LMFDB - Embedded newform 230.2.j.a.29.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(9,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 10]))

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

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

chi := DirichletCharacter("230.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.j (of order $22$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			29.8
Character	$\chi$	$=$	230.29
Dual form			230.2.j.a.119.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.909632 + 0.415415i) q^{2} +(-0.537451 + 1.83039i) q^{3} +(0.654861 + 0.755750i) q^{4} +(1.72616 + 1.42140i) q^{5} +(-1.24925 + 1.44172i) q^{6} +(-2.93634 - 0.422181i) q^{7} +(0.281733 + 0.959493i) q^{8} +(-0.537711 - 0.345566i) q^{9} +O(q^{10})$	\(q+(0.909632 + 0.415415i) q^{2} +(-0.537451 + 1.83039i) q^{3} +(0.654861 + 0.755750i) q^{4} +(1.72616 + 1.42140i) q^{5} +(-1.24925 + 1.44172i) q^{6} +(-2.93634 - 0.422181i) q^{7} +(0.281733 + 0.959493i) q^{8} +(-0.537711 - 0.345566i) q^{9} +(0.979700 + 2.01002i) q^{10} +(-1.22793 - 2.68879i) q^{11} +(-1.73527 + 0.792472i) q^{12} +(1.87656 - 0.269809i) q^{13} +(-2.49560 - 1.60383i) q^{14} +(-3.52944 + 2.39561i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(0.719853 + 0.623756i) q^{17} +(-0.345566 - 0.537711i) q^{18} +(0.167681 + 0.193515i) q^{19} +(0.0561727 + 2.23536i) q^{20} +(2.35089 - 5.14774i) q^{21} -2.95591i q^{22} +(4.04295 - 2.57964i) q^{23} -1.90766 q^{24} +(0.959253 + 4.90712i) q^{25} +(1.81906 + 0.534125i) q^{26} +(-3.40363 + 2.94926i) q^{27} +(-1.60383 - 2.49560i) q^{28} +(-0.0268070 + 0.0309369i) q^{29} +(-4.20566 + 0.712944i) q^{30} +(5.13506 - 1.50779i) q^{31} +(-0.540641 + 0.841254i) q^{32} +(5.58149 - 0.802497i) q^{33} +(0.395684 + 0.866426i) q^{34} +(-4.46849 - 4.90245i) q^{35} +(-0.0909646 - 0.632673i) q^{36} +(-2.00856 + 3.12538i) q^{37} +(0.0721395 + 0.245685i) q^{38} +(-0.514704 + 3.57985i) q^{39} +(-0.877507 + 2.05669i) q^{40} +(7.88484 - 5.06728i) q^{41} +(4.27689 - 3.70595i) q^{42} +(3.10755 - 10.5833i) q^{43} +(1.22793 - 2.68879i) q^{44} +(-0.436988 - 1.36080i) q^{45} +(4.74922 - 0.667022i) q^{46} -8.07309i q^{47} +(-1.73527 - 0.792472i) q^{48} +(1.72738 + 0.507204i) q^{49} +(-1.16592 + 4.86216i) q^{50} +(-1.52860 + 0.982373i) q^{51} +(1.43279 + 1.24152i) q^{52} +(-12.5053 - 1.79799i) q^{53} +(-4.32122 + 1.26883i) q^{54} +(1.70224 - 6.38666i) q^{55} +(-0.422181 - 2.93634i) q^{56} +(-0.444328 + 0.202918i) q^{57} +(-0.0372362 + 0.0170052i) q^{58} +(0.794391 + 5.52511i) q^{59} +(-4.12177 - 1.09858i) q^{60} +(8.08881 - 2.37509i) q^{61} +(5.29738 + 0.761648i) q^{62} +(1.43301 + 1.24171i) q^{63} +(-0.841254 + 0.540641i) q^{64} +(3.62275 + 2.20161i) q^{65} +(5.41047 + 1.58866i) q^{66} +(-5.22758 - 2.38735i) q^{67} +0.952502i q^{68} +(2.54886 + 8.78660i) q^{69} +(-2.02813 - 6.31571i) q^{70} +(-5.95566 + 13.0411i) q^{71} +(0.180077 - 0.613288i) q^{72} +(-0.785633 + 0.680754i) q^{73} +(-3.12538 + 2.00856i) q^{74} +(-9.49749 - 0.881530i) q^{75} +(-0.0364407 + 0.253450i) q^{76} +(2.47046 + 8.41360i) q^{77} +(-1.95531 + 3.04253i) q^{78} +(-0.123952 - 0.862106i) q^{79} +(-1.65259 + 1.50630i) q^{80} +(-4.36559 - 9.55931i) q^{81} +(9.27732 - 1.33388i) q^{82} +(-6.11445 + 9.51428i) q^{83} +(5.42991 - 1.59436i) q^{84} +(0.355975 + 2.09990i) q^{85} +(7.22320 - 8.33602i) q^{86} +(-0.0422192 - 0.0656944i) q^{87} +(2.23393 - 1.93571i) q^{88} +(-15.5804 - 4.57482i) q^{89} +(0.167800 - 1.41936i) q^{90} -5.62412 q^{91} +(4.59713 + 1.36615i) q^{92} +10.2095i q^{93} +(3.35368 - 7.34354i) q^{94} +(0.0143834 + 0.572379i) q^{95} +(-1.24925 - 1.44172i) q^{96} +(-1.81420 - 2.82294i) q^{97} +(1.36058 + 1.17895i) q^{98} +(-0.268883 + 1.87012i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41} - 8 q^{44} + 16 q^{45} - 4 q^{46} - 58 q^{49} + 12 q^{50} - 24 q^{51} - 6 q^{54} - 36 q^{55} + 22 q^{56} - 102 q^{59} - 38 q^{60} + 72 q^{61} + 12 q^{64} - 138 q^{65} + 80 q^{66} - 212 q^{69} - 108 q^{70} + 176 q^{71} - 88 q^{74} - 100 q^{75} + 16 q^{76} - 104 q^{79} - 22 q^{80} - 28 q^{81} - 22 q^{84} + 2 q^{85} + 62 q^{86} + 48 q^{89} + 24 q^{90} - 56 q^{91} + 24 q^{94} + 18 q^{95} - 4 q^{96} + 188 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	0.909632	+	0.415415i	0.643207	+	0.293743i
$2$	0.909632	+	0.415415i	0.643207	+	0.293743i
$3$	−0.537451	+	1.83039i	−0.310297	+	1.05678i	0.645746	+	0.763552i	$0.276546\pi$
$3$	−0.537451	+	1.83039i	−0.310297	+	1.05678i	−0.956044	+	0.293224i	$0.905272\pi$
$4$	0.654861	+	0.755750i	0.327430	+	0.377875i
$5$	1.72616	+	1.42140i	0.771962	+	0.635669i
$5$	1.72616	+	1.42140i	0.771962	+	0.635669i
$6$	−1.24925	+	1.44172i	−0.510006	+	0.588578i
$7$	−2.93634	−	0.422181i	−1.10983	−	0.159570i	−0.437068	−	0.899428i	$-0.643983\pi$
$7$	−2.93634	−	0.422181i	−1.10983	−	0.159570i	−0.672762	+	0.739859i	$0.734892\pi$
$8$	0.281733	+	0.959493i	0.0996075	+	0.339232i
$9$	−0.537711	−	0.345566i	−0.179237	−	0.115189i
$10$	0.979700	+	2.01002i	0.309808	+	0.635625i
$11$	−1.22793	−	2.68879i	−0.370235	−	0.810701i	−0.999440	−	0.0334618i	$-0.989347\pi$
$11$	−1.22793	−	2.68879i	−0.370235	−	0.810701i	0.629205	−	0.777239i	$-0.283380\pi$
$12$	−1.73527	+	0.792472i	−0.500930	+	0.228767i
$13$	1.87656	−	0.269809i	0.520464	−	0.0748315i	0.122924	−	0.992416i	$-0.460773\pi$
$13$	1.87656	−	0.269809i	0.520464	−	0.0748315i	0.397540	+	0.917585i	$0.369864\pi$
$14$	−2.49560	−	1.60383i	−0.666978	−	0.428641i
$15$	−3.52944	+	2.39561i	−0.911297	+	0.618544i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	0.719853	+	0.623756i	0.174590	+	0.151283i	0.737772	−	0.675049i	$-0.235878\pi$
$17$	0.719853	+	0.623756i	0.174590	+	0.151283i	−0.563182	+	0.826333i	$0.690423\pi$
$18$	−0.345566	−	0.537711i	−0.0814507	−	0.126740i
$19$	0.167681	+	0.193515i	0.0384688	+	0.0443953i	0.774658	−	0.632381i	$-0.217922\pi$
$19$	0.167681	+	0.193515i	0.0384688	+	0.0443953i	−0.736189	+	0.676776i	$0.763377\pi$
$20$	0.0561727	+	2.23536i	0.0125606	+	0.499842i
$21$	2.35089	−	5.14774i	0.513007	−	1.12333i
$22$		−	2.95591i		−	0.630202i
$23$	4.04295	−	2.57964i	0.843014	−	0.537892i
$23$	4.04295	−	2.57964i	0.843014	−	0.537892i
$24$	−1.90766			−0.389400
$25$	0.959253	+	4.90712i	0.191851	+	0.981424i
$26$	1.81906	+	0.534125i	0.356747	+	0.104751i
$27$	−3.40363	+	2.94926i	−0.655029	+	0.567586i
$28$	−1.60383	−	2.49560i	−0.303095	−	0.471625i
$29$	−0.0268070	+	0.0309369i	−0.00497794	+	0.00574485i	−0.758233	−	0.651984i	$-0.773937\pi$
$29$	−0.0268070	+	0.0309369i	−0.00497794	+	0.00574485i	0.753255	+	0.657728i	$0.228483\pi$
$30$	−4.20566	+	0.712944i	−0.767846	+	0.130165i
$31$	5.13506	−	1.50779i	0.922285	−	0.270807i	0.214081	−	0.976816i	$-0.431324\pi$
$31$	5.13506	−	1.50779i	0.922285	−	0.270807i	0.708203	+	0.706009i	$0.249506\pi$
$32$	−0.540641	+	0.841254i	−0.0955727	+	0.148714i
$33$	5.58149	−	0.802497i	0.971612	−	0.139697i
$34$	0.395684	+	0.866426i	0.0678592	+	0.148591i
$35$	−4.46849	−	4.90245i	−0.755314	−	0.828666i
$36$	−0.0909646	−	0.632673i	−0.0151608	−	0.105445i
$37$	−2.00856	+	3.12538i	−0.330205	+	0.513809i	−0.966169	−	0.257909i	$-0.916966\pi$
$37$	−2.00856	+	3.12538i	−0.330205	+	0.513809i	0.635964	+	0.771719i	$0.280603\pi$
$38$	0.0721395	+	0.245685i	0.0117026	+	0.0398553i
$39$	−0.514704	+	3.57985i	−0.0824186	+	0.573234i
$40$	−0.877507	+	2.05669i	−0.138746	+	0.325192i
$41$	7.88484	−	5.06728i	1.23140	−	0.791376i	0.247295	−	0.968940i	$-0.420458\pi$
$41$	7.88484	−	5.06728i	1.23140	−	0.791376i	0.984109	+	0.177564i	$0.0568218\pi$
$42$	4.27689	−	3.70595i	0.659939	−	0.571840i
$43$	3.10755	−	10.5833i	0.473897	−	1.61394i	−0.282111	−	0.959382i	$-0.591035\pi$
$43$	3.10755	−	10.5833i	0.473897	−	1.61394i	0.756008	−	0.654563i	$-0.227147\pi$
$44$	1.22793	−	2.68879i	0.185117	−	0.405351i
$45$	−0.436988	−	1.36080i	−0.0651424	−	0.202857i
$46$	4.74922	−	0.667022i	0.700234	−	0.0983470i
$47$		−	8.07309i		−	1.17758i	−0.808286	−	0.588790i	$-0.799604\pi$
$47$		−	8.07309i		−	1.17758i	0.808286	−	0.588790i	$-0.200396\pi$
$48$	−1.73527	−	0.792472i	−0.250465	−	0.114383i
$49$	1.72738	+	0.507204i	0.246768	+	0.0724577i
$50$	−1.16592	+	4.86216i	−0.164887	+	0.687614i
$51$	−1.52860	+	0.982373i	−0.214047	+	0.137560i
$52$	1.43279	+	1.24152i	0.198693	+	0.172168i
$53$	−12.5053	−	1.79799i	−1.71773	−	0.246972i	−0.788122	−	0.615520i	$-0.788946\pi$
$53$	−12.5053	−	1.79799i	−1.71773	−	0.246972i	−0.929609	+	0.368547i	$0.879855\pi$
$54$	−4.32122	+	1.26883i	−0.588044	+	0.172665i
$55$	1.70224	−	6.38666i	0.229530	−	0.861177i
$56$	−0.422181	−	2.93634i	−0.0564163	−	0.392384i
$57$	−0.444328	+	0.202918i	−0.0588526	+	0.0268771i
$58$	−0.0372362	+	0.0170052i	−0.00488935	+	0.00223289i
$59$	0.794391	+	5.52511i	0.103421	+	0.719308i	0.973879	+	0.227066i	$0.0729134\pi$
$59$	0.794391	+	5.52511i	0.103421	+	0.719308i	−0.870458	+	0.492242i	$0.836178\pi$
$60$	−4.12177	−	1.09858i	−0.532119	−	0.141826i
$61$	8.08881	−	2.37509i	1.03567	−	0.304099i	0.280653	−	0.959809i	$-0.409449\pi$
$61$	8.08881	−	2.37509i	1.03567	−	0.304099i	0.755012	+	0.655710i	$0.227631\pi$
$62$	5.29738	+	0.761648i	0.672767	+	0.0967294i
$63$	1.43301	+	1.24171i	0.180542	+	0.156441i
$64$	−0.841254	+	0.540641i	−0.105157	+	0.0675801i
$65$	3.62275	+	2.20161i	0.449347	+	0.273076i
$66$	5.41047	+	1.58866i	0.665983	+	0.195550i
$67$	−5.22758	−	2.38735i	−0.638650	−	0.291662i	0.0696517	−	0.997571i	$-0.477811\pi$
$67$	−5.22758	−	2.38735i	−0.638650	−	0.291662i	−0.708302	+	0.705910i	$0.750538\pi$
$68$			0.952502i			0.115508i
$69$	2.54886	+	8.78660i	0.306847	+	1.05778i
$70$	−2.02813	−	6.31571i	−0.242408	−	0.754872i
$71$	−5.95566	+	13.0411i	−0.706807	+	1.54769i	0.124712	+	0.992193i	$0.460199\pi$
$71$	−5.95566	+	13.0411i	−0.706807	+	1.54769i	−0.831518	+	0.555498i	$0.812528\pi$
$72$	0.180077	−	0.613288i	0.0212223	−	0.0722766i
$73$	−0.785633	+	0.680754i	−0.0919513	+	0.0796763i	−0.699624	−	0.714512i	$-0.746649\pi$
$73$	−0.785633	+	0.680754i	−0.0919513	+	0.0796763i	0.607672	+	0.794188i	$0.292103\pi$
$74$	−3.12538	+	2.00856i	−0.363318	+	0.233490i
$75$	−9.49749	−	0.881530i	−1.09668	−	0.101790i
$76$	−0.0364407	+	0.253450i	−0.00418003	+	0.0290727i
$77$	2.47046	+	8.41360i	0.281535	+	0.958819i
$78$	−1.95531	+	3.04253i	−0.221396	+	0.344498i
$79$	−0.123952	−	0.862106i	−0.0139457	−	0.0969945i	0.981660	−	0.190641i	$-0.0610567\pi$
$79$	−0.123952	−	0.862106i	−0.0139457	−	0.0969945i	−0.995605	+	0.0936467i	$0.970148\pi$
$80$	−1.65259	+	1.50630i	−0.184765	+	0.168410i
$81$	−4.36559	−	9.55931i	−0.485066	−	1.06215i
$82$	9.27732	−	1.33388i	1.02451	−	0.147302i
$83$	−6.11445	+	9.51428i	−0.671149	+	1.04433i	0.324011	+	0.946053i	$0.394969\pi$
$83$	−6.11445	+	9.51428i	−0.671149	+	1.04433i	−0.995159	+	0.0982742i	$0.968668\pi$
$84$	5.42991	−	1.59436i	0.592451	−	0.173959i
$85$	0.355975	+	2.09990i	0.0386109	+	0.227766i
$86$	7.22320	−	8.33602i	0.778898	−	0.898896i
$87$	−0.0422192	−	0.0656944i	−0.00452637	−	0.00704318i
$88$	2.23393	−	1.93571i	0.238138	−	0.206347i
$89$	−15.5804	−	4.57482i	−1.65152	−	0.484930i	−0.682288	−	0.731083i	$-0.739015\pi$
$89$	−15.5804	−	4.57482i	−1.65152	−	0.484930i	−0.969231	+	0.246153i	$0.920833\pi$
$90$	0.167800	−	1.41936i	0.0176877	−	0.149614i
$91$	−5.62412			−0.589568
$92$	4.59713	+	1.36615i	0.479284	+	0.142431i
$93$			10.2095i			1.05868i
$94$	3.35368	−	7.34354i	0.345906	−	0.757428i
$95$	0.0143834	+	0.572379i	0.00147571	+	0.0587249i
$96$	−1.24925	−	1.44172i	−0.127501	−	0.147144i
$97$	−1.81420	−	2.82294i	−0.184204	−	0.286626i	0.736855	−	0.676051i	$-0.236310\pi$
$97$	−1.81420	−	2.82294i	−0.184204	−	0.286626i	−0.921058	+	0.389425i	$0.872674\pi$
$98$	1.36058	+	1.17895i	0.137439	+	0.119092i
$99$	−0.268883	+	1.87012i	−0.0270238	+	0.187955i
$100$	−3.08038	+	3.93844i	−0.308038	+	0.393844i
$101$	−0.243652	−	0.156585i	−0.0242443	−	0.0155808i	0.528463	−	0.848957i	$-0.322769\pi$
$101$	−0.243652	−	0.156585i	−0.0242443	−	0.0155808i	−0.552707	+	0.833376i	$0.686405\pi$
$102$	−1.79856	+	0.258594i	−0.178084	+	0.0256046i
$103$	8.77628	−	4.00799i	0.864753	−	0.394919i	0.0668915	−	0.997760i	$-0.478692\pi$
$103$	8.77628	−	4.00799i	0.864753	−	0.394919i	0.797861	+	0.602841i	$0.205965\pi$
$104$	0.787568	+	1.72453i	0.0772274	+	0.169104i
$105$	11.3750	−	5.54426i	1.11009	−	0.541064i
$106$	−10.6283	−	6.83038i	−1.03231	−	0.663425i
$107$	4.41635	+	15.0407i	0.426944	+	1.45404i	0.839627	+	0.543164i	$0.182774\pi$
$107$	4.41635	+	15.0407i	0.426944	+	1.45404i	−0.412683	+	0.910875i	$0.635408\pi$
$108$	−4.45781	−	0.640936i	−0.428953	−	0.0616741i
$109$	4.51086	−	5.20580i	0.432062	−	0.498626i	−0.497412	−	0.867514i	$-0.665716\pi$
$109$	4.51086	−	5.20580i	0.432062	−	0.498626i	0.929474	+	0.368889i	$0.120262\pi$
$110$	4.20153	−	5.10237i	0.400600	−	0.486492i
$111$	−4.64116	−	5.35619i	−0.440520	−	0.508387i
$112$	0.835768	−	2.84636i	0.0789727	−	0.268956i
$113$	−9.78064	−	4.46667i	−0.920085	−	0.420189i	−0.101671	−	0.994818i	$-0.532419\pi$
$113$	−9.78064	−	4.46667i	−0.920085	−	0.420189i	−0.818414	+	0.574629i	$0.805146\pi$
$114$	−0.488470			−0.0457494
$115$	10.6455	+	1.29377i	0.992696	+	0.120645i
$116$	−0.0409355			−0.00380076
$117$	−1.10228	−	0.503397i	−0.101906	−	0.0465390i
$118$	−1.57261	+	5.35582i	−0.144771	+	0.493043i
$119$	−1.85039	−	2.13547i	−0.169625	−	0.195758i
$120$	−3.29293	−	2.71155i	−0.300602	−	0.247529i
$121$	1.48168	−	1.70995i	0.134698	−	0.155450i
$122$	8.34448	+	1.19976i	0.755474	+	0.108621i
$123$	5.03738	+	17.1557i	0.454205	+	1.54688i
$124$	4.50226	+	2.89343i	0.404315	+	0.259838i
$125$	−5.31915	+	9.83395i	−0.475759	+	0.879576i
$126$	0.787686	+	1.72479i	0.0701727	+	0.153657i
$127$	−1.59832	+	0.729926i	−0.141828	+	0.0647705i	−0.485065	−	0.874478i	$-0.661204\pi$
$127$	−1.59832	+	0.729926i	−0.141828	+	0.0647705i	0.343237	+	0.939249i	$0.388477\pi$
$128$	−0.989821	+	0.142315i	−0.0874887	+	0.0125790i
$129$	17.7015	+	11.3761i	1.55853	+	1.00161i
$130$	2.38079	+	3.50760i	0.208809	+	0.307637i
$131$	−0.739637	+	5.14428i	−0.0646223	+	0.449458i	0.931661	+	0.363327i	$0.118359\pi$
$131$	−0.739637	+	5.14428i	−0.0646223	+	0.449458i	−0.996284	+	0.0861308i	$0.972550\pi$
$132$	4.26158	+	3.69268i	0.370923	+	0.321407i
$133$	−0.410671	−	0.639016i	−0.0356097	−	0.0554097i
$134$	−3.76343	−	4.34323i	−0.325111	−	0.375198i
$135$	−10.0673	+	0.252982i	−0.866455	+	0.0217733i
$136$	−0.395684	+	0.866426i	−0.0339296	+	0.0742954i
$137$		−	3.53527i		−	0.302038i	−0.988531	−	0.151019i	$-0.951744\pi$
$137$		−	3.53527i		−	0.302038i	0.988531	−	0.151019i	$-0.0482555\pi$
$138$	−1.33156	+	9.05141i	−0.113350	+	0.770507i
$139$	−18.7922			−1.59393			−0.796967	−	0.604023i	$-0.793564\pi$
$139$	−18.7922			−1.59393			−0.796967	+	0.604023i	$0.793564\pi$
$140$	0.778786	−	6.58749i	0.0658194	−	0.556744i
$141$	14.7769	+	4.33889i	1.24444	+	0.365400i
$142$	−10.8349	+	9.38851i	−0.909246	+	0.787866i
$143$	−3.02974	−	4.71437i	−0.253360	−	0.394236i
$144$	0.418573	−	0.483059i	0.0348811	−	0.0402549i
$145$	−0.0902469	+	0.0152987i	−0.00749460	+	0.00127048i
$146$	−0.997432	+	0.292872i	−0.0825481	+	0.0242383i
$147$	−1.85676	+	2.88918i	−0.153143	+	0.238295i
$148$	−3.67733	+	0.528721i	−0.302275	+	0.0434606i
$149$	−6.53477	−	14.3091i	−0.535349	−	1.17225i	−0.963295	−	0.268446i	$-0.913490\pi$
$149$	−6.53477	−	14.3091i	−0.535349	−	1.17225i	0.427946	−	0.903804i	$-0.359237\pi$
$150$	−8.27302	−	4.74727i	−0.675489	−	0.387613i
$151$	2.82587	+	19.6544i	0.229966	+	1.59945i	0.698239	+	0.715865i	$0.253967\pi$
$151$	2.82587	+	19.6544i	0.229966	+	1.59945i	−0.468272	+	0.883584i	$0.655123\pi$
$152$	−0.138435	+	0.215409i	−0.0112285	+	0.0174719i
$153$	−0.171524	−	0.584157i	−0.0138669	−	0.0472263i
$154$	−1.24793	+	8.67955i	−0.100561	+	0.699418i
$155$	11.0071	+	4.69628i	0.884112	+	0.377215i
$156$	−3.04253	+	1.95531i	−0.243597	+	0.156550i
$157$	1.59778	−	1.38448i	0.127517	−	0.110494i	−0.588768	−	0.808302i	$-0.700387\pi$
$157$	1.59778	−	1.38448i	0.127517	−	0.110494i	0.716284	+	0.697808i	$0.245841\pi$
$158$	0.245381	−	0.835691i	0.0195215	−	0.0664840i
$159$	10.0120	−	21.9232i	0.794002	−	1.73862i
$160$	−2.12899	+	0.683672i	−0.168311	+	0.0540490i
$161$	−12.9605	+	5.86783i	−1.02143	+	0.462450i
$162$		−	10.5090i		−	0.825664i
$163$	6.14991	+	2.80857i	0.481698	+	0.219984i	0.641438	−	0.767175i	$-0.278338\pi$
$163$	6.14991	+	2.80857i	0.481698	+	0.219984i	−0.159740	+	0.987159i	$0.551066\pi$
$164$	8.99306	+	2.64060i	0.702240	+	0.206196i
$165$	10.7752	+	6.54828i	0.838848	+	0.509783i
$166$	−9.51428	+	6.11445i	−0.738451	+	0.474574i
$167$	−14.0030	−	12.1337i	−1.08358	−	0.938931i	−0.0852349	−	0.996361i	$-0.527164\pi$
$167$	−14.0030	−	12.1337i	−1.08358	−	0.938931i	−0.998350	+	0.0574296i	$0.981710\pi$
$168$	5.60154	+	0.805380i	0.432168	+	0.0621364i
$169$	−9.02473	+	2.64990i	−0.694210	+	0.203838i
$170$	−0.548524	+	2.05801i	−0.0420699	+	0.157842i
$171$	−0.0232921	−	0.162000i	−0.00178119	−	0.0123885i
$172$	10.0334	−	4.58209i	0.765037	−	0.349381i
$173$	16.7785	−	7.66249i	1.27565	−	0.582568i	0.341642	−	0.939830i	$-0.389017\pi$
$173$	16.7785	−	7.66249i	1.27565	−	0.582568i	0.934004	+	0.357262i	$0.116290\pi$
$174$	−0.0111135	−	0.0772962i	−0.000842513	−	0.00585981i
$175$	−0.744993	−	14.8139i	−0.0563162	−	1.11983i
$176$	2.83618	−	0.832776i	0.213785	−	0.0627729i
$177$	−10.5401	−	1.51543i	−0.792239	−	0.113907i
$178$	−12.2720	−	10.6337i	−0.919824	−	0.797032i
$179$	−20.7148	+	13.3126i	−1.54830	+	0.995030i	−0.562556	+	0.826759i	$0.690182\pi$
$179$	−20.7148	+	13.3126i	−1.54830	+	0.995030i	−0.985741	+	0.168271i	$0.946182\pi$
$180$	0.742261	−	1.22139i	0.0553249	−	0.0910371i
$181$	4.53803	+	1.33249i	0.337309	+	0.0990429i	0.446001	−	0.895033i	$-0.352848\pi$
$181$	4.53803	+	1.33249i	0.337309	+	0.0990429i	−0.108692	+	0.994076i	$0.534666\pi$
$182$	−5.11588	−	2.33634i	−0.379214	−	0.173181i
$183$			16.0822i			1.18883i
$184$	3.61418	+	3.15241i	0.266441	+	0.232399i
$185$	−7.90951	+	2.53994i	−0.581519	+	0.186740i
$186$	−4.24119	+	9.28691i	−0.310979	+	0.680950i
$187$	0.793221	−	2.70146i	0.0580061	−	0.197551i
$188$	6.10123	−	5.28675i	0.444978	−	0.385576i
$189$	11.2393	−	7.22308i	0.817541	−	0.525402i
$190$	−0.224691	+	0.526630i	−0.0163008	+	0.0382057i
$191$	−1.33212	+	9.26507i	−0.0963885	+	0.670397i	0.883143	+	0.469105i	$0.155423\pi$
$191$	−1.33212	+	9.26507i	−0.0963885	+	0.670397i	−0.979531	+	0.201292i	$0.935486\pi$
$192$	−0.537451	−	1.83039i	−0.0387872	−	0.132097i
$193$	10.9915	−	17.1030i	0.791182	−	1.23110i	−0.177823	−	0.984062i	$-0.556905\pi$
$193$	10.9915	−	17.1030i	0.791182	−	1.23110i	0.969005	−	0.247041i	$-0.0794582\pi$
$194$	−0.477557	−	3.32148i	−0.0342866	−	0.238469i
$195$	−5.97685	+	5.44778i	−0.428011	+	0.390124i
$196$	0.747872	+	1.63761i	0.0534195	+	0.116972i
$197$	−5.50214	+	0.791089i	−0.392011	+	0.0563627i	−0.335502	−	0.942039i	$-0.608906\pi$
$197$	−5.50214	+	0.791089i	−0.392011	+	0.0563627i	−0.0565091	+	0.998402i	$0.517997\pi$
$198$	−1.02146	+	1.58943i	−0.0725922	+	0.112956i
$199$	26.0943	−	7.66198i	1.84978	−	0.543143i	0.849907	−	0.526932i	$-0.176658\pi$
$199$	26.0943	−	7.66198i	1.84978	−	0.543143i	0.999869	−	0.0162109i	$-0.00516030\pi$
$200$	−4.43810	+	2.30289i	−0.313821	+	0.162839i
$201$	7.17936	−	8.28542i	0.506393	−	0.584408i
$202$	−0.156585	−	0.243652i	−0.0110173	−	0.0171433i
$203$	0.0917754	−	0.0795238i	0.00644137	−	0.00558148i
$204$	−1.74345	−	0.511923i	−0.122066	−	0.0358418i
$205$	20.8131	+	2.46057i	1.45365	+	0.171853i
$206$	9.64817			0.672220
$207$	−3.06538	−	0.0100043i	−0.213058	−	0.000695348i
$208$			1.89586i			0.131454i
$209$	0.314420	−	0.688483i	0.0217489	−	0.0476233i
$210$	12.6502	−	0.317889i	0.872949	−	0.0219365i
$211$	−6.20313	−	7.15880i	−0.427041	−	0.492832i	0.500928	−	0.865489i	$-0.332992\pi$
$211$	−6.20313	−	7.15880i	−0.427041	−	0.492832i	−0.927969	+	0.372657i	$0.878447\pi$
$212$	−6.83038	−	10.6283i	−0.469112	−	0.729953i
$213$	−20.6694	−	17.9101i	−1.41624	−	1.22718i
$214$	−2.23088	+	15.5161i	−0.152500	+	1.06066i
$215$	20.4073	−	13.8515i	1.39176	−	0.944662i
$216$	−3.78871	−	2.43486i	−0.257789	−	0.165671i
$217$	−15.7148	+	2.25945i	−1.06679	+	0.153382i
$218$	6.26579	−	2.86149i	0.424373	−	0.193805i
$219$	−0.823807	−	1.80389i	−0.0556677	−	0.121895i
$220$	5.94145	−	2.89590i	0.400572	−	0.195242i
$221$	1.51914	+	0.976294i	0.102189	+	0.0656726i
$222$	−1.99671	−	6.80017i	−0.134010	−	0.456397i
$223$	−2.74318	−	0.394410i	−0.183697	−	0.0264116i	0.0498523	−	0.998757i	$-0.484125\pi$
$223$	−2.74318	−	0.394410i	−0.183697	−	0.0264116i	−0.233549	+	0.972345i	$0.575034\pi$
$224$	1.94266	−	2.24195i	0.129800	−	0.149797i
$225$	1.17993	−	2.97010i	0.0786622	−	0.198007i
$226$	−7.04126	−	8.12605i	−0.468378	−	0.540537i
$227$	1.37919	−	4.69707i	0.0915398	−	0.311756i	−0.900977	−	0.433868i	$-0.857149\pi$
$227$	1.37919	−	4.69707i	0.0915398	−	0.311756i	0.992516	+	0.122112i	$0.0389667\pi$
$228$	−0.444328	−	0.202918i	−0.0294263	−	0.0134386i
$229$	18.3691			1.21386			0.606932	−	0.794754i	$-0.292400\pi$
$229$	18.3691			1.21386			0.606932	+	0.794754i	$0.292400\pi$
$230$	9.14601	+	5.59915i	0.603070	+	0.369197i
$231$	−16.7279			−1.10062
$232$	−0.0372362	−	0.0170052i	−0.00244468	−	0.00111645i
$233$	−6.00281	+	20.4437i	−0.393257	+	1.33931i	0.490531	+	0.871424i	$0.336803\pi$
$233$	−6.00281	+	20.4437i	−0.393257	+	1.33931i	−0.883788	+	0.467887i	$0.845015\pi$
$234$	−0.793555	−	0.915811i	−0.0518763	−	0.0598685i
$235$	11.4751	−	13.9354i	0.748551	−	0.909047i
$236$	−3.65539	+	4.21854i	−0.237945	+	0.274604i
$237$	1.64461	+	0.236459i	0.106829	+	0.0153597i
$238$	−0.796071	−	2.71117i	−0.0516016	−	0.175739i
$239$	−0.909109	−	0.584249i	−0.0588054	−	0.0377919i	0.510908	−	0.859636i	$-0.329309\pi$
$239$	−0.909109	−	0.584249i	−0.0588054	−	0.0377919i	−0.569713	+	0.821844i	$0.692946\pi$
$240$	−1.86894	−	3.83445i	−0.120639	−	0.247512i
$241$	−6.08250	−	13.3188i	−0.391809	−	0.857941i	−0.998036	−	0.0626494i	$-0.980045\pi$
$241$	−6.08250	−	13.3188i	−0.391809	−	0.857941i	0.606227	−	0.795292i	$-0.292682\pi$
$242$	2.05812	−	0.939914i	0.132301	−	0.0604200i
$243$	6.47012	−	0.930263i	0.415058	−	0.0596764i
$244$	7.09201	+	4.55776i	0.454020	+	0.291781i
$245$	2.26079	+	3.33081i	0.144437	+	0.212797i
$246$	−2.54459	+	17.6980i	−0.162237	+	1.12838i
$247$	0.366876	+	0.317900i	0.0233438	+	0.0202275i
$248$	2.89343	+	4.50226i	0.183733	+	0.285894i
$249$	−14.1286	−	16.3053i	−0.895365	−	1.03331i
$250$	−8.92364	+	6.73562i	−0.564381	+	0.425998i
$251$	4.64552	−	10.1723i	0.293223	−	0.642068i	−0.704487	−	0.709717i	$-0.748823\pi$
$251$	4.64552	−	10.1723i	0.293223	−	0.642068i	0.997709	+	0.0676494i	$0.0215499\pi$
$252$			1.89614i			0.119446i
$253$	−11.9006	−	7.70303i	−0.748183	−	0.484285i
$254$	−1.75710			−0.110250
$255$	−4.03495	−	0.477020i	−0.252679	−	0.0298722i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	22.6797	−	19.6521i	1.41472	−	1.22586i	0.476800	−	0.879012i	$-0.341797\pi$
$257$	22.6797	−	19.6521i	1.41472	−	1.22586i	0.937920	−	0.346851i	$-0.112749\pi$
$258$	11.3761	+	17.7015i	0.708242	+	1.10205i
$259$	7.21728	−	8.32919i	0.448460	−	0.517551i
$260$	0.708532	+	4.17964i	0.0439413	+	0.259210i
$261$	0.0251052	−	0.00737155i	0.00155397	−	0.000456288i
$262$	−2.80981	+	4.37215i	−0.173591	+	0.270112i
$263$	16.0629	−	2.30950i	0.990483	−	0.142410i	0.372021	−	0.928224i	$-0.378665\pi$
$263$	16.0629	−	2.30950i	0.990483	−	0.142410i	0.618462	+	0.785814i	$0.287756\pi$
$264$	2.34248	+	5.12931i	0.144169	+	0.315687i
$265$	−19.0304	−	20.8786i	−1.16903	−	1.28256i
$266$	−0.108102	−	0.751868i	−0.00662818	−	0.0461000i
$267$	16.7474	−	26.0595i	1.02492	−	1.59481i
$268$	−1.61909	−	5.51412i	−0.0989019	−	0.336829i
$269$	−2.72536	+	18.9553i	−0.166168	+	1.15572i	0.720546	+	0.693407i	$0.243891\pi$
$269$	−2.72536	+	18.9553i	−0.166168	+	1.15572i	−0.886714	+	0.462318i	$0.847018\pi$
$270$	−9.26262	−	3.95198i	−0.563705	−	0.240510i
$271$	−1.18119	+	0.759102i	−0.0717519	+	0.0461122i	−0.576025	−	0.817432i	$-0.695397\pi$
$271$	−1.18119	+	0.759102i	−0.0717519	+	0.0461122i	0.504273	+	0.863544i	$0.331761\pi$
$272$	−0.719853	+	0.623756i	−0.0436475	+	0.0378208i
$273$	3.02269	−	10.2943i	0.182941	−	0.623041i
$274$	1.46860	−	3.21579i	0.0887216	−	0.194273i
$275$	12.0163	−	8.60483i	0.724612	−	0.518891i
$276$	−4.97132	+	7.68030i	−0.299239	+	0.462300i
$277$			17.5234i			1.05288i	0.850212	+	0.526441i	$0.176474\pi$
$277$			17.5234i			1.05288i	−0.850212	+	0.526441i	$0.823526\pi$
$278$	−17.0940	−	7.80656i	−1.02523	−	0.468207i
$279$	−3.28222	−	0.963748i	−0.196502	−	0.0576981i
$280$	3.44495	−	5.66867i	0.205875	−	0.338768i
$281$	−26.9954	+	17.3489i	−1.61041	+	1.03495i	−0.648639	+	0.761096i	$0.724661\pi$
$281$	−26.9954	+	17.3489i	−1.61041	+	1.03495i	−0.961772	+	0.273852i	$0.911702\pi$
$282$	11.6391	+	10.0853i	0.693098	+	0.600573i
$283$	3.58275	+	0.515121i	0.212972	+	0.0306208i	0.247975	−	0.968766i	$-0.420235\pi$
$283$	3.58275	+	0.515121i	0.212972	+	0.0306208i	−0.0350028	+	0.999387i	$0.511144\pi$
$284$	−13.7559	+	4.03910i	−0.816263	+	0.239676i
$285$	−1.05541	−	0.281298i	−0.0625169	−	0.0166627i
$286$	−0.797530	−	5.54695i	−0.0471590	−	0.327998i
$287$	−25.2918	+	11.5504i	−1.49293	+	0.681798i
$288$	0.581417	−	0.265524i	0.0342604	−	0.0156462i
$289$	−2.29024	−	15.9289i	−0.134720	−	0.936996i
$290$	−0.0884468	−	0.0235738i	−0.00519377	−	0.00138430i
$291$	6.14212	−	1.80349i	0.360058	−	0.105722i
$292$	−1.02896	−	0.147942i	−0.0602153	−	0.00865766i
$293$	−5.14803	−	4.46079i	−0.300751	−	0.260602i	0.491391	−	0.870939i	$-0.336489\pi$
$293$	−5.14803	−	4.46079i	−0.300751	−	0.260602i	−0.792142	+	0.610337i	$0.791034\pi$
$294$	−2.88918	+	1.85676i	−0.168500	+	0.108288i
$295$	−6.48214	+	10.6664i	−0.377405	+	0.621020i
$296$	−3.56466	−	1.04668i	−0.207192	−	0.0608369i
$297$	12.1094	+	5.53017i	0.702657	+	0.320893i
$298$		−	15.7307i		−	0.911255i
$299$	6.89083	−	5.93168i	0.398507	−	0.343038i
$300$	−5.55332	−	7.75501i	−0.320621	−	0.447735i
$301$	−13.5929	+	29.7643i	−0.783481	+	1.71558i
$302$	−5.59421	+	19.0521i	−0.321911	+	1.09633i
$303$	0.417563	−	0.361821i	0.0239884	−	0.0207860i
$304$	−0.215409	+	0.138435i	−0.0123545	+	0.00793977i
$305$	17.3385	+	7.39764i	0.992800	+	0.423587i
$306$	0.0866440	−	0.602622i	0.00495311	−	0.0344496i
$307$	0.958041	+	3.26279i	0.0546783	+	0.186217i	0.982304	−	0.187294i	$-0.0599718\pi$
$307$	0.958041	+	3.26279i	0.0546783	+	0.186217i	−0.927626	+	0.373511i	$0.878154\pi$
$308$	−4.74077	+	7.37678i	−0.270130	+	0.420331i
$309$	2.61937	+	18.2181i	0.149011	+	1.03639i
$310$	8.06151	+	8.84441i	0.457863	+	0.502329i
$311$	8.33365	+	18.2481i	0.472558	+	1.03476i	0.984443	+	0.175703i	$0.0562200\pi$
$311$	8.33365	+	18.2481i	0.472558	+	1.03476i	−0.511885	+	0.859054i	$0.671053\pi$
$312$	−3.57985	+	0.514704i	−0.202669	+	0.0291394i
$313$	−8.02235	+	12.4830i	−0.453450	+	0.705582i	−0.990430	−	0.138013i	$-0.955928\pi$
$313$	−8.02235	+	12.4830i	−0.453450	+	0.705582i	0.536981	+	0.843595i	$0.319565\pi$
$314$	2.02852	−	0.595628i	0.114476	−	0.0336133i
$315$	0.708638	+	4.18027i	0.0399272	+	0.235531i
$316$	0.570365	−	0.658236i	0.0320855	−	0.0370287i
$317$	9.60462	+	14.9451i	0.539449	+	0.839400i	0.998806	−	0.0488523i	$-0.0155564\pi$
$317$	9.60462	+	14.9451i	0.539449	+	0.839400i	−0.459357	+	0.888252i	$0.651920\pi$
$318$	18.2144	−	15.7829i	1.02141	−	0.885061i
$319$	0.116100	+	0.0340901i	0.00650036	+	0.00190868i
$320$	−2.22060	−	0.262524i	−0.124136	−	0.0146756i
$321$	−29.9039			−1.66907
$322$	−14.2269	−	0.0464316i	−0.792834	−	0.00258753i
$323$			0.243894i			0.0135706i
$324$	4.36559	−	9.55931i	0.242533	−	0.531073i
$325$	3.12408	+	8.94970i	0.173293	+	0.496440i
$326$	4.42743	+	5.10953i	0.245213	+	0.282990i
$327$	7.10429	+	11.0545i	0.392868	+	0.611314i
$328$	7.08343	+	6.13783i	0.391117	+	0.338905i
$329$	−3.40831	+	23.7053i	−0.187906	+	1.30691i
$330$	7.08122	+	10.4327i	0.389808	+	0.574302i
$331$	−9.47608	−	6.08991i	−0.520852	−	0.334731i	0.253657	−	0.967294i	$-0.418367\pi$
$331$	−9.47608	−	6.08991i	−0.520852	−	0.334731i	−0.774509	+	0.632563i	$0.782003\pi$
$332$	−11.1945	+	1.60953i	−0.614380	+	0.0883344i
$333$	2.16005	−	0.986463i	0.118370	−	0.0540578i
$334$	−7.69707	−	16.8542i	−0.421165	−	0.922222i
$335$	−5.63025	−	11.5514i	−0.307613	−	0.631122i
$336$	4.76077	+	3.05956i	0.259721	+	0.166913i
$337$	7.65302	+	26.0638i	0.416887	+	1.41979i	0.853950	+	0.520355i	$0.174200\pi$
$337$	7.65302	+	26.0638i	0.416887	+	1.41979i	−0.437063	+	0.899431i	$0.643981\pi$
$338$	−9.30999	−	1.33857i	−0.506397	−	0.0728088i
$339$	13.4323	−	15.5018i	0.729545	−	0.841940i
$340$	−1.35388	+	1.64417i	−0.0734247	+	0.0891676i
$341$	−10.3596	−	11.9557i	−0.561005	−	0.647435i
$342$	0.0461100	−	0.157036i	0.00249334	−	0.00849155i
$343$	14.0311	+	6.40780i	0.757610	+	0.345989i
$344$	11.0301			0.594705
$345$	−8.08953	+	18.7900i	−0.435525	+	1.01162i
$346$	18.4454			0.991630
$347$	16.1094	+	7.35691i	0.864797	+	0.394940i	0.797878	−	0.602819i	$-0.205956\pi$
$347$	16.1094	+	7.35691i	0.864797	+	0.394940i	0.0669191	+	0.997758i	$0.478683\pi$
$348$	0.0220008	−	0.0749278i	0.00117937	−	0.00401655i
$349$	13.4559	+	15.5289i	0.720275	+	0.831242i	0.991340	−	0.131319i	$-0.0419212\pi$
$349$	13.4559	+	15.5289i	0.720275	+	0.831242i	−0.271065	+	0.962561i	$0.587376\pi$
$350$	5.47626	−	13.7847i	0.292718	−	0.736824i
$351$	−5.59139	+	6.45280i	−0.298446	+	0.344425i
$352$	2.92582	+	0.420670i	0.155947	+	0.0224218i
$353$	−7.24558	−	24.6762i	−0.385643	−	1.31338i	−0.892382	−	0.451281i	$-0.850967\pi$
$353$	−7.24558	−	24.6762i	−0.385643	−	1.31338i	0.506738	−	0.862100i	$-0.330851\pi$
$354$	−8.95804	−	5.75698i	−0.476114	−	0.305980i
$355$	−28.8170	+	14.0456i	−1.52945	+	0.745463i
$356$	−6.74558	−	14.7707i	−0.357515	−	0.782848i
$357$	4.90323	−	2.23923i	0.259506	−	0.118513i
$358$	−24.3731	+	3.50432i	−1.28816	+	0.185209i
$359$	−0.532753	−	0.342380i	−0.0281177	−	0.0180701i	0.526506	−	0.850171i	$-0.323502\pi$
$359$	−0.532753	−	0.342380i	−0.0281177	−	0.0180701i	−0.554624	+	0.832101i	$0.687138\pi$
$360$	1.18257	−	0.802670i	0.0623268	−	0.0423044i
$361$	2.69465	−	18.7417i	0.141824	−	0.986406i
$362$	3.57440	+	3.09724i	0.187866	+	0.162787i
$363$	2.33355	+	3.63107i	0.122479	+	0.190582i
$364$	−3.68301	−	4.25043i	−0.193042	−	0.222783i
$365$	−2.32375	+	0.0583939i	−0.121631	+	0.00305647i
$366$	−6.68077	+	14.6288i	−0.349209	+	0.764662i
$367$		−	6.01653i		−	0.314060i	−0.987594	−	0.157030i	$-0.949808\pi$
$367$		−	6.01653i		−	0.314060i	0.987594	−	0.157030i	$-0.0501920\pi$
$368$	1.97801	+	4.36892i	0.103111	+	0.227746i
$369$	−5.99085			−0.311871
$370$	−8.24987	−	0.975316i	−0.428890	−	0.0507043i
$371$	35.9606	+	10.5590i	1.86698	+	0.548195i
$372$	−7.71585	+	6.68582i	−0.400048	+	0.346644i
$373$	18.0163	+	28.0339i	0.932848	+	1.45154i	0.891824	+	0.452382i	$0.149426\pi$
$373$	18.0163	+	28.0339i	0.932848	+	1.45154i	0.0410244	+	0.999158i	$0.486938\pi$
$374$	1.84377	−	2.12782i	0.0953389	−	0.110027i
$375$	−15.1412	−	15.0214i	−0.781887	−	0.775701i
$376$	7.74607	−	2.27445i	0.399473	−	0.117296i
$377$	−0.0419579	+	0.0652878i	−0.00216094	+	0.00336249i
$378$	13.2242	−	1.90136i	0.680181	−	0.0977953i
$379$	4.92740	+	10.7895i	0.253103	+	0.554219i	0.992947	−	0.118560i	$-0.0378278\pi$
$379$	4.92740	+	10.7895i	0.253103	+	0.554219i	−0.739844	+	0.672779i	$0.765101\pi$
$380$	−0.423156	+	0.385699i	−0.0217075	+	0.0197859i
$381$	−0.477033	−	3.31784i	−0.0244392	−	0.169978i
$382$	−5.06058	+	7.87442i	−0.258922	+	0.402891i
$383$	−3.83003	−	13.0439i	−0.195706	−	0.666512i	−0.997612	−	0.0690628i	$-0.977999\pi$
$383$	−3.83003	−	13.0439i	−0.195706	−	0.666512i	0.801907	−	0.597449i	$-0.203819\pi$
$384$	0.271489	−	1.88825i	0.0138544	−	0.0963591i
$385$	−7.69468	+	18.0347i	−0.392157	+	0.919134i
$386$	17.1030	−	10.9915i	0.870522	−	0.559450i
$387$	−5.32821	+	4.61692i	−0.270848	+	0.234691i
$388$	0.945393	−	3.21971i	0.0479950	−	0.163456i
$389$	−4.79087	+	10.4905i	−0.242907	+	0.531891i	−0.991340	−	0.131318i	$-0.958079\pi$
$389$	−4.79087	+	10.4905i	−0.242907	+	0.531891i	0.748434	+	0.663210i	$0.230806\pi$
$390$	−7.69982	+	2.47261i	−0.389896	+	0.125205i
$391$	4.51940	+	0.664853i	0.228556	+	0.0336231i
$392$			1.80030i			0.0909290i
$393$	−9.01853	−	4.11862i	−0.454924	−	0.207757i
$394$	−5.33356	−	1.56607i	−0.268701	−	0.0788976i
$395$	1.01143	−	1.66432i	0.0508908	−	0.0837409i
$396$	−1.58943	+	1.02146i	−0.0798717	+	0.0513304i
$397$	12.0135	+	10.4097i	0.602939	+	0.522450i	0.901973	−	0.431793i	$-0.142119\pi$
$397$	12.0135	+	10.4097i	0.602939	+	0.522450i	−0.299034	+	0.954243i	$0.596664\pi$
$398$	26.9191	+	3.87038i	1.34933	+	0.194005i
$399$	1.39036	−	0.408247i	0.0696052	−	0.0204379i
$400$	−4.99369	+	0.251133i	−0.249684	+	0.0125566i
$401$	1.46816	+	10.2113i	0.0733166	+	0.509928i	0.993079	+	0.117452i	$0.0374725\pi$
$401$	1.46816	+	10.2113i	0.0733166	+	0.509928i	−0.919762	+	0.392477i	$0.871618\pi$
$402$	9.97246	−	4.55427i	0.497381	−	0.227146i
$403$	9.22944	−	4.21495i	0.459751	−	0.209961i
$404$	−0.0412186	−	0.286681i	−0.00205070	−	0.0142629i
$405$	6.05188	−	22.7061i	0.300721	−	1.12828i
$406$	0.116517	−	0.0342125i	0.00578265	−	0.00169794i
$407$	10.8699	+	1.56285i	0.538799	+	0.0774676i
$408$	−1.37324	−	1.18992i	−0.0679854	−	0.0589096i
$409$	−7.78549	+	5.00343i	−0.384968	+	0.247404i	−0.718783	−	0.695235i	$-0.755300\pi$
$409$	−7.78549	+	5.00343i	−0.384968	+	0.247404i	0.333815	+	0.942639i	$0.391664\pi$
$410$	17.9101	+	10.8843i	0.884517	+	0.537537i
$411$	6.47092	+	1.90003i	0.319187	+	0.0937217i
$412$	8.77628	+	4.00799i	0.432376	+	0.197460i
$413$		−	16.5590i		−	0.814813i
$414$	−2.78421	−	1.28250i	−0.136836	−	0.0630316i
$415$	−24.0781	+	7.73208i	−1.18195	+	0.379553i
$416$	−0.787568	+	1.72453i	−0.0386137	+	0.0845522i
$417$	10.0999	−	34.3971i	0.494594	−	1.68443i
$418$	0.572012	−	0.495651i	0.0279780	−	0.0242431i
$419$	−10.2420	+	6.58215i	−0.500356	+	0.321559i	−0.766359	−	0.642413i	$-0.777933\pi$
$419$	−10.2420	+	6.58215i	−0.500356	+	0.321559i	0.266003	+	0.963972i	$0.414297\pi$
$420$	11.6391	+	4.96593i	0.567930	+	0.242313i
$421$	−2.31536	+	16.1037i	−0.112844	+	0.784845i	0.852287	+	0.523075i	$0.175215\pi$
$421$	−2.31536	+	16.1037i	−0.112844	+	0.784845i	−0.965130	+	0.261770i	$0.915694\pi$
$422$	−2.66870	−	9.08874i	−0.129910	−	0.442433i
$423$	−2.78978	+	4.34099i	−0.135644	+	0.211066i
$424$	−1.79799	−	12.5053i	−0.0873179	−	0.607309i
$425$	−2.37033	+	4.13074i	−0.114978	+	0.200371i
$426$	−11.3614	−	24.8780i	−0.550461	−	1.20534i
$427$	−24.7542	+	3.55911i	−1.19794	+	0.172237i
$428$	−8.47491	+	13.1872i	−0.409650	+	0.637428i
$429$	10.2575	−	3.01187i	0.495236	−	0.145414i
$430$	24.3172	−	4.12225i	1.17268	−	0.198793i
$431$	25.2443	−	29.1334i	1.21597	−	1.40331i	0.327205	−	0.944953i	$-0.393893\pi$
$431$	25.2443	−	29.1334i	1.21597	−	1.40331i	0.888769	−	0.458355i	$-0.151561\pi$
$432$	−2.43486	−	3.78871i	−0.117147	−	0.182285i
$433$	−17.8974	+	15.5082i	−0.860094	+	0.745276i	−0.968548	−	0.248826i	$-0.919955\pi$
$433$	−17.8974	+	15.5082i	−0.860094	+	0.745276i	0.108454	+	0.994101i	$0.465410\pi$
$434$	−15.2333	−	4.47291i	−0.731223	−	0.214706i
$435$	0.0205008	−	0.173409i	0.000982938	−	0.00831434i
$436$	6.88827			0.329888
$437$	1.17713	+	0.349812i	0.0563096	+	0.0167338i
$438$		−	1.98309i		−	0.0947559i
$439$	−0.427987	+	0.937161i	−0.0204267	+	0.0447283i	−0.919570	−	0.392925i	$-0.871463\pi$
$439$	−0.427987	+	0.937161i	−0.0204267	+	0.0447283i	0.899144	+	0.437654i	$0.144190\pi$
$440$	6.60753	−	0.166042i	0.315002	−	0.00791572i
$441$	−0.753558	−	0.869652i	−0.0358837	−	0.0414120i
$442$	0.976294	+	1.51914i	0.0464375	+	0.0722582i
$443$	−1.42284	−	1.23290i	−0.0676012	−	0.0585768i	0.620405	−	0.784282i	$-0.286968\pi$
$443$	−1.42284	−	1.23290i	−0.0676012	−	0.0585768i	−0.688006	+	0.725705i	$0.741514\pi$
$444$	1.00862	−	7.01511i	0.0478670	−	0.332922i
$445$	−20.3916	−	30.0428i	−0.966655	−	1.42417i
$446$	−2.33144	−	1.49833i	−0.110397	−	0.0709478i
$447$	29.7034	−	4.27071i	1.40492	−	0.201997i
$448$	2.69845	−	1.23234i	0.127490	−	0.0582226i
$449$	−12.7865	−	27.9986i	−0.603434	−	1.32134i	−0.926975	−	0.375122i	$-0.877601\pi$
$449$	−12.7865	−	27.9986i	−0.603434	−	1.32134i	0.323542	−	0.946214i	$-0.395126\pi$
$450$	2.30713	−	2.21154i	0.108759	−	0.104253i
$451$	−23.3069	−	14.9784i	−1.09748	−	0.705306i
$452$	−3.02927	−	10.3168i	−0.142485	−	0.485259i
$453$	−37.4939	−	5.39081i	−1.76162	−	0.253282i
$454$	3.20579	−	3.69967i	0.150455	−	0.173634i
$455$	−9.70813	−	7.99411i	−0.455124	−	0.374770i
$456$	−0.319880	−	0.369161i	−0.0149797	−	0.0172875i
$457$	3.27623	−	11.1578i	0.153255	−	0.521940i	−0.846693	−	0.532081i	$-0.821410\pi$
$457$	3.27623	−	11.1578i	0.153255	−	0.521940i	0.999949	+	0.0101415i	$0.00322819\pi$
$458$	16.7091	+	7.63079i	0.780765	+	0.356564i
$459$	−4.28974			−0.200228
$460$	5.99354	+	8.89255i	0.279450	+	0.414617i
$461$	−1.25915			−0.0586445			−0.0293223	−	0.999570i	$-0.509335\pi$
$461$	−1.25915			−0.0586445			−0.0293223	+	0.999570i	$0.509335\pi$
$462$	−15.2162	−	6.94903i	−0.707924	−	0.323298i
$463$	−3.83011	+	13.0442i	−0.178000	+	0.606213i	0.821359	+	0.570412i	$0.193216\pi$
$463$	−3.83011	+	13.0442i	−0.178000	+	0.606213i	−0.999359	+	0.0358012i	$0.988602\pi$
$464$	−0.0268070	−	0.0309369i	−0.00124448	−	0.00143621i
$465$	−14.5118	+	17.6233i	−0.672969	+	0.817260i
$466$	−13.9530	+	16.1026i	−0.646359	+	0.745938i
$467$	−22.0760	−	3.17405i	−1.02156	−	0.146877i	−0.388875	−	0.921291i	$-0.627136\pi$
$467$	−22.0760	−	3.17405i	−1.02156	−	0.146877i	−0.632680	+	0.774413i	$0.718045\pi$
$468$	−0.341401	−	1.16271i	−0.0157813	−	0.0537461i
$469$	14.3420	+	9.21706i	0.662253	+	0.425604i
$470$	16.2271	−	7.90920i	0.748499	−	0.364824i
$471$	1.67541	+	3.66865i	0.0771990	+	0.169042i
$472$	−5.07750	+	2.31882i	−0.233711	+	0.106732i
$473$	−32.2722	+	4.64005i	−1.48388	+	0.213350i
$474$	1.39776	+	0.898285i	0.0642012	+	0.0412596i
$475$	−0.788751	+	1.00846i	−0.0361904	+	0.0462714i
$476$	0.402128	−	2.79686i	0.0184315	−	0.128194i
$477$	6.10290	+	5.28819i	0.279433	+	0.242130i
$478$	−0.584249	−	0.909109i	−0.0267229	−	0.0415817i
$479$	0.174615	+	0.201516i	0.00797836	+	0.00920751i	0.759725	−	0.650245i	$-0.225334\pi$
$479$	0.174615	+	0.201516i	0.00797836	+	0.00920751i	−0.751746	+	0.659452i	$0.770788\pi$
$480$	−0.107159	−	4.26432i	−0.00489110	−	0.194639i
$481$	−2.92593	+	6.40689i	−0.133411	+	0.292129i
$482$		−	14.6420i		−	0.666925i
$483$	−3.77477	−	26.8765i	−0.171758	−	1.22292i
$484$	2.26259			0.102845
$485$	0.880936	−	7.45154i	0.0400013	−	0.338357i
$486$	6.27187	+	1.84159i	0.284498	+	0.0835361i
$487$	−0.649982	+	0.563213i	−0.0294535	+	0.0255216i	−0.669463	−	0.742845i	$-0.733476\pi$
$487$	−0.649982	+	0.563213i	−0.0294535	+	0.0255216i	0.640010	+	0.768367i	$0.278930\pi$
$488$	4.55776	+	7.09201i	0.206320	+	0.321040i
$489$	−8.44604	+	9.74725i	−0.381943	+	0.440786i
$490$	0.672820	+	3.96897i	0.0303949	+	0.179300i
$491$	31.2363	−	9.17181i	1.40968	−	0.413918i	0.513680	−	0.857982i	$-0.328282\pi$
$491$	31.2363	−	9.17181i	1.40968	−	0.413918i	0.895995	+	0.444064i	$0.146464\pi$
$492$	−9.66666	+	15.0416i	−0.435807	+	0.678128i
$493$	−0.0385942	+	0.00554901i	−0.00173820	+	0.000249915i
$494$	0.201662	+	0.441578i	0.00907320	+	0.0198675i
$495$	−3.12233	+	2.84594i	−0.140338	+	0.127916i
$496$	0.761648	+	5.29738i	0.0341990	+	0.237859i
$497$	22.9935	−	35.7786i	1.03140	−	1.60489i
$498$	−6.07838	−	20.7011i	−0.272379	−	0.927636i
$499$	−2.09574	+	14.5762i	−0.0938184	+	0.652521i	0.887596	+	0.460622i	$0.152374\pi$
$499$	−2.09574	+	14.5762i	−0.0938184	+	0.652521i	−0.981415	+	0.191899i	$0.938535\pi$
$500$	−10.9153	+	2.41992i	−0.488147	+	0.108222i
$501$	29.7353	−	19.1097i	1.32847	−	0.853758i
$502$	8.45143	−	7.32320i	0.377206	−	0.326851i
$503$	−6.57420	+	22.3897i	−0.293129	+	0.998306i	0.672870	+	0.739761i	$0.265061\pi$
$503$	−6.57420	+	22.3897i	−0.293129	+	0.998306i	−0.965999	+	0.258545i	$0.916757\pi$
$504$	−0.787686	+	1.72479i	−0.0350863	+	0.0768284i
$505$	−0.198011	−	0.616618i	−0.00881139	−	0.0274391i
$506$	−7.62519	−	11.9506i	−0.338981	−	0.531269i
$507$		−	17.9430i		−	0.796874i
$508$	−1.59832	−	0.729926i	−0.0709138	−	0.0323852i
$509$	−32.1300	−	9.43422i	−1.42414	−	0.418165i	−0.523236	−	0.852188i	$-0.675275\pi$
$509$	−32.1300	−	9.43422i	−1.42414	−	0.418165i	−0.900902	+	0.434023i	$0.857094\pi$
$510$	−3.47216	−	2.11009i	−0.153750	−	0.0934365i
$511$	2.59428	−	1.66724i	0.114764	−	0.0737545i
$512$	−0.755750	−	0.654861i	−0.0333997	−	0.0289410i
$513$	−1.14145	−	0.164116i	−0.0503963	−	0.00724590i
$514$	28.7939	−	8.45466i	1.27005	−	0.372919i
$515$	20.8462	+	5.55616i	0.918594	+	0.244834i
$516$	2.99456	+	20.8276i	0.131828	+	0.916885i
$517$	−21.7068	+	9.91318i	−0.954666	+	0.435981i
$518$	10.0251	−	4.57833i	0.440479	−	0.201160i
$519$	5.00771	+	34.8294i	0.219814	+	1.52884i
$520$	−1.09178	+	4.09627i	−0.0478778	+	0.179633i
$521$	−4.03729	+	1.18546i	−0.176877	+	0.0519357i	−0.368972	−	0.929441i	$-0.620290\pi$
$521$	−4.03729	+	1.18546i	−0.176877	+	0.0519357i	0.192095	+	0.981376i	$0.438472\pi$
$522$	0.0258987	+	0.00372368i	0.00113356	+	0.000162981i
$523$	24.2454	+	21.0088i	1.06018	+	0.918650i	0.996847	−	0.0793426i	$-0.0252821\pi$
$523$	24.2454	+	21.0088i	1.06018	+	0.918650i	0.0633312	+	0.997993i	$0.479828\pi$
$524$	−4.37215	+	2.80981i	−0.190998	+	0.122747i
$525$	27.5157	+	6.59813i	1.20088	+	0.287966i
$526$	15.5708	+	4.57199i	0.678917	+	0.199348i
$527$	4.63698	+	2.11764i	0.201990	+	0.0922458i
$528$			5.63888i			0.245401i
$529$	9.69090	−	20.8587i	0.421344	−	0.906901i
$530$	−8.63741	−	26.8973i	−0.375185	−	1.16835i
$531$	1.48214	−	3.24543i	0.0643193	−	0.140840i
$532$	0.214004	−	0.728831i	0.00927825	−	0.0315988i
$533$	13.4292	−	11.6364i	0.581682	−	0.504031i
$534$	26.0595	−	16.7474i	1.12770	−	0.724731i
$535$	−13.7555	+	32.2400i	−0.594702	+	1.39386i
$536$	0.817871	−	5.68842i	0.0353267	−	0.245702i
$537$	−13.2340	−	45.0710i	−0.571091	−	1.94496i
$538$	−10.3534	+	16.1102i	−0.446366	+	0.694560i
$539$	−0.757333	−	5.26737i	−0.0326206	−	0.226882i
$540$	−6.78387	−	7.44268i	−0.291931	−	0.320282i
$541$	9.77877	+	21.4125i	0.420422	+	0.920596i	0.994785	+	0.101995i	$0.0325226\pi$
$541$	9.77877	+	21.4125i	0.420422	+	0.920596i	−0.574363	+	0.818601i	$0.694750\pi$
$542$	−1.38979	+	0.199821i	−0.0596965	+	0.00858305i
$543$	−4.87794	+	7.59022i	−0.209332	+	0.325727i
$544$	−0.913919	+	0.268351i	−0.0391839	+	0.0115054i
$545$	15.1860	−	2.57433i	0.650496	−	0.110272i
$546$	7.02595	−	8.10838i	0.300683	−	0.347007i
$547$	−8.01047	−	12.4645i	−0.342503	−	0.532945i	0.626683	−	0.779274i	$-0.284412\pi$
$547$	−8.01047	−	12.4645i	−0.342503	−	0.532945i	−0.969186	+	0.246329i	$0.920776\pi$
$548$	2.67178	−	2.31511i	0.114133	−	0.0988966i
$549$	−5.17019	−	1.51811i	−0.220658	−	0.0647912i
$550$	14.5050	−	2.83547i	0.618496	−	0.120905i
$551$	−0.0104818			−0.000446539
$552$	−7.71259	+	4.92109i	−0.328270	+	0.209455i
$553$			2.58376i			0.109873i
$554$	−7.27950	+	15.9399i	−0.309276	+	0.677221i
$555$	−0.398110	−	15.8426i	−0.0168988	−	0.672480i
$556$	−12.3063	−	14.2022i	−0.521902	−	0.602308i
$557$	−6.01408	−	9.35810i	−0.254825	−	0.396515i	0.690146	−	0.723670i	$-0.257546\pi$
$557$	−6.01408	−	9.35810i	−0.254825	−	0.396515i	−0.944971	+	0.327155i	$0.893910\pi$
$558$	−2.58526	−	2.24014i	−0.109443	−	0.0948327i
$559$	2.97603	−	20.6987i	0.125873	−	0.875463i
$560$	5.48849	−	3.72532i	0.231931	−	0.157424i
$561$	4.51841	+	2.90381i	0.190767	+	0.122599i
$562$	−31.7629	+	4.56681i	−1.33984	+	0.192639i
$563$	12.4961	−	5.70679i	0.526649	−	0.240512i	−0.134304	−	0.990940i	$-0.542880\pi$
$563$	12.4961	−	5.70679i	0.526649	−	0.240512i	0.660952	+	0.750428i	$0.270152\pi$
$564$	6.39769	+	14.0090i	0.269391	+	0.589885i
$565$	−10.5340	−	21.6124i	−0.443170	−	0.909239i
$566$	3.04499	+	1.95690i	0.127991	+	0.0822546i
$567$	8.78308	+	29.9124i	0.368855	+	1.25620i
$568$	−14.1907	−	2.04032i	−0.595429	−	0.0856098i
$569$	−8.21383	+	9.47926i	−0.344342	+	0.397391i	−0.901333	−	0.433127i	$-0.857410\pi$
$569$	−8.21383	+	9.47926i	−0.344342	+	0.397391i	0.556991	+	0.830518i	$0.311956\pi$
$570$	−0.843177	−	0.694310i	−0.0353168	−	0.0290815i
$571$	−12.6512	−	14.6003i	−0.529436	−	0.611002i	0.426532	−	0.904473i	$-0.359735\pi$
$571$	−12.6512	−	14.6003i	−0.529436	−	0.611002i	−0.955968	+	0.293471i	$0.905190\pi$
$572$	1.57883	−	5.37699i	0.0660140	−	0.224823i
$573$	−16.2427	−	7.41781i	−0.678550	−	0.309883i
$574$	−27.8045			−1.16054
$575$	16.5368	+	17.3647i	0.689633	+	0.724159i
$576$	0.639179			0.0266324
$577$	−5.00558	−	2.28597i	−0.208385	−	0.0951663i	0.308488	−	0.951228i	$-0.400177\pi$
$577$	−5.00558	−	2.28597i	−0.208385	−	0.0951663i	−0.516873	+	0.856062i	$0.672904\pi$
$578$	4.53385	−	15.4409i	0.188583	−	0.642256i
$579$	25.3978	+	29.3107i	1.05550	+	1.21811i
$580$	−0.0706611	−	0.0581856i	−0.00293404	−	0.00241603i
$581$	21.9708	−	25.3557i	0.911504	−	1.05193i
$582$	6.33627	+	0.911018i	0.262647	+	0.0377629i
$583$	10.5212	+	35.8319i	0.435743	+	1.48400i
$584$	−0.874517	−	0.562018i	−0.0361878	−	0.0232565i
$585$	−1.18719	−	2.43573i	−0.0490844	−	0.100705i
$586$	−2.82973	−	6.19625i	−0.116895	−	0.255965i
$587$	9.60539	−	4.38663i	0.396457	−	0.181056i	−0.207203	−	0.978298i	$-0.566436\pi$
$587$	9.60539	−	4.38663i	0.396457	−	0.181056i	0.603659	+	0.797242i	$0.293709\pi$
$588$	−3.39941	+	0.488762i	−0.140189	+	0.0201562i
$589$	1.15283	+	0.740882i	0.0475017	+	0.0305275i
$590$	−10.3273	+	7.00969i	−0.425170	+	0.288585i
$591$	1.50913	−	10.4962i	0.0620774	−	0.431757i
$592$	−2.80772	−	2.43290i	−0.115397	−	0.0999917i
$593$	8.27934	+	12.8829i	0.339992	+	0.529038i	0.968580	−	0.248700i	$-0.0800035\pi$
$593$	8.27934	+	12.8829i	0.339992	+	0.529038i	−0.628589	+	0.777738i	$0.716367\pi$
$594$	8.71776	+	10.0608i	0.357694	+	0.412801i
$595$	−0.158723	−	6.31630i	−0.00650701	−	0.258943i
$596$	6.53477	−	14.3091i	0.267674	−	0.586125i
$597$			51.8807i			2.12333i
$598$	8.73223	−	2.53309i	0.357087	−	0.103586i
$599$	5.42374			0.221608			0.110804	−	0.993842i	$-0.464657\pi$
$599$	5.42374			0.221608			0.110804	+	0.993842i	$0.464657\pi$
$600$	−1.82993	−	9.36113i	−0.0747066	−	0.382167i
$601$	30.5924	+	8.98275i	1.24789	+	0.366414i	0.837975	−	0.545709i	$-0.183740\pi$
$601$	30.5924	+	8.98275i	1.24789	+	0.366414i	0.409916	+	0.912123i	$0.365558\pi$
$602$	−24.7291	+	21.4279i	−1.00788	+	0.873334i
$603$	1.98594	+	3.09018i	0.0808737	+	0.125842i
$604$	−13.0032	+	15.0065i	−0.529094	+	0.610607i
$605$	4.98814	−	0.845589i	0.202797	−	0.0343781i
$606$	0.530135	−	0.155662i	0.0215352	−	0.00632332i
$607$	23.1899	−	36.0841i	0.941248	−	1.46461i	0.0565743	−	0.998398i	$-0.481982\pi$
$607$	23.1899	−	36.0841i	0.941248	−	1.46461i	0.884673	−	0.466211i	$-0.154381\pi$
$608$	−0.253450	+	0.0364407i	−0.0102788	+	0.00147786i
$609$	0.0962348	+	0.210725i	0.00389963	+	0.00853900i
$610$	12.6986	+	13.9318i	0.514150	+	0.564082i
$611$	−2.17819	−	15.1496i	−0.0881201	−	0.612889i
$612$	0.329152	−	0.512171i	0.0133052	−	0.0207033i
$613$	−10.6884	−	36.4012i	−0.431699	−	1.47023i	−0.832479	−	0.554057i	$-0.813079\pi$
$613$	−10.6884	−	36.4012i	−0.431699	−	1.47023i	0.400780	−	0.916174i	$-0.368739\pi$
$614$	−0.483946	+	3.36592i	−0.0195305	+	0.135837i
$615$	−15.6898	+	36.7737i	−0.632674	+	1.48286i
$616$	−7.37678	+	4.74077i	−0.297219	+	0.191011i
$617$	−4.64812	+	4.02762i	−0.187126	+	0.162146i	−0.743386	−	0.668863i	$-0.766781\pi$
$617$	−4.64812	+	4.02762i	−0.187126	+	0.162146i	0.556260	+	0.831008i	$0.312236\pi$
$618$	−5.18542	+	17.6599i	−0.208588	+	0.710386i
$619$	−4.96800	+	10.8784i	−0.199681	+	0.437240i	−0.982810	−	0.184619i	$-0.940895\pi$
$619$	−4.96800	+	10.8784i	−0.199681	+	0.437240i	0.783130	+	0.621859i	$0.213622\pi$
$620$	3.65891	+	11.3940i	0.146945	+	0.457595i
$621$	−6.15268	+	20.7039i	−0.246898	+	0.830818i
$622$			20.0610i			0.804374i
$623$	43.8179	+	20.0110i	1.75553	+	0.801722i
$624$	−3.47016	−	1.01893i	−0.138917	−	0.0407899i
$625$	−23.1597	+	9.41434i	−0.926387	+	0.376574i
$626$	−12.4830	+	8.02235i	−0.498922	+	0.320637i
$627$	1.09121	+	0.945536i	0.0435786	+	0.0377611i
$628$	2.09264	+	0.300877i	0.0835056	+	0.0120063i
$629$	−3.39534	+	0.996963i	−0.135381	+	0.0397515i
$630$	−1.09195	+	4.09688i	−0.0435041	+	0.163224i
$631$	−6.21662	−	43.2375i	−0.247480	−	1.72126i	−0.612682	−	0.790330i	$-0.709909\pi$
$631$	−6.21662	−	43.2375i	−0.247480	−	1.72126i	0.365202	−	0.930928i	$-0.381000\pi$
$632$	0.792263	−	0.361815i	0.0315145	−	0.0143922i
$633$	16.4373	−	7.50665i	0.653323	−	0.298362i
$634$	2.52826	+	17.5844i	0.100410	+	0.698367i
$635$	−3.79646	−	1.01187i	−0.150658	−	0.0401550i
$636$	23.1249	−	6.79008i	0.916961	−	0.269244i
$637$	3.37838	+	0.485737i	0.133856	+	0.0192456i
$638$	0.0914469	+	0.0792392i	0.00362042	+	0.00313711i
$639$	7.70898	−	4.95426i	0.304962	−	0.195987i
$640$	−1.91088	−	1.16127i	−0.0755340	−	0.0459033i
$641$	10.8536	+	3.18690i	0.428691	+	0.125875i	0.488958	−	0.872307i	$-0.337377\pi$
$641$	10.8536	+	3.18690i	0.428691	+	0.125875i	−0.0602670	+	0.998182i	$0.519195\pi$
$642$	−27.2015	−	12.4225i	−1.07356	−	0.490278i
$643$			26.3024i			1.03727i	0.854997	+	0.518634i	$0.173559\pi$
$643$			26.3024i			1.03727i	−0.854997	+	0.518634i	$0.826441\pi$
$644$	−12.9220	−	5.95231i	−0.509196	−	0.234554i
$645$	14.3857	+	44.7977i	0.566435	+	1.76391i
$646$	−0.101317	+	0.221854i	−0.00398628	+	0.00872873i
$647$	3.90089	−	13.2852i	0.153360	−	0.522296i	−0.846591	−	0.532245i	$-0.821349\pi$
$647$	3.90089	−	13.2852i	0.153360	−	0.522296i	0.999951	+	0.00994875i	$0.00316684\pi$
$648$	7.94216	−	6.88192i	0.311998	−	0.270347i
$649$	13.8804	−	8.92040i	0.544854	−	0.350156i
$650$	−0.876075	+	9.43872i	−0.0343625	+	0.370217i
$651$	4.31027	−	29.9786i	0.168933	−	1.17495i
$652$	1.90476	+	6.48701i	0.0745961	+	0.254051i
$653$	−14.2893	+	22.2347i	−0.559185	+	0.870110i	−0.999617	−	0.0276767i	$-0.991189\pi$
$653$	−14.2893	+	22.2347i	−0.559185	+	0.870110i	0.440431	+	0.897786i	$0.354825\pi$
$654$	1.87009	+	13.0067i	0.0731262	+	0.508604i
$655$	−8.58881	+	7.82854i	−0.335593	+	0.305886i
$656$	3.89357	+	8.52573i	0.152018	+	0.332874i
$657$	0.657689	−	0.0945614i	0.0256589	−	0.00368919i
$658$	−12.9478	+	20.1472i	−0.504759	+	0.785421i
$659$	−42.4985	+	12.4787i	−1.65551	+	0.486100i	−0.970231	−	0.242183i	$-0.922136\pi$
$659$	−42.4985	+	12.4787i	−1.65551	+	0.486100i	−0.685276	+	0.728284i	$0.740318\pi$
$660$	2.10740	+	12.4316i	0.0820304	+	0.483898i
$661$	−24.2167	+	27.9476i	−0.941921	+	1.08703i	0.0541553	+	0.998533i	$0.482753\pi$
$661$	−24.2167	+	27.9476i	−0.941921	+	1.08703i	−0.996076	+	0.0885019i	$0.971792\pi$
$662$	−6.08991	−	9.47608i	−0.236691	−	0.368298i
$663$	−2.60346	+	2.25591i	−0.101110	+	0.0876124i
$664$	−10.8515	−	3.18629i	−0.421121	−	0.123652i
$665$	0.199413	−	1.68677i	0.00773292	−	0.0654101i
$666$	2.37464			0.0920156
$667$	−0.0285732	+	0.194229i	−0.00110636	+	0.00752058i
$668$		−	18.5286i		−	0.716894i
$669$	2.19625	−	4.80912i	0.0849119	−	0.185931i
$670$	−0.322820	−	12.8464i	−0.0124716	−	0.496301i
$671$	−16.3186	−	18.8327i	−0.629973	−	0.727027i
$672$	3.05956	+	4.76077i	0.118025	+	0.183651i
$673$	−20.6317	−	17.8775i	−0.795295	−	0.689127i	0.159236	−	0.987241i	$-0.449097\pi$
$673$	−20.6317	−	17.8775i	−0.795295	−	0.689127i	−0.954530	+	0.298114i	$0.903642\pi$
$674$	−3.86586	+	26.8877i	−0.148907	+	1.03567i
$675$	−17.7373	−	13.8729i	−0.682711	−	0.533970i
$676$	−7.91260	−	5.08512i	−0.304331	−	0.195581i
$677$	17.5137	−	2.51809i	0.673106	−	0.0967780i	0.202717	−	0.979237i	$-0.435023\pi$
$677$	17.5137	−	2.51809i	0.673106	−	0.0967780i	0.470389	+	0.882459i	$0.344114\pi$
$678$	18.6582	−	8.52090i	0.716562	−	0.327243i
$679$	4.13529	+	9.05503i	0.158698	+	0.347500i
$680$	−1.91455	+	0.933166i	−0.0734196	+	0.0357853i
$681$	7.85623	+	5.04889i	0.301051	+	0.193474i
$682$	−4.45689	−	15.1788i	−0.170663	−	0.581226i
$683$	−30.3133	−	4.35840i	−1.15991	−	0.166770i	−0.464626	−	0.885507i	$-0.653811\pi$
$683$	−30.3133	−	4.35840i	−1.15991	−	0.166770i	−0.695282	+	0.718737i	$0.744720\pi$
$684$	0.107178	−	0.123690i	0.00409807	−	0.00472942i
$685$	5.02503	−	6.10244i	0.191996	−	0.233162i
$686$	10.1013	+	11.6575i	0.385668	+	0.445085i
$687$	−9.87248	+	33.6226i	−0.376659	+	1.28278i
$688$	10.0334	+	4.58209i	0.382519	+	0.174690i
$689$	−23.9520			−0.912499
$690$	−15.1642	+	13.7315i	−0.577289	+	0.522749i
$691$	21.1619			0.805035			0.402517	−	0.915412i	$-0.368135\pi$
$691$	21.1619			0.805035			0.402517	+	0.915412i	$0.368135\pi$
$692$	16.7785	+	7.66249i	0.637823	+	0.291284i
$693$	1.57906	−	5.37780i	0.0599836	−	0.204286i
$694$	11.5974	+	13.3842i	0.440233	+	0.508056i
$695$	−32.4383	−	26.7112i	−1.23046	−	1.01321i
$696$	0.0511388	−	0.0590173i	0.00193841	−	0.00223704i
$697$	8.83667	+	1.27052i	0.334713	+	0.0481244i
$698$	5.78894	+	19.7153i	0.219115	+	0.746236i
$699$	−34.1937	−	21.9750i	−1.29333	−	0.831170i
$700$	10.7078	−	10.2641i	0.404715	−	0.387946i
$701$	−9.47002	−	20.7364i	−0.357678	−	0.783205i	−0.999861	−	0.0166540i	$-0.994699\pi$
$701$	−9.47002	−	20.7364i	−0.357678	−	0.783205i	0.642184	−	0.766551i	$-0.278029\pi$
$702$	−7.76670	+	3.54693i	−0.293135	+	0.133870i
$703$	−0.941605	+	0.135382i	−0.0355133	+	0.00510604i
$704$	2.48667	+	1.59809i	0.0937199	+	0.0602301i
$705$	19.3400	+	28.4935i	0.728386	+	1.07313i
$706$	3.66005	−	25.4562i	0.137748	−	0.958056i
$707$	0.649336	+	0.562653i	0.0244208	+	0.0211607i
$708$	−5.75698	−	8.95804i	−0.216361	−	0.336664i
$709$	−12.8245	−	14.8002i	−0.481633	−	0.555834i	0.461978	−	0.886891i	$-0.347140\pi$
$709$	−12.8245	−	14.8002i	−0.481633	−	0.555834i	−0.943610	+	0.331058i	$0.892594\pi$
$710$	−32.0476	+	0.805329i	−1.20272	+	0.0302234i
$711$	−0.231264	+	0.506398i	−0.00867308	+	0.0189914i
$712$		−	16.2382i		−	0.608551i
$713$	16.8712	−	19.3425i	0.631833	−	0.724384i
$714$	5.39034			0.201728
$715$	1.47118	−	12.4442i	0.0550191	−	0.465388i
$716$	−23.6263	−	6.93731i	−0.882956	−	0.259259i
$717$	1.55800	−	1.35002i	0.0581847	−	0.0504174i
$718$	−0.342380	−	0.532753i	−0.0127775	−	0.0198822i
$719$	22.8049	−	26.3183i	0.850481	−	0.981507i	−0.149493	−	0.988763i	$-0.547764\pi$
$719$	22.8049	−	26.3183i	0.850481	−	0.981507i	0.999974	+	0.00725573i	$0.00230959\pi$
$720$	1.40914	−	0.238878i	0.0525157	−	0.00890245i
$721$	−27.4622	+	8.06363i	−1.02275	+	0.300305i
$722$	10.2367	−	15.9287i	0.380972	−	0.592803i
$723$	27.6477	−	3.97514i	1.02823	−	0.147837i
$724$	1.96475	+	4.30221i	0.0730195	+	0.159890i
$725$	−0.177526	−	0.101869i	−0.00659315	−	0.00378332i
$726$	0.614268	+	4.27233i	0.0227976	+	0.158561i
$727$	−11.1869	+	17.4071i	−0.414898	+	0.645594i	−0.984308	−	0.176460i	$-0.943535\pi$
$727$	−11.1869	+	17.4071i	−0.414898	+	0.645594i	0.569410	+	0.822054i	$0.307172\pi$
$728$	−1.58450	−	5.39630i	−0.0587254	−	0.200000i
$729$	2.71213	−	18.8633i	0.100449	−	0.698639i
$730$	−2.13802	−	0.912204i	−0.0791315	−	0.0337622i
$731$	8.83840	−	5.68010i	0.326900	−	0.210086i
$732$	−12.1541	+	10.5316i	−0.449228	+	0.389258i
$733$	2.20751	−	7.51810i	0.0815364	−	0.277688i	−0.908626	−	0.417611i	$-0.862867\pi$
$733$	2.20751	−	7.51810i	0.0815364	−	0.277688i	0.990162	+	0.139924i	$0.0446857\pi$
$734$	2.49936	−	5.47283i	0.0922530	−	0.202006i
$735$	−7.31173	+	2.34798i	−0.269697	+	0.0866066i
$736$	−0.0156518	+	4.79581i	−0.000576934	+	0.176776i
$737$			16.9874i			0.625738i
$738$	−5.44946	−	2.48869i	−0.200598	−	0.0916098i
$739$	−9.88396	−	2.90219i	−0.363587	−	0.106759i	0.0948358	−	0.995493i	$-0.469767\pi$
$739$	−9.88396	−	2.90219i	−0.363587	−	0.106759i	−0.458423	+	0.888734i	$0.651586\pi$
$740$	−7.09919	−	4.31430i	−0.260971	−	0.158597i
$741$	−0.779059	+	0.500671i	−0.0286194	+	0.0183926i
$742$	28.3245	+	24.5433i	1.03983	+	0.901015i
$743$	−25.9834	−	3.73584i	−0.953237	−	0.137055i	−0.351889	−	0.936042i	$-0.614461\pi$
$743$	−25.9834	−	3.73584i	−0.953237	−	0.137055i	−0.601348	+	0.798987i	$0.705370\pi$
$744$	−9.79597	+	2.87636i	−0.359138	+	0.105452i
$745$	9.05894	−	33.9884i	0.331894	−	1.24524i
$746$	4.74249	+	32.9848i	0.173635	+	1.20766i
$747$	6.57562	−	3.00299i	0.240590	−	0.109874i
$748$	2.56108	−	1.16961i	0.0936423	−	0.0427650i
$749$	−6.61797	−	46.0290i	−0.241815	−	1.68186i
$750$	−7.53280	−	19.9538i	−0.275059	−	0.728610i
$751$	−19.6037	+	5.75615i	−0.715347	+	0.210045i	−0.619100	−	0.785312i	$-0.712502\pi$
$751$	−19.6037	+	5.75615i	−0.715347	+	0.210045i	−0.0962478	+	0.995357i	$0.530684\pi$
$752$	7.99091	+	1.14892i	0.291399	+	0.0418968i
$753$	16.1225	+	13.9702i	0.587536	+	0.509103i
$754$	−0.0652878	+	0.0419579i	−0.00237764	+	0.00152802i
$755$	−23.0588	+	37.9432i	−0.839195	+	1.38090i
$756$	12.8190	+	3.76401i	0.466224	+	0.136896i
$757$	18.7288	+	8.55314i	0.680709	+	0.310869i	0.725594	−	0.688123i	$-0.241565\pi$
$757$	18.7288	+	8.55314i	0.680709	+	0.310869i	−0.0448854	+	0.998992i	$0.514292\pi$
$758$			11.8614i			0.430825i
$759$	20.4955	−	17.6427i	0.743940	−	0.640389i
$760$	−0.545142	+	0.175059i	−0.0197744	+	0.00635004i
$761$	16.3218	−	35.7399i	0.591667	−	1.29557i	−0.342763	−	0.939422i	$-0.611363\pi$
$761$	16.3218	−	35.7399i	0.591667	−	1.29557i	0.934430	−	0.356147i	$-0.115910\pi$
$762$	0.944356	−	3.21618i	0.0342104	−	0.116510i
$763$	−15.4432	+	13.3816i	−0.559081	+	0.484446i
$764$	−7.87442	+	5.06058i	−0.284887	+	0.183086i
$765$	0.534243	−	1.25215i	0.0193156	−	0.0452717i
$766$	1.93471	−	13.4562i	0.0699039	−	0.486192i
$767$	2.98145	+	10.1539i	0.107654	+	0.366635i
$768$	1.03136	−	1.60483i	0.0372160	−	0.0579093i
$769$	−1.35535	−	9.42668i	−0.0488752	−	0.339935i	−0.999557	−	0.0297663i	$-0.990524\pi$
$769$	−1.35535	−	9.42668i	−0.0488752	−	0.339935i	0.950682	−	0.310168i	$-0.100385\pi$
$770$	−14.4912	+	13.2085i	−0.522227	+	0.476000i
$771$	23.7817	+	52.0747i	0.856478	+	1.87542i
$772$	20.1235	−	2.89332i	0.724260	−	0.104133i
$773$	−14.4452	+	22.4772i	−0.519559	+	0.808450i	−0.997553	−	0.0699132i	$-0.977728\pi$
$773$	−14.4452	+	22.4772i	−0.519559	+	0.808450i	0.477994	+	0.878363i	$0.341364\pi$
$774$	−6.76465	+	1.98628i	−0.243150	+	0.0713953i
$775$	12.3247	+	23.7520i	0.442717	+	0.853198i
$776$	2.19748	−	2.53602i	0.0788848	−	0.0910379i
$777$	11.3667	+	17.6870i	0.407779	+	0.634517i
$778$	−8.71585	+	7.55233i	−0.312478	+	0.270764i
$779$	2.30273	+	0.676143i	0.0825040	+	0.0242253i
$780$	−8.03116	−	0.949460i	−0.287562	−	0.0339961i
$781$	42.3779			1.51640
$782$	3.83480	+	2.48220i	0.137132	+	0.0887632i
$783$		−	0.184359i		−	0.00658845i
$784$	−0.747872	+	1.63761i	−0.0267097	+	0.0584861i
$785$	4.72592	−	0.118758i	0.168675	−	0.00423867i
$786$	−6.49260	−	7.49286i	−0.231583	−	0.267262i
$787$	−23.6155	−	36.7464i	−0.841800	−	1.30987i	−0.948887	−	0.315617i	$-0.897789\pi$
$787$	−23.6155	−	36.7464i	−0.841800	−	1.30987i	0.107086	−	0.994250i	$-0.465848\pi$
$788$	−4.20100	−	3.64019i	−0.149655	−	0.129676i
$789$	−4.40575	+	30.6427i	−0.156849	+	1.09091i
$790$	1.61142	−	1.09375i	0.0573316	−	0.0389139i
$791$	26.8335	+	17.2448i	0.954089	+	0.613156i
$792$	−1.87012	+	0.268883i	−0.0664520	+	0.00955435i
$793$	14.5383	−	6.63943i	0.516271	−	0.235773i
$794$	6.60348	+	14.4596i	0.234349	+	0.513152i
$795$	48.4438	−	23.6119i	1.71813	−	0.837427i
$796$	22.8787	+	14.7032i	0.810913	+	0.521142i
$797$	−0.176676	−	0.601704i	−0.00625820	−	0.0213135i	0.956305	−	0.292372i	$-0.0944445\pi$
$797$	−0.176676	−	0.601704i	−0.00625820	−	0.0213135i	−0.962563	+	0.271058i	$0.912626\pi$
$798$	1.43431	+	0.206223i	0.0507741	+	0.00730021i
$799$	5.03564	−	5.81143i	0.178148	−	0.205594i
$800$	−4.64674	−	1.84602i	−0.164287	−	0.0652665i
$801$	6.79686	+	7.84399i	0.240155	+	0.277154i
$802$	−2.90644	+	9.89842i	−0.102630	+	0.349526i
$803$	2.79511	+	1.27648i	0.0986372	+	0.0450461i
$804$	10.9632			0.386642
$805$	−30.7125	−	8.29327i	−1.08247	−	0.292299i
$806$	10.1463			0.357390
$807$	−33.2308	−	15.1760i	−1.16978	−	0.534221i
$808$	0.0815980	−	0.277897i	0.00287061	−	0.00977639i
$809$	−1.88040	−	2.17009i	−0.0661113	−	0.0762965i	0.721731	−	0.692174i	$-0.243347\pi$
$809$	−1.88040	−	2.17009i	−0.0661113	−	0.0762965i	−0.787842	+	0.615878i	$0.788802\pi$
$810$	14.9375	−	18.1402i	0.524849	−	0.637381i
$811$	−3.78957	+	4.37340i	−0.133070	+	0.153571i	−0.818374	−	0.574687i	$-0.805124\pi$
$811$	−3.78957	+	4.37340i	−0.133070	+	0.153571i	0.685304	+	0.728257i	$0.259669\pi$
$812$	0.120200	+	0.0172822i	0.00421820	+	0.000606486i
$813$	−0.754623	−	2.57001i	−0.0264658	−	0.0901342i
$814$	9.23835	+	5.93713i	0.323804	+	0.208096i
$815$	6.62362	+	13.5895i	0.232015	+	0.476019i
$816$	−0.754831	−	1.65285i	−0.0264244	−	0.0578613i
$817$	2.56911	−	1.17327i	0.0898818	−	0.0410476i
$818$	−9.16044	+	1.31707i	−0.320287	+	0.0460503i
$819$	3.02415	+	1.94351i	0.105672	+	0.0679116i
$820$	11.7701	+	17.3408i	0.411030	+	0.605568i
$821$	−1.56214	+	10.8649i	−0.0545189	+	0.379188i	0.944235	+	0.329274i	$0.106804\pi$
$821$	−1.56214	+	10.8649i	−0.0545189	+	0.379188i	−0.998754	+	0.0499140i	$0.984105\pi$
$822$	5.09685	+	4.41645i	0.177773	+	0.154041i
$823$	−16.1743	−	25.1677i	−0.563801	−	0.877291i	0.435942	−	0.899975i	$-0.356415\pi$
$823$	−16.1743	−	25.1677i	−0.563801	−	0.877291i	−0.999743	+	0.0226835i	$0.992779\pi$
$824$	6.31821	+	7.29160i	0.220105	+	0.254015i
$825$	9.29200	+	26.6192i	0.323506	+	0.926763i
$826$	6.87884	−	15.0626i	0.239345	−	0.524093i
$827$			24.7192i			0.859572i	0.902931	+	0.429786i	$0.141411\pi$
$827$			24.7192i			0.859572i	−0.902931	+	0.429786i	$0.858589\pi$
$828$	−1.99983	−	2.32321i	−0.0694991	−	0.0807371i
$829$	42.4718			1.47511			0.737553	−	0.675289i	$-0.235981\pi$
$829$	42.4718			1.47511			0.737553	+	0.675289i	$0.235981\pi$
$830$	−25.1142	−	2.96906i	−0.871728	−	0.103057i
$831$	−32.0747	−	9.41799i	−1.11266	−	0.326706i
$832$	−1.43279	+	1.24152i	−0.0496732	+	0.0430421i
$833$	0.927086	+	1.44257i	0.0321216	+	0.0499822i
$834$	23.4762	−	27.0930i	0.812916	−	0.938155i
$835$	−6.92463	−	40.8485i	−0.239637	−	1.41362i
$836$	0.726222	−	0.213238i	0.0251169	−	0.00737499i
$837$	−13.0310	+	20.2766i	−0.450417	+	0.700863i
$838$	−12.0508	+	1.73264i	−0.416288	+	0.0598532i
$839$	16.1329	+	35.3261i	0.556970	+	1.21959i	0.953450	+	0.301550i	$0.0975041\pi$
$839$	16.1329	+	35.3261i	0.556970	+	1.21959i	−0.396481	+	0.918043i	$0.629769\pi$
$840$	8.52438	+	9.35223i	0.294119	+	0.322683i
$841$	4.12689	+	28.7032i	0.142307	+	0.989764i
$842$	−8.79583	+	13.6866i	−0.303124	+	0.471671i
$843$	−17.2465	−	58.7363i	−0.594002	−	2.02298i
$844$	1.34807	−	9.37603i	0.0464025	−	0.322736i
$845$	−19.3447	−	8.25358i	−0.665477	−	0.283932i
$846$	−4.34099	+	2.78978i	−0.149246	+	0.0959148i
$847$	−5.07262	+	4.39545i	−0.174297	+	0.151030i
$848$	3.55937	−	12.1221i	0.122229	−	0.416275i
$849$	−2.86842	+	6.28097i	−0.0984440	+	0.215562i
$850$	−3.87210	+	2.77279i	−0.132812	+	0.0951059i
$851$	−0.0581488	+	17.8171i	−0.00199332	+	0.610763i
$852$		−	27.3495i		−	0.936978i
$853$	22.7063	+	10.3696i	0.777448	+	0.355049i	0.764297	−	0.644865i	$-0.223086\pi$
$853$	22.7063	+	10.3696i	0.777448	+	0.355049i	0.0131515	+	0.999914i	$0.495814\pi$
$854$	−23.9957	−	7.04577i	−0.821116	−	0.241101i
$855$	0.190061	−	0.312745i	0.00649994	−	0.0106957i
$856$	−13.1872	+	8.47491i	−0.450730	+	0.289666i
$857$	7.02875	+	6.09044i	0.240097	+	0.208046i	0.766595	−	0.642131i	$-0.221950\pi$
$857$	7.02875	+	6.09044i	0.240097	+	0.208046i	−0.526497	+	0.850177i	$0.676495\pi$
$858$	10.5817	+	1.52142i	0.361253	+	0.0519404i
$859$	−38.5439	+	11.3175i	−1.31510	+	0.386149i	−0.862723	−	0.505677i	$-0.831243\pi$
$859$	−38.5439	+	11.3175i	−1.31510	+	0.386149i	−0.452379	+	0.891826i	$0.649424\pi$
$860$	23.8322	+	6.35200i	0.812670	+	0.216602i
$861$	−7.54860	−	52.5017i	−0.257256	−	1.78925i
$862$	35.0655	−	16.0139i	1.19433	−	0.545434i
$863$	15.7189	−	7.17860i	0.535079	−	0.244362i	−0.129501	−	0.991579i	$-0.541338\pi$
$863$	15.7189	−	7.17860i	0.535079	−	0.244362i	0.664580	+	0.747217i	$0.268610\pi$
$864$	−0.640936	−	4.45781i	−0.0218051	−	0.151658i
$865$	39.8538	+	10.6223i	1.35507	+	0.361168i
$866$	−22.7224	+	6.67189i	−0.772138	+	0.226720i
$867$	30.3871	+	4.36900i	1.03200	+	0.148379i
$868$	−11.9986	−	10.3968i	−0.407259	−	0.352892i
$869$	−2.16582	+	1.39189i	−0.0734704	+	0.0472165i
$870$	0.0906850	−	0.149222i	0.00307451	−	0.00505911i
$871$	−10.4540	−	3.06957i	−0.354220	−	0.104008i
$872$	6.26579	+	2.86149i	0.212186	+	0.0969023i
$873$			2.14485i			0.0725923i
$874$	0.925434	+	0.807196i	0.0313033	+	0.0273038i
$875$	19.7705	−	26.6301i	0.668366	−	0.900263i
$876$	0.823807	−	1.80389i	0.0278339	−	0.0609476i
$877$	1.66330	−	5.66466i	0.0561655	−	0.191282i	−0.926632	−	0.375971i	$-0.877309\pi$
$877$	1.66330	−	5.66466i	0.0561655	−	0.191282i	0.982797	+	0.184688i	$0.0591276\pi$
$878$	−0.778622	+	0.674680i	−0.0262772	+	0.0227693i
$879$	10.9318	−	7.02544i	0.368720	−	0.236962i
$880$	6.07940	+	2.59383i	0.204936	+	0.0874380i
$881$	−1.54156	+	10.7218i	−0.0519364	+	0.361226i	0.947236	+	0.320538i	$0.103864\pi$
$881$	−1.54156	+	10.7218i	−0.0519364	+	0.361226i	−0.999172	+	0.0406872i	$0.987045\pi$
$882$	−0.324194	−	1.10410i	−0.0109162	−	0.0371771i
$883$	16.4724	−	25.6316i	0.554341	−	0.862571i	−0.445118	−	0.895472i	$-0.646838\pi$
$883$	16.4724	−	25.6316i	0.554341	−	0.862571i	0.999459	+	0.0329012i	$0.0104747\pi$
$884$	0.256993	+	1.78743i	0.00864362	+	0.0601177i
$885$	−16.0398	−	17.5975i	−0.539171	−	0.591533i
$886$	−0.782097	−	1.71255i	−0.0262751	−	0.0575343i
$887$	36.5190	−	5.25063i	1.22619	−	0.176299i	0.501365	−	0.865236i	$-0.332831\pi$
$887$	36.5190	−	5.25063i	1.22619	−	0.176299i	0.724821	+	0.688937i	$0.241922\pi$
$888$	3.83166	−	5.96217i	0.128582	−	0.200077i
$889$	5.00135	−	1.46853i	0.167740	−	0.0492529i
$890$	−6.06863	−	35.7989i	−0.203421	−	1.19998i
$891$	−20.3424	+	23.4763i	−0.681494	+	0.786486i
$892$	−1.49833	−	2.33144i	−0.0501677	−	0.0780625i
$893$	1.56226	−	1.35371i	0.0522791	−	0.0453001i
$894$	28.7933	+	8.45447i	0.962992	+	0.282760i
$895$	−54.6795	−	6.46433i	−1.82774	−	0.216079i
$896$	2.96653			0.0991048
$897$	7.15379	+	15.8009i	0.238858	+	0.527576i
$898$		−	30.7801i		−	1.02715i
$899$	−0.0910093	+	0.199283i	−0.00303533	+	0.00664645i
$900$	3.01734	−	1.05327i	0.100578	−	0.0351089i
$901$	−7.88045	−	9.09452i	−0.262536	−	0.302982i
$902$	−14.9784	−	23.3069i	−0.498727	−	0.776034i
$903$	−47.1747	−	40.8771i	−1.56988	−	1.36031i
$904$	1.53021	−	10.6429i	0.0508941	−	0.353976i
$905$	5.93937	+	8.75043i	0.197431	+	0.290874i
$906$	−31.8662	−	20.4792i	−1.05868	−	0.680375i
$907$	22.8093	−	3.27948i	0.757370	−	0.108893i	0.247197	−	0.968965i	$-0.420491\pi$
$907$	22.8093	−	3.27948i	0.757370	−	0.108893i	0.510173	+	0.860072i	$0.329581\pi$
$908$	4.45299	−	2.03361i	0.147778	−	0.0674877i
$909$	0.0769037	+	0.168396i	0.00255073	+	0.00558533i
$910$	−5.50995	−	11.3046i	−0.182653	−	0.374744i
$911$	−4.54236	−	2.91920i	−0.150495	−	0.0967173i	0.463226	−	0.886240i	$-0.346692\pi$
$911$	−4.54236	−	2.91920i	−0.150495	−	0.0967173i	−0.613721	+	0.789523i	$0.710328\pi$
$912$	−0.137618	−	0.468683i	−0.00455698	−	0.0155197i
$913$	33.0900	+	4.75763i	1.09512	+	0.157454i
$914$	7.61528	−	8.78850i	0.251891	−	0.290698i
$915$	−22.8592	+	27.7604i	−0.755700	+	0.917729i
$916$	12.0292	+	13.8824i	0.397456	+	0.458688i
$917$	4.34364	−	14.7931i	0.143440	−	0.488511i
$918$	−3.90208	−	1.78202i	−0.128788	−	0.0588155i
$919$	−15.4108			−0.508357			−0.254178	−	0.967157i	$-0.581805\pi$
$919$	−15.4108			−0.508357			−0.254178	+	0.967157i	$0.581805\pi$
$920$	1.75781	+	10.5788i	0.0579533	+	0.348771i
$921$	−6.48707			−0.213756
$922$	−1.14536	−	0.523071i	−0.0377206	−	0.0172264i
$923$	−7.65756	+	26.0793i	−0.252052	+	0.858409i
$924$	−10.9545	−	12.6421i	−0.360375	−	0.415895i
$925$	−17.2633	−	6.85822i	−0.567615	−	0.225497i
$926$	−8.90273	+	10.2743i	−0.292562	+	0.337634i
$927$	−6.10414	−	0.877642i	−0.200486	−	0.0288256i
$928$	−0.0115328	−	0.0392773i	−0.000378584	−	0.00128934i
$929$	28.3735	+	18.2345i	0.930904	+	0.598256i	0.915802	−	0.401630i	$-0.131556\pi$
$929$	28.3735	+	18.2345i	0.930904	+	0.598256i	0.0151020	+	0.999886i	$0.495193\pi$
$930$	−20.5214	+	10.0023i	−0.672922	+	0.327987i
$931$	0.191498	+	0.419321i	0.00627608	+	0.0137427i
$932$	−19.3813	+	8.85115i	−0.634856	+	0.289929i
$933$	−37.8801	+	5.44634i	−1.24014	+	0.178305i
$934$	−18.7625	−	12.0579i	−0.613927	−	0.394547i
$935$	5.20908	−	3.53567i	0.170355	−	0.115629i
$936$	0.172456	−	1.19946i	0.00563690	−	0.0392055i
$937$	−36.4029	−	31.5433i	−1.18923	−	1.03048i	−0.998810	−	0.0487727i	$-0.984469\pi$
$937$	−36.4029	−	31.5433i	−1.18923	−	1.03048i	−0.190422	−	0.981702i	$-0.560986\pi$
$938$	9.21706	+	14.3420i	0.300948	+	0.468284i
$939$	−18.5372	−	21.3930i	−0.604937	−	0.698135i
$940$	18.0463	−	0.453487i	0.588604	−	0.0147911i
$941$	−17.4801	+	38.2762i	−0.569837	+	1.24777i	0.377048	+	0.926194i	$0.376939\pi$
$941$	−17.4801	+	38.2762i	−0.569837	+	1.24777i	−0.946884	+	0.321574i	$0.895788\pi$
$942$			4.03311i			0.131406i
$943$	18.8062	−	40.8268i	0.612416	−	1.32950i
$944$	−5.58193			−0.181676
$945$	29.6678	+	3.50738i	0.965092	+	0.114095i
$946$	−31.2834	−	9.18564i	−1.01711	−	0.298651i
$947$	−8.14693	+	7.05935i	−0.264740	+	0.229398i	−0.777107	−	0.629368i	$-0.783314\pi$
$947$	−8.14693	+	7.05935i	−0.264740	+	0.229398i	0.512368	+	0.858766i	$0.328768\pi$
$948$	0.898285	+	1.39776i	0.0291750	+	0.0453971i
$949$	−1.29061	+	1.48945i	−0.0418951	+	0.0483495i
$950$	−1.13640	+	0.589671i	−0.0368698	+	0.0191314i
$951$	−32.5173	+	9.54795i	−1.05445	+	0.309614i
$952$	1.52765	−	2.37707i	0.0495114	−	0.0770412i
$953$	−10.8376	+	1.55822i	−0.351065	+	0.0504755i	−0.315592	−	0.948895i	$-0.602203\pi$
$953$	−10.8376	+	1.55822i	−0.351065	+	0.0504755i	−0.0354734	+	0.999371i	$0.511294\pi$
$954$	3.35460	+	7.34555i	0.108609	+	0.237821i
$955$	−15.4688	+	14.0995i	−0.500559	+	0.456250i
$956$	−0.153794	−	1.06966i	−0.00497405	−	0.0345953i
$957$	−0.124796	+	0.194187i	−0.00403409	+	0.00627717i
$958$	0.0751224	+	0.255843i	0.00242709	+	0.00826592i
$959$	−1.49252	+	10.3807i	−0.0481961	+	0.335211i
$960$	1.67399	−	3.92348i	0.0540277	−	0.126630i
$961$	−1.98342	+	1.27467i	−0.0639813	+	0.0411183i
$962$	−5.32304	+	4.61244i	−0.171622	+	0.148711i
$963$	2.82283	−	9.61369i	0.0909646	−	0.309797i
$964$	6.08250	−	13.3188i	0.195904	−	0.428971i
$965$	43.2832	−	13.8993i	1.39334	−	0.447435i
$966$	7.73125	−	26.0158i	0.248749	−	0.837045i
$967$		−	47.8039i		−	1.53727i	−0.639688	−	0.768635i	$-0.720936\pi$
$967$		−	47.8039i		−	1.53727i	0.639688	−	0.768635i	$-0.279064\pi$
$968$	2.05812	+	0.939914i	0.0661506	+	0.0302100i
$969$	−0.446422	−	0.131081i	−0.0143411	−	0.00421094i
$970$	3.89681	−	6.41221i	0.125119	−	0.205884i
$971$	15.2084	−	9.77384i	0.488061	−	0.313658i	−0.273364	−	0.961911i	$-0.588136\pi$
$971$	15.2084	−	9.77384i	0.488061	−	0.313658i	0.761425	+	0.648253i	$0.224500\pi$
$972$	4.94007	+	4.28060i	0.158453	+	0.137300i
$973$	55.1802	+	7.93372i	1.76900	+	0.254343i
$974$	−0.825211	+	0.242304i	−0.0264415	+	0.00776392i
$975$	−18.0605	+	0.908262i	−0.578398	+	0.0290877i
$976$	1.19976	+	8.34448i	0.0384032	+	0.267100i
$977$	−50.3011	+	22.9717i	−1.60927	+	0.734931i	−0.998386	−	0.0567870i	$-0.981914\pi$
$977$	−50.3011	+	22.9717i	−1.60927	+	0.734931i	−0.610887	+	0.791718i	$0.709187\pi$
$978$	−11.7319	+	5.35780i	−0.375146	+	0.171324i
$979$	6.83091	+	47.5100i	0.218317	+	1.51843i
$980$	−1.03675	+	3.88980i	−0.0331178	+	0.124255i
$981$	−4.22449	+	1.24042i	−0.134878	+	0.0396036i
$982$	32.2237	+	4.63306i	1.02830	+	0.147847i
$983$	−31.6087	−	27.3891i	−1.00816	−	0.873578i	−0.0161692	−	0.999869i	$-0.505147\pi$
$983$	−31.6087	−	27.3891i	−1.00816	−	0.873578i	−0.991993	+	0.126292i	$0.959692\pi$
$984$	−15.0416	+	9.66666i	−0.479509	+	0.308162i
$985$	−10.6220	−	6.45519i	−0.338446	−	0.205680i
$986$	−0.0374117	−	0.0109851i	−0.00119143	−	0.000349836i
$987$	−41.5581	−	18.9790i	−1.32281	−	0.604107i
$988$			0.485447i			0.0154441i
$989$	−14.7376	−	50.8043i	−0.468627	−	1.61548i
$990$	−4.02242	+	1.29170i	−0.127841	+	0.0410529i
$991$	2.51570	−	5.50862i	0.0799140	−	0.174987i	−0.865457	−	0.500983i	$-0.832972\pi$
$991$	2.51570	−	5.50862i	0.0799140	−	0.174987i	0.945371	+	0.325995i	$0.105699\pi$
$992$	−1.50779	+	5.13506i	−0.0478724	+	0.163038i
$993$	16.2398	−	14.0719i	0.515355	−	0.446558i
$994$	35.7786	−	22.9935i	1.13483	−	0.729310i
$995$	55.9336	+	23.8646i	1.77322	+	0.756559i
$996$	3.07044	−	21.3554i	0.0972907	−	0.676671i
$997$	16.2761	+	55.4314i	0.515470	+	1.75553i	0.645235	+	0.763984i	$0.276759\pi$
$997$	16.2761	+	55.4314i	0.515470	+	1.75553i	−0.129766	+	0.991545i	$0.541422\pi$
$998$	−7.96154	+	12.3884i	−0.252018	+	0.392148i
$999$	−2.38117	−	16.5614i	−0.0753370	−	0.523980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.j.a.29.8	yes	120
5.4	even	2	inner	230.2.j.a.29.5	✓	120
23.4	even	11	inner	230.2.j.a.119.5	yes	120
115.4	even	22	inner	230.2.j.a.119.8	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.j.a.29.5	✓	120	5.4	even	2	inner
230.2.j.a.29.8	yes	120	1.1	even	1	trivial
230.2.j.a.119.5	yes	120	23.4	even	11	inner
230.2.j.a.119.8	yes	120	115.4	even	22	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.909632 + 0.415415i) q^{2} +(-0.537451 + 1.83039i) q^{3} +(0.654861 + 0.755750i) q^{4} +(1.72616 + 1.42140i) q^{5} +(-1.24925 + 1.44172i) q^{6} +(-2.93634 - 0.422181i) q^{7} +(0.281733 + 0.959493i) q^{8} +(-0.537711 - 0.345566i) q^{9} +O(q^{10})\)	\(q+(0.909632 + 0.415415i) q^{2} +(-0.537451 + 1.83039i) q^{3} +(0.654861 + 0.755750i) q^{4} +(1.72616 + 1.42140i) q^{5} +(-1.24925 + 1.44172i) q^{6} +(-2.93634 - 0.422181i) q^{7} +(0.281733 + 0.959493i) q^{8} +(-0.537711 - 0.345566i) q^{9} +(0.979700 + 2.01002i) q^{10} +(-1.22793 - 2.68879i) q^{11} +(-1.73527 + 0.792472i) q^{12} +(1.87656 - 0.269809i) q^{13} +(-2.49560 - 1.60383i) q^{14} +(-3.52944 + 2.39561i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(0.719853 + 0.623756i) q^{17} +(-0.345566 - 0.537711i) q^{18} +(0.167681 + 0.193515i) q^{19} +(0.0561727 + 2.23536i) q^{20} +(2.35089 - 5.14774i) q^{21} -2.95591i q^{22} +(4.04295 - 2.57964i) q^{23} -1.90766 q^{24} +(0.959253 + 4.90712i) q^{25} +(1.81906 + 0.534125i) q^{26} +(-3.40363 + 2.94926i) q^{27} +(-1.60383 - 2.49560i) q^{28} +(-0.0268070 + 0.0309369i) q^{29} +(-4.20566 + 0.712944i) q^{30} +(5.13506 - 1.50779i) q^{31} +(-0.540641 + 0.841254i) q^{32} +(5.58149 - 0.802497i) q^{33} +(0.395684 + 0.866426i) q^{34} +(-4.46849 - 4.90245i) q^{35} +(-0.0909646 - 0.632673i) q^{36} +(-2.00856 + 3.12538i) q^{37} +(0.0721395 + 0.245685i) q^{38} +(-0.514704 + 3.57985i) q^{39} +(-0.877507 + 2.05669i) q^{40} +(7.88484 - 5.06728i) q^{41} +(4.27689 - 3.70595i) q^{42} +(3.10755 - 10.5833i) q^{43} +(1.22793 - 2.68879i) q^{44} +(-0.436988 - 1.36080i) q^{45} +(4.74922 - 0.667022i) q^{46} -8.07309i q^{47} +(-1.73527 - 0.792472i) q^{48} +(1.72738 + 0.507204i) q^{49} +(-1.16592 + 4.86216i) q^{50} +(-1.52860 + 0.982373i) q^{51} +(1.43279 + 1.24152i) q^{52} +(-12.5053 - 1.79799i) q^{53} +(-4.32122 + 1.26883i) q^{54} +(1.70224 - 6.38666i) q^{55} +(-0.422181 - 2.93634i) q^{56} +(-0.444328 + 0.202918i) q^{57} +(-0.0372362 + 0.0170052i) q^{58} +(0.794391 + 5.52511i) q^{59} +(-4.12177 - 1.09858i) q^{60} +(8.08881 - 2.37509i) q^{61} +(5.29738 + 0.761648i) q^{62} +(1.43301 + 1.24171i) q^{63} +(-0.841254 + 0.540641i) q^{64} +(3.62275 + 2.20161i) q^{65} +(5.41047 + 1.58866i) q^{66} +(-5.22758 - 2.38735i) q^{67} +0.952502i q^{68} +(2.54886 + 8.78660i) q^{69} +(-2.02813 - 6.31571i) q^{70} +(-5.95566 + 13.0411i) q^{71} +(0.180077 - 0.613288i) q^{72} +(-0.785633 + 0.680754i) q^{73} +(-3.12538 + 2.00856i) q^{74} +(-9.49749 - 0.881530i) q^{75} +(-0.0364407 + 0.253450i) q^{76} +(2.47046 + 8.41360i) q^{77} +(-1.95531 + 3.04253i) q^{78} +(-0.123952 - 0.862106i) q^{79} +(-1.65259 + 1.50630i) q^{80} +(-4.36559 - 9.55931i) q^{81} +(9.27732 - 1.33388i) q^{82} +(-6.11445 + 9.51428i) q^{83} +(5.42991 - 1.59436i) q^{84} +(0.355975 + 2.09990i) q^{85} +(7.22320 - 8.33602i) q^{86} +(-0.0422192 - 0.0656944i) q^{87} +(2.23393 - 1.93571i) q^{88} +(-15.5804 - 4.57482i) q^{89} +(0.167800 - 1.41936i) q^{90} -5.62412 q^{91} +(4.59713 + 1.36615i) q^{92} +10.2095i q^{93} +(3.35368 - 7.34354i) q^{94} +(0.0143834 + 0.572379i) q^{95} +(-1.24925 - 1.44172i) q^{96} +(-1.81420 - 2.82294i) q^{97} +(1.36058 + 1.17895i) q^{98} +(-0.268883 + 1.87012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41} - 8 q^{44} + 16 q^{45} - 4 q^{46} - 58 q^{49} + 12 q^{50} - 24 q^{51} - 6 q^{54} - 36 q^{55} + 22 q^{56} - 102 q^{59} - 38 q^{60} + 72 q^{61} + 12 q^{64} - 138 q^{65} + 80 q^{66} - 212 q^{69} - 108 q^{70} + 176 q^{71} - 88 q^{74} - 100 q^{75} + 16 q^{76} - 104 q^{79} - 22 q^{80} - 28 q^{81} - 22 q^{84} + 2 q^{85} + 62 q^{86} + 48 q^{89} + 24 q^{90} - 56 q^{91} + 24 q^{94} + 18 q^{95} - 4 q^{96} + 188 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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