LMFDB - Embedded newform 231.2.c.a.76.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(76,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("231.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.1
Root			$-0.917186 - 1.66637i$ of defining polynomial
Character	$\chi$	$=$	231.76
Dual form			231.2.c.a.76.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30927i q^{2} -1.00000i q^{3} -3.33275 q^{4} -3.77447i q^{5} -2.30927 q^{6} +(-0.474903 + 2.60278i) q^{7} +3.07768i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.30927i q^{2} -1.00000i q^{3} -3.33275 q^{4} -3.77447i q^{5} -2.30927 q^{6} +(-0.474903 + 2.60278i) q^{7} +3.07768i q^{8} -1.00000 q^{9} -8.71628 q^{10} +(3.23607 + 0.726543i) q^{11} +3.33275i q^{12} +3.32932 q^{13} +(6.01054 + 1.09668i) q^{14} -3.77447 q^{15} +0.441718 q^{16} -5.12183 q^{17} +2.30927i q^{18} +2.74231 q^{19} +12.5794i q^{20} +(2.60278 + 0.474903i) q^{21} +(1.67779 - 7.47297i) q^{22} +2.19336 q^{23} +3.07768 q^{24} -9.24660 q^{25} -7.68832i q^{26} +1.00000i q^{27} +(1.58273 - 8.67441i) q^{28} -4.27913i q^{29} +8.71628i q^{30} -1.11656i q^{31} +5.13532i q^{32} +(0.726543 - 3.23607i) q^{33} +11.8277i q^{34} +(9.82411 + 1.79251i) q^{35} +3.33275 q^{36} +8.24660 q^{37} -6.33275i q^{38} -3.32932i q^{39} +11.6166 q^{40} -3.75248 q^{41} +(1.09668 - 6.01054i) q^{42} -6.74238i q^{43} +(-10.7850 - 2.42138i) q^{44} +3.77447i q^{45} -5.06508i q^{46} +5.58111i q^{47} -0.441718i q^{48} +(-6.54893 - 2.47214i) q^{49} +21.3529i q^{50} +5.12183i q^{51} -11.0958 q^{52} +6.66550 q^{53} +2.30927 q^{54} +(2.74231 - 12.2144i) q^{55} +(-8.01054 - 1.46160i) q^{56} -2.74231i q^{57} -9.88168 q^{58} -7.36317i q^{59} +12.5794 q^{60} -9.23710 q^{61} -2.57845 q^{62} +(0.474903 - 2.60278i) q^{63} +12.7423 q^{64} -12.5664i q^{65} +(-7.47297 - 1.67779i) q^{66} +1.96783 q^{67} +17.0698 q^{68} -2.19336i q^{69} +(4.13939 - 22.6866i) q^{70} -5.07680 q^{71} -3.07768i q^{72} +12.7339 q^{73} -19.0437i q^{74} +9.24660i q^{75} -9.13943 q^{76} +(-3.42785 + 8.07774i) q^{77} -7.68832 q^{78} +5.88440i q^{79} -1.66725i q^{80} +1.00000 q^{81} +8.66550i q^{82} +16.2585 q^{83} +(-8.67441 - 1.58273i) q^{84} +19.3322i q^{85} -15.5700 q^{86} -4.27913 q^{87} +(-2.23607 + 9.95959i) q^{88} +10.0211i q^{89} +8.71628 q^{90} +(-1.58111 + 8.66550i) q^{91} -7.30993 q^{92} -1.11656 q^{93} +12.8883 q^{94} -10.3508i q^{95} +5.13532 q^{96} +14.4476i q^{97} +(-5.70884 + 15.1233i) q^{98} +(-3.23607 - 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{4} - 16 q^{9}+O(q^{10}) $ 16 * q - 12 * q^4 - 16 * q^9	$ 16 q - 12 q^{4} - 16 q^{9} + 16 q^{11} + 8 q^{14} - 8 q^{15} - 4 q^{16} - 20 q^{22} + 24 q^{23} - 24 q^{25} + 12 q^{36} + 8 q^{37} + 12 q^{42} - 32 q^{44} + 24 q^{53} - 40 q^{56} - 12 q^{58} + 36 q^{60} + 88 q^{64} - 32 q^{67} + 36 q^{70} - 48 q^{71} + 12 q^{78} + 16 q^{81} + 32 q^{86} + 16 q^{91} - 128 q^{92} - 40 q^{93} - 16 q^{99}+O(q^{100}) $ 16 * q - 12 * q^4 - 16 * q^9 + 16 * q^11 + 8 * q^14 - 8 * q^15 - 4 * q^16 - 20 * q^22 + 24 * q^23 - 24 * q^25 + 12 * q^36 + 8 * q^37 + 12 * q^42 - 32 * q^44 + 24 * q^53 - 40 * q^56 - 12 * q^58 + 36 * q^60 + 88 * q^64 - 32 * q^67 + 36 * q^70 - 48 * q^71 + 12 * q^78 + 16 * q^81 + 32 * q^86 + 16 * q^91 - 128 * q^92 - 40 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$		−	2.30927i		−	1.63290i	−0.577414	−	0.816452i	$-0.695938\pi$
$2$		−	2.30927i		−	1.63290i	0.577414	−	0.816452i	$-0.304062\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−3.33275			−1.66637
$5$		−	3.77447i		−	1.68799i	−0.536349	−	0.843997i	$-0.680197\pi$
$5$		−	3.77447i		−	1.68799i	0.536349	−	0.843997i	$-0.319803\pi$
$6$	−2.30927			−0.942757
$7$	−0.474903	+	2.60278i	−0.179496	+	0.983759i
$7$	−0.474903	+	2.60278i	−0.179496	+	0.983759i
$8$			3.07768i			1.08813i
$9$	−1.00000			−0.333333
$10$	−8.71628			−2.75633
$11$	3.23607	+	0.726543i	0.975711	+	0.219061i
$11$	3.23607	+	0.726543i	0.975711	+	0.219061i
$12$			3.33275i			0.962082i
$13$	3.32932			0.923388			0.461694	−	0.887039i	$-0.347242\pi$
$13$	3.32932			0.923388			0.461694	+	0.887039i	$0.347242\pi$
$14$	6.01054	+	1.09668i	1.60638	+	0.293100i
$15$	−3.77447			−0.974563
$16$	0.441718			0.110430
$17$	−5.12183			−1.24223			−0.621113	−	0.783721i	$-0.713319\pi$
$17$	−5.12183			−1.24223			−0.621113	+	0.783721i	$0.713319\pi$
$18$			2.30927i			0.544301i
$19$	2.74231			0.629129			0.314565	−	0.949236i	$-0.398141\pi$
$19$	2.74231			0.629129			0.314565	+	0.949236i	$0.398141\pi$
$20$			12.5794i			2.81283i
$21$	2.60278	+	0.474903i	0.567973	+	0.103632i
$22$	1.67779	−	7.47297i	0.357705	−	1.59324i
$23$	2.19336			0.457348			0.228674	−	0.973503i	$-0.426561\pi$
$23$	2.19336			0.457348			0.228674	+	0.973503i	$0.426561\pi$
$24$	3.07768			0.628230
$25$	−9.24660			−1.84932
$26$		−	7.68832i		−	1.50780i
$27$			1.00000i			0.192450i
$28$	1.58273	−	8.67441i	0.299108	−	1.63931i
$29$		−	4.27913i		−	0.794614i	−0.917686	−	0.397307i	$-0.869945\pi$
$29$		−	4.27913i		−	0.794614i	0.917686	−	0.397307i	$-0.130055\pi$
$30$			8.71628i			1.59137i
$31$		−	1.11656i		−	0.200541i	−0.994960	−	0.100270i	$-0.968029\pi$
$31$		−	1.11656i		−	0.200541i	0.994960	−	0.100270i	$-0.0319708\pi$
$32$			5.13532i			0.907805i
$33$	0.726543	−	3.23607i	0.126475	−	0.563327i
$34$			11.8277i			2.02844i
$35$	9.82411	+	1.79251i	1.66058	+	0.302989i
$36$	3.33275			0.555458
$37$	8.24660			1.35573			0.677867	−	0.735185i	$-0.262905\pi$
$37$	8.24660			1.35573			0.677867	+	0.735185i	$0.262905\pi$
$38$		−	6.33275i		−	1.02731i
$39$		−	3.32932i		−	0.533118i
$40$	11.6166			1.83675
$41$	−3.75248			−0.586038			−0.293019	−	0.956107i	$-0.594660\pi$
$41$	−3.75248			−0.586038			−0.293019	+	0.956107i	$0.594660\pi$
$42$	1.09668	−	6.01054i	0.169222	−	0.927446i
$43$		−	6.74238i		−	1.02820i	−0.857729	−	0.514102i	$-0.828125\pi$
$43$		−	6.74238i		−	1.02820i	0.857729	−	0.514102i	$-0.171875\pi$
$44$	−10.7850	−	2.42138i	−1.62590	−	0.365037i
$45$			3.77447i			0.562664i
$46$		−	5.06508i		−	0.746805i
$47$			5.58111i			0.814088i	0.913409	+	0.407044i	$0.133440\pi$
$47$			5.58111i			0.814088i	−0.913409	+	0.407044i	$0.866560\pi$
$48$		−	0.441718i		−	0.0637565i
$49$	−6.54893	−	2.47214i	−0.935562	−	0.353162i
$50$			21.3529i			3.01976i
$51$			5.12183i			0.717199i
$52$	−11.0958			−1.53871
$53$	6.66550			0.915577			0.457788	−	0.889061i	$-0.348642\pi$
$53$	6.66550			0.915577			0.457788	+	0.889061i	$0.348642\pi$
$54$	2.30927			0.314252
$55$	2.74231	−	12.2144i	0.369773	−	1.64699i
$56$	−8.01054	−	1.46160i	−1.07045	−	0.195315i
$57$		−	2.74231i		−	0.363228i
$58$	−9.88168			−1.29753
$59$		−	7.36317i		−	0.958603i	−0.877650	−	0.479301i	$-0.840890\pi$
$59$		−	7.36317i		−	0.958603i	0.877650	−	0.479301i	$-0.159110\pi$
$60$	12.5794			1.62399
$61$	−9.23710			−1.18269			−0.591345	−	0.806419i	$-0.701403\pi$
$61$	−9.23710			−1.18269			−0.591345	+	0.806419i	$0.701403\pi$
$62$	−2.57845			−0.327464
$63$	0.474903	−	2.60278i	0.0598321	−	0.327920i
$64$	12.7423			1.59279
$65$		−	12.5664i		−	1.55867i
$66$	−7.47297	−	1.67779i	−0.919859	−	0.206521i
$67$	1.96783			0.240409			0.120204	−	0.992749i	$-0.461645\pi$
$67$	1.96783			0.240409			0.120204	+	0.992749i	$0.461645\pi$
$68$	17.0698			2.07001
$69$		−	2.19336i		−	0.264050i
$70$	4.13939	−	22.6866i	0.494751	−	2.71156i
$71$	−5.07680			−0.602505			−0.301253	−	0.953544i	$-0.597405\pi$
$71$	−5.07680			−0.602505			−0.301253	+	0.953544i	$0.597405\pi$
$72$		−	3.07768i		−	0.362708i
$73$	12.7339			1.49039			0.745194	−	0.666847i	$-0.232357\pi$
$73$	12.7339			1.49039			0.745194	+	0.666847i	$0.232357\pi$
$74$		−	19.0437i		−	2.21378i
$75$			9.24660i			1.06771i
$76$	−9.13943			−1.04837
$77$	−3.42785	+	8.07774i	−0.390640	+	0.920544i
$78$	−7.68832			−0.870531
$79$			5.88440i			0.662047i	0.943623	+	0.331023i	$0.107394\pi$
$79$			5.88440i			0.662047i	−0.943623	+	0.331023i	$0.892606\pi$
$80$		−	1.66725i		−	0.186404i
$81$	1.00000			0.111111
$82$			8.66550i			0.956944i
$83$	16.2585			1.78461			0.892303	−	0.451437i	$-0.149088\pi$
$83$	16.2585			1.78461			0.892303	+	0.451437i	$0.149088\pi$
$84$	−8.67441	−	1.58273i	−0.946456	−	0.172690i
$85$			19.3322i			2.09687i
$86$	−15.5700			−1.67896
$87$	−4.27913			−0.458771
$88$	−2.23607	+	9.95959i	−0.238366	+	1.06170i
$89$			10.0211i			1.06223i	0.847299	+	0.531116i	$0.178227\pi$
$89$			10.0211i			1.06223i	−0.847299	+	0.531116i	$0.821773\pi$
$90$	8.71628			0.918777
$91$	−1.58111	+	8.66550i	−0.165745	+	0.908391i
$92$	−7.30993			−0.762112
$93$	−1.11656			−0.115782
$94$	12.8883			1.32933
$95$		−	10.3508i		−	1.06197i
$96$	5.13532			0.524121
$97$			14.4476i			1.46693i	0.679729	+	0.733464i	$0.262098\pi$
$97$			14.4476i			1.46693i	−0.679729	+	0.733464i	$0.737902\pi$
$98$	−5.70884	+	15.1233i	−0.576680	+	1.52768i
$99$	−3.23607	−	0.726543i	−0.325237	−	0.0730203i
$100$	30.8166			3.08166
$101$	−15.5797			−1.55024			−0.775119	−	0.631815i	$-0.782310\pi$
$101$	−15.5797			−1.55024			−0.775119	+	0.631815i	$0.782310\pi$
$102$	11.8277			1.17112
$103$			16.4932i			1.62512i	0.582875	+	0.812562i	$0.301928\pi$
$103$			16.4932i			1.62512i	−0.582875	+	0.812562i	$0.698072\pi$
$104$			10.2466i			1.00476i
$105$	1.79251	−	9.82411i	0.174931	−	0.958735i
$106$		−	15.3925i		−	1.49505i
$107$		−	5.09846i		−	0.492886i	−0.969157	−	0.246443i	$-0.920738\pi$
$107$		−	5.09846i		−	0.492886i	0.969157	−	0.246443i	$-0.0792619\pi$
$108$		−	3.33275i		−	0.320694i
$109$			13.6801i			1.31031i	0.755492	+	0.655157i	$0.227398\pi$
$109$			13.6801i			1.31031i	−0.755492	+	0.655157i	$0.772602\pi$
$110$	−28.2065	−	6.33275i	−2.68938	−	0.603804i
$111$		−	8.24660i		−	0.782733i
$112$	−0.209773	+	1.14970i	−0.0198217	+	0.108636i
$113$	17.0979			1.60843			0.804216	−	0.594337i	$-0.202585\pi$
$113$	17.0979			1.60843			0.804216	+	0.594337i	$0.202585\pi$
$114$	−6.33275			−0.593116
$115$		−	8.27877i		−	0.772000i
$116$			14.2613i			1.32413i
$117$	−3.32932			−0.307796
$118$	−17.0036			−1.56531
$119$	2.43237	−	13.3310i	0.222975	−	1.22205i
$120$		−	11.6166i		−	1.06045i
$121$	9.94427	+	4.70228i	0.904025	+	0.427480i
$122$			21.3310i			1.93122i
$123$			3.75248i			0.338349i
$124$			3.72123i			0.334176i
$125$			16.0287i			1.43365i
$126$	−6.01054	−	1.09668i	−0.535461	−	0.0977001i
$127$		−	3.66874i		−	0.325548i	−0.986663	−	0.162774i	$-0.947956\pi$
$127$		−	3.66874i		−	0.325548i	0.986663	−	0.162774i	$-0.0520442\pi$
$128$		−	19.1548i		−	1.69306i
$129$	−6.74238			−0.593633
$130$	−29.0193			−2.54516
$131$	8.55826			0.747738			0.373869	−	0.927481i	$-0.378031\pi$
$131$	8.55826			0.747738			0.373869	+	0.927481i	$0.378031\pi$
$132$	−2.42138	+	10.7850i	−0.210754	+	0.938714i
$133$	−1.30233	+	7.13763i	−0.112926	+	0.618911i
$134$		−	4.54426i		−	0.392564i
$135$	3.77447			0.324854
$136$		−	15.7634i		−	1.35170i
$137$	−8.44756			−0.721724			−0.360862	−	0.932619i	$-0.617517\pi$
$137$	−8.44756			−0.721724			−0.360862	+	0.932619i	$0.617517\pi$
$138$	−5.06508			−0.431168
$139$	2.12383			0.180141			0.0900705	−	0.995935i	$-0.471291\pi$
$139$	2.12383			0.180141			0.0900705	+	0.995935i	$0.471291\pi$
$140$	−32.7413	−	5.97397i	−2.76714	−	0.504893i
$141$	5.58111			0.470014
$142$			11.7237i			0.983833i
$143$	10.7739	+	2.41889i	0.900960	+	0.202278i
$144$	−0.441718			−0.0368099
$145$	−16.1514			−1.34130
$146$		−	29.4060i		−	2.43366i
$147$	−2.47214	+	6.54893i	−0.203898	+	0.540147i
$148$	−27.4839			−2.25916
$149$			5.45315i			0.446740i	0.974734	+	0.223370i	$0.0717058\pi$
$149$			5.45315i			0.446740i	−0.974734	+	0.223370i	$0.928294\pi$
$150$	21.3529			1.74346
$151$		−	7.42122i		−	0.603930i	−0.953319	−	0.301965i	$-0.902357\pi$
$151$		−	7.42122i		−	0.603930i	0.953319	−	0.301965i	$-0.0976426\pi$
$152$			8.43997i			0.684572i
$153$	5.12183			0.414075
$154$	18.6537	+	7.91584i	1.50316	+	0.637877i
$155$	−4.21443			−0.338511
$156$			11.0958i			0.888375i
$157$		−	1.83121i		−	0.146147i	−0.997327	−	0.0730734i	$-0.976719\pi$
$157$		−	1.83121i		−	0.146147i	0.997327	−	0.0730734i	$-0.0232807\pi$
$158$	13.5887			1.08106
$159$		−	6.66550i		−	0.528608i
$160$	19.3831			1.53237
$161$	−1.04163	+	5.70884i	−0.0820923	+	0.449920i
$162$		−	2.30927i		−	0.181434i
$163$	−7.73470			−0.605829			−0.302914	−	0.953018i	$-0.597960\pi$
$163$	−7.73470			−0.605829			−0.302914	+	0.953018i	$0.597960\pi$
$164$	12.5061			0.976559
$165$	−12.2144	−	2.74231i	−0.950892	−	0.213489i
$166$		−	37.5454i		−	2.91409i
$167$	0.316047			0.0244564			0.0122282	−	0.999925i	$-0.496108\pi$
$167$	0.316047			0.0244564			0.0122282	+	0.999925i	$0.496108\pi$
$168$	−1.46160	+	8.01054i	−0.112765	+	0.618026i
$169$	−1.91561			−0.147354
$170$	44.6433			3.42398
$171$	−2.74231			−0.209710
$172$			22.4707i			1.71337i
$173$	−20.1434			−1.53147			−0.765737	−	0.643153i	$-0.777626\pi$
$173$	−20.1434			−1.53147			−0.765737	+	0.643153i	$0.777626\pi$
$174$			9.88168i			0.749129i
$175$	4.39124	−	24.0669i	0.331946	−	1.81929i
$176$	1.42943	+	0.320927i	0.107747	+	0.0241908i
$177$	−7.36317			−0.553450
$178$	23.1414			1.73452
$179$	8.25420			0.616948			0.308474	−	0.951233i	$-0.400182\pi$
$179$	8.25420			0.616948			0.308474	+	0.951233i	$0.400182\pi$
$180$		−	12.5794i		−	0.937610i
$181$		−	10.4324i		−	0.775432i	−0.921779	−	0.387716i	$-0.873264\pi$
$181$		−	10.4324i		−	0.775432i	0.921779	−	0.387716i	$-0.126736\pi$
$182$	20.0110	+	3.65121i	1.48332	+	0.270645i
$183$			9.23710i			0.682826i
$184$			6.75047i			0.497652i
$185$		−	31.1265i		−	2.28847i
$186$			2.57845i			0.189061i
$187$	−16.5746	−	3.72123i	−1.21205	−	0.272123i
$188$		−	18.6004i		−	1.35658i
$189$	−2.60278	−	0.474903i	−0.189324	−	0.0345441i
$190$	−23.9028			−1.73409
$191$	−10.2998			−0.745271			−0.372635	−	0.927978i	$-0.621546\pi$
$191$	−10.2998			−0.745271			−0.372635	+	0.927978i	$0.621546\pi$
$192$		−	12.7423i		−	0.919596i
$193$			0.195328i			0.0140600i	0.999975	+	0.00703000i	$0.00223774\pi$
$193$			0.195328i			0.0140600i	−0.999975	+	0.00703000i	$0.997762\pi$
$194$	33.3634			2.39535
$195$	−12.5664			−0.899900
$196$	21.8260	+	8.23901i	1.55900	+	0.588501i
$197$			5.87631i			0.418669i	0.977844	+	0.209335i	$0.0671298\pi$
$197$			5.87631i			0.418669i	−0.977844	+	0.209335i	$0.932870\pi$
$198$	−1.67779	+	7.47297i	−0.119235	+	0.531081i
$199$		−	0.214433i		−	0.0152007i	−0.999971	−	0.00760037i	$-0.997581\pi$
$199$		−	0.214433i		−	0.0152007i	0.999971	−	0.00760037i	$-0.00241929\pi$
$200$		−	28.4581i		−	2.01229i
$201$		−	1.96783i		−	0.138800i
$202$			35.9778i			2.53139i
$203$	11.1376	+	2.03217i	0.781709	+	0.142630i
$204$		−	17.0698i		−	1.19512i
$205$			14.1636i			0.989229i
$206$	38.0873			2.65367
$207$	−2.19336			−0.152449
$208$	1.47062			0.101969
$209$	8.87430	+	1.99241i	0.613848	+	0.137818i
$210$	−22.6866	−	4.13939i	−1.56552	−	0.285645i
$211$			19.2017i			1.32190i	0.750430	+	0.660950i	$0.229846\pi$
$211$			19.2017i			1.32190i	−0.750430	+	0.660950i	$0.770154\pi$
$212$	−22.2144			−1.52569
$213$			5.07680i			0.347857i
$214$	−11.7737			−0.804836
$215$	−25.4489			−1.73560
$216$	−3.07768			−0.209410
$217$	2.90617	+	0.530259i	0.197284	+	0.0359963i
$218$	31.5911			2.13962
$219$		−	12.7339i		−	0.860476i
$220$	−9.13943	+	40.7076i	−0.616181	+	2.74451i
$221$	−17.0522			−1.14706
$222$	−19.0437			−1.27813
$223$		−	3.62846i		−	0.242980i	−0.992593	−	0.121490i	$-0.961233\pi$
$223$		−	3.62846i		−	0.242980i	0.992593	−	0.121490i	$-0.0387672\pi$
$224$	−13.3661	−	2.43878i	−0.893061	−	0.162948i
$225$	9.24660			0.616440
$226$		−	39.4837i		−	2.62641i
$227$	−3.07364			−0.204004			−0.102002	−	0.994784i	$-0.532525\pi$
$227$	−3.07364			−0.204004			−0.102002	+	0.994784i	$0.532525\pi$
$228$			9.13943i			0.605274i
$229$		−	15.3766i		−	1.01612i	−0.861323	−	0.508059i	$-0.830363\pi$
$229$		−	15.3766i		−	1.01612i	0.861323	−	0.508059i	$-0.169637\pi$
$230$	−19.1180			−1.26060
$231$	8.07774	+	3.42785i	0.531476	+	0.225536i
$232$	13.1698			0.864640
$233$		−	16.2874i		−	1.06702i	−0.845792	−	0.533512i	$-0.820872\pi$
$233$		−	16.2874i		−	1.06702i	0.845792	−	0.533512i	$-0.179128\pi$
$234$			7.68832i			0.502601i
$235$	21.0657			1.37417
$236$			24.5396i			1.59739i
$237$	5.88440			0.382233
$238$	−30.7849	−	5.61701i	−1.99549	−	0.364097i
$239$		−	13.8242i		−	0.894212i	−0.894481	−	0.447106i	$-0.852455\pi$
$239$		−	13.8242i		−	0.894212i	0.894481	−	0.447106i	$-0.147545\pi$
$240$	−1.66725			−0.107621
$241$	−5.22893			−0.336825			−0.168413	−	0.985717i	$-0.553864\pi$
$241$	−5.22893			−0.336825			−0.168413	+	0.985717i	$0.553864\pi$
$242$	10.8589	−	22.9641i	0.698034	−	1.47619i
$243$		−	1.00000i		−	0.0641500i
$244$	30.7849			1.97080
$245$	−9.33100	+	24.7187i	−0.596135	+	1.57922i
$246$	8.66550			0.552492
$247$	9.13004			0.580931
$248$	3.43643			0.218213
$249$		−	16.2585i		−	1.03034i
$250$	37.0146			2.34101
$251$		−	1.19438i		−	0.0753886i	−0.999289	−	0.0376943i	$-0.987999\pi$
$251$		−	1.19438i		−	0.0753886i	0.999289	−	0.0376943i	$-0.0120013\pi$
$252$	−1.58273	+	8.67441i	−0.0997027	+	0.546437i
$253$	7.09787	+	1.59357i	0.446239	+	0.100187i
$254$	−8.47214			−0.531589
$255$	19.3322			1.21063
$256$	−18.7492			−1.17182
$257$			15.8166i			0.986613i	0.869856	+	0.493306i	$0.164212\pi$
$257$			15.8166i			0.986613i	−0.869856	+	0.493306i	$0.835788\pi$
$258$			15.5700i			0.969346i
$259$	−3.91634	+	21.4641i	−0.243349	+	1.33371i
$260$			41.8807i			2.59733i
$261$			4.27913i			0.264871i
$262$		−	19.7634i		−	1.22098i
$263$			24.7467i			1.52595i	0.646431	+	0.762973i	$0.276261\pi$
$263$			24.7467i			1.52595i	−0.646431	+	0.762973i	$0.723739\pi$
$264$	9.95959	+	2.23607i	0.612971	+	0.137620i
$265$		−	25.1587i		−	1.54549i
$266$	16.4828	+	3.00744i	1.01062	+	0.184398i
$267$	10.0211			0.613280
$268$	−6.55828			−0.400611
$269$		−	13.0768i		−	0.797306i	−0.917102	−	0.398653i	$-0.869478\pi$
$269$		−	13.0768i		−	0.797306i	0.917102	−	0.398653i	$-0.130522\pi$
$270$		−	8.71628i		−	0.530456i
$271$	24.8015			1.50658			0.753292	−	0.657686i	$-0.228464\pi$
$271$	24.8015			1.50658			0.753292	+	0.657686i	$0.228464\pi$
$272$	−2.26240			−0.137178
$273$	8.66550	+	1.58111i	0.524460	+	0.0956928i
$274$			19.5077i			1.17851i
$275$	−29.9226	−	6.71805i	−1.80440	−	0.405114i
$276$			7.30993i			0.440006i
$277$		−	4.26385i		−	0.256190i	−0.991762	−	0.128095i	$-0.959114\pi$
$277$		−	4.26385i		−	0.256190i	0.991762	−	0.128095i	$-0.0408862\pi$
$278$		−	4.90451i		−	0.294153i
$279$			1.11656i			0.0668469i
$280$	−5.51676	+	30.2355i	−0.329690	+	1.80692i
$281$		−	17.4290i		−	1.03972i	−0.854250	−	0.519862i	$-0.825983\pi$
$281$		−	17.4290i		−	1.03972i	0.854250	−	0.519862i	$-0.174017\pi$
$282$		−	12.8883i		−	0.767487i
$283$	−10.5750			−0.628617			−0.314309	−	0.949321i	$-0.601773\pi$
$283$	−10.5750			−0.628617			−0.314309	+	0.949321i	$0.601773\pi$
$284$	16.9197			1.00400
$285$	−10.3508			−0.613126
$286$	5.58589	−	24.8799i	0.330301	−	1.47118i
$287$	1.78206	−	9.76687i	0.105192	−	0.576520i
$288$		−	5.13532i		−	0.302602i
$289$	9.23313			0.543125
$290$			37.2981i			2.19022i
$291$	14.4476			0.846931
$292$	−42.4389			−2.48355
$293$	−21.3804			−1.24905			−0.624527	−	0.781003i	$-0.714708\pi$
$293$	−21.3804			−1.24905			−0.624527	+	0.781003i	$0.714708\pi$
$294$	15.1233	+	5.70884i	0.882008	+	0.332946i
$295$	−27.7920			−1.61811
$296$			25.3804i			1.47521i
$297$	−0.726543	+	3.23607i	−0.0421583	+	0.187776i
$298$	12.5928			0.729483
$299$	7.30241			0.422309
$300$		−	30.8166i		−	1.77920i
$301$	17.5489	+	3.20198i	1.01150	+	0.184559i
$302$	−17.1376			−0.986160
$303$			15.5797i			0.895030i
$304$	1.21133			0.0694745
$305$			34.8651i			1.99637i
$306$		−	11.8277i		−	0.676145i
$307$	26.2034			1.49551			0.747753	−	0.663977i	$-0.231133\pi$
$307$	26.2034			1.49551			0.747753	+	0.663977i	$0.231133\pi$
$308$	11.4242	−	26.9211i	0.650952	−	1.53397i
$309$	16.4932			0.938266
$310$			9.73228i			0.552756i
$311$			17.3731i			0.985140i	0.870273	+	0.492570i	$0.163942\pi$
$311$			17.3731i			0.985140i	−0.870273	+	0.492570i	$0.836058\pi$
$312$	10.2466			0.580100
$313$			3.33450i			0.188477i	0.995550	+	0.0942386i	$0.0300417\pi$
$313$			3.33450i			0.188477i	−0.995550	+	0.0942386i	$0.969958\pi$
$314$	−4.22878			−0.238644
$315$	−9.82411	−	1.79251i	−0.553526	−	0.100996i
$316$		−	19.6112i		−	1.10322i
$317$	−4.83428			−0.271520			−0.135760	−	0.990742i	$-0.543348\pi$
$317$	−4.83428			−0.271520			−0.135760	+	0.990742i	$0.543348\pi$
$318$	−15.3925			−0.863167
$319$	3.10897	−	13.8476i	0.174069	−	0.775314i
$320$		−	48.0954i		−	2.68861i
$321$	−5.09846			−0.284568
$322$	13.1833	+	2.40542i	0.734676	+	0.134049i
$323$	−14.0456			−0.781521
$324$	−3.33275			−0.185153
$325$	−30.7849			−1.70764
$326$			17.8616i			0.989260i
$327$	13.6801			0.756511
$328$		−	11.5489i		−	0.637683i
$329$	−14.5264	−	2.65048i	−0.800866	−	0.146126i
$330$	−6.33275	+	28.2065i	−0.348606	+	1.55272i
$331$	−9.71772			−0.534134			−0.267067	−	0.963678i	$-0.586055\pi$
$331$	−9.71772			−0.534134			−0.267067	+	0.963678i	$0.586055\pi$
$332$	−54.1856			−2.97382
$333$	−8.24660			−0.451911
$334$		−	0.729839i		−	0.0399350i
$335$		−	7.42751i		−	0.405808i
$336$	1.14970	+	0.209773i	0.0627210	+	0.0114441i
$337$		−	22.5895i		−	1.23053i	−0.788322	−	0.615263i	$-0.789050\pi$
$337$		−	22.5895i		−	1.23053i	0.788322	−	0.615263i	$-0.210950\pi$
$338$			4.42366i			0.240616i
$339$		−	17.0979i		−	0.928629i
$340$		−	64.4293i		−	3.49417i
$341$	0.811231	−	3.61328i	0.0439306	−	0.195670i
$342$			6.33275i			0.342436i
$343$	9.54454	−	15.8714i	0.515356	−	0.856976i
$344$	20.7509			1.11881
$345$	−8.27877			−0.445714
$346$			46.5167i			2.50075i
$347$			9.12550i			0.489883i	0.969538	+	0.244941i	$0.0787687\pi$
$347$			9.12550i			0.489883i	−0.969538	+	0.244941i	$0.921231\pi$
$348$	14.2613			0.764484
$349$	−21.8035			−1.16712			−0.583558	−	0.812072i	$-0.698340\pi$
$349$	−21.8035			−1.16712			−0.583558	+	0.812072i	$0.698340\pi$
$350$	−55.5770	−	10.1406i	−2.97072	−	0.542037i
$351$			3.32932i			0.177706i
$352$	−3.73103	+	16.6182i	−0.198864	+	0.885755i
$353$		−	2.50080i		−	0.133104i	−0.997783	−	0.0665521i	$-0.978800\pi$
$353$		−	2.50080i		−	0.133104i	0.997783	−	0.0665521i	$-0.0211999\pi$
$354$			17.0036i			0.903730i
$355$			19.1622i			1.01702i
$356$		−	33.3977i		−	1.77008i
$357$	−13.3310	−	2.43237i	−0.705551	−	0.128735i
$358$		−	19.0612i		−	1.00742i
$359$			32.0706i			1.69262i	0.532692	+	0.846309i	$0.321181\pi$
$359$			32.0706i			1.69262i	−0.532692	+	0.846309i	$0.678819\pi$
$360$	−11.6166			−0.612249
$361$	−11.4797			−0.604196
$362$	−24.0912			−1.26621
$363$	4.70228	−	9.94427i	0.246806	−	0.521939i
$364$	5.26943	−	28.8799i	0.276193	−	1.51372i
$365$		−	48.0636i		−	2.51577i
$366$	21.3310			1.11499
$367$		−	4.77345i		−	0.249172i	−0.992209	−	0.124586i	$-0.960240\pi$
$367$		−	4.77345i		−	0.249172i	0.992209	−	0.124586i	$-0.0397603\pi$
$368$	0.968848			0.0505047
$369$	3.75248			0.195346
$370$	−71.8797			−3.73685
$371$	−3.16546	+	17.3488i	−0.164343	+	0.900706i
$372$	3.72123			0.192937
$373$		−	4.27552i		−	0.221378i	−0.993855	−	0.110689i	$-0.964694\pi$
$373$		−	4.27552i		−	0.221378i	0.993855	−	0.110689i	$-0.0353058\pi$
$374$	−8.59333	+	38.2753i	−0.444351	+	1.97917i
$375$	16.0287			0.827717
$376$	−17.1769			−0.885830
$377$		−	14.2466i		−	0.733737i
$378$	−1.09668	+	6.01054i	−0.0564072	+	0.309149i
$379$	−2.41889			−0.124250			−0.0621251	−	0.998068i	$-0.519788\pi$
$379$	−2.41889			−0.124250			−0.0621251	+	0.998068i	$0.519788\pi$
$380$			34.4965i			1.76963i
$381$	−3.66874			−0.187955
$382$			23.7852i			1.21696i
$383$			24.9443i			1.27459i	0.770619	+	0.637296i	$0.219947\pi$
$383$			24.9443i			1.27459i	−0.770619	+	0.637296i	$0.780053\pi$
$384$	−19.1548			−0.977491
$385$	30.4892	+	12.9383i	1.55387	+	0.659397i
$386$	0.451065			0.0229586
$387$			6.74238i			0.342734i
$388$		−	48.1501i		−	2.44445i
$389$	−24.2753			−1.23080			−0.615402	−	0.788213i	$-0.711007\pi$
$389$	−24.2753			−1.23080			−0.615402	+	0.788213i	$0.711007\pi$
$390$			29.0193i			1.46945i
$391$	−11.2340			−0.568129
$392$	7.60845	−	20.1555i	0.384285	−	1.01801i
$393$		−	8.55826i		−	0.431707i
$394$	13.5700			0.683647
$395$	22.2105			1.11753
$396$	10.7850	+	2.42138i	0.541967	+	0.121679i
$397$			29.0944i			1.46020i	0.683338	+	0.730102i	$0.260528\pi$
$397$			29.0944i			1.46020i	−0.683338	+	0.730102i	$0.739472\pi$
$398$	−0.495184			−0.0248213
$399$	7.13763	+	1.30233i	0.357329	+	0.0651981i
$400$	−4.08439			−0.204220
$401$	−12.0456			−0.601531			−0.300765	−	0.953698i	$-0.597242\pi$
$401$	−12.0456			−0.601531			−0.300765	+	0.953698i	$0.597242\pi$
$402$	−4.54426			−0.226647
$403$		−	3.71740i		−	0.185177i
$404$	51.9232			2.58328
$405$		−	3.77447i		−	0.187555i
$406$	4.69284	−	25.7199i	0.232902	−	1.27645i
$407$	26.6866	+	5.99151i	1.32280	+	0.296988i
$408$	−15.7634			−0.780403
$409$	14.9359			0.738534			0.369267	−	0.929323i	$-0.379609\pi$
$409$	14.9359			0.738534			0.369267	+	0.929323i	$0.379609\pi$
$410$	32.7076			1.61532
$411$			8.44756i			0.416687i
$412$		−	54.9677i		−	2.70807i
$413$	19.1647	+	3.49679i	0.943034	+	0.172066i
$414$			5.06508i			0.248935i
$415$		−	61.3673i		−	3.01240i
$416$			17.0971i			0.838256i
$417$		−	2.12383i		−	0.104004i
$418$	4.60101	−	20.4932i	0.225043	−	1.00236i
$419$			8.29225i			0.405103i	0.979272	+	0.202551i	$0.0649233\pi$
$419$			8.29225i			0.405103i	−0.979272	+	0.202551i	$0.935077\pi$
$420$	−5.97397	+	32.7413i	−0.291500	+	1.59761i
$421$	−2.54407			−0.123990			−0.0619952	−	0.998076i	$-0.519746\pi$
$421$	−2.54407			−0.123990			−0.0619952	+	0.998076i	$0.519746\pi$
$422$	44.3420			2.15853
$423$		−	5.58111i		−	0.271363i
$424$			20.5143i			0.996262i
$425$	47.3595			2.29727
$426$	11.7237			0.568016
$427$	4.38672	−	24.0421i	0.212288	−	1.16348i
$428$			16.9919i			0.821333i
$429$	2.41889	−	10.7739i	0.116785	−	0.520170i
$430$			58.7685i			2.83407i
$431$			22.4454i			1.08116i	0.841294	+	0.540578i	$0.181794\pi$
$431$			22.4454i			1.08116i	−0.841294	+	0.540578i	$0.818206\pi$
$432$			0.441718i			0.0212522i
$433$			28.4137i			1.36547i	0.730664	+	0.682737i	$0.239211\pi$
$433$			28.4137i			1.36547i	−0.730664	+	0.682737i	$0.760789\pi$
$434$	1.22451	−	6.71114i	0.0587786	−	0.322145i
$435$			16.1514i			0.774402i
$436$		−	45.5923i		−	2.18347i
$437$	6.01488			0.287731
$438$	−29.4060			−1.40508
$439$	23.3503			1.11445			0.557226	−	0.830361i	$-0.311866\pi$
$439$	23.3503			1.11445			0.557226	+	0.830361i	$0.311866\pi$
$440$	37.5922	+	8.43997i	1.79214	+	0.402360i
$441$	6.54893	+	2.47214i	0.311854	+	0.117721i
$442$			39.3783i			1.87303i
$443$	−7.37427			−0.350362			−0.175181	−	0.984536i	$-0.556051\pi$
$443$	−7.37427			−0.350362			−0.175181	+	0.984536i	$0.556051\pi$
$444$			27.4839i			1.30433i
$445$	37.8242			1.79304
$446$	−8.37912			−0.396763
$447$	5.45315			0.257925
$448$	−6.05135	+	33.1654i	−0.285900	+	1.56692i
$449$	−26.0270			−1.22829			−0.614144	−	0.789194i	$-0.710499\pi$
$449$	−26.0270			−1.22829			−0.614144	+	0.789194i	$0.710499\pi$
$450$		−	21.3529i		−	1.00659i
$451$	−12.1433	−	2.72633i	−0.571804	−	0.128378i
$452$	−56.9829			−2.68025
$453$	−7.42122			−0.348679
$454$			7.09787i			0.333120i
$455$	32.7076	+	5.96783i	1.53336	+	0.279776i
$456$	8.43997			0.395238
$457$			11.2853i			0.527904i	0.964536	+	0.263952i	$0.0850260\pi$
$457$			11.2853i			0.527904i	−0.964536	+	0.263952i	$0.914974\pi$
$458$	−35.5089			−1.65922
$459$		−	5.12183i		−	0.239066i
$460$			27.5911i			1.28644i
$461$	11.1367			0.518688			0.259344	−	0.965785i	$-0.416494\pi$
$461$	11.1367			0.518688			0.259344	+	0.965785i	$0.416494\pi$
$462$	7.91584	−	18.6537i	0.368278	−	0.867849i
$463$	0.572492			0.0266060			0.0133030	−	0.999912i	$-0.495765\pi$
$463$	0.572492			0.0266060			0.0133030	+	0.999912i	$0.495765\pi$
$464$		−	1.89017i		−	0.0877489i
$465$			4.21443i			0.195440i
$466$	−37.6121			−1.74235
$467$		−	9.06570i		−	0.419510i	−0.977754	−	0.209755i	$-0.932733\pi$
$467$		−	9.06570i		−	0.419510i	0.977754	−	0.209755i	$-0.0672667\pi$
$468$	11.0958			0.512903
$469$	−0.934528	+	5.12183i	−0.0431525	+	0.236504i
$470$		−	48.6465i		−	2.24389i
$471$	−1.83121			−0.0843779
$472$	22.6615			1.04308
$473$	4.89863	−	21.8188i	0.225239	−	1.00323i
$474$		−	13.5887i		−	0.624150i
$475$	−25.3571			−1.16346
$476$	−8.10648	+	44.4289i	−0.371560	+	2.03639i
$477$	−6.66550			−0.305192
$478$	−31.9238			−1.46016
$479$	−36.0275			−1.64614			−0.823069	−	0.567942i	$-0.807740\pi$
$479$	−36.0275			−1.64614			−0.823069	+	0.567942i	$0.807740\pi$
$480$		−	19.3831i		−	0.884713i
$481$	27.4556			1.25187
$482$			12.0750i			0.550003i
$483$	5.70884	+	1.04163i	0.259761	+	0.0473960i
$484$	−33.1418	−	15.6715i	−1.50644	−	0.712342i
$485$	54.5318			2.47616
$486$	−2.30927			−0.104751
$487$	−36.8156			−1.66827			−0.834137	−	0.551558i	$-0.814034\pi$
$487$	−36.8156			−1.66827			−0.834137	+	0.551558i	$0.814034\pi$
$488$		−	28.4289i		−	1.28691i
$489$			7.73470i			0.349775i
$490$	57.0824	+	21.5478i	2.57872	+	0.973432i
$491$		−	8.85093i		−	0.399437i	−0.979853	−	0.199718i	$-0.935997\pi$
$491$		−	8.85093i		−	0.399437i	0.979853	−	0.199718i	$-0.0640028\pi$
$492$		−	12.5061i		−	0.563817i
$493$			21.9170i			0.987090i
$494$		−	21.0838i		−	0.948604i
$495$	−2.74231	+	12.2144i	−0.123258	+	0.548998i
$496$		−	0.493206i		−	0.0221456i
$497$	2.41099	−	13.2138i	0.108148	−	0.592720i
$498$	−37.5454			−1.68245
$499$	20.3074			0.909086			0.454543	−	0.890725i	$-0.349803\pi$
$499$	20.3074			0.909086			0.454543	+	0.890725i	$0.349803\pi$
$500$		−	53.4195i		−	2.38899i
$501$		−	0.316047i		−	0.0141199i
$502$	−2.75815			−0.123102
$503$	−14.0240			−0.625299			−0.312650	−	0.949869i	$-0.601217\pi$
$503$	−14.0240			−0.625299			−0.312650	+	0.949869i	$0.601217\pi$
$504$	8.01054	+	1.46160i	0.356818	+	0.0651049i
$505$			58.8051i			2.61679i
$506$	3.67999	−	16.3909i	0.163596	−	0.728666i
$507$			1.91561i			0.0850751i
$508$			12.2270i			0.542485i
$509$		−	16.2963i		−	0.722323i	−0.932503	−	0.361161i	$-0.882380\pi$
$509$		−	16.2963i		−	0.722323i	0.932503	−	0.361161i	$-0.117620\pi$
$510$		−	44.6433i		−	1.97684i
$511$	−6.04736	+	33.1435i	−0.267519	+	1.46618i
$512$			4.98730i			0.220410i
$513$			2.74231i			0.121076i
$514$	36.5249			1.61104
$515$	62.2531			2.74320
$516$	22.4707			0.989216
$517$	−4.05491	+	18.0608i	−0.178335	+	0.794315i
$518$	49.5665	+	9.04389i	2.17783	+	0.397366i
$519$			20.1434i			0.884197i
$520$	38.6755			1.69603
$521$			6.83020i			0.299236i	0.988744	+	0.149618i	$0.0478044\pi$
$521$			6.83020i			0.299236i	−0.988744	+	0.149618i	$0.952196\pi$
$522$	9.88168			0.432510
$523$	18.7983			0.821993			0.410996	−	0.911637i	$-0.365181\pi$
$523$	18.7983			0.821993			0.410996	+	0.911637i	$0.365181\pi$
$524$	−28.5225			−1.24601
$525$	−24.0669	−	4.39124i	−1.05036	−	0.191649i
$526$	57.1469			2.49172
$527$			5.71885i			0.249117i
$528$	0.320927	−	1.42943i	0.0139666	−	0.0622080i
$529$	−18.1892			−0.790833
$530$	−58.0984			−2.52363
$531$			7.36317i			0.319534i
$532$	4.34034	−	23.7879i	0.188178	−	1.03134i
$533$	−12.4932			−0.541141
$534$		−	23.1414i		−	1.00143i
$535$	−19.2440			−0.831989
$536$			6.05636i			0.261595i
$537$		−	8.25420i		−	0.356195i
$538$	−30.1979			−1.30192
$539$	−19.3967	−	12.7581i	−0.835474	−	0.549529i
$540$	−12.5794			−0.541329
$541$		−	5.76559i		−	0.247882i	−0.992290	−	0.123941i	$-0.960447\pi$
$541$		−	5.76559i		−	0.247882i	0.992290	−	0.123941i	$-0.0395534\pi$
$542$		−	57.2735i		−	2.46011i
$543$	−10.4324			−0.447696
$544$		−	26.3022i		−	1.12770i
$545$	51.6350			2.21180
$546$	3.65121	−	20.0110i	0.156257	−	0.856392i
$547$			13.2686i			0.567326i	0.958924	+	0.283663i	$0.0915497\pi$
$547$			13.2686i			0.567326i	−0.958924	+	0.283663i	$0.908450\pi$
$548$	28.1536			1.20266
$549$	9.23710			0.394230
$550$	−15.5138	+	69.0996i	−0.661512	+	2.94642i
$551$		−	11.7347i		−	0.499915i
$552$	6.75047			0.287319
$553$	−15.3158	−	2.79452i	−0.651294	−	0.118835i
$554$	−9.84640			−0.418334
$555$	−31.1265			−1.32125
$556$	−7.07819			−0.300182
$557$		−	26.6733i		−	1.13018i	−0.825028	−	0.565091i	$-0.808841\pi$
$557$		−	26.6733i		−	1.13018i	0.825028	−	0.565091i	$-0.191159\pi$
$558$	2.57845			0.109155
$559$		−	22.4476i		−	0.949431i
$560$	4.33949	+	0.791782i	0.183377	+	0.0334589i
$561$	−3.72123	+	16.5746i	−0.157110	+	0.699780i
$562$	−40.2482			−1.69777
$563$	18.7902			0.791914			0.395957	−	0.918269i	$-0.370413\pi$
$563$	18.7902			0.791914			0.395957	+	0.918269i	$0.370413\pi$
$564$	−18.6004			−0.783219
$565$		−	64.5353i		−	2.71502i
$566$			24.4205i			1.02647i
$567$	−0.474903	+	2.60278i	−0.0199440	+	0.109307i
$568$		−	15.6248i		−	0.655601i
$569$			35.6007i			1.49246i	0.665688	+	0.746230i	$0.268138\pi$
$569$			35.6007i			1.49246i	−0.665688	+	0.746230i	$0.731862\pi$
$570$			23.9028i			1.00118i
$571$		−	35.3746i		−	1.48038i	−0.672398	−	0.740190i	$-0.734735\pi$
$571$		−	35.3746i		−	1.48038i	0.672398	−	0.740190i	$-0.265265\pi$
$572$	−35.9068	−	8.06157i	−1.50134	−	0.337071i
$573$			10.2998i			0.430282i
$574$	−22.5544	−	4.11527i	−0.941402	−	0.171768i
$575$	−20.2811			−0.845782
$576$	−12.7423			−0.530929
$577$		−	36.2144i		−	1.50763i	−0.657089	−	0.753813i	$-0.728212\pi$
$577$		−	36.2144i		−	1.50763i	0.657089	−	0.753813i	$-0.271788\pi$
$578$		−	21.3218i		−	0.886871i
$579$	0.195328			0.00811754
$580$	53.8287			2.23511
$581$	−7.72123	+	42.3174i	−0.320330	+	1.75562i
$582$		−	33.3634i		−	1.38296i
$583$	21.5700	+	4.84277i	0.893338	+	0.200567i
$584$			39.1909i			1.62173i
$585$			12.5664i			0.519558i
$586$			49.3731i			2.03959i
$587$		−	6.46104i		−	0.266675i	−0.991071	−	0.133338i	$-0.957430\pi$
$587$		−	6.46104i		−	0.266675i	0.991071	−	0.133338i	$-0.0425695\pi$
$588$	8.23901	−	21.8260i	0.339771	−	0.900087i
$589$		−	3.06196i		−	0.126166i
$590$			64.1794i			2.64223i
$591$	5.87631			0.241719
$592$	3.64267			0.149713
$593$	42.9282			1.76285			0.881425	−	0.472324i	$-0.156585\pi$
$593$	42.9282			1.76285			0.881425	+	0.472324i	$0.156585\pi$
$594$	7.47297	+	1.67779i	0.306620	+	0.0688404i
$595$	−50.3174	−	9.18090i	−2.06281	−	0.376380i
$596$		−	18.1740i		−	0.744436i
$597$	−0.214433			−0.00877615
$598$		−	16.8633i		−	0.689591i
$599$	−33.0698			−1.35119			−0.675597	−	0.737271i	$-0.736114\pi$
$599$	−33.0698			−1.35119			−0.675597	+	0.737271i	$0.736114\pi$
$600$	−28.4581			−1.16180
$601$	25.2049			1.02813			0.514064	−	0.857752i	$-0.328139\pi$
$601$	25.2049			1.02813			0.514064	+	0.857752i	$0.328139\pi$
$602$	7.39424	−	40.5253i	0.301367	−	1.65169i
$603$	−1.96783			−0.0801362
$604$			24.7331i			1.00637i
$605$	17.7486	−	37.5343i	0.721584	−	1.52599i
$606$	35.9778			1.46150
$607$	−26.0963			−1.05921			−0.529607	−	0.848243i	$-0.677661\pi$
$607$	−26.0963			−1.05921			−0.529607	+	0.848243i	$0.677661\pi$
$608$			14.0826i			0.571126i
$609$	2.03217	−	11.1376i	0.0823477	−	0.451320i
$610$	80.5131			3.25988
$611$			18.5813i			0.751719i
$612$	−17.0698			−0.690005
$613$		−	14.0078i		−	0.565770i	−0.959154	−	0.282885i	$-0.908709\pi$
$613$		−	14.0078i		−	0.565770i	0.959154	−	0.282885i	$-0.0912915\pi$
$614$		−	60.5108i		−	2.44202i
$615$	14.1636			0.571131
$616$	−24.8607	−	10.5498i	−1.00167	−	0.425065i
$617$	23.7025			0.954228			0.477114	−	0.878841i	$-0.341683\pi$
$617$	23.7025			0.954228			0.477114	+	0.878841i	$0.341683\pi$
$618$		−	38.0873i		−	1.53210i
$619$		−	17.4881i		−	0.702906i	−0.936206	−	0.351453i	$-0.885688\pi$
$619$		−	17.4881i		−	0.702906i	0.936206	−	0.351453i	$-0.114312\pi$
$620$	14.0456			0.564087
$621$			2.19336i			0.0880166i
$622$	40.1193			1.60864
$623$	−26.0826	−	4.75903i	−1.04498	−	0.190667i
$624$		−	1.47062i		−	0.0588720i
$625$	14.2667			0.570666
$626$	7.70028			0.307765
$627$	1.99241	−	8.87430i	0.0795690	−	0.354406i
$628$			6.10298i			0.243535i
$629$	−42.2377			−1.68413
$630$	−4.13939	+	22.6866i	−0.164917	+	0.903855i
$631$	−3.00658			−0.119690			−0.0598449	−	0.998208i	$-0.519061\pi$
$631$	−3.00658			−0.119690			−0.0598449	+	0.998208i	$0.519061\pi$
$632$	−18.1103			−0.720390
$633$	19.2017			0.763199
$634$			11.1637i			0.443367i
$635$	−13.8476			−0.549523
$636$			22.2144i			0.880860i
$637$	−21.8035	−	8.23054i	−0.863887	−	0.326106i
$638$	−31.9778	−	7.17946i	−1.26601	−	0.284238i
$639$	5.07680			0.200835
$640$	−72.2993			−2.85788
$641$	14.1501			0.558895			0.279448	−	0.960161i	$-0.409849\pi$
$641$	14.1501			0.558895			0.279448	+	0.960161i	$0.409849\pi$
$642$			11.7737i			0.464672i
$643$		−	13.4238i		−	0.529381i	−0.964333	−	0.264691i	$-0.914730\pi$
$643$		−	13.4238i		−	0.529381i	0.964333	−	0.264691i	$-0.0852699\pi$
$644$	3.47150	−	19.0261i	0.136796	−	0.749735i
$645$			25.4489i			1.00205i
$646$			32.4353i			1.27615i
$647$			21.0809i			0.828775i	0.910100	+	0.414388i	$0.136004\pi$
$647$			21.0809i			0.828775i	−0.910100	+	0.414388i	$0.863996\pi$
$648$			3.07768i			0.120903i
$649$	5.34965	−	23.8277i	0.209992	−	0.935319i
$650$			71.0909i			2.78841i
$651$	0.530259	−	2.90617i	0.0207825	−	0.113902i
$652$	25.7778			1.00954
$653$	−2.87993			−0.112700			−0.0563502	−	0.998411i	$-0.517946\pi$
$653$	−2.87993			−0.112700			−0.0563502	+	0.998411i	$0.517946\pi$
$654$		−	31.5911i		−	1.23531i
$655$		−	32.3029i		−	1.26218i
$656$	−1.65754			−0.0647160
$657$	−12.7339			−0.496796
$658$	−6.12069	+	33.5454i	−0.238609	+	1.30774i
$659$		−	41.2473i		−	1.60677i	−0.595462	−	0.803383i	$-0.703031\pi$
$659$		−	41.2473i		−	1.60677i	0.595462	−	0.803383i	$-0.296969\pi$
$660$	40.7076	+	9.13943i	1.58454	+	0.355752i
$661$			3.22802i			0.125555i	0.998028	+	0.0627777i	$0.0199959\pi$
$661$			3.22802i			0.125555i	−0.998028	+	0.0627777i	$0.980004\pi$
$662$			22.4409i			0.872190i
$663$			17.0522i			0.662253i
$664$			50.0386i			1.94188i
$665$	26.9408	+	4.91561i	1.04472	+	0.190619i
$666$			19.0437i			0.737927i
$667$		−	9.38568i		−	0.363415i
$668$	−1.05331			−0.0407536
$669$	−3.62846			−0.140285
$670$	−17.1522			−0.662646
$671$	−29.8919	−	6.71114i	−1.15396	−	0.259081i
$672$	−2.43878	+	13.3661i	−0.0940779	+	0.515609i
$673$			15.0845i			0.581465i	0.956804	+	0.290733i	$0.0938990\pi$
$673$			15.0845i			0.581465i	−0.956804	+	0.290733i	$0.906101\pi$
$674$	−52.1653			−2.00933
$675$		−	9.24660i		−	0.355902i
$676$	6.38424			0.245548
$677$	−24.9654			−0.959497			−0.479749	−	0.877406i	$-0.659272\pi$
$677$	−24.9654			−0.959497			−0.479749	+	0.877406i	$0.659272\pi$
$678$	−39.4837			−1.51636
$679$	−37.6038	−	6.86119i	−1.44310	−	0.263308i
$680$	−59.4983			−2.28166
$681$			3.07364i			0.117782i
$682$	−8.34405	−	1.87335i	−0.319510	−	0.0717345i
$683$	6.67138			0.255273			0.127637	−	0.991821i	$-0.459261\pi$
$683$	6.67138			0.255273			0.127637	+	0.991821i	$0.459261\pi$
$684$	9.13943			0.349455
$685$			31.8850i			1.21826i
$686$	−36.6515	−	22.0410i	−1.39936	−	0.841527i
$687$	−15.3766			−0.586656
$688$		−	2.97823i		−	0.113544i
$689$	22.1916			0.845433
$690$			19.1180i			0.727808i
$691$			37.8885i			1.44135i	0.693274	+	0.720674i	$0.256168\pi$
$691$			37.8885i			1.44135i	−0.693274	+	0.720674i	$0.743832\pi$
$692$	67.1329			2.55201
$693$	3.42785	−	8.07774i	0.130213	−	0.306848i
$694$	21.0733			0.799931
$695$		−	8.01633i		−	0.304077i
$696$		−	13.1698i		−	0.499200i
$697$	19.2195			0.727992
$698$			50.3503i			1.90579i
$699$	−16.2874			−0.616047
$700$	−14.6349	+	80.2089i	−0.553147	+	3.03161i
$701$			18.3545i			0.693240i	0.938006	+	0.346620i	$0.112671\pi$
$701$			18.3545i			0.693240i	−0.938006	+	0.346620i	$0.887329\pi$
$702$	7.68832			0.290177
$703$	22.6148			0.852931
$704$	41.2349	+	9.25782i	1.55410	+	0.348917i
$705$		−	21.0657i		−	0.793380i
$706$	−5.77504			−0.217346
$707$	7.39884	−	40.5505i	0.278262	−	1.52506i
$708$	24.5396			0.922254
$709$	−10.2937			−0.386589			−0.193294	−	0.981141i	$-0.561917\pi$
$709$	−10.2937			−0.386589			−0.193294	+	0.981141i	$0.561917\pi$
$710$	44.2508			1.66070
$711$		−	5.88440i		−	0.220682i
$712$	−30.8417			−1.15584
$713$		−	2.44903i		−	0.0917168i
$714$	−5.61701	+	30.7849i	−0.210211	+	1.15210i
$715$	9.13004	−	40.6658i	0.341444	−	1.52081i
$716$	−27.5092			−1.02807
$717$	−13.8242			−0.516273
$718$	74.0597			2.76388
$719$		−	31.8412i		−	1.18748i	−0.804659	−	0.593738i	$-0.797652\pi$
$719$		−	31.8412i		−	1.18748i	0.804659	−	0.593738i	$-0.202348\pi$
$720$			1.66725i			0.0621348i
$721$	−42.9282	−	7.83267i	−1.59873	−	0.291704i
$722$			26.5098i			0.986594i
$723$			5.22893i			0.194466i
$724$			34.7685i			1.29216i
$725$			39.5674i			1.46950i
$726$	−22.9641	−	10.8589i	−0.852276	−	0.403010i
$727$			20.1501i			0.747326i	0.927565	+	0.373663i	$0.121898\pi$
$727$			20.1501i			0.747326i	−0.927565	+	0.373663i	$0.878102\pi$
$728$	−26.6697	−	4.86614i	−0.988443	−	0.180351i
$729$	−1.00000			−0.0370370
$730$	−110.992			−4.10800
$731$			34.5333i			1.27726i
$732$		−	30.7849i		−	1.13784i
$733$	16.7421			0.618382			0.309191	−	0.951000i	$-0.399942\pi$
$733$	16.7421			0.618382			0.309191	+	0.951000i	$0.399942\pi$
$734$	−11.0232			−0.406874
$735$	24.7187	+	9.33100i	0.911764	+	0.344179i
$736$			11.2636i			0.415182i
$737$	6.36803	+	1.42971i	0.234569	+	0.0526641i
$738$		−	8.66550i		−	0.318981i
$739$			9.60180i			0.353208i	0.984282	+	0.176604i	$0.0565112\pi$
$739$			9.60180i			0.353208i	−0.984282	+	0.176604i	$0.943489\pi$
$740$			103.737i			3.81345i
$741$		−	9.13004i		−	0.335400i
$742$	40.0632	+	7.30993i	1.47077	+	0.268356i
$743$			9.95098i			0.365066i	0.983200	+	0.182533i	$0.0584297\pi$
$743$			9.95098i			0.365066i	−0.983200	+	0.182533i	$0.941570\pi$
$744$		−	3.43643i		−	0.125986i
$745$	20.5827			0.754094
$746$	−9.87335			−0.361489
$747$	−16.2585			−0.594869
$748$	55.2389	+	12.4019i	2.01974	+	0.453459i
$749$	13.2702	+	2.42127i	0.484881	+	0.0884713i
$750$		−	37.0146i		−	1.35158i
$751$	53.5437			1.95384			0.976919	−	0.213610i	$-0.0685222\pi$
$751$	53.5437			1.95384			0.976919	+	0.213610i	$0.0685222\pi$
$752$			2.46528i			0.0898994i
$753$	−1.19438			−0.0435257
$754$	−32.8993			−1.19812
$755$	−28.0112			−1.01943
$756$	8.67441	+	1.58273i	0.315485	+	0.0575634i
$757$	−38.4423			−1.39721			−0.698605	−	0.715507i	$-0.746196\pi$
$757$	−38.4423			−1.39721			−0.698605	+	0.715507i	$0.746196\pi$
$758$			5.58589i			0.202889i
$759$	1.59357	−	7.09787i	0.0578430	−	0.257636i
$760$	31.8564			1.15555
$761$	−34.1863			−1.23925			−0.619626	−	0.784897i	$-0.712716\pi$
$761$	−34.1863			−1.23925			−0.619626	+	0.784897i	$0.712716\pi$
$762$			8.47214i			0.306913i
$763$	−35.6063	−	6.49671i	−1.28903	−	0.235197i
$764$	34.3268			1.24190
$765$		−	19.3322i		−	0.698956i
$766$	57.6032			2.08129
$767$		−	24.5144i		−	0.885162i
$768$			18.7492i			0.676552i
$769$	1.52320			0.0549282			0.0274641	−	0.999623i	$-0.491257\pi$
$769$	1.52320			0.0549282			0.0274641	+	0.999623i	$0.491257\pi$
$770$	29.8781	−	70.4078i	1.07673	−	2.53732i
$771$	15.8166			0.569621
$772$		−	0.650978i		−	0.0234292i
$773$		−	43.8809i		−	1.57829i	−0.614208	−	0.789144i	$-0.710524\pi$
$773$		−	43.8809i		−	1.57829i	0.614208	−	0.789144i	$-0.289476\pi$
$774$	15.5700			0.559652
$775$			10.3244i			0.370864i
$776$	−44.4650			−1.59620
$777$	21.4641	+	3.91634i	0.770020	+	0.140498i
$778$			56.0583i			2.00979i
$779$	−10.2905			−0.368694
$780$	41.8807			1.49957
$781$	−16.4289	−	3.68851i	−0.587871	−	0.131985i
$782$			25.9424i			0.927700i
$783$	4.27913			0.152924
$784$	−2.89278	−	1.09199i	−0.103314	−	0.0389996i
$785$	−6.91186			−0.246695
$786$	−19.7634			−0.704936
$787$	7.83628			0.279333			0.139667	−	0.990199i	$-0.455397\pi$
$787$	7.83628			0.279333			0.139667	+	0.990199i	$0.455397\pi$
$788$		−	19.5843i		−	0.697660i
$789$	24.7467			0.881005
$790$		−	51.2901i		−	1.82482i
$791$	−8.11983	+	44.5020i	−0.288708	+	1.58231i
$792$	2.23607	−	9.95959i	0.0794552	−	0.353899i
$793$	−30.7533			−1.09208
$794$	67.1869			2.38437
$795$	−25.1587			−0.892287
$796$			0.714650i			0.0253301i
$797$			12.2255i			0.433051i	0.976277	+	0.216525i	$0.0694724\pi$
$797$			12.2255i			0.433051i	−0.976277	+	0.216525i	$0.930528\pi$
$798$	3.00744	−	16.4828i	0.106462	−	0.583483i
$799$		−	28.5855i		−	1.01128i
$800$		−	47.4843i		−	1.67882i
$801$		−	10.0211i		−	0.354077i
$802$			27.8167i			0.982242i
$803$	41.2077	+	9.25171i	1.45419	+	0.326486i
$804$			6.55828i			0.231293i
$805$	21.5478	+	3.93161i	0.759461	+	0.138571i
$806$	−8.58450			−0.302376
$807$	−13.0768			−0.460325
$808$		−	47.9494i		−	1.68685i
$809$		−	5.29290i		−	0.186088i	−0.995662	−	0.0930442i	$-0.970340\pi$
$809$		−	5.29290i		−	0.186088i	0.995662	−	0.0930442i	$-0.0296598\pi$
$810$	−8.71628			−0.306259
$811$	−43.0993			−1.51342			−0.756710	−	0.653751i	$-0.773195\pi$
$811$	−43.0993			−1.51342			−0.756710	+	0.653751i	$0.773195\pi$
$812$	−37.1189	−	6.77271i	−1.30262	−	0.237676i
$813$		−	24.8015i		−	0.869827i
$814$	13.8360	−	61.6266i	0.484953	−	2.16001i
$815$			29.1944i			1.02263i
$816$			2.26240i			0.0792000i
$817$		−	18.4897i		−	0.646873i
$818$		−	34.4912i		−	1.20596i
$819$	1.58111	−	8.66550i	0.0552483	−	0.302797i
$820$		−	47.2037i		−	1.64843i
$821$		−	44.6289i		−	1.55756i	−0.627298	−	0.778779i	$-0.715839\pi$
$821$		−	44.6289i		−	1.55756i	0.627298	−	0.778779i	$-0.284161\pi$
$822$	19.5077			0.680410
$823$	−12.6942			−0.442491			−0.221245	−	0.975218i	$-0.571012\pi$
$823$	−12.6942			−0.442491			−0.221245	+	0.975218i	$0.571012\pi$
$824$	−50.7609			−1.76834
$825$	−6.71805	+	29.9226i	−0.233892	+	1.04177i
$826$	8.07505	−	44.2566i	0.280967	−	1.53988i
$827$			0.667138i			0.0231987i	0.999933	+	0.0115993i	$0.00369227\pi$
$827$			0.667138i			0.0231987i	−0.999933	+	0.0115993i	$0.996308\pi$
$828$	7.30993			0.254037
$829$			3.13526i			0.108892i	0.998517	+	0.0544460i	$0.0173393\pi$
$829$			3.13526i			0.108892i	−0.998517	+	0.0544460i	$0.982661\pi$
$830$	−141.714			−4.91896
$831$	−4.26385			−0.147911
$832$	42.4232			1.47076
$833$	33.5425	+	12.6619i	1.16218	+	0.438707i
$834$	−4.90451			−0.169829
$835$		−	1.19291i		−	0.0412823i
$836$	−29.5758	−	6.64019i	−1.02290	−	0.229656i
$837$	1.11656			0.0385941
$838$	19.1491			0.661494
$839$		−	11.7195i		−	0.404603i	−0.979323	−	0.202301i	$-0.935158\pi$
$839$		−	11.7195i		−	0.404603i	0.979323	−	0.202301i	$-0.0648420\pi$
$840$	30.2355	+	5.51676i	1.04322	+	0.190346i
$841$	10.6891			0.368588
$842$			5.87496i			0.202464i
$843$	−17.4290			−0.600285
$844$		−	63.9944i		−	2.20278i
$845$			7.23040i			0.248733i
$846$	−12.8883			−0.443109
$847$	−16.9616	+	23.6496i	−0.582807	+	0.812611i
$848$	2.94427			0.101107
$849$			10.5750i			0.362932i
$850$		−	109.366i		−	3.75123i
$851$	18.0878			0.620041
$852$		−	16.9197i		−	0.579659i
$853$	9.96269			0.341116			0.170558	−	0.985348i	$-0.445443\pi$
$853$	9.96269			0.341116			0.170558	+	0.985348i	$0.445443\pi$
$854$	−55.5199	−	10.1302i	−1.89985	−	0.346647i
$855$			10.3508i			0.353989i
$856$	15.6914			0.536322
$857$	−49.5868			−1.69385			−0.846927	−	0.531709i	$-0.821550\pi$
$857$	−49.5868			−1.69385			−0.846927	+	0.531709i	$0.821550\pi$
$858$	−24.8799	−	5.58589i	−0.849387	−	0.190699i
$859$			42.5977i			1.45341i	0.686948	+	0.726707i	$0.258950\pi$
$859$			42.5977i			1.45341i	−0.686948	+	0.726707i	$0.741050\pi$
$860$	84.8148			2.89216
$861$	−9.76687	−	1.78206i	−0.332854	−	0.0607325i
$862$	51.8325			1.76542
$863$	41.7996			1.42288			0.711438	−	0.702749i	$-0.248044\pi$
$863$	41.7996			1.42288			0.711438	+	0.702749i	$0.248044\pi$
$864$	−5.13532			−0.174707
$865$			76.0306i			2.58512i
$866$	65.6150			2.22969
$867$		−	9.23313i		−	0.313573i
$868$	−9.68554	−	1.76722i	−0.328749	−	0.0599834i
$869$	−4.27527	+	19.0423i	−0.145029	+	0.645967i
$870$	37.2981			1.26452
$871$	6.55154			0.221990
$872$	−42.1030			−1.42579
$873$		−	14.4476i		−	0.488976i
$874$		−	13.8900i		−	0.469837i
$875$	−41.7191	−	7.61206i	−1.41036	−	0.257335i
$876$			42.4389i			1.43388i
$877$			30.2663i			1.02202i	0.859574	+	0.511011i	$0.170729\pi$
$877$			30.2663i			1.02202i	−0.859574	+	0.511011i	$0.829271\pi$
$878$		−	53.9224i		−	1.81979i
$879$			21.3804i			0.721142i
$880$	1.21133	−	5.39534i	0.0408339	−	0.181877i
$881$		−	36.1238i		−	1.21704i	−0.793538	−	0.608521i	$-0.791763\pi$
$881$		−	36.1238i		−	1.21704i	0.793538	−	0.608521i	$-0.208237\pi$
$882$	5.70884	−	15.1233i	0.192227	−	0.509228i
$883$	45.6654			1.53676			0.768381	−	0.639992i	$-0.221062\pi$
$883$	45.6654			1.53676			0.768381	+	0.639992i	$0.221062\pi$
$884$	56.8308			1.91143
$885$			27.7920i			0.934219i
$886$			17.0292i			0.572107i
$887$	−14.2454			−0.478314			−0.239157	−	0.970981i	$-0.576871\pi$
$887$	−14.2454			−0.478314			−0.239157	+	0.970981i	$0.576871\pi$
$888$	25.3804			0.851712
$889$	9.54893	+	1.74230i	0.320261	+	0.0584348i
$890$		−	87.3465i		−	2.92786i
$891$	3.23607	+	0.726543i	0.108412	+	0.0243401i
$892$			12.0928i			0.404896i
$893$			15.3051i			0.512167i
$894$		−	12.5928i		−	0.421167i
$895$		−	31.1552i		−	1.04140i
$896$	49.8558	+	9.09668i	1.66557	+	0.303899i
$897$		−	7.30241i		−	0.243820i
$898$			60.1034i			2.00568i
$899$	−4.77792			−0.159353
$900$	−30.8166			−1.02722
$901$	−34.1395			−1.13735
$902$	−6.29585	+	28.0421i	−0.209629	+	0.933701i
$903$	3.20198	−	17.5489i	0.106555	−	0.583992i
$904$			52.6218i			1.75018i
$905$	−39.3766			−1.30892
$906$			17.1376i			0.569360i
$907$	19.1774			0.636775			0.318388	−	0.947961i	$-0.396859\pi$
$907$	19.1774			0.636775			0.318388	+	0.947961i	$0.396859\pi$
$908$	10.2437			0.339948
$909$	15.5797			0.516746
$910$	13.7814	−	75.5309i	0.456848	−	2.50383i
$911$	23.4737			0.777720			0.388860	−	0.921297i	$-0.372869\pi$
$911$	23.4737			0.777720			0.388860	+	0.921297i	$0.372869\pi$
$912$		−	1.21133i		−	0.0401111i
$913$	52.6137	+	11.8125i	1.74126	+	0.390937i
$914$	26.0608			0.862016
$915$	34.8651			1.15261
$916$			51.2465i			1.69323i
$917$	−4.06434	+	22.2753i	−0.134216	+	0.735594i
$918$	−11.8277			−0.390373
$919$		−	12.8519i		−	0.423944i	−0.977276	−	0.211972i	$-0.932011\pi$
$919$		−	12.8519i		−	0.423944i	0.977276	−	0.211972i	$-0.0679886\pi$
$920$	25.4794			0.840032
$921$		−	26.2034i		−	0.863430i
$922$		−	25.7177i		−	0.846968i
$923$	−16.9023			−0.556346
$924$	−26.9211	−	11.4242i	−0.885638	−	0.375827i
$925$	−76.2531			−2.50719
$926$		−	1.32204i		−	0.0434450i
$927$		−	16.4932i		−	0.541708i
$928$	21.9747			0.721355
$929$			12.9195i			0.423873i	0.977283	+	0.211937i	$0.0679771\pi$
$929$			12.9195i			0.423873i	−0.977283	+	0.211937i	$0.932023\pi$
$930$	9.73228			0.319134
$931$	−17.9592	−	6.77937i	−0.588590	−	0.222185i
$932$			54.2819i			1.77806i
$933$	17.3731			0.568771
$934$	−20.9352			−0.685020
$935$	−14.0456	+	62.5602i	−0.459342	+	2.04594i
$936$		−	10.2466i		−	0.334921i
$937$	5.64487			0.184410			0.0922050	−	0.995740i	$-0.470608\pi$
$937$	5.64487			0.184410			0.0922050	+	0.995740i	$0.470608\pi$
$938$	11.8277	+	2.15808i	0.386188	+	0.0704639i
$939$	3.33450			0.108817
$940$	−70.2067			−2.28989
$941$	−20.5341			−0.669391			−0.334696	−	0.942326i	$-0.608633\pi$
$941$	−20.5341			−0.669391			−0.334696	+	0.942326i	$0.608633\pi$
$942$			4.22878i			0.137781i
$943$	−8.23054			−0.268023
$944$		−	3.25244i		−	0.105858i
$945$	−1.79251	+	9.82411i	−0.0583102	+	0.319578i
$946$	−50.3856	−	11.3123i	−1.63818	−	0.367794i
$947$	−28.7170			−0.933178			−0.466589	−	0.884474i	$-0.654517\pi$
$947$	−28.7170			−0.933178			−0.466589	+	0.884474i	$0.654517\pi$
$948$	−19.6112			−0.636943
$949$	42.3952			1.37621
$950$			58.5564i			1.89982i
$951$			4.83428i			0.156762i
$952$	41.0286	+	7.48607i	1.32974	+	0.242625i
$953$		−	33.3085i		−	1.07897i	−0.841996	−	0.539484i	$-0.818619\pi$
$953$		−	33.3085i		−	1.07897i	0.841996	−	0.539484i	$-0.181381\pi$
$954$			15.3925i			0.498349i
$955$			38.8764i			1.25801i
$956$			46.0725i			1.49009i
$957$	−13.8476	−	3.10897i	−0.447628	−	0.100499i
$958$			83.1973i			2.68798i
$959$	4.01177	−	21.9871i	0.129547	−	0.710002i
$960$	−48.0954			−1.55227
$961$	29.7533			0.959783
$962$		−	63.4025i		−	2.04418i
$963$			5.09846i			0.164295i
$964$	17.4267			0.561277
$965$	0.737258			0.0237332
$966$	2.40542	−	13.1833i	0.0773931	−	0.424165i
$967$			4.50338i			0.144819i	0.997375	+	0.0724094i	$0.0230688\pi$
$967$			4.50338i			0.144819i	−0.997375	+	0.0724094i	$0.976931\pi$
$968$	−14.4721	+	30.6053i	−0.465152	+	0.983692i
$969$			14.0456i			0.451211i
$970$		−	125.929i		−	4.04334i
$971$			28.7585i			0.922904i	0.887165	+	0.461452i	$0.152671\pi$
$971$			28.7585i			0.922904i	−0.887165	+	0.461452i	$0.847329\pi$
$972$			3.33275i			0.106898i
$973$	−1.00861	+	5.52786i	−0.0323346	+	0.177215i
$974$			85.0173i			2.72413i
$975$			30.7849i			0.985907i
$976$	−4.08019			−0.130604
$977$	47.5454			1.52111			0.760557	−	0.649272i	$-0.224926\pi$
$977$	47.5454			1.52111			0.760557	+	0.649272i	$0.224926\pi$
$978$	17.8616			0.571149
$979$	−7.28073	+	32.4289i	−0.232693	+	1.03643i
$980$	31.0979	−	82.3814i	0.993385	−	2.63158i
$981$		−	13.6801i		−	0.436772i
$982$	−20.4392			−0.652242
$983$			33.3731i			1.06444i	0.846607	+	0.532219i	$0.178642\pi$
$983$			33.3731i			1.06444i	−0.846607	+	0.532219i	$0.821358\pi$
$984$	−11.5489			−0.368167
$985$	22.1799			0.706711
$986$	50.6123			1.61182
$987$	−2.65048	+	14.5264i	−0.0843658	+	0.462380i
$988$	−30.4281			−0.968048
$989$		−	14.7885i		−	0.470246i
$990$	28.2065	+	6.33275i	0.896461	+	0.201268i
$991$	−24.1788			−0.768064			−0.384032	−	0.923320i	$-0.625465\pi$
$991$	−24.1788			−0.768064			−0.384032	+	0.923320i	$0.625465\pi$
$992$	5.73391			0.182052
$993$			9.71772i			0.308383i
$994$	−30.5143	−	5.56763i	−0.967854	−	0.176594i
$995$	−0.809369			−0.0256587
$996$			54.1856i			1.71694i
$997$	5.14071			0.162808			0.0814040	−	0.996681i	$-0.474060\pi$
$997$	5.14071			0.162808			0.0814040	+	0.996681i	$0.474060\pi$
$998$		−	46.8955i		−	1.48445i
$999$			8.24660i			0.260911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.c.a.76.1	✓	16
3.2	odd	2		693.2.c.e.307.16		16
4.3	odd	2		3696.2.q.e.769.10		16
7.6	odd	2	inner	231.2.c.a.76.2	yes	16
11.10	odd	2	inner	231.2.c.a.76.15	yes	16
21.20	even	2		693.2.c.e.307.15		16
28.27	even	2		3696.2.q.e.769.7		16
33.32	even	2		693.2.c.e.307.2		16
44.43	even	2		3696.2.q.e.769.9		16
77.76	even	2	inner	231.2.c.a.76.16	yes	16
231.230	odd	2		693.2.c.e.307.1		16
308.307	odd	2		3696.2.q.e.769.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.c.a.76.1	✓	16	1.1	even	1	trivial
231.2.c.a.76.2	yes	16	7.6	odd	2	inner
231.2.c.a.76.15	yes	16	11.10	odd	2	inner
231.2.c.a.76.16	yes	16	77.76	even	2	inner
693.2.c.e.307.1		16	231.230	odd	2
693.2.c.e.307.2		16	33.32	even	2
693.2.c.e.307.15		16	21.20	even	2
693.2.c.e.307.16		16	3.2	odd	2
3696.2.q.e.769.7		16	28.27	even	2
3696.2.q.e.769.8		16	308.307	odd	2
3696.2.q.e.769.9		16	44.43	even	2
3696.2.q.e.769.10		16	4.3	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.30927i q^{2} -1.00000i q^{3} -3.33275 q^{4} -3.77447i q^{5} -2.30927 q^{6} +(-0.474903 + 2.60278i) q^{7} +3.07768i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.30927i q^{2} -1.00000i q^{3} -3.33275 q^{4} -3.77447i q^{5} -2.30927 q^{6} +(-0.474903 + 2.60278i) q^{7} +3.07768i q^{8} -1.00000 q^{9} -8.71628 q^{10} +(3.23607 + 0.726543i) q^{11} +3.33275i q^{12} +3.32932 q^{13} +(6.01054 + 1.09668i) q^{14} -3.77447 q^{15} +0.441718 q^{16} -5.12183 q^{17} +2.30927i q^{18} +2.74231 q^{19} +12.5794i q^{20} +(2.60278 + 0.474903i) q^{21} +(1.67779 - 7.47297i) q^{22} +2.19336 q^{23} +3.07768 q^{24} -9.24660 q^{25} -7.68832i q^{26} +1.00000i q^{27} +(1.58273 - 8.67441i) q^{28} -4.27913i q^{29} +8.71628i q^{30} -1.11656i q^{31} +5.13532i q^{32} +(0.726543 - 3.23607i) q^{33} +11.8277i q^{34} +(9.82411 + 1.79251i) q^{35} +3.33275 q^{36} +8.24660 q^{37} -6.33275i q^{38} -3.32932i q^{39} +11.6166 q^{40} -3.75248 q^{41} +(1.09668 - 6.01054i) q^{42} -6.74238i q^{43} +(-10.7850 - 2.42138i) q^{44} +3.77447i q^{45} -5.06508i q^{46} +5.58111i q^{47} -0.441718i q^{48} +(-6.54893 - 2.47214i) q^{49} +21.3529i q^{50} +5.12183i q^{51} -11.0958 q^{52} +6.66550 q^{53} +2.30927 q^{54} +(2.74231 - 12.2144i) q^{55} +(-8.01054 - 1.46160i) q^{56} -2.74231i q^{57} -9.88168 q^{58} -7.36317i q^{59} +12.5794 q^{60} -9.23710 q^{61} -2.57845 q^{62} +(0.474903 - 2.60278i) q^{63} +12.7423 q^{64} -12.5664i q^{65} +(-7.47297 - 1.67779i) q^{66} +1.96783 q^{67} +17.0698 q^{68} -2.19336i q^{69} +(4.13939 - 22.6866i) q^{70} -5.07680 q^{71} -3.07768i q^{72} +12.7339 q^{73} -19.0437i q^{74} +9.24660i q^{75} -9.13943 q^{76} +(-3.42785 + 8.07774i) q^{77} -7.68832 q^{78} +5.88440i q^{79} -1.66725i q^{80} +1.00000 q^{81} +8.66550i q^{82} +16.2585 q^{83} +(-8.67441 - 1.58273i) q^{84} +19.3322i q^{85} -15.5700 q^{86} -4.27913 q^{87} +(-2.23607 + 9.95959i) q^{88} +10.0211i q^{89} +8.71628 q^{90} +(-1.58111 + 8.66550i) q^{91} -7.30993 q^{92} -1.11656 q^{93} +12.8883 q^{94} -10.3508i q^{95} +5.13532 q^{96} +14.4476i q^{97} +(-5.70884 + 15.1233i) q^{98} +(-3.23607 - 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4} - 16 q^{9}+O(q^{10}) \) 16 * q - 12 * q^4 - 16 * q^9	\( 16 q - 12 q^{4} - 16 q^{9} + 16 q^{11} + 8 q^{14} - 8 q^{15} - 4 q^{16} - 20 q^{22} + 24 q^{23} - 24 q^{25} + 12 q^{36} + 8 q^{37} + 12 q^{42} - 32 q^{44} + 24 q^{53} - 40 q^{56} - 12 q^{58} + 36 q^{60} + 88 q^{64} - 32 q^{67} + 36 q^{70} - 48 q^{71} + 12 q^{78} + 16 q^{81} + 32 q^{86} + 16 q^{91} - 128 q^{92} - 40 q^{93} - 16 q^{99}+O(q^{100}) \) 16 * q - 12 * q^4 - 16 * q^9 + 16 * q^11 + 8 * q^14 - 8 * q^15 - 4 * q^16 - 20 * q^22 + 24 * q^23 - 24 * q^25 + 12 * q^36 + 8 * q^37 + 12 * q^42 - 32 * q^44 + 24 * q^53 - 40 * q^56 - 12 * q^58 + 36 * q^60 + 88 * q^64 - 32 * q^67 + 36 * q^70 - 48 * q^71 + 12 * q^78 + 16 * q^81 + 32 * q^86 + 16 * q^91 - 128 * q^92 - 40 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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