LMFDB - Embedded newform 841.2.d.j.571.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(190,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

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

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

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

chi := DirichletCharacter("841.190");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	12.0.74049191673856.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 2x^{10} + 4x^{8} + 8x^{6} + 16x^{4} + 32x^{2} + 64 $ x^12 + 2x^10 + 4x^8 + 8x^6 + 16x^4 + 32*x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			571.2
Root			$0.314692 + 1.37876i$ of defining polynomial
Character	$\chi$	$=$	841.571
Dual form			841.2.d.j.190.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.17513 - 1.04749i) q^{2} +(1.50524 + 1.88751i) q^{3} +(2.38699 - 2.99318i) q^{4} +(0.900969 - 0.433884i) q^{5} +(5.25123 + 2.52886i) q^{6} +(-1.76350 - 2.21135i) q^{7} +(0.982255 - 4.30354i) q^{8} +(-0.629384 + 2.75751i) q^{9} +(1.50524 - 1.88751i) q^{10} +(0.0921712 + 0.403828i) q^{11} +9.24264 q^{12} +(0.851905 + 3.73244i) q^{13} +(-6.15220 - 2.96274i) q^{14} +(2.17513 + 1.04749i) q^{15} +(-0.667563 - 2.92478i) q^{16} +0.828427 q^{17} +(1.51947 + 6.65722i) q^{18} +(3.74094 - 4.69099i) q^{19} +(0.851905 - 3.73244i) q^{20} +(1.51947 - 6.65722i) q^{21} +(0.623490 + 0.781831i) q^{22} +(-3.29471 - 1.58665i) q^{23} +(9.60149 - 4.62384i) q^{24} +(-2.49396 + 3.12733i) q^{25} +(5.76269 + 7.22619i) q^{26} +(0.373194 - 0.179721i) q^{27} -10.8284 q^{28} +5.82843 q^{30} +(-9.07372 + 4.36967i) q^{31} +(0.988722 + 1.23982i) q^{32} +(-0.623490 + 0.781831i) q^{33} +(1.80194 - 0.867767i) q^{34} +(-2.54832 - 1.22721i) q^{35} +(6.75141 + 8.46601i) q^{36} +(0.890084 - 3.89971i) q^{37} +(3.22328 - 14.1221i) q^{38} +(-5.76269 + 7.22619i) q^{39} +(-0.982255 - 4.30354i) q^{40} -4.48528 q^{41} +(-3.66832 - 16.0720i) q^{42} +(-3.23068 - 1.55581i) q^{43} +(1.42874 + 0.688047i) q^{44} +(0.629384 + 2.75751i) q^{45} -8.82843 q^{46} +(0.721555 + 3.16134i) q^{47} +(4.51571 - 5.66252i) q^{48} +(-0.222521 + 0.974928i) q^{49} +(-2.14885 + 9.41474i) q^{50} +(1.24698 + 1.56366i) q^{51} +(13.2054 + 6.35937i) q^{52} +(-8.54594 + 4.11551i) q^{53} +(0.623490 - 0.781831i) q^{54} +(0.258258 + 0.323845i) q^{55} +(-11.2488 + 5.41716i) q^{56} +14.4853 q^{57} -3.65685 q^{59} +(8.32733 - 4.01023i) q^{60} +(-3.01048 - 3.77502i) q^{61} +(-15.1593 + 19.0092i) q^{62} +(7.20775 - 3.47107i) q^{63} +(8.85511 + 4.26439i) q^{64} +(2.38699 + 2.99318i) q^{65} +(-0.537213 + 2.35368i) q^{66} +(-1.25877 + 5.51503i) q^{67} +(1.97744 - 2.47964i) q^{68} +(-1.96451 - 8.60708i) q^{69} -6.82843 q^{70} +(1.96451 + 8.60708i) q^{71} +(11.2488 + 5.41716i) q^{72} +(-3.60388 - 1.73553i) q^{73} +(-2.14885 - 9.41474i) q^{74} -9.65685 q^{75} +(-5.11143 - 22.3946i) q^{76} +(0.730464 - 0.915973i) q^{77} +(-4.96527 + 21.7543i) q^{78} +(0.537213 - 2.35368i) q^{79} +(-1.87047 - 2.34549i) q^{80} +(8.54594 + 4.11551i) q^{81} +(-9.75608 + 4.69828i) q^{82} +(4.77397 - 5.98637i) q^{83} +(-16.2994 - 20.4387i) q^{84} +(0.746387 - 0.359441i) q^{85} -8.65685 q^{86} +1.82843 q^{88} +(11.2488 - 5.41716i) q^{89} +(4.25745 + 5.33868i) q^{90} +(6.75141 - 8.46601i) q^{91} +(-12.6136 + 6.07437i) q^{92} +(-21.9059 - 10.5493i) q^{93} +(4.88094 + 6.12051i) q^{94} +(1.33513 - 5.84957i) q^{95} +(-0.851905 + 3.73244i) q^{96} +(2.79653 - 3.50673i) q^{97} +(0.537213 + 2.35368i) q^{98} -1.17157 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8} - 2 q^{10} - 2 q^{11} + 60 q^{12} + 2 q^{13} - 8 q^{14} + 2 q^{15} - 6 q^{16} - 24 q^{17} + 8 q^{18} - 12 q^{19} + 2 q^{20} + 8 q^{21} - 2 q^{22}+ \cdots - 48 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 6 * q^6 + 6 * q^8 - 2 * q^10 - 2 * q^11 + 60 * q^12 + 2 * q^13 - 8 * q^14 + 2 * q^15 - 6 * q^16 - 24 * q^17 + 8 * q^18 - 12 * q^19 + 2 * q^20 + 8 * q^21 - 2 * q^22 + 4 * q^23 + 10 * q^24 + 8 * q^25 - 10 * q^26 - 2 * q^27 - 96 * q^28 + 36 * q^30 - 6 * q^31 - 6 * q^32 + 2 * q^33 + 4 * q^34 - 16 * q^36 + 8 * q^37 + 12 * q^38 + 10 * q^39 - 6 * q^40 + 48 * q^41 - 16 * q^42 - 10 * q^43 + 6 * q^44 - 72 * q^46 - 2 * q^47 - 6 * q^48 - 2 * q^49 - 8 * q^50 - 4 * q^51 + 18 * q^52 - 2 * q^53 - 2 * q^54 + 2 * q^55 - 8 * q^56 + 72 * q^57 + 24 * q^59 + 10 * q^60 + 4 * q^61 + 26 * q^62 + 16 * q^63 + 14 * q^64 - 2 * q^65 - 2 * q^66 - 12 * q^68 - 12 * q^69 - 48 * q^70 + 12 * q^71 + 8 * q^72 - 8 * q^73 - 8 * q^74 - 48 * q^75 - 12 * q^76 - 8 * q^77 - 22 * q^78 + 2 * q^79 + 6 * q^80 + 2 * q^81 - 16 * q^82 - 4 * q^83 + 24 * q^84 - 4 * q^85 - 36 * q^86 - 12 * q^88 + 8 * q^89 - 8 * q^90 - 16 * q^91 - 28 * q^92 - 26 * q^93 - 10 * q^94 + 12 * q^95 - 2 * q^96 + 8 * q^97 + 2 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	2.17513	−	1.04749i	1.53805	−	0.740686i	0.542969	−	0.839753i	$-0.317300\pi$
$2$	2.17513	−	1.04749i	1.53805	−	0.740686i	0.995081	+	0.0990667i	$0.0315857\pi$
$3$	1.50524	+	1.88751i	0.869049	+	1.08975i	0.995212	+	0.0977437i	$0.0311626\pi$
$3$	1.50524	+	1.88751i	0.869049	+	1.08975i	−0.126162	+	0.992010i	$0.540266\pi$
$4$	2.38699	−	2.99318i	1.19349	−	1.49659i
$5$	0.900969	−	0.433884i	0.402926	−	0.194039i	−0.221435	−	0.975175i	$-0.571074\pi$
$5$	0.900969	−	0.433884i	0.402926	−	0.194039i	0.624360	+	0.781136i	$0.285360\pi$
$6$	5.25123	+	2.52886i	2.14381	+	1.03240i
$7$	−1.76350	−	2.21135i	−0.666539	−	0.835813i	0.327499	−	0.944852i	$-0.393794\pi$
$7$	−1.76350	−	2.21135i	−0.666539	−	0.835813i	−0.994038	+	0.109039i	$0.965223\pi$
$8$	0.982255	−	4.30354i	0.347280	−	1.52153i
$9$	−0.629384	+	2.75751i	−0.209795	+	0.919171i
$10$	1.50524	−	1.88751i	0.475998	−	0.596882i
$11$	0.0921712	+	0.403828i	0.0277907	+	0.121759i	0.986921	−	0.161207i	$-0.0515388\pi$
$11$	0.0921712	+	0.403828i	0.0277907	+	0.121759i	−0.959130	+	0.282966i	$0.908682\pi$
$12$	9.24264			2.66812
$13$	0.851905	+	3.73244i	0.236276	+	1.03519i	0.944321	+	0.329025i	$0.106720\pi$
$13$	0.851905	+	3.73244i	0.236276	+	1.03519i	−0.708045	+	0.706167i	$0.750423\pi$
$14$	−6.15220	−	2.96274i	−1.64424	−	0.791827i
$15$	2.17513	+	1.04749i	0.561616	+	0.270460i
$16$	−0.667563	−	2.92478i	−0.166891	−	0.731196i
$17$	0.828427			0.200923			0.100462	−	0.994941i	$-0.467968\pi$
$17$	0.828427			0.200923			0.100462	+	0.994941i	$0.467968\pi$
$18$	1.51947	+	6.65722i	0.358142	+	1.56912i
$19$	3.74094	−	4.69099i	0.858230	−	1.07619i	−0.138085	−	0.990420i	$-0.544095\pi$
$19$	3.74094	−	4.69099i	0.858230	−	1.07619i	0.996315	−	0.0857663i	$-0.0273338\pi$
$20$	0.851905	−	3.73244i	0.190492	−	0.834599i
$21$	1.51947	−	6.65722i	0.331575	−	1.45273i
$22$	0.623490	+	0.781831i	0.132928	+	0.166687i
$23$	−3.29471	−	1.58665i	−0.686995	−	0.330839i	0.0576153	−	0.998339i	$-0.481650\pi$
$23$	−3.29471	−	1.58665i	−0.686995	−	0.330839i	−0.744610	+	0.667500i	$0.767365\pi$
$24$	9.60149	−	4.62384i	1.95990	−	0.943837i
$25$	−2.49396	+	3.12733i	−0.498792	+	0.625465i
$26$	5.76269	+	7.22619i	1.13016	+	1.41717i
$27$	0.373194	−	0.179721i	0.0718211	−	0.0345872i
$28$	−10.8284			−2.04638
$29$		0			0
$29$		0			0
$30$	5.82843			1.06412
$31$	−9.07372	+	4.36967i	−1.62969	+	0.784816i	−0.629720	+	0.776822i	$0.716830\pi$
$31$	−9.07372	+	4.36967i	−1.62969	+	0.784816i	−0.999968	+	0.00799410i	$0.997455\pi$
$32$	0.988722	+	1.23982i	0.174783	+	0.219171i
$33$	−0.623490	+	0.781831i	−0.108536	+	0.136099i
$34$	1.80194	−	0.867767i	0.309030	−	0.148821i
$35$	−2.54832	−	1.22721i	−0.430746	−	0.207436i
$36$	6.75141	+	8.46601i	1.12524	+	1.41100i
$37$	0.890084	−	3.89971i	0.146329	−	0.641109i	−0.847558	−	0.530703i	$-0.821928\pi$
$37$	0.890084	−	3.89971i	0.146329	−	0.641109i	0.993887	−	0.110405i	$-0.0352149\pi$
$38$	3.22328	−	14.1221i	0.522885	−	2.29091i
$39$	−5.76269	+	7.22619i	−0.922769	+	1.15712i
$40$	−0.982255	−	4.30354i	−0.155308	−	0.680449i
$41$	−4.48528			−0.700483			−0.350242	−	0.936659i	$-0.613901\pi$
$41$	−4.48528			−0.700483			−0.350242	+	0.936659i	$0.613901\pi$
$42$	−3.66832	−	16.0720i	−0.566034	−	2.47996i
$43$	−3.23068	−	1.55581i	−0.492674	−	0.237259i	0.171014	−	0.985269i	$-0.445296\pi$
$43$	−3.23068	−	1.55581i	−0.492674	−	0.237259i	−0.663688	+	0.748009i	$0.731010\pi$
$44$	1.42874	+	0.688047i	0.215391	+	0.103727i
$45$	0.629384	+	2.75751i	0.0938231	+	0.411066i
$46$	−8.82843			−1.30168
$47$	0.721555	+	3.16134i	0.105250	+	0.461129i	0.999897	+	0.0143558i	$0.00456975\pi$
$47$	0.721555	+	3.16134i	0.105250	+	0.461129i	−0.894647	+	0.446773i	$0.852573\pi$
$48$	4.51571	−	5.66252i	0.651787	−	0.817315i
$49$	−0.222521	+	0.974928i	−0.0317887	+	0.139275i
$50$	−2.14885	+	9.41474i	−0.303894	+	1.33144i
$51$	1.24698	+	1.56366i	0.174612	+	0.218957i
$52$	13.2054	+	6.35937i	1.83126	+	0.881886i
$53$	−8.54594	+	4.11551i	−1.17388	+	0.565309i	−0.916121	−	0.400902i	$-0.868697\pi$
$53$	−8.54594	+	4.11551i	−1.17388	+	0.565309i	−0.257755	+	0.966210i	$0.582983\pi$
$54$	0.623490	−	0.781831i	0.0848462	−	0.106394i
$55$	0.258258	+	0.323845i	0.0348235	+	0.0436673i
$56$	−11.2488	+	5.41716i	−1.50319	+	0.723899i
$57$	14.4853			1.91862
$58$		0			0
$59$	−3.65685			−0.476082			−0.238041	−	0.971255i	$-0.576505\pi$
$59$	−3.65685			−0.476082			−0.238041	+	0.971255i	$0.576505\pi$
$60$	8.32733	−	4.01023i	1.07505	−	0.517719i
$61$	−3.01048	−	3.77502i	−0.385452	−	0.483341i	0.550817	−	0.834626i	$-0.314316\pi$
$61$	−3.01048	−	3.77502i	−0.385452	−	0.483341i	−0.936269	+	0.351285i	$0.885745\pi$
$62$	−15.1593	+	19.0092i	−1.92524	+	2.41417i
$63$	7.20775	−	3.47107i	0.908091	−	0.437314i
$64$	8.85511	+	4.26439i	1.10689	+	0.533049i
$65$	2.38699	+	2.99318i	0.296069	+	0.371259i
$66$	−0.537213	+	2.35368i	−0.0661264	+	0.289718i
$67$	−1.25877	+	5.51503i	−0.153783	+	0.673768i	0.837982	+	0.545698i	$0.183735\pi$
$67$	−1.25877	+	5.51503i	−0.153783	+	0.673768i	−0.991765	+	0.128070i	$0.959122\pi$
$68$	1.97744	−	2.47964i	0.239800	−	0.300700i
$69$	−1.96451	−	8.60708i	−0.236499	−	1.03617i
$70$	−6.82843			−0.816153
$71$	1.96451	+	8.60708i	0.233144	+	1.02147i	0.947014	+	0.321193i	$0.104084\pi$
$71$	1.96451	+	8.60708i	0.233144	+	1.02147i	−0.713869	+	0.700279i	$0.753059\pi$
$72$	11.2488	+	5.41716i	1.32569	+	0.638418i
$73$	−3.60388	−	1.73553i	−0.421802	−	0.203129i	0.210928	−	0.977502i	$-0.432351\pi$
$73$	−3.60388	−	1.73553i	−0.421802	−	0.203129i	−0.632730	+	0.774373i	$0.718066\pi$
$74$	−2.14885	−	9.41474i	−0.249799	−	1.09444i
$75$	−9.65685			−1.11508
$76$	−5.11143	−	22.3946i	−0.586321	−	2.56884i
$77$	0.730464	−	0.915973i	0.0832441	−	0.104385i
$78$	−4.96527	+	21.7543i	−0.562206	+	2.46318i
$79$	0.537213	−	2.35368i	0.0604412	−	0.264810i	−0.935674	−	0.352864i	$-0.885208\pi$
$79$	0.537213	−	2.35368i	0.0604412	−	0.264810i	0.996116	+	0.0880542i	$0.0280649\pi$
$80$	−1.87047	−	2.34549i	−0.209125	−	0.262234i
$81$	8.54594	+	4.11551i	0.949549	+	0.457279i
$82$	−9.75608	+	4.69828i	−1.07738	+	0.518838i
$83$	4.77397	−	5.98637i	0.524011	−	0.657089i	−0.447444	−	0.894312i	$-0.647666\pi$
$83$	4.77397	−	5.98637i	0.524011	−	0.657089i	0.971455	+	0.237223i	$0.0762370\pi$
$84$	−16.2994	−	20.4387i	−1.77841	−	2.23005i
$85$	0.746387	−	0.359441i	0.0809570	−	0.0389869i
$86$	−8.65685			−0.933493
$87$		0			0
$88$	1.82843			0.194911
$89$	11.2488	−	5.41716i	1.19238	−	0.574218i	0.270883	−	0.962612i	$-0.412685\pi$
$89$	11.2488	−	5.41716i	1.19238	−	0.574218i	0.921493	+	0.388395i	$0.126970\pi$
$90$	4.25745	+	5.33868i	0.448775	+	0.562746i
$91$	6.75141	−	8.46601i	0.707740	−	0.887478i
$92$	−12.6136	+	6.07437i	−1.31505	+	0.633297i
$93$	−21.9059	−	10.5493i	−2.27154	−	1.09391i
$94$	4.88094	+	6.12051i	0.503431	+	0.631282i
$95$	1.33513	−	5.84957i	0.136981	−	0.600153i
$96$	−0.851905	+	3.73244i	−0.0869472	+	0.380941i
$97$	2.79653	−	3.50673i	0.283944	−	0.356055i	−0.619321	−	0.785138i	$-0.712592\pi$
$97$	2.79653	−	3.50673i	0.283944	−	0.356055i	0.903265	+	0.429083i	$0.141163\pi$
$98$	0.537213	+	2.35368i	0.0542667	+	0.237758i
$99$	−1.17157			−0.117748
$100$	3.40762	+	14.9298i	0.340762	+	1.49298i
$101$	2.11110	+	1.01665i	0.210062	+	0.101161i	0.535957	−	0.844246i	$-0.319951\pi$
$101$	2.11110	+	1.01665i	0.210062	+	0.101161i	−0.325894	+	0.945406i	$0.605665\pi$
$102$	4.35026	+	2.09498i	0.430740	+	0.207434i
$103$	1.07443	+	4.70737i	0.105866	+	0.463831i	0.999875	+	0.0157820i	$0.00502377\pi$
$103$	1.07443	+	4.70737i	0.105866	+	0.463831i	−0.894009	+	0.448049i	$0.852119\pi$
$104$	16.8995			1.65713
$105$	−1.51947	−	6.65722i	−0.148285	−	0.649679i
$106$	−14.2776	+	17.9035i	−1.38676	+	1.73895i
$107$	3.29964	−	14.4566i	0.318988	−	1.39758i	−0.520344	−	0.853957i	$-0.674196\pi$
$107$	3.29964	−	14.4566i	0.318988	−	1.39758i	0.839331	−	0.543620i	$-0.182947\pi$
$108$	0.352871	−	1.54603i	0.0339550	−	0.148767i
$109$	7.89142	+	9.89553i	0.755861	+	0.947820i	0.999758	−	0.0219814i	$-0.00699747\pi$
$109$	7.89142	+	9.89553i	0.755861	+	0.947820i	−0.243897	+	0.969801i	$0.578426\pi$
$110$	0.900969	+	0.433884i	0.0859040	+	0.0413692i
$111$	8.70053	−	4.18995i	0.825817	−	0.397693i
$112$	−5.29049	+	6.63406i	−0.499904	+	0.626860i
$113$	−8.30096	−	10.4091i	−0.780889	−	0.979204i	−0.999994	−	0.00350228i	$-0.998885\pi$
$113$	−8.30096	−	10.4091i	−0.780889	−	0.979204i	0.219105	−	0.975701i	$-0.429686\pi$
$114$	31.5074	−	15.1732i	2.95094	−	1.42110i
$115$	−3.65685			−0.341003
$116$		0			0
$117$	−10.8284			−1.00109
$118$	−7.95414	+	3.83051i	−0.732238	+	0.352627i
$119$	−1.46093	−	1.83195i	−0.133923	−	0.167934i
$120$	6.64444	−	8.33186i	0.606552	−	0.760592i
$121$	9.75608	−	4.69828i	0.886916	−	0.427116i
$122$	−10.5025	−	5.05772i	−0.950848	−	0.457904i
$123$	−6.75141	−	8.46601i	−0.608754	−	0.763354i
$124$	−8.57959	+	37.5897i	−0.770470	+	3.37565i
$125$	−2.00269	+	8.77435i	−0.179126	+	0.784802i
$126$	12.0419	−	15.1001i	1.07278	−	1.34522i
$127$	0.966441	+	4.23425i	0.0857578	+	0.375729i	0.999535	−	0.0304859i	$-0.00970547\pi$
$127$	0.966441	+	4.23425i	0.0857578	+	0.375729i	−0.913777	+	0.406215i	$0.866848\pi$
$128$	20.5563			1.81694
$129$	−1.92633	−	8.43981i	−0.169604	−	0.743084i
$130$	8.32733	+	4.01023i	0.730355	+	0.351721i
$131$	−19.2030	−	9.24767i	−1.67777	−	0.807973i	−0.997159	−	0.0753308i	$-0.975999\pi$
$131$	−19.2030	−	9.24767i	−1.67777	−	0.807973i	−0.680614	−	0.732642i	$-0.738287\pi$
$132$	0.851905	+	3.73244i	0.0741488	+	0.324867i
$133$	−16.9706			−1.47153
$134$	3.03894	+	13.3144i	0.262524	+	1.15019i
$135$	0.258258	−	0.323845i	0.0222273	−	0.0278722i
$136$	0.813727	−	3.56517i	0.0697765	−	0.305711i
$137$	−2.67025	+	11.6991i	−0.228135	+	0.999525i	0.723024	+	0.690823i	$0.242752\pi$
$137$	−2.67025	+	11.6991i	−0.228135	+	0.999525i	−0.951159	+	0.308702i	$0.900106\pi$
$138$	−13.2889	−	16.6637i	−1.13122	−	1.41851i
$139$	−12.6136	−	6.07437i	−1.06987	−	0.515222i	−0.185804	−	0.982587i	$-0.559489\pi$
$139$	−12.6136	−	6.07437i	−1.06987	−	0.515222i	−0.884064	+	0.467365i	$0.845203\pi$
$140$	−9.75608	+	4.69828i	−0.824539	+	0.397077i
$141$	−4.88094	+	6.12051i	−0.411050	+	0.515440i
$142$	13.2889	+	16.6637i	1.11518	+	1.39839i
$143$	−1.42874	+	0.688047i	−0.119478	+	0.0575374i
$144$	8.48528			0.707107
$145$		0			0
$146$	−9.65685			−0.799207
$147$	−2.17513	+	1.04749i	−0.179402	+	0.0863954i
$148$	−9.54794	−	11.9727i	−0.784836	−	0.984153i
$149$	−4.88094	+	6.12051i	−0.399863	+	0.501412i	−0.940476	−	0.339859i	$-0.889621\pi$
$149$	−4.88094	+	6.12051i	−0.399863	+	0.501412i	0.540614	+	0.841271i	$0.318192\pi$
$150$	−21.0049	+	10.1154i	−1.71504	+	0.825922i
$151$	12.7416	+	6.13604i	1.03690	+	0.499344i	0.873300	−	0.487183i	$-0.161975\pi$
$151$	12.7416	+	6.13604i	1.03690	+	0.499344i	0.163599	+	0.986527i	$0.447690\pi$
$152$	−16.5133	−	20.7070i	−1.33941	−	1.67956i
$153$	−0.521399	+	2.28440i	−0.0421526	+	0.184683i
$154$	0.629384	−	2.75751i	0.0507172	−	0.222207i
$155$	−6.27921	+	7.87388i	−0.504358	+	0.632445i
$156$	7.87385	+	34.4976i	0.630413	+	2.76202i
$157$	8.48528			0.677199			0.338600	−	0.940931i	$-0.390047\pi$
$157$	8.48528			0.677199			0.338600	+	0.940931i	$0.390047\pi$
$158$	−1.29695	−	5.68230i	−0.103180	−	0.452059i
$159$	−20.6317	−	9.93572i	−1.63620	−	0.787954i
$160$	1.42874	+	0.688047i	0.112952	+	0.0543949i
$161$	2.30157	+	10.0838i	0.181389	+	0.794716i
$162$	22.8995			1.79915
$163$	−0.874270	−	3.83043i	−0.0684781	−	0.300022i	0.929079	−	0.369882i	$-0.120602\pi$
$163$	−0.874270	−	3.83043i	−0.0684781	−	0.300022i	−0.997557	+	0.0698599i	$0.977745\pi$
$164$	−10.7063	+	13.4253i	−0.836022	+	1.04834i
$165$	−0.222521	+	0.974928i	−0.0173232	+	0.0758980i
$166$	4.11336	−	18.0218i	0.319259	−	1.39876i
$167$	−1.97744	−	2.47964i	−0.153019	−	0.191880i	0.699413	−	0.714718i	$-0.253445\pi$
$167$	−1.97744	−	2.47964i	−0.153019	−	0.191880i	−0.852432	+	0.522838i	$0.824873\pi$
$168$	−27.1571	−	13.0782i	−2.09522	−	1.00900i
$169$	−1.49277	+	0.718882i	−0.114829	+	0.0552986i
$170$	1.24698	−	1.56366i	0.0956390	−	0.119927i
$171$	10.5810	+	13.2681i	0.809147	+	1.01464i
$172$	−12.3684	+	5.95632i	−0.943084	+	0.454165i
$173$	12.3431			0.938432			0.469216	−	0.883083i	$-0.344537\pi$
$173$	12.3431			0.938432			0.469216	+	0.883083i	$0.344537\pi$
$174$		0			0
$175$	11.3137			0.855236
$176$	1.11958	−	0.539162i	0.0843916	−	0.0406408i
$177$	−5.50443	−	6.90234i	−0.413739	−	0.518812i
$178$	18.7933	−	23.5661i	1.40862	−	1.76635i
$179$	5.84304	−	2.81386i	0.436729	−	0.210318i	−0.202583	−	0.979265i	$-0.564934\pi$
$179$	5.84304	−	2.81386i	0.436729	−	0.210318i	0.639312	+	0.768947i	$0.279219\pi$
$180$	9.75608	+	4.69828i	0.727175	+	0.350189i
$181$	5.18351	+	6.49992i	0.385287	+	0.483135i	0.936220	−	0.351415i	$-0.114299\pi$
$181$	5.18351	+	6.49992i	0.385287	+	0.483135i	−0.550932	+	0.834550i	$0.685728\pi$
$182$	5.81717	−	25.4867i	0.431198	−	1.88920i
$183$	2.59389	−	11.3646i	0.191746	−	0.840095i
$184$	−10.0645	+	12.6204i	−0.741962	+	0.930390i
$185$	−0.890084	−	3.89971i	−0.0654403	−	0.286713i
$186$	−58.6985			−4.30398
$187$	0.0763571	+	0.334542i	0.00558379	+	0.0244642i
$188$	11.1848	+	5.38633i	0.815737	+	0.392838i
$189$	−1.05555	−	0.508326i	−0.0767800	−	0.0369753i
$190$	−3.22328	−	14.1221i	−0.233841	−	1.02453i
$191$	25.3137			1.83164			0.915818	−	0.401594i	$-0.131544\pi$
$191$	25.3137			1.83164			0.915818	+	0.401594i	$0.131544\pi$
$192$	5.27996	+	23.1330i	0.381048	+	1.66948i
$193$	−3.22442	+	4.04330i	−0.232099	+	0.291043i	−0.884219	−	0.467073i	$-0.845309\pi$
$193$	−3.22442	+	4.04330i	−0.232099	+	0.291043i	0.652120	+	0.758116i	$0.273880\pi$
$194$	2.40955	−	10.5569i	0.172996	−	0.757944i
$195$	−2.05668	+	9.01091i	−0.147282	+	0.645285i
$196$	2.38699	+	2.99318i	0.170499	+	0.213799i
$197$	−1.80194	−	0.867767i	−0.128383	−	0.0618259i	0.368590	−	0.929592i	$-0.379841\pi$
$197$	−1.80194	−	0.867767i	−0.128383	−	0.0618259i	−0.496972	+	0.867766i	$0.665555\pi$
$198$	−2.54832	+	1.22721i	−0.181102	+	0.0872139i
$199$	−0.302568	+	0.379408i	−0.0214485	+	0.0268955i	−0.792440	−	0.609950i	$-0.791190\pi$
$199$	−0.302568	+	0.379408i	−0.0214485	+	0.0268955i	0.770992	+	0.636845i	$0.219761\pi$
$200$	11.0089	+	13.8047i	0.778445	+	0.976139i
$201$	−12.3044	+	5.92549i	−0.867885	+	0.417952i
$202$	5.65685			0.398015
$203$		0			0
$204$	7.65685			0.536087
$205$	−4.04110	+	1.94609i	−0.282243	+	0.135921i
$206$	7.26793	+	9.11370i	0.506381	+	0.634981i
$207$	6.44885	−	8.08660i	0.448226	−	0.562057i
$208$	10.3479	−	4.98328i	0.717496	−	0.345528i
$209$	2.23916	+	1.07832i	0.154886	+	0.0745892i
$210$	−10.2784	−	12.8887i	−0.709277	−	0.889406i
$211$	4.31352	−	18.8988i	0.296955	−	1.30104i	−0.577681	−	0.816263i	$-0.696042\pi$
$211$	4.31352	−	18.8988i	0.296955	−	1.30104i	0.874635	−	0.484781i	$-0.161101\pi$
$212$	−8.08056	+	35.4032i	−0.554975	+	2.43151i
$213$	−13.2889	+	16.6637i	−0.910539	+	1.14178i
$214$	−7.96602	−	34.9014i	−0.544546	−	2.38581i
$215$	−3.58579			−0.244549
$216$	−0.406863	−	1.78258i	−0.0276835	−	0.121290i
$217$	25.6644	+	12.3593i	1.74221	+	0.839004i
$218$	27.5303	+	13.2579i	1.86459	+	0.897938i
$219$	−2.14885	−	9.41474i	−0.145206	−	0.636189i
$220$	1.58579			0.106914
$221$	0.705741	+	3.09205i	0.0474733	+	0.207994i
$222$	14.5359	−	18.2274i	0.975583	−	1.22334i
$223$	0.705741	−	3.09205i	0.0472599	−	0.207059i	−0.945785	−	0.324792i	$-0.894706\pi$
$223$	0.705741	−	3.09205i	0.0472599	−	0.207059i	0.993045	+	0.117733i	$0.0375627\pi$
$224$	0.998069	−	4.37283i	0.0666863	−	0.292172i
$225$	−7.05398	−	8.84541i	−0.470265	−	0.589694i
$226$	−28.9591	−	13.9459i	−1.92633	−	0.927671i
$227$	7.33581	−	3.53274i	0.486895	−	0.234476i	−0.174297	−	0.984693i	$-0.555765\pi$
$227$	7.33581	−	3.53274i	0.486895	−	0.234476i	0.661192	+	0.750217i	$0.270051\pi$
$228$	34.5762	−	43.3571i	2.28986	−	2.87140i
$229$	−2.19139	−	2.74792i	−0.144811	−	0.181588i	0.704136	−	0.710065i	$-0.251334\pi$
$229$	−2.19139	−	2.74792i	−0.144811	−	0.181588i	−0.848947	+	0.528478i	$0.822763\pi$
$230$	−7.95414	+	3.83051i	−0.524480	+	0.252576i
$231$	2.82843			0.186097
$232$		0			0
$233$	18.3137			1.19977			0.599885	−	0.800086i	$-0.295213\pi$
$233$	18.3137			1.19977			0.599885	+	0.800086i	$0.295213\pi$
$234$	−23.5533	+	11.3426i	−1.53972	+	0.741492i
$235$	2.02175	+	2.53520i	0.131885	+	0.165378i
$236$	−8.72886	+	10.9456i	−0.568200	+	0.712501i
$237$	5.25123	−	2.52886i	0.341104	−	0.164267i
$238$	−5.09665	−	2.45442i	−0.330367	−	0.159096i
$239$	−12.2558	−	15.3683i	−0.792765	−	0.994096i	−0.999876	−	0.0157782i	$-0.994977\pi$
$239$	−12.2558	−	15.3683i	−0.792765	−	0.994096i	0.207111	−	0.978318i	$-0.433594\pi$
$240$	1.61164	−	7.06105i	0.104031	−	0.455789i
$241$	4.07518	−	17.8545i	0.262506	−	1.15011i	−0.656018	−	0.754746i	$-0.727760\pi$
$241$	4.07518	−	17.8545i	0.262506	−	1.15011i	0.918523	−	0.395367i	$-0.129383\pi$
$242$	16.2994	−	20.4387i	1.04776	−	1.31385i
$243$	4.81910	+	21.1139i	0.309146	+	1.35446i
$244$	−18.4853			−1.18340
$245$	0.222521	+	0.974928i	0.0142163	+	0.0622859i
$246$	−23.5533	−	11.3426i	−1.50170	−	0.723181i
$247$	20.6958	+	9.96655i	1.31684	+	0.634157i
$248$	9.89236	+	43.3412i	0.628165	+	2.75217i
$249$	18.4853			1.17146
$250$	4.83492	+	21.1832i	0.305787	+	1.33974i
$251$	12.5141	−	15.6922i	0.789883	−	0.990482i	−0.210035	−	0.977694i	$-0.567358\pi$
$251$	12.5141	−	15.6922i	0.789883	−	0.990482i	0.999918	−	0.0127885i	$-0.00407082\pi$
$252$	6.81524	−	29.8595i	0.429320	−	1.88097i
$253$	0.337057	−	1.47674i	0.0211906	−	0.0928419i
$254$	6.53747	+	8.19772i	0.410197	+	0.514371i
$255$	1.80194	+	0.867767i	0.112842	+	0.0543417i
$256$	27.0025	−	13.0037i	1.68766	−	0.812734i
$257$	−11.3298	+	14.2071i	−0.706733	+	0.886215i	−0.997506	−	0.0705769i	$-0.977516\pi$
$257$	−11.3298	+	14.2071i	−0.706733	+	0.886215i	0.290773	+	0.956792i	$0.406087\pi$
$258$	−13.0306	−	16.3399i	−0.811251	−	1.01728i
$259$	−10.1933	+	4.90883i	−0.633381	+	0.305020i
$260$	14.6569			0.908980
$261$		0			0
$262$	−51.4558			−3.17895
$263$	−2.48429	+	1.19637i	−0.153188	+	0.0737715i	−0.508907	−	0.860821i	$-0.669950\pi$
$263$	−2.48429	+	1.19637i	−0.153188	+	0.0737715i	0.355719	+	0.934593i	$0.384236\pi$
$264$	2.75222	+	3.45117i	0.169387	+	0.212405i
$265$	−5.91398	+	7.41589i	−0.363293	+	0.455555i
$266$	−36.9132	+	17.7765i	−2.26329	+	1.08994i
$267$	27.1571	+	13.0782i	1.66199	+	0.800372i
$268$	13.5028	+	16.9320i	0.824816	+	1.03429i
$269$	−6.99958	+	30.6672i	−0.426772	+	1.86981i	0.0630848	+	0.998008i	$0.479906\pi$
$269$	−6.99958	+	30.6672i	−0.426772	+	1.86981i	−0.489857	+	0.871803i	$0.662951\pi$
$270$	0.222521	−	0.974928i	0.0135422	−	0.0593322i
$271$	10.3227	−	12.9443i	0.627060	−	0.786309i	−0.362258	−	0.932078i	$-0.617994\pi$
$271$	10.3227	−	12.9443i	0.627060	−	0.786309i	0.989319	+	0.145769i	$0.0465656\pi$
$272$	−0.553027	−	2.42297i	−0.0335322	−	0.146914i
$273$	26.1421			1.58219
$274$	6.44656	+	28.2442i	0.389451	+	1.70630i
$275$	−1.49277	−	0.718882i	−0.0900177	−	0.0433502i
$276$	−30.4518	−	14.6648i	−1.83299	−	0.882719i
$277$	3.85266	+	16.8796i	0.231484	+	1.01420i	0.948409	+	0.317048i	$0.102692\pi$
$277$	3.85266	+	16.8796i	0.231484	+	1.01420i	−0.716925	+	0.697150i	$0.754451\pi$
$278$	−33.7990			−2.02713
$279$	−6.33857	−	27.7711i	−0.379480	−	1.66261i
$280$	−7.78445	+	9.76139i	−0.465210	+	0.583354i
$281$	−7.11412	+	31.1690i	−0.424393	+	1.85939i	0.0813255	+	0.996688i	$0.474085\pi$
$281$	−7.11412	+	31.1690i	−0.424393	+	1.85939i	−0.505718	+	0.862699i	$0.668772\pi$
$282$	−4.20553	+	18.4256i	−0.250436	+	1.09723i
$283$	7.26793	+	9.11370i	0.432034	+	0.541753i	0.949424	−	0.313996i	$-0.101668\pi$
$283$	7.26793	+	9.11370i	0.432034	+	0.541753i	−0.517391	+	0.855749i	$0.673097\pi$
$284$	30.4518	+	14.6648i	1.80698	+	0.870198i
$285$	13.0508	−	6.28493i	0.773062	−	0.372287i
$286$	−2.38699	+	2.99318i	−0.141145	+	0.176991i
$287$	7.90977	+	9.91854i	0.466899	+	0.585473i
$288$	−4.04110	+	1.94609i	−0.238124	+	0.114674i
$289$	−16.3137			−0.959630
$290$		0			0
$291$	10.8284			0.634774
$292$	−13.7972	+	6.64437i	−0.807419	+	0.388832i
$293$	4.77397	+	5.98637i	0.278898	+	0.349727i	0.901475	−	0.432831i	$-0.142485\pi$
$293$	4.77397	+	5.98637i	0.278898	+	0.349727i	−0.622577	+	0.782559i	$0.713914\pi$
$294$	−3.63396	+	4.55685i	−0.211937	+	0.265761i
$295$	−3.29471	+	1.58665i	−0.191826	+	0.0923783i
$296$	−15.9083	−	7.66102i	−0.924650	−	0.445288i
$297$	0.106974	+	0.134141i	0.00620726	+	0.00778365i
$298$	−4.20553	+	18.4256i	−0.243620	+	1.06737i
$299$	3.11529	−	13.6490i	0.180162	−	0.789342i
$300$	−23.0508	+	28.9047i	−1.33084	+	1.66882i
$301$	2.25684	+	9.88785i	0.130082	+	0.569926i
$302$	34.1421			1.96466
$303$	1.25877	+	5.51503i	0.0723144	+	0.316830i
$304$	−16.2174	−	7.80991i	−0.930134	−	0.447929i
$305$	−4.35026	−	2.09498i	−0.249095	−	0.119958i
$306$	1.25877	+	5.51503i	0.0719590	+	0.315273i
$307$	2.89949			0.165483			0.0827415	−	0.996571i	$-0.473632\pi$
$307$	2.89949			0.165483			0.0827415	+	0.996571i	$0.473632\pi$
$308$	−0.998069	−	4.37283i	−0.0568703	−	0.249165i
$309$	−7.26793	+	9.11370i	−0.413458	+	0.518460i
$310$	−5.41031	+	23.7041i	−0.307285	+	1.34630i
$311$	−0.597756	+	2.61894i	−0.0338956	+	0.148506i	−0.989044	−	0.147621i	$-0.952838\pi$
$311$	−0.597756	+	2.61894i	−0.0338956	+	0.148506i	0.955148	+	0.296128i	$0.0956954\pi$
$312$	25.4378	+	31.8979i	1.44013	+	1.80586i
$313$	−8.85511	−	4.26439i	−0.500520	−	0.241038i	0.166550	−	0.986033i	$-0.446737\pi$
$313$	−8.85511	−	4.26439i	−0.500520	−	0.241038i	−0.667070	+	0.744995i	$0.732452\pi$
$314$	18.4566	−	8.88823i	1.04157	−	0.501592i
$315$	4.98792	−	6.25465i	0.281037	−	0.352410i
$316$	−5.76269	−	7.22619i	−0.324177	−	0.406505i
$317$	28.3407	−	13.6482i	1.59177	−	0.766558i	0.592535	−	0.805545i	$-0.298127\pi$
$317$	28.3407	−	13.6482i	1.59177	−	0.766558i	0.999240	+	0.0389869i	$0.0124131\pi$
$318$	−55.2843			−3.10019
$319$		0			0
$320$	9.82843			0.549426
$321$	32.2538	−	15.5326i	1.80023	−	0.866945i
$322$	15.5689	+	19.5228i	0.867620	+	1.08796i
$323$	3.09910	−	3.88614i	0.172438	−	0.216231i
$324$	32.7175	−	15.7559i	1.81764	−	0.875329i
$325$	−13.7972	−	6.64437i	−0.765330	−	0.368563i
$326$	−5.91398	−	7.41589i	−0.327545	−	0.410728i
$327$	−6.79943	+	29.7902i	−0.376009	+	1.64740i
$328$	−4.40569	+	19.3026i	−0.243264	+	1.06581i
$329$	5.71838	−	7.17062i	0.315265	−	0.395329i
$330$	0.537213	+	2.35368i	0.0295726	+	0.129566i
$331$	−2.41421			−0.132697			−0.0663486	−	0.997797i	$-0.521135\pi$
$331$	−2.41421			−0.132697			−0.0663486	+	0.997797i	$0.521135\pi$
$332$	−6.52291	−	28.5788i	−0.357991	−	1.56846i
$333$	10.1933	+	4.90883i	0.558589	+	0.269002i
$334$	−6.89859	−	3.32218i	−0.377474	−	0.181782i
$335$	1.25877	+	5.51503i	0.0687739	+	0.301318i
$336$	−20.4853			−1.11756
$337$	−4.85073	−	21.2524i	−0.264236	−	1.15769i	−0.916605	−	0.399793i	$-0.869082\pi$
$337$	−4.85073	−	21.2524i	−0.264236	−	1.15769i	0.652369	−	0.757901i	$-0.273775\pi$
$338$	−2.49396	+	3.12733i	−0.135653	+	0.170104i
$339$	7.15230	−	31.3363i	0.388460	−	1.70195i
$340$	0.705741	−	3.09205i	0.0382742	−	0.167690i
$341$	−2.60093	−	3.26147i	−0.140848	−	0.176618i
$342$	36.9132	+	17.7765i	1.99604	+	0.961241i
$343$	−15.2899	+	7.36325i	−0.825580	+	0.397578i
$344$	−9.86886	+	12.3752i	−0.532093	+	0.667224i
$345$	−5.50443	−	6.90234i	−0.296349	−	0.371610i
$346$	26.8480	−	12.9293i	1.44336	−	0.695083i
$347$	2.48528			0.133417			0.0667084	−	0.997773i	$-0.478750\pi$
$347$	2.48528			0.133417			0.0667084	+	0.997773i	$0.478750\pi$
$348$		0			0
$349$	−5.14214			−0.275252			−0.137626	−	0.990484i	$-0.543947\pi$
$349$	−5.14214			−0.275252			−0.137626	+	0.990484i	$0.543947\pi$
$350$	24.6088	−	11.8510i	1.31540	−	0.633461i
$351$	0.988722	+	1.23982i	0.0527741	+	0.0661766i
$352$	−0.409542	+	0.513549i	−0.0218287	+	0.0273723i
$353$	−24.2996	+	11.7021i	−1.29334	+	0.622839i	−0.948784	−	0.315927i	$-0.897685\pi$
$353$	−24.2996	+	11.7021i	−1.29334	+	0.622839i	−0.344556	+	0.938766i	$0.611970\pi$
$354$	−19.2030	−	9.24767i	−1.02063	−	0.491508i
$355$	5.50443	+	6.90234i	0.292145	+	0.366338i
$356$	10.6363	−	46.6006i	0.563721	−	2.46983i
$357$	1.25877	−	5.51503i	0.0666211	−	0.291886i
$358$	9.76189	−	12.2410i	0.515932	−	0.646958i
$359$	−0.874270	−	3.83043i	−0.0461422	−	0.202162i	0.946603	−	0.322403i	$-0.104491\pi$
$359$	−0.874270	−	3.83043i	−0.0461422	−	0.202162i	−0.992745	+	0.120241i	$0.961633\pi$
$360$	12.4853			0.658032
$361$	−3.78286	−	16.5738i	−0.199098	−	0.872304i
$362$	18.0834	+	8.70851i	0.950443	+	0.457709i
$363$	23.5533	+	11.3426i	1.23623	+	0.595335i
$364$	−9.22479	−	40.4165i	−0.483511	−	2.11840i
$365$	−4.00000			−0.209370
$366$	−6.26221	−	27.4366i	−0.327331	−	1.43413i
$367$	11.2228	−	14.0730i	0.585826	−	0.734603i	−0.397268	−	0.917703i	$-0.630042\pi$
$367$	11.2228	−	14.0730i	0.585826	−	0.734603i	0.983094	+	0.183100i	$0.0586131\pi$
$368$	−2.44118	+	10.6955i	−0.127255	+	0.557542i
$369$	2.82297	−	12.3682i	0.146958	−	0.643864i
$370$	−6.02095	−	7.55003i	−0.313014	−	0.392508i
$371$	24.1716	+	11.6404i	1.25493	+	0.604340i
$372$	−83.8651	+	40.3873i	−4.34820	+	2.09398i
$373$	−16.4063	+	20.5729i	−0.849488	+	1.06522i	0.147607	+	0.989046i	$0.452843\pi$
$373$	−16.4063	+	20.5729i	−0.849488	+	1.06522i	−0.997094	+	0.0761775i	$0.975728\pi$
$374$	0.516516	+	0.647690i	0.0267084	+	0.0334913i
$375$	−19.5762	+	9.42739i	−1.01091	+	0.486828i
$376$	14.3137			0.738173
$377$		0			0
$378$	−2.82843			−0.145479
$379$	6.28026	−	3.02441i	0.322595	−	0.155354i	−0.265576	−	0.964090i	$-0.585562\pi$
$379$	6.28026	−	3.02441i	0.322595	−	0.155354i	0.588172	+	0.808736i	$0.299848\pi$
$380$	−14.3219	−	17.9591i	−0.734699	−	0.921283i
$381$	−6.53747	+	8.19772i	−0.334925	+	0.419982i
$382$	55.0606	−	26.5158i	2.81715	−	1.35667i
$383$	3.16665	+	1.52498i	0.161808	+	0.0779228i	0.513035	−	0.858368i	$-0.328521\pi$
$383$	3.16665	+	1.52498i	0.161808	+	0.0779228i	−0.351227	+	0.936290i	$0.614235\pi$
$384$	30.9422	+	38.8003i	1.57901	+	1.98002i
$385$	0.260699	−	1.14220i	0.0132865	−	0.0582119i
$386$	−2.77824	+	12.1722i	−0.141409	+	0.619551i
$387$	6.32352	−	7.92944i	0.321442	−	0.403076i
$388$	−3.82103	−	16.7410i	−0.193984	−	0.849898i
$389$	3.02944			0.153599			0.0767993	−	0.997047i	$-0.475530\pi$
$389$	3.02944			0.153599			0.0767993	+	0.997047i	$0.475530\pi$
$390$	4.96527	+	21.7543i	0.251426	+	1.10157i
$391$	−2.72943	−	1.31442i	−0.138033	−	0.0664733i
$392$	3.97707	+	1.91526i	0.200872	+	0.0967350i
$393$	−11.4500	−	50.1657i	−0.577576	−	2.53053i
$394$	−4.82843			−0.243253
$395$	−0.537213	−	2.35368i	−0.0270301	−	0.118427i
$396$	−2.79653	+	3.50673i	−0.140531	+	0.176220i
$397$	−4.30425	+	18.8582i	−0.216024	+	0.946465i	0.744358	+	0.667780i	$0.232755\pi$
$397$	−4.30425	+	18.8582i	−0.216024	+	0.946465i	−0.960383	+	0.278684i	$0.910102\pi$
$398$	−0.260699	+	1.14220i	−0.0130677	+	0.0572533i
$399$	−25.5447	−	32.0321i	−1.27884	−	1.60361i
$400$	10.8116	+	5.20660i	0.540581	+	0.260330i
$401$	16.8092	−	8.09491i	0.839414	−	0.404240i	0.0357764	−	0.999360i	$-0.488610\pi$
$401$	16.8092	−	8.09491i	0.839414	−	0.404240i	0.803637	+	0.595120i	$0.202895\pi$
$402$	−20.5568	+	25.7774i	−1.02528	+	1.28566i
$403$	−24.0395	−	30.1446i	−1.19749	−	1.50161i
$404$	8.08220	−	3.89218i	0.402104	−	0.193643i
$405$	9.48528			0.471327
$406$		0			0
$407$	1.65685			0.0821272
$408$	7.95414	−	3.83051i	0.393789	−	0.189639i
$409$	−11.8280	−	14.8318i	−0.584855	−	0.733384i	0.398078	−	0.917352i	$-0.369677\pi$
$409$	−11.8280	−	14.8318i	−0.584855	−	0.733384i	−0.982932	+	0.183967i	$0.941106\pi$
$410$	−6.75141	+	8.46601i	−0.333429	+	0.418106i
$411$	−26.1016	+	12.5699i	−1.28750	+	0.620025i
$412$	16.6547	+	8.02046i	0.820516	+	0.395140i
$413$	6.44885	+	8.08660i	0.317327	+	0.397915i
$414$	5.55647	−	24.3445i	0.273086	−	1.19647i
$415$	1.70381	−	7.46488i	0.0836368	−	0.366437i
$416$	−3.78525	+	4.74655i	−0.185587	+	0.232719i
$417$	−7.52098	−	32.9516i	−0.368304	−	1.61365i
$418$	6.00000			0.293470
$419$	2.11722	+	9.27616i	0.103433	+	0.453170i	0.999948	+	0.0101574i	$0.00323326\pi$
$419$	2.11722	+	9.27616i	0.103433	+	0.453170i	−0.896515	+	0.443013i	$0.853910\pi$
$420$	−23.5533	−	11.3426i	−1.14928	−	0.553465i
$421$	−33.4374	−	16.1026i	−1.62964	−	0.784793i	−0.999969	−	0.00792973i	$-0.997476\pi$
$421$	−33.4374	−	16.1026i	−1.62964	−	0.784793i	−0.629670	−	0.776863i	$-0.716810\pi$
$422$	−10.4138	−	45.6256i	−0.506934	−	2.22102i
$423$	−9.17157			−0.445937
$424$	9.31696	+	40.8203i	0.452472	+	1.98241i
$425$	−2.06606	+	2.59076i	−0.100219	+	0.125670i
$426$	−11.4500	+	50.1657i	−0.554754	+	2.43054i
$427$	−3.03894	+	13.3144i	−0.147064	+	0.644331i
$428$	−35.3952	−	44.3842i	−1.71089	−	2.14539i
$429$	−3.44929	−	1.66109i	−0.166533	−	0.0801983i
$430$	−7.79956	+	3.75607i	−0.376128	+	0.181134i
$431$	12.2558	−	15.3683i	0.590343	−	0.740267i	−0.393495	−	0.919327i	$-0.628734\pi$
$431$	12.2558	−	15.3683i	0.590343	−	0.740267i	0.983838	+	0.179060i	$0.0573055\pi$
$432$	−0.774774	−	0.971536i	−0.0372763	−	0.0467430i
$433$	−27.5943	+	13.2887i	−1.32610	+	0.638616i	−0.956814	−	0.290700i	$-0.906112\pi$
$433$	−27.5943	+	13.2887i	−1.32610	+	0.638616i	−0.369286	+	0.929316i	$0.620398\pi$
$434$	68.7696			3.30104
$435$		0			0
$436$	48.4558			2.32061
$437$	−19.7683	+	9.51990i	−0.945645	+	0.455398i
$438$	−14.5359	−	18.2274i	−0.694550	−	0.870938i
$439$	−0.213948	+	0.268282i	−0.0102112	+	0.0128044i	−0.786911	−	0.617067i	$-0.788321\pi$
$439$	−0.213948	+	0.268282i	−0.0102112	+	0.0128044i	0.776700	+	0.629871i	$0.216892\pi$
$440$	1.64736	−	0.793325i	0.0785346	−	0.0378203i
$441$	−2.54832	−	1.22721i	−0.121349	−	0.0584385i
$442$	4.77397	+	5.98637i	0.227075	+	0.284743i
$443$	5.41686	−	23.7328i	0.257363	−	1.12758i	−0.666696	−	0.745330i	$-0.732292\pi$
$443$	5.41686	−	23.7328i	0.257363	−	1.12758i	0.924059	−	0.382250i	$-0.124851\pi$
$444$	8.22672	−	36.0436i	0.390423	−	1.71056i
$445$	7.78445	−	9.76139i	0.369018	−	0.462734i
$446$	−1.70381	−	7.46488i	−0.0806778	−	0.353472i
$447$	−18.8995			−0.893915
$448$	−6.18586	−	27.1020i	−0.292254	−	1.28045i
$449$	31.5074	+	15.1732i	1.48693	+	0.716066i	0.988550	−	0.150895i	$-0.0482157\pi$
$449$	31.5074	+	15.1732i	1.48693	+	0.716066i	0.498376	+	0.866961i	$0.333930\pi$
$450$	−24.6088	−	11.8510i	−1.16007	−	0.558660i
$451$	−0.413414	−	1.81128i	−0.0194669	−	0.0852900i
$452$	−50.9706			−2.39745
$453$	7.59734	+	33.2861i	0.356954	+	1.56392i
$454$	12.2558	−	15.3683i	0.575195	−	0.721272i
$455$	2.40955	−	10.5569i	0.112962	−	0.494917i
$456$	14.2282	−	62.3380i	0.666298	−	2.91924i
$457$	0.641844	+	0.804846i	0.0300242	+	0.0376491i	0.796617	−	0.604484i	$-0.206621\pi$
$457$	0.641844	+	0.804846i	0.0300242	+	0.0376491i	−0.766593	+	0.642134i	$0.778049\pi$
$458$	−7.64497	−	3.68163i	−0.357226	−	0.172031i
$459$	0.309164	−	0.148885i	0.0144305	−	0.00694937i
$460$	−8.72886	+	10.9456i	−0.406985	+	0.510343i
$461$	8.72886	+	10.9456i	0.406543	+	0.509789i	0.942385	−	0.334529i	$-0.108577\pi$
$461$	8.72886	+	10.9456i	0.406543	+	0.509789i	−0.535842	+	0.844318i	$0.680006\pi$
$462$	6.15220	−	2.96274i	0.286226	−	0.137839i
$463$	−26.0000			−1.20832			−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000			−1.20832			−0.604161	+	0.796862i	$0.706492\pi$
$464$		0			0
$465$	−24.3137			−1.12752
$466$	39.8347	−	19.1834i	1.84531	−	0.888653i
$467$	−23.9142	−	29.9874i	−1.10662	−	1.38765i	−0.913677	−	0.406441i	$-0.866770\pi$
$467$	−23.9142	−	29.9874i	−1.10662	−	1.38765i	−0.192938	−	0.981211i	$-0.561802\pi$
$468$	−25.8473	+	32.4115i	−1.19479	+	1.49822i
$469$	14.4155	−	6.94214i	0.665646	−	0.320558i
$470$	7.05317	+	3.39663i	0.325338	+	0.156675i
$471$	12.7724	+	16.0160i	0.588519	+	0.737980i
$472$	−3.59196	+	15.7374i	−0.165334	+	0.724373i
$473$	0.330506	−	1.44804i	0.0151967	−	0.0665811i
$474$	8.77317	−	11.0012i	0.402965	−	0.505302i
$475$	5.34050	+	23.3983i	0.245039	+	1.07359i
$476$	−8.97056			−0.411165
$477$	−5.96989	−	26.1558i	−0.273342	−	1.19759i
$478$	−42.7562	−	20.5903i	−1.95562	−	0.941779i
$479$	−6.21623	−	2.99358i	−0.284027	−	0.136780i	0.286447	−	0.958096i	$-0.407526\pi$
$479$	−6.21623	−	2.99358i	−0.284027	−	0.136780i	−0.570473	+	0.821316i	$0.693240\pi$
$480$	0.851905	+	3.73244i	0.0388840	+	0.170362i
$481$	15.3137			0.698245
$482$	−9.83836	−	43.1047i	−0.448125	−	1.96336i
$483$	−15.5689	+	19.5228i	−0.708409	+	0.888317i
$484$	9.22479	−	40.4165i	0.419309	−	1.83711i
$485$	0.998069	−	4.37283i	0.0453200	−	0.198560i
$486$	32.5987	+	40.8775i	1.47871	+	1.85424i
$487$	10.3744	+	4.99605i	0.470109	+	0.226393i	0.653912	−	0.756570i	$-0.273127\pi$
$487$	10.3744	+	4.99605i	0.470109	+	0.226393i	−0.183803	+	0.982963i	$0.558841\pi$
$488$	−19.2030	+	9.24767i	−0.869278	+	0.418622i
$489$	5.91398	−	7.41589i	0.267439	−	0.335358i
$490$	1.50524	+	1.88751i	0.0679997	+	0.0852689i
$491$	19.1390	−	9.21684i	0.863729	−	0.415950i	0.0510739	−	0.998695i	$-0.483736\pi$
$491$	19.1390	−	9.21684i	0.863729	−	0.415950i	0.812655	+	0.582745i	$0.198021\pi$
$492$	−41.4558			−1.86897
$493$		0			0
$494$	55.4558			2.49508
$495$	−1.05555	+	0.508326i	−0.0474435	+	0.0228476i
$496$	18.8376	+	23.6216i	0.845834	+	1.06064i
$497$	15.5689	−	19.5228i	0.698360	−	0.875716i
$498$	40.2079	−	19.3631i	1.80176	−	0.867682i
$499$	−17.0919	−	8.23102i	−0.765138	−	0.368471i	0.0102572	−	0.999947i	$-0.496735\pi$
$499$	−17.0919	−	8.23102i	−0.765138	−	0.368471i	−0.775395	+	0.631476i	$0.782449\pi$
$500$	21.4829	+	26.9387i	0.960743	+	1.20473i
$501$	1.70381	−	7.46488i	0.0761206	−	0.333506i
$502$	10.7824	−	47.2410i	0.481244	−	2.10847i
$503$	0.169638	−	0.212719i	0.00756378	−	0.00948468i	−0.778035	−	0.628221i	$-0.783784\pi$
$503$	0.169638	−	0.212719i	0.00756378	−	0.00948468i	0.785599	+	0.618736i	$0.212355\pi$
$504$	−7.85804	−	34.4283i	−0.350025	−	1.53356i
$505$	2.34315			0.104269
$506$	−0.813727	−	3.56517i	−0.0361746	−	0.158491i
$507$	−3.60388	−	1.73553i	−0.160054	−	0.0770778i
$508$	14.9808	+	7.21437i	0.664665	+	0.320086i
$509$	2.33975	+	10.2511i	0.103707	+	0.454372i	0.999942	+	0.0107909i	$0.00343493\pi$
$509$	2.33975	+	10.2511i	0.103707	+	0.454372i	−0.896234	+	0.443581i	$0.853708\pi$
$510$	4.82843			0.213806
$511$	2.51754	+	11.0301i	0.111369	+	0.487941i
$512$	19.4795	−	24.4265i	0.860879	−	1.07951i
$513$	0.553027	−	2.42297i	0.0244167	−	0.106977i
$514$	−9.76201	+	42.7701i	−0.430584	+	1.88651i
$515$	3.01048	+	3.77502i	0.132657	+	0.166347i
$516$	−29.8600	−	14.3798i	−1.31451	−	0.633037i
$517$	−1.21013	+	0.582769i	−0.0532216	+	0.0256302i
$518$	−17.0298	+	21.3547i	−0.748247	+	0.938272i
$519$	18.5794	+	23.2978i	0.815544	+	1.02266i
$520$	15.2259	−	7.33242i	0.667701	−	0.321548i
$521$	−29.1421			−1.27674			−0.638370	−	0.769730i	$-0.720391\pi$
$521$	−29.1421			−1.27674			−0.638370	+	0.769730i	$0.720391\pi$
$522$		0			0
$523$	4.68629			0.204917			0.102459	−	0.994737i	$-0.467329\pi$
$523$	4.68629			0.204917			0.102459	+	0.994737i	$0.467329\pi$
$524$	−73.5172	+	35.4040i	−3.21162	+	1.54663i
$525$	17.0298	+	21.3547i	0.743242	+	0.931996i
$526$	−4.15048	+	5.20454i	−0.180970	+	0.226929i
$527$	−7.51691	+	3.61996i	−0.327442	+	0.157688i
$528$	2.70291	+	1.30165i	0.117629	+	0.0566471i
$529$	−6.00260	−	7.52702i	−0.260982	−	0.327262i
$530$	−5.09562	+	22.3254i	−0.221339	+	0.969752i
$531$	2.30157	−	10.0838i	0.0998795	−	0.437601i
$532$	−40.5085	+	50.7960i	−1.75627	+	2.20229i
$533$	−3.82103	−	16.7410i	−0.165507	−	0.725135i
$534$	72.7696			3.14905
$535$	−3.29964	−	14.4566i	−0.142656	−	0.625015i
$536$	22.4977	+	10.8343i	0.971753	+	0.467971i
$537$	14.1063	+	6.79325i	0.608733	+	0.293151i
$538$	16.8985	+	74.0371i	0.728546	+	3.19197i
$539$	−0.414214			−0.0178414
$540$	−0.352871	−	1.54603i	−0.0151851	−	0.0665304i
$541$	−6.44885	+	8.08660i	−0.277258	+	0.347670i	−0.900890	−	0.434048i	$-0.857085\pi$
$541$	−6.44885	+	8.08660i	−0.277258	+	0.347670i	0.623632	+	0.781718i	$0.285656\pi$
$542$	8.89429	−	38.9684i	0.382042	−	1.67384i
$543$	−4.46623	+	19.5678i	−0.191664	+	0.839737i
$544$	0.819084	+	1.02710i	0.0351179	+	0.0440365i
$545$	11.4034	+	5.49160i	0.488469	+	0.235234i
$546$	56.8626	−	27.3836i	2.43349	−	1.17191i
$547$	22.3203	−	27.9888i	0.954347	−	1.19671i	−0.0260455	−	0.999661i	$-0.508291\pi$
$547$	22.3203	−	27.9888i	0.954347	−	1.19671i	0.980393	−	0.197053i	$-0.0631371\pi$
$548$	28.6438	+	35.9182i	1.22360	+	1.53435i
$549$	12.3044	−	5.92549i	0.525139	−	0.252894i
$550$	−4.00000			−0.170561
$551$		0			0
$552$	−38.9706			−1.65870
$553$	−6.15220	+	2.96274i	−0.261618	+	0.125989i
$554$	26.0612	+	32.6798i	1.10724	+	1.38843i
$555$	6.02095	−	7.55003i	0.255575	−	0.320481i
$556$	−48.2901	+	23.2553i	−2.04796	+	0.986244i
$557$	15.5991	+	7.51214i	0.660956	+	0.318299i	0.734119	−	0.679021i	$-0.237595\pi$
$557$	15.5991	+	7.51214i	0.660956	+	0.318299i	−0.0731637	+	0.997320i	$0.523310\pi$
$558$	−42.8771	−	53.7662i	−1.81513	−	2.27610i
$559$	3.05475	−	13.3837i	0.129202	−	0.566072i
$560$	−1.88815	+	8.27254i	−0.0797890	+	0.349579i
$561$	−0.516516	+	0.647690i	−0.0218073	+	0.0273455i
$562$	17.1750	+	75.2486i	0.724484	+	3.17417i
$563$	−0.757359			−0.0319189			−0.0159594	−	0.999873i	$-0.505080\pi$
$563$	−0.757359			−0.0319189			−0.0159594	+	0.999873i	$0.505080\pi$
$564$	6.66908	+	29.2191i	0.280819	+	1.23035i
$565$	−11.9952	−	5.77660i	−0.504643	−	0.243023i
$566$	25.3552	+	12.2104i	1.06576	+	0.513242i
$567$	−5.96989	−	26.1558i	−0.250712	−	1.09844i
$568$	38.9706			1.63517
$569$	8.82448	+	38.6626i	0.369941	+	1.62082i	0.726931	+	0.686711i	$0.240946\pi$
$569$	8.82448	+	38.6626i	0.369941	+	1.62082i	−0.356989	+	0.934109i	$0.616197\pi$
$570$	21.8038	−	27.3411i	0.913260	−	1.14519i
$571$	−3.25491	+	14.2607i	−0.136214	+	0.596791i	0.860034	+	0.510237i	$0.170442\pi$
$571$	−3.25491	+	14.2607i	−0.136214	+	0.596791i	−0.996247	+	0.0865534i	$0.972415\pi$
$572$	−1.35094	+	5.91885i	−0.0564856	+	0.247480i
$573$	38.1031	+	47.7798i	1.59178	+	1.99603i
$574$	27.5943	+	13.2887i	1.15177	+	0.554661i
$575$	13.1788	−	6.34660i	0.549596	−	0.264671i
$576$	−17.3324	+	21.7341i	−0.722183	+	0.905589i
$577$	−18.5794	−	23.2978i	−0.773469	−	0.969900i	0.226522	−	0.974006i	$-0.427264\pi$
$577$	−18.5794	−	23.2978i	−0.773469	−	0.969900i	−0.999992	+	0.00410633i	$0.998693\pi$
$578$	−35.4845	+	17.0884i	−1.47596	+	0.710784i
$579$	−12.4853			−0.518871
$580$		0			0
$581$	−21.6569			−0.898478
$582$	23.5533	−	11.3426i	0.976314	−	0.470168i
$583$	−2.44965	−	3.07176i	−0.101454	−	0.127219i
$584$	−11.0089	+	13.8047i	−0.455550	+	0.571242i
$585$	−9.75608	+	4.69828i	−0.403364	+	0.194250i
$586$	16.6547	+	8.02046i	0.687998	+	0.331322i
$587$	4.77397	+	5.98637i	0.197043	+	0.247084i	0.870530	−	0.492115i	$-0.163776\pi$
$587$	4.77397	+	5.98637i	0.197043	+	0.247084i	−0.673488	+	0.739199i	$0.735204\pi$
$588$	−2.05668	+	9.01091i	−0.0848161	+	0.371604i
$589$	−13.4461	+	58.9114i	−0.554039	+	2.42740i
$590$	−5.50443	+	6.90234i	−0.226614	+	0.284165i
$591$	−1.07443	−	4.70737i	−0.0441960	−	0.193635i
$592$	−12.0000			−0.493197
$593$	4.33588	+	18.9967i	0.178053	+	0.780103i	0.982528	+	0.186116i	$0.0595899\pi$
$593$	4.33588	+	18.9967i	0.178053	+	0.780103i	−0.804474	+	0.593987i	$0.797553\pi$
$594$	0.373194	+	0.179721i	0.0153123	+	0.00737402i
$595$	−2.11110	−	1.01665i	−0.0865467	−	0.0416787i
$596$	6.66908	+	29.2191i	0.273176	+	1.19686i
$597$	−1.17157			−0.0479493
$598$	−7.52098	−	32.9516i	−0.307556	−	1.34749i
$599$	6.15388	−	7.71672i	0.251441	−	0.315297i	−0.640052	−	0.768332i	$-0.721087\pi$
$599$	6.15388	−	7.71672i	0.251441	−	0.315297i	0.891493	+	0.453035i	$0.149659\pi$
$600$	−9.48549	+	41.5587i	−0.387244	+	1.69663i
$601$	3.82103	−	16.7410i	0.155863	−	0.682881i	−0.835251	−	0.549869i	$-0.814678\pi$
$601$	3.82103	−	16.7410i	0.155863	−	0.682881i	0.991114	−	0.133013i	$-0.0424651\pi$
$602$	15.2663	+	19.1434i	0.622209	+	0.780225i
$603$	−14.4155	−	6.94214i	−0.587045	−	0.282706i
$604$	48.7804	−	23.4914i	1.98485	−	0.955851i
$605$	6.75141	−	8.46601i	0.274484	−	0.344192i
$606$	8.51491	+	10.6774i	0.345895	+	0.433738i
$607$	6.96262	−	3.35302i	0.282604	−	0.136095i	−0.287213	−	0.957867i	$-0.592729\pi$
$607$	6.96262	−	3.35302i	0.282604	−	0.136095i	0.569816	+	0.821772i	$0.307014\pi$
$608$	9.51472			0.385873
$609$		0			0
$610$	−11.6569			−0.471972
$611$	−11.1848	+	5.38633i	−0.452489	+	0.217907i
$612$	5.59305	+	7.01347i	0.226086	+	0.283503i
$613$	−5.61141	+	7.03648i	−0.226643	+	0.284201i	−0.882131	−	0.471005i	$-0.843892\pi$
$613$	−5.61141	+	7.03648i	−0.226643	+	0.284201i	0.655488	+	0.755205i	$0.272463\pi$
$614$	6.30678	−	3.03719i	0.254521	−	0.122571i
$615$	−9.75608	−	4.69828i	−0.393403	−	0.189453i
$616$	−3.22442	−	4.04330i	−0.129916	−	0.162909i
$617$	−0.152714	+	0.669085i	−0.00614804	+	0.0269363i	−0.977909	−	0.209032i	$-0.932969\pi$
$617$	−0.152714	+	0.669085i	−0.00614804	+	0.0269363i	0.971761	+	0.235968i	$0.0758260\pi$
$618$	−6.26221	+	27.4366i	−0.251903	+	1.10366i
$619$	20.9404	−	26.2584i	0.841666	−	1.05542i	−0.156043	−	0.987750i	$-0.549874\pi$
$619$	20.9404	−	26.2584i	0.841666	−	1.05542i	0.997708	−	0.0676649i	$-0.0215549\pi$
$620$	8.57959	+	37.5897i	0.344565	+	1.50964i
$621$	−1.51472			−0.0607836
$622$	1.44311	+	6.32268i	0.0578635	+	0.253516i
$623$	−31.8166	−	15.3220i	−1.27470	−	0.613865i
$624$	24.9820	+	12.0307i	1.00008	+	0.481613i
$625$	−2.44773	−	10.7242i	−0.0979092	−	0.428968i
$626$	−23.7279			−0.948358
$627$	1.33513	+	5.84957i	0.0533198	+	0.233609i
$628$	20.2542	−	25.3980i	0.808232	−	1.01349i
$629$	0.737370	−	3.23063i	0.0294008	−	0.128814i
$630$	4.29770	−	18.8295i	0.171225	−	0.750184i
$631$	−22.9621	−	28.7936i	−0.914109	−	1.14626i	−0.988829	−	0.149052i	$-0.952378\pi$
$631$	−22.9621	−	28.7936i	−0.914109	−	1.14626i	0.0747207	−	0.997204i	$-0.476193\pi$
$632$	−9.60149	−	4.62384i	−0.381927	−	0.183926i
$633$	42.1644	−	20.3053i	1.67589	−	0.807064i
$634$	47.3485	−	59.3732i	1.88045	−	2.35801i
$635$	2.70791	+	3.39561i	0.107460	+	0.134751i
$636$	−78.9871	+	38.0382i	−3.13204	+	1.50831i
$637$	−3.82843			−0.151688
$638$		0			0
$639$	−24.9706			−0.987820
$640$	18.5206	−	8.91907i	0.732092	−	0.352557i
$641$	11.0975	+	13.9158i	0.438324	+	0.549641i	0.951101	−	0.308881i	$-0.0999544\pi$
$641$	11.0975	+	13.9158i	0.438324	+	0.549641i	−0.512776	+	0.858522i	$0.671383\pi$
$642$	53.8860	−	67.5709i	2.12671	−	2.66681i
$643$	−29.2682	+	14.0948i	−1.15423	+	0.555846i	−0.910301	−	0.413948i	$-0.864150\pi$
$643$	−29.2682	+	14.0948i	−1.15423	+	0.555846i	−0.243926	+	0.969794i	$0.578435\pi$
$644$	35.6765	+	17.1809i	1.40585	+	0.677023i
$645$	−5.39746	−	6.76820i	−0.212525	−	0.266498i
$646$	2.67025	−	11.6991i	0.105060	−	0.460296i
$647$	−8.82448	+	38.6626i	−0.346926	+	1.51998i	0.437190	+	0.899369i	$0.355974\pi$
$647$	−8.82448	+	38.6626i	−0.346926	+	1.51998i	−0.784117	+	0.620614i	$0.786884\pi$
$648$	26.1056	−	32.7353i	1.02552	−	1.28597i
$649$	−0.337057	−	1.47674i	−0.0132306	−	0.0579672i
$650$	−36.9706			−1.45010
$651$	15.3027	+	67.0454i	0.599759	+	2.62771i
$652$	−13.5520	−	6.52632i	−0.530739	−	0.255590i
$653$	27.1571	+	13.0782i	1.06274	+	0.511789i	0.881760	−	0.471698i	$-0.156359\pi$
$653$	27.1571	+	13.0782i	1.06274	+	0.511789i	0.180980	+	0.983487i	$0.442073\pi$
$654$	16.4153	+	71.9200i	0.641888	+	2.81229i
$655$	−21.3137			−0.832796
$656$	2.99421	+	13.1185i	0.116904	+	0.512191i
$657$	7.05398	−	8.84541i	0.275202	−	0.345092i
$658$	4.92709	−	21.5870i	0.192078	−	0.841548i
$659$	−3.20746	+	14.0528i	−0.124945	+	0.547420i	0.873245	+	0.487281i	$0.162011\pi$
$659$	−3.20746	+	14.0528i	−0.124945	+	0.547420i	−0.998190	+	0.0601386i	$0.980846\pi$
$660$	2.38699	+	2.99318i	0.0929133	+	0.116510i
$661$	−30.0146	−	14.4543i	−1.16743	−	0.562206i	−0.253208	−	0.967412i	$-0.581486\pi$
$661$	−30.0146	−	14.4543i	−1.16743	−	0.562206i	−0.914226	+	0.405206i	$0.867200\pi$
$662$	−5.25123	+	2.52886i	−0.204095	+	0.0982869i
$663$	−4.77397	+	5.98637i	−0.185406	+	0.232491i
$664$	−21.0733	−	26.4251i	−0.817804	−	1.02549i
$665$	−15.2899	+	7.36325i	−0.592919	+	0.285535i
$666$	27.3137			1.05838
$667$		0			0
$668$	−12.1421			−0.469793
$669$	6.89859	−	3.32218i	0.266715	−	0.128443i
$670$	8.51491	+	10.6774i	0.328960	+	0.412502i
$671$	1.24698	−	1.56366i	0.0481391	−	0.0603645i
$672$	9.75608	−	4.69828i	0.376349	−	0.181240i
$673$	19.4856	+	9.38378i	0.751116	+	0.361718i	0.769950	−	0.638104i	$-0.220281\pi$
$673$	19.4856	+	9.38378i	0.751116	+	0.361718i	−0.0188341	+	0.999823i	$0.505995\pi$
$674$	−32.8127	−	41.1458i	−1.26390	−	1.58488i
$675$	−0.368685	+	1.61531i	−0.0141907	+	0.0621734i
$676$	−1.41148	+	6.18411i	−0.0542878	+	0.237850i
$677$	−13.7168	+	17.2003i	−0.527179	+	0.661061i	−0.972116	−	0.234501i	$-0.924654\pi$
$677$	−13.7168	+	17.2003i	−0.527179	+	0.661061i	0.444937	+	0.895562i	$0.353226\pi$
$678$	−17.2672	−	75.6524i	−0.663142	−	2.90541i
$679$	−12.6863			−0.486855
$680$	−0.813727	−	3.56517i	−0.0312050	−	0.136718i
$681$	17.7102	+	8.52879i	0.678657	+	0.326824i
$682$	−9.07372	−	4.36967i	−0.347451	−	0.167323i
$683$	−4.66639	−	20.4448i	−0.178554	−	0.782298i	−0.982298	−	0.187323i	$-0.940019\pi$
$683$	−4.66639	−	20.4448i	−0.178554	−	0.782298i	0.803744	−	0.594975i	$-0.202838\pi$
$684$	64.9706			2.48421
$685$	2.67025	+	11.6991i	0.102025	+	0.447001i
$686$	−25.5447	+	32.0321i	−0.975302	+	1.22299i
$687$	1.88815	−	8.27254i	0.0720375	−	0.315617i
$688$	−2.39374	+	10.4876i	−0.0912604	+	0.399838i
$689$	−22.6412	−	28.3912i	−0.862562	−	1.08162i
$690$	−19.2030	−	9.24767i	−0.731045	−	0.352053i
$691$	−43.2465	+	20.8264i	−1.64517	+	0.792274i	−0.645583	+	0.763690i	$0.723386\pi$
$691$	−43.2465	+	20.8264i	−1.64517	+	0.792274i	−0.999591	+	0.0285844i	$0.990900\pi$
$692$	29.4629	−	36.9453i	1.12001	−	1.40445i
$693$	2.06606	+	2.59076i	0.0784833	+	0.0984149i
$694$	5.40581	−	2.60330i	0.205202	−	0.0988200i
$695$	−14.0000			−0.531050
$696$		0			0
$697$	−3.71573			−0.140743
$698$	−11.1848	+	5.38633i	−0.423352	+	0.203875i
$699$	27.5665	+	34.5673i	1.04266	+	1.30745i
$700$	27.0057	−	33.8640i	1.02072	−	1.27994i
$701$	36.1403	−	17.4042i	1.36500	−	0.657349i	0.399254	−	0.916840i	$-0.369269\pi$
$701$	36.1403	−	17.4042i	1.36500	−	0.657349i	0.965746	+	0.259491i	$0.0835547\pi$
$702$	3.44929	+	1.66109i	0.130185	+	0.0626939i
$703$	−14.9638	−	18.7640i	−0.564369	−	0.707696i
$704$	−0.905898	+	3.96900i	−0.0341423	+	0.149587i
$705$	−1.74199	+	7.63215i	−0.0656071	+	0.287443i
$706$	−40.5971	+	50.9072i	−1.52789	+	1.91592i
$707$	−1.47474	−	6.46125i	−0.0554633	−	0.243000i
$708$	−33.7990			−1.27024
$709$	−6.48474	−	28.4115i	−0.243539	−	1.06702i	−0.937768	−	0.347261i	$-0.887112\pi$
$709$	−6.48474	−	28.4115i	−0.243539	−	1.06702i	0.694229	−	0.719754i	$-0.255745\pi$
$710$	19.2030	+	9.24767i	0.720675	+	0.347059i
$711$	6.15220	+	2.96274i	0.230726	+	0.111112i
$712$	−12.2637	−	53.7309i	−0.459603	−	2.01365i
$713$	36.8284			1.37924
$714$	−3.03894	−	13.3144i	−0.113729	−	0.498281i
$715$	−0.988722	+	1.23982i	−0.0369761	+	0.0463666i
$716$	5.52484	−	24.2059i	0.206473	−	0.904618i
$717$	10.5599	−	46.2660i	0.394367	−	1.72784i
$718$	−5.91398	−	7.41589i	−0.220708	−	0.276759i
$719$	18.1474	+	8.73935i	0.676785	+	0.325923i	0.740510	−	0.672045i	$-0.234584\pi$
$719$	18.1474	+	8.73935i	0.676785	+	0.325923i	−0.0637252	+	0.997967i	$0.520298\pi$
$720$	7.64497	−	3.68163i	0.284911	−	0.137206i
$721$	8.51491	−	10.6774i	0.317112	−	0.397646i
$722$	−25.5890	−	32.0876i	−0.952325	−	1.19418i
$723$	39.8347	−	19.1834i	1.48147	−	0.713438i
$724$	31.8284			1.18289
$725$		0			0
$726$	63.1127			2.34233
$727$	−1.18361	+	0.569997i	−0.0438977	+	0.0211400i	−0.455704	−	0.890131i	$-0.650612\pi$
$727$	−1.18361	+	0.569997i	−0.0438977	+	0.0211400i	0.411806	+	0.911271i	$0.364898\pi$
$728$	−29.8022	−	37.3708i	−1.10454	−	1.38505i
$729$	−14.8568	+	18.6298i	−0.550251	+	0.689993i
$730$	−8.70053	+	4.18995i	−0.322021	+	0.155077i
$731$	−2.67638	−	1.28888i	−0.0989897	−	0.0476709i
$732$	−27.8247	−	34.8911i	−1.02843	−	1.28961i
$733$	9.18006	−	40.2205i	0.339073	−	1.48558i	−0.461929	−	0.886917i	$-0.652843\pi$
$733$	9.18006	−	40.2205i	0.339073	−	1.48558i	0.801003	−	0.598661i	$-0.204300\pi$
$734$	9.66984	−	42.3663i	0.356920	−	1.56377i
$735$	−1.50524	+	1.88751i	−0.0555215	+	0.0696218i
$736$	−1.29040	−	5.65360i	−0.0475647	−	0.208394i
$737$	−2.34315			−0.0863109
$738$	−6.81524	−	29.8595i	−0.250873	−	1.09914i
$739$	−3.66791	−	1.76637i	−0.134926	−	0.0649770i	0.365203	−	0.930928i	$-0.381000\pi$
$739$	−3.66791	−	1.76637i	−0.134926	−	0.0649770i	−0.500129	+	0.865951i	$0.666714\pi$
$740$	−13.7972	−	6.64437i	−0.507194	−	0.244252i
$741$	12.3401	+	54.0655i	0.453324	+	1.98614i
$742$	64.7696			2.37777
$743$	−5.26415	−	23.0637i	−0.193123	−	0.846126i	−0.974913	−	0.222585i	$-0.928551\pi$
$743$	−5.26415	−	23.0637i	−0.193123	−	0.846126i	0.781791	−	0.623541i	$-0.214307\pi$
$744$	−66.9166	+	83.9108i	−2.45328	+	3.07632i
$745$	−1.74199	+	7.63215i	−0.0638215	+	0.279620i
$746$	−14.1361	+	61.9342i	−0.517558	+	2.26757i
$747$	13.5028	+	16.9320i	0.494043	+	0.619510i
$748$	1.18361	+	0.569997i	0.0432771	+	0.0208411i
$749$	−37.7876	+	18.1976i	−1.38073	+	0.664925i
$750$	−32.7057	+	41.0116i	−1.19424	+	1.49753i
$751$	15.7828	+	19.7911i	0.575924	+	0.722186i	0.981412	−	0.191915i	$-0.0614697\pi$
$751$	15.7828	+	19.7911i	0.575924	+	0.722186i	−0.405488	+	0.914101i	$0.632898\pi$
$752$	8.76455	−	4.22079i	0.319610	−	0.153916i
$753$	48.4558			1.76583
$754$		0			0
$755$	14.1421			0.514685
$756$	−4.04110	+	1.94609i	−0.146973	+	0.0707786i
$757$	15.9082	+	19.9482i	0.578192	+	0.725030i	0.981803	−	0.189901i	$-0.0608166\pi$
$757$	15.9082	+	19.9482i	0.578192	+	0.725030i	−0.403611	+	0.914931i	$0.632245\pi$
$758$	10.4924	−	13.1570i	0.381099	−	0.477884i
$759$	3.29471	−	1.58665i	0.119590	−	0.0575917i
$760$	−23.8624	−	11.4915i	−0.865581	−	0.416842i
$761$	28.4299	+	35.6499i	1.03058	+	1.29231i	0.955456	+	0.295135i	$0.0953647\pi$
$761$	28.4299	+	35.6499i	1.03058	+	1.29231i	0.0751267	+	0.997174i	$0.476064\pi$
$762$	−5.63283	+	24.6790i	−0.204056	+	0.894027i
$763$	7.96602	−	34.9014i	0.288389	−	1.26352i
$764$	60.4234	−	75.7686i	2.18604	−	2.74121i
$765$	0.521399	+	2.28440i	0.0188512	+	0.0825926i
$766$	8.48528			0.306586
$767$	−3.11529	−	13.6490i	−0.112487	−	0.492836i
$768$	65.1899	+	31.3938i	2.35234	+	1.13283i
$769$	44.2490	+	21.3092i	1.59566	+	0.768429i	0.999409	−	0.0343686i	$-0.0109420\pi$
$769$	44.2490	+	21.3092i	1.59566	+	0.768429i	0.596251	+	0.802798i	$0.296656\pi$
$770$	−0.629384	−	2.75751i	−0.0226814	−	0.0993739i
$771$	−43.8701			−1.57994
$772$	4.40569	+	19.3026i	0.158564	+	0.694715i
$773$	−12.1672	+	15.2572i	−0.437625	+	0.548764i	−0.950915	−	0.309451i	$-0.899855\pi$
$773$	−12.1672	+	15.2572i	−0.437625	+	0.548764i	0.513291	+	0.858215i	$0.328426\pi$
$774$	5.44849	−	23.8714i	0.195842	−	0.858039i
$775$	8.96409	−	39.2743i	0.322000	−	1.41077i
$776$	−12.3445	−	15.4795i	−0.443141	−	0.555681i
$777$	−24.6088	−	11.8510i	−0.882836	−	0.425151i
$778$	6.58942	−	3.17330i	0.236242	−	0.113768i
$779$	−16.7792	+	21.0404i	−0.601176	+	0.753851i
$780$	22.0620	+	27.6649i	0.789948	+	0.990563i
$781$	−3.29471	+	1.58665i	−0.117894	+	0.0567748i
$782$	−7.31371			−0.261538
$783$		0			0
$784$	3.00000			0.107143
$785$	7.64497	−	3.68163i	0.272861	−	0.131403i
$786$	−77.4533	−	97.1233i	−2.76267	−	3.46427i
$787$	−33.7204	+	42.2840i	−1.20200	+	1.50726i	−0.392912	+	0.919576i	$0.628532\pi$
$787$	−33.7204	+	42.2840i	−1.20200	+	1.50726i	−0.809090	+	0.587685i	$0.800039\pi$
$788$	−6.89859	+	3.32218i	−0.245752	+	0.118348i
$789$	−5.99762	−	2.88830i	−0.213521	−	0.102826i
$790$	−3.63396	−	4.55685i	−0.129291	−	0.162125i
$791$	−8.37944	+	36.7127i	−0.297939	+	1.30535i
$792$	−1.15078	+	5.04191i	−0.0408913	+	0.179156i
$793$	11.5254	−	14.4524i	0.409278	−	0.513219i
$794$	10.3914	+	45.5277i	0.368777	+	1.61572i
$795$	−22.8995			−0.812161
$796$	0.413414	+	1.81128i	0.0146531	+	0.0641993i
$797$	−46.6162	−	22.4492i	−1.65123	−	0.795191i	−0.999319	−	0.0368972i	$-0.988253\pi$
$797$	−46.6162	−	22.4492i	−1.65123	−	0.795191i	−0.651913	−	0.758294i	$-0.726033\pi$
$798$	−89.1164	−	42.9162i	−3.15468	−	1.51922i
$799$	0.597756	+	2.61894i	0.0211471	+	0.0926515i
$800$	−6.34315			−0.224264
$801$	7.85804	+	34.4283i	0.277650	+	1.21646i
$802$	28.0830	−	35.2150i	0.991645	−	1.24348i
$803$	0.368685	−	1.61531i	0.0130106	−	0.0570032i
$804$	−11.6343	+	50.9734i	−0.410312	+	1.79769i
$805$	6.44885	+	8.08660i	0.227292	+	0.285015i
$806$	−83.8651	−	40.3873i	−2.95402	−	1.42258i
$807$	−68.4206	+	32.9496i	−2.40852	+	1.15988i
$808$	6.44885	−	8.08660i	0.226870	−	0.284485i
$809$	22.6229	+	28.3682i	0.795378	+	0.997372i	0.999829	+	0.0184955i	$0.00588764\pi$
$809$	22.6229	+	28.3682i	0.795378	+	0.997372i	−0.204451	+	0.978877i	$0.565541\pi$
$810$	20.6317	−	9.93572i	0.724925	−	0.349106i
$811$	10.8284			0.380238			0.190119	−	0.981761i	$-0.439113\pi$
$811$	10.8284			0.380238			0.190119	+	0.981761i	$0.439113\pi$
$812$		0			0
$813$	39.9706			1.40183
$814$	3.60388	−	1.73553i	0.126316	−	0.0608305i
$815$	−2.44965	−	3.07176i	−0.0858075	−	0.107599i
$816$	3.74094	−	4.69099i	0.130959	−	0.164217i
$817$	−19.3841	+	9.33489i	−0.678164	+	0.326586i
$818$	−41.2635	−	19.8714i	−1.44274	−	0.694789i
$819$	19.0959	+	23.9455i	0.667264	+	0.836723i
$820$	−3.82103	+	16.7410i	−0.133436	+	0.584623i
$821$	0.330506	−	1.44804i	0.0115347	−	0.0505370i	−0.968833	−	0.247715i	$-0.920320\pi$
$821$	0.330506	−	1.44804i	0.0115347	−	0.0505370i	0.980368	+	0.197178i	$0.0631776\pi$
$822$	−43.6076	+	54.6822i	−1.52099	+	1.90726i
$823$	12.0794	+	52.9233i	0.421061	+	1.84479i	0.526241	+	0.850335i	$0.323601\pi$
$823$	12.0794	+	52.9233i	0.421061	+	1.84479i	−0.105180	+	0.994453i	$0.533542\pi$
$824$	21.3137			0.742498
$825$	−0.890084	−	3.89971i	−0.0309887	−	0.135771i
$826$	22.4977	+	10.8343i	0.782795	+	0.376974i
$827$	−29.6414	−	14.2746i	−1.03073	−	0.496375i	−0.159476	−	0.987202i	$-0.550980\pi$
$827$	−29.6414	−	14.2746i	−1.03073	−	0.496375i	−0.871257	+	0.490827i	$0.836695\pi$
$828$	−8.81138	−	38.6052i	−0.306217	−	1.34162i
$829$	−29.7990			−1.03496			−0.517481	−	0.855695i	$-0.673130\pi$
$829$	−29.7990			−1.03496			−0.517481	+	0.855695i	$0.673130\pi$
$830$	−4.11336	−	18.0218i	−0.142777	−	0.625546i
$831$	−26.0612	+	32.6798i	−0.904055	+	1.13365i
$832$	−8.37289	+	36.6840i	−0.290278	+	1.27179i
$833$	−0.184342	+	0.807657i	−0.00638708	+	0.0279836i
$834$	−50.8755	−	63.7959i	−1.76167	−	2.20907i
$835$	−2.85749	−	1.37609i	−0.0988875	−	0.0476217i
$836$	8.57247	−	4.12828i	0.296485	−	0.142780i
$837$	−2.60093	+	3.26147i	−0.0899014	+	0.112733i
$838$	14.3219	+	17.9591i	0.494742	+	0.620387i
$839$	7.14372	−	3.44023i	0.246629	−	0.118770i	−0.306486	−	0.951875i	$-0.599153\pi$
$839$	7.14372	−	3.44023i	0.246629	−	0.118770i	0.553115	+	0.833105i	$0.313439\pi$
$840$	−30.1421			−1.04000
$841$		0			0
$842$	−89.5980			−3.08775
$843$	−69.5402	+	33.4888i	−2.39509	+	1.15341i
$844$	−46.2712	−	58.0222i	−1.59272	−	1.99721i
$845$	−1.03303	+	1.29538i	−0.0355374	+	0.0445625i
$846$	−19.9494	+	9.60711i	−0.685874	+	0.330299i
$847$	−27.5943	−	13.2887i	−0.948153	−	0.456606i
$848$	17.7419	+	22.2477i	0.609260	+	0.763988i
$849$	−6.26221	+	27.4366i	−0.214919	+	0.941620i
$850$	−1.78017	+	7.79942i	−0.0610592	+	0.267518i
$851$	−9.12005	+	11.4362i	−0.312631	+	0.392027i
$852$	18.1573	+	79.5521i	0.622057	+	2.72541i
$853$	−22.9706			−0.786497			−0.393249	−	0.919432i	$-0.628649\pi$
$853$	−22.9706			−0.786497			−0.393249	+	0.919432i	$0.628649\pi$
$854$	7.33664	+	32.1439i	0.251055	+	1.09994i
$855$	15.2899	+	7.36325i	0.522905	+	0.251818i
$856$	−58.9737	−	28.4002i	−2.01568	−	0.970700i
$857$	1.37330	+	6.01684i	0.0469112	+	0.205531i	0.992952	−	0.118516i	$-0.0378136\pi$
$857$	1.37330	+	6.01684i	0.0469112	+	0.205531i	−0.946041	+	0.324047i	$0.894956\pi$
$858$	−9.24264			−0.315539
$859$	−4.38988	−	19.2333i	−0.149781	−	0.656232i	−0.992945	−	0.118576i	$-0.962167\pi$
$859$	−4.38988	−	19.2333i	−0.149781	−	0.656232i	0.843164	−	0.537656i	$-0.180690\pi$
$860$	−8.55922	+	10.7329i	−0.291867	+	0.365990i
$861$	−6.81524	+	29.8595i	−0.232263	+	1.01761i
$862$	10.5599	−	46.2660i	0.359672	−	1.57583i
$863$	10.6696	+	13.3792i	0.363197	+	0.455435i	0.929533	−	0.368740i	$-0.120211\pi$
$863$	10.6696	+	13.3792i	0.363197	+	0.455435i	−0.566335	+	0.824175i	$0.691639\pi$
$864$	0.591805	+	0.284998i	0.0201336	+	0.00969584i
$865$	11.1208	−	5.35549i	0.378118	−	0.182092i
$866$	−46.1015	+	57.8095i	−1.56659	+	1.96445i
$867$	−24.5560	−	30.7923i	−0.833966	−	1.04576i
$868$	98.2541	−	47.3167i	3.33496	−	1.60603i
$869$	1.00000			0.0339227
$870$		0			0
$871$	−21.6569			−0.733815
$872$	50.3372	−	24.2411i	1.70463	−	0.820908i
$873$	7.90977	+	9.91854i	0.267705	+	0.335692i
$874$	−33.0266	+	41.4141i	−1.11714	+	1.40085i
$875$	22.9349	−	11.0449i	0.775342	−	0.373385i
$876$	−33.3093	−	16.0409i	−1.12542	−	0.541973i
$877$	−23.1577	−	29.0389i	−0.781981	−	0.980574i	−0.999989	−	0.00462667i	$-0.998527\pi$
$877$	−23.1577	−	29.0389i	−0.781981	−	0.980574i	0.218008	−	0.975947i	$-0.430044\pi$
$878$	−0.184342	+	0.807657i	−0.00622125	+	0.0272571i
$879$	−4.11336	+	18.0218i	−0.138740	+	0.607861i
$880$	0.774774	−	0.971536i	0.0261176	−	0.0327505i
$881$	−3.11529	−	13.6490i	−0.104957	−	0.459846i	−0.999906	−	0.0136788i	$-0.995646\pi$
$881$	−3.11529	−	13.6490i	−0.104957	−	0.459846i	0.894950	−	0.446167i	$-0.147211\pi$
$882$	−6.82843			−0.229925
$883$	−8.55068	−	37.4630i	−0.287753	−	1.26073i	−0.887600	−	0.460615i	$-0.847629\pi$
$883$	−8.55068	−	37.4630i	−0.287753	−	1.26073i	0.599847	−	0.800115i	$-0.295228\pi$
$884$	10.9397	+	5.26828i	0.367941	+	0.177191i
$885$	−7.95414	−	3.83051i	−0.267375	−	0.128761i
$886$	−13.0775	−	57.2961i	−0.439346	−	1.92490i
$887$	17.1005			0.574179			0.287089	−	0.957904i	$-0.407312\pi$
$887$	17.1005			0.574179			0.287089	+	0.957904i	$0.407312\pi$
$888$	−9.48549	−	41.5587i	−0.318312	−	1.39462i
$889$	7.65912	−	9.60423i	0.256879	−	0.322116i
$890$	6.70726	−	29.3864i	0.224828	−	0.985035i
$891$	−0.874270	+	3.83043i	−0.0292891	+	0.128324i
$892$	−7.57050	−	9.49310i	−0.253479	−	0.317853i
$893$	17.5291	+	8.44157i	0.586589	+	0.282487i
$894$	−41.1089	+	19.7970i	−1.37489	+	0.662111i
$895$	4.04351	−	5.07040i	0.135160	−	0.169485i
$896$	−36.2510	−	45.4574i	−1.21106	−	1.51862i
$897$	30.4518	−	14.6648i	1.01676	−	0.489644i
$898$	84.4264			2.81735
$899$		0			0
$900$	−43.3137			−1.44379
$901$	−7.07969	+	3.40940i	−0.235859	+	0.113584i
$902$	−2.79653	−	3.50673i	−0.0931142	−	0.116761i
$903$	−15.2663	+	19.1434i	−0.508031	+	0.637051i
$904$	−52.9495	+	25.4992i	−1.76108	+	0.848089i
$905$	7.49039	+	3.60718i	0.248989	+	0.119907i
$906$	51.3920	+	64.4436i	1.70739	+	2.14099i
$907$	−4.95872	+	21.7256i	−0.164651	+	0.721385i	0.823425	+	0.567424i	$0.192060\pi$
$907$	−4.95872	+	21.7256i	−0.164651	+	0.721385i	−0.988077	+	0.153961i	$0.950797\pi$
$908$	6.93633	−	30.3900i	0.230190	−	1.00853i
$909$	−4.13213	+	5.18152i	−0.137054	+	0.171860i
$910$	−5.81717	−	25.4867i	−0.192837	−	0.844876i
$911$	−15.4437			−0.511671			−0.255835	−	0.966720i	$-0.582351\pi$
$911$	−15.4437			−0.511671			−0.255835	+	0.966720i	$0.582351\pi$
$912$	−9.66984	−	42.3663i	−0.320200	−	1.40289i
$913$	2.85749	+	1.37609i	0.0945691	+	0.0455421i
$914$	2.23916	+	1.07832i	0.0740649	+	0.0356678i
$915$	−2.59389	−	11.3646i	−0.0857515	−	0.375702i
$916$	−13.4558			−0.444594
$917$	13.4145	+	58.7728i	0.442986	+	1.94085i
$918$	0.516516	−	0.647690i	0.0170476	−	0.0213770i
$919$	−1.81180	+	7.93800i	−0.0597656	+	0.261850i	−0.995980	−	0.0895801i	$-0.971447\pi$
$919$	−1.81180	+	7.93800i	−0.0597656	+	0.261850i	0.936214	+	0.351430i	$0.114305\pi$
$920$	−3.59196	+	15.7374i	−0.118424	+	0.518847i
$921$	4.36443	+	5.47282i	0.143813	+	0.180336i
$922$	30.4518	+	14.6648i	1.00288	+	0.482961i
$923$	−30.4518	+	14.6648i	−1.00233	+	0.482699i
$924$	6.75141	−	8.46601i	0.222105	−	0.278511i
$925$	9.97584	+	12.5093i	0.328003	+	0.411303i
$926$	−56.5534	+	27.2347i	−1.85846	+	0.894987i
$927$	−13.6569			−0.448550
$928$		0			0
$929$	18.6863			0.613077			0.306539	−	0.951858i	$-0.400829\pi$
$929$	18.6863			0.613077			0.306539	+	0.951858i	$0.400829\pi$
$930$	−52.8855	+	25.4683i	−1.73418	+	0.835139i
$931$	3.74094	+	4.69099i	0.122604	+	0.153741i
$932$	43.7146	−	54.8163i	1.43192	−	1.79557i
$933$	−5.84304	+	2.81386i	−0.191292	+	0.0921216i
$934$	−83.4279	−	40.1768i	−2.72984	−	1.31462i
$935$	0.213948	+	0.268282i	0.00699684	+	0.00877376i
$936$	−10.6363	+	46.6006i	−0.347658	+	1.52319i
$937$	3.69995	−	16.2105i	0.120872	−	0.529575i	−0.877845	−	0.478944i	$-0.841020\pi$
$937$	3.69995	−	16.2105i	0.120872	−	0.529575i	0.998717	−	0.0506309i	$-0.0161232\pi$
$938$	24.0838	−	30.2001i	0.786364	−	0.986069i
$939$	−5.27996	−	23.1330i	−0.172305	−	0.754917i
$940$	12.4142			0.404907
$941$	12.5942	+	55.1790i	0.410560	+	1.79878i	0.581551	+	0.813510i	$0.302446\pi$
$941$	12.5942	+	55.1790i	0.410560	+	1.79878i	−0.170991	+	0.985273i	$0.554697\pi$
$942$	44.5582	+	21.4581i	1.45178	+	0.699142i
$943$	14.7777	+	7.11657i	0.481228	+	0.231747i
$944$	2.44118	+	10.6955i	0.0794536	+	0.348109i
$945$	−1.17157			−0.0381113
$946$	−0.797913	−	3.49588i	−0.0259424	−	0.113661i
$947$	1.63057	−	2.04466i	0.0529863	−	0.0664427i	−0.754632	−	0.656148i	$-0.772185\pi$
$947$	1.63057	−	2.04466i	0.0529863	−	0.0664427i	0.807618	+	0.589705i	$0.200756\pi$
$948$	4.96527	−	21.7543i	0.161264	−	0.706545i
$949$	3.40762	−	14.9298i	0.110616	−	0.484641i
$950$	36.1257	+	45.3002i	1.17207	+	1.46973i
$951$	68.4206	+	32.9496i	2.21869	+	1.06846i
$952$	−9.31885	+	4.48772i	−0.302026	+	0.145448i
$953$	−22.2133	+	27.8546i	−0.719560	+	0.902300i	−0.998313	−	0.0580628i	$-0.981508\pi$
$953$	−22.2133	+	27.8546i	−0.719560	+	0.902300i	0.278753	+	0.960363i	$0.410079\pi$
$954$	−40.3832	−	50.6389i	−1.30745	−	1.63949i
$955$	22.8069	−	10.9832i	0.738013	−	0.355408i
$956$	−75.2548			−2.43392
$957$		0			0
$958$	−16.6569			−0.538159
$959$	30.5799	−	14.7265i	0.987476	−	0.475544i
$960$	14.7941	+	18.5512i	0.477478	+	0.598739i
$961$	43.9101	−	55.0616i	1.41646	−	1.77618i
$962$	33.3093	−	16.0409i	1.07394	−	0.517180i
$963$	37.7876	+	18.1976i	1.21769	+	0.586409i
$964$	−43.7146	−	54.8163i	−1.40795	−	1.76551i
$965$	−1.15078	+	5.04191i	−0.0370450	+	0.162305i
$966$	−13.4145	+	58.7728i	−0.431605	+	1.89098i
$967$	−21.9734	+	27.5538i	−0.706618	+	0.886071i	−0.997498	−	0.0706887i	$-0.977480\pi$
$967$	−21.9734	+	27.5538i	−0.706618	+	0.886071i	0.290881	+	0.956759i	$0.406052\pi$
$968$	−10.6363	−	46.6006i	−0.341863	−	1.49780i
$969$	12.0000			0.385496
$970$	−2.40955	−	10.5569i	−0.0773660	−	0.338963i
$971$	14.1063	+	6.79325i	0.452694	+	0.218006i	0.646315	−	0.763070i	$-0.276309\pi$
$971$	14.1063	+	6.79325i	0.452694	+	0.218006i	−0.193621	+	0.981076i	$0.562023\pi$
$972$	74.7008	+	35.9740i	2.39603	+	1.15387i
$973$	8.81138	+	38.6052i	0.282480	+	1.23763i
$974$	27.7990			0.890737
$975$	−8.22672	−	36.0436i	−0.263466	−	1.15432i
$976$	−9.03143	+	11.3250i	−0.289089	+	0.362506i
$977$	−8.04893	+	35.2647i	−0.257508	+	1.12822i	0.666398	+	0.745597i	$0.267835\pi$
$977$	−8.04893	+	35.2647i	−0.257508	+	1.12822i	−0.923906	+	0.382620i	$0.875022\pi$
$978$	5.09562	−	22.3254i	0.162940	−	0.713886i
$979$	3.22442	+	4.04330i	0.103053	+	0.129224i
$980$	3.44929	+	1.66109i	0.110184	+	0.0530616i
$981$	−32.2538	+	15.5326i	−1.02978	+	0.495918i
$982$	31.9752	−	40.0957i	1.02037	−	1.27950i
$983$	−13.6358	−	17.0987i	−0.434913	−	0.545364i	0.515281	−	0.857021i	$-0.327687\pi$
$983$	−13.6358	−	17.0987i	−0.434913	−	0.545364i	−0.950195	+	0.311657i	$0.899116\pi$
$984$	−43.0654	+	20.7392i	−1.37287	+	0.661142i
$985$	−2.00000			−0.0637253
$986$		0			0
$987$	22.1421			0.704792
$988$	79.2322	−	38.1562i	2.52071	−	1.21391i
$989$	8.17563	+	10.2519i	0.259970	+	0.325992i
$990$	−1.76350	+	2.21135i	−0.0560476	+	0.0702814i
$991$	11.5580	−	5.56605i	0.367152	−	0.176811i	−0.241206	−	0.970474i	$-0.577543\pi$
$991$	11.5580	−	5.56605i	0.367152	−	0.176811i	0.608358	+	0.793663i	$0.291829\pi$
$992$	−14.3890	−	6.92937i	−0.456851	−	0.220008i
$993$	−3.63396	−	4.55685i	−0.115320	−	0.144607i
$994$	13.4145	−	58.7728i	0.425482	−	1.86416i
$995$	−0.107985	+	0.473114i	−0.00342336	+	0.0149987i
$996$	44.1241	−	55.3299i	1.39813	−	1.75319i
$997$	−6.29384	−	27.5751i	−0.199328	−	0.873313i	−0.971338	−	0.237703i	$-0.923606\pi$
$997$	−6.29384	−	27.5751i	−0.199328	−	0.873313i	0.772010	−	0.635610i	$-0.219252\pi$
$998$	−45.7990			−1.44974
$999$	−0.368685	−	1.61531i	−0.0116647	−	0.0511063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.j.571.2		12
29.2	odd	28		841.2.e.k.196.4		24
29.3	odd	28		841.2.e.k.267.4		24
29.4	even	14		841.2.a.d.1.2		2
29.5	even	14		841.2.d.f.645.1		12
29.6	even	14		841.2.d.f.778.2		12
29.7	even	7	inner	841.2.d.j.574.1		12
29.8	odd	28		841.2.e.k.236.4		24
29.9	even	14		841.2.d.f.605.1		12
29.10	odd	28		841.2.b.a.840.1		4
29.11	odd	28		841.2.e.k.651.4		24
29.12	odd	4		841.2.e.k.270.4		24
29.13	even	14		841.2.d.f.190.1		12
29.14	odd	28		841.2.e.k.63.1		24
29.15	odd	28		841.2.e.k.63.4		24
29.16	even	7	inner	841.2.d.j.190.2		12
29.17	odd	4		841.2.e.k.270.1		24
29.18	odd	28		841.2.e.k.651.1		24
29.19	odd	28		841.2.b.a.840.4		4
29.20	even	7	inner	841.2.d.j.605.2		12
29.21	odd	28		841.2.e.k.236.1		24
29.22	even	14		841.2.d.f.574.2		12
29.23	even	7	inner	841.2.d.j.778.1		12
29.24	even	7	inner	841.2.d.j.645.2		12
29.25	even	7		29.2.a.a.1.1	✓	2
29.26	odd	28		841.2.e.k.267.1		24
29.27	odd	28		841.2.e.k.196.1		24
29.28	even	2		841.2.d.f.571.1		12
87.62	odd	14		7569.2.a.c.1.1		2
87.83	odd	14		261.2.a.d.1.2		2
116.83	odd	14		464.2.a.h.1.1		2
145.54	even	14		725.2.a.b.1.2		2
145.83	odd	28		725.2.b.b.349.4		4
145.112	odd	28		725.2.b.b.349.1		4
203.83	odd	14		1421.2.a.j.1.1		2
232.83	odd	14		1856.2.a.w.1.2		2
232.141	even	14		1856.2.a.r.1.1		2
319.54	odd	14		3509.2.a.j.1.2		2
348.83	even	14		4176.2.a.bq.1.2		2
377.25	even	14		4901.2.a.g.1.2		2
435.344	odd	14		6525.2.a.o.1.1		2
493.373	even	14		8381.2.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.a.a.1.1	✓	2	29.25	even	7
261.2.a.d.1.2		2	87.83	odd	14
464.2.a.h.1.1		2	116.83	odd	14
725.2.a.b.1.2		2	145.54	even	14
725.2.b.b.349.1		4	145.112	odd	28
725.2.b.b.349.4		4	145.83	odd	28
841.2.a.d.1.2		2	29.4	even	14
841.2.b.a.840.1		4	29.10	odd	28
841.2.b.a.840.4		4	29.19	odd	28
841.2.d.f.190.1		12	29.13	even	14
841.2.d.f.571.1		12	29.28	even	2
841.2.d.f.574.2		12	29.22	even	14
841.2.d.f.605.1		12	29.9	even	14
841.2.d.f.645.1		12	29.5	even	14
841.2.d.f.778.2		12	29.6	even	14
841.2.d.j.190.2		12	29.16	even	7	inner
841.2.d.j.571.2		12	1.1	even	1	trivial
841.2.d.j.574.1		12	29.7	even	7	inner
841.2.d.j.605.2		12	29.20	even	7	inner
841.2.d.j.645.2		12	29.24	even	7	inner
841.2.d.j.778.1		12	29.23	even	7	inner
841.2.e.k.63.1		24	29.14	odd	28
841.2.e.k.63.4		24	29.15	odd	28
841.2.e.k.196.1		24	29.27	odd	28
841.2.e.k.196.4		24	29.2	odd	28
841.2.e.k.236.1		24	29.21	odd	28
841.2.e.k.236.4		24	29.8	odd	28
841.2.e.k.267.1		24	29.26	odd	28
841.2.e.k.267.4		24	29.3	odd	28
841.2.e.k.270.1		24	29.17	odd	4
841.2.e.k.270.4		24	29.12	odd	4
841.2.e.k.651.1		24	29.18	odd	28
841.2.e.k.651.4		24	29.11	odd	28
1421.2.a.j.1.1		2	203.83	odd	14
1856.2.a.r.1.1		2	232.141	even	14
1856.2.a.w.1.2		2	232.83	odd	14
3509.2.a.j.1.2		2	319.54	odd	14
4176.2.a.bq.1.2		2	348.83	even	14
4901.2.a.g.1.2		2	377.25	even	14
6525.2.a.o.1.1		2	435.344	odd	14
7569.2.a.c.1.1		2	87.62	odd	14
8381.2.a.e.1.1		2	493.373	even	14

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.17513 - 1.04749i) q^{2} +(1.50524 + 1.88751i) q^{3} +(2.38699 - 2.99318i) q^{4} +(0.900969 - 0.433884i) q^{5} +(5.25123 + 2.52886i) q^{6} +(-1.76350 - 2.21135i) q^{7} +(0.982255 - 4.30354i) q^{8} +(-0.629384 + 2.75751i) q^{9} +(1.50524 - 1.88751i) q^{10} +(0.0921712 + 0.403828i) q^{11} +9.24264 q^{12} +(0.851905 + 3.73244i) q^{13} +(-6.15220 - 2.96274i) q^{14} +(2.17513 + 1.04749i) q^{15} +(-0.667563 - 2.92478i) q^{16} +0.828427 q^{17} +(1.51947 + 6.65722i) q^{18} +(3.74094 - 4.69099i) q^{19} +(0.851905 - 3.73244i) q^{20} +(1.51947 - 6.65722i) q^{21} +(0.623490 + 0.781831i) q^{22} +(-3.29471 - 1.58665i) q^{23} +(9.60149 - 4.62384i) q^{24} +(-2.49396 + 3.12733i) q^{25} +(5.76269 + 7.22619i) q^{26} +(0.373194 - 0.179721i) q^{27} -10.8284 q^{28} +5.82843 q^{30} +(-9.07372 + 4.36967i) q^{31} +(0.988722 + 1.23982i) q^{32} +(-0.623490 + 0.781831i) q^{33} +(1.80194 - 0.867767i) q^{34} +(-2.54832 - 1.22721i) q^{35} +(6.75141 + 8.46601i) q^{36} +(0.890084 - 3.89971i) q^{37} +(3.22328 - 14.1221i) q^{38} +(-5.76269 + 7.22619i) q^{39} +(-0.982255 - 4.30354i) q^{40} -4.48528 q^{41} +(-3.66832 - 16.0720i) q^{42} +(-3.23068 - 1.55581i) q^{43} +(1.42874 + 0.688047i) q^{44} +(0.629384 + 2.75751i) q^{45} -8.82843 q^{46} +(0.721555 + 3.16134i) q^{47} +(4.51571 - 5.66252i) q^{48} +(-0.222521 + 0.974928i) q^{49} +(-2.14885 + 9.41474i) q^{50} +(1.24698 + 1.56366i) q^{51} +(13.2054 + 6.35937i) q^{52} +(-8.54594 + 4.11551i) q^{53} +(0.623490 - 0.781831i) q^{54} +(0.258258 + 0.323845i) q^{55} +(-11.2488 + 5.41716i) q^{56} +14.4853 q^{57} -3.65685 q^{59} +(8.32733 - 4.01023i) q^{60} +(-3.01048 - 3.77502i) q^{61} +(-15.1593 + 19.0092i) q^{62} +(7.20775 - 3.47107i) q^{63} +(8.85511 + 4.26439i) q^{64} +(2.38699 + 2.99318i) q^{65} +(-0.537213 + 2.35368i) q^{66} +(-1.25877 + 5.51503i) q^{67} +(1.97744 - 2.47964i) q^{68} +(-1.96451 - 8.60708i) q^{69} -6.82843 q^{70} +(1.96451 + 8.60708i) q^{71} +(11.2488 + 5.41716i) q^{72} +(-3.60388 - 1.73553i) q^{73} +(-2.14885 - 9.41474i) q^{74} -9.65685 q^{75} +(-5.11143 - 22.3946i) q^{76} +(0.730464 - 0.915973i) q^{77} +(-4.96527 + 21.7543i) q^{78} +(0.537213 - 2.35368i) q^{79} +(-1.87047 - 2.34549i) q^{80} +(8.54594 + 4.11551i) q^{81} +(-9.75608 + 4.69828i) q^{82} +(4.77397 - 5.98637i) q^{83} +(-16.2994 - 20.4387i) q^{84} +(0.746387 - 0.359441i) q^{85} -8.65685 q^{86} +1.82843 q^{88} +(11.2488 - 5.41716i) q^{89} +(4.25745 + 5.33868i) q^{90} +(6.75141 - 8.46601i) q^{91} +(-12.6136 + 6.07437i) q^{92} +(-21.9059 - 10.5493i) q^{93} +(4.88094 + 6.12051i) q^{94} +(1.33513 - 5.84957i) q^{95} +(-0.851905 + 3.73244i) q^{96} +(2.79653 - 3.50673i) q^{97} +(0.537213 + 2.35368i) q^{98} -1.17157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8} - 2 q^{10} - 2 q^{11} + 60 q^{12} + 2 q^{13} - 8 q^{14} + 2 q^{15} - 6 q^{16} - 24 q^{17} + 8 q^{18} - 12 q^{19} + 2 q^{20} + 8 q^{21} - 2 q^{22}+ \cdots - 48 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 6 * q^6 + 6 * q^8 - 2 * q^10 - 2 * q^11 + 60 * q^12 + 2 * q^13 - 8 * q^14 + 2 * q^15 - 6 * q^16 - 24 * q^17 + 8 * q^18 - 12 * q^19 + 2 * q^20 + 8 * q^21 - 2 * q^22 + 4 * q^23 + 10 * q^24 + 8 * q^25 - 10 * q^26 - 2 * q^27 - 96 * q^28 + 36 * q^30 - 6 * q^31 - 6 * q^32 + 2 * q^33 + 4 * q^34 - 16 * q^36 + 8 * q^37 + 12 * q^38 + 10 * q^39 - 6 * q^40 + 48 * q^41 - 16 * q^42 - 10 * q^43 + 6 * q^44 - 72 * q^46 - 2 * q^47 - 6 * q^48 - 2 * q^49 - 8 * q^50 - 4 * q^51 + 18 * q^52 - 2 * q^53 - 2 * q^54 + 2 * q^55 - 8 * q^56 + 72 * q^57 + 24 * q^59 + 10 * q^60 + 4 * q^61 + 26 * q^62 + 16 * q^63 + 14 * q^64 - 2 * q^65 - 2 * q^66 - 12 * q^68 - 12 * q^69 - 48 * q^70 + 12 * q^71 + 8 * q^72 - 8 * q^73 - 8 * q^74 - 48 * q^75 - 12 * q^76 - 8 * q^77 - 22 * q^78 + 2 * q^79 + 6 * q^80 + 2 * q^81 - 16 * q^82 - 4 * q^83 + 24 * q^84 - 4 * q^85 - 36 * q^86 - 12 * q^88 + 8 * q^89 - 8 * q^90 - 16 * q^91 - 28 * q^92 - 26 * q^93 - 10 * q^94 + 12 * q^95 - 2 * q^96 + 8 * q^97 + 2 * q^98 - 48 * q^99

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