LMFDB - Embedded newform 1155.2.c.c.694.2

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:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.2
Root			$0.403032 - 0.403032i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.c.694.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.67513i q^{2} +1.00000i q^{3} -0.806063 q^{4} +(-1.48119 - 1.67513i) q^{5} +1.67513 q^{6} +1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.67513i q^{2} +1.00000i q^{3} -0.806063 q^{4} +(-1.48119 - 1.67513i) q^{5} +1.67513 q^{6} +1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +(-2.80606 + 2.48119i) q^{10} -1.00000 q^{11} -0.806063i q^{12} -0.481194i q^{13} +1.67513 q^{14} +(1.67513 - 1.48119i) q^{15} -4.96239 q^{16} +0.193937i q^{17} +1.67513i q^{18} -3.96239 q^{19} +(1.19394 + 1.35026i) q^{20} -1.00000 q^{21} +1.67513i q^{22} -3.15633i q^{23} +2.00000 q^{24} +(-0.612127 + 4.96239i) q^{25} -0.806063 q^{26} -1.00000i q^{27} -0.806063i q^{28} +0.130933 q^{29} +(-2.48119 - 2.80606i) q^{30} -8.24965 q^{31} +4.31265i q^{32} -1.00000i q^{33} +0.324869 q^{34} +(1.67513 - 1.48119i) q^{35} +0.806063 q^{36} -0.481194i q^{37} +6.63752i q^{38} +0.481194 q^{39} +(-3.35026 + 2.96239i) q^{40} -4.48119 q^{41} +1.67513i q^{42} +0.130933i q^{43} +0.806063 q^{44} +(1.48119 + 1.67513i) q^{45} -5.28726 q^{46} +1.28726i q^{47} -4.96239i q^{48} -1.00000 q^{49} +(8.31265 + 1.02539i) q^{50} -0.193937 q^{51} +0.387873i q^{52} -3.64974i q^{53} -1.67513 q^{54} +(1.48119 + 1.67513i) q^{55} +2.00000 q^{56} -3.96239i q^{57} -0.219329i q^{58} +3.32487 q^{59} +(-1.35026 + 1.19394i) q^{60} -14.5066 q^{61} +13.8192i q^{62} -1.00000i q^{63} -2.70052 q^{64} +(-0.806063 + 0.712742i) q^{65} -1.67513 q^{66} +2.00000i q^{67} -0.156325i q^{68} +3.15633 q^{69} +(-2.48119 - 2.80606i) q^{70} -5.25694 q^{71} +2.00000i q^{72} +4.64974i q^{73} -0.806063 q^{74} +(-4.96239 - 0.612127i) q^{75} +3.19394 q^{76} -1.00000i q^{77} -0.806063i q^{78} +4.24965 q^{79} +(7.35026 + 8.31265i) q^{80} +1.00000 q^{81} +7.50659i q^{82} -5.23155i q^{83} +0.806063 q^{84} +(0.324869 - 0.287258i) q^{85} +0.219329 q^{86} +0.130933i q^{87} +2.00000i q^{88} -1.79384 q^{89} +(2.80606 - 2.48119i) q^{90} +0.481194 q^{91} +2.54420i q^{92} -8.24965i q^{93} +2.15633 q^{94} +(5.86907 + 6.63752i) q^{95} -4.31265 q^{96} +5.21933i q^{97} +1.67513i q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9}+O(q^{10}) $ 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9	$ 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9} - 16 q^{10} - 6 q^{11} - 8 q^{16} - 2 q^{19} + 8 q^{20} - 6 q^{21} + 12 q^{24} - 2 q^{25} - 4 q^{26} + 10 q^{29} - 4 q^{30} - 16 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} - 16 q^{41} + 4 q^{44} - 2 q^{45} - 20 q^{46} - 6 q^{49} + 8 q^{50} - 2 q^{51} - 2 q^{55} + 12 q^{56} + 30 q^{59} + 12 q^{60} - 46 q^{61} + 24 q^{64} - 4 q^{65} - 2 q^{69} - 4 q^{70} - 24 q^{71} - 4 q^{74} - 8 q^{75} + 20 q^{76} - 8 q^{79} + 24 q^{80} + 6 q^{81} + 4 q^{84} + 12 q^{85} - 28 q^{86} + 42 q^{89} + 16 q^{90} - 8 q^{91} - 8 q^{94} + 26 q^{95} + 16 q^{96} + 6 q^{99}+O(q^{100}) $ 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9 - 16 * q^10 - 6 * q^11 - 8 * q^16 - 2 * q^19 + 8 * q^20 - 6 * q^21 + 12 * q^24 - 2 * q^25 - 4 * q^26 + 10 * q^29 - 4 * q^30 - 16 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 - 16 * q^41 + 4 * q^44 - 2 * q^45 - 20 * q^46 - 6 * q^49 + 8 * q^50 - 2 * q^51 - 2 * q^55 + 12 * q^56 + 30 * q^59 + 12 * q^60 - 46 * q^61 + 24 * q^64 - 4 * q^65 - 2 * q^69 - 4 * q^70 - 24 * q^71 - 4 * q^74 - 8 * q^75 + 20 * q^76 - 8 * q^79 + 24 * q^80 + 6 * q^81 + 4 * q^84 + 12 * q^85 - 28 * q^86 + 42 * q^89 + 16 * q^90 - 8 * q^91 - 8 * q^94 + 26 * q^95 + 16 * q^96 + 6 * 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 $

$2$		−	1.67513i		−	1.18450i	−0.805756	−	0.592248i	$-0.798240\pi$
$2$		−	1.67513i		−	1.18450i	0.805756	−	0.592248i	$-0.201760\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.806063			−0.403032
$5$	−1.48119	−	1.67513i	−0.662410	−	0.749141i
$5$	−1.48119	−	1.67513i	−0.662410	−	0.749141i
$6$	1.67513			0.683869
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		−	2.00000i		−	0.707107i
$9$	−1.00000			−0.333333
$10$	−2.80606	+	2.48119i	−0.887355	+	0.784623i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		−	0.806063i		−	0.232690i
$13$		−	0.481194i		−	0.133459i	−0.997771	−	0.0667296i	$-0.978743\pi$
$13$		−	0.481194i		−	0.133459i	0.997771	−	0.0667296i	$-0.0212565\pi$
$14$	1.67513			0.447698
$15$	1.67513	−	1.48119i	0.432517	−	0.382443i
$16$	−4.96239			−1.24060
$17$			0.193937i			0.0470365i	0.999723	+	0.0235183i	$0.00748679\pi$
$17$			0.193937i			0.0470365i	−0.999723	+	0.0235183i	$0.992513\pi$
$18$			1.67513i			0.394832i
$19$	−3.96239			−0.909034			−0.454517	−	0.890738i	$-0.650188\pi$
$19$	−3.96239			−0.909034			−0.454517	+	0.890738i	$0.650188\pi$
$20$	1.19394	+	1.35026i	0.266972	+	0.301928i
$21$	−1.00000			−0.218218
$22$			1.67513i			0.357139i
$23$		−	3.15633i		−	0.658139i	−0.944306	−	0.329070i	$-0.893265\pi$
$23$		−	3.15633i		−	0.658139i	0.944306	−	0.329070i	$-0.106735\pi$
$24$	2.00000			0.408248
$25$	−0.612127	+	4.96239i	−0.122425	+	0.992478i
$26$	−0.806063			−0.158082
$27$		−	1.00000i		−	0.192450i
$28$		−	0.806063i		−	0.152332i
$29$	0.130933			0.0243136			0.0121568	−	0.999926i	$-0.496130\pi$
$29$	0.130933			0.0243136			0.0121568	+	0.999926i	$0.496130\pi$
$30$	−2.48119	−	2.80606i	−0.453002	−	0.512315i
$31$	−8.24965			−1.48168			−0.740840	−	0.671681i	$-0.765572\pi$
$31$	−8.24965			−1.48168			−0.740840	+	0.671681i	$0.765572\pi$
$32$			4.31265i			0.762376i
$33$		−	1.00000i		−	0.174078i
$34$	0.324869			0.0557146
$35$	1.67513	−	1.48119i	0.283149	−	0.250368i
$36$	0.806063			0.134344
$37$		−	0.481194i		−	0.0791079i	−0.999217	−	0.0395539i	$-0.987406\pi$
$37$		−	0.481194i		−	0.0791079i	0.999217	−	0.0395539i	$-0.0125937\pi$
$38$			6.63752i			1.07675i
$39$	0.481194			0.0770528
$40$	−3.35026	+	2.96239i	−0.529723	+	0.468395i
$41$	−4.48119			−0.699845			−0.349922	−	0.936779i	$-0.613792\pi$
$41$	−4.48119			−0.699845			−0.349922	+	0.936779i	$0.613792\pi$
$42$			1.67513i			0.258478i
$43$			0.130933i			0.0199670i	0.999950	+	0.00998351i	$0.00317790\pi$
$43$			0.130933i			0.0199670i	−0.999950	+	0.00998351i	$0.996822\pi$
$44$	0.806063			0.121519
$45$	1.48119	+	1.67513i	0.220803	+	0.249714i
$46$	−5.28726			−0.779564
$47$			1.28726i			0.187766i	0.995583	+	0.0938829i	$0.0299279\pi$
$47$			1.28726i			0.187766i	−0.995583	+	0.0938829i	$0.970072\pi$
$48$		−	4.96239i		−	0.716259i
$49$	−1.00000			−0.142857
$50$	8.31265	+	1.02539i	1.17559	+	0.145012i
$51$	−0.193937			−0.0271566
$52$			0.387873i			0.0537883i
$53$		−	3.64974i		−	0.501330i	−0.968074	−	0.250665i	$-0.919351\pi$
$53$		−	3.64974i		−	0.501330i	0.968074	−	0.250665i	$-0.0806493\pi$
$54$	−1.67513			−0.227956
$55$	1.48119	+	1.67513i	0.199724	+	0.225875i
$56$	2.00000			0.267261
$57$		−	3.96239i		−	0.524831i
$58$		−	0.219329i		−	0.0287993i
$59$	3.32487			0.432861			0.216431	−	0.976298i	$-0.430559\pi$
$59$	3.32487			0.432861			0.216431	+	0.976298i	$0.430559\pi$
$60$	−1.35026	+	1.19394i	−0.174318	+	0.154137i
$61$	−14.5066			−1.85738			−0.928689	−	0.370859i	$-0.879063\pi$
$61$	−14.5066			−1.85738			−0.928689	+	0.370859i	$0.879063\pi$
$62$			13.8192i			1.75504i
$63$		−	1.00000i		−	0.125988i
$64$	−2.70052			−0.337565
$65$	−0.806063	+	0.712742i	−0.0999799	+	0.0884048i
$66$	−1.67513			−0.206194
$67$			2.00000i			0.244339i	0.992509	+	0.122169i	$0.0389851\pi$
$67$			2.00000i			0.244339i	−0.992509	+	0.122169i	$0.961015\pi$
$68$		−	0.156325i		−	0.0189572i
$69$	3.15633			0.379977
$70$	−2.48119	−	2.80606i	−0.296559	−	0.335389i
$71$	−5.25694			−0.623884			−0.311942	−	0.950101i	$-0.600979\pi$
$71$	−5.25694			−0.623884			−0.311942	+	0.950101i	$0.600979\pi$
$72$			2.00000i			0.235702i
$73$			4.64974i			0.544211i	0.962267	+	0.272105i	$0.0877199\pi$
$73$			4.64974i			0.544211i	−0.962267	+	0.272105i	$0.912280\pi$
$74$	−0.806063			−0.0937030
$75$	−4.96239	−	0.612127i	−0.573007	−	0.0706823i
$76$	3.19394			0.366370
$77$		−	1.00000i		−	0.113961i
$78$		−	0.806063i		−	0.0912687i
$79$	4.24965			0.478123			0.239061	−	0.971004i	$-0.423160\pi$
$79$	4.24965			0.478123			0.239061	+	0.971004i	$0.423160\pi$
$80$	7.35026	+	8.31265i	0.821784	+	0.929383i
$81$	1.00000			0.111111
$82$			7.50659i			0.828964i
$83$		−	5.23155i		−	0.574237i	−0.957895	−	0.287118i	$-0.907303\pi$
$83$		−	5.23155i		−	0.574237i	0.957895	−	0.287118i	$-0.0926973\pi$
$84$	0.806063			0.0879487
$85$	0.324869	−	0.287258i	0.0352370	−	0.0311575i
$86$	0.219329			0.0236509
$87$			0.130933i			0.0140374i
$88$			2.00000i			0.213201i
$89$	−1.79384			−0.190147			−0.0950736	−	0.995470i	$-0.530309\pi$
$89$	−1.79384			−0.190147			−0.0950736	+	0.995470i	$0.530309\pi$
$90$	2.80606	−	2.48119i	0.295785	−	0.261541i
$91$	0.481194			0.0504429
$92$			2.54420i			0.265251i
$93$		−	8.24965i		−	0.855448i
$94$	2.15633			0.222408
$95$	5.86907	+	6.63752i	0.602154	+	0.680995i
$96$	−4.31265			−0.440158
$97$			5.21933i			0.529943i	0.964256	+	0.264971i	$0.0853625\pi$
$97$			5.21933i			0.529943i	−0.964256	+	0.264971i	$0.914638\pi$
$98$			1.67513i			0.169214i
$99$	1.00000			0.100504
$100$	0.493413	−	4.00000i	0.0493413	−	0.400000i
$101$	−11.9248			−1.18656			−0.593280	−	0.804996i	$-0.702167\pi$
$101$	−11.9248			−1.18656			−0.593280	+	0.804996i	$0.702167\pi$
$102$			0.324869i			0.0321668i
$103$			4.70545i			0.463642i	0.972759	+	0.231821i	$0.0744683\pi$
$103$			4.70545i			0.463642i	−0.972759	+	0.231821i	$0.925532\pi$
$104$	−0.962389			−0.0943700
$105$	1.48119	+	1.67513i	0.144550	+	0.163476i
$106$	−6.11379			−0.593824
$107$			1.36248i			0.131716i	0.997829	+	0.0658580i	$0.0209784\pi$
$107$			1.36248i			0.131716i	−0.997829	+	0.0658580i	$0.979022\pi$
$108$			0.806063i			0.0775635i
$109$	1.10062			0.105420			0.0527099	−	0.998610i	$-0.483214\pi$
$109$	1.10062			0.105420			0.0527099	+	0.998610i	$0.483214\pi$
$110$	2.80606	−	2.48119i	0.267548	−	0.236573i
$111$	0.481194			0.0456729
$112$		−	4.96239i		−	0.468902i
$113$		−	14.8945i		−	1.40115i	−0.713577	−	0.700576i	$-0.752926\pi$
$113$		−	14.8945i		−	1.40115i	0.713577	−	0.700576i	$-0.247074\pi$
$114$	−6.63752			−0.621661
$115$	−5.28726	+	4.67513i	−0.493039	+	0.435958i
$116$	−0.105540			−0.00979914
$117$			0.481194i			0.0444864i
$118$		−	5.56959i		−	0.512722i
$119$	−0.193937			−0.0177781
$120$	−2.96239	−	3.35026i	−0.270428	−	0.305836i
$121$	1.00000			0.0909091
$122$			24.3004i			2.20006i
$123$		−	4.48119i		−	0.404056i
$124$	6.64974			0.597164
$125$	9.21933	−	6.32487i	0.824602	−	0.565713i
$126$	−1.67513			−0.149233
$127$		−	8.59991i		−	0.763118i	−0.924344	−	0.381559i	$-0.875387\pi$
$127$		−	8.59991i		−	0.763118i	0.924344	−	0.381559i	$-0.124613\pi$
$128$			13.1490i			1.16222i
$129$	−0.130933			−0.0115280
$130$	1.19394	+	1.35026i	0.104715	+	0.118426i
$131$	3.83146			0.334756			0.167378	−	0.985893i	$-0.446470\pi$
$131$	3.83146			0.334756			0.167378	+	0.985893i	$0.446470\pi$
$132$			0.806063i			0.0701588i
$133$		−	3.96239i		−	0.343583i
$134$	3.35026			0.289419
$135$	−1.67513	+	1.48119i	−0.144172	+	0.127481i
$136$	0.387873			0.0332598
$137$		−	8.28233i		−	0.707607i	−0.935320	−	0.353804i	$-0.884888\pi$
$137$		−	8.28233i		−	0.707607i	0.935320	−	0.353804i	$-0.115112\pi$
$138$		−	5.28726i		−	0.450081i
$139$	14.0059			1.18796			0.593982	−	0.804479i	$-0.297555\pi$
$139$	14.0059			1.18796			0.593982	+	0.804479i	$0.297555\pi$
$140$	−1.35026	+	1.19394i	−0.114118	+	0.100906i
$141$	−1.28726			−0.108407
$142$			8.80606i			0.738988i
$143$			0.481194i			0.0402395i
$144$	4.96239			0.413532
$145$	−0.193937	−	0.219329i	−0.0161056	−	0.0182143i
$146$	7.78892			0.644616
$147$		−	1.00000i		−	0.0824786i
$148$			0.387873i			0.0318830i
$149$	−10.0000			−0.819232			−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000			−0.819232			−0.409616	+	0.912258i	$0.634337\pi$
$150$	−1.02539	+	8.31265i	−0.0837230	+	0.678725i
$151$	6.31265			0.513716			0.256858	−	0.966449i	$-0.417313\pi$
$151$	6.31265			0.513716			0.256858	+	0.966449i	$0.417313\pi$
$152$			7.92478i			0.642784i
$153$		−	0.193937i		−	0.0156788i
$154$	−1.67513			−0.134986
$155$	12.2193	+	13.8192i	0.981480	+	1.10999i
$156$	−0.387873			−0.0310547
$157$		−	9.95017i		−	0.794110i	−0.917795	−	0.397055i	$-0.870032\pi$
$157$		−	9.95017i		−	0.794110i	0.917795	−	0.397055i	$-0.129968\pi$
$158$		−	7.11871i		−	0.566334i
$159$	3.64974			0.289443
$160$	7.22425	−	6.38787i	0.571127	−	0.505006i
$161$	3.15633			0.248753
$162$		−	1.67513i		−	0.131611i
$163$		−	0.481194i		−	0.0376900i	−0.999822	−	0.0188450i	$-0.994001\pi$
$163$		−	0.481194i		−	0.0376900i	0.999822	−	0.0188450i	$-0.00599891\pi$
$164$	3.61213			0.282060
$165$	−1.67513	+	1.48119i	−0.130409	+	0.115311i
$166$	−8.76353			−0.680182
$167$			1.06793i			0.0826388i	0.999146	+	0.0413194i	$0.0131561\pi$
$167$			1.06793i			0.0826388i	−0.999146	+	0.0413194i	$0.986844\pi$
$168$			2.00000i			0.154303i
$169$	12.7685			0.982189
$170$	−0.481194	−	0.544198i	−0.0369059	−	0.0417381i
$171$	3.96239			0.303011
$172$		−	0.105540i		−	0.00804735i
$173$		−	18.5198i		−	1.40803i	−0.710184	−	0.704016i	$-0.751388\pi$
$173$		−	18.5198i		−	1.40803i	0.710184	−	0.704016i	$-0.248612\pi$
$174$	0.219329			0.0166273
$175$	−4.96239	−	0.612127i	−0.375121	−	0.0462724i
$176$	4.96239			0.374054
$177$			3.32487i			0.249912i
$178$			3.00492i			0.225229i
$179$	23.5550			1.76058			0.880292	−	0.474433i	$-0.157347\pi$
$179$	23.5550			1.76058			0.880292	+	0.474433i	$0.157347\pi$
$180$	−1.19394	−	1.35026i	−0.0889908	−	0.100643i
$181$	20.2882			1.50801			0.754005	−	0.656868i	$-0.228119\pi$
$181$	20.2882			1.50801			0.754005	+	0.656868i	$0.228119\pi$
$182$		−	0.806063i		−	0.0597494i
$183$		−	14.5066i		−	1.07236i
$184$	−6.31265			−0.465375
$185$	−0.806063	+	0.712742i	−0.0592630	+	0.0524019i
$186$	−13.8192			−1.01328
$187$		−	0.193937i		−	0.0141820i
$188$		−	1.03761i		−	0.0756756i
$189$	1.00000			0.0727393
$190$	11.1187	−	9.83146i	0.806636	−	0.713249i
$191$	20.1622			1.45889			0.729443	−	0.684042i	$-0.239779\pi$
$191$	20.1622			1.45889			0.729443	+	0.684042i	$0.239779\pi$
$192$		−	2.70052i		−	0.194893i
$193$		−	19.4617i		−	1.40088i	−0.713710	−	0.700441i	$-0.752987\pi$
$193$		−	19.4617i		−	1.40088i	0.713710	−	0.700441i	$-0.247013\pi$
$194$	8.74306			0.627715
$195$	−0.712742	−	0.806063i	−0.0510405	−	0.0577234i
$196$	0.806063			0.0575760
$197$		−	6.06063i		−	0.431802i	−0.976415	−	0.215901i	$-0.930731\pi$
$197$		−	6.06063i		−	0.431802i	0.976415	−	0.215901i	$-0.0692689\pi$
$198$		−	1.67513i		−	0.119046i
$199$	−2.49929			−0.177170			−0.0885851	−	0.996069i	$-0.528235\pi$
$199$	−2.49929			−0.177170			−0.0885851	+	0.996069i	$0.528235\pi$
$200$	9.92478	+	1.22425i	0.701788	+	0.0865678i
$201$	−2.00000			−0.141069
$202$			19.9756i			1.40548i
$203$			0.130933i			0.00918966i
$204$	0.156325			0.0109450
$205$	6.63752	+	7.50659i	0.463584	+	0.524283i
$206$	7.88224			0.549182
$207$			3.15633i			0.219380i
$208$			2.38787i			0.165569i
$209$	3.96239			0.274084
$210$	2.80606	−	2.48119i	0.193637	−	0.171219i
$211$	−7.16362			−0.493164			−0.246582	−	0.969122i	$-0.579307\pi$
$211$	−7.16362			−0.493164			−0.246582	+	0.969122i	$0.579307\pi$
$212$			2.94192i			0.202052i
$213$		−	5.25694i		−	0.360200i
$214$	2.28233			0.156017
$215$	0.219329	−	0.193937i	0.0149581	−	0.0132264i
$216$	−2.00000			−0.136083
$217$		−	8.24965i		−	0.560022i
$218$		−	1.84367i		−	0.124869i
$219$	−4.64974			−0.314200
$220$	−1.19394	−	1.35026i	−0.0804952	−	0.0910346i
$221$	0.0933212			0.00627746
$222$		−	0.806063i		−	0.0540994i
$223$			6.89209i			0.461529i	0.973010	+	0.230764i	$0.0741226\pi$
$223$			6.89209i			0.461529i	−0.973010	+	0.230764i	$0.925877\pi$
$224$	−4.31265			−0.288151
$225$	0.612127	−	4.96239i	0.0408085	−	0.330826i
$226$	−24.9502			−1.65966
$227$			3.76116i			0.249637i	0.992180	+	0.124818i	$0.0398348\pi$
$227$			3.76116i			0.249637i	−0.992180	+	0.124818i	$0.960165\pi$
$228$			3.19394i			0.211524i
$229$	−18.9502			−1.25226			−0.626131	−	0.779718i	$-0.715363\pi$
$229$	−18.9502			−1.25226			−0.626131	+	0.779718i	$0.715363\pi$
$230$	7.83146	+	8.85685i	0.516391	+	0.584003i
$231$	1.00000			0.0657952
$232$		−	0.261865i		−	0.0171923i
$233$		−	11.0860i		−	0.726270i	−0.931737	−	0.363135i	$-0.881706\pi$
$233$		−	11.0860i		−	0.726270i	0.931737	−	0.363135i	$-0.118294\pi$
$234$	0.806063			0.0526940
$235$	2.15633	−	1.90668i	0.140663	−	0.124378i
$236$	−2.68006			−0.174457
$237$			4.24965i			0.276044i
$238$			0.324869i			0.0210581i
$239$	−16.9370			−1.09556			−0.547782	−	0.836621i	$-0.684528\pi$
$239$	−16.9370			−1.09556			−0.547782	+	0.836621i	$0.684528\pi$
$240$	−8.31265	+	7.35026i	−0.536579	+	0.474457i
$241$	−30.2071			−1.94581			−0.972906	−	0.231203i	$-0.925734\pi$
$241$	−30.2071			−1.94581			−0.972906	+	0.231203i	$0.925734\pi$
$242$		−	1.67513i		−	0.107681i
$243$			1.00000i			0.0641500i
$244$	11.6932			0.748582
$245$	1.48119	+	1.67513i	0.0946300	+	0.107020i
$246$	−7.50659			−0.478603
$247$			1.90668i			0.121319i
$248$			16.4993i			1.04771i
$249$	5.23155			0.331536
$250$	−10.5950	−	15.4436i	−0.670086	−	0.976738i
$251$	26.0263			1.64277			0.821384	−	0.570375i	$-0.193202\pi$
$251$	26.0263			1.64277			0.821384	+	0.570375i	$0.193202\pi$
$252$			0.806063i			0.0507772i
$253$			3.15633i			0.198436i
$254$	−14.4060			−0.903911
$255$	0.287258	+	0.324869i	0.0179888	+	0.0203441i
$256$	16.6253			1.03908
$257$			15.1612i			0.945733i	0.881134	+	0.472866i	$0.156781\pi$
$257$			15.1612i			0.945733i	−0.881134	+	0.472866i	$0.843219\pi$
$258$			0.219329i			0.0136548i
$259$	0.481194			0.0299000
$260$	0.649738	−	0.574515i	0.0402951	−	0.0356299i
$261$	−0.130933			−0.00810452
$262$		−	6.41819i		−	0.396517i
$263$		−	7.29948i		−	0.450105i	−0.974347	−	0.225053i	$-0.927745\pi$
$263$		−	7.29948i		−	0.450105i	0.974347	−	0.225053i	$-0.0722554\pi$
$264$	−2.00000			−0.123091
$265$	−6.11379	+	5.40597i	−0.375567	+	0.332086i
$266$	−6.63752			−0.406972
$267$		−	1.79384i		−	0.109782i
$268$		−	1.61213i		−	0.0984763i
$269$	−19.0992			−1.16450			−0.582249	−	0.813010i	$-0.697827\pi$
$269$	−19.0992			−1.16450			−0.582249	+	0.813010i	$0.697827\pi$
$270$	2.48119	+	2.80606i	0.151001	+	0.170772i
$271$	18.4821			1.12271			0.561355	−	0.827575i	$-0.310280\pi$
$271$	18.4821			1.12271			0.561355	+	0.827575i	$0.310280\pi$
$272$		−	0.962389i		−	0.0583534i
$273$			0.481194i			0.0291232i
$274$	−13.8740			−0.838159
$275$	0.612127	−	4.96239i	0.0369126	−	0.299243i
$276$	−2.54420			−0.153143
$277$		−	31.8945i		−	1.91635i	−0.286179	−	0.958176i	$-0.592385\pi$
$277$		−	31.8945i		−	1.91635i	0.286179	−	0.958176i	$-0.407615\pi$
$278$		−	23.4617i		−	1.40714i
$279$	8.24965			0.493893
$280$	−2.96239	−	3.35026i	−0.177037	−	0.200216i
$281$	−19.8945			−1.18680			−0.593402	−	0.804906i	$-0.702216\pi$
$281$	−19.8945			−1.18680			−0.593402	+	0.804906i	$0.702216\pi$
$282$			2.15633i			0.128407i
$283$		−	12.2701i		−	0.729383i	−0.931128	−	0.364691i	$-0.881175\pi$
$283$		−	12.2701i		−	0.729383i	0.931128	−	0.364691i	$-0.118825\pi$
$284$	4.23743			0.251445
$285$	−6.63752	+	5.86907i	−0.393173	+	0.347654i
$286$	0.806063			0.0476635
$287$		−	4.48119i		−	0.264517i
$288$		−	4.31265i		−	0.254125i
$289$	16.9624			0.997788
$290$	−0.367405	+	0.324869i	−0.0215748	+	0.0190770i
$291$	−5.21933			−0.305962
$292$		−	3.74798i		−	0.219334i
$293$			12.4109i			0.725052i	0.931974	+	0.362526i	$0.118086\pi$
$293$			12.4109i			0.725052i	−0.931974	+	0.362526i	$0.881914\pi$
$294$	−1.67513			−0.0976956
$295$	−4.92478	−	5.56959i	−0.286732	−	0.324274i
$296$	−0.962389			−0.0559377
$297$			1.00000i			0.0580259i
$298$			16.7513i			0.970377i
$299$	−1.51881			−0.0878348
$300$	4.00000	+	0.493413i	0.230940	+	0.0284872i
$301$	−0.130933			−0.00754683
$302$		−	10.5745i		−	0.608495i
$303$		−	11.9248i		−	0.685061i
$304$	19.6629			1.12775
$305$	21.4871	+	24.3004i	1.23035	+	1.39144i
$306$	−0.324869			−0.0185715
$307$		−	22.4387i		−	1.28064i	−0.768107	−	0.640321i	$-0.778801\pi$
$307$		−	22.4387i		−	1.28064i	0.768107	−	0.640321i	$-0.221199\pi$
$308$			0.806063i			0.0459297i
$309$	−4.70545			−0.267684
$310$	23.1490	−	20.4690i	1.31478	−	1.16256i
$311$	−22.1768			−1.25753			−0.628765	−	0.777595i	$-0.716439\pi$
$311$	−22.1768			−1.25753			−0.628765	+	0.777595i	$0.716439\pi$
$312$		−	0.962389i		−	0.0544845i
$313$			16.5393i			0.934855i	0.884031	+	0.467428i	$0.154819\pi$
$313$			16.5393i			0.934855i	−0.884031	+	0.467428i	$0.845181\pi$
$314$	−16.6678			−0.940620
$315$	−1.67513	+	1.48119i	−0.0943829	+	0.0834558i
$316$	−3.42548			−0.192699
$317$		−	24.6556i		−	1.38480i	−0.721515	−	0.692399i	$-0.756554\pi$
$317$		−	24.6556i		−	1.38480i	0.721515	−	0.692399i	$-0.243446\pi$
$318$		−	6.11379i		−	0.342844i
$319$	−0.130933			−0.00733082
$320$	4.00000	+	4.52373i	0.223607	+	0.252884i
$321$	−1.36248			−0.0760462
$322$		−	5.28726i		−	0.294647i
$323$		−	0.768452i		−	0.0427578i
$324$	−0.806063			−0.0447813
$325$	2.38787	+	0.294552i	0.132455	+	0.0163388i
$326$	−0.806063			−0.0446437
$327$			1.10062i			0.0608642i
$328$			8.96239i			0.494865i
$329$	−1.28726			−0.0709688
$330$	2.48119	+	2.80606i	0.136585	+	0.154469i
$331$	−2.78892			−0.153293			−0.0766465	−	0.997058i	$-0.524421\pi$
$331$	−2.78892			−0.153293			−0.0766465	+	0.997058i	$0.524421\pi$
$332$			4.21696i			0.231436i
$333$			0.481194i			0.0263693i
$334$	1.78892			0.0978854
$335$	3.35026	−	2.96239i	0.183044	−	0.161853i
$336$	4.96239			0.270720
$337$		−	8.44358i		−	0.459951i	−0.973196	−	0.229976i	$-0.926135\pi$
$337$		−	8.44358i		−	0.459951i	0.973196	−	0.229976i	$-0.0738647\pi$
$338$		−	21.3888i		−	1.16340i
$339$	14.8945			0.808956
$340$	−0.261865	+	0.231548i	−0.0142016	+	0.0125575i
$341$	8.24965			0.446743
$342$		−	6.63752i		−	0.358916i
$343$		−	1.00000i		−	0.0539949i
$344$	0.261865			0.0141188
$345$	−4.67513	−	5.28726i	−0.251701	−	0.284656i
$346$	−31.0230			−1.66781
$347$		−	7.40105i		−	0.397309i	−0.980070	−	0.198655i	$-0.936343\pi$
$347$		−	7.40105i		−	0.397309i	0.980070	−	0.198655i	$-0.0636572\pi$
$348$		−	0.105540i		−	0.00565754i
$349$	3.32724			0.178103			0.0890515	−	0.996027i	$-0.471616\pi$
$349$	3.32724			0.178103			0.0890515	+	0.996027i	$0.471616\pi$
$350$	−1.02539	+	8.31265i	−0.0548095	+	0.444330i
$351$	−0.481194			−0.0256843
$352$		−	4.31265i		−	0.229865i
$353$			19.0640i			1.01467i	0.861748	+	0.507336i	$0.169370\pi$
$353$			19.0640i			1.01467i	−0.861748	+	0.507336i	$0.830630\pi$
$354$	5.56959			0.296020
$355$	7.78655	+	8.80606i	0.413267	+	0.467377i
$356$	1.44595			0.0766353
$357$		−	0.193937i		−	0.0102642i
$358$		−	39.4577i		−	2.08540i
$359$	−10.1817			−0.537371			−0.268685	−	0.963228i	$-0.586589\pi$
$359$	−10.1817			−0.537371			−0.268685	+	0.963228i	$0.586589\pi$
$360$	3.35026	−	2.96239i	0.176574	−	0.156132i
$361$	−3.29948			−0.173657
$362$		−	33.9854i		−	1.78623i
$363$			1.00000i			0.0524864i
$364$	−0.387873			−0.0203301
$365$	7.78892	−	6.88717i	0.407691	−	0.360491i
$366$	−24.3004			−1.27020
$367$		−	21.8895i		−	1.14262i	−0.820733	−	0.571312i	$-0.806435\pi$
$367$		−	21.8895i		−	1.14262i	0.820733	−	0.571312i	$-0.193565\pi$
$368$			15.6629i			0.816486i
$369$	4.48119			0.233282
$370$	1.19394	+	1.35026i	0.0620698	+	0.0701968i
$371$	3.64974			0.189485
$372$			6.64974i			0.344773i
$373$			3.13823i			0.162491i	0.996694	+	0.0812456i	$0.0258898\pi$
$373$			3.13823i			0.162491i	−0.996694	+	0.0812456i	$0.974110\pi$
$374$	−0.324869			−0.0167986
$375$	6.32487	+	9.21933i	0.326615	+	0.476084i
$376$	2.57452			0.132770
$377$		−	0.0630040i		−	0.00324487i
$378$		−	1.67513i		−	0.0861594i
$379$	22.0943			1.13491			0.567453	−	0.823406i	$-0.307929\pi$
$379$	22.0943			1.13491			0.567453	+	0.823406i	$0.307929\pi$
$380$	−4.73084	−	5.35026i	−0.242687	−	0.274463i
$381$	8.59991			0.440587
$382$		−	33.7743i		−	1.72805i
$383$			9.36248i			0.478400i	0.970970	+	0.239200i	$0.0768852\pi$
$383$			9.36248i			0.478400i	−0.970970	+	0.239200i	$0.923115\pi$
$384$	−13.1490			−0.671009
$385$	−1.67513	+	1.48119i	−0.0853726	+	0.0754887i
$386$	−32.6009			−1.65934
$387$		−	0.130933i		−	0.00665568i
$388$		−	4.20711i		−	0.213584i
$389$	8.27996			0.419811			0.209905	−	0.977722i	$-0.432684\pi$
$389$	8.27996			0.419811			0.209905	+	0.977722i	$0.432684\pi$
$390$	−1.35026	+	1.19394i	−0.0683732	+	0.0604573i
$391$	0.612127			0.0309566
$392$			2.00000i			0.101015i
$393$			3.83146i			0.193271i
$394$	−10.1524			−0.511468
$395$	−6.29455	−	7.11871i	−0.316713	−	0.358181i
$396$	−0.806063			−0.0405062
$397$			14.8061i			0.743095i	0.928414	+	0.371548i	$0.121173\pi$
$397$			14.8061i			0.743095i	−0.928414	+	0.371548i	$0.878827\pi$
$398$			4.18664i			0.209857i
$399$	3.96239			0.198368
$400$	3.03761	−	24.6253i	0.151881	−	1.23127i
$401$	−28.1197			−1.40423			−0.702115	−	0.712064i	$-0.747761\pi$
$401$	−28.1197			−1.40423			−0.702115	+	0.712064i	$0.747761\pi$
$402$			3.35026i			0.167096i
$403$			3.96968i			0.197744i
$404$	9.61213			0.478221
$405$	−1.48119	−	1.67513i	−0.0736011	−	0.0832379i
$406$	0.219329			0.0108851
$407$			0.481194i			0.0238519i
$408$			0.387873i			0.0192026i
$409$	19.0435			0.941640			0.470820	−	0.882229i	$-0.343958\pi$
$409$	19.0435			0.941640			0.470820	+	0.882229i	$0.343958\pi$
$410$	12.5745	−	11.1187i	0.621011	−	0.549114i
$411$	8.28233			0.408537
$412$		−	3.79289i		−	0.186862i
$413$			3.32487i			0.163606i
$414$	5.28726			0.259855
$415$	−8.76353	+	7.74894i	−0.430185	+	0.380380i
$416$	2.07522			0.101746
$417$			14.0059i			0.685871i
$418$		−	6.63752i		−	0.324652i
$419$	−4.29314			−0.209733			−0.104867	−	0.994486i	$-0.533442\pi$
$419$	−4.29314			−0.209733			−0.104867	+	0.994486i	$0.533442\pi$
$420$	−1.19394	−	1.35026i	−0.0582581	−	0.0658860i
$421$	−17.0508			−0.831004			−0.415502	−	0.909592i	$-0.636394\pi$
$421$	−17.0508			−0.831004			−0.415502	+	0.909592i	$0.636394\pi$
$422$			12.0000i			0.584151i
$423$		−	1.28726i		−	0.0625886i
$424$	−7.29948			−0.354494
$425$	−0.962389	−	0.118714i	−0.0466827	−	0.00575846i
$426$	−8.80606			−0.426655
$427$		−	14.5066i		−	0.702023i
$428$		−	1.09825i		−	0.0530857i
$429$	−0.481194			−0.0232323
$430$	−0.324869	−	0.367405i	−0.0156666	−	0.0177178i
$431$	21.6483			1.04276			0.521382	−	0.853324i	$-0.325417\pi$
$431$	21.6483			1.04276			0.521382	+	0.853324i	$0.325417\pi$
$432$			4.96239i			0.238753i
$433$			40.7123i			1.95651i	0.207412	+	0.978254i	$0.433496\pi$
$433$			40.7123i			1.95651i	−0.207412	+	0.978254i	$0.566504\pi$
$434$	−13.8192			−0.663345
$435$	0.219329	−	0.193937i	0.0105160	−	0.00929855i
$436$	−0.887166			−0.0424875
$437$			12.5066i			0.598271i
$438$			7.78892i			0.372169i
$439$	−20.4617			−0.976583			−0.488291	−	0.872681i	$-0.662380\pi$
$439$	−20.4617			−0.976583			−0.488291	+	0.872681i	$0.662380\pi$
$440$	3.35026	−	2.96239i	0.159717	−	0.141226i
$441$	1.00000			0.0476190
$442$		−	0.156325i		−	0.00743563i
$443$		−	28.3938i		−	1.34903i	−0.738262	−	0.674514i	$-0.764353\pi$
$443$		−	28.3938i		−	1.34903i	0.738262	−	0.674514i	$-0.235647\pi$
$444$	−0.387873			−0.0184076
$445$	2.65703	+	3.00492i	0.125955	+	0.142447i
$446$	11.5452			0.546679
$447$		−	10.0000i		−	0.472984i
$448$		−	2.70052i		−	0.127588i
$449$	−3.49437			−0.164909			−0.0824547	−	0.996595i	$-0.526276\pi$
$449$	−3.49437			−0.164909			−0.0824547	+	0.996595i	$0.526276\pi$
$450$	−8.31265	−	1.02539i	−0.391862	−	0.0483375i
$451$	4.48119			0.211011
$452$			12.0059i			0.564709i
$453$			6.31265i			0.296594i
$454$	6.30043			0.295694
$455$	−0.712742	−	0.806063i	−0.0334139	−	0.0377888i
$456$	−7.92478			−0.371112
$457$			2.46802i			0.115449i	0.998333	+	0.0577246i	$0.0183845\pi$
$457$			2.46802i			0.115449i	−0.998333	+	0.0577246i	$0.981615\pi$
$458$			31.7440i			1.48330i
$459$	0.193937			0.00905218
$460$	4.26187	−	3.76845i	0.198710	−	0.175705i
$461$	−8.28821			−0.386021			−0.193010	−	0.981197i	$-0.561825\pi$
$461$	−8.28821			−0.386021			−0.193010	+	0.981197i	$0.561825\pi$
$462$		−	1.67513i		−	0.0779341i
$463$			40.8119i			1.89669i	0.317238	+	0.948346i	$0.397245\pi$
$463$			40.8119i			1.89669i	−0.317238	+	0.948346i	$0.602755\pi$
$464$	−0.649738			−0.0301633
$465$	−13.8192	+	12.2193i	−0.640852	+	0.566658i
$466$	−18.5705			−0.860264
$467$		−	14.7757i		−	0.683740i	−0.939747	−	0.341870i	$-0.888940\pi$
$467$		−	14.7757i		−	0.683740i	0.939747	−	0.341870i	$-0.111060\pi$
$468$		−	0.387873i		−	0.0179294i
$469$	−2.00000			−0.0923514
$470$	−3.19394	−	3.61213i	−0.147325	−	0.166615i
$471$	9.95017			0.458480
$472$		−	6.64974i		−	0.306079i
$473$		−	0.130933i		−	0.00602029i
$474$	7.11871			0.326973
$475$	2.42548	−	19.6629i	0.111289	−	0.902196i
$476$	0.156325			0.00716515
$477$			3.64974i			0.167110i
$478$			28.3717i			1.29769i
$479$	9.46802			0.432605			0.216302	−	0.976326i	$-0.430600\pi$
$479$	9.46802			0.432605			0.216302	+	0.976326i	$0.430600\pi$
$480$	6.38787	+	7.22425i	0.291565	+	0.329741i
$481$	−0.231548			−0.0105577
$482$			50.6009i			2.30481i
$483$			3.15633i			0.143618i
$484$	−0.806063			−0.0366392
$485$	8.74306	−	7.73084i	0.397002	−	0.351039i
$486$	1.67513			0.0759855
$487$			35.3620i			1.60241i	0.598393	+	0.801203i	$0.295806\pi$
$487$			35.3620i			1.60241i	−0.598393	+	0.801203i	$0.704194\pi$
$488$			29.0132i			1.31336i
$489$	0.481194			0.0217604
$490$	2.80606	−	2.48119i	0.126765	−	0.112089i
$491$	−28.1124			−1.26869			−0.634347	−	0.773049i	$-0.718731\pi$
$491$	−28.1124			−1.26869			−0.634347	+	0.773049i	$0.718731\pi$
$492$			3.61213i			0.162847i
$493$			0.0253926i			0.00114363i
$494$	3.19394			0.143702
$495$	−1.48119	−	1.67513i	−0.0665747	−	0.0752915i
$496$	40.9380			1.83817
$497$		−	5.25694i		−	0.235806i
$498$		−	8.76353i		−	0.392703i
$499$	29.1417			1.30456			0.652282	−	0.757977i	$-0.273812\pi$
$499$	29.1417			1.30456			0.652282	+	0.757977i	$0.273812\pi$
$500$	−7.43136	+	5.09825i	−0.332341	+	0.228000i
$501$	−1.06793			−0.0477115
$502$		−	43.5975i		−	1.94585i
$503$			2.73813i			0.122087i	0.998135	+	0.0610437i	$0.0194429\pi$
$503$			2.73813i			0.122087i	−0.998135	+	0.0610437i	$0.980557\pi$
$504$	−2.00000			−0.0890871
$505$	17.6629	+	19.9756i	0.785989	+	0.888901i
$506$	5.28726			0.235047
$507$			12.7685i			0.567067i
$508$			6.93207i			0.307561i
$509$	4.45343			0.197395			0.0986975	−	0.995117i	$-0.468532\pi$
$509$	4.45343			0.197395			0.0986975	+	0.995117i	$0.468532\pi$
$510$	0.544198	−	0.481194i	0.0240975	−	0.0213076i
$511$	−4.64974			−0.205692
$512$		−	1.55149i		−	0.0685669i
$513$			3.96239i			0.174944i
$514$	25.3971			1.12022
$515$	7.88224	−	6.96968i	0.347333	−	0.307121i
$516$	0.105540			0.00464614
$517$		−	1.28726i		−	0.0566135i
$518$		−	0.806063i		−	0.0354164i
$519$	18.5198			0.812927
$520$	1.42548	+	1.61213i	0.0625116	+	0.0706964i
$521$	−5.88954			−0.258025			−0.129013	−	0.991643i	$-0.541181\pi$
$521$	−5.88954			−0.258025			−0.129013	+	0.991643i	$0.541181\pi$
$522$			0.219329i			0.00959978i
$523$			4.72496i			0.206608i	0.994650	+	0.103304i	$0.0329415\pi$
$523$			4.72496i			0.206608i	−0.994650	+	0.103304i	$0.967059\pi$
$524$	−3.08840			−0.134917
$525$	0.612127	−	4.96239i	0.0267154	−	0.216576i
$526$	−12.2276			−0.533148
$527$		−	1.59991i		−	0.0696931i
$528$			4.96239i			0.215960i
$529$	13.0376			0.566853
$530$	9.05571	+	10.2414i	0.393355	+	0.444858i
$531$	−3.32487			−0.144287
$532$			3.19394i			0.138475i
$533$			2.15633i			0.0934008i
$534$	−3.00492			−0.130036
$535$	2.28233	−	2.01810i	0.0986739	−	0.0872500i
$536$	4.00000			0.172774
$537$			23.5550i			1.01647i
$538$			31.9937i			1.37934i
$539$	1.00000			0.0430730
$540$	1.35026	−	1.19394i	0.0581060	−	0.0513788i
$541$	33.8129			1.45373			0.726865	−	0.686780i	$-0.240977\pi$
$541$	33.8129			1.45373			0.726865	+	0.686780i	$0.240977\pi$
$542$		−	30.9600i		−	1.32985i
$543$			20.2882i			0.870651i
$544$	−0.836381			−0.0358595
$545$	−1.63023	−	1.84367i	−0.0698312	−	0.0789744i
$546$	0.806063			0.0344963
$547$			36.2990i			1.55203i	0.630712	+	0.776017i	$0.282763\pi$
$547$			36.2990i			1.55203i	−0.630712	+	0.776017i	$0.717237\pi$
$548$			6.67609i			0.285188i
$549$	14.5066			0.619126
$550$	−8.31265	−	1.02539i	−0.354453	−	0.0437229i
$551$	−0.518806			−0.0221019
$552$		−	6.31265i		−	0.268684i
$553$			4.24965i			0.180713i
$554$	−53.4274			−2.26991
$555$	−0.712742	−	0.806063i	−0.0302542	−	0.0342155i
$556$	−11.2896			−0.478787
$557$		−	15.0640i		−	0.638280i	−0.947708	−	0.319140i	$-0.896606\pi$
$557$		−	15.0640i		−	0.638280i	0.947708	−	0.319140i	$-0.103394\pi$
$558$		−	13.8192i		−	0.585015i
$559$	0.0630040			0.00266479
$560$	−8.31265	+	7.35026i	−0.351274	+	0.310605i
$561$	0.193937			0.00818801
$562$			33.3258i			1.40577i
$563$			23.0943i			0.973308i	0.873595	+	0.486654i	$0.161783\pi$
$563$			23.0943i			0.973308i	−0.873595	+	0.486654i	$0.838217\pi$
$564$	1.03761			0.0436913
$565$	−24.9502	+	22.0616i	−1.04966	+	0.928138i
$566$	−20.5540			−0.863951
$567$			1.00000i			0.0419961i
$568$			10.5139i			0.441153i
$569$	−37.9013			−1.58890			−0.794452	−	0.607326i	$-0.792242\pi$
$569$	−37.9013			−1.58890			−0.794452	+	0.607326i	$0.792242\pi$
$570$	9.83146	+	11.1187i	0.411794	+	0.465712i
$571$	1.95158			0.0816713			0.0408356	−	0.999166i	$-0.486998\pi$
$571$	1.95158			0.0816713			0.0408356	+	0.999166i	$0.486998\pi$
$572$		−	0.387873i		−	0.0162178i
$573$			20.1622i			0.842288i
$574$	−7.50659			−0.313319
$575$	15.6629	+	1.93207i	0.653189	+	0.0805729i
$576$	2.70052			0.112522
$577$		−	1.71179i		−	0.0712626i	−0.999365	−	0.0356313i	$-0.988656\pi$
$577$		−	1.71179i		−	0.0712626i	0.999365	−	0.0356313i	$-0.0113442\pi$
$578$		−	28.4142i		−	1.18188i
$579$	19.4617			0.808800
$580$	0.156325	+	0.176793i	0.00649105	+	0.00734094i
$581$	5.23155			0.217041
$582$			8.74306i			0.362411i
$583$			3.64974i			0.151157i
$584$	9.29948			0.384815
$585$	0.806063	−	0.712742i	0.0333266	−	0.0294683i
$586$	20.7899			0.858822
$587$			25.1006i			1.03601i	0.855377	+	0.518007i	$0.173326\pi$
$587$			25.1006i			1.03601i	−0.855377	+	0.518007i	$0.826674\pi$
$588$			0.806063i			0.0332415i
$589$	32.6883			1.34690
$590$	−9.32979	+	8.24965i	−0.384102	+	0.339633i
$591$	6.06063			0.249301
$592$			2.38787i			0.0981410i
$593$			2.54420i			0.104478i	0.998635	+	0.0522389i	$0.0166357\pi$
$593$			2.54420i			0.104478i	−0.998635	+	0.0522389i	$0.983364\pi$
$594$	1.67513			0.0687315
$595$	0.287258	+	0.324869i	0.0117764	+	0.0133183i
$596$	8.06063			0.330176
$597$		−	2.49929i		−	0.102289i
$598$			2.54420i			0.104040i
$599$	−27.1246			−1.10828			−0.554140	−	0.832423i	$-0.686953\pi$
$599$	−27.1246			−1.10828			−0.554140	+	0.832423i	$0.686953\pi$
$600$	−1.22425	+	9.92478i	−0.0499799	+	0.405177i
$601$	6.96968			0.284299			0.142150	−	0.989845i	$-0.454599\pi$
$601$	6.96968			0.284299			0.142150	+	0.989845i	$0.454599\pi$
$602$			0.219329i			0.00893919i
$603$		−	2.00000i		−	0.0814463i
$604$	−5.08840			−0.207044
$605$	−1.48119	−	1.67513i	−0.0602191	−	0.0681038i
$606$	−19.9756			−0.811452
$607$		−	29.6893i		−	1.20505i	−0.798100	−	0.602525i	$-0.794161\pi$
$607$		−	29.6893i		−	1.20505i	0.798100	−	0.602525i	$-0.205839\pi$
$608$		−	17.0884i		−	0.693026i
$609$	−0.130933			−0.00530566
$610$	40.7064	−	35.9937i	1.64815	−	1.45734i
$611$	0.619421			0.0250591
$612$			0.156325i			0.00631907i
$613$			48.0019i			1.93878i	0.245528	+	0.969389i	$0.421039\pi$
$613$			48.0019i			1.93878i	−0.245528	+	0.969389i	$0.578961\pi$
$614$	−37.5877			−1.51692
$615$	−7.50659	+	6.63752i	−0.302695	+	0.267651i
$616$	−2.00000			−0.0805823
$617$			48.6966i			1.96045i	0.197888	+	0.980225i	$0.436592\pi$
$617$			48.6966i			1.96045i	−0.197888	+	0.980225i	$0.563408\pi$
$618$			7.88224i			0.317070i
$619$	22.4749			0.903341			0.451670	−	0.892185i	$-0.350828\pi$
$619$	22.4749			0.903341			0.451670	+	0.892185i	$0.350828\pi$
$620$	−9.84955	−	11.1392i	−0.395568	−	0.447360i
$621$	−3.15633			−0.126659
$622$			37.1490i			1.48954i
$623$		−	1.79384i		−	0.0718689i
$624$	−2.38787			−0.0955914
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$	27.7054			1.10733
$627$			3.96239i			0.158243i
$628$			8.02047i			0.320052i
$629$	0.0933212			0.00372096
$630$	2.48119	+	2.80606i	0.0988531	+	0.111796i
$631$	−1.96827			−0.0783555			−0.0391778	−	0.999232i	$-0.512474\pi$
$631$	−1.96827			−0.0783555			−0.0391778	+	0.999232i	$0.512474\pi$
$632$		−	8.49929i		−	0.338084i
$633$		−	7.16362i		−	0.284728i
$634$	−41.3014			−1.64029
$635$	−14.4060	+	12.7381i	−0.571684	+	0.505497i
$636$	−2.94192			−0.116655
$637$			0.481194i			0.0190656i
$638$			0.219329i			0.00868333i
$639$	5.25694			0.207961
$640$	22.0263	−	19.4763i	0.870668	−	0.769867i
$641$	28.0870			1.10937			0.554685	−	0.832061i	$-0.312839\pi$
$641$	28.0870			1.10937			0.554685	+	0.832061i	$0.312839\pi$
$642$			2.28233i			0.0900765i
$643$			34.9779i			1.37939i	0.724098	+	0.689697i	$0.242256\pi$
$643$			34.9779i			1.37939i	−0.724098	+	0.689697i	$0.757744\pi$
$644$	−2.54420			−0.100255
$645$	0.193937	+	0.219329i	0.00763624	+	0.00863608i
$646$	−1.28726			−0.0506465
$647$		−	31.5731i		−	1.24127i	−0.784101	−	0.620633i	$-0.786876\pi$
$647$		−	31.5731i		−	1.24127i	0.784101	−	0.620633i	$-0.213124\pi$
$648$		−	2.00000i		−	0.0785674i
$649$	−3.32487			−0.130513
$650$	0.493413	−	4.00000i	0.0193533	−	0.156893i
$651$	8.24965			0.323329
$652$			0.387873i			0.0151903i
$653$			16.7137i			0.654058i	0.945014	+	0.327029i	$0.106047\pi$
$653$			16.7137i			0.654058i	−0.945014	+	0.327029i	$0.893953\pi$
$654$	1.84367			0.0720934
$655$	−5.67513	−	6.41819i	−0.221746	−	0.250779i
$656$	22.2374			0.868226
$657$		−	4.64974i		−	0.181404i
$658$			2.15633i			0.0840623i
$659$	12.5148			0.487509			0.243754	−	0.969837i	$-0.421621\pi$
$659$	12.5148			0.487509			0.243754	+	0.969837i	$0.421621\pi$
$660$	1.35026	−	1.19394i	0.0525589	−	0.0464739i
$661$	−35.5510			−1.38277			−0.691387	−	0.722484i	$-0.743000\pi$
$661$	−35.5510			−1.38277			−0.691387	+	0.722484i	$0.743000\pi$
$662$			4.67181i			0.181575i
$663$			0.0933212i			0.00362429i
$664$	−10.4631			−0.406047
$665$	−6.63752	+	5.86907i	−0.257392	+	0.227593i
$666$	0.806063			0.0312343
$667$		−	0.413266i		−	0.0160017i
$668$		−	0.860818i		−	0.0333061i
$669$	−6.89209			−0.266464
$670$	−4.96239	−	5.61213i	−0.191714	−	0.216815i
$671$	14.5066			0.560021
$672$		−	4.31265i		−	0.166364i
$673$			27.1646i			1.04712i	0.851990	+	0.523559i	$0.175396\pi$
$673$			27.1646i			1.04712i	−0.851990	+	0.523559i	$0.824604\pi$
$674$	−14.1441			−0.544811
$675$	4.96239	+	0.612127i	0.191002	+	0.0235608i
$676$	−10.2922			−0.395853
$677$		−	37.3693i		−	1.43622i	−0.695930	−	0.718110i	$-0.745008\pi$
$677$		−	37.3693i		−	1.43622i	0.695930	−	0.718110i	$-0.254992\pi$
$678$		−	24.9502i		−	0.958205i
$679$	−5.21933			−0.200299
$680$	−0.574515	−	0.649738i	−0.0220317	−	0.0249163i
$681$	−3.76116			−0.144128
$682$		−	13.8192i		−	0.529166i
$683$		−	44.6253i		−	1.70754i	−0.520651	−	0.853770i	$-0.674311\pi$
$683$		−	44.6253i		−	1.70754i	0.520651	−	0.853770i	$-0.325689\pi$
$684$	−3.19394			−0.122123
$685$	−13.8740	+	12.2677i	−0.530098	+	0.468726i
$686$	−1.67513			−0.0639568
$687$		−	18.9502i		−	0.722994i
$688$		−	0.649738i		−	0.0247710i
$689$	−1.75623			−0.0669072
$690$	−8.85685	+	7.83146i	−0.337174	+	0.298138i
$691$	−47.9365			−1.82359			−0.911796	−	0.410644i	$-0.865304\pi$
$691$	−47.9365			−1.82359			−0.911796	+	0.410644i	$0.865304\pi$
$692$			14.9281i			0.567481i
$693$			1.00000i			0.0379869i
$694$	−12.3977			−0.470611
$695$	−20.7454	−	23.4617i	−0.786919	−	0.889952i
$696$	0.261865			0.00992597
$697$		−	0.869067i		−	0.0329183i
$698$		−	5.57356i		−	0.210962i
$699$	11.0860			0.419312
$700$	4.00000	+	0.493413i	0.151186	+	0.0186493i
$701$	−38.3947			−1.45015			−0.725074	−	0.688671i	$-0.758194\pi$
$701$	−38.3947			−1.45015			−0.725074	+	0.688671i	$0.758194\pi$
$702$			0.806063i			0.0304229i
$703$			1.90668i			0.0719118i
$704$	2.70052			0.101780
$705$	1.90668	+	2.15633i	0.0718097	+	0.0812119i
$706$	31.9346			1.20188
$707$		−	11.9248i		−	0.448477i
$708$		−	2.68006i		−	0.100723i
$709$	30.4558			1.14379			0.571896	−	0.820326i	$-0.306208\pi$
$709$	30.4558			1.14379			0.571896	+	0.820326i	$0.306208\pi$
$710$	14.7513	−	13.0435i	0.553607	−	0.489513i
$711$	−4.24965			−0.159374
$712$			3.58769i			0.134454i
$713$			26.0386i			0.975152i
$714$	−0.324869			−0.0121579
$715$	0.806063	−	0.712742i	0.0301451	−	0.0266550i
$716$	−18.9868			−0.709571
$717$		−	16.9370i		−	0.632524i
$718$			17.0557i			0.636513i
$719$	29.8096			1.11171			0.555855	−	0.831279i	$-0.312391\pi$
$719$	29.8096			1.11171			0.555855	+	0.831279i	$0.312391\pi$
$720$	−7.35026	−	8.31265i	−0.273928	−	0.309794i
$721$	−4.70545			−0.175240
$722$			5.52705i			0.205696i
$723$		−	30.2071i		−	1.12341i
$724$	−16.3536			−0.607776
$725$	−0.0801473	+	0.649738i	−0.00297660	+	0.0241307i
$726$	1.67513			0.0621699
$727$			1.38550i			0.0513855i	0.999670	+	0.0256927i	$0.00817915\pi$
$727$			1.38550i			0.0513855i	−0.999670	+	0.0256927i	$0.991821\pi$
$728$		−	0.962389i		−	0.0356685i
$729$	−1.00000			−0.0370370
$730$	−11.5369	−	13.0475i	−0.427000	−	0.482908i
$731$	−0.0253926			−0.000939180
$732$			11.6932i			0.432194i
$733$		−	47.8858i		−	1.76870i	−0.466824	−	0.884350i	$-0.654602\pi$
$733$		−	47.8858i		−	1.76870i	0.466824	−	0.884350i	$-0.345398\pi$
$734$	−36.6678			−1.35343
$735$	−1.67513	+	1.48119i	−0.0617881	+	0.0546347i
$736$	13.6121			0.501750
$737$		−	2.00000i		−	0.0736709i
$738$		−	7.50659i		−	0.276321i
$739$	−43.6893			−1.60714			−0.803568	−	0.595213i	$-0.797068\pi$
$739$	−43.6893			−1.60714			−0.803568	+	0.595213i	$0.797068\pi$
$740$	0.649738	−	0.574515i	0.0238849	−	0.0211196i
$741$	−1.90668			−0.0700436
$742$		−	6.11379i		−	0.224444i
$743$			7.74798i			0.284246i	0.989849	+	0.142123i	$0.0453928\pi$
$743$			7.74798i			0.284246i	−0.989849	+	0.142123i	$0.954607\pi$
$744$	−16.4993			−0.604893
$745$	14.8119	+	16.7513i	0.542668	+	0.613720i
$746$	5.25694			0.192470
$747$			5.23155i			0.191412i
$748$			0.156325i			0.00571581i
$749$	−1.36248			−0.0497840
$750$	15.4436	−	10.5950i	0.563920	−	0.386874i
$751$	−5.07522			−0.185198			−0.0925988	−	0.995704i	$-0.529517\pi$
$751$	−5.07522			−0.185198			−0.0925988	+	0.995704i	$0.529517\pi$
$752$		−	6.38787i		−	0.232942i
$753$			26.0263i			0.948453i
$754$	−0.105540			−0.00384354
$755$	−9.35026	−	10.5745i	−0.340291	−	0.384846i
$756$	−0.806063			−0.0293162
$757$			38.9478i			1.41558i	0.706422	+	0.707791i	$0.250308\pi$
$757$			38.9478i			1.41558i	−0.706422	+	0.707791i	$0.749692\pi$
$758$		−	37.0108i		−	1.34429i
$759$	−3.15633			−0.114567
$760$	13.2750	−	11.7381i	0.481536	−	0.425787i
$761$	−46.6107			−1.68964			−0.844818	−	0.535053i	$-0.820292\pi$
$761$	−46.6107			−1.68964			−0.844818	+	0.535053i	$0.820292\pi$
$762$		−	14.4060i		−	0.521873i
$763$			1.10062i			0.0398450i
$764$	−16.2520			−0.587977
$765$	−0.324869	+	0.287258i	−0.0117457	+	0.0103858i
$766$	15.6834			0.566664
$767$		−	1.59991i		−	0.0577693i
$768$			16.6253i			0.599914i
$769$	−25.0870			−0.904660			−0.452330	−	0.891851i	$-0.649407\pi$
$769$	−25.0870			−0.904660			−0.452330	+	0.891851i	$0.649407\pi$
$770$	2.48119	+	2.80606i	0.0894160	+	0.101124i
$771$	−15.1612			−0.546019
$772$			15.6873i			0.564600i
$773$		−	45.9464i		−	1.65258i	−0.563247	−	0.826288i	$-0.690448\pi$
$773$		−	45.9464i		−	1.65258i	0.563247	−	0.826288i	$-0.309552\pi$
$774$	−0.219329			−0.00788362
$775$	5.04983	−	40.9380i	0.181395	−	1.47053i
$776$	10.4387			0.374726
$777$			0.481194i			0.0172627i
$778$		−	13.8700i		−	0.497264i
$779$	17.7562			0.636183
$780$	0.574515	+	0.649738i	0.0205710	+	0.0232644i
$781$	5.25694			0.188108
$782$		−	1.02539i		−	0.0366680i
$783$		−	0.130933i		−	0.00467915i
$784$	4.96239			0.177228
$785$	−16.6678	+	14.7381i	−0.594901	+	0.526027i
$786$	6.41819			0.228929
$787$		−	42.0870i		−	1.50024i	−0.661302	−	0.750119i	$-0.729996\pi$
$787$		−	42.0870i		−	1.50024i	0.661302	−	0.750119i	$-0.270004\pi$
$788$			4.88526i			0.174030i
$789$	7.29948			0.259868
$790$	−11.9248	+	10.5442i	−0.424265	+	0.375146i
$791$	14.8945			0.529586
$792$		−	2.00000i		−	0.0710669i
$793$			6.98049i			0.247884i
$794$	24.8021			0.880193
$795$	−5.40597	−	6.11379i	−0.191730	−	0.216834i
$796$	2.01459			0.0714052
$797$			5.96380i			0.211249i	0.994406	+	0.105624i	$0.0336841\pi$
$797$			5.96380i			0.211249i	−0.994406	+	0.105624i	$0.966316\pi$
$798$		−	6.63752i		−	0.234966i
$799$	−0.249646			−0.00883185
$800$	−21.4010	−	2.63989i	−0.756641	−	0.0933342i
$801$	1.79384			0.0633824
$802$			47.1041i			1.66330i
$803$		−	4.64974i		−	0.164086i
$804$	1.61213			0.0568553
$805$	−4.67513	−	5.28726i	−0.164777	−	0.186351i
$806$	6.64974			0.234227
$807$		−	19.0992i		−	0.672324i
$808$			23.8496i			0.839024i
$809$	22.6859			0.797595			0.398798	−	0.917039i	$-0.369428\pi$
$809$	22.6859			0.797595			0.398798	+	0.917039i	$0.369428\pi$
$810$	−2.80606	+	2.48119i	−0.0985950	+	0.0871803i
$811$	33.3160			1.16988			0.584941	−	0.811076i	$-0.301118\pi$
$811$	33.3160			1.16988			0.584941	+	0.811076i	$0.301118\pi$
$812$		−	0.105540i		−	0.00370373i
$813$			18.4821i			0.648197i
$814$	0.806063			0.0282525
$815$	−0.806063	+	0.712742i	−0.0282352	+	0.0249663i
$816$	0.962389			0.0336903
$817$		−	0.518806i		−	0.0181507i
$818$		−	31.9003i		−	1.11537i
$819$	−0.481194			−0.0168143
$820$	−5.35026	−	6.05079i	−0.186839	−	0.211303i
$821$	−25.8848			−0.903386			−0.451693	−	0.892174i	$-0.649180\pi$
$821$	−25.8848			−0.903386			−0.451693	+	0.892174i	$0.649180\pi$
$822$		−	13.8740i		−	0.483911i
$823$		−	22.7548i		−	0.793183i	−0.917995	−	0.396592i	$-0.870193\pi$
$823$		−	22.7548i		−	0.793183i	0.917995	−	0.396592i	$-0.129807\pi$
$824$	9.41090			0.327844
$825$	4.96239	+	0.612127i	0.172768	+	0.0213115i
$826$	5.56959			0.193791
$827$			11.4499i			0.398153i	0.979984	+	0.199076i	$0.0637942\pi$
$827$			11.4499i			0.398153i	−0.979984	+	0.199076i	$0.936206\pi$
$828$		−	2.54420i		−	0.0884170i
$829$	40.4749			1.40575			0.702875	−	0.711313i	$-0.251899\pi$
$829$	40.4749			1.40575			0.702875	+	0.711313i	$0.251899\pi$
$830$	12.9805	+	14.6801i	0.450559	+	0.509552i
$831$	31.8945			1.10641
$832$			1.29948i			0.0450512i
$833$		−	0.193937i		−	0.00671950i
$834$	23.4617			0.812412
$835$	1.78892	−	1.58181i	0.0619081	−	0.0547408i
$836$	−3.19394			−0.110465
$837$			8.24965i			0.285149i
$838$			7.19157i			0.248429i
$839$	29.5682			1.02081			0.510403	−	0.859935i	$-0.329496\pi$
$839$	29.5682			1.02081			0.510403	+	0.859935i	$0.329496\pi$
$840$	3.35026	−	2.96239i	0.115595	−	0.102212i
$841$	−28.9829			−0.999409
$842$			28.5623i			0.984322i
$843$		−	19.8945i		−	0.685202i
$844$	5.77433			0.198761
$845$	−18.9126	−	21.3888i	−0.650612	−	0.735798i
$846$	−2.15633			−0.0741360
$847$			1.00000i			0.0343604i
$848$			18.1114i			0.621949i
$849$	12.2701			0.421109
$850$	−0.198861	+	1.61213i	−0.00682088	+	0.0552955i
$851$	−1.51881			−0.0520640
$852$			4.23743i			0.145172i
$853$		−	9.88224i		−	0.338361i	−0.985585	−	0.169181i	$-0.945888\pi$
$853$		−	9.88224i		−	0.338361i	0.985585	−	0.169181i	$-0.0541122\pi$
$854$	−24.3004			−0.831544
$855$	−5.86907	−	6.63752i	−0.200718	−	0.226998i
$856$	2.72496			0.0931373
$857$		−	47.1002i		−	1.60891i	−0.594013	−	0.804455i	$-0.702457\pi$
$857$		−	47.1002i		−	1.60891i	0.594013	−	0.804455i	$-0.297543\pi$
$858$			0.806063i			0.0275186i
$859$	−30.8096			−1.05121			−0.525605	−	0.850729i	$-0.676161\pi$
$859$	−30.8096			−1.05121			−0.525605	+	0.850729i	$0.676161\pi$
$860$	−0.176793	+	0.156325i	−0.00602860	+	0.00533064i
$861$	4.48119			0.152719
$862$		−	36.2638i		−	1.23515i
$863$			19.5040i			0.663925i	0.943293	+	0.331962i	$0.107711\pi$
$863$			19.5040i			0.663925i	−0.943293	+	0.331962i	$0.892289\pi$
$864$	4.31265			0.146719
$865$	−31.0230	+	27.4314i	−1.05481	+	0.932694i
$866$	68.1984			2.31748
$867$			16.9624i			0.576073i
$868$			6.64974i			0.225707i
$869$	−4.24965			−0.144159
$870$	−0.324869	−	0.367405i	−0.0110141	−	0.0124562i
$871$	0.962389			0.0326093
$872$		−	2.20123i		−	0.0745431i
$873$		−	5.21933i		−	0.176648i
$874$	20.9502			0.708650
$875$	6.32487	+	9.21933i	0.213820	+	0.311670i
$876$	3.74798			0.126633
$877$			33.6697i			1.13695i	0.822702	+	0.568473i	$0.192466\pi$
$877$			33.6697i			1.13695i	−0.822702	+	0.568473i	$0.807534\pi$
$878$			34.2760i			1.15676i
$879$	−12.4109			−0.418609
$880$	−7.35026	−	8.31265i	−0.247777	−	0.280219i
$881$	−44.4191			−1.49652			−0.748260	−	0.663406i	$-0.769110\pi$
$881$	−44.4191			−1.49652			−0.748260	+	0.663406i	$0.769110\pi$
$882$		−	1.67513i		−	0.0564046i
$883$			33.1100i			1.11424i	0.830432	+	0.557120i	$0.188094\pi$
$883$			33.1100i			1.11424i	−0.830432	+	0.557120i	$0.811906\pi$
$884$	−0.0752228			−0.00253002
$885$	5.56959	−	4.92478i	0.187220	−	0.165545i
$886$	−47.5633			−1.59792
$887$		−	40.5877i		−	1.36280i	−0.731911	−	0.681401i	$-0.761371\pi$
$887$		−	40.5877i		−	1.36280i	0.731911	−	0.681401i	$-0.238629\pi$
$888$		−	0.962389i		−	0.0322956i
$889$	8.59991			0.288432
$890$	5.03364	−	4.45088i	0.168728	−	0.149194i
$891$	−1.00000			−0.0335013
$892$		−	5.55546i		−	0.186011i
$893$		−	5.10062i		−	0.170686i
$894$	−16.7513			−0.560248
$895$	−34.8895	−	39.4577i	−1.16623	−	1.31893i
$896$	−13.1490			−0.439278
$897$		−	1.51881i		−	0.0507114i
$898$			5.85352i			0.195335i
$899$	−1.08015			−0.0360249
$900$	−0.493413	+	4.00000i	−0.0164471	+	0.133333i
$901$	0.707818			0.0235808
$902$		−	7.50659i		−	0.249942i
$903$		−	0.130933i		−	0.00435716i
$904$	−29.7889			−0.990765
$905$	−30.0508	−	33.9854i	−0.998922	−	1.12971i
$906$	10.5745			0.351315
$907$		−	6.39612i		−	0.212380i	−0.994346	−	0.106190i	$-0.966135\pi$
$907$		−	6.39612i		−	0.212380i	0.994346	−	0.106190i	$-0.0338651\pi$
$908$		−	3.03173i		−	0.100612i
$909$	11.9248			0.395520
$910$	−1.35026	+	1.19394i	−0.0447607	+	0.0395786i
$911$	−24.0362			−0.796355			−0.398177	−	0.917308i	$-0.630357\pi$
$911$	−24.0362			−0.796355			−0.398177	+	0.917308i	$0.630357\pi$
$912$			19.6629i			0.651104i
$913$			5.23155i			0.173139i
$914$	4.13426			0.136749
$915$	−24.3004	+	21.4871i	−0.803347	+	0.710341i
$916$	15.2750			0.504701
$917$			3.83146i			0.126526i
$918$		−	0.324869i		−	0.0107223i
$919$	3.81336			0.125791			0.0628955	−	0.998020i	$-0.479967\pi$
$919$	3.81336			0.125791			0.0628955	+	0.998020i	$0.479967\pi$
$920$	9.35026	+	10.5745i	0.308269	+	0.348631i
$921$	22.4387			0.739379
$922$			13.8838i			0.457240i
$923$			2.52961i			0.0832631i
$924$	−0.806063			−0.0265175
$925$	2.38787	+	0.294552i	0.0785128	+	0.00968481i
$926$	68.3653			2.24662
$927$		−	4.70545i		−	0.154547i
$928$			0.564666i			0.0185361i
$929$	−20.4591			−0.671242			−0.335621	−	0.941997i	$-0.608946\pi$
$929$	−20.4591			−0.671242			−0.335621	+	0.941997i	$0.608946\pi$
$930$	20.4690	+	23.1490i	0.671204	+	0.759087i
$931$	3.96239			0.129862
$932$			8.93604i			0.292710i
$933$		−	22.1768i		−	0.726036i
$934$	−24.7513			−0.809888
$935$	−0.324869	+	0.287258i	−0.0106244	+	0.00939433i
$936$	0.962389			0.0314567
$937$		−	41.1065i		−	1.34289i	−0.741054	−	0.671445i	$-0.765674\pi$
$937$		−	41.1065i		−	1.34289i	0.741054	−	0.671445i	$-0.234326\pi$
$938$			3.35026i			0.109390i
$939$	−16.5393			−0.539739
$940$	−1.73813	+	1.53690i	−0.0566917	+	0.0501283i
$941$	4.80369			0.156596			0.0782980	−	0.996930i	$-0.475051\pi$
$941$	4.80369			0.156596			0.0782980	+	0.996930i	$0.475051\pi$
$942$		−	16.6678i		−	0.543067i
$943$			14.1441i			0.460595i
$944$	−16.4993			−0.537006
$945$	−1.48119	−	1.67513i	−0.0481833	−	0.0544920i
$946$	−0.219329			−0.00713101
$947$			2.07267i			0.0673527i	0.999433	+	0.0336763i	$0.0107215\pi$
$947$			2.07267i			0.0673527i	−0.999433	+	0.0336763i	$0.989278\pi$
$948$		−	3.42548i		−	0.111255i
$949$	2.23743			0.0726300
$950$	−32.9380	−	4.06300i	−1.06865	−	0.131821i
$951$	24.6556			0.799513
$952$			0.387873i			0.0125710i
$953$		−	36.3996i		−	1.17910i	−0.807732	−	0.589550i	$-0.799305\pi$
$953$		−	36.3996i		−	1.17910i	0.807732	−	0.589550i	$-0.200695\pi$
$954$	6.11379			0.197941
$955$	−29.8641	−	33.7743i	−0.966381	−	1.09291i
$956$	13.6523			0.441547
$957$		−	0.130933i		−	0.00423245i
$958$		−	15.8602i		−	0.512419i
$959$	8.28233			0.267450
$960$	−4.52373	+	4.00000i	−0.146003	+	0.129099i
$961$	37.0567			1.19538
$962$			0.387873i			0.0125055i
$963$		−	1.36248i		−	0.0439053i
$964$	24.3488			0.784224
$965$	−32.6009	+	28.8265i	−1.04946	+	0.927959i
$966$	5.28726			0.170115
$967$		−	5.15869i		−	0.165892i	−0.996554	−	0.0829462i	$-0.973567\pi$
$967$		−	5.15869i		−	0.165892i	0.996554	−	0.0829462i	$-0.0264330\pi$
$968$		−	2.00000i		−	0.0642824i
$969$	0.768452			0.0246862
$970$	−12.9502	−	14.6458i	−0.415805	−	0.470247i
$971$	24.0919			0.773146			0.386573	−	0.922259i	$-0.373659\pi$
$971$	24.0919			0.773146			0.386573	+	0.922259i	$0.373659\pi$
$972$		−	0.806063i		−	0.0258545i
$973$			14.0059i			0.449008i
$974$	59.2360			1.89804
$975$	−0.294552	+	2.38787i	−0.00943321	+	0.0764731i
$976$	71.9873			2.30426
$977$		−	8.62198i		−	0.275841i	−0.990443	−	0.137921i	$-0.955958\pi$
$977$		−	8.62198i		−	0.275841i	0.990443	−	0.137921i	$-0.0440419\pi$
$978$		−	0.806063i		−	0.0257751i
$979$	1.79384			0.0573315
$980$	−1.19394	−	1.35026i	−0.0381389	−	0.0431325i
$981$	−1.10062			−0.0351399
$982$			47.0919i			1.50276i
$983$		−	16.2228i		−	0.517428i	−0.965954	−	0.258714i	$-0.916701\pi$
$983$		−	16.2228i		−	0.517428i	0.965954	−	0.258714i	$-0.0832988\pi$
$984$	−8.96239			−0.285711
$985$	−10.1524	+	8.97698i	−0.323481	+	0.286030i
$986$	0.0425359			0.00135462
$987$		−	1.28726i		−	0.0409739i
$988$		−	1.53690i		−	0.0488954i
$989$	0.413266			0.0131411
$990$	−2.80606	+	2.48119i	−0.0891826	+	0.0788575i
$991$	−40.4880			−1.28614			−0.643072	−	0.765805i	$-0.722341\pi$
$991$	−40.4880			−1.28614			−0.643072	+	0.765805i	$0.722341\pi$
$992$		−	35.5778i		−	1.12960i
$993$		−	2.78892i		−	0.0885037i
$994$	−8.80606			−0.279311
$995$	3.70194	+	4.18664i	0.117359	+	0.132725i
$996$	−4.21696			−0.133619
$997$			16.8627i			0.534048i	0.963690	+	0.267024i	$0.0860403\pi$
$997$			16.8627i			0.534048i	−0.963690	+	0.267024i	$0.913960\pi$
$998$		−	48.8162i		−	1.54525i
$999$	−0.481194			−0.0152243

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.c.694.2	✓	6
5.2	odd	4		5775.2.a.bu.1.3		3
5.3	odd	4		5775.2.a.bt.1.1		3
5.4	even	2	inner	1155.2.c.c.694.5	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.c.694.2	✓	6	1.1	even	1	trivial
1155.2.c.c.694.5	yes	6	5.4	even	2	inner
5775.2.a.bt.1.1		3	5.3	odd	4
5775.2.a.bu.1.3		3	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)

\(f(q)\)	\(=\)	\(q-1.67513i q^{2} +1.00000i q^{3} -0.806063 q^{4} +(-1.48119 - 1.67513i) q^{5} +1.67513 q^{6} +1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.67513i q^{2} +1.00000i q^{3} -0.806063 q^{4} +(-1.48119 - 1.67513i) q^{5} +1.67513 q^{6} +1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +(-2.80606 + 2.48119i) q^{10} -1.00000 q^{11} -0.806063i q^{12} -0.481194i q^{13} +1.67513 q^{14} +(1.67513 - 1.48119i) q^{15} -4.96239 q^{16} +0.193937i q^{17} +1.67513i q^{18} -3.96239 q^{19} +(1.19394 + 1.35026i) q^{20} -1.00000 q^{21} +1.67513i q^{22} -3.15633i q^{23} +2.00000 q^{24} +(-0.612127 + 4.96239i) q^{25} -0.806063 q^{26} -1.00000i q^{27} -0.806063i q^{28} +0.130933 q^{29} +(-2.48119 - 2.80606i) q^{30} -8.24965 q^{31} +4.31265i q^{32} -1.00000i q^{33} +0.324869 q^{34} +(1.67513 - 1.48119i) q^{35} +0.806063 q^{36} -0.481194i q^{37} +6.63752i q^{38} +0.481194 q^{39} +(-3.35026 + 2.96239i) q^{40} -4.48119 q^{41} +1.67513i q^{42} +0.130933i q^{43} +0.806063 q^{44} +(1.48119 + 1.67513i) q^{45} -5.28726 q^{46} +1.28726i q^{47} -4.96239i q^{48} -1.00000 q^{49} +(8.31265 + 1.02539i) q^{50} -0.193937 q^{51} +0.387873i q^{52} -3.64974i q^{53} -1.67513 q^{54} +(1.48119 + 1.67513i) q^{55} +2.00000 q^{56} -3.96239i q^{57} -0.219329i q^{58} +3.32487 q^{59} +(-1.35026 + 1.19394i) q^{60} -14.5066 q^{61} +13.8192i q^{62} -1.00000i q^{63} -2.70052 q^{64} +(-0.806063 + 0.712742i) q^{65} -1.67513 q^{66} +2.00000i q^{67} -0.156325i q^{68} +3.15633 q^{69} +(-2.48119 - 2.80606i) q^{70} -5.25694 q^{71} +2.00000i q^{72} +4.64974i q^{73} -0.806063 q^{74} +(-4.96239 - 0.612127i) q^{75} +3.19394 q^{76} -1.00000i q^{77} -0.806063i q^{78} +4.24965 q^{79} +(7.35026 + 8.31265i) q^{80} +1.00000 q^{81} +7.50659i q^{82} -5.23155i q^{83} +0.806063 q^{84} +(0.324869 - 0.287258i) q^{85} +0.219329 q^{86} +0.130933i q^{87} +2.00000i q^{88} -1.79384 q^{89} +(2.80606 - 2.48119i) q^{90} +0.481194 q^{91} +2.54420i q^{92} -8.24965i q^{93} +2.15633 q^{94} +(5.86907 + 6.63752i) q^{95} -4.31265 q^{96} +5.21933i q^{97} +1.67513i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9	\( 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9} - 16 q^{10} - 6 q^{11} - 8 q^{16} - 2 q^{19} + 8 q^{20} - 6 q^{21} + 12 q^{24} - 2 q^{25} - 4 q^{26} + 10 q^{29} - 4 q^{30} - 16 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} - 16 q^{41} + 4 q^{44} - 2 q^{45} - 20 q^{46} - 6 q^{49} + 8 q^{50} - 2 q^{51} - 2 q^{55} + 12 q^{56} + 30 q^{59} + 12 q^{60} - 46 q^{61} + 24 q^{64} - 4 q^{65} - 2 q^{69} - 4 q^{70} - 24 q^{71} - 4 q^{74} - 8 q^{75} + 20 q^{76} - 8 q^{79} + 24 q^{80} + 6 q^{81} + 4 q^{84} + 12 q^{85} - 28 q^{86} + 42 q^{89} + 16 q^{90} - 8 q^{91} - 8 q^{94} + 26 q^{95} + 16 q^{96} + 6 q^{99}+O(q^{100}) \) 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9 - 16 * q^10 - 6 * q^11 - 8 * q^16 - 2 * q^19 + 8 * q^20 - 6 * q^21 + 12 * q^24 - 2 * q^25 - 4 * q^26 + 10 * q^29 - 4 * q^30 - 16 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 - 16 * q^41 + 4 * q^44 - 2 * q^45 - 20 * q^46 - 6 * q^49 + 8 * q^50 - 2 * q^51 - 2 * q^55 + 12 * q^56 + 30 * q^59 + 12 * q^60 - 46 * q^61 + 24 * q^64 - 4 * q^65 - 2 * q^69 - 4 * q^70 - 24 * q^71 - 4 * q^74 - 8 * q^75 + 20 * q^76 - 8 * q^79 + 24 * q^80 + 6 * q^81 + 4 * q^84 + 12 * q^85 - 28 * q^86 + 42 * q^89 + 16 * q^90 - 8 * q^91 - 8 * q^94 + 26 * q^95 + 16 * q^96 + 6 * q^99

Introduction

L-functions

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