LMFDB - Embedded newform 1155.2.c.e.694.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(694,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.694");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15194 x^{12} + 40320 x^{10} + 61593 x^{8} + 48545 x^{6} + \cdots + 100 $ x^20 + 33x^18 + 456x^16 + 3426x^14 + 15194x^12 + 40320x^10 + 61593x^8 + 48545x^6 + 15624x^4 + 2116*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.4
Root			$-2.02181i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.e.694.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.02181i q^{2} +1.00000i q^{3} -2.08773 q^{4} +(-0.549616 + 2.16747i) q^{5} +2.02181 q^{6} -1.00000i q^{7} +0.177380i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.02181i q^{2} +1.00000i q^{3} -2.08773 q^{4} +(-0.549616 + 2.16747i) q^{5} +2.02181 q^{6} -1.00000i q^{7} +0.177380i q^{8} -1.00000 q^{9} +(4.38222 + 1.11122i) q^{10} -1.00000 q^{11} -2.08773i q^{12} +5.44833i q^{13} -2.02181 q^{14} +(-2.16747 - 0.549616i) q^{15} -3.81684 q^{16} -2.57671i q^{17} +2.02181i q^{18} +0.801918 q^{19} +(1.14745 - 4.52510i) q^{20} +1.00000 q^{21} +2.02181i q^{22} +4.06135i q^{23} -0.177380 q^{24} +(-4.39584 - 2.38255i) q^{25} +11.0155 q^{26} -1.00000i q^{27} +2.08773i q^{28} -4.72983 q^{29} +(-1.11122 + 4.38222i) q^{30} -9.50964 q^{31} +8.07170i q^{32} -1.00000i q^{33} -5.20963 q^{34} +(2.16747 + 0.549616i) q^{35} +2.08773 q^{36} -0.369366i q^{37} -1.62133i q^{38} -5.44833 q^{39} +(-0.384465 - 0.0974908i) q^{40} -6.07185 q^{41} -2.02181i q^{42} +12.8198i q^{43} +2.08773 q^{44} +(0.549616 - 2.16747i) q^{45} +8.21129 q^{46} -10.4673i q^{47} -3.81684i q^{48} -1.00000 q^{49} +(-4.81708 + 8.88758i) q^{50} +2.57671 q^{51} -11.3747i q^{52} +8.19730i q^{53} -2.02181 q^{54} +(0.549616 - 2.16747i) q^{55} +0.177380 q^{56} +0.801918i q^{57} +9.56284i q^{58} +0.232249 q^{59} +(4.52510 + 1.14745i) q^{60} +15.4328 q^{61} +19.2267i q^{62} +1.00000i q^{63} +8.68579 q^{64} +(-11.8091 - 2.99449i) q^{65} -2.02181 q^{66} +14.9167i q^{67} +5.37949i q^{68} -4.06135 q^{69} +(1.11122 - 4.38222i) q^{70} -9.27387 q^{71} -0.177380i q^{72} +10.5828i q^{73} -0.746790 q^{74} +(2.38255 - 4.39584i) q^{75} -1.67419 q^{76} +1.00000i q^{77} +11.0155i q^{78} -13.3303 q^{79} +(2.09779 - 8.27288i) q^{80} +1.00000 q^{81} +12.2761i q^{82} +5.21440i q^{83} -2.08773 q^{84} +(5.58494 + 1.41620i) q^{85} +25.9193 q^{86} -4.72983i q^{87} -0.177380i q^{88} +10.5734 q^{89} +(-4.38222 - 1.11122i) q^{90} +5.44833 q^{91} -8.47901i q^{92} -9.50964i q^{93} -21.1629 q^{94} +(-0.440747 + 1.73813i) q^{95} -8.07170 q^{96} +12.2790i q^{97} +2.02181i q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} - 2 q^{10} - 20 q^{11} - 6 q^{14} + 2 q^{15} + 38 q^{16} + 2 q^{19} + 4 q^{20} + 20 q^{21} - 18 q^{24} + 12 q^{25} + 20 q^{26} - 38 q^{29} + 6 q^{30} + 20 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} + 2 q^{40} + 12 q^{41} + 26 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{49} - 6 q^{50} + 26 q^{51} - 6 q^{54} + 2 q^{55} + 18 q^{56} - 22 q^{59} + 16 q^{60} + 34 q^{61} - 26 q^{64} - 28 q^{65} - 6 q^{66} - 26 q^{69} - 6 q^{70} + 72 q^{71} - 72 q^{74} - 8 q^{75} + 44 q^{76} + 4 q^{79} - 8 q^{80} + 20 q^{81} - 26 q^{84} - 16 q^{85} + 52 q^{86} + 6 q^{89} + 2 q^{90} + 16 q^{94} + 14 q^{95} + 62 q^{96} + 20 q^{99}+O(q^{100}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 - 2 * q^10 - 20 * q^11 - 6 * q^14 + 2 * q^15 + 38 * q^16 + 2 * q^19 + 4 * q^20 + 20 * q^21 - 18 * q^24 + 12 * q^25 + 20 * q^26 - 38 * q^29 + 6 * q^30 + 20 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 + 2 * q^40 + 12 * q^41 + 26 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^49 - 6 * q^50 + 26 * q^51 - 6 * q^54 + 2 * q^55 + 18 * q^56 - 22 * q^59 + 16 * q^60 + 34 * q^61 - 26 * q^64 - 28 * q^65 - 6 * q^66 - 26 * q^69 - 6 * q^70 + 72 * q^71 - 72 * q^74 - 8 * q^75 + 44 * q^76 + 4 * q^79 - 8 * q^80 + 20 * q^81 - 26 * q^84 - 16 * q^85 + 52 * q^86 + 6 * q^89 + 2 * q^90 + 16 * q^94 + 14 * q^95 + 62 * q^96 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		−	2.02181i		−	1.42964i	−0.699309	−	0.714819i	$-0.746509\pi$
$2$		−	2.02181i		−	1.42964i	0.699309	−	0.714819i	$-0.253491\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−2.08773			−1.04387
$5$	−0.549616	+	2.16747i	−0.245796	+	0.969322i
$5$	−0.549616	+	2.16747i	−0.245796	+	0.969322i
$6$	2.02181			0.825402
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			0.177380i			0.0627132i
$9$	−1.00000			−0.333333
$10$	4.38222	+	1.11122i	1.38578	+	0.351399i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		−	2.08773i		−	0.602677i
$13$			5.44833i			1.51110i	0.655094	+	0.755548i	$0.272629\pi$
$13$			5.44833i			1.51110i	−0.655094	+	0.755548i	$0.727371\pi$
$14$	−2.02181			−0.540353
$15$	−2.16747	−	0.549616i	−0.559638	−	0.141910i
$16$	−3.81684			−0.954209
$17$		−	2.57671i		−	0.624944i	−0.949927	−	0.312472i	$-0.898843\pi$
$17$		−	2.57671i		−	0.624944i	0.949927	−	0.312472i	$-0.101157\pi$
$18$			2.02181i			0.476546i
$19$	0.801918			0.183973			0.0919863	−	0.995760i	$-0.470678\pi$
$19$	0.801918			0.183973			0.0919863	+	0.995760i	$0.470678\pi$
$20$	1.14745	−	4.52510i	0.256578	−	1.01184i
$21$	1.00000			0.218218
$22$			2.02181i			0.431052i
$23$			4.06135i			0.846849i	0.905931	+	0.423425i	$0.139172\pi$
$23$			4.06135i			0.846849i	−0.905931	+	0.423425i	$0.860828\pi$
$24$	−0.177380			−0.0362075
$25$	−4.39584	−	2.38255i	−0.879169	−	0.476510i
$26$	11.0155			2.16032
$27$		−	1.00000i		−	0.192450i
$28$			2.08773i			0.394544i
$29$	−4.72983			−0.878307			−0.439154	−	0.898412i	$-0.644722\pi$
$29$	−4.72983			−0.878307			−0.439154	+	0.898412i	$0.644722\pi$
$30$	−1.11122	+	4.38222i	−0.202880	+	0.800080i
$31$	−9.50964			−1.70798			−0.853991	−	0.520288i	$-0.825825\pi$
$31$	−9.50964			−1.70798			−0.853991	+	0.520288i	$0.825825\pi$
$32$			8.07170i			1.42689i
$33$		−	1.00000i		−	0.174078i
$34$	−5.20963			−0.893445
$35$	2.16747	+	0.549616i	0.366369	+	0.0929021i
$36$	2.08773			0.347955
$37$		−	0.369366i		−	0.0607234i	−0.999539	−	0.0303617i	$-0.990334\pi$
$37$		−	0.369366i		−	0.0607234i	0.999539	−	0.0303617i	$-0.00966592\pi$
$38$		−	1.62133i		−	0.263014i
$39$	−5.44833			−0.872431
$40$	−0.384465	−	0.0974908i	−0.0607893	−	0.0154146i
$41$	−6.07185			−0.948263			−0.474132	−	0.880454i	$-0.657238\pi$
$41$	−6.07185			−0.948263			−0.474132	+	0.880454i	$0.657238\pi$
$42$		−	2.02181i		−	0.311973i
$43$			12.8198i			1.95500i	0.210926	+	0.977502i	$0.432352\pi$
$43$			12.8198i			1.95500i	−0.210926	+	0.977502i	$0.567648\pi$
$44$	2.08773			0.314738
$45$	0.549616	−	2.16747i	0.0819319	−	0.323107i
$46$	8.21129			1.21069
$47$		−	10.4673i		−	1.52681i	−0.645920	−	0.763405i	$-0.723526\pi$
$47$		−	10.4673i		−	1.52681i	0.645920	−	0.763405i	$-0.276474\pi$
$48$		−	3.81684i		−	0.550913i
$49$	−1.00000			−0.142857
$50$	−4.81708	+	8.88758i	−0.681237	+	1.25689i
$51$	2.57671			0.360812
$52$		−	11.3747i		−	1.57738i
$53$			8.19730i			1.12599i	0.826462	+	0.562993i	$0.190350\pi$
$53$			8.19730i			1.12599i	−0.826462	+	0.562993i	$0.809650\pi$
$54$	−2.02181			−0.275134
$55$	0.549616	−	2.16747i	0.0741102	−	0.292261i
$56$	0.177380			0.0237034
$57$			0.801918i			0.106217i
$58$			9.56284i			1.25566i
$59$	0.232249			0.0302362			0.0151181	−	0.999886i	$-0.495188\pi$
$59$	0.232249			0.0302362			0.0151181	+	0.999886i	$0.495188\pi$
$60$	4.52510	+	1.14745i	0.584187	+	0.148135i
$61$	15.4328			1.97597			0.987984	−	0.154559i	$-0.0493955\pi$
$61$	15.4328			1.97597			0.987984	+	0.154559i	$0.0493955\pi$
$62$			19.2267i			2.44180i
$63$			1.00000i			0.125988i
$64$	8.68579			1.08572
$65$	−11.8091	−	2.99449i	−1.46474	−	0.371421i
$66$	−2.02181			−0.248868
$67$			14.9167i			1.82236i	0.412004	+	0.911182i	$0.364829\pi$
$67$			14.9167i			1.82236i	−0.412004	+	0.911182i	$0.635171\pi$
$68$			5.37949i			0.652358i
$69$	−4.06135			−0.488929
$70$	1.11122	−	4.38222i	0.132816	−	0.523775i
$71$	−9.27387			−1.10061			−0.550303	−	0.834965i	$-0.685488\pi$
$71$	−9.27387			−1.10061			−0.550303	+	0.834965i	$0.685488\pi$
$72$		−	0.177380i		−	0.0209044i
$73$			10.5828i			1.23862i	0.785145	+	0.619312i	$0.212588\pi$
$73$			10.5828i			1.23862i	−0.785145	+	0.619312i	$0.787412\pi$
$74$	−0.746790			−0.0868126
$75$	2.38255	−	4.39584i	0.275113	−	0.507588i
$76$	−1.67419			−0.192043
$77$			1.00000i			0.113961i
$78$			11.0155i			1.24726i
$79$	−13.3303			−1.49978			−0.749891	−	0.661562i	$-0.769894\pi$
$79$	−13.3303			−1.49978			−0.749891	+	0.661562i	$0.769894\pi$
$80$	2.09779	−	8.27288i	0.234541	−	0.924936i
$81$	1.00000			0.111111
$82$			12.2761i			1.35567i
$83$			5.21440i			0.572355i	0.958177	+	0.286177i	$0.0923847\pi$
$83$			5.21440i			0.572355i	−0.958177	+	0.286177i	$0.907615\pi$
$84$	−2.08773			−0.227790
$85$	5.58494	+	1.41620i	0.605772	+	0.153609i
$86$	25.9193			2.79495
$87$		−	4.72983i		−	0.507091i
$88$		−	0.177380i		−	0.0189088i
$89$	10.5734			1.12078			0.560389	−	0.828230i	$-0.310652\pi$
$89$	10.5734			1.12078			0.560389	+	0.828230i	$0.310652\pi$
$90$	−4.38222	−	1.11122i	−0.461927	−	0.117133i
$91$	5.44833			0.571140
$92$		−	8.47901i		−	0.883998i
$93$		−	9.50964i		−	0.986104i
$94$	−21.1629			−2.18279
$95$	−0.440747	+	1.73813i	−0.0452197	+	0.178329i
$96$	−8.07170			−0.823814
$97$			12.2790i			1.24675i	0.781924	+	0.623374i	$0.214239\pi$
$97$			12.2790i			1.24675i	−0.781924	+	0.623374i	$0.785761\pi$
$98$			2.02181i			0.204234i
$99$	1.00000			0.100504
$100$	9.17735	+	4.97413i	0.917735	+	0.497413i
$101$	2.21466			0.220367			0.110183	−	0.993911i	$-0.464856\pi$
$101$	2.21466			0.220367			0.110183	+	0.993911i	$0.464856\pi$
$102$		−	5.20963i		−	0.515830i
$103$		−	14.9953i		−	1.47753i	−0.673964	−	0.738765i	$-0.735410\pi$
$103$		−	14.9953i		−	1.47753i	0.673964	−	0.738765i	$-0.264590\pi$
$104$	−0.966424			−0.0947657
$105$	−0.549616	+	2.16747i	−0.0536370	+	0.211523i
$106$	16.5734			1.60975
$107$		−	9.79736i		−	0.947147i	−0.880754	−	0.473573i	$-0.842964\pi$
$107$		−	9.79736i		−	0.947147i	0.880754	−	0.473573i	$-0.157036\pi$
$108$			2.08773i			0.200892i
$109$	0.805348			0.0771384			0.0385692	−	0.999256i	$-0.487720\pi$
$109$	0.805348			0.0771384			0.0385692	+	0.999256i	$0.487720\pi$
$110$	−4.38222	−	1.11122i	−0.417828	−	0.105951i
$111$	0.369366			0.0350587
$112$			3.81684i			0.360657i
$113$		−	18.3292i		−	1.72427i	−0.506681	−	0.862134i	$-0.669128\pi$
$113$		−	18.3292i		−	1.72427i	0.506681	−	0.862134i	$-0.330872\pi$
$114$	1.62133			0.151851
$115$	−8.80284	−	2.23218i	−0.820869	−	0.208152i
$116$	9.87462			0.916836
$117$		−	5.44833i		−	0.503698i
$118$		−	0.469564i		−	0.0432269i
$119$	−2.57671			−0.236207
$120$	0.0974908	−	0.384465i	0.00889965	−	0.0350967i
$121$	1.00000			0.0909091
$122$		−	31.2023i		−	2.82492i
$123$		−	6.07185i		−	0.547480i
$124$	19.8536			1.78291
$125$	7.58013	−	8.21837i	0.677988	−	0.735073i
$126$	2.02181			0.180118
$127$			4.11772i			0.365388i	0.983170	+	0.182694i	$0.0584818\pi$
$127$			4.11772i			0.365388i	−0.983170	+	0.182694i	$0.941518\pi$
$128$		−	1.41767i		−	0.125306i
$129$	−12.8198			−1.12872
$130$	−6.05430	+	23.8758i	−0.530998	+	2.09405i
$131$	−7.41340			−0.647712			−0.323856	−	0.946106i	$-0.604979\pi$
$131$	−7.41340			−0.647712			−0.323856	+	0.946106i	$0.604979\pi$
$132$			2.08773i			0.181714i
$133$		−	0.801918i		−	0.0695351i
$134$	30.1588			2.60532
$135$	2.16747	+	0.549616i	0.186546	+	0.0473034i
$136$	0.457057			0.0391923
$137$		−	9.06835i		−	0.774762i	−0.921920	−	0.387381i	$-0.873380\pi$
$137$		−	9.06835i		−	0.774762i	0.921920	−	0.387381i	$-0.126620\pi$
$138$			8.21129i			0.698991i
$139$	7.21710			0.612146			0.306073	−	0.952008i	$-0.400985\pi$
$139$	7.21710			0.612146			0.306073	+	0.952008i	$0.400985\pi$
$140$	−4.52510	−	1.14745i	−0.382440	−	0.0969774i
$141$	10.4673			0.881505
$142$			18.7501i			1.57347i
$143$		−	5.44833i		−	0.455612i
$144$	3.81684			0.318070
$145$	2.59959	−	10.2518i	0.215884	−	0.851362i
$146$	21.3965			1.77078
$147$		−	1.00000i		−	0.0824786i
$148$			0.771138i			0.0633872i
$149$	6.63108			0.543240			0.271620	−	0.962405i	$-0.412441\pi$
$149$	6.63108			0.543240			0.271620	+	0.962405i	$0.412441\pi$
$150$	−8.88758	−	4.81708i	−0.725668	−	0.393313i
$151$	−19.2917			−1.56993			−0.784967	−	0.619538i	$-0.787320\pi$
$151$	−19.2917			−1.56993			−0.784967	+	0.619538i	$0.787320\pi$
$152$			0.142244i			0.0115375i
$153$			2.57671i			0.208315i
$154$	2.02181			0.162922
$155$	5.22665	−	20.6119i	0.419815	−	1.65558i
$156$	11.3747			0.910702
$157$		−	9.60329i		−	0.766426i	−0.923660	−	0.383213i	$-0.874818\pi$
$157$		−	9.60329i		−	0.766426i	0.923660	−	0.383213i	$-0.125182\pi$
$158$			26.9515i			2.14415i
$159$	−8.19730			−0.650088
$160$	−17.4951	−	4.43633i	−1.38311	−	0.350723i
$161$	4.06135			0.320079
$162$		−	2.02181i		−	0.158849i
$163$		−	1.09563i		−	0.0858166i	−0.999079	−	0.0429083i	$-0.986338\pi$
$163$		−	1.09563i		−	0.0858166i	0.999079	−	0.0429083i	$-0.0136623\pi$
$164$	12.6764			0.989860
$165$	2.16747	+	0.549616i	0.168737	+	0.0427875i
$166$	10.5425			0.818260
$167$		−	14.3675i		−	1.11179i	−0.831253	−	0.555895i	$-0.812376\pi$
$167$		−	14.3675i		−	1.11179i	0.831253	−	0.555895i	$-0.187624\pi$
$168$			0.177380i			0.0136852i
$169$	−16.6843			−1.28341
$170$	2.86330	−	11.2917i	0.219605	−	0.866035i
$171$	−0.801918			−0.0613242
$172$		−	26.7644i		−	2.04076i
$173$			14.5699i			1.10773i	0.832607	+	0.553864i	$0.186847\pi$
$173$			14.5699i			1.10773i	−0.832607	+	0.553864i	$0.813153\pi$
$174$	−9.56284			−0.724957
$175$	−2.38255	+	4.39584i	−0.180104	+	0.332295i
$176$	3.81684			0.287705
$177$			0.232249i			0.0174569i
$178$		−	21.3774i		−	1.60231i
$179$	−22.2817			−1.66542			−0.832708	−	0.553713i	$-0.813211\pi$
$179$	−22.2817			−1.66542			−0.832708	+	0.553713i	$0.813211\pi$
$180$	−1.14745	+	4.52510i	−0.0855260	+	0.337281i
$181$	−0.314870			−0.0234041			−0.0117021	−	0.999932i	$-0.503725\pi$
$181$	−0.314870			−0.0234041			−0.0117021	+	0.999932i	$0.503725\pi$
$182$		−	11.0155i		−	0.816524i
$183$			15.4328i			1.14083i
$184$	−0.720401			−0.0531087
$185$	0.800590	+	0.203010i	0.0588605	+	0.0149256i
$186$	−19.2267			−1.40977
$187$			2.57671i			0.188428i
$188$			21.8529i			1.59379i
$189$	−1.00000			−0.0727393
$190$	3.51418	+	0.891108i	0.254945	+	0.0646478i
$191$	25.0569			1.81306			0.906528	−	0.422145i	$-0.138723\pi$
$191$	25.0569			1.81306			0.906528	+	0.422145i	$0.138723\pi$
$192$			8.68579i			0.626843i
$193$			9.45610i			0.680665i	0.940305	+	0.340333i	$0.110540\pi$
$193$			9.45610i			0.680665i	−0.940305	+	0.340333i	$0.889460\pi$
$194$	24.8260			1.78240
$195$	2.99449	−	11.8091i	0.214440	−	0.845667i
$196$	2.08773			0.149124
$197$		−	4.03568i		−	0.287530i	−0.989612	−	0.143765i	$-0.954079\pi$
$197$		−	4.03568i		−	0.287530i	0.989612	−	0.143765i	$-0.0459210\pi$
$198$		−	2.02181i		−	0.143684i
$199$	27.6266			1.95840			0.979199	−	0.202903i	$-0.0650377\pi$
$199$	27.6266			1.95840			0.979199	+	0.202903i	$0.0650377\pi$
$200$	0.422617	−	0.779734i	0.0298835	−	0.0551355i
$201$	−14.9167			−1.05214
$202$		−	4.47763i		−	0.315045i
$203$			4.72983i			0.331969i
$204$	−5.37949			−0.376639
$205$	3.33718	−	13.1605i	0.233079	−	0.919172i
$206$	−30.3177			−2.11233
$207$		−	4.06135i		−	0.282283i
$208$		−	20.7954i		−	1.44190i
$209$	−0.801918			−0.0554698
$210$	4.38222	+	1.11122i	0.302402	+	0.0766816i
$211$	−12.9896			−0.894244			−0.447122	−	0.894473i	$-0.647551\pi$
$211$	−12.9896			−0.894244			−0.447122	+	0.894473i	$0.647551\pi$
$212$		−	17.1138i		−	1.17538i
$213$		−	9.27387i		−	0.635435i
$214$	−19.8085			−1.35408
$215$	−27.7866	−	7.04598i	−1.89503	−	0.480532i
$216$	0.177380			0.0120692
$217$			9.50964i			0.645557i
$218$		−	1.62827i		−	0.110280i
$219$	−10.5828			−0.715119
$220$	−1.14745	+	4.52510i	−0.0773612	+	0.305082i
$221$	14.0388			0.944350
$222$		−	0.746790i		−	0.0501213i
$223$			5.10103i			0.341590i	0.985307	+	0.170795i	$0.0546336\pi$
$223$			5.10103i			0.341590i	−0.985307	+	0.170795i	$0.945366\pi$
$224$	8.07170			0.539313
$225$	4.39584	+	2.38255i	0.293056	+	0.158837i
$226$	−37.0583			−2.46508
$227$		−	8.23018i		−	0.546256i	−0.961978	−	0.273128i	$-0.911942\pi$
$227$		−	8.23018i		−	0.546256i	0.961978	−	0.273128i	$-0.0880583\pi$
$228$		−	1.67419i		−	0.110876i
$229$	−3.29195			−0.217538			−0.108769	−	0.994067i	$-0.534691\pi$
$229$	−3.29195			−0.217538			−0.108769	+	0.994067i	$0.534691\pi$
$230$	−4.51306	+	17.7977i	−0.297582	+	1.17355i
$231$	−1.00000			−0.0657952
$232$		−	0.838976i		−	0.0550815i
$233$		−	3.13826i		−	0.205594i	−0.994702	−	0.102797i	$-0.967221\pi$
$233$		−	3.13826i		−	0.205594i	0.994702	−	0.102797i	$-0.0327793\pi$
$234$	−11.0155			−0.720107
$235$	22.6875	+	5.75299i	1.47997	+	0.375284i
$236$	−0.484874			−0.0315626
$237$		−	13.3303i		−	0.865899i
$238$			5.20963i			0.337690i
$239$	25.5582			1.65322			0.826610	−	0.562775i	$-0.190266\pi$
$239$	25.5582			1.65322			0.826610	+	0.562775i	$0.190266\pi$
$240$	8.27288	+	2.09779i	0.534012	+	0.135412i
$241$	1.88461			0.121398			0.0606991	−	0.998156i	$-0.480667\pi$
$241$	1.88461			0.121398			0.0606991	+	0.998156i	$0.480667\pi$
$242$		−	2.02181i		−	0.129967i
$243$			1.00000i			0.0641500i
$244$	−32.2196			−2.06265
$245$	0.549616	−	2.16747i	0.0351137	−	0.138475i
$246$	−12.2761			−0.782699
$247$			4.36911i			0.278000i
$248$		−	1.68682i		−	0.107113i
$249$	−5.21440			−0.330449
$250$	−16.6160	−	15.3256i	−1.05089	−	0.969277i
$251$	−9.74338			−0.614997			−0.307498	−	0.951549i	$-0.599492\pi$
$251$	−9.74338			−0.614997			−0.307498	+	0.951549i	$0.599492\pi$
$252$		−	2.08773i		−	0.131515i
$253$		−	4.06135i		−	0.255335i
$254$	8.32526			0.522373
$255$	−1.41620	+	5.58494i	−0.0886860	+	0.349743i
$256$	14.5053			0.906582
$257$			17.6638i			1.10184i	0.834558	+	0.550920i	$0.185723\pi$
$257$			17.6638i			1.10184i	−0.834558	+	0.550920i	$0.814277\pi$
$258$			25.9193i			1.61366i
$259$	−0.369366			−0.0229513
$260$	24.6542	+	6.25170i	1.52899	+	0.387714i
$261$	4.72983			0.292769
$262$			14.9885i			0.925994i
$263$		−	22.9064i		−	1.41247i	−0.707976	−	0.706236i	$-0.750392\pi$
$263$		−	22.9064i		−	1.41247i	0.707976	−	0.706236i	$-0.249608\pi$
$264$	0.177380			0.0109170
$265$	−17.7674	−	4.50536i	−1.09144	−	0.276762i
$266$	−1.62133			−0.0994100
$267$			10.5734i			0.647081i
$268$		−	31.1421i		−	1.90230i
$269$	−8.26091			−0.503677			−0.251838	−	0.967769i	$-0.581035\pi$
$269$	−8.26091			−0.503677			−0.251838	+	0.967769i	$0.581035\pi$
$270$	1.11122	−	4.38222i	0.0676268	−	0.266693i
$271$	23.9284			1.45355			0.726773	−	0.686878i	$-0.241019\pi$
$271$	23.9284			1.45355			0.726773	+	0.686878i	$0.241019\pi$
$272$			9.83489i			0.596328i
$273$			5.44833i			0.329748i
$274$	−18.3345			−1.10763
$275$	4.39584	+	2.38255i	0.265079	+	0.143673i
$276$	8.47901			0.510376
$277$			17.0380i			1.02371i	0.859071	+	0.511857i	$0.171042\pi$
$277$			17.0380i			1.02371i	−0.859071	+	0.511857i	$0.828958\pi$
$278$		−	14.5916i		−	0.875148i
$279$	9.50964			0.569327
$280$	−0.0974908	+	0.384465i	−0.00582619	+	0.0229762i
$281$	−19.6769			−1.17382			−0.586912	−	0.809651i	$-0.699656\pi$
$281$	−19.6769			−1.17382			−0.586912	+	0.809651i	$0.699656\pi$
$282$		−	21.1629i		−	1.26023i
$283$		−	4.63518i		−	0.275533i	−0.990465	−	0.137766i	$-0.956008\pi$
$283$		−	4.63518i		−	0.275533i	0.990465	−	0.137766i	$-0.0439923\pi$
$284$	19.3614			1.14889
$285$	−1.73813	−	0.440747i	−0.102958	−	0.0261076i
$286$	−11.0155			−0.651361
$287$			6.07185i			0.358410i
$288$		−	8.07170i		−	0.475629i
$289$	10.3606			0.609445
$290$	−20.7272	−	5.25589i	−1.21714	−	0.308636i
$291$	−12.2790			−0.719811
$292$		−	22.0941i		−	1.29296i
$293$			17.7414i			1.03646i	0.855241	+	0.518231i	$0.173409\pi$
$293$			17.7414i			1.03646i	−0.855241	+	0.518231i	$0.826591\pi$
$294$	−2.02181			−0.117915
$295$	−0.127648	+	0.503392i	−0.00743194	+	0.0293086i
$296$	0.0655181			0.00380816
$297$			1.00000i			0.0580259i
$298$		−	13.4068i		−	0.776636i
$299$	−22.1276			−1.27967
$300$	−4.97413	+	9.17735i	−0.287182	+	0.529855i
$301$	12.8198			0.738922
$302$			39.0042i			2.24444i
$303$			2.21466i			0.127229i
$304$	−3.06079			−0.175548
$305$	−8.48211	+	33.4501i	−0.485684	+	1.91535i
$306$	5.20963			0.297815
$307$			13.7194i			0.783008i	0.920176	+	0.391504i	$0.128045\pi$
$307$			13.7194i			0.783008i	−0.920176	+	0.391504i	$0.871955\pi$
$308$		−	2.08773i		−	0.118960i
$309$	14.9953			0.853052
$310$	−41.6733	−	10.5673i	−2.36689	−	0.600183i
$311$	−0.512264			−0.0290478			−0.0145239	−	0.999895i	$-0.504623\pi$
$311$	−0.512264			−0.0290478			−0.0145239	+	0.999895i	$0.504623\pi$
$312$		−	0.966424i		−	0.0547130i
$313$		−	3.12863i		−	0.176841i	−0.996083	−	0.0884204i	$-0.971818\pi$
$313$		−	3.12863i		−	0.176841i	0.996083	−	0.0884204i	$-0.0281819\pi$
$314$	−19.4161			−1.09571
$315$	−2.16747	−	0.549616i	−0.122123	−	0.0309674i
$316$	27.8302			1.56557
$317$			7.61306i			0.427592i	0.976878	+	0.213796i	$0.0685828\pi$
$317$			7.61306i			0.427592i	−0.976878	+	0.213796i	$0.931417\pi$
$318$			16.5734i			0.929391i
$319$	4.72983			0.264820
$320$	−4.77385	+	18.8262i	−0.266866	+	1.05242i
$321$	9.79736			0.546836
$322$		−	8.21129i		−	0.457597i
$323$		−	2.06631i		−	0.114973i
$324$	−2.08773			−0.115985
$325$	12.9809	−	23.9500i	0.720052	−	1.32851i
$326$	−2.21517			−0.122687
$327$			0.805348i			0.0445359i
$328$		−	1.07702i		−	0.0594687i
$329$	−10.4673			−0.577080
$330$	1.11122	−	4.38222i	0.0611707	−	0.241233i
$331$	−4.56072			−0.250680			−0.125340	−	0.992114i	$-0.540002\pi$
$331$	−4.56072			−0.250680			−0.125340	+	0.992114i	$0.540002\pi$
$332$		−	10.8863i		−	0.597462i
$333$			0.369366i			0.0202411i
$334$	−29.0484			−1.58946
$335$	−32.3315	−	8.19845i	−1.76646	−	0.447929i
$336$	−3.81684			−0.208226
$337$			10.3709i			0.564938i	0.959276	+	0.282469i	$0.0911535\pi$
$337$			10.3709i			0.564938i	−0.959276	+	0.282469i	$0.908847\pi$
$338$			33.7326i			1.83481i
$339$	18.3292			0.995506
$340$	−11.6599	−	2.95665i	−0.632345	−	0.160347i
$341$	9.50964			0.514976
$342$			1.62133i			0.0876714i
$343$			1.00000i			0.0539949i
$344$	−2.27398			−0.122605
$345$	2.23218	−	8.80284i	0.120177	−	0.473929i
$346$	29.4576			1.58365
$347$			1.74157i			0.0934922i	0.998907	+	0.0467461i	$0.0148852\pi$
$347$			1.74157i			0.0934922i	−0.998907	+	0.0467461i	$0.985115\pi$
$348$			9.87462i			0.529335i
$349$	−25.0894			−1.34301			−0.671503	−	0.741002i	$-0.734351\pi$
$349$	−25.0894			−1.34301			−0.671503	+	0.741002i	$0.734351\pi$
$350$	8.88758	+	4.81708i	0.475061	+	0.257484i
$351$	5.44833			0.290810
$352$		−	8.07170i		−	0.430223i
$353$			18.4717i			0.983150i	0.870835	+	0.491575i	$0.163579\pi$
$353$			18.4717i			0.983150i	−0.870835	+	0.491575i	$0.836421\pi$
$354$	0.469564			0.0249570
$355$	5.09707	−	20.1008i	0.270524	−	1.06684i
$356$	−22.0744			−1.16994
$357$		−	2.57671i		−	0.136374i
$358$			45.0495i			2.38094i
$359$	19.7245			1.04102			0.520509	−	0.853856i	$-0.325742\pi$
$359$	19.7245			1.04102			0.520509	+	0.853856i	$0.325742\pi$
$360$	0.384465	+	0.0974908i	0.0202631	+	0.00513822i
$361$	−18.3569			−0.966154
$362$			0.636610i			0.0334595i
$363$			1.00000i			0.0524864i
$364$	−11.3747			−0.596194
$365$	−22.9379	−	5.81648i	−1.20062	−	0.304448i
$366$	31.2023			1.63097
$367$		−	14.4499i		−	0.754277i	−0.926157	−	0.377138i	$-0.876908\pi$
$367$		−	14.4499i		−	0.754277i	0.926157	−	0.377138i	$-0.123092\pi$
$368$		−	15.5015i		−	0.808071i
$369$	6.07185			0.316088
$370$	0.410448	−	1.61864i	0.0213382	−	0.0841493i
$371$	8.19730			0.425582
$372$			19.8536i			1.02936i
$373$		−	18.6903i		−	0.967746i	−0.875138	−	0.483873i	$-0.839230\pi$
$373$		−	18.6903i		−	0.967746i	0.875138	−	0.483873i	$-0.160770\pi$
$374$	5.20963			0.269384
$375$	8.21837	+	7.58013i	0.424395	+	0.391436i
$376$	1.85669			0.0957513
$377$		−	25.7697i		−	1.32721i
$378$			2.02181i			0.103991i
$379$	18.7279			0.961988			0.480994	−	0.876724i	$-0.340276\pi$
$379$	18.7279			0.961988			0.480994	+	0.876724i	$0.340276\pi$
$380$	0.920162	−	3.62875i	0.0472033	−	0.186151i
$381$	−4.11772			−0.210957
$382$		−	50.6605i		−	2.59202i
$383$		−	28.9782i		−	1.48072i	−0.672213	−	0.740358i	$-0.734656\pi$
$383$		−	28.9782i		−	1.48072i	0.672213	−	0.740358i	$-0.265344\pi$
$384$	1.41767			0.0723453
$385$	−2.16747	−	0.549616i	−0.110464	−	0.0280110i
$386$	19.1185			0.973105
$387$		−	12.8198i		−	0.651668i
$388$		−	25.6354i		−	1.30144i
$389$	−0.520340			−0.0263823			−0.0131911	−	0.999913i	$-0.504199\pi$
$389$	−0.520340			−0.0263823			−0.0131911	+	0.999913i	$0.504199\pi$
$390$	−23.8758	−	6.05430i	−1.20900	−	0.306572i
$391$	10.4649			0.529234
$392$		−	0.177380i		−	0.00895903i
$393$		−	7.41340i		−	0.373957i
$394$	−8.15940			−0.411065
$395$	7.32657	−	28.8931i	0.368640	−	1.45377i
$396$	−2.08773			−0.104913
$397$		−	5.41741i		−	0.271892i	−0.990716	−	0.135946i	$-0.956593\pi$
$397$		−	5.41741i		−	0.271892i	0.990716	−	0.135946i	$-0.0434074\pi$
$398$		−	55.8559i		−	2.79980i
$399$	0.801918			0.0401461
$400$	16.7782	+	9.09381i	0.838911	+	0.454691i
$401$	2.98876			0.149251			0.0746257	−	0.997212i	$-0.476224\pi$
$401$	2.98876			0.149251			0.0746257	+	0.997212i	$0.476224\pi$
$402$			30.1588i			1.50418i
$403$		−	51.8117i		−	2.58092i
$404$	−4.62361			−0.230033
$405$	−0.549616	+	2.16747i	−0.0273106	+	0.107702i
$406$	9.56284			0.474596
$407$			0.369366i			0.0183088i
$408$			0.457057i			0.0226277i
$409$	15.0596			0.744648			0.372324	−	0.928103i	$-0.378561\pi$
$409$	15.0596			0.744648			0.372324	+	0.928103i	$0.378561\pi$
$410$	−26.6082	−	6.74717i	−1.31408	−	0.333219i
$411$	9.06835			0.447309
$412$			31.3061i			1.54234i
$413$		−	0.232249i		−	0.0114282i
$414$	−8.21129			−0.403563
$415$	−11.3021	−	2.86592i	−0.554796	−	0.140682i
$416$	−43.9773			−2.15616
$417$			7.21710i			0.353423i
$418$			1.62133i			0.0793018i
$419$	25.7411			1.25753			0.628767	−	0.777594i	$-0.283560\pi$
$419$	25.7411			1.25753			0.628767	+	0.777594i	$0.283560\pi$
$420$	1.14745	−	4.52510i	0.0559899	−	0.220802i
$421$	5.47012			0.266597			0.133299	−	0.991076i	$-0.457443\pi$
$421$	5.47012			0.266597			0.133299	+	0.991076i	$0.457443\pi$
$422$			26.2627i			1.27845i
$423$			10.4673i			0.508937i
$424$	−1.45403			−0.0706142
$425$	−6.13915	+	11.3268i	−0.297792	+	0.549432i
$426$	−18.7501			−0.908443
$427$		−	15.4328i		−	0.746845i
$428$			20.4543i			0.988695i
$429$	5.44833			0.263048
$430$	−14.2457	+	56.1793i	−0.686987	+	2.70920i
$431$	−2.40289			−0.115743			−0.0578715	−	0.998324i	$-0.518431\pi$
$431$	−2.40289			−0.115743			−0.0578715	+	0.998324i	$0.518431\pi$
$432$			3.81684i			0.183638i
$433$		−	5.28854i		−	0.254151i	−0.991893	−	0.127075i	$-0.959441\pi$
$433$		−	5.28854i		−	0.254151i	0.991893	−	0.127075i	$-0.0405590\pi$
$434$	19.2267			0.922913
$435$	10.2518	+	2.59959i	0.491534	+	0.124641i
$436$	−1.68135			−0.0805222
$437$			3.25687i			0.155797i
$438$			21.3965i			1.02236i
$439$	−3.58440			−0.171074			−0.0855370	−	0.996335i	$-0.527261\pi$
$439$	−3.58440			−0.171074			−0.0855370	+	0.996335i	$0.527261\pi$
$440$	0.384465	+	0.0974908i	0.0183287	+	0.00464769i
$441$	1.00000			0.0476190
$442$		−	28.3838i		−	1.35008i
$443$			0.658409i			0.0312820i	0.999878	+	0.0156410i	$0.00497888\pi$
$443$			0.658409i			0.0312820i	−0.999878	+	0.0156410i	$0.995021\pi$
$444$	−0.771138			−0.0365966
$445$	−5.81131	+	22.9175i	−0.275482	+	1.08639i
$446$	10.3133			0.488350
$447$			6.63108i			0.313639i
$448$		−	8.68579i		−	0.410365i
$449$	−18.7482			−0.884781			−0.442391	−	0.896823i	$-0.645869\pi$
$449$	−18.7482			−0.884781			−0.442391	+	0.896823i	$0.645869\pi$
$450$	4.81708	−	8.88758i	0.227079	−	0.418965i
$451$	6.07185			0.285912
$452$			38.2665i			1.79991i
$453$		−	19.2917i		−	0.906402i
$454$	−16.6399			−0.780949
$455$	−2.99449	+	11.8091i	−0.140384	+	0.553619i
$456$	−0.142244			−0.00666119
$457$			29.2056i			1.36618i	0.730335	+	0.683090i	$0.239364\pi$
$457$			29.2056i			1.36618i	−0.730335	+	0.683090i	$0.760636\pi$
$458$			6.65570i			0.311001i
$459$	−2.57671			−0.120271
$460$	18.3780	+	4.66020i	0.856878	+	0.217283i
$461$	−3.97847			−0.185296			−0.0926480	−	0.995699i	$-0.529533\pi$
$461$	−3.97847			−0.185296			−0.0926480	+	0.995699i	$0.529533\pi$
$462$			2.02181i			0.0940633i
$463$		−	40.1219i		−	1.86463i	−0.361654	−	0.932313i	$-0.617788\pi$
$463$		−	40.1219i		−	1.86463i	0.361654	−	0.932313i	$-0.382212\pi$
$464$	18.0530			0.838089
$465$	20.6119	+	5.22665i	0.955852	+	0.242380i
$466$	−6.34498			−0.293926
$467$			33.0723i			1.53040i	0.643790	+	0.765202i	$0.277361\pi$
$467$			33.0723i			1.53040i	−0.643790	+	0.765202i	$0.722639\pi$
$468$			11.3747i			0.525794i
$469$	14.9167			0.688789
$470$	11.6315	−	45.8700i	0.536520	−	2.11582i
$471$	9.60329			0.442496
$472$			0.0411963i			0.00189621i
$473$		−	12.8198i		−	0.589456i
$474$	−26.9515			−1.23792
$475$	−3.52511	−	1.91061i	−0.161743	−	0.0876648i
$476$	5.37949			0.246568
$477$		−	8.19730i		−	0.375328i
$478$		−	51.6739i		−	2.36351i
$479$	12.7565			0.582859			0.291429	−	0.956592i	$-0.405869\pi$
$479$	12.7565			0.582859			0.291429	+	0.956592i	$0.405869\pi$
$480$	4.43633	−	17.4951i	0.202490	−	0.798541i
$481$	2.01243			0.0917589
$482$		−	3.81032i		−	0.173555i
$483$			4.06135i			0.184798i
$484$	−2.08773			−0.0948970
$485$	−26.6145	−	6.74876i	−1.20850	−	0.306445i
$486$	2.02181			0.0917114
$487$			17.8968i			0.810980i	0.914100	+	0.405490i	$0.132899\pi$
$487$			17.8968i			0.810980i	−0.914100	+	0.405490i	$0.867101\pi$
$488$			2.73747i			0.123919i
$489$	1.09563			0.0495463
$490$	−4.38222	−	1.11122i	−0.197969	−	0.0501999i
$491$	−12.4841			−0.563399			−0.281699	−	0.959503i	$-0.590898\pi$
$491$	−12.4841			−0.563399			−0.281699	+	0.959503i	$0.590898\pi$
$492$			12.6764i			0.571496i
$493$			12.1874i			0.548893i
$494$	8.83354			0.397440
$495$	−0.549616	+	2.16747i	−0.0247034	+	0.0974205i
$496$	36.2968			1.62977
$497$			9.27387i			0.415990i
$498$			10.5425i			0.472423i
$499$	−24.5411			−1.09861			−0.549306	−	0.835621i	$-0.685108\pi$
$499$	−24.5411			−1.09861			−0.549306	+	0.835621i	$0.685108\pi$
$500$	−15.8253	+	17.1578i	−0.707729	+	0.767318i
$501$	14.3675			0.641892
$502$			19.6993i			0.879223i
$503$			39.7756i			1.77350i	0.462245	+	0.886752i	$0.347044\pi$
$503$			39.7756i			1.77350i	−0.462245	+	0.886752i	$0.652956\pi$
$504$	−0.177380			−0.00790113
$505$	−1.21721	+	4.80020i	−0.0541652	+	0.213606i
$506$	−8.21129			−0.365036
$507$		−	16.6843i		−	0.740977i
$508$		−	8.59670i		−	0.381417i
$509$	−14.2699			−0.632502			−0.316251	−	0.948676i	$-0.602424\pi$
$509$	−14.2699			−0.632502			−0.316251	+	0.948676i	$0.602424\pi$
$510$	11.2917	+	2.86330i	0.500006	+	0.126789i
$511$	10.5828			0.468156
$512$		−	32.1624i		−	1.42139i
$513$		−	0.801918i		−	0.0354055i
$514$	35.7130			1.57523
$515$	32.5018	+	8.24165i	1.43220	+	0.363170i
$516$	26.7644			1.17824
$517$			10.4673i			0.460351i
$518$			0.746790i			0.0328121i
$519$	−14.5699			−0.639547
$520$	0.531162	−	2.09469i	0.0232930	−	0.0918584i
$521$	12.4960			0.547461			0.273731	−	0.961806i	$-0.411742\pi$
$521$	12.4960			0.547461			0.273731	+	0.961806i	$0.411742\pi$
$522$		−	9.56284i		−	0.418554i
$523$		−	29.4581i		−	1.28811i	−0.764977	−	0.644057i	$-0.777250\pi$
$523$		−	29.4581i		−	1.28811i	0.764977	−	0.644057i	$-0.222750\pi$
$524$	15.4772			0.676125
$525$	−4.39584	−	2.38255i	−0.191850	−	0.103983i
$526$	−46.3126			−2.01932
$527$			24.5036i			1.06739i
$528$			3.81684i			0.166107i
$529$	6.50546			0.282846
$530$	−9.10901	+	35.9223i	−0.395670	+	1.56037i
$531$	−0.232249			−0.0100787
$532$			1.67419i			0.0725853i
$533$		−	33.0814i		−	1.43292i
$534$	21.3774			0.925092
$535$	21.2355	+	5.38479i	0.918090	+	0.232805i
$536$	−2.64592			−0.114286
$537$		−	22.2817i		−	0.961528i
$538$			16.7020i			0.720076i
$539$	1.00000			0.0430730
$540$	−4.52510	−	1.14745i	−0.194729	−	0.0493785i
$541$	21.0046			0.903060			0.451530	−	0.892256i	$-0.350878\pi$
$541$	21.0046			0.903060			0.451530	+	0.892256i	$0.350878\pi$
$542$		−	48.3787i		−	2.07805i
$543$		−	0.314870i		−	0.0135124i
$544$	20.7984			0.891725
$545$	−0.442632	+	1.74557i	−0.0189603	+	0.0747719i
$546$	11.0155			0.471421
$547$			16.8542i			0.720634i	0.932830	+	0.360317i	$0.117331\pi$
$547$			16.8542i			0.720634i	−0.932830	+	0.360317i	$0.882669\pi$
$548$			18.9323i			0.808748i
$549$	−15.4328			−0.658656
$550$	4.81708	−	8.88758i	0.205401	−	0.378968i
$551$	−3.79293			−0.161584
$552$		−	0.720401i		−	0.0306623i
$553$			13.3303i			0.566864i
$554$	34.4477			1.46354
$555$	−0.203010	+	0.800590i	−0.00861728	+	0.0339832i
$556$	−15.0674			−0.638999
$557$			21.2648i			0.901019i	0.892772	+	0.450509i	$0.148758\pi$
$557$			21.2648i			0.901019i	−0.892772	+	0.450509i	$0.851242\pi$
$558$		−	19.2267i		−	0.813932i
$559$	−69.8466			−2.95420
$560$	−8.27288	−	2.09779i	−0.349593	−	0.0886480i
$561$	−2.57671			−0.108789
$562$			39.7830i			1.67814i
$563$			29.7983i			1.25585i	0.778274	+	0.627925i	$0.216095\pi$
$563$			29.7983i			1.25585i	−0.778274	+	0.627925i	$0.783905\pi$
$564$	−21.8529			−0.920173
$565$	39.7280	+	10.0740i	1.67137	+	0.423818i
$566$	−9.37147			−0.393912
$567$		−	1.00000i		−	0.0419961i
$568$		−	1.64500i		−	0.0690226i
$569$	14.3258			0.600569			0.300284	−	0.953850i	$-0.402918\pi$
$569$	14.3258			0.600569			0.300284	+	0.953850i	$0.402918\pi$
$570$	−0.891108	+	3.51418i	−0.0373244	+	0.147193i
$571$	15.8350			0.662676			0.331338	−	0.943512i	$-0.392500\pi$
$571$	15.8350			0.662676			0.331338	+	0.943512i	$0.392500\pi$
$572$			11.3747i			0.475598i
$573$			25.0569i			1.04677i
$574$	12.2761			0.512397
$575$	9.67637	−	17.8530i	0.403532	−	0.744524i
$576$	−8.68579			−0.361908
$577$			32.4932i			1.35271i	0.736576	+	0.676355i	$0.236441\pi$
$577$			32.4932i			1.35271i	−0.736576	+	0.676355i	$0.763559\pi$
$578$		−	20.9471i		−	0.871285i
$579$	−9.45610			−0.392982
$580$	−5.42725	+	21.4029i	−0.225354	+	0.888709i
$581$	5.21440			0.216330
$582$			24.8260i			1.02907i
$583$		−	8.19730i		−	0.339497i
$584$	−1.87718			−0.0776781
$585$	11.8091	+	2.99449i	0.488246	+	0.123807i
$586$	35.8697			1.48177
$587$			9.23858i			0.381317i	0.981656	+	0.190659i	$0.0610623\pi$
$587$			9.23858i			0.381317i	−0.981656	+	0.190659i	$0.938938\pi$
$588$			2.08773i			0.0860967i
$589$	−7.62595			−0.314222
$590$	1.01777	+	0.258080i	0.0419007	+	0.0106250i
$591$	4.03568			0.166006
$592$			1.40981i			0.0579429i
$593$			45.0180i			1.84867i	0.381586	+	0.924333i	$0.375378\pi$
$593$			45.0180i			1.84867i	−0.381586	+	0.924333i	$0.624622\pi$
$594$	2.02181			0.0829560
$595$	1.41620	−	5.58494i	0.0580586	−	0.228960i
$596$	−13.8439			−0.567070
$597$			27.6266i			1.13068i
$598$			44.7378i			1.82947i
$599$	−12.0839			−0.493735			−0.246867	−	0.969049i	$-0.579401\pi$
$599$	−12.0839			−0.493735			−0.246867	+	0.969049i	$0.579401\pi$
$600$	0.779734	+	0.422617i	0.0318325	+	0.0172532i
$601$	9.97876			0.407042			0.203521	−	0.979071i	$-0.434761\pi$
$601$	9.97876			0.407042			0.203521	+	0.979071i	$0.434761\pi$
$602$		−	25.9193i		−	1.05639i
$603$		−	14.9167i		−	0.607455i
$604$	40.2759			1.63880
$605$	−0.549616	+	2.16747i	−0.0223451	+	0.0881201i
$606$	4.47763			0.181891
$607$		−	9.78393i		−	0.397118i	−0.980089	−	0.198559i	$-0.936374\pi$
$607$		−	9.78393i		−	0.397118i	0.980089	−	0.198559i	$-0.0636261\pi$
$608$			6.47283i			0.262508i
$609$	−4.72983			−0.191662
$610$	67.6299	+	17.1493i	2.73826	+	0.694353i
$611$	57.0293			2.30716
$612$		−	5.37949i		−	0.217453i
$613$			35.1588i			1.42005i	0.704176	+	0.710025i	$0.251317\pi$
$613$			35.1588i			1.42005i	−0.704176	+	0.710025i	$0.748683\pi$
$614$	27.7381			1.11942
$615$	13.1605	+	3.33718i	0.530684	+	0.134568i
$616$	−0.177380			−0.00714684
$617$			21.5575i			0.867871i	0.900944	+	0.433936i	$0.142875\pi$
$617$			21.5575i			0.867871i	−0.900944	+	0.433936i	$0.857125\pi$
$618$		−	30.3177i		−	1.21956i
$619$	10.2962			0.413840			0.206920	−	0.978358i	$-0.433656\pi$
$619$	10.2962			0.413840			0.206920	+	0.978358i	$0.433656\pi$
$620$	−10.9119	+	43.0321i	−0.438231	+	1.72821i
$621$	4.06135			0.162976
$622$			1.03570i			0.0415279i
$623$		−	10.5734i		−	0.423614i
$624$	20.7954			0.832482
$625$	13.6469	+	20.9467i	0.545876	+	0.837866i
$626$	−6.32552			−0.252818
$627$		−	0.801918i		−	0.0320255i
$628$			20.0491i			0.800046i
$629$	−0.951750			−0.0379488
$630$	−1.11122	+	4.38222i	−0.0442721	+	0.174592i
$631$	−43.4243			−1.72869			−0.864347	−	0.502896i	$-0.832268\pi$
$631$	−43.4243			−1.72869			−0.864347	+	0.502896i	$0.832268\pi$
$632$		−	2.36453i		−	0.0940561i
$633$		−	12.9896i		−	0.516292i
$634$	15.3922			0.611302
$635$	−8.92503	−	2.26316i	−0.354179	−	0.0898109i
$636$	17.1138			0.678605
$637$		−	5.44833i		−	0.215871i
$638$		−	9.56284i		−	0.378596i
$639$	9.27387			0.366869
$640$	3.07276	+	0.779176i	0.121462	+	0.0307996i
$641$	−16.6086			−0.656002			−0.328001	−	0.944677i	$-0.606375\pi$
$641$	−16.6086			−0.656002			−0.328001	+	0.944677i	$0.606375\pi$
$642$		−	19.8085i		−	0.781777i
$643$		−	45.9180i		−	1.81083i	−0.424527	−	0.905415i	$-0.639560\pi$
$643$		−	45.9180i		−	1.81083i	0.424527	−	0.905415i	$-0.360440\pi$
$644$	−8.47901			−0.334120
$645$	7.04598	−	27.7866i	0.277435	−	1.09409i
$646$	−4.17770			−0.164369
$647$		−	14.0765i		−	0.553403i	−0.960956	−	0.276701i	$-0.910759\pi$
$647$		−	14.0765i		−	0.553403i	0.960956	−	0.276701i	$-0.0892412\pi$
$648$			0.177380i			0.00696814i
$649$	−0.232249			−0.00911657
$650$	−48.4225	−	26.2450i	−1.89929	−	1.02941i
$651$	−9.50964			−0.372712
$652$			2.28739i			0.0895811i
$653$		−	7.20161i		−	0.281821i	−0.990022	−	0.140910i	$-0.954997\pi$
$653$		−	7.20161i		−	0.281821i	0.990022	−	0.140910i	$-0.0450030\pi$
$654$	1.62827			0.0636702
$655$	4.07453	−	16.0683i	0.159205	−	0.627841i
$656$	23.1753			0.904842
$657$		−	10.5828i		−	0.412874i
$658$			21.1629i			0.825016i
$659$	−5.49951			−0.214231			−0.107115	−	0.994247i	$-0.534161\pi$
$659$	−5.49951			−0.214231			−0.107115	+	0.994247i	$0.534161\pi$
$660$	−4.52510	−	1.14745i	−0.176139	−	0.0446645i
$661$	33.5903			1.30651			0.653256	−	0.757137i	$-0.273403\pi$
$661$	33.5903			1.30651			0.653256	+	0.757137i	$0.273403\pi$
$662$			9.22093i			0.358381i
$663$			14.0388i			0.545221i
$664$	−0.924929			−0.0358942
$665$	1.73813	+	0.440747i	0.0674019	+	0.0170914i
$666$	0.746790			0.0289375
$667$		−	19.2095i		−	0.743794i
$668$			29.9955i			1.16056i
$669$	−5.10103			−0.197217
$670$	−16.5757	+	65.3682i	−0.640377	+	2.52539i
$671$	−15.4328			−0.595777
$672$			8.07170i			0.311372i
$673$		−	35.9603i		−	1.38617i	−0.720857	−	0.693084i	$-0.756251\pi$
$673$		−	35.9603i		−	1.38617i	0.720857	−	0.693084i	$-0.243749\pi$
$674$	20.9680			0.807657
$675$	−2.38255	+	4.39584i	−0.0917044	+	0.169196i
$676$	34.8324			1.33971
$677$			8.06821i			0.310087i	0.987908	+	0.155043i	$0.0495517\pi$
$677$			8.06821i			0.310087i	−0.987908	+	0.155043i	$0.950448\pi$
$678$		−	37.0583i		−	1.42321i
$679$	12.2790			0.471227
$680$	−0.251206	+	0.990656i	−0.00963330	+	0.0379899i
$681$	8.23018			0.315381
$682$		−	19.2267i		−	0.736230i
$683$			11.8720i			0.454271i	0.973863	+	0.227135i	$0.0729360\pi$
$683$			11.8720i			0.454271i	−0.973863	+	0.227135i	$0.927064\pi$
$684$	1.67419			0.0640142
$685$	19.6554	+	4.98411i	0.750993	+	0.190433i
$686$	2.02181			0.0771932
$687$		−	3.29195i		−	0.125596i
$688$		−	48.9312i		−	1.86548i
$689$	−44.6616			−1.70147
$690$	−17.7977	−	4.51306i	−0.677547	−	0.171809i
$691$	16.5331			0.628950			0.314475	−	0.949266i	$-0.398172\pi$
$691$	16.5331			0.628950			0.314475	+	0.949266i	$0.398172\pi$
$692$		−	30.4180i		−	1.15632i
$693$		−	1.00000i		−	0.0379869i
$694$	3.52112			0.133660
$695$	−3.96663	+	15.6428i	−0.150463	+	0.593366i
$696$	0.838976			0.0318013
$697$			15.6454i			0.592612i
$698$			50.7261i			1.92001i
$699$	3.13826			0.118700
$700$	4.97413	−	9.17735i	0.188004	−	0.346871i
$701$	−10.4860			−0.396052			−0.198026	−	0.980197i	$-0.563453\pi$
$701$	−10.4860			−0.396052			−0.198026	+	0.980197i	$0.563453\pi$
$702$		−	11.0155i		−	0.415754i
$703$		−	0.296201i		−	0.0111714i
$704$	−8.68579			−0.327358
$705$	−5.75299	+	22.6875i	−0.216670	+	0.854462i
$706$	37.3464			1.40555
$707$		−	2.21466i		−	0.0832908i
$708$		−	0.484874i		−	0.0182227i
$709$	−14.3256			−0.538009			−0.269004	−	0.963139i	$-0.586695\pi$
$709$	−14.3256			−0.538009			−0.269004	+	0.963139i	$0.586695\pi$
$710$	−40.6402	−	10.3053i	−1.52520	−	0.386752i
$711$	13.3303			0.499927
$712$			1.87551i			0.0702876i
$713$		−	38.6220i		−	1.44640i
$714$	−5.20963			−0.194966
$715$	11.8091	+	2.99449i	0.441635	+	0.111988i
$716$	46.5183			1.73847
$717$			25.5582i			0.954487i
$718$		−	39.8792i		−	1.48828i
$719$	−9.03703			−0.337024			−0.168512	−	0.985700i	$-0.553896\pi$
$719$	−9.03703			−0.337024			−0.168512	+	0.985700i	$0.553896\pi$
$720$	−2.09779	+	8.27288i	−0.0781802	+	0.308312i
$721$	−14.9953			−0.558454
$722$			37.1143i			1.38125i
$723$			1.88461i			0.0700893i
$724$	0.657366			0.0244308
$725$	20.7916	+	11.2691i	0.772181	+	0.418522i
$726$	2.02181			0.0750366
$727$			16.0207i			0.594176i	0.954850	+	0.297088i	$0.0960155\pi$
$727$			16.0207i			0.594176i	−0.954850	+	0.297088i	$0.903984\pi$
$728$			0.966424i			0.0358181i
$729$	−1.00000			−0.0370370
$730$	−11.7598	+	46.3762i	−0.435251	+	1.71646i
$731$	33.0330			1.22177
$732$		−	32.2196i		−	1.19087i
$733$			6.95247i			0.256796i	0.991723	+	0.128398i	$0.0409834\pi$
$733$			6.95247i			0.256796i	−0.991723	+	0.128398i	$0.959017\pi$
$734$	−29.2149			−1.07834
$735$	2.16747	+	0.549616i	0.0799483	+	0.0202729i
$736$	−32.7820			−1.20836
$737$		−	14.9167i		−	0.549463i
$738$		−	12.2761i		−	0.451891i
$739$	14.9743			0.550837			0.275419	−	0.961324i	$-0.411184\pi$
$739$	14.9743			0.550837			0.275419	+	0.961324i	$0.411184\pi$
$740$	−1.67142	−	0.423830i	−0.0614426	−	0.0155803i
$741$	−4.36911			−0.160503
$742$		−	16.5734i		−	0.608429i
$743$		−	22.7811i		−	0.835757i	−0.908503	−	0.417878i	$-0.862774\pi$
$743$		−	22.7811i		−	0.835757i	0.908503	−	0.417878i	$-0.137226\pi$
$744$	1.68682			0.0618418
$745$	−3.64455	+	14.3727i	−0.133526	+	0.526574i
$746$	−37.7883			−1.38353
$747$		−	5.21440i		−	0.190785i
$748$		−	5.37949i		−	0.196693i
$749$	−9.79736			−0.357988
$750$	15.3256	−	16.6160i	0.559613	−	0.606731i
$751$	−15.6340			−0.570494			−0.285247	−	0.958454i	$-0.592076\pi$
$751$	−15.6340			−0.570494			−0.285247	+	0.958454i	$0.592076\pi$
$752$			39.9519i			1.45690i
$753$		−	9.74338i		−	0.355068i
$754$	−52.1015			−1.89743
$755$	10.6030	−	41.8141i	0.385883	−	1.52177i
$756$	2.08773			0.0759301
$757$		−	31.0417i		−	1.12823i	−0.825696	−	0.564115i	$-0.809218\pi$
$757$		−	31.0417i		−	1.12823i	0.825696	−	0.564115i	$-0.190782\pi$
$758$		−	37.8644i		−	1.37530i
$759$	4.06135			0.147418
$760$	−0.308309	−	0.0781796i	−0.0111836	−	0.00283587i
$761$	16.9582			0.614734			0.307367	−	0.951591i	$-0.400552\pi$
$761$	16.9582			0.614734			0.307367	+	0.951591i	$0.400552\pi$
$762$			8.32526i			0.301592i
$763$		−	0.805348i		−	0.0291556i
$764$	−52.3122			−1.89259
$765$	−5.58494	−	1.41620i	−0.201924	−	0.0512029i
$766$	−58.5885			−2.11689
$767$			1.26537i			0.0456898i
$768$			14.5053i			0.523416i
$769$	17.6273			0.635657			0.317829	−	0.948148i	$-0.397046\pi$
$769$	17.6273			0.635657			0.317829	+	0.948148i	$0.397046\pi$
$770$	−1.11122	+	4.38222i	−0.0400456	+	0.157924i
$771$	−17.6638			−0.636148
$772$		−	19.7418i		−	0.710524i
$773$			25.9014i			0.931608i	0.884888	+	0.465804i	$0.154235\pi$
$773$			25.9014i			0.931608i	−0.884888	+	0.465804i	$0.845765\pi$
$774$	−25.9193			−0.931650
$775$	41.8029	+	22.6572i	1.50160	+	0.813871i
$776$	−2.17806			−0.0781876
$777$		−	0.369366i		−	0.0132509i
$778$			1.05203i			0.0377171i
$779$	−4.86912			−0.174454
$780$	−6.25170	+	24.6542i	−0.223847	+	0.882763i
$781$	9.27387			0.331845
$782$		−	21.1581i		−	0.756613i
$783$			4.72983i			0.169030i
$784$	3.81684			0.136316
$785$	20.8148	+	5.27812i	0.742913	+	0.188384i
$786$	−14.9885			−0.534623
$787$			14.9659i			0.533478i	0.963769	+	0.266739i	$0.0859461\pi$
$787$			14.9659i			0.533478i	−0.963769	+	0.266739i	$0.914054\pi$
$788$			8.42543i			0.300143i
$789$	22.9064			0.815491
$790$	−58.4165	−	14.8130i	−2.07837	−	0.527022i
$791$	−18.3292			−0.651712
$792$			0.177380i			0.00630292i
$793$			84.0830i			2.98587i
$794$	−10.9530			−0.388707
$795$	4.50536	−	17.7674i	0.159789	−	0.630144i
$796$	−57.6770			−2.04431
$797$		−	2.54301i		−	0.0900781i	−0.998985	−	0.0450390i	$-0.985659\pi$
$797$		−	2.54301i		−	0.0900781i	0.998985	−	0.0450390i	$-0.0143412\pi$
$798$		−	1.62133i		−	0.0573944i
$799$	−26.9712			−0.954172
$800$	19.2312	−	35.4819i	0.679927	−	1.25448i
$801$	−10.5734			−0.373593
$802$		−	6.04271i		−	0.213376i
$803$		−	10.5828i		−	0.373459i
$804$	31.1421			1.09830
$805$	−2.23218	+	8.80284i	−0.0786740	+	0.310259i
$806$	−104.754			−3.68979
$807$		−	8.26091i		−	0.290798i
$808$			0.392836i			0.0138199i
$809$	−39.3893			−1.38485			−0.692426	−	0.721488i	$-0.743458\pi$
$809$	−39.3893			−1.38485			−0.692426	+	0.721488i	$0.743458\pi$
$810$	4.38222	+	1.11122i	0.153976	+	0.0390443i
$811$	−4.84482			−0.170125			−0.0850623	−	0.996376i	$-0.527109\pi$
$811$	−4.84482			−0.170125			−0.0850623	+	0.996376i	$0.527109\pi$
$812$		−	9.87462i		−	0.346531i
$813$			23.9284i			0.839205i
$814$	0.746790			0.0261750
$815$	2.37475	+	0.602178i	0.0831839	+	0.0210934i
$816$	−9.83489			−0.344290
$817$			10.2804i			0.359667i
$818$		−	30.4477i		−	1.06458i
$819$	−5.44833			−0.190380
$820$	−6.96715	+	27.4757i	−0.243303	+	0.959493i
$821$	−29.1027			−1.01569			−0.507845	−	0.861448i	$-0.669558\pi$
$821$	−29.1027			−1.01569			−0.507845	+	0.861448i	$0.669558\pi$
$822$		−	18.3345i		−	0.639490i
$823$			13.4746i			0.469695i	0.972032	+	0.234847i	$0.0754591\pi$
$823$			13.4746i			0.469695i	−0.972032	+	0.234847i	$0.924541\pi$
$824$	2.65986			0.0926606
$825$	−2.38255	+	4.39584i	−0.0829498	+	0.153044i
$826$	−0.469564			−0.0163382
$827$		−	22.3530i		−	0.777291i	−0.921387	−	0.388645i	$-0.872943\pi$
$827$		−	22.3530i		−	0.777291i	0.921387	−	0.388645i	$-0.127057\pi$
$828$			8.47901i			0.294666i
$829$	26.1762			0.909138			0.454569	−	0.890711i	$-0.349793\pi$
$829$	26.1762			0.909138			0.454569	+	0.890711i	$0.349793\pi$
$830$	−5.79435	+	22.8506i	−0.201125	+	0.793158i
$831$	−17.0380			−0.591042
$832$			47.3231i			1.64063i
$833$			2.57671i			0.0892778i
$834$	14.5916			0.505267
$835$	31.1411	+	7.89660i	1.07768	+	0.273273i
$836$	1.67419			0.0579031
$837$			9.50964i			0.328701i
$838$		−	52.0437i		−	1.79782i
$839$	−47.8883			−1.65329			−0.826644	−	0.562725i	$-0.809753\pi$
$839$	−47.8883			−1.65329			−0.826644	+	0.562725i	$0.809753\pi$
$840$	−0.384465	−	0.0974908i	−0.0132653	−	0.00336375i
$841$	−6.62871			−0.228576
$842$		−	11.0596i		−	0.381138i
$843$		−	19.6769i		−	0.677707i
$844$	27.1189			0.933471
$845$	9.16997	−	36.1627i	0.315456	−	1.24404i
$846$	21.1629			0.727596
$847$		−	1.00000i		−	0.0343604i
$848$		−	31.2877i		−	1.07443i
$849$	4.63518			0.159079
$850$	22.9007	+	12.4122i	0.785489	+	0.425736i
$851$	1.50012			0.0514236
$852$			19.3614i			0.663310i
$853$			7.31318i			0.250399i	0.992132	+	0.125199i	$0.0399570\pi$
$853$			7.31318i			0.250399i	−0.992132	+	0.125199i	$0.960043\pi$
$854$	−31.2023			−1.06772
$855$	0.440747	−	1.73813i	0.0150732	−	0.0594428i
$856$	1.73785			0.0593986
$857$			35.1097i			1.19932i	0.800253	+	0.599662i	$0.204698\pi$
$857$			35.1097i			1.19932i	−0.800253	+	0.599662i	$0.795302\pi$
$858$		−	11.0155i		−	0.376063i
$859$	−47.7724			−1.62997			−0.814987	−	0.579480i	$-0.803256\pi$
$859$	−47.7724			−1.62997			−0.814987	+	0.579480i	$0.803256\pi$
$860$	58.0109	+	14.7101i	1.97816	+	0.501611i
$861$	−6.07185			−0.206928
$862$			4.85819i			0.165471i
$863$		−	17.8620i		−	0.608028i	−0.952668	−	0.304014i	$-0.901673\pi$
$863$		−	17.8620i		−	0.608028i	0.952668	−	0.304014i	$-0.0983270\pi$
$864$	8.07170			0.274605
$865$	−31.5798	−	8.00785i	−1.07375	−	0.272275i
$866$	−10.6924			−0.363344
$867$			10.3606i			0.351863i
$868$		−	19.8536i		−	0.673875i
$869$	13.3303			0.452201
$870$	5.25589	−	20.7272i	0.178191	−	0.702716i
$871$	−81.2711			−2.75377
$872$			0.142853i			0.00483760i
$873$		−	12.2790i		−	0.415583i
$874$	6.58478			0.222733
$875$	−8.21837	−	7.58013i	−0.277832	−	0.256255i
$876$	22.0941			0.746489
$877$			28.4812i			0.961742i	0.876791	+	0.480871i	$0.159679\pi$
$877$			28.4812i			0.961742i	−0.876791	+	0.480871i	$0.840321\pi$
$878$			7.24699i			0.244574i
$879$	−17.7414			−0.598401
$880$	−2.09779	+	8.27288i	−0.0707166	+	0.278879i
$881$	28.9224			0.974420			0.487210	−	0.873285i	$-0.338015\pi$
$881$	28.9224			0.974420			0.487210	+	0.873285i	$0.338015\pi$
$882$		−	2.02181i		−	0.0680780i
$883$			37.4549i			1.26046i	0.776410	+	0.630228i	$0.217039\pi$
$883$			37.4549i			1.26046i	−0.776410	+	0.630228i	$0.782961\pi$
$884$	−29.3092			−0.985776
$885$	−0.503392	−	0.127648i	−0.0169213	−	0.00429083i
$886$	1.33118			0.0447219
$887$			3.59533i			0.120719i	0.998177	+	0.0603597i	$0.0192248\pi$
$887$			3.59533i			0.120719i	−0.998177	+	0.0603597i	$0.980775\pi$
$888$			0.0655181i			0.00219864i
$889$	4.11772			0.138104
$890$	46.3349	+	11.7494i	1.55315	+	0.393840i
$891$	−1.00000			−0.0335013
$892$		−	10.6496i		−	0.356575i
$893$		−	8.39390i		−	0.280891i
$894$	13.4068			0.448391
$895$	12.2464	−	48.2950i	0.409352	−	1.61432i
$896$	−1.41767			−0.0473611
$897$		−	22.1276i		−	0.738818i
$898$			37.9053i			1.26492i
$899$	44.9790			1.50013
$900$	−9.17735	−	4.97413i	−0.305912	−	0.165804i
$901$	21.1221			0.703678
$902$		−	12.2761i		−	0.408751i
$903$			12.8198i			0.426617i
$904$	3.25123			0.108134
$905$	0.173058	−	0.682472i	0.00575264	−	0.0226861i
$906$	−39.0042			−1.29583
$907$			8.77625i			0.291411i	0.989328	+	0.145705i	$0.0465451\pi$
$907$			8.77625i			0.291411i	−0.989328	+	0.145705i	$0.953455\pi$
$908$			17.1824i			0.570219i
$909$	−2.21466			−0.0734556
$910$	23.8758	+	6.05430i	0.791475	+	0.200698i
$911$	32.2659			1.06902			0.534509	−	0.845163i	$-0.320497\pi$
$911$	32.2659			1.06902			0.534509	+	0.845163i	$0.320497\pi$
$912$		−	3.06079i		−	0.101353i
$913$		−	5.21440i		−	0.172571i
$914$	59.0483			1.95314
$915$	−33.4501	−	8.48211i	−1.10583	−	0.280410i
$916$	6.87270			0.227081
$917$			7.41340i			0.244812i
$918$			5.20963i			0.171943i
$919$	−8.81522			−0.290787			−0.145394	−	0.989374i	$-0.546445\pi$
$919$	−8.81522			−0.290787			−0.145394	+	0.989374i	$0.546445\pi$
$920$	0.395944	−	1.56145i	0.0130539	−	0.0514794i
$921$	−13.7194			−0.452070
$922$			8.04373i			0.264906i
$923$		−	50.5271i		−	1.66312i
$924$	2.08773			0.0686814
$925$	−0.880034	+	1.62368i	−0.0289353	+	0.0533862i
$926$	−81.1191			−2.66574
$927$			14.9953i			0.492510i
$928$		−	38.1777i		−	1.25325i
$929$	−12.1528			−0.398722			−0.199361	−	0.979926i	$-0.563887\pi$
$929$	−12.1528			−0.398722			−0.199361	+	0.979926i	$0.563887\pi$
$930$	10.5673	−	41.6733i	0.346516	−	1.36652i
$931$	−0.801918			−0.0262818
$932$			6.55185i			0.214613i
$933$		−	0.512264i		−	0.0167708i
$934$	66.8661			2.18792
$935$	−5.58494	−	1.41620i	−0.182647	−	0.0463148i
$936$	0.966424			0.0315886
$937$			0.710001i			0.0231947i	0.999933	+	0.0115974i	$0.00369164\pi$
$937$			0.710001i			0.0231947i	−0.999933	+	0.0115974i	$0.996308\pi$
$938$		−	30.1588i		−	0.984719i
$939$	3.12863			0.102099
$940$	−47.3655	−	12.0107i	−1.54489	−	0.391746i
$941$	7.19633			0.234594			0.117297	−	0.993097i	$-0.462577\pi$
$941$	7.19633			0.234594			0.117297	+	0.993097i	$0.462577\pi$
$942$		−	19.4161i		−	0.632610i
$943$		−	24.6599i		−	0.803036i
$944$	−0.886456			−0.0288517
$945$	0.549616	−	2.16747i	0.0178790	−	0.0705078i
$946$	−25.9193			−0.842709
$947$			24.8433i			0.807300i	0.914913	+	0.403650i	$0.132259\pi$
$947$			24.8433i			0.807300i	−0.914913	+	0.403650i	$0.867741\pi$
$948$			27.8302i			0.903883i
$949$	−57.6586			−1.87168
$950$	−3.86290	+	7.12711i	−0.125329	+	0.231234i
$951$	−7.61306			−0.246870
$952$		−	0.457057i		−	0.0148133i
$953$		−	4.52824i		−	0.146684i	−0.997307	−	0.0733421i	$-0.976634\pi$
$953$		−	4.52824i		−	0.146684i	0.997307	−	0.0733421i	$-0.0233665\pi$
$954$	−16.5734			−0.536584
$955$	−13.7717	+	54.3102i	−0.445642	+	1.75744i
$956$	−53.3586			−1.72574
$957$			4.72983i			0.152894i
$958$		−	25.7912i		−	0.833277i
$959$	−9.06835			−0.292832
$960$	−18.8262	−	4.77385i	−0.607613	−	0.154075i
$961$	59.4333			1.91720
$962$		−	4.06876i		−	0.131182i
$963$			9.79736i			0.315716i
$964$	−3.93455			−0.126723
$965$	−20.4958	−	5.19723i	−0.659783	−	0.167305i
$966$	8.21129			0.264194
$967$		−	6.58048i		−	0.211614i	−0.994387	−	0.105807i	$-0.966257\pi$
$967$		−	6.58048i		−	0.211614i	0.994387	−	0.105807i	$-0.0337426\pi$
$968$			0.177380i			0.00570120i
$969$	2.06631			0.0663795
$970$	−13.6447	+	53.8095i	−0.438106	+	1.72772i
$971$	−7.15664			−0.229667			−0.114834	−	0.993385i	$-0.536634\pi$
$971$	−7.15664			−0.229667			−0.114834	+	0.993385i	$0.536634\pi$
$972$		−	2.08773i		−	0.0669641i
$973$		−	7.21710i		−	0.231369i
$974$	36.1839			1.15941
$975$	23.9500	+	12.9809i	0.767014	+	0.415722i
$976$	−58.9045			−1.88549
$977$			59.7619i			1.91195i	0.293446	+	0.955976i	$0.405198\pi$
$977$			59.7619i			1.91195i	−0.293446	+	0.955976i	$0.594802\pi$
$978$		−	2.21517i		−	0.0708332i
$979$	−10.5734			−0.337927
$980$	−1.14745	+	4.52510i	−0.0366540	+	0.144549i
$981$	−0.805348			−0.0257128
$982$			25.2405i			0.805457i
$983$			30.2137i			0.963668i	0.876262	+	0.481834i	$0.160029\pi$
$983$			30.2137i			0.963668i	−0.876262	+	0.481834i	$0.839971\pi$
$984$	1.07702			0.0343342
$985$	8.74722	+	2.21808i	0.278710	+	0.0706738i
$986$	24.6407			0.784719
$987$		−	10.4673i		−	0.333177i
$988$		−	9.12154i		−	0.290195i
$989$	−52.0657			−1.65559
$990$	4.38222	+	1.11122i	0.139276	+	0.0353169i
$991$	−38.0074			−1.20734			−0.603672	−	0.797233i	$-0.706296\pi$
$991$	−38.0074			−1.20734			−0.603672	+	0.797233i	$0.706296\pi$
$992$		−	76.7589i		−	2.43710i
$993$		−	4.56072i		−	0.144730i
$994$	18.7501			0.594715
$995$	−15.1840	+	59.8798i	−0.481366	+	1.89832i
$996$	10.8863			0.344945
$997$		−	28.2891i		−	0.895925i	−0.894052	−	0.447963i	$-0.852150\pi$
$997$		−	28.2891i		−	0.895925i	0.894052	−	0.447963i	$-0.147850\pi$
$998$			49.6176i			1.57062i
$999$	−0.369366			−0.0116862

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.e.694.4	✓	20
5.2	odd	4		5775.2.a.cp.1.8		10
5.3	odd	4		5775.2.a.cm.1.3		10
5.4	even	2	inner	1155.2.c.e.694.17	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.e.694.4	✓	20	1.1	even	1	trivial
1155.2.c.e.694.17	yes	20	5.4	even	2	inner
5775.2.a.cm.1.3		10	5.3	odd	4
5775.2.a.cp.1.8		10	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.02181i q^{2} +1.00000i q^{3} -2.08773 q^{4} +(-0.549616 + 2.16747i) q^{5} +2.02181 q^{6} -1.00000i q^{7} +0.177380i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.02181i q^{2} +1.00000i q^{3} -2.08773 q^{4} +(-0.549616 + 2.16747i) q^{5} +2.02181 q^{6} -1.00000i q^{7} +0.177380i q^{8} -1.00000 q^{9} +(4.38222 + 1.11122i) q^{10} -1.00000 q^{11} -2.08773i q^{12} +5.44833i q^{13} -2.02181 q^{14} +(-2.16747 - 0.549616i) q^{15} -3.81684 q^{16} -2.57671i q^{17} +2.02181i q^{18} +0.801918 q^{19} +(1.14745 - 4.52510i) q^{20} +1.00000 q^{21} +2.02181i q^{22} +4.06135i q^{23} -0.177380 q^{24} +(-4.39584 - 2.38255i) q^{25} +11.0155 q^{26} -1.00000i q^{27} +2.08773i q^{28} -4.72983 q^{29} +(-1.11122 + 4.38222i) q^{30} -9.50964 q^{31} +8.07170i q^{32} -1.00000i q^{33} -5.20963 q^{34} +(2.16747 + 0.549616i) q^{35} +2.08773 q^{36} -0.369366i q^{37} -1.62133i q^{38} -5.44833 q^{39} +(-0.384465 - 0.0974908i) q^{40} -6.07185 q^{41} -2.02181i q^{42} +12.8198i q^{43} +2.08773 q^{44} +(0.549616 - 2.16747i) q^{45} +8.21129 q^{46} -10.4673i q^{47} -3.81684i q^{48} -1.00000 q^{49} +(-4.81708 + 8.88758i) q^{50} +2.57671 q^{51} -11.3747i q^{52} +8.19730i q^{53} -2.02181 q^{54} +(0.549616 - 2.16747i) q^{55} +0.177380 q^{56} +0.801918i q^{57} +9.56284i q^{58} +0.232249 q^{59} +(4.52510 + 1.14745i) q^{60} +15.4328 q^{61} +19.2267i q^{62} +1.00000i q^{63} +8.68579 q^{64} +(-11.8091 - 2.99449i) q^{65} -2.02181 q^{66} +14.9167i q^{67} +5.37949i q^{68} -4.06135 q^{69} +(1.11122 - 4.38222i) q^{70} -9.27387 q^{71} -0.177380i q^{72} +10.5828i q^{73} -0.746790 q^{74} +(2.38255 - 4.39584i) q^{75} -1.67419 q^{76} +1.00000i q^{77} +11.0155i q^{78} -13.3303 q^{79} +(2.09779 - 8.27288i) q^{80} +1.00000 q^{81} +12.2761i q^{82} +5.21440i q^{83} -2.08773 q^{84} +(5.58494 + 1.41620i) q^{85} +25.9193 q^{86} -4.72983i q^{87} -0.177380i q^{88} +10.5734 q^{89} +(-4.38222 - 1.11122i) q^{90} +5.44833 q^{91} -8.47901i q^{92} -9.50964i q^{93} -21.1629 q^{94} +(-0.440747 + 1.73813i) q^{95} -8.07170 q^{96} +12.2790i q^{97} +2.02181i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} - 2 q^{10} - 20 q^{11} - 6 q^{14} + 2 q^{15} + 38 q^{16} + 2 q^{19} + 4 q^{20} + 20 q^{21} - 18 q^{24} + 12 q^{25} + 20 q^{26} - 38 q^{29} + 6 q^{30} + 20 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} + 2 q^{40} + 12 q^{41} + 26 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{49} - 6 q^{50} + 26 q^{51} - 6 q^{54} + 2 q^{55} + 18 q^{56} - 22 q^{59} + 16 q^{60} + 34 q^{61} - 26 q^{64} - 28 q^{65} - 6 q^{66} - 26 q^{69} - 6 q^{70} + 72 q^{71} - 72 q^{74} - 8 q^{75} + 44 q^{76} + 4 q^{79} - 8 q^{80} + 20 q^{81} - 26 q^{84} - 16 q^{85} + 52 q^{86} + 6 q^{89} + 2 q^{90} + 16 q^{94} + 14 q^{95} + 62 q^{96} + 20 q^{99}+O(q^{100}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 - 2 * q^10 - 20 * q^11 - 6 * q^14 + 2 * q^15 + 38 * q^16 + 2 * q^19 + 4 * q^20 + 20 * q^21 - 18 * q^24 + 12 * q^25 + 20 * q^26 - 38 * q^29 + 6 * q^30 + 20 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 + 2 * q^40 + 12 * q^41 + 26 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^49 - 6 * q^50 + 26 * q^51 - 6 * q^54 + 2 * q^55 + 18 * q^56 - 22 * q^59 + 16 * q^60 + 34 * q^61 - 26 * q^64 - 28 * q^65 - 6 * q^66 - 26 * q^69 - 6 * q^70 + 72 * q^71 - 72 * q^74 - 8 * q^75 + 44 * q^76 + 4 * q^79 - 8 * q^80 + 20 * q^81 - 26 * q^84 - 16 * q^85 + 52 * q^86 + 6 * q^89 + 2 * q^90 + 16 * q^94 + 14 * q^95 + 62 * q^96 + 20 * q^99

Introduction

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