LMFDB - Embedded newform 300.3.c.g.151.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("300.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.4069419264.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 7x^{6} + 50x^{4} - 84x^{3} + 55x^{2} - 12x + 1 $ x^8 - 7x^6 + 50x^4 - 84x^3 + 55x^2 - 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.8
Root			$1.65359 - 0.954702i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.3.c.g.151.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.97650 + 0.305673i) q^{2} +1.73205i q^{3} +(3.81313 + 1.20833i) q^{4} +(-0.529441 + 3.42340i) q^{6} -0.329898i q^{7} +(7.16731 + 3.55383i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.97650 + 0.305673i) q^{2} +1.73205i q^{3} +(3.81313 + 1.20833i) q^{4} +(-0.529441 + 3.42340i) q^{6} -0.329898i q^{7} +(7.16731 + 3.55383i) q^{8} -3.00000 q^{9} +20.4920i q^{11} +(-2.09288 + 6.60453i) q^{12} +0.416712 q^{13} +(0.100841 - 0.652044i) q^{14} +(13.0799 + 9.21501i) q^{16} +18.5884 q^{17} +(-5.92951 - 0.917019i) q^{18} -12.4503i q^{19} +0.571400 q^{21} +(-6.26384 + 40.5024i) q^{22} -23.2304i q^{23} +(-6.15542 + 12.4141i) q^{24} +(0.823633 + 0.127378i) q^{26} -5.19615i q^{27} +(0.398624 - 1.25794i) q^{28} -23.9166 q^{29} +42.0148i q^{31} +(23.0357 + 22.2117i) q^{32} -35.4931 q^{33} +(36.7400 + 5.68197i) q^{34} +(-11.4394 - 3.62498i) q^{36} -50.9523 q^{37} +(3.80573 - 24.6081i) q^{38} +0.721767i q^{39} +46.7073 q^{41} +(1.12937 + 0.174661i) q^{42} -55.5866i q^{43} +(-24.7610 + 78.1385i) q^{44} +(7.10090 - 45.9149i) q^{46} -81.7616i q^{47} +(-15.9609 + 22.6550i) q^{48} +48.8912 q^{49} +32.1960i q^{51} +(1.58898 + 0.503524i) q^{52} +29.9744 q^{53} +(1.58832 - 10.2702i) q^{54} +(1.17240 - 2.36448i) q^{56} +21.5646 q^{57} +(-47.2713 - 7.31067i) q^{58} -24.3311i q^{59} -74.8416 q^{61} +(-12.8428 + 83.0424i) q^{62} +0.989693i q^{63} +(38.7406 + 50.9428i) q^{64} +(-70.1523 - 10.8493i) q^{66} -72.8008i q^{67} +(70.8799 + 22.4608i) q^{68} +40.2362 q^{69} -39.2803i q^{71} +(-21.5019 - 10.6615i) q^{72} +46.5814 q^{73} +(-100.707 - 15.5747i) q^{74} +(15.0441 - 47.4747i) q^{76} +6.76026 q^{77} +(-0.220625 + 1.42657i) q^{78} -101.920i q^{79} +9.00000 q^{81} +(92.3170 + 14.2771i) q^{82} -5.88913i q^{83} +(2.17882 + 0.690438i) q^{84} +(16.9913 - 109.867i) q^{86} -41.4248i q^{87} +(-72.8250 + 146.872i) q^{88} -61.0100 q^{89} -0.137472i q^{91} +(28.0699 - 88.5804i) q^{92} -72.7718 q^{93} +(24.9923 - 161.602i) q^{94} +(-38.4717 + 39.8989i) q^{96} -95.5437 q^{97} +(96.6335 + 14.9447i) q^{98} -61.4759i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 8 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 8 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9	$ 8 q + 2 q^{2} - 8 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9} + 8 q^{13} + 22 q^{14} + 40 q^{16} - 6 q^{18} + 24 q^{21} + 4 q^{22} - 36 q^{24} - 66 q^{26} + 104 q^{28} - 32 q^{29} + 112 q^{32} + 124 q^{34} + 24 q^{36} - 176 q^{37} - 170 q^{38} - 16 q^{41} + 54 q^{42} + 40 q^{44} - 76 q^{46} + 24 q^{48} + 16 q^{49} + 56 q^{52} - 304 q^{53} + 18 q^{54} - 172 q^{56} + 72 q^{57} - 12 q^{58} + 136 q^{61} - 238 q^{62} + 16 q^{64} - 108 q^{66} + 88 q^{68} - 96 q^{69} - 60 q^{72} + 240 q^{73} - 108 q^{74} + 120 q^{76} - 384 q^{77} + 150 q^{78} + 72 q^{81} + 320 q^{82} - 144 q^{84} + 214 q^{86} - 200 q^{88} + 128 q^{89} + 312 q^{92} + 72 q^{93} + 12 q^{94} + 96 q^{96} + 216 q^{97} + 60 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 8 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9 + 8 * q^13 + 22 * q^14 + 40 * q^16 - 6 * q^18 + 24 * q^21 + 4 * q^22 - 36 * q^24 - 66 * q^26 + 104 * q^28 - 32 * q^29 + 112 * q^32 + 124 * q^34 + 24 * q^36 - 176 * q^37 - 170 * q^38 - 16 * q^41 + 54 * q^42 + 40 * q^44 - 76 * q^46 + 24 * q^48 + 16 * q^49 + 56 * q^52 - 304 * q^53 + 18 * q^54 - 172 * q^56 + 72 * q^57 - 12 * q^58 + 136 * q^61 - 238 * q^62 + 16 * q^64 - 108 * q^66 + 88 * q^68 - 96 * q^69 - 60 * q^72 + 240 * q^73 - 108 * q^74 + 120 * q^76 - 384 * q^77 + 150 * q^78 + 72 * q^81 + 320 * q^82 - 144 * q^84 + 214 * q^86 - 200 * q^88 + 128 * q^89 + 312 * q^92 + 72 * q^93 + 12 * q^94 + 96 * q^96 + 216 * q^97 + 60 * 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 $

$2$	1.97650	+	0.305673i	0.988251	+	0.152836i
$2$	1.97650	+	0.305673i	0.988251	+	0.152836i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	3.81313	+	1.20833i	0.953282	+	0.302082i
$5$		0			0
$5$		0			0
$6$	−0.529441	+	3.42340i	−0.0882402	+	0.570567i
$7$		−	0.329898i		−	0.0471283i	−0.999722	−	0.0235641i	$-0.992499\pi$
$7$		−	0.329898i		−	0.0471283i	0.999722	−	0.0235641i	$-0.00750139\pi$
$8$	7.16731	+	3.55383i	0.895913	+	0.444229i
$9$	−3.00000			−0.333333
$10$		0			0
$11$			20.4920i			1.86291i	0.363861	+	0.931453i	$0.381458\pi$
$11$			20.4920i			1.86291i	−0.363861	+	0.931453i	$0.618542\pi$
$12$	−2.09288	+	6.60453i	−0.174407	+	0.550378i
$13$	0.416712			0.0320548			0.0160274	−	0.999872i	$-0.494898\pi$
$13$	0.416712			0.0320548			0.0160274	+	0.999872i	$0.494898\pi$
$14$	0.100841	−	0.652044i	0.00720292	−	0.0465746i
$15$		0			0
$16$	13.0799	+	9.21501i	0.817493	+	0.575938i
$17$	18.5884			1.09343			0.546717	−	0.837317i	$-0.315877\pi$
$17$	18.5884			1.09343			0.546717	+	0.837317i	$0.315877\pi$
$18$	−5.92951	−	0.917019i	−0.329417	−	0.0509455i
$19$		−	12.4503i		−	0.655281i	−0.944803	−	0.327640i	$-0.893747\pi$
$19$		−	12.4503i		−	0.655281i	0.944803	−	0.327640i	$-0.106253\pi$
$20$		0			0
$21$	0.571400			0.0272095
$22$	−6.26384	+	40.5024i	−0.284720	+	1.84102i
$23$		−	23.2304i		−	1.01002i	−0.863114	−	0.505008i	$-0.831489\pi$
$23$		−	23.2304i		−	1.01002i	0.863114	−	0.505008i	$-0.168511\pi$
$24$	−6.15542	+	12.4141i	−0.256476	+	0.517256i
$25$		0			0
$26$	0.823633	+	0.127378i	0.0316782	+	0.00489914i
$27$		−	5.19615i		−	0.192450i
$28$	0.398624	−	1.25794i	0.0142366	−	0.0449265i
$29$	−23.9166			−0.824712			−0.412356	−	0.911023i	$-0.635294\pi$
$29$	−23.9166			−0.824712			−0.412356	+	0.911023i	$0.635294\pi$
$30$		0			0
$31$			42.0148i			1.35532i	0.735377	+	0.677658i	$0.237005\pi$
$31$			42.0148i			1.35532i	−0.735377	+	0.677658i	$0.762995\pi$
$32$	23.0357	+	22.2117i	0.719865	+	0.694115i
$33$	−35.4931			−1.07555
$34$	36.7400	+	5.68197i	1.08059	+	0.167117i
$35$		0			0
$36$	−11.4394	−	3.62498i	−0.317761	−	0.100694i
$37$	−50.9523			−1.37709			−0.688545	−	0.725194i	$-0.741750\pi$
$37$	−50.9523			−1.37709			−0.688545	+	0.725194i	$0.741750\pi$
$38$	3.80573	−	24.6081i	0.100151	−	0.647582i
$39$			0.721767i			0.0185068i
$40$		0			0
$41$	46.7073			1.13920			0.569601	−	0.821921i	$-0.307098\pi$
$41$	46.7073			1.13920			0.569601	+	0.821921i	$0.307098\pi$
$42$	1.12937	+	0.174661i	0.0268898	+	0.00415861i
$43$		−	55.5866i		−	1.29271i	−0.763036	−	0.646356i	$-0.776292\pi$
$43$		−	55.5866i		−	1.29271i	0.763036	−	0.646356i	$-0.223708\pi$
$44$	−24.7610	+	78.1385i	−0.562750	+	1.77588i
$45$		0			0
$46$	7.10090	−	45.9149i	0.154367	−	0.998151i
$47$		−	81.7616i		−	1.73961i	−0.493397	−	0.869804i	$-0.664245\pi$
$47$		−	81.7616i		−	1.73961i	0.493397	−	0.869804i	$-0.335755\pi$
$48$	−15.9609	+	22.6550i	−0.332518	+	0.471980i
$49$	48.8912			0.997779
$50$		0			0
$51$			32.1960i			0.631295i
$52$	1.58898	+	0.503524i	0.0305572	+	0.00968316i
$53$	29.9744			0.565554			0.282777	−	0.959186i	$-0.408744\pi$
$53$	29.9744			0.565554			0.282777	+	0.959186i	$0.408744\pi$
$54$	1.58832	−	10.2702i	0.0294134	−	0.190189i
$55$		0			0
$56$	1.17240	−	2.36448i	0.0209357	−	0.0422228i
$57$	21.5646			0.378326
$58$	−47.2713	−	7.31067i	−0.815023	−	0.126046i
$59$		−	24.3311i		−	0.412391i	−0.978511	−	0.206196i	$-0.933892\pi$
$59$		−	24.3311i		−	0.412391i	0.978511	−	0.206196i	$-0.0661083\pi$
$60$		0			0
$61$	−74.8416			−1.22691			−0.613456	−	0.789729i	$-0.710221\pi$
$61$	−74.8416			−1.22691			−0.613456	+	0.789729i	$0.710221\pi$
$62$	−12.8428	+	83.0424i	−0.207142	+	1.33939i
$63$			0.989693i			0.0157094i
$64$	38.7406	+	50.9428i	0.605321	+	0.795981i
$65$		0			0
$66$	−70.1523	−	10.8493i	−1.06291	−	0.164383i
$67$		−	72.8008i		−	1.08658i	−0.839545	−	0.543290i	$-0.817178\pi$
$67$		−	72.8008i		−	1.08658i	0.839545	−	0.543290i	$-0.182822\pi$
$68$	70.8799	+	22.4608i	1.04235	+	0.330307i
$69$	40.2362			0.583133
$70$		0			0
$71$		−	39.2803i		−	0.553244i	−0.960979	−	0.276622i	$-0.910785\pi$
$71$		−	39.2803i		−	0.553244i	0.960979	−	0.276622i	$-0.0892150\pi$
$72$	−21.5019	−	10.6615i	−0.298638	−	0.148076i
$73$	46.5814			0.638101			0.319051	−	0.947738i	$-0.396636\pi$
$73$	46.5814			0.638101			0.319051	+	0.947738i	$0.396636\pi$
$74$	−100.707	−	15.5747i	−1.36091	−	0.210469i
$75$		0			0
$76$	15.0441	−	47.4747i	0.197948	−	0.624667i
$77$	6.76026			0.0877955
$78$	−0.220625	+	1.42657i	−0.00282852	+	0.0182894i
$79$		−	101.920i		−	1.29012i	−0.764131	−	0.645062i	$-0.776832\pi$
$79$		−	101.920i		−	1.29012i	0.764131	−	0.645062i	$-0.223168\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	92.3170	+	14.2771i	1.12582	+	0.174112i
$83$		−	5.88913i		−	0.0709534i	−0.999371	−	0.0354767i	$-0.988705\pi$
$83$		−	5.88913i		−	0.0709534i	0.999371	−	0.0354767i	$-0.0112950\pi$
$84$	2.17882	+	0.690438i	0.0259383	+	0.00821950i
$85$		0			0
$86$	16.9913	−	109.867i	0.197574	−	1.27752i
$87$		−	41.4248i		−	0.476148i
$88$	−72.8250	+	146.872i	−0.827557	+	1.66900i
$89$	−61.0100			−0.685506			−0.342753	−	0.939426i	$-0.611359\pi$
$89$	−61.0100			−0.685506			−0.342753	+	0.939426i	$0.611359\pi$
$90$		0			0
$91$		−	0.137472i		−	0.00151069i
$92$	28.0699	−	88.5804i	0.305108	−	0.962831i
$93$	−72.7718			−0.782492
$94$	24.9923	−	161.602i	0.265876	−	1.71917i
$95$		0			0
$96$	−38.4717	+	39.8989i	−0.400747	+	0.415614i
$97$	−95.5437			−0.984987			−0.492494	−	0.870316i	$-0.663914\pi$
$97$	−95.5437			−0.984987			−0.492494	+	0.870316i	$0.663914\pi$
$98$	96.6335	+	14.9447i	0.986057	+	0.152497i
$99$		−	61.4759i		−	0.620969i
$100$		0			0
$101$	162.675			1.61064			0.805322	−	0.592838i	$-0.201992\pi$
$101$	162.675			1.61064			0.805322	+	0.592838i	$0.201992\pi$
$102$	−9.84145	+	63.6355i	−0.0964848	+	0.623878i
$103$			158.196i			1.53588i	0.640521	+	0.767941i	$0.278718\pi$
$103$			158.196i			1.53588i	−0.640521	+	0.767941i	$0.721282\pi$
$104$	2.98670	+	1.48092i	0.0287183	+	0.0142397i
$105$		0			0
$106$	59.2445	+	9.16236i	0.558910	+	0.0864373i
$107$			18.1827i			0.169932i	0.996384	+	0.0849660i	$0.0270782\pi$
$107$			18.1827i			0.169932i	−0.996384	+	0.0849660i	$0.972922\pi$
$108$	6.27865	−	19.8136i	0.0581357	−	0.183459i
$109$	−156.842			−1.43891			−0.719457	−	0.694537i	$-0.755609\pi$
$109$	−156.842			−1.43891			−0.719457	+	0.694537i	$0.755609\pi$
$110$		0			0
$111$		−	88.2520i		−	0.795063i
$112$	3.04001	−	4.31503i	0.0271430	−	0.0385270i
$113$	98.7245			0.873668			0.436834	−	0.899542i	$-0.356100\pi$
$113$	98.7245			0.873668			0.436834	+	0.899542i	$0.356100\pi$
$114$	42.6225	+	6.59172i	0.373882	+	0.0578221i
$115$		0			0
$116$	−91.1972	−	28.8991i	−0.786183	−	0.249130i
$117$	−1.25014			−0.0106849
$118$	7.43735	−	48.0904i	0.0630284	−	0.407546i
$119$		−	6.13227i		−	0.0515317i
$120$		0			0
$121$	−298.921			−2.47042
$122$	−147.925	−	22.8770i	−1.21250	−	0.187517i
$123$			80.8994i			0.657718i
$124$	−50.7676	+	160.208i	−0.409416	+	1.29200i
$125$		0			0
$126$	−0.302523	+	1.95613i	−0.00240097	+	0.0155249i
$127$			27.0938i			0.213337i	0.994295	+	0.106669i	$0.0340184\pi$
$127$			27.0938i			0.213337i	−0.994295	+	0.106669i	$0.965982\pi$
$128$	60.9990	+	112.531i	0.476555	+	0.879145i
$129$	96.2789			0.746348
$130$		0			0
$131$			4.45811i			0.0340314i	0.999855	+	0.0170157i	$0.00541653\pi$
$131$			4.45811i			0.0340314i	−0.999855	+	0.0170157i	$0.994583\pi$
$132$	−135.340	−	42.8873i	−1.02530	−	0.324904i
$133$	−4.10734			−0.0308822
$134$	22.2533	−	143.891i	0.166069	−	1.07381i
$135$		0			0
$136$	133.229	+	66.0600i	0.979622	+	0.485735i
$137$	181.700			1.32628			0.663139	−	0.748496i	$-0.269224\pi$
$137$	181.700			1.32628			0.663139	+	0.748496i	$0.269224\pi$
$138$	79.5270	+	12.2991i	0.576282	+	0.0891241i
$139$			223.419i			1.60733i	0.595083	+	0.803664i	$0.297119\pi$
$139$			223.419i			1.60733i	−0.595083	+	0.803664i	$0.702881\pi$
$140$		0			0
$141$	141.615			1.00436
$142$	12.0069	−	77.6377i	0.0845559	−	0.546744i
$143$			8.53925i			0.0597151i
$144$	−39.2397	−	27.6450i	−0.272498	−	0.191979i
$145$		0			0
$146$	92.0683	+	14.2387i	0.630604	+	0.0975251i
$147$			84.6820i			0.576068i
$148$	−194.288	−	61.5670i	−1.31275	−	0.415994i
$149$	123.867			0.831324			0.415662	−	0.909519i	$-0.363550\pi$
$149$	123.867			0.831324			0.415662	+	0.909519i	$0.363550\pi$
$150$		0			0
$151$		−	76.0961i		−	0.503948i	−0.967734	−	0.251974i	$-0.918920\pi$
$151$		−	76.0961i		−	0.503948i	0.967734	−	0.251974i	$-0.0810797\pi$
$152$	44.2464	−	89.2353i	0.291095	−	0.587075i
$153$	−55.7651			−0.364478
$154$	13.3617	+	2.06643i	0.0867641	+	0.0134184i
$155$		0			0
$156$	−0.872130	+	2.75219i	−0.00559058	+	0.0176422i
$157$	−34.2940			−0.218433			−0.109217	−	0.994018i	$-0.534834\pi$
$157$	−34.2940			−0.218433			−0.109217	+	0.994018i	$0.534834\pi$
$158$	31.1541	−	201.445i	0.197178	−	1.27497i
$159$			51.9172i			0.326523i
$160$		0			0
$161$	−7.66365			−0.0476003
$162$	17.7885	+	2.75106i	0.109806	+	0.0169818i
$163$		−	165.538i		−	1.01557i	−0.861483	−	0.507786i	$-0.830464\pi$
$163$		−	165.538i		−	1.01557i	0.861483	−	0.507786i	$-0.169536\pi$
$164$	178.101	+	56.4377i	1.08598	+	0.344132i
$165$		0			0
$166$	1.80015	−	11.6399i	0.0108443	−	0.0701198i
$167$			83.6064i			0.500637i	0.968164	+	0.250319i	$0.0805353\pi$
$167$			83.6064i			0.500637i	−0.968164	+	0.250319i	$0.919465\pi$
$168$	4.09540	+	2.03066i	0.0243774	+	0.0120873i
$169$	−168.826			−0.998972
$170$		0			0
$171$			37.3510i			0.218427i
$172$	67.1668	−	211.959i	0.390505	−	1.23232i
$173$	−192.900			−1.11503			−0.557513	−	0.830168i	$-0.688244\pi$
$173$	−192.900			−1.11503			−0.557513	+	0.830168i	$0.688244\pi$
$174$	12.6625	−	81.8763i	0.0727727	−	0.470554i
$175$		0			0
$176$	−188.834	+	268.033i	−1.07292	+	1.52291i
$177$	42.1427			0.238094
$178$	−120.587	−	18.6491i	−0.677452	−	0.104770i
$179$			120.939i			0.675637i	0.941211	+	0.337819i	$0.109689\pi$
$179$			120.939i			0.675637i	−0.941211	+	0.337819i	$0.890311\pi$
$180$		0			0
$181$	−107.583			−0.594381			−0.297191	−	0.954818i	$-0.596050\pi$
$181$	−107.583			−0.594381			−0.297191	+	0.954818i	$0.596050\pi$
$182$	0.0420216	−	0.271715i	0.000230888	−	0.00149294i
$183$		−	129.629i		−	0.708357i
$184$	82.5569	−	166.499i	0.448679	−	0.904887i
$185$		0			0
$186$	−143.834	−	22.2444i	−0.773299	−	0.119593i
$187$			380.913i			2.03697i
$188$	98.7947	−	311.767i	0.525504	−	1.65834i
$189$	−1.71420			−0.00906984
$190$		0			0
$191$		−	279.706i		−	1.46443i	−0.681075	−	0.732214i	$-0.738487\pi$
$191$		−	279.706i		−	1.46443i	0.681075	−	0.732214i	$-0.261513\pi$
$192$	−88.2355	+	67.1006i	−0.459560	+	0.349482i
$193$	102.534			0.531263			0.265632	−	0.964075i	$-0.414420\pi$
$193$	102.534			0.531263			0.265632	+	0.964075i	$0.414420\pi$
$194$	−188.842	−	29.2051i	−0.973415	−	0.150542i
$195$		0			0
$196$	186.428	+	59.0765i	0.951165	+	0.301411i
$197$	−38.9632			−0.197783			−0.0988913	−	0.995098i	$-0.531530\pi$
$197$	−38.9632			−0.197783			−0.0988913	+	0.995098i	$0.531530\pi$
$198$	18.7915	−	121.507i	0.0949067	−	0.613673i
$199$			147.646i			0.741940i	0.928645	+	0.370970i	$0.120975\pi$
$199$			147.646i			0.741940i	−0.928645	+	0.370970i	$0.879025\pi$
$200$		0			0
$201$	126.095			0.627337
$202$	321.528	+	49.7254i	1.59172	+	0.246165i
$203$			7.89005i			0.0388672i
$204$	−38.9033	+	122.768i	−0.190703	+	0.601802i
$205$		0			0
$206$	−48.3562	+	312.674i	−0.234739	+	1.51784i
$207$			69.6912i			0.336672i
$208$	5.45055	+	3.84001i	0.0262046	+	0.0184616i
$209$	255.132			1.22073
$210$		0			0
$211$			233.336i			1.10586i	0.833229	+	0.552928i	$0.186490\pi$
$211$			233.336i			1.10586i	−0.833229	+	0.552928i	$0.813510\pi$
$212$	114.296	+	36.2189i	0.539133	+	0.170844i
$213$	68.0355			0.319416
$214$	−5.55797	+	35.9382i	−0.0259718	+	0.167936i
$215$		0			0
$216$	18.4663	−	37.2424i	0.0854919	−	0.172419i
$217$	13.8606			0.0638737
$218$	−309.998	−	47.9422i	−1.42201	−	0.219918i
$219$			80.6813i			0.368408i
$220$		0			0
$221$	7.74600			0.0350498
$222$	26.9762	−	174.430i	0.121515	−	0.785722i
$223$			82.7105i			0.370899i	0.982654	+	0.185450i	$0.0593741\pi$
$223$			82.7105i			0.370899i	−0.982654	+	0.185450i	$0.940626\pi$
$224$	7.32758	−	7.59941i	0.0327124	−	0.0339260i
$225$		0			0
$226$	195.129	+	30.1774i	0.863403	+	0.133528i
$227$			361.534i			1.59266i	0.604862	+	0.796330i	$0.293228\pi$
$227$			361.534i			1.59266i	−0.604862	+	0.796330i	$0.706772\pi$
$228$	82.2286	+	26.0571i	0.360652	+	0.114286i
$229$	121.818			0.531955			0.265977	−	0.963979i	$-0.414305\pi$
$229$	121.818			0.531955			0.265977	+	0.963979i	$0.414305\pi$
$230$		0			0
$231$			11.7091i			0.0506888i
$232$	−171.418	−	84.9957i	−0.738870	−	0.366361i
$233$	−136.615			−0.586329			−0.293164	−	0.956062i	$-0.594708\pi$
$233$	−136.615			−0.586329			−0.293164	+	0.956062i	$0.594708\pi$
$234$	−2.47090	−	0.382133i	−0.0105594	−	0.00163305i
$235$		0			0
$236$	29.3999	−	92.7775i	0.124576	−	0.393125i
$237$	176.530			0.744853
$238$	1.87447	−	12.1204i	0.00787592	−	0.0509262i
$239$			56.4632i			0.236248i	0.992999	+	0.118124i	$0.0376880\pi$
$239$			56.4632i			0.236248i	−0.992999	+	0.118124i	$0.962312\pi$
$240$		0			0
$241$	−2.24158			−0.00930117			−0.00465059	−	0.999989i	$-0.501480\pi$
$241$	−2.24158			−0.00930117			−0.00465059	+	0.999989i	$0.501480\pi$
$242$	−590.818	−	91.3720i	−2.44140	−	0.377570i
$243$			15.5885i			0.0641500i
$244$	−285.381	−	90.4331i	−1.16959	−	0.370627i
$245$		0			0
$246$	−24.7287	+	159.898i	−0.100523	+	0.649991i
$247$		−	5.18820i		−	0.0210049i
$248$	−149.314	+	301.133i	−0.602071	+	1.21425i
$249$	10.2003			0.0409650
$250$		0			0
$251$			395.809i			1.57693i	0.615081	+	0.788464i	$0.289123\pi$
$251$			395.809i			1.57693i	−0.615081	+	0.788464i	$0.710877\pi$
$252$	−1.19587	+	3.77383i	−0.00474553	+	0.0149755i
$253$	476.036			1.88157
$254$	−8.28184	+	53.5510i	−0.0326057	+	0.210831i
$255$		0			0
$256$	86.1671	+	241.063i	0.336590	+	0.941651i
$257$	−109.778			−0.427151			−0.213576	−	0.976927i	$-0.568511\pi$
$257$	−109.778			−0.427151			−0.213576	+	0.976927i	$0.568511\pi$
$258$	190.295	+	29.4298i	0.737579	+	0.114069i
$259$			16.8091i			0.0648998i
$260$		0			0
$261$	71.7499			0.274904
$262$	−1.36272	+	8.81147i	−0.00520124	+	0.0336316i
$263$			327.702i			1.24601i	0.782216	+	0.623007i	$0.214089\pi$
$263$			327.702i			1.24601i	−0.782216	+	0.623007i	$0.785911\pi$
$264$	−254.390	−	126.137i	−0.963599	−	0.477790i
$265$		0			0
$266$	−8.11816	−	1.25550i	−0.0305194	−	0.00471993i
$267$		−	105.673i		−	0.395777i
$268$	87.9672	−	277.599i	0.328236	−	1.03582i
$269$	−130.032			−0.483392			−0.241696	−	0.970352i	$-0.577704\pi$
$269$	−130.032			−0.483392			−0.241696	+	0.970352i	$0.577704\pi$
$270$		0			0
$271$		−	329.669i		−	1.21649i	−0.793750	−	0.608245i	$-0.791874\pi$
$271$		−	329.669i		−	1.21649i	0.793750	−	0.608245i	$-0.208126\pi$
$272$	243.134	+	171.292i	0.893875	+	0.629751i
$273$	0.238109			0.000872195
$274$	359.131	+	55.5408i	1.31070	+	0.202704i
$275$		0			0
$276$	153.426	+	48.6185i	0.555891	+	0.176154i
$277$	−304.124			−1.09792			−0.548960	−	0.835849i	$-0.684976\pi$
$277$	−304.124			−1.09792			−0.548960	+	0.835849i	$0.684976\pi$
$278$	−68.2930	+	441.588i	−0.245658	+	1.58844i
$279$		−	126.044i		−	0.451772i
$280$		0			0
$281$	240.099			0.854446			0.427223	−	0.904146i	$-0.359492\pi$
$281$	240.099			0.854446			0.427223	+	0.904146i	$0.359492\pi$
$282$	279.903	+	43.2879i	0.992563	+	0.153503i
$283$		−	86.6730i		−	0.306265i	−0.988206	−	0.153133i	$-0.951064\pi$
$283$		−	86.6730i		−	0.306265i	0.988206	−	0.153133i	$-0.0489362\pi$
$284$	47.4635	−	149.781i	0.167125	−	0.527398i
$285$		0			0
$286$	−2.61022	+	16.8779i	−0.00912664	+	0.0590135i
$287$		−	15.4086i		−	0.0536886i
$288$	−69.1070	−	66.6350i	−0.239955	−	0.231372i
$289$	56.5280			0.195599
$290$		0			0
$291$		−	165.487i		−	0.568683i
$292$	177.621	+	56.2856i	0.608290	+	0.192759i
$293$	−390.339			−1.33222			−0.666108	−	0.745855i	$-0.732041\pi$
$293$	−390.339			−1.33222			−0.666108	+	0.745855i	$0.732041\pi$
$294$	−25.8850	+	167.374i	−0.0880442	+	0.569300i
$295$		0			0
$296$	−365.191	−	181.076i	−1.23375	−	0.611743i
$297$	106.479			0.358517
$298$	244.824	+	37.8629i	0.821557	+	0.127057i
$299$		−	9.68038i		−	0.0323759i
$300$		0			0
$301$	−18.3379			−0.0609233
$302$	23.2605	−	150.404i	0.0770216	−	0.498027i
$303$			281.761i			0.929906i
$304$	114.730	−	162.849i	0.377401	−	0.535687i
$305$		0			0
$306$	−110.220	−	17.0459i	−0.360196	−	0.0557056i
$307$		−	60.2318i		−	0.196195i	−0.995177	−	0.0980973i	$-0.968724\pi$
$307$		−	60.2318i		−	0.196195i	0.995177	−	0.0980973i	$-0.0312757\pi$
$308$	25.7777	+	8.16860i	0.0836939	+	0.0265214i
$309$	−274.003			−0.886741
$310$		0			0
$311$		−	106.594i		−	0.342747i	−0.985206	−	0.171373i	$-0.945180\pi$
$311$		−	106.594i		−	0.342747i	0.985206	−	0.171373i	$-0.0548205\pi$
$312$	−2.56504	+	5.17312i	−0.00822127	+	0.0165805i
$313$	46.2243			0.147682			0.0738408	−	0.997270i	$-0.476474\pi$
$313$	46.2243			0.147682			0.0738408	+	0.997270i	$0.476474\pi$
$314$	−67.7823	−	10.4828i	−0.215867	−	0.0333846i
$315$		0			0
$316$	123.152	−	388.633i	0.389723	−	1.22985i
$317$	8.36780			0.0263969			0.0131984	−	0.999913i	$-0.495799\pi$
$317$	8.36780			0.0263969			0.0131984	+	0.999913i	$0.495799\pi$
$318$	−15.8697	+	102.614i	−0.0499046	+	0.322687i
$319$		−	490.099i		−	1.53636i
$320$		0			0
$321$	−31.4934			−0.0981103
$322$	−15.1472	−	2.34257i	−0.0470411	−	0.00727507i
$323$		−	231.432i		−	0.716506i
$324$	34.3182	+	10.8749i	0.105920	+	0.0335646i
$325$		0			0
$326$	50.6006	−	327.187i	0.155217	−	1.00364i
$327$		−	271.658i		−	0.830757i
$328$	334.765	+	165.990i	1.02063	+	0.506066i
$329$	−26.9730			−0.0819847
$330$		0			0
$331$			111.072i			0.335564i	0.985824	+	0.167782i	$0.0536605\pi$
$331$			111.072i			0.335564i	−0.985824	+	0.167782i	$0.946339\pi$
$332$	7.11600	−	22.4560i	0.0214337	−	0.0676386i
$333$	152.857			0.459030
$334$	−25.5562	+	165.248i	−0.0765156	+	0.494755i
$335$		0			0
$336$	7.47385	+	5.26546i	0.0222436	+	0.0156710i
$337$	231.853			0.687990			0.343995	−	0.938972i	$-0.388220\pi$
$337$	231.853			0.687990			0.343995	+	0.938972i	$0.388220\pi$
$338$	−333.686	−	51.6057i	−0.987236	−	0.152679i
$339$			170.996i			0.504412i
$340$		0			0
$341$	−860.966			−2.52483
$342$	−11.4172	+	73.8244i	−0.0333836	+	0.215861i
$343$		−	32.2941i		−	0.0941518i
$344$	197.546	−	398.406i	0.574260	−	1.15816i
$345$		0			0
$346$	−381.266	−	58.9642i	−1.10193	−	0.170417i
$347$		−	402.088i		−	1.15875i	−0.815059	−	0.579377i	$-0.803296\pi$
$347$		−	402.088i		−	1.15875i	0.815059	−	0.579377i	$-0.196704\pi$
$348$	50.0548	−	157.958i	0.143835	−	0.453903i
$349$	−163.284			−0.467864			−0.233932	−	0.972253i	$-0.575159\pi$
$349$	−163.284			−0.467864			−0.233932	+	0.972253i	$0.575159\pi$
$350$		0			0
$351$		−	2.16530i		−	0.00616894i
$352$	−455.161	+	472.046i	−1.29307	+	1.34104i
$353$	−175.851			−0.498161			−0.249081	−	0.968483i	$-0.580128\pi$
$353$	−175.851			−0.498161			−0.249081	+	0.968483i	$0.580128\pi$
$354$	83.2951	+	12.8819i	0.235297	+	0.0363895i
$355$		0			0
$356$	−232.639	−	73.7201i	−0.653481	−	0.207079i
$357$	10.6214			0.0297518
$358$	−36.9678	+	239.037i	−0.103262	+	0.667700i
$359$		−	345.628i		−	0.962753i	−0.876514	−	0.481377i	$-0.840137\pi$
$359$		−	345.628i		−	0.962753i	0.876514	−	0.481377i	$-0.159863\pi$
$360$		0			0
$361$	205.989			0.570607
$362$	−212.638	−	32.8852i	−0.587398	−	0.0908431i
$363$		−	517.746i		−	1.42630i
$364$	0.166112	−	0.524200i	0.000456351	−	0.00144011i
$365$		0			0
$366$	39.6242	−	256.213i	0.108263	−	0.700035i
$367$		−	728.998i		−	1.98637i	−0.116546	−	0.993185i	$-0.537182\pi$
$367$		−	728.998i		−	1.98637i	0.116546	−	0.993185i	$-0.462818\pi$
$368$	214.068	−	303.851i	0.581707	−	0.825682i
$369$	−140.122			−0.379734
$370$		0			0
$371$		−	9.88848i		−	0.0266536i
$372$	−277.488	−	87.9321i	−0.745936	−	0.236377i
$373$	46.6749			0.125134			0.0625668	−	0.998041i	$-0.480071\pi$
$373$	46.6749			0.125134			0.0625668	+	0.998041i	$0.480071\pi$
$374$	−116.435	+	752.875i	−0.311323	+	2.01303i
$375$		0			0
$376$	290.567	−	586.010i	0.772784	−	1.55854i
$377$	−9.96635			−0.0264360
$378$	−3.38812	−	0.523984i	−0.00896328	−	0.00138620i
$379$		−	117.629i		−	0.310368i	−0.987886	−	0.155184i	$-0.950403\pi$
$379$		−	117.629i		−	0.310368i	0.987886	−	0.155184i	$-0.0495970\pi$
$380$		0			0
$381$	−46.9278			−0.123170
$382$	85.4985	−	552.839i	0.223818	−	1.44722i
$383$			251.669i			0.657100i	0.944487	+	0.328550i	$0.106560\pi$
$383$			251.669i			0.657100i	−0.944487	+	0.328550i	$0.893440\pi$
$384$	−194.909	+	105.653i	−0.507575	+	0.275139i
$385$		0			0
$386$	202.658	+	31.3418i	0.525022	+	0.0811964i
$387$			166.760i			0.430904i
$388$	−364.321	−	115.448i	−0.938970	−	0.297547i
$389$	356.890			0.917454			0.458727	−	0.888577i	$-0.348306\pi$
$389$	356.890			0.917454			0.458727	+	0.888577i	$0.348306\pi$
$390$		0			0
$391$		−	431.815i		−	1.10439i
$392$	350.418	+	173.751i	0.893923	+	0.443242i
$393$	−7.72168			−0.0196480
$394$	−77.0108	−	11.9100i	−0.195459	−	0.0302284i
$395$		0			0
$396$	74.2830	−	234.416i	0.187583	−	0.591958i
$397$	103.819			0.261508			0.130754	−	0.991415i	$-0.458260\pi$
$397$	103.819			0.261508			0.130754	+	0.991415i	$0.458260\pi$
$398$	−45.1314	+	291.823i	−0.113396	+	0.733224i
$399$		−	7.11412i		−	0.0178299i
$400$		0			0
$401$	−121.598			−0.303237			−0.151618	−	0.988439i	$-0.548449\pi$
$401$	−121.598			−0.303237			−0.151618	+	0.988439i	$0.548449\pi$
$402$	249.227	+	38.5438i	0.619967	+	0.0958800i
$403$			17.5081i			0.0434444i
$404$	620.301	+	196.565i	1.53540	+	0.486546i
$405$		0			0
$406$	−2.41177	+	15.5947i	−0.00594033	+	0.0384106i
$407$		−	1044.11i		−	2.56539i
$408$	−114.419	+	230.759i	−0.280439	+	0.565585i
$409$	182.788			0.446915			0.223457	−	0.974714i	$-0.428266\pi$
$409$	182.788			0.446915			0.223457	+	0.974714i	$0.428266\pi$
$410$		0			0
$411$			314.714i			0.765727i
$412$	−191.152	+	603.221i	−0.463962	+	1.46413i
$413$	−8.02677			−0.0194353
$414$	−21.3027	+	137.745i	−0.0514558	+	0.332717i
$415$		0			0
$416$	9.59924	+	9.25587i	0.0230751	+	0.0222497i
$417$	−386.972			−0.927991
$418$	504.269	+	77.9869i	1.20638	+	0.186572i
$419$		−	168.020i		−	0.401003i	−0.979693	−	0.200502i	$-0.935743\pi$
$419$		−	168.020i		−	0.401003i	0.979693	−	0.200502i	$-0.0642572\pi$
$420$		0			0
$421$	625.291			1.48525			0.742626	−	0.669706i	$-0.233580\pi$
$421$	625.291			1.48525			0.742626	+	0.669706i	$0.233580\pi$
$422$	−71.3244	+	461.189i	−0.169015	+	1.09286i
$423$			245.285i			0.579869i
$424$	214.836	+	106.524i	0.506688	+	0.251236i
$425$		0			0
$426$	134.472	+	20.7966i	0.315663	+	0.0488184i
$427$			24.6901i			0.0578222i
$428$	−21.9707	+	69.3331i	−0.0513334	+	0.161993i
$429$	−14.7904			−0.0344765
$430$		0			0
$431$		−	133.413i		−	0.309544i	−0.987950	−	0.154772i	$-0.950536\pi$
$431$		−	133.413i		−	0.309544i	0.987950	−	0.154772i	$-0.0494643\pi$
$432$	47.8826	−	67.9651i	0.110839	−	0.157327i
$433$	−706.716			−1.63214			−0.816069	−	0.577954i	$-0.803851\pi$
$433$	−706.716			−1.63214			−0.816069	+	0.577954i	$0.803851\pi$
$434$	27.3955	+	4.23681i	0.0631233	+	0.00976223i
$435$		0			0
$436$	−598.057	−	189.516i	−1.37169	−	0.434670i
$437$	−289.226			−0.661844
$438$	−24.6621	+	159.467i	−0.0563062	+	0.364080i
$439$			507.488i			1.15601i	0.816033	+	0.578005i	$0.196169\pi$
$439$			507.488i			1.15601i	−0.816033	+	0.578005i	$0.803831\pi$
$440$		0			0
$441$	−146.674			−0.332593
$442$	15.3100	+	2.36774i	0.0346380	+	0.00535689i
$443$		−	412.172i		−	0.930410i	−0.885203	−	0.465205i	$-0.845981\pi$
$443$		−	412.172i		−	0.930410i	0.885203	−	0.465205i	$-0.154019\pi$
$444$	106.637	−	336.516i	0.240174	−	0.757919i
$445$		0			0
$446$	−25.2824	+	163.478i	−0.0566869	+	0.366542i
$447$			214.544i			0.479965i
$448$	16.8059	−	12.7804i	0.0375132	−	0.0285277i
$449$	−808.617			−1.80093			−0.900465	−	0.434929i	$-0.856773\pi$
$449$	−808.617			−1.80093			−0.900465	+	0.434929i	$0.856773\pi$
$450$		0			0
$451$			957.124i			2.12223i
$452$	376.449	+	119.291i	0.832852	+	0.263919i
$453$	131.802			0.290955
$454$	−110.511	+	714.573i	−0.243417	+	1.57395i
$455$		0			0
$456$	154.560	+	76.6370i	0.338948	+	0.168064i
$457$	−472.873			−1.03473			−0.517367	−	0.855764i	$-0.673088\pi$
$457$	−472.873			−1.03473			−0.517367	+	0.855764i	$0.673088\pi$
$458$	240.773	+	37.2364i	0.525705	+	0.0813021i
$459$		−	96.5881i		−	0.210432i
$460$		0			0
$461$	433.776			0.940946			0.470473	−	0.882414i	$-0.344083\pi$
$461$	433.776			0.940946			0.470473	+	0.882414i	$0.344083\pi$
$462$	−3.57916	+	23.1431i	−0.00774709	+	0.0500933i
$463$		−	530.624i		−	1.14606i	−0.819536	−	0.573028i	$-0.805769\pi$
$463$		−	530.624i		−	1.14606i	0.819536	−	0.573028i	$-0.194231\pi$
$464$	−312.827	−	220.392i	−0.674196	−	0.474983i
$465$		0			0
$466$	−270.019	−	41.7594i	−0.579440	−	0.0896124i
$467$			355.266i			0.760741i	0.924834	+	0.380370i	$0.124203\pi$
$467$			355.266i			0.760741i	−0.924834	+	0.380370i	$0.875797\pi$
$468$	−4.76693	−	1.51057i	−0.0101857	−	0.00322772i
$469$	−24.0168			−0.0512086
$470$		0			0
$471$		−	59.3990i		−	0.126113i
$472$	86.4686	−	174.388i	0.183196	−	0.369467i
$473$	1139.08			2.40820
$474$	348.912	+	53.9605i	0.736102	+	0.113841i
$475$		0			0
$476$	7.40978	−	23.3831i	0.0155668	−	0.0491242i
$477$	−89.9232			−0.188518
$478$	−17.2593	+	111.600i	−0.0361072	+	0.233472i
$479$		−	548.640i		−	1.14539i	−0.819770	−	0.572693i	$-0.805899\pi$
$479$		−	548.640i		−	1.14539i	0.819770	−	0.572693i	$-0.194101\pi$
$480$		0			0
$481$	−21.2324			−0.0441423
$482$	−4.43050	−	0.685191i	−0.00919190	−	0.00142156i
$483$		−	13.2738i		−	0.0274821i
$484$	−1139.82	−	361.194i	−2.35501	−	0.746269i
$485$		0			0
$486$	−4.76497	+	30.8106i	−0.00980446	+	0.0633964i
$487$		−	134.618i		−	0.276422i	−0.990403	−	0.138211i	$-0.955865\pi$
$487$		−	134.618i		−	0.276422i	0.990403	−	0.138211i	$-0.0441352\pi$
$488$	−536.412	−	265.974i	−1.09921	−	0.545029i
$489$	286.721			0.586341
$490$		0			0
$491$			756.810i			1.54136i	0.637220	+	0.770682i	$0.280084\pi$
$491$			756.810i			1.54136i	−0.637220	+	0.770682i	$0.719916\pi$
$492$	−97.7529	+	308.480i	−0.198685	+	0.626991i
$493$	−444.572			−0.901768
$494$	1.58589	−	10.2545i	0.00321031	−	0.0207581i
$495$		0			0
$496$	−387.167	+	549.549i	−0.780579	+	1.10796i
$497$	−12.9585			−0.0260734
$498$	20.1609	+	3.11795i	0.0404837	+	0.00626094i
$499$		−	706.956i		−	1.41675i	−0.705838	−	0.708373i	$-0.749430\pi$
$499$		−	706.956i		−	1.41675i	0.705838	−	0.708373i	$-0.250570\pi$
$500$		0			0
$501$	−144.811			−0.289043
$502$	−120.988	+	782.318i	−0.241012	+	1.55840i
$503$			100.567i			0.199935i	0.994991	+	0.0999673i	$0.0318738\pi$
$503$			100.567i			0.199935i	−0.994991	+	0.0999673i	$0.968126\pi$
$504$	−3.51720	+	7.09344i	−0.00697858	+	0.0140743i
$505$		0			0
$506$	940.887	+	145.511i	1.85946	+	0.287572i
$507$		−	292.416i		−	0.576757i
$508$	−32.7382	+	103.312i	−0.0644452	+	0.203370i
$509$	753.185			1.47973			0.739867	−	0.672753i	$-0.234888\pi$
$509$	753.185			1.47973			0.739867	+	0.672753i	$0.234888\pi$
$510$		0			0
$511$		−	15.3671i		−	0.0300726i
$512$	96.6232	+	502.800i	0.188717	+	0.982031i
$513$	−64.6938			−0.126109
$514$	−216.976	−	33.5561i	−0.422133	−	0.0652843i
$515$		0			0
$516$	367.124	+	116.336i	0.711480	+	0.225458i
$517$	1675.46			3.24073
$518$	−5.13807	+	33.2231i	−0.00991906	+	0.0641373i
$519$		−	334.112i		−	0.643761i
$520$		0			0
$521$	117.708			0.225926			0.112963	−	0.993599i	$-0.463966\pi$
$521$	117.708			0.225926			0.112963	+	0.993599i	$0.463966\pi$
$522$	141.814	+	21.9320i	0.271674	+	0.0420153i
$523$			617.411i			1.18052i	0.807214	+	0.590259i	$0.200974\pi$
$523$			617.411i			1.18052i	−0.807214	+	0.590259i	$0.799026\pi$
$524$	−5.38686	+	16.9994i	−0.0102803	+	0.0324415i
$525$		0			0
$526$	−100.170	+	647.704i	−0.190437	+	1.23138i
$527$			780.988i			1.48195i
$528$	−464.246	−	327.070i	−0.879254	−	0.619450i
$529$	−10.6508			−0.0201338
$530$		0			0
$531$			72.9932i			0.137464i
$532$	−15.6618	−	4.96301i	−0.0294395	−	0.00932896i
$533$	19.4635			0.0365169
$534$	32.3012	−	208.862i	0.0604892	−	0.391127i
$535$		0			0
$536$	258.722	−	521.786i	0.482690	−	0.973481i
$537$	−209.473			−0.390079
$538$	−257.009	−	39.7474i	−0.477713	−	0.0738799i
$539$			1001.88i			1.85877i
$540$		0			0
$541$	352.762			0.652056			0.326028	−	0.945360i	$-0.394290\pi$
$541$	352.762			0.652056			0.326028	+	0.945360i	$0.394290\pi$
$542$	100.771	−	651.591i	0.185924	−	1.20220i
$543$		−	186.339i		−	0.343166i
$544$	428.196	+	412.879i	0.787125	+	0.758969i
$545$		0			0
$546$	0.470623	+	0.0727835i	0.000861948	+	0.000133303i
$547$			295.110i			0.539507i	0.962929	+	0.269753i	$0.0869422\pi$
$547$			295.110i			0.539507i	−0.962929	+	0.269753i	$0.913058\pi$
$548$	692.846	+	219.553i	1.26432	+	0.400644i
$549$	224.525			0.408970
$550$		0			0
$551$			297.770i			0.540418i
$552$	288.385	+	142.993i	0.522437	+	0.259045i
$553$	−33.6231			−0.0608013
$554$	−601.102	−	92.9624i	−1.08502	−	0.167802i
$555$		0			0
$556$	−269.963	+	851.924i	−0.485545	+	1.53224i
$557$	−31.8538			−0.0571882			−0.0285941	−	0.999591i	$-0.509103\pi$
$557$	−31.8538			−0.0571882			−0.0285941	+	0.999591i	$0.509103\pi$
$558$	38.5284	−	249.127i	0.0690473	−	0.446465i
$559$		−	23.1636i		−	0.0414376i
$560$		0			0
$561$	−659.760			−1.17604
$562$	474.557	+	73.3919i	0.844408	+	0.130591i
$563$		−	906.668i		−	1.61042i	−0.592988	−	0.805211i	$-0.702052\pi$
$563$		−	906.668i		−	1.61042i	0.592988	−	0.805211i	$-0.297948\pi$
$564$	539.997	+	171.117i	0.957441	+	0.303400i
$565$		0			0
$566$	26.4936	−	171.310i	0.0468085	−	0.302667i
$567$		−	2.96908i		−	0.00523647i
$568$	139.596	−	281.534i	0.245767	−	0.495659i
$569$	−465.009			−0.817239			−0.408620	−	0.912705i	$-0.633990\pi$
$569$	−465.009			−0.817239			−0.408620	+	0.912705i	$0.633990\pi$
$570$		0			0
$571$			265.895i			0.465666i	0.972517	+	0.232833i	$0.0747995\pi$
$571$			265.895i			0.465666i	−0.972517	+	0.232833i	$0.925200\pi$
$572$	−10.3182	+	32.5613i	−0.0180388	+	0.0569253i
$573$	484.464			0.845488
$574$	4.71000	−	30.4552i	0.00820557	−	0.0530578i
$575$		0			0
$576$	−116.222	−	152.828i	−0.201774	−	0.265327i
$577$	−138.097			−0.239336			−0.119668	−	0.992814i	$-0.538183\pi$
$577$	−138.097			−0.239336			−0.119668	+	0.992814i	$0.538183\pi$
$578$	111.728	+	17.2791i	0.193301	+	0.0298946i
$579$			177.594i			0.306725i
$580$		0			0
$581$	−1.94281			−0.00334391
$582$	50.5848	−	327.085i	0.0869154	−	0.562001i
$583$			614.234i			1.05358i
$584$	333.863	+	165.542i	0.571683	+	0.283463i
$585$		0			0
$586$	−771.507	−	119.316i	−1.31656	−	0.203611i
$587$			648.473i			1.10472i	0.833604	+	0.552362i	$0.186273\pi$
$587$			648.473i			1.10472i	−0.833604	+	0.552362i	$0.813727\pi$
$588$	−102.324	+	322.903i	−0.174020	+	0.549155i
$589$	523.098			0.888113
$590$		0			0
$591$		−	67.4862i		−	0.114190i
$592$	−666.451	−	469.526i	−1.12576	−	0.793118i
$593$	350.392			0.590880			0.295440	−	0.955361i	$-0.404534\pi$
$593$	350.392			0.590880			0.295440	+	0.955361i	$0.404534\pi$
$594$	210.457	+	32.5479i	0.354304	+	0.0547944i
$595$		0			0
$596$	472.322	+	149.672i	0.792486	+	0.251128i
$597$	−255.731			−0.428359
$598$	2.95903	−	19.1333i	0.00494821	−	0.0319955i
$599$			276.745i			0.462012i	0.972952	+	0.231006i	$0.0742017\pi$
$599$			276.745i			0.462012i	−0.972952	+	0.231006i	$0.925798\pi$
$600$		0			0
$601$	815.487			1.35688			0.678442	−	0.734654i	$-0.262656\pi$
$601$	815.487			1.35688			0.678442	+	0.734654i	$0.262656\pi$
$602$	−36.2449	−	5.60540i	−0.0602075	−	0.00931130i
$603$			218.403i			0.362193i
$604$	91.9490	−	290.164i	0.152233	−	0.480405i
$605$		0			0
$606$	−86.1269	+	556.902i	−0.142124	+	0.918981i
$607$		−	247.049i		−	0.407001i	−0.979075	−	0.203500i	$-0.934768\pi$
$607$		−	247.049i		−	0.407001i	0.979075	−	0.203500i	$-0.0652318\pi$
$608$	276.543	−	286.802i	0.454840	−	0.471713i
$609$	−13.6660			−0.0224400
$610$		0			0
$611$		−	34.0710i		−	0.0557627i
$612$	−212.640	−	67.3825i	−0.347450	−	0.110102i
$613$	−1005.15			−1.63972			−0.819862	−	0.572561i	$-0.805950\pi$
$613$	−1005.15			−1.63972			−0.819862	+	0.572561i	$0.805950\pi$
$614$	18.4112	−	119.048i	0.0299857	−	0.193890i
$615$		0			0
$616$	48.4528	+	24.0248i	0.0786572	+	0.0390013i
$617$	−533.282			−0.864314			−0.432157	−	0.901798i	$-0.642247\pi$
$617$	−533.282			−0.864314			−0.432157	+	0.901798i	$0.642247\pi$
$618$	−541.568	−	83.7553i	−0.876324	−	0.135526i
$619$			1136.85i			1.83659i	0.395900	+	0.918294i	$0.370433\pi$
$619$			1136.85i			1.83659i	−0.395900	+	0.918294i	$0.629567\pi$
$620$		0			0
$621$	−120.709			−0.194378
$622$	32.5830	−	210.684i	0.0523842	−	0.338720i
$623$			20.1271i			0.0323067i
$624$	−6.65109	+	9.44063i	−0.0106588	+	0.0151292i
$625$		0			0
$626$	91.3625	+	14.1295i	0.145946	+	0.0225711i
$627$			441.901i			0.704787i
$628$	−130.768	−	41.4384i	−0.208229	−	0.0659847i
$629$	−947.121			−1.50576
$630$		0			0
$631$		−	936.738i		−	1.48453i	−0.670107	−	0.742265i	$-0.733752\pi$
$631$		−	936.738i		−	1.48453i	0.670107	−	0.742265i	$-0.266248\pi$
$632$	362.206	−	730.490i	0.573110	−	1.15584i
$633$	−404.149			−0.638466
$634$	16.5390	+	2.55781i	0.0260867	+	0.00403440i
$635$		0			0
$636$	−62.7329	+	197.967i	−0.0986366	+	0.311269i
$637$	20.3735			0.0319836
$638$	149.810	−	968.682i	0.234812	−	1.51831i
$639$			117.841i			0.184415i
$640$		0			0
$641$	214.558			0.334723			0.167362	−	0.985896i	$-0.446475\pi$
$641$	214.558			0.334723			0.167362	+	0.985896i	$0.446475\pi$
$642$	−62.2468	−	9.62669i	−0.0969577	−	0.0149948i
$643$		−	786.394i		−	1.22301i	−0.791241	−	0.611504i	$-0.790565\pi$
$643$		−	786.394i		−	1.22301i	0.791241	−	0.611504i	$-0.209435\pi$
$644$	−29.2225	−	9.26020i	−0.0453765	−	0.0143792i
$645$		0			0
$646$	70.7424	−	457.425i	0.109508	−	0.708088i
$647$		−	316.550i		−	0.489258i	−0.969617	−	0.244629i	$-0.921334\pi$
$647$		−	316.550i		−	0.489258i	0.969617	−	0.244629i	$-0.0786661\pi$
$648$	64.5058	+	31.9845i	0.0995459	+	0.0493588i
$649$	498.592			0.768246
$650$		0			0
$651$			24.0073i			0.0368775i
$652$	200.024	−	631.219i	0.306786	−	0.968127i
$653$	516.391			0.790797			0.395399	−	0.918510i	$-0.370606\pi$
$653$	516.391			0.790797			0.395399	+	0.918510i	$0.370606\pi$
$654$	83.0384	−	536.932i	0.126970	−	0.820997i
$655$		0			0
$656$	610.926	+	430.408i	0.931290	+	0.656110i
$657$	−139.744			−0.212700
$658$	−53.3121	−	8.24491i	−0.0810215	−	0.0125303i
$659$			285.118i			0.432653i	0.976321	+	0.216326i	$0.0694076\pi$
$659$			285.118i			0.432653i	−0.976321	+	0.216326i	$0.930592\pi$
$660$		0			0
$661$	−391.847			−0.592809			−0.296405	−	0.955062i	$-0.595788\pi$
$661$	−391.847			−0.592809			−0.296405	+	0.955062i	$0.595788\pi$
$662$	−33.9516	+	219.534i	−0.0512865	+	0.331622i
$663$			13.4165i			0.0202360i
$664$	20.9290	−	42.2092i	0.0315196	−	0.0635681i
$665$		0			0
$666$	302.122	+	46.7242i	0.453637	+	0.0701565i
$667$			555.593i			0.832973i
$668$	−101.024	+	318.802i	−0.151233	+	0.477248i
$669$	−143.259			−0.214139
$670$		0			0
$671$		−	1533.65i		−	2.28562i
$672$	13.1626	+	12.6917i	0.0195872	+	0.0188865i
$673$	−1213.59			−1.80325			−0.901626	−	0.432517i	$-0.857625\pi$
$673$	−1213.59			−1.80325			−0.901626	+	0.432517i	$0.857625\pi$
$674$	458.257	+	70.8711i	0.679907	+	0.105150i
$675$		0			0
$676$	−643.756	−	203.997i	−0.952303	−	0.301771i
$677$	251.863			0.372028			0.186014	−	0.982547i	$-0.440443\pi$
$677$	251.863			0.372028			0.186014	+	0.982547i	$0.440443\pi$
$678$	−52.2688	+	337.974i	−0.0770926	+	0.498486i
$679$			31.5197i			0.0464207i
$680$		0			0
$681$	−626.195			−0.919523
$682$	−1701.70	−	263.174i	−2.49517	−	0.385886i
$683$			664.793i			0.973342i	0.873585	+	0.486671i	$0.161789\pi$
$683$			664.793i			0.973342i	−0.873585	+	0.486671i	$0.838211\pi$
$684$	−45.1322	+	142.424i	−0.0659828	+	0.208222i
$685$		0			0
$686$	9.87143	−	63.8293i	0.0143898	−	0.0930457i
$687$			210.994i			0.307124i
$688$	512.231	−	727.067i	0.744522	−	1.05678i
$689$	12.4907			0.0181287
$690$		0			0
$691$		−	654.347i		−	0.946957i	−0.880805	−	0.473479i	$-0.842998\pi$
$691$		−	654.347i		−	0.946957i	0.880805	−	0.473479i	$-0.157002\pi$
$692$	−735.551	−	233.086i	−1.06293	−	0.336829i
$693$	−20.2808			−0.0292652
$694$	122.907	−	794.728i	0.177100	−	1.14514i
$695$		0			0
$696$	147.217	−	296.904i	0.211519	−	0.426587i
$697$	868.213			1.24564
$698$	−322.732	−	49.9117i	−0.462367	−	0.0715067i
$699$		−	236.623i		−	0.338517i
$700$		0			0
$701$	−1266.25			−1.80635			−0.903174	−	0.429275i	$-0.858769\pi$
$701$	−1266.25			−1.80635			−0.903174	+	0.429275i	$0.858769\pi$
$702$	0.661874	−	4.27972i	0.000942840	−	0.00609647i
$703$			634.373i			0.902380i
$704$	−1043.92	+	793.870i	−1.48284	+	1.12766i
$705$		0			0
$706$	−347.570	−	53.7529i	−0.492309	−	0.0761372i
$707$		−	53.6661i		−	0.0759068i
$708$	160.695	+	50.9221i	0.226971	+	0.0719239i
$709$	−493.220			−0.695656			−0.347828	−	0.937558i	$-0.613081\pi$
$709$	−493.220			−0.695656			−0.347828	+	0.937558i	$0.613081\pi$
$710$		0			0
$711$			305.759i			0.430041i
$712$	−437.278	−	216.819i	−0.614154	−	0.304522i
$713$	976.020			1.36889
$714$	20.9932	+	3.24667i	0.0294023	+	0.00454716i
$715$		0			0
$716$	−146.134	+	461.156i	−0.204098	+	0.644073i
$717$	−97.7971			−0.136398
$718$	105.649	−	683.135i	0.147144	−	0.951442i
$719$			60.3910i			0.0839930i	0.999118	+	0.0419965i	$0.0133718\pi$
$719$			60.3910i			0.0839930i	−0.999118	+	0.0419965i	$0.986628\pi$
$720$		0			0
$721$	52.1884			0.0723834
$722$	407.138	+	62.9653i	0.563904	+	0.0872096i
$723$		−	3.88254i		−	0.00537003i
$724$	−410.228	−	129.995i	−0.566613	−	0.179552i
$725$		0			0
$726$	158.261	−	1023.33i	0.217990	−	1.40954i
$727$			994.690i			1.36821i	0.729383	+	0.684106i	$0.239807\pi$
$727$			994.690i			1.36821i	−0.729383	+	0.684106i	$0.760193\pi$
$728$	0.488554	−	0.985307i	0.000671090	−	0.00135344i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		−	1033.27i		−	1.41350i
$732$	156.635	−	494.294i	0.213982	−	0.675264i
$733$	1167.65			1.59298			0.796488	−	0.604654i	$-0.206689\pi$
$733$	1167.65			1.59298			0.796488	+	0.604654i	$0.206689\pi$
$734$	222.835	−	1440.87i	0.303590	−	1.96303i
$735$		0			0
$736$	515.986	−	535.127i	0.701067	−	0.727075i
$737$	1491.83			2.02420
$738$	−276.951	−	42.8314i	−0.375273	−	0.0580372i
$739$		−	79.9863i		−	0.108236i	−0.998535	−	0.0541179i	$-0.982765\pi$
$739$		−	79.9863i		−	0.108236i	0.998535	−	0.0541179i	$-0.0172347\pi$
$740$		0			0
$741$	8.98623			0.0121272
$742$	3.02264	−	19.5446i	0.00407364	−	0.0263405i
$743$			402.122i			0.541214i	0.962690	+	0.270607i	$0.0872244\pi$
$743$			402.122i			0.541214i	−0.962690	+	0.270607i	$0.912776\pi$
$744$	−521.578	−	258.619i	−0.701045	−	0.347606i
$745$		0			0
$746$	92.2530	+	14.2672i	0.123664	+	0.0191250i
$747$			17.6674i			0.0236511i
$748$	−460.267	+	1452.47i	−0.615330	+	1.94180i
$749$	5.99844			0.00800860
$750$		0			0
$751$		−	58.7486i		−	0.0782271i	−0.999235	−	0.0391136i	$-0.987547\pi$
$751$		−	58.7486i		−	0.0782271i	0.999235	−	0.0391136i	$-0.0124534\pi$
$752$	753.434	−	1069.43i	1.00191	−	1.42212i
$753$	−685.561			−0.910440
$754$	−19.6985	−	3.04644i	−0.0261254	−	0.00404038i
$755$		0			0
$756$	−6.53646	−	2.07131i	−0.00864611	−	0.00273983i
$757$	−1040.91			−1.37504			−0.687522	−	0.726164i	$-0.741301\pi$
$757$	−1040.91			−1.37504			−0.687522	+	0.726164i	$0.741301\pi$
$758$	35.9561	−	232.495i	0.0474355	−	0.306721i
$759$			824.519i			1.08632i
$760$		0			0
$761$	750.095			0.985670			0.492835	−	0.870123i	$-0.335961\pi$
$761$	750.095			0.985670			0.492835	+	0.870123i	$0.335961\pi$
$762$	−92.7530	−	14.3446i	−0.121723	−	0.0188249i
$763$			51.7417i			0.0678135i
$764$	337.976	−	1066.55i	0.442377	−	1.39601i
$765$		0			0
$766$	−76.9285	+	497.425i	−0.100429	+	0.649380i
$767$		−	10.1391i		−	0.0132191i
$768$	−417.533	+	149.246i	−0.543663	+	0.194331i
$769$	1065.98			1.38619			0.693094	−	0.720847i	$-0.256247\pi$
$769$	1065.98			1.38619			0.693094	+	0.720847i	$0.256247\pi$
$770$		0			0
$771$		−	190.141i		−	0.246616i
$772$	390.975	+	123.894i	0.506444	+	0.160485i
$773$	−947.271			−1.22545			−0.612724	−	0.790297i	$-0.709926\pi$
$773$	−947.271			−1.22545			−0.612724	+	0.790297i	$0.709926\pi$
$774$	−50.9740	+	329.601i	−0.0658579	+	0.425842i
$775$		0			0
$776$	−684.791	−	339.546i	−0.882463	−	0.437560i
$777$	−29.1141			−0.0374699
$778$	705.393	+	109.092i	0.906675	+	0.140220i
$779$		−	581.521i		−	0.746497i
$780$		0			0
$781$	804.931			1.03064
$782$	131.994	−	853.484i	0.168791	−	1.09141i
$783$			124.275i			0.158716i
$784$	639.491	+	450.533i	0.815678	+	0.574659i
$785$		0			0
$786$	−15.2619	−	2.36031i	−0.0194172	−	0.00300294i
$787$		−	11.5874i		−	0.0147236i	−0.999973	−	0.00736178i	$-0.997657\pi$
$787$		−	11.5874i		−	0.0147236i	0.999973	−	0.00736178i	$-0.00234335\pi$
$788$	−148.572	−	47.0803i	−0.188543	−	0.0597465i
$789$	−567.596			−0.719387
$790$		0			0
$791$		−	32.5690i		−	0.0411744i
$792$	218.475	−	440.617i	0.275852	−	0.556334i
$793$	−31.1874			−0.0393284
$794$	205.198	+	31.7345i	0.258436	+	0.0399679i
$795$		0			0
$796$	−178.405	+	562.994i	−0.224127	+	0.707278i
$797$	−780.220			−0.978946			−0.489473	−	0.872018i	$-0.662811\pi$
$797$	−780.220			−0.978946			−0.489473	+	0.872018i	$0.662811\pi$
$798$	2.17459	−	14.0611i	0.00272505	−	0.0176204i
$799$		−	1519.82i		−	1.90215i
$800$		0			0
$801$	183.030			0.228502
$802$	−240.339	−	37.1692i	−0.299674	−	0.0463457i
$803$			954.545i			1.18872i
$804$	480.815	+	152.364i	0.598029	+	0.189507i
$805$		0			0
$806$	−5.35175	+	34.6048i	−0.00663989	+	0.0429340i
$807$		−	225.223i		−	0.279086i
$808$	1165.94	+	578.120i	1.44300	+	0.715495i
$809$	−1061.80			−1.31249			−0.656243	−	0.754549i	$-0.727855\pi$
$809$	−1061.80			−1.31249			−0.656243	+	0.754549i	$0.727855\pi$
$810$		0			0
$811$		−	309.236i		−	0.381302i	−0.981658	−	0.190651i	$-0.938940\pi$
$811$		−	309.236i		−	0.381302i	0.981658	−	0.190651i	$-0.0610599\pi$
$812$	−9.53376	+	30.0858i	−0.0117411	+	0.0370514i
$813$	571.003			0.702341
$814$	319.157	−	2063.69i	0.392085	−	2.53525i
$815$		0			0
$816$	−296.687	+	421.121i	−0.363587	+	0.516079i
$817$	−692.072			−0.847089
$818$	361.281	+	55.8734i	0.441664	+	0.0683049i
$819$			0.412417i			0.000503562i
$820$		0			0
$821$	−1156.76			−1.40897			−0.704483	−	0.709721i	$-0.748821\pi$
$821$	−1156.76			−1.40897			−0.704483	+	0.709721i	$0.748821\pi$
$822$	−96.1995	+	622.033i	−0.117031	+	0.756731i
$823$			1441.89i			1.75200i	0.482314	+	0.875998i	$0.339796\pi$
$823$			1441.89i			1.75200i	−0.482314	+	0.875998i	$0.660204\pi$
$824$	−562.201	+	1133.84i	−0.682283	+	1.37602i
$825$		0			0
$826$	−15.8649	−	2.45357i	−0.0192069	−	0.00297042i
$827$		−	367.599i		−	0.444497i	−0.974990	−	0.222249i	$-0.928660\pi$
$827$		−	367.599i		−	0.444497i	0.974990	−	0.222249i	$-0.0713397\pi$
$828$	−84.2097	+	265.741i	−0.101703	+	0.320944i
$829$	172.743			0.208375			0.104188	−	0.994558i	$-0.466776\pi$
$829$	172.743			0.208375			0.104188	+	0.994558i	$0.466776\pi$
$830$		0			0
$831$		−	526.758i		−	0.633884i
$832$	16.1437	+	21.2285i	0.0194034	+	0.0255150i
$833$	908.808			1.09101
$834$	−764.852	−	118.287i	−0.917089	−	0.141831i
$835$		0			0
$836$	972.850	+	308.283i	1.16370	+	0.368759i
$837$	218.315			0.260831
$838$	51.3593	−	332.093i	0.0612879	−	0.396292i
$839$			1083.17i			1.29103i	0.763748	+	0.645514i	$0.223357\pi$
$839$			1083.17i			1.29103i	−0.763748	+	0.645514i	$0.776643\pi$
$840$		0			0
$841$	−268.994			−0.319850
$842$	1235.89	+	191.135i	1.46780	+	0.227001i
$843$			415.864i			0.493315i
$844$	−281.946	+	889.739i	−0.334059	+	1.05419i
$845$		0			0
$846$	−74.9769	+	484.806i	−0.0886252	+	0.573057i
$847$			98.6133i			0.116427i
$848$	392.062	+	276.214i	0.462337	+	0.325724i
$849$	150.122			0.176822
$850$		0			0
$851$			1183.64i			1.39088i
$852$	259.428	+	82.2092i	0.304493	+	0.0964896i
$853$	1218.00			1.42790			0.713951	−	0.700196i	$-0.246904\pi$
$853$	1218.00			1.42790			0.713951	+	0.700196i	$0.246904\pi$
$854$	−7.54709	+	48.8000i	−0.00883734	+	0.0571429i
$855$		0			0
$856$	−64.6184	+	130.321i	−0.0754888	+	0.152244i
$857$	−207.055			−0.241604			−0.120802	−	0.992677i	$-0.538547\pi$
$857$	−207.055			−0.241604			−0.120802	+	0.992677i	$0.538547\pi$
$858$	−29.2333	−	4.52103i	−0.0340715	−	0.00526927i
$859$			1186.36i			1.38109i	0.723290	+	0.690544i	$0.242629\pi$
$859$			1186.36i			1.38109i	−0.723290	+	0.690544i	$0.757371\pi$
$860$		0			0
$861$	26.6885			0.0309971
$862$	40.7809	−	263.692i	0.0473096	−	0.305907i
$863$		−	885.953i		−	1.02660i	−0.858210	−	0.513298i	$-0.828423\pi$
$863$		−	885.953i		−	1.02660i	0.858210	−	0.513298i	$-0.171577\pi$
$864$	115.415	−	119.697i	0.133582	−	0.138538i
$865$		0			0
$866$	−1396.83	−	216.024i	−1.61296	−	0.249450i
$867$			97.9093i			0.112929i
$868$	52.8522	+	16.7481i	0.0608897	+	0.0192951i
$869$	2088.54			2.40338
$870$		0			0
$871$		−	30.3370i		−	0.0348301i
$872$	−1124.13	−	557.389i	−1.28914	−	0.639207i
$873$	286.631			0.328329
$874$	−571.656	−	88.4086i	−0.654069	−	0.101154i
$875$		0			0
$876$	−97.4894	+	307.648i	−0.111289	+	0.351197i
$877$	643.339			0.733567			0.366784	−	0.930306i	$-0.380459\pi$
$877$	643.339			0.733567			0.366784	+	0.930306i	$0.380459\pi$
$878$	−155.125	+	1003.05i	−0.176680	+	1.14243i
$879$		−	676.088i		−	0.769155i
$880$		0			0
$881$	353.918			0.401723			0.200861	−	0.979620i	$-0.435626\pi$
$881$	353.918			0.401723			0.200861	+	0.979620i	$0.435626\pi$
$882$	−289.901	−	44.8341i	−0.328686	−	0.0508323i
$883$		−	1093.51i		−	1.23840i	−0.785233	−	0.619200i	$-0.787457\pi$
$883$		−	1093.51i		−	1.23840i	0.785233	−	0.619200i	$-0.212543\pi$
$884$	29.5365	+	9.35971i	0.0334123	+	0.0105879i
$885$		0			0
$886$	125.990	−	814.659i	0.142201	−	0.919479i
$887$			520.234i			0.586510i	0.956034	+	0.293255i	$0.0947384\pi$
$887$			520.234i			0.586510i	−0.956034	+	0.293255i	$0.905262\pi$
$888$	313.633	−	632.529i	0.353190	−	0.712307i
$889$	8.93819			0.0100542
$890$		0			0
$891$			184.428i			0.206990i
$892$	−99.9413	+	315.386i	−0.112042	+	0.353571i
$893$	−1017.96			−1.13993
$894$	−65.5804	+	424.048i	−0.0733562	+	0.474326i
$895$		0			0
$896$	37.1236	−	20.1234i	0.0414326	−	0.0224592i
$897$	16.7669			0.0186922
$898$	−1598.23	−	247.172i	−1.77977	−	0.275248i
$899$		−	1004.85i		−	1.11775i
$900$		0			0
$901$	557.175			0.618397
$902$	−292.567	+	1891.76i	−0.324354	+	2.09729i
$903$		−	31.7622i		−	0.0351741i
$904$	707.588	+	350.850i	0.782730	+	0.388109i
$905$		0			0
$906$	260.508	+	40.2884i	0.287536	+	0.0444685i
$907$		−	567.834i		−	0.626057i	−0.949744	−	0.313029i	$-0.898656\pi$
$907$		−	567.834i		−	0.626057i	0.949744	−	0.313029i	$-0.101344\pi$
$908$	−436.851	+	1378.58i	−0.481114	+	1.51825i
$909$	−488.025			−0.536881
$910$		0			0
$911$			1180.19i			1.29549i	0.761858	+	0.647744i	$0.224287\pi$
$911$			1180.19i			1.29549i	−0.761858	+	0.647744i	$0.775713\pi$
$912$	282.063	+	198.718i	0.309279	+	0.217893i
$913$	120.680			0.132180
$914$	−934.635	−	144.545i	−1.02258	−	0.158145i
$915$		0			0
$916$	464.506	+	147.196i	0.507103	+	0.160694i
$917$	1.47072			0.00160384
$918$	29.5244	−	190.907i	0.0321616	−	0.207959i
$919$			54.5449i			0.0593524i	0.999560	+	0.0296762i	$0.00944761\pi$
$919$			54.5449i			0.0593524i	−0.999560	+	0.0296762i	$0.990552\pi$
$920$		0			0
$921$	104.324			0.113273
$922$	857.360	+	132.594i	0.929892	+	0.143811i
$923$		−	16.3686i		−	0.0177341i
$924$	−14.1484	+	44.6483i	−0.0153122	+	0.0483207i
$925$		0			0
$926$	162.197	−	1048.78i	0.175159	−	1.13259i
$927$		−	474.587i		−	0.511960i
$928$	−550.936	−	531.228i	−0.593681	−	0.572444i
$929$	175.428			0.188835			0.0944175	−	0.995533i	$-0.469901\pi$
$929$	175.428			0.188835			0.0944175	+	0.995533i	$0.469901\pi$
$930$		0			0
$931$		−	608.711i		−	0.653825i
$932$	−520.929	−	165.075i	−0.558937	−	0.177119i
$933$	184.627			0.197885
$934$	−108.595	+	702.184i	−0.116269	+	0.751803i
$935$		0			0
$936$	−8.96011	−	4.44277i	−0.00957277	−	0.00474655i
$937$	335.374			0.357923			0.178962	−	0.983856i	$-0.442726\pi$
$937$	335.374			0.357923			0.178962	+	0.983856i	$0.442726\pi$
$938$	−47.4694	−	7.34130i	−0.0506070	−	0.00782654i
$939$			80.0629i			0.0852640i
$940$		0			0
$941$	709.182			0.753647			0.376823	−	0.926285i	$-0.377016\pi$
$941$	709.182			0.753647			0.376823	+	0.926285i	$0.377016\pi$
$942$	18.1567	−	117.402i	0.0192746	−	0.124631i
$943$		−	1085.03i		−	1.15061i
$944$	224.211	−	318.248i	0.237512	−	0.337127i
$945$		0			0
$946$	2251.39	+	348.186i	2.37991	+	0.368061i
$947$			992.486i			1.04803i	0.851708	+	0.524016i	$0.175567\pi$
$947$			992.486i			1.04803i	−0.851708	+	0.524016i	$0.824433\pi$
$948$	673.132	+	213.306i	0.710055	+	0.225007i
$949$	19.4110			0.0204542
$950$		0			0
$951$			14.4935i			0.0152402i
$952$	21.7930	−	43.9518i	0.0228919	−	0.0461679i
$953$	−1438.16			−1.50908			−0.754542	−	0.656251i	$-0.772141\pi$
$953$	−1438.16			−1.50908			−0.754542	+	0.656251i	$0.772141\pi$
$954$	−177.733	−	27.4871i	−0.186303	−	0.0288124i
$955$		0			0
$956$	−68.2260	+	215.301i	−0.0713661	+	0.225211i
$957$	848.877			0.887018
$958$	167.704	−	1084.39i	0.175057	−	1.13193i
$959$		−	59.9425i		−	0.0625052i
$960$		0			0
$961$	−804.245			−0.836883
$962$	−41.9660	−	6.49018i	−0.0436237	−	0.00674655i
$963$		−	54.5482i		−	0.0566440i
$964$	−8.54744	−	2.70857i	−0.00886664	−	0.00280971i
$965$		0			0
$966$	4.05745	−	26.2358i	0.00420026	−	0.0271592i
$967$		−	1376.32i		−	1.42329i	−0.702539	−	0.711646i	$-0.747950\pi$
$967$		−	1376.32i		−	1.42329i	0.702539	−	0.711646i	$-0.252050\pi$
$968$	−2142.46	−	1062.31i	−2.21328	−	1.09743i
$969$	400.851			0.413675
$970$		0			0
$971$			652.667i			0.672159i	0.941834	+	0.336080i	$0.109101\pi$
$971$			652.667i			0.672159i	−0.941834	+	0.336080i	$0.890899\pi$
$972$	−18.8360	+	59.4408i	−0.0193786	+	0.0611531i
$973$	73.7053			0.0757506
$974$	41.1490	−	266.072i	0.0422474	−	0.273175i
$975$		0			0
$976$	−978.920	−	689.666i	−1.00299	−	0.706625i
$977$	−467.260			−0.478260			−0.239130	−	0.970988i	$-0.576862\pi$
$977$	−467.260			−0.478260			−0.239130	+	0.970988i	$0.576862\pi$
$978$	566.705	+	87.6428i	0.579453	+	0.0896143i
$979$		−	1250.22i		−	1.27703i
$980$		0			0
$981$	470.525			0.479638
$982$	−231.336	+	1495.84i	−0.235577	+	1.52326i
$983$		−	1044.27i		−	1.06233i	−0.847268	−	0.531165i	$-0.821754\pi$
$983$		−	1044.27i		−	1.06233i	0.847268	−	0.531165i	$-0.178246\pi$
$984$	−287.503	+	579.830i	−0.292178	+	0.589259i
$985$		0			0
$986$	−878.697	−	135.894i	−0.891174	−	0.137823i
$987$		−	46.7185i		−	0.0473339i
$988$	6.26905	−	19.7833i	0.00634519	−	0.0200236i
$989$	−1291.30			−1.30566
$990$		0			0
$991$			1705.99i			1.72148i	0.509044	+	0.860740i	$0.329999\pi$
$991$			1705.99i			1.72148i	−0.509044	+	0.860740i	$0.670001\pi$
$992$	−933.219	+	967.839i	−0.940745	+	0.975644i
$993$	−192.382			−0.193738
$994$	−25.6125	−	3.96106i	−0.0257671	−	0.00398497i
$995$		0			0
$996$	38.8950	+	12.3253i	0.0390512	+	0.0123748i
$997$	−1262.24			−1.26604			−0.633020	−	0.774136i	$-0.718185\pi$
$997$	−1262.24			−1.26604			−0.633020	+	0.774136i	$0.718185\pi$
$998$	216.097	−	1397.30i	0.216530	−	1.40010i
$999$			264.756i			0.265021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.c.g.151.8	yes	8
3.2	odd	2		900.3.c.n.451.1		8
4.3	odd	2	inner	300.3.c.g.151.7	yes	8
5.2	odd	4		300.3.f.c.199.8		16
5.3	odd	4		300.3.f.c.199.9		16
5.4	even	2		300.3.c.e.151.1	✓	8
12.11	even	2		900.3.c.n.451.2		8
15.2	even	4		900.3.f.h.199.9		16
15.8	even	4		900.3.f.h.199.8		16
15.14	odd	2		900.3.c.t.451.8		8
20.3	even	4		300.3.f.c.199.7		16
20.7	even	4		300.3.f.c.199.10		16
20.19	odd	2		300.3.c.e.151.2	yes	8
60.23	odd	4		900.3.f.h.199.10		16
60.47	odd	4		900.3.f.h.199.7		16
60.59	even	2		900.3.c.t.451.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.3.c.e.151.1	✓	8	5.4	even	2
300.3.c.e.151.2	yes	8	20.19	odd	2
300.3.c.g.151.7	yes	8	4.3	odd	2	inner
300.3.c.g.151.8	yes	8	1.1	even	1	trivial
300.3.f.c.199.7		16	20.3	even	4
300.3.f.c.199.8		16	5.2	odd	4
300.3.f.c.199.9		16	5.3	odd	4
300.3.f.c.199.10		16	20.7	even	4
900.3.c.n.451.1		8	3.2	odd	2
900.3.c.n.451.2		8	12.11	even	2
900.3.c.t.451.7		8	60.59	even	2
900.3.c.t.451.8		8	15.14	odd	2
900.3.f.h.199.7		16	60.47	odd	4
900.3.f.h.199.8		16	15.8	even	4
900.3.f.h.199.9		16	15.2	even	4
900.3.f.h.199.10		16	60.23	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.97650 + 0.305673i) q^{2} +1.73205i q^{3} +(3.81313 + 1.20833i) q^{4} +(-0.529441 + 3.42340i) q^{6} -0.329898i q^{7} +(7.16731 + 3.55383i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(1.97650 + 0.305673i) q^{2} +1.73205i q^{3} +(3.81313 + 1.20833i) q^{4} +(-0.529441 + 3.42340i) q^{6} -0.329898i q^{7} +(7.16731 + 3.55383i) q^{8} -3.00000 q^{9} +20.4920i q^{11} +(-2.09288 + 6.60453i) q^{12} +0.416712 q^{13} +(0.100841 - 0.652044i) q^{14} +(13.0799 + 9.21501i) q^{16} +18.5884 q^{17} +(-5.92951 - 0.917019i) q^{18} -12.4503i q^{19} +0.571400 q^{21} +(-6.26384 + 40.5024i) q^{22} -23.2304i q^{23} +(-6.15542 + 12.4141i) q^{24} +(0.823633 + 0.127378i) q^{26} -5.19615i q^{27} +(0.398624 - 1.25794i) q^{28} -23.9166 q^{29} +42.0148i q^{31} +(23.0357 + 22.2117i) q^{32} -35.4931 q^{33} +(36.7400 + 5.68197i) q^{34} +(-11.4394 - 3.62498i) q^{36} -50.9523 q^{37} +(3.80573 - 24.6081i) q^{38} +0.721767i q^{39} +46.7073 q^{41} +(1.12937 + 0.174661i) q^{42} -55.5866i q^{43} +(-24.7610 + 78.1385i) q^{44} +(7.10090 - 45.9149i) q^{46} -81.7616i q^{47} +(-15.9609 + 22.6550i) q^{48} +48.8912 q^{49} +32.1960i q^{51} +(1.58898 + 0.503524i) q^{52} +29.9744 q^{53} +(1.58832 - 10.2702i) q^{54} +(1.17240 - 2.36448i) q^{56} +21.5646 q^{57} +(-47.2713 - 7.31067i) q^{58} -24.3311i q^{59} -74.8416 q^{61} +(-12.8428 + 83.0424i) q^{62} +0.989693i q^{63} +(38.7406 + 50.9428i) q^{64} +(-70.1523 - 10.8493i) q^{66} -72.8008i q^{67} +(70.8799 + 22.4608i) q^{68} +40.2362 q^{69} -39.2803i q^{71} +(-21.5019 - 10.6615i) q^{72} +46.5814 q^{73} +(-100.707 - 15.5747i) q^{74} +(15.0441 - 47.4747i) q^{76} +6.76026 q^{77} +(-0.220625 + 1.42657i) q^{78} -101.920i q^{79} +9.00000 q^{81} +(92.3170 + 14.2771i) q^{82} -5.88913i q^{83} +(2.17882 + 0.690438i) q^{84} +(16.9913 - 109.867i) q^{86} -41.4248i q^{87} +(-72.8250 + 146.872i) q^{88} -61.0100 q^{89} -0.137472i q^{91} +(28.0699 - 88.5804i) q^{92} -72.7718 q^{93} +(24.9923 - 161.602i) q^{94} +(-38.4717 + 39.8989i) q^{96} -95.5437 q^{97} +(96.6335 + 14.9447i) q^{98} -61.4759i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 8 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 8 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9	\( 8 q + 2 q^{2} - 8 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9} + 8 q^{13} + 22 q^{14} + 40 q^{16} - 6 q^{18} + 24 q^{21} + 4 q^{22} - 36 q^{24} - 66 q^{26} + 104 q^{28} - 32 q^{29} + 112 q^{32} + 124 q^{34} + 24 q^{36} - 176 q^{37} - 170 q^{38} - 16 q^{41} + 54 q^{42} + 40 q^{44} - 76 q^{46} + 24 q^{48} + 16 q^{49} + 56 q^{52} - 304 q^{53} + 18 q^{54} - 172 q^{56} + 72 q^{57} - 12 q^{58} + 136 q^{61} - 238 q^{62} + 16 q^{64} - 108 q^{66} + 88 q^{68} - 96 q^{69} - 60 q^{72} + 240 q^{73} - 108 q^{74} + 120 q^{76} - 384 q^{77} + 150 q^{78} + 72 q^{81} + 320 q^{82} - 144 q^{84} + 214 q^{86} - 200 q^{88} + 128 q^{89} + 312 q^{92} + 72 q^{93} + 12 q^{94} + 96 q^{96} + 216 q^{97} + 60 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 8 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9 + 8 * q^13 + 22 * q^14 + 40 * q^16 - 6 * q^18 + 24 * q^21 + 4 * q^22 - 36 * q^24 - 66 * q^26 + 104 * q^28 - 32 * q^29 + 112 * q^32 + 124 * q^34 + 24 * q^36 - 176 * q^37 - 170 * q^38 - 16 * q^41 + 54 * q^42 + 40 * q^44 - 76 * q^46 + 24 * q^48 + 16 * q^49 + 56 * q^52 - 304 * q^53 + 18 * q^54 - 172 * q^56 + 72 * q^57 - 12 * q^58 + 136 * q^61 - 238 * q^62 + 16 * q^64 - 108 * q^66 + 88 * q^68 - 96 * q^69 - 60 * q^72 + 240 * q^73 - 108 * q^74 + 120 * q^76 - 384 * q^77 + 150 * q^78 + 72 * q^81 + 320 * q^82 - 144 * q^84 + 214 * q^86 - 200 * q^88 + 128 * q^89 + 312 * q^92 + 72 * q^93 + 12 * q^94 + 96 * q^96 + 216 * q^97 + 60 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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