LMFDB - Embedded newform 46.2.c.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [46,2,Mod(3,46)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(46, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("46.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 46 = 2 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	46.c (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.367311849298$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			29.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	46.29
Dual form			46.2.c.a.27.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(-0.524075 - 0.153882i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.767092 - 0.492980i) q^{5} +(-0.357685 + 0.412791i) q^{6} +(-0.601808 + 4.18567i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-2.27279 - 1.46063i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(-0.524075 - 0.153882i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.767092 - 0.492980i) q^{5} +(-0.357685 + 0.412791i) q^{6} +(-0.601808 + 4.18567i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-2.27279 - 1.46063i) q^{9} +(-0.129769 - 0.902563i) q^{10} +(0.630972 + 1.38164i) q^{11} +(0.226900 + 0.496841i) q^{12} +(-0.0694846 - 0.483276i) q^{13} +(3.55742 + 2.28621i) q^{14} +(-0.477875 + 0.140317i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(2.10926 - 2.43422i) q^{17} +(-2.27279 + 1.46063i) q^{18} +(-3.48325 - 4.01989i) q^{19} +(-0.874908 - 0.256896i) q^{20} +(0.959493 - 2.10100i) q^{21} +1.51890 q^{22} +(2.89510 - 3.82340i) q^{23} +0.546200 q^{24} +(-1.73167 + 3.79184i) q^{25} +(-0.468468 - 0.137555i) q^{26} +(2.03940 + 2.35359i) q^{27} +(3.55742 - 2.28621i) q^{28} +(5.24460 - 6.05259i) q^{29} +(-0.0708798 + 0.492980i) q^{30} +(-7.89071 + 2.31692i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-0.118067 - 0.821177i) q^{33} +(-1.33803 - 2.92987i) q^{34} +(1.60181 + 3.50747i) q^{35} +(0.384487 + 2.67417i) q^{36} +(6.47324 + 4.16010i) q^{37} +(-5.10362 + 1.49856i) q^{38} +(-0.0379525 + 0.263965i) q^{39} +(-0.597131 + 0.689126i) q^{40} +(-7.73806 + 4.97295i) q^{41} +(-1.51255 - 1.74557i) q^{42} +(4.30093 + 1.26287i) q^{43} +(0.630972 - 1.38164i) q^{44} -2.46350 q^{45} +(-2.27522 - 4.22177i) q^{46} -0.273137 q^{47} +(0.226900 - 0.496841i) q^{48} +(-10.4412 - 3.06580i) q^{49} +(2.72981 + 3.15037i) q^{50} +(-1.48000 + 0.951137i) q^{51} +(-0.319733 + 0.368991i) q^{52} +(-1.04432 + 7.26339i) q^{53} +(2.98810 - 0.877386i) q^{54} +(1.16513 + 0.748786i) q^{55} +(-0.601808 - 4.18567i) q^{56} +(1.20690 + 2.64274i) q^{57} +(-3.32694 - 7.28499i) q^{58} +(0.161473 + 1.12307i) q^{59} +(0.418986 + 0.269266i) q^{60} +(13.8768 - 4.07459i) q^{61} +(-1.17037 + 8.14013i) q^{62} +(7.48149 - 8.63410i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.291546 - 0.336462i) q^{65} +(-0.796016 - 0.233731i) q^{66} +(0.851175 - 1.86381i) q^{67} -3.22094 q^{68} +(-2.10560 + 1.55825i) q^{69} +3.85592 q^{70} +(4.40736 - 9.65077i) q^{71} +(2.59223 + 0.761147i) q^{72} +(-0.420749 - 0.485571i) q^{73} +(6.47324 - 4.16010i) q^{74} +(1.49103 - 1.72073i) q^{75} +(-0.756983 + 5.26493i) q^{76} +(-6.16279 + 1.80956i) q^{77} +(0.224345 + 0.144178i) q^{78} +(0.230973 + 1.60645i) q^{79} +(0.378794 + 0.829443i) q^{80} +(2.66031 + 5.82527i) q^{81} +(1.30905 + 9.10463i) q^{82} +(-10.0793 - 6.47759i) q^{83} +(-2.21616 + 0.650724i) q^{84} +(0.417977 - 2.90710i) q^{85} +(2.93542 - 3.38765i) q^{86} +(-3.67995 + 2.36496i) q^{87} +(-0.994666 - 1.14791i) q^{88} +(-8.97609 - 2.63562i) q^{89} +(-1.02337 + 2.24088i) q^{90} +2.06465 q^{91} +(-4.78542 + 0.315828i) q^{92} +4.49186 q^{93} +(-0.113465 + 0.248454i) q^{94} +(-4.65370 - 1.36645i) q^{95} +(-0.357685 - 0.412791i) q^{96} +(-3.83870 + 2.46698i) q^{97} +(-7.12617 + 8.22404i) q^{98} +(0.583996 - 4.06178i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9}+O(q^{10}) $ 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9	\( 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9} - 6 q^{10} - 12 q^{11} + 7 q^{12} - 14 q^{13} + 3 q^{14} - 13 q^{15} - q^{16} + 15 q^{17} + 9 q^{18} + 2 q^{19} + 5 q^{20} + q^{21} + 10 q^{22} - q^{23} - 4 q^{24} + 13 q^{25} - 3 q^{26} + 26 q^{27} + 3 q^{28} - 8 q^{29} + 20 q^{30} - 21 q^{31} - q^{32} - 15 q^{33} - 7 q^{34} + 7 q^{35} - 13 q^{36} + 28 q^{37} - 9 q^{38} - 12 q^{39} - 6 q^{40} - 31 q^{41} - 10 q^{42} + 11 q^{43} - 12 q^{44} + 10 q^{45} - 12 q^{46} + 18 q^{47} + 7 q^{48} - 24 q^{49} + 2 q^{50} - 17 q^{51} + 8 q^{52} - 21 q^{53} - 29 q^{54} + 5 q^{55} + 3 q^{56} + 19 q^{57} - 8 q^{58} - 5 q^{59} - 13 q^{60} + 37 q^{61} + q^{62} + 17 q^{63} - q^{64} + 37 q^{65} + 29 q^{66} - 13 q^{67} + 26 q^{68} - 15 q^{69} + 18 q^{70} + 49 q^{71} + 20 q^{72} - 8 q^{73} + 28 q^{74} + 8 q^{75} - 20 q^{76} - 8 q^{77} + 10 q^{78} + 8 q^{79} + 5 q^{80} - 11 q^{81} + 2 q^{82} - 7 q^{83} + q^{84} - 42 q^{85} + 22 q^{86} - 21 q^{87} - q^{88} - 13 q^{89} - 45 q^{90} - 24 q^{91} - 23 q^{92} - 40 q^{93} - 37 q^{94} - 10 q^{95} - 4 q^{96} - 32 q^{97} - 24 q^{98} + 20 q^{99}+O(q^{100}) \) 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9 - 6 * q^10 - 12 * q^11 + 7 * q^12 - 14 * q^13 + 3 * q^14 - 13 * q^15 - q^16 + 15 * q^17 + 9 * q^18 + 2 * q^19 + 5 * q^20 + q^21 + 10 * q^22 - q^23 - 4 * q^24 + 13 * q^25 - 3 * q^26 + 26 * q^27 + 3 * q^28 - 8 * q^29 + 20 * q^30 - 21 * q^31 - q^32 - 15 * q^33 - 7 * q^34 + 7 * q^35 - 13 * q^36 + 28 * q^37 - 9 * q^38 - 12 * q^39 - 6 * q^40 - 31 * q^41 - 10 * q^42 + 11 * q^43 - 12 * q^44 + 10 * q^45 - 12 * q^46 + 18 * q^47 + 7 * q^48 - 24 * q^49 + 2 * q^50 - 17 * q^51 + 8 * q^52 - 21 * q^53 - 29 * q^54 + 5 * q^55 + 3 * q^56 + 19 * q^57 - 8 * q^58 - 5 * q^59 - 13 * q^60 + 37 * q^61 + q^62 + 17 * q^63 - q^64 + 37 * q^65 + 29 * q^66 - 13 * q^67 + 26 * q^68 - 15 * q^69 + 18 * q^70 + 49 * q^71 + 20 * q^72 - 8 * q^73 + 28 * q^74 + 8 * q^75 - 20 * q^76 - 8 * q^77 + 10 * q^78 + 8 * q^79 + 5 * q^80 - 11 * q^81 + 2 * q^82 - 7 * q^83 + q^84 - 42 * q^85 + 22 * q^86 - 21 * q^87 - q^88 - 13 * q^89 - 45 * q^90 - 24 * q^91 - 23 * q^92 - 40 * q^93 - 37 * q^94 - 10 * q^95 - 4 * q^96 - 32 * q^97 - 24 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/46\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$	−0.524075	−	0.153882i	−0.302575	−	0.0888441i	0.126921	−	0.991913i	$-0.459491\pi$
$3$	−0.524075	−	0.153882i	−0.302575	−	0.0888441i	−0.429496	+	0.903069i	$0.641309\pi$
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	0.767092	−	0.492980i	0.343054	−	0.220467i	−0.357757	−	0.933815i	$-0.616458\pi$
$5$	0.767092	−	0.492980i	0.343054	−	0.220467i	0.700810	+	0.713347i	$0.252822\pi$
$6$	−0.357685	+	0.412791i	−0.146024	+	0.168521i
$7$	−0.601808	+	4.18567i	−0.227462	+	1.58203i	0.481281	+	0.876566i	$0.340172\pi$
$7$	−0.601808	+	4.18567i	−0.227462	+	1.58203i	−0.708743	+	0.705467i	$0.750738\pi$
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	−2.27279	−	1.46063i	−0.757595	−	0.486877i
$10$	−0.129769	−	0.902563i	−0.0410365	−	0.285415i
$11$	0.630972	+	1.38164i	0.190245	+	0.416579i	0.980586	−	0.196088i	$-0.0628239\pi$
$11$	0.630972	+	1.38164i	0.190245	+	0.416579i	−0.790341	+	0.612667i	$0.790097\pi$
$12$	0.226900	+	0.496841i	0.0655003	+	0.143426i
$13$	−0.0694846	−	0.483276i	−0.0192715	−	0.134037i	0.977914	−	0.209007i	$-0.0670230\pi$
$13$	−0.0694846	−	0.483276i	−0.0192715	−	0.134037i	−0.997186	+	0.0749700i	$0.976114\pi$
$14$	3.55742	+	2.28621i	0.950759	+	0.611016i
$15$	−0.477875	+	0.140317i	−0.123387	+	0.0362296i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	2.10926	−	2.43422i	0.511572	−	0.590385i	−0.439929	−	0.898033i	$-0.644996\pi$
$17$	2.10926	−	2.43422i	0.511572	−	0.590385i	0.951500	+	0.307647i	$0.0995417\pi$
$18$	−2.27279	+	1.46063i	−0.535701	+	0.344274i
$19$	−3.48325	−	4.01989i	−0.799113	−	0.922226i	0.199219	−	0.979955i	$-0.436159\pi$
$19$	−3.48325	−	4.01989i	−0.799113	−	0.922226i	−0.998332	+	0.0577292i	$0.981614\pi$
$20$	−0.874908	−	0.256896i	−0.195635	−	0.0574437i
$21$	0.959493	−	2.10100i	0.209379	−	0.458475i
$22$	1.51890			0.323830
$23$	2.89510	−	3.82340i	0.603670	−	0.797235i
$23$	2.89510	−	3.82340i	0.603670	−	0.797235i
$24$	0.546200			0.111493
$25$	−1.73167	+	3.79184i	−0.346335	+	0.758368i
$26$	−0.468468	−	0.137555i	−0.0918741	−	0.0269767i
$27$	2.03940	+	2.35359i	0.392483	+	0.452949i
$28$	3.55742	−	2.28621i	0.672288	−	0.432053i
$29$	5.24460	−	6.05259i	0.973898	−	1.12394i	−0.0183713	−	0.999831i	$-0.505848\pi$
$29$	5.24460	−	6.05259i	0.973898	−	1.12394i	0.992269	−	0.124107i	$-0.0396064\pi$
$30$	−0.0708798	+	0.492980i	−0.0129408	+	0.0900054i
$31$	−7.89071	+	2.31692i	−1.41721	+	0.416131i	−0.898559	−	0.438853i	$-0.855385\pi$
$31$	−7.89071	+	2.31692i	−1.41721	+	0.416131i	−0.518654	+	0.854984i	$0.673567\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$	−0.118067	−	0.821177i	−0.0205529	−	0.142949i
$34$	−1.33803	−	2.92987i	−0.229469	−	0.502468i
$35$	1.60181	+	3.50747i	0.270755	+	0.592871i
$36$	0.384487	+	2.67417i	0.0640812	+	0.445694i
$37$	6.47324	+	4.16010i	1.06419	+	0.683916i	0.950854	−	0.309640i	$-0.100209\pi$
$37$	6.47324	+	4.16010i	1.06419	+	0.683916i	0.113341	+	0.993556i	$0.463845\pi$
$38$	−5.10362	+	1.49856i	−0.827916	+	0.243098i
$39$	−0.0379525	+	0.263965i	−0.00607726	+	0.0422683i
$40$	−0.597131	+	0.689126i	−0.0944147	+	0.108960i
$41$	−7.73806	+	4.97295i	−1.20848	+	0.776644i	−0.980404	−	0.196998i	$-0.936881\pi$
$41$	−7.73806	+	4.97295i	−1.20848	+	0.776644i	−0.228078	+	0.973643i	$0.573244\pi$
$42$	−1.51255	−	1.74557i	−0.233391	−	0.269347i
$43$	4.30093	+	1.26287i	0.655886	+	0.192586i	0.592709	−	0.805417i	$-0.298058\pi$
$43$	4.30093	+	1.26287i	0.655886	+	0.192586i	0.0631773	+	0.998002i	$0.479877\pi$
$44$	0.630972	−	1.38164i	0.0951227	−	0.208290i
$45$	−2.46350			−0.367237
$46$	−2.27522	−	4.22177i	−0.335463	−	0.622466i
$47$	−0.273137			−0.0398411			−0.0199205	−	0.999802i	$-0.506341\pi$
$47$	−0.273137			−0.0398411			−0.0199205	+	0.999802i	$0.506341\pi$
$48$	0.226900	−	0.496841i	0.0327502	−	0.0717129i
$49$	−10.4412	−	3.06580i	−1.49160	−	0.437972i
$50$	2.72981	+	3.15037i	0.386054	+	0.445530i
$51$	−1.48000	+	0.951137i	−0.207241	+	0.133186i
$52$	−0.319733	+	0.368991i	−0.0443389	+	0.0511699i
$53$	−1.04432	+	7.26339i	−0.143448	+	0.997704i	0.783199	+	0.621771i	$0.213587\pi$
$53$	−1.04432	+	7.26339i	−0.143448	+	0.997704i	−0.926647	+	0.375933i	$0.877322\pi$
$54$	2.98810	−	0.877386i	0.406629	−	0.119397i
$55$	1.16513	+	0.748786i	0.157107	+	0.100966i
$56$	−0.601808	−	4.18567i	−0.0804200	−	0.559333i
$57$	1.20690	+	2.64274i	0.159857	+	0.350039i
$58$	−3.32694	−	7.28499i	−0.436849	−	0.956566i
$59$	0.161473	+	1.12307i	0.0210220	+	0.146211i	0.997629	−	0.0688206i	$-0.0219236\pi$
$59$	0.161473	+	1.12307i	0.0210220	+	0.146211i	−0.976607	+	0.215032i	$0.931015\pi$
$60$	0.418986	+	0.269266i	0.0540909	+	0.0347621i
$61$	13.8768	−	4.07459i	1.77674	−	0.521698i	0.781922	−	0.623377i	$-0.214240\pi$
$61$	13.8768	−	4.07459i	1.77674	−	0.521698i	0.994817	+	0.101679i	$0.0324215\pi$
$62$	−1.17037	+	8.14013i	−0.148638	+	1.03380i
$63$	7.48149	−	8.63410i	0.942579	−	1.08779i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−0.291546	−	0.336462i	−0.0361619	−	0.0417330i
$66$	−0.796016	−	0.233731i	−0.0979828	−	0.0287704i
$67$	0.851175	−	1.86381i	0.103988	−	0.227701i	−0.850485	−	0.525999i	$-0.823692\pi$
$67$	0.851175	−	1.86381i	0.103988	−	0.227701i	0.954473	+	0.298298i	$0.0964189\pi$
$68$	−3.22094			−0.390596
$69$	−2.10560	+	1.55825i	−0.253485	+	0.187591i
$70$	3.85592			0.460871
$71$	4.40736	−	9.65077i	0.523057	−	1.14534i	−0.445212	−	0.895425i	$-0.646872\pi$
$71$	4.40736	−	9.65077i	0.523057	−	1.14534i	0.968269	−	0.249910i	$-0.0804011\pi$
$72$	2.59223	+	0.761147i	0.305497	+	0.0897020i
$73$	−0.420749	−	0.485571i	−0.0492450	−	0.0568317i	0.730593	−	0.682814i	$-0.239244\pi$
$73$	−0.420749	−	0.485571i	−0.0492450	−	0.0568317i	−0.779838	+	0.625982i	$0.784698\pi$
$74$	6.47324	−	4.16010i	0.752499	−	0.483602i
$75$	1.49103	−	1.72073i	0.172169	−	0.198693i
$76$	−0.756983	+	5.26493i	−0.0868319	+	0.603929i
$77$	−6.16279	+	1.80956i	−0.702316	+	0.206218i
$78$	0.224345	+	0.144178i	0.0254021	+	0.0163249i
$79$	0.230973	+	1.60645i	0.0259865	+	0.180740i	0.998681	−	0.0513506i	$-0.0163526\pi$
$79$	0.230973	+	1.60645i	0.0259865	+	0.180740i	−0.972694	+	0.232090i	$0.925443\pi$
$80$	0.378794	+	0.829443i	0.0423504	+	0.0927345i
$81$	2.66031	+	5.82527i	0.295590	+	0.647253i
$82$	1.30905	+	9.10463i	0.144560	+	1.00544i
$83$	−10.0793	−	6.47759i	−1.10635	−	0.711008i	−0.145855	−	0.989306i	$-0.546593\pi$
$83$	−10.0793	−	6.47759i	−1.10635	−	0.711008i	−0.960495	+	0.278298i	$0.910230\pi$
$84$	−2.21616	+	0.650724i	−0.241803	+	0.0709998i
$85$	0.417977	−	2.90710i	0.0453360	−	0.315319i
$86$	2.93542	−	3.38765i	0.316534	−	0.365300i
$87$	−3.67995	+	2.36496i	−0.394532	+	0.253551i
$88$	−0.994666	−	1.14791i	−0.106032	−	0.122367i
$89$	−8.97609	−	2.63562i	−0.951463	−	0.279375i	−0.231067	−	0.972938i	$-0.574222\pi$
$89$	−8.97609	−	2.63562i	−0.951463	−	0.279375i	−0.720396	+	0.693563i	$0.756040\pi$
$90$	−1.02337	+	2.24088i	−0.107873	+	0.236209i
$91$	2.06465			0.216434
$92$	−4.78542	+	0.315828i	−0.498915	+	0.0329273i
$93$	4.49186			0.465784
$94$	−0.113465	+	0.248454i	−0.0117030	+	0.0256260i
$95$	−4.65370	−	1.36645i	−0.477460	−	0.140195i
$96$	−0.357685	−	0.412791i	−0.0365061	−	0.0421303i
$97$	−3.83870	+	2.46698i	−0.389761	+	0.250484i	−0.720815	−	0.693128i	$-0.756232\pi$
$97$	−3.83870	+	2.46698i	−0.389761	+	0.250484i	0.331054	+	0.943612i	$0.392596\pi$
$98$	−7.12617	+	8.22404i	−0.719852	+	0.830754i
$99$	0.583996	−	4.06178i	0.0586938	−	0.408224i
$100$	3.99969	−	1.17441i	0.399969	−	0.117441i
$101$	−0.793605	−	0.510019i	−0.0789666	−	0.0507488i	0.500562	−	0.865701i	$-0.333127\pi$
$101$	−0.793605	−	0.510019i	−0.0789666	−	0.0507488i	−0.579528	+	0.814952i	$0.696763\pi$
$102$	0.250371	+	1.74137i	0.0247904	+	0.172421i
$103$	3.83595	+	8.39955i	0.377967	+	0.827632i	0.999037	+	0.0438773i	$0.0139710\pi$
$103$	3.83595	+	8.39955i	0.377967	+	0.827632i	−0.621070	+	0.783755i	$0.713302\pi$
$104$	0.202824	+	0.444124i	0.0198886	+	0.0435499i
$105$	−0.299730	−	2.08467i	−0.0292507	−	0.203443i
$106$	6.17319	+	3.96727i	0.599593	+	0.385335i
$107$	3.67940	−	1.08037i	0.355701	−	0.104443i	−0.0990000	−	0.995087i	$-0.531564\pi$
$107$	3.67940	−	1.08037i	0.355701	−	0.104443i	0.454701	+	0.890644i	$0.349746\pi$
$108$	0.443204	−	3.08255i	0.0426473	−	0.296619i
$109$	−5.92480	+	6.83758i	−0.567493	+	0.654921i	−0.964868	−	0.262735i	$-0.915376\pi$
$109$	−5.92480	+	6.83758i	−0.567493	+	0.654921i	0.397376	+	0.917656i	$0.369921\pi$
$110$	1.16513	−	0.748786i	0.111091	−	0.0713939i
$111$	−2.75230	−	3.17632i	−0.261237	−	0.301483i
$112$	−4.05742	−	1.19136i	−0.383390	−	0.112573i
$113$	−4.66678	+	10.2188i	−0.439013	+	0.961305i	0.552765	+	0.833337i	$0.313573\pi$
$113$	−4.66678	+	10.2188i	−0.439013	+	0.961305i	−0.991778	+	0.127968i	$0.959154\pi$
$114$	2.90528			0.272104
$115$	0.335945	−	4.36013i	0.0313270	−	0.406584i
$116$	−8.00872			−0.743591
$117$	−0.547964	+	1.19987i	−0.0506593	+	0.110928i
$118$	1.08866	+	0.319659i	0.100219	+	0.0294270i
$119$	8.91946	+	10.2936i	0.817646	+	0.943614i
$120$	0.418986	−	0.269266i	0.0382480	−	0.0245805i
$121$	5.69267	−	6.56970i	0.517516	−	0.597245i
$122$	2.05824	−	14.3154i	0.186345	−	1.29606i
$123$	4.82058	−	1.41545i	0.434657	−	0.127627i
$124$	6.91833	+	4.44614i	0.621284	+	0.399275i
$125$	1.18979	+	8.27518i	0.106418	+	0.740155i
$126$	−4.74593	−	10.3921i	−0.422801	−	0.925805i
$127$	1.86599	+	4.08594i	0.165580	+	0.362569i	0.974174	−	0.225797i	$-0.0724987\pi$
$127$	1.86599	+	4.08594i	0.165580	+	0.362569i	−0.808595	+	0.588366i	$0.799771\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$	−2.05968	−	1.32368i	−0.181345	−	0.116543i
$130$	−0.427170	+	0.125428i	−0.0374653	+	0.0110008i
$131$	1.14934	−	7.99383i	0.100418	−	0.698424i	−0.875964	−	0.482376i	$-0.839774\pi$
$131$	1.14934	−	7.99383i	0.100418	−	0.698424i	0.976383	−	0.216048i	$-0.0693169\pi$
$132$	−0.543287	+	0.626986i	−0.0472870	+	0.0545722i
$133$	18.9222	−	12.1605i	1.64076	−	1.05445i
$134$	−1.34179	−	1.54851i	−0.115913	−	0.133771i
$135$	2.72468	+	0.800039i	0.234503	+	0.0688564i
$136$	−1.33803	+	2.92987i	−0.114735	+	0.251234i
$137$	−0.602808			−0.0515013			−0.0257507	−	0.999668i	$-0.508198\pi$
$137$	−0.602808			−0.0515013			−0.0257507	+	0.999668i	$0.508198\pi$
$138$	0.542732	+	2.56264i	0.0462004	+	0.218147i
$139$	−15.6895			−1.33077			−0.665384	−	0.746501i	$-0.731732\pi$
$139$	−15.6895			−1.33077			−0.665384	+	0.746501i	$0.731732\pi$
$140$	1.60181	−	3.50747i	0.135377	−	0.296435i
$141$	0.143144	+	0.0420309i	0.0120549	+	0.00353964i
$142$	−6.94777	−	8.01815i	−0.583044	−	0.672868i
$143$	0.623869	−	0.400936i	0.0521705	−	0.0335280i
$144$	1.76921	−	2.04178i	0.147435	−	0.170149i
$145$	1.03928	−	7.22838i	0.0863078	−	0.600284i
$146$	−0.616476	+	0.181014i	−0.0510199	+	0.0149808i
$147$	5.00019	+	3.21343i	0.412408	+	0.265039i
$148$	−1.09508	−	7.61644i	−0.0900149	−	0.626067i
$149$	−1.68160	−	3.68220i	−0.137762	−	0.301658i	0.828159	−	0.560493i	$-0.189388\pi$
$149$	−1.68160	−	3.68220i	−0.137762	−	0.301658i	−0.965921	+	0.258836i	$0.916661\pi$
$150$	−0.945841	−	2.07110i	−0.0772276	−	0.169105i
$151$	0.0103213	+	0.0717863i	0.000839936	+	0.00584189i	0.990237	−	0.139393i	$-0.0445152\pi$
$151$	0.0103213	+	0.0717863i	0.000839936	+	0.00584189i	−0.989397	+	0.145235i	$0.953606\pi$
$152$	4.47469	+	2.87571i	0.362945	+	0.233251i
$153$	−8.34940	+	2.45161i	−0.675009	+	0.198201i
$154$	−0.914084	+	6.35759i	−0.0736590	+	0.512309i
$155$	−4.91070	+	5.66726i	−0.394437	+	0.455205i
$156$	0.224345	−	0.144178i	0.0179620	−	0.0115435i
$157$	−0.0235791	−	0.0272118i	−0.00188182	−	0.00217174i	0.754808	−	0.655946i	$-0.227730\pi$
$157$	−0.0235791	−	0.0272118i	−0.00188182	−	0.00217174i	−0.756690	+	0.653774i	$0.773185\pi$
$158$	1.55723	+	0.457243i	0.123886	+	0.0363763i
$159$	1.66501	−	3.64586i	0.132044	−	0.289136i
$160$	0.911844			0.0720876
$161$	14.2612	+	14.4189i	1.12394	+	1.13637i
$162$	6.40399			0.503145
$163$	−6.64774	+	14.5565i	−0.520691	+	1.14015i	0.448486	+	0.893790i	$0.351963\pi$
$163$	−6.64774	+	14.5565i	−0.520691	+	1.14015i	−0.969177	+	0.246365i	$0.920764\pi$
$164$	8.82566	+	2.59145i	0.689168	+	0.202358i
$165$	−0.495393	−	0.571714i	−0.0385663	−	0.0445079i
$166$	−10.0793	+	6.47759i	−0.782307	+	0.502758i
$167$	−3.00660	+	3.46980i	−0.232657	+	0.268501i	−0.860059	−	0.510195i	$-0.829573\pi$
$167$	−3.00660	+	3.46980i	−0.232657	+	0.268501i	0.627401	+	0.778696i	$0.284119\pi$
$168$	−0.328708	+	2.28621i	−0.0253603	+	0.176385i
$169$	12.2447	−	3.59536i	0.941899	−	0.276566i
$170$	−2.47075	−	1.58786i	−0.189498	−	0.121783i
$171$	2.04512	+	14.2241i	0.156394	+	1.08774i
$172$	−1.86210	−	4.07743i	−0.141984	−	0.310901i
$173$	−8.60729	−	18.8473i	−0.654400	−	1.43294i	−0.887650	−	0.460519i	$-0.847663\pi$
$173$	−8.60729	−	18.8473i	−0.654400	−	1.43294i	0.233250	−	0.972417i	$-0.425064\pi$
$174$	0.622537	+	4.32984i	0.0471944	+	0.328245i
$175$	−14.8292	−	9.53017i	−1.12098	−	0.720413i
$176$	−1.45737	+	0.427923i	−0.109853	+	0.0322559i
$177$	0.0881966	−	0.613421i	0.00662926	−	0.0461075i
$178$	−6.12624	+	7.07006i	−0.459181	+	0.529923i
$179$	−0.458738	+	0.294813i	−0.0342877	+	0.0220354i	−0.557672	−	0.830061i	$-0.688305\pi$
$179$	−0.458738	+	0.294813i	−0.0342877	+	0.0220354i	0.523385	+	0.852097i	$0.324669\pi$
$180$	1.61325	+	1.86179i	0.120244	+	0.138769i
$181$	2.45842	+	0.721857i	0.182733	+	0.0536552i	0.371819	−	0.928305i	$-0.378734\pi$
$181$	2.45842	+	0.721857i	0.182733	+	0.0536552i	−0.189086	+	0.981961i	$0.560552\pi$
$182$	0.857685	−	1.87807i	0.0635759	−	0.139212i
$183$	−7.89948			−0.583947
$184$	−1.70065	+	4.48417i	−0.125373	+	0.330578i
$185$	7.01642			0.515857
$186$	1.86599	−	4.08594i	0.136821	−	0.299596i
$187$	4.69410	+	1.37831i	0.343266	+	0.100792i
$188$	0.178866	+	0.206423i	0.0130452	+	0.0150549i
$189$	−11.0787	+	7.11984i	−0.805856	+	0.517892i
$190$	−3.17618	+	3.66551i	−0.230425	+	0.265924i
$191$	0.554917	−	3.85953i	0.0401524	−	0.279266i	−0.959847	−	0.280525i	$-0.909492\pi$
$191$	0.554917	−	3.85953i	0.0401524	−	0.279266i	0.999999	+	0.00125875i	$0.000400672\pi$
$192$	−0.524075	+	0.153882i	−0.0378219	+	0.0111055i
$193$	−11.2055	−	7.20135i	−0.806590	−	0.518364i	0.0711699	−	0.997464i	$-0.477327\pi$
$193$	−11.2055	−	7.20135i	−0.806590	−	0.518364i	−0.877760	+	0.479100i	$0.840963\pi$
$194$	0.649393	+	4.51662i	0.0466237	+	0.324275i
$195$	0.101017	+	0.221196i	0.00723395	+	0.0158401i
$196$	4.52053	+	9.89858i	0.322895	+	0.707042i
$197$	−2.37532	−	16.5207i	−0.169235	−	1.17705i	−0.880471	−	0.474100i	$-0.842774\pi$
$197$	−2.37532	−	16.5207i	−0.169235	−	1.17705i	0.711237	−	0.702953i	$-0.248135\pi$
$198$	−3.45213	−	2.21855i	−0.245332	−	0.157665i
$199$	2.86040	−	0.839888i	0.202768	−	0.0595381i	−0.178771	−	0.983891i	$-0.557212\pi$
$199$	2.86040	−	0.839888i	0.202768	−	0.0595381i	0.381539	+	0.924353i	$0.375394\pi$
$200$	0.593245	−	4.12611i	0.0419488	−	0.291760i
$201$	−0.732888	+	0.845798i	−0.0516939	+	0.0596580i
$202$	−0.793605	+	0.510019i	−0.0558378	+	0.0358848i
$203$	22.1779	+	25.5946i	1.55658	+	1.79639i
$204$	1.68801	+	0.495645i	0.118185	+	0.0347021i
$205$	−3.48424	+	7.62942i	−0.243350	+	0.532862i
$206$	9.23401			0.643364
$207$	−12.1645	+	4.46111i	−0.845492	+	0.310068i
$208$	0.488245			0.0338537
$209$	3.35619	−	7.34903i	0.232153	−	0.508343i
$210$	−2.02079	−	0.593359i	−0.139448	−	0.0409456i
$211$	−16.0787	−	18.5558i	−1.10690	−	1.27743i	−0.957430	−	0.288664i	$-0.906789\pi$
$211$	−16.0787	−	18.5558i	−1.10690	−	1.27743i	−0.149470	−	0.988766i	$-0.547757\pi$
$212$	6.17319	−	3.96727i	0.423976	−	0.272473i
$213$	−3.79487	+	4.37952i	−0.260020	+	0.300079i
$214$	0.545739	−	3.79570i	0.0373060	−	0.259469i
$215$	3.92178	−	1.15154i	0.267463	−	0.0785343i
$216$	−2.61988	−	1.68369i	−0.178260	−	0.114561i
$217$	−4.94917	−	34.4222i	−0.335971	−	2.33673i
$218$	3.75843	+	8.22982i	0.254553	+	0.557394i
$219$	0.145784	+	0.319222i	0.00985114	+	0.0215710i
$220$	−0.197106	−	1.37090i	−0.0132889	−	0.0924260i
$221$	−1.32296	−	0.850215i	−0.0889920	−	0.0571917i
$222$	−4.03263	+	1.18409i	−0.270653	+	0.0794708i
$223$	0.840553	−	5.84618i	0.0562876	−	0.391489i	−0.942130	−	0.335249i	$-0.891180\pi$
$223$	0.840553	−	5.84618i	0.0562876	−	0.391489i	0.998417	−	0.0562402i	$-0.0179113\pi$
$224$	−2.76921	+	3.19584i	−0.185026	+	0.213531i
$225$	9.47420	−	6.08870i	0.631613	−	0.405913i
$226$	7.35671	+	8.49010i	0.489361	+	0.564753i
$227$	5.19631	+	1.52578i	0.344892	+	0.101269i	0.449591	−	0.893235i	$-0.351570\pi$
$227$	5.19631	+	1.52578i	0.344892	+	0.101269i	−0.104699	+	0.994504i	$0.533388\pi$
$228$	1.20690	−	2.64274i	0.0799287	−	0.175019i
$229$	14.7114			0.972154			0.486077	−	0.873916i	$-0.338427\pi$
$229$	14.7114			0.972154			0.486077	+	0.873916i	$0.338427\pi$
$230$	−3.82656	−	2.11685i	−0.252316	−	0.139581i
$231$	3.50823			0.230824
$232$	−3.32694	+	7.28499i	−0.218425	+	0.478283i
$233$	24.5668	+	7.21346i	1.60942	+	0.472569i	0.958148	−	0.286272i	$-0.0924162\pi$
$233$	24.5668	+	7.21346i	1.60942	+	0.472569i	0.651275	+	0.758842i	$0.274234\pi$
$234$	0.863811	+	0.996891i	0.0564691	+	0.0651688i
$235$	−0.209521	+	0.134651i	−0.0136676	+	0.00878365i
$236$	0.743017	−	0.857487i	0.0483663	−	0.0558176i
$237$	0.126157	−	0.877444i	0.00819480	−	0.0569961i
$238$	13.0687	−	3.83731i	0.847116	−	0.248736i
$239$	1.70531	+	1.09594i	0.110307	+	0.0708903i	0.594631	−	0.803998i	$-0.297298\pi$
$239$	1.70531	+	1.09594i	0.110307	+	0.0708903i	−0.484324	+	0.874889i	$0.660934\pi$
$240$	−0.0708798	−	0.492980i	−0.00457527	−	0.0318217i
$241$	7.69901	+	16.8585i	0.495937	+	1.08595i	0.977769	+	0.209687i	$0.0672444\pi$
$241$	7.69901	+	16.8585i	0.495937	+	1.08595i	−0.481832	+	0.876264i	$0.660028\pi$
$242$	−3.61118	−	7.90739i	−0.232136	−	0.508306i
$243$	−1.82741	−	12.7099i	−0.117228	−	0.815342i
$244$	−12.1667	−	7.81908i	−0.778895	−	0.500565i
$245$	−9.52072	+	2.79554i	−0.608256	+	0.178600i
$246$	0.715002	−	4.97295i	0.0455869	−	0.317064i
$247$	−1.70068	+	1.96269i	−0.108212	+	0.124883i
$248$	6.91833	−	4.44614i	0.439314	−	0.282330i
$249$	4.28554	+	4.94577i	0.271585	+	0.313426i
$250$	8.02163	+	2.35536i	0.507332	+	0.148966i
$251$	9.74401	−	21.3364i	0.615036	−	1.34674i	−0.304039	−	0.952660i	$-0.598335\pi$
$251$	9.74401	−	21.3364i	0.615036	−	1.34674i	0.919075	−	0.394082i	$-0.128937\pi$
$252$	−11.4246			−0.719679
$253$	7.10928	+	1.58751i	0.446957	+	0.0998060i
$254$	4.49186			0.281844
$255$	−0.666403	+	1.45922i	−0.0417318	+	0.0913798i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−6.80351	−	7.85166i	−0.424391	−	0.489773i	0.502779	−	0.864415i	$-0.332311\pi$
$257$	−6.80351	−	7.85166i	−0.424391	−	0.489773i	−0.927170	+	0.374642i	$0.877766\pi$
$258$	−2.05968	+	1.32368i	−0.128230	+	0.0824085i
$259$	−21.3084	+	24.5912i	−1.32404	+	1.52803i
$260$	−0.0633591	+	0.440672i	−0.00392936	+	0.0273293i
$261$	−20.7604	+	6.09582i	−1.28504	+	0.377322i
$262$	−6.79399	−	4.36623i	−0.419734	−	0.269747i
$263$	3.68520	+	25.6312i	0.227239	+	1.58049i	0.709659	+	0.704545i	$0.248849\pi$
$263$	3.68520	+	25.6312i	0.227239	+	1.58049i	−0.482420	+	0.875940i	$0.660242\pi$
$264$	0.344637	+	0.754651i	0.0212110	+	0.0464455i
$265$	2.77962	+	6.08652i	0.170751	+	0.373892i
$266$	−3.20106	−	22.2639i	−0.196270	−	1.36509i
$267$	4.29857	+	2.76252i	0.263068	+	0.169064i
$268$	−1.96598	+	0.577263i	−0.120091	+	0.0352620i
$269$	−1.83374	+	12.7540i	−0.111805	+	0.777623i	0.854357	+	0.519687i	$0.173951\pi$
$269$	−1.83374	+	12.7540i	−0.111805	+	0.777623i	−0.966162	+	0.257936i	$0.916958\pi$
$270$	1.85962	−	2.14611i	0.113173	−	0.130608i
$271$	−13.5616	+	8.71552i	−0.823809	+	0.529430i	−0.883305	−	0.468799i	$-0.844687\pi$
$271$	−13.5616	+	8.71552i	−0.823809	+	0.529430i	0.0594961	+	0.998229i	$0.481051\pi$
$272$	2.10926	+	2.43422i	0.127893	+	0.147596i
$273$	−1.08203	−	0.317713i	−0.0654875	−	0.0192289i
$274$	−0.250415	+	0.548333i	−0.0151281	+	0.0331260i
$275$	−6.33158			−0.381809
$276$	2.55652	+	0.570875i	0.153885	+	0.0343626i
$277$	−4.14896			−0.249287			−0.124643	−	0.992202i	$-0.539779\pi$
$277$	−4.14896			−0.249287			−0.124643	+	0.992202i	$0.539779\pi$
$278$	−6.51767	+	14.2717i	−0.390904	+	0.855960i
$279$	21.3181	+	6.25955i	1.27628	+	0.374749i
$280$	−2.52509	−	2.91411i	−0.150903	−	0.174151i
$281$	−4.37371	+	2.81081i	−0.260914	+	0.167679i	−0.664557	−	0.747237i	$-0.731380\pi$
$281$	−4.37371	+	2.81081i	−0.260914	+	0.167679i	0.403644	+	0.914916i	$0.367744\pi$
$282$	0.0976969	−	0.112748i	0.00581776	−	0.00671406i
$283$	1.98080	−	13.7768i	0.117746	−	0.818944i	−0.842281	−	0.539038i	$-0.818788\pi$
$283$	1.98080	−	13.7768i	0.117746	−	0.818944i	0.960028	−	0.279905i	$-0.0903031\pi$
$284$	−10.1798	+	2.98905i	−0.604058	+	0.177368i
$285$	2.22862	+	1.43225i	0.132012	+	0.0848389i
$286$	−0.105540	−	0.734046i	−0.00624070	−	0.0434050i
$287$	−16.1583	−	35.3817i	−0.953793	−	2.08852i
$288$	−1.12231	−	2.45752i	−0.0661329	−	0.144811i
$289$	0.942917	+	6.55813i	0.0554657	+	0.385773i
$290$	−6.14343	−	3.94814i	−0.360755	−	0.231843i
$291$	2.39139	−	0.702176i	0.140186	−	0.0411623i
$292$	−0.0914376	+	0.635962i	−0.00535098	+	0.0372169i
$293$	−16.9201	+	19.5268i	−0.988481	+	1.14077i	0.00156123	+	0.999999i	$0.499503\pi$
$293$	−16.9201	+	19.5268i	−0.988481	+	1.14077i	−0.990042	+	0.140769i	$0.955042\pi$
$294$	5.00019	−	3.21343i	0.291617	−	0.187411i
$295$	0.677515	+	0.781894i	0.0394465	+	0.0455237i
$296$	−7.38307	−	2.16786i	−0.429132	−	0.126005i
$297$	−1.96501	+	4.30276i	−0.114021	+	0.249672i
$298$	−4.04801			−0.234495
$299$	−2.04892	−	1.13346i	−0.118492	−	0.0655498i
$300$	−2.27686			−0.131454
$301$	−7.87428	+	17.2423i	−0.453866	+	0.993828i
$302$	0.0695867	+	0.0204325i	0.00400427	+	0.00117576i
$303$	0.337426	+	0.389410i	0.0193846	+	0.0223710i
$304$	4.47469	−	2.87571i	0.256641	−	0.164933i
$305$	8.63607	−	9.96656i	0.494500	−	0.570684i
$306$	−1.23841	+	8.61332i	−0.0707951	+	0.492391i
$307$	31.6662	−	9.29803i	1.80728	−	0.530667i	0.808924	−	0.587913i	$-0.200050\pi$
$307$	31.6662	−	9.29803i	1.80728	−	0.530667i	0.998360	+	0.0572466i	$0.0182321\pi$
$308$	5.40335	+	3.47252i	0.307884	+	0.197865i
$309$	−0.717782	−	4.99228i	−0.0408332	−	0.284001i
$310$	3.11514	+	6.82120i	0.176928	+	0.387418i
$311$	6.17137	+	13.5134i	0.349946	+	0.766276i	0.999980	+	0.00637009i	$0.00202768\pi$
$311$	6.17137	+	13.5134i	0.349946	+	0.766276i	−0.650033	+	0.759906i	$0.725245\pi$
$312$	−0.0379525	−	0.263965i	−0.00214864	−	0.0149441i
$313$	5.85184	+	3.76075i	0.330765	+	0.212570i	0.695473	−	0.718552i	$-0.255195\pi$
$313$	5.85184	+	3.76075i	0.330765	+	0.212570i	−0.364708	+	0.931122i	$0.618831\pi$
$314$	−0.0345478	+	0.0101442i	−0.00194965	+	0.000572468i
$315$	1.48255	−	10.3114i	0.0835323	−	0.580980i
$316$	1.06282	−	1.22656i	0.0597882	−	0.0689993i
$317$	3.72494	−	2.39388i	0.209214	−	0.134453i	−0.431838	−	0.901951i	$-0.642135\pi$
$317$	3.72494	−	2.39388i	0.209214	−	0.134453i	0.641052	+	0.767498i	$0.278498\pi$
$318$	−2.62472	−	3.02909i	−0.147187	−	0.169863i
$319$	11.6717	+	3.42711i	0.653489	+	0.191882i
$320$	0.378794	−	0.829443i	0.0211752	−	0.0463672i
$321$	−2.09453			−0.116905
$322$	19.0402	−	6.98262i	1.06107	−	0.389126i
$323$	−17.1324			−0.953272
$324$	2.66031	−	5.82527i	0.147795	−	0.323626i
$325$	1.95283	+	0.573402i	0.108323	+	0.0318066i
$326$	10.4795	+	12.0940i	0.580406	+	0.669824i
$327$	4.15722	−	2.67169i	0.229895	−	0.147745i
$328$	6.02357	−	6.95157i	0.332596	−	0.383836i
$329$	0.164376	−	1.14326i	0.00906233	−	0.0630299i
$330$	−0.725843	+	0.213127i	−0.0399563	+	0.0117322i
$331$	4.30350	+	2.76569i	0.236542	+	0.152016i	0.653542	−	0.756890i	$-0.273282\pi$
$331$	4.30350	+	2.76569i	0.236542	+	0.152016i	−0.417000	+	0.908906i	$0.636919\pi$
$332$	1.70512	+	11.8594i	0.0935805	+	0.650867i
$333$	−8.63592	−	18.9100i	−0.473246	−	1.03626i
$334$	1.90725	+	4.17630i	0.104360	+	0.228517i
$335$	−0.265893	−	1.84933i	−0.0145273	−	0.101040i
$336$	1.94306	+	1.24873i	0.106003	+	0.0681238i
$337$	−11.5860	+	3.40195i	−0.631129	+	0.185316i	−0.581624	−	0.813458i	$-0.697583\pi$
$337$	−11.5860	+	3.40195i	−0.631129	+	0.185316i	−0.0495050	+	0.998774i	$0.515764\pi$
$338$	1.81617	−	12.6317i	0.0987865	−	0.687075i
$339$	4.01824	−	4.63730i	0.218241	−	0.251863i
$340$	−2.47075	+	1.58786i	−0.133995	+	0.0861137i
$341$	−8.17996	−	9.44018i	−0.442970	−	0.511215i
$342$	13.7883	+	4.04860i	0.745584	+	0.218923i
$343$	6.81933	−	14.9322i	0.368209	−	0.806266i
$344$	−4.48251			−0.241681
$345$	−0.847007	+	2.23334i	−0.0456013	+	0.120239i
$346$	−20.7197			−1.11390
$347$	8.34765	−	18.2788i	0.448125	−	0.981257i	−0.541910	−	0.840437i	$-0.682299\pi$
$347$	8.34765	−	18.2788i	0.448125	−	0.981257i	0.990035	−	0.140821i	$-0.0449741\pi$
$348$	4.19718	+	1.23240i	0.224992	+	0.0660637i
$349$	−5.83909	−	6.73867i	−0.312559	−	0.360713i	0.577634	−	0.816296i	$-0.303976\pi$
$349$	−5.83909	−	6.73867i	−0.312559	−	0.360713i	−0.890193	+	0.455583i	$0.849431\pi$
$350$	−14.8292	+	9.53017i	−0.792656	+	0.509409i
$351$	0.995728	−	1.14913i	0.0531480	−	0.0613361i
$352$	−0.216162	+	1.50344i	−0.0115214	+	0.0801334i
$353$	12.1485	−	3.56713i	0.646601	−	0.189859i	0.0580428	−	0.998314i	$-0.481514\pi$
$353$	12.1485	−	3.56713i	0.646601	−	0.189859i	0.588558	+	0.808455i	$0.299696\pi$
$354$	−0.521349	−	0.335051i	−0.0277094	−	0.0178077i
$355$	−1.37679	−	9.57577i	−0.0730723	−	0.508229i
$356$	3.88622	+	8.50964i	0.205969	+	0.451010i
$357$	−3.09047	−	6.76718i	−0.163565	−	0.358157i
$358$	0.0776047	+	0.539753i	0.00410154	+	0.0285268i
$359$	8.24006	+	5.29557i	0.434894	+	0.279489i	0.739715	−	0.672920i	$-0.234960\pi$
$359$	8.24006	+	5.29557i	0.434894	+	0.279489i	−0.304821	+	0.952410i	$0.598597\pi$
$360$	2.36371	−	0.694047i	0.124578	−	0.0365795i
$361$	−1.32247	+	9.19798i	−0.0696037	+	0.484104i
$362$	1.67789	−	1.93639i	0.0881878	−	0.101774i
$363$	−3.99435	+	2.56701i	−0.209649	+	0.134733i
$364$	−1.35206	−	1.56036i	−0.0708670	−	0.0817849i
$365$	−0.562130	−	0.165056i	−0.0294232	−	0.00863944i
$366$	−3.28156	+	7.18562i	−0.171530	+	0.375599i
$367$	10.9305			0.570568			0.285284	−	0.958443i	$-0.407912\pi$
$367$	10.9305			0.570568			0.285284	+	0.958443i	$0.407912\pi$
$368$	3.37247	+	3.40976i	0.175802	+	0.177746i
$369$	24.8506			1.29367
$370$	2.91473	−	6.38236i	0.151529	−	0.331803i
$371$	−29.7737	−	8.74233i	−1.54577	−	0.453879i
$372$	−2.94154	−	3.39472i	−0.152512	−	0.176008i
$373$	7.62102	−	4.89773i	0.394601	−	0.253595i	−0.328261	−	0.944587i	$-0.606463\pi$
$373$	7.62102	−	4.89773i	0.394601	−	0.253595i	0.722862	+	0.690992i	$0.242826\pi$
$374$	3.20375	−	3.69733i	0.165662	−	0.191184i
$375$	0.649865	−	4.51991i	0.0335589	−	0.233407i
$376$	0.262073	−	0.0769515i	0.0135154	−	0.00396847i
$377$	−3.28949	−	2.11403i	−0.169417	−	0.108878i
$378$	1.87418	+	13.0352i	0.0963975	+	0.670459i
$379$	6.75852	+	14.7991i	0.347162	+	0.760179i	0.999996	+	0.00267820i	$0.000852497\pi$
$379$	6.75852	+	14.7991i	0.347162	+	0.760179i	−0.652834	+	0.757501i	$0.726420\pi$
$380$	2.01483	+	4.41187i	0.103359	+	0.226324i
$381$	−0.349163	−	2.42848i	−0.0178882	−	0.124415i
$382$	−3.28023	−	2.10808i	−0.167831	−	0.107859i
$383$	−28.0369	+	8.23237i	−1.43262	+	0.420655i	−0.903754	−	0.428052i	$-0.859200\pi$
$383$	−28.0369	+	8.23237i	−1.43262	+	0.420655i	−0.528864	+	0.848707i	$0.677382\pi$
$384$	−0.0777324	+	0.540641i	−0.00396677	+	0.0275895i
$385$	−3.83535	+	4.42623i	−0.195468	+	0.225582i
$386$	−11.2055	+	7.20135i	−0.570346	+	0.366539i
$387$	−7.93052	−	9.15230i	−0.403131	−	0.465238i
$388$	4.37823	+	1.28557i	0.222271	+	0.0652647i
$389$	−11.3460	+	24.8442i	−0.575264	+	1.25965i	0.368682	+	0.929555i	$0.379809\pi$
$389$	−11.3460	+	24.8442i	−0.575264	+	1.25965i	−0.943947	+	0.330098i	$0.892918\pi$
$390$	0.243170			0.0123134
$391$	−3.20048	−	15.1119i	−0.161855	−	0.764240i
$392$	10.8820			0.549622
$393$	−1.83245	+	4.01251i	−0.0924349	+	0.202404i
$394$	−16.0145	−	4.70229i	−0.806800	−	0.236898i
$395$	0.969125	+	1.11843i	0.0487620	+	0.0562743i
$396$	−3.45213	+	2.21855i	−0.173476	+	0.111486i
$397$	−7.92826	+	9.14970i	−0.397908	+	0.459210i	−0.918981	−	0.394302i	$-0.870986\pi$
$397$	−7.92826	+	9.14970i	−0.397908	+	0.459210i	0.521073	+	0.853512i	$0.325532\pi$
$398$	0.424262	−	2.95081i	0.0212663	−	0.147911i
$399$	−11.7879	+	3.46125i	−0.590135	+	0.173279i
$400$	−3.50680	−	2.25368i	−0.175340	−	0.112684i
$401$	0.192189	+	1.33671i	0.00959747	+	0.0667519i	0.994057	−	0.108858i	$-0.0347194\pi$
$401$	0.192189	+	1.33671i	0.00959747	+	0.0667519i	−0.984460	+	0.175610i	$0.943810\pi$
$402$	0.464912	+	1.01802i	0.0231877	+	0.0507740i
$403$	1.66799	+	3.65240i	0.0830887	+	0.181939i
$404$	0.134254	+	0.933758i	0.00667939	+	0.0464562i
$405$	4.91245	+	3.15704i	0.244102	+	0.156875i
$406$	32.4947	−	9.54131i	1.61269	−	0.473527i
$407$	−1.66331	+	11.5686i	−0.0824472	+	0.573433i
$408$	1.15208	−	1.32957i	0.0570365	−	0.0658236i
$409$	8.13725	−	5.22949i	0.402361	−	0.258582i	−0.323773	−	0.946135i	$-0.604951\pi$
$409$	8.13725	−	5.22949i	0.402361	−	0.258582i	0.726134	+	0.687553i	$0.241315\pi$
$410$	5.49256	+	6.33875i	0.271258	+	0.313049i
$411$	0.315917	+	0.0927615i	0.0155830	+	0.00457559i
$412$	3.83595	−	8.39955i	0.188984	−	0.413816i
$413$	−4.79797			−0.236093
$414$	−0.995357	+	12.9184i	−0.0489191	+	0.634907i
$415$	−10.9251			−0.536292
$416$	0.202824	−	0.444124i	0.00994429	−	0.0217749i
$417$	8.22250	+	2.41434i	0.402657	+	0.118231i
$418$	−5.29070	−	6.10580i	−0.258777	−	0.298644i
$419$	21.6263	−	13.8984i	1.05652	−	0.678981i	0.107498	−	0.994205i	$-0.465716\pi$
$419$	21.6263	−	13.8984i	1.05652	−	0.678981i	0.949017	+	0.315224i	$0.102080\pi$
$420$	−1.37921	+	1.59169i	−0.0672984	+	0.0776665i
$421$	−2.25678	+	15.6963i	−0.109989	+	0.764989i	0.857937	+	0.513754i	$0.171746\pi$
$421$	−2.25678	+	15.6963i	−0.109989	+	0.764989i	−0.967926	+	0.251235i	$0.919163\pi$
$422$	−23.5582	+	6.91732i	−1.14680	+	0.336730i
$423$	0.620781	+	0.398952i	0.0301834	+	0.0193977i
$424$	−1.04432	−	7.26339i	−0.0507166	−	0.352742i
$425$	5.57761	+	12.2133i	0.270554	+	0.592430i
$426$	2.40730	+	5.27125i	0.116634	+	0.255393i
$427$	8.70371	+	60.5357i	0.421202	+	2.92953i
$428$	−3.22598	−	2.07321i	−0.155934	−	0.100212i
$429$	−0.388651	+	0.114118i	−0.0187643	+	0.00550968i
$430$	0.581690	−	4.04574i	0.0280516	−	0.195103i
$431$	25.0732	−	28.9361i	1.20774	−	1.39380i	0.311486	−	0.950251i	$-0.399173\pi$
$431$	25.0732	−	28.9361i	1.20774	−	1.39380i	0.896249	−	0.443550i	$-0.146281\pi$
$432$	−2.61988	+	1.68369i	−0.126049	+	0.0810066i
$433$	−7.92749	−	9.14881i	−0.380971	−	0.439664i	0.532585	−	0.846376i	$-0.321221\pi$
$433$	−7.92749	−	9.14881i	−0.380971	−	0.439664i	−0.913556	+	0.406712i	$0.866675\pi$
$434$	−33.3675	−	9.79758i	−1.60169	−	0.470299i
$435$	−1.65698	+	3.62829i	−0.0794463	+	0.173963i
$436$	9.04741			0.433293
$437$	−25.4540	+	1.67991i	−1.21763	+	0.0803610i
$438$	0.350935			0.0167683
$439$	9.63515	−	21.0980i	0.459861	−	1.00695i	−0.527658	−	0.849457i	$-0.676930\pi$
$439$	9.63515	−	21.0980i	0.459861	−	1.00695i	0.987519	−	0.157498i	$-0.0503428\pi$
$440$	−1.32889	−	0.390199i	−0.0633526	−	0.0186020i
$441$	19.2525	+	22.2186i	0.916787	+	1.05803i
$442$	−1.32296	+	0.850215i	−0.0629268	+	0.0404406i
$443$	−6.10576	+	7.04642i	−0.290093	+	0.334786i	−0.882025	−	0.471203i	$-0.843820\pi$
$443$	−6.10576	+	7.04642i	−0.290093	+	0.334786i	0.591932	+	0.805988i	$0.298366\pi$
$444$	−0.598132	+	4.16010i	−0.0283861	+	0.197430i
$445$	−8.18479	+	2.40327i	−0.387996	+	0.113926i
$446$	−4.96869	−	3.19318i	−0.235274	−	0.151202i
$447$	0.314662	+	2.18852i	0.0148830	+	0.103513i
$448$	1.75667	+	3.84657i	0.0829948	+	0.181733i
$449$	−17.3174	−	37.9197i	−0.817256	−	1.78954i	−0.572382	−	0.819987i	$-0.693980\pi$
$449$	−17.3174	−	37.9197i	−0.817256	−	1.78954i	−0.244875	−	0.969555i	$-0.578747\pi$
$450$	−1.60275	−	11.1474i	−0.0755543	−	0.525492i
$451$	−11.7533	−	7.55340i	−0.553442	−	0.355676i
$452$	10.7790	−	3.16499i	0.506999	−	0.148868i
$453$	0.00563750	−	0.0392097i	0.000264873	−	0.00184223i
$454$	3.54652	−	4.09290i	0.166446	−	0.192089i
$455$	1.58377	−	1.01783i	0.0742485	−	0.0477166i
$456$	−1.90255	−	2.19566i	−0.0890953	−	0.102821i
$457$	−26.1393	−	7.67519i	−1.22274	−	0.359030i	−0.394237	−	0.919009i	$-0.628991\pi$
$457$	−26.1393	−	7.67519i	−1.22274	−	0.359030i	−0.828507	+	0.559979i	$0.810809\pi$
$458$	6.11132	−	13.3819i	0.285563	−	0.625296i
$459$	10.0308			0.468198
$460$	−3.51516	+	2.60139i	−0.163895	+	0.121290i
$461$	29.0881			1.35477			0.677384	−	0.735629i	$-0.263114\pi$
$461$	29.0881			1.35477			0.677384	+	0.735629i	$0.263114\pi$
$462$	1.45737	−	3.19120i	0.0678030	−	0.148468i
$463$	−1.99904	−	0.586970i	−0.0929031	−	0.0272788i	0.234951	−	0.972007i	$-0.424507\pi$
$463$	−1.99904	−	0.586970i	−0.0929031	−	0.0272788i	−0.327854	+	0.944728i	$0.606325\pi$
$464$	5.24460	+	6.05259i	0.243474	+	0.280984i
$465$	3.44567	−	2.21440i	0.159789	−	0.102690i
$466$	16.7670	−	19.3502i	0.776716	−	0.896379i
$467$	−3.78800	+	26.3461i	−0.175288	+	1.21915i	0.692205	+	0.721701i	$0.256640\pi$
$467$	−3.78800	+	26.3461i	−0.175288	+	1.21915i	−0.867492	+	0.497451i	$0.834270\pi$
$468$	1.26564	−	0.371626i	0.0585044	−	0.0171784i
$469$	7.28906	+	4.68439i	0.336577	+	0.216305i
$470$	0.0354446	+	0.246523i	0.00163494	+	0.0113713i
$471$	0.00816984	+	0.0178894i	0.000376446	+	0.000824302i
$472$	−0.471337	−	1.03208i	−0.0216951	−	0.0475055i
$473$	0.968945	+	6.73916i	0.0445522	+	0.309867i
$474$	−0.745743	−	0.479260i	−0.0342531	−	0.0220131i
$475$	21.2746	−	6.24679i	0.976147	−	0.286623i
$476$	1.93838	−	13.4818i	0.0888457	−	0.617935i
$477$	12.9826	−	14.9828i	0.594434	−	0.686014i
$478$	1.70531	−	1.09594i	0.0779992	−	0.0501270i
$479$	−2.98599	−	3.44602i	−0.136434	−	0.157453i	0.683421	−	0.730024i	$-0.260491\pi$
$479$	−2.98599	−	3.44602i	−0.136434	−	0.157453i	−0.819855	+	0.572572i	$0.805946\pi$
$480$	−0.477875	−	0.140317i	−0.0218119	−	0.00640456i
$481$	1.56068	−	3.41742i	0.0711611	−	0.155821i
$482$	18.5333			0.844169
$483$	−5.25513	−	9.75112i	−0.239117	−	0.443691i
$484$	−8.69295			−0.395134
$485$	−1.72846	+	3.78480i	−0.0784854	+	0.171859i
$486$	−12.3205	−	3.61762i	−0.558868	−	0.164099i
$487$	7.71086	+	8.89881i	0.349413	+	0.403244i	0.903065	−	0.429504i	$-0.141312\pi$
$487$	7.71086	+	8.89881i	0.349413	+	0.403244i	−0.553652	+	0.832748i	$0.686766\pi$
$488$	−12.1667	+	7.81908i	−0.550762	+	0.353953i
$489$	5.72391	−	6.60574i	0.258844	−	0.298722i
$490$	−1.41214	+	9.82166i	−0.0637940	+	0.443697i
$491$	−8.20130	+	2.40812i	−0.370119	+	0.108677i	−0.461502	−	0.887139i	$-0.652689\pi$
$491$	−8.20130	+	2.40812i	−0.370119	+	0.108677i	0.0913831	+	0.995816i	$0.470871\pi$
$492$	−4.22653	−	2.71623i	−0.190547	−	0.122457i
$493$	−3.67109	−	25.5330i	−0.165338	−	1.14995i
$494$	1.07884	+	2.36233i	0.0485392	+	0.106286i
$495$	−1.55440	−	3.40366i	−0.0698650	−	0.152983i
$496$	−1.17037	−	8.14013i	−0.0525513	−	0.365502i
$497$	37.7425	+	24.2556i	1.69298	+	1.08801i
$498$	6.27911	−	1.84371i	0.281374	−	0.0826188i
$499$	−1.71847	+	11.9522i	−0.0769291	+	0.535054i	0.914518	+	0.404545i	$0.132570\pi$
$499$	−1.71847	+	11.9522i	−0.0769291	+	0.535054i	−0.991447	+	0.130509i	$0.958339\pi$
$500$	5.47482	−	6.31828i	0.244841	−	0.282562i
$501$	2.10962	−	1.35577i	0.0942510	−	0.0605715i
$502$	−15.3605	−	17.7269i	−0.685571	−	0.791191i
$503$	6.26872	+	1.84066i	0.279508	+	0.0820711i	0.418482	−	0.908225i	$-0.362562\pi$
$503$	6.26872	+	1.84066i	0.279508	+	0.0820711i	−0.138974	+	0.990296i	$0.544380\pi$
$504$	−4.74593	+	10.3921i	−0.211401	+	0.462903i
$505$	−0.860197			−0.0382783
$506$	4.39735	−	5.80735i	0.195486	−	0.258168i
$507$	−6.97040			−0.309566
$508$	1.86599	−	4.08594i	0.0827898	−	0.181284i
$509$	−21.6949	−	6.37019i	−0.961608	−	0.282354i	−0.236996	−	0.971511i	$-0.576163\pi$
$509$	−21.6949	−	6.37019i	−0.961608	−	0.282354i	−0.724612	+	0.689157i	$0.757981\pi$
$510$	1.05052	+	1.21236i	0.0465177	+	0.0536843i
$511$	2.28565	−	1.46890i	0.101111	−	0.0649801i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	2.35744	−	16.3963i	0.104083	−	0.723916i
$514$	−9.96840	+	2.92699i	−0.439687	+	0.129104i
$515$	7.08334	+	4.55218i	0.312129	+	0.200593i
$516$	0.348436	+	2.42343i	0.0153390	+	0.106685i
$517$	−0.172342	−	0.377376i	−0.00757958	−	0.0165970i
$518$	13.5171	+	29.5984i	0.593909	+	1.30048i
$519$	1.61059	+	11.2019i	0.0706973	+	0.491710i
$520$	0.374529	+	0.240695i	0.0164242	+	0.0105552i
$521$	15.6623	−	4.59886i	0.686176	−	0.201480i	0.0799822	−	0.996796i	$-0.474514\pi$
$521$	15.6623	−	4.59886i	0.686176	−	0.201480i	0.606194	+	0.795317i	$0.292695\pi$
$522$	−3.07925	+	21.4167i	−0.134775	+	0.937382i
$523$	−12.8909	+	14.8769i	−0.563680	+	0.650522i	−0.964015	−	0.265847i	$-0.914348\pi$
$523$	−12.8909	+	14.8769i	−0.563680	+	0.650522i	0.400335	+	0.916369i	$0.368894\pi$
$524$	−6.79399	+	4.36623i	−0.296797	+	0.190740i
$525$	6.30511	+	7.27648i	0.275178	+	0.317572i
$526$	24.8458	+	7.29539i	1.08333	+	0.318094i
$527$	−11.0037	+	24.0947i	−0.479329	+	1.04958i
$528$	0.829622			0.0361047
$529$	−6.23682	−	22.1382i	−0.271166	−	0.962533i
$530$	6.69119			0.290647
$531$	1.27340	−	2.78835i	0.0552607	−	0.121004i
$532$	−21.5817	−	6.33696i	−0.935685	−	0.274742i
$533$	2.94098	+	3.39407i	0.127388	+	0.147014i
$534$	4.29857	−	2.76252i	0.186017	−	0.119546i
$535$	2.28984	−	2.64261i	0.0989983	−	0.114250i
$536$	−0.291600	+	2.02812i	−0.0125952	+	0.0876014i
$537$	0.285780	−	0.0839126i	0.0123323	−	0.00362109i
$538$	10.8396	+	6.96622i	0.467330	+	0.300335i
$539$	−2.35226	−	16.3603i	−0.101319	−	0.704690i
$540$	−1.17966	−	2.58309i	−0.0507644	−	0.111159i
$541$	1.09643	+	2.40084i	0.0471390	+	0.103220i	0.931736	−	0.363136i	$-0.118294\pi$
$541$	1.09643	+	2.40084i	0.0471390	+	0.103220i	−0.884597	+	0.466356i	$0.845567\pi$
$542$	2.29422	+	15.9566i	0.0985450	+	0.685396i
$543$	−1.17732	−	0.756615i	−0.0505235	−	0.0324694i
$544$	3.09047	−	0.907443i	0.132503	−	0.0389063i
$545$	−1.17407	+	8.16586i	−0.0502918	+	0.349787i
$546$	−0.738493	+	0.852267i	−0.0316046	+	0.0364737i
$547$	−13.8142	+	8.87783i	−0.590651	+	0.379589i	−0.801558	−	0.597918i	$-0.795995\pi$
$547$	−13.8142	+	8.87783i	−0.590651	+	0.379589i	0.210906	+	0.977506i	$0.432359\pi$
$548$	0.394755	+	0.455572i	0.0168631	+	0.0194611i
$549$	−37.4904	−	11.0082i	−1.60005	−	0.469817i
$550$	−2.63023	+	5.75941i	−0.112154	+	0.245582i
$551$	−42.5990			−1.81478
$552$	1.58130	−	2.08834i	0.0673047	−	0.0888858i
$553$	−6.86306			−0.291847
$554$	−1.72354	+	3.77402i	−0.0732262	+	0.160343i
$555$	−3.67713	−	1.07970i	−0.156086	−	0.0458309i
$556$	10.2745	+	11.8574i	0.435734	+	0.502864i
$557$	27.4471	−	17.6391i	1.16297	−	0.747395i	0.190789	−	0.981631i	$-0.438895\pi$
$557$	27.4471	−	17.6391i	1.16297	−	0.747395i	0.972180	+	0.234236i	$0.0752590\pi$
$558$	14.5497	−	16.7913i	0.615939	−	0.710831i
$559$	0.311465	−	2.16629i	0.0131736	−	0.0916242i
$560$	−3.69973	+	1.08634i	−0.156342	+	0.0459062i
$561$	−2.24796	−	1.44468i	−0.0949091	−	0.0609944i
$562$	0.739901	+	5.14612i	0.0312108	+	0.217076i
$563$	−9.24940	−	20.2534i	−0.389816	−	0.853577i	−0.998202	−	0.0599365i	$-0.980910\pi$
$563$	−9.24940	−	20.2534i	−0.389816	−	0.853577i	0.608386	−	0.793641i	$-0.291817\pi$
$564$	−0.0619746	−	0.135706i	−0.00260960	−	0.00571423i
$565$	1.45783	+	10.1394i	0.0613312	+	0.426568i
$566$	−11.7089	−	7.52487i	−0.492163	−	0.316294i
$567$	−25.9836	+	7.62949i	−1.09121	+	0.320408i
$568$	−1.50989	+	10.5015i	−0.0633537	+	0.440635i
$569$	8.55133	−	9.86876i	0.358490	−	0.413720i	−0.547643	−	0.836712i	$-0.684475\pi$
$569$	8.55133	−	9.86876i	0.358490	−	0.413720i	0.906133	+	0.422992i	$0.139020\pi$
$570$	2.22862	−	1.43225i	0.0933465	−	0.0599902i
$571$	−26.3070	−	30.3599i	−1.10092	−	1.27052i	−0.959847	−	0.280525i	$-0.909492\pi$
$571$	−26.3070	−	30.3599i	−1.10092	−	1.27052i	−0.141069	−	0.990000i	$-0.545054\pi$
$572$	−0.711554	−	0.208931i	−0.0297516	−	0.00873585i
$573$	−0.884732	+	1.93729i	−0.0369602	+	0.0809316i
$574$	−38.8967			−1.62352
$575$	9.48436	+	17.5986i	0.395525	+	0.733914i
$576$	−2.70167			−0.112569
$577$	−9.65310	+	21.1373i	−0.401864	+	0.879959i	0.595214	+	0.803567i	$0.297067\pi$
$577$	−9.65310	+	21.1373i	−0.401864	+	0.879959i	−0.997078	+	0.0763918i	$0.975660\pi$
$578$	6.35719	+	1.86664i	0.264424	+	0.0776420i
$579$	4.76437	+	5.49838i	0.198001	+	0.228505i
$580$	−6.14343	+	3.94814i	−0.255092	+	0.163938i
$581$	33.1788	−	38.2904i	1.37649	−	1.58855i
$582$	0.354698	−	2.46698i	0.0147027	−	0.102260i
$583$	−10.6943	+	3.14013i	−0.442913	+	0.130051i
$584$	0.540507	+	0.347363i	0.0223663	+	0.0143740i
$585$	0.171175	+	1.19055i	0.00707722	+	0.0492231i
$586$	10.7334	+	23.5028i	0.443391	+	0.970890i
$587$	3.17611	+	6.95471i	0.131092	+	0.287051i	0.963784	−	0.266686i	$-0.0859285\pi$
$587$	3.17611	+	6.95471i	0.131092	+	0.287051i	−0.832692	+	0.553737i	$0.813201\pi$
$588$	−0.845882	−	5.88324i	−0.0348836	−	0.242621i
$589$	36.7991	+	23.6494i	1.51628	+	0.974455i
$590$	0.992686	−	0.291479i	0.0408682	−	0.0120000i
$591$	−1.29740	+	9.02362i	−0.0533679	+	0.371182i
$592$	−5.03899	+	5.81531i	−0.207101	+	0.239008i
$593$	−25.5201	+	16.4007i	−1.04798	+	0.673498i	−0.946949	−	0.321385i	$-0.895852\pi$
$593$	−25.5201	+	16.4007i	−1.04798	+	0.673498i	−0.101035	+	0.994883i	$0.532215\pi$
$594$	3.09764	+	3.57487i	0.127098	+	0.146679i
$595$	11.9166	+	3.49903i	0.488533	+	0.143446i
$596$	−1.68160	+	3.68220i	−0.0688812	+	0.150829i
$597$	−1.62831			−0.0666422
$598$	−1.88219	+	1.39291i	−0.0769684	+	0.0569602i
$599$	4.69418			0.191799			0.0958995	−	0.995391i	$-0.469427\pi$
$599$	4.69418			0.191799			0.0958995	+	0.995391i	$0.469427\pi$
$600$	−0.945841	+	2.07110i	−0.0386138	+	0.0845524i
$601$	−37.4716	−	11.0026i	−1.52850	−	0.448807i	−0.593907	−	0.804533i	$-0.702415\pi$
$601$	−37.4716	−	11.0026i	−1.52850	−	0.448807i	−0.934590	+	0.355726i	$0.884234\pi$
$602$	12.4130	+	14.3254i	0.505917	+	0.583859i
$603$	−4.65688	+	2.99280i	−0.189643	+	0.121876i
$604$	0.0474934	−	0.0548104i	0.00193248	−	0.00223020i
$605$	1.12808	−	7.84594i	0.0458628	−	0.318983i
$606$	0.494392	−	0.145166i	0.0200833	−	0.00589698i
$607$	39.3317	+	25.2769i	1.59642	+	1.02596i	0.968929	+	0.247338i	$0.0795558\pi$
$607$	39.3317	+	25.2769i	1.59642	+	1.02596i	0.627494	+	0.778621i	$0.284081\pi$
$608$	−0.756983	−	5.26493i	−0.0306997	−	0.213521i
$609$	−7.68431	−	16.8263i	−0.311384	−	0.681836i
$610$	−5.47835	−	11.9959i	−0.221812	−	0.485700i
$611$	0.0189788	+	0.132000i	0.000767799	+	0.00534016i
$612$	7.32050	+	4.70460i	0.295914	+	0.190172i
$613$	21.3373	−	6.26519i	0.861804	−	0.253049i	0.179178	−	0.983817i	$-0.442656\pi$
$613$	21.3373	−	6.26519i	0.861804	−	0.253049i	0.682626	+	0.730768i	$0.260838\pi$
$614$	4.69682	−	32.6671i	0.189548	−	1.31834i
$615$	3.00004	−	3.46223i	0.120973	−	0.139611i
$616$	5.40335	−	3.47252i	0.217707	−	0.139912i
$617$	−16.6962	−	19.2685i	−0.672165	−	0.775719i	0.312549	−	0.949902i	$-0.398817\pi$
$617$	−16.6962	−	19.2685i	−0.672165	−	0.775719i	−0.984713	+	0.174182i	$0.944272\pi$
$618$	−4.83932	−	1.42095i	−0.194666	−	0.0571591i
$619$	7.07356	−	15.4889i	0.284310	−	0.622553i	−0.712560	−	0.701612i	$-0.752464\pi$
$619$	7.07356	−	15.4889i	0.284310	−	0.622553i	0.996870	+	0.0790587i	$0.0251915\pi$
$620$	7.49885			0.301161
$621$	14.9030	−	0.983567i	0.598037	−	0.0394692i
$622$	14.8559			0.595668
$623$	16.4337	−	35.9848i	0.658402	−	1.44170i
$624$	−0.255877	−	0.0751324i	−0.0102433	−	0.00300770i
$625$	−8.65689	−	9.99058i	−0.346275	−	0.399623i
$626$	5.85184	−	3.76075i	0.233887	−	0.150310i
$627$	−2.88978	+	3.33499i	−0.115407	+	0.133187i
$628$	−0.00512424	+	0.0356399i	−0.000204479	+	0.00142219i
$629$	23.7804	−	6.98255i	0.948186	−	0.278413i
$630$	−8.76368	−	5.63208i	−0.349153	−	0.224387i
$631$	3.24308	+	22.5561i	0.129105	+	0.897945i	0.946692	+	0.322140i	$0.104402\pi$
$631$	3.24308	+	22.5561i	0.129105	+	0.897945i	−0.817587	+	0.575805i	$0.804689\pi$
$632$	−0.674206	−	1.47631i	−0.0268185	−	0.0587243i
$633$	5.57102	+	12.1988i	0.221428	+	0.484860i
$634$	−0.630148	−	4.38278i	−0.0250264	−	0.174062i
$635$	3.44567	+	2.21440i	0.136737	+	0.0878757i
$636$	−3.84571	+	1.12920i	−0.152492	+	0.0447758i
$637$	−0.756129	+	5.25899i	−0.0299589	+	0.208369i
$638$	7.96600	−	9.19326i	0.315377	−	0.363965i
$639$	−24.1132	+	15.4966i	−0.953903	+	0.613036i
$640$	−0.597131	−	0.689126i	−0.0236037	−	0.0272401i
$641$	2.51720	+	0.739116i	0.0994234	+	0.0291933i	0.331066	−	0.943608i	$-0.392592\pi$
$641$	2.51720	+	0.739116i	0.0994234	+	0.0291933i	−0.231642	+	0.972801i	$0.574410\pi$
$642$	−0.870100	+	1.90525i	−0.0343401	+	0.0751943i
$643$	44.5362			1.75634			0.878168	−	0.478352i	$-0.158766\pi$
$643$	44.5362			1.75634			0.878168	+	0.478352i	$0.158766\pi$
$644$	1.55796	−	20.2202i	0.0613920	−	0.796789i
$645$	−2.23251			−0.0879050
$646$	−7.11706	+	15.5842i	−0.280017	+	0.613151i
$647$	35.6308	+	10.4622i	1.40079	+	0.411310i	0.892956	−	0.450144i	$-0.148627\pi$
$647$	35.6308	+	10.4622i	1.40079	+	0.411310i	0.507836	+	0.861454i	$0.330446\pi$
$648$	−4.19372	−	4.83981i	−0.164745	−	0.190126i
$649$	−1.44979	+	0.931723i	−0.0569092	+	0.0365733i
$650$	1.33282	−	1.53815i	0.0522774	−	0.0603314i
$651$	−2.70324	+	18.8014i	−0.105948	+	0.736886i
$652$	15.3544	−	4.50847i	0.601326	−	0.176565i
$653$	−21.8542	−	14.0448i	−0.855221	−	0.549617i	0.0379778	−	0.999279i	$-0.487908\pi$
$653$	−21.8542	−	14.0448i	−0.855221	−	0.549617i	−0.893199	+	0.449661i	$0.851545\pi$
$654$	−0.703277	−	4.89140i	−0.0275003	−	0.191269i
$655$	−3.05915	−	6.69861i	−0.119531	−	0.261736i
$656$	−3.82109	−	8.36702i	−0.149189	−	0.326677i
$657$	0.247034	+	1.71816i	0.00963770	+	0.0670317i
$658$	−0.971660	−	0.624448i	−0.0378792	−	0.0243435i
$659$	8.36443	−	2.45602i	0.325832	−	0.0956728i	−0.114726	−	0.993397i	$-0.536599\pi$
$659$	8.36443	−	2.45602i	0.325832	−	0.0956728i	0.440558	+	0.897724i	$0.354781\pi$
$660$	−0.107659	+	0.748786i	−0.00419063	+	0.0291464i
$661$	−2.00404	+	2.31278i	−0.0779480	+	0.0899568i	−0.793384	−	0.608722i	$-0.791683\pi$
$661$	−2.00404	+	2.31278i	−0.0779480	+	0.0899568i	0.715436	+	0.698678i	$0.246228\pi$
$662$	4.30350	−	2.76569i	0.167260	−	0.107492i
$663$	0.562498	+	0.649157i	0.0218456	+	0.0252112i
$664$	11.4960	+	3.37553i	0.446131	+	0.130996i
$665$	8.52014	−	18.6565i	0.330397	−	0.723468i
$666$	−20.7887			−0.805544
$667$	−7.95786	−	37.5751i	−0.308130	−	1.45491i
$668$	4.59120			0.177639
$669$	−1.34014	+	2.93449i	−0.0518127	+	0.113454i
$670$	−1.79266	−	0.526374i	−0.0692567	−	0.0203356i
$671$	14.3855	+	16.6017i	0.555345	+	0.640902i
$672$	1.94306	−	1.24873i	0.0749552	−	0.0481708i
$673$	−22.7134	+	26.2126i	−0.875536	+	1.01042i	0.124298	+	0.992245i	$0.460332\pi$
$673$	−22.7134	+	26.2126i	−0.875536	+	1.01042i	−0.999835	+	0.0181779i	$0.994213\pi$
$674$	−1.71847	+	11.9522i	−0.0661929	+	0.460382i
$675$	−12.4560	+	3.65742i	−0.479433	+	0.140774i
$676$	−10.7358	−	6.89945i	−0.412914	−	0.265363i
$677$	−2.16688	−	15.0710i	−0.0832801	−	0.579226i	−0.988145	−	0.153526i	$-0.950937\pi$
$677$	−2.16688	−	15.0710i	−0.0832801	−	0.579226i	0.904864	−	0.425700i	$-0.139972\pi$
$678$	−2.54900	−	5.58152i	−0.0978936	−	0.214357i
$679$	−8.01580	−	17.5522i	−0.307618	−	0.673590i
$680$	0.417977	+	2.90710i	0.0160287	+	0.111482i
$681$	−2.48847	−	1.59924i	−0.0953584	−	0.0612831i
$682$	−11.9852	+	3.51916i	−0.458936	+	0.134756i
$683$	−5.32744	+	37.0532i	−0.203849	+	1.41780i	0.588877	+	0.808222i	$0.299570\pi$
$683$	−5.32744	+	37.0532i	−0.203849	+	1.41780i	−0.792726	+	0.609578i	$0.791339\pi$
$684$	9.41058	−	10.8604i	0.359823	−	0.415258i
$685$	−0.462409	+	0.297172i	−0.0176677	+	0.0113544i
$686$	−10.7500	−	12.4062i	−0.410437	−	0.473669i
$687$	−7.70986	−	2.26382i	−0.294150	−	0.0863701i
$688$	−1.86210	+	4.07743i	−0.0709919	+	0.155451i
$689$	3.58279			0.136493
$690$	1.67966	+	1.69823i	0.0639435	+	0.0646504i
$691$	−6.04705			−0.230041			−0.115020	−	0.993363i	$-0.536693\pi$
$691$	−6.04705			−0.230041			−0.115020	+	0.993363i	$0.536693\pi$
$692$	−8.60729	+	18.8473i	−0.327200	+	0.716468i
$693$	16.6498	+	4.88882i	0.632474	+	0.185711i
$694$	−13.1592	−	15.1866i	−0.499518	−	0.576474i
$695$	−12.0353	+	7.73463i	−0.456526	+	0.293391i
$696$	2.86460	−	3.30593i	0.108582	−	0.125311i
$697$	−4.21636	+	29.3254i	−0.159706	+	1.11078i
$698$	−8.55535	+	2.51208i	−0.323825	+	0.0950836i
$699$	−11.7648	−	7.56079i	−0.444986	−	0.285975i
$700$	2.50866	+	17.4481i	0.0948184	+	0.659477i
$701$	12.4636	+	27.2915i	0.470744	+	1.03079i	0.984906	+	0.173093i	$0.0553761\pi$
$701$	12.4636	+	27.2915i	0.470744	+	1.03079i	−0.514161	+	0.857694i	$0.671897\pi$
$702$	−0.631646	−	1.38311i	−0.0238400	−	0.0522022i
$703$	−5.82480	−	40.5124i	−0.219687	−	1.52795i
$704$	1.27778	+	0.821177i	0.0481580	+	0.0309493i
$705$	0.130525	−	0.0383256i	0.00491586	−	0.00144343i
$706$	1.80191	−	12.5325i	0.0678156	−	0.471668i
$707$	2.61237	−	3.01483i	0.0982481	−	0.113384i
$708$	−0.521349	+	0.335051i	−0.0195935	+	0.0125920i
$709$	15.8016	+	18.2361i	0.593443	+	0.684869i	0.970439	−	0.241345i	$-0.0775887\pi$
$709$	15.8016	+	18.2361i	0.593443	+	0.684869i	−0.376997	+	0.926215i	$0.623043\pi$
$710$	−9.28236	−	2.72555i	−0.348361	−	0.102288i
$711$	1.82148	−	3.98848i	0.0683108	−	0.149580i
$712$	9.35503			0.350595
$713$	−13.9859	+	36.8771i	−0.523774	+	1.38106i
$714$	−7.43946			−0.278415
$715$	0.280911	−	0.615110i	0.0105055	−	0.0230038i
$716$	0.523214	+	0.153630i	0.0195534	+	0.00574141i
$717$	−0.725067	−	0.836772i	−0.0270781	−	0.0312498i
$718$	8.24006	−	5.29557i	0.307516	−	0.197629i
$719$	−14.6435	+	16.8995i	−0.546110	+	0.630245i	−0.959972	−	0.280095i	$-0.909634\pi$
$719$	−14.6435	+	16.8995i	−0.546110	+	0.630245i	0.413862	+	0.910340i	$0.364180\pi$
$720$	0.350592	−	2.43842i	0.0130658	−	0.0908746i
$721$	−37.4662	+	11.0011i	−1.39531	+	0.409701i
$722$	7.81740	+	5.02394i	0.290934	+	0.186972i
$723$	−1.44064	−	10.0199i	−0.0535779	−	0.372643i
$724$	−1.06438	−	2.33066i	−0.0395573	−	0.0866185i
$725$	13.8685	+	30.3678i	0.515063	+	1.12783i
$726$	0.675724	+	4.69977i	0.0250785	+	0.174425i
$727$	−8.62131	−	5.54058i	−0.319747	−	0.205489i	0.370915	−	0.928667i	$-0.379044\pi$
$727$	−8.62131	−	5.54058i	−0.319747	−	0.205489i	−0.690661	+	0.723178i	$0.742681\pi$
$728$	−1.98101	+	0.581678i	−0.0734213	+	0.0215584i
$729$	1.73602	−	12.0743i	0.0642969	−	0.447195i
$730$	−0.383658	+	0.442765i	−0.0141998	+	0.0163875i
$731$	12.1459	−	7.80570i	0.449233	−	0.288704i
$732$	5.17306	+	5.97003i	0.191202	+	0.220659i
$733$	−5.50513	−	1.61645i	−0.203337	−	0.0597050i	0.178478	−	0.983944i	$-0.442883\pi$
$733$	−5.50513	−	1.61645i	−0.203337	−	0.0597050i	−0.381815	+	0.924239i	$0.624701\pi$
$734$	4.54070	−	9.94275i	0.167600	−	0.366994i
$735$	5.41976			0.199911
$736$	4.50260	−	1.65124i	0.165968	−	0.0608656i
$737$	3.11218			0.114639
$738$	10.3233	−	22.6049i	0.380006	−	0.832098i
$739$	−16.3476	−	4.80010i	−0.601357	−	0.176574i	−0.0331367	−	0.999451i	$-0.510550\pi$
$739$	−16.3476	−	4.80010i	−0.601357	−	0.176574i	−0.568220	+	0.822876i	$0.692368\pi$
$740$	−4.59478	−	5.30266i	−0.168907	−	0.194930i
$741$	1.19331	−	0.766893i	0.0438373	−	0.0281725i
$742$	−20.3207	+	23.4514i	−0.745997	+	0.860927i
$743$	0.877334	−	6.10199i	0.0321863	−	0.223860i	−0.967379	−	0.253332i	$-0.918473\pi$
$743$	0.877334	−	6.10199i	0.0321863	−	0.223860i	0.999566	+	0.0294718i	$0.00938252\pi$
$744$	−4.30991	+	1.26550i	−0.158009	+	0.0463956i
$745$	−3.10520	−	1.99559i	−0.113766	−	0.0731127i
$746$	−1.28925	−	8.96691i	−0.0472027	−	0.328302i
$747$	13.4468	+	29.4443i	0.491992	+	1.07731i
$748$	−2.03232	−	4.45016i	−0.0743090	−	0.162714i
$749$	2.30777	+	16.0509i	0.0843241	+	0.586487i
$750$	−3.84149	−	2.46878i	−0.140271	−	0.0901469i
$751$	1.66332	−	0.488395i	0.0606955	−	0.0178218i	−0.251244	−	0.967924i	$-0.580840\pi$
$751$	1.66332	−	0.488395i	0.0606955	−	0.0178218i	0.311939	+	0.950102i	$0.399021\pi$
$752$	0.0388714	−	0.270356i	0.00141749	−	0.00985888i
$753$	−8.38989	+	9.68245i	−0.305745	+	0.352848i
$754$	−3.28949	+	2.11403i	−0.119796	+	0.0769883i
$755$	0.0433066	+	0.0499785i	0.00157609	+	0.00181890i
$756$	12.6358	+	3.71021i	0.459560	+	0.134939i
$757$	9.81588	−	21.4938i	0.356764	−	0.781204i	−0.643117	−	0.765768i	$-0.722359\pi$
$757$	9.81588	−	21.4938i	0.356764	−	0.781204i	0.999881	−	0.0154362i	$-0.00491370\pi$
$758$	16.2693			0.590929
$759$	−3.48151	−	1.92597i	−0.126371	−	0.0699083i
$760$	4.85017			0.175934
$761$	1.02392	−	2.24208i	0.0371172	−	0.0812752i	−0.890165	−	0.455638i	$-0.849411\pi$
$761$	1.02392	−	2.24208i	0.0371172	−	0.0812752i	0.927282	+	0.374363i	$0.122138\pi$
$762$	−2.35407	−	0.691218i	−0.0852791	−	0.0250402i
$763$	−25.0542	−	28.9141i	−0.907024	−	1.04676i
$764$	−3.28023	+	2.10808i	−0.118675	+	0.0762675i
$765$	−5.19617	+	5.99670i	−0.187868	+	0.216811i
$766$	−4.15851	+	28.9231i	−0.150253	+	1.04503i
$767$	0.531532	−	0.156072i	0.0191925	−	0.00563543i
$768$	0.459493	+	0.295298i	0.0165805	+	0.0106557i
$769$	2.83570	+	19.7227i	0.102258	+	0.711220i	0.974865	+	0.222797i	$0.0715186\pi$
$769$	2.83570	+	19.7227i	0.102258	+	0.711220i	−0.872607	+	0.488423i	$0.837572\pi$
$770$	2.43298	+	5.32748i	0.0876785	+	0.191989i
$771$	2.35732	+	5.16180i	0.0848967	+	0.185898i
$772$	1.89564	+	13.1844i	0.0682254	+	0.474518i
$773$	−12.1822	−	7.82904i	−0.438164	−	0.281591i	0.302904	−	0.953021i	$-0.402044\pi$
$773$	−12.1822	−	7.82904i	−0.438164	−	0.281591i	−0.741068	+	0.671430i	$0.765680\pi$
$774$	−11.6197	+	3.41185i	−0.417661	+	0.122636i
$775$	4.87875	−	33.9324i	0.175250	−	1.21889i
$776$	2.98818	−	3.44854i	0.107269	−	0.123795i
$777$	14.9514	−	9.60867i	0.536378	−	0.344709i
$778$	17.8858	+	20.6413i	0.641238	+	0.740028i
$779$	46.9443	+	13.7841i	1.68196	+	0.493867i
$780$	0.101017	−	0.221196i	0.00361698	−	0.00792007i
$781$	16.1148			0.576632
$782$	−15.0758	−	3.36644i	−0.539109	−	0.120384i
$783$	24.9412			0.891325
$784$	4.52053	−	9.89858i	0.161448	−	0.353521i
$785$	−0.0315022	−	0.00924989i	−0.00112436	−	0.000330143i
$786$	2.88868	+	3.33371i	0.103036	+	0.118910i
$787$	26.6603	−	17.1336i	0.950338	−	0.610745i	0.0290302	−	0.999579i	$-0.490758\pi$
$787$	26.6603	−	17.1336i	0.950338	−	0.610745i	0.921308	+	0.388833i	$0.127122\pi$
$788$	−10.9300	+	12.6139i	−0.389366	+	0.449352i
$789$	2.01286	−	13.9997i	0.0716597	−	0.498404i
$790$	1.41995	−	0.416935i	0.0505195	−	0.0148339i
$791$	−39.9640	−	25.6833i	−1.42096	−	0.913194i
$792$	0.583996	+	4.06178i	0.0207514	+	0.144329i
$793$	−2.93337	−	6.42319i	−0.104167	−	0.228094i
$794$	5.02934	+	11.0127i	0.178485	+	0.390827i
$795$	−0.520122	−	3.61753i	−0.0184468	−	0.128301i
$796$	−2.50791	−	1.61173i	−0.0888903	−	0.0571264i
$797$	−46.4770	+	13.6469i	−1.64630	+	0.483398i	−0.967909	−	0.251302i	$-0.919141\pi$
$797$	−46.4770	+	13.6469i	−1.64630	+	0.483398i	−0.678393	+	0.734700i	$0.737323\pi$
$798$	−1.74842	+	12.1605i	−0.0618934	+	0.430478i
$799$	−0.576117	+	0.664875i	−0.0203816	+	0.0235216i
$800$	−3.50680	+	2.25368i	−0.123984	+	0.0796797i
$801$	16.5511	+	19.1009i	0.584803	+	0.674898i
$802$	1.29575	+	0.380466i	0.0457545	+	0.0134347i
$803$	0.405401	−	0.887704i	0.0143063	−	0.0313264i
$804$	1.11915			0.0394694
$805$	18.0479	+	4.03011i	0.636103	+	0.142043i
$806$	4.01525			0.141431
$807$	2.92363	−	6.40185i	0.102917	−	0.225356i
$808$	0.905147	+	0.265775i	0.0318430	+	0.00934994i
$809$	−16.6402	−	19.2039i	−0.585040	−	0.675172i	0.383641	−	0.923483i	$-0.374670\pi$
$809$	−16.6402	−	19.2039i	−0.585040	−	0.675172i	−0.968681	+	0.248310i	$0.920125\pi$
$810$	4.91245	−	3.15704i	0.172606	−	0.110927i
$811$	18.9473	−	21.8663i	0.665329	−	0.767830i	−0.318309	−	0.947987i	$-0.603115\pi$
$811$	18.9473	−	21.8663i	0.665329	−	0.767830i	0.983638	+	0.180157i	$0.0576605\pi$
$812$	4.81971	−	33.5218i	0.169139	−	1.17639i
$813$	8.44847	−	2.48069i	0.296301	−	0.0870017i
$814$	9.83219	+	6.31876i	0.344618	+	0.221472i
$815$	2.07665	+	14.4434i	0.0727417	+	0.505930i
$816$	−0.730830	−	1.60029i	−0.0255842	−	0.0560215i
$817$	−9.90465	−	21.6882i	−0.346520	−	0.758773i
$818$	−1.37658	−	9.57431i	−0.0481309	−	0.334758i
$819$	−4.69250	−	3.01569i	−0.163969	−	0.105377i
$820$	8.04762	−	2.36300i	0.281035	−	0.0825194i
$821$	4.14106	−	28.8017i	0.144524	−	1.00519i	−0.780467	−	0.625197i	$-0.785019\pi$
$821$	4.14106	−	28.8017i	0.144524	−	1.00519i	0.924991	−	0.379989i	$-0.124072\pi$
$822$	0.215615	−	0.248833i	0.00752045	−	0.00867906i
$823$	11.7641	−	7.56035i	0.410072	−	0.263537i	−0.319301	−	0.947653i	$-0.603448\pi$
$823$	11.7641	−	7.56035i	0.410072	−	0.263537i	0.729373	+	0.684116i	$0.239812\pi$
$824$	−6.04699	−	6.97860i	−0.210657	−	0.243111i
$825$	3.31823	+	0.974319i	0.115526	+	0.0339214i
$826$	−1.99315	+	4.36438i	−0.0693505	+	0.151856i
$827$	−36.4585			−1.26779			−0.633894	−	0.773420i	$-0.718544\pi$
$827$	−36.4585			−1.26779			−0.633894	+	0.773420i	$0.718544\pi$
$828$	11.3375	+	6.27192i	0.394007	+	0.217964i
$829$	−19.6791			−0.683482			−0.341741	−	0.939794i	$-0.611017\pi$
$829$	−19.6791			−0.683482			−0.341741	+	0.939794i	$0.611017\pi$
$830$	−4.53845	+	9.93781i	−0.157532	+	0.344946i
$831$	2.17437	+	0.638452i	0.0754279	+	0.0221476i
$832$	−0.319733	−	0.368991i	−0.0110847	−	0.0127925i
$833$	−29.4860	+	18.9495i	−1.02163	+	0.656562i
$834$	5.61191	−	6.47649i	0.194325	−	0.224263i
$835$	−0.595795	+	4.14385i	−0.0206183	+	0.143404i
$836$	−7.75186	+	2.27615i	−0.268104	+	0.0787224i
$837$	−21.5454	−	13.8464i	−0.744718	−	0.478602i
$838$	−3.65852	−	25.4456i	−0.126382	−	0.879004i
$839$	−15.3408	−	33.5917i	−0.529624	−	1.15971i	−0.965666	−	0.259788i	$-0.916347\pi$
$839$	−15.3408	−	33.5917i	−0.529624	−	1.15971i	0.436042	−	0.899926i	$-0.356380\pi$
$840$	0.874908	+	1.91578i	0.0301872	+	0.0661007i
$841$	−5.00090	−	34.7820i	−0.172445	−	1.19938i
$842$	13.3403	+	8.57330i	0.459738	+	0.295456i
$843$	2.72469	−	0.800041i	0.0938433	−	0.0275549i
$844$	−3.49422	+	24.3029i	−0.120276	+	0.836539i
$845$	7.62036	−	8.79436i	0.262148	−	0.302535i
$846$	0.620781	−	0.398952i	0.0213429	−	0.0137162i
$847$	24.0727	+	27.7813i	0.827146	+	0.954577i
$848$	−7.04084	−	2.06738i	−0.241783	−	0.0709940i
$849$	−3.15809	+	6.91525i	−0.108385	+	0.237331i
$850$	13.4266			0.460529
$851$	34.6464	−	12.7059i	1.18766	−	0.435553i
$852$	5.79493			0.198531
$853$	−0.861454	+	1.88632i	−0.0294956	+	0.0645864i	−0.923806	−	0.382860i	$-0.874939\pi$
$853$	−0.861454	+	1.88632i	−0.0294956	+	0.0645864i	0.894311	+	0.447446i	$0.147666\pi$
$854$	58.6808	+	17.2302i	2.00802	+	0.589607i
$855$	8.58099	+	9.90299i	0.293464	+	0.338675i
$856$	−3.22598	+	2.07321i	−0.110262	+	0.0708609i
$857$	−0.262276	+	0.302682i	−0.00895916	+	0.0103394i	−0.760211	−	0.649676i	$-0.774905\pi$
$857$	−0.262276	+	0.302682i	−0.00895916	+	0.0103394i	0.751252	+	0.660015i	$0.229450\pi$
$858$	−0.0576459	+	0.400936i	−0.00196800	+	0.0136877i
$859$	38.8368	−	11.4035i	1.32509	−	0.389083i	0.458765	−	0.888557i	$-0.348292\pi$
$859$	38.8368	−	11.4035i	1.32509	−	0.389083i	0.866328	+	0.499475i	$0.166474\pi$
$860$	−3.43850	−	2.20979i	−0.117252	−	0.0753531i
$861$	3.02354	+	21.0292i	0.103042	+	0.716672i
$862$	−15.9054	−	34.8279i	−0.541739	−	1.18624i
$863$	1.77473	+	3.88613i	0.0604127	+	0.132285i	0.937430	−	0.348173i	$-0.113198\pi$
$863$	1.77473	+	3.88613i	0.0604127	+	0.132285i	−0.877018	+	0.480458i	$0.840470\pi$
$864$	0.443204	+	3.08255i	0.0150781	+	0.104871i
$865$	−15.8939	−	10.2144i	−0.540410	−	0.347301i
$866$	−11.6153	+	3.41055i	−0.394702	+	0.115895i
$867$	0.515022	−	3.58205i	0.0174911	−	0.121653i
$868$	−22.7736	+	26.2821i	−0.772985	+	0.892072i
$869$	−2.07379	+	1.33275i	−0.0703486	+	0.0452103i
$870$	2.61207	+	3.01449i	0.0885575	+	0.102201i
$871$	−0.959879	−	0.281846i	−0.0325243	−	0.00954999i
$872$	3.75843	−	8.22982i	0.127277	−	0.278697i
$873$	12.3279			0.417236
$874$	−9.04588	+	23.8516i	−0.305981	+	0.806794i
$875$	−35.3532			−1.19516
$876$	0.145784	−	0.319222i	0.00492557	−	0.0107855i
$877$	32.9543	+	9.67625i	1.11279	+	0.326744i	0.785921	−	0.618327i	$-0.212189\pi$
$877$	32.9543	+	9.67625i	1.11279	+	0.326744i	0.326866	+	0.945071i	$0.394007\pi$
$878$	−15.1889	−	17.5289i	−0.512600	−	0.591571i
$879$	11.8722	−	7.62982i	0.400440	−	0.257347i
$880$	−0.906980	+	1.04671i	−0.0305743	+	0.0352846i
$881$	−4.50512	+	31.3338i	−0.151781	+	1.05566i	0.761450	+	0.648223i	$0.224488\pi$
$881$	−4.50512	+	31.3338i	−0.151781	+	1.05566i	−0.913232	+	0.407440i	$0.866421\pi$
$882$	28.2085	−	8.28278i	0.949831	−	0.278896i
$883$	26.9690	+	17.3319i	0.907578	+	0.583265i	0.909028	−	0.416734i	$-0.136825\pi$
$883$	26.9690	+	17.3319i	0.907578	+	0.583265i	−0.00145064	+	0.999999i	$0.500462\pi$
$884$	0.223805	+	1.55660i	0.00752739	+	0.0523541i
$885$	−0.234749	−	0.514029i	−0.00789101	−	0.0172789i
$886$	3.87323	+	8.48118i	0.130124	+	0.284931i
$887$	−0.175049	−	1.21749i	−0.00587757	−	0.0408794i	0.986672	−	0.162724i	$-0.0520281\pi$
$887$	−0.175049	−	1.21749i	−0.00587757	−	0.0408794i	−0.992549	+	0.121845i	$0.961119\pi$
$888$	3.53569	+	2.27225i	0.118650	+	0.0762517i
$889$	−18.2253	+	5.35144i	−0.611258	+	0.179482i
$890$	−1.21399	+	8.44350i	−0.0406931	+	0.283027i
$891$	−6.36983	+	7.35118i	−0.213397	+	0.246274i
$892$	−4.96869	+	3.19318i	−0.166364	+	0.106916i
$893$	0.951404	+	1.09798i	0.0318375	+	0.0367424i
$894$	2.12146	+	0.622918i	0.0709523	+	0.0208335i
$895$	−0.206557	+	0.452298i	−0.00690445	+	0.0151186i
$896$	4.22871			0.141271
$897$	0.899370	+	0.909313i	0.0300291	+	0.0303611i
$898$	−41.6869			−1.39111
$899$	−27.3602	+	59.9106i	−0.912515	+	1.99813i
$900$	−10.8058	−	3.17287i	−0.360194	−	0.105762i
$901$	15.4780	+	17.8625i	0.515646	+	0.595087i
$902$	−11.7533	+	7.55340i	−0.391343	+	0.251501i
$903$	6.78000	−	7.82453i	0.225624	−	0.260384i
$904$	1.59877	−	11.1197i	0.0531742	−	0.369835i
$905$	2.24169	−	0.658221i	0.0745164	−	0.0218800i
$906$	−0.0333245	−	0.0214164i	−0.00110713	−	0.000711511i
$907$	−4.30921	−	29.9712i	−0.143085	−	0.995178i	−0.927201	−	0.374564i	$-0.877792\pi$
$907$	−4.30921	−	29.9712i	−0.143085	−	0.995178i	0.784116	−	0.620614i	$-0.213117\pi$
$908$	−2.24976	−	4.92628i	−0.0746608	−	0.163484i
$909$	1.05874	+	2.31833i	0.0351163	+	0.0768940i
$910$	−0.267927	−	1.86347i	−0.00888169	−	0.0617735i
$911$	−41.7100	−	26.8054i	−1.38192	−	0.888103i	−0.382557	−	0.923932i	$-0.624957\pi$
$911$	−41.7100	−	26.8054i	−1.38192	−	0.888103i	−0.999358	+	0.0358289i	$0.988593\pi$
$912$	−2.78760	+	0.818512i	−0.0923065	+	0.0271036i
$913$	2.58990	−	18.0131i	0.0857131	−	0.596148i
$914$	−17.8402	+	20.5887i	−0.590103	+	0.681015i
$915$	−6.05963	+	3.89429i	−0.200325	+	0.128741i
$916$	−9.63389	−	11.1181i	−0.318313	−	0.367353i
$917$	32.7678	+	9.62150i	1.08209	+	0.317730i
$918$	4.16695	−	9.12434i	0.137530	−	0.301148i
$919$	−30.4532			−1.00456			−0.502279	−	0.864705i	$-0.667505\pi$
$919$	−30.4532			−1.00456			−0.502279	+	0.864705i	$0.667505\pi$
$920$	0.906053	+	4.27816i	0.0298717	+	0.141047i
$921$	−18.0263			−0.593986
$922$	12.0836	−	26.4595i	0.397953	−	0.871396i
$923$	−4.97023	−	1.45939i	−0.163597	−	0.0480364i
$924$	−2.29740	−	2.65134i	−0.0755789	−	0.0872227i
$925$	−26.9840	+	17.3415i	−0.887228	+	0.570187i
$926$	−1.36436	+	1.57455i	−0.0448355	+	0.0517430i
$927$	3.55036	−	24.6933i	0.116609	−	0.811034i
$928$	7.68431	−	2.25632i	0.252250	−	0.0740673i
$929$	48.6422	+	31.2604i	1.59590	+	1.02562i	0.969173	+	0.246382i	$0.0792419\pi$
$929$	48.6422	+	31.2604i	1.59590	+	1.02562i	0.626726	+	0.779240i	$0.284394\pi$
$930$	−0.582904	−	4.05419i	−0.0191142	−	0.132942i
$931$	24.0451	+	52.6513i	0.788045	+	1.72558i
$932$	−10.6363	−	23.2901i	−0.348402	−	0.762894i
$933$	−1.15479	−	8.03172i	−0.0378060	−	0.262947i
$934$	22.3917	+	14.3902i	0.732678	+	0.470863i
$935$	4.28028	−	1.25681i	0.139980	−	0.0411019i
$936$	0.187724	−	1.30565i	0.00613595	−	0.0426765i
$937$	−29.9525	+	34.5670i	−0.978505	+	1.12926i	0.0130948	+	0.999914i	$0.495832\pi$
$937$	−29.9525	+	34.5670i	−0.978505	+	1.12926i	−0.991600	+	0.129341i	$0.958714\pi$
$938$	7.28906	−	4.68439i	0.237996	−	0.152951i
$939$	−2.48809	−	2.87141i	−0.0811958	−	0.0937049i
$940$	0.238969	+	0.0701677i	0.00779432	+	0.00228862i
$941$	−13.1150	+	28.7179i	−0.427538	+	0.936178i	0.566182	+	0.824280i	$0.308420\pi$
$941$	−13.1150	+	28.7179i	−0.427538	+	0.936178i	−0.993720	+	0.111897i	$0.964307\pi$
$942$	0.0196667			0.000640775
$943$	−3.38885	+	43.9829i	−0.110356	+	1.43228i
$944$	−1.13462			−0.0369287
$945$	−4.98843	+	10.9231i	−0.162274	+	0.355330i
$946$	6.53267	+	1.91817i	0.212396	+	0.0623650i
$947$	−19.0440	−	21.9780i	−0.618848	−	0.714188i	0.356640	−	0.934242i	$-0.383922\pi$
$947$	−19.0440	−	21.9780i	−0.618848	−	0.714188i	−0.975488	+	0.220054i	$0.929377\pi$
$948$	−0.745743	+	0.479260i	−0.0242206	+	0.0155656i
$949$	−0.205429	+	0.237078i	−0.00666850	+	0.00769586i
$950$	3.15552	−	21.9471i	0.102378	−	0.712058i
$951$	−2.32053	+	0.681368i	−0.0752482	+	0.0220949i
$952$	−11.4582	−	7.36374i	−0.371363	−	0.238660i
$953$	2.79626	+	19.4484i	0.0905797	+	0.629996i	0.983652	+	0.180082i	$0.0576363\pi$
$953$	2.79626	+	19.4484i	0.0905797	+	0.629996i	−0.893072	+	0.449914i	$0.851455\pi$
$954$	−8.23562	−	18.0335i	−0.266638	−	0.583856i
$955$	−1.47700	−	3.23418i	−0.0477946	−	0.104656i
$956$	−0.288488	−	2.00648i	−0.00933036	−	0.0648941i
$957$	−5.58947	−	3.59213i	−0.180682	−	0.116117i
$958$	−4.37504	+	1.28463i	−0.141351	+	0.0415044i
$959$	0.362774	−	2.52315i	0.0117146	−	0.0814768i
$960$	−0.326153	+	0.376401i	−0.0105265	+	0.0121483i
$961$	30.8163	−	19.8044i	0.994075	−	0.638853i
$962$	−2.46027	−	2.83930i	−0.0793221	−	0.0915426i
$963$	−9.94050	−	2.91879i	−0.320328	−	0.0940568i
$964$	7.69901	−	16.8585i	0.247968	−	0.542975i
$965$	−12.1458			−0.390986
$966$	−11.0530	+	0.729474i	−0.355624	+	0.0234704i
$967$	26.2117			0.842911			0.421455	−	0.906849i	$-0.361519\pi$
$967$	26.2117			0.842911			0.421455	+	0.906849i	$0.361519\pi$
$968$	−3.61118	+	7.90739i	−0.116068	+	0.254153i
$969$	8.97867	+	2.63638i	0.288436	+	0.0846926i
$970$	2.72475	+	3.14453i	0.0874865	+	0.100965i
$971$	−49.8758	+	32.0532i	−1.60059	+	1.02864i	−0.633656	+	0.773615i	$0.718447\pi$
$971$	−49.8758	+	32.0532i	−1.60059	+	1.02864i	−0.966935	+	0.255023i	$0.917917\pi$
$972$	−8.40882	+	9.70429i	−0.269713	+	0.311265i
$973$	9.44208	−	65.6711i	0.302699	−	2.10532i
$974$	11.2979	−	3.31735i	0.362007	−	0.106295i
$975$	−0.935192	−	0.601012i	−0.0299501	−	0.0192478i
$976$	2.05824	+	14.3154i	0.0658828	+	0.458225i
$977$	−12.0987	−	26.4926i	−0.387073	−	0.847572i	−0.998419	−	0.0562085i	$-0.982099\pi$
$977$	−12.0987	−	26.4926i	−0.387073	−	0.847572i	0.611346	−	0.791363i	$-0.290628\pi$
$978$	−3.63100	−	7.95077i	−0.116106	−	0.254238i
$979$	−2.02220	−	14.0647i	−0.0646297	−	0.449510i
$980$	8.34747	+	5.36459i	0.266650	+	0.171366i
$981$	23.4530	−	6.88641i	0.748796	−	0.219866i
$982$	−1.21644	+	8.46053i	−0.0388182	+	0.269986i
$983$	−1.37496	+	1.58678i	−0.0438543	+	0.0506105i	−0.777253	−	0.629188i	$-0.783387\pi$
$983$	−1.37496	+	1.58678i	−0.0438543	+	0.0506105i	0.733399	+	0.679799i	$0.237933\pi$
$984$	−4.22653	+	2.71623i	−0.134737	+	0.0865902i
$985$	−9.96647	−	11.5019i	−0.317558	−	0.366482i
$986$	−24.7507	−	7.26746i	−0.788222	−	0.231443i
$987$	−0.262073	+	0.573859i	−0.00834186	+	0.0182661i
$988$	2.59701			0.0826220
$989$	17.2801	−	12.7881i	0.549474	−	0.406637i
$990$	−3.74180			−0.118922
$991$	−17.3984	+	38.0972i	−0.552679	+	1.21020i	0.402841	+	0.915270i	$0.368023\pi$
$991$	−17.3984	+	38.0972i	−0.552679	+	1.21020i	−0.955520	+	0.294928i	$0.904704\pi$
$992$	−7.89071	−	2.31692i	−0.250530	−	0.0735623i
$993$	−1.82977	−	2.11166i	−0.0580659	−	0.0670117i
$994$	37.7425	−	24.2556i	1.19712	−	0.769342i
$995$	1.78014	−	2.05439i	0.0564342	−	0.0651285i
$996$	0.931336	−	6.47759i	0.0295105	−	0.205250i
$997$	5.06282	−	1.48658i	0.160341	−	0.0470804i	−0.200577	−	0.979678i	$-0.564282\pi$
$997$	5.06282	−	1.48658i	0.160341	−	0.0470804i	0.360918	+	0.932598i	$0.382463\pi$
$998$	10.1582	+	6.52829i	0.321553	+	0.206650i
$999$	3.41035	+	23.7195i	0.107899	+	0.750452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.2.c.a.29.1	yes	10
3.2	odd	2		414.2.i.f.397.1		10
4.3	odd	2		368.2.m.b.305.1		10
23.2	even	11		1058.2.a.m.1.4		5
23.4	even	11	inner	46.2.c.a.27.1	✓	10
23.21	odd	22		1058.2.a.l.1.4		5
69.2	odd	22		9522.2.a.bp.1.4		5
69.44	even	22		9522.2.a.bu.1.2		5
69.50	odd	22		414.2.i.f.73.1		10
92.27	odd	22		368.2.m.b.257.1		10
92.67	even	22		8464.2.a.bw.1.2		5
92.71	odd	22		8464.2.a.bx.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.a.27.1	✓	10	23.4	even	11	inner
46.2.c.a.29.1	yes	10	1.1	even	1	trivial
368.2.m.b.257.1		10	92.27	odd	22
368.2.m.b.305.1		10	4.3	odd	2
414.2.i.f.73.1		10	69.50	odd	22
414.2.i.f.397.1		10	3.2	odd	2
1058.2.a.l.1.4		5	23.21	odd	22
1058.2.a.m.1.4		5	23.2	even	11
8464.2.a.bw.1.2		5	92.67	even	22
8464.2.a.bx.1.2		5	92.71	odd	22
9522.2.a.bp.1.4		5	69.2	odd	22
9522.2.a.bu.1.2		5	69.44	even	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	46.c (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.524075 - 0.153882i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.767092 - 0.492980i) q^{5} +(-0.357685 + 0.412791i) q^{6} +(-0.601808 + 4.18567i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-2.27279 - 1.46063i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.524075 - 0.153882i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.767092 - 0.492980i) q^{5} +(-0.357685 + 0.412791i) q^{6} +(-0.601808 + 4.18567i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-2.27279 - 1.46063i) q^{9} +(-0.129769 - 0.902563i) q^{10} +(0.630972 + 1.38164i) q^{11} +(0.226900 + 0.496841i) q^{12} +(-0.0694846 - 0.483276i) q^{13} +(3.55742 + 2.28621i) q^{14} +(-0.477875 + 0.140317i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(2.10926 - 2.43422i) q^{17} +(-2.27279 + 1.46063i) q^{18} +(-3.48325 - 4.01989i) q^{19} +(-0.874908 - 0.256896i) q^{20} +(0.959493 - 2.10100i) q^{21} +1.51890 q^{22} +(2.89510 - 3.82340i) q^{23} +0.546200 q^{24} +(-1.73167 + 3.79184i) q^{25} +(-0.468468 - 0.137555i) q^{26} +(2.03940 + 2.35359i) q^{27} +(3.55742 - 2.28621i) q^{28} +(5.24460 - 6.05259i) q^{29} +(-0.0708798 + 0.492980i) q^{30} +(-7.89071 + 2.31692i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-0.118067 - 0.821177i) q^{33} +(-1.33803 - 2.92987i) q^{34} +(1.60181 + 3.50747i) q^{35} +(0.384487 + 2.67417i) q^{36} +(6.47324 + 4.16010i) q^{37} +(-5.10362 + 1.49856i) q^{38} +(-0.0379525 + 0.263965i) q^{39} +(-0.597131 + 0.689126i) q^{40} +(-7.73806 + 4.97295i) q^{41} +(-1.51255 - 1.74557i) q^{42} +(4.30093 + 1.26287i) q^{43} +(0.630972 - 1.38164i) q^{44} -2.46350 q^{45} +(-2.27522 - 4.22177i) q^{46} -0.273137 q^{47} +(0.226900 - 0.496841i) q^{48} +(-10.4412 - 3.06580i) q^{49} +(2.72981 + 3.15037i) q^{50} +(-1.48000 + 0.951137i) q^{51} +(-0.319733 + 0.368991i) q^{52} +(-1.04432 + 7.26339i) q^{53} +(2.98810 - 0.877386i) q^{54} +(1.16513 + 0.748786i) q^{55} +(-0.601808 - 4.18567i) q^{56} +(1.20690 + 2.64274i) q^{57} +(-3.32694 - 7.28499i) q^{58} +(0.161473 + 1.12307i) q^{59} +(0.418986 + 0.269266i) q^{60} +(13.8768 - 4.07459i) q^{61} +(-1.17037 + 8.14013i) q^{62} +(7.48149 - 8.63410i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.291546 - 0.336462i) q^{65} +(-0.796016 - 0.233731i) q^{66} +(0.851175 - 1.86381i) q^{67} -3.22094 q^{68} +(-2.10560 + 1.55825i) q^{69} +3.85592 q^{70} +(4.40736 - 9.65077i) q^{71} +(2.59223 + 0.761147i) q^{72} +(-0.420749 - 0.485571i) q^{73} +(6.47324 - 4.16010i) q^{74} +(1.49103 - 1.72073i) q^{75} +(-0.756983 + 5.26493i) q^{76} +(-6.16279 + 1.80956i) q^{77} +(0.224345 + 0.144178i) q^{78} +(0.230973 + 1.60645i) q^{79} +(0.378794 + 0.829443i) q^{80} +(2.66031 + 5.82527i) q^{81} +(1.30905 + 9.10463i) q^{82} +(-10.0793 - 6.47759i) q^{83} +(-2.21616 + 0.650724i) q^{84} +(0.417977 - 2.90710i) q^{85} +(2.93542 - 3.38765i) q^{86} +(-3.67995 + 2.36496i) q^{87} +(-0.994666 - 1.14791i) q^{88} +(-8.97609 - 2.63562i) q^{89} +(-1.02337 + 2.24088i) q^{90} +2.06465 q^{91} +(-4.78542 + 0.315828i) q^{92} +4.49186 q^{93} +(-0.113465 + 0.248454i) q^{94} +(-4.65370 - 1.36645i) q^{95} +(-0.357685 - 0.412791i) q^{96} +(-3.83870 + 2.46698i) q^{97} +(-7.12617 + 8.22404i) q^{98} +(0.583996 - 4.06178i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9}+O(q^{10}) \) 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9	\( 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9} - 6 q^{10} - 12 q^{11} + 7 q^{12} - 14 q^{13} + 3 q^{14} - 13 q^{15} - q^{16} + 15 q^{17} + 9 q^{18} + 2 q^{19} + 5 q^{20} + q^{21} + 10 q^{22} - q^{23} - 4 q^{24} + 13 q^{25} - 3 q^{26} + 26 q^{27} + 3 q^{28} - 8 q^{29} + 20 q^{30} - 21 q^{31} - q^{32} - 15 q^{33} - 7 q^{34} + 7 q^{35} - 13 q^{36} + 28 q^{37} - 9 q^{38} - 12 q^{39} - 6 q^{40} - 31 q^{41} - 10 q^{42} + 11 q^{43} - 12 q^{44} + 10 q^{45} - 12 q^{46} + 18 q^{47} + 7 q^{48} - 24 q^{49} + 2 q^{50} - 17 q^{51} + 8 q^{52} - 21 q^{53} - 29 q^{54} + 5 q^{55} + 3 q^{56} + 19 q^{57} - 8 q^{58} - 5 q^{59} - 13 q^{60} + 37 q^{61} + q^{62} + 17 q^{63} - q^{64} + 37 q^{65} + 29 q^{66} - 13 q^{67} + 26 q^{68} - 15 q^{69} + 18 q^{70} + 49 q^{71} + 20 q^{72} - 8 q^{73} + 28 q^{74} + 8 q^{75} - 20 q^{76} - 8 q^{77} + 10 q^{78} + 8 q^{79} + 5 q^{80} - 11 q^{81} + 2 q^{82} - 7 q^{83} + q^{84} - 42 q^{85} + 22 q^{86} - 21 q^{87} - q^{88} - 13 q^{89} - 45 q^{90} - 24 q^{91} - 23 q^{92} - 40 q^{93} - 37 q^{94} - 10 q^{95} - 4 q^{96} - 32 q^{97} - 24 q^{98} + 20 q^{99}+O(q^{100}) \) 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9 - 6 * q^10 - 12 * q^11 + 7 * q^12 - 14 * q^13 + 3 * q^14 - 13 * q^15 - q^16 + 15 * q^17 + 9 * q^18 + 2 * q^19 + 5 * q^20 + q^21 + 10 * q^22 - q^23 - 4 * q^24 + 13 * q^25 - 3 * q^26 + 26 * q^27 + 3 * q^28 - 8 * q^29 + 20 * q^30 - 21 * q^31 - q^32 - 15 * q^33 - 7 * q^34 + 7 * q^35 - 13 * q^36 + 28 * q^37 - 9 * q^38 - 12 * q^39 - 6 * q^40 - 31 * q^41 - 10 * q^42 + 11 * q^43 - 12 * q^44 + 10 * q^45 - 12 * q^46 + 18 * q^47 + 7 * q^48 - 24 * q^49 + 2 * q^50 - 17 * q^51 + 8 * q^52 - 21 * q^53 - 29 * q^54 + 5 * q^55 + 3 * q^56 + 19 * q^57 - 8 * q^58 - 5 * q^59 - 13 * q^60 + 37 * q^61 + q^62 + 17 * q^63 - q^64 + 37 * q^65 + 29 * q^66 - 13 * q^67 + 26 * q^68 - 15 * q^69 + 18 * q^70 + 49 * q^71 + 20 * q^72 - 8 * q^73 + 28 * q^74 + 8 * q^75 - 20 * q^76 - 8 * q^77 + 10 * q^78 + 8 * q^79 + 5 * q^80 - 11 * q^81 + 2 * q^82 - 7 * q^83 + q^84 - 42 * q^85 + 22 * q^86 - 21 * q^87 - q^88 - 13 * q^89 - 45 * q^90 - 24 * q^91 - 23 * q^92 - 40 * q^93 - 37 * q^94 - 10 * q^95 - 4 * q^96 - 32 * q^97 - 24 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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