LMFDB - Embedded newform 300.3.c.e.151.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("300.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			151.7
Root			$0.151747 - 0.0876113i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.3.c.e.151.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33290 - 1.49110i) q^{2} -1.73205i q^{3} +(-0.446749 - 3.97497i) q^{4} +(-2.58266 - 2.30865i) q^{6} -6.56834i q^{7} +(-6.52255 - 4.63210i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.33290 - 1.49110i) q^{2} -1.73205i q^{3} +(-0.446749 - 3.97497i) q^{4} +(-2.58266 - 2.30865i) q^{6} -6.56834i q^{7} +(-6.52255 - 4.63210i) q^{8} -3.00000 q^{9} +2.26696i q^{11} +(-6.88486 + 0.773791i) q^{12} -14.8772 q^{13} +(-9.79404 - 8.75495i) q^{14} +(-15.6008 + 3.55163i) q^{16} +26.8250 q^{17} +(-3.99870 + 4.47330i) q^{18} +10.8680i q^{19} -11.3767 q^{21} +(3.38027 + 3.02164i) q^{22} -36.4610i q^{23} +(-8.02303 + 11.2974i) q^{24} +(-19.8298 + 22.1834i) q^{26} +5.19615i q^{27} +(-26.1090 + 2.93440i) q^{28} -35.2510 q^{29} -23.8330i q^{31} +(-15.4985 + 27.9963i) q^{32} +3.92650 q^{33} +(35.7550 - 39.9987i) q^{34} +(1.34025 + 11.9249i) q^{36} +54.7495 q^{37} +(16.2053 + 14.4860i) q^{38} +25.7680i q^{39} -23.8298 q^{41} +(-15.1640 + 16.9638i) q^{42} +56.2515i q^{43} +(9.01112 - 1.01276i) q^{44} +(-54.3670 - 48.5989i) q^{46} -51.4177i q^{47} +(6.15160 + 27.0214i) q^{48} +5.85689 q^{49} -46.4622i q^{51} +(6.64636 + 59.1364i) q^{52} +30.6465 q^{53} +(7.74797 + 6.92596i) q^{54} +(-30.4252 + 42.8423i) q^{56} +18.8240 q^{57} +(-46.9861 + 52.5627i) q^{58} -6.92483i q^{59} +107.426 q^{61} +(-35.5374 - 31.7671i) q^{62} +19.7050i q^{63} +(21.0873 + 60.4262i) q^{64} +(5.23363 - 5.85479i) q^{66} -111.444i q^{67} +(-11.9840 - 106.629i) q^{68} -63.1524 q^{69} -31.3190i q^{71} +(19.5676 + 13.8963i) q^{72} +110.909 q^{73} +(72.9757 - 81.6369i) q^{74} +(43.2002 - 4.85528i) q^{76} +14.8902 q^{77} +(38.4227 + 34.3463i) q^{78} +59.0065i q^{79} +9.00000 q^{81} +(-31.7628 + 35.5326i) q^{82} -142.416i q^{83} +(5.08253 + 45.2221i) q^{84} +(83.8765 + 74.9776i) q^{86} +61.0565i q^{87} +(10.5008 - 14.7864i) q^{88} +7.14798 q^{89} +97.7185i q^{91} +(-144.932 + 16.2889i) q^{92} -41.2800 q^{93} +(-76.6689 - 68.5347i) q^{94} +(48.4911 + 26.8443i) q^{96} -126.308 q^{97} +(7.80665 - 8.73319i) q^{98} -6.80089i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 8 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 8 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9	$ 8 q - 2 q^{2} - 8 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9} - 8 q^{13} + 22 q^{14} + 40 q^{16} + 6 q^{18} + 24 q^{21} - 4 q^{22} - 36 q^{24} - 66 q^{26} - 104 q^{28} - 32 q^{29} - 112 q^{32} + 124 q^{34} + 24 q^{36} + 176 q^{37} + 170 q^{38} - 16 q^{41} - 54 q^{42} + 40 q^{44} - 76 q^{46} - 24 q^{48} + 16 q^{49} - 56 q^{52} + 304 q^{53} + 18 q^{54} - 172 q^{56} - 72 q^{57} + 12 q^{58} + 136 q^{61} + 238 q^{62} + 16 q^{64} - 108 q^{66} - 88 q^{68} - 96 q^{69} + 60 q^{72} - 240 q^{73} - 108 q^{74} + 120 q^{76} + 384 q^{77} - 150 q^{78} + 72 q^{81} - 320 q^{82} - 144 q^{84} + 214 q^{86} + 200 q^{88} + 128 q^{89} - 312 q^{92} - 72 q^{93} + 12 q^{94} + 96 q^{96} - 216 q^{97} - 60 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 8 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9 - 8 * q^13 + 22 * q^14 + 40 * q^16 + 6 * q^18 + 24 * q^21 - 4 * q^22 - 36 * q^24 - 66 * q^26 - 104 * q^28 - 32 * q^29 - 112 * q^32 + 124 * q^34 + 24 * q^36 + 176 * q^37 + 170 * q^38 - 16 * q^41 - 54 * q^42 + 40 * q^44 - 76 * q^46 - 24 * q^48 + 16 * q^49 - 56 * q^52 + 304 * q^53 + 18 * q^54 - 172 * q^56 - 72 * q^57 + 12 * q^58 + 136 * q^61 + 238 * q^62 + 16 * q^64 - 108 * q^66 - 88 * q^68 - 96 * q^69 + 60 * q^72 - 240 * q^73 - 108 * q^74 + 120 * q^76 + 384 * q^77 - 150 * q^78 + 72 * q^81 - 320 * q^82 - 144 * q^84 + 214 * q^86 + 200 * q^88 + 128 * q^89 - 312 * q^92 - 72 * q^93 + 12 * q^94 + 96 * q^96 - 216 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.33290	−	1.49110i	0.666451	−	0.745549i
$2$	1.33290	−	1.49110i	0.666451	−	0.745549i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−0.446749	−	3.97497i	−0.111687	−	0.993743i
$5$		0			0
$5$		0			0
$6$	−2.58266	−	2.30865i	−0.430443	−	0.384775i
$7$		−	6.56834i		−	0.938335i	−0.883109	−	0.469167i	$-0.844554\pi$
$7$		−	6.56834i		−	0.938335i	0.883109	−	0.469167i	$-0.155446\pi$
$8$	−6.52255	−	4.63210i	−0.815319	−	0.579013i
$9$	−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	$0.967142\pi$
$12$	−6.88486	+	0.773791i	−0.573738	+	0.0644826i
$13$	−14.8772			−1.14440			−0.572200	−	0.820114i	$-0.693910\pi$
$13$	−14.8772			−1.14440			−0.572200	+	0.820114i	$0.693910\pi$
$14$	−9.79404	−	8.75495i	−0.699575	−	0.625354i
$15$		0			0
$16$	−15.6008	+	3.55163i	−0.975052	+	0.221977i
$17$	26.8250			1.57794			0.788969	−	0.614432i	$-0.210615\pi$
$17$	26.8250			1.57794			0.788969	+	0.614432i	$0.210615\pi$
$18$	−3.99870	+	4.47330i	−0.222150	+	0.248516i
$19$			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
$22$	3.38027	+	3.02164i	0.153648	+	0.137347i
$23$		−	36.4610i		−	1.58526i	−0.609702	−	0.792631i	$-0.708711\pi$
$23$		−	36.4610i		−	1.58526i	0.609702	−	0.792631i	$-0.291289\pi$
$24$	−8.02303	+	11.2974i	−0.334293	+	0.470724i
$25$		0			0
$26$	−19.8298	+	22.1834i	−0.762685	+	0.853206i
$27$			5.19615i			0.192450i
$28$	−26.1090	+	2.93440i	−0.932464	+	0.104800i
$29$	−35.2510			−1.21555			−0.607775	−	0.794109i	$-0.707938\pi$
$29$	−35.2510			−1.21555			−0.607775	+	0.794109i	$0.707938\pi$
$30$		0			0
$31$		−	23.8330i		−	0.768808i	−0.923165	−	0.384404i	$-0.874407\pi$
$31$		−	23.8330i		−	0.768808i	0.923165	−	0.384404i	$-0.125593\pi$
$32$	−15.4985	+	27.9963i	−0.484329	+	0.874886i
$33$	3.92650			0.118985
$34$	35.7550	−	39.9987i	1.05162	−	1.17643i
$35$		0			0
$36$	1.34025	+	11.9249i	0.0372290	+	0.331248i
$37$	54.7495			1.47972			0.739858	−	0.672763i	$-0.234893\pi$
$37$	54.7495			1.47972			0.739858	+	0.672763i	$0.234893\pi$
$38$	16.2053	+	14.4860i	0.426455	+	0.381211i
$39$			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	$0.593857\pi$
$42$	−15.1640	+	16.9638i	−0.361048	+	0.403900i
$43$			56.2515i			1.30817i	0.756420	+	0.654087i	$0.226947\pi$
$43$			56.2515i			1.30817i	−0.756420	+	0.654087i	$0.773053\pi$
$44$	9.01112	−	1.01276i	0.204798	−	0.0230173i
$45$		0			0
$46$	−54.3670	−	48.5989i	−1.18189	−	1.05650i
$47$		−	51.4177i		−	1.09399i	−0.837135	−	0.546997i	$-0.815771\pi$
$47$		−	51.4177i		−	1.09399i	0.837135	−	0.546997i	$-0.184229\pi$
$48$	6.15160	+	27.0214i	0.128158	+	0.562947i
$49$	5.85689			0.119528
$50$		0			0
$51$		−	46.4622i		−	0.911023i
$52$	6.64636	+	59.1364i	0.127815	+	1.13724i
$53$	30.6465			0.578236			0.289118	−	0.957293i	$-0.406638\pi$
$53$	30.6465			0.578236			0.289118	+	0.957293i	$0.406638\pi$
$54$	7.74797	+	6.92596i	0.143481	+	0.128258i
$55$		0			0
$56$	−30.4252	+	42.8423i	−0.543308	+	0.765042i
$57$	18.8240			0.330245
$58$	−46.9861	+	52.5627i	−0.810105	+	0.906253i
$59$		−	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	$0.157182\pi$
$62$	−35.5374	−	31.7671i	−0.573184	−	0.512372i
$63$			19.7050i			0.312778i
$64$	21.0873	+	60.4262i	0.329489	+	0.944160i
$65$		0			0
$66$	5.23363	−	5.85479i	0.0792975	−	0.0887090i
$67$		−	111.444i		−	1.66334i	−0.555271	−	0.831670i	$-0.687385\pi$
$67$		−	111.444i		−	1.66334i	0.555271	−	0.831670i	$-0.312615\pi$
$68$	−11.9840	−	106.629i	−0.176235	−	1.56807i
$69$	−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	$-0.0707873\pi$
$72$	19.5676	+	13.8963i	0.271773	+	0.193004i
$73$	110.909			1.51930			0.759652	−	0.650330i	$-0.225369\pi$
$73$	110.909			1.51930			0.759652	+	0.650330i	$0.225369\pi$
$74$	72.9757	−	81.6369i	0.986158	−	1.10320i
$75$		0			0
$76$	43.2002	−	4.85528i	0.568423	−	0.0638853i
$77$	14.8902			0.193379
$78$	38.4227	+	34.3463i	0.492599	+	0.440337i
$79$			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
$82$	−31.7628	+	35.5326i	−0.387351	+	0.433325i
$83$		−	142.416i		−	1.71586i	−0.513767	−	0.857930i	$-0.671751\pi$
$83$		−	142.416i		−	1.71586i	0.513767	−	0.857930i	$-0.328249\pi$
$84$	5.08253	+	45.2221i	0.0605063	+	0.538358i
$85$		0			0
$86$	83.8765	+	74.9776i	0.975308	+	0.871833i
$87$			61.0565i			0.701799i
$88$	10.5008	−	14.7864i	0.119327	−	0.168027i
$89$	7.14798			0.0803144			0.0401572	−	0.999193i	$-0.487214\pi$
$89$	7.14798			0.0803144			0.0401572	+	0.999193i	$0.487214\pi$
$90$		0			0
$91$			97.7185i			1.07383i
$92$	−144.932	+	16.2889i	−1.57534	+	0.177053i
$93$	−41.2800			−0.443871
$94$	−76.6689	−	68.5347i	−0.815626	−	0.729093i
$95$		0			0
$96$	48.4911	+	26.8443i	0.505116	+	0.279628i
$97$	−126.308			−1.30214			−0.651070	−	0.759017i	$-0.725680\pi$
$97$	−126.308			−1.30214			−0.651070	+	0.759017i	$0.725680\pi$
$98$	7.80665	−	8.73319i	0.0796597	−	0.0891142i
$99$		−	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	$0.358770\pi$
$102$	−69.2797	−	61.9295i	−0.679213	−	0.607152i
$103$			21.9281i			0.212895i	0.994318	+	0.106447i	$0.0339475\pi$
$103$			21.9281i			0.212895i	−0.994318	+	0.106447i	$0.966052\pi$
$104$	97.0372	+	68.9126i	0.933050	+	0.662622i
$105$		0			0
$106$	40.8488	−	45.6970i	0.385366	−	0.431104i
$107$		−	7.17725i		−	0.0670771i	−0.999437	−	0.0335385i	$-0.989322\pi$
$107$		−	7.17725i		−	0.0670771i	0.999437	−	0.0335385i	$-0.0106777\pi$
$108$	20.6546	−	2.32137i	0.191246	−	0.0214942i
$109$	25.4256			0.233262			0.116631	−	0.993175i	$-0.462790\pi$
$109$	25.4256			0.233262			0.116631	+	0.993175i	$0.462790\pi$
$110$		0			0
$111$		−	94.8289i		−	0.854315i
$112$	23.3283	+	102.472i	0.208288	+	0.914925i
$113$	−78.3588			−0.693441			−0.346720	−	0.937968i	$-0.612705\pi$
$113$	−78.3588			−0.693441			−0.346720	+	0.937968i	$0.612705\pi$
$114$	25.0905	−	28.0684i	0.220092	−	0.246214i
$115$		0			0
$116$	15.7483	+	140.122i	0.135761	+	1.20795i
$117$	44.6316			0.381466
$118$	−10.3256	−	9.23012i	−0.0875052	−	0.0782214i
$119$		−	176.196i		−	1.48063i
$120$		0			0
$121$	115.861			0.957528
$122$	143.188	−	160.182i	1.17367	−	1.31297i
$123$			41.2745i			0.335565i
$124$	−94.7357	+	10.6474i	−0.763997	+	0.0858659i
$125$		0			0
$126$	29.3821	+	26.2649i	0.233192	+	0.208451i
$127$			71.6077i			0.563840i	0.959438	+	0.281920i	$0.0909713\pi$
$127$			71.6077i			0.563840i	−0.959438	+	0.281920i	$0.909029\pi$
$128$	118.209	+	49.0990i	0.923505	+	0.383586i
$129$	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	$0.870098\pi$
$132$	−1.75416	−	15.6077i	−0.0132891	−	0.118240i
$133$	71.3850			0.536729
$134$	−166.174	−	148.543i	−1.24010	−	1.10853i
$135$		0			0
$136$	−174.967	−	124.256i	−1.28652	−	0.913647i
$137$	7.16645			0.0523099			0.0261549	−	0.999658i	$-0.491674\pi$
$137$	7.16645			0.0523099			0.0261549	+	0.999658i	$0.491674\pi$
$138$	−84.1758	+	94.1664i	−0.609970	+	0.682365i
$139$			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
$142$	−46.6997	−	41.7451i	−0.328871	−	0.293980i
$143$		−	33.7261i		−	0.235847i
$144$	46.8025	−	10.6549i	0.325017	−	0.0739922i
$145$		0			0
$146$	147.831	−	165.376i	1.01254	−	1.13272i
$147$		−	10.1444i		−	0.0690097i
$148$	−24.4593	−	217.628i	−0.165265	−	1.47046i
$149$	79.6054			0.534265			0.267132	−	0.963660i	$-0.413924\pi$
$149$	79.6054			0.534265			0.267132	+	0.963660i	$0.413924\pi$
$150$		0			0
$151$			182.722i			1.21008i	0.796196	+	0.605039i	$0.206842\pi$
$151$			182.722i			1.21008i	−0.796196	+	0.605039i	$0.793158\pi$
$152$	50.3418	−	70.8873i	0.331196	−	0.466364i
$153$	−80.4749			−0.525980
$154$	19.8472	−	22.2027i	0.128878	−	0.144174i
$155$		0			0
$156$	102.427	−	11.5118i	0.656585	−	0.0737938i
$157$	−212.182			−1.35148			−0.675739	−	0.737141i	$-0.736175\pi$
$157$	−212.182			−1.35148			−0.675739	+	0.737141i	$0.736175\pi$
$158$	87.9844	+	78.6498i	0.556864	+	0.497783i
$159$		−	53.0813i		−	0.333845i
$160$		0			0
$161$	−239.488			−1.48751
$162$	11.9961	−	13.4199i	0.0740501	−	0.0828388i
$163$			243.400i			1.49325i	0.665244	+	0.746626i	$0.268327\pi$
$163$			243.400i			1.49325i	−0.665244	+	0.746626i	$0.731673\pi$
$164$	10.6459	+	94.7229i	0.0649143	+	0.577579i
$165$		0			0
$166$	−212.357	−	189.827i	−1.27926	−	1.14354i
$167$			211.395i			1.26584i	0.774218	+	0.632919i	$0.218143\pi$
$167$			211.395i			1.26584i	−0.774218	+	0.632919i	$0.781857\pi$
$168$	74.2051	+	52.6980i	0.441697	+	0.313679i
$169$	52.3307			0.309649
$170$		0			0
$171$		−	32.6041i		−	0.190667i
$172$	223.598	−	25.1303i	1.29999	−	0.146106i
$173$	22.3138			0.128982			0.0644909	−	0.997918i	$-0.479458\pi$
$173$	22.3138			0.128982			0.0644909	+	0.997918i	$0.479458\pi$
$174$	91.0412	+	81.3823i	0.523225	+	0.467714i
$175$		0			0
$176$	−8.05141	−	35.3665i	−0.0457467	−	0.200946i
$177$	−11.9942			−0.0677636
$178$	9.52755	−	10.6583i	0.0535255	−	0.0598783i
$179$			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	$0.571488\pi$
$182$	145.708	+	130.249i	0.800592	+	0.715654i
$183$		−	186.067i		−	1.01676i
$184$	−168.891	+	237.819i	−0.917887	+	1.29249i
$185$		0			0
$186$	−55.0222	+	61.5526i	−0.295818	+	0.330928i
$187$			60.8112i			0.325194i
$188$	−204.384	+	22.9708i	−1.08715	+	0.122185i
$189$	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	$-0.332865\pi$
$192$	104.661	−	36.5242i	0.545111	−	0.190230i
$193$	−103.609			−0.536836			−0.268418	−	0.963303i	$-0.586501\pi$
$193$	−103.609			−0.536836			−0.268418	+	0.963303i	$0.586501\pi$
$194$	−168.356	+	188.337i	−0.867812	+	0.970810i
$195$		0			0
$196$	−2.61656	−	23.2810i	−0.0133498	−	0.118780i
$197$	160.633			0.815394			0.407697	−	0.913117i	$-0.366332\pi$
$197$	160.633			0.815394			0.407697	+	0.913117i	$0.366332\pi$
$198$	−10.1408	−	9.06492i	−0.0512162	−	0.0457824i
$199$		−	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
$202$	115.580	−	129.298i	0.572179	−	0.640089i
$203$			231.540i			1.14059i
$204$	−184.686	+	20.7569i	−0.905324	+	0.101750i
$205$		0			0
$206$	32.6970	+	29.2280i	0.158723	+	0.141884i
$207$			109.383i			0.528421i
$208$	232.097	−	52.8382i	1.11585	−	0.254030i
$209$	−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	$0.779201\pi$
$212$	−13.6913	−	121.819i	−0.0645816	−	0.574618i
$213$	−54.2461			−0.254677
$214$	−10.7020	−	9.56656i	−0.0500093	−	0.0447036i
$215$		0			0
$216$	24.0691	−	33.8922i	0.111431	−	0.156908i
$217$	−156.544			−0.721399
$218$	33.8898	−	37.9120i	0.155458	−	0.173908i
$219$		−	192.100i		−	0.877170i
$220$		0			0
$221$	−399.080			−1.80579
$222$	−141.399	−	126.398i	−0.636934	−	0.569359i
$223$		−	41.3345i		−	0.185356i	−0.995696	−	0.0926782i	$-0.970457\pi$
$223$		−	41.3345i		−	0.185356i	0.995696	−	0.0926782i	$-0.0295428\pi$
$224$	183.890	+	101.800i	0.820935	+	0.454463i
$225$		0			0
$226$	−104.445	+	116.841i	−0.462144	+	0.516994i
$227$			149.837i			0.660076i	0.943968	+	0.330038i	$0.107061\pi$
$227$			149.837i			0.660076i	−0.943968	+	0.330038i	$0.892939\pi$
$228$	−8.40959	−	74.8249i	−0.0368842	−	0.328179i
$229$	−61.6770			−0.269332			−0.134666	−	0.990891i	$-0.542996\pi$
$229$	−61.6770			−0.269332			−0.134666	+	0.990891i	$0.542996\pi$
$230$		0			0
$231$		−	25.7906i		−	0.111648i
$232$	229.926	+	163.286i	0.991061	+	0.703819i
$233$	−405.585			−1.74071			−0.870355	−	0.492425i	$-0.836110\pi$
$233$	−405.585			−1.74071			−0.870355	+	0.492425i	$0.836110\pi$
$234$	59.4895	−	66.5501i	0.254228	−	0.284402i
$235$		0			0
$236$	−27.5260	+	3.09366i	−0.116636	+	0.0131087i
$237$	102.202			0.431233
$238$	−262.725	−	234.851i	−1.10389	−	0.986770i
$239$		−	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	$0.559476\pi$
$242$	154.431	−	172.760i	0.638145	−	0.713884i
$243$		−	15.5885i		−	0.0641500i
$244$	−47.9922	−	427.014i	−0.196689	−	1.75006i
$245$		0			0
$246$	61.5443	+	55.0148i	0.250180	+	0.223637i
$247$		−	161.686i		−	0.654598i
$248$	−110.397	+	155.452i	−0.445149	+	0.626823i
$249$	−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	$0.850042\pi$
$252$	78.3270	−	8.80319i	0.310821	−	0.0349333i
$253$	82.6559			0.326703
$254$	106.774	+	95.4460i	0.420371	+	0.375772i
$255$		0			0
$256$	230.772	−	110.817i	0.901453	−	0.432878i
$257$	−442.129			−1.72035			−0.860173	−	0.510003i	$-0.829644\pi$
$257$	−442.129			−1.72035			−0.860173	+	0.510003i	$0.829644\pi$
$258$	129.865	−	145.278i	0.503353	−	0.563094i
$259$		−	359.614i		−	1.38847i
$260$		0			0
$261$	105.753			0.405184
$262$	155.042	+	138.593i	0.591763	+	0.528981i
$263$			34.1556i			0.129869i	0.997890	+	0.0649346i	$0.0206839\pi$
$263$			34.1556i			0.129869i	−0.997890	+	0.0649346i	$0.979316\pi$
$264$	−25.6108	−	18.1879i	−0.0970105	−	0.0688937i
$265$		0			0
$266$	95.1491	−	106.442i	0.357703	−	0.400158i
$267$		−	12.3807i		−	0.0463695i
$268$	−442.986	+	49.7873i	−1.65293	+	0.185774i
$269$	−9.96085			−0.0370292			−0.0185146	−	0.999829i	$-0.505894\pi$
$269$	−9.96085			−0.0370292			−0.0185146	+	0.999829i	$0.505894\pi$
$270$		0			0
$271$		−	56.5791i		−	0.208779i	−0.994536	−	0.104390i	$-0.966711\pi$
$271$		−	56.5791i		−	0.208779i	0.994536	−	0.104390i	$-0.0332889\pi$
$272$	−418.492	+	95.2723i	−1.53857	+	0.350266i
$273$	169.253			0.619976
$274$	9.55218	−	10.6859i	0.0348620	−	0.0389996i
$275$		0			0
$276$	28.2132	+	251.029i	0.102222	+	0.909525i
$277$	103.794			0.374708			0.187354	−	0.982292i	$-0.440009\pi$
$277$	103.794			0.374708			0.187354	+	0.982292i	$0.440009\pi$
$278$	219.056	+	195.815i	0.787969	+	0.704370i
$279$			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	$0.253446\pi$
$282$	−118.706	+	132.794i	−0.420942	+	0.470902i
$283$		−	114.027i		−	0.402923i	−0.979496	−	0.201462i	$-0.935431\pi$
$283$		−	114.027i		−	0.402923i	0.979496	−	0.201462i	$-0.0645692\pi$
$284$	−124.492	+	13.9917i	−0.438353	+	0.0492666i
$285$		0			0
$286$	−50.2889	−	44.9535i	−0.175835	−	0.157180i
$287$			156.522i			0.545374i
$288$	46.4956	−	83.9890i	0.161443	−	0.291629i
$289$	430.579			1.48989
$290$		0			0
$291$			218.771i			0.751791i
$292$	−49.5485	−	440.861i	−0.169687	−	1.50980i
$293$	126.796			0.432750			0.216375	−	0.976310i	$-0.430577\pi$
$293$	126.796			0.432750			0.216375	+	0.976310i	$0.430577\pi$
$294$	−15.1263	−	13.5215i	−0.0514501	−	0.0459915i
$295$		0			0
$296$	−357.106	−	253.605i	−1.20644	−	0.856775i
$297$	−11.7795			−0.0396616
$298$	106.106	−	118.700i	0.356061	−	0.398321i
$299$			542.438i			1.81417i
$300$		0			0
$301$	369.479			1.22750
$302$	272.456	+	243.550i	0.902172	+	0.806457i
$303$		−	150.192i		−	0.495683i
$304$	−38.5992	−	169.550i	−0.126971	−	0.557732i
$305$		0			0
$306$	−107.265	+	119.996i	−0.350539	+	0.392144i
$307$		−	408.420i		−	1.33036i	−0.746683	−	0.665180i	$-0.768355\pi$
$307$		−	408.420i		−	1.33036i	0.746683	−	0.665180i	$-0.231645\pi$
$308$	−6.65217	−	59.1881i	−0.0215980	−	0.192169i
$309$	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	$-0.274624\pi$
$312$	119.360	−	168.073i	0.382565	−	0.538697i
$313$	54.6519			0.174607			0.0873033	−	0.996182i	$-0.472175\pi$
$313$	54.6519			0.174607			0.0873033	+	0.996182i	$0.472175\pi$
$314$	−282.818	+	316.384i	−0.900693	+	1.00759i
$315$		0			0
$316$	234.549	−	26.3611i	0.742244	−	0.0834211i
$317$	−63.3734			−0.199916			−0.0999581	−	0.994992i	$-0.531871\pi$
$317$	−63.3734			−0.199916			−0.0999581	+	0.994992i	$0.531871\pi$
$318$	−79.1495	−	70.7522i	−0.248898	−	0.222491i
$319$		−	79.9127i		−	0.250510i
$320$		0			0
$321$	−12.4314			−0.0387270
$322$	−319.215	+	357.101i	−0.991349	+	1.10901i
$323$			291.535i			0.902584i
$324$	−4.02074	−	35.7748i	−0.0124097	−	0.110416i
$325$		0			0
$326$	362.933	+	324.428i	1.11329	+	0.995179i
$327$		−	44.0384i		−	0.134674i
$328$	155.431	+	110.382i	0.473876	+	0.336531i
$329$	−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	$0.773949\pi$
$332$	−566.101	+	63.6243i	−1.70512	+	0.191639i
$333$	−164.249			−0.493239
$334$	315.211	+	281.768i	0.943744	+	0.843618i
$335$		0			0
$336$	177.486	−	40.4058i	0.528232	−	0.120255i
$337$	486.091			1.44241			0.721203	−	0.692723i	$-0.243589\pi$
$337$	486.091			1.44241			0.721203	+	0.692723i	$0.243589\pi$
$338$	69.7517	−	78.0303i	0.206366	−	0.230859i
$339$			135.721i			0.400358i
$340$		0			0
$341$	54.0286			0.158442
$342$	−48.6159	−	43.4581i	−0.142152	−	0.127070i
$343$		−	360.319i		−	1.05049i
$344$	260.562	−	366.903i	0.757449	−	1.06658i
$345$		0			0
$346$	29.7422	−	33.2721i	0.0859600	−	0.0961623i
$347$		−	294.297i		−	0.848119i	−0.905634	−	0.424060i	$-0.860605\pi$
$347$		−	294.297i		−	0.848119i	0.905634	−	0.424060i	$-0.139395\pi$
$348$	242.698	−	27.2769i	0.697408	−	0.0783819i
$349$	83.0428			0.237945			0.118972	−	0.992898i	$-0.462040\pi$
$349$	83.0428			0.237945			0.118972	+	0.992898i	$0.462040\pi$
$350$		0			0
$351$		−	77.3041i		−	0.220240i
$352$	−63.4667	−	35.1346i	−0.180303	−	0.0998143i
$353$	570.733			1.61681			0.808404	−	0.588628i	$-0.200332\pi$
$353$	570.733			1.61681			0.808404	+	0.588628i	$0.200332\pi$
$354$	−15.9870	+	17.8845i	−0.0451611	+	0.0505211i
$355$		0			0
$356$	−3.19335	−	28.4130i	−0.00897008	−	0.0798119i
$357$	−305.180			−0.854845
$358$	140.941	+	125.988i	0.393691	+	0.351923i
$359$			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
$362$	−107.456	+	120.209i	−0.296839	+	0.332070i
$363$		−	200.677i		−	0.552829i
$364$	388.428	−	43.6556i	1.06711	−	0.119933i
$365$		0			0
$366$	−277.444	−	248.008i	−0.758042	−	0.677618i
$367$			446.467i			1.21653i	0.793734	+	0.608265i	$0.208134\pi$
$367$			446.467i			1.21653i	−0.793734	+	0.608265i	$0.791866\pi$
$368$	129.496	+	568.822i	0.351891	+	1.54571i
$369$	71.4895			0.193738
$370$		0			0
$371$		−	201.297i		−	0.542579i
$372$	18.4418	+	164.087i	0.0495747	+	0.441094i
$373$	112.924			0.302744			0.151372	−	0.988477i	$-0.451631\pi$
$373$	112.924			0.302744			0.151372	+	0.988477i	$0.451631\pi$
$374$	90.6755	+	81.0554i	0.242448	+	0.216726i
$375$		0			0
$376$	−238.172	+	335.375i	−0.633436	+	0.891954i
$377$	524.435			1.39108
$378$	45.4921	−	50.8913i	0.120349	−	0.134633i
$379$			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
$382$	−492.868	−	440.577i	−1.29023	−	1.15334i
$383$			89.2269i			0.232968i	0.993193	+	0.116484i	$0.0371624\pi$
$383$			89.2269i			0.232968i	−0.993193	+	0.116484i	$0.962838\pi$
$384$	85.0419	−	204.743i	0.221463	−	0.533186i
$385$		0			0
$386$	−138.101	+	154.492i	−0.357775	+	0.400238i
$387$		−	168.754i		−	0.436058i
$388$	56.4278	+	502.069i	0.145432	+	1.29399i
$389$	260.714			0.670217			0.335108	−	0.942180i	$-0.391227\pi$
$389$	260.714			0.670217			0.335108	+	0.942180i	$0.391227\pi$
$390$		0			0
$391$		−	978.066i		−	2.50145i
$392$	−38.2018	−	27.1297i	−0.0974536	−	0.0692084i
$393$	180.096			0.458259
$394$	214.107	−	239.519i	0.543420	−	0.607916i
$395$		0			0
$396$	−27.0334	+	3.03829i	−0.0682661	+	0.00767245i
$397$	−112.607			−0.283644			−0.141822	−	0.989892i	$-0.545296\pi$
$397$	−112.607			−0.283644			−0.141822	+	0.989892i	$0.545296\pi$
$398$	−41.0824	−	36.7238i	−0.103222	−	0.0922708i
$399$		−	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	$0.244100\pi$
$402$	−257.285	+	287.821i	−0.640012	+	0.715973i
$403$			354.569i			0.879823i
$404$	−38.7390	−	344.683i	−0.0958887	−	0.853176i
$405$		0			0
$406$	345.250	+	308.621i	0.850368	+	0.760149i
$407$			124.115i			0.304951i
$408$	−215.218	+	303.052i	−0.527494	+	0.742774i
$409$	−276.255			−0.675441			−0.337721	−	0.941246i	$-0.609656\pi$
$409$	−276.255			−0.675441			−0.337721	+	0.941246i	$0.609656\pi$
$410$		0			0
$411$		−	12.4127i		−	0.0302011i
$412$	87.1638	−	9.79636i	0.211563	−	0.0237776i
$413$	−45.4847			−0.110132
$414$	163.101	+	145.797i	0.393964	+	0.352166i
$415$		0			0
$416$	230.575	−	416.507i	0.554266	−	1.00122i
$417$	254.454			0.610200
$418$	−32.8393	+	36.7369i	−0.0785629	+	0.0878872i
$419$		−	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	$0.529427\pi$
$422$	402.310	+	359.627i	0.953342	+	0.852197i
$423$			154.253i			0.364665i
$424$	−199.893	−	141.958i	−0.471447	−	0.334806i
$425$		0			0
$426$	−72.3047	+	80.8863i	−0.169729	+	0.189874i
$427$		−	705.608i		−	1.65248i
$428$	−28.5294	+	3.20643i	−0.0666574	+	0.00749165i
$429$	−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	$0.880055\pi$
$432$	−18.4548	−	81.0643i	−0.0427194	−	0.187649i
$433$	82.9688			0.191614			0.0958069	−	0.995400i	$-0.469457\pi$
$433$	82.9688			0.191614			0.0958069	+	0.995400i	$0.469457\pi$
$434$	−208.657	+	233.422i	−0.480777	+	0.537838i
$435$		0			0
$436$	−11.3588	−	101.066i	−0.0260524	−	0.231803i
$437$	396.260			0.906773
$438$	−286.440	−	256.051i	−0.653974	−	0.584591i
$439$		−	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
$442$	−531.934	+	595.068i	−1.20347	+	1.34631i
$443$			35.1780i			0.0794086i	0.999211	+	0.0397043i	$0.0126416\pi$
$443$			35.1780i			0.0794086i	−0.999211	+	0.0397043i	$0.987358\pi$
$444$	−376.943	+	42.3647i	−0.848970	+	0.0954160i
$445$		0			0
$446$	−61.6337	−	55.0948i	−0.138192	−	0.123531i
$447$		−	137.881i		−	0.308458i
$448$	396.900	−	138.508i	0.885938	−	0.309171i
$449$	−67.4253			−0.150168			−0.0750838	−	0.997177i	$-0.523922\pi$
$449$	−67.4253			−0.150168			−0.0750838	+	0.997177i	$0.523922\pi$
$450$		0			0
$451$		−	54.0214i		−	0.119781i
$452$	35.0067	+	311.474i	0.0774484	+	0.689102i
$453$	316.483			0.698638
$454$	223.422	+	199.718i	0.492119	+	0.439908i
$455$		0			0
$456$	−122.780	−	87.1946i	−0.269255	−	0.191216i
$457$	204.153			0.446724			0.223362	−	0.974736i	$-0.428297\pi$
$457$	204.153			0.446724			0.223362	+	0.974736i	$0.428297\pi$
$458$	−82.2094	+	91.9665i	−0.179496	+	0.200800i
$459$			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	$0.456446\pi$
$462$	−38.4563	−	34.3763i	−0.0832387	−	0.0744076i
$463$		−	553.629i		−	1.19574i	−0.801592	−	0.597871i	$-0.796013\pi$
$463$		−	553.629i		−	1.19574i	0.801592	−	0.597871i	$-0.203987\pi$
$464$	549.944	−	125.198i	1.18523	−	0.269824i
$465$		0			0
$466$	−540.605	+	604.768i	−1.16010	+	1.29778i
$467$		−	625.772i		−	1.33998i	−0.742369	−	0.669991i	$-0.766298\pi$
$467$		−	625.772i		−	1.33998i	0.742369	−	0.669991i	$-0.233702\pi$
$468$	−19.9391	−	177.409i	−0.0426049	−	0.379080i
$469$	−732.000			−1.56077
$470$		0			0
$471$			367.510i			0.780276i
$472$	−32.0765	+	45.1676i	−0.0679588	+	0.0956940i
$473$	−127.520			−0.269598
$474$	136.225	−	152.394i	0.287395	−	0.321505i
$475$		0			0
$476$	−700.373	+	78.7151i	−1.47137	+	0.165368i
$477$	−91.9396			−0.192745
$478$	−399.269	−	356.909i	−0.835291	−	0.746672i
$479$		−	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
$482$	−119.345	+	133.509i	−0.247604	+	0.276991i
$483$			414.806i			0.858812i
$484$	−51.7607	−	460.544i	−0.106944	−	0.951537i
$485$		0			0
$486$	−23.2439	−	20.7779i	−0.0478270	−	0.0427528i
$487$			609.476i			1.25149i	0.780027	+	0.625746i	$0.215205\pi$
$487$			609.476i			1.25149i	−0.780027	+	0.625746i	$0.784795\pi$
$488$	−700.689	−	497.606i	−1.43584	−	1.01968i
$489$	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	$0.752422\pi$
$492$	164.065	−	18.4393i	0.333465	−	0.0374783i
$493$	−945.606			−1.91806
$494$	−241.089	−	215.511i	−0.488035	−	0.436257i
$495$		0			0
$496$	84.6461	+	371.815i	0.170657	+	0.749627i
$497$	−205.714			−0.413911
$498$	−328.790	+	367.813i	−0.660220	+	0.738580i
$499$			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
$502$	339.738	+	303.694i	0.676769	+	0.604967i
$503$		−	943.945i		−	1.87663i	−0.345782	−	0.938315i	$-0.612386\pi$
$503$		−	943.945i		−	1.87663i	0.345782	−	0.938315i	$-0.387614\pi$
$504$	91.2757	−	128.527i	0.181103	−	0.255014i
$505$		0			0
$506$	110.172	−	123.248i	0.217731	−	0.243573i
$507$		−	90.6395i		−	0.178776i
$508$	284.639	−	31.9906i	0.560313	−	0.0629737i
$509$	−357.147			−0.701665			−0.350832	−	0.936438i	$-0.614101\pi$
$509$	−357.147			−0.701665			−0.350832	+	0.936438i	$0.614101\pi$
$510$		0			0
$511$		−	728.489i		−	1.42562i
$512$	142.358	−	491.811i	0.278042	−	0.960569i
$513$	−56.4720			−0.110082
$514$	−589.314	+	659.258i	−1.14653	+	1.28260i
$515$		0			0
$516$	−43.5269	−	387.283i	−0.0843544	−	0.750549i
$517$	116.562			0.225459
$518$	−536.219	−	479.329i	−1.03517	−	0.925346i
$519$		−	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	$0.527172\pi$
$522$	140.958	−	157.688i	0.270035	−	0.302084i
$523$		−	220.427i		−	0.421467i	−0.977544	−	0.210734i	$-0.932415\pi$
$523$		−	220.427i		−	0.421467i	0.977544	−	0.210734i	$-0.0675852\pi$
$524$	413.311	−	46.4522i	0.788762	−	0.0886492i
$525$		0			0
$526$	50.9294	+	45.5261i	0.0968239	+	0.0865514i
$527$		−	639.320i		−	1.21313i
$528$	−61.2566	+	13.9455i	−0.116016	+	0.0264119i
$529$	−800.407			−1.51306
$530$		0			0
$531$			20.7745i			0.0391234i
$532$	−31.8911	−	283.753i	−0.0599457	−	0.533371i
$533$	354.521			0.665142
$534$	−18.4608	−	16.5022i	−0.0345708	−	0.0309030i
$535$		0			0
$536$	−516.219	+	726.897i	−0.963094	+	1.35615i
$537$	163.717			0.304873
$538$	−13.2768	+	14.8526i	−0.0246781	+	0.0276071i
$539$			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	$0.624203\pi$
$542$	−84.3651	−	75.4144i	−0.155655	−	0.139141i
$543$			139.634i			0.257154i
$544$	−415.748	+	751.001i	−0.764242	+	1.38052i
$545$		0			0
$546$	225.598	−	252.373i	0.413183	−	0.462222i
$547$			851.537i			1.55674i	0.627806	+	0.778370i	$0.283953\pi$
$547$			851.537i			1.55674i	−0.627806	+	0.778370i	$0.716047\pi$
$548$	−3.20160	−	28.4865i	−0.00584234	−	0.0519826i
$549$	−322.277			−0.587025
$550$		0			0
$551$		−	383.109i		−	0.695297i
$552$	411.914	+	292.528i	0.746222	+	0.529942i
$553$	387.575			0.700858
$554$	138.347	−	154.767i	0.249724	−	0.279363i
$555$		0			0
$556$	583.959	−	65.6313i	1.05029	−	0.118042i
$557$	−211.553			−0.379808			−0.189904	−	0.981803i	$-0.560818\pi$
$557$	−211.553			−0.379808			−0.189904	+	0.981803i	$0.560818\pi$
$558$	106.612	+	95.3012i	0.191061	+	0.170791i
$559$		−	836.864i		−	1.49707i
$560$		0			0
$561$	105.328			0.187751
$562$	523.922	−	586.104i	0.932246	−	1.04289i
$563$			404.044i			0.717663i	0.933402	+	0.358832i	$0.116825\pi$
$563$			404.044i			0.717663i	−0.933402	+	0.358832i	$0.883175\pi$
$564$	39.7866	+	354.004i	0.0705436	+	0.627666i
$565$		0			0
$566$	−170.026	−	151.987i	−0.300399	−	0.268529i
$567$		−	59.1151i		−	0.104259i
$568$	−145.073	+	204.280i	−0.255410	+	0.359647i
$569$	230.465			0.405036			0.202518	−	0.979279i	$-0.435088\pi$
$569$	230.465			0.405036			0.202518	+	0.979279i	$0.435088\pi$
$570$		0			0
$571$		−	351.234i		−	0.615121i	−0.951529	−	0.307560i	$-0.900487\pi$
$571$		−	351.234i		−	0.615121i	0.951529	−	0.307560i	$-0.0995126\pi$
$572$	−134.060	+	15.0671i	−0.234371	+	0.0263410i
$573$	−572.512			−0.999149
$574$	233.390	+	208.629i	0.406603	+	0.363465i
$575$		0			0
$576$	−63.2618	−	181.279i	−0.109830	−	0.314720i
$577$	638.575			1.10672			0.553358	−	0.832944i	$-0.313346\pi$
$577$	638.575			1.10672			0.553358	+	0.832944i	$0.313346\pi$
$578$	573.919	−	642.035i	0.992939	−	1.11079i
$579$			179.457i			0.309942i
$580$		0			0
$581$	−935.439			−1.61005
$582$	326.209	+	291.600i	0.560497	+	0.501032i
$583$			69.4746i			0.119167i
$584$	−723.410	−	513.742i	−1.23872	−	0.879696i
$585$		0			0
$586$	169.006	−	189.065i	0.288407	−	0.322637i
$587$		−	105.047i		−	0.178956i	−0.995989	−	0.0894779i	$-0.971480\pi$
$587$		−	105.047i		−	0.178956i	0.995989	−	0.0894779i	$-0.0285198\pi$
$588$	−40.3238	+	4.53201i	−0.0685779	+	0.00770749i
$589$	259.018			0.439759
$590$		0			0
$591$		−	278.224i		−	0.470768i
$592$	−854.138	+	194.450i	−1.44280	+	0.328463i
$593$	−990.175			−1.66977			−0.834886	−	0.550422i	$-0.814467\pi$
$593$	−990.175			−1.66977			−0.834886	+	0.550422i	$0.814467\pi$
$594$	−15.7009	+	17.5644i	−0.0264325	+	0.0295697i
$595$		0			0
$596$	−35.5636	−	316.429i	−0.0596705	−	0.530922i
$597$	−47.7210			−0.0799347
$598$	808.828	+	723.016i	1.35255	+	1.20906i
$599$		−	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	$0.671426\pi$
$602$	492.479	−	550.929i	0.818071	−	0.915165i
$603$			334.331i			0.554446i
$604$	726.314	−	81.6306i	1.20251	−	0.135150i
$605$		0			0
$606$	−223.951	−	200.191i	−0.369556	−	0.330348i
$607$		−	226.520i		−	0.373179i	−0.982438	−	0.186590i	$-0.940257\pi$
$607$		−	226.520i		−	0.373179i	0.982438	−	0.186590i	$-0.0597435\pi$
$608$	−304.265	−	168.439i	−0.500436	−	0.277037i
$609$	401.040			0.658522
$610$		0			0
$611$			764.951i			1.25197i
$612$	35.9520	+	319.886i	0.0587452	+	0.522689i
$613$	−732.519			−1.19497			−0.597487	−	0.801879i	$-0.703834\pi$
$613$	−732.519			−1.19497			−0.597487	+	0.801879i	$0.703834\pi$
$614$	−608.995	−	544.384i	−0.991848	−	0.886619i
$615$		0			0
$616$	−97.1220	−	68.9729i	−0.157666	−	0.111969i
$617$	−350.585			−0.568209			−0.284105	−	0.958793i	$-0.591696\pi$
$617$	−350.585			−0.568209			−0.284105	+	0.958793i	$0.591696\pi$
$618$	50.6245	−	56.6329i	0.0819166	−	0.0916390i
$619$		−	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
$622$	−704.537	−	629.790i	−1.13270	−	1.01252i
$623$		−	46.9504i		−	0.0753617i
$624$	−91.5185	−	402.003i	−0.146664	−	0.644235i
$625$		0			0
$626$	72.8455	−	81.4913i	0.116367	−	0.130178i
$627$			42.6733i			0.0680595i
$628$	94.7920	+	843.417i	0.150943	+	1.34302i
$629$	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	$0.949105\pi$
$632$	273.324	−	384.873i	0.432475	−	0.608976i
$633$	467.321			0.738264
$634$	−84.4705	+	94.4960i	−0.133234	+	0.149047i
$635$		0			0
$636$	−210.997	+	23.7140i	−0.331756	+	0.0372862i
$637$	−87.1340			−0.136788
$638$	−119.158	−	106.516i	−0.186768	−	0.166953i
$639$			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	$0.445895\pi$
$642$	−16.5698	+	18.5364i	−0.0258096	+	0.0288729i
$643$		−	37.5349i		−	0.0583746i	−0.999574	−	0.0291873i	$-0.990708\pi$
$643$		−	37.5349i		−	0.0583746i	0.999574	−	0.0291873i	$-0.00929193\pi$
$644$	106.991	+	951.960i	0.166135	+	1.47820i
$645$		0			0
$646$	434.707	+	388.587i	0.672921	+	0.601528i
$647$			1192.56i			1.84321i	0.388125	+	0.921607i	$0.373123\pi$
$647$			1192.56i			1.84321i	−0.388125	+	0.921607i	$0.626877\pi$
$648$	−58.7029	−	41.6889i	−0.0905910	−	0.0643347i
$649$	15.6984			0.0241885
$650$		0			0
$651$			271.141i			0.416500i
$652$	967.509	−	108.739i	1.48391	−	0.166777i
$653$	1087.78			1.66582			0.832908	−	0.553412i	$-0.186675\pi$
$653$	1087.78			1.66582			0.832908	+	0.553412i	$0.186675\pi$
$654$	−65.6656	−	58.6988i	−0.100406	−	0.0897535i
$655$		0			0
$656$	371.765	−	84.6347i	0.566715	−	0.129016i
$657$	−332.727			−0.506435
$658$	−450.160	+	503.587i	−0.684133	+	0.765330i
$659$		−	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	$0.624746\pi$
$662$	643.550	+	575.273i	0.972130	+	0.868992i
$663$			691.227i			1.04257i
$664$	−659.687	+	928.917i	−0.993504	+	1.39897i
$665$		0			0
$666$	−218.927	+	244.911i	−0.328719	+	0.367734i
$667$			1285.29i			1.92697i
$668$	840.289	−	94.4403i	1.25792	−	0.141378i
$669$	−71.5934			−0.107016
$670$		0			0
$671$			243.530i			0.362936i
$672$	176.322	−	318.506i	0.262384	−	0.473967i
$673$	902.689			1.34129			0.670646	−	0.741778i	$-0.266017\pi$
$673$	902.689			1.34129			0.670646	+	0.741778i	$0.266017\pi$
$674$	647.911	−	724.810i	0.961293	−	1.07539i
$675$		0			0
$676$	−23.3787	−	208.013i	−0.0345838	−	0.307712i
$677$	−930.750			−1.37482			−0.687408	−	0.726272i	$-0.741252\pi$
$677$	−930.750			−1.37482			−0.687408	+	0.726272i	$0.741252\pi$
$678$	202.374	+	180.903i	0.298487	+	0.266819i
$679$			829.632i			1.22184i
$680$		0			0
$681$	259.526			0.381095
$682$	72.0148	−	80.5620i	0.105594	−	0.118126i
$683$		−	64.9023i		−	0.0950253i	−0.998871	−	0.0475127i	$-0.984871\pi$
$683$		−	64.9023i		−	0.0950253i	0.998871	−	0.0475127i	$-0.0151294\pi$
$684$	−129.600	+	14.5658i	−0.189474	+	0.0212951i
$685$		0			0
$686$	−537.271	−	480.269i	−0.783193	−	0.700101i
$687$			106.828i			0.155499i
$688$	−199.784	−	877.570i	−0.290384	−	1.27554i
$689$	−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	$0.918896\pi$
$692$	−9.96868	−	88.6970i	−0.0144056	−	0.128175i
$693$	−44.6706			−0.0644597
$694$	−438.826	−	392.269i	−0.632315	−	0.565230i
$695$		0			0
$696$	282.820	−	398.244i	0.406350	−	0.572189i
$697$	−639.234			−0.917122
$698$	110.688	−	123.825i	0.158579	−	0.177400i
$699$			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	$0.302495\pi$
$702$	−115.268	−	103.039i	−0.164200	−	0.146779i
$703$			595.020i			0.846401i
$704$	−136.984	+	47.8041i	−0.194580	+	0.0679036i
$705$		0			0
$706$	760.731	−	851.020i	1.07752	−	1.20541i
$707$		−	569.562i		−	0.805605i
$708$	5.35838	+	47.6765i	0.00756833	+	0.0673397i
$709$	1300.08			1.83368			0.916839	−	0.399257i	$-0.130732\pi$
$709$	1300.08			1.83368			0.916839	+	0.399257i	$0.130732\pi$
$710$		0			0
$711$		−	177.019i		−	0.248972i
$712$	−46.6230	−	33.1102i	−0.0654818	−	0.0465030i
$713$	−868.977			−1.21876
$714$	−406.774	+	455.053i	−0.569712	+	0.637329i
$715$		0			0
$716$	375.722	−	42.2275i	0.524751	−	0.0589770i
$717$	−463.789			−0.646846
$718$	832.428	+	744.112i	1.15937	+	1.03637i
$719$			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
$722$	323.743	−	362.167i	0.448397	−	0.501616i
$723$			155.084i			0.214500i
$724$	36.0160	+	320.454i	0.0497458	+	0.442616i
$725$		0			0
$726$	−299.229	−	267.483i	−0.412161	−	0.368433i
$727$			850.638i			1.17007i	0.811009	+	0.585033i	$0.198919\pi$
$727$			850.638i			1.17007i	−0.811009	+	0.585033i	$0.801081\pi$
$728$	452.642	−	637.373i	0.621761	−	0.875513i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$			1508.94i			2.06422i
$732$	−739.610	+	83.1250i	−1.01040	+	0.113559i
$733$	−365.781			−0.499019			−0.249510	−	0.968372i	$-0.580269\pi$
$733$	−365.781			−0.499019			−0.249510	+	0.968372i	$0.580269\pi$
$734$	665.726	+	595.096i	0.906984	+	0.810758i
$735$		0			0
$736$	1020.78	+	565.093i	1.38692	+	0.767789i
$737$	252.639			0.342794
$738$	95.2884	−	106.598i	0.129117	−	0.144442i
$739$		−	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
$742$	−300.153	−	268.309i	−0.404519	−	0.361602i
$743$		−	481.526i		−	0.648083i	−0.946043	−	0.324041i	$-0.894958\pi$
$743$		−	481.526i		−	0.648083i	0.946043	−	0.324041i	$-0.105042\pi$
$744$	269.251	+	191.213i	0.361896	+	0.257007i
$745$		0			0
$746$	150.516	−	168.380i	0.201764	−	0.225711i
$747$			427.249i			0.571953i
$748$	241.723	−	27.1673i	0.323159	−	0.0363200i
$749$	−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	$-0.340039\pi$
$752$	182.617	+	802.159i	0.242841	+	1.06670i
$753$	394.637			0.524087
$754$	699.021	−	781.985i	0.927083	−	1.03711i
$755$		0			0
$756$	−15.2476	−	135.666i	−0.0201688	−	0.179453i
$757$	−483.813			−0.639118			−0.319559	−	0.947566i	$-0.603535\pi$
$757$	−483.813			−0.639118			−0.319559	+	0.947566i	$0.603535\pi$
$758$	479.325	+	428.471i	0.632354	+	0.565265i
$759$		−	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	$0.264235\pi$
$762$	165.317	−	184.938i	0.216952	−	0.242701i
$763$		−	167.004i		−	0.218878i
$764$	−1313.89	+	147.668i	−1.71975	+	0.193283i
$765$		0			0
$766$	133.046	+	118.931i	0.173689	+	0.155262i
$767$			103.022i			0.134318i
$768$	−191.940	−	399.709i	−0.249922	−	0.520454i
$769$	1024.79			1.33263			0.666314	−	0.745671i	$-0.267871\pi$
$769$	1024.79			1.33263			0.666314	+	0.745671i	$0.267871\pi$
$770$		0			0
$771$			765.790i			0.993242i
$772$	46.2873	+	411.844i	0.0599577	+	0.533477i
$773$	1092.74			1.41364			0.706819	−	0.707395i	$-0.250130\pi$
$773$	1092.74			1.41364			0.706819	+	0.707395i	$0.250130\pi$
$774$	−251.629	−	224.933i	−0.325103	−	0.290611i
$775$		0			0
$776$	823.848	+	585.070i	1.06166	+	0.753956i
$777$	−622.869			−0.801633
$778$	347.506	−	388.751i	0.446666	−	0.499679i
$779$		−	258.983i		−	0.332456i
$780$		0			0
$781$	70.9991			0.0909079
$782$	−1458.39	−	1303.66i	−1.86495	−	1.66709i
$783$		−	183.169i		−	0.233933i
$784$	−91.3723	+	20.8015i	−0.116546	+	0.0265325i
$785$		0			0
$786$	240.050	−	268.541i	0.305407	−	0.341655i
$787$		−	1385.63i		−	1.76064i	−0.474376	−	0.880322i	$-0.657326\pi$
$787$		−	1385.63i		−	1.76064i	0.474376	−	0.880322i	$-0.342674\pi$
$788$	−71.7624	−	638.511i	−0.0910691	−	0.810293i
$789$	59.1593			0.0749800
$790$		0			0
$791$			514.688i			0.650680i
$792$	−31.5024	+	44.3592i	−0.0397758	+	0.0560090i
$793$	−1598.19			−2.01537
$794$	−150.093	+	167.907i	−0.189034	+	0.211470i
$795$		0			0
$796$	−109.518	+	12.3087i	−0.137585	+	0.0154632i
$797$	98.5251			0.123620			0.0618100	−	0.998088i	$-0.480313\pi$
$797$	98.5251			0.123620			0.0618100	+	0.998088i	$0.480313\pi$
$798$	−184.363	−	164.803i	−0.231031	−	0.206520i
$799$		−	1379.28i		−	1.72626i
$800$		0			0
$801$	−21.4439			−0.0267715
$802$	769.767	−	861.128i	0.959810	−	1.07373i
$803$			251.427i			0.313110i
$804$	86.2342	+	767.274i	0.107256	+	0.954321i
$805$		0			0
$806$	528.697	+	472.605i	0.655951	+	0.586358i
$807$			17.2527i			0.0213788i
$808$	−565.592	−	401.665i	−0.699990	−	0.497110i
$809$	−212.100			−0.262176			−0.131088	−	0.991371i	$-0.541847\pi$
$809$	−212.100			−0.262176			−0.131088	+	0.991371i	$0.541847\pi$
$810$		0			0
$811$		−	485.409i		−	0.598531i	−0.954170	−	0.299266i	$-0.903258\pi$
$811$		−	485.409i		−	0.598531i	0.954170	−	0.299266i	$-0.0967417\pi$
$812$	920.367	−	103.440i	1.13346	−	0.127390i
$813$	−97.9980			−0.120539
$814$	185.068	+	165.433i	0.227356	+	0.203235i
$815$		0			0
$816$	165.016	+	724.849i	0.202226	+	0.888295i
$817$	−611.343			−0.748278
$818$	−368.221	+	411.924i	−0.450148	+	0.503575i
$819$		−	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	$0.675976\pi$
$822$	−18.5085	−	16.5449i	−0.0225164	−	0.0201276i
$823$		−	485.042i		−	0.589358i	−0.955596	−	0.294679i	$-0.904787\pi$
$823$		−	485.042i		−	0.589358i	0.955596	−	0.294679i	$-0.0952127\pi$
$824$	101.573	−	143.027i	0.123269	−	0.173577i
$825$		0			0
$826$	−60.6266	+	67.8221i	−0.0733978	+	0.0821091i
$827$			590.547i			0.714084i	0.934088	+	0.357042i	$0.116215\pi$
$827$			590.547i			0.714084i	−0.934088	+	0.357042i	$0.883785\pi$
$828$	434.795	−	48.8667i	0.525115	−	0.0590178i
$829$	−1071.30			−1.29228			−0.646139	−	0.763220i	$-0.723617\pi$
$829$	−1071.30			−1.29228			−0.646139	+	0.763220i	$0.723617\pi$
$830$		0			0
$831$		−	179.777i		−	0.216338i
$832$	−313.719	−	898.972i	−0.377067	−	1.08050i
$833$	157.111			0.188608
$834$	339.161	−	379.415i	0.406668	−	0.454934i
$835$		0			0
$836$	11.0067	+	97.9332i	0.0131660	+	0.117145i
$837$	123.840			0.147957
$838$	−369.076	−	329.919i	−0.440425	−	0.393698i
$839$		−	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
$842$	−103.607	+	115.903i	−0.123048	+	0.137653i
$843$		−	680.815i		−	0.807610i
$844$	1072.48	−	120.536i	1.27071	−	0.142816i
$845$		0			0
$846$	230.007	+	205.604i	0.271875	+	0.243031i
$847$		−	761.014i		−	0.898481i
$848$	−478.111	+	108.845i	−0.563810	+	0.128355i
$849$	−197.501			−0.232628
$850$		0			0
$851$		−	1996.22i		−	2.34574i
$852$	24.2344	+	215.627i	0.0284441	+	0.253083i
$853$	104.807			0.122868			0.0614341	−	0.998111i	$-0.480433\pi$
$853$	104.807			0.122868			0.0614341	+	0.998111i	$0.480433\pi$
$854$	−1052.13	−	940.506i	−1.23200	−	1.10129i
$855$		0			0
$856$	−33.2457	+	46.8140i	−0.0388385	+	0.0546892i
$857$	−1163.30			−1.35741			−0.678705	−	0.734411i	$-0.737458\pi$
$857$	−1163.30			−1.35741			−0.678705	+	0.734411i	$0.737458\pi$
$858$	−77.8617	+	87.1029i	−0.0907480	+	0.101518i
$859$			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
$862$	472.953	+	422.775i	0.548669	+	0.490458i
$863$			199.699i			0.231400i	0.993284	+	0.115700i	$0.0369112\pi$
$863$			199.699i			0.231400i	−0.993284	+	0.115700i	$0.963089\pi$
$864$	−145.473	−	80.5328i	−0.168372	−	0.0932092i
$865$		0			0
$866$	110.589	−	123.715i	0.127701	−	0.142858i
$867$		−	745.784i		−	0.860189i
$868$	69.9356	+	622.256i	0.0805710	+	0.716885i
$869$	−133.766			−0.153930
$870$		0			0
$871$			1657.97i			1.90352i
$872$	−165.840	−	117.774i	−0.190183	−	0.135062i
$873$	378.923			0.434047
$874$	528.175	−	590.862i	0.604319	−	0.676044i
$875$		0			0
$876$	−763.594	+	85.8205i	−0.871682	+	0.0979687i
$877$	1032.82			1.17767			0.588836	−	0.808252i	$-0.299586\pi$
$877$	1032.82			1.17767			0.588836	+	0.808252i	$0.299586\pi$
$878$	−175.385	−	156.777i	−0.199755	−	0.178562i
$879$		−	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	$0.607805\pi$
$882$	−23.4199	+	26.1996i	−0.0265532	+	0.0297047i
$883$			536.231i			0.607283i	0.952786	+	0.303641i	$0.0982025\pi$
$883$			536.231i			0.607283i	−0.952786	+	0.303641i	$0.901797\pi$
$884$	178.288	+	1586.33i	0.201684	+	1.79449i
$885$		0			0
$886$	52.4539	+	46.8888i	0.0592030	+	0.0529219i
$887$		−	173.466i		−	0.195564i	−0.995208	−	0.0977822i	$-0.968825\pi$
$887$		−	173.466i		−	0.195564i	0.995208	−	0.0977822i	$-0.0311749\pi$
$888$	−439.257	+	618.526i	−0.494659	+	0.696539i
$889$	470.344			0.529071
$890$		0			0
$891$			20.4027i			0.0228986i
$892$	−164.303	+	18.4661i	−0.184197	+	0.0207019i
$893$	558.810			0.625767
$894$	−205.594	−	183.781i	−0.229970	−	0.205572i
$895$		0			0
$896$	322.499	−	776.435i	0.359932	−	0.866557i
$897$	939.529			1.04741
$898$	−89.8712	+	100.538i	−0.100079	+	0.111957i
$899$			840.138i			0.934525i
$900$		0			0
$901$	822.092			0.912421
$902$	−80.5512	−	72.0051i	−0.0893028	−	0.0798283i
$903$		−	639.956i		−	0.708700i
$904$	511.099	+	362.966i	0.565375	+	0.401511i
$905$		0			0
$906$	421.841	−	471.908i	0.465608	−	0.520869i
$907$			817.237i			0.901033i	0.892768	+	0.450516i	$0.148760\pi$
$907$			817.237i			0.901033i	−0.892768	+	0.450516i	$0.851240\pi$
$908$	595.599	−	66.9395i	0.655946	−	0.0737220i
$909$	−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	$0.960079\pi$
$912$	−293.670	+	66.8558i	−0.322006	+	0.0733068i
$913$	322.853			0.353617
$914$	272.115	−	304.412i	0.297719	−	0.333055i
$915$		0			0
$916$	27.5541	+	245.165i	0.0300809	+	0.267647i
$917$	682.966			0.744783
$918$	207.839	+	185.789i	0.226404	+	0.202384i
$919$			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
$922$	167.628	−	187.523i	0.181809	−	0.203387i
$923$			465.939i			0.504809i
$924$	−102.517	+	11.5219i	−0.110949	+	0.0124696i
$925$		0			0
$926$	−825.515	−	737.933i	−0.891485	−	0.796904i
$927$		−	65.7844i		−	0.0709648i
$928$	546.339	−	986.898i	0.588727	−	1.06347i
$929$	−1192.84			−1.28400			−0.642000	−	0.766705i	$-0.721895\pi$
$929$	−1192.84			−1.28400			−0.642000	+	0.766705i	$0.721895\pi$
$930$		0			0
$931$			63.6528i			0.0683704i
$932$	181.195	+	1612.19i	0.194415	+	1.72982i
$933$	−818.386			−0.877156
$934$	−933.088	−	834.092i	−0.999023	−	0.893032i
$935$		0			0
$936$	−291.112	−	206.738i	−0.311017	−	0.220874i
$937$	530.621			0.566298			0.283149	−	0.959076i	$-0.408621\pi$
$937$	530.621			0.566298			0.283149	+	0.959076i	$0.408621\pi$
$938$	−975.684	+	1091.48i	−1.04018	+	1.16363i
$939$		−	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	$0.586899\pi$
$942$	547.993	+	489.854i	0.581734	+	0.520015i
$943$			868.860i			0.921378i
$944$	24.5944	+	108.033i	0.0260534	+	0.114442i
$945$		0			0
$946$	−169.972	+	190.145i	−0.179674	+	0.200999i
$947$		−	453.872i		−	0.479274i	−0.970863	−	0.239637i	$-0.922972\pi$
$947$		−	453.872i		−	0.479274i	0.970863	−	0.239637i	$-0.0770284\pi$
$948$	−45.6587	−	406.251i	−0.0481632	−	0.428535i
$949$	−1650.02			−1.73869
$950$		0			0
$951$			109.766i			0.115422i
$952$	−816.155	+	1149.24i	−0.857306	+	1.20719i
$953$	−1220.52			−1.28071			−0.640356	−	0.768078i	$-0.721213\pi$
$953$	−1220.52			−1.28071			−0.640356	+	0.768078i	$0.721213\pi$
$954$	−122.546	+	137.091i	−0.128455	+	0.143701i
$955$		0			0
$956$	−1064.37	+	119.625i	−1.11336	+	0.125131i
$957$	−138.413			−0.144632
$958$	−727.964	−	650.731i	−0.759879	−	0.679260i
$959$		−	47.0717i		−	0.0490842i
$960$		0			0
$961$	392.986			0.408935
$962$	−1085.67	+	1214.53i	−1.12856	+	1.26250i
$963$			21.5317i			0.0223590i
$964$	40.0008	+	355.910i	0.0414946	+	0.369201i
$965$		0			0
$966$	618.517	+	552.896i	0.640287	+	0.572356i
$967$		−	292.088i		−	0.302056i	−0.988530	−	0.151028i	$-0.951742\pi$
$967$		−	292.088i		−	0.302056i	0.988530	−	0.151028i	$-0.0482583\pi$
$968$	−755.708	−	536.679i	−0.780690	−	0.554421i
$969$	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	$-0.191215\pi$
$972$	−61.9637	+	6.96412i	−0.0637487	+	0.00716473i
$973$	964.947			0.991724
$974$	908.789	+	812.372i	0.933048	+	0.834057i
$975$		0			0
$976$	−1675.93	+	381.536i	−1.71714	+	0.390918i
$977$	−338.550			−0.346520			−0.173260	−	0.984876i	$-0.555430\pi$
$977$	−338.550			−0.346520			−0.173260	+	0.984876i	$0.555430\pi$
$978$	561.926	−	628.619i	0.574567	−	0.642760i
$979$			16.2042i			0.0165518i
$980$		0			0
$981$	−76.2767			−0.0777540
$982$	1027.48	+	918.468i	1.04631	+	0.935304i
$983$			346.346i			0.352336i	0.984360	+	0.176168i	$0.0563702\pi$
$983$			346.346i			0.352336i	−0.984360	+	0.176168i	$0.943630\pi$
$984$	191.188	−	269.215i	0.194296	−	0.273592i
$985$		0			0
$986$	−1260.40	+	1409.99i	−1.27830	+	1.43001i
$987$			584.964i			0.592669i
$988$	−642.697	+	72.2329i	−0.650503	+	0.0731102i
$989$	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	$0.961033\pi$
$992$	667.238	+	369.377i	0.672619	+	0.372356i
$993$	747.544			0.752813
$994$	−274.196	+	306.740i	−0.275851	+	0.308591i
$995$		0			0
$996$	110.200	+	980.516i	0.110643	+	0.984454i
$997$	178.452			0.178989			0.0894946	−	0.995987i	$-0.471475\pi$
$997$	178.452			0.178989			0.0894946	+	0.995987i	$0.471475\pi$
$998$	1044.37	+	933.565i	1.04646	+	0.935436i
$999$			284.487i			0.284772i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.33290 - 1.49110i) q^{2} -1.73205i q^{3} +(-0.446749 - 3.97497i) q^{4} +(-2.58266 - 2.30865i) q^{6} -6.56834i q^{7} +(-6.52255 - 4.63210i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(1.33290 - 1.49110i) q^{2} -1.73205i q^{3} +(-0.446749 - 3.97497i) q^{4} +(-2.58266 - 2.30865i) q^{6} -6.56834i q^{7} +(-6.52255 - 4.63210i) q^{8} -3.00000 q^{9} +2.26696i q^{11} +(-6.88486 + 0.773791i) q^{12} -14.8772 q^{13} +(-9.79404 - 8.75495i) q^{14} +(-15.6008 + 3.55163i) q^{16} +26.8250 q^{17} +(-3.99870 + 4.47330i) q^{18} +10.8680i q^{19} -11.3767 q^{21} +(3.38027 + 3.02164i) q^{22} -36.4610i q^{23} +(-8.02303 + 11.2974i) q^{24} +(-19.8298 + 22.1834i) q^{26} +5.19615i q^{27} +(-26.1090 + 2.93440i) q^{28} -35.2510 q^{29} -23.8330i q^{31} +(-15.4985 + 27.9963i) q^{32} +3.92650 q^{33} +(35.7550 - 39.9987i) q^{34} +(1.34025 + 11.9249i) q^{36} +54.7495 q^{37} +(16.2053 + 14.4860i) q^{38} +25.7680i q^{39} -23.8298 q^{41} +(-15.1640 + 16.9638i) q^{42} +56.2515i q^{43} +(9.01112 - 1.01276i) q^{44} +(-54.3670 - 48.5989i) q^{46} -51.4177i q^{47} +(6.15160 + 27.0214i) q^{48} +5.85689 q^{49} -46.4622i q^{51} +(6.64636 + 59.1364i) q^{52} +30.6465 q^{53} +(7.74797 + 6.92596i) q^{54} +(-30.4252 + 42.8423i) q^{56} +18.8240 q^{57} +(-46.9861 + 52.5627i) q^{58} -6.92483i q^{59} +107.426 q^{61} +(-35.5374 - 31.7671i) q^{62} +19.7050i q^{63} +(21.0873 + 60.4262i) q^{64} +(5.23363 - 5.85479i) q^{66} -111.444i q^{67} +(-11.9840 - 106.629i) q^{68} -63.1524 q^{69} -31.3190i q^{71} +(19.5676 + 13.8963i) q^{72} +110.909 q^{73} +(72.9757 - 81.6369i) q^{74} +(43.2002 - 4.85528i) q^{76} +14.8902 q^{77} +(38.4227 + 34.3463i) q^{78} +59.0065i q^{79} +9.00000 q^{81} +(-31.7628 + 35.5326i) q^{82} -142.416i q^{83} +(5.08253 + 45.2221i) q^{84} +(83.8765 + 74.9776i) q^{86} +61.0565i q^{87} +(10.5008 - 14.7864i) q^{88} +7.14798 q^{89} +97.7185i q^{91} +(-144.932 + 16.2889i) q^{92} -41.2800 q^{93} +(-76.6689 - 68.5347i) q^{94} +(48.4911 + 26.8443i) q^{96} -126.308 q^{97} +(7.80665 - 8.73319i) q^{98} -6.80089i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 8 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 8 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9	\( 8 q - 2 q^{2} - 8 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9} - 8 q^{13} + 22 q^{14} + 40 q^{16} + 6 q^{18} + 24 q^{21} - 4 q^{22} - 36 q^{24} - 66 q^{26} - 104 q^{28} - 32 q^{29} - 112 q^{32} + 124 q^{34} + 24 q^{36} + 176 q^{37} + 170 q^{38} - 16 q^{41} - 54 q^{42} + 40 q^{44} - 76 q^{46} - 24 q^{48} + 16 q^{49} - 56 q^{52} + 304 q^{53} + 18 q^{54} - 172 q^{56} - 72 q^{57} + 12 q^{58} + 136 q^{61} + 238 q^{62} + 16 q^{64} - 108 q^{66} - 88 q^{68} - 96 q^{69} + 60 q^{72} - 240 q^{73} - 108 q^{74} + 120 q^{76} + 384 q^{77} - 150 q^{78} + 72 q^{81} - 320 q^{82} - 144 q^{84} + 214 q^{86} + 200 q^{88} + 128 q^{89} - 312 q^{92} - 72 q^{93} + 12 q^{94} + 96 q^{96} - 216 q^{97} - 60 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 8 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9 - 8 * q^13 + 22 * q^14 + 40 * q^16 + 6 * q^18 + 24 * q^21 - 4 * q^22 - 36 * q^24 - 66 * q^26 - 104 * q^28 - 32 * q^29 - 112 * q^32 + 124 * q^34 + 24 * q^36 + 176 * q^37 + 170 * q^38 - 16 * q^41 - 54 * q^42 + 40 * q^44 - 76 * q^46 - 24 * q^48 + 16 * q^49 - 56 * q^52 + 304 * q^53 + 18 * q^54 - 172 * q^56 - 72 * q^57 + 12 * q^58 + 136 * q^61 + 238 * q^62 + 16 * q^64 - 108 * q^66 - 88 * q^68 - 96 * q^69 + 60 * q^72 - 240 * q^73 - 108 * q^74 + 120 * q^76 + 384 * q^77 - 150 * q^78 + 72 * q^81 - 320 * q^82 - 144 * q^84 + 214 * q^86 + 200 * q^88 + 128 * q^89 - 312 * q^92 - 72 * q^93 + 12 * q^94 + 96 * q^96 - 216 * q^97 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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