LMFDB - Embedded newform 345.2.m.a.211.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,2,Mod(16,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("345.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.m (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:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			211.3
Character	$\chi$	$=$	345.211
Dual form			345.2.m.a.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.597726 + 1.30884i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.0460597 + 0.0531557i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(0.942257 + 1.08742i) q^{6} +(0.462869 + 3.21932i) q^{7} +(2.66406 + 0.782239i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(0.597726 + 1.30884i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.0460597 + 0.0531557i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(0.942257 + 1.08742i) q^{6} +(0.462869 + 3.21932i) q^{7} +(2.66406 + 0.782239i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.204772 - 1.42422i) q^{10} +(1.08101 - 2.36709i) q^{11} +(-0.0292182 + 0.0639790i) q^{12} +(0.116463 - 0.810015i) q^{13} +(-3.93690 + 2.53009i) q^{14} +(-0.959493 - 0.281733i) q^{15} +(0.588575 + 4.09363i) q^{16} +(0.275075 + 0.317453i) q^{17} +(1.21045 + 0.777910i) q^{18} +(-3.12049 + 3.60124i) q^{19} +(0.0674860 - 0.0198157i) q^{20} +(1.35111 + 2.95851i) q^{21} +3.74428 q^{22} +(4.71379 - 0.883258i) q^{23} +2.77653 q^{24} +(0.415415 + 0.909632i) q^{25} +(1.12979 - 0.331737i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-0.192445 - 0.123677i) q^{28} +(-5.61944 - 6.48518i) q^{29} +(-0.204772 - 1.42422i) q^{30} +(-1.49213 - 0.438130i) q^{31} +(-0.334561 + 0.215009i) q^{32} +(0.370338 - 2.57576i) q^{33} +(-0.251075 + 0.549778i) q^{34} +(1.35111 - 2.95851i) q^{35} +(-0.0100097 + 0.0696192i) q^{36} +(-3.76312 + 2.41841i) q^{37} +(-6.57864 - 1.93166i) q^{38} +(-0.116463 - 0.810015i) q^{39} +(-1.81824 - 2.09836i) q^{40} +(-2.76464 - 1.77673i) q^{41} +(-3.06462 + 3.53676i) q^{42} +(-6.91281 + 2.02978i) q^{43} +(0.0760331 + 0.166489i) q^{44} -1.00000 q^{45} +(3.97360 + 5.64165i) q^{46} -4.01828 q^{47} +(1.71804 + 3.76199i) q^{48} +(-3.43334 + 1.00812i) q^{49} +(-0.942257 + 1.08742i) q^{50} +(0.353369 + 0.227096i) q^{51} +(0.0376927 + 0.0434997i) q^{52} +(-0.974824 - 6.78005i) q^{53} +(1.38058 + 0.405375i) q^{54} +(-2.18915 + 1.40688i) q^{55} +(-1.28517 + 8.93854i) q^{56} +(-1.97950 + 4.33451i) q^{57} +(5.12916 - 11.2313i) q^{58} +(1.42209 - 9.89086i) q^{59} +(0.0591696 - 0.0380260i) q^{60} +(-6.66840 - 1.95802i) q^{61} +(-0.318446 - 2.21484i) q^{62} +(2.12989 + 2.45802i) q^{63} +(6.47700 + 4.16251i) q^{64} +(-0.535902 + 0.618464i) q^{65} +(3.59261 - 1.05489i) q^{66} +(-2.21282 - 4.84540i) q^{67} -0.0295443 q^{68} +(4.27401 - 2.17551i) q^{69} +4.67981 q^{70} +(3.31278 + 7.25398i) q^{71} +(2.66406 - 0.782239i) q^{72} +(9.10592 - 10.5088i) q^{73} +(-5.41463 - 3.47977i) q^{74} +(0.654861 + 0.755750i) q^{75} +(-0.0476976 - 0.331744i) q^{76} +(8.12078 + 2.38448i) q^{77} +(0.990566 - 0.636598i) q^{78} +(-0.517191 + 3.59714i) q^{79} +(1.71804 - 3.76199i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.672949 - 4.68047i) q^{82} +(-2.30887 + 1.48382i) q^{83} +(-0.219493 - 0.0644491i) q^{84} +(-0.0597794 - 0.415775i) q^{85} +(-6.78863 - 7.83450i) q^{86} +(-7.21890 - 4.63931i) q^{87} +(4.73151 - 5.46045i) q^{88} +(-10.5657 + 3.10236i) q^{89} +(-0.597726 - 1.30884i) q^{90} +2.66161 q^{91} +(-0.170166 + 0.291248i) q^{92} -1.55513 q^{93} +(-2.40184 - 5.25929i) q^{94} +(4.57210 - 1.34249i) q^{95} +(-0.260433 + 0.300556i) q^{96} +(7.33379 + 4.71314i) q^{97} +(-3.37166 - 3.89111i) q^{98} +(-0.370338 - 2.57576i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9} - 7 q^{11} - 2 q^{12} + 7 q^{13} - 47 q^{14} - 3 q^{15} + 26 q^{16} + 15 q^{17} - 7 q^{19} - 2 q^{20} - 12 q^{21} - 18 q^{22} + 12 q^{23} - 3 q^{25} - 18 q^{26} + 3 q^{27} + 2 q^{28} - 6 q^{29} + 22 q^{31} + 33 q^{32} - 4 q^{33} - 53 q^{34} - 12 q^{35} - 9 q^{36} - 23 q^{37} + 21 q^{38} - 7 q^{39} + 11 q^{40} + 26 q^{41} + 3 q^{42} - 19 q^{43} - 47 q^{44} - 30 q^{45} - 44 q^{46} + 14 q^{47} + 7 q^{48} + 2 q^{49} - 11 q^{50} - 15 q^{51} + 55 q^{52} - 14 q^{53} - 11 q^{54} - 4 q^{55} + 6 q^{56} - 26 q^{57} - 18 q^{58} + 40 q^{59} - 9 q^{60} + 37 q^{61} + 19 q^{62} - 10 q^{63} + 14 q^{64} + 4 q^{65} - 4 q^{66} - 108 q^{67} + 54 q^{68} + 21 q^{69} - 30 q^{70} + 39 q^{71} + 22 q^{72} + 57 q^{73} - 11 q^{74} + 3 q^{75} + 22 q^{76} + 2 q^{77} + 7 q^{78} + 55 q^{79} + 7 q^{80} - 3 q^{81} - 26 q^{82} - 79 q^{83} - 2 q^{84} + 18 q^{85} - 44 q^{86} - 5 q^{87} - 8 q^{88} - 30 q^{89} + 40 q^{91} + 35 q^{92} + 44 q^{93} - 29 q^{94} + 7 q^{95} + 22 q^{96} - 52 q^{97} + 28 q^{98} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9 - 7 * q^11 - 2 * q^12 + 7 * q^13 - 47 * q^14 - 3 * q^15 + 26 * q^16 + 15 * q^17 - 7 * q^19 - 2 * q^20 - 12 * q^21 - 18 * q^22 + 12 * q^23 - 3 * q^25 - 18 * q^26 + 3 * q^27 + 2 * q^28 - 6 * q^29 + 22 * q^31 + 33 * q^32 - 4 * q^33 - 53 * q^34 - 12 * q^35 - 9 * q^36 - 23 * q^37 + 21 * q^38 - 7 * q^39 + 11 * q^40 + 26 * q^41 + 3 * q^42 - 19 * q^43 - 47 * q^44 - 30 * q^45 - 44 * q^46 + 14 * q^47 + 7 * q^48 + 2 * q^49 - 11 * q^50 - 15 * q^51 + 55 * q^52 - 14 * q^53 - 11 * q^54 - 4 * q^55 + 6 * q^56 - 26 * q^57 - 18 * q^58 + 40 * q^59 - 9 * q^60 + 37 * q^61 + 19 * q^62 - 10 * q^63 + 14 * q^64 + 4 * q^65 - 4 * q^66 - 108 * q^67 + 54 * q^68 + 21 * q^69 - 30 * q^70 + 39 * q^71 + 22 * q^72 + 57 * q^73 - 11 * q^74 + 3 * q^75 + 22 * q^76 + 2 * q^77 + 7 * q^78 + 55 * q^79 + 7 * q^80 - 3 * q^81 - 26 * q^82 - 79 * q^83 - 2 * q^84 + 18 * q^85 - 44 * q^86 - 5 * q^87 - 8 * q^88 - 30 * q^89 + 40 * q^91 + 35 * q^92 + 44 * q^93 - 29 * q^94 + 7 * q^95 + 22 * q^96 - 52 * q^97 + 28 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	0.597726	+	1.30884i	0.422656	+	0.925489i	0.994462	+	0.105099i	$0.0335160\pi$
$2$	0.597726	+	1.30884i	0.422656	+	0.925489i	−0.571805	+	0.820389i	$0.693757\pi$
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$	−0.0460597	+	0.0531557i	−0.0230298	+	0.0265779i
$5$	−0.841254	−	0.540641i	−0.376220	−	0.241782i
$5$	−0.841254	−	0.540641i	−0.376220	−	0.241782i
$6$	0.942257	+	1.08742i	0.384675	+	0.443938i
$7$	0.462869	+	3.21932i	0.174948	+	1.21679i	0.868244	+	0.496137i	$0.165249\pi$
$7$	0.462869	+	3.21932i	0.174948	+	1.21679i	−0.693296	+	0.720653i	$0.743842\pi$
$8$	2.66406	+	0.782239i	0.941887	+	0.276563i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	0.204772	−	1.42422i	0.0647546	−	0.450378i
$11$	1.08101	−	2.36709i	0.325938	−	0.713704i	−0.673743	−	0.738965i	$-0.735315\pi$
$11$	1.08101	−	2.36709i	0.325938	−	0.713704i	0.999681	+	0.0252618i	$0.00804193\pi$
$12$	−0.0292182	+	0.0639790i	−0.00843458	+	0.0184692i
$13$	0.116463	−	0.810015i	0.0323009	−	0.224658i	−0.967277	−	0.253724i	$-0.918344\pi$
$13$	0.116463	−	0.810015i	0.0323009	−	0.224658i	0.999577	+	0.0290666i	$0.00925347\pi$
$14$	−3.93690	+	2.53009i	−1.05218	+	0.676196i
$15$	−0.959493	−	0.281733i	−0.247740	−	0.0727430i
$16$	0.588575	+	4.09363i	0.147144	+	1.02341i
$17$	0.275075	+	0.317453i	0.0667154	+	0.0769937i	0.788126	−	0.615514i	$-0.211051\pi$
$17$	0.275075	+	0.317453i	0.0667154	+	0.0769937i	−0.721411	+	0.692507i	$0.756506\pi$
$18$	1.21045	+	0.777910i	0.285306	+	0.183355i
$19$	−3.12049	+	3.60124i	−0.715890	+	0.826181i	−0.990806	−	0.135287i	$-0.956804\pi$
$19$	−3.12049	+	3.60124i	−0.715890	+	0.826181i	0.274916	+	0.961468i	$0.411350\pi$
$20$	0.0674860	−	0.0198157i	0.0150903	−	0.00443092i
$21$	1.35111	+	2.95851i	0.294836	+	0.645600i
$22$	3.74428			0.798284
$23$	4.71379	−	0.883258i	0.982894	−	0.184172i
$23$	4.71379	−	0.883258i	0.982894	−	0.184172i
$24$	2.77653			0.566757
$25$	0.415415	+	0.909632i	0.0830830	+	0.181926i
$26$	1.12979	−	0.331737i	0.221570	−	0.0650589i
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$	−0.192445	−	0.123677i	−0.0363687	−	0.0233727i
$29$	−5.61944	−	6.48518i	−1.04350	−	1.20427i	−0.978471	−	0.206385i	$-0.933830\pi$
$29$	−5.61944	−	6.48518i	−1.04350	−	1.20427i	−0.0650330	−	0.997883i	$-0.520715\pi$
$30$	−0.204772	−	1.42422i	−0.0373861	−	0.260026i
$31$	−1.49213	−	0.438130i	−0.267995	−	0.0786905i	0.144974	−	0.989435i	$-0.453690\pi$
$31$	−1.49213	−	0.438130i	−0.267995	−	0.0786905i	−0.412969	+	0.910745i	$0.635508\pi$
$32$	−0.334561	+	0.215009i	−0.0591425	+	0.0380086i
$33$	0.370338	−	2.57576i	0.0644676	−	0.448382i
$34$	−0.251075	+	0.549778i	−0.0430591	+	0.0942862i
$35$	1.35111	−	2.95851i	0.228379	−	0.500080i
$36$	−0.0100097	+	0.0696192i	−0.00166829	+	0.0116032i
$37$	−3.76312	+	2.41841i	−0.618653	+	0.397584i	−0.812093	−	0.583528i	$-0.801672\pi$
$37$	−3.76312	+	2.41841i	−0.618653	+	0.397584i	0.193440	+	0.981112i	$0.438036\pi$
$38$	−6.57864	−	1.93166i	−1.06720	−	0.313357i
$39$	−0.116463	−	0.810015i	−0.0186489	−	0.129706i
$40$	−1.81824	−	2.09836i	−0.287489	−	0.331780i
$41$	−2.76464	−	1.77673i	−0.431764	−	0.277478i	0.306654	−	0.951821i	$-0.400791\pi$
$41$	−2.76464	−	1.77673i	−0.431764	−	0.277478i	−0.738418	+	0.674343i	$0.764427\pi$
$42$	−3.06462	+	3.53676i	−0.472881	+	0.545734i
$43$	−6.91281	+	2.02978i	−1.05419	+	0.309539i	−0.762511	−	0.646976i	$-0.776034\pi$
$43$	−6.91281	+	2.02978i	−1.05419	+	0.309539i	−0.291683	+	0.956515i	$0.594215\pi$
$44$	0.0760331	+	0.166489i	0.0114624	+	0.0250992i
$45$	−1.00000			−0.149071
$46$	3.97360	+	5.64165i	0.585876	+	0.831816i
$47$	−4.01828			−0.586127			−0.293064	−	0.956093i	$-0.594675\pi$
$47$	−4.01828			−0.586127			−0.293064	+	0.956093i	$0.594675\pi$
$48$	1.71804	+	3.76199i	0.247978	+	0.542996i
$49$	−3.43334	+	1.00812i	−0.490477	+	0.144017i
$50$	−0.942257	+	1.08742i	−0.133255	+	0.153785i
$51$	0.353369	+	0.227096i	0.0494816	+	0.0317999i
$52$	0.0376927	+	0.0434997i	0.00522704	+	0.00603232i
$53$	−0.974824	−	6.78005i	−0.133902	−	0.931311i	−0.940399	−	0.340073i	$-0.889548\pi$
$53$	−0.974824	−	6.78005i	−0.133902	−	0.931311i	0.806497	−	0.591238i	$-0.201361\pi$
$54$	1.38058	+	0.405375i	0.187873	+	0.0551646i
$55$	−2.18915	+	1.40688i	−0.295185	+	0.189704i
$56$	−1.28517	+	8.93854i	−0.171738	+	1.19446i
$57$	−1.97950	+	4.33451i	−0.262192	+	0.574120i
$58$	5.12916	−	11.2313i	0.673492	−	1.47474i
$59$	1.42209	−	9.89086i	0.185140	−	1.28768i	−0.659239	−	0.751934i	$-0.729121\pi$
$59$	1.42209	−	9.89086i	0.185140	−	1.28768i	0.844379	−	0.535746i	$-0.179970\pi$
$60$	0.0591696	−	0.0380260i	0.00763877	−	0.00490914i
$61$	−6.66840	−	1.95802i	−0.853801	−	0.250699i	−0.174590	−	0.984641i	$-0.555860\pi$
$61$	−6.66840	−	1.95802i	−0.853801	−	0.250699i	−0.679211	+	0.733943i	$0.737678\pi$
$62$	−0.318446	−	2.21484i	−0.0404427	−	0.281285i
$63$	2.12989	+	2.45802i	0.268341	+	0.309681i
$64$	6.47700	+	4.16251i	0.809624	+	0.520314i
$65$	−0.535902	+	0.618464i	−0.0664704	+	0.0767110i
$66$	3.59261	−	1.05489i	0.442220	−	0.129848i
$67$	−2.21282	−	4.84540i	−0.270339	−	0.591960i	0.724962	−	0.688789i	$-0.241857\pi$
$67$	−2.21282	−	4.84540i	−0.270339	−	0.591960i	−0.995301	+	0.0968288i	$0.969130\pi$
$68$	−0.0295443			−0.00358277
$69$	4.27401	−	2.17551i	0.514530	−	0.261901i
$70$	4.67981			0.559344
$71$	3.31278	+	7.25398i	0.393155	+	0.860888i	0.997919	+	0.0644839i	$0.0205401\pi$
$71$	3.31278	+	7.25398i	0.393155	+	0.860888i	−0.604764	+	0.796405i	$0.706733\pi$
$72$	2.66406	−	0.782239i	0.313962	−	0.0921877i
$73$	9.10592	−	10.5088i	1.06577	−	1.22996i	0.0936158	−	0.995608i	$-0.470157\pi$
$73$	9.10592	−	10.5088i	1.06577	−	1.22996i	0.972152	−	0.234353i	$-0.0752971\pi$
$74$	−5.41463	−	3.47977i	−0.629438	−	0.404515i
$75$	0.654861	+	0.755750i	0.0756168	+	0.0872664i
$76$	−0.0476976	−	0.331744i	−0.00547129	−	0.0380536i
$77$	8.12078	+	2.38448i	0.925449	+	0.271736i
$78$	0.990566	−	0.636598i	0.112160	−	0.0720806i
$79$	−0.517191	+	3.59714i	−0.0581885	+	0.404710i	0.939822	+	0.341664i	$0.110991\pi$
$79$	−0.517191	+	3.59714i	−0.0581885	+	0.404710i	−0.998011	+	0.0630459i	$0.979919\pi$
$80$	1.71804	−	3.76199i	0.192083	−	0.420603i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	0.672949	−	4.68047i	0.0743148	−	0.516871i
$83$	−2.30887	+	1.48382i	−0.253431	+	0.162870i	−0.661188	−	0.750220i	$-0.729947\pi$
$83$	−2.30887	+	1.48382i	−0.253431	+	0.162870i	0.407757	+	0.913091i	$0.366311\pi$
$84$	−0.219493	−	0.0644491i	−0.0239487	−	0.00703197i
$85$	−0.0597794	−	0.415775i	−0.00648399	−	0.0450971i
$86$	−6.78863	−	7.83450i	−0.732037	−	0.844816i
$87$	−7.21890	−	4.63931i	−0.773947	−	0.497386i
$88$	4.73151	−	5.46045i	0.504381	−	0.582086i
$89$	−10.5657	+	3.10236i	−1.11996	+	0.328849i	−0.788754	−	0.614710i	$-0.789273\pi$
$89$	−10.5657	+	3.10236i	−1.11996	+	0.328849i	−0.331205	+	0.943559i	$0.607455\pi$
$90$	−0.597726	−	1.30884i	−0.0630059	−	0.137964i
$91$	2.66161			0.279012
$92$	−0.170166	+	0.291248i	−0.0177410	+	0.0303647i
$93$	−1.55513			−0.161259
$94$	−2.40184	−	5.25929i	−0.247730	−	0.542454i
$95$	4.57210	−	1.34249i	0.469088	−	0.137737i
$96$	−0.260433	+	0.300556i	−0.0265804	+	0.0306754i
$97$	7.33379	+	4.71314i	0.744634	+	0.478547i	0.857127	−	0.515105i	$-0.172247\pi$
$97$	7.33379	+	4.71314i	0.744634	+	0.478547i	−0.112493	+	0.993653i	$0.535884\pi$
$98$	−3.37166	−	3.89111i	−0.340589	−	0.393061i
$99$	−0.370338	−	2.57576i	−0.0372204	−	0.258874i
$100$	−0.0674860	−	0.0198157i	−0.00674860	−	0.00198157i
$101$	−15.5596	+	9.99957i	−1.54824	+	0.994995i	−0.562487	+	0.826806i	$0.690155\pi$
$101$	−15.5596	+	9.99957i	−1.54824	+	0.994995i	−0.985755	+	0.168189i	$0.946208\pi$
$102$	−0.0860146	+	0.598244i	−0.00851671	+	0.0592350i
$103$	−1.78216	+	3.90238i	−0.175601	+	0.384513i	−0.976883	−	0.213774i	$-0.931424\pi$
$103$	−1.78216	+	3.90238i	−0.175601	+	0.384513i	0.801282	+	0.598287i	$0.204152\pi$
$104$	0.943889	−	2.06683i	0.0925559	−	0.202669i
$105$	0.462869	−	3.21932i	0.0451714	−	0.314174i
$106$	8.29131	−	5.32850i	0.805323	−	0.517550i
$107$	11.2220	+	3.29508i	1.08487	+	0.318547i	0.774826	−	0.632174i	$-0.217837\pi$
$107$	11.2220	+	3.29508i	1.08487	+	0.318547i	0.310046	+	0.950721i	$0.399655\pi$
$108$	0.0100097	+	0.0696192i	0.000963186	+	0.00669911i
$109$	11.0039	+	12.6992i	1.05398	+	1.21636i	0.975627	+	0.219436i	$0.0704216\pi$
$109$	11.0039	+	12.6992i	1.05398	+	1.21636i	0.0783558	+	0.996925i	$0.475033\pi$
$110$	−3.14989	−	2.02431i	−0.300330	−	0.193011i
$111$	−2.92934	+	3.38064i	−0.278041	+	0.320876i
$112$	−12.9063	+	3.78962i	−1.21953	+	0.358086i
$113$	−5.18606	−	11.3559i	−0.487863	−	1.06827i	−0.980226	−	0.197881i	$-0.936594\pi$
$113$	−5.18606	−	11.3559i	−0.487863	−	1.06827i	0.492363	−	0.870390i	$-0.336133\pi$
$114$	−6.85638			−0.642158
$115$	−4.44302	−	1.80543i	−0.414314	−	0.168357i
$116$	0.603554			0.0560386
$117$	−0.339953	−	0.744393i	−0.0314286	−	0.0688191i
$118$	13.7956	−	4.05074i	1.26998	−	0.372901i
$119$	−0.894660	+	1.03249i	−0.0820134	+	0.0946485i
$120$	−2.33576	−	1.50110i	−0.213225	−	0.137032i
$121$	2.76895	+	3.19554i	0.251723	+	0.290504i
$122$	−1.42315	−	9.89822i	−0.128846	−	0.896142i
$123$	−3.15322	−	0.925868i	−0.284316	−	0.0834827i
$124$	0.0920163	−	0.0591353i	0.00826331	−	0.00531051i
$125$	0.142315	−	0.989821i	0.0127290	−	0.0885323i
$126$	−1.94406	+	4.25690i	−0.173191	+	0.379235i
$127$	4.24098	−	9.28645i	0.376326	−	0.824039i	−0.622806	−	0.782377i	$-0.714007\pi$
$127$	4.24098	−	9.28645i	0.376326	−	0.824039i	0.999132	−	0.0416627i	$-0.0132655\pi$
$128$	−1.68978	+	11.7527i	−0.149357	+	1.03880i
$129$	−6.06094	+	3.89513i	−0.533636	+	0.342947i
$130$	−1.12979	−	0.331737i	−0.0990893	−	0.0290952i
$131$	0.279466	+	1.94373i	0.0244171	+	0.169825i	0.998381	−	0.0568779i	$-0.0181146\pi$
$131$	0.279466	+	1.94373i	0.0244171	+	0.169825i	−0.973964	+	0.226702i	$0.927205\pi$
$132$	0.119859	+	0.138324i	0.0104324	+	0.0120396i
$133$	−13.0379	−	8.37897i	−1.13053	−	0.726549i
$134$	5.01919	−	5.79245i	0.433592	−	0.500392i
$135$	−0.959493	+	0.281733i	−0.0825800	+	0.0242477i
$136$	0.484491	+	1.06089i	0.0415448	+	0.0909704i
$137$	21.0132			1.79528			0.897639	−	0.440732i	$-0.145281\pi$
$137$	21.0132			1.79528			0.897639	+	0.440732i	$0.145281\pi$
$138$	5.40208	+	4.29363i	0.459856	+	0.365498i
$139$	12.2031			1.03506			0.517528	−	0.855666i	$-0.326852\pi$
$139$	12.2031			1.03506			0.517528	+	0.855666i	$0.326852\pi$
$140$	0.0950302	+	0.208087i	0.00803152	+	0.0175866i
$141$	−3.85552	+	1.13208i	−0.324693	+	0.0953385i
$142$	−7.51415	+	8.67179i	−0.630573	+	0.727720i
$143$	−1.79148	−	1.15131i	−0.149811	−	0.0962777i
$144$	2.70832	+	3.12557i	0.225694	+	0.260464i
$145$	1.22122	+	8.49378i	0.101417	+	0.705370i
$146$	19.1972	+	5.63680i	1.58877	+	0.466505i
$147$	−3.01024	+	1.93457i	−0.248281	+	0.159560i
$148$	0.0447758	−	0.311423i	0.00368055	−	0.0255988i
$149$	−2.57832	+	5.64574i	−0.211224	+	0.462517i	−0.985356	−	0.170507i	$-0.945459\pi$
$149$	−2.57832	+	5.64574i	−0.211224	+	0.462517i	0.774132	+	0.633024i	$0.218187\pi$
$150$	−0.597726	+	1.30884i	−0.0488042	+	0.106866i
$151$	1.27680	−	8.88031i	0.103904	−	0.722670i	−0.869559	−	0.493828i	$-0.835597\pi$
$151$	1.27680	−	8.88031i	0.103904	−	0.722670i	0.973464	−	0.228841i	$-0.0734937\pi$
$152$	−11.1302	+	7.15295i	−0.902779	+	0.580181i
$153$	0.403035	+	0.118342i	0.0325835	+	0.00956738i
$154$	1.73311	+	12.0541i	0.139658	+	0.971344i
$155$	1.01839	+	1.17529i	0.0817992	+	0.0944013i
$156$	0.0484212	+	0.0311184i	0.00387680	+	0.00249147i
$157$	−6.63046	+	7.65196i	−0.529168	+	0.610693i	−0.955902	−	0.293684i	$-0.905119\pi$
$157$	−6.63046	+	7.65196i	−0.529168	+	0.610693i	0.426734	+	0.904377i	$0.359664\pi$
$158$	−5.01722	+	1.47319i	−0.399148	+	0.117201i
$159$	−2.84550	−	6.23077i	−0.225663	−	0.494132i
$160$	0.397693			0.0314404
$161$	5.02536	+	14.7664i	0.396054	+	1.16375i
$162$	1.43887			0.113048
$163$	−6.61238	−	14.4791i	−0.517921	−	1.13409i	−0.970221	−	0.242223i	$-0.922123\pi$
$163$	−6.61238	−	14.4791i	−0.517921	−	1.13409i	0.452299	−	0.891866i	$-0.350604\pi$
$164$	0.221782	−	0.0651210i	0.0173182	−	0.00508509i
$165$	−1.70411	+	1.96665i	−0.132665	+	0.153103i
$166$	−3.32215	−	2.13502i	−0.257849	−	0.165710i
$167$	10.2086	+	11.7814i	0.789965	+	0.911669i	0.997787	−	0.0664983i	$-0.0211827\pi$
$167$	10.2086	+	11.7814i	0.789965	+	0.911669i	−0.207821	+	0.978167i	$0.566637\pi$
$168$	1.28517	+	8.93854i	0.0991529	+	0.689623i
$169$	11.8308	+	3.47385i	0.910065	+	0.267219i
$170$	0.508451	−	0.326761i	0.0389964	−	0.0250614i
$171$	−0.678148	+	4.71662i	−0.0518593	+	0.360689i
$172$	0.210507	−	0.460947i	0.0160510	−	0.0351469i
$173$	−4.46884	+	9.78541i	−0.339760	+	0.743971i	−0.999975	−	0.00710627i	$-0.997738\pi$
$173$	−4.46884	+	9.78541i	−0.339760	+	0.743971i	0.660215	+	0.751077i	$0.270465\pi$
$174$	1.75717	−	12.2214i	0.133211	−	0.926503i
$175$	−2.73612	+	1.75839i	−0.206831	+	0.132922i
$176$	10.3262	+	3.03205i	0.778369	+	0.228550i
$177$	−1.42209	−	9.89086i	−0.106891	−	0.743442i
$178$	−10.3759	−	11.9744i	−0.777704	−	0.897518i
$179$	−10.3510	−	6.65216i	−0.773667	−	0.497206i	0.0932592	−	0.995642i	$-0.470271\pi$
$179$	−10.3510	−	6.65216i	−0.773667	−	0.497206i	−0.866926	+	0.498436i	$0.833908\pi$
$180$	0.0460597	−	0.0531557i	0.00343309	−	0.00396199i
$181$	−24.3973	+	7.16369i	−1.81344	+	0.532473i	−0.998867	−	0.0475946i	$-0.984844\pi$
$181$	−24.3973	+	7.16369i	−1.81344	+	0.532473i	−0.814569	+	0.580067i	$0.803026\pi$
$182$	1.59091	+	3.48361i	0.117926	+	0.258223i
$183$	−6.94992			−0.513753
$184$	13.2487	+	1.33426i	0.976711	+	0.0983628i
$185$	4.47323			0.328878
$186$	−0.929541	−	2.03541i	−0.0681572	−	0.149244i
$187$	1.04880	−	0.307955i	0.0766957	−	0.0225199i
$188$	0.185081	−	0.213595i	0.0134984	−	0.0155780i
$189$	2.73612	+	1.75839i	0.199023	+	0.127904i
$190$	4.48997	+	5.18170i	0.325737	+	0.375920i
$191$	0.0800099	+	0.556481i	0.00578932	+	0.0402656i	0.992511	−	0.122153i	$-0.0389797\pi$
$191$	0.0800099	+	0.556481i	0.00578932	+	0.0402656i	−0.986722	+	0.162418i	$0.948071\pi$
$192$	7.38735	+	2.16912i	0.533136	+	0.156543i
$193$	−15.6818	+	10.0781i	−1.12880	+	0.725438i	−0.965310	−	0.261106i	$-0.915913\pi$
$193$	−15.6818	+	10.0781i	−1.12880	+	0.725438i	−0.163494	+	0.986544i	$0.552276\pi$
$194$	−1.78514	+	12.4159i	−0.128166	+	0.891411i
$195$	−0.339953	+	0.744393i	−0.0243445	+	0.0533071i
$196$	0.104551	−	0.228935i	0.00746794	−	0.0163525i
$197$	−1.87075	+	13.0113i	−0.133285	+	0.927019i	0.807946	+	0.589256i	$0.200579\pi$
$197$	−1.87075	+	13.0113i	−0.133285	+	0.927019i	−0.941231	+	0.337763i	$0.890330\pi$
$198$	3.14989	−	2.02431i	0.223853	−	0.143862i
$199$	12.8905	+	3.78498i	0.913780	+	0.268310i	0.704631	−	0.709574i	$-0.251113\pi$
$199$	12.8905	+	3.78498i	0.913780	+	0.268310i	0.209149	+	0.977884i	$0.432931\pi$
$200$	0.395141	+	2.74827i	0.0279407	+	0.194332i
$201$	−3.48829	−	4.02571i	−0.246045	−	0.283951i
$202$	−22.3882	−	14.3880i	−1.57523	−	1.01234i
$203$	18.2768	−	21.0926i	1.28278	−	1.48041i
$204$	−0.0283475	+	0.00832359i	−0.00198472	+	0.000582768i
$205$	1.36519	+	2.98936i	0.0953492	+	0.208786i
$206$	−6.17282			−0.430081
$207$	3.48797	−	3.29151i	0.242431	−	0.228776i
$208$	3.38445			0.234669
$209$	5.15116	+	11.2795i	0.356313	+	0.780217i
$210$	4.49024	−	1.31845i	0.309856	−	0.0909820i
$211$	−9.61515	+	11.0965i	−0.661934	+	0.763912i	−0.983092	−	0.183113i	$-0.941383\pi$
$211$	−9.61515	+	11.0965i	−0.661934	+	0.763912i	0.321158	+	0.947026i	$0.395928\pi$
$212$	0.405298	+	0.260469i	0.0278360	+	0.0178891i
$213$	5.22227	+	6.02682i	0.357824	+	0.412951i
$214$	2.39497	+	16.6574i	0.163717	+	1.13867i
$215$	6.91281	+	2.02978i	0.471450	+	0.138430i
$216$	2.33576	−	1.50110i	0.158929	−	0.102137i
$217$	0.719820	−	5.00646i	0.0488645	−	0.339860i
$218$	−10.0439	+	21.9930i	−0.680256	+	1.48955i
$219$	5.77640	−	12.6485i	0.390333	−	0.854710i
$220$	0.0260478	−	0.181166i	0.00175614	−	0.0122142i
$221$	0.289178	−	0.185843i	0.0194522	−	0.0125012i
$222$	−6.17566	−	1.81334i	−0.414483	−	0.121703i
$223$	2.48833	+	17.3067i	0.166631	+	1.15894i	0.885786	+	0.464094i	$0.153620\pi$
$223$	2.48833	+	17.3067i	0.166631	+	1.15894i	−0.719155	+	0.694850i	$0.755471\pi$
$224$	−0.847041	−	0.977537i	−0.0565953	−	0.0653145i
$225$	0.841254	+	0.540641i	0.0560836	+	0.0360427i
$226$	11.7632	−	13.5754i	0.782475	−	0.903024i
$227$	8.65405	−	2.54106i	0.574390	−	0.168656i	0.0183789	−	0.999831i	$-0.494149\pi$
$227$	8.65405	−	2.54106i	0.574390	−	0.168656i	0.556011	+	0.831175i	$0.312331\pi$
$228$	−0.139229	−	0.304868i	−0.00922064	−	0.0201904i
$229$	−10.4603			−0.691236			−0.345618	−	0.938375i	$-0.612331\pi$
$229$	−10.4603			−0.691236			−0.345618	+	0.938375i	$0.612331\pi$
$230$	−0.292702	−	6.89435i	−0.0193002	−	0.454600i
$231$	8.46362			0.556865
$232$	−9.89757	−	21.6727i	−0.649807	−	1.42288i
$233$	6.87225	−	2.01788i	0.450216	−	0.132195i	−0.0487610	−	0.998810i	$-0.515527\pi$
$233$	6.87225	−	2.01788i	0.450216	−	0.132195i	0.498977	+	0.866615i	$0.333709\pi$
$234$	0.771091	−	0.889886i	0.0504078	−	0.0581737i
$235$	3.38040	+	2.17245i	0.220513	+	0.141715i
$236$	0.460254	+	0.531162i	0.0299600	+	0.0345757i
$237$	0.517191	+	3.59714i	0.0335952	+	0.233659i
$238$	−1.88613	−	0.553817i	−0.122260	−	0.0358986i
$239$	20.9993	−	13.4955i	1.35833	−	0.872949i	0.360133	−	0.932901i	$-0.382731\pi$
$239$	20.9993	−	13.4955i	1.35833	−	0.872949i	0.998201	+	0.0599521i	$0.0190948\pi$
$240$	0.588575	−	4.09363i	0.0379923	−	0.264243i
$241$	4.61591	−	10.1074i	0.297337	−	0.651077i	−0.700717	−	0.713440i	$-0.747136\pi$
$241$	4.61591	−	10.1074i	0.297337	−	0.651077i	0.998054	+	0.0623626i	$0.0198635\pi$
$242$	−2.52737	+	5.53417i	−0.162466	+	0.355750i
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$	0.411224	−	0.264278i	0.0263259	−	0.0169186i
$245$	3.43334	+	1.00812i	0.219348	+	0.0644064i
$246$	−0.672949	−	4.68047i	−0.0429057	−	0.298416i
$247$	2.55364	+	2.94706i	0.162484	+	0.187517i
$248$	−3.63241	−	2.33441i	−0.230658	−	0.148235i
$249$	−1.79730	+	2.07420i	−0.113899	+	0.131447i
$250$	1.38058	−	0.405375i	0.0873157	−	0.0256382i
$251$	−6.83327	−	14.9628i	−0.431312	−	0.944442i	−0.993112	−	0.117169i	$-0.962618\pi$
$251$	−6.83327	−	14.9628i	−0.431312	−	0.944442i	0.561800	−	0.827273i	$-0.310109\pi$
$252$	−0.228760			−0.0144105
$253$	3.00492	−	12.1128i	0.188918	−	0.761524i
$254$	14.6894			0.921696
$255$	−0.174495	−	0.382091i	−0.0109273	−	0.0239275i
$256$	−1.61768	+	0.474995i	−0.101105	+	0.0296872i
$257$	4.15287	−	4.79267i	0.259049	−	0.298958i	−0.611295	−	0.791403i	$-0.709351\pi$
$257$	4.15287	−	4.79267i	0.259049	−	0.298958i	0.870344	+	0.492445i	$0.163897\pi$
$258$	−8.72088	−	5.60457i	−0.542938	−	0.348925i
$259$	−9.52748	−	10.9953i	−0.592009	−	0.683214i
$260$	−0.00819141	−	0.0569725i	−0.000508009	−	0.00353328i
$261$	−8.23353	−	2.41758i	−0.509643	−	0.149645i
$262$	−2.37699	+	1.52760i	−0.146851	+	0.0943752i
$263$	−0.575515	+	4.00280i	−0.0354878	+	0.246823i	−0.999842	−	0.0177929i	$-0.994336\pi$
$263$	−0.575515	+	4.00280i	−0.0354878	+	0.246823i	0.964354	+	0.264616i	$0.0852451\pi$
$264$	3.00146	−	6.57229i	0.184727	−	0.404496i
$265$	−2.84550	+	6.23077i	−0.174797	+	0.382753i
$266$	3.17360	−	22.0729i	0.194586	−	1.35338i
$267$	−9.26364	+	5.95338i	−0.566926	+	0.364341i
$268$	0.359483	+	0.105554i	0.0219589	+	0.00644771i
$269$	1.63397	+	11.3645i	0.0996249	+	0.692906i	0.977022	+	0.213140i	$0.0683692\pi$
$269$	1.63397	+	11.3645i	0.0996249	+	0.692906i	−0.877397	+	0.479766i	$0.840722\pi$
$270$	−0.942257	−	1.08742i	−0.0573439	−	0.0661784i
$271$	−10.9410	−	7.03136i	−0.664619	−	0.427125i	0.164363	−	0.986400i	$-0.447443\pi$
$271$	−10.9410	−	7.03136i	−0.664619	−	0.427125i	−0.828982	+	0.559275i	$0.811080\pi$
$272$	−1.13763	+	1.31290i	−0.0689791	+	0.0796061i
$273$	2.55379	−	0.749861i	0.154563	−	0.0453837i
$274$	12.5601	+	27.5029i	0.758786	+	1.66151i
$275$	2.60225			0.156921
$276$	−0.0812188	+	0.327391i	−0.00488880	+	0.0197066i
$277$	20.0794			1.20645			0.603226	−	0.797570i	$-0.293882\pi$
$277$	20.0794			1.20645			0.603226	+	0.797570i	$0.293882\pi$
$278$	7.29414	+	15.9719i	0.437473	+	0.957933i
$279$	−1.49213	+	0.438130i	−0.0893317	+	0.0262302i
$280$	5.91369	−	6.82477i	0.353411	−	0.407858i
$281$	−4.23488	−	2.72159i	−0.252632	−	0.162357i	0.408196	−	0.912894i	$-0.366158\pi$
$281$	−4.23488	−	2.72159i	−0.252632	−	0.162357i	−0.660827	+	0.750538i	$0.729794\pi$
$282$	−3.78626	−	4.36957i	−0.225468	−	0.260204i
$283$	−1.05707	−	7.35206i	−0.0628361	−	0.437035i	−0.996818	−	0.0797138i	$-0.974599\pi$
$283$	−1.05707	−	7.35206i	−0.0628361	−	0.437035i	0.933982	−	0.357321i	$-0.116310\pi$
$284$	−0.538176	−	0.158023i	−0.0319349	−	0.00937692i
$285$	4.00868	−	2.57622i	0.237454	−	0.152602i
$286$	0.436069	−	3.03293i	0.0257853	−	0.179341i
$287$	4.44019	−	9.72266i	0.262096	−	0.573911i
$288$	−0.165208	+	0.361754i	−0.00973495	+	0.0213166i
$289$	2.39424	−	16.6523i	0.140838	−	0.979548i
$290$	−10.3870	+	6.67534i	−0.609947	+	0.391989i
$291$	8.36457	+	2.45606i	0.490340	+	0.143977i
$292$	0.139186	+	0.968063i	0.00814527	+	0.0566516i
$293$	21.8155	+	25.1764i	1.27448	+	1.47082i	0.811386	+	0.584511i	$0.198714\pi$
$293$	21.8155	+	25.1764i	1.27448	+	1.47082i	0.463090	+	0.886311i	$0.346741\pi$
$294$	−4.33134	−	2.78358i	−0.252609	−	0.162342i
$295$	−6.54374	+	7.55188i	−0.380991	+	0.439687i
$296$	−11.9170	+	3.49913i	−0.692659	+	0.203383i
$297$	−1.08101	−	2.36709i	−0.0627267	−	0.137352i
$298$	−8.93049			−0.517329
$299$	−0.166472	−	3.92111i	−0.00962733	−	0.226764i
$300$	−0.0703351			−0.00406080
$301$	−9.73426	−	21.3150i	−0.561073	−	1.22858i
$302$	12.3861	−	3.63688i	0.712738	−	0.209279i
$303$	−12.1122	+	13.9782i	−0.695825	+	0.803025i
$304$	−16.5788	−	10.6545i	−0.950858	−	0.611080i
$305$	4.55123	+	5.25240i	0.260603	+	0.300751i
$306$	0.0860146	+	0.598244i	0.00491713	+	0.0341994i
$307$	25.8852	+	7.60058i	1.47735	+	0.433788i	0.918479	−	0.395470i	$-0.129418\pi$
$307$	25.8852	+	7.60058i	1.47735	+	0.433788i	0.558867	+	0.829257i	$0.311236\pi$
$308$	−0.500789	+	0.321838i	−0.0285351	+	0.0183384i
$309$	−0.610540	+	4.24640i	−0.0347324	+	0.241569i
$310$	−0.929541	+	2.03541i	−0.0527944	+	0.115604i
$311$	7.41770	−	16.2425i	0.420619	−	0.921028i	−0.574138	−	0.818759i	$-0.694663\pi$
$311$	7.41770	−	16.2425i	0.420619	−	0.921028i	0.994757	−	0.102269i	$-0.0326102\pi$
$312$	0.323362	−	2.24903i	0.0183068	−	0.127326i
$313$	−14.2243	+	9.14140i	−0.804005	+	0.516703i	−0.876921	−	0.480635i	$-0.840406\pi$
$313$	−14.2243	+	9.14140i	−0.804005	+	0.516703i	0.0729154	+	0.997338i	$0.476770\pi$
$314$	−13.9784	−	4.10442i	−0.788846	−	0.231626i
$315$	−0.462869	−	3.21932i	−0.0260797	−	0.181388i
$316$	−0.167387	−	0.193175i	−0.00941625	−	0.0108669i
$317$	−23.1128	−	14.8537i	−1.29814	−	0.834266i	−0.305135	−	0.952309i	$-0.598701\pi$
$317$	−23.1128	−	14.8537i	−1.29814	−	0.834266i	−0.993008	+	0.118043i	$0.962338\pi$
$318$	6.45424	−	7.44859i	0.361936	−	0.417696i
$319$	−21.4257	+	6.29115i	−1.19961	+	0.352237i
$320$	−3.19837	−	7.00346i	−0.178794	−	0.391505i
$321$	11.6958			0.652794
$322$	−16.3230	+	15.4036i	−0.909647	+	0.858412i
$323$	−2.00159			−0.111372
$324$	0.0292182	+	0.0639790i	0.00162324	+	0.00355439i
$325$	0.785196	−	0.230554i	0.0435548	−	0.0127889i
$326$	14.9984	−	17.3091i	0.830684	−	0.958660i
$327$	14.1359	+	9.08462i	0.781719	+	0.502381i
$328$	−5.97535	−	6.89592i	−0.329933	−	0.380763i
$329$	−1.85994	−	12.9362i	−0.102542	−	0.713193i
$330$	−3.59261	−	1.05489i	−0.197767	−	0.0580696i
$331$	24.2173	−	15.5635i	1.33110	−	0.855449i	0.334880	−	0.942261i	$-0.391304\pi$
$331$	24.2173	−	15.5635i	1.33110	−	0.855449i	0.996225	+	0.0868116i	$0.0276678\pi$
$332$	0.0274723	−	0.191074i	0.00150774	−	0.0104865i
$333$	−1.85825	+	4.06899i	−0.101831	+	0.222980i
$334$	−9.31794	+	20.4034i	−0.509855	+	1.11643i
$335$	−0.758079	+	5.27255i	−0.0414183	+	0.288070i
$336$	−11.3158	+	7.27223i	−0.617328	+	0.396733i
$337$	−17.9224	−	5.26248i	−0.976294	−	0.286666i	−0.245600	−	0.969371i	$-0.578985\pi$
$337$	−17.9224	−	5.26248i	−0.976294	−	0.286666i	−0.730694	+	0.682705i	$0.760803\pi$
$338$	2.52490	+	17.5611i	0.137337	+	0.955197i
$339$	−8.17531	−	9.43481i	−0.444022	−	0.512428i
$340$	0.0248542	+	0.0159728i	0.00134791	+	0.000866249i
$341$	−2.65011	+	3.05839i	−0.143511	+	0.165621i
$342$	−6.57864	+	1.93166i	−0.355732	+	0.104452i
$343$	4.62311	+	10.1232i	0.249624	+	0.546601i
$344$	−20.0039			−1.07854
$345$	−4.77169	−	0.480549i	−0.256899	−	0.0258719i
$346$	−15.4787			−0.832138
$347$	−0.0939332	−	0.205685i	−0.00504260	−	0.0110417i	0.907094	−	0.420928i	$-0.138296\pi$
$347$	−0.0939332	−	0.205685i	−0.00504260	−	0.0110417i	−0.912137	+	0.409886i	$0.865568\pi$
$348$	0.579106	−	0.170041i	0.0310433	−	0.00911514i
$349$	−11.8497	+	13.6753i	−0.634301	+	0.732022i	−0.978356	−	0.206927i	$-0.933654\pi$
$349$	−11.8497	+	13.6753i	−0.634301	+	0.732022i	0.344056	+	0.938949i	$0.388199\pi$
$350$	−3.93690	−	2.53009i	−0.210436	−	0.135239i
$351$	−0.535902	−	0.618464i	−0.0286043	−	0.0330112i
$352$	0.147281	+	1.02436i	0.00785010	+	0.0545986i
$353$	−2.66331	−	0.782019i	−0.141754	−	0.0416227i	0.210086	−	0.977683i	$-0.432626\pi$
$353$	−2.66331	−	0.782019i	−0.141754	−	0.0416227i	−0.351840	+	0.936060i	$0.614444\pi$
$354$	12.0955	−	7.77331i	0.642869	−	0.413147i
$355$	1.13491	−	7.89346i	0.0602346	−	0.418941i
$356$	0.321743	−	0.704519i	0.0170523	−	0.0373394i
$357$	−0.567533	+	1.24272i	−0.0300370	+	0.0657719i
$358$	2.51956	−	17.5239i	0.133163	−	0.926167i
$359$	23.2907	−	14.9680i	1.22924	−	0.789983i	0.245465	−	0.969405i	$-0.421059\pi$
$359$	23.2907	−	14.9680i	1.22924	−	0.789983i	0.983772	+	0.179423i	$0.0574230\pi$
$360$	−2.66406	−	0.782239i	−0.140408	−	0.0412276i
$361$	−0.527478	−	3.66869i	−0.0277620	−	0.193089i
$362$	−23.9590	−	27.6502i	−1.25926	−	1.45326i
$363$	3.55708	+	2.28600i	0.186698	+	0.119984i
$364$	−0.122593	+	0.141480i	−0.00642561	+	0.00741555i
$365$	−13.3419	+	3.91753i	−0.698345	+	0.205053i
$366$	−4.15415	−	9.09632i	−0.217141	−	0.475472i
$367$	18.9631			0.989864			0.494932	−	0.868932i	$-0.335193\pi$
$367$	18.9631			0.989864			0.494932	+	0.868932i	$0.335193\pi$
$368$	6.39015	+	18.7767i	0.333110	+	0.978801i
$369$	−3.28634			−0.171080
$370$	2.67377	+	5.85474i	0.139003	+	0.304373i
$371$	21.3759	−	6.27654i	1.10978	−	0.325862i
$372$	0.0716287	−	0.0826639i	0.00371377	−	0.00428592i
$373$	11.4176	+	7.33763i	0.591180	+	0.379928i	0.801758	−	0.597649i	$-0.203898\pi$
$373$	11.4176	+	7.33763i	0.591180	+	0.379928i	−0.210578	+	0.977577i	$0.567535\pi$
$374$	1.02996	+	1.18863i	0.0532578	+	0.0614628i
$375$	−0.142315	−	0.989821i	−0.00734911	−	0.0511142i
$376$	−10.7050	−	3.14326i	−0.552066	−	0.162101i
$377$	−5.90755	+	3.79655i	−0.304254	+	0.195532i
$378$	−0.666006	+	4.63217i	−0.0342556	+	0.238253i
$379$	1.99491	−	4.36825i	0.102472	−	0.224382i	−0.851451	−	0.524434i	$-0.824277\pi$
$379$	1.99491	−	4.36825i	0.102472	−	0.224382i	0.953923	+	0.300052i	$0.0970041\pi$
$380$	−0.139229	+	0.304868i	−0.00714228	+	0.0156394i
$381$	1.45290	−	10.1051i	0.0744341	−	0.517700i
$382$	−0.680520	+	0.437344i	−0.0348184	+	0.0223764i
$383$	−11.6288	−	3.41452i	−0.594204	−	0.174474i	−0.0292160	−	0.999573i	$-0.509301\pi$
$383$	−11.6288	−	3.41452i	−0.594204	−	0.174474i	−0.564988	+	0.825099i	$0.691119\pi$
$384$	1.68978	+	11.7527i	0.0862312	+	0.599751i
$385$	−5.54249	−	6.39638i	−0.282472	−	0.325990i
$386$	−22.5641	−	14.5010i	−1.14848	−	0.738084i
$387$	−4.71804	+	5.44491i	−0.239832	+	0.276780i
$388$	−0.588323	+	0.172747i	−0.0298676	+	0.00876990i
$389$	−11.1450	−	24.4042i	−0.565076	−	1.23734i	−0.949378	−	0.314137i	$-0.898285\pi$
$389$	−11.1450	−	24.4042i	−0.565076	−	1.23734i	0.384302	−	0.923208i	$-0.374442\pi$
$390$	−1.17749			−0.0596244
$391$	1.57704	+	1.25345i	0.0797542	+	0.0633895i
$392$	−9.93521			−0.501804
$393$	0.815758	+	1.78626i	0.0411496	+	0.0901050i
$394$	−18.1479	+	5.32871i	−0.914279	+	0.268457i
$395$	2.37985	−	2.74649i	0.119743	−	0.138191i
$396$	0.153974	+	0.0989531i	0.00773749	+	0.00497258i
$397$	17.0465	+	19.6727i	0.855539	+	0.987344i	0.999998	−	0.00216648i	$-0.000689613\pi$
$397$	17.0465	+	19.6727i	0.855539	+	0.987344i	−0.144459	+	0.989511i	$0.546144\pi$
$398$	2.75104	+	19.1339i	0.137897	+	0.959096i
$399$	−14.8704	−	4.36635i	−0.744453	−	0.218591i
$400$	−3.47919	+	2.23594i	−0.173960	+	0.111797i
$401$	−3.22558	+	22.4344i	−0.161078	+	1.12032i	0.735530	+	0.677492i	$0.236933\pi$
$401$	−3.22558	+	22.4344i	−0.161078	+	1.12032i	−0.896607	+	0.442827i	$0.853976\pi$
$402$	3.18395	−	6.97188i	0.158801	−	0.347726i
$403$	−0.528670	+	1.15763i	−0.0263349	+	0.0576654i
$404$	0.185138	−	1.28766i	0.00921094	−	0.0640635i
$405$	−0.841254	+	0.540641i	−0.0418022	+	0.0268647i
$406$	38.5313	+	11.3138i	1.91228	+	0.561495i
$407$	1.65661	+	11.5220i	0.0821151	+	0.571123i
$408$	0.763753	+	0.881417i	0.0378114	+	0.0436367i
$409$	−27.8704	−	17.9112i	−1.37810	−	0.885654i	−0.378897	−	0.925439i	$-0.623696\pi$
$409$	−27.8704	−	17.9112i	−1.37810	−	0.885654i	−0.999208	+	0.0397849i	$0.987333\pi$
$410$	−3.09657	+	3.57363i	−0.152929	+	0.176489i
$411$	20.1620	−	5.92010i	0.994518	−	0.292017i
$412$	−0.125348	−	0.274474i	−0.00617546	−	0.0135224i
$413$	32.5001			1.59923
$414$	6.39291	+	2.59776i	0.314194	+	0.127673i
$415$	2.74456			0.134725
$416$	0.135197	+	0.296040i	0.00662857	+	0.0145145i
$417$	11.7088	−	3.43802i	0.573384	−	0.168361i
$418$	−11.6840	+	13.4841i	−0.571484	+	0.659528i
$419$	−12.9993	−	8.35414i	−0.635057	−	0.408126i	0.183122	−	0.983090i	$-0.441380\pi$
$419$	−12.9993	−	8.35414i	−0.635057	−	0.408126i	−0.818179	+	0.574964i	$0.805016\pi$
$420$	0.149806	+	0.172885i	0.00730977	+	0.00843593i
$421$	−4.85887	−	33.7942i	−0.236807	−	1.64703i	−0.667559	−	0.744557i	$-0.732661\pi$
$421$	−4.85887	−	33.7942i	−0.236807	−	1.64703i	0.430752	−	0.902470i	$-0.358248\pi$
$422$	−20.2707	−	5.95202i	−0.986763	−	0.289740i
$423$	−3.38040	+	2.17245i	−0.164360	+	0.105628i
$424$	2.70663	−	18.8250i	0.131445	−	0.914223i
$425$	−0.174495	+	0.382091i	−0.00846426	+	0.0185342i
$426$	−4.76665	+	10.4375i	−0.230945	+	0.505698i
$427$	3.21690	−	22.3740i	0.155677	−	1.08276i
$428$	−0.692035	+	0.444744i	−0.0334508	+	0.0214975i
$429$	−2.04327	−	0.599959i	−0.0986502	−	0.0289663i
$430$	1.47531	+	10.2610i	0.0711458	+	0.494830i
$431$	24.7344	+	28.5450i	1.19141	+	1.37497i	0.909594	+	0.415499i	$0.136393\pi$
$431$	24.7344	+	28.5450i	1.19141	+	1.37497i	0.281821	+	0.959467i	$0.409062\pi$
$432$	3.47919	+	2.23594i	0.167393	+	0.107577i
$433$	9.61570	−	11.0971i	0.462101	−	0.533293i	−0.476097	−	0.879393i	$-0.657949\pi$
$433$	9.61570	−	11.0971i	0.462101	−	0.533293i	0.938198	+	0.346100i	$0.112494\pi$
$434$	6.98290	−	2.05036i	0.335190	−	0.0984206i
$435$	3.56473	+	7.80566i	0.170916	+	0.374253i
$436$	−1.18187			−0.0566013
$437$	−11.5285	+	19.7317i	−0.551485	+	0.943896i
$438$	20.0076			0.956001
$439$	0.621538	+	1.36098i	0.0296644	+	0.0649559i	0.923884	−	0.382672i	$-0.124996\pi$
$439$	0.621538	+	1.36098i	0.0296644	+	0.0649559i	−0.894220	+	0.447628i	$0.852269\pi$
$440$	−6.93254	+	2.03558i	−0.330496	+	0.0970424i
$441$	−2.34328	+	2.70429i	−0.111585	+	0.128776i
$442$	0.416088	+	0.267403i	0.0197913	+	0.0127191i
$443$	−2.81243	−	3.24572i	−0.133623	−	0.154209i	0.684995	−	0.728548i	$-0.259805\pi$
$443$	−2.81243	−	3.24572i	−0.133623	−	0.154209i	−0.818617	+	0.574339i	$0.805259\pi$
$444$	−0.0447758	−	0.311423i	−0.00212497	−	0.0147795i
$445$	10.5657	+	3.10236i	0.500861	+	0.147066i
$446$	−21.1644	+	13.6015i	−1.00216	+	0.644050i
$447$	−0.883293	+	6.14344i	−0.0417783	+	0.290575i
$448$	−10.4025	+	22.7782i	−0.491471	+	1.07617i
$449$	−13.6825	+	29.9605i	−0.645717	+	1.41392i	0.249537	+	0.968365i	$0.419722\pi$
$449$	−13.6825	+	29.9605i	−0.645717	+	1.41392i	−0.895253	+	0.445557i	$0.853006\pi$
$450$	−0.204772	+	1.42422i	−0.00965304	+	0.0671384i
$451$	−7.19428	+	4.62348i	−0.338765	+	0.217711i
$452$	0.842498	+	0.247380i	0.0396278	+	0.0116358i
$453$	−1.27680	−	8.88031i	−0.0599891	−	0.417234i
$454$	8.49859	+	9.80790i	0.398859	+	0.460307i
$455$	−2.23909	−	1.43897i	−0.104970	−	0.0674601i
$456$	−8.66414	+	9.99895i	−0.405736	+	0.468244i
$457$	20.5859	−	6.04456i	0.962966	−	0.282752i	0.237791	−	0.971316i	$-0.423577\pi$
$457$	20.5859	−	6.04456i	0.962966	−	0.282752i	0.725176	+	0.688564i	$0.241759\pi$
$458$	−6.25240	−	13.6908i	−0.292155	−	0.639731i
$459$	0.420050			0.0196063
$460$	0.300613	−	0.153015i	0.0140161	−	0.00713434i
$461$	−5.90185			−0.274877			−0.137438	−	0.990510i	$-0.543887\pi$
$461$	−5.90185			−0.274877			−0.137438	+	0.990510i	$0.543887\pi$
$462$	5.05893	+	11.0775i	0.235363	+	0.515372i
$463$	25.8587	−	7.59279i	1.20175	−	0.352867i	0.381231	−	0.924480i	$-0.375500\pi$
$463$	25.8587	−	7.59279i	1.20175	−	0.352867i	0.820524	+	0.571613i	$0.193682\pi$
$464$	23.2405	−	26.8209i	1.07891	−	1.24513i
$465$	1.30826	+	0.840765i	0.0606689	+	0.0389896i
$466$	6.74880	+	7.78853i	0.312632	+	0.360797i
$467$	−5.28126	−	36.7319i	−0.244387	−	1.69975i	−0.629597	−	0.776922i	$-0.716780\pi$
$467$	−5.28126	−	36.7319i	−0.244387	−	1.69975i	0.385209	−	0.922829i	$-0.374129\pi$
$468$	0.0552268	+	0.0162161i	0.00255286	+	0.000749588i
$469$	14.5747	−	9.36657i	0.672996	−	0.432508i
$470$	−0.822832	+	5.72292i	−0.0379544	+	0.263979i
$471$	−4.20607	+	9.21002i	−0.193806	+	0.424375i
$472$	11.5255	−	25.2374i	0.530506	−	1.16165i
$473$	−2.66816	+	18.5575i	−0.122682	+	0.853273i
$474$	−4.39894	+	2.82703i	−0.202050	+	0.129850i
$475$	−4.57210	−	1.34249i	−0.209783	−	0.0615977i
$476$	−0.0136751	−	0.0951126i	−0.000626798	−	0.00435948i
$477$	−4.48564	−	5.17671i	−0.205384	−	0.237025i
$478$	30.2152	+	19.4182i	1.38201	+	0.888166i
$479$	2.61951	−	3.02308i	0.119689	−	0.138128i	−0.692743	−	0.721185i	$-0.743598\pi$
$479$	2.61951	−	3.02308i	0.119689	−	0.138128i	0.812432	+	0.583057i	$0.198143\pi$
$480$	0.381584	−	0.112043i	0.0174168	−	0.00511404i
$481$	1.52069	+	3.32984i	0.0693374	+	0.151828i
$482$	15.9881			0.728236
$483$	8.98197	+	12.7524i	0.408694	+	0.580256i
$484$	−0.297398			−0.0135181
$485$	−3.62146	−	7.92989i	−0.164442	−	0.360078i
$486$	1.38058	−	0.405375i	0.0626245	−	0.0183882i
$487$	0.592636	−	0.683939i	0.0268549	−	0.0309922i	−0.742163	−	0.670219i	$-0.766200\pi$
$487$	0.592636	−	0.683939i	0.0268549	−	0.0309922i	0.769018	+	0.639227i	$0.220746\pi$
$488$	−16.2334	−	10.4326i	−0.734850	−	0.472260i
$489$	−10.4238	−	12.0297i	−0.471379	−	0.544000i
$490$	0.732732	+	5.09626i	0.0331015	+	0.230226i
$491$	−17.0739	−	5.01336i	−0.770536	−	0.226250i	−0.127245	−	0.991871i	$-0.540613\pi$
$491$	−17.0739	−	5.01336i	−0.770536	−	0.226250i	−0.643291	+	0.765621i	$0.722432\pi$
$492$	0.194451	−	0.124966i	0.00876654	−	0.00563391i
$493$	0.512975	−	3.56782i	0.0231032	−	0.160686i
$494$	−2.33084	+	5.10384i	−0.104870	+	0.229632i
$495$	−1.08101	+	2.36709i	−0.0485879	+	0.106393i
$496$	0.915309	−	6.36611i	0.0410986	−	0.285847i
$497$	−21.8195	+	14.0225i	−0.978738	+	0.628997i
$498$	−3.78909	−	1.11258i	−0.169793	−	0.0498557i
$499$	4.12329	+	28.6781i	0.184584	+	1.28381i	0.845754	+	0.533574i	$0.179151\pi$
$499$	4.12329	+	28.6781i	0.184584	+	1.28381i	−0.661170	+	0.750236i	$0.729940\pi$
$500$	0.0460597	+	0.0531557i	0.00205985	+	0.00237720i
$501$	13.1143	+	8.42803i	0.585902	+	0.376537i
$502$	15.4994	−	17.8873i	0.691773	−	0.798349i
$503$	−3.38291	+	0.993313i	−0.150837	+	0.0442896i	−0.356279	−	0.934380i	$-0.615955\pi$
$503$	−3.38291	+	0.993313i	−0.150837	+	0.0442896i	0.205443	+	0.978669i	$0.434137\pi$
$504$	3.75139	+	8.21439i	0.167100	+	0.365898i
$505$	18.4958			0.823051
$506$	17.6498	−	3.30717i	0.784629	−	0.147022i
$507$	12.3303			0.547608
$508$	0.298290	+	0.653163i	0.0132345	+	0.0289794i
$509$	6.84507	−	2.00989i	0.303402	−	0.0890870i	−0.126488	−	0.991968i	$-0.540370\pi$
$509$	6.84507	−	2.00989i	0.303402	−	0.0890870i	0.429890	+	0.902881i	$0.358552\pi$
$510$	0.395795	−	0.456772i	0.0175261	−	0.0202262i
$511$	38.0460	+	24.4507i	1.68306	+	1.08164i
$512$	13.9624	+	16.1135i	0.617056	+	0.712121i
$513$	0.678148	+	4.71662i	0.0299410	+	0.208244i
$514$	8.75511	+	2.57073i	0.386171	+	0.113390i
$515$	3.60903	−	2.31938i	0.159033	−	0.102204i
$516$	0.0721166	−	0.501582i	0.00317476	−	0.0220809i
$517$	−4.34382	+	9.51163i	−0.191041	+	0.418321i
$518$	8.69624	−	19.0421i	0.382091	−	0.836662i
$519$	−1.53096	+	10.6480i	−0.0672016	+	0.467397i
$520$	−1.91146	+	1.22842i	−0.0838231	+	0.0538698i
$521$	−26.7478	−	7.85387i	−1.17184	−	0.344084i	−0.362819	−	0.931859i	$-0.618186\pi$
$521$	−26.7478	−	7.85387i	−1.17184	−	0.344084i	−0.809024	+	0.587775i	$0.800004\pi$
$522$	−1.75717	−	12.2214i	−0.0769094	−	0.534917i
$523$	2.65624	+	3.06546i	0.116149	+	0.134043i	0.810846	−	0.585259i	$-0.199007\pi$
$523$	2.65624	+	3.06546i	0.116149	+	0.134043i	−0.694697	+	0.719302i	$0.744462\pi$
$524$	−0.116193	−	0.0746724i	−0.00507589	−	0.00326208i
$525$	−2.12989	+	2.45802i	−0.0929559	+	0.107277i
$526$	−5.58301	+	1.63932i	−0.243431	+	0.0714778i
$527$	−0.271362	−	0.594201i	−0.0118207	−	0.0258838i
$528$	10.7622			0.468363
$529$	21.4397	−	8.32700i	0.932161	−	0.362043i
$530$	−9.85590			−0.428113
$531$	−4.15106	−	9.08956i	−0.180141	−	0.394453i
$532$	1.04591	−	0.307108i	0.0453461	−	0.0133148i
$533$	−1.76115	+	2.03248i	−0.0762840	+	0.0880365i
$534$	−13.3291	−	8.56612i	−0.576808	−	0.370692i
$535$	−7.65910	−	8.83908i	−0.331132	−	0.382147i
$536$	−2.10483	−	14.6394i	−0.0909147	−	0.632326i
$537$	−11.8058	−	3.46650i	−0.509458	−	0.149590i
$538$	−13.8976	+	8.93147i	−0.599170	+	0.385063i
$539$	−1.32518	+	9.21680i	−0.0570794	+	0.396996i
$540$	0.0292182	−	0.0639790i	0.00125735	−	0.00275322i
$541$	−8.67367	+	18.9927i	−0.372910	+	0.816559i	0.626403	+	0.779499i	$0.284527\pi$
$541$	−8.67367	+	18.9927i	−0.372910	+	0.816559i	−0.999313	+	0.0370599i	$0.988201\pi$
$542$	2.66318	−	18.5229i	0.114394	−	0.795625i
$543$	−21.3908	+	13.7470i	−0.917966	+	0.589941i
$544$	−0.160284	−	0.0470637i	−0.00687213	−	0.00201784i
$545$	−2.39138	−	16.6324i	−0.102435	−	0.712453i
$546$	2.50792	+	2.89429i	0.107329	+	0.123864i
$547$	25.1764	+	16.1799i	1.07646	+	0.691802i	0.953738	−	0.300639i	$-0.0971999\pi$
$547$	25.1764	+	16.1799i	1.07646	+	0.691802i	0.122726	+	0.992441i	$0.460836\pi$
$548$	−0.967861	+	1.11697i	−0.0413450	+	0.0477146i
$549$	−6.66840	+	1.95802i	−0.284600	+	0.0835662i
$550$	1.55543	+	3.40592i	0.0663238	+	0.145229i
$551$	40.8901			1.74198
$552$	13.0880	−	2.45239i	0.557062	−	0.104381i
$553$	−11.8197			−0.502627
$554$	12.0020	+	26.2806i	0.509915	+	1.11656i
$555$	4.29203	−	1.26025i	0.182187	−	0.0534948i
$556$	−0.562073	+	0.648666i	−0.0238372	+	0.0275096i
$557$	−18.7993	−	12.0816i	−0.796554	−	0.511914i	0.0779358	−	0.996958i	$-0.475167\pi$
$557$	−18.7993	−	12.0816i	−0.796554	−	0.511914i	−0.874490	+	0.485044i	$0.838803\pi$
$558$	−1.46533	−	1.69108i	−0.0620323	−	0.0715891i
$559$	0.839072	+	5.83588i	0.0354890	+	0.246831i
$560$	12.9063	+	3.78962i	0.545390	+	0.160141i
$561$	0.919553	−	0.590961i	0.0388236	−	0.0249504i
$562$	1.03082	−	7.16954i	0.0434827	−	0.302429i
$563$	−12.9027	+	28.2529i	−0.543783	+	1.19072i	0.415842	+	0.909437i	$0.363487\pi$
$563$	−12.9027	+	28.2529i	−0.543783	+	1.19072i	−0.959625	+	0.281282i	$0.909240\pi$
$564$	0.117407	−	0.257086i	0.00494374	−	0.0108253i
$565$	−1.77666	+	12.3570i	−0.0747448	+	0.519862i
$566$	8.99082	−	5.77805i	0.377913	−	0.242870i
$567$	3.12068	+	0.916315i	0.131056	+	0.0384816i
$568$	3.15110	+	21.9164i	0.132217	+	0.919592i
$569$	−6.23617	−	7.19693i	−0.261434	−	0.301711i	0.609823	−	0.792537i	$-0.291240\pi$
$569$	−6.23617	−	7.19693i	−0.261434	−	0.301711i	−0.871257	+	0.490827i	$0.836695\pi$
$570$	5.76795	+	3.70684i	0.241593	+	0.155262i
$571$	12.0920	−	13.9549i	0.506034	−	0.583994i	−0.444045	−	0.896005i	$-0.646457\pi$
$571$	12.0920	−	13.9549i	0.506034	−	0.583994i	0.950079	+	0.312010i	$0.101002\pi$
$572$	0.143714	−	0.0421982i	0.00600898	−	0.00176440i
$573$	0.233548	+	0.511398i	0.00975660	+	0.0213640i
$574$	15.3794			0.641924
$575$	2.76162	+	3.92090i	0.115168	+	0.163513i
$576$	7.69922			0.320801
$577$	10.0740	+	22.0589i	0.419384	+	0.918324i	0.994931	+	0.100555i	$0.0320618\pi$
$577$	10.0740	+	22.0589i	0.419384	+	0.918324i	−0.575547	+	0.817769i	$0.695211\pi$
$578$	23.2263	−	6.81986i	0.966087	−	0.283669i
$579$	−12.2073	+	14.0880i	−0.507317	+	0.585476i
$580$	−0.507742	−	0.326306i	−0.0210828	−	0.0135491i
$581$	−5.84560	−	6.74618i	−0.242516	−	0.279879i
$582$	1.78514	+	12.4159i	0.0739964	+	0.514656i
$583$	−17.1028	−	5.02182i	−0.708324	−	0.207983i
$584$	32.4791	−	20.8731i	1.34399	−	0.863733i
$585$	−0.116463	+	0.810015i	−0.00481514	+	0.0334900i
$586$	−19.9122	+	43.6016i	−0.822564	+	1.80116i
$587$	−5.82431	+	12.7535i	−0.240395	+	0.526391i	−0.990920	−	0.134450i	$-0.957073\pi$
$587$	−5.82431	+	12.7535i	−0.240395	+	0.526391i	0.750525	+	0.660842i	$0.229800\pi$
$588$	0.0358176	−	0.249117i	0.00147709	−	0.0102734i
$589$	6.23400	−	4.00635i	0.256868	−	0.165079i
$590$	−13.7956	−	4.05074i	−0.567954	−	0.166766i
$591$	1.87075	+	13.0113i	0.0769523	+	0.535215i
$592$	−12.1150	−	13.9814i	−0.497922	−	0.574632i
$593$	16.0341	+	10.3045i	0.658442	+	0.423155i	0.826742	−	0.562581i	$-0.190191\pi$
$593$	16.0341	+	10.3045i	0.658442	+	0.423155i	−0.168300	+	0.985736i	$0.553828\pi$
$594$	2.45199	−	2.82974i	0.100606	−	0.116106i
$595$	1.31084	−	0.384898i	0.0537393	−	0.0157793i
$596$	−0.181346	−	0.397093i	−0.00742824	−	0.0162656i
$597$	13.4346			0.549844
$598$	5.03260	−	2.56164i	0.205798	−	0.104753i
$599$	−26.0691			−1.06515			−0.532577	−	0.846381i	$-0.678777\pi$
$599$	−26.0691			−1.06515			−0.532577	+	0.846381i	$0.678777\pi$
$600$	1.15341	+	2.52562i	0.0470878	+	0.103108i
$601$	−35.3131	+	10.3688i	−1.44045	+	0.422954i	−0.906372	−	0.422481i	$-0.861159\pi$
$601$	−35.3131	+	10.3688i	−1.44045	+	0.422954i	−0.534078	+	0.845435i	$0.679341\pi$
$602$	22.0795	−	25.4811i	0.899894	−	1.03853i
$603$	−4.48117	−	2.87987i	−0.182487	−	0.117277i
$604$	0.413230	+	0.476893i	0.0168141	+	0.0194045i
$605$	−0.601751	−	4.18527i	−0.0244647	−	0.170155i
$606$	−25.5349	−	7.49773i	−1.03729	−	0.304575i
$607$	−33.7235	+	21.6728i	−1.36880	+	0.879672i	−0.998781	−	0.0493545i	$-0.984284\pi$
$607$	−33.7235	+	21.6728i	−1.36880	+	0.879672i	−0.370014	+	0.929026i	$0.620647\pi$
$608$	0.269695	−	1.87577i	0.0109376	−	0.0760724i
$609$	11.5940	−	25.3874i	0.469813	−	1.02875i
$610$	−4.15415	+	9.09632i	−0.168197	+	0.368299i
$611$	−0.467980	+	3.25487i	−0.0189324	+	0.131678i
$612$	−0.0248542	+	0.0159728i	−0.00100467	+	0.000645664i
$613$	40.7355	+	11.9610i	1.64529	+	0.483101i	0.967651	−	0.252294i	$-0.0811850\pi$
$613$	40.7355	+	11.9610i	1.64529	+	0.483101i	0.677639	+	0.735395i	$0.263003\pi$
$614$	5.52434	+	38.4226i	0.222944	+	1.55061i
$615$	2.15209	+	2.48365i	0.0867807	+	0.100150i
$616$	19.7690	+	12.7048i	0.796517	+	0.511890i
$617$	−27.4730	+	31.7055i	−1.10602	+	1.27642i	−0.148230	+	0.988953i	$0.547358\pi$
$617$	−27.4730	+	31.7055i	−1.10602	+	1.27642i	−0.957791	+	0.287464i	$0.907188\pi$
$618$	−5.92278	+	1.73909i	−0.238249	+	0.0699563i
$619$	−7.35457	−	16.1043i	−0.295605	−	0.647285i	0.702307	−	0.711874i	$-0.252153\pi$
$619$	−7.35457	−	16.1043i	−0.295605	−	0.647285i	−0.997912	+	0.0645896i	$0.979426\pi$
$620$	−0.109380			−0.00439281
$621$	2.41936	−	4.14086i	0.0970854	−	0.166167i
$622$	25.6926			1.03018
$623$	−14.8780	−	32.5783i	−0.596075	−	1.30522i
$624$	3.24735	−	0.953509i	0.129998	−	0.0381709i
$625$	−0.654861	+	0.755750i	−0.0261944	+	0.0302300i
$626$	−20.4669	−	13.1533i	−0.818020	−	0.525710i
$627$	8.12029	+	9.37132i	0.324293	+	0.374254i
$628$	−0.101348	−	0.704894i	−0.00404424	−	0.0281283i
$629$	−1.80287	−	0.529371i	−0.0718852	−	0.0211074i
$630$	3.93690	−	2.53009i	0.156850	−	0.100801i
$631$	5.01736	−	34.8965i	0.199738	−	1.38921i	−0.605307	−	0.795992i	$-0.706949\pi$
$631$	5.01736	−	34.8965i	0.199738	−	1.38921i	0.805044	−	0.593215i	$-0.202141\pi$
$632$	−4.19165	+	9.17843i	−0.166735	+	0.365099i
$633$	−6.09943	+	13.3559i	−0.242430	+	0.530849i
$634$	5.62595	−	39.1293i	0.223435	−	1.55402i
$635$	−8.58837	+	5.51941i	−0.340819	+	0.219031i
$636$	0.462263	+	0.135733i	0.0183299	+	0.00538216i
$637$	0.416736	+	2.89846i	0.0165117	+	0.114841i
$638$	−21.0408	−	24.2824i	−0.833013	−	0.961348i
$639$	6.70868	+	4.31141i	0.265391	+	0.170557i
$640$	7.77551	−	8.97342i	0.307354	−	0.354705i
$641$	11.0388	−	3.24127i	0.436005	−	0.128023i	−0.0563618	−	0.998410i	$-0.517950\pi$
$641$	11.0388	−	3.24127i	0.436005	−	0.128023i	0.492367	+	0.870388i	$0.336132\pi$
$642$	6.99087	+	15.3079i	0.275908	+	0.604154i
$643$	−37.6329			−1.48410			−0.742049	−	0.670346i	$-0.766146\pi$
$643$	−37.6329			−1.48410			−0.742049	+	0.670346i	$0.766146\pi$
$644$	−1.01638	−	0.413009i	−0.0400512	−	0.0162748i
$645$	7.20465			0.283683
$646$	−1.19641	−	2.61976i	−0.0470719	−	0.103073i
$647$	−39.0295	+	11.4601i	−1.53441	+	0.450543i	−0.936397	−	0.350943i	$-0.885861\pi$
$647$	−39.0295	+	11.4601i	−1.53441	+	0.450543i	−0.598013	+	0.801487i	$0.704043\pi$
$648$	1.81824	−	2.09836i	0.0714272	−	0.0824314i
$649$	−21.8752	−	14.0584i	−0.858678	−	0.551839i
$650$	0.771091	+	0.889886i	0.0302447	+	0.0349042i
$651$	−0.719820	−	5.00646i	−0.0282120	−	0.196218i
$652$	1.07421	+	0.315416i	0.0420693	+	0.0123527i
$653$	11.9041	−	7.65029i	0.465843	−	0.299379i	−0.286584	−	0.958055i	$-0.592520\pi$
$653$	11.9041	−	7.65029i	0.465843	−	0.299379i	0.752427	+	0.658676i	$0.228883\pi$
$654$	−3.44087	+	23.9318i	−0.134549	+	0.935807i
$655$	0.815758	−	1.78626i	0.0318743	−	0.0697950i
$656$	5.64606	−	12.3631i	0.220442	−	0.482700i
$657$	1.97891	−	13.7636i	0.0772045	−	0.536969i
$658$	15.8196	−	10.1666i	0.616712	−	0.396337i
$659$	−10.8982	−	3.20001i	−0.424534	−	0.124655i	0.0624846	−	0.998046i	$-0.480098\pi$
$659$	−10.8982	−	3.20001i	−0.424534	−	0.124655i	−0.487019	+	0.873391i	$0.661916\pi$
$660$	−0.0260478	−	0.181166i	−0.00101391	−	0.00705189i
$661$	−13.4878	−	15.5658i	−0.524616	−	0.605439i	0.430165	−	0.902750i	$-0.358455\pi$
$661$	−13.4878	−	15.5658i	−0.524616	−	0.605439i	−0.954781	+	0.297312i	$0.903910\pi$
$662$	34.8455	+	22.3938i	1.35431	+	0.870361i
$663$	0.225106	−	0.259786i	0.00874239	−	0.0100893i
$664$	−7.31167	+	2.14690i	−0.283748	+	0.0833159i
$665$	6.43819	+	14.0977i	0.249662	+	0.546685i
$666$	−6.43638			−0.249405
$667$	−32.2170	−	25.6064i	−1.24745	−	0.991483i
$668$	−1.09645			−0.0424230
$669$	7.26340	+	15.9046i	0.280819	+	0.614909i
$670$	−7.35404	+	2.15934i	−0.284112	+	0.0834227i
$671$	−11.8434	+	13.6680i	−0.457210	+	0.527649i
$672$	−1.08813	−	0.699301i	−0.0419757	−	0.0269761i
$673$	−3.70312	−	4.27363i	−0.142745	−	0.164736i	0.679875	−	0.733328i	$-0.262034\pi$
$673$	−3.70312	−	4.27363i	−0.142745	−	0.164736i	−0.822620	+	0.568592i	$0.807489\pi$
$674$	−3.82494	−	26.6030i	−0.147331	−	1.02471i
$675$	0.959493	+	0.281733i	0.0369309	+	0.0108439i
$676$	−0.729580	+	0.468873i	−0.0280608	+	0.0180336i
$677$	2.31736	−	16.1176i	0.0890634	−	0.619449i	−0.895584	−	0.444893i	$-0.853242\pi$
$677$	2.31736	−	16.1176i	0.0890634	−	0.619449i	0.984647	−	0.174557i	$-0.0558492\pi$
$678$	7.46204	−	16.3396i	0.286578	−	0.627518i
$679$	−11.7785	+	25.7914i	−0.452019	+	0.989783i
$680$	0.165979	−	1.15441i	0.00636502	−	0.0442697i
$681$	7.58760	−	4.87626i	0.290758	−	0.186859i
$682$	−5.58697	−	1.64048i	−0.213936	−	0.0628173i
$683$	−3.37402	−	23.4669i	−0.129103	−	0.897934i	−0.946694	−	0.322134i	$-0.895600\pi$
$683$	−3.37402	−	23.4669i	−0.129103	−	0.897934i	0.817591	−	0.575800i	$-0.195309\pi$
$684$	−0.219480	−	0.253294i	−0.00839203	−	0.00968492i
$685$	−17.6774	−	11.3606i	−0.675419	−	0.434066i
$686$	−10.4863	+	12.1018i	−0.400368	+	0.462049i
$687$	−10.0366	+	2.94701i	−0.382920	+	0.112435i
$688$	−12.3779	−	27.1038i	−0.471903	−	1.03332i
$689$	−5.60547			−0.213551
$690$	−2.22321	−	6.53261i	−0.0846361	−	0.248692i
$691$	10.6344			0.404551			0.202275	−	0.979329i	$-0.435166\pi$
$691$	10.6344			0.404551			0.202275	+	0.979329i	$0.435166\pi$
$692$	−0.314317	−	0.688257i	−0.0119485	−	0.0261636i
$693$	8.12078	−	2.38448i	0.308483	−	0.0905788i
$694$	0.213062	−	0.245887i	0.00808773	−	0.00933373i
$695$	−10.2659	−	6.59751i	−0.389409	−	0.250258i
$696$	−15.6025	−	18.0063i	−0.591413	−	0.682527i
$697$	−0.196455	−	1.36638i	−0.00744127	−	0.0517552i
$698$	−24.9816	−	7.33527i	−0.945569	−	0.277644i
$699$	6.02538	−	3.87228i	0.227901	−	0.146463i
$700$	0.0325559	−	0.226431i	0.00123050	−	0.00855830i
$701$	−9.84374	+	21.5548i	−0.371793	+	0.814113i	0.627575	+	0.778556i	$0.284048\pi$
$701$	−9.84374	+	21.5548i	−0.371793	+	0.814113i	−0.999368	+	0.0355568i	$0.988680\pi$
$702$	0.489146	−	1.07108i	0.0184616	−	0.0404254i
$703$	3.03351	−	21.0985i	0.114411	−	0.795747i
$704$	16.8547	−	10.8319i	0.635237	−	0.408242i
$705$	3.85552	+	1.13208i	0.145207	+	0.0426367i
$706$	−0.568396	−	3.95328i	−0.0213919	−	0.148784i
$707$	−39.3939	−	45.4630i	−1.48156	−	1.70981i
$708$	0.591257	+	0.379977i	0.0222208	+	0.0142804i
$709$	0.477125	−	0.550631i	0.0179188	−	0.0206794i	−0.746719	−	0.665139i	$-0.768372\pi$
$709$	0.477125	−	0.550631i	0.0179188	−	0.0206794i	0.764638	+	0.644460i	$0.222918\pi$
$710$	11.0096	−	3.23272i	0.413184	−	0.121322i
$711$	1.50967	+	3.30572i	0.0566172	+	0.123974i
$712$	−30.5743			−1.14582
$713$	−7.42059	−	0.747315i	−0.277903	−	0.0279872i
$714$	−1.96576			−0.0735665
$715$	0.884641	+	1.93709i	0.0330837	+	0.0724432i
$716$	0.830362	−	0.243816i	0.0310321	−	0.00911185i
$717$	16.3466	−	18.8650i	0.610475	−	0.704526i
$718$	33.5122	+	21.5370i	1.25066	+	0.803753i
$719$	2.77350	+	3.20080i	0.103434	+	0.119370i	0.805106	−	0.593131i	$-0.202108\pi$
$719$	2.77350	+	3.20080i	0.103434	+	0.119370i	−0.701672	+	0.712500i	$0.747563\pi$
$720$	−0.588575	−	4.09363i	−0.0219349	−	0.152560i
$721$	−13.3879	−	3.93105i	−0.498592	−	0.146400i
$722$	4.48643	−	2.88326i	0.166968	−	0.107304i
$723$	1.58134	−	10.9985i	0.0588107	−	0.409037i
$724$	0.742940	−	1.62681i	0.0276111	−	0.0604600i
$725$	3.56473	−	7.80566i	0.132391	−	0.289895i
$726$	−0.865839	+	6.02204i	−0.0321343	+	0.223499i
$727$	−21.6522	+	13.9150i	−0.803035	+	0.516079i	−0.876605	−	0.481211i	$-0.840197\pi$
$727$	−21.6522	+	13.9150i	−0.803035	+	0.516079i	0.0735702	+	0.997290i	$0.476561\pi$
$728$	7.09068	+	2.08201i	0.262798	+	0.0771645i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	−13.1022	−	15.1207i	−0.484934	−	0.559644i
$731$	−2.54590	−	1.63615i	−0.0941635	−	0.0605152i
$732$	0.320111	−	0.369428i	0.0118316	−	0.0136544i
$733$	15.2490	−	4.47751i	0.563235	−	0.165381i	0.0122931	−	0.999924i	$-0.496087\pi$
$733$	15.2490	−	4.47751i	0.563235	−	0.165381i	0.550942	+	0.834544i	$0.314269\pi$
$734$	11.3347	+	24.8196i	0.418372	+	0.916108i
$735$	3.57828			0.131987
$736$	−1.38714	+	1.30901i	−0.0511307	+	0.0482508i
$737$	−13.8616			−0.510598
$738$	−1.96433	−	4.30128i	−0.0723080	−	0.158332i
$739$	−19.5145	+	5.72996i	−0.717851	+	0.210780i	−0.620204	−	0.784441i	$-0.712950\pi$
$739$	−19.5145	+	5.72996i	−0.717851	+	0.210780i	−0.0976476	+	0.995221i	$0.531132\pi$
$740$	−0.206036	+	0.237778i	−0.00757402	+	0.00874088i
$741$	3.28048	+	2.10824i	0.120511	+	0.0774480i
$742$	20.9919	+	24.2260i	0.770639	+	0.889364i
$743$	−1.10395	−	7.67816i	−0.0405001	−	0.281684i	0.959500	−	0.281709i	$-0.0909013\pi$
$743$	−1.10395	−	7.67816i	−0.0405001	−	0.281684i	−1.00000		2.45336e-5i	$0.999992\pi$
$744$	−4.14295	−	1.21648i	−0.151888	−	0.0445983i
$745$	5.22134	−	3.35555i	0.191295	−	0.122938i
$746$	−2.77919	+	19.3297i	−0.101753	+	0.707709i
$747$	−1.14013	+	2.49654i	−0.0417152	+	0.0913436i
$748$	−0.0319377	+	0.0699339i	−0.00116776	+	0.00255704i
$749$	−5.41361	+	37.6525i	−0.197809	+	1.37579i
$750$	1.21045	−	0.777910i	0.0441994	−	0.0284052i
$751$	−45.4698	−	13.3512i	−1.65922	−	0.487190i	−0.688065	−	0.725649i	$-0.741540\pi$
$751$	−45.4698	−	13.3512i	−1.65922	−	0.487190i	−0.971153	+	0.238458i	$0.923358\pi$
$752$	−2.36506	−	16.4494i	−0.0862449	−	0.599846i
$753$	−10.7720	−	12.4315i	−0.392553	−	0.453030i
$754$	−8.50017	−	5.46273i	−0.309558	−	0.198941i
$755$	−5.87517	+	6.78031i	−0.213819	+	0.246761i
$756$	−0.219493	+	0.0644491i	−0.00798290	+	0.00234399i
$757$	12.5801	+	27.5465i	0.457230	+	1.00119i	0.988110	+	0.153747i	$0.0491341\pi$
$757$	12.5801	+	27.5465i	0.457230	+	1.00119i	−0.530880	+	0.847447i	$0.678139\pi$
$758$	6.90975			0.250973
$759$	−0.529363	−	12.4687i	−0.0192147	−	0.452585i
$760$	13.2305			0.479921
$761$	−5.28053	−	11.5627i	−0.191419	−	0.419149i	0.789451	−	0.613814i	$-0.210365\pi$
$761$	−5.28053	−	11.5627i	−0.191419	−	0.419149i	−0.980870	+	0.194665i	$0.937638\pi$
$762$	14.0944	−	4.13849i	0.510586	−	0.149922i
$763$	−35.7894	+	41.3032i	−1.29566	+	1.49527i
$764$	−0.0332654	−	0.0213784i	−0.00120350	−	0.000773442i
$765$	−0.275075	−	0.317453i	−0.00994534	−	0.0114775i
$766$	−2.48178	−	17.2612i	−0.0896705	−	0.623672i
$767$	−7.84612	−	2.30383i	−0.283307	−	0.0831865i
$768$	−1.41834	+	0.911509i	−0.0511798	+	0.0328912i
$769$	2.10663	−	14.6519i	0.0759670	−	0.528362i	−0.915932	−	0.401333i	$-0.868547\pi$
$769$	2.10663	−	14.6519i	0.0759670	−	0.528362i	0.991899	−	0.127029i	$-0.0405440\pi$
$770$	5.05893	−	11.0775i	0.182311	−	0.399206i
$771$	2.63440	−	5.76853i	0.0948756	−	0.207748i
$772$	0.186592	−	1.29777i	0.00671558	−	0.0467079i
$773$	7.50323	−	4.82203i	0.269872	−	0.173436i	−0.398705	−	0.917079i	$-0.630540\pi$
$773$	7.50323	−	4.82203i	0.269872	−	0.173436i	0.668577	+	0.743643i	$0.266904\pi$
$774$	−9.94661	−	2.92059i	−0.357524	−	0.104978i
$775$	−0.221318	−	1.53930i	−0.00794996	−	0.0552932i
$776$	15.8509	+	18.2929i	0.569013	+	0.656676i
$777$	−12.2393	−	7.86571i	−0.439082	−	0.282181i
$778$	25.2795	−	29.1741i	0.906315	−	1.04594i
$779$	15.0255	−	4.41188i	0.538343	−	0.158072i
$780$	−0.0239106	−	0.0523569i	−0.000856137	−	0.00187468i
$781$	20.7519			0.742563
$782$	−0.697921	+	2.81331i	−0.0249576	+	0.100604i
$783$	−8.58112			−0.306664
$784$	−6.14764	−	13.4615i	−0.219559	−	0.480766i
$785$	9.71486	−	2.85254i	0.346738	−	0.101812i
$786$	−1.85033	+	2.13539i	−0.0659990	+	0.0761669i
$787$	7.49702	+	4.81804i	0.267240	+	0.171745i	0.667397	−	0.744702i	$-0.267408\pi$
$787$	7.49702	+	4.81804i	0.267240	+	0.171745i	−0.400158	+	0.916446i	$0.631045\pi$
$788$	−0.605460	−	0.698739i	−0.0215686	−	0.0248915i
$789$	0.575515	+	4.00280i	0.0204889	+	0.142503i
$790$	5.01722	+	1.47319i	0.178505	+	0.0524137i
$791$	34.1578	−	21.9519i	1.21451	−	0.780519i
$792$	1.02826	−	7.15167i	0.0365375	−	0.254124i
$793$	−2.36264	+	5.17347i	−0.0839000	+	0.183715i
$794$	−15.5592	+	34.0700i	−0.552177	+	1.20910i
$795$	−0.974824	+	6.78005i	−0.0345734	+	0.240463i
$796$	−0.794923	+	0.510866i	−0.0281753	+	0.0181072i
$797$	43.0228	+	12.6326i	1.52395	+	0.447471i	0.933191	−	0.359381i	$-0.117012\pi$
$797$	43.0228	+	12.6326i	1.52395	+	0.447471i	0.590754	+	0.806852i	$0.298830\pi$
$798$	−3.17360	−	22.0729i	−0.112344	−	0.781372i
$799$	−1.10533	−	1.27562i	−0.0391037	−	0.0451281i
$800$	−0.334561	−	0.215009i	−0.0118285	−	0.00760172i
$801$	−7.21114	+	8.32210i	−0.254793	+	0.294047i
$802$	−31.2910	+	9.18786i	−1.10492	+	0.324435i
$803$	−15.0316	−	32.9146i	−0.530454	−	1.16153i
$804$	0.374659			0.0132132
$805$	3.75571	−	15.1392i	0.132371	−	0.533586i
$806$	−1.83114			−0.0644993
$807$	4.76953	+	10.4438i	0.167896	+	0.367640i
$808$	−49.2739	+	14.4681i	−1.73345	+	0.508986i
$809$	−0.587041	+	0.677482i	−0.0206393	+	0.0238190i	−0.765975	−	0.642870i	$-0.777744\pi$
$809$	−0.587041	+	0.677482i	−0.0206393	+	0.0238190i	0.745336	+	0.666689i	$0.232289\pi$
$810$	−1.21045	−	0.777910i	−0.0425309	−	0.0273330i
$811$	12.5033	+	14.4296i	0.439050	+	0.506691i	0.931546	−	0.363624i	$-0.118461\pi$
$811$	12.5033	+	14.4296i	0.439050	+	0.506691i	−0.492495	+	0.870315i	$0.663915\pi$
$812$	0.279366	+	1.94303i	0.00980383	+	0.0681872i
$813$	−12.4788	−	3.66410i	−0.437650	−	0.128506i
$814$	−14.0902	+	9.05522i	−0.493861	+	0.317385i
$815$	−2.26530	+	15.7555i	−0.0793500	+	0.551891i
$816$	−0.721664	+	1.58022i	−0.0252633	+	0.0553189i
$817$	14.2616	−	31.2286i	0.498952	−	1.09255i
$818$	6.78403	−	47.1839i	0.237198	−	1.64975i
$819$	2.23909	−	1.43897i	0.0782400	−	0.0502818i
$820$	−0.221782	−	0.0651210i	−0.00774495	−	0.00227412i
$821$	1.35094	+	9.39598i	0.0471481	+	0.327922i	0.999721	+	0.0236122i	$0.00751669\pi$
$821$	1.35094	+	9.39598i	0.0471481	+	0.327922i	−0.952573	+	0.304310i	$0.901574\pi$
$822$	19.7998	+	22.8502i	0.690598	+	0.796992i
$823$	−13.0743	−	8.40234i	−0.455741	−	0.292887i	0.292559	−	0.956248i	$-0.405493\pi$
$823$	−13.0743	−	8.40234i	−0.455741	−	0.292887i	−0.748300	+	0.663360i	$0.769130\pi$
$824$	−7.80036	+	9.00210i	−0.271739	+	0.313603i
$825$	2.49684	−	0.733138i	0.0869287	−	0.0255246i
$826$	19.4262	+	42.5374i	0.675923	+	1.48006i
$827$	39.4779			1.37278			0.686391	−	0.727233i	$-0.259194\pi$
$827$	39.4779			1.37278			0.686391	+	0.727233i	$0.259194\pi$
$828$	0.0143079	+	0.337012i	0.000497235	+	0.0117120i
$829$	36.3776			1.26345			0.631723	−	0.775194i	$-0.282348\pi$
$829$	36.3776			1.26345			0.631723	+	0.775194i	$0.282348\pi$
$830$	1.64050	+	3.59218i	0.0569424	+	0.124687i
$831$	19.2660	−	5.65701i	0.668330	−	0.196239i
$832$	4.12603	−	4.76169i	0.143044	−	0.165082i
$833$	−1.26445	−	0.812615i	−0.0438107	−	0.0281555i
$834$	11.4985	+	13.2700i	0.398160	+	0.459501i
$835$	−2.21854	−	15.4303i	−0.0767758	−	0.533987i
$836$	−0.836829	−	0.245715i	−0.0289423	−	0.00849823i
$837$	−1.30826	+	0.840765i	−0.0452199	+	0.0290611i
$838$	3.16419	−	22.0075i	0.109305	−	0.760235i
$839$	19.3778	−	42.4315i	0.668997	−	1.46490i	−0.204897	−	0.978784i	$-0.565686\pi$
$839$	19.3778	−	42.4315i	0.668997	−	1.46490i	0.873894	−	0.486116i	$-0.161587\pi$
$840$	3.75139	−	8.21439i	0.129435	−	0.283424i
$841$	−6.35232	+	44.1814i	−0.219045	+	1.52349i
$842$	41.3268	−	26.5591i	1.42422	−	0.915289i
$843$	−4.83010	−	1.41824i	−0.166357	−	0.0488469i
$844$	−0.146970	−	1.02220i	−0.00505892	−	0.0351856i
$845$	−8.07464	−	9.31863i	−0.277776	−	0.320571i
$846$	−4.86394	−	3.12586i	−0.167226	−	0.107469i
$847$	−9.00582	+	10.3933i	−0.309444	+	0.357117i
$848$	27.1812	−	7.98113i	0.933407	−	0.274073i
$849$	−3.08556	−	6.75644i	−0.105896	−	0.231880i
$850$	−0.604396			−0.0207306
$851$	−15.6025	+	14.7237i	−0.534847	+	0.504722i
$852$	−0.560896			−0.0192160
$853$	−18.7143	−	40.9787i	−0.640767	−	1.40308i	−0.899408	−	0.437110i	$-0.856002\pi$
$853$	−18.7143	−	40.9787i	−0.640767	−	1.40308i	0.258641	−	0.965974i	$-0.416725\pi$
$854$	31.2068	−	9.16315i	1.06788	−	0.313556i
$855$	3.12049	−	3.60124i	0.106719	−	0.123160i
$856$	27.3186	+	17.5566i	0.933730	+	0.600072i
$857$	−21.0868	−	24.3355i	−0.720312	−	0.831285i	0.271032	−	0.962570i	$-0.412635\pi$
$857$	−21.0868	−	24.3355i	−0.720312	−	0.831285i	−0.991345	+	0.131286i	$0.958089\pi$
$858$	−0.436069	−	3.03293i	−0.0148872	−	0.103542i
$859$	39.3177	+	11.5447i	1.34150	+	0.393900i	0.872205	−	0.489140i	$-0.162689\pi$
$859$	39.3177	+	11.5447i	1.34150	+	0.393900i	0.469296	+	0.883041i	$0.344508\pi$
$860$	−0.426297	+	0.273964i	−0.0145366	+	0.00934210i
$861$	1.52114	−	10.5798i	0.0518404	−	0.360558i
$862$	−22.5764	+	49.4355i	−0.768956	+	1.68378i
$863$	−12.6606	+	27.7229i	−0.430973	+	0.943698i	0.562195	+	0.827004i	$0.309957\pi$
$863$	−12.6606	+	27.7229i	−0.430973	+	0.943698i	−0.993168	+	0.116694i	$0.962770\pi$
$864$	−0.0565976	+	0.393645i	−0.00192549	+	0.0133921i
$865$	9.04982	−	5.81597i	0.307703	−	0.197749i
$866$	20.2719	+	5.95236i	0.688866	+	0.202269i
$867$	−2.39424	−	16.6523i	−0.0813127	−	0.565542i
$868$	0.232967	+	0.268858i	0.00790742	+	0.00912564i
$869$	7.95566	+	5.11279i	0.269877	+	0.173440i
$870$	−8.08562	+	9.33130i	−0.274128	+	0.316361i
$871$	−4.18256	+	1.22811i	−0.141721	+	0.0416129i
$872$	19.3813	+	42.4391i	0.656333	+	1.43717i
$873$	8.71770			0.295049
$874$	−32.7165	−	3.29482i	−1.10665	−	0.111449i
$875$	3.25243			0.109952
$876$	0.406283	+	0.889637i	0.0137270	+	0.0300580i
$877$	−33.5204	+	9.84247i	−1.13190	+	0.332357i	−0.793455	−	0.608629i	$-0.791720\pi$
$877$	−33.5204	+	9.84247i	−1.13190	+	0.332357i	−0.338448	+	0.940985i	$0.609902\pi$
$878$	−1.40979	+	1.62699i	−0.0475781	+	0.0549081i
$879$	28.0248	+	18.0105i	0.945254	+	0.607478i
$880$	−7.04773	−	8.13351i	−0.237579	−	0.274181i
$881$	2.78281	+	19.3549i	0.0937552	+	0.652082i	0.981460	+	0.191668i	$0.0613898\pi$
$881$	2.78281	+	19.3549i	0.0937552	+	0.652082i	−0.887705	+	0.460414i	$0.847701\pi$
$882$	−4.94011	−	1.45055i	−0.166342	−	0.0488425i
$883$	26.2702	−	16.8829i	0.884064	−	0.568154i	−0.0179602	−	0.999839i	$-0.505717\pi$
$883$	26.2702	−	16.8829i	0.884064	−	0.568154i	0.902024	+	0.431685i	$0.142081\pi$
$884$	−0.00344080	+	0.0239313i	−0.000115727	+	0.000804897i
$885$	−4.15106	+	9.08956i	−0.139536	+	0.305542i
$886$	2.56706	−	5.62107i	0.0862420	−	0.188844i
$887$	−5.75386	+	40.0190i	−0.193196	+	1.34371i	0.630286	+	0.776363i	$0.282937\pi$
$887$	−5.75386	+	40.0190i	−0.193196	+	1.34371i	−0.823482	+	0.567342i	$0.807972\pi$
$888$	−10.4484	+	6.71479i	−0.350626	+	0.225334i
$889$	31.8591	+	9.35468i	1.06852	+	0.313746i
$890$	2.25489	+	15.6831i	0.0755841	+	0.525699i
$891$	−1.70411	−	1.96665i	−0.0570898	−	0.0658852i
$892$	−1.03456	−	0.664873i	−0.0346397	−	0.0222616i
$893$	12.5390	−	14.4708i	0.419603	−	0.484247i
$894$	−8.56874	+	2.51601i	−0.286582	+	0.0841479i
$895$	5.11135	+	11.1923i	0.170854	+	0.374118i
$896$	−38.6178			−1.29013
$897$	−1.26443	−	3.71538i	−0.0422182	−	0.124053i
$898$	−47.3918			−1.58149
$899$	5.54360	+	12.1388i	0.184890	+	0.404852i
$900$	−0.0674860	+	0.0198157i	−0.00224953	+	0.000660523i
$901$	1.88420	−	2.17448i	0.0627717	−	0.0724424i
$902$	−10.3516	−	6.65257i	−0.344671	−	0.221506i
$903$	−15.3451	−	17.7092i	−0.510653	−	0.589325i
$904$	−4.93296	−	34.3095i	−0.164068	−	1.14112i
$905$	24.3973	+	7.16369i	0.810993	+	0.238129i
$906$	10.8597	−	6.97912i	0.360790	−	0.231866i
$907$	2.75833	−	19.1846i	0.0915888	−	0.637014i	−0.891382	−	0.453253i	$-0.850264\pi$
$907$	2.75833	−	19.1846i	0.0915888	−	0.637014i	0.982971	−	0.183761i	$-0.0588274\pi$
$908$	−0.263531	+	0.577053i	−0.00874559	+	0.0191502i
$909$	−7.68342	+	16.8244i	−0.254843	+	0.558029i
$910$	0.545023	−	3.79071i	0.0180673	−	0.125661i
$911$	−19.0996	+	12.2745i	−0.632797	+	0.406674i	−0.817344	−	0.576150i	$-0.804554\pi$
$911$	−19.0996	+	12.2745i	−0.632797	+	0.406674i	0.184547	+	0.982824i	$0.440918\pi$
$912$	−18.9090	−	5.55217i	−0.626138	−	0.183851i
$913$	1.01642	+	7.06932i	0.0336384	+	0.233961i
$914$	20.2161	+	23.3306i	0.668688	+	0.771707i
$915$	5.84664	+	3.75741i	0.193284	+	0.124216i
$916$	0.481798	−	0.556025i	0.0159191	−	0.0183716i
$917$	−6.12814	+	1.79938i	−0.202369	+	0.0594209i
$918$	0.251075	+	0.549778i	0.00828672	+	0.0181454i
$919$	−34.5552			−1.13987			−0.569936	−	0.821689i	$-0.693032\pi$
$919$	−34.5552			−1.13987			−0.569936	+	0.821689i	$0.693032\pi$
$920$	−10.4242	−	8.28526i	−0.343676	−	0.273157i
$921$	26.9780			0.888955
$922$	−3.52769	−	7.72457i	−0.116178	−	0.254395i
$923$	6.26165	−	1.83859i	0.206105	−	0.0605178i
$924$	−0.389832	+	0.449890i	−0.0128245	+	0.0148003i
$925$	−3.76312	−	2.41841i	−0.123731	−	0.0795169i
$926$	25.3942	+	29.3064i	0.834504	+	0.963069i
$927$	0.610540	+	4.24640i	0.0200527	+	0.139470i
$928$	3.27442	+	0.961455i	0.107488	+	0.0315613i
$929$	31.6235	−	20.3232i	1.03753	−	0.666783i	0.0931586	−	0.995651i	$-0.470304\pi$
$929$	31.6235	−	20.3232i	1.03753	−	0.666783i	0.944376	+	0.328868i	$0.106667\pi$
$930$	−0.318446	+	2.21484i	−0.0104423	+	0.0726276i
$931$	7.08323	−	15.5101i	0.232143	−	0.508323i
$932$	−0.209272	+	0.458242i	−0.00685494	+	0.0150102i
$933$	2.54119	−	17.6744i	0.0831949	−	0.578633i
$934$	44.9194	−	28.8680i	1.46981	−	0.944589i
$935$	−1.04880	−	0.307955i	−0.0342994	−	0.0100712i
$936$	−0.323362	−	2.24903i	−0.0105694	−	0.0735119i
$937$	5.99477	+	6.91834i	0.195841	+	0.226012i	0.845173	−	0.534492i	$-0.179497\pi$
$937$	5.99477	+	6.91834i	0.195841	+	0.226012i	−0.649333	+	0.760505i	$0.724952\pi$
$938$	20.9710	+	13.4772i	0.684727	+	0.440047i
$939$	−11.0727	+	12.7786i	−0.361343	+	0.417013i
$940$	−0.271178	+	0.0796250i	−0.00884485	+	0.00259708i
$941$	−15.8794	−	34.7710i	−0.517654	−	1.13350i	−0.970320	−	0.241824i	$-0.922254\pi$
$941$	−15.8794	−	34.7710i	−0.517654	−	1.13350i	0.452666	−	0.891680i	$-0.350473\pi$
$942$	−14.5685			−0.474668
$943$	−14.6013	−	5.93323i	−0.475482	−	0.193213i
$944$	41.3265			1.34506
$945$	−1.35111	−	2.95851i	−0.0439515	−	0.0962404i
$946$	−25.8835	+	7.60009i	−0.841546	+	0.247100i
$947$	7.07631	−	8.16650i	0.229949	−	0.265376i	−0.629036	−	0.777376i	$-0.716550\pi$
$947$	7.07631	−	8.16650i	0.229949	−	0.265376i	0.858985	+	0.512001i	$0.171096\pi$
$948$	−0.215030	−	0.138192i	−0.00698386	−	0.00448825i
$949$	−7.45178	−	8.59982i	−0.241895	−	0.279162i
$950$	−0.975764	−	6.78659i	−0.0316580	−	0.220186i
$951$	−26.3613	−	7.74038i	−0.854824	−	0.250999i
$952$	−3.19108	+	2.05079i	−0.103424	+	0.0664663i
$953$	1.77448	−	12.3418i	0.0574810	−	0.399789i	−0.940687	−	0.339277i	$-0.889818\pi$
$953$	1.77448	−	12.3418i	0.0574810	−	0.399789i	0.998167	−	0.0605119i	$-0.0192733\pi$
$954$	4.09429	−	8.96524i	0.132557	−	0.290260i
$955$	0.233548	−	0.511398i	0.00755743	−	0.0165485i
$956$	−0.249862	+	1.73783i	−0.00808113	+	0.0562055i
$957$	−18.7854	+	12.0726i	−0.607245	+	0.390252i
$958$	5.52248	+	1.62155i	0.178423	+	0.0523897i
$959$	9.72634	+	67.6482i	0.314080	+	2.18447i
$960$	−5.04192	−	5.81868i	−0.162727	−	0.187797i
$961$	−24.0444	−	15.4524i	−0.775624	−	0.498464i
$962$	−3.44927	+	3.98067i	−0.111209	+	0.128342i
$963$	11.2220	−	3.29508i	0.361624	−	0.106182i
$964$	0.324660	+	0.710907i	0.0104566	+	0.0228968i
$965$	18.6410			0.600076
$966$	−11.3221	+	19.3784i	−0.364283	+	0.623490i
$967$	37.0043			1.18998			0.594988	−	0.803734i	$-0.297157\pi$
$967$	37.0043			1.18998			0.594988	+	0.803734i	$0.297157\pi$
$968$	4.87698	+	10.6791i	0.156752	+	0.343239i
$969$	−1.92051	+	0.563914i	−0.0616958	+	0.0181155i
$970$	8.21431	−	9.47982i	0.263746	−	0.304379i
$971$	6.50118	+	4.17805i	0.208633	+	0.134080i	0.640785	−	0.767721i	$-0.278609\pi$
$971$	6.50118	+	4.17805i	0.208633	+	0.134080i	−0.432152	+	0.901801i	$0.642246\pi$
$972$	0.0460597	+	0.0531557i	0.00147736	+	0.00170497i
$973$	5.64845	+	39.2858i	0.181081	+	1.25945i
$974$	1.24940	+	0.366857i	0.0400333	+	0.0117549i
$975$	0.688435	−	0.442431i	0.0220476	−	0.0141691i
$976$	4.09055	−	28.4504i	0.130935	−	0.910675i
$977$	−22.4639	+	49.1892i	−0.718685	+	1.57370i	0.0970529	+	0.995279i	$0.469058\pi$
$977$	−22.4639	+	49.1892i	−0.718685	+	1.57370i	−0.815738	+	0.578422i	$0.803669\pi$
$978$	9.51432	−	20.8335i	0.304234	−	0.666181i
$979$	−4.07806	+	28.3635i	−0.130335	+	0.906503i
$980$	−0.211726	+	0.136068i	−0.00676333	+	0.00434653i
$981$	16.1228	+	4.73407i	0.514760	+	0.151147i
$982$	−3.64387	−	25.3437i	−0.116280	−	0.808749i
$983$	−26.3920	−	30.4580i	−0.841774	−	0.971459i	0.158099	−	0.987423i	$-0.449464\pi$
$983$	−26.3920	−	30.4580i	−0.841774	−	0.971459i	−0.999873	+	0.0159645i	$0.994918\pi$
$984$	−7.67611	−	4.93313i	−0.244705	−	0.157263i
$985$	8.60823	−	9.93443i	0.274281	−	0.316537i
$986$	4.97631	−	1.46118i	0.158478	−	0.0465334i
$987$	−5.42913	−	11.8881i	−0.172811	−	0.378404i
$988$	−0.274273			−0.00872578
$989$	−30.7927	+	15.6738i	−0.979152	+	0.498397i
$990$	−3.74428			−0.119001
$991$	21.0134	+	46.0130i	0.667514	+	1.46165i	0.875351	+	0.483488i	$0.160630\pi$
$991$	21.0134	+	46.0130i	0.667514	+	1.46165i	−0.207838	+	0.978163i	$0.566643\pi$
$992$	0.593411	−	0.174241i	0.0188408	−	0.00553216i
$993$	18.8516	−	21.7559i	0.598238	−	0.690403i
$994$	−31.3953	−	20.1766i	−0.995800	−	0.639962i
$995$	−8.79782	−	10.1532i	−0.278910	−	0.321879i
$996$	−0.0274723	−	0.191074i	−0.000870492	−	0.00605441i
$997$	16.2958	+	4.78487i	0.516092	+	0.151538i	0.529399	−	0.848373i	$-0.322418\pi$
$997$	16.2958	+	4.78487i	0.516092	+	0.151538i	−0.0133067	+	0.999911i	$0.504236\pi$
$998$	−35.0705	+	22.5384i	−1.11014	+	0.713441i
$999$	−0.636607	+	4.42770i	−0.0201414	+	0.140086i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.m.a.211.3	yes	30
23.6	even	11	inner	345.2.m.a.121.3	✓	30
23.11	odd	22		7935.2.a.bq.1.12		15
23.12	even	11		7935.2.a.bp.1.12		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.a.121.3	✓	30	23.6	even	11	inner
345.2.m.a.211.3	yes	30	1.1	even	1	trivial
7935.2.a.bp.1.12		15	23.12	even	11
7935.2.a.bq.1.12		15	23.11	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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.597726 + 1.30884i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.0460597 + 0.0531557i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(0.942257 + 1.08742i) q^{6} +(0.462869 + 3.21932i) q^{7} +(2.66406 + 0.782239i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.597726 + 1.30884i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.0460597 + 0.0531557i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(0.942257 + 1.08742i) q^{6} +(0.462869 + 3.21932i) q^{7} +(2.66406 + 0.782239i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.204772 - 1.42422i) q^{10} +(1.08101 - 2.36709i) q^{11} +(-0.0292182 + 0.0639790i) q^{12} +(0.116463 - 0.810015i) q^{13} +(-3.93690 + 2.53009i) q^{14} +(-0.959493 - 0.281733i) q^{15} +(0.588575 + 4.09363i) q^{16} +(0.275075 + 0.317453i) q^{17} +(1.21045 + 0.777910i) q^{18} +(-3.12049 + 3.60124i) q^{19} +(0.0674860 - 0.0198157i) q^{20} +(1.35111 + 2.95851i) q^{21} +3.74428 q^{22} +(4.71379 - 0.883258i) q^{23} +2.77653 q^{24} +(0.415415 + 0.909632i) q^{25} +(1.12979 - 0.331737i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-0.192445 - 0.123677i) q^{28} +(-5.61944 - 6.48518i) q^{29} +(-0.204772 - 1.42422i) q^{30} +(-1.49213 - 0.438130i) q^{31} +(-0.334561 + 0.215009i) q^{32} +(0.370338 - 2.57576i) q^{33} +(-0.251075 + 0.549778i) q^{34} +(1.35111 - 2.95851i) q^{35} +(-0.0100097 + 0.0696192i) q^{36} +(-3.76312 + 2.41841i) q^{37} +(-6.57864 - 1.93166i) q^{38} +(-0.116463 - 0.810015i) q^{39} +(-1.81824 - 2.09836i) q^{40} +(-2.76464 - 1.77673i) q^{41} +(-3.06462 + 3.53676i) q^{42} +(-6.91281 + 2.02978i) q^{43} +(0.0760331 + 0.166489i) q^{44} -1.00000 q^{45} +(3.97360 + 5.64165i) q^{46} -4.01828 q^{47} +(1.71804 + 3.76199i) q^{48} +(-3.43334 + 1.00812i) q^{49} +(-0.942257 + 1.08742i) q^{50} +(0.353369 + 0.227096i) q^{51} +(0.0376927 + 0.0434997i) q^{52} +(-0.974824 - 6.78005i) q^{53} +(1.38058 + 0.405375i) q^{54} +(-2.18915 + 1.40688i) q^{55} +(-1.28517 + 8.93854i) q^{56} +(-1.97950 + 4.33451i) q^{57} +(5.12916 - 11.2313i) q^{58} +(1.42209 - 9.89086i) q^{59} +(0.0591696 - 0.0380260i) q^{60} +(-6.66840 - 1.95802i) q^{61} +(-0.318446 - 2.21484i) q^{62} +(2.12989 + 2.45802i) q^{63} +(6.47700 + 4.16251i) q^{64} +(-0.535902 + 0.618464i) q^{65} +(3.59261 - 1.05489i) q^{66} +(-2.21282 - 4.84540i) q^{67} -0.0295443 q^{68} +(4.27401 - 2.17551i) q^{69} +4.67981 q^{70} +(3.31278 + 7.25398i) q^{71} +(2.66406 - 0.782239i) q^{72} +(9.10592 - 10.5088i) q^{73} +(-5.41463 - 3.47977i) q^{74} +(0.654861 + 0.755750i) q^{75} +(-0.0476976 - 0.331744i) q^{76} +(8.12078 + 2.38448i) q^{77} +(0.990566 - 0.636598i) q^{78} +(-0.517191 + 3.59714i) q^{79} +(1.71804 - 3.76199i) q^{80} +(0.415415 - 0.909632i) q^{81} +(0.672949 - 4.68047i) q^{82} +(-2.30887 + 1.48382i) q^{83} +(-0.219493 - 0.0644491i) q^{84} +(-0.0597794 - 0.415775i) q^{85} +(-6.78863 - 7.83450i) q^{86} +(-7.21890 - 4.63931i) q^{87} +(4.73151 - 5.46045i) q^{88} +(-10.5657 + 3.10236i) q^{89} +(-0.597726 - 1.30884i) q^{90} +2.66161 q^{91} +(-0.170166 + 0.291248i) q^{92} -1.55513 q^{93} +(-2.40184 - 5.25929i) q^{94} +(4.57210 - 1.34249i) q^{95} +(-0.260433 + 0.300556i) q^{96} +(7.33379 + 4.71314i) q^{97} +(-3.37166 - 3.89111i) q^{98} +(-0.370338 - 2.57576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9} - 7 q^{11} - 2 q^{12} + 7 q^{13} - 47 q^{14} - 3 q^{15} + 26 q^{16} + 15 q^{17} - 7 q^{19} - 2 q^{20} - 12 q^{21} - 18 q^{22} + 12 q^{23} - 3 q^{25} - 18 q^{26} + 3 q^{27} + 2 q^{28} - 6 q^{29} + 22 q^{31} + 33 q^{32} - 4 q^{33} - 53 q^{34} - 12 q^{35} - 9 q^{36} - 23 q^{37} + 21 q^{38} - 7 q^{39} + 11 q^{40} + 26 q^{41} + 3 q^{42} - 19 q^{43} - 47 q^{44} - 30 q^{45} - 44 q^{46} + 14 q^{47} + 7 q^{48} + 2 q^{49} - 11 q^{50} - 15 q^{51} + 55 q^{52} - 14 q^{53} - 11 q^{54} - 4 q^{55} + 6 q^{56} - 26 q^{57} - 18 q^{58} + 40 q^{59} - 9 q^{60} + 37 q^{61} + 19 q^{62} - 10 q^{63} + 14 q^{64} + 4 q^{65} - 4 q^{66} - 108 q^{67} + 54 q^{68} + 21 q^{69} - 30 q^{70} + 39 q^{71} + 22 q^{72} + 57 q^{73} - 11 q^{74} + 3 q^{75} + 22 q^{76} + 2 q^{77} + 7 q^{78} + 55 q^{79} + 7 q^{80} - 3 q^{81} - 26 q^{82} - 79 q^{83} - 2 q^{84} + 18 q^{85} - 44 q^{86} - 5 q^{87} - 8 q^{88} - 30 q^{89} + 40 q^{91} + 35 q^{92} + 44 q^{93} - 29 q^{94} + 7 q^{95} + 22 q^{96} - 52 q^{97} + 28 q^{98} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9 - 7 * q^11 - 2 * q^12 + 7 * q^13 - 47 * q^14 - 3 * q^15 + 26 * q^16 + 15 * q^17 - 7 * q^19 - 2 * q^20 - 12 * q^21 - 18 * q^22 + 12 * q^23 - 3 * q^25 - 18 * q^26 + 3 * q^27 + 2 * q^28 - 6 * q^29 + 22 * q^31 + 33 * q^32 - 4 * q^33 - 53 * q^34 - 12 * q^35 - 9 * q^36 - 23 * q^37 + 21 * q^38 - 7 * q^39 + 11 * q^40 + 26 * q^41 + 3 * q^42 - 19 * q^43 - 47 * q^44 - 30 * q^45 - 44 * q^46 + 14 * q^47 + 7 * q^48 + 2 * q^49 - 11 * q^50 - 15 * q^51 + 55 * q^52 - 14 * q^53 - 11 * q^54 - 4 * q^55 + 6 * q^56 - 26 * q^57 - 18 * q^58 + 40 * q^59 - 9 * q^60 + 37 * q^61 + 19 * q^62 - 10 * q^63 + 14 * q^64 + 4 * q^65 - 4 * q^66 - 108 * q^67 + 54 * q^68 + 21 * q^69 - 30 * q^70 + 39 * q^71 + 22 * q^72 + 57 * q^73 - 11 * q^74 + 3 * q^75 + 22 * q^76 + 2 * q^77 + 7 * q^78 + 55 * q^79 + 7 * q^80 - 3 * q^81 - 26 * q^82 - 79 * q^83 - 2 * q^84 + 18 * q^85 - 44 * q^86 - 5 * q^87 - 8 * q^88 - 30 * q^89 + 40 * q^91 + 35 * q^92 + 44 * q^93 - 29 * q^94 + 7 * q^95 + 22 * q^96 - 52 * q^97 + 28 * q^98 + 4 * q^99

Introduction

L-functions

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