LMFDB - Embedded newform 231.2.c.a.76.6

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			76.6
Root			$1.86824 - 0.357358i$ of defining polynomial
Character	$\chi$	$=$	231.76
Dual form			231.2.c.a.76.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.13370i q^{2} +1.00000i q^{3} +0.714715 q^{4} -2.77447i q^{5} +1.13370 q^{6} +(-2.60278 - 0.474903i) q^{7} -3.07768i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.13370i q^{2} +1.00000i q^{3} +0.714715 q^{4} -2.77447i q^{5} +1.13370 q^{6} +(-2.60278 - 0.474903i) q^{7} -3.07768i q^{8} -1.00000 q^{9} -3.14542 q^{10} +(3.23607 - 0.726543i) q^{11} +0.714715i q^{12} +1.20145 q^{13} +(-0.538399 + 2.95078i) q^{14} +2.77447 q^{15} -2.05975 q^{16} +6.01988 q^{17} +1.13370i q^{18} -2.01577 q^{19} -1.98295i q^{20} +(0.474903 - 2.60278i) q^{21} +(-0.823684 - 3.66874i) q^{22} -5.90157 q^{23} +3.07768 q^{24} -2.69767 q^{25} -1.36208i q^{26} -1.00000i q^{27} +(-1.86025 - 0.339420i) q^{28} +6.40701i q^{29} -3.14542i q^{30} +6.11950i q^{31} -3.82022i q^{32} +(0.726543 + 3.23607i) q^{33} -6.82477i q^{34} +(-1.31760 + 7.22133i) q^{35} -0.714715 q^{36} +1.69767 q^{37} +2.28528i q^{38} +1.20145i q^{39} -8.53893 q^{40} +0.503279 q^{41} +(-2.95078 - 0.538399i) q^{42} +9.37258i q^{43} +(2.31287 - 0.519271i) q^{44} +2.77447i q^{45} +6.69063i q^{46} -7.12710i q^{47} -2.05975i q^{48} +(6.54893 + 2.47214i) q^{49} +3.05836i q^{50} +6.01988i q^{51} +0.858691 q^{52} -1.42943 q^{53} -1.13370 q^{54} +(-2.01577 - 8.97836i) q^{55} +(-1.46160 + 8.01054i) q^{56} -2.01577i q^{57} +7.26365 q^{58} +5.81717i q^{59} +1.98295 q^{60} +4.53482 q^{61} +6.93771 q^{62} +(2.60278 + 0.474903i) q^{63} -8.45050 q^{64} -3.33337i q^{65} +(3.66874 - 0.823684i) q^{66} -12.6760 q^{67} +4.30250 q^{68} -5.90157i q^{69} +(8.18685 + 1.49377i) q^{70} +8.02107 q^{71} +3.07768i q^{72} +10.6060 q^{73} -1.92465i q^{74} -2.69767i q^{75} -1.44070 q^{76} +(-8.76781 + 0.354213i) q^{77} +1.36208 q^{78} +16.3990i q^{79} +5.71472i q^{80} +1.00000 q^{81} -0.570570i q^{82} -0.143578 q^{83} +(0.339420 - 1.86025i) q^{84} -16.7020i q^{85} +10.6257 q^{86} -6.40701 q^{87} +(-2.23607 - 9.95959i) q^{88} +3.07680i q^{89} +3.14542 q^{90} +(-3.12710 - 0.570570i) q^{91} -4.21794 q^{92} -6.11950 q^{93} -8.08002 q^{94} +5.59268i q^{95} +3.82022 q^{96} -3.26064i q^{97} +(2.80267 - 7.42455i) q^{98} +(-3.23607 + 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.13370i		−	0.801650i	−0.916155	−	0.400825i	$-0.868724\pi$
$2$		−	1.13370i		−	0.801650i	0.916155	−	0.400825i	$-0.131276\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.714715			0.357358
$5$		−	2.77447i		−	1.24078i	−0.784294	−	0.620390i	$-0.786974\pi$
$5$		−	2.77447i		−	1.24078i	0.784294	−	0.620390i	$-0.213026\pi$
$6$	1.13370			0.462833
$7$	−2.60278	−	0.474903i	−0.983759	−	0.179496i
$7$	−2.60278	−	0.474903i	−0.983759	−	0.179496i
$8$		−	3.07768i		−	1.08813i
$9$	−1.00000			−0.333333
$10$	−3.14542			−0.994671
$11$	3.23607	−	0.726543i	0.975711	−	0.219061i
$11$	3.23607	−	0.726543i	0.975711	−	0.219061i
$12$			0.714715i			0.206320i
$13$	1.20145			0.333221			0.166610	−	0.986023i	$-0.446718\pi$
$13$	1.20145			0.333221			0.166610	+	0.986023i	$0.446718\pi$
$14$	−0.538399	+	2.95078i	−0.143893	+	0.788630i
$15$	2.77447			0.716364
$16$	−2.05975			−0.514938
$17$	6.01988			1.46004			0.730018	−	0.683428i	$-0.239512\pi$
$17$	6.01988			1.46004			0.730018	+	0.683428i	$0.239512\pi$
$18$			1.13370i			0.267217i
$19$	−2.01577			−0.462449			−0.231225	−	0.972900i	$-0.574273\pi$
$19$	−2.01577			−0.462449			−0.231225	+	0.972900i	$0.574273\pi$
$20$		−	1.98295i		−	0.443402i
$21$	0.474903	−	2.60278i	0.103632	−	0.567973i
$22$	−0.823684	−	3.66874i	−0.175610	−	0.782179i
$23$	−5.90157			−1.23056			−0.615281	−	0.788308i	$-0.710957\pi$
$23$	−5.90157			−1.23056			−0.615281	+	0.788308i	$0.710957\pi$
$24$	3.07768			0.628230
$25$	−2.69767			−0.539534
$26$		−	1.36208i		−	0.267127i
$27$		−	1.00000i		−	0.192450i
$28$	−1.86025	−	0.339420i	−0.351554	−	0.0641444i
$29$			6.40701i			1.18975i	0.803818	+	0.594876i	$0.202799\pi$
$29$			6.40701i			1.18975i	−0.803818	+	0.594876i	$0.797201\pi$
$30$		−	3.14542i		−	0.574273i
$31$			6.11950i			1.09910i	0.835462	+	0.549548i	$0.185200\pi$
$31$			6.11950i			1.09910i	−0.835462	+	0.549548i	$0.814800\pi$
$32$		−	3.82022i		−	0.675325i
$33$	0.726543	+	3.23607i	0.126475	+	0.563327i
$34$		−	6.82477i		−	1.17044i
$35$	−1.31760	+	7.22133i	−0.222715	+	1.22063i
$36$	−0.714715			−0.119119
$37$	1.69767			0.279095			0.139548	−	0.990215i	$-0.455435\pi$
$37$	1.69767			0.279095			0.139548	+	0.990215i	$0.455435\pi$
$38$			2.28528i			0.370722i
$39$			1.20145i			0.192385i
$40$	−8.53893			−1.35012
$41$	0.503279			0.0785990			0.0392995	−	0.999227i	$-0.487487\pi$
$41$	0.503279			0.0785990			0.0392995	+	0.999227i	$0.487487\pi$
$42$	−2.95078	−	0.538399i	−0.455316	−	0.0830768i
$43$			9.37258i			1.42931i	0.699480	+	0.714653i	$0.253415\pi$
$43$			9.37258i			1.42931i	−0.699480	+	0.714653i	$0.746585\pi$
$44$	2.31287	−	0.519271i	0.348678	−	0.0782830i
$45$			2.77447i			0.413593i
$46$			6.69063i			0.986480i
$47$		−	7.12710i		−	1.03959i	−0.854290	−	0.519797i	$-0.826008\pi$
$47$		−	7.12710i		−	1.03959i	0.854290	−	0.519797i	$-0.173992\pi$
$48$		−	2.05975i		−	0.297300i
$49$	6.54893	+	2.47214i	0.935562	+	0.353162i
$50$			3.05836i			0.432517i
$51$			6.01988i			0.842952i
$52$	0.858691			0.119079
$53$	−1.42943			−0.196347			−0.0981737	−	0.995169i	$-0.531300\pi$
$53$	−1.42943			−0.196347			−0.0981737	+	0.995169i	$0.531300\pi$
$54$	−1.13370			−0.154278
$55$	−2.01577	−	8.97836i	−0.271806	−	1.21064i
$56$	−1.46160	+	8.01054i	−0.195315	+	1.07045i
$57$		−	2.01577i		−	0.266995i
$58$	7.26365			0.953764
$59$			5.81717i			0.757331i	0.925534	+	0.378666i	$0.123617\pi$
$59$			5.81717i			0.757331i	−0.925534	+	0.378666i	$0.876383\pi$
$60$	1.98295			0.255998
$61$	4.53482			0.580624			0.290312	−	0.956932i	$-0.406241\pi$
$61$	4.53482			0.580624			0.290312	+	0.956932i	$0.406241\pi$
$62$	6.93771			0.881090
$63$	2.60278	+	0.474903i	0.327920	+	0.0598321i
$64$	−8.45050			−1.05631
$65$		−	3.33337i		−	0.413454i
$66$	3.66874	−	0.823684i	0.451591	−	0.101389i
$67$	−12.6760			−1.54862			−0.774312	−	0.632804i	$-0.781904\pi$
$67$	−12.6760			−1.54862			−0.774312	+	0.632804i	$0.781904\pi$
$68$	4.30250			0.521755
$69$		−	5.90157i		−	0.710465i
$70$	8.18685	+	1.49377i	0.978516	+	0.178540i
$71$	8.02107			0.951926			0.475963	−	0.879465i	$-0.342100\pi$
$71$	8.02107			0.951926			0.475963	+	0.879465i	$0.342100\pi$
$72$			3.07768i			0.362708i
$73$	10.6060			1.24134			0.620670	−	0.784072i	$-0.286861\pi$
$73$	10.6060			1.24134			0.620670	+	0.784072i	$0.286861\pi$
$74$		−	1.92465i		−	0.223736i
$75$		−	2.69767i		−	0.311500i
$76$	−1.44070			−0.165260
$77$	−8.76781	+	0.354213i	−0.999185	+	0.0403663i
$78$	1.36208			0.154226
$79$			16.3990i			1.84503i	0.385956	+	0.922517i	$0.373872\pi$
$79$			16.3990i			1.84503i	−0.385956	+	0.922517i	$0.626128\pi$
$80$			5.71472i			0.638925i
$81$	1.00000			0.111111
$82$		−	0.570570i		−	0.0630089i
$83$	−0.143578			−0.0157597			−0.00787987	−	0.999969i	$-0.502508\pi$
$83$	−0.143578			−0.0157597			−0.00787987	+	0.999969i	$0.502508\pi$
$84$	0.339420	−	1.86025i	0.0370338	−	0.202970i
$85$		−	16.7020i		−	1.81158i
$86$	10.6257			1.14580
$87$	−6.40701			−0.686903
$88$	−2.23607	−	9.95959i	−0.238366	−	1.06170i
$89$			3.07680i			0.326140i	0.986615	+	0.163070i	$0.0521396\pi$
$89$			3.07680i			0.326140i	−0.986615	+	0.163070i	$0.947860\pi$
$90$	3.14542			0.331557
$91$	−3.12710	−	0.570570i	−0.327809	−	0.0598120i
$92$	−4.21794			−0.439750
$93$	−6.11950			−0.634563
$94$	−8.08002			−0.833391
$95$			5.59268i			0.573797i
$96$	3.82022			0.389899
$97$		−	3.26064i		−	0.331068i	−0.986204	−	0.165534i	$-0.947065\pi$
$97$		−	3.26064i		−	0.331068i	0.986204	−	0.165534i	$-0.0529348\pi$
$98$	2.80267	−	7.42455i	0.283112	−	0.749993i
$99$	−3.23607	+	0.726543i	−0.325237	+	0.0730203i
$100$	−1.92806			−0.192806
$101$	−17.2053			−1.71199			−0.855993	−	0.516987i	$-0.827054\pi$
$101$	−17.2053			−1.71199			−0.855993	+	0.516987i	$0.827054\pi$
$102$	6.82477			0.675753
$103$		−	3.39534i		−	0.334553i	−0.985910	−	0.167276i	$-0.946503\pi$
$103$		−	3.39534i		−	0.334553i	0.985910	−	0.167276i	$-0.0534972\pi$
$104$		−	3.69767i		−	0.362586i
$105$	−7.22133	−	1.31760i	−0.704730	−	0.128585i
$106$			1.62055i			0.157402i
$107$		−	16.6826i		−	1.61277i	−0.591389	−	0.806386i	$-0.701420\pi$
$107$		−	16.6826i		−	1.61277i	0.591389	−	0.806386i	$-0.298580\pi$
$108$		−	0.714715i		−	0.0687735i
$109$		−	6.79413i		−	0.650760i	−0.945583	−	0.325380i	$-0.894508\pi$
$109$		−	6.79413i		−	0.650760i	0.945583	−	0.325380i	$-0.105492\pi$
$110$	−10.1788	+	2.28528i	−0.970511	+	0.217893i
$111$			1.69767i			0.161136i
$112$	5.36108	+	0.978182i	0.506575	+	0.0924295i
$113$	−9.09787			−0.855856			−0.427928	−	0.903813i	$-0.640756\pi$
$113$	−9.09787			−0.855856			−0.427928	+	0.903813i	$0.640756\pi$
$114$	−2.28528			−0.214037
$115$			16.3737i			1.52686i
$116$			4.57918i			0.425167i
$117$	−1.20145			−0.111074
$118$	6.59495			0.607115
$119$	−15.6684	−	2.85886i	−1.43632	−	0.262071i
$120$		−	8.53893i		−	0.779494i
$121$	9.94427	−	4.70228i	0.904025	−	0.427480i
$122$		−	5.14114i		−	0.465457i
$123$			0.503279i			0.0453792i
$124$			4.37370i			0.392770i
$125$		−	6.38774i		−	0.571337i
$126$	0.538399	−	2.95078i	0.0479644	−	0.262877i
$127$		−	7.47297i		−	0.663119i	−0.943434	−	0.331559i	$-0.892425\pi$
$127$		−	7.47297i		−	0.663119i	0.943434	−	0.331559i	$-0.107575\pi$
$128$			1.93993i			0.171467i
$129$	−9.37258			−0.825210
$130$	−3.77906			−0.331445
$131$	12.8140			1.11957			0.559783	−	0.828639i	$-0.310885\pi$
$131$	12.8140			1.11957			0.559783	+	0.828639i	$0.310885\pi$
$132$	0.519271	+	2.31287i	0.0451967	+	0.201309i
$133$	5.24660	+	0.957294i	0.454938	+	0.0830079i
$134$			14.3709i			1.24145i
$135$	−2.77447			−0.238788
$136$		−	18.5273i		−	1.58870i
$137$	2.73936			0.234039			0.117019	−	0.993130i	$-0.462666\pi$
$137$	2.73936			0.234039			0.117019	+	0.993130i	$0.462666\pi$
$138$	−6.69063			−0.569544
$139$	11.6400			0.987291			0.493645	−	0.869663i	$-0.335664\pi$
$139$	11.6400			0.987291			0.493645	+	0.869663i	$0.335664\pi$
$140$	−0.941710	+	5.16119i	−0.0795890	+	0.436200i
$141$	7.12710			0.600210
$142$		−	9.09352i		−	0.763111i
$143$	3.88796	−	0.872901i	0.325127	−	0.0729957i
$144$	2.05975			0.171646
$145$	17.7760			1.47622
$146$		−	12.0241i		−	0.995120i
$147$	−2.47214	+	6.54893i	−0.203898	+	0.540147i
$148$	1.21335			0.0997367
$149$		−	12.8414i		−	1.05201i	−0.850481	−	0.526006i	$-0.823689\pi$
$149$		−	12.8414i		−	1.05201i	0.850481	−	0.526006i	$-0.176311\pi$
$150$	−3.05836			−0.249714
$151$		−	7.97625i		−	0.649098i	−0.945869	−	0.324549i	$-0.894787\pi$
$151$		−	7.97625i		−	0.649098i	0.945869	−	0.324549i	$-0.105213\pi$
$152$			6.20390i			0.503203i
$153$	−6.01988			−0.486679
$154$	0.401573	+	9.94010i	0.0323596	+	0.800996i
$155$	16.9784			1.36374
$156$			0.858691i			0.0687503i
$157$			21.1131i			1.68501i	0.538692	+	0.842503i	$0.318919\pi$
$157$			21.1131i			1.68501i	−0.538692	+	0.842503i	$0.681081\pi$
$158$	18.5916			1.47907
$159$		−	1.42943i		−	0.113361i
$160$	−10.5991			−0.837930
$161$	15.3605	+	2.80267i	1.21058	+	0.220881i
$162$		−	1.13370i		−	0.0890722i
$163$	16.9150			1.32489			0.662444	−	0.749111i	$-0.269519\pi$
$163$	16.9150			1.32489			0.662444	+	0.749111i	$0.269519\pi$
$164$	0.359701			0.0280880
$165$	8.97836	−	2.01577i	0.698965	−	0.156927i
$166$			0.162775i			0.0126338i
$167$	−19.3372			−1.49636			−0.748178	−	0.663498i	$-0.769071\pi$
$167$	−19.3372			−1.49636			−0.748178	+	0.663498i	$0.769071\pi$
$168$	−8.01054	−	1.46160i	−0.618026	−	0.112765i
$169$	−11.5565			−0.888964
$170$	−18.9351			−1.45226
$171$	2.01577			0.154150
$172$			6.69872i			0.510773i
$173$	−21.1481			−1.60786			−0.803928	−	0.594726i	$-0.797260\pi$
$173$	−21.1481			−1.60786			−0.803928	+	0.594726i	$0.797260\pi$
$174$			7.26365i			0.550656i
$175$	7.02144	+	1.28113i	0.530771	+	0.0968444i
$176$	−6.66550	+	1.49650i	−0.502431	+	0.112803i
$177$	−5.81717			−0.437246
$178$	3.48818			0.261450
$179$	5.16221			0.385842			0.192921	−	0.981214i	$-0.438204\pi$
$179$	5.16221			0.385842			0.192921	+	0.981214i	$0.438204\pi$
$180$			1.98295i			0.147801i
$181$		−	7.66844i		−	0.569991i	−0.958529	−	0.284995i	$-0.908008\pi$
$181$		−	7.66844i		−	0.569991i	0.958529	−	0.284995i	$-0.0919920\pi$
$182$	−0.646857	+	3.54520i	−0.0479483	+	0.262788i
$183$			4.53482i			0.335223i
$184$			18.1632i			1.33901i
$185$		−	4.71013i		−	0.346295i
$186$			6.93771i			0.508697i
$187$	19.4808	−	4.37370i	1.42457	−	0.319837i
$188$		−	5.09385i		−	0.371507i
$189$	−0.474903	+	2.60278i	−0.0345441	+	0.189324i
$190$	6.34045			0.459984
$191$	−5.29690			−0.383270			−0.191635	−	0.981466i	$-0.561379\pi$
$191$	−5.29690			−0.383270			−0.191635	+	0.981466i	$0.561379\pi$
$192$		−	8.45050i		−	0.609862i
$193$			11.9510i			0.860254i	0.902768	+	0.430127i	$0.141531\pi$
$193$			11.9510i			0.860254i	−0.902768	+	0.430127i	$0.858469\pi$
$194$	−3.69661			−0.265401
$195$	3.33337			0.238708
$196$	4.68062	+	1.76687i	0.334330	+	0.126205i
$197$		−	11.1367i		−	0.793458i	−0.917936	−	0.396729i	$-0.870145\pi$
$197$		−	11.1367i		−	0.793458i	0.917936	−	0.396729i	$-0.129855\pi$
$198$	0.823684	+	3.66874i	0.0585367	+	0.260726i
$199$		−	20.9784i		−	1.48712i	−0.668671	−	0.743558i	$-0.733137\pi$
$199$		−	20.9784i		−	1.48712i	0.668671	−	0.743558i	$-0.266863\pi$
$200$			8.30257i			0.587080i
$201$		−	12.6760i		−	0.894098i
$202$			19.5057i			1.37241i
$203$	3.04271	−	16.6760i	0.213556	−	1.17043i
$204$			4.30250i			0.301235i
$205$		−	1.39633i		−	0.0975241i
$206$	−3.84931			−0.268194
$207$	5.90157			0.410187
$208$	−2.47468			−0.171588
$209$	−6.52316	+	1.46454i	−0.451217	+	0.101304i
$210$	−1.49377	+	8.18685i	−0.103080	+	0.564946i
$211$			11.5932i			0.798112i	0.916927	+	0.399056i	$0.130662\pi$
$211$			11.5932i			0.798112i	−0.916927	+	0.399056i	$0.869338\pi$
$212$	−1.02164			−0.0701662
$213$			8.02107i			0.549595i
$214$	−18.9132			−1.29288
$215$	26.0039			1.77345
$216$	−3.07768			−0.209410
$217$	2.90617	−	15.9277i	0.197284	−	1.08124i
$218$	−7.70253			−0.521681
$219$			10.6060i			0.716688i
$220$	−1.44070	−	6.41697i	−0.0971320	−	0.432632i
$221$	7.23256			0.486515
$222$	1.92465			0.129174
$223$			26.7322i			1.79012i	0.445944	+	0.895061i	$0.352868\pi$
$223$			26.7322i			1.79012i	−0.445944	+	0.895061i	$0.647132\pi$
$224$	−1.81423	+	9.94319i	−0.121218	+	0.664357i
$225$	2.69767			0.179845
$226$			10.3143i			0.686096i
$227$	−16.8456			−1.11808			−0.559039	−	0.829141i	$-0.688830\pi$
$227$	−16.8456			−1.11808			−0.559039	+	0.829141i	$0.688830\pi$
$228$		−	1.44070i		−	0.0954127i
$229$		−	2.72417i		−	0.180018i	−0.995941	−	0.0900090i	$-0.971310\pi$
$229$		−	2.72417i		−	0.180018i	0.995941	−	0.0900090i	$-0.0286896\pi$
$230$	18.5629			1.22400
$231$	−0.354213	−	8.76781i	−0.0233055	−	0.576880i
$232$	19.7187			1.29460
$233$			13.0363i			0.854038i	0.904243	+	0.427019i	$0.140436\pi$
$233$			13.0363i			0.854038i	−0.904243	+	0.427019i	$0.859564\pi$
$234$			1.36208i			0.0890422i
$235$	−19.7739			−1.28991
$236$			4.15762i			0.270638i
$237$	−16.3990			−1.06523
$238$	−3.24110	+	17.7634i	−0.210089	+	1.15143i
$239$			10.0707i			0.651422i	0.945469	+	0.325711i	$0.105604\pi$
$239$			10.0707i			0.651422i	−0.945469	+	0.325711i	$0.894396\pi$
$240$	−5.71472			−0.368883
$241$	−11.6126			−0.748031			−0.374016	−	0.927422i	$-0.622019\pi$
$241$	−11.6126			−0.748031			−0.374016	+	0.927422i	$0.622019\pi$
$242$	−5.33100	−	11.2739i	−0.342689	−	0.724711i
$243$			1.00000i			0.0641500i
$244$	3.24110			0.207490
$245$	6.85886	−	18.1698i	0.438197	−	1.16083i
$246$	0.570570			0.0363782
$247$	−2.42184			−0.154098
$248$	18.8339			1.19595
$249$		−	0.143578i		−	0.00909889i
$250$	−7.24181			−0.458012
$251$			18.9302i			1.19487i	0.801919	+	0.597433i	$0.203813\pi$
$251$			18.9302i			1.19487i	−0.801919	+	0.597433i	$0.796187\pi$
$252$	1.86025	+	0.339420i	0.117185	+	0.0213815i
$253$	−19.0979	+	4.28774i	−1.20067	+	0.269568i
$254$	−8.47214			−0.531589
$255$	16.7020			1.04592
$256$	−14.7017			−0.918856
$257$			16.9281i			1.05594i	0.849262	+	0.527972i	$0.177047\pi$
$257$			16.9281i			1.05594i	−0.849262	+	0.527972i	$0.822953\pi$
$258$			10.6257i			0.661529i
$259$	−4.41866	−	0.806228i	−0.274562	−	0.0500966i
$260$		−	2.38241i		−	0.147751i
$261$		−	6.40701i		−	0.396584i
$262$		−	14.5273i		−	0.897500i
$263$			19.3179i			1.19119i	0.803285	+	0.595595i	$0.203084\pi$
$263$			19.3179i			1.19119i	−0.803285	+	0.595595i	$0.796916\pi$
$264$	9.95959	−	2.23607i	0.612971	−	0.137620i
$265$			3.96591i			0.243624i
$266$	1.08529	−	5.94810i	0.0665433	−	0.364701i
$267$	−3.07680			−0.188297
$268$	−9.05975			−0.553412
$269$		−	0.0210705i		−	0.00128469i	−1.00000		0.000642346i	$-0.999796\pi$
$269$		−	0.0210705i		−	0.00128469i	1.00000		0.000642346i	$-0.000204465\pi$
$270$			3.14542i			0.191424i
$271$	−25.5281			−1.55072			−0.775360	−	0.631520i	$-0.782431\pi$
$271$	−25.5281			−1.55072			−0.775360	+	0.631520i	$0.782431\pi$
$272$	−12.3995			−0.751828
$273$	0.570570	−	3.12710i	0.0345325	−	0.189261i
$274$		−	3.10562i		−	0.187617i
$275$	−8.72984	+	1.95997i	−0.526429	+	0.118191i
$276$		−	4.21794i		−	0.253890i
$277$		−	31.7915i		−	1.91017i	−0.296339	−	0.955083i	$-0.595766\pi$
$277$		−	31.7915i		−	1.91017i	0.296339	−	0.955083i	$-0.404234\pi$
$278$		−	13.1963i		−	0.791462i
$279$		−	6.11950i		−	0.366365i
$280$	22.2250	+	4.05516i	1.32820	+	0.242342i
$281$		−	2.72659i		−	0.162655i	−0.996687	−	0.0813274i	$-0.974084\pi$
$281$		−	2.72659i		−	0.162655i	0.996687	−	0.0813274i	$-0.0259159\pi$
$282$		−	8.08002i		−	0.481158i
$283$	−6.82155			−0.405499			−0.202750	−	0.979231i	$-0.564988\pi$
$283$	−6.82155			−0.405499			−0.202750	+	0.979231i	$0.564988\pi$
$284$	5.73278			0.340178
$285$	−5.59268			−0.331282
$286$	−0.989612	−	4.40779i	−0.0585170	−	0.260638i
$287$	−1.30993	−	0.239009i	−0.0773225	−	0.0141082i
$288$			3.82022i			0.225108i
$289$	19.2390			1.13171
$290$		−	20.1528i		−	1.18341i
$291$	3.26064			0.191142
$292$	7.58027			0.443602
$293$	6.16346			0.360073			0.180037	−	0.983660i	$-0.442378\pi$
$293$	6.16346			0.360073			0.180037	+	0.983660i	$0.442378\pi$
$294$	7.42455	+	2.80267i	0.433009	+	0.163455i
$295$	16.1396			0.939681
$296$		−	5.22489i		−	0.303690i
$297$	−0.726543	−	3.23607i	−0.0421583	−	0.187776i
$298$	−14.5584			−0.843345
$299$	−7.09041			−0.410049
$300$		−	1.92806i		−	0.111317i
$301$	4.45107	−	24.3948i	0.256555	−	1.40609i
$302$	−9.04271			−0.520349
$303$		−	17.2053i		−	0.988416i
$304$	4.15198			0.238133
$305$		−	12.5817i		−	0.720426i
$306$			6.82477i			0.390146i
$307$	−8.84732			−0.504944			−0.252472	−	0.967604i	$-0.581243\pi$
$307$	−8.84732			−0.504944			−0.252472	+	0.967604i	$0.581243\pi$
$308$	−6.26649	+	0.253161i	−0.357066	+	0.0144252i
$309$	3.39534			0.193154
$310$		−	19.2484i		−	1.09324i
$311$			25.0125i			1.41833i	0.705044	+	0.709163i	$0.250927\pi$
$311$			25.0125i			1.41833i	−0.705044	+	0.709163i	$0.749073\pi$
$312$	3.69767			0.209339
$313$		−	11.4294i		−	0.646030i	−0.946394	−	0.323015i	$-0.895304\pi$
$313$		−	11.4294i		−	0.646030i	0.946394	−	0.323015i	$-0.104696\pi$
$314$	23.9360			1.35078
$315$	1.31760	−	7.22133i	0.0742385	−	0.406876i
$316$			11.7206i			0.659337i
$317$	22.5425			1.26611			0.633056	−	0.774106i	$-0.281800\pi$
$317$	22.5425			1.26611			0.633056	+	0.774106i	$0.281800\pi$
$318$	−1.62055			−0.0908760
$319$	4.65496	+	20.7335i	0.260628	+	1.16085i
$320$			23.4456i			1.31065i
$321$	16.6826			0.931135
$322$	3.17740	−	17.4142i	0.177070	−	0.970458i
$323$	−12.1347			−0.675192
$324$	0.714715			0.0397064
$325$	−3.24110			−0.179784
$326$		−	19.1767i		−	1.06210i
$327$	6.79413			0.375716
$328$		−	1.54893i		−	0.0855256i
$329$	−3.38468	+	18.5503i	−0.186603	+	1.02271i
$330$	−2.28528	−	10.1788i	−0.125801	−	0.560325i
$331$	22.6620			1.24562			0.622808	−	0.782375i	$-0.285992\pi$
$331$	22.6620			1.24562			0.622808	+	0.782375i	$0.285992\pi$
$332$	−0.102617			−0.00563186
$333$	−1.69767			−0.0930317
$334$			21.9226i			1.19955i
$335$			35.1692i			1.92150i
$336$	−0.978182	+	5.36108i	−0.0533642	+	0.292471i
$337$		−	7.58456i		−	0.413158i	−0.978430	−	0.206579i	$-0.933767\pi$
$337$		−	7.58456i		−	0.413158i	0.978430	−	0.206579i	$-0.0662330\pi$
$338$			13.1017i			0.712638i
$339$		−	9.09787i		−	0.494128i
$340$		−	11.9372i		−	0.647383i
$341$	4.44608	+	19.8031i	0.240769	+	1.07240i
$342$		−	2.28528i		−	0.123574i
$343$	−15.8714	−	9.54454i	−0.856976	−	0.515356i
$344$	28.8458			1.55526
$345$	−16.3737			−0.881530
$346$			23.9756i			1.28894i
$347$		−	14.3859i		−	0.772276i	−0.922441	−	0.386138i	$-0.873809\pi$
$347$		−	14.3859i		−	0.772276i	0.922441	−	0.386138i	$-0.126191\pi$
$348$	−4.57918			−0.245470
$349$	7.86819			0.421174			0.210587	−	0.977575i	$-0.432462\pi$
$349$	7.86819			0.421174			0.210587	+	0.977575i	$0.432462\pi$
$350$	1.45242	−	7.96024i	0.0776353	−	0.425492i
$351$		−	1.20145i		−	0.0641284i
$352$	−2.77555	−	12.3625i	−0.147937	−	0.658923i
$353$		−	7.14012i		−	0.380030i	−0.981781	−	0.190015i	$-0.939146\pi$
$353$		−	7.14012i		−	0.380030i	0.981781	−	0.190015i	$-0.0608537\pi$
$354$			6.59495i			0.350518i
$355$		−	22.2542i		−	1.18113i
$356$			2.19903i			0.116549i
$357$	2.85886	−	15.6684i	0.151307	−	0.829262i
$358$		−	5.85242i		−	0.309310i
$359$			9.24519i			0.487943i	0.969782	+	0.243971i	$0.0784503\pi$
$359$			9.24519i			0.487943i	−0.969782	+	0.243971i	$0.921550\pi$
$360$	8.53893			0.450041
$361$	−14.9367			−0.786141
$362$	−8.69374			−0.456933
$363$	4.70228	+	9.94427i	0.246806	+	0.521939i
$364$	−2.23498	−	0.407795i	−0.117145	−	0.0213743i
$365$		−	29.4260i		−	1.54023i
$366$	5.14114			0.268732
$367$		−	27.6063i		−	1.44104i	−0.693437	−	0.720518i	$-0.743904\pi$
$367$		−	27.6063i		−	1.44104i	0.693437	−	0.720518i	$-0.256096\pi$
$368$	12.1558			0.633663
$369$	−0.503279			−0.0261997
$370$	−5.33989			−0.277608
$371$	3.72049	+	0.678840i	0.193158	+	0.0352436i
$372$	−4.37370			−0.226766
$373$		−	2.61043i		−	0.135163i	−0.997714	−	0.0675816i	$-0.978472\pi$
$373$		−	2.61043i		−	0.135163i	0.997714	−	0.0675816i	$-0.0215283\pi$
$374$	−4.95848	−	22.0854i	−0.256397	−	1.14201i
$375$	6.38774			0.329862
$376$	−21.9350			−1.13121
$377$			7.69767i			0.396450i
$378$	2.95078	+	0.538399i	0.151772	+	0.0276923i
$379$	−0.872901			−0.0448379			−0.0224190	−	0.999749i	$-0.507137\pi$
$379$	−0.872901			−0.0448379			−0.0224190	+	0.999749i	$0.507137\pi$
$380$			3.99718i			0.205051i
$381$	7.47297			0.382852
$382$			6.00512i			0.307249i
$383$		−	24.9443i		−	1.27459i	−0.770619	−	0.637296i	$-0.780053\pi$
$383$		−	24.9443i		−	1.27459i	0.770619	−	0.637296i	$-0.219947\pi$
$384$	−1.93993			−0.0989967
$385$	0.982752	+	24.3260i	0.0500857	+	1.23977i
$386$	13.5489			0.689623
$387$		−	9.37258i		−	0.476435i
$388$		−	2.33043i		−	0.118310i
$389$	−8.08541			−0.409947			−0.204973	−	0.978768i	$-0.565711\pi$
$389$	−8.08541			−0.409947			−0.204973	+	0.978768i	$0.565711\pi$
$390$		−	3.77906i		−	0.191360i
$391$	−35.5267			−1.79666
$392$	7.60845	−	20.1555i	0.384285	−	1.01801i
$393$			12.8140i			0.646381i
$394$	−12.6257			−0.636075
$395$	45.4986			2.28928
$396$	−2.31287	+	0.519271i	−0.116226	+	0.0260943i
$397$			21.3862i			1.07334i	0.843792	+	0.536670i	$0.180318\pi$
$397$			21.3862i			1.07334i	−0.843792	+	0.536670i	$0.819682\pi$
$398$	−23.7833			−1.19215
$399$	−0.957294	+	5.24660i	−0.0479247	+	0.262659i
$400$	5.55653			0.277826
$401$	−10.1347			−0.506102			−0.253051	−	0.967453i	$-0.581434\pi$
$401$	−10.1347			−0.506102			−0.253051	+	0.967453i	$0.581434\pi$
$402$	−14.3709			−0.716754
$403$			7.35225i			0.366242i
$404$	−12.2969			−0.611791
$405$		−	2.77447i		−	0.137864i
$406$	−18.9057	−	3.44953i	−0.938273	−	0.171197i
$407$	5.49377	−	1.23343i	0.272316	−	0.0611388i
$408$	18.5273			0.917238
$409$	26.6986			1.32016			0.660079	−	0.751196i	$-0.270523\pi$
$409$	26.6986			1.32016			0.660079	+	0.751196i	$0.270523\pi$
$410$	−1.58303			−0.0781801
$411$			2.73936i			0.135122i
$412$		−	2.42670i		−	0.119555i
$413$	2.76259	−	15.1408i	0.135938	−	0.745031i
$414$		−	6.69063i		−	0.328827i
$415$			0.398352i			0.0195544i
$416$		−	4.58978i		−	0.225033i
$417$			11.6400i			0.570013i
$418$	1.66036	+	7.39534i	0.0812107	+	0.361718i
$419$			0.167638i			0.00818965i	0.999992	+	0.00409483i	$0.00130343\pi$
$419$			0.167638i			0.00818965i	−0.999992	+	0.00409483i	$0.998697\pi$
$420$	−5.16119	−	0.941710i	−0.251840	−	0.0459508i
$421$	−35.2887			−1.71987			−0.859934	−	0.510405i	$-0.829495\pi$
$421$	−35.2887			−1.71987			−0.859934	+	0.510405i	$0.829495\pi$
$422$	13.1433			0.639806
$423$			7.12710i			0.346531i
$424$			4.39933i			0.213651i
$425$	−16.2397			−0.787739
$426$	9.09352			0.440582
$427$	−11.8031	−	2.15360i	−0.571194	−	0.104220i
$428$		−	11.9233i		−	0.576336i
$429$	0.872901	+	3.88796i	0.0421441	+	0.187712i
$430$		−	29.4807i		−	1.42169i
$431$			10.8612i			0.523165i	0.965181	+	0.261582i	$0.0842443\pi$
$431$			10.8612i			0.523165i	−0.965181	+	0.261582i	$0.915756\pi$
$432$			2.05975i			0.0990999i
$433$			20.8858i			1.00371i	0.864952	+	0.501854i	$0.167349\pi$
$433$			20.8858i			1.00371i	−0.864952	+	0.501854i	$0.832651\pi$
$434$	−18.0573	−	3.29474i	−0.866780	−	0.158152i
$435$			17.7760i			0.852295i
$436$		−	4.85587i		−	0.232554i
$437$	11.8962			0.569072
$438$	12.0241			0.574533
$439$	−33.4815			−1.59798			−0.798991	−	0.601343i	$-0.794633\pi$
$439$	−33.4815			−1.59798			−0.798991	+	0.601343i	$0.794633\pi$
$440$	−27.6326	+	6.20390i	−1.31733	+	0.295759i
$441$	−6.54893	−	2.47214i	−0.311854	−	0.117721i
$442$		−	8.19959i		−	0.390015i
$443$	−33.5700			−1.59496			−0.797480	−	0.603346i	$-0.793834\pi$
$443$	−33.5700			−1.59496			−0.797480	+	0.603346i	$0.793834\pi$
$444$			1.21335i			0.0575830i
$445$	8.53648			0.404668
$446$	30.3064			1.43505
$447$	12.8414			0.607379
$448$	21.9948	+	4.01317i	1.03916	+	0.189604i
$449$	7.08268			0.334252			0.167126	−	0.985936i	$-0.446551\pi$
$449$	7.08268			0.334252			0.167126	+	0.985936i	$0.446551\pi$
$450$		−	3.05836i		−	0.144172i
$451$	1.62865	−	0.365654i	0.0766900	−	0.0172180i
$452$	−6.50238			−0.305846
$453$	7.97625			0.374757
$454$			19.0979i			0.896307i
$455$	−1.58303	+	8.67603i	−0.0742135	+	0.406739i
$456$	−6.20390			−0.290524
$457$			27.4003i			1.28173i	0.767654	+	0.640865i	$0.221424\pi$
$457$			27.4003i			1.28173i	−0.767654	+	0.640865i	$0.778576\pi$
$458$	−3.08840			−0.144311
$459$		−	6.01988i		−	0.280984i
$460$			11.7025i			0.545633i
$461$	5.87631			0.273687			0.136843	−	0.990593i	$-0.456304\pi$
$461$	5.87631			0.273687			0.136843	+	0.990593i	$0.456304\pi$
$462$	−9.94010	+	0.401573i	−0.462456	+	0.0186829i
$463$	−27.1692			−1.26266			−0.631331	−	0.775514i	$-0.717491\pi$
$463$	−27.1692			−1.26266			−0.631331	+	0.775514i	$0.717491\pi$
$464$		−	13.1968i		−	0.612648i
$465$			16.9784i			0.787353i
$466$	14.7793			0.684639
$467$		−	31.7739i		−	1.47032i	−0.677893	−	0.735160i	$-0.737107\pi$
$467$		−	31.7739i		−	1.47032i	0.677893	−	0.735160i	$-0.262893\pi$
$468$	−0.858691			−0.0396930
$469$	32.9929	+	6.01988i	1.52347	+	0.277972i
$470$			22.4178i			1.03405i
$471$	−21.1131			−0.972838
$472$	17.9034			0.824072
$473$	6.80958	+	30.3303i	0.313105	+	1.39459i
$474$			18.5916i			0.853942i
$475$	5.43788			0.249507
$476$	−11.1985	−	2.04327i	−0.513281	−	0.0936532i
$477$	1.42943			0.0654491
$478$	11.4172			0.522213
$479$	10.1649			0.464447			0.232224	−	0.972662i	$-0.425400\pi$
$479$	10.1649			0.464447			0.232224	+	0.972662i	$0.425400\pi$
$480$		−	10.5991i		−	0.483779i
$481$	2.03966			0.0930003
$482$			13.1652i			0.599659i
$483$	−2.80267	+	15.3605i	−0.127526	+	0.698926i
$484$	7.10732	−	3.36079i	0.323060	−	0.152763i
$485$	−9.04655			−0.410783
$486$	1.13370			0.0514259
$487$	21.7599			0.986033			0.493017	−	0.870020i	$-0.335894\pi$
$487$	21.7599			0.986033			0.493017	+	0.870020i	$0.335894\pi$
$488$		−	13.9567i		−	0.631791i
$489$			16.9150i			0.764925i
$490$	−20.5992	−	7.77592i	−0.930576	−	0.351280i
$491$		−	17.1859i		−	0.775590i	−0.921746	−	0.387795i	$-0.873237\pi$
$491$		−	17.1859i		−	0.775590i	0.921746	−	0.387795i	$-0.126763\pi$
$492$			0.359701i			0.0162166i
$493$			38.5694i			1.73708i
$494$			2.74565i			0.123532i
$495$	2.01577	+	8.97836i	0.0906021	+	0.403547i
$496$		−	12.6047i		−	0.565966i
$497$	−20.8771	−	3.80923i	−0.936465	−	0.170867i
$498$	−0.162775			−0.00729412
$499$	18.7614			0.839878			0.419939	−	0.907552i	$-0.362052\pi$
$499$	18.7614			0.839878			0.419939	+	0.907552i	$0.362052\pi$
$500$		−	4.56542i		−	0.204172i
$501$		−	19.3372i		−	0.863921i
$502$	21.4613			0.957864
$503$	38.4335			1.71366			0.856832	−	0.515596i	$-0.172430\pi$
$503$	38.4335			1.71366			0.856832	+	0.515596i	$0.172430\pi$
$504$	1.46160	−	8.01054i	0.0651049	−	0.356818i
$505$			47.7354i			2.12420i
$506$	4.86103	+	21.6513i	0.216099	+	0.962519i
$507$		−	11.5565i		−	0.513243i
$508$		−	5.34104i		−	0.236971i
$509$		−	12.9914i		−	0.575833i	−0.957656	−	0.287917i	$-0.907037\pi$
$509$		−	12.9914i		−	0.575833i	0.957656	−	0.287917i	$-0.0929626\pi$
$510$		−	18.9351i		−	0.838460i
$511$	−27.6051	−	5.03682i	−1.22118	−	0.222816i
$512$			20.5472i			0.908068i
$513$			2.01577i			0.0889984i
$514$	19.1914			0.846497
$515$	−9.42025			−0.415106
$516$	−6.69872			−0.294895
$517$	−5.17814	−	23.0638i	−0.227734	−	1.01434i
$518$	−0.914024	+	5.00945i	−0.0401599	+	0.220103i
$519$		−	21.1481i		−	0.928296i
$520$	−10.2591			−0.449890
$521$		−	0.281261i		−	0.0123223i	−0.999981	−	0.00616113i	$-0.998039\pi$
$521$		−	0.281261i		−	0.0123223i	0.999981	−	0.00616113i	$-0.00196116\pi$
$522$	−7.26365			−0.317921
$523$	−8.24320			−0.360450			−0.180225	−	0.983625i	$-0.557683\pi$
$523$	−8.24320			−0.360450			−0.180225	+	0.983625i	$0.557683\pi$
$524$	9.15837			0.400085
$525$	−1.28113	+	7.02144i	−0.0559131	+	0.306441i
$526$	21.9007			0.954917
$527$			36.8387i			1.60472i
$528$	−1.49650	−	6.66550i	−0.0651267	−	0.290079i
$529$	11.8285			0.514282
$530$	4.49617			0.195301
$531$		−	5.81717i		−	0.252444i
$532$	3.74983	+	0.684193i	0.162576	+	0.0296635i
$533$	0.604663			0.0261908
$534$			3.48818i			0.150948i
$535$	−46.2855			−2.00109
$536$			39.0128i			1.68510i
$537$			5.16221i			0.222766i
$538$	−0.0238877			−0.00102987
$539$	22.9889	+	3.24192i	0.990202	+	0.139639i
$540$	−1.98295			−0.0853327
$541$		−	15.5132i		−	0.666964i	−0.942756	−	0.333482i	$-0.891776\pi$
$541$		−	15.5132i		−	0.666964i	0.942756	−	0.333482i	$-0.108224\pi$
$542$			28.9413i			1.24313i
$543$	7.66844			0.329084
$544$		−	22.9973i		−	0.986000i
$545$	−18.8501			−0.807449
$546$	−3.54520	−	0.646857i	−0.151721	−	0.0276829i
$547$			10.0194i			0.428400i	0.976790	+	0.214200i	$0.0687145\pi$
$547$			10.0194i			0.428400i	−0.976790	+	0.214200i	$0.931286\pi$
$548$	1.95786			0.0836356
$549$	−4.53482			−0.193541
$550$	2.22203	+	9.89705i	0.0947476	+	0.422012i
$551$		−	12.9150i		−	0.550199i
$552$	−18.1632			−0.773075
$553$	7.78794	−	42.6831i	0.331177	−	1.81507i
$554$	−36.0421			−1.53128
$555$	4.71013			0.199934
$556$	8.31928			0.352816
$557$			10.7735i			0.456487i	0.973604	+	0.228243i	$0.0732982\pi$
$557$			10.7735i			0.456487i	−0.973604	+	0.228243i	$0.926702\pi$
$558$	−6.93771			−0.293697
$559$			11.2606i			0.476274i
$560$	2.71393	−	14.8742i	0.114685	−	0.628548i
$561$	4.37370	+	19.4808i	0.184658	+	0.822478i
$562$	−3.09115			−0.130392
$563$	−28.4068			−1.19720			−0.598602	−	0.801046i	$-0.704277\pi$
$563$	−28.4068			−1.19720			−0.598602	+	0.801046i	$0.704277\pi$
$564$	5.09385			0.214490
$565$			25.2417i			1.06193i
$566$			7.73362i			0.325068i
$567$	−2.60278	−	0.474903i	−0.109307	−	0.0199440i
$568$		−	24.6863i		−	1.03581i
$569$			17.4776i			0.732701i	0.930477	+	0.366350i	$0.119393\pi$
$569$			17.4776i			0.732701i	−0.930477	+	0.366350i	$0.880607\pi$
$570$			6.34045i			0.265572i
$571$		−	12.2062i		−	0.510814i	−0.966834	−	0.255407i	$-0.917791\pi$
$571$		−	12.2062i		−	0.510814i	0.966834	−	0.255407i	$-0.0822094\pi$
$572$	2.77878	−	0.623876i	0.116187	−	0.0260856i
$573$		−	5.29690i		−	0.221281i
$574$	−0.270965	+	1.48507i	−0.0113099	+	0.0619855i
$575$	15.9205			0.663929
$576$	8.45050			0.352104
$577$			15.0216i			0.625359i	0.949859	+	0.312679i	$0.101227\pi$
$577$			15.0216i			0.625359i	−0.949859	+	0.312679i	$0.898773\pi$
$578$		−	21.8113i		−	0.907232i
$579$	−11.9510			−0.496668
$580$	12.7048			0.527538
$581$	0.373702	+	0.0681856i	0.0155038	+	0.00282882i
$582$		−	3.69661i		−	0.153229i
$583$	−4.62573	+	1.03854i	−0.191578	+	0.0430120i
$584$		−	32.6419i		−	1.35073i
$585$			3.33337i			0.137818i
$586$		−	6.98754i		−	0.288653i
$587$		−	21.2807i		−	0.878348i	−0.898402	−	0.439174i	$-0.855271\pi$
$587$		−	21.2807i		−	0.878348i	0.898402	−	0.439174i	$-0.144729\pi$
$588$	−1.76687	+	4.68062i	−0.0728646	+	0.193026i
$589$		−	12.3355i		−	0.508276i
$590$		−	18.2975i		−	0.753295i
$591$	11.1367			0.458103
$592$	−3.49678			−0.143717
$593$	1.61246			0.0662156			0.0331078	−	0.999452i	$-0.489460\pi$
$593$	1.61246			0.0662156			0.0331078	+	0.999452i	$0.489460\pi$
$594$	−3.66874	+	0.823684i	−0.150530	+	0.0337962i
$595$	−7.93181	+	43.4716i	−0.325173	+	1.78216i
$596$		−	9.17797i		−	0.375944i
$597$	20.9784			0.858587
$598$			8.03843i			0.328716i
$599$	28.5977			1.16847			0.584234	−	0.811585i	$-0.301395\pi$
$599$	28.5977			1.16847			0.584234	+	0.811585i	$0.301395\pi$
$600$	−8.30257			−0.338951
$601$	18.8212			0.767734			0.383867	−	0.923388i	$-0.374592\pi$
$601$	18.8212			0.767734			0.383867	+	0.923388i	$0.374592\pi$
$602$	−27.6565	−	5.04619i	−1.12719	−	0.205667i
$603$	12.6760			0.516208
$604$		−	5.70075i		−	0.231960i
$605$	−13.0463	−	27.5901i	−0.530409	−	1.12170i
$606$	−19.5057			−0.792363
$607$	26.4798			1.07478			0.537391	−	0.843334i	$-0.319410\pi$
$607$	26.4798			1.07478			0.537391	+	0.843334i	$0.319410\pi$
$608$			7.70067i			0.312304i
$609$	16.6760	+	3.04271i	0.675747	+	0.123297i
$610$	−14.2639			−0.577529
$611$		−	8.56282i		−	0.346415i
$612$	−4.30250			−0.173918
$613$			16.6380i			0.672003i	0.941861	+	0.336001i	$0.109075\pi$
$613$			16.6380i			0.672003i	−0.941861	+	0.336001i	$0.890925\pi$
$614$			10.0302i			0.404788i
$615$	1.39633			0.0563055
$616$	1.09016	+	26.9846i	0.0439236	+	1.08724i
$617$	−15.5911			−0.627673			−0.313837	−	0.949477i	$-0.601614\pi$
$617$	−15.5911			−0.627673			−0.313837	+	0.949477i	$0.601614\pi$
$618$		−	3.84931i		−	0.154842i
$619$		−	0.612711i		−	0.0246269i	−0.999924	−	0.0123135i	$-0.996080\pi$
$619$		−	0.612711i		−	0.0246269i	0.999924	−	0.0123135i	$-0.00391960\pi$
$620$	12.1347			0.487341
$621$			5.90157i			0.236822i
$622$	28.3567			1.13700
$623$	1.46118	−	8.00823i	0.0585410	−	0.320843i
$624$		−	2.47468i		−	0.0990665i
$625$	−31.2109			−1.24844
$626$	−12.9576			−0.517890
$627$	−1.46454	−	6.52316i	−0.0584882	−	0.260510i
$628$			15.0898i			0.602149i
$629$	10.2198			0.407489
$630$	−8.18685	−	1.49377i	−0.326172	−	0.0595133i
$631$	19.3673			0.770998			0.385499	−	0.922708i	$-0.374029\pi$
$631$	19.3673			0.770998			0.385499	+	0.922708i	$0.374029\pi$
$632$	50.4710			2.00763
$633$	−11.5932			−0.460790
$634$		−	25.5565i		−	1.01498i
$635$	−20.7335			−0.822784
$636$		−	1.02164i		−	0.0405105i
$637$	7.86819	+	2.97014i	0.311749	+	0.117681i
$638$	23.5057	−	5.27735i	0.930598	−	0.208932i
$639$	−8.02107			−0.317309
$640$	5.38228			0.212753
$641$	−36.3304			−1.43497			−0.717483	−	0.696576i	$-0.754706\pi$
$641$	−36.3304			−1.43497			−0.717483	+	0.696576i	$0.754706\pi$
$642$		−	18.9132i		−	0.746444i
$643$		−	33.9648i		−	1.33944i	−0.742614	−	0.669720i	$-0.766414\pi$
$643$		−	33.9648i		−	1.33944i	0.742614	−	0.669720i	$-0.233586\pi$
$644$	10.9784	+	2.00311i	0.432608	+	0.0789336i
$645$			26.0039i			1.02390i
$646$			13.7572i			0.541268i
$647$			12.8448i			0.504982i	0.967599	+	0.252491i	$0.0812498\pi$
$647$			12.8448i			0.504982i	−0.967599	+	0.252491i	$0.918750\pi$
$648$		−	3.07768i		−	0.120903i
$649$	4.22642	+	18.8248i	0.165902	+	0.738937i
$650$			3.67445i			0.144124i
$651$	15.9277	+	2.90617i	0.624257	+	0.113902i
$652$	12.0894			0.473459
$653$	26.4078			1.03342			0.516708	−	0.856161i	$-0.327157\pi$
$653$	26.4078			1.03342			0.516708	+	0.856161i	$0.327157\pi$
$654$		−	7.70253i		−	0.301193i
$655$		−	35.5521i		−	1.38913i
$656$	−1.03663			−0.0404736
$657$	−10.6060			−0.413780
$658$	21.0305	+	3.83723i	0.819855	+	0.149591i
$659$		−	10.0869i		−	0.392931i	−0.980511	−	0.196466i	$-0.937054\pi$
$659$		−	10.0869i		−	0.392931i	0.980511	−	0.196466i	$-0.0629464\pi$
$660$	6.41697	−	1.44070i	0.249780	−	0.0560792i
$661$		−	8.23096i		−	0.320147i	−0.987105	−	0.160074i	$-0.948827\pi$
$661$		−	8.23096i		−	0.320147i	0.987105	−	0.160074i	$-0.0511732\pi$
$662$		−	25.6920i		−	0.998548i
$663$			7.23256i			0.280889i
$664$			0.441888i			0.0171486i
$665$	2.65598	−	14.5565i	0.102995	−	0.564478i
$666$			1.92465i			0.0745788i
$667$		−	37.8114i		−	1.46406i
$668$	−13.8206			−0.534734
$669$	−26.7322			−1.03353
$670$	39.8715			1.54037
$671$	14.6750	−	3.29474i	0.566521	−	0.127192i
$672$	−9.94319	−	1.81423i	−0.383567	−	0.0699855i
$673$			6.57801i			0.253563i	0.991931	+	0.126782i	$0.0404648\pi$
$673$			6.57801i			0.253563i	−0.991931	+	0.126782i	$0.959535\pi$
$674$	−8.59865			−0.331208
$675$			2.69767i			0.103833i
$676$	−8.25963			−0.317678
$677$	20.6061			0.791958			0.395979	−	0.918260i	$-0.370405\pi$
$677$	20.6061			0.791958			0.395979	+	0.918260i	$0.370405\pi$
$678$	−10.3143			−0.396118
$679$	−1.54849	+	8.48674i	−0.0594256	+	0.325691i
$680$	−51.4034			−1.97123
$681$		−	16.8456i		−	0.645523i
$682$	22.4509	−	5.04054i	0.859689	−	0.193012i
$683$	−21.4353			−0.820199			−0.410100	−	0.912041i	$-0.634506\pi$
$683$	−21.4353			−0.820199			−0.410100	+	0.912041i	$0.634506\pi$
$684$	1.44070			0.0550865
$685$		−	7.60025i		−	0.290391i
$686$	−10.8207	+	17.9935i	−0.413135	+	0.686995i
$687$	2.72417			0.103933
$688$		−	19.3052i		−	0.736004i
$689$	−1.71738			−0.0654271
$690$			18.5629i			0.706679i
$691$		−	37.8885i		−	1.44135i	−0.693274	−	0.720674i	$-0.743832\pi$
$691$		−	37.8885i		−	1.44135i	0.693274	−	0.720674i	$-0.256168\pi$
$692$	−15.1148			−0.574580
$693$	8.76781	−	0.354213i	0.333062	−	0.0134554i
$694$	−16.3094			−0.619095
$695$		−	32.2948i		−	1.22501i
$696$			19.7187i			0.747437i
$697$	3.02968			0.114757
$698$		−	8.92020i		−	0.337634i
$699$	−13.0363			−0.493079
$700$	5.01833	+	0.915643i	0.189675	+	0.0346081i
$701$		−	37.3868i		−	1.41208i	−0.708172	−	0.706040i	$-0.750480\pi$
$701$		−	37.3868i		−	1.41208i	0.708172	−	0.706040i	$-0.249520\pi$
$702$	−1.36208			−0.0514085
$703$	−3.42211			−0.129067
$704$	−27.3464	+	6.13965i	−1.03066	+	0.231397i
$705$		−	19.7739i		−	0.744728i
$706$	−8.09478			−0.304651
$707$	44.7815	+	8.17082i	1.68418	+	0.307295i
$708$	−4.15762			−0.156253
$709$	25.5429			0.959285			0.479643	−	0.877464i	$-0.340766\pi$
$709$	25.5429			0.959285			0.479643	+	0.877464i	$0.340766\pi$
$710$	−25.2297			−0.946853
$711$		−	16.3990i		−	0.615011i
$712$	9.46941			0.354881
$713$		−	36.1147i		−	1.35250i
$714$	−17.7634	−	3.24110i	−0.664778	−	0.121295i
$715$	−2.42184	−	10.7870i	−0.0905715	−	0.403411i
$716$	3.68951			0.137883
$717$	−10.0707			−0.376099
$718$	10.4813			0.391159
$719$			10.2834i			0.383507i	0.981443	+	0.191754i	$0.0614174\pi$
$719$			10.2834i			0.383507i	−0.981443	+	0.191754i	$0.938583\pi$
$720$		−	5.71472i		−	0.212975i
$721$	−1.61246	+	8.83732i	−0.0600510	+	0.329119i
$722$			16.9338i			0.630210i
$723$		−	11.6126i		−	0.431876i
$724$		−	5.48075i		−	0.203690i
$725$		−	17.2840i		−	0.641911i
$726$	11.2739	−	5.33100i	0.418412	−	0.197852i
$727$			30.3304i			1.12489i	0.826834	+	0.562447i	$0.190140\pi$
$727$			30.3304i			1.12489i	−0.826834	+	0.562447i	$0.809860\pi$
$728$	−1.75603	+	9.62422i	−0.0650829	+	0.356697i
$729$	−1.00000			−0.0370370
$730$	−33.3604			−1.23472
$731$			56.4219i			2.08684i
$732$			3.24110i			0.119795i
$733$	−5.54137			−0.204675			−0.102338	−	0.994750i	$-0.532632\pi$
$733$	−5.54137			−0.204675			−0.102338	+	0.994750i	$0.532632\pi$
$734$	−31.2973			−1.15521
$735$	18.1698	+	6.85886i	0.670203	+	0.252993i
$736$			22.5453i			0.831030i
$737$	−41.0205	+	9.20968i	−1.51101	+	0.339243i
$738$			0.570570i			0.0210030i
$739$			9.04677i			0.332791i	0.986059	+	0.166395i	$0.0532128\pi$
$739$			9.04677i			0.332791i	−0.986059	+	0.166395i	$0.946787\pi$
$740$		−	3.36640i		−	0.123751i
$741$		−	2.42184i		−	0.0889684i
$742$	0.769604	−	4.21794i	0.0282531	−	0.154845i
$743$		−	17.9602i		−	0.658895i	−0.944174	−	0.329447i	$-0.893138\pi$
$743$		−	17.9602i		−	0.658895i	0.944174	−	0.329447i	$-0.106862\pi$
$744$			18.8339i			0.690484i
$745$	−35.6281			−1.30531
$746$	−2.95946			−0.108354
$747$	0.143578			0.00525324
$748$	13.9232	−	3.12595i	0.509082	−	0.114296i
$749$	−7.92264	+	43.4213i	−0.289487	+	1.58658i
$750$		−	7.24181i		−	0.264434i
$751$	−7.30765			−0.266660			−0.133330	−	0.991072i	$-0.542567\pi$
$751$	−7.30765			−0.266660			−0.133330	+	0.991072i	$0.542567\pi$
$752$			14.6801i			0.535327i
$753$	−18.9302			−0.689856
$754$	8.72688			0.317814
$755$	−22.1298			−0.805387
$756$	−0.339420	+	1.86025i	−0.0123446	+	0.0676565i
$757$	20.4981			0.745015			0.372508	−	0.928029i	$-0.378498\pi$
$757$	20.4981			0.745015			0.372508	+	0.928029i	$0.378498\pi$
$758$			0.989612i			0.0359443i
$759$	−4.28774	−	19.0979i	−0.155635	−	0.693209i
$760$	17.2125			0.624363
$761$	−29.9305			−1.08498			−0.542490	−	0.840062i	$-0.682519\pi$
$761$	−29.9305			−1.08498			−0.542490	+	0.840062i	$0.682519\pi$
$762$		−	8.47214i		−	0.306913i
$763$	−3.22655	+	17.6836i	−0.116809	+	0.640190i
$764$	−3.78578			−0.136965
$765$			16.7020i			0.603861i
$766$	−28.2794			−1.02178
$767$			6.98902i			0.252359i
$768$		−	14.7017i		−	0.530502i
$769$	33.4414			1.20593			0.602963	−	0.797769i	$-0.293987\pi$
$769$	33.4414			1.20593			0.602963	+	0.797769i	$0.293987\pi$
$770$	27.5785	−	1.11415i	0.993860	−	0.0401512i
$771$	−16.9281			−0.609649
$772$			8.54158i			0.307418i
$773$			40.4240i			1.45395i	0.686664	+	0.726975i	$0.259074\pi$
$773$			40.4240i			1.45395i	−0.686664	+	0.726975i	$0.740926\pi$
$774$	−10.6257			−0.381934
$775$		−	16.5084i		−	0.592999i
$776$	−10.0352			−0.360244
$777$	0.806228	−	4.41866i	0.0289233	−	0.158519i
$778$			9.16646i			0.328634i
$779$	−1.01449			−0.0363480
$780$	2.38241			0.0853040
$781$	25.9567	−	5.82765i	0.928805	−	0.208530i
$782$			40.2768i			1.44030i
$783$	6.40701			0.228968
$784$	−13.4892	−	5.09199i	−0.481757	−	0.181857i
$785$	58.5775			2.09072
$786$	14.5273			0.518172
$787$	17.8548			0.636453			0.318227	−	0.948015i	$-0.396913\pi$
$787$	17.8548			0.636453			0.318227	+	0.948015i	$0.396913\pi$
$788$		−	7.95957i		−	0.283548i
$789$	−19.3179			−0.687734
$790$		−	51.5819i		−	1.83520i
$791$	23.6798	+	4.32060i	0.841955	+	0.153623i
$792$	2.23607	+	9.95959i	0.0794552	+	0.353899i
$793$	5.44833			0.193476
$794$	24.2456			0.860443
$795$	−3.96591			−0.140656
$796$		−	14.9936i		−	0.531432i
$797$		−	18.7745i		−	0.665026i	−0.943099	−	0.332513i	$-0.892104\pi$
$797$		−	18.7745i		−	0.665026i	0.943099	−	0.332513i	$-0.107896\pi$
$798$	5.94810	+	1.08529i	0.210560	+	0.0384188i
$799$		−	42.9043i		−	1.51785i
$800$			10.3057i			0.364361i
$801$		−	3.07680i		−	0.108713i
$802$			11.4897i			0.405717i
$803$	34.3218	−	7.70572i	1.21119	−	0.271929i
$804$		−	9.05975i		−	0.319513i
$805$	7.77592	−	42.6172i	0.274065	−	1.50206i
$806$	8.33528			0.293598
$807$	0.0210705			0.000741717
$808$			52.9523i			1.86286i
$809$			16.9369i			0.595471i	0.954648	+	0.297736i	$0.0962314\pi$
$809$			16.9369i			0.595471i	−0.954648	+	0.297736i	$0.903769\pi$
$810$	−3.14542			−0.110519
$811$	−24.5693			−0.862744			−0.431372	−	0.902174i	$-0.641970\pi$
$811$	−24.5693			−0.862744			−0.431372	+	0.902174i	$0.641970\pi$
$812$	2.17467	−	11.9186i	0.0763159	−	0.418261i
$813$		−	25.5281i		−	0.895308i
$814$	−1.39834	−	6.22831i	−0.0490119	−	0.218302i
$815$		−	46.9302i		−	1.64389i
$816$		−	12.3995i		−	0.434068i
$817$		−	18.8930i		−	0.660981i
$818$		−	30.2683i		−	1.05830i
$819$	3.12710	+	0.570570i	0.109270	+	0.0199373i
$820$		−	0.997980i		−	0.0348510i
$821$			14.9572i			0.522009i	0.965338	+	0.261004i	$0.0840537\pi$
$821$			14.9572i			0.522009i	−0.965338	+	0.261004i	$0.915946\pi$
$822$	3.10562			0.108321
$823$	5.04169			0.175742			0.0878711	−	0.996132i	$-0.471994\pi$
$823$	5.04169			0.175742			0.0878711	+	0.996132i	$0.471994\pi$
$824$	−10.4498			−0.364035
$825$	−1.95997	−	8.72984i	−0.0682374	−	0.303934i
$826$	−17.1652	−	3.13196i	−0.597254	−	0.108975i
$827$		−	1.16946i		−	0.0406662i	−0.999793	−	0.0203331i	$-0.993527\pi$
$827$		−	1.16946i		−	0.0406662i	0.999793	−	0.0203331i	$-0.00647267\pi$
$828$	4.21794			0.146583
$829$		−	39.3369i		−	1.36623i	−0.730313	−	0.683113i	$-0.760626\pi$
$829$		−	39.3369i		−	1.36623i	0.730313	−	0.683113i	$-0.239374\pi$
$830$	0.451614			0.0156757
$831$	31.7915			1.10283
$832$	−10.1528			−0.351986
$833$	39.4238	+	14.8820i	1.36595	+	0.515630i
$834$	13.1963			0.456951
$835$			53.6504i			1.85665i
$836$	−4.66220	+	1.04673i	−0.161246	+	0.0362019i
$837$	6.11950			0.211521
$838$	0.190052			0.00656524
$839$		−	19.8441i		−	0.685095i	−0.939500	−	0.342548i	$-0.888710\pi$
$839$		−	19.8441i		−	0.685095i	0.939500	−	0.342548i	$-0.111290\pi$
$840$	−4.05516	+	22.2250i	−0.139916	+	0.766834i
$841$	−12.0497			−0.415508
$842$			40.0070i			1.37873i
$843$	2.72659			0.0939088
$844$			8.28587i			0.285211i
$845$			32.0632i			1.10301i
$846$	8.08002			0.277797
$847$	−28.1159	+	7.51645i	−0.966073	+	0.258268i
$848$	2.94427			0.101107
$849$		−	6.82155i		−	0.234115i
$850$			18.4110i			0.631491i
$851$	−10.0189			−0.343444
$852$			5.73278i			0.196402i
$853$	−0.558121			−0.0191097			−0.00955485	−	0.999954i	$-0.503041\pi$
$853$	−0.558121			−0.0191097			−0.00955485	+	0.999954i	$0.503041\pi$
$854$	−2.44154	+	13.3813i	−0.0835478	+	0.457897i
$855$		−	5.59268i		−	0.191266i
$856$	−51.3439			−1.75490
$857$	−4.01535			−0.137162			−0.0685808	−	0.997646i	$-0.521847\pi$
$857$	−4.01535			−0.137162			−0.0685808	+	0.997646i	$0.521847\pi$
$858$	4.40779	−	0.989612i	0.150480	−	0.0337848i
$859$			19.0698i			0.650653i	0.945602	+	0.325326i	$0.105474\pi$
$859$			19.0698i			0.650653i	−0.945602	+	0.325326i	$0.894526\pi$
$860$	18.5854			0.633757
$861$	0.239009	−	1.30993i	0.00814540	−	0.0446422i
$862$	12.3134			0.419395
$863$	1.32499			0.0451030			0.0225515	−	0.999746i	$-0.492821\pi$
$863$	1.32499			0.0451030			0.0225515	+	0.999746i	$0.492821\pi$
$864$	−3.82022			−0.129966
$865$			58.6746i			1.99500i
$866$	23.6783			0.804622
$867$			19.2390i			0.653391i
$868$	2.07708	−	11.3838i	0.0705008	−	0.386391i
$869$	11.9146	+	53.0684i	0.404175	+	1.80022i
$870$	20.1528			0.683242
$871$	−15.2296			−0.516034
$872$	−20.9102			−0.708108
$873$			3.26064i			0.110356i
$874$		−	13.4868i		−	0.456196i
$875$	−3.03356	+	16.6259i	−0.102553	+	0.562058i
$876$			7.58027i			0.256114i
$877$		−	16.4944i		−	0.556977i	−0.960440	−	0.278489i	$-0.910167\pi$
$877$		−	16.4944i		−	0.556977i	0.960440	−	0.278489i	$-0.0898335\pi$
$878$			37.9581i			1.28102i
$879$			6.16346i			0.207888i
$880$	4.15198	+	18.4932i	0.139963	+	0.623406i
$881$		−	49.0123i		−	1.65127i	−0.564206	−	0.825634i	$-0.690818\pi$
$881$		−	49.0123i		−	1.65127i	0.564206	−	0.825634i	$-0.309182\pi$
$882$	−2.80267	+	7.42455i	−0.0943708	+	0.249998i
$883$	−5.18010			−0.174324			−0.0871620	−	0.996194i	$-0.527780\pi$
$883$	−5.18010			−0.174324			−0.0871620	+	0.996194i	$0.527780\pi$
$884$	5.16922			0.173860
$885$			16.1396i			0.542525i
$886$			38.0585i			1.27860i
$887$	−14.8663			−0.499162			−0.249581	−	0.968354i	$-0.580293\pi$
$887$	−14.8663			−0.499162			−0.249581	+	0.968354i	$0.580293\pi$
$888$	5.22489			0.175336
$889$	−3.54893	+	19.4505i	−0.119027	+	0.652349i
$890$		−	9.67784i		−	0.324402i
$891$	3.23607	−	0.726543i	0.108412	−	0.0243401i
$892$			19.1059i			0.639713i
$893$			14.3666i			0.480759i
$894$		−	14.5584i		−	0.486905i
$895$		−	14.3224i		−	0.478744i
$896$	0.921279	−	5.04922i	0.0307778	−	0.168682i
$897$		−	7.09041i		−	0.236742i
$898$		−	8.02966i		−	0.267953i
$899$	−39.2077			−1.30765
$900$	1.92806			0.0642688
$901$	−8.60500			−0.286674
$902$	−0.414543	−	1.84640i	−0.0138028	−	0.0614785i
$903$	24.3948	+	4.45107i	0.811807	+	0.148122i
$904$			28.0004i			0.931278i
$905$	−21.2758			−0.707233
$906$		−	9.04271i		−	0.300424i
$907$	29.1833			0.969015			0.484507	−	0.874787i	$-0.338999\pi$
$907$	29.1833			0.969015			0.484507	+	0.874787i	$0.338999\pi$
$908$	−12.0398			−0.399554
$909$	17.2053			0.570662
$910$	9.83605	+	1.79468i	0.326062	+	0.0594932i
$911$	4.19189			0.138884			0.0694418	−	0.997586i	$-0.477878\pi$
$911$	4.19189			0.138884			0.0694418	+	0.997586i	$0.477878\pi$
$912$			4.15198i			0.137486i
$913$	−0.464628	+	0.104316i	−0.0153769	+	0.00345234i
$914$	31.0638			1.02750
$915$	12.5817			0.415938
$916$		−	1.94700i		−	0.0643308i
$917$	−33.3521	−	6.08541i	−1.10138	−	0.200958i
$918$	−6.82477			−0.225251
$919$		−	51.3682i		−	1.69448i	−0.531210	−	0.847240i	$-0.678262\pi$
$919$		−	51.3682i		−	1.69448i	0.531210	−	0.847240i	$-0.321738\pi$
$920$	50.3931			1.66141
$921$		−	8.84732i		−	0.291529i
$922$		−	6.66199i		−	0.219401i
$923$	9.63688			0.317202
$924$	−0.253161	−	6.26649i	−0.00832840	−	0.206152i
$925$	−4.57975			−0.150581
$926$			30.8019i			1.01221i
$927$			3.39534i			0.111518i
$928$	24.4762			0.803469
$929$			49.1129i			1.61134i	0.592362	+	0.805672i	$0.298195\pi$
$929$			49.1129i			1.61134i	−0.592362	+	0.805672i	$0.701805\pi$
$930$	19.2484			0.631181
$931$	−13.2011	−	4.98325i	−0.432650	−	0.163320i
$932$			9.31726i			0.305197i
$933$	−25.0125			−0.818871
$934$	−36.0222			−1.17868
$935$	−12.1347	−	54.0487i	−0.396847	−	1.76758i
$936$			3.69767i			0.120862i
$937$	−8.12704			−0.265499			−0.132749	−	0.991150i	$-0.542381\pi$
$937$	−8.12704			−0.265499			−0.132749	+	0.991150i	$0.542381\pi$
$938$	6.82477	−	37.4042i	0.222837	−	1.22129i
$939$	11.4294			0.372985
$940$	−14.1327			−0.460958
$941$	2.75401			0.0897783			0.0448891	−	0.998992i	$-0.485707\pi$
$941$	2.75401			0.0897783			0.0448891	+	0.998992i	$0.485707\pi$
$942$			23.9360i			0.779876i
$943$	−2.97014			−0.0967209
$944$		−	11.9819i		−	0.389979i
$945$	7.22133	+	1.31760i	0.234910	+	0.0428616i
$946$	34.3856	−	7.72005i	1.11797	−	0.251000i
$947$	1.30062			0.0422644			0.0211322	−	0.999777i	$-0.493273\pi$
$947$	1.30062			0.0422644			0.0211322	+	0.999777i	$0.493273\pi$
$948$	−11.7206			−0.380668
$949$	12.7425			0.413640
$950$		−	6.16494i		−	0.200017i
$951$			22.5425i			0.730990i
$952$	−8.79867	+	48.2225i	−0.285166	+	1.56290i
$953$			50.2130i			1.62656i	0.581875	+	0.813278i	$0.302319\pi$
$953$			50.2130i			1.62656i	−0.581875	+	0.813278i	$0.697681\pi$
$954$		−	1.62055i		−	0.0524673i
$955$			14.6961i			0.475554i
$956$			7.19771i			0.232791i
$957$	−20.7335	+	4.65496i	−0.670219	+	0.150474i
$958$		−	11.5240i		−	0.372324i
$959$	−7.12994	−	1.30093i	−0.230238	−	0.0420092i
$960$	−23.4456			−0.756705
$961$	−6.44833			−0.208011
$962$		−	2.31237i		−	0.0745537i
$963$			16.6826i			0.537591i
$964$	−8.29968			−0.267315
$965$	33.1577			1.06739
$966$	17.4142	+	3.17740i	0.560294	+	0.102231i
$967$			40.0635i			1.28835i	0.764876	+	0.644177i	$0.222800\pi$
$967$			40.0635i			1.28835i	−0.764876	+	0.644177i	$0.777200\pi$
$968$	−14.4721	−	30.6053i	−0.465152	−	0.983692i
$969$		−	12.1347i		−	0.389823i
$970$			10.2561i			0.329304i
$971$		−	40.3104i		−	1.29362i	−0.762650	−	0.646811i	$-0.776102\pi$
$971$		−	40.3104i		−	1.29362i	0.762650	−	0.646811i	$-0.223898\pi$
$972$			0.714715i			0.0229245i
$973$	−30.2963	−	5.52786i	−0.971256	−	0.177215i
$974$		−	24.6692i		−	0.790454i
$975$		−	3.24110i		−	0.103798i
$976$	−9.34060			−0.298985
$977$	10.1628			0.325136			0.162568	−	0.986697i	$-0.448022\pi$
$977$	10.1628			0.325136			0.162568	+	0.986697i	$0.448022\pi$
$978$	19.1767			0.613202
$979$	2.23543	+	9.95673i	0.0714445	+	0.318218i
$980$	4.90213	−	12.9862i	0.156593	−	0.414830i
$981$			6.79413i			0.216920i
$982$	−19.4838			−0.621752
$983$			9.01246i			0.287453i	0.989617	+	0.143726i	$0.0459085\pi$
$983$			9.01246i			0.287453i	−0.989617	+	0.143726i	$0.954091\pi$
$984$	1.54893			0.0493782
$985$	−30.8984			−0.984506
$986$	43.7263			1.39253
$987$	−18.5503	−	3.38468i	−0.590462	−	0.107736i
$988$	−1.73092			−0.0550680
$989$		−	55.3129i		−	1.75885i
$990$	10.1788	−	2.28528i	0.323504	−	0.0726311i
$991$	35.9427			1.14176			0.570879	−	0.821035i	$-0.306603\pi$
$991$	35.9427			1.14176			0.570879	+	0.821035i	$0.306603\pi$
$992$	23.3778			0.742247
$993$			22.6620i			0.719157i
$994$	−4.31854	+	23.6684i	−0.136976	+	0.750717i
$995$	−58.2038			−1.84518
$996$		−	0.102617i		−	0.00325156i
$997$	41.1961			1.30469			0.652346	−	0.757921i	$-0.273785\pi$
$997$	41.1961			1.30469			0.652346	+	0.757921i	$0.273785\pi$
$998$		−	21.2699i		−	0.673288i
$999$		−	1.69767i		−	0.0537119i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.c.a.76.6	yes	16
3.2	odd	2		693.2.c.e.307.12		16
4.3	odd	2		3696.2.q.e.769.2		16
7.6	odd	2	inner	231.2.c.a.76.5	✓	16
11.10	odd	2	inner	231.2.c.a.76.12	yes	16
21.20	even	2		693.2.c.e.307.11		16
28.27	even	2		3696.2.q.e.769.15		16
33.32	even	2		693.2.c.e.307.6		16
44.43	even	2		3696.2.q.e.769.1		16
77.76	even	2	inner	231.2.c.a.76.11	yes	16
231.230	odd	2		693.2.c.e.307.5		16
308.307	odd	2		3696.2.q.e.769.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.c.a.76.5	✓	16	7.6	odd	2	inner
231.2.c.a.76.6	yes	16	1.1	even	1	trivial
231.2.c.a.76.11	yes	16	77.76	even	2	inner
231.2.c.a.76.12	yes	16	11.10	odd	2	inner
693.2.c.e.307.5		16	231.230	odd	2
693.2.c.e.307.6		16	33.32	even	2
693.2.c.e.307.11		16	21.20	even	2
693.2.c.e.307.12		16	3.2	odd	2
3696.2.q.e.769.1		16	44.43	even	2
3696.2.q.e.769.2		16	4.3	odd	2
3696.2.q.e.769.15		16	28.27	even	2
3696.2.q.e.769.16		16	308.307	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)

\(f(q)\)	\(=\)	\(q-1.13370i q^{2} +1.00000i q^{3} +0.714715 q^{4} -2.77447i q^{5} +1.13370 q^{6} +(-2.60278 - 0.474903i) q^{7} -3.07768i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.13370i q^{2} +1.00000i q^{3} +0.714715 q^{4} -2.77447i q^{5} +1.13370 q^{6} +(-2.60278 - 0.474903i) q^{7} -3.07768i q^{8} -1.00000 q^{9} -3.14542 q^{10} +(3.23607 - 0.726543i) q^{11} +0.714715i q^{12} +1.20145 q^{13} +(-0.538399 + 2.95078i) q^{14} +2.77447 q^{15} -2.05975 q^{16} +6.01988 q^{17} +1.13370i q^{18} -2.01577 q^{19} -1.98295i q^{20} +(0.474903 - 2.60278i) q^{21} +(-0.823684 - 3.66874i) q^{22} -5.90157 q^{23} +3.07768 q^{24} -2.69767 q^{25} -1.36208i q^{26} -1.00000i q^{27} +(-1.86025 - 0.339420i) q^{28} +6.40701i q^{29} -3.14542i q^{30} +6.11950i q^{31} -3.82022i q^{32} +(0.726543 + 3.23607i) q^{33} -6.82477i q^{34} +(-1.31760 + 7.22133i) q^{35} -0.714715 q^{36} +1.69767 q^{37} +2.28528i q^{38} +1.20145i q^{39} -8.53893 q^{40} +0.503279 q^{41} +(-2.95078 - 0.538399i) q^{42} +9.37258i q^{43} +(2.31287 - 0.519271i) q^{44} +2.77447i q^{45} +6.69063i q^{46} -7.12710i q^{47} -2.05975i q^{48} +(6.54893 + 2.47214i) q^{49} +3.05836i q^{50} +6.01988i q^{51} +0.858691 q^{52} -1.42943 q^{53} -1.13370 q^{54} +(-2.01577 - 8.97836i) q^{55} +(-1.46160 + 8.01054i) q^{56} -2.01577i q^{57} +7.26365 q^{58} +5.81717i q^{59} +1.98295 q^{60} +4.53482 q^{61} +6.93771 q^{62} +(2.60278 + 0.474903i) q^{63} -8.45050 q^{64} -3.33337i q^{65} +(3.66874 - 0.823684i) q^{66} -12.6760 q^{67} +4.30250 q^{68} -5.90157i q^{69} +(8.18685 + 1.49377i) q^{70} +8.02107 q^{71} +3.07768i q^{72} +10.6060 q^{73} -1.92465i q^{74} -2.69767i q^{75} -1.44070 q^{76} +(-8.76781 + 0.354213i) q^{77} +1.36208 q^{78} +16.3990i q^{79} +5.71472i q^{80} +1.00000 q^{81} -0.570570i q^{82} -0.143578 q^{83} +(0.339420 - 1.86025i) q^{84} -16.7020i q^{85} +10.6257 q^{86} -6.40701 q^{87} +(-2.23607 - 9.95959i) q^{88} +3.07680i q^{89} +3.14542 q^{90} +(-3.12710 - 0.570570i) q^{91} -4.21794 q^{92} -6.11950 q^{93} -8.08002 q^{94} +5.59268i q^{95} +3.82022 q^{96} -3.26064i q^{97} +(2.80267 - 7.42455i) q^{98} +(-3.23607 + 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4} - 16 q^{9}+O(q^{10}) \) 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

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