LMFDB - Embedded newform 1755.2.i.h.1171.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1755,2,Mod(586,1755)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1755, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 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("1755.586");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1755 = 3^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1755.i (of order $3$, degree $2$, not 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:	$14.0137455547$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 585)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1171.11
Character	$\chi$	$=$	1755.1171
Dual form			1755.2.i.h.586.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.644173 + 1.11574i) q^{2} +(0.170081 - 0.294590i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.40888 + 2.44026i) q^{7} +3.01494 q^{8} +O(q^{10})$	\(q+(0.644173 + 1.11574i) q^{2} +(0.170081 - 0.294590i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.40888 + 2.44026i) q^{7} +3.01494 q^{8} -1.28835 q^{10} +(-2.57577 - 4.46137i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(-1.81513 + 3.14390i) q^{14} +(1.60198 + 2.77471i) q^{16} +6.95944 q^{17} +5.29545 q^{19} +(0.170081 + 0.294590i) q^{20} +(3.31849 - 5.74779i) q^{22} +(0.178608 - 0.309358i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.28835 q^{26} +0.958499 q^{28} +(-2.41921 - 4.19019i) q^{29} +(-3.69084 + 6.39272i) q^{31} +(0.951033 - 1.64724i) q^{32} +(4.48308 + 7.76493i) q^{34} -2.81777 q^{35} +5.70885 q^{37} +(3.41119 + 5.90835i) q^{38} +(-1.50747 + 2.61102i) q^{40} +(-3.03414 + 5.25529i) q^{41} +(4.89119 + 8.47179i) q^{43} -1.75236 q^{44} +0.460217 q^{46} +(-3.06257 - 5.30452i) q^{47} +(-0.469900 + 0.813891i) q^{49} +(0.644173 - 1.11574i) q^{50} +(0.170081 + 0.294590i) q^{52} -3.26565 q^{53} +5.15154 q^{55} +(4.24770 + 7.35723i) q^{56} +(3.11678 - 5.39842i) q^{58} +(0.656449 - 1.13700i) q^{59} +(4.58881 + 7.94805i) q^{61} -9.51016 q^{62} +8.85845 q^{64} +(-0.500000 - 0.866025i) q^{65} +(-0.894026 + 1.54850i) q^{67} +(1.18367 - 2.05018i) q^{68} +(-1.81513 - 3.14390i) q^{70} +4.91564 q^{71} +4.67778 q^{73} +(3.67749 + 6.36960i) q^{74} +(0.900658 - 1.55999i) q^{76} +(7.25792 - 12.5711i) q^{77} +(-4.43554 - 7.68258i) q^{79} -3.20396 q^{80} -7.81806 q^{82} +(7.47911 + 12.9542i) q^{83} +(-3.47972 + 6.02705i) q^{85} +(-6.30155 + 10.9146i) q^{86} +(-7.76580 - 13.4508i) q^{88} -6.44960 q^{89} -2.81777 q^{91} +(-0.0607557 - 0.105232i) q^{92} +(3.94565 - 6.83406i) q^{94} +(-2.64773 + 4.58600i) q^{95} +(-5.62800 - 9.74798i) q^{97} -1.21079 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - q^{2} - 21 q^{4} - 15 q^{5} - 10 q^{7}+O(q^{10}) $ 30 * q - q^2 - 21 * q^4 - 15 * q^5 - 10 * q^7	$ 30 q - q^{2} - 21 q^{4} - 15 q^{5} - 10 q^{7} + 2 q^{10} - 9 q^{11} - 15 q^{13} - 3 q^{14} - 33 q^{16} - 6 q^{17} + 30 q^{19} - 21 q^{20} - 10 q^{22} + 6 q^{23} - 15 q^{25} + 2 q^{26} + 70 q^{28} - 8 q^{29} - 22 q^{31} - 21 q^{32} - 9 q^{34} + 20 q^{35} + 8 q^{37} + 14 q^{38} - 13 q^{41} - 24 q^{43} - 10 q^{44} - 6 q^{46} + q^{47} - 37 q^{49} - q^{50} - 21 q^{52} - 14 q^{53} + 18 q^{55} - 17 q^{56} - 22 q^{58} - 19 q^{59} - 16 q^{61} - 26 q^{62} + 72 q^{64} - 15 q^{65} - 11 q^{67} + 28 q^{68} - 3 q^{70} + 56 q^{71} + 52 q^{73} - 8 q^{74} - 18 q^{76} + 24 q^{77} - 44 q^{79} + 66 q^{80} + 70 q^{82} + 3 q^{83} + 3 q^{85} - 40 q^{86} - 37 q^{88} + 8 q^{89} + 20 q^{91} + 74 q^{92} - 2 q^{94} - 15 q^{95} - 33 q^{97} - 6 q^{98}+O(q^{100}) $ 30 * q - q^2 - 21 * q^4 - 15 * q^5 - 10 * q^7 + 2 * q^10 - 9 * q^11 - 15 * q^13 - 3 * q^14 - 33 * q^16 - 6 * q^17 + 30 * q^19 - 21 * q^20 - 10 * q^22 + 6 * q^23 - 15 * q^25 + 2 * q^26 + 70 * q^28 - 8 * q^29 - 22 * q^31 - 21 * q^32 - 9 * q^34 + 20 * q^35 + 8 * q^37 + 14 * q^38 - 13 * q^41 - 24 * q^43 - 10 * q^44 - 6 * q^46 + q^47 - 37 * q^49 - q^50 - 21 * q^52 - 14 * q^53 + 18 * q^55 - 17 * q^56 - 22 * q^58 - 19 * q^59 - 16 * q^61 - 26 * q^62 + 72 * q^64 - 15 * q^65 - 11 * q^67 + 28 * q^68 - 3 * q^70 + 56 * q^71 + 52 * q^73 - 8 * q^74 - 18 * q^76 + 24 * q^77 - 44 * q^79 + 66 * q^80 + 70 * q^82 + 3 * q^83 + 3 * q^85 - 40 * q^86 - 37 * q^88 + 8 * q^89 + 20 * q^91 + 74 * q^92 - 2 * q^94 - 15 * q^95 - 33 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1755\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.644173	+	1.11574i	0.455499	+	0.788948i	0.998717	−	0.0506441i	$-0.0161274\pi$
$2$	0.644173	+	1.11574i	0.455499	+	0.788948i	−0.543217	+	0.839592i	$0.682794\pi$
$3$		0			0
$3$		0			0
$4$	0.170081	−	0.294590i	0.0850407	−	0.147295i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	1.40888	+	2.44026i	0.532508	+	0.922330i	0.999280	+	0.0379524i	$0.0120835\pi$
$7$	1.40888	+	2.44026i	0.532508	+	0.922330i	−0.466772	+	0.884378i	$0.654583\pi$
$8$	3.01494			1.06594
$9$		0			0
$10$	−1.28835			−0.407411
$11$	−2.57577	−	4.46137i	−0.776625	−	1.34515i	−0.933877	−	0.357595i	$-0.883597\pi$
$11$	−2.57577	−	4.46137i	−0.776625	−	1.34515i	0.157252	−	0.987558i	$-0.449736\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−1.81513	+	3.14390i	−0.485114	+	0.840242i
$15$		0			0
$16$	1.60198	+	2.77471i	0.400495	+	0.693678i
$17$	6.95944			1.68791			0.843956	−	0.536413i	$-0.180221\pi$
$17$	6.95944			1.68791			0.843956	+	0.536413i	$0.180221\pi$
$18$		0			0
$19$	5.29545			1.21486			0.607430	−	0.794373i	$-0.292200\pi$
$19$	5.29545			1.21486			0.607430	+	0.794373i	$0.292200\pi$
$20$	0.170081	+	0.294590i	0.0380314	+	0.0658723i
$21$		0			0
$22$	3.31849	−	5.74779i	0.707504	−	1.22543i
$23$	0.178608	−	0.309358i	0.0372423	−	0.0645055i	−0.846803	−	0.531906i	$-0.821476\pi$
$23$	0.178608	−	0.309358i	0.0372423	−	0.0645055i	0.884046	+	0.467400i	$0.154809\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.28835			−0.252666
$27$		0			0
$28$	0.958499			0.181139
$29$	−2.41921	−	4.19019i	−0.449235	−	0.778099i	0.549101	−	0.835756i	$-0.314970\pi$
$29$	−2.41921	−	4.19019i	−0.449235	−	0.778099i	−0.998336	+	0.0576574i	$0.981637\pi$
$30$		0			0
$31$	−3.69084	+	6.39272i	−0.662894	+	1.14817i	0.316957	+	0.948440i	$0.397339\pi$
$31$	−3.69084	+	6.39272i	−0.662894	+	1.14817i	−0.979852	+	0.199727i	$0.935994\pi$
$32$	0.951033	−	1.64724i	0.168121	−	0.291193i
$33$		0			0
$34$	4.48308	+	7.76493i	0.768843	+	1.33167i
$35$	−2.81777			−0.476289
$36$		0			0
$37$	5.70885			0.938530			0.469265	−	0.883058i	$-0.344519\pi$
$37$	5.70885			0.938530			0.469265	+	0.883058i	$0.344519\pi$
$38$	3.41119	+	5.90835i	0.553368	+	0.958461i
$39$		0			0
$40$	−1.50747	+	2.61102i	−0.238352	+	0.412838i
$41$	−3.03414	+	5.25529i	−0.473854	+	0.820739i	−0.999552	−	0.0299323i	$-0.990471\pi$
$41$	−3.03414	+	5.25529i	−0.473854	+	0.820739i	0.525698	+	0.850671i	$0.323804\pi$
$42$		0			0
$43$	4.89119	+	8.47179i	0.745900	+	1.29194i	0.949773	+	0.312939i	$0.101314\pi$
$43$	4.89119	+	8.47179i	0.745900	+	1.29194i	−0.203873	+	0.978997i	$0.565353\pi$
$44$	−1.75236			−0.264179
$45$		0			0
$46$	0.460217			0.0678553
$47$	−3.06257	−	5.30452i	−0.446721	−	0.773744i	0.551449	−	0.834208i	$-0.314075\pi$
$47$	−3.06257	−	5.30452i	−0.446721	−	0.773744i	−0.998170	+	0.0604648i	$0.980742\pi$
$48$		0			0
$49$	−0.469900	+	0.813891i	−0.0671286	+	0.116270i
$50$	0.644173	−	1.11574i	0.0910999	−	0.157790i
$51$		0			0
$52$	0.170081	+	0.294590i	0.0235861	+	0.0408522i
$53$	−3.26565			−0.448572			−0.224286	−	0.974523i	$-0.572005\pi$
$53$	−3.26565			−0.448572			−0.224286	+	0.974523i	$0.572005\pi$
$54$		0			0
$55$	5.15154			0.694634
$56$	4.24770	+	7.35723i	0.567623	+	0.983151i
$57$		0			0
$58$	3.11678	−	5.39842i	0.409253	−	0.708847i
$59$	0.656449	−	1.13700i	0.0854624	−	0.148025i	−0.820126	−	0.572183i	$-0.806097\pi$
$59$	0.656449	−	1.13700i	0.0854624	−	0.148025i	0.905588	+	0.424158i	$0.139430\pi$
$60$		0			0
$61$	4.58881	+	7.94805i	0.587537	+	1.01764i	0.994554	+	0.104223i	$0.0332356\pi$
$61$	4.58881	+	7.94805i	0.587537	+	1.01764i	−0.407017	+	0.913421i	$0.633431\pi$
$62$	−9.51016			−1.20779
$63$		0			0
$64$	8.85845			1.10731
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$		0			0
$67$	−0.894026	+	1.54850i	−0.109223	+	0.189179i	−0.915456	−	0.402419i	$-0.868169\pi$
$67$	−0.894026	+	1.54850i	−0.109223	+	0.189179i	0.806233	+	0.591598i	$0.201503\pi$
$68$	1.18367	−	2.05018i	0.143541	−	0.248621i
$69$		0			0
$70$	−1.81513	−	3.14390i	−0.216949	−	0.375767i
$71$	4.91564			0.583379			0.291689	−	0.956513i	$-0.405783\pi$
$71$	4.91564			0.583379			0.291689	+	0.956513i	$0.405783\pi$
$72$		0			0
$73$	4.67778			0.547493			0.273746	−	0.961802i	$-0.411737\pi$
$73$	4.67778			0.547493			0.273746	+	0.961802i	$0.411737\pi$
$74$	3.67749	+	6.36960i	0.427500	+	0.740451i
$75$		0			0
$76$	0.900658	−	1.55999i	0.103313	−	0.178943i
$77$	7.25792	−	12.5711i	0.827117	−	1.43261i
$78$		0			0
$79$	−4.43554	−	7.68258i	−0.499037	−	0.864358i	0.500962	−	0.865469i	$-0.332980\pi$
$79$	−4.43554	−	7.68258i	−0.499037	−	0.864358i	−0.999999	+	0.00111120i	$0.999646\pi$
$80$	−3.20396			−0.358214
$81$		0			0
$82$	−7.81806			−0.863360
$83$	7.47911	+	12.9542i	0.820939	+	1.42191i	0.904984	+	0.425446i	$0.139883\pi$
$83$	7.47911	+	12.9542i	0.820939	+	1.42191i	−0.0840448	+	0.996462i	$0.526784\pi$
$84$		0			0
$85$	−3.47972	+	6.02705i	−0.377429	+	0.653725i
$86$	−6.30155	+	10.9146i	−0.679514	+	1.17695i
$87$		0			0
$88$	−7.76580	−	13.4508i	−0.827837	−	1.43386i
$89$	−6.44960			−0.683656			−0.341828	−	0.939763i	$-0.611046\pi$
$89$	−6.44960			−0.683656			−0.341828	+	0.939763i	$0.611046\pi$
$90$		0			0
$91$	−2.81777			−0.295382
$92$	−0.0607557	−	0.105232i	−0.00633422	−	0.0109712i
$93$		0			0
$94$	3.94565	−	6.83406i	0.406962	−	0.704879i
$95$	−2.64773	+	4.58600i	−0.271651	+	0.470513i
$96$		0			0
$97$	−5.62800	−	9.74798i	−0.571437	−	0.989757i	−0.996419	−	0.0845556i	$-0.973053\pi$
$97$	−5.62800	−	9.74798i	−0.571437	−	0.989757i	0.424982	−	0.905202i	$-0.360280\pi$
$98$	−1.21079			−0.122308
$99$		0			0
$100$	−0.340163			−0.0340163
$101$	4.87922	+	8.45106i	0.485501	+	0.840912i	0.999861	−	0.0166623i	$-0.00530402\pi$
$101$	4.87922	+	8.45106i	0.485501	+	0.840912i	−0.514361	+	0.857574i	$0.671971\pi$
$102$		0			0
$103$	−3.96888	+	6.87431i	−0.391066	+	0.677345i	−0.992590	−	0.121509i	$-0.961227\pi$
$103$	−3.96888	+	6.87431i	−0.391066	+	0.677345i	0.601525	+	0.798854i	$0.294560\pi$
$104$	−1.50747	+	2.61102i	−0.147820	+	0.256031i
$105$		0			0
$106$	−2.10365	−	3.64362i	−0.204324	−	0.353900i
$107$	−4.45095			−0.430290			−0.215145	−	0.976582i	$-0.569022\pi$
$107$	−4.45095			−0.430290			−0.215145	+	0.976582i	$0.569022\pi$
$108$		0			0
$109$	−8.58876			−0.822654			−0.411327	−	0.911488i	$-0.634935\pi$
$109$	−8.58876			−0.822654			−0.411327	+	0.911488i	$0.634935\pi$
$110$	3.31849	+	5.74779i	0.316405	+	0.548030i
$111$		0			0
$112$	−4.51401	+	7.81849i	−0.426534	+	0.738778i
$113$	9.61749	−	16.6580i	0.904738	−	1.56705i	0.0834690	−	0.996510i	$-0.473400\pi$
$113$	9.61749	−	16.6580i	0.904738	−	1.56705i	0.821269	−	0.570541i	$-0.193267\pi$
$114$		0			0
$115$	0.178608	+	0.309358i	0.0166553	+	0.0288477i
$116$	−1.64585			−0.152813
$117$		0			0
$118$	1.69147			0.155712
$119$	9.80503	+	16.9828i	0.898826	+	1.55681i
$120$		0			0
$121$	−7.76921	+	13.4567i	−0.706291	+	1.22333i
$122$	−5.91198	+	10.2398i	−0.535245	+	0.927072i
$123$		0			0
$124$	1.25549	+	2.17457i	0.112746	+	0.195282i
$125$	1.00000			0.0894427
$126$		0			0
$127$	7.98997			0.708995			0.354497	−	0.935057i	$-0.384652\pi$
$127$	7.98997			0.708995			0.354497	+	0.935057i	$0.384652\pi$
$128$	3.80431	+	6.58926i	0.336257	+	0.582414i
$129$		0			0
$130$	0.644173	−	1.11574i	0.0564977	−	0.0978570i
$131$	−1.73503	+	3.00516i	−0.151590	+	0.262562i	−0.931812	−	0.362941i	$-0.881773\pi$
$131$	−1.73503	+	3.00516i	−0.151590	+	0.262562i	0.780222	+	0.625503i	$0.215106\pi$
$132$		0			0
$133$	7.46067	+	12.9223i	0.646922	+	1.12050i
$134$	−2.30363			−0.199003
$135$		0			0
$136$	20.9823			1.79922
$137$	2.87915	+	4.98683i	0.245982	+	0.426054i	0.962407	−	0.271610i	$-0.0875562\pi$
$137$	2.87915	+	4.98683i	0.245982	+	0.426054i	−0.716425	+	0.697664i	$0.754223\pi$
$138$		0			0
$139$	3.79217	−	6.56823i	0.321647	−	0.557110i	−0.659181	−	0.751985i	$-0.729097\pi$
$139$	3.79217	−	6.56823i	0.321647	−	0.557110i	0.980828	+	0.194875i	$0.0624301\pi$
$140$	−0.479250	+	0.830085i	−0.0405040	+	0.0701550i
$141$		0			0
$142$	3.16652	+	5.48458i	0.265729	+	0.460256i
$143$	5.15154			0.430794
$144$		0			0
$145$	4.83841			0.401808
$146$	3.01330	+	5.21919i	0.249383	+	0.431943i
$147$		0			0
$148$	0.970970	−	1.68177i	0.0798132	−	0.138241i
$149$	3.00953	−	5.21267i	0.246551	−	0.427038i	−0.716016	−	0.698084i	$-0.754036\pi$
$149$	3.00953	−	5.21267i	0.246551	−	0.427038i	0.962566	+	0.271046i	$0.0873695\pi$
$150$		0			0
$151$	−4.91595	−	8.51467i	−0.400054	−	0.692914i	0.593678	−	0.804703i	$-0.297675\pi$
$151$	−4.91595	−	8.51467i	−0.400054	−	0.692914i	−0.993732	+	0.111789i	$0.964342\pi$
$152$	15.9655			1.29497
$153$		0			0
$154$	18.7014			1.50700
$155$	−3.69084	−	6.39272i	−0.296455	−	0.513476i
$156$		0			0
$157$	1.25443	−	2.17274i	0.100115	−	0.173403i	−0.811617	−	0.584190i	$-0.801412\pi$
$157$	1.25443	−	2.17274i	0.100115	−	0.173403i	0.911732	+	0.410786i	$0.134746\pi$
$158$	5.71451	−	9.89783i	0.454622	−	0.787429i
$159$		0			0
$160$	0.951033	+	1.64724i	0.0751858	+	0.130226i
$161$	1.00655			0.0793272
$162$		0			0
$163$	−19.8235			−1.55269			−0.776347	−	0.630306i	$-0.782929\pi$
$163$	−19.8235			−1.55269			−0.776347	+	0.630306i	$0.782929\pi$
$164$	1.03210	+	1.78766i	0.0805938	+	0.139592i
$165$		0			0
$166$	−9.63569	+	16.6895i	−0.747874	+	1.29536i
$167$	−11.8886	+	20.5916i	−0.919964	+	1.59342i	−0.120497	+	0.992714i	$0.538449\pi$
$167$	−11.8886	+	20.5916i	−0.919964	+	1.59342i	−0.799467	+	0.600710i	$0.794885\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−8.96617			−0.687674
$171$		0			0
$172$	3.32760			0.253727
$173$	−2.89292	−	5.01068i	−0.219944	−	0.380955i	0.734846	−	0.678234i	$-0.237254\pi$
$173$	−2.89292	−	5.01068i	−0.219944	−	0.380955i	−0.954791	+	0.297279i	$0.903921\pi$
$174$		0			0
$175$	1.40888	−	2.44026i	0.106502	−	0.184466i
$176$	8.25268	−	14.2941i	0.622069	−	1.07746i
$177$		0			0
$178$	−4.15466	−	7.19608i	−0.311405	−	0.539369i
$179$	20.1982			1.50969			0.754844	−	0.655905i	$-0.227713\pi$
$179$	20.1982			1.50969			0.754844	+	0.655905i	$0.227713\pi$
$180$		0			0
$181$	−10.0801			−0.749249			−0.374625	−	0.927177i	$-0.622228\pi$
$181$	−10.0801			−0.749249			−0.374625	+	0.927177i	$0.622228\pi$
$182$	−1.81513	−	3.14390i	−0.134546	−	0.233041i
$183$		0			0
$184$	0.538492	−	0.932695i	0.0396981	−	0.0687592i
$185$	−2.85443	+	4.94401i	−0.209862	+	0.363491i
$186$		0			0
$187$	−17.9259	−	31.0486i	−1.31087	−	2.27050i
$188$	−2.08354			−0.151958
$189$		0			0
$190$	−6.82238			−0.494947
$191$	−9.12892	−	15.8118i	−0.660545	−	1.14410i	−0.980473	−	0.196656i	$-0.936992\pi$
$191$	−9.12892	−	15.8118i	−0.660545	−	1.14410i	0.319927	−	0.947442i	$-0.396342\pi$
$192$		0			0
$193$	1.08415	−	1.87780i	0.0780388	−	0.135167i	−0.824365	−	0.566059i	$-0.808468\pi$
$193$	1.08415	−	1.87780i	0.0780388	−	0.135167i	0.902404	+	0.430892i	$0.141801\pi$
$194$	7.25081	−	12.5588i	0.520578	−	0.901668i
$195$		0			0
$196$	0.159843	+	0.276856i	0.0114173	+	0.0197754i
$197$	−14.9589			−1.06578			−0.532890	−	0.846185i	$-0.678894\pi$
$197$	−14.9589			−1.06578			−0.532890	+	0.846185i	$0.678894\pi$
$198$		0			0
$199$	4.81279			0.341170			0.170585	−	0.985343i	$-0.445434\pi$
$199$	4.81279			0.341170			0.170585	+	0.985343i	$0.445434\pi$
$200$	−1.50747	−	2.61102i	−0.106594	−	0.184627i
$201$		0			0
$202$	−6.28613	+	10.8879i	−0.442290	+	0.766069i
$203$	6.81676	−	11.8070i	0.478443	−	0.828687i
$204$		0			0
$205$	−3.03414	−	5.25529i	−0.211914	−	0.367046i
$206$	−10.2266			−0.712520
$207$		0			0
$208$	−3.20396			−0.222155
$209$	−13.6399	−	23.6250i	−0.943490	−	1.63417i
$210$		0			0
$211$	−4.80298	+	8.31901i	−0.330651	+	0.572704i	−0.982640	−	0.185524i	$-0.940602\pi$
$211$	−4.80298	+	8.31901i	−0.330651	+	0.572704i	0.651989	+	0.758229i	$0.273935\pi$
$212$	−0.555427	+	0.962028i	−0.0381469	+	0.0660724i
$213$		0			0
$214$	−2.86718	−	4.96611i	−0.195997	−	0.339476i
$215$	−9.78238			−0.667153
$216$		0			0
$217$	−20.7998			−1.41199
$218$	−5.53265	−	9.58283i	−0.374718	−	0.649031i
$219$		0			0
$220$	0.876182	−	1.51759i	0.0590722	−	0.102316i
$221$	−3.47972	+	6.02705i	−0.234071	+	0.405423i
$222$		0			0
$223$	3.17548	+	5.50009i	0.212646	+	0.368313i	0.952542	−	0.304408i	$-0.0984587\pi$
$223$	3.17548	+	5.50009i	0.212646	+	0.368313i	−0.739896	+	0.672721i	$0.765125\pi$
$224$	5.35958			0.358102
$225$		0			0
$226$	24.7813			1.64843
$227$	2.84962	+	4.93569i	0.189136	+	0.327593i	0.944962	−	0.327179i	$-0.106098\pi$
$227$	2.84962	+	4.93569i	0.189136	+	0.327593i	−0.755826	+	0.654772i	$0.772765\pi$
$228$		0			0
$229$	10.9728	−	19.0054i	0.725102	−	1.25591i	−0.233830	−	0.972277i	$-0.575126\pi$
$229$	10.9728	−	19.0054i	0.725102	−	1.25591i	0.958932	−	0.283636i	$-0.0915407\pi$
$230$	−0.230109	+	0.398560i	−0.0151729	+	0.0262803i
$231$		0			0
$232$	−7.29377	−	12.6332i	−0.478859	−	0.829408i
$233$	−25.7672			−1.68806			−0.844031	−	0.536294i	$-0.819824\pi$
$233$	−25.7672			−1.68806			−0.844031	+	0.536294i	$0.819824\pi$
$234$		0			0
$235$	6.12513			0.399560
$236$	−0.223300	−	0.386766i	−0.0145356	−	0.0251763i
$237$		0			0
$238$	−12.6323	+	21.8797i	−0.818829	+	1.41825i
$239$	−2.97550	+	5.15372i	−0.192469	+	0.333366i	−0.946068	−	0.323968i	$-0.894983\pi$
$239$	−2.97550	+	5.15372i	−0.192469	+	0.333366i	0.753599	+	0.657335i	$0.228316\pi$
$240$		0			0
$241$	−11.6495	−	20.1774i	−0.750407	−	1.29974i	−0.947625	−	0.319384i	$-0.896524\pi$
$241$	−11.6495	−	20.1774i	−0.750407	−	1.29974i	0.197218	−	0.980360i	$-0.436809\pi$
$242$	−20.0189			−1.28686
$243$		0			0
$244$	3.12189			0.199858
$245$	−0.469900	−	0.813891i	−0.0300208	−	0.0519976i
$246$		0			0
$247$	−2.64773	+	4.58600i	−0.168471	+	0.291800i
$248$	−11.1277	+	19.2737i	−0.706607	+	1.22388i
$249$		0			0
$250$	0.644173	+	1.11574i	0.0407411	+	0.0705657i
$251$	−16.6483			−1.05083			−0.525417	−	0.850845i	$-0.676091\pi$
$251$	−16.6483			−1.05083			−0.525417	+	0.850845i	$0.676091\pi$
$252$		0			0
$253$	−1.84021			−0.115693
$254$	5.14692	+	8.91473i	0.322947	+	0.559360i
$255$		0			0
$256$	3.95718	−	6.85404i	0.247324	−	0.428377i
$257$	−3.29768	+	5.71175i	−0.205704	+	0.356289i	−0.950357	−	0.311163i	$-0.899282\pi$
$257$	−3.29768	+	5.71175i	−0.205704	+	0.356289i	0.744653	+	0.667452i	$0.232615\pi$
$258$		0			0
$259$	8.04310	+	13.9311i	0.499774	+	0.865634i
$260$	−0.340163			−0.0210960
$261$		0			0
$262$	−4.47064			−0.276197
$263$	−8.83438	−	15.3016i	−0.544751	−	0.943536i	−0.998623	−	0.0524693i	$-0.983291\pi$
$263$	−8.83438	−	15.3016i	−0.544751	−	0.943536i	0.453872	−	0.891067i	$-0.350042\pi$
$264$		0			0
$265$	1.63283	−	2.82814i	0.100304	−	0.173731i
$266$	−9.61193	+	16.6484i	−0.589345	+	1.02078i
$267$		0			0
$268$	0.304115	+	0.526742i	0.0185768	+	0.0321759i
$269$	6.09803			0.371804			0.185902	−	0.982568i	$-0.440479\pi$
$269$	6.09803			0.371804			0.185902	+	0.982568i	$0.440479\pi$
$270$		0			0
$271$	−19.9160			−1.20981			−0.604906	−	0.796297i	$-0.706789\pi$
$271$	−19.9160			−1.20981			−0.604906	+	0.796297i	$0.706789\pi$
$272$	11.1489	+	19.3104i	0.676001	+	1.17087i
$273$		0			0
$274$	−3.70934	+	6.42477i	−0.224090	+	0.388134i
$275$	−2.57577	+	4.46137i	−0.155325	+	0.269031i
$276$		0			0
$277$	−16.1804	−	28.0254i	−0.972189	−	1.68388i	−0.688916	−	0.724841i	$-0.741913\pi$
$277$	−16.1804	−	28.0254i	−0.972189	−	1.68388i	−0.283272	−	0.959040i	$-0.591420\pi$
$278$	9.77125			0.586041
$279$		0			0
$280$	−8.49540			−0.507697
$281$	−16.0058	−	27.7228i	−0.954825	−	1.65381i	−0.734768	−	0.678319i	$-0.762709\pi$
$281$	−16.0058	−	27.7228i	−0.954825	−	1.65381i	−0.220057	−	0.975487i	$-0.570624\pi$
$282$		0			0
$283$	14.4870	−	25.0921i	0.861160	−	1.49157i	−0.00965008	−	0.999953i	$-0.503072\pi$
$283$	14.4870	−	25.0921i	0.861160	−	1.49157i	0.870810	−	0.491620i	$-0.163595\pi$
$284$	0.836059	−	1.44810i	0.0496110	−	0.0859287i
$285$		0			0
$286$	3.31849	+	5.74779i	0.196226	+	0.339874i
$287$	−17.0990			−1.00932
$288$		0			0
$289$	31.4338			1.84905
$290$	3.11678	+	5.39842i	0.183023	+	0.317006i
$291$		0			0
$292$	0.795603	−	1.37803i	0.0465592	−	0.0806429i
$293$	2.02909	−	3.51448i	0.118541	−	0.205318i	−0.800649	−	0.599134i	$-0.795512\pi$
$293$	2.02909	−	3.51448i	0.118541	−	0.205318i	0.919190	+	0.393815i	$0.128845\pi$
$294$		0			0
$295$	0.656449	+	1.13700i	0.0382199	+	0.0661989i
$296$	17.2119			1.00042
$297$		0			0
$298$	7.75465			0.449215
$299$	0.178608	+	0.309358i	0.0103292	+	0.0178906i
$300$		0			0
$301$	−13.7822	+	23.8715i	−0.794395	+	1.37593i
$302$	6.33345	−	10.9698i	0.364449	−	0.631244i
$303$		0			0
$304$	8.48322	+	14.6934i	0.486546	+	0.842722i
$305$	−9.17762			−0.525509
$306$		0			0
$307$	10.2358			0.584185			0.292093	−	0.956390i	$-0.405648\pi$
$307$	10.2358			0.584185			0.292093	+	0.956390i	$0.405648\pi$
$308$	−2.46888	−	4.27622i	−0.140677	−	0.243660i
$309$		0			0
$310$	4.75508	−	8.23604i	0.270070	−	0.467776i
$311$	11.1128	−	19.2479i	0.630149	−	1.09145i	−0.357372	−	0.933962i	$-0.616327\pi$
$311$	11.1128	−	19.2479i	0.630149	−	1.09145i	0.987521	−	0.157488i	$-0.0503397\pi$
$312$		0			0
$313$	4.81602	+	8.34160i	0.272218	+	0.471495i	0.969429	−	0.245370i	$-0.0789096\pi$
$313$	4.81602	+	8.34160i	0.272218	+	0.471495i	−0.697212	+	0.716865i	$0.745576\pi$
$314$	3.23228			0.182408
$315$		0			0
$316$	−3.01761			−0.169754
$317$	15.3523	+	26.5910i	0.862273	+	1.49350i	0.869730	+	0.493528i	$0.164293\pi$
$317$	15.3523	+	26.5910i	0.862273	+	1.49350i	−0.00745758	+	0.999972i	$0.502374\pi$
$318$		0			0
$319$	−12.4627	+	21.5859i	−0.697775	+	1.20858i
$320$	−4.42922	+	7.67164i	−0.247601	+	0.428858i
$321$		0			0
$322$	0.648392	+	1.12305i	0.0361335	+	0.0625850i
$323$	36.8534			2.05058
$324$		0			0
$325$	1.00000			0.0554700
$326$	−12.7697	−	22.1179i	−0.707251	−	1.22499i
$327$		0			0
$328$	−9.14777	+	15.8444i	−0.505101	+	0.874861i
$329$	8.62959	−	14.9469i	0.475765	−	0.824049i
$330$		0			0
$331$	1.75825	+	3.04538i	0.0966424	+	0.167389i	0.910293	−	0.413965i	$-0.135856\pi$
$331$	1.75825	+	3.04538i	0.0966424	+	0.167389i	−0.813651	+	0.581354i	$0.802523\pi$
$332$	5.08823			0.279253
$333$		0			0
$334$	−30.6331			−1.67617
$335$	−0.894026	−	1.54850i	−0.0488459	−	0.0846035i
$336$		0			0
$337$	9.81302	−	16.9967i	0.534549	−	0.925867i	−0.464636	−	0.885502i	$-0.653815\pi$
$337$	9.81302	−	16.9967i	0.534549	−	0.925867i	0.999185	−	0.0403646i	$-0.0128520\pi$
$338$	0.644173	−	1.11574i	0.0350384	−	0.0606883i
$339$		0			0
$340$	1.18367	+	2.05018i	0.0641936	+	0.111187i
$341$	38.0271			2.05928
$342$		0			0
$343$	17.0762			0.922029
$344$	14.7467	+	25.5420i	0.795086	+	1.37713i
$345$		0			0
$346$	3.72708	−	6.45549i	0.200369	−	0.347049i
$347$	12.6960	−	21.9902i	0.681559	−	1.18049i	−0.292946	−	0.956129i	$-0.594636\pi$
$347$	12.6960	−	21.9902i	0.681559	−	1.18049i	0.974505	−	0.224366i	$-0.0720310\pi$
$348$		0			0
$349$	6.09864	+	10.5632i	0.326453	+	0.565433i	0.981805	−	0.189890i	$-0.0608132\pi$
$349$	6.09864	+	10.5632i	0.326453	+	0.565433i	−0.655352	+	0.755323i	$0.727480\pi$
$350$	3.63026			0.194045
$351$		0			0
$352$	−9.79858			−0.522266
$353$	−8.97537	−	15.5458i	−0.477711	−	0.827419i	0.521963	−	0.852968i	$-0.325200\pi$
$353$	−8.97537	−	15.5458i	−0.477711	−	0.827419i	−0.999674	+	0.0255491i	$0.991867\pi$
$354$		0			0
$355$	−2.45782	+	4.25707i	−0.130447	+	0.225942i
$356$	−1.09696	+	1.89999i	−0.0581386	+	0.100699i
$357$		0			0
$358$	13.0112	+	22.5360i	0.687662	+	1.19106i
$359$	−20.1656			−1.06430			−0.532149	−	0.846651i	$-0.678615\pi$
$359$	−20.1656			−1.06430			−0.532149	+	0.846651i	$0.678615\pi$
$360$		0			0
$361$	9.04182			0.475885
$362$	−6.49334	−	11.2468i	−0.341283	−	0.591119i
$363$		0			0
$364$	−0.479250	+	0.830085i	−0.0251195	+	0.0435083i
$365$	−2.33889	+	4.05108i	−0.122423	+	0.212043i
$366$		0			0
$367$	−14.9418	−	25.8799i	−0.779953	−	1.35092i	−0.931968	−	0.362540i	$-0.881910\pi$
$367$	−14.9418	−	25.8799i	−0.779953	−	1.35092i	0.152015	−	0.988378i	$-0.451424\pi$
$368$	1.14451			0.0596615
$369$		0			0
$370$	−7.35498			−0.382367
$371$	−4.60092	−	7.96903i	−0.238868	−	0.413732i
$372$		0			0
$373$	1.82808	−	3.16632i	0.0946542	−	0.163946i	−0.814810	−	0.579728i	$-0.803159\pi$
$373$	1.82808	−	3.16632i	0.0946542	−	0.163946i	0.909464	+	0.415782i	$0.136492\pi$
$374$	23.0948	−	40.0014i	1.19420	−	2.06842i
$375$		0			0
$376$	−9.23346	−	15.9928i	−0.476179	−	0.824766i
$377$	4.83841			0.249191
$378$		0			0
$379$	24.0635			1.23606			0.618028	−	0.786156i	$-0.287932\pi$
$379$	24.0635			1.23606			0.618028	+	0.786156i	$0.287932\pi$
$380$	0.900658	+	1.55999i	0.0462028	+	0.0800256i
$381$		0			0
$382$	11.7612	−	20.3710i	0.601756	−	1.04227i
$383$	−14.8405	+	25.7045i	−0.758314	+	1.31344i	0.185396	+	0.982664i	$0.440643\pi$
$383$	−14.8405	+	25.7045i	−0.758314	+	1.31344i	−0.943710	+	0.330775i	$0.892690\pi$
$384$		0			0
$385$	7.25792	+	12.5711i	0.369898	+	0.640682i
$386$	2.79352			0.142187
$387$		0			0
$388$	−3.82887			−0.194382
$389$	2.84354	+	4.92516i	0.144173	+	0.249715i	0.929064	−	0.369919i	$-0.120614\pi$
$389$	2.84354	+	4.92516i	0.144173	+	0.249715i	−0.784891	+	0.619634i	$0.787281\pi$
$390$		0			0
$391$	1.24301	−	2.15296i	0.0628617	−	0.108880i
$392$	−1.41672	+	2.45383i	−0.0715552	+	0.123937i
$393$		0			0
$394$	−9.63614	−	16.6903i	−0.485462	−	0.840845i
$395$	8.87108			0.446353
$396$		0			0
$397$	−1.64080			−0.0823496			−0.0411748	−	0.999152i	$-0.513110\pi$
$397$	−1.64080			−0.0823496			−0.0411748	+	0.999152i	$0.513110\pi$
$398$	3.10027	+	5.36983i	0.155403	+	0.269165i
$399$		0			0
$400$	1.60198	−	2.77471i	0.0800991	−	0.138736i
$401$	−6.65233	+	11.5222i	−0.332201	+	0.575390i	−0.982943	−	0.183909i	$-0.941125\pi$
$401$	−6.65233	+	11.5222i	−0.332201	+	0.575390i	0.650742	+	0.759299i	$0.274458\pi$
$402$		0			0
$403$	−3.69084	−	6.39272i	−0.183854	−	0.318444i
$404$	3.31946			0.165149
$405$		0			0
$406$	17.5647			0.871721
$407$	−14.7047	−	25.4693i	−0.728885	−	1.26247i
$408$		0			0
$409$	−5.27938	+	9.14416i	−0.261049	+	0.452150i	−0.966521	−	0.256588i	$-0.917402\pi$
$409$	−5.27938	+	9.14416i	−0.261049	+	0.452150i	0.705472	+	0.708738i	$0.250735\pi$
$410$	3.90903	−	6.77064i	0.193053	−	0.334378i
$411$		0			0
$412$	1.35007	+	2.33838i	0.0665130	+	0.115204i
$413$	3.69944			0.182037
$414$		0			0
$415$	−14.9582			−0.734270
$416$	0.951033	+	1.64724i	0.0466282	+	0.0807625i
$417$		0			0
$418$	17.5729	−	30.4371i	0.859518	−	1.48873i
$419$	10.2745	−	17.7960i	0.501944	−	0.869393i	−0.498053	−	0.867146i	$-0.665952\pi$
$419$	10.2745	−	17.7960i	0.501944	−	0.869393i	0.999997	−	0.00224654i	$-0.000715097\pi$
$420$		0			0
$421$	18.1358	+	31.4121i	0.883885	+	1.53093i	0.846987	+	0.531614i	$0.178414\pi$
$421$	18.1358	+	31.4121i	0.883885	+	1.53093i	0.0368980	+	0.999319i	$0.488252\pi$
$422$	−12.3758			−0.602445
$423$		0			0
$424$	−9.84576			−0.478152
$425$	−3.47972	−	6.02705i	−0.168791	−	0.292355i
$426$		0			0
$427$	−12.9302	+	22.3957i	−0.625736	+	1.08381i
$428$	−0.757024	+	1.31120i	−0.0365921	+	0.0633794i
$429$		0			0
$430$	−6.30155	−	10.9146i	−0.303888	−	0.526349i
$431$	−15.4318			−0.743323			−0.371661	−	0.928368i	$-0.621212\pi$
$431$	−15.4318			−0.743323			−0.371661	+	0.928368i	$0.621212\pi$
$432$		0			0
$433$	−23.3484			−1.12205			−0.561027	−	0.827797i	$-0.689594\pi$
$433$	−23.3484			−1.12205			−0.561027	+	0.827797i	$0.689594\pi$
$434$	−13.3987	−	23.2072i	−0.643158	−	1.11398i
$435$		0			0
$436$	−1.46079	+	2.53016i	−0.0699591	+	0.121173i
$437$	0.945809	−	1.63819i	0.0452442	−	0.0783652i
$438$		0			0
$439$	−6.22486	−	10.7818i	−0.297096	−	0.514586i	0.678374	−	0.734717i	$-0.262685\pi$
$439$	−6.22486	−	10.7818i	−0.297096	−	0.514586i	−0.975470	+	0.220131i	$0.929352\pi$
$440$	15.5316			0.740440
$441$		0			0
$442$	−8.96617			−0.426477
$443$	−3.63184	−	6.29053i	−0.172554	−	0.298872i	0.766758	−	0.641936i	$-0.221869\pi$
$443$	−3.63184	−	6.29053i	−0.172554	−	0.298872i	−0.939312	+	0.343064i	$0.888535\pi$
$444$		0			0
$445$	3.22480	−	5.58552i	0.152870	−	0.264779i
$446$	−4.09111	+	7.08602i	−0.193720	+	0.335533i
$447$		0			0
$448$	12.4805	+	21.6169i	0.589649	+	1.02130i
$449$	14.7385			0.695555			0.347777	−	0.937577i	$-0.386936\pi$
$449$	14.7385			0.695555			0.347777	+	0.937577i	$0.386936\pi$
$450$		0			0
$451$	31.2611			1.47203
$452$	−3.27152	−	5.66643i	−0.153879	−	0.266526i
$453$		0			0
$454$	−3.67130	+	6.35888i	−0.172303	+	0.298437i
$455$	1.40888	−	2.44026i	0.0660494	−	0.114401i
$456$		0			0
$457$	−3.70139	−	6.41099i	−0.173143	−	0.299893i	0.766374	−	0.642395i	$-0.222059\pi$
$457$	−3.70139	−	6.41099i	−0.173143	−	0.299893i	−0.939517	+	0.342502i	$0.888726\pi$
$458$	28.2735			1.32113
$459$		0			0
$460$	0.121511			0.00566550
$461$	−1.52205	−	2.63626i	−0.0708888	−	0.122783i	0.828402	−	0.560134i	$-0.189250\pi$
$461$	−1.52205	−	2.63626i	−0.0708888	−	0.122783i	−0.899291	+	0.437351i	$0.855917\pi$
$462$		0			0
$463$	−6.99042	+	12.1078i	−0.324872	+	0.562695i	−0.981487	−	0.191531i	$-0.938655\pi$
$463$	−6.99042	+	12.1078i	−0.324872	+	0.562695i	0.656614	+	0.754227i	$0.271988\pi$
$464$	7.75105	−	13.4252i	0.359833	−	0.623250i
$465$		0			0
$466$	−16.5985	−	28.7495i	−0.768911	−	1.33179i
$467$	−30.6445			−1.41806			−0.709030	−	0.705178i	$-0.750867\pi$
$467$	−30.6445			−1.41806			−0.709030	+	0.705178i	$0.750867\pi$
$468$		0			0
$469$	−5.03831			−0.232648
$470$	3.94565	+	6.83406i	0.181999	+	0.315232i
$471$		0			0
$472$	1.97915	−	3.42800i	0.0910980	−	0.157786i
$473$	25.1972	−	43.6428i	1.15857	−	2.00670i
$474$		0			0
$475$	−2.64773	−	4.58600i	−0.121486	−	0.210420i
$476$	6.67062			0.305747
$477$		0			0
$478$	−7.66695			−0.350678
$479$	−1.48202	−	2.56693i	−0.0677152	−	0.117286i	0.830180	−	0.557495i	$-0.188238\pi$
$479$	−1.48202	−	2.56693i	−0.0677152	−	0.117286i	−0.897895	+	0.440209i	$0.854904\pi$
$480$		0			0
$481$	−2.85443	+	4.94401i	−0.130151	+	0.225428i
$482$	15.0085	−	25.9955i	0.683620	−	1.18406i
$483$		0			0
$484$	2.64280	+	4.57746i	0.120127	+	0.208066i
$485$	11.2560			0.511109
$486$		0			0
$487$	−17.5341			−0.794546			−0.397273	−	0.917700i	$-0.630043\pi$
$487$	−17.5341			−0.794546			−0.397273	+	0.917700i	$0.630043\pi$
$488$	13.8350	+	23.9629i	0.626281	+	1.08475i
$489$		0			0
$490$	0.605394	−	1.04857i	0.0273489	−	0.0473697i
$491$	−10.5572	+	18.2856i	−0.476439	+	0.825216i	−0.999636	−	0.0269956i	$-0.991406\pi$
$491$	−10.5572	+	18.2856i	−0.476439	+	0.825216i	0.523197	+	0.852212i	$0.324739\pi$
$492$		0			0
$493$	−16.8363	−	29.1614i	−0.758270	−	1.31336i
$494$	−6.82238			−0.306953
$495$		0			0
$496$	−23.6506			−1.06194
$497$	6.92556	+	11.9954i	0.310654	+	0.538068i
$498$		0			0
$499$	−16.5523	+	28.6694i	−0.740981	+	1.28342i	0.211068	+	0.977471i	$0.432306\pi$
$499$	−16.5523	+	28.6694i	−0.740981	+	1.28342i	−0.952049	+	0.305945i	$0.901028\pi$
$500$	0.170081	−	0.294590i	0.00760627	−	0.0131745i
$501$		0			0
$502$	−10.7244	−	18.5752i	−0.478654	−	0.829053i
$503$	−20.4002			−0.909601			−0.454800	−	0.890593i	$-0.650289\pi$
$503$	−20.4002			−0.909601			−0.454800	+	0.890593i	$0.650289\pi$
$504$		0			0
$505$	−9.75844			−0.434245
$506$	−1.18541	−	2.05320i	−0.0526981	−	0.0912758i
$507$		0			0
$508$	1.35895	−	2.35376i	0.0602934	−	0.104431i
$509$	−15.9675	+	27.6564i	−0.707745	+	1.22585i	0.257947	+	0.966159i	$0.416954\pi$
$509$	−15.9675	+	27.6564i	−0.707745	+	1.22585i	−0.965692	+	0.259691i	$0.916379\pi$
$510$		0			0
$511$	6.59044	+	11.4150i	0.291544	+	0.504969i
$512$	25.4137			1.12314
$513$		0			0
$514$	−8.49711			−0.374791
$515$	−3.96888	−	6.87431i	−0.174890	−	0.302918i
$516$		0			0
$517$	−15.7769	+	27.3265i	−0.693869	+	1.20182i
$518$	−10.3623	+	17.9480i	−0.455294	+	0.788591i
$519$		0			0
$520$	−1.50747	−	2.61102i	−0.0661070	−	0.114501i
$521$	20.4121			0.894270			0.447135	−	0.894467i	$-0.352444\pi$
$521$	20.4121			0.894270			0.447135	+	0.894467i	$0.352444\pi$
$522$		0			0
$523$	16.5405			0.723264			0.361632	−	0.932321i	$-0.382220\pi$
$523$	16.5405			0.723264			0.361632	+	0.932321i	$0.382220\pi$
$524$	0.590193	+	1.02224i	0.0257827	+	0.0446570i
$525$		0			0
$526$	11.3817	−	19.7138i	0.496267	−	0.859560i
$527$	−25.6862	+	44.4898i	−1.11891	+	1.93800i
$528$		0			0
$529$	11.4362	+	19.8081i	0.497226	+	0.861221i
$530$	4.20729			0.182753
$531$		0			0
$532$	5.07569			0.220059
$533$	−3.03414	−	5.25529i	−0.131423	−	0.227632i
$534$		0			0
$535$	2.22547	−	3.85464i	0.0962157	−	0.166650i
$536$	−2.69544	+	4.66863i	−0.116425	+	0.201654i
$537$		0			0
$538$	3.92819	+	6.80382i	0.169356	+	0.293334i
$539$	4.84142			0.208535
$540$		0			0
$541$	13.3791			0.575211			0.287606	−	0.957749i	$-0.407141\pi$
$541$	13.3791			0.575211			0.287606	+	0.957749i	$0.407141\pi$
$542$	−12.8294	−	22.2211i	−0.551069	−	0.954479i
$543$		0			0
$544$	6.61866	−	11.4639i	0.283773	−	0.491509i
$545$	4.29438	−	7.43809i	0.183951	−	0.318613i
$546$		0			0
$547$	−13.9133	−	24.0986i	−0.594892	−	1.03038i	−0.993562	−	0.113288i	$-0.963862\pi$
$547$	−13.9133	−	24.0986i	−0.594892	−	1.03038i	0.398671	−	0.917094i	$-0.369472\pi$
$548$	1.95876			0.0836741
$549$		0			0
$550$	−6.63698			−0.283002
$551$	−12.8108	−	22.1889i	−0.545758	−	0.945281i
$552$		0			0
$553$	12.4983	−	21.6477i	0.531482	−	0.920554i
$554$	20.8460	−	36.1064i	0.885663	−	1.53401i
$555$		0			0
$556$	−1.28995	−	2.23427i	−0.0547063	−	0.0947540i
$557$	6.61513			0.280292			0.140146	−	0.990131i	$-0.455243\pi$
$557$	6.61513			0.280292			0.140146	+	0.990131i	$0.455243\pi$
$558$		0			0
$559$	−9.78238			−0.413751
$560$	−4.51401	−	7.81849i	−0.190752	−	0.330392i
$561$		0			0
$562$	20.6210	−	35.7166i	0.869844	−	1.50661i
$563$	8.40891	−	14.5647i	0.354393	−	0.613827i	−0.632621	−	0.774462i	$-0.718021\pi$
$563$	8.40891	−	14.5647i	0.354393	−	0.613827i	0.987014	+	0.160634i	$0.0513540\pi$
$564$		0			0
$565$	9.61749	+	16.6580i	0.404611	+	0.700807i
$566$	37.3284			1.56903
$567$		0			0
$568$	14.8204			0.621848
$569$	−14.8185	−	25.6664i	−0.621223	−	1.07599i	−0.989258	−	0.146178i	$-0.953303\pi$
$569$	−14.8185	−	25.6664i	−0.621223	−	1.07599i	0.368035	−	0.929812i	$-0.380031\pi$
$570$		0			0
$571$	−12.4637	+	21.5878i	−0.521590	+	0.903421i	0.478094	+	0.878308i	$0.341328\pi$
$571$	−12.4637	+	21.5878i	−0.521590	+	0.903421i	−0.999685	+	0.0251123i	$0.992006\pi$
$572$	0.876182	−	1.51759i	0.0366350	−	0.0634537i
$573$		0			0
$574$	−11.0147	−	19.0781i	−0.459746	−	0.796303i
$575$	−0.357215			−0.0148969
$576$		0			0
$577$	25.6134			1.06630			0.533151	−	0.846020i	$-0.321008\pi$
$577$	25.6134			1.06630			0.533151	+	0.846020i	$0.321008\pi$
$578$	20.2488	+	35.0720i	0.842239	+	1.45880i
$579$		0			0
$580$	0.822924	−	1.42535i	0.0341701	−	0.0591843i
$581$	−21.0744	+	36.5019i	−0.874312	+	1.51435i
$582$		0			0
$583$	8.41158	+	14.5693i	0.348372	+	0.603398i
$584$	14.1032			0.583596
$585$		0			0
$586$	5.22834			0.215981
$587$	13.1566	+	22.7878i	0.543029	+	0.940554i	0.998728	+	0.0504202i	$0.0160561\pi$
$587$	13.1566	+	22.7878i	0.543029	+	0.940554i	−0.455699	+	0.890134i	$0.650611\pi$
$588$		0			0
$589$	−19.5447	+	33.8524i	−0.805324	+	1.39486i
$590$	−0.845734	+	1.46485i	−0.0348183	+	0.0603071i
$591$		0			0
$592$	9.14548	+	15.8404i	0.375877	+	0.651038i
$593$	28.9470			1.18871			0.594356	−	0.804202i	$-0.297407\pi$
$593$	28.9470			1.18871			0.594356	+	0.804202i	$0.297407\pi$
$594$		0			0
$595$	−19.6101			−0.803934
$596$	−1.02373	−	1.77316i	−0.0419337	−	0.0726313i
$597$		0			0
$598$	−0.230109	+	0.398560i	−0.00940984	+	0.0162983i
$599$	−17.8935	+	30.9925i	−0.731110	+	1.26632i	0.225299	+	0.974290i	$0.427664\pi$
$599$	−17.8935	+	30.9925i	−0.731110	+	1.26632i	−0.956409	+	0.292031i	$0.905669\pi$
$600$		0			0
$601$	−23.1849	−	40.1574i	−0.945731	−	1.63805i	−0.754281	−	0.656552i	$-0.772014\pi$
$601$	−23.1849	−	40.1574i	−0.945731	−	1.63805i	−0.191450	−	0.981502i	$-0.561319\pi$
$602$	−35.5126			−1.44738
$603$		0			0
$604$	−3.34445			−0.136084
$605$	−7.76921	−	13.4567i	−0.315863	−	0.547091i
$606$		0			0
$607$	−1.97001	+	3.41216i	−0.0799603	+	0.138495i	−0.903233	−	0.429151i	$-0.858813\pi$
$607$	−1.97001	+	3.41216i	−0.0799603	+	0.138495i	0.823272	+	0.567647i	$0.192146\pi$
$608$	5.03615	−	8.72287i	0.204243	−	0.353759i
$609$		0			0
$610$	−5.91198	−	10.2398i	−0.239369	−	0.414599i
$611$	6.12513			0.247796
$612$		0			0
$613$	−36.4623			−1.47270			−0.736349	−	0.676602i	$-0.763452\pi$
$613$	−36.4623			−1.47270			−0.736349	+	0.676602i	$0.763452\pi$
$614$	6.59360	+	11.4205i	0.266096	+	0.460892i
$615$		0			0
$616$	21.8822	−	37.9011i	0.881659	−	1.52708i
$617$	6.07505	−	10.5223i	0.244572	−	0.423612i	−0.717439	−	0.696621i	$-0.754686\pi$
$617$	6.07505	−	10.5223i	0.244572	−	0.423612i	0.962011	+	0.273010i	$0.0880191\pi$
$618$		0			0
$619$	−4.37235	−	7.57314i	−0.175740	−	0.304390i	0.764677	−	0.644413i	$-0.222898\pi$
$619$	−4.37235	−	7.57314i	−0.175740	−	0.304390i	−0.940417	+	0.340023i	$0.889565\pi$
$620$	−2.51097			−0.100843
$621$		0			0
$622$	28.6343			1.14813
$623$	−9.08673	−	15.7387i	−0.364052	−	0.630557i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−6.20471	+	10.7469i	−0.247990	+	0.429531i
$627$		0			0
$628$	−0.426711	−	0.739085i	−0.0170276	−	0.0294927i
$629$	39.7304			1.58415
$630$		0			0
$631$	8.53562			0.339798			0.169899	−	0.985462i	$-0.445656\pi$
$631$	8.53562			0.339798			0.169899	+	0.985462i	$0.445656\pi$
$632$	−13.3729	−	23.1625i	−0.531945	−	0.921356i
$633$		0			0
$634$	−19.7791	+	34.2584i	−0.785529	+	1.36058i
$635$	−3.99498	+	6.91951i	−0.158536	+	0.274592i
$636$		0			0
$637$	−0.469900	−	0.813891i	−0.0186181	−	0.0322475i
$638$	−32.1124			−1.27134
$639$		0			0
$640$	−7.60862			−0.300757
$641$	9.66780	+	16.7451i	0.381855	+	0.661393i	0.991327	−	0.131415i	$-0.0419520\pi$
$641$	9.66780	+	16.7451i	0.381855	+	0.661393i	−0.609472	+	0.792807i	$0.708619\pi$
$642$		0			0
$643$	19.7501	−	34.2082i	0.778868	−	1.34904i	−0.153726	−	0.988113i	$-0.549127\pi$
$643$	19.7501	−	34.2082i	0.778868	−	1.34904i	0.932594	−	0.360926i	$-0.117539\pi$
$644$	0.171195	−	0.296519i	0.00674604	−	0.0116845i
$645$		0			0
$646$	23.7400	+	41.1188i	0.934036	+	1.61780i
$647$	−35.0901			−1.37954			−0.689768	−	0.724031i	$-0.742287\pi$
$647$	−35.0901			−1.37954			−0.689768	+	0.724031i	$0.742287\pi$
$648$		0			0
$649$	−6.76345			−0.265489
$650$	0.644173	+	1.11574i	0.0252666	+	0.0437630i
$651$		0			0
$652$	−3.37160	+	5.83979i	−0.132042	+	0.228704i
$653$	−5.16552	+	8.94694i	−0.202142	+	0.350121i	−0.949218	−	0.314618i	$-0.898124\pi$
$653$	−5.16552	+	8.94694i	−0.202142	+	0.350121i	0.747076	+	0.664738i	$0.231457\pi$
$654$		0			0
$655$	−1.73503	−	3.00516i	−0.0677933	−	0.117421i
$656$	−19.4426			−0.759105
$657$		0			0
$658$	22.2358			0.866842
$659$	16.6368	+	28.8158i	0.648078	+	1.12250i	0.983581	+	0.180465i	$0.0577602\pi$
$659$	16.6368	+	28.8158i	0.648078	+	1.12250i	−0.335504	+	0.942039i	$0.608906\pi$
$660$		0			0
$661$	10.6134	−	18.3829i	0.412812	−	0.715011i	−0.582384	−	0.812914i	$-0.697880\pi$
$661$	10.6134	−	18.3829i	0.412812	−	0.715011i	0.995196	+	0.0979025i	$0.0312133\pi$
$662$	−2.26524	+	3.92351i	−0.0880411	+	0.152492i
$663$		0			0
$664$	22.5491	+	39.0561i	0.875074	+	1.51567i
$665$	−14.9213			−0.578625
$666$		0			0
$667$	−1.72836			−0.0669222
$668$	4.04404	+	7.00449i	0.156469	+	0.271012i
$669$		0			0
$670$	1.15182	−	1.99500i	0.0444985	−	0.0770737i
$671$	23.6395	−	40.9447i	0.912591	−	1.58065i
$672$		0			0
$673$	0.618753	+	1.07171i	0.0238512	+	0.0413115i	0.877705	−	0.479202i	$-0.159074\pi$
$673$	0.618753	+	1.07171i	0.0238512	+	0.0413115i	−0.853853	+	0.520513i	$0.825741\pi$
$674$	25.2851			0.973947
$675$		0			0
$676$	−0.340163			−0.0130832
$677$	11.3996	+	19.7446i	0.438121	+	0.758848i	0.997545	−	0.0700341i	$-0.0223108\pi$
$677$	11.3996	+	19.7446i	0.438121	+	0.758848i	−0.559424	+	0.828882i	$0.688977\pi$
$678$		0			0
$679$	15.8584	−	27.4675i	0.608589	−	1.05411i
$680$	−10.4911	+	18.1712i	−0.402317	+	0.696834i
$681$		0			0
$682$	24.4960	+	42.4283i	0.938001	+	1.62467i
$683$	−2.63501			−0.100826			−0.0504130	−	0.998728i	$-0.516054\pi$
$683$	−2.63501			−0.100826			−0.0504130	+	0.998728i	$0.516054\pi$
$684$		0			0
$685$	−5.75830			−0.220013
$686$	11.0000	+	19.0526i	0.419984	+	0.727433i
$687$		0			0
$688$	−15.6712	+	27.1433i	−0.597459	+	1.03483i
$689$	1.63283	−	2.82814i	0.0622058	−	0.107744i
$690$		0			0
$691$	11.8570	+	20.5370i	0.451063	+	0.781264i	0.998452	−	0.0556138i	$-0.0177116\pi$
$691$	11.8570	+	20.5370i	0.451063	+	0.781264i	−0.547389	+	0.836878i	$0.684378\pi$
$692$	−1.96813			−0.0748169
$693$		0			0
$694$	32.7138			1.24180
$695$	3.79217	+	6.56823i	0.143845	+	0.249147i
$696$		0			0
$697$	−21.1159	+	36.5739i	−0.799823	+	1.38533i
$698$	−7.85717	+	13.6090i	−0.297398	+	0.515109i
$699$		0			0
$700$	−0.479250	−	0.830085i	−0.0181139	−	0.0313743i
$701$	−36.6440			−1.38403			−0.692013	−	0.721885i	$-0.743276\pi$
$701$	−36.6440			−1.38403			−0.692013	+	0.721885i	$0.743276\pi$
$702$		0			0
$703$	30.2310			1.14018
$704$	−22.8173	−	39.5208i	−0.859961	−	1.48950i
$705$		0			0
$706$	11.5634	−	20.0284i	0.435194	−	0.753778i
$707$	−13.7485	+	23.8131i	−0.517065	+	0.895584i
$708$		0			0
$709$	−12.7783	−	22.1327i	−0.479900	−	0.831211i	0.519834	−	0.854267i	$-0.325994\pi$
$709$	−12.7783	−	22.1327i	−0.479900	−	0.831211i	−0.999734	+	0.0230560i	$0.992660\pi$
$710$	−6.33305			−0.237675
$711$		0			0
$712$	−19.4452			−0.728738
$713$	1.31842	+	2.28358i	0.0493754	+	0.0855207i
$714$		0			0
$715$	−2.57577	+	4.46137i	−0.0963284	+	0.166846i
$716$	3.43535	−	5.95019i	0.128385	−	0.222369i
$717$		0			0
$718$	−12.9901	−	22.4996i	−0.484787	−	0.839676i
$719$	−3.51637			−0.131139			−0.0655693	−	0.997848i	$-0.520886\pi$
$719$	−3.51637			−0.131139			−0.0655693	+	0.997848i	$0.520886\pi$
$720$		0			0
$721$	−22.3668			−0.832981
$722$	5.82450	+	10.0883i	0.216765	+	0.375449i
$723$		0			0
$724$	−1.71444	+	2.96950i	−0.0637167	+	0.110361i
$725$	−2.41921	+	4.19019i	−0.0898471	+	0.155620i
$726$		0			0
$727$	9.54123	+	16.5259i	0.353865	+	0.612912i	0.986923	−	0.161192i	$-0.0515340\pi$
$727$	9.54123	+	16.5259i	0.353865	+	0.612912i	−0.633058	+	0.774104i	$0.718201\pi$
$728$	−8.49540			−0.314860
$729$		0			0
$730$	−6.02660			−0.223054
$731$	34.0399	+	58.9589i	1.25901	+	2.18067i
$732$		0			0
$733$	8.11234	−	14.0510i	0.299636	−	0.518985i	−0.676417	−	0.736519i	$-0.736468\pi$
$733$	8.11234	−	14.0510i	0.299636	−	0.518985i	0.976053	+	0.217534i	$0.0698014\pi$
$734$	19.2502	−	33.3423i	0.710536	−	1.23068i
$735$		0			0
$736$	−0.339724	−	0.588419i	−0.0125224	−	0.0216894i
$737$	9.21123			0.339300
$738$		0			0
$739$	17.3100			0.636760			0.318380	−	0.947963i	$-0.396861\pi$
$739$	17.3100			0.636760			0.318380	+	0.947963i	$0.396861\pi$
$740$	0.970970	+	1.68177i	0.0356936	+	0.0618231i
$741$		0			0
$742$	5.92758	−	10.2669i	0.217608	−	0.376909i
$743$	−22.3620	+	38.7321i	−0.820381	+	1.42094i	0.0850183	+	0.996379i	$0.472905\pi$
$743$	−22.3620	+	38.7321i	−0.820381	+	1.42094i	−0.905399	+	0.424562i	$0.860428\pi$
$744$		0			0
$745$	3.00953	+	5.21267i	0.110261	+	0.190977i
$746$	4.71039			0.172460
$747$		0			0
$748$	−12.1955			−0.445911
$749$	−6.27086	−	10.8615i	−0.229132	−	0.396869i
$750$		0			0
$751$	−14.4998	+	25.1143i	−0.529104	+	0.916435i	0.470320	+	0.882496i	$0.344139\pi$
$751$	−14.4998	+	25.1143i	−0.529104	+	0.916435i	−0.999424	+	0.0339392i	$0.989195\pi$
$752$	9.81235	−	16.9955i	0.357820	−	0.619762i
$753$		0			0
$754$	3.11678	+	5.39842i	0.113506	+	0.196599i
$755$	9.83190			0.357819
$756$		0			0
$757$	32.0762			1.16583			0.582914	−	0.812534i	$-0.301912\pi$
$757$	32.0762			1.16583			0.582914	+	0.812534i	$0.301912\pi$
$758$	15.5010	+	26.8486i	0.563023	+	0.975184i
$759$		0			0
$760$	−7.98274	+	13.8265i	−0.289564	+	0.501540i
$761$	−12.4399	+	21.5465i	−0.450944	+	0.781059i	−0.998445	−	0.0557467i	$-0.982246\pi$
$761$	−12.4399	+	21.5465i	−0.450944	+	0.781059i	0.547501	+	0.836805i	$0.315579\pi$
$762$		0			0
$763$	−12.1006	−	20.9588i	−0.438070	−	0.758759i
$764$	−6.21064			−0.224693
$765$		0			0
$766$	−38.2394			−1.38165
$767$	0.656449	+	1.13700i	0.0237030	+	0.0410548i
$768$		0			0
$769$	20.1005	−	34.8150i	0.724842	−	1.25546i	−0.234198	−	0.972189i	$-0.575246\pi$
$769$	20.1005	−	34.8150i	0.724842	−	1.25546i	0.959039	−	0.283273i	$-0.0914204\pi$
$770$	−9.35072	+	16.1959i	−0.336977	+	0.583660i
$771$		0			0
$772$	−0.368788	−	0.638759i	−0.0132730	−	0.0229894i
$773$	2.03131			0.0730612			0.0365306	−	0.999333i	$-0.488369\pi$
$773$	2.03131			0.0730612			0.0365306	+	0.999333i	$0.488369\pi$
$774$		0			0
$775$	7.38168			0.265158
$776$	−16.9681	−	29.3896i	−0.609119	−	1.05502i
$777$		0			0
$778$	−3.66346	+	6.34531i	−0.131342	+	0.227490i
$779$	−16.0672	+	27.8292i	−0.575666	+	0.997083i
$780$		0			0
$781$	−12.6616	−	21.9305i	−0.453066	−	0.784734i
$782$	3.20285			0.114534
$783$		0			0
$784$	−3.01109			−0.107539
$785$	1.25443	+	2.17274i	0.0447726	+	0.0775484i
$786$		0			0
$787$	−18.7372	+	32.4537i	−0.667908	+	1.15685i	0.310580	+	0.950547i	$0.399477\pi$
$787$	−18.7372	+	32.4537i	−0.667908	+	1.15685i	−0.978488	+	0.206303i	$0.933857\pi$
$788$	−2.54424	+	4.40675i	−0.0906347	+	0.156984i
$789$		0			0
$790$	5.71451	+	9.89783i	0.203313	+	0.352149i
$791$	54.1997			1.92712
$792$		0			0
$793$	−9.17762			−0.325907
$794$	−1.05696	−	1.83071i	−0.0375102	−	0.0649696i
$795$		0			0
$796$	0.818567	−	1.41780i	0.0290133	−	0.0502526i
$797$	−6.95827	+	12.0521i	−0.246475	+	0.426907i	−0.962545	−	0.271121i	$-0.912606\pi$
$797$	−6.95827	+	12.0521i	−0.246475	+	0.426907i	0.716070	+	0.698028i	$0.245939\pi$
$798$		0			0
$799$	−21.3137	−	36.9165i	−0.754026	−	1.30601i
$800$	−1.90207			−0.0672482
$801$		0			0
$802$	−17.1410			−0.605270
$803$	−12.0489	−	20.8693i	−0.425196	−	0.736461i
$804$		0			0
$805$	−0.503275	+	0.871697i	−0.0177381	+	0.0307233i
$806$	4.75508	−	8.23604i	0.167491	−	0.290102i
$807$		0			0
$808$	14.7106	+	25.4794i	0.517516	+	0.896364i
$809$	−7.77442			−0.273334			−0.136667	−	0.990617i	$-0.543639\pi$
$809$	−7.77442			−0.273334			−0.136667	+	0.990617i	$0.543639\pi$
$810$		0			0
$811$	−29.5307			−1.03696			−0.518482	−	0.855089i	$-0.673503\pi$
$811$	−29.5307			−1.03696			−0.518482	+	0.855089i	$0.673503\pi$
$812$	−2.31881	−	4.01629i	−0.0813742	−	0.140944i
$813$		0			0
$814$	18.9448	−	32.8133i	0.664013	−	1.15010i
$815$	9.91173	−	17.1676i	0.347193	−	0.601356i
$816$		0			0
$817$	25.9011	+	44.8620i	0.906164	+	1.56952i
$818$	−13.6034			−0.475630
$819$		0			0
$820$	−2.06421			−0.0720852
$821$	−9.69370	−	16.7900i	−0.338312	−	0.585974i	0.645803	−	0.763504i	$-0.276523\pi$
$821$	−9.69370	−	16.7900i	−0.338312	−	0.585974i	−0.984115	+	0.177530i	$0.943189\pi$
$822$		0			0
$823$	−19.9843	+	34.6138i	−0.696609	+	1.20656i	0.273027	+	0.962006i	$0.411975\pi$
$823$	−19.9843	+	34.6138i	−0.696609	+	1.20656i	−0.969635	+	0.244555i	$0.921358\pi$
$824$	−11.9659	+	20.7256i	−0.416853	+	0.722011i
$825$		0			0
$826$	2.38308	+	4.12761i	0.0829179	+	0.143618i
$827$	−39.8289			−1.38499			−0.692494	−	0.721424i	$-0.743488\pi$
$827$	−39.8289			−1.38499			−0.692494	+	0.721424i	$0.743488\pi$
$828$		0			0
$829$	32.8078			1.13946			0.569731	−	0.821831i	$-0.307047\pi$
$829$	32.8078			1.13946			0.569731	+	0.821831i	$0.307047\pi$
$830$	−9.63569	−	16.6895i	−0.334460	−	0.579301i
$831$		0			0
$832$	−4.42922	+	7.67164i	−0.153556	+	0.265966i
$833$	−3.27024	+	5.66422i	−0.113307	+	0.196254i
$834$		0			0
$835$	−11.8886	−	20.5916i	−0.411420	−	0.712601i
$836$	−9.27956			−0.320940
$837$		0			0
$838$	26.4743			0.914541
$839$	24.7549	+	42.8767i	0.854633	+	1.48027i	0.876985	+	0.480517i	$0.159551\pi$
$839$	24.7549	+	42.8767i	0.854633	+	1.48027i	−0.0223528	+	0.999750i	$0.507116\pi$
$840$		0			0
$841$	2.79488	−	4.84087i	0.0963751	−	0.166927i
$842$	−23.3652	+	40.4697i	−0.805218	+	1.39468i
$843$		0			0
$844$	1.63380	+	2.82982i	0.0562376	+	0.0974064i
$845$	1.00000			0.0344010
$846$		0			0
$847$	−43.7836			−1.50442
$848$	−5.23152	−	9.06126i	−0.179651	−	0.311165i
$849$		0			0
$850$	4.48308	−	7.76493i	0.153769	−	0.266335i
$851$	1.01965	−	1.76608i	0.0349530	−	0.0605403i
$852$		0			0
$853$	9.43866	+	16.3482i	0.323174	+	0.559753i	0.981141	−	0.193293i	$-0.0619168\pi$
$853$	9.43866	+	16.3482i	0.323174	+	0.559753i	−0.657967	+	0.753046i	$0.728584\pi$
$854$	−33.3171			−1.14009
$855$		0			0
$856$	−13.4193			−0.458664
$857$	−19.0881	−	33.0616i	−0.652037	−	1.12936i	−0.982628	−	0.185587i	$-0.940581\pi$
$857$	−19.0881	−	33.0616i	−0.652037	−	1.12936i	0.330591	−	0.943774i	$-0.392752\pi$
$858$		0			0
$859$	−17.1791	+	29.7551i	−0.586144	+	1.01523i	0.408588	+	0.912719i	$0.366021\pi$
$859$	−17.1791	+	29.7551i	−0.586144	+	1.01523i	−0.994732	+	0.102512i	$0.967312\pi$
$860$	−1.66380	+	2.88179i	−0.0567352	+	0.0982682i
$861$		0			0
$862$	−9.94074	−	17.2179i	−0.338583	−	0.586443i
$863$	−38.0198			−1.29421			−0.647105	−	0.762401i	$-0.724020\pi$
$863$	−38.0198			−1.29421			−0.647105	+	0.762401i	$0.724020\pi$
$864$		0			0
$865$	5.78584			0.196724
$866$	−15.0404	−	26.0508i	−0.511095	−	0.885243i
$867$		0			0
$868$	−3.53767	+	6.12742i	−0.120076	+	0.207978i
$869$	−22.8499	+	39.5772i	−0.775129	+	1.34256i
$870$		0			0
$871$	−0.894026	−	1.54850i	−0.0302929	−	0.0524689i
$872$	−25.8946			−0.876902
$873$		0			0
$874$	2.43706			0.0824347
$875$	1.40888	+	2.44026i	0.0476289	+	0.0824957i
$876$		0			0
$877$	15.8916	−	27.5251i	0.536622	−	0.929456i	−0.462461	−	0.886640i	$-0.653034\pi$
$877$	15.8916	−	27.5251i	0.536622	−	0.929456i	0.999083	−	0.0428167i	$-0.0136331\pi$
$878$	8.01978	−	13.8907i	0.270654	−	0.468787i
$879$		0			0
$880$	8.25268	+	14.2941i	0.278198	+	0.481853i
$881$	9.08373			0.306039			0.153019	−	0.988223i	$-0.451100\pi$
$881$	9.08373			0.306039			0.153019	+	0.988223i	$0.451100\pi$
$882$		0			0
$883$	49.6414			1.67057			0.835283	−	0.549820i	$-0.185304\pi$
$883$	49.6414			1.67057			0.835283	+	0.549820i	$0.185304\pi$
$884$	1.18367	+	2.05018i	0.0398112	+	0.0689550i
$885$		0			0
$886$	4.67907	−	8.10438i	0.157196	−	0.272272i
$887$	14.9338	−	25.8661i	0.501429	−	0.868500i	−0.498570	−	0.866850i	$-0.666141\pi$
$887$	14.9338	−	25.8661i	0.501429	−	0.868500i	0.999999	−	0.00165060i	$-0.000525401\pi$
$888$		0			0
$889$	11.2569	+	19.4976i	0.377545	+	0.653927i
$890$	8.30932			0.278529
$891$		0			0
$892$	2.16036			0.0723342
$893$	−16.2177	−	28.0898i	−0.542704	−	0.939990i
$894$		0			0
$895$	−10.0991	+	17.4922i	−0.337576	+	0.584699i
$896$	−10.7196	+	18.5670i	−0.358118	+	0.620279i
$897$		0			0
$898$	9.49418	+	16.4444i	0.316825	+	0.548757i
$899$	35.7156			1.19118
$900$		0			0
$901$	−22.7271			−0.757150
$902$	20.1375	+	34.8793i	0.670507	+	1.16135i
$903$		0			0
$904$	28.9962	−	50.2229i	0.964399	−	1.67039i
$905$	5.04006	−	8.72964i	0.167537	−	0.290183i
$906$		0			0
$907$	9.22113	+	15.9715i	0.306183	+	0.530324i	0.977524	−	0.210824i	$-0.0676148\pi$
$907$	9.22113	+	15.9715i	0.306183	+	0.530324i	−0.671341	+	0.741148i	$0.734282\pi$
$908$	1.93867			0.0643371
$909$		0			0
$910$	3.63026			0.120342
$911$	−4.10456	−	7.10930i	−0.135990	−	0.235542i	0.789985	−	0.613126i	$-0.210088\pi$
$911$	−4.10456	−	7.10930i	−0.135990	−	0.235542i	−0.925975	+	0.377584i	$0.876755\pi$
$912$		0			0
$913$	38.5290	−	66.7341i	1.27512	−	2.20858i
$914$	4.76867	−	8.25957i	0.157733	−	0.273202i
$915$		0			0
$916$	−3.73253	−	6.46494i	−0.123326	−	0.213608i
$917$	−9.77782			−0.322892
$918$		0			0
$919$	−1.11177			−0.0366738			−0.0183369	−	0.999832i	$-0.505837\pi$
$919$	−1.11177			−0.0366738			−0.0183369	+	0.999832i	$0.505837\pi$
$920$	0.538492	+	0.932695i	0.0177535	+	0.0307500i
$921$		0			0
$922$	1.96093	−	3.39642i	0.0645796	−	0.111855i
$923$	−2.45782	+	4.25707i	−0.0809001	+	0.140123i
$924$		0			0
$925$	−2.85443	−	4.94401i	−0.0938530	−	0.162558i
$926$	−18.0122			−0.591916
$927$		0			0
$928$	−9.20299			−0.302103
$929$	5.88119	+	10.1865i	0.192956	+	0.334209i	0.946228	−	0.323499i	$-0.104859\pi$
$929$	5.88119	+	10.1865i	0.192956	+	0.334209i	−0.753273	+	0.657708i	$0.771526\pi$
$930$		0			0
$931$	−2.48833	+	4.30992i	−0.0815519	+	0.141252i
$932$	−4.38252	+	7.59074i	−0.143554	+	0.248643i
$933$		0			0
$934$	−19.7404	−	34.1914i	−0.645926	−	1.11878i
$935$	35.8519			1.17248
$936$		0			0
$937$	−50.7176			−1.65687			−0.828436	−	0.560084i	$-0.810769\pi$
$937$	−50.7176			−1.65687			−0.828436	+	0.560084i	$0.810769\pi$
$938$	−3.24555	−	5.62145i	−0.105971	−	0.183547i
$939$		0			0
$940$	1.04177	−	1.80440i	0.0339788	−	0.0588531i
$941$	13.3852	−	23.1839i	0.436345	−	0.755772i	−0.561059	−	0.827776i	$-0.689606\pi$
$941$	13.3852	−	23.1839i	0.436345	−	0.755772i	0.997404	+	0.0720035i	$0.0229393\pi$
$942$		0			0
$943$	1.08384	+	1.87727i	0.0352948	+	0.0611324i
$944$	4.20648			0.136909
$945$		0			0
$946$	64.9254			2.11091
$947$	−11.4159	−	19.7730i	−0.370968	−	0.642536i	0.618746	−	0.785591i	$-0.287641\pi$
$947$	−11.4159	−	19.7730i	−0.370968	−	0.642536i	−0.989715	+	0.143055i	$0.954307\pi$
$948$		0			0
$949$	−2.33889	+	4.05108i	−0.0759236	+	0.131503i
$950$	3.41119	−	5.90835i	0.110674	−	0.191692i
$951$		0			0
$952$	29.5616	+	51.2022i	0.958097	+	1.65947i
$953$	4.98857			0.161596			0.0807979	−	0.996731i	$-0.474253\pi$
$953$	4.98857			0.161596			0.0807979	+	0.996731i	$0.474253\pi$
$954$		0			0
$955$	18.2578			0.590810
$956$	1.01216	+	1.75310i	0.0327354	+	0.0566994i
$957$		0			0
$958$	1.90936	−	3.30710i	0.0616885	−	0.106848i
$959$	−8.11277	+	14.0517i	−0.261975	+	0.453754i
$960$		0			0
$961$	−11.7446	−	20.3422i	−0.378858	−	0.656201i
$962$	−7.35498			−0.237134
$963$		0			0
$964$	−7.92542			−0.255261
$965$	1.08415	+	1.87780i	0.0349000	+	0.0604486i
$966$		0			0
$967$	8.44142	−	14.6210i	0.271458	−	0.470179i	−0.697778	−	0.716314i	$-0.745828\pi$
$967$	8.44142	−	14.6210i	0.271458	−	0.470179i	0.969235	+	0.246136i	$0.0791610\pi$
$968$	−23.4237	+	40.5710i	−0.752866	+	1.30400i
$969$		0			0
$970$	7.25081	+	12.5588i	0.232810	+	0.403238i
$971$	12.3303			0.395699			0.197850	−	0.980232i	$-0.436604\pi$
$971$	12.3303			0.395699			0.197850	+	0.980232i	$0.436604\pi$
$972$		0			0
$973$	21.3709			0.685119
$974$	−11.2950	−	19.5635i	−0.361915	−	0.626856i
$975$		0			0
$976$	−14.7024	+	25.4653i	−0.470612	+	0.815123i
$977$	30.0983	−	52.1317i	0.962929	−	1.66784i	0.247850	−	0.968798i	$-0.420276\pi$
$977$	30.0983	−	52.1317i	0.962929	−	1.66784i	0.715079	−	0.699044i	$-0.246391\pi$
$978$		0			0
$979$	16.6127	+	28.7740i	0.530944	+	0.919622i
$980$	−0.319685			−0.0102120
$981$		0			0
$982$	−27.2026			−0.868070
$983$	−1.13564	−	1.96698i	−0.0362212	−	0.0627370i	0.847346	−	0.531040i	$-0.178199\pi$
$983$	−1.13564	−	1.96698i	−0.0362212	−	0.0627370i	−0.883568	+	0.468303i	$0.844865\pi$
$984$		0			0
$985$	7.47946	−	12.9548i	0.238316	−	0.412775i
$986$	21.6910	−	37.5699i	0.690783	−	1.19647i
$987$		0			0
$988$	0.900658	+	1.55999i	0.0286538	+	0.0496298i
$989$	3.49442			0.111116
$990$		0			0
$991$	55.9580			1.77756			0.888782	−	0.458331i	$-0.151552\pi$
$991$	55.9580			1.77756			0.888782	+	0.458331i	$0.151552\pi$
$992$	7.02022	+	12.1594i	0.222892	+	0.386061i
$993$		0			0
$994$	−8.92252	+	15.4543i	−0.283005	+	0.490179i
$995$	−2.40640	+	4.16800i	−0.0762879	+	0.132135i
$996$		0			0
$997$	−1.41267	−	2.44682i	−0.0447397	−	0.0774915i	0.842788	−	0.538245i	$-0.180913\pi$
$997$	−1.41267	−	2.44682i	−0.0447397	−	0.0774915i	−0.887528	+	0.460754i	$0.847579\pi$
$998$	−42.6501			−1.35007
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1755.2.i.h.1171.11		30
3.2	odd	2		585.2.i.h.391.5	yes	30
9.2	odd	6		585.2.i.h.196.5	✓	30
9.4	even	3		5265.2.a.bl.1.5		15
9.5	odd	6		5265.2.a.bk.1.11		15
9.7	even	3	inner	1755.2.i.h.586.11		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.h.196.5	✓	30	9.2	odd	6
585.2.i.h.391.5	yes	30	3.2	odd	2
1755.2.i.h.586.11		30	9.7	even	3	inner
1755.2.i.h.1171.11		30	1.1	even	1	trivial
5265.2.a.bk.1.11		15	9.5	odd	6
5265.2.a.bl.1.5		15	9.4	even	3

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:	\( N \)	\(=\)	\( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1755.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.644173 + 1.11574i) q^{2} +(0.170081 - 0.294590i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.40888 + 2.44026i) q^{7} +3.01494 q^{8} +O(q^{10})\)	\(q+(0.644173 + 1.11574i) q^{2} +(0.170081 - 0.294590i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.40888 + 2.44026i) q^{7} +3.01494 q^{8} -1.28835 q^{10} +(-2.57577 - 4.46137i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(-1.81513 + 3.14390i) q^{14} +(1.60198 + 2.77471i) q^{16} +6.95944 q^{17} +5.29545 q^{19} +(0.170081 + 0.294590i) q^{20} +(3.31849 - 5.74779i) q^{22} +(0.178608 - 0.309358i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.28835 q^{26} +0.958499 q^{28} +(-2.41921 - 4.19019i) q^{29} +(-3.69084 + 6.39272i) q^{31} +(0.951033 - 1.64724i) q^{32} +(4.48308 + 7.76493i) q^{34} -2.81777 q^{35} +5.70885 q^{37} +(3.41119 + 5.90835i) q^{38} +(-1.50747 + 2.61102i) q^{40} +(-3.03414 + 5.25529i) q^{41} +(4.89119 + 8.47179i) q^{43} -1.75236 q^{44} +0.460217 q^{46} +(-3.06257 - 5.30452i) q^{47} +(-0.469900 + 0.813891i) q^{49} +(0.644173 - 1.11574i) q^{50} +(0.170081 + 0.294590i) q^{52} -3.26565 q^{53} +5.15154 q^{55} +(4.24770 + 7.35723i) q^{56} +(3.11678 - 5.39842i) q^{58} +(0.656449 - 1.13700i) q^{59} +(4.58881 + 7.94805i) q^{61} -9.51016 q^{62} +8.85845 q^{64} +(-0.500000 - 0.866025i) q^{65} +(-0.894026 + 1.54850i) q^{67} +(1.18367 - 2.05018i) q^{68} +(-1.81513 - 3.14390i) q^{70} +4.91564 q^{71} +4.67778 q^{73} +(3.67749 + 6.36960i) q^{74} +(0.900658 - 1.55999i) q^{76} +(7.25792 - 12.5711i) q^{77} +(-4.43554 - 7.68258i) q^{79} -3.20396 q^{80} -7.81806 q^{82} +(7.47911 + 12.9542i) q^{83} +(-3.47972 + 6.02705i) q^{85} +(-6.30155 + 10.9146i) q^{86} +(-7.76580 - 13.4508i) q^{88} -6.44960 q^{89} -2.81777 q^{91} +(-0.0607557 - 0.105232i) q^{92} +(3.94565 - 6.83406i) q^{94} +(-2.64773 + 4.58600i) q^{95} +(-5.62800 - 9.74798i) q^{97} -1.21079 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - q^{2} - 21 q^{4} - 15 q^{5} - 10 q^{7}+O(q^{10}) \) 30 * q - q^2 - 21 * q^4 - 15 * q^5 - 10 * q^7	\( 30 q - q^{2} - 21 q^{4} - 15 q^{5} - 10 q^{7} + 2 q^{10} - 9 q^{11} - 15 q^{13} - 3 q^{14} - 33 q^{16} - 6 q^{17} + 30 q^{19} - 21 q^{20} - 10 q^{22} + 6 q^{23} - 15 q^{25} + 2 q^{26} + 70 q^{28} - 8 q^{29} - 22 q^{31} - 21 q^{32} - 9 q^{34} + 20 q^{35} + 8 q^{37} + 14 q^{38} - 13 q^{41} - 24 q^{43} - 10 q^{44} - 6 q^{46} + q^{47} - 37 q^{49} - q^{50} - 21 q^{52} - 14 q^{53} + 18 q^{55} - 17 q^{56} - 22 q^{58} - 19 q^{59} - 16 q^{61} - 26 q^{62} + 72 q^{64} - 15 q^{65} - 11 q^{67} + 28 q^{68} - 3 q^{70} + 56 q^{71} + 52 q^{73} - 8 q^{74} - 18 q^{76} + 24 q^{77} - 44 q^{79} + 66 q^{80} + 70 q^{82} + 3 q^{83} + 3 q^{85} - 40 q^{86} - 37 q^{88} + 8 q^{89} + 20 q^{91} + 74 q^{92} - 2 q^{94} - 15 q^{95} - 33 q^{97} - 6 q^{98}+O(q^{100}) \) 30 * q - q^2 - 21 * q^4 - 15 * q^5 - 10 * q^7 + 2 * q^10 - 9 * q^11 - 15 * q^13 - 3 * q^14 - 33 * q^16 - 6 * q^17 + 30 * q^19 - 21 * q^20 - 10 * q^22 + 6 * q^23 - 15 * q^25 + 2 * q^26 + 70 * q^28 - 8 * q^29 - 22 * q^31 - 21 * q^32 - 9 * q^34 + 20 * q^35 + 8 * q^37 + 14 * q^38 - 13 * q^41 - 24 * q^43 - 10 * q^44 - 6 * q^46 + q^47 - 37 * q^49 - q^50 - 21 * q^52 - 14 * q^53 + 18 * q^55 - 17 * q^56 - 22 * q^58 - 19 * q^59 - 16 * q^61 - 26 * q^62 + 72 * q^64 - 15 * q^65 - 11 * q^67 + 28 * q^68 - 3 * q^70 + 56 * q^71 + 52 * q^73 - 8 * q^74 - 18 * q^76 + 24 * q^77 - 44 * q^79 + 66 * q^80 + 70 * q^82 + 3 * q^83 + 3 * q^85 - 40 * q^86 - 37 * q^88 + 8 * q^89 + 20 * q^91 + 74 * q^92 - 2 * q^94 - 15 * q^95 - 33 * q^97 - 6 * q^98

Introduction

L-functions

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