LMFDB - Embedded newform 322.2.i.e.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			71.1
Character	$\chi$	$=$	322.71
Dual form			322.2.i.e.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 - 0.540641i) q^{2} +(-0.459025 - 3.19259i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-1.51548 - 0.444984i) q^{5} +(-1.33989 + 2.93395i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-7.10346 + 2.08576i) q^{9} +O(q^{10})$	\(q+(-0.841254 - 0.540641i) q^{2} +(-0.459025 - 3.19259i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-1.51548 - 0.444984i) q^{5} +(-1.33989 + 2.93395i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-7.10346 + 2.08576i) q^{9} +(1.03432 + 1.19367i) q^{10} +(-3.31676 + 2.13155i) q^{11} +(2.71340 - 1.74379i) q^{12} +(1.69975 + 1.96161i) q^{13} +(0.959493 - 0.281733i) q^{14} +(-0.725010 + 5.04255i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(2.89606 - 6.34148i) q^{17} +(7.10346 + 2.08576i) q^{18} +(-0.897585 - 1.96544i) q^{19} +(-0.224780 - 1.56338i) q^{20} +(2.71340 + 1.74379i) q^{21} +3.94264 q^{22} +(-3.68001 + 3.07531i) q^{23} -3.22542 q^{24} +(-2.10761 - 1.35448i) q^{25} +(-0.369391 - 2.56917i) q^{26} +(5.90000 + 12.9192i) q^{27} +(-0.959493 - 0.281733i) q^{28} +(2.53672 - 5.55464i) q^{29} +(3.33613 - 3.85010i) q^{30} +(-1.46075 + 10.1598i) q^{31} +(0.959493 - 0.281733i) q^{32} +(8.32765 + 9.61062i) q^{33} +(-5.86478 + 3.76907i) q^{34} +(1.32872 - 0.853917i) q^{35} +(-4.84816 - 5.59508i) q^{36} +(1.02666 - 0.301455i) q^{37} +(-0.307499 + 2.13870i) q^{38} +(5.48241 - 6.32704i) q^{39} +(-0.656129 + 1.43672i) q^{40} +(-9.85631 - 2.89407i) q^{41} +(-1.33989 - 2.93395i) q^{42} +(-0.247191 - 1.71925i) q^{43} +(-3.31676 - 2.13155i) q^{44} +11.6933 q^{45} +(4.75846 - 0.597548i) q^{46} -6.77019 q^{47} +(2.71340 + 1.74379i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(1.04075 + 2.27892i) q^{50} +(-21.5751 - 6.33503i) q^{51} +(-1.07825 + 2.36103i) q^{52} +(-2.61584 + 3.01884i) q^{53} +(2.02125 - 14.0581i) q^{54} +(5.97497 - 1.75441i) q^{55} +(0.654861 + 0.755750i) q^{56} +(-5.86283 + 3.76781i) q^{57} +(-5.13709 + 3.30141i) q^{58} +(-0.713448 - 0.823363i) q^{59} +(-4.88805 + 1.43526i) q^{60} +(1.25414 - 8.72276i) q^{61} +(6.72164 - 7.75719i) q^{62} +(3.07546 - 6.73432i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.70304 - 3.72914i) q^{65} +(-1.80977 - 12.5872i) q^{66} +(-4.61008 - 2.96272i) q^{67} +6.97148 q^{68} +(11.5074 + 10.3371i) q^{69} -1.57945 q^{70} +(-3.57835 - 2.29967i) q^{71} +(1.05361 + 7.32799i) q^{72} +(1.57632 + 3.45166i) q^{73} +(-1.02666 - 0.301455i) q^{74} +(-3.35686 + 7.35049i) q^{75} +(1.41495 - 1.63294i) q^{76} +(0.561096 - 3.90251i) q^{77} +(-8.03275 + 2.35863i) q^{78} +(-5.51737 - 6.36739i) q^{79} +(1.32872 - 0.853917i) q^{80} +(19.8532 - 12.7589i) q^{81} +(6.72700 + 7.76338i) q^{82} +(6.31081 - 1.85302i) q^{83} +(-0.459025 + 3.19259i) q^{84} +(-7.21076 + 8.32166i) q^{85} +(-0.721547 + 1.57997i) q^{86} +(-18.8981 - 5.54899i) q^{87} +(1.63783 + 3.58635i) q^{88} +(-1.88932 - 13.1405i) q^{89} +(-9.83699 - 6.32185i) q^{90} -2.59559 q^{91} +(-4.32613 - 2.06993i) q^{92} +33.1065 q^{93} +(5.69545 + 3.66024i) q^{94} +(0.485681 + 3.37798i) q^{95} +(-1.33989 - 2.93395i) q^{96} +(0.931081 + 0.273390i) q^{97} +(-0.415415 + 0.909632i) q^{98} +(19.1146 - 22.0594i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	$ 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} + 2 q^{12} + 4 q^{13} + 4 q^{14} - 11 q^{15} - 4 q^{16} - 21 q^{17} + 4 q^{19} + 2 q^{20} + 2 q^{21} - 11 q^{23} - 2 q^{24} + 5 q^{25} - 15 q^{26} + 95 q^{27} - 4 q^{28} + 22 q^{30} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 10 q^{34} - 9 q^{35} + 41 q^{37} + 7 q^{38} - 38 q^{39} - 13 q^{40} + 25 q^{41} - 2 q^{42} - 59 q^{43} - 6 q^{45} + 11 q^{46} - 60 q^{47} + 2 q^{48} - 4 q^{49} + 61 q^{50} - 87 q^{51} + 4 q^{52} + 47 q^{53} - 29 q^{54} - 30 q^{55} + 4 q^{56} + 20 q^{57} - 96 q^{59} - 11 q^{60} + 84 q^{61} - 65 q^{62} - 4 q^{64} + 52 q^{65} - 3 q^{66} + 11 q^{67} - 10 q^{68} - 42 q^{69} - 2 q^{70} - 13 q^{71} + 11 q^{72} - 48 q^{73} - 41 q^{74} + 23 q^{75} + 26 q^{76} - 83 q^{78} + 80 q^{79} - 9 q^{80} + 2 q^{81} + 30 q^{82} - 20 q^{83} + 2 q^{84} - 71 q^{85} - 40 q^{86} + 99 q^{87} - 30 q^{89} + 116 q^{90} + 26 q^{91} - 22 q^{92} + 20 q^{93} - 17 q^{94} - 4 q^{95} - 2 q^{96} - 56 q^{97} + 4 q^{98} + 138 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 + 2 * q^12 + 4 * q^13 + 4 * q^14 - 11 * q^15 - 4 * q^16 - 21 * q^17 + 4 * q^19 + 2 * q^20 + 2 * q^21 - 11 * q^23 - 2 * q^24 + 5 * q^25 - 15 * q^26 + 95 * q^27 - 4 * q^28 + 22 * q^30 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 10 * q^34 - 9 * q^35 + 41 * q^37 + 7 * q^38 - 38 * q^39 - 13 * q^40 + 25 * q^41 - 2 * q^42 - 59 * q^43 - 6 * q^45 + 11 * q^46 - 60 * q^47 + 2 * q^48 - 4 * q^49 + 61 * q^50 - 87 * q^51 + 4 * q^52 + 47 * q^53 - 29 * q^54 - 30 * q^55 + 4 * q^56 + 20 * q^57 - 96 * q^59 - 11 * q^60 + 84 * q^61 - 65 * q^62 - 4 * q^64 + 52 * q^65 - 3 * q^66 + 11 * q^67 - 10 * q^68 - 42 * q^69 - 2 * q^70 - 13 * q^71 + 11 * q^72 - 48 * q^73 - 41 * q^74 + 23 * q^75 + 26 * q^76 - 83 * q^78 + 80 * q^79 - 9 * q^80 + 2 * q^81 + 30 * q^82 - 20 * q^83 + 2 * q^84 - 71 * q^85 - 40 * q^86 + 99 * q^87 - 30 * q^89 + 116 * q^90 + 26 * q^91 - 22 * q^92 + 20 * q^93 - 17 * q^94 - 4 * q^95 - 2 * q^96 - 56 * q^97 + 4 * q^98 + 138 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$

Coefficient data

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

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

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

$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$3$	−0.459025	−	3.19259i	−0.265018	−	1.84324i	−0.493562	−	0.869710i	$-0.664306\pi$
$3$	−0.459025	−	3.19259i	−0.265018	−	1.84324i	0.228544	−	0.973534i	$-0.426604\pi$
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	−1.51548	−	0.444984i	−0.677741	−	0.199003i	−0.0752938	−	0.997161i	$-0.523989\pi$
$5$	−1.51548	−	0.444984i	−0.677741	−	0.199003i	−0.602447	+	0.798159i	$0.705808\pi$
$6$	−1.33989	+	2.93395i	−0.547007	+	1.19778i
$7$	−0.654861	+	0.755750i	−0.247514	+	0.285646i
$7$	−0.654861	+	0.755750i	−0.247514	+	0.285646i
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	−7.10346	+	2.08576i	−2.36782	+	0.695255i
$10$	1.03432	+	1.19367i	0.327082	+	0.377472i
$11$	−3.31676	+	2.13155i	−1.00004	+	0.642687i	−0.934797	−	0.355183i	$-0.884419\pi$
$11$	−3.31676	+	2.13155i	−1.00004	+	0.642687i	−0.0652432	+	0.997869i	$0.520782\pi$
$12$	2.71340	−	1.74379i	0.783291	−	0.503390i
$13$	1.69975	+	1.96161i	0.471426	+	0.544054i	0.940808	−	0.338941i	$-0.110069\pi$
$13$	1.69975	+	1.96161i	0.471426	+	0.544054i	−0.469382	+	0.882995i	$0.655523\pi$
$14$	0.959493	−	0.281733i	0.256435	−	0.0752962i
$15$	−0.725010	+	5.04255i	−0.187197	+	1.30198i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	2.89606	−	6.34148i	0.702397	−	1.53804i	−0.134643	−	0.990894i	$-0.542989\pi$
$17$	2.89606	−	6.34148i	0.702397	−	1.53804i	0.837040	−	0.547141i	$-0.184284\pi$
$18$	7.10346	+	2.08576i	1.67430	+	0.491619i
$19$	−0.897585	−	1.96544i	−0.205920	−	0.450902i	0.778290	−	0.627905i	$-0.216087\pi$
$19$	−0.897585	−	1.96544i	−0.205920	−	0.450902i	−0.984210	+	0.177002i	$0.943360\pi$
$20$	−0.224780	−	1.56338i	−0.0502623	−	0.349582i
$21$	2.71340	+	1.74379i	0.592112	+	0.380527i
$22$	3.94264			0.840573
$23$	−3.68001	+	3.07531i	−0.767336	+	0.641246i
$23$	−3.68001	+	3.07531i	−0.767336	+	0.641246i
$24$	−3.22542			−0.658387
$25$	−2.10761	−	1.35448i	−0.421523	−	0.270896i
$26$	−0.369391	−	2.56917i	−0.0724435	−	0.503855i
$27$	5.90000	+	12.9192i	1.13546	+	2.48630i
$28$	−0.959493	−	0.281733i	−0.181327	−	0.0532424i
$29$	2.53672	−	5.55464i	0.471057	−	1.03147i	−0.513770	−	0.857928i	$-0.671751\pi$
$29$	2.53672	−	5.55464i	0.471057	−	1.03147i	0.984826	−	0.173542i	$-0.0555213\pi$
$30$	3.33613	−	3.85010i	0.609091	−	0.702928i
$31$	−1.46075	+	10.1598i	−0.262359	+	1.82475i	0.252646	+	0.967559i	$0.418699\pi$
$31$	−1.46075	+	10.1598i	−0.262359	+	1.82475i	−0.515005	+	0.857187i	$0.672210\pi$
$32$	0.959493	−	0.281733i	0.169616	−	0.0498038i
$33$	8.32765	+	9.61062i	1.44966	+	1.67299i
$34$	−5.86478	+	3.76907i	−1.00580	+	0.646390i
$35$	1.32872	−	0.853917i	0.224595	−	0.144338i
$36$	−4.84816	−	5.59508i	−0.808027	−	0.932513i
$37$	1.02666	−	0.301455i	0.168782	−	0.0495589i	−0.196250	−	0.980554i	$-0.562876\pi$
$37$	1.02666	−	0.301455i	0.168782	−	0.0495589i	0.365032	+	0.930995i	$0.381058\pi$
$38$	−0.307499	+	2.13870i	−0.0498829	+	0.346943i
$39$	5.48241	−	6.32704i	0.877888	−	1.01314i
$40$	−0.656129	+	1.43672i	−0.103743	+	0.227166i
$41$	−9.85631	−	2.89407i	−1.53930	−	0.451978i	−0.601416	−	0.798936i	$-0.705397\pi$
$41$	−9.85631	−	2.89407i	−1.53930	−	0.451978i	−0.937881	+	0.346957i	$0.887215\pi$
$42$	−1.33989	−	2.93395i	−0.206749	−	0.452718i
$43$	−0.247191	−	1.71925i	−0.0376963	−	0.262183i	0.962254	−	0.272153i	$-0.0877357\pi$
$43$	−0.247191	−	1.71925i	−0.0376963	−	0.262183i	−0.999950	+	0.00996948i	$0.996827\pi$
$44$	−3.31676	−	2.13155i	−0.500020	−	0.321343i
$45$	11.6933			1.74313
$46$	4.75846	−	0.597548i	0.701597	−	0.0881036i
$47$	−6.77019			−0.987534			−0.493767	−	0.869594i	$-0.664381\pi$
$47$	−6.77019			−0.987534			−0.493767	+	0.869594i	$0.664381\pi$
$48$	2.71340	+	1.74379i	0.391645	+	0.251695i
$49$	−0.142315	−	0.989821i	−0.0203307	−	0.141403i
$50$	1.04075	+	2.27892i	0.147184	+	0.322288i
$51$	−21.5751	−	6.33503i	−3.02112	−	0.887082i
$52$	−1.07825	+	2.36103i	−0.149526	+	0.327416i
$53$	−2.61584	+	3.01884i	−0.359314	+	0.414670i	−0.906410	−	0.422400i	$-0.861188\pi$
$53$	−2.61584	+	3.01884i	−0.359314	+	0.414670i	0.547096	+	0.837070i	$0.315733\pi$
$54$	2.02125	−	14.0581i	0.275057	−	1.91307i
$55$	5.97497	−	1.75441i	0.805665	−	0.236565i
$56$	0.654861	+	0.755750i	0.0875094	+	0.100991i
$57$	−5.86283	+	3.76781i	−0.776550	+	0.499059i
$58$	−5.13709	+	3.30141i	−0.674533	+	0.433496i
$59$	−0.713448	−	0.823363i	−0.0928830	−	0.107193i	0.707405	−	0.706808i	$-0.249866\pi$
$59$	−0.713448	−	0.823363i	−0.0928830	−	0.107193i	−0.800288	+	0.599616i	$0.795320\pi$
$60$	−4.88805	+	1.43526i	−0.631044	+	0.185291i
$61$	1.25414	−	8.72276i	0.160577	−	1.11684i	−0.736973	−	0.675922i	$-0.763746\pi$
$61$	1.25414	−	8.72276i	0.160577	−	1.11684i	0.897550	−	0.440913i	$-0.145345\pi$
$62$	6.72164	−	7.75719i	0.853649	−	0.985164i
$63$	3.07546	−	6.73432i	0.387472	−	0.848445i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−1.70304	−	3.72914i	−0.211236	−	0.462543i
$66$	−1.80977	−	12.5872i	−0.222767	−	1.54938i
$67$	−4.61008	−	2.96272i	−0.563210	−	0.361953i	0.227845	−	0.973697i	$-0.426832\pi$
$67$	−4.61008	−	2.96272i	−0.563210	−	0.361953i	−0.791056	+	0.611744i	$0.790468\pi$
$68$	6.97148			0.845416
$69$	11.5074	+	10.3371i	1.38533	+	1.24444i
$70$	−1.57945			−0.188781
$71$	−3.57835	−	2.29967i	−0.424672	−	0.272920i	0.310800	−	0.950475i	$-0.399403\pi$
$71$	−3.57835	−	2.29967i	−0.424672	−	0.272920i	−0.735472	+	0.677555i	$0.763039\pi$
$72$	1.05361	+	7.32799i	0.124169	+	0.863612i
$73$	1.57632	+	3.45166i	0.184494	+	0.403986i	0.979168	−	0.203050i	$-0.0650855\pi$
$73$	1.57632	+	3.45166i	0.184494	+	0.403986i	−0.794674	+	0.607036i	$0.792358\pi$
$74$	−1.02666	−	0.301455i	−0.119347	−	0.0350434i
$75$	−3.35686	+	7.35049i	−0.387616	+	0.848762i
$76$	1.41495	−	1.63294i	0.162306	−	0.187312i
$77$	0.561096	−	3.90251i	0.0639428	−	0.444732i
$78$	−8.03275	+	2.35863i	−0.909530	+	0.267062i
$79$	−5.51737	−	6.36739i	−0.620753	−	0.716387i	0.355097	−	0.934829i	$-0.384448\pi$
$79$	−5.51737	−	6.36739i	−0.620753	−	0.716387i	−0.975850	+	0.218443i	$0.929902\pi$
$80$	1.32872	−	0.853917i	0.148556	−	0.0954709i
$81$	19.8532	−	12.7589i	2.20591	−	1.41765i
$82$	6.72700	+	7.76338i	0.742873	+	0.857321i
$83$	6.31081	−	1.85302i	0.692702	−	0.203396i	0.0836138	−	0.996498i	$-0.473354\pi$
$83$	6.31081	−	1.85302i	0.692702	−	0.203396i	0.609088	+	0.793103i	$0.291536\pi$
$84$	−0.459025	+	3.19259i	−0.0500838	+	0.348340i
$85$	−7.21076	+	8.32166i	−0.782117	+	0.902611i
$86$	−0.721547	+	1.57997i	−0.0778064	+	0.170372i
$87$	−18.8981	−	5.54899i	−2.02609	−	0.594914i
$88$	1.63783	+	3.58635i	0.174593	+	0.382306i
$89$	−1.88932	−	13.1405i	−0.200268	−	1.39289i	−0.803489	−	0.595320i	$-0.797025\pi$
$89$	−1.88932	−	13.1405i	−0.200268	−	1.39289i	0.603221	−	0.797574i	$-0.293884\pi$
$90$	−9.83699	−	6.32185i	−1.03691	−	0.666381i
$91$	−2.59559			−0.272092
$92$	−4.32613	−	2.06993i	−0.451030	−	0.215805i
$93$	33.1065			3.43298
$94$	5.69545	+	3.66024i	0.587441	+	0.377525i
$95$	0.485681	+	3.37798i	0.0498298	+	0.346574i
$96$	−1.33989	−	2.93395i	−0.136752	−	0.299445i
$97$	0.931081	+	0.273390i	0.0945370	+	0.0277586i	0.328659	−	0.944449i	$-0.393403\pi$
$97$	0.931081	+	0.273390i	0.0945370	+	0.0277586i	−0.234122	+	0.972207i	$0.575222\pi$
$98$	−0.415415	+	0.909632i	−0.0419633	+	0.0918867i
$99$	19.1146	−	22.0594i	1.92108	−	2.21705i
$100$	0.356545	−	2.47982i	0.0356545	−	0.247982i
$101$	4.98162	−	1.46274i	0.495690	−	0.145548i	−0.0243263	−	0.999704i	$-0.507744\pi$
$101$	4.98162	−	1.46274i	0.495690	−	0.145548i	0.520016	+	0.854156i	$0.325926\pi$
$102$	14.7252	+	16.9938i	1.45801	+	1.68263i
$103$	0.816718	−	0.524873i	0.0804736	−	0.0517172i	−0.499785	−	0.866149i	$-0.666588\pi$
$103$	0.816718	−	0.524873i	0.0804736	−	0.0517172i	0.580259	+	0.814432i	$0.302951\pi$
$104$	2.18355	−	1.40328i	0.214114	−	0.137603i
$105$	−3.33613	−	3.85010i	−0.325573	−	0.375731i
$106$	3.83270	−	1.12538i	0.372264	−	0.109307i
$107$	1.78786	−	12.4349i	0.172839	−	1.20212i	−0.700009	−	0.714134i	$-0.746821\pi$
$107$	1.78786	−	12.4349i	0.172839	−	1.20212i	0.872849	−	0.487991i	$-0.162270\pi$
$108$	−9.30077	+	10.7337i	−0.894967	+	1.03285i
$109$	−7.44330	+	16.2985i	−0.712938	+	1.56112i	0.110605	+	0.993864i	$0.464721\pi$
$109$	−7.44330	+	16.2985i	−0.712938	+	1.56112i	−0.823544	+	0.567253i	$0.808006\pi$
$110$	−5.97497	−	1.75441i	−0.569691	−	0.167276i
$111$	−1.43369	−	3.13934i	−0.136080	−	0.297973i
$112$	−0.142315	−	0.989821i	−0.0134475	−	0.0935293i
$113$	−2.93542	−	1.88648i	−0.276141	−	0.177465i	0.395239	−	0.918578i	$-0.370662\pi$
$113$	−2.93542	−	1.88648i	−0.276141	−	0.177465i	−0.671380	+	0.741113i	$0.734298\pi$
$114$	6.96916			0.652721
$115$	6.94543	−	3.02301i	0.647665	−	0.281897i
$116$	6.10647			0.566971
$117$	−16.1656	−	10.3890i	−1.49451	−	0.960461i
$118$	0.155047	+	1.07838i	0.0142732	+	0.0992725i
$119$	2.89606	+	6.34148i	0.265481	+	0.581323i
$120$	4.88805	+	1.43526i	0.446216	+	0.131021i
$121$	1.88781	−	4.13373i	0.171619	−	0.375793i
$122$	−5.77093	+	6.66001i	−0.522476	+	0.602969i
$123$	−4.71530	+	32.7956i	−0.425164	+	2.95708i
$124$	−9.84846	+	2.89177i	−0.884418	+	0.259688i
$125$	7.76293	+	8.95889i	0.694337	+	0.801308i
$126$	−6.22809	+	4.00255i	−0.554843	+	0.356576i
$127$	1.32487	−	0.851443i	0.117563	−	0.0755533i	−0.480538	−	0.876974i	$-0.659558\pi$
$127$	1.32487	−	0.851443i	0.117563	−	0.0755533i	0.598101	+	0.801421i	$0.295922\pi$
$128$	0.654861	+	0.755750i	0.0578821	+	0.0667995i
$129$	−5.37540	+	1.57836i	−0.473278	+	0.138967i
$130$	−0.583436	+	4.05788i	−0.0511707	+	0.355900i
$131$	−12.4195	+	14.3329i	−1.08510	+	1.25227i	−0.119329	+	0.992855i	$0.538074\pi$
$131$	−12.4195	+	14.3329i	−1.08510	+	1.25227i	−0.965767	+	0.259412i	$0.916471\pi$
$132$	−5.28270	+	11.5675i	−0.459800	+	1.00682i
$133$	2.07317	+	0.608738i	0.179767	+	0.0527843i
$134$	2.27648	+	4.98479i	0.196658	+	0.430620i
$135$	−3.19247	−	22.2041i	−0.274764	−	1.91103i
$136$	−5.86478	−	3.76907i	−0.502901	−	0.323195i
$137$	−12.1371			−1.03694			−0.518472	−	0.855094i	$-0.673499\pi$
$137$	−12.1371			−1.03694			−0.518472	+	0.855094i	$0.673499\pi$
$138$	−4.09198	−	14.9175i	−0.348333	−	1.26986i
$139$	15.6737			1.32943			0.664715	−	0.747097i	$-0.268553\pi$
$139$	15.6737			1.32943			0.664715	+	0.747097i	$0.268553\pi$
$140$	1.32872	+	0.853917i	0.112297	+	0.0721692i
$141$	3.10769	+	21.6145i	0.261715	+	1.82027i
$142$	1.76701	+	3.86921i	0.148284	+	0.324697i
$143$	−9.81894	−	2.88310i	−0.821101	−	0.241097i
$144$	3.07546	−	6.73432i	0.256289	−	0.561194i
$145$	−6.31606	+	7.28912i	−0.524520	+	0.605328i
$146$	0.540023	−	3.75594i	0.0446926	−	0.310844i
$147$	−3.09477	+	0.908706i	−0.255252	+	0.0749488i
$148$	0.700704	+	0.808655i	0.0575975	+	0.0664711i
$149$	8.86940	−	5.70001i	0.726609	−	0.466963i	−0.124321	−	0.992242i	$-0.539675\pi$
$149$	8.86940	−	5.70001i	0.726609	−	0.466963i	0.850930	+	0.525279i	$0.176039\pi$
$150$	6.79794	−	4.36877i	0.555050	−	0.356709i
$151$	−4.23592	−	4.88851i	−0.344714	−	0.397821i	0.556746	−	0.830682i	$-0.312049\pi$
$151$	−4.23592	−	4.88851i	−0.344714	−	0.397821i	−0.901461	+	0.432861i	$0.857504\pi$
$152$	−2.07317	+	0.608738i	−0.168156	+	0.0493752i
$153$	−7.34520	+	51.0870i	−0.593824	+	4.13014i
$154$	−2.58188	+	2.97965i	−0.208054	+	0.240107i
$155$	6.73466	−	14.7468i	0.540941	−	1.18450i
$156$	8.03275	+	2.35863i	0.643135	+	0.188841i
$157$	−0.158995	−	0.348151i	−0.0126892	−	0.0277855i	0.903181	−	0.429259i	$-0.141225\pi$
$157$	−0.158995	−	0.348151i	−0.0126892	−	0.0277855i	−0.915870	+	0.401474i	$0.868498\pi$
$158$	1.19904	+	8.33950i	0.0953905	+	0.663455i
$159$	10.8387	+	6.96559i	0.859563	+	0.552408i
$160$	−1.57945			−0.124867
$161$	0.0857335	−	4.79507i	0.00675675	−	0.377904i
$162$	−23.5995			−1.85415
$163$	−3.07643	−	1.97710i	−0.240965	−	0.154859i	0.414585	−	0.910011i	$-0.363927\pi$
$163$	−3.07643	−	1.97710i	−0.240965	−	0.154859i	−0.655550	+	0.755152i	$0.727563\pi$
$164$	−1.46192	−	10.1679i	−0.114157	−	0.793976i
$165$	−8.34378	−	18.2703i	−0.649562	−	1.42234i
$166$	−6.31081	−	1.85302i	−0.489814	−	0.143822i
$167$	3.53692	−	7.74477i	0.273695	−	0.599308i	−0.722011	−	0.691882i	$-0.756782\pi$
$167$	3.53692	−	7.74477i	0.273695	−	0.599308i	0.995706	+	0.0925734i	$0.0295093\pi$
$168$	2.11220	−	2.43761i	0.162960	−	0.188066i
$169$	0.891307	−	6.19917i	0.0685621	−	0.476860i
$170$	10.5651	−	3.10220i	0.810307	−	0.237928i
$171$	10.4754	+	12.0893i	0.801074	+	0.924489i
$172$	1.46120	−	0.939056i	0.111415	−	0.0716023i
$173$	13.1355	−	8.44168i	0.998674	−	0.641809i	0.0642362	−	0.997935i	$-0.479539\pi$
$173$	13.1355	−	8.44168i	0.998674	−	0.641809i	0.934438	+	0.356126i	$0.115903\pi$
$174$	12.8981	+	14.8852i	0.977802	+	1.12844i
$175$	2.40384	−	0.705831i	0.181713	−	0.0533558i
$176$	0.561096	−	3.90251i	0.0422942	−	0.294163i
$177$	−2.30117	+	2.65569i	−0.172967	+	0.199614i
$178$	−5.51491	+	12.0760i	−0.413360	+	0.905132i
$179$	−0.936282	−	0.274917i	−0.0699810	−	0.0205483i	0.246555	−	0.969129i	$-0.420702\pi$
$179$	−0.936282	−	0.274917i	−0.0699810	−	0.0205483i	−0.316536	+	0.948581i	$0.602520\pi$
$180$	4.85755	+	10.6366i	0.362061	+	0.792802i
$181$	−3.45685	−	24.0429i	−0.256946	−	1.78710i	−0.554286	−	0.832326i	$-0.687009\pi$
$181$	−3.45685	−	24.0429i	−0.256946	−	1.78710i	0.297340	−	0.954772i	$-0.403901\pi$
$182$	2.18355	+	1.40328i	0.161855	+	0.104018i
$183$	−28.4239			−2.10116
$184$	2.52028	+	4.08022i	0.185798	+	0.300798i
$185$	−1.69002			−0.124253
$186$	−27.8509	−	17.8987i	−2.04213	−	1.31240i
$187$	3.91167	+	27.2063i	0.286050	+	1.98952i
$188$	−2.81244	−	6.15839i	−0.205118	−	0.449146i
$189$	−13.6274	−	4.00135i	−0.991244	−	0.291056i
$190$	1.41769	−	3.10432i	0.102850	−	0.225211i
$191$	5.54057	−	6.39416i	0.400901	−	0.462665i	−0.519023	−	0.854760i	$-0.673704\pi$
$191$	5.54057	−	6.39416i	0.400901	−	0.462665i	0.919925	+	0.392095i	$0.128250\pi$
$192$	−0.459025	+	3.19259i	−0.0331273	+	0.230405i
$193$	−8.52827	+	2.50413i	−0.613879	+	0.180251i	−0.573867	−	0.818948i	$-0.694558\pi$
$193$	−8.52827	+	2.50413i	−0.613879	+	0.180251i	−0.0400112	+	0.999199i	$0.512739\pi$
$194$	−0.635470	−	0.733371i	−0.0456241	−	0.0526530i
$195$	−11.1239	+	7.14888i	−0.796598	+	0.511942i
$196$	0.841254	−	0.540641i	0.0600895	−	0.0386172i
$197$	4.85624	+	5.60440i	0.345993	+	0.399297i	0.901898	−	0.431948i	$-0.142174\pi$
$197$	4.85624	+	5.60440i	0.345993	+	0.399297i	−0.555905	+	0.831246i	$0.687628\pi$
$198$	−28.0064	+	8.22341i	−1.99033	+	0.584413i
$199$	1.29013	−	8.97307i	0.0914551	−	0.636084i	−0.891607	−	0.452811i	$-0.850421\pi$
$199$	1.29013	−	8.97307i	0.0914551	−	0.636084i	0.983062	−	0.183274i	$-0.0586695\pi$
$200$	−1.64064	+	1.89340i	−0.116011	+	0.133883i
$201$	−7.34260	+	16.0781i	−0.517907	+	1.13406i
$202$	−4.98162	−	1.46274i	−0.350506	−	0.102918i
$203$	2.53672	+	5.55464i	0.178043	+	0.389859i
$204$	−3.20009	−	22.2571i	−0.224051	−	1.55831i
$205$	13.6492	+	8.77180i	0.953300	+	0.612649i
$206$	−0.970834			−0.0676412
$207$	19.7265	−	29.5210i	1.37108	−	2.05185i
$208$	−2.59559			−0.179972
$209$	7.16650	+	4.60563i	0.495717	+	0.318578i
$210$	0.725010	+	5.04255i	0.0500304	+	0.347969i
$211$	9.99072	+	21.8766i	0.687790	+	1.50605i	0.854173	+	0.519988i	$0.174064\pi$
$211$	9.99072	+	21.8766i	0.687790	+	1.50605i	−0.166384	+	0.986061i	$0.553209\pi$
$212$	−3.83270	−	1.12538i	−0.263231	−	0.0772915i
$213$	−5.69934	+	12.4798i	−0.390513	+	0.855103i
$214$	−8.22685	+	9.49429i	−0.562376	+	0.649016i
$215$	−0.390427	+	2.71548i	−0.0266269	+	0.185194i
$216$	13.6274	−	4.00135i	0.927224	−	0.272258i
$217$	−6.72164	−	7.75719i	−0.456295	−	0.526592i
$218$	15.0734	−	9.68706i	1.02090	−	0.656090i
$219$	10.2962	−	6.61694i	0.695750	−	0.447131i
$220$	4.07796	+	4.70622i	0.274936	+	0.317293i
$221$	17.3621	−	5.09798i	1.16790	−	0.342927i
$222$	−0.491159	+	3.41609i	−0.0329645	+	0.229273i
$223$	15.1756	−	17.5136i	1.01624	−	1.17280i	0.0313661	−	0.999508i	$-0.490014\pi$
$223$	15.1756	−	17.5136i	1.01624	−	1.17280i	0.984871	−	0.173292i	$-0.0554403\pi$
$224$	−0.415415	+	0.909632i	−0.0277561	+	0.0607773i
$225$	17.7965	+	5.22552i	1.18643	+	0.348368i
$226$	1.44952	+	3.17401i	0.0964208	+	0.211132i
$227$	2.37743	+	16.5354i	0.157795	+	1.09749i	0.902684	+	0.430303i	$0.141593\pi$
$227$	2.37743	+	16.5354i	0.157795	+	1.09749i	−0.744889	+	0.667188i	$0.767498\pi$
$228$	−5.86283	−	3.76781i	−0.388275	−	0.249529i
$229$	1.60396			0.105993			0.0529963	−	0.998595i	$-0.483123\pi$
$229$	1.60396			0.105993			0.0529963	+	0.998595i	$0.483123\pi$
$230$	−7.47723	−	1.21187i	−0.493034	−	0.0799082i
$231$	−12.7167			−0.836696
$232$	−5.13709	−	3.30141i	−0.337266	−	0.216748i
$233$	3.11641	+	21.6751i	0.204163	+	1.41998i	0.791762	+	0.610830i	$0.209164\pi$
$233$	3.11641	+	21.6751i	0.204163	+	1.41998i	−0.587599	+	0.809152i	$0.699927\pi$
$234$	7.98263	+	17.4795i	0.521841	+	1.14267i
$235$	10.2601	+	3.01263i	0.669293	+	0.196522i
$236$	0.452580	−	0.991012i	0.0294605	−	0.0645094i
$237$	−17.7959	+	20.5375i	−1.15596	+	1.33405i
$238$	0.992145	−	6.90052i	0.0643112	−	0.447294i
$239$	8.23980	−	2.41942i	0.532989	−	0.156500i	−0.00415342	−	0.999991i	$-0.501322\pi$
$239$	8.23980	−	2.41942i	0.532989	−	0.156500i	0.537142	+	0.843492i	$0.319504\pi$
$240$	−3.33613	−	3.85010i	−0.215346	−	0.248523i
$241$	16.6283	−	10.6864i	1.07113	−	0.688371i	0.118635	−	0.992938i	$-0.462148\pi$
$241$	16.6283	−	10.6864i	1.07113	−	0.688371i	0.952491	+	0.304567i	$0.0985118\pi$
$242$	−3.82299	+	2.45688i	−0.245751	+	0.157935i
$243$	−21.9447	−	25.3255i	−1.40775	−	1.62463i
$244$	8.45549	−	2.48276i	0.541307	−	0.158942i
$245$	−0.224780	+	1.56338i	−0.0143607	+	0.0998805i
$246$	21.6974	−	25.0402i	1.38338	−	1.59650i
$247$	2.32976	−	5.10147i	0.148239	−	0.324599i
$248$	9.84846	+	2.89177i	0.625378	+	0.183627i
$249$	−8.81277	−	19.2973i	−0.558487	−	1.22291i
$250$	−1.68705	−	11.7337i	−0.106698	−	0.742102i
$251$	−13.1238	−	8.43413i	−0.828364	−	0.532357i	0.0563935	−	0.998409i	$-0.482040\pi$
$251$	−13.1238	−	8.43413i	−0.828364	−	0.532357i	−0.884758	+	0.466051i	$0.845676\pi$
$252$	7.40335			0.466367
$253$	5.65054	−	18.0442i	0.355246	−	1.13443i
$254$	−1.57488			−0.0988166
$255$	29.8776	+	19.2012i	1.87101	+	1.20242i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	11.9499	+	26.1666i	0.745414	+	1.63223i	0.774438	+	0.632650i	$0.218033\pi$
$257$	11.9499	+	26.1666i	0.745414	+	1.63223i	−0.0290245	+	0.999579i	$0.509240\pi$
$258$	5.37540	+	1.57836i	0.334658	+	0.0982644i
$259$	−0.444496	+	0.973310i	−0.0276196	+	0.0604786i
$260$	2.68468	−	3.09828i	0.166497	−	0.192147i
$261$	−6.43381	+	44.7482i	−0.398243	+	2.76984i
$262$	18.1969	−	5.34308i	1.12421	−	0.330097i
$263$	−7.21825	−	8.33031i	−0.445097	−	0.513669i	0.488221	−	0.872720i	$-0.337646\pi$
$263$	−7.21825	−	8.33031i	−0.445097	−	0.513669i	−0.933318	+	0.359051i	$0.883100\pi$
$264$	10.6979	−	6.87515i	0.658413	−	0.423136i
$265$	5.30758	−	3.41098i	0.326042	−	0.209535i
$266$	−1.41495	−	1.63294i	−0.0867564	−	0.100122i
$267$	−41.0851	+	12.0637i	−2.51437	+	0.738285i
$268$	0.779886	−	5.42423i	0.0476391	−	0.331338i
$269$	−3.52156	+	4.06409i	−0.214713	+	0.247792i	−0.852881	−	0.522105i	$-0.825147\pi$
$269$	−3.52156	+	4.06409i	−0.214713	+	0.247792i	0.638168	+	0.769897i	$0.279692\pi$
$270$	−9.31878	+	20.4053i	−0.567123	+	1.24183i
$271$	−1.16323	−	0.341554i	−0.0706610	−	0.0207479i	0.246211	−	0.969216i	$-0.420814\pi$
$271$	−1.16323	−	0.341554i	−0.0706610	−	0.0207479i	−0.316872	+	0.948468i	$0.602633\pi$
$272$	2.89606	+	6.34148i	0.175599	+	0.384509i
$273$	1.19144	+	8.28665i	0.0721093	+	0.501531i
$274$	10.2104	+	6.56183i	0.616833	+	0.396414i
$275$	9.87759			0.595641
$276$	−4.62263	+	14.7617i	−0.278250	+	0.888551i
$277$	12.1964			0.732812			0.366406	−	0.930455i	$-0.380588\pi$
$277$	12.1964			0.732812			0.366406	+	0.930455i	$0.380588\pi$
$278$	−13.1856	−	8.47386i	−0.790819	−	0.508228i
$279$	−10.8145	−	75.2162i	−0.647445	−	4.50308i
$280$	−0.656129	−	1.43672i	−0.0392112	−	0.0858606i
$281$	−21.3968	−	6.28268i	−1.27643	−	0.374793i	−0.427843	−	0.903853i	$-0.640727\pi$
$281$	−21.3968	−	6.28268i	−1.27643	−	0.374793i	−0.848585	+	0.529060i	$0.822545\pi$
$282$	9.07131	−	19.8634i	0.540189	−	1.18285i
$283$	20.5420	−	23.7067i	1.22109	−	1.40922i	0.337263	−	0.941410i	$-0.390499\pi$
$283$	20.5420	−	23.7067i	1.22109	−	1.40922i	0.883831	−	0.467807i	$-0.154956\pi$
$284$	0.605350	−	4.21030i	0.0359209	−	0.249835i
$285$	10.5616	−	3.10116i	0.625614	−	0.183697i
$286$	6.70149	+	7.73394i	0.396268	+	0.457317i
$287$	8.64171	−	5.55369i	0.510104	−	0.327824i
$288$	−6.22809	+	4.00255i	−0.366994	+	0.235853i
$289$	−20.6946	−	23.8829i	−1.21733	−	1.40487i
$290$	9.25420	−	2.71728i	0.543425	−	0.159564i
$291$	0.445433	−	3.09806i	0.0261118	−	0.181611i
$292$	−2.48491	+	2.86774i	−0.145418	+	0.167822i
$293$	6.53246	−	14.3041i	0.381631	−	0.835654i	−0.617176	−	0.786825i	$-0.711724\pi$
$293$	6.53246	−	14.3041i	0.381631	−	0.835654i	0.998807	−	0.0488297i	$-0.0155492\pi$
$294$	3.09477	+	0.908706i	0.180491	+	0.0529968i
$295$	0.714829	+	1.56526i	0.0416190	+	0.0911329i
$296$	−0.152278	−	1.05911i	−0.00885095	−	0.0615597i
$297$	−47.1068	−	30.2737i	−2.73341	−	1.75666i
$298$	−10.5431			−0.610744
$299$	−12.2877	−	1.99152i	−0.710614	−	0.115172i
$300$	−8.08073			−0.466541
$301$	1.46120	+	0.939056i	0.0842221	+	0.0541263i
$302$	0.920553	+	6.40259i	0.0529719	+	0.368427i
$303$	−6.95661	−	15.2329i	−0.399647	−	0.875105i
$304$	2.07317	+	0.608738i	0.118905	+	0.0349135i
$305$	−5.78211	+	12.6611i	−0.331083	+	0.724970i
$306$	33.7989	−	39.0060i	1.93215	−	2.22982i
$307$	−2.62558	+	18.2613i	−0.149850	+	1.04223i	0.766613	+	0.642109i	$0.221940\pi$
$307$	−2.62558	+	18.2613i	−0.149850	+	1.04223i	−0.916463	+	0.400119i	$0.868969\pi$
$308$	3.78293	−	1.11077i	0.215553	−	0.0632920i
$309$	−2.05060	−	2.36652i	−0.116654	−	0.134626i
$310$	−13.6383	+	8.76480i	−0.774604	+	0.497807i
$311$	−17.7386	+	11.3999i	−1.00586	+	0.646428i	−0.936319	−	0.351151i	$-0.885790\pi$
$311$	−17.7386	+	11.3999i	−1.00586	+	0.646428i	−0.0695423	+	0.997579i	$0.522154\pi$
$312$	−5.48241	−	6.32704i	−0.310380	−	0.358198i
$313$	−9.64993	+	2.83348i	−0.545447	+	0.160158i	−0.542836	−	0.839839i	$-0.682649\pi$
$313$	−9.64993	+	2.83348i	−0.545447	+	0.160158i	−0.00261102	+	0.999997i	$0.500831\pi$
$314$	−0.0544693	+	0.378842i	−0.00307388	+	0.0213793i
$315$	−7.65745	+	8.83717i	−0.431448	+	0.497918i
$316$	3.49998	−	7.66389i	0.196889	−	0.431127i
$317$	23.7682	+	6.97898i	1.33496	+	0.391979i	0.869868	−	0.493285i	$-0.164204\pi$
$317$	23.7682	+	6.97898i	1.33496	+	0.391979i	0.465089	+	0.885264i	$0.346022\pi$
$318$	−5.35219	−	11.7197i	−0.300136	−	0.657206i
$319$	3.42631	+	23.8305i	0.191837	+	1.33425i
$320$	1.32872	+	0.853917i	0.0742778	+	0.0477354i
$321$	−40.5201			−2.26161
$322$	−2.66453	+	3.98751i	−0.148489	+	0.222215i
$323$	−15.0632			−0.838142
$324$	19.8532	+	12.7589i	1.10296	+	0.708826i
$325$	−0.925444	−	6.43660i	−0.0513344	−	0.357038i
$326$	1.51916	+	3.32649i	0.0841382	+	0.184237i
$327$	55.4513	+	16.2820i	3.06646	+	0.900394i
$328$	−4.26732	+	9.34412i	−0.235623	+	0.515943i
$329$	4.43353	−	5.11657i	0.244429	−	0.282086i
$330$	−2.85845	+	19.8810i	−0.157353	+	1.09441i
$331$	−19.6507	+	5.76997i	−1.08010	+	0.317146i	−0.772919	−	0.634505i	$-0.781204\pi$
$331$	−19.6507	+	5.76997i	−1.08010	+	0.317146i	−0.307181	+	0.951651i	$0.599386\pi$
$332$	4.30718	+	4.97075i	0.236387	+	0.272805i
$333$	−6.66409	+	4.28275i	−0.365190	+	0.234693i
$334$	−7.16258	+	4.60311i	−0.391919	+	0.251871i
$335$	5.66810	+	6.54133i	0.309681	+	0.357391i
$336$	−3.09477	+	0.908706i	−0.168834	+	0.0495740i
$337$	1.54039	−	10.7137i	0.0839105	−	0.583611i	−0.903876	−	0.427795i	$-0.859290\pi$
$337$	1.54039	−	10.7137i	0.0839105	−	0.583611i	0.987786	−	0.155815i	$-0.0498005\pi$
$338$	−4.10134	+	4.73320i	−0.223084	+	0.257452i
$339$	−4.67532	+	10.2375i	−0.253929	+	0.556026i
$340$	−10.5651	−	3.10220i	−0.572973	−	0.168240i
$341$	−16.8111	−	36.8111i	−0.910371	−	1.99343i
$342$	−2.27652	−	15.8336i	−0.123100	−	0.856181i
$343$	0.841254	+	0.540641i	0.0454234	+	0.0291919i
$344$	−1.73693			−0.0936491
$345$	−12.8394	−	20.7863i	−0.691248	−	1.11910i
$346$	−15.6142			−0.839425
$347$	−6.26807	−	4.02824i	−0.336488	−	0.216247i	0.361475	−	0.932382i	$-0.382273\pi$
$347$	−6.26807	−	4.02824i	−0.336488	−	0.216247i	−0.697962	+	0.716134i	$0.745910\pi$
$348$	−2.80302	−	19.4955i	−0.150258	−	1.04507i
$349$	0.0802023	+	0.175619i	0.00429313	+	0.00940065i	0.911766	−	0.410709i	$-0.134719\pi$
$349$	0.0802023	+	0.175619i	0.00429313	+	0.00940065i	−0.907473	+	0.420110i	$0.861992\pi$
$350$	−2.40384	−	0.705831i	−0.128491	−	0.0377283i
$351$	−15.3140	+	33.5329i	−0.817399	+	1.78985i
$352$	−2.58188	+	2.97965i	−0.137615	+	0.158816i
$353$	2.82815	−	19.6702i	0.150527	−	1.04694i	−0.764812	−	0.644254i	$-0.777168\pi$
$353$	2.82815	−	19.6702i	0.150527	−	1.04694i	0.915339	−	0.402685i	$-0.131923\pi$
$354$	3.37164	−	0.990004i	0.179201	−	0.0526181i
$355$	4.39959	+	5.07740i	0.233506	+	0.269480i
$356$	11.1682	−	7.17737i	0.591913	−	0.380400i
$357$	18.9164	−	12.1568i	1.00116	−	0.643408i
$358$	0.639019	+	0.737467i	0.0337732	+	0.0389764i
$359$	−21.9575	+	6.44732i	−1.15887	+	0.340276i	−0.803995	−	0.594636i	$-0.797296\pi$
$359$	−21.9575	+	6.44732i	−1.15887	+	0.340276i	−0.354880	+	0.934912i	$0.615478\pi$
$360$	1.66412	−	11.5742i	0.0877070	−	0.610016i
$361$	9.38507	−	10.8309i	0.493951	−	0.570050i
$362$	−10.0905	+	22.0951i	−0.530345	+	1.16129i
$363$	−14.0639	−	4.12952i	−0.738161	−	0.216744i
$364$	−1.07825	−	2.36103i	−0.0565155	−	0.123752i
$365$	−0.852941	−	5.93234i	−0.0446450	−	0.310513i
$366$	23.9117	+	15.3671i	1.24988	+	0.803252i
$367$	−9.36285			−0.488737			−0.244368	−	0.969682i	$-0.578581\pi$
$367$	−9.36285			−0.488737			−0.244368	+	0.969682i	$0.578581\pi$
$368$	0.0857335	−	4.79507i	0.00446917	−	0.249960i
$369$	76.0503			3.95902
$370$	1.42174	+	0.913696i	0.0739126	+	0.0475008i
$371$	−0.568477	−	3.95384i	−0.0295139	−	0.205273i
$372$	13.7529	+	30.1147i	0.713056	+	1.56138i
$373$	−19.6058	−	5.75679i	−1.01515	−	0.298075i	−0.268492	−	0.963282i	$-0.586525\pi$
$373$	−19.6058	−	5.75679i	−1.01515	−	0.298075i	−0.746659	+	0.665206i	$0.768344\pi$
$374$	11.4181	−	25.0022i	0.590416	−	1.29283i
$375$	25.0387	−	28.8962i	1.29299	−	1.49219i
$376$	−0.963499	+	6.70128i	−0.0496887	+	0.345592i
$377$	15.2078	−	4.46543i	0.783244	−	0.229981i
$378$	9.30077	+	10.7337i	0.478380	+	0.552080i
$379$	−10.5603	+	6.78672i	−0.542448	+	0.348610i	−0.782996	−	0.622027i	$-0.786309\pi$
$379$	−10.5603	+	6.78672i	−0.542448	+	0.348610i	0.240548	+	0.970637i	$0.422673\pi$
$380$	−2.87096	+	1.84506i	−0.147277	+	0.0946494i
$381$	−3.32646	−	3.83894i	−0.170420	−	0.196675i
$382$	−8.11796	+	2.38365i	−0.415351	+	0.121958i
$383$	1.18669	−	8.25361i	0.0606370	−	0.421740i	−0.936780	−	0.349918i	$-0.886210\pi$
$383$	1.18669	−	8.25361i	0.0606370	−	0.421740i	0.997417	−	0.0718220i	$-0.0228813\pi$
$384$	2.11220	−	2.43761i	0.107788	−	0.124394i
$385$	−2.58688	+	5.66447i	−0.131840	+	0.288688i
$386$	8.52827	+	2.50413i	0.434078	+	0.127457i
$387$	5.34187	+	11.6971i	0.271542	+	0.594595i
$388$	0.138101	+	0.960512i	0.00701100	+	0.0487626i
$389$	20.3025	+	13.0476i	1.02938	+	0.661542i	0.942338	−	0.334663i	$-0.108622\pi$
$389$	20.3025	+	13.0476i	1.02938	+	0.661542i	0.0870415	+	0.996205i	$0.472259\pi$
$390$	13.2230			0.669572
$391$	8.84448	+	32.2430i	0.447284	+	1.63060i
$392$	−1.00000			−0.0505076
$393$	51.4598	+	33.0712i	2.59580	+	1.66822i
$394$	−1.05536	−	7.34021i	−0.0531684	−	0.369794i
$395$	5.52806	+	12.1048i	0.278147	+	0.609056i
$396$	28.0064	+	8.22341i	1.40737	+	0.413242i
$397$	5.45971	−	11.9551i	0.274015	−	0.600010i	−0.721728	−	0.692176i	$-0.756652\pi$
$397$	5.45971	−	11.9551i	0.274015	−	0.600010i	0.995744	+	0.0921668i	$0.0293793\pi$
$398$	−5.93654	+	6.85113i	−0.297572	+	0.343416i
$399$	0.991814	−	6.89822i	0.0496528	−	0.345343i
$400$	2.40384	−	0.705831i	0.120192	−	0.0352916i
$401$	16.1523	+	18.6407i	0.806606	+	0.930873i	0.998724	−	0.0504991i	$-0.0160812\pi$
$401$	16.1523	+	18.6407i	0.806606	+	0.930873i	−0.192118	+	0.981372i	$0.561536\pi$
$402$	14.8694	−	9.55601i	0.741620	−	0.476610i
$403$	−22.4124	+	14.4036i	−1.11644	+	0.717494i
$404$	3.39999	+	3.92380i	0.169156	+	0.195216i
$405$	−35.7645	+	10.5014i	−1.77715	+	0.521819i
$406$	0.869041	−	6.04431i	0.0431298	−	0.299974i
$407$	−2.76262	+	3.18824i	−0.136938	+	0.158035i
$408$	−9.34101	+	20.4540i	−0.462449	+	1.01262i
$409$	−22.4841	−	6.60191i	−1.11177	−	0.326444i	−0.326248	−	0.945284i	$-0.605785\pi$
$409$	−22.4841	−	6.60191i	−1.11177	−	0.326444i	−0.785517	+	0.618840i	$0.787603\pi$
$410$	−6.74003	−	14.7586i	−0.332866	−	0.728876i
$411$	5.57125	+	38.7489i	0.274810	+	1.91134i
$412$	0.816718	+	0.524873i	0.0402368	+	0.0258586i
$413$	1.08946			0.0536091
$414$	−32.5552	+	14.1697i	−1.60000	+	0.696402i
$415$	−10.3884			−0.509949
$416$	2.18355	+	1.40328i	0.107057	+	0.0688015i
$417$	−7.19464	−	50.0399i	−0.352323	−	2.45046i
$418$	−3.53885	−	7.74901i	−0.173091	−	0.379016i
$419$	−12.7494	−	3.74356i	−0.622849	−	0.182885i	−0.0449446	−	0.998989i	$-0.514311\pi$
$419$	−12.7494	−	3.74356i	−0.622849	−	0.182885i	−0.577904	+	0.816105i	$0.696129\pi$
$420$	2.11629	−	4.63404i	0.103265	−	0.226118i
$421$	−4.61323	+	5.32395i	−0.224835	+	0.259473i	−0.856948	−	0.515403i	$-0.827642\pi$
$421$	−4.61323	+	5.32395i	−0.224835	+	0.259473i	0.632113	+	0.774876i	$0.282188\pi$
$422$	3.42267	−	23.8052i	0.166613	−	1.15882i
$423$	48.0918	−	14.1210i	2.33830	−	0.686588i
$424$	2.61584	+	3.01884i	0.127037	+	0.146608i
$425$	−14.6932	+	9.44274i	−0.712724	+	0.458040i
$426$	11.5417	−	7.41740i	0.559197	−	0.359374i
$427$	5.77093	+	6.66001i	0.279275	+	0.322301i
$428$	12.0539	−	3.53933i	0.582645	−	0.171080i
$429$	−4.69742	+	32.6713i	−0.226794	+	1.57738i
$430$	1.79655	−	2.07333i	0.0866372	−	0.0999846i
$431$	−17.0855	+	37.4121i	−0.822982	+	1.80208i	−0.286757	+	0.958003i	$0.592577\pi$
$431$	−17.0855	+	37.4121i	−0.822982	+	1.80208i	−0.536225	+	0.844075i	$0.680150\pi$
$432$	−13.6274	−	4.00135i	−0.655646	−	0.192515i
$433$	0.722146	+	1.58128i	0.0347041	+	0.0759915i	0.926190	−	0.377057i	$-0.123064\pi$
$433$	0.722146	+	1.58128i	0.0347041	+	0.0759915i	−0.891486	+	0.453048i	$0.850337\pi$
$434$	1.46075	+	10.1598i	0.0701184	+	0.487684i
$435$	26.1704	+	16.8187i	1.25478	+	0.806395i
$436$	−17.9177			−0.858104
$437$	9.34745	+	4.47248i	0.447149	+	0.213948i
$438$	−12.2391			−0.584805
$439$	4.60112	+	2.95696i	0.219599	+	0.141128i	0.645816	−	0.763493i	$-0.276517\pi$
$439$	4.60112	+	2.95696i	0.219599	+	0.141128i	−0.426216	+	0.904621i	$0.640154\pi$
$440$	−0.886225	−	6.16383i	−0.0422491	−	0.293849i
$441$	3.07546	+	6.73432i	0.146451	+	0.320682i
$442$	−17.3621	−	5.09798i	−0.825832	−	0.242486i
$443$	−14.6971	+	32.1821i	−0.698278	+	1.52902i	0.143768	+	0.989611i	$0.454078\pi$
$443$	−14.6971	+	32.1821i	−0.698278	+	1.52902i	−0.842047	+	0.539405i	$0.818649\pi$
$444$	2.26007	−	2.60826i	0.107258	−	0.123782i
$445$	−2.98410	+	20.7549i	−0.141460	+	0.983876i
$446$	−22.2352	+	6.52883i	−1.05287	+	0.309149i
$447$	−22.2691	−	25.6999i	−1.05329	−	1.21556i
$448$	0.841254	−	0.540641i	0.0397455	−	0.0255429i
$449$	−17.6668	+	11.3538i	−0.833750	+	0.535818i	−0.886467	−	0.462791i	$-0.846848\pi$
$449$	−17.6668	+	11.3538i	−0.833750	+	0.535818i	0.0527176	+	0.998609i	$0.483212\pi$
$450$	−12.1462	−	14.0175i	−0.572578	−	0.660791i
$451$	38.8599	−	11.4103i	1.82984	−	0.537289i
$452$	0.496584	−	3.45382i	0.0233574	−	0.162454i
$453$	−13.6626	+	15.7675i	−0.641926	+	0.740822i
$454$	6.93968	−	15.1958i	0.325695	−	0.713173i
$455$	3.93355	+	1.15499i	0.184408	+	0.0541470i
$456$	2.89509	+	6.33937i	0.135575	+	0.296868i
$457$	−1.45351	−	10.1094i	−0.0679921	−	0.472896i	−0.995161	−	0.0982531i	$-0.968675\pi$
$457$	−1.45351	−	10.1094i	−0.0679921	−	0.472896i	0.927169	−	0.374643i	$-0.122235\pi$
$458$	−1.34934	−	0.867166i	−0.0630504	−	0.0405200i
$459$	99.0136			4.62156
$460$	5.63506	+	5.06198i	0.262736	+	0.236016i
$461$	−36.2066			−1.68631			−0.843154	−	0.537672i	$-0.819304\pi$
$461$	−36.2066			−1.68631			−0.843154	+	0.537672i	$0.819304\pi$
$462$	10.6979	+	6.87515i	0.497713	+	0.319861i
$463$	1.32392	+	9.20806i	0.0615277	+	0.427935i	0.997182	+	0.0750173i	$0.0239012\pi$
$463$	1.32392	+	9.20806i	0.0615277	+	0.427935i	−0.935655	+	0.352917i	$0.885190\pi$
$464$	2.53672	+	5.55464i	0.117764	+	0.257868i
$465$	−50.1720	−	14.7318i	−2.32667	−	0.683173i
$466$	9.09675	−	19.9191i	0.421399	−	0.922735i
$467$	3.54146	−	4.08706i	0.163879	−	0.189127i	−0.667870	−	0.744278i	$-0.732794\pi$
$467$	3.54146	−	4.08706i	0.163879	−	0.189127i	0.831750	+	0.555151i	$0.187339\pi$
$468$	2.73473	−	19.0205i	0.126413	−	0.879221i
$469$	5.25803	−	1.54390i	0.242793	−	0.0712905i
$470$	−7.00256	−	8.08139i	−0.323004	−	0.372767i
$471$	−1.03852	+	0.667417i	−0.0478525	+	0.0307529i
$472$	−0.916516	+	0.589009i	−0.0421861	+	0.0271113i
$473$	4.48455	+	5.17544i	0.206200	+	0.237967i
$474$	26.0742	−	7.65609i	1.19763	−	0.351656i
$475$	−0.770385	+	5.35814i	−0.0353477	+	0.245849i
$476$	−4.56535	+	5.26869i	−0.209252	+	0.241490i
$477$	12.2849	−	26.9003i	0.562489	−	1.23168i
$478$	−8.23980	−	2.41942i	−0.376880	−	0.110662i
$479$	0.291423	+	0.638128i	0.0133155	+	0.0291568i	0.916173	−	0.400783i	$-0.131262\pi$
$479$	0.291423	+	0.638128i	0.0133155	+	0.0291568i	−0.902857	+	0.429940i	$0.858535\pi$
$480$	0.725010	+	5.04255i	0.0330920	+	0.230160i
$481$	2.33641	+	1.50152i	0.106531	+	0.0684633i
$482$	−19.7662			−0.900324
$483$	−15.3480	+	1.92734i	−0.698360	+	0.0876972i
$484$	4.54439			0.206563
$485$	−1.28938	−	0.828632i	−0.0585476	−	0.0376262i
$486$	4.76904	+	33.1694i	0.216328	+	1.50459i
$487$	−3.32707	−	7.28526i	−0.150764	−	0.330127i	0.819148	−	0.573582i	$-0.194446\pi$
$487$	−3.32707	−	7.28526i	−0.150764	−	0.330127i	−0.969912	+	0.243455i	$0.921719\pi$
$488$	−8.45549	−	2.48276i	−0.382762	−	0.112389i
$489$	−4.89992	+	10.7293i	−0.221582	+	0.485197i
$490$	1.03432	−	1.19367i	0.0467259	−	0.0539246i
$491$	1.76401	−	12.2690i	0.0796088	−	0.553691i	−0.910513	−	0.413481i	$-0.864313\pi$
$491$	1.76401	−	12.2690i	0.0796088	−	0.553691i	0.990122	−	0.140211i	$-0.0447780\pi$
$492$	−31.7908	+	9.33461i	−1.43324	+	0.420837i
$493$	−27.8782	−	32.1731i	−1.25557	−	1.44900i
$494$	−4.71798	+	3.03206i	−0.212272	+	0.136419i
$495$	−38.7837	+	24.9248i	−1.74320	+	1.12028i
$496$	−6.72164	−	7.75719i	−0.301811	−	0.348308i
$497$	4.08129	−	1.19838i	0.183071	−	0.0537545i
$498$	−3.01912	+	20.9984i	−0.135290	+	0.940963i
$499$	25.0955	−	28.9618i	1.12343	−	1.29651i	0.173226	−	0.984882i	$-0.444581\pi$
$499$	25.0955	−	28.9618i	1.12343	−	1.29651i	0.950205	−	0.311626i	$-0.100874\pi$
$500$	−4.92446	+	10.7831i	−0.220229	+	0.482233i
$501$	−26.3494	−	7.73689i	−1.17721	−	0.345659i
$502$	6.48057	+	14.1905i	0.289242	+	0.633352i
$503$	3.21208	+	22.3405i	0.143219	+	0.996113i	0.926996	+	0.375071i	$0.122382\pi$
$503$	3.21208	+	22.3405i	0.143219	+	0.996113i	−0.783777	+	0.621043i	$0.786709\pi$
$504$	−6.22809	−	4.00255i	−0.277421	−	0.178288i
$505$	−8.20042			−0.364914
$506$	−14.5090	+	12.1248i	−0.645002	+	0.539014i
$507$	−20.2006			−0.897139
$508$	1.32487	+	0.851443i	0.0587817	+	0.0377767i
$509$	−2.30942	−	16.0624i	−0.102363	−	0.711952i	−0.974777	−	0.223183i	$-0.928355\pi$
$509$	−2.30942	−	16.0624i	−0.102363	−	0.711952i	0.872413	−	0.488769i	$-0.162554\pi$
$510$	−14.7537	−	32.3061i	−0.653305	−	1.43054i
$511$	−3.64086	−	1.06905i	−0.161062	−	0.0472921i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	20.0961	−	23.1922i	0.887265	−	1.02396i
$514$	4.09385	−	28.4734i	0.180572	−	1.25591i
$515$	−1.47127	+	0.432005i	−0.0648321	+	0.0190364i
$516$	−3.66875	−	4.23396i	−0.161508	−	0.186390i
$517$	22.4551	−	14.4310i	0.987574	−	0.634675i
$518$	0.900145	−	0.578488i	0.0395501	−	0.0254173i
$519$	−32.9804	−	38.0614i	−1.44768	−	1.67071i
$520$	−3.93355	+	1.15499i	−0.172498	+	0.0506499i
$521$	−3.49150	+	24.2839i	−0.152966	+	1.06390i	0.758248	+	0.651966i	$0.226055\pi$
$521$	−3.49150	+	24.2839i	−0.152966	+	1.06390i	−0.911214	+	0.411933i	$0.864854\pi$
$522$	29.6051	−	34.1662i	1.29578	−	1.49541i
$523$	7.20482	−	15.7764i	0.315045	−	0.689852i	−0.684176	−	0.729317i	$-0.739838\pi$
$523$	7.20482	−	15.7764i	0.315045	−	0.689852i	0.999221	+	0.0394647i	$0.0125653\pi$
$524$	−18.1969	−	5.34308i	−0.794934	−	0.233414i
$525$	−3.35686	−	7.35049i	−0.146505	−	0.320802i
$526$	1.56868	+	10.9104i	0.0683975	+	0.475715i
$527$	60.1975	+	38.6866i	2.62224	+	1.68521i
$528$	−12.7167			−0.553422
$529$	4.08498	−	22.6343i	0.177608	−	0.984101i
$530$	−6.30913			−0.274051
$531$	6.78529	+	4.36064i	0.294456	+	0.189236i
$532$	0.307499	+	2.13870i	0.0133318	+	0.0927245i
$533$	−11.0762	−	24.2535i	−0.479763	−	1.05054i
$534$	41.0851	+	12.0637i	1.77793	+	0.522047i
$535$	−8.24278	+	18.0492i	−0.356366	+	0.780334i
$536$	−3.58864	+	4.14151i	−0.155006	+	0.178886i
$537$	−0.447921	+	3.11536i	−0.0193292	+	0.134438i
$538$	5.15974	−	1.51504i	0.222452	−	0.0653178i
$539$	2.58188	+	2.97965i	0.111209	+	0.128342i
$540$	18.8714	−	12.1279i	0.812095	−	0.521902i
$541$	−16.3505	+	10.5079i	−0.702965	+	0.451768i	−0.842674	−	0.538425i	$-0.819020\pi$
$541$	−16.3505	+	10.5079i	−0.702965	+	0.451768i	0.139709	+	0.990193i	$0.455383\pi$
$542$	0.793911	+	0.916222i	0.0341014	+	0.0393551i
$543$	−75.1725	+	22.0726i	−3.22596	+	0.947228i
$544$	0.992145	−	6.90052i	0.0425379	−	0.295857i
$545$	18.5327	−	21.3879i	0.793854	−	0.916157i
$546$	3.47780	−	7.61532i	0.148836	−	0.325906i
$547$	−36.8392	−	10.8170i	−1.57513	−	0.462500i	−0.626641	−	0.779308i	$-0.715571\pi$
$547$	−36.8392	−	10.8170i	−1.57513	−	0.462500i	−0.948490	+	0.316809i	$0.897389\pi$
$548$	−5.04195	−	11.0403i	−0.215381	−	0.471619i
$549$	9.28486	+	64.5776i	0.396268	+	2.75611i
$550$	−8.30956	−	5.34023i	−0.354321	−	0.227708i
$551$	−13.1942			−0.562092
$552$	11.8696	−	9.91916i	0.505203	−	0.422188i
$553$	8.42526			0.358278
$554$	−10.2603	−	6.59388i	−0.435918	−	0.280147i
$555$	0.775764	+	5.39555i	0.0329293	+	0.229029i
$556$	6.51111	+	14.2573i	0.276132	+	0.604646i
$557$	22.8458	+	6.70813i	0.968008	+	0.284233i	0.727265	−	0.686356i	$-0.240791\pi$
$557$	22.8458	+	6.70813i	0.968008	+	0.284233i	0.240742	+	0.970589i	$0.422609\pi$
$558$	−31.5673	+	69.1226i	−1.33635	+	2.92620i
$559$	2.95235	−	3.40719i	0.124871	−	0.144109i
$560$	−0.224780	+	1.56338i	−0.00949868	+	0.0660648i
$561$	85.0629	−	24.9767i	3.59136	−	1.05452i
$562$	14.6035	+	16.8533i	0.616011	+	0.710915i
$563$	−2.82245	+	1.81388i	−0.118952	+	0.0764460i	−0.598764	−	0.800925i	$-0.704341\pi$
$563$	−2.82245	+	1.81388i	−0.118952	+	0.0764460i	0.479812	+	0.877371i	$0.340705\pi$
$564$	−18.3702	+	11.8058i	−0.773526	+	0.497115i
$565$	3.60910	+	4.16512i	0.151836	+	0.175228i
$566$	−30.0978	+	8.83752i	−1.26511	+	0.371469i
$567$	−3.35856	+	23.3593i	−0.141046	+	0.980999i
$568$	−2.78551	+	3.21465i	−0.116877	+	0.134884i
$569$	−12.3416	+	27.0244i	−0.517389	+	1.13292i	0.453030	+	0.891495i	$0.350343\pi$
$569$	−12.3416	+	27.0244i	−0.517389	+	1.13292i	−0.970419	+	0.241428i	$0.922384\pi$
$570$	−10.5616	−	3.10116i	−0.442376	−	0.129893i
$571$	−9.45896	−	20.7122i	−0.395845	−	0.866780i	−0.997675	−	0.0681552i	$-0.978289\pi$
$571$	−9.45896	−	20.7122i	−0.395845	−	0.866780i	0.601830	−	0.798624i	$-0.294439\pi$
$572$	−1.45637	−	10.1293i	−0.0608941	−	0.423527i
$573$	−22.9572	−	14.7537i	−0.959051	−	0.616344i
$574$	−10.2724			−0.428762
$575$	11.9215	−	1.49705i	0.497160	−	0.0624314i
$576$	7.40335			0.308473
$577$	−7.47680	−	4.80505i	−0.311263	−	0.200037i	0.375677	−	0.926751i	$-0.377410\pi$
$577$	−7.47680	−	4.80505i	−0.311263	−	0.200037i	−0.686940	+	0.726714i	$0.741047\pi$
$578$	4.49737	+	31.2799i	0.187066	+	1.30107i
$579$	11.9094	+	26.0778i	0.494936	+	1.08376i
$580$	−9.25420	−	2.71728i	−0.384260	−	0.112829i
$581$	−2.73228	+	5.98287i	−0.113354	+	0.248211i
$582$	−2.04966	+	2.36543i	−0.0849610	+	0.0980503i
$583$	2.24130	−	15.5886i	0.0928251	−	0.645613i
$584$	3.64086	−	1.06905i	0.150660	−	0.0442377i
$585$	19.8756	+	22.9377i	0.821755	+	0.948355i
$586$	−13.2288	+	8.50166i	−0.546478	+	0.351200i
$587$	3.06619	−	1.97052i	0.126555	−	0.0813321i	−0.475832	−	0.879536i	$-0.657853\pi$
$587$	3.06619	−	1.97052i	0.126555	−	0.0813321i	0.602387	+	0.798204i	$0.294216\pi$
$588$	−2.11220	−	2.43761i	−0.0871058	−	0.100525i
$589$	21.2795	−	6.24823i	0.876807	−	0.257454i
$590$	0.244890	−	1.70325i	0.0100819	−	0.0701215i
$591$	15.6634	−	18.0766i	0.644308	−	0.743571i
$592$	−0.444496	+	0.973310i	−0.0182687	+	0.0400028i
$593$	10.0590	+	2.95359i	0.413074	+	0.121289i	0.481665	−	0.876355i	$-0.340032\pi$
$593$	10.0590	+	2.95359i	0.413074	+	0.121289i	−0.0685913	+	0.997645i	$0.521850\pi$
$594$	23.2616	+	50.9357i	0.954433	+	2.08992i
$595$	−1.56705	−	10.8991i	−0.0642427	−	0.446818i
$596$	8.86940	+	5.70001i	0.363305	+	0.233482i
$597$	−29.2396			−1.19670
$598$	9.26034	+	8.31858i	0.378684	+	0.340172i
$599$	−33.3206			−1.36144			−0.680721	−	0.732543i	$-0.738333\pi$
$599$	−33.3206			−1.36144			−0.680721	+	0.732543i	$0.738333\pi$
$600$	6.79794	+	4.36877i	0.277525	+	0.178354i
$601$	2.60355	+	18.1081i	0.106201	+	0.738644i	0.971440	+	0.237285i	$0.0762575\pi$
$601$	2.60355	+	18.1081i	0.106201	+	0.738644i	−0.865239	+	0.501359i	$0.832833\pi$
$602$	−0.721547	−	1.57997i	−0.0294081	−	0.0643947i
$603$	38.9270	+	11.4300i	1.58523	+	0.465466i
$604$	2.68708	−	5.88389i	0.109336	−	0.239412i
$605$	−4.70037	+	5.42452i	−0.191097	+	0.220538i
$606$	−2.38323	+	16.5757i	−0.0968121	+	0.673343i
$607$	−4.22590	+	1.24084i	−0.171524	+	0.0503640i	−0.366367	−	0.930470i	$-0.619398\pi$
$607$	−4.22590	+	1.24084i	−0.171524	+	0.0503640i	0.194843	+	0.980834i	$0.437580\pi$
$608$	−1.41495	−	1.63294i	−0.0573840	−	0.0662247i
$609$	16.5693	−	10.6484i	0.671421	−	0.431496i
$610$	11.7093	−	7.52511i	0.474096	−	0.304683i
$611$	−11.5076	−	13.2805i	−0.465549	−	0.537272i
$612$	−49.5217	+	14.5409i	−2.00179	+	0.587780i
$613$	4.34516	−	30.2213i	0.175499	−	1.22062i	−0.691523	−	0.722355i	$-0.743060\pi$
$613$	4.34516	−	30.2213i	0.175499	−	1.22062i	0.867022	−	0.498270i	$-0.166031\pi$
$614$	12.0816	−	13.9429i	0.487573	−	0.562690i
$615$	21.7394	−	47.6027i	0.876619	−	1.91953i
$616$	−3.78293	−	1.11077i	−0.152419	−	0.0447542i
$617$	17.9612	+	39.3296i	0.723092	+	1.58335i	0.809520	+	0.587092i	$0.199727\pi$
$617$	17.9612	+	39.3296i	0.723092	+	1.58335i	−0.0864283	+	0.996258i	$0.527545\pi$
$618$	0.445638	+	3.09948i	0.0179262	+	0.124679i
$619$	−18.4821	−	11.8777i	−0.742858	−	0.477406i	0.113662	−	0.993519i	$-0.463742\pi$
$619$	−18.4821	−	11.8777i	−0.742858	−	0.477406i	−0.856520	+	0.516114i	$0.827378\pi$
$620$	16.2119			0.651085
$621$	−61.4426	−	29.3985i	−2.46560	−	1.17972i
$622$	21.0859			0.845466
$623$	11.1682	+	7.17737i	0.447445	+	0.287555i
$624$	1.19144	+	8.28665i	0.0476958	+	0.331732i
$625$	−2.57421	−	5.63674i	−0.102969	−	0.225470i
$626$	9.64993	+	2.83348i	0.385689	+	0.113248i
$627$	11.4143	−	24.9938i	0.455843	−	0.998157i
$628$	0.250640	−	0.289254i	0.0100016	−	0.0115425i
$629$	1.06160	−	7.38359i	0.0423288	−	0.294403i
$630$	11.2196	−	3.29437i	0.446999	−	0.131251i
$631$	10.3504	+	11.9450i	0.412042	+	0.475522i	0.923396	−	0.383848i	$-0.125401\pi$
$631$	10.3504	+	11.9450i	0.412042	+	0.475522i	−0.511354	+	0.859370i	$0.670856\pi$
$632$	−7.08778	+	4.55504i	−0.281937	+	0.181190i
$633$	65.2572	−	41.9382i	2.59374	−	1.66690i
$634$	−16.2220	−	18.7212i	−0.644257	−	0.743512i
$635$	−2.38669	+	0.700795i	−0.0947128	+	0.0278102i
$636$	−1.83358	+	12.7528i	−0.0727061	+	0.505682i
$637$	1.69975	−	1.96161i	0.0673465	−	0.0777220i
$638$	10.0014	−	21.8999i	0.395958	−	0.867026i
$639$	30.2152	+	8.87200i	1.19530	+	0.350971i
$640$	−0.656129	−	1.43672i	−0.0259358	−	0.0567914i
$641$	1.70187	+	11.8368i	0.0672200	+	0.467525i	0.995432	+	0.0954736i	$0.0304365\pi$
$641$	1.70187	+	11.8368i	0.0672200	+	0.467525i	−0.928212	+	0.372052i	$0.878654\pi$
$642$	34.0877	+	21.9068i	1.34533	+	0.864594i
$643$	−8.03903			−0.317028			−0.158514	−	0.987357i	$-0.550670\pi$
$643$	−8.03903			−0.317028			−0.158514	+	0.987357i	$0.550670\pi$
$644$	4.39736	−	1.91396i	0.173280	−	0.0754204i
$645$	8.84863			0.348415
$646$	12.6720	+	8.14381i	0.498574	+	0.320414i
$647$	0.780966	+	5.43174i	0.0307030	+	0.213544i	0.999397	−	0.0347125i	$-0.0110516\pi$
$647$	0.780966	+	5.43174i	0.0307030	+	0.213544i	−0.968694	+	0.248256i	$0.920142\pi$
$648$	−9.80360	−	21.4669i	−0.385122	−	0.843299i
$649$	4.12137	+	1.21014i	0.161778	+	0.0475023i
$650$	−2.70136	+	5.91515i	−0.105956	+	0.232011i
$651$	−21.6801	+	25.0202i	−0.849711	+	0.980619i
$652$	0.520440	−	3.61974i	0.0203820	−	0.141760i
$653$	20.7329	−	6.08772i	0.811340	−	0.238231i	0.150357	−	0.988632i	$-0.451958\pi$
$653$	20.7329	−	6.08772i	0.811340	−	0.238231i	0.660983	+	0.750401i	$0.270139\pi$
$654$	−37.8459	−	43.6765i	−1.47989	−	1.70789i
$655$	25.1993	−	16.1946i	0.984618	−	0.632776i
$656$	8.64171	−	5.55369i	0.337402	−	0.216835i
$657$	−18.3967	−	21.2309i	−0.717722	−	0.828296i
$658$	−6.49595	+	1.90738i	−0.253239	+	0.0743576i
$659$	2.52957	−	17.5935i	0.0985380	−	0.685347i	−0.879344	−	0.476188i	$-0.842018\pi$
$659$	2.52957	−	17.5935i	0.0985380	−	0.685347i	0.977882	−	0.209159i	$-0.0670727\pi$
$660$	13.1531	−	15.1795i	0.511985	−	0.590863i
$661$	−0.325799	+	0.713399i	−0.0126721	+	0.0277480i	−0.915862	−	0.401493i	$-0.868492\pi$
$661$	−0.325799	+	0.713399i	−0.0126721	+	0.0277480i	0.903190	+	0.429241i	$0.141219\pi$
$662$	19.6507	+	5.76997i	0.763746	+	0.224256i
$663$	−24.2454	−	53.0901i	−0.941614	−	2.06185i
$664$	−0.936039	−	6.51029i	−0.0363253	−	0.252648i
$665$	−2.87096	−	1.84506i	−0.111331	−	0.0715482i
$666$	7.92162			0.306956
$667$	7.74706	+	28.2423i	0.299967	+	1.09355i
$668$	8.51418			0.329423
$669$	−62.8799	−	40.4105i	−2.43108	−	1.56236i
$670$	−1.23179	−	8.56732i	−0.0475884	−	0.330984i
$671$	14.4333	+	31.6046i	0.557192	+	1.22008i
$672$	3.09477	+	0.908706i	0.119383	+	0.0350541i
$673$	−8.81076	+	19.2929i	−0.339630	+	0.743686i	−0.999974	−	0.00727779i	$-0.997683\pi$
$673$	−8.81076	+	19.2929i	−0.339630	+	0.743686i	0.660344	+	0.750964i	$0.270411\pi$
$674$	−7.08811	+	8.18011i	−0.273024	+	0.315086i
$675$	5.06389	−	35.2201i	0.194909	−	1.35562i
$676$	6.00923	−	1.76447i	0.231124	−	0.0678642i
$677$	7.16811	+	8.27244i	0.275493	+	0.317936i	0.876588	−	0.481242i	$-0.159814\pi$
$677$	7.16811	+	8.27244i	0.275493	+	0.317936i	−0.601095	+	0.799178i	$0.705269\pi$
$678$	9.46796	−	6.08469i	0.363615	−	0.233681i
$679$	−0.816343	+	0.524632i	−0.0313284	+	0.0201335i
$680$	7.21076	+	8.32166i	0.276520	+	0.319121i
$681$	51.6994	−	15.1803i	1.98113	−	0.581711i
$682$	−5.75922	+	40.0562i	−0.220532	+	1.53383i
$683$	15.6391	−	18.0485i	0.598413	−	0.690606i	−0.373046	−	0.927813i	$-0.621687\pi$
$683$	15.6391	−	18.0485i	0.598413	−	0.690606i	0.971459	+	0.237207i	$0.0762320\pi$
$684$	−6.64514	+	14.5508i	−0.254083	+	0.556365i
$685$	18.3935	+	5.40082i	0.702780	+	0.206355i
$686$	−0.415415	−	0.909632i	−0.0158606	−	0.0347299i
$687$	−0.736259	−	5.12079i	−0.0280900	−	0.195370i
$688$	1.46120	+	0.939056i	0.0557077	+	0.0358012i
$689$	−10.3681			−0.394993
$690$	−0.436762	+	24.4280i	−0.0166272	+	0.929959i
$691$	20.8592			0.793521			0.396761	−	0.917922i	$-0.370134\pi$
$691$	20.8592			0.793521			0.396761	+	0.917922i	$0.370134\pi$
$692$	13.1355	+	8.44168i	0.499337	+	0.320904i
$693$	4.15399	+	28.8916i	0.157797	+	1.09750i
$694$	3.09520	+	6.77755i	0.117492	+	0.257272i
$695$	−23.7532	−	6.97456i	−0.901009	−	0.264560i
$696$	−8.18199	+	17.9161i	−0.310137	+	0.679106i
$697$	−46.8972	+	54.1222i	−1.77636	+	2.05003i
$698$	0.0274761	−	0.191100i	0.00103999	−	0.00723326i
$699$	67.7692	−	19.8988i	2.56327	−	0.752643i
$700$	1.64064	+	1.89340i	0.0620103	+	0.0715637i
$701$	−39.7299	+	25.5328i	−1.50058	+	0.964362i	−0.505760	+	0.862674i	$0.668788\pi$
$701$	−39.7299	+	25.5328i	−1.50058	+	0.964362i	−0.994816	+	0.101688i	$0.967576\pi$
$702$	31.0122	−	19.9303i	1.17048	−	0.752222i
$703$	−1.51401	−	1.74726i	−0.0571019	−	0.0658991i
$704$	3.78293	−	1.11077i	0.142575	−	0.0418637i
$705$	4.90846	−	34.1391i	0.184863	−	1.28575i
$706$	−13.0137	+	15.0186i	−0.489777	+	0.565233i
$707$	−2.15681	+	4.72275i	−0.0811150	+	0.177617i
$708$	−3.37164	−	0.990004i	−0.126714	−	0.0372066i
$709$	7.84356	+	17.1750i	0.294571	+	0.645021i	0.997825	−	0.0659180i	$-0.0209976\pi$
$709$	7.84356	+	17.1750i	0.294571	+	0.645021i	−0.703254	+	0.710939i	$0.748270\pi$
$710$	−0.956122	−	6.64997i	−0.0358826	−	0.249569i
$711$	52.4733	+	33.7225i	1.96790	+	1.26469i
$712$	−13.2757			−0.497527
$713$	−25.8688	−	41.8803i	−0.968793	−	1.56843i
$714$	−22.4860			−0.841516
$715$	13.5974	+	8.73853i	0.508515	+	0.326803i
$716$	−0.138872	−	0.965877i	−0.00518989	−	0.0360965i
$717$	−11.5065	−	25.1958i	−0.429719	−	0.940953i
$718$	21.9575	+	6.44732i	0.819448	+	0.240612i
$719$	9.87659	−	21.6267i	0.368335	−	0.806540i	−0.631188	−	0.775630i	$-0.717432\pi$
$719$	9.87659	−	21.6267i	0.368335	−	0.806540i	0.999522	−	0.0309100i	$-0.00984053\pi$
$720$	−7.65745	+	8.83717i	−0.285376	+	0.329342i
$721$	−0.138164	+	0.960952i	−0.00514550	+	0.0357877i
$722$	−13.7509	+	4.03762i	−0.511754	+	0.150265i
$723$	−41.7501	−	48.1822i	−1.55270	−	1.79192i
$724$	20.4342	−	13.1323i	0.759431	−	0.488057i
$725$	−12.8701	+	8.27109i	−0.477982	+	0.307181i
$726$	9.59868	+	11.0775i	0.356240	+	0.411123i
$727$	44.7003	−	13.1252i	1.65784	−	0.486787i	0.687032	−	0.726627i	$-0.258913\pi$
$727$	44.7003	−	13.1252i	1.65784	−	0.486787i	0.970812	+	0.239840i	$0.0770951\pi$
$728$	−0.369391	+	2.56917i	−0.0136905	+	0.0952197i
$729$	−24.4177	+	28.1795i	−0.904359	+	1.04369i
$730$	−2.48972	+	5.45173i	−0.0921488	+	0.201778i
$731$	−11.6185	−	3.41149i	−0.429725	−	0.126179i
$732$	−11.8077	−	25.8553i	−0.436426	−	0.955639i
$733$	2.51189	+	17.4706i	0.0927787	+	0.645290i	0.982149	+	0.188103i	$0.0602339\pi$
$733$	2.51189	+	17.4706i	0.0927787	+	0.645290i	−0.889371	+	0.457187i	$0.848857\pi$
$734$	7.87653	+	5.06194i	0.290728	+	0.186840i
$735$	5.09441			0.187910
$736$	−2.66453	+	3.98751i	−0.0982159	+	0.146982i
$737$	21.6057			0.795856
$738$	−63.9776	−	41.1159i	−2.35505	−	1.51350i
$739$	−5.55250	−	38.6185i	−0.204252	−	1.42060i	−0.791487	−	0.611186i	$-0.790693\pi$
$739$	−5.55250	−	38.6185i	−0.204252	−	1.42060i	0.587235	−	0.809417i	$-0.300216\pi$
$740$	−0.702061	−	1.53730i	−0.0258083	−	0.0565122i
$741$	−17.3563	−	5.09628i	−0.637601	−	0.187216i
$742$	−1.65938	+	3.63353i	−0.0609176	+	0.133391i
$743$	−23.7337	+	27.3902i	−0.870707	+	1.00485i	0.129206	+	0.991618i	$0.458757\pi$
$743$	−23.7337	+	27.3902i	−0.870707	+	1.00485i	−0.999912	+	0.0132313i	$0.995788\pi$
$744$	4.71154	−	32.7695i	0.172734	−	1.20139i
$745$	−15.9778	+	4.69149i	−0.585380	+	0.171883i
$746$	13.3811	+	15.4426i	0.489918	+	0.565395i
$747$	−40.9637	+	26.3257i	−1.49878	+	0.963209i
$748$	−23.1227	+	14.8601i	−0.845450	+	0.543338i
$749$	8.22685	+	9.49429i	0.300602	+	0.346914i
$750$	−36.6864	+	10.7721i	−1.33960	+	0.393341i
$751$	1.97529	−	13.7384i	0.0720793	−	0.501323i	−0.921517	−	0.388337i	$-0.873050\pi$
$751$	1.97529	−	13.7384i	0.0720793	−	0.501323i	0.993597	−	0.112985i	$-0.0360414\pi$
$752$	4.43353	−	5.11657i	0.161674	−	0.186582i
$753$	−20.9026	+	45.7703i	−0.761733	+	1.66796i
$754$	−15.2078	−	4.46543i	−0.553837	−	0.162621i
$755$	4.24412	+	9.29333i	0.154459	+	0.338219i
$756$	−2.02125	−	14.0581i	−0.0735121	−	0.511288i
$757$	−25.0231	−	16.0814i	−0.909480	−	0.584488i	0.000107102	−	1.00000i	$-0.499966\pi$
$757$	−25.0231	−	16.0814i	−0.909480	−	0.584488i	−0.909587	+	0.415512i	$0.863602\pi$
$758$	12.5531			0.455949
$759$	−60.2015	−	9.75712i	−2.18517	−	0.354161i
$760$	3.41272			0.123792
$761$	−30.7633	−	19.7704i	−1.11517	−	0.716676i	−0.152756	−	0.988264i	$-0.548815\pi$
$761$	−30.7633	−	19.7704i	−1.11517	−	0.716676i	−0.962414	+	0.271588i	$0.912451\pi$
$762$	0.722909	+	5.02794i	0.0261882	+	0.182143i
$763$	−7.44330	−	16.2985i	−0.269465	−	0.590047i
$764$	8.11796	+	2.38365i	0.293698	+	0.0862374i
$765$	33.8643	−	74.1525i	1.22437	−	2.68099i
$766$	−5.46054	+	6.30180i	−0.197297	+	0.227693i
$767$	0.402438	−	2.79902i	0.0145312	−	0.101067i
$768$	−3.09477	+	0.908706i	−0.111673	+	0.0327901i
$769$	17.9197	+	20.6804i	0.646200	+	0.745755i	0.980458	−	0.196727i	$-0.0630311\pi$
$769$	17.9197	+	20.6804i	0.646200	+	0.745755i	−0.334258	+	0.942482i	$0.608486\pi$
$770$	5.23867	−	3.36669i	0.188788	−	0.121327i
$771$	78.0540	−	50.1623i	2.81105	−	1.80655i
$772$	−5.82061	−	6.71734i	−0.209488	−	0.241762i
$773$	3.75932	−	1.10384i	0.135213	−	0.0397023i	−0.213426	−	0.976959i	$-0.568462\pi$
$773$	3.75932	−	1.10384i	0.135213	−	0.0397023i	0.348639	+	0.937257i	$0.386644\pi$
$774$	1.83004	−	12.7282i	0.0657795	−	0.457506i
$775$	16.8399	−	19.4343i	0.604907	−	0.698100i
$776$	0.403114	−	0.882697i	0.0144710	−	0.0316870i
$777$	3.31142	+	0.972320i	0.118796	+	0.0348818i
$778$	−10.0255	−	21.9528i	−0.359431	−	0.787045i
$779$	3.15876	+	21.9696i	0.113174	+	0.787144i
$780$	−11.1239	−	7.14888i	−0.398299	−	0.255971i
$781$	16.7704			0.600091
$782$	9.99143	−	31.9062i	0.357293	−	1.14096i
$783$	86.7281			3.09941
$784$	0.841254	+	0.540641i	0.0300448	+	0.0193086i
$785$	0.0860318	+	0.598364i	0.00307061	+	0.0213565i
$786$	−25.4111	−	55.6425i	−0.906384	−	1.98470i
$787$	0.694264	+	0.203854i	0.0247478	+	0.00726662i	0.294083	−	0.955780i	$-0.404986\pi$
$787$	0.694264	+	0.203854i	0.0247478	+	0.00726662i	−0.269335	+	0.963046i	$0.586804\pi$
$788$	−3.08059	+	6.74555i	−0.109741	+	0.240300i
$789$	−23.2819	+	26.8688i	−0.828858	+	0.956553i
$790$	1.89383	−	13.1719i	0.0673794	−	0.468634i
$791$	3.34799	−	0.983060i	0.119041	−	0.0349536i
$792$	−19.1146	−	22.0594i	−0.679206	−	0.783846i
$793$	19.2424	−	12.3664i	0.683319	−	0.439142i
$794$	−11.0564	+	7.10553i	−0.392378	+	0.252166i
$795$	−13.3262	−	15.3792i	−0.472630	−	0.545445i
$796$	8.69814	−	2.55400i	0.308297	−	0.0905242i
$797$	3.37974	−	23.5066i	0.119717	−	0.832647i	−0.838151	−	0.545438i	$-0.816363\pi$
$797$	3.37974	−	23.5066i	0.119717	−	0.832647i	0.957868	−	0.287209i	$-0.0927276\pi$
$798$	−4.56383	+	5.26694i	−0.161558	+	0.186448i
$799$	−19.6069	+	42.9331i	−0.693641	+	1.51886i
$800$	−2.40384	−	0.705831i	−0.0849886	−	0.0249549i
$801$	40.8288	+	89.4026i	1.44262	+	3.15889i
$802$	−3.51022	−	24.4141i	−0.123950	−	0.862093i
$803$	−12.5857	−	8.08831i	−0.444138	−	0.285430i
$804$	−17.6753			−0.623361
$805$	−2.26365	+	7.22865i	−0.0797833	+	0.254777i
$806$	26.6417			0.938414
$807$	14.5915	+	9.37737i	0.513644	+	0.330099i
$808$	−0.738889	−	5.13909i	−0.0259940	−	0.180792i
$809$	−0.326961	−	0.715945i	−0.0114953	−	0.0251713i	0.903797	−	0.427961i	$-0.140768\pi$
$809$	−0.326961	−	0.715945i	−0.0114953	−	0.0251713i	−0.915293	+	0.402790i	$0.868041\pi$
$810$	35.7645	+	10.5014i	1.25664	+	0.368982i
$811$	6.07235	−	13.2966i	0.213229	−	0.466907i	−0.772550	−	0.634954i	$-0.781019\pi$
$811$	6.07235	−	13.2966i	0.213229	−	0.466907i	0.985779	+	0.168048i	$0.0537462\pi$
$812$	−3.99889	+	4.61496i	−0.140333	+	0.161953i
$813$	−0.556493	+	3.87049i	−0.0195170	+	0.135744i
$814$	4.04776	−	1.18853i	0.141874	−	0.0416579i
$815$	3.78247	+	4.36521i	0.132494	+	0.152907i
$816$	18.9164	−	12.1568i	0.662207	−	0.425574i
$817$	−3.15721	+	2.02901i	−0.110457	+	0.0709862i
$818$	15.3455	+	17.7097i	0.536544	+	0.619205i
$819$	18.4377	−	5.41379i	0.644264	−	0.189173i
$820$	−2.30903	+	16.0597i	−0.0806349	+	0.560828i
$821$	23.3185	−	26.9110i	0.813822	−	0.939200i	−0.185232	−	0.982695i	$-0.559304\pi$
$821$	23.3185	−	26.9110i	0.813822	−	0.939200i	0.999054	+	0.0434944i	$0.0138491\pi$
$822$	16.2624	−	35.6097i	0.567216	−	1.24203i
$823$	21.0365	+	6.17687i	0.733286	+	0.215312i	0.626995	−	0.779023i	$-0.284284\pi$
$823$	21.0365	+	6.17687i	0.733286	+	0.215312i	0.106291	+	0.994335i	$0.466103\pi$
$824$	−0.403299	−	0.883102i	−0.0140496	−	0.0307643i
$825$	−4.53406	−	31.5351i	−0.157856	−	1.09791i
$826$	−0.916516	−	0.589009i	−0.0318897	−	0.0204943i
$827$	11.1908			0.389142			0.194571	−	0.980888i	$-0.437668\pi$
$827$	11.1908			0.389142			0.194571	+	0.980888i	$0.437668\pi$
$828$	35.0479	+	5.68037i	1.21800	+	0.197406i
$829$	−27.8448			−0.967090			−0.483545	−	0.875319i	$-0.660651\pi$
$829$	−27.8448			−0.967090			−0.483545	+	0.875319i	$0.660651\pi$
$830$	8.73932	+	5.61642i	0.303346	+	0.194949i
$831$	−5.59847	−	38.9382i	−0.194209	−	1.35075i
$832$	−1.07825	−	2.36103i	−0.0373815	−	0.0818540i
$833$	−6.68909	−	1.96409i	−0.231763	−	0.0680518i
$834$	−21.0011	+	45.9859i	−0.727207	+	1.59236i
$835$	−8.80641	+	10.1631i	−0.304758	+	0.351710i
$836$	−1.21236	+	8.43213i	−0.0419303	+	0.291631i
$837$	−139.874	+	41.0708i	−4.83476	+	1.41961i
$838$	8.70155	+	10.0421i	0.300590	+	0.346900i
$839$	11.1934	−	7.19354i	0.386438	−	0.248349i	−0.332969	−	0.942938i	$-0.608050\pi$
$839$	11.1934	−	7.19354i	0.386438	−	0.248349i	0.719406	+	0.694589i	$0.244414\pi$
$840$	−4.28569	+	2.75424i	−0.147870	+	0.0950305i
$841$	−5.42810	−	6.26436i	−0.187176	−	0.216012i
$842$	6.75923	−	1.98469i	0.232939	−	0.0683969i
$843$	−10.2363	+	71.1953i	−0.352558	+	2.45210i
$844$	−15.7494	+	18.1758i	−0.542116	+	0.625635i
$845$	−4.10928	+	8.99808i	−0.141364	+	0.309543i
$846$	−48.0918	−	14.1210i	−1.65343	−	0.485491i
$847$	1.88781	+	4.13373i	0.0648659	+	0.142037i
$848$	−0.568477	−	3.95384i	−0.0195216	−	0.135776i
$849$	−85.1151	−	54.7002i	−2.92114	−	1.87731i
$850$	17.4658			0.599073
$851$	−2.85106	+	4.26666i	−0.0977331	+	0.146259i
$852$	−13.7196			−0.470027
$853$	5.72461	+	3.67898i	0.196007	+	0.125966i	0.634963	−	0.772543i	$-0.281015\pi$
$853$	5.72461	+	3.67898i	0.196007	+	0.125966i	−0.438956	+	0.898508i	$0.644652\pi$
$854$	−1.25414	−	8.72276i	−0.0429159	−	0.298487i
$855$	−10.4957	−	22.9824i	−0.358945	−	0.785980i
$856$	−12.0539	−	3.53933i	−0.411993	−	0.120972i
$857$	15.9375	−	34.8982i	0.544414	−	1.19210i	−0.414928	−	0.909854i	$-0.636193\pi$
$857$	15.9375	−	34.8982i	0.544414	−	1.19210i	0.959342	−	0.282247i	$-0.0910796\pi$
$858$	21.6151	−	24.9452i	0.737929	−	0.851616i
$859$	−2.78160	+	19.3465i	−0.0949071	+	0.660093i	0.885721	+	0.464217i	$0.153664\pi$
$859$	−2.78160	+	19.3465i	−0.0949071	+	0.660093i	−0.980629	+	0.195876i	$0.937245\pi$
$860$	−2.63228	+	0.772906i	−0.0897599	+	0.0263559i
$861$	−21.6974	−	25.0402i	−0.739446	−	0.853366i
$862$	34.5998	−	22.2359i	1.17847	−	0.757359i
$863$	−35.9051	+	23.0748i	−1.22222	+	0.785475i	−0.982662	−	0.185407i	$-0.940640\pi$
$863$	−35.9051	+	23.0748i	−1.22222	+	0.785475i	−0.239560	+	0.970881i	$0.577003\pi$
$864$	9.30077	+	10.7337i	0.316418	+	0.365166i
$865$	−23.6629	+	6.94807i	−0.804564	+	0.236241i
$866$	0.247396	−	1.72068i	0.00840687	−	0.0584711i
$867$	−66.7489	+	77.0323i	−2.26691	+	2.61615i
$868$	4.26392	−	9.33667i	0.144727	−	0.316907i
$869$	31.8722	+	9.35852i	1.08119	+	0.317466i
$870$	−12.9231	−	28.2976i	−0.438133	−	0.959378i
$871$	−2.02426	−	14.0791i	−0.0685896	−	0.477051i
$872$	15.0734	+	9.68706i	0.510448	+	0.328045i
$873$	−7.18413			−0.243146
$874$	−5.44557	−	8.81611i	−0.184199	−	0.298209i
$875$	−11.8543			−0.400749
$876$	10.2962	+	6.61694i	0.347875	+	0.223566i
$877$	6.47484	+	45.0335i	0.218640	+	1.52067i	0.743066	+	0.669218i	$0.233371\pi$
$877$	6.47484	+	45.0335i	0.218640	+	1.52067i	−0.524426	+	0.851456i	$0.675720\pi$
$878$	−2.27205	−	4.97511i	−0.0766781	−	0.167902i
$879$	−48.6657	−	14.2895i	−1.64145	−	0.481974i
$880$	−2.58688	+	5.66447i	−0.0872037	+	0.190949i
$881$	−20.6868	+	23.8738i	−0.696954	+	0.804328i	−0.988338	−	0.152278i	$-0.951339\pi$
$881$	−20.6868	+	23.8738i	−0.696954	+	0.804328i	0.291383	+	0.956606i	$0.405884\pi$
$882$	1.05361	−	7.32799i	0.0354768	−	0.246746i
$883$	29.5139	−	8.66607i	0.993223	−	0.291636i	0.255551	−	0.966796i	$-0.417743\pi$
$883$	29.5139	−	8.66607i	0.993223	−	0.291636i	0.737672	+	0.675159i	$0.235925\pi$
$884$	11.8498	+	13.6754i	0.398551	+	0.459952i
$885$	4.66911	−	3.00065i	0.156950	−	0.100866i
$886$	29.7629	−	19.1275i	0.999904	−	0.642599i
$887$	−22.2260	−	25.6501i	−0.746274	−	0.861247i	0.247927	−	0.968779i	$-0.420251\pi$
$887$	−22.2260	−	25.6501i	−0.746274	−	0.861247i	−0.994202	+	0.107532i	$0.965705\pi$
$888$	−3.31142	+	0.972320i	−0.111124	+	0.0326289i
$889$	−0.224128	+	1.55885i	−0.00751703	+	0.0522821i
$890$	13.7313	−	15.8468i	0.460275	−	0.531186i
$891$	−38.6521	+	84.6362i	−1.29489	+	2.83542i
$892$	22.2352	+	6.52883i	0.744488	+	0.218601i
$893$	6.07683	+	13.3064i	0.203353	+	0.445282i
$894$	4.83954	+	33.6597i	0.161858	+	1.12575i
$895$	1.29658	+	0.833260i	0.0433398	+	0.0278528i
$896$	−1.00000			−0.0334077
$897$	−0.717750	+	40.1437i	−0.0239650	+	1.34036i
$898$	21.0006			0.700800
$899$	52.7282	+	33.8864i	1.75859	+	1.13017i
$900$	2.63963	+	18.3590i	0.0879875	+	0.611967i
$901$	11.5683	+	25.3311i	0.385396	+	0.843900i
$902$	−38.8599	−	11.4103i	−1.29389	−	0.379921i
$903$	2.32729	−	5.09606i	0.0774475	−	0.169586i
$904$	−2.28503	+	2.63706i	−0.0759989	+	0.0877075i
$905$	−5.45994	+	37.9747i	−0.181495	+	1.26232i
$906$	20.0183	−	5.87790i	0.665063	−	0.195280i
$907$	16.1879	+	18.6818i	0.537509	+	0.620319i	0.957927	−	0.287012i	$-0.0926619\pi$
$907$	16.1879	+	18.6818i	0.537509	+	0.620319i	−0.420418	+	0.907331i	$0.638116\pi$
$908$	−14.0535	+	9.03163i	−0.466381	+	0.299725i
$909$	−32.3358	+	20.7810i	−1.07251	+	0.689262i
$910$	−2.68468	−	3.09828i	−0.0889961	−	0.102707i
$911$	29.5820	−	8.68604i	0.980094	−	0.287781i	0.247831	−	0.968803i	$-0.420282\pi$
$911$	29.5820	−	8.68604i	0.980094	−	0.287781i	0.732263	+	0.681022i	$0.238464\pi$
$912$	0.991814	−	6.89822i	0.0328423	−	0.228423i
$913$	−16.9816	+	19.5978i	−0.562010	+	0.648594i
$914$	−4.24276	+	9.29035i	−0.140338	+	0.307298i
$915$	43.0757	+	12.6482i	1.42404	+	0.418136i
$916$	0.666309	+	1.45901i	0.0220155	+	0.0482072i
$917$	−2.69901	−	18.7720i	−0.0891292	−	0.619907i
$918$	−83.2955	−	53.5308i	−2.74916	−	1.76678i
$919$	32.9310			1.08629			0.543146	−	0.839638i	$-0.317233\pi$
$919$	32.9310			1.08629			0.543146	+	0.839638i	$0.317233\pi$
$920$	−2.00380	−	7.30495i	−0.0660633	−	0.240837i
$921$	59.5061			1.96079
$922$	30.4589	+	19.5748i	1.00311	+	0.644660i
$923$	−1.57124	−	10.9282i	−0.0517179	−	0.359706i
$924$	−5.28270	−	11.5675i	−0.173788	−	0.380543i
$925$	−2.57212	−	0.755243i	−0.0845708	−	0.0248322i
$926$	3.86450	−	8.46207i	0.126995	−	0.278081i
$927$	−4.70676	+	5.43189i	−0.154590	+	0.178407i
$928$	0.869041	−	6.04431i	0.0285277	−	0.198414i
$929$	16.4017	−	4.81597i	0.538122	−	0.158007i	−0.00136770	−	0.999999i	$-0.500435\pi$
$929$	16.4017	−	4.81597i	0.538122	−	0.158007i	0.539490	+	0.841992i	$0.318617\pi$
$930$	34.2428	+	39.5183i	1.12286	+	1.29586i
$931$	−1.81769	+	1.16816i	−0.0595725	+	0.0382849i
$932$	−18.4218	+	11.8389i	−0.603425	+	0.387798i
$933$	44.5376	+	51.3991i	1.45810	+	1.68273i
$934$	−5.18890	+	1.52360i	−0.169786	+	0.0498537i
$935$	6.17830	−	42.9710i	0.202052	−	1.40530i
$936$	−12.5838	+	14.5225i	−0.411316	+	0.474683i
$937$	9.59380	−	21.0075i	0.313416	−	0.686285i	−0.685719	−	0.727866i	$-0.740512\pi$
$937$	9.59380	−	21.0075i	0.313416	−	0.686285i	0.999135	+	0.0415812i	$0.0132395\pi$
$938$	−5.25803	−	1.54390i	−0.171681	−	0.0504100i
$939$	13.4757	+	29.5077i	0.439763	+	0.962946i
$940$	1.52180	+	10.5844i	0.0496357	+	0.345224i
$941$	42.0677	+	27.0353i	1.37137	+	0.881326i	0.998908	−	0.0467220i	$-0.0148775\pi$
$941$	42.0677	+	27.0353i	1.37137	+	0.881326i	0.372461	+	0.928048i	$0.378514\pi$
$942$	1.23449			0.0402219
$943$	45.1715	−	19.6610i	1.47099	−	0.640249i
$944$	1.08946			0.0354591
$945$	18.8714	+	12.1279i	0.613886	+	0.394521i
$946$	−0.974585	−	6.77839i	−0.0316865	−	0.220384i
$947$	−0.0859614	−	0.188229i	−0.00279337	−	0.00611662i	0.908230	−	0.418471i	$-0.137434\pi$
$947$	−0.0859614	−	0.188229i	−0.00279337	−	0.00611662i	−0.911024	+	0.412354i	$0.864707\pi$
$948$	−26.0742	−	7.65609i	−0.846852	−	0.248658i
$949$	−4.09147	+	8.95908i	−0.132815	+	0.290824i
$950$	3.54492	−	4.09106i	0.115012	−	0.132731i
$951$	11.3708	−	79.0858i	0.368724	−	2.56453i
$952$	6.68909	−	1.96409i	0.216795	−	0.0636566i
$953$	−35.8350	−	41.3558i	−1.16081	−	1.33965i	−0.930397	−	0.366553i	$-0.880538\pi$
$953$	−35.8350	−	41.3558i	−1.16081	−	1.33965i	−0.230413	−	0.973093i	$-0.574008\pi$
$954$	−24.8781	+	15.9882i	−0.805459	+	0.517637i
$955$	−11.2419	+	7.22472i	−0.363779	+	0.233787i
$956$	5.62372	+	6.49012i	0.181884	+	0.209906i
$957$	74.5084	−	21.8776i	2.40851	−	0.707204i
$958$	0.0998371	−	0.694382i	0.00322559	−	0.0224345i
$959$	7.94813	−	9.17263i	0.256658	−	0.296200i
$960$	2.11629	−	4.63404i	0.0683031	−	0.149563i
$961$	−71.3425	−	20.9481i	−2.30137	−	0.675744i
$962$	−1.15373	−	2.52631i	−0.0371977	−	0.0814516i
$963$	13.2362	+	92.0597i	0.426530	+	2.96658i
$964$	16.6283	+	10.6864i	0.535563	+	0.344185i
$965$	14.0387			0.451921
$966$	13.9536	+	6.67639i	0.448950	+	0.214809i
$967$	−28.6222			−0.920429			−0.460214	−	0.887808i	$-0.652227\pi$
$967$	−28.6222			−0.920429			−0.460214	+	0.887808i	$0.652227\pi$
$968$	−3.82299	−	2.45688i	−0.122875	−	0.0789673i
$969$	6.91441	+	48.0908i	0.222123	+	1.54490i
$970$	0.636700	+	1.39418i	0.0204432	+	0.0447644i
$971$	4.15710	+	1.22063i	0.133408	+	0.0391720i	0.347755	−	0.937586i	$-0.386944\pi$
$971$	4.15710	+	1.22063i	0.133408	+	0.0391720i	−0.214347	+	0.976758i	$0.568762\pi$
$972$	13.9208	−	30.4822i	0.446509	−	0.977717i
$973$	−10.2641	+	11.8454i	−0.329052	+	0.379747i
$974$	−1.13980	+	7.92750i	−0.0365216	+	0.254014i
$975$	−20.1246	+	5.90913i	−0.644504	+	0.189244i
$976$	5.77093	+	6.66001i	0.184723	+	0.213182i
$977$	1.05215	−	0.676179i	0.0336614	−	0.0216329i	−0.523702	−	0.851902i	$-0.675449\pi$
$977$	1.05215	−	0.676179i	0.0336614	−	0.0216329i	0.557363	+	0.830269i	$0.311813\pi$
$978$	9.92278	−	6.37699i	0.317296	−	0.203914i
$979$	34.2762	+	39.5568i	1.09547	+	1.26424i
$980$	−1.51548	+	0.444984i	−0.0484101	+	0.0142145i
$981$	18.8782	−	131.301i	0.602736	−	4.19212i
$982$	−8.11709	+	9.36762i	−0.259027	+	0.298933i
$983$	21.6466	−	47.3995i	0.690419	−	1.51181i	−0.160794	−	0.986988i	$-0.551405\pi$
$983$	21.6466	−	47.3995i	0.690419	−	1.51181i	0.851213	−	0.524820i	$-0.175867\pi$
$984$	31.7908	+	9.33461i	1.01345	+	0.297577i
$985$	−4.86565	−	10.6543i	−0.155032	−	0.339474i
$986$	6.05850	+	42.1378i	0.192942	+	1.34194i
$987$	−18.3702	−	11.8058i	−0.584731	−	0.375784i
$988$	5.60828			0.178423
$989$	6.19689	+	5.56668i	0.197050	+	0.177010i
$990$	46.1023			1.46523
$991$	9.38147	+	6.02910i	0.298012	+	0.191521i	0.681099	−	0.732192i	$-0.261502\pi$
$991$	9.38147	+	6.02910i	0.298012	+	0.191521i	−0.383086	+	0.923713i	$0.625139\pi$
$992$	1.46075	+	10.1598i	0.0463789	+	0.322573i
$993$	27.4413	+	60.0881i	0.870824	+	1.90684i
$994$	−4.08129	−	1.19838i	−0.129451	−	0.0380102i
$995$	−5.94804	+	13.0244i	−0.188565	+	0.412901i
$996$	13.8925	−	16.0328i	0.440199	−	0.508017i
$997$	−1.89653	+	13.1906i	−0.0600636	+	0.417751i	0.937500	+	0.347986i	$0.113134\pi$
$997$	−1.89653	+	13.1906i	−0.0600636	+	0.417751i	−0.997563	+	0.0697657i	$0.977775\pi$
$998$	−36.7696	+	10.7965i	−1.16392	+	0.341758i
$999$	9.95186	+	11.4851i	0.314863	+	0.363371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.e.71.1	✓	40
23.9	even	11		7406.2.a.bt.1.19		20
23.12	even	11	inner	322.2.i.e.127.1	yes	40
23.14	odd	22		7406.2.a.bs.1.19		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.e.71.1	✓	40	1.1	even	1	trivial
322.2.i.e.127.1	yes	40	23.12	even	11	inner
7406.2.a.bs.1.19		20	23.14	odd	22
7406.2.a.bt.1.19		20	23.9	even	11

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 - 0.540641i) q^{2} +(-0.459025 - 3.19259i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-1.51548 - 0.444984i) q^{5} +(-1.33989 + 2.93395i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-7.10346 + 2.08576i) q^{9} +O(q^{10})\)	\(q+(-0.841254 - 0.540641i) q^{2} +(-0.459025 - 3.19259i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-1.51548 - 0.444984i) q^{5} +(-1.33989 + 2.93395i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-7.10346 + 2.08576i) q^{9} +(1.03432 + 1.19367i) q^{10} +(-3.31676 + 2.13155i) q^{11} +(2.71340 - 1.74379i) q^{12} +(1.69975 + 1.96161i) q^{13} +(0.959493 - 0.281733i) q^{14} +(-0.725010 + 5.04255i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(2.89606 - 6.34148i) q^{17} +(7.10346 + 2.08576i) q^{18} +(-0.897585 - 1.96544i) q^{19} +(-0.224780 - 1.56338i) q^{20} +(2.71340 + 1.74379i) q^{21} +3.94264 q^{22} +(-3.68001 + 3.07531i) q^{23} -3.22542 q^{24} +(-2.10761 - 1.35448i) q^{25} +(-0.369391 - 2.56917i) q^{26} +(5.90000 + 12.9192i) q^{27} +(-0.959493 - 0.281733i) q^{28} +(2.53672 - 5.55464i) q^{29} +(3.33613 - 3.85010i) q^{30} +(-1.46075 + 10.1598i) q^{31} +(0.959493 - 0.281733i) q^{32} +(8.32765 + 9.61062i) q^{33} +(-5.86478 + 3.76907i) q^{34} +(1.32872 - 0.853917i) q^{35} +(-4.84816 - 5.59508i) q^{36} +(1.02666 - 0.301455i) q^{37} +(-0.307499 + 2.13870i) q^{38} +(5.48241 - 6.32704i) q^{39} +(-0.656129 + 1.43672i) q^{40} +(-9.85631 - 2.89407i) q^{41} +(-1.33989 - 2.93395i) q^{42} +(-0.247191 - 1.71925i) q^{43} +(-3.31676 - 2.13155i) q^{44} +11.6933 q^{45} +(4.75846 - 0.597548i) q^{46} -6.77019 q^{47} +(2.71340 + 1.74379i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(1.04075 + 2.27892i) q^{50} +(-21.5751 - 6.33503i) q^{51} +(-1.07825 + 2.36103i) q^{52} +(-2.61584 + 3.01884i) q^{53} +(2.02125 - 14.0581i) q^{54} +(5.97497 - 1.75441i) q^{55} +(0.654861 + 0.755750i) q^{56} +(-5.86283 + 3.76781i) q^{57} +(-5.13709 + 3.30141i) q^{58} +(-0.713448 - 0.823363i) q^{59} +(-4.88805 + 1.43526i) q^{60} +(1.25414 - 8.72276i) q^{61} +(6.72164 - 7.75719i) q^{62} +(3.07546 - 6.73432i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.70304 - 3.72914i) q^{65} +(-1.80977 - 12.5872i) q^{66} +(-4.61008 - 2.96272i) q^{67} +6.97148 q^{68} +(11.5074 + 10.3371i) q^{69} -1.57945 q^{70} +(-3.57835 - 2.29967i) q^{71} +(1.05361 + 7.32799i) q^{72} +(1.57632 + 3.45166i) q^{73} +(-1.02666 - 0.301455i) q^{74} +(-3.35686 + 7.35049i) q^{75} +(1.41495 - 1.63294i) q^{76} +(0.561096 - 3.90251i) q^{77} +(-8.03275 + 2.35863i) q^{78} +(-5.51737 - 6.36739i) q^{79} +(1.32872 - 0.853917i) q^{80} +(19.8532 - 12.7589i) q^{81} +(6.72700 + 7.76338i) q^{82} +(6.31081 - 1.85302i) q^{83} +(-0.459025 + 3.19259i) q^{84} +(-7.21076 + 8.32166i) q^{85} +(-0.721547 + 1.57997i) q^{86} +(-18.8981 - 5.54899i) q^{87} +(1.63783 + 3.58635i) q^{88} +(-1.88932 - 13.1405i) q^{89} +(-9.83699 - 6.32185i) q^{90} -2.59559 q^{91} +(-4.32613 - 2.06993i) q^{92} +33.1065 q^{93} +(5.69545 + 3.66024i) q^{94} +(0.485681 + 3.37798i) q^{95} +(-1.33989 - 2.93395i) q^{96} +(0.931081 + 0.273390i) q^{97} +(-0.415415 + 0.909632i) q^{98} +(19.1146 - 22.0594i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	\( 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} + 2 q^{12} + 4 q^{13} + 4 q^{14} - 11 q^{15} - 4 q^{16} - 21 q^{17} + 4 q^{19} + 2 q^{20} + 2 q^{21} - 11 q^{23} - 2 q^{24} + 5 q^{25} - 15 q^{26} + 95 q^{27} - 4 q^{28} + 22 q^{30} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 10 q^{34} - 9 q^{35} + 41 q^{37} + 7 q^{38} - 38 q^{39} - 13 q^{40} + 25 q^{41} - 2 q^{42} - 59 q^{43} - 6 q^{45} + 11 q^{46} - 60 q^{47} + 2 q^{48} - 4 q^{49} + 61 q^{50} - 87 q^{51} + 4 q^{52} + 47 q^{53} - 29 q^{54} - 30 q^{55} + 4 q^{56} + 20 q^{57} - 96 q^{59} - 11 q^{60} + 84 q^{61} - 65 q^{62} - 4 q^{64} + 52 q^{65} - 3 q^{66} + 11 q^{67} - 10 q^{68} - 42 q^{69} - 2 q^{70} - 13 q^{71} + 11 q^{72} - 48 q^{73} - 41 q^{74} + 23 q^{75} + 26 q^{76} - 83 q^{78} + 80 q^{79} - 9 q^{80} + 2 q^{81} + 30 q^{82} - 20 q^{83} + 2 q^{84} - 71 q^{85} - 40 q^{86} + 99 q^{87} - 30 q^{89} + 116 q^{90} + 26 q^{91} - 22 q^{92} + 20 q^{93} - 17 q^{94} - 4 q^{95} - 2 q^{96} - 56 q^{97} + 4 q^{98} + 138 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 + 2 * q^12 + 4 * q^13 + 4 * q^14 - 11 * q^15 - 4 * q^16 - 21 * q^17 + 4 * q^19 + 2 * q^20 + 2 * q^21 - 11 * q^23 - 2 * q^24 + 5 * q^25 - 15 * q^26 + 95 * q^27 - 4 * q^28 + 22 * q^30 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 10 * q^34 - 9 * q^35 + 41 * q^37 + 7 * q^38 - 38 * q^39 - 13 * q^40 + 25 * q^41 - 2 * q^42 - 59 * q^43 - 6 * q^45 + 11 * q^46 - 60 * q^47 + 2 * q^48 - 4 * q^49 + 61 * q^50 - 87 * q^51 + 4 * q^52 + 47 * q^53 - 29 * q^54 - 30 * q^55 + 4 * q^56 + 20 * q^57 - 96 * q^59 - 11 * q^60 + 84 * q^61 - 65 * q^62 - 4 * q^64 + 52 * q^65 - 3 * q^66 + 11 * q^67 - 10 * q^68 - 42 * q^69 - 2 * q^70 - 13 * q^71 + 11 * q^72 - 48 * q^73 - 41 * q^74 + 23 * q^75 + 26 * q^76 - 83 * q^78 + 80 * q^79 - 9 * q^80 + 2 * q^81 + 30 * q^82 - 20 * q^83 + 2 * q^84 - 71 * q^85 - 40 * q^86 + 99 * q^87 - 30 * q^89 + 116 * q^90 + 26 * q^91 - 22 * q^92 + 20 * q^93 - 17 * q^94 - 4 * q^95 - 2 * q^96 - 56 * q^97 + 4 * q^98 + 138 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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