LMFDB - Embedded newform 322.2.i.d.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, degree $10$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			29.4
Character	$\chi$	$=$	322.29
Dual form			322.2.i.d.211.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(2.84549 + 0.835512i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.221294 + 0.142217i) q^{5} +(1.94207 - 2.24127i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(4.87498 + 3.13296i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(2.84549 + 0.835512i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.221294 + 0.142217i) q^{5} +(1.94207 - 2.24127i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(4.87498 + 3.13296i) q^{9} +(0.0374364 + 0.260376i) q^{10} +(-0.940420 - 2.05923i) q^{11} +(-1.23196 - 2.69762i) q^{12} +(0.349844 + 2.43322i) q^{13} +(-0.841254 - 0.540641i) q^{14} +(-0.748515 + 0.219784i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-0.0868517 + 0.100232i) q^{17} +(4.87498 - 3.13296i) q^{18} +(-3.38188 - 3.90290i) q^{19} +(0.252398 + 0.0741106i) q^{20} +(1.23196 - 2.69762i) q^{21} -2.26381 q^{22} +(4.01087 + 2.62925i) q^{23} -2.96562 q^{24} +(-2.04833 + 4.48522i) q^{25} +(2.35867 + 0.692567i) q^{26} +(5.42789 + 6.26412i) q^{27} +(-0.841254 + 0.540641i) q^{28} +(-0.566666 + 0.653967i) q^{29} +(-0.111022 + 0.772175i) q^{30} +(-8.27222 + 2.42894i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-0.955444 - 6.64526i) q^{33} +(0.0550949 + 0.120641i) q^{34} +(0.109276 + 0.239282i) q^{35} +(-0.824700 - 5.73592i) q^{36} +(-4.71366 - 3.02929i) q^{37} +(-4.95509 + 1.45495i) q^{38} +(-1.03751 + 7.21601i) q^{39} +(0.172263 - 0.198802i) q^{40} +(1.66935 - 1.07282i) q^{41} +(-1.94207 - 2.24127i) q^{42} +(8.88983 + 2.61029i) q^{43} +(-0.940420 + 2.05923i) q^{44} -1.52437 q^{45} +(4.05782 - 2.55618i) q^{46} -10.1098 q^{47} +(-1.23196 + 2.69762i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(3.22899 + 3.72645i) q^{50} +(-0.330881 + 0.212644i) q^{51} +(1.60981 - 1.85782i) q^{52} +(1.21404 - 8.44385i) q^{53} +(7.95287 - 2.33517i) q^{54} +(0.500968 + 0.321952i) q^{55} +(0.142315 + 0.989821i) q^{56} +(-6.36220 - 13.9313i) q^{57} +(0.359468 + 0.787125i) q^{58} +(-1.14099 - 7.93573i) q^{59} +(0.656275 + 0.421762i) q^{60} +(-5.34592 + 1.56970i) q^{61} +(-1.22696 + 8.53369i) q^{62} +(3.79485 - 4.37949i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.423465 - 0.488704i) q^{65} +(-6.44164 - 1.89144i) q^{66} +(1.08736 - 2.38100i) q^{67} +0.132626 q^{68} +(9.21612 + 10.8326i) q^{69} +0.263053 q^{70} +(-0.253605 + 0.555318i) q^{71} +(-5.56017 - 1.63261i) q^{72} +(4.66442 + 5.38303i) q^{73} +(-4.71366 + 3.02929i) q^{74} +(-9.57596 + 11.0512i) q^{75} +(-0.734954 + 5.11172i) q^{76} +(-2.17211 + 0.637788i) q^{77} +(6.13292 + 3.94139i) q^{78} +(0.391691 + 2.72427i) q^{79} +(-0.109276 - 0.239282i) q^{80} +(2.98940 + 6.54588i) q^{81} +(-0.282403 - 1.96416i) q^{82} +(13.1707 + 8.46432i) q^{83} +(-2.84549 + 0.835512i) q^{84} +(0.00496504 - 0.0345326i) q^{85} +(6.06737 - 7.00212i) q^{86} +(-2.15884 + 1.38740i) q^{87} +(1.48248 + 1.71087i) q^{88} +(1.57153 + 0.461444i) q^{89} +(-0.633245 + 1.38661i) q^{90} +2.45824 q^{91} +(-0.639507 - 4.75300i) q^{92} -25.5679 q^{93} +(-4.19975 + 9.19617i) q^{94} +(1.30345 + 0.382728i) q^{95} +(1.94207 + 2.24127i) q^{96} +(-9.34160 + 6.00348i) q^{97} +(-0.654861 + 0.755750i) q^{98} +(1.86696 - 12.9850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$	2.84549	+	0.835512i	1.64285	+	0.482383i	0.967025	−	0.254683i	$-0.0819712\pi$
$3$	2.84549	+	0.835512i	1.64285	+	0.482383i	0.675821	+	0.737066i	$0.263789\pi$
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−0.221294	+	0.142217i	−0.0989658	+	0.0636015i	−0.589188	−	0.807996i	$-0.700552\pi$
$5$	−0.221294	+	0.142217i	−0.0989658	+	0.0636015i	0.490222	+	0.871598i	$0.336916\pi$
$6$	1.94207	−	2.24127i	0.792846	−	0.914993i
$7$	0.142315	−	0.989821i	0.0537900	−	0.374117i
$7$	0.142315	−	0.989821i	0.0537900	−	0.374117i
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	4.87498	+	3.13296i	1.62499	+	1.04432i
$10$	0.0374364	+	0.260376i	0.0118384	+	0.0823380i
$11$	−0.940420	−	2.05923i	−0.283547	−	0.620882i	0.713245	−	0.700915i	$-0.247225\pi$
$11$	−0.940420	−	2.05923i	−0.283547	−	0.620882i	−0.996792	+	0.0800331i	$0.974497\pi$
$12$	−1.23196	−	2.69762i	−0.355637	−	0.778737i
$13$	0.349844	+	2.43322i	0.0970294	+	0.674854i	0.979046	+	0.203637i	$0.0652762\pi$
$13$	0.349844	+	2.43322i	0.0970294	+	0.674854i	−0.882017	+	0.471217i	$0.843815\pi$
$14$	−0.841254	−	0.540641i	−0.224834	−	0.144492i
$15$	−0.748515	+	0.219784i	−0.193266	+	0.0567480i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−0.0868517	+	0.100232i	−0.0210646	+	0.0243099i	−0.766184	−	0.642621i	$-0.777847\pi$
$17$	−0.0868517	+	0.100232i	−0.0210646	+	0.0243099i	0.745120	+	0.666931i	$0.232392\pi$
$18$	4.87498	−	3.13296i	1.14904	−	0.738446i
$19$	−3.38188	−	3.90290i	−0.775857	−	0.895387i	0.220946	−	0.975286i	$-0.429086\pi$
$19$	−3.38188	−	3.90290i	−0.775857	−	0.895387i	−0.996803	+	0.0798989i	$0.974540\pi$
$20$	0.252398	+	0.0741106i	0.0564378	+	0.0165716i
$21$	1.23196	−	2.69762i	0.268836	−	0.588670i
$22$	−2.26381			−0.482645
$23$	4.01087	+	2.62925i	0.836324	+	0.548236i
$23$	4.01087	+	2.62925i	0.836324	+	0.548236i
$24$	−2.96562			−0.605355
$25$	−2.04833	+	4.48522i	−0.409666	+	0.897043i
$26$	2.35867	+	0.692567i	0.462573	+	0.135824i
$27$	5.42789	+	6.26412i	1.04460	+	1.20553i
$28$	−0.841254	+	0.540641i	−0.158982	+	0.102172i
$29$	−0.566666	+	0.653967i	−0.105227	+	0.121439i	−0.805920	−	0.592024i	$-0.798329\pi$
$29$	−0.566666	+	0.653967i	−0.105227	+	0.121439i	0.700693	+	0.713463i	$0.252874\pi$
$30$	−0.111022	+	0.772175i	−0.0202698	+	0.140979i
$31$	−8.27222	+	2.42894i	−1.48573	+	0.436251i	−0.921177	−	0.389143i	$-0.872771\pi$
$31$	−8.27222	+	2.42894i	−1.48573	+	0.436251i	−0.564557	+	0.825394i	$0.690953\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$	−0.955444	−	6.64526i	−0.166321	−	1.15679i
$34$	0.0550949	+	0.120641i	0.00944870	+	0.0206898i
$35$	0.109276	+	0.239282i	0.0184711	+	0.0404460i
$36$	−0.824700	−	5.73592i	−0.137450	−	0.955986i
$37$	−4.71366	−	3.02929i	−0.774921	−	0.498012i	0.0924233	−	0.995720i	$-0.470539\pi$
$37$	−4.71366	−	3.02929i	−0.774921	−	0.498012i	−0.867345	+	0.497708i	$0.834175\pi$
$38$	−4.95509	+	1.45495i	−0.803822	+	0.236023i
$39$	−1.03751	+	7.21601i	−0.166134	+	1.15549i
$40$	0.172263	−	0.198802i	0.0272372	−	0.0314334i
$41$	1.66935	−	1.07282i	0.260708	−	0.167547i	−0.403757	−	0.914866i	$-0.632296\pi$
$41$	1.66935	−	1.07282i	0.260708	−	0.167547i	0.664465	+	0.747319i	$0.268659\pi$
$42$	−1.94207	−	2.24127i	−0.299668	−	0.345835i
$43$	8.88983	+	2.61029i	1.35569	+	0.398065i	0.877240	−	0.480051i	$-0.159382\pi$
$43$	8.88983	+	2.61029i	1.35569	+	0.398065i	0.478446	+	0.878117i	$0.341200\pi$
$44$	−0.940420	+	2.05923i	−0.141774	+	0.310441i
$45$	−1.52437			−0.227239
$46$	4.05782	−	2.55618i	0.598293	−	0.376889i
$47$	−10.1098			−1.47466			−0.737331	−	0.675532i	$-0.763914\pi$
$47$	−10.1098			−1.47466			−0.737331	+	0.675532i	$0.763914\pi$
$48$	−1.23196	+	2.69762i	−0.177819	+	0.389368i
$49$	−0.959493	−	0.281733i	−0.137070	−	0.0402475i
$50$	3.22899	+	3.72645i	0.456648	+	0.527000i
$51$	−0.330881	+	0.212644i	−0.0463326	+	0.0297761i
$52$	1.60981	−	1.85782i	0.223240	−	0.257633i
$53$	1.21404	−	8.44385i	0.166761	−	1.15985i	−0.718762	−	0.695256i	$-0.755291\pi$
$53$	1.21404	−	8.44385i	0.166761	−	1.15985i	0.885523	−	0.464595i	$-0.153800\pi$
$54$	7.95287	−	2.33517i	1.08225	−	0.317777i
$55$	0.500968	+	0.321952i	0.0675505	+	0.0434121i
$56$	0.142315	+	0.989821i	0.0190176	+	0.132270i
$57$	−6.36220	−	13.9313i	−0.842694	−	1.84524i
$58$	0.359468	+	0.787125i	0.0472005	+	0.103355i
$59$	−1.14099	−	7.93573i	−0.148544	−	1.03314i	−0.918606	−	0.395175i	$-0.870684\pi$
$59$	−1.14099	−	7.93573i	−0.148544	−	1.03314i	0.770062	−	0.637969i	$-0.220225\pi$
$60$	0.656275	+	0.421762i	0.0847247	+	0.0544493i
$61$	−5.34592	+	1.56970i	−0.684475	+	0.200980i	−0.605439	−	0.795892i	$-0.707002\pi$
$61$	−5.34592	+	1.56970i	−0.684475	+	0.200980i	−0.0790359	+	0.996872i	$0.525184\pi$
$62$	−1.22696	+	8.53369i	−0.155824	+	1.08378i
$63$	3.79485	−	4.37949i	0.478107	−	0.551764i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−0.423465	−	0.488704i	−0.0525243	−	0.0606163i
$66$	−6.44164	−	1.89144i	−0.792912	−	0.232820i
$67$	1.08736	−	2.38100i	0.132843	−	0.290885i	−0.831508	−	0.555513i	$-0.812522\pi$
$67$	1.08736	−	2.38100i	0.132843	−	0.290885i	0.964351	+	0.264628i	$0.0852492\pi$
$68$	0.132626			0.0160833
$69$	9.21612	+	10.8326i	1.10949	+	1.30410i
$70$	0.263053			0.0314409
$71$	−0.253605	+	0.555318i	−0.0300974	+	0.0659041i	−0.924084	−	0.382190i	$-0.875170\pi$
$71$	−0.253605	+	0.555318i	−0.0300974	+	0.0659041i	0.893986	+	0.448094i	$0.147897\pi$
$72$	−5.56017	−	1.63261i	−0.655272	−	0.192405i
$73$	4.66442	+	5.38303i	0.545929	+	0.630036i	0.959930	−	0.280241i	$-0.0904144\pi$
$73$	4.66442	+	5.38303i	0.545929	+	0.630036i	−0.414001	+	0.910277i	$0.635869\pi$
$74$	−4.71366	+	3.02929i	−0.547952	+	0.352147i
$75$	−9.57596	+	11.0512i	−1.10574	+	1.27609i
$76$	−0.734954	+	5.11172i	−0.0843050	+	0.586354i
$77$	−2.17211	+	0.637788i	−0.247535	+	0.0726827i
$78$	6.13292	+	3.94139i	0.694416	+	0.446274i
$79$	0.391691	+	2.72427i	0.0440687	+	0.306505i	0.999920	+	0.0126536i	$0.00402788\pi$
$79$	0.391691	+	2.72427i	0.0440687	+	0.306505i	−0.955851	+	0.293851i	$0.905063\pi$
$80$	−0.109276	−	0.239282i	−0.0122175	−	0.0267525i
$81$	2.98940	+	6.54588i	0.332156	+	0.727320i
$82$	−0.282403	−	1.96416i	−0.0311862	−	0.216905i
$83$	13.1707	+	8.46432i	1.44568	+	0.929079i	0.999416	+	0.0341761i	$0.0108807\pi$
$83$	13.1707	+	8.46432i	1.44568	+	0.929079i	0.446260	+	0.894903i	$0.352756\pi$
$84$	−2.84549	+	0.835512i	−0.310469	+	0.0911618i
$85$	0.00496504	−	0.0345326i	0.000538534	−	0.00374559i
$86$	6.06737	−	7.00212i	0.654262	−	0.755058i
$87$	−2.15884	+	1.38740i	−0.231452	+	0.148745i
$88$	1.48248	+	1.71087i	0.158033	+	0.182380i
$89$	1.57153	+	0.461444i	0.166582	+	0.0489129i	0.363960	−	0.931415i	$-0.381424\pi$
$89$	1.57153	+	0.461444i	0.166582	+	0.0489129i	−0.197378	+	0.980327i	$0.563243\pi$
$90$	−0.633245	+	1.38661i	−0.0667499	+	0.146162i
$91$	2.45824			0.257694
$92$	−0.639507	−	4.75300i	−0.0666732	−	0.495535i
$93$	−25.5679			−2.65127
$94$	−4.19975	+	9.19617i	−0.433171	+	0.948512i
$95$	1.30345	+	0.382728i	0.133731	+	0.0392671i
$96$	1.94207	+	2.24127i	0.198211	+	0.228748i
$97$	−9.34160	+	6.00348i	−0.948496	+	0.609561i	−0.920792	−	0.390055i	$-0.872456\pi$
$97$	−9.34160	+	6.00348i	−0.948496	+	0.609561i	−0.0277044	+	0.999616i	$0.508820\pi$
$98$	−0.654861	+	0.755750i	−0.0661509	+	0.0763422i
$99$	1.86696	−	12.9850i	0.187637	−	1.30504i
$100$	4.73107	−	1.38917i	0.473107	−	0.138917i
$101$	12.4845	+	8.02328i	1.24225	+	0.798346i	0.985753	−	0.168198i	$-0.0537949\pi$
$101$	12.4845	+	8.02328i	1.24225	+	0.798346i	0.256498	+	0.966545i	$0.417431\pi$
$102$	0.0559751	+	0.389315i	0.00554236	+	0.0385480i
$103$	−2.12190	−	4.64632i	−0.209077	−	0.457815i	0.775820	−	0.630954i	$-0.217336\pi$
$103$	−2.12190	−	4.64632i	−0.209077	−	0.457815i	−0.984897	+	0.173139i	$0.944609\pi$
$104$	−1.02119	−	2.23610i	−0.100136	−	0.219267i
$105$	0.111022	+	0.772175i	0.0108346	+	0.0753566i
$106$	−7.17646	−	4.61203i	−0.697040	−	0.447960i
$107$	9.86672	−	2.89713i	0.953851	−	0.280076i	0.232462	−	0.972606i	$-0.425322\pi$
$107$	9.86672	−	2.89713i	0.953851	−	0.280076i	0.721390	+	0.692529i	$0.243504\pi$
$108$	1.17959	−	8.20425i	0.113506	−	0.789454i
$109$	−13.2606	+	15.3035i	−1.27013	+	1.46581i	−0.450653	+	0.892699i	$0.648809\pi$
$109$	−13.2606	+	15.3035i	−1.27013	+	1.46581i	−0.819478	+	0.573111i	$0.805737\pi$
$110$	0.500968	−	0.321952i	0.0477654	−	0.0306970i
$111$	−10.8817	−	12.5581i	−1.03284	−	1.19196i
$112$	0.959493	+	0.281733i	0.0906636	+	0.0266212i
$113$	2.08678	−	4.56940i	0.196307	−	0.429853i	−0.785722	−	0.618579i	$-0.787709\pi$
$113$	2.08678	−	4.56940i	0.196307	−	0.429853i	0.982030	+	0.188726i	$0.0604358\pi$
$114$	−15.3153			−1.43441
$115$	−1.26151	−	0.0114231i	−0.117636	−	0.00106521i
$116$	0.865322			0.0803432
$117$	−5.91770	+	12.9580i	−0.547092	+	1.19796i
$118$	−7.69258	−	2.25874i	−0.708159	−	0.207934i
$119$	0.0868517	+	0.100232i	0.00796168	+	0.00918827i
$120$	0.656275	−	0.421762i	0.0599094	−	0.0385015i
$121$	3.84742	−	4.44016i	0.349766	−	0.403651i
$122$	−0.792922	+	5.51490i	−0.0717878	+	0.499295i
$123$	5.64647	−	1.65795i	0.509125	−	0.149493i
$124$	7.25282	+	4.66111i	0.651323	+	0.418580i
$125$	−0.371773	−	2.58574i	−0.0332524	−	0.231276i
$126$	−2.40729	−	5.27123i	−0.214458	−	0.469598i
$127$	1.09319	+	2.39376i	0.0970052	+	0.212412i	0.951913	−	0.306368i	$-0.0991138\pi$
$127$	1.09319	+	2.39376i	0.0970052	+	0.212412i	−0.854908	+	0.518780i	$0.826387\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$	23.1150	+	14.8551i	2.03516	+	1.30792i
$130$	−0.620455	+	0.182182i	−0.0544175	+	0.0159784i
$131$	1.12839	−	7.84813i	0.0985880	−	0.685694i	−0.879255	−	0.476352i	$-0.841959\pi$
$131$	1.12839	−	7.84813i	0.0985880	−	0.685694i	0.977842	−	0.209342i	$-0.0671322\pi$
$132$	−4.39647	+	5.07379i	−0.382663	+	0.441617i
$133$	−4.34447	+	2.79202i	−0.376713	+	0.242099i
$134$	−1.71412	−	1.97820i	−0.148078	−	0.170891i
$135$	−2.09203	−	0.614275i	−0.180053	−	0.0528683i
$136$	0.0550949	−	0.120641i	0.00472435	−	0.0103449i
$137$	13.5240			1.15544			0.577718	−	0.816237i	$-0.303943\pi$
$137$	13.5240			1.15544			0.577718	+	0.816237i	$0.303943\pi$
$138$	13.6822	−	3.88324i	1.16471	−	0.330564i
$139$	15.4322			1.30894			0.654471	−	0.756087i	$-0.272891\pi$
$139$	15.4322			1.30894			0.654471	+	0.756087i	$0.272891\pi$
$140$	0.109276	−	0.239282i	0.00923553	−	0.0202230i
$141$	−28.7673	−	8.44683i	−2.42264	−	0.711351i
$142$	0.399784	+	0.461375i	0.0335491	+	0.0387177i
$143$	4.68157	−	3.00866i	0.391492	−	0.251597i
$144$	−3.79485	+	4.37949i	−0.316238	+	0.364958i
$145$	0.0323945	−	0.225309i	0.00269022	−	0.0187109i
$146$	6.83424	−	2.00671i	0.565606	−	0.166077i
$147$	−2.49484	−	1.60334i	−0.205771	−	0.132241i
$148$	0.797410	+	5.54611i	0.0655467	+	0.455887i
$149$	−8.73393	−	19.1246i	−0.715511	−	1.56675i	−0.820090	−	0.572234i	$-0.806077\pi$
$149$	−8.73393	−	19.1246i	−0.715511	−	1.56675i	0.104579	−	0.994517i	$-0.466650\pi$
$150$	6.07457	+	13.3014i	0.495986	+	1.08606i
$151$	−1.82295	−	12.6789i	−0.148349	−	1.03179i	−0.918922	−	0.394440i	$-0.870938\pi$
$151$	−1.82295	−	12.6789i	−0.148349	−	1.03179i	0.770572	−	0.637353i	$-0.219971\pi$
$152$	4.34447	+	2.79202i	0.352383	+	0.226463i
$153$	−0.737424	+	0.216527i	−0.0596172	+	0.0175052i
$154$	−0.322173	+	2.24077i	−0.0259615	+	0.180566i
$155$	1.48516	−	1.71396i	0.119291	−	0.137669i
$156$	6.13292	−	3.94139i	0.491026	−	0.315564i
$157$	8.06342	+	9.30568i	0.643531	+	0.742674i	0.979995	−	0.199022i	$-0.0637766\pi$
$157$	8.06342	+	9.30568i	0.643531	+	0.742674i	−0.336464	+	0.941696i	$0.609231\pi$
$158$	2.64080	+	0.775409i	0.210091	+	0.0616882i
$159$	10.5095	−	23.0125i	0.833456	−	1.82501i
$160$	−0.263053			−0.0207962
$161$	3.17329	−	3.59586i	0.250090	−	0.283394i
$162$	7.19618			0.565385
$163$	3.52643	−	7.72181i	0.276212	−	0.604819i	−0.719786	−	0.694196i	$-0.755760\pi$
$163$	3.52643	−	7.72181i	0.276212	−	0.604819i	0.995998	+	0.0893768i	$0.0284875\pi$
$164$	−1.90398	−	0.559058i	−0.148676	−	0.0436551i
$165$	1.15650	+	1.33468i	0.0900338	+	0.103904i
$166$	13.1707	−	8.46432i	1.02225	−	0.656958i
$167$	13.3823	−	15.4440i	1.03556	−	1.19509i	0.0550739	−	0.998482i	$-0.482461\pi$
$167$	13.3823	−	15.4440i	1.03556	−	1.19509i	0.980481	−	0.196612i	$-0.0629940\pi$
$168$	−0.422052	+	2.93543i	−0.0325620	+	0.226474i
$169$	6.67523	−	1.96002i	0.513479	−	0.150771i
$170$	−0.0293494	−	0.0188617i	−0.00225100	−	0.00144663i
$171$	−4.25898	−	29.6219i	−0.325693	−	2.26524i
$172$	−3.84888	−	8.42786i	−0.293474	−	0.642619i
$173$	7.61523	+	16.6750i	0.578975	+	1.26778i	0.941879	+	0.335952i	$0.109058\pi$
$173$	7.61523	+	16.6750i	0.578975	+	1.26778i	−0.362904	+	0.931827i	$0.618215\pi$
$174$	0.365211	+	2.54010i	0.0276866	+	0.192564i
$175$	4.14806	+	2.66579i	0.313564	+	0.201515i
$176$	2.17211	−	0.637788i	0.163729	−	0.0480751i
$177$	3.38373	−	23.5344i	0.254337	−	1.76895i
$178$	1.07258	−	1.23783i	0.0803935	−	0.0927790i
$179$	10.2519	−	6.58851i	0.766264	−	0.492448i	−0.0981850	−	0.995168i	$-0.531304\pi$
$179$	10.2519	−	6.58851i	0.766264	−	0.492448i	0.864449	+	0.502720i	$0.167667\pi$
$180$	0.998248	+	1.15204i	0.0744050	+	0.0858680i
$181$	−20.5780	−	6.04224i	−1.52955	−	0.449116i	−0.594637	−	0.803994i	$-0.702704\pi$
$181$	−20.5780	−	6.04224i	−1.52955	−	0.449116i	−0.934913	+	0.354878i	$0.884522\pi$
$182$	1.02119	−	2.23610i	0.0756957	−	0.165751i
$183$	−16.5233			−1.22144
$184$	−4.58914	−	1.39275i	−0.338316	−	0.102675i
$185$	1.47392			0.108365
$186$	−10.6213	+	23.2574i	−0.778792	+	1.70532i
$187$	0.288078	+	0.0845874i	0.0210664	+	0.00618564i
$188$	6.62049	+	7.64045i	0.482849	+	0.557237i
$189$	6.97283	−	4.48116i	0.507199	−	0.325957i
$190$	0.889615	−	1.02667i	0.0645395	−	0.0744825i
$191$	2.45469	−	17.0728i	0.177615	−	1.23534i	−0.684646	−	0.728876i	$-0.740043\pi$
$191$	2.45469	−	17.0728i	0.177615	−	1.23534i	0.862261	−	0.506465i	$-0.169048\pi$
$192$	2.84549	−	0.835512i	0.205356	−	0.0602979i
$193$	−6.75882	−	4.34363i	−0.486510	−	0.312661i	0.274290	−	0.961647i	$-0.411557\pi$
$193$	−6.75882	−	4.34363i	−0.486510	−	0.312661i	−0.760801	+	0.648986i	$0.775193\pi$
$194$	1.58032	+	10.9914i	0.113460	+	0.789134i
$195$	−0.796647	−	1.74441i	−0.0570491	−	0.124920i
$196$	0.415415	+	0.909632i	0.0296725	+	0.0649737i
$197$	3.35346	+	23.3238i	0.238924	+	1.66175i	0.657411	+	0.753532i	$0.271651\pi$
$197$	3.35346	+	23.3238i	0.238924	+	1.66175i	−0.418487	+	0.908223i	$0.637439\pi$
$198$	−11.0360	−	7.09242i	−0.784296	−	0.504036i
$199$	−8.79355	+	2.58202i	−0.623358	+	0.183034i	−0.578133	−	0.815942i	$-0.696219\pi$
$199$	−8.79355	+	2.58202i	−0.623358	+	0.183034i	−0.0452248	+	0.998977i	$0.514400\pi$
$200$	0.701726	−	4.88061i	0.0496196	−	0.345112i
$201$	5.08344	−	5.86660i	0.358558	−	0.413798i
$202$	12.4845	−	8.02328i	0.878404	−	0.564516i
$203$	0.566666	+	0.653967i	0.0397721	+	0.0458995i
$204$	0.377387	+	0.110811i	0.0264224	+	0.00775830i
$205$	−0.216843	+	0.474820i	−0.0151450	+	0.0331629i
$206$	−5.10791			−0.355885
$207$	11.3156	+	25.3834i	0.786487	+	1.76427i
$208$	−2.45824			−0.170448
$209$	−4.85659	+	10.6344i	−0.335937	+	0.735600i
$210$	0.748515	+	0.219784i	0.0516525	+	0.0151665i
$211$	−5.93976	−	6.85485i	−0.408910	−	0.471907i	0.513517	−	0.858080i	$-0.328342\pi$
$211$	−5.93976	−	6.85485i	−0.408910	−	0.471907i	−0.922427	+	0.386172i	$0.873797\pi$
$212$	−7.17646	+	4.61203i	−0.492881	+	0.316756i
$213$	−1.18561	+	1.36826i	−0.0812364	+	0.0937518i
$214$	1.46346	−	10.1786i	0.100040	−	0.695794i
$215$	−2.33850	+	0.686645i	−0.159484	+	0.0468288i
$216$	−6.97283	−	4.48116i	−0.474441	−	0.304905i
$217$	1.22696	+	8.53369i	0.0832915	+	0.579305i
$218$	8.41192	+	18.4195i	0.569727	+	1.24753i
$219$	8.77498	+	19.2145i	0.592958	+	1.29840i
$220$	−0.0847487	−	0.589440i	−0.00571376	−	0.0397401i
$221$	−0.274272	−	0.176264i	−0.0184495	−	0.0118568i
$222$	−15.9437	+	4.68149i	−1.07007	+	0.314201i
$223$	−2.03950	+	14.1850i	−0.136575	+	0.949899i	0.800142	+	0.599811i	$0.204758\pi$
$223$	−2.03950	+	14.1850i	−0.136575	+	0.949899i	−0.936717	+	0.350088i	$0.886152\pi$
$224$	0.654861	−	0.755750i	0.0437547	−	0.0504956i
$225$	−24.0376	+	15.4480i	−1.60250	+	1.02987i
$226$	−3.28960	−	3.79640i	−0.218821	−	0.252533i
$227$	−2.44342	−	0.717453i	−0.162175	−	0.0476190i	0.199637	−	0.979870i	$-0.436024\pi$
$227$	−2.44342	−	0.717453i	−0.162175	−	0.0476190i	−0.361812	+	0.932251i	$0.617842\pi$
$228$	−6.36220	+	13.9313i	−0.421347	+	0.922622i
$229$	−5.23545			−0.345969			−0.172984	−	0.984925i	$-0.555341\pi$
$229$	−5.23545			−0.345969			−0.172984	+	0.984925i	$0.555341\pi$
$230$	−0.534440	+	1.14276i	−0.0352399	+	0.0753515i
$231$	−6.71359			−0.441722
$232$	0.359468	−	0.787125i	0.0236002	−	0.0516773i
$233$	−13.8184	−	4.05744i	−0.905271	−	0.265812i	−0.204222	−	0.978925i	$-0.565466\pi$
$233$	−13.8184	−	4.05744i	−0.905271	−	0.265812i	−0.701049	+	0.713113i	$0.747285\pi$
$234$	9.32867	+	10.7659i	0.609834	+	0.703786i
$235$	2.23723	−	1.43778i	0.145941	−	0.0937907i
$236$	−5.25024	+	6.05910i	−0.341761	+	0.394414i
$237$	−1.16161	+	8.07916i	−0.0754545	+	0.524798i
$238$	0.127254	−	0.0373651i	0.00824864	−	0.00242202i
$239$	23.2012	+	14.9105i	1.50076	+	0.964480i	0.994792	+	0.101927i	$0.0325009\pi$
$239$	23.2012	+	14.9105i	1.50076	+	0.964480i	0.505968	+	0.862552i	$0.331135\pi$
$240$	−0.111022	−	0.772175i	−0.00716644	−	0.0498437i
$241$	−5.21865	−	11.4272i	−0.336163	−	0.736094i	0.663767	−	0.747939i	$-0.268957\pi$
$241$	−5.21865	−	11.4272i	−0.336163	−	0.736094i	−0.999930	+	0.0118455i	$0.996229\pi$
$242$	−2.44064	−	5.34425i	−0.156890	−	0.343541i
$243$	−0.501619	−	3.48884i	−0.0321789	−	0.223809i
$244$	4.68713	+	3.01224i	0.300063	+	0.192839i
$245$	0.252398	−	0.0741106i	0.0161251	−	0.00473475i
$246$	0.837501	−	5.82495i	0.0533971	−	0.371385i
$247$	8.31349	−	9.59428i	0.528975	−	0.610470i
$248$	7.25282	−	4.66111i	0.460555	−	0.295981i
$249$	30.4052	+	35.0894i	1.92685	+	2.22370i
$250$	−2.50651	−	0.735978i	−0.158526	−	0.0465473i
$251$	−6.89388	+	15.0955i	−0.435138	+	0.952820i	0.557327	+	0.830293i	$0.311827\pi$
$251$	−6.89388	+	15.0955i	−0.435138	+	0.952820i	−0.992465	+	0.122527i	$0.960900\pi$
$252$	−5.79490			−0.365044
$253$	1.64233	−	10.7319i	0.103252	−	0.674709i
$254$	2.63157			0.165119
$255$	0.0429804	−	0.0941139i	0.00269154	−	0.00589364i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−16.1883	−	18.6823i	−1.00980	−	1.16537i	−0.986185	−	0.165649i	$-0.947028\pi$
$257$	−16.1883	−	18.6823i	−1.00980	−	1.16537i	−0.0236144	−	0.999721i	$-0.507517\pi$
$258$	23.1150	−	14.8551i	1.43908	−	0.924839i
$259$	−3.66928	+	4.23457i	−0.227998	+	0.263123i
$260$	−0.0920277	+	0.640067i	−0.00570731	+	0.0396952i
$261$	−4.81134	+	1.41274i	−0.297814	+	0.0874462i
$262$	−6.67016	−	4.28665i	−0.412084	−	0.264830i
$263$	−2.09022	−	14.5378i	−0.128889	−	0.896441i	−0.946966	−	0.321333i	$-0.895869\pi$
$263$	−2.09022	−	14.5378i	−0.128889	−	0.896441i	0.818078	−	0.575108i	$-0.195040\pi$
$264$	2.78893	+	6.10690i	0.171647	+	0.375854i
$265$	0.932200	+	2.04123i	0.0572646	+	0.125392i
$266$	0.734954	+	5.11172i	0.0450629	+	0.313419i
$267$	4.08624	+	2.62607i	0.250074	+	0.160713i
$268$	−2.51151	+	0.737446i	−0.153415	+	0.0450467i
$269$	−0.664831	+	4.62400i	−0.0405355	+	0.281930i	0.959465	+	0.281829i	$0.0909412\pi$
$269$	−0.664831	+	4.62400i	−0.0405355	+	0.281930i	−1.00000		0.000100994i	$0.999968\pi$
$270$	−1.42782	+	1.64780i	−0.0868945	+	0.100282i
$271$	14.4713	−	9.30012i	0.879067	−	0.564942i	−0.0214467	−	0.999770i	$-0.506827\pi$
$271$	14.4713	−	9.30012i	0.879067	−	0.564942i	0.900513	+	0.434828i	$0.143191\pi$
$272$	−0.0868517	−	0.100232i	−0.00526616	−	0.00607747i
$273$	6.99491	+	2.05389i	0.423351	+	0.124307i
$274$	5.61808	−	12.3019i	0.339401	−	0.743184i
$275$	11.1624			0.673117
$276$	2.15148	−	14.0589i	0.129504	−	0.846249i
$277$	13.1278			0.788775			0.394388	−	0.918944i	$-0.370957\pi$
$277$	13.1278			0.788775			0.394388	+	0.918944i	$0.370957\pi$
$278$	6.41077	−	14.0376i	0.384493	−	0.841921i
$279$	−47.9367	−	14.0755i	−2.86989	−	0.842677i
$280$	−0.172263	−	0.198802i	−0.0102947	−	0.0118807i
$281$	−6.33300	+	4.06997i	−0.377795	+	0.242794i	−0.715733	−	0.698374i	$-0.753907\pi$
$281$	−6.33300	+	4.06997i	−0.377795	+	0.242794i	0.337938	+	0.941168i	$0.390271\pi$
$282$	−19.6339	+	22.6587i	−1.16918	+	1.34930i
$283$	−3.07891	+	21.4143i	−0.183022	+	1.27295i	0.666544	+	0.745466i	$0.267773\pi$
$283$	−3.07891	+	21.4143i	−0.183022	+	1.27295i	−0.849566	+	0.527482i	$0.823136\pi$
$284$	0.585757	−	0.171994i	0.0347583	−	0.0102060i
$285$	3.38919	+	2.17810i	0.200758	+	0.129019i
$286$	−0.791980	−	5.50835i	−0.0468308	−	0.325715i
$287$	−0.824332	−	1.80503i	−0.0486588	−	0.106548i
$288$	2.40729	+	5.27123i	0.141851	+	0.310610i
$289$	2.41685	+	16.8096i	0.142168	+	0.988797i
$290$	−0.191491	−	0.123064i	−0.0112447	−	0.00722655i
$291$	−31.5974	+	9.27784i	−1.85227	+	0.543877i
$292$	1.01368	−	7.05027i	0.0593209	−	0.412586i
$293$	−2.66040	+	3.07027i	−0.155422	+	0.179367i	−0.828121	−	0.560550i	$-0.810590\pi$
$293$	−2.66040	+	3.07027i	−0.155422	+	0.179367i	0.672698	+	0.739917i	$0.265135\pi$
$294$	−2.49484	+	1.60334i	−0.145502	+	0.0935084i
$295$	1.38109	+	1.59386i	0.0804102	+	0.0927984i
$296$	5.37617	+	1.57859i	0.312484	+	0.0917535i
$297$	7.79478	−	17.0682i	0.452299	−	0.990396i
$298$	−21.0246			−1.21792
$299$	−4.99436	+	10.6792i	−0.288831	+	0.617592i
$300$	14.6229			0.844253
$301$	3.84888	−	8.42786i	0.221846	−	0.485774i
$302$	−12.2904	−	3.60879i	−0.707233	−	0.207662i
$303$	28.8209	+	33.2611i	1.65572	+	1.91080i
$304$	4.34447	−	2.79202i	0.249172	−	0.160133i
$305$	0.959783	−	1.10765i	0.0549570	−	0.0634237i
$306$	−0.109377	+	0.760733i	−0.00625266	+	0.0434882i
$307$	−31.6878	+	9.30439i	−1.80852	+	0.531029i	−0.998468	−	0.0553284i	$-0.982379\pi$
$307$	−31.6878	+	9.30439i	−1.80852	+	0.531029i	−0.810052	+	0.586358i	$0.800561\pi$
$308$	1.90444	+	1.22391i	0.108515	+	0.0697386i
$309$	−2.15580	−	14.9939i	−0.122639	−	0.852975i
$310$	−0.942119	−	2.06295i	−0.0535088	−	0.117168i
$311$	2.78141	+	6.09043i	0.157719	+	0.345357i	0.971951	−	0.235183i	$-0.0755689\pi$
$311$	2.78141	+	6.09043i	0.157719	+	0.345357i	−0.814232	+	0.580540i	$0.802842\pi$
$312$	−1.03751	−	7.21601i	−0.0587372	−	0.408526i
$313$	−15.6996	−	10.0895i	−0.887396	−	0.570295i	0.0156316	−	0.999878i	$-0.495024\pi$
$313$	−15.6996	−	10.0895i	−0.887396	−	0.570295i	−0.903027	+	0.429583i	$0.858660\pi$
$314$	11.8144	−	3.46902i	0.666726	−	0.195768i
$315$	−0.216940	+	1.50885i	−0.0122232	+	0.0850141i
$316$	1.80237	−	2.08004i	0.101391	−	0.117011i
$317$	14.5122	−	9.32640i	0.815084	−	0.523823i	−0.0654220	−	0.997858i	$-0.520839\pi$
$317$	14.5122	−	9.32640i	0.815084	−	0.523823i	0.880506	+	0.474035i	$0.157203\pi$
$318$	−16.5672	−	19.1195i	−0.929040	−	1.07217i
$319$	1.87957	+	0.551892i	0.105236	+	0.0309000i
$320$	−0.109276	+	0.239282i	−0.00610873	+	0.0133762i
$321$	30.4962			1.70213
$322$	−1.95268	−	4.38030i	−0.108818	−	0.244105i
$323$	0.684919			0.0381099
$324$	2.98940	−	6.54588i	0.166078	−	0.363660i
$325$	−11.6301	−	3.41491i	−0.645123	−	0.189425i
$326$	−5.55907	−	6.41551i	−0.307889	−	0.355322i
$327$	−50.5191	+	32.4666i	−2.79371	+	1.79541i
$328$	−1.29948	+	1.49968i	−0.0717516	+	0.0828058i
$329$	−1.43877	+	10.0069i	−0.0793220	+	0.551696i
$330$	1.69449	−	0.497549i	0.0932789	−	0.0273891i
$331$	28.8241	+	18.5241i	1.58432	+	1.01818i	0.974150	+	0.225903i	$0.0725333\pi$
$331$	28.8241	+	18.5241i	1.58432	+	1.01818i	0.610165	+	0.792274i	$0.291103\pi$
$332$	−2.22809	−	15.4967i	−0.122282	−	0.850493i
$333$	−13.4884	−	29.5354i	−0.739159	−	1.61853i
$334$	−8.48916	−	18.5887i	−0.464506	−	1.01713i
$335$	0.0979911	+	0.681543i	0.00535382	+	0.0372367i
$336$	2.49484	+	1.60334i	0.136105	+	0.0874691i
$337$	−2.95459	+	0.867545i	−0.160947	+	0.0472582i	−0.361213	−	0.932483i	$-0.617637\pi$
$337$	−2.95459	+	0.867545i	−0.160947	+	0.0472582i	0.200267	+	0.979741i	$0.435819\pi$
$338$	0.990090	−	6.88623i	0.0538538	−	0.374561i
$339$	9.75569	−	11.2587i	0.529857	−	0.611487i
$340$	−0.0293494	+	0.0188617i	−0.00159170	+	0.00102292i
$341$	12.7811	+	14.7502i	0.692136	+	0.798767i
$342$	−28.7143	−	8.43127i	−1.55269	−	0.455911i
$343$	−0.415415	+	0.909632i	−0.0224303	+	0.0491155i
$344$	−9.26513			−0.499543
$345$	−3.58006	−	1.08651i	−0.192744	−	0.0584956i
$346$	18.3316			0.985514
$347$	13.6277	−	29.8405i	0.731572	−	1.60192i	−0.0653673	−	0.997861i	$-0.520822\pi$
$347$	13.6277	−	29.8405i	0.731572	−	1.60192i	0.796940	−	0.604059i	$-0.206451\pi$
$348$	2.46227	+	0.722987i	0.131991	+	0.0387562i
$349$	6.70088	+	7.73323i	0.358690	+	0.413950i	0.906200	−	0.422849i	$-0.138970\pi$
$349$	6.70088	+	7.73323i	0.358690	+	0.413950i	−0.547510	+	0.836799i	$0.684424\pi$
$350$	4.14806	−	2.66579i	0.221723	−	0.142493i
$351$	−13.3431	+	15.3987i	−0.712200	+	0.821923i
$352$	0.322173	−	2.24077i	0.0171719	−	0.119433i
$353$	−10.3498	+	3.03899i	−0.550867	+	0.161749i	−0.545308	−	0.838235i	$-0.683587\pi$
$353$	−10.3498	+	3.03899i	−0.550867	+	0.161749i	−0.00555837	+	0.999985i	$0.501769\pi$
$354$	−20.0020	−	12.8545i	−1.06309	−	0.683208i
$355$	−0.0228544	−	0.158956i	−0.00121298	−	0.00843650i
$356$	−0.680400	−	1.48987i	−0.0360611	−	0.0789628i
$357$	0.163391	+	0.357775i	0.00864754	+	0.0189355i
$358$	−1.73432	−	12.0624i	−0.0916615	−	0.637520i
$359$	−13.9654	−	8.97505i	−0.737068	−	0.473685i	0.117468	−	0.993077i	$-0.462522\pi$
$359$	−13.9654	−	8.97505i	−0.737068	−	0.473685i	−0.854536	+	0.519392i	$0.826159\pi$
$360$	1.46262	−	0.429464i	0.0770868	−	0.0226347i
$361$	−1.09152	+	7.59172i	−0.0574487	+	0.399564i
$362$	−14.0446	+	16.2084i	−0.738169	+	0.851892i
$363$	14.6576	−	9.41988i	0.769325	−	0.494415i
$364$	−1.60981	−	1.85782i	−0.0843768	−	0.0973760i
$365$	−1.79777	−	0.527873i	−0.0940995	−	0.0276301i
$366$	−6.86401	+	15.0301i	−0.358788	+	0.785636i
$367$	24.7829			1.29366			0.646829	−	0.762635i	$-0.276095\pi$
$367$	24.7829			1.29366			0.646829	+	0.762635i	$0.276095\pi$
$368$	−3.17329	+	3.59586i	−0.165419	+	0.187447i
$369$	11.4992			0.598622
$370$	0.612290	−	1.34073i	0.0318314	−	0.0697011i
$371$	−8.18512	−	2.40337i	−0.424950	−	0.124777i
$372$	16.7434	+	19.3230i	0.868107	+	1.00185i
$373$	−5.42411	+	3.48586i	−0.280850	+	0.180491i	−0.673480	−	0.739205i	$-0.735201\pi$
$373$	−5.42411	+	3.48586i	−0.280850	+	0.180491i	0.392631	+	0.919696i	$0.371565\pi$
$374$	0.196615	−	0.226906i	0.0101667	−	0.0117330i
$375$	1.10254	−	7.66832i	0.0569348	−	0.395990i
$376$	9.70025	−	2.84825i	0.500252	−	0.146887i
$377$	−1.78949	−	1.15004i	−0.0921635	−	0.0592299i
$378$	−1.17959	−	8.20425i	−0.0606717	−	0.421981i
$379$	−0.139156	−	0.304709i	−0.00714797	−	0.0156519i	0.906024	−	0.423226i	$-0.139102\pi$
$379$	−0.139156	−	0.304709i	−0.00714797	−	0.0156519i	−0.913172	+	0.407574i	$0.866375\pi$
$380$	−0.564333	−	1.23572i	−0.0289497	−	0.0633909i
$381$	1.11066	+	7.72479i	0.0569007	+	0.395753i
$382$	−14.5102	−	9.32514i	−0.742407	−	0.477116i
$383$	−11.0720	+	3.25103i	−0.565752	+	0.166120i	−0.552087	−	0.833787i	$-0.686168\pi$
$383$	−11.0720	+	3.25103i	−0.565752	+	0.166120i	−0.0136657	+	0.999907i	$0.504350\pi$
$384$	0.422052	−	2.93543i	0.0215377	−	0.149798i
$385$	0.389971	−	0.450050i	0.0198747	−	0.0229367i
$386$	−6.75882	+	4.34363i	−0.344015	+	0.221085i
$387$	35.1598	+	40.5766i	1.78727	+	2.06262i
$388$	10.6546	+	3.12847i	0.540904	+	0.158824i
$389$	5.34178	−	11.6969i	0.270839	−	0.593055i	−0.724523	−	0.689250i	$-0.757940\pi$
$389$	5.34178	−	11.6969i	0.270839	−	0.593055i	0.995362	+	0.0961955i	$0.0306674\pi$
$390$	−1.91771			−0.0971072
$391$	−0.611886	+	0.173663i	−0.0309444	+	0.00878254i
$392$	1.00000			0.0505076
$393$	9.76803	−	21.3890i	0.492732	−	1.07893i
$394$	22.6092	+	6.63866i	1.13903	+	0.334451i
$395$	−0.474118	−	0.547161i	−0.0238555	−	0.0275307i
$396$	−11.0360	+	7.09242i	−0.554581	+	0.356407i
$397$	−6.95440	+	8.02580i	−0.349031	+	0.402804i	−0.902935	−	0.429777i	$-0.858592\pi$
$397$	−6.95440	+	8.02580i	−0.349031	+	0.402804i	0.553904	+	0.832581i	$0.313138\pi$
$398$	−1.30428	+	9.07150i	−0.0653779	+	0.454713i
$399$	−14.6949	+	4.31482i	−0.735666	+	0.216011i
$400$	−4.14806	−	2.66579i	−0.207403	−	0.133290i
$401$	4.57450	+	31.8164i	0.228440	+	1.58883i	0.704684	+	0.709521i	$0.251089\pi$
$401$	4.57450	+	31.8164i	0.228440	+	1.58883i	−0.476244	+	0.879313i	$0.658002\pi$
$402$	−3.22471	−	7.06113i	−0.160834	−	0.352177i
$403$	−8.80414	−	19.2784i	−0.438566	−	0.960325i
$404$	−2.11200	−	14.6893i	−0.105076	−	0.730818i
$405$	−1.59247	−	1.02342i	−0.0791307	−	0.0508542i
$406$	0.830271	−	0.243790i	0.0412056	−	0.0120991i
$407$	−1.80518	+	12.5553i	−0.0894796	+	0.622344i
$408$	0.257569	−	0.297251i	0.0127516	−	0.0147161i
$409$	−21.8046	+	14.0130i	−1.07817	+	0.692897i	−0.954134	−	0.299381i	$-0.903220\pi$
$409$	−21.8046	+	14.0130i	−1.07817	+	0.692897i	−0.124035	+	0.992278i	$0.539584\pi$
$410$	0.341832	+	0.394495i	0.0168819	+	0.0194827i
$411$	38.4825	+	11.2995i	1.89820	+	0.557362i
$412$	−2.12190	+	4.64632i	−0.104539	+	0.228908i
$413$	−8.01733			−0.394507
$414$	27.7902	+	0.251643i	1.36582	+	0.0123676i
$415$	−4.11838			−0.202163
$416$	−1.02119	+	2.23610i	−0.0500680	+	0.109634i
$417$	43.9122	+	12.8938i	2.15039	+	0.631412i
$418$	7.65593	+	8.83542i	0.374464	+	0.432154i
$419$	−23.2849	+	14.9643i	−1.13754	+	0.731054i	−0.967121	−	0.254317i	$-0.918149\pi$
$419$	−23.2849	+	14.9643i	−1.13754	+	0.731054i	−0.170421	+	0.985371i	$0.554513\pi$
$420$	0.510867	−	0.589572i	0.0249278	−	0.0287682i
$421$	−4.81005	+	33.4546i	−0.234427	+	1.63048i	0.444152	+	0.895951i	$0.353505\pi$
$421$	−4.81005	+	33.4546i	−0.234427	+	1.63048i	−0.678580	+	0.734527i	$0.737404\pi$
$422$	−8.70285	+	2.55539i	−0.423648	+	0.124394i
$423$	−49.2849	−	31.6735i	−2.39632	−	1.54002i
$424$	1.21404	+	8.44385i	0.0589591	+	0.410069i
$425$	−0.271662	−	0.594857i	−0.0131775	−	0.0288548i
$426$	0.752097	+	1.64686i	0.0364392	+	0.0797907i
$427$	0.792922	+	5.51490i	0.0383722	+	0.266885i
$428$	−8.65083	−	5.55955i	−0.418154	−	0.268731i
$429$	15.8351	−	4.64961i	0.764527	−	0.224485i
$430$	−0.346853	+	2.41241i	−0.0167267	+	0.116337i
$431$	−16.7327	+	19.3105i	−0.805983	+	0.930154i	−0.998693	−	0.0511013i	$-0.983727\pi$
$431$	−16.7327	+	19.3105i	−0.805983	+	0.930154i	0.192710	+	0.981256i	$0.438272\pi$
$432$	−6.97283	+	4.48116i	−0.335480	+	0.215600i
$433$	−22.9884	−	26.5300i	−1.10475	−	1.27495i	−0.958310	−	0.285732i	$-0.907763\pi$
$433$	−22.9884	−	26.5300i	−1.10475	−	1.27495i	−0.146442	−	0.989219i	$-0.546782\pi$
$434$	8.27222	+	2.42894i	0.397079	+	0.116593i
$435$	0.280427	−	0.614048i	0.0134454	−	0.0294414i
$436$	20.2494			0.969772
$437$	−3.30259	−	24.5458i	−0.157984	−	1.17419i
$438$	21.1234			1.00932
$439$	7.38746	−	16.1763i	0.352584	−	0.772052i	−0.647367	−	0.762178i	$-0.724130\pi$
$439$	7.38746	−	16.1763i	0.352584	−	0.772052i	0.999951	−	0.00987320i	$-0.00314279\pi$
$440$	−0.571380	−	0.167772i	−0.0272395	−	0.00799822i
$441$	−3.79485	−	4.37949i	−0.180707	−	0.208547i
$442$	−0.274272	+	0.176264i	−0.0130458	+	0.00838401i
$443$	−19.6760	+	22.7073i	−0.934836	+	1.07886i	0.0618966	+	0.998083i	$0.480285\pi$
$443$	−19.6760	+	22.7073i	−0.934836	+	1.07886i	−0.996732	+	0.0807753i	$0.974260\pi$
$444$	−2.36482	+	16.4477i	−0.112229	+	0.780571i
$445$	−0.413397	+	0.121384i	−0.0195969	+	0.00575416i
$446$	12.0559	+	7.74786i	0.570864	+	0.366872i
$447$	−8.87346	−	61.7163i	−0.419700	−	2.91908i
$448$	−0.415415	−	0.909632i	−0.0196265	−	0.0429761i
$449$	1.51278	+	3.31252i	0.0713923	+	0.156327i	0.941964	−	0.335715i	$-0.108978\pi$
$449$	1.51278	+	3.31252i	0.0713923	+	0.156327i	−0.870571	+	0.492042i	$0.836251\pi$
$450$	4.06644	+	28.2827i	0.191694	+	1.33326i
$451$	−3.77908	−	2.42867i	−0.177950	−	0.114361i
$452$	−4.81987	+	1.41524i	−0.226708	+	0.0665674i
$453$	5.40617	−	37.6008i	0.254004	−	1.76664i
$454$	−1.66765	+	1.92457i	−0.0782668	+	0.0903247i
$455$	−0.543995	+	0.349605i	−0.0255029	+	0.0163897i
$456$	10.0294	+	11.5745i	0.469669	+	0.542027i
$457$	−27.4149	−	8.04975i	−1.28242	−	0.376552i	−0.431625	−	0.902053i	$-0.642059\pi$
$457$	−27.4149	−	8.04975i	−1.28242	−	0.376552i	−0.850793	+	0.525502i	$0.823878\pi$
$458$	−2.17489	+	4.76234i	−0.101626	+	0.222529i
$459$	−1.09929			−0.0513103
$460$	0.817478	+	0.960864i	0.0381151	+	0.0448005i
$461$	16.1455			0.751971			0.375985	−	0.926626i	$-0.377304\pi$
$461$	16.1455			0.751971			0.375985	+	0.926626i	$0.377304\pi$
$462$	−2.78893	+	6.10690i	−0.129753	+	0.284119i
$463$	24.8908	+	7.30860i	1.15677	+	0.339659i	0.803178	−	0.595739i	$-0.203141\pi$
$463$	24.8908	+	7.30860i	1.15677	+	0.339659i	0.353595	+	0.935398i	$0.384959\pi$
$464$	−0.566666	−	0.653967i	−0.0263068	−	0.0303597i
$465$	5.65804	−	3.63620i	0.262385	−	0.168625i
$466$	−9.43113	+	10.8841i	−0.436889	+	0.504196i
$467$	−3.37237	+	23.4553i	−0.156054	+	1.08538i	0.749760	+	0.661709i	$0.230169\pi$
$467$	−3.37237	+	23.4553i	−0.156054	+	1.08538i	−0.905815	+	0.423673i	$0.860740\pi$
$468$	13.6682	−	4.01336i	0.631815	−	0.185518i
$469$	−2.20201	−	1.41515i	−0.101679	−	0.0653454i
$470$	−0.378473	−	2.63234i	−0.0174577	−	0.121421i
$471$	15.1694	+	33.2163i	0.698968	+	1.53053i
$472$	3.33052	+	7.29282i	0.153300	+	0.335679i
$473$	−2.98498	−	20.7610i	−0.137250	−	0.954591i
$474$	6.86651	+	4.41284i	0.315389	+	0.202688i
$475$	24.4326	−	7.17405i	1.12104	−	0.329168i
$476$	0.0188747	−	0.131276i	0.000865119	−	0.00601704i
$477$	32.3727	−	37.3601i	1.48224	−	1.71060i
$478$	23.2012	−	14.9105i	1.06120	−	0.681990i
$479$	−0.639131	−	0.737597i	−0.0292027	−	0.0337017i	0.740960	−	0.671549i	$-0.234371\pi$
$479$	−0.639131	−	0.737597i	−0.0292027	−	0.0337017i	−0.770163	+	0.637847i	$0.779825\pi$
$480$	−0.748515	−	0.219784i	−0.0341649	−	0.0100317i
$481$	5.72188	−	12.5292i	0.260895	−	0.571281i
$482$	−12.5625			−0.572206
$483$	12.0340	−	7.58067i	0.547564	−	0.344933i
$484$	−5.87518			−0.267053
$485$	1.21345	−	2.65707i	0.0550997	−	0.120652i
$486$	−3.38194	−	0.993026i	−0.153408	−	0.0450446i
$487$	−21.8188	−	25.1802i	−0.988702	−	1.14102i	−0.990006	−	0.141024i	$-0.954961\pi$
$487$	−21.8188	−	25.1802i	−0.988702	−	1.14102i	0.00130397	−	0.999999i	$-0.499585\pi$
$488$	4.68713	−	3.01224i	0.212177	−	0.136358i
$489$	16.4861	−	19.0260i	0.745527	−	0.860384i
$490$	0.0374364	−	0.260376i	0.00169120	−	0.0117626i
$491$	−25.0330	+	7.35036i	−1.12972	+	0.331717i	−0.792599	−	0.609743i	$-0.791273\pi$
$491$	−25.0330	+	7.35036i	−1.12972	+	0.331717i	−0.337125	+	0.941460i	$0.609455\pi$
$492$	−4.95065	−	3.18159i	−0.223193	−	0.143437i
$493$	−0.0163327	−	0.113596i	−0.000735587	−	0.00511612i
$494$	−5.27372	−	11.5478i	−0.237276	−	0.519561i
$495$	1.43354	+	3.13902i	0.0644330	+	0.141089i
$496$	−1.22696	−	8.53369i	−0.0550921	−	0.383174i
$497$	0.513574	+	0.330054i	0.0230369	+	0.0148049i
$498$	44.5492	−	13.0808i	1.99630	−	0.586166i
$499$	−2.95897	+	20.5801i	−0.132462	+	0.921293i	0.809869	+	0.586610i	$0.199538\pi$
$499$	−2.95897	+	20.5801i	−0.132462	+	0.921293i	−0.942331	+	0.334682i	$0.891371\pi$
$500$	−1.71071	+	1.97427i	−0.0765053	+	0.0882919i
$501$	50.9829	−	32.7648i	2.27775	−	1.46382i
$502$	10.8675	+	12.5418i	0.485042	+	0.559768i
$503$	9.15105	+	2.68699i	0.408025	+	0.119807i	0.479303	−	0.877649i	$-0.340889\pi$
$503$	9.15105	+	2.68699i	0.408025	+	0.119807i	−0.0712778	+	0.997457i	$0.522708\pi$
$504$	−2.40729	+	5.27123i	−0.107229	+	0.234799i
$505$	−3.90379			−0.173716
$506$	−9.07983	−	5.95211i	−0.403648	−	0.264604i
$507$	20.6319			0.916297
$508$	1.09319	−	2.39376i	0.0485026	−	0.106206i
$509$	−1.14827	−	0.337163i	−0.0508963	−	0.0149445i	0.256185	−	0.966628i	$-0.417534\pi$
$509$	−1.14827	−	0.337163i	−0.0508963	−	0.0149445i	−0.307082	+	0.951683i	$0.599352\pi$
$510$	−0.0677543	−	0.0781927i	−0.00300021	−	0.00346243i
$511$	5.99205	−	3.85086i	0.265073	−	0.170352i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	6.09175	−	42.3690i	0.268957	−	1.87064i
$514$	−23.7189	+	6.96450i	−1.04620	+	0.307191i
$515$	1.13035	+	0.726433i	0.0498092	+	0.0320105i
$516$	−3.91037	−	27.1972i	−0.172144	−	1.19729i
$517$	9.50742	+	20.8184i	0.418136	+	0.915590i
$518$	2.32763	+	5.09680i	0.102270	+	0.223940i
$519$	7.73689	+	53.8113i	0.339612	+	2.36205i
$520$	0.543995	+	0.349605i	0.0238558	+	0.0153312i
$521$	15.2493	−	4.47761i	0.668086	−	0.196168i	0.0699352	−	0.997552i	$-0.477721\pi$
$521$	15.2493	−	4.47761i	0.668086	−	0.196168i	0.598150	+	0.801384i	$0.295903\pi$
$522$	−0.713632	+	4.96342i	−0.0312348	+	0.217243i
$523$	−0.579336	+	0.668589i	−0.0253326	+	0.0292354i	−0.768274	−	0.640121i	$-0.778884\pi$
$523$	−0.579336	+	0.668589i	−0.0253326	+	0.0292354i	0.742942	+	0.669356i	$0.233430\pi$
$524$	−6.67016	+	4.28665i	−0.291387	+	0.187263i
$525$	9.57596	+	11.0512i	0.417929	+	0.482316i
$526$	−14.0924	−	4.13790i	−0.614457	−	0.180421i
$527$	0.474998	−	1.04010i	0.0206912	−	0.0453075i
$528$	6.71359			0.292172
$529$	9.17412	+	21.0911i	0.398875	+	0.917005i
$530$	2.24402			0.0974740
$531$	19.3000	−	42.2612i	0.837550	−	1.83398i
$532$	4.95509	+	1.45495i	0.214830	+	0.0630799i
$533$	3.19443	+	3.68657i	0.138366	+	0.159683i
$534$	4.08624	−	2.62607i	0.176829	−	0.113641i
$535$	−1.77143	+	2.04434i	−0.0765855	+	0.0883843i
$536$	−0.372514	+	2.59089i	−0.0160902	+	0.111910i
$537$	34.6765	−	10.1819i	1.49640	−	0.439383i
$538$	3.92996	+	2.52563i	0.169433	+	0.108888i
$539$	0.322173	+	2.24077i	0.0138770	+	0.0965166i
$540$	0.905749	+	1.98331i	0.0389772	+	0.0853482i
$541$	−8.70831	−	19.0685i	−0.374399	−	0.819820i	−0.999237	−	0.0390652i	$-0.987562\pi$
$541$	−8.70831	−	19.0685i	−0.374399	−	0.819820i	0.624837	−	0.780755i	$-0.285165\pi$
$542$	−2.44810	−	17.0269i	−0.105155	−	0.731369i
$543$	−53.5061	−	34.3863i	−2.29617	−	1.47566i
$544$	−0.127254	+	0.0373651i	−0.00545597	+	0.00160202i
$545$	0.758065	−	5.27246i	0.0324719	−	0.225847i
$546$	4.77408	−	5.50958i	0.204312	−	0.235788i
$547$	24.2013	−	15.5532i	1.03477	−	0.665008i	0.0910841	−	0.995843i	$-0.470967\pi$
$547$	24.2013	−	15.5532i	1.03477	−	0.665008i	0.943689	+	0.330835i	$0.107330\pi$
$548$	−8.85635	−	10.2208i	−0.378325	−	0.436610i
$549$	−30.9791	−	9.09628i	−1.32215	−	0.388220i
$550$	4.63702	−	10.1537i	0.197723	−	0.432954i
$551$	4.46877			0.190376
$552$	−11.8947	−	7.79735i	−0.506272	−	0.331877i
$553$	2.75229			0.117039
$554$	5.45350	−	11.9415i	0.231697	−	0.507346i
$555$	4.19404	+	1.23148i	0.178027	+	0.0522734i
$556$	−10.1059	−	11.6629i	−0.428588	−	0.494617i
$557$	−3.84048	+	2.46813i	−0.162726	+	0.104578i	−0.619469	−	0.785021i	$-0.712652\pi$
$557$	−3.84048	+	2.46813i	−0.162726	+	0.104578i	0.456743	+	0.889599i	$0.349016\pi$
$558$	−32.7171	+	37.7576i	−1.38503	+	1.59841i
$559$	−3.24136	+	22.5441i	−0.137095	+	0.953515i
$560$	−0.252398	+	0.0741106i	−0.0106657	+	0.00313175i
$561$	0.749051	+	0.481386i	0.0316249	+	0.0203241i
$562$	1.07135	+	7.45142i	0.0451923	+	0.314319i
$563$	0.682146	+	1.49369i	0.0287490	+	0.0629515i	0.923462	−	0.383690i	$-0.125347\pi$
$563$	0.682146	+	1.49369i	0.0287490	+	0.0629515i	−0.894713	+	0.446642i	$0.852620\pi$
$564$	12.4549	+	27.2723i	0.524444	+	1.14837i
$565$	0.188056	+	1.30796i	0.00791158	+	0.0550262i
$566$	18.2001	+	11.6965i	0.765008	+	0.491640i
$567$	6.90468	−	2.02740i	0.289969	−	0.0851427i
$568$	0.0868813	−	0.604272i	0.00364546	−	0.0253547i
$569$	−1.16089	+	1.33974i	−0.0486670	+	0.0561647i	−0.779561	−	0.626326i	$-0.784558\pi$
$569$	−1.16089	+	1.33974i	−0.0486670	+	0.0561647i	0.730894	+	0.682491i	$0.239103\pi$
$570$	3.38919	−	2.17810i	0.141957	−	0.0912305i
$571$	25.4134	+	29.3286i	1.06352	+	1.22736i	0.972839	+	0.231483i	$0.0743577\pi$
$571$	25.4134	+	29.3286i	1.06352	+	1.22736i	0.0906771	+	0.995880i	$0.471097\pi$
$572$	−5.33957	−	1.56784i	−0.223259	−	0.0655546i
$573$	21.2493	−	46.5294i	0.887702	−	1.94380i
$574$	−1.98436			−0.0828255
$575$	−20.0083	+	12.6040i	−0.834405	+	0.525625i
$576$	5.79490			0.241454
$577$	−6.33133	+	13.8637i	−0.263577	+	0.577153i	−0.994432	−	0.105380i	$-0.966394\pi$
$577$	−6.33133	+	13.8637i	−0.263577	+	0.577153i	0.730855	+	0.682532i	$0.239121\pi$
$578$	16.2945	+	4.78450i	0.677762	+	0.199009i
$579$	−15.6030	−	18.0068i	−0.648439	−	0.748338i
$580$	−0.191491	+	0.123064i	−0.00795123	+	0.00510995i
$581$	10.2526	−	11.8321i	0.425348	−	0.490877i
$582$	−4.68662	+	32.5962i	−0.194267	+	1.35116i
$583$	−18.5295	+	5.44077i	−0.767415	+	0.225333i
$584$	−5.99205	−	3.85086i	−0.247953	−	0.159350i
$585$	−0.533291	−	3.70912i	−0.0220489	−	0.153353i
$586$	1.68764	+	3.69543i	0.0697159	+	0.152657i
$587$	−3.88688	−	8.51108i	−0.160429	−	0.351290i	0.812298	−	0.583242i	$-0.198216\pi$
$587$	−3.88688	−	8.51108i	−0.160429	−	0.351290i	−0.972727	+	0.231952i	$0.925489\pi$
$588$	0.422052	+	2.93543i	0.0174051	+	0.121055i
$589$	37.4556	+	24.0713i	1.54333	+	0.991839i
$590$	2.02356	−	0.594170i	0.0833085	−	0.0244616i
$591$	−9.94509	+	69.1696i	−0.409086	+	2.84526i
$592$	3.66928	−	4.23457i	0.150806	−	0.174040i
$593$	−21.3371	+	13.7125i	−0.876211	+	0.563106i	−0.899647	−	0.436619i	$-0.856176\pi$
$593$	−21.3371	+	13.7125i	−0.876211	+	0.563106i	0.0234358	+	0.999725i	$0.492539\pi$
$594$	−12.2877	−	14.1808i	−0.504170	−	0.581843i
$595$	−0.0334745	−	0.00982901i	−0.00137232	−	0.000402950i
$596$	−8.73393	+	19.1246i	−0.357756	+	0.783375i
$597$	−27.1793			−1.11237
$598$	7.63937	+	8.97931i	0.312397	+	0.367191i
$599$	−34.2953			−1.40127			−0.700635	−	0.713520i	$-0.747100\pi$
$599$	−34.2953			−1.40127			−0.700635	+	0.713520i	$0.747100\pi$
$600$	6.07457	−	13.3014i	0.247993	−	0.543029i
$601$	−21.7861	−	6.39698i	−0.888675	−	0.260938i	−0.194635	−	0.980876i	$-0.562352\pi$
$601$	−21.7861	−	6.39698i	−0.888675	−	0.260938i	−0.694039	+	0.719937i	$0.744171\pi$
$602$	−6.06737	−	7.00212i	−0.247288	−	0.285385i
$603$	12.7604	−	8.20064i	0.519646	−	0.333956i
$604$	−8.38829	+	9.68060i	−0.341315	+	0.393898i
$605$	−0.219945	+	1.52975i	−0.00894204	+	0.0621933i
$606$	42.2280	−	12.3993i	1.71540	−	0.503686i
$607$	−4.57788	−	2.94202i	−0.185810	−	0.119413i	0.444429	−	0.895814i	$-0.353407\pi$
$607$	−4.57788	−	2.94202i	−0.185810	−	0.119413i	−0.630239	+	0.776401i	$0.717043\pi$
$608$	−0.734954	−	5.11172i	−0.0298063	−	0.207307i
$609$	1.06605	+	2.33431i	0.0431983	+	0.0945912i
$610$	−0.608844	−	1.33318i	−0.0246514	−	0.0539790i
$611$	−3.53685	−	24.5993i	−0.143085	−	0.995181i
$612$	0.646550	+	0.415513i	0.0261352	+	0.0167961i
$613$	7.70038	−	2.26103i	0.311015	−	0.0913223i	−0.122500	−	0.992469i	$-0.539091\pi$
$613$	7.70038	−	2.26103i	0.311015	−	0.0913223i	0.433515	+	0.901146i	$0.357273\pi$
$614$	−4.70003	+	32.6895i	−0.189678	+	1.31924i
$615$	−1.01374	+	1.16992i	−0.0408780	+	0.0471758i
$616$	1.90444	−	1.22391i	0.0767319	−	0.0493126i
$617$	−13.2016	−	15.2355i	−0.531476	−	0.613356i	0.424990	−	0.905198i	$-0.360277\pi$
$617$	−13.2016	−	15.2355i	−0.531476	−	0.613356i	−0.956467	+	0.291841i	$0.905732\pi$
$618$	−14.5345	−	4.26772i	−0.584664	−	0.171673i
$619$	12.8384	−	28.1122i	0.516018	−	1.12992i	−0.454907	−	0.890539i	$-0.650327\pi$
$619$	12.8384	−	28.1122i	0.516018	−	1.12992i	0.970925	−	0.239384i	$-0.0769454\pi$
$620$	−2.26790			−0.0910810
$621$	5.30063	+	39.3958i	0.212707	+	1.58090i
$622$	6.69549			0.268465
$623$	0.680400	−	1.48987i	0.0272596	−	0.0596903i
$624$	−6.99491	−	2.05389i	−0.280020	−	0.0822214i
$625$	−15.6949	−	18.1129i	−0.627798	−	0.724517i
$626$	−15.6996	+	10.0895i	−0.627483	+	0.403259i
$627$	−22.7046	+	26.2025i	−0.906734	+	1.04643i
$628$	1.75235	−	12.1878i	0.0699263	−	0.486348i
$629$	0.713021	−	0.209362i	0.0284300	−	0.00834781i
$630$	1.28238	+	0.824135i	0.0510912	+	0.0328343i
$631$	−0.469272	−	3.26386i	−0.0186814	−	0.129932i	0.978346	−	0.206974i	$-0.0663616\pi$
$631$	−0.469272	−	3.26386i	−0.0186814	−	0.129932i	−0.997028	+	0.0770419i	$0.975452\pi$
$632$	−1.14334	−	2.50357i	−0.0454797	−	0.0995866i
$633$	−11.1742	−	24.4681i	−0.444136	−	0.972522i
$634$	−2.45502	−	17.0750i	−0.0975014	−	0.678137i
$635$	−0.582351	−	0.374254i	−0.0231099	−	0.0148518i
$636$	−24.2740	+	7.12748i	−0.962525	+	0.282623i
$637$	0.349844	−	2.43322i	0.0138613	−	0.0964078i
$638$	1.28282	−	1.48046i	0.0507874	−	0.0586118i
$639$	−2.97611	+	1.91263i	−0.117733	+	0.0756625i
$640$	0.172263	+	0.198802i	0.00680930	+	0.00785835i
$641$	−24.8041	−	7.28313i	−0.979701	−	0.287666i	−0.247600	−	0.968862i	$-0.579642\pi$
$641$	−24.8041	−	7.28313i	−0.979701	−	0.287666i	−0.732101	+	0.681196i	$0.761460\pi$
$642$	12.6686	−	27.7404i	0.499990	−	1.09482i
$643$	−21.7804			−0.858935			−0.429468	−	0.903082i	$-0.641299\pi$
$643$	−21.7804			−0.858935			−0.429468	+	0.903082i	$0.641299\pi$
$644$	−4.79563	−	0.0434249i	−0.188974	−	0.00171118i
$645$	−7.22788			−0.284597
$646$	0.284526	−	0.623024i	0.0111945	−	0.0245125i
$647$	−11.9684	−	3.51424i	−0.470526	−	0.138159i	0.0378691	−	0.999283i	$-0.487943\pi$
$647$	−11.9684	−	3.51424i	−0.470526	−	0.138159i	−0.508396	+	0.861124i	$0.669761\pi$
$648$	−4.71250	−	5.43851i	−0.185124	−	0.213645i
$649$	−15.2685	+	9.81247i	−0.599341	+	0.385173i
$650$	−7.93764	+	9.16053i	−0.311340	+	0.359305i
$651$	−3.63870	+	25.3077i	−0.142612	+	0.991887i
$652$	−8.14508	+	2.39161i	−0.318986	+	0.0936627i
$653$	−19.0050	−	12.2138i	−0.743723	−	0.477962i	0.113092	−	0.993584i	$-0.463924\pi$
$653$	−19.0050	−	12.2138i	−0.743723	−	0.477962i	−0.856816	+	0.515622i	$0.827561\pi$
$654$	8.54631	+	59.4409i	0.334187	+	2.32432i
$655$	0.866433	+	1.89722i	0.0338543	+	0.0741307i
$656$	0.824332	+	1.80503i	0.0321847	+	0.0704748i
$657$	5.87415	+	40.8556i	0.229172	+	1.59393i
$658$	8.50488	+	5.46575i	0.331555	+	0.213077i
$659$	11.0120	−	3.23342i	0.428967	−	0.125956i	−0.0601197	−	0.998191i	$-0.519148\pi$
$659$	11.0120	−	3.23342i	0.428967	−	0.125956i	0.489087	+	0.872235i	$0.337330\pi$
$660$	0.251332	−	1.74806i	0.00978310	−	0.0680430i
$661$	4.35775	−	5.02911i	0.169497	−	0.195610i	−0.664646	−	0.747159i	$-0.731418\pi$
$661$	4.35775	−	5.02911i	0.169497	−	0.195610i	0.834143	+	0.551549i	$0.185963\pi$
$662$	28.8241	−	18.5241i	1.12028	−	0.719960i
$663$	−0.633167	−	0.730714i	−0.0245902	−	0.0283786i
$664$	−15.0219	−	4.41083i	−0.582963	−	0.171173i
$665$	0.564333	−	1.23572i	0.0218839	−	0.0479190i
$666$	−32.4696			−1.25817
$667$	−3.99226	+	1.13307i	−0.154581	+	0.0438727i
$668$	−20.4354			−0.790668
$669$	−17.6551	+	38.6593i	−0.682587	+	1.49466i
$670$	0.660660	+	0.193987i	0.0255235	+	0.00749438i
$671$	8.25979	+	9.53230i	0.318866	+	0.367990i
$672$	2.49484	−	1.60334i	0.0962405	−	0.0618500i
$673$	−11.5161	+	13.2903i	−0.443914	+	0.512304i	−0.932973	−	0.359947i	$-0.882795\pi$
$673$	−11.5161	+	13.2903i	−0.443914	+	0.512304i	0.489059	+	0.872251i	$0.337340\pi$
$674$	−0.438233	+	3.04798i	−0.0168801	+	0.117404i
$675$	−39.2140	+	11.5143i	−1.50935	+	0.443185i
$676$	−5.85264	−	3.76126i	−0.225101	−	0.144664i
$677$	0.802189	+	5.57934i	0.0308306	+	0.214432i	0.999413	−	0.0342617i	$-0.0109080\pi$
$677$	0.802189	+	5.57934i	0.0308306	+	0.214432i	−0.968582	+	0.248693i	$0.919999\pi$
$678$	−6.18859	−	13.5511i	−0.237671	−	0.520427i
$679$	4.61293	+	10.1009i	0.177028	+	0.387637i
$680$	0.00496504	+	0.0345326i	0.000190401	+	0.00132427i
$681$	−6.35329	−	4.08301i	−0.243459	−	0.156461i
$682$	18.7267	−	5.49866i	0.717083	−	0.210554i
$683$	4.61758	−	32.1160i	0.176687	−	1.22888i	−0.687676	−	0.726017i	$-0.741369\pi$
$683$	4.61758	−	32.1160i	0.176687	−	1.22888i	0.864363	−	0.502868i	$-0.167722\pi$
$684$	−19.5977	+	22.6169i	−0.749336	+	0.864780i
$685$	−2.99279	+	1.92335i	−0.114349	+	0.0734874i
$686$	0.654861	+	0.755750i	0.0250027	+	0.0288547i
$687$	−14.8974	−	4.37428i	−0.568373	−	0.166889i
$688$	−3.84888	+	8.42786i	−0.146737	+	0.321309i
$689$	20.9705			0.798912
$690$	−2.47553	+	2.80519i	−0.0942420	+	0.106792i
$691$	45.0090			1.71222			0.856111	−	0.516792i	$-0.172874\pi$
$691$	45.0090			1.71222			0.856111	+	0.516792i	$0.172874\pi$
$692$	7.61523	−	16.6750i	0.289488	−	0.633890i
$693$	−12.5871	−	3.69592i	−0.478146	−	0.140396i
$694$	−21.4827	−	24.7924i	−0.815472	−	0.941105i
$695$	−3.41506	+	2.19473i	−0.129541	+	0.0832507i
$696$	1.68052	−	1.93942i	0.0636998	−	0.0735134i
$697$	−0.0374541	+	0.260499i	−0.00141867	+	0.00986710i
$698$	9.81804	−	2.88284i	0.371618	−	0.109117i
$699$	−35.9300	−	23.0908i	−1.35900	−	0.873374i
$700$	−0.701726	−	4.88061i	−0.0265228	−	0.184470i
$701$	−12.7216	−	27.8565i	−0.480489	−	1.05212i	−0.982329	−	0.187164i	$-0.940070\pi$
$701$	−12.7216	−	27.8565i	−0.480489	−	1.05212i	0.501839	−	0.864961i	$-0.332657\pi$
$702$	8.46426	+	18.5341i	0.319463	+	0.699526i
$703$	4.11805	+	28.6417i	0.155315	+	1.08024i
$704$	−1.90444	−	1.22391i	−0.0717761	−	0.0461277i
$705$	7.56732	−	2.22196i	0.285002	−	0.0836840i
$706$	−1.53512	+	10.6770i	−0.0577750	+	0.401834i
$707$	9.71834	−	11.2156i	0.365496	−	0.421805i
$708$	−20.0020	+	12.8545i	−0.751719	+	0.483101i
$709$	24.3624	+	28.1157i	0.914949	+	1.05591i	0.998235	+	0.0593819i	$0.0189130\pi$
$709$	24.3624	+	28.1157i	0.914949	+	1.05591i	−0.0832863	+	0.996526i	$0.526542\pi$
$710$	−0.154085	−	0.0452435i	−0.00578272	−	0.00169796i
$711$	−6.62555	+	14.5079i	−0.248478	+	0.544090i
$712$	−1.63788			−0.0613821
$713$	−39.5651	−	12.0075i	−1.48172	−	0.449686i
$714$	0.393319			0.0147196
$715$	−0.608121	+	1.33160i	−0.0227424	+	0.0497990i
$716$	−11.6928	−	3.43333i	−0.436982	−	0.128309i
$717$	53.5609	+	61.8125i	2.00027	+	2.30843i
$718$	−13.9654	+	8.97505i	−0.521186	+	0.334946i
$719$	−15.3495	+	17.7143i	−0.572441	+	0.660632i	−0.965962	−	0.258684i	$-0.916711\pi$
$719$	−15.3495	+	17.7143i	−0.572441	+	0.660632i	0.393521	+	0.919315i	$0.371257\pi$
$720$	0.216940	−	1.50885i	0.00808488	−	0.0562316i
$721$	−4.90100	+	1.43906i	−0.182523	+	0.0535936i
$722$	6.45224	+	4.14660i	0.240127	+	0.154320i
$723$	−5.30202	−	36.8764i	−0.197184	−	1.37145i
$724$	8.90929	+	19.5086i	0.331111	+	0.725033i
$725$	−1.77247	−	3.88116i	−0.0658277	−	0.144143i
$726$	−2.47963	−	17.2462i	−0.0920276	−	0.640066i
$727$	−37.8086	−	24.2981i	−1.40224	−	0.901166i	−0.402345	−	0.915488i	$-0.631805\pi$
$727$	−37.8086	−	24.2981i	−1.40224	−	0.901166i	−0.999897	+	0.0143221i	$0.995441\pi$
$728$	−2.35867	+	0.692567i	−0.0874180	+	0.0256682i
$729$	4.55998	−	31.7154i	0.168888	−	1.17464i
$730$	−1.22699	+	1.41602i	−0.0454129	+	0.0524093i
$731$	−1.03373	+	0.664339i	−0.0382340	+	0.0245715i
$732$	10.8204	+	12.4875i	0.399935	+	0.461550i
$733$	25.2049	+	7.40083i	0.930965	+	0.273356i	0.711841	−	0.702341i	$-0.247862\pi$
$733$	25.2049	+	7.40083i	0.930965	+	0.273356i	0.219124	+	0.975697i	$0.429680\pi$
$734$	10.2952	−	22.5433i	0.380002	−	0.832089i
$735$	0.780116			0.0287750
$736$	1.95268	+	4.38030i	0.0719767	+	0.161460i
$737$	−5.92560			−0.218272
$738$	4.77692	−	10.4600i	0.175841	−	0.385038i
$739$	14.2070	+	4.17155i	0.522613	+	0.153453i	0.532390	−	0.846499i	$-0.321294\pi$
$739$	14.2070	+	4.17155i	0.522613	+	0.153453i	−0.00977714	+	0.999952i	$0.503112\pi$
$740$	−0.965215	−	1.11392i	−0.0354820	−	0.0409484i
$741$	31.6721	−	20.3544i	1.16350	−	0.747739i
$742$	−5.58641	+	6.44706i	−0.205083	+	0.236679i
$743$	−3.35507	+	23.3350i	−0.123085	+	0.856078i	0.830942	+	0.556359i	$0.187802\pi$
$743$	−3.35507	+	23.3350i	−0.123085	+	0.856078i	−0.954027	+	0.299719i	$0.903107\pi$
$744$	24.5323	−	7.20332i	0.899396	−	0.264087i
$745$	4.65262	+	2.99006i	0.170459	+	0.109547i
$746$	0.917597	+	6.38202i	0.0335956	+	0.233663i
$747$	37.6887	+	82.5268i	1.37896	+	3.01950i
$748$	−0.124724	−	0.273108i	−0.00456037	−	0.00998582i
$749$	−1.46346	−	10.1786i	−0.0534737	−	0.371918i
$750$	−6.51734	−	4.18844i	−0.237980	−	0.152940i
$751$	7.63357	−	2.24142i	0.278553	−	0.0817906i	−0.139472	−	0.990226i	$-0.544541\pi$
$751$	7.63357	−	2.24142i	0.278553	−	0.0817906i	0.418025	+	0.908435i	$0.362722\pi$
$752$	1.43877	−	10.0069i	0.0524665	−	0.364913i
$753$	−32.2290	+	37.1942i	−1.17449	+	1.35543i
$754$	−1.78949	+	1.15004i	−0.0651694	+	0.0418819i
$755$	2.20657	+	2.54651i	0.0803051	+	0.0926771i
$756$	−7.95287	−	2.33517i	−0.289243	−	0.0849294i
$757$	14.0737	−	30.8171i	0.511518	−	1.12007i	−0.461034	−	0.887382i	$-0.652521\pi$
$757$	14.0737	−	30.8171i	0.511518	−	1.12007i	0.972552	−	0.232686i	$-0.0747514\pi$
$758$	−0.334981			−0.0121671
$759$	13.6399	−	29.1653i	0.495096	−	1.05863i
$760$	−1.35848			−0.0492772
$761$	−19.2106	+	42.0654i	−0.696384	+	1.52487i	0.147918	+	0.989000i	$0.452743\pi$
$761$	−19.2106	+	42.0654i	−0.696384	+	1.52487i	−0.844302	+	0.535868i	$0.819984\pi$
$762$	7.48810	+	2.19871i	0.271265	+	0.0796507i
$763$	13.2606	+	15.3035i	0.480065	+	0.554024i
$764$	−14.5102	+	9.32514i	−0.524961	+	0.337372i
$765$	0.132394	−	0.152791i	0.00478671	−	0.00552416i
$766$	−1.64223	+	11.4220i	−0.0593362	+	0.412692i
$767$	18.9102	−	5.55254i	0.682809	−	0.200491i
$768$	−2.49484	−	1.60334i	−0.0900247	−	0.0578554i
$769$	6.47905	+	45.0628i	0.233641	+	1.62501i	0.682139	+	0.731222i	$0.261050\pi$
$769$	6.47905	+	45.0628i	0.233641	+	1.62501i	−0.448499	+	0.893784i	$0.648041\pi$
$770$	−0.247380	−	0.541687i	−0.00891497	−	0.0195211i
$771$	−30.4544	−	66.6859i	−1.09679	−	2.40163i
$772$	1.14339	+	7.95244i	0.0411515	+	0.286215i
$773$	19.8566	+	12.7610i	0.714191	+	0.458983i	0.846612	−	0.532211i	$-0.178639\pi$
$773$	19.8566	+	12.7610i	0.714191	+	0.458983i	−0.132421	+	0.991194i	$0.542275\pi$
$774$	51.5157	−	15.1264i	1.85169	−	0.543706i
$775$	6.04990	−	42.0780i	0.217319	−	1.51148i
$776$	7.27183	−	8.39213i	0.261043	−	0.301260i
$777$	−13.9789	+	8.98371i	−0.501491	+	0.322289i
$778$	−8.42079	−	9.71811i	−0.301900	−	0.348411i
$779$	−9.83267	−	2.88713i	−0.352292	−	0.103442i
$780$	−0.796647	+	1.74441i	−0.0285245	+	0.0624600i
$781$	1.38202			0.0494527
$782$	−0.0962167	+	0.628733i	−0.00344070	+	0.0224835i
$783$	−7.17233			−0.256318
$784$	0.415415	−	0.909632i	0.0148363	−	0.0324869i
$785$	−3.10782	−	0.912537i	−0.110923	−	0.0325699i
$786$	−15.3983	−	17.7706i	−0.549240	−	0.633857i
$787$	23.9659	−	15.4020i	0.854293	−	0.549021i	−0.0386179	−	0.999254i	$-0.512296\pi$
$787$	23.9659	−	15.4020i	0.854293	−	0.549021i	0.892911	+	0.450233i	$0.148659\pi$
$788$	15.4309	−	17.8082i	0.549704	−	0.634392i
$789$	6.19881	−	43.1137i	0.220683	−	1.53489i
$790$	−0.694671	+	0.203974i	−0.0247153	+	0.00725706i
$791$	−4.22591	−	2.71583i	−0.150256	−	0.0965638i
$792$	1.86696	+	12.9850i	0.0663396	+	0.461402i
$793$	−5.68968	−	12.4587i	−0.202046	−	0.442420i
$794$	4.41157	+	9.65998i	0.156561	+	0.342820i
$795$	0.947093	+	6.58718i	0.0335899	+	0.233623i
$796$	7.70991	+	4.95486i	0.273270	+	0.175620i
$797$	−4.08151	+	1.19844i	−0.144575	+	0.0424509i	−0.353219	−	0.935541i	$-0.614913\pi$
$797$	−4.08151	+	1.19844i	−0.144575	+	0.0424509i	0.208645	+	0.977992i	$0.433095\pi$
$798$	−2.17959	+	15.1594i	−0.0771568	+	0.536637i
$799$	0.878050	−	1.01332i	0.0310632	−	0.0358488i
$800$	−4.14806	+	2.66579i	−0.146656	+	0.0942500i
$801$	6.21551	+	7.17308i	0.219614	+	0.253448i
$802$	30.8415	+	9.05588i	1.08905	+	0.319774i
$803$	6.69839	−	14.6674i	0.236381	−	0.517602i
$804$	−7.76262			−0.273767
$805$	−0.190838	+	1.24704i	−0.00672615	+	0.0439524i
$806$	−21.1936			−0.746513
$807$	−5.75518	+	12.6021i	−0.202592	+	0.443614i
$808$	−14.2392	−	4.18100i	−0.500933	−	0.147087i
$809$	−3.86275	−	4.45785i	−0.135807	−	0.156730i	0.683772	−	0.729695i	$-0.260338\pi$
$809$	−3.86275	−	4.45785i	−0.135807	−	0.156730i	−0.819579	+	0.572966i	$0.805793\pi$
$810$	−1.59247	+	1.02342i	−0.0559538	+	0.0359593i
$811$	36.3986	−	42.0063i	1.27813	−	1.47504i	0.474073	−	0.880485i	$-0.342783\pi$
$811$	36.3986	−	42.0063i	1.27813	−	1.47504i	0.804056	−	0.594554i	$-0.202671\pi$
$812$	0.123148	−	0.856515i	0.00432166	−	0.0300578i
$813$	48.9482	−	14.3725i	1.71669	−	0.504065i
$814$	10.6708	+	6.85772i	0.374012	+	0.240363i
$815$	0.317795	+	2.21031i	0.0111319	+	0.0774239i
$816$	−0.163391	−	0.357775i	−0.00571981	−	0.0125246i
$817$	−19.8767	−	43.5238i	−0.695397	−	1.52271i
$818$	3.68869	+	25.6554i	0.128972	+	0.897019i
$819$	11.9839	+	7.70158i	0.418751	+	0.269115i
$820$	0.500847	−	0.147062i	0.0174903	−	0.00513563i
$821$	1.78063	−	12.3845i	0.0621443	−	0.432223i	−0.934869	−	0.354993i	$-0.884483\pi$
$821$	1.78063	−	12.3845i	0.0621443	−	0.432223i	0.997013	−	0.0772302i	$-0.0246077\pi$
$822$	26.2646	−	30.3109i	0.916082	−	1.05722i
$823$	18.0090	−	11.5737i	0.627755	−	0.403433i	−0.187723	−	0.982222i	$-0.560111\pi$
$823$	18.0090	−	11.5737i	0.627755	−	0.403433i	0.815478	+	0.578789i	$0.196474\pi$
$824$	3.34497	+	3.86030i	0.116528	+	0.134480i
$825$	31.7625	+	9.32631i	1.10583	+	0.324700i
$826$	−3.33052	+	7.29282i	−0.115884	+	0.253750i
$827$	43.7954			1.52292			0.761458	−	0.648214i	$-0.224484\pi$
$827$	43.7954			1.52292			0.761458	+	0.648214i	$0.224484\pi$
$828$	11.7734	−	25.1743i	0.409153	−	0.874869i
$829$	−8.37285			−0.290801			−0.145401	−	0.989373i	$-0.546447\pi$
$829$	−8.37285			−0.290801			−0.145401	+	0.989373i	$0.546447\pi$
$830$	−1.71084	+	3.74621i	−0.0593840	+	0.130033i
$831$	37.3551	+	10.9685i	1.29584	+	0.380492i
$832$	1.60981	+	1.85782i	0.0558100	+	0.0644082i
$833$	0.111572	−	0.0717031i	0.00386575	−	0.00248437i
$834$	29.9704	−	34.5877i	1.03779	−	1.19767i
$835$	−0.765026	+	5.32087i	−0.0264748	+	0.184136i
$836$	11.2174	−	3.29372i	0.387961	−	0.113916i
$837$	−60.1159	−	38.6341i	−2.07791	−	1.33539i
$838$	3.93911	+	27.3971i	0.136074	+	0.946417i
$839$	−17.5287	−	38.3824i	−0.605157	−	1.32511i	−0.925838	−	0.377921i	$-0.876639\pi$
$839$	−17.5287	−	38.3824i	−0.605157	−	1.32511i	0.320681	−	0.947187i	$-0.396088\pi$
$840$	−0.324072	−	0.709618i	−0.0111815	−	0.0244841i
$841$	4.02057	+	27.9637i	0.138640	+	0.964264i
$842$	28.4332	+	18.2729i	0.979873	+	0.629726i
$843$	−21.4210	+	6.28977i	−0.737778	+	0.216631i
$844$	−1.29083	+	8.97794i	−0.0444323	+	0.309033i
$845$	−1.19844	+	1.38308i	−0.0412277	+	0.0475792i
$846$	−49.2849	+	31.6735i	−1.69445	+	1.08896i
$847$	−3.84742	−	4.44016i	−0.132199	−	0.152566i
$848$	8.18512	+	2.40337i	0.281078	+	0.0825320i
$849$	−26.6529	+	58.3617i	−0.914726	+	2.00297i
$850$	−0.653954			−0.0224304
$851$	−10.9411	−	24.5435i	−0.375057	−	0.841339i
$852$	1.81047			0.0620257
$853$	−8.44378	+	18.4893i	−0.289109	+	0.633061i	−0.997338	−	0.0729223i	$-0.976767\pi$
$853$	−8.44378	+	18.4893i	−0.289109	+	0.633061i	0.708228	+	0.705984i	$0.249495\pi$
$854$	5.34592	+	1.56970i	0.182934	+	0.0537141i
$855$	5.15523	+	5.94946i	0.176305	+	0.203467i
$856$	−8.65083	+	5.55955i	−0.295679	+	0.190022i
$857$	3.12418	−	3.60549i	0.106720	−	0.123161i	−0.699877	−	0.714264i	$-0.746762\pi$
$857$	3.12418	−	3.60549i	0.106720	−	0.123161i	0.806596	+	0.591103i	$0.201307\pi$
$858$	2.34871	−	16.3357i	0.0801837	−	0.557690i
$859$	−9.00311	+	2.64355i	−0.307182	+	0.0901968i	−0.431691	−	0.902022i	$-0.642083\pi$
$859$	−9.00311	+	2.64355i	−0.307182	+	0.0901968i	0.124509	+	0.992219i	$0.460265\pi$
$860$	2.05032	+	1.31766i	0.0699154	+	0.0449319i
$861$	−0.837501	−	5.82495i	−0.0285420	−	0.198514i
$862$	10.6145	+	23.2424i	0.361530	+	0.791640i
$863$	−21.9019	−	47.9586i	−0.745551	−	1.63253i	−0.774201	−	0.632939i	$-0.781848\pi$
$863$	−21.9019	−	47.9586i	−0.745551	−	1.63253i	0.0286504	−	0.999589i	$-0.490879\pi$
$864$	1.17959	+	8.20425i	0.0401306	+	0.279114i
$865$	−4.05668	−	2.60707i	−0.137931	−	0.0886431i
$866$	−33.6823	+	9.89001i	−1.14457	+	0.336076i
$867$	−7.16746	+	49.8507i	−0.243420	+	1.69302i
$868$	5.64585	−	6.51565i	0.191633	−	0.221156i
$869$	5.24156	−	3.36854i	0.177808	−	0.114270i
$870$	−0.442065	−	0.510170i	−0.0149874	−	0.0172964i
$871$	6.17390	+	1.81282i	0.209195	+	0.0614251i
$872$	8.41192	−	18.4195i	0.284864	−	0.623764i
$873$	−64.3488			−2.17788
$874$	−23.6996	−	7.19256i	−0.801652	−	0.243292i
$875$	−2.61233			−0.0883128
$876$	8.77498	−	19.2145i	0.296479	−	0.649199i
$877$	−21.6401	−	6.35410i	−0.730734	−	0.214563i	−0.104860	−	0.994487i	$-0.533439\pi$
$877$	−21.6401	−	6.35410i	−0.730734	−	0.214563i	−0.625874	+	0.779924i	$0.715258\pi$
$878$	−11.6456	−	13.4397i	−0.393020	−	0.453569i
$879$	−10.1354	+	6.51363i	−0.341859	+	0.219699i
$880$	−0.389971	+	0.450050i	−0.0131459	+	0.0151712i
$881$	−2.50441	+	17.4186i	−0.0843758	+	0.586847i	0.903142	+	0.429341i	$0.141254\pi$
$881$	−2.50441	+	17.4186i	−0.0843758	+	0.586847i	−0.987518	+	0.157505i	$0.949655\pi$
$882$	−5.56017	+	1.63261i	−0.187221	+	0.0549729i
$883$	5.61940	+	3.61137i	0.189108	+	0.121532i	0.631769	−	0.775157i	$-0.282329\pi$
$883$	5.61940	+	3.61137i	0.189108	+	0.121532i	−0.442661	+	0.896689i	$0.645966\pi$
$884$	0.0463985	+	0.322709i	0.00156055	+	0.0108539i
$885$	2.59819	+	5.68925i	0.0873372	+	0.191242i
$886$	12.4816	+	27.3309i	0.419328	+	0.918200i
$887$	−0.315554	−	2.19473i	−0.0105953	−	0.0736917i	0.983838	−	0.179062i	$-0.0573063\pi$
$887$	−0.315554	−	2.19473i	−0.0105953	−	0.0736917i	−0.994433	+	0.105370i	$0.966397\pi$
$888$	13.9789	+	8.98371i	0.469102	+	0.301474i
$889$	2.52497	−	0.741398i	0.0846848	−	0.0248657i
$890$	−0.0613162	+	0.426464i	−0.00205532	+	0.0142951i
$891$	10.6682	−	12.3117i	0.357398	−	0.412459i
$892$	12.0559	−	7.74786i	0.403662	−	0.259418i
$893$	34.1901	+	39.4574i	1.14413	+	1.32039i
$894$	−59.8253	−	17.5663i	−2.00086	−	0.587504i
$895$	−1.33169	+	2.91600i	−0.0445136	+	0.0974711i
$896$	−1.00000			−0.0334077
$897$	−23.1340	+	26.2146i	−0.772421	+	0.875280i
$898$	3.64160			0.121522
$899$	3.09913	−	6.78616i	0.103362	−	0.226331i
$900$	27.4161	+	8.05009i	0.913870	+	0.268336i
$901$	0.740904	+	0.855048i	0.0246831	+	0.0284858i
$902$	−3.77908	+	2.42867i	−0.125830	+	0.0808658i
$903$	17.9935	−	20.7656i	0.598787	−	0.691037i
$904$	−0.714898	+	4.97222i	−0.0237771	+	0.165374i
$905$	5.41310	−	1.58943i	0.179938	−	0.0528345i
$906$	−31.9571	−	20.5376i	−1.06170	−	0.682314i
$907$	6.19635	+	43.0965i	0.205746	+	1.43100i	0.786838	+	0.617159i	$0.211717\pi$
$907$	6.19635	+	43.0965i	0.205746	+	1.43100i	−0.581092	+	0.813838i	$0.697374\pi$
$908$	1.05789	+	2.31645i	0.0351072	+	0.0768739i
$909$	35.7249	+	78.2267i	1.18492	+	2.59462i
$910$	0.0920277	+	0.640067i	0.00305069	+	0.0212180i
$911$	35.4634	+	22.7909i	1.17495	+	0.755097i	0.974452	−	0.224596i	$-0.0721063\pi$
$911$	35.4634	+	22.7909i	1.17495	+	0.755097i	0.200502	+	0.979693i	$0.435743\pi$
$912$	14.6949	−	4.31482i	0.486597	−	0.142878i
$913$	5.04397	−	35.0816i	0.166931	−	1.16103i
$914$	−18.7109	+	21.5935i	−0.618901	+	0.714250i
$915$	3.65651	−	2.34989i	0.120880	−	0.0776851i
$916$	3.42849	+	3.95669i	0.113281	+	0.130733i
$917$	−7.60766	−	2.23381i	−0.251227	−	0.0737669i
$918$	−0.456660	+	0.999947i	−0.0150720	+	0.0330032i
$919$	−23.4481			−0.773482			−0.386741	−	0.922188i	$-0.626399\pi$
$919$	−23.4481			−0.773482			−0.386741	+	0.922188i	$0.626399\pi$
$920$	1.21363	−	0.344447i	0.0400120	−	0.0113561i
$921$	−97.9414			−3.22728
$922$	6.70708	−	14.6865i	0.220886	−	0.483673i
$923$	−1.43993	−	0.422803i	−0.0473960	−	0.0139167i
$924$	4.39647	+	5.07379i	0.144633	+	0.166916i
$925$	23.2421	−	14.9368i	0.764197	−	0.491119i
$926$	16.9881	−	19.6054i	0.558265	−	0.644272i
$927$	4.21249	−	29.2985i	0.138356	−	0.962290i
$928$	−0.830271	+	0.243790i	−0.0272550	+	0.00800278i
$929$	28.1527	+	18.0926i	0.923659	+	0.593599i	0.913717	−	0.406351i	$-0.133199\pi$
$929$	28.1527	+	18.0926i	0.923659	+	0.593599i	0.00994163	+	0.999951i	$0.496835\pi$
$930$	−0.957170	−	6.65727i	−0.0313869	−	0.218300i
$931$	2.14532	+	4.69759i	0.0703100	+	0.153957i
$932$	5.98270	+	13.1003i	0.195970	+	0.429114i
$933$	2.82584	+	19.6542i	0.0925139	+	0.643449i
$934$	19.9348	+	12.8113i	0.652286	+	0.419199i
$935$	−0.0757799	+	0.0222510i	−0.00247827	+	0.000727685i
$936$	2.02731	−	14.1003i	0.0662648	−	0.460882i
$937$	37.2301	−	42.9658i	1.21625	−	1.40363i	0.327749	−	0.944765i	$-0.393710\pi$
$937$	37.2301	−	42.9658i	1.21625	−	1.40363i	0.888505	−	0.458867i	$-0.151745\pi$
$938$	−2.20201	+	1.41515i	−0.0718983	+	0.0462062i
$939$	−36.2432	−	41.8269i	−1.18275	−	1.36497i
$940$	−2.55168	−	0.749241i	−0.0832267	−	0.0244376i
$941$	13.2422	−	28.9963i	0.431682	−	0.945252i	−0.561369	−	0.827566i	$-0.689725\pi$
$941$	13.2422	−	28.9963i	0.431682	−	0.945252i	0.993051	−	0.117686i	$-0.0375476\pi$
$942$	36.5162			1.18976
$943$	9.51625	+	0.0861705i	0.309892	+	0.00280610i
$944$	8.01733			0.260942
$945$	−0.905749	+	1.98331i	−0.0294640	+	0.0645172i
$946$	−20.1249	−	5.90919i	−0.654316	−	0.192124i
$947$	1.76037	+	2.03157i	0.0572043	+	0.0660172i	0.783631	−	0.621227i	$-0.213366\pi$
$947$	1.76037	+	2.03157i	0.0572043	+	0.0660172i	−0.726426	+	0.687244i	$0.758820\pi$
$948$	6.86651	−	4.41284i	0.223014	−	0.143322i
$949$	−11.4663	+	13.2328i	−0.372211	+	0.429554i
$950$	3.62391	−	25.2049i	0.117575	−	0.817754i
$951$	49.0865	−	14.4131i	1.59174	−	0.467377i
$952$	−0.111572	−	0.0717031i	−0.00361608	−	0.00232391i
$953$	−3.29790	−	22.9374i	−0.106830	−	0.743016i	−0.970872	−	0.239597i	$-0.922985\pi$
$953$	−3.29790	−	22.9374i	−0.106830	−	0.743016i	0.864043	−	0.503418i	$-0.167924\pi$
$954$	−20.5358	−	44.9671i	−0.664871	−	1.45586i
$955$	1.88483	+	4.12720i	0.0609917	+	0.133553i
$956$	−3.92494	−	27.2986i	−0.126942	−	0.882899i
$957$	4.88720	+	3.14081i	0.157981	+	0.101528i
$958$	−0.936446	+	0.274965i	−0.0302552	+	0.00888373i
$959$	1.92467	−	13.3864i	0.0621508	−	0.432268i
$960$	−0.510867	+	0.589572i	−0.0164882	+	0.0190284i
$961$	36.4510	−	23.4256i	1.17584	−	0.755665i
$962$	−9.01997	−	10.4096i	−0.290816	−	0.335619i
$963$	57.1766	+	16.7886i	1.84249	+	0.541004i
$964$	−5.21865	+	11.4272i	−0.168081	+	0.368047i
$965$	2.11343			0.0680336
$966$	−1.89653	−	14.0956i	−0.0610200	−	0.453518i
$967$	48.9666			1.57466			0.787329	−	0.616533i	$-0.211463\pi$
$967$	48.9666			1.57466			0.787329	+	0.616533i	$0.211463\pi$
$968$	−2.44064	+	5.34425i	−0.0784450	+	0.171771i
$969$	1.94893	+	0.572258i	0.0626087	+	0.0183836i
$970$	−1.91288	−	2.20758i	−0.0614188	−	0.0708810i
$971$	−43.2798	+	27.8142i	−1.38891	+	0.892601i	−0.999594	−	0.0285018i	$-0.990926\pi$
$971$	−43.2798	+	27.8142i	−1.38891	+	0.892601i	−0.389320	+	0.921103i	$0.627290\pi$
$972$	−2.30820	+	2.66380i	−0.0740354	+	0.0854414i
$973$	2.19623	−	15.2751i	0.0704080	−	0.489698i
$974$	−31.9685	+	9.38681i	−1.02434	+	0.300773i
$975$	−30.2402	−	19.4342i	−0.968462	−	0.622393i
$976$	−0.792922	−	5.51490i	−0.0253808	−	0.176528i
$977$	1.84989	+	4.05069i	0.0591832	+	0.129593i	0.936913	−	0.349563i	$-0.113670\pi$
$977$	1.84989	+	4.05069i	0.0591832	+	0.129593i	−0.877730	+	0.479156i	$0.840943\pi$
$978$	−10.4581	−	22.9000i	−0.334412	−	0.732260i
$979$	−0.527681	−	3.67010i	−0.0168648	−	0.117297i
$980$	−0.221294	−	0.142217i	−0.00706899	−	0.00454296i
$981$	−112.590	+	33.0595i	−3.59473	+	1.05551i
$982$	−3.71297	+	25.8243i	−0.118486	+	0.824086i
$983$	−2.17499	+	2.51007i	−0.0693714	+	0.0800588i	−0.789374	−	0.613912i	$-0.789595\pi$
$983$	−2.17499	+	2.51007i	−0.0693714	+	0.0800588i	0.720003	+	0.693971i	$0.244140\pi$
$984$	−4.95065	+	3.18159i	−0.157821	+	0.101425i
$985$	−4.05915	−	4.68451i	−0.129335	−	0.149261i
$986$	−0.110116	−	0.0323329i	−0.00350680	−	0.00102969i
$987$	−12.4549	+	27.2723i	−0.396443	+	0.868088i
$988$	−12.6951			−0.403884
$989$	28.7928	+	33.8431i	0.915559	+	1.07615i
$990$	3.45087			0.109676
$991$	8.14962	−	17.8452i	0.258881	−	0.566871i	−0.734906	−	0.678169i	$-0.762774\pi$
$991$	8.14962	−	17.8452i	0.258881	−	0.566871i	0.993787	+	0.111298i	$0.0355009\pi$
$992$	−8.27222	−	2.42894i	−0.262643	−	0.0771190i
$993$	66.5416	+	76.7931i	2.11163	+	2.43695i
$994$	0.513574	−	0.330054i	0.0162896	−	0.0104687i
$995$	1.57875	−	1.82198i	0.0500499	−	0.0577607i
$996$	6.60768	−	45.9574i	0.209372	−	1.45622i
$997$	−43.5023	+	12.7734i	−1.37773	+	0.404538i	−0.884979	−	0.465631i	$-0.845827\pi$
$997$	−43.5023	+	12.7734i	−1.37773	+	0.404538i	−0.492752	+	0.870170i	$0.664009\pi$
$998$	17.4911	+	11.2409i	0.553672	+	0.355823i
$999$	−6.60943	−	45.9696i	−0.209113	−	1.45441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.d.29.4	✓	40
23.2	even	11		7406.2.a.bu.1.1		20
23.4	even	11	inner	322.2.i.d.211.4	yes	40
23.21	odd	22		7406.2.a.bv.1.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.d.29.4	✓	40	1.1	even	1	trivial
322.2.i.d.211.4	yes	40	23.4	even	11	inner
7406.2.a.bu.1.1		20	23.2	even	11
7406.2.a.bv.1.1		20	23.21	odd	22

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(2.84549 + 0.835512i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.221294 + 0.142217i) q^{5} +(1.94207 - 2.24127i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(4.87498 + 3.13296i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(2.84549 + 0.835512i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.221294 + 0.142217i) q^{5} +(1.94207 - 2.24127i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(4.87498 + 3.13296i) q^{9} +(0.0374364 + 0.260376i) q^{10} +(-0.940420 - 2.05923i) q^{11} +(-1.23196 - 2.69762i) q^{12} +(0.349844 + 2.43322i) q^{13} +(-0.841254 - 0.540641i) q^{14} +(-0.748515 + 0.219784i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-0.0868517 + 0.100232i) q^{17} +(4.87498 - 3.13296i) q^{18} +(-3.38188 - 3.90290i) q^{19} +(0.252398 + 0.0741106i) q^{20} +(1.23196 - 2.69762i) q^{21} -2.26381 q^{22} +(4.01087 + 2.62925i) q^{23} -2.96562 q^{24} +(-2.04833 + 4.48522i) q^{25} +(2.35867 + 0.692567i) q^{26} +(5.42789 + 6.26412i) q^{27} +(-0.841254 + 0.540641i) q^{28} +(-0.566666 + 0.653967i) q^{29} +(-0.111022 + 0.772175i) q^{30} +(-8.27222 + 2.42894i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-0.955444 - 6.64526i) q^{33} +(0.0550949 + 0.120641i) q^{34} +(0.109276 + 0.239282i) q^{35} +(-0.824700 - 5.73592i) q^{36} +(-4.71366 - 3.02929i) q^{37} +(-4.95509 + 1.45495i) q^{38} +(-1.03751 + 7.21601i) q^{39} +(0.172263 - 0.198802i) q^{40} +(1.66935 - 1.07282i) q^{41} +(-1.94207 - 2.24127i) q^{42} +(8.88983 + 2.61029i) q^{43} +(-0.940420 + 2.05923i) q^{44} -1.52437 q^{45} +(4.05782 - 2.55618i) q^{46} -10.1098 q^{47} +(-1.23196 + 2.69762i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(3.22899 + 3.72645i) q^{50} +(-0.330881 + 0.212644i) q^{51} +(1.60981 - 1.85782i) q^{52} +(1.21404 - 8.44385i) q^{53} +(7.95287 - 2.33517i) q^{54} +(0.500968 + 0.321952i) q^{55} +(0.142315 + 0.989821i) q^{56} +(-6.36220 - 13.9313i) q^{57} +(0.359468 + 0.787125i) q^{58} +(-1.14099 - 7.93573i) q^{59} +(0.656275 + 0.421762i) q^{60} +(-5.34592 + 1.56970i) q^{61} +(-1.22696 + 8.53369i) q^{62} +(3.79485 - 4.37949i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.423465 - 0.488704i) q^{65} +(-6.44164 - 1.89144i) q^{66} +(1.08736 - 2.38100i) q^{67} +0.132626 q^{68} +(9.21612 + 10.8326i) q^{69} +0.263053 q^{70} +(-0.253605 + 0.555318i) q^{71} +(-5.56017 - 1.63261i) q^{72} +(4.66442 + 5.38303i) q^{73} +(-4.71366 + 3.02929i) q^{74} +(-9.57596 + 11.0512i) q^{75} +(-0.734954 + 5.11172i) q^{76} +(-2.17211 + 0.637788i) q^{77} +(6.13292 + 3.94139i) q^{78} +(0.391691 + 2.72427i) q^{79} +(-0.109276 - 0.239282i) q^{80} +(2.98940 + 6.54588i) q^{81} +(-0.282403 - 1.96416i) q^{82} +(13.1707 + 8.46432i) q^{83} +(-2.84549 + 0.835512i) q^{84} +(0.00496504 - 0.0345326i) q^{85} +(6.06737 - 7.00212i) q^{86} +(-2.15884 + 1.38740i) q^{87} +(1.48248 + 1.71087i) q^{88} +(1.57153 + 0.461444i) q^{89} +(-0.633245 + 1.38661i) q^{90} +2.45824 q^{91} +(-0.639507 - 4.75300i) q^{92} -25.5679 q^{93} +(-4.19975 + 9.19617i) q^{94} +(1.30345 + 0.382728i) q^{95} +(1.94207 + 2.24127i) q^{96} +(-9.34160 + 6.00348i) q^{97} +(-0.654861 + 0.755750i) q^{98} +(1.86696 - 12.9850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more