LMFDB - Embedded newform 1155.2.i.c.76.12

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			76.12
Root			$-0.644389 - 0.983224i$ of defining polynomial
Character	$\chi$	$=$	1155.76
Dual form			1155.2.i.c.76.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.47195i q^{2} +1.00000i q^{3} -0.166634 q^{4} -1.00000i q^{5} -1.47195 q^{6} +(1.47195 - 2.19849i) q^{7} +2.69862i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.47195i q^{2} +1.00000i q^{3} -0.166634 q^{4} -1.00000i q^{5} -1.47195 q^{6} +(1.47195 - 2.19849i) q^{7} +2.69862i q^{8} -1.00000 q^{9} +1.47195 q^{10} +(-1.23607 + 3.07768i) q^{11} -0.166634i q^{12} +1.98480 q^{13} +(3.23607 + 2.16663i) q^{14} +1.00000 q^{15} -4.30550 q^{16} +0.152649 q^{17} -1.47195i q^{18} +6.00272 q^{19} +0.166634i q^{20} +(2.19849 + 1.47195i) q^{21} +(-4.53019 - 1.81943i) q^{22} +1.16663 q^{23} -2.69862 q^{24} -1.00000 q^{25} +2.92152i q^{26} -1.00000i q^{27} +(-0.245277 + 0.366344i) q^{28} +5.77630i q^{29} +1.47195i q^{30} +0.696828i q^{31} -0.940237i q^{32} +(-3.07768 - 1.23607i) q^{33} +0.224692i q^{34} +(-2.19849 - 1.47195i) q^{35} +0.166634 q^{36} +0.696828 q^{37} +8.83570i q^{38} +1.98480i q^{39} +2.69862 q^{40} +7.38204 q^{41} +(-2.16663 + 3.23607i) q^{42} +10.9060i q^{43} +(0.205971 - 0.512848i) q^{44} +1.00000i q^{45} +1.71723i q^{46} +10.6968i q^{47} -4.30550i q^{48} +(-2.66673 - 6.47214i) q^{49} -1.47195i q^{50} +0.152649i q^{51} -0.330735 q^{52} -4.56029 q^{53} +1.47195 q^{54} +(3.07768 + 1.23607i) q^{55} +(5.93290 + 3.97223i) q^{56} +6.00272i q^{57} -8.50243 q^{58} -7.53019i q^{59} -0.166634 q^{60} +3.81694 q^{61} -1.02570 q^{62} +(-1.47195 + 2.19849i) q^{63} -7.22702 q^{64} -1.98480i q^{65} +(1.81943 - 4.53019i) q^{66} +3.19460 q^{67} -0.0254366 q^{68} +1.16663i q^{69} +(2.16663 - 3.23607i) q^{70} -0.224692 q^{71} -2.69862i q^{72} -0.732688 q^{73} +1.02570i q^{74} -1.00000i q^{75} -1.00026 q^{76} +(4.94683 + 7.24768i) q^{77} -2.92152 q^{78} -2.98506i q^{79} +4.30550i q^{80} +1.00000 q^{81} +10.8660i q^{82} -9.97231 q^{83} +(-0.366344 - 0.245277i) q^{84} -0.152649i q^{85} -16.0530 q^{86} -5.77630 q^{87} +(-8.30550 - 3.33568i) q^{88} -12.0023i q^{89} -1.47195 q^{90} +(2.92152 - 4.36356i) q^{91} -0.194401 q^{92} -0.696828 q^{93} -15.7452 q^{94} -6.00272i q^{95} +0.940237 q^{96} +4.13654i q^{97} +(9.52666 - 3.92529i) q^{98} +(1.23607 - 3.07768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.174222\pi$
$2$			1.47195i			1.04083i	−0.853915	+	0.520413i	$0.825778\pi$
$3$			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	$-0.411242\pi$
$13$	1.98480			0.550484			0.275242	+	0.961375i	$0.411242\pi$
$14$	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	$-0.494107\pi$
$17$	0.152649			0.0370229			0.0185114	+	0.999829i	$0.494107\pi$
$18$		−	1.47195i		−	0.346942i
$19$	6.00272			1.37712			0.688559	−	0.725180i	$-0.258244\pi$
$19$	6.00272			1.37712			0.688559	+	0.725180i	$0.258244\pi$
$20$			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	$0.180185\pi$
$29$			5.77630i			1.07263i	−0.844017	+	0.536316i	$0.819815\pi$
$30$			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	$-0.304441\pi$
$41$	7.38204			1.15288			0.576440	+	0.817139i	$0.304441\pi$
$42$	−2.16663	+	3.23607i	−0.334319	+	0.499336i
$43$			10.9060i			1.66315i	0.555416	+	0.831573i	$0.312559\pi$
$43$			10.9060i			1.66315i	−0.555416	+	0.831573i	$0.687441\pi$
$44$	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	$-0.421424\pi$
$61$	3.81694			0.488710			0.244355	+	0.969686i	$0.421424\pi$
$62$	−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	$-0.513652\pi$
$73$	−0.732688			−0.0857547			−0.0428773	+	0.999080i	$0.513652\pi$
$74$			1.02570i			0.119235i
$75$		−	1.00000i		−	0.115470i
$76$	−1.00026			−0.114738
$77$	4.94683	+	7.24768i	0.563744	+	0.825950i
$78$	−2.92152			−0.330797
$79$		−	2.98506i		−	0.335845i	−0.985800	−	0.167922i	$-0.946294\pi$
$79$		−	2.98506i		−	0.335845i	0.985800	−	0.167922i	$-0.0537058\pi$
$80$			4.30550i			0.481370i
$81$	1.00000			0.111111
$82$			10.8660i			1.19995i
$83$	−9.97231			−1.09460			−0.547302	−	0.836935i	$-0.684345\pi$
$83$	−9.97231			−1.09460			−0.547302	+	0.836935i	$0.684345\pi$
$84$	−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	$-0.476968\pi$
$101$	1.45309			0.144587			0.0722937	+	0.997383i	$0.476968\pi$
$102$	−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	$-0.851586\pi$
$107$		−	9.30024i		−	0.899088i	0.893258	−	0.449544i	$-0.148414\pi$
$108$			0.166634i			0.0160344i
$109$		−	5.92895i		−	0.567891i	−0.958840	−	0.283945i	$-0.908357\pi$
$109$		−	5.92895i		−	0.567891i	0.958840	−	0.283945i	$-0.0916434\pi$
$110$	−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	$0.00913347\pi$
$127$			0.646633i			0.0573794i	−0.999588	+	0.0286897i	$0.990867\pi$
$128$		−	12.5183i		−	1.10647i
$129$	−10.9060			−0.960218
$130$	2.92152			0.256234
$131$	15.7863			1.37926			0.689630	−	0.724162i	$-0.257773\pi$
$131$	15.7863			1.37926			0.689630	+	0.724162i	$0.257773\pi$
$132$	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	$-0.594360\pi$
$139$	−6.88806			−0.584237			−0.292119	+	0.956382i	$0.594360\pi$
$140$	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	$0.0476226\pi$
$149$			3.63886i			0.298107i	−0.988829	+	0.149053i	$0.952377\pi$
$150$	1.47195			0.120184
$151$		−	23.0606i		−	1.87665i	−0.345758	−	0.938324i	$-0.612378\pi$
$151$		−	23.0606i		−	1.87665i	0.345758	−	0.938324i	$-0.387622\pi$
$152$			16.1991i			1.31392i
$153$	−0.152649			−0.0123410
$154$	−10.6682	+	7.28149i	−0.859669	+	0.586759i
$155$	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	$-0.604440\pi$
$167$	−8.32885			−0.644506			−0.322253	+	0.946654i	$0.604440\pi$
$168$	−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	$-0.755701\pi$
$173$	−18.9312			−1.43931			−0.719657	+	0.694330i	$0.755701\pi$
$174$		−	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	$-0.966211\pi$
$193$		−	2.94390i		−	0.211906i	0.994371	−	0.105953i	$-0.0337894\pi$
$194$	−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	$0.302233\pi$
$197$			22.8254i			1.62624i	−0.582097	+	0.813120i	$0.697767\pi$
$198$	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	$0.147051\pi$
$211$			12.9488i			0.891433i	−0.895174	+	0.445717i	$0.852949\pi$
$212$	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	$-0.437753\pi$
$227$	5.85519			0.388623			0.194311	+	0.980940i	$0.437753\pi$
$228$		−	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
$231$	−7.24768	+	4.94683i	−0.476862	+	0.325478i
$232$	−15.5881			−1.02341
$233$		−	9.33797i		−	0.611751i	−0.952072	−	0.305875i	$-0.901051\pi$
$233$		−	9.33797i		−	0.611751i	0.952072	−	0.305875i	$-0.0989491\pi$
$234$		−	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	$-0.960050\pi$
$239$		−	3.87039i		−	0.250355i	0.992134	−	0.125177i	$-0.0399500\pi$
$240$	−4.30550			−0.277919
$241$	2.19806			0.141590			0.0707949	−	0.997491i	$-0.477446\pi$
$241$	2.19806			0.141590			0.0707949	+	0.997491i	$0.477446\pi$
$242$	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	$-0.936423\pi$
$263$		−	6.43523i		−	0.396813i	0.980120	−	0.198407i	$-0.0635767\pi$
$264$	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	$-0.577338\pi$
$271$	−7.92092			−0.481162			−0.240581	+	0.970629i	$0.577338\pi$
$272$	−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	$0.160802\pi$
$277$			16.1094i			0.967921i	−0.875090	+	0.483960i	$0.839198\pi$
$278$		−	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	$0.356543\pi$
$281$			30.1785i			1.80030i	−0.435580	+	0.900150i	$0.643457\pi$
$282$		−	15.7452i		−	0.937612i
$283$	−1.23896			−0.0736487			−0.0368244	−	0.999322i	$-0.511724\pi$
$283$	−1.23896			−0.0736487			−0.0368244	+	0.999322i	$0.511724\pi$
$284$	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	$-0.641137\pi$
$293$	−14.6869			−0.858017			−0.429008	+	0.903300i	$0.641137\pi$
$294$	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	$-0.423146\pi$
$307$	8.37887			0.478207			0.239104	+	0.970994i	$0.423146\pi$
$308$	−0.824312	−	1.20771i	−0.0469695	−	0.0688158i
$309$	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	$-0.879494\pi$
$337$		−	13.5700i		−	0.739206i	0.929190	−	0.369603i	$-0.120506\pi$
$338$		−	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	$-0.791283\pi$
$347$		−	22.7156i		−	1.21943i	0.792619	−	0.609717i	$-0.208717\pi$
$348$	0.962531			0.0515971
$349$	31.2114			1.67071			0.835354	−	0.549713i	$-0.185263\pi$
$349$	31.2114			1.67071			0.835354	+	0.549713i	$0.185263\pi$
$350$	−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	$-0.651429\pi$
$359$		−	33.6867i		−	1.77792i	0.457986	−	0.888959i	$-0.348571\pi$
$360$	−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	$0.145859\pi$
$373$			17.0868i			0.884720i	−0.896838	+	0.442360i	$0.854141\pi$
$374$	−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
$385$	7.24768	−	4.94683i	0.369376	−	0.252114i
$386$	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	$-0.285938\pi$
$409$	25.1964			1.24588			0.622941	+	0.782269i	$0.285938\pi$
$410$	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	$0.236773\pi$
$431$			28.1148i			1.35424i	−0.735871	+	0.677122i	$0.763227\pi$
$432$			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	$-0.640703\pi$
$439$	−17.9258			−0.855554			−0.427777	+	0.903884i	$0.640703\pi$
$440$	−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	$-0.856535\pi$
$457$		−	18.6242i		−	0.871205i	0.900139	−	0.435602i	$-0.143465\pi$
$458$	30.9621			1.44676
$459$		−	0.152649i		−	0.00712506i
$460$			0.194401i			0.00906401i
$461$	−29.9110			−1.39309			−0.696546	−	0.717512i	$-0.745281\pi$
$461$	−29.9110			−1.39309			−0.696546	+	0.717512i	$0.745281\pi$
$462$	−7.28149	−	10.6682i	−0.338765	−	0.496330i
$463$	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	$-0.637586\pi$
$479$	−18.3363			−0.837809			−0.418904	+	0.908030i	$0.637586\pi$
$480$		−	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	$-0.854131\pi$
$491$		−	19.6053i		−	0.884776i	0.896824	−	0.442388i	$-0.145869\pi$
$492$		−	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	$-0.520406\pi$
$503$	−2.87356			−0.128126			−0.0640629	+	0.997946i	$0.520406\pi$
$504$	−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	$-0.433124\pi$
$523$	9.53895			0.417109			0.208555	+	0.978011i	$0.433124\pi$
$524$	−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
$539$	23.2154	−	0.207355i	0.999960	−	0.00893142i
$540$	0.166634			0.00717080
$541$		−	27.7409i		−	1.19267i	−0.802734	−	0.596337i	$-0.796622\pi$
$541$		−	27.7409i		−	1.19267i	0.802734	−	0.596337i	$-0.203378\pi$
$542$		−	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	$-0.714181\pi$
$547$		−	36.5806i		−	1.56407i	0.623232	−	0.782037i	$-0.285819\pi$
$548$	−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	$-0.925358\pi$
$557$		−	10.9674i		−	0.464706i	0.972632	−	0.232353i	$-0.0746424\pi$
$558$	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	$-0.217655\pi$
$563$	36.7867			1.55038			0.775188	+	0.631731i	$0.217655\pi$
$564$	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	$0.122815\pi$
$569$			17.9539i			0.752665i	−0.926485	+	0.376332i	$0.877185\pi$
$570$			8.83570i			0.370087i
$571$			16.6543i			0.696959i	0.937316	+	0.348480i	$0.113302\pi$
$571$			16.6543i			0.696959i	−0.937316	+	0.348480i	$0.886698\pi$
$572$	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	$-0.721678\pi$
$593$	−31.2420			−1.28295			−0.641477	+	0.767143i	$0.721678\pi$
$594$	−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	$-0.553746\pi$
$601$	−8.23936			−0.336091			−0.168045	+	0.985779i	$0.553746\pi$
$602$	−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	$-0.336992\pi$
$607$	24.1453			0.980026			0.490013	+	0.871715i	$0.336992\pi$
$608$		−	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	$-0.830705\pi$
$613$		−	25.1120i		−	1.01427i	0.861868	−	0.507133i	$-0.169295\pi$
$614$			12.3333i			0.497730i
$615$	7.38204			0.297673
$616$	−19.5587	+	13.3496i	−0.788044	+	0.537872i
$617$	−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	$0.165983\pi$
$659$			25.5754i			0.996278i	−0.867097	+	0.498139i	$0.834017\pi$
$660$	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	$0.378419\pi$
$673$			48.1455i			1.85587i	−0.372738	+	0.927937i	$0.621581\pi$
$674$	19.9744			0.769384
$675$			1.00000i			0.0384900i
$676$	1.50980			0.0580694
$677$	−2.45847			−0.0944865			−0.0472433	−	0.998883i	$-0.515044\pi$
$677$	−2.45847			−0.0944865			−0.0472433	+	0.998883i	$0.515044\pi$
$678$	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
$693$	−4.94683	−	7.24768i	−0.187915	−	0.275317i
$694$	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	$0.0570543\pi$
$701$			9.44060i			0.356567i	−0.983979	+	0.178283i	$0.942946\pi$
$702$	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	$-0.659283\pi$
$733$	−25.9791			−0.959560			−0.479780	+	0.877389i	$0.659283\pi$
$734$	−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	$0.123940\pi$
$739$			20.6387i			0.759208i	−0.925149	+	0.379604i	$0.876060\pi$
$740$			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	$0.219396\pi$
$743$			34.6701i			1.27192i	−0.771721	+	0.635962i	$0.780604\pi$
$744$		−	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	$-0.485829\pi$
$761$	2.45539			0.0890079			0.0445039	+	0.999009i	$0.485829\pi$
$762$		−	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	$-0.701960\pi$
$769$	−32.8752			−1.18551			−0.592755	+	0.805383i	$0.701960\pi$
$770$	7.28149	+	10.6682i	0.262407	+	0.384456i
$771$	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	$-0.119852\pi$
$787$	52.1766			1.85989			0.929947	+	0.367693i	$0.119852\pi$
$788$		−	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	$0.198092\pi$
$809$			33.1602i			1.16585i	−0.812526	+	0.582925i	$0.801908\pi$
$810$	1.47195			0.0517190
$811$	26.6028			0.934152			0.467076	−	0.884217i	$-0.345307\pi$
$811$	26.6028			0.934152			0.467076	+	0.884217i	$0.345307\pi$
$812$	−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	$-0.756707\pi$
$821$		−	39.6589i		−	1.38411i	0.721847	−	0.692053i	$-0.243293\pi$
$822$	−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	$0.0122406\pi$
$827$			2.21121i			0.0768913i	−0.999261	+	0.0384457i	$0.987759\pi$
$828$	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
$847$	−28.4207	+	6.26616i	−0.976546	+	0.215308i
$848$	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	$-0.329381\pi$
$853$	29.8321			1.02143			0.510715	+	0.859750i	$0.329381\pi$
$854$	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	$-0.109883\pi$
$857$	55.0951			1.88201			0.941006	+	0.338391i	$0.109883\pi$
$858$	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	$0.138070\pi$
$877$			24.8928i			0.840569i	−0.907392	+	0.420285i	$0.861930\pi$
$878$		−	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	$-0.527676\pi$
$887$	−5.17252			−0.173676			−0.0868381	+	0.996222i	$0.527676\pi$
$888$	−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	$-0.941325\pi$
$919$		−	11.1129i		−	0.366582i	0.983059	−	0.183291i	$-0.0586750\pi$
$920$	3.14830			0.103797
$921$			8.37887i			0.276093i
$922$		−	44.0274i		−	1.44997i
$923$	−0.445968			−0.0146792
$924$	1.20771	−	0.824312i	0.0397308	−	0.0271179i
$925$	−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	$-0.354690\pi$
$937$	26.9870			0.881628			0.440814	+	0.897599i	$0.354690\pi$
$938$	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	$-0.368427\pi$
$941$	24.6435			0.803354			0.401677	+	0.915781i	$0.368427\pi$
$942$		−	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	$0.144312\pi$
$953$			27.0425i			0.875993i	−0.898977	+	0.437997i	$0.855688\pi$
$954$			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	$0.216469\pi$
$967$			39.1094i			1.25767i	−0.777537	+	0.628837i	$0.783531\pi$
$968$	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	$-0.593616\pi$
$997$	−18.3063			−0.579766			−0.289883	+	0.957062i	$0.593616\pi$
$998$		−	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.76.12	yes	16
7.6	odd	2	inner	1155.2.i.c.76.11	yes	16
11.10	odd	2	inner	1155.2.i.c.76.6	yes	16
77.76	even	2	inner	1155.2.i.c.76.5	✓	16

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

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)

\(f(q)\)	\(=\)	\(q+1.47195i q^{2} +1.00000i q^{3} -0.166634 q^{4} -1.00000i q^{5} -1.47195 q^{6} +(1.47195 - 2.19849i) q^{7} +2.69862i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.47195i q^{2} +1.00000i q^{3} -0.166634 q^{4} -1.00000i q^{5} -1.47195 q^{6} +(1.47195 - 2.19849i) q^{7} +2.69862i q^{8} -1.00000 q^{9} +1.47195 q^{10} +(-1.23607 + 3.07768i) q^{11} -0.166634i q^{12} +1.98480 q^{13} +(3.23607 + 2.16663i) q^{14} +1.00000 q^{15} -4.30550 q^{16} +0.152649 q^{17} -1.47195i q^{18} +6.00272 q^{19} +0.166634i q^{20} +(2.19849 + 1.47195i) q^{21} +(-4.53019 - 1.81943i) q^{22} +1.16663 q^{23} -2.69862 q^{24} -1.00000 q^{25} +2.92152i q^{26} -1.00000i q^{27} +(-0.245277 + 0.366344i) q^{28} +5.77630i q^{29} +1.47195i q^{30} +0.696828i q^{31} -0.940237i q^{32} +(-3.07768 - 1.23607i) q^{33} +0.224692i q^{34} +(-2.19849 - 1.47195i) q^{35} +0.166634 q^{36} +0.696828 q^{37} +8.83570i q^{38} +1.98480i q^{39} +2.69862 q^{40} +7.38204 q^{41} +(-2.16663 + 3.23607i) q^{42} +10.9060i q^{43} +(0.205971 - 0.512848i) q^{44} +1.00000i q^{45} +1.71723i q^{46} +10.6968i q^{47} -4.30550i q^{48} +(-2.66673 - 6.47214i) q^{49} -1.47195i q^{50} +0.152649i q^{51} -0.330735 q^{52} -4.56029 q^{53} +1.47195 q^{54} +(3.07768 + 1.23607i) q^{55} +(5.93290 + 3.97223i) q^{56} +6.00272i q^{57} -8.50243 q^{58} -7.53019i q^{59} -0.166634 q^{60} +3.81694 q^{61} -1.02570 q^{62} +(-1.47195 + 2.19849i) q^{63} -7.22702 q^{64} -1.98480i q^{65} +(1.81943 - 4.53019i) q^{66} +3.19460 q^{67} -0.0254366 q^{68} +1.16663i q^{69} +(2.16663 - 3.23607i) q^{70} -0.224692 q^{71} -2.69862i q^{72} -0.732688 q^{73} +1.02570i q^{74} -1.00000i q^{75} -1.00026 q^{76} +(4.94683 + 7.24768i) q^{77} -2.92152 q^{78} -2.98506i q^{79} +4.30550i q^{80} +1.00000 q^{81} +10.8660i q^{82} -9.97231 q^{83} +(-0.366344 - 0.245277i) q^{84} -0.152649i q^{85} -16.0530 q^{86} -5.77630 q^{87} +(-8.30550 - 3.33568i) q^{88} -12.0023i q^{89} -1.47195 q^{90} +(2.92152 - 4.36356i) q^{91} -0.194401 q^{92} -0.696828 q^{93} -15.7452 q^{94} -6.00272i q^{95} +0.940237 q^{96} +4.13654i q^{97} +(9.52666 - 3.92529i) q^{98} +(1.23607 - 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) \) 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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