LMFDB - Embedded newform 414.2.m.a.25.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(13,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([22, 42]))

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

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

chi := DirichletCharacter("414.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.m (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			25.6
Character	$\chi$	$=$	414.25
Dual form			414.2.m.a.265.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.888835 - 0.458227i) q^{2} +(0.143725 - 1.72608i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-0.196850 - 0.811428i) q^{5} +(-0.663187 - 1.60006i) q^{6} +(-1.10397 - 3.18970i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-2.95869 - 0.496161i) q^{9} +O(q^{10})$	\(q+(0.888835 - 0.458227i) q^{2} +(0.143725 - 1.72608i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-0.196850 - 0.811428i) q^{5} +(-0.663187 - 1.60006i) q^{6} +(-1.10397 - 3.18970i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-2.95869 - 0.496161i) q^{9} +(-0.546785 - 0.631024i) q^{10} +(0.108882 + 2.28571i) q^{11} +(-1.32265 - 1.11830i) q^{12} +(-1.57591 + 4.55328i) q^{13} +(-2.44285 - 2.32925i) q^{14} +(-1.42888 + 0.223156i) q^{15} +(-0.327068 - 0.945001i) q^{16} +(2.81051 - 6.15416i) q^{17} +(-2.85714 + 0.914743i) q^{18} +(1.29911 + 2.84465i) q^{19} +(-0.775154 - 0.310325i) q^{20} +(-5.66434 + 1.44709i) q^{21} +(1.14415 + 1.98173i) q^{22} +(3.19053 + 3.58058i) q^{23} +(-1.68805 - 0.387909i) q^{24} +(3.82451 - 1.97167i) q^{25} +(0.685713 + 4.76924i) q^{26} +(-1.28165 + 5.03561i) q^{27} +(-3.23862 - 0.950944i) q^{28} +(-6.11245 - 8.58374i) q^{29} +(-1.16778 + 0.853100i) q^{30} +(4.24974 - 1.70134i) q^{31} +(-0.723734 - 0.690079i) q^{32} +(3.96096 + 0.140575i) q^{33} +(-0.321918 - 6.75789i) q^{34} +(-2.37090 + 1.52368i) q^{35} +(-2.12037 + 2.12227i) q^{36} +(10.1097 - 2.96848i) q^{37} +(2.45819 + 1.93314i) q^{38} +(7.63282 + 3.37456i) q^{39} +(-0.831184 + 0.0793684i) q^{40} +(-1.55510 - 6.41022i) q^{41} +(-4.37157 + 3.88178i) q^{42} +(-1.12842 - 0.451751i) q^{43} +(1.92504 + 1.23715i) q^{44} +(0.179819 + 2.49843i) q^{45} +(4.47657 + 1.72056i) q^{46} +(-3.09441 + 5.35967i) q^{47} +(-1.67815 + 0.428724i) q^{48} +(-3.45308 + 2.71553i) q^{49} +(2.49589 - 3.50499i) q^{50} +(-10.2186 - 5.73567i) q^{51} +(2.79488 + 3.92486i) q^{52} +(-8.01652 + 9.25156i) q^{53} +(1.16827 + 5.06312i) q^{54} +(1.83326 - 0.538292i) q^{55} +(-3.31435 + 0.638788i) q^{56} +(5.09681 - 1.83352i) q^{57} +(-9.36626 - 4.82864i) q^{58} +(2.75125 - 7.94920i) q^{59} +(-0.647054 + 1.29337i) q^{60} +(9.72258 + 7.64592i) q^{61} +(2.99772 - 3.45955i) q^{62} +(1.68368 + 9.98507i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(4.00488 + 0.382419i) q^{65} +(3.58506 - 1.69007i) q^{66} +(-0.245875 + 5.16156i) q^{67} +(-3.38278 - 5.85914i) q^{68} +(6.63891 - 4.99248i) q^{69} +(-1.40915 + 2.44071i) q^{70} +(3.46698 + 2.22810i) q^{71} +(-0.912176 + 2.85796i) q^{72} +(-0.979365 - 2.14451i) q^{73} +(7.62564 - 7.27103i) q^{74} +(-2.85358 - 6.88478i) q^{75} +(3.07074 + 0.591837i) q^{76} +(7.17053 - 2.87065i) q^{77} +(8.33063 - 0.498135i) q^{78} +(0.0200833 - 0.00387073i) q^{79} +(-0.702417 + 0.451416i) q^{80} +(8.50765 + 2.93597i) q^{81} +(-4.31956 - 4.98504i) q^{82} +(0.182557 - 0.752511i) q^{83} +(-2.10687 + 5.45343i) q^{84} +(-5.54691 - 1.06908i) q^{85} +(-1.20998 + 0.115539i) q^{86} +(-15.6947 + 9.31687i) q^{87} +(2.27794 + 0.217517i) q^{88} +(0.395747 + 2.75248i) q^{89} +(1.30468 + 2.13830i) q^{90} +16.2634 q^{91} +(4.76734 - 0.521986i) q^{92} +(-2.32585 - 7.57990i) q^{93} +(-0.294476 + 6.18180i) q^{94} +(2.05250 - 1.61410i) q^{95} +(-1.29515 + 1.15004i) q^{96} +(0.839000 - 0.799985i) q^{97} +(-1.82489 + 3.99595i) q^{98} +(0.811933 - 6.81672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) $ 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.888835	−	0.458227i	0.628502	−	0.324015i
$2$	0.888835	−	0.458227i	0.628502	−	0.324015i
$3$	0.143725	−	1.72608i	0.0829797	−	0.996551i
$3$	0.143725	−	1.72608i	0.0829797	−	0.996551i
$4$	0.580057	−	0.814576i	0.290028	−	0.407288i
$5$	−0.196850	−	0.811428i	−0.0880341	−	0.362882i	0.910706	−	0.413054i	$-0.135538\pi$
$5$	−0.196850	−	0.811428i	−0.0880341	−	0.362882i	−0.998741	+	0.0501726i	$0.984023\pi$
$6$	−0.663187	−	1.60006i	−0.270745	−	0.653221i
$7$	−1.10397	−	3.18970i	−0.417260	−	1.20559i	−0.936409	−	0.350910i	$-0.885872\pi$
$7$	−1.10397	−	3.18970i	−0.417260	−	1.20559i	0.519149	−	0.854684i	$-0.326249\pi$
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	−2.95869	−	0.496161i	−0.986229	−	0.165387i
$10$	−0.546785	−	0.631024i	−0.172909	−	0.199547i
$11$	0.108882	+	2.28571i	0.0328291	+	0.689167i	0.953963	+	0.299923i	$0.0969609\pi$
$11$	0.108882	+	2.28571i	0.0328291	+	0.689167i	−0.921134	+	0.389245i	$0.872736\pi$
$12$	−1.32265	−	1.11830i	−0.381817	−	0.322825i
$13$	−1.57591	+	4.55328i	−0.437078	+	1.26285i	0.484545	+	0.874766i	$0.338985\pi$
$13$	−1.57591	+	4.55328i	−0.437078	+	1.26285i	−0.921623	+	0.388087i	$0.873136\pi$
$14$	−2.44285	−	2.32925i	−0.652879	−	0.622519i
$15$	−1.42888	+	0.223156i	−0.368935	+	0.0576187i
$16$	−0.327068	−	0.945001i	−0.0817670	−	0.236250i
$17$	2.81051	−	6.15416i	0.681649	−	1.49260i	−0.179237	−	0.983806i	$-0.557363\pi$
$17$	2.81051	−	6.15416i	0.681649	−	1.49260i	0.860886	−	0.508798i	$-0.169910\pi$
$18$	−2.85714	+	0.914743i	−0.673434	+	0.215607i
$19$	1.29911	+	2.84465i	0.298036	+	0.652608i	0.998109	−	0.0614629i	$-0.0195766\pi$
$19$	1.29911	+	2.84465i	0.298036	+	0.652608i	−0.700073	+	0.714071i	$0.746849\pi$
$20$	−0.775154	−	0.310325i	−0.173330	−	0.0693908i
$21$	−5.66434	+	1.44709i	−1.23606	+	0.315781i
$22$	1.14415	+	1.98173i	0.243934	+	0.422506i
$23$	3.19053	+	3.58058i	0.665271	+	0.746602i
$23$	3.19053	+	3.58058i	0.665271	+	0.746602i
$24$	−1.68805	−	0.387909i	−0.344573	−	0.0791815i
$25$	3.82451	−	1.97167i	0.764902	−	0.394335i
$26$	0.685713	+	4.76924i	0.134479	+	0.935325i
$27$	−1.28165	+	5.03561i	−0.246654	+	0.969104i
$28$	−3.23862	−	0.950944i	−0.612041	−	0.179711i
$29$	−6.11245	−	8.58374i	−1.13505	−	1.59396i	−0.735920	−	0.677068i	$-0.763250\pi$
$29$	−6.11245	−	8.58374i	−1.13505	−	1.59396i	−0.399134	−	0.916893i	$-0.630689\pi$
$30$	−1.16778	+	0.853100i	−0.213207	+	0.155754i
$31$	4.24974	−	1.70134i	0.763276	−	0.305570i	0.0428315	−	0.999082i	$-0.486362\pi$
$31$	4.24974	−	1.70134i	0.763276	−	0.305570i	0.720444	+	0.693513i	$0.243938\pi$
$32$	−0.723734	−	0.690079i	−0.127939	−	0.121990i
$33$	3.96096	+	0.140575i	0.689515	+	0.0244710i
$34$	−0.321918	−	6.75789i	−0.0552085	−	1.15897i
$35$	−2.37090	+	1.52368i	−0.400755	+	0.257549i
$36$	−2.12037	+	2.12227i	−0.353395	+	0.353712i
$37$	10.1097	−	2.96848i	1.66203	−	0.488015i	0.690182	−	0.723636i	$-0.257530\pi$
$37$	10.1097	−	2.96848i	1.66203	−	0.488015i	0.971845	+	0.235621i	$0.0757122\pi$
$38$	2.45819	+	1.93314i	0.398771	+	0.313597i
$39$	7.63282	+	3.37456i	1.22223	+	0.540361i
$40$	−0.831184	+	0.0793684i	−0.131422	+	0.0125492i
$41$	−1.55510	−	6.41022i	−0.242866	−	1.00111i	−0.954418	−	0.298474i	$-0.903522\pi$
$41$	−1.55510	−	6.41022i	−0.242866	−	1.00111i	0.711551	−	0.702634i	$-0.247993\pi$
$42$	−4.37157	+	3.88178i	−0.674548	+	0.598971i
$43$	−1.12842	−	0.451751i	−0.172082	−	0.0688913i	0.284022	−	0.958818i	$-0.408331\pi$
$43$	−1.12842	−	0.451751i	−0.172082	−	0.0688913i	−0.456104	+	0.889927i	$0.650755\pi$
$44$	1.92504	+	1.23715i	0.290211	+	0.186507i
$45$	0.179819	+	2.49843i	0.0268059	+	0.372444i
$46$	4.47657	+	1.72056i	0.660034	+	0.253683i
$47$	−3.09441	+	5.35967i	−0.451366	+	0.781788i	−0.998471	−	0.0552755i	$-0.982396\pi$
$47$	−3.09441	+	5.35967i	−0.451366	+	0.781788i	0.547106	+	0.837064i	$0.315730\pi$
$48$	−1.67815	+	0.428724i	−0.242220	+	0.0618810i
$49$	−3.45308	+	2.71553i	−0.493297	+	0.387933i
$50$	2.49589	−	3.50499i	0.352972	−	0.495680i
$51$	−10.2186	−	5.73567i	−1.43089	−	0.803154i
$52$	2.79488	+	3.92486i	0.387580	+	0.544280i
$53$	−8.01652	+	9.25156i	−1.10115	+	1.27080i	−0.141402	+	0.989952i	$0.545161\pi$
$53$	−8.01652	+	9.25156i	−1.10115	+	1.27080i	−0.959752	+	0.280848i	$0.909384\pi$
$54$	1.16827	+	5.06312i	0.158982	+	0.689003i
$55$	1.83326	−	0.538292i	0.247196	−	0.0725833i
$56$	−3.31435	+	0.638788i	−0.442898	+	0.0853616i
$57$	5.09681	−	1.83352i	0.675089	−	0.242855i
$58$	−9.36626	−	4.82864i	−1.22985	−	0.634032i
$59$	2.75125	−	7.94920i	0.358182	−	1.03490i	−0.611651	−	0.791128i	$-0.709494\pi$
$59$	2.75125	−	7.94920i	0.358182	−	1.03490i	0.969833	−	0.243771i	$-0.0783844\pi$
$60$	−0.647054	+	1.29337i	−0.0835343	+	0.166974i
$61$	9.72258	+	7.64592i	1.24485	+	0.978960i	0.999956	+	0.00941036i	$0.00299546\pi$
$61$	9.72258	+	7.64592i	1.24485	+	0.978960i	0.244894	+	0.969550i	$0.421247\pi$
$62$	2.99772	−	3.45955i	0.380711	−	0.439364i
$63$	1.68368	+	9.98507i	0.212124	+	1.25800i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	4.00488	+	0.382419i	0.496744	+	0.0474333i
$66$	3.58506	−	1.69007i	0.441290	−	0.208033i
$67$	−0.245875	+	5.16156i	−0.0300384	+	0.630584i	0.932782	+	0.360441i	$0.117374\pi$
$67$	−0.245875	+	5.16156i	−0.0300384	+	0.630584i	−0.962820	+	0.270143i	$0.912929\pi$
$68$	−3.38278	−	5.85914i	−0.410222	−	0.710525i
$69$	6.63891	−	4.99248i	0.799231	−	0.601023i
$70$	−1.40915	+	2.44071i	−0.168425	+	0.291721i
$71$	3.46698	+	2.22810i	0.411455	+	0.264426i	0.729953	−	0.683497i	$-0.239542\pi$
$71$	3.46698	+	2.22810i	0.411455	+	0.264426i	−0.318498	+	0.947924i	$0.603178\pi$
$72$	−0.912176	+	2.85796i	−0.107501	+	0.336814i
$73$	−0.979365	−	2.14451i	−0.114626	−	0.250996i	0.843620	−	0.536940i	$-0.180420\pi$
$73$	−0.979365	−	2.14451i	−0.114626	−	0.250996i	−0.958246	+	0.285944i	$0.907693\pi$
$74$	7.62564	−	7.27103i	0.886462	−	0.845240i
$75$	−2.85358	−	6.88478i	−0.329503	−	0.794986i
$76$	3.07074	+	0.591837i	0.352238	+	0.0678884i
$77$	7.17053	−	2.87065i	0.817158	−	0.327141i
$78$	8.33063	−	0.498135i	0.943258	−	0.0564027i
$79$	0.0200833	−	0.00387073i	0.00225955	−	0.000435492i	−0.188121	−	0.982146i	$-0.560240\pi$
$79$	0.0200833	−	0.00387073i	0.00225955	−	0.000435492i	0.190381	+	0.981710i	$0.439028\pi$
$80$	−0.702417	+	0.451416i	−0.0785326	+	0.0504698i
$81$	8.50765	+	2.93597i	0.945294	+	0.326219i
$82$	−4.31956	−	4.98504i	−0.477016	−	0.550506i
$83$	0.182557	−	0.752511i	0.0200383	−	0.0825988i	−0.960914	−	0.276845i	$-0.910711\pi$
$83$	0.182557	−	0.752511i	0.0200383	−	0.0825988i	0.980953	+	0.194247i	$0.0622262\pi$
$84$	−2.10687	+	5.45343i	−0.229879	+	0.595018i
$85$	−5.54691	−	1.06908i	−0.601647	−	0.115958i
$86$	−1.20998	+	0.115539i	−0.130476	+	0.0124589i
$87$	−15.6947	+	9.31687i	−1.68265	+	0.998873i
$88$	2.27794	+	0.217517i	0.242829	+	0.0231874i
$89$	0.395747	+	2.75248i	0.0419491	+	0.291763i	0.999987	+	0.00512057i	$0.00162994\pi$
$89$	0.395747	+	2.75248i	0.0419491	+	0.291763i	−0.958038	+	0.286642i	$0.907461\pi$
$90$	1.30468	+	2.13830i	0.137525	+	0.225396i
$91$	16.2634			1.70486
$92$	4.76734	−	0.521986i	0.497030	−	0.0544208i
$93$	−2.32585	−	7.57990i	−0.241179	−	0.786000i
$94$	−0.294476	+	6.18180i	−0.0303728	+	0.637604i
$95$	2.05250	−	1.61410i	0.210582	−	0.165604i
$96$	−1.29515	+	1.15004i	−0.132186	+	0.117375i
$97$	0.839000	−	0.799985i	0.0851875	−	0.0812261i	−0.646289	−	0.763093i	$-0.723680\pi$
$97$	0.839000	−	0.799985i	0.0851875	−	0.0812261i	0.731477	+	0.681867i	$0.238832\pi$
$98$	−1.82489	+	3.99595i	−0.184342	+	0.403652i
$99$	0.811933	−	6.81672i	0.0816023	−	0.685106i
$100$	0.612357	−	4.25904i	0.0612357	−	0.425904i
$101$	1.97493	−	8.14077i	0.196513	−	0.810037i	−0.785133	−	0.619327i	$-0.787406\pi$
$101$	1.97493	−	8.14077i	0.196513	−	0.810037i	0.981646	−	0.190711i	$-0.0610792\pi$
$102$	−11.7109	−	0.415622i	−1.15955	−	0.0411528i
$103$	14.7659	+	7.61237i	1.45493	+	0.750069i	0.990754	−	0.135674i	$-0.0433199\pi$
$103$	14.7659	+	7.61237i	1.45493	+	0.750069i	0.464177	+	0.885743i	$0.346350\pi$
$104$	4.28266	+	2.20787i	0.419949	+	0.216499i
$105$	2.28924	+	4.31134i	0.223407	+	0.420744i
$106$	−2.88606	+	11.8965i	−0.280319	+	1.15549i
$107$	−2.52418	+	17.5560i	−0.244021	+	1.69721i	0.387517	+	0.921862i	$0.373333\pi$
$107$	−2.52418	+	17.5560i	−0.244021	+	1.69721i	−0.631539	+	0.775344i	$0.717576\pi$
$108$	3.35846	+	3.96494i	0.323168	+	0.381527i
$109$	−6.44499	+	14.1125i	−0.617318	+	1.35174i	0.300137	+	0.953896i	$0.402968\pi$
$109$	−6.44499	+	14.1125i	−0.617318	+	1.35174i	−0.917454	+	0.397841i	$0.869760\pi$
$110$	1.38280	−	1.31850i	0.131845	−	0.125714i
$111$	−3.67081	−	17.8768i	−0.348418	−	1.69679i
$112$	−2.65320	+	2.08650i	−0.250704	+	0.197156i
$113$	0.0662131	−	1.38998i	0.00622881	−	0.130759i	−0.993611	−	0.112859i	$-0.963999\pi$
$113$	0.0662131	−	1.38998i	0.00622881	−	0.130759i	0.999840	−	0.0178995i	$-0.00569790\pi$
$114$	3.69006	−	3.96519i	0.345605	−	0.371374i
$115$	2.27733	−	3.29372i	0.212362	−	0.307141i
$116$	−10.5377			−0.978399
$117$	6.92177	−	12.6898i	0.639918	−	1.17318i
$118$	−1.19713	−	8.32623i	−0.110205	−	0.766491i
$119$	−22.7327	−	2.17071i	−2.08390	−	0.198988i
$120$	0.0175342	+	1.44609i	0.00160064	+	0.132010i
$121$	5.73758	−	0.547872i	0.521598	−	0.0498066i
$122$	12.1453	+	2.34082i	1.09959	+	0.211928i
$123$	−11.2880	+	1.76292i	−1.01781	+	0.158957i
$124$	1.07922	−	4.44861i	0.0969169	−	0.399497i
$125$	−5.08665	−	5.87031i	−0.454964	−	0.525057i
$126$	6.07194	+	8.10357i	0.540932	+	0.721924i
$127$	−15.2477	+	9.79911i	−1.35302	+	0.869530i	−0.997867	−	0.0652796i	$-0.979206\pi$
$127$	−15.2477	+	9.79911i	−1.35302	+	0.869530i	−0.355148	+	0.934810i	$0.615570\pi$
$128$	−0.981929	+	0.189251i	−0.0867911	+	0.0167276i
$129$	−0.941939	+	1.88281i	−0.0829331	+	0.165772i
$130$	3.73491	−	1.49523i	0.327573	−	0.131141i
$131$	−1.78131	−	0.343320i	−0.155634	−	0.0299960i	0.110839	−	0.993838i	$-0.464646\pi$
$131$	−1.78131	−	0.343320i	−0.155634	−	0.0299960i	−0.266473	+	0.963842i	$0.585858\pi$
$132$	2.41209	−	3.14496i	0.209946	−	0.273734i
$133$	7.63942	−	7.28417i	0.662422	−	0.631618i
$134$	2.14662	+	4.70044i	0.185440	+	0.406056i
$135$	4.33833	+	0.0487047i	0.373384	+	0.00419183i
$136$	−5.69155	−	3.65773i	−0.488046	−	0.313648i
$137$	−1.92446	+	3.33327i	−0.164418	+	0.284780i	−0.936448	−	0.350805i	$-0.885908\pi$
$137$	−1.92446	+	3.33327i	−0.164418	+	0.284780i	0.772031	+	0.635585i	$0.219241\pi$
$138$	3.61322	−	7.47962i	0.307578	−	0.636707i
$139$	6.11028	+	10.5833i	0.518267	+	0.897665i	0.999775	+	0.0212231i	$0.00675603\pi$
$139$	6.11028	+	10.5833i	0.518267	+	0.897665i	−0.481508	+	0.876442i	$0.659911\pi$
$140$	−0.134100	+	2.81510i	−0.0113335	+	0.237919i
$141$	8.80646	+	6.11150i	0.741638	+	0.514681i
$142$	4.10255	+	0.391746i	0.344279	+	0.0328746i
$143$	−10.5791	−	3.10629i	−0.884666	−	0.259761i
$144$	0.498819	+	2.95824i	0.0415682	+	0.246520i
$145$	−5.76185	+	6.64953i	−0.478496	+	0.552213i
$146$	−1.85317	−	1.45735i	−0.153369	−	0.120611i
$147$	4.19092	+	6.35057i	0.345662	+	0.523786i
$148$	3.44616	−	9.95702i	0.283272	−	0.818462i
$149$	1.25878	+	0.648945i	0.103123	+	0.0531637i	0.509016	−	0.860757i	$-0.330009\pi$
$149$	1.25878	+	0.648945i	0.103123	+	0.0531637i	−0.405893	+	0.913920i	$0.633040\pi$
$150$	−5.69115	−	4.81185i	−0.464681	−	0.392886i
$151$	−17.7372	+	3.41856i	−1.44343	+	0.278198i	−0.850040	−	0.526718i	$-0.823422\pi$
$151$	−17.7372	+	3.41856i	−1.44343	+	0.278198i	−0.593389	+	0.804916i	$0.702210\pi$
$152$	3.00058	−	0.881050i	0.243379	−	0.0714626i
$153$	−11.3689	+	16.8138i	−0.919120	+	1.35931i
$154$	5.05801	−	5.83726i	0.407586	−	0.470380i
$155$	−2.21708	−	3.11345i	−0.178080	−	0.250078i
$156$	7.17630	−	4.26008i	0.574564	−	0.341079i
$157$	−8.83716	+	12.4101i	−0.705282	+	0.990431i	0.294117	+	0.955770i	$0.404975\pi$
$157$	−8.83716	+	12.4101i	−0.705282	+	0.990431i	−0.999399	+	0.0346610i	$0.988965\pi$
$158$	0.0160771	−	0.0126431i	0.00127902	−	0.00100583i
$159$	14.8167	+	15.1668i	1.17504	+	1.20281i
$160$	−0.417482	+	0.723100i	−0.0330049	+	0.0571661i
$161$	7.89874	−	14.1297i	0.622508	−	1.11357i
$162$	8.90724	−	1.28884i	0.699819	−	0.101261i
$163$	−5.79117	−	3.72176i	−0.453599	−	0.291511i	0.293823	−	0.955860i	$-0.405072\pi$
$163$	−5.79117	−	3.72176i	−0.453599	−	0.291511i	−0.747422	+	0.664349i	$0.768709\pi$
$164$	−6.12366	−	2.45154i	−0.478178	−	0.191433i
$165$	−0.665650	−	3.24171i	−0.0518208	−	0.252367i
$166$	−0.182557	−	0.752511i	−0.0141692	−	0.0584062i
$167$	5.18050	−	0.494678i	0.400879	−	0.0382793i	0.107330	−	0.994223i	$-0.465770\pi$
$167$	5.18050	−	0.494678i	0.400879	−	0.0382793i	0.293549	+	0.955944i	$0.405164\pi$
$168$	0.626243	+	5.81263i	0.0483157	+	0.448454i
$169$	−8.03020	−	6.31502i	−0.617708	−	0.485771i
$170$	−5.42017	+	1.59151i	−0.415708	+	0.122063i
$171$	−2.43225	−	9.06100i	−0.185999	−	0.692912i
$172$	−1.02253	+	0.657142i	−0.0779674	+	0.0501066i
$173$	−0.485296	−	10.1876i	−0.0368964	−	0.774550i	−0.939184	−	0.343415i	$-0.888416\pi$
$173$	−0.485296	−	10.1876i	−0.0368964	−	0.774550i	0.902287	−	0.431135i	$-0.141887\pi$
$174$	−9.68078	+	15.4729i	−0.733898	+	1.17300i
$175$	−10.5112	−	10.0224i	−0.794570	−	0.757621i
$176$	2.12439	−	0.850476i	0.160132	−	0.0641070i
$177$	−13.3255	−	5.89136i	−1.00161	−	0.442822i
$178$	1.61301	+	2.26516i	0.120901	+	0.169781i
$179$	−10.4959	−	3.08189i	−0.784503	−	0.230351i	−0.135137	−	0.990827i	$-0.543148\pi$
$179$	−10.4959	−	3.08189i	−0.784503	−	0.230351i	−0.649366	+	0.760476i	$0.724966\pi$
$180$	2.13947	+	1.30276i	0.159466	+	0.0971016i
$181$	−0.646313	−	4.49520i	−0.0480401	−	0.334126i	−0.999641	−	0.0267898i	$-0.991472\pi$
$181$	−0.646313	−	4.49520i	−0.0480401	−	0.334126i	0.951601	−	0.307336i	$-0.0994376\pi$
$182$	14.4554	−	7.45230i	1.07151	−	0.552401i
$183$	14.5948	−	15.6830i	1.07888	−	1.15932i
$184$	3.99819	−	2.64848i	0.294751	−	0.195249i
$185$	−4.39881	−	7.61896i	−0.323407	−	0.560157i
$186$	−5.54061	−	5.67152i	−0.406257	−	0.415856i
$187$	14.3726	+	5.75394i	1.05103	+	0.420770i
$188$	2.57093	+	5.62954i	0.187504	+	0.410577i
$189$	17.4770	−	1.47107i	1.27126	−	0.107004i
$190$	1.08471	−	2.37518i	0.0786932	−	0.172314i
$191$	−3.67259	−	10.6112i	−0.265739	−	0.767803i	−0.996378	−	0.0850383i	$-0.972899\pi$
$191$	−3.67259	−	10.6112i	−0.265739	−	0.767803i	0.730639	−	0.682764i	$-0.239222\pi$
$192$	−0.624195	+	1.61567i	−0.0450474	+	0.116601i
$193$	−10.7224	−	10.2238i	−0.771814	−	0.735923i	0.197885	−	0.980225i	$-0.436593\pi$
$193$	−10.7224	−	10.2238i	−0.771814	−	0.735923i	−0.969699	+	0.244302i	$0.921441\pi$
$194$	0.379159	−	1.09551i	0.0272220	−	0.0786528i
$195$	1.23569	−	6.85777i	0.0884894	−	0.491095i
$196$	0.209024	+	4.38796i	0.0149303	+	0.313426i
$197$	8.51414	+	9.82585i	0.606608	+	0.700063i	0.973106	−	0.230356i	$-0.0739891\pi$
$197$	8.51414	+	9.82585i	0.606608	+	0.700063i	−0.366499	+	0.930419i	$0.619444\pi$
$198$	−2.40193	−	6.43099i	−0.170698	−	0.457031i
$199$	−0.927731	+	6.45251i	−0.0657651	+	0.457406i	0.930155	+	0.367167i	$0.119672\pi$
$199$	−0.927731	+	6.45251i	−0.0657651	+	0.457406i	−0.995920	+	0.0902393i	$0.971237\pi$
$200$	−1.40732	−	4.06618i	−0.0995125	−	0.287523i
$201$	8.87391	+	1.16624i	0.625917	+	0.0822605i
$202$	−1.97493	−	8.14077i	−0.138956	−	0.572783i
$203$	−20.6316	+	28.9731i	−1.44806	+	2.03351i
$204$	−10.5995	+	4.99683i	−0.742115	+	0.349848i
$205$	−4.89531	+	2.52371i	−0.341903	+	0.176263i
$206$	16.6127			1.15746
$207$	−7.66322	−	12.1768i	−0.532631	−	0.846348i
$208$	4.81828			0.334088
$209$	−6.36060	+	3.27912i	−0.439972	+	0.226821i
$210$	4.01033	+	2.78308i	0.276739	+	0.192051i
$211$	9.35622	−	13.1390i	0.644109	−	0.904524i	−0.355436	−	0.934701i	$-0.615668\pi$
$211$	9.35622	−	13.1390i	0.644109	−	0.904524i	0.999545	+	0.0301767i	$0.00960701\pi$
$212$	2.88606	+	11.8965i	0.198215	+	0.817055i
$213$	4.34416	−	5.66405i	0.297657	−	0.388094i
$214$	5.80107	+	16.7611i	0.396553	+	1.14576i
$215$	−0.144434	+	1.00456i	−0.00985029	+	0.0685103i
$216$	4.80196	+	1.98525i	0.326732	+	0.135079i
$217$	−10.1183	−	11.6772i	−0.686877	−	0.792699i
$218$	0.738213	+	15.4970i	0.0499981	+	1.04959i
$219$	−3.84235	+	1.38224i	−0.259642	+	0.0934031i
$220$	0.624913	−	1.80557i	0.0421316	−	0.121731i
$221$	23.5925	+	22.4954i	1.58701	+	1.51321i
$222$	−11.4544	−	14.2075i	−0.768767	−	0.953543i
$223$	4.07080	+	11.7618i	0.272601	+	0.787629i	0.995333	+	0.0965006i	$0.0307650\pi$
$223$	4.07080	+	11.7618i	0.272601	+	0.787629i	−0.722732	+	0.691129i	$0.757114\pi$
$224$	−1.40217	+	3.07032i	−0.0936863	+	0.205144i
$225$	−12.2938	+	3.93599i	−0.819587	+	0.262399i
$226$	−0.578075	−	1.26581i	−0.0384530	−	0.0842003i
$227$	2.22910	+	0.892399i	0.147951	+	0.0592306i	0.444456	−	0.895801i	$-0.353397\pi$
$227$	2.22910	+	0.892399i	0.147951	+	0.0592306i	−0.296505	+	0.955031i	$0.595821\pi$
$228$	1.46290	−	5.21528i	0.0968829	−	0.345390i
$229$	−1.81593	−	3.14528i	−0.120000	−	0.207846i	0.799767	−	0.600310i	$-0.204956\pi$
$229$	−1.81593	−	3.14528i	−0.120000	−	0.207846i	−0.919767	+	0.392464i	$0.871623\pi$
$230$	0.514898	−	3.97111i	0.0339514	−	0.261847i
$231$	−3.92437	−	12.7895i	−0.258205	−	0.841485i
$232$	−9.36626	+	4.82864i	−0.614925	+	0.317016i
$233$	0.203631	+	1.41628i	0.0133403	+	0.0927838i	0.995404	−	0.0957665i	$-0.0305302\pi$
$233$	0.203631	+	1.41628i	0.0133403	+	0.0927838i	−0.982064	+	0.188550i	$0.939621\pi$
$234$	0.337500	−	14.4509i	0.0220631	−	0.944686i
$235$	4.95812	+	1.45584i	0.323432	+	0.0949682i
$236$	−4.87935	−	6.85209i	−0.317619	−	0.446033i
$237$	−0.00379472	−	0.0352216i	−0.000246493	−	0.00228789i
$238$	−21.2003	+	8.48731i	−1.37421	+	0.550150i
$239$	−15.1443	−	14.4401i	−0.979605	−	0.934052i	0.0182287	−	0.999834i	$-0.494197\pi$
$239$	−15.1443	−	14.4401i	−0.979605	−	0.934052i	−0.997834	+	0.0657820i	$0.979046\pi$
$240$	0.678224	+	1.27731i	0.0437792	+	0.0824497i
$241$	−0.821734	−	17.2503i	−0.0529325	−	1.11119i	−0.856557	−	0.516053i	$-0.827401\pi$
$241$	−0.821734	−	17.2503i	−0.0529325	−	1.11119i	0.803624	−	0.595137i	$-0.202902\pi$
$242$	4.84871	−	3.11608i	0.311687	−	0.200309i
$243$	6.29047	−	14.2629i	0.403534	−	0.914965i
$244$	11.8678	−	3.48471i	0.759760	−	0.223086i
$245$	2.88320	+	2.26737i	0.184201	+	0.144857i
$246$	−9.22540	+	6.73943i	−0.588190	+	0.429690i
$247$	−14.9998	+	1.43231i	−0.954413	+	0.0911354i
$248$	−1.07922	−	4.44861i	−0.0685306	−	0.282487i
$249$	−1.27265	−	0.423262i	−0.0806512	−	0.0268232i
$250$	−7.21113	−	2.88690i	−0.456072	−	0.182584i
$251$	11.3922	+	7.32132i	0.719069	+	0.462118i	0.848313	−	0.529495i	$-0.177619\pi$
$251$	11.3922	+	7.32132i	0.719069	+	0.462118i	−0.129244	+	0.991613i	$0.541255\pi$
$252$	9.11023	+	4.42042i	0.573891	+	0.278460i
$253$	−7.83677	+	7.68248i	−0.492694	+	0.482993i
$254$	−9.06249	+	15.6967i	−0.568631	+	0.984899i
$255$	−2.64254	+	9.42074i	−0.165483	+	0.589950i
$256$	−0.786053	+	0.618159i	−0.0491283	+	0.0386349i
$257$	5.36536	−	7.53460i	0.334682	−	0.469995i	−0.612601	−	0.790392i	$-0.709877\pi$
$257$	5.36536	−	7.53460i	0.334682	−	0.469995i	0.947283	+	0.320397i	$0.103816\pi$
$258$	0.0255251	+	2.10513i	0.00158912	+	0.131060i
$259$	−20.6294	−	28.9699i	−1.28185	−	1.80010i
$260$	2.63457	−	3.04045i	0.163389	−	0.188561i
$261$	13.8259	+	28.4294i	0.855803	+	1.75973i
$262$	−1.74061	+	0.511090i	−0.107535	+	0.0315753i
$263$	4.30763	−	0.830228i	0.265620	−	0.0511941i	−0.0547022	−	0.998503i	$-0.517421\pi$
$263$	4.30763	−	0.830228i	0.265620	−	0.0511941i	0.320322	+	0.947309i	$0.396209\pi$
$264$	0.702848	−	3.90064i	0.0432573	−	0.240068i
$265$	9.08503	+	4.68366i	0.558089	+	0.287715i
$266$	3.45239	−	9.97502i	0.211679	−	0.611607i
$267$	4.80788	−	0.287490i	0.294237	−	0.0175941i
$268$	4.06186	+	3.19428i	0.248117	+	0.195122i
$269$	−1.37635	+	1.58840i	−0.0839178	+	0.0968463i	−0.796156	−	0.605092i	$-0.793136\pi$
$269$	−1.37635	+	1.58840i	−0.0839178	+	0.0968463i	0.712238	+	0.701938i	$0.247682\pi$
$270$	3.87838	−	1.94465i	0.236031	−	0.118347i
$271$	−11.6089	−	3.40867i	−0.705188	−	0.207062i	−0.0905737	−	0.995890i	$-0.528870\pi$
$271$	−11.6089	−	3.40867i	−0.705188	−	0.207062i	−0.614614	+	0.788828i	$0.710688\pi$
$272$	−6.73492	−	0.643107i	−0.408364	−	0.0389941i
$273$	2.33745	−	28.0718i	0.141469	−	1.69898i
$274$	−0.183139	+	3.84456i	−0.0110638	+	0.232259i
$275$	4.92309	+	8.52705i	0.296874	+	0.514200i
$276$	−0.215802	−	8.30382i	−0.0129898	−	0.499831i
$277$	6.71408	−	11.6291i	0.403410	−	0.698726i	−0.590725	−	0.806873i	$-0.701158\pi$
$277$	6.71408	−	11.6291i	0.403410	−	0.698726i	0.994135	+	0.108147i	$0.0344916\pi$
$278$	10.2806	+	6.60693i	0.616589	+	0.396257i
$279$	−13.4178	+	2.92517i	−0.803302	+	0.175126i
$280$	1.17076	+	2.56361i	0.0699663	+	0.153205i
$281$	−3.39677	+	3.23881i	−0.202634	+	0.193211i	−0.784601	−	0.620002i	$-0.787132\pi$
$281$	−3.39677	+	3.23881i	−0.202634	+	0.193211i	0.581967	+	0.813213i	$0.302283\pi$
$282$	10.6279	+	1.39677i	0.632885	+	0.0831763i
$283$	7.76698	+	1.49696i	0.461699	+	0.0889852i	0.414796	−	0.909914i	$-0.363853\pi$
$283$	7.76698	+	1.49696i	0.461699	+	0.0889852i	0.0469026	+	0.998899i	$0.485065\pi$
$284$	3.82600	−	1.53170i	0.227031	−	0.0908897i
$285$	−2.49107	−	3.77476i	−0.147558	−	0.223598i
$286$	−10.8264	+	2.08662i	−0.640181	+	0.123385i
$287$	−18.7299	+	12.0370i	−1.10559	+	0.710521i
$288$	1.79891	+	2.40082i	0.106002	+	0.141469i
$289$	−18.8421	−	21.7450i	−1.10836	−	1.27912i
$290$	−2.07435	+	8.55057i	−0.121810	+	0.502107i
$291$	−1.26025	−	1.56316i	−0.0738772	−	0.0916338i
$292$	−2.31495	−	0.446171i	−0.135472	−	0.0261102i
$293$	5.51135	−	0.526270i	0.321976	−	0.0307450i	0.0671834	−	0.997741i	$-0.478599\pi$
$293$	5.51135	−	0.526270i	0.321976	−	0.0307450i	0.254793	+	0.966996i	$0.417993\pi$
$294$	6.63504	+	3.72422i	0.386963	+	0.217201i
$295$	−6.99179	−	0.667635i	−0.407078	−	0.0388712i
$296$	−1.49950	−	10.4293i	−0.0871568	−	0.606189i
$297$	−11.6495	−	2.38119i	−0.675972	−	0.138171i
$298$	1.41621			0.0820389
$299$	−21.3314	+	8.88471i	−1.23362	+	0.513816i
$300$	−7.26342	−	1.66911i	−0.419354	−	0.0963659i
$301$	−0.195214	+	4.09804i	−0.0112519	+	0.236207i
$302$	−14.1989	+	11.1662i	−0.817057	+	0.642541i
$303$	−13.7678	−	4.57892i	−0.790937	−	0.263052i
$304$	2.26330	−	2.15805i	0.129809	−	0.123773i
$305$	4.29022	−	9.39428i	0.245657	−	0.537915i
$306$	−2.40055	+	20.1542i	−0.137230	+	1.15214i
$307$	−0.514206	+	3.57638i	−0.0293473	+	0.204115i	−0.999220	−	0.0394990i	$-0.987424\pi$
$307$	−0.514206	+	3.57638i	−0.0293473	+	0.204115i	0.969872	+	0.243614i	$0.0783329\pi$
$308$	1.82096	−	7.50608i	0.103759	−	0.427699i
$309$	15.2618	−	24.3930i	0.868212	−	1.38767i
$310$	−3.39728	−	1.75142i	−0.192953	−	0.0994740i
$311$	19.0760	+	9.83436i	1.08170	+	0.557655i	0.904480	−	0.426516i	$-0.140259\pi$
$311$	19.0760	+	9.83436i	1.08170	+	0.557655i	0.177220	+	0.984171i	$0.443290\pi$
$312$	4.42647	−	7.07488i	0.250600	−	0.400536i
$313$	5.64539	−	23.2706i	0.319096	−	1.31533i	−0.555919	−	0.831236i	$-0.687634\pi$
$313$	5.64539	−	23.2706i	0.319096	−	1.31533i	0.875015	−	0.484095i	$-0.160851\pi$
$314$	−2.16817	+	15.0799i	−0.122357	+	0.851009i
$315$	7.77073	−	3.33175i	0.437831	−	0.187723i
$316$	0.00849644	−	0.0186046i	0.000477962	−	0.00104659i
$317$	−22.4455	+	21.4018i	−1.26067	+	1.20204i	−0.291243	+	0.956649i	$0.594069\pi$
$317$	−22.4455	+	21.4018i	−1.26067	+	1.20204i	−0.969424	+	0.245393i	$0.921083\pi$
$318$	20.1195	+	6.69139i	1.12824	+	0.375234i
$319$	18.9544	−	14.9059i	1.06124	−	0.834571i
$320$	−0.0397292	+	0.834019i	−0.00222093	+	0.0466231i
$321$	29.9403	+	6.88017i	1.67110	+	0.384014i
$322$	0.546097	−	16.1784i	0.0304328	−	0.901585i
$323$	21.1576			1.17724
$324$	7.32649	−	5.22710i	0.407027	−	0.290394i
$325$	2.95051	+	20.5213i	0.163665	+	1.13831i
$326$	−6.85280	−	0.654363i	−0.379542	−	0.0362418i
$327$	23.4330	+	13.1529i	1.29585	+	0.727355i
$328$	−6.56629	+	0.627005i	−0.362563	+	0.0346205i
$329$	20.5119	+	3.95334i	1.13086	+	0.217955i
$330$	−2.07709	−	2.57633i	−0.114340	−	0.141822i
$331$	−7.57425	+	31.2215i	−0.416318	+	1.71609i	0.248107	+	0.968733i	$0.420192\pi$
$331$	−7.57425	+	31.2215i	−0.416318	+	1.71609i	−0.664425	+	0.747355i	$0.731323\pi$
$332$	−0.507084	−	0.585206i	−0.0278298	−	0.0321173i
$333$	−31.3843	+	3.76676i	−1.71985	+	0.206417i
$334$	4.37794	−	2.81353i	0.239550	−	0.153949i
$335$	4.23663	−	0.816544i	0.231472	−	0.0446125i
$336$	3.22013	+	4.87951i	0.175672	+	0.266199i
$337$	7.50887	−	3.00610i	0.409034	−	0.163753i	−0.158015	−	0.987437i	$-0.550509\pi$
$337$	7.50887	−	3.00610i	0.409034	−	0.163753i	0.567049	+	0.823684i	$0.308085\pi$
$338$	−10.0312	−	1.93336i	−0.545628	−	0.105161i
$339$	−2.38971	−	0.314065i	−0.129791	−	0.0170576i
$340$	−4.08837	+	3.89825i	−0.221723	+	0.211412i
$341$	4.35149	+	9.52843i	0.235646	+	0.515993i
$342$	−6.31386	−	6.93922i	−0.341415	−	0.375230i
$343$	−7.40281	−	4.75750i	−0.399714	−	0.256881i
$344$	−0.607743	+	1.05264i	−0.0327673	+	0.0567547i
$345$	−5.35791	−	4.40423i	−0.288460	−	0.237116i
$346$	−5.09958	−	8.83274i	−0.274155	−	0.474851i
$347$	0.540214	−	11.3405i	0.0290002	−	0.608789i	−0.936857	−	0.349713i	$-0.886279\pi$
$347$	0.540214	−	11.3405i	0.0290002	−	0.608789i	0.965857	−	0.259076i	$-0.0834180\pi$
$348$	−1.51453	+	18.1889i	−0.0811872	+	0.975025i
$349$	15.4931	+	1.47941i	0.829328	+	0.0791912i	0.501081	−	0.865401i	$-0.332936\pi$
$349$	15.4931	+	1.47941i	0.829328	+	0.0791912i	0.328247	+	0.944592i	$0.393542\pi$
$350$	−13.9352	−	4.09175i	−0.744870	−	0.218713i
$351$	−20.9088	−	13.7714i	−1.11603	−	0.735061i
$352$	1.49852	−	1.72938i	0.0798713	−	0.0921764i
$353$	8.44866	+	6.64410i	0.449677	+	0.353630i	0.817170	−	0.576396i	$-0.195541\pi$
$353$	8.44866	+	6.64410i	0.449677	+	0.353630i	−0.367493	+	0.930026i	$0.619784\pi$
$354$	−14.5438	+	0.869653i	−0.772993	+	0.0462216i
$355$	1.12546	−	3.25181i	0.0597333	−	0.172588i
$356$	2.47166	+	1.27423i	0.130998	+	0.0675341i
$357$	−7.01406	+	38.9263i	−0.371223	+	2.06020i
$358$	−10.7414	+	2.07023i	−0.567699	+	0.109415i
$359$	0.490808	−	0.144114i	0.0259039	−	0.00760606i	−0.268755	−	0.963209i	$-0.586612\pi$
$359$	0.490808	−	0.144114i	0.0259039	−	0.00760606i	0.294659	+	0.955603i	$0.404794\pi$
$360$	2.49859	+	0.177575i	0.131687	+	0.00935900i
$361$	6.03799	−	6.96821i	0.317789	−	0.366748i
$362$	−2.63429	−	3.69934i	−0.138455	−	0.194433i
$363$	−0.121037	−	9.98224i	−0.00635277	−	0.523932i
$364$	9.43367	−	13.2477i	0.494459	−	0.694370i
$365$	−1.54733	+	1.21683i	−0.0809908	+	0.0636919i
$366$	5.78603	−	20.6274i	0.302441	−	1.07821i
$367$	−12.9336	+	22.4017i	−0.675128	+	1.16936i	0.301303	+	0.953528i	$0.402578\pi$
$367$	−12.9336	+	22.4017i	−0.675128	+	1.16936i	−0.976431	+	0.215828i	$0.930755\pi$
$368$	2.34013	−	4.18614i	0.121988	−	0.218218i
$369$	1.42056	+	19.7374i	0.0739514	+	1.02749i
$370$	−7.40103	−	4.75635i	−0.384761	−	0.247271i
$371$	38.3597	+	15.3569i	1.99154	+	0.797291i
$372$	−7.52353	−	2.50220i	−0.390077	−	0.129733i
$373$	−0.582419	−	2.40077i	−0.0301565	−	0.124307i	0.954744	−	0.297430i	$-0.0961294\pi$
$373$	−0.582419	−	2.40077i	−0.0301565	−	0.124307i	−0.984900	+	0.173123i	$0.944614\pi$
$374$	15.4115	−	1.47162i	0.796911	−	0.0760958i
$375$	−10.8637	+	7.93625i	−0.560999	+	0.409826i
$376$	4.86474	+	3.82567i	0.250880	+	0.197294i
$377$	48.7168	−	14.3046i	2.50905	−	0.736722i
$378$	14.8601	−	9.31596i	0.764320	−	0.479161i
$379$	13.4942	−	8.67221i	0.693151	−	0.445461i	−0.146054	−	0.989277i	$-0.546657\pi$
$379$	13.4942	−	8.67221i	0.693151	−	0.445461i	0.839205	+	0.543815i	$0.183021\pi$
$380$	−0.124243	−	2.60819i	−0.00637355	−	0.133797i
$381$	14.7225	+	27.7271i	0.754259	+	1.42050i
$382$	−8.12668	−	7.74877i	−0.415797	−	0.396462i
$383$	−15.6584	+	6.26870i	−0.800109	+	0.320315i	−0.735439	−	0.677591i	$-0.763024\pi$
$383$	−15.6584	+	6.26870i	−0.800109	+	0.320315i	−0.0646704	+	0.997907i	$0.520600\pi$
$384$	0.185535	+	1.72209i	0.00946802	+	0.0878798i
$385$	−3.74084	−	5.25328i	−0.190651	−	0.267732i
$386$	−14.2152	−	4.17397i	−0.723536	−	0.212449i
$387$	3.11450	+	1.89647i	0.158319	+	0.0964028i
$388$	−0.164981	−	1.14747i	−0.00837562	−	0.0582537i
$389$	−9.34753	+	4.81898i	−0.473938	+	0.244332i	−0.678610	−	0.734498i	$-0.737418\pi$
$389$	−9.34753	+	4.81898i	−0.473938	+	0.244332i	0.204672	+	0.978831i	$0.434387\pi$
$390$	−2.04409	−	6.66165i	−0.103506	−	0.337326i
$391$	31.0025	−	9.57176i	1.56786	−	0.484065i
$392$	2.19647	+	3.80439i	0.110938	+	0.192151i
$393$	−0.848617	+	3.02534i	−0.0428071	+	0.152608i
$394$	12.0701	+	4.83215i	0.608085	+	0.243440i
$395$	−0.00709422	−	0.0155342i	−0.000356949	−	0.000781609i
$396$	−5.08177	−	4.61547i	−0.255369	−	0.231936i
$397$	−14.0141	+	30.6867i	−0.703350	+	1.54012i	0.132512	+	0.991181i	$0.457696\pi$
$397$	−14.0141	+	30.6867i	−0.703350	+	1.54012i	−0.835862	+	0.548939i	$0.815032\pi$
$398$	2.13211	+	6.16033i	0.106873	+	0.308790i
$399$	−11.4751	−	14.2331i	−0.574472	−	0.712549i
$400$	−3.11411	−	2.96930i	−0.155705	−	0.148465i
$401$	0.606890	−	1.75349i	0.0303066	−	0.0875653i	−0.928833	−	0.370499i	$-0.879187\pi$
$401$	0.606890	−	1.75349i	0.0303066	−	0.0875653i	0.959139	+	0.282934i	$0.0913078\pi$
$402$	8.42185	−	3.02966i	0.420043	−	0.151106i
$403$	1.04949	+	22.0314i	0.0522786	+	1.09746i
$404$	−5.48571	−	6.33084i	−0.272924	−	0.314971i
$405$	0.707594	−	7.48129i	0.0351606	−	0.371748i
$406$	−5.06189	+	35.2062i	−0.251218	+	1.74726i
$407$	7.88585	+	22.7847i	0.390887	+	1.12939i
$408$	−7.13155	+	9.29834i	−0.353064	+	0.460336i
$409$	0.783436	+	3.22937i	0.0387384	+	0.159682i	0.987895	−	0.155121i	$-0.0495767\pi$
$409$	0.783436	+	3.22937i	0.0387384	+	0.159682i	−0.949157	+	0.314803i	$0.898062\pi$
$410$	−3.19470	+	4.48632i	−0.157775	+	0.221564i
$411$	5.47688	+	3.80084i	0.270155	+	0.187482i
$412$	14.7659	−	7.61237i	0.727465	−	0.375034i
$413$	−28.3929			−1.39712
$414$	−12.3911	−	7.31170i	−0.608989	−	0.359351i
$415$	−0.646545			−0.0317376
$416$	4.28266	−	2.20787i	0.209975	−	0.108249i
$417$	19.1458	−	9.02573i	0.937575	−	0.441992i
$418$	−4.15095	+	5.82919i	−0.203030	+	0.285115i
$419$	1.34136	+	5.52915i	0.0655295	+	0.270116i	0.995146	−	0.0984128i	$-0.0313766\pi$
$419$	1.34136	+	5.52915i	0.0655295	+	0.270116i	−0.929616	+	0.368529i	$0.879861\pi$
$420$	4.83980	+	0.636066i	0.236158	+	0.0310369i
$421$	−10.8465	−	31.3388i	−0.528625	−	1.52736i	−0.820926	−	0.571034i	$-0.806542\pi$
$421$	−10.8465	−	31.3388i	−0.528625	−	1.52736i	0.292302	−	0.956326i	$-0.405579\pi$
$422$	2.29551	−	15.9656i	0.111744	−	0.777196i
$423$	11.8146	−	14.3223i	0.574447	−	0.696372i
$424$	8.01652	+	9.25156i	0.389317	+	0.449296i
$425$	−1.38516	−	29.0781i	−0.0671901	−	1.41049i
$426$	1.26582	−	7.02502i	0.0613293	−	0.340363i
$427$	13.6548	−	39.4530i	0.660802	−	1.90926i
$428$	12.8366	+	12.2396i	0.620479	+	0.591625i
$429$	−6.88218	+	17.8138i	−0.332275	+	0.860060i
$430$	0.331937	+	0.959070i	0.0160074	+	0.0462505i
$431$	−12.3034	+	26.9406i	−0.592633	+	1.29768i	0.341206	+	0.939989i	$0.389165\pi$
$431$	−12.3034	+	26.9406i	−0.592633	+	1.29768i	−0.933838	+	0.357696i	$0.883563\pi$
$432$	5.17784	−	0.435827i	0.249119	−	0.0209687i
$433$	3.57826	+	7.83530i	0.171960	+	0.376541i	0.975915	−	0.218150i	$-0.0700020\pi$
$433$	3.57826	+	7.83530i	0.171960	+	0.376541i	−0.803955	+	0.594690i	$0.797275\pi$
$434$	−14.3443	−	5.74260i	−0.688550	−	0.275654i
$435$	10.6495	+	10.9011i	0.510603	+	0.522668i
$436$	7.75728	+	13.4360i	0.371507	+	0.643468i
$437$	−6.04066	+	13.7275i	−0.288964	+	0.656676i
$438$	−2.78184	+	2.98925i	−0.132921	+	0.142832i
$439$	7.11469	−	3.66788i	0.339566	−	0.175058i	−0.280006	−	0.959998i	$-0.590337\pi$
$439$	7.11469	−	3.66788i	0.339566	−	0.175058i	0.619572	+	0.784940i	$0.287306\pi$
$440$	−0.271914	−	1.89120i	−0.0129630	−	0.0901596i
$441$	11.5639	−	6.32112i	0.550663	−	0.301006i
$442$	31.2779	+	9.18402i	1.48774	+	0.436839i
$443$	0.461928	+	0.648688i	0.0219469	+	0.0308201i	0.825404	−	0.564543i	$-0.190948\pi$
$443$	0.461928	+	0.648688i	0.0219469	+	0.0308201i	−0.803457	+	0.595363i	$0.797008\pi$
$444$	−16.6913	−	7.37941i	−0.792133	−	0.350211i
$445$	2.15554	−	0.862947i	0.102182	−	0.0409076i
$446$	9.00785	+	8.58897i	0.426534	+	0.406699i
$447$	1.30105	−	2.07948i	0.0615374	−	0.0983560i
$448$	0.160605	+	3.37152i	0.00758788	+	0.159289i
$449$	−22.3045	+	14.3343i	−1.05262	+	0.676475i	−0.948076	−	0.318045i	$-0.896974\pi$
$449$	−22.3045	+	14.3343i	−1.05262	+	0.676475i	−0.104541	+	0.994521i	$0.533337\pi$
$450$	−9.12359	+	9.13179i	−0.430090	+	0.430477i
$451$	14.4826	−	4.25247i	0.681958	−	0.200241i
$452$	−1.09384	−	0.860206i	−0.0514499	−	0.0404607i
$453$	3.35142	+	31.1070i	0.157463	+	1.46154i
$454$	2.39023	−	0.228239i	0.112179	−	0.0107118i
$455$	−3.20145	−	13.1965i	−0.150086	−	0.618663i
$456$	−1.08950	−	5.30586i	−0.0510206	−	0.248470i
$457$	13.6057	+	5.44689i	0.636447	+	0.254795i	0.667369	−	0.744727i	$-0.267420\pi$
$457$	13.6057	+	5.44689i	0.636447	+	0.254795i	−0.0309224	+	0.999522i	$0.509844\pi$
$458$	−3.05531	−	1.96353i	−0.142765	−	0.0917498i
$459$	27.3879	+	22.0401i	1.27836	+	1.02875i
$460$	−1.36201	−	3.76560i	−0.0635039	−	0.175572i
$461$	8.63480	−	14.9559i	0.402163	−	0.696567i	−0.591824	−	0.806067i	$-0.701592\pi$
$461$	8.63480	−	14.9559i	0.402163	−	0.696567i	0.993987	+	0.109501i	$0.0349252\pi$
$462$	−9.34860	−	9.56948i	−0.434936	−	0.445213i
$463$	4.17708	−	3.28489i	0.194125	−	0.152662i	−0.516366	−	0.856368i	$-0.672715\pi$
$463$	4.17708	−	3.28489i	0.194125	−	0.152662i	0.710491	+	0.703707i	$0.248473\pi$
$464$	−6.11245	+	8.58374i	−0.283764	+	0.398490i
$465$	−5.69270	+	3.37937i	−0.263993	+	0.156714i
$466$	0.829973	+	1.16553i	0.0384478	+	0.0539923i
$467$	20.6052	−	23.7797i	0.953495	−	1.10039i	−0.0413662	−	0.999144i	$-0.513171\pi$
$467$	20.6052	−	23.7797i	0.953495	−	1.10039i	0.994861	−	0.101248i	$-0.0322835\pi$
$468$	−6.32181	−	12.9991i	−0.292226	−	0.600885i
$469$	16.7353	−	4.91391i	0.772762	−	0.226903i
$470$	5.07406	−	0.977944i	0.234049	−	0.0451092i
$471$	20.1506	+	17.0373i	0.928491	+	0.785036i
$472$	−7.47675	−	3.85453i	−0.344145	−	0.177419i
$473$	0.909707	−	2.62843i	0.0418284	−	0.120855i
$474$	−0.0195124	−	0.0295674i	−0.000896232	−	0.00135807i
$475$	10.5772	+	8.31799i	0.485315	+	0.381656i
$476$	−14.9544	+	17.2583i	−0.685436	+	0.791035i
$477$	28.3086	−	23.3950i	1.29616	−	1.07118i
$478$	−20.0777	−	5.89533i	−0.918330	−	0.269646i
$479$	15.5348	+	1.48339i	0.709802	+	0.0677779i	0.443711	−	0.896170i	$-0.353662\pi$
$479$	15.5348	+	1.48339i	0.709802	+	0.0677779i	0.266091	+	0.963948i	$0.414268\pi$
$480$	1.18812	+	0.824534i	0.0542302	+	0.0376347i
$481$	−2.41564	+	50.7104i	−0.110144	+	2.31220i
$482$	−8.63494	−	14.9561i	−0.393311	−	0.681234i
$483$	−23.2536	−	15.6646i	−1.05808	−	0.712765i
$484$	2.88184	−	4.99149i	0.130993	−	0.226886i
$485$	−0.814287	−	0.523311i	−0.0369749	−	0.0237623i
$486$	−0.944439	−	15.5598i	−0.0428406	−	0.705808i
$487$	11.1016	+	24.3091i	0.503062	+	1.10155i	0.975462	+	0.220167i	$0.0706603\pi$
$487$	11.1016	+	24.3091i	0.503062	+	1.10155i	−0.472400	+	0.881384i	$0.656612\pi$
$488$	8.95177	−	8.53549i	0.405227	−	0.386384i
$489$	−7.25638	+	9.46110i	−0.328145	+	0.427846i
$490$	3.60166	+	0.694163i	0.162706	+	0.0313591i
$491$	8.67486	−	3.47289i	0.391491	−	0.156729i	−0.167562	−	0.985862i	$-0.553589\pi$
$491$	8.67486	−	3.47289i	0.391491	−	0.156729i	0.559052	+	0.829132i	$0.311165\pi$
$492$	−5.11168	+	10.2176i	−0.230452	+	0.460643i
$493$	−70.0049	+	13.4923i	−3.15286	+	0.607664i
$494$	−12.6760	+	8.14638i	−0.570321	+	0.366523i
$495$	−5.69111	+	0.683049i	−0.255796	+	0.0307007i
$496$	−2.99772	−	3.45955i	−0.134602	−	0.155339i
$497$	3.27953	−	13.5184i	0.147107	−	0.606383i
$498$	−1.32513	+	0.206953i	−0.0593805	+	0.00927379i
$499$	−27.0744	−	5.21817i	−1.21202	−	0.233597i	−0.457099	−	0.889416i	$-0.651112\pi$
$499$	−27.0744	−	5.21817i	−1.21202	−	0.233597i	−0.754919	+	0.655818i	$0.772324\pi$
$500$	−7.73236	+	0.738351i	−0.345802	+	0.0330201i
$501$	−0.109285	−	9.01304i	−0.00488248	−	0.402673i
$502$	13.4806	+	1.28724i	0.601669	+	0.0574524i
$503$	0.733337	+	5.10047i	0.0326979	+	0.227419i	0.999617	−	0.0276633i	$-0.00880664\pi$
$503$	0.733337	+	5.10047i	0.0326979	+	0.227419i	−0.966919	+	0.255082i	$0.917898\pi$
$504$	10.1230	−	0.245524i	0.450916	−	0.0109365i
$505$	−6.99442			−0.311247
$506$	−3.44529	+	10.4195i	−0.153162	+	0.463202i
$507$	−12.0544	+	12.9531i	−0.535353	+	0.575269i
$508$	−0.862422	+	18.1045i	−0.0382638	+	0.803255i
$509$	4.72310	−	3.71429i	0.209348	−	0.164633i	−0.507980	−	0.861369i	$-0.669608\pi$
$509$	4.72310	−	3.71429i	0.209348	−	0.164633i	0.717328	+	0.696736i	$0.245365\pi$
$510$	1.96805	+	9.58438i	0.0871466	+	0.424403i
$511$	−5.75916	+	5.49135i	−0.254770	+	0.242923i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	−15.9896	+	2.89596i	−0.705957	+	0.127860i
$514$	1.31637	−	9.15557i	0.0580627	−	0.403835i
$515$	3.27021	−	13.4800i	0.144103	−	0.593999i
$516$	0.987314	+	1.85942i	0.0434641	+	0.0818563i
$517$	−12.5876	−	6.48935i	−0.553601	−	0.285401i
$518$	−31.6109	−	16.2965i	−1.38890	−	0.716029i
$519$	−17.6544	−	0.626557i	−0.774941	−	0.0275028i
$520$	0.948481	−	3.90969i	0.0415936	−	0.171451i
$521$	1.22199	−	8.49913i	0.0535363	−	0.372353i	−0.945387	−	0.325951i	$-0.894315\pi$
$521$	1.22199	−	8.49913i	0.0535363	−	0.372353i	0.998923	−	0.0464020i	$-0.0147755\pi$
$522$	25.3161	+	18.9336i	1.10805	+	0.828702i
$523$	8.93183	−	19.5580i	0.390562	−	0.855210i	−0.607579	−	0.794259i	$-0.707859\pi$
$523$	8.93183	−	19.5580i	0.390562	−	0.855210i	0.998141	−	0.0609514i	$-0.0194135\pi$
$524$	−1.31292	+	1.25187i	−0.0573554	+	0.0546882i
$525$	−18.8101	+	16.7026i	−0.820942	+	0.728963i
$526$	3.44835	−	2.71181i	0.150355	−	0.118240i
$527$	1.47363	−	30.9352i	0.0641922	−	1.34756i
$528$	−1.16266	−	3.78909i	−0.0505983	−	0.164899i
$529$	−2.64109	+	22.8479i	−0.114830	+	0.993385i
$530$	10.2213			0.443984
$531$	−12.0842	+	22.1541i	−0.524408	+	0.961408i
$532$	−1.50221	−	10.4481i	−0.0651292	−	0.452984i
$533$	31.6382	+	3.02109i	1.37040	+	0.130858i
$534$	4.14168	−	2.45863i	0.179228	−	0.106395i
$535$	14.7423	−	1.40772i	0.637367	−	0.0608612i
$536$	5.07403	+	0.977938i	0.219165	+	0.0422405i
$537$	−6.82810	+	17.6739i	−0.294654	+	0.762683i
$538$	−0.495507	+	2.04251i	−0.0213628	+	0.0880587i
$539$	−6.58289	−	7.59707i	−0.283545	−	0.327229i
$540$	2.55615	−	3.50565i	0.109999	−	0.150859i
$541$	−17.3150	+	11.1277i	−0.744431	+	0.478417i	−0.857058	−	0.515221i	$-0.827710\pi$
$541$	−17.3150	+	11.1277i	−0.744431	+	0.478417i	0.112627	+	0.993637i	$0.464074\pi$
$542$	−11.8803	+	2.28974i	−0.510303	+	0.0983528i
$543$	−7.85196	+	0.469513i	−0.336960	+	0.0201487i
$544$	−6.28092	+	2.51450i	−0.269292	+	0.107808i
$545$	12.7200	+	2.45158i	0.544866	+	0.105014i
$546$	−10.7856	−	26.0223i	−0.461583	−	1.11365i
$547$	17.9788	−	17.1427i	0.768716	−	0.732969i	−0.200363	−	0.979722i	$-0.564212\pi$
$547$	17.9788	−	17.1427i	0.768716	−	0.732969i	0.969078	+	0.246753i	$0.0793635\pi$
$548$	1.59890	+	3.50110i	0.0683017	+	0.149560i
$549$	−24.9725	−	27.4459i	−1.06580	−	1.17136i
$550$	8.28314	+	5.32325i	0.353194	+	0.226984i
$551$	16.4770	−	28.5390i	0.701945	−	1.21580i
$552$	−3.99684	−	7.28184i	−0.170117	−	0.309936i
$553$	−0.0345177	−	0.0597865i	−0.00146784	−	0.00254238i
$554$	0.638937	−	13.4129i	0.0271458	−	0.569861i
$555$	−13.7831	+	6.49765i	−0.585061	+	0.275810i
$556$	12.1652	+	1.16164i	0.515920	+	0.0492644i
$557$	19.6445	+	5.76816i	0.832366	+	0.244405i	0.670033	−	0.742331i	$-0.266280\pi$
$557$	19.6445	+	5.76816i	0.832366	+	0.244405i	0.162333	+	0.986736i	$0.448098\pi$
$558$	−10.5858	+	8.74838i	−0.448133	+	0.370349i
$559$	3.83523	−	4.42609i	0.162213	−	0.187204i
$560$	2.21533	+	1.74215i	0.0936146	+	0.0736193i
$561$	11.9975	−	23.9813i	0.506533	−	1.01249i
$562$	−1.53506	+	4.43526i	−0.0647525	+	0.187090i
$563$	−26.4624	−	13.6423i	−1.11526	−	0.574956i	−0.200798	−	0.979633i	$-0.564354\pi$
$563$	−26.4624	−	13.6423i	−1.11526	−	0.574956i	−0.914460	+	0.404677i	$0.867384\pi$
$564$	10.0865	−	3.62851i	0.424720	−	0.152788i
$565$	−1.14091	+	0.219892i	−0.0479983	+	0.00925092i
$566$	7.58951	−	2.22848i	0.319011	−	0.0936701i
$567$	−0.0272934	−	30.3781i	−0.00114622	−	1.27576i
$568$	2.69882	−	3.11460i	0.113240	−	0.130686i
$569$	−11.0015	−	15.4494i	−0.461206	−	0.647673i	0.516835	−	0.856085i	$-0.327110\pi$
$569$	−11.0015	−	15.4494i	−0.461206	−	0.647673i	−0.978041	+	0.208412i	$0.933171\pi$
$570$	−3.94385	−	2.21367i	−0.165190	−	0.0927203i
$571$	0.247020	−	0.346892i	0.0103375	−	0.0145170i	−0.809375	−	0.587292i	$-0.800194\pi$
$571$	0.247020	−	0.346892i	0.0103375	−	0.0145170i	0.819712	+	0.572775i	$0.194133\pi$
$572$	−8.66678	+	6.81563i	−0.362376	+	0.284976i
$573$	−18.8437	+	4.81407i	−0.787206	+	0.201111i
$574$	−11.1321	+	19.2814i	−0.464647	+	0.804792i
$575$	19.2619	+	7.40329i	0.803278	+	0.308739i
$576$	2.69905	+	1.30962i	0.112461	+	0.0545675i
$577$	−32.8719	−	21.1255i	−1.36847	−	0.879465i	−0.369709	−	0.929148i	$-0.620543\pi$
$577$	−32.8719	−	21.1255i	−1.36847	−	0.879465i	−0.998765	+	0.0496827i	$0.984179\pi$
$578$	−26.7117	−	10.6937i	−1.11106	−	0.444801i
$579$	−19.1881	+	17.0382i	−0.797430	+	0.708085i
$580$	2.07435	+	8.55057i	0.0861325	+	0.355043i
$581$	−2.60182	+	0.248444i	−0.107942	+	0.0103072i
$582$	−1.83643	−	0.811909i	−0.0761227	−	0.0336547i
$583$	−22.0192	−	17.3161i	−0.911944	−	0.717161i
$584$	−2.26206	+	0.664201i	−0.0936047	+	0.0274848i
$585$	−11.6594	−	3.11852i	−0.482058	−	0.128935i
$586$	4.65753	−	2.99321i	0.192401	−	0.123648i
$587$	1.24141	+	26.0604i	0.0512384	+	1.07563i	0.867339	+	0.497717i	$0.165828\pi$
$587$	1.24141	+	26.0604i	0.0512384	+	1.07563i	−0.816101	+	0.577909i	$0.803869\pi$
$588$	7.60400	+	0.269867i	0.313584	+	0.0111291i
$589$	10.3606	+	9.87881i	0.426901	+	0.407049i
$590$	−6.52048	+	2.61041i	−0.268444	+	0.107469i
$591$	18.1839	−	13.2839i	0.747984	−	0.546425i
$592$	−6.11178	−	8.58280i	−0.251193	−	0.352751i
$593$	−15.5017	−	4.55170i	−0.636577	−	0.186916i	−0.0525091	−	0.998620i	$-0.516722\pi$
$593$	−15.5017	−	4.55170i	−0.636577	−	0.186916i	−0.584068	+	0.811704i	$0.698540\pi$
$594$	−11.4456	+	3.22162i	−0.469619	+	0.132185i
$595$	2.71356	+	18.8732i	0.111245	+	0.773726i
$596$	1.25878	−	0.648945i	0.0515616	−	0.0265818i
$597$	11.0042	+	2.52872i	0.450372	+	0.103494i
$598$	−14.8889	+	17.6716i	−0.608851	+	0.722647i
$599$	−18.1435	−	31.4254i	−0.741322	−	1.28401i	−0.951894	−	0.306428i	$-0.900866\pi$
$599$	−18.1435	−	31.4254i	−0.741322	−	1.28401i	0.210572	−	0.977578i	$-0.432467\pi$
$600$	−7.22081	+	1.84473i	−0.294788	+	0.0753108i
$601$	−10.5195	−	4.21136i	−0.429098	−	0.171785i	0.147052	−	0.989129i	$-0.453021\pi$
$601$	−10.5195	−	4.21136i	−0.429098	−	0.171785i	−0.576150	+	0.817344i	$0.695446\pi$
$602$	1.70432	+	3.73193i	0.0694627	+	0.152102i
$603$	3.28843	−	15.1494i	0.133915	−	0.616932i
$604$	−7.50388	+	16.4312i	−0.305329	+	0.668577i
$605$	−1.57400	−	4.54778i	−0.0639923	−	0.184894i
$606$	−14.3355	+	2.23885i	−0.582338	+	0.0909471i
$607$	17.1680	+	16.3697i	0.696829	+	0.664425i	0.953265	−	0.302136i	$-0.0976998\pi$
$607$	17.1680	+	16.3697i	0.696829	+	0.664425i	−0.256436	+	0.966561i	$0.582548\pi$
$608$	1.02283	−	2.95526i	0.0414811	−	0.119852i
$609$	47.0445	+	39.7759i	1.90634	+	1.61180i
$610$	−0.491405	−	10.3159i	−0.0198964	−	0.417677i
$611$	−19.5276	−	22.5360i	−0.790002	−	0.911711i
$612$	7.10150	+	19.0138i	0.287061	+	0.768586i
$613$	−1.40193	+	9.75064i	−0.0566235	+	0.393825i	0.941725	+	0.336383i	$0.109204\pi$
$613$	−1.40193	+	9.75064i	−0.0566235	+	0.393825i	−0.998349	+	0.0574421i	$0.981706\pi$
$614$	1.18175	+	3.41444i	0.0476914	+	0.137795i
$615$	3.65254	+	8.81241i	0.147285	+	0.355351i
$616$	−1.82096	−	7.50608i	−0.0733684	−	0.302429i
$617$	2.29382	−	3.22122i	0.0923457	−	0.129681i	−0.765818	−	0.643057i	$-0.777666\pi$
$617$	2.29382	−	3.22122i	0.0923457	−	0.129681i	0.858164	+	0.513376i	$0.171605\pi$
$618$	2.38766	−	28.6748i	0.0960456	−	1.15347i
$619$	8.82934	−	4.55184i	0.354881	−	0.182954i	−0.271562	−	0.962421i	$-0.587540\pi$
$619$	8.82934	−	4.55184i	0.354881	−	0.182954i	0.626443	+	0.779467i	$0.284510\pi$
$620$	−3.82217			−0.153502
$621$	−22.1195	+	11.4772i	−0.887626	+	0.460564i
$622$	21.4618			0.860539
$623$	8.34271	−	4.30096i	0.334243	−	0.172314i
$624$	0.692508	−	8.31673i	0.0277225	−	0.332936i
$625$	8.71742	−	12.2419i	0.348697	−	0.489676i
$626$	−5.64539	−	23.2706i	−0.225635	−	0.930080i
$627$	4.74584	+	11.4502i	0.189530	+	0.457276i
$628$	4.98288	+	14.3971i	0.198838	+	0.574506i
$629$	10.1450	−	70.5598i	0.404506	−	2.81340i
$630$	5.38020	−	6.52213i	0.214352	−	0.259848i
$631$	9.00646	+	10.3940i	0.358541	+	0.413779i	0.906150	−	0.422955i	$-0.139007\pi$
$631$	9.00646	+	10.3940i	0.358541	+	0.413779i	−0.547609	+	0.836734i	$0.684462\pi$
$632$	−0.000973188	−	0.0204297i	−3.87113e−5	−	0.000812651i
$633$	−21.3342	−	18.0380i	−0.847956	−	0.716944i
$634$	−10.1435	+	29.3078i	−0.402851	+	1.16396i
$635$	10.9528	+	10.4435i	0.434648	+	0.414436i
$636$	20.9491	−	3.27174i	0.830685	−	0.129733i
$637$	−6.92285	−	20.0023i	−0.274293	−	0.792519i
$638$	10.0171	−	21.9343i	0.396579	−	0.868388i
$639$	−9.15223	−	8.31242i	−0.362056	−	0.328834i
$640$	0.346857	+	0.759510i	0.0137107	+	0.0300223i
$641$	−25.1633	−	10.0739i	−0.993891	−	0.397894i	−0.183014	−	0.983110i	$-0.558585\pi$
$641$	−25.1633	−	10.0739i	−0.993891	−	0.397894i	−0.810877	+	0.585217i	$0.801010\pi$
$642$	29.7647	−	7.60410i	1.17472	−	0.300110i
$643$	−6.21563	−	10.7658i	−0.245120	−	0.424561i	0.717045	−	0.697027i	$-0.245494\pi$
$643$	−6.21563	−	10.7658i	−0.245120	−	0.424561i	−0.962165	+	0.272466i	$0.912161\pi$
$644$	−6.92796	−	14.6301i	−0.273000	−	0.576508i
$645$	1.71319	+	0.393684i	0.0674566	+	0.0155013i
$646$	18.8056	−	9.69499i	0.739898	−	0.381444i
$647$	2.65770	+	18.4847i	0.104485	+	0.726709i	0.972960	+	0.230975i	$0.0741917\pi$
$647$	2.65770	+	18.4847i	0.104485	+	0.726709i	−0.868475	+	0.495734i	$0.834899\pi$
$648$	4.11685	−	8.00322i	0.161725	−	0.314396i
$649$	18.4691	+	5.42303i	0.724977	+	0.212872i
$650$	12.0259	+	16.8880i	0.471695	+	0.662402i
$651$	−21.6100	+	15.7867i	−0.846962	+	0.618730i
$652$	−6.39086	+	2.55852i	−0.250285	+	0.100199i
$653$	−10.8150	−	10.3121i	−0.423225	−	0.403544i	0.448309	−	0.893878i	$-0.352026\pi$
$653$	−10.8150	−	10.3121i	−0.423225	−	0.403544i	−0.871535	+	0.490334i	$0.836875\pi$
$654$	26.8551	+	0.953093i	1.05012	+	0.0372689i
$655$	0.0720727	+	1.51299i	0.00281611	+	0.0591175i
$656$	−5.54904	+	3.56615i	−0.216654	+	0.139235i
$657$	1.83361	+	6.83086i	0.0715360	+	0.266497i
$658$	20.0432	−	5.88521i	0.781365	−	0.229429i
$659$	−5.16275	−	4.06003i	−0.201112	−	0.158156i	0.512524	−	0.858673i	$-0.328711\pi$
$659$	−5.16275	−	4.06003i	−0.201112	−	0.158156i	−0.713636	+	0.700517i	$0.752953\pi$
$660$	−3.02673	−	1.33815i	−0.117815	−	0.0520875i
$661$	22.4237	−	2.14120i	0.872181	−	0.0832832i	0.350641	−	0.936510i	$-0.385964\pi$
$661$	22.4237	−	2.14120i	0.872181	−	0.0832832i	0.521540	+	0.853227i	$0.325358\pi$
$662$	7.57425	+	31.2215i	0.294382	+	1.21346i
$663$	42.2197	−	37.4894i	1.63968	−	1.45597i
$664$	−0.718871	−	0.287792i	−0.0278976	−	0.0111685i
$665$	−7.41440	−	4.76495i	−0.287518	−	0.184777i
$666$	−26.1695	+	17.7292i	−1.01405	+	0.686991i
$667$	11.2328	−	49.2728i	0.434936	−	1.90785i
$668$	2.60203	−	4.50685i	0.100676	−	0.174375i
$669$	20.8869	−	5.33605i	0.807533	−	0.206304i
$670$	3.39151	−	2.66711i	0.131025	−	0.103039i
$671$	−16.4178	+	23.0555i	−0.633800	+	0.890048i
$672$	5.09808	+	2.86153i	0.196663	+	0.110386i
$673$	−17.4889	−	24.5597i	−0.674146	−	0.946706i	−0.999999	−	0.00128559i	$-0.999591\pi$
$673$	−17.4889	−	24.5597i	−0.674146	−	0.946706i	0.325853	−	0.945421i	$-0.394349\pi$
$674$	5.29668	−	6.11269i	0.204020	−	0.235452i
$675$	5.02689	+	21.7857i	0.193485	+	0.838534i
$676$	−9.80204	+	2.87814i	−0.377002	+	0.110698i
$677$	−16.7837	+	3.23479i	−0.645050	+	0.124323i	−0.501276	−	0.865287i	$-0.667136\pi$
$677$	−16.7837	+	3.23479i	−0.645050	+	0.124323i	−0.143774	+	0.989611i	$0.545924\pi$
$678$	−2.26797	+	0.815875i	−0.0871008	+	0.0313335i
$679$	−3.47794	−	1.79300i	−0.133471	−	0.0688091i
$680$	−1.84761	+	5.33831i	−0.0708524	+	0.204715i
$681$	1.86073	−	3.71935i	0.0713032	−	0.142526i
$682$	8.23393	+	6.47524i	0.315294	+	0.247950i
$683$	−16.7091	+	19.2833i	−0.639356	+	0.737856i	−0.979261	−	0.202604i	$-0.935060\pi$
$683$	−16.7091	+	19.2833i	−0.639356	+	0.737856i	0.339905	+	0.940460i	$0.389605\pi$
$684$	−8.79172	−	3.27464i	−0.336160	−	0.125209i
$685$	3.08354	+	0.905408i	0.117816	+	0.0345939i
$686$	−8.75989	−	0.836468i	−0.334454	−	0.0319365i
$687$	−5.68999	+	2.68238i	−0.217087	+	0.102339i
$688$	−0.0578352	+	1.21411i	−0.00220495	+	0.0462875i
$689$	−29.4917	−	51.0811i	−1.12354	−	1.94603i
$690$	−6.78043	−	1.45950i	−0.258127	−	0.0555623i
$691$	16.0216	−	27.7502i	0.609489	−	1.05567i	−0.381835	−	0.924230i	$-0.624708\pi$
$691$	16.0216	−	27.7502i	0.609489	−	1.05567i	0.991325	−	0.131436i	$-0.0419588\pi$
$692$	−8.58009	−	5.51409i	−0.326166	−	0.209614i
$693$	−22.6396	+	4.93561i	−0.860009	+	0.187488i
$694$	−4.71635	−	10.3274i	−0.179030	−	0.392022i
$695$	7.38479	−	7.04138i	0.280121	−	0.267095i
$696$	6.98845	+	16.8609i	0.264896	+	0.639111i
$697$	−43.8202	−	8.44565i	−1.65981	−	0.319902i
$698$	14.4487	−	5.78440i	0.546893	−	0.218943i
$699$	2.47388	−	0.147927i	0.0935708	−	0.00559512i
$700$	−14.2611	+	2.74860i	−0.539018	+	0.103887i
$701$	−21.7728	+	13.9926i	−0.822349	+	0.528492i	−0.882838	−	0.469677i	$-0.844370\pi$
$701$	−21.7728	+	13.9926i	−0.822349	+	0.528492i	0.0604892	+	0.998169i	$0.480734\pi$
$702$	−24.8949	−	2.65951i	−0.939597	−	0.100377i
$703$	21.5779	+	24.9023i	0.813827	+	0.939206i
$704$	0.539488	−	2.22380i	0.0203327	−	0.0838125i
$705$	3.22549	−	8.34886i	0.121479	−	0.314436i
$706$	10.5540	+	2.03411i	0.397204	+	0.0765548i
$707$	−28.1469	+	2.68770i	−1.05857	+	0.101081i
$708$	−12.5285	+	7.43732i	−0.470851	+	0.279512i
$709$	40.7476	+	3.89092i	1.53031	+	0.146127i	0.825960	−	0.563728i	$-0.190634\pi$
$709$	40.7476	+	3.89092i	1.53031	+	0.146127i	0.704348	+	0.709855i	$0.251240\pi$
$710$	−0.489715	−	3.40604i	−0.0183787	−	0.127826i
$711$	−0.0613406	+	0.00148775i	−0.00230045	+	5.57950e-5i
$712$	2.78079			0.104214
$713$	19.6507	+	9.78836i	0.735924	+	0.366577i
$714$	11.6027	+	37.8131i	0.434222	+	1.41512i
$715$	−0.438042	+	9.19563i	−0.0163818	+	0.343897i
$716$	−8.59867	+	6.76207i	−0.321348	+	0.252710i
$717$	−27.1013	+	24.0649i	−1.01212	+	0.898720i
$718$	0.370211	−	0.352995i	0.0138161	−	0.0131737i
$719$	−6.37497	+	13.9592i	−0.237746	+	0.520592i	−0.990467	−	0.137748i	$-0.956014\pi$
$719$	−6.37497	+	13.9592i	−0.237746	+	0.520592i	0.752721	+	0.658340i	$0.228741\pi$
$720$	2.30221	−	0.987086i	0.0857981	−	0.0367865i
$721$	7.98008	−	55.5027i	0.297194	−	2.06703i
$722$	2.17376	−	8.96036i	0.0808989	−	0.333470i
$723$	−29.8935	−	1.06093i	−1.11175	−	0.0394562i
$724$	−4.03658	−	2.08100i	−0.150018	−	0.0773399i
$725$	−40.3015	−	20.7769i	−1.49676	−	0.771633i
$726$	−4.68171	−	8.81711i	−0.173755	−	0.327234i
$727$	−4.62844	+	19.0787i	−0.171659	+	0.707589i	0.819293	+	0.573375i	$0.194366\pi$
$727$	−4.62844	+	19.0787i	−0.171659	+	0.707589i	−0.990952	+	0.134214i	$0.957149\pi$
$728$	2.31452	−	16.0978i	0.0857817	−	0.596625i
$729$	−23.7147	−	12.9078i	−0.878324	−	0.478066i
$730$	−0.817735	+	1.79059i	−0.0302657	+	0.0662727i
$731$	−5.95158	+	5.67482i	−0.220127	+	0.209891i
$732$	−4.30918	−	20.9856i	−0.159272	−	0.775652i
$733$	−3.86542	+	3.03980i	−0.142773	+	0.112278i	−0.686991	−	0.726666i	$-0.741069\pi$
$733$	−3.86542	+	3.03980i	−0.142773	+	0.112278i	0.544218	+	0.838944i	$0.316826\pi$
$734$	−1.23081	+	25.8379i	−0.0454301	+	0.953694i
$735$	4.32805	−	4.65074i	0.159642	−	0.171545i
$736$	0.161790	−	4.79310i	0.00596366	−	0.176676i
$737$	−11.8246			−0.435564
$738$	10.3069	+	16.8924i	0.379401	+	0.621817i
$739$	6.33061	+	44.0303i	0.232875	+	1.61968i	0.685563	+	0.728013i	$0.259556\pi$
$739$	6.33061	+	44.0303i	0.232875	+	1.61968i	−0.452688	+	0.891669i	$0.649535\pi$
$740$	−8.75778	−	0.836267i	−0.321942	−	0.0307418i
$741$	0.316427	+	26.0966i	0.0116242	+	0.958684i
$742$	41.1324	−	3.92767i	1.51002	−	0.144189i
$743$	−5.72410	−	1.10323i	−0.209997	−	0.0404736i	0.0831677	−	0.996536i	$-0.473496\pi$
$743$	−5.72410	−	1.10323i	−0.209997	−	0.0404736i	−0.293165	+	0.956062i	$0.594708\pi$
$744$	−7.83376	+	1.22344i	−0.287199	+	0.0448536i
$745$	0.278781	−	1.14915i	0.0102138	−	0.0421017i
$746$	−1.61777	−	1.86701i	−0.0592308	−	0.0683559i
$747$	−0.913496	+	2.13587i	−0.0334231	+	0.0781473i
$748$	13.0240	−	8.37000i	0.476204	−	0.306038i
$749$	58.7851	−	11.3299i	2.14796	−	0.413986i
$750$	−6.01943	+	12.0320i	−0.219799	+	0.439348i
$751$	−6.40730	+	2.56510i	−0.233806	+	0.0936017i	−0.485607	−	0.874177i	$-0.661401\pi$
$751$	−6.40730	+	2.56510i	−0.233806	+	0.0936017i	0.251801	+	0.967779i	$0.418977\pi$
$752$	6.07697	+	1.17124i	0.221604	+	0.0427107i
$753$	14.2745	−	18.6116i	0.520192	−	0.678243i
$754$	36.7465	−	35.0377i	1.33823	−	1.27600i
$755$	6.26548	+	13.7195i	0.228024	+	0.499303i
$756$	8.93935	−	15.0896i	0.325121	−	0.548805i
$757$	−21.8163	−	14.0205i	−0.792928	−	0.509584i	0.0803729	−	0.996765i	$-0.474389\pi$
$757$	−21.8163	−	14.0205i	−0.792928	−	0.509584i	−0.873301	+	0.487181i	$0.838025\pi$
$758$	8.02030	−	13.8916i	0.291311	−	0.504565i
$759$	12.1342	+	14.6310i	0.440444	+	0.531073i
$760$	−1.30557	−	2.26132i	−0.0473582	−	0.0820267i
$761$	−1.46826	+	30.8225i	−0.0532243	+	1.11732i	0.801420	+	0.598102i	$0.204078\pi$
$761$	−1.46826	+	30.8225i	−0.0532243	+	1.11732i	−0.854645	+	0.519214i	$0.826225\pi$
$762$	25.7912	+	17.8986i	0.934317	+	0.648397i
$763$	52.1299	+	4.97780i	1.88723	+	0.180208i
$764$	−10.7740	−	3.16352i	−0.389789	−	0.114452i
$765$	15.8811	+	5.91523i	0.574184	+	0.213866i
$766$	−11.0453	+	12.7470i	−0.399083	+	0.460566i
$767$	31.8593	+	25.0544i	1.15037	+	0.904662i
$768$	0.954015	+	1.44563i	0.0344250	+	0.0521648i
$769$	10.5285	−	30.4200i	0.379666	−	1.09697i	−0.579705	−	0.814827i	$-0.696832\pi$
$769$	10.5285	−	30.4200i	0.379666	−	1.09697i	0.959371	−	0.282147i	$-0.0910467\pi$
$770$	−5.73219	−	2.95515i	−0.206574	−	0.106496i
$771$	−12.2342	−	10.3439i	−0.440603	−	0.372528i
$772$	−14.5476	+	2.80383i	−0.523581	+	0.100912i
$773$	15.2555	−	4.47943i	0.548703	−	0.161114i	0.00438155	−	0.999990i	$-0.498605\pi$
$773$	15.2555	−	4.47943i	0.548703	−	0.161114i	0.544322	+	0.838877i	$0.316787\pi$
$774$	3.63729	+	0.258502i	0.130740	+	0.00929165i
$775$	12.8987	−	14.8859i	0.463335	−	0.534717i
$776$	−0.672440	−	0.944310i	−0.0241392	−	0.0338987i
$777$	−52.9692	+	31.4442i	−1.90026	+	1.12805i
$778$	−6.10023	+	8.56657i	−0.218704	+	0.307126i
$779$	16.2146	−	12.7513i	0.580949	−	0.456863i
$780$	−4.86940	−	4.98446i	−0.174353	−	0.178472i
$781$	−4.71529	+	8.16712i	−0.168726	+	0.292243i
$782$	23.1701	−	22.7139i	0.828560	−	0.812247i
$783$	51.0584	−	19.7786i	1.82468	−	0.706829i
$784$	3.69557	+	2.37500i	0.131985	+	0.0848214i
$785$	11.8095	+	4.72780i	0.421498	+	0.168742i
$786$	0.632012	+	3.07789i	0.0225431	+	0.109785i
$787$	0.342953	+	1.41367i	0.0122249	+	0.0503919i	0.977597	−	0.210484i	$-0.0675039\pi$
$787$	0.342953	+	1.41367i	0.0122249	+	0.0503919i	−0.965372	+	0.260876i	$0.915989\pi$
$788$	12.9426	−	1.23587i	0.461061	−	0.0440259i
$789$	−0.813924	−	7.55463i	−0.0289765	−	0.268952i
$790$	−0.0134238	−	0.0105566i	−0.000477596	−	0.000375586i
$791$	−4.50673	+	1.32330i	−0.160241	+	0.0470510i
$792$	−6.63179	−	1.77379i	−0.235650	−	0.0630289i
$793$	−50.1359	+	32.2204i	−1.78038	+	1.14418i
$794$	1.60519	+	33.6971i	0.0569660	+	1.19586i
$795$	9.39011	−	15.0083i	0.333033	−	0.532290i
$796$	4.71792	+	4.49853i	0.167222	+	0.159446i
$797$	−35.3505	+	14.1522i	−1.25218	+	0.501296i	−0.900513	−	0.434830i	$-0.856809\pi$
$797$	−35.3505	+	14.1522i	−1.25218	+	0.501296i	−0.351665	+	0.936126i	$0.614384\pi$
$798$	−16.7215	−	7.39275i	−0.591933	−	0.261700i
$799$	24.2874	+	34.1069i	0.859227	+	1.20662i
$800$	−4.12854	−	1.21225i	−0.145966	−	0.0428595i
$801$	0.194782	−	8.34009i	0.00688230	−	0.294682i
$802$	−0.264072	−	1.83666i	−0.00932470	−	0.0648547i
$803$	4.79509	−	2.47204i	0.169215	−	0.0872365i
$804$	6.09736	−	6.55198i	0.215037	−	0.231071i
$805$	−13.0201	−	3.62783i	−0.458897	−	0.127864i
$806$	11.0282	+	19.1014i	0.388452	+	0.672818i
$807$	2.54388	+	2.60399i	0.0895489	+	0.0916647i
$808$	−7.77685	−	3.11338i	−0.273589	−	0.109528i
$809$	−10.2669	−	22.4814i	−0.360965	−	0.790403i	−0.999779	−	0.0210412i	$-0.993302\pi$
$809$	−10.2669	−	22.4814i	−0.360965	−	0.790403i	0.638814	−	0.769361i	$-0.279425\pi$
$810$	−2.79919	−	6.97387i	−0.0983535	−	0.245037i
$811$	19.9619	−	43.7104i	0.700957	−	1.53488i	−0.137851	−	0.990453i	$-0.544020\pi$
$811$	19.9619	−	43.7104i	0.700957	−	1.53488i	0.838808	−	0.544428i	$-0.183253\pi$
$812$	11.6332	+	33.6121i	0.408247	+	1.17955i
$813$	−7.55211	+	19.5479i	−0.264864	+	0.685574i
$814$	17.4498	+	16.6383i	0.611614	+	0.583173i
$815$	−1.87995	+	5.43175i	−0.0658516	+	0.190266i
$816$	−2.07803	+	11.5326i	−0.0727455	+	0.403720i
$817$	−0.180866	−	3.79683i	−0.00632768	−	0.132834i
$818$	2.17613	+	2.51138i	0.0760865	+	0.0878085i
$819$	−48.1182	−	8.06924i	−1.68138	−	0.281962i
$820$	−0.783807	+	5.45150i	−0.0273717	+	0.190375i
$821$	13.8772	+	40.0956i	0.484319	+	1.39935i	0.877363	+	0.479828i	$0.159301\pi$
$821$	13.8772	+	40.0956i	0.484319	+	1.39935i	−0.393044	+	0.919520i	$0.628578\pi$
$822$	6.60969	+	0.868672i	0.230540	+	0.0302984i
$823$	7.22071	+	29.7642i	0.251698	+	1.03751i	0.947621	+	0.319397i	$0.103480\pi$
$823$	7.22071	+	29.7642i	0.251698	+	1.03751i	−0.695923	+	0.718117i	$0.745004\pi$
$824$	9.63629	−	13.5323i	0.335696	−	0.471419i
$825$	15.4259	−	7.27209i	0.537061	−	0.253182i
$826$	−25.2366	+	13.0104i	−0.878093	+	0.452689i
$827$	27.9119			0.970592			0.485296	−	0.874350i	$-0.338712\pi$
$827$	27.9119			0.970592			0.485296	+	0.874350i	$0.338712\pi$
$828$	−14.3641	−	0.820975i	−0.499185	−	0.0285308i
$829$	2.47662			0.0860166			0.0430083	−	0.999075i	$-0.486306\pi$
$829$	2.47662			0.0860166			0.0430083	+	0.999075i	$0.486306\pi$
$830$	−0.574672	+	0.296264i	−0.0199472	+	0.0102835i
$831$	−19.1078	−	13.2604i	−0.662842	−	0.459999i
$832$	2.79488	−	3.92486i	0.0968950	−	0.136070i
$833$	7.00690	+	28.8829i	0.242775	+	1.00073i
$834$	12.8817	−	16.7955i	0.446055	−	0.581581i
$835$	−1.42118	−	4.10622i	−0.0491819	−	0.142102i
$836$	−1.01842	+	7.08327i	−0.0352228	+	0.244980i
$837$	3.12061	+	23.5806i	0.107864	+	0.815063i
$838$	3.72585	+	4.29986i	0.128707	+	0.148536i
$839$	−0.733951	−	15.4075i	−0.0253388	−	0.531927i	−0.975477	−	0.220099i	$-0.929362\pi$
$839$	−0.733951	−	15.4075i	−0.0253388	−	0.531927i	0.950139	−	0.311828i	$-0.100941\pi$
$840$	4.59325	−	1.65237i	0.158482	−	0.0570121i
$841$	−26.8335	+	77.5304i	−0.925295	+	2.67346i
$842$	−24.0010	−	22.8849i	−0.827129	−	0.788666i
$843$	5.10224	+	6.32858i	0.175730	+	0.217968i
$844$	−5.27555	−	15.2427i	−0.181592	−	0.524675i
$845$	−3.54344	+	7.75905i	−0.121898	+	0.266919i
$846$	3.93843	−	18.1439i	0.135406	−	0.623800i
$847$	−8.08164	−	17.6963i	−0.277688	−	0.608053i
$848$	11.3647	+	4.54973i	0.390265	+	0.156238i
$849$	3.70018	−	13.1913i	0.126990	−	0.452723i
$850$	−14.5555	−	25.2109i	−0.499251	−	0.864727i
$851$	42.8842	+	26.7276i	1.47005	+	0.916211i
$852$	−2.09394	−	6.82412i	−0.0717372	−	0.233790i
$853$	−39.4801	+	20.3534i	−1.35177	+	0.696887i	−0.973474	−	0.228797i	$-0.926521\pi$
$853$	−39.4801	+	20.3534i	−1.35177	+	0.696887i	−0.378298	+	0.925684i	$0.623490\pi$
$854$	−5.94152	−	41.3242i	−0.203315	−	1.41409i
$855$	−6.87356	+	3.75726i	−0.235071	+	0.128496i
$856$	17.0181	+	4.99697i	0.581667	+	0.170793i
$857$	11.0407	+	15.5046i	0.377145	+	0.529626i	0.958902	−	0.283737i	$-0.0915741\pi$
$857$	11.0407	+	15.5046i	0.377145	+	0.529626i	−0.581757	+	0.813362i	$0.697635\pi$
$858$	2.04565	+	18.9872i	0.0698372	+	0.648211i
$859$	−18.4708	+	7.39458i	−0.630214	+	0.252300i	−0.664706	−	0.747105i	$-0.731443\pi$
$859$	−18.4708	+	7.39458i	−0.630214	+	0.252300i	0.0344915	+	0.999405i	$0.489019\pi$
$860$	0.734509	+	0.700353i	0.0250465	+	0.0238818i
$861$	18.0848	+	34.0593i	0.616329	+	1.16074i
$862$	1.40924	+	29.5835i	0.0479988	+	1.00762i
$863$	25.4198	−	16.3363i	0.865300	−	0.556095i	−0.0310115	−	0.999519i	$-0.509873\pi$
$863$	25.4198	−	16.3363i	0.865300	−	0.556095i	0.896312	+	0.443424i	$0.146236\pi$
$864$	4.40254	−	2.76000i	0.149778	−	0.0938972i
$865$	−8.17099	+	2.39922i	−0.277822	+	0.0815759i
$866$	6.77083	+	5.32464i	0.230082	+	0.180939i
$867$	−40.2416	+	29.3977i	−1.36668	+	0.998397i
$868$	−15.3812	+	1.46872i	−0.522071	+	0.0498517i
$869$	0.0110341	+	0.0454831i	0.000374305	+	0.00154291i
$870$	14.4608	+	4.80941i	0.490267	+	0.163054i
$871$	−23.1145	−	9.25367i	−0.783206	−	0.313548i
$872$	13.0517	+	8.38781i	0.441986	+	0.284047i
$873$	−2.87926	+	1.95062i	−0.0974481	+	0.0660186i
$874$	0.921152	+	14.9695i	0.0311584	+	0.506350i
$875$	−13.1090	+	22.7055i	−0.443167	+	0.767587i
$876$	−1.10284	+	3.93166i	−0.0372616	+	0.132839i
$877$	13.1161	−	10.3146i	0.442900	−	0.348300i	−0.371671	−	0.928364i	$-0.621215\pi$
$877$	13.1161	−	10.3146i	0.442900	−	0.348300i	0.814571	+	0.580064i	$0.196973\pi$
$878$	4.64307	−	6.52028i	0.156696	−	0.220049i
$879$	−0.116264	−	9.58865i	−0.00392149	−	0.323417i
$880$	−1.10829	−	1.55637i	−0.0373603	−	0.0524652i
$881$	18.2003	−	21.0042i	0.613183	−	0.707651i	−0.361215	−	0.932483i	$-0.617638\pi$
$881$	18.2003	−	21.0042i	0.613183	−	0.707651i	0.974398	+	0.224832i	$0.0721832\pi$
$882$	7.38191	−	10.9173i	0.248562	−	0.367606i
$883$	−26.2723	+	7.71425i	−0.884134	+	0.259605i	−0.692116	−	0.721786i	$-0.743321\pi$
$883$	−26.2723	+	7.71425i	−0.884134	+	0.259605i	−0.192018	+	0.981391i	$0.561503\pi$
$884$	32.0093	−	6.16928i	1.07659	−	0.207495i
$885$	−2.15728	+	11.9724i	−0.0725163	+	0.402448i
$886$	0.707824	+	0.364909i	0.0237798	+	0.0122593i
$887$	−0.460719	+	1.33116i	−0.0154694	+	0.0446960i	−0.952471	−	0.304629i	$-0.901468\pi$
$887$	−0.460719	+	1.33116i	−0.0154694	+	0.0446960i	0.937002	+	0.349324i	$0.113589\pi$
$888$	−18.2172	+	1.08931i	−0.611331	+	0.0365549i
$889$	48.0892	+	37.8178i	1.61286	+	1.26837i
$890$	1.52049	−	1.75474i	0.0509671	−	0.0588191i
$891$	−5.78445	+	19.7657i	−0.193786	+	0.662176i
$892$	11.9422	+	3.50654i	0.399854	+	0.117408i
$893$	−19.2664	−	1.83972i	−0.644725	−	0.0615637i
$894$	0.203545	−	2.44449i	0.00680756	−	0.0817559i
$895$	−0.434600	+	9.12337i	−0.0145271	+	0.304961i
$896$	1.68767	+	2.92313i	0.0563811	+	0.0976550i
$897$	12.2698	+	38.0965i	0.409678	+	1.27201i
$898$	−13.2567	+	22.9613i	−0.442383	+	0.766229i
$899$	−40.5802	−	26.0793i	−1.35343	−	0.869794i
$900$	−3.92494	+	12.2973i	−0.130831	+	0.409911i
$901$	34.4051	+	75.3366i	1.14620	+	2.50983i
$902$	10.9240	−	10.4161i	0.363731	−	0.346817i
$903$	7.04547	+	0.925944i	0.234459	+	0.0308135i
$904$	−1.36641	−	0.263355i	−0.0454462	−	0.00875905i
$905$	−3.52031	+	1.40932i	−0.117019	+	0.0468473i
$906$	17.2329	+	26.1133i	0.572526	+	0.867557i
$907$	−0.0418252	+	0.00806116i	−0.00138878	+	0.000267666i	−0.189946	−	0.981795i	$-0.560831\pi$
$907$	−0.0418252	+	0.00806116i	−0.00138878	+	0.000267666i	0.188557	+	0.982062i	$0.439619\pi$
$908$	2.01993	−	1.29813i	0.0670339	−	0.0430800i
$909$	−9.88233	+	23.1061i	−0.327776	+	0.766381i
$910$	−8.89256	−	10.2626i	−0.294786	−	0.340201i
$911$	8.22718	−	33.9129i	0.272579	−	1.12358i	−0.656684	−	0.754166i	$-0.728042\pi$
$911$	8.22718	−	33.9129i	0.272579	−	1.12358i	0.929263	−	0.369419i	$-0.120443\pi$
$912$	−3.39968	−	4.21680i	−0.112575	−	0.139632i
$913$	1.73990	+	0.335338i	0.0575823	+	0.0110981i
$914$	14.5891	−	1.39309i	0.482565	−	0.0460794i
$915$	−15.5986	−	8.75545i	−0.515675	−	0.289446i
$916$	−3.61541	−	0.345230i	−0.119457	−	0.0114067i
$917$	0.871422	+	6.06088i	0.0287769	+	0.200148i
$918$	34.4427	+	7.04019i	1.13678	+	0.232361i
$919$	−16.0393			−0.529088			−0.264544	−	0.964374i	$-0.585221\pi$
$919$	−16.0393			−0.529088			−0.264544	+	0.964374i	$0.585221\pi$
$920$	−2.93610	−	2.72289i	−0.0968003	−	0.0897711i
$921$	6.09920	+	1.40157i	0.200976	+	0.0461834i
$922$	0.821721	−	17.2500i	0.0270619	−	0.568100i
$923$	−15.6088	+	12.2749i	−0.513770	+	0.404033i
$924$	−12.6944	−	4.22192i	−0.417614	−	0.138891i
$925$	32.8119	−	31.2860i	1.07885	−	1.02868i
$926$	2.20751	−	4.83377i	0.0725433	−	0.158848i
$927$	−39.9108	−	29.8489i	−1.31084	−	0.980366i
$928$	−1.49967	+	10.4304i	−0.0492290	+	0.342395i
$929$	−10.5620	+	43.5373i	−0.346529	+	1.42841i	0.485771	+	0.874086i	$0.338539\pi$
$929$	−10.5620	+	43.5373i	−0.346529	+	1.42841i	−0.832300	+	0.554325i	$0.812976\pi$
$930$	−3.51136	+	5.61225i	−0.115142	+	0.184033i
$931$	−12.2107	−	6.29504i	−0.400189	−	0.206312i
$932$	1.27179	+	0.655652i	0.0416588	+	0.0214766i
$933$	19.7166	−	31.5132i	0.645491	−	1.03170i
$934$	7.41816	−	30.5781i	0.242730	−	1.00054i
$935$	1.83965	−	12.7950i	0.0601629	−	0.418442i
$936$	−11.5756	−	8.65727i	−0.378360	−	0.282972i
$937$	23.5191	−	51.4997i	0.768337	−	1.68242i	0.0380567	−	0.999276i	$-0.487883\pi$
$937$	23.5191	−	51.4997i	0.768337	−	1.68242i	0.730280	−	0.683148i	$-0.239389\pi$
$938$	12.6232	−	12.0362i	0.412162	−	0.392996i
$939$	−39.3555	−	13.0889i	−1.28432	−	0.427141i
$940$	4.06188	−	3.19430i	0.132484	−	0.104187i
$941$	0.274198	−	5.75613i	0.00893861	−	0.187644i	−0.989982	−	0.141194i	$-0.954906\pi$
$941$	0.274198	−	5.75613i	0.00893861	−	0.187644i	0.998921	−	0.0464507i	$-0.0147910\pi$
$942$	25.7175	+	5.90978i	0.837921	+	0.192551i
$943$	17.9907	−	26.0201i	0.585858	−	0.847333i
$944$	−8.41185			−0.273782
$945$	−4.63401	−	13.8917i	−0.150745	−	0.451898i
$946$	−0.395835	−	2.75309i	−0.0128697	−	0.0895107i
$947$	−34.5489	−	3.29902i	−1.12269	−	0.107204i	−0.482842	−	0.875707i	$-0.660396\pi$
$947$	−34.5489	−	3.29902i	−1.12269	−	0.107204i	−0.639845	+	0.768504i	$0.721002\pi$
$948$	−0.0308918	−	0.0173395i	−0.00100332	−	0.000563159i
$949$	11.3079	−	1.07978i	0.367072	−	0.0350511i
$950$	13.2129	+	2.54658i	0.428683	+	0.0826219i
$951$	33.7151	+	41.8187i	1.09329	+	1.35606i
$952$	−5.38380	+	22.1923i	−0.174490	+	0.719258i
$953$	18.8298	+	21.7307i	0.609956	+	0.703927i	0.973767	−	0.227546i	$-0.0730701\pi$
$953$	18.8298	+	21.7307i	0.609956	+	0.703927i	−0.363811	+	0.931473i	$0.618525\pi$
$954$	14.4415	−	33.7661i	0.467562	−	1.09322i
$955$	−7.88731	+	5.06887i	−0.255227	+	0.164025i
$956$	−20.5471	+	3.96013i	−0.664542	+	0.128080i
$957$	−23.0045	−	34.8591i	−0.743631	−	1.12684i
$958$	14.4876	−	5.79996i	0.468073	−	0.187388i
$959$	12.7567	+	2.45865i	0.411934	+	0.0793938i
$960$	1.43387	+	0.188445i	0.0462780	+	0.00608204i
$961$	−7.27002	+	6.93195i	−0.234517	+	0.223611i
$962$	21.0898	+	46.1801i	0.679961	+	1.48891i
$963$	16.1789	−	50.6904i	0.521357	−	1.63348i
$964$	−14.5283	−	9.33680i	−0.467926	−	0.300718i
$965$	−6.18515	+	10.7130i	−0.199107	+	0.344863i
$966$	−27.8466	−	3.26784i	−0.895950	−	0.105141i
$967$	−13.8508	−	23.9904i	−0.445413	−	0.771478i	0.552668	−	0.833402i	$-0.313610\pi$
$967$	−13.8508	−	23.9904i	−0.445413	−	0.771478i	−0.998081	+	0.0619234i	$0.980277\pi$
$968$	0.274247	−	5.75715i	0.00881462	−	0.185042i
$969$	3.04088	−	36.5197i	0.0976871	−	1.17318i
$970$	−0.963562	−	0.0920090i	−0.0309381	−	0.00295423i
$971$	44.3592	+	13.0250i	1.42355	+	0.417993i	0.900705	−	0.434431i	$-0.143051\pi$
$971$	44.3592	+	13.0250i	1.42355	+	0.417993i	0.522850	+	0.852425i	$0.324869\pi$
$972$	−7.96937	−	13.3974i	−0.255618	−	0.429720i
$973$	27.0121	−	31.1736i	0.865967	−	0.999379i
$974$	21.0066	+	16.5198i	0.673094	+	0.529327i
$975$	35.8453	−	2.14339i	1.14797	−	0.0686435i
$976$	4.04546	−	11.6886i	0.129492	−	0.374143i
$977$	17.8179	+	9.18579i	0.570046	+	0.293879i	0.719051	−	0.694957i	$-0.244577\pi$
$977$	17.8179	+	9.18579i	0.570046	+	0.293879i	−0.149005	+	0.988836i	$0.547607\pi$
$978$	−2.11440	+	11.7344i	−0.0676111	+	0.375225i
$979$	−6.24829	+	1.20426i	−0.199696	+	0.0384883i
$980$	3.51937	−	1.03338i	0.112422	−	0.0330101i
$981$	26.0708	−	38.5569i	0.832376	−	1.23103i
$982$	6.11915	−	7.06188i	0.195270	−	0.225354i
$983$	7.54782	+	10.5994i	0.240738	+	0.338069i	0.917214	−	0.398396i	$-0.130433\pi$
$983$	7.54782	+	10.5994i	0.240738	+	0.338069i	−0.676476	+	0.736465i	$0.736494\pi$
$984$	0.138519	+	11.4240i	0.00441581	+	0.364185i
$985$	6.29695	−	8.84284i	0.200638	−	0.281756i
$986$	−56.0403	+	44.0706i	−1.78469	+	1.40349i
$987$	9.77183	−	34.8369i	0.311041	−	1.10887i
$988$	−7.53401	+	13.0493i	−0.239689	+	0.415153i
$989$	−1.98272	−	5.48172i	−0.0630468	−	0.174308i
$990$	−4.74547	+	3.21493i	−0.150821	+	0.102177i
$991$	−46.5145	−	29.8931i	−1.47758	−	0.949584i	−0.997373	−	0.0724300i	$-0.976925\pi$
$991$	−46.5145	−	29.8931i	−1.47758	−	0.949584i	−0.480209	−	0.877154i	$-0.659439\pi$
$992$	−4.24974	−	1.70134i	−0.134929	−	0.0540176i
$993$	52.8021	+	17.5610i	1.67562	+	0.557283i
$994$	−3.27953	−	13.5184i	−0.104020	−	0.428777i
$995$	5.41837	−	0.517392i	0.171774	−	0.0164024i
$996$	−1.08299	+	0.791157i	−0.0343159	+	0.0250688i
$997$	−0.346704	−	0.272651i	−0.0109802	−	0.00863495i	0.612654	−	0.790351i	$-0.290102\pi$
$997$	−0.346704	−	0.272651i	−0.0109802	−	0.00863495i	−0.623634	+	0.781716i	$0.714344\pi$
$998$	−26.4558	+	7.76813i	−0.837444	+	0.245896i
$999$	1.99100	+	54.7132i	0.0629925	+	1.73105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.m.a.25.6	✓	240
9.4	even	3	inner	414.2.m.a.301.6	yes	240
23.12	even	11	inner	414.2.m.a.403.6	yes	240
207.58	even	33	inner	414.2.m.a.265.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.m.a.25.6	✓	240	1.1	even	1	trivial
414.2.m.a.265.6	yes	240	207.58	even	33	inner
414.2.m.a.301.6	yes	240	9.4	even	3	inner
414.2.m.a.403.6	yes	240	23.12	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.888835 - 0.458227i) q^{2} +(0.143725 - 1.72608i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-0.196850 - 0.811428i) q^{5} +(-0.663187 - 1.60006i) q^{6} +(-1.10397 - 3.18970i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-2.95869 - 0.496161i) q^{9} +O(q^{10})\)	\(q+(0.888835 - 0.458227i) q^{2} +(0.143725 - 1.72608i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-0.196850 - 0.811428i) q^{5} +(-0.663187 - 1.60006i) q^{6} +(-1.10397 - 3.18970i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-2.95869 - 0.496161i) q^{9} +(-0.546785 - 0.631024i) q^{10} +(0.108882 + 2.28571i) q^{11} +(-1.32265 - 1.11830i) q^{12} +(-1.57591 + 4.55328i) q^{13} +(-2.44285 - 2.32925i) q^{14} +(-1.42888 + 0.223156i) q^{15} +(-0.327068 - 0.945001i) q^{16} +(2.81051 - 6.15416i) q^{17} +(-2.85714 + 0.914743i) q^{18} +(1.29911 + 2.84465i) q^{19} +(-0.775154 - 0.310325i) q^{20} +(-5.66434 + 1.44709i) q^{21} +(1.14415 + 1.98173i) q^{22} +(3.19053 + 3.58058i) q^{23} +(-1.68805 - 0.387909i) q^{24} +(3.82451 - 1.97167i) q^{25} +(0.685713 + 4.76924i) q^{26} +(-1.28165 + 5.03561i) q^{27} +(-3.23862 - 0.950944i) q^{28} +(-6.11245 - 8.58374i) q^{29} +(-1.16778 + 0.853100i) q^{30} +(4.24974 - 1.70134i) q^{31} +(-0.723734 - 0.690079i) q^{32} +(3.96096 + 0.140575i) q^{33} +(-0.321918 - 6.75789i) q^{34} +(-2.37090 + 1.52368i) q^{35} +(-2.12037 + 2.12227i) q^{36} +(10.1097 - 2.96848i) q^{37} +(2.45819 + 1.93314i) q^{38} +(7.63282 + 3.37456i) q^{39} +(-0.831184 + 0.0793684i) q^{40} +(-1.55510 - 6.41022i) q^{41} +(-4.37157 + 3.88178i) q^{42} +(-1.12842 - 0.451751i) q^{43} +(1.92504 + 1.23715i) q^{44} +(0.179819 + 2.49843i) q^{45} +(4.47657 + 1.72056i) q^{46} +(-3.09441 + 5.35967i) q^{47} +(-1.67815 + 0.428724i) q^{48} +(-3.45308 + 2.71553i) q^{49} +(2.49589 - 3.50499i) q^{50} +(-10.2186 - 5.73567i) q^{51} +(2.79488 + 3.92486i) q^{52} +(-8.01652 + 9.25156i) q^{53} +(1.16827 + 5.06312i) q^{54} +(1.83326 - 0.538292i) q^{55} +(-3.31435 + 0.638788i) q^{56} +(5.09681 - 1.83352i) q^{57} +(-9.36626 - 4.82864i) q^{58} +(2.75125 - 7.94920i) q^{59} +(-0.647054 + 1.29337i) q^{60} +(9.72258 + 7.64592i) q^{61} +(2.99772 - 3.45955i) q^{62} +(1.68368 + 9.98507i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(4.00488 + 0.382419i) q^{65} +(3.58506 - 1.69007i) q^{66} +(-0.245875 + 5.16156i) q^{67} +(-3.38278 - 5.85914i) q^{68} +(6.63891 - 4.99248i) q^{69} +(-1.40915 + 2.44071i) q^{70} +(3.46698 + 2.22810i) q^{71} +(-0.912176 + 2.85796i) q^{72} +(-0.979365 - 2.14451i) q^{73} +(7.62564 - 7.27103i) q^{74} +(-2.85358 - 6.88478i) q^{75} +(3.07074 + 0.591837i) q^{76} +(7.17053 - 2.87065i) q^{77} +(8.33063 - 0.498135i) q^{78} +(0.0200833 - 0.00387073i) q^{79} +(-0.702417 + 0.451416i) q^{80} +(8.50765 + 2.93597i) q^{81} +(-4.31956 - 4.98504i) q^{82} +(0.182557 - 0.752511i) q^{83} +(-2.10687 + 5.45343i) q^{84} +(-5.54691 - 1.06908i) q^{85} +(-1.20998 + 0.115539i) q^{86} +(-15.6947 + 9.31687i) q^{87} +(2.27794 + 0.217517i) q^{88} +(0.395747 + 2.75248i) q^{89} +(1.30468 + 2.13830i) q^{90} +16.2634 q^{91} +(4.76734 - 0.521986i) q^{92} +(-2.32585 - 7.57990i) q^{93} +(-0.294476 + 6.18180i) q^{94} +(2.05250 - 1.61410i) q^{95} +(-1.29515 + 1.15004i) q^{96} +(0.839000 - 0.799985i) q^{97} +(-1.82489 + 3.99595i) q^{98} +(0.811933 - 6.81672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

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