LMFDB - Embedded newform 847.2.e.f.606.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(485,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("847.485");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.e (of order $3$, 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 11 x^{12} - 2 x^{11} + 88 x^{10} - 10 x^{9} + 310 x^{8} + 46 x^{7} + 791 x^{6} + 186 x^{5} + \cdots + 81 $ x^14 + 11x^12 - 2x^11 + 88x^10 - 10x^9 + 310x^8 + 46x^7 + 791x^6 + 186x^5 + 901x^4 + 567x^3 + 738x^2 + 243x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			606.2
Root			$0.944230 + 1.63545i$ of defining polynomial
Character	$\chi$	$=$	847.606
Dual form			847.2.e.f.485.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.944230 - 1.63545i) q^{2} +(0.0669258 - 0.115919i) q^{3} +(-0.783142 + 1.35644i) q^{4} +(1.17111 + 2.02842i) q^{5} -0.252774 q^{6} +(1.25670 - 2.32824i) q^{7} -0.819057 q^{8} +(1.49104 + 2.58256i) q^{9} +O(q^{10})$	\(q+(-0.944230 - 1.63545i) q^{2} +(0.0669258 - 0.115919i) q^{3} +(-0.783142 + 1.35644i) q^{4} +(1.17111 + 2.02842i) q^{5} -0.252774 q^{6} +(1.25670 - 2.32824i) q^{7} -0.819057 q^{8} +(1.49104 + 2.58256i) q^{9} +(2.21159 - 3.83059i) q^{10} +(0.104825 + 0.181562i) q^{12} +2.32218 q^{13} +(-4.99435 + 0.143121i) q^{14} +0.313510 q^{15} +(2.33966 + 4.05241i) q^{16} +(-2.93527 + 5.08404i) q^{17} +(2.81577 - 4.87706i) q^{18} +(2.32786 + 4.03198i) q^{19} -3.66857 q^{20} +(-0.185782 - 0.301495i) q^{21} +(-1.41779 - 2.45568i) q^{23} +(-0.0548161 + 0.0949442i) q^{24} +(-0.242988 + 0.420868i) q^{25} +(-2.19267 - 3.79782i) q^{26} +0.800712 q^{27} +(2.17395 + 3.52798i) q^{28} -2.08944 q^{29} +(-0.296025 - 0.512731i) q^{30} +(-3.51854 + 6.09429i) q^{31} +(3.59930 - 6.23417i) q^{32} +11.0863 q^{34} +(6.19438 - 0.177510i) q^{35} -4.67079 q^{36} +(4.63228 + 8.02334i) q^{37} +(4.39608 - 7.61423i) q^{38} +(0.155414 - 0.269184i) q^{39} +(-0.959204 - 1.66139i) q^{40} +2.21575 q^{41} +(-0.317660 + 0.588518i) q^{42} +11.0789 q^{43} +(-3.49234 + 6.04891i) q^{45} +(-2.67744 + 4.63746i) q^{46} +(2.16584 + 3.75135i) q^{47} +0.626335 q^{48} +(-3.84141 - 5.85180i) q^{49} +0.917748 q^{50} +(0.392891 + 0.680507i) q^{51} +(-1.81859 + 3.14990i) q^{52} +(1.98183 - 3.43263i) q^{53} +(-0.756057 - 1.30953i) q^{54} +(-1.02931 + 1.90696i) q^{56} +0.623177 q^{57} +(1.97291 + 3.41719i) q^{58} +(1.17594 - 2.03678i) q^{59} +(-0.245522 + 0.425257i) q^{60} +(-4.41596 - 7.64867i) q^{61} +13.2892 q^{62} +(7.88661 - 0.226004i) q^{63} -4.23563 q^{64} +(2.71952 + 4.71035i) q^{65} +(7.38216 - 12.7863i) q^{67} +(-4.59747 - 7.96305i) q^{68} -0.379547 q^{69} +(-6.13923 - 9.96302i) q^{70} +7.76013 q^{71} +(-1.22125 - 2.11526i) q^{72} +(-4.82484 + 8.35687i) q^{73} +(8.74787 - 15.1518i) q^{74} +(0.0325244 + 0.0563339i) q^{75} -7.29219 q^{76} -0.586985 q^{78} +(-3.84690 - 6.66302i) q^{79} +(-5.47999 + 9.49163i) q^{80} +(-4.41954 + 7.65486i) q^{81} +(-2.09218 - 3.62375i) q^{82} -3.82583 q^{83} +(0.554453 - 0.0158888i) q^{84} -13.7501 q^{85} +(-10.4610 - 18.1191i) q^{86} +(-0.139838 + 0.242206i) q^{87} +(-7.79272 - 13.4974i) q^{89} +13.1903 q^{90} +(2.91828 - 5.40659i) q^{91} +4.44131 q^{92} +(0.470962 + 0.815731i) q^{93} +(4.09011 - 7.08427i) q^{94} +(-5.45236 + 9.44376i) q^{95} +(-0.481773 - 0.834455i) q^{96} +14.8326 q^{97} +(-5.94317 + 11.8079i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{3} - 8 q^{4} - 4 q^{5} - 4 q^{6} + 2 q^{7} - 6 q^{8} - 10 q^{9}+O(q^{10}) $ 14 * q - 3 * q^3 - 8 * q^4 - 4 * q^5 - 4 * q^6 + 2 * q^7 - 6 * q^8 - 10 * q^9	$ 14 q - 3 q^{3} - 8 q^{4} - 4 q^{5} - 4 q^{6} + 2 q^{7} - 6 q^{8} - 10 q^{9} - 6 q^{10} - 13 q^{12} + 12 q^{13} + 12 q^{14} - 2 q^{15} - 6 q^{16} + 3 q^{17} - 14 q^{18} + 9 q^{19} + 4 q^{20} - 6 q^{21} + 6 q^{23} - 4 q^{24} - 7 q^{25} - 25 q^{26} + 24 q^{27} - 36 q^{28} + 12 q^{29} - 16 q^{30} - 14 q^{31} + 36 q^{32} + 16 q^{34} + 18 q^{35} - 4 q^{36} + 8 q^{37} + 10 q^{38} + 9 q^{39} - 18 q^{40} - 20 q^{41} - 8 q^{42} + 34 q^{43} - 12 q^{45} - 16 q^{46} - 30 q^{47} + 112 q^{48} + 14 q^{49} + 42 q^{50} + 20 q^{51} + 37 q^{52} + 10 q^{53} + 7 q^{54} - 33 q^{56} - 62 q^{57} + 13 q^{58} - 20 q^{59} - 42 q^{60} - 7 q^{61} + 52 q^{62} + 37 q^{63} + 42 q^{64} - 12 q^{65} - 7 q^{67} - 7 q^{68} + 18 q^{69} - 39 q^{70} - 22 q^{71} + q^{72} + 6 q^{73} - 8 q^{74} + q^{75} - 112 q^{76} + 30 q^{78} + 14 q^{79} - 12 q^{80} - 35 q^{81} + 7 q^{82} + 34 q^{83} + 40 q^{84} - 4 q^{85} + 15 q^{87} - 40 q^{89} + 136 q^{90} - 32 q^{91} - 52 q^{92} - 19 q^{94} - 20 q^{95} + 63 q^{96} - 44 q^{97} + 21 q^{98}+O(q^{100}) $ 14 * q - 3 * q^3 - 8 * q^4 - 4 * q^5 - 4 * q^6 + 2 * q^7 - 6 * q^8 - 10 * q^9 - 6 * q^10 - 13 * q^12 + 12 * q^13 + 12 * q^14 - 2 * q^15 - 6 * q^16 + 3 * q^17 - 14 * q^18 + 9 * q^19 + 4 * q^20 - 6 * q^21 + 6 * q^23 - 4 * q^24 - 7 * q^25 - 25 * q^26 + 24 * q^27 - 36 * q^28 + 12 * q^29 - 16 * q^30 - 14 * q^31 + 36 * q^32 + 16 * q^34 + 18 * q^35 - 4 * q^36 + 8 * q^37 + 10 * q^38 + 9 * q^39 - 18 * q^40 - 20 * q^41 - 8 * q^42 + 34 * q^43 - 12 * q^45 - 16 * q^46 - 30 * q^47 + 112 * q^48 + 14 * q^49 + 42 * q^50 + 20 * q^51 + 37 * q^52 + 10 * q^53 + 7 * q^54 - 33 * q^56 - 62 * q^57 + 13 * q^58 - 20 * q^59 - 42 * q^60 - 7 * q^61 + 52 * q^62 + 37 * q^63 + 42 * q^64 - 12 * q^65 - 7 * q^67 - 7 * q^68 + 18 * q^69 - 39 * q^70 - 22 * q^71 + q^72 + 6 * q^73 - 8 * q^74 + q^75 - 112 * q^76 + 30 * q^78 + 14 * q^79 - 12 * q^80 - 35 * q^81 + 7 * q^82 + 34 * q^83 + 40 * q^84 - 4 * q^85 + 15 * q^87 - 40 * q^89 + 136 * q^90 - 32 * q^91 - 52 * q^92 - 19 * q^94 - 20 * q^95 + 63 * q^96 - 44 * q^97 + 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.944230	−	1.63545i	−0.667672	−	1.15644i	−0.978554	−	0.205993i	$-0.933958\pi$
$2$	−0.944230	−	1.63545i	−0.667672	−	1.15644i	0.310882	−	0.950449i	$-0.399376\pi$
$3$	0.0669258	−	0.115919i	0.0386397	−	0.0669258i	−0.846059	−	0.533090i	$-0.821031\pi$
$3$	0.0669258	−	0.115919i	0.0386397	−	0.0669258i	0.884698	+	0.466164i	$0.154364\pi$
$4$	−0.783142	+	1.35644i	−0.391571	+	0.678221i
$5$	1.17111	+	2.02842i	0.523735	+	0.907136i	0.999618	+	0.0276277i	$0.00879530\pi$
$5$	1.17111	+	2.02842i	0.523735	+	0.907136i	−0.475883	+	0.879509i	$0.657871\pi$
$6$	−0.252774			−0.103194
$7$	1.25670	−	2.32824i	0.474988	−	0.879992i
$7$	1.25670	−	2.32824i	0.474988	−	0.879992i
$8$	−0.819057			−0.289580
$9$	1.49104	+	2.58256i	0.497014	+	0.860853i
$10$	2.21159	−	3.83059i	0.699367	−	1.21134i
$11$		0			0
$11$		0			0
$12$	0.104825	+	0.181562i	0.0302603	+	0.0524124i
$13$	2.32218			0.644056			0.322028	−	0.946730i	$-0.395635\pi$
$13$	2.32218			0.644056			0.322028	+	0.946730i	$0.395635\pi$
$14$	−4.99435	+	0.143121i	−1.33480	+	0.0382507i
$15$	0.313510			0.0809478
$16$	2.33966	+	4.05241i	0.584915	+	1.01310i
$17$	−2.93527	+	5.08404i	−0.711908	+	1.23306i	0.252232	+	0.967667i	$0.418835\pi$
$17$	−2.93527	+	5.08404i	−0.711908	+	1.23306i	−0.964140	+	0.265394i	$0.914498\pi$
$18$	2.81577	−	4.87706i	0.663684	−	1.14953i
$19$	2.32786	+	4.03198i	0.534048	+	0.924999i	0.999209	+	0.0397725i	$0.0126633\pi$
$19$	2.32786	+	4.03198i	0.534048	+	0.924999i	−0.465160	+	0.885226i	$0.654003\pi$
$20$	−3.66857			−0.820318
$21$	−0.185782	−	0.301495i	−0.0405409	−	0.0657916i
$22$		0			0
$23$	−1.41779	−	2.45568i	−0.295629	−	0.512045i	0.679502	−	0.733674i	$-0.262196\pi$
$23$	−1.41779	−	2.45568i	−0.295629	−	0.512045i	−0.975131	+	0.221629i	$0.928863\pi$
$24$	−0.0548161	+	0.0949442i	−0.0111893	+	0.0193804i
$25$	−0.242988	+	0.420868i	−0.0485977	+	0.0841737i
$26$	−2.19267	−	3.79782i	−0.430018	−	0.744813i
$27$	0.800712			0.154097
$28$	2.17395	+	3.52798i	0.410838	+	0.666726i
$29$	−2.08944			−0.388000			−0.194000	−	0.981002i	$-0.562146\pi$
$29$	−2.08944			−0.388000			−0.194000	+	0.981002i	$0.562146\pi$
$30$	−0.296025	−	0.512731i	−0.0540466	−	0.0936114i
$31$	−3.51854	+	6.09429i	−0.631948	+	1.09457i	0.355205	+	0.934789i	$0.384411\pi$
$31$	−3.51854	+	6.09429i	−0.631948	+	1.09457i	−0.987153	+	0.159778i	$0.948922\pi$
$32$	3.59930	−	6.23417i	0.636273	−	1.10206i
$33$		0			0
$34$	11.0863			1.90128
$35$	6.19438	−	0.177510i	1.04704	−	0.0300047i
$36$	−4.67079			−0.778465
$37$	4.63228	+	8.02334i	0.761541	+	1.31903i	0.942056	+	0.335456i	$0.108890\pi$
$37$	4.63228	+	8.02334i	0.761541	+	1.31903i	−0.180514	+	0.983572i	$0.557776\pi$
$38$	4.39608	−	7.61423i	0.713138	−	1.23519i
$39$	0.155414	−	0.269184i	0.0248861	−	0.0431040i
$40$	−0.959204	−	1.66139i	−0.151664	−	0.262689i
$41$	2.21575			0.346042			0.173021	−	0.984918i	$-0.444647\pi$
$41$	2.21575			0.346042			0.173021	+	0.984918i	$0.444647\pi$
$42$	−0.317660	+	0.588518i	−0.0490161	+	0.0908103i
$43$	11.0789			1.68952			0.844759	−	0.535147i	$-0.179744\pi$
$43$	11.0789			1.68952			0.844759	+	0.535147i	$0.179744\pi$
$44$		0			0
$45$	−3.49234	+	6.04891i	−0.520608	+	0.901719i
$46$	−2.67744	+	4.63746i	−0.394766	+	0.683756i
$47$	2.16584	+	3.75135i	0.315920	+	0.547190i	0.979633	−	0.200798i	$-0.0643534\pi$
$47$	2.16584	+	3.75135i	0.315920	+	0.547190i	−0.663712	+	0.747988i	$0.731020\pi$
$48$	0.626335			0.0904037
$49$	−3.84141	−	5.85180i	−0.548773	−	0.835971i
$50$	0.917748			0.129789
$51$	0.392891	+	0.680507i	0.0550158	+	0.0952901i
$52$	−1.81859	+	3.14990i	−0.252194	+	0.436812i
$53$	1.98183	−	3.43263i	0.272225	−	0.471508i	−0.697206	−	0.716871i	$-0.745574\pi$
$53$	1.98183	−	3.43263i	0.272225	−	0.471508i	0.969431	+	0.245363i	$0.0789071\pi$
$54$	−0.756057	−	1.30953i	−0.102886	−	0.178204i
$55$		0			0
$56$	−1.02931	+	1.90696i	−0.137547	+	0.254829i
$57$	0.623177			0.0825418
$58$	1.97291	+	3.41719i	0.259056	+	0.448699i
$59$	1.17594	−	2.03678i	0.153094	−	0.265166i	−0.779269	−	0.626689i	$-0.784410\pi$
$59$	1.17594	−	2.03678i	0.153094	−	0.265166i	0.932363	+	0.361523i	$0.117743\pi$
$60$	−0.245522	+	0.425257i	−0.0316968	+	0.0549005i
$61$	−4.41596	−	7.64867i	−0.565406	−	0.979312i	−0.997012	−	0.0772500i	$-0.975386\pi$
$61$	−4.41596	−	7.64867i	−0.565406	−	0.979312i	0.431605	−	0.902062i	$-0.357947\pi$
$62$	13.2892			1.68774
$63$	7.88661	−	0.226004i	0.993620	−	0.0284738i
$64$	−4.23563			−0.529454
$65$	2.71952	+	4.71035i	0.337315	+	0.584247i
$66$		0			0
$67$	7.38216	−	12.7863i	0.901875	−	1.56209i	0.0768170	−	0.997045i	$-0.475524\pi$
$67$	7.38216	−	12.7863i	0.901875	−	1.56209i	0.825058	−	0.565048i	$-0.191142\pi$
$68$	−4.59747	−	7.96305i	−0.557525	−	0.965661i
$69$	−0.379547			−0.0456920
$70$	−6.13923	−	9.96302i	−0.733778	−	1.19081i
$71$	7.76013			0.920957			0.460479	−	0.887671i	$-0.347678\pi$
$71$	7.76013			0.920957			0.460479	+	0.887671i	$0.347678\pi$
$72$	−1.22125	−	2.11526i	−0.143925	−	0.249286i
$73$	−4.82484	+	8.35687i	−0.564705	+	0.978097i	0.432372	+	0.901695i	$0.357677\pi$
$73$	−4.82484	+	8.35687i	−0.564705	+	0.978097i	−0.997077	+	0.0764022i	$0.975657\pi$
$74$	8.74787	−	15.1518i	1.01692	−	1.76136i
$75$	0.0325244	+	0.0563339i	0.00375560	+	0.00650488i
$76$	−7.29219			−0.836471
$77$		0			0
$78$	−0.586985			−0.0664630
$79$	−3.84690	−	6.66302i	−0.432810	−	0.749648i	0.564304	−	0.825567i	$-0.309144\pi$
$79$	−3.84690	−	6.66302i	−0.432810	−	0.749648i	−0.997114	+	0.0759186i	$0.975811\pi$
$80$	−5.47999	+	9.49163i	−0.612682	+	1.06120i
$81$	−4.41954	+	7.65486i	−0.491060	+	0.850540i
$82$	−2.09218	−	3.62375i	−0.231042	−	0.400177i
$83$	−3.82583			−0.419940			−0.209970	−	0.977708i	$-0.567337\pi$
$83$	−3.82583			−0.419940			−0.209970	+	0.977708i	$0.567337\pi$
$84$	0.554453	−	0.0158888i	0.0604958	−	0.00173361i
$85$	−13.7501			−1.49141
$86$	−10.4610	−	18.1191i	−1.12804	−	1.95383i
$87$	−0.139838	+	0.242206i	−0.0149922	+	0.0259672i
$88$		0			0
$89$	−7.79272	−	13.4974i	−0.826027	−	1.43072i	−0.901132	−	0.433545i	$-0.857263\pi$
$89$	−7.79272	−	13.4974i	−0.826027	−	1.43072i	0.0751051	−	0.997176i	$-0.476071\pi$
$90$	13.1903			1.39038
$91$	2.91828	−	5.40659i	0.305919	−	0.566765i
$92$	4.44131			0.463039
$93$	0.470962	+	0.815731i	0.0488365	+	0.0845873i
$94$	4.09011	−	7.08427i	0.421862	−	0.730687i
$95$	−5.45236	+	9.44376i	−0.559400	+	0.968909i
$96$	−0.481773	−	0.834455i	−0.0491707	−	0.0851662i
$97$	14.8326			1.50603			0.753013	−	0.658005i	$-0.228600\pi$
$97$	14.8326			1.50603			0.753013	+	0.658005i	$0.228600\pi$
$98$	−5.94317	+	11.8079i	−0.600351	+	1.19278i
$99$		0			0
$100$	−0.380589	−	0.659199i	−0.0380589	−	0.0659199i
$101$	−7.36776	+	12.7613i	−0.733119	+	1.26980i	0.222424	+	0.974950i	$0.428603\pi$
$101$	−7.36776	+	12.7613i	−0.733119	+	1.26980i	−0.955544	+	0.294850i	$0.904730\pi$
$102$	0.741959	−	1.28511i	0.0734649	−	0.127245i
$103$	−3.39494	−	5.88020i	−0.334513	−	0.579394i	0.648878	−	0.760892i	$-0.275239\pi$
$103$	−3.39494	−	5.88020i	−0.334513	−	0.579394i	−0.983391	+	0.181499i	$0.941905\pi$
$104$	−1.90200			−0.186506
$105$	0.393987	−	0.729926i	0.0384492	−	0.0712335i
$106$	−7.48521			−0.727028
$107$	−8.87325	−	15.3689i	−0.857810	−	1.48577i	−0.874014	−	0.485901i	$-0.838491\pi$
$107$	−8.87325	−	15.3689i	−0.857810	−	1.48577i	0.0162041	−	0.999869i	$-0.494842\pi$
$108$	−0.627071	+	1.08612i	−0.0603399	+	0.104512i
$109$	−0.486421	+	0.842506i	−0.0465907	+	0.0806975i	−0.888380	−	0.459108i	$-0.848169\pi$
$109$	−0.486421	+	0.842506i	−0.0465907	+	0.0806975i	0.841790	+	0.539806i	$0.181502\pi$
$110$		0			0
$111$	1.24008			0.117703
$112$	12.3752	−	0.354633i	1.16935	−	0.0335097i
$113$	−3.04752			−0.286687			−0.143343	−	0.989673i	$-0.545785\pi$
$113$	−3.04752			−0.286687			−0.143343	+	0.989673i	$0.545785\pi$
$114$	−0.588422	−	1.01918i	−0.0551108	−	0.0954547i
$115$	3.32077	−	5.75173i	0.309663	−	0.536352i
$116$	1.63633	−	2.83421i	0.151929	−	0.263149i
$117$	3.46246	+	5.99716i	0.320105	+	0.554438i
$118$	−4.44142			−0.408866
$119$	8.14812	+	13.2231i	0.746937	+	1.21216i
$120$	−0.256782			−0.0234409
$121$		0			0
$122$	−8.33937	+	14.4442i	−0.755011	+	1.30772i
$123$	0.148291	−	0.256847i	0.0133709	−	0.0231591i
$124$	−5.51103	−	9.54538i	−0.494905	−	0.857201i
$125$	10.5728			0.945662
$126$	−7.81640	−	12.6848i	−0.696340	−	1.13005i
$127$	4.06723			0.360908			0.180454	−	0.983583i	$-0.442243\pi$
$127$	4.06723			0.360908			0.180454	+	0.983583i	$0.442243\pi$
$128$	−3.19919	−	5.54116i	−0.282771	−	0.489774i
$129$	0.741465	−	1.28426i	0.0652824	−	0.113072i
$130$	5.13571	−	8.89531i	0.450431	−	0.780170i
$131$	6.18763	+	10.7173i	0.540615	+	0.936373i	0.998869	+	0.0475518i	$0.0151419\pi$
$131$	6.18763	+	10.7173i	0.540615	+	0.936373i	−0.458253	+	0.888822i	$0.651525\pi$
$132$		0			0
$133$	12.3128	−	0.352845i	1.06766	−	0.0305955i
$134$	−27.8819			−2.40863
$135$	0.937720	+	1.62418i	0.0807061	+	0.139787i
$136$	2.40415	−	4.16412i	0.206155	−	0.357070i
$137$	−5.15525	+	8.92915i	−0.440442	+	0.762868i	−0.997722	−	0.0674562i	$-0.978512\pi$
$137$	−5.15525	+	8.92915i	−0.440442	+	0.762868i	0.557280	+	0.830325i	$0.311845\pi$
$138$	0.358379	+	0.620731i	0.0305073	+	0.0528402i
$139$	10.3357			0.876664			0.438332	−	0.898813i	$-0.355569\pi$
$139$	10.3357			0.876664			0.438332	+	0.898813i	$0.355569\pi$
$140$	−4.61029	+	8.54133i	−0.389641	+	0.721874i
$141$	0.579803			0.0488282
$142$	−7.32735	−	12.6913i	−0.614897	−	1.06503i
$143$		0			0
$144$	−6.97707	+	12.0846i	−0.581422	+	1.00705i
$145$	−2.44696	−	4.23826i	−0.203209	−	0.351969i
$146$	18.2230			1.50815
$147$	−0.935424	+	0.0536563i	−0.0771525	+	0.00442550i
$148$	−14.5109			−1.19279
$149$	−2.65909	−	4.60569i	−0.217841	−	0.377313i	0.736306	−	0.676648i	$-0.236568\pi$
$149$	−2.65909	−	4.60569i	−0.217841	−	0.377313i	−0.954148	+	0.299336i	$0.903235\pi$
$150$	0.0614211	−	0.106384i	0.00501501	−	0.00868625i
$151$	−7.18742	+	12.4490i	−0.584904	+	1.01308i	0.409983	+	0.912093i	$0.365535\pi$
$151$	−7.18742	+	12.4490i	−0.584904	+	1.01308i	−0.994887	+	0.100991i	$0.967799\pi$
$152$	−1.90665	−	3.30242i	−0.154650	−	0.267862i
$153$	−17.5065			−1.41531
$154$		0			0
$155$	−16.4824			−1.32389
$156$	0.243422	+	0.421619i	0.0194893	+	0.0337565i
$157$	7.23205	−	12.5263i	0.577180	−	0.999706i	−0.418621	−	0.908161i	$-0.637486\pi$
$157$	7.23205	−	12.5263i	0.577180	−	0.999706i	0.995801	−	0.0915444i	$-0.0291803\pi$
$158$	−7.26471	+	12.5828i	−0.577949	+	1.00104i
$159$	−0.265271	−	0.459463i	−0.0210374	−	0.0364378i
$160$	16.8607			1.33295
$161$	−7.49915	+	0.214900i	−0.591016	+	0.0169365i
$162$	16.6922			1.31147
$163$	0.234108	+	0.405488i	0.0183368	+	0.0317603i	0.875048	−	0.484036i	$-0.160830\pi$
$163$	0.234108	+	0.405488i	0.0183368	+	0.0317603i	−0.856711	+	0.515796i	$0.827496\pi$
$164$	−1.73524	+	3.00553i	−0.135500	+	0.234692i
$165$		0			0
$166$	3.61247	+	6.25697i	0.280382	+	0.485635i
$167$	22.4939			1.74063			0.870313	−	0.492498i	$-0.163916\pi$
$167$	22.4939			1.74063			0.870313	+	0.492498i	$0.163916\pi$
$168$	0.152166	+	0.246941i	0.0117398	+	0.0190519i
$169$	−7.60749			−0.585192
$170$	12.9832	+	22.4876i	0.995769	+	1.72472i
$171$	−6.94188	+	12.0237i	−0.530859	+	0.919475i
$172$	−8.67635	+	15.0279i	−0.661566	+	1.14587i
$173$	7.80382	+	13.5166i	0.593314	+	1.02765i	0.993782	+	0.111339i	$0.0355139\pi$
$173$	7.80382	+	13.5166i	0.593314	+	1.02765i	−0.400469	+	0.916310i	$0.631153\pi$
$174$	0.528156			0.0400394
$175$	0.674520	+	1.09464i	0.0509889	+	0.0827470i
$176$		0			0
$177$	−0.157401	−	0.272627i	−0.0118310	−	0.0204919i
$178$	−14.7162	+	25.4893i	−1.10303	+	1.91050i
$179$	0.465286	−	0.805899i	0.0347771	−	0.0602357i	−0.848113	−	0.529815i	$-0.822261\pi$
$179$	0.465286	−	0.805899i	0.0347771	−	0.0602357i	0.882890	+	0.469580i	$0.155595\pi$
$180$	−5.47000	−	9.47431i	−0.407710	−	0.706174i
$181$	−6.03439			−0.448533			−0.224267	−	0.974528i	$-0.571999\pi$
$181$	−6.03439			−0.448533			−0.224267	+	0.974528i	$0.571999\pi$
$182$	−11.5978	+	0.332353i	−0.859683	+	0.0246356i
$183$	−1.18217			−0.0873884
$184$	1.16125	+	2.01134i	0.0856084	+	0.148278i
$185$	−10.8498	+	18.7924i	−0.797693	+	1.38164i
$186$	0.889394	−	1.54048i	0.0652135	−	0.112953i
$187$		0			0
$188$	−6.78464			−0.494821
$189$	1.00625	−	1.86425i	0.0731942	−	0.135604i
$190$	20.5931			1.49398
$191$	4.51107	+	7.81340i	0.326410	+	0.565358i	0.981797	−	0.189935i	$-0.0608278\pi$
$191$	4.51107	+	7.81340i	0.326410	+	0.565358i	−0.655387	+	0.755293i	$0.727494\pi$
$192$	−0.283473	+	0.490990i	−0.0204579	+	0.0354342i
$193$	0.464055	−	0.803767i	0.0334034	−	0.0578564i	−0.848840	−	0.528649i	$-0.822699\pi$
$193$	0.464055	−	0.803767i	0.0334034	−	0.0578564i	0.882244	+	0.470793i	$0.156032\pi$
$194$	−14.0054	−	24.2581i	−1.00553	−	1.74163i
$195$	0.728025			0.0521349
$196$	10.9460	−	0.627866i	0.781856	−	0.0448476i
$197$	−17.8169			−1.26940			−0.634701	−	0.772758i	$-0.718877\pi$
$197$	−17.8169			−1.26940			−0.634701	+	0.772758i	$0.718877\pi$
$198$		0			0
$199$	−1.14410	+	1.98164i	−0.0811030	+	0.140474i	−0.903724	−	0.428116i	$-0.859178\pi$
$199$	−1.14410	+	1.98164i	−0.0811030	+	0.140474i	0.822621	+	0.568590i	$0.192511\pi$
$200$	0.199021	−	0.344715i	0.0140729	−	0.0243750i
$201$	−0.988115	−	1.71147i	−0.0696963	−	0.120717i
$202$	27.8274			1.95793
$203$	−2.62580	+	4.86473i	−0.184295	+	0.341437i
$204$	−1.23076			−0.0861703
$205$	2.59488	+	4.49446i	0.181234	+	0.313907i
$206$	−6.41121	+	11.1045i	−0.446690	+	0.773689i
$207$	4.22796	−	7.32304i	0.293864	−	0.508987i
$208$	5.43311	+	9.41042i	0.376718	+	0.652495i
$209$		0			0
$210$	−1.56578	+	0.0448699i	−0.108049	+	0.00309632i
$211$	−4.55916			−0.313866			−0.156933	−	0.987609i	$-0.550161\pi$
$211$	−4.55916			−0.313866			−0.156933	+	0.987609i	$0.550161\pi$
$212$	3.10411	+	5.37647i	0.213191	+	0.369257i
$213$	0.519353	−	0.899546i	0.0355855	−	0.0616359i
$214$	−16.7568	+	29.0236i	−1.14547	+	1.98401i
$215$	12.9746	+	22.4727i	0.884860	+	1.53262i
$216$	−0.655829			−0.0446235
$217$	9.76723	+	15.8507i	0.663043	+	1.07602i
$218$	1.83717			0.124429
$219$	0.645813	+	1.11858i	0.0436400	+	0.0755867i
$220$		0			0
$221$	−6.81622	+	11.8060i	−0.458509	+	0.794160i
$222$	−1.17092	−	2.02809i	−0.0785868	−	0.136116i
$223$	−3.25507			−0.217976			−0.108988	−	0.994043i	$-0.534761\pi$
$223$	−3.25507			−0.217976			−0.108988	+	0.994043i	$0.534761\pi$
$224$	−9.99142	−	16.2145i	−0.667580	−	1.08338i
$225$	−1.44922			−0.0966149
$226$	2.87756	+	4.98408i	0.191412	+	0.331536i
$227$	2.32962	−	4.03503i	0.154623	−	0.267814i	−0.778299	−	0.627894i	$-0.783917\pi$
$227$	2.32962	−	4.03503i	0.154623	−	0.267814i	0.932922	+	0.360080i	$0.117251\pi$
$228$	−0.488036	+	0.845303i	−0.0323210	+	0.0559815i
$229$	0.255838	+	0.443124i	0.0169062	+	0.0292824i	0.874355	−	0.485287i	$-0.161285\pi$
$229$	0.255838	+	0.443124i	0.0169062	+	0.0292824i	−0.857449	+	0.514570i	$0.827952\pi$
$230$	−12.5423			−0.827013
$231$		0			0
$232$	1.71137			0.112357
$233$	−10.3927	−	18.0008i	−0.680851	−	1.17927i	−0.974721	−	0.223424i	$-0.928277\pi$
$233$	−10.3927	−	18.0008i	−0.680851	−	1.17927i	0.293870	−	0.955845i	$-0.405057\pi$
$234$	6.53873	−	11.3254i	0.427450	−	0.740365i
$235$	−5.07287	+	8.78647i	−0.330917	+	0.573166i
$236$	1.84185	+	3.19018i	0.119894	+	0.207663i
$237$	−1.02983			−0.0668945
$238$	13.9321	−	25.8116i	0.903086	−	1.67311i
$239$	0.578108			0.0373947			0.0186973	−	0.999825i	$-0.494048\pi$
$239$	0.578108			0.0373947			0.0186973	+	0.999825i	$0.494048\pi$
$240$	0.733506	+	1.27047i	0.0473476	+	0.0820085i
$241$	6.09896	−	10.5637i	0.392868	−	0.680468i	−0.599958	−	0.800031i	$-0.704816\pi$
$241$	6.09896	−	10.5637i	0.392868	−	0.680468i	0.992827	+	0.119563i	$0.0381495\pi$
$242$		0			0
$243$	1.79263	+	3.10493i	0.114997	+	0.199181i
$244$	13.8333			0.885586
$245$	7.37118	−	14.6451i	0.470928	−	0.935640i
$246$	−0.560082			−0.0357096
$247$	5.40571	+	9.36297i	0.343957	+	0.595751i
$248$	2.88188	−	4.99157i	0.183000	−	0.316965i
$249$	−0.256047	+	0.443486i	−0.0162263	+	0.0281048i
$250$	−9.98318	−	17.2914i	−0.631391	−	1.09360i
$251$	−15.7638			−0.995004			−0.497502	−	0.867463i	$-0.665749\pi$
$251$	−15.7638			−0.995004			−0.497502	+	0.867463i	$0.665749\pi$
$252$	−5.86978	+	10.8747i	−0.369761	+	0.685043i
$253$		0			0
$254$	−3.84040	−	6.65177i	−0.240968	−	0.417369i
$255$	−0.920236	+	1.59390i	−0.0576274	+	0.0998136i
$256$	−10.2772	+	17.8006i	−0.642324	+	1.11254i
$257$	12.8643	+	22.2817i	0.802454	+	1.38989i	0.917996	+	0.396589i	$0.129806\pi$
$257$	12.8643	+	22.2817i	0.802454	+	1.38989i	−0.115542	+	0.993303i	$0.536861\pi$
$258$	−2.80046			−0.174349
$259$	24.5016	−	0.702135i	1.52246	−	0.0436285i
$260$	−8.51908			−0.528331
$261$	−3.11545	−	5.39611i	−0.192841	−	0.334011i
$262$	11.6851	−	20.2392i	0.721907	−	1.25038i
$263$	3.74405	−	6.48488i	0.230868	−	0.399875i	−0.727196	−	0.686430i	$-0.759177\pi$
$263$	3.74405	−	6.48488i	0.230868	−	0.399875i	0.958064	+	0.286555i	$0.0925101\pi$
$264$		0			0
$265$	9.28374			0.570296
$266$	−12.2032	−	19.8039i	−0.748227	−	1.21426i
$267$	−2.08614			−0.127670
$268$	11.5626	+	20.0269i	0.706296	+	1.22334i
$269$	−7.63566	+	13.2253i	−0.465554	+	0.806364i	−0.999226	−	0.0393279i	$-0.987478\pi$
$269$	−7.63566	+	13.2253i	−0.465554	+	0.806364i	0.533672	+	0.845691i	$0.320812\pi$
$270$	1.77085	−	3.06720i	0.107770	−	0.186664i
$271$	−6.62341	−	11.4721i	−0.402343	−	0.696879i	0.591665	−	0.806184i	$-0.298471\pi$
$271$	−6.62341	−	11.4721i	−0.402343	−	0.696879i	−0.994008	+	0.109305i	$0.965137\pi$
$272$	−27.4702			−1.66562
$273$	−0.431418	−	0.700124i	−0.0261106	−	0.0423735i
$274$	19.4710			1.17628
$275$		0			0
$276$	0.297239	−	0.514833i	0.0178917	−	0.0309893i
$277$	−2.86568	+	4.96351i	−0.172182	+	0.298228i	−0.939183	−	0.343418i	$-0.888415\pi$
$277$	−2.86568	+	4.96351i	−0.172182	+	0.298228i	0.767000	+	0.641647i	$0.221748\pi$
$278$	−9.75930	−	16.9036i	−0.585324	−	1.01381i
$279$	−20.9852			−1.25635
$280$	−5.07355	+	0.145391i	−0.303203	+	0.00868877i
$281$	−18.4652			−1.10154			−0.550769	−	0.834657i	$-0.685666\pi$
$281$	−18.4652			−1.10154			−0.550769	+	0.834657i	$0.685666\pi$
$282$	−0.547468	−	0.948242i	−0.0326012	−	0.0564670i
$283$	−3.77408	+	6.53689i	−0.224346	+	0.388578i	−0.956123	−	0.292966i	$-0.905358\pi$
$283$	−3.77408	+	6.53689i	−0.224346	+	0.388578i	0.731777	+	0.681544i	$0.238691\pi$
$284$	−6.07728	+	10.5262i	−0.360620	+	0.624612i
$285$	0.729807	+	1.26406i	0.0432301	+	0.0748767i
$286$		0			0
$287$	2.78453	−	5.15879i	0.164365	−	0.304514i
$288$	21.4668			1.26495
$289$	−8.73165	−	15.1237i	−0.513626	−	0.889627i
$290$	−4.62099	+	8.00380i	−0.271354	+	0.469999i
$291$	0.992687	−	1.71938i	0.0581923	−	0.100792i
$292$	−7.55707	−	13.0892i	−0.442244	−	0.765989i
$293$	−9.85925			−0.575983			−0.287992	−	0.957633i	$-0.592988\pi$
$293$	−9.85925			−0.575983			−0.287992	+	0.957633i	$0.592988\pi$
$294$	0.971008	+	1.47918i	0.0566304	+	0.0862675i
$295$	5.50859			0.320723
$296$	−3.79410	−	6.57157i	−0.220527	−	0.381965i
$297$		0			0
$298$	−5.02159	+	8.69766i	−0.290893	+	0.503842i
$299$	−3.29235	−	5.70253i	−0.190402	−	0.329786i
$300$	−0.101885			−0.00588233
$301$	13.9229	−	25.7944i	0.802500	−	1.48676i
$302$	27.1463			1.56210
$303$	0.986187	+	1.70813i	0.0566550	+	0.0981293i
$304$	−10.8928	+	18.8669i	−0.624746	+	1.08209i
$305$	10.3431	−	17.9148i	0.592247	−	1.02580i
$306$	16.5301	+	28.6310i	0.944964	+	1.63673i
$307$	−25.7388			−1.46899			−0.734495	−	0.678615i	$-0.762581\pi$
$307$	−25.7388			−1.46899			−0.734495	+	0.678615i	$0.762581\pi$
$308$		0			0
$309$	−0.908836			−0.0517019
$310$	15.5631	+	26.9561i	0.883927	+	1.53101i
$311$	−0.462529	+	0.801124i	−0.0262276	+	0.0454276i	−0.878841	−	0.477114i	$-0.841683\pi$
$311$	−0.462529	+	0.801124i	−0.0262276	+	0.0454276i	0.852614	+	0.522542i	$0.175016\pi$
$312$	−0.127293	+	0.220477i	−0.00720653	+	0.0124821i
$313$	−14.8181	−	25.6657i	−0.837570	−	1.45071i	−0.891921	−	0.452192i	$-0.850642\pi$
$313$	−14.8181	−	25.6657i	−0.837570	−	1.45071i	0.0543508	−	0.998522i	$-0.482691\pi$
$314$	−27.3149			−1.54147
$315$	9.69451	+	15.7327i	0.546224	+	0.886436i
$316$	12.0507			0.677902
$317$	−7.81751	−	13.5403i	−0.439075	−	0.760501i	0.558543	−	0.829475i	$-0.311361\pi$
$317$	−7.81751	−	13.5403i	−0.439075	−	0.760501i	−0.997618	+	0.0689748i	$0.978027\pi$
$318$	−0.500954	+	0.867678i	−0.0280921	+	0.0486570i
$319$		0			0
$320$	−4.96038	−	8.59164i	−0.277294	−	0.480287i
$321$	−2.37540			−0.132582
$322$	7.43238	+	12.0616i	0.414191	+	0.672167i
$323$	−27.3316			−1.52077
$324$	−6.92225	−	11.9897i	−0.384569	−	0.666094i
$325$	−0.564262	+	0.977331i	−0.0312996	+	0.0542126i
$326$	0.442105	−	0.765748i	0.0244859	−	0.0424108i
$327$	0.0651083	+	0.112771i	0.00360050	+	0.00623624i
$328$	−1.81482			−0.100207
$329$	11.4559	−	0.328286i	0.631582	−	0.0180990i
$330$		0			0
$331$	−7.92315	−	13.7233i	−0.435496	−	0.754300i	0.561840	−	0.827246i	$-0.310093\pi$
$331$	−7.92315	−	13.7233i	−0.435496	−	0.754300i	−0.997336	+	0.0729453i	$0.976760\pi$
$332$	2.99617	−	5.18951i	0.164436	−	0.284812i
$333$	−13.8138	+	23.9263i	−0.756993	+	1.31115i
$334$	−21.2394	−	36.7877i	−1.16217	−	2.01293i
$335$	34.5813			1.88938
$336$	0.787115	−	1.45826i	0.0429407	−	0.0795546i
$337$	15.6689			0.853539			0.426769	−	0.904361i	$-0.359652\pi$
$337$	15.6689			0.853539			0.426769	+	0.904361i	$0.359652\pi$
$338$	7.18322	+	12.4417i	0.390716	+	0.676740i
$339$	−0.203958	+	0.353265i	−0.0110775	+	0.0191867i
$340$	10.7683	−	18.6512i	0.583991	−	1.01150i
$341$		0			0
$342$	26.2189			1.41776
$343$	−18.4519	+	1.58979i	−0.996309	+	0.0858406i
$344$	−9.07426			−0.489251
$345$	−0.444490	−	0.769879i	−0.0239305	−	0.0414489i
$346$	14.7372	−	25.5256i	0.792277	−	1.37226i
$347$	3.76137	−	6.51488i	0.201921	−	0.349737i	−0.747227	−	0.664569i	$-0.768615\pi$
$347$	3.76137	−	6.51488i	0.201921	−	0.349737i	0.949147	+	0.314832i	$0.101948\pi$
$348$	−0.219025	−	0.379363i	−0.0117410	−	0.0203360i
$349$	7.66830			0.410475			0.205237	−	0.978712i	$-0.434203\pi$
$349$	7.66830			0.410475			0.205237	+	0.978712i	$0.434203\pi$
$350$	1.15333	−	2.13674i	0.0616483	−	0.114214i
$351$	1.85940			0.0992472
$352$		0			0
$353$	3.50035	−	6.06278i	0.186305	−	0.322689i	−0.757711	−	0.652591i	$-0.773682\pi$
$353$	3.50035	−	6.06278i	0.186305	−	0.322689i	0.944015	+	0.329902i	$0.107016\pi$
$354$	−0.297246	+	0.514845i	−0.0157984	+	0.0273637i
$355$	9.08795	+	15.7408i	0.482338	+	0.835434i
$356$	24.4112			1.29379
$357$	2.07813	−	0.0595523i	0.109986	−	0.00315184i
$358$	−1.75735			−0.0928788
$359$	13.2782	+	22.9986i	0.700799	+	1.21382i	0.968186	+	0.250231i	$0.0805064\pi$
$359$	13.2782	+	22.9986i	0.700799	+	1.21382i	−0.267387	+	0.963589i	$0.586160\pi$
$360$	2.86043	−	4.95441i	0.150758	−	0.261120i
$361$	−1.33789	+	2.31730i	−0.0704153	+	0.121963i
$362$	5.69786	+	9.86898i	0.299473	+	0.518702i
$363$		0			0
$364$	5.04829	+	8.19260i	0.264603	+	0.429409i
$365$	−22.6016			−1.18302
$366$	1.11624	+	1.93338i	0.0583468	+	0.101060i
$367$	1.70859	−	2.95936i	0.0891875	−	0.154477i	−0.817980	−	0.575246i	$-0.804906\pi$
$367$	1.70859	−	2.95936i	0.0891875	−	0.154477i	0.907168	+	0.420769i	$0.138240\pi$
$368$	6.63429	−	11.4909i	0.345836	−	0.599006i
$369$	3.30377	+	5.72230i	0.171987	+	0.297891i
$370$	40.9788			2.13039
$371$	−5.50142	−	8.92796i	−0.285620	−	0.463516i
$372$	−1.47532			−0.0764918
$373$	6.27649	+	10.8712i	0.324984	+	0.562889i	0.981509	−	0.191415i	$-0.0613077\pi$
$373$	6.27649	+	10.8712i	0.324984	+	0.562889i	−0.656525	+	0.754304i	$0.727974\pi$
$374$		0			0
$375$	0.707595	−	1.22559i	0.0365400	−	0.0632892i
$376$	−1.77395	−	3.07257i	−0.0914843	−	0.158456i
$377$	−4.85206			−0.249894
$378$	−3.99903	+	0.114599i	−0.205688	+	0.00589433i
$379$	−17.1416			−0.880506			−0.440253	−	0.897874i	$-0.645111\pi$
$379$	−17.1416			−0.880506			−0.440253	+	0.897874i	$0.645111\pi$
$380$	−8.53994	−	14.7916i	−0.438090	−	0.758793i
$381$	0.272203	−	0.471469i	0.0139454	−	0.0241541i
$382$	8.51898	−	14.7553i	0.435869	−	0.754947i
$383$	−16.8758	−	29.2297i	−0.862313	−	1.49357i	−0.869690	−	0.493598i	$-0.835682\pi$
$383$	−16.8758	−	29.2297i	−0.862313	−	1.49357i	0.00737725	−	0.999973i	$-0.497652\pi$
$384$	−0.856434			−0.0437047
$385$		0			0
$386$	−1.75270			−0.0892100
$387$	16.5191	+	28.6119i	0.839714	+	1.45443i
$388$	−11.6161	+	20.1196i	−0.589716	+	1.02142i
$389$	1.86561	−	3.23132i	0.0945899	−	0.163835i	−0.814847	−	0.579675i	$-0.803179\pi$
$389$	1.86561	−	3.23132i	0.0945899	−	0.163835i	0.909437	+	0.415841i	$0.136513\pi$
$390$	−0.687423	−	1.19065i	−0.0348090	−	0.0602910i
$391$	16.6464			0.841843
$392$	3.14634	+	4.79296i	0.158914	+	0.242081i
$393$	1.65645			0.0835568
$394$	16.8233	+	29.1388i	0.847544	+	1.46799i
$395$	9.01026	−	15.6062i	0.453355	−	0.785235i
$396$		0			0
$397$	6.51237	+	11.2798i	0.326847	+	0.566115i	0.981884	−	0.189481i	$-0.0606806\pi$
$397$	6.51237	+	11.2798i	0.326847	+	0.566115i	−0.655038	+	0.755596i	$0.727347\pi$
$398$	4.32117			0.216601
$399$	0.783146	−	1.45091i	0.0392063	−	0.0726361i
$400$	−2.27404			−0.113702
$401$	−14.0941	−	24.4117i	−0.703825	−	1.21906i	−0.967114	−	0.254343i	$-0.918141\pi$
$401$	−14.0941	−	24.4117i	−0.703825	−	1.21906i	0.263289	−	0.964717i	$-0.415193\pi$
$402$	−1.86602	+	3.23204i	−0.0930685	+	0.161199i
$403$	−8.17067	+	14.1520i	−0.407010	+	0.704962i
$404$	−11.5400	−	19.9879i	−0.574136	−	0.994433i
$405$	−20.7030			−1.02874
$406$	10.4354	−	0.299043i	0.517900	−	0.0148413i
$407$		0			0
$408$	−0.321800	−	0.557374i	−0.0159315	−	0.0275941i
$409$	19.3826	−	33.5717i	0.958410	−	1.66001i	0.232045	−	0.972705i	$-0.425458\pi$
$409$	19.3826	−	33.5717i	0.958410	−	1.66001i	0.726365	−	0.687309i	$-0.241208\pi$
$410$	4.90033	−	8.48762i	0.242010	−	0.419173i
$411$	0.690038	+	1.19518i	0.0340371	+	0.0589540i
$412$	10.6349			0.523942
$413$	−3.26432	−	5.29748i	−0.160627	−	0.260672i
$414$	−15.9687			−0.784818
$415$	−4.48046	−	7.76039i	−0.219937	−	0.380942i
$416$	8.35822	−	14.4769i	0.409795	−	0.709786i
$417$	0.691727	−	1.19811i	0.0338740	−	0.0586715i
$418$		0			0
$419$	−2.65722			−0.129814			−0.0649069	−	0.997891i	$-0.520675\pi$
$419$	−2.65722			−0.129814			−0.0649069	+	0.997891i	$0.520675\pi$
$420$	0.681554	+	1.10606i	0.0332564	+	0.0539700i
$421$	−24.7026			−1.20393			−0.601967	−	0.798521i	$-0.705616\pi$
$421$	−24.7026			−1.20393			−0.601967	+	0.798521i	$0.705616\pi$
$422$	4.30490	+	7.45630i	0.209559	+	0.362967i
$423$	−6.45872	+	11.1868i	−0.314034	+	0.543922i
$424$	−1.62323	+	2.81152i	−0.0788311	+	0.136539i
$425$	−1.42647	−	2.47073i	−0.0691942	−	0.119848i
$426$	−1.96156			−0.0950377
$427$	−23.3575	+	0.669347i	−1.13035	+	0.0323920i
$428$	27.7961			1.34357
$429$		0			0
$430$	24.5020	−	42.4387i	1.18159	−	2.04658i
$431$	−5.20756	+	9.01976i	−0.250839	+	0.434466i	−0.963757	−	0.266781i	$-0.914040\pi$
$431$	−5.20756	+	9.01976i	−0.250839	+	0.434466i	0.712918	+	0.701248i	$0.247373\pi$
$432$	1.87340	+	3.24482i	0.0901338	+	0.156116i
$433$	19.9276			0.957660			0.478830	−	0.877908i	$-0.341061\pi$
$433$	19.9276			0.957660			0.478830	+	0.877908i	$0.341061\pi$
$434$	16.7006	−	30.9406i	0.801654	−	1.48519i
$435$	−0.655060			−0.0314077
$436$	−0.761873	−	1.31960i	−0.0364871	−	0.0631975i
$437$	6.60083	−	11.4330i	0.315761	−	0.546913i
$438$	1.21959	−	2.11240i	0.0582744	−	0.100934i
$439$	10.8711	+	18.8293i	0.518850	+	0.898674i	0.999760	+	0.0219043i	$0.00697291\pi$
$439$	10.8711	+	18.8293i	0.518850	+	0.898674i	−0.480910	+	0.876770i	$0.659694\pi$
$440$		0			0
$441$	9.38491	−	18.6460i	0.446900	−	0.887903i
$442$	25.7443			1.22453
$443$	13.5115	+	23.4027i	0.641952	+	1.11189i	0.984996	+	0.172574i	$0.0552085\pi$
$443$	13.5115	+	23.4027i	0.641952	+	1.11189i	−0.343044	+	0.939319i	$0.611458\pi$
$444$	−0.971155	+	1.68209i	−0.0460890	+	0.0798285i
$445$	18.2522	−	31.6138i	0.865239	−	1.49864i
$446$	3.07354	+	5.32352i	0.145536	+	0.252076i
$447$	−0.711849			−0.0336693
$448$	−5.32292	+	9.86157i	−0.251484	+	0.465916i
$449$	−8.05030			−0.379917			−0.189959	−	0.981792i	$-0.560835\pi$
$449$	−8.05030			−0.379917			−0.189959	+	0.981792i	$0.560835\pi$
$450$	1.36840	+	2.37014i	0.0645070	+	0.111729i
$451$		0			0
$452$	2.38664	−	4.13378i	0.112258	−	0.194437i
$453$	0.962049	+	1.66632i	0.0452010	+	0.0782904i
$454$	−8.79880			−0.412948
$455$	14.3844	−	0.412210i	0.674353	−	0.0193247i
$456$	−0.510417			−0.0239025
$457$	−0.699411	−	1.21142i	−0.0327171	−	0.0566676i	0.849203	−	0.528066i	$-0.177083\pi$
$457$	−0.699411	−	1.21142i	−0.0327171	−	0.0566676i	−0.881920	+	0.471399i	$0.843749\pi$
$458$	0.483139	−	0.836821i	0.0225756	−	0.0391021i
$459$	−2.35031	+	4.07085i	−0.109703	+	0.190011i
$460$	5.20126	+	9.00885i	0.242510	+	0.420040i
$461$	19.9578			0.929528			0.464764	−	0.885435i	$-0.346139\pi$
$461$	19.9578			0.929528			0.464764	+	0.885435i	$0.346139\pi$
$462$		0			0
$463$	6.11640			0.284253			0.142127	−	0.989848i	$-0.454606\pi$
$463$	6.11640			0.284253			0.142127	+	0.989848i	$0.454606\pi$
$464$	−4.88859	−	8.46728i	−0.226947	−	0.393084i
$465$	−1.10310	+	1.91062i	−0.0511548	+	0.0886028i
$466$	−19.6263	+	33.9937i	−0.909170	+	1.57473i
$467$	−7.52100	−	13.0268i	−0.348030	−	0.602806i	0.637869	−	0.770145i	$-0.279816\pi$
$467$	−7.52100	−	13.0268i	−0.348030	−	0.602806i	−0.985900	+	0.167338i	$0.946483\pi$
$468$	−10.8464			−0.501375
$469$	−20.4924	−	33.2560i	−0.946251	−	1.53562i
$470$	19.1598			0.883777
$471$	−0.968022	−	1.67666i	−0.0446041	−	0.0772566i
$472$	−0.963159	+	1.66824i	−0.0443330	+	0.0767869i
$473$		0			0
$474$	0.972394	+	1.68424i	0.0446635	+	0.0773595i
$475$	−2.26257			−0.103814
$476$	−24.3175	+	0.696859i	−1.11459	+	0.0319405i
$477$	11.8200			0.541199
$478$	−0.545867	−	0.945469i	−0.0249674	−	0.0432448i
$479$	15.9669	−	27.6555i	0.729546	−	1.26361i	−0.227530	−	0.973771i	$-0.573065\pi$
$479$	15.9669	−	27.6555i	0.729546	−	1.26361i	0.957075	−	0.289839i	$-0.0936018\pi$
$480$	1.12842	−	1.95447i	0.0515049	−	0.0892091i
$481$	10.7570	+	18.6316i	0.490475	+	0.849528i
$482$	−23.0353			−1.04923
$483$	−0.476976	+	0.883676i	−0.0217032	+	0.0402087i
$484$		0			0
$485$	17.3706	+	30.0868i	0.788759	+	1.36617i
$486$	3.38531	−	5.86353i	0.153561	−	0.265975i
$487$	6.46614	−	11.1997i	0.293009	−	0.507506i	−0.681511	−	0.731808i	$-0.738677\pi$
$487$	6.46614	−	11.1997i	0.293009	−	0.507506i	0.974520	+	0.224302i	$0.0720101\pi$
$488$	3.61693	+	6.26470i	0.163731	+	0.283590i
$489$	0.0626716			0.00283411
$490$	−30.9115	+	1.77309i	−1.39644	+	0.0801002i
$491$	18.4054			0.830624			0.415312	−	0.909679i	$-0.363672\pi$
$491$	18.4054			0.830624			0.415312	+	0.909679i	$0.363672\pi$
$492$	0.232265	+	0.402295i	0.0104713	+	0.0181369i
$493$	6.13308	−	10.6228i	0.276220	−	0.478427i
$494$	10.2085	−	17.6816i	0.459301	−	0.795532i
$495$		0			0
$496$	−32.9288			−1.47854
$497$	9.75214	−	18.0674i	0.437443	−	0.810436i
$498$	0.967069			0.0433354
$499$	−20.0955	−	34.8064i	−0.899598	−	1.55815i	−0.828009	−	0.560715i	$-0.810526\pi$
$499$	−20.0955	−	34.8064i	−0.899598	−	1.55815i	−0.0715895	−	0.997434i	$-0.522807\pi$
$500$	−8.28001	+	14.3414i	−0.370293	+	0.641367i
$501$	1.50542	−	2.60746i	0.0672572	−	0.116493i
$502$	14.8847	+	25.7810i	0.664336	+	1.15066i
$503$	3.28902			0.146650			0.0733250	−	0.997308i	$-0.476639\pi$
$503$	3.28902			0.146650			0.0733250	+	0.997308i	$0.476639\pi$
$504$	−6.45959	+	0.185110i	−0.287733	+	0.00824546i
$505$	−34.5138			−1.53584
$506$		0			0
$507$	−0.509138	+	0.881853i	−0.0226116	+	0.0391645i
$508$	−3.18522	+	5.51696i	−0.141321	+	0.244775i
$509$	−6.43702	−	11.1492i	−0.285316	−	0.494181i	0.687370	−	0.726307i	$-0.258765\pi$
$509$	−6.43702	−	11.1492i	−0.285316	−	0.494181i	−0.972686	+	0.232126i	$0.925432\pi$
$510$	3.47566			0.153905
$511$	13.3934	+	21.7355i	0.592491	+	0.961520i
$512$	26.0193			1.14990
$513$	1.86395	+	3.22845i	0.0822953	+	0.142540i
$514$	24.2938	−	42.0780i	1.07155	−	1.85598i
$515$	7.95168	−	13.7727i	0.350393	−	0.606898i
$516$	1.16134	+	2.01151i	0.0511254	+	0.0885517i
$517$		0			0
$518$	−24.2835	−	39.4084i	−1.06696	−	1.73150i
$519$	2.08911			0.0917017
$520$	−2.22744	−	3.85804i	−0.0976798	−	0.169186i
$521$	−8.14791	+	14.1126i	−0.356966	+	0.618284i	−0.987452	−	0.157917i	$-0.949522\pi$
$521$	−8.14791	+	14.1126i	−0.356966	+	0.618284i	0.630486	+	0.776201i	$0.282856\pi$
$522$	−5.88340	+	10.1903i	−0.257509	+	0.446019i
$523$	2.13193	+	3.69262i	0.0932230	+	0.161467i	0.908866	−	0.417089i	$-0.136950\pi$
$523$	2.13193	+	3.69262i	0.0932230	+	0.161467i	−0.815643	+	0.578556i	$0.803616\pi$
$524$	−19.3832			−0.846757
$525$	0.172032	−	0.00492987i	0.00750811	−	0.000215157i
$526$	−14.1410			−0.616576
$527$	−20.6557	−	35.7768i	−0.899778	−	1.55846i
$528$		0			0
$529$	7.47976	−	12.9553i	0.325207	−	0.563275i
$530$	−8.76599	−	15.1831i	−0.380770	−	0.659514i
$531$	7.01348			0.304359
$532$	−9.16408	+	16.9780i	−0.397313	+	0.736088i
$533$	5.14536			0.222870
$534$	1.96979	+	3.41178i	0.0852414	+	0.147642i
$535$	20.7831	−	35.9973i	0.898531	−	1.55630i
$536$	−6.04641	+	10.4727i	−0.261165	+	0.452352i
$537$	−0.0622793	−	0.107871i	−0.00268755	−	0.00465498i
$538$	28.8393			1.24335
$539$		0			0
$540$	−2.93747			−0.126409
$541$	3.94815	+	6.83840i	0.169744	+	0.294006i	0.938330	−	0.345741i	$-0.112372\pi$
$541$	3.94815	+	6.83840i	0.169744	+	0.294006i	−0.768586	+	0.639747i	$0.779039\pi$
$542$	−12.5080	+	21.6646i	−0.537266	+	0.930573i
$543$	−0.403857	+	0.699501i	−0.0173312	+	0.0300185i
$544$	21.1299	+	36.5980i	0.905935	+	1.56913i
$545$	−2.27861			−0.0976048
$546$	−0.737664	+	1.36664i	−0.0315691	+	0.0584869i
$547$	−19.8598			−0.849144			−0.424572	−	0.905394i	$-0.639575\pi$
$547$	−19.8598			−0.849144			−0.424572	+	0.905394i	$0.639575\pi$
$548$	−8.07457	−	13.9856i	−0.344929	−	0.597434i
$549$	13.1688	−	22.8090i	0.562030	−	0.973464i
$550$		0			0
$551$	−4.86394	−	8.42458i	−0.207211	−	0.358899i
$552$	0.310870			0.0132315
$553$	−20.3475	+	0.583091i	−0.865264	+	0.0247956i
$554$	10.8235			0.459845
$555$	1.45226	+	2.51539i	0.0616451	+	0.106773i
$556$	−8.09433	+	14.0198i	−0.343276	+	0.594572i
$557$	11.4695	−	19.8657i	0.485977	−	0.841737i	−0.513893	−	0.857854i	$-0.671797\pi$
$557$	11.4695	−	19.8657i	0.485977	−	0.841737i	0.999870	+	0.0161172i	$0.00513048\pi$
$558$	19.8148	+	34.3203i	0.838828	+	1.45289i
$559$	25.7272			1.08814
$560$	15.2121	+	24.6869i	0.642828	+	1.04321i
$561$		0			0
$562$	17.4354	+	30.1989i	0.735466	+	1.27386i
$563$	6.74745	−	11.6869i	0.284371	−	0.492545i	−0.688085	−	0.725630i	$-0.741549\pi$
$563$	6.74745	−	11.6869i	0.284371	−	0.492545i	0.972456	+	0.233084i	$0.0748819\pi$
$564$	−0.454068	+	0.786469i	−0.0191197	+	0.0331163i
$565$	−3.56898	−	6.18165i	−0.150148	−	0.260064i
$566$	14.2544			0.599157
$567$	12.2683	+	19.9096i	0.515222	+	0.836125i
$568$	−6.35598			−0.266691
$569$	−3.83250	−	6.63809i	−0.160667	−	0.278283i	0.774441	−	0.632646i	$-0.218031\pi$
$569$	−3.83250	−	6.63809i	−0.160667	−	0.278283i	−0.935108	+	0.354363i	$0.884698\pi$
$570$	1.37821	−	2.38713i	0.0577270	−	0.0999860i
$571$	−4.90915	+	8.50289i	−0.205441	+	0.355835i	−0.950273	−	0.311417i	$-0.899196\pi$
$571$	−4.90915	+	8.50289i	−0.205441	+	0.355835i	0.744832	+	0.667252i	$0.232530\pi$
$572$		0			0
$573$	1.20763			0.0504494
$574$	−11.0662	+	0.317120i	−0.461895	+	0.0132363i
$575$	1.37802			0.0574676
$576$	−6.31551	−	10.9388i	−0.263146	−	0.455782i
$577$	−16.9945	+	29.4353i	−0.707488	+	1.22541i	0.258298	+	0.966065i	$0.416839\pi$
$577$	−16.9945	+	29.4353i	−0.707488	+	1.22541i	−0.965786	+	0.259341i	$0.916495\pi$
$578$	−16.4894	+	28.5604i	−0.685867	+	1.18796i
$579$	−0.0621145	−	0.107586i	−0.00258139	−	0.00447110i
$580$	7.66527			0.318283
$581$	−4.80792	+	8.90746i	−0.199466	+	0.369544i
$582$	−3.74930			−0.155414
$583$		0			0
$584$	3.95182	−	6.84475i	0.163527	−	0.283238i
$585$	−8.10984	+	14.0467i	−0.335301	+	0.580758i
$586$	9.30940	+	16.1243i	0.384568	+	0.666091i
$587$	18.0573			0.745304			0.372652	−	0.927971i	$-0.378448\pi$
$587$	18.0573			0.745304			0.372652	+	0.927971i	$0.378448\pi$
$588$	0.659788	−	1.31087i	0.0272092	−	0.0540593i
$589$	−32.7627			−1.34996
$590$	−5.20138	−	9.00905i	−0.214137	−	0.370897i
$591$	−1.19241	+	2.06532i	−0.0490493	+	0.0849558i
$592$	−21.6759	+	37.5438i	−0.890875	+	1.54304i
$593$	−3.68463	−	6.38197i	−0.151310	−	0.262076i	0.780399	−	0.625281i	$-0.215016\pi$
$593$	−3.68463	−	6.38197i	−0.151310	−	0.262076i	−0.931709	+	0.363205i	$0.881682\pi$
$594$		0			0
$595$	−17.2797	+	32.0135i	−0.708399	+	1.31243i
$596$	8.32979			0.341201
$597$	0.153140	+	0.265245i	0.00626758	+	0.0108558i
$598$	−6.21748	+	10.7690i	−0.254252	+	0.440377i
$599$	−6.67462	+	11.5608i	−0.272718	+	0.472361i	−0.969557	−	0.244867i	$-0.921256\pi$
$599$	−6.67462	+	11.5608i	−0.272718	+	0.472361i	0.696839	+	0.717228i	$0.254589\pi$
$600$	−0.0266393	−	0.0461407i	−0.00108755	−	0.00188369i
$601$	14.5167			0.592149			0.296075	−	0.955165i	$-0.404322\pi$
$601$	14.5167			0.592149			0.296075	+	0.955165i	$0.404322\pi$
$602$	−55.3319	+	1.58563i	−2.25516	+	0.0646253i
$603$	44.0285			1.79298
$604$	−11.2575	−	19.4986i	−0.458063	−	0.793388i
$605$		0			0
$606$	1.86238	−	3.22573i	0.0756538	−	0.131036i
$607$	7.63093	+	13.2172i	0.309730	+	0.536468i	0.978303	−	0.207178i	$-0.0664280\pi$
$607$	7.63093	+	13.2172i	0.309730	+	0.536468i	−0.668573	+	0.743646i	$0.733095\pi$
$608$	33.5147			1.35920
$609$	0.388180	+	0.629956i	0.0157299	+	0.0255271i
$610$	−39.0652			−1.58171
$611$	5.02947	+	8.71129i	0.203470	+	0.352421i
$612$	13.7100	−	23.7465i	0.554195	−	0.959894i
$613$	−6.63639	+	11.4946i	−0.268041	+	0.464261i	−0.968356	−	0.249573i	$-0.919710\pi$
$613$	−6.63639	+	11.4946i	−0.268041	+	0.464261i	0.700315	+	0.713834i	$0.253043\pi$
$614$	24.3033	+	42.0946i	0.980802	+	1.69880i
$615$	0.694658			0.0280113
$616$		0			0
$617$	38.8365			1.56350			0.781748	−	0.623594i	$-0.214328\pi$
$617$	38.8365			1.56350			0.781748	+	0.623594i	$0.214328\pi$
$618$	0.858151	+	1.48636i	0.0345199	+	0.0597902i
$619$	11.9578	−	20.7115i	0.480624	−	0.832465i	−0.519129	−	0.854696i	$-0.673744\pi$
$619$	11.9578	−	20.7115i	0.480624	−	0.832465i	0.999753	+	0.0222310i	$0.00707694\pi$
$620$	12.9080	−	22.3573i	0.518399	−	0.897893i
$621$	−1.13524	−	1.96629i	−0.0455556	−	0.0789046i
$622$	1.74694			0.0700458
$623$	−41.2183	+	1.18118i	−1.65138	+	0.0473229i
$624$	1.45446			0.0582251
$625$	13.5969	+	23.5504i	0.543874	+	0.942018i
$626$	−27.9834	+	48.4687i	−1.11844	+	1.93720i
$627$		0			0
$628$	11.3274	+	19.6197i	0.452014	+	0.782911i
$629$	−54.3880			−2.16859
$630$	16.5762	−	30.7102i	0.660413	−	1.22352i
$631$	−35.1637			−1.39984			−0.699922	−	0.714219i	$-0.746782\pi$
$631$	−35.1637			−1.39984			−0.699922	+	0.714219i	$0.746782\pi$
$632$	3.15083	+	5.45739i	0.125333	+	0.217083i
$633$	−0.305126	+	0.528493i	−0.0121277	+	0.0210057i
$634$	−14.7631	+	25.5704i	−0.586316	+	1.01553i
$635$	4.76317	+	8.25005i	0.189021	+	0.327393i
$636$	0.830980			0.0329505
$637$	−8.92045	−	13.5889i	−0.353441	−	0.538412i
$638$		0			0
$639$	11.5707	+	20.0410i	0.457729	+	0.792809i
$640$	7.49320	−	12.9786i	0.296195	−	0.513024i
$641$	6.14805	−	10.6487i	0.242833	−	0.420600i	−0.718687	−	0.695334i	$-0.755257\pi$
$641$	6.14805	−	10.6487i	0.242833	−	0.420600i	0.961520	+	0.274734i	$0.0885898\pi$
$642$	2.24292	+	3.88486i	0.0885212	+	0.153323i
$643$	37.4991			1.47882			0.739409	−	0.673256i	$-0.235105\pi$
$643$	37.4991			1.47882			0.739409	+	0.673256i	$0.235105\pi$
$644$	5.58140	−	10.3405i	0.219938	−	0.407471i
$645$	3.47334			0.136763
$646$	25.8074	+	44.6997i	1.01538	+	1.75868i
$647$	−15.6537	+	27.1130i	−0.615409	+	1.06592i	0.374903	+	0.927064i	$0.377676\pi$
$647$	−15.6537	+	27.1130i	−0.615409	+	1.06592i	−0.990313	+	0.138856i	$0.955657\pi$
$648$	3.61985	−	6.26977i	0.142201	−	0.246300i
$649$		0			0
$650$	2.13117			0.0835915
$651$	2.49108	−	0.0713859i	0.0976330	−	0.00279783i
$652$	−0.733360			−0.0287206
$653$	−12.2890	−	21.2852i	−0.480907	−	0.832955i	0.518853	−	0.854863i	$-0.326359\pi$
$653$	−12.2890	−	21.2852i	−0.480907	−	0.832955i	−0.999760	+	0.0219084i	$0.993026\pi$
$654$	0.122954	−	0.212963i	0.00480790	−	0.00832753i
$655$	−14.4928	+	25.1022i	−0.566279	+	0.980824i
$656$	5.18410	+	8.97912i	0.202405	+	0.350576i
$657$	−28.7762			−1.12266
$658$	−11.3539	−	18.4256i	−0.442620	−	0.718303i
$659$	31.1674			1.21411			0.607054	−	0.794660i	$-0.292351\pi$
$659$	31.1674			1.21411			0.607054	+	0.794660i	$0.292351\pi$
$660$		0			0
$661$	−16.0378	+	27.7782i	−0.623797	+	1.08045i	0.364976	+	0.931017i	$0.381077\pi$
$661$	−16.0378	+	27.7782i	−0.623797	+	1.08045i	−0.988772	+	0.149430i	$0.952256\pi$
$662$	−14.9625	+	25.9159i	−0.581536	+	1.00725i
$663$	0.912363	+	1.58026i	0.0354332	+	0.0613722i
$664$	3.13357			0.121606
$665$	15.1354	+	24.5624i	0.586925	+	0.952488i
$666$	52.1738			2.02169
$667$	2.96239	+	5.13100i	0.114704	+	0.198673i
$668$	−17.6159	+	30.5116i	−0.681579	+	1.18053i
$669$	−0.217848	+	0.377324i	−0.00842250	+	0.0145882i
$670$	−32.6527	−	56.5561i	−1.26148	−	2.18495i
$671$		0			0
$672$	−2.54826	+	0.0730244i	−0.0983011	+	0.00281698i
$673$	26.3445			1.01551			0.507753	−	0.861503i	$-0.330476\pi$
$673$	26.3445			1.01551			0.507753	+	0.861503i	$0.330476\pi$
$674$	−14.7950	−	25.6258i	−0.569884	−	0.987067i
$675$	−0.194564	+	0.336994i	−0.00748876	+	0.0129709i
$676$	5.95774	−	10.3191i	0.229144	−	0.396889i
$677$	−20.5398	−	35.5759i	−0.789407	−	1.36729i	−0.926331	−	0.376711i	$-0.877055\pi$
$677$	−20.5398	−	35.5759i	−0.789407	−	1.36729i	0.136924	−	0.990582i	$-0.456278\pi$
$678$	0.770333			0.0295845
$679$	18.6402	−	34.5340i	0.715344	−	1.32529i
$680$	11.2621			0.431882
$681$	−0.311824	−	0.540095i	−0.0119491	−	0.0206965i
$682$		0			0
$683$	−11.2471	+	19.4806i	−0.430360	+	0.745405i	−0.996904	−	0.0786265i	$-0.974947\pi$
$683$	−11.2471	+	19.4806i	−0.430360	+	0.745405i	0.566545	+	0.824031i	$0.308280\pi$
$684$	−10.8730	−	18.8325i	−0.415738	−	0.720079i
$685$	−24.1494			−0.922701
$686$	20.0229	+	28.6761i	0.764477	+	1.09486i
$687$	0.0684886			0.00261300
$688$	25.9209	+	44.8963i	0.988225	+	1.71166i
$689$	4.60216	−	7.97117i	0.175328	−	0.303677i
$690$	−0.839402	+	1.45389i	−0.0319555	+	0.0553485i
$691$	−13.6251	−	23.5994i	−0.518325	−	0.897764i	−0.999773	−	0.0212902i	$-0.993223\pi$
$691$	−13.6251	−	23.5994i	−0.518325	−	0.897764i	0.481449	−	0.876474i	$-0.340111\pi$
$692$	−24.4460			−0.929297
$693$		0			0
$694$	−14.2064			−0.539267
$695$	12.1042	+	20.9652i	0.459140	+	0.795254i
$696$	0.114535	−	0.198381i	0.00434144	−	0.00751959i
$697$	−6.50382	+	11.2649i	−0.246350	+	0.426690i
$698$	−7.24064	−	12.5412i	−0.274062	−	0.474690i
$699$	−2.78217			−0.105231
$700$	−2.01306	+	0.0576875i	−0.0760865	+	0.00218038i
$701$	−6.70947			−0.253413			−0.126707	−	0.991940i	$-0.540441\pi$
$701$	−6.70947			−0.253413			−0.126707	+	0.991940i	$0.540441\pi$
$702$	−1.75570	−	3.04096i	−0.0662645	−	0.114774i
$703$	−21.5666	+	37.3545i	−0.813400	+	1.40885i
$704$		0			0
$705$	0.679012	+	1.17608i	0.0255731	+	0.0442939i
$706$	−13.2205			−0.497561
$707$	20.4524	+	33.1911i	0.769192	+	1.24828i
$708$	0.493069			0.0185307
$709$	−15.0500	−	26.0673i	−0.565213	−	0.978978i	−0.997030	−	0.0770168i	$-0.975460\pi$
$709$	−15.0500	−	26.0673i	−0.565213	−	0.978978i	0.431816	−	0.901962i	$-0.357873\pi$
$710$	17.1622	−	29.7258i	0.644087	−	1.11559i
$711$	11.4718	−	19.8697i	0.430225	−	0.745171i
$712$	6.38268	+	11.0551i	0.239201	+	0.414309i
$713$	19.9542			0.747289
$714$	−2.05963	−	3.34246i	−0.0770797	−	0.125088i
$715$		0			0
$716$	0.728770	+	1.26227i	0.0272354	+	0.0471731i
$717$	0.0386904	−	0.0670137i	0.00144492	−	0.00250267i
$718$	25.0755	−	43.4320i	0.935807	−	1.62087i
$719$	−11.5300	−	19.9705i	−0.429995	−	0.744773i	0.566878	−	0.823802i	$-0.308151\pi$
$719$	−11.5300	−	19.9705i	−0.429995	−	0.744773i	−0.996872	+	0.0790294i	$0.974818\pi$
$720$	−32.6836			−1.21805
$721$	−17.9569	+	0.514586i	−0.668752	+	0.0191642i
$722$	5.05311			0.188057
$723$	−0.816356	−	1.41397i	−0.0303606	−	0.0525861i
$724$	4.72579	−	8.18530i	0.175632	−	0.304204i
$725$	0.507710	−	0.879380i	0.0188559	−	0.0326594i
$726$		0			0
$727$	−52.1592			−1.93448			−0.967239	−	0.253869i	$-0.918297\pi$
$727$	−52.1592			−1.93448			−0.967239	+	0.253869i	$0.918297\pi$
$728$	−2.39024	+	4.42830i	−0.0885880	+	0.164124i
$729$	−26.0373			−0.964346
$730$	21.3411	+	36.9640i	0.789871	+	1.36810i
$731$	−32.5196	+	56.3256i	−1.20278	+	2.08328i
$732$	0.925806	−	1.60354i	0.0342188	−	0.0592686i
$733$	−22.3988	−	38.7959i	−0.827320	−	1.43296i	−0.900133	−	0.435615i	$-0.856531\pi$
$733$	−22.3988	−	38.7959i	−0.827320	−	1.43296i	0.0728132	−	0.997346i	$-0.476802\pi$
$734$	−6.45320			−0.238192
$735$	−1.20432	−	1.83459i	−0.0444220	−	0.0676701i
$736$	−20.4122			−0.752403
$737$		0			0
$738$	6.23904	−	10.8063i	0.229662	−	0.397787i
$739$	3.35660	−	5.81379i	0.123474	−	0.213864i	−0.797661	−	0.603106i	$-0.793930\pi$
$739$	3.35660	−	5.81379i	0.123474	−	0.213864i	0.921136	+	0.389242i	$0.127263\pi$
$740$	−16.9938	−	29.4342i	−0.624706	−	1.08202i
$741$	1.44713			0.0531615
$742$	−9.40666	+	17.4274i	−0.345329	+	0.639779i
$743$	21.8223			0.800581			0.400291	−	0.916388i	$-0.368909\pi$
$743$	21.8223			0.800581			0.400291	+	0.916388i	$0.368909\pi$
$744$	−0.385745	−	0.668130i	−0.0141421	−	0.0244948i
$745$	6.22817	−	10.7875i	0.228183	−	0.395224i
$746$	11.8529	−	20.5298i	0.433965	−	0.751650i
$747$	−5.70447	−	9.88044i	−0.208716	−	0.361506i
$748$		0			0
$749$	−46.9336	+	1.34496i	−1.71492	+	0.0491437i
$750$	−2.67253			−0.0975870
$751$	7.99460	+	13.8470i	0.291727	+	0.505286i	0.974218	−	0.225608i	$-0.0724368\pi$
$751$	7.99460	+	13.8470i	0.291727	+	0.505286i	−0.682491	+	0.730894i	$0.739103\pi$
$752$	−10.1347	+	17.5538i	−0.369573	+	0.640120i
$753$	−1.05501	+	1.82733i	−0.0384466	+	0.0665915i
$754$	4.58146	+	7.93532i	0.166847	+	0.288987i
$755$	−33.6690			−1.22534
$756$	1.74071	+	2.82490i	0.0633089	+	0.102741i
$757$	−5.92288			−0.215271			−0.107635	−	0.994190i	$-0.534328\pi$
$757$	−5.92288			−0.215271			−0.107635	+	0.994190i	$0.534328\pi$
$758$	16.1856	+	28.0343i	0.587889	+	1.01825i
$759$		0			0
$760$	4.46579	−	7.73498i	0.161991	−	0.280577i
$761$	21.7607	+	37.6907i	0.788825	+	1.36629i	0.926687	+	0.375834i	$0.122644\pi$
$761$	21.7607	+	37.6907i	0.788825	+	1.36629i	−0.137861	+	0.990452i	$0.544023\pi$
$762$	−1.02809			−0.0372437
$763$	1.35027	+	2.19128i	0.0488832	+	0.0793298i
$764$	−14.1312			−0.511250
$765$	−20.5020	−	35.5104i	−0.741250	−	1.28388i
$766$	−31.8693	+	55.1992i	−1.15148	+	1.99443i
$767$	2.73073	−	4.72977i	0.0986010	−	0.170782i
$768$	1.37562	+	2.38264i	0.0496383	+	0.0859761i
$769$	−3.83360			−0.138243			−0.0691215	−	0.997608i	$-0.522020\pi$
$769$	−3.83360			−0.138243			−0.0691215	+	0.997608i	$0.522020\pi$
$770$		0			0
$771$	3.44382			0.124026
$772$	0.726841	+	1.25893i	0.0261596	+	0.0453098i
$773$	−4.40968	+	7.63779i	−0.158605	+	0.274712i	−0.934366	−	0.356315i	$-0.884033\pi$
$773$	−4.40968	+	7.63779i	−0.158605	+	0.274712i	0.775761	+	0.631027i	$0.217366\pi$
$774$	31.1957	−	54.0325i	1.12131	−	1.94216i
$775$	−1.70993	−	2.96168i	−0.0614224	−	0.106387i
$776$	−12.1488			−0.436116
$777$	1.55840	−	2.88720i	0.0559074	−	0.103578i
$778$	−7.04624			−0.252620
$779$	5.15796	+	8.93384i	0.184803	+	0.320088i
$780$	−0.570147	+	0.987523i	−0.0204145	+	0.0353590i
$781$		0			0
$782$	−15.7180	−	27.2244i	−0.562075	−	0.973542i
$783$	−1.67304			−0.0597896
$784$	14.7263	−	29.2582i	0.525939	−	1.04494i
$785$	33.8780			1.20916
$786$	−1.56407	−	2.70905i	−0.0557885	−	0.0966285i
$787$	−3.44246	+	5.96252i	−0.122711	+	0.212541i	−0.920836	−	0.389951i	$-0.872492\pi$
$787$	−3.44246	+	5.96252i	−0.122711	+	0.212541i	0.798125	+	0.602492i	$0.205825\pi$
$788$	13.9532	−	24.1676i	0.497061	−	0.860935i
$789$	−0.501147	−	0.868013i	−0.0178413	−	0.0309021i
$790$	−34.0310			−1.21077
$791$	−3.82982	+	7.09536i	−0.136173	+	0.252282i
$792$		0			0
$793$	−10.2547	−	17.7616i	−0.364153	−	0.630732i
$794$	12.2984	−	21.3014i	0.436453	−	0.755958i
$795$	0.621322	−	1.07616i	0.0220360	−	0.0381675i
$796$	−1.79198	−	3.10380i	−0.0635151	−	0.110011i
$797$	8.85703			0.313732			0.156866	−	0.987620i	$-0.449861\pi$
$797$	8.85703			0.313732			0.156866	+	0.987620i	$0.449861\pi$
$798$	−3.11236	+	0.0891898i	−0.110176	+	0.00315728i
$799$	−25.4293			−0.899625
$800$	1.74918	+	3.02966i	0.0618428	+	0.107115i
$801$	23.2385	−	40.2503i	0.821094	−	1.42218i
$802$	−26.6161	+	46.1005i	−0.939848	+	1.62786i
$803$		0			0
$804$	3.09534			0.109164
$805$	−9.21822	−	14.9597i	−0.324900	−	0.527262i
$806$	30.8600			1.08700
$807$	1.02205	+	1.77024i	0.0359777	+	0.0623152i
$808$	6.03461	−	10.4523i	0.212297	−	0.367709i
$809$	8.72770	−	15.1168i	0.306850	−	0.531479i	−0.670822	−	0.741619i	$-0.734058\pi$
$809$	8.72770	−	15.1168i	0.306850	−	0.531479i	0.977671	+	0.210140i	$0.0673918\pi$
$810$	19.5484	+	33.8589i	0.686862	+	1.18968i
$811$	2.12038			0.0744566			0.0372283	−	0.999307i	$-0.488147\pi$
$811$	2.12038			0.0744566			0.0372283	+	0.999307i	$0.488147\pi$
$812$	−4.54234	−	7.37151i	−0.159405	−	0.258689i
$813$	−1.77311			−0.0621856
$814$		0			0
$815$	−0.548333	+	0.949740i	−0.0192073	+	0.0332679i
$816$	−1.83846	+	3.18431i	−0.0643591	+	0.111473i
$817$	25.7902	+	44.6699i	0.902284	+	1.56280i
$818$	−73.2067			−2.55961
$819$	18.3141	−	0.524821i	0.639947	−	0.0183387i
$820$	−8.12863			−0.283864
$821$	3.19448	+	5.53301i	0.111488	+	0.193103i	0.916371	−	0.400331i	$-0.131105\pi$
$821$	3.19448	+	5.53301i	0.111488	+	0.193103i	−0.804882	+	0.593435i	$0.797772\pi$
$822$	1.30311	−	2.25705i	0.0454512	−	0.0787238i
$823$	3.31229	−	5.73706i	0.115459	−	0.199981i	−0.802504	−	0.596647i	$-0.796499\pi$
$823$	3.31229	−	5.73706i	0.115459	−	0.199981i	0.917963	+	0.396665i	$0.129833\pi$
$824$	2.78065	+	4.81622i	0.0968684	+	0.167781i
$825$		0			0
$826$	−5.58153	+	10.3407i	−0.194206	+	0.359799i
$827$	−5.59803			−0.194663			−0.0973314	−	0.995252i	$-0.531031\pi$
$827$	−5.59803			−0.194663			−0.0973314	+	0.995252i	$0.531031\pi$
$828$	6.62219	+	11.4700i	0.230137	+	0.398609i
$829$	−7.34314	+	12.7187i	−0.255038	+	0.441738i	−0.964906	−	0.262597i	$-0.915421\pi$
$829$	−7.34314	+	12.7187i	−0.255038	+	0.441738i	0.709868	+	0.704335i	$0.248755\pi$
$830$	−8.46118	+	14.6552i	−0.293692	+	0.508689i
$831$	0.383577	+	0.664374i	0.0133061	+	0.0230469i
$832$	−9.83589			−0.340998
$833$	41.0264	−	2.35329i	1.42148	−	0.0815366i
$834$	−2.61260			−0.0904668
$835$	26.3427	+	45.6270i	0.911628	+	1.57899i
$836$		0			0
$837$	−2.81734	+	4.87977i	−0.0973814	+	0.168670i
$838$	2.50903	+	4.34577i	0.0866730	+	0.150122i
$839$	49.1555			1.69703			0.848517	−	0.529168i	$-0.177496\pi$
$839$	49.1555			1.69703			0.848517	+	0.529168i	$0.177496\pi$
$840$	−0.322698	+	0.597851i	−0.0111341	+	0.0206278i
$841$	−24.6342			−0.849456
$842$	23.3250	+	40.4001i	0.803832	+	1.39228i
$843$	−1.23580	+	2.14046i	−0.0425631	+	0.0737214i
$844$	3.57047	−	6.18423i	0.122901	−	0.212870i
$845$	−8.90920	−	15.4312i	−0.306486	−	0.530849i
$846$	24.3941			0.838686
$847$		0			0
$848$	18.5472			0.636915
$849$	0.505166	+	0.874974i	0.0173373	+	0.0300290i
$850$	−2.69384	+	4.66587i	−0.0923980	+	0.160038i
$851$	13.1352	−	22.7508i	0.450268	−	0.779887i
$852$	0.813454	+	1.40894i	0.0278685	+	0.0482696i
$853$	4.13154			0.141461			0.0707307	−	0.997495i	$-0.477467\pi$
$853$	4.13154			0.141461			0.0707307	+	0.997495i	$0.477467\pi$
$854$	23.1495	+	37.5681i	0.792161	+	1.28555i
$855$	−32.5188			−1.11212
$856$	7.26770	+	12.5880i	0.248405	+	0.430250i
$857$	3.56179	−	6.16919i	0.121668	−	0.210736i	−0.798757	−	0.601653i	$-0.794509\pi$
$857$	3.56179	−	6.16919i	0.121668	−	0.210736i	0.920426	+	0.390918i	$0.127842\pi$
$858$		0			0
$859$	3.31319	+	5.73861i	0.113045	+	0.195799i	0.916996	−	0.398896i	$-0.130606\pi$
$859$	3.31319	+	5.73861i	0.113045	+	0.195799i	−0.803952	+	0.594694i	$0.797273\pi$
$860$	−40.6438			−1.38594
$861$	−0.411645	−	0.668036i	−0.0140288	−	0.0227666i
$862$	19.6685			0.669913
$863$	−17.9669	−	31.1196i	−0.611601	−	1.05932i	−0.990971	−	0.134079i	$-0.957192\pi$
$863$	−17.9669	−	31.1196i	−0.611601	−	1.05932i	0.379370	−	0.925245i	$-0.376141\pi$
$864$	2.88200	−	4.99178i	0.0980478	−	0.169824i
$865$	−18.2782	+	31.6588i	−0.621479	+	1.07643i
$866$	−18.8163	−	32.5907i	−0.639402	−	1.10748i
$867$	−2.33749			−0.0793854
$868$	−29.1497	+	0.835331i	−0.989404	+	0.0283530i
$869$		0			0
$870$	0.618528	+	1.07132i	0.0209701	+	0.0363212i
$871$	17.1427	−	29.6920i	0.580858	−	1.00608i
$872$	0.398407	−	0.690061i	0.0134918	−	0.0233684i
$873$	22.1161	+	38.3062i	0.748516	+	1.29647i
$874$	−24.9308			−0.843298
$875$	13.2869	−	24.6161i	0.449178	−	0.832175i
$876$	−2.02305			−0.0683526
$877$	1.94150	+	3.36277i	0.0655597	+	0.113553i	0.896942	−	0.442148i	$-0.145783\pi$
$877$	1.94150	+	3.36277i	0.0655597	+	0.113553i	−0.831382	+	0.555701i	$0.812450\pi$
$878$	20.5297	−	35.5584i	0.692842	−	1.20004i
$879$	−0.659838	+	1.14287i	−0.0222558	+	0.0385482i
$880$		0			0
$881$	53.8472			1.81416			0.907079	−	0.420961i	$-0.138307\pi$
$881$	53.8472			1.81416			0.907079	+	0.420961i	$0.138307\pi$
$882$	−39.3561	+	2.25748i	−1.32519	+	0.0760134i
$883$	34.8518			1.17286			0.586429	−	0.810001i	$-0.300533\pi$
$883$	34.8518			1.17286			0.586429	+	0.810001i	$0.300533\pi$
$884$	−10.6761	−	18.4916i	−0.359077	−	0.621940i
$885$	0.368667	−	0.638550i	0.0123926	−	0.0214646i
$886$	25.5160	−	44.1950i	0.857226	−	1.48476i
$887$	13.4514	+	23.2985i	0.451653	+	0.782286i	0.998489	−	0.0549535i	$-0.0175011\pi$
$887$	13.4514	+	23.2985i	0.451653	+	0.782286i	−0.546836	+	0.837240i	$0.684168\pi$
$888$	−1.01569			−0.0340844
$889$	5.11129	−	9.46950i	0.171427	−	0.317597i
$890$	−68.9373			−2.31078
$891$		0			0
$892$	2.54918	−	4.41531i	0.0853529	−	0.147836i
$893$	−10.0836	+	17.4652i	−0.337434	+	0.584452i
$894$	0.672149	+	1.16420i	0.0224800	+	0.0389365i
$895$	2.17960			0.0728560
$896$	−16.9216	+	0.484916i	−0.565310	+	0.0161999i
$897$	−0.881375			−0.0294282
$898$	7.60134	+	13.1659i	0.253660	+	0.439352i
$899$	7.35178	−	12.7337i	0.245196	−	0.424691i
$900$	1.13495	−	1.96579i	0.0378316	−	0.0655262i
$901$	11.6344	+	20.1514i	0.387599	+	0.671340i
$902$		0			0
$903$	−2.05826	−	3.34023i	−0.0684945	−	0.111156i
$904$	2.49609			0.0830188
$905$	−7.06693	−	12.2403i	−0.234913	−	0.406881i
$906$	1.81679	−	3.14678i	0.0603589	−	0.104545i
$907$	24.2637	−	42.0260i	0.805663	−	1.39545i	−0.110179	−	0.993912i	$-0.535143\pi$
$907$	24.2637	−	42.0260i	0.805663	−	1.39545i	0.915843	−	0.401538i	$-0.131524\pi$
$908$	3.64885	+	6.31999i	0.121091	+	0.209736i
$909$	−43.9425			−1.45748
$910$	−14.2564	−	23.1359i	−0.472594	−	0.766947i
$911$	11.3831			0.377139			0.188570	−	0.982060i	$-0.439615\pi$
$911$	11.3831			0.377139			0.188570	+	0.982060i	$0.439615\pi$
$912$	1.45802	+	2.52537i	0.0482800	+	0.0836233i
$913$		0			0
$914$	−1.32081	+	2.28771i	−0.0436885	+	0.0756707i
$915$	−1.38445	−	2.39793i	−0.0457684	−	0.0792732i
$916$	−0.801428			−0.0264799
$917$	32.7284	−	0.937886i	1.08079	−	0.0309717i
$918$	8.87693			0.292982
$919$	−16.8169	−	29.1277i	−0.554738	−	0.960834i	−0.997924	−	0.0644041i	$-0.979485\pi$
$919$	−16.8169	−	29.1277i	−0.554738	−	0.960834i	0.443186	−	0.896430i	$-0.353848\pi$
$920$	−2.71990	+	4.71100i	−0.0896723	+	0.155317i
$921$	−1.72259	+	2.98361i	−0.0567612	+	0.0983133i
$922$	−18.8448	−	32.6401i	−0.620619	−	1.07494i
$923$	18.0204			0.593148
$924$		0			0
$925$	−4.50236			−0.148037
$926$	−5.77529	−	10.0031i	−0.189788	−	0.328722i
$927$	10.1240	−	17.5353i	0.332515	−	0.575934i
$928$	−7.52053	+	13.0259i	−0.246874	+	0.427598i
$929$	11.7453	+	20.3435i	0.385351	+	0.667448i	0.991818	−	0.127661i	$-0.0407469\pi$
$929$	11.7453	+	20.3435i	0.385351	+	0.667448i	−0.606467	+	0.795109i	$0.707414\pi$
$930$	4.16631			0.136619
$931$	14.6520	−	29.1107i	0.480201	−	0.954064i
$932$	32.5560			1.06641
$933$	0.0619103	+	0.107232i	0.00202685	+	0.00351061i
$934$	−14.2031	+	24.6005i	−0.464740	+	0.804953i
$935$		0			0
$936$	−2.83595	−	4.91202i	−0.0926961	−	0.160554i
$937$	−10.1132			−0.330383			−0.165192	−	0.986261i	$-0.552824\pi$
$937$	−10.1132			−0.330383			−0.165192	+	0.986261i	$0.552824\pi$
$938$	−35.0391	+	64.9157i	−1.14407	+	2.11957i
$939$	−3.96686			−0.129454
$940$	−7.94555	−	13.7621i	−0.259155	−	0.448870i
$941$	−15.8667	+	27.4820i	−0.517240	+	0.895886i	0.482559	+	0.875863i	$0.339707\pi$
$941$	−15.8667	+	27.4820i	−0.517240	+	0.895886i	−0.999800	+	0.0200229i	$0.993626\pi$
$942$	−1.82807	+	3.16631i	−0.0595618	+	0.103164i
$943$	−3.14146	−	5.44117i	−0.102300	−	0.177189i
$944$	11.0052			0.358188
$945$	4.95991	−	0.142134i	0.161346	−	0.00462363i
$946$		0			0
$947$	−17.5526	−	30.4019i	−0.570382	−	0.987931i	−0.996527	−	0.0832755i	$-0.973462\pi$
$947$	−17.5526	−	30.4019i	−0.570382	−	0.987931i	0.426145	−	0.904655i	$-0.359871\pi$
$948$	0.806500	−	1.39690i	0.0261939	−	0.0453692i
$949$	−11.2041	+	19.4061i	−0.363702	+	0.629950i
$950$	2.13639	+	3.70034i	0.0693137	+	0.120055i
$951$	−2.09277			−0.0678629
$952$	−6.67377	−	10.8305i	−0.216298	−	0.351018i
$953$	37.2800			1.20762			0.603809	−	0.797129i	$-0.293649\pi$
$953$	37.2800			1.20762			0.603809	+	0.797129i	$0.293649\pi$
$954$	−11.1608	−	19.3310i	−0.361343	−	0.625865i
$955$	−10.5659	+	18.3007i	−0.341905	+	0.592196i
$956$	−0.452740	+	0.784169i	−0.0146427	+	0.0253618i
$957$		0			0
$958$	−60.3057			−1.94839
$959$	14.3106	+	23.2239i	0.462114	+	0.749939i
$960$	−1.32791			−0.0428582
$961$	−9.26023	−	16.0392i	−0.298717	−	0.517393i
$962$	20.3141	−	35.1851i	0.654953	−	1.13441i
$963$	26.4608	−	45.8314i	0.852687	−	1.47690i
$964$	9.55269	+	16.5458i	0.307672	+	0.532903i
$965$	2.17383			0.0699782
$966$	1.89559	−	0.0543212i	0.0609895	−	0.00174775i
$967$	26.9529			0.866746			0.433373	−	0.901215i	$-0.357323\pi$
$967$	26.9529			0.866746			0.433373	+	0.901215i	$0.357323\pi$
$968$		0			0
$969$	−1.82919	+	3.16826i	−0.0587622	+	0.101779i
$970$	32.8037	−	56.8177i	1.05326	−	1.82431i
$971$	−15.5830	−	26.9906i	−0.500083	−	0.866168i	−1.00000		9.53589e-5i	$-0.999970\pi$
$971$	−15.5830	−	26.9906i	−0.500083	−	0.866168i	0.499917	−	0.866073i	$-0.333364\pi$
$972$	−5.61553			−0.180118
$973$	12.9889	−	24.0640i	0.416405	−	0.771458i
$974$	−24.4221			−0.782535
$975$	0.0755275	+	0.130817i	0.00241881	+	0.00418951i
$976$	20.6637	−	35.7906i	0.661430	−	1.14563i
$977$	17.7170	−	30.6868i	0.566818	−	0.981757i	−0.430060	−	0.902800i	$-0.641508\pi$
$977$	17.7170	−	30.6868i	0.566818	−	0.981757i	0.996878	−	0.0789569i	$-0.0251589\pi$
$978$	−0.0591765	−	0.102497i	−0.00189225	−	0.00327748i
$979$		0			0
$980$	14.0925	+	21.4678i	0.450169	+	0.685762i
$981$	−2.90110			−0.0926249
$982$	−17.3789	−	30.1012i	−0.554584	−	0.960567i
$983$	27.7848	−	48.1248i	0.886199	−	1.53494i	0.0418660	−	0.999123i	$-0.486670\pi$
$983$	27.7848	−	48.1248i	0.886199	−	1.53494i	0.844333	−	0.535819i	$-0.179997\pi$
$984$	−0.121459	+	0.210372i	−0.00387196	+	0.00670643i
$985$	−20.8655	−	36.1402i	−0.664831	−	1.15152i
$986$	−23.1642			−0.737697
$987$	0.728638	−	1.34992i	0.0231928	−	0.0429685i
$988$	−16.9337			−0.538734
$989$	−15.7075	−	27.2063i	−0.499471	−	0.865109i
$990$		0			0
$991$	−2.94716	+	5.10464i	−0.0936197	+	0.162154i	−0.909032	−	0.416727i	$-0.863177\pi$
$991$	−2.94716	+	5.10464i	−0.0936197	+	0.162154i	0.815412	+	0.578881i	$0.196510\pi$
$992$	25.3286	+	43.8704i	0.804183	+	1.39289i
$993$	−2.12105			−0.0673096
$994$	−38.7568	+	1.11064i	−1.22929	+	0.0352273i
$995$	−5.35945			−0.169906
$996$	−0.401042	−	0.694625i	−0.0127075	−	0.0220100i
$997$	8.42497	−	14.5925i	0.266821	−	0.462148i	−0.701218	−	0.712947i	$-0.747360\pi$
$997$	8.42497	−	14.5925i	0.266821	−	0.462148i	0.968039	+	0.250799i	$0.0806933\pi$
$998$	−37.9496	+	65.7306i	−1.20127	+	2.08066i
$999$	3.70912	+	6.42438i	0.117351	+	0.203258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.e.f.606.2	yes	14
7.2	even	3	inner	847.2.e.f.485.2	✓	14
7.3	odd	6		5929.2.a.bo.1.6		7
7.4	even	3		5929.2.a.bp.1.6		7
11.2	odd	10		847.2.n.l.81.6		56
11.3	even	5		847.2.n.m.130.2		56
11.4	even	5		847.2.n.m.753.6		56
11.5	even	5		847.2.n.m.487.6		56
11.6	odd	10		847.2.n.l.487.2		56
11.7	odd	10		847.2.n.l.753.2		56
11.8	odd	10		847.2.n.l.130.6		56
11.9	even	5		847.2.n.m.81.2		56
11.10	odd	2		847.2.e.g.606.6	yes	14
77.2	odd	30		847.2.n.l.807.2		56
77.9	even	15		847.2.n.m.807.6		56
77.10	even	6		5929.2.a.bn.1.2		7
77.16	even	15		847.2.n.m.366.2		56
77.30	odd	30		847.2.n.l.9.2		56
77.32	odd	6		5929.2.a.bq.1.2		7
77.37	even	15		847.2.n.m.632.2		56
77.51	odd	30		847.2.n.l.632.6		56
77.58	even	15		847.2.n.m.9.6		56
77.65	odd	6		847.2.e.g.485.6	yes	14
77.72	odd	30		847.2.n.l.366.6		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.e.f.485.2	✓	14	7.2	even	3	inner
847.2.e.f.606.2	yes	14	1.1	even	1	trivial
847.2.e.g.485.6	yes	14	77.65	odd	6
847.2.e.g.606.6	yes	14	11.10	odd	2
847.2.n.l.9.2		56	77.30	odd	30
847.2.n.l.81.6		56	11.2	odd	10
847.2.n.l.130.6		56	11.8	odd	10
847.2.n.l.366.6		56	77.72	odd	30
847.2.n.l.487.2		56	11.6	odd	10
847.2.n.l.632.6		56	77.51	odd	30
847.2.n.l.753.2		56	11.7	odd	10
847.2.n.l.807.2		56	77.2	odd	30
847.2.n.m.9.6		56	77.58	even	15
847.2.n.m.81.2		56	11.9	even	5
847.2.n.m.130.2		56	11.3	even	5
847.2.n.m.366.2		56	77.16	even	15
847.2.n.m.487.6		56	11.5	even	5
847.2.n.m.632.2		56	77.37	even	15
847.2.n.m.753.6		56	11.4	even	5
847.2.n.m.807.6		56	77.9	even	15
5929.2.a.bn.1.2		7	77.10	even	6
5929.2.a.bo.1.6		7	7.3	odd	6
5929.2.a.bp.1.6		7	7.4	even	3
5929.2.a.bq.1.2		7	77.32	odd	6

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.944230 - 1.63545i) q^{2} +(0.0669258 - 0.115919i) q^{3} +(-0.783142 + 1.35644i) q^{4} +(1.17111 + 2.02842i) q^{5} -0.252774 q^{6} +(1.25670 - 2.32824i) q^{7} -0.819057 q^{8} +(1.49104 + 2.58256i) q^{9} +O(q^{10})\)	\(q+(-0.944230 - 1.63545i) q^{2} +(0.0669258 - 0.115919i) q^{3} +(-0.783142 + 1.35644i) q^{4} +(1.17111 + 2.02842i) q^{5} -0.252774 q^{6} +(1.25670 - 2.32824i) q^{7} -0.819057 q^{8} +(1.49104 + 2.58256i) q^{9} +(2.21159 - 3.83059i) q^{10} +(0.104825 + 0.181562i) q^{12} +2.32218 q^{13} +(-4.99435 + 0.143121i) q^{14} +0.313510 q^{15} +(2.33966 + 4.05241i) q^{16} +(-2.93527 + 5.08404i) q^{17} +(2.81577 - 4.87706i) q^{18} +(2.32786 + 4.03198i) q^{19} -3.66857 q^{20} +(-0.185782 - 0.301495i) q^{21} +(-1.41779 - 2.45568i) q^{23} +(-0.0548161 + 0.0949442i) q^{24} +(-0.242988 + 0.420868i) q^{25} +(-2.19267 - 3.79782i) q^{26} +0.800712 q^{27} +(2.17395 + 3.52798i) q^{28} -2.08944 q^{29} +(-0.296025 - 0.512731i) q^{30} +(-3.51854 + 6.09429i) q^{31} +(3.59930 - 6.23417i) q^{32} +11.0863 q^{34} +(6.19438 - 0.177510i) q^{35} -4.67079 q^{36} +(4.63228 + 8.02334i) q^{37} +(4.39608 - 7.61423i) q^{38} +(0.155414 - 0.269184i) q^{39} +(-0.959204 - 1.66139i) q^{40} +2.21575 q^{41} +(-0.317660 + 0.588518i) q^{42} +11.0789 q^{43} +(-3.49234 + 6.04891i) q^{45} +(-2.67744 + 4.63746i) q^{46} +(2.16584 + 3.75135i) q^{47} +0.626335 q^{48} +(-3.84141 - 5.85180i) q^{49} +0.917748 q^{50} +(0.392891 + 0.680507i) q^{51} +(-1.81859 + 3.14990i) q^{52} +(1.98183 - 3.43263i) q^{53} +(-0.756057 - 1.30953i) q^{54} +(-1.02931 + 1.90696i) q^{56} +0.623177 q^{57} +(1.97291 + 3.41719i) q^{58} +(1.17594 - 2.03678i) q^{59} +(-0.245522 + 0.425257i) q^{60} +(-4.41596 - 7.64867i) q^{61} +13.2892 q^{62} +(7.88661 - 0.226004i) q^{63} -4.23563 q^{64} +(2.71952 + 4.71035i) q^{65} +(7.38216 - 12.7863i) q^{67} +(-4.59747 - 7.96305i) q^{68} -0.379547 q^{69} +(-6.13923 - 9.96302i) q^{70} +7.76013 q^{71} +(-1.22125 - 2.11526i) q^{72} +(-4.82484 + 8.35687i) q^{73} +(8.74787 - 15.1518i) q^{74} +(0.0325244 + 0.0563339i) q^{75} -7.29219 q^{76} -0.586985 q^{78} +(-3.84690 - 6.66302i) q^{79} +(-5.47999 + 9.49163i) q^{80} +(-4.41954 + 7.65486i) q^{81} +(-2.09218 - 3.62375i) q^{82} -3.82583 q^{83} +(0.554453 - 0.0158888i) q^{84} -13.7501 q^{85} +(-10.4610 - 18.1191i) q^{86} +(-0.139838 + 0.242206i) q^{87} +(-7.79272 - 13.4974i) q^{89} +13.1903 q^{90} +(2.91828 - 5.40659i) q^{91} +4.44131 q^{92} +(0.470962 + 0.815731i) q^{93} +(4.09011 - 7.08427i) q^{94} +(-5.45236 + 9.44376i) q^{95} +(-0.481773 - 0.834455i) q^{96} +14.8326 q^{97} +(-5.94317 + 11.8079i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{3} - 8 q^{4} - 4 q^{5} - 4 q^{6} + 2 q^{7} - 6 q^{8} - 10 q^{9}+O(q^{10}) \) 14 * q - 3 * q^3 - 8 * q^4 - 4 * q^5 - 4 * q^6 + 2 * q^7 - 6 * q^8 - 10 * q^9	\( 14 q - 3 q^{3} - 8 q^{4} - 4 q^{5} - 4 q^{6} + 2 q^{7} - 6 q^{8} - 10 q^{9} - 6 q^{10} - 13 q^{12} + 12 q^{13} + 12 q^{14} - 2 q^{15} - 6 q^{16} + 3 q^{17} - 14 q^{18} + 9 q^{19} + 4 q^{20} - 6 q^{21} + 6 q^{23} - 4 q^{24} - 7 q^{25} - 25 q^{26} + 24 q^{27} - 36 q^{28} + 12 q^{29} - 16 q^{30} - 14 q^{31} + 36 q^{32} + 16 q^{34} + 18 q^{35} - 4 q^{36} + 8 q^{37} + 10 q^{38} + 9 q^{39} - 18 q^{40} - 20 q^{41} - 8 q^{42} + 34 q^{43} - 12 q^{45} - 16 q^{46} - 30 q^{47} + 112 q^{48} + 14 q^{49} + 42 q^{50} + 20 q^{51} + 37 q^{52} + 10 q^{53} + 7 q^{54} - 33 q^{56} - 62 q^{57} + 13 q^{58} - 20 q^{59} - 42 q^{60} - 7 q^{61} + 52 q^{62} + 37 q^{63} + 42 q^{64} - 12 q^{65} - 7 q^{67} - 7 q^{68} + 18 q^{69} - 39 q^{70} - 22 q^{71} + q^{72} + 6 q^{73} - 8 q^{74} + q^{75} - 112 q^{76} + 30 q^{78} + 14 q^{79} - 12 q^{80} - 35 q^{81} + 7 q^{82} + 34 q^{83} + 40 q^{84} - 4 q^{85} + 15 q^{87} - 40 q^{89} + 136 q^{90} - 32 q^{91} - 52 q^{92} - 19 q^{94} - 20 q^{95} + 63 q^{96} - 44 q^{97} + 21 q^{98}+O(q^{100}) \) 14 * q - 3 * q^3 - 8 * q^4 - 4 * q^5 - 4 * q^6 + 2 * q^7 - 6 * q^8 - 10 * q^9 - 6 * q^10 - 13 * q^12 + 12 * q^13 + 12 * q^14 - 2 * q^15 - 6 * q^16 + 3 * q^17 - 14 * q^18 + 9 * q^19 + 4 * q^20 - 6 * q^21 + 6 * q^23 - 4 * q^24 - 7 * q^25 - 25 * q^26 + 24 * q^27 - 36 * q^28 + 12 * q^29 - 16 * q^30 - 14 * q^31 + 36 * q^32 + 16 * q^34 + 18 * q^35 - 4 * q^36 + 8 * q^37 + 10 * q^38 + 9 * q^39 - 18 * q^40 - 20 * q^41 - 8 * q^42 + 34 * q^43 - 12 * q^45 - 16 * q^46 - 30 * q^47 + 112 * q^48 + 14 * q^49 + 42 * q^50 + 20 * q^51 + 37 * q^52 + 10 * q^53 + 7 * q^54 - 33 * q^56 - 62 * q^57 + 13 * q^58 - 20 * q^59 - 42 * q^60 - 7 * q^61 + 52 * q^62 + 37 * q^63 + 42 * q^64 - 12 * q^65 - 7 * q^67 - 7 * q^68 + 18 * q^69 - 39 * q^70 - 22 * q^71 + q^72 + 6 * q^73 - 8 * q^74 + q^75 - 112 * q^76 + 30 * q^78 + 14 * q^79 - 12 * q^80 - 35 * q^81 + 7 * q^82 + 34 * q^83 + 40 * q^84 - 4 * q^85 + 15 * q^87 - 40 * q^89 + 136 * q^90 - 32 * q^91 - 52 * q^92 - 19 * q^94 - 20 * q^95 + 63 * q^96 - 44 * q^97 + 21 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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