LMFDB - Embedded newform 300.3.f.c.199.12

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			199.12
Root			$-0.637499 - 1.26238i$ of defining polynomial
Character	$\chi$	$=$	300.199
Dual form			300.3.f.c.199.11

$q$-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	$-0.344554\pi$
$7$	6.56834			0.938335			0.469167	+	0.883109i	$0.344554\pi$
$8$	−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	$0.0328582\pi$
$11$			2.26696i			0.206088i	−0.994677	+	0.103044i	$0.967142\pi$
$12$	−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	$-0.907674\pi$
$19$		−	10.8680i		−	0.572002i	0.958229	−	0.286001i	$-0.0923260\pi$
$20$		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	$-0.791289\pi$
$23$	−36.4610			−1.58526			−0.792631	+	0.609702i	$0.791289\pi$
$24$	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	$-0.874407\pi$
$31$		−	23.8330i		−	0.768808i	0.923165	−	0.384404i	$-0.125593\pi$
$32$	−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	$-0.273053\pi$
$43$	56.2515			1.30817			0.654087	+	0.756420i	$0.273053\pi$
$44$	−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	$-0.315771\pi$
$47$	51.4177			1.09399			0.546997	+	0.837135i	$0.315771\pi$
$48$	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	$0.0186908\pi$
$59$			6.92483i			0.117370i	−0.998277	+	0.0586850i	$0.981309\pi$
$60$		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	$-0.187385\pi$
$67$	111.444			1.66334			0.831670	+	0.555271i	$0.187385\pi$
$68$	−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	$-0.929213\pi$
$71$		−	31.3190i		−	0.441113i	0.975374	−	0.220556i	$-0.0707873\pi$
$72$	−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	$-0.878172\pi$
$79$		−	59.0065i		−	0.746917i	0.927647	−	0.373459i	$-0.121828\pi$
$80$		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	$-0.828249\pi$
$83$	−142.416			−1.71586			−0.857930	+	0.513767i	$0.828249\pi$
$84$	−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	$-0.466052\pi$
$103$	21.9281			0.212895			0.106447	+	0.994318i	$0.466052\pi$
$104$	−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	$-0.489322\pi$
$107$	7.17725			0.0670771			0.0335385	+	0.999437i	$0.489322\pi$
$108$	−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	$-0.590971\pi$
$127$	−71.6077			−0.563840			−0.281920	+	0.959438i	$0.590971\pi$
$128$	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	$0.129902\pi$
$131$			103.978i			0.793728i	−0.917877	+	0.396864i	$0.870098\pi$
$132$	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	$-0.822774\pi$
$139$		−	146.909i		−	1.05690i	0.848965	−	0.528449i	$-0.177226\pi$
$140$		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	$0.206842\pi$
$151$			182.722i			1.21008i	−0.796196	+	0.605039i	$0.793158\pi$
$152$	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	$-0.231673\pi$
$163$	243.400			1.49325			0.746626	+	0.665244i	$0.231673\pi$
$164$	−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	$-0.718143\pi$
$167$	−211.395			−1.26584			−0.632919	+	0.774218i	$0.718143\pi$
$168$	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	$-0.914949\pi$
$179$		−	94.5219i		−	0.528055i	0.964515	−	0.264028i	$-0.0850510\pi$
$180$		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	$-0.667135\pi$
$191$		−	330.540i		−	1.73058i	0.501275	−	0.865288i	$-0.332865\pi$
$192$	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	$0.0220528\pi$
$199$			27.5518i			0.138451i	−0.997601	+	0.0692255i	$0.977947\pi$
$200$		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	$0.220799\pi$
$211$			269.808i			1.27871i	−0.768911	+	0.639355i	$0.779201\pi$
$212$	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	$-0.529543\pi$
$223$	−41.3345			−0.185356			−0.0926782	+	0.995696i	$0.529543\pi$
$224$	−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	$-0.607061\pi$
$227$	−149.837			−0.660076			−0.330038	+	0.943968i	$0.607061\pi$
$228$	−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	$0.189270\pi$
$239$			267.769i			1.12037i	−0.828367	+	0.560185i	$0.810730\pi$
$240$		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	$0.149958\pi$
$251$			227.844i			0.907745i	−0.891067	+	0.453873i	$0.850042\pi$
$252$	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	$-0.479316\pi$
$263$	34.1556			0.129869			0.0649346	+	0.997890i	$0.479316\pi$
$264$	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	$-0.966711\pi$
$271$		−	56.5791i		−	0.208779i	0.994536	−	0.104390i	$-0.0332889\pi$
$272$	−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	$-0.564569\pi$
$283$	−114.027			−0.402923			−0.201462	+	0.979496i	$0.564569\pi$
$284$	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	$-0.268355\pi$
$307$	408.420			1.33036			0.665180	+	0.746683i	$0.268355\pi$
$308$	−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	$-0.725376\pi$
$311$		−	472.495i		−	1.51928i	0.650345	−	0.759639i	$-0.274624\pi$
$312$	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	$0.226051\pi$
$331$			431.595i			1.30391i	−0.758257	+	0.651955i	$0.773949\pi$
$332$	−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	$-0.360605\pi$
$347$	294.297			0.848119			0.424060	+	0.905634i	$0.360605\pi$
$348$	−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	$-0.716473\pi$
$359$		−	558.265i		−	1.55506i	0.628848	−	0.777528i	$-0.283527\pi$
$360$		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	$-0.708134\pi$
$367$	−446.467			−1.21653			−0.608265	+	0.793734i	$0.708134\pi$
$368$	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	$-0.860595\pi$
$379$		−	321.457i		−	0.848173i	0.905622	−	0.424086i	$-0.139405\pi$
$380$		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	$-0.462838\pi$
$383$	89.2269			0.232968			0.116484	+	0.993193i	$0.462838\pi$
$384$	−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	$0.0954428\pi$
$419$			247.520i			0.590739i	−0.955383	+	0.295370i	$0.904557\pi$
$420$		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	$0.119945\pi$
$431$			317.184i			0.735926i	−0.929840	+	0.367963i	$0.880055\pi$
$432$	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	$0.0427709\pi$
$439$			117.621i			0.267930i	−0.990986	+	0.133965i	$0.957229\pi$
$440$		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	$-0.487358\pi$
$443$	35.1780			0.0794086			0.0397043	+	0.999211i	$0.487358\pi$
$444$	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	$-0.703987\pi$
$463$	−553.629			−1.19574			−0.597871	+	0.801592i	$0.703987\pi$
$464$	−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	$-0.266298\pi$
$467$	625.772			1.33998			0.669991	+	0.742369i	$0.266298\pi$
$468$	−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	$0.170210\pi$
$479$			488.207i			1.01922i	−0.860405	+	0.509610i	$0.829790\pi$
$480$		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	$-0.715205\pi$
$487$	−609.476			−1.25149			−0.625746	+	0.780027i	$0.715205\pi$
$488$	−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	$0.247578\pi$
$491$			689.074i			1.40341i	−0.712468	+	0.701705i	$0.752422\pi$
$492$	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	$-0.752378\pi$
$499$		−	700.401i		−	1.40361i	0.712370	−	0.701804i	$-0.247622\pi$
$500$		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	$-0.887614\pi$
$503$	−943.945			−1.87663			−0.938315	+	0.345782i	$0.887614\pi$
$504$	−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	$-0.567585\pi$
$523$	−220.427			−0.421467			−0.210734	+	0.977544i	$0.567585\pi$
$524$	−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	$-0.783953\pi$
$547$	−851.537			−1.55674			−0.778370	+	0.627806i	$0.783953\pi$
$548$	−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	$-0.383175\pi$
$563$	404.044			0.717663			0.358832	+	0.933402i	$0.383175\pi$
$564$	−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	$-0.900487\pi$
$571$		−	351.234i		−	0.615121i	0.951529	−	0.307560i	$-0.0995126\pi$
$572$	−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	$-0.471480\pi$
$587$	105.047			0.178956			0.0894779	+	0.995989i	$0.471480\pi$
$588$	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	$0.0207592\pi$
$599$			78.0745i			0.130341i	−0.997874	+	0.0651707i	$0.979241\pi$
$600$		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	$-0.440257\pi$
$607$	226.520			0.373179			0.186590	+	0.982438i	$0.440257\pi$
$608$	−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	$0.0615569\pi$
$619$			237.923i			0.384367i	−0.981359	+	0.192184i	$0.938443\pi$
$620$		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	$0.0508946\pi$
$631$			200.923i			0.318419i	−0.987245	+	0.159210i	$0.949105\pi$
$632$	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	$-0.509292\pi$
$643$	−37.5349			−0.0583746			−0.0291873	+	0.999574i	$0.509292\pi$
$644$	−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	$-0.873123\pi$
$647$	−1192.56			−1.84321			−0.921607	+	0.388125i	$0.873123\pi$
$648$	−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	$0.224044\pi$
$659$			852.957i			1.29432i	−0.762354	+	0.647160i	$0.775956\pi$
$660$		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	$-0.515129\pi$
$683$	−64.9023			−0.0950253			−0.0475127	+	0.998871i	$0.515129\pi$
$684$	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	$0.0811038\pi$
$691$			348.329i			0.504094i	−0.967715	+	0.252047i	$0.918896\pi$
$692$	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	$-0.816819\pi$
$719$		−	782.612i		−	1.08847i	0.838932	−	0.544237i	$-0.183181\pi$
$720$		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	$-0.698919\pi$
$727$	−850.638			−1.17007			−0.585033	+	0.811009i	$0.698919\pi$
$728$	−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	$0.163772\pi$
$739$			727.328i			0.984205i	−0.870537	+	0.492103i	$0.836228\pi$
$740$		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	$-0.605042\pi$
$743$	−481.526			−0.648083			−0.324041	+	0.946043i	$0.605042\pi$
$744$	−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	$-0.659961\pi$
$751$		−	1316.30i		−	1.75273i	0.481647	−	0.876365i	$-0.340039\pi$
$752$	−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	$-0.157326\pi$
$787$	1385.63			1.76064			0.880322	+	0.474376i	$0.157326\pi$
$788$	−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	$-0.903258\pi$
$811$		−	485.409i		−	0.598531i	0.954170	−	0.299266i	$-0.0967417\pi$
$812$	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	$-0.595213\pi$
$823$	−485.042			−0.589358			−0.294679	+	0.955596i	$0.595213\pi$
$824$	−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	$-0.616215\pi$
$827$	−590.547			−0.714084			−0.357042	+	0.934088i	$0.616215\pi$
$828$	−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	$0.154655\pi$
$839$			783.581i			0.933946i	−0.884272	+	0.466973i	$0.845345\pi$
$840$		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	$-0.936999\pi$
$859$		−	337.818i		−	0.393269i	0.980477	−	0.196634i	$-0.0630012\pi$
$860$		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	$-0.463089\pi$
$863$	199.699			0.231400			0.115700	+	0.993284i	$0.463089\pi$
$864$	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	$-0.401797\pi$
$883$	536.231			0.607283			0.303641	+	0.952786i	$0.401797\pi$
$884$	−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	$-0.468825\pi$
$887$	173.466			0.195564			0.0977822	+	0.995208i	$0.468825\pi$
$888$	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	$-0.648760\pi$
$907$	−817.237			−0.901033			−0.450516	+	0.892768i	$0.648760\pi$
$908$	−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	$0.0399215\pi$
$911$			227.911i			0.250177i	−0.992146	+	0.125088i	$0.960079\pi$
$912$	−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	$-0.881400\pi$
$919$		−	669.088i		−	0.728061i	0.931387	−	0.364031i	$-0.118600\pi$
$920$		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	$-0.422972\pi$
$947$	453.872			0.479274			0.239637	+	0.970863i	$0.422972\pi$
$948$	−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	$-0.451742\pi$
$967$	292.088			0.302056			0.151028	+	0.988530i	$0.451742\pi$
$968$	−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	$-0.808785\pi$
$971$		−	1097.69i		−	1.13047i	0.824928	−	0.565237i	$-0.191215\pi$
$972$	−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	$-0.443630\pi$
$983$	346.346			0.352336			0.176168	+	0.984360i	$0.443630\pi$
$984$	−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	$0.0389673\pi$
$991$			242.030i			0.244228i	−0.992516	+	0.122114i	$0.961033\pi$
$992$	−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.199.12		16
3.2	odd	2		900.3.f.h.199.5		16
4.3	odd	2	inner	300.3.f.c.199.6		16
5.2	odd	4		300.3.c.g.151.2	yes	8
5.3	odd	4		300.3.c.e.151.7	✓	8
5.4	even	2	inner	300.3.f.c.199.5		16
12.11	even	2		900.3.f.h.199.11		16
15.2	even	4		900.3.c.n.451.7		8
15.8	even	4		900.3.c.t.451.2		8
15.14	odd	2		900.3.f.h.199.12		16
20.3	even	4		300.3.c.e.151.8	yes	8
20.7	even	4		300.3.c.g.151.1	yes	8
20.19	odd	2	inner	300.3.f.c.199.11		16
60.23	odd	4		900.3.c.t.451.1		8
60.47	odd	4		900.3.c.n.451.8		8
60.59	even	2		900.3.f.h.199.6		16

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

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Database

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