LMFDB - Embedded newform 231.2.c.a.76.7

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			76.7
Root			$0.644389 + 0.983224i$ of defining polynomial
Character	$\chi$	$=$	231.76
Dual form			231.2.c.a.76.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.183172i q^{2} -1.00000i q^{3} +1.96645 q^{4} -1.83337i q^{5} -0.183172 q^{6} +(-1.47195 - 2.19849i) q^{7} -0.726543i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.183172i q^{2} -1.00000i q^{3} +1.96645 q^{4} -1.83337i q^{5} -0.183172 q^{6} +(-1.47195 - 2.19849i) q^{7} -0.726543i q^{8} -1.00000 q^{9} -0.335821 q^{10} +(-1.23607 + 3.07768i) q^{11} -1.96645i q^{12} +0.879192 q^{13} +(-0.402702 + 0.269620i) q^{14} -1.83337 q^{15} +3.79981 q^{16} -3.57781 q^{17} +0.183172i q^{18} +5.64252 q^{19} -3.60522i q^{20} +(-2.19849 + 1.47195i) q^{21} +(0.563746 + 0.226413i) q^{22} +0.539240 q^{23} -0.726543 q^{24} +1.63877 q^{25} -0.161043i q^{26} +1.00000i q^{27} +(-2.89451 - 4.32322i) q^{28} -3.82309i q^{29} +0.335821i q^{30} +5.59963i q^{31} -2.14910i q^{32} +(3.07768 + 1.23607i) q^{33} +0.655355i q^{34} +(-4.03064 + 2.69862i) q^{35} -1.96645 q^{36} -2.63877 q^{37} -1.03355i q^{38} -0.879192i q^{39} -1.33202 q^{40} +10.5524 q^{41} +(0.269620 + 0.402702i) q^{42} +6.21641i q^{43} +(-2.43066 + 6.05210i) q^{44} +1.83337i q^{45} -0.0987737i q^{46} +5.29413i q^{47} -3.79981i q^{48} +(-2.66673 + 6.47214i) q^{49} -0.300177i q^{50} +3.57781i q^{51} +1.72889 q^{52} -3.93290 q^{53} +0.183172 q^{54} +(5.64252 + 2.26616i) q^{55} +(-1.59730 + 1.06943i) q^{56} -5.64252i q^{57} -0.700283 q^{58} +10.2384i q^{59} -3.60522 q^{60} -0.732688 q^{61} +1.02570 q^{62} +(1.47195 + 2.19849i) q^{63} +7.20597 q^{64} -1.61188i q^{65} +(0.226413 - 0.563746i) q^{66} -1.62739 q^{67} -7.03558 q^{68} -0.539240i q^{69} +(0.494312 + 0.738301i) q^{70} -10.1389 q^{71} +0.726543i q^{72} -14.3377 q^{73} +0.483349i q^{74} -1.63877i q^{75} +11.0957 q^{76} +(8.58569 - 1.81271i) q^{77} -0.161043 q^{78} -11.3105i q^{79} -6.96645i q^{80} +1.00000 q^{81} -1.93290i q^{82} +10.1983 q^{83} +(-4.32322 + 2.89451i) q^{84} +6.55944i q^{85} +1.13867 q^{86} -3.82309 q^{87} +(2.23607 + 0.898056i) q^{88} -2.80540i q^{89} +0.335821 q^{90} +(-1.29413 - 1.93290i) q^{91} +1.06039 q^{92} +5.59963 q^{93} +0.969736 q^{94} -10.3448i q^{95} -2.14910 q^{96} -13.4654i q^{97} +(1.18551 + 0.488471i) q^{98} +(1.23607 - 3.07768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	0.183172i		−	0.129522i	−0.997901	−	0.0647611i	$-0.979371\pi$
$2$		−	0.183172i		−	0.129522i	0.997901	−	0.0647611i	$-0.0206285\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.96645			0.983224
$5$		−	1.83337i		−	0.819906i	−0.912107	−	0.409953i	$-0.865545\pi$
$5$		−	1.83337i		−	0.819906i	0.912107	−	0.409953i	$-0.134455\pi$
$6$	−0.183172			−0.0747797
$7$	−1.47195	−	2.19849i	−0.556344	−	0.830952i
$7$	−1.47195	−	2.19849i	−0.556344	−	0.830952i
$8$		−	0.726543i		−	0.256872i
$9$	−1.00000			−0.333333
$10$	−0.335821			−0.106196
$11$	−1.23607	+	3.07768i	−0.372689	+	0.927957i
$11$	−1.23607	+	3.07768i	−0.372689	+	0.927957i
$12$		−	1.96645i		−	0.567665i
$13$	0.879192			0.243844			0.121922	−	0.992540i	$-0.461094\pi$
$13$	0.879192			0.243844			0.121922	+	0.992540i	$0.461094\pi$
$14$	−0.402702	+	0.269620i	−0.107627	+	0.0720590i
$15$	−1.83337			−0.473373
$16$	3.79981			0.949953
$17$	−3.57781			−0.867747			−0.433874	−	0.900974i	$-0.642854\pi$
$17$	−3.57781			−0.867747			−0.433874	+	0.900974i	$0.642854\pi$
$18$			0.183172i			0.0431741i
$19$	5.64252			1.29448			0.647241	−	0.762285i	$-0.275923\pi$
$19$	5.64252			1.29448			0.647241	+	0.762285i	$0.275923\pi$
$20$		−	3.60522i		−	0.806151i
$21$	−2.19849	+	1.47195i	−0.479750	+	0.321206i
$22$	0.563746	+	0.226413i	0.120191	+	0.0482714i
$23$	0.539240			0.112439			0.0562197	−	0.998418i	$-0.482095\pi$
$23$	0.539240			0.112439			0.0562197	+	0.998418i	$0.482095\pi$
$24$	−0.726543			−0.148305
$25$	1.63877			0.327754
$26$		−	0.161043i		−	0.0315832i
$27$			1.00000i			0.192450i
$28$	−2.89451	−	4.32322i	−0.547011	−	0.817012i
$29$		−	3.82309i		−	0.709930i	−0.934880	−	0.354965i	$-0.884493\pi$
$29$		−	3.82309i		−	0.709930i	0.934880	−	0.354965i	$-0.115507\pi$
$30$			0.335821i			0.0613123i
$31$			5.59963i			1.00572i	0.864367	+	0.502861i	$0.167719\pi$
$31$			5.59963i			1.00572i	−0.864367	+	0.502861i	$0.832281\pi$
$32$		−	2.14910i		−	0.379912i
$33$	3.07768	+	1.23607i	0.535756	+	0.215172i
$34$			0.655355i			0.112393i
$35$	−4.03064	+	2.69862i	−0.681302	+	0.456150i
$36$	−1.96645			−0.327741
$37$	−2.63877			−0.433811			−0.216906	−	0.976193i	$-0.569596\pi$
$37$	−2.63877			−0.433811			−0.216906	+	0.976193i	$0.569596\pi$
$38$		−	1.03355i		−	0.167664i
$39$		−	0.879192i		−	0.140783i
$40$	−1.33202			−0.210611
$41$	10.5524			1.64800			0.824000	−	0.566590i	$-0.191737\pi$
$41$	10.5524			1.64800			0.824000	+	0.566590i	$0.191737\pi$
$42$	0.269620	+	0.402702i	0.0416033	+	0.0621383i
$43$			6.21641i			0.947994i	0.880526	+	0.473997i	$0.157189\pi$
$43$			6.21641i			0.947994i	−0.880526	+	0.473997i	$0.842811\pi$
$44$	−2.43066	+	6.05210i	−0.366436	+	0.912389i
$45$			1.83337i			0.273302i
$46$		−	0.0987737i		−	0.0145634i
$47$			5.29413i			0.772228i	0.922451	+	0.386114i	$0.126183\pi$
$47$			5.29413i			0.772228i	−0.922451	+	0.386114i	$0.873817\pi$
$48$		−	3.79981i		−	0.548456i
$49$	−2.66673	+	6.47214i	−0.380962	+	0.924591i
$50$		−	0.300177i		−	0.0424514i
$51$			3.57781i			0.500994i
$52$	1.72889			0.239753
$53$	−3.93290			−0.540225			−0.270112	−	0.962829i	$-0.587061\pi$
$53$	−3.93290			−0.540225			−0.270112	+	0.962829i	$0.587061\pi$
$54$	0.183172			0.0249266
$55$	5.64252	+	2.26616i	0.760837	+	0.305570i
$56$	−1.59730	+	1.06943i	−0.213448	+	0.142909i
$57$		−	5.64252i		−	0.747370i
$58$	−0.700283			−0.0919517
$59$			10.2384i			1.33293i	0.745538	+	0.666463i	$0.232193\pi$
$59$			10.2384i			1.33293i	−0.745538	+	0.666463i	$0.767807\pi$
$60$	−3.60522			−0.465432
$61$	−0.732688			−0.0938111			−0.0469056	−	0.998899i	$-0.514936\pi$
$61$	−0.732688			−0.0938111			−0.0469056	+	0.998899i	$0.514936\pi$
$62$	1.02570			0.130263
$63$	1.47195	+	2.19849i	0.185448	+	0.276984i
$64$	7.20597			0.900746
$65$		−	1.61188i		−	0.199929i
$66$	0.226413	−	0.563746i	0.0278695	−	0.0693923i
$67$	−1.62739			−0.198818			−0.0994089	−	0.995047i	$-0.531695\pi$
$67$	−1.62739			−0.198818			−0.0994089	+	0.995047i	$0.531695\pi$
$68$	−7.03558			−0.853190
$69$		−	0.539240i		−	0.0649169i
$70$	0.494312	+	0.738301i	0.0590816	+	0.0882438i
$71$	−10.1389			−1.20326			−0.601631	−	0.798774i	$-0.705482\pi$
$71$	−10.1389			−1.20326			−0.601631	+	0.798774i	$0.705482\pi$
$72$			0.726543i			0.0856239i
$73$	−14.3377			−1.67810			−0.839051	−	0.544053i	$-0.816889\pi$
$73$	−14.3377			−1.67810			−0.839051	+	0.544053i	$0.816889\pi$
$74$			0.483349i			0.0561882i
$75$		−	1.63877i		−	0.189229i
$76$	11.0957			1.27277
$77$	8.58569	−	1.81271i	0.978430	−	0.206577i
$78$	−0.161043			−0.0182346
$79$		−	11.3105i		−	1.27253i	−0.771471	−	0.636264i	$-0.780479\pi$
$79$		−	11.3105i		−	1.27253i	0.771471	−	0.636264i	$-0.219521\pi$
$80$		−	6.96645i		−	0.778873i
$81$	1.00000			0.111111
$82$		−	1.93290i		−	0.213453i
$83$	10.1983			1.11941			0.559704	−	0.828692i	$-0.310915\pi$
$83$	10.1983			1.11941			0.559704	+	0.828692i	$0.310915\pi$
$84$	−4.32322	+	2.89451i	−0.471702	+	0.315817i
$85$			6.55944i			0.711471i
$86$	1.13867			0.122786
$87$	−3.82309			−0.409878
$88$	2.23607	+	0.898056i	0.238366	+	0.0957331i
$89$		−	2.80540i		−	0.297372i	−0.988884	−	0.148686i	$-0.952496\pi$
$89$		−	2.80540i		−	0.297372i	0.988884	−	0.148686i	$-0.0475044\pi$
$90$	0.335821			0.0353987
$91$	−1.29413	−	1.93290i	−0.135661	−	0.202623i
$92$	1.06039			0.110553
$93$	5.59963			0.580654
$94$	0.969736			0.100021
$95$		−	10.3448i		−	1.06135i
$96$	−2.14910			−0.219342
$97$		−	13.4654i		−	1.36721i	−0.729854	−	0.683603i	$-0.760412\pi$
$97$		−	13.4654i		−	1.36721i	0.729854	−	0.683603i	$-0.239588\pi$
$98$	1.18551	+	0.488471i	0.119755	+	0.0493430i
$99$	1.23607	−	3.07768i	0.124230	−	0.309319i
$100$	3.22256			0.322256
$101$	−17.1118			−1.70269			−0.851343	−	0.524609i	$-0.824212\pi$
$101$	−17.1118			−1.70269			−0.851343	+	0.524609i	$0.824212\pi$
$102$	0.655355			0.0648899
$103$		−	5.27754i		−	0.520012i	−0.965607	−	0.260006i	$-0.916276\pi$
$103$		−	5.27754i		−	0.520012i	0.965607	−	0.260006i	$-0.0837245\pi$
$104$		−	0.638770i		−	0.0626366i
$105$	2.69862	+	4.03064i	0.263358	+	0.393350i
$106$			0.720397i			0.0699711i
$107$			7.58616i			0.733382i	0.930343	+	0.366691i	$0.119509\pi$
$107$			7.58616i			0.733382i	−0.930343	+	0.366691i	$0.880491\pi$
$108$			1.96645i			0.189222i
$109$			11.2240i			1.07506i	0.843243	+	0.537532i	$0.180643\pi$
$109$			11.2240i			1.07506i	−0.843243	+	0.537532i	$0.819357\pi$
$110$	0.415098	−	1.03355i	0.0395780	−	0.0985453i
$111$			2.63877i			0.250461i
$112$	−5.59313	−	8.35386i	−0.528501	−	0.789365i
$113$	9.33346			0.878018			0.439009	−	0.898483i	$-0.355330\pi$
$113$	9.33346			0.878018			0.439009	+	0.898483i	$0.355330\pi$
$114$	−1.03355			−0.0968010
$115$		−	0.988624i		−	0.0921897i
$116$		−	7.51791i		−	0.698020i
$117$	−0.879192			−0.0812813
$118$	1.87539			0.172644
$119$	5.26636	+	7.86579i	0.482766	+	0.721056i
$120$			1.33202i			0.121596i
$121$	−7.94427	−	7.60845i	−0.722207	−	0.691677i
$122$			0.134208i			0.0121506i
$123$		−	10.5524i		−	0.951473i
$124$			11.0114i			0.988851i
$125$		−	12.1713i		−	1.08863i
$126$	0.402702	−	0.269620i	0.0358756	−	0.0240197i
$127$			2.57755i			0.228721i	0.993439	+	0.114360i	$0.0364819\pi$
$127$			2.57755i			0.228721i	−0.993439	+	0.114360i	$0.963518\pi$
$128$		−	5.61814i		−	0.496578i
$129$	6.21641			0.547325
$130$	−0.295251			−0.0258953
$131$	7.64618			0.668050			0.334025	−	0.942564i	$-0.391593\pi$
$131$	7.64618			0.668050			0.334025	+	0.942564i	$0.391593\pi$
$132$	6.05210	+	2.43066i	0.526768	+	0.211562i
$133$	−8.30550	−	12.4050i	−0.720178	−	1.07565i
$134$			0.298093i			0.0257513i
$135$	1.83337			0.157791
$136$			2.59943i			0.222900i
$137$	19.4654			1.66304			0.831522	−	0.555493i	$-0.187470\pi$
$137$	19.4654			1.66304			0.831522	+	0.555493i	$0.187470\pi$
$138$	−0.0987737			−0.00840818
$139$	−6.58276			−0.558342			−0.279171	−	0.960241i	$-0.590060\pi$
$139$	−6.58276			−0.558342			−0.279171	+	0.960241i	$0.590060\pi$
$140$	−7.92604	+	5.30670i	−0.669873	+	0.448498i
$141$	5.29413			0.445846
$142$			1.85716i			0.155849i
$143$	−1.08674	+	2.70587i	−0.0908778	+	0.226277i
$144$	−3.79981			−0.316651
$145$	−7.00912			−0.582076
$146$			2.62627i			0.217352i
$147$	6.47214	+	2.66673i	0.533813	+	0.219948i
$148$	−5.18900			−0.426534
$149$		−	5.70356i		−	0.467254i	−0.972326	−	0.233627i	$-0.924940\pi$
$149$		−	5.70356i		−	0.467254i	0.972326	−	0.233627i	$-0.0750595\pi$
$150$	−0.300177			−0.0245093
$151$			13.1299i			1.06850i	0.845328	+	0.534248i	$0.179405\pi$
$151$			13.1299i			1.06850i	−0.845328	+	0.534248i	$0.820595\pi$
$152$		−	4.09953i		−	0.332516i
$153$	3.57781			0.289249
$154$	−0.332038	−	1.57266i	−0.0267564	−	0.126728i
$155$	10.2662			0.824598
$156$		−	1.72889i		−	0.138422i
$157$		−	22.4540i		−	1.79203i	−0.444026	−	0.896014i	$-0.646450\pi$
$157$		−	22.4540i		−	1.79203i	0.444026	−	0.896014i	$-0.353550\pi$
$158$	−2.07176			−0.164821
$159$			3.93290i			0.311899i
$160$	−3.94010			−0.311492
$161$	−0.793734	−	1.18551i	−0.0625550	−	0.0934316i
$162$		−	0.183172i		−	0.0143914i
$163$	−17.5719			−1.37633			−0.688167	−	0.725552i	$-0.741584\pi$
$163$	−17.5719			−1.37633			−0.688167	+	0.725552i	$0.741584\pi$
$164$	20.7506			1.62035
$165$	2.26616	−	5.64252i	0.176421	−	0.439270i
$166$		−	1.86804i		−	0.144988i
$167$	−14.6207			−1.13139			−0.565693	−	0.824616i	$-0.691391\pi$
$167$	−14.6207			−1.13139			−0.565693	+	0.824616i	$0.691391\pi$
$168$	1.06943	+	1.59730i	0.0825086	+	0.123234i
$169$	−12.2270			−0.940540
$170$	1.20151			0.0921513
$171$	−5.64252			−0.431494
$172$			12.2243i			0.932090i
$173$	10.6744			0.811563			0.405781	−	0.913970i	$-0.366999\pi$
$173$	10.6744			0.811563			0.405781	+	0.913970i	$0.366999\pi$
$174$			0.700283i			0.0530883i
$175$	−2.41219	−	3.60282i	−0.182344	−	0.272348i
$176$	−4.69683	+	11.6946i	−0.354037	+	0.881515i
$177$	10.2384			0.769565
$178$	−0.513872			−0.0385163
$179$	−18.0047			−1.34573			−0.672866	−	0.739765i	$-0.734937\pi$
$179$	−18.0047			−1.34573			−0.672866	+	0.739765i	$0.734937\pi$
$180$			3.60522i			0.268717i
$181$		−	13.2664i		−	0.986081i	−0.870006	−	0.493040i	$-0.835885\pi$
$181$		−	13.2664i		−	0.986081i	0.870006	−	0.493040i	$-0.164115\pi$
$182$	−0.354053	+	0.237048i	−0.0262441	+	0.0175711i
$183$			0.732688i			0.0541619i
$184$		−	0.391781i		−	0.0288825i
$185$			4.83783i			0.355684i
$186$		−	1.02570i		−	0.0752076i
$187$	4.42242	−	11.0114i	0.323399	−	0.805232i
$188$			10.4106i			0.759273i
$189$	2.19849	−	1.47195i	0.159917	−	0.107069i
$190$	−1.89488			−0.137469
$191$	9.81678			0.710317			0.355159	−	0.934806i	$-0.384427\pi$
$191$	9.81678			0.710317			0.355159	+	0.934806i	$0.384427\pi$
$192$		−	7.20597i		−	0.520046i
$193$			23.6568i			1.70286i	0.524472	+	0.851428i	$0.324263\pi$
$193$			23.6568i			1.70286i	−0.524472	+	0.851428i	$0.675737\pi$
$194$	−2.46649			−0.177084
$195$	−1.61188			−0.115429
$196$	−5.24399	+	12.7271i	−0.374571	+	0.909080i
$197$		−	17.1351i		−	1.22083i	−0.792083	−	0.610413i	$-0.791004\pi$
$197$		−	17.1351i		−	1.22083i	0.792083	−	0.610413i	$-0.208996\pi$
$198$	−0.563746	−	0.226413i	−0.0400637	−	0.0160905i
$199$			14.2662i			1.01130i	0.862738	+	0.505651i	$0.168748\pi$
$199$			14.2662i			1.01130i	−0.862738	+	0.505651i	$0.831252\pi$
$200$		−	1.19064i		−	0.0841907i
$201$			1.62739i			0.114788i
$202$			3.13440i			0.220536i
$203$	−8.40503	+	5.62739i	−0.589918	+	0.394966i
$204$			7.03558i			0.492589i
$205$		−	19.3463i		−	1.35121i
$206$	−0.966698			−0.0673530
$207$	−0.539240			−0.0374798
$208$	3.34077			0.231640
$209$	−6.97454	+	17.3659i	−0.482439	+	1.20122i
$210$	0.738301	−	0.494312i	0.0509476	−	0.0341108i
$211$		−	7.79371i		−	0.536541i	−0.963344	−	0.268270i	$-0.913548\pi$
$211$		−	7.79371i		−	0.536541i	0.963344	−	0.268270i	$-0.0864521\pi$
$212$	−7.73384			−0.531162
$213$			10.1389i			0.694704i
$214$	1.38957			0.0949892
$215$	11.3970			0.777266
$216$	0.726543			0.0494350
$217$	12.3107	−	8.24237i	0.835707	−	0.559528i
$218$	2.05592			0.139245
$219$			14.3377i			0.968853i
$220$	11.0957	+	4.45629i	0.748073	+	0.300443i
$221$	−3.14558			−0.211595
$222$	0.483349			0.0324403
$223$			23.8103i			1.59445i	0.603680	+	0.797226i	$0.293700\pi$
$223$			23.8103i			1.59445i	−0.603680	+	0.797226i	$0.706300\pi$
$224$	−4.72479	+	3.16337i	−0.315688	+	0.211362i
$225$	−1.63877			−0.109251
$226$		−	1.70963i		−	0.113723i
$227$	3.63886			0.241520			0.120760	−	0.992682i	$-0.461467\pi$
$227$	3.63886			0.241520			0.120760	+	0.992682i	$0.461467\pi$
$228$		−	11.0957i		−	0.734832i
$229$		−	0.322087i		−	0.0212841i	−0.999943	−	0.0106420i	$-0.996612\pi$
$229$		−	0.322087i		−	0.0212841i	0.999943	−	0.0106420i	$-0.00338753\pi$
$230$	−0.181088			−0.0119406
$231$	−1.81271	−	8.58569i	−0.119267	−	0.564897i
$232$	−2.77764			−0.182361
$233$			25.9291i			1.69867i	0.527854	+	0.849335i	$0.322997\pi$
$233$			25.9291i			1.69867i	−0.527854	+	0.849335i	$0.677003\pi$
$234$			0.161043i			0.0105277i
$235$	9.70607			0.633154
$236$			20.1333i			1.31056i
$237$	−11.3105			−0.734694
$238$	1.44079	−	0.964650i	0.0933928	−	0.0625290i
$239$			15.8896i			1.02781i	0.857847	+	0.513905i	$0.171802\pi$
$239$			15.8896i			1.02781i	−0.857847	+	0.513905i	$0.828198\pi$
$240$	−6.96645			−0.449682
$241$	−6.76699			−0.435900			−0.217950	−	0.975960i	$-0.569937\pi$
$241$	−6.76699			−0.435900			−0.217950	+	0.975960i	$0.569937\pi$
$242$	−1.39366	+	1.45517i	−0.0895876	+	0.0935418i
$243$		−	1.00000i		−	0.0641500i
$244$	−1.44079			−0.0922374
$245$	11.8658	+	4.88909i	0.758078	+	0.312353i
$246$	−1.93290			−0.123237
$247$	4.96086			0.315652
$248$	4.06837			0.258342
$249$		−	10.1983i		−	0.646291i
$250$	−2.22944			−0.141002
$251$		−	4.21565i		−	0.266089i	−0.991110	−	0.133045i	$-0.957525\pi$
$251$		−	4.21565i		−	0.266089i	0.991110	−	0.133045i	$-0.0424754\pi$
$252$	2.89451	+	4.32322i	0.182337	+	0.272337i
$253$	−0.666537	+	1.65961i	−0.0419048	+	0.104339i
$254$	0.472136			0.0296244
$255$	6.55944			0.410768
$256$	13.3829			0.836428
$257$		−	11.7774i		−	0.734657i	−0.930091	−	0.367328i	$-0.880273\pi$
$257$		−	11.7774i		−	0.734657i	0.930091	−	0.367328i	$-0.119727\pi$
$258$		−	1.13867i		−	0.0708907i
$259$	3.88414	+	5.80131i	0.241348	+	0.360476i
$260$		−	3.16968i		−	0.196575i
$261$			3.82309i			0.236643i
$262$		−	1.40057i		−	0.0865273i
$263$		−	15.6474i		−	0.964862i	−0.875934	−	0.482431i	$-0.839754\pi$
$263$		−	15.6474i		−	0.964862i	0.875934	−	0.482431i	$-0.160246\pi$
$264$	0.898056	−	2.23607i	0.0552715	−	0.137620i
$265$			7.21044i			0.442934i
$266$	−2.27226	+	1.52134i	−0.139321	+	0.0932791i
$267$	−2.80540			−0.171688
$268$	−3.20019			−0.195482
$269$		−	18.1389i		−	1.10595i	−0.833199	−	0.552973i	$-0.813493\pi$
$269$		−	18.1389i		−	1.10595i	0.833199	−	0.552973i	$-0.186507\pi$
$270$		−	0.335821i		−	0.0204374i
$271$	12.5051			0.759633			0.379817	−	0.925062i	$-0.375987\pi$
$271$	12.5051			0.759633			0.379817	+	0.925062i	$0.375987\pi$
$272$	−13.5950			−0.824319
$273$	−1.93290	+	1.29413i	−0.116984	+	0.0783241i
$274$		−	3.56552i		−	0.215401i
$275$	−2.02563	+	5.04362i	−0.122150	+	0.304142i
$276$		−	1.06039i		−	0.0638278i
$277$			1.51625i			0.0911026i	0.998962	+	0.0455513i	$0.0145045\pi$
$277$			1.51625i			0.0911026i	−0.998962	+	0.0455513i	$0.985496\pi$
$278$			1.20578i			0.0723177i
$279$		−	5.59963i		−	0.335241i
$280$	1.96066	+	2.92843i	0.117172	+	0.175007i
$281$		−	23.2895i		−	1.38933i	−0.719332	−	0.694666i	$-0.755552\pi$
$281$		−	23.2895i		−	1.38933i	0.719332	−	0.694666i	$-0.244448\pi$
$282$		−	0.969736i		−	0.0577469i
$283$	2.12575			0.126363			0.0631814	−	0.998002i	$-0.479875\pi$
$283$	2.12575			0.126363			0.0631814	+	0.998002i	$0.479875\pi$
$284$	−19.9376			−1.18308
$285$	−10.3448			−0.612773
$286$	0.495641	+	0.199061i	0.0293078	+	0.0117707i
$287$	−15.5325	−	23.1993i	−0.916856	−	1.36941i
$288$			2.14910i			0.126637i
$289$	−4.19925			−0.247015
$290$			1.28388i			0.0753918i
$291$	−13.4654			−0.789357
$292$	−28.1944			−1.64995
$293$	−13.7761			−0.804809			−0.402404	−	0.915462i	$-0.631825\pi$
$293$	−13.7761			−0.804809			−0.402404	+	0.915462i	$0.631825\pi$
$294$	0.488471	−	1.18551i	0.0284882	−	0.0691406i
$295$	18.7707			1.09287
$296$			1.91718i			0.111434i
$297$	−3.07768	−	1.23607i	−0.178585	−	0.0717239i
$298$	−1.04473			−0.0605198
$299$	0.474095			0.0274176
$300$		−	3.22256i		−	0.186054i
$301$	13.6667	−	9.15024i	0.787737	−	0.527411i
$302$	2.40503			0.138394
$303$			17.1118i			0.983047i
$304$	21.4405			1.22970
$305$			1.34329i			0.0769163i
$306$		−	0.655355i		−	0.0374642i
$307$	−32.1099			−1.83261			−0.916304	−	0.400484i	$-0.868842\pi$
$307$	−32.1099			−1.83261			−0.916304	+	0.400484i	$0.868842\pi$
$308$	16.8833	−	3.56460i	0.962016	−	0.203112i
$309$	−5.27754			−0.300229
$310$		−	1.88047i		−	0.106804i
$311$		−	29.4766i		−	1.67146i	−0.549137	−	0.835732i	$-0.685043\pi$
$311$		−	29.4766i		−	1.67146i	0.549137	−	0.835732i	$-0.314957\pi$
$312$	−0.638770			−0.0361632
$313$			13.9329i			0.787534i	0.919210	+	0.393767i	$0.128828\pi$
$313$			13.9329i			0.787534i	−0.919210	+	0.393767i	$0.871172\pi$
$314$	−4.11295			−0.232107
$315$	4.03064	−	2.69862i	0.227101	−	0.152050i
$316$		−	22.2415i		−	1.25118i
$317$	26.3869			1.48204			0.741019	−	0.671484i	$-0.234343\pi$
$317$	26.3869			1.48204			0.741019	+	0.671484i	$0.234343\pi$
$318$	0.720397			0.0403978
$319$	11.7663	+	4.72560i	0.658784	+	0.264583i
$320$		−	13.2112i		−	0.738527i
$321$	7.58616			0.423418
$322$	−0.217153	+	0.145390i	−0.0121015	+	0.00810226i
$323$	−20.1879			−1.12328
$324$	1.96645			0.109247
$325$	1.44079			0.0799208
$326$			3.21867i			0.178266i
$327$	11.2240			0.620688
$328$		−	7.66673i		−	0.423324i
$329$	11.6391	−	7.79268i	0.641684	−	0.429625i
$330$	−1.03355	−	0.415098i	−0.0568952	−	0.0228504i
$331$	14.7873			0.812784			0.406392	−	0.913699i	$-0.366787\pi$
$331$	14.7873			0.812784			0.406392	+	0.913699i	$0.366787\pi$
$332$	20.0544			1.10063
$333$	2.63877			0.144604
$334$			2.67811i			0.146540i
$335$			2.98361i			0.163012i
$336$	−8.35386	+	5.59313i	−0.455740	+	0.305130i
$337$			1.37975i			0.0751597i	0.999294	+	0.0375798i	$0.0119648\pi$
$337$			1.37975i			0.0751597i	−0.999294	+	0.0375798i	$0.988035\pi$
$338$			2.23965i			0.121821i
$339$		−	9.33346i		−	0.506924i
$340$			12.8988i			0.699535i
$341$	−17.2339	−	6.92152i	−0.933267	−	0.374821i
$342$			1.03355i			0.0558881i
$343$	18.1542	−	3.66387i	0.980236	−	0.197830i
$344$	4.51649			0.243513
$345$	−0.988624			−0.0532257
$346$		−	1.95526i		−	0.105115i
$347$		−	30.8989i		−	1.65874i	−0.558699	−	0.829371i	$-0.688699\pi$
$347$		−	30.8989i		−	1.65874i	0.558699	−	0.829371i	$-0.311301\pi$
$348$	−7.51791			−0.403002
$349$	−2.34457			−0.125502			−0.0627509	−	0.998029i	$-0.519987\pi$
$349$	−2.34457			−0.125502			−0.0627509	+	0.998029i	$0.519987\pi$
$350$	−0.659937	+	0.441845i	−0.0352751	+	0.0236176i
$351$			0.879192i			0.0469278i
$352$	6.61426	+	2.65644i	0.352541	+	0.141589i
$353$			34.6434i			1.84388i	0.387328	+	0.921942i	$0.373398\pi$
$353$			34.6434i			1.84388i	−0.387328	+	0.921942i	$0.626602\pi$
$354$		−	1.87539i		−	0.0996758i
$355$			18.5883i			0.986562i
$356$		−	5.51668i		−	0.292384i
$357$	7.86579	−	5.26636i	0.416302	−	0.278725i
$358$			3.29795i			0.174302i
$359$			20.6642i			1.09061i	0.838237	+	0.545306i	$0.183587\pi$
$359$			20.6642i			1.09061i	−0.838237	+	0.545306i	$0.816413\pi$
$360$	1.33202			0.0702035
$361$	12.8380			0.675686
$362$	−2.43003			−0.127719
$363$	−7.60845	+	7.94427i	−0.399340	+	0.416966i
$364$	−2.54483	−	3.80094i	−0.133385	−	0.199223i
$365$			26.2863i			1.37589i
$366$	0.134208			0.00701517
$367$			1.84304i			0.0962059i	0.998842	+	0.0481030i	$0.0153176\pi$
$367$			1.84304i			0.0962059i	−0.998842	+	0.0481030i	$0.984682\pi$
$368$	2.04901			0.106812
$369$	−10.5524			−0.549333
$370$	0.886156			0.0460690
$371$	5.78902	+	8.64644i	0.300551	+	0.448901i
$372$	11.0114			0.570913
$373$		−	26.4409i		−	1.36906i	−0.728986	−	0.684529i	$-0.760008\pi$
$373$		−	26.4409i		−	1.36906i	0.728986	−	0.684529i	$-0.239992\pi$
$374$	−2.01698	−	0.810064i	−0.104295	−	0.0418874i
$375$	−12.1713			−0.628523
$376$	3.84641			0.198363
$377$		−	3.36123i		−	0.173112i
$378$	−0.269620	−	0.402702i	−0.0138678	−	0.0207128i
$379$	−2.70587			−0.138991			−0.0694957	−	0.997582i	$-0.522139\pi$
$379$	−2.70587			−0.138991			−0.0694957	+	0.997582i	$0.522139\pi$
$380$		−	20.3425i		−	1.04355i
$381$	2.57755			0.132052
$382$		−	1.79816i		−	0.0920019i
$383$			7.05573i			0.360531i	0.983618	+	0.180265i	$0.0576957\pi$
$383$			7.05573i			0.360531i	−0.983618	+	0.180265i	$0.942304\pi$
$384$	−5.61814			−0.286700
$385$	−3.32336	−	15.7407i	−0.169374	−	0.802221i
$386$	4.33327			0.220558
$387$		−	6.21641i		−	0.315998i
$388$		−	26.4790i		−	1.34427i
$389$	14.8101			0.750900			0.375450	−	0.926843i	$-0.377488\pi$
$389$	14.8101			0.750900			0.375450	+	0.926843i	$0.377488\pi$
$390$			0.295251i			0.0149506i
$391$	−1.92930			−0.0975689
$392$	4.70228	+	1.93749i	0.237501	+	0.0978582i
$393$		−	7.64618i		−	0.385699i
$394$	−3.13867			−0.158124
$395$	−20.7362			−1.04335
$396$	2.43066	−	6.05210i	0.122145	−	0.304130i
$397$		−	10.4652i		−	0.525235i	−0.964900	−	0.262617i	$-0.915414\pi$
$397$		−	10.4652i		−	0.525235i	0.964900	−	0.262617i	$-0.0845857\pi$
$398$	2.61316			0.130986
$399$	−12.4050	+	8.30550i	−0.621028	+	0.415795i
$400$	6.22702			0.311351
$401$	−18.1879			−0.908259			−0.454130	−	0.890936i	$-0.650050\pi$
$401$	−18.1879			−0.908259			−0.454130	+	0.890936i	$0.650050\pi$
$402$	0.298093			0.0148675
$403$			4.92315i			0.245239i
$404$	−33.6494			−1.67412
$405$		−	1.83337i		−	0.0911007i
$406$	1.03078	+	1.53957i	0.0511568	+	0.0764074i
$407$	3.26170	−	8.12130i	0.161676	−	0.402558i
$408$	2.59943			0.128691
$409$	18.3961			0.909628			0.454814	−	0.890587i	$-0.349706\pi$
$409$	18.3961			0.909628			0.454814	+	0.890587i	$0.349706\pi$
$410$	−3.54371			−0.175011
$411$		−	19.4654i		−	0.960158i
$412$		−	10.3780i		−	0.511288i
$413$	22.5090	−	15.0704i	1.10760	−	0.741566i
$414$			0.0987737i			0.00485446i
$415$		−	18.6972i		−	0.917810i
$416$		−	1.88948i		−	0.0926392i
$417$			6.58276i			0.322359i
$418$	3.18095	+	1.27754i	0.155585	+	0.0624866i
$419$			3.54911i			0.173385i	0.996235	+	0.0866926i	$0.0276298\pi$
$419$			3.54911i			0.173385i	−0.996235	+	0.0866926i	$0.972370\pi$
$420$	5.30670	+	7.92604i	0.258940	+	0.386751i
$421$	14.5832			0.710743			0.355372	−	0.934725i	$-0.384354\pi$
$421$	14.5832			0.710743			0.355372	+	0.934725i	$0.384354\pi$
$422$	−1.42759			−0.0694940
$423$		−	5.29413i		−	0.257409i
$424$			2.85742i			0.138768i
$425$	−5.86321			−0.284408
$426$	1.85716			0.0899796
$427$	1.07848	+	1.61081i	0.0521913	+	0.0779525i
$428$			14.9178i			0.721078i
$429$	2.70587	+	1.08674i	0.130641	+	0.0524683i
$430$		−	2.08760i		−	0.100673i
$431$			25.7338i			1.23955i	0.784778	+	0.619777i	$0.212777\pi$
$431$			25.7338i			1.23955i	−0.784778	+	0.619777i	$0.787223\pi$
$432$			3.79981i			0.182819i
$433$			30.1994i			1.45129i	0.688068	+	0.725646i	$0.258459\pi$
$433$			30.1994i			1.45129i	−0.688068	+	0.725646i	$0.741541\pi$
$434$	−1.50977	−	2.25498i	−0.0724713	−	0.108243i
$435$			7.00912i			0.336062i
$436$			22.0714i			1.05703i
$437$	3.04267			0.145551
$438$	2.62627			0.125488
$439$	−18.3238			−0.874546			−0.437273	−	0.899329i	$-0.644056\pi$
$439$	−18.3238			−0.874546			−0.437273	+	0.899329i	$0.644056\pi$
$440$	1.64646	−	4.09953i	0.0784921	−	0.195437i
$441$	2.66673	−	6.47214i	0.126987	−	0.308197i
$442$			0.576183i			0.0274062i
$443$	−6.19440			−0.294305			−0.147152	−	0.989114i	$-0.547011\pi$
$443$	−6.19440			−0.294305			−0.147152	+	0.989114i	$0.547011\pi$
$444$			5.18900i			0.246259i
$445$	−5.14333			−0.243817
$446$	4.36137			0.206517
$447$	−5.70356			−0.269769
$448$	−10.6068	−	15.8423i	−0.501125	−	0.748477i
$449$	−31.1210			−1.46869			−0.734345	−	0.678777i	$-0.762510\pi$
$449$	−31.1210			−1.46869			−0.734345	+	0.678777i	$0.762510\pi$
$450$			0.300177i			0.0141505i
$451$	−13.0434	+	32.4768i	−0.614191	+	1.52927i
$452$	18.3538			0.863289
$453$	13.1299			0.616897
$454$		−	0.666537i		−	0.0312821i
$455$	−3.54371	+	2.37261i	−0.166131	+	0.111229i
$456$	−4.09953			−0.191978
$457$			7.94936i			0.371855i	0.982563	+	0.185928i	$0.0595290\pi$
$457$			7.94936i			0.371855i	−0.982563	+	0.185928i	$0.940471\pi$
$458$	−0.0589973			−0.00275676
$459$		−	3.57781i		−	0.166998i
$460$		−	1.94408i		−	0.0906431i
$461$	6.62048			0.308347			0.154173	−	0.988044i	$-0.450729\pi$
$461$	6.62048			0.308347			0.154173	+	0.988044i	$0.450729\pi$
$462$	−1.57266	+	0.332038i	−0.0731667	+	0.0154478i
$463$	10.9836			0.510452			0.255226	−	0.966881i	$-0.417850\pi$
$463$	10.9836			0.510452			0.255226	+	0.966881i	$0.417850\pi$
$464$		−	14.5270i		−	0.674400i
$465$		−	10.2662i		−	0.476082i
$466$	4.74948			0.220016
$467$			2.29393i			0.106150i	0.998591	+	0.0530752i	$0.0169023\pi$
$467$			2.29393i			0.106150i	−0.998591	+	0.0530752i	$0.983098\pi$
$468$	−1.72889			−0.0799177
$469$	2.39544	+	3.57781i	0.110611	+	0.165208i
$470$		−	1.77788i		−	0.0820075i
$471$	−22.4540			−1.03463
$472$	7.43863			0.342391
$473$	−19.1322	−	7.68391i	−0.879697	−	0.353306i
$474$			2.07176i			0.0951592i
$475$	9.24679			0.424272
$476$	10.3560	+	15.4677i	0.474667	+	0.708960i
$477$	3.93290			0.180075
$478$	2.91053			0.133124
$479$	36.1405			1.65130			0.825651	−	0.564181i	$-0.190808\pi$
$479$	36.1405			1.65130			0.825651	+	0.564181i	$0.190808\pi$
$480$			3.94010i			0.179840i
$481$	−2.31999			−0.105782
$482$			1.23952i			0.0564587i
$483$	−1.18551	+	0.793734i	−0.0539428	+	0.0361161i
$484$	−15.6220	−	14.9616i	−0.710091	−	0.680074i
$485$	−24.6870			−1.12098
$486$	−0.183172			−0.00830885
$487$	−4.54615			−0.206006			−0.103003	−	0.994681i	$-0.532845\pi$
$487$	−4.54615			−0.206006			−0.103003	+	0.994681i	$0.532845\pi$
$488$			0.532329i			0.0240974i
$489$			17.5719i			0.794627i
$490$	0.895545	−	2.17348i	0.0404566	−	0.0981879i
$491$			18.1385i			0.818579i	0.912404	+	0.409290i	$0.134223\pi$
$491$			18.1385i			0.818579i	−0.912404	+	0.409290i	$0.865777\pi$
$492$		−	20.7506i		−	0.935511i
$493$			13.6783i			0.616040i
$494$		−	0.908691i		−	0.0408839i
$495$	−5.64252	−	2.26616i	−0.253612	−	0.101857i
$496$			21.2775i			0.955390i
$497$	14.9239	+	22.2902i	0.669428	+	0.999853i
$498$	−1.86804			−0.0837090
$499$	−15.1827			−0.679670			−0.339835	−	0.940485i	$-0.610371\pi$
$499$	−15.1827			−0.679670			−0.339835	+	0.940485i	$0.610371\pi$
$500$		−	23.9342i		−	1.07037i
$501$			14.6207i			0.653206i
$502$	−0.772189			−0.0344645
$503$	−36.2097			−1.61451			−0.807255	−	0.590203i	$-0.799048\pi$
$503$	−36.2097			−1.61451			−0.807255	+	0.590203i	$0.799048\pi$
$504$	1.59730	−	1.06943i	0.0711493	−	0.0476364i
$505$			31.3722i			1.39604i
$506$	0.303994	+	0.122091i	0.0135142	+	0.00542761i
$507$			12.2270i			0.543021i
$508$			5.06863i			0.224884i
$509$			35.6155i			1.57863i	0.613990	+	0.789314i	$0.289564\pi$
$509$			35.6155i			1.57863i	−0.613990	+	0.789314i	$0.710436\pi$
$510$		−	1.20151i		−	0.0532036i
$511$	21.1044	+	31.5213i	0.933603	+	1.39442i
$512$		−	13.6877i		−	0.604914i
$513$			5.64252i			0.249123i
$514$	−2.15730			−0.0951544
$515$	−9.67566			−0.426361
$516$	12.2243			0.538143
$517$	−16.2936	−	6.54390i	−0.716594	−	0.287800i
$518$	1.06264	−	0.711465i	0.0466897	−	0.0312600i
$519$		−	10.6744i		−	0.468556i
$520$	−1.17110			−0.0513561
$521$			22.7776i			0.997906i	0.866629	+	0.498953i	$0.166282\pi$
$521$			22.7776i			0.997906i	−0.866629	+	0.498953i	$0.833718\pi$
$522$	0.700283			0.0306506
$523$	37.4196			1.63625			0.818123	−	0.575044i	$-0.195015\pi$
$523$	37.4196			1.63625			0.818123	+	0.575044i	$0.195015\pi$
$524$	15.0358			0.656843
$525$	−3.60282	+	2.41219i	−0.157240	+	0.105276i
$526$	−2.86617			−0.124971
$527$		−	20.0344i		−	0.872713i
$528$	11.6946	+	4.69683i	0.508943	+	0.204403i
$529$	−22.7092			−0.987357
$530$	1.32075			0.0573697
$531$		−	10.2384i		−	0.444309i
$532$	−16.3323	−	24.3939i	−0.708097	−	1.05761i
$533$	9.27754			0.401855
$534$			0.513872i			0.0222374i
$535$	13.9082			0.601304
$536$			1.18237i			0.0510707i
$537$			18.0047i			0.776958i
$538$	−3.32253			−0.143245
$539$	−16.6229	−	16.2074i	−0.716000	−	0.698100i
$540$	3.60522			0.155144
$541$		−	2.29352i		−	0.0986063i	−0.998784	−	0.0493032i	$-0.984300\pi$
$541$		−	2.29352i		−	0.0986063i	0.998784	−	0.0493032i	$-0.0157000\pi$
$542$		−	2.29059i		−	0.0983894i
$543$	−13.2664			−0.569314
$544$			7.68910i			0.329667i
$545$	20.5777			0.881451
$546$	0.237048	+	0.354053i	0.0101447	+	0.0151521i
$547$			5.86236i			0.250656i	0.992115	+	0.125328i	$0.0399984\pi$
$547$			5.86236i			0.250656i	−0.992115	+	0.125328i	$0.960002\pi$
$548$	38.2777			1.63514
$549$	0.732688			0.0312704
$550$	0.923850	+	0.371039i	0.0393931	+	0.0158212i
$551$		−	21.5719i		−	0.918992i
$552$	−0.391781			−0.0166753
$553$	−24.8660	+	16.6484i	−1.05741	+	0.707964i
$554$	0.277735			0.0117998
$555$	4.83783			0.205354
$556$	−12.9446			−0.548975
$557$			21.2135i			0.898844i	0.893320	+	0.449422i	$0.148370\pi$
$557$			21.2135i			0.898844i	−0.893320	+	0.449422i	$0.851630\pi$
$558$	−1.02570			−0.0434211
$559$			5.46542i			0.231163i
$560$	−15.3157	+	10.2543i	−0.647206	+	0.433321i
$561$	−11.0114	−	4.42242i	−0.464901	−	0.186715i
$562$	−4.26598			−0.179949
$563$	−13.1553			−0.554432			−0.277216	−	0.960808i	$-0.589412\pi$
$563$	−13.1553			−0.554432			−0.277216	+	0.960808i	$0.589412\pi$
$564$	10.4106			0.438366
$565$		−	17.1117i		−	0.719893i
$566$		−	0.389378i		−	0.0163668i
$567$	−1.47195	−	2.19849i	−0.0618161	−	0.0923280i
$568$			7.36632i			0.309084i
$569$		−	2.09117i		−	0.0876663i	−0.999039	−	0.0438331i	$-0.986043\pi$
$569$		−	2.09117i		−	0.0876663i	0.999039	−	0.0438331i	$-0.0139570\pi$
$570$			1.89488i			0.0793677i
$571$		−	35.0529i		−	1.46692i	−0.679733	−	0.733460i	$-0.737904\pi$
$571$		−	35.0529i		−	1.46692i	0.679733	−	0.733460i	$-0.262096\pi$
$572$	−2.13702	+	5.32096i	−0.0893533	+	0.222481i
$573$		−	9.81678i		−	0.410102i
$574$	−4.24946	+	2.84512i	−0.177369	+	0.118753i
$575$	0.883690			0.0368524
$576$	−7.20597			−0.300249
$577$		−	21.7338i		−	0.904791i	−0.891817	−	0.452396i	$-0.850569\pi$
$577$		−	21.7338i		−	0.904791i	0.891817	−	0.452396i	$-0.149431\pi$
$578$			0.769186i			0.0319939i
$579$	23.6568			0.983144
$580$	−13.7831			−0.572311
$581$	−15.0114	−	22.4209i	−0.622777	−	0.930175i
$582$			2.46649i			0.102239i
$583$	4.86133	−	12.1042i	0.201336	−	0.501305i
$584$			10.4170i			0.431057i
$585$			1.61188i			0.0666430i
$586$			2.52340i			0.104241i
$587$			18.9049i			0.780290i	0.920753	+	0.390145i	$0.127575\pi$
$587$			18.9049i			0.780290i	−0.920753	+	0.390145i	$0.872425\pi$
$588$	12.7271	+	5.24399i	0.524858	+	0.216258i
$589$			31.5960i			1.30189i
$590$		−	3.43827i		−	0.141551i
$591$	−17.1351			−0.704844
$592$	−10.0268			−0.412100
$593$	11.6026			0.476463			0.238231	−	0.971208i	$-0.423432\pi$
$593$	11.6026			0.476463			0.238231	+	0.971208i	$0.423432\pi$
$594$	−0.226413	+	0.563746i	−0.00928984	+	0.0231308i
$595$	14.4209	−	9.65516i	0.591198	−	0.395823i
$596$		−	11.2158i		−	0.459416i
$597$	14.2662			0.583875
$598$		−	0.0868410i		−	0.00355119i
$599$	25.4585			1.04021			0.520103	−	0.854103i	$-0.325893\pi$
$599$	25.4585			1.04021			0.520103	+	0.854103i	$0.325893\pi$
$600$	−1.19064			−0.0486075
$601$	12.0421			0.491209			0.245605	−	0.969370i	$-0.421014\pi$
$601$	12.0421			0.491209			0.245605	+	0.969370i	$0.421014\pi$
$602$	−1.67607	−	2.50336i	−0.0683115	−	0.102029i
$603$	1.62739			0.0662726
$604$			25.8193i			1.05057i
$605$	−13.9491	+	14.5648i	−0.567111	+	0.592142i
$606$	3.13440			0.127326
$607$	35.2991			1.43274			0.716372	−	0.697718i	$-0.245801\pi$
$607$	35.2991			1.43274			0.716372	+	0.697718i	$0.245801\pi$
$608$		−	12.1264i		−	0.491789i
$609$	5.62739	+	8.40503i	0.228034	+	0.340589i
$610$	0.246052			0.00996237
$611$			4.65455i			0.188303i
$612$	7.03558			0.284397
$613$		−	24.5604i		−	0.991986i	−0.868326	−	0.495993i	$-0.834804\pi$
$613$		−	24.5604i		−	0.991986i	0.868326	−	0.495993i	$-0.165196\pi$
$614$			5.88163i			0.237363i
$615$	−19.3463			−0.780119
$616$	−1.31701	−	6.23787i	−0.0530638	−	0.251331i
$617$	29.9445			1.20552			0.602759	−	0.797923i	$-0.294068\pi$
$617$	29.9445			1.20552			0.602759	+	0.797923i	$0.294068\pi$
$618$			0.966698i			0.0388863i
$619$		−	38.2106i		−	1.53581i	−0.640561	−	0.767907i	$-0.721298\pi$
$619$		−	38.2106i		−	1.53581i	0.640561	−	0.767907i	$-0.278702\pi$
$620$	20.1879			0.810765
$621$			0.539240i			0.0216390i
$622$	−5.39929			−0.216492
$623$	−6.16766	+	4.12941i	−0.247102	+	0.165441i
$624$		−	3.34077i		−	0.133738i
$625$	−14.1206			−0.564823
$626$	2.55212			0.102003
$627$	17.3659	+	6.97454i	0.693527	+	0.278536i
$628$		−	44.1547i		−	1.76196i
$629$	9.44103			0.376438
$630$	−0.494312	−	0.738301i	−0.0196939	−	0.0294146i
$631$	17.0423			0.678443			0.339222	−	0.940707i	$-0.389836\pi$
$631$	17.0423			0.678443			0.339222	+	0.940707i	$0.389836\pi$
$632$	−8.21754			−0.326876
$633$	−7.79371			−0.309772
$634$		−	4.83335i		−	0.191957i
$635$	4.72560			0.187530
$636$			7.73384i			0.306667i
$637$	−2.34457	+	5.69025i	−0.0928952	+	0.225456i
$638$	0.865598	−	2.15525i	0.0342693	−	0.0853272i
$639$	10.1389			0.401087
$640$	−10.3001			−0.407148
$641$	−7.52095			−0.297060			−0.148530	−	0.988908i	$-0.547454\pi$
$641$	−7.52095			−0.297060			−0.148530	+	0.988908i	$0.547454\pi$
$642$		−	1.38957i		−	0.0548421i
$643$		−	26.9558i		−	1.06303i	−0.847047	−	0.531517i	$-0.821622\pi$
$643$		−	26.9558i		−	1.06303i	0.847047	−	0.531517i	$-0.178378\pi$
$644$	−1.56084	−	2.33125i	−0.0615056	−	0.0918642i
$645$		−	11.3970i		−	0.448755i
$646$			3.69786i			0.145490i
$647$		−	21.0257i		−	0.826606i	−0.910594	−	0.413303i	$-0.864375\pi$
$647$		−	21.0257i		−	0.826606i	0.910594	−	0.413303i	$-0.135625\pi$
$648$		−	0.726543i		−	0.0285413i
$649$	−31.5105	−	12.6554i	−1.23690	−	0.496766i
$650$		−	0.263913i		−	0.0103515i
$651$	−8.24237	−	12.3107i	−0.323044	−	0.482496i
$652$	−34.5541			−1.35324
$653$	22.1991			0.868716			0.434358	−	0.900740i	$-0.356975\pi$
$653$	22.1991			0.868716			0.434358	+	0.900740i	$0.356975\pi$
$654$		−	2.05592i		−	0.0803929i
$655$		−	14.0182i		−	0.547738i
$656$	40.0970			1.56552
$657$	14.3377			0.559367
$658$	−1.42740	−	2.13196i	−0.0556459	−	0.0831123i
$659$		−	40.5356i		−	1.57904i	−0.613722	−	0.789522i	$-0.710329\pi$
$659$		−	40.5356i		−	1.57904i	0.613722	−	0.789522i	$-0.289671\pi$
$660$	4.45629	−	11.0957i	0.173461	−	0.431900i
$661$			32.2889i			1.25589i	0.778256	+	0.627947i	$0.216104\pi$
$661$			32.2889i			1.25589i	−0.778256	+	0.627947i	$0.783896\pi$
$662$		−	2.70862i		−	0.105274i
$663$			3.14558i			0.122164i
$664$		−	7.40950i		−	0.287544i
$665$	−22.7430	+	15.2270i	−0.881934	+	0.590479i
$666$		−	0.483349i		−	0.0187294i
$667$		−	2.06156i		−	0.0798240i
$668$	−28.7509			−1.11240
$669$	23.8103			0.920558
$670$	0.546514			0.0211137
$671$	0.905653	−	2.25498i	0.0349623	−	0.0870526i
$672$	3.16337	+	4.72479i	0.122030	+	0.182263i
$673$			19.7250i			0.760341i	0.924916	+	0.380171i	$0.124135\pi$
$673$			19.7250i			0.760341i	−0.924916	+	0.380171i	$0.875865\pi$
$674$	0.252731			0.00973485
$675$			1.63877i			0.0630763i
$676$	−24.0438			−0.924762
$677$	−19.1734			−0.736892			−0.368446	−	0.929649i	$-0.620110\pi$
$677$	−19.1734			−0.736892			−0.368446	+	0.929649i	$0.620110\pi$
$678$	−1.70963			−0.0656579
$679$	−29.6036	+	19.8204i	−1.13608	+	0.760638i
$680$	4.76571			0.182757
$681$		−	3.63886i		−	0.139441i
$682$	−1.26783	+	3.15677i	−0.0485477	+	0.120879i
$683$	13.9935			0.535446			0.267723	−	0.963496i	$-0.413729\pi$
$683$	13.9935			0.535446			0.267723	+	0.963496i	$0.413729\pi$
$684$	−11.0957			−0.424255
$685$		−	35.6872i		−	1.36354i
$686$	−0.671118	−	3.32535i	−0.0256234	−	0.126962i
$687$	−0.322087			−0.0122884
$688$			23.6212i			0.900550i
$689$	−3.45777			−0.131731
$690$			0.181088i			0.00689391i
$691$			2.11146i			0.0803236i	0.999193	+	0.0401618i	$0.0127873\pi$
$691$			2.11146i			0.0803236i	−0.999193	+	0.0401618i	$0.987213\pi$
$692$	20.9907			0.797948
$693$	−8.58569	+	1.81271i	−0.326143	+	0.0688591i
$694$	−5.65982			−0.214844
$695$			12.0686i			0.457788i
$696$			2.77764i			0.105286i
$697$	−37.7543			−1.43005
$698$			0.429459i			0.0162553i
$699$	25.9291			0.980728
$700$	−4.74344	−	7.08476i	−0.179285	−	0.267779i
$701$		−	35.9909i		−	1.35936i	−0.733510	−	0.679678i	$-0.762119\pi$
$701$		−	35.9909i		−	1.35936i	0.733510	−	0.679678i	$-0.237881\pi$
$702$	0.161043			0.00607819
$703$	−14.8893			−0.561561
$704$	−8.90707	+	22.1777i	−0.335698	+	0.835853i
$705$		−	9.70607i		−	0.365552i
$706$	6.34571			0.238824
$707$	25.1877	+	37.6201i	0.947280	+	1.41485i
$708$	20.1333			0.756655
$709$	−27.9950			−1.05137			−0.525687	−	0.850678i	$-0.676192\pi$
$709$	−27.9950			−1.05137			−0.525687	+	0.850678i	$0.676192\pi$
$710$	3.40485			0.127782
$711$			11.3105i			0.424176i
$712$	−2.03825			−0.0763865
$713$			3.01954i			0.113083i
$714$	−0.964650	−	1.44079i	−0.0361011	−	0.0539203i
$715$	4.96086	+	1.99239i	0.185526	+	0.0745113i
$716$	−35.4052			−1.32316
$717$	15.8896			0.593407
$718$	3.78510			0.141259
$719$		−	23.2158i		−	0.865805i	−0.901441	−	0.432902i	$-0.857489\pi$
$719$		−	23.2158i		−	0.865805i	0.901441	−	0.432902i	$-0.142511\pi$
$720$			6.96645i			0.259624i
$721$	−11.6026	+	7.76827i	−0.432104	+	0.289306i
$722$		−	2.35157i		−	0.0875163i
$723$			6.76699i			0.251667i
$724$		−	26.0876i		−	0.969538i
$725$		−	6.26517i		−	0.232682i
$726$	1.45517	+	1.39366i	0.0540064	+	0.0517234i
$727$		−	1.52095i		−	0.0564090i	−0.999602	−	0.0282045i	$-0.991021\pi$
$727$		−	1.52095i		−	0.0564090i	0.999602	−	0.0282045i	$-0.00897897\pi$
$728$	−1.40433	+	0.940237i	−0.0520480	+	0.0348475i
$729$	−1.00000			−0.0370370
$730$	4.81491			0.178208
$731$		−	22.2412i		−	0.822619i
$732$			1.44079i			0.0532533i
$733$	−20.3720			−0.752457			−0.376229	−	0.926527i	$-0.622779\pi$
$733$	−20.3720			−0.752457			−0.376229	+	0.926527i	$0.622779\pi$
$734$	0.337593			0.0124608
$735$	4.88909	−	11.8658i	0.180337	−	0.437676i
$736$		−	1.15888i		−	0.0427170i
$737$	2.01157	−	5.00860i	0.0740971	−	0.184494i
$738$			1.93290i			0.0711509i
$739$		−	16.2336i		−	0.597163i	−0.954384	−	0.298582i	$-0.903486\pi$
$739$		−	16.2336i		−	0.597163i	0.954384	−	0.298582i	$-0.0965135\pi$
$740$			9.51334i			0.349717i
$741$		−	4.96086i		−	0.182242i
$742$	1.58379	−	1.06039i	0.0581426	−	0.0389280i
$743$			32.9403i			1.20846i	0.796809	+	0.604231i	$0.206520\pi$
$743$			32.9403i			1.20846i	−0.796809	+	0.604231i	$0.793480\pi$
$744$		−	4.06837i		−	0.149154i
$745$	−10.4567			−0.383105
$746$	−4.84323			−0.177323
$747$	−10.1983			−0.373136
$748$	8.69646	−	21.6533i	0.317974	−	0.791723i
$749$	16.6781	−	11.1664i	0.609405	−	0.408013i
$750$			2.22944i			0.0814077i
$751$	51.1603			1.86687			0.933433	−	0.358752i	$-0.116798\pi$
$751$	51.1603			1.86687			0.933433	+	0.358752i	$0.116798\pi$
$752$			20.1167i			0.733580i
$753$	−4.21565			−0.153627
$754$	−0.615683			−0.0224219
$755$	24.0719			0.876067
$756$	4.32322	−	2.89451i	0.157234	−	0.105272i
$757$	−12.0282			−0.437171			−0.218585	−	0.975818i	$-0.570144\pi$
$757$	−12.0282			−0.437171			−0.218585	+	0.975818i	$0.570144\pi$
$758$			0.495641i			0.0180025i
$759$	1.65961	+	0.666537i	0.0602400	+	0.0241938i
$760$	−7.51594			−0.272632
$761$	−8.25678			−0.299308			−0.149654	−	0.988738i	$-0.547816\pi$
$761$	−8.25678			−0.299308			−0.149654	+	0.988738i	$0.547816\pi$
$762$		−	0.472136i		−	0.0171037i
$763$	24.6759	−	16.5211i	0.893326	−	0.598106i
$764$	19.3042			0.698401
$765$		−	6.55944i		−	0.237157i
$766$	1.29241			0.0466968
$767$			9.00152i			0.325026i
$768$		−	13.3829i		−	0.482912i
$769$	39.6473			1.42972			0.714859	−	0.699269i	$-0.246491\pi$
$769$	39.6473			1.42972			0.714859	+	0.699269i	$0.246491\pi$
$770$	−2.88326	+	0.608746i	−0.103905	+	0.0219377i
$771$	−11.7774			−0.424154
$772$			46.5199i			1.67429i
$773$		−	23.4773i		−	0.844421i	−0.906498	−	0.422211i	$-0.861254\pi$
$773$		−	23.4773i		−	0.844421i	0.906498	−	0.422211i	$-0.138746\pi$
$774$	−1.13867			−0.0409288
$775$			9.17650i			0.329630i
$776$	−9.78320			−0.351196
$777$	5.80131	−	3.88414i	0.208121	−	0.139343i
$778$		−	2.71279i		−	0.0972582i
$779$	59.5418			2.13331
$780$	−3.16968			−0.113493
$781$	12.5323	−	31.2042i	0.448442	−	1.11657i
$782$			0.353394i			0.0126373i
$783$	3.82309			0.136626
$784$	−10.1331	+	24.5929i	−0.361896	+	0.878318i
$785$	−41.1665			−1.46929
$786$	−1.40057			−0.0499566
$787$	−30.3861			−1.08315			−0.541573	−	0.840653i	$-0.682171\pi$
$787$	−30.3861			−1.08315			−0.541573	+	0.840653i	$0.682171\pi$
$788$		−	33.6953i		−	1.20035i
$789$	−15.6474			−0.557064
$790$			3.79830i			0.135137i
$791$	−13.7384	−	20.5195i	−0.488481	−	0.729591i
$792$	−2.23607	−	0.898056i	−0.0794552	−	0.0319110i
$793$	−0.644174			−0.0228753
$794$	−1.91694			−0.0680296
$795$	7.21044			0.255728
$796$			28.0537i			0.994336i
$797$			14.1666i			0.501808i	0.968012	+	0.250904i	$0.0807278\pi$
$797$			14.1666i			0.501808i	−0.968012	+	0.250904i	$0.919272\pi$
$798$	1.52134	+	2.27226i	0.0538547	+	0.0804370i
$799$		−	18.9414i		−	0.670098i
$800$		−	3.52189i		−	0.124518i
$801$			2.80540i			0.0991241i
$802$			3.33151i			0.117640i
$803$	17.7224	−	44.1269i	0.625409	−	1.55721i
$804$			3.20019i			0.112862i
$805$	−2.17348	+	1.45520i	−0.0766052	+	0.0512892i
$806$	0.901783			0.0317640
$807$	−18.1389			−0.638518
$808$			12.4324i			0.437372i
$809$			34.9896i			1.23017i	0.788461	+	0.615084i	$0.210878\pi$
$809$			34.9896i			1.23017i	−0.788461	+	0.615084i	$0.789122\pi$
$810$	−0.335821			−0.0117996
$811$	26.9648			0.946861			0.473431	−	0.880831i	$-0.343015\pi$
$811$	26.9648			0.946861			0.473431	+	0.880831i	$0.343015\pi$
$812$	−16.5281	+	11.0660i	−0.580021	+	0.388340i
$813$		−	12.5051i		−	0.438574i
$814$	−1.48760	−	0.597452i	−0.0521402	−	0.0209407i
$815$			32.2156i			1.12846i
$816$			13.5950i			0.475921i
$817$			35.0762i			1.22716i
$818$		−	3.36965i		−	0.117817i
$819$	1.29413	+	1.93290i	0.0452204	+	0.0675409i
$820$		−	38.0435i		−	1.32854i
$821$		−	16.4514i		−	0.574158i	−0.957907	−	0.287079i	$-0.907316\pi$
$821$		−	16.4514i		−	0.574158i	0.957907	−	0.287079i	$-0.0926843\pi$
$822$	−3.56552			−0.124362
$823$	26.1042			0.909935			0.454967	−	0.890508i	$-0.349651\pi$
$823$	26.1042			0.909935			0.454967	+	0.890508i	$0.349651\pi$
$824$	−3.83436			−0.133576
$825$	5.04362	+	2.02563i	0.175596	+	0.0705234i
$826$	−2.76048	−	4.12303i	−0.0960493	−	0.143458i
$827$			9.87968i			0.343550i	0.985136	+	0.171775i	$0.0549502\pi$
$827$			9.87968i			0.343550i	−0.985136	+	0.171775i	$0.945050\pi$
$828$	−1.06039			−0.0368510
$829$		−	2.53272i		−	0.0879649i	−0.999032	−	0.0439825i	$-0.985995\pi$
$829$		−	2.53272i		−	0.0879649i	0.999032	−	0.0439825i	$-0.0140046\pi$
$830$	−3.42481			−0.118877
$831$	1.51625			0.0525981
$832$	6.33543			0.219642
$833$	9.54107	−	23.1561i	0.330578	−	0.802311i
$834$	1.20578			0.0417527
$835$			26.8051i			0.927630i
$836$	−13.7151	+	34.1491i	−0.474345	+	1.18107i
$837$	−5.59963			−0.193551
$838$	0.650098			0.0224572
$839$		−	52.3036i		−	1.80572i	−0.429932	−	0.902861i	$-0.641463\pi$
$839$		−	52.3036i		−	1.80572i	0.429932	−	0.902861i	$-0.358537\pi$
$840$	2.92843	−	1.96066i	0.101040	−	0.0676493i
$841$	14.3840			0.495999
$842$		−	2.67124i		−	0.0920571i
$843$	−23.2895			−0.802131
$844$		−	15.3259i		−	0.527540i
$845$			22.4166i			0.771155i
$846$	−0.969736			−0.0333402
$847$	−5.03355	+	28.6647i	−0.172955	+	0.984930i
$848$	−14.9443			−0.513188
$849$		−	2.12575i		−	0.0729556i
$850$			1.07398i			0.0368371i
$851$	−1.42293			−0.0487774
$852$			19.9376i			0.683049i
$853$	16.1471			0.552868			0.276434	−	0.961033i	$-0.410847\pi$
$853$	16.1471			0.552868			0.276434	+	0.961033i	$0.410847\pi$
$854$	0.295055	−	0.197547i	0.0100966	−	0.00675993i
$855$			10.3448i			0.353785i
$856$	5.51167			0.188385
$857$	−13.3610			−0.456403			−0.228202	−	0.973614i	$-0.573285\pi$
$857$	−13.3610			−0.456403			−0.228202	+	0.973614i	$0.573285\pi$
$858$	0.199061	−	0.495641i	0.00679582	−	0.0169209i
$859$		−	6.98637i		−	0.238372i	−0.992872	−	0.119186i	$-0.961972\pi$
$859$		−	6.98637i		−	0.238372i	0.992872	−	0.119186i	$-0.0380285\pi$
$860$	22.4115			0.764227
$861$	−23.1993	+	15.5325i	−0.790628	+	0.529347i
$862$	4.71372			0.160550
$863$	−20.1366			−0.685458			−0.342729	−	0.939434i	$-0.611351\pi$
$863$	−20.1366			−0.685458			−0.342729	+	0.939434i	$0.611351\pi$
$864$	2.14910			0.0731140
$865$		−	19.5702i		−	0.665405i
$866$	5.53170			0.187975
$867$			4.19925i			0.142614i
$868$	24.2084	−	16.2082i	0.821687	−	0.550142i
$869$	34.8101	+	13.9805i	1.18085	+	0.474257i
$870$	1.28388			0.0435275
$871$	−1.43079			−0.0484805
$872$	8.15471			0.276153
$873$			13.4654i			0.455735i
$874$		−	0.557333i		−	0.0188521i
$875$	−26.7585	+	17.9155i	−0.904602	+	0.605655i
$876$			28.1944i			0.952599i
$877$			34.7587i			1.17372i	0.809689	+	0.586859i	$0.199636\pi$
$877$			34.7587i			1.17372i	−0.809689	+	0.586859i	$0.800364\pi$
$878$			3.35640i			0.113273i
$879$			13.7761i			0.464657i
$880$	21.4405	+	8.61100i	0.722760	+	0.290277i
$881$		−	28.7780i		−	0.969556i	−0.874637	−	0.484778i	$-0.838900\pi$
$881$		−	28.7780i		−	0.969556i	0.874637	−	0.484778i	$-0.161100\pi$
$882$	−1.18551	−	0.488471i	−0.0399184	−	0.0164477i
$883$	−5.92749			−0.199476			−0.0997380	−	0.995014i	$-0.531800\pi$
$883$	−5.92749			−0.199476			−0.0997380	+	0.995014i	$0.531800\pi$
$884$	−6.18563			−0.208045
$885$		−	18.7707i		−	0.630971i
$886$			1.13464i			0.0381190i
$887$	2.64758			0.0888969			0.0444485	−	0.999012i	$-0.485847\pi$
$887$	2.64758			0.0888969			0.0444485	+	0.999012i	$0.485847\pi$
$888$	1.91718			0.0643363
$889$	5.66673	−	3.79403i	0.190056	−	0.127248i
$890$			0.942115i			0.0315798i
$891$	−1.23607	+	3.07768i	−0.0414098	+	0.103106i
$892$			46.8216i			1.56770i
$893$			29.8722i			0.999635i
$894$			1.04473i			0.0349411i
$895$			33.0091i			1.10337i
$896$	−12.3514	+	8.26962i	−0.412633	+	0.276269i
$897$		−	0.474095i		−	0.0158296i
$898$			5.70049i			0.190228i
$899$	21.4079			0.713993
$900$	−3.22256			−0.107419
$901$	14.0712			0.468779
$902$	5.94884	+	2.38919i	0.198075	+	0.0795514i
$903$	−9.15024	−	13.6667i	−0.304501	−	0.454800i
$904$		−	6.78116i		−	0.225538i
$905$	−24.3221			−0.808494
$906$		−	2.40503i		−	0.0799018i
$907$	−12.1435			−0.403219			−0.201610	−	0.979466i	$-0.564617\pi$
$907$	−12.1435			−0.403219			−0.201610	+	0.979466i	$0.564617\pi$
$908$	7.15563			0.237468
$909$	17.1118			0.567562
$910$	0.434595	+	0.649108i	0.0144067	+	0.0215177i
$911$	−59.7590			−1.97990			−0.989952	−	0.141404i	$-0.954838\pi$
$911$	−59.7590			−1.97990			−0.989952	+	0.141404i	$0.954838\pi$
$912$		−	21.4405i		−	0.709967i
$913$	−12.6058	+	31.3871i	−0.417191	+	1.03876i
$914$	1.45610			0.0481635
$915$	1.34329			0.0444077
$916$		−	0.633367i		−	0.0209270i
$917$	−11.2548	−	16.8101i	−0.371666	−	0.555117i
$918$	−0.655355			−0.0216300
$919$		−	21.0628i		−	0.694798i	−0.937717	−	0.347399i	$-0.887065\pi$
$919$		−	21.0628i		−	0.694798i	0.937717	−	0.347399i	$-0.112935\pi$
$920$	−0.718277			−0.0236809
$921$			32.1099i			1.05806i
$922$		−	1.21269i		−	0.0399378i
$923$	−8.91401			−0.293408
$924$	−3.56460	−	16.8833i	−0.117267	−	0.555420i
$925$	−4.32434			−0.142183
$926$		−	2.01189i		−	0.0661148i
$927$			5.27754i			0.173337i
$928$	−8.21622			−0.269711
$929$			31.8006i			1.04334i	0.853146	+	0.521672i	$0.174691\pi$
$929$			31.8006i			1.04334i	−0.853146	+	0.521672i	$0.825309\pi$
$930$	−1.88047			−0.0616632
$931$	−15.0471	+	36.5192i	−0.493148	+	1.19687i
$932$			50.9882i			1.67017i
$933$	−29.4766			−0.965021
$934$	0.420184			0.0137488
$935$	−20.1879	−	8.10791i	−0.660214	−	0.265157i
$936$			0.638770i			0.0208789i
$937$	40.5711			1.32540			0.662699	−	0.748886i	$-0.269411\pi$
$937$	40.5711			1.32540			0.662699	+	0.748886i	$0.269411\pi$
$938$	0.655355	−	0.438778i	0.0213981	−	0.0143266i
$939$	13.9329			0.454683
$940$	19.0865			0.622532
$941$	−36.6392			−1.19440			−0.597202	−	0.802091i	$-0.703721\pi$
$941$	−36.6392			−1.19440			−0.597202	+	0.802091i	$0.703721\pi$
$942$			4.11295i			0.134007i
$943$	5.69025			0.185300
$944$			38.9040i			1.26622i
$945$	−2.69862	−	4.03064i	−0.0877861	−	0.131117i
$946$	−1.40748	+	3.50448i	−0.0457610	+	0.113940i
$947$	−42.1814			−1.37071			−0.685355	−	0.728209i	$-0.740353\pi$
$947$	−42.1814			−1.37071			−0.685355	+	0.728209i	$0.740353\pi$
$948$	−22.2415			−0.722369
$949$	−12.6056			−0.409195
$950$		−	1.69375i		−	0.0549526i
$951$		−	26.3869i		−	0.855655i
$952$	5.71483	−	3.82623i	0.185219	−	0.124009i
$953$		−	14.1313i		−	0.457756i	−0.973455	−	0.228878i	$-0.926494\pi$
$953$		−	14.1313i		−	0.457756i	0.973455	−	0.228878i	$-0.0735057\pi$
$954$		−	0.720397i		−	0.0233237i
$955$		−	17.9977i		−	0.582393i
$956$			31.2460i			1.01057i
$957$	4.72560	−	11.7663i	0.152757	−	0.380349i
$958$		−	6.61993i		−	0.213880i
$959$	−28.6521	−	42.7946i	−0.925225	−	1.38191i
$960$	−13.2112			−0.426389
$961$	−0.355826			−0.0114783
$962$			0.424957i			0.0137011i
$963$		−	7.58616i		−	0.244461i
$964$	−13.3069			−0.428587
$965$	43.3716			1.39618
$966$	0.145390	+	0.217153i	0.00467784	+	0.00698679i
$967$		−	53.3978i		−	1.71716i	−0.512682	−	0.858579i	$-0.671348\pi$
$967$		−	53.3978i		−	1.71716i	0.512682	−	0.858579i	$-0.328652\pi$
$968$	−5.52786	+	5.77185i	−0.177672	+	0.185514i
$969$			20.1879i			0.648528i
$970$			4.52198i			0.145192i
$971$		−	2.84940i		−	0.0914416i	−0.998954	−	0.0457208i	$-0.985442\pi$
$971$		−	2.84940i		−	0.0914416i	0.998954	−	0.0457208i	$-0.0145585\pi$
$972$		−	1.96645i		−	0.0630738i
$973$	9.68948	+	14.4721i	0.310631	+	0.463955i
$974$			0.832728i			0.0266823i
$975$		−	1.44079i		−	0.0461423i
$976$	−2.78408			−0.0891162
$977$	11.8680			0.379692			0.189846	−	0.981814i	$-0.439201\pi$
$977$	11.8680			0.379692			0.189846	+	0.981814i	$0.439201\pi$
$978$	3.21867			0.102922
$979$	8.63415	+	3.46767i	0.275949	+	0.110827i
$980$	23.3335	+	9.61415i	0.745360	+	0.307113i
$981$		−	11.2240i		−	0.358355i
$982$	3.32247			0.106024
$983$		−	13.4766i		−	0.429837i	−0.976632	−	0.214918i	$-0.931051\pi$
$983$		−	13.4766i		−	0.429837i	0.976632	−	0.214918i	$-0.0689486\pi$
$984$	−7.66673			−0.244406
$985$	−31.4149			−1.00096
$986$	2.50548			0.0797908
$987$	−7.79268	−	11.6391i	−0.248044	−	0.370476i
$988$	9.75527			0.310356
$989$			3.35214i			0.106592i
$990$	−0.415098	+	1.03355i	−0.0131927	+	0.0328484i
$991$	25.6922			0.816141			0.408071	−	0.912950i	$-0.366202\pi$
$991$	25.6922			0.816141			0.408071	+	0.912950i	$0.366202\pi$
$992$	12.0342			0.382086
$993$		−	14.7873i		−	0.469261i
$994$	4.08295	−	2.73364i	0.129503	−	0.0867058i
$995$	26.1551			0.829172
$996$		−	20.0544i		−	0.635449i
$997$	−13.7007			−0.433904			−0.216952	−	0.976182i	$-0.569612\pi$
$997$	−13.7007			−0.433904			−0.216952	+	0.976182i	$0.569612\pi$
$998$			2.78104i			0.0880323i
$999$		−	2.63877i		−	0.0834870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.c.a.76.7	✓	16
3.2	odd	2		693.2.c.e.307.10		16
4.3	odd	2		3696.2.q.e.769.12		16
7.6	odd	2	inner	231.2.c.a.76.8	yes	16
11.10	odd	2	inner	231.2.c.a.76.9	yes	16
21.20	even	2		693.2.c.e.307.9		16
28.27	even	2		3696.2.q.e.769.5		16
33.32	even	2		693.2.c.e.307.8		16
44.43	even	2		3696.2.q.e.769.11		16
77.76	even	2	inner	231.2.c.a.76.10	yes	16
231.230	odd	2		693.2.c.e.307.7		16
308.307	odd	2		3696.2.q.e.769.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.c.a.76.7	✓	16	1.1	even	1	trivial
231.2.c.a.76.8	yes	16	7.6	odd	2	inner
231.2.c.a.76.9	yes	16	11.10	odd	2	inner
231.2.c.a.76.10	yes	16	77.76	even	2	inner
693.2.c.e.307.7		16	231.230	odd	2
693.2.c.e.307.8		16	33.32	even	2
693.2.c.e.307.9		16	21.20	even	2
693.2.c.e.307.10		16	3.2	odd	2
3696.2.q.e.769.5		16	28.27	even	2
3696.2.q.e.769.6		16	308.307	odd	2
3696.2.q.e.769.11		16	44.43	even	2
3696.2.q.e.769.12		16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.183172i q^{2} -1.00000i q^{3} +1.96645 q^{4} -1.83337i q^{5} -0.183172 q^{6} +(-1.47195 - 2.19849i) q^{7} -0.726543i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.183172i q^{2} -1.00000i q^{3} +1.96645 q^{4} -1.83337i q^{5} -0.183172 q^{6} +(-1.47195 - 2.19849i) q^{7} -0.726543i q^{8} -1.00000 q^{9} -0.335821 q^{10} +(-1.23607 + 3.07768i) q^{11} -1.96645i q^{12} +0.879192 q^{13} +(-0.402702 + 0.269620i) q^{14} -1.83337 q^{15} +3.79981 q^{16} -3.57781 q^{17} +0.183172i q^{18} +5.64252 q^{19} -3.60522i q^{20} +(-2.19849 + 1.47195i) q^{21} +(0.563746 + 0.226413i) q^{22} +0.539240 q^{23} -0.726543 q^{24} +1.63877 q^{25} -0.161043i q^{26} +1.00000i q^{27} +(-2.89451 - 4.32322i) q^{28} -3.82309i q^{29} +0.335821i q^{30} +5.59963i q^{31} -2.14910i q^{32} +(3.07768 + 1.23607i) q^{33} +0.655355i q^{34} +(-4.03064 + 2.69862i) q^{35} -1.96645 q^{36} -2.63877 q^{37} -1.03355i q^{38} -0.879192i q^{39} -1.33202 q^{40} +10.5524 q^{41} +(0.269620 + 0.402702i) q^{42} +6.21641i q^{43} +(-2.43066 + 6.05210i) q^{44} +1.83337i q^{45} -0.0987737i q^{46} +5.29413i q^{47} -3.79981i q^{48} +(-2.66673 + 6.47214i) q^{49} -0.300177i q^{50} +3.57781i q^{51} +1.72889 q^{52} -3.93290 q^{53} +0.183172 q^{54} +(5.64252 + 2.26616i) q^{55} +(-1.59730 + 1.06943i) q^{56} -5.64252i q^{57} -0.700283 q^{58} +10.2384i q^{59} -3.60522 q^{60} -0.732688 q^{61} +1.02570 q^{62} +(1.47195 + 2.19849i) q^{63} +7.20597 q^{64} -1.61188i q^{65} +(0.226413 - 0.563746i) q^{66} -1.62739 q^{67} -7.03558 q^{68} -0.539240i q^{69} +(0.494312 + 0.738301i) q^{70} -10.1389 q^{71} +0.726543i q^{72} -14.3377 q^{73} +0.483349i q^{74} -1.63877i q^{75} +11.0957 q^{76} +(8.58569 - 1.81271i) q^{77} -0.161043 q^{78} -11.3105i q^{79} -6.96645i q^{80} +1.00000 q^{81} -1.93290i q^{82} +10.1983 q^{83} +(-4.32322 + 2.89451i) q^{84} +6.55944i q^{85} +1.13867 q^{86} -3.82309 q^{87} +(2.23607 + 0.898056i) q^{88} -2.80540i q^{89} +0.335821 q^{90} +(-1.29413 - 1.93290i) q^{91} +1.06039 q^{92} +5.59963 q^{93} +0.969736 q^{94} -10.3448i q^{95} -2.14910 q^{96} -13.4654i q^{97} +(1.18551 + 0.488471i) q^{98} +(1.23607 - 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4} - 16 q^{9}+O(q^{10}) \) 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

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Database

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