LMFDB - Embedded newform 300.3.c.d.151.4

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:	8.0.85100625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + x^5 + 3x^4 + 2x^3 - 8x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.4
Root			$-0.600040 - 1.28061i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.3.c.d.151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.67986 + 1.08539i) q^{2} -1.73205i q^{3} +(1.64388 - 3.64660i) q^{4} +(1.87994 + 2.90961i) q^{6} -0.596540i q^{7} +(1.19648 + 7.91002i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-1.67986 + 1.08539i) q^{2} -1.73205i q^{3} +(1.64388 - 3.64660i) q^{4} +(1.87994 + 2.90961i) q^{6} -0.596540i q^{7} +(1.19648 + 7.91002i) q^{8} -3.00000 q^{9} +9.27963i q^{11} +(-6.31609 - 2.84728i) q^{12} +23.5117 q^{13} +(0.647476 + 1.00210i) q^{14} +(-10.5953 - 11.9891i) q^{16} -3.97751 q^{17} +(5.03959 - 3.25616i) q^{18} -7.04756i q^{19} -1.03324 q^{21} +(-10.0720 - 15.5885i) q^{22} -32.0793i q^{23} +(13.7006 - 2.07237i) q^{24} +(-39.4964 + 25.5192i) q^{26} +5.19615i q^{27} +(-2.17534 - 0.980637i) q^{28} +35.6734 q^{29} -59.2585i q^{31} +(30.8115 + 8.64000i) q^{32} +16.0728 q^{33} +(6.68167 - 4.31713i) q^{34} +(-4.93163 + 10.9398i) q^{36} +5.38761 q^{37} +(7.64932 + 11.8389i) q^{38} -40.7234i q^{39} +40.0791 q^{41} +(1.73570 - 1.12146i) q^{42} -36.1157i q^{43} +(33.8391 + 15.2545i) q^{44} +(34.8184 + 53.8888i) q^{46} +74.0131i q^{47} +(-20.7657 + 18.3517i) q^{48} +48.6441 q^{49} +6.88925i q^{51} +(38.6503 - 85.7376i) q^{52} +2.55123 q^{53} +(-5.63983 - 8.72882i) q^{54} +(4.71864 - 0.713748i) q^{56} -12.2067 q^{57} +(-59.9265 + 38.7194i) q^{58} +36.4026i q^{59} -8.73223 q^{61} +(64.3183 + 99.5461i) q^{62} +1.78962i q^{63} +(-61.1369 + 18.9284i) q^{64} +(-27.0001 + 17.4452i) q^{66} -69.7379i q^{67} +(-6.53853 + 14.5044i) q^{68} -55.5630 q^{69} -59.2170i q^{71} +(-3.58944 - 23.7301i) q^{72} +83.0019 q^{73} +(-9.05044 + 5.84763i) q^{74} +(-25.6996 - 11.5853i) q^{76} +5.53566 q^{77} +(44.2006 + 68.4098i) q^{78} +65.8705i q^{79} +9.00000 q^{81} +(-67.3274 + 43.5013i) q^{82} -129.909i q^{83} +(-1.69851 + 3.76780i) q^{84} +(39.1995 + 60.6695i) q^{86} -61.7882i q^{87} +(-73.4020 + 11.1029i) q^{88} -130.466 q^{89} -14.0256i q^{91} +(-116.980 - 52.7344i) q^{92} -102.639 q^{93} +(-80.3327 - 124.332i) q^{94} +(14.9649 - 53.3671i) q^{96} -93.1113 q^{97} +(-81.7155 + 52.7977i) q^{98} -27.8389i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9	$ 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9} - 16 q^{13} - 20 q^{14} + 34 q^{16} + 12 q^{18} - 48 q^{21} - 68 q^{22} + 18 q^{24} - 36 q^{26} - 28 q^{28} + 64 q^{29} + 76 q^{32} - 92 q^{34} - 30 q^{36} + 112 q^{37} + 40 q^{38} - 16 q^{41} - 108 q^{42} + 172 q^{44} + 152 q^{46} - 48 q^{48} - 56 q^{49} + 128 q^{52} - 352 q^{53} + 18 q^{54} + 116 q^{56} - 144 q^{57} + 204 q^{58} - 176 q^{61} + 56 q^{62} - 110 q^{64} + 108 q^{66} + 184 q^{68} - 96 q^{69} - 60 q^{72} + 240 q^{73} + 132 q^{74} - 24 q^{76} + 288 q^{77} + 240 q^{78} + 72 q^{81} - 40 q^{82} - 36 q^{84} - 200 q^{86} - 140 q^{88} + 80 q^{89} - 144 q^{92} - 144 q^{93} - 96 q^{94} - 174 q^{96} - 432 q^{97} - 660 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9 - 16 * q^13 - 20 * q^14 + 34 * q^16 + 12 * q^18 - 48 * q^21 - 68 * q^22 + 18 * q^24 - 36 * q^26 - 28 * q^28 + 64 * q^29 + 76 * q^32 - 92 * q^34 - 30 * q^36 + 112 * q^37 + 40 * q^38 - 16 * q^41 - 108 * q^42 + 172 * q^44 + 152 * q^46 - 48 * q^48 - 56 * q^49 + 128 * q^52 - 352 * q^53 + 18 * q^54 + 116 * q^56 - 144 * q^57 + 204 * q^58 - 176 * q^61 + 56 * q^62 - 110 * q^64 + 108 * q^66 + 184 * q^68 - 96 * q^69 - 60 * q^72 + 240 * q^73 + 132 * q^74 - 24 * q^76 + 288 * q^77 + 240 * q^78 + 72 * q^81 - 40 * q^82 - 36 * q^84 - 200 * q^86 - 140 * q^88 + 80 * q^89 - 144 * q^92 - 144 * q^93 - 96 * q^94 - 174 * q^96 - 432 * q^97 - 660 * 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 $

$2$	−1.67986	+	1.08539i	−0.839931	+	0.542693i
$2$	−1.67986	+	1.08539i	−0.839931	+	0.542693i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	1.64388	−	3.64660i	0.410969	−	0.911649i
$5$		0			0
$5$		0			0
$6$	1.87994	+	2.90961i	0.313324	+	0.484935i
$7$		−	0.596540i		−	0.0852199i	−0.999092	−	0.0426100i	$-0.986433\pi$
$7$		−	0.596540i		−	0.0852199i	0.999092	−	0.0426100i	$-0.0135673\pi$
$8$	1.19648	+	7.91002i	0.149560	+	0.988753i
$9$	−3.00000			−0.333333
$10$		0			0
$11$			9.27963i			0.843602i	0.906688	+	0.421801i	$0.138602\pi$
$11$			9.27963i			0.843602i	−0.906688	+	0.421801i	$0.861398\pi$
$12$	−6.31609	−	2.84728i	−0.526341	−	0.237273i
$13$	23.5117			1.80859			0.904295	−	0.426907i	$-0.140397\pi$
$13$	23.5117			1.80859			0.904295	+	0.426907i	$0.140397\pi$
$14$	0.647476	+	1.00210i	0.0462483	+	0.0715789i
$15$		0			0
$16$	−10.5953	−	11.9891i	−0.662209	−	0.749319i
$17$	−3.97751			−0.233971			−0.116986	−	0.993134i	$-0.537323\pi$
$17$	−3.97751			−0.233971			−0.116986	+	0.993134i	$0.537323\pi$
$18$	5.03959	−	3.25616i	0.279977	−	0.180898i
$19$		−	7.04756i		−	0.370924i	−0.982651	−	0.185462i	$-0.940622\pi$
$19$		−	7.04756i		−	0.370924i	0.982651	−	0.185462i	$-0.0593782\pi$
$20$		0			0
$21$	−1.03324			−0.0492018
$22$	−10.0720	−	15.5885i	−0.457817	−	0.708568i
$23$		−	32.0793i		−	1.39475i	−0.716705	−	0.697376i	$-0.754351\pi$
$23$		−	32.0793i		−	1.39475i	0.716705	−	0.697376i	$-0.245649\pi$
$24$	13.7006	−	2.07237i	0.570857	−	0.0863486i
$25$		0			0
$26$	−39.4964	+	25.5192i	−1.51909	+	0.981509i
$27$			5.19615i			0.192450i
$28$	−2.17534	−	0.980637i	−0.0776907	−	0.0350227i
$29$	35.6734			1.23012			0.615059	−	0.788481i	$-0.289132\pi$
$29$	35.6734			1.23012			0.615059	+	0.788481i	$0.289132\pi$
$30$		0			0
$31$		−	59.2585i		−	1.91156i	−0.294076	−	0.955782i	$-0.595012\pi$
$31$		−	59.2585i		−	1.91156i	0.294076	−	0.955782i	$-0.404988\pi$
$32$	30.8115	+	8.64000i	0.962860	+	0.270000i
$33$	16.0728			0.487054
$34$	6.68167	−	4.31713i	0.196520	−	0.126974i
$35$		0			0
$36$	−4.93163	+	10.9398i	−0.136990	+	0.303883i
$37$	5.38761			0.145611			0.0728055	−	0.997346i	$-0.476805\pi$
$37$	5.38761			0.145611			0.0728055	+	0.997346i	$0.476805\pi$
$38$	7.64932	+	11.8389i	0.201298	+	0.311551i
$39$		−	40.7234i		−	1.04419i
$40$		0			0
$41$	40.0791			0.977539			0.488769	−	0.872413i	$-0.337446\pi$
$41$	40.0791			0.977539			0.488769	+	0.872413i	$0.337446\pi$
$42$	1.73570	−	1.12146i	0.0413261	−	0.0267014i
$43$		−	36.1157i		−	0.839901i	−0.907547	−	0.419950i	$-0.862047\pi$
$43$		−	36.1157i		−	0.839901i	0.907547	−	0.419950i	$-0.137953\pi$
$44$	33.8391	+	15.2545i	0.769070	+	0.346694i
$45$		0			0
$46$	34.8184	+	53.8888i	0.756922	+	1.17150i
$47$			74.0131i			1.57475i	0.616477	+	0.787373i	$0.288559\pi$
$47$			74.0131i			1.57475i	−0.616477	+	0.787373i	$0.711441\pi$
$48$	−20.7657	+	18.3517i	−0.432620	+	0.382327i
$49$	48.6441			0.992738
$50$		0			0
$51$			6.88925i			0.135083i
$52$	38.6503	−	85.7376i	0.743275	−	1.64880i
$53$	2.55123			0.0481364			0.0240682	−	0.999710i	$-0.492338\pi$
$53$	2.55123			0.0481364			0.0240682	+	0.999710i	$0.492338\pi$
$54$	−5.63983	−	8.72882i	−0.104441	−	0.161645i
$55$		0			0
$56$	4.71864	−	0.713748i	0.0842614	−	0.0127455i
$57$	−12.2067			−0.214153
$58$	−59.9265	+	38.7194i	−1.03321	+	0.667576i
$59$			36.4026i			0.616993i	0.951225	+	0.308497i	$0.0998259\pi$
$59$			36.4026i			0.616993i	−0.951225	+	0.308497i	$0.900174\pi$
$60$		0			0
$61$	−8.73223			−0.143151			−0.0715757	−	0.997435i	$-0.522803\pi$
$61$	−8.73223			−0.143151			−0.0715757	+	0.997435i	$0.522803\pi$
$62$	64.3183	+	99.5461i	1.03739	+	1.60558i
$63$			1.78962i			0.0284066i
$64$	−61.1369	+	18.9284i	−0.955264	+	0.295756i
$65$		0			0
$66$	−27.0001	+	17.4452i	−0.409092	+	0.264321i
$67$		−	69.7379i		−	1.04086i	−0.853903	−	0.520432i	$-0.825771\pi$
$67$		−	69.7379i		−	1.04086i	0.853903	−	0.520432i	$-0.174229\pi$
$68$	−6.53853	+	14.5044i	−0.0961548	+	0.213300i
$69$	−55.5630			−0.805261
$70$		0			0
$71$		−	59.2170i		−	0.834043i	−0.908897	−	0.417021i	$-0.863074\pi$
$71$		−	59.2170i		−	0.834043i	0.908897	−	0.417021i	$-0.136926\pi$
$72$	−3.58944	−	23.7301i	−0.0498534	−	0.329584i
$73$	83.0019			1.13701			0.568506	−	0.822679i	$-0.307522\pi$
$73$	83.0019			1.13701			0.568506	+	0.822679i	$0.307522\pi$
$74$	−9.05044	+	5.84763i	−0.122303	+	0.0790220i
$75$		0			0
$76$	−25.6996	−	11.5853i	−0.338153	−	0.152438i
$77$	5.53566			0.0718917
$78$	44.2006	+	68.4098i	0.566675	+	0.877048i
$79$			65.8705i			0.833804i	0.908951	+	0.416902i	$0.136884\pi$
$79$			65.8705i			0.833804i	−0.908951	+	0.416902i	$0.863116\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	−67.3274	+	43.5013i	−0.821065	+	0.530503i
$83$		−	129.909i		−	1.56517i	−0.622542	−	0.782586i	$-0.713900\pi$
$83$		−	129.909i		−	1.56517i	0.622542	−	0.782586i	$-0.286100\pi$
$84$	−1.69851	+	3.76780i	−0.0202204	+	0.0448547i
$85$		0			0
$86$	39.1995	+	60.6695i	0.455808	+	0.705459i
$87$		−	61.7882i		−	0.710209i
$88$	−73.4020	+	11.1029i	−0.834114	+	0.126169i
$89$	−130.466			−1.46591			−0.732956	−	0.680277i	$-0.761860\pi$
$89$	−130.466			−1.46591			−0.732956	+	0.680277i	$0.761860\pi$
$90$		0			0
$91$		−	14.0256i		−	0.154128i
$92$	−116.980	−	52.7344i	−1.27152	−	0.573200i
$93$	−102.639			−1.10364
$94$	−80.3327	−	124.332i	−0.854603	−	1.32268i
$95$		0			0
$96$	14.9649	−	53.3671i	0.155885	−	0.555908i
$97$	−93.1113			−0.959911			−0.479955	−	0.877293i	$-0.659347\pi$
$97$	−93.1113			−0.959911			−0.479955	+	0.877293i	$0.659347\pi$
$98$	−81.7155	+	52.7977i	−0.833831	+	0.538752i
$99$		−	27.8389i		−	0.281201i
$100$		0			0
$101$	−3.66081			−0.0362457			−0.0181228	−	0.999836i	$-0.505769\pi$
$101$	−3.66081			−0.0362457			−0.0181228	+	0.999836i	$0.505769\pi$
$102$	−7.47749	−	11.5730i	−0.0733087	−	0.113461i
$103$			151.417i			1.47007i	0.678032	+	0.735033i	$0.262833\pi$
$103$			151.417i			1.47007i	−0.678032	+	0.735033i	$0.737167\pi$
$104$	28.1313	+	185.978i	0.270493	+	1.78825i
$105$		0			0
$106$	−4.28571	+	2.76907i	−0.0404313	+	0.0261233i
$107$			82.8092i			0.773918i	0.922097	+	0.386959i	$0.126474\pi$
$107$			82.8092i			0.773918i	−0.922097	+	0.386959i	$0.873526\pi$
$108$	18.9483	+	8.54183i	0.175447	+	0.0790910i
$109$	−7.36835			−0.0675996			−0.0337998	−	0.999429i	$-0.510761\pi$
$109$	−7.36835			−0.0675996			−0.0337998	+	0.999429i	$0.510761\pi$
$110$		0			0
$111$		−	9.33161i		−	0.0840685i
$112$	−7.15197	+	6.32054i	−0.0638569	+	0.0564334i
$113$	−65.0370			−0.575549			−0.287774	−	0.957698i	$-0.592915\pi$
$113$	−65.0370			−0.575549			−0.287774	+	0.957698i	$0.592915\pi$
$114$	20.5056	−	13.2490i	0.179874	−	0.116219i
$115$		0			0
$116$	58.6427	−	130.087i	0.505540	−	1.12144i
$117$	−70.5350			−0.602864
$118$	−39.5109	−	61.1514i	−0.334838	−	0.518232i
$119$			2.37274i			0.0199390i
$120$		0			0
$121$	34.8885			0.288335
$122$	14.6689	−	9.47784i	0.120237	−	0.0776872i
$123$		−	69.4190i		−	0.564382i
$124$	−216.092	−	97.4136i	−1.74268	−	0.785593i
$125$		0			0
$126$	−1.94243	−	3.00631i	−0.0154161	−	0.0238596i
$127$			139.469i			1.09818i	0.835763	+	0.549091i	$0.185026\pi$
$127$			139.469i			1.09818i	−0.835763	+	0.549091i	$0.814974\pi$
$128$	82.1569	−	98.1542i	0.641851	−	0.766829i
$129$	−62.5543			−0.484917
$130$		0			0
$131$			63.4856i			0.484623i	0.970198	+	0.242312i	$0.0779056\pi$
$131$			63.4856i			0.484623i	−0.970198	+	0.242312i	$0.922094\pi$
$132$	26.4217	−	58.6110i	0.200164	−	0.444023i
$133$	−4.20415			−0.0316101
$134$	75.6925	+	117.150i	0.564870	+	0.874254i
$135$		0			0
$136$	−4.75901	−	31.4622i	−0.0349927	−	0.231340i
$137$	138.157			1.00845			0.504223	−	0.863573i	$-0.331779\pi$
$137$	138.157			1.00845			0.504223	+	0.863573i	$0.331779\pi$
$138$	93.3382	−	60.3073i	0.676363	−	0.437009i
$139$		−	29.9578i		−	0.215523i	−0.994177	−	0.107762i	$-0.965632\pi$
$139$		−	29.9578i		−	0.215523i	0.994177	−	0.107762i	$-0.0343684\pi$
$140$		0			0
$141$	128.194			0.909180
$142$	64.2733	+	99.4765i	0.452629	+	0.700539i
$143$			218.180i			1.52573i
$144$	31.7860	+	35.9673i	0.220736	+	0.249773i
$145$		0			0
$146$	−139.432	+	90.0891i	−0.955012	+	0.617048i
$147$		−	84.2541i		−	0.573157i
$148$	8.85655	−	19.6464i	0.0598416	−	0.132746i
$149$	−47.3823			−0.318002			−0.159001	−	0.987278i	$-0.550827\pi$
$149$	−47.3823			−0.318002			−0.159001	+	0.987278i	$0.550827\pi$
$150$		0			0
$151$			109.604i			0.725852i	0.931818	+	0.362926i	$0.118222\pi$
$151$			109.604i			0.725852i	−0.931818	+	0.362926i	$0.881778\pi$
$152$	55.7463	−	8.43227i	0.366752	−	0.0554755i
$153$	11.9325			0.0779904
$154$	−9.29915	+	6.00833i	−0.0603841	+	0.0390151i
$155$		0			0
$156$	−148.502	−	66.9442i	−0.951936	−	0.429130i
$157$	177.588			1.13113			0.565566	−	0.824703i	$-0.308658\pi$
$157$	177.588			1.13113			0.565566	+	0.824703i	$0.308658\pi$
$158$	−71.4950	−	110.653i	−0.452500	−	0.700338i
$159$		−	4.41886i		−	0.0277916i
$160$		0			0
$161$	−19.1366			−0.118861
$162$	−15.1188	+	9.76847i	−0.0933257	+	0.0602992i
$163$			96.8778i			0.594342i	0.954824	+	0.297171i	$0.0960432\pi$
$163$			96.8778i			0.594342i	−0.954824	+	0.297171i	$0.903957\pi$
$164$	65.8850	−	146.152i	0.401738	−	0.891173i
$165$		0			0
$166$	141.002	+	218.230i	0.849408	+	1.31464i
$167$		−	152.605i		−	0.913801i	−0.889518	−	0.456901i	$-0.848960\pi$
$167$		−	152.605i		−	0.913801i	0.889518	−	0.456901i	$-0.151040\pi$
$168$	−1.23625	−	8.17292i	−0.00735862	−	0.0486484i
$169$	383.799			2.27100
$170$		0			0
$171$			21.1427i			0.123641i
$172$	−131.700	−	59.3698i	−0.765695	−	0.345173i
$173$	−155.773			−0.900422			−0.450211	−	0.892922i	$-0.648651\pi$
$173$	−155.773			−0.900422			−0.450211	+	0.892922i	$0.648651\pi$
$174$	67.0640	+	103.796i	0.385425	+	0.596527i
$175$		0			0
$176$	111.254	−	98.3209i	0.632127	−	0.558641i
$177$	63.0512			0.356221
$178$	219.165	−	141.606i	1.23126	−	0.795540i
$179$		−	126.001i		−	0.703915i	−0.936016	−	0.351957i	$-0.885516\pi$
$179$		−	126.001i		−	0.703915i	0.936016	−	0.351957i	$-0.114484\pi$
$180$		0			0
$181$	−346.725			−1.91561			−0.957803	−	0.287424i	$-0.907201\pi$
$181$	−346.725			−1.91561			−0.957803	+	0.287424i	$0.907201\pi$
$182$	15.2232	+	23.5612i	0.0836442	+	0.129457i
$183$			15.1247i			0.0826485i
$184$	253.748	−	38.3823i	1.37906	−	0.208599i
$185$		0			0
$186$	172.419	−	111.403i	0.926983	−	0.598939i
$187$		−	36.9098i		−	0.197379i
$188$	269.896	+	121.668i	1.43562	+	0.647171i
$189$	3.09971			0.0164006
$190$		0			0
$191$			133.159i			0.697167i	0.937278	+	0.348584i	$0.113337\pi$
$191$			133.159i			0.697167i	−0.937278	+	0.348584i	$0.886663\pi$
$192$	32.7849	+	105.892i	0.170755	+	0.551522i
$193$	136.246			0.705940			0.352970	−	0.935635i	$-0.385172\pi$
$193$	136.246			0.705940			0.352970	+	0.935635i	$0.385172\pi$
$194$	156.414	−	101.062i	0.806259	−	0.520937i
$195$		0			0
$196$	79.9649	−	177.386i	0.407984	−	0.905029i
$197$	−74.8945			−0.380175			−0.190087	−	0.981767i	$-0.560877\pi$
$197$	−74.8945			−0.380175			−0.190087	+	0.981767i	$0.560877\pi$
$198$	30.2159	+	46.7655i	0.152606	+	0.236189i
$199$			251.605i			1.26434i	0.774828	+	0.632172i	$0.217836\pi$
$199$			251.605i			1.26434i	−0.774828	+	0.632172i	$0.782164\pi$
$200$		0			0
$201$	−120.790			−0.600943
$202$	6.14966	−	3.97339i	0.0304439	−	0.0196703i
$203$		−	21.2806i		−	0.104831i
$204$	25.1223	+	11.3251i	0.123149	+	0.0555150i
$205$		0			0
$206$	−164.346	−	254.359i	−0.797794	−	1.23475i
$207$			96.2379i			0.464917i
$208$	−249.114	−	281.884i	−1.19767	−	1.35521i
$209$	65.3987			0.312913
$210$		0			0
$211$			228.203i			1.08153i	0.841173	+	0.540766i	$0.181865\pi$
$211$			228.203i			1.08153i	−0.841173	+	0.540766i	$0.818135\pi$
$212$	4.19390	−	9.30331i	0.0197826	−	0.0438835i
$213$	−102.567			−0.481535
$214$	−89.8799	−	139.108i	−0.420000	−	0.650038i
$215$		0			0
$216$	−41.1017	+	6.21710i	−0.190286	+	0.0287829i
$217$	−35.3500			−0.162903
$218$	12.3778	−	7.99751i	0.0567790	−	0.0366858i
$219$		−	143.763i		−	0.656454i
$220$		0			0
$221$	−93.5179			−0.423158
$222$	10.1284	+	15.6758i	0.0456234	+	0.0706118i
$223$			85.9549i			0.385448i	0.981253	+	0.192724i	$0.0617322\pi$
$223$			85.9549i			0.385448i	−0.981253	+	0.192724i	$0.938268\pi$
$224$	5.15410	−	18.3803i	0.0230094	−	0.0820549i
$225$		0			0
$226$	109.253	−	70.5902i	0.483421	−	0.312346i
$227$		−	282.357i		−	1.24386i	−0.783071	−	0.621932i	$-0.786348\pi$
$227$		−	282.357i		−	1.24386i	0.783071	−	0.621932i	$-0.213652\pi$
$228$	−20.0663	+	44.5130i	−0.0880103	+	0.195233i
$229$	138.263			0.603768			0.301884	−	0.953345i	$-0.402385\pi$
$229$	138.263			0.603768			0.301884	+	0.953345i	$0.402385\pi$
$230$		0			0
$231$		−	9.58805i		−	0.0415067i
$232$	42.6826	+	282.178i	0.183977	+	1.21628i
$233$	0.522939			0.00224438			0.00112219	−	0.999999i	$-0.499643\pi$
$233$	0.522939			0.00224438			0.00112219	+	0.999999i	$0.499643\pi$
$234$	118.489	−	76.5577i	0.506364	−	0.327170i
$235$		0			0
$236$	132.746	+	59.8413i	0.562482	+	0.253565i
$237$	114.091			0.481397
$238$	−2.57534	−	3.98588i	−0.0108208	−	0.0167474i
$239$			73.6928i			0.308338i	0.988044	+	0.154169i	$0.0492700\pi$
$239$			73.6928i			0.308338i	−0.988044	+	0.154169i	$0.950730\pi$
$240$		0			0
$241$	31.3705			0.130168			0.0650840	−	0.997880i	$-0.479268\pi$
$241$	31.3705			0.130168			0.0650840	+	0.997880i	$0.479268\pi$
$242$	−58.6080	+	37.8675i	−0.242182	+	0.156477i
$243$		−	15.5885i		−	0.0641500i
$244$	−14.3547	+	31.8429i	−0.0588307	+	0.130504i
$245$		0			0
$246$	75.3464	+	116.614i	0.306286	+	0.474042i
$247$		−	165.700i		−	0.670850i
$248$	468.736	−	70.9016i	1.89006	−	0.285894i
$249$	−225.010			−0.903653
$250$		0			0
$251$			78.7478i			0.313736i	0.987620	+	0.156868i	$0.0501398\pi$
$251$			78.7478i			0.313736i	−0.987620	+	0.156868i	$0.949860\pi$
$252$	6.52602	+	2.94191i	0.0258969	+	0.0116742i
$253$	297.684			1.17662
$254$	−151.378	−	234.289i	−0.595975	−	0.922397i
$255$		0			0
$256$	−31.4772	+	254.057i	−0.122958	+	0.992412i
$257$	−243.954			−0.949236			−0.474618	−	0.880192i	$-0.657414\pi$
$257$	−243.954			−0.949236			−0.474618	+	0.880192i	$0.657414\pi$
$258$	105.083	−	67.8956i	0.407297	−	0.263161i
$259$		−	3.21392i		−	0.0124090i
$260$		0			0
$261$	−107.020			−0.410039
$262$	−68.9064	−	106.647i	−0.263002	−	0.407050i
$263$		−	102.737i		−	0.390635i	−0.980740	−	0.195317i	$-0.937426\pi$
$263$		−	102.737i		−	0.390635i	0.980740	−	0.195317i	$-0.0625737\pi$
$264$	19.2308	+	127.136i	0.0728439	+	0.481576i
$265$		0			0
$266$	7.06239	−	4.56312i	0.0265503	−	0.0171546i
$267$			225.974i			0.846344i
$268$	−254.306	−	114.640i	−0.948903	−	0.427763i
$269$	−123.646			−0.459651			−0.229825	−	0.973232i	$-0.573816\pi$
$269$	−123.646			−0.459651			−0.229825	+	0.973232i	$0.573816\pi$
$270$		0			0
$271$		−	332.371i		−	1.22646i	−0.789904	−	0.613230i	$-0.789870\pi$
$271$		−	332.371i		−	1.22646i	0.789904	−	0.613230i	$-0.210130\pi$
$272$	42.1431	+	47.6868i	0.154938	+	0.175319i
$273$	−24.2931			−0.0889858
$274$	−232.085	+	149.954i	−0.847026	+	0.547277i
$275$		0			0
$276$	−91.3386	+	202.616i	−0.330937	+	0.734115i
$277$	125.916			0.454571			0.227286	−	0.973828i	$-0.427015\pi$
$277$	125.916			0.454571			0.227286	+	0.973828i	$0.427015\pi$
$278$	32.5157	+	50.3249i	0.116963	+	0.181025i
$279$			177.775i			0.637188i
$280$		0			0
$281$	52.5628			0.187056			0.0935281	−	0.995617i	$-0.470186\pi$
$281$	52.5628			0.187056			0.0935281	+	0.995617i	$0.470186\pi$
$282$	−215.349	+	139.140i	−0.763649	+	0.493405i
$283$			199.288i			0.704199i	0.935963	+	0.352100i	$0.114532\pi$
$283$			199.288i			0.704199i	−0.935963	+	0.352100i	$0.885468\pi$
$284$	−215.941	−	97.3454i	−0.760355	−	0.342766i
$285$		0			0
$286$	−236.809	−	366.512i	−0.828004	−	1.28151i
$287$		−	23.9088i		−	0.0833058i
$288$	−92.4346	−	25.9200i	−0.320953	−	0.0900001i
$289$	−273.179			−0.945258
$290$		0			0
$291$			161.274i			0.554205i
$292$	136.445	−	302.674i	0.467276	−	1.03656i
$293$	−102.161			−0.348672			−0.174336	−	0.984686i	$-0.555778\pi$
$293$	−102.161			−0.348672			−0.174336	+	0.984686i	$0.555778\pi$
$294$	91.4482	+	141.535i	0.311048	+	0.481413i
$295$		0			0
$296$	6.44617	+	42.6161i	0.0217776	+	0.143973i
$297$	−48.2184			−0.162351
$298$	79.5957	−	51.4281i	0.267100	−	0.172577i
$299$		−	754.238i		−	2.52254i
$300$		0			0
$301$	−21.5445			−0.0715763
$302$	−118.962	−	184.119i	−0.393915	−	0.609666i
$303$			6.34071i			0.0209264i
$304$	−84.4939	+	74.6713i	−0.277941	+	0.245629i
$305$		0			0
$306$	−20.0450	+	12.9514i	−0.0655065	+	0.0423248i
$307$			328.391i			1.06968i	0.844954	+	0.534839i	$0.179628\pi$
$307$			328.391i			1.06968i	−0.844954	+	0.534839i	$0.820372\pi$
$308$	9.09994	−	20.1863i	0.0295453	−	0.0655401i
$309$	262.262			0.848743
$310$		0			0
$311$		−	95.4377i		−	0.306874i	−0.988158	−	0.153437i	$-0.950966\pi$
$311$		−	95.4377i		−	0.306874i	0.988158	−	0.153437i	$-0.0490342\pi$
$312$	322.123	−	48.7248i	1.03245	−	0.156169i
$313$	−550.408			−1.75849			−0.879246	−	0.476368i	$-0.841953\pi$
$313$	−550.408			−1.75849			−0.879246	+	0.476368i	$0.841953\pi$
$314$	−298.323	+	192.751i	−0.950073	+	0.613858i
$315$		0			0
$316$	240.203	+	108.283i	0.760137	+	0.342668i
$317$	−439.394			−1.38610			−0.693051	−	0.720889i	$-0.743734\pi$
$317$	−439.394			−1.38610			−0.693051	+	0.720889i	$0.743734\pi$
$318$	4.79617	+	7.42307i	0.0150823	+	0.0233430i
$319$			331.036i			1.03773i
$320$		0			0
$321$	143.430			0.446822
$322$	32.1468	−	20.7706i	0.0998348	−	0.0645048i
$323$			28.0317i			0.0867855i
$324$	14.7949	−	32.8194i	0.0456632	−	0.101294i
$325$		0			0
$326$	−105.150	−	162.741i	−0.322545	−	0.499206i
$327$			12.7624i			0.0390286i
$328$	47.9539	+	317.026i	0.146201	+	0.966544i
$329$	44.1517			0.134200
$330$		0			0
$331$		−	479.922i		−	1.44992i	−0.688794	−	0.724958i	$-0.741859\pi$
$331$		−	479.922i		−	1.44992i	0.688794	−	0.724958i	$-0.258141\pi$
$332$	−473.727	−	213.555i	−1.42689	−	0.643237i
$333$	−16.1628			−0.0485370
$334$	165.635	+	256.355i	0.495913	+	0.767530i
$335$		0			0
$336$	10.9475	+	12.3876i	0.0325819	+	0.0368678i
$337$	−58.8437			−0.174610			−0.0873052	−	0.996182i	$-0.527826\pi$
$337$	−58.8437			−0.174610			−0.0873052	+	0.996182i	$0.527826\pi$
$338$	−644.730	+	416.570i	−1.90748	+	1.23246i
$339$			112.647i			0.332293i
$340$		0			0
$341$	549.897			1.61260
$342$	−22.9480	−	35.5168i	−0.0670993	−	0.103850i
$343$		−	58.2486i		−	0.169821i
$344$	285.676	−	43.2118i	0.830454	−	0.125616i
$345$		0			0
$346$	261.677	−	169.074i	0.756293	−	0.488653i
$347$		−	12.1484i		−	0.0350099i	−0.999847	−	0.0175049i	$-0.994428\pi$
$347$		−	12.1484i		−	0.0350099i	0.999847	−	0.0175049i	$-0.00557228\pi$
$348$	−225.317	−	101.572i	−0.647462	−	0.291874i
$349$	−30.9277			−0.0886180			−0.0443090	−	0.999018i	$-0.514109\pi$
$349$	−30.9277			−0.0886180			−0.0443090	+	0.999018i	$0.514109\pi$
$350$		0			0
$351$			122.170i			0.348063i
$352$	−80.1760	+	285.919i	−0.227773	+	0.812271i
$353$	288.065			0.816048			0.408024	−	0.912971i	$-0.366218\pi$
$353$	288.065			0.816048			0.408024	+	0.912971i	$0.366218\pi$
$354$	−105.917	+	68.4348i	−0.299201	+	0.193319i
$355$		0			0
$356$	−214.470	+	475.757i	−0.602444	+	1.33640i
$357$	4.10971			0.0115118
$358$	136.759	+	211.664i	0.382010	+	0.591240i
$359$			663.911i			1.84933i	0.380776	+	0.924667i	$0.375657\pi$
$359$			663.911i			1.84933i	−0.380776	+	0.924667i	$0.624343\pi$
$360$		0			0
$361$	311.332			0.862415
$362$	582.450	−	376.330i	1.60898	−	1.03959i
$363$		−	60.4287i		−	0.166470i
$364$	−51.1459	−	23.0564i	−0.140511	−	0.0633418i
$365$		0			0
$366$	−16.4161	−	25.4074i	−0.0448527	−	0.0694190i
$367$		−	6.08529i		−	0.0165812i	−0.999966	−	0.00829059i	$-0.997361\pi$
$367$		−	6.08529i		−	0.0165812i	0.999966	−	0.00829059i	$-0.00263901\pi$
$368$	−384.602	+	339.891i	−1.04511	+	0.923618i
$369$	−120.237			−0.325846
$370$		0			0
$371$		−	1.52191i		−	0.00410218i
$372$	−168.725	+	374.282i	−0.453562	+	1.00613i
$373$	204.741			0.548903			0.274451	−	0.961601i	$-0.411504\pi$
$373$	204.741			0.548903			0.274451	+	0.961601i	$0.411504\pi$
$374$	40.0614	+	62.0034i	0.107116	+	0.165784i
$375$		0			0
$376$	−585.445	+	88.5552i	−1.55703	+	0.235519i
$377$	838.742			2.22478
$378$	−5.20709	+	3.36438i	−0.0137754	+	0.00890048i
$379$		−	402.331i		−	1.06156i	−0.847510	−	0.530780i	$-0.821899\pi$
$379$		−	402.331i		−	1.06156i	0.847510	−	0.530780i	$-0.178101\pi$
$380$		0			0
$381$	241.568			0.634036
$382$	−144.529	−	223.689i	−0.378348	−	0.585573i
$383$			331.751i			0.866191i	0.901348	+	0.433096i	$0.142579\pi$
$383$			331.751i			0.866191i	−0.901348	+	0.433096i	$0.857421\pi$
$384$	−170.008	−	142.300i	−0.442729	−	0.370573i
$385$		0			0
$386$	−228.875	+	147.880i	−0.592941	+	0.383109i
$387$			108.347i			0.279967i
$388$	−153.063	+	339.540i	−0.394493	+	0.875102i
$389$	−623.310			−1.60234			−0.801169	−	0.598438i	$-0.795788\pi$
$389$	−623.310			−1.60234			−0.801169	+	0.598438i	$0.795788\pi$
$390$		0			0
$391$			127.596i			0.326332i
$392$	58.2018	+	384.776i	0.148474	+	0.981572i
$393$	109.960			0.279797
$394$	125.812	−	81.2894i	0.319321	−	0.206318i
$395$		0			0
$396$	−101.517	−	45.7636i	−0.256357	−	0.115565i
$397$	355.449			0.895338			0.447669	−	0.894199i	$-0.352254\pi$
$397$	355.449			0.895338			0.447669	+	0.894199i	$0.352254\pi$
$398$	−273.088	−	422.661i	−0.686151	−	1.06196i
$399$			7.28180i			0.0182501i
$400$		0			0
$401$	−542.927			−1.35393			−0.676966	−	0.736014i	$-0.736706\pi$
$401$	−542.927			−1.35393			−0.676966	+	0.736014i	$0.736706\pi$
$402$	202.910	−	131.103i	0.504751	−	0.326128i
$403$		−	1393.27i		−	3.45724i
$404$	−6.01792	+	13.3495i	−0.0148958	+	0.0330433i
$405$		0			0
$406$	23.0977	+	35.7485i	0.0568908	+	0.0880505i
$407$			49.9950i			0.122838i
$408$	−54.4941	+	8.24285i	−0.133564	+	0.0202031i
$409$	−108.497			−0.265273			−0.132636	−	0.991165i	$-0.542344\pi$
$409$	−108.497			−0.265273			−0.132636	+	0.991165i	$0.542344\pi$
$410$		0			0
$411$		−	239.295i		−	0.582227i
$412$	552.156	+	248.910i	1.34018	+	0.604151i
$413$	21.7156			0.0525801
$414$	−104.455	−	161.666i	−0.252307	−	0.390499i
$415$		0			0
$416$	724.431	+	203.141i	1.74142	+	0.488320i
$417$	−51.8884			−0.124433
$418$	−109.861	+	70.9828i	−0.262825	+	0.169815i
$419$		−	172.176i		−	0.410921i	−0.978665	−	0.205460i	$-0.934131\pi$
$419$		−	172.176i		−	0.410921i	0.978665	−	0.205460i	$-0.0658691\pi$
$420$		0			0
$421$	478.522			1.13663			0.568316	−	0.822810i	$-0.307595\pi$
$421$	478.522			1.13663			0.568316	+	0.822810i	$0.307595\pi$
$422$	−247.688	−	383.350i	−0.586940	−	0.908412i
$423$		−	222.039i		−	0.524915i
$424$	3.05250	+	20.1803i	0.00719929	+	0.0475950i
$425$		0			0
$426$	172.298	−	111.325i	0.404456	−	0.261326i
$427$			5.20912i			0.0121993i
$428$	301.972	+	136.128i	0.705541	+	0.318056i
$429$	377.898			0.880882
$430$		0			0
$431$		−	290.722i		−	0.674530i	−0.941410	−	0.337265i	$-0.890498\pi$
$431$		−	290.722i		−	0.674530i	0.941410	−	0.337265i	$-0.109502\pi$
$432$	62.2972	−	55.0550i	0.144207	−	0.127442i
$433$	−53.7726			−0.124186			−0.0620931	−	0.998070i	$-0.519778\pi$
$433$	−53.7726			−0.124186			−0.0620931	+	0.998070i	$0.519778\pi$
$434$	59.3832	−	38.3684i	0.136828	−	0.0884065i
$435$		0			0
$436$	−12.1127	+	26.8694i	−0.0277813	+	0.0616271i
$437$	−226.081			−0.517347
$438$	156.039	+	241.503i	0.356253	+	0.551376i
$439$			328.657i			0.748650i	0.927298	+	0.374325i	$0.122126\pi$
$439$			328.657i			0.748650i	−0.927298	+	0.374325i	$0.877874\pi$
$440$		0			0
$441$	−145.932			−0.330913
$442$	157.097	−	101.503i	0.355424	−	0.229645i
$443$		−	428.910i		−	0.968194i	−0.875014	−	0.484097i	$-0.839148\pi$
$443$		−	428.910i		−	0.968194i	0.875014	−	0.484097i	$-0.160852\pi$
$444$	−34.0286	−	15.3400i	−0.0766410	−	0.0345496i
$445$		0			0
$446$	−93.2942	−	144.392i	−0.209180	−	0.323750i
$447$			82.0685i			0.183599i
$448$	11.2915	+	36.4706i	0.0252043	+	0.0814075i
$449$	409.229			0.911423			0.455711	−	0.890128i	$-0.349385\pi$
$449$	409.229			0.911423			0.455711	+	0.890128i	$0.349385\pi$
$450$		0			0
$451$			371.919i			0.824654i
$452$	−106.913	+	237.164i	−0.236533	+	0.524698i
$453$	189.839			0.419071
$454$	306.466	+	474.321i	0.675036	+	1.04476i
$455$		0			0
$456$	−14.6051	−	96.5555i	−0.0320288	−	0.211745i
$457$	−768.561			−1.68175			−0.840876	−	0.541228i	$-0.817960\pi$
$457$	−768.561			−1.68175			−0.840876	+	0.541228i	$0.817960\pi$
$458$	−232.262	+	150.068i	−0.507123	+	0.327660i
$459$		−	20.6677i		−	0.0450278i
$460$		0			0
$461$	−316.563			−0.686687			−0.343343	−	0.939210i	$-0.611559\pi$
$461$	−316.563			−0.686687			−0.343343	+	0.939210i	$0.611559\pi$
$462$	10.4067	+	16.1066i	0.0225254	+	0.0348628i
$463$			491.208i			1.06093i	0.847708	+	0.530463i	$0.177982\pi$
$463$			491.208i			1.06093i	−0.847708	+	0.530463i	$0.822018\pi$
$464$	−377.972	−	427.692i	−0.814596	−	0.921751i
$465$		0			0
$466$	−0.878466	+	0.567591i	−0.00188512	+	0.00121801i
$467$			410.393i			0.878785i	0.898295	+	0.439393i	$0.144806\pi$
$467$			410.393i			0.878785i	−0.898295	+	0.439393i	$0.855194\pi$
$468$	−115.951	+	257.213i	−0.247758	+	0.549600i
$469$	−41.6014			−0.0887024
$470$		0			0
$471$		−	307.591i		−	0.653060i
$472$	−287.945	+	43.5550i	−0.610054	+	0.0922776i
$473$	335.141			0.708542
$474$	−191.657	+	123.833i	−0.404341	+	0.261251i
$475$		0			0
$476$	8.65243	+	3.90049i	0.0181774	+	0.00819431i
$477$	−7.65369			−0.0160455
$478$	−79.9851	−	123.794i	−0.167333	−	0.258983i
$479$		−	198.918i		−	0.415277i	−0.978206	−	0.207638i	$-0.933422\pi$
$479$		−	198.918i		−	0.415277i	0.978206	−	0.207638i	$-0.0665778\pi$
$480$		0			0
$481$	126.672			0.263351
$482$	−52.6981	+	34.0491i	−0.109332	+	0.0706413i
$483$			33.1455i			0.0686242i
$484$	57.3524	−	127.224i	0.118497	−	0.262860i
$485$		0			0
$486$	16.9195	+	26.1865i	0.0348138	+	0.0538816i
$487$		−	204.762i		−	0.420456i	−0.977652	−	0.210228i	$-0.932579\pi$
$487$		−	204.762i		−	0.420456i	0.977652	−	0.210228i	$-0.0674206\pi$
$488$	−10.4479	−	69.0721i	−0.0214097	−	0.141541i
$489$	167.797			0.343144
$490$		0			0
$491$		−	788.598i		−	1.60611i	−0.595908	−	0.803053i	$-0.703208\pi$
$491$		−	788.598i		−	1.60611i	0.595908	−	0.803053i	$-0.296792\pi$
$492$	−253.143	−	114.116i	−0.514519	−	0.231944i
$493$	−141.891			−0.287812
$494$	179.848	+	278.353i	0.364066	+	0.563468i
$495$		0			0
$496$	−710.456	+	627.864i	−1.43237	+	1.26586i
$497$	−35.3253			−0.0710771
$498$	377.985	−	244.222i	0.759006	−	0.490406i
$499$		−	740.385i		−	1.48374i	−0.670545	−	0.741869i	$-0.733940\pi$
$499$		−	740.385i		−	1.48374i	0.670545	−	0.741869i	$-0.266060\pi$
$500$		0			0
$501$	−264.319			−0.527583
$502$	−85.4717	−	132.285i	−0.170262	−	0.263517i
$503$			70.8800i			0.140914i	0.997515	+	0.0704572i	$0.0224458\pi$
$503$			70.8800i			0.140914i	−0.997515	+	0.0704572i	$0.977554\pi$
$504$	−14.1559	+	2.14124i	−0.0280871	+	0.00424850i
$505$		0			0
$506$	−500.068	+	323.102i	−0.988277	+	0.638541i
$507$		−	664.760i		−	1.31116i
$508$	508.588	+	229.270i	1.00116	+	0.451318i
$509$	522.642			1.02680			0.513400	−	0.858149i	$-0.328386\pi$
$509$	522.642			1.02680			0.513400	+	0.858149i	$0.328386\pi$
$510$		0			0
$511$		−	49.5139i		−	0.0968961i
$512$	−222.873	−	460.946i	−0.435299	−	0.900286i
$513$	36.6202			0.0713844
$514$	409.809	−	264.784i	0.797293	−	0.515144i
$515$		0			0
$516$	−102.831	+	228.110i	−0.199286	+	0.442074i
$517$	−686.813			−1.32846
$518$	3.48834	+	5.39894i	0.00673425	+	0.0104227i
$519$			269.807i			0.519859i
$520$		0			0
$521$	304.082			0.583650			0.291825	−	0.956472i	$-0.405738\pi$
$521$	304.082			0.583650			0.291825	+	0.956472i	$0.405738\pi$
$522$	179.779	−	116.158i	0.344405	−	0.222525i
$523$		−	174.416i		−	0.333491i	−0.986000	−	0.166746i	$-0.946674\pi$
$523$		−	174.416i		−	0.333491i	0.986000	−	0.166746i	$-0.0533259\pi$
$524$	231.507	+	104.362i	0.441806	+	0.199165i
$525$		0			0
$526$	111.509	+	172.584i	0.211995	+	0.328106i
$527$			235.701i			0.447251i
$528$	−170.297	−	192.698i	−0.322532	−	0.364959i
$529$	−500.081			−0.945333
$530$		0			0
$531$		−	109.208i		−	0.205664i
$532$	−6.91109	+	15.3308i	−0.0129908	+	0.0288174i
$533$	942.327			1.76797
$534$	−245.269	−	379.605i	−0.459305	−	0.710871i
$535$		0			0
$536$	551.628	−	83.4401i	1.02916	−	0.155672i
$537$	−218.240			−0.406405
$538$	207.708	−	134.204i	0.386075	−	0.249449i
$539$			451.399i			0.837476i
$540$		0			0
$541$	−262.199			−0.484655			−0.242328	−	0.970194i	$-0.577911\pi$
$541$	−262.199			−0.484655			−0.242328	+	0.970194i	$0.577911\pi$
$542$	360.750	+	558.337i	0.665591	+	1.03014i
$543$			600.545i			1.10598i
$544$	−122.553	−	34.3657i	−0.225281	−	0.0631722i
$545$		0			0
$546$	40.8091	−	26.3674i	0.0747420	−	0.0482920i
$547$			146.179i			0.267237i	0.991033	+	0.133619i	$0.0426598\pi$
$547$			146.179i			0.267237i	−0.991033	+	0.133619i	$0.957340\pi$
$548$	227.113	−	503.804i	0.414440	−	0.919350i
$549$	26.1967			0.0477171
$550$		0			0
$551$		−	251.411i		−	0.456281i
$552$	−66.4800	−	439.504i	−0.120435	−	0.796203i
$553$	39.2944			0.0710568
$554$	−211.522	+	136.668i	−0.381809	+	0.246693i
$555$		0			0
$556$	−109.244	−	49.2468i	−0.196482	−	0.0885734i
$557$	−187.700			−0.336984			−0.168492	−	0.985703i	$-0.553890\pi$
$557$	−187.700			−0.336984			−0.168492	+	0.985703i	$0.553890\pi$
$558$	−192.955	−	298.638i	−0.345797	−	0.535194i
$559$		−	849.142i		−	1.51904i
$560$		0			0
$561$	−63.9296			−0.113957
$562$	−88.2982	+	57.0509i	−0.157114	+	0.101514i
$563$		−	447.848i		−	0.795467i	−0.917501	−	0.397734i	$-0.869797\pi$
$563$		−	447.848i		−	0.795467i	0.917501	−	0.397734i	$-0.130203\pi$
$564$	210.736	−	467.473i	0.373645	−	0.828853i
$565$		0			0
$566$	−216.305	−	334.777i	−0.382164	−	0.591479i
$567$		−	5.36886i		−	0.00946888i
$568$	468.408	−	70.8520i	0.824662	−	0.124740i
$569$	1078.91			1.89615			0.948077	−	0.318042i	$-0.103025\pi$
$569$	1078.91			1.89615			0.948077	+	0.318042i	$0.103025\pi$
$570$		0			0
$571$			936.324i			1.63980i	0.572509	+	0.819899i	$0.305970\pi$
$571$			936.324i			1.63980i	−0.572509	+	0.819899i	$0.694030\pi$
$572$	795.613	+	358.660i	1.39093	+	0.627028i
$573$	230.638			0.402510
$574$	25.9502	+	40.1634i	0.0452095	+	0.0699711i
$575$		0			0
$576$	183.411	−	56.7851i	0.318421	−	0.0985853i
$577$	544.832			0.944250			0.472125	−	0.881532i	$-0.343487\pi$
$577$	544.832			0.944250			0.472125	+	0.881532i	$0.343487\pi$
$578$	458.904	−	296.505i	0.793951	−	0.512985i
$579$		−	235.986i		−	0.407575i
$580$		0			0
$581$	−77.4960			−0.133384
$582$	−175.044	−	270.917i	−0.300763	−	0.465494i
$583$			23.6745i			0.0406080i
$584$	99.3101	+	656.547i	0.170052	+	1.12422i
$585$		0			0
$586$	171.616	−	110.884i	0.292861	−	0.189222i
$587$		−	337.889i		−	0.575619i	−0.957688	−	0.287810i	$-0.907073\pi$
$587$		−	337.889i		−	0.575619i	0.957688	−	0.287810i	$-0.0929271\pi$
$588$	−307.241	−	138.503i	−0.522519	−	0.235550i
$589$	−417.628			−0.709045
$590$		0			0
$591$			129.721i			0.219494i
$592$	−57.0836	−	64.5926i	−0.0964249	−	0.109109i
$593$	−567.269			−0.956608			−0.478304	−	0.878194i	$-0.658748\pi$
$593$	−567.269			−0.956608			−0.478304	+	0.878194i	$0.658748\pi$
$594$	81.0002	−	52.3355i	0.136364	−	0.0881069i
$595$		0			0
$596$	−77.8906	+	172.784i	−0.130689	+	0.289906i
$597$	435.792			0.729969
$598$	818.640	+	1267.02i	1.36896	+	2.11876i
$599$			762.966i			1.27373i	0.770974	+	0.636867i	$0.219770\pi$
$599$			762.966i			1.27373i	−0.770974	+	0.636867i	$0.780230\pi$
$600$		0			0
$601$	−790.102			−1.31464			−0.657322	−	0.753609i	$-0.728311\pi$
$601$	−790.102			−1.31464			−0.657322	+	0.753609i	$0.728311\pi$
$602$	36.1917	−	23.3841i	0.0601192	−	0.0388440i
$603$			209.214i			0.346955i
$604$	399.680	+	180.175i	0.661722	+	0.298302i
$605$		0			0
$606$	−6.88212	−	10.6515i	−0.0113566	−	0.0175768i
$607$			522.994i			0.861605i	0.902446	+	0.430802i	$0.141769\pi$
$607$			522.994i			0.861605i	−0.902446	+	0.430802i	$0.858231\pi$
$608$	60.8909	−	217.146i	0.100150	−	0.357148i
$609$	−36.8591			−0.0605240
$610$		0			0
$611$			1740.17i			2.84807i
$612$	19.6156	−	43.5131i	0.0320516	−	0.0710999i
$613$	−1026.91			−1.67522			−0.837609	−	0.546270i	$-0.816047\pi$
$613$	−1026.91			−1.67522			−0.837609	+	0.546270i	$0.816047\pi$
$614$	−356.431	−	551.652i	−0.580506	−	0.898455i
$615$		0			0
$616$	6.62332	+	43.7872i	0.0107521	+	0.0710831i
$617$	479.223			0.776698			0.388349	−	0.921512i	$-0.373046\pi$
$617$	479.223			0.776698			0.388349	+	0.921512i	$0.373046\pi$
$618$	−440.563	+	284.655i	−0.712886	+	0.460607i
$619$		−	507.654i		−	0.820119i	−0.912059	−	0.410059i	$-0.865508\pi$
$619$		−	507.654i		−	0.820119i	0.912059	−	0.410059i	$-0.134492\pi$
$620$		0			0
$621$	166.689			0.268420
$622$	103.587	+	160.322i	0.166538	+	0.257753i
$623$			77.8282i			0.124925i
$624$	−488.237	+	431.479i	−0.782432	+	0.691473i
$625$		0			0
$626$	924.609	−	597.405i	1.47701	−	0.954321i
$627$		−	113.274i		−	0.180660i
$628$	291.932	−	647.591i	0.464860	−	1.03120i
$629$	−21.4293			−0.0340688
$630$		0			0
$631$		−	460.186i		−	0.729297i	−0.931145	−	0.364648i	$-0.881189\pi$
$631$		−	460.186i		−	0.729297i	0.931145	−	0.364648i	$-0.118811\pi$
$632$	−521.037	+	78.8128i	−0.824426	+	0.124704i
$633$	395.259			0.624423
$634$	738.122	−	476.912i	1.16423	−	0.752228i
$635$		0			0
$636$	−16.1138	−	7.26405i	−0.0253362	−	0.0114215i
$637$	1143.71			1.79546
$638$	−359.302	−	556.095i	−0.563169	−	0.871622i
$639$			177.651i			0.278014i
$640$		0			0
$641$	250.774			0.391223			0.195612	−	0.980681i	$-0.437331\pi$
$641$	250.774			0.391223			0.195612	+	0.980681i	$0.437331\pi$
$642$	−240.942	+	155.677i	−0.375299	+	0.242487i
$643$			590.355i			0.918126i	0.888404	+	0.459063i	$0.151815\pi$
$643$			590.355i			0.918126i	−0.888404	+	0.459063i	$0.848185\pi$
$644$	−31.4581	+	69.7834i	−0.0488480	+	0.108359i
$645$		0			0
$646$	−30.4252	−	47.0894i	−0.0470979	−	0.0728939i
$647$			319.341i			0.493572i	0.969070	+	0.246786i	$0.0793744\pi$
$647$			319.341i			0.493572i	−0.969070	+	0.246786i	$0.920626\pi$
$648$	10.7683	+	71.1902i	0.0166178	+	0.109861i
$649$	−337.803			−0.520497
$650$		0			0
$651$			61.2280i			0.0940523i
$652$	353.274	+	159.255i	0.541832	+	0.244256i
$653$	−88.5949			−0.135674			−0.0678369	−	0.997696i	$-0.521610\pi$
$653$	−88.5949			−0.135674			−0.0678369	+	0.997696i	$0.521610\pi$
$654$	−13.8521	−	21.4390i	−0.0211806	−	0.0327814i
$655$		0			0
$656$	−424.652	−	480.512i	−0.647335	−	0.732488i
$657$	−249.006			−0.379004
$658$	−74.1688	+	47.9216i	−0.112719	+	0.0728292i
$659$			758.423i			1.15087i	0.817847	+	0.575435i	$0.195167\pi$
$659$			758.423i			1.15087i	−0.817847	+	0.575435i	$0.804833\pi$
$660$		0			0
$661$	527.327			0.797771			0.398885	−	0.917001i	$-0.369397\pi$
$661$	527.327			0.797771			0.398885	+	0.917001i	$0.369397\pi$
$662$	520.900	+	806.203i	0.786859	+	1.21783i
$663$			161.978i			0.244310i
$664$	1027.59	−	155.434i	1.54757	−	0.234087i
$665$		0			0
$666$	27.1513	−	17.5429i	0.0407677	−	0.0263407i
$667$		−	1144.38i		−	1.71571i
$668$	−556.488	−	250.863i	−0.833066	−	0.375544i
$669$	148.878			0.222538
$670$		0			0
$671$		−	81.0318i		−	0.120763i
$672$	−31.8356	−	8.92717i	−0.0473744	−	0.0132845i
$673$	−120.657			−0.179283			−0.0896415	−	0.995974i	$-0.528572\pi$
$673$	−120.657			−0.179283			−0.0896415	+	0.995974i	$0.528572\pi$
$674$	98.8493	−	63.8681i	0.146661	−	0.0947598i
$675$		0			0
$676$	630.918	−	1399.56i	0.933311	−	2.07036i
$677$	219.196			0.323776			0.161888	−	0.986809i	$-0.448242\pi$
$677$	219.196			0.323776			0.161888	+	0.986809i	$0.448242\pi$
$678$	−122.266	−	189.232i	−0.180333	−	0.279103i
$679$			55.5446i			0.0818035i
$680$		0			0
$681$	−489.057			−0.718145
$682$	−923.751	+	596.850i	−1.35447	+	0.875146i
$683$			205.502i			0.300881i	0.988619	+	0.150441i	$0.0480693\pi$
$683$			205.502i			0.300881i	−0.988619	+	0.150441i	$0.951931\pi$
$684$	77.0988	+	34.7559i	0.112718	+	0.0508128i
$685$		0			0
$686$	63.2222	+	97.8496i	0.0921606	+	0.142638i
$687$		−	239.478i		−	0.348585i
$688$	−432.995	+	382.659i	−0.629354	+	0.556190i
$689$	59.9837			0.0870591
$690$		0			0
$691$		−	109.536i		−	0.158519i	−0.996854	−	0.0792593i	$-0.974744\pi$
$691$		−	109.536i		−	0.158519i	0.996854	−	0.0792593i	$-0.0252555\pi$
$692$	−256.071	+	568.042i	−0.370045	+	0.820869i
$693$	−16.6070			−0.0239639
$694$	13.1857	+	20.4077i	0.0189996	+	0.0294059i
$695$		0			0
$696$	488.746	−	73.9284i	0.702221	−	0.106219i
$697$	−159.415			−0.228716
$698$	51.9543	−	33.5685i	0.0744331	−	0.0480924i
$699$		−	0.905758i		−	0.00129579i
$700$		0			0
$701$	168.847			0.240865			0.120433	−	0.992721i	$-0.461572\pi$
$701$	168.847			0.240865			0.120433	+	0.992721i	$0.461572\pi$
$702$	−132.602	−	205.229i	−0.188892	−	0.292349i
$703$		−	37.9695i		−	0.0540106i
$704$	−175.648	−	567.327i	−0.249500	−	0.805863i
$705$		0			0
$706$	−483.909	+	312.661i	−0.685424	+	0.442863i
$707$			2.18382i			0.00308885i
$708$	103.648	−	229.922i	0.146396	−	0.324749i
$709$	−554.846			−0.782576			−0.391288	−	0.920268i	$-0.627970\pi$
$709$	−554.846			−0.782576			−0.391288	+	0.920268i	$0.627970\pi$
$710$		0			0
$711$		−	197.612i		−	0.277935i
$712$	−156.100	−	1031.99i	−0.219242	−	1.44942i
$713$	−1900.97			−2.66616
$714$	−6.90374	+	4.46062i	−0.00966911	+	0.00624737i
$715$		0			0
$716$	−459.474	−	207.130i	−0.641723	−	0.289287i
$717$	127.640			0.178019
$718$	−720.600	−	1115.28i	−1.00362	−	1.55331i
$719$			377.485i			0.525014i	0.964930	+	0.262507i	$0.0845494\pi$
$719$			377.485i			0.525014i	−0.964930	+	0.262507i	$0.915451\pi$
$720$		0			0
$721$	90.3261			0.125279
$722$	−522.995	+	337.915i	−0.724369	+	0.468027i
$723$		−	54.3353i		−	0.0751525i
$724$	−569.972	+	1264.37i	−0.787255	+	1.74636i
$725$		0			0
$726$	65.5885	+	101.512i	0.0903423	+	0.139824i
$727$		−	173.183i		−	0.238216i	−0.992881	−	0.119108i	$-0.961997\pi$
$727$		−	173.183i		−	0.238216i	0.992881	−	0.119108i	$-0.0380035\pi$
$728$	110.943	−	16.7814i	0.152394	−	0.0230514i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$			143.651i			0.196513i
$732$	55.1536	+	24.8631i	0.0753464	+	0.0339659i
$733$	−278.722			−0.380249			−0.190124	−	0.981760i	$-0.560889\pi$
$733$	−278.722			−0.380249			−0.190124	+	0.981760i	$0.560889\pi$
$734$	6.60489	+	10.2225i	0.00899849	+	0.0139270i
$735$		0			0
$736$	277.165	−	988.412i	0.376583	−	1.34295i
$737$	647.142			0.878075
$738$	201.982	−	130.504i	0.273688	−	0.176834i
$739$			521.363i			0.705498i	0.935718	+	0.352749i	$0.114753\pi$
$739$			521.363i			0.705498i	−0.935718	+	0.352749i	$0.885247\pi$
$740$		0			0
$741$	−287.001			−0.387315
$742$	1.65186	+	2.55660i	0.00222622	+	0.00344555i
$743$			1277.93i			1.71996i	0.510326	+	0.859981i	$0.329525\pi$
$743$			1277.93i			1.71996i	−0.510326	+	0.859981i	$0.670475\pi$
$744$	−122.805	−	811.874i	−0.165061	−	1.09123i
$745$		0			0
$746$	−343.936	+	222.223i	−0.461041	+	0.297886i
$747$			389.728i			0.521724i
$748$	−134.595	−	60.6751i	−0.179940	−	0.0811164i
$749$	49.3989			0.0659532
$750$		0			0
$751$			1165.31i			1.55168i	0.630930	+	0.775840i	$0.282673\pi$
$751$			1165.31i			1.55168i	−0.630930	+	0.775840i	$0.717327\pi$
$752$	887.350	−	784.194i	1.17999	−	1.04281i
$753$	136.395			0.181136
$754$	−1408.97	+	910.359i	−1.86866	+	1.20737i
$755$		0			0
$756$	5.09554	−	11.3034i	0.00674013	−	0.0149516i
$757$	−1063.75			−1.40522			−0.702611	−	0.711574i	$-0.747983\pi$
$757$	−1063.75			−1.40522			−0.702611	+	0.711574i	$0.747983\pi$
$758$	436.685	+	675.861i	0.576101	+	0.891638i
$759$		−	515.604i		−	0.679320i
$760$		0			0
$761$	−677.847			−0.890732			−0.445366	−	0.895349i	$-0.646926\pi$
$761$	−677.847			−0.890732			−0.445366	+	0.895349i	$0.646926\pi$
$762$	−405.800	+	262.194i	−0.532546	+	0.344087i
$763$			4.39551i			0.00576083i
$764$	485.577	+	218.897i	0.635572	+	0.286514i
$765$		0			0
$766$	−360.078	−	557.296i	−0.470076	−	0.727541i
$767$			855.887i			1.11589i
$768$	440.040	+	54.5201i	0.572969	+	0.0709898i
$769$	−1289.59			−1.67697			−0.838486	−	0.544922i	$-0.816559\pi$
$769$	−1289.59			−1.67697			−0.838486	+	0.544922i	$0.816559\pi$
$770$		0			0
$771$			422.540i			0.548042i
$772$	223.972	−	496.836i	0.290119	−	0.643570i
$773$	750.339			0.970684			0.485342	−	0.874324i	$-0.338695\pi$
$773$	750.339			0.970684			0.485342	+	0.874324i	$0.338695\pi$
$774$	−117.599	−	182.008i	−0.151936	−	0.235153i
$775$		0			0
$776$	−111.406	−	736.513i	−0.143564	−	0.949114i
$777$	−5.56667			−0.00716432
$778$	1047.07	−	676.532i	1.34585	−	0.869578i
$779$		−	282.460i		−	0.362593i
$780$		0			0
$781$	549.512			0.703600
$782$	−138.491	−	214.343i	−0.177098	−	0.274096i
$783$			185.365i			0.236736i
$784$	−515.402	−	583.200i	−0.657400	−	0.743877i
$785$		0			0
$786$	−184.718	+	119.349i	−0.235011	+	0.151844i
$787$		−	825.185i		−	1.04852i	−0.851558	−	0.524260i	$-0.824342\pi$
$787$		−	825.185i		−	1.04852i	0.851558	−	0.524260i	$-0.175658\pi$
$788$	−123.117	+	273.110i	−0.156240	+	0.346586i
$789$	−177.946			−0.225533
$790$		0			0
$791$			38.7971i			0.0490482i
$792$	220.206	−	33.3087i	0.278038	−	0.0420564i
$793$	−205.309			−0.258902
$794$	−597.106	+	385.799i	−0.752022	+	0.485893i
$795$		0			0
$796$	917.500	+	413.606i	1.15264	+	0.519606i
$797$	−1113.70			−1.39737			−0.698684	−	0.715430i	$-0.746231\pi$
$797$	−1113.70			−1.39737			−0.698684	+	0.715430i	$0.746231\pi$
$798$	−7.90356	−	12.2324i	−0.00990421	−	0.0153288i
$799$		−	294.388i		−	0.368445i
$800$		0			0
$801$	391.398			0.488637
$802$	912.043	−	589.285i	1.13721	−	0.734770i
$803$			770.226i			0.959186i
$804$	−198.563	+	440.471i	−0.246969	+	0.547849i
$805$		0			0
$806$	1512.23	+	2340.50i	1.87622	+	2.90384i
$807$			214.161i			0.265379i
$808$	−4.38009	−	28.9571i	−0.00542090	−	0.0358380i
$809$	−1049.54			−1.29733			−0.648664	−	0.761075i	$-0.724672\pi$
$809$	−1049.54			−1.29733			−0.648664	+	0.761075i	$0.724672\pi$
$810$		0			0
$811$		−	424.482i		−	0.523406i	−0.965148	−	0.261703i	$-0.915716\pi$
$811$		−	424.482i		−	0.523406i	0.965148	−	0.261703i	$-0.0842841\pi$
$812$	−77.6018	−	34.9827i	−0.0955688	−	0.0430821i
$813$	−575.683			−0.708097
$814$	−54.2638	−	83.9847i	−0.0666632	−	0.103175i
$815$		0			0
$816$	82.5959	−	72.9940i	0.101220	−	0.0894534i
$817$	−254.528			−0.311540
$818$	182.259	−	117.761i	0.222811	−	0.143962i
$819$			42.0769i			0.0513760i
$820$		0			0
$821$	−1257.98			−1.53225			−0.766126	−	0.642690i	$-0.777818\pi$
$821$	−1257.98			−1.53225			−0.766126	+	0.642690i	$0.777818\pi$
$822$	259.728	+	401.983i	0.315970	+	0.489031i
$823$			729.181i			0.886004i	0.896521	+	0.443002i	$0.146087\pi$
$823$			729.181i			0.886004i	−0.896521	+	0.443002i	$0.853913\pi$
$824$	−1197.71	+	181.167i	−1.45353	+	0.219863i
$825$		0			0
$826$	−36.4792	+	23.5698i	−0.0441637	+	0.0285349i
$827$		−	72.5882i		−	0.0877729i	−0.999037	−	0.0438865i	$-0.986026\pi$
$827$		−	72.5882i		−	0.0877729i	0.999037	−	0.0438865i	$-0.0139740\pi$
$828$	350.941	+	158.203i	0.423842	+	0.191067i
$829$	900.257			1.08596			0.542978	−	0.839747i	$-0.317297\pi$
$829$	900.257			1.08596			0.542978	+	0.839747i	$0.317297\pi$
$830$		0			0
$831$		−	218.093i		−	0.262447i
$832$	−1437.43	+	445.038i	−1.72768	+	0.534901i
$833$	−193.482			−0.232272
$834$	87.1653	−	56.3189i	0.104515	−	0.0675286i
$835$		0			0
$836$	107.507	−	238.483i	0.128597	−	0.285266i
$837$	307.916			0.367881
$838$	186.877	+	289.232i	0.223004	+	0.345145i
$839$		−	71.4721i		−	0.0851872i	−0.999092	−	0.0425936i	$-0.986438\pi$
$839$		−	71.4721i		−	0.0851872i	0.999092	−	0.0425936i	$-0.0135621\pi$
$840$		0			0
$841$	431.594			0.513191
$842$	−803.851	+	519.381i	−0.954693	+	0.616842i
$843$		−	91.0414i		−	0.107997i
$844$	832.165	+	375.138i	0.985978	+	0.444476i
$845$		0			0
$846$	240.998	+	372.995i	0.284868	+	0.440893i
$847$		−	20.8124i		−	0.0245719i
$848$	−27.0312	−	30.5870i	−0.0318764	−	0.0360695i
$849$	345.178			0.406570
$850$		0			0
$851$		−	172.831i		−	0.203091i
$852$	−168.607	+	374.020i	−0.197896	+	0.438991i
$853$	−882.349			−1.03441			−0.517203	−	0.855862i	$-0.673027\pi$
$853$	−882.349			−1.03441			−0.517203	+	0.855862i	$0.673027\pi$
$854$	−5.65391	−	8.75061i	−0.00662050	−	0.0102466i
$855$		0			0
$856$	−655.022	+	99.0796i	−0.765213	+	0.115747i
$857$	370.111			0.431868			0.215934	−	0.976408i	$-0.430720\pi$
$857$	370.111			0.431868			0.215934	+	0.976408i	$0.430720\pi$
$858$	−634.817	+	410.165i	−0.739880	+	0.478048i
$859$			1039.00i			1.20955i	0.796397	+	0.604774i	$0.206736\pi$
$859$			1039.00i			1.20955i	−0.796397	+	0.604774i	$0.793264\pi$
$860$		0			0
$861$	−41.4112			−0.0480966
$862$	315.546	+	488.373i	0.366062	+	0.566558i
$863$			72.0666i			0.0835071i	0.999128	+	0.0417535i	$0.0132944\pi$
$863$			72.0666i			0.0835071i	−0.999128	+	0.0417535i	$0.986706\pi$
$864$	−44.8948	+	160.101i	−0.0519616	+	0.185303i
$865$		0			0
$866$	90.3306	−	58.3640i	0.104308	−	0.0673950i
$867$			473.161i			0.545745i
$868$	−58.1110	+	128.907i	−0.0669482	+	0.148511i
$869$	−611.254			−0.703399
$870$		0			0
$871$		−	1639.66i		−	1.88250i
$872$	−8.81609	−	58.2838i	−0.0101102	−	0.0668393i
$873$	279.334			0.319970
$874$	379.785	−	245.385i	0.434536	−	0.280761i
$875$		0			0
$876$	−524.247	−	236.329i	−0.598456	−	0.269782i
$877$	−14.4444			−0.0164703			−0.00823514	−	0.999966i	$-0.502621\pi$
$877$	−14.4444			−0.0164703			−0.00823514	+	0.999966i	$0.502621\pi$
$878$	−356.720	−	552.099i	−0.406287	−	0.628815i
$879$			176.948i			0.201306i
$880$		0			0
$881$	1589.22			1.80388			0.901942	−	0.431858i	$-0.142142\pi$
$881$	1589.22			1.80388			0.901942	+	0.431858i	$0.142142\pi$
$882$	245.146	−	158.393i	0.277944	−	0.179584i
$883$		−	495.149i		−	0.560758i	−0.959889	−	0.280379i	$-0.909540\pi$
$883$		−	495.149i		−	0.560758i	0.959889	−	0.280379i	$-0.0904601\pi$
$884$	−153.732	+	341.022i	−0.173905	+	0.385772i
$885$		0			0
$886$	465.533	+	720.510i	0.525432	+	0.813216i
$887$		−	1384.20i		−	1.56054i	−0.625440	−	0.780272i	$-0.715081\pi$
$887$		−	1384.20i		−	1.56054i	0.625440	−	0.780272i	$-0.284919\pi$
$888$	73.8132	−	11.1651i	0.0831230	−	0.0125733i
$889$	83.1988			0.0935870
$890$		0			0
$891$			83.5166i			0.0937336i
$892$	313.443	+	141.299i	0.351393	+	0.158407i
$893$	521.611			0.584111
$894$	−89.0760	−	137.864i	−0.0996376	−	0.154210i
$895$		0			0
$896$	−58.5528	−	49.0099i	−0.0653491	−	0.0546985i
$897$	−1306.38			−1.45639
$898$	−687.448	+	444.171i	−0.765533	+	0.494623i
$899$		−	2113.95i		−	2.35145i
$900$		0			0
$901$	−10.1475			−0.0112625
$902$	−403.676	−	624.773i	−0.447534	−	0.692653i
$903$			37.3161i			0.0413246i
$904$	−77.8155	−	514.444i	−0.0860791	−	0.569075i
$905$		0			0
$906$	−318.903	+	206.049i	−0.351991	+	0.227427i
$907$			957.750i			1.05595i	0.849259	+	0.527977i	$0.177049\pi$
$907$			957.750i			1.05595i	−0.849259	+	0.527977i	$0.822951\pi$
$908$	−1029.64	−	464.160i	−1.13397	−	0.511189i
$909$	10.9824			0.0120819
$910$		0			0
$911$			704.979i			0.773852i	0.922111	+	0.386926i	$0.126463\pi$
$911$			704.979i			0.773852i	−0.922111	+	0.386926i	$0.873537\pi$
$912$	129.335	+	146.348i	0.141814	+	0.160469i
$913$	1205.51			1.32038
$914$	1291.08	−	834.185i	1.41256	−	0.912675i
$915$		0			0
$916$	227.287	−	504.189i	0.248130	−	0.550424i
$917$	37.8717			0.0412996
$918$	22.4325	+	34.7190i	0.0244362	+	0.0378202i
$919$			607.048i			0.660553i	0.943884	+	0.330277i	$0.107142\pi$
$919$			607.048i			0.660553i	−0.943884	+	0.330277i	$0.892858\pi$
$920$		0			0
$921$	568.790			0.617578
$922$	531.782	−	343.593i	0.576770	−	0.372660i
$923$		−	1392.29i		−	1.50844i
$924$	−34.9638	−	15.7616i	−0.0378396	−	0.0170580i
$925$		0			0
$926$	−533.151	−	825.163i	−0.575757	−	0.891104i
$927$		−	454.250i		−	0.490022i
$928$	1099.15	+	308.219i	1.18443	+	0.332132i
$929$	1011.21			1.08849			0.544247	−	0.838925i	$-0.316815\pi$
$929$	1011.21			1.08849			0.544247	+	0.838925i	$0.316815\pi$
$930$		0			0
$931$		−	342.822i		−	0.368230i
$932$	0.859647	−	1.90695i	0.000922368	−	0.00204608i
$933$	−165.303			−0.177174
$934$	−445.434	−	689.403i	−0.476910	−	0.738119i
$935$		0			0
$936$	−84.3938	−	557.934i	−0.0901643	−	0.596083i
$937$	363.105			0.387519			0.193760	−	0.981049i	$-0.437932\pi$
$937$	363.105			0.387519			0.193760	+	0.981049i	$0.437932\pi$
$938$	69.8846	−	45.1536i	0.0745039	−	0.0481381i
$939$			953.334i			1.01527i
$940$		0			0
$941$	−1106.51			−1.17588			−0.587942	−	0.808903i	$-0.700061\pi$
$941$	−1106.51			−1.17588			−0.587942	+	0.808903i	$0.700061\pi$
$942$	333.855	+	516.711i	0.354411	+	0.548525i
$943$		−	1285.71i		−	1.36342i
$944$	436.435	−	385.698i	0.462325	−	0.408579i
$945$		0			0
$946$	−562.990	+	363.757i	−0.595127	+	0.384521i
$947$			553.561i			0.584541i	0.956336	+	0.292271i	$0.0944108\pi$
$947$			553.561i			0.584541i	−0.956336	+	0.292271i	$0.905589\pi$
$948$	187.552	−	416.044i	0.197839	−	0.438865i
$949$	1951.51			2.05639
$950$		0			0
$951$			761.053i			0.800266i
$952$	−18.7684	+	2.83894i	−0.0197147	+	0.00298208i
$953$	1674.84			1.75744			0.878718	−	0.477342i	$-0.158400\pi$
$953$	1674.84			1.75744			0.878718	+	0.477342i	$0.158400\pi$
$954$	12.8571	−	8.30720i	0.0134771	−	0.00870776i
$955$		0			0
$956$	268.728	+	121.142i	0.281096	+	0.126717i
$957$	573.371			0.599134
$958$	215.902	+	334.154i	0.225368	+	0.348804i
$959$		−	82.4162i		−	0.0859398i
$960$		0			0
$961$	−2550.57			−2.65408
$962$	−212.791	+	137.488i	−0.221196	+	0.142919i
$963$		−	248.428i		−	0.257973i
$964$	51.5692	−	114.396i	0.0534950	−	0.118668i
$965$		0			0
$966$	−35.9757	−	55.6799i	−0.0372419	−	0.0576396i
$967$		−	786.720i		−	0.813568i	−0.913524	−	0.406784i	$-0.866650\pi$
$967$		−	786.720i		−	0.813568i	0.913524	−	0.406784i	$-0.133350\pi$
$968$	41.7435	+	275.969i	0.0431234	+	0.285092i
$969$	48.5524			0.0501057
$970$		0			0
$971$		−	1289.75i		−	1.32827i	−0.747612	−	0.664135i	$-0.768800\pi$
$971$		−	1289.75i		−	1.32827i	0.747612	−	0.664135i	$-0.231200\pi$
$972$	−56.8448	−	25.6255i	−0.0584823	−	0.0263637i
$973$	−17.8710			−0.0183669
$974$	222.246	+	343.972i	0.228178	+	0.353154i
$975$		0			0
$976$	92.5210	+	104.692i	0.0947961	+	0.107266i
$977$	−495.847			−0.507520			−0.253760	−	0.967267i	$-0.581667\pi$
$977$	−495.847			−0.507520			−0.253760	+	0.967267i	$0.581667\pi$
$978$	−281.876	+	182.125i	−0.288217	+	0.186222i
$979$		−	1210.68i		−	1.23665i
$980$		0			0
$981$	22.1051			0.0225332
$982$	855.933	+	1324.74i	0.871622	+	1.34902i
$983$		−	967.035i		−	0.983759i	−0.870663	−	0.491880i	$-0.836310\pi$
$983$		−	967.035i		−	0.983759i	0.870663	−	0.491880i	$-0.163690\pi$
$984$	549.106	−	83.0585i	0.558035	−	0.0844091i
$985$		0			0
$986$	238.358	−	154.007i	0.241742	−	0.156194i
$987$		−	76.4730i		−	0.0774803i
$988$	−604.241	−	272.390i	−0.611580	−	0.275698i
$989$	−1158.57			−1.17145
$990$		0			0
$991$			1203.68i			1.21461i	0.794469	+	0.607305i	$0.207749\pi$
$991$			1203.68i			1.21461i	−0.794469	+	0.607305i	$0.792251\pi$
$992$	511.994	−	1825.84i	0.516123	−	1.84057i
$993$	−831.249			−0.837109
$994$	59.3417	−	38.3416i	0.0596999	−	0.0385730i
$995$		0			0
$996$	−369.888	+	820.519i	−0.371373	+	0.823814i
$997$	1274.55			1.27838			0.639192	−	0.769047i	$-0.279269\pi$
$997$	1274.55			1.27838			0.639192	+	0.769047i	$0.279269\pi$
$998$	803.603	+	1243.74i	0.805214	+	1.24624i
$999$			27.9948i			0.0280228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.c.d.151.4		8
3.2	odd	2		900.3.c.u.451.5		8
4.3	odd	2	inner	300.3.c.d.151.3		8
5.2	odd	4		300.3.f.b.199.3		16
5.3	odd	4		300.3.f.b.199.14		16
5.4	even	2		60.3.c.a.31.5	✓	8
12.11	even	2		900.3.c.u.451.6		8
15.2	even	4		900.3.f.f.199.14		16
15.8	even	4		900.3.f.f.199.3		16
15.14	odd	2		180.3.c.b.91.4		8
20.3	even	4		300.3.f.b.199.4		16
20.7	even	4		300.3.f.b.199.13		16
20.19	odd	2		60.3.c.a.31.6	yes	8
40.19	odd	2		960.3.e.c.511.6		8
40.29	even	2		960.3.e.c.511.1		8
60.23	odd	4		900.3.f.f.199.13		16
60.47	odd	4		900.3.f.f.199.4		16
60.59	even	2		180.3.c.b.91.3		8
120.29	odd	2		2880.3.e.j.2431.7		8
120.59	even	2		2880.3.e.j.2431.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.5	✓	8	5.4	even	2
60.3.c.a.31.6	yes	8	20.19	odd	2
180.3.c.b.91.3		8	60.59	even	2
180.3.c.b.91.4		8	15.14	odd	2
300.3.c.d.151.3		8	4.3	odd	2	inner
300.3.c.d.151.4		8	1.1	even	1	trivial
300.3.f.b.199.3		16	5.2	odd	4
300.3.f.b.199.4		16	20.3	even	4
300.3.f.b.199.13		16	20.7	even	4
300.3.f.b.199.14		16	5.3	odd	4
900.3.c.u.451.5		8	3.2	odd	2
900.3.c.u.451.6		8	12.11	even	2
900.3.f.f.199.3		16	15.8	even	4
900.3.f.f.199.4		16	60.47	odd	4
900.3.f.f.199.13		16	60.23	odd	4
900.3.f.f.199.14		16	15.2	even	4
960.3.e.c.511.1		8	40.29	even	2
960.3.e.c.511.6		8	40.19	odd	2
2880.3.e.j.2431.6		8	120.59	even	2
2880.3.e.j.2431.7		8	120.29	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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67986 + 1.08539i) q^{2} -1.73205i q^{3} +(1.64388 - 3.64660i) q^{4} +(1.87994 + 2.90961i) q^{6} -0.596540i q^{7} +(1.19648 + 7.91002i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-1.67986 + 1.08539i) q^{2} -1.73205i q^{3} +(1.64388 - 3.64660i) q^{4} +(1.87994 + 2.90961i) q^{6} -0.596540i q^{7} +(1.19648 + 7.91002i) q^{8} -3.00000 q^{9} +9.27963i q^{11} +(-6.31609 - 2.84728i) q^{12} +23.5117 q^{13} +(0.647476 + 1.00210i) q^{14} +(-10.5953 - 11.9891i) q^{16} -3.97751 q^{17} +(5.03959 - 3.25616i) q^{18} -7.04756i q^{19} -1.03324 q^{21} +(-10.0720 - 15.5885i) q^{22} -32.0793i q^{23} +(13.7006 - 2.07237i) q^{24} +(-39.4964 + 25.5192i) q^{26} +5.19615i q^{27} +(-2.17534 - 0.980637i) q^{28} +35.6734 q^{29} -59.2585i q^{31} +(30.8115 + 8.64000i) q^{32} +16.0728 q^{33} +(6.68167 - 4.31713i) q^{34} +(-4.93163 + 10.9398i) q^{36} +5.38761 q^{37} +(7.64932 + 11.8389i) q^{38} -40.7234i q^{39} +40.0791 q^{41} +(1.73570 - 1.12146i) q^{42} -36.1157i q^{43} +(33.8391 + 15.2545i) q^{44} +(34.8184 + 53.8888i) q^{46} +74.0131i q^{47} +(-20.7657 + 18.3517i) q^{48} +48.6441 q^{49} +6.88925i q^{51} +(38.6503 - 85.7376i) q^{52} +2.55123 q^{53} +(-5.63983 - 8.72882i) q^{54} +(4.71864 - 0.713748i) q^{56} -12.2067 q^{57} +(-59.9265 + 38.7194i) q^{58} +36.4026i q^{59} -8.73223 q^{61} +(64.3183 + 99.5461i) q^{62} +1.78962i q^{63} +(-61.1369 + 18.9284i) q^{64} +(-27.0001 + 17.4452i) q^{66} -69.7379i q^{67} +(-6.53853 + 14.5044i) q^{68} -55.5630 q^{69} -59.2170i q^{71} +(-3.58944 - 23.7301i) q^{72} +83.0019 q^{73} +(-9.05044 + 5.84763i) q^{74} +(-25.6996 - 11.5853i) q^{76} +5.53566 q^{77} +(44.2006 + 68.4098i) q^{78} +65.8705i q^{79} +9.00000 q^{81} +(-67.3274 + 43.5013i) q^{82} -129.909i q^{83} +(-1.69851 + 3.76780i) q^{84} +(39.1995 + 60.6695i) q^{86} -61.7882i q^{87} +(-73.4020 + 11.1029i) q^{88} -130.466 q^{89} -14.0256i q^{91} +(-116.980 - 52.7344i) q^{92} -102.639 q^{93} +(-80.3327 - 124.332i) q^{94} +(14.9649 - 53.3671i) q^{96} -93.1113 q^{97} +(-81.7155 + 52.7977i) q^{98} -27.8389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9	\( 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9} - 16 q^{13} - 20 q^{14} + 34 q^{16} + 12 q^{18} - 48 q^{21} - 68 q^{22} + 18 q^{24} - 36 q^{26} - 28 q^{28} + 64 q^{29} + 76 q^{32} - 92 q^{34} - 30 q^{36} + 112 q^{37} + 40 q^{38} - 16 q^{41} - 108 q^{42} + 172 q^{44} + 152 q^{46} - 48 q^{48} - 56 q^{49} + 128 q^{52} - 352 q^{53} + 18 q^{54} + 116 q^{56} - 144 q^{57} + 204 q^{58} - 176 q^{61} + 56 q^{62} - 110 q^{64} + 108 q^{66} + 184 q^{68} - 96 q^{69} - 60 q^{72} + 240 q^{73} + 132 q^{74} - 24 q^{76} + 288 q^{77} + 240 q^{78} + 72 q^{81} - 40 q^{82} - 36 q^{84} - 200 q^{86} - 140 q^{88} + 80 q^{89} - 144 q^{92} - 144 q^{93} - 96 q^{94} - 174 q^{96} - 432 q^{97} - 660 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9 - 16 * q^13 - 20 * q^14 + 34 * q^16 + 12 * q^18 - 48 * q^21 - 68 * q^22 + 18 * q^24 - 36 * q^26 - 28 * q^28 + 64 * q^29 + 76 * q^32 - 92 * q^34 - 30 * q^36 + 112 * q^37 + 40 * q^38 - 16 * q^41 - 108 * q^42 + 172 * q^44 + 152 * q^46 - 48 * q^48 - 56 * q^49 + 128 * q^52 - 352 * q^53 + 18 * q^54 + 116 * q^56 - 144 * q^57 + 204 * q^58 - 176 * q^61 + 56 * q^62 - 110 * q^64 + 108 * q^66 + 184 * q^68 - 96 * q^69 - 60 * q^72 + 240 * q^73 + 132 * q^74 - 24 * q^76 + 288 * q^77 + 240 * q^78 + 72 * q^81 - 40 * q^82 - 36 * q^84 - 200 * q^86 - 140 * q^88 + 80 * q^89 - 144 * q^92 - 144 * q^93 - 96 * q^94 - 174 * q^96 - 432 * q^97 - 660 * q^98

Introduction

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