LMFDB - Embedded newform 1155.2.l.e.1121.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1121,1155)]

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([1, 0, 0, 1]))

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

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

chi := DirichletCharacter("1155.1121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.l (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:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.15
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.e.1121.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.805231 q^{2} +(-0.972634 + 1.43317i) q^{3} -1.35160 q^{4} +1.00000i q^{5} +(0.783195 - 1.15404i) q^{6} -1.00000i q^{7} +2.69881 q^{8} +(-1.10797 - 2.78790i) q^{9} +O(q^{10})$	\(q-0.805231 q^{2} +(-0.972634 + 1.43317i) q^{3} -1.35160 q^{4} +1.00000i q^{5} +(0.783195 - 1.15404i) q^{6} -1.00000i q^{7} +2.69881 q^{8} +(-1.10797 - 2.78790i) q^{9} -0.805231i q^{10} +(-0.889838 - 3.19503i) q^{11} +(1.31461 - 1.93708i) q^{12} +0.669710i q^{13} +0.805231i q^{14} +(-1.43317 - 0.972634i) q^{15} +0.530036 q^{16} +5.06106 q^{17} +(0.892170 + 2.24491i) q^{18} +8.50615i q^{19} -1.35160i q^{20} +(1.43317 + 0.972634i) q^{21} +(0.716525 + 2.57273i) q^{22} +6.77356i q^{23} +(-2.62496 + 3.86787i) q^{24} -1.00000 q^{25} -0.539271i q^{26} +(5.07319 + 1.12370i) q^{27} +1.35160i q^{28} -2.44686 q^{29} +(1.15404 + 0.783195i) q^{30} +5.73402 q^{31} -5.82443 q^{32} +(5.44451 + 1.83230i) q^{33} -4.07533 q^{34} +1.00000 q^{35} +(1.49753 + 3.76814i) q^{36} -4.26879 q^{37} -6.84942i q^{38} +(-0.959810 - 0.651382i) q^{39} +2.69881i q^{40} -10.5633 q^{41} +(-1.15404 - 0.783195i) q^{42} -1.79024i q^{43} +(1.20271 + 4.31841i) q^{44} +(2.78790 - 1.10797i) q^{45} -5.45428i q^{46} -7.04997i q^{47} +(-0.515531 + 0.759633i) q^{48} -1.00000 q^{49} +0.805231 q^{50} +(-4.92256 + 7.25338i) q^{51} -0.905182i q^{52} -9.79006i q^{53} +(-4.08509 - 0.904838i) q^{54} +(3.19503 - 0.889838i) q^{55} -2.69881i q^{56} +(-12.1908 - 8.27337i) q^{57} +1.97029 q^{58} -11.6161i q^{59} +(1.93708 + 1.31461i) q^{60} +7.58641i q^{61} -4.61721 q^{62} +(-2.78790 + 1.10797i) q^{63} +3.62994 q^{64} -0.669710 q^{65} +(-4.38409 - 1.47542i) q^{66} -9.11307 q^{67} -6.84055 q^{68} +(-9.70768 - 6.58819i) q^{69} -0.805231 q^{70} +11.8970i q^{71} +(-2.99020 - 7.52404i) q^{72} +12.3309i q^{73} +3.43737 q^{74} +(0.972634 - 1.43317i) q^{75} -11.4969i q^{76} +(-3.19503 + 0.889838i) q^{77} +(0.772869 + 0.524513i) q^{78} +11.9518i q^{79} +0.530036i q^{80} +(-6.54481 + 6.17782i) q^{81} +8.50589 q^{82} +6.36979 q^{83} +(-1.93708 - 1.31461i) q^{84} +5.06106i q^{85} +1.44156i q^{86} +(2.37990 - 3.50678i) q^{87} +(-2.40151 - 8.62278i) q^{88} +8.93224i q^{89} +(-2.24491 + 0.892170i) q^{90} +0.669710 q^{91} -9.15516i q^{92} +(-5.57710 + 8.21784i) q^{93} +5.67686i q^{94} -8.50615 q^{95} +(5.66504 - 8.34742i) q^{96} -9.76091 q^{97} +0.805231 q^{98} +(-7.92151 + 6.02077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9	$ 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9} - 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} + 40 q^{18} - 2 q^{21} - 4 q^{22} - 12 q^{24} - 40 q^{25} + 32 q^{27} - 24 q^{29} - 8 q^{31} + 52 q^{32} - 16 q^{33} + 32 q^{34} + 40 q^{35} - 48 q^{37} + 66 q^{39} - 16 q^{41} + 32 q^{44} + 32 q^{48} - 40 q^{49} + 4 q^{50} - 14 q^{51} - 72 q^{54} + 8 q^{55} - 24 q^{57} - 80 q^{58} + 24 q^{60} + 48 q^{62} + 76 q^{64} + 4 q^{65} - 76 q^{66} - 48 q^{67} - 32 q^{68} - 20 q^{69} - 4 q^{70} + 128 q^{72} + 4 q^{75} - 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} - 24 q^{83} - 24 q^{84} - 32 q^{87} - 16 q^{88} + 8 q^{90} - 4 q^{91} - 20 q^{93} - 12 q^{95} + 12 q^{96} + 100 q^{97} + 4 q^{98} - 54 q^{99}+O(q^{100}) $ 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9 - 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 + 40 * q^18 - 2 * q^21 - 4 * q^22 - 12 * q^24 - 40 * q^25 + 32 * q^27 - 24 * q^29 - 8 * q^31 + 52 * q^32 - 16 * q^33 + 32 * q^34 + 40 * q^35 - 48 * q^37 + 66 * q^39 - 16 * q^41 + 32 * q^44 + 32 * q^48 - 40 * q^49 + 4 * q^50 - 14 * q^51 - 72 * q^54 + 8 * q^55 - 24 * q^57 - 80 * q^58 + 24 * q^60 + 48 * q^62 + 76 * q^64 + 4 * q^65 - 76 * q^66 - 48 * q^67 - 32 * q^68 - 20 * q^69 - 4 * q^70 + 128 * q^72 + 4 * q^75 - 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 - 24 * q^83 - 24 * q^84 - 32 * q^87 - 16 * q^88 + 8 * q^90 - 4 * q^91 - 20 * q^93 - 12 * q^95 + 12 * q^96 + 100 * q^97 + 4 * q^98 - 54 * 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 $

$2$	−0.805231			−0.569384			−0.284692	−	0.958619i	$-0.591891\pi$
$2$	−0.805231			−0.569384			−0.284692	+	0.958619i	$0.591891\pi$
$3$	−0.972634	+	1.43317i	−0.561550	+	0.827443i
$3$	−0.972634	+	1.43317i	−0.561550	+	0.827443i
$4$	−1.35160			−0.675801
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.783195	−	1.15404i	0.319738	−	0.471133i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.69881			0.954175
$9$	−1.10797	−	2.78790i	−0.369323	−	0.929301i
$10$		−	0.805231i		−	0.254636i
$11$	−0.889838	−	3.19503i	−0.268296	−	0.963336i
$11$	−0.889838	−	3.19503i	−0.268296	−	0.963336i
$12$	1.31461	−	1.93708i	0.379496	−	0.559187i
$13$			0.669710i			0.185744i	0.995678	+	0.0928721i	$0.0296048\pi$
$13$			0.669710i			0.185744i	−0.995678	+	0.0928721i	$0.970395\pi$
$14$			0.805231i			0.215207i
$15$	−1.43317	−	0.972634i	−0.370044	−	0.251133i
$16$	0.530036			0.132509
$17$	5.06106			1.22749			0.613744	−	0.789505i	$-0.289663\pi$
$17$	5.06106			1.22749			0.613744	+	0.789505i	$0.289663\pi$
$18$	0.892170	+	2.24491i	0.210287	+	0.529130i
$19$			8.50615i			1.95144i	0.219011	+	0.975722i	$0.429717\pi$
$19$			8.50615i			1.95144i	−0.219011	+	0.975722i	$0.570283\pi$
$20$		−	1.35160i		−	0.302228i
$21$	1.43317	+	0.972634i	0.312744	+	0.212246i
$22$	0.716525	+	2.57273i	0.152764	+	0.548509i
$23$			6.77356i			1.41238i	0.708020	+	0.706192i	$0.249589\pi$
$23$			6.77356i			1.41238i	−0.708020	+	0.706192i	$0.750411\pi$
$24$	−2.62496	+	3.86787i	−0.535817	+	0.789525i
$25$	−1.00000			−0.200000
$26$		−	0.539271i		−	0.105760i
$27$	5.07319	+	1.12370i	0.976337	+	0.216256i
$28$			1.35160i			0.255429i
$29$	−2.44686			−0.454371			−0.227185	−	0.973852i	$-0.572952\pi$
$29$	−2.44686			−0.454371			−0.227185	+	0.973852i	$0.572952\pi$
$30$	1.15404	+	0.783195i	0.210697	+	0.142991i
$31$	5.73402			1.02986			0.514930	−	0.857232i	$-0.327818\pi$
$31$	5.73402			1.02986			0.514930	+	0.857232i	$0.327818\pi$
$32$	−5.82443			−1.02962
$33$	5.44451	+	1.83230i	0.947768	+	0.318962i
$34$	−4.07533			−0.698913
$35$	1.00000			0.169031
$36$	1.49753	+	3.76814i	0.249589	+	0.628023i
$37$	−4.26879			−0.701785			−0.350893	−	0.936416i	$-0.614122\pi$
$37$	−4.26879			−0.701785			−0.350893	+	0.936416i	$0.614122\pi$
$38$		−	6.84942i		−	1.11112i
$39$	−0.959810	−	0.651382i	−0.153693	−	0.104305i
$40$			2.69881i			0.426720i
$41$	−10.5633			−1.64971			−0.824854	−	0.565346i	$-0.808743\pi$
$41$	−10.5633			−1.64971			−0.824854	+	0.565346i	$0.808743\pi$
$42$	−1.15404	−	0.783195i	−0.178071	−	0.120850i
$43$		−	1.79024i		−	0.273010i	−0.990639	−	0.136505i	$-0.956413\pi$
$43$		−	1.79024i		−	0.273010i	0.990639	−	0.136505i	$-0.0435869\pi$
$44$	1.20271	+	4.31841i	0.181315	+	0.651024i
$45$	2.78790	−	1.10797i	0.415596	−	0.165166i
$46$		−	5.45428i		−	0.804190i
$47$		−	7.04997i		−	1.02834i	−0.857687	−	0.514172i	$-0.828099\pi$
$47$		−	7.04997i		−	1.02834i	0.857687	−	0.514172i	$-0.171901\pi$
$48$	−0.515531	+	0.759633i	−0.0744105	+	0.109644i
$49$	−1.00000			−0.142857
$50$	0.805231			0.113877
$51$	−4.92256	+	7.25338i	−0.689296	+	1.01568i
$52$		−	0.905182i		−	0.125526i
$53$		−	9.79006i		−	1.34477i	−0.740202	−	0.672384i	$-0.765270\pi$
$53$		−	9.79006i		−	1.34477i	0.740202	−	0.672384i	$-0.234730\pi$
$54$	−4.08509	−	0.904838i	−0.555911	−	0.123133i
$55$	3.19503	−	0.889838i	0.430817	−	0.119986i
$56$		−	2.69881i		−	0.360644i
$57$	−12.1908	−	8.27337i	−1.61471	−	1.09583i
$58$	1.97029			0.258712
$59$		−	11.6161i		−	1.51229i	−0.654406	−	0.756144i	$-0.727081\pi$
$59$		−	11.6161i		−	1.51229i	0.654406	−	0.756144i	$-0.272919\pi$
$60$	1.93708	+	1.31461i	0.250076	+	0.169716i
$61$			7.58641i			0.971340i	0.874142	+	0.485670i	$0.161424\pi$
$61$			7.58641i			0.971340i	−0.874142	+	0.485670i	$0.838576\pi$
$62$	−4.61721			−0.586386
$63$	−2.78790	+	1.10797i	−0.351243	+	0.139591i
$64$	3.62994			0.453743
$65$	−0.669710			−0.0830673
$66$	−4.38409	−	1.47542i	−0.539644	−	0.181612i
$67$	−9.11307			−1.11334			−0.556669	−	0.830734i	$-0.687921\pi$
$67$	−9.11307			−1.11334			−0.556669	+	0.830734i	$0.687921\pi$
$68$	−6.84055			−0.829539
$69$	−9.70768	−	6.58819i	−1.16867	−	0.793125i
$70$	−0.805231			−0.0962435
$71$			11.8970i			1.41192i	0.708254	+	0.705958i	$0.249483\pi$
$71$			11.8970i			1.41192i	−0.708254	+	0.705958i	$0.750517\pi$
$72$	−2.99020	−	7.52404i	−0.352398	−	0.886716i
$73$			12.3309i			1.44322i	0.692300	+	0.721610i	$0.256597\pi$
$73$			12.3309i			1.44322i	−0.692300	+	0.721610i	$0.743403\pi$
$74$	3.43737			0.399586
$75$	0.972634	−	1.43317i	0.112310	−	0.165489i
$76$		−	11.4969i		−	1.31879i
$77$	−3.19503	+	0.889838i	−0.364107	+	0.101406i
$78$	0.772869	+	0.524513i	0.0875102	+	0.0593894i
$79$			11.9518i			1.34468i	0.740243	+	0.672340i	$0.234711\pi$
$79$			11.9518i			1.34468i	−0.740243	+	0.672340i	$0.765289\pi$
$80$			0.530036i			0.0592598i
$81$	−6.54481	+	6.17782i	−0.727202	+	0.686424i
$82$	8.50589			0.939318
$83$	6.36979			0.699175			0.349588	−	0.936904i	$-0.386322\pi$
$83$	6.36979			0.699175			0.349588	+	0.936904i	$0.386322\pi$
$84$	−1.93708	−	1.31461i	−0.211353	−	0.143436i
$85$			5.06106i			0.548950i
$86$			1.44156i			0.155447i
$87$	2.37990	−	3.50678i	0.255152	−	0.375966i
$88$	−2.40151	−	8.62278i	−0.256002	−	0.919192i
$89$			8.93224i			0.946815i	0.880844	+	0.473408i	$0.156976\pi$
$89$			8.93224i			0.946815i	−0.880844	+	0.473408i	$0.843024\pi$
$90$	−2.24491	+	0.892170i	−0.236634	+	0.0940430i
$91$	0.669710			0.0702047
$92$		−	9.15516i		−	0.954492i
$93$	−5.57710	+	8.21784i	−0.578318	+	0.852150i
$94$			5.67686i			0.585523i
$95$	−8.50615			−0.872713
$96$	5.66504	−	8.34742i	0.578185	−	0.851955i
$97$	−9.76091			−0.991070			−0.495535	−	0.868588i	$-0.665028\pi$
$97$	−9.76091			−0.991070			−0.495535	+	0.868588i	$0.665028\pi$
$98$	0.805231			0.0813406
$99$	−7.92151	+	6.02077i	−0.796142	+	0.605110i
$100$	1.35160			0.135160
$101$	−8.10895			−0.806871			−0.403435	−	0.915008i	$-0.632184\pi$
$101$	−8.10895			−0.806871			−0.403435	+	0.915008i	$0.632184\pi$
$102$	3.96380	−	5.84065i	0.392475	−	0.578310i
$103$	−3.71194			−0.365748			−0.182874	−	0.983136i	$-0.558540\pi$
$103$	−3.71194			−0.365748			−0.182874	+	0.983136i	$0.558540\pi$
$104$			1.80742i			0.177232i
$105$	−0.972634	+	1.43317i	−0.0949193	+	0.139863i
$106$			7.88326i			0.765690i
$107$	−1.77046			−0.171157			−0.0855785	−	0.996331i	$-0.527274\pi$
$107$	−1.77046			−0.171157			−0.0855785	+	0.996331i	$0.527274\pi$
$108$	−6.85694	−	1.51880i	−0.659810	−	0.146146i
$109$			3.28733i			0.314869i	0.987529	+	0.157435i	$0.0503224\pi$
$109$			3.28733i			0.314869i	−0.987529	+	0.157435i	$0.949678\pi$
$110$	−2.57273	+	0.716525i	−0.245301	+	0.0683180i
$111$	4.15197	−	6.11792i	0.394088	−	0.580687i
$112$		−	0.530036i		−	0.0500837i
$113$			6.55921i			0.617039i	0.951218	+	0.308519i	$0.0998335\pi$
$113$			6.55921i			0.617039i	−0.951218	+	0.308519i	$0.900167\pi$
$114$	9.81640	+	6.66197i	0.919390	+	0.623951i
$115$	−6.77356			−0.631638
$116$	3.30719			0.307065
$117$	1.86709	−	0.742017i	0.172612	−	0.0685995i
$118$			9.35364i			0.861073i
$119$		−	5.06106i		−	0.463947i
$120$	−3.86787	−	2.62496i	−0.353086	−	0.239625i
$121$	−9.41638	+	5.68611i	−0.856034	+	0.516919i
$122$		−	6.10881i		−	0.553066i
$123$	10.2742	−	15.1390i	0.926394	−	1.36504i
$124$	−7.75011			−0.695981
$125$		−	1.00000i		−	0.0894427i
$126$	2.24491	−	0.892170i	0.199992	−	0.0794808i
$127$		−	6.91444i		−	0.613558i	−0.951781	−	0.306779i	$-0.900749\pi$
$127$		−	6.91444i		−	0.613558i	0.951781	−	0.306779i	$-0.0992512\pi$
$128$	8.72592			0.771270
$129$	2.56573	+	1.74125i	0.225900	+	0.153309i
$130$	0.539271			0.0472972
$131$	2.08390			0.182072			0.0910358	−	0.995848i	$-0.470982\pi$
$131$	2.08390			0.182072			0.0910358	+	0.995848i	$0.470982\pi$
$132$	−7.35882	−	2.47654i	−0.640503	−	0.215555i
$133$	8.50615			0.737577
$134$	7.33812			0.633917
$135$	−1.12370	+	5.07319i	−0.0967126	+	0.436631i
$136$	13.6589			1.17124
$137$		−	12.4736i		−	1.06569i	−0.846212	−	0.532846i	$-0.821122\pi$
$137$		−	12.4736i		−	1.06569i	0.846212	−	0.532846i	$-0.178878\pi$
$138$	7.81693	+	5.30502i	0.665421	+	0.451593i
$139$			18.7127i			1.58719i	0.608444	+	0.793597i	$0.291794\pi$
$139$			18.7127i			1.58719i	−0.608444	+	0.793597i	$0.708206\pi$
$140$	−1.35160			−0.114231
$141$	10.1038	+	6.85704i	0.850896	+	0.577467i
$142$		−	9.57985i		−	0.803923i
$143$	2.13974	−	0.595934i	0.178934	−	0.0498345i
$144$	−0.587263	−	1.47769i	−0.0489386	−	0.123141i
$145$		−	2.44686i		−	0.203201i
$146$		−	9.92920i		−	0.821746i
$147$	0.972634	−	1.43317i	0.0802215	−	0.118206i
$148$	5.76971			0.474268
$149$	−9.56736			−0.783789			−0.391894	−	0.920010i	$-0.628180\pi$
$149$	−9.56736			−0.783789			−0.391894	+	0.920010i	$0.628180\pi$
$150$	−0.783195	+	1.15404i	−0.0639476	+	0.0942266i
$151$		−	1.94620i		−	0.158379i	−0.996860	−	0.0791897i	$-0.974767\pi$
$151$		−	1.94620i		−	0.158379i	0.996860	−	0.0791897i	$-0.0252333\pi$
$152$			22.9565i			1.86202i
$153$	−5.60750	−	14.1098i	−0.453339	−	1.14071i
$154$	2.57273	−	0.716525i	0.207317	−	0.0577393i
$155$			5.73402i			0.460567i
$156$	1.29728	+	0.880410i	0.103866	+	0.0704892i
$157$	3.30917			0.264101			0.132050	−	0.991243i	$-0.457844\pi$
$157$	3.30917			0.264101			0.132050	+	0.991243i	$0.457844\pi$
$158$		−	9.62394i		−	0.765640i
$159$	14.0308	+	9.52214i	1.11272	+	0.755155i
$160$		−	5.82443i		−	0.460462i
$161$	6.77356			0.533831
$162$	5.27009	−	4.97457i	0.414057	−	0.390839i
$163$	−15.1867			−1.18951			−0.594757	−	0.803906i	$-0.702752\pi$
$163$	−15.1867			−1.18951			−0.594757	+	0.803906i	$0.702752\pi$
$164$	14.2774			1.11488
$165$	−1.83230	+	5.44451i	−0.142644	+	0.423855i
$166$	−5.12915			−0.398099
$167$	11.9307			0.923224			0.461612	−	0.887082i	$-0.347271\pi$
$167$	11.9307			0.923224			0.461612	+	0.887082i	$0.347271\pi$
$168$	3.86787	+	2.62496i	0.298412	+	0.202520i
$169$	12.5515			0.965499
$170$		−	4.07533i		−	0.312563i
$171$	23.7143	−	9.42454i	1.81348	−	0.720713i
$172$			2.41970i			0.184500i
$173$	−16.9899			−1.29171			−0.645857	−	0.763458i	$-0.723500\pi$
$173$	−16.9899			−1.29171			−0.645857	+	0.763458i	$0.723500\pi$
$174$	−1.91637	+	2.82377i	−0.145280	+	0.214069i
$175$			1.00000i			0.0755929i
$176$	−0.471647	−	1.69348i	−0.0355517	−	0.127651i
$177$	16.6479	+	11.2982i	1.25133	+	0.849225i
$178$		−	7.19251i		−	0.539102i
$179$			2.16756i			0.162011i	0.996714	+	0.0810056i	$0.0258132\pi$
$179$			2.16756i			0.162011i	−0.996714	+	0.0810056i	$0.974187\pi$
$180$	−3.76814	+	1.49753i	−0.280860	+	0.111619i
$181$	−16.1899			−1.20338			−0.601691	−	0.798729i	$-0.705506\pi$
$181$	−16.1899			−1.20338			−0.601691	+	0.798729i	$0.705506\pi$
$182$	−0.539271			−0.0399735
$183$	−10.8726	−	7.37879i	−0.803728	−	0.545456i
$184$			18.2806i			1.34766i
$185$		−	4.26879i		−	0.313848i
$186$	4.49085	−	6.61726i	0.329285	−	0.485201i
$187$	−4.50353	−	16.1702i	−0.329331	−	1.18248i
$188$			9.52877i			0.694957i
$189$	1.12370	−	5.07319i	0.0817371	−	0.369021i
$190$	6.84942			0.496909
$191$			20.8721i			1.51025i	0.655579	+	0.755126i	$0.272424\pi$
$191$			20.8721i			1.51025i	−0.655579	+	0.755126i	$0.727576\pi$
$192$	−3.53060	+	5.20233i	−0.254799	+	0.375446i
$193$			22.9994i			1.65554i	0.561071	+	0.827768i	$0.310390\pi$
$193$			22.9994i			1.65554i	−0.561071	+	0.827768i	$0.689610\pi$
$194$	7.85979			0.564300
$195$	0.651382	−	0.959810i	0.0466465	−	0.0687334i
$196$	1.35160			0.0965431
$197$	−20.9422			−1.49207			−0.746034	−	0.665907i	$-0.768045\pi$
$197$	−20.9422			−1.49207			−0.746034	+	0.665907i	$0.768045\pi$
$198$	6.37865	−	4.84811i	0.453311	−	0.344540i
$199$	−25.3288			−1.79551			−0.897755	−	0.440495i	$-0.854803\pi$
$199$	−25.3288			−1.79551			−0.897755	+	0.440495i	$0.854803\pi$
$200$	−2.69881			−0.190835
$201$	8.86367	−	13.0606i	0.625195	−	0.921223i
$202$	6.52958			0.459420
$203$			2.44686i			0.171736i
$204$	6.65335	−	9.80369i	0.465828	−	0.686396i
$205$		−	10.5633i		−	0.737772i
$206$	2.98897			0.208251
$207$	18.8840	−	7.50489i	1.31253	−	0.521626i
$208$			0.354971i			0.0246128i
$209$	27.1774	−	7.56910i	1.87990	−	0.523566i
$210$	0.783195	−	1.15404i	0.0540456	−	0.0796360i
$211$		−	3.35803i		−	0.231176i	−0.993297	−	0.115588i	$-0.963125\pi$
$211$		−	3.35803i		−	0.231176i	0.993297	−	0.115588i	$-0.0368753\pi$
$212$			13.2323i			0.908796i
$213$	−17.0505	−	11.5714i	−1.16828	−	0.792862i
$214$	1.42563			0.0974541
$215$	1.79024			0.122094
$216$	13.6916	+	3.03266i	0.931596	+	0.206346i
$217$		−	5.73402i		−	0.389250i
$218$		−	2.64706i		−	0.179282i
$219$	−17.6723	−	11.9934i	−1.19418	−	0.810440i
$220$	−4.31841	+	1.20271i	−0.291147	+	0.0810866i
$221$			3.38945i			0.227999i
$222$	−3.34330	+	4.92634i	−0.224387	+	0.330634i
$223$	2.29034			0.153372			0.0766861	−	0.997055i	$-0.475566\pi$
$223$	2.29034			0.153372			0.0766861	+	0.997055i	$0.475566\pi$
$224$			5.82443i			0.389161i
$225$	1.10797	+	2.78790i	0.0738645	+	0.185860i
$226$		−	5.28168i		−	0.351332i
$227$	13.2053			0.876468			0.438234	−	0.898861i	$-0.355604\pi$
$227$	13.2053			0.876468			0.438234	+	0.898861i	$0.355604\pi$
$228$	16.4771	+	11.1823i	1.09122	+	0.740566i
$229$	−1.13007			−0.0746774			−0.0373387	−	0.999303i	$-0.511888\pi$
$229$	−1.13007			−0.0746774			−0.0373387	+	0.999303i	$0.511888\pi$
$230$	5.45428			0.359645
$231$	1.83230	−	5.44451i	0.120556	−	0.358222i
$232$	−6.60363			−0.433549
$233$	11.6502			0.763231			0.381616	−	0.924321i	$-0.375368\pi$
$233$	11.6502			0.763231			0.381616	+	0.924321i	$0.375368\pi$
$234$	−1.50344	+	0.597495i	−0.0982827	+	0.0390595i
$235$	7.04997			0.459890
$236$			15.7004i			1.02201i
$237$	−17.1290	−	11.6247i	−1.11265	−	0.755105i
$238$			4.07533i			0.264164i
$239$	24.2314			1.56740			0.783699	−	0.621141i	$-0.213330\pi$
$239$	24.2314			1.56740			0.783699	+	0.621141i	$0.213330\pi$
$240$	−0.759633	−	0.515531i	−0.0490341	−	0.0332774i
$241$			27.0505i			1.74248i	0.490858	+	0.871239i	$0.336683\pi$
$241$			27.0505i			1.74248i	−0.490858	+	0.871239i	$0.663317\pi$
$242$	7.58236	−	4.57863i	0.487412	−	0.294326i
$243$	−2.48817	−	15.3886i	−0.159616	−	0.987179i
$244$		−	10.2538i		−	0.656433i
$245$		−	1.00000i		−	0.0638877i
$246$	−8.27311	+	12.1904i	−0.527474	+	0.777232i
$247$	−5.69665			−0.362469
$248$	15.4750			0.982667
$249$	−6.19547	+	9.12901i	−0.392622	+	0.578527i
$250$			0.805231i			0.0509273i
$251$		−	16.1221i		−	1.01762i	−0.860879	−	0.508810i	$-0.830086\pi$
$251$		−	16.1221i		−	1.01762i	0.860879	−	0.508810i	$-0.169914\pi$
$252$	3.76814	−	1.49753i	0.237370	−	0.0943357i
$253$	21.6417	−	6.02737i	1.36060	−	0.378938i
$254$			5.56772i			0.349350i
$255$	−7.25338	−	4.92256i	−0.454224	−	0.308263i
$256$	−14.2863			−0.892892
$257$		−	2.35496i		−	0.146898i	−0.997299	−	0.0734492i	$-0.976599\pi$
$257$		−	2.35496i		−	0.146898i	0.997299	−	0.0734492i	$-0.0234007\pi$
$258$	−2.06600	−	1.40211i	−0.128624	−	0.0872915i
$259$			4.26879i			0.265250i
$260$	0.905182			0.0561370
$261$	2.71105	+	6.82162i	0.167810	+	0.422248i
$262$	−1.67802			−0.103669
$263$	−17.1377			−1.05676			−0.528378	−	0.849009i	$-0.677200\pi$
$263$	−17.1377			−1.05676			−0.528378	+	0.849009i	$0.677200\pi$
$264$	14.6937	+	4.94503i	0.904336	+	0.304346i
$265$	9.79006			0.601399
$266$	−6.84942			−0.419965
$267$	−12.8014	−	8.68779i	−0.783435	−	0.531684i
$268$	12.3172			0.752396
$269$			10.1651i			0.619776i	0.950773	+	0.309888i	$0.100292\pi$
$269$			10.1651i			0.619776i	−0.950773	+	0.309888i	$0.899708\pi$
$270$	0.904838	−	4.08509i	0.0550667	−	0.248611i
$271$			13.8170i			0.839325i	0.907680	+	0.419663i	$0.137852\pi$
$271$			13.8170i			0.839325i	−0.907680	+	0.419663i	$0.862148\pi$
$272$	2.68255			0.162653
$273$	−0.651382	+	0.959810i	−0.0394235	+	0.0580904i
$274$			10.0441i			0.606789i
$275$	0.889838	+	3.19503i	0.0536593	+	0.192667i
$276$	13.1209	+	8.90462i	0.789787	+	0.535995i
$277$		−	11.2372i		−	0.675177i	−0.941294	−	0.337588i	$-0.890389\pi$
$277$		−	11.2372i		−	0.675177i	0.941294	−	0.337588i	$-0.109611\pi$
$278$		−	15.0681i		−	0.903723i
$279$	−6.35311	−	15.9859i	−0.380351	−	0.957050i
$280$	2.69881			0.161285
$281$	−27.9364			−1.66654			−0.833272	−	0.552864i	$-0.813535\pi$
$281$	−27.9364			−1.66654			−0.833272	+	0.552864i	$0.813535\pi$
$282$	−8.13592	−	5.52150i	−0.484487	−	0.328801i
$283$			16.8529i			1.00180i	0.865505	+	0.500900i	$0.166997\pi$
$283$			16.8529i			1.00180i	−0.865505	+	0.500900i	$0.833003\pi$
$284$		−	16.0800i		−	0.954175i
$285$	8.27337	−	12.1908i	0.490072	−	0.722120i
$286$	−1.72299	+	0.479864i	−0.101882	+	0.0283750i
$287$			10.5633i			0.623531i
$288$	6.45328	+	16.2380i	0.380263	+	0.956831i
$289$	8.61438			0.506728
$290$			1.97029i			0.115699i
$291$	9.49379	−	13.9891i	0.556536	−	0.820054i
$292$		−	16.6664i		−	0.975330i
$293$	4.53039			0.264668			0.132334	−	0.991205i	$-0.457753\pi$
$293$	4.53039			0.264668			0.132334	+	0.991205i	$0.457753\pi$
$294$	−0.783195	+	1.15404i	−0.0456768	+	0.0673047i
$295$	11.6161			0.676315
$296$	−11.5207			−0.669626
$297$	−0.924075	−	17.2089i	−0.0536203	−	0.998561i
$298$	7.70394			0.446277
$299$	−4.53632			−0.262342
$300$	−1.31461	+	1.93708i	−0.0758993	+	0.111837i
$301$	−1.79024			−0.103188
$302$			1.56714i			0.0901787i
$303$	7.88704	−	11.6215i	0.453098	−	0.667639i
$304$			4.50857i			0.258584i
$305$	−7.58641			−0.434396
$306$	4.51533	+	11.3616i	0.258124	+	0.649500i
$307$		−	16.8864i		−	0.963758i	−0.876238	−	0.481879i	$-0.839955\pi$
$307$		−	16.8864i		−	0.963758i	0.876238	−	0.481879i	$-0.160045\pi$
$308$	4.31841	−	1.20271i	0.246064	−	0.0685307i
$309$	3.61036	−	5.31985i	0.205386	−	0.302636i
$310$		−	4.61721i		−	0.262240i
$311$			18.2203i			1.03318i	0.856234	+	0.516588i	$0.172798\pi$
$311$			18.2203i			1.03318i	−0.856234	+	0.516588i	$0.827202\pi$
$312$	−2.59035	−	1.75796i	−0.146650	−	0.0995249i
$313$	23.3136			1.31777			0.658883	−	0.752246i	$-0.271029\pi$
$313$	23.3136			1.31777			0.658883	+	0.752246i	$0.271029\pi$
$314$	−2.66465			−0.150375
$315$	−1.10797	−	2.78790i	−0.0624269	−	0.157081i
$316$		−	16.1541i		−	0.908736i
$317$		−	8.88079i		−	0.498795i	−0.968401	−	0.249397i	$-0.919767\pi$
$317$		−	8.88079i		−	0.498795i	0.968401	−	0.249397i	$-0.0802325\pi$
$318$	−11.2981	−	7.66752i	−0.633565	−	0.429973i
$319$	2.17731	+	7.81779i	0.121906	+	0.437712i
$320$			3.62994i			0.202920i
$321$	1.72201	−	2.53738i	0.0961133	−	0.141623i
$322$	−5.45428			−0.303955
$323$			43.0502i			2.39538i
$324$	8.84599	−	8.34995i	0.491444	−	0.463886i
$325$		−	0.669710i		−	0.0371488i
$326$	12.2288			0.677290
$327$	−4.71131	−	3.19737i	−0.260536	−	0.176815i
$328$	−28.5084			−1.57411
$329$	−7.04997			−0.388678
$330$	1.47542	−	4.38409i	0.0812193	−	0.241336i
$331$	18.2838			1.00497			0.502484	−	0.864586i	$-0.332419\pi$
$331$	18.2838			1.00497			0.502484	+	0.864586i	$0.332419\pi$
$332$	−8.60942			−0.472503
$333$	4.72969	+	11.9010i	0.259185	+	0.652170i
$334$	−9.60696			−0.525669
$335$		−	9.11307i		−	0.497900i
$336$	0.759633	+	0.515531i	0.0414414	+	0.0281245i
$337$			26.1754i			1.42587i	0.701231	+	0.712934i	$0.252634\pi$
$337$			26.1754i			1.42587i	−0.701231	+	0.712934i	$0.747366\pi$
$338$	−10.1068			−0.549740
$339$	−9.40048	−	6.37971i	−0.510564	−	0.346498i
$340$		−	6.84055i		−	0.370981i
$341$	−5.10235	−	18.3203i	−0.276308	−	0.992101i
$342$	−19.0955	+	7.58893i	−1.03257	+	0.410363i
$343$			1.00000i			0.0539949i
$344$		−	4.83154i		−	0.260499i
$345$	6.58819	−	9.70768i	0.354696	−	0.522644i
$346$	13.6808			0.735482
$347$	27.2695			1.46390			0.731952	−	0.681356i	$-0.238610\pi$
$347$	27.2695			1.46390			0.731952	+	0.681356i	$0.238610\pi$
$348$	−3.21668	+	4.73977i	−0.172432	+	0.254078i
$349$		−	28.3670i		−	1.51845i	−0.650827	−	0.759226i	$-0.725578\pi$
$349$		−	28.3670i		−	1.51845i	0.650827	−	0.759226i	$-0.274422\pi$
$350$		−	0.805231i		−	0.0430414i
$351$	−0.752553	+	3.39757i	−0.0401683	+	0.181349i
$352$	5.18280	+	18.6092i	0.276244	+	0.991874i
$353$		−	8.61212i		−	0.458377i	−0.973382	−	0.229188i	$-0.926393\pi$
$353$		−	8.61212i		−	0.458377i	0.973382	−	0.229188i	$-0.0736072\pi$
$354$	−13.4054	−	9.09767i	−0.712488	−	0.483536i
$355$	−11.8970			−0.631428
$356$		−	12.0728i		−	0.639859i
$357$	7.25338	+	4.92256i	0.383890	+	0.260530i
$358$		−	1.74539i		−	0.0922466i
$359$	30.1123			1.58926			0.794632	−	0.607092i	$-0.207664\pi$
$359$	30.1123			1.58926			0.794632	+	0.607092i	$0.207664\pi$
$360$	7.52404	−	2.99020i	0.396552	−	0.157597i
$361$	−53.3546			−2.80814
$362$	13.0366			0.685187
$363$	1.00950	−	19.0258i	0.0529851	−	0.998595i
$364$	−0.905182			−0.0474444
$365$	−12.3309			−0.645427
$366$	8.75498	+	5.94163i	0.457630	+	0.310574i
$367$	16.8620			0.880187			0.440094	−	0.897952i	$-0.354945\pi$
$367$	16.8620			0.880187			0.440094	+	0.897952i	$0.354945\pi$
$368$			3.59023i			0.187154i
$369$	11.7038	+	29.4494i	0.609275	+	1.53308i
$370$			3.43737i			0.178700i
$371$	−9.79006			−0.508275
$372$	7.53802	−	11.1073i	0.390828	−	0.575884i
$373$		−	15.9570i		−	0.826224i	−0.910680	−	0.413112i	$-0.864442\pi$
$373$		−	15.9570i		−	0.826224i	0.910680	−	0.413112i	$-0.135558\pi$
$374$	3.62638	+	13.0208i	0.187516	+	0.673288i
$375$	1.43317	+	0.972634i	0.0740087	+	0.0502266i
$376$		−	19.0266i		−	0.981221i
$377$		−	1.63869i		−	0.0843967i
$378$	−0.904838	+	4.08509i	−0.0465398	+	0.210115i
$379$	−9.77971			−0.502350			−0.251175	−	0.967942i	$-0.580817\pi$
$379$	−9.77971			−0.502350			−0.251175	+	0.967942i	$0.580817\pi$
$380$	11.4969			0.589780
$381$	9.90959	+	6.72522i	0.507684	+	0.344543i
$382$		−	16.8069i		−	0.859914i
$383$		−	8.74402i		−	0.446798i	−0.974727	−	0.223399i	$-0.928285\pi$
$383$		−	8.74402i		−	0.446798i	0.974727	−	0.223399i	$-0.0717154\pi$
$384$	−8.48712	+	12.5058i	−0.433107	+	0.638182i
$385$	−0.889838	−	3.19503i	−0.0453504	−	0.162834i
$386$		−	18.5199i		−	0.942636i
$387$	−4.99103	+	1.98353i	−0.253708	+	0.100829i
$388$	13.1929			0.669766
$389$			6.65387i			0.337364i	0.985670	+	0.168682i	$0.0539512\pi$
$389$			6.65387i			0.337364i	−0.985670	+	0.168682i	$0.946049\pi$
$390$	−0.524513	+	0.772869i	−0.0265598	+	0.0391357i
$391$			34.2814i			1.73369i
$392$	−2.69881			−0.136311
$393$	−2.02687	+	2.98659i	−0.102242	+	0.150654i
$394$	16.8633			0.849561
$395$	−11.9518			−0.601359
$396$	10.7067	−	8.13769i	0.538034	−	0.408934i
$397$	29.9140			1.50134			0.750671	−	0.660676i	$-0.229730\pi$
$397$	29.9140			1.50134			0.750671	+	0.660676i	$0.229730\pi$
$398$	20.3955			1.02234
$399$	−8.27337	+	12.1908i	−0.414186	+	0.610302i
$400$	−0.530036			−0.0265018
$401$		−	0.00731824i		−	0.000365456i	−1.00000		0.000182728i	$-0.999942\pi$
$401$		−	0.00731824i		−	0.000365456i	1.00000		0.000182728i	$-5.81641e-5\pi$
$402$	−7.13730	+	10.5168i	−0.355976	+	0.524530i
$403$			3.84013i			0.191290i
$404$	10.9601			0.545284
$405$	−6.17782	−	6.54481i	−0.306978	−	0.325214i
$406$		−	1.97029i		−	0.0977838i
$407$	3.79854	+	13.6389i	0.188286	+	0.676055i
$408$	−13.2851	+	19.5755i	−0.657710	+	0.969133i
$409$		−	39.1600i		−	1.93634i	−0.250299	−	0.968169i	$-0.580529\pi$
$409$		−	39.1600i		−	1.93634i	0.250299	−	0.968169i	$-0.419471\pi$
$410$			8.50589i			0.420076i
$411$	17.8768	+	12.1323i	0.881800	+	0.598440i
$412$	5.01707			0.247173
$413$	−11.6161			−0.571591
$414$	−15.2060	+	6.04317i	−0.747335	+	0.297006i
$415$			6.36979i			0.312681i
$416$		−	3.90068i		−	0.191247i
$417$	−26.8186	−	18.2006i	−1.31331	−	0.891289i
$418$	−21.8841	+	6.09487i	−1.07038	+	0.298110i
$419$		−	10.7859i		−	0.526927i	−0.964669	−	0.263463i	$-0.915135\pi$
$419$		−	10.7859i		−	0.526927i	0.964669	−	0.263463i	$-0.0848648\pi$
$420$	1.31461	−	1.93708i	0.0641466	−	0.0945198i
$421$	−3.85845			−0.188050			−0.0940248	−	0.995570i	$-0.529973\pi$
$421$	−3.85845			−0.188050			−0.0940248	+	0.995570i	$0.529973\pi$
$422$			2.70399i			0.131628i
$423$	−19.6546	+	7.81115i	−0.955642	+	0.379791i
$424$		−	26.4216i		−	1.28314i
$425$	−5.06106			−0.245498
$426$	13.7296	+	9.31768i	0.665200	+	0.451443i
$427$	7.58641			0.367132
$428$	2.39296			0.115668
$429$	−1.22711	+	3.64624i	−0.0592453	+	0.176042i
$430$	−1.44156			−0.0695182
$431$	5.78115			0.278468			0.139234	−	0.990259i	$-0.455536\pi$
$431$	5.78115			0.278468			0.139234	+	0.990259i	$0.455536\pi$
$432$	2.68898	+	0.595601i	0.129373	+	0.0286559i
$433$	−4.93767			−0.237289			−0.118645	−	0.992937i	$-0.537855\pi$
$433$	−4.93767			−0.237289			−0.118645	+	0.992937i	$0.537855\pi$
$434$			4.61721i			0.221633i
$435$	3.50678	+	2.37990i	0.168137	+	0.114108i
$436$		−	4.44317i		−	0.212789i
$437$	−57.6169			−2.75619
$438$	14.2303	+	9.65747i	0.679948	+	0.461452i
$439$		−	11.3559i		−	0.541990i	−0.962581	−	0.270995i	$-0.912647\pi$
$439$		−	11.3559i		−	0.541990i	0.962581	−	0.270995i	$-0.0873526\pi$
$440$	8.62278	−	2.40151i	0.411075	−	0.114487i
$441$	1.10797	+	2.78790i	0.0527604	+	0.132757i
$442$		−	2.72929i		−	0.129819i
$443$			2.46312i			0.117026i	0.998287	+	0.0585131i	$0.0186360\pi$
$443$			2.46312i			0.117026i	−0.998287	+	0.0585131i	$0.981364\pi$
$444$	−5.61182	+	8.26900i	−0.266325	+	0.392429i
$445$	−8.93224			−0.423429
$446$	−1.84425			−0.0873278
$447$	9.30554	−	13.7117i	0.440137	−	0.648540i
$448$		−	3.62994i		−	0.171499i
$449$			18.7503i			0.884884i	0.896797	+	0.442442i	$0.145888\pi$
$449$			18.7503i			0.884884i	−0.896797	+	0.442442i	$0.854112\pi$
$450$	−0.892170	−	2.24491i	−0.0420573	−	0.105826i
$451$	9.39962	+	33.7500i	0.442611	+	1.58922i
$452$		−	8.86545i		−	0.416996i
$453$	2.78924	+	1.89294i	0.131050	+	0.0889380i
$454$	−10.6333			−0.499047
$455$			0.669710i			0.0313965i
$456$	−32.9007	−	22.3283i	−1.54071	−	1.04562i
$457$			14.7678i			0.690810i	0.938454	+	0.345405i	$0.112258\pi$
$457$			14.7678i			0.690810i	−0.938454	+	0.345405i	$0.887742\pi$
$458$	0.909971			0.0425201
$459$	25.6758	+	5.68711i	1.19844	+	0.265452i
$460$	9.15516			0.426862
$461$	−13.1124			−0.610706			−0.305353	−	0.952239i	$-0.598774\pi$
$461$	−13.1124			−0.610706			−0.305353	+	0.952239i	$0.598774\pi$
$462$	−1.47542	+	4.38409i	−0.0686429	+	0.203966i
$463$	9.89142			0.459693			0.229847	−	0.973227i	$-0.426178\pi$
$463$	9.89142			0.459693			0.229847	+	0.973227i	$0.426178\pi$
$464$	−1.29693			−0.0602083
$465$	−8.21784	−	5.57710i	−0.381093	−	0.258632i
$466$	−9.38112			−0.434572
$467$			3.71218i			0.171779i	0.996305	+	0.0858896i	$0.0273732\pi$
$467$			3.71218i			0.171779i	−0.996305	+	0.0858896i	$0.972627\pi$
$468$	−2.52356	+	1.00291i	−0.116652	+	0.0463597i
$469$			9.11307i			0.420802i
$470$	−5.67686			−0.261854
$471$	−3.21861	+	4.74262i	−0.148306	+	0.218528i
$472$		−	31.3497i		−	1.44299i
$473$	−5.71987	+	1.59303i	−0.263000	+	0.0732475i
$474$	13.7928	+	9.36057i	0.633523	+	0.429945i
$475$		−	8.50615i		−	0.390289i
$476$			6.84055i			0.313536i
$477$	−27.2937	+	10.8471i	−1.24969	+	0.496653i
$478$	−19.5119			−0.892452
$479$	−13.8435			−0.632528			−0.316264	−	0.948671i	$-0.602429\pi$
$479$	−13.8435			−0.632528			−0.316264	+	0.948671i	$0.602429\pi$
$480$	8.34742	+	5.66504i	0.381006	+	0.258572i
$481$		−	2.85885i		−	0.130353i
$482$		−	21.7819i		−	0.992140i
$483$	−6.58819	+	9.70768i	−0.299773	+	0.441715i
$484$	12.7272	−	7.68537i	0.578509	−	0.349335i
$485$		−	9.76091i		−	0.443220i
$486$	2.00355	+	12.3914i	0.0908830	+	0.562084i
$487$	18.8757			0.855338			0.427669	−	0.903935i	$-0.359335\pi$
$487$	18.8757			0.855338			0.427669	+	0.903935i	$0.359335\pi$
$488$			20.4743i			0.926828i
$489$	14.7711	−	21.7651i	0.667971	−	0.984254i
$490$			0.805231i			0.0363766i
$491$	19.1707			0.865161			0.432580	−	0.901595i	$-0.357603\pi$
$491$	19.1707			0.865161			0.432580	+	0.901595i	$0.357603\pi$
$492$	−13.8866	+	20.4619i	−0.626058	+	0.922495i
$493$	−12.3837			−0.557735
$494$	4.58712			0.206384
$495$	−6.02077	−	7.92151i	−0.270613	−	0.356045i
$496$	3.03924			0.136466
$497$	11.8970			0.533654
$498$	4.98878	−	7.35096i	0.223553	−	0.329404i
$499$	23.6446			1.05848			0.529239	−	0.848473i	$-0.322478\pi$
$499$	23.6446			1.05848			0.529239	+	0.848473i	$0.322478\pi$
$500$			1.35160i			0.0604455i
$501$	−11.6042	+	17.0987i	−0.518437	+	0.763915i
$502$			12.9820i			0.579417i
$503$	−25.3152			−1.12875			−0.564375	−	0.825518i	$-0.690883\pi$
$503$	−25.3152			−1.12875			−0.564375	+	0.825518i	$0.690883\pi$
$504$	−7.52404	+	2.99020i	−0.335147	+	0.133194i
$505$		−	8.10895i		−	0.360844i
$506$	−17.4266	+	4.85343i	−0.774705	+	0.215761i
$507$	−12.2080	+	17.9885i	−0.542176	+	0.798895i
$508$			9.34558i			0.414643i
$509$			11.5858i			0.513532i	0.966474	+	0.256766i	$0.0826569\pi$
$509$			11.5858i			0.513532i	−0.966474	+	0.256766i	$0.917343\pi$
$510$	5.84065	+	3.96380i	0.258628	+	0.175520i
$511$	12.3309			0.545486
$512$	−5.94810			−0.262871
$513$	−9.55835	+	43.1534i	−0.422012	+	1.90527i
$514$			1.89629i			0.0836416i
$515$		−	3.71194i		−	0.163568i
$516$	−3.46785	−	2.35348i	−0.152663	−	0.103606i
$517$	−22.5248	+	6.27334i	−0.990642	+	0.275901i
$518$		−	3.43737i		−	0.151029i
$519$	16.5249	−	24.3494i	0.725363	−	1.06882i
$520$	−1.80742			−0.0792608
$521$		−	30.4904i		−	1.33581i	−0.744248	−	0.667903i	$-0.767192\pi$
$521$		−	30.4904i		−	1.33581i	0.744248	−	0.667903i	$-0.232808\pi$
$522$	−2.18302	−	5.49298i	−0.0955481	−	0.240421i
$523$		−	7.32640i		−	0.320361i	−0.987088	−	0.160181i	$-0.948792\pi$
$523$		−	7.32640i		−	0.320361i	0.987088	−	0.160181i	$-0.0512076\pi$
$524$	−2.81661			−0.123044
$525$	−1.43317	−	0.972634i	−0.0625488	−	0.0424492i
$526$	13.7998			0.601701
$527$	29.0202			1.26414
$528$	2.88579	+	0.971184i	0.125588	+	0.0422653i
$529$	−22.8811			−0.994831
$530$	−7.88326			−0.342427
$531$	−32.3846	+	12.8703i	−1.40537	+	0.558522i
$532$	−11.4969			−0.498455
$533$		−	7.07434i		−	0.306424i
$534$	10.3081	+	6.99568i	0.446076	+	0.302733i
$535$		−	1.77046i		−	0.0765437i
$536$	−24.5945			−1.06232
$537$	−3.10649	−	2.10824i	−0.134055	−	0.0909774i
$538$		−	8.18524i		−	0.352891i
$539$	0.889838	+	3.19503i	0.0383280	+	0.137619i
$540$	1.51880	−	6.85694i	0.0653585	−	0.295076i
$541$			7.99959i			0.343929i	0.985103	+	0.171965i	$0.0550115\pi$
$541$			7.99959i			0.343929i	−0.985103	+	0.171965i	$0.944989\pi$
$542$		−	11.1259i		−	0.477899i
$543$	15.7468	−	23.2029i	0.675760	−	0.995730i
$544$	−29.4778			−1.26385
$545$	−3.28733			−0.140814
$546$	0.524513	−	0.772869i	0.0224471	−	0.0330757i
$547$		−	8.86354i		−	0.378978i	−0.981883	−	0.189489i	$-0.939317\pi$
$547$		−	8.86354i		−	0.378978i	0.981883	−	0.189489i	$-0.0606831\pi$
$548$			16.8594i			0.720197i
$549$	21.1502	−	8.40550i	0.902667	−	0.358738i
$550$	−0.716525	−	2.57273i	−0.0305527	−	0.109702i
$551$		−	20.8134i		−	0.886680i
$552$	−26.1992	−	17.7803i	−1.11511	−	0.756780i
$553$	11.9518			0.508241
$554$			9.04853i			0.384435i
$555$	6.11792	+	4.15197i	0.259691	+	0.176241i
$556$		−	25.2922i		−	1.07263i
$557$	−3.81742			−0.161749			−0.0808745	−	0.996724i	$-0.525771\pi$
$557$	−3.81742			−0.161749			−0.0808745	+	0.996724i	$0.525771\pi$
$558$	5.11572	+	12.8723i	0.216566	+	0.544929i
$559$	1.19894			0.0507099
$560$	0.530036			0.0223981
$561$	27.5550	+	9.27337i	1.16337	+	0.391522i
$562$	22.4952			0.948904
$563$	13.7850			0.580969			0.290485	−	0.956880i	$-0.406184\pi$
$563$	13.7850			0.580969			0.290485	+	0.956880i	$0.406184\pi$
$564$	−13.6564	−	9.26800i	−0.575037	−	0.390253i
$565$	−6.55921			−0.275948
$566$		−	13.5705i		−	0.570409i
$567$	6.17782	+	6.54481i	0.259444	+	0.274856i
$568$			32.1078i			1.34722i
$569$	4.54623			0.190588			0.0952939	−	0.995449i	$-0.469621\pi$
$569$	4.54623			0.190588			0.0952939	+	0.995449i	$0.469621\pi$
$570$	−6.66197	+	9.81640i	−0.279039	+	0.411164i
$571$		−	1.70071i		−	0.0711726i	−0.999367	−	0.0355863i	$-0.988670\pi$
$571$		−	1.70071i		−	0.0711726i	0.999367	−	0.0355863i	$-0.0113299\pi$
$572$	−2.89208	+	0.805466i	−0.120924	+	0.0336782i
$573$	−29.9133	−	20.3009i	−1.24965	−	0.848083i
$574$		−	8.50589i		−	0.355029i
$575$		−	6.77356i		−	0.282477i
$576$	−4.02186	−	10.1199i	−0.167577	−	0.421664i
$577$	−6.86724			−0.285887			−0.142943	−	0.989731i	$-0.545657\pi$
$577$	−6.86724			−0.285887			−0.142943	+	0.989731i	$0.545657\pi$
$578$	−6.93656			−0.288523
$579$	−32.9622	−	22.3700i	−1.36986	−	0.929667i
$580$			3.30719i			0.137323i
$581$		−	6.36979i		−	0.264263i
$582$	−7.64469	+	11.2644i	−0.316883	+	0.466926i
$583$	−31.2795	+	8.71157i	−1.29546	+	0.360796i
$584$			33.2787i			1.37708i
$585$	0.742017	+	1.86709i	0.0306786	+	0.0771945i
$586$	−3.64801			−0.150698
$587$			0.194423i			0.00802469i	0.999992	+	0.00401234i	$0.00127717\pi$
$587$			0.194423i			0.00802469i	−0.999992	+	0.00401234i	$0.998723\pi$
$588$	−1.31461	+	1.93708i	−0.0542138	+	0.0798838i
$589$			48.7744i			2.00971i
$590$	−9.35364			−0.385083
$591$	20.3691	−	30.0138i	0.837872	−	1.23460i
$592$	−2.26262			−0.0929929
$593$	−22.6249			−0.929092			−0.464546	−	0.885549i	$-0.653782\pi$
$593$	−22.6249			−0.929092			−0.464546	+	0.885549i	$0.653782\pi$
$594$	0.744094	+	13.8571i	0.0305305	+	0.568565i
$595$	5.06106			0.207483
$596$	12.9313			0.529686
$597$	24.6356	−	36.3005i	1.00827	−	1.48568i
$598$	3.65279			0.149374
$599$			33.7504i			1.37901i	0.724283	+	0.689503i	$0.242171\pi$
$599$			33.7504i			1.37901i	−0.724283	+	0.689503i	$0.757829\pi$
$600$	2.62496	−	3.86787i	0.107163	−	0.157905i
$601$		−	13.2712i		−	0.541343i	−0.962672	−	0.270672i	$-0.912754\pi$
$601$		−	13.2712i		−	0.541343i	0.962672	−	0.270672i	$-0.0872458\pi$
$602$	1.44156			0.0587536
$603$	10.0970	+	25.4063i	0.411181	+	1.03463i
$604$			2.63049i			0.107033i
$605$	−5.68611	−	9.41638i	−0.231173	−	0.382830i
$606$	−6.35089	+	9.35801i	−0.257987	+	0.380143i
$607$			12.7378i			0.517010i	0.966010	+	0.258505i	$0.0832299\pi$
$607$			12.7378i			0.517010i	−0.966010	+	0.258505i	$0.916770\pi$
$608$		−	49.5435i		−	2.00925i
$609$	−3.50678	−	2.37990i	−0.142102	−	0.0964384i
$610$	6.10881			0.247339
$611$	4.72144			0.191009
$612$	7.57911	+	19.0708i	0.306367	+	0.770891i
$613$			6.54462i			0.264335i	0.991227	+	0.132167i	$0.0421936\pi$
$613$			6.54462i			0.264335i	−0.991227	+	0.132167i	$0.957806\pi$
$614$			13.5975i			0.548749i
$615$	15.1390	+	10.2742i	0.610464	+	0.414296i
$616$	−8.62278	+	2.40151i	−0.347422	+	0.0967595i
$617$			13.8372i			0.557064i	0.960427	+	0.278532i	$0.0898479\pi$
$617$			13.8372i			0.557064i	−0.960427	+	0.278532i	$0.910152\pi$
$618$	−2.90717	+	4.28371i	−0.116944	+	0.172316i
$619$	16.3201			0.655960			0.327980	−	0.944685i	$-0.393632\pi$
$619$	16.3201			0.655960			0.327980	+	0.944685i	$0.393632\pi$
$620$		−	7.75011i		−	0.311252i
$621$	−7.61144	+	34.3636i	−0.305437	+	1.37896i
$622$		−	14.6715i		−	0.588275i
$623$	8.93224			0.357862
$624$	−0.508734	−	0.345256i	−0.0203657	−	0.0138213i
$625$	1.00000			0.0400000
$626$	−18.7729			−0.750315
$627$	−15.5858	+	46.3118i	−0.622437	+	1.84952i
$628$	−4.47269			−0.178480
$629$	−21.6046			−0.861434
$630$	0.892170	+	2.24491i	0.0355449	+	0.0894392i
$631$	1.15803			0.0461006			0.0230503	−	0.999734i	$-0.492662\pi$
$631$	1.15803			0.0461006			0.0230503	+	0.999734i	$0.492662\pi$
$632$			32.2556i			1.28306i
$633$	4.81264	+	3.26614i	0.191285	+	0.129817i
$634$			7.15109i			0.284006i
$635$	6.91444			0.274391
$636$	−18.9641	−	12.8702i	−0.751977	−	0.510335i
$637$		−	0.669710i		−	0.0265349i
$638$	−1.75324	−	6.29513i	−0.0694114	−	0.249226i
$639$	33.1677	−	13.1815i	1.31210	−	0.521453i
$640$			8.72592i			0.344922i
$641$			18.4932i			0.730439i	0.930922	+	0.365219i	$0.119006\pi$
$641$			18.4932i			0.730439i	−0.930922	+	0.365219i	$0.880994\pi$
$642$	−1.38662	+	2.04318i	−0.0547254	+	0.0806377i
$643$	35.8202			1.41261			0.706306	−	0.707906i	$-0.250360\pi$
$643$	35.8202			1.41261			0.706306	+	0.707906i	$0.250360\pi$
$644$	−9.15516			−0.360764
$645$	−1.74125	+	2.56573i	−0.0685617	+	0.101025i
$646$		−	34.6653i		−	1.36389i
$647$			30.1269i			1.18441i	0.805787	+	0.592205i	$0.201743\pi$
$647$			30.1269i			1.18441i	−0.805787	+	0.592205i	$0.798257\pi$
$648$	−17.6632	+	16.6728i	−0.693878	+	0.654969i
$649$	−37.1137	+	10.3364i	−1.45684	+	0.405741i
$650$			0.539271i			0.0211520i
$651$	8.21784	+	5.57710i	0.322082	+	0.218584i
$652$	20.5264			0.803875
$653$		−	17.4302i		−	0.682096i	−0.940046	−	0.341048i	$-0.889218\pi$
$653$		−	17.4302i		−	0.682096i	0.940046	−	0.341048i	$-0.110782\pi$
$654$	3.79370	+	2.57462i	0.148345	+	0.100676i
$655$			2.08390i			0.0814249i
$656$	−5.59892			−0.218601
$657$	34.3773	−	13.6622i	1.34119	−	0.533013i
$658$	5.67686			0.221307
$659$	−5.97500			−0.232753			−0.116376	−	0.993205i	$-0.537128\pi$
$659$	−5.97500			−0.232753			−0.116376	+	0.993205i	$0.537128\pi$
$660$	2.47654	−	7.35882i	0.0963991	−	0.286441i
$661$	13.9146			0.541214			0.270607	−	0.962690i	$-0.412776\pi$
$661$	13.9146			0.541214			0.270607	+	0.962690i	$0.412776\pi$
$662$	−14.7227			−0.572214
$663$	−4.85766	−	3.29669i	−0.188656	−	0.128033i
$664$	17.1909			0.667135
$665$			8.50615i			0.329854i
$666$	−3.80849	−	9.58304i	−0.147576	−	0.371335i
$667$		−	16.5740i		−	0.641747i
$668$	−16.1256			−0.623916
$669$	−2.22766	+	3.28245i	−0.0861262	+	0.126907i
$670$			7.33812i			0.283496i
$671$	24.2388	−	6.75068i	0.935727	−	0.260607i
$672$	−8.34742	−	5.66504i	−0.322009	−	0.218534i
$673$		−	22.1580i		−	0.854129i	−0.904221	−	0.427064i	$-0.859548\pi$
$673$		−	22.1580i		−	0.854129i	0.904221	−	0.427064i	$-0.140452\pi$
$674$		−	21.0773i		−	0.811867i
$675$	−5.07319	−	1.12370i	−0.195267	−	0.0432512i
$676$	−16.9646			−0.652486
$677$	−3.79395			−0.145813			−0.0729067	−	0.997339i	$-0.523228\pi$
$677$	−3.79395			−0.145813			−0.0729067	+	0.997339i	$0.523228\pi$
$678$	7.56956	+	5.13714i	0.290707	+	0.197291i
$679$			9.76091i			0.374589i
$680$			13.6589i			0.523794i
$681$	−12.8439	+	18.9255i	−0.492181	+	0.725227i
$682$	4.10857	+	14.7521i	0.157325	+	0.564887i
$683$		−	4.59887i		−	0.175971i	−0.996122	−	0.0879855i	$-0.971957\pi$
$683$		−	4.59887i		−	0.175971i	0.996122	−	0.0879855i	$-0.0280429\pi$
$684$	−32.0524	+	12.7382i	−1.22555	+	0.487059i
$685$	12.4736			0.476592
$686$		−	0.805231i		−	0.0307439i
$687$	1.09915	−	1.61959i	0.0419351	−	0.0617913i
$688$		−	0.948894i		−	0.0361762i
$689$	6.55650			0.249783
$690$	−5.30502	+	7.81693i	−0.201959	+	0.297585i
$691$	−47.8095			−1.81876			−0.909380	−	0.415965i	$-0.863444\pi$
$691$	−47.8095			−1.81876			−0.909380	+	0.415965i	$0.863444\pi$
$692$	22.9635			0.872943
$693$	6.02077	+	7.92151i	0.228710	+	0.300913i
$694$	−21.9583			−0.833524
$695$	−18.7127			−0.709814
$696$	6.42291	−	9.46414i	0.243460	−	0.358737i
$697$	−53.4615			−2.02500
$698$			22.8420i			0.864583i
$699$	−11.3314	+	16.6968i	−0.428593	+	0.631530i
$700$		−	1.35160i		−	0.0510858i
$701$	−45.8011			−1.72988			−0.864942	−	0.501872i	$-0.832645\pi$
$701$	−45.8011			−1.72988			−0.864942	+	0.501872i	$0.832645\pi$
$702$	0.605979	−	2.73583i	0.0228712	−	0.103257i
$703$		−	36.3110i		−	1.36950i
$704$	−3.23006	−	11.5978i	−0.121737	−	0.437107i
$705$	−6.85704	+	10.1038i	−0.258251	+	0.380532i
$706$			6.93475i			0.260993i
$707$			8.10895i			0.304968i
$708$	−22.5013	−	15.2707i	−0.845651	−	0.573908i
$709$	9.31674			0.349898			0.174949	−	0.984578i	$-0.444024\pi$
$709$	9.31674			0.349898			0.174949	+	0.984578i	$0.444024\pi$
$710$	9.57985			0.359525
$711$	33.3204	−	13.2422i	1.24961	−	0.496621i
$712$			24.1065i			0.903427i
$713$			38.8397i			1.45456i
$714$	−5.84065	−	3.96380i	−0.218581	−	0.148341i
$715$	0.595934	+	2.13974i	0.0222867	+	0.0800218i
$716$		−	2.92968i		−	0.109487i
$717$	−23.5683	+	34.7278i	−0.880173	+	1.29693i
$718$	−24.2473			−0.904902
$719$		−	2.30617i		−	0.0860056i	−0.999075	−	0.0430028i	$-0.986308\pi$
$719$		−	2.30617i		−	0.0860056i	0.999075	−	0.0430028i	$-0.0136924\pi$
$720$	1.47769	−	0.587263i	0.0550703	−	0.0218860i
$721$			3.71194i			0.138240i
$722$	42.9628			1.59891
$723$	−38.7681	−	26.3103i	−1.44180	−	0.978489i
$724$	21.8823			0.813248
$725$	2.44686			0.0908742
$726$	−0.812882	+	15.3202i	−0.0301689	+	0.568585i
$727$	−3.42816			−0.127143			−0.0635717	−	0.997977i	$-0.520249\pi$
$727$	−3.42816			−0.127143			−0.0635717	+	0.997977i	$0.520249\pi$
$728$	1.80742			0.0669876
$729$	24.4746	+	11.4015i	0.906467	+	0.422277i
$730$	9.92920			0.367496
$731$		−	9.06054i		−	0.335116i
$732$	14.6955	+	9.97320i	0.543161	+	0.368620i
$733$			16.5785i			0.612342i	0.951977	+	0.306171i	$0.0990479\pi$
$733$			16.5785i			0.612342i	−0.951977	+	0.306171i	$0.900952\pi$
$734$	−13.5778			−0.501165
$735$	1.43317	+	0.972634i	0.0528634	+	0.0358761i
$736$		−	39.4521i		−	1.45423i
$737$	8.10915	+	29.1165i	0.298705	+	1.07252i
$738$	−9.42425	−	23.7136i	−0.346911	−	0.872909i
$739$		−	30.9376i		−	1.13806i	−0.822317	−	0.569030i	$-0.807319\pi$
$739$		−	30.9376i		−	1.13806i	0.822317	−	0.569030i	$-0.192681\pi$
$740$			5.76971i			0.212099i
$741$	5.54076	−	8.16429i	0.203545	−	0.299923i
$742$	7.88326			0.289404
$743$	9.03623			0.331507			0.165754	−	0.986167i	$-0.446994\pi$
$743$	9.03623			0.331507			0.165754	+	0.986167i	$0.446994\pi$
$744$	−15.0516	+	22.1784i	−0.551817	+	0.813100i
$745$		−	9.56736i		−	0.350521i
$746$			12.8491i			0.470439i
$747$	−7.05752	−	17.7584i	−0.258221	−	0.649744i
$748$	6.08698	+	21.8557i	0.222562	+	0.799125i
$749$			1.77046i			0.0646913i
$750$	−1.15404	−	0.783195i	−0.0421394	−	0.0285982i
$751$	−16.1740			−0.590197			−0.295099	−	0.955467i	$-0.595353\pi$
$751$	−16.1740			−0.590197			−0.295099	+	0.955467i	$0.595353\pi$
$752$		−	3.73674i		−	0.136265i
$753$	23.1058	+	15.6809i	0.842022	+	0.571444i
$754$			1.31952i			0.0480542i
$755$	1.94620			0.0708294
$756$	−1.51880	+	6.85694i	−0.0552380	+	0.249385i
$757$	17.9378			0.651959			0.325979	−	0.945377i	$-0.394306\pi$
$757$	17.9378			0.651959			0.325979	+	0.945377i	$0.394306\pi$
$758$	7.87492			0.286030
$759$	−12.4112	+	36.8787i	−0.450497	+	1.33861i
$760$	−22.9565			−0.832721
$761$	−34.7910			−1.26117			−0.630586	−	0.776119i	$-0.717185\pi$
$761$	−34.7910			−1.26117			−0.630586	+	0.776119i	$0.717185\pi$
$762$	−7.97951	−	5.41536i	−0.289067	−	0.196178i
$763$	3.28733			0.119009
$764$		−	28.2108i		−	1.02063i
$765$	14.1098	−	5.60750i	0.510139	−	0.202740i
$766$			7.04096i			0.254400i
$767$	7.77942			0.280898
$768$	13.8953	−	20.4747i	0.501403	−	0.738817i
$769$			34.3351i			1.23816i	0.785330	+	0.619078i	$0.212494\pi$
$769$			34.3351i			1.23816i	−0.785330	+	0.619078i	$0.787506\pi$
$770$	0.716525	+	2.57273i	0.0258218	+	0.0927149i
$771$	3.37506	+	2.29051i	0.121550	+	0.0824908i
$772$		−	31.0861i		−	1.11881i
$773$		−	38.4105i		−	1.38153i	−0.723079	−	0.690765i	$-0.757274\pi$
$773$		−	38.4105i		−	1.38153i	0.723079	−	0.690765i	$-0.242726\pi$
$774$	4.01893	−	1.59720i	0.144457	−	0.0574102i
$775$	−5.73402			−0.205972
$776$	−26.3429			−0.945654
$777$	−6.11792	−	4.15197i	−0.219479	−	0.148951i
$778$		−	5.35790i		−	0.192090i
$779$		−	89.8529i		−	3.21931i
$780$	−0.880410	+	1.29728i	−0.0315237	+	0.0464502i
$781$	38.0113	−	10.5864i	1.36015	−	0.378812i
$782$		−	27.6045i		−	0.987134i
$783$	−12.4134	−	2.74954i	−0.443619	−	0.0982605i
$784$	−0.530036			−0.0189299
$785$			3.30917i			0.118110i
$786$	1.63210	−	2.40490i	0.0582152	−	0.0857799i
$787$		−	1.16812i		−	0.0416390i	−0.999783	−	0.0208195i	$-0.993372\pi$
$787$		−	1.16812i		−	0.0416390i	0.999783	−	0.0208195i	$-0.00662753\pi$
$788$	28.3055			1.00834
$789$	16.6687	−	24.5613i	0.593422	−	0.874406i
$790$	9.62394			0.342404
$791$	6.55921			0.233219
$792$	−21.3787	+	16.2489i	−0.759659	+	0.577381i
$793$	−5.08069			−0.180421
$794$	−24.0877			−0.854841
$795$	−9.52214	+	14.0308i	−0.337716	+	0.497623i
$796$	34.2345			1.21341
$797$		−	33.1337i		−	1.17366i	−0.809712	−	0.586828i	$-0.800377\pi$
$797$		−	33.1337i		−	1.17366i	0.809712	−	0.586828i	$-0.199623\pi$
$798$	6.66197	−	9.81640i	0.235831	−	0.347497i
$799$		−	35.6804i		−	1.26228i
$800$	5.82443			0.205925
$801$	24.9022	−	9.89663i	0.879876	−	0.349680i
$802$			0.00589288i			0.000208085i
$803$	39.3974	−	10.9725i	1.39031	−	0.387210i
$804$	−11.9802	+	17.6527i	−0.422508	+	0.622564i
$805$			6.77356i			0.238737i
$806$		−	3.09219i		−	0.108918i
$807$	−14.5683	−	9.88690i	−0.512829	−	0.348035i
$808$	−21.8846			−0.769896
$809$	−8.38468			−0.294790			−0.147395	−	0.989078i	$-0.547089\pi$
$809$	−8.38468			−0.294790			−0.147395	+	0.989078i	$0.547089\pi$
$810$	4.97457	+	5.27009i	0.174789	+	0.185172i
$811$		−	27.1176i		−	0.952227i	−0.879384	−	0.476114i	$-0.842045\pi$
$811$		−	27.1176i		−	0.952227i	0.879384	−	0.476114i	$-0.157955\pi$
$812$		−	3.30719i		−	0.116059i
$813$	−19.8022	−	13.4389i	−0.694494	−	0.471323i
$814$	−3.05870	−	10.9825i	−0.107207	−	0.384935i
$815$		−	15.1867i		−	0.531966i
$816$	−2.60914	+	3.84455i	−0.0913380	+	0.134586i
$817$	15.2281			0.532763
$818$			31.5328i			1.10252i
$819$	−0.742017	−	1.86709i	−0.0259282	−	0.0652413i
$820$			14.2774i			0.498587i
$821$	20.0161			0.698567			0.349284	−	0.937017i	$-0.386425\pi$
$821$	20.0161			0.698567			0.349284	+	0.937017i	$0.386425\pi$
$822$	−14.3950	−	9.76927i	−0.502083	−	0.340742i
$823$	52.7595			1.83908			0.919541	−	0.392994i	$-0.128561\pi$
$823$	52.7595			1.83908			0.919541	+	0.392994i	$0.128561\pi$
$824$	−10.0178			−0.348988
$825$	−5.44451	−	1.83230i	−0.189554	−	0.0637924i
$826$	9.35364			0.325455
$827$	−41.3711			−1.43862			−0.719308	−	0.694692i	$-0.755541\pi$
$827$	−41.3711			−1.43862			−0.719308	+	0.694692i	$0.755541\pi$
$828$	−25.5237	+	10.1436i	−0.887010	+	0.352515i
$829$	26.4238			0.917738			0.458869	−	0.888504i	$-0.348255\pi$
$829$	26.4238			0.917738			0.458869	+	0.888504i	$0.348255\pi$
$830$		−	5.12915i		−	0.178035i
$831$	16.1048	+	10.9297i	0.558670	+	0.379146i
$832$			2.43101i			0.0842800i
$833$	−5.06106			−0.175356
$834$	21.5952	+	14.6557i	0.747779	+	0.507486i
$835$			11.9307i			0.412878i
$836$	−36.7330	+	10.2304i	−1.27044	+	0.353826i
$837$	29.0898	+	6.44331i	1.00549	+	0.222713i
$838$			8.68516i			0.300024i
$839$		−	0.543844i		−	0.0187756i	−0.999956	−	0.00938779i	$-0.997012\pi$
$839$		−	0.543844i		−	0.0187756i	0.999956	−	0.00938779i	$-0.00298827\pi$
$840$	−2.62496	+	3.86787i	−0.0905697	+	0.133454i
$841$	−23.0129			−0.793547
$842$	3.10695			0.107072
$843$	27.1718	−	40.0376i	0.935848	−	1.37897i
$844$			4.53873i			0.156229i
$845$			12.5515i			0.431784i
$846$	15.8265	−	6.28978i	0.544127	−	0.216247i
$847$	5.68611	+	9.41638i	0.195377	+	0.323550i
$848$		−	5.18909i		−	0.178194i
$849$	−24.1531	−	16.3917i	−0.828931	−	0.562561i
$850$	4.07533			0.139783
$851$		−	28.9149i		−	0.991191i
$852$	23.0455	+	15.6400i	0.789525	+	0.535817i
$853$			36.3286i			1.24387i	0.783070	+	0.621933i	$0.213653\pi$
$853$			36.3286i			1.24387i	−0.783070	+	0.621933i	$0.786347\pi$
$854$	−6.10881			−0.209039
$855$	9.42454	+	23.7143i	0.322313	+	0.811013i
$856$	−4.77815			−0.163314
$857$	56.8864			1.94320			0.971601	−	0.236624i	$-0.0760410\pi$
$857$	56.8864			1.94320			0.971601	+	0.236624i	$0.0760410\pi$
$858$	0.988105	−	2.93607i	0.0337334	−	0.100236i
$859$	9.30868			0.317608			0.158804	−	0.987310i	$-0.449236\pi$
$859$	9.30868			0.317608			0.158804	+	0.987310i	$0.449236\pi$
$860$	−2.41970			−0.0825110
$861$	−15.1390	−	10.2742i	−0.515936	−	0.350144i
$862$	−4.65516			−0.158555
$863$			11.4902i			0.391132i	0.980691	+	0.195566i	$0.0626543\pi$
$863$			11.4902i			0.391132i	−0.980691	+	0.195566i	$0.937346\pi$
$864$	−29.5485	−	6.54491i	−1.00526	−	0.222662i
$865$		−	16.9899i		−	0.577672i
$866$	3.97597			0.135109
$867$	−8.37863	+	12.3459i	−0.284553	+	0.419288i
$868$			7.75011i			0.263056i
$869$	38.1862	−	10.6351i	1.29538	−	0.360773i
$870$	−2.82377	−	1.91637i	−0.0957346	−	0.0649710i
$871$		−	6.10311i		−	0.206796i
$872$			8.87190i			0.300440i
$873$	10.8148	+	27.2125i	0.366025	+	0.921003i
$874$	46.3949			1.56933
$875$	−1.00000			−0.0338062
$876$	23.8859	+	16.2103i	0.807029	+	0.547697i
$877$		−	12.9975i		−	0.438895i	−0.975624	−	0.219447i	$-0.929575\pi$
$877$		−	12.9975i		−	0.438895i	0.975624	−	0.219447i	$-0.0704254\pi$
$878$			9.14416i			0.308600i
$879$	−4.40641	+	6.49283i	−0.148624	+	0.218998i
$880$	1.69348	−	0.471647i	0.0570872	−	0.0158992i
$881$			13.5765i			0.457403i	0.973497	+	0.228702i	$0.0734480\pi$
$881$			13.5765i			0.457403i	−0.973497	+	0.228702i	$0.926552\pi$
$882$	−0.892170	−	2.24491i	−0.0300409	−	0.0755899i
$883$	16.2175			0.545761			0.272881	−	0.962048i	$-0.412024\pi$
$883$	16.2175			0.545761			0.272881	+	0.962048i	$0.412024\pi$
$884$		−	4.58118i		−	0.154082i
$885$	−11.2982	+	16.6479i	−0.379785	+	0.559612i
$886$		−	1.98338i		−	0.0666329i
$887$	42.7254			1.43458			0.717290	−	0.696775i	$-0.245382\pi$
$887$	42.7254			1.43458			0.717290	+	0.696775i	$0.245382\pi$
$888$	11.2054	−	16.5111i	0.376029	−	0.554077i
$889$	−6.91444			−0.231903
$890$	7.19251			0.241094
$891$	25.5621	+	15.4136i	0.856363	+	0.516375i
$892$	−3.09563			−0.103649
$893$	59.9681			2.00676
$894$	−7.49311	+	11.0411i	−0.250607	+	0.369269i
$895$	−2.16756			−0.0724536
$896$		−	8.72592i		−	0.291513i
$897$	4.41218	−	6.50133i	0.147318	−	0.217073i
$898$		−	15.0984i		−	0.503839i
$899$	−14.0303			−0.467938
$900$	−1.49753	−	3.76814i	−0.0499178	−	0.125605i
$901$		−	49.5481i		−	1.65069i
$902$	−7.56886	−	27.1765i	−0.252016	−	0.904879i
$903$	1.74125	−	2.56573i	0.0579452	−	0.0853821i
$904$			17.7021i			0.588763i
$905$		−	16.1899i		−	0.538169i
$906$	−2.24598	−	1.52425i	−0.0746177	−	0.0506399i
$907$	−11.6076			−0.385425			−0.192713	−	0.981255i	$-0.561729\pi$
$907$	−11.6076			−0.385425			−0.192713	+	0.981255i	$0.561729\pi$
$908$	−17.8484			−0.592318
$909$	8.98446	+	22.6070i	0.297996	+	0.749826i
$910$		−	0.539271i		−	0.0178767i
$911$		−	24.9537i		−	0.826752i	−0.910560	−	0.413376i	$-0.864349\pi$
$911$		−	24.9537i		−	0.826752i	0.910560	−	0.413376i	$-0.135651\pi$
$912$	−6.46156	−	4.38518i	−0.213964	−	0.145208i
$913$	−5.66808	−	20.3516i	−0.187586	−	0.673541i
$914$		−	11.8915i		−	0.393337i
$915$	7.37879	−	10.8726i	0.243935	−	0.359438i
$916$	1.52741			0.0504671
$917$		−	2.08390i		−	0.0688166i
$918$	−20.6749	−	4.57944i	−0.682374	−	0.151144i
$919$			38.8182i			1.28049i	0.768169	+	0.640247i	$0.221168\pi$
$919$			38.8182i			1.28049i	−0.768169	+	0.640247i	$0.778832\pi$
$920$	−18.2806			−0.602693
$921$	24.2011	+	16.4243i	0.797454	+	0.541198i
$922$	10.5585			0.347726
$923$	−7.96755			−0.262255
$924$	−2.47654	+	7.35882i	−0.0814721	+	0.242087i
$925$	4.26879			0.140357
$926$	−7.96488			−0.261742
$927$	4.11271	+	10.3485i	0.135079	+	0.339890i
$928$	14.2516			0.467831
$929$		−	23.4080i		−	0.767990i	−0.923335	−	0.383995i	$-0.874548\pi$
$929$		−	23.4080i		−	0.767990i	0.923335	−	0.383995i	$-0.125452\pi$
$930$	6.61726	+	4.49085i	0.216988	+	0.147261i
$931$		−	8.50615i		−	0.278778i
$932$	−15.7465			−0.515793
$933$	−26.1128	−	17.7216i	−0.854895	−	0.580181i
$934$		−	2.98916i		−	0.0978084i
$935$	16.1702	−	4.50353i	0.528823	−	0.147281i
$936$	5.03892	−	2.00257i	0.164702	−	0.0654560i
$937$			33.5612i			1.09640i	0.836348	+	0.548199i	$0.184686\pi$
$937$			33.5612i			1.09640i	−0.836348	+	0.548199i	$0.815314\pi$
$938$		−	7.33812i		−	0.239598i
$939$	−22.6756	+	33.4125i	−0.739991	+	1.09038i
$940$	−9.52877			−0.310794
$941$	−3.96520			−0.129262			−0.0646309	−	0.997909i	$-0.520587\pi$
$941$	−3.96520			−0.129262			−0.0646309	+	0.997909i	$0.520587\pi$
$942$	2.59173	−	3.81890i	0.0844431	−	0.124427i
$943$		−	71.5511i		−	2.33002i
$944$		−	6.15695i		−	0.200392i
$945$	5.07319	+	1.12370i	0.165031	+	0.0365539i
$946$	4.60582	−	1.28276i	0.149748	−	0.0417060i
$947$			18.8834i			0.613628i	0.951770	+	0.306814i	$0.0992629\pi$
$947$			18.8834i			0.613628i	−0.951770	+	0.306814i	$0.900737\pi$
$948$	23.1515	+	15.7120i	0.751927	+	0.510301i
$949$	−8.25811			−0.268069
$950$			6.84942i			0.222224i
$951$	12.7277	+	8.63775i	0.412724	+	0.280098i
$952$		−	13.6589i		−	0.442687i
$953$	18.7909			0.608697			0.304348	−	0.952561i	$-0.401561\pi$
$953$	18.7909			0.608697			0.304348	+	0.952561i	$0.401561\pi$
$954$	21.9778	−	8.73440i	0.711557	−	0.282787i
$955$	−20.8721			−0.675406
$956$	−32.7512			−1.05925
$957$	−13.3220	−	4.48338i	−0.430638	−	0.144927i
$958$	11.1473			0.360151
$959$	−12.4736			−0.402794
$960$	−5.20233	−	3.53060i	−0.167905	−	0.113950i
$961$	1.87894			0.0606110
$962$			2.30204i			0.0742207i
$963$	1.96162	+	4.93588i	0.0632122	+	0.159056i
$964$		−	36.5616i		−	1.17757i
$965$	−22.9994			−0.740378
$966$	5.30502	−	7.81693i	0.170686	−	0.251506i
$967$			50.8100i			1.63394i	0.576679	+	0.816970i	$0.304348\pi$
$967$			50.8100i			1.63394i	−0.576679	+	0.816970i	$0.695652\pi$
$968$	−25.4131	+	15.3458i	−0.816806	+	0.493232i
$969$	−61.6983	−	41.8720i	−1.98204	−	1.34512i
$970$			7.85979i			0.252363i
$971$			25.2423i			0.810065i	0.914302	+	0.405032i	$0.132740\pi$
$971$			25.2423i			0.810065i	−0.914302	+	0.405032i	$0.867260\pi$
$972$	3.36302	+	20.7993i	0.107869	+	0.667137i
$973$	18.7127			0.599903
$974$	−15.1993			−0.487016
$975$	0.959810	+	0.651382i	0.0307385	+	0.0208609i
$976$			4.02107i			0.128711i
$977$			15.8515i			0.507134i	0.967318	+	0.253567i	$0.0816038\pi$
$977$			15.8515i			0.507134i	−0.967318	+	0.253567i	$0.918396\pi$
$978$	−11.8941	+	17.5260i	−0.380332	+	0.560419i
$979$	28.5387	−	7.94825i	0.912101	−	0.254027i
$980$			1.35160i			0.0431754i
$981$	9.16476	−	3.64226i	0.292608	−	0.116288i
$982$	−15.4368			−0.492609
$983$		−	41.3786i		−	1.31977i	−0.751366	−	0.659886i	$-0.770605\pi$
$983$		−	41.3786i		−	1.31977i	0.751366	−	0.659886i	$-0.229395\pi$
$984$	27.7282	−	40.8574i	0.883942	−	1.30249i
$985$		−	20.9422i		−	0.667274i
$986$	9.97176			0.317566
$987$	6.85704	−	10.1038i	0.218262	−	0.321608i
$988$	7.69961			0.244957
$989$	12.1263			0.385595
$990$	4.84811	+	6.37865i	0.154083	+	0.202727i
$991$	−50.6507			−1.60897			−0.804486	−	0.593971i	$-0.797559\pi$
$991$	−50.6507			−1.60897			−0.804486	+	0.593971i	$0.797559\pi$
$992$	−33.3974			−1.06037
$993$	−17.7834	+	26.2039i	−0.564341	+	0.831554i
$994$	−9.57985			−0.303854
$995$		−	25.3288i		−	0.802977i
$996$	8.37381	−	12.3388i	0.265334	−	0.390970i
$997$		−	36.0992i		−	1.14327i	−0.820507	−	0.571636i	$-0.806309\pi$
$997$		−	36.0992i		−	1.14327i	0.820507	−	0.571636i	$-0.193691\pi$
$998$	−19.0394			−0.602680
$999$	−21.6564	−	4.79684i	−0.685179	−	0.151765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.e.1121.15	✓	40
3.2	odd	2		1155.2.l.f.1121.26	yes	40
11.10	odd	2		1155.2.l.f.1121.25	yes	40
33.32	even	2	inner	1155.2.l.e.1121.16	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.15	✓	40	1.1	even	1	trivial
1155.2.l.e.1121.16	yes	40	33.32	even	2	inner
1155.2.l.f.1121.25	yes	40	11.10	odd	2
1155.2.l.f.1121.26	yes	40	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.805231 q^{2} +(-0.972634 + 1.43317i) q^{3} -1.35160 q^{4} +1.00000i q^{5} +(0.783195 - 1.15404i) q^{6} -1.00000i q^{7} +2.69881 q^{8} +(-1.10797 - 2.78790i) q^{9} +O(q^{10})\)	\(q-0.805231 q^{2} +(-0.972634 + 1.43317i) q^{3} -1.35160 q^{4} +1.00000i q^{5} +(0.783195 - 1.15404i) q^{6} -1.00000i q^{7} +2.69881 q^{8} +(-1.10797 - 2.78790i) q^{9} -0.805231i q^{10} +(-0.889838 - 3.19503i) q^{11} +(1.31461 - 1.93708i) q^{12} +0.669710i q^{13} +0.805231i q^{14} +(-1.43317 - 0.972634i) q^{15} +0.530036 q^{16} +5.06106 q^{17} +(0.892170 + 2.24491i) q^{18} +8.50615i q^{19} -1.35160i q^{20} +(1.43317 + 0.972634i) q^{21} +(0.716525 + 2.57273i) q^{22} +6.77356i q^{23} +(-2.62496 + 3.86787i) q^{24} -1.00000 q^{25} -0.539271i q^{26} +(5.07319 + 1.12370i) q^{27} +1.35160i q^{28} -2.44686 q^{29} +(1.15404 + 0.783195i) q^{30} +5.73402 q^{31} -5.82443 q^{32} +(5.44451 + 1.83230i) q^{33} -4.07533 q^{34} +1.00000 q^{35} +(1.49753 + 3.76814i) q^{36} -4.26879 q^{37} -6.84942i q^{38} +(-0.959810 - 0.651382i) q^{39} +2.69881i q^{40} -10.5633 q^{41} +(-1.15404 - 0.783195i) q^{42} -1.79024i q^{43} +(1.20271 + 4.31841i) q^{44} +(2.78790 - 1.10797i) q^{45} -5.45428i q^{46} -7.04997i q^{47} +(-0.515531 + 0.759633i) q^{48} -1.00000 q^{49} +0.805231 q^{50} +(-4.92256 + 7.25338i) q^{51} -0.905182i q^{52} -9.79006i q^{53} +(-4.08509 - 0.904838i) q^{54} +(3.19503 - 0.889838i) q^{55} -2.69881i q^{56} +(-12.1908 - 8.27337i) q^{57} +1.97029 q^{58} -11.6161i q^{59} +(1.93708 + 1.31461i) q^{60} +7.58641i q^{61} -4.61721 q^{62} +(-2.78790 + 1.10797i) q^{63} +3.62994 q^{64} -0.669710 q^{65} +(-4.38409 - 1.47542i) q^{66} -9.11307 q^{67} -6.84055 q^{68} +(-9.70768 - 6.58819i) q^{69} -0.805231 q^{70} +11.8970i q^{71} +(-2.99020 - 7.52404i) q^{72} +12.3309i q^{73} +3.43737 q^{74} +(0.972634 - 1.43317i) q^{75} -11.4969i q^{76} +(-3.19503 + 0.889838i) q^{77} +(0.772869 + 0.524513i) q^{78} +11.9518i q^{79} +0.530036i q^{80} +(-6.54481 + 6.17782i) q^{81} +8.50589 q^{82} +6.36979 q^{83} +(-1.93708 - 1.31461i) q^{84} +5.06106i q^{85} +1.44156i q^{86} +(2.37990 - 3.50678i) q^{87} +(-2.40151 - 8.62278i) q^{88} +8.93224i q^{89} +(-2.24491 + 0.892170i) q^{90} +0.669710 q^{91} -9.15516i q^{92} +(-5.57710 + 8.21784i) q^{93} +5.67686i q^{94} -8.50615 q^{95} +(5.66504 - 8.34742i) q^{96} -9.76091 q^{97} +0.805231 q^{98} +(-7.92151 + 6.02077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9} - 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} + 40 q^{18} - 2 q^{21} - 4 q^{22} - 12 q^{24} - 40 q^{25} + 32 q^{27} - 24 q^{29} - 8 q^{31} + 52 q^{32} - 16 q^{33} + 32 q^{34} + 40 q^{35} - 48 q^{37} + 66 q^{39} - 16 q^{41} + 32 q^{44} + 32 q^{48} - 40 q^{49} + 4 q^{50} - 14 q^{51} - 72 q^{54} + 8 q^{55} - 24 q^{57} - 80 q^{58} + 24 q^{60} + 48 q^{62} + 76 q^{64} + 4 q^{65} - 76 q^{66} - 48 q^{67} - 32 q^{68} - 20 q^{69} - 4 q^{70} + 128 q^{72} + 4 q^{75} - 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} - 24 q^{83} - 24 q^{84} - 32 q^{87} - 16 q^{88} + 8 q^{90} - 4 q^{91} - 20 q^{93} - 12 q^{95} + 12 q^{96} + 100 q^{97} + 4 q^{98} - 54 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9 - 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 + 40 * q^18 - 2 * q^21 - 4 * q^22 - 12 * q^24 - 40 * q^25 + 32 * q^27 - 24 * q^29 - 8 * q^31 + 52 * q^32 - 16 * q^33 + 32 * q^34 + 40 * q^35 - 48 * q^37 + 66 * q^39 - 16 * q^41 + 32 * q^44 + 32 * q^48 - 40 * q^49 + 4 * q^50 - 14 * q^51 - 72 * q^54 + 8 * q^55 - 24 * q^57 - 80 * q^58 + 24 * q^60 + 48 * q^62 + 76 * q^64 + 4 * q^65 - 76 * q^66 - 48 * q^67 - 32 * q^68 - 20 * q^69 - 4 * q^70 + 128 * q^72 + 4 * q^75 - 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 - 24 * q^83 - 24 * q^84 - 32 * q^87 - 16 * q^88 + 8 * q^90 - 4 * q^91 - 20 * q^93 - 12 * q^95 + 12 * q^96 + 100 * q^97 + 4 * q^98 - 54 * q^99

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