LMFDB - Embedded newform 1155.2.c.f.694.12

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} + 15210 x^{12} + 40640 x^{10} + 63865 x^{8} + 55281 x^{6} + \cdots + 4 $ x^20 + 33x^18 + 456x^16 + 3426x^14 + 15210x^12 + 40640x^10 + 63865x^8 + 55281x^6 + 22984x^4 + 3428*x^2 + 4
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			694.12
Root			$0.568210i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.f.694.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.568210i q^{2} +1.00000i q^{3} +1.67714 q^{4} +(1.08688 + 1.95415i) q^{5} -0.568210 q^{6} +1.00000i q^{7} +2.08939i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+0.568210i q^{2} +1.00000i q^{3} +1.67714 q^{4} +(1.08688 + 1.95415i) q^{5} -0.568210 q^{6} +1.00000i q^{7} +2.08939i q^{8} -1.00000 q^{9} +(-1.11037 + 0.617578i) q^{10} +1.00000 q^{11} +1.67714i q^{12} -4.29449i q^{13} -0.568210 q^{14} +(-1.95415 + 1.08688i) q^{15} +2.16706 q^{16} +6.71715i q^{17} -0.568210i q^{18} +4.32394 q^{19} +(1.82285 + 3.27737i) q^{20} -1.00000 q^{21} +0.568210i q^{22} -1.44198i q^{23} -2.08939 q^{24} +(-2.63738 + 4.24785i) q^{25} +2.44018 q^{26} -1.00000i q^{27} +1.67714i q^{28} -2.91660 q^{29} +(-0.617578 - 1.11037i) q^{30} -3.49098 q^{31} +5.41012i q^{32} +1.00000i q^{33} -3.81675 q^{34} +(-1.95415 + 1.08688i) q^{35} -1.67714 q^{36} -4.94242i q^{37} +2.45691i q^{38} +4.29449 q^{39} +(-4.08297 + 2.27092i) q^{40} +3.95634 q^{41} -0.568210i q^{42} +6.03102i q^{43} +1.67714 q^{44} +(-1.08688 - 1.95415i) q^{45} +0.819349 q^{46} -2.12631i q^{47} +2.16706i q^{48} -1.00000 q^{49} +(-2.41367 - 1.49858i) q^{50} -6.71715 q^{51} -7.20245i q^{52} -11.9318i q^{53} +0.568210 q^{54} +(1.08688 + 1.95415i) q^{55} -2.08939 q^{56} +4.32394i q^{57} -1.65725i q^{58} -2.84709 q^{59} +(-3.27737 + 1.82285i) q^{60} +0.0957071 q^{61} -1.98361i q^{62} -1.00000i q^{63} +1.26004 q^{64} +(8.39207 - 4.66761i) q^{65} -0.568210 q^{66} -11.3006i q^{67} +11.2656i q^{68} +1.44198 q^{69} +(-0.617578 - 1.11037i) q^{70} -0.0842254 q^{71} -2.08939i q^{72} -0.741211i q^{73} +2.80834 q^{74} +(-4.24785 - 2.63738i) q^{75} +7.25184 q^{76} +1.00000i q^{77} +2.44018i q^{78} -13.6518 q^{79} +(2.35534 + 4.23476i) q^{80} +1.00000 q^{81} +2.24803i q^{82} +17.6251i q^{83} -1.67714 q^{84} +(-13.1263 + 7.30075i) q^{85} -3.42689 q^{86} -2.91660i q^{87} +2.08939i q^{88} +15.6046 q^{89} +(1.11037 - 0.617578i) q^{90} +4.29449 q^{91} -2.41840i q^{92} -3.49098i q^{93} +1.20819 q^{94} +(4.69961 + 8.44961i) q^{95} -5.41012 q^{96} +7.99194i q^{97} -0.568210i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 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 - 34 * q^19 + 4 * q^20 - 20 * q^21 - 18 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^29 - 6 * q^30 + 12 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 - 2 * q^40 + 52 * q^41 - 26 * q^44 + 2 * q^45 + 40 * q^46 - 20 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^54 - 2 * q^55 - 18 * q^56 - 14 * q^59 - 28 * q^60 + 78 * q^61 - 26 * q^64 - 4 * q^65 + 6 * q^66 - 18 * q^69 - 6 * q^70 - 8 * q^74 - 8 * q^75 + 84 * q^76 - 52 * q^79 - 40 * q^80 + 20 * q^81 + 26 * q^84 - 24 * q^85 + 4 * q^86 - 10 * q^89 - 2 * q^90 - 96 * q^94 - 30 * 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 $

$2$			0.568210i			0.401785i	0.979613	+	0.200893i	$0.0643843\pi$
$2$			0.568210i			0.401785i	−0.979613	+	0.200893i	$0.935616\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.67714			0.838569
$5$	1.08688	+	1.95415i	0.486068	+	0.873921i
$5$	1.08688	+	1.95415i	0.486068	+	0.873921i
$6$	−0.568210			−0.231971
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			2.08939i			0.738710i
$9$	−1.00000			−0.333333
$10$	−1.11037	+	0.617578i	−0.351129	+	0.195295i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$			1.67714i			0.484148i
$13$		−	4.29449i		−	1.19108i	−0.803326	−	0.595539i	$-0.796938\pi$
$13$		−	4.29449i		−	1.19108i	0.803326	−	0.595539i	$-0.203062\pi$
$14$	−0.568210			−0.151861
$15$	−1.95415	+	1.08688i	−0.504558	+	0.280632i
$16$	2.16706			0.541766
$17$			6.71715i			1.62915i	0.580060	+	0.814574i	$0.303029\pi$
$17$			6.71715i			1.62915i	−0.580060	+	0.814574i	$0.696971\pi$
$18$		−	0.568210i		−	0.133928i
$19$	4.32394			0.991980			0.495990	−	0.868328i	$-0.334805\pi$
$19$	4.32394			0.991980			0.495990	+	0.868328i	$0.334805\pi$
$20$	1.82285	+	3.27737i	0.407602	+	0.732842i
$21$	−1.00000			−0.218218
$22$			0.568210i			0.121143i
$23$		−	1.44198i		−	0.300674i	−0.988635	−	0.150337i	$-0.951964\pi$
$23$		−	1.44198i		−	0.300674i	0.988635	−	0.150337i	$-0.0480359\pi$
$24$	−2.08939			−0.426494
$25$	−2.63738	+	4.24785i	−0.527475	+	0.849571i
$26$	2.44018			0.478558
$27$		−	1.00000i		−	0.192450i
$28$			1.67714i			0.316949i
$29$	−2.91660			−0.541600			−0.270800	−	0.962636i	$-0.587288\pi$
$29$	−2.91660			−0.541600			−0.270800	+	0.962636i	$0.587288\pi$
$30$	−0.617578	−	1.11037i	−0.112754	−	0.202724i
$31$	−3.49098			−0.626999			−0.313499	−	0.949588i	$-0.601501\pi$
$31$	−3.49098			−0.626999			−0.313499	+	0.949588i	$0.601501\pi$
$32$			5.41012i			0.956383i
$33$			1.00000i			0.174078i
$34$	−3.81675			−0.654568
$35$	−1.95415	+	1.08688i	−0.330311	+	0.183717i
$36$	−1.67714			−0.279523
$37$		−	4.94242i		−	0.812529i	−0.913755	−	0.406265i	$-0.866831\pi$
$37$		−	4.94242i		−	0.812529i	0.913755	−	0.406265i	$-0.133169\pi$
$38$			2.45691i			0.398563i
$39$	4.29449			0.687669
$40$	−4.08297	+	2.27092i	−0.645574	+	0.359064i
$41$	3.95634			0.617877			0.308938	−	0.951082i	$-0.400026\pi$
$41$	3.95634			0.617877			0.308938	+	0.951082i	$0.400026\pi$
$42$		−	0.568210i		−	0.0876768i
$43$			6.03102i			0.919722i	0.887991	+	0.459861i	$0.152101\pi$
$43$			6.03102i			0.919722i	−0.887991	+	0.459861i	$0.847899\pi$
$44$	1.67714			0.252838
$45$	−1.08688	−	1.95415i	−0.162023	−	0.291307i
$46$	0.819349			0.120806
$47$		−	2.12631i		−	0.310155i	−0.987902	−	0.155077i	$-0.950437\pi$
$47$		−	2.12631i		−	0.310155i	0.987902	−	0.155077i	$-0.0495627\pi$
$48$			2.16706i			0.312789i
$49$	−1.00000			−0.142857
$50$	−2.41367	−	1.49858i	−0.341345	−	0.211932i
$51$	−6.71715			−0.940589
$52$		−	7.20245i		−	0.998801i
$53$		−	11.9318i		−	1.63896i	−0.573106	−	0.819481i	$-0.694262\pi$
$53$		−	11.9318i		−	1.63896i	0.573106	−	0.819481i	$-0.305738\pi$
$54$	0.568210			0.0773236
$55$	1.08688	+	1.95415i	0.146555	+	0.263497i
$56$	−2.08939			−0.279206
$57$			4.32394i			0.572720i
$58$		−	1.65725i		−	0.217607i
$59$	−2.84709			−0.370659			−0.185330	−	0.982676i	$-0.559335\pi$
$59$	−2.84709			−0.370659			−0.185330	+	0.982676i	$0.559335\pi$
$60$	−3.27737	+	1.82285i	−0.423107	+	0.235329i
$61$	0.0957071			0.0122540			0.00612702	−	0.999981i	$-0.498050\pi$
$61$	0.0957071			0.0122540			0.00612702	+	0.999981i	$0.498050\pi$
$62$		−	1.98361i		−	0.251919i
$63$		−	1.00000i		−	0.125988i
$64$	1.26004			0.157505
$65$	8.39207	−	4.66761i	1.04091	−	0.578946i
$66$	−0.568210			−0.0699419
$67$		−	11.3006i		−	1.38058i	−0.723531	−	0.690292i	$-0.757482\pi$
$67$		−	11.3006i		−	1.38058i	0.723531	−	0.690292i	$-0.242518\pi$
$68$			11.2656i			1.36615i
$69$	1.44198			0.173594
$70$	−0.617578	−	1.11037i	−0.0738146	−	0.132714i
$71$	−0.0842254			−0.00999572			−0.00499786	−	0.999988i	$-0.501591\pi$
$71$	−0.0842254			−0.00999572			−0.00499786	+	0.999988i	$0.501591\pi$
$72$		−	2.08939i		−	0.246237i
$73$		−	0.741211i		−	0.0867522i	−0.999059	−	0.0433761i	$-0.986189\pi$
$73$		−	0.741211i		−	0.0867522i	0.999059	−	0.0433761i	$-0.0138114\pi$
$74$	2.80834			0.326462
$75$	−4.24785	−	2.63738i	−0.490500	−	0.304538i
$76$	7.25184			0.831843
$77$			1.00000i			0.113961i
$78$			2.44018i			0.276296i
$79$	−13.6518			−1.53594			−0.767972	−	0.640483i	$-0.778734\pi$
$79$	−13.6518			−1.53594			−0.767972	+	0.640483i	$0.778734\pi$
$80$	2.35534	+	4.23476i	0.263335	+	0.473460i
$81$	1.00000			0.111111
$82$			2.24803i			0.248254i
$83$			17.6251i			1.93460i	0.253629	+	0.967301i	$0.418376\pi$
$83$			17.6251i			1.93460i	−0.253629	+	0.967301i	$0.581624\pi$
$84$	−1.67714			−0.182991
$85$	−13.1263	+	7.30075i	−1.42375	+	0.791877i
$86$	−3.42689			−0.369531
$87$		−	2.91660i		−	0.312693i
$88$			2.08939i			0.222729i
$89$	15.6046			1.65409			0.827044	−	0.562137i	$-0.190021\pi$
$89$	15.6046			1.65409			0.827044	+	0.562137i	$0.190021\pi$
$90$	1.11037	−	0.617578i	0.117043	−	0.0650984i
$91$	4.29449			0.450185
$92$		−	2.41840i		−	0.252136i
$93$		−	3.49098i		−	0.361998i
$94$	1.20819			0.124616
$95$	4.69961	+	8.44961i	0.482170	+	0.866912i
$96$	−5.41012			−0.552168
$97$			7.99194i			0.811459i	0.913993	+	0.405729i	$0.132982\pi$
$97$			7.99194i			0.811459i	−0.913993	+	0.405729i	$0.867018\pi$
$98$		−	0.568210i		−	0.0573979i
$99$	−1.00000			−0.100504
$100$	−4.42324	+	7.12423i	−0.442324	+	0.712423i
$101$	2.15535			0.214465			0.107233	−	0.994234i	$-0.465801\pi$
$101$	2.15535			0.214465			0.107233	+	0.994234i	$0.465801\pi$
$102$		−	3.81675i		−	0.377915i
$103$		−	14.7669i		−	1.45503i	−0.686093	−	0.727514i	$-0.740676\pi$
$103$		−	14.7669i		−	1.45503i	0.686093	−	0.727514i	$-0.259324\pi$
$104$	8.97286			0.879861
$105$	−1.08688	−	1.95415i	−0.106069	−	0.190705i
$106$	6.77979			0.658511
$107$		−	4.20683i		−	0.406689i	−0.979107	−	0.203345i	$-0.934819\pi$
$107$		−	4.20683i		−	0.406689i	0.979107	−	0.203345i	$-0.0651812\pi$
$108$		−	1.67714i		−	0.161383i
$109$	−12.8803			−1.23371			−0.616855	−	0.787076i	$-0.711594\pi$
$109$	−12.8803			−1.23371			−0.616855	+	0.787076i	$0.711594\pi$
$110$	−1.11037	+	0.617578i	−0.105869	+	0.0588837i
$111$	4.94242			0.469114
$112$			2.16706i			0.204768i
$113$			3.47264i			0.326679i	0.986570	+	0.163339i	$0.0522265\pi$
$113$			3.47264i			0.326679i	−0.986570	+	0.163339i	$0.947773\pi$
$114$	−2.45691			−0.230110
$115$	2.81784	−	1.56726i	0.262765	−	0.146148i
$116$	−4.89155			−0.454169
$117$			4.29449i			0.397026i
$118$		−	1.61774i		−	0.148925i
$119$	−6.71715			−0.615760
$120$	−2.27092	−	4.08297i	−0.207305	−	0.372722i
$121$	1.00000			0.0909091
$122$			0.0543818i			0.00492349i
$123$			3.95634i			0.356731i
$124$	−5.85485			−0.525781
$125$	−11.1674	−	0.536902i	−0.998846	−	0.0480220i
$126$	0.568210			0.0506202
$127$		−	17.5676i		−	1.55888i	−0.626479	−	0.779438i	$-0.715505\pi$
$127$		−	17.5676i		−	1.55888i	0.626479	−	0.779438i	$-0.284495\pi$
$128$			11.5362i			1.01967i
$129$	−6.03102			−0.531002
$130$	2.65218	+	4.76846i	0.232612	+	0.418222i
$131$	5.58466			0.487934			0.243967	−	0.969783i	$-0.421551\pi$
$131$	5.58466			0.487934			0.243967	+	0.969783i	$0.421551\pi$
$132$			1.67714i			0.145976i
$133$			4.32394i			0.374933i
$134$	6.42109			0.554698
$135$	1.95415	−	1.08688i	0.168186	−	0.0935439i
$136$	−14.0347			−1.20347
$137$			7.65615i			0.654109i	0.945005	+	0.327054i	$0.106056\pi$
$137$			7.65615i			0.654109i	−0.945005	+	0.327054i	$0.893944\pi$
$138$			0.819349i			0.0697476i
$139$	8.89291			0.754287			0.377143	−	0.926155i	$-0.376906\pi$
$139$	8.89291			0.754287			0.377143	+	0.926155i	$0.376906\pi$
$140$	−3.27737	+	1.82285i	−0.276988	+	0.154059i
$141$	2.12631			0.179068
$142$		−	0.0478578i		−	0.00401613i
$143$		−	4.29449i		−	0.359124i
$144$	−2.16706			−0.180589
$145$	−3.17001	−	5.69947i	−0.263255	−	0.473315i
$146$	0.421164			0.0348558
$147$		−	1.00000i		−	0.0824786i
$148$		−	8.28912i		−	0.681361i
$149$	−21.0244			−1.72239			−0.861193	−	0.508279i	$-0.830282\pi$
$149$	−21.0244			−1.72239			−0.861193	+	0.508279i	$0.830282\pi$
$150$	1.49858	−	2.41367i	0.122359	−	0.197076i
$151$	12.3892			1.00822			0.504108	−	0.863641i	$-0.331821\pi$
$151$	12.3892			1.00822			0.504108	+	0.863641i	$0.331821\pi$
$152$			9.03438i			0.732785i
$153$		−	6.71715i		−	0.543049i
$154$	−0.568210			−0.0457877
$155$	−3.79428	−	6.82189i	−0.304764	−	0.547947i
$156$	7.20245			0.576658
$157$			9.62438i			0.768109i	0.923310	+	0.384055i	$0.125473\pi$
$157$			9.62438i			0.768109i	−0.923310	+	0.384055i	$0.874527\pi$
$158$		−	7.75708i		−	0.617120i
$159$	11.9318			0.946256
$160$	−10.5722	+	5.88016i	−0.835803	+	0.464868i
$161$	1.44198			0.113644
$162$			0.568210i			0.0446428i
$163$		−	17.6354i		−	1.38131i	−0.723185	−	0.690655i	$-0.757322\pi$
$163$		−	17.6354i		−	1.38131i	0.723185	−	0.690655i	$-0.242678\pi$
$164$	6.63533			0.518132
$165$	−1.95415	+	1.08688i	−0.152130	+	0.0846136i
$166$	−10.0147			−0.777295
$167$			15.7103i			1.21570i	0.794051	+	0.607851i	$0.207968\pi$
$167$			15.7103i			1.21570i	−0.794051	+	0.607851i	$0.792032\pi$
$168$		−	2.08939i		−	0.161200i
$169$	−5.44268			−0.418668
$170$	−4.14836	−	7.45849i	−0.318165	−	0.572040i
$171$	−4.32394			−0.330660
$172$			10.1148i			0.771250i
$173$		−	12.8955i		−	0.980427i	−0.871602	−	0.490214i	$-0.836919\pi$
$173$		−	12.8955i		−	0.980427i	0.871602	−	0.490214i	$-0.163081\pi$
$174$	1.65725			0.125635
$175$	−4.24785	−	2.63738i	−0.321107	−	0.199367i
$176$	2.16706			0.163348
$177$		−	2.84709i		−	0.214000i
$178$			8.86672i			0.664588i
$179$	10.5794			0.790745			0.395373	−	0.918521i	$-0.370615\pi$
$179$	10.5794			0.790745			0.395373	+	0.918521i	$0.370615\pi$
$180$	−1.82285	−	3.27737i	−0.135867	−	0.244281i
$181$	10.1821			0.756829			0.378414	−	0.925636i	$-0.376469\pi$
$181$	10.1821			0.756829			0.378414	+	0.925636i	$0.376469\pi$
$182$			2.44018i			0.180878i
$183$			0.0957071i			0.00707487i
$184$	3.01286			0.222111
$185$	9.65822	−	5.37183i	0.710086	−	0.394945i
$186$	1.98361			0.145445
$187$			6.71715i			0.491206i
$188$		−	3.56612i		−	0.260086i
$189$	1.00000			0.0727393
$190$	−4.80116	+	2.67037i	−0.348312	+	0.193729i
$191$	25.1437			1.81933			0.909666	−	0.415340i	$-0.136337\pi$
$191$	25.1437			1.81933			0.909666	+	0.415340i	$0.136337\pi$
$192$			1.26004i			0.0909354i
$193$			15.6737i			1.12822i	0.825700	+	0.564109i	$0.190780\pi$
$193$			15.6737i			1.12822i	−0.825700	+	0.564109i	$0.809220\pi$
$194$	−4.54110			−0.326032
$195$	4.66761	+	8.39207i	0.334254	+	0.600969i
$196$	−1.67714			−0.119796
$197$		−	7.89608i		−	0.562572i	−0.959624	−	0.281286i	$-0.909239\pi$
$197$		−	7.89608i		−	0.562572i	0.959624	−	0.281286i	$-0.0907610\pi$
$198$		−	0.568210i		−	0.0403810i
$199$	23.1995			1.64457			0.822286	−	0.569074i	$-0.192698\pi$
$199$	23.1995			1.64457			0.822286	+	0.569074i	$0.192698\pi$
$200$	−8.87541	−	5.51050i	−0.627586	−	0.389651i
$201$	11.3006			0.797080
$202$			1.22469i			0.0861691i
$203$		−	2.91660i		−	0.204706i
$204$	−11.2656			−0.788748
$205$	4.30008	+	7.73127i	0.300330	+	0.539975i
$206$	8.39071			0.584609
$207$			1.44198i			0.100225i
$208$		−	9.30644i		−	0.645285i
$209$	4.32394			0.299093
$210$	1.11037	−	0.617578i	0.0766225	−	0.0426169i
$211$	−0.000165629	0		−1.14024e−5	0		−5.70120e−6	−	1.00000i	$-0.500002\pi$
$211$	−0.000165629	0		−1.14024e−5	0		−5.70120e−6		1.00000i	$0.500002\pi$
$212$		−	20.0113i		−	1.37438i
$213$		−	0.0842254i		−	0.00577103i
$214$	2.39036			0.163402
$215$	−11.7855	+	6.55501i	−0.803764	+	0.447048i
$216$	2.08939			0.142165
$217$		−	3.49098i		−	0.236983i
$218$		−	7.31873i		−	0.495687i
$219$	0.741211			0.0500864
$220$	1.82285	+	3.27737i	0.122897	+	0.220960i
$221$	28.8467			1.94044
$222$			2.80834i			0.188483i
$223$		−	10.0823i		−	0.675160i	−0.941297	−	0.337580i	$-0.890392\pi$
$223$		−	10.0823i		−	0.675160i	0.941297	−	0.337580i	$-0.109608\pi$
$224$	−5.41012			−0.361479
$225$	2.63738	−	4.24785i	0.175825	−	0.283190i
$226$	−1.97319			−0.131255
$227$		−	20.7750i		−	1.37889i	−0.724339	−	0.689444i	$-0.757855\pi$
$227$		−	20.7750i		−	1.37889i	0.724339	−	0.689444i	$-0.242145\pi$
$228$			7.25184i			0.480265i
$229$	−26.3609			−1.74197			−0.870987	−	0.491305i	$-0.836520\pi$
$229$	−26.3609			−1.74197			−0.870987	+	0.491305i	$0.836520\pi$
$230$	0.890536	+	1.60113i	0.0587202	+	0.105575i
$231$	−1.00000			−0.0657952
$232$		−	6.09392i		−	0.400085i
$233$		−	1.46351i		−	0.0958780i	−0.998850	−	0.0479390i	$-0.984735\pi$
$233$		−	1.46351i		−	0.0958780i	0.998850	−	0.0479390i	$-0.0152653\pi$
$234$	−2.44018			−0.159519
$235$	4.15513	−	2.31105i	0.271051	−	0.150756i
$236$	−4.77496			−0.310823
$237$		−	13.6518i		−	0.886778i
$238$		−	3.81675i		−	0.247403i
$239$	8.43462			0.545590			0.272795	−	0.962072i	$-0.412052\pi$
$239$	8.43462			0.545590			0.272795	+	0.962072i	$0.412052\pi$
$240$	−4.23476	+	2.35534i	−0.273352	+	0.152037i
$241$	22.5350			1.45161			0.725803	−	0.687903i	$-0.241468\pi$
$241$	22.5350			1.45161			0.725803	+	0.687903i	$0.241468\pi$
$242$			0.568210i			0.0365259i
$243$			1.00000i			0.0641500i
$244$	0.160514			0.0102759
$245$	−1.08688	−	1.95415i	−0.0694383	−	0.124846i
$246$	−2.24803			−0.143329
$247$		−	18.5691i		−	1.18153i
$248$		−	7.29401i		−	0.463170i
$249$	−17.6251			−1.11694
$250$	0.305074	−	6.34546i	0.0192945	−	0.401322i
$251$	11.6291			0.734024			0.367012	−	0.930216i	$-0.380381\pi$
$251$	11.6291			0.734024			0.367012	+	0.930216i	$0.380381\pi$
$252$		−	1.67714i		−	0.105650i
$253$		−	1.44198i		−	0.0906566i
$254$	9.98212			0.626334
$255$	−7.30075	−	13.1263i	−0.457190	−	0.822000i
$256$	−4.03492			−0.252182
$257$			0.174409i			0.0108793i	0.999985	+	0.00543966i	$0.00173151\pi$
$257$			0.174409i			0.0108793i	−0.999985	+	0.00543966i	$0.998268\pi$
$258$		−	3.42689i		−	0.213349i
$259$	4.94242			0.307107
$260$	14.0746	−	7.82822i	0.872873	−	0.485485i
$261$	2.91660			0.180533
$262$			3.17326i			0.196045i
$263$		−	15.6380i		−	0.964279i	−0.876095	−	0.482139i	$-0.839860\pi$
$263$		−	15.6380i		−	0.964279i	0.876095	−	0.482139i	$-0.160140\pi$
$264$	−2.08939			−0.128593
$265$	23.3165	−	12.9685i	1.43232	−	0.796648i
$266$	−2.45691			−0.150643
$267$			15.6046i			0.954988i
$268$		−	18.9526i		−	1.15771i
$269$	−19.6732			−1.19949			−0.599747	−	0.800190i	$-0.704732\pi$
$269$	−19.6732			−1.19949			−0.599747	+	0.800190i	$0.704732\pi$
$270$	0.617578	+	1.11037i	0.0375846	+	0.0675747i
$271$	24.7767			1.50508			0.752540	−	0.658547i	$-0.228829\pi$
$271$	24.7767			1.50508			0.752540	+	0.658547i	$0.228829\pi$
$272$			14.5565i			0.882616i
$273$			4.29449i			0.259915i
$274$	−4.35030			−0.262811
$275$	−2.63738	+	4.24785i	−0.159040	+	0.256155i
$276$	2.41840			0.145571
$277$			18.7968i			1.12939i	0.825300	+	0.564695i	$0.191006\pi$
$277$			18.7968i			1.12939i	−0.825300	+	0.564695i	$0.808994\pi$
$278$			5.05304i			0.303061i
$279$	3.49098			0.209000
$280$	−2.27092	−	4.08297i	−0.135713	−	0.244004i
$281$	4.07551			0.243124			0.121562	−	0.992584i	$-0.461210\pi$
$281$	4.07551			0.243124			0.121562	+	0.992584i	$0.461210\pi$
$282$			1.20819i			0.0719468i
$283$		−	3.45803i		−	0.205559i	−0.994704	−	0.102779i	$-0.967226\pi$
$283$		−	3.45803i		−	0.205559i	0.994704	−	0.102779i	$-0.0327736\pi$
$284$	−0.141258			−0.00838209
$285$	−8.44961	+	4.69961i	−0.500512	+	0.278381i
$286$	2.44018			0.144291
$287$			3.95634i			0.233535i
$288$		−	5.41012i		−	0.318794i
$289$	−28.1201			−1.65412
$290$	3.23850	−	1.80123i	0.190171	−	0.105772i
$291$	−7.99194			−0.468496
$292$		−	1.24311i		−	0.0727477i
$293$			18.9700i			1.10824i	0.832438	+	0.554118i	$0.186945\pi$
$293$			18.9700i			1.10824i	−0.832438	+	0.554118i	$0.813055\pi$
$294$	0.568210			0.0331387
$295$	−3.09445	−	5.56362i	−0.180166	−	0.323927i
$296$	10.3266			0.600223
$297$		−	1.00000i		−	0.0580259i
$298$		−	11.9463i		−	0.692029i
$299$	−6.19258			−0.358126
$300$	−7.12423	−	4.42324i	−0.411318	−	0.255376i
$301$	−6.03102			−0.347622
$302$			7.03965i			0.405086i
$303$			2.15535i			0.123822i
$304$	9.37025			0.537421
$305$	0.104022	+	0.187026i	0.00595630	+	0.0107091i
$306$	3.81675			0.218189
$307$		−	9.80079i		−	0.559361i	−0.960093	−	0.279680i	$-0.909772\pi$
$307$		−	9.80079i		−	0.559361i	0.960093	−	0.279680i	$-0.0902285\pi$
$308$			1.67714i			0.0955638i
$309$	14.7669			0.840061
$310$	3.87627	−	2.15595i	0.220157	−	0.122450i
$311$	3.62724			0.205682			0.102841	−	0.994698i	$-0.467207\pi$
$311$	3.62724			0.205682			0.102841	+	0.994698i	$0.467207\pi$
$312$			8.97286i			0.507988i
$313$		−	21.1258i		−	1.19410i	−0.802203	−	0.597052i	$-0.796339\pi$
$313$		−	21.1258i		−	1.19410i	0.802203	−	0.597052i	$-0.203661\pi$
$314$	−5.46867			−0.308615
$315$	1.95415	−	1.08688i	0.110104	−	0.0612389i
$316$	−22.8959			−1.28799
$317$		−	20.1710i		−	1.13291i	−0.824091	−	0.566457i	$-0.808314\pi$
$317$		−	20.1710i		−	1.13291i	0.824091	−	0.566457i	$-0.191686\pi$
$318$			6.77979i			0.380192i
$319$	−2.91660			−0.163299
$320$	1.36951	+	2.46230i	0.0765581	+	0.137647i
$321$	4.20683			0.234802
$322$			0.819349i			0.0456605i
$323$			29.0445i			1.61608i
$324$	1.67714			0.0931743
$325$	18.2424	+	11.3262i	1.01191	+	0.628264i
$326$	10.0206			0.554990
$327$		−	12.8803i		−	0.712283i
$328$			8.26633i			0.456432i
$329$	2.12631			0.117227
$330$	−0.617578	−	1.11037i	−0.0339965	−	0.0611236i
$331$	14.4524			0.794375			0.397187	−	0.917738i	$-0.369986\pi$
$331$	14.4524			0.794375			0.397187	+	0.917738i	$0.369986\pi$
$332$			29.5597i			1.62230i
$333$			4.94242i			0.270843i
$334$	−8.92677			−0.488451
$335$	22.0829	−	12.2824i	1.20652	−	0.671058i
$336$	−2.16706			−0.118223
$337$		−	15.2464i		−	0.830525i	−0.909702	−	0.415263i	$-0.863690\pi$
$337$		−	15.2464i		−	0.830525i	0.909702	−	0.415263i	$-0.136310\pi$
$338$		−	3.09259i		−	0.168214i
$339$	−3.47264			−0.188608
$340$	−22.0146	+	12.2444i	−1.19391	+	0.664043i
$341$	−3.49098			−0.189047
$342$		−	2.45691i		−	0.132854i
$343$		−	1.00000i		−	0.0539949i
$344$	−12.6011			−0.679408
$345$	1.56726	+	2.81784i	0.0843787	+	0.151708i
$346$	7.32736			0.393921
$347$		−	26.3548i		−	1.41480i	−0.706812	−	0.707401i	$-0.749867\pi$
$347$		−	26.3548i		−	1.41480i	0.706812	−	0.707401i	$-0.250133\pi$
$348$		−	4.89155i		−	0.262214i
$349$	25.9611			1.38966			0.694832	−	0.719172i	$-0.255479\pi$
$349$	25.9611			1.38966			0.694832	+	0.719172i	$0.255479\pi$
$350$	1.49858	−	2.41367i	0.0801027	−	0.129016i
$351$	−4.29449			−0.229223
$352$			5.41012i			0.288360i
$353$			19.3671i			1.03081i	0.856948	+	0.515404i	$0.172358\pi$
$353$			19.3671i			1.03081i	−0.856948	+	0.515404i	$0.827642\pi$
$354$	1.61774			0.0859821
$355$	−0.0915431	−	0.164589i	−0.00485860	−	0.00873547i
$356$	26.1711			1.38707
$357$		−	6.71715i		−	0.355509i
$358$			6.01135i			0.317710i
$359$	−26.7037			−1.40937			−0.704684	−	0.709521i	$-0.748911\pi$
$359$	−26.7037			−1.40937			−0.704684	+	0.709521i	$0.748911\pi$
$360$	4.08297	−	2.27092i	0.215191	−	0.119688i
$361$	−0.303551			−0.0159763
$362$			5.78557i			0.304083i
$363$			1.00000i			0.0524864i
$364$	7.20245			0.377511
$365$	1.44844	−	0.805609i	0.0758146	−	0.0421675i
$366$	−0.0543818			−0.00284258
$367$		−	10.0165i		−	0.522855i	−0.965223	−	0.261428i	$-0.915807\pi$
$367$		−	10.0165i		−	0.522855i	0.965223	−	0.261428i	$-0.0841933\pi$
$368$		−	3.12487i		−	0.162895i
$369$	−3.95634			−0.205959
$370$	3.05233	+	5.48790i	0.158683	+	0.285302i
$371$	11.9318			0.619470
$372$		−	5.85485i		−	0.303560i
$373$		−	2.57505i		−	0.133331i	−0.997775	−	0.0666655i	$-0.978764\pi$
$373$		−	2.57505i		−	0.133331i	0.997775	−	0.0666655i	$-0.0212360\pi$
$374$	−3.81675			−0.197360
$375$	0.536902	−	11.1674i	0.0277255	−	0.576684i
$376$	4.44269			0.229114
$377$			12.5253i			0.645088i
$378$			0.568210i			0.0292256i
$379$	−11.5448			−0.593018			−0.296509	−	0.955030i	$-0.595823\pi$
$379$	−11.5448			−0.593018			−0.296509	+	0.955030i	$0.595823\pi$
$380$	7.88189	+	14.1712i	0.404333	+	0.726965i
$381$	17.5676			0.900018
$382$			14.2869i			0.730981i
$383$		−	26.9281i		−	1.37596i	−0.725729	−	0.687981i	$-0.758497\pi$
$383$		−	26.9281i		−	1.37596i	0.725729	−	0.687981i	$-0.241503\pi$
$384$	−11.5362			−0.588705
$385$	−1.95415	+	1.08688i	−0.0995925	+	0.0553926i
$386$	−8.90596			−0.453301
$387$		−	6.03102i		−	0.306574i
$388$			13.4036i			0.680464i
$389$	16.2758			0.825214			0.412607	−	0.910909i	$-0.364618\pi$
$389$	16.2758			0.825214			0.412607	+	0.910909i	$0.364618\pi$
$390$	−4.76846	+	2.65218i	−0.241460	+	0.134299i
$391$	9.68600			0.489842
$392$		−	2.08939i		−	0.105530i
$393$			5.58466i			0.281709i
$394$	4.48663			0.226033
$395$	−14.8379	−	26.6776i	−0.746574	−	1.34229i
$396$	−1.67714			−0.0842793
$397$		−	7.25428i		−	0.364082i	−0.983291	−	0.182041i	$-0.941730\pi$
$397$		−	7.25428i		−	0.364082i	0.983291	−	0.182041i	$-0.0582704\pi$
$398$			13.1822i			0.660765i
$399$	−4.32394			−0.216468
$400$	−5.71536	+	9.20536i	−0.285768	+	0.460268i
$401$	−17.4126			−0.869542			−0.434771	−	0.900541i	$-0.643171\pi$
$401$	−17.4126			−0.869542			−0.434771	+	0.900541i	$0.643171\pi$
$402$			6.42109i			0.320255i
$403$			14.9920i			0.746805i
$404$	3.61482			0.179844
$405$	1.08688	+	1.95415i	0.0540076	+	0.0971023i
$406$	1.65725			0.0822477
$407$		−	4.94242i		−	0.244987i
$408$		−	14.0347i		−	0.694822i
$409$	−20.9104			−1.03395			−0.516976	−	0.856000i	$-0.672943\pi$
$409$	−20.9104			−1.03395			−0.516976	+	0.856000i	$0.672943\pi$
$410$	−4.39299	+	2.44335i	−0.216954	+	0.120668i
$411$	−7.65615			−0.377650
$412$		−	24.7661i		−	1.22014i
$413$		−	2.84709i		−	0.140096i
$414$	−0.819349			−0.0402688
$415$	−34.4420	+	19.1564i	−1.69069	+	0.940349i
$416$	23.2337			1.13913
$417$			8.89291i			0.435488i
$418$			2.45691i			0.120171i
$419$	−28.0774			−1.37167			−0.685836	−	0.727757i	$-0.740563\pi$
$419$	−28.0774			−1.37167			−0.685836	+	0.727757i	$0.740563\pi$
$420$	−1.82285	−	3.27737i	−0.0889460	−	0.159919i
$421$	−26.5958			−1.29620			−0.648101	−	0.761555i	$-0.724436\pi$
$421$	−26.5958			−1.29620			−0.648101	+	0.761555i	$0.724436\pi$
$422$		0	9.41123e-5i		0	4.58132e-6i
$423$			2.12631i			0.103385i
$424$	24.9302			1.21072
$425$	−28.5334	−	17.7156i	−1.38408	−	0.859335i
$426$	0.0478578			0.00231872
$427$			0.0957071i			0.00463159i
$428$		−	7.05543i		−	0.341037i
$429$	4.29449			0.207340
$430$	−3.72462	−	6.69664i	−0.179617	−	0.322941i
$431$	−19.7169			−0.949732			−0.474866	−	0.880058i	$-0.657503\pi$
$431$	−19.7169			−0.949732			−0.474866	+	0.880058i	$0.657503\pi$
$432$		−	2.16706i		−	0.104263i
$433$			25.6261i			1.23151i	0.787937	+	0.615756i	$0.211149\pi$
$433$			25.6261i			1.23151i	−0.787937	+	0.615756i	$0.788851\pi$
$434$	1.98361			0.0952164
$435$	5.69947	−	3.17001i	0.273269	−	0.151990i
$436$	−21.6021			−1.03455
$437$		−	6.23504i		−	0.298263i
$438$			0.421164i			0.0201240i
$439$	7.14100			0.340821			0.170411	−	0.985373i	$-0.445491\pi$
$439$	7.14100			0.340821			0.170411	+	0.985373i	$0.445491\pi$
$440$	−4.08297	+	2.27092i	−0.194648	+	0.108262i
$441$	1.00000			0.0476190
$442$			16.3910i			0.779641i
$443$			36.1557i			1.71781i	0.512136	+	0.858905i	$0.328855\pi$
$443$			36.1557i			1.71781i	−0.512136	+	0.858905i	$0.671145\pi$
$444$	8.28912			0.393384
$445$	16.9604	+	30.4937i	0.804000	+	1.44554i
$446$	5.72886			0.271269
$447$		−	21.0244i		−	0.994420i
$448$			1.26004i			0.0595312i
$449$	−7.96435			−0.375861			−0.187930	−	0.982182i	$-0.560178\pi$
$449$	−7.96435			−0.375861			−0.187930	+	0.982182i	$0.560178\pi$
$450$	2.41367	+	1.49858i	0.113782	+	0.0706439i
$451$	3.95634			0.186297
$452$			5.82410i			0.273942i
$453$			12.3892i			0.582094i
$454$	11.8046			0.554017
$455$	4.66761	+	8.39207i	0.218821	+	0.393426i
$456$	−9.03438			−0.423074
$457$			23.6841i			1.10790i	0.832551	+	0.553948i	$0.186880\pi$
$457$			23.6841i			1.10790i	−0.832551	+	0.553948i	$0.813120\pi$
$458$		−	14.9785i		−	0.699900i
$459$	6.71715			0.313530
$460$	4.72591	−	2.62852i	0.220347	−	0.122555i
$461$	7.72513			0.359795			0.179897	−	0.983685i	$-0.442423\pi$
$461$	7.72513			0.359795			0.179897	+	0.983685i	$0.442423\pi$
$462$		−	0.568210i		−	0.0264355i
$463$		−	29.8278i		−	1.38622i	−0.720834	−	0.693108i	$-0.756241\pi$
$463$		−	29.8278i		−	1.38622i	0.720834	−	0.693108i	$-0.243759\pi$
$464$	−6.32047			−0.293420
$465$	6.82189	−	3.79428i	0.316357	−	0.175956i
$466$	0.831583			0.0385224
$467$		−	5.89001i		−	0.272557i	−0.990671	−	0.136279i	$-0.956486\pi$
$467$		−	5.89001i		−	0.272557i	0.990671	−	0.136279i	$-0.0435143\pi$
$468$			7.20245i			0.332934i
$469$	11.3006			0.521811
$470$	1.31316	+	2.36099i	0.0605717	+	0.108904i
$471$	−9.62438			−0.443468
$472$		−	5.94867i		−	0.273810i
$473$			6.03102i			0.277307i
$474$	7.75708			0.356295
$475$	−11.4038	+	18.3675i	−0.523245	+	0.842757i
$476$	−11.2656			−0.516357
$477$			11.9318i			0.546321i
$478$			4.79264i			0.219210i
$479$	−12.2774			−0.560967			−0.280483	−	0.959859i	$-0.590495\pi$
$479$	−12.2774			−0.560967			−0.280483	+	0.959859i	$0.590495\pi$
$480$	−5.88016	−	10.5722i	−0.268392	−	0.482551i
$481$	−21.2252			−0.967786
$482$			12.8046i			0.583234i
$483$			1.44198i			0.0656124i
$484$	1.67714			0.0762335
$485$	−15.6174	+	8.68630i	−0.709151	+	0.394424i
$486$	−0.568210			−0.0257745
$487$			29.2746i			1.32656i	0.748371	+	0.663280i	$0.230836\pi$
$487$			29.2746i			1.32656i	−0.748371	+	0.663280i	$0.769164\pi$
$488$			0.199969i			0.00905218i
$489$	17.6354			0.797500
$490$	1.11037	−	0.617578i	0.0501612	−	0.0278993i
$491$	8.35789			0.377186			0.188593	−	0.982055i	$-0.439607\pi$
$491$	8.35789			0.377186			0.188593	+	0.982055i	$0.439607\pi$
$492$			6.63533i			0.299144i
$493$		−	19.5913i		−	0.882346i
$494$	10.5512			0.474720
$495$	−1.08688	−	1.95415i	−0.0488517	−	0.0878323i
$496$	−7.56517			−0.339686
$497$		−	0.0842254i		−	0.00377803i
$498$		−	10.0147i		−	0.448772i
$499$	−34.4127			−1.54052			−0.770262	−	0.637727i	$-0.779875\pi$
$499$	−34.4127			−1.54052			−0.770262	+	0.637727i	$0.779875\pi$
$500$	−18.7293	−	0.900459i	−0.837601	−	0.0402698i
$501$	−15.7103			−0.701886
$502$			6.60779i			0.294920i
$503$			34.6175i			1.54352i	0.635915	+	0.771760i	$0.280623\pi$
$503$			34.6175i			1.54352i	−0.635915	+	0.771760i	$0.719377\pi$
$504$	2.08939			0.0930687
$505$	2.34261	+	4.21187i	0.104245	+	0.187426i
$506$	0.819349			0.0364245
$507$		−	5.44268i		−	0.241718i
$508$		−	29.4633i		−	1.30722i
$509$	−21.4226			−0.949540			−0.474770	−	0.880110i	$-0.657469\pi$
$509$	−21.4226			−0.949540			−0.474770	+	0.880110i	$0.657469\pi$
$510$	7.45849	−	4.14836i	0.330268	−	0.183692i
$511$	0.741211			0.0327893
$512$			20.7797i			0.918343i
$513$		−	4.32394i		−	0.190907i
$514$	−0.0991009			−0.00437115
$515$	28.8567	−	16.0499i	1.27158	−	0.707243i
$516$	−10.1148			−0.445281
$517$		−	2.12631i		−	0.0935151i
$518$			2.80834i			0.123391i
$519$	12.8955			0.566050
$520$	9.75244	+	17.5343i	0.427673	+	0.768929i
$521$	10.9302			0.478863			0.239431	−	0.970913i	$-0.423039\pi$
$521$	10.9302			0.478863			0.239431	+	0.970913i	$0.423039\pi$
$522$			1.65725i			0.0725356i
$523$		−	8.46577i		−	0.370182i	−0.982721	−	0.185091i	$-0.940742\pi$
$523$		−	8.46577i		−	0.370182i	0.982721	−	0.185091i	$-0.0592581\pi$
$524$	9.36625			0.409166
$525$	2.63738	−	4.24785i	0.115104	−	0.185391i
$526$	8.88566			0.387433
$527$		−	23.4494i		−	1.02147i
$528$			2.16706i			0.0943093i
$529$	20.9207			0.909595
$530$	7.36883	+	13.2487i	0.320082	+	0.575487i
$531$	2.84709			0.123553
$532$			7.25184i			0.314407i
$533$		−	16.9905i		−	0.735940i
$534$	−8.86672			−0.383700
$535$	8.22076	−	4.57233i	0.355414	−	0.197679i
$536$	23.6112			1.01985
$537$			10.5794i			0.456537i
$538$		−	11.1785i		−	0.481939i
$539$	−1.00000			−0.0430730
$540$	3.27737	−	1.82285i	0.141036	−	0.0784430i
$541$	21.9104			0.942003			0.471002	−	0.882132i	$-0.343893\pi$
$541$	21.9104			0.942003			0.471002	+	0.882132i	$0.343893\pi$
$542$			14.0784i			0.604719i
$543$			10.1821i			0.436955i
$544$	−36.3406			−1.55809
$545$	−13.9994	−	25.1700i	−0.599668	−	1.07817i
$546$	−2.44018			−0.104430
$547$		−	7.66283i		−	0.327639i	−0.986490	−	0.163820i	$-0.947619\pi$
$547$		−	7.66283i		−	0.327639i	0.986490	−	0.163820i	$-0.0523815\pi$
$548$			12.8404i			0.548515i
$549$	−0.0957071			−0.00408468
$550$	−2.41367	−	1.49858i	−0.102919	−	0.0638998i
$551$	−12.6112			−0.537256
$552$			3.01286i			0.128236i
$553$		−	13.6518i		−	0.580533i
$554$	−10.6805			−0.453772
$555$	5.37183	+	9.65822i	0.228021	+	0.409968i
$556$	14.9146			0.632521
$557$			6.00613i			0.254488i	0.991871	+	0.127244i	$0.0406131\pi$
$557$			6.00613i			0.254488i	−0.991871	+	0.127244i	$0.959387\pi$
$558$			1.98361i			0.0839730i
$559$	25.9002			1.09546
$560$	−4.23476	+	2.35534i	−0.178951	+	0.0995313i
$561$	−6.71715			−0.283598
$562$			2.31575i			0.0976838i
$563$		−	5.67905i		−	0.239343i	−0.992814	−	0.119672i	$-0.961816\pi$
$563$		−	5.67905i		−	0.239343i	0.992814	−	0.119672i	$-0.0381842\pi$
$564$	3.56612			0.150161
$565$	−6.78605	+	3.77435i	−0.285491	+	0.158788i
$566$	1.96489			0.0825905
$567$			1.00000i			0.0419961i
$568$		−	0.175980i		−	0.00738394i
$569$	−37.1186			−1.55609			−0.778047	−	0.628206i	$-0.783790\pi$
$569$	−37.1186			−1.55609			−0.778047	+	0.628206i	$0.783790\pi$
$570$	−2.67037	−	4.80116i	−0.111849	−	0.201098i
$571$	−15.3033			−0.640422			−0.320211	−	0.947346i	$-0.603754\pi$
$571$	−15.3033			−0.640422			−0.320211	+	0.947346i	$0.603754\pi$
$572$		−	7.20245i		−	0.301150i
$573$			25.1437i			1.05039i
$574$	−2.24803			−0.0938311
$575$	6.12533	+	3.80305i	0.255444	+	0.158598i
$576$	−1.26004			−0.0525016
$577$			34.4946i			1.43603i	0.696029	+	0.718014i	$0.254948\pi$
$577$			34.4946i			1.43603i	−0.696029	+	0.718014i	$0.745052\pi$
$578$		−	15.9781i		−	0.664602i
$579$	−15.6737			−0.651377
$580$	−5.31653	−	9.55880i	−0.220757	−	0.396907i
$581$	−17.6251			−0.731211
$582$		−	4.54110i		−	0.188235i
$583$		−	11.9318i		−	0.494166i
$584$	1.54868			0.0640847
$585$	−8.39207	+	4.66761i	−0.346969	+	0.192982i
$586$	−10.7789			−0.445273
$587$		−	9.29884i		−	0.383804i	−0.981414	−	0.191902i	$-0.938534\pi$
$587$		−	9.29884i		−	0.383804i	0.981414	−	0.191902i	$-0.0614656\pi$
$588$		−	1.67714i		−	0.0691640i
$589$	−15.0948			−0.621970
$590$	3.16131	−	1.75830i	0.130149	−	0.0723879i
$591$	7.89608			0.324801
$592$		−	10.7105i		−	0.440200i
$593$		−	29.3616i		−	1.20574i	−0.797841	−	0.602868i	$-0.794024\pi$
$593$		−	29.3616i		−	1.20574i	0.797841	−	0.602868i	$-0.205976\pi$
$594$	0.568210			0.0233140
$595$	−7.30075	−	13.1263i	−0.299301	−	0.538125i
$596$	−35.2608			−1.44434
$597$			23.1995i			0.949494i
$598$		−	3.51869i		−	0.143890i
$599$	7.60915			0.310902			0.155451	−	0.987844i	$-0.450317\pi$
$599$	7.60915			0.310902			0.155451	+	0.987844i	$0.450317\pi$
$600$	5.51050	−	8.87541i	0.224965	−	0.362337i
$601$	−7.40844			−0.302197			−0.151098	−	0.988519i	$-0.548281\pi$
$601$	−7.40844			−0.302197			−0.151098	+	0.988519i	$0.548281\pi$
$602$		−	3.42689i		−	0.139670i
$603$			11.3006i			0.460194i
$604$	20.7783			0.845458
$605$	1.08688	+	1.95415i	0.0441880	+	0.0794473i
$606$	−1.22469			−0.0497497
$607$			40.8961i			1.65992i	0.557823	+	0.829960i	$0.311637\pi$
$607$			40.8961i			1.65992i	−0.557823	+	0.829960i	$0.688363\pi$
$608$			23.3930i			0.948713i
$609$	2.91660			0.118187
$610$	−0.106270	+	0.0591066i	−0.00430274	+	0.00239315i
$611$	−9.13144			−0.369418
$612$		−	11.2656i		−	0.455384i
$613$			0.933437i			0.0377012i	0.999822	+	0.0188506i	$0.00600068\pi$
$613$			0.933437i			0.0377012i	−0.999822	+	0.0188506i	$0.993999\pi$
$614$	5.56891			0.224743
$615$	−7.73127	+	4.30008i	−0.311755	+	0.173396i
$616$	−2.08939			−0.0841838
$617$		−	24.7428i		−	0.996109i	−0.867146	−	0.498054i	$-0.834048\pi$
$617$		−	24.7428i		−	0.996109i	0.867146	−	0.498054i	$-0.165952\pi$
$618$			8.39071i			0.337524i
$619$	22.7962			0.916258			0.458129	−	0.888886i	$-0.348520\pi$
$619$	22.7962			0.916258			0.458129	+	0.888886i	$0.348520\pi$
$620$	−6.36353	−	11.4412i	−0.255566	−	0.459491i
$621$	−1.44198			−0.0578647
$622$			2.06104i			0.0826400i
$623$			15.6046i			0.625187i
$624$	9.30644			0.372556
$625$	−11.0885	−	22.4064i	−0.443540	−	0.896254i
$626$	12.0039			0.479773
$627$			4.32394i			0.172681i
$628$			16.1414i			0.644112i
$629$	33.1990			1.32373
$630$	0.617578	+	1.11037i	0.0246049	+	0.0442380i
$631$	31.8523			1.26802			0.634010	−	0.773325i	$-0.281408\pi$
$631$	31.8523			1.26802			0.634010	+	0.773325i	$0.281408\pi$
$632$		−	28.5238i		−	1.13462i
$633$		0	0.000165629i		0	6.58318e-6i
$634$	11.4614			0.455188
$635$	34.3297	−	19.0940i	1.36233	−	0.757721i
$636$	20.0113			0.793500
$637$			4.29449i			0.170154i
$638$		−	1.65725i		−	0.0656110i
$639$	0.0842254			0.00333191
$640$	−22.5434	+	12.5385i	−0.891108	+	0.495628i
$641$	−3.38759			−0.133802			−0.0669008	−	0.997760i	$-0.521311\pi$
$641$	−3.38759			−0.133802			−0.0669008	+	0.997760i	$0.521311\pi$
$642$			2.39036i			0.0943401i
$643$		−	11.9008i		−	0.469323i	−0.972077	−	0.234662i	$-0.924602\pi$
$643$		−	11.9008i		−	0.469323i	0.972077	−	0.234662i	$-0.0753982\pi$
$644$	2.41840			0.0952984
$645$	−6.55501	−	11.7855i	−0.258103	−	0.464053i
$646$	−16.5034			−0.649318
$647$			31.5833i			1.24167i	0.783943	+	0.620833i	$0.213206\pi$
$647$			31.5833i			1.24167i	−0.783943	+	0.620833i	$0.786794\pi$
$648$			2.08939i			0.0820789i
$649$	−2.84709			−0.111758
$650$	−6.43566	+	10.3655i	−0.252427	+	0.406569i
$651$	3.49098			0.136822
$652$		−	29.5770i		−	1.15832i
$653$			22.1364i			0.866263i	0.901331	+	0.433131i	$0.142591\pi$
$653$			22.1364i			0.866263i	−0.901331	+	0.433131i	$0.857409\pi$
$654$	7.31873			0.286185
$655$	6.06987	+	10.9133i	0.237169	+	0.426416i
$656$	8.57364			0.334744
$657$			0.741211i			0.0289174i
$658$			1.20819i			0.0471003i
$659$	−7.20849			−0.280803			−0.140402	−	0.990095i	$-0.544839\pi$
$659$	−7.20849			−0.280803			−0.140402	+	0.990095i	$0.544839\pi$
$660$	−3.27737	+	1.82285i	−0.127571	+	0.0709543i
$661$	−21.8599			−0.850252			−0.425126	−	0.905134i	$-0.639770\pi$
$661$	−21.8599			−0.850252			−0.425126	+	0.905134i	$0.639770\pi$
$662$			8.21199i			0.319168i
$663$			28.8467i			1.12031i
$664$	−36.8256			−1.42911
$665$	−8.44961	+	4.69961i	−0.327662	+	0.182243i
$666$	−2.80834			−0.108821
$667$			4.20569i			0.162845i
$668$			26.3484i			1.01945i
$669$	10.0823			0.389804
$670$	6.97897	+	12.5478i	0.269621	+	0.484762i
$671$	0.0957071			0.00369473
$672$		−	5.41012i		−	0.208700i
$673$			37.2294i			1.43509i	0.696514	+	0.717544i	$0.254734\pi$
$673$			37.2294i			1.43509i	−0.696514	+	0.717544i	$0.745266\pi$
$674$	8.66317			0.333693
$675$	4.24785	+	2.63738i	0.163500	+	0.101513i
$676$	−9.12812			−0.351081
$677$			4.63765i			0.178240i	0.996021	+	0.0891198i	$0.0284054\pi$
$677$			4.63765i			0.178240i	−0.996021	+	0.0891198i	$0.971595\pi$
$678$		−	1.97319i		−	0.0757800i
$679$	−7.99194			−0.306703
$680$	−15.2541	−	27.4259i	−0.584967	−	1.05174i
$681$	20.7750			0.796102
$682$		−	1.98361i		−	0.0759564i
$683$		−	42.5332i		−	1.62749i	−0.581225	−	0.813743i	$-0.697426\pi$
$683$		−	42.5332i		−	1.62749i	0.581225	−	0.813743i	$-0.302574\pi$
$684$	−7.25184			−0.277281
$685$	−14.9612	+	8.32133i	−0.571639	+	0.317942i
$686$	0.568210			0.0216944
$687$		−	26.3609i		−	1.00573i
$688$			13.0696i			0.498274i
$689$	−51.2412			−1.95213
$690$	−1.60113	+	0.890536i	−0.0609539	+	0.0339021i
$691$	42.7590			1.62663			0.813314	−	0.581824i	$-0.197661\pi$
$691$	42.7590			1.62663			0.813314	+	0.581824i	$0.197661\pi$
$692$		−	21.6275i		−	0.822155i
$693$		−	1.00000i		−	0.0379869i
$694$	14.9751			0.568447
$695$	9.66554	+	17.3780i	0.366635	+	0.659187i
$696$	6.09392			0.230989
$697$			26.5753i			1.00661i
$698$			14.7514i			0.558347i
$699$	1.46351			0.0553552
$700$	−7.12423	−	4.42324i	−0.269271	−	0.167183i
$701$	−46.5737			−1.75906			−0.879532	−	0.475841i	$-0.842144\pi$
$701$	−46.5737			−1.75906			−0.879532	+	0.475841i	$0.842144\pi$
$702$		−	2.44018i		−	0.0920985i
$703$		−	21.3707i		−	0.806013i
$704$	1.26004			0.0474895
$705$	2.31105	+	4.15513i	0.0870392	+	0.156491i
$706$	−11.0046			−0.414163
$707$			2.15535i			0.0810603i
$708$		−	4.77496i		−	0.179454i
$709$	47.1584			1.77107			0.885535	−	0.464572i	$-0.153792\pi$
$709$	47.1584			1.77107			0.885535	+	0.464572i	$0.153792\pi$
$710$	0.0935210	−	0.0520157i	0.00350978	−	0.00195212i
$711$	13.6518			0.511982
$712$			32.6041i			1.22189i
$713$			5.03393i			0.188522i
$714$	3.81675			0.142838
$715$	8.39207	−	4.66761i	0.313846	−	0.174559i
$716$	17.7432			0.663094
$717$			8.43462i			0.314997i
$718$		−	15.1733i		−	0.566263i
$719$	−51.2634			−1.91180			−0.955900	−	0.293691i	$-0.905116\pi$
$719$	−51.2634			−1.91180			−0.955900	+	0.293691i	$0.905116\pi$
$720$	−2.35534	−	4.23476i	−0.0877784	−	0.157820i
$721$	14.7669			0.549949
$722$		−	0.172481i		−	0.00641906i
$723$			22.5350i			0.838085i
$724$	17.0768			0.634653
$725$	7.69218	−	12.3893i	0.285680	−	0.460127i
$726$	−0.568210			−0.0210883
$727$			13.7680i			0.510628i	0.966858	+	0.255314i	$0.0821788\pi$
$727$			13.7680i			0.510628i	−0.966858	+	0.255314i	$0.917821\pi$
$728$			8.97286i			0.332556i
$729$	−1.00000			−0.0370370
$730$	0.457755	+	0.823016i	0.0169423	+	0.0304612i
$731$	−40.5112			−1.49836
$732$			0.160514i			0.00593277i
$733$		−	6.00424i		−	0.221772i	−0.993833	−	0.110886i	$-0.964631\pi$
$733$		−	6.00424i		−	0.221772i	0.993833	−	0.110886i	$-0.0353688\pi$
$734$	5.69146			0.210076
$735$	1.95415	−	1.08688i	0.0720798	−	0.0400902i
$736$	7.80130			0.287560
$737$		−	11.3006i		−	0.416261i
$738$		−	2.24803i		−	0.0827513i
$739$	34.2308			1.25920			0.629600	−	0.776920i	$-0.283219\pi$
$739$	34.2308			1.25920			0.629600	+	0.776920i	$0.283219\pi$
$740$	16.1982	−	9.00930i	0.595456	−	0.331188i
$741$	18.5691			0.682154
$742$			6.77979i			0.248894i
$743$			33.5261i			1.22995i	0.788546	+	0.614976i	$0.210834\pi$
$743$			33.5261i			1.22995i	−0.788546	+	0.614976i	$0.789166\pi$
$744$	7.29401			0.267411
$745$	−22.8510	−	41.0847i	−0.837197	−	1.50523i
$746$	1.46317			0.0535704
$747$		−	17.6251i		−	0.644868i
$748$			11.2656i			0.411910i
$749$	4.20683			0.153714
$750$	6.34546	+	0.305074i	0.231703	+	0.0111397i
$751$	−27.6113			−1.00755			−0.503776	−	0.863834i	$-0.668056\pi$
$751$	−27.6113			−1.00755			−0.503776	+	0.863834i	$0.668056\pi$
$752$		−	4.60785i		−	0.168031i
$753$			11.6291i			0.423789i
$754$	−7.11703			−0.259187
$755$	13.4656	+	24.2102i	0.490062	+	0.881101i
$756$	1.67714			0.0609969
$757$			38.8029i			1.41031i	0.709051	+	0.705157i	$0.249124\pi$
$757$			38.8029i			1.41031i	−0.709051	+	0.705157i	$0.750876\pi$
$758$		−	6.55989i		−	0.238266i
$759$	1.44198			0.0523406
$760$	−17.6545	+	9.81931i	−0.640396	+	0.356184i
$761$	−27.5844			−0.999934			−0.499967	−	0.866045i	$-0.666654\pi$
$761$	−27.5844			−0.999934			−0.499967	+	0.866045i	$0.666654\pi$
$762$			9.98212i			0.361614i
$763$		−	12.8803i		−	0.466299i
$764$	42.1694			1.52563
$765$	13.1263	−	7.30075i	0.474582	−	0.263959i
$766$	15.3008			0.552841
$767$			12.2268i			0.441484i
$768$		−	4.03492i		−	0.145598i
$769$	−30.2908			−1.09232			−0.546158	−	0.837682i	$-0.683910\pi$
$769$	−30.2908			−1.09232			−0.546158	+	0.837682i	$0.683910\pi$
$770$	−0.617578	−	1.11037i	−0.0222560	−	0.0400148i
$771$	−0.174409			−0.00628118
$772$			26.2869i			0.946088i
$773$			41.9610i			1.50923i	0.656166	+	0.754617i	$0.272177\pi$
$773$			41.9610i			1.50923i	−0.656166	+	0.754617i	$0.727823\pi$
$774$	3.42689			0.123177
$775$	9.20703	−	14.8292i	0.330726	−	0.532680i
$776$	−16.6983			−0.599433
$777$			4.94242i			0.177308i
$778$			9.24806i			0.331559i
$779$	17.1070			0.612921
$780$	7.82822	+	14.0746i	0.280295	+	0.503953i
$781$	−0.0842254			−0.00301382
$782$			5.50369i			0.196811i
$783$			2.91660i			0.104231i
$784$	−2.16706			−0.0773951
$785$	−18.8075	+	10.4606i	−0.671267	+	0.373354i
$786$	−3.17326			−0.113187
$787$			10.7014i			0.381463i	0.981642	+	0.190731i	$0.0610859\pi$
$787$			10.7014i			0.381463i	−0.981642	+	0.190731i	$0.938914\pi$
$788$		−	13.2428i		−	0.471755i
$789$	15.6380			0.556727
$790$	15.1585	−	8.43103i	0.539314	−	0.299963i
$791$	−3.47264			−0.123473
$792$		−	2.08939i		−	0.0742431i
$793$		−	0.411014i		−	0.0145955i
$794$	4.12196			0.146283
$795$	12.9685	+	23.3165i	0.459945	+	0.826953i
$796$	38.9088			1.37909
$797$			1.26443i			0.0447883i	0.999749	+	0.0223942i	$0.00712888\pi$
$797$			1.26443i			0.0447883i	−0.999749	+	0.0223942i	$0.992871\pi$
$798$		−	2.45691i		−	0.0869736i
$799$	14.2828			0.505288
$800$	−22.9814	−	14.2685i	−0.812515	−	0.504468i
$801$	−15.6046			−0.551363
$802$		−	9.89400i		−	0.349369i
$803$		−	0.741211i		−	0.0261568i
$804$	18.9526			0.668406
$805$	1.56726	+	2.81784i	0.0552388	+	0.0993159i
$806$	−8.51861			−0.300055
$807$		−	19.6732i		−	0.692528i
$808$			4.50336i			0.158428i
$809$	−35.3809			−1.24392			−0.621962	−	0.783047i	$-0.713664\pi$
$809$	−35.3809			−1.24392			−0.621962	+	0.783047i	$0.713664\pi$
$810$	−1.11037	+	0.617578i	−0.0390143	+	0.0216995i
$811$	9.52408			0.334436			0.167218	−	0.985920i	$-0.446522\pi$
$811$	9.52408			0.334436			0.167218	+	0.985920i	$0.446522\pi$
$812$		−	4.89155i		−	0.171660i
$813$			24.7767i			0.868958i
$814$	2.80834			0.0984321
$815$	34.4621	−	19.1676i	1.20716	−	0.671411i
$816$	−14.5565			−0.509579
$817$			26.0778i			0.912345i
$818$		−	11.8815i		−	0.415427i
$819$	−4.29449			−0.150062
$820$	7.21182	+	12.9664i	0.251848	+	0.452806i
$821$	−40.1557			−1.40144			−0.700722	−	0.713434i	$-0.747139\pi$
$821$	−40.1557			−1.40144			−0.700722	+	0.713434i	$0.747139\pi$
$822$		−	4.35030i		−	0.151734i
$823$			15.0684i			0.525253i	0.964898	+	0.262626i	$0.0845886\pi$
$823$			15.0684i			0.525253i	−0.964898	+	0.262626i	$0.915411\pi$
$824$	30.8538			1.07484
$825$	−4.24785	−	2.63738i	−0.147891	−	0.0918216i
$826$	1.61774			0.0562885
$827$		−	4.11172i		−	0.142978i	−0.997441	−	0.0714892i	$-0.977225\pi$
$827$		−	4.11172i		−	0.142978i	0.997441	−	0.0714892i	$-0.0227751\pi$
$828$			2.41840i			0.0840453i
$829$	−30.0427			−1.04342			−0.521712	−	0.853121i	$-0.674707\pi$
$829$	−30.0427			−1.04342			−0.521712	+	0.853121i	$0.674707\pi$
$830$	−10.8848	−	19.5703i	−0.377819	−	0.679294i
$831$	−18.7968			−0.652053
$832$		−	5.41123i		−	0.187600i
$833$		−	6.71715i		−	0.232735i
$834$	−5.05304			−0.174973
$835$	−30.7003	+	17.0753i	−1.06243	+	0.590914i
$836$	7.25184			0.250810
$837$			3.49098i			0.120666i
$838$		−	15.9539i		−	0.551117i
$839$	−25.2937			−0.873235			−0.436617	−	0.899647i	$-0.643824\pi$
$839$	−25.2937			−0.873235			−0.436617	+	0.899647i	$0.643824\pi$
$840$	4.08297	−	2.27092i	0.140876	−	0.0783541i
$841$	−20.4934			−0.706670
$842$		−	15.1120i		−	0.520795i
$843$			4.07551i			0.140368i
$844$	−0.000277783	0		−9.56169e−6	0
$845$	−5.91555	−	10.6358i	−0.203501	−	0.365882i
$846$	−1.20819			−0.0415385
$847$			1.00000i			0.0343604i
$848$		−	25.8570i		−	0.887934i
$849$	3.45803			0.118679
$850$	10.0662	−	16.2130i	0.345268	−	0.556101i
$851$	−7.12688			−0.244306
$852$		−	0.141258i		−	0.00483940i
$853$		−	8.15289i		−	0.279150i	−0.990212	−	0.139575i	$-0.955426\pi$
$853$		−	8.15289i		−	0.279150i	0.990212	−	0.139575i	$-0.0445736\pi$
$854$	−0.0543818			−0.00186091
$855$	−4.69961	−	8.44961i	−0.160723	−	0.288971i
$856$	8.78969			0.300426
$857$			38.9369i			1.33006i	0.746817	+	0.665029i	$0.231581\pi$
$857$			38.9369i			1.33006i	−0.746817	+	0.665029i	$0.768419\pi$
$858$			2.44018i			0.0833062i
$859$	5.95131			0.203056			0.101528	−	0.994833i	$-0.467627\pi$
$859$	5.95131			0.203056			0.101528	+	0.994833i	$0.467627\pi$
$860$	−19.7659	+	10.9936i	−0.674011	+	0.374880i
$861$	−3.95634			−0.134832
$862$		−	11.2034i		−	0.381588i
$863$			4.36170i			0.148474i	0.997241	+	0.0742369i	$0.0236521\pi$
$863$			4.36170i			0.148474i	−0.997241	+	0.0742369i	$0.976348\pi$
$864$	5.41012			0.184056
$865$	25.1997	−	14.0159i	0.856816	−	0.476555i
$866$	−14.5610			−0.494803
$867$		−	28.1201i		−	0.955007i
$868$		−	5.85485i		−	0.198727i
$869$	−13.6518			−0.463105
$870$	1.80123	+	3.23850i	0.0610674	+	0.109795i
$871$	−48.5302			−1.64438
$872$		−	26.9120i		−	0.911354i
$873$		−	7.99194i		−	0.270486i
$874$	3.54282			0.119838
$875$	0.536902	−	11.1674i	0.0181506	−	0.377528i
$876$	1.24311			0.0420009
$877$		−	58.6844i		−	1.98163i	−0.135217	−	0.990816i	$-0.543173\pi$
$877$		−	58.6844i		−	1.98163i	0.135217	−	0.990816i	$-0.456827\pi$
$878$			4.05759i			0.136937i
$879$	−18.9700			−0.639841
$880$	2.35534	+	4.23476i	0.0793985	+	0.142754i
$881$	−17.0829			−0.575537			−0.287768	−	0.957700i	$-0.592913\pi$
$881$	−17.0829			−0.575537			−0.287768	+	0.957700i	$0.592913\pi$
$882$			0.568210i			0.0191326i
$883$		−	16.1472i		−	0.543396i	−0.962383	−	0.271698i	$-0.912415\pi$
$883$		−	16.1472i		−	0.543396i	0.962383	−	0.271698i	$-0.0875851\pi$
$884$	48.3799			1.62719
$885$	5.56362	−	3.09445i	0.187019	−	0.104019i
$886$	−20.5440			−0.690191
$887$		−	57.8400i		−	1.94208i	−0.238924	−	0.971038i	$-0.576795\pi$
$887$		−	57.8400i		−	1.94208i	0.238924	−	0.971038i	$-0.423205\pi$
$888$			10.3266i			0.346539i
$889$	17.5676			0.589200
$890$	−17.3269	+	9.63707i	−0.580798	+	0.323035i
$891$	1.00000			0.0335013
$892$		−	16.9094i		−	0.566168i
$893$		−	9.19405i		−	0.307667i
$894$	11.9463			0.399543
$895$	11.4986	+	20.6738i	0.384356	+	0.691049i
$896$	−11.5362			−0.385398
$897$		−	6.19258i		−	0.206764i
$898$		−	4.52542i		−	0.151015i
$899$	10.1818			0.339582
$900$	4.42324	−	7.12423i	0.147441	−	0.237474i
$901$	80.1479			2.67011
$902$			2.24803i			0.0748514i
$903$		−	6.03102i		−	0.200700i
$904$	−7.25569			−0.241321
$905$	11.0667	+	19.8973i	0.367871	+	0.661409i
$906$	−7.03965			−0.233877
$907$		−	38.6123i		−	1.28210i	−0.767499	−	0.641050i	$-0.778499\pi$
$907$		−	38.6123i		−	1.28210i	0.767499	−	0.641050i	$-0.221501\pi$
$908$		−	34.8426i		−	1.15629i
$909$	−2.15535			−0.0714885
$910$	−4.76846	+	2.65218i	−0.158073	+	0.0879190i
$911$	−49.0131			−1.62388			−0.811938	−	0.583744i	$-0.801587\pi$
$911$	−49.0131			−1.62388			−0.811938	+	0.583744i	$0.801587\pi$
$912$			9.37025i			0.310280i
$913$			17.6251i			0.583305i
$914$	−13.4576			−0.445137
$915$	−0.187026	+	0.104022i	−0.00618288	+	0.00343887i
$916$	−44.2108			−1.46077
$917$			5.58466i			0.184422i
$918$			3.81675i			0.125972i
$919$	24.4400			0.806200			0.403100	−	0.915156i	$-0.367933\pi$
$919$	24.4400			0.806200			0.403100	+	0.915156i	$0.367933\pi$
$920$	3.27462	+	5.88757i	0.107961	+	0.194107i
$921$	9.80079			0.322947
$922$			4.38950i			0.144560i
$923$			0.361706i			0.0119057i
$924$	−1.67714			−0.0551738
$925$	20.9947	+	13.0350i	0.690301	+	0.428589i
$926$	16.9485			0.556961
$927$			14.7669i			0.485009i
$928$		−	15.7792i		−	0.517977i
$929$	3.93277			0.129030			0.0645150	−	0.997917i	$-0.479450\pi$
$929$	3.93277			0.129030			0.0645150	+	0.997917i	$0.479450\pi$
$930$	2.15595	+	3.87627i	0.0706964	+	0.127108i
$931$	−4.32394			−0.141711
$932$		−	2.45451i		−	0.0804002i
$933$			3.62724i			0.118751i
$934$	3.34677			0.109510
$935$	−13.1263	+	7.30075i	−0.429275	+	0.238760i
$936$	−8.97286			−0.293287
$937$		−	41.0616i		−	1.34142i	−0.741718	−	0.670712i	$-0.765989\pi$
$937$		−	41.0616i		−	1.34142i	0.741718	−	0.670712i	$-0.234011\pi$
$938$			6.42109i			0.209656i
$939$	21.1258			0.689416
$940$	6.96872	−	3.87595i	0.227294	−	0.126420i
$941$	−43.5332			−1.41914			−0.709570	−	0.704635i	$-0.751111\pi$
$941$	−43.5332			−1.41914			−0.709570	+	0.704635i	$0.751111\pi$
$942$		−	5.46867i		−	0.178179i
$943$		−	5.70497i		−	0.185780i
$944$	−6.16982			−0.200810
$945$	1.08688	+	1.95415i	0.0353563	+	0.0635684i
$946$	−3.42689			−0.111418
$947$		−	14.0748i		−	0.457371i	−0.973500	−	0.228685i	$-0.926557\pi$
$947$		−	14.0748i		−	0.457371i	0.973500	−	0.228685i	$-0.0734427\pi$
$948$		−	22.8959i		−	0.743624i
$949$	−3.18313			−0.103329
$950$	−10.4366	−	6.47979i	−0.338607	−	0.210232i
$951$	20.1710			0.654089
$952$		−	14.0347i		−	0.454868i
$953$			17.1825i			0.556596i	0.960495	+	0.278298i	$0.0897703\pi$
$953$			17.1825i			0.556596i	−0.960495	+	0.278298i	$0.910230\pi$
$954$	−6.77979			−0.219504
$955$	27.3282	+	49.1344i	0.884320	+	1.58995i
$956$	14.1460			0.457515
$957$		−	2.91660i		−	0.0942804i
$958$		−	6.97612i		−	0.225388i
$959$	−7.65615			−0.247230
$960$	−2.46230	+	1.36951i	−0.0794703	+	0.0442008i
$961$	−18.8131			−0.606873
$962$		−	12.0604i		−	0.388842i
$963$			4.20683i			0.135563i
$964$	37.7943			1.21727
$965$	−30.6287	+	17.0355i	−0.985973	+	0.548391i
$966$	−0.819349			−0.0263621
$967$			19.5724i			0.629404i	0.949190	+	0.314702i	$0.101905\pi$
$967$			19.5724i			0.629404i	−0.949190	+	0.314702i	$0.898095\pi$
$968$			2.08939i			0.0671554i
$969$	−29.0445			−0.933045
$970$	−4.93564	−	8.87398i	−0.158474	−	0.284926i
$971$	40.0210			1.28433			0.642167	−	0.766564i	$-0.278035\pi$
$971$	40.0210			1.28433			0.642167	+	0.766564i	$0.278035\pi$
$972$			1.67714i			0.0537942i
$973$			8.89291i			0.285094i
$974$	−16.6342			−0.532993
$975$	−11.3262	+	18.2424i	−0.362728	+	0.584224i
$976$	0.207403			0.00663882
$977$		−	39.7738i		−	1.27248i	−0.771493	−	0.636238i	$-0.780490\pi$
$977$		−	39.7738i		−	1.27248i	0.771493	−	0.636238i	$-0.219510\pi$
$978$			10.0206i			0.320424i
$979$	15.6046			0.498726
$980$	−1.82285	−	3.27737i	−0.0582288	−	0.104692i
$981$	12.8803			0.411237
$982$			4.74904i			0.151548i
$983$			25.2728i			0.806078i	0.915183	+	0.403039i	$0.132046\pi$
$983$			25.2728i			0.806078i	−0.915183	+	0.403039i	$0.867954\pi$
$984$	−8.26633			−0.263521
$985$	15.4301	−	8.58210i	0.491644	−	0.273449i
$986$	11.1320			0.354514
$987$			2.12631i			0.0676813i
$988$		−	31.1430i		−	0.990790i
$989$	8.69662			0.276536
$990$	1.11037	−	0.617578i	0.0352898	−	0.0196279i
$991$	8.91847			0.283305			0.141652	−	0.989916i	$-0.454759\pi$
$991$	8.91847			0.283305			0.141652	+	0.989916i	$0.454759\pi$
$992$		−	18.8866i		−	0.599651i
$993$			14.4524i			0.458632i
$994$	0.0478578			0.00151796
$995$	25.2152	+	45.3353i	0.799375	+	1.43723i
$996$	−29.5597			−0.936634
$997$		−	1.95523i		−	0.0619229i	−0.999521	−	0.0309614i	$-0.990143\pi$
$997$		−	1.95523i		−	0.0619229i	0.999521	−	0.0309614i	$-0.00985691\pi$
$998$		−	19.5537i		−	0.618960i
$999$	−4.94242			−0.156371

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.f.694.12	yes	20
5.2	odd	4		5775.2.a.co.1.4		10
5.3	odd	4		5775.2.a.cn.1.7		10
5.4	even	2	inner	1155.2.c.f.694.9	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.f.694.9	✓	20	5.4	even	2	inner
1155.2.c.f.694.12	yes	20	1.1	even	1	trivial
5775.2.a.cn.1.7		10	5.3	odd	4
5775.2.a.co.1.4		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)

\(f(q)\)	\(=\)	\(q+0.568210i q^{2} +1.00000i q^{3} +1.67714 q^{4} +(1.08688 + 1.95415i) q^{5} -0.568210 q^{6} +1.00000i q^{7} +2.08939i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+0.568210i q^{2} +1.00000i q^{3} +1.67714 q^{4} +(1.08688 + 1.95415i) q^{5} -0.568210 q^{6} +1.00000i q^{7} +2.08939i q^{8} -1.00000 q^{9} +(-1.11037 + 0.617578i) q^{10} +1.00000 q^{11} +1.67714i q^{12} -4.29449i q^{13} -0.568210 q^{14} +(-1.95415 + 1.08688i) q^{15} +2.16706 q^{16} +6.71715i q^{17} -0.568210i q^{18} +4.32394 q^{19} +(1.82285 + 3.27737i) q^{20} -1.00000 q^{21} +0.568210i q^{22} -1.44198i q^{23} -2.08939 q^{24} +(-2.63738 + 4.24785i) q^{25} +2.44018 q^{26} -1.00000i q^{27} +1.67714i q^{28} -2.91660 q^{29} +(-0.617578 - 1.11037i) q^{30} -3.49098 q^{31} +5.41012i q^{32} +1.00000i q^{33} -3.81675 q^{34} +(-1.95415 + 1.08688i) q^{35} -1.67714 q^{36} -4.94242i q^{37} +2.45691i q^{38} +4.29449 q^{39} +(-4.08297 + 2.27092i) q^{40} +3.95634 q^{41} -0.568210i q^{42} +6.03102i q^{43} +1.67714 q^{44} +(-1.08688 - 1.95415i) q^{45} +0.819349 q^{46} -2.12631i q^{47} +2.16706i q^{48} -1.00000 q^{49} +(-2.41367 - 1.49858i) q^{50} -6.71715 q^{51} -7.20245i q^{52} -11.9318i q^{53} +0.568210 q^{54} +(1.08688 + 1.95415i) q^{55} -2.08939 q^{56} +4.32394i q^{57} -1.65725i q^{58} -2.84709 q^{59} +(-3.27737 + 1.82285i) q^{60} +0.0957071 q^{61} -1.98361i q^{62} -1.00000i q^{63} +1.26004 q^{64} +(8.39207 - 4.66761i) q^{65} -0.568210 q^{66} -11.3006i q^{67} +11.2656i q^{68} +1.44198 q^{69} +(-0.617578 - 1.11037i) q^{70} -0.0842254 q^{71} -2.08939i q^{72} -0.741211i q^{73} +2.80834 q^{74} +(-4.24785 - 2.63738i) q^{75} +7.25184 q^{76} +1.00000i q^{77} +2.44018i q^{78} -13.6518 q^{79} +(2.35534 + 4.23476i) q^{80} +1.00000 q^{81} +2.24803i q^{82} +17.6251i q^{83} -1.67714 q^{84} +(-13.1263 + 7.30075i) q^{85} -3.42689 q^{86} -2.91660i q^{87} +2.08939i q^{88} +15.6046 q^{89} +(1.11037 - 0.617578i) q^{90} +4.29449 q^{91} -2.41840i q^{92} -3.49098i q^{93} +1.20819 q^{94} +(4.69961 + 8.44961i) q^{95} -5.41012 q^{96} +7.99194i q^{97} -0.568210i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} + 2 q^{10} + 20 q^{11} + 6 q^{14} - 2 q^{15} + 38 q^{16} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 q^{95} + 62 q^{96} - 20 q^{99}+O(q^{100}) \) 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 - 34 * q^19 + 4 * q^20 - 20 * q^21 - 18 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^29 - 6 * q^30 + 12 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 - 2 * q^40 + 52 * q^41 - 26 * q^44 + 2 * q^45 + 40 * q^46 - 20 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^54 - 2 * q^55 - 18 * q^56 - 14 * q^59 - 28 * q^60 + 78 * q^61 - 26 * q^64 - 4 * q^65 + 6 * q^66 - 18 * q^69 - 6 * q^70 - 8 * q^74 - 8 * q^75 + 84 * q^76 - 52 * q^79 - 40 * q^80 + 20 * q^81 + 26 * q^84 - 24 * q^85 + 4 * q^86 - 10 * q^89 - 2 * q^90 - 96 * q^94 - 30 * q^95 + 62 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

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Database

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