LMFDB - Embedded newform 300.3.f.c.199.6

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} - 4 x^{15} + 8 x^{14} - 14 x^{13} + 23 x^{12} - 26 x^{11} + 18 x^{10} - 10 x^{9} + 9 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 8x^14 - 14x^13 + 23x^12 - 26x^11 + 18x^10 - 10x^9 + 9x^8 - 20x^7 + 72x^6 - 208x^5 + 368x^4 - 448x^3 + 512x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.6
Root			$1.26238 + 0.637499i$ of defining polynomial
Character	$\chi$	$=$	300.199
Dual form			300.3.f.c.199.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49110 + 1.33290i) q^{2} +1.73205 q^{3} +(0.446749 - 3.97497i) q^{4} +(-2.58266 + 2.30865i) q^{6} -6.56834 q^{7} +(4.63210 + 6.52255i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-1.49110 + 1.33290i) q^{2} +1.73205 q^{3} +(0.446749 - 3.97497i) q^{4} +(-2.58266 + 2.30865i) q^{6} -6.56834 q^{7} +(4.63210 + 6.52255i) q^{8} +3.00000 q^{9} -2.26696i q^{11} +(0.773791 - 6.88486i) q^{12} +14.8772i q^{13} +(9.79404 - 8.75495i) q^{14} +(-15.6008 - 3.55163i) q^{16} +26.8250i q^{17} +(-4.47330 + 3.99870i) q^{18} +10.8680i q^{19} -11.3767 q^{21} +(3.02164 + 3.38027i) q^{22} +36.4610 q^{23} +(8.02303 + 11.2974i) q^{24} +(-19.8298 - 22.1834i) q^{26} +5.19615 q^{27} +(-2.93440 + 26.1090i) q^{28} +35.2510 q^{29} +23.8330i q^{31} +(27.9963 - 15.4985i) q^{32} -3.92650i q^{33} +(-35.7550 - 39.9987i) q^{34} +(1.34025 - 11.9249i) q^{36} +54.7495i q^{37} +(-14.4860 - 16.2053i) q^{38} +25.7680i q^{39} -23.8298 q^{41} +(16.9638 - 15.1640i) q^{42} -56.2515 q^{43} +(-9.01112 - 1.01276i) q^{44} +(-54.3670 + 48.5989i) q^{46} -51.4177 q^{47} +(-27.0214 - 6.15160i) q^{48} -5.85689 q^{49} +46.4622i q^{51} +(59.1364 + 6.64636i) q^{52} -30.6465i q^{53} +(-7.74797 + 6.92596i) q^{54} +(-30.4252 - 42.8423i) q^{56} +18.8240i q^{57} +(-52.5627 + 46.9861i) q^{58} -6.92483i q^{59} +107.426 q^{61} +(-31.7671 - 35.5374i) q^{62} -19.7050 q^{63} +(-21.0873 + 60.4262i) q^{64} +(5.23363 + 5.85479i) q^{66} -111.444 q^{67} +(106.629 + 11.9840i) q^{68} +63.1524 q^{69} +31.3190i q^{71} +(13.8963 + 19.5676i) q^{72} -110.909i q^{73} +(-72.9757 - 81.6369i) q^{74} +(43.2002 + 4.85528i) q^{76} +14.8902i q^{77} +(-34.3463 - 38.4227i) q^{78} +59.0065i q^{79} +9.00000 q^{81} +(35.5326 - 31.7628i) q^{82} +142.416 q^{83} +(-5.08253 + 45.2221i) q^{84} +(83.8765 - 74.9776i) q^{86} +61.0565 q^{87} +(14.7864 - 10.5008i) q^{88} -7.14798 q^{89} -97.7185i q^{91} +(16.2889 - 144.932i) q^{92} +41.2800i q^{93} +(76.6689 - 68.5347i) q^{94} +(48.4911 - 26.8443i) q^{96} -126.308i q^{97} +(8.73319 - 7.80665i) q^{98} -6.80089i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} - 12 q^{6} + 48 q^{9}+O(q^{10}) $ 16 * q + 16 * q^4 - 12 * q^6 + 48 * q^9	$ 16 q + 16 q^{4} - 12 q^{6} + 48 q^{9} - 44 q^{14} + 80 q^{16} + 48 q^{21} + 72 q^{24} - 132 q^{26} + 64 q^{29} - 248 q^{34} + 48 q^{36} - 32 q^{41} - 80 q^{44} - 152 q^{46} - 32 q^{49} - 36 q^{54} - 344 q^{56} + 272 q^{61} - 32 q^{64} - 216 q^{66} + 192 q^{69} + 216 q^{74} + 240 q^{76} + 144 q^{81} + 288 q^{84} + 428 q^{86} - 256 q^{89} - 24 q^{94} + 192 q^{96}+O(q^{100}) $ 16 * q + 16 * q^4 - 12 * q^6 + 48 * q^9 - 44 * q^14 + 80 * q^16 + 48 * q^21 + 72 * q^24 - 132 * q^26 + 64 * q^29 - 248 * q^34 + 48 * q^36 - 32 * q^41 - 80 * q^44 - 152 * q^46 - 32 * q^49 - 36 * q^54 - 344 * q^56 + 272 * q^61 - 32 * q^64 - 216 * q^66 + 192 * q^69 + 216 * q^74 + 240 * q^76 + 144 * q^81 + 288 * q^84 + 428 * q^86 - 256 * q^89 - 24 * q^94 + 192 * 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 $

$2$	−1.49110	+	1.33290i	−0.745549	+	0.666451i
$2$	−1.49110	+	1.33290i	−0.745549	+	0.666451i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	0.446749	−	3.97497i	0.111687	−	0.993743i
$5$		0			0
$5$		0			0
$6$	−2.58266	+	2.30865i	−0.430443	+	0.384775i
$7$	−6.56834			−0.938335			−0.469167	−	0.883109i	$-0.655446\pi$
$7$	−6.56834			−0.938335			−0.469167	+	0.883109i	$0.655446\pi$
$8$	4.63210	+	6.52255i	0.579013	+	0.815319i
$9$	3.00000			0.333333
$10$		0			0
$11$		−	2.26696i		−	0.206088i	−0.994677	−	0.103044i	$-0.967142\pi$
$11$		−	2.26696i		−	0.206088i	0.994677	−	0.103044i	$-0.0328582\pi$
$12$	0.773791	−	6.88486i	0.0644826	−	0.573738i
$13$			14.8772i			1.14440i	0.820114	+	0.572200i	$0.193910\pi$
$13$			14.8772i			1.14440i	−0.820114	+	0.572200i	$0.806090\pi$
$14$	9.79404	−	8.75495i	0.699575	−	0.625354i
$15$		0			0
$16$	−15.6008	−	3.55163i	−0.975052	−	0.221977i
$17$			26.8250i			1.57794i	0.614432	+	0.788969i	$0.289385\pi$
$17$			26.8250i			1.57794i	−0.614432	+	0.788969i	$0.710615\pi$
$18$	−4.47330	+	3.99870i	−0.248516	+	0.222150i
$19$			10.8680i			0.572002i	0.958229	+	0.286001i	$0.0923260\pi$
$19$			10.8680i			0.572002i	−0.958229	+	0.286001i	$0.907674\pi$
$20$		0			0
$21$	−11.3767			−0.541748
$22$	3.02164	+	3.38027i	0.137347	+	0.153648i
$23$	36.4610			1.58526			0.792631	−	0.609702i	$-0.208711\pi$
$23$	36.4610			1.58526			0.792631	+	0.609702i	$0.208711\pi$
$24$	8.02303	+	11.2974i	0.334293	+	0.470724i
$25$		0			0
$26$	−19.8298	−	22.1834i	−0.762685	−	0.853206i
$27$	5.19615			0.192450
$28$	−2.93440	+	26.1090i	−0.104800	+	0.932464i
$29$	35.2510			1.21555			0.607775	−	0.794109i	$-0.292062\pi$
$29$	35.2510			1.21555			0.607775	+	0.794109i	$0.292062\pi$
$30$		0			0
$31$			23.8330i			0.768808i	0.923165	+	0.384404i	$0.125593\pi$
$31$			23.8330i			0.768808i	−0.923165	+	0.384404i	$0.874407\pi$
$32$	27.9963	−	15.4985i	0.874886	−	0.484329i
$33$		−	3.92650i		−	0.118985i
$34$	−35.7550	−	39.9987i	−1.05162	−	1.17643i
$35$		0			0
$36$	1.34025	−	11.9249i	0.0372290	−	0.331248i
$37$			54.7495i			1.47972i	0.672763	+	0.739858i	$0.265107\pi$
$37$			54.7495i			1.47972i	−0.672763	+	0.739858i	$0.734893\pi$
$38$	−14.4860	−	16.2053i	−0.381211	−	0.426455i
$39$			25.7680i			0.660719i
$40$		0			0
$41$	−23.8298			−0.581215			−0.290608	−	0.956842i	$-0.593857\pi$
$41$	−23.8298			−0.581215			−0.290608	+	0.956842i	$0.593857\pi$
$42$	16.9638	−	15.1640i	0.403900	−	0.361048i
$43$	−56.2515			−1.30817			−0.654087	−	0.756420i	$-0.726947\pi$
$43$	−56.2515			−1.30817			−0.654087	+	0.756420i	$0.726947\pi$
$44$	−9.01112	−	1.01276i	−0.204798	−	0.0230173i
$45$		0			0
$46$	−54.3670	+	48.5989i	−1.18189	+	1.05650i
$47$	−51.4177			−1.09399			−0.546997	−	0.837135i	$-0.684229\pi$
$47$	−51.4177			−1.09399			−0.546997	+	0.837135i	$0.684229\pi$
$48$	−27.0214	−	6.15160i	−0.562947	−	0.128158i
$49$	−5.85689			−0.119528
$50$		0			0
$51$			46.4622i			0.911023i
$52$	59.1364	+	6.64636i	1.13724	+	0.127815i
$53$		−	30.6465i		−	0.578236i	−0.957293	−	0.289118i	$-0.906638\pi$
$53$		−	30.6465i		−	0.578236i	0.957293	−	0.289118i	$-0.0933620\pi$
$54$	−7.74797	+	6.92596i	−0.143481	+	0.128258i
$55$		0			0
$56$	−30.4252	−	42.8423i	−0.543308	−	0.765042i
$57$			18.8240i			0.330245i
$58$	−52.5627	+	46.9861i	−0.906253	+	0.810105i
$59$		−	6.92483i		−	0.117370i	−0.998277	−	0.0586850i	$-0.981309\pi$
$59$		−	6.92483i		−	0.117370i	0.998277	−	0.0586850i	$-0.0186908\pi$
$60$		0			0
$61$	107.426			1.76107			0.880537	−	0.473977i	$-0.157182\pi$
$61$	107.426			1.76107			0.880537	+	0.473977i	$0.157182\pi$
$62$	−31.7671	−	35.5374i	−0.512372	−	0.573184i
$63$	−19.7050			−0.312778
$64$	−21.0873	+	60.4262i	−0.329489	+	0.944160i
$65$		0			0
$66$	5.23363	+	5.85479i	0.0792975	+	0.0887090i
$67$	−111.444			−1.66334			−0.831670	−	0.555271i	$-0.812615\pi$
$67$	−111.444			−1.66334			−0.831670	+	0.555271i	$0.812615\pi$
$68$	106.629	+	11.9840i	1.56807	+	0.176235i
$69$	63.1524			0.915251
$70$		0			0
$71$			31.3190i			0.441113i	0.975374	+	0.220556i	$0.0707873\pi$
$71$			31.3190i			0.441113i	−0.975374	+	0.220556i	$0.929213\pi$
$72$	13.8963	+	19.5676i	0.193004	+	0.271773i
$73$		−	110.909i		−	1.51930i	−0.650330	−	0.759652i	$-0.725369\pi$
$73$		−	110.909i		−	1.51930i	0.650330	−	0.759652i	$-0.274631\pi$
$74$	−72.9757	−	81.6369i	−0.986158	−	1.10320i
$75$		0			0
$76$	43.2002	+	4.85528i	0.568423	+	0.0638853i
$77$			14.8902i			0.193379i
$78$	−34.3463	−	38.4227i	−0.440337	−	0.492599i
$79$			59.0065i			0.746917i	0.927647	+	0.373459i	$0.121828\pi$
$79$			59.0065i			0.746917i	−0.927647	+	0.373459i	$0.878172\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	35.5326	−	31.7628i	0.433325	−	0.387351i
$83$	142.416			1.71586			0.857930	−	0.513767i	$-0.171751\pi$
$83$	142.416			1.71586			0.857930	+	0.513767i	$0.171751\pi$
$84$	−5.08253	+	45.2221i	−0.0605063	+	0.538358i
$85$		0			0
$86$	83.8765	−	74.9776i	0.975308	−	0.871833i
$87$	61.0565			0.701799
$88$	14.7864	−	10.5008i	0.168027	−	0.119327i
$89$	−7.14798			−0.0803144			−0.0401572	−	0.999193i	$-0.512786\pi$
$89$	−7.14798			−0.0803144			−0.0401572	+	0.999193i	$0.512786\pi$
$90$		0			0
$91$		−	97.7185i		−	1.07383i
$92$	16.2889	−	144.932i	0.177053	−	1.57534i
$93$			41.2800i			0.443871i
$94$	76.6689	−	68.5347i	0.815626	−	0.729093i
$95$		0			0
$96$	48.4911	−	26.8443i	0.505116	−	0.279628i
$97$		−	126.308i		−	1.30214i	−0.759017	−	0.651070i	$-0.774320\pi$
$97$		−	126.308i		−	1.30214i	0.759017	−	0.651070i	$-0.225680\pi$
$98$	8.73319	−	7.80665i	0.0891142	−	0.0796597i
$99$		−	6.80089i		−	0.0686959i
$100$		0			0
$101$	86.7133			0.858547			0.429274	−	0.903174i	$-0.358770\pi$
$101$	86.7133			0.858547			0.429274	+	0.903174i	$0.358770\pi$
$102$	−61.9295	−	69.2797i	−0.607152	−	0.679213i
$103$	−21.9281			−0.212895			−0.106447	−	0.994318i	$-0.533948\pi$
$103$	−21.9281			−0.212895			−0.106447	+	0.994318i	$0.533948\pi$
$104$	−97.0372	+	68.9126i	−0.933050	+	0.662622i
$105$		0			0
$106$	40.8488	+	45.6970i	0.385366	+	0.431104i
$107$	−7.17725			−0.0670771			−0.0335385	−	0.999437i	$-0.510678\pi$
$107$	−7.17725			−0.0670771			−0.0335385	+	0.999437i	$0.510678\pi$
$108$	2.32137	−	20.6546i	0.0214942	−	0.191246i
$109$	−25.4256			−0.233262			−0.116631	−	0.993175i	$-0.537210\pi$
$109$	−25.4256			−0.233262			−0.116631	+	0.993175i	$0.537210\pi$
$110$		0			0
$111$			94.8289i			0.854315i
$112$	102.472	+	23.3283i	0.914925	+	0.208288i
$113$			78.3588i			0.693441i	0.937968	+	0.346720i	$0.112705\pi$
$113$			78.3588i			0.693441i	−0.937968	+	0.346720i	$0.887295\pi$
$114$	−25.0905	−	28.0684i	−0.220092	−	0.246214i
$115$		0			0
$116$	15.7483	−	140.122i	0.135761	−	1.20795i
$117$			44.6316i			0.381466i
$118$	9.23012	+	10.3256i	0.0782214	+	0.0875052i
$119$		−	176.196i		−	1.48063i
$120$		0			0
$121$	115.861			0.957528
$122$	−160.182	+	143.188i	−1.31297	+	1.17367i
$123$	−41.2745			−0.335565
$124$	94.7357	+	10.6474i	0.763997	+	0.0858659i
$125$		0			0
$126$	29.3821	−	26.2649i	0.233192	−	0.208451i
$127$	71.6077			0.563840			0.281920	−	0.959438i	$-0.409029\pi$
$127$	71.6077			0.563840			0.281920	+	0.959438i	$0.409029\pi$
$128$	−49.0990	−	118.209i	−0.383586	−	0.923505i
$129$	−97.4304			−0.755274
$130$		0			0
$131$		−	103.978i		−	0.793728i	−0.917877	−	0.396864i	$-0.870098\pi$
$131$		−	103.978i		−	0.793728i	0.917877	−	0.396864i	$-0.129902\pi$
$132$	−15.6077	−	1.75416i	−0.118240	−	0.0132891i
$133$		−	71.3850i		−	0.536729i
$134$	166.174	−	148.543i	1.24010	−	1.10853i
$135$		0			0
$136$	−174.967	+	124.256i	−1.28652	+	0.913647i
$137$			7.16645i			0.0523099i	0.999658	+	0.0261549i	$0.00832633\pi$
$137$			7.16645i			0.0523099i	−0.999658	+	0.0261549i	$0.991674\pi$
$138$	−94.1664	+	84.1758i	−0.682365	+	0.609970i
$139$			146.909i			1.05690i	0.848965	+	0.528449i	$0.177226\pi$
$139$			146.909i			1.05690i	−0.848965	+	0.528449i	$0.822774\pi$
$140$		0			0
$141$	−89.0581			−0.631618
$142$	−41.7451	−	46.6997i	−0.293980	−	0.328871i
$143$	33.7261			0.235847
$144$	−46.8025	−	10.6549i	−0.325017	−	0.0739922i
$145$		0			0
$146$	147.831	+	165.376i	1.01254	+	1.13272i
$147$	−10.1444			−0.0690097
$148$	217.628	+	24.4593i	1.47046	+	0.165265i
$149$	−79.6054			−0.534265			−0.267132	−	0.963660i	$-0.586076\pi$
$149$	−79.6054			−0.534265			−0.267132	+	0.963660i	$0.586076\pi$
$150$		0			0
$151$		−	182.722i		−	1.21008i	−0.796196	−	0.605039i	$-0.793158\pi$
$151$		−	182.722i		−	1.21008i	0.796196	−	0.605039i	$-0.206842\pi$
$152$	−70.8873	+	50.3418i	−0.466364	+	0.331196i
$153$			80.4749i			0.525980i
$154$	−19.8472	−	22.2027i	−0.128878	−	0.144174i
$155$		0			0
$156$	102.427	+	11.5118i	0.656585	+	0.0737938i
$157$		−	212.182i		−	1.35148i	−0.737141	−	0.675739i	$-0.763825\pi$
$157$		−	212.182i		−	1.35148i	0.737141	−	0.675739i	$-0.236175\pi$
$158$	−78.6498	−	87.9844i	−0.497783	−	0.556864i
$159$		−	53.0813i		−	0.333845i
$160$		0			0
$161$	−239.488			−1.48751
$162$	−13.4199	+	11.9961i	−0.0828388	+	0.0740501i
$163$	−243.400			−1.49325			−0.746626	−	0.665244i	$-0.768327\pi$
$163$	−243.400			−1.49325			−0.746626	+	0.665244i	$0.768327\pi$
$164$	−10.6459	+	94.7229i	−0.0649143	+	0.577579i
$165$		0			0
$166$	−212.357	+	189.827i	−1.27926	+	1.14354i
$167$	211.395			1.26584			0.632919	−	0.774218i	$-0.281857\pi$
$167$	211.395			1.26584			0.632919	+	0.774218i	$0.281857\pi$
$168$	−52.6980	−	74.2051i	−0.313679	−	0.441697i
$169$	−52.3307			−0.309649
$170$		0			0
$171$			32.6041i			0.190667i
$172$	−25.1303	+	223.598i	−0.146106	+	1.29999i
$173$		−	22.3138i		−	0.128982i	−0.997918	−	0.0644909i	$-0.979458\pi$
$173$		−	22.3138i		−	0.128982i	0.997918	−	0.0644909i	$-0.0205423\pi$
$174$	−91.0412	+	81.3823i	−0.523225	+	0.467714i
$175$		0			0
$176$	−8.05141	+	35.3665i	−0.0457467	+	0.200946i
$177$		−	11.9942i		−	0.0677636i
$178$	10.6583	−	9.52755i	0.0598783	−	0.0535255i
$179$			94.5219i			0.528055i	0.964515	+	0.264028i	$0.0850510\pi$
$179$			94.5219i			0.528055i	−0.964515	+	0.264028i	$0.914949\pi$
$180$		0			0
$181$	−80.6179			−0.445403			−0.222702	−	0.974887i	$-0.571488\pi$
$181$	−80.6179			−0.445403			−0.222702	+	0.974887i	$0.571488\pi$
$182$	130.249	+	145.708i	0.715654	+	0.800592i
$183$	186.067			1.01676
$184$	168.891	+	237.819i	0.917887	+	1.29249i
$185$		0			0
$186$	−55.0222	−	61.5526i	−0.295818	−	0.330928i
$187$	60.8112			0.325194
$188$	−22.9708	+	204.384i	−0.122185	+	1.08715i
$189$	−34.1301			−0.180583
$190$		0			0
$191$			330.540i			1.73058i	0.501275	+	0.865288i	$0.332865\pi$
$191$			330.540i			1.73058i	−0.501275	+	0.865288i	$0.667135\pi$
$192$	−36.5242	+	104.661i	−0.190230	+	0.545111i
$193$			103.609i			0.536836i	0.963303	+	0.268418i	$0.0865008\pi$
$193$			103.609i			0.536836i	−0.963303	+	0.268418i	$0.913499\pi$
$194$	168.356	+	188.337i	0.867812	+	0.970810i
$195$		0			0
$196$	−2.61656	+	23.2810i	−0.0133498	+	0.118780i
$197$			160.633i			0.815394i	0.913117	+	0.407697i	$0.133668\pi$
$197$			160.633i			0.815394i	−0.913117	+	0.407697i	$0.866332\pi$
$198$	9.06492	+	10.1408i	0.0457824	+	0.0512162i
$199$		−	27.5518i		−	0.138451i	−0.997601	−	0.0692255i	$-0.977947\pi$
$199$		−	27.5518i		−	0.138451i	0.997601	−	0.0692255i	$-0.0220528\pi$
$200$		0			0
$201$	−193.026			−0.960329
$202$	−129.298	+	115.580i	−0.640089	+	0.572179i
$203$	−231.540			−1.14059
$204$	184.686	+	20.7569i	0.905324	+	0.101750i
$205$		0			0
$206$	32.6970	−	29.2280i	0.158723	−	0.141884i
$207$	109.383			0.528421
$208$	52.8382	−	232.097i	0.254030	−	1.11585i
$209$	24.6374			0.117883
$210$		0			0
$211$		−	269.808i		−	1.27871i	−0.768911	−	0.639355i	$-0.779201\pi$
$211$		−	269.808i		−	1.27871i	0.768911	−	0.639355i	$-0.220799\pi$
$212$	−121.819	−	13.6913i	−0.574618	−	0.0645816i
$213$			54.2461i			0.254677i
$214$	10.7020	−	9.56656i	0.0500093	−	0.0447036i
$215$		0			0
$216$	24.0691	+	33.8922i	0.111431	+	0.156908i
$217$		−	156.544i		−	0.721399i
$218$	37.9120	−	33.8898i	0.173908	−	0.155458i
$219$		−	192.100i		−	0.877170i
$220$		0			0
$221$	−399.080			−1.80579
$222$	−126.398	−	141.399i	−0.569359	−	0.636934i
$223$	41.3345			0.185356			0.0926782	−	0.995696i	$-0.470457\pi$
$223$	41.3345			0.185356			0.0926782	+	0.995696i	$0.470457\pi$
$224$	−183.890	+	101.800i	−0.820935	+	0.454463i
$225$		0			0
$226$	−104.445	−	116.841i	−0.462144	−	0.516994i
$227$	149.837			0.660076			0.330038	−	0.943968i	$-0.392939\pi$
$227$	149.837			0.660076			0.330038	+	0.943968i	$0.392939\pi$
$228$	74.8249	+	8.40959i	0.328179	+	0.0368842i
$229$	61.6770			0.269332			0.134666	−	0.990891i	$-0.457004\pi$
$229$	61.6770			0.269332			0.134666	+	0.990891i	$0.457004\pi$
$230$		0			0
$231$			25.7906i			0.111648i
$232$	163.286	+	229.926i	0.703819	+	0.991061i
$233$			405.585i			1.74071i	0.492425	+	0.870355i	$0.336110\pi$
$233$			405.585i			1.74071i	−0.492425	+	0.870355i	$0.663890\pi$
$234$	−59.4895	−	66.5501i	−0.254228	−	0.284402i
$235$		0			0
$236$	−27.5260	−	3.09366i	−0.116636	−	0.0131087i
$237$			102.202i			0.431233i
$238$	234.851	+	262.725i	0.986770	+	1.10389i
$239$		−	267.769i		−	1.12037i	−0.828367	−	0.560185i	$-0.810730\pi$
$239$		−	267.769i		−	1.12037i	0.828367	−	0.560185i	$-0.189270\pi$
$240$		0			0
$241$	−89.5377			−0.371526			−0.185763	−	0.982595i	$-0.559476\pi$
$241$	−89.5377			−0.371526			−0.185763	+	0.982595i	$0.559476\pi$
$242$	−172.760	+	154.431i	−0.713884	+	0.638145i
$243$	15.5885			0.0641500
$244$	47.9922	−	427.014i	0.196689	−	1.75006i
$245$		0			0
$246$	61.5443	−	55.0148i	0.250180	−	0.223637i
$247$	−161.686			−0.654598
$248$	−155.452	+	110.397i	−0.626823	+	0.445149i
$249$	246.672			0.990652
$250$		0			0
$251$		−	227.844i		−	0.907745i	−0.891067	−	0.453873i	$-0.850042\pi$
$251$		−	227.844i		−	0.907745i	0.891067	−	0.453873i	$-0.149958\pi$
$252$	−8.80319	+	78.3270i	−0.0349333	+	0.310821i
$253$		−	82.6559i		−	0.326703i
$254$	−106.774	+	95.4460i	−0.420371	+	0.375772i
$255$		0			0
$256$	230.772	+	110.817i	0.901453	+	0.432878i
$257$		−	442.129i		−	1.72035i	−0.510003	−	0.860173i	$-0.670356\pi$
$257$		−	442.129i		−	1.72035i	0.510003	−	0.860173i	$-0.329644\pi$
$258$	145.278	−	129.865i	0.563094	−	0.503353i
$259$		−	359.614i		−	1.38847i
$260$		0			0
$261$	105.753			0.405184
$262$	138.593	+	155.042i	0.528981	+	0.591763i
$263$	−34.1556			−0.129869			−0.0649346	−	0.997890i	$-0.520684\pi$
$263$	−34.1556			−0.129869			−0.0649346	+	0.997890i	$0.520684\pi$
$264$	25.6108	−	18.1879i	0.0970105	−	0.0688937i
$265$		0			0
$266$	95.1491	+	106.442i	0.357703	+	0.400158i
$267$	−12.3807			−0.0463695
$268$	−49.7873	+	442.986i	−0.185774	+	1.65293i
$269$	9.96085			0.0370292			0.0185146	−	0.999829i	$-0.494106\pi$
$269$	9.96085			0.0370292			0.0185146	+	0.999829i	$0.494106\pi$
$270$		0			0
$271$			56.5791i			0.208779i	0.994536	+	0.104390i	$0.0332889\pi$
$271$			56.5791i			0.208779i	−0.994536	+	0.104390i	$0.966711\pi$
$272$	95.2723	−	418.492i	0.350266	−	1.53857i
$273$		−	169.253i		−	0.619976i
$274$	−9.55218	−	10.6859i	−0.0348620	−	0.0389996i
$275$		0			0
$276$	28.2132	−	251.029i	0.102222	−	0.909525i
$277$			103.794i			0.374708i	0.982292	+	0.187354i	$0.0599911\pi$
$277$			103.794i			0.374708i	−0.982292	+	0.187354i	$0.940009\pi$
$278$	−195.815	−	219.056i	−0.704370	−	0.787969i
$279$			71.4991i			0.256269i
$280$		0			0
$281$	393.069			1.39882			0.699411	−	0.714720i	$-0.253446\pi$
$281$	393.069			1.39882			0.699411	+	0.714720i	$0.253446\pi$
$282$	132.794	−	118.706i	0.470902	−	0.420942i
$283$	114.027			0.402923			0.201462	−	0.979496i	$-0.435431\pi$
$283$	114.027			0.402923			0.201462	+	0.979496i	$0.435431\pi$
$284$	124.492	+	13.9917i	0.438353	+	0.0492666i
$285$		0			0
$286$	−50.2889	+	44.9535i	−0.175835	+	0.157180i
$287$	156.522			0.545374
$288$	83.9890	−	46.4956i	0.291629	−	0.161443i
$289$	−430.579			−1.48989
$290$		0			0
$291$		−	218.771i		−	0.751791i
$292$	−440.861	−	49.5485i	−1.50980	−	0.169687i
$293$		−	126.796i		−	0.432750i	−0.976310	−	0.216375i	$-0.930577\pi$
$293$		−	126.796i		−	0.432750i	0.976310	−	0.216375i	$-0.0694234\pi$
$294$	15.1263	−	13.5215i	0.0514501	−	0.0459915i
$295$		0			0
$296$	−357.106	+	253.605i	−1.20644	+	0.856775i
$297$		−	11.7795i		−	0.0396616i
$298$	118.700	−	106.106i	0.398321	−	0.356061i
$299$			542.438i			1.81417i
$300$		0			0
$301$	369.479			1.22750
$302$	243.550	+	272.456i	0.806457	+	0.902172i
$303$	150.192			0.495683
$304$	38.5992	−	169.550i	0.126971	−	0.557732i
$305$		0			0
$306$	−107.265	−	119.996i	−0.350539	−	0.392144i
$307$	−408.420			−1.33036			−0.665180	−	0.746683i	$-0.731645\pi$
$307$	−408.420			−1.33036			−0.665180	+	0.746683i	$0.731645\pi$
$308$	59.1881	+	6.65217i	0.192169	+	0.0215980i
$309$	−37.9806			−0.122915
$310$		0			0
$311$			472.495i			1.51928i	0.650345	+	0.759639i	$0.274624\pi$
$311$			472.495i			1.51928i	−0.650345	+	0.759639i	$0.725376\pi$
$312$	−168.073	+	119.360i	−0.538697	+	0.382565i
$313$		−	54.6519i		−	0.174607i	−0.996182	−	0.0873033i	$-0.972175\pi$
$313$		−	54.6519i		−	0.174607i	0.996182	−	0.0873033i	$-0.0278249\pi$
$314$	282.818	+	316.384i	0.900693	+	1.00759i
$315$		0			0
$316$	234.549	+	26.3611i	0.742244	+	0.0834211i
$317$		−	63.3734i		−	0.199916i	−0.994992	−	0.0999581i	$-0.968129\pi$
$317$		−	63.3734i		−	0.199916i	0.994992	−	0.0999581i	$-0.0318709\pi$
$318$	70.7522	+	79.1495i	0.222491	+	0.248898i
$319$		−	79.9127i		−	0.250510i
$320$		0			0
$321$	−12.4314			−0.0387270
$322$	357.101	−	319.215i	1.10901	−	0.991349i
$323$	−291.535			−0.902584
$324$	4.02074	−	35.7748i	0.0124097	−	0.110416i
$325$		0			0
$326$	362.933	−	324.428i	1.11329	−	0.995179i
$327$	−44.0384			−0.134674
$328$	−110.382	−	155.431i	−0.336531	−	0.473876i
$329$	337.729			1.02653
$330$		0			0
$331$		−	431.595i		−	1.30391i	−0.758257	−	0.651955i	$-0.773949\pi$
$331$		−	431.595i		−	1.30391i	0.758257	−	0.651955i	$-0.226051\pi$
$332$	63.6243	−	566.101i	0.191639	−	1.70512i
$333$			164.249i			0.493239i
$334$	−315.211	+	281.768i	−0.943744	+	0.843618i
$335$		0			0
$336$	177.486	+	40.4058i	0.528232	+	0.120255i
$337$			486.091i			1.44241i	0.692723	+	0.721203i	$0.256411\pi$
$337$			486.091i			1.44241i	−0.692723	+	0.721203i	$0.743589\pi$
$338$	78.0303	−	69.7517i	0.230859	−	0.206366i
$339$			135.721i			0.400358i
$340$		0			0
$341$	54.0286			0.158442
$342$	−43.4581	−	48.6159i	−0.127070	−	0.142152i
$343$	360.319			1.05049
$344$	−260.562	−	366.903i	−0.757449	−	1.06658i
$345$		0			0
$346$	29.7422	+	33.2721i	0.0859600	+	0.0961623i
$347$	−294.297			−0.848119			−0.424060	−	0.905634i	$-0.639395\pi$
$347$	−294.297			−0.848119			−0.424060	+	0.905634i	$0.639395\pi$
$348$	27.2769	−	242.698i	0.0783819	−	0.697408i
$349$	−83.0428			−0.237945			−0.118972	−	0.992898i	$-0.537960\pi$
$349$	−83.0428			−0.237945			−0.118972	+	0.992898i	$0.537960\pi$
$350$		0			0
$351$			77.3041i			0.220240i
$352$	−35.1346	−	63.4667i	−0.0998143	−	0.180303i
$353$		−	570.733i		−	1.61681i	−0.588628	−	0.808404i	$-0.700332\pi$
$353$		−	570.733i		−	1.61681i	0.588628	−	0.808404i	$-0.299668\pi$
$354$	15.9870	+	17.8845i	0.0451611	+	0.0505211i
$355$		0			0
$356$	−3.19335	+	28.4130i	−0.00897008	+	0.0798119i
$357$		−	305.180i		−	0.854845i
$358$	−125.988	−	140.941i	−0.351923	−	0.393691i
$359$			558.265i			1.55506i	0.628848	+	0.777528i	$0.283527\pi$
$359$			558.265i			1.55506i	−0.628848	+	0.777528i	$0.716473\pi$
$360$		0			0
$361$	242.886			0.672814
$362$	120.209	−	107.456i	0.332070	−	0.296839i
$363$	200.677			0.552829
$364$	−388.428	−	43.6556i	−1.06711	−	0.119933i
$365$		0			0
$366$	−277.444	+	248.008i	−0.758042	+	0.677618i
$367$	446.467			1.21653			0.608265	−	0.793734i	$-0.291866\pi$
$367$	446.467			1.21653			0.608265	+	0.793734i	$0.291866\pi$
$368$	−568.822	−	129.496i	−1.54571	−	0.351891i
$369$	−71.4895			−0.193738
$370$		0			0
$371$			201.297i			0.542579i
$372$	164.087	+	18.4418i	0.441094	+	0.0495747i
$373$		−	112.924i		−	0.302744i	−0.988477	−	0.151372i	$-0.951631\pi$
$373$		−	112.924i		−	0.302744i	0.988477	−	0.151372i	$-0.0483692\pi$
$374$	−90.6755	+	81.0554i	−0.242448	+	0.216726i
$375$		0			0
$376$	−238.172	−	335.375i	−0.633436	−	0.891954i
$377$			524.435i			1.39108i
$378$	50.8913	−	45.4921i	0.134633	−	0.120349i
$379$			321.457i			0.848173i	0.905622	+	0.424086i	$0.139405\pi$
$379$			321.457i			0.848173i	−0.905622	+	0.424086i	$0.860595\pi$
$380$		0			0
$381$	124.028			0.325533
$382$	−440.577	−	492.868i	−1.15334	−	1.29023i
$383$	−89.2269			−0.232968			−0.116484	−	0.993193i	$-0.537162\pi$
$383$	−89.2269			−0.232968			−0.116484	+	0.993193i	$0.537162\pi$
$384$	−85.0419	−	204.743i	−0.221463	−	0.533186i
$385$		0			0
$386$	−138.101	−	154.492i	−0.357775	−	0.400238i
$387$	−168.754			−0.436058
$388$	−502.069	−	56.4278i	−1.29399	−	0.145432i
$389$	−260.714			−0.670217			−0.335108	−	0.942180i	$-0.608773\pi$
$389$	−260.714			−0.670217			−0.335108	+	0.942180i	$0.608773\pi$
$390$		0			0
$391$			978.066i			2.50145i
$392$	−27.1297	−	38.2018i	−0.0692084	−	0.0974536i
$393$		−	180.096i		−	0.458259i
$394$	−214.107	−	239.519i	−0.543420	−	0.607916i
$395$		0			0
$396$	−27.0334	−	3.03829i	−0.0682661	−	0.00767245i
$397$		−	112.607i		−	0.283644i	−0.989892	−	0.141822i	$-0.954704\pi$
$397$		−	112.607i		−	0.283644i	0.989892	−	0.141822i	$-0.0452960\pi$
$398$	36.7238	+	41.0824i	0.0922708	+	0.103222i
$399$		−	123.642i		−	0.309881i
$400$		0			0
$401$	577.513			1.44018			0.720091	−	0.693880i	$-0.244100\pi$
$401$	577.513			1.44018			0.720091	+	0.693880i	$0.244100\pi$
$402$	287.821	−	257.285i	0.715973	−	0.640012i
$403$	−354.569			−0.879823
$404$	38.7390	−	344.683i	0.0958887	−	0.853176i
$405$		0			0
$406$	345.250	−	308.621i	0.850368	−	0.760149i
$407$	124.115			0.304951
$408$	−303.052	+	215.218i	−0.742774	+	0.527494i
$409$	276.255			0.675441			0.337721	−	0.941246i	$-0.390344\pi$
$409$	276.255			0.675441			0.337721	+	0.941246i	$0.390344\pi$
$410$		0			0
$411$			12.4127i			0.0302011i
$412$	−9.79636	+	87.1638i	−0.0237776	+	0.211563i
$413$			45.4847i			0.110132i
$414$	−163.101	+	145.797i	−0.393964	+	0.352166i
$415$		0			0
$416$	230.575	+	416.507i	0.554266	+	1.00122i
$417$			254.454i			0.610200i
$418$	−36.7369	+	32.8393i	−0.0878872	+	0.0785629i
$419$		−	247.520i		−	0.590739i	−0.955383	−	0.295370i	$-0.904557\pi$
$419$		−	247.520i		−	0.590739i	0.955383	−	0.295370i	$-0.0954428\pi$
$420$		0			0
$421$	−77.7303			−0.184632			−0.0923162	−	0.995730i	$-0.529427\pi$
$421$	−77.7303			−0.184632			−0.0923162	+	0.995730i	$0.529427\pi$
$422$	359.627	+	402.310i	0.852197	+	0.953342i
$423$	−154.253			−0.364665
$424$	199.893	−	141.958i	0.471447	−	0.334806i
$425$		0			0
$426$	−72.3047	−	80.8863i	−0.169729	−	0.189874i
$427$	−705.608			−1.65248
$428$	−3.20643	+	28.5294i	−0.00749165	+	0.0666574i
$429$	58.4152			0.136166
$430$		0			0
$431$		−	317.184i		−	0.735926i	−0.929840	−	0.367963i	$-0.880055\pi$
$431$		−	317.184i		−	0.735926i	0.929840	−	0.367963i	$-0.119945\pi$
$432$	−81.0643	−	18.4548i	−0.187649	−	0.0427194i
$433$		−	82.9688i		−	0.191614i	−0.995400	−	0.0958069i	$-0.969457\pi$
$433$		−	82.9688i		−	0.191614i	0.995400	−	0.0958069i	$-0.0305431\pi$
$434$	208.657	+	233.422i	0.480777	+	0.537838i
$435$		0			0
$436$	−11.3588	+	101.066i	−0.0260524	+	0.231803i
$437$			396.260i			0.906773i
$438$	256.051	+	286.440i	0.584591	+	0.653974i
$439$		−	117.621i		−	0.267930i	−0.990986	−	0.133965i	$-0.957229\pi$
$439$		−	117.621i		−	0.267930i	0.990986	−	0.133965i	$-0.0427709\pi$
$440$		0			0
$441$	−17.5707			−0.0398428
$442$	595.068	−	531.934i	1.34631	−	1.20347i
$443$	−35.1780			−0.0794086			−0.0397043	−	0.999211i	$-0.512642\pi$
$443$	−35.1780			−0.0794086			−0.0397043	+	0.999211i	$0.512642\pi$
$444$	376.943	+	42.3647i	0.848970	+	0.0954160i
$445$		0			0
$446$	−61.6337	+	55.0948i	−0.138192	+	0.123531i
$447$	−137.881			−0.308458
$448$	138.508	−	396.900i	0.309171	−	0.885938i
$449$	67.4253			0.150168			0.0750838	−	0.997177i	$-0.476078\pi$
$449$	67.4253			0.150168			0.0750838	+	0.997177i	$0.476078\pi$
$450$		0			0
$451$			54.0214i			0.119781i
$452$	311.474	+	35.0067i	0.689102	+	0.0774484i
$453$		−	316.483i		−	0.698638i
$454$	−223.422	+	199.718i	−0.492119	+	0.439908i
$455$		0			0
$456$	−122.780	+	87.1946i	−0.269255	+	0.191216i
$457$			204.153i			0.446724i	0.974736	+	0.223362i	$0.0717032\pi$
$457$			204.153i			0.446724i	−0.974736	+	0.223362i	$0.928297\pi$
$458$	−91.9665	+	82.2094i	−0.200800	+	0.179496i
$459$			139.387i			0.303674i
$460$		0			0
$461$	125.762			0.272802			0.136401	−	0.990654i	$-0.456446\pi$
$461$	125.762			0.272802			0.136401	+	0.990654i	$0.456446\pi$
$462$	−34.3763	−	38.4563i	−0.0744076	−	0.0832387i
$463$	553.629			1.19574			0.597871	−	0.801592i	$-0.296013\pi$
$463$	553.629			1.19574			0.597871	+	0.801592i	$0.296013\pi$
$464$	−549.944	−	125.198i	−1.18523	−	0.269824i
$465$		0			0
$466$	−540.605	−	604.768i	−1.16010	−	1.29778i
$467$	−625.772			−1.33998			−0.669991	−	0.742369i	$-0.733702\pi$
$467$	−625.772			−1.33998			−0.669991	+	0.742369i	$0.733702\pi$
$468$	177.409	+	19.9391i	0.379080	+	0.0426049i
$469$	732.000			1.56077
$470$		0			0
$471$		−	367.510i		−	0.780276i
$472$	45.1676	−	32.0765i	0.0956940	−	0.0679588i
$473$			127.520i			0.269598i
$474$	−136.225	−	152.394i	−0.287395	−	0.321505i
$475$		0			0
$476$	−700.373	−	78.7151i	−1.47137	−	0.165368i
$477$		−	91.9396i		−	0.192745i
$478$	356.909	+	399.269i	0.746672	+	0.835291i
$479$		−	488.207i		−	1.01922i	−0.860405	−	0.509610i	$-0.829790\pi$
$479$		−	488.207i		−	1.01922i	0.860405	−	0.509610i	$-0.170210\pi$
$480$		0			0
$481$	−814.519			−1.69339
$482$	133.509	−	119.345i	0.276991	−	0.247604i
$483$	−414.806			−0.858812
$484$	51.7607	−	460.544i	0.106944	−	0.951537i
$485$		0			0
$486$	−23.2439	+	20.7779i	−0.0478270	+	0.0427528i
$487$	609.476			1.25149			0.625746	−	0.780027i	$-0.284795\pi$
$487$	609.476			1.25149			0.625746	+	0.780027i	$0.284795\pi$
$488$	497.606	+	700.689i	1.01968	+	1.43584i
$489$	−421.581			−0.862129
$490$		0			0
$491$		−	689.074i		−	1.40341i	−0.712468	−	0.701705i	$-0.752422\pi$
$491$		−	689.074i		−	1.40341i	0.712468	−	0.701705i	$-0.247578\pi$
$492$	−18.4393	+	164.065i	−0.0374783	+	0.333465i
$493$			945.606i			1.91806i
$494$	241.089	−	215.511i	0.488035	−	0.436257i
$495$		0			0
$496$	84.6461	−	371.815i	0.170657	−	0.749627i
$497$		−	205.714i		−	0.413911i
$498$	−367.813	+	328.790i	−0.738580	+	0.660220i
$499$			700.401i			1.40361i	0.712370	+	0.701804i	$0.247622\pi$
$499$			700.401i			1.40361i	−0.712370	+	0.701804i	$0.752378\pi$
$500$		0			0
$501$	366.147			0.730832
$502$	303.694	+	339.738i	0.604967	+	0.676769i
$503$	943.945			1.87663			0.938315	−	0.345782i	$-0.112386\pi$
$503$	943.945			1.87663			0.938315	+	0.345782i	$0.112386\pi$
$504$	−91.2757	−	128.527i	−0.181103	−	0.255014i
$505$		0			0
$506$	110.172	+	123.248i	0.217731	+	0.243573i
$507$	−90.6395			−0.178776
$508$	31.9906	−	284.639i	0.0629737	−	0.560313i
$509$	357.147			0.701665			0.350832	−	0.936438i	$-0.385899\pi$
$509$	357.147			0.701665			0.350832	+	0.936438i	$0.385899\pi$
$510$		0			0
$511$			728.489i			1.42562i
$512$	−491.811	+	142.358i	−0.960569	+	0.278042i
$513$			56.4720i			0.110082i
$514$	589.314	+	659.258i	1.14653	+	1.28260i
$515$		0			0
$516$	−43.5269	+	387.283i	−0.0843544	+	0.750549i
$517$			116.562i			0.225459i
$518$	479.329	+	536.219i	0.925346	+	1.03517i
$519$		−	38.6487i		−	0.0744677i
$520$		0			0
$521$	−88.8415			−0.170521			−0.0852605	−	0.996359i	$-0.527172\pi$
$521$	−88.8415			−0.170521			−0.0852605	+	0.996359i	$0.527172\pi$
$522$	−157.688	+	140.958i	−0.302084	+	0.270035i
$523$	220.427			0.421467			0.210734	−	0.977544i	$-0.432415\pi$
$523$	220.427			0.421467			0.210734	+	0.977544i	$0.432415\pi$
$524$	−413.311	−	46.4522i	−0.788762	−	0.0886492i
$525$		0			0
$526$	50.9294	−	45.5261i	0.0968239	−	0.0865514i
$527$	−639.320			−1.21313
$528$	−13.9455	+	61.2566i	−0.0264119	+	0.116016i
$529$	800.407			1.51306
$530$		0			0
$531$		−	20.7745i		−	0.0391234i
$532$	−283.753	−	31.8911i	−0.533371	−	0.0599457i
$533$		−	354.521i		−	0.665142i
$534$	18.4608	−	16.5022i	0.0345708	−	0.0309030i
$535$		0			0
$536$	−516.219	−	726.897i	−0.963094	−	1.35615i
$537$			163.717i			0.304873i
$538$	−14.8526	+	13.2768i	−0.0276071	+	0.0246781i
$539$			13.2774i			0.0246333i
$540$		0			0
$541$	−411.560			−0.760740			−0.380370	−	0.924834i	$-0.624203\pi$
$541$	−411.560			−0.760740			−0.380370	+	0.924834i	$0.624203\pi$
$542$	−75.4144	−	84.3651i	−0.139141	−	0.155655i
$543$	−139.634			−0.257154
$544$	415.748	+	751.001i	0.764242	+	1.38052i
$545$		0			0
$546$	225.598	+	252.373i	0.413183	+	0.462222i
$547$	851.537			1.55674			0.778370	−	0.627806i	$-0.216047\pi$
$547$	851.537			1.55674			0.778370	+	0.627806i	$0.216047\pi$
$548$	28.4865	+	3.20160i	0.0519826	+	0.00584234i
$549$	322.277			0.587025
$550$		0			0
$551$			383.109i			0.695297i
$552$	292.528	+	411.914i	0.529942	+	0.746222i
$553$		−	387.575i		−	0.700858i
$554$	−138.347	−	154.767i	−0.249724	−	0.279363i
$555$		0			0
$556$	583.959	+	65.6313i	1.05029	+	0.118042i
$557$		−	211.553i		−	0.379808i	−0.981803	−	0.189904i	$-0.939182\pi$
$557$		−	211.553i		−	0.379808i	0.981803	−	0.189904i	$-0.0608177\pi$
$558$	−95.3012	−	106.612i	−0.170791	−	0.191061i
$559$		−	836.864i		−	1.49707i
$560$		0			0
$561$	105.328			0.187751
$562$	−586.104	+	523.922i	−1.04289	+	0.932246i
$563$	−404.044			−0.717663			−0.358832	−	0.933402i	$-0.616825\pi$
$563$	−404.044			−0.717663			−0.358832	+	0.933402i	$0.616825\pi$
$564$	−39.7866	+	354.004i	−0.0705436	+	0.627666i
$565$		0			0
$566$	−170.026	+	151.987i	−0.300399	+	0.268529i
$567$	−59.1151			−0.104259
$568$	−204.280	+	145.073i	−0.359647	+	0.255410i
$569$	−230.465			−0.405036			−0.202518	−	0.979279i	$-0.564912\pi$
$569$	−230.465			−0.405036			−0.202518	+	0.979279i	$0.564912\pi$
$570$		0			0
$571$			351.234i			0.615121i	0.951529	+	0.307560i	$0.0995126\pi$
$571$			351.234i			0.615121i	−0.951529	+	0.307560i	$0.900487\pi$
$572$	15.0671	−	134.060i	0.0263410	−	0.234371i
$573$			572.512i			0.999149i
$574$	−233.390	+	208.629i	−0.406603	+	0.363465i
$575$		0			0
$576$	−63.2618	+	181.279i	−0.109830	+	0.314720i
$577$			638.575i			1.10672i	0.832944	+	0.553358i	$0.186654\pi$
$577$			638.575i			1.10672i	−0.832944	+	0.553358i	$0.813346\pi$
$578$	642.035	−	573.919i	1.11079	−	0.992939i
$579$			179.457i			0.309942i
$580$		0			0
$581$	−935.439			−1.61005
$582$	291.600	+	326.209i	0.501032	+	0.560497i
$583$	−69.4746			−0.119167
$584$	723.410	−	513.742i	1.23872	−	0.879696i
$585$		0			0
$586$	169.006	+	189.065i	0.288407	+	0.322637i
$587$	−105.047			−0.178956			−0.0894779	−	0.995989i	$-0.528520\pi$
$587$	−105.047			−0.178956			−0.0894779	+	0.995989i	$0.528520\pi$
$588$	−4.53201	+	40.3238i	−0.00770749	+	0.0685779i
$589$	−259.018			−0.439759
$590$		0			0
$591$			278.224i			0.470768i
$592$	194.450	−	854.138i	0.328463	−	1.44280i
$593$			990.175i			1.66977i	0.550422	+	0.834886i	$0.314467\pi$
$593$			990.175i			1.66977i	−0.550422	+	0.834886i	$0.685533\pi$
$594$	15.7009	+	17.5644i	0.0264325	+	0.0295697i
$595$		0			0
$596$	−35.5636	+	316.429i	−0.0596705	+	0.530922i
$597$		−	47.7210i		−	0.0799347i
$598$	−723.016	−	808.828i	−1.20906	−	1.35255i
$599$		−	78.0745i		−	0.130341i	−0.997874	−	0.0651707i	$-0.979241\pi$
$599$		−	78.0745i		−	0.130341i	0.997874	−	0.0651707i	$-0.0207592\pi$
$600$		0			0
$601$	−616.498			−1.02579			−0.512893	−	0.858452i	$-0.671426\pi$
$601$	−616.498			−1.02579			−0.512893	+	0.858452i	$0.671426\pi$
$602$	−550.929	+	492.479i	−0.915165	+	0.818071i
$603$	−334.331			−0.554446
$604$	−726.314	−	81.6306i	−1.20251	−	0.135150i
$605$		0			0
$606$	−223.951	+	200.191i	−0.369556	+	0.330348i
$607$	−226.520			−0.373179			−0.186590	−	0.982438i	$-0.559743\pi$
$607$	−226.520			−0.373179			−0.186590	+	0.982438i	$0.559743\pi$
$608$	168.439	+	304.265i	0.277037	+	0.500436i
$609$	−401.040			−0.658522
$610$		0			0
$611$		−	764.951i		−	1.25197i
$612$	319.886	+	35.9520i	0.522689	+	0.0587452i
$613$			732.519i			1.19497i	0.801879	+	0.597487i	$0.203834\pi$
$613$			732.519i			1.19497i	−0.801879	+	0.597487i	$0.796166\pi$
$614$	608.995	−	544.384i	0.991848	−	0.886619i
$615$		0			0
$616$	−97.1220	+	68.9729i	−0.157666	+	0.111969i
$617$		−	350.585i		−	0.568209i	−0.958793	−	0.284105i	$-0.908304\pi$
$617$		−	350.585i		−	0.568209i	0.958793	−	0.284105i	$-0.0916963\pi$
$618$	56.6329	−	50.6245i	0.0916390	−	0.0819166i
$619$		−	237.923i		−	0.384367i	−0.981359	−	0.192184i	$-0.938443\pi$
$619$		−	237.923i		−	0.384367i	0.981359	−	0.192184i	$-0.0615569\pi$
$620$		0			0
$621$	189.457			0.305084
$622$	−629.790	−	704.537i	−1.01252	−	1.13270i
$623$	46.9504			0.0753617
$624$	91.5185	−	402.003i	0.146664	−	0.644235i
$625$		0			0
$626$	72.8455	+	81.4913i	0.116367	+	0.130178i
$627$	42.6733			0.0680595
$628$	−843.417	−	94.7920i	−1.34302	−	0.150943i
$629$	−1468.65			−2.33490
$630$		0			0
$631$		−	200.923i		−	0.318419i	−0.987245	−	0.159210i	$-0.949105\pi$
$631$		−	200.923i		−	0.318419i	0.987245	−	0.159210i	$-0.0508946\pi$
$632$	−384.873	+	273.324i	−0.608976	+	0.432475i
$633$		−	467.321i		−	0.738264i
$634$	84.4705	+	94.4960i	0.133234	+	0.149047i
$635$		0			0
$636$	−210.997	−	23.7140i	−0.331756	−	0.0372862i
$637$		−	87.1340i		−	0.136788i
$638$	106.516	+	119.158i	0.166953	+	0.186768i
$639$			93.9570i			0.147038i
$640$		0			0
$641$	216.861			0.338316			0.169158	−	0.985589i	$-0.445895\pi$
$641$	216.861			0.338316			0.169158	+	0.985589i	$0.445895\pi$
$642$	18.5364	−	16.5698i	0.0288729	−	0.0258096i
$643$	37.5349			0.0583746			0.0291873	−	0.999574i	$-0.490708\pi$
$643$	37.5349			0.0583746			0.0291873	+	0.999574i	$0.490708\pi$
$644$	−106.991	+	951.960i	−0.166135	+	1.47820i
$645$		0			0
$646$	434.707	−	388.587i	0.672921	−	0.601528i
$647$	1192.56			1.84321			0.921607	−	0.388125i	$-0.126877\pi$
$647$	1192.56			1.84321			0.921607	+	0.388125i	$0.126877\pi$
$648$	41.6889	+	58.7029i	0.0643347	+	0.0905910i
$649$	−15.6984			−0.0241885
$650$		0			0
$651$		−	271.141i		−	0.416500i
$652$	−108.739	+	967.509i	−0.166777	+	1.48391i
$653$		−	1087.78i		−	1.66582i	−0.553412	−	0.832908i	$-0.686675\pi$
$653$		−	1087.78i		−	1.66582i	0.553412	−	0.832908i	$-0.313325\pi$
$654$	65.6656	−	58.6988i	0.100406	−	0.0897535i
$655$		0			0
$656$	371.765	+	84.6347i	0.566715	+	0.129016i
$657$		−	332.727i		−	0.506435i
$658$	−503.587	+	450.160i	−0.765330	+	0.684133i
$659$		−	852.957i		−	1.29432i	−0.762354	−	0.647160i	$-0.775956\pi$
$659$		−	852.957i		−	1.29432i	0.762354	−	0.647160i	$-0.224044\pi$
$660$		0			0
$661$	−504.933			−0.763892			−0.381946	−	0.924185i	$-0.624746\pi$
$661$	−504.933			−0.763892			−0.381946	+	0.924185i	$0.624746\pi$
$662$	575.273	+	643.550i	0.868992	+	0.972130i
$663$	−691.227			−1.04257
$664$	659.687	+	928.917i	0.993504	+	1.39897i
$665$		0			0
$666$	−218.927	−	244.911i	−0.328719	−	0.367734i
$667$	1285.29			1.92697
$668$	94.4403	−	840.289i	0.141378	−	1.25792i
$669$	71.5934			0.107016
$670$		0			0
$671$		−	243.530i		−	0.362936i
$672$	−318.506	+	176.322i	−0.473967	+	0.262384i
$673$		−	902.689i		−	1.34129i	−0.741778	−	0.670646i	$-0.766017\pi$
$673$		−	902.689i		−	1.34129i	0.741778	−	0.670646i	$-0.233983\pi$
$674$	−647.911	−	724.810i	−0.961293	−	1.07539i
$675$		0			0
$676$	−23.3787	+	208.013i	−0.0345838	+	0.307712i
$677$		−	930.750i		−	1.37482i	−0.726272	−	0.687408i	$-0.758748\pi$
$677$		−	930.750i		−	1.37482i	0.726272	−	0.687408i	$-0.241252\pi$
$678$	−180.903	−	202.374i	−0.266819	−	0.298487i
$679$			829.632i			1.22184i
$680$		0			0
$681$	259.526			0.381095
$682$	−80.5620	+	72.0148i	−0.118126	+	0.105594i
$683$	64.9023			0.0950253			0.0475127	−	0.998871i	$-0.484871\pi$
$683$	64.9023			0.0950253			0.0475127	+	0.998871i	$0.484871\pi$
$684$	129.600	+	14.5658i	0.189474	+	0.0212951i
$685$		0			0
$686$	−537.271	+	480.269i	−0.783193	+	0.700101i
$687$	106.828			0.155499
$688$	877.570	+	199.784i	1.27554	+	0.290384i
$689$	455.934			0.661733
$690$		0			0
$691$		−	348.329i		−	0.504094i	−0.967715	−	0.252047i	$-0.918896\pi$
$691$		−	348.329i		−	0.504094i	0.967715	−	0.252047i	$-0.0811038\pi$
$692$	−88.6970	−	9.96868i	−0.128175	−	0.0144056i
$693$			44.6706i			0.0644597i
$694$	438.826	−	392.269i	0.632315	−	0.565230i
$695$		0			0
$696$	282.820	+	398.244i	0.406350	+	0.572189i
$697$		−	639.234i		−	0.917122i
$698$	123.825	−	110.688i	0.177400	−	0.158579i
$699$			702.494i			1.00500i
$700$		0			0
$701$	815.159			1.16285			0.581426	−	0.813600i	$-0.302495\pi$
$701$	815.159			1.16285			0.581426	+	0.813600i	$0.302495\pi$
$702$	−103.039	−	115.268i	−0.146779	−	0.164200i
$703$	−595.020			−0.846401
$704$	136.984	+	47.8041i	0.194580	+	0.0679036i
$705$		0			0
$706$	760.731	+	851.020i	1.07752	+	1.20541i
$707$	−569.562			−0.805605
$708$	−47.6765	−	5.35838i	−0.0673397	−	0.00756833i
$709$	−1300.08			−1.83368			−0.916839	−	0.399257i	$-0.869268\pi$
$709$	−1300.08			−1.83368			−0.916839	+	0.399257i	$0.869268\pi$
$710$		0			0
$711$			177.019i			0.248972i
$712$	−33.1102	−	46.6230i	−0.0465030	−	0.0654818i
$713$			868.977i			1.21876i
$714$	406.774	+	455.053i	0.569712	+	0.637329i
$715$		0			0
$716$	375.722	+	42.2275i	0.524751	+	0.0589770i
$717$		−	463.789i		−	0.646846i
$718$	−744.112	−	832.428i	−1.03637	−	1.15937i
$719$			782.612i			1.08847i	0.838932	+	0.544237i	$0.183181\pi$
$719$			782.612i			1.08847i	−0.838932	+	0.544237i	$0.816819\pi$
$720$		0			0
$721$	144.031			0.199766
$722$	−362.167	+	323.743i	−0.501616	+	0.448397i
$723$	−155.084			−0.214500
$724$	−36.0160	+	320.454i	−0.0497458	+	0.442616i
$725$		0			0
$726$	−299.229	+	267.483i	−0.412161	+	0.368433i
$727$	850.638			1.17007			0.585033	−	0.811009i	$-0.301081\pi$
$727$	850.638			1.17007			0.585033	+	0.811009i	$0.301081\pi$
$728$	637.373	−	452.642i	0.875513	−	0.621761i
$729$	27.0000			0.0370370
$730$		0			0
$731$		−	1508.94i		−	2.06422i
$732$	83.1250	−	739.610i	0.113559	−	1.01040i
$733$			365.781i			0.499019i	0.968372	+	0.249510i	$0.0802694\pi$
$733$			365.781i			0.499019i	−0.968372	+	0.249510i	$0.919731\pi$
$734$	−665.726	+	595.096i	−0.906984	+	0.810758i
$735$		0			0
$736$	1020.78	−	565.093i	1.38692	−	0.767789i
$737$			252.639i			0.342794i
$738$	106.598	−	95.2884i	0.144442	−	0.129117i
$739$		−	727.328i		−	0.984205i	−0.870537	−	0.492103i	$-0.836228\pi$
$739$		−	727.328i		−	0.984205i	0.870537	−	0.492103i	$-0.163772\pi$
$740$		0			0
$741$	−280.048			−0.377933
$742$	−268.309	−	300.153i	−0.361602	−	0.404519i
$743$	481.526			0.648083			0.324041	−	0.946043i	$-0.394958\pi$
$743$	481.526			0.648083			0.324041	+	0.946043i	$0.394958\pi$
$744$	−269.251	+	191.213i	−0.361896	+	0.257007i
$745$		0			0
$746$	150.516	+	168.380i	0.201764	+	0.225711i
$747$	427.249			0.571953
$748$	27.1673	−	241.723i	0.0363200	−	0.323159i
$749$	47.1426			0.0629408
$750$		0			0
$751$			1316.30i			1.75273i	0.481647	+	0.876365i	$0.340039\pi$
$751$			1316.30i			1.75273i	−0.481647	+	0.876365i	$0.659961\pi$
$752$	802.159	+	182.617i	1.06670	+	0.242841i
$753$		−	394.637i		−	0.524087i
$754$	−699.021	−	781.985i	−0.927083	−	1.03711i
$755$		0			0
$756$	−15.2476	+	135.666i	−0.0201688	+	0.179453i
$757$		−	483.813i		−	0.639118i	−0.947566	−	0.319559i	$-0.896465\pi$
$757$		−	483.813i		−	0.639118i	0.947566	−	0.319559i	$-0.103535\pi$
$758$	−428.471	−	479.325i	−0.565265	−	0.632354i
$759$		−	143.164i		−	0.188622i
$760$		0			0
$761$	1027.03			1.34958			0.674789	−	0.738011i	$-0.264235\pi$
$761$	1027.03			1.34958			0.674789	+	0.738011i	$0.264235\pi$
$762$	−184.938	+	165.317i	−0.242701	+	0.216952i
$763$	167.004			0.218878
$764$	1313.89	+	147.668i	1.71975	+	0.193283i
$765$		0			0
$766$	133.046	−	118.931i	0.173689	−	0.155262i
$767$	103.022			0.134318
$768$	399.709	+	191.940i	0.520454	+	0.249922i
$769$	−1024.79			−1.33263			−0.666314	−	0.745671i	$-0.732129\pi$
$769$	−1024.79			−1.33263			−0.666314	+	0.745671i	$0.732129\pi$
$770$		0			0
$771$		−	765.790i		−	0.993242i
$772$	411.844	+	46.2873i	0.533477	+	0.0599577i
$773$		−	1092.74i		−	1.41364i	−0.707395	−	0.706819i	$-0.750130\pi$
$773$		−	1092.74i		−	1.41364i	0.707395	−	0.706819i	$-0.249870\pi$
$774$	251.629	−	224.933i	0.325103	−	0.290611i
$775$		0			0
$776$	823.848	−	585.070i	1.06166	−	0.753956i
$777$		−	622.869i		−	0.801633i
$778$	388.751	−	347.506i	0.499679	−	0.446666i
$779$		−	258.983i		−	0.332456i
$780$		0			0
$781$	70.9991			0.0909079
$782$	−1303.66	−	1458.39i	−1.66709	−	1.86495i
$783$	183.169			0.233933
$784$	91.3723	+	20.8015i	0.116546	+	0.0265325i
$785$		0			0
$786$	240.050	+	268.541i	0.305407	+	0.341655i
$787$	−1385.63			−1.76064			−0.880322	−	0.474376i	$-0.842674\pi$
$787$	−1385.63			−1.76064			−0.880322	+	0.474376i	$0.842674\pi$
$788$	638.511	+	71.7624i	0.810293	+	0.0910691i
$789$	−59.1593			−0.0749800
$790$		0			0
$791$		−	514.688i		−	0.650680i
$792$	44.3592	−	31.5024i	0.0560090	−	0.0397758i
$793$			1598.19i			2.01537i
$794$	150.093	+	167.907i	0.189034	+	0.211470i
$795$		0			0
$796$	−109.518	−	12.3087i	−0.137585	−	0.0154632i
$797$			98.5251i			0.123620i	0.998088	+	0.0618100i	$0.0196873\pi$
$797$			98.5251i			0.123620i	−0.998088	+	0.0618100i	$0.980313\pi$
$798$	164.803	+	184.363i	0.206520	+	0.231031i
$799$		−	1379.28i		−	1.72626i
$800$		0			0
$801$	−21.4439			−0.0267715
$802$	−861.128	+	769.767i	−1.07373	+	0.959810i
$803$	−251.427			−0.313110
$804$	−86.2342	+	767.274i	−0.107256	+	0.954321i
$805$		0			0
$806$	528.697	−	472.605i	0.655951	−	0.586358i
$807$	17.2527			0.0213788
$808$	401.665	+	565.592i	0.497110	+	0.699990i
$809$	212.100			0.262176			0.131088	−	0.991371i	$-0.458153\pi$
$809$	212.100			0.262176			0.131088	+	0.991371i	$0.458153\pi$
$810$		0			0
$811$			485.409i			0.598531i	0.954170	+	0.299266i	$0.0967417\pi$
$811$			485.409i			0.598531i	−0.954170	+	0.299266i	$0.903258\pi$
$812$	−103.440	+	920.367i	−0.127390	+	1.13346i
$813$			97.9980i			0.120539i
$814$	−185.068	+	165.433i	−0.227356	+	0.203235i
$815$		0			0
$816$	165.016	−	724.849i	0.202226	−	0.888295i
$817$		−	611.343i		−	0.748278i
$818$	−411.924	+	368.221i	−0.503575	+	0.450148i
$819$		−	293.155i		−	0.357943i
$820$		0			0
$821$	−862.231			−1.05022			−0.525110	−	0.851034i	$-0.675976\pi$
$821$	−862.231			−1.05022			−0.525110	+	0.851034i	$0.675976\pi$
$822$	−16.5449	−	18.5085i	−0.0201276	−	0.0225164i
$823$	485.042			0.589358			0.294679	−	0.955596i	$-0.404787\pi$
$823$	485.042			0.589358			0.294679	+	0.955596i	$0.404787\pi$
$824$	−101.573	−	143.027i	−0.123269	−	0.173577i
$825$		0			0
$826$	−60.6266	−	67.8221i	−0.0733978	−	0.0821091i
$827$	590.547			0.714084			0.357042	−	0.934088i	$-0.383785\pi$
$827$	590.547			0.714084			0.357042	+	0.934088i	$0.383785\pi$
$828$	48.8667	−	434.795i	0.0590178	−	0.525115i
$829$	1071.30			1.29228			0.646139	−	0.763220i	$-0.276383\pi$
$829$	1071.30			1.29228			0.646139	+	0.763220i	$0.276383\pi$
$830$		0			0
$831$			179.777i			0.216338i
$832$	−898.972	−	313.719i	−1.08050	−	0.377067i
$833$		−	157.111i		−	0.188608i
$834$	−339.161	−	379.415i	−0.406668	−	0.454934i
$835$		0			0
$836$	11.0067	−	97.9332i	0.0131660	−	0.117145i
$837$			123.840i			0.147957i
$838$	329.919	+	369.076i	0.393698	+	0.440425i
$839$		−	783.581i		−	0.933946i	−0.884272	−	0.466973i	$-0.845345\pi$
$839$		−	783.581i		−	0.933946i	0.884272	−	0.466973i	$-0.154655\pi$
$840$		0			0
$841$	401.631			0.477564
$842$	115.903	−	103.607i	0.137653	−	0.123048i
$843$	680.815			0.807610
$844$	−1072.48	−	120.536i	−1.27071	−	0.142816i
$845$		0			0
$846$	230.007	−	205.604i	0.271875	−	0.243031i
$847$	−761.014			−0.898481
$848$	−108.845	+	478.111i	−0.128355	+	0.563810i
$849$	197.501			0.232628
$850$		0			0
$851$			1996.22i			2.34574i
$852$	215.627	+	24.2344i	0.253083	+	0.0284441i
$853$		−	104.807i		−	0.122868i	−0.998111	−	0.0614341i	$-0.980433\pi$
$853$		−	104.807i		−	0.122868i	0.998111	−	0.0614341i	$-0.0195674\pi$
$854$	1052.13	−	940.506i	1.23200	−	1.10129i
$855$		0			0
$856$	−33.2457	−	46.8140i	−0.0388385	−	0.0546892i
$857$		−	1163.30i		−	1.35741i	−0.734411	−	0.678705i	$-0.762542\pi$
$857$		−	1163.30i		−	1.35741i	0.734411	−	0.678705i	$-0.237458\pi$
$858$	−87.1029	+	77.8617i	−0.101518	+	0.0907480i
$859$			337.818i			0.393269i	0.980477	+	0.196634i	$0.0630012\pi$
$859$			337.818i			0.393269i	−0.980477	+	0.196634i	$0.936999\pi$
$860$		0			0
$861$	271.105			0.314872
$862$	422.775	+	472.953i	0.490458	+	0.548669i
$863$	−199.699			−0.231400			−0.115700	−	0.993284i	$-0.536911\pi$
$863$	−199.699			−0.231400			−0.115700	+	0.993284i	$0.536911\pi$
$864$	145.473	−	80.5328i	0.168372	−	0.0932092i
$865$		0			0
$866$	110.589	+	123.715i	0.127701	+	0.142858i
$867$	−745.784			−0.860189
$868$	−622.256	−	69.9356i	−0.716885	−	0.0805710i
$869$	133.766			0.153930
$870$		0			0
$871$		−	1657.97i		−	1.90352i
$872$	−117.774	−	165.840i	−0.135062	−	0.190183i
$873$		−	378.923i		−	0.434047i
$874$	−528.175	−	590.862i	−0.604319	−	0.676044i
$875$		0			0
$876$	−763.594	−	85.8205i	−0.871682	−	0.0979687i
$877$			1032.82i			1.17767i	0.808252	+	0.588836i	$0.200414\pi$
$877$			1032.82i			1.17767i	−0.808252	+	0.588836i	$0.799586\pi$
$878$	156.777	+	175.385i	0.178562	+	0.199755i
$879$		−	219.617i		−	0.249849i
$880$		0			0
$881$	−585.412			−0.664486			−0.332243	−	0.943194i	$-0.607805\pi$
$881$	−585.412			−0.664486			−0.332243	+	0.943194i	$0.607805\pi$
$882$	26.1996	−	23.4199i	0.0297047	−	0.0265532i
$883$	−536.231			−0.607283			−0.303641	−	0.952786i	$-0.598203\pi$
$883$	−536.231			−0.607283			−0.303641	+	0.952786i	$0.598203\pi$
$884$	−178.288	+	1586.33i	−0.201684	+	1.79449i
$885$		0			0
$886$	52.4539	−	46.8888i	0.0592030	−	0.0529219i
$887$	−173.466			−0.195564			−0.0977822	−	0.995208i	$-0.531175\pi$
$887$	−173.466			−0.195564			−0.0977822	+	0.995208i	$0.531175\pi$
$888$	−618.526	+	439.257i	−0.696539	+	0.494659i
$889$	−470.344			−0.529071
$890$		0			0
$891$		−	20.4027i		−	0.0228986i
$892$	18.4661	−	164.303i	0.0207019	−	0.184197i
$893$		−	558.810i		−	0.625767i
$894$	205.594	−	183.781i	0.229970	−	0.205572i
$895$		0			0
$896$	322.499	+	776.435i	0.359932	+	0.866557i
$897$			939.529i			1.04741i
$898$	−100.538	+	89.8712i	−0.111957	+	0.100079i
$899$			840.138i			0.934525i
$900$		0			0
$901$	822.092			0.912421
$902$	−72.0051	−	80.5512i	−0.0798283	−	0.0893028i
$903$	639.956			0.708700
$904$	−511.099	+	362.966i	−0.565375	+	0.401511i
$905$		0			0
$906$	421.841	+	471.908i	0.465608	+	0.520869i
$907$	817.237			0.901033			0.450516	−	0.892768i	$-0.351240\pi$
$907$	817.237			0.901033			0.450516	+	0.892768i	$0.351240\pi$
$908$	66.9395	−	595.599i	0.0737220	−	0.655946i
$909$	260.140			0.286182
$910$		0			0
$911$		−	227.911i		−	0.250177i	−0.992146	−	0.125088i	$-0.960079\pi$
$911$		−	227.911i		−	0.250177i	0.992146	−	0.125088i	$-0.0399215\pi$
$912$	66.8558	−	293.670i	0.0733068	−	0.322006i
$913$		−	322.853i		−	0.353617i
$914$	−272.115	−	304.412i	−0.297719	−	0.333055i
$915$		0			0
$916$	27.5541	−	245.165i	0.0300809	−	0.267647i
$917$			682.966i			0.744783i
$918$	−185.789	−	207.839i	−0.202384	−	0.226404i
$919$			669.088i			0.728061i	0.931387	+	0.364031i	$0.118600\pi$
$919$			669.088i			0.728061i	−0.931387	+	0.364031i	$0.881400\pi$
$920$		0			0
$921$	−707.405			−0.768083
$922$	−187.523	+	167.628i	−0.203387	+	0.181809i
$923$	−465.939			−0.504809
$924$	102.517	+	11.5219i	0.110949	+	0.0124696i
$925$		0			0
$926$	−825.515	+	737.933i	−0.891485	+	0.796904i
$927$	−65.7844			−0.0709648
$928$	986.898	−	546.339i	1.06347	−	0.588727i
$929$	1192.84			1.28400			0.642000	−	0.766705i	$-0.278105\pi$
$929$	1192.84			1.28400			0.642000	+	0.766705i	$0.278105\pi$
$930$		0			0
$931$		−	63.6528i		−	0.0683704i
$932$	1612.19	+	181.195i	1.72982	+	0.194415i
$933$			818.386i			0.877156i
$934$	933.088	−	834.092i	0.999023	−	0.893032i
$935$		0			0
$936$	−291.112	+	206.738i	−0.311017	+	0.220874i
$937$			530.621i			0.566298i	0.959076	+	0.283149i	$0.0913790\pi$
$937$			530.621i			0.566298i	−0.959076	+	0.283149i	$0.908621\pi$
$938$	−1091.48	+	975.684i	−1.16363	+	1.04018i
$939$		−	94.6598i		−	0.100809i
$940$		0			0
$941$	−507.433			−0.539248			−0.269624	−	0.962966i	$-0.586899\pi$
$941$	−507.433			−0.539248			−0.269624	+	0.962966i	$0.586899\pi$
$942$	489.854	+	547.993i	0.520015	+	0.581734i
$943$	−868.860			−0.921378
$944$	−24.5944	+	108.033i	−0.0260534	+	0.114442i
$945$		0			0
$946$	−169.972	−	190.145i	−0.179674	−	0.200999i
$947$	−453.872			−0.479274			−0.239637	−	0.970863i	$-0.577028\pi$
$947$	−453.872			−0.479274			−0.239637	+	0.970863i	$0.577028\pi$
$948$	406.251	+	45.6587i	0.428535	+	0.0481632i
$949$	1650.02			1.73869
$950$		0			0
$951$		−	109.766i		−	0.115422i
$952$	1149.24	−	816.155i	1.20719	−	0.857306i
$953$			1220.52i			1.28071i	0.768078	+	0.640356i	$0.221213\pi$
$953$			1220.52i			1.28071i	−0.768078	+	0.640356i	$0.778787\pi$
$954$	122.546	+	137.091i	0.128455	+	0.143701i
$955$		0			0
$956$	−1064.37	−	119.625i	−1.11336	−	0.125131i
$957$		−	138.413i		−	0.144632i
$958$	650.731	+	727.964i	0.679260	+	0.759879i
$959$		−	47.0717i		−	0.0490842i
$960$		0			0
$961$	392.986			0.408935
$962$	1214.53	−	1085.67i	1.26250	−	1.12856i
$963$	−21.5317			−0.0223590
$964$	−40.0008	+	355.910i	−0.0414946	+	0.369201i
$965$		0			0
$966$	618.517	−	552.896i	0.640287	−	0.572356i
$967$	−292.088			−0.302056			−0.151028	−	0.988530i	$-0.548258\pi$
$967$	−292.088			−0.302056			−0.151028	+	0.988530i	$0.548258\pi$
$968$	536.679	+	755.708i	0.554421	+	0.780690i
$969$	−504.953			−0.521107
$970$		0			0
$971$			1097.69i			1.13047i	0.824928	+	0.565237i	$0.191215\pi$
$971$			1097.69i			1.13047i	−0.824928	+	0.565237i	$0.808785\pi$
$972$	6.96412	−	61.9637i	0.00716473	−	0.0637487i
$973$		−	964.947i		−	0.991724i
$974$	−908.789	+	812.372i	−0.933048	+	0.834057i
$975$		0			0
$976$	−1675.93	−	381.536i	−1.71714	−	0.390918i
$977$		−	338.550i		−	0.346520i	−0.984876	−	0.173260i	$-0.944570\pi$
$977$		−	338.550i		−	0.346520i	0.984876	−	0.173260i	$-0.0554301\pi$
$978$	628.619	−	561.926i	0.642760	−	0.574567i
$979$			16.2042i			0.0165518i
$980$		0			0
$981$	−76.2767			−0.0777540
$982$	918.468	+	1027.48i	0.935304	+	1.04631i
$983$	−346.346			−0.352336			−0.176168	−	0.984360i	$-0.556370\pi$
$983$	−346.346			−0.352336			−0.176168	+	0.984360i	$0.556370\pi$
$984$	−191.188	−	269.215i	−0.194296	−	0.273592i
$985$		0			0
$986$	−1260.40	−	1409.99i	−1.27830	−	1.43001i
$987$	584.964			0.592669
$988$	−72.2329	+	642.697i	−0.0731102	+	0.650503i
$989$	−2050.99			−2.07380
$990$		0			0
$991$		−	242.030i		−	0.244228i	−0.992516	−	0.122114i	$-0.961033\pi$
$991$		−	242.030i		−	0.244228i	0.992516	−	0.122114i	$-0.0389673\pi$
$992$	369.377	+	667.238i	0.372356	+	0.672619i
$993$		−	747.544i		−	0.752813i
$994$	274.196	+	306.740i	0.275851	+	0.308591i
$995$		0			0
$996$	110.200	−	980.516i	0.110643	−	0.984454i
$997$			178.452i			0.178989i	0.995987	+	0.0894946i	$0.0285252\pi$
$997$			178.452i			0.178989i	−0.995987	+	0.0894946i	$0.971475\pi$
$998$	−933.565	−	1044.37i	−0.935436	−	1.04646i
$999$			284.487i			0.284772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.f.c.199.6		16
3.2	odd	2		900.3.f.h.199.11		16
4.3	odd	2	inner	300.3.f.c.199.12		16
5.2	odd	4		300.3.c.g.151.1	yes	8
5.3	odd	4		300.3.c.e.151.8	yes	8
5.4	even	2	inner	300.3.f.c.199.11		16
12.11	even	2		900.3.f.h.199.5		16
15.2	even	4		900.3.c.n.451.8		8
15.8	even	4		900.3.c.t.451.1		8
15.14	odd	2		900.3.f.h.199.6		16
20.3	even	4		300.3.c.e.151.7	✓	8
20.7	even	4		300.3.c.g.151.2	yes	8
20.19	odd	2	inner	300.3.f.c.199.5		16
60.23	odd	4		900.3.c.t.451.2		8
60.47	odd	4		900.3.c.n.451.7		8
60.59	even	2		900.3.f.h.199.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.3.c.e.151.7	✓	8	20.3	even	4
300.3.c.e.151.8	yes	8	5.3	odd	4
300.3.c.g.151.1	yes	8	5.2	odd	4
300.3.c.g.151.2	yes	8	20.7	even	4
300.3.f.c.199.5		16	20.19	odd	2	inner
300.3.f.c.199.6		16	1.1	even	1	trivial
300.3.f.c.199.11		16	5.4	even	2	inner
300.3.f.c.199.12		16	4.3	odd	2	inner
900.3.c.n.451.7		8	60.47	odd	4
900.3.c.n.451.8		8	15.2	even	4
900.3.c.t.451.1		8	15.8	even	4
900.3.c.t.451.2		8	60.23	odd	4
900.3.f.h.199.5		16	12.11	even	2
900.3.f.h.199.6		16	15.14	odd	2
900.3.f.h.199.11		16	3.2	odd	2
900.3.f.h.199.12		16	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.49110 + 1.33290i) q^{2} +1.73205 q^{3} +(0.446749 - 3.97497i) q^{4} +(-2.58266 + 2.30865i) q^{6} -6.56834 q^{7} +(4.63210 + 6.52255i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-1.49110 + 1.33290i) q^{2} +1.73205 q^{3} +(0.446749 - 3.97497i) q^{4} +(-2.58266 + 2.30865i) q^{6} -6.56834 q^{7} +(4.63210 + 6.52255i) q^{8} +3.00000 q^{9} -2.26696i q^{11} +(0.773791 - 6.88486i) q^{12} +14.8772i q^{13} +(9.79404 - 8.75495i) q^{14} +(-15.6008 - 3.55163i) q^{16} +26.8250i q^{17} +(-4.47330 + 3.99870i) q^{18} +10.8680i q^{19} -11.3767 q^{21} +(3.02164 + 3.38027i) q^{22} +36.4610 q^{23} +(8.02303 + 11.2974i) q^{24} +(-19.8298 - 22.1834i) q^{26} +5.19615 q^{27} +(-2.93440 + 26.1090i) q^{28} +35.2510 q^{29} +23.8330i q^{31} +(27.9963 - 15.4985i) q^{32} -3.92650i q^{33} +(-35.7550 - 39.9987i) q^{34} +(1.34025 - 11.9249i) q^{36} +54.7495i q^{37} +(-14.4860 - 16.2053i) q^{38} +25.7680i q^{39} -23.8298 q^{41} +(16.9638 - 15.1640i) q^{42} -56.2515 q^{43} +(-9.01112 - 1.01276i) q^{44} +(-54.3670 + 48.5989i) q^{46} -51.4177 q^{47} +(-27.0214 - 6.15160i) q^{48} -5.85689 q^{49} +46.4622i q^{51} +(59.1364 + 6.64636i) q^{52} -30.6465i q^{53} +(-7.74797 + 6.92596i) q^{54} +(-30.4252 - 42.8423i) q^{56} +18.8240i q^{57} +(-52.5627 + 46.9861i) q^{58} -6.92483i q^{59} +107.426 q^{61} +(-31.7671 - 35.5374i) q^{62} -19.7050 q^{63} +(-21.0873 + 60.4262i) q^{64} +(5.23363 + 5.85479i) q^{66} -111.444 q^{67} +(106.629 + 11.9840i) q^{68} +63.1524 q^{69} +31.3190i q^{71} +(13.8963 + 19.5676i) q^{72} -110.909i q^{73} +(-72.9757 - 81.6369i) q^{74} +(43.2002 + 4.85528i) q^{76} +14.8902i q^{77} +(-34.3463 - 38.4227i) q^{78} +59.0065i q^{79} +9.00000 q^{81} +(35.5326 - 31.7628i) q^{82} +142.416 q^{83} +(-5.08253 + 45.2221i) q^{84} +(83.8765 - 74.9776i) q^{86} +61.0565 q^{87} +(14.7864 - 10.5008i) q^{88} -7.14798 q^{89} -97.7185i q^{91} +(16.2889 - 144.932i) q^{92} +41.2800i q^{93} +(76.6689 - 68.5347i) q^{94} +(48.4911 - 26.8443i) q^{96} -126.308i q^{97} +(8.73319 - 7.80665i) q^{98} -6.80089i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 12 q^{6} + 48 q^{9}+O(q^{10}) \) 16 * q + 16 * q^4 - 12 * q^6 + 48 * q^9	\( 16 q + 16 q^{4} - 12 q^{6} + 48 q^{9} - 44 q^{14} + 80 q^{16} + 48 q^{21} + 72 q^{24} - 132 q^{26} + 64 q^{29} - 248 q^{34} + 48 q^{36} - 32 q^{41} - 80 q^{44} - 152 q^{46} - 32 q^{49} - 36 q^{54} - 344 q^{56} + 272 q^{61} - 32 q^{64} - 216 q^{66} + 192 q^{69} + 216 q^{74} + 240 q^{76} + 144 q^{81} + 288 q^{84} + 428 q^{86} - 256 q^{89} - 24 q^{94} + 192 q^{96}+O(q^{100}) \) 16 * q + 16 * q^4 - 12 * q^6 + 48 * q^9 - 44 * q^14 + 80 * q^16 + 48 * q^21 + 72 * q^24 - 132 * q^26 + 64 * q^29 - 248 * q^34 + 48 * q^36 - 32 * q^41 - 80 * q^44 - 152 * q^46 - 32 * q^49 - 36 * q^54 - 344 * q^56 + 272 * q^61 - 32 * q^64 - 216 * q^66 + 192 * q^69 + 216 * q^74 + 240 * q^76 + 144 * q^81 + 288 * q^84 + 428 * q^86 - 256 * q^89 - 24 * q^94 + 192 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more