LMFDB - Embedded newform 231.2.c.a.76.12

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			76.12
Root			$-1.86824 - 0.357358i$ of defining polynomial
Character	$\chi$	$=$	231.76
Dual form			231.2.c.a.76.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.13370i q^{2} +1.00000i q^{3} +0.714715 q^{4} -2.77447i q^{5} -1.13370 q^{6} +(2.60278 + 0.474903i) q^{7} +3.07768i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.13370i q^{2} +1.00000i q^{3} +0.714715 q^{4} -2.77447i q^{5} -1.13370 q^{6} +(2.60278 + 0.474903i) q^{7} +3.07768i q^{8} -1.00000 q^{9} +3.14542 q^{10} +(3.23607 + 0.726543i) q^{11} +0.714715i q^{12} -1.20145 q^{13} +(-0.538399 + 2.95078i) q^{14} +2.77447 q^{15} -2.05975 q^{16} -6.01988 q^{17} -1.13370i q^{18} +2.01577 q^{19} -1.98295i q^{20} +(-0.474903 + 2.60278i) q^{21} +(-0.823684 + 3.66874i) q^{22} -5.90157 q^{23} -3.07768 q^{24} -2.69767 q^{25} -1.36208i q^{26} -1.00000i q^{27} +(1.86025 + 0.339420i) q^{28} -6.40701i q^{29} +3.14542i q^{30} +6.11950i q^{31} +3.82022i q^{32} +(-0.726543 + 3.23607i) q^{33} -6.82477i q^{34} +(1.31760 - 7.22133i) q^{35} -0.714715 q^{36} +1.69767 q^{37} +2.28528i q^{38} -1.20145i q^{39} +8.53893 q^{40} -0.503279 q^{41} +(-2.95078 - 0.538399i) q^{42} -9.37258i q^{43} +(2.31287 + 0.519271i) q^{44} +2.77447i q^{45} -6.69063i q^{46} -7.12710i q^{47} -2.05975i q^{48} +(6.54893 + 2.47214i) q^{49} -3.05836i q^{50} -6.01988i q^{51} -0.858691 q^{52} -1.42943 q^{53} +1.13370 q^{54} +(2.01577 - 8.97836i) q^{55} +(-1.46160 + 8.01054i) q^{56} +2.01577i q^{57} +7.26365 q^{58} +5.81717i q^{59} +1.98295 q^{60} -4.53482 q^{61} -6.93771 q^{62} +(-2.60278 - 0.474903i) q^{63} -8.45050 q^{64} +3.33337i q^{65} +(-3.66874 - 0.823684i) q^{66} -12.6760 q^{67} -4.30250 q^{68} -5.90157i q^{69} +(8.18685 + 1.49377i) q^{70} +8.02107 q^{71} -3.07768i q^{72} -10.6060 q^{73} +1.92465i q^{74} -2.69767i q^{75} +1.44070 q^{76} +(8.07774 + 3.42785i) q^{77} +1.36208 q^{78} -16.3990i q^{79} +5.71472i q^{80} +1.00000 q^{81} -0.570570i q^{82} +0.143578 q^{83} +(-0.339420 + 1.86025i) q^{84} +16.7020i q^{85} +10.6257 q^{86} +6.40701 q^{87} +(-2.23607 + 9.95959i) q^{88} +3.07680i q^{89} -3.14542 q^{90} +(-3.12710 - 0.570570i) q^{91} -4.21794 q^{92} -6.11950 q^{93} +8.08002 q^{94} -5.59268i q^{95} -3.82022 q^{96} -3.26064i q^{97} +(-2.80267 + 7.42455i) q^{98} +(-3.23607 - 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.131276\pi$
$2$			1.13370i			0.801650i	−0.916155	+	0.400825i	$0.868724\pi$
$3$			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	$-0.553282\pi$
$13$	−1.20145			−0.333221			−0.166610	+	0.986023i	$0.553282\pi$
$14$	−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	$-0.760488\pi$
$17$	−6.01988			−1.46004			−0.730018	+	0.683428i	$0.760488\pi$
$18$		−	1.13370i		−	0.267217i
$19$	2.01577			0.462449			0.231225	−	0.972900i	$-0.425727\pi$
$19$	2.01577			0.462449			0.231225	+	0.972900i	$0.425727\pi$
$20$		−	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	$-0.797201\pi$
$29$		−	6.40701i		−	1.18975i	0.803818	−	0.594876i	$-0.202799\pi$
$30$			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	$-0.512513\pi$
$41$	−0.503279			−0.0785990			−0.0392995	+	0.999227i	$0.512513\pi$
$42$	−2.95078	−	0.538399i	−0.455316	−	0.0830768i
$43$		−	9.37258i		−	1.42931i	−0.699480	−	0.714653i	$-0.746585\pi$
$43$		−	9.37258i		−	1.42931i	0.699480	−	0.714653i	$-0.253415\pi$
$44$	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	$-0.593759\pi$
$61$	−4.53482			−0.580624			−0.290312	+	0.956932i	$0.593759\pi$
$62$	−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	$-0.713139\pi$
$73$	−10.6060			−1.24134			−0.620670	+	0.784072i	$0.713139\pi$
$74$			1.92465i			0.223736i
$75$		−	2.69767i		−	0.311500i
$76$	1.44070			0.165260
$77$	8.07774	+	3.42785i	0.920544	+	0.390640i
$78$	1.36208			0.154226
$79$		−	16.3990i		−	1.84503i	−0.385956	−	0.922517i	$-0.626128\pi$
$79$		−	16.3990i		−	1.84503i	0.385956	−	0.922517i	$-0.373872\pi$
$80$			5.71472i			0.638925i
$81$	1.00000			0.111111
$82$		−	0.570570i		−	0.0630089i
$83$	0.143578			0.0157597			0.00787987	−	0.999969i	$-0.497492\pi$
$83$	0.143578			0.0157597			0.00787987	+	0.999969i	$0.497492\pi$
$84$	−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	$-0.172946\pi$
$101$	17.2053			1.71199			0.855993	+	0.516987i	$0.172946\pi$
$102$	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	$0.298580\pi$
$107$			16.6826i			1.61277i	−0.591389	+	0.806386i	$0.701420\pi$
$108$		−	0.714715i		−	0.0687735i
$109$			6.79413i			0.650760i	0.945583	+	0.325380i	$0.105492\pi$
$109$			6.79413i			0.650760i	−0.945583	+	0.325380i	$0.894508\pi$
$110$	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	$0.107575\pi$
$127$			7.47297i			0.663119i	−0.943434	+	0.331559i	$0.892425\pi$
$128$		−	1.93993i		−	0.171467i
$129$	9.37258			0.825210
$130$	−3.77906			−0.331445
$131$	−12.8140			−1.11957			−0.559783	−	0.828639i	$-0.689115\pi$
$131$	−12.8140			−1.11957			−0.559783	+	0.828639i	$0.689115\pi$
$132$	−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	$-0.664336\pi$
$139$	−11.6400			−0.987291			−0.493645	+	0.869663i	$0.664336\pi$
$140$	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	$0.176311\pi$
$149$			12.8414i			1.05201i	−0.850481	+	0.526006i	$0.823689\pi$
$150$	3.05836			0.249714
$151$			7.97625i			0.649098i	0.945869	+	0.324549i	$0.105213\pi$
$151$			7.97625i			0.649098i	−0.945869	+	0.324549i	$0.894787\pi$
$152$			6.20390i			0.503203i
$153$	6.01988			0.486679
$154$	−3.88617	+	9.15776i	−0.313156	+	0.737954i
$155$	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	$-0.230929\pi$
$167$	19.3372			1.49636			0.748178	+	0.663498i	$0.230929\pi$
$168$	−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	$-0.202740\pi$
$173$	21.1481			1.60786			0.803928	+	0.594726i	$0.202740\pi$
$174$			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	$-0.858469\pi$
$193$		−	11.9510i		−	0.860254i	0.902768	−	0.430127i	$-0.141531\pi$
$194$	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	$0.129855\pi$
$197$			11.1367i			0.793458i	−0.917936	+	0.396729i	$0.870145\pi$
$198$	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	$-0.869338\pi$
$211$		−	11.5932i		−	0.798112i	0.916927	−	0.399056i	$-0.130662\pi$
$212$	−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	$-0.311170\pi$
$227$	16.8456			1.11808			0.559039	+	0.829141i	$0.311170\pi$
$228$			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
$231$	−3.42785	+	8.07774i	−0.225536	+	0.531476i
$232$	19.7187			1.29460
$233$		−	13.0363i		−	0.854038i	−0.904243	−	0.427019i	$-0.859564\pi$
$233$		−	13.0363i		−	0.854038i	0.904243	−	0.427019i	$-0.140436\pi$
$234$			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	$-0.894396\pi$
$239$		−	10.0707i		−	0.651422i	0.945469	−	0.325711i	$-0.105604\pi$
$240$	−5.71472			−0.368883
$241$	11.6126			0.748031			0.374016	−	0.927422i	$-0.377981\pi$
$241$	11.6126			0.748031			0.374016	+	0.927422i	$0.377981\pi$
$242$	−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	$-0.796916\pi$
$263$		−	19.3179i		−	1.19119i	0.803285	−	0.595595i	$-0.203084\pi$
$264$	−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	$-0.217569\pi$
$271$	25.5281			1.55072			0.775360	+	0.631520i	$0.217569\pi$
$272$	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	$0.404234\pi$
$277$			31.7915i			1.91017i	−0.296339	+	0.955083i	$0.595766\pi$
$278$		−	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	$0.0259159\pi$
$281$			2.72659i			0.162655i	−0.996687	+	0.0813274i	$0.974084\pi$
$282$			8.08002i			0.481158i
$283$	6.82155			0.405499			0.202750	−	0.979231i	$-0.435012\pi$
$283$	6.82155			0.405499			0.202750	+	0.979231i	$0.435012\pi$
$284$	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	$-0.557622\pi$
$293$	−6.16346			−0.360073			−0.180037	+	0.983660i	$0.557622\pi$
$294$	−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	$-0.418757\pi$
$307$	8.84732			0.504944			0.252472	+	0.967604i	$0.418757\pi$
$308$	5.77328	+	2.44994i	0.328963	+	0.139598i
$309$	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	$0.0662330\pi$
$337$			7.58456i			0.413158i	−0.978430	+	0.206579i	$0.933767\pi$
$338$		−	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	$0.126191\pi$
$347$			14.3859i			0.772276i	−0.922441	+	0.386138i	$0.873809\pi$
$348$	4.57918			0.245470
$349$	−7.86819			−0.421174			−0.210587	−	0.977575i	$-0.567538\pi$
$349$	−7.86819			−0.421174			−0.210587	+	0.977575i	$0.567538\pi$
$350$	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	$-0.921550\pi$
$359$		−	9.24519i		−	0.487943i	0.969782	−	0.243971i	$-0.0784503\pi$
$360$	−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	$0.0215283\pi$
$373$			2.61043i			0.135163i	−0.997714	+	0.0675816i	$0.978472\pi$
$374$	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
$385$	9.51045	−	22.4114i	0.484698	−	1.14219i
$386$	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	$-0.729477\pi$
$409$	−26.6986			−1.32016			−0.660079	+	0.751196i	$0.729477\pi$
$410$	−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	$-0.915756\pi$
$431$		−	10.8612i		−	0.523165i	0.965181	−	0.261582i	$-0.0842443\pi$
$432$			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	$-0.205367\pi$
$439$	33.4815			1.59798			0.798991	+	0.601343i	$0.205367\pi$
$440$	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	$-0.778576\pi$
$457$		−	27.4003i		−	1.28173i	0.767654	−	0.640865i	$-0.221424\pi$
$458$	3.08840			0.144311
$459$			6.01988i			0.280984i
$460$			11.7025i			0.545633i
$461$	−5.87631			−0.273687			−0.136843	−	0.990593i	$-0.543696\pi$
$461$	−5.87631			−0.273687			−0.136843	+	0.990593i	$0.543696\pi$
$462$	−9.15776	−	3.88617i	−0.426058	−	0.180801i
$463$	−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	$-0.574600\pi$
$479$	−10.1649			−0.464447			−0.232224	+	0.972662i	$0.574600\pi$
$480$			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	$0.126763\pi$
$491$			17.1859i			0.775590i	−0.921746	+	0.387795i	$0.873237\pi$
$492$		−	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	$-0.827570\pi$
$503$	−38.4335			−1.71366			−0.856832	+	0.515596i	$0.827570\pi$
$504$	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	$-0.442317\pi$
$523$	8.24320			0.360450			0.180225	+	0.983625i	$0.442317\pi$
$524$	−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
$539$	19.3967	+	12.7581i	0.835474	+	0.549529i
$540$	−1.98295			−0.0853327
$541$			15.5132i			0.666964i	0.942756	+	0.333482i	$0.108224\pi$
$541$			15.5132i			0.666964i	−0.942756	+	0.333482i	$0.891776\pi$
$542$			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	$-0.931286\pi$
$547$		−	10.0194i		−	0.428400i	0.976790	−	0.214200i	$-0.0687145\pi$
$548$	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	$-0.926702\pi$
$557$		−	10.7735i		−	0.456487i	0.973604	−	0.228243i	$-0.0732982\pi$
$558$	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	$-0.295723\pi$
$563$	28.4068			1.19720			0.598602	+	0.801046i	$0.295723\pi$
$564$	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	$-0.880607\pi$
$569$		−	17.4776i		−	0.732701i	0.930477	−	0.366350i	$-0.119393\pi$
$570$			6.34045i			0.265572i
$571$			12.2062i			0.510814i	0.966834	+	0.255407i	$0.0822094\pi$
$571$			12.2062i			0.510814i	−0.966834	+	0.255407i	$0.917791\pi$
$572$	−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	$-0.510540\pi$
$593$	−1.61246			−0.0662156			−0.0331078	+	0.999452i	$0.510540\pi$
$594$	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	$-0.625408\pi$
$601$	−18.8212			−0.767734			−0.383867	+	0.923388i	$0.625408\pi$
$602$	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	$-0.680590\pi$
$607$	−26.4798			−1.07478			−0.537391	+	0.843334i	$0.680590\pi$
$608$			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	$-0.890925\pi$
$613$		−	16.6380i		−	0.672003i	0.941861	−	0.336001i	$-0.109075\pi$
$614$			10.0302i			0.404788i
$615$	−1.39633			−0.0563055
$616$	−10.5498	+	24.8607i	−0.425065	+	1.00167i
$617$	−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	$0.0629464\pi$
$659$			10.0869i			0.392931i	−0.980511	+	0.196466i	$0.937054\pi$
$660$	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	$-0.959535\pi$
$673$		−	6.57801i		−	0.253563i	0.991931	−	0.126782i	$-0.0404648\pi$
$674$	−8.59865			−0.331208
$675$			2.69767i			0.103833i
$676$	−8.25963			−0.317678
$677$	−20.6061			−0.791958			−0.395979	−	0.918260i	$-0.629595\pi$
$677$	−20.6061			−0.791958			−0.395979	+	0.918260i	$0.629595\pi$
$678$	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
$693$	−8.07774	−	3.42785i	−0.306848	−	0.130213i
$694$	−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	$0.249520\pi$
$701$			37.3868i			1.41208i	−0.708172	+	0.706040i	$0.750480\pi$
$702$	−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	$-0.467368\pi$
$733$	5.54137			0.204675			0.102338	+	0.994750i	$0.467368\pi$
$734$	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	$-0.946787\pi$
$739$		−	9.04677i		−	0.332791i	0.986059	−	0.166395i	$-0.0532128\pi$
$740$		−	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	$0.106862\pi$
$743$			17.9602i			0.658895i	−0.944174	+	0.329447i	$0.893138\pi$
$744$		−	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	$-0.317481\pi$
$761$	29.9305			1.08498			0.542490	+	0.840062i	$0.317481\pi$
$762$		−	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	$-0.706013\pi$
$769$	−33.4414			−1.20593			−0.602963	+	0.797769i	$0.706013\pi$
$770$	25.4079	+	10.7820i	0.915638	+	0.388558i
$771$	−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	$-0.603087\pi$
$787$	−17.8548			−0.636453			−0.318227	+	0.948015i	$0.603087\pi$
$788$			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	$-0.903769\pi$
$809$		−	16.9369i		−	0.595471i	0.954648	−	0.297736i	$-0.0962314\pi$
$810$	3.14542			0.110519
$811$	24.5693			0.862744			0.431372	−	0.902174i	$-0.358030\pi$
$811$	24.5693			0.862744			0.431372	+	0.902174i	$0.358030\pi$
$812$	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	$-0.915946\pi$
$821$		−	14.9572i		−	0.522009i	0.965338	−	0.261004i	$-0.0840537\pi$
$822$	−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	$0.00647267\pi$
$827$			1.16946i			0.0406662i	−0.999793	+	0.0203331i	$0.993527\pi$
$828$	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
$847$	23.6496	+	16.9616i	0.812611	+	0.582807i
$848$	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	$-0.496959\pi$
$853$	0.558121			0.0191097			0.00955485	+	0.999954i	$0.496959\pi$
$854$	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	$-0.478153\pi$
$857$	4.01535			0.137162			0.0685808	+	0.997646i	$0.478153\pi$
$858$	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	$0.0898335\pi$
$877$			16.4944i			0.556977i	−0.960440	+	0.278489i	$0.910167\pi$
$878$			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	$-0.419707\pi$
$887$	14.8663			0.499162			0.249581	+	0.968354i	$0.419707\pi$
$888$	−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	$0.321738\pi$
$919$			51.3682i			1.69448i	−0.531210	+	0.847240i	$0.678262\pi$
$920$	−50.3931			−1.66141
$921$			8.84732i			0.291529i
$922$		−	6.66199i		−	0.219401i
$923$	−9.63688			−0.317202
$924$	−2.44994	+	5.77328i	−0.0805970	+	0.189927i
$925$	−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	$-0.457619\pi$
$937$	8.12704			0.265499			0.132749	+	0.991150i	$0.457619\pi$
$938$	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	$-0.514293\pi$
$941$	−2.75401			−0.0897783			−0.0448891	+	0.998992i	$0.514293\pi$
$942$		−	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	$-0.697681\pi$
$953$		−	50.2130i		−	1.62656i	0.581875	−	0.813278i	$-0.302319\pi$
$954$			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	$-0.777200\pi$
$967$		−	40.0635i		−	1.28835i	0.764876	−	0.644177i	$-0.222800\pi$
$968$	−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	$-0.726215\pi$
$997$	−41.1961			−1.30469			−0.652346	+	0.757921i	$0.726215\pi$
$998$			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.76.12	yes	16
3.2	odd	2		693.2.c.e.307.6		16
4.3	odd	2		3696.2.q.e.769.1		16
7.6	odd	2	inner	231.2.c.a.76.11	yes	16
11.10	odd	2	inner	231.2.c.a.76.6	yes	16
21.20	even	2		693.2.c.e.307.5		16
28.27	even	2		3696.2.q.e.769.16		16
33.32	even	2		693.2.c.e.307.12		16
44.43	even	2		3696.2.q.e.769.2		16
77.76	even	2	inner	231.2.c.a.76.5	✓	16
231.230	odd	2		693.2.c.e.307.11		16
308.307	odd	2		3696.2.q.e.769.15		16

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

\(f(q)\)	\(=\)	\(q+1.13370i q^{2} +1.00000i q^{3} +0.714715 q^{4} -2.77447i q^{5} -1.13370 q^{6} +(2.60278 + 0.474903i) q^{7} +3.07768i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.13370i q^{2} +1.00000i q^{3} +0.714715 q^{4} -2.77447i q^{5} -1.13370 q^{6} +(2.60278 + 0.474903i) q^{7} +3.07768i q^{8} -1.00000 q^{9} +3.14542 q^{10} +(3.23607 + 0.726543i) q^{11} +0.714715i q^{12} -1.20145 q^{13} +(-0.538399 + 2.95078i) q^{14} +2.77447 q^{15} -2.05975 q^{16} -6.01988 q^{17} -1.13370i q^{18} +2.01577 q^{19} -1.98295i q^{20} +(-0.474903 + 2.60278i) q^{21} +(-0.823684 + 3.66874i) q^{22} -5.90157 q^{23} -3.07768 q^{24} -2.69767 q^{25} -1.36208i q^{26} -1.00000i q^{27} +(1.86025 + 0.339420i) q^{28} -6.40701i q^{29} +3.14542i q^{30} +6.11950i q^{31} +3.82022i q^{32} +(-0.726543 + 3.23607i) q^{33} -6.82477i q^{34} +(1.31760 - 7.22133i) q^{35} -0.714715 q^{36} +1.69767 q^{37} +2.28528i q^{38} -1.20145i q^{39} +8.53893 q^{40} -0.503279 q^{41} +(-2.95078 - 0.538399i) q^{42} -9.37258i q^{43} +(2.31287 + 0.519271i) q^{44} +2.77447i q^{45} -6.69063i q^{46} -7.12710i q^{47} -2.05975i q^{48} +(6.54893 + 2.47214i) q^{49} -3.05836i q^{50} -6.01988i q^{51} -0.858691 q^{52} -1.42943 q^{53} +1.13370 q^{54} +(2.01577 - 8.97836i) q^{55} +(-1.46160 + 8.01054i) q^{56} +2.01577i q^{57} +7.26365 q^{58} +5.81717i q^{59} +1.98295 q^{60} -4.53482 q^{61} -6.93771 q^{62} +(-2.60278 - 0.474903i) q^{63} -8.45050 q^{64} +3.33337i q^{65} +(-3.66874 - 0.823684i) q^{66} -12.6760 q^{67} -4.30250 q^{68} -5.90157i q^{69} +(8.18685 + 1.49377i) q^{70} +8.02107 q^{71} -3.07768i q^{72} -10.6060 q^{73} +1.92465i q^{74} -2.69767i q^{75} +1.44070 q^{76} +(8.07774 + 3.42785i) q^{77} +1.36208 q^{78} -16.3990i q^{79} +5.71472i q^{80} +1.00000 q^{81} -0.570570i q^{82} +0.143578 q^{83} +(-0.339420 + 1.86025i) q^{84} +16.7020i q^{85} +10.6257 q^{86} +6.40701 q^{87} +(-2.23607 + 9.95959i) q^{88} +3.07680i q^{89} -3.14542 q^{90} +(-3.12710 - 0.570570i) q^{91} -4.21794 q^{92} -6.11950 q^{93} +8.08002 q^{94} -5.59268i q^{95} -3.82022 q^{96} -3.26064i q^{97} +(-2.80267 + 7.42455i) q^{98} +(-3.23607 - 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4} - 16 q^{9}+O(q^{10}) \) 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

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Groups

Database

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