LMFDB - Embedded newform 464.2.bi.a.45.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,2,Mod(45,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([0, 21, 4]))

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

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

chi := DirichletCharacter("464.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.bi (of order $28$, degree $12$, 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:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$696$
Relative dimension:	$58$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			45.18
Character	$\chi$	$=$	464.45
Dual form			464.2.bi.a.165.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.783622 - 1.17726i) q^{2} +(0.957676 - 0.107904i) q^{3} +(-0.771873 + 1.84505i) q^{4} +(-2.16233 + 0.756630i) q^{5} +(-0.877487 - 1.04288i) q^{6} +(0.390747 + 0.311610i) q^{7} +(2.77696 - 0.537129i) q^{8} +(-2.01928 + 0.460888i) q^{9} +O(q^{10})$	\(q+(-0.783622 - 1.17726i) q^{2} +(0.957676 - 0.107904i) q^{3} +(-0.771873 + 1.84505i) q^{4} +(-2.16233 + 0.756630i) q^{5} +(-0.877487 - 1.04288i) q^{6} +(0.390747 + 0.311610i) q^{7} +(2.77696 - 0.537129i) q^{8} +(-2.01928 + 0.460888i) q^{9} +(2.58520 + 1.95270i) q^{10} +(-1.73835 - 2.76657i) q^{11} +(-0.540115 + 1.85025i) q^{12} +(0.749269 - 0.470797i) q^{13} +(0.0606477 - 0.704194i) q^{14} +(-1.98916 + 0.957931i) q^{15} +(-2.80842 - 2.84829i) q^{16} -7.44845 q^{17} +(2.12494 + 2.01606i) q^{18} +(-0.586173 + 5.20243i) q^{19} +(0.273019 - 4.57362i) q^{20} +(0.407833 + 0.256258i) q^{21} +(-1.89476 + 4.21444i) q^{22} +(1.68499 + 3.49891i) q^{23} +(2.60147 - 0.814041i) q^{24} +(0.194004 - 0.154713i) q^{25} +(-1.14139 - 0.513156i) q^{26} +(-4.61305 + 1.61418i) q^{27} +(-0.876543 + 0.480424i) q^{28} +(-5.38432 - 0.0954760i) q^{29} +(2.68648 + 1.59110i) q^{30} +(-6.66152 - 3.20802i) q^{31} +(-1.15243 + 5.53822i) q^{32} +(-1.96330 - 2.46190i) q^{33} +(5.83677 + 8.76875i) q^{34} +(-1.08070 - 0.378152i) q^{35} +(0.708268 - 4.08143i) q^{36} +(8.18227 + 5.14126i) q^{37} +(6.58394 - 3.38666i) q^{38} +(0.666756 - 0.531720i) q^{39} +(-5.59828 + 3.26258i) q^{40} +2.27608i q^{41} +(-0.0179046 - 0.680934i) q^{42} +(0.257367 - 0.735512i) q^{43} +(6.44625 - 1.07191i) q^{44} +(4.01763 - 2.52444i) q^{45} +(2.79873 - 4.72549i) q^{46} +(2.75421 - 12.0670i) q^{47} +(-2.99690 - 2.42470i) q^{48} +(-1.50206 - 6.58097i) q^{49} +(-0.334163 - 0.107156i) q^{50} +(-7.13321 + 0.803719i) q^{51} +(0.290304 + 1.74583i) q^{52} +(1.68772 - 0.590559i) q^{53} +(5.51519 + 4.16585i) q^{54} +(5.85215 + 4.66694i) q^{55} +(1.25246 + 0.655447i) q^{56} +5.04549i q^{57} +(4.10687 + 6.41355i) q^{58} +(-8.57529 + 8.57529i) q^{59} +(-0.232049 - 4.40951i) q^{60} +(8.10028 - 0.912682i) q^{61} +(1.44345 + 10.3562i) q^{62} +(-0.932646 - 0.449139i) q^{63} +(7.42299 - 2.98317i) q^{64} +(-1.26394 + 1.58494i) q^{65} +(-1.35981 + 4.24052i) q^{66} +(-4.27138 + 6.79786i) q^{67} +(5.74926 - 13.7428i) q^{68} +(1.99122 + 3.16901i) q^{69} +(0.401675 + 1.56858i) q^{70} +(2.40891 + 0.549818i) q^{71} +(-5.35991 + 2.36448i) q^{72} +(-2.14122 - 4.44630i) q^{73} +(-0.359217 - 13.6615i) q^{74} +(0.169099 - 0.169099i) q^{75} +(-9.14629 - 5.09713i) q^{76} +(0.182836 - 1.62272i) q^{77} +(-1.14846 - 0.368276i) q^{78} +(1.68060 + 7.36319i) q^{79} +(8.22783 + 4.03399i) q^{80} +(1.35467 - 0.652373i) q^{81} +(2.67954 - 1.78359i) q^{82} +(-1.26423 + 11.2203i) q^{83} +(-0.787605 + 0.554673i) q^{84} +(16.1060 - 5.63573i) q^{85} +(-1.06757 + 0.273376i) q^{86} +(-5.16673 + 0.489555i) q^{87} +(-6.31334 - 6.74893i) q^{88} +(7.62694 - 15.8375i) q^{89} +(-6.12022 - 2.75157i) q^{90} +(0.439479 + 0.0495174i) q^{91} +(-7.75627 + 0.408172i) q^{92} +(-6.72574 - 2.35344i) q^{93} +(-16.3642 + 6.21354i) q^{94} +(-2.66882 - 11.6929i) q^{95} +(-0.506055 + 5.42817i) q^{96} +(5.09277 + 6.38613i) q^{97} +(-6.57045 + 6.92531i) q^{98} +(4.78531 + 4.78531i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 696 q - 10 q^{2} - 10 q^{3} - 14 q^{4} - 10 q^{5} - 22 q^{6} - 10 q^{8}+O(q^{10}) $ 696 * q - 10 * q^2 - 10 * q^3 - 14 * q^4 - 10 * q^5 - 22 * q^6 - 10 * q^8	\( 696 q - 10 q^{2} - 10 q^{3} - 14 q^{4} - 10 q^{5} - 22 q^{6} - 10 q^{8} - 10 q^{10} + 10 q^{11} - 36 q^{12} - 10 q^{13} - 22 q^{14} - 20 q^{15} + 10 q^{16} - 48 q^{17} + 2 q^{18} - 10 q^{19} - 38 q^{20} - 22 q^{21} - 32 q^{22} - 10 q^{24} - 10 q^{26} + 2 q^{27} + 52 q^{28} - 20 q^{29} - 44 q^{30} - 20 q^{31} - 10 q^{32} - 20 q^{33} - 62 q^{34} - 30 q^{35} - 14 q^{36} - 26 q^{37} - 88 q^{38} + 22 q^{40} - 34 q^{42} - 2 q^{43} - 4 q^{44} - 18 q^{45} - 20 q^{46} - 20 q^{47} + 70 q^{48} + 72 q^{49} - 46 q^{50} - 40 q^{51} + 12 q^{52} + 6 q^{53} + 10 q^{54} - 38 q^{56} - 2 q^{58} - 48 q^{59} - 86 q^{60} - 10 q^{61} + 56 q^{62} - 36 q^{63} + 100 q^{64} - 36 q^{65} - 182 q^{66} + 30 q^{67} - 140 q^{68} - 22 q^{69} + 32 q^{70} + 104 q^{72} + 18 q^{74} - 72 q^{75} - 10 q^{76} - 22 q^{77} - 42 q^{78} - 20 q^{79} + 160 q^{80} + 64 q^{81} - 46 q^{82} - 10 q^{83} + 16 q^{84} - 60 q^{85} - 24 q^{86} - 4 q^{88} - 142 q^{90} - 14 q^{91} - 32 q^{92} + 122 q^{93} - 92 q^{94} - 20 q^{95} + 86 q^{96} - 20 q^{97} + 66 q^{98} - 88 q^{99}+O(q^{100}) \) 696 * q - 10 * q^2 - 10 * q^3 - 14 * q^4 - 10 * q^5 - 22 * q^6 - 10 * q^8 - 10 * q^10 + 10 * q^11 - 36 * q^12 - 10 * q^13 - 22 * q^14 - 20 * q^15 + 10 * q^16 - 48 * q^17 + 2 * q^18 - 10 * q^19 - 38 * q^20 - 22 * q^21 - 32 * q^22 - 10 * q^24 - 10 * q^26 + 2 * q^27 + 52 * q^28 - 20 * q^29 - 44 * q^30 - 20 * q^31 - 10 * q^32 - 20 * q^33 - 62 * q^34 - 30 * q^35 - 14 * q^36 - 26 * q^37 - 88 * q^38 + 22 * q^40 - 34 * q^42 - 2 * q^43 - 4 * q^44 - 18 * q^45 - 20 * q^46 - 20 * q^47 + 70 * q^48 + 72 * q^49 - 46 * q^50 - 40 * q^51 + 12 * q^52 + 6 * q^53 + 10 * q^54 - 38 * q^56 - 2 * q^58 - 48 * q^59 - 86 * q^60 - 10 * q^61 + 56 * q^62 - 36 * q^63 + 100 * q^64 - 36 * q^65 - 182 * q^66 + 30 * q^67 - 140 * q^68 - 22 * q^69 + 32 * q^70 + 104 * q^72 + 18 * q^74 - 72 * q^75 - 10 * q^76 - 22 * q^77 - 42 * q^78 - 20 * q^79 + 160 * q^80 + 64 * q^81 - 46 * q^82 - 10 * q^83 + 16 * q^84 - 60 * q^85 - 24 * q^86 - 4 * q^88 - 142 * q^90 - 14 * q^91 - 32 * q^92 + 122 * q^93 - 92 * q^94 - 20 * q^95 + 86 * q^96 - 20 * q^97 + 66 * q^98 - 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{7}\right)$

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 $

$2$	−0.783622	−	1.17726i	−0.554104	−	0.832447i
$2$	−0.783622	−	1.17726i	−0.554104	−	0.832447i
$3$	0.957676	−	0.107904i	0.552914	−	0.0622985i	0.168913	−	0.985631i	$-0.445974\pi$
$3$	0.957676	−	0.107904i	0.552914	−	0.0622985i	0.384001	+	0.923332i	$0.374546\pi$
$4$	−0.771873	+	1.84505i	−0.385936	+	0.922525i
$5$	−2.16233	+	0.756630i	−0.967021	+	0.338375i	−0.767165	−	0.641450i	$-0.778333\pi$
$5$	−2.16233	+	0.756630i	−0.967021	+	0.338375i	−0.199856	+	0.979825i	$0.564048\pi$
$6$	−0.877487	−	1.04288i	−0.358233	−	0.425752i
$7$	0.390747	+	0.311610i	0.147688	+	0.117778i	0.694547	−	0.719448i	$-0.255605\pi$
$7$	0.390747	+	0.311610i	0.147688	+	0.117778i	−0.546858	+	0.837225i	$0.684176\pi$
$8$	2.77696	−	0.537129i	0.981803	−	0.189904i
$9$	−2.01928	+	0.460888i	−0.673095	+	0.153629i
$10$	2.58520	+	1.95270i	0.817510	+	0.617499i
$11$	−1.73835	−	2.76657i	−0.524133	−	0.834153i	0.474812	−	0.880087i	$-0.342516\pi$
$11$	−1.73835	−	2.76657i	−0.524133	−	0.834153i	−0.998944	+	0.0459348i	$0.985373\pi$
$12$	−0.540115	+	1.85025i	−0.155918	+	0.534121i
$13$	0.749269	−	0.470797i	0.207810	−	0.130576i	−0.424106	−	0.905613i	$-0.639412\pi$
$13$	0.749269	−	0.470797i	0.207810	−	0.130576i	0.631916	+	0.775037i	$0.282269\pi$
$14$	0.0606477	−	0.704194i	0.0162088	−	0.188204i
$15$	−1.98916	+	0.957931i	−0.513600	+	0.247337i
$16$	−2.80842	−	2.84829i	−0.702106	−	0.712072i
$17$	−7.44845			−1.80652			−0.903258	−	0.429098i	$-0.858831\pi$
$17$	−7.44845			−1.80652			−0.903258	+	0.429098i	$0.858831\pi$
$18$	2.12494	+	2.01606i	0.500853	+	0.475189i
$19$	−0.586173	+	5.20243i	−0.134477	+	1.19352i	0.727332	+	0.686286i	$0.240760\pi$
$19$	−0.586173	+	5.20243i	−0.134477	+	1.19352i	−0.861809	+	0.507233i	$0.830668\pi$
$20$	0.273019	−	4.57362i	0.0610489	−	1.02269i
$21$	0.407833	+	0.256258i	0.0889964	+	0.0559201i
$22$	−1.89476	+	4.21444i	−0.403964	+	0.898521i
$23$	1.68499	+	3.49891i	0.351344	+	0.729574i	0.999490	−	0.0319427i	$-0.0101694\pi$
$23$	1.68499	+	3.49891i	0.351344	+	0.729574i	−0.648145	+	0.761517i	$0.724455\pi$
$24$	2.60147	−	0.814041i	0.531022	−	0.166165i
$25$	0.194004	−	0.154713i	0.0388008	−	0.0309426i
$26$	−1.14139	−	0.513156i	−0.223846	−	0.100638i
$27$	−4.61305	+	1.61418i	−0.887782	+	0.310648i
$28$	−0.876543	+	0.480424i	−0.165651	+	0.0907916i
$29$	−5.38432	−	0.0954760i	−0.999843	−	0.0177294i
$29$	−5.38432	−	0.0954760i	−0.999843	−	0.0177294i
$30$	2.68648	+	1.59110i	0.490483	+	0.290494i
$31$	−6.66152	−	3.20802i	−1.19644	−	0.576177i	−0.273784	−	0.961791i	$-0.588275\pi$
$31$	−6.66152	−	3.20802i	−1.19644	−	0.576177i	−0.922660	+	0.385614i	$0.873990\pi$
$32$	−1.15243	+	5.53822i	−0.203722	+	0.979029i
$33$	−1.96330	−	2.46190i	−0.341767	−	0.428562i
$34$	5.83677	+	8.76875i	1.00100	+	1.50383i
$35$	−1.08070	−	0.378152i	−0.182671	−	0.0639193i
$36$	0.708268	−	4.08143i	0.118045	−	0.680238i
$37$	8.18227	+	5.14126i	1.34516	+	0.845218i	0.995781	−	0.0917642i	$-0.0292506\pi$
$37$	8.18227	+	5.14126i	1.34516	+	0.845218i	0.349376	+	0.936982i	$0.386393\pi$
$38$	6.58394	−	3.38666i	1.06806	−	0.549389i
$39$	0.666756	−	0.531720i	0.106766	−	0.0851434i
$40$	−5.59828	+	3.26258i	−0.885165	+	0.515859i
$41$			2.27608i			0.355464i	0.984079	+	0.177732i	$0.0568761\pi$
$41$			2.27608i			0.355464i	−0.984079	+	0.177732i	$0.943124\pi$
$42$	−0.0179046	−	0.680934i	−0.00276274	−	0.105070i
$43$	0.257367	−	0.735512i	0.0392481	−	0.112165i	−0.922592	−	0.385778i	$-0.873933\pi$
$43$	0.257367	−	0.735512i	0.0392481	−	0.112165i	0.961840	+	0.273613i	$0.0882188\pi$
$44$	6.44625	−	1.07191i	0.971809	−	0.161596i
$45$	4.01763	−	2.52444i	0.598912	−	0.376322i
$46$	2.79873	−	4.72549i	0.412650	−	0.696736i
$47$	2.75421	−	12.0670i	0.401743	−	1.76015i	−0.218593	−	0.975816i	$-0.570147\pi$
$47$	2.75421	−	12.0670i	0.401743	−	1.76015i	0.620336	−	0.784336i	$-0.286996\pi$
$48$	−2.99690	−	2.42470i	−0.432566	−	0.349975i
$49$	−1.50206	−	6.58097i	−0.214581	−	0.940139i
$50$	−0.334163	−	0.107156i	−0.0472578	−	0.0151542i
$51$	−7.13321	+	0.803719i	−0.998849	+	0.112543i
$52$	0.290304	+	1.74583i	0.0402579	+	0.242104i
$53$	1.68772	−	0.590559i	0.231826	−	0.0811196i	−0.211866	−	0.977299i	$-0.567954\pi$
$53$	1.68772	−	0.590559i	0.231826	−	0.0811196i	0.443692	+	0.896179i	$0.353668\pi$
$54$	5.51519	+	4.16585i	0.750522	+	0.566900i
$55$	5.85215	+	4.66694i	0.789104	+	0.629290i
$56$	1.25246	+	0.655447i	0.167367	+	0.0875877i
$57$			5.04549i			0.668292i
$58$	4.10687	+	6.41355i	0.539259	+	0.842140i
$59$	−8.57529	+	8.57529i	−1.11641	+	1.11641i	−0.124144	+	0.992264i	$0.539618\pi$
$59$	−8.57529	+	8.57529i	−1.11641	+	1.11641i	−0.992264	+	0.124144i	$0.960382\pi$
$60$	−0.232049	−	4.40951i	−0.0299574	−	0.569265i
$61$	8.10028	−	0.912682i	1.03713	−	0.116857i	0.423057	−	0.906103i	$-0.360957\pi$
$61$	8.10028	−	0.912682i	1.03713	−	0.116857i	0.614077	+	0.789246i	$0.289528\pi$
$62$	1.44345	+	10.3562i	0.183318	+	1.31524i
$63$	−0.932646	−	0.449139i	−0.117502	−	0.0565861i
$64$	7.42299	−	2.98317i	0.927873	−	0.372896i
$65$	−1.26394	+	1.58494i	−0.156773	+	0.196587i
$66$	−1.35981	+	4.24052i	−0.167381	+	0.521971i
$67$	−4.27138	+	6.79786i	−0.521832	+	0.830490i	−0.998827	−	0.0484154i	$-0.984583\pi$
$67$	−4.27138	+	6.79786i	−0.521832	+	0.830490i	0.476996	+	0.878906i	$0.341726\pi$
$68$	5.74926	−	13.7428i	0.697200	−	1.66656i
$69$	1.99122	+	3.16901i	0.239715	+	0.381504i
$70$	0.401675	+	1.56858i	0.0480093	+	0.187482i
$71$	2.40891	+	0.549818i	0.285885	+	0.0652514i	0.363059	−	0.931766i	$-0.381732\pi$
$71$	2.40891	+	0.549818i	0.285885	+	0.0652514i	−0.0771735	+	0.997018i	$0.524590\pi$
$72$	−5.35991	+	2.36448i	−0.631671	+	0.278657i
$73$	−2.14122	−	4.44630i	−0.250611	−	0.520400i	0.737272	−	0.675596i	$-0.236113\pi$
$73$	−2.14122	−	4.44630i	−0.250611	−	0.520400i	−0.987884	+	0.155196i	$0.950399\pi$
$74$	−0.359217	−	13.6615i	−0.0417581	−	1.58811i
$75$	0.169099	−	0.169099i	0.0195258	−	0.0195258i
$76$	−9.14629	−	5.09713i	−1.04915	−	0.584681i
$77$	0.182836	−	1.62272i	0.0208361	−	0.184926i
$78$	−1.14846	−	0.368276i	−0.130037	−	0.0416991i
$79$	1.68060	+	7.36319i	0.189082	+	0.828424i	0.977102	+	0.212773i	$0.0682496\pi$
$79$	1.68060	+	7.36319i	0.189082	+	0.828424i	−0.788019	+	0.615651i	$0.788893\pi$
$80$	8.22783	+	4.03399i	0.919899	+	0.451014i
$81$	1.35467	−	0.652373i	0.150518	−	0.0724858i
$82$	2.67954	−	1.78359i	0.295905	−	0.196964i
$83$	−1.26423	+	11.2203i	−0.138767	+	1.23159i	0.710526	+	0.703671i	$0.248457\pi$
$83$	−1.26423	+	11.2203i	−0.138767	+	1.23159i	−0.849293	+	0.527922i	$0.822971\pi$
$84$	−0.787605	+	0.554673i	−0.0859347	+	0.0605198i
$85$	16.1060	−	5.63573i	1.74694	−	0.611280i
$86$	−1.06757	+	0.273376i	−0.115119	+	0.0294789i
$87$	−5.16673	+	0.489555i	−0.553932	+	0.0524858i
$88$	−6.31334	−	6.74893i	−0.673004	−	0.719439i
$89$	7.62694	−	15.8375i	0.808454	−	1.67877i	0.0768496	−	0.997043i	$-0.475514\pi$
$89$	7.62694	−	15.8375i	0.808454	−	1.67877i	0.731604	−	0.681729i	$-0.238772\pi$
$90$	−6.12022	−	2.75157i	−0.645128	−	0.290041i
$91$	0.439479	+	0.0495174i	0.0460700	+	0.00519084i
$92$	−7.75627	+	0.408172i	−0.808647	+	0.0425548i
$93$	−6.72574	−	2.35344i	−0.697427	−	0.244040i
$94$	−16.3642	+	6.21354i	−1.68784	+	0.640878i
$95$	−2.66882	−	11.6929i	−0.273815	−	1.19966i
$96$	−0.506055	+	5.42817i	−0.0516491	+	0.554011i
$97$	5.09277	+	6.38613i	0.517092	+	0.648413i	0.969989	−	0.243150i	$-0.0781808\pi$
$97$	5.09277	+	6.38613i	0.517092	+	0.648413i	−0.452897	+	0.891563i	$0.649609\pi$
$98$	−6.57045	+	6.92531i	−0.663716	+	0.699562i
$99$	4.78531	+	4.78531i	0.480941	+	0.480941i
$100$	0.135707	+	0.477366i	0.0135707	+	0.0477366i
$101$	2.84530	−	8.13139i	0.283118	−	0.809103i	−0.711233	−	0.702956i	$-0.751863\pi$
$101$	2.84530	−	8.13139i	0.283118	−	0.809103i	0.994350	−	0.106147i	$-0.0338514\pi$
$102$	6.53592	+	7.76781i	0.647153	+	0.769128i
$103$	−12.3467	−	2.81805i	−1.21655	−	0.277671i	−0.434380	−	0.900730i	$-0.643032\pi$
$103$	−12.3467	−	2.81805i	−1.21655	−	0.277671i	−0.782175	+	0.623059i	$0.785890\pi$
$104$	1.82781	−	1.70984i	0.179231	−	0.167663i
$105$	−1.07576	−	0.245535i	−0.104983	−	0.0239618i
$106$	−2.01778	−	1.52411i	−0.195984	−	0.148034i
$107$	−7.61734	−	4.78629i	−0.736396	−	0.462708i	0.110899	−	0.993832i	$-0.464627\pi$
$107$	−7.61734	−	4.78629i	−0.736396	−	0.462708i	−0.847294	+	0.531124i	$0.821770\pi$
$108$	0.582452	−	9.75725i	0.0560464	−	0.938892i
$109$	−4.62046	+	0.520601i	−0.442560	+	0.0498646i	−0.330433	−	0.943829i	$-0.607195\pi$
$109$	−4.62046	+	0.520601i	−0.442560	+	0.0498646i	−0.112127	+	0.993694i	$0.535766\pi$
$110$	0.908312	−	10.5466i	0.0866042	−	1.00558i
$111$	8.39073	+	4.04076i	0.796413	+	0.383532i
$112$	−0.209827	−	1.98809i	−0.0198268	−	0.187857i
$113$	0.842824	−	1.05687i	0.0792862	−	0.0994218i	−0.740606	−	0.671939i	$-0.765462\pi$
$113$	0.842824	−	1.05687i	0.0792862	−	0.0994218i	0.819893	+	0.572517i	$0.194033\pi$
$114$	5.93984	−	3.95376i	0.556317	−	0.370303i
$115$	−6.29088	−	6.29088i	−0.586627	−	0.586627i
$116$	4.33217	−	9.86065i	0.402232	−	0.915538i
$117$	−1.29600	+	1.29600i	−0.119815	+	0.119815i
$118$	16.8151	+	3.37554i	1.54796	+	0.310744i
$119$	−2.91046	−	2.32101i	−0.266801	−	0.212767i
$120$	−5.00929	+	3.72857i	−0.457284	+	0.340370i
$121$	0.140671	−	0.292107i	0.0127883	−	0.0265552i
$122$	−7.42202	−	8.82092i	−0.671958	−	0.798608i
$123$	0.245599	+	2.17975i	0.0221449	+	0.196541i
$124$	11.0608	−	9.81466i	0.993290	−	0.881383i
$125$	5.79167	−	9.21740i	0.518023	−	0.824429i
$126$	0.202090	+	1.44992i	0.0180036	+	0.129169i
$127$	0.247942	−	1.08631i	0.0220013	−	0.0963940i	−0.962735	−	0.270446i	$-0.912829\pi$
$127$	0.247942	−	1.08631i	0.0220013	−	0.0963940i	0.984736	+	0.174052i	$0.0556860\pi$
$128$	−9.32877	−	6.40109i	−0.824555	−	0.565782i
$129$	0.167109	−	0.732153i	0.0147131	−	0.0644625i
$130$	2.85633	+	0.245998i	0.250517	+	0.0215754i
$131$	2.44244	+	0.854647i	0.213397	+	0.0746708i	0.434861	−	0.900498i	$-0.356798\pi$
$131$	2.44244	+	0.854647i	0.213397	+	0.0746708i	−0.221464	+	0.975169i	$0.571083\pi$
$132$	6.05776	−	1.72212i	0.527260	−	0.149891i
$133$	−1.85017	+	1.85017i	−0.160430	+	0.160430i
$134$	11.3500	−	0.298438i	0.980488	−	0.0257811i
$135$	8.75358	−	6.98075i	0.753388	−	0.600807i
$136$	−20.6840	+	4.00078i	−1.77364	+	0.343064i
$137$	−9.99707	+	2.28177i	−0.854107	+	0.194944i	−0.627091	−	0.778946i	$-0.715754\pi$
$137$	−9.99707	+	2.28177i	−0.854107	+	0.194944i	−0.227017	+	0.973891i	$0.572897\pi$
$138$	2.17038	−	4.82748i	0.184755	−	0.410943i
$139$	7.03238	−	20.0974i	0.596479	−	1.70464i	−0.107306	−	0.994226i	$-0.534223\pi$
$139$	7.03238	−	20.0974i	0.596479	−	1.70464i	0.703785	−	0.710413i	$-0.251492\pi$
$140$	1.53187	−	1.70205i	0.129466	−	0.143850i
$141$	1.33556	−	11.8535i	0.112475	−	0.998242i
$142$	−1.24040	−	3.26676i	−0.104092	−	0.274140i
$143$	−2.60499	−	1.25450i	−0.217840	−	0.104906i
$144$	6.98375	+	4.45713i	0.581979	+	0.371428i
$145$	11.7149	−	3.86749i	0.972869	−	0.321177i
$146$	−3.55653	+	6.00499i	−0.294340	+	0.496976i
$147$	−2.14861	−	6.14036i	−0.177214	−	0.506449i
$148$	−15.8016	+	11.1283i	−1.29888	+	0.914741i
$149$	2.05450	+	0.231486i	0.168311	+	0.0189641i	0.195718	−	0.980660i	$-0.437296\pi$
$149$	2.05450	+	0.231486i	0.168311	+	0.0189641i	−0.0274068	+	0.999624i	$0.508725\pi$
$150$	−0.331582	−	0.0665633i	−0.0270736	−	0.00543487i
$151$	8.13493	+	16.8924i	0.662012	+	1.37468i	0.913507	+	0.406823i	$0.133363\pi$
$151$	8.13493	+	16.8924i	0.662012	+	1.37468i	−0.251495	+	0.967858i	$0.580922\pi$
$152$	1.16660	+	14.7618i	0.0946235	+	1.19734i
$153$	15.0405	−	3.43291i	1.21596	−	0.277534i
$154$	−2.05363	+	1.05635i	−0.165486	+	0.0851232i
$155$	16.8317	+	1.89647i	1.35195	+	0.152328i
$156$	0.466400	+	1.64062i	0.0373419	+	0.131355i
$157$	9.96781	+	9.96781i	0.795518	+	0.795518i	0.982385	−	0.186867i	$-0.0598334\pi$
$157$	9.96781	+	9.96781i	0.795518	+	0.795518i	−0.186867	+	0.982385i	$0.559833\pi$
$158$	7.35142	−	7.74846i	0.584848	−	0.616434i
$159$	1.55257	−	0.747677i	0.123127	−	0.0592946i
$160$	−1.69846	−	12.8474i	−0.134275	−	1.01568i
$161$	−0.431893	+	1.89225i	−0.0340380	+	0.149130i
$162$	−1.82956	−	1.08358i	−0.143744	−	0.0851339i
$163$	−13.1901	+	8.28786i	−1.03312	+	0.649155i	−0.938116	−	0.346321i	$-0.887431\pi$
$163$	−13.1901	+	8.28786i	−1.03312	+	0.649155i	−0.0950089	+	0.995476i	$0.530288\pi$
$164$	−4.19949	−	1.75685i	−0.327925	−	0.137187i
$165$	6.10805	+	3.83794i	0.475511	+	0.298783i
$166$	14.1999	−	7.30418i	1.10213	−	0.566915i
$167$	−9.85176	−	7.85652i	−0.762352	−	0.607956i	0.163192	−	0.986594i	$-0.447821\pi$
$167$	−9.85176	−	7.85652i	−0.762352	−	0.607956i	−0.925545	+	0.378639i	$0.876392\pi$
$168$	1.27018	+	0.492560i	0.0979963	+	0.0380018i
$169$	−5.30073	+	11.0071i	−0.407749	+	0.846699i
$170$	−19.2557	−	14.5446i	−1.47685	−	1.11552i
$171$	−1.21409	−	10.7753i	−0.0928437	−	0.824011i
$172$	1.15840	+	1.04258i	0.0883274	+	0.0794957i
$173$	1.53233	+	1.53233i	0.116501	+	0.116501i	0.762954	−	0.646453i	$-0.223748\pi$
$173$	1.53233	+	1.53233i	0.116501	+	0.116501i	−0.646453	+	0.762954i	$0.723748\pi$
$174$	4.62510	+	5.69895i	0.350628	+	0.432037i
$175$	0.124017			0.00937477
$176$	−2.99797	+	12.7210i	−0.225980	+	0.958884i
$177$	−7.28704	+	9.13766i	−0.547728	+	0.686829i
$178$	−24.6215	+	3.43174i	−1.84546	+	0.257220i
$179$	4.44185	+	12.6941i	0.332000	+	0.948800i	0.982002	+	0.188869i	$0.0604820\pi$
$179$	4.44185	+	12.6941i	0.332000	+	0.948800i	−0.650003	+	0.759932i	$0.725232\pi$
$180$	1.55663	+	9.36127i	0.116024	+	0.697748i
$181$	2.23978	+	19.8786i	0.166481	+	1.47756i	0.747821	+	0.663900i	$0.231100\pi$
$181$	2.23978	+	19.8786i	0.166481	+	1.47756i	−0.581340	+	0.813661i	$0.697471\pi$
$182$	−0.286091	−	0.556184i	−0.0212065	−	0.0412271i
$183$	7.65896	−	1.74811i	0.566166	−	0.129224i
$184$	6.55851	+	8.81128i	0.483500	+	0.649576i
$185$	−21.5828	−	4.92613i	−1.58680	−	0.362176i
$186$	2.49983	+	9.76213i	0.183297	+	0.715794i
$187$	12.9480	+	20.6067i	0.946854	+	1.50691i
$188$	20.1383	+	14.3958i	1.46874	+	1.04993i
$189$	−2.30553	−	0.806739i	−0.167702	−	0.0586816i
$190$	−11.6742	+	12.3047i	−0.846933	+	0.892675i
$191$	−2.79424			−0.202184			−0.101092	−	0.994877i	$-0.532234\pi$
$191$	−2.79424			−0.202184			−0.101092	+	0.994877i	$0.532234\pi$
$192$	6.78692	−	3.65788i	0.489804	−	0.263985i
$193$	−10.3515	−	12.9803i	−0.745116	−	0.934346i	0.254347	−	0.967113i	$-0.418139\pi$
$193$	−10.3515	−	12.9803i	−0.745116	−	0.934346i	−0.999463	+	0.0327672i	$0.989568\pi$
$194$	3.52731	−	10.9998i	0.253246	−	0.789740i
$195$	−1.03943	+	1.65424i	−0.0744350	+	0.118463i
$196$	13.3016	+	2.30829i	0.950117	+	0.164878i
$197$	0.356748	−	1.01953i	0.0254173	−	0.0726383i	−0.930476	−	0.366354i	$-0.880606\pi$
$197$	0.356748	−	1.01953i	0.0254173	−	0.0726383i	0.955893	+	0.293715i	$0.0948918\pi$
$198$	1.88367	−	9.38341i	0.133867	−	0.666850i
$199$	−6.40120	+	5.10479i	−0.453769	+	0.361869i	−0.823544	−	0.567253i	$-0.808006\pi$
$199$	−6.40120	+	5.10479i	−0.453769	+	0.361869i	0.369775	+	0.929121i	$0.379435\pi$
$200$	0.455640	−	0.533837i	0.0322186	−	0.0377479i
$201$	−3.35708	+	6.97104i	−0.236790	+	0.491699i
$202$	−11.8024	+	3.02229i	−0.830412	+	0.212647i
$203$	−2.07415	−	1.71511i	−0.145577	−	0.120377i
$204$	4.02303	−	13.7815i	0.281668	−	0.964898i
$205$	−1.72215	−	4.92163i	−0.120280	−	0.343741i
$206$	6.35756	+	16.7435i	0.442952	+	1.16658i
$207$	−5.01508	−	6.28871i	−0.348572	−	0.437095i
$208$	−3.44523	−	0.811937i	−0.238884	−	0.0562977i
$209$	15.4119	−	7.42196i	1.06606	−	0.513388i
$210$	0.553931	+	1.45885i	0.0382249	+	0.100670i
$211$	−3.69537	+	5.88115i	−0.254400	+	0.404875i	−0.949368	−	0.314165i	$-0.898275\pi$
$211$	−3.69537	+	5.88115i	−0.254400	+	0.404875i	0.694968	+	0.719040i	$0.255418\pi$
$212$	−0.213095	+	3.56977i	−0.0146354	+	0.245173i
$213$	2.36628	+	0.266616i	0.162135	+	0.0182682i
$214$	0.334415	+	12.7182i	0.0228601	+	0.869399i
$215$			1.78515i			0.121746i
$216$	−11.9432	+	6.96030i	−0.812633	+	0.473588i
$217$	−1.60332	−	3.32932i	−0.108840	−	0.226009i
$218$	4.23358	+	5.03152i	0.286734	+	0.340778i
$219$	−2.53037	−	4.02706i	−0.170987	−	0.272124i
$220$	−13.1279	+	7.19524i	−0.885080	+	0.485103i
$221$	−5.58090	+	3.50671i	−0.375412	+	0.235887i
$222$	−1.81814	−	13.0445i	−0.122026	−	0.875488i
$223$	−2.68578	−	11.7672i	−0.179853	−	0.787989i	−0.981696	−	0.190454i	$-0.939004\pi$
$223$	−2.68578	−	11.7672i	−0.179853	−	0.787989i	0.801843	−	0.597535i	$-0.203853\pi$
$224$	−2.17607	+	1.80493i	−0.145395	+	0.120597i
$225$	−0.320444	+	0.401824i	−0.0213629	+	0.0267882i
$226$	−1.90466	−	0.164036i	−0.126696	−	0.0109115i
$227$	2.59090	+	7.40436i	0.171964	+	0.491445i	0.997320	−	0.0731686i	$-0.0233111\pi$
$227$	2.59090	+	7.40436i	0.171964	+	0.491445i	−0.825356	+	0.564613i	$0.809025\pi$
$228$	−9.30919	−	3.89448i	−0.616516	−	0.257918i
$229$	1.47683	+	13.1072i	0.0975914	+	0.866148i	0.943173	+	0.332302i	$0.107825\pi$
$229$	1.47683	+	13.1072i	0.0975914	+	0.866148i	−0.845582	+	0.533846i	$0.820746\pi$
$230$	−2.47632	+	12.3357i	−0.163283	+	0.813389i
$231$		−	1.57377i		−	0.103546i
$232$	−15.0033	+	2.62694i	−0.985015	+	0.172467i
$233$			1.85196i			0.121326i	0.998158	+	0.0606629i	$0.0193215\pi$
$233$			1.85196i			0.121326i	−0.998158	+	0.0606629i	$0.980679\pi$
$234$	2.54130	+	0.510153i	0.166130	+	0.0333497i
$235$	3.17475	+	28.1767i	0.207098	+	1.83804i
$236$	−9.20281	−	22.4409i	−0.599052	−	1.46078i
$237$	2.40399	+	6.87021i	0.156156	+	0.446268i
$238$	−0.451732	+	5.24516i	−0.0292814	+	0.339993i
$239$	−10.6510	+	13.3560i	−0.688958	+	0.863926i	−0.996145	−	0.0877232i	$-0.972041\pi$
$239$	−10.6510	+	13.3560i	−0.688958	+	0.863926i	0.307187	+	0.951649i	$0.400612\pi$
$240$	8.31488	+	2.97544i	0.536723	+	0.192064i
$241$	−6.35993	−	27.8647i	−0.409679	−	1.79492i	−0.585691	−	0.810534i	$-0.699177\pi$
$241$	−6.35993	−	27.8647i	−0.409679	−	1.79492i	0.176012	−	0.984388i	$-0.443680\pi$
$242$	−0.454119	+	0.0632951i	−0.0291918	+	0.00406876i
$243$	13.6415	−	8.57155i	0.875106	−	0.549865i
$244$	−4.56844	+	15.6499i	−0.292464	+	1.00188i
$245$	8.22732	+	13.0937i	0.525624	+	0.836526i
$246$	2.37367	−	1.99723i	0.151340	−	0.127339i
$247$	2.01009	+	4.17399i	0.127899	+	0.265584i
$248$	−20.2219	−	5.33044i	−1.28409	−	0.338483i
$249$			10.8819i			0.689610i
$250$	−15.3897	+	0.404661i	−0.973333	+	0.0255930i
$251$	7.75389	+	0.873654i	0.489421	+	0.0551445i	0.353227	−	0.935538i	$-0.385084\pi$
$251$	7.75389	+	0.873654i	0.489421	+	0.0551445i	0.136194	+	0.990682i	$0.456513\pi$
$252$	1.54857	−	1.37410i	0.0975506	−	0.0865602i
$253$	6.75089	−	10.7440i	0.424425	−	0.675468i
$254$	−1.47315	+	0.559361i	−0.0924339	+	0.0350974i
$255$	14.8162	−	7.13510i	0.927826	−	0.446817i
$256$	−0.225505	+	15.9984i	−0.0140940	+	0.999901i
$257$	8.36063	+	10.4839i	0.521522	+	0.653968i	0.970931	−	0.239358i	$-0.0769370\pi$
$257$	8.36063	+	10.4839i	0.521522	+	0.653968i	−0.449410	+	0.893326i	$0.648366\pi$
$258$	−0.992884	+	0.377001i	−0.0618142	+	0.0234710i
$259$	1.59513	+	4.55861i	0.0991163	+	0.283258i
$260$	−1.94868	−	3.55541i	−0.120852	−	0.220497i
$261$	10.9165	−	2.28878i	0.675713	−	0.141672i
$262$	−0.907810	−	3.54510i	−0.0560847	−	0.219017i
$263$	3.82074	−	7.93385i	0.235597	−	0.489222i	−0.749329	−	0.662198i	$-0.769624\pi$
$263$	3.82074	−	7.93385i	0.235597	−	0.489222i	0.984926	+	0.172976i	$0.0553382\pi$
$264$	−6.77437	−	5.78205i	−0.416933	−	0.355861i
$265$	−3.20257	+	2.55396i	−0.196732	+	0.156889i
$266$	3.62797	+	0.728295i	0.222445	+	0.0446546i
$267$	5.59520	−	15.9902i	0.342421	−	0.978583i
$268$	−9.24543	−	13.1280i	−0.564754	−	0.801919i
$269$	−16.8643	+	26.8393i	−1.02823	+	1.63642i	−0.296233	+	0.955116i	$0.595731\pi$
$269$	−16.8643	+	26.8393i	−1.02823	+	1.63642i	−0.731999	+	0.681306i	$0.761412\pi$
$270$	−15.0776	−	4.83496i	−0.917596	−	0.294246i
$271$	4.76850	+	5.97951i	0.289666	+	0.363230i	0.905278	−	0.424820i	$-0.139663\pi$
$271$	4.76850	+	5.97951i	0.289666	+	0.363230i	−0.615612	+	0.788049i	$0.711091\pi$
$272$	20.9184	+	21.2154i	1.26837	+	1.28637i
$273$	0.426222			0.0257961
$274$	10.5202	+	9.98109i	0.635546	+	0.602980i
$275$	−0.765272	−	0.267780i	−0.0461476	−	0.0161478i
$276$	−7.38395	+	1.22783i	−0.444462	+	0.0739067i
$277$	−12.4548	−	19.8218i	−0.748338	−	1.19097i	−0.976114	−	0.217260i	$-0.930288\pi$
$277$	−12.4548	−	19.8218i	−0.748338	−	1.19097i	0.227775	−	0.973714i	$-0.426855\pi$
$278$	−29.1705	+	7.46983i	−1.74953	+	0.448011i
$279$	14.9300	+	3.40768i	0.893838	+	0.204013i
$280$	−3.20416	−	0.469638i	−0.191485	−	0.0280663i
$281$	−17.7659	+	4.05495i	−1.05982	+	0.241898i	−0.716692	−	0.697389i	$-0.754345\pi$
$281$	−17.7659	+	4.05495i	−1.05982	+	0.241898i	−0.343132	+	0.939287i	$0.611488\pi$
$282$	−15.0012	+	7.71633i	−0.893306	+	0.459501i
$283$	0.0581534	+	0.516126i	0.00345686	+	0.0306805i	0.995322	−	0.0966109i	$-0.0308002\pi$
$283$	0.0581534	+	0.516126i	0.00345686	+	0.0306805i	−0.991865	+	0.127291i	$0.959372\pi$
$284$	−2.87382	+	4.02018i	−0.170530	+	0.238554i
$285$	−3.81757	−	10.9100i	−0.226133	−	0.646252i
$286$	0.564460	+	4.04979i	0.0333772	+	0.239469i
$287$	−0.709250	+	0.889371i	−0.0418657	+	0.0524979i
$288$	−0.225423	−	11.7144i	−0.0132832	−	0.690277i
$289$	38.4795			2.26350
$290$	−13.7331	−	10.7608i	−0.806434	−	0.631896i
$291$	5.56631	+	5.56631i	0.326303	+	0.326303i
$292$	9.85639	−	0.518690i	0.576802	−	0.0303540i
$293$	−0.322703	−	2.86407i	−0.0188525	−	0.167321i	0.980758	−	0.195227i	$-0.0625445\pi$
$293$	−0.322703	−	2.86407i	−0.0188525	−	0.167321i	−0.999611	+	0.0279067i	$0.991116\pi$
$294$	−5.54510	+	7.34119i	−0.323397	+	0.428147i
$295$	12.0542	−	25.0309i	0.701825	−	1.45736i
$296$	25.4833	+	9.88213i	1.48119	+	0.574387i
$297$	12.4848	+	9.95633i	0.724444	+	0.577725i
$298$	−1.33743	−	2.60007i	−0.0774752	−	0.150618i
$299$	2.90979	+	1.82834i	0.168277	+	0.105736i
$300$	0.181473	+	0.442519i	0.0104774	+	0.0255488i
$301$	0.329758	−	0.207201i	0.0190069	−	0.0119429i
$302$	13.5120	−	22.8141i	0.777526	−	1.31281i
$303$	1.84746	−	8.09425i	0.106134	−	0.465003i
$304$	16.4642	−	12.9410i	0.944289	−	0.742219i
$305$	−16.8249	+	8.10243i	−0.963389	+	0.463944i
$306$	−15.8275	−	15.0165i	−0.904799	−	0.858436i
$307$	2.56027	+	2.56027i	0.146122	+	0.146122i	0.776383	−	0.630261i	$-0.217052\pi$
$307$	2.56027	+	2.56027i	0.146122	+	0.146122i	−0.630261	+	0.776383i	$0.717052\pi$
$308$	2.85287	+	1.58987i	0.162557	+	0.0905914i
$309$	−12.1282	−	1.36652i	−0.689949	−	0.0777386i
$310$	−10.9570	−	21.3013i	−0.622317	−	1.20983i
$311$	0.384112	−	0.0876711i	0.0217810	−	0.00497137i	−0.211617	−	0.977353i	$-0.567873\pi$
$311$	0.384112	−	0.0876711i	0.0217810	−	0.00497137i	0.233398	+	0.972381i	$0.425016\pi$
$312$	1.56595	−	1.83470i	0.0886545	−	0.103869i
$313$	−2.62297	−	5.44666i	−0.148259	−	0.307863i	0.813592	−	0.581436i	$-0.197509\pi$
$313$	−2.62297	−	5.44666i	−0.148259	−	0.307863i	−0.961851	+	0.273573i	$0.911795\pi$
$314$	3.92369	−	19.5457i	0.221427	−	1.10303i
$315$	2.35652	+	0.265516i	0.132775	+	0.0149601i
$316$	−14.8827	−	2.58266i	−0.837216	−	0.145286i
$317$	7.25026	+	20.7201i	0.407215	+	1.16375i	0.946800	+	0.321823i	$0.104296\pi$
$317$	7.25026	+	20.7201i	0.407215	+	1.16375i	−0.539585	+	0.841931i	$0.681419\pi$
$318$	−2.09683	−	1.24188i	−0.117585	−	0.0696409i
$319$	9.09570	+	15.0621i	0.509261	+	0.843314i
$320$	−13.7938	+	12.0670i	−0.771094	+	0.674568i
$321$	−7.81140	−	3.76177i	−0.435990	−	0.209962i
$322$	2.56611	−	0.974357i	0.143003	−	0.0542988i
$323$	4.36608	−	38.7500i	0.242935	−	2.15611i
$324$	0.158031	+	3.00298i	0.00877949	+	0.166832i
$325$	0.0725228	−	0.207258i	0.00402284	−	0.0114966i
$326$	20.0930	+	9.03355i	1.11285	+	0.500322i
$327$	−4.36873	+	0.997135i	−0.241591	+	0.0551417i
$328$	1.22255	+	6.32058i	0.0675040	+	0.348996i
$329$	4.83640	−	3.85690i	0.266639	−	0.212638i
$330$	−0.268155	−	10.1982i	−0.0147614	−	0.561395i
$331$	−14.4308	+	14.4308i	−0.793189	+	0.793189i	−0.982011	−	0.188822i	$-0.939533\pi$
$331$	−14.4308	+	14.4308i	−0.793189	+	0.793189i	0.188822	+	0.982011i	$0.439533\pi$
$332$	−19.7263	−	10.9932i	−1.08262	−	0.603333i
$333$	−18.8919	−	6.61055i	−1.03527	−	0.362256i
$334$	−1.52909	+	17.7546i	−0.0836681	+	0.971489i
$335$	4.09264	−	17.9310i	0.223605	−	0.979677i
$336$	−0.415470	−	1.88131i	−0.0226657	−	0.102634i
$337$	−4.66094	+	20.4209i	−0.253898	+	1.11240i	0.673755	+	0.738954i	$0.264680\pi$
$337$	−4.66094	+	20.4209i	−0.253898	+	1.11240i	−0.927653	+	0.373443i	$0.878177\pi$
$338$	17.1120	−	2.38507i	0.930768	−	0.129730i
$339$	0.693112	−	1.10308i	0.0376447	−	0.0599111i
$340$	−2.03357	+	34.0664i	−0.110286	+	1.84751i
$341$	2.70485	+	24.0062i	0.146476	+	1.30001i
$342$	−11.7340	+	9.87309i	−0.634500	+	0.533876i
$343$	2.98171	−	6.19158i	0.160997	−	0.334314i
$344$	0.319632	−	2.18073i	0.0172334	−	0.117577i
$345$	−6.70343	−	5.34581i	−0.360901	−	0.287809i
$346$	0.603182	−	3.00472i	0.0324272	−	0.161535i
$347$	−3.77068	+	3.77068i	−0.202421	+	0.202421i	−0.801036	−	0.598616i	$-0.795718\pi$
$347$	−3.77068	+	3.77068i	−0.202421	+	0.202421i	0.598616	+	0.801036i	$0.295718\pi$
$348$	3.08481	−	9.91076i	0.165363	−	0.531273i
$349$	−3.45250	−	3.45250i	−0.184808	−	0.184808i	0.608639	−	0.793447i	$-0.291716\pi$
$349$	−3.45250	−	3.45250i	−0.184808	−	0.184808i	−0.793447	+	0.608639i	$0.791716\pi$
$350$	−0.0971821	−	0.145999i	−0.00519460	−	0.00780400i
$351$	−2.69647	+	3.38126i	−0.143927	+	0.180478i
$352$	17.3252	−	6.43911i	0.923437	−	0.343205i
$353$	−17.3358	−	8.34848i	−0.922692	−	0.444345i	−0.0886603	−	0.996062i	$-0.528259\pi$
$353$	−17.3358	−	8.34848i	−0.922692	−	0.444345i	−0.834031	+	0.551717i	$0.813973\pi$
$354$	16.4677	+	1.41826i	0.875247	+	0.0753794i
$355$	−5.62486	+	0.633770i	−0.298537	+	0.0336370i
$356$	23.3340	+	26.2966i	1.23670	+	1.39372i
$357$	−3.03772	−	1.90873i	−0.160773	−	0.101021i
$358$	11.4635	−	15.1766i	0.605864	−	0.802107i
$359$	19.8277	+	4.52554i	1.04647	+	0.238849i	0.710992	−	0.703201i	$-0.248246\pi$
$359$	19.8277	+	4.52554i	1.04647	+	0.238849i	0.335474	+	0.942049i	$0.391104\pi$
$360$	9.80083	−	9.16825i	0.516549	−	0.483209i
$361$	−8.19803	−	1.87115i	−0.431475	−	0.0984814i
$362$	21.6470	−	18.2141i	1.13774	−	0.957310i
$363$	0.103198	−	0.294923i	0.00541649	−	0.0154794i
$364$	−0.430584	+	0.772641i	−0.0225688	+	0.0404974i
$365$	7.99422	+	7.99422i	0.418437	+	0.418437i
$366$	−8.05970	−	7.64671i	−0.421287	−	0.399700i
$367$	−7.22122	−	9.05512i	−0.376944	−	0.472673i	0.556783	−	0.830658i	$-0.312035\pi$
$367$	−7.22122	−	9.05512i	−0.376944	−	0.472673i	−0.933727	+	0.357985i	$0.883464\pi$
$368$	5.23376	−	14.6258i	0.272828	−	0.762421i
$369$	−1.04902	−	4.59605i	−0.0546098	−	0.239261i
$370$	11.1134	+	29.2687i	0.577759	+	1.52161i
$371$	0.843496	+	0.295152i	0.0437921	+	0.0153235i
$372$	9.53363	−	10.5928i	0.494296	−	0.549210i
$373$	−5.26243	−	0.592934i	−0.272478	−	0.0307009i	−0.0253320	−	0.999679i	$-0.508064\pi$
$373$	−5.26243	−	0.592934i	−0.272478	−	0.0307009i	−0.247146	+	0.968978i	$0.579493\pi$
$374$	14.1130	−	31.3910i	0.729767	−	1.62319i
$375$	4.55195	−	9.45223i	0.235062	−	0.488111i
$376$	1.16680	−	34.9889i	0.0601731	−	1.80441i
$377$	−4.07925	+	2.46338i	−0.210092	+	0.126871i
$378$	0.856922	+	3.34638i	0.0440753	+	0.172119i
$379$	−8.67518	+	3.03558i	−0.445614	+	0.155927i	−0.543752	−	0.839246i	$-0.682997\pi$
$379$	−8.67518	+	3.03558i	−0.445614	+	0.155927i	0.0981383	+	0.995173i	$0.468711\pi$
$380$	23.6339	+	4.10129i	1.21239	+	0.210392i
$381$	0.120231	−	1.06708i	0.00615964	−	0.0546683i
$382$	2.18963	+	3.28954i	0.112031	+	0.168307i
$383$	−1.92900	+	0.928959i	−0.0985675	+	0.0474676i	−0.482518	−	0.875886i	$-0.660278\pi$
$383$	−1.92900	+	0.928959i	−0.0985675	+	0.0474676i	0.383950	+	0.923354i	$0.374563\pi$
$384$	−9.62465	−	5.12356i	−0.491156	−	0.261461i
$385$	0.832445	+	3.64718i	0.0424253	+	0.185878i
$386$	−7.16957	+	22.3581i	−0.364921	+	1.13799i
$387$	−0.180708	+	1.60383i	−0.00918589	+	0.0815270i
$388$	−15.7137	+	4.46713i	−0.797742	+	0.226784i
$389$	21.1052	−	21.1052i	1.07008	−	1.07008i	0.0727263	−	0.997352i	$-0.476830\pi$
$389$	21.1052	−	21.1052i	1.07008	−	1.07008i	0.997352	−	0.0727263i	$-0.0231700\pi$
$390$	2.76199	−	0.0726241i	0.139859	−	0.00367747i
$391$	−12.5506	−	26.0615i	−0.634709	−	1.31799i
$392$	−7.70600	−	17.4683i	−0.389212	−	0.882282i
$393$	2.43129	+	0.554925i	0.122642	+	0.0279923i
$394$	−1.47980	+	0.378940i	−0.0745514	+	0.0190907i
$395$	−9.20522	−	14.6500i	−0.463165	−	0.737123i
$396$	−12.5228	+	5.13549i	−0.629293	+	0.258068i
$397$	1.60817	−	2.55938i	0.0807116	−	0.128452i	−0.803929	−	0.594725i	$-0.797261\pi$
$397$	1.60817	−	2.55938i	0.0807116	−	0.128452i	0.884641	+	0.466273i	$0.154404\pi$
$398$	11.0258	+	3.53564i	0.552672	+	0.177226i
$399$	−1.57223	+	1.97151i	−0.0787097	+	0.0986989i
$400$	−0.985513	−	0.118080i	−0.0492756	−	0.00590398i
$401$	−5.86319	−	2.82356i	−0.292794	−	0.141002i	0.281721	−	0.959496i	$-0.409095\pi$
$401$	−5.86319	−	2.82356i	−0.292794	−	0.141002i	−0.574514	+	0.818494i	$0.694809\pi$
$402$	10.8374	−	1.51052i	0.540520	−	0.0753377i
$403$	−6.50160	+	0.732554i	−0.323868	+	0.0364911i
$404$	12.8066	+	11.5261i	0.637153	+	0.573446i
$405$	−2.43562	+	2.43562i	−0.121027	+	0.121027i
$406$	−0.393780	+	3.78582i	−0.0195430	+	0.187887i
$407$		−	31.5742i		−	1.56507i
$408$	−19.3769	+	6.06335i	−0.959300	+	0.300180i
$409$	−5.02606	−	4.00815i	−0.248523	−	0.198190i	0.491303	−	0.870989i	$-0.336521\pi$
$409$	−5.02606	−	4.00815i	−0.248523	−	0.198190i	−0.739826	+	0.672798i	$0.765092\pi$
$410$	−4.44451	+	5.88411i	−0.219499	+	0.290596i
$411$	−9.32774	+	3.26392i	−0.460104	+	0.160997i
$412$	14.7295	−	20.6051i	0.725671	−	1.01514i
$413$	−6.02291	+	0.678619i	−0.296368	+	0.0333927i
$414$	−3.47351	+	10.8320i	−0.170714	+	0.532364i
$415$	−5.75598	−	25.2186i	−0.282550	−	1.23793i
$416$	1.74390	+	4.69218i	0.0855017	+	0.230053i
$417$	4.56615	−	20.0056i	0.223605	−	0.979679i
$418$	−20.8146	−	12.3277i	−1.01808	−	0.602969i
$419$	−21.9401	+	13.7859i	−1.07184	+	0.673484i	−0.947824	−	0.318795i	$-0.896722\pi$
$419$	−21.9401	+	13.7859i	−1.07184	+	0.673484i	−0.124021	+	0.992280i	$0.539579\pi$
$420$	1.28337	−	1.79531i	0.0626223	−	0.0876021i
$421$	10.1126	−	28.9001i	0.492857	−	1.40850i	−0.382018	−	0.924155i	$-0.624771\pi$
$421$	10.1126	−	28.9001i	0.492857	−	1.40850i	0.874875	−	0.484349i	$-0.160944\pi$
$422$	9.81941	−	0.258193i	0.478002	−	0.0125687i
$423$			25.6361i			1.24647i
$424$	4.36952	−	2.54648i	0.212203	−	0.123668i
$425$	−1.44503	+	1.15237i	−0.0700942	+	0.0558983i
$426$	−1.54040	−	2.99465i	−0.0746325	−	0.145091i
$427$	3.44956	+	2.16750i	0.166936	+	0.104893i
$428$	14.7106	−	10.3600i	0.711062	−	0.500768i
$429$	−2.63010	−	0.920311i	−0.126982	−	0.0444330i
$430$	2.10158	−	1.39888i	0.101347	−	0.0674601i
$431$	12.7490	+	15.9867i	0.614096	+	0.770052i	0.987500	−	0.157617i	$-0.0503810\pi$
$431$	12.7490	+	15.9867i	0.614096	+	0.770052i	−0.373404	+	0.927669i	$0.621810\pi$
$432$	17.5530	+	8.60601i	0.844521	+	0.414057i
$433$	−30.1017	−	14.4962i	−1.44660	−	0.696644i	−0.464596	−	0.885523i	$-0.653800\pi$
$433$	−30.1017	−	14.4962i	−1.44660	−	0.696644i	−0.982000	+	0.188879i	$0.939515\pi$
$434$	−2.66308	+	4.49645i	−0.127832	+	0.215836i
$435$	10.8017	−	4.96789i	0.517904	−	0.238192i
$436$	2.60588	−	8.92683i	0.124799	−	0.427518i
$437$	−19.1905	+	6.71506i	−0.918008	+	0.321225i
$438$	−2.75804	+	6.13460i	−0.131784	+	0.293122i
$439$	−6.68741	+	5.33303i	−0.319173	+	0.254532i	−0.769949	−	0.638105i	$-0.779719\pi$
$439$	−6.68741	+	5.33303i	−0.319173	+	0.254532i	0.450777	+	0.892637i	$0.351147\pi$
$440$	18.7579	+	9.81653i	0.894249	+	0.467985i
$441$	6.06619	+	12.5966i	0.288866	+	0.599837i
$442$	8.50162	+	3.82222i	0.404381	+	0.181804i
$443$	−10.5622	−	6.63665i	−0.501824	−	0.315317i	0.257224	−	0.966352i	$-0.417192\pi$
$443$	−10.5622	−	6.63665i	−0.501824	−	0.315317i	−0.759048	+	0.651035i	$0.774335\pi$
$444$	−13.9320	+	12.3624i	−0.661183	+	0.586692i
$445$	−4.50879	+	40.0166i	−0.213737	+	1.89697i
$446$	−11.7484	+	12.3829i	−0.556301	+	0.586346i
$447$	1.99252			0.0942429
$448$	3.83009	+	1.14741i	0.180955	+	0.0542102i
$449$	−24.1133	+	11.6124i	−1.13798	+	0.548022i	−0.905402	−	0.424556i	$-0.860430\pi$
$449$	−24.1133	+	11.6124i	−1.13798	+	0.548022i	−0.232577	+	0.972578i	$0.574716\pi$
$450$	0.724157	+	0.0623670i	0.0341371	+	0.00294001i
$451$	6.29694	−	3.95663i	0.296511	−	0.186310i
$452$	1.29942	+	2.37082i	0.0611197	+	0.111514i
$453$	9.61339	+	15.2996i	0.451676	+	0.718839i
$454$	6.68656	−	8.85237i	0.313816	−	0.415462i
$455$	−0.987764	+	0.225451i	−0.0463071	+	0.0105693i
$456$	2.71008	+	14.0111i	0.126911	+	0.656131i
$457$	−20.2084	−	16.1157i	−0.945311	−	0.753860i	0.0239969	−	0.999712i	$-0.492361\pi$
$457$	−20.2084	−	16.1157i	−0.945311	−	0.753860i	−0.969307	+	0.245852i	$0.920932\pi$
$458$	14.2733	−	12.0097i	0.666946	−	0.561176i
$459$	34.3601	−	12.0231i	1.60379	−	0.561191i
$460$	16.4627	−	6.75123i	0.767579	−	0.314778i
$461$	7.34010	−	0.827030i	0.341862	−	0.0385186i	0.0606355	−	0.998160i	$-0.480687\pi$
$461$	7.34010	−	0.827030i	0.341862	−	0.0385186i	0.281227	+	0.959641i	$0.409259\pi$
$462$	−1.85273	+	1.23324i	−0.0861967	+	0.0573754i
$463$	−32.2440			−1.49851			−0.749254	−	0.662283i	$-0.769588\pi$
$463$	−32.2440			−1.49851			−0.749254	+	0.662283i	$0.769588\pi$
$464$	14.8495	+	15.6042i	0.689371	+	0.724408i
$465$	16.3239			0.757003
$466$	2.18023	−	1.45123i	0.100997	−	0.0672271i
$467$	−1.80216	+	0.203055i	−0.0833941	+	0.00939625i	−0.153563	−	0.988139i	$-0.549075\pi$
$467$	−1.80216	+	0.203055i	−0.0833941	+	0.00939625i	0.0701688	+	0.997535i	$0.477646\pi$
$468$	−1.39084	−	3.39154i	−0.0642916	−	0.156774i
$469$	−3.78731	+	1.32524i	−0.174882	+	0.0611937i
$470$	30.6834	−	25.8174i	1.41532	−	1.19087i
$471$	10.6215	+	8.47037i	0.489413	+	0.390294i
$472$	−19.2072	+	28.4193i	−0.884082	+	1.30810i
$473$	−2.48224	+	0.566555i	−0.114134	+	0.0260502i
$474$	6.20419	−	8.21376i	0.284968	−	0.377271i
$475$	0.691163	+	1.09998i	0.0317128	+	0.0504706i
$476$	6.52889	−	3.57842i	0.299251	−	0.164016i
$477$	−3.13581	+	1.97036i	−0.143579	+	0.0902165i
$478$	24.0698	+	2.07298i	1.10093	+	0.0948158i
$479$	−27.3000	+	13.1470i	−1.24737	+	0.600702i	−0.936806	−	0.349851i	$-0.886232\pi$
$479$	−27.3000	+	13.1470i	−1.24737	+	0.600702i	−0.310564	+	0.950552i	$0.600518\pi$
$480$	−3.01286	−	12.1204i	−0.137518	−	0.553217i
$481$	8.55121			0.389902
$482$	−27.8201	+	29.3227i	−1.26717	+	1.33561i
$483$	−0.209432	+	1.85876i	−0.00952950	+	0.0845767i
$484$	0.430372	+	0.485015i	0.0195624	+	0.0220462i
$485$	−15.8442	−	9.95554i	−0.719446	−	0.452058i
$486$	−20.7807	−	9.34276i	−0.942634	−	0.423796i
$487$	7.59889	+	15.7793i	0.344339	+	0.715026i	0.999169	−	0.0407490i	$-0.0129744\pi$
$487$	7.59889	+	15.7793i	0.344339	+	0.715026i	−0.654831	+	0.755776i	$0.727260\pi$
$488$	22.0039	−	6.88537i	0.996069	−	0.311686i
$489$	−11.7375	+	9.36035i	−0.530788	+	0.423290i
$490$	8.96756	−	19.9462i	0.405113	−	0.901077i
$491$	24.1774	−	8.46005i	1.09111	−	0.381797i	0.276034	−	0.961148i	$-0.410980\pi$
$491$	24.1774	−	8.46005i	1.09111	−	0.381797i	0.815078	+	0.579351i	$0.196694\pi$
$492$	−4.21132	−	1.22935i	−0.189861	−	0.0554232i
$493$	40.1049	+	0.711149i	1.80623	+	0.0320285i
$494$	3.33871	−	5.63722i	0.150216	−	0.253630i
$495$	−13.9681	−	6.72668i	−0.627819	−	0.302342i
$496$	9.57101	+	27.9834i	0.429751	+	1.25649i
$497$	0.769945	+	0.965481i	0.0345368	+	0.0433077i
$498$	12.8108	−	8.52727i	0.574064	−	0.382116i
$499$	−28.3324	−	9.91395i	−1.26833	−	0.443809i	−0.389540	−	0.921010i	$-0.627366\pi$
$499$	−28.3324	−	9.91395i	−1.26833	−	0.443809i	−0.878794	+	0.477200i	$0.841652\pi$
$500$	12.5361	+	17.8006i	0.560633	+	0.796067i
$501$	−10.2825	−	6.46095i	−0.459390	−	0.288654i
$502$	−5.04760	−	9.81294i	−0.225286	−	0.437973i
$503$	−7.85988	+	6.26805i	−0.350455	+	0.279478i	−0.782856	−	0.622203i	$-0.786238\pi$
$503$	−7.85988	+	6.26805i	−0.350455	+	0.279478i	0.432401	+	0.901681i	$0.357666\pi$
$504$	−2.83116	−	0.746288i	−0.126110	−	0.0332423i
$505$			19.7355i			0.878220i
$506$	−17.9386	+	0.471680i	−0.797467	+	0.0209688i
$507$	−3.88868	+	11.1132i	−0.172702	+	0.493554i
$508$	1.81291	+	1.29596i	0.0804348	+	0.0574987i
$509$	5.13175	−	3.22449i	0.227461	−	0.142923i	−0.413481	−	0.910513i	$-0.635687\pi$
$509$	5.13175	−	3.22449i	0.227461	−	0.142923i	0.640941	+	0.767590i	$0.278544\pi$
$510$	−20.0102	−	11.8513i	−0.886064	−	0.524783i
$511$	0.548835	−	2.40460i	0.0242790	−	0.106373i
$512$	19.0110	−	12.2712i	0.840174	−	0.542317i
$513$	−5.69359	−	24.9452i	−0.251378	−	1.10136i
$514$	5.79068	−	18.0580i	0.255416	−	0.796506i
$515$	28.8298	−	3.24833i	1.27039	−	0.143139i
$516$	1.22187	+	0.873454i	0.0537900	+	0.0384517i
$517$	−38.1720	+	13.3570i	−1.67880	+	0.587438i
$518$	4.11668	−	5.45010i	0.180877	−	0.239464i
$519$	1.63282	+	1.30213i	0.0716730	+	0.0571573i
$520$	−2.65860	+	5.08020i	−0.116588	+	0.222782i
$521$			4.62824i			0.202767i	0.994847	+	0.101384i	$0.0323269\pi$
$521$			4.62824i			0.202767i	−0.994847	+	0.101384i	$0.967673\pi$
$522$	−11.2489	−	11.0580i	−0.492350	−	0.483994i
$523$	3.41920	−	3.41920i	0.149511	−	0.149511i	−0.628388	−	0.777900i	$-0.716285\pi$
$523$	3.41920	−	3.41920i	0.149511	−	0.149511i	0.777900	+	0.628388i	$0.216285\pi$
$524$	−3.46212	+	3.84675i	−0.151243	+	0.168046i
$525$	0.118768	−	0.0133819i	0.00518344	−	0.000584034i
$526$	−12.3342	+	1.71914i	−0.537797	+	0.0749581i
$527$	49.6180	+	23.8948i	2.16140	+	1.04087i
$528$	−1.49843	+	12.5061i	−0.0652107	+	0.544259i
$529$	4.93705	−	6.19087i	0.214655	−	0.269168i
$530$	5.51628	+	1.76891i	0.239612	+	0.0768364i
$531$	13.3637	−	21.2682i	0.579935	−	0.922961i
$532$	−1.98557	−	4.84176i	−0.0860852	−	0.209917i
$533$	1.07157	+	1.70540i	0.0464149	+	0.0738690i
$534$	−23.2091	+	5.94326i	−1.00436	+	0.257190i
$535$	20.0926	+	4.58601i	0.868679	+	0.198270i
$536$	−8.21010	+	21.1716i	−0.354622	+	0.914475i
$537$	5.62360	+	11.6775i	0.242676	+	0.503922i
$538$	44.8120	−	1.17829i	1.93198	−	0.0507999i
$539$	−15.5956	+	15.5956i	−0.671751	+	0.671751i
$540$	6.12318	+	21.5390i	0.263500	+	0.926893i
$541$	0.100299	−	0.890176i	0.00431218	−	0.0382717i	−0.991372	−	0.131080i	$-0.958156\pi$
$541$	0.100299	−	0.890176i	0.00431218	−	0.0382717i	0.995684	+	0.0928079i	$0.0295842\pi$
$542$	3.30273	−	10.2994i	0.141864	−	0.442399i
$543$	4.28996	+	18.7955i	0.184100	+	0.806593i
$544$	8.58381	−	41.2512i	0.368028	−	1.76863i
$545$	9.59705	−	4.62169i	0.411092	−	0.197972i
$546$	−0.333997	−	0.501773i	−0.0142938	−	0.0214739i
$547$	0.0307889	−	0.273259i	0.00131644	−	0.0116837i	−0.993037	−	0.117804i	$-0.962414\pi$
$547$	0.0307889	−	0.273259i	0.00131644	−	0.0116837i	0.994353	+	0.106121i	$0.0338430\pi$
$548$	3.50649	−	20.2063i	0.149790	−	0.863172i
$549$	−15.9361	+	5.57629i	−0.680137	+	0.237990i
$550$	0.284437	+	1.11076i	0.0121285	+	0.0473630i
$551$	3.65285	−	27.9556i	0.155617	−	1.19095i
$552$	7.23170	+	7.73066i	0.307802	+	0.329039i
$553$	−1.63776	+	3.40084i	−0.0696445	+	0.144618i
$554$	−13.5754	+	30.1953i	−0.576765	+	1.28288i
$555$	−21.2008	−	2.38876i	−0.899926	−	0.101397i
$556$	31.6526	+	28.4877i	1.34237	+	1.20815i
$557$	−30.7359	−	10.7550i	−1.30232	−	0.455702i	−0.412062	−	0.911156i	$-0.635191\pi$
$557$	−30.7359	−	10.7550i	−1.30232	−	0.455702i	−0.890259	+	0.455454i	$0.849477\pi$
$558$	−7.68779	−	20.2468i	−0.325450	−	0.857117i
$559$	−0.153440	−	0.672264i	−0.00648982	−	0.0284337i
$560$	1.95797	+	4.14014i	0.0827391	+	0.174953i
$561$	14.6236	+	18.3374i	0.617408	+	0.774205i
$562$	18.6955	+	17.7375i	0.788621	+	0.748211i
$563$	3.77289	+	3.77289i	0.159008	+	0.159008i	0.782127	−	0.623119i	$-0.214135\pi$
$563$	3.77289	+	3.77289i	0.159008	+	0.159008i	−0.623119	+	0.782127i	$0.714135\pi$
$564$	20.8394	+	11.6136i	0.877495	+	0.489019i
$565$	−1.02280	+	2.92300i	−0.0430296	+	0.122971i
$566$	0.562043	−	0.472909i	0.0236244	−	0.0198779i
$567$	0.732617	+	0.167215i	0.0307670	+	0.00702237i
$568$	6.98477	+	0.232926i	0.293074	+	0.00977337i
$569$	0.428439	+	0.0977885i	0.0179611	+	0.00409951i	0.231492	−	0.972837i	$-0.425639\pi$
$569$	0.428439	+	0.0977885i	0.0179611	+	0.00409951i	−0.213531	+	0.976936i	$0.568496\pi$
$570$	−9.85234	+	13.0436i	−0.412669	+	0.546335i
$571$	19.9113	+	12.5111i	0.833262	+	0.523573i	0.879800	−	0.475343i	$-0.157676\pi$
$571$	19.9113	+	12.5111i	0.833262	+	0.523573i	−0.0465383	+	0.998917i	$0.514819\pi$
$572$	4.32533	−	3.83802i	0.180851	−	0.160476i
$573$	−2.67598	+	0.301510i	−0.111790	+	0.0125958i
$574$	1.60280	+	0.138039i	0.0668997	+	0.00576165i
$575$	0.868222	+	0.418114i	0.0362073	+	0.0174365i
$576$	−13.6142	+	9.44503i	−0.567259	+	0.393543i
$577$	3.42700	−	4.29733i	0.142668	−	0.178900i	−0.705364	−	0.708846i	$-0.749216\pi$
$577$	3.42700	−	4.29733i	0.142668	−	0.178900i	0.848032	+	0.529946i	$0.177788\pi$
$578$	−30.1534	−	45.3003i	−1.25421	−	1.88424i
$579$	−11.3140	−	11.3140i	−0.470194	−	0.470194i
$580$	−1.90669	+	24.5998i	−0.0791711	+	1.02145i
$581$	−3.99036	+	3.99036i	−0.165548	+	0.165548i
$582$	2.19110	−	10.9149i	0.0908240	−	0.452436i
$583$	−4.56768	−	3.64260i	−0.189174	−	0.150861i
$584$	−8.33432	−	11.1971i	−0.344877	−	0.463338i
$585$	1.82178	−	3.78297i	0.0753215	−	0.156407i
$586$	−3.11887	+	2.62425i	−0.128839	+	0.108407i
$587$	−2.04149	−	18.1187i	−0.0842614	−	0.747841i	−0.962808	−	0.270185i	$-0.912915\pi$
$587$	−2.04149	−	18.1187i	−0.0842614	−	0.747841i	0.878547	−	0.477656i	$-0.158513\pi$
$588$	12.9877	+	0.775293i	0.535605	+	0.0319725i
$589$	20.5943	−	32.7756i	0.848573	−	1.35050i
$590$	−38.9138	+	5.42381i	−1.60206	+	0.223295i
$591$	0.231638	−	1.01487i	0.00952831	−	0.0417462i
$592$	−8.33549	−	37.7443i	−0.342586	−	1.55128i
$593$	−9.58390	+	41.9898i	−0.393564	+	1.72432i	0.258376	+	0.966044i	$0.416813\pi$
$593$	−9.58390	+	41.9898i	−0.393564	+	1.72432i	−0.651940	+	0.758271i	$0.726044\pi$
$594$	1.93777	−	22.4999i	0.0795077	−	0.923181i
$595$	8.04951	+	2.81664i	0.329998	+	0.115471i
$596$	−2.01291	+	3.61197i	−0.0824521	+	0.147952i
$597$	−5.57945	+	5.57945i	−0.228352	+	0.228352i
$598$	−0.127745	−	4.85830i	−0.00522388	−	0.198671i
$599$	−21.8722	+	17.4425i	−0.893672	+	0.712680i	−0.958462	−	0.285219i	$-0.907934\pi$
$599$	−21.8722	+	17.4425i	−0.893672	+	0.712680i	0.0647904	+	0.997899i	$0.479362\pi$
$600$	0.378752	−	0.560408i	0.0154625	−	0.0228786i
$601$	40.8230	−	9.31759i	1.66521	−	0.380072i	0.716837	−	0.697241i	$-0.245589\pi$
$601$	40.8230	−	9.31759i	1.66521	−	0.380072i	0.948369	+	0.317168i	$0.102732\pi$
$602$	−0.502335	−	0.225843i	−0.0204736	−	0.00920469i
$603$	5.49207	−	15.6954i	0.223654	−	0.639167i
$604$	−37.4464	+	1.97061i	−1.52367	+	0.0801829i
$605$	−0.0831602	+	0.738067i	−0.00338094	+	0.0300067i
$606$	−10.9767	+	4.16790i	−0.445899	+	0.169309i
$607$	23.3848	+	11.2615i	0.949159	+	0.457091i	0.843391	−	0.537300i	$-0.180556\pi$
$607$	23.3848	+	11.2615i	0.949159	+	0.457091i	0.105768	+	0.994391i	$0.466270\pi$
$608$	−28.1367	−	9.24178i	−1.14109	−	0.374804i
$609$	−2.17143	−	1.41871i	−0.0879910	−	0.0574892i
$610$	22.7230	+	13.4580i	0.920027	+	0.544897i
$611$	−3.61746	−	10.3381i	−0.146347	−	0.418235i
$612$	−5.27550	+	30.4003i	−0.213250	+	1.22886i
$613$	−17.8326	−	2.00926i	−0.720253	−	0.0811531i	−0.255773	−	0.966737i	$-0.582330\pi$
$613$	−17.8326	−	2.00926i	−0.720253	−	0.0811531i	−0.464480	+	0.885584i	$0.653759\pi$
$614$	1.00782	−	5.02039i	0.0406721	−	0.202606i
$615$	−2.18033	−	4.52750i	−0.0879193	−	0.182566i
$616$	−0.363879	−	4.60442i	−0.0146611	−	0.185517i
$617$	25.7416	−	5.87536i	1.03632	−	0.236533i	0.329670	−	0.944096i	$-0.393063\pi$
$617$	25.7416	−	5.87536i	1.03632	−	0.236533i	0.706650	+	0.707563i	$0.250206\pi$
$618$	7.89518	+	15.3489i	0.317591	+	0.617421i
$619$	−6.68087	−	0.752753i	−0.268527	−	0.0302557i	−0.0233256	−	0.999728i	$-0.507425\pi$
$619$	−6.68087	−	0.752753i	−0.268527	−	0.0302557i	−0.245201	+	0.969472i	$0.578854\pi$
$620$	−16.4910	+	29.5914i	−0.662294	+	1.18842i
$621$	−13.4208	−	13.4208i	−0.538558	−	0.538558i
$622$	−0.404210	−	0.383498i	−0.0162074	−	0.0153769i
$623$	7.91533	−	3.81182i	0.317121	−	0.152717i
$624$	−3.38703	−	0.405818i	−0.135590	−	0.0162457i
$625$	−5.82540	+	25.5228i	−0.233016	+	1.02091i
$626$	−4.35670	+	7.35604i	−0.174129	+	0.294006i
$627$	13.9587	−	8.77084i	0.557457	−	0.350274i
$628$	−26.0850	+	10.6972i	−1.04091	+	0.426866i
$629$	−60.9453	−	38.2945i	−2.43005	−	1.52690i
$630$	−1.53404	−	2.98229i	−0.0611175	−	0.118817i
$631$	10.2598	+	8.18194i	0.408438	+	0.325718i	0.806063	−	0.591830i	$-0.201594\pi$
$631$	10.2598	+	8.18194i	0.408438	+	0.325718i	−0.397625	+	0.917548i	$0.630166\pi$
$632$	8.62194	+	19.5446i	0.342962	+	0.777441i
$633$	−2.90437	+	6.03099i	−0.115438	+	0.239710i
$634$	18.7114	−	24.7721i	0.743124	−	0.983827i
$635$	0.285800	+	2.53655i	0.0113416	+	0.100660i
$636$	0.181117	+	3.44168i	0.00718177	+	0.136471i
$637$	−4.22375	−	4.22375i	−0.167351	−	0.167351i
$638$	10.6044	−	22.5110i	0.419830	−	0.891217i
$639$	−5.11768			−0.202452
$640$	25.0151	+	6.78281i	0.988809	+	0.268114i
$641$	−26.1308	+	32.7670i	−1.03210	+	1.29422i	−0.0772910	+	0.997009i	$0.524627\pi$
$641$	−26.1308	+	32.7670i	−1.03210	+	1.29422i	−0.954813	+	0.297208i	$0.903944\pi$
$642$	1.69261	+	12.1438i	0.0668020	+	0.479279i
$643$	1.20247	+	3.43647i	0.0474209	+	0.135521i	0.965158	−	0.261666i	$-0.0842720\pi$
$643$	1.20247	+	3.43647i	0.0474209	+	0.135521i	−0.917738	+	0.397187i	$0.869986\pi$
$644$	−3.15793	−	2.25744i	−0.124440	−	0.0889556i
$645$	0.192625	+	1.70959i	0.00758460	+	0.0673152i
$646$	−49.0402	+	25.2254i	−1.92946	+	0.992480i
$647$	−47.5398	+	10.8506i	−1.86898	+	0.426583i	−0.997913	−	0.0645790i	$-0.979430\pi$
$647$	−47.5398	+	10.8506i	−1.86898	+	0.426583i	−0.871068	+	0.491162i	$0.836572\pi$
$648$	3.41144	−	2.53924i	0.134014	−	0.0997508i
$649$	38.6310	+	8.81728i	1.51640	+	0.346109i
$650$	−0.300827	+	0.0770340i	−0.0117994	+	0.00302152i
$651$	−1.89470	−	3.01541i	−0.0742593	−	0.118183i
$652$	−5.11048	−	30.7335i	−0.200142	−	1.20362i
$653$	2.05817	+	0.720185i	0.0805424	+	0.0281830i	0.370250	−	0.928932i	$-0.379272\pi$
$653$	2.05817	+	0.720185i	0.0805424	+	0.0281830i	−0.289707	+	0.957115i	$0.593558\pi$
$654$	4.59732	+	4.36175i	0.179769	+	0.170558i
$655$	−5.92800			−0.231626
$656$	6.48294	−	6.39220i	0.253116	−	0.249574i
$657$	6.37298	+	7.99147i	0.248634	+	0.311777i
$658$	−8.33047	−	2.67134i	−0.324756	−	0.104140i
$659$	−11.8959	+	18.9322i	−0.463399	+	0.737495i	−0.993911	−	0.110182i	$-0.964857\pi$
$659$	−11.8959	+	18.9322i	−0.463399	+	0.737495i	0.530513	+	0.847677i	$0.321999\pi$
$660$	−11.7958	+	8.30726i	−0.459152	+	0.323360i
$661$	9.19103	−	26.2665i	0.357490	−	1.02165i	−0.614965	−	0.788554i	$-0.710830\pi$
$661$	9.19103	−	26.2665i	0.357490	−	1.02165i	0.972455	−	0.233092i	$-0.0748844\pi$
$662$	28.2971	+	5.68049i	1.09980	+	0.220778i
$663$	−4.96630	+	3.96049i	−0.192875	+	0.153813i
$664$	2.51606	+	31.8375i	0.0976421	+	1.23553i
$665$	2.60078	−	5.40058i	0.100854	−	0.209425i
$666$	7.02176	+	27.4208i	0.272088	+	1.06253i
$667$	−8.73845	−	19.0001i	−0.338354	−	0.735688i
$668$	22.1000	−	12.1128i	0.855074	−	0.468657i
$669$	−3.84184	−	10.9793i	−0.148534	−	0.424486i
$670$	−24.3165	+	9.23306i	−0.939430	+	0.356704i
$671$	−16.6061	−	20.8234i	−0.641073	−	0.803880i
$672$	−1.88921	+	1.96335i	−0.0728780	+	0.0757378i
$673$	3.74944	−	1.80564i	0.144530	−	0.0696022i	−0.360221	−	0.932867i	$-0.617299\pi$
$673$	3.74944	−	1.80564i	0.144530	−	0.0696022i	0.504751	+	0.863265i	$0.331584\pi$
$674$	27.6931	−	10.5151i	1.06670	−	0.405028i
$675$	−0.645216	+	1.02686i	−0.0248344	+	0.0395237i
$676$	−16.2171	−	18.2762i	−0.623736	−	0.702931i
$677$	35.2728	+	3.97430i	1.35565	+	0.152745i	0.759697	−	0.650278i	$-0.225347\pi$
$677$	35.2728	+	3.97430i	1.35565	+	0.152745i	0.595949	+	0.803022i	$0.296776\pi$
$678$	−1.84175	+	0.0484273i	−0.0707319	+	0.00185984i
$679$			4.08231i			0.156665i
$680$	41.6985	−	24.3012i	1.59907	−	0.931907i
$681$	3.28020	+	6.81141i	0.125698	+	0.261014i
$682$	26.1420	−	21.9961i	1.00103	−	0.842275i
$683$	13.6862	+	21.7814i	0.523687	+	0.833444i	0.998922	−	0.0464153i	$-0.0147798\pi$
$683$	13.6862	+	21.7814i	0.523687	+	0.833444i	−0.475235	+	0.879859i	$0.657637\pi$
$684$	20.8182	+	6.07714i	0.796003	+	0.232365i
$685$	19.8905	−	12.4980i	0.759976	−	0.477524i
$686$	−9.62562	+	1.34162i	−0.367508	+	0.0512233i
$687$	2.82864	+	12.3931i	0.107919	+	0.472826i
$688$	−2.81775	+	1.33258i	−0.107426	+	0.0508039i
$689$	0.986524	−	1.23706i	0.0375836	−	0.0471283i
$690$	−1.04044	+	12.0808i	−0.0396088	+	0.459907i
$691$	−12.9228	−	36.9311i	−0.491605	−	1.40493i	−0.876248	−	0.481861i	$-0.839961\pi$
$691$	−12.9228	−	36.9311i	−0.491605	−	1.40493i	0.384643	−	0.923066i	$-0.374325\pi$
$692$	−4.01000	+	1.64447i	−0.152437	+	0.0625132i
$693$	0.378693	+	3.36099i	0.0143854	+	0.127674i
$694$	7.39386	+	1.48428i	0.280667	+	0.0563424i
$695$			48.7780i			1.85026i
$696$	−14.0848	+	4.13468i	−0.533885	+	0.156725i
$697$		−	16.9533i		−	0.642152i
$698$	−1.35903	+	6.76994i	−0.0514400	+	0.256246i
$699$	0.199834	+	1.77357i	0.00755841	+	0.0670828i
$700$	−0.0957250	+	0.228817i	−0.00361806	+	0.00864846i
$701$	9.60068	+	27.4372i	0.362613	+	1.03629i	0.970257	+	0.242078i	$0.0778291\pi$
$701$	9.60068	+	27.4372i	0.362613	+	1.03629i	−0.607644	+	0.794210i	$0.707885\pi$
$702$	6.09363	+	0.524805i	0.229989	+	0.0198075i
$703$	−31.5433	+	39.5540i	−1.18968	+	1.49181i
$704$	−21.1569	−	15.3504i	−0.797381	−	0.578541i
$705$	6.08076	+	26.6416i	0.229015	+	1.00338i
$706$	3.75640	+	26.9508i	0.141374	+	1.01431i
$707$	3.64561	−	2.29069i	0.137107	−	0.0861503i
$708$	−11.2348	−	20.4981i	−0.422229	−	0.770365i
$709$	−5.13971	−	8.17980i	−0.193026	−	0.307199i	0.736163	−	0.676804i	$-0.236636\pi$
$709$	−5.13971	−	8.17980i	−0.193026	−	0.307199i	−0.929189	+	0.369606i	$0.879493\pi$
$710$	5.15388	+	6.12528i	0.193422	+	0.229878i
$711$	−6.78722	−	14.0938i	−0.254541	−	0.528559i
$712$	12.6729	−	48.0767i	0.474937	−	1.80175i
$713$		−	28.7136i		−	1.07533i
$714$	0.133362	+	5.07191i	0.00499093	+	0.189811i
$715$	6.58202	+	0.741615i	0.246154	+	0.0277348i
$716$	−26.8498	−	1.60278i	−1.00342	−	0.0598986i
$717$	−8.75907	+	13.9400i	−0.327114	+	0.520598i
$718$	−10.2097	−	26.8886i	−0.381022	−	1.00347i
$719$	9.87529	−	4.75569i	0.368286	−	0.177357i	−0.240582	−	0.970629i	$-0.577338\pi$
$719$	9.87529	−	4.75569i	0.368286	−	0.177357i	0.608868	+	0.793272i	$0.291624\pi$
$720$	−18.4735	−	4.35366i	−0.688468	−	0.162251i
$721$	−3.94629	−	4.94849i	−0.146968	−	0.184292i
$722$	4.22133	+	11.1175i	0.157102	+	0.413749i
$723$	−9.09747	−	25.9991i	−0.338339	−	0.966916i
$724$	−38.4058	−	11.2112i	−1.42734	−	0.416662i
$725$	−1.05935	+	0.814501i	−0.0393433	+	0.0302498i
$726$	−0.428069	+	0.109617i	−0.0158871	+	0.00406829i
$727$	−12.5753	+	26.1129i	−0.466392	+	0.968473i	0.526580	+	0.850125i	$0.323474\pi$
$727$	−12.5753	+	26.1129i	−0.466392	+	0.968473i	−0.992972	+	0.118348i	$0.962240\pi$
$728$	1.24701	−	0.0985493i	0.0462174	−	0.00365248i
$729$	8.61267	−	6.86838i	0.318988	−	0.254384i
$730$	3.14681	−	15.6757i	0.116469	−	0.580184i
$731$	−1.91699	+	5.47843i	−0.0709023	+	0.202627i
$732$	−2.68640	+	15.4805i	−0.0992920	+	0.572175i
$733$	6.51144	−	10.3629i	0.240505	−	0.382762i	−0.704560	−	0.709645i	$-0.748855\pi$
$733$	6.51144	−	10.3629i	0.240505	−	0.382762i	0.945065	+	0.326883i	$0.105998\pi$
$734$	−5.00151	+	15.5970i	−0.184609	+	0.575697i
$735$	9.29197	+	11.6518i	0.342739	+	0.429782i
$736$	−21.3196	+	5.29959i	−0.785850	+	0.195346i
$737$	26.2319			0.966265
$738$	−4.58871	+	4.83654i	−0.168913	+	0.178035i
$739$	20.8567	+	7.29808i	0.767227	+	0.268464i	0.685385	−	0.728181i	$-0.259634\pi$
$739$	20.8567	+	7.29808i	0.767227	+	0.268464i	0.0818421	+	0.996645i	$0.473920\pi$
$740$	25.7481	−	36.0190i	0.946519	−	1.32408i
$741$	2.37540	+	3.78043i	0.0872626	+	0.138878i
$742$	−0.313512	−	1.22430i	−0.0115094	−	0.0449455i
$743$	−37.6745	−	8.59896i	−1.38214	−	0.315465i	−0.534113	−	0.845413i	$-0.679354\pi$
$743$	−37.6745	−	8.59896i	−1.38214	−	0.315465i	−0.848030	+	0.529948i	$0.822212\pi$
$744$	−19.9412	−	2.92281i	−0.731079	−	0.107155i
$745$	−4.61764	+	1.05395i	−0.169177	+	0.0386136i
$746$	3.42572	+	6.65988i	0.125425	+	0.243835i
$747$	−2.61849	−	23.2397i	−0.0958055	−	0.850297i
$748$	−48.0146	+	7.98404i	−1.75559	+	0.291926i
$749$	−1.48499	−	4.24387i	−0.0542605	−	0.155067i
$750$	−14.6947	+	2.04815i	−0.536575	+	0.0747879i
$751$	14.5824	−	18.2857i	0.532118	−	0.667255i	−0.441015	−	0.897500i	$-0.645381\pi$
$751$	14.5824	−	18.2857i	0.532118	−	0.667255i	0.973133	+	0.230245i	$0.0739528\pi$
$752$	−42.1053	+	26.0444i	−1.53542	+	0.949743i
$753$	7.51998			0.274043
$754$	6.09663	+	2.87197i	0.222026	+	0.104591i
$755$	−30.3717	−	30.3717i	−1.10534	−	1.10534i
$756$	3.26805	−	3.63112i	0.118858	−	0.132062i
$757$	−0.875563	−	7.77084i	−0.0318229	−	0.282436i	−0.999538	−	0.0303898i	$-0.990325\pi$
$757$	−0.875563	−	7.77084i	−0.0318229	−	0.282436i	0.967715	−	0.252046i	$-0.0811034\pi$
$758$	10.3717	+	7.83418i	0.376718	+	0.284550i
$759$	5.30585	−	11.0177i	0.192590	−	0.399917i
$760$	−13.6918	−	31.0371i	−0.496653	−	1.12583i
$761$	−2.46587	−	1.96647i	−0.0893879	−	0.0712844i	0.577776	−	0.816195i	$-0.303921\pi$
$761$	−2.46587	−	1.96647i	−0.0893879	−	0.0712844i	−0.667164	+	0.744911i	$0.732492\pi$
$762$	−1.35045	+	0.694646i	−0.0489215	+	0.0251644i
$763$	−1.96766	−	1.23636i	−0.0712339	−	0.0447592i
$764$	2.15680	−	5.15551i	0.0780302	−	0.186520i
$765$	−29.9251	+	18.8032i	−1.08194	+	0.679831i
$766$	2.60523	+	1.54298i	0.0941309	+	0.0557502i
$767$	−2.38798	+	10.4624i	−0.0862250	+	0.377776i
$768$	1.51033	+	15.3456i	0.0544995	+	0.553738i
$769$	46.7036	−	22.4913i	1.68418	−	0.811056i	0.687809	−	0.725892i	$-0.258573\pi$
$769$	46.7036	−	22.4913i	1.68418	−	0.811056i	0.996367	−	0.0851649i	$-0.0271417\pi$
$770$	3.64135	−	3.83801i	0.131225	−	0.138312i
$771$	9.13803	+	9.13803i	0.329098	+	0.329098i
$772$	31.9394	−	9.07983i	1.14953	−	0.326790i
$773$	−28.8572	−	3.25143i	−1.03792	−	0.116946i	−0.423478	−	0.905906i	$-0.639191\pi$
$773$	−28.8572	−	3.25143i	−1.03792	−	0.116946i	−0.614444	+	0.788960i	$0.710620\pi$
$774$	2.02972	−	1.04405i	0.0729569	−	0.0375277i
$775$	−1.78868	+	0.408255i	−0.0642514	+	0.0146650i
$776$	17.5726	+	14.9985i	0.630818	+	0.538416i
$777$	2.01951	+	4.19355i	0.0724494	+	0.150443i
$778$	−41.3848	−	8.30778i	−1.48372	−	0.297848i
$779$	−11.8412	−	1.33418i	−0.424253	−	0.0478019i
$780$	−2.24985	−	3.19466i	−0.0805576	−	0.114387i
$781$	−2.66643	−	7.62021i	−0.0954122	−	0.272672i
$782$	−20.8462	+	35.1976i	−0.745459	+	1.25866i
$783$	24.9922	−	8.25080i	0.893150	−	0.294860i
$784$	−14.5261	+	22.7605i	−0.518789	+	0.812874i
$785$	−29.0956	−	14.0117i	−1.03847	−	0.500099i
$786$	−1.25192	−	3.29710i	−0.0446545	−	0.117604i
$787$	5.33735	−	47.3703i	0.190256	−	1.68857i	−0.428941	−	0.903332i	$-0.641113\pi$
$787$	5.33735	−	47.3703i	0.190256	−	1.68857i	0.619197	−	0.785236i	$-0.287458\pi$
$788$	1.60572	+	1.44516i	0.0572013	+	0.0514818i
$789$	2.80294	−	8.01033i	0.0997871	−	0.285175i
$790$	−10.0334	+	22.3170i	−0.356974	+	0.794003i
$791$	0.658661	−	0.150335i	0.0234193	−	0.00534530i
$792$	15.8589	+	10.7183i	0.563522	+	0.380857i
$793$	5.63960	−	4.49743i	0.200268	−	0.159708i
$794$	−4.27325	+	0.112362i	−0.151652	+	0.00398756i
$795$	−2.79144	+	2.79144i	−0.0990021	+	0.0990021i
$796$	−4.47768	−	15.7508i	−0.158707	−	0.558272i
$797$	14.1803	+	4.96192i	0.502293	+	0.175760i	0.569520	−	0.821978i	$-0.307129\pi$
$797$	14.1803	+	4.96192i	0.502293	+	0.175760i	−0.0672263	+	0.997738i	$0.521415\pi$
$798$	3.55301	+	0.305998i	0.125775	+	0.0108322i
$799$	−20.5146	+	89.8805i	−0.725755	+	3.17974i
$800$	0.633259	+	1.25273i	0.0223891	+	0.0442908i
$801$	−8.10164	+	35.4956i	−0.286257	+	1.25417i
$802$	1.27046	+	9.11509i	0.0448616	+	0.321865i
$803$	−8.57880	+	13.6531i	−0.302739	+	0.481807i
$804$	−10.2707	−	11.5747i	−0.362219	−	0.408209i
$805$	−0.497839	−	4.41844i	−0.0175465	−	0.155730i
$806$	5.95720	+	7.08001i	0.209833	+	0.249383i
$807$	−13.2544	+	27.5231i	−0.466578	+	0.968859i
$808$	3.53366	−	24.1088i	0.124314	−	0.848145i
$809$	22.7028	+	18.1049i	0.798187	+	0.636533i	0.935234	−	0.354031i	$-0.115189\pi$
$809$	22.7028	+	18.1049i	0.798187	+	0.636533i	−0.137046	+	0.990565i	$0.543761\pi$
$810$	4.77596	+	0.958749i	0.167810	+	0.0336870i
$811$	9.24601	−	9.24601i	0.324671	−	0.324671i	−0.525885	−	0.850556i	$-0.676266\pi$
$811$	9.24601	−	9.24601i	0.324671	−	0.324671i	0.850556	+	0.525885i	$0.176266\pi$
$812$	4.76546	−	2.50307i	0.167235	−	0.0878404i
$813$	5.21189	+	5.21189i	0.182789	+	0.182789i
$814$	−37.1709	+	24.7422i	−1.30284	+	0.867214i
$815$	22.2503	−	27.9011i	0.779396	−	0.977331i
$816$	22.3223	+	18.0602i	0.781437	+	0.632235i
$817$	3.67559	+	1.77007i	0.128593	+	0.0619269i
$818$	−0.780095	+	9.05785i	−0.0272754	+	0.316700i
$819$	−0.910256	+	0.102561i	−0.0318069	+	0.00358378i
$820$	10.4099	+	0.621413i	0.363531	+	0.0217007i
$821$	21.5362	+	13.5321i	0.751618	+	0.472273i	0.852567	−	0.522619i	$-0.175045\pi$
$821$	21.5362	+	13.5321i	0.751618	+	0.472273i	−0.100948	+	0.994892i	$0.532188\pi$
$822$	11.1519	+	8.42348i	0.388967	+	0.293803i
$823$	13.7488	+	3.13806i	0.479252	+	0.109386i	0.455321	−	0.890328i	$-0.349525\pi$
$823$	13.7488	+	3.13806i	0.479252	+	0.109386i	0.0239310	+	0.999714i	$0.492382\pi$
$824$	−35.7999	−	1.19384i	−1.24715	−	0.0415895i
$825$	−0.761777	−	0.173871i	−0.0265217	−	0.00605340i
$826$	5.51860	+	6.55874i	0.192017	+	0.228208i
$827$	−18.2969	+	52.2897i	−0.636247	+	1.81829i	−0.0644091	+	0.997924i	$0.520516\pi$
$827$	−18.2969	+	52.2897i	−0.636247	+	1.81829i	−0.571838	+	0.820366i	$0.693769\pi$
$828$	15.4740	−	4.39899i	0.537758	−	0.152875i
$829$	−12.2584	−	12.2584i	−0.425753	−	0.425753i	0.461426	−	0.887179i	$-0.347338\pi$
$829$	−12.2584	−	12.2584i	−0.425753	−	0.425753i	−0.887179	+	0.461426i	$0.847338\pi$
$830$	−25.1783	+	26.5381i	−0.873951	+	0.921151i
$831$	−14.0665	−	17.6389i	−0.487963	−	0.611886i
$832$	4.15735	−	5.72991i	0.144130	−	0.198649i
$833$	11.1881	+	49.0181i	0.387643	+	1.69838i
$834$	−27.1299	+	10.3013i	−0.939432	+	0.356705i
$835$	27.2472	+	9.53421i	0.942928	+	0.329945i
$836$	1.79790	+	34.1645i	0.0621816	+	1.18160i
$837$	35.9082	+	4.04589i	1.24117	+	0.139846i
$838$	33.4223	+	15.0262i	1.15455	+	0.519073i
$839$	9.53594	−	19.8016i	0.329217	−	0.683627i	−0.669003	−	0.743260i	$-0.733279\pi$
$839$	9.53594	−	19.8016i	0.329217	−	0.683627i	0.998220	+	0.0596329i	$0.0189930\pi$
$840$	−3.11922	−	0.104019i	−0.107623	−	0.00358900i
$841$	28.9818	+	1.02815i	0.999371	+	0.0354533i
$842$	−41.9473	+	10.7416i	−1.44560	+	0.370181i
$843$	−16.5764	+	5.80034i	−0.570922	+	0.199774i
$844$	−7.99867	−	11.3577i	−0.275326	−	0.390947i
$845$	3.13361	−	27.8116i	0.107800	−	0.956748i
$846$	30.1803	−	20.0890i	1.03762	−	0.690674i
$847$	0.145990	−	0.0703053i	0.00501629	−	0.00241572i
$848$	−6.42192	−	3.14858i	−0.220530	−	0.108123i
$849$	0.111384	+	0.488007i	0.00382270	+	0.0167483i
$850$	2.48900	+	0.798148i	0.0853719	+	0.0273763i
$851$	−4.20180	+	37.2920i	−0.144036	+	1.27835i
$852$	−2.31839	+	4.16012i	−0.0794268	+	0.142523i
$853$	17.2262	−	17.2262i	0.589815	−	0.589815i	−0.347766	−	0.937581i	$-0.613060\pi$
$853$	17.2262	−	17.2262i	0.589815	−	0.589815i	0.937581	+	0.347766i	$0.113060\pi$
$854$	−0.151442	−	5.75952i	−0.00518223	−	0.197087i
$855$	10.7782	+	22.3812i	0.368607	+	0.765420i
$856$	−23.7239	−	9.19983i	−0.810865	−	0.314444i
$857$	−11.3887	−	2.59939i	−0.389029	−	0.0887933i	0.0235326	−	0.999723i	$-0.492509\pi$
$857$	−11.3887	−	2.59939i	−0.389029	−	0.0887933i	−0.412561	+	0.910930i	$0.635366\pi$
$858$	0.977559	+	3.81748i	0.0333733	+	0.130327i
$859$	5.89454	+	9.38111i	0.201119	+	0.320079i	0.932022	−	0.362402i	$-0.118043\pi$
$859$	5.89454	+	9.38111i	0.201119	+	0.320079i	−0.730902	+	0.682482i	$0.760901\pi$
$860$	−3.29369	−	1.37791i	−0.112314	−	0.0469863i
$861$	−0.583265	+	0.928260i	−0.0198776	+	0.0316350i
$862$	8.83009	−	27.5363i	0.300754	−	0.937892i
$863$	−4.01079	+	5.02937i	−0.136529	+	0.171202i	−0.845396	−	0.534141i	$-0.820635\pi$
$863$	−4.01079	+	5.02937i	−0.136529	+	0.171202i	0.708867	+	0.705342i	$0.249207\pi$
$864$	−3.62346	−	27.4083i	−0.123273	−	0.932450i
$865$	−4.47281	−	2.15399i	−0.152080	−	0.0732380i
$866$	6.52258	+	46.7971i	0.221646	+	1.59023i
$867$	36.8509	−	4.15210i	1.25152	−	0.141013i
$868$	7.38032	−	0.388387i	0.250504	−	0.0131827i
$869$	17.4493	−	17.4493i	0.591928	−	0.591928i
$870$	−14.3130	−	8.82350i	−0.485255	−	0.299145i
$871$			7.10437i			0.240723i
$872$	−12.5512	+	3.92747i	−0.425037	+	0.133001i
$873$	−13.2270	−	10.5482i	−0.447667	−	0.357003i
$874$	22.9435	+	17.3301i	0.776075	+	0.586201i
$875$	5.13531	−	1.79692i	0.173605	−	0.0607471i
$876$	9.38326	−	1.56028i	0.317031	−	0.0527171i
$877$	−41.6275	+	4.69030i	−1.40566	+	0.158380i	−0.781983	−	0.623300i	$-0.785791\pi$
$877$	−41.6275	+	4.69030i	−1.40566	+	0.158380i	−0.623679	+	0.781680i	$0.714363\pi$
$878$	11.5188	+	3.69372i	0.388739	+	0.124657i
$879$	−0.618090	−	2.70803i	−0.0208476	−	0.0913395i
$880$	−3.14255	−	29.7754i	−0.105935	−	1.00373i
$881$	6.94170	−	30.4136i	0.233872	−	1.02466i	−0.712523	−	0.701648i	$-0.752448\pi$
$881$	6.94170	−	30.4136i	0.233872	−	1.02466i	0.946395	−	0.323011i	$-0.104695\pi$
$882$	10.0758	−	17.0124i	0.339270	−	0.572838i
$883$	7.07665	−	4.44655i	0.238148	−	0.149638i	−0.407671	−	0.913129i	$-0.633659\pi$
$883$	7.07665	−	4.44655i	0.238148	−	0.149638i	0.645819	+	0.763491i	$0.276516\pi$
$884$	−2.16231	−	13.0038i	−0.0727265	−	0.437364i
$885$	8.84312	−	25.2722i	0.297258	−	0.849515i
$886$	0.463699	+	17.6350i	0.0155783	+	0.592461i
$887$			6.47250i			0.217325i	0.994079	+	0.108663i	$0.0346568\pi$
$887$			6.47250i			0.217325i	−0.994079	+	0.108663i	$0.965343\pi$
$888$	25.4711	+	6.71412i	0.854754	+	0.225311i
$889$	0.435386	−	0.347209i	0.0146024	−	0.0116450i
$890$	50.6431	−	26.0499i	1.69756	−	0.873194i
$891$	−4.15972	−	2.61373i	−0.139356	−	0.0875631i
$892$	23.7841	+	4.12736i	0.796351	+	0.138194i
$893$	61.1632	+	21.4019i	2.04675	+	0.716189i
$894$	−1.56138	−	2.34571i	−0.0522204	−	0.0784523i
$895$	−19.2095	−	24.0879i	−0.642101	−	0.805170i
$896$	−1.65054	−	5.40815i	−0.0551407	−	0.180673i
$897$	2.98392	+	1.43698i	0.0996301	+	0.0479793i
$898$	32.5665	+	19.2879i	1.08676	+	0.643646i
$899$	35.5615	+	17.9090i	1.18604	+	0.597299i
$900$	−0.494043	−	0.901392i	−0.0164681	−	0.0300464i
$901$	−12.5709	+	4.39875i	−0.418798	+	0.146544i
$902$	−9.59240	−	4.31262i	−0.319392	−	0.143595i
$903$	0.293444	−	0.234014i	0.00976519	−	0.00778748i
$904$	1.77281	−	3.38758i	0.0589629	−	0.112669i
$905$	−19.8838	−	41.2892i	−0.660961	−	1.37250i
$906$	10.4783	−	23.3066i	0.348119	−	0.774309i
$907$	−44.7093	−	28.0927i	−1.48455	−	0.932804i	−0.998258	−	0.0590066i	$-0.981207\pi$
$907$	−44.7093	−	28.0927i	−1.48455	−	0.932804i	−0.486291	−	0.873797i	$-0.661650\pi$
$908$	−15.6613	−	0.934887i	−0.519737	−	0.0310253i
$909$	−1.99780	+	17.7309i	−0.0662628	+	0.588098i
$910$	1.03945	+	0.986185i	0.0344573	+	0.0326917i
$911$	53.3666			1.76811			0.884057	−	0.467380i	$-0.154802\pi$
$911$	53.3666			1.76811			0.884057	+	0.467380i	$0.154802\pi$
$912$	14.3710	−	14.1699i	0.475872	−	0.469212i
$913$	33.2396	−	16.0073i	1.10007	−	0.529765i
$914$	−3.13655	+	36.4191i	−0.103748	+	1.20464i
$915$	−15.2385	+	9.57498i	−0.503769	+	0.316539i
$916$	−25.3234	−	7.39227i	−0.836707	−	0.244247i
$917$	0.688059	+	1.09504i	0.0227217	+	0.0361614i
$918$	−41.0796	−	31.0291i	−1.35583	−	1.02411i
$919$	23.8241	−	5.43769i	0.785883	−	0.179373i	0.189295	−	0.981920i	$-0.439380\pi$
$919$	23.8241	−	5.43769i	0.785883	−	0.179373i	0.596588	+	0.802547i	$0.296523\pi$
$920$	−20.8485	−	14.0905i	−0.687355	−	0.464549i
$921$	2.72818	+	2.17565i	0.0898965	+	0.0716900i
$922$	−6.72549	−	7.99311i	−0.221492	−	0.263239i
$923$	2.06378	−	0.722147i	0.0679300	−	0.0237697i
$924$	2.90368	+	1.21475i	0.0955240	+	0.0399622i
$925$	2.38281	−	0.268479i	0.0783464	−	0.00882752i
$926$	25.2671	+	37.9595i	0.830330	+	1.24743i
$927$	26.2303			0.861515
$928$	6.73381	−	29.7095i	0.221048	−	0.975263i
$929$	−14.6441			−0.480459			−0.240229	−	0.970716i	$-0.577223\pi$
$929$	−14.6441			−0.480459			−0.240229	+	0.970716i	$0.577223\pi$
$930$	−12.7918	−	19.2175i	−0.419459	−	0.630165i
$931$	35.1175	−	3.95679i	1.15093	−	0.129679i
$932$	−3.41695	−	1.42948i	−0.111926	−	0.0468240i
$933$	0.358395	−	0.125408i	0.0117333	−	0.00410567i
$934$	1.65126	+	1.96249i	0.0540309	+	0.0642146i
$935$	−43.5895	−	34.7615i	−1.42553	−	1.13682i
$936$	−2.90282	+	4.29506i	−0.0948817	+	0.140389i
$937$	12.4969	−	2.85234i	0.408257	−	0.0931819i	−0.0134604	−	0.999909i	$-0.504285\pi$
$937$	12.4969	−	2.85234i	0.408257	−	0.0931819i	0.421717	+	0.906727i	$0.361428\pi$
$938$	4.52796	+	3.42015i	0.147843	+	0.111672i
$939$	−3.09967	−	4.93310i	−0.101154	−	0.160986i
$940$	−54.4379	−	15.8912i	−1.77557	−	0.518315i
$941$	24.2122	−	15.2135i	0.789295	−	0.495947i	−0.0760616	−	0.997103i	$-0.524235\pi$
$941$	24.2122	−	15.2135i	0.789295	−	0.495947i	0.865357	+	0.501156i	$0.167092\pi$
$942$	1.64856	−	19.1418i	0.0537131	−	0.623674i
$943$	−7.96381	+	3.83517i	−0.259337	+	0.124890i
$944$	48.5080	+	0.341854i	1.57880	+	0.0111264i
$945$	5.59570			0.182028
$946$	2.61212	+	2.47827i	0.0849274	+	0.0805756i
$947$	−3.38270	+	30.0223i	−0.109923	+	0.975594i	0.810786	+	0.585343i	$0.199040\pi$
$947$	−3.38270	+	30.0223i	−0.109923	+	0.975594i	−0.920709	+	0.390251i	$0.872388\pi$
$948$	−14.5315	−	0.867445i	−0.471960	−	0.0281733i
$949$	−3.69766	−	2.32339i	−0.120031	−	0.0754205i
$950$	0.753350	−	1.67565i	0.0244419	−	0.0543651i
$951$	9.17918	+	19.0608i	0.297655	+	0.618088i
$952$	−9.32890	−	4.88206i	−0.302351	−	0.158229i
$953$	41.5876	−	33.1650i	1.34716	−	1.07432i	0.357036	−	0.934090i	$-0.383787\pi$
$953$	41.5876	−	33.1650i	1.34716	−	1.07432i	0.990119	−	0.140230i	$-0.0447842\pi$
$954$	4.77691	+	2.14764i	0.154658	+	0.0695323i
$955$	6.04205	−	2.11421i	0.195516	−	0.0684141i
$956$	−16.4212	−	29.9608i	−0.531100	−	0.969002i
$957$	10.3360	+	13.4431i	0.334115	+	0.434554i
$958$	36.8703	+	21.8369i	1.19123	+	0.705518i
$959$	−4.61734	−	2.22360i	−0.149102	−	0.0718036i
$960$	−11.9079	+	13.0447i	−0.384325	+	0.421016i
$961$	14.7563	+	18.5038i	0.476010	+	0.596897i
$962$	−6.70092	−	10.0670i	−0.216046	−	0.324573i
$963$	17.5875	+	6.15414i	0.566750	+	0.198314i
$964$	56.3208	+	9.77360i	1.81397	+	0.314786i
$965$	32.2046	+	20.2355i	1.03670	+	0.651403i
$966$	2.35236	−	1.21001i	0.0756859	−	0.0389315i
$967$	−1.29879	+	1.03575i	−0.0417663	+	0.0333075i	−0.644150	−	0.764899i	$-0.722789\pi$
$967$	−1.29879	+	1.03575i	−0.0417663	+	0.0333075i	0.602384	+	0.798206i	$0.294218\pi$
$968$	0.233739	−	0.886728i	0.00751266	−	0.0285005i
$969$		−	37.5811i		−	1.20728i
$970$	0.695587	+	26.4540i	0.0223340	+	0.849388i
$971$	−0.925090	+	2.64376i	−0.0296876	+	0.0848422i	−0.957773	−	0.287524i	$-0.907168\pi$
$971$	−0.925090	+	2.64376i	−0.0296876	+	0.0848422i	0.928086	+	0.372366i	$0.121454\pi$
$972$	5.28541	+	31.7855i	0.169530	+	1.01952i
$973$	9.01043	−	5.66163i	0.288861	−	0.181503i
$974$	12.6216	−	21.3108i	0.404422	−	0.682843i
$975$	0.0470893	−	0.206312i	0.00150806	−	0.00660726i
$976$	−25.3486	−	20.5087i	−0.811389	−	0.656469i
$977$	6.66035	+	29.1809i	0.213084	+	0.933580i	0.962457	+	0.271433i	$0.0874975\pi$
$977$	6.66035	+	29.1809i	0.213084	+	0.933580i	−0.749374	+	0.662147i	$0.769645\pi$
$978$	20.2173	+	6.48310i	0.646478	+	0.207307i
$979$	−57.0739	+	6.43068i	−1.82409	+	0.205526i
$980$	−30.5090	+	5.07314i	−0.974574	+	0.162056i
$981$	9.09009	−	3.18076i	0.290224	−	0.101554i
$982$	−28.9056	−	21.8336i	−0.922416	−	0.696738i
$983$	−46.3357	−	36.9515i	−1.47788	−	1.17857i	−0.942614	−	0.333884i	$-0.891641\pi$
$983$	−46.3357	−	36.9515i	−1.47788	−	1.17857i	−0.535264	−	0.844685i	$-0.679788\pi$
$984$	1.85282	+	5.92115i	0.0590658	+	0.188759i
$985$			2.47448i			0.0788434i
$986$	−30.5898	−	47.7710i	−0.974179	−	1.52134i
$987$	4.21553	−	4.21553i	0.134182	−	0.134182i
$988$	−9.25275	+	0.486923i	−0.294369	+	0.0154911i
$989$	3.00715	−	0.338825i	0.0956219	−	0.0107740i
$990$	3.02667	+	21.7152i	0.0961939	+	0.690155i
$991$	8.12953	+	3.91497i	0.258243	+	0.124363i	0.558526	−	0.829487i	$-0.311367\pi$
$991$	8.12953	+	3.91497i	0.258243	+	0.124363i	−0.300283	+	0.953850i	$0.597081\pi$
$992$	25.4437	−	33.1960i	0.807837	−	1.05397i
$993$	−12.2629	+	15.3772i	−0.389151	+	0.487980i
$994$	0.533274	−	1.66300i	0.0169144	−	0.0527471i
$995$	9.97904	−	15.8816i	0.316357	−	0.503479i
$996$	−20.0776	−	8.39942i	−0.636183	−	0.266146i
$997$	−3.54858	−	5.64754i	−0.112385	−	0.178859i	0.785796	−	0.618486i	$-0.212254\pi$
$997$	−3.54858	−	5.64754i	−0.112385	−	0.178859i	−0.898181	+	0.439627i	$0.855111\pi$
$998$	10.5306	+	41.1234i	0.333342	+	1.30174i
$999$	−46.0441	−	10.5093i	−1.45677	−	0.332499i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.bi.a.45.18	✓	696
16.5	even	4	inner	464.2.bi.a.277.1	yes	696
29.20	even	7	inner	464.2.bi.a.397.1	yes	696
464.165	even	28	inner	464.2.bi.a.165.18	yes	696

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
464.2.bi.a.45.18	✓	696	1.1	even	1	trivial
464.2.bi.a.165.18	yes	696	464.165	even	28	inner
464.2.bi.a.277.1	yes	696	16.5	even	4	inner
464.2.bi.a.397.1	yes	696	29.20	even	7	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.bi (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.783622 - 1.17726i) q^{2} +(0.957676 - 0.107904i) q^{3} +(-0.771873 + 1.84505i) q^{4} +(-2.16233 + 0.756630i) q^{5} +(-0.877487 - 1.04288i) q^{6} +(0.390747 + 0.311610i) q^{7} +(2.77696 - 0.537129i) q^{8} +(-2.01928 + 0.460888i) q^{9} +O(q^{10})\)	\(q+(-0.783622 - 1.17726i) q^{2} +(0.957676 - 0.107904i) q^{3} +(-0.771873 + 1.84505i) q^{4} +(-2.16233 + 0.756630i) q^{5} +(-0.877487 - 1.04288i) q^{6} +(0.390747 + 0.311610i) q^{7} +(2.77696 - 0.537129i) q^{8} +(-2.01928 + 0.460888i) q^{9} +(2.58520 + 1.95270i) q^{10} +(-1.73835 - 2.76657i) q^{11} +(-0.540115 + 1.85025i) q^{12} +(0.749269 - 0.470797i) q^{13} +(0.0606477 - 0.704194i) q^{14} +(-1.98916 + 0.957931i) q^{15} +(-2.80842 - 2.84829i) q^{16} -7.44845 q^{17} +(2.12494 + 2.01606i) q^{18} +(-0.586173 + 5.20243i) q^{19} +(0.273019 - 4.57362i) q^{20} +(0.407833 + 0.256258i) q^{21} +(-1.89476 + 4.21444i) q^{22} +(1.68499 + 3.49891i) q^{23} +(2.60147 - 0.814041i) q^{24} +(0.194004 - 0.154713i) q^{25} +(-1.14139 - 0.513156i) q^{26} +(-4.61305 + 1.61418i) q^{27} +(-0.876543 + 0.480424i) q^{28} +(-5.38432 - 0.0954760i) q^{29} +(2.68648 + 1.59110i) q^{30} +(-6.66152 - 3.20802i) q^{31} +(-1.15243 + 5.53822i) q^{32} +(-1.96330 - 2.46190i) q^{33} +(5.83677 + 8.76875i) q^{34} +(-1.08070 - 0.378152i) q^{35} +(0.708268 - 4.08143i) q^{36} +(8.18227 + 5.14126i) q^{37} +(6.58394 - 3.38666i) q^{38} +(0.666756 - 0.531720i) q^{39} +(-5.59828 + 3.26258i) q^{40} +2.27608i q^{41} +(-0.0179046 - 0.680934i) q^{42} +(0.257367 - 0.735512i) q^{43} +(6.44625 - 1.07191i) q^{44} +(4.01763 - 2.52444i) q^{45} +(2.79873 - 4.72549i) q^{46} +(2.75421 - 12.0670i) q^{47} +(-2.99690 - 2.42470i) q^{48} +(-1.50206 - 6.58097i) q^{49} +(-0.334163 - 0.107156i) q^{50} +(-7.13321 + 0.803719i) q^{51} +(0.290304 + 1.74583i) q^{52} +(1.68772 - 0.590559i) q^{53} +(5.51519 + 4.16585i) q^{54} +(5.85215 + 4.66694i) q^{55} +(1.25246 + 0.655447i) q^{56} +5.04549i q^{57} +(4.10687 + 6.41355i) q^{58} +(-8.57529 + 8.57529i) q^{59} +(-0.232049 - 4.40951i) q^{60} +(8.10028 - 0.912682i) q^{61} +(1.44345 + 10.3562i) q^{62} +(-0.932646 - 0.449139i) q^{63} +(7.42299 - 2.98317i) q^{64} +(-1.26394 + 1.58494i) q^{65} +(-1.35981 + 4.24052i) q^{66} +(-4.27138 + 6.79786i) q^{67} +(5.74926 - 13.7428i) q^{68} +(1.99122 + 3.16901i) q^{69} +(0.401675 + 1.56858i) q^{70} +(2.40891 + 0.549818i) q^{71} +(-5.35991 + 2.36448i) q^{72} +(-2.14122 - 4.44630i) q^{73} +(-0.359217 - 13.6615i) q^{74} +(0.169099 - 0.169099i) q^{75} +(-9.14629 - 5.09713i) q^{76} +(0.182836 - 1.62272i) q^{77} +(-1.14846 - 0.368276i) q^{78} +(1.68060 + 7.36319i) q^{79} +(8.22783 + 4.03399i) q^{80} +(1.35467 - 0.652373i) q^{81} +(2.67954 - 1.78359i) q^{82} +(-1.26423 + 11.2203i) q^{83} +(-0.787605 + 0.554673i) q^{84} +(16.1060 - 5.63573i) q^{85} +(-1.06757 + 0.273376i) q^{86} +(-5.16673 + 0.489555i) q^{87} +(-6.31334 - 6.74893i) q^{88} +(7.62694 - 15.8375i) q^{89} +(-6.12022 - 2.75157i) q^{90} +(0.439479 + 0.0495174i) q^{91} +(-7.75627 + 0.408172i) q^{92} +(-6.72574 - 2.35344i) q^{93} +(-16.3642 + 6.21354i) q^{94} +(-2.66882 - 11.6929i) q^{95} +(-0.506055 + 5.42817i) q^{96} +(5.09277 + 6.38613i) q^{97} +(-6.57045 + 6.92531i) q^{98} +(4.78531 + 4.78531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 696 q - 10 q^{2} - 10 q^{3} - 14 q^{4} - 10 q^{5} - 22 q^{6} - 10 q^{8}+O(q^{10}) \) 696 * q - 10 * q^2 - 10 * q^3 - 14 * q^4 - 10 * q^5 - 22 * q^6 - 10 * q^8	\( 696 q - 10 q^{2} - 10 q^{3} - 14 q^{4} - 10 q^{5} - 22 q^{6} - 10 q^{8} - 10 q^{10} + 10 q^{11} - 36 q^{12} - 10 q^{13} - 22 q^{14} - 20 q^{15} + 10 q^{16} - 48 q^{17} + 2 q^{18} - 10 q^{19} - 38 q^{20} - 22 q^{21} - 32 q^{22} - 10 q^{24} - 10 q^{26} + 2 q^{27} + 52 q^{28} - 20 q^{29} - 44 q^{30} - 20 q^{31} - 10 q^{32} - 20 q^{33} - 62 q^{34} - 30 q^{35} - 14 q^{36} - 26 q^{37} - 88 q^{38} + 22 q^{40} - 34 q^{42} - 2 q^{43} - 4 q^{44} - 18 q^{45} - 20 q^{46} - 20 q^{47} + 70 q^{48} + 72 q^{49} - 46 q^{50} - 40 q^{51} + 12 q^{52} + 6 q^{53} + 10 q^{54} - 38 q^{56} - 2 q^{58} - 48 q^{59} - 86 q^{60} - 10 q^{61} + 56 q^{62} - 36 q^{63} + 100 q^{64} - 36 q^{65} - 182 q^{66} + 30 q^{67} - 140 q^{68} - 22 q^{69} + 32 q^{70} + 104 q^{72} + 18 q^{74} - 72 q^{75} - 10 q^{76} - 22 q^{77} - 42 q^{78} - 20 q^{79} + 160 q^{80} + 64 q^{81} - 46 q^{82} - 10 q^{83} + 16 q^{84} - 60 q^{85} - 24 q^{86} - 4 q^{88} - 142 q^{90} - 14 q^{91} - 32 q^{92} + 122 q^{93} - 92 q^{94} - 20 q^{95} + 86 q^{96} - 20 q^{97} + 66 q^{98} - 88 q^{99}+O(q^{100}) \) 696 * q - 10 * q^2 - 10 * q^3 - 14 * q^4 - 10 * q^5 - 22 * q^6 - 10 * q^8 - 10 * q^10 + 10 * q^11 - 36 * q^12 - 10 * q^13 - 22 * q^14 - 20 * q^15 + 10 * q^16 - 48 * q^17 + 2 * q^18 - 10 * q^19 - 38 * q^20 - 22 * q^21 - 32 * q^22 - 10 * q^24 - 10 * q^26 + 2 * q^27 + 52 * q^28 - 20 * q^29 - 44 * q^30 - 20 * q^31 - 10 * q^32 - 20 * q^33 - 62 * q^34 - 30 * q^35 - 14 * q^36 - 26 * q^37 - 88 * q^38 + 22 * q^40 - 34 * q^42 - 2 * q^43 - 4 * q^44 - 18 * q^45 - 20 * q^46 - 20 * q^47 + 70 * q^48 + 72 * q^49 - 46 * q^50 - 40 * q^51 + 12 * q^52 + 6 * q^53 + 10 * q^54 - 38 * q^56 - 2 * q^58 - 48 * q^59 - 86 * q^60 - 10 * q^61 + 56 * q^62 - 36 * q^63 + 100 * q^64 - 36 * q^65 - 182 * q^66 + 30 * q^67 - 140 * q^68 - 22 * q^69 + 32 * q^70 + 104 * q^72 + 18 * q^74 - 72 * q^75 - 10 * q^76 - 22 * q^77 - 42 * q^78 - 20 * q^79 + 160 * q^80 + 64 * q^81 - 46 * q^82 - 10 * q^83 + 16 * q^84 - 60 * q^85 - 24 * q^86 - 4 * q^88 - 142 * q^90 - 14 * q^91 - 32 * q^92 + 122 * q^93 - 92 * q^94 - 20 * q^95 + 86 * q^96 - 20 * q^97 + 66 * q^98 - 88 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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