LMFDB - Embedded newform 400.2.be.a.21.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(21,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 5, 12]))

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

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

chi := DirichletCharacter("400.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.be (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$58$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			21.18
Character	$\chi$	$=$	400.21
Dual form			400.2.be.a.381.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.741429 + 1.20428i) q^{2} +(-1.38564 + 0.219464i) q^{3} +(-0.900567 - 1.78577i) q^{4} +(0.522765 - 2.17410i) q^{5} +(0.763059 - 1.83141i) q^{6} -1.14575i q^{7} +(2.81827 + 0.239491i) q^{8} +(-0.981331 + 0.318854i) q^{9} +O(q^{10})$	\(q+(-0.741429 + 1.20428i) q^{2} +(-1.38564 + 0.219464i) q^{3} +(-0.900567 - 1.78577i) q^{4} +(0.522765 - 2.17410i) q^{5} +(0.763059 - 1.83141i) q^{6} -1.14575i q^{7} +(2.81827 + 0.239491i) q^{8} +(-0.981331 + 0.318854i) q^{9} +(2.23063 + 2.24149i) q^{10} +(-4.84717 + 2.46976i) q^{11} +(1.63978 + 2.27680i) q^{12} +(4.50615 + 2.29600i) q^{13} +(1.37980 + 0.849495i) q^{14} +(-0.247227 + 3.12725i) q^{15} +(-2.37796 + 3.21641i) q^{16} +(-3.23203 + 2.34820i) q^{17} +(0.343599 - 1.41820i) q^{18} +(-0.980964 + 6.19356i) q^{19} +(-4.35323 + 1.02439i) q^{20} +(0.251452 + 1.58760i) q^{21} +(0.619561 - 7.66849i) q^{22} +(-0.792657 - 0.257550i) q^{23} +(-3.95767 + 0.286661i) q^{24} +(-4.45343 - 2.27309i) q^{25} +(-6.10600 + 3.72433i) q^{26} +(5.03981 - 2.56791i) q^{27} +(-2.04605 + 1.03183i) q^{28} +(7.20173 - 1.14064i) q^{29} +(-3.58278 - 2.61637i) q^{30} +(-5.56106 + 4.04035i) q^{31} +(-2.11036 - 5.24846i) q^{32} +(6.17442 - 4.48598i) q^{33} +(-0.431572 - 5.63328i) q^{34} +(-2.49098 - 0.598959i) q^{35} +(1.45315 + 1.46528i) q^{36} +(-2.81057 + 5.51605i) q^{37} +(-6.73145 - 5.77344i) q^{38} +(-6.74779 - 2.19249i) q^{39} +(1.99397 - 6.00201i) q^{40} +(-10.5651 + 3.43282i) q^{41} +(-2.09835 - 0.874278i) q^{42} +(-0.250889 - 0.250889i) q^{43} +(8.77563 + 6.43176i) q^{44} +(0.180215 + 2.30020i) q^{45} +(0.897860 - 0.763624i) q^{46} +(-1.22571 - 0.890528i) q^{47} +(2.58911 - 4.97867i) q^{48} +5.68725 q^{49} +(6.03933 - 3.67784i) q^{50} +(3.96308 - 3.96308i) q^{51} +(0.0420395 - 10.1146i) q^{52} +(-1.24024 - 7.83054i) q^{53} +(-0.644184 + 7.97326i) q^{54} +(2.83558 + 11.8294i) q^{55} +(0.274397 - 3.22904i) q^{56} -8.79734i q^{57} +(-3.96592 + 9.51858i) q^{58} +(-0.782428 + 1.53560i) q^{59} +(5.80720 - 2.37481i) q^{60} +(0.966208 + 1.89629i) q^{61} +(-0.742567 - 9.69268i) q^{62} +(0.365328 + 1.12436i) q^{63} +(7.88529 + 1.34990i) q^{64} +(7.34738 - 8.59656i) q^{65} +(0.824469 + 10.7618i) q^{66} +(-1.44398 + 9.11693i) q^{67} +(7.10401 + 3.65695i) q^{68} +(1.15486 + 0.182912i) q^{69} +(2.56820 - 2.55575i) q^{70} +(-6.56203 + 9.03186i) q^{71} +(-2.84202 + 0.663597i) q^{72} +(11.2412 + 3.65248i) q^{73} +(-4.55902 - 7.47446i) q^{74} +(6.66972 + 2.17231i) q^{75} +(11.9437 - 3.82594i) q^{76} +(2.82974 + 5.55367i) q^{77} +(7.64338 - 6.50064i) q^{78} +(-8.92591 - 6.48505i) q^{79} +(5.74969 + 6.85135i) q^{80} +(-3.91550 + 2.84478i) q^{81} +(3.69923 - 15.2686i) q^{82} +(-0.877457 + 5.54004i) q^{83} +(2.60865 - 1.87878i) q^{84} +(3.41565 + 8.25431i) q^{85} +(0.488156 - 0.116124i) q^{86} +(-9.72869 + 3.16104i) q^{87} +(-14.2521 + 5.79959i) q^{88} +(-17.7865 - 5.77918i) q^{89} +(-2.90369 - 1.48841i) q^{90} +(2.63065 - 5.16293i) q^{91} +(0.253915 + 1.64745i) q^{92} +(6.81892 - 6.81892i) q^{93} +(1.98122 - 0.815828i) q^{94} +(12.9526 + 5.37049i) q^{95} +(4.07606 + 6.80934i) q^{96} +(-0.0422810 - 0.0307189i) q^{97} +(-4.21669 + 6.84902i) q^{98} +(3.96919 - 3.96919i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8}+O(q^{10}) $ 464 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 + 12 * q^8	$ 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8} - 14 q^{10} - 6 q^{11} + 10 q^{12} - 6 q^{13} + 6 q^{14} - 16 q^{15} - 6 q^{16} - 12 q^{17} - 24 q^{18} - 6 q^{19} - 22 q^{20} + 12 q^{21} + 10 q^{22} - 16 q^{24} + 4 q^{26} - 18 q^{27} + 18 q^{28} - 6 q^{29} - 6 q^{30} + 12 q^{31} - 36 q^{32} - 12 q^{33} - 30 q^{34} + 44 q^{35} - 82 q^{36} - 6 q^{37} - 76 q^{38} - 52 q^{40} - 10 q^{42} - 48 q^{43} + 36 q^{44} - 12 q^{45} - 14 q^{46} - 12 q^{47} - 116 q^{48} - 400 q^{49} + 10 q^{50} - 4 q^{51} + 32 q^{52} - 6 q^{53} - 30 q^{54} + 36 q^{56} + 26 q^{58} - 6 q^{59} + 48 q^{60} - 6 q^{61} - 34 q^{62} + 72 q^{63} - 24 q^{64} + 16 q^{65} + 92 q^{66} + 30 q^{67} + 28 q^{68} - 18 q^{69} + 60 q^{70} + 22 q^{72} + 28 q^{74} - 26 q^{75} - 76 q^{76} + 36 q^{77} + 14 q^{78} - 52 q^{79} - 34 q^{80} + 72 q^{81} + 56 q^{82} - 46 q^{83} + 112 q^{84} + 2 q^{85} - 46 q^{86} - 136 q^{88} - 42 q^{90} + 36 q^{91} - 4 q^{93} + 50 q^{94} - 40 q^{95} - 66 q^{96} - 12 q^{97} - 8 q^{98} - 40 q^{99}+O(q^{100}) $ 464 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 + 12 * q^8 - 14 * q^10 - 6 * q^11 + 10 * q^12 - 6 * q^13 + 6 * q^14 - 16 * q^15 - 6 * q^16 - 12 * q^17 - 24 * q^18 - 6 * q^19 - 22 * q^20 + 12 * q^21 + 10 * q^22 - 16 * q^24 + 4 * q^26 - 18 * q^27 + 18 * q^28 - 6 * q^29 - 6 * q^30 + 12 * q^31 - 36 * q^32 - 12 * q^33 - 30 * q^34 + 44 * q^35 - 82 * q^36 - 6 * q^37 - 76 * q^38 - 52 * q^40 - 10 * q^42 - 48 * q^43 + 36 * q^44 - 12 * q^45 - 14 * q^46 - 12 * q^47 - 116 * q^48 - 400 * q^49 + 10 * q^50 - 4 * q^51 + 32 * q^52 - 6 * q^53 - 30 * q^54 + 36 * q^56 + 26 * q^58 - 6 * q^59 + 48 * q^60 - 6 * q^61 - 34 * q^62 + 72 * q^63 - 24 * q^64 + 16 * q^65 + 92 * q^66 + 30 * q^67 + 28 * q^68 - 18 * q^69 + 60 * q^70 + 22 * q^72 + 28 * q^74 - 26 * q^75 - 76 * q^76 + 36 * q^77 + 14 * q^78 - 52 * q^79 - 34 * q^80 + 72 * q^81 + 56 * q^82 - 46 * q^83 + 112 * q^84 + 2 * q^85 - 46 * q^86 - 136 * q^88 - 42 * q^90 + 36 * q^91 - 4 * q^93 + 50 * q^94 - 40 * q^95 - 66 * q^96 - 12 * q^97 - 8 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.741429	+	1.20428i	−0.524269	+	0.851553i
$2$	−0.741429	+	1.20428i	−0.524269	+	0.851553i
$3$	−1.38564	+	0.219464i	−0.800001	+	0.126708i	−0.543032	−	0.839712i	$-0.682724\pi$
$3$	−1.38564	+	0.219464i	−0.800001	+	0.126708i	−0.256969	+	0.966420i	$0.582724\pi$
$4$	−0.900567	−	1.78577i	−0.450283	−	0.892886i
$5$	0.522765	−	2.17410i	0.233787	−	0.972288i
$5$	0.522765	−	2.17410i	0.233787	−	0.972288i
$6$	0.763059	−	1.83141i	0.311518	−	0.747671i
$7$		−	1.14575i		−	0.433054i	−0.976277	−	0.216527i	$-0.930527\pi$
$7$		−	1.14575i		−	0.433054i	0.976277	−	0.216527i	$-0.0694730\pi$
$8$	2.81827	+	0.239491i	0.996409	+	0.0846727i
$9$	−0.981331	+	0.318854i	−0.327110	+	0.106285i
$10$	2.23063	+	2.24149i	0.705386	+	0.708823i
$11$	−4.84717	+	2.46976i	−1.46148	+	0.744660i	−0.990504	−	0.137486i	$-0.956098\pi$
$11$	−4.84717	+	2.46976i	−1.46148	+	0.744660i	−0.470975	+	0.882147i	$0.656098\pi$
$12$	1.63978	+	2.27680i	0.473362	+	0.657255i
$13$	4.50615	+	2.29600i	1.24978	+	0.636795i	0.948511	−	0.316744i	$-0.102590\pi$
$13$	4.50615	+	2.29600i	1.24978	+	0.636795i	0.301269	+	0.953539i	$0.402590\pi$
$14$	1.37980	+	0.849495i	0.368768	+	0.227037i
$15$	−0.247227	+	3.12725i	−0.0638338	+	0.807453i
$16$	−2.37796	+	3.21641i	−0.594490	+	0.804103i
$17$	−3.23203	+	2.34820i	−0.783882	+	0.569523i	−0.906141	−	0.422975i	$-0.860986\pi$
$17$	−3.23203	+	2.34820i	−0.783882	+	0.569523i	0.122260	+	0.992498i	$0.460986\pi$
$18$	0.343599	−	1.41820i	0.0809870	−	0.334274i
$19$	−0.980964	+	6.19356i	−0.225048	+	1.42090i	0.573616	+	0.819124i	$0.305540\pi$
$19$	−0.980964	+	6.19356i	−0.225048	+	1.42090i	−0.798665	+	0.601776i	$0.794460\pi$
$20$	−4.35323	+	1.02439i	−0.973412	+	0.229059i
$21$	0.251452	+	1.58760i	0.0548713	+	0.346444i
$22$	0.619561	−	7.66849i	0.132091	−	1.63493i
$23$	−0.792657	−	0.257550i	−0.165280	−	0.0537029i	0.225208	−	0.974311i	$-0.427694\pi$
$23$	−0.792657	−	0.257550i	−0.165280	−	0.0537029i	−0.390488	+	0.920608i	$0.627694\pi$
$24$	−3.95767	+	0.286661i	−0.807856	+	0.0585144i
$25$	−4.45343	−	2.27309i	−0.890687	−	0.454617i
$26$	−6.10600	+	3.72433i	−1.19749	+	0.730402i
$27$	5.03981	−	2.56791i	0.969912	−	0.494195i
$28$	−2.04605	+	1.03183i	−0.386668	+	0.194997i
$29$	7.20173	−	1.14064i	1.33733	−	0.211812i	0.553530	−	0.832829i	$-0.313280\pi$
$29$	7.20173	−	1.14064i	1.33733	−	0.211812i	0.783797	+	0.621017i	$0.213280\pi$
$30$	−3.58278	−	2.61637i	−0.654123	−	0.477681i
$31$	−5.56106	+	4.04035i	−0.998796	+	0.725667i	−0.961830	−	0.273649i	$-0.911769\pi$
$31$	−5.56106	+	4.04035i	−0.998796	+	0.725667i	−0.0369660	+	0.999317i	$0.511769\pi$
$32$	−2.11036	−	5.24846i	−0.373063	−	0.927806i
$33$	6.17442	−	4.48598i	1.07483	−	0.780909i
$34$	−0.431572	−	5.63328i	−0.0740139	−	0.966100i
$35$	−2.49098	−	0.598959i	−0.421053	−	0.101243i
$36$	1.45315	+	1.46528i	0.242192	+	0.244214i
$37$	−2.81057	+	5.51605i	−0.462054	+	0.906833i	0.535984	+	0.844228i	$0.319941\pi$
$37$	−2.81057	+	5.51605i	−0.462054	+	0.906833i	−0.998038	+	0.0626046i	$0.980059\pi$
$38$	−6.73145	−	5.77344i	−1.09199	−	0.936575i
$39$	−6.74779	−	2.19249i	−1.08051	−	0.351080i
$40$	1.99397	−	6.00201i	0.315274	−	0.949001i
$41$	−10.5651	+	3.43282i	−1.65000	+	0.536117i	−0.978740	−	0.205107i	$-0.934246\pi$
$41$	−10.5651	+	3.43282i	−1.65000	+	0.536117i	−0.671258	+	0.741224i	$0.734246\pi$
$42$	−2.09835	−	0.874278i	−0.323782	−	0.134904i
$43$	−0.250889	−	0.250889i	−0.0382602	−	0.0382602i	0.687718	−	0.725978i	$-0.258613\pi$
$43$	−0.250889	−	0.250889i	−0.0382602	−	0.0382602i	−0.725978	+	0.687718i	$0.758613\pi$
$44$	8.77563	+	6.43176i	1.32298	+	0.969625i
$45$	0.180215	+	2.30020i	0.0268649	+	0.342894i
$46$	0.897860	−	0.763624i	0.132382	−	0.112590i
$47$	−1.22571	−	0.890528i	−0.178788	−	0.129897i	0.494792	−	0.869011i	$-0.335244\pi$
$47$	−1.22571	−	0.890528i	−0.178788	−	0.129897i	−0.673580	+	0.739114i	$0.735244\pi$
$48$	2.58911	−	4.97867i	0.373706	−	0.718609i
$49$	5.68725			0.812464
$50$	6.03933	−	3.67784i	0.854090	−	0.520125i
$51$	3.96308	−	3.96308i	0.554943	−	0.554943i
$52$	0.0420395	−	10.1146i	0.00582982	−	1.40265i
$53$	−1.24024	−	7.83054i	−0.170360	−	1.07561i	−0.913609	−	0.406593i	$-0.866717\pi$
$53$	−1.24024	−	7.83054i	−0.170360	−	1.07561i	0.743250	−	0.669014i	$-0.233283\pi$
$54$	−0.644184	+	7.97326i	−0.0876623	+	1.08502i
$55$	2.83558	+	11.8294i	0.382349	+	1.59507i
$56$	0.274397	−	3.22904i	0.0366679	−	0.431499i
$57$		−	8.79734i		−	1.16524i
$58$	−3.96592	+	9.51858i	−0.520751	+	1.24985i
$59$	−0.782428	+	1.53560i	−0.101863	+	0.199918i	−0.936313	−	0.351165i	$-0.885785\pi$
$59$	−0.782428	+	1.53560i	−0.101863	+	0.199918i	0.834450	+	0.551084i	$0.185785\pi$
$60$	5.80720	−	2.37481i	0.749707	−	0.306586i
$61$	0.966208	+	1.89629i	0.123710	+	0.242795i	0.944553	−	0.328359i	$-0.106496\pi$
$61$	0.966208	+	1.89629i	0.123710	+	0.242795i	−0.820843	+	0.571155i	$0.806496\pi$
$62$	−0.742567	−	9.69268i	−0.0943061	−	1.23097i
$63$	0.365328	+	1.12436i	0.0460270	+	0.141657i
$64$	7.88529	+	1.34990i	0.985661	+	0.168737i
$65$	7.34738	−	8.59656i	0.911331	−	1.06627i
$66$	0.824469	+	10.7618i	0.101485	+	1.32468i
$67$	−1.44398	+	9.11693i	−0.176410	+	1.11381i	0.727506	+	0.686101i	$0.240679\pi$
$67$	−1.44398	+	9.11693i	−0.176410	+	1.11381i	−0.903916	+	0.427709i	$0.859321\pi$
$68$	7.10401	+	3.65695i	0.861488	+	0.443470i
$69$	1.15486	+	0.182912i	0.139029	+	0.0220200i
$70$	2.56820	−	2.55575i	0.306959	−	0.305471i
$71$	−6.56203	+	9.03186i	−0.778770	+	1.07188i	0.216647	+	0.976250i	$0.430488\pi$
$71$	−6.56203	+	9.03186i	−0.778770	+	1.07188i	−0.995417	+	0.0956345i	$0.969512\pi$
$72$	−2.84202	+	0.663597i	−0.334935	+	0.0782056i
$73$	11.2412	+	3.65248i	1.31568	+	0.427491i	0.881010	−	0.473099i	$-0.156865\pi$
$73$	11.2412	+	3.65248i	1.31568	+	0.427491i	0.434671	+	0.900589i	$0.356865\pi$
$74$	−4.55902	−	7.47446i	−0.529975	−	0.868888i
$75$	6.66972	+	2.17231i	0.770153	+	0.250837i
$76$	11.9437	−	3.82594i	1.37004	−	0.438865i
$77$	2.82974	+	5.55367i	0.322478	+	0.632899i
$78$	7.64338	−	6.50064i	0.865442	−	0.736052i
$79$	−8.92591	−	6.48505i	−1.00424	−	0.729626i	−0.0412496	−	0.999149i	$-0.513134\pi$
$79$	−8.92591	−	6.48505i	−1.00424	−	0.729626i	−0.962994	+	0.269523i	$0.913134\pi$
$80$	5.74969	+	6.85135i	0.642835	+	0.766004i
$81$	−3.91550	+	2.84478i	−0.435055	+	0.316086i
$82$	3.69923	−	15.2686i	0.408512	−	1.68613i
$83$	−0.877457	+	5.54004i	−0.0963134	+	0.608099i	0.891568	+	0.452887i	$0.149606\pi$
$83$	−0.877457	+	5.54004i	−0.0963134	+	0.608099i	−0.987881	+	0.155212i	$0.950394\pi$
$84$	2.60865	−	1.87878i	0.284627	−	0.204992i
$85$	3.41565	+	8.25431i	0.370479	+	0.895306i
$86$	0.488156	−	0.116124i	0.0526393	−	0.0125219i
$87$	−9.72869	+	3.16104i	−1.04302	+	0.338899i
$88$	−14.2521	+	5.79959i	−1.51928	+	0.618239i
$89$	−17.7865	−	5.77918i	−1.88536	−	0.612592i	−0.983600	−	0.180362i	$-0.942273\pi$
$89$	−17.7865	−	5.77918i	−1.88536	−	0.612592i	−0.901763	−	0.432230i	$-0.857727\pi$
$90$	−2.90369	−	1.48841i	−0.306076	−	0.156892i
$91$	2.63065	−	5.16293i	0.275767	−	0.541223i
$92$	0.253915	+	1.64745i	0.0264725	+	0.171758i
$93$	6.81892	−	6.81892i	0.707089	−	0.707089i
$94$	1.98122	−	0.815828i	0.204347	−	0.0841462i
$95$	12.9526	+	5.37049i	1.32891	+	0.551001i
$96$	4.07606	+	6.80934i	0.416011	+	0.694975i
$97$	−0.0422810	−	0.0307189i	−0.00429298	−	0.00311904i	0.585637	−	0.810574i	$-0.300845\pi$
$97$	−0.0422810	−	0.0307189i	−0.00429298	−	0.00311904i	−0.589930	+	0.807455i	$0.700845\pi$
$98$	−4.21669	+	6.84902i	−0.425950	+	0.691856i
$99$	3.96919	−	3.96919i	0.398919	−	0.398919i
$100$	−0.0485988	+	9.99988i	−0.00485988	+	0.999988i
$101$	−5.60094	−	5.60094i	−0.557315	−	0.557315i	0.371227	−	0.928542i	$-0.378937\pi$
$101$	−5.60094	−	5.60094i	−0.557315	−	0.557315i	−0.928542	+	0.371227i	$0.878937\pi$
$102$	1.83431	+	7.71100i	0.181623	+	0.763502i
$103$	9.21869	−	12.6884i	0.908345	−	1.25023i	−0.0593841	−	0.998235i	$-0.518914\pi$
$103$	9.21869	−	12.6884i	0.908345	−	1.25023i	0.967729	−	0.251994i	$-0.0810863\pi$
$104$	12.1497	+	7.54992i	1.19137	+	0.740330i
$105$	3.58306	+	0.283261i	0.349671	+	0.0276435i
$106$	10.3497	+	4.31220i	1.00525	+	0.418838i
$107$	7.21156	+	7.21156i	0.697168	+	0.697168i	0.963799	−	0.266631i	$-0.0859103\pi$
$107$	7.21156	+	7.21156i	0.697168	+	0.697168i	−0.266631	+	0.963799i	$0.585910\pi$
$108$	−9.12439	−	6.68738i	−0.877995	−	0.643493i
$109$	0.868681	+	0.442615i	0.0832046	+	0.0423948i	0.495098	−	0.868837i	$-0.335132\pi$
$109$	0.868681	+	0.442615i	0.0832046	+	0.0423948i	−0.411893	+	0.911232i	$0.635132\pi$
$110$	−16.3482	−	5.35580i	−1.55874	−	0.510656i
$111$	2.68386	−	8.26008i	0.254741	−	0.784012i
$112$	3.68522	+	2.72456i	0.348220	+	0.257446i
$113$	1.40753	+	4.33193i	0.132409	+	0.407514i	0.995178	−	0.0980850i	$-0.0312717\pi$
$113$	1.40753	+	4.33193i	0.132409	+	0.407514i	−0.862769	+	0.505599i	$0.831272\pi$
$114$	10.5944	+	6.52260i	0.992260	+	0.610898i
$115$	−0.974313	+	1.58868i	−0.0908551	+	0.148145i
$116$	−8.52256	−	11.8334i	−0.791300	−	1.09871i
$117$	−5.15411	−	0.816331i	−0.476498	−	0.0754698i
$118$	−1.26917	−	2.08080i	−0.116837	−	0.191553i
$119$	2.69046	+	3.70311i	0.246634	+	0.339463i
$120$	−1.44570	+	8.75423i	−0.131974	+	0.799149i
$121$	10.9298	−	15.0435i	0.993614	−	1.36759i
$122$	−3.00003	−	0.242382i	−0.271610	−	0.0219442i
$123$	13.8861	−	7.07533i	1.25207	−	0.637961i
$124$	12.2232	+	6.29218i	1.09768	+	0.565054i
$125$	−7.27002	+	8.49393i	−0.650250	+	0.759720i
$126$	−1.62491	−	0.393680i	−0.144759	−	0.0350718i
$127$	1.87251	−	5.76300i	0.166158	−	0.511383i	−0.832961	−	0.553331i	$-0.813356\pi$
$127$	1.87251	−	5.76300i	0.166158	−	0.511383i	0.999120	+	0.0419480i	$0.0133564\pi$
$128$	−7.47203	+	8.49522i	−0.660441	+	0.750878i
$129$	0.402703	+	0.292581i	0.0354561	+	0.0257603i
$130$	4.90507	+	15.2220i	0.430203	+	1.33506i
$131$	1.69937	−	10.7294i	0.148474	−	0.937431i	−0.795150	−	0.606413i	$-0.792608\pi$
$131$	1.69937	−	10.7294i	0.148474	−	0.937431i	0.943624	−	0.331018i	$-0.107392\pi$
$132$	−13.5714	−	6.98618i	−1.18124	−	0.608069i
$133$	7.09629	+	1.12394i	0.615327	+	0.0974582i
$134$	−9.90870	−	8.49851i	−0.855981	−	0.734159i
$135$	−2.94827	−	12.2995i	−0.253746	−	1.05857i
$136$	−9.67110	+	5.84383i	−0.829290	+	0.501105i
$137$	−4.96309	+	1.61260i	−0.424025	+	0.137774i	−0.513253	−	0.858237i	$-0.671560\pi$
$137$	−4.96309	+	1.61260i	−0.424025	+	0.137774i	0.0892284	+	0.996011i	$0.471560\pi$
$138$	−1.07652	+	1.25516i	−0.0916398	+	0.106846i
$139$	3.97403	−	2.02487i	0.337073	−	0.171747i	−0.277259	−	0.960795i	$-0.589426\pi$
$139$	3.97403	−	2.02487i	0.337073	−	0.171747i	0.614331	+	0.789048i	$0.289426\pi$
$140$	1.17369	+	4.98773i	0.0991952	+	0.421540i
$141$	1.89383	+	0.964954i	0.159489	+	0.0812638i
$142$	−6.01158	−	14.5990i	−0.504481	−	1.22512i
$143$	−27.5126			−2.30072
$144$	1.30800	−	3.91459i	0.109000	−	0.326216i
$145$	1.28494	−	16.2536i	0.106708	−	1.34979i
$146$	−12.7331	+	10.8294i	−1.05380	+	0.896251i
$147$	−7.88049	+	1.24815i	−0.649972	+	0.102945i
$148$	12.3815	+	0.0514612i	1.01775	+	0.00423008i
$149$	4.67705	+	4.67705i	0.383159	+	0.383159i	0.872239	−	0.489080i	$-0.162667\pi$
$149$	4.67705	+	4.67705i	0.383159	+	0.383159i	−0.489080	+	0.872239i	$0.662667\pi$
$150$	−7.56119	+	6.42158i	−0.617369	+	0.524320i
$151$		−	12.4128i		−	1.01014i	−0.863078	−	0.505070i	$-0.831466\pi$
$151$		−	12.4128i		−	1.01014i	0.863078	−	0.505070i	$-0.168534\pi$
$152$	−4.24792	+	17.2202i	−0.344552	+	1.39674i
$153$	2.42296	−	3.33491i	0.195884	−	0.269612i
$154$	−8.78620	−	0.709864i	−0.708012	−	0.0572025i
$155$	5.87700	+	14.2025i	0.472052	+	1.14077i
$156$	2.16155	+	14.0245i	0.173063	+	1.12286i
$157$	−2.92799	+	2.92799i	−0.233679	+	0.233679i	−0.814226	−	0.580548i	$-0.802839\pi$
$157$	−2.92799	+	2.92799i	−0.233679	+	0.233679i	0.580548	+	0.814226i	$0.302839\pi$
$158$	14.4277	−	5.94106i	1.14781	−	0.472646i
$159$	3.43704	+	10.5781i	0.272575	+	0.838901i
$160$	−12.5139	+	1.84444i	−0.989312	+	0.145815i
$161$	−0.295089	+	0.908190i	−0.0232562	+	0.0715754i
$162$	−0.522835	−	6.82454i	−0.0410778	−	0.536187i
$163$	−2.37316	−	1.20919i	−0.185880	−	0.0947107i	0.358574	−	0.933501i	$-0.383263\pi$
$163$	−2.37316	−	1.20919i	−0.185880	−	0.0947107i	−0.544454	+	0.838791i	$0.683263\pi$
$164$	15.6449	+	15.7754i	1.22166	+	1.23186i
$165$	−6.52521	−	15.7689i	−0.507987	−	1.22761i
$166$	−6.02118	−	5.16425i	−0.467334	−	0.400823i
$167$	−8.25867	−	11.3671i	−0.639075	−	0.879611i	0.359491	−	0.933149i	$-0.382950\pi$
$167$	−8.25867	−	11.3671i	−0.639075	−	0.879611i	−0.998566	+	0.0535375i	$0.982950\pi$
$168$	0.328443	+	4.53452i	0.0253399	+	0.349845i
$169$	7.39256	+	10.1750i	0.568658	+	0.782691i
$170$	−12.4729	−	2.00660i	−0.956631	−	0.153899i
$171$	−1.01219	−	6.39072i	−0.0774042	−	0.488711i
$172$	−0.222088	+	0.673973i	−0.0169341	+	0.0513899i
$173$	−1.53406	−	3.01075i	−0.116632	−	0.228903i	0.825309	−	0.564681i	$-0.191001\pi$
$173$	−1.53406	−	3.01075i	−0.116632	−	0.228903i	−0.941941	+	0.335778i	$0.891001\pi$
$174$	3.40636	−	14.0597i	0.258235	−	1.06586i
$175$	−2.60440	+	5.10254i	−0.196874	+	0.385716i
$176$	3.58262	−	21.4635i	0.270050	−	1.61787i
$177$	0.747155	−	2.29951i	0.0561596	−	0.172842i
$178$	20.1471	−	17.1350i	1.51009	−	1.28432i
$179$	2.71482	−	0.429986i	0.202915	−	0.0321386i	−0.0541493	−	0.998533i	$-0.517245\pi$
$179$	2.71482	−	0.429986i	0.202915	−	0.0321386i	0.257065	+	0.966394i	$0.417245\pi$
$180$	3.94534	−	2.39331i	0.294068	−	0.178387i
$181$	−2.31764	−	0.367078i	−0.172269	−	0.0272847i	0.0697041	−	0.997568i	$-0.477794\pi$
$181$	−2.31764	−	0.367078i	−0.172269	−	0.0272847i	−0.241973	+	0.970283i	$0.577794\pi$
$182$	4.26717	+	6.99598i	0.316303	+	0.518576i
$183$	−1.75499	−	2.41553i	−0.129732	−	0.178561i
$184$	−2.17224	−	0.915679i	−0.160140	−	0.0675047i
$185$	10.5232	+	8.99405i	0.773680	+	0.661256i
$186$	3.15613	+	13.2676i	0.231418	+	0.972829i
$187$	9.86670	−	19.3645i	0.721524	−	1.41607i
$188$	−0.486449	+	2.99081i	−0.0354780	+	0.218127i
$189$	−2.94220	−	5.77438i	−0.214013	−	0.420025i
$190$	−16.0710	+	11.6167i	−1.16591	+	0.842764i
$191$	3.39252	+	10.4411i	0.245474	+	0.755492i	0.995558	+	0.0941493i	$0.0300131\pi$
$191$	3.39252	+	10.4411i	0.245474	+	0.755492i	−0.750084	+	0.661343i	$0.769987\pi$
$192$	−11.2224	−	0.139938i	−0.809910	−	0.0100991i
$193$	−9.37493			−0.674822			−0.337411	−	0.941357i	$-0.609551\pi$
$193$	−9.37493			−0.674822			−0.337411	+	0.941357i	$0.609551\pi$
$194$	0.0683425	−	0.0281421i	0.00490670	−	0.00202049i
$195$	−8.29421	+	13.5242i	−0.593960	+	0.968490i
$196$	−5.12175	−	10.1561i	−0.365839	−	0.725438i
$197$	2.02989	+	12.8162i	0.144623	+	0.913117i	0.948144	+	0.317840i	$0.102958\pi$
$197$	2.02989	+	12.8162i	0.144623	+	0.913117i	−0.803521	+	0.595277i	$0.797042\pi$
$198$	1.83713	+	7.72288i	0.130559	+	0.548841i
$199$			10.7021i			0.758651i	0.925263	+	0.379326i	$0.123844\pi$
$199$			10.7021i			0.758651i	−0.925263	+	0.379326i	$0.876156\pi$
$200$	−12.0066	−	7.47273i	−0.848995	−	0.528402i
$201$		−	12.9497i		−	0.913401i
$202$	10.8978	−	2.59239i	0.766766	−	0.182400i
$203$	−1.30689	−	8.25141i	−0.0917260	−	0.579135i
$204$	−10.6462	−	3.50814i	−0.745382	−	0.245619i
$205$	1.94022	+	24.7642i	0.135511	+	1.72961i
$206$	8.44539	+	20.5094i	0.588419	+	1.42896i
$207$	0.859980			0.0597727
$208$	−18.1003	+	9.03384i	−1.25503	+	0.626384i
$209$	−10.5417	−	32.4440i	−0.729185	−	2.24420i
$210$	−2.99771	+	4.10498i	−0.206862	+	0.283271i
$211$	−1.36964	−	2.68807i	−0.0942900	−	0.185055i	0.839044	−	0.544063i	$-0.183115\pi$
$211$	−1.36964	−	2.68807i	−0.0942900	−	0.185055i	−0.933334	+	0.359009i	$0.883115\pi$
$212$	−12.8666	+	9.26670i	−0.883685	+	0.636440i
$213$	7.11045	−	13.9550i	0.487200	−	0.956184i
$214$	−14.0316	+	3.33786i	−0.959179	+	0.228171i
$215$	−0.676614	+	0.414302i	−0.0461447	+	0.0282552i
$216$	14.8185	−	6.03008i	1.00827	−	0.410295i
$217$	4.62924	+	6.37160i	0.314253	+	0.432533i
$218$	−1.17710	+	0.717965i	−0.0797230	+	0.0486267i
$219$	−16.3778	−	2.59399i	−1.10671	−	0.175286i
$220$	18.5709	−	15.7168i	1.25205	−	1.05963i
$221$	−19.9555	+	3.16063i	−1.34235	+	0.212607i
$222$	7.95754	+	9.35638i	0.534075	+	0.627959i
$223$	0.0959964	−	0.295447i	0.00642840	−	0.0197846i	−0.947791	−	0.318893i	$-0.896689\pi$
$223$	0.0959964	−	0.295447i	0.00642840	−	0.0197846i	0.954219	+	0.299108i	$0.0966891\pi$
$224$	−6.01344	+	2.41796i	−0.401790	+	0.161557i
$225$	5.09508	+	0.810656i	0.339672	+	0.0540438i
$226$	−6.26043	−	1.51676i	−0.416437	−	0.100893i
$227$	−4.67088	−	9.16712i	−0.310017	−	0.608443i	0.682453	−	0.730930i	$-0.260913\pi$
$227$	−4.67088	−	9.16712i	−0.310017	−	0.608443i	−0.992470	+	0.122486i	$0.960913\pi$
$228$	−15.7100	+	7.92259i	−1.04042	+	0.524686i
$229$	3.08001	+	19.4464i	0.203533	+	1.28506i	0.851890	+	0.523721i	$0.175456\pi$
$229$	3.08001	+	19.4464i	0.203533	+	1.28506i	−0.648357	+	0.761336i	$0.724544\pi$
$230$	−1.19083	−	2.35123i	−0.0785207	−	0.155036i
$231$	−5.13983	−	7.07437i	−0.338176	−	0.465459i
$232$	20.5696	−	1.48989i	1.35046	−	0.0978161i
$233$	−9.82452	−	13.5223i	−0.643626	−	0.885875i	0.355176	−	0.934799i	$-0.384421\pi$
$233$	−9.82452	−	13.5223i	−0.643626	−	0.885875i	−0.998803	+	0.0489240i	$0.984421\pi$
$234$	4.80450	−	5.60173i	0.314080	−	0.366196i
$235$	−2.57686	+	2.19927i	−0.168096	+	0.143465i
$236$	3.44686	+	0.0143262i	0.224372	+	0.000932554i
$237$	13.7913	+	7.02704i	0.895844	+	0.456456i
$238$	−6.45435	+	0.494475i	−0.418374	+	0.0320520i
$239$	1.63733	−	5.03918i	0.105910	−	0.325958i	−0.884033	−	0.467425i	$-0.845182\pi$
$239$	1.63733	−	5.03918i	0.105910	−	0.325958i	0.989943	+	0.141467i	$0.0451819\pi$
$240$	−9.47064	−	8.23167i	−0.611327	−	0.531352i
$241$	2.87014	+	8.83339i	0.184882	+	0.569009i	0.999946	−	0.0103618i	$-0.00329833\pi$
$241$	2.87014	+	8.83339i	0.184882	+	0.569009i	−0.815064	+	0.579371i	$0.803298\pi$
$242$	10.0129	+	24.3162i	0.643656	+	1.56310i
$243$	−7.19770	+	7.19770i	−0.461733	+	0.461733i
$244$	2.51621	−	3.43316i	0.161084	−	0.219786i
$245$	2.97309	−	12.3647i	0.189944	−	0.789949i
$246$	−1.77491	+	21.9686i	−0.113164	+	1.40067i
$247$	−18.6408	+	25.6568i	−1.18608	+	1.63250i
$248$	−16.6402	+	10.0550i	−1.05665	+	0.638491i
$249$		−	7.86908i		−	0.498683i
$250$	−4.83884	−	15.0528i	−0.306035	−	0.952020i
$251$	−20.1511	−	20.1511i	−1.27192	−	1.27192i	−0.945078	−	0.326845i	$-0.894014\pi$
$251$	−20.1511	−	20.1511i	−1.27192	−	1.27192i	−0.326845	−	0.945078i	$-0.605986\pi$
$252$	1.67885	−	1.66496i	0.105758	−	0.104882i
$253$	4.47823	−	0.709282i	0.281544	−	0.0445922i
$254$	5.55191	+	6.52787i	0.348358	+	0.409595i
$255$	−6.54439	−	10.6879i	−0.409825	−	0.669303i
$256$	−4.69062	−	15.2970i	−0.293164	−	0.956062i
$257$	7.38217			0.460487			0.230244	−	0.973133i	$-0.426048\pi$
$257$	7.38217			0.460487			0.230244	+	0.973133i	$0.426048\pi$
$258$	−0.650925	+	0.268038i	−0.0405248	+	0.0166873i
$259$	6.32003	+	3.22022i	0.392708	+	0.200095i
$260$	−21.9683	−	5.37898i	−1.36242	−	0.333590i
$261$	−6.70359	+	3.41565i	−0.414942	+	0.211423i
$262$	11.6612	+	10.0016i	0.720431	+	0.617900i
$263$	4.23765	−	1.37690i	0.261305	−	0.0849030i	−0.175435	−	0.984491i	$-0.556133\pi$
$263$	4.23765	−	1.37690i	0.261305	−	0.0849030i	0.436739	+	0.899588i	$0.356133\pi$
$264$	18.4755	−	11.1640i	1.13709	−	0.687096i
$265$	−17.6727	−	1.39713i	−1.08563	−	0.0858251i
$266$	−6.61493	+	7.71258i	−0.405588	+	0.472889i
$267$	25.9140	+	4.10438i	1.58591	+	0.251184i
$268$	17.5812	−	5.63179i	1.07394	−	0.344016i
$269$	−0.280145	+	1.76876i	−0.0170807	+	0.107843i	−0.994756	−	0.102279i	$-0.967386\pi$
$269$	−0.280145	+	1.76876i	−0.0170807	+	0.107843i	0.977675	+	0.210123i	$0.0673864\pi$
$270$	16.9979	+	5.56866i	1.03446	+	0.338898i
$271$	14.3753	+	10.4442i	0.873234	+	0.634442i	0.931453	−	0.363862i	$-0.118542\pi$
$271$	14.3753	+	10.4442i	0.873234	+	0.634442i	−0.0582186	+	0.998304i	$0.518542\pi$
$272$	0.132833	−	15.9795i	0.00805418	−	0.968897i
$273$	−2.51205	+	7.73131i	−0.152036	+	0.467920i
$274$	1.73775	−	7.17256i	0.104981	−	0.433310i
$275$	27.2006	+	0.0191392i	1.64025	+	0.00115414i
$276$	−0.713391	−	2.22704i	−0.0429411	−	0.134052i
$277$	−23.9420	+	12.1991i	−1.43854	+	0.732972i	−0.987216	−	0.159389i	$-0.949048\pi$
$277$	−23.9420	+	12.1991i	−1.43854	+	0.732972i	−0.451322	+	0.892361i	$0.649048\pi$
$278$	−0.507956	+	6.28713i	−0.0304652	+	0.377077i
$279$	4.16896	−	5.73808i	0.249589	−	0.343530i
$280$	−6.87682	−	2.28460i	−0.410969	−	0.136531i
$281$	12.7732	+	17.5808i	0.761985	+	1.04878i	0.997046	+	0.0768015i	$0.0244708\pi$
$281$	12.7732	+	17.5808i	0.761985	+	1.04878i	−0.235062	+	0.971980i	$0.575529\pi$
$282$	−2.56621	+	1.56525i	−0.152816	+	0.0932093i
$283$	1.08604	+	0.172012i	0.0645584	+	0.0102250i	0.188630	−	0.982048i	$-0.439595\pi$
$283$	1.08604	+	0.172012i	0.0645584	+	0.0102250i	−0.124072	+	0.992273i	$0.539595\pi$
$284$	22.0384	+	3.58449i	1.30774	+	0.212701i
$285$	−19.1263	−	4.59894i	−1.13294	−	0.272418i
$286$	20.3987	−	33.1328i	1.20620	−	1.95919i
$287$	3.93317	+	12.1050i	0.232168	+	0.714538i
$288$	3.74446	+	4.47758i	0.220644	+	0.263844i
$289$	−0.321359	+	0.989041i	−0.0189035	+	0.0581789i
$290$	18.6211	+	13.5983i	1.09347	+	0.798519i
$291$	0.0653280	+	0.0332863i	0.00382960	+	0.00195128i
$292$	−3.60094	−	23.3635i	−0.210729	−	1.36724i
$293$	13.7806	+	13.7806i	0.805074	+	0.805074i	0.983884	−	0.178810i	$-0.0572247\pi$
$293$	13.7806	+	13.7806i	0.805074	+	0.805074i	−0.178810	+	0.983884i	$0.557225\pi$
$294$	4.33971	−	10.4157i	0.253097	−	0.607456i
$295$	2.92953	+	2.50384i	0.170564	+	0.145779i
$296$	−9.24198	+	14.8726i	−0.537179	+	0.864453i
$297$	−18.0867	+	24.8942i	−1.04950	+	1.44451i
$298$	−9.10016	+	2.16476i	−0.527158	+	0.125401i
$299$	−2.98050	−	2.98050i	−0.172367	−	0.172367i
$300$	−2.12727	−	13.8669i	−0.122818	−	0.800607i
$301$	−0.287457	+	0.287457i	−0.0165687	+	0.0165687i
$302$	14.9485	+	9.20322i	0.860188	+	0.529586i
$303$	8.99011	+	6.53169i	0.516468	+	0.375236i
$304$	−17.5884	−	17.8832i	−1.00876	−	1.02567i
$305$	4.62783	−	1.10932i	0.264989	−	0.0635195i
$306$	2.21971	+	5.39051i	0.126892	+	0.308155i
$307$	22.6578	−	22.6578i	1.29315	−	1.29315i	0.360317	−	0.932830i	$-0.382668\pi$
$307$	22.6578	−	22.6578i	1.29315	−	1.29315i	0.932830	−	0.360317i	$-0.117332\pi$
$308$	7.36922	−	10.0547i	0.419900	−	0.572920i
$309$	−9.98915	+	19.6048i	−0.568263	+	1.11528i
$310$	−21.4611	−	3.45258i	−1.21891	−	0.196093i
$311$	25.4975	+	8.28464i	1.44583	+	0.469779i	0.923710	−	0.383093i	$-0.125141\pi$
$311$	25.4975	+	8.28464i	1.44583	+	0.469779i	0.522121	+	0.852872i	$0.325141\pi$
$312$	−18.4920	−	7.79506i	−1.04690	−	0.441309i
$313$	−11.4698	+	3.72677i	−0.648313	+	0.210650i	−0.614670	−	0.788784i	$-0.710711\pi$
$313$	−11.4698	+	3.72677i	−0.648313	+	0.210650i	−0.0336426	+	0.999434i	$0.510711\pi$
$314$	−1.35521	−	5.69700i	−0.0764791	−	0.321500i
$315$	2.63546	−	0.206482i	0.148491	−	0.0116340i
$316$	−3.54245	+	21.7799i	−0.199278	+	1.22521i
$317$	−0.327659	+	2.06876i	−0.0184032	+	0.116193i	−0.995180	−	0.0980670i	$-0.968734\pi$
$317$	−0.327659	+	2.06876i	−0.0184032	+	0.116193i	0.976777	+	0.214260i	$0.0687340\pi$
$318$	−15.2873	−	3.70378i	−0.857271	−	0.207698i
$319$	−32.0909	+	23.3154i	−1.79675	+	1.30541i
$320$	7.05697	−	16.4377i	0.394496	−	0.918897i
$321$	−11.5753	−	8.40996i	−0.646072	−	0.469398i
$322$	−0.874925	−	1.02873i	−0.0487576	−	0.0573287i
$323$	−11.3732	−	22.3213i	−0.632824	−	1.24199i
$324$	8.60629	+	4.43027i	0.478127	+	0.246126i
$325$	−14.8488	−	20.4679i	−0.823665	−	1.13536i
$326$	3.21572	−	1.96142i	0.178102	−	0.108633i
$327$	−1.30082	−	0.422662i	−0.0719355	−	0.0233732i
$328$	−30.5975	+	7.14437i	−1.68947	+	0.394482i
$329$	−1.02033	+	1.40436i	−0.0562524	+	0.0774248i
$330$	23.8281	+	3.83338i	1.31170	+	0.211021i
$331$	22.1003	+	3.50035i	1.21474	+	0.192397i	0.730732	−	0.682665i	$-0.239179\pi$
$331$	22.1003	+	3.50035i	1.21474	+	0.192397i	0.484012	+	0.875061i	$0.339179\pi$
$332$	10.6835	−	3.42224i	0.586331	−	0.187820i
$333$	0.999284	−	6.30923i	0.0547604	−	0.345744i
$334$	19.8123	−	1.51784i	1.08408	−	0.0830527i
$335$	19.0663	+	7.90537i	1.04170	+	0.431916i
$336$	−5.70433	−	2.96648i	−0.311197	−	0.161835i
$337$	3.51758	+	10.8260i	0.191615	+	0.589729i	0.999999	+	0.00107483i	$0.000342130\pi$
$337$	3.51758	+	10.8260i	0.191615	+	0.589729i	−0.808385	+	0.588654i	$0.799658\pi$
$338$	−17.7345	+	1.35866i	−0.964632	+	0.0739015i
$339$	−2.90103	−	5.69360i	−0.157563	−	0.309234i
$340$	11.6643	−	13.5331i	0.632585	−	0.733937i
$341$	16.9767	−	33.3187i	0.919342	−	1.80431i
$342$	8.44666	+	3.51931i	0.456743	+	0.190302i
$343$		−	14.5365i		−	0.784895i
$344$	−0.646987	−	0.767159i	−0.0348832	−	0.0413624i
$345$	1.00139	−	2.41517i	0.0539130	−	0.130028i
$346$	4.76317	+	0.384831i	0.256070	+	0.0206887i
$347$	−0.495114	−	3.12603i	−0.0265791	−	0.167814i	0.970828	−	0.239776i	$-0.0770740\pi$
$347$	−0.495114	−	3.12603i	−0.0265791	−	0.167814i	−0.997407	+	0.0719620i	$0.977074\pi$
$348$	14.4062	+	14.5265i	0.772255	+	0.778701i
$349$	2.84991	−	2.84991i	0.152552	−	0.152552i	−0.626705	−	0.779257i	$-0.715597\pi$
$349$	2.84991	−	2.84991i	0.152552	−	0.152552i	0.779257	+	0.626705i	$0.215597\pi$
$350$	−4.21389	−	6.91958i	−0.225242	−	0.369867i
$351$	28.6061			1.52688
$352$	23.1917	+	20.2281i	1.23612	+	1.07816i
$353$	26.5068	+	19.2583i	1.41081	+	1.02502i	0.993203	+	0.116391i	$0.0371325\pi$
$353$	26.5068	+	19.2583i	1.41081	+	1.02502i	0.417611	+	0.908626i	$0.362867\pi$
$354$	2.21528	+	2.60470i	0.117741	+	0.138438i
$355$	16.2058	+	18.9881i	0.860114	+	1.00778i
$356$	5.69762	+	36.9671i	0.301973	+	1.95925i
$357$	−4.54072	−	4.54072i	−0.240320	−	0.240320i
$358$	−1.49503	+	3.58820i	−0.0790146	+	0.189642i
$359$	−17.8007	+	5.78378i	−0.939482	+	0.305256i	−0.738435	−	0.674325i	$-0.764435\pi$
$359$	−17.8007	+	5.78378i	−0.939482	+	0.305256i	−0.201048	+	0.979581i	$0.564435\pi$
$360$	−0.0429806	+	6.52574i	−0.00226528	+	0.343937i
$361$	−19.3278	−	6.27999i	−1.01725	−	0.330526i
$362$	2.16043	−	2.51892i	0.113550	−	0.132391i
$363$	−11.8432	+	23.2436i	−0.621608	+	1.21997i
$364$	−11.5889	−	0.0481668i	−0.607423	−	0.00252463i
$365$	13.8174	−	22.5301i	0.723234	−	1.17928i
$366$	4.21017	−	0.322545i	0.220069	−	0.0168597i
$367$	11.0501	−	8.02835i	0.576809	−	0.419076i	−0.260763	−	0.965403i	$-0.583974\pi$
$367$	11.0501	−	8.02835i	0.576809	−	0.419076i	0.837572	+	0.546326i	$0.183974\pi$
$368$	2.71329	−	1.93707i	0.141440	−	0.100977i
$369$	9.27334	−	6.73747i	0.482751	−	0.350739i
$370$	−18.6335	+	6.00438i	−0.968711	+	0.312153i
$371$	−8.97187	+	1.42100i	−0.465796	+	0.0737749i
$372$	−18.3179	−	6.03614i	−0.949741	−	0.312959i
$373$	11.9901	−	6.10927i	0.620825	−	0.316326i	−0.115137	−	0.993350i	$-0.536731\pi$
$373$	11.9901	−	6.10927i	0.620825	−	0.316326i	0.735961	+	0.677024i	$0.236731\pi$
$374$	16.0048	+	26.2396i	0.827586	+	1.35682i
$375$	8.20953	−	13.3650i	0.423938	−	0.690168i
$376$	−3.24110	−	2.80329i	−0.167147	−	0.144569i
$377$	35.0710	+	11.3952i	1.80625	+	0.586885i
$378$	9.13539	+	0.738076i	0.469874	+	0.0379625i
$379$	−1.36126	−	8.59465i	−0.0699232	−	0.441478i	−0.997667	−	0.0682612i	$-0.978255\pi$
$379$	−1.36126	−	8.59465i	−0.0699232	−	0.441478i	0.927744	−	0.373216i	$-0.121745\pi$
$380$	−2.07423	−	27.9669i	−0.106406	−	1.43467i
$381$	−1.32986	+	8.39640i	−0.0681307	+	0.430160i
$382$	−15.0893	−	3.65580i	−0.772036	−	0.187047i
$383$	5.88246	−	4.27385i	0.300579	−	0.218384i	−0.427264	−	0.904127i	$-0.640523\pi$
$383$	5.88246	−	4.27385i	0.300579	−	0.218384i	0.727844	+	0.685743i	$0.240523\pi$
$384$	8.48916	−	13.4112i	0.433211	−	0.684386i
$385$	13.5535	−	3.24887i	0.690751	−	0.165578i
$386$	6.95084	−	11.2900i	0.353789	−	0.574646i
$387$	0.326202	+	0.166208i	0.0165818	+	0.00844885i
$388$	−0.0167802	+	0.103169i	−0.000851883	+	0.00523759i
$389$	3.59579	−	1.83215i	0.182314	−	0.0928935i	−0.360451	−	0.932778i	$-0.617377\pi$
$389$	3.59579	−	1.83215i	0.182314	−	0.0928935i	0.542765	+	0.839884i	$0.317377\pi$
$390$	−10.1374	−	20.0158i	−0.513325	−	1.01354i
$391$	3.16667	−	1.02891i	0.160145	−	0.0520344i
$392$	16.0282	+	1.36204i	0.809546	+	0.0687935i
$393$			15.2400i			0.768758i
$394$	−16.9393	−	7.05776i	−0.853388	−	0.355565i
$395$	−18.7653	+	16.0157i	−0.944185	+	0.805836i
$396$	−10.6626	−	3.51355i	−0.535816	−	0.176562i
$397$	−24.7868	+	3.92585i	−1.24402	+	0.197033i	−0.743525	−	0.668709i	$-0.766847\pi$
$397$	−24.7868	+	3.92585i	−1.24402	+	0.197033i	−0.500492	+	0.865741i	$0.666847\pi$
$398$	−12.8883	−	7.93484i	−0.646032	−	0.397738i
$399$	−10.0796			−0.504610
$400$	17.9013	−	8.91877i	0.895064	−	0.445939i
$401$	−32.5445			−1.62519			−0.812597	−	0.582826i	$-0.801947\pi$
$401$	−32.5445			−1.62519			−0.812597	+	0.582826i	$0.801947\pi$
$402$	15.5950	+	9.60128i	0.777809	+	0.478868i
$403$	−34.3356	+	5.43822i	−1.71038	+	0.270897i
$404$	−4.95798	+	15.0460i	−0.246669	+	0.748568i
$405$	4.13795	+	9.99984i	0.205616	+	0.496896i
$406$	10.9059	+	4.54397i	0.541253	+	0.225513i
$407$		−	33.6787i		−	1.66939i
$408$	12.1182	−	10.2199i	0.599938	−	0.505961i
$409$	−7.05290	+	2.29162i	−0.348743	+	0.113314i	−0.478150	−	0.878278i	$-0.658693\pi$
$409$	−7.05290	+	2.29162i	−0.348743	+	0.113314i	0.129407	+	0.991592i	$0.458693\pi$
$410$	−31.2616	−	16.0244i	−1.54390	−	0.791387i
$411$	6.52315	−	3.32371i	0.321763	−	0.163947i
$412$	−30.9607	−	5.03569i	−1.52532	−	0.248091i
$413$	1.75942	+	0.896469i	0.0865754	+	0.0441124i
$414$	−0.637614	+	1.03565i	−0.0313370	+	0.0508996i
$415$	11.5859	+	4.80382i	0.568730	+	0.235810i
$416$	2.54084	−	28.4957i	0.124575	−	1.39712i
$417$	−5.06219	+	3.67790i	−0.247897	+	0.180108i
$418$	46.8875	+	11.3598i	2.29334	+	0.555626i
$419$	−0.189047	+	1.19359i	−0.00923554	+	0.0583109i	−0.991876	−	0.127211i	$-0.959398\pi$
$419$	−0.189047	+	1.19359i	−0.00923554	+	0.0583109i	0.982640	+	0.185522i	$0.0593975\pi$
$420$	−2.72095	−	6.65362i	−0.132769	−	0.324664i
$421$	2.90616	+	18.3487i	0.141637	+	0.894263i	0.951501	+	0.307645i	$0.0995410\pi$
$421$	2.90616	+	18.3487i	0.141637	+	0.894263i	−0.809864	+	0.586618i	$0.800459\pi$
$422$	4.25268	+	0.343587i	0.207017	+	0.0167255i
$423$	1.48677	+	0.483082i	0.0722894	+	0.0234882i
$424$	−1.61998	−	22.3656i	−0.0786731	−	1.08617i
$425$	19.7313	−	3.11090i	0.957108	−	0.150901i
$426$	11.5339	+	18.9096i	0.558817	+	0.916175i
$427$	2.17268	−	1.10704i	0.105143	−	0.0535733i
$428$	6.38371	−	19.3727i	0.308568	−	0.936415i
$429$	38.1227	−	6.03804i	1.84058	−	0.291519i
$430$	0.00272643	−	1.12201i	0.000131480	−	0.0541080i
$431$	−0.592238	+	0.430286i	−0.0285271	+	0.0207261i	−0.601957	−	0.798528i	$-0.705612\pi$
$431$	−0.592238	+	0.430286i	−0.0285271	+	0.0207261i	0.573430	+	0.819254i	$0.305612\pi$
$432$	−3.72500	+	22.3165i	−0.179219	+	1.07370i
$433$	−14.0067	+	10.1765i	−0.673121	+	0.489051i	−0.871068	−	0.491162i	$-0.836572\pi$
$433$	−14.0067	+	10.1765i	−0.673121	+	0.489051i	0.197948	+	0.980213i	$0.436572\pi$
$434$	−11.1054	+	0.850798i	−0.533078	+	0.0408396i
$435$	1.78661	+	22.8036i	0.0856615	+	1.09335i
$436$	0.00810424	−	1.94987i	0.000388123	−	0.0933819i
$437$	2.37272	−	4.65672i	0.113503	−	0.222761i
$438$	15.2669	−	17.8002i	0.729480	−	0.850526i
$439$	−1.62197	−	0.527010i	−0.0774124	−	0.0251528i	0.270055	−	0.962845i	$-0.412958\pi$
$439$	−1.62197	−	0.527010i	−0.0774124	−	0.0251528i	−0.347467	+	0.937692i	$0.612958\pi$
$440$	5.15840	+	34.0174i	0.245917	+	1.62172i
$441$	−5.58108	+	1.81340i	−0.265766	+	0.0863525i
$442$	10.9893	−	26.3753i	0.522706	−	1.25454i
$443$	7.01099	+	7.01099i	0.333102	+	0.333102i	0.853763	−	0.520661i	$-0.174315\pi$
$443$	7.01099	+	7.01099i	0.333102	+	0.333102i	−0.520661	+	0.853763i	$0.674315\pi$
$444$	−17.1676	+	2.64599i	−0.814739	+	0.125573i
$445$	−21.8627	+	35.6485i	−1.03639	+	1.68990i
$446$	0.284625	+	0.334659i	0.0134774	+	0.0158466i
$447$	−7.50715	−	5.45427i	−0.355076	−	0.257978i
$448$	1.54665	−	9.03460i	0.0730724	−	0.426845i
$449$	−32.4855			−1.53309			−0.766544	−	0.642192i	$-0.778025\pi$
$449$	−32.4855			−1.53309			−0.766544	+	0.642192i	$0.778025\pi$
$450$	−4.75389	+	5.53484i	−0.224101	+	0.260915i
$451$	42.7328	−	42.7328i	2.01221	−	2.01221i
$452$	6.46826	−	6.41472i	0.304241	−	0.301723i
$453$	2.72417	+	17.1997i	0.127993	+	0.808113i
$454$	14.5029	+	1.17173i	0.680654	+	0.0549921i
$455$	−9.84953	−	8.41829i	−0.461753	−	0.394656i
$456$	2.10688	−	24.7933i	0.0986637	−	1.16105i
$457$		−	8.27193i		−	0.386944i	−0.981106	−	0.193472i	$-0.938025\pi$
$457$		−	8.27193i		−	0.386944i	0.981106	−	0.193472i	$-0.0619749\pi$
$458$	−25.7025	−	10.7090i	−1.20100	−	0.500397i
$459$	−10.2588	+	20.1341i	−0.478841	+	0.939778i
$460$	3.71445	+	0.309188i	0.173187	+	0.0144160i
$461$	−9.97738	−	19.5817i	−0.464693	−	0.912011i	−0.997821	−	0.0659768i	$-0.978984\pi$
$461$	−9.97738	−	19.5817i	−0.464693	−	0.912011i	0.533128	−	0.846034i	$-0.321016\pi$
$462$	12.3303	−	0.944638i	0.573658	−	0.0439486i
$463$	−9.36064	−	28.8091i	−0.435026	−	1.33887i	−0.893060	−	0.449938i	$-0.851446\pi$
$463$	−9.36064	−	28.8091i	−0.435026	−	1.33887i	0.458034	−	0.888935i	$-0.348554\pi$
$464$	−13.4566	+	25.8761i	−0.624709	+	1.20127i
$465$	−11.2603	−	18.3897i	−0.522186	−	0.852803i
$466$	23.5688	−	1.80563i	1.09180	−	0.0836441i
$467$	−3.23080	+	20.3985i	−0.149504	+	0.943930i	0.792876	+	0.609383i	$0.208583\pi$
$467$	−3.23080	+	20.3985i	−0.149504	+	0.943930i	−0.942379	+	0.334546i	$0.891417\pi$
$468$	3.18384	+	9.93923i	0.147173	+	0.459441i
$469$	10.4458	+	1.65444i	0.482340	+	0.0763952i
$470$	−0.737982	−	4.73385i	−0.0340406	−	0.218356i
$471$	3.41455	−	4.69973i	0.157334	−	0.216552i
$472$	−2.57285	+	4.14035i	−0.118425	+	0.190575i
$473$	1.83574	+	0.596468i	0.0844074	+	0.0274256i
$474$	−18.6878	+	11.3986i	−0.858360	+	0.523553i
$475$	18.4472	−	25.3528i	0.846414	−	1.16327i
$476$	4.18996	−	8.13945i	0.192046	−	0.373071i
$477$	3.71388	+	7.28890i	0.170047	+	0.333736i
$478$	4.85461	+	5.70799i	0.222045	+	0.261078i
$479$	15.4967	+	11.2590i	0.708063	+	0.514438i	0.882548	−	0.470222i	$-0.155826\pi$
$479$	15.4967	+	11.2590i	0.708063	+	0.514438i	−0.174485	+	0.984660i	$0.555826\pi$
$480$	16.9350	−	5.30208i	0.772974	−	0.242006i
$481$	−25.3297	+	18.4031i	−1.15493	+	0.839108i
$482$	−12.7659	−	3.09288i	−0.581469	−	0.140877i
$483$	0.209572	−	1.32319i	0.00953586	−	0.0602071i
$484$	−36.7073	−	5.97036i	−1.66851	−	0.271380i
$485$	−0.0888891	+	0.0758644i	−0.00403625	+	0.00344482i
$486$	−3.33144	−	14.0046i	−0.151117	−	0.635262i
$487$	−18.8800	+	6.13448i	−0.855535	+	0.277980i	−0.703762	−	0.710435i	$-0.748498\pi$
$487$	−18.8800	+	6.13448i	−0.855535	+	0.277980i	−0.151772	+	0.988416i	$0.548498\pi$
$488$	2.26889	+	5.57566i	0.102708	+	0.252398i
$489$	3.55372	+	1.15467i	0.160705	+	0.0522162i
$490$	12.6861	+	12.7479i	0.573101	+	0.575893i
$491$	−14.0282	+	27.5318i	−0.633083	+	1.24249i	0.322164	+	0.946684i	$0.395590\pi$
$491$	−14.0282	+	27.5318i	−0.633083	+	1.24249i	−0.955247	+	0.295811i	$0.904410\pi$
$492$	−25.1403	−	18.4256i	−1.13341	−	0.830691i
$493$	−20.5977	+	20.5977i	−0.927675	+	0.927675i
$494$	−17.0771	−	41.4713i	−0.768335	−	1.86588i
$495$	−6.55447	−	10.7044i	−0.294602	−	0.481126i
$496$	0.228554	−	27.4944i	0.0102624	−	1.23454i
$497$	10.3483	+	7.51847i	0.464184	+	0.337249i
$498$	9.47656	+	5.83437i	0.424655	+	0.261444i
$499$	2.85393	−	2.85393i	0.127759	−	0.127759i	−0.640336	−	0.768095i	$-0.721205\pi$
$499$	2.85393	−	2.85393i	0.127759	−	0.127759i	0.768095	+	0.640336i	$0.221205\pi$
$500$	21.7154	+	5.33324i	0.971140	+	0.238510i
$501$	13.9382	+	13.9382i	0.622714	+	0.622714i
$502$	39.2080	−	9.32688i	1.74994	−	0.416279i
$503$	7.05592	−	9.71164i	0.314608	−	0.433021i	−0.622203	−	0.782856i	$-0.713762\pi$
$503$	7.05592	−	9.71164i	0.314608	−	0.433021i	0.936811	+	0.349835i	$0.113762\pi$
$504$	0.760318	+	3.25625i	0.0338673	+	0.145045i
$505$	−15.1050	+	9.24904i	−0.672163	+	0.411577i
$506$	−2.46612	+	5.91892i	−0.109632	+	0.263128i
$507$	−12.4765	−	12.4765i	−0.554100	−	0.554100i
$508$	−11.9777	+	1.84609i	−0.531425	+	0.0819068i
$509$	8.83946	+	4.50393i	0.391802	+	0.199633i	0.638783	−	0.769387i	$-0.279438\pi$
$509$	8.83946	+	4.50393i	0.391802	+	0.199633i	−0.246980	+	0.969020i	$0.579438\pi$
$510$	17.7234	+	0.0430671i	0.784805	+	0.00190704i
$511$	4.18484	−	12.8796i	0.185127	−	0.569761i
$512$	21.8996	+	5.69283i	0.967834	+	0.251590i
$513$	10.9607	+	33.7334i	0.483925	+	1.48937i
$514$	−5.47335	+	8.89018i	−0.241419	+	0.392129i
$515$	−22.7668	−	26.6754i	−1.00322	−	1.17546i
$516$	0.159822	−	0.982625i	0.00703576	−	0.0432577i
$517$	8.14061	+	1.28935i	0.358023	+	0.0567054i
$518$	−8.56389	+	5.22351i	−0.376276	+	0.229508i
$519$	2.78640	+	3.83515i	0.122310	+	0.168345i
$520$	22.7657	−	22.4678i	0.998342	−	0.985278i
$521$	10.7887	−	14.8494i	0.472662	−	0.650563i	−0.504412	−	0.863463i	$-0.668291\pi$
$521$	10.7887	−	14.8494i	0.472662	−	0.650563i	0.977074	+	0.212900i	$0.0682907\pi$
$522$	0.856845	−	10.6054i	0.0375031	−	0.464187i
$523$	−32.0227	+	16.3164i	−1.40025	+	0.713465i	−0.980928	−	0.194371i	$-0.937733\pi$
$523$	−32.0227	+	16.3164i	−1.40025	+	0.713465i	−0.419325	+	0.907836i	$0.637733\pi$
$524$	−20.6906	+	6.62784i	−0.903874	+	0.289539i
$525$	2.48894	−	7.64186i	0.108626	−	0.333518i
$526$	−1.48375	+	6.12417i	−0.0646946	+	0.267027i
$527$	8.48593	−	26.1170i	0.369653	−	1.13767i
$528$	−0.253763	+	30.5270i	−0.0110436	+	1.32852i
$529$	−18.0454	−	13.1108i	−0.784583	−	0.570033i
$530$	14.7856	−	20.2470i	0.642246	−	0.879474i
$531$	0.278189	−	1.75641i	0.0120724	−	0.0762219i
$532$	−4.38358	−	13.6845i	−0.190052	−	0.593300i
$533$	−55.4898	−	8.78873i	−2.40353	−	0.380682i
$534$	−24.1562	+	28.1646i	−1.04534	+	1.21880i
$535$	19.4486	−	11.9087i	0.840837	−	0.514859i
$536$	−6.25294	+	25.3481i	−0.270086	+	1.09487i
$537$	−3.66740	+	1.19161i	−0.158260	+	0.0514218i
$538$	−1.92238	−	1.64879i	−0.0828795	−	0.0710842i
$539$	−27.5671	+	14.0461i	−1.18740	+	0.605010i
$540$	−19.3089	+	16.3414i	−0.830925	+	0.703223i
$541$	11.2656	+	5.74013i	0.484348	+	0.246787i	0.679073	−	0.734070i	$-0.262382\pi$
$541$	11.2656	+	5.74013i	0.484348	+	0.246787i	−0.194726	+	0.980858i	$0.562382\pi$
$542$	−23.2360	+	9.56813i	−0.998070	+	0.410986i
$543$	3.29198			0.141272
$544$	19.1452	+	12.0076i	0.820844	+	0.514822i
$545$	1.41641	−	1.65722i	0.0606722	−	0.0709874i
$546$	−7.44813	−	8.75742i	−0.318750	−	0.374783i
$547$	−4.10413	+	0.650031i	−0.175480	+	0.0277933i	−0.243556	−	0.969887i	$-0.578314\pi$
$547$	−4.10413	+	0.650031i	−0.175480	+	0.0277933i	0.0680760	+	0.997680i	$0.478314\pi$
$548$	7.34933	+	7.41068i	0.313948	+	0.316569i
$549$	−1.55281	−	1.55281i	−0.0662723	−	0.0662723i
$550$	−20.1903	+	32.7428i	−0.860918	+	1.39616i
$551$			45.7233i			1.94788i
$552$	3.21091	+	0.792074i	0.136665	+	0.0337129i
$553$	−7.43027	+	10.2269i	−0.315967	+	0.434892i
$554$	3.06025	−	37.8776i	0.130017	−	1.60927i
$555$	−16.5552	−	10.1531i	−0.702730	−	0.430974i
$556$	−7.19483	−	5.27318i	−0.305129	−	0.223633i
$557$	12.8857	−	12.8857i	0.545983	−	0.545983i	−0.379293	−	0.925277i	$-0.623833\pi$
$557$	12.8857	−	12.8857i	0.545983	−	0.545983i	0.925277	+	0.379293i	$0.123833\pi$
$558$	3.81925	+	9.27497i	0.161682	+	0.392641i
$559$	−0.554503	−	1.70658i	−0.0234530	−	0.0721808i
$560$	7.84996	−	6.58773i	0.331721	−	0.278382i
$561$	−9.42190	+	28.9976i	−0.397793	+	1.22428i
$562$	−30.6426	+	2.34756i	−1.29258	+	0.0990257i
$563$	22.5872	+	11.5087i	0.951935	+	0.485035i	0.859755	−	0.510707i	$-0.170616\pi$
$563$	22.5872	+	11.5087i	0.951935	+	0.485035i	0.0921805	+	0.995742i	$0.470616\pi$
$564$	0.0176682	−	4.25095i	0.000743966	−	0.178997i
$565$	10.1539	−	0.795532i	0.427176	−	0.0334683i
$566$	−1.01237	+	1.18036i	−0.0425532	+	0.0496142i
$567$	3.25941	+	4.48620i	0.136882	+	0.188403i
$568$	−20.6566	+	23.8827i	−0.866732	+	1.00209i
$569$	2.00146	+	2.75478i	0.0839057	+	0.115486i	0.848907	−	0.528543i	$-0.177261\pi$
$569$	2.00146	+	2.75478i	0.0839057	+	0.115486i	−0.765001	+	0.644029i	$0.777261\pi$
$570$	19.7192	−	19.6236i	0.825946	−	0.821942i
$571$	5.10658	+	32.2417i	0.213704	+	1.34927i	0.828235	+	0.560381i	$0.189345\pi$
$571$	5.10658	+	32.2417i	0.213704	+	1.34927i	−0.614531	+	0.788892i	$0.710655\pi$
$572$	24.7770	+	49.1313i	1.03598	+	2.05428i
$573$	−6.99227	−	13.7231i	−0.292106	−	0.573291i
$574$	−17.4940	−	4.23841i	−0.730185	−	0.176908i
$575$	2.94461	+	2.94876i	0.122799	+	0.122972i
$576$	−8.16850	+	1.18956i	−0.340354	+	0.0495649i
$577$	5.11080	−	15.7294i	0.212765	−	0.654824i	−0.786539	−	0.617540i	$-0.788129\pi$
$577$	5.11080	−	15.7294i	0.212765	−	0.654824i	0.999305	−	0.0372841i	$-0.0118706\pi$
$578$	−0.952815	−	1.12031i	−0.0396319	−	0.0465987i
$579$	12.9903	−	2.05746i	0.539858	−	0.0855051i
$580$	−30.1823	+	12.3428i	−1.25325	+	0.512508i
$581$	6.34752	+	1.00535i	0.263340	+	0.0417089i
$582$	−0.0885220	+	0.0539936i	−0.00366935	+	0.00223811i
$583$	25.3512	+	34.8929i	1.04994	+	1.44512i
$584$	30.8059	+	12.9858i	1.27476	+	0.537358i
$585$	−4.46917	+	10.7788i	−0.184778	+	0.445649i
$586$	−26.8131	+	6.37835i	−1.10764	+	0.263487i
$587$	1.08385	−	2.12718i	0.0447354	−	0.0877981i	−0.867557	−	0.497338i	$-0.834311\pi$
$587$	1.08385	−	2.12718i	0.0447354	−	0.0877981i	0.912292	+	0.409540i	$0.134311\pi$
$588$	9.32581	+	12.9487i	0.384590	+	0.533996i
$589$	−19.5689	−	38.4062i	−0.806324	−	1.58250i
$590$	−5.18735	+	1.67155i	−0.213560	+	0.0688165i
$591$	−5.62539	−	17.3132i	−0.231398	−	0.712169i
$592$	−11.0585	−	22.1569i	−0.454500	−	0.910642i
$593$	38.3362			1.57428			0.787139	−	0.616775i	$-0.211561\pi$
$593$	38.3362			1.57428			0.787139	+	0.616775i	$0.211561\pi$
$594$	−16.5695	−	40.2387i	−0.679857	−	1.65102i
$595$	9.45741	−	3.91349i	0.387716	−	0.160437i
$596$	4.14014	−	12.5641i	0.169587	−	0.514647i
$597$	−2.34873	−	14.8293i	−0.0961269	−	0.606922i
$598$	5.79917	−	1.37952i	0.237146	−	0.0564127i
$599$			19.8758i			0.812101i	0.913851	+	0.406051i	$0.133094\pi$
$599$			19.8758i			0.812101i	−0.913851	+	0.406051i	$0.866906\pi$
$600$	18.2768	+	7.71950i	0.746149	+	0.315147i
$601$			6.33790i			0.258528i	0.991610	+	0.129264i	$0.0412615\pi$
$601$			6.33790i			0.258528i	−0.991610	+	0.129264i	$0.958739\pi$
$602$	−0.133049	−	0.559307i	−0.00542267	−	0.0227956i
$603$	−1.48995	−	9.40715i	−0.0606753	−	0.383089i
$604$	−22.1665	+	11.1786i	−0.901940	+	0.454850i
$605$	−26.9925	−	31.6266i	−1.09740	−	1.28581i
$606$	−14.5315	+	5.98379i	−0.590302	+	0.243075i
$607$	−9.03871			−0.366870			−0.183435	−	0.983032i	$-0.558722\pi$
$607$	−9.03871			−0.366870			−0.183435	+	0.983032i	$0.558722\pi$
$608$	34.5769	−	7.92212i	1.40228	−	0.321284i
$609$	3.62177	+	11.1467i	0.146762	+	0.451686i
$610$	−2.09527	+	6.39567i	−0.0848352	+	0.258953i
$611$	−3.47857	−	6.82707i	−0.140728	−	0.276194i
$612$	−8.13742	−	1.32353i	−0.328936	−	0.0535007i
$613$	−6.30343	+	12.3712i	−0.254593	+	0.499667i	−0.982560	−	0.185945i	$-0.940465\pi$
$613$	−6.30343	+	12.3712i	−0.254593	+	0.499667i	0.727967	+	0.685612i	$0.240465\pi$
$614$	10.4871	+	44.0854i	0.423225	+	1.77914i
$615$	−8.12332	−	33.8886i	−0.327564	−	1.36652i
$616$	6.64491	+	16.3294i	0.267731	+	0.657931i
$617$	1.99032	+	2.73944i	0.0801272	+	0.110286i	0.847199	−	0.531275i	$-0.178287\pi$
$617$	1.99032	+	2.73944i	0.0801272	+	0.110286i	−0.767072	+	0.641561i	$0.778287\pi$
$618$	−16.2034	−	26.5653i	−0.651795	−	1.06861i
$619$	−17.8879	−	2.83317i	−0.718977	−	0.113875i	−0.213784	−	0.976881i	$-0.568579\pi$
$619$	−17.8879	−	2.83317i	−0.718977	−	0.113875i	−0.505193	+	0.863006i	$0.668579\pi$
$620$	20.0697	−	23.2852i	0.806019	−	0.935157i
$621$	−4.65621	+	0.737471i	−0.186847	+	0.0295937i
$622$	−28.8816	+	24.5636i	−1.15805	+	0.984910i
$623$	−6.62152	+	20.3789i	−0.265285	+	0.816465i
$624$	23.0979	−	16.4900i	0.924657	−	0.660130i
$625$	14.6662	+	20.2461i	0.586646	+	0.809843i
$626$	4.01599	−	16.5760i	0.160511	−	0.662509i
$627$	21.7273	+	42.6423i	0.867705	+	1.70297i
$628$	7.86556	+	2.59187i	0.313870	+	0.103427i
$629$	−3.86898	−	24.4278i	−0.154266	−	0.974000i
$630$	−1.70535	+	3.32692i	−0.0679426	+	0.132548i
$631$	27.5607	+	37.9341i	1.09718	+	1.51013i	0.839077	+	0.544013i	$0.183096\pi$
$631$	27.5607	+	37.9341i	1.09718	+	1.51013i	0.258099	+	0.966119i	$0.416904\pi$
$632$	−23.6025	−	20.4143i	−0.938858	−	0.812037i
$633$	2.48777	+	3.42412i	0.0988799	+	0.136096i
$634$	−2.24842	−	1.92843i	−0.0892963	−	0.0765878i
$635$	−11.5505	−	7.08372i	−0.458366	−	0.281109i
$636$	15.7948	−	15.6641i	0.626306	−	0.621122i
$637$	25.6276	+	13.0579i	1.01540	+	0.517373i
$638$	−4.28509	−	55.9331i	−0.169648	−	2.21441i
$639$	3.55968	−	10.9556i	0.140819	−	0.433396i
$640$	14.5634	+	20.6860i	0.575667	+	0.817684i
$641$	9.08558	+	27.9625i	0.358859	+	1.10445i	0.953738	+	0.300639i	$0.0971998\pi$
$641$	9.08558	+	27.9625i	0.358859	+	1.10445i	−0.594879	+	0.803815i	$0.702800\pi$
$642$	18.7102	−	7.70451i	0.738433	−	0.304073i
$643$	3.12033	−	3.12033i	0.123054	−	0.123054i	−0.642898	−	0.765952i	$-0.722268\pi$
$643$	3.12033	−	3.12033i	0.123054	−	0.123054i	0.765952	+	0.642898i	$0.222268\pi$
$644$	1.88757	−	0.290924i	0.0743805	−	0.0114640i
$645$	0.846620	−	0.722567i	0.0333356	−	0.0284510i
$646$	35.3134	+	2.85308i	1.38939	+	0.112253i
$647$	−11.4451	+	15.7528i	−0.449952	+	0.619305i	−0.972387	−	0.233373i	$-0.925024\pi$
$647$	−11.4451	+	15.7528i	−0.449952	+	0.619305i	0.522435	+	0.852679i	$0.325024\pi$
$648$	−11.7162	+	7.07962i	−0.460257	+	0.278114i
$649$		−	9.37574i		−	0.368030i
$650$	35.6584	−	2.70659i	1.39864	−	0.106161i
$651$	−7.81281	−	7.81281i	−0.306208	−	0.306208i
$652$	−0.0221401	+	5.32687i	−0.000867071	+	0.208616i
$653$	5.87749	−	0.930903i	0.230004	−	0.0364291i	−0.0403684	−	0.999185i	$-0.512853\pi$
$653$	5.87749	−	0.930903i	0.230004	−	0.0364291i	0.270372	+	0.962756i	$0.412853\pi$
$654$	1.47347	−	1.25317i	0.0576171	−	0.0490029i
$655$	−22.4384	−	9.30354i	−0.876741	−	0.363519i
$656$	14.0821	−	42.1450i	0.549814	−	1.64548i
$657$	−12.1959			−0.475809
$658$	−0.934737	−	2.26999i	−0.0364399	−	0.0884933i
$659$	24.3901	+	12.4274i	0.950103	+	0.484102i	0.859133	−	0.511752i	$-0.171003\pi$
$659$	24.3901	+	12.4274i	0.950103	+	0.484102i	0.0909700	+	0.995854i	$0.471003\pi$
$660$	−22.2833	+	25.8535i	−0.867377	+	1.00635i
$661$	5.67480	−	2.89145i	0.220724	−	0.112464i	−0.340133	−	0.940378i	$-0.610472\pi$
$661$	5.67480	−	2.89145i	0.220724	−	0.112464i	0.560857	+	0.827913i	$0.310472\pi$
$662$	−20.6012	+	24.0197i	−0.800689	+	0.933551i
$663$	26.9575	−	8.75901i	1.04694	−	0.340172i
$664$	−3.79970	+	15.4032i	−0.147457	+	0.597760i
$665$	6.15326	−	14.8405i	0.238613	−	0.575490i
$666$	6.85717	+	5.88126i	0.265710	+	0.227894i
$667$	−6.00227	−	0.950667i	−0.232409	−	0.0368100i
$668$	−12.8615	+	24.9849i	−0.497627	+	0.966695i
$669$	−0.0681767	+	0.430451i	−0.00263586	+	0.0166422i
$670$	−23.6565	+	17.0998i	−0.913932	+	0.660623i
$671$	−9.36676	−	6.80535i	−0.361600	−	0.262718i
$672$	7.80182	−	4.67016i	0.300962	−	0.180155i
$673$	2.47104	−	7.60509i	0.0952517	−	0.293155i	−0.892067	−	0.451902i	$-0.850746\pi$
$673$	2.47104	−	7.60509i	0.0952517	−	0.293155i	0.987319	+	0.158748i	$0.0507456\pi$
$674$	−15.6455	−	3.79056i	−0.602643	−	0.146007i
$675$	−28.2816	−	0.0198998i	−1.08856	−	0.000765944i
$676$	11.5127	−	22.3647i	0.442796	−	0.860179i
$677$	−22.7433	+	11.5883i	−0.874096	+	0.445374i	−0.832672	−	0.553767i	$-0.813190\pi$
$677$	−22.7433	+	11.5883i	−0.874096	+	0.445374i	−0.0414249	+	0.999142i	$0.513190\pi$
$678$	9.00758	+	0.727750i	0.345934	+	0.0279491i
$679$	−0.0351963	+	0.0484436i	−0.00135071	+	0.00185909i
$680$	7.64938	+	24.0809i	0.293340	+	0.923460i
$681$	8.48402	+	11.6773i	0.325108	+	0.447473i
$682$	27.5379	+	45.1482i	1.05448	+	1.72881i
$683$	32.0785	+	5.08074i	1.22745	+	0.194409i	0.736294	−	0.676662i	$-0.236574\pi$
$683$	32.0785	+	5.08074i	1.22745	+	0.194409i	0.491157	+	0.871071i	$0.336574\pi$
$684$	−10.5008	+	7.56281i	−0.401509	+	0.289171i
$685$	0.911440	+	11.6333i	0.0348243	+	0.444484i
$686$	17.5059	+	10.7778i	0.668379	+	0.411496i
$687$	−8.53559	−	26.2698i	−0.325653	−	1.00226i
$688$	1.40357	−	0.210359i	0.0535105	−	0.00801985i
$689$	12.3902	−	38.1332i	0.472030	−	1.45276i
$690$	2.16607	+	2.99662i	0.0824609	+	0.114080i
$691$	−16.9986	−	8.66120i	−0.646656	−	0.329488i	0.0997167	−	0.995016i	$-0.468206\pi$
$691$	−16.9986	−	8.66120i	−0.646656	−	0.329488i	−0.746373	+	0.665528i	$0.768206\pi$
$692$	−3.99500	+	5.45086i	−0.151867	+	0.207210i
$693$	−4.54772	−	4.54772i	−0.172753	−	0.172753i
$694$	4.13170	+	1.72147i	0.156837	+	0.0653462i
$695$	−2.32479	−	9.69847i	−0.0881843	−	0.367884i
$696$	−28.1751	+	6.57874i	−1.06797	+	0.249366i
$697$	26.0858	−	35.9041i	0.988072	−	1.35996i
$698$	1.31907	+	5.54508i	0.0499277	+	0.209884i
$699$	16.5809	+	16.5809i	0.627148	+	0.627148i
$700$	11.4574	+	0.0556823i	0.433049	+	0.00210459i
$701$	−14.5582	+	14.5582i	−0.549857	+	0.549857i	−0.926399	−	0.376542i	$-0.877113\pi$
$701$	−14.5582	+	14.5582i	−0.549857	+	0.549857i	0.376542	+	0.926399i	$0.377113\pi$
$702$	−21.2094	+	34.4496i	−0.800496	+	1.30022i
$703$	−31.4069	−	22.8185i	−1.18453	−	0.860614i
$704$	−41.5553	+	12.9316i	−1.56617	+	0.487377i
$705$	3.08794	−	3.61293i	0.116298	−	0.136071i
$706$	−42.8453	+	17.6429i	−1.61250	+	0.663998i
$707$	−6.41730	+	6.41730i	−0.241347	+	0.241347i
$708$	−4.77926	+	0.736611i	−0.179616	+	0.0276835i
$709$	13.7712	−	27.0274i	0.517187	−	1.01504i	−0.473744	−	0.880662i	$-0.657098\pi$
$709$	13.7712	−	27.0274i	0.517187	−	1.01504i	0.990931	−	0.134373i	$-0.0429021\pi$
$710$	−34.8823	+	5.43796i	−1.30911	+	0.204083i
$711$	10.8271	+	3.51793i	0.406047	+	0.131933i
$712$	−48.7431	−	20.5470i	−1.82672	−	0.770031i
$713$	5.44860	−	1.77036i	0.204052	−	0.0663004i
$714$	8.83490	−	2.10166i	0.330638	−	0.0786528i
$715$	−14.3826	+	59.8153i	−0.537880	+	2.23696i
$716$	−3.21273	−	4.46082i	−0.120066	−	0.166709i
$717$	−1.16283	+	7.34184i	−0.0434268	+	0.274186i
$718$	6.23264	−	25.7252i	0.232600	−	0.960055i
$719$	24.1529	−	17.5481i	0.900752	−	0.654435i	−0.0379071	−	0.999281i	$-0.512069\pi$
$719$	24.1529	−	17.5481i	0.900752	−	0.654435i	0.938659	+	0.344847i	$0.112069\pi$
$720$	−7.82694	−	4.89013i	−0.291693	−	0.182245i
$721$	−14.5378	−	10.5623i	−0.541417	−	0.393362i
$722$	21.8931	−	18.6199i	0.814775	−	0.692961i
$723$	−5.91560	−	11.6100i	−0.220004	−	0.431781i
$724$	1.43167	+	4.46935i	0.0532076	+	0.166102i
$725$	−34.6652	−	11.2904i	−1.28743	−	0.419314i
$726$	−19.2109	−	31.4960i	−0.712982	−	1.16893i
$727$	3.87469	+	1.25896i	0.143704	+	0.0466923i	0.379986	−	0.924992i	$-0.375929\pi$
$727$	3.87469	+	1.25896i	0.143704	+	0.0466923i	−0.236282	+	0.971685i	$0.575929\pi$
$728$	8.65035	−	13.9205i	0.320603	−	0.515929i
$729$	16.9281	−	23.2996i	0.626968	−	0.862947i
$730$	16.8879	+	33.3444i	0.625048	+	1.23413i
$731$	1.40002	+	0.221741i	0.0517816	+	0.00820140i
$732$	−2.73310	+	5.30935i	−0.101018	+	0.196239i
$733$	7.16155	−	45.2163i	0.264518	−	1.67010i	−0.395206	−	0.918593i	$-0.629327\pi$
$733$	7.16155	−	45.2163i	0.264518	−	1.67010i	0.659724	−	0.751508i	$-0.270673\pi$
$734$	1.47551	+	19.2598i	0.0544622	+	0.710892i
$735$	−1.40604	+	17.7855i	−0.0518627	+	0.656027i
$736$	0.321054	+	4.70375i	0.0118342	+	0.173383i
$737$	−15.5174	−	47.7576i	−0.571591	−	1.75918i
$738$	1.23827	+	16.1630i	0.0455812	+	0.594969i
$739$	3.35168	+	6.57804i	0.123293	+	0.241977i	0.944401	−	0.328797i	$-0.106643\pi$
$739$	3.35168	+	6.57804i	0.123293	+	0.241977i	−0.821107	+	0.570774i	$0.806643\pi$
$740$	6.58449	−	26.8917i	0.242051	−	0.988560i
$741$	20.1987	−	39.6421i	0.742017	−	1.45629i
$742$	4.94072	−	11.8582i	0.181380	−	0.435328i
$743$		−	2.98133i		−	0.109374i	−0.998504	−	0.0546871i	$-0.982584\pi$
$743$		−	2.98133i		−	0.109374i	0.998504	−	0.0546871i	$-0.0174161\pi$
$744$	20.8506	−	17.5845i	0.764421	−	0.644679i
$745$	12.6134	−	7.72338i	0.462118	−	0.282963i
$746$	−1.53256	+	18.9690i	−0.0561112	+	0.694505i
$747$	−0.905389	−	5.71640i	−0.0331264	−	0.209152i
$748$	−43.4662	−	0.180658i	−1.58928	−	0.00660552i
$749$	8.26268	−	8.26268i	0.301912	−	0.301912i
$750$	10.0084	+	19.7958i	0.365457	+	0.722840i
$751$	−39.3159			−1.43466			−0.717329	−	0.696734i	$-0.754636\pi$
$751$	−39.3159			−1.43466			−0.717329	+	0.696734i	$0.754636\pi$
$752$	5.77899	−	1.82474i	0.210738	−	0.0665414i
$753$	32.3446	+	23.4997i	1.17870	+	0.856377i
$754$	−39.7257	+	33.7864i	−1.44672	+	1.23043i
$755$	−26.9867	−	6.48898i	−0.982148	−	0.236158i
$756$	−7.66209	+	10.4543i	−0.278667	+	0.380219i
$757$	28.7807	+	28.7807i	1.04605	+	1.04605i	0.998887	+	0.0471642i	$0.0150184\pi$
$757$	28.7807	+	28.7807i	1.04605	+	1.04605i	0.0471642	+	0.998887i	$0.484982\pi$
$758$	11.3596	+	4.73299i	0.412600	+	0.171910i
$759$	−6.04956	+	1.96562i	−0.219585	+	0.0713476i
$760$	35.2178	+	18.2375i	1.27748	+	0.661544i
$761$	−4.23364	−	1.37559i	−0.153469	−	0.0498652i	0.231275	−	0.972888i	$-0.425710\pi$
$761$	−4.23364	−	1.37559i	−0.153469	−	0.0498652i	−0.384744	+	0.923023i	$0.625710\pi$
$762$	−9.12559	−	7.82685i	−0.330585	−	0.283537i
$763$	0.507128	−	0.995295i	0.0183593	−	0.0360321i
$764$	15.5902	−	15.4612i	0.564035	−	0.559366i
$765$	−5.98380	−	7.01112i	−0.216345	−	0.253488i
$766$	0.785483	+	10.2529i	0.0283806	+	0.370451i
$767$	−7.05147	+	5.12319i	−0.254614	+	0.184988i
$768$	9.85666	+	20.1667i	0.355671	+	0.727704i
$769$	−20.5069	+	14.8991i	−0.739497	+	0.537276i	−0.892554	−	0.450941i	$-0.851088\pi$
$769$	−20.5069	+	14.8991i	−0.739497	+	0.537276i	0.153057	+	0.988217i	$0.451088\pi$
$770$	−6.13643	+	18.7310i	−0.221142	+	0.675018i
$771$	−10.2290	+	1.62012i	−0.368390	+	0.0583472i
$772$	8.44275	+	16.7415i	0.303861	+	0.602539i
$773$	46.2633	−	23.5723i	1.66398	−	0.847838i	0.669507	−	0.742805i	$-0.266505\pi$
$773$	46.2633	−	23.5723i	1.66398	−	0.847838i	0.994469	−	0.105033i	$-0.0334947\pi$
$774$	−0.442017	+	0.269606i	−0.0158880	+	0.00969080i
$775$	33.9499	−	5.35265i	1.21952	−	0.192273i
$776$	−0.111802	−	0.0967001i	−0.00401347	−	0.00347133i
$777$	−9.46402	−	3.07505i	−0.339520	−	0.110317i
$778$	−0.459610	+	5.68873i	−0.0164778	+	0.203951i
$779$	−10.8974	−	68.8033i	−0.390439	−	2.46513i
$780$	31.6207	+	2.63208i	1.13220	+	0.0942437i
$781$	9.50079	−	59.9856i	0.339965	−	2.14645i
$782$	−1.10876	+	4.57641i	−0.0396493	+	0.163652i
$783$	33.3663	−	24.2420i	1.19241	−	0.866340i
$784$	−13.5240	+	18.2925i	−0.483002	+	0.653305i
$785$	4.83509	+	7.89639i	0.172572	+	0.281834i
$786$	−18.3532	−	11.2994i	−0.654638	−	0.403036i
$787$	1.30639	+	0.665640i	0.0465679	+	0.0237275i	0.477119	−	0.878838i	$-0.341681\pi$
$787$	1.30639	+	0.665640i	0.0465679	+	0.0237275i	−0.430552	+	0.902566i	$0.641681\pi$
$788$	21.0588	−	15.1668i	0.750187	−	0.540293i
$789$	−5.56968	+	2.83789i	−0.198286	+	0.101032i
$790$	−5.37417	−	34.4731i	−0.191204	−	1.22650i
$791$	4.96332	−	1.61268i	0.176475	−	0.0573403i
$792$	12.1368	−	10.2357i	0.431264	−	0.363709i
$793$			10.7634i			0.382219i
$794$	13.6499	−	32.7610i	0.484416	−	1.16264i
$795$	24.7947	−	1.94261i	0.879378	−	0.0688972i
$796$	19.1115	−	9.63795i	0.677389	−	0.341608i
$797$	−2.52499	+	0.399919i	−0.0894398	+	0.0141659i	−0.200994	−	0.979592i	$-0.564417\pi$
$797$	−2.52499	+	0.399919i	−0.0894398	+	0.0141659i	0.111554	+	0.993758i	$0.464417\pi$
$798$	7.47329	−	12.1386i	0.264552	−	0.429702i
$799$	6.05266			0.214128
$800$	−2.53184	+	28.1707i	−0.0895141	+	0.995986i
$801$	19.2972			0.681831
$802$	24.1294	−	39.1926i	0.852039	−	1.38394i
$803$	−63.5087	+	10.0588i	−2.24117	+	0.354967i
$804$	−23.1252	+	11.6621i	−0.815563	+	0.411289i
$805$	1.82023	+	1.11632i	0.0641548	+	0.0393452i
$806$	18.9083	−	45.3816i	0.666015	−	1.59850i
$807$		−	2.51236i		−	0.0884391i
$808$	−14.4436	−	17.1263i	−0.508124	−	0.602503i
$809$	26.6004	−	8.64299i	0.935220	−	0.303871i	0.198524	−	0.980096i	$-0.436385\pi$
$809$	26.6004	−	8.64299i	0.935220	−	0.303871i	0.736696	+	0.676225i	$0.236385\pi$
$810$	−15.1106	−	2.43093i	−0.530931	−	0.0854143i
$811$	−24.2899	+	12.3763i	−0.852934	+	0.434591i	−0.825077	−	0.565020i	$-0.808868\pi$
$811$	−24.2899	+	12.3763i	−0.852934	+	0.434591i	−0.0278569	+	0.999612i	$0.508868\pi$
$812$	−13.5582	+	9.76476i	−0.475799	+	0.342676i
$813$	−22.2111	−	11.3171i	−0.778977	−	0.396908i
$814$	40.5585	+	24.9703i	1.42157	+	0.875210i
$815$	−3.86950	+	4.52737i	−0.135543	+	0.158587i
$816$	3.32286	+	22.1710i	0.116323	+	0.776139i
$817$	1.80001	−	1.30778i	0.0629744	−	0.0457536i
$818$	2.46947	−	10.1927i	0.0863430	−	0.356380i
$819$	−0.935314	+	5.90534i	−0.0326825	+	0.206349i
$820$	42.4760	−	25.7666i	1.48333	−	0.899810i
$821$	−1.63402	−	10.3168i	−0.0570276	−	0.360058i	−0.999656	−	0.0262153i	$-0.991654\pi$
$821$	−1.63402	−	10.3168i	−0.0570276	−	0.360058i	0.942629	−	0.333843i	$-0.108346\pi$
$822$	−0.833782	+	10.3200i	−0.0290815	+	0.359950i
$823$	17.2294	+	5.59816i	0.600578	+	0.195140i	0.593498	−	0.804835i	$-0.297746\pi$
$823$	17.2294	+	5.59816i	0.600578	+	0.195140i	0.00707999	+	0.999975i	$0.497746\pi$
$824$	29.0195	−	33.5517i	1.01094	−	1.16883i
$825$	−37.6944	+	5.94302i	−1.31235	+	0.206910i
$826$	−2.38408	+	1.45416i	−0.0829528	+	0.0505967i
$827$	−15.0972	+	7.69241i	−0.524981	+	0.267491i	−0.696333	−	0.717719i	$-0.745186\pi$
$827$	−15.0972	+	7.69241i	−0.524981	+	0.267491i	0.171352	+	0.985210i	$0.445186\pi$
$828$	−0.774469	−	1.53573i	−0.0269147	−	0.0533702i
$829$	−12.1142	+	1.91871i	−0.420745	+	0.0666394i	−0.363217	−	0.931705i	$-0.618322\pi$
$829$	−12.1142	+	1.91871i	−0.420745	+	0.0666394i	−0.0575275	+	0.998344i	$0.518322\pi$
$830$	−14.3753	+	10.3910i	−0.498972	+	0.360675i
$831$	30.4978	−	22.1580i	1.05796	−	0.768652i
$832$	32.4329	+	24.1874i	1.12441	+	0.838549i
$833$	−18.3813	+	13.3548i	−0.636876	+	0.462717i
$834$	−0.675953	−	8.82319i	−0.0234064	−	0.305522i
$835$	−29.0305	+	12.0129i	−1.00464	+	0.415723i
$836$	−48.4441	+	48.0431i	−1.67547	+	1.66160i
$837$	−17.6514	+	34.6429i	−0.610123	+	1.19743i
$838$	−1.29725	−	1.11263i	−0.0448129	−	0.0384352i
$839$	5.56077	+	1.80680i	0.191979	+	0.0623778i	0.403429	−	0.915011i	$-0.367818\pi$
$839$	5.56077	+	1.80680i	0.191979	+	0.0623778i	−0.211449	+	0.977389i	$0.567818\pi$
$840$	10.0302	+	1.65642i	0.346075	+	0.0571518i
$841$	22.9832	−	7.46769i	0.792524	−	0.257507i
$842$	−24.2517	−	10.1045i	−0.835768	−	0.348223i
$843$	−21.5574	−	21.5574i	−0.742477	−	0.742477i
$844$	−3.56683	+	4.86666i	−0.122775	+	0.167517i
$845$	25.9860	−	10.7530i	0.893946	−	0.369916i
$846$	−1.68410	+	1.43232i	−0.0579006	+	0.0492440i
$847$	−17.2362	−	12.5228i	−0.592242	−	0.430289i
$848$	28.1355	+	14.6316i	0.966176	+	0.502451i
$849$	−1.54261			−0.0529424
$850$	−10.8830	+	26.0685i	−0.373283	+	0.894141i
$851$	3.64847	−	3.64847i	0.125068	−	0.125068i
$852$	−31.3240	−	0.130192i	−1.07314	−	0.00446029i
$853$	1.83593	+	11.5916i	0.0628609	+	0.396888i	0.998978	+	0.0451997i	$0.0143924\pi$
$853$	1.83593	+	11.5916i	0.0628609	+	0.396888i	−0.936117	+	0.351689i	$0.885608\pi$
$854$	−0.277710	+	3.43730i	−0.00950304	+	0.117622i
$855$	−14.4232	−	1.14024i	−0.493263	−	0.0389953i
$856$	18.5970	+	22.0512i	0.635633	+	0.753696i
$857$		−	28.2305i		−	0.964334i	−0.876079	−	0.482167i	$-0.839850\pi$
$857$		−	28.2305i		−	0.964334i	0.876079	−	0.482167i	$-0.160150\pi$
$858$	−20.9938	+	50.3870i	−0.716716	+	1.72018i
$859$	17.4114	−	34.1717i	0.594068	−	1.16592i	−0.376797	−	0.926296i	$-0.622974\pi$
$859$	17.4114	−	34.1717i	0.594068	−	1.16592i	0.970865	−	0.239628i	$-0.0770256\pi$
$860$	1.34919	+	0.835171i	0.0460068	+	0.0284791i
$861$	−8.10658	−	15.9101i	−0.276272	−	0.542214i
$862$	−0.0790813	−	1.03224i	−0.00269352	−	0.0351584i
$863$	13.8946	+	42.7633i	0.472979	+	1.45568i	0.848665	+	0.528931i	$0.177407\pi$
$863$	13.8946	+	42.7633i	0.472979	+	1.45568i	−0.375686	+	0.926747i	$0.622593\pi$
$864$	−24.1134	−	21.0320i	−0.820356	−	0.715524i
$865$	−7.34763	+	1.76128i	−0.249827	+	0.0598852i
$866$	−1.87032	−	24.4131i	−0.0635559	−	0.829592i
$867$	0.228229	−	1.44098i	0.00775107	−	0.0489384i
$868$	7.20929	−	14.0048i	0.244699	−	0.475354i
$869$	59.2820	+	9.38934i	2.01100	+	0.318512i
$870$	−28.7865	−	14.7557i	−0.975955	−	0.500265i
$871$	−27.4392	+	37.7669i	−0.929743	+	1.27968i
$872$	2.34218	+	1.45545i	0.0793161	+	0.0492878i
$873$	0.0512865	+	0.0166640i	0.00173579	+	0.000563991i
$874$	3.84878	+	6.31004i	0.130187	+	0.213440i
$875$	9.73195	+	8.32965i	0.329000	+	0.281594i
$876$	10.1171	+	31.5831i	0.341824	+	1.06710i
$877$	8.63146	+	16.9402i	0.291464	+	0.572030i	0.989585	−	0.143950i	$-0.0459804\pi$
$877$	8.63146	+	16.9402i	0.291464	+	0.572030i	−0.698121	+	0.715979i	$0.745980\pi$
$878$	1.83724	−	1.56256i	0.0620039	−	0.0527339i
$879$	−22.1194	−	16.0707i	−0.746068	−	0.542050i
$880$	−44.7910	−	19.0093i	−1.50990	−	0.640805i
$881$	−9.59057	+	6.96796i	−0.323115	+	0.234756i	−0.737503	−	0.675343i	$-0.763995\pi$
$881$	−9.59057	+	6.96796i	−0.323115	+	0.234756i	0.414389	+	0.910100i	$0.363995\pi$
$882$	1.95413	−	8.06567i	0.0657991	−	0.271585i
$883$	2.88674	−	18.2262i	0.0971466	−	0.613359i	−0.890296	−	0.455382i	$-0.849503\pi$
$883$	2.88674	−	18.2262i	0.0971466	−	0.613359i	0.987443	−	0.157977i	$-0.0504973\pi$
$884$	23.6154	+	32.7895i	0.794272	+	1.10283i
$885$	−4.60878	−	2.82649i	−0.154922	−	0.0950115i
$886$	−13.6413	+	3.24502i	−0.458289	+	0.109019i
$887$	35.1571	−	11.4232i	1.18046	−	0.383555i	0.347923	−	0.937523i	$-0.386887\pi$
$887$	35.1571	−	11.4232i	1.18046	−	0.383555i	0.832538	+	0.553968i	$0.186887\pi$
$888$	9.54207	−	22.6364i	0.320211	−	0.759627i
$889$	−6.60297	−	2.14544i	−0.221457	−	0.0719556i
$890$	−26.7210	−	52.7595i	−0.895691	−	1.76850i
$891$	11.9532	−	23.4595i	0.400447	−	0.785922i
$892$	−0.614051	+	0.0946417i	−0.0205600	+	0.00316884i
$893$	6.71792	−	6.71792i	0.224806	−	0.224806i
$894$	12.1345	−	4.99674i	0.405837	−	0.167116i
$895$	0.484381	−	6.12708i	0.0161911	−	0.204806i
$896$	9.73343	+	8.56111i	0.325171	+	0.286006i
$897$	4.78401	+	3.47579i	0.159733	+	0.116053i
$898$	24.0857	−	39.1216i	0.803751	−	1.30550i
$899$	−35.4406	+	35.4406i	−1.18201	+	1.18201i
$900$	−3.14081	−	9.82869i	−0.104694	−	0.327623i
$901$	22.3962	+	22.3962i	0.746125	+	0.746125i
$902$	19.7788	+	83.1455i	0.658563	+	2.76844i
$903$	0.335226	−	0.461399i	0.0111556	−	0.0153544i
$904$	2.92934	+	12.5456i	0.0974284	+	0.417262i
$905$	−2.00964	+	4.84689i	−0.0668028	+	0.161116i
$906$	−22.7330	−	9.47171i	−0.755253	−	0.314677i
$907$	−10.6512	−	10.6512i	−0.353668	−	0.353668i	0.507804	−	0.861472i	$-0.330457\pi$
$907$	−10.6512	−	10.6512i	−0.353668	−	0.353668i	−0.861472	+	0.507804i	$0.830457\pi$
$908$	−12.1639	+	16.5967i	−0.403675	+	0.550782i
$909$	7.28226	+	3.71050i	0.241537	+	0.123069i
$910$	17.4407	−	5.62000i	0.578153	−	0.186301i
$911$	−5.97422	+	18.3868i	−0.197935	+	0.609180i	0.801995	+	0.597331i	$0.203772\pi$
$911$	−5.97422	+	18.3868i	−0.197935	+	0.609180i	−0.999930	+	0.0118497i	$0.996228\pi$
$912$	28.2959	+	20.9197i	0.936970	+	0.692721i
$913$	−9.42939	−	29.0207i	−0.312067	−	0.960444i
$914$	9.96169	+	6.13305i	0.329504	+	0.202863i
$915$	−6.16905	+	2.55276i	−0.203943	+	0.0843918i
$916$	31.9531	−	23.0130i	1.05576	−	0.760372i
$917$	−12.2932	−	1.94706i	−0.405958	−	0.0642975i
$918$	−16.6408	−	27.2824i	−0.549229	−	0.900455i
$919$	31.1184	+	42.8308i	1.02650	+	1.41286i	0.907544	+	0.419958i	$0.137955\pi$
$919$	31.1184	+	42.8308i	1.02650	+	1.41286i	0.118957	+	0.992899i	$0.462045\pi$
$920$	−3.12635	+	4.24399i	−0.103073	+	0.139920i
$921$	−26.4230	+	36.3681i	−0.870667	+	1.19837i
$922$	30.9793	+	2.50291i	1.02025	+	0.0824291i
$923$	−50.3066	+	25.6325i	−1.65586	+	0.843704i
$924$	−8.00445	+	15.5495i	−0.263327	+	0.511541i
$925$	25.0551	−	18.1767i	0.823808	−	0.597646i
$926$	41.6344	+	10.0871i	1.36819	+	0.331482i
$927$	−5.00083	+	15.3910i	−0.164249	+	0.505506i
$928$	−21.1849	−	35.3908i	−0.695428	−	1.16176i
$929$	37.9239	+	27.5533i	1.24424	+	0.903995i	0.997873	−	0.0651806i	$-0.0207624\pi$
$929$	37.9239	+	27.5533i	1.24424	+	0.903995i	0.246369	+	0.969176i	$0.420762\pi$
$930$	30.4951	+	0.0741016i	0.999972	+	0.00242989i
$931$	−5.57898	+	35.2243i	−0.182844	+	1.15443i
$932$	−15.3001	+	29.7221i	−0.501171	+	0.973579i
$933$	−37.1486	−	5.88376i	−1.21619	−	0.192626i
$934$	−22.1700	−	19.0148i	−0.725425	−	0.622184i
$935$	−36.9424	−	31.5743i	−1.20815	−	1.03259i
$936$	−14.3302	−	3.53500i	−0.468396	−	0.115545i
$937$	36.8324	−	11.9676i	1.20326	−	0.390964i	0.362303	−	0.932060i	$-0.381991\pi$
$937$	36.8324	−	11.9676i	1.20326	−	0.390964i	0.840961	+	0.541096i	$0.181991\pi$
$938$	−9.73719	+	11.3529i	−0.317931	+	0.370686i
$939$	15.0752	−	7.68118i	0.491959	−	0.250666i
$940$	6.24803	+	2.62108i	0.203788	+	0.0854902i
$941$	−1.55775	−	0.793713i	−0.0507812	−	0.0258743i	0.428416	−	0.903582i	$-0.359072\pi$
$941$	−1.55775	−	0.793713i	−0.0507812	−	0.0258743i	−0.479197	+	0.877708i	$0.659072\pi$
$942$	3.12813	+	7.59658i	0.101920	+	0.247510i
$943$	9.25866			0.301503
$944$	−3.07854	−	6.16821i	−0.100198	−	0.200758i
$945$	−14.0922	+	3.37799i	−0.458418	+	0.109886i
$946$	−2.07938	+	1.76850i	−0.0676065	+	0.0574989i
$947$	31.9183	−	5.05537i	1.03721	−	0.164277i	0.385468	−	0.922721i	$-0.374040\pi$
$947$	31.9183	−	5.05537i	1.03721	−	0.164277i	0.651738	+	0.758444i	$0.274040\pi$
$948$	0.128664	−	30.9565i	0.00417883	−	1.00542i
$949$	42.2683	+	42.2683i	1.37209	+	1.37209i
$950$	16.8545	+	41.0128i	0.546834	+	1.33063i
$951$		−	2.93847i		−	0.0952864i
$952$	6.69559	+	11.0807i	0.217005	+	0.359127i
$953$	7.44583	−	10.2483i	0.241194	−	0.331975i	−0.671209	−	0.741268i	$-0.734225\pi$
$953$	7.44583	−	10.2483i	0.241194	−	0.331975i	0.912403	+	0.409293i	$0.134225\pi$
$954$	−11.5314	−	0.931660i	−0.373344	−	0.0301636i
$955$	24.4735	−	1.91744i	0.791944	−	0.0620470i
$956$	−10.4734	+	1.61422i	−0.338732	+	0.0522077i
$957$	39.3496	−	39.3496i	1.27199	−	1.27199i
$958$	−25.0487	+	10.3146i	−0.809286	+	0.333249i
$959$	1.84765	+	5.68647i	0.0596636	+	0.183626i
$960$	−6.17093	+	24.3256i	−0.199166	+	0.785104i
$961$	5.02145	−	15.4544i	0.161982	−	0.498530i
$962$	−3.38226	−	44.1485i	−0.109049	−	1.42340i
$963$	−9.37637	−	4.77750i	−0.302149	−	0.153953i
$964$	13.1897	−	13.0805i	0.424811	−	0.421294i
$965$	−4.90088	+	20.3820i	−0.157765	+	0.656121i
$966$	1.43810	+	1.23343i	0.0462701	+	0.0396850i
$967$	−25.4764	−	35.0653i	−0.819267	−	1.12762i	−0.989827	−	0.142277i	$-0.954558\pi$
$967$	−25.4764	−	35.0653i	−0.819267	−	1.12762i	0.170560	−	0.985347i	$-0.445442\pi$
$968$	34.4058	−	39.7791i	1.10584	−	1.27855i
$969$	20.6580	+	28.4332i	0.663629	+	0.913407i
$970$	−0.0254568	−	0.163295i	−0.000817369	−	0.00524309i
$971$	1.30615	+	8.24669i	0.0419162	+	0.264649i	0.999742	−	0.0226998i	$-0.00722619\pi$
$971$	1.30615	+	8.24669i	0.0419162	+	0.264649i	−0.957826	+	0.287349i	$0.907226\pi$
$972$	19.3355	+	6.37144i	0.620185	+	0.204364i
$973$	−2.32000	−	4.55326i	−0.0743758	−	0.145971i
$974$	6.61056	−	27.2850i	0.211816	−	0.874269i
$975$	25.0671	+	25.1024i	0.802791	+	0.803921i
$976$	−8.39686	−	1.40158i	−0.268777	−	0.0448634i
$977$	13.4017	−	41.2461i	0.428758	−	1.31958i	−0.470592	−	0.882351i	$-0.655960\pi$
$977$	13.4017	−	41.2461i	0.428758	−	1.31958i	0.899350	−	0.437230i	$-0.144040\pi$
$978$	−4.02538	+	3.42356i	−0.128717	+	0.109473i
$979$	100.487	−	15.9156i	3.21159	−	0.508666i
$980$	−24.7579	+	5.82593i	−0.790863	+	0.186103i
$981$	−0.993594	−	0.157370i	−0.0317230	−	0.00502443i
$982$	−22.7551	−	37.3067i	−0.726144	−	1.19051i
$983$	0.695693	+	0.957539i	0.0221891	+	0.0305407i	0.819967	−	0.572410i	$-0.193991\pi$
$983$	0.695693	+	0.957539i	0.0221891	+	0.0305407i	−0.797778	+	0.602951i	$0.793991\pi$
$984$	40.8293	−	16.6146i	1.30159	−	0.529654i
$985$	28.9249	+	2.28668i	0.921623	+	0.0728596i
$986$	−9.53362	−	40.0771i	−0.303612	−	1.27631i
$987$	1.10560	−	2.16986i	0.0351916	−	0.0690675i
$988$	62.6044	+	10.1825i	1.99171	+	0.323948i
$989$	0.134253	+	0.263485i	0.00426898	+	0.00837835i
$990$	17.7507	+	0.0431335i	0.564155	+	0.00137087i
$991$	11.6884	+	35.9733i	0.371295	+	1.14273i	0.945944	+	0.324330i	$0.105139\pi$
$991$	11.6884	+	35.9733i	0.371295	+	1.14273i	−0.574649	+	0.818400i	$0.694861\pi$
$992$	32.9415	+	20.6604i	1.04589	+	0.655969i
$993$	−31.3913			−0.996174
$994$	−16.7268	+	6.88779i	−0.530543	+	0.218468i
$995$	23.2674	+	5.59468i	0.737628	+	0.177363i
$996$	−14.0524	+	7.08663i	−0.445267	+	0.224549i
$997$	−4.84825	−	30.6106i	−0.153546	−	0.969449i	−0.937337	−	0.348425i	$-0.886717\pi$
$997$	−4.84825	−	30.6106i	−0.153546	−	0.969449i	0.783791	−	0.621024i	$-0.213283\pi$
$998$	1.32094	+	5.55290i	0.0418135	+	0.175774i
$999$			35.0171i			1.10789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.be.a.21.18	✓	464
16.13	even	4	inner	400.2.be.a.221.29	yes	464
25.6	even	5	inner	400.2.be.a.181.29	yes	464
400.381	even	20	inner	400.2.be.a.381.18	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.be.a.21.18	✓	464	1.1	even	1	trivial
400.2.be.a.181.29	yes	464	25.6	even	5	inner
400.2.be.a.221.29	yes	464	16.13	even	4	inner
400.2.be.a.381.18	yes	464	400.381	even	20	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.be (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.741429 + 1.20428i) q^{2} +(-1.38564 + 0.219464i) q^{3} +(-0.900567 - 1.78577i) q^{4} +(0.522765 - 2.17410i) q^{5} +(0.763059 - 1.83141i) q^{6} -1.14575i q^{7} +(2.81827 + 0.239491i) q^{8} +(-0.981331 + 0.318854i) q^{9} +O(q^{10})\)	\(q+(-0.741429 + 1.20428i) q^{2} +(-1.38564 + 0.219464i) q^{3} +(-0.900567 - 1.78577i) q^{4} +(0.522765 - 2.17410i) q^{5} +(0.763059 - 1.83141i) q^{6} -1.14575i q^{7} +(2.81827 + 0.239491i) q^{8} +(-0.981331 + 0.318854i) q^{9} +(2.23063 + 2.24149i) q^{10} +(-4.84717 + 2.46976i) q^{11} +(1.63978 + 2.27680i) q^{12} +(4.50615 + 2.29600i) q^{13} +(1.37980 + 0.849495i) q^{14} +(-0.247227 + 3.12725i) q^{15} +(-2.37796 + 3.21641i) q^{16} +(-3.23203 + 2.34820i) q^{17} +(0.343599 - 1.41820i) q^{18} +(-0.980964 + 6.19356i) q^{19} +(-4.35323 + 1.02439i) q^{20} +(0.251452 + 1.58760i) q^{21} +(0.619561 - 7.66849i) q^{22} +(-0.792657 - 0.257550i) q^{23} +(-3.95767 + 0.286661i) q^{24} +(-4.45343 - 2.27309i) q^{25} +(-6.10600 + 3.72433i) q^{26} +(5.03981 - 2.56791i) q^{27} +(-2.04605 + 1.03183i) q^{28} +(7.20173 - 1.14064i) q^{29} +(-3.58278 - 2.61637i) q^{30} +(-5.56106 + 4.04035i) q^{31} +(-2.11036 - 5.24846i) q^{32} +(6.17442 - 4.48598i) q^{33} +(-0.431572 - 5.63328i) q^{34} +(-2.49098 - 0.598959i) q^{35} +(1.45315 + 1.46528i) q^{36} +(-2.81057 + 5.51605i) q^{37} +(-6.73145 - 5.77344i) q^{38} +(-6.74779 - 2.19249i) q^{39} +(1.99397 - 6.00201i) q^{40} +(-10.5651 + 3.43282i) q^{41} +(-2.09835 - 0.874278i) q^{42} +(-0.250889 - 0.250889i) q^{43} +(8.77563 + 6.43176i) q^{44} +(0.180215 + 2.30020i) q^{45} +(0.897860 - 0.763624i) q^{46} +(-1.22571 - 0.890528i) q^{47} +(2.58911 - 4.97867i) q^{48} +5.68725 q^{49} +(6.03933 - 3.67784i) q^{50} +(3.96308 - 3.96308i) q^{51} +(0.0420395 - 10.1146i) q^{52} +(-1.24024 - 7.83054i) q^{53} +(-0.644184 + 7.97326i) q^{54} +(2.83558 + 11.8294i) q^{55} +(0.274397 - 3.22904i) q^{56} -8.79734i q^{57} +(-3.96592 + 9.51858i) q^{58} +(-0.782428 + 1.53560i) q^{59} +(5.80720 - 2.37481i) q^{60} +(0.966208 + 1.89629i) q^{61} +(-0.742567 - 9.69268i) q^{62} +(0.365328 + 1.12436i) q^{63} +(7.88529 + 1.34990i) q^{64} +(7.34738 - 8.59656i) q^{65} +(0.824469 + 10.7618i) q^{66} +(-1.44398 + 9.11693i) q^{67} +(7.10401 + 3.65695i) q^{68} +(1.15486 + 0.182912i) q^{69} +(2.56820 - 2.55575i) q^{70} +(-6.56203 + 9.03186i) q^{71} +(-2.84202 + 0.663597i) q^{72} +(11.2412 + 3.65248i) q^{73} +(-4.55902 - 7.47446i) q^{74} +(6.66972 + 2.17231i) q^{75} +(11.9437 - 3.82594i) q^{76} +(2.82974 + 5.55367i) q^{77} +(7.64338 - 6.50064i) q^{78} +(-8.92591 - 6.48505i) q^{79} +(5.74969 + 6.85135i) q^{80} +(-3.91550 + 2.84478i) q^{81} +(3.69923 - 15.2686i) q^{82} +(-0.877457 + 5.54004i) q^{83} +(2.60865 - 1.87878i) q^{84} +(3.41565 + 8.25431i) q^{85} +(0.488156 - 0.116124i) q^{86} +(-9.72869 + 3.16104i) q^{87} +(-14.2521 + 5.79959i) q^{88} +(-17.7865 - 5.77918i) q^{89} +(-2.90369 - 1.48841i) q^{90} +(2.63065 - 5.16293i) q^{91} +(0.253915 + 1.64745i) q^{92} +(6.81892 - 6.81892i) q^{93} +(1.98122 - 0.815828i) q^{94} +(12.9526 + 5.37049i) q^{95} +(4.07606 + 6.80934i) q^{96} +(-0.0422810 - 0.0307189i) q^{97} +(-4.21669 + 6.84902i) q^{98} +(3.96919 - 3.96919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8}+O(q^{10}) \) 464 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 + 12 * q^8	\( 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8} - 14 q^{10} - 6 q^{11} + 10 q^{12} - 6 q^{13} + 6 q^{14} - 16 q^{15} - 6 q^{16} - 12 q^{17} - 24 q^{18} - 6 q^{19} - 22 q^{20} + 12 q^{21} + 10 q^{22} - 16 q^{24} + 4 q^{26} - 18 q^{27} + 18 q^{28} - 6 q^{29} - 6 q^{30} + 12 q^{31} - 36 q^{32} - 12 q^{33} - 30 q^{34} + 44 q^{35} - 82 q^{36} - 6 q^{37} - 76 q^{38} - 52 q^{40} - 10 q^{42} - 48 q^{43} + 36 q^{44} - 12 q^{45} - 14 q^{46} - 12 q^{47} - 116 q^{48} - 400 q^{49} + 10 q^{50} - 4 q^{51} + 32 q^{52} - 6 q^{53} - 30 q^{54} + 36 q^{56} + 26 q^{58} - 6 q^{59} + 48 q^{60} - 6 q^{61} - 34 q^{62} + 72 q^{63} - 24 q^{64} + 16 q^{65} + 92 q^{66} + 30 q^{67} + 28 q^{68} - 18 q^{69} + 60 q^{70} + 22 q^{72} + 28 q^{74} - 26 q^{75} - 76 q^{76} + 36 q^{77} + 14 q^{78} - 52 q^{79} - 34 q^{80} + 72 q^{81} + 56 q^{82} - 46 q^{83} + 112 q^{84} + 2 q^{85} - 46 q^{86} - 136 q^{88} - 42 q^{90} + 36 q^{91} - 4 q^{93} + 50 q^{94} - 40 q^{95} - 66 q^{96} - 12 q^{97} - 8 q^{98} - 40 q^{99}+O(q^{100}) \) 464 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 + 12 * q^8 - 14 * q^10 - 6 * q^11 + 10 * q^12 - 6 * q^13 + 6 * q^14 - 16 * q^15 - 6 * q^16 - 12 * q^17 - 24 * q^18 - 6 * q^19 - 22 * q^20 + 12 * q^21 + 10 * q^22 - 16 * q^24 + 4 * q^26 - 18 * q^27 + 18 * q^28 - 6 * q^29 - 6 * q^30 + 12 * q^31 - 36 * q^32 - 12 * q^33 - 30 * q^34 + 44 * q^35 - 82 * q^36 - 6 * q^37 - 76 * q^38 - 52 * q^40 - 10 * q^42 - 48 * q^43 + 36 * q^44 - 12 * q^45 - 14 * q^46 - 12 * q^47 - 116 * q^48 - 400 * q^49 + 10 * q^50 - 4 * q^51 + 32 * q^52 - 6 * q^53 - 30 * q^54 + 36 * q^56 + 26 * q^58 - 6 * q^59 + 48 * q^60 - 6 * q^61 - 34 * q^62 + 72 * q^63 - 24 * q^64 + 16 * q^65 + 92 * q^66 + 30 * q^67 + 28 * q^68 - 18 * q^69 + 60 * q^70 + 22 * q^72 + 28 * q^74 - 26 * q^75 - 76 * q^76 + 36 * q^77 + 14 * q^78 - 52 * q^79 - 34 * q^80 + 72 * q^81 + 56 * q^82 - 46 * q^83 + 112 * q^84 + 2 * q^85 - 46 * q^86 - 136 * q^88 - 42 * q^90 + 36 * q^91 - 4 * q^93 + 50 * q^94 - 40 * q^95 - 66 * q^96 - 12 * q^97 - 8 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

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