LMFDB - Embedded newform 1638.2.y.b.827.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(827,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("1638.827");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.y (of order $4$, degree $2$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 4 x^{10} + 12 x^{9} - 40 x^{8} + 12 x^{7} + 230 x^{6} - 144 x^{5} + 129 x^{4} + \cdots + 2 $ x^12 - 4x^11 + 4x^10 + 12x^9 - 40x^8 + 12x^7 + 230x^6 - 144x^5 + 129x^4 - 56x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			827.1
Root			$0.218790 + 0.528206i$ of defining polynomial
Character	$\chi$	$=$	1638.827
Dual form			1638.2.y.b.1331.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.24541 + 2.24541i) q^{5} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.24541 + 2.24541i) q^{5} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -3.17548i q^{10} +(1.49250 + 1.49250i) q^{11} +(-3.59471 - 0.279383i) q^{13} +1.00000i q^{14} -1.00000 q^{16} +0.776275 q^{17} +(-2.73940 - 2.73940i) q^{19} +(2.24541 + 2.24541i) q^{20} -2.11071 q^{22} -2.11071 q^{23} -5.08369i q^{25} +(2.73940 - 2.34429i) q^{26} +(-0.707107 - 0.707107i) q^{28} +4.11071i q^{29} +(-2.19049 - 2.19049i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.548909 + 0.548909i) q^{34} +3.17548i q^{35} +(1.51160 - 1.51160i) q^{37} +3.87409 q^{38} -3.17548 q^{40} +(1.17548 - 1.17548i) q^{41} +4.06950i q^{43} +(1.49250 - 1.49250i) q^{44} +(1.49250 - 1.49250i) q^{46} +(-4.65447 - 4.65447i) q^{47} -1.00000i q^{49} +(3.59471 + 3.59471i) q^{50} +(-0.279383 + 3.59471i) q^{52} -0.828427i q^{53} -6.70252 q^{55} +1.00000 q^{56} +(-2.90671 - 2.90671i) q^{58} +(-8.37799 - 8.37799i) q^{59} +5.91811 q^{61} +3.09782 q^{62} +1.00000i q^{64} +(8.69891 - 7.44425i) q^{65} +(-6.16029 - 6.16029i) q^{67} -0.776275i q^{68} +(-2.24541 - 2.24541i) q^{70} +(-1.86015 + 1.86015i) q^{71} +(10.8392 - 10.8392i) q^{73} +2.13773i q^{74} +(-2.73940 + 2.73940i) q^{76} +2.11071 q^{77} +10.9928 q^{79} +(2.24541 - 2.24541i) q^{80} +1.66238i q^{82} +(2.13985 - 2.13985i) q^{83} +(-1.74305 + 1.74305i) q^{85} +(-2.87757 - 2.87757i) q^{86} +2.11071i q^{88} +(-2.33033 - 2.33033i) q^{89} +(-2.73940 + 2.34429i) q^{91} +2.11071i q^{92} +6.58241 q^{94} +12.3021 q^{95} +(-12.2393 - 12.2393i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{5}+O(q^{10}) $ 12 * q + 4 * q^5	$ 12 q + 4 q^{5} + 8 q^{11} - 16 q^{13} - 12 q^{16} + 8 q^{17} - 4 q^{20} + 8 q^{22} + 8 q^{23} - 8 q^{31} + 8 q^{34} + 16 q^{38} - 24 q^{41} + 8 q^{44} + 8 q^{46} + 4 q^{47} + 16 q^{50} - 16 q^{55} + 12 q^{56} - 8 q^{58} - 48 q^{59} + 32 q^{61} + 8 q^{62} + 8 q^{65} + 28 q^{67} + 4 q^{70} - 8 q^{71} + 16 q^{73} - 8 q^{77} - 32 q^{79} - 4 q^{80} + 40 q^{83} + 8 q^{85} + 40 q^{86} - 24 q^{89} - 8 q^{94} + 8 q^{95} + 8 q^{97}+O(q^{100}) $ 12 * q + 4 * q^5 + 8 * q^11 - 16 * q^13 - 12 * q^16 + 8 * q^17 - 4 * q^20 + 8 * q^22 + 8 * q^23 - 8 * q^31 + 8 * q^34 + 16 * q^38 - 24 * q^41 + 8 * q^44 + 8 * q^46 + 4 * q^47 + 16 * q^50 - 16 * q^55 + 12 * q^56 - 8 * q^58 - 48 * q^59 + 32 * q^61 + 8 * q^62 + 8 * q^65 + 28 * q^67 + 4 * q^70 - 8 * q^71 + 16 * q^73 - 8 * q^77 - 32 * q^79 - 4 * q^80 + 40 * q^83 + 8 * q^85 + 40 * q^86 - 24 * q^89 - 8 * q^94 + 8 * q^95 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−2.24541	+	2.24541i	−1.00418	+	1.00418i	−0.00418447	+	0.999991i	$0.501332\pi$
$5$	−2.24541	+	2.24541i	−1.00418	+	1.00418i	−0.999991	+	0.00418447i	$0.998668\pi$
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$		−	3.17548i		−	1.00418i
$11$	1.49250	+	1.49250i	0.450005	+	0.450005i	0.895356	−	0.445351i	$-0.146921\pi$
$11$	1.49250	+	1.49250i	0.450005	+	0.450005i	−0.445351	+	0.895356i	$0.646921\pi$
$12$		0			0
$13$	−3.59471	−	0.279383i	−0.996993	−	0.0774869i
$13$	−3.59471	−	0.279383i	−0.996993	−	0.0774869i
$14$			1.00000i			0.267261i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	0.776275			0.188274			0.0941372	−	0.995559i	$-0.469991\pi$
$17$	0.776275			0.188274			0.0941372	+	0.995559i	$0.469991\pi$
$18$		0			0
$19$	−2.73940	−	2.73940i	−0.628461	−	0.628461i	0.319220	−	0.947681i	$-0.396579\pi$
$19$	−2.73940	−	2.73940i	−0.628461	−	0.628461i	−0.947681	+	0.319220i	$0.896579\pi$
$20$	2.24541	+	2.24541i	0.502088	+	0.502088i
$21$		0			0
$22$	−2.11071			−0.450005
$23$	−2.11071			−0.440113			−0.220057	−	0.975487i	$-0.570624\pi$
$23$	−2.11071			−0.440113			−0.220057	+	0.975487i	$0.570624\pi$
$24$		0			0
$25$		−	5.08369i		−	1.01674i
$26$	2.73940	−	2.34429i	0.537240	−	0.459753i
$27$		0			0
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$			4.11071i			0.763340i	0.924299	+	0.381670i	$0.124651\pi$
$29$			4.11071i			0.763340i	−0.924299	+	0.381670i	$0.875349\pi$
$30$		0			0
$31$	−2.19049	−	2.19049i	−0.393423	−	0.393423i	0.482482	−	0.875906i	$-0.339735\pi$
$31$	−2.19049	−	2.19049i	−0.393423	−	0.393423i	−0.875906	+	0.482482i	$0.839735\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−0.548909	+	0.548909i	−0.0941372	+	0.0941372i
$35$			3.17548i			0.536754i
$36$		0			0
$37$	1.51160	−	1.51160i	0.248506	−	0.248506i	−0.571851	−	0.820357i	$-0.693775\pi$
$37$	1.51160	−	1.51160i	0.248506	−	0.248506i	0.820357	+	0.571851i	$0.193775\pi$
$38$	3.87409			0.628461
$39$		0			0
$40$	−3.17548			−0.502088
$41$	1.17548	−	1.17548i	0.183580	−	0.183580i	−0.609334	−	0.792914i	$-0.708563\pi$
$41$	1.17548	−	1.17548i	0.183580	−	0.183580i	0.792914	+	0.609334i	$0.208563\pi$
$42$		0			0
$43$			4.06950i			0.620594i	0.950640	+	0.310297i	$0.100428\pi$
$43$			4.06950i			0.620594i	−0.950640	+	0.310297i	$0.899572\pi$
$44$	1.49250	−	1.49250i	0.225002	−	0.225002i
$45$		0			0
$46$	1.49250	−	1.49250i	0.220057	−	0.220057i
$47$	−4.65447	−	4.65447i	−0.678924	−	0.678924i	0.280833	−	0.959757i	$-0.409389\pi$
$47$	−4.65447	−	4.65447i	−0.678924	−	0.678924i	−0.959757	+	0.280833i	$0.909389\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	3.59471	+	3.59471i	0.508369	+	0.508369i
$51$		0			0
$52$	−0.279383	+	3.59471i	−0.0387434	+	0.498497i
$53$		−	0.828427i		−	0.113793i	−0.998380	−	0.0568966i	$-0.981879\pi$
$53$		−	0.828427i		−	0.113793i	0.998380	−	0.0568966i	$-0.0181205\pi$
$54$		0			0
$55$	−6.70252			−0.903768
$56$	1.00000			0.133631
$57$		0			0
$58$	−2.90671	−	2.90671i	−0.381670	−	0.381670i
$59$	−8.37799	−	8.37799i	−1.09072	−	1.09072i	−0.995452	−	0.0952693i	$-0.969629\pi$
$59$	−8.37799	−	8.37799i	−1.09072	−	1.09072i	−0.0952693	−	0.995452i	$-0.530371\pi$
$60$		0			0
$61$	5.91811			0.757736			0.378868	−	0.925451i	$-0.376313\pi$
$61$	5.91811			0.757736			0.378868	+	0.925451i	$0.376313\pi$
$62$	3.09782			0.393423
$63$		0			0
$64$			1.00000i			0.125000i
$65$	8.69891	−	7.44425i	1.07897	−	0.923346i
$66$		0			0
$67$	−6.16029	−	6.16029i	−0.752599	−	0.752599i	0.222365	−	0.974964i	$-0.428622\pi$
$67$	−6.16029	−	6.16029i	−0.752599	−	0.752599i	−0.974964	+	0.222365i	$0.928622\pi$
$68$		−	0.776275i		−	0.0941372i
$69$		0			0
$70$	−2.24541	−	2.24541i	−0.268377	−	0.268377i
$71$	−1.86015	+	1.86015i	−0.220760	+	0.220760i	−0.808818	−	0.588059i	$-0.799892\pi$
$71$	−1.86015	+	1.86015i	−0.220760	+	0.220760i	0.588059	+	0.808818i	$0.299892\pi$
$72$		0			0
$73$	10.8392	−	10.8392i	1.26863	−	1.26863i	0.321838	−	0.946795i	$-0.395699\pi$
$73$	10.8392	−	10.8392i	1.26863	−	1.26863i	0.946795	−	0.321838i	$-0.104301\pi$
$74$			2.13773i			0.248506i
$75$		0			0
$76$	−2.73940	+	2.73940i	−0.314230	+	0.314230i
$77$	2.11071			0.240538
$78$		0			0
$79$	10.9928			1.23679			0.618394	−	0.785868i	$-0.287784\pi$
$79$	10.9928			1.23679			0.618394	+	0.785868i	$0.287784\pi$
$80$	2.24541	−	2.24541i	0.251044	−	0.251044i
$81$		0			0
$82$			1.66238i			0.183580i
$83$	2.13985	−	2.13985i	0.234879	−	0.234879i	−0.579847	−	0.814725i	$-0.696888\pi$
$83$	2.13985	−	2.13985i	0.234879	−	0.234879i	0.814725	+	0.579847i	$0.196888\pi$
$84$		0			0
$85$	−1.74305	+	1.74305i	−0.189061	+	0.189061i
$86$	−2.87757	−	2.87757i	−0.310297	−	0.310297i
$87$		0			0
$88$			2.11071i			0.225002i
$89$	−2.33033	−	2.33033i	−0.247015	−	0.247015i	0.572730	−	0.819744i	$-0.305885\pi$
$89$	−2.33033	−	2.33033i	−0.247015	−	0.247015i	−0.819744	+	0.572730i	$0.805885\pi$
$90$		0			0
$91$	−2.73940	+	2.34429i	−0.287167	+	0.245748i
$92$			2.11071i			0.220057i
$93$		0			0
$94$	6.58241			0.678924
$95$	12.3021			1.26217
$96$		0			0
$97$	−12.2393	−	12.2393i	−1.24271	−	1.24271i	−0.958873	−	0.283837i	$-0.908393\pi$
$97$	−12.2393	−	12.2393i	−1.24271	−	1.24271i	−0.283837	−	0.958873i	$-0.591607\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		0			0
$100$	−5.08369			−0.508369
$101$	6.79021			0.675652			0.337826	−	0.941209i	$-0.390309\pi$
$101$	6.79021			0.675652			0.337826	+	0.941209i	$0.390309\pi$
$102$		0			0
$103$		−	14.6543i		−	1.44393i	−0.691930	−	0.721964i	$-0.743239\pi$
$103$		−	14.6543i		−	1.44393i	0.691930	−	0.721964i	$-0.256761\pi$
$104$	−2.34429	−	2.73940i	−0.229877	−	0.268620i
$105$		0			0
$106$	0.585786	+	0.585786i	0.0568966	+	0.0568966i
$107$		−	12.9758i		−	1.25442i	−0.778850	−	0.627210i	$-0.784197\pi$
$107$		−	12.9758i		−	1.25442i	0.778850	−	0.627210i	$-0.215803\pi$
$108$		0			0
$109$	1.50041	+	1.50041i	0.143713	+	0.143713i	0.775303	−	0.631590i	$-0.217597\pi$
$109$	1.50041	+	1.50041i	0.143713	+	0.143713i	−0.631590	+	0.775303i	$0.717597\pi$
$110$	4.73940	−	4.73940i	0.451884	−	0.451884i
$111$		0			0
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$			13.1041i			1.23273i	0.787460	+	0.616366i	$0.211396\pi$
$113$			13.1041i			1.23273i	−0.787460	+	0.616366i	$0.788604\pi$
$114$		0			0
$115$	4.73940	−	4.73940i	0.441951	−	0.441951i
$116$	4.11071			0.381670
$117$		0			0
$118$	11.8483			1.09072
$119$	0.548909	−	0.548909i	0.0503184	−	0.0503184i
$120$		0			0
$121$		−	6.54491i		−	0.594991i
$122$	−4.18473	+	4.18473i	−0.378868	+	0.378868i
$123$		0			0
$124$	−2.19049	+	2.19049i	−0.196712	+	0.196712i
$125$	0.187915	+	0.187915i	0.0168076	+	0.0168076i
$126$		0			0
$127$			4.69888i			0.416958i	0.978027	+	0.208479i	$0.0668513\pi$
$127$			4.69888i			0.416958i	−0.978027	+	0.208479i	$0.933149\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−0.887175	+	11.4149i	−0.0778104	+	1.00116i
$131$		−	11.5443i		−	1.00863i	−0.863520	−	0.504315i	$-0.831745\pi$
$131$		−	11.5443i		−	1.00863i	0.863520	−	0.504315i	$-0.168255\pi$
$132$		0			0
$133$	−3.87409			−0.335927
$134$	8.71196			0.752599
$135$		0			0
$136$	0.548909	+	0.548909i	0.0470686	+	0.0470686i
$137$	−7.06627	−	7.06627i	−0.603712	−	0.603712i	0.337584	−	0.941296i	$-0.390390\pi$
$137$	−7.06627	−	7.06627i	−0.603712	−	0.603712i	−0.941296	+	0.337584i	$0.890390\pi$
$138$		0			0
$139$	−17.6560			−1.49756			−0.748782	−	0.662816i	$-0.769361\pi$
$139$	−17.6560			−1.49756			−0.748782	+	0.662816i	$0.769361\pi$
$140$	3.17548			0.268377
$141$		0			0
$142$		−	2.63066i		−	0.220760i
$143$	−4.94812	−	5.78207i	−0.413782	−	0.483521i
$144$		0			0
$145$	−9.23021	−	9.23021i	−0.766527	−	0.766527i
$146$			15.3289i			1.26863i
$147$		0			0
$148$	−1.51160	−	1.51160i	−0.124253	−	0.124253i
$149$	−7.45670	+	7.45670i	−0.610876	+	0.610876i	−0.943174	−	0.332298i	$-0.892176\pi$
$149$	−7.45670	+	7.45670i	−0.610876	+	0.610876i	0.332298	+	0.943174i	$0.392176\pi$
$150$		0			0
$151$	5.65080	−	5.65080i	0.459855	−	0.459855i	−0.438753	−	0.898608i	$-0.644580\pi$
$151$	5.65080	−	5.65080i	0.459855	−	0.459855i	0.898608	+	0.438753i	$0.144580\pi$
$152$		−	3.87409i		−	0.314230i
$153$		0			0
$154$	−1.49250	+	1.49250i	−0.120269	+	0.120269i
$155$	9.83707			0.790132
$156$		0			0
$157$	3.00219			0.239601			0.119801	−	0.992798i	$-0.461774\pi$
$157$	3.00219			0.239601			0.119801	+	0.992798i	$0.461774\pi$
$158$	−7.77309	+	7.77309i	−0.618394	+	0.618394i
$159$		0			0
$160$			3.17548i			0.251044i
$161$	−1.49250	+	1.49250i	−0.117625	+	0.117625i
$162$		0			0
$163$	−8.98784	+	8.98784i	−0.703982	+	0.703982i	−0.965263	−	0.261281i	$-0.915855\pi$
$163$	−8.98784	+	8.98784i	−0.703982	+	0.703982i	0.261281	+	0.965263i	$0.415855\pi$
$164$	−1.17548	−	1.17548i	−0.0917898	−	0.0917898i
$165$		0			0
$166$			3.02620i			0.234879i
$167$	3.09934	+	3.09934i	0.239834	+	0.239834i	0.816782	−	0.576947i	$-0.195756\pi$
$167$	3.09934	+	3.09934i	0.239834	+	0.239834i	−0.576947	+	0.816782i	$0.695756\pi$
$168$		0			0
$169$	12.8439	+	2.00860i	0.987992	+	0.154508i
$170$		−	2.46505i		−	0.189061i
$171$		0			0
$172$	4.06950			0.310297
$173$	11.9700			0.910061			0.455031	−	0.890476i	$-0.349628\pi$
$173$	11.9700			0.910061			0.455031	+	0.890476i	$0.349628\pi$
$174$		0			0
$175$	−3.59471	−	3.59471i	−0.271735	−	0.271735i
$176$	−1.49250	−	1.49250i	−0.112501	−	0.112501i
$177$		0			0
$178$	3.29559			0.247015
$179$	−14.6928			−1.09819			−0.549094	−	0.835761i	$-0.685027\pi$
$179$	−14.6928			−1.09819			−0.549094	+	0.835761i	$0.685027\pi$
$180$		0			0
$181$			5.43608i			0.404061i	0.979379	+	0.202030i	$0.0647540\pi$
$181$			5.43608i			0.404061i	−0.979379	+	0.202030i	$0.935246\pi$
$182$	0.279383	−	3.59471i	0.0207092	−	0.266458i
$183$		0			0
$184$	−1.49250	−	1.49250i	−0.110028	−	0.110028i
$185$			6.78832i			0.499088i
$186$		0			0
$187$	1.15859	+	1.15859i	0.0847243	+	0.0847243i
$188$	−4.65447	+	4.65447i	−0.339462	+	0.339462i
$189$		0			0
$190$	−8.69891	+	8.69891i	−0.631085	+	0.631085i
$191$		−	12.2699i		−	0.887818i	−0.896072	−	0.443909i	$-0.853591\pi$
$191$		−	12.2699i		−	0.887818i	0.896072	−	0.443909i	$-0.146409\pi$
$192$		0			0
$193$	9.62335	−	9.62335i	0.692704	−	0.692704i	−0.270122	−	0.962826i	$-0.587064\pi$
$193$	9.62335	−	9.62335i	0.692704	−	0.692704i	0.962826	+	0.270122i	$0.0870641\pi$
$194$	17.3089			1.24271
$195$		0			0
$196$	−1.00000			−0.0714286
$197$	−13.9162	+	13.9162i	−0.991489	+	0.991489i	−0.999964	−	0.00847473i	$-0.997302\pi$
$197$	−13.9162	+	13.9162i	−0.991489	+	0.991489i	0.00847473	+	0.999964i	$0.497302\pi$
$198$		0			0
$199$			6.23086i			0.441694i	0.975308	+	0.220847i	$0.0708821\pi$
$199$			6.23086i			0.441694i	−0.975308	+	0.220847i	$0.929118\pi$
$200$	3.59471	−	3.59471i	0.254184	−	0.254184i
$201$		0			0
$202$	−4.80141	+	4.80141i	−0.337826	+	0.337826i
$203$	2.90671	+	2.90671i	0.204011	+	0.204011i
$204$		0			0
$205$			5.27887i			0.368692i
$206$	10.3621	+	10.3621i	0.721964	+	0.721964i
$207$		0			0
$208$	3.59471	+	0.279383i	0.249248	+	0.0193717i
$209$		−	8.17709i		−	0.565621i
$210$		0			0
$211$	11.9614			0.823458			0.411729	−	0.911306i	$-0.364925\pi$
$211$	11.9614			0.823458			0.411729	+	0.911306i	$0.364925\pi$
$212$	−0.828427			−0.0568966
$213$		0			0
$214$	9.17529	+	9.17529i	0.627210	+	0.627210i
$215$	−9.13769	−	9.13769i	−0.623185	−	0.623185i
$216$		0			0
$217$	−3.09782			−0.210294
$218$	−2.12190			−0.143713
$219$		0			0
$220$			6.70252i			0.451884i
$221$	−2.79048	−	0.216878i	−0.187708	−	0.0145888i
$222$		0			0
$223$	2.75654	+	2.75654i	0.184591	+	0.184591i	0.793353	−	0.608762i	$-0.208333\pi$
$223$	2.75654	+	2.75654i	0.184591	+	0.184591i	−0.608762	+	0.793353i	$0.708333\pi$
$224$		−	1.00000i		−	0.0668153i
$225$		0			0
$226$	−9.26602	−	9.26602i	−0.616366	−	0.616366i
$227$	2.31035	−	2.31035i	0.153343	−	0.153343i	−0.626266	−	0.779609i	$-0.715418\pi$
$227$	2.31035	−	2.31035i	0.153343	−	0.153343i	0.779609	+	0.626266i	$0.215418\pi$
$228$		0			0
$229$	9.83707	−	9.83707i	0.650052	−	0.650052i	−0.302954	−	0.953005i	$-0.597973\pi$
$229$	9.83707	−	9.83707i	0.650052	−	0.650052i	0.953005	+	0.302954i	$0.0979727\pi$
$230$			6.70252i			0.441951i
$231$		0			0
$232$	−2.90671	+	2.90671i	−0.190835	+	0.190835i
$233$	−19.1178			−1.25245			−0.626225	−	0.779642i	$-0.715401\pi$
$233$	−19.1178			−1.25245			−0.626225	+	0.779642i	$0.715401\pi$
$234$		0			0
$235$	20.9023			1.36352
$236$	−8.37799	+	8.37799i	−0.545360	+	0.545360i
$237$		0			0
$238$			0.776275i			0.0503184i
$239$	−12.0163	+	12.0163i	−0.777272	+	0.777272i	−0.979366	−	0.202094i	$-0.935225\pi$
$239$	−12.0163	+	12.0163i	−0.777272	+	0.777272i	0.202094	+	0.979366i	$0.435225\pi$
$240$		0			0
$241$	4.71196	−	4.71196i	0.303524	−	0.303524i	−0.538867	−	0.842391i	$-0.681147\pi$
$241$	4.71196	−	4.71196i	0.303524	−	0.303524i	0.842391	+	0.538867i	$0.181147\pi$
$242$	4.62795	+	4.62795i	0.297496	+	0.297496i
$243$		0			0
$244$		−	5.91811i		−	0.378868i
$245$	2.24541	+	2.24541i	0.143454	+	0.143454i
$246$		0			0
$247$	9.08200	+	10.6127i	0.577874	+	0.675269i
$248$		−	3.09782i		−	0.196712i
$249$		0			0
$250$	−0.265752			−0.0168076
$251$	15.1414			0.955718			0.477859	−	0.878437i	$-0.341413\pi$
$251$	15.1414			0.955718			0.477859	+	0.878437i	$0.341413\pi$
$252$		0			0
$253$	−3.15023	−	3.15023i	−0.198053	−	0.198053i
$254$	−3.32261	−	3.32261i	−0.208479	−	0.208479i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−4.34063			−0.270761			−0.135381	−	0.990794i	$-0.543226\pi$
$257$	−4.34063			−0.270761			−0.135381	+	0.990794i	$0.543226\pi$
$258$		0			0
$259$		−	2.13773i		−	0.132832i
$260$	−7.44425	−	8.69891i	−0.461673	−	0.539483i
$261$		0			0
$262$	8.16305	+	8.16305i	0.504315	+	0.504315i
$263$		−	29.2722i		−	1.80500i	−0.430690	−	0.902500i	$-0.641730\pi$
$263$		−	29.2722i		−	1.80500i	0.430690	−	0.902500i	$-0.358270\pi$
$264$		0			0
$265$	1.86015	+	1.86015i	0.114268	+	0.114268i
$266$	2.73940	−	2.73940i	0.167963	−	0.167963i
$267$		0			0
$268$	−6.16029	+	6.16029i	−0.376299	+	0.376299i
$269$			25.4815i			1.55363i	0.629728	+	0.776816i	$0.283167\pi$
$269$			25.4815i			1.55363i	−0.629728	+	0.776816i	$0.716833\pi$
$270$		0			0
$271$	2.03093	−	2.03093i	0.123370	−	0.123370i	−0.642726	−	0.766096i	$-0.722197\pi$
$271$	2.03093	−	2.03093i	0.123370	−	0.123370i	0.766096	+	0.642726i	$0.222197\pi$
$272$	−0.776275			−0.0470686
$273$		0			0
$274$	9.99321			0.603712
$275$	7.58739	−	7.58739i	0.457537	−	0.457537i
$276$		0			0
$277$			19.0405i			1.14403i	0.820243	+	0.572015i	$0.193838\pi$
$277$			19.0405i			1.14403i	−0.820243	+	0.572015i	$0.806162\pi$
$278$	12.4847	−	12.4847i	0.748782	−	0.748782i
$279$		0			0
$280$	−2.24541	+	2.24541i	−0.134189	+	0.134189i
$281$	−1.20679	−	1.20679i	−0.0719913	−	0.0719913i	0.670194	−	0.742186i	$-0.266211\pi$
$281$	−1.20679	−	1.20679i	−0.0719913	−	0.0719913i	−0.742186	+	0.670194i	$0.766211\pi$
$282$		0			0
$283$			19.3274i			1.14890i	0.818541	+	0.574448i	$0.194783\pi$
$283$			19.3274i			1.14890i	−0.818541	+	0.574448i	$0.805217\pi$
$284$	1.86015	+	1.86015i	0.110380	+	0.110380i
$285$		0			0
$286$	7.58739	+	0.589696i	0.448652	+	0.0348695i
$287$		−	1.66238i		−	0.0981274i
$288$		0			0
$289$	−16.3974			−0.964553
$290$	13.0535			0.766527
$291$		0			0
$292$	−10.8392	−	10.8392i	−0.634316	−	0.634316i
$293$	−15.2038	−	15.2038i	−0.888217	−	0.888217i	0.106135	−	0.994352i	$-0.466152\pi$
$293$	−15.2038	−	15.2038i	−0.888217	−	0.888217i	−0.994352	+	0.106135i	$0.966152\pi$
$294$		0			0
$295$	37.6239			2.19055
$296$	2.13773			0.124253
$297$		0			0
$298$		−	10.5454i		−	0.610876i
$299$	7.58739	+	0.589696i	0.438790	+	0.0341030i
$300$		0			0
$301$	2.87757	+	2.87757i	0.165861	+	0.165861i
$302$			7.99143i			0.459855i
$303$		0			0
$304$	2.73940	+	2.73940i	0.157115	+	0.157115i
$305$	−13.2885	+	13.2885i	−0.760900	+	0.760900i
$306$		0			0
$307$	2.76627	−	2.76627i	0.157879	−	0.157879i	−0.623747	−	0.781626i	$-0.714390\pi$
$307$	2.76627	−	2.76627i	0.157879	−	0.157879i	0.781626	+	0.623747i	$0.214390\pi$
$308$		−	2.11071i		−	0.120269i
$309$		0			0
$310$	−6.95586	+	6.95586i	−0.395066	+	0.395066i
$311$	−15.6951			−0.889986			−0.444993	−	0.895534i	$-0.646794\pi$
$311$	−15.6951			−0.889986			−0.444993	+	0.895534i	$0.646794\pi$
$312$		0			0
$313$	1.36775			0.0773098			0.0386549	−	0.999253i	$-0.487693\pi$
$313$	1.36775			0.0773098			0.0386549	+	0.999253i	$0.487693\pi$
$314$	−2.12287	+	2.12287i	−0.119801	+	0.119801i
$315$		0			0
$316$		−	10.9928i		−	0.618394i
$317$	−1.78226	+	1.78226i	−0.100102	+	0.100102i	−0.755384	−	0.655282i	$-0.772550\pi$
$317$	−1.78226	+	1.78226i	−0.100102	+	0.100102i	0.655282	+	0.755384i	$0.272550\pi$
$318$		0			0
$319$	−6.13522	+	6.13522i	−0.343506	+	0.343506i
$320$	−2.24541	−	2.24541i	−0.125522	−	0.125522i
$321$		0			0
$322$		−	2.11071i		−	0.117625i
$323$	−2.12653	−	2.12653i	−0.118323	−	0.118323i
$324$		0			0
$325$	−1.42030	+	18.2744i	−0.0787838	+	1.01368i
$326$		−	12.7107i		−	0.703982i
$327$		0			0
$328$	1.66238			0.0917898
$329$	−6.58241			−0.362900
$330$		0			0
$331$	8.17788	+	8.17788i	0.449497	+	0.449497i	0.895187	−	0.445690i	$-0.147042\pi$
$331$	8.17788	+	8.17788i	0.449497	+	0.449497i	−0.445690	+	0.895187i	$0.647042\pi$
$332$	−2.13985	−	2.13985i	−0.117439	−	0.117439i
$333$		0			0
$334$	−4.38313			−0.239834
$335$	27.6647			1.51148
$336$		0			0
$337$			23.4017i			1.27477i	0.770545	+	0.637386i	$0.219984\pi$
$337$			23.4017i			1.27477i	−0.770545	+	0.637386i	$0.780016\pi$
$338$	−10.5023	+	7.66171i	−0.571250	+	0.416742i
$339$		0			0
$340$	1.74305	+	1.74305i	0.0945303	+	0.0945303i
$341$		−	6.53859i		−	0.354085i
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−2.87757	+	2.87757i	−0.155148	+	0.155148i
$345$		0			0
$346$	−8.46406	+	8.46406i	−0.455031	+	0.455031i
$347$		−	26.9081i		−	1.44450i	−0.691630	−	0.722252i	$-0.743107\pi$
$347$		−	26.9081i		−	1.44450i	0.691630	−	0.722252i	$-0.256893\pi$
$348$		0			0
$349$	−23.9941	+	23.9941i	−1.28438	+	1.28438i	−0.346226	+	0.938151i	$0.612537\pi$
$349$	−23.9941	+	23.9941i	−1.28438	+	1.28438i	−0.938151	+	0.346226i	$0.887463\pi$
$350$	5.08369			0.271735
$351$		0			0
$352$	2.11071			0.112501
$353$	−10.3230	+	10.3230i	−0.549439	+	0.549439i	−0.926279	−	0.376839i	$-0.877011\pi$
$353$	−10.3230	+	10.3230i	−0.549439	+	0.549439i	0.376839	+	0.926279i	$0.377011\pi$
$354$		0			0
$355$		−	8.35360i		−	0.443363i
$356$	−2.33033	+	2.33033i	−0.123507	+	0.123507i
$357$		0			0
$358$	10.3893	−	10.3893i	0.549094	−	0.549094i
$359$	−3.26430	−	3.26430i	−0.172283	−	0.172283i	0.615699	−	0.787982i	$-0.288874\pi$
$359$	−3.26430	−	3.26430i	−0.172283	−	0.172283i	−0.787982	+	0.615699i	$0.788874\pi$
$360$		0			0
$361$		−	3.99140i		−	0.210074i
$362$	−3.84389	−	3.84389i	−0.202030	−	0.202030i
$363$		0			0
$364$	2.34429	+	2.73940i	0.122874	+	0.143583i
$365$			48.6768i			2.54786i
$366$		0			0
$367$	−22.4767			−1.17327			−0.586637	−	0.809850i	$-0.699549\pi$
$367$	−22.4767			−1.17327			−0.586637	+	0.809850i	$0.699549\pi$
$368$	2.11071			0.110028
$369$		0			0
$370$	−4.80007	−	4.80007i	−0.249544	−	0.249544i
$371$	−0.585786	−	0.585786i	−0.0304125	−	0.0304125i
$372$		0			0
$373$	6.68130			0.345945			0.172972	−	0.984927i	$-0.444663\pi$
$373$	6.68130			0.345945			0.172972	+	0.984927i	$0.444663\pi$
$374$	−1.63849			−0.0847243
$375$		0			0
$376$		−	6.58241i		−	0.339462i
$377$	1.14846	−	14.7768i	0.0591488	−	0.761044i
$378$		0			0
$379$	13.3139	+	13.3139i	0.683888	+	0.683888i	0.960874	−	0.276986i	$-0.0893355\pi$
$379$	13.3139	+	13.3139i	0.683888	+	0.683888i	−0.276986	+	0.960874i	$0.589336\pi$
$380$		−	12.3021i		−	0.631085i
$381$		0			0
$382$	8.67612	+	8.67612i	0.443909	+	0.443909i
$383$	−4.65014	+	4.65014i	−0.237611	+	0.237611i	−0.815860	−	0.578249i	$-0.803736\pi$
$383$	−4.65014	+	4.65014i	−0.237611	+	0.237611i	0.578249	+	0.815860i	$0.303736\pi$
$384$		0			0
$385$	−4.73940	+	4.73940i	−0.241542	+	0.241542i
$386$			13.6095i			0.692704i
$387$		0			0
$388$	−12.2393	+	12.2393i	−0.621355	+	0.621355i
$389$	−26.6042			−1.34889			−0.674444	−	0.738326i	$-0.735617\pi$
$389$	−26.6042			−1.34889			−0.674444	+	0.738326i	$0.735617\pi$
$390$		0			0
$391$	−1.63849			−0.0828620
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$		0			0
$394$		−	19.6805i		−	0.991489i
$395$	−24.6833	+	24.6833i	−1.24195	+	1.24195i
$396$		0			0
$397$	−24.1752	+	24.1752i	−1.21332	+	1.21332i	−0.243390	+	0.969929i	$0.578259\pi$
$397$	−24.1752	+	24.1752i	−1.21332	+	1.21332i	−0.969929	+	0.243390i	$0.921741\pi$
$398$	−4.40588	−	4.40588i	−0.220847	−	0.220847i
$399$		0			0
$400$			5.08369i			0.254184i
$401$	10.5700	+	10.5700i	0.527839	+	0.527839i	0.919927	−	0.392089i	$-0.128247\pi$
$401$	10.5700	+	10.5700i	0.527839	+	0.527839i	−0.392089	+	0.919927i	$0.628247\pi$
$402$		0			0
$403$	7.26219	+	8.48616i	0.361755	+	0.422726i
$404$		−	6.79021i		−	0.337826i
$405$		0			0
$406$	−4.11071			−0.204011
$407$	4.51213			0.223658
$408$		0			0
$409$	−20.0847	−	20.0847i	−0.993124	−	0.993124i	0.00685277	−	0.999977i	$-0.497819\pi$
$409$	−20.0847	−	20.0847i	−0.993124	−	0.993124i	−0.999977	+	0.00685277i	$0.997819\pi$
$410$	−3.73272	−	3.73272i	−0.184346	−	0.184346i
$411$		0			0
$412$	−14.6543			−0.721964
$413$	−11.8483			−0.583015
$414$		0			0
$415$			9.60964i			0.471719i
$416$	−2.73940	+	2.34429i	−0.134310	+	0.114938i
$417$		0			0
$418$	5.78207	+	5.78207i	0.282810	+	0.282810i
$419$			9.54891i			0.466495i	0.972417	+	0.233247i	$0.0749352\pi$
$419$			9.54891i			0.466495i	−0.972417	+	0.233247i	$0.925065\pi$
$420$		0			0
$421$	21.4769	+	21.4769i	1.04672	+	1.04672i	0.998854	+	0.0478679i	$0.0152427\pi$
$421$	21.4769	+	21.4769i	1.04672	+	1.04672i	0.0478679	+	0.998854i	$0.484757\pi$
$422$	−8.45800	+	8.45800i	−0.411729	+	0.411729i
$423$		0			0
$424$	0.585786	−	0.585786i	0.0284483	−	0.0284483i
$425$		−	3.94634i		−	0.191426i
$426$		0			0
$427$	4.18473	−	4.18473i	0.202513	−	0.202513i
$428$	−12.9758			−0.627210
$429$		0			0
$430$	12.9226			0.623185
$431$	−21.9899	+	21.9899i	−1.05922	+	1.05922i	−0.0610825	+	0.998133i	$0.519455\pi$
$431$	−21.9899	+	21.9899i	−1.05922	+	1.05922i	−0.998133	+	0.0610825i	$0.980545\pi$
$432$		0			0
$433$		−	35.8033i		−	1.72060i	−0.509789	−	0.860299i	$-0.670277\pi$
$433$		−	35.8033i		−	1.72060i	0.509789	−	0.860299i	$-0.329723\pi$
$434$	2.19049	−	2.19049i	0.105147	−	0.105147i
$435$		0			0
$436$	1.50041	−	1.50041i	0.0718567	−	0.0718567i
$437$	5.78207	+	5.78207i	0.276594	+	0.276594i
$438$		0			0
$439$			33.9406i			1.61990i	0.586500	+	0.809949i	$0.300505\pi$
$439$			33.9406i			1.61990i	−0.586500	+	0.809949i	$0.699495\pi$
$440$	−4.73940	−	4.73940i	−0.225942	−	0.225942i
$441$		0			0
$442$	2.12653	−	1.81981i	0.101149	−	0.0865597i
$443$			18.4490i			0.876539i	0.898844	+	0.438270i	$0.144409\pi$
$443$			18.4490i			0.876539i	−0.898844	+	0.438270i	$0.855591\pi$
$444$		0			0
$445$	10.4651			0.496093
$446$	−3.89833			−0.184591
$447$		0			0
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	−20.1372	−	20.1372i	−0.950331	−	0.950331i	0.0484926	−	0.998824i	$-0.484558\pi$
$449$	−20.1372	−	20.1372i	−0.950331	−	0.950331i	−0.998824	+	0.0484926i	$0.984558\pi$
$450$		0			0
$451$	3.50881			0.165223
$452$	13.1041			0.616366
$453$		0			0
$454$			3.26733i			0.153343i
$455$	0.887175	−	11.4149i	0.0415914	−	0.535141i
$456$		0			0
$457$	−22.4634	−	22.4634i	−1.05079	−	1.05079i	−0.998639	−	0.0521540i	$-0.983391\pi$
$457$	−22.4634	−	22.4634i	−1.05079	−	1.05079i	−0.0521540	−	0.998639i	$-0.516609\pi$
$458$			13.9117i			0.650052i
$459$		0			0
$460$	−4.73940	−	4.73940i	−0.220976	−	0.220976i
$461$	7.65204	−	7.65204i	0.356391	−	0.356391i	−0.506090	−	0.862481i	$-0.668910\pi$
$461$	7.65204	−	7.65204i	0.356391	−	0.356391i	0.862481	+	0.506090i	$0.168910\pi$
$462$		0			0
$463$	17.7157	−	17.7157i	0.823319	−	0.823319i	−0.163264	−	0.986582i	$-0.552202\pi$
$463$	17.7157	−	17.7157i	0.823319	−	0.823319i	0.986582	+	0.163264i	$0.0522022\pi$
$464$		−	4.11071i		−	0.190835i
$465$		0			0
$466$	13.5183	−	13.5183i	0.626225	−	0.626225i
$467$	−1.94747			−0.0901180			−0.0450590	−	0.998984i	$-0.514348\pi$
$467$	−1.94747			−0.0901180			−0.0450590	+	0.998984i	$0.514348\pi$
$468$		0			0
$469$	−8.71196			−0.402281
$470$	−14.7802	+	14.7802i	−0.681759	+	0.681759i
$471$		0			0
$472$		−	11.8483i		−	0.545360i
$473$	−6.07372	+	6.07372i	−0.279270	+	0.279270i
$474$		0			0
$475$	−13.9262	+	13.9262i	−0.638980	+	0.638980i
$476$	−0.548909	−	0.548909i	−0.0251592	−	0.0251592i
$477$		0			0
$478$		−	16.9937i		−	0.777272i
$479$	19.9875	+	19.9875i	0.913252	+	0.913252i	0.996527	−	0.0832746i	$-0.0265379\pi$
$479$	19.9875	+	19.9875i	0.913252	+	0.913252i	−0.0832746	+	0.996527i	$0.526538\pi$
$480$		0			0
$481$	−5.85609	+	5.01146i	−0.267015	+	0.228503i
$482$			6.66372i			0.303524i
$483$		0			0
$484$	−6.54491			−0.297496
$485$	54.9642			2.49580
$486$		0			0
$487$	−10.8624	−	10.8624i	−0.492223	−	0.492223i	0.416783	−	0.909006i	$-0.363157\pi$
$487$	−10.8624	−	10.8624i	−0.492223	−	0.492223i	−0.909006	+	0.416783i	$0.863157\pi$
$488$	4.18473	+	4.18473i	0.189434	+	0.189434i
$489$		0			0
$490$	−3.17548			−0.143454
$491$	1.83750			0.0829252			0.0414626	−	0.999140i	$-0.486798\pi$
$491$	1.83750			0.0829252			0.0414626	+	0.999140i	$0.486798\pi$
$492$		0			0
$493$			3.19104i			0.143717i
$494$	−13.9262	−	1.08236i	−0.626571	−	0.0486975i
$495$		0			0
$496$	2.19049	+	2.19049i	0.0983558	+	0.0983558i
$497$			2.63066i			0.118001i
$498$		0			0
$499$	6.61414	+	6.61414i	0.296090	+	0.296090i	0.839480	−	0.543390i	$-0.182860\pi$
$499$	6.61414	+	6.61414i	0.296090	+	0.296090i	−0.543390	+	0.839480i	$0.682860\pi$
$500$	0.187915	−	0.187915i	0.00840381	−	0.00840381i
$501$		0			0
$502$	−10.7066	+	10.7066i	−0.477859	+	0.477859i
$503$		−	5.15307i		−	0.229764i	−0.993379	−	0.114882i	$-0.963351\pi$
$503$		−	5.15307i		−	0.229764i	0.993379	−	0.114882i	$-0.0366490\pi$
$504$		0			0
$505$	−15.2468	+	15.2468i	−0.678473	+	0.678473i
$506$	4.45509			0.198053
$507$		0			0
$508$	4.69888			0.208479
$509$	−20.1271	+	20.1271i	−0.892117	+	0.892117i	−0.994722	−	0.102605i	$-0.967282\pi$
$509$	−20.1271	+	20.1271i	−0.892117	+	0.892117i	0.102605	+	0.994722i	$0.467282\pi$
$510$		0			0
$511$		−	15.3289i		−	0.678113i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	3.06929	−	3.06929i	0.135381	−	0.135381i
$515$	32.9048	+	32.9048i	1.44996	+	1.44996i
$516$		0			0
$517$		−	13.8936i		−	0.611038i
$518$	1.51160	+	1.51160i	0.0664160	+	0.0664160i
$519$		0			0
$520$	11.4149	+	0.887175i	0.500578	+	0.0389052i
$521$			39.5009i			1.73057i	0.501283	+	0.865284i	$0.332862\pi$
$521$			39.5009i			1.73057i	−0.501283	+	0.865284i	$0.667138\pi$
$522$		0			0
$523$	−42.2831			−1.84891			−0.924454	−	0.381293i	$-0.875479\pi$
$523$	−42.2831			−1.84891			−0.924454	+	0.381293i	$0.875479\pi$
$524$	−11.5443			−0.504315
$525$		0			0
$526$	20.6986	+	20.6986i	0.902500	+	0.902500i
$527$	−1.70042	−	1.70042i	−0.0740715	−	0.0740715i
$528$		0			0
$529$	−18.5449			−0.806300
$530$	−2.63066			−0.114268
$531$		0			0
$532$			3.87409i			0.167963i
$533$	−4.55393	+	3.89711i	−0.197253	+	0.168803i
$534$		0			0
$535$	29.1360	+	29.1360i	1.25966	+	1.25966i
$536$		−	8.71196i		−	0.376299i
$537$		0			0
$538$	−18.0181	−	18.0181i	−0.776816	−	0.776816i
$539$	1.49250	−	1.49250i	0.0642864	−	0.0642864i
$540$		0			0
$541$	−18.4350	+	18.4350i	−0.792580	+	0.792580i	−0.981913	−	0.189333i	$-0.939368\pi$
$541$	−18.4350	+	18.4350i	−0.792580	+	0.792580i	0.189333	+	0.981913i	$0.439368\pi$
$542$			2.87217i			0.123370i
$543$		0			0
$544$	0.548909	−	0.548909i	0.0235343	−	0.0235343i
$545$	−6.73806			−0.288627
$546$		0			0
$547$	45.1589			1.93086			0.965428	−	0.260670i	$-0.0839436\pi$
$547$	45.1589			1.93086			0.965428	+	0.260670i	$0.0839436\pi$
$548$	−7.06627	+	7.06627i	−0.301856	+	0.301856i
$549$		0			0
$550$			10.7302i			0.457537i
$551$	11.2609	−	11.2609i	0.479729	−	0.479729i
$552$		0			0
$553$	7.77309	−	7.77309i	0.330546	−	0.330546i
$554$	−13.4636	−	13.4636i	−0.572015	−	0.572015i
$555$		0			0
$556$			17.6560i			0.748782i
$557$	−33.1438	−	33.1438i	−1.40435	−	1.40435i	−0.785552	−	0.618796i	$-0.787621\pi$
$557$	−33.1438	−	33.1438i	−1.40435	−	1.40435i	−0.618796	−	0.785552i	$-0.712379\pi$
$558$		0			0
$559$	1.13695	−	14.6287i	0.0480879	−	0.618728i
$560$		−	3.17548i		−	0.134189i
$561$		0			0
$562$	1.70667			0.0719913
$563$	−41.3570			−1.74299			−0.871495	−	0.490404i	$-0.836849\pi$
$563$	−41.3570			−1.74299			−0.871495	+	0.490404i	$0.836849\pi$
$564$		0			0
$565$	−29.4241	−	29.4241i	−1.23788	−	1.23788i
$566$	−13.6666	−	13.6666i	−0.574448	−	0.574448i
$567$		0			0
$568$	−2.63066			−0.110380
$569$	43.7396			1.83366			0.916830	−	0.399278i	$-0.130739\pi$
$569$	43.7396			1.83366			0.916830	+	0.399278i	$0.130739\pi$
$570$		0			0
$571$		−	29.5378i		−	1.23612i	−0.786132	−	0.618059i	$-0.787919\pi$
$571$		−	29.5378i		−	1.23612i	0.786132	−	0.618059i	$-0.212081\pi$
$572$	−5.78207	+	4.94812i	−0.241761	+	0.206891i
$573$		0			0
$574$	1.17548	+	1.17548i	0.0490637	+	0.0490637i
$575$			10.7302i			0.447480i
$576$		0			0
$577$	−7.45672	−	7.45672i	−0.310427	−	0.310427i	0.534648	−	0.845075i	$-0.320444\pi$
$577$	−7.45672	−	7.45672i	−0.310427	−	0.310427i	−0.845075	+	0.534648i	$0.820444\pi$
$578$	11.5947	−	11.5947i	0.482276	−	0.482276i
$579$		0			0
$580$	−9.23021	+	9.23021i	−0.383264	+	0.383264i
$581$		−	3.02620i		−	0.125548i
$582$		0			0
$583$	1.23642	−	1.23642i	0.0512075	−	0.0512075i
$584$	15.3289			0.634316
$585$		0			0
$586$	21.5015			0.888217
$587$	27.2779	−	27.2779i	1.12588	−	1.12588i	0.135040	−	0.990840i	$-0.456884\pi$
$587$	27.2779	−	27.2779i	1.12588	−	1.12588i	0.990840	−	0.135040i	$-0.0431163\pi$
$588$		0			0
$589$			12.0012i			0.494502i
$590$	−26.6041	+	26.6041i	−1.09528	+	1.09528i
$591$		0			0
$592$	−1.51160	+	1.51160i	−0.0621265	+	0.0621265i
$593$	−11.8561	−	11.8561i	−0.486873	−	0.486873i	0.420445	−	0.907318i	$-0.361874\pi$
$593$	−11.8561	−	11.8561i	−0.486873	−	0.486873i	−0.907318	+	0.420445i	$0.861874\pi$
$594$		0			0
$595$			2.46505i			0.101057i
$596$	7.45670	+	7.45670i	0.305438	+	0.305438i
$597$		0			0
$598$	−5.78207	+	4.94812i	−0.236447	+	0.202344i
$599$		−	4.42953i		−	0.180986i	−0.995897	−	0.0904928i	$-0.971156\pi$
$599$		−	4.42953i		−	0.180986i	0.995897	−	0.0904928i	$-0.0288442\pi$
$600$		0			0
$601$	−36.6575			−1.49529			−0.747645	−	0.664098i	$-0.768816\pi$
$601$	−36.6575			−1.49529			−0.747645	+	0.664098i	$0.768816\pi$
$602$	−4.06950			−0.165861
$603$		0			0
$604$	−5.65080	−	5.65080i	−0.229928	−	0.229928i
$605$	14.6960	+	14.6960i	0.597476	+	0.597476i
$606$		0			0
$607$	20.2160			0.820540			0.410270	−	0.911964i	$-0.365434\pi$
$607$	20.2160			0.820540			0.410270	+	0.911964i	$0.365434\pi$
$608$	−3.87409			−0.157115
$609$		0			0
$610$		−	18.7928i		−	0.760900i
$611$	15.4311	+	18.0318i	0.624275	+	0.729491i
$612$		0			0
$613$	12.4598	+	12.4598i	0.503246	+	0.503246i	0.912445	−	0.409199i	$-0.134192\pi$
$613$	12.4598	+	12.4598i	0.503246	+	0.503246i	−0.409199	+	0.912445i	$0.634192\pi$
$614$			3.91210i			0.157879i
$615$		0			0
$616$	1.49250	+	1.49250i	0.0601344	+	0.0601344i
$617$	2.21026	−	2.21026i	0.0889815	−	0.0889815i	−0.661215	−	0.750196i	$-0.729959\pi$
$617$	2.21026	−	2.21026i	0.0889815	−	0.0889815i	0.750196	+	0.661215i	$0.229959\pi$
$618$		0			0
$619$	5.55485	−	5.55485i	0.223268	−	0.223268i	−0.586605	−	0.809873i	$-0.699536\pi$
$619$	5.55485	−	5.55485i	0.223268	−	0.223268i	0.809873	+	0.586605i	$0.199536\pi$
$620$		−	9.83707i		−	0.395066i
$621$		0			0
$622$	11.0981	−	11.0981i	0.444993	−	0.444993i
$623$	−3.29559			−0.132035
$624$		0			0
$625$	24.5746			0.982982
$626$	−0.967145	+	0.967145i	−0.0386549	+	0.0386549i
$627$		0			0
$628$		−	3.00219i		−	0.119801i
$629$	1.17342	−	1.17342i	0.0467873	−	0.0467873i
$630$		0			0
$631$	3.49283	−	3.49283i	0.139047	−	0.139047i	−0.634157	−	0.773204i	$-0.718653\pi$
$631$	3.49283	−	3.49283i	0.139047	−	0.139047i	0.773204	+	0.634157i	$0.218653\pi$
$632$	7.77309	+	7.77309i	0.309197	+	0.309197i
$633$		0			0
$634$		−	2.52050i		−	0.100102i
$635$	−10.5509	−	10.5509i	−0.418699	−	0.418699i
$636$		0			0
$637$	−0.279383	+	3.59471i	−0.0110696	+	0.142428i
$638$		−	8.67651i		−	0.343506i
$639$		0			0
$640$	3.17548			0.125522
$641$	28.0466			1.10777			0.553887	−	0.832592i	$-0.313144\pi$
$641$	28.0466			1.10777			0.553887	+	0.832592i	$0.313144\pi$
$642$		0			0
$643$	2.00360	+	2.00360i	0.0790143	+	0.0790143i	0.745509	−	0.666495i	$-0.232206\pi$
$643$	2.00360	+	2.00360i	0.0790143	+	0.0790143i	−0.666495	+	0.745509i	$0.732206\pi$
$644$	1.49250	+	1.49250i	0.0588126	+	0.0588126i
$645$		0			0
$646$	3.00736			0.118323
$647$	35.3219			1.38865			0.694323	−	0.719663i	$-0.255704\pi$
$647$	35.3219			1.38865			0.694323	+	0.719663i	$0.255704\pi$
$648$		0			0
$649$		−	25.0082i		−	0.981659i
$650$	−11.9176	−	13.9262i	−0.467448	−	0.546232i
$651$		0			0
$652$	8.98784	+	8.98784i	0.351991	+	0.351991i
$653$		−	9.44791i		−	0.369725i	−0.982764	−	0.184863i	$-0.940816\pi$
$653$		−	9.44791i		−	0.369725i	0.982764	−	0.184863i	$-0.0591840\pi$
$654$		0			0
$655$	25.9216	+	25.9216i	1.01284	+	1.01284i
$656$	−1.17548	+	1.17548i	−0.0458949	+	0.0458949i
$657$		0			0
$658$	4.65447	−	4.65447i	0.181450	−	0.181450i
$659$		−	38.4902i		−	1.49937i	−0.661797	−	0.749683i	$-0.730206\pi$
$659$		−	38.4902i		−	1.49937i	0.661797	−	0.749683i	$-0.269794\pi$
$660$		0			0
$661$	6.96665	−	6.96665i	0.270971	−	0.270971i	−0.558520	−	0.829491i	$-0.688631\pi$
$661$	6.96665	−	6.96665i	0.270971	−	0.270971i	0.829491	+	0.558520i	$0.188631\pi$
$662$	−11.5653			−0.449497
$663$		0			0
$664$	3.02620			0.117439
$665$	8.69891	−	8.69891i	0.337329	−	0.337329i
$666$		0			0
$667$		−	8.67651i		−	0.335956i
$668$	3.09934	−	3.09934i	0.119917	−	0.119917i
$669$		0			0
$670$	−19.5619	+	19.5619i	−0.755741	+	0.755741i
$671$	8.83275	+	8.83275i	0.340985	+	0.340985i
$672$		0			0
$673$			6.46472i			0.249196i	0.992207	+	0.124598i	$0.0397642\pi$
$673$			6.46472i			0.249196i	−0.992207	+	0.124598i	$0.960236\pi$
$674$	−16.5475	−	16.5475i	−0.637386	−	0.637386i
$675$		0			0
$676$	2.00860	−	12.8439i	0.0772539	−	0.493996i
$677$		−	5.73152i		−	0.220280i	−0.993916	−	0.110140i	$-0.964870\pi$
$677$		−	5.73152i		−	0.220280i	0.993916	−	0.110140i	$-0.0351300\pi$
$678$		0			0
$679$	−17.3089			−0.664256
$680$	−2.46505			−0.0945303
$681$		0			0
$682$	4.62348	+	4.62348i	0.177042	+	0.177042i
$683$	−13.4588	−	13.4588i	−0.514987	−	0.514987i	0.401063	−	0.916050i	$-0.368641\pi$
$683$	−13.4588	−	13.4588i	−0.514987	−	0.514987i	−0.916050	+	0.401063i	$0.868641\pi$
$684$		0			0
$685$	31.7333			1.21247
$686$	1.00000			0.0381802
$687$		0			0
$688$		−	4.06950i		−	0.155148i
$689$	−0.231448	+	2.97796i	−0.00881748	+	0.113451i
$690$		0			0
$691$	−12.3647	−	12.3647i	−0.470374	−	0.470374i	0.431662	−	0.902036i	$-0.357927\pi$
$691$	−12.3647	−	12.3647i	−0.470374	−	0.470374i	−0.902036	+	0.431662i	$0.857927\pi$
$692$		−	11.9700i		−	0.455031i
$693$		0			0
$694$	19.0269	+	19.0269i	0.722252	+	0.722252i
$695$	39.6449	−	39.6449i	1.50382	−	1.50382i
$696$		0			0
$697$	0.912498	−	0.912498i	0.0345633	−	0.0345633i
$698$		−	33.9328i		−	1.28438i
$699$		0			0
$700$	−3.59471	+	3.59471i	−0.135867	+	0.135867i
$701$	28.1009			1.06136			0.530678	−	0.847574i	$-0.321938\pi$
$701$	28.1009			1.06136			0.530678	+	0.847574i	$0.321938\pi$
$702$		0			0
$703$	−8.28177			−0.312353
$704$	−1.49250	+	1.49250i	−0.0562506	+	0.0562506i
$705$		0			0
$706$		−	14.5990i		−	0.549439i
$707$	4.80141	−	4.80141i	0.180575	−	0.180575i
$708$		0			0
$709$	3.39704	−	3.39704i	0.127578	−	0.127578i	−0.640434	−	0.768013i	$-0.721246\pi$
$709$	3.39704	−	3.39704i	0.127578	−	0.127578i	0.768013	+	0.640434i	$0.221246\pi$
$710$	5.90689	+	5.90689i	0.221682	+	0.221682i
$711$		0			0
$712$		−	3.29559i		−	0.123507i
$713$	4.62348	+	4.62348i	0.173151	+	0.173151i
$714$		0			0
$715$	24.0936	+	1.87257i	0.901050	+	0.0700301i
$716$			14.6928i			0.549094i
$717$		0			0
$718$	4.61642			0.172283
$719$	20.1669			0.752098			0.376049	−	0.926600i	$-0.377282\pi$
$719$	20.1669			0.752098			0.376049	+	0.926600i	$0.377282\pi$
$720$		0			0
$721$	−10.3621	−	10.3621i	−0.385906	−	0.385906i
$722$	2.82235	+	2.82235i	0.105037	+	0.105037i
$723$		0			0
$724$	5.43608			0.202030
$725$	20.8976			0.776116
$726$		0			0
$727$			7.67609i			0.284690i	0.989817	+	0.142345i	$0.0454643\pi$
$727$			7.67609i			0.284690i	−0.989817	+	0.142345i	$0.954536\pi$
$728$	−3.59471	−	0.279383i	−0.133229	−	0.0103546i
$729$		0			0
$730$	−34.4197	−	34.4197i	−1.27393	−	1.27393i
$731$			3.15905i			0.116842i
$732$		0			0
$733$	−5.09299	−	5.09299i	−0.188114	−	0.188114i	0.606766	−	0.794880i	$-0.292466\pi$
$733$	−5.09299	−	5.09299i	−0.188114	−	0.188114i	−0.794880	+	0.606766i	$0.792466\pi$
$734$	15.8934	−	15.8934i	0.586637	−	0.586637i
$735$		0			0
$736$	−1.49250	+	1.49250i	−0.0550142	+	0.0550142i
$737$		−	18.3884i		−	0.677346i
$738$		0			0
$739$	28.2291	−	28.2291i	1.03842	−	1.03842i	0.0391921	−	0.999232i	$-0.487522\pi$
$739$	28.2291	−	28.2291i	1.03842	−	1.03842i	0.999232	−	0.0391921i	$-0.0124784\pi$
$740$	6.78832			0.249544
$741$		0			0
$742$	0.828427			0.0304125
$743$	27.4605	−	27.4605i	1.00743	−	1.00743i	0.00745721	−	0.999972i	$-0.497626\pi$
$743$	27.4605	−	27.4605i	1.00743	−	1.00743i	0.999972	−	0.00745721i	$-0.00237373\pi$
$744$		0			0
$745$		−	33.4866i		−	1.22685i
$746$	−4.72439	+	4.72439i	−0.172972	+	0.172972i
$747$		0			0
$748$	1.15859	−	1.15859i	0.0423622	−	0.0423622i
$749$	−9.17529	−	9.17529i	−0.335258	−	0.335258i
$750$		0			0
$751$			2.87888i			0.105052i	0.998620	+	0.0525259i	$0.0167272\pi$
$751$			2.87888i			0.105052i	−0.998620	+	0.0525259i	$0.983273\pi$
$752$	4.65447	+	4.65447i	0.169731	+	0.169731i
$753$		0			0
$754$	9.63670	+	11.2609i	0.350948	+	0.410097i
$755$			25.3767i			0.923551i
$756$		0			0
$757$	−31.8866			−1.15894			−0.579469	−	0.814994i	$-0.696740\pi$
$757$	−31.8866			−1.15894			−0.579469	+	0.814994i	$0.696740\pi$
$758$	−18.8287			−0.683888
$759$		0			0
$760$	8.69891	+	8.69891i	0.315543	+	0.315543i
$761$	−1.77090	−	1.77090i	−0.0641949	−	0.0641949i	0.674280	−	0.738475i	$-0.264454\pi$
$761$	−1.77090	−	1.77090i	−0.0641949	−	0.0641949i	−0.738475	+	0.674280i	$0.764454\pi$
$762$		0			0
$763$	2.12190			0.0768180
$764$	−12.2699			−0.443909
$765$		0			0
$766$		−	6.57629i		−	0.237611i
$767$	27.7758	+	32.4571i	1.00292	+	1.17196i
$768$		0			0
$769$	30.1443	+	30.1443i	1.08703	+	1.08703i	0.995833	+	0.0911968i	$0.0290692\pi$
$769$	30.1443	+	30.1443i	1.08703	+	1.08703i	0.0911968	+	0.995833i	$0.470931\pi$
$770$		−	6.70252i		−	0.241542i
$771$		0			0
$772$	−9.62335	−	9.62335i	−0.346352	−	0.346352i
$773$	8.74956	−	8.74956i	0.314700	−	0.314700i	−0.532027	−	0.846727i	$-0.678570\pi$
$773$	8.74956	−	8.74956i	0.314700	−	0.314700i	0.846727	+	0.532027i	$0.178570\pi$
$774$		0			0
$775$	−11.1358	+	11.1358i	−0.400008	+	0.400008i
$776$		−	17.3089i		−	0.621355i
$777$		0			0
$778$	18.8120	−	18.8120i	0.674444	−	0.674444i
$779$	−6.44023			−0.230745
$780$		0			0
$781$	−5.55255			−0.198686
$782$	1.15859	−	1.15859i	0.0414310	−	0.0414310i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$	−6.74114	+	6.74114i	−0.240602	+	0.240602i
$786$		0			0
$787$	−18.1068	+	18.1068i	−0.645437	+	0.645437i	−0.951887	−	0.306450i	$-0.900859\pi$
$787$	−18.1068	+	18.1068i	−0.645437	+	0.645437i	0.306450	+	0.951887i	$0.400859\pi$
$788$	13.9162	+	13.9162i	0.495745	+	0.495745i
$789$		0			0
$790$		−	34.9075i		−	1.24195i
$791$	9.26602	+	9.26602i	0.329462	+	0.329462i
$792$		0			0
$793$	−21.2739	−	1.65342i	−0.755458	−	0.0587146i
$794$		−	34.1889i		−	1.21332i
$795$		0			0
$796$	6.23086			0.220847
$797$	3.19339			0.113116			0.0565578	−	0.998399i	$-0.481987\pi$
$797$	3.19339			0.113116			0.0565578	+	0.998399i	$0.481987\pi$
$798$		0			0
$799$	−3.61315	−	3.61315i	−0.127824	−	0.127824i
$800$	−3.59471	−	3.59471i	−0.127092	−	0.127092i
$801$		0			0
$802$	−14.9482			−0.527839
$803$	32.3550			1.14178
$804$		0			0
$805$		−	6.70252i		−	0.236233i
$806$	−11.1358	−	0.865477i	−0.392240	−	0.0304851i
$807$		0			0
$808$	4.80141	+	4.80141i	0.168913	+	0.168913i
$809$			3.29721i			0.115924i	0.998319	+	0.0579618i	$0.0184602\pi$
$809$			3.29721i			0.115924i	−0.998319	+	0.0579618i	$0.981540\pi$
$810$		0			0
$811$	11.8498	+	11.8498i	0.416103	+	0.416103i	0.883858	−	0.467755i	$-0.154937\pi$
$811$	11.8498	+	11.8498i	0.416103	+	0.416103i	−0.467755	+	0.883858i	$0.654937\pi$
$812$	2.90671	−	2.90671i	0.102006	−	0.102006i
$813$		0			0
$814$	−3.19056	+	3.19056i	−0.111829	+	0.111829i
$815$		−	40.3627i		−	1.41384i
$816$		0			0
$817$	11.1480	−	11.1480i	0.390019	−	0.390019i
$818$	28.4040			0.993124
$819$		0			0
$820$	5.27887			0.184346
$821$	21.2487	−	21.2487i	0.741585	−	0.741585i	−0.231298	−	0.972883i	$-0.574297\pi$
$821$	21.2487	−	21.2487i	0.741585	−	0.741585i	0.972883	+	0.231298i	$0.0742971\pi$
$822$		0			0
$823$		−	24.3031i		−	0.847153i	−0.905860	−	0.423576i	$-0.860775\pi$
$823$		−	24.3031i		−	0.847153i	0.905860	−	0.423576i	$-0.139225\pi$
$824$	10.3621	−	10.3621i	0.360982	−	0.360982i
$825$		0			0
$826$	8.37799	−	8.37799i	0.291507	−	0.291507i
$827$	12.4911	+	12.4911i	0.434358	+	0.434358i	0.890108	−	0.455750i	$-0.150629\pi$
$827$	12.4911	+	12.4911i	0.434358	+	0.434358i	−0.455750	+	0.890108i	$0.650629\pi$
$828$		0			0
$829$		−	18.4052i		−	0.639240i	−0.947546	−	0.319620i	$-0.896445\pi$
$829$		−	18.4052i		−	0.639240i	0.947546	−	0.319620i	$-0.103555\pi$
$830$	−6.79504	−	6.79504i	−0.235859	−	0.235859i
$831$		0			0
$832$	0.279383	−	3.59471i	0.00968586	−	0.124624i
$833$		−	0.776275i		−	0.0268963i
$834$		0			0
$835$	−13.9186			−0.481672
$836$	−8.17709			−0.282810
$837$		0			0
$838$	−6.75210	−	6.75210i	−0.233247	−	0.233247i
$839$	−32.0133	−	32.0133i	−1.10522	−	1.10522i	−0.993770	−	0.111452i	$-0.964450\pi$
$839$	−32.0133	−	32.0133i	−1.10522	−	1.10522i	−0.111452	−	0.993770i	$-0.535550\pi$
$840$		0			0
$841$	12.1021			0.417313
$842$	−30.3730			−1.04672
$843$		0			0
$844$		−	11.9614i		−	0.411729i
$845$	−33.3499	+	24.3296i	−1.14727	+	0.836964i
$846$		0			0
$847$	−4.62795	−	4.62795i	−0.159018	−	0.159018i
$848$			0.828427i			0.0284483i
$849$		0			0
$850$	2.79048	+	2.79048i	0.0957128	+	0.0957128i
$851$	−3.19056	+	3.19056i	−0.109371	+	0.109371i
$852$		0			0
$853$	−23.3258	+	23.3258i	−0.798662	+	0.798662i	−0.982884	−	0.184223i	$-0.941023\pi$
$853$	−23.3258	+	23.3258i	−0.798662	+	0.798662i	0.184223	+	0.982884i	$0.441023\pi$
$854$			5.91811i			0.202513i
$855$		0			0
$856$	9.17529	−	9.17529i	0.313605	−	0.313605i
$857$	−4.28784			−0.146470			−0.0732349	−	0.997315i	$-0.523332\pi$
$857$	−4.28784			−0.146470			−0.0732349	+	0.997315i	$0.523332\pi$
$858$		0			0
$859$	−38.3593			−1.30880			−0.654401	−	0.756147i	$-0.727079\pi$
$859$	−38.3593			−1.30880			−0.654401	+	0.756147i	$0.727079\pi$
$860$	−9.13769	+	9.13769i	−0.311593	+	0.311593i
$861$		0			0
$862$		−	31.0984i		−	1.05922i
$863$	19.2661	−	19.2661i	0.655826	−	0.655826i	−0.298564	−	0.954390i	$-0.596508\pi$
$863$	19.2661	−	19.2661i	0.655826	−	0.655826i	0.954390	+	0.298564i	$0.0965075\pi$
$864$		0			0
$865$	−26.8775	+	26.8775i	−0.913861	+	0.913861i
$866$	25.3168	+	25.3168i	0.860299	+	0.860299i
$867$		0			0
$868$			3.09782i			0.105147i
$869$	16.4067	+	16.4067i	0.556561	+	0.556561i
$870$		0			0
$871$	20.4234	+	23.8655i	0.692019	+	0.808652i
$872$			2.12190i			0.0718567i
$873$		0			0
$874$	−8.17709			−0.276594
$875$	0.265752			0.00898405
$876$		0			0
$877$	−4.82953	−	4.82953i	−0.163082	−	0.163082i	0.620849	−	0.783930i	$-0.286788\pi$
$877$	−4.82953	−	4.82953i	−0.163082	−	0.163082i	−0.783930	+	0.620849i	$0.786788\pi$
$878$	−23.9997	−	23.9997i	−0.809949	−	0.809949i
$879$		0			0
$880$	6.70252			0.225942
$881$	32.9708			1.11081			0.555407	−	0.831578i	$-0.312562\pi$
$881$	32.9708			1.11081			0.555407	+	0.831578i	$0.312562\pi$
$882$		0			0
$883$		−	17.8603i		−	0.601047i	−0.953774	−	0.300523i	$-0.902839\pi$
$883$		−	17.8603i		−	0.601047i	0.953774	−	0.300523i	$-0.0971613\pi$
$884$	−0.216878	+	2.79048i	−0.00729439	+	0.0938541i
$885$		0			0
$886$	−13.0454	−	13.0454i	−0.438270	−	0.438270i
$887$		−	28.0378i		−	0.941417i	−0.882289	−	0.470708i	$-0.843998\pi$
$887$		−	28.0378i		−	0.941417i	0.882289	−	0.470708i	$-0.156002\pi$
$888$		0			0
$889$	3.32261	+	3.32261i	0.111437	+	0.111437i
$890$	−7.39993	+	7.39993i	−0.248046	+	0.248046i
$891$		0			0
$892$	2.75654	−	2.75654i	0.0922957	−	0.0922957i
$893$			25.5009i			0.853355i
$894$		0			0
$895$	32.9912	−	32.9912i	1.10277	−	1.10277i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	28.4782			0.950331
$899$	9.00446	−	9.00446i	0.300316	−	0.300316i
$900$		0			0
$901$		−	0.643087i		−	0.0214243i
$902$	−2.48110	+	2.48110i	−0.0826117	+	0.0826117i
$903$		0			0
$904$	−9.26602	+	9.26602i	−0.308183	+	0.308183i
$905$	−12.2062	−	12.2062i	−0.405748	−	0.405748i
$906$		0			0
$907$			34.2895i			1.13856i	0.822142	+	0.569282i	$0.192779\pi$
$907$			34.2895i			1.13856i	−0.822142	+	0.569282i	$0.807221\pi$
$908$	−2.31035	−	2.31035i	−0.0766717	−	0.0766717i
$909$		0			0
$910$	7.44425	+	8.69891i	0.246775	+	0.288366i
$911$			50.9612i			1.68842i	0.536013	+	0.844210i	$0.319930\pi$
$911$			50.9612i			1.68842i	−0.536013	+	0.844210i	$0.680070\pi$
$912$		0			0
$913$	6.38743			0.211393
$914$	31.7680			1.05079
$915$		0			0
$916$	−9.83707	−	9.83707i	−0.325026	−	0.325026i
$917$	−8.16305	−	8.16305i	−0.269568	−	0.269568i
$918$		0			0
$919$	−41.0295			−1.35344			−0.676719	−	0.736241i	$-0.736599\pi$
$919$	−41.0295			−1.35344			−0.676719	+	0.736241i	$0.736599\pi$
$920$	6.70252			0.220976
$921$		0			0
$922$			10.8216i			0.356391i
$923$	7.20641	−	6.16702i	0.237202	−	0.202990i
$924$		0			0
$925$	−7.68452	−	7.68452i	−0.252666	−	0.252666i
$926$			25.0538i			0.823319i
$927$		0			0
$928$	2.90671	+	2.90671i	0.0954174	+	0.0954174i
$929$	25.0532	−	25.0532i	0.821968	−	0.821968i	−0.164422	−	0.986390i	$-0.552576\pi$
$929$	25.0532	−	25.0532i	0.821968	−	0.821968i	0.986390	+	0.164422i	$0.0525760\pi$
$930$		0			0
$931$	−2.73940	+	2.73940i	−0.0897801	+	0.0897801i
$932$			19.1178i			0.626225i
$933$		0			0
$934$	1.37707	−	1.37707i	0.0450590	−	0.0450590i
$935$	−5.20300			−0.170156
$936$		0			0
$937$	18.0500			0.589667			0.294833	−	0.955549i	$-0.404736\pi$
$937$	18.0500			0.589667			0.294833	+	0.955549i	$0.404736\pi$
$938$	6.16029	−	6.16029i	0.201140	−	0.201140i
$939$		0			0
$940$		−	20.9023i		−	0.681759i
$941$	−27.4575	+	27.4575i	−0.895090	+	0.895090i	−0.994997	−	0.0999065i	$-0.968146\pi$
$941$	−27.4575	+	27.4575i	−0.895090	+	0.895090i	0.0999065	+	0.994997i	$0.468146\pi$
$942$		0			0
$943$	−2.48110	+	2.48110i	−0.0807958	+	0.0807958i
$944$	8.37799	+	8.37799i	0.272680	+	0.272680i
$945$		0			0
$946$		−	8.58954i		−	0.279270i
$947$	6.69702	+	6.69702i	0.217624	+	0.217624i	0.807496	−	0.589872i	$-0.200822\pi$
$947$	6.69702	+	6.69702i	0.217624	+	0.217624i	−0.589872	+	0.807496i	$0.700822\pi$
$948$		0			0
$949$	−41.9921	+	35.9355i	−1.36312	+	1.16652i
$950$		−	19.6947i		−	0.638980i
$951$		0			0
$952$	0.776275			0.0251592
$953$	−21.3942			−0.693026			−0.346513	−	0.938045i	$-0.612634\pi$
$953$	−21.3942			−0.693026			−0.346513	+	0.938045i	$0.612634\pi$
$954$		0			0
$955$	27.5509	+	27.5509i	0.891525	+	0.891525i
$956$	12.0163	+	12.0163i	0.388636	+	0.388636i
$957$		0			0
$958$	−28.2666			−0.913252
$959$	−9.99321			−0.322698
$960$		0			0
$961$		−	21.4035i		−	0.690436i
$962$	0.597245	−	7.68452i	0.0192560	−	0.247759i
$963$		0			0
$964$	−4.71196	−	4.71196i	−0.151762	−	0.151762i
$965$			43.2166i			1.39119i
$966$		0			0
$967$	−7.47277	−	7.47277i	−0.240308	−	0.240308i	0.576669	−	0.816978i	$-0.304352\pi$
$967$	−7.47277	−	7.47277i	−0.240308	−	0.240308i	−0.816978	+	0.576669i	$0.804352\pi$
$968$	4.62795	−	4.62795i	0.148748	−	0.148748i
$969$		0			0
$970$	−38.8656	+	38.8656i	−1.24790	+	1.24790i
$971$			11.7285i			0.376387i	0.982132	+	0.188193i	$0.0602632\pi$
$971$			11.7285i			0.376387i	−0.982132	+	0.188193i	$0.939737\pi$
$972$		0			0
$973$	−12.4847	+	12.4847i	−0.400241	+	0.400241i
$974$	15.3618			0.492223
$975$		0			0
$976$	−5.91811			−0.189434
$977$	−31.5989	+	31.5989i	−1.01094	+	1.01094i	−0.0109989	+	0.999940i	$0.503501\pi$
$977$	−31.5989	+	31.5989i	−1.01094	+	1.01094i	−0.999940	+	0.0109989i	$0.996499\pi$
$978$		0			0
$979$		−	6.95603i		−	0.222316i
$980$	2.24541	−	2.24541i	0.0717268	−	0.0717268i
$981$		0			0
$982$	−1.29931	+	1.29931i	−0.0414626	+	0.0414626i
$983$	−25.0458	−	25.0458i	−0.798838	−	0.798838i	0.184074	−	0.982912i	$-0.441071\pi$
$983$	−25.0458	−	25.0458i	−0.798838	−	0.798838i	−0.982912	+	0.184074i	$0.941071\pi$
$984$		0			0
$985$		−	62.4951i		−	1.99126i
$986$	−2.25641	−	2.25641i	−0.0718586	−	0.0718586i
$987$		0			0
$988$	10.6127	−	9.08200i	0.337634	−	0.288937i
$989$		−	8.58954i		−	0.273132i
$990$		0			0
$991$	40.1577			1.27565			0.637825	−	0.770181i	$-0.279834\pi$
$991$	40.1577			1.27565			0.637825	+	0.770181i	$0.279834\pi$
$992$	−3.09782			−0.0983558
$993$		0			0
$994$	−1.86015	−	1.86015i	−0.0590005	−	0.0590005i
$995$	−13.9908	−	13.9908i	−0.443538	−	0.443538i
$996$		0			0
$997$	0.239160			0.00757426			0.00378713	−	0.999993i	$-0.498795\pi$
$997$	0.239160			0.00757426			0.00378713	+	0.999993i	$0.498795\pi$
$998$	−9.35381			−0.296090
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.y.b.827.1	yes	12
3.2	odd	2		1638.2.y.a.827.6	✓	12
13.5	odd	4		1638.2.y.a.1331.6	yes	12
39.5	even	4	inner	1638.2.y.b.1331.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.y.a.827.6	✓	12	3.2	odd	2
1638.2.y.a.1331.6	yes	12	13.5	odd	4
1638.2.y.b.827.1	yes	12	1.1	even	1	trivial
1638.2.y.b.1331.1	yes	12	39.5	even	4	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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.24541 + 2.24541i) q^{5} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.24541 + 2.24541i) q^{5} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -3.17548i q^{10} +(1.49250 + 1.49250i) q^{11} +(-3.59471 - 0.279383i) q^{13} +1.00000i q^{14} -1.00000 q^{16} +0.776275 q^{17} +(-2.73940 - 2.73940i) q^{19} +(2.24541 + 2.24541i) q^{20} -2.11071 q^{22} -2.11071 q^{23} -5.08369i q^{25} +(2.73940 - 2.34429i) q^{26} +(-0.707107 - 0.707107i) q^{28} +4.11071i q^{29} +(-2.19049 - 2.19049i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.548909 + 0.548909i) q^{34} +3.17548i q^{35} +(1.51160 - 1.51160i) q^{37} +3.87409 q^{38} -3.17548 q^{40} +(1.17548 - 1.17548i) q^{41} +4.06950i q^{43} +(1.49250 - 1.49250i) q^{44} +(1.49250 - 1.49250i) q^{46} +(-4.65447 - 4.65447i) q^{47} -1.00000i q^{49} +(3.59471 + 3.59471i) q^{50} +(-0.279383 + 3.59471i) q^{52} -0.828427i q^{53} -6.70252 q^{55} +1.00000 q^{56} +(-2.90671 - 2.90671i) q^{58} +(-8.37799 - 8.37799i) q^{59} +5.91811 q^{61} +3.09782 q^{62} +1.00000i q^{64} +(8.69891 - 7.44425i) q^{65} +(-6.16029 - 6.16029i) q^{67} -0.776275i q^{68} +(-2.24541 - 2.24541i) q^{70} +(-1.86015 + 1.86015i) q^{71} +(10.8392 - 10.8392i) q^{73} +2.13773i q^{74} +(-2.73940 + 2.73940i) q^{76} +2.11071 q^{77} +10.9928 q^{79} +(2.24541 - 2.24541i) q^{80} +1.66238i q^{82} +(2.13985 - 2.13985i) q^{83} +(-1.74305 + 1.74305i) q^{85} +(-2.87757 - 2.87757i) q^{86} +2.11071i q^{88} +(-2.33033 - 2.33033i) q^{89} +(-2.73940 + 2.34429i) q^{91} +2.11071i q^{92} +6.58241 q^{94} +12.3021 q^{95} +(-12.2393 - 12.2393i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{5}+O(q^{10}) \) 12 * q + 4 * q^5	\( 12 q + 4 q^{5} + 8 q^{11} - 16 q^{13} - 12 q^{16} + 8 q^{17} - 4 q^{20} + 8 q^{22} + 8 q^{23} - 8 q^{31} + 8 q^{34} + 16 q^{38} - 24 q^{41} + 8 q^{44} + 8 q^{46} + 4 q^{47} + 16 q^{50} - 16 q^{55} + 12 q^{56} - 8 q^{58} - 48 q^{59} + 32 q^{61} + 8 q^{62} + 8 q^{65} + 28 q^{67} + 4 q^{70} - 8 q^{71} + 16 q^{73} - 8 q^{77} - 32 q^{79} - 4 q^{80} + 40 q^{83} + 8 q^{85} + 40 q^{86} - 24 q^{89} - 8 q^{94} + 8 q^{95} + 8 q^{97}+O(q^{100}) \) 12 * q + 4 * q^5 + 8 * q^11 - 16 * q^13 - 12 * q^16 + 8 * q^17 - 4 * q^20 + 8 * q^22 + 8 * q^23 - 8 * q^31 + 8 * q^34 + 16 * q^38 - 24 * q^41 + 8 * q^44 + 8 * q^46 + 4 * q^47 + 16 * q^50 - 16 * q^55 + 12 * q^56 - 8 * q^58 - 48 * q^59 + 32 * q^61 + 8 * q^62 + 8 * q^65 + 28 * q^67 + 4 * q^70 - 8 * q^71 + 16 * q^73 - 8 * q^77 - 32 * q^79 - 4 * q^80 + 40 * q^83 + 8 * q^85 + 40 * q^86 - 24 * q^89 - 8 * q^94 + 8 * q^95 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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