LMFDB - Embedded newform 1155.2.i.c.76.6

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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.6
Root			$0.644389 - 0.983224i$ of defining polynomial
Character	$\chi$	$=$	1155.76
Dual form			1155.2.i.c.76.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.47195i q^{2} +1.00000i q^{3} -0.166634 q^{4} -1.00000i q^{5} +1.47195 q^{6} +(-1.47195 + 2.19849i) q^{7} -2.69862i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.47195i q^{2} +1.00000i q^{3} -0.166634 q^{4} -1.00000i q^{5} +1.47195 q^{6} +(-1.47195 + 2.19849i) q^{7} -2.69862i q^{8} -1.00000 q^{9} -1.47195 q^{10} +(-1.23607 - 3.07768i) q^{11} -0.166634i q^{12} -1.98480 q^{13} +(3.23607 + 2.16663i) q^{14} +1.00000 q^{15} -4.30550 q^{16} -0.152649 q^{17} +1.47195i q^{18} -6.00272 q^{19} +0.166634i q^{20} +(-2.19849 - 1.47195i) q^{21} +(-4.53019 + 1.81943i) q^{22} +1.16663 q^{23} +2.69862 q^{24} -1.00000 q^{25} +2.92152i q^{26} -1.00000i q^{27} +(0.245277 - 0.366344i) q^{28} -5.77630i q^{29} -1.47195i q^{30} +0.696828i q^{31} +0.940237i q^{32} +(3.07768 - 1.23607i) q^{33} +0.224692i q^{34} +(2.19849 + 1.47195i) q^{35} +0.166634 q^{36} +0.696828 q^{37} +8.83570i q^{38} -1.98480i q^{39} -2.69862 q^{40} -7.38204 q^{41} +(-2.16663 + 3.23607i) q^{42} -10.9060i q^{43} +(0.205971 + 0.512848i) q^{44} +1.00000i q^{45} -1.71723i q^{46} +10.6968i q^{47} -4.30550i q^{48} +(-2.66673 - 6.47214i) q^{49} +1.47195i q^{50} -0.152649i q^{51} +0.330735 q^{52} -4.56029 q^{53} -1.47195 q^{54} +(-3.07768 + 1.23607i) q^{55} +(5.93290 + 3.97223i) q^{56} -6.00272i q^{57} -8.50243 q^{58} -7.53019i q^{59} -0.166634 q^{60} -3.81694 q^{61} +1.02570 q^{62} +(1.47195 - 2.19849i) q^{63} -7.22702 q^{64} +1.98480i q^{65} +(-1.81943 - 4.53019i) q^{66} +3.19460 q^{67} +0.0254366 q^{68} +1.16663i q^{69} +(2.16663 - 3.23607i) q^{70} -0.224692 q^{71} +2.69862i q^{72} +0.732688 q^{73} -1.02570i q^{74} -1.00000i q^{75} +1.00026 q^{76} +(8.58569 + 1.81271i) q^{77} -2.92152 q^{78} +2.98506i q^{79} +4.30550i q^{80} +1.00000 q^{81} +10.8660i q^{82} +9.97231 q^{83} +(0.366344 + 0.245277i) q^{84} +0.152649i q^{85} -16.0530 q^{86} +5.77630 q^{87} +(-8.30550 + 3.33568i) q^{88} -12.0023i q^{89} +1.47195 q^{90} +(2.92152 - 4.36356i) q^{91} -0.194401 q^{92} -0.696828 q^{93} +15.7452 q^{94} +6.00272i q^{95} -0.940237 q^{96} +4.13654i q^{97} +(-9.52666 + 3.92529i) q^{98} +(1.23607 + 3.07768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) $ 16 * q - 24 * q^4 - 16 * q^9	$ 16 q - 24 q^{4} - 16 q^{9} + 16 q^{11} + 16 q^{14} + 16 q^{15} + 24 q^{16} + 40 q^{23} - 16 q^{25} + 24 q^{36} - 40 q^{37} - 56 q^{42} - 24 q^{44} + 8 q^{53} + 8 q^{56} + 72 q^{58} - 24 q^{60} + 8 q^{64} + 80 q^{67} + 56 q^{70} - 24 q^{71} - 16 q^{78} + 16 q^{81} - 8 q^{86} - 40 q^{88} + 16 q^{91} - 160 q^{92} + 40 q^{93} - 16 q^{99}+O(q^{100}) $ 16 * q - 24 * q^4 - 16 * q^9 + 16 * q^11 + 16 * q^14 + 16 * q^15 + 24 * q^16 + 40 * q^23 - 16 * q^25 + 24 * q^36 - 40 * q^37 - 56 * q^42 - 24 * q^44 + 8 * q^53 + 8 * q^56 + 72 * q^58 - 24 * q^60 + 8 * q^64 + 80 * q^67 + 56 * q^70 - 24 * q^71 - 16 * q^78 + 16 * q^81 - 8 * q^86 - 40 * q^88 + 16 * q^91 - 160 * q^92 + 40 * q^93 - 16 * 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 $

$2$		−	1.47195i		−	1.04083i	−0.853915	−	0.520413i	$-0.825778\pi$
$2$		−	1.47195i		−	1.04083i	0.853915	−	0.520413i	$-0.174222\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.166634			−0.0833172
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.47195			0.600921
$7$	−1.47195	+	2.19849i	−0.556344	+	0.830952i
$7$	−1.47195	+	2.19849i	−0.556344	+	0.830952i
$8$		−	2.69862i		−	0.954107i
$9$	−1.00000			−0.333333
$10$	−1.47195			−0.465471
$11$	−1.23607	−	3.07768i	−0.372689	−	0.927957i
$11$	−1.23607	−	3.07768i	−0.372689	−	0.927957i
$12$		−	0.166634i		−	0.0481032i
$13$	−1.98480			−0.550484			−0.275242	−	0.961375i	$-0.588758\pi$
$13$	−1.98480			−0.550484			−0.275242	+	0.961375i	$0.588758\pi$
$14$	3.23607	+	2.16663i	0.864876	+	0.579057i
$15$	1.00000			0.258199
$16$	−4.30550			−1.07638
$17$	−0.152649			−0.0370229			−0.0185114	−	0.999829i	$-0.505893\pi$
$17$	−0.152649			−0.0370229			−0.0185114	+	0.999829i	$0.505893\pi$
$18$			1.47195i			0.346942i
$19$	−6.00272			−1.37712			−0.688559	−	0.725180i	$-0.741756\pi$
$19$	−6.00272			−1.37712			−0.688559	+	0.725180i	$0.741756\pi$
$20$			0.166634i			0.0372606i
$21$	−2.19849	−	1.47195i	−0.479750	−	0.321206i
$22$	−4.53019	+	1.81943i	−0.965841	+	0.387904i
$23$	1.16663			0.243260			0.121630	−	0.992576i	$-0.461188\pi$
$23$	1.16663			0.243260			0.121630	+	0.992576i	$0.461188\pi$
$24$	2.69862			0.550854
$25$	−1.00000			−0.200000
$26$			2.92152i			0.572957i
$27$		−	1.00000i		−	0.192450i
$28$	0.245277	−	0.366344i	0.0463530	−	0.0692325i
$29$		−	5.77630i		−	1.07263i	−0.844017	−	0.536316i	$-0.819815\pi$
$29$		−	5.77630i		−	1.07263i	0.844017	−	0.536316i	$-0.180185\pi$
$30$		−	1.47195i		−	0.268740i
$31$			0.696828i			0.125154i	0.998040	+	0.0625770i	$0.0199319\pi$
$31$			0.696828i			0.125154i	−0.998040	+	0.0625770i	$0.980068\pi$
$32$			0.940237i			0.166212i
$33$	3.07768	−	1.23607i	0.535756	−	0.215172i
$34$			0.224692i			0.0385344i
$35$	2.19849	+	1.47195i	0.371613	+	0.248805i
$36$	0.166634			0.0277724
$37$	0.696828			0.114558			0.0572789	−	0.998358i	$-0.481758\pi$
$37$	0.696828			0.114558			0.0572789	+	0.998358i	$0.481758\pi$
$38$			8.83570i			1.43334i
$39$		−	1.98480i		−	0.317822i
$40$	−2.69862			−0.426689
$41$	−7.38204			−1.15288			−0.576440	−	0.817139i	$-0.695559\pi$
$41$	−7.38204			−1.15288			−0.576440	+	0.817139i	$0.695559\pi$
$42$	−2.16663	+	3.23607i	−0.334319	+	0.499336i
$43$		−	10.9060i		−	1.66315i	−0.555416	−	0.831573i	$-0.687441\pi$
$43$		−	10.9060i		−	1.66315i	0.555416	−	0.831573i	$-0.312559\pi$
$44$	0.205971	+	0.512848i	0.0310513	+	0.0773147i
$45$			1.00000i			0.149071i
$46$		−	1.71723i		−	0.253191i
$47$			10.6968i			1.56029i	0.625597	+	0.780146i	$0.284855\pi$
$47$			10.6968i			1.56029i	−0.625597	+	0.780146i	$0.715145\pi$
$48$		−	4.30550i		−	0.621446i
$49$	−2.66673	−	6.47214i	−0.380962	−	0.924591i
$50$			1.47195i			0.208165i
$51$		−	0.152649i		−	0.0213752i
$52$	0.330735			0.0458647
$53$	−4.56029			−0.626404			−0.313202	−	0.949687i	$-0.601402\pi$
$53$	−4.56029			−0.626404			−0.313202	+	0.949687i	$0.601402\pi$
$54$	−1.47195			−0.200307
$55$	−3.07768	+	1.23607i	−0.414995	+	0.166671i
$56$	5.93290	+	3.97223i	0.792817	+	0.530812i
$57$		−	6.00272i		−	0.795079i
$58$	−8.50243			−1.11642
$59$		−	7.53019i		−	0.980348i	−0.871625	−	0.490174i	$-0.836933\pi$
$59$		−	7.53019i		−	0.980348i	0.871625	−	0.490174i	$-0.163067\pi$
$60$	−0.166634			−0.0215124
$61$	−3.81694			−0.488710			−0.244355	−	0.969686i	$-0.578576\pi$
$61$	−3.81694			−0.488710			−0.244355	+	0.969686i	$0.578576\pi$
$62$	1.02570			0.130263
$63$	1.47195	−	2.19849i	0.185448	−	0.276984i
$64$	−7.22702			−0.903378
$65$			1.98480i			0.246184i
$66$	−1.81943	−	4.53019i	−0.223956	−	0.557628i
$67$	3.19460			0.390282			0.195141	−	0.980775i	$-0.437484\pi$
$67$	3.19460			0.390282			0.195141	+	0.980775i	$0.437484\pi$
$68$	0.0254366			0.00308464
$69$			1.16663i			0.140446i
$70$	2.16663	−	3.23607i	0.258962	−	0.386784i
$71$	−0.224692			−0.0266660			−0.0133330	−	0.999911i	$-0.504244\pi$
$71$	−0.224692			−0.0266660			−0.0133330	+	0.999911i	$0.504244\pi$
$72$			2.69862i			0.318036i
$73$	0.732688			0.0857547			0.0428773	−	0.999080i	$-0.486348\pi$
$73$	0.732688			0.0857547			0.0428773	+	0.999080i	$0.486348\pi$
$74$		−	1.02570i		−	0.119235i
$75$		−	1.00000i		−	0.115470i
$76$	1.00026			0.114738
$77$	8.58569	+	1.81271i	0.978430	+	0.206577i
$78$	−2.92152			−0.330797
$79$			2.98506i			0.335845i	0.985800	+	0.167922i	$0.0537058\pi$
$79$			2.98506i			0.335845i	−0.985800	+	0.167922i	$0.946294\pi$
$80$			4.30550i			0.481370i
$81$	1.00000			0.111111
$82$			10.8660i			1.19995i
$83$	9.97231			1.09460			0.547302	−	0.836935i	$-0.315655\pi$
$83$	9.97231			1.09460			0.547302	+	0.836935i	$0.315655\pi$
$84$	0.366344	+	0.245277i	0.0399714	+	0.0267619i
$85$			0.152649i			0.0165571i
$86$	−16.0530			−1.73104
$87$	5.77630			0.619285
$88$	−8.30550	+	3.33568i	−0.885369	+	0.355585i
$89$		−	12.0023i		−	1.27224i	−0.771588	−	0.636122i	$-0.780537\pi$
$89$		−	12.0023i		−	1.27224i	0.771588	−	0.636122i	$-0.219463\pi$
$90$	1.47195			0.155157
$91$	2.92152	−	4.36356i	0.306259	−	0.457425i
$92$	−0.194401			−0.0202677
$93$	−0.696828			−0.0722577
$94$	15.7452			1.62399
$95$			6.00272i			0.615866i
$96$	−0.940237			−0.0959626
$97$			4.13654i			0.420002i	0.977701	+	0.210001i	$0.0673467\pi$
$97$			4.13654i			0.420002i	−0.977701	+	0.210001i	$0.932653\pi$
$98$	−9.52666	+	3.92529i	−0.962337	+	0.396514i
$99$	1.23607	+	3.07768i	0.124230	+	0.309319i
$100$	0.166634			0.0166634
$101$	−1.45309			−0.144587			−0.0722937	−	0.997383i	$-0.523032\pi$
$101$	−1.45309			−0.144587			−0.0722937	+	0.997383i	$0.523032\pi$
$102$	−0.224692			−0.0222478
$103$		−	7.66906i		−	0.755655i	−0.925876	−	0.377828i	$-0.876671\pi$
$103$		−	7.66906i		−	0.755655i	0.925876	−	0.377828i	$-0.123329\pi$
$104$			5.35621i			0.525220i
$105$	−1.47195	+	2.19849i	−0.143648	+	0.214551i
$106$			6.71252i			0.651977i
$107$			9.30024i			0.899088i	0.893258	+	0.449544i	$0.148414\pi$
$107$			9.30024i			0.899088i	−0.893258	+	0.449544i	$0.851586\pi$
$108$			0.166634i			0.0160344i
$109$			5.92895i			0.567891i	0.958840	+	0.283945i	$0.0916434\pi$
$109$			5.92895i			0.567891i	−0.958840	+	0.283945i	$0.908357\pi$
$110$	1.81943	+	4.53019i	0.173476	+	0.431937i
$111$			0.696828i			0.0661400i
$112$	6.33748	−	9.46561i	0.598836	−	0.894416i
$113$	−15.8938			−1.49516			−0.747579	−	0.664173i	$-0.768784\pi$
$113$	−15.8938			−1.49516			−0.747579	+	0.664173i	$0.768784\pi$
$114$	−8.83570			−0.827539
$115$		−	1.16663i		−	0.108789i
$116$			0.962531i			0.0893687i
$117$	1.98480			0.183495
$118$	−11.0841			−1.02037
$119$	0.224692	−	0.335598i	0.0205975	−	0.0307642i
$120$		−	2.69862i		−	0.246349i
$121$	−7.94427	+	7.60845i	−0.722207	+	0.691677i
$122$			5.61835i			0.508661i
$123$		−	7.38204i		−	0.665616i
$124$		−	0.116115i		−	0.0104275i
$125$			1.00000i			0.0894427i
$126$	−3.23607	−	2.16663i	−0.288292	−	0.193019i
$127$		−	0.646633i		−	0.0573794i	−0.999588	−	0.0286897i	$-0.990867\pi$
$127$		−	0.646633i		−	0.0573794i	0.999588	−	0.0286897i	$-0.00913347\pi$
$128$			12.5183i			1.10647i
$129$	10.9060			0.960218
$130$	2.92152			0.256234
$131$	−15.7863			−1.37926			−0.689630	−	0.724162i	$-0.742227\pi$
$131$	−15.7863			−1.37926			−0.689630	+	0.724162i	$0.742227\pi$
$132$	−0.512848	+	0.205971i	−0.0446377	+	0.0179275i
$133$	8.83570	−	13.1969i	0.766152	−	1.14432i
$134$		−	4.70228i		−	0.406215i
$135$	−1.00000			−0.0860663
$136$			0.411943i			0.0353238i
$137$	22.4768			1.92032			0.960161	−	0.279447i	$-0.0901511\pi$
$137$	22.4768			1.92032			0.960161	+	0.279447i	$0.0901511\pi$
$138$	1.71723			0.146180
$139$	6.88806			0.584237			0.292119	−	0.956382i	$-0.405640\pi$
$139$	6.88806			0.584237			0.292119	+	0.956382i	$0.405640\pi$
$140$	−0.366344	−	0.245277i	−0.0309617	−	0.0207297i
$141$	−10.6968			−0.900835
$142$			0.330735i			0.0277547i
$143$	2.45334	+	6.10858i	0.205159	+	0.510825i
$144$	4.30550			0.358792
$145$	−5.77630			−0.479696
$146$		−	1.07848i		−	0.0892556i
$147$	6.47214	−	2.66673i	0.533813	−	0.219948i
$148$	−0.116115			−0.00954463
$149$		−	3.63886i		−	0.298107i	−0.988829	−	0.149053i	$-0.952377\pi$
$149$		−	3.63886i		−	0.298107i	0.988829	−	0.149053i	$-0.0476226\pi$
$150$	−1.47195			−0.120184
$151$			23.0606i			1.87665i	0.345758	+	0.938324i	$0.387622\pi$
$151$			23.0606i			1.87665i	−0.345758	+	0.938324i	$0.612378\pi$
$152$			16.1991i			1.31392i
$153$	0.152649			0.0123410
$154$	2.66821	−	12.6377i	0.215011	−	1.01837i
$155$	0.696828			0.0559706
$156$			0.330735i			0.0264800i
$157$			7.14100i			0.569914i	0.958540	+	0.284957i	$0.0919793\pi$
$157$			7.14100i			0.569914i	−0.958540	+	0.284957i	$0.908021\pi$
$158$	4.39385			0.349556
$159$		−	4.56029i		−	0.361655i
$160$	0.940237			0.0743323
$161$	−1.71723	+	2.56484i	−0.135336	+	0.202137i
$162$		−	1.47195i		−	0.115647i
$163$	8.50243			0.665961			0.332981	−	0.942934i	$-0.391946\pi$
$163$	8.50243			0.665961			0.332981	+	0.942934i	$0.391946\pi$
$164$	1.23010			0.0960548
$165$	−1.23607	−	3.07768i	−0.0962278	−	0.239597i
$166$		−	14.6787i		−	1.13929i
$167$	8.32885			0.644506			0.322253	−	0.946654i	$-0.395560\pi$
$167$	8.32885			0.644506			0.322253	+	0.946654i	$0.395560\pi$
$168$	−3.97223	+	5.93290i	−0.306464	+	0.457733i
$169$	−9.06058			−0.696968
$170$	0.224692			0.0172331
$171$	6.00272			0.459039
$172$			1.81731i			0.138569i
$173$	18.9312			1.43931			0.719657	−	0.694330i	$-0.244299\pi$
$173$	18.9312			1.43931			0.719657	+	0.694330i	$0.244299\pi$
$174$		−	8.50243i		−	0.644567i
$175$	1.47195	−	2.19849i	0.111269	−	0.166190i
$176$	5.32189	+	13.2510i	0.401153	+	0.998830i
$177$	7.53019			0.566004
$178$	−17.6668			−1.32418
$179$	19.5628			1.46219			0.731097	−	0.682274i	$-0.239009\pi$
$179$	19.5628			1.46219			0.731097	+	0.682274i	$0.239009\pi$
$180$		−	0.166634i		−	0.0124202i
$181$		−	18.6110i		−	1.38334i	−0.722211	−	0.691672i	$-0.756874\pi$
$181$		−	18.6110i		−	1.38334i	0.722211	−	0.691672i	$-0.243126\pi$
$182$	−6.42294	−	4.30033i	−0.476100	−	0.318762i
$183$		−	3.81694i		−	0.282157i
$184$		−	3.14830i		−	0.232096i
$185$		−	0.696828i		−	0.0512318i
$186$			1.02570i			0.0752076i
$187$	0.188685	+	0.469806i	0.0137980	+	0.0343556i
$188$		−	1.78246i		−	0.129999i
$189$	2.19849	+	1.47195i	0.159917	+	0.107069i
$190$	8.83570			0.641009
$191$	11.4723			0.830109			0.415054	−	0.909797i	$-0.363763\pi$
$191$	11.4723			0.830109			0.415054	+	0.909797i	$0.363763\pi$
$192$		−	7.22702i		−	0.521565i
$193$			2.94390i			0.211906i	0.994371	+	0.105953i	$0.0337894\pi$
$193$			2.94390i			0.211906i	−0.994371	+	0.105953i	$0.966211\pi$
$194$	6.08877			0.437148
$195$	−1.98480			−0.142134
$196$	0.444369	+	1.07848i	0.0317406	+	0.0770343i
$197$		−	22.8254i		−	1.62624i	−0.582097	−	0.813120i	$-0.697767\pi$
$197$		−	22.8254i		−	1.62624i	0.582097	−	0.813120i	$-0.302233\pi$
$198$	4.53019	−	1.81943i	0.321947	−	0.129301i
$199$			5.06039i			0.358721i	0.983783	+	0.179361i	$0.0574029\pi$
$199$			5.06039i			0.358721i	−0.983783	+	0.179361i	$0.942597\pi$
$200$			2.69862i			0.190821i
$201$			3.19460i			0.225329i
$202$			2.13887i			0.150490i
$203$	12.6992	+	8.50243i	0.891306	+	0.596753i
$204$			0.0254366i			0.00178092i
$205$			7.38204i			0.515584i
$206$	−11.2885			−0.786505
$207$	−1.16663			−0.0810867
$208$	8.54555			0.592527
$209$	7.41977	+	18.4745i	0.513236	+	1.27791i
$210$	3.23607	+	2.16663i	0.223310	+	0.149512i
$211$		−	12.9488i		−	0.891433i	−0.895174	−	0.445717i	$-0.852949\pi$
$211$		−	12.9488i		−	0.891433i	0.895174	−	0.445717i	$-0.147051\pi$
$212$	0.759901			0.0521902
$213$		−	0.224692i		−	0.0153956i
$214$	13.6895			0.935794
$215$	−10.9060			−0.743781
$216$	−2.69862			−0.183618
$217$	−1.53197	−	1.02570i	−0.103997	−	0.0696287i
$218$	8.72712			0.591075
$219$			0.732688i			0.0495105i
$220$	0.512848	−	0.205971i	0.0345762	−	0.0138866i
$221$	0.302978			0.0203805
$222$	1.02570			0.0688402
$223$		−	4.33560i		−	0.290333i	−0.989407	−	0.145167i	$-0.953628\pi$
$223$		−	4.33560i		−	0.290333i	0.989407	−	0.145167i	$-0.0463718\pi$
$224$	−2.06710	−	1.38398i	−0.138114	−	0.0924712i
$225$	1.00000			0.0666667
$226$			23.3948i			1.55620i
$227$	−5.85519			−0.388623			−0.194311	−	0.980940i	$-0.562247\pi$
$227$	−5.85519			−0.388623			−0.194311	+	0.980940i	$0.562247\pi$
$228$			1.00026i			0.0662438i
$229$		−	21.0348i		−	1.39002i	−0.719002	−	0.695008i	$-0.755401\pi$
$229$		−	21.0348i		−	1.39002i	0.719002	−	0.695008i	$-0.244599\pi$
$230$	−1.71723			−0.113231
$231$	−1.81271	+	8.58569i	−0.119267	+	0.564897i
$232$	−15.5881			−1.02341
$233$			9.33797i			0.611751i	0.952072	+	0.305875i	$0.0989491\pi$
$233$			9.33797i			0.611751i	−0.952072	+	0.305875i	$0.901051\pi$
$234$		−	2.92152i		−	0.190986i
$235$	10.6968			0.697784
$236$			1.25479i			0.0816798i
$237$	−2.98506			−0.193900
$238$	−0.493984	−	0.330735i	−0.0320202	−	0.0214384i
$239$			3.87039i			0.250355i	0.992134	+	0.125177i	$0.0399500\pi$
$239$			3.87039i			0.250355i	−0.992134	+	0.125177i	$0.960050\pi$
$240$	−4.30550			−0.277919
$241$	−2.19806			−0.141590			−0.0707949	−	0.997491i	$-0.522554\pi$
$241$	−2.19806			−0.141590			−0.0707949	+	0.997491i	$0.522554\pi$
$242$	11.1993	+	11.6936i	0.719915	+	0.751691i
$243$			1.00000i			0.0641500i
$244$	0.636034			0.0407179
$245$	−6.47214	+	2.66673i	−0.413490	+	0.170371i
$246$	−10.8660			−0.692790
$247$	11.9142			0.758081
$248$	1.88047			0.119410
$249$			9.97231i			0.631970i
$250$	1.47195			0.0930942
$251$			8.53233i			0.538556i	0.963063	+	0.269278i	$0.0867850\pi$
$251$			8.53233i			0.538556i	−0.963063	+	0.269278i	$0.913215\pi$
$252$	−0.245277	+	0.366344i	−0.0154510	+	0.0230775i
$253$	−1.44204	−	3.59053i	−0.0906602	−	0.225735i
$254$	−0.951811			−0.0597219
$255$	−0.152649			−0.00955927
$256$	3.97223			0.248265
$257$		−	1.90952i		−	0.119112i	−0.998225	−	0.0595562i	$-0.981031\pi$
$257$		−	1.90952i		−	0.119112i	0.998225	−	0.0595562i	$-0.0189685\pi$
$258$		−	16.0530i		−	0.999419i
$259$	−1.02570	+	1.53197i	−0.0637336	+	0.0951920i
$260$		−	0.330735i		−	0.0205113i
$261$			5.77630i			0.357544i
$262$			23.2367i			1.43557i
$263$			6.43523i			0.396813i	0.980120	+	0.198407i	$0.0635767\pi$
$263$			6.43523i			0.396813i	−0.980120	+	0.198407i	$0.936423\pi$
$264$	−3.33568	−	8.30550i	−0.205297	−	0.511168i
$265$			4.56029i			0.280136i
$266$	−19.4252	−	13.0057i	−1.19104	−	0.797430i
$267$	12.0023			0.734531
$268$	−0.532329			−0.0325172
$269$		−	17.0025i		−	1.03666i	−0.855180	−	0.518331i	$-0.826553\pi$
$269$		−	17.0025i		−	1.03666i	0.855180	−	0.518331i	$-0.173447\pi$
$270$			1.47195i			0.0895800i
$271$	7.92092			0.481162			0.240581	−	0.970629i	$-0.422662\pi$
$271$	7.92092			0.481162			0.240581	+	0.970629i	$0.422662\pi$
$272$	0.657232			0.0398505
$273$	4.36356	+	2.92152i	0.264095	+	0.176818i
$274$		−	33.0847i		−	1.99872i
$275$	1.23607	+	3.07768i	0.0745377	+	0.185591i
$276$		−	0.194401i		−	0.0117016i
$277$		−	16.1094i		−	0.967921i	−0.875090	−	0.483960i	$-0.839198\pi$
$277$		−	16.1094i		−	0.967921i	0.875090	−	0.483960i	$-0.160802\pi$
$278$		−	10.1389i		−	0.608089i
$279$		−	0.696828i		−	0.0417180i
$280$	3.97223	−	5.93290i	0.237386	−	0.354558i
$281$		−	30.1785i		−	1.80030i	−0.435580	−	0.900150i	$-0.643457\pi$
$281$		−	30.1785i		−	1.80030i	0.435580	−	0.900150i	$-0.356543\pi$
$282$			15.7452i			0.937612i
$283$	1.23896			0.0736487			0.0368244	−	0.999322i	$-0.488276\pi$
$283$	1.23896			0.0736487			0.0368244	+	0.999322i	$0.488276\pi$
$284$	0.0374414			0.00222174
$285$	−6.00272			−0.355570
$286$	8.99151	−	3.61120i	0.531679	−	0.213535i
$287$	10.8660	−	16.2294i	0.641399	−	0.957988i
$288$		−	0.940237i		−	0.0554040i
$289$	−16.9767			−0.998629
$290$			8.50243i			0.499280i
$291$	−4.13654			−0.242488
$292$	−0.122091			−0.00714484
$293$	14.6869			0.858017			0.429008	−	0.903300i	$-0.358863\pi$
$293$	14.6869			0.858017			0.429008	+	0.903300i	$0.358863\pi$
$294$	−3.92529	−	9.52666i	−0.228928	−	0.555606i
$295$	−7.53019			−0.438425
$296$		−	1.88047i		−	0.109300i
$297$	−3.07768	+	1.23607i	−0.178585	+	0.0717239i
$298$	−5.35621			−0.310277
$299$	−2.31553			−0.133911
$300$			0.166634i			0.00962064i
$301$	23.9767	+	16.0530i	1.38199	+	0.925282i
$302$	33.9441			1.95326
$303$		−	1.45309i		−	0.0834776i
$304$	25.8447			1.48230
$305$			3.81694i			0.218558i
$306$		−	0.224692i		−	0.0128448i
$307$	−8.37887			−0.478207			−0.239104	−	0.970994i	$-0.576854\pi$
$307$	−8.37887			−0.478207			−0.239104	+	0.970994i	$0.576854\pi$
$308$	−1.43067	−	0.302059i	−0.0815200	−	0.0172114i
$309$	7.66906			0.436278
$310$		−	1.02570i		−	0.0582556i
$311$		−	29.7543i		−	1.68721i	−0.536961	−	0.843607i	$-0.680428\pi$
$311$		−	29.7543i		−	1.68721i	0.536961	−	0.843607i	$-0.319572\pi$
$312$	−5.35621			−0.303236
$313$		−	23.8681i		−	1.34911i	−0.738226	−	0.674553i	$-0.764336\pi$
$313$		−	23.8681i		−	1.34911i	0.738226	−	0.674553i	$-0.235664\pi$
$314$	10.5112			0.593181
$315$	−2.19849	−	1.47195i	−0.123871	−	0.0829349i
$316$		−	0.497413i		−	0.0279817i
$317$	−5.53252			−0.310737			−0.155369	−	0.987857i	$-0.549657\pi$
$317$	−5.53252			−0.310737			−0.155369	+	0.987857i	$0.549657\pi$
$318$	−6.71252			−0.376419
$319$	−17.7776	+	7.13991i	−0.995357	+	0.399758i
$320$			7.22702i			0.404003i
$321$	−9.30024			−0.519089
$322$	3.77531	+	2.52767i	0.210390	+	0.140862i
$323$	0.916311			0.0509849
$324$	−0.166634			−0.00925746
$325$	1.98480			0.110097
$326$		−	12.5151i		−	0.693149i
$327$	−5.92895			−0.327872
$328$			19.9213i			1.09997i
$329$	−23.5169	−	15.7452i	−1.29653	−	0.868060i
$330$	−4.53019	+	1.81943i	−0.249379	+	0.100156i
$331$	26.3100			1.44613			0.723063	−	0.690782i	$-0.242733\pi$
$331$	26.3100			1.44613			0.723063	+	0.690782i	$0.242733\pi$
$332$	−1.66173			−0.0911992
$333$	−0.696828			−0.0381859
$334$		−	12.2596i		−	0.670818i
$335$		−	3.19460i		−	0.174539i
$336$	9.46561	+	6.33748i	0.516391	+	0.345738i
$337$			13.5700i			0.739206i	0.929190	+	0.369603i	$0.120506\pi$
$337$			13.5700i			0.739206i	−0.929190	+	0.369603i	$0.879494\pi$
$338$			13.3367i			0.725422i
$339$		−	15.8938i		−	0.863230i
$340$		−	0.0254366i		−	0.00137949i
$341$	2.14462	−	0.861327i	0.116137	−	0.0466435i
$342$		−	8.83570i		−	0.477780i
$343$	18.1542	+	3.66387i	0.980236	+	0.197830i
$344$	−29.4311			−1.58682
$345$	1.16663			0.0628095
$346$		−	27.8658i		−	1.49807i
$347$			22.7156i			1.21943i	0.792619	+	0.609717i	$0.208717\pi$
$347$			22.7156i			1.21943i	−0.792619	+	0.609717i	$0.791283\pi$
$348$	−0.962531			−0.0515971
$349$	−31.2114			−1.67071			−0.835354	−	0.549713i	$-0.814737\pi$
$349$	−31.2114			−1.67071			−0.835354	+	0.549713i	$0.814737\pi$
$350$	−3.23607	−	2.16663i	−0.172975	−	0.115811i
$351$			1.98480i			0.105941i
$352$	2.89375	−	1.16220i	0.154238	−	0.0619453i
$353$		−	24.3426i		−	1.29563i	−0.761800	−	0.647813i	$-0.775684\pi$
$353$		−	24.3426i		−	1.29563i	0.761800	−	0.647813i	$-0.224316\pi$
$354$		−	11.0841i		−	0.589111i
$355$			0.224692i			0.0119254i
$356$			2.00000i			0.106000i
$357$	0.335598	+	0.224692i	0.0177617	+	0.0118920i
$358$		−	28.7955i		−	1.52189i
$359$			33.6867i			1.77792i	0.457986	+	0.888959i	$0.348571\pi$
$359$			33.6867i			1.77792i	−0.457986	+	0.888959i	$0.651429\pi$
$360$	2.69862			0.142230
$361$	17.0326			0.896454
$362$	−27.3945			−1.43982
$363$	−7.60845	−	7.94427i	−0.399340	−	0.416966i
$364$	−0.486825	+	0.727119i	−0.0255166	+	0.0381114i
$365$		−	0.732688i		−	0.0383507i
$366$	−5.61835			−0.293676
$367$			11.0025i			0.574327i	0.957882	+	0.287164i	$0.0927123\pi$
$367$			11.0025i			0.574327i	−0.957882	+	0.287164i	$0.907288\pi$
$368$	−5.02295			−0.261839
$369$	7.38204			0.384294
$370$	−1.02570			−0.0533234
$371$	6.71252	−	10.0258i	0.348496	−	0.520512i
$372$	0.116115			0.00602031
$373$		−	17.0868i		−	0.884720i	−0.896838	−	0.442360i	$-0.854141\pi$
$373$		−	17.0868i		−	0.884720i	0.896838	−	0.442360i	$-0.145859\pi$
$374$	0.691531	−	0.277735i	0.0357582	−	0.0143613i
$375$	−1.00000			−0.0516398
$376$	28.8667			1.48869
$377$			11.4648i			0.590467i
$378$	2.16663	−	3.23607i	0.111440	−	0.166445i
$379$	27.4865			1.41189			0.705943	−	0.708269i	$-0.250524\pi$
$379$	27.4865			1.41189			0.705943	+	0.708269i	$0.250524\pi$
$380$		−	1.00026i		−	0.0513122i
$381$	0.646633			0.0331280
$382$		−	16.8867i		−	0.863998i
$383$		−	9.08602i		−	0.464274i	−0.972683	−	0.232137i	$-0.925428\pi$
$383$		−	9.08602i		−	0.464274i	0.972683	−	0.232137i	$-0.0745717\pi$
$384$	−12.5183			−0.638821
$385$	1.81271	−	8.58569i	0.0923842	−	0.437567i
$386$	4.33327			0.220558
$387$			10.9060i			0.554382i
$388$		−	0.689289i		−	0.0349934i
$389$	−21.6458			−1.09748			−0.548742	−	0.835992i	$-0.684893\pi$
$389$	−21.6458			−1.09748			−0.548742	+	0.835992i	$0.684893\pi$
$390$			2.92152i			0.147937i
$391$	−0.178086			−0.00900619
$392$	−17.4658	+	7.19650i	−0.882158	+	0.363478i
$393$		−	15.7863i		−	0.796316i
$394$	−33.5978			−1.69263
$395$	2.98506			0.150194
$396$	−0.205971	−	0.512848i	−0.0103504	−	0.0257716i
$397$			25.9264i			1.30121i	0.759417	+	0.650604i	$0.225484\pi$
$397$			25.9264i			1.30121i	−0.759417	+	0.650604i	$0.774516\pi$
$398$	7.44863			0.373366
$399$	13.1969	+	8.83570i	0.660673	+	0.442338i
$400$	4.30550			0.215275
$401$	2.41948			0.120823			0.0604116	−	0.998174i	$-0.480759\pi$
$401$	2.41948			0.120823			0.0604116	+	0.998174i	$0.480759\pi$
$402$	4.70228			0.234529
$403$		−	1.38306i		−	0.0688952i
$404$	0.242134			0.0120466
$405$		−	1.00000i		−	0.0496904i
$406$	12.5151	−	18.6925i	0.621116	−	0.927694i
$407$	−0.861327	−	2.14462i	−0.0426944	−	0.106305i
$408$	−0.411943			−0.0203942
$409$	−25.1964			−1.24588			−0.622941	−	0.782269i	$-0.714062\pi$
$409$	−25.1964			−1.24588			−0.622941	+	0.782269i	$0.714062\pi$
$410$	10.8660			0.536633
$411$			22.4768i			1.10870i
$412$			1.27793i			0.0629590i
$413$	16.5551	+	11.0841i	0.814622	+	0.545411i
$414$			1.71723i			0.0843971i
$415$		−	9.97231i		−	0.489522i
$416$		−	1.86618i		−	0.0914970i
$417$			6.88806i			0.337310i
$418$	27.1935	−	10.9215i	1.33008	−	0.534189i
$419$		−	17.8635i		−	0.872687i	−0.899780	−	0.436344i	$-0.856273\pi$
$419$		−	17.8635i		−	0.872687i	0.899780	−	0.436344i	$-0.143727\pi$
$420$	0.245277	−	0.366344i	0.0119683	−	0.0178758i
$421$	−17.9720			−0.875904			−0.437952	−	0.898998i	$-0.644296\pi$
$421$	−17.9720			−0.875904			−0.437952	+	0.898998i	$0.644296\pi$
$422$	−19.0600			−0.927826
$423$		−	10.6968i		−	0.520098i
$424$			12.3065i			0.597656i
$425$	0.152649			0.00740458
$426$	−0.330735			−0.0160242
$427$	5.61835	−	8.39152i	0.271891	−	0.406094i
$428$		−	1.54974i		−	0.0749095i
$429$	−6.10858	+	2.45334i	−0.294925	+	0.118449i
$430$			16.0530i			0.774146i
$431$		−	28.1148i		−	1.35424i	−0.735871	−	0.677122i	$-0.763227\pi$
$431$		−	28.1148i		−	1.35424i	0.735871	−	0.677122i	$-0.236773\pi$
$432$			4.30550i			0.207149i
$433$			31.0878i			1.49398i	0.664833	+	0.746992i	$0.268503\pi$
$433$			31.0878i			1.49398i	−0.664833	+	0.746992i	$0.731497\pi$
$434$	−1.50977	+	2.25498i	−0.0724713	+	0.108243i
$435$		−	5.77630i		−	0.276953i
$436$		−	0.987967i		−	0.0473150i
$437$	−7.00298			−0.334998
$438$	1.07848			0.0515318
$439$	17.9258			0.855554			0.427777	−	0.903884i	$-0.359297\pi$
$439$	17.9258			0.855554			0.427777	+	0.903884i	$0.359297\pi$
$440$	3.33568	+	8.30550i	0.159022	+	0.395949i
$441$	2.66673	+	6.47214i	0.126987	+	0.308197i
$442$		−	0.445968i		−	0.0212125i
$443$	−10.3560			−0.492029			−0.246015	−	0.969266i	$-0.579121\pi$
$443$	−10.3560			−0.492029			−0.246015	+	0.969266i	$0.579121\pi$
$444$		−	0.116115i		−	0.00551060i
$445$	−12.0023			−0.568965
$446$	−6.38178			−0.302186
$447$	3.63886			0.172112
$448$	10.6378	−	15.8885i	0.502589	−	0.750663i
$449$	8.91398			0.420677			0.210338	−	0.977629i	$-0.432543\pi$
$449$	8.91398			0.420677			0.210338	+	0.977629i	$0.432543\pi$
$450$		−	1.47195i		−	0.0693883i
$451$	9.12470	+	22.7196i	0.429665	+	1.06982i
$452$	2.64844			0.124572
$453$	−23.0606			−1.08348
$454$			8.61854i			0.404488i
$455$	−4.36356	−	2.92152i	−0.204567	−	0.136963i
$456$	−16.1991			−0.758591
$457$			18.6242i			0.871205i	0.900139	+	0.435602i	$0.143465\pi$
$457$			18.6242i			0.871205i	−0.900139	+	0.435602i	$0.856535\pi$
$458$	−30.9621			−1.44676
$459$			0.152649i			0.00712506i
$460$			0.194401i			0.00906401i
$461$	29.9110			1.39309			0.696546	−	0.717512i	$-0.254719\pi$
$461$	29.9110			1.39309			0.696546	+	0.717512i	$0.254719\pi$
$462$	12.6377	+	2.66821i	0.587959	+	0.124137i
$463$	7.41641			0.344670			0.172335	−	0.985038i	$-0.444869\pi$
$463$	7.41641			0.344670			0.172335	+	0.985038i	$0.444869\pi$
$464$			24.8699i			1.15456i
$465$			0.696828i			0.0323146i
$466$	13.7450			0.636726
$467$			23.6112i			1.09260i	0.837591	+	0.546298i	$0.183963\pi$
$467$			23.6112i			1.09260i	−0.837591	+	0.546298i	$0.816037\pi$
$468$	−0.330735			−0.0152882
$469$	−4.70228	+	7.02329i	−0.217131	+	0.324305i
$470$		−	15.7452i		−	0.726271i
$471$	−7.14100			−0.329040
$472$	−20.3211			−0.935356
$473$	−33.5651	+	13.4805i	−1.54333	+	0.619835i
$474$			4.39385i			0.201816i
$475$	6.00272			0.275424
$476$	−0.0374414	+	0.0559222i	−0.00171612	+	0.00256319i
$477$	4.56029			0.208801
$478$	5.69702			0.260576
$479$	18.3363			0.837809			0.418904	−	0.908030i	$-0.362414\pi$
$479$	18.3363			0.837809			0.418904	+	0.908030i	$0.362414\pi$
$480$			0.940237i			0.0429158i
$481$	−1.38306			−0.0630622
$482$			3.23544i			0.147370i
$483$	−2.56484	−	1.71723i	−0.116704	−	0.0781365i
$484$	1.32379	−	1.26783i	0.0601722	−	0.0576286i
$485$	4.13654			0.187831
$486$	1.47195			0.0667690
$487$	−31.6941			−1.43620			−0.718099	−	0.695941i	$-0.754988\pi$
$487$	−31.6941			−1.43620			−0.718099	+	0.695941i	$0.754988\pi$
$488$			10.3005i			0.466281i
$489$			8.50243i			0.384493i
$490$	3.92529	+	9.52666i	0.177327	+	0.430370i
$491$			19.6053i			0.884776i	0.896824	+	0.442388i	$0.145869\pi$
$491$			19.6053i			0.884776i	−0.896824	+	0.442388i	$0.854131\pi$
$492$			1.23010i			0.0554572i
$493$			0.881749i			0.0397120i
$494$		−	17.5371i		−	0.789030i
$495$	3.07768	−	1.23607i	0.138332	−	0.0555571i
$496$		−	3.00019i		−	0.134713i
$497$	0.330735	−	0.493984i	0.0148355	−	0.0221582i
$498$	14.6787			0.657770
$499$	−9.18939			−0.411373			−0.205687	−	0.978618i	$-0.565943\pi$
$499$	−9.18939			−0.411373			−0.205687	+	0.978618i	$0.565943\pi$
$500$		−	0.166634i		−	0.00745211i
$501$			8.32885i			0.372106i
$502$	12.5592			0.560543
$503$	2.87356			0.128126			0.0640629	−	0.997946i	$-0.479594\pi$
$503$	2.87356			0.128126			0.0640629	+	0.997946i	$0.479594\pi$
$504$	−5.93290	−	3.97223i	−0.264272	−	0.176937i
$505$			1.45309i			0.0646614i
$506$	−5.28508	+	2.12261i	−0.234950	+	0.0943615i
$507$		−	9.06058i		−	0.402395i
$508$			0.107751i			0.00478069i
$509$		−	23.6135i		−	1.04665i	−0.852133	−	0.523326i	$-0.824691\pi$
$509$		−	23.6135i		−	1.04665i	0.852133	−	0.523326i	$-0.175309\pi$
$510$			0.224692i			0.00994953i
$511$	−1.07848	+	1.61081i	−0.0477091	+	0.0712580i
$512$			19.1896i			0.848070i
$513$			6.00272i			0.265026i
$514$	−2.81071			−0.123975
$515$	−7.66906			−0.337939
$516$	−1.81731			−0.0800026
$517$	32.9215	−	13.2220i	1.44788	−	0.581503i
$518$	2.25498	+	1.50977i	0.0990783	+	0.0663355i
$519$			18.9312i			0.830988i
$520$	5.35621			0.234886
$521$		−	0.886020i		−	0.0388172i	−0.999812	−	0.0194086i	$-0.993822\pi$
$521$		−	0.886020i		−	0.0388172i	0.999812	−	0.0194086i	$-0.00617834\pi$
$522$	8.50243			0.372141
$523$	−9.53895			−0.417109			−0.208555	−	0.978011i	$-0.566876\pi$
$523$	−9.53895			−0.417109			−0.208555	+	0.978011i	$0.566876\pi$
$524$	2.63055			0.114916
$525$	2.19849	+	1.47195i	0.0959500	+	0.0642411i
$526$	9.47233			0.413013
$527$		−	0.106370i		−	0.00463356i
$528$	−13.2510	+	5.32189i	−0.576675	+	0.231606i
$529$	−21.6390			−0.940825
$530$	6.71252			0.291573
$531$			7.53019i			0.326783i
$532$	−1.47233	+	2.19906i	−0.0638336	+	0.0953414i
$533$	14.6518			0.634642
$534$		−	17.6668i		−	0.764518i
$535$	9.30024			0.402085
$536$		−	8.62100i		−	0.372371i
$537$			19.5628i			0.844198i
$538$	−25.0269			−1.07898
$539$	−16.6229	+	16.2074i	−0.716000	+	0.698100i
$540$	0.166634			0.00717080
$541$			27.7409i			1.19267i	0.802734	+	0.596337i	$0.203378\pi$
$541$			27.7409i			1.19267i	−0.802734	+	0.596337i	$0.796622\pi$
$542$		−	11.6592i		−	0.500805i
$543$	18.6110			0.798675
$544$		−	0.143527i		−	0.00615365i
$545$	5.92895			0.253968
$546$	4.30033	−	6.42294i	0.184037	−	0.274876i
$547$			36.5806i			1.56407i	0.623232	+	0.782037i	$0.285819\pi$
$547$			36.5806i			1.56407i	−0.623232	+	0.782037i	$0.714181\pi$
$548$	−3.74541			−0.159996
$549$	3.81694			0.162903
$550$	4.53019	−	1.81943i	0.193168	−	0.0775807i
$551$			34.6735i			1.47714i
$552$	3.14830			0.134001
$553$	−6.56262	−	4.39385i	−0.279071	−	0.186846i
$554$	−23.7122			−1.00744
$555$	0.696828			0.0295787
$556$	−1.14779			−0.0486770
$557$			10.9674i			0.464706i	0.972632	+	0.232353i	$0.0746424\pi$
$557$			10.9674i			0.464706i	−0.972632	+	0.232353i	$0.925358\pi$
$558$	−1.02570			−0.0434211
$559$			21.6461i			0.915534i
$560$	−9.46561	−	6.33748i	−0.399995	−	0.267807i
$561$	−0.469806	+	0.188685i	−0.0198352	+	0.00796628i
$562$	−44.4213			−1.87380
$563$	−36.7867			−1.55038			−0.775188	−	0.631731i	$-0.782345\pi$
$563$	−36.7867			−1.55038			−0.775188	+	0.631731i	$0.782345\pi$
$564$	1.78246			0.0750550
$565$			15.8938i			0.668655i
$566$		−	1.82369i		−	0.0766555i
$567$	−1.47195	+	2.19849i	−0.0618161	+	0.0923280i
$568$			0.606359i			0.0254422i
$569$		−	17.9539i		−	0.752665i	−0.926485	−	0.376332i	$-0.877185\pi$
$569$		−	17.9539i		−	0.752665i	0.926485	−	0.376332i	$-0.122815\pi$
$570$			8.83570i			0.370087i
$571$		−	16.6543i		−	0.696959i	−0.937316	−	0.348480i	$-0.886698\pi$
$571$		−	16.6543i		−	0.696959i	0.937316	−	0.348480i	$-0.113302\pi$
$572$	−0.408811	−	1.01790i	−0.0170933	−	0.0425605i
$573$			11.4723i			0.479263i
$574$	−23.8888	−	15.9942i	−0.997098	−	0.667584i
$575$	−1.16663			−0.0486520
$576$	7.22702			0.301126
$577$			37.3802i			1.55616i	0.628166	+	0.778080i	$0.283806\pi$
$577$			37.3802i			1.55616i	−0.628166	+	0.778080i	$0.716194\pi$
$578$			24.9888i			1.03940i
$579$	−2.94390			−0.122344
$580$	0.962531			0.0399669
$581$	−14.6787	+	21.9240i	−0.608977	+	0.909563i
$582$			6.08877i			0.252388i
$583$	5.63683	+	14.0351i	0.233454	+	0.581276i
$584$		−	1.97725i		−	0.0818191i
$585$		−	1.98480i		−	0.0820613i
$586$		−	21.6183i		−	0.893046i
$587$		−	48.0951i		−	1.98510i	−0.121842	−	0.992550i	$-0.538880\pi$
$587$		−	48.0951i		−	1.98510i	0.121842	−	0.992550i	$-0.461120\pi$
$588$	−1.07848	+	0.444369i	−0.0444758	+	0.0183255i
$589$		−	4.18286i		−	0.172352i
$590$			11.0841i			0.456324i
$591$	22.8254			0.938910
$592$	−3.00019			−0.123307
$593$	31.2420			1.28295			0.641477	−	0.767143i	$-0.278322\pi$
$593$	31.2420			1.28295			0.641477	+	0.767143i	$0.278322\pi$
$594$	1.81943	+	4.53019i	0.0746521	+	0.185876i
$595$	−0.335598	−	0.224692i	−0.0137582	−	0.00921148i
$596$			0.606359i			0.0248374i
$597$	−5.06039			−0.207108
$598$			3.40835i			0.139378i
$599$	−8.86599			−0.362254			−0.181127	−	0.983460i	$-0.557975\pi$
$599$	−8.86599			−0.362254			−0.181127	+	0.983460i	$0.557975\pi$
$600$	−2.69862			−0.110171
$601$	8.23936			0.336091			0.168045	−	0.985779i	$-0.446254\pi$
$601$	8.23936			0.336091			0.168045	+	0.985779i	$0.446254\pi$
$602$	23.6293	−	35.2925i	0.963057	−	1.43841i
$603$	−3.19460			−0.130094
$604$		−	3.84269i		−	0.156357i
$605$	7.60845	+	7.94427i	0.309328	+	0.322981i
$606$	−2.13887			−0.0868855
$607$	−24.1453			−0.980026			−0.490013	−	0.871715i	$-0.663008\pi$
$607$	−24.1453			−0.980026			−0.490013	+	0.871715i	$0.663008\pi$
$608$		−	5.64398i		−	0.228894i
$609$	−8.50243	+	12.6992i	−0.344536	+	0.514596i
$610$	5.61835			0.227480
$611$		−	21.2310i		−	0.858916i
$612$	−0.0254366			−0.00102821
$613$			25.1120i			1.01427i	0.861868	+	0.507133i	$0.169295\pi$
$613$			25.1120i			1.01427i	−0.861868	+	0.507133i	$0.830705\pi$
$614$			12.3333i			0.497730i
$615$	−7.38204			−0.297673
$616$	4.89181	−	23.1695i	0.197097	−	0.933527i
$617$	−29.7497			−1.19768			−0.598838	−	0.800870i	$-0.704371\pi$
$617$	−29.7497			−1.19768			−0.598838	+	0.800870i	$0.704371\pi$
$618$		−	11.2885i		−	0.454089i
$619$			31.6201i			1.27092i	0.772134	+	0.635460i	$0.219190\pi$
$619$			31.6201i			1.27092i	−0.772134	+	0.635460i	$0.780810\pi$
$620$	−0.116115			−0.00466331
$621$		−	1.16663i		−	0.0468154i
$622$	−43.7969			−1.75609
$623$	26.3870	+	17.6668i	1.05717	+	0.707806i
$624$			8.54555i			0.342096i
$625$	1.00000			0.0400000
$626$	−35.1327			−1.40418
$627$	−18.4745	+	7.41977i	−0.737799	+	0.296317i
$628$		−	1.18994i		−	0.0474836i
$629$	−0.106370			−0.00424126
$630$	−2.16663	+	3.23607i	−0.0863208	+	0.128928i
$631$	26.8049			1.06708			0.533542	−	0.845773i	$-0.320861\pi$
$631$	26.8049			1.06708			0.533542	+	0.845773i	$0.320861\pi$
$632$	8.05553			0.320432
$633$	12.9488			0.514669
$634$			8.14359i			0.323423i
$635$	−0.646633			−0.0256608
$636$			0.759901i			0.0301320i
$637$	5.29292	+	12.8459i	0.209713	+	0.508972i
$638$	10.5096	+	26.1678i	0.416078	+	1.03599i
$639$	0.224692			0.00888868
$640$	12.5183			0.494829
$641$	−47.1812			−1.86354			−0.931772	−	0.363044i	$-0.881737\pi$
$641$	−47.1812			−1.86354			−0.931772	+	0.363044i	$0.881737\pi$
$642$			13.6895i			0.540281i
$643$		−	8.83049i		−	0.348240i	−0.984724	−	0.174120i	$-0.944292\pi$
$643$		−	8.83049i		−	0.348240i	0.984724	−	0.174120i	$-0.0557081\pi$
$644$	0.286149	−	0.427390i	0.0112758	−	0.0168415i
$645$		−	10.9060i		−	0.429422i
$646$		−	1.34876i		−	0.0530664i
$647$		−	6.78265i		−	0.266654i	−0.991072	−	0.133327i	$-0.957434\pi$
$647$		−	6.78265i		−	0.266654i	0.991072	−	0.133327i	$-0.0425660\pi$
$648$		−	2.69862i		−	0.106012i
$649$	−23.1756	+	9.30783i	−0.909720	+	0.365364i
$650$		−	2.92152i		−	0.114591i
$651$	1.02570	−	1.53197i	0.0402002	−	0.0600427i
$652$	−1.41680			−0.0554860
$653$	−45.5046			−1.78073			−0.890366	−	0.455246i	$-0.849551\pi$
$653$	−45.5046			−1.78073			−0.890366	+	0.455246i	$0.849551\pi$
$654$			8.72712i			0.341257i
$655$			15.7863i			0.616824i
$656$	31.7834			1.24093
$657$	−0.732688			−0.0285849
$658$	−23.1761	+	34.6157i	−0.903499	+	1.34946i
$659$		−	25.5754i		−	0.996278i	−0.867097	−	0.498139i	$-0.834017\pi$
$659$		−	25.5754i		−	0.996278i	0.867097	−	0.498139i	$-0.165983\pi$
$660$	0.205971	+	0.512848i	0.00801742	+	0.0199626i
$661$			42.0909i			1.63715i	0.574403	+	0.818573i	$0.305234\pi$
$661$			42.0909i			1.63715i	−0.574403	+	0.818573i	$0.694766\pi$
$662$		−	38.7269i		−	1.50517i
$663$			0.302978i			0.0117667i
$664$		−	26.9115i		−	1.04437i
$665$	−13.1969	−	8.83570i	−0.511755	−	0.342634i
$666$			1.02570i			0.0397449i
$667$		−	6.73884i		−	0.260929i
$668$	−1.38787			−0.0536984
$669$	4.33560			0.167624
$670$	−4.70228			−0.181665
$671$	4.71800	+	11.7473i	0.182136	+	0.453501i
$672$	1.38398	−	2.06710i	0.0533882	−	0.0797403i
$673$		−	48.1455i		−	1.85587i	−0.372738	−	0.927937i	$-0.621581\pi$
$673$		−	48.1455i		−	1.85587i	0.372738	−	0.927937i	$-0.378419\pi$
$674$	19.9744			0.769384
$675$			1.00000i			0.0384900i
$676$	1.50980			0.0580694
$677$	2.45847			0.0944865			0.0472433	−	0.998883i	$-0.484956\pi$
$677$	2.45847			0.0944865			0.0472433	+	0.998883i	$0.484956\pi$
$678$	−23.3948			−0.898472
$679$	−9.09414	−	6.08877i	−0.349001	−	0.233666i
$680$	0.411943			0.0157973
$681$		−	5.85519i		−	0.224371i
$682$	−1.26783	−	3.15677i	−0.0485477	−	0.120879i
$683$	−10.0421			−0.384250			−0.192125	−	0.981370i	$-0.561538\pi$
$683$	−10.0421			−0.384250			−0.192125	+	0.981370i	$0.561538\pi$
$684$	−1.00026			−0.0382459
$685$		−	22.4768i		−	0.858794i
$686$	5.39303	−	26.7221i	0.205907	−	1.02025i
$687$	21.0348			0.802526
$688$			46.9557i			1.79017i
$689$	9.05125			0.344825
$690$		−	1.71723i		−	0.0653737i
$691$		−	35.8885i		−	1.36526i	−0.730762	−	0.682632i	$-0.760835\pi$
$691$		−	35.8885i		−	1.36526i	0.730762	−	0.682632i	$-0.239165\pi$
$692$	−3.15459			−0.119920
$693$	−8.58569	−	1.81271i	−0.326143	−	0.0688591i
$694$	33.4361			1.26922
$695$		−	6.88806i		−	0.261279i
$696$		−	15.5881i		−	0.590864i
$697$	1.12686			0.0426830
$698$			45.9416i			1.73891i
$699$	−9.33797			−0.353194
$700$	−0.245277	+	0.366344i	−0.00927061	+	0.0138465i
$701$		−	9.44060i		−	0.356567i	−0.983979	−	0.178283i	$-0.942946\pi$
$701$		−	9.44060i		−	0.356567i	0.983979	−	0.178283i	$-0.0570543\pi$
$702$	2.92152			0.110266
$703$	−4.18286			−0.157760
$704$	8.93309	+	22.2425i	0.336679	+	0.838295i
$705$			10.6968i			0.402866i
$706$	−35.8311			−1.34852
$707$	2.13887	−	3.19460i	0.0804404	−	0.120145i
$708$	−1.25479			−0.0471578
$709$	−23.1940			−0.871071			−0.435535	−	0.900172i	$-0.643441\pi$
$709$	−23.1940			−0.871071			−0.435535	+	0.900172i	$0.643441\pi$
$710$	0.330735			0.0124123
$711$		−	2.98506i		−	0.111948i
$712$	−32.3897			−1.21386
$713$			0.812943i			0.0304450i
$714$	0.330735	−	0.493984i	0.0123775	−	0.0184869i
$715$	6.10858	−	2.45334i	0.228448	−	0.0917499i
$716$	−3.25984			−0.121826
$717$	−3.87039			−0.144542
$718$	49.5852			1.85050
$719$		−	45.1503i		−	1.68382i	−0.539616	−	0.841911i	$-0.681430\pi$
$719$		−	45.1503i		−	1.68382i	0.539616	−	0.841911i	$-0.318570\pi$
$720$		−	4.30550i		−	0.160457i
$721$	16.8604	+	11.2885i	0.627913	+	0.420405i
$722$		−	25.0712i		−	0.933052i
$723$		−	2.19806i		−	0.0817469i
$724$			3.10123i			0.115256i
$725$			5.77630i			0.214527i
$726$	−11.6936	+	11.1993i	−0.433989	+	0.415643i
$727$		−	24.1231i		−	0.894676i	−0.894365	−	0.447338i	$-0.852372\pi$
$727$		−	24.1231i		−	0.894676i	0.894365	−	0.447338i	$-0.147628\pi$
$728$	−11.7756	−	7.88408i	−0.436433	−	0.292203i
$729$	−1.00000			−0.0370370
$730$	−1.07848			−0.0399163
$731$			1.66479i			0.0615745i
$732$			0.636034i			0.0235085i
$733$	25.9791			0.959560			0.479780	−	0.877389i	$-0.340717\pi$
$733$	25.9791			0.959560			0.479780	+	0.877389i	$0.340717\pi$
$734$	16.1952			0.597774
$735$	−2.66673	−	6.47214i	−0.0983639	−	0.238728i
$736$			1.09691i			0.0404328i
$737$	−3.94874	−	9.83195i	−0.145454	−	0.362165i
$738$		−	10.8660i		−	0.399982i
$739$		−	20.6387i		−	0.759208i	−0.925149	−	0.379604i	$-0.876060\pi$
$739$		−	20.6387i		−	0.759208i	0.925149	−	0.379604i	$-0.123940\pi$
$740$			0.116115i			0.00426849i
$741$			11.9142i			0.437678i
$742$	−14.7574	−	9.88048i	−0.541762	−	0.362724i
$743$		−	34.6701i		−	1.27192i	−0.771721	−	0.635962i	$-0.780604\pi$
$743$		−	34.6701i		−	1.27192i	0.771721	−	0.635962i	$-0.219396\pi$
$744$			1.88047i			0.0689415i
$745$	−3.63886			−0.133317
$746$	−25.1509			−0.920839
$747$	−9.97231			−0.364868
$748$	−0.0314414	−	0.0782859i	−0.00114961	−	0.00286241i
$749$	−20.4465	−	13.6895i	−0.747099	−	0.500203i
$750$			1.47195i			0.0537480i
$751$	−1.18473			−0.0432313			−0.0216156	−	0.999766i	$-0.506881\pi$
$751$	−1.18473			−0.0432313			−0.0216156	+	0.999766i	$0.506881\pi$
$752$		−	46.0552i		−	1.67946i
$753$	−8.53233			−0.310935
$754$	16.8756			0.614573
$755$	23.0606			0.839262
$756$	−0.366344	−	0.245277i	−0.0133238	−	0.00892065i
$757$	26.1212			0.949390			0.474695	−	0.880150i	$-0.342558\pi$
$757$	26.1212			0.949390			0.474695	+	0.880150i	$0.342558\pi$
$758$		−	40.4587i		−	1.46953i
$759$	3.59053	−	1.44204i	0.130328	−	0.0523427i
$760$	16.1991			0.587602
$761$	−2.45539			−0.0890079			−0.0445039	−	0.999009i	$-0.514171\pi$
$761$	−2.45539			−0.0890079			−0.0445039	+	0.999009i	$0.514171\pi$
$762$		−	0.951811i		−	0.0344805i
$763$	−13.0348	−	8.72712i	−0.471890	−	0.315943i
$764$	−1.91168			−0.0691623
$765$		−	0.152649i		−	0.00551905i
$766$	−13.3742			−0.483228
$767$			14.9459i			0.539665i
$768$			3.97223i			0.143336i
$769$	32.8752			1.18551			0.592755	−	0.805383i	$-0.298040\pi$
$769$	32.8752			1.18551			0.592755	+	0.805383i	$0.298040\pi$
$770$	−12.6377	−	2.66821i	−0.455431	−	0.0961558i
$771$	1.90952			0.0687695
$772$		−	0.490554i		−	0.0176554i
$773$		−	42.7364i		−	1.53712i	−0.639776	−	0.768561i	$-0.720973\pi$
$773$		−	42.7364i		−	1.53712i	0.639776	−	0.768561i	$-0.279027\pi$
$774$	16.0530			0.577015
$775$		−	0.696828i		−	0.0250308i
$776$	11.1629			0.400726
$777$	−1.53197	−	1.02570i	−0.0549591	−	0.0367966i
$778$			31.8615i			1.14229i
$779$	44.3123			1.58765
$780$	0.330735			0.0118422
$781$	0.277735	+	0.691531i	0.00993813	+	0.0247449i
$782$			0.262133i			0.00937387i
$783$	−5.77630			−0.206428
$784$	11.4816	+	27.8658i	0.410058	+	0.995207i
$785$	7.14100			0.254873
$786$	−23.2367			−0.828826
$787$	−52.1766			−1.85989			−0.929947	−	0.367693i	$-0.880148\pi$
$787$	−52.1766			−1.85989			−0.929947	+	0.367693i	$0.880148\pi$
$788$			3.80349i			0.135494i
$789$	−6.43523			−0.229100
$790$		−	4.39385i		−	0.156326i
$791$	23.3948	−	34.9423i	0.831823	−	1.24240i
$792$	8.30550	−	3.33568i	0.295123	−	0.118528i
$793$	7.57586			0.269027
$794$	38.1623			1.35433
$795$	−4.56029			−0.161737
$796$		−	0.843234i		−	0.0298876i
$797$		−	3.72265i		−	0.131863i	−0.997824	−	0.0659316i	$-0.978998\pi$
$797$		−	3.72265i		−	0.131863i	0.997824	−	0.0659316i	$-0.0210019\pi$
$798$	13.0057	−	19.4252i	0.460397	−	0.687645i
$799$		−	1.63286i		−	0.0577666i
$800$		−	0.940237i		−	0.0332424i
$801$			12.0023i			0.424081i
$802$		−	3.56135i		−	0.125756i
$803$	−0.905653	−	2.25498i	−0.0319598	−	0.0795766i
$804$		−	0.532329i		−	0.0187738i
$805$	2.56484	+	1.71723i	0.0903986	+	0.0605243i
$806$	−2.03580			−0.0717079
$807$	17.0025			0.598517
$808$			3.92133i			0.137952i
$809$		−	33.1602i		−	1.16585i	−0.812526	−	0.582925i	$-0.801908\pi$
$809$		−	33.1602i		−	1.16585i	0.812526	−	0.582925i	$-0.198092\pi$
$810$	−1.47195			−0.0517190
$811$	−26.6028			−0.934152			−0.467076	−	0.884217i	$-0.654693\pi$
$811$	−26.6028			−0.934152			−0.467076	+	0.884217i	$0.654693\pi$
$812$	−2.11612	−	1.41680i	−0.0742611	−	0.0497198i
$813$			7.92092i			0.277799i
$814$	−3.15677	+	1.26783i	−0.110645	+	0.0444374i
$815$		−	8.50243i		−	0.297827i
$816$			0.657232i			0.0230077i
$817$			65.4655i			2.29035i
$818$			37.0878i			1.29674i
$819$	−2.92152	+	4.36356i	−0.102086	+	0.152475i
$820$		−	1.23010i		−	0.0429570i
$821$			39.6589i			1.38411i	0.721847	+	0.692053i	$0.243293\pi$
$821$			39.6589i			1.38411i	−0.721847	+	0.692053i	$0.756707\pi$
$822$	33.0847			1.15396
$823$	−49.9613			−1.74154			−0.870771	−	0.491689i	$-0.836380\pi$
$823$	−49.9613			−1.74154			−0.870771	+	0.491689i	$0.836380\pi$
$824$	−20.6959			−0.720975
$825$	−3.07768	+	1.23607i	−0.107151	+	0.0430344i
$826$	16.3152	−	24.3682i	0.567678	−	0.847879i
$827$		−	2.21121i		−	0.0768913i	−0.999261	−	0.0384457i	$-0.987759\pi$
$827$		−	2.21121i		−	0.0768913i	0.999261	−	0.0384457i	$-0.0122406\pi$
$828$	0.194401			0.00675591
$829$			55.7409i			1.93596i	0.251024	+	0.967981i	$0.419233\pi$
$829$			55.7409i			1.93596i	−0.251024	+	0.967981i	$0.580767\pi$
$830$	−14.6787			−0.509506
$831$	16.1094			0.558829
$832$	14.3442			0.497295
$833$	0.407075	+	0.987967i	0.0141043	+	0.0342310i
$834$	10.1389			0.351080
$835$		−	8.32885i		−	0.288232i
$836$	−1.23639	−	3.07848i	−0.0427614	−	0.106471i
$837$	0.696828			0.0240859
$838$	−26.2941			−0.908315
$839$			18.5300i			0.639727i	0.947464	+	0.319863i	$0.103637\pi$
$839$			18.5300i			0.639727i	−0.947464	+	0.319863i	$0.896363\pi$
$840$	5.93290	+	3.97223i	0.204704	+	0.137055i
$841$	−4.36569			−0.150541
$842$			26.4539i			0.911663i
$843$	30.1785			1.03940
$844$			2.15772i			0.0742717i
$845$			9.06058i			0.311693i
$846$	−15.7452			−0.541331
$847$	−5.03355	−	28.6647i	−0.172955	−	0.984930i
$848$	19.6343			0.674246
$849$			1.23896i			0.0425211i
$850$		−	0.224692i		−	0.00770687i
$851$	0.812943			0.0278673
$852$			0.0374414i			0.00128272i
$853$	−29.8321			−1.02143			−0.510715	−	0.859750i	$-0.670619\pi$
$853$	−29.8321			−1.02143			−0.510715	+	0.859750i	$0.670619\pi$
$854$	−12.3519	−	8.26992i	−0.422673	−	0.282991i
$855$		−	6.00272i		−	0.205289i
$856$	25.0978			0.857826
$857$	−55.0951			−1.88201			−0.941006	−	0.338391i	$-0.890117\pi$
$857$	−55.0951			−1.88201			−0.941006	+	0.338391i	$0.890117\pi$
$858$	3.61120	+	8.99151i	0.123284	+	0.306965i
$859$		−	58.3775i		−	1.99182i	−0.0903736	−	0.995908i	$-0.528806\pi$
$859$		−	58.3775i		−	1.99182i	0.0903736	−	0.995908i	$-0.471194\pi$
$860$	1.81731			0.0619698
$861$	16.2294	+	10.8660i	0.553095	+	0.370312i
$862$	−41.3836			−1.40953
$863$	−6.16683			−0.209921			−0.104961	−	0.994476i	$-0.533472\pi$
$863$	−6.16683			−0.209921			−0.104961	+	0.994476i	$0.533472\pi$
$864$	0.940237			0.0319875
$865$		−	18.9312i		−	0.643681i
$866$	45.7597			1.55498
$867$		−	16.9767i		−	0.576559i
$868$	0.255279	+	0.170916i	0.00866473	+	0.00580127i
$869$	9.18706	−	3.68973i	0.311650	−	0.125166i
$870$	−8.50243			−0.288259
$871$	−6.34062			−0.214844
$872$	16.0000			0.541828
$873$		−	4.13654i		−	0.140001i
$874$			10.3080i			0.348674i
$875$	−2.19849	−	1.47195i	−0.0743226	−	0.0497610i
$876$		−	0.122091i		−	0.00412507i
$877$		−	24.8928i		−	0.840569i	−0.907392	−	0.420285i	$-0.861930\pi$
$877$		−	24.8928i		−	0.840569i	0.907392	−	0.420285i	$-0.138070\pi$
$878$		−	26.3859i		−	0.890482i
$879$			14.6869i			0.495376i
$880$	13.2510	−	5.32189i	0.446690	−	0.179401i
$881$			31.7339i			1.06914i	0.845123	+	0.534571i	$0.179527\pi$
$881$			31.7339i			1.06914i	−0.845123	+	0.534571i	$0.820473\pi$
$882$	9.52666	−	3.92529i	0.320779	−	0.132171i
$883$	10.4768			0.352572			0.176286	−	0.984339i	$-0.443592\pi$
$883$	10.4768			0.352572			0.176286	+	0.984339i	$0.443592\pi$
$884$	−0.0504865			−0.00169805
$885$		−	7.53019i		−	0.253125i
$886$			15.2435i			0.512117i
$887$	5.17252			0.173676			0.0868381	−	0.996222i	$-0.472324\pi$
$887$	5.17252			0.173676			0.0868381	+	0.996222i	$0.472324\pi$
$888$	1.88047			0.0631046
$889$	1.42162	+	0.951811i	0.0476795	+	0.0319227i
$890$			17.6668i			0.592193i
$891$	−1.23607	−	3.07768i	−0.0414098	−	0.103106i
$892$			0.722459i			0.0241897i
$893$		−	64.2100i		−	2.14871i
$894$		−	5.35621i		−	0.179139i
$895$		−	19.5628i		−	0.653913i
$896$	−27.5213	−	18.4263i	−0.919423	−	0.615579i
$897$		−	2.31553i		−	0.0773134i
$898$		−	13.1209i		−	0.437851i
$899$	4.02509			0.134244
$900$	−0.166634			−0.00555448
$901$	0.696125			0.0231913
$902$	33.4421	−	13.4311i	1.11350	−	0.447207i
$903$	−16.0530	+	23.9767i	−0.534212	+	0.797895i
$904$			42.8912i			1.42654i
$905$	−18.6110			−0.618651
$906$			33.9441i			1.12772i
$907$	−51.5721			−1.71242			−0.856212	−	0.516624i	$-0.827188\pi$
$907$	−51.5721			−1.71242			−0.856212	+	0.516624i	$0.827188\pi$
$908$	0.975676			0.0323789
$909$	1.45309			0.0481958
$910$	−4.30033	+	6.42294i	−0.142555	+	0.212918i
$911$	42.0425			1.39293			0.696465	−	0.717591i	$-0.254755\pi$
$911$	42.0425			1.39293			0.696465	+	0.717591i	$0.254755\pi$
$912$			25.8447i			0.855804i
$913$	−12.3265	−	30.6916i	−0.407946	−	1.01574i
$914$	27.4139			0.906772
$915$	−3.81694			−0.126184
$916$			3.50511i			0.115812i
$917$	23.2367	−	34.7061i	0.767343	−	1.14610i
$918$	0.224692			0.00741594
$919$			11.1129i			0.366582i	0.983059	+	0.183291i	$0.0586750\pi$
$919$			11.1129i			0.366582i	−0.983059	+	0.183291i	$0.941325\pi$
$920$	−3.14830			−0.103797
$921$		−	8.37887i		−	0.276093i
$922$		−	44.0274i		−	1.44997i
$923$	0.445968			0.0146792
$924$	0.302059	−	1.43067i	0.00993703	−	0.0470656i
$925$	−0.696828			−0.0229116
$926$		−	10.9166i		−	0.358741i
$927$			7.66906i			0.251885i
$928$	5.43110			0.178285
$929$			13.8284i			0.453693i	0.973930	+	0.226847i	$0.0728416\pi$
$929$			13.8284i			0.453693i	−0.973930	+	0.226847i	$0.927158\pi$
$930$	1.02570			0.0336339
$931$	16.0076	+	38.8504i	0.524629	+	1.27327i
$932$		−	1.55603i		−	0.0509693i
$933$	29.7543			0.974113
$934$	34.7545			1.13720
$935$	0.469806	−	0.188685i	0.0153643	−	0.00617066i
$936$		−	5.35621i		−	0.175073i
$937$	−26.9870			−0.881628			−0.440814	−	0.897599i	$-0.645310\pi$
$937$	−26.9870			−0.881628			−0.440814	+	0.897599i	$0.645310\pi$
$938$	10.3379	+	6.92152i	0.337545	+	0.225996i
$939$	23.8681			0.778907
$940$	−1.78246			−0.0581374
$941$	−24.6435			−0.803354			−0.401677	−	0.915781i	$-0.631573\pi$
$941$	−24.6435			−0.803354			−0.401677	+	0.915781i	$0.631573\pi$
$942$			10.5112i			0.342473i
$943$	−8.61214			−0.280450
$944$			32.4213i			1.05522i
$945$	1.47195	−	2.19849i	0.0478825	−	0.0715169i
$946$	19.8427	+	49.4062i	0.645140	+	1.60633i
$947$	0.448834			0.0145851			0.00729257	−	0.999973i	$-0.497679\pi$
$947$	0.448834			0.0145851			0.00729257	+	0.999973i	$0.497679\pi$
$948$	0.497413			0.0161552
$949$	−1.45424			−0.0472065
$950$		−	8.83570i		−	0.286668i
$951$		−	5.53252i		−	0.179404i
$952$	−0.905653	−	0.606359i	−0.0293524	−	0.0196522i
$953$		−	27.0425i		−	0.875993i	−0.898977	−	0.437997i	$-0.855688\pi$
$953$		−	27.0425i		−	0.875993i	0.898977	−	0.437997i	$-0.144312\pi$
$954$		−	6.71252i		−	0.217326i
$955$		−	11.4723i		−	0.371236i
$956$		−	0.644940i		−	0.0208589i
$957$	−7.13991	−	17.7776i	−0.230800	−	0.574669i
$958$		−	26.9902i		−	0.872013i
$959$	−33.0847	+	49.4150i	−1.06836	+	1.59570i
$960$	−7.22702			−0.233251
$961$	30.5144			0.984336
$962$			2.03580i			0.0656367i
$963$		−	9.30024i		−	0.299696i
$964$	0.366273			0.0117969
$965$	2.94390			0.0947674
$966$	−2.52767	+	3.77531i	−0.0813264	+	0.121469i
$967$		−	39.1094i		−	1.25767i	−0.777537	−	0.628837i	$-0.783531\pi$
$967$		−	39.1094i		−	1.25767i	0.777537	−	0.628837i	$-0.216469\pi$
$968$	20.5323	+	21.4386i	0.659934	+	0.689062i
$969$			0.916311i			0.0294361i
$970$		−	6.08877i		−	0.195499i
$971$		−	11.2980i		−	0.362569i	−0.983431	−	0.181284i	$-0.941975\pi$
$971$		−	11.2980i		−	0.362569i	0.983431	−	0.181284i	$-0.0580255\pi$
$972$		−	0.166634i		−	0.00534480i
$973$	−10.1389	+	15.1433i	−0.325037	+	0.485473i
$974$			46.6522i			1.49483i
$975$			1.98480i			0.0635644i
$976$	16.4339			0.526035
$977$	−3.67660			−0.117625			−0.0588124	−	0.998269i	$-0.518731\pi$
$977$	−3.67660			−0.117625			−0.0588124	+	0.998269i	$0.518731\pi$
$978$	12.5151			0.400190
$979$	−36.9394	+	14.8357i	−1.18059	+	0.474151i
$980$	1.07848	−	0.444369i	0.0344508	−	0.0141948i
$981$		−	5.92895i		−	0.189297i
$982$	28.8581			0.920898
$983$		−	46.8421i		−	1.49403i	−0.664806	−	0.747016i	$-0.731486\pi$
$983$		−	46.8421i		−	1.49403i	0.664806	−	0.747016i	$-0.268514\pi$
$984$	−19.9213			−0.635069
$985$	−22.8254			−0.727276
$986$	1.29789			0.0413332
$987$	15.7452	−	23.5169i	0.501175	−	0.748551i
$988$	−1.98531			−0.0631611
$989$		−	12.7233i		−	0.404577i
$990$	−1.81943	−	4.53019i	−0.0578253	−	0.143979i
$991$	48.5228			1.54138			0.770690	−	0.637211i	$-0.219912\pi$
$991$	48.5228			1.54138			0.770690	+	0.637211i	$0.219912\pi$
$992$	−0.655184			−0.0208021
$993$			26.3100i			0.834922i
$994$	−0.727119	−	0.486825i	−0.0230628	−	0.0154412i
$995$	5.06039			0.160425
$996$		−	1.66173i		−	0.0526539i
$997$	18.3063			0.579766			0.289883	−	0.957062i	$-0.406384\pi$
$997$	18.3063			0.579766			0.289883	+	0.957062i	$0.406384\pi$
$998$			13.5263i			0.428168i
$999$		−	0.696828i		−	0.0220467i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.i.c.76.6	yes	16
7.6	odd	2	inner	1155.2.i.c.76.5	✓	16
11.10	odd	2	inner	1155.2.i.c.76.12	yes	16
77.76	even	2	inner	1155.2.i.c.76.11	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.i.c.76.5	✓	16	7.6	odd	2	inner
1155.2.i.c.76.6	yes	16	1.1	even	1	trivial
1155.2.i.c.76.11	yes	16	77.76	even	2	inner
1155.2.i.c.76.12	yes	16	11.10	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)

\(f(q)\)	\(=\)	\(q-1.47195i q^{2} +1.00000i q^{3} -0.166634 q^{4} -1.00000i q^{5} +1.47195 q^{6} +(-1.47195 + 2.19849i) q^{7} -2.69862i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.47195i q^{2} +1.00000i q^{3} -0.166634 q^{4} -1.00000i q^{5} +1.47195 q^{6} +(-1.47195 + 2.19849i) q^{7} -2.69862i q^{8} -1.00000 q^{9} -1.47195 q^{10} +(-1.23607 - 3.07768i) q^{11} -0.166634i q^{12} -1.98480 q^{13} +(3.23607 + 2.16663i) q^{14} +1.00000 q^{15} -4.30550 q^{16} -0.152649 q^{17} +1.47195i q^{18} -6.00272 q^{19} +0.166634i q^{20} +(-2.19849 - 1.47195i) q^{21} +(-4.53019 + 1.81943i) q^{22} +1.16663 q^{23} +2.69862 q^{24} -1.00000 q^{25} +2.92152i q^{26} -1.00000i q^{27} +(0.245277 - 0.366344i) q^{28} -5.77630i q^{29} -1.47195i q^{30} +0.696828i q^{31} +0.940237i q^{32} +(3.07768 - 1.23607i) q^{33} +0.224692i q^{34} +(2.19849 + 1.47195i) q^{35} +0.166634 q^{36} +0.696828 q^{37} +8.83570i q^{38} -1.98480i q^{39} -2.69862 q^{40} -7.38204 q^{41} +(-2.16663 + 3.23607i) q^{42} -10.9060i q^{43} +(0.205971 + 0.512848i) q^{44} +1.00000i q^{45} -1.71723i q^{46} +10.6968i q^{47} -4.30550i q^{48} +(-2.66673 - 6.47214i) q^{49} +1.47195i q^{50} -0.152649i q^{51} +0.330735 q^{52} -4.56029 q^{53} -1.47195 q^{54} +(-3.07768 + 1.23607i) q^{55} +(5.93290 + 3.97223i) q^{56} -6.00272i q^{57} -8.50243 q^{58} -7.53019i q^{59} -0.166634 q^{60} -3.81694 q^{61} +1.02570 q^{62} +(1.47195 - 2.19849i) q^{63} -7.22702 q^{64} +1.98480i q^{65} +(-1.81943 - 4.53019i) q^{66} +3.19460 q^{67} +0.0254366 q^{68} +1.16663i q^{69} +(2.16663 - 3.23607i) q^{70} -0.224692 q^{71} +2.69862i q^{72} +0.732688 q^{73} -1.02570i q^{74} -1.00000i q^{75} +1.00026 q^{76} +(8.58569 + 1.81271i) q^{77} -2.92152 q^{78} +2.98506i q^{79} +4.30550i q^{80} +1.00000 q^{81} +10.8660i q^{82} +9.97231 q^{83} +(0.366344 + 0.245277i) q^{84} +0.152649i q^{85} -16.0530 q^{86} +5.77630 q^{87} +(-8.30550 + 3.33568i) q^{88} -12.0023i q^{89} +1.47195 q^{90} +(2.92152 - 4.36356i) q^{91} -0.194401 q^{92} -0.696828 q^{93} +15.7452 q^{94} +6.00272i q^{95} -0.940237 q^{96} +4.13654i q^{97} +(-9.52666 + 3.92529i) q^{98} +(1.23607 + 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) \) 16 * q - 24 * q^4 - 16 * q^9	\( 16 q - 24 q^{4} - 16 q^{9} + 16 q^{11} + 16 q^{14} + 16 q^{15} + 24 q^{16} + 40 q^{23} - 16 q^{25} + 24 q^{36} - 40 q^{37} - 56 q^{42} - 24 q^{44} + 8 q^{53} + 8 q^{56} + 72 q^{58} - 24 q^{60} + 8 q^{64} + 80 q^{67} + 56 q^{70} - 24 q^{71} - 16 q^{78} + 16 q^{81} - 8 q^{86} - 40 q^{88} + 16 q^{91} - 160 q^{92} + 40 q^{93} - 16 q^{99}+O(q^{100}) \) 16 * q - 24 * q^4 - 16 * q^9 + 16 * q^11 + 16 * q^14 + 16 * q^15 + 24 * q^16 + 40 * q^23 - 16 * q^25 + 24 * q^36 - 40 * q^37 - 56 * q^42 - 24 * q^44 + 8 * q^53 + 8 * q^56 + 72 * q^58 - 24 * q^60 + 8 * q^64 + 80 * q^67 + 56 * q^70 - 24 * q^71 - 16 * q^78 + 16 * q^81 - 8 * q^86 - 40 * q^88 + 16 * q^91 - 160 * q^92 + 40 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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