LMFDB - Embedded newform 1155.2.i.d.76.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(76,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))

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

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

chi := DirichletCharacter("1155.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.i (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:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.14
Character	$\chi$	$=$	1155.76
Dual form			1155.2.i.d.76.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.54704i q^{2} +1.00000i q^{3} -0.393347 q^{4} +1.00000i q^{5} -1.54704 q^{6} +(-2.51711 + 0.814965i) q^{7} +2.48556i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.54704i q^{2} +1.00000i q^{3} -0.393347 q^{4} +1.00000i q^{5} -1.54704 q^{6} +(-2.51711 + 0.814965i) q^{7} +2.48556i q^{8} -1.00000 q^{9} -1.54704 q^{10} +(1.71987 - 2.83585i) q^{11} -0.393347i q^{12} -2.83183 q^{13} +(-1.26079 - 3.89408i) q^{14} -1.00000 q^{15} -4.63197 q^{16} -1.11146 q^{17} -1.54704i q^{18} -2.57562 q^{19} -0.393347i q^{20} +(-0.814965 - 2.51711i) q^{21} +(4.38719 + 2.66072i) q^{22} -4.41867 q^{23} -2.48556 q^{24} -1.00000 q^{25} -4.38097i q^{26} -1.00000i q^{27} +(0.990098 - 0.320564i) q^{28} -2.50888i q^{29} -1.54704i q^{30} +4.63764i q^{31} -2.19474i q^{32} +(2.83585 + 1.71987i) q^{33} -1.71947i q^{34} +(-0.814965 - 2.51711i) q^{35} +0.393347 q^{36} +3.30505 q^{37} -3.98459i q^{38} -2.83183i q^{39} -2.48556 q^{40} -4.46980 q^{41} +(3.89408 - 1.26079i) q^{42} +6.92036i q^{43} +(-0.676507 + 1.11547i) q^{44} -1.00000i q^{45} -6.83588i q^{46} +3.19790i q^{47} -4.63197i q^{48} +(5.67167 - 4.10271i) q^{49} -1.54704i q^{50} -1.11146i q^{51} +1.11389 q^{52} -3.06018 q^{53} +1.54704 q^{54} +(2.83585 + 1.71987i) q^{55} +(-2.02565 - 6.25643i) q^{56} -2.57562i q^{57} +3.88135 q^{58} -4.55256i q^{59} +0.393347 q^{60} -2.53745 q^{61} -7.17464 q^{62} +(2.51711 - 0.814965i) q^{63} -5.86858 q^{64} -2.83183i q^{65} +(-2.66072 + 4.38719i) q^{66} +14.7029 q^{67} +0.437189 q^{68} -4.41867i q^{69} +(3.89408 - 1.26079i) q^{70} -3.76969 q^{71} -2.48556i q^{72} -4.86845 q^{73} +5.11306i q^{74} -1.00000i q^{75} +1.01311 q^{76} +(-2.01798 + 8.53977i) q^{77} +4.38097 q^{78} +4.77430i q^{79} -4.63197i q^{80} +1.00000 q^{81} -6.91498i q^{82} -14.3185 q^{83} +(0.320564 + 0.990098i) q^{84} -1.11146i q^{85} -10.7061 q^{86} +2.50888 q^{87} +(7.04869 + 4.27485i) q^{88} +0.588850i q^{89} +1.54704 q^{90} +(7.12803 - 2.30784i) q^{91} +1.73807 q^{92} -4.63764 q^{93} -4.94729 q^{94} -2.57562i q^{95} +2.19474 q^{96} +7.73585i q^{97} +(6.34707 + 8.77432i) q^{98} +(-1.71987 + 2.83585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) $ 32 * q - 36 * q^4 - 32 * q^9	$ 32 q - 36 q^{4} - 32 q^{9} - 8 q^{11} - 28 q^{14} - 32 q^{15} + 44 q^{16} - 12 q^{22} + 4 q^{23} - 32 q^{25} + 36 q^{36} - 16 q^{37} + 8 q^{42} + 56 q^{44} + 16 q^{49} - 20 q^{53} + 52 q^{56} - 48 q^{58} + 36 q^{60} - 156 q^{64} - 72 q^{67} + 8 q^{70} + 48 q^{71} - 20 q^{77} - 8 q^{78} + 32 q^{81} + 56 q^{86} + 4 q^{88} - 80 q^{91} + 64 q^{92} + 32 q^{93} + 8 q^{99}+O(q^{100}) $ 32 * q - 36 * q^4 - 32 * q^9 - 8 * q^11 - 28 * q^14 - 32 * q^15 + 44 * q^16 - 12 * q^22 + 4 * q^23 - 32 * q^25 + 36 * q^36 - 16 * q^37 + 8 * q^42 + 56 * q^44 + 16 * q^49 - 20 * q^53 + 52 * q^56 - 48 * q^58 + 36 * q^60 - 156 * q^64 - 72 * q^67 + 8 * q^70 + 48 * q^71 - 20 * q^77 - 8 * q^78 + 32 * q^81 + 56 * q^86 + 4 * q^88 - 80 * q^91 + 64 * q^92 + 32 * q^93 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.54704i			1.09393i	0.837157	+	0.546963i	$0.184216\pi$
$2$			1.54704i			1.09393i	−0.837157	+	0.546963i	$0.815784\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.393347			−0.196674
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−1.54704			−0.631578
$7$	−2.51711	+	0.814965i	−0.951377	+	0.308028i
$7$	−2.51711	+	0.814965i	−0.951377	+	0.308028i
$8$			2.48556i			0.878779i
$9$	−1.00000			−0.333333
$10$	−1.54704			−0.489218
$11$	1.71987	−	2.83585i	0.518561	−	0.855041i
$11$	1.71987	−	2.83585i	0.518561	−	0.855041i
$12$		−	0.393347i		−	0.113550i
$13$	−2.83183			−0.785409			−0.392705	−	0.919665i	$-0.628460\pi$
$13$	−2.83183			−0.785409			−0.392705	+	0.919665i	$0.628460\pi$
$14$	−1.26079	−	3.89408i	−0.336959	−	1.04074i
$15$	−1.00000			−0.258199
$16$	−4.63197			−1.15799
$17$	−1.11146			−0.269568			−0.134784	−	0.990875i	$-0.543034\pi$
$17$	−1.11146			−0.269568			−0.134784	+	0.990875i	$0.543034\pi$
$18$		−	1.54704i		−	0.364642i
$19$	−2.57562			−0.590887			−0.295444	−	0.955360i	$-0.595467\pi$
$19$	−2.57562			−0.590887			−0.295444	+	0.955360i	$0.595467\pi$
$20$		−	0.393347i		−	0.0879551i
$21$	−0.814965	−	2.51711i	−0.177840	−	0.549278i
$22$	4.38719	+	2.66072i	0.935351	+	0.567267i
$23$	−4.41867			−0.921356			−0.460678	−	0.887567i	$-0.652394\pi$
$23$	−4.41867			−0.921356			−0.460678	+	0.887567i	$0.652394\pi$
$24$	−2.48556			−0.507364
$25$	−1.00000			−0.200000
$26$		−	4.38097i		−	0.859179i
$27$		−	1.00000i		−	0.192450i
$28$	0.990098	−	0.320564i	0.187111	−	0.0605809i
$29$		−	2.50888i		−	0.465888i	−0.972490	−	0.232944i	$-0.925164\pi$
$29$		−	2.50888i		−	0.465888i	0.972490	−	0.232944i	$-0.0748358\pi$
$30$		−	1.54704i		−	0.282450i
$31$			4.63764i			0.832945i	0.909148	+	0.416472i	$0.136734\pi$
$31$			4.63764i			0.832945i	−0.909148	+	0.416472i	$0.863266\pi$
$32$		−	2.19474i		−	0.387979i
$33$	2.83585	+	1.71987i	0.493658	+	0.299391i
$34$		−	1.71947i		−	0.294887i
$35$	−0.814965	−	2.51711i	−0.137754	−	0.425469i
$36$	0.393347			0.0655579
$37$	3.30505			0.543347			0.271674	−	0.962389i	$-0.412423\pi$
$37$	3.30505			0.543347			0.271674	+	0.962389i	$0.412423\pi$
$38$		−	3.98459i		−	0.646387i
$39$		−	2.83183i		−	0.453456i
$40$	−2.48556			−0.393002
$41$	−4.46980			−0.698065			−0.349032	−	0.937111i	$-0.613490\pi$
$41$	−4.46980			−0.698065			−0.349032	+	0.937111i	$0.613490\pi$
$42$	3.89408	−	1.26079i	0.600869	−	0.194544i
$43$			6.92036i			1.05535i	0.849448	+	0.527673i	$0.176935\pi$
$43$			6.92036i			1.05535i	−0.849448	+	0.527673i	$0.823065\pi$
$44$	−0.676507	+	1.11547i	−0.101987	+	0.168164i
$45$		−	1.00000i		−	0.149071i
$46$		−	6.83588i		−	1.00789i
$47$			3.19790i			0.466462i	0.972421	+	0.233231i	$0.0749298\pi$
$47$			3.19790i			0.466462i	−0.972421	+	0.233231i	$0.925070\pi$
$48$		−	4.63197i		−	0.668568i
$49$	5.67167	−	4.10271i	0.810238	−	0.586101i
$50$		−	1.54704i		−	0.218785i
$51$		−	1.11146i		−	0.155635i
$52$	1.11389			0.154469
$53$	−3.06018			−0.420348			−0.210174	−	0.977664i	$-0.567403\pi$
$53$	−3.06018			−0.420348			−0.210174	+	0.977664i	$0.567403\pi$
$54$	1.54704			0.210526
$55$	2.83585	+	1.71987i	0.382386	+	0.231907i
$56$	−2.02565	−	6.25643i	−0.270688	−	0.836051i
$57$		−	2.57562i		−	0.341149i
$58$	3.88135			0.509646
$59$		−	4.55256i		−	0.592693i	−0.955080	−	0.296347i	$-0.904232\pi$
$59$		−	4.55256i		−	0.592693i	0.955080	−	0.296347i	$-0.0957683\pi$
$60$	0.393347			0.0507809
$61$	−2.53745			−0.324887			−0.162443	−	0.986718i	$-0.551937\pi$
$61$	−2.53745			−0.324887			−0.162443	+	0.986718i	$0.551937\pi$
$62$	−7.17464			−0.911180
$63$	2.51711	−	0.814965i	0.317126	−	0.102676i
$64$	−5.86858			−0.733573
$65$		−	2.83183i		−	0.351246i
$66$	−2.66072	+	4.38719i	−0.327512	+	0.540025i
$67$	14.7029			1.79624			0.898122	−	0.439746i	$-0.144932\pi$
$67$	14.7029			1.79624			0.898122	+	0.439746i	$0.144932\pi$
$68$	0.437189			0.0530169
$69$		−	4.41867i		−	0.531945i
$70$	3.89408	−	1.26079i	0.465431	−	0.150693i
$71$	−3.76969			−0.447380			−0.223690	−	0.974660i	$-0.571810\pi$
$71$	−3.76969			−0.447380			−0.223690	+	0.974660i	$0.571810\pi$
$72$		−	2.48556i		−	0.292926i
$73$	−4.86845			−0.569809			−0.284904	−	0.958556i	$-0.591962\pi$
$73$	−4.86845			−0.569809			−0.284904	+	0.958556i	$0.591962\pi$
$74$			5.11306i			0.594381i
$75$		−	1.00000i		−	0.115470i
$76$	1.01311			0.116212
$77$	−2.01798	+	8.53977i	−0.229970	+	0.973198i
$78$	4.38097			0.496047
$79$			4.77430i			0.537151i	0.963259	+	0.268575i	$0.0865529\pi$
$79$			4.77430i			0.537151i	−0.963259	+	0.268575i	$0.913447\pi$
$80$		−	4.63197i		−	0.517870i
$81$	1.00000			0.111111
$82$		−	6.91498i		−	0.763631i
$83$	−14.3185			−1.57166			−0.785829	−	0.618444i	$-0.787763\pi$
$83$	−14.3185			−1.57166			−0.785829	+	0.618444i	$0.787763\pi$
$84$	0.320564	+	0.990098i	0.0349764	+	0.108029i
$85$		−	1.11146i		−	0.120554i
$86$	−10.7061			−1.15447
$87$	2.50888			0.268980
$88$	7.04869	+	4.27485i	0.751392	+	0.455700i
$89$			0.588850i			0.0624179i	0.999513	+	0.0312090i	$0.00993574\pi$
$89$			0.588850i			0.0624179i	−0.999513	+	0.0312090i	$0.990064\pi$
$90$	1.54704			0.163073
$91$	7.12803	−	2.30784i	0.747220	−	0.241928i
$92$	1.73807			0.181206
$93$	−4.63764			−0.480901
$94$	−4.94729			−0.510274
$95$		−	2.57562i		−	0.264253i
$96$	2.19474			0.224000
$97$			7.73585i			0.785457i	0.919655	+	0.392728i	$0.128469\pi$
$97$			7.73585i			0.785457i	−0.919655	+	0.392728i	$0.871531\pi$
$98$	6.34707	+	8.77432i	0.641151	+	0.886340i
$99$	−1.71987	+	2.83585i	−0.172854	+	0.285014i
$100$	0.393347			0.0393347
$101$	14.3930			1.43216			0.716078	−	0.698020i	$-0.245935\pi$
$101$	14.3930			1.43216			0.716078	+	0.698020i	$0.245935\pi$
$102$	1.71947			0.170253
$103$			0.277430i			0.0273360i	0.999907	+	0.0136680i	$0.00435079\pi$
$103$			0.277430i			0.0273360i	−0.999907	+	0.0136680i	$0.995649\pi$
$104$		−	7.03870i		−	0.690201i
$105$	2.51711	−	0.814965i	0.245645	−	0.0795324i
$106$		−	4.73423i		−	0.459829i
$107$		−	3.04381i		−	0.294256i	−0.989117	−	0.147128i	$-0.952997\pi$
$107$		−	3.04381i		−	0.294256i	0.989117	−	0.147128i	$-0.0470029\pi$
$108$			0.393347i			0.0378499i
$109$			13.0411i			1.24911i	0.780980	+	0.624556i	$0.214720\pi$
$109$			13.0411i			1.24911i	−0.780980	+	0.624556i	$0.785280\pi$
$110$	−2.66072	+	4.38719i	−0.253689	+	0.418302i
$111$			3.30505i			0.313702i
$112$	11.6592	−	3.77489i	1.10169	−	0.356694i
$113$	−11.1090			−1.04504			−0.522521	−	0.852626i	$-0.675008\pi$
$113$	−11.1090			−1.04504			−0.522521	+	0.852626i	$0.675008\pi$
$114$	3.98459			0.373191
$115$		−	4.41867i		−	0.412043i
$116$			0.986862i			0.0916278i
$117$	2.83183			0.261803
$118$	7.04302			0.648362
$119$	2.79766	−	0.905798i	0.256461	−	0.0830344i
$120$		−	2.48556i		−	0.226900i
$121$	−5.08409	−	9.75459i	−0.462190	−	0.886781i
$122$		−	3.92554i		−	0.355402i
$123$		−	4.46980i		−	0.403028i
$124$		−	1.82420i		−	0.163818i
$125$		−	1.00000i		−	0.0894427i
$126$	1.26079	+	3.89408i	0.112320	+	0.346912i
$127$			17.3736i			1.54166i	0.637041	+	0.770830i	$0.280158\pi$
$127$			17.3736i			1.54166i	−0.637041	+	0.770830i	$0.719842\pi$
$128$		−	13.4684i		−	1.19045i
$129$	−6.92036			−0.609304
$130$	4.38097			0.384237
$131$	15.0601			1.31581			0.657903	−	0.753103i	$-0.271444\pi$
$131$	15.0601			1.31581			0.657903	+	0.753103i	$0.271444\pi$
$132$	−1.11547	−	0.676507i	−0.0970896	−	0.0588823i
$133$	6.48311	−	2.09904i	0.562157	−	0.182010i
$134$			22.7460i			1.96496i
$135$	1.00000			0.0860663
$136$		−	2.76260i		−	0.236891i
$137$	4.33359			0.370243			0.185122	−	0.982716i	$-0.440732\pi$
$137$	4.33359			0.370243			0.185122	+	0.982716i	$0.440732\pi$
$138$	6.83588			0.581908
$139$	10.9554			0.929222			0.464611	−	0.885515i	$-0.346194\pi$
$139$	10.9554			0.929222			0.464611	+	0.885515i	$0.346194\pi$
$140$	0.320564	+	0.990098i	0.0270926	+	0.0836785i
$141$	−3.19790			−0.269312
$142$		−	5.83189i		−	0.489401i
$143$	−4.87039	+	8.03065i	−0.407282	+	0.671557i
$144$	4.63197			0.385998
$145$	2.50888			0.208351
$146$		−	7.53170i		−	0.623328i
$147$	4.10271	+	5.67167i	0.338386	+	0.467791i
$148$	−1.30003			−0.106862
$149$		−	3.61456i		−	0.296116i	−0.988979	−	0.148058i	$-0.952698\pi$
$149$		−	3.61456i		−	0.296116i	0.988979	−	0.148058i	$-0.0473022\pi$
$150$	1.54704			0.126316
$151$		−	9.24176i		−	0.752083i	−0.926603	−	0.376042i	$-0.877285\pi$
$151$		−	9.24176i		−	0.752083i	0.926603	−	0.376042i	$-0.122715\pi$
$152$		−	6.40186i		−	0.519259i
$153$	1.11146			0.0898559
$154$	−13.2114	−	3.12191i	−1.06461	−	0.251571i
$155$	−4.63764			−0.372504
$156$			1.11389i			0.0891829i
$157$			5.84300i			0.466322i	0.972438	+	0.233161i	$0.0749070\pi$
$157$			5.84300i			0.466322i	−0.972438	+	0.233161i	$0.925093\pi$
$158$	−7.38606			−0.587603
$159$		−	3.06018i		−	0.242688i
$160$	2.19474			0.173510
$161$	11.1223	−	3.60106i	0.876557	−	0.283803i
$162$			1.54704i			0.121547i
$163$	−9.75792			−0.764300			−0.382150	−	0.924100i	$-0.624816\pi$
$163$	−9.75792			−0.764300			−0.382150	+	0.924100i	$0.624816\pi$
$164$	1.75818			0.137291
$165$	−1.71987	+	2.83585i	−0.133892	+	0.220771i
$166$		−	22.1513i		−	1.71928i
$167$	9.45478			0.731633			0.365816	−	0.930687i	$-0.380790\pi$
$167$	9.45478			0.731633			0.365816	+	0.930687i	$0.380790\pi$
$168$	6.25643	−	2.02565i	0.482694	−	0.156282i
$169$	−4.98072			−0.383133
$170$	1.71947			0.131878
$171$	2.57562			0.196962
$172$		−	2.72211i		−	0.207559i
$173$	6.13078			0.466115			0.233057	−	0.972463i	$-0.425127\pi$
$173$	6.13078			0.466115			0.233057	+	0.972463i	$0.425127\pi$
$174$			3.88135i			0.294245i
$175$	2.51711	−	0.814965i	0.190275	−	0.0616055i
$176$	−7.96639	+	13.1356i	−0.600490	+	0.990132i
$177$	4.55256			0.342192
$178$	−0.910977			−0.0682806
$179$	−25.1893			−1.88273			−0.941367	−	0.337385i	$-0.890457\pi$
$179$	−25.1893			−1.88273			−0.941367	+	0.337385i	$0.890457\pi$
$180$			0.393347i			0.0293184i
$181$		−	3.44629i		−	0.256161i	−0.991764	−	0.128080i	$-0.959118\pi$
$181$		−	3.44629i		−	0.256161i	0.991764	−	0.128080i	$-0.0408815\pi$
$182$	3.57034	+	11.0274i	0.264651	+	0.817404i
$183$		−	2.53745i		−	0.187573i
$184$		−	10.9829i		−	0.809669i
$185$			3.30505i			0.242992i
$186$		−	7.17464i		−	0.526070i
$187$	−1.91156	+	3.15192i	−0.139787	+	0.230492i
$188$		−	1.25789i		−	0.0917407i
$189$	0.814965	+	2.51711i	0.0592800	+	0.183093i
$190$	3.98459			0.289073
$191$	−10.4878			−0.758870			−0.379435	−	0.925218i	$-0.623882\pi$
$191$	−10.4878			−0.758870			−0.379435	+	0.925218i	$0.623882\pi$
$192$		−	5.86858i		−	0.423528i
$193$			8.80647i			0.633903i	0.948442	+	0.316952i	$0.102659\pi$
$193$			8.80647i			0.633903i	−0.948442	+	0.316952i	$0.897341\pi$
$194$	−11.9677			−0.859231
$195$	2.83183			0.202792
$196$	−2.23093	+	1.61379i	−0.159352	+	0.115271i
$197$			3.67764i			0.262021i	0.991381	+	0.131011i	$0.0418222\pi$
$197$			3.67764i			0.262021i	−0.991381	+	0.131011i	$0.958178\pi$
$198$	−4.38719	−	2.66072i	−0.311784	−	0.189089i
$199$			17.7841i			1.26068i	0.776319	+	0.630340i	$0.217084\pi$
$199$			17.7841i			1.26068i	−0.776319	+	0.630340i	$0.782916\pi$
$200$		−	2.48556i		−	0.175756i
$201$			14.7029i			1.03706i
$202$			22.2666i			1.56667i
$203$	2.04465	+	6.31513i	0.143506	+	0.443235i
$204$			0.437189i			0.0306093i
$205$		−	4.46980i		−	0.312184i
$206$	−0.429196			−0.0299035
$207$	4.41867			0.307119
$208$	13.1170			0.909498
$209$	−4.42973	+	7.30406i	−0.306411	+	0.505233i
$210$	1.26079	+	3.89408i	0.0870026	+	0.268717i
$211$			15.0841i			1.03843i	0.854644	+	0.519215i	$0.173776\pi$
$211$			15.0841i			1.03843i	−0.854644	+	0.519215i	$0.826224\pi$
$212$	1.20371			0.0826713
$213$		−	3.76969i		−	0.258295i
$214$	4.70891			0.321894
$215$	−6.92036			−0.471965
$216$	2.48556			0.169121
$217$	−3.77951	−	11.6734i	−0.256570	−	0.792445i
$218$	−20.1752			−1.36644
$219$		−	4.86845i		−	0.328979i
$220$	−1.11547	−	0.676507i	−0.0752052	−	0.0456101i
$221$	3.14746			0.211721
$222$	−5.11306			−0.343166
$223$			21.2206i			1.42104i	0.703677	+	0.710520i	$0.251540\pi$
$223$			21.2206i			1.42104i	−0.703677	+	0.710520i	$0.748460\pi$
$224$	1.78864	+	5.52440i	0.119508	+	0.369115i
$225$	1.00000			0.0666667
$226$		−	17.1860i		−	1.14320i
$227$	−6.71340			−0.445584			−0.222792	−	0.974866i	$-0.571517\pi$
$227$	−6.71340			−0.445584			−0.222792	+	0.974866i	$0.571517\pi$
$228$			1.01311i			0.0670950i
$229$			25.9762i			1.71655i	0.513186	+	0.858277i	$0.328465\pi$
$229$			25.9762i			1.71655i	−0.513186	+	0.858277i	$0.671535\pi$
$230$	6.83588			0.450744
$231$	−8.53977	−	2.01798i	−0.561876	−	0.132774i
$232$	6.23598			0.409412
$233$		−	0.0686068i		−	0.00449458i	−0.999997	−	0.00224729i	$-0.999285\pi$
$233$		−	0.0686068i		−	0.00449458i	0.999997	−	0.00224729i	$-0.000715335\pi$
$234$			4.38097i			0.286393i
$235$	−3.19790			−0.208608
$236$			1.79074i			0.116567i
$237$	−4.77430			−0.310124
$238$	1.40131	+	4.32810i	0.0908334	+	0.280549i
$239$			21.9557i			1.42019i	0.704104	+	0.710097i	$0.251349\pi$
$239$			21.9557i			1.42019i	−0.704104	+	0.710097i	$0.748651\pi$
$240$	4.63197			0.298993
$241$	−3.80239			−0.244933			−0.122467	−	0.992473i	$-0.539080\pi$
$241$	−3.80239			−0.244933			−0.122467	+	0.992473i	$0.539080\pi$
$242$	15.0908	−	7.86531i	0.970073	−	0.505602i
$243$			1.00000i			0.0641500i
$244$	0.998098			0.0638967
$245$	4.10271	+	5.67167i	0.262112	+	0.362349i
$246$	6.91498			0.440883
$247$	7.29372			0.464088
$248$	−11.5272			−0.731975
$249$		−	14.3185i		−	0.907397i
$250$	1.54704			0.0978437
$251$			18.0105i			1.13681i	0.822748	+	0.568407i	$0.192440\pi$
$251$			18.0105i			1.13681i	−0.822748	+	0.568407i	$0.807560\pi$
$252$	−0.990098	+	0.320564i	−0.0623703	+	0.0201936i
$253$	−7.59954	+	12.5307i	−0.477779	+	0.787797i
$254$	−26.8778			−1.68646
$255$	1.11146			0.0696021
$256$	9.09912			0.568695
$257$		−	11.0756i		−	0.690875i	−0.938442	−	0.345437i	$-0.887731\pi$
$257$		−	11.0756i		−	0.690875i	0.938442	−	0.345437i	$-0.112269\pi$
$258$		−	10.7061i		−	0.666533i
$259$	−8.31917	+	2.69350i	−0.516928	+	0.167366i
$260$			1.11389i			0.0690808i
$261$			2.50888i			0.155296i
$262$			23.2986i			1.43939i
$263$			3.71325i			0.228969i	0.993425	+	0.114484i	$0.0365216\pi$
$263$			3.71325i			0.228969i	−0.993425	+	0.114484i	$0.963478\pi$
$264$	−4.27485	+	7.04869i	−0.263099	+	0.433817i
$265$		−	3.06018i		−	0.187985i
$266$	3.24730	+	10.0297i	0.199105	+	0.614958i
$267$	−0.588850			−0.0360370
$268$	−5.78334			−0.353274
$269$		−	26.7827i		−	1.63297i	−0.577366	−	0.816486i	$-0.695919\pi$
$269$		−	26.7827i		−	1.63297i	0.577366	−	0.816486i	$-0.304081\pi$
$270$			1.54704i			0.0941501i
$271$	−18.8021			−1.14215			−0.571074	−	0.820899i	$-0.693473\pi$
$271$	−18.8021			−1.14215			−0.571074	+	0.820899i	$0.693473\pi$
$272$	5.14824			0.312158
$273$	2.30784	+	7.12803i	0.139677	+	0.431408i
$274$			6.70425i			0.405019i
$275$	−1.71987	+	2.83585i	−0.103712	+	0.171008i
$276$			1.73807i			0.104620i
$277$		−	18.8093i		−	1.13014i	−0.825042	−	0.565071i	$-0.808849\pi$
$277$		−	18.8093i		−	1.13014i	0.825042	−	0.565071i	$-0.191151\pi$
$278$			16.9484i			1.01650i
$279$		−	4.63764i		−	0.277648i
$280$	6.25643	−	2.02565i	0.373893	−	0.121056i
$281$			6.00260i			0.358085i	0.983841	+	0.179043i	$0.0573000\pi$
$281$			6.00260i			0.358085i	−0.983841	+	0.179043i	$0.942700\pi$
$282$		−	4.94729i		−	0.294607i
$283$	5.80703			0.345192			0.172596	−	0.984993i	$-0.444784\pi$
$283$	5.80703			0.345192			0.172596	+	0.984993i	$0.444784\pi$
$284$	1.48280			0.0879880
$285$	2.57562			0.152566
$286$	−12.4238	−	7.53470i	−0.734633	−	0.445536i
$287$	11.2510	−	3.64273i	0.664123	−	0.215023i
$288$			2.19474i			0.129326i
$289$	−15.7647			−0.927333
$290$			3.88135i			0.227921i
$291$	−7.73585			−0.453484
$292$	1.91499			0.112066
$293$	−23.9606			−1.39979			−0.699897	−	0.714244i	$-0.746771\pi$
$293$	−23.9606			−1.39979			−0.699897	+	0.714244i	$0.746771\pi$
$294$	−8.77432	+	6.34707i	−0.511729	+	0.370169i
$295$	4.55256			0.265060
$296$			8.21492i			0.477482i
$297$	−2.83585	−	1.71987i	−0.164553	−	0.0997970i
$298$	5.59188			0.323929
$299$	12.5129			0.723641
$300$			0.393347i			0.0227099i
$301$	−5.63985	−	17.4193i	−0.325076	−	1.00403i
$302$	14.2974			0.822723
$303$			14.3930i			0.826856i
$304$	11.9302			0.684243
$305$		−	2.53745i		−	0.145294i
$306$			1.71947i			0.0982957i
$307$	31.6593			1.80689			0.903445	−	0.428703i	$-0.141029\pi$
$307$	31.6593			1.80689			0.903445	+	0.428703i	$0.141029\pi$
$308$	0.793768	−	3.35910i	0.0452291	−	0.191402i
$309$	−0.277430			−0.0157824
$310$		−	7.17464i		−	0.407492i
$311$			13.8570i			0.785759i	0.919590	+	0.392880i	$0.128521\pi$
$311$			13.8570i			0.785759i	−0.919590	+	0.392880i	$0.871479\pi$
$312$	7.03870			0.398488
$313$		−	19.7086i		−	1.11399i	−0.830515	−	0.556997i	$-0.811954\pi$
$313$		−	19.7086i		−	1.11399i	0.830515	−	0.556997i	$-0.188046\pi$
$314$	−9.03939			−0.510122
$315$	0.814965	+	2.51711i	0.0459181	+	0.141823i
$316$		−	1.87796i		−	0.105643i
$317$	12.5949			0.707403			0.353701	−	0.935358i	$-0.384923\pi$
$317$	12.5949			0.707403			0.353701	+	0.935358i	$0.384923\pi$
$318$	4.73423			0.265483
$319$	−7.11481	−	4.31495i	−0.398353	−	0.241591i
$320$		−	5.86858i		−	0.328064i
$321$	3.04381			0.169889
$322$	5.57100	+	17.2066i	0.310460	+	0.958888i
$323$	2.86269			0.159284
$324$	−0.393347			−0.0218526
$325$	2.83183			0.157082
$326$		−	15.0959i		−	0.836087i
$327$	−13.0411			−0.721175
$328$		−	11.1100i		−	0.613445i
$329$	−2.60618	−	8.04946i	−0.143683	−	0.443781i
$330$	−4.38719	−	2.66072i	−0.241507	−	0.146468i
$331$	−12.5054			−0.687359			−0.343679	−	0.939087i	$-0.611673\pi$
$331$	−12.5054			−0.687359			−0.343679	+	0.939087i	$0.611673\pi$
$332$	5.63214			0.309104
$333$	−3.30505			−0.181116
$334$			14.6270i			0.800352i
$335$			14.7029i			0.803305i
$336$	3.77489	+	11.6592i	0.205937	+	0.636060i
$337$			3.88910i			0.211853i	0.994374	+	0.105926i	$0.0337808\pi$
$337$			3.88910i			0.211853i	−0.994374	+	0.105926i	$0.966219\pi$
$338$		−	7.70540i		−	0.419119i
$339$		−	11.1090i		−	0.603355i
$340$			0.437189i			0.0237099i
$341$	13.1517	+	7.97614i	0.712202	+	0.431932i
$342$			3.98459i			0.215462i
$343$	−10.9326	+	14.9492i	−0.590307	+	0.807179i
$344$	−17.2010			−0.927416
$345$	4.41867			0.237893
$346$			9.48460i			0.509895i
$347$			5.63633i			0.302574i	0.988490	+	0.151287i	$0.0483417\pi$
$347$			5.63633i			0.302574i	−0.988490	+	0.151287i	$0.951658\pi$
$348$	−0.986862			−0.0529014
$349$	5.20232			0.278474			0.139237	−	0.990259i	$-0.455535\pi$
$349$	5.20232			0.278474			0.139237	+	0.990259i	$0.455535\pi$
$350$	1.26079	+	3.89408i	0.0673919	+	0.208147i
$351$			2.83183i			0.151152i
$352$	−6.22396	−	3.77467i	−0.331738	−	0.201191i
$353$		−	3.66618i		−	0.195131i	−0.995229	−	0.0975655i	$-0.968894\pi$
$353$		−	3.66618i		−	0.195131i	0.995229	−	0.0975655i	$-0.0311055\pi$
$354$			7.04302i			0.374332i
$355$		−	3.76969i		−	0.200075i
$356$		−	0.231622i		−	0.0122760i
$357$	0.905798	+	2.79766i	0.0479399	+	0.148068i
$358$		−	38.9689i		−	2.05957i
$359$		−	7.36337i		−	0.388624i	−0.980940	−	0.194312i	$-0.937753\pi$
$359$		−	7.36337i		−	0.388624i	0.980940	−	0.194312i	$-0.0622474\pi$
$360$	2.48556			0.131001
$361$	−12.3662			−0.650853
$362$	5.33156			0.280221
$363$	9.75459	−	5.08409i	0.511983	−	0.266846i
$364$	−2.80379	+	0.907784i	−0.146959	+	0.0475808i
$365$		−	4.86845i		−	0.254826i
$366$	3.92554			0.205191
$367$			32.7650i			1.71032i	0.518365	+	0.855159i	$0.326541\pi$
$367$			32.7650i			1.71032i	−0.518365	+	0.855159i	$0.673459\pi$
$368$	20.4671			1.06692
$369$	4.46980			0.232688
$370$	−5.11306			−0.265815
$371$	7.70280	−	2.49394i	0.399909	−	0.129479i
$372$	1.82420			0.0945806
$373$		−	4.31273i		−	0.223305i	−0.993747	−	0.111652i	$-0.964386\pi$
$373$		−	4.31273i		−	0.223305i	0.993747	−	0.111652i	$-0.0356143\pi$
$374$	−4.87617	−	2.95727i	−0.252141	−	0.152917i
$375$	1.00000			0.0516398
$376$	−7.94858			−0.409917
$377$			7.10473i			0.365912i
$378$	−3.89408	+	1.26079i	−0.200290	+	0.0648479i
$379$	−34.2848			−1.76109			−0.880545	−	0.473962i	$-0.842823\pi$
$379$	−34.2848			−1.76109			−0.880545	+	0.473962i	$0.842823\pi$
$380$			1.01311i			0.0519716i
$381$	−17.3736			−0.890078
$382$		−	16.2251i		−	0.830147i
$383$			19.0897i			0.975439i	0.873000	+	0.487720i	$0.162171\pi$
$383$			19.0897i			0.975439i	−0.873000	+	0.487720i	$0.837829\pi$
$384$	13.4684			0.687309
$385$	−8.53977	−	2.01798i	−0.435227	−	0.102846i
$386$	−13.6240			−0.693443
$387$		−	6.92036i		−	0.351782i
$388$		−	3.04288i		−	0.154479i
$389$	−25.8528			−1.31079			−0.655394	−	0.755287i	$-0.727498\pi$
$389$	−25.8528			−1.31079			−0.655394	+	0.755287i	$0.727498\pi$
$390$			4.38097i			0.221839i
$391$	4.91116			0.248368
$392$	10.1975	+	14.0973i	0.515054	+	0.712020i
$393$			15.0601i			0.759681i
$394$	−5.68948			−0.286632
$395$	−4.77430			−0.240221
$396$	0.676507	−	1.11547i	0.0339957	−	0.0560547i
$397$		−	26.8639i		−	1.34826i	−0.738612	−	0.674131i	$-0.764518\pi$
$397$		−	26.8639i		−	1.34826i	0.738612	−	0.674131i	$-0.235482\pi$
$398$	−27.5128			−1.37909
$399$	2.09904	+	6.48311i	0.105083	+	0.324561i
$400$	4.63197			0.231599
$401$	38.2162			1.90842			0.954212	−	0.299130i	$-0.0966964\pi$
$401$	38.2162			1.90842			0.954212	+	0.299130i	$0.0966964\pi$
$402$	−22.7460			−1.13447
$403$		−	13.1330i		−	0.654202i
$404$	−5.66144			−0.281667
$405$			1.00000i			0.0496904i
$406$	−9.76978	+	3.16316i	−0.484866	+	0.156985i
$407$	5.68426	−	9.37263i	0.281758	−	0.464584i
$408$	2.76260			0.136769
$409$	33.7421			1.66844			0.834221	−	0.551431i	$-0.185918\pi$
$409$	33.7421			1.66844			0.834221	+	0.551431i	$0.185918\pi$
$410$	6.91498			0.341506
$411$			4.33359i			0.213760i
$412$		−	0.109126i		−	0.00537626i
$413$	3.71018	+	11.4593i	0.182566	+	0.563875i
$414$			6.83588i			0.335965i
$415$		−	14.3185i		−	0.702866i
$416$			6.21514i			0.304722i
$417$			10.9554i			0.536487i
$418$	−11.2997	−	6.85299i	−0.552687	−	0.335191i
$419$		−	4.94856i		−	0.241753i	−0.992668	−	0.120876i	$-0.961429\pi$
$419$		−	4.94856i		−	0.241753i	0.992668	−	0.120876i	$-0.0385705\pi$
$420$	−0.990098	+	0.320564i	−0.0483118	+	0.0156419i
$421$	36.7108			1.78917			0.894587	−	0.446893i	$-0.147470\pi$
$421$	36.7108			1.78917			0.894587	+	0.446893i	$0.147470\pi$
$422$	−23.3357			−1.13596
$423$		−	3.19790i		−	0.155487i
$424$		−	7.60627i		−	0.369393i
$425$	1.11146			0.0539136
$426$	5.83189			0.282556
$427$	6.38703	−	2.06793i	0.309090	−	0.100074i
$428$			1.19727i			0.0578724i
$429$	−8.03065	−	4.87039i	−0.387724	−	0.235144i
$430$		−	10.7061i		−	0.516294i
$431$		−	19.1239i		−	0.921167i	−0.887616	−	0.460583i	$-0.847640\pi$
$431$		−	19.1239i		−	0.921167i	0.887616	−	0.460583i	$-0.152360\pi$
$432$			4.63197i			0.222856i
$433$		−	23.0731i		−	1.10882i	−0.832243	−	0.554412i	$-0.812943\pi$
$433$		−	23.0731i		−	1.10882i	0.832243	−	0.554412i	$-0.187057\pi$
$434$	18.0593	−	5.84708i	0.866876	−	0.280669i
$435$			2.50888i			0.120292i
$436$		−	5.12969i		−	0.245668i
$437$	11.3808			0.544417
$438$	7.53170			0.359879
$439$	25.6104			1.22232			0.611159	−	0.791508i	$-0.290704\pi$
$439$	25.6104			1.22232			0.611159	+	0.791508i	$0.290704\pi$
$440$	−4.27485	+	7.04869i	−0.203795	+	0.336033i
$441$	−5.67167	+	4.10271i	−0.270079	+	0.195367i
$442$			4.86926i			0.231607i
$443$	−9.64017			−0.458018			−0.229009	−	0.973424i	$-0.573549\pi$
$443$	−9.64017			−0.458018			−0.229009	+	0.973424i	$0.573549\pi$
$444$		−	1.30003i		−	0.0616969i
$445$	−0.588850			−0.0279142
$446$	−32.8293			−1.55451
$447$	3.61456			0.170963
$448$	14.7719	−	4.78269i	0.697904	−	0.225961i
$449$	36.1350			1.70532			0.852658	−	0.522469i	$-0.174989\pi$
$449$	36.1350			1.70532			0.852658	+	0.522469i	$0.174989\pi$
$450$			1.54704i			0.0729284i
$451$	−7.68747	+	12.6757i	−0.361989	+	0.596874i
$452$	4.36968			0.205532
$453$	9.24176			0.434216
$454$		−	10.3859i		−	0.487436i
$455$	2.30784	+	7.12803i	0.108193	+	0.334167i
$456$	6.40186			0.299795
$457$		−	27.3776i		−	1.28067i	−0.768096	−	0.640335i	$-0.778795\pi$
$457$		−	27.3776i		−	1.28067i	0.768096	−	0.640335i	$-0.221205\pi$
$458$	−40.1863			−1.87778
$459$			1.11146i			0.0518784i
$460$			1.73807i			0.0810380i
$461$	16.9958			0.791571			0.395786	−	0.918343i	$-0.370472\pi$
$461$	16.9958			0.791571			0.395786	+	0.918343i	$0.370472\pi$
$462$	3.12191	−	13.2114i	0.145244	−	0.614651i
$463$	5.32300			0.247381			0.123690	−	0.992321i	$-0.460527\pi$
$463$	5.32300			0.247381			0.123690	+	0.992321i	$0.460527\pi$
$464$			11.6211i			0.539495i
$465$		−	4.63764i		−	0.215065i
$466$	0.106138			0.00491674
$467$		−	34.3107i		−	1.58771i	−0.608108	−	0.793855i	$-0.708071\pi$
$467$		−	34.3107i		−	1.58771i	0.608108	−	0.793855i	$-0.291929\pi$
$468$	−1.11389			−0.0514898
$469$	−37.0088	+	11.9823i	−1.70891	+	0.553293i
$470$		−	4.94729i		−	0.228202i
$471$	−5.84300			−0.269231
$472$	11.3157			0.520846
$473$	19.6251	+	11.9021i	0.902363	+	0.547260i
$474$		−	7.38606i		−	0.339253i
$475$	2.57562			0.118177
$476$	−1.10045	+	0.356293i	−0.0504391	+	0.0163307i
$477$	3.06018			0.140116
$478$	−33.9664			−1.55359
$479$	41.8127			1.91047			0.955236	−	0.295845i	$-0.0956012\pi$
$479$	41.8127			1.91047			0.955236	+	0.295845i	$0.0956012\pi$
$480$			2.19474i			0.100176i
$481$	−9.35935			−0.426750
$482$		−	5.88246i		−	0.267939i
$483$	3.60106	+	11.1223i	0.163854	+	0.506080i
$484$	1.99981	+	3.83694i	0.0909006	+	0.174406i
$485$	−7.73585			−0.351267
$486$	−1.54704			−0.0701754
$487$	−35.9454			−1.62884			−0.814420	−	0.580275i	$-0.802945\pi$
$487$	−35.9454			−1.62884			−0.814420	+	0.580275i	$0.802945\pi$
$488$		−	6.30698i		−	0.285504i
$489$		−	9.75792i		−	0.441269i
$490$	−8.77432	+	6.34707i	−0.396383	+	0.286732i
$491$			37.1012i			1.67436i	0.546931	+	0.837178i	$0.315796\pi$
$491$			37.1012i			1.67436i	−0.546931	+	0.837178i	$0.684204\pi$
$492$			1.75818i			0.0792650i
$493$			2.78851i			0.125588i
$494$			11.2837i			0.507678i
$495$	−2.83585	−	1.71987i	−0.127462	−	0.0773024i
$496$		−	21.4814i		−	0.964544i
$497$	9.48873	−	3.07217i	0.425628	−	0.137806i
$498$	22.1513			0.992625
$499$	22.3917			1.00239			0.501196	−	0.865334i	$-0.332894\pi$
$499$	22.3917			1.00239			0.501196	+	0.865334i	$0.332894\pi$
$500$			0.393347i			0.0175910i
$501$			9.45478i			0.422408i
$502$	−27.8631			−1.24359
$503$	−5.47272			−0.244016			−0.122008	−	0.992529i	$-0.538933\pi$
$503$	−5.47272			−0.244016			−0.122008	+	0.992529i	$0.538933\pi$
$504$	2.02565	+	6.25643i	0.0902295	+	0.278684i
$505$			14.3930i			0.640480i
$506$	−19.3855	−	11.7568i	−0.861791	−	0.522655i
$507$		−	4.98072i		−	0.221202i
$508$		−	6.83387i		−	0.303204i
$509$			13.3419i			0.591370i	0.955286	+	0.295685i	$0.0955478\pi$
$509$			13.3419i			0.591370i	−0.955286	+	0.295685i	$0.904452\pi$
$510$			1.71947i			0.0761396i
$511$	12.2544	−	3.96761i	0.542103	−	0.175517i
$512$		−	12.8601i		−	0.568343i
$513$			2.57562i			0.113716i
$514$	17.1344			0.755766
$515$	−0.277430			−0.0122250
$516$	2.72211			0.119834
$517$	9.06876	+	5.49997i	0.398844	+	0.241889i
$518$	−4.16697	−	12.8701i	−0.183086	−	0.565481i
$519$			6.13078i			0.269111i
$520$	7.03870			0.308667
$521$		−	40.4466i		−	1.77200i	−0.463689	−	0.885998i	$-0.653475\pi$
$521$		−	40.4466i		−	1.77200i	0.463689	−	0.885998i	$-0.346525\pi$
$522$	−3.88135			−0.169882
$523$	28.0390			1.22606			0.613030	−	0.790059i	$-0.289950\pi$
$523$	28.0390			1.22606			0.613030	+	0.790059i	$0.289950\pi$
$524$	−5.92385			−0.258784
$525$	0.814965	+	2.51711i	0.0355680	+	0.109856i
$526$	−5.74456			−0.250475
$527$		−	5.15454i		−	0.224535i
$528$	−13.1356	−	7.96639i	−0.571653	−	0.346693i
$529$	−3.47538			−0.151103
$530$	4.73423			0.205642
$531$			4.55256i			0.197564i
$532$	−2.55011	+	0.825651i	−0.110561	+	0.0357965i
$533$	12.6577			0.548267
$534$		−	0.910977i		−	0.0394218i
$535$	3.04381			0.131595
$536$			36.5450i			1.57850i
$537$		−	25.1893i		−	1.08700i
$538$	41.4341			1.78635
$539$	−1.88013	−	23.1401i	−0.0809831	−	0.996715i
$540$	−0.393347			−0.0169270
$541$			30.5495i			1.31343i	0.754141	+	0.656713i	$0.228054\pi$
$541$			30.5495i			1.31343i	−0.754141	+	0.656713i	$0.771946\pi$
$542$		−	29.0877i		−	1.24943i
$543$	3.44629			0.147894
$544$			2.43936i			0.104587i
$545$	−13.0411			−0.558620
$546$	−11.0274	+	3.57034i	−0.471928	+	0.152796i
$547$			14.4756i			0.618932i	0.950910	+	0.309466i	$0.100150\pi$
$547$			14.4756i			0.618932i	−0.950910	+	0.309466i	$0.899850\pi$
$548$	−1.70461			−0.0728171
$549$	2.53745			0.108296
$550$	−4.38719	−	2.66072i	−0.187070	−	0.113453i
$551$			6.46192i			0.275287i
$552$	10.9829			0.467462
$553$	−3.89089	−	12.0174i	−0.165457	−	0.511033i
$554$	29.0988			1.23629
$555$	−3.30505			−0.140292
$556$	−4.30926			−0.182754
$557$		−	29.9998i		−	1.27113i	−0.772046	−	0.635566i	$-0.780767\pi$
$557$		−	29.9998i		−	1.27113i	0.772046	−	0.635566i	$-0.219233\pi$
$558$	7.17464			0.303727
$559$		−	19.5973i		−	0.828878i
$560$	3.77489	+	11.6592i	0.159518	+	0.492690i
$561$	−3.15192	−	1.91156i	−0.133074	−	0.0807062i
$562$	−9.28630			−0.391719
$563$	19.7699			0.833202			0.416601	−	0.909089i	$-0.363221\pi$
$563$	19.7699			0.833202			0.416601	+	0.909089i	$0.363221\pi$
$564$	1.25789			0.0529665
$565$		−	11.1090i		−	0.467357i
$566$			8.98374i			0.377615i
$567$	−2.51711	+	0.814965i	−0.105709	+	0.0342253i
$568$		−	9.36981i		−	0.393149i
$569$		−	27.3273i		−	1.14562i	−0.819689	−	0.572810i	$-0.805853\pi$
$569$		−	27.3273i		−	1.14562i	0.819689	−	0.572810i	$-0.194147\pi$
$570$			3.98459i			0.166896i
$571$			10.7124i			0.448299i	0.974555	+	0.224149i	$0.0719604\pi$
$571$			10.7124i			0.448299i	−0.974555	+	0.224149i	$0.928040\pi$
$572$	1.91575	−	3.15884i	0.0801017	−	0.132078i
$573$		−	10.4878i		−	0.438134i
$574$	5.63546	+	17.4057i	0.235220	+	0.726502i
$575$	4.41867			0.184271
$576$	5.86858			0.244524
$577$		−	18.1629i		−	0.756130i	−0.925779	−	0.378065i	$-0.876590\pi$
$577$		−	18.1629i		−	0.756130i	0.925779	−	0.378065i	$-0.123410\pi$
$578$		−	24.3886i		−	1.01443i
$579$	−8.80647			−0.365984
$580$	−0.986862			−0.0409772
$581$	36.0412	−	11.6691i	1.49524	−	0.484114i
$582$		−	11.9677i		−	0.496077i
$583$	−5.26311	+	8.67821i	−0.217976	+	0.359415i
$584$		−	12.1008i		−	0.500736i
$585$			2.83183i			0.117082i
$586$		−	37.0681i		−	1.53127i
$587$			18.4262i			0.760532i	0.924877	+	0.380266i	$0.124168\pi$
$587$			18.4262i			0.760532i	−0.924877	+	0.380266i	$0.875832\pi$
$588$	−1.61379	−	2.23093i	−0.0665516	−	0.0920022i
$589$		−	11.9448i		−	0.492176i
$590$			7.04302i			0.289956i
$591$	−3.67764			−0.151278
$592$	−15.3089			−0.629192
$593$	−11.6023			−0.476448			−0.238224	−	0.971210i	$-0.576565\pi$
$593$	−11.6023			−0.476448			−0.238224	+	0.971210i	$0.576565\pi$
$594$	2.66072	−	4.38719i	0.109171	−	0.180008i
$595$	0.905798	+	2.79766i	0.0371341	+	0.114693i
$596$			1.42178i			0.0582382i
$597$	−17.7841			−0.727854
$598$			19.3581i			0.791610i
$599$	−2.82975			−0.115620			−0.0578102	−	0.998328i	$-0.518412\pi$
$599$	−2.82975			−0.115620			−0.0578102	+	0.998328i	$0.518412\pi$
$600$	2.48556			0.101473
$601$	−34.0478			−1.38884			−0.694420	−	0.719570i	$-0.744339\pi$
$601$	−34.0478			−1.38884			−0.694420	+	0.719570i	$0.744339\pi$
$602$	26.9484	−	8.72510i	1.09834	−	0.355609i
$603$	−14.7029			−0.598748
$604$			3.63522i			0.147915i
$605$	9.75459	−	5.08409i	0.396580	−	0.206698i
$606$	−22.2666			−0.904519
$607$	9.36820			0.380244			0.190122	−	0.981761i	$-0.439112\pi$
$607$	9.36820			0.380244			0.190122	+	0.981761i	$0.439112\pi$
$608$			5.65281i			0.229252i
$609$	−6.31513	+	2.04465i	−0.255902	+	0.0828534i
$610$	3.92554			0.158941
$611$		−	9.05592i		−	0.366363i
$612$	−0.437189			−0.0176723
$613$			16.8291i			0.679722i	0.940476	+	0.339861i	$0.110380\pi$
$613$			16.8291i			0.679722i	−0.940476	+	0.339861i	$0.889620\pi$
$614$			48.9783i			1.97660i
$615$	4.46980			0.180240
$616$	−21.2262	−	5.01582i	−0.855226	−	0.202093i
$617$	45.4929			1.83148			0.915739	−	0.401775i	$-0.131606\pi$
$617$	45.4929			1.83148			0.915739	+	0.401775i	$0.131606\pi$
$618$		−	0.429196i		−	0.0172648i
$619$		−	2.73967i		−	0.110116i	−0.998483	−	0.0550582i	$-0.982466\pi$
$619$		−	2.73967i		−	0.110116i	0.998483	−	0.0550582i	$-0.0175344\pi$
$620$	1.82420			0.0732618
$621$			4.41867i			0.177315i
$622$	−21.4374			−0.859562
$623$	−0.479892	−	1.48220i	−0.0192265	−	0.0593830i
$624$			13.1170i			0.525099i
$625$	1.00000			0.0400000
$626$	30.4900			1.21863
$627$	−7.30406	−	4.42973i	−0.291696	−	0.176906i
$628$		−	2.29833i		−	0.0917133i
$629$	−3.67342			−0.146469
$630$	−3.89408	+	1.26079i	−0.155144	+	0.0502309i
$631$	32.1434			1.27961			0.639805	−	0.768537i	$-0.279015\pi$
$631$	32.1434			1.27961			0.639805	+	0.768537i	$0.279015\pi$
$632$	−11.8668			−0.472037
$633$	−15.0841			−0.599538
$634$			19.4849i			0.773846i
$635$	−17.3736			−0.689451
$636$			1.20371i			0.0477303i
$637$	−16.0612	+	11.6182i	−0.636368	+	0.460329i
$638$	6.67542	−	11.0069i	0.264283	−	0.435769i
$639$	3.76969			0.149127
$640$	13.4684			0.532387
$641$	20.5371			0.811168			0.405584	−	0.914058i	$-0.367068\pi$
$641$	20.5371			0.811168			0.405584	+	0.914058i	$0.367068\pi$
$642$			4.70891i			0.185846i
$643$		−	20.8311i		−	0.821500i	−0.911748	−	0.410750i	$-0.865267\pi$
$643$		−	20.8311i		−	0.821500i	0.911748	−	0.410750i	$-0.134733\pi$
$644$	−4.37491	+	1.41647i	−0.172396	+	0.0558166i
$645$		−	6.92036i		−	0.272489i
$646$			4.42870i			0.174245i
$647$		−	38.0636i		−	1.49643i	−0.663454	−	0.748217i	$-0.730910\pi$
$647$		−	38.0636i		−	1.49643i	0.663454	−	0.748217i	$-0.269090\pi$
$648$			2.48556i			0.0976422i
$649$	−12.9104	−	7.82982i	−0.506777	−	0.307347i
$650$			4.38097i			0.171836i
$651$	11.6734	−	3.77951i	0.457518	−	0.148131i
$652$	3.83825			0.150318
$653$	8.11098			0.317407			0.158704	−	0.987326i	$-0.449269\pi$
$653$	8.11098			0.317407			0.158704	+	0.987326i	$0.449269\pi$
$654$		−	20.1752i		−	0.788912i
$655$			15.0601i			0.588446i
$656$	20.7040			0.808354
$657$	4.86845			0.189936
$658$	12.4529	−	4.03187i	0.485463	−	0.157179i
$659$		−	47.7491i		−	1.86004i	−0.367505	−	0.930021i	$-0.619788\pi$
$659$		−	47.7491i		−	1.86004i	0.367505	−	0.930021i	$-0.380212\pi$
$660$	0.676507	−	1.11547i	0.0263330	−	0.0434198i
$661$		−	10.3686i		−	0.403293i	−0.979458	−	0.201646i	$-0.935371\pi$
$661$		−	10.3686i		−	0.403293i	0.979458	−	0.201646i	$-0.0646292\pi$
$662$		−	19.3464i		−	0.751919i
$663$			3.14746i			0.122237i
$664$		−	35.5895i		−	1.38114i
$665$	2.09904	+	6.48311i	0.0813972	+	0.251404i
$666$		−	5.11306i		−	0.198127i
$667$			11.0859i			0.429248i
$668$	−3.71901			−0.143893
$669$	−21.2206			−0.820438
$670$	−22.7460			−0.878756
$671$	−4.36408	+	7.19582i	−0.168473	+	0.277791i
$672$	−5.52440	+	1.78864i	−0.213108	+	0.0689982i
$673$			32.3798i			1.24815i	0.781365	+	0.624074i	$0.214524\pi$
$673$			32.3798i			1.24815i	−0.781365	+	0.624074i	$0.785476\pi$
$674$	−6.01661			−0.231751
$675$			1.00000i			0.0384900i
$676$	1.95915			0.0753521
$677$	−24.5861			−0.944922			−0.472461	−	0.881351i	$-0.656634\pi$
$677$	−24.5861			−0.944922			−0.472461	+	0.881351i	$0.656634\pi$
$678$	17.1860			0.660026
$679$	−6.30445	−	19.4720i	−0.241942	−	0.747266i
$680$	2.76260			0.105941
$681$		−	6.71340i		−	0.257258i
$682$	−12.3394	+	20.3462i	−0.472502	+	0.779096i
$683$	−38.3901			−1.46896			−0.734478	−	0.678633i	$-0.762573\pi$
$683$	−38.3901			−1.46896			−0.734478	+	0.678633i	$0.762573\pi$
$684$	−1.01311			−0.0387373
$685$			4.33359i			0.165578i
$686$	−23.1270	−	16.9133i	−0.882994	−	0.645752i
$687$	−25.9762			−0.991053
$688$		−	32.0549i		−	1.22208i
$689$	8.66591			0.330145
$690$			6.83588i			0.260237i
$691$			13.7707i			0.523863i	0.965086	+	0.261932i	$0.0843595\pi$
$691$			13.7707i			0.523863i	−0.965086	+	0.261932i	$0.915640\pi$
$692$	−2.41153			−0.0916725
$693$	2.01798	−	8.53977i	0.0766568	−	0.324399i
$694$	−8.71965			−0.330993
$695$			10.9554i			0.415561i
$696$			6.23598i			0.236374i
$697$	4.96799			0.188176
$698$			8.04822i			0.304630i
$699$	0.0686068			0.00259495
$700$	−0.990098	+	0.320564i	−0.0374222	+	0.0121162i
$701$			19.7289i			0.745149i	0.928002	+	0.372575i	$0.121525\pi$
$701$			19.7289i			0.745149i	−0.928002	+	0.372575i	$0.878475\pi$
$702$	−4.38097			−0.165349
$703$	−8.51255			−0.321057
$704$	−10.0932	+	16.6424i	−0.380402	+	0.627235i
$705$		−	3.19790i		−	0.120440i
$706$	5.67174			0.213459
$707$	−36.2287	+	11.7298i	−1.36252	+	0.441144i
$708$	−1.79074			−0.0673001
$709$	−1.84456			−0.0692737			−0.0346369	−	0.999400i	$-0.511027\pi$
$709$	−1.84456			−0.0692737			−0.0346369	+	0.999400i	$0.511027\pi$
$710$	5.83189			0.218867
$711$		−	4.77430i		−	0.179050i
$712$	−1.46362			−0.0548516
$713$		−	20.4922i		−	0.767439i
$714$	−4.32810	+	1.40131i	−0.161975	+	0.0524427i
$715$	−8.03065	−	4.87039i	−0.300329	−	0.182142i
$716$	9.90813			0.370284
$717$	−21.9557			−0.819949
$718$	11.3915			0.425126
$719$		−	5.92835i		−	0.221090i	−0.993871	−	0.110545i	$-0.964740\pi$
$719$		−	5.92835i		−	0.221090i	0.993871	−	0.110545i	$-0.0352597\pi$
$720$			4.63197i			0.172623i
$721$	−0.226095	−	0.698320i	−0.00842023	−	0.0260068i
$722$		−	19.1311i		−	0.711984i
$723$		−	3.80239i		−	0.141412i
$724$			1.35559i			0.0503801i
$725$			2.50888i			0.0931775i
$726$	7.86531	+	15.0908i	0.291909	+	0.560072i
$727$			24.2778i			0.900414i	0.892924	+	0.450207i	$0.148650\pi$
$727$			24.2778i			0.900414i	−0.892924	+	0.450207i	$0.851350\pi$
$728$	5.73629	+	17.7172i	0.212601	+	0.656642i
$729$	−1.00000			−0.0370370
$730$	7.53170			0.278761
$731$		−	7.69168i		−	0.284487i
$732$			0.998098i			0.0368908i
$733$	−6.93569			−0.256175			−0.128088	−	0.991763i	$-0.540884\pi$
$733$	−6.93569			−0.256175			−0.128088	+	0.991763i	$0.540884\pi$
$734$	−50.6889			−1.87096
$735$	−5.67167	+	4.10271i	−0.209203	+	0.151331i
$736$			9.69783i			0.357467i
$737$	25.2871	−	41.6952i	0.931461	−	1.53586i
$738$			6.91498i			0.254544i
$739$		−	19.8673i		−	0.730829i	−0.930845	−	0.365414i	$-0.880927\pi$
$739$		−	19.8673i		−	0.730829i	0.930845	−	0.365414i	$-0.119073\pi$
$740$		−	1.30003i		−	0.0477902i
$741$			7.29372i			0.267941i
$742$	3.85823	+	11.9166i	0.141640	+	0.437471i
$743$			20.2006i			0.741088i	0.928815	+	0.370544i	$0.120829\pi$
$743$			20.2006i			0.741088i	−0.928815	+	0.370544i	$0.879171\pi$
$744$		−	11.5272i		−	0.422606i
$745$	3.61456			0.132427
$746$	6.67199			0.244279
$747$	14.3185			0.523886
$748$	0.751908	−	1.23980i	0.0274925	−	0.0453316i
$749$	2.48060	+	7.66159i	0.0906390	+	0.279948i
$750$			1.54704i			0.0564901i
$751$	42.8386			1.56320			0.781601	−	0.623779i	$-0.214404\pi$
$751$	42.8386			1.56320			0.781601	+	0.623779i	$0.214404\pi$
$752$		−	14.8126i		−	0.540159i
$753$	−18.0105			−0.656339
$754$	−10.9913			−0.400281
$755$	9.24176			0.336342
$756$	−0.320564	−	0.990098i	−0.0116588	−	0.0360095i
$757$	−8.12642			−0.295360			−0.147680	−	0.989035i	$-0.547181\pi$
$757$	−8.12642			−0.295360			−0.147680	+	0.989035i	$0.547181\pi$
$758$		−	53.0401i		−	1.92650i
$759$	−12.5307	−	7.59954i	−0.454835	−	0.275846i
$760$	6.40186			0.232220
$761$	16.4058			0.594708			0.297354	−	0.954767i	$-0.403896\pi$
$761$	16.4058			0.594708			0.297354	+	0.954767i	$0.403896\pi$
$762$		−	26.8778i		−	0.973679i
$763$	−10.6280	−	32.8259i	−0.384761	−	1.18838i
$764$	4.12535			0.149250
$765$			1.11146i			0.0401848i
$766$	−29.5326			−1.06706
$767$			12.8921i			0.465506i
$768$			9.09912i			0.328336i
$769$	−42.1218			−1.51895			−0.759475	−	0.650536i	$-0.774544\pi$
$769$	−42.1218			−1.51895			−0.759475	+	0.650536i	$0.774544\pi$
$770$	3.12191	−	13.2114i	0.112506	−	0.476106i
$771$	11.0756			0.398877
$772$		−	3.46400i		−	0.124672i
$773$		−	22.5199i		−	0.809983i	−0.914320	−	0.404991i	$-0.867275\pi$
$773$		−	22.5199i		−	0.809983i	0.914320	−	0.404991i	$-0.132725\pi$
$774$	10.7061			0.384823
$775$		−	4.63764i		−	0.166589i
$776$	−19.2279			−0.690243
$777$	−2.69350	−	8.31917i	−0.0966288	−	0.298449i
$778$		−	39.9954i		−	1.43391i
$779$	11.5125			0.412478
$780$	−1.11389			−0.0398838
$781$	−6.48339	+	10.6903i	−0.231994	+	0.382529i
$782$			7.59778i			0.271696i
$783$	−2.50888			−0.0896601
$784$	−26.2710	+	19.0036i	−0.938250	+	0.678701i
$785$	−5.84300			−0.208546
$786$	−23.2986			−0.831035
$787$	22.5618			0.804242			0.402121	−	0.915587i	$-0.368273\pi$
$787$	22.5618			0.804242			0.402121	+	0.915587i	$0.368273\pi$
$788$		−	1.44659i		−	0.0515327i
$789$	−3.71325			−0.132195
$790$		−	7.38606i		−	0.262784i
$791$	27.9624	−	9.05340i	0.994230	−	0.321902i
$792$	−7.04869	−	4.27485i	−0.250464	−	0.151900i
$793$	7.18562			0.255169
$794$	41.5597			1.47490
$795$	3.06018			0.108533
$796$		−	6.99532i		−	0.247942i
$797$			39.0541i			1.38337i	0.722201	+	0.691683i	$0.243131\pi$
$797$			39.0541i			1.38337i	−0.722201	+	0.691683i	$0.756869\pi$
$798$	−10.0297	+	3.24730i	−0.355046	+	0.114953i
$799$		−	3.55433i		−	0.125743i
$800$			2.19474i			0.0775958i
$801$		−	0.588850i		−	0.0208060i
$802$			59.1221i			2.08768i
$803$	−8.37310	+	13.8062i	−0.295480	+	0.487210i
$804$		−	5.78334i		−	0.203963i
$805$	3.60106	+	11.1223i	0.126921	+	0.392008i
$806$	20.3174			0.715649
$807$	26.7827			0.942796
$808$			35.7747i			1.25855i
$809$		−	6.16340i		−	0.216694i	−0.994113	−	0.108347i	$-0.965444\pi$
$809$		−	6.16340i		−	0.216694i	0.994113	−	0.108347i	$-0.0345557\pi$
$810$	−1.54704			−0.0543576
$811$	−2.18332			−0.0766668			−0.0383334	−	0.999265i	$-0.512205\pi$
$811$	−2.18332			−0.0766668			−0.0383334	+	0.999265i	$0.512205\pi$
$812$	−0.804258	−	2.48404i	−0.0282239	−	0.0871726i
$813$		−	18.8021i		−	0.659420i
$814$	14.4999	+	8.79381i	0.508221	+	0.308223i
$815$		−	9.75792i		−	0.341805i
$816$			5.14824i			0.180224i
$817$		−	17.8242i		−	0.623590i
$818$			52.2006i			1.82515i
$819$	−7.12803	+	2.30784i	−0.249073	+	0.0806426i
$820$			1.75818i			0.0613984i
$821$		−	0.700047i		−	0.0244318i	−0.999925	−	0.0122159i	$-0.996111\pi$
$821$		−	0.700047i		−	0.0244318i	0.999925	−	0.0122159i	$-0.00388854\pi$
$822$	−6.70425			−0.233838
$823$	−4.81852			−0.167963			−0.0839815	−	0.996467i	$-0.526764\pi$
$823$	−4.81852			−0.167963			−0.0839815	+	0.996467i	$0.526764\pi$
$824$	−0.689569			−0.0240223
$825$	−2.83585	−	1.71987i	−0.0987316	−	0.0598782i
$826$	−17.7280	+	5.73981i	−0.616837	+	0.199714i
$827$		−	19.7114i		−	0.685431i	−0.939439	−	0.342716i	$-0.888653\pi$
$827$		−	19.7114i		−	0.685431i	0.939439	−	0.342716i	$-0.111347\pi$
$828$	−1.73807			−0.0604021
$829$			38.4947i			1.33698i	0.743722	+	0.668489i	$0.233059\pi$
$829$			38.4947i			1.33698i	−0.743722	+	0.668489i	$0.766941\pi$
$830$	22.1513			0.768884
$831$	18.8093			0.652487
$832$	16.6188			0.576155
$833$	−6.30381	+	4.55998i	−0.218414	+	0.157994i
$834$	−16.9484			−0.586877
$835$			9.45478i			0.327196i
$836$	1.74242	−	2.87303i	0.0602629	−	0.0993660i
$837$	4.63764			0.160300
$838$	7.65564			0.264460
$839$		−	36.7334i		−	1.26818i	−0.773260	−	0.634089i	$-0.781375\pi$
$839$		−	36.7334i		−	1.26818i	0.773260	−	0.634089i	$-0.218625\pi$
$840$	2.02565	+	6.25643i	0.0698914	+	0.215867i
$841$	22.7055			0.782949
$842$			56.7932i			1.95722i
$843$	−6.00260			−0.206741
$844$		−	5.93327i		−	0.204232i
$845$		−	4.98072i		−	0.171342i
$846$	4.94729			0.170091
$847$	20.7468	+	20.4100i	0.712870	+	0.701296i
$848$	14.1747			0.486760
$849$			5.80703i			0.199297i
$850$			1.71947i			0.0589774i
$851$	−14.6039			−0.500616
$852$			1.48280i			0.0507999i
$853$	−15.9526			−0.546206			−0.273103	−	0.961985i	$-0.588050\pi$
$853$	−15.9526			−0.546206			−0.273103	+	0.961985i	$0.588050\pi$
$854$	3.19918	+	9.88101i	0.109474	+	0.338121i
$855$			2.57562i			0.0880842i
$856$	7.56558			0.258586
$857$	−24.7265			−0.844642			−0.422321	−	0.906446i	$-0.638784\pi$
$857$	−24.7265			−0.844642			−0.422321	+	0.906446i	$0.638784\pi$
$858$	7.53470	−	12.4238i	0.257231	−	0.424141i
$859$			42.5190i			1.45073i	0.688365	+	0.725364i	$0.258329\pi$
$859$			42.5190i			1.45073i	−0.688365	+	0.725364i	$0.741671\pi$
$860$	2.72211			0.0928230
$861$	3.64273	+	11.2510i	0.124144	+	0.383432i
$862$	29.5856			1.00769
$863$	21.7576			0.740639			0.370319	−	0.928904i	$-0.379248\pi$
$863$	21.7576			0.740639			0.370319	+	0.928904i	$0.379248\pi$
$864$	−2.19474			−0.0746666
$865$			6.13078i			0.208453i
$866$	35.6952			1.21297
$867$		−	15.7647i		−	0.535396i
$868$	1.48666	+	4.59172i	0.0504606	+	0.155853i
$869$	13.5392	+	8.21118i	0.459286	+	0.278545i
$870$	−3.88135			−0.131590
$871$	−41.6361			−1.41079
$872$	−32.4145			−1.09769
$873$		−	7.73585i		−	0.261819i
$874$			17.6066i			0.595552i
$875$	0.814965	+	2.51711i	0.0275508	+	0.0850938i
$876$			1.91499i			0.0647015i
$877$		−	47.3365i		−	1.59844i	−0.601039	−	0.799220i	$-0.705246\pi$
$877$		−	47.3365i		−	1.59844i	0.601039	−	0.799220i	$-0.294754\pi$
$878$			39.6204i			1.33712i
$879$		−	23.9606i		−	0.808172i
$880$	−13.1356	−	7.96639i	−0.442800	−	0.268547i
$881$			17.6494i			0.594624i	0.954780	+	0.297312i	$0.0960902\pi$
$881$			17.6494i			0.594624i	−0.954780	+	0.297312i	$0.903910\pi$
$882$	−6.34707	−	8.77432i	−0.213717	−	0.295447i
$883$	−4.14662			−0.139545			−0.0697724	−	0.997563i	$-0.522227\pi$
$883$	−4.14662			−0.139545			−0.0697724	+	0.997563i	$0.522227\pi$
$884$	−1.23804			−0.0416400
$885$			4.55256i			0.153033i
$886$		−	14.9138i		−	0.501038i
$887$	−43.7710			−1.46969			−0.734843	−	0.678237i	$-0.762744\pi$
$887$	−43.7710			−1.46969			−0.734843	+	0.678237i	$0.762744\pi$
$888$	−8.21492			−0.275675
$889$	−14.1589	−	43.7313i	−0.474874	−	1.46670i
$890$		−	0.910977i		−	0.0305360i
$891$	1.71987	−	2.83585i	0.0576178	−	0.0950045i
$892$		−	8.34709i		−	0.279481i
$893$		−	8.23656i		−	0.275626i
$894$			5.59188i			0.187020i
$895$		−	25.1893i		−	0.841984i
$896$	10.9763	+	33.9015i	0.366693	+	1.13257i
$897$			12.5129i			0.417794i
$898$			55.9025i			1.86549i
$899$	11.6353			0.388059
$900$	−0.393347			−0.0131116
$901$	3.40126			0.113312
$902$	−19.6098	−	11.8929i	−0.652936	−	0.395989i
$903$	17.4193	−	5.63985i	0.579678	−	0.187682i
$904$		−	27.6120i		−	0.918362i
$905$	3.44629			0.114559
$906$			14.2974i			0.475000i
$907$	−30.0208			−0.996824			−0.498412	−	0.866940i	$-0.666083\pi$
$907$	−30.0208			−0.996824			−0.498412	+	0.866940i	$0.666083\pi$
$908$	2.64070			0.0876346
$909$	−14.3930			−0.477385
$910$	−11.0274	+	3.57034i	−0.365554	+	0.118356i
$911$	26.2565			0.869916			0.434958	−	0.900451i	$-0.356763\pi$
$911$	26.2565			0.869916			0.434958	+	0.900451i	$0.356763\pi$
$912$			11.9302i			0.395048i
$913$	−24.6259	+	40.6051i	−0.814999	+	1.34383i
$914$	42.3544			1.40096
$915$	2.53745			0.0838854
$916$		−	10.2177i		−	0.337601i
$917$	−37.9079	+	12.2734i	−1.25183	+	0.405305i
$918$	−1.71947			−0.0567511
$919$		−	7.49311i		−	0.247175i	−0.992334	−	0.123587i	$-0.960560\pi$
$919$		−	7.49311i		−	0.247175i	0.992334	−	0.123587i	$-0.0394399\pi$
$920$	10.9829			0.362095
$921$			31.6593i			1.04321i
$922$			26.2932i			0.865920i
$923$	10.6751			0.351377
$924$	3.35910	+	0.793768i	0.110506	+	0.0261131i
$925$	−3.30505			−0.108669
$926$			8.23491i			0.270616i
$927$		−	0.277430i		−	0.00911198i
$928$	−5.50635			−0.180755
$929$			33.5283i			1.10003i	0.835155	+	0.550014i	$0.185378\pi$
$929$			33.5283i			1.10003i	−0.835155	+	0.550014i	$0.814622\pi$
$930$	7.17464			0.235266
$931$	−14.6080	+	10.5670i	−0.478759	+	0.346320i
$932$			0.0269863i			0.000883966i
$933$	−13.8570			−0.453658
$934$	53.0802			1.73684
$935$	−3.15192	−	1.91156i	−0.103079	−	0.0625148i
$936$			7.03870i			0.230067i
$937$	32.9338			1.07590			0.537951	−	0.842976i	$-0.319199\pi$
$937$	32.9338			1.07590			0.537951	+	0.842976i	$0.319199\pi$
$938$	−18.5372	−	57.2542i	−0.605261	−	1.86942i
$939$	19.7086			0.643165
$940$	1.25789			0.0410277
$941$	5.85991			0.191028			0.0955138	−	0.995428i	$-0.469551\pi$
$941$	5.85991			0.191028			0.0955138	+	0.995428i	$0.469551\pi$
$942$		−	9.03939i		−	0.294519i
$943$	19.7505			0.643166
$944$			21.0873i			0.686335i
$945$	−2.51711	+	0.814965i	−0.0818815	+	0.0265108i
$946$	−18.4131	+	30.3609i	−0.598662	+	0.987119i
$947$	35.0508			1.13900			0.569499	−	0.821992i	$-0.307137\pi$
$947$	35.0508			1.13900			0.569499	+	0.821992i	$0.307137\pi$
$948$	1.87796			0.0609933
$949$	13.7866			0.447533
$950$			3.98459i			0.129277i
$951$			12.5949i			0.408419i
$952$	2.25142	+	6.95375i	0.0729689	+	0.225372i
$953$		−	54.5247i		−	1.76623i	−0.469157	−	0.883115i	$-0.655442\pi$
$953$		−	54.5247i		−	1.76623i	0.469157	−	0.883115i	$-0.344558\pi$
$954$			4.73423i			0.153276i
$955$		−	10.4878i		−	0.339377i
$956$		−	8.63620i		−	0.279315i
$957$	4.31495	−	7.11481i	0.139483	−	0.229989i
$958$			64.6861i			2.08991i
$959$	−10.9081	+	3.53172i	−0.352241	+	0.114045i
$960$	5.86858			0.189408
$961$	9.49229			0.306203
$962$		−	14.4793i		−	0.466833i
$963$			3.04381i			0.0980853i
$964$	1.49566			0.0481719
$965$	−8.80647			−0.283490
$966$	−17.2066	+	5.57100i	−0.553614	+	0.179244i
$967$			51.3259i			1.65053i	0.564746	+	0.825265i	$0.308974\pi$
$967$			51.3259i			1.65053i	−0.564746	+	0.825265i	$0.691026\pi$
$968$	24.2457	−	12.6368i	0.779285	−	0.406163i
$969$			2.86269i			0.0919627i
$970$		−	11.9677i		−	0.384260i
$971$			54.7672i			1.75756i	0.477223	+	0.878782i	$0.341643\pi$
$971$			54.7672i			1.75756i	−0.477223	+	0.878782i	$0.658357\pi$
$972$		−	0.393347i		−	0.0126166i
$973$	−27.5758	+	8.92824i	−0.884041	+	0.286226i
$974$		−	55.6091i		−	1.78183i
$975$			2.83183i			0.0906912i
$976$	11.7534			0.376217
$977$	−4.96135			−0.158728			−0.0793638	−	0.996846i	$-0.525289\pi$
$977$	−4.96135			−0.158728			−0.0793638	+	0.996846i	$0.525289\pi$
$978$	15.0959			0.482715
$979$	1.66989	+	1.01275i	0.0533699	+	0.0323675i
$980$	−1.61379	−	2.23093i	−0.0515506	−	0.0712646i
$981$		−	13.0411i		−	0.416371i
$982$	−57.3973			−1.83162
$983$			5.00619i			0.159673i	0.996808	+	0.0798363i	$0.0254397\pi$
$983$			5.00619i			0.159673i	−0.996808	+	0.0798363i	$0.974560\pi$
$984$	11.1100			0.354173
$985$	−3.67764			−0.117180
$986$	−4.31395			−0.137384
$987$	8.04946	−	2.60618i	0.256217	−	0.0829555i
$988$	−2.86896			−0.0912739
$989$		−	30.5788i		−	0.972348i
$990$	2.66072	−	4.38719i	0.0845631	−	0.139434i
$991$	−52.4293			−1.66547			−0.832735	−	0.553671i	$-0.813226\pi$
$991$	−52.4293			−1.66547			−0.832735	+	0.553671i	$0.813226\pi$
$992$	10.1784			0.323165
$993$		−	12.5054i		−	0.396847i
$994$	4.75278	+	14.6795i	0.150749	+	0.465605i
$995$	−17.7841			−0.563793
$996$			5.63214i			0.178461i
$997$	−5.93448			−0.187947			−0.0939734	−	0.995575i	$-0.529957\pi$
$997$	−5.93448			−0.187947			−0.0939734	+	0.995575i	$0.529957\pi$
$998$			34.6410i			1.09654i
$999$		−	3.30505i		−	0.104567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.i.d.76.14	yes	32
7.6	odd	2	inner	1155.2.i.d.76.20	yes	32
11.10	odd	2	inner	1155.2.i.d.76.19	yes	32
77.76	even	2	inner	1155.2.i.d.76.13	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.i.d.76.13	✓	32	77.76	even	2	inner
1155.2.i.d.76.14	yes	32	1.1	even	1	trivial
1155.2.i.d.76.19	yes	32	11.10	odd	2	inner
1155.2.i.d.76.20	yes	32	7.6	odd	2	inner

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.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.54704i q^{2} +1.00000i q^{3} -0.393347 q^{4} +1.00000i q^{5} -1.54704 q^{6} +(-2.51711 + 0.814965i) q^{7} +2.48556i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.54704i q^{2} +1.00000i q^{3} -0.393347 q^{4} +1.00000i q^{5} -1.54704 q^{6} +(-2.51711 + 0.814965i) q^{7} +2.48556i q^{8} -1.00000 q^{9} -1.54704 q^{10} +(1.71987 - 2.83585i) q^{11} -0.393347i q^{12} -2.83183 q^{13} +(-1.26079 - 3.89408i) q^{14} -1.00000 q^{15} -4.63197 q^{16} -1.11146 q^{17} -1.54704i q^{18} -2.57562 q^{19} -0.393347i q^{20} +(-0.814965 - 2.51711i) q^{21} +(4.38719 + 2.66072i) q^{22} -4.41867 q^{23} -2.48556 q^{24} -1.00000 q^{25} -4.38097i q^{26} -1.00000i q^{27} +(0.990098 - 0.320564i) q^{28} -2.50888i q^{29} -1.54704i q^{30} +4.63764i q^{31} -2.19474i q^{32} +(2.83585 + 1.71987i) q^{33} -1.71947i q^{34} +(-0.814965 - 2.51711i) q^{35} +0.393347 q^{36} +3.30505 q^{37} -3.98459i q^{38} -2.83183i q^{39} -2.48556 q^{40} -4.46980 q^{41} +(3.89408 - 1.26079i) q^{42} +6.92036i q^{43} +(-0.676507 + 1.11547i) q^{44} -1.00000i q^{45} -6.83588i q^{46} +3.19790i q^{47} -4.63197i q^{48} +(5.67167 - 4.10271i) q^{49} -1.54704i q^{50} -1.11146i q^{51} +1.11389 q^{52} -3.06018 q^{53} +1.54704 q^{54} +(2.83585 + 1.71987i) q^{55} +(-2.02565 - 6.25643i) q^{56} -2.57562i q^{57} +3.88135 q^{58} -4.55256i q^{59} +0.393347 q^{60} -2.53745 q^{61} -7.17464 q^{62} +(2.51711 - 0.814965i) q^{63} -5.86858 q^{64} -2.83183i q^{65} +(-2.66072 + 4.38719i) q^{66} +14.7029 q^{67} +0.437189 q^{68} -4.41867i q^{69} +(3.89408 - 1.26079i) q^{70} -3.76969 q^{71} -2.48556i q^{72} -4.86845 q^{73} +5.11306i q^{74} -1.00000i q^{75} +1.01311 q^{76} +(-2.01798 + 8.53977i) q^{77} +4.38097 q^{78} +4.77430i q^{79} -4.63197i q^{80} +1.00000 q^{81} -6.91498i q^{82} -14.3185 q^{83} +(0.320564 + 0.990098i) q^{84} -1.11146i q^{85} -10.7061 q^{86} +2.50888 q^{87} +(7.04869 + 4.27485i) q^{88} +0.588850i q^{89} +1.54704 q^{90} +(7.12803 - 2.30784i) q^{91} +1.73807 q^{92} -4.63764 q^{93} -4.94729 q^{94} -2.57562i q^{95} +2.19474 q^{96} +7.73585i q^{97} +(6.34707 + 8.77432i) q^{98} +(-1.71987 + 2.83585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) \) 32 * q - 36 * q^4 - 32 * q^9	\( 32 q - 36 q^{4} - 32 q^{9} - 8 q^{11} - 28 q^{14} - 32 q^{15} + 44 q^{16} - 12 q^{22} + 4 q^{23} - 32 q^{25} + 36 q^{36} - 16 q^{37} + 8 q^{42} + 56 q^{44} + 16 q^{49} - 20 q^{53} + 52 q^{56} - 48 q^{58} + 36 q^{60} - 156 q^{64} - 72 q^{67} + 8 q^{70} + 48 q^{71} - 20 q^{77} - 8 q^{78} + 32 q^{81} + 56 q^{86} + 4 q^{88} - 80 q^{91} + 64 q^{92} + 32 q^{93} + 8 q^{99}+O(q^{100}) \) 32 * q - 36 * q^4 - 32 * q^9 - 8 * q^11 - 28 * q^14 - 32 * q^15 + 44 * q^16 - 12 * q^22 + 4 * q^23 - 32 * q^25 + 36 * q^36 - 16 * q^37 + 8 * q^42 + 56 * q^44 + 16 * q^49 - 20 * q^53 + 52 * q^56 - 48 * q^58 + 36 * q^60 - 156 * q^64 - 72 * q^67 + 8 * q^70 + 48 * q^71 - 20 * q^77 - 8 * q^78 + 32 * q^81 + 56 * q^86 + 4 * q^88 - 80 * q^91 + 64 * q^92 + 32 * q^93 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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