LMFDB - Embedded newform 483.2.q.d.127.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.5
Character	$\chi$	$=$	483.127
Dual form			483.2.q.d.232.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.84770 - 1.18744i) q^{2} +(0.142315 - 0.989821i) q^{3} +(1.17314 - 2.56882i) q^{4} +(2.35208 - 0.690633i) q^{5} +(-0.912403 - 1.99788i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.257569 - 1.79143i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(1.84770 - 1.18744i) q^{2} +(0.142315 - 0.989821i) q^{3} +(1.17314 - 2.56882i) q^{4} +(2.35208 - 0.690633i) q^{5} +(-0.912403 - 1.99788i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.257569 - 1.79143i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(3.52585 - 4.06905i) q^{10} +(-0.863864 - 0.555172i) q^{11} +(-2.37572 - 1.52678i) q^{12} +(-1.90088 + 2.19373i) q^{13} +(-2.10740 - 0.618788i) q^{14} +(-0.348867 - 2.42643i) q^{15} +(1.09555 + 1.26433i) q^{16} +(0.500171 + 1.09522i) q^{17} +(-2.10740 + 0.618788i) q^{18} +(-1.81228 + 3.96835i) q^{19} +(0.985209 - 6.85228i) q^{20} +(-0.841254 + 0.540641i) q^{21} -2.25540 q^{22} +(4.63908 - 1.21611i) q^{23} -1.80985 q^{24} +(0.849039 - 0.545644i) q^{25} +(-0.907321 + 6.31055i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-2.70963 + 0.795619i) q^{28} +(-0.173655 - 0.380251i) q^{29} +(-3.52585 - 4.06905i) q^{30} +(-0.954577 - 6.63923i) q^{31} +(6.99864 + 2.05499i) q^{32} +(-0.672462 + 0.776062i) q^{33} +(2.22468 + 1.42972i) q^{34} +(-2.06223 - 1.32532i) q^{35} +(-1.84934 + 2.13425i) q^{36} +(-2.68567 - 0.788584i) q^{37} +(1.36364 + 9.48430i) q^{38} +(1.90088 + 2.19373i) q^{39} +(-1.84304 - 4.03570i) q^{40} +(-5.89531 + 1.73102i) q^{41} +(-0.912403 + 1.99788i) q^{42} +(-0.0677671 + 0.471330i) q^{43} +(-2.43957 + 1.56782i) q^{44} -2.45138 q^{45} +(7.12756 - 7.75566i) q^{46} -4.95991 q^{47} +(1.40737 - 0.904464i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(0.920847 - 2.01637i) q^{50} +(1.15526 - 0.339214i) q^{51} +(3.40531 + 7.45658i) q^{52} +(4.62185 + 5.33389i) q^{53} +(0.312575 + 2.17401i) q^{54} +(-2.41530 - 0.709195i) q^{55} +(-1.18520 + 1.36779i) q^{56} +(3.67004 + 2.35859i) q^{57} +(-0.772389 - 0.496384i) q^{58} +(-3.11116 + 3.59046i) q^{59} +(-6.64232 - 1.95036i) q^{60} +(1.29575 + 9.01212i) q^{61} +(-9.64749 - 11.1338i) q^{62} +(0.415415 + 0.909632i) q^{63} +(12.1612 - 3.57086i) q^{64} +(-2.95596 + 6.47265i) q^{65} +(-0.320977 + 2.23244i) q^{66} +(5.08487 - 3.26784i) q^{67} +3.40020 q^{68} +(-0.543523 - 4.76493i) q^{69} -5.38412 q^{70} +(11.2966 - 7.25987i) q^{71} +(-0.257569 + 1.79143i) q^{72} +(2.92821 - 6.41189i) q^{73} +(-5.89872 + 1.73202i) q^{74} +(-0.419259 - 0.918050i) q^{75} +(8.06791 + 9.31086i) q^{76} +(0.146140 + 1.01643i) q^{77} +(6.11720 + 1.79617i) q^{78} +(8.60185 - 9.92706i) q^{79} +(3.45000 + 2.21718i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-8.83728 + 10.1988i) q^{82} +(-5.98611 - 1.75768i) q^{83} +(0.401900 + 2.79528i) q^{84} +(1.93284 + 2.23062i) q^{85} +(0.434466 + 0.951347i) q^{86} +(-0.401094 + 0.117772i) q^{87} +(-0.772047 + 1.69055i) q^{88} +(-2.51357 + 17.4822i) q^{89} +(-4.52941 + 2.91088i) q^{90} +2.90273 q^{91} +(2.31832 - 13.3436i) q^{92} -6.70750 q^{93} +(-9.16443 + 5.88962i) q^{94} +(-1.52196 + 10.5855i) q^{95} +(3.03008 - 6.63495i) q^{96} +(2.09088 - 0.613937i) q^{97} +(0.912403 + 1.99788i) q^{98} +(0.672462 + 0.776062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	1.84770	−	1.18744i	1.30652	−	0.839650i	0.312615	−	0.949880i	$-0.398795\pi$
$2$	1.84770	−	1.18744i	1.30652	−	0.839650i	0.993906	+	0.110230i	$0.0351586\pi$
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$	1.17314	−	2.56882i	0.586570	−	1.28441i
$5$	2.35208	−	0.690633i	1.05188	−	0.308860i	0.290305	−	0.956934i	$-0.406243\pi$
$5$	2.35208	−	0.690633i	1.05188	−	0.308860i	0.761578	+	0.648074i	$0.224425\pi$
$6$	−0.912403	−	1.99788i	−0.372487	−	0.815633i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$8$	−0.257569	−	1.79143i	−0.0910643	−	0.633366i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	3.52585	−	4.06905i	1.11497	−	1.28675i
$11$	−0.863864	−	0.555172i	−0.260465	−	0.167391i	0.403891	−	0.914807i	$-0.367658\pi$
$11$	−0.863864	−	0.555172i	−0.260465	−	0.167391i	−0.664356	+	0.747417i	$0.731294\pi$
$12$	−2.37572	−	1.52678i	−0.685811	−	0.440744i
$13$	−1.90088	+	2.19373i	−0.527210	+	0.608432i	−0.955421	−	0.295246i	$-0.904598\pi$
$13$	−1.90088	+	2.19373i	−0.527210	+	0.608432i	0.428212	+	0.903679i	$0.359144\pi$
$14$	−2.10740	−	0.618788i	−0.563226	−	0.165378i
$15$	−0.348867	−	2.42643i	−0.0900772	−	0.626501i
$16$	1.09555	+	1.26433i	0.273887	+	0.316082i
$17$	0.500171	+	1.09522i	0.121309	+	0.265630i	0.960538	−	0.278148i	$-0.0897205\pi$
$17$	0.500171	+	1.09522i	0.121309	+	0.265630i	−0.839229	+	0.543778i	$0.816993\pi$
$18$	−2.10740	+	0.618788i	−0.496718	+	0.145850i
$19$	−1.81228	+	3.96835i	−0.415766	+	0.910402i	0.579659	+	0.814859i	$0.303186\pi$
$19$	−1.81228	+	3.96835i	−0.415766	+	0.910402i	−0.995425	+	0.0955423i	$0.969541\pi$
$20$	0.985209	−	6.85228i	0.220299	−	1.53222i
$21$	−0.841254	+	0.540641i	−0.183577	+	0.117977i
$22$	−2.25540			−0.480852
$23$	4.63908	−	1.21611i	0.967315	−	0.253577i
$23$	4.63908	−	1.21611i	0.967315	−	0.253577i
$24$	−1.80985			−0.369434
$25$	0.849039	−	0.545644i	0.169808	−	0.109129i
$26$	−0.907321	+	6.31055i	−0.177940	+	1.23760i
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$	−2.70963	+	0.795619i	−0.512072	+	0.150358i
$29$	−0.173655	−	0.380251i	−0.0322469	−	0.0706108i	0.892823	−	0.450407i	$-0.148721\pi$
$29$	−0.173655	−	0.380251i	−0.0322469	−	0.0706108i	−0.925070	+	0.379797i	$0.875994\pi$
$30$	−3.52585	−	4.06905i	−0.643729	−	0.742903i
$31$	−0.954577	−	6.63923i	−0.171447	−	1.19244i	−0.875830	−	0.482620i	$-0.839685\pi$
$31$	−0.954577	−	6.63923i	−0.171447	−	1.19244i	0.704383	−	0.709820i	$-0.251224\pi$
$32$	6.99864	+	2.05499i	1.23720	+	0.363274i
$33$	−0.672462	+	0.776062i	−0.117061	+	0.135095i
$34$	2.22468	+	1.42972i	0.381530	+	0.245194i
$35$	−2.06223	−	1.32532i	−0.348581	−	0.224019i
$36$	−1.84934	+	2.13425i	−0.308223	+	0.355709i
$37$	−2.68567	−	0.788584i	−0.441522	−	0.129642i	0.0534132	−	0.998572i	$-0.482990\pi$
$37$	−2.68567	−	0.788584i	−0.441522	−	0.129642i	−0.494935	+	0.868930i	$0.664808\pi$
$38$	1.36364	+	9.48430i	0.221211	+	1.53856i
$39$	1.90088	+	2.19373i	0.304385	+	0.351279i
$40$	−1.84304	−	4.03570i	−0.291411	−	0.638100i
$41$	−5.89531	+	1.73102i	−0.920693	+	0.270340i	−0.707536	−	0.706678i	$-0.750193\pi$
$41$	−5.89531	+	1.73102i	−0.920693	+	0.270340i	−0.213158	+	0.977018i	$0.568375\pi$
$42$	−0.912403	+	1.99788i	−0.140787	+	0.308280i
$43$	−0.0677671	+	0.471330i	−0.0103344	+	0.0718772i	−0.994336	−	0.106282i	$-0.966105\pi$
$43$	−0.0677671	+	0.471330i	−0.0103344	+	0.0718772i	0.984002	+	0.178160i	$0.0570143\pi$
$44$	−2.43957	+	1.56782i	−0.367779	+	0.236357i
$45$	−2.45138			−0.365430
$46$	7.12756	−	7.75566i	1.05090	−	1.14351i
$47$	−4.95991			−0.723477			−0.361739	−	0.932280i	$-0.617817\pi$
$47$	−4.95991			−0.723477			−0.361739	+	0.932280i	$0.617817\pi$
$48$	1.40737	−	0.904464i	0.203137	−	0.130548i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	0.920847	−	2.01637i	0.130227	−	0.285158i
$51$	1.15526	−	0.339214i	0.161768	−	0.0474994i
$52$	3.40531	+	7.45658i	0.472231	+	1.03404i
$53$	4.62185	+	5.33389i	0.634859	+	0.732667i	0.978457	−	0.206450i	$-0.0661912\pi$
$53$	4.62185	+	5.33389i	0.634859	+	0.732667i	−0.343598	+	0.939117i	$0.611646\pi$
$54$	0.312575	+	2.17401i	0.0425361	+	0.295845i
$55$	−2.41530	−	0.709195i	−0.325679	−	0.0956279i
$56$	−1.18520	+	1.36779i	−0.158379	+	0.182779i
$57$	3.67004	+	2.35859i	0.486109	+	0.312403i
$58$	−0.772389	−	0.496384i	−0.101420	−	0.0651785i
$59$	−3.11116	+	3.59046i	−0.405038	+	0.467439i	−0.921221	−	0.389040i	$-0.872807\pi$
$59$	−3.11116	+	3.59046i	−0.405038	+	0.467439i	0.516183	+	0.856478i	$0.327352\pi$
$60$	−6.64232	−	1.95036i	−0.857520	−	0.251791i
$61$	1.29575	+	9.01212i	0.165903	+	1.15388i	0.887243	+	0.461302i	$0.152618\pi$
$61$	1.29575	+	9.01212i	0.165903	+	1.15388i	−0.721339	+	0.692582i	$0.756473\pi$
$62$	−9.64749	−	11.1338i	−1.22523	−	1.41399i
$63$	0.415415	+	0.909632i	0.0523374	+	0.114603i
$64$	12.1612	−	3.57086i	1.52015	−	0.446357i
$65$	−2.95596	+	6.47265i	−0.366642	+	0.802833i
$66$	−0.320977	+	2.23244i	−0.0395095	+	0.274795i
$67$	5.08487	−	3.26784i	0.621215	−	0.399231i	−0.191833	−	0.981428i	$-0.561443\pi$
$67$	5.08487	−	3.26784i	0.621215	−	0.399231i	0.813048	+	0.582197i	$0.197807\pi$
$68$	3.40020			0.412335
$69$	−0.543523	−	4.76493i	−0.0654325	−	0.573630i
$70$	−5.38412			−0.643526
$71$	11.2966	−	7.25987i	1.34066	−	0.861588i	0.343665	−	0.939092i	$-0.388331\pi$
$71$	11.2966	−	7.25987i	1.34066	−	0.861588i	0.996992	+	0.0775041i	$0.0246951\pi$
$72$	−0.257569	+	1.79143i	−0.0303548	+	0.211122i
$73$	2.92821	−	6.41189i	0.342721	−	0.750455i	−0.657274	−	0.753652i	$-0.728290\pi$
$73$	2.92821	−	6.41189i	0.342721	−	0.750455i	0.999995	+	0.00319718i	$0.00101770\pi$
$74$	−5.89872	+	1.73202i	−0.685712	+	0.201343i
$75$	−0.419259	−	0.918050i	−0.0484119	−	0.106007i
$76$	8.06791	+	9.31086i	0.925452	+	1.06803i
$77$	0.146140	+	1.01643i	0.0166542	+	0.115832i
$78$	6.11720	+	1.79617i	0.692636	+	0.203376i
$79$	8.60185	−	9.92706i	0.967783	−	1.11688i	−0.0253249	−	0.999679i	$-0.508062\pi$
$79$	8.60185	−	9.92706i	0.967783	−	1.11688i	0.993108	−	0.117202i	$-0.0373925\pi$
$80$	3.45000	+	2.21718i	0.385722	+	0.247889i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−8.83728	+	10.1988i	−0.975915	+	1.12627i
$83$	−5.98611	−	1.75768i	−0.657061	−	0.192931i	−0.0638276	−	0.997961i	$-0.520331\pi$
$83$	−5.98611	−	1.75768i	−0.657061	−	0.192931i	−0.593234	+	0.805030i	$0.702149\pi$
$84$	0.401900	+	2.79528i	0.0438509	+	0.304990i
$85$	1.93284	+	2.23062i	0.209646	+	0.241944i
$86$	0.434466	+	0.951347i	0.0468496	+	0.102586i
$87$	−0.401094	+	0.117772i	−0.0430018	+	0.0126265i
$88$	−0.772047	+	1.69055i	−0.0823005	+	0.180213i
$89$	−2.51357	+	17.4822i	−0.266437	+	1.85311i	0.214976	+	0.976619i	$0.431033\pi$
$89$	−2.51357	+	17.4822i	−0.266437	+	1.85311i	−0.481413	+	0.876494i	$0.659876\pi$
$90$	−4.52941	+	2.91088i	−0.477442	+	0.306833i
$91$	2.90273			0.304288
$92$	2.31832	−	13.3436i	0.241702	−	1.39117i
$93$	−6.70750			−0.695535
$94$	−9.16443	+	5.88962i	−0.945238	+	0.607468i
$95$	−1.52196	+	10.5855i	−0.156150	+	1.08605i
$96$	3.03008	−	6.63495i	0.309256	−	0.677177i
$97$	2.09088	−	0.613937i	0.212297	−	0.0623359i	−0.173855	−	0.984771i	$-0.555622\pi$
$97$	2.09088	−	0.613937i	0.212297	−	0.0623359i	0.386151	+	0.922435i	$0.373804\pi$
$98$	0.912403	+	1.99788i	0.0921666	+	0.201817i
$99$	0.672462	+	0.776062i	0.0675849	+	0.0779972i
$100$	−0.405619	−	2.82115i	−0.0405619	−	0.282115i
$101$	−12.1433	−	3.56560i	−1.20831	−	0.354790i	−0.385282	−	0.922799i	$-0.625896\pi$
$101$	−12.1433	−	3.56560i	−1.20831	−	0.354790i	−0.823023	+	0.568008i	$0.807714\pi$
$102$	1.73177	−	1.99857i	0.171471	−	0.197888i
$103$	1.43707	+	0.923547i	0.141598	+	0.0909998i	0.609522	−	0.792769i	$-0.291361\pi$
$103$	1.43707	+	0.923547i	0.141598	+	0.0909998i	−0.467924	+	0.883769i	$0.654998\pi$
$104$	4.41953	+	2.84026i	0.433370	+	0.278510i
$105$	−1.60531	+	1.85263i	−0.156662	+	0.180798i
$106$	14.8735	+	4.36725i	1.44464	+	0.424185i
$107$	1.15025	+	8.00016i	0.111199	+	0.773405i	0.966757	+	0.255698i	$0.0823052\pi$
$107$	1.15025	+	8.00016i	0.111199	+	0.773405i	−0.855558	+	0.517707i	$0.826786\pi$
$108$	1.84934	+	2.13425i	0.177953	+	0.205369i
$109$	1.04118	+	2.27986i	0.0997266	+	0.218371i	0.952919	−	0.303226i	$-0.0980638\pi$
$109$	1.04118	+	2.27986i	0.0997266	+	0.218371i	−0.853192	+	0.521597i	$0.825336\pi$
$110$	−5.30488	+	1.55765i	−0.505800	+	0.148516i
$111$	−1.16277	+	2.54611i	−0.110365	+	0.241666i
$112$	0.238085	−	1.65592i	0.0224969	−	0.156470i
$113$	8.05676	−	5.17777i	0.757917	−	0.487083i	−0.103722	−	0.994606i	$-0.533075\pi$
$113$	8.05676	−	5.17777i	0.757917	−	0.487083i	0.861638	+	0.507523i	$0.169439\pi$
$114$	9.58183			0.897421
$115$	10.0716	−	6.06429i	0.939182	−	0.565498i
$116$	−1.18052			−0.109608
$117$	2.44193	−	1.56933i	0.225756	−	0.145085i
$118$	−1.48500	+	10.3284i	−0.136706	+	0.950809i
$119$	0.500171	−	1.09522i	0.0458506	−	0.100399i
$120$	−4.25691	+	1.24994i	−0.388601	+	0.114104i
$121$	−4.13152	−	9.04677i	−0.375593	−	0.822433i
$122$	13.0956	+	15.1131i	1.18562	+	1.36827i
$123$	0.874410	+	6.08166i	0.0788429	+	0.548365i
$124$	−18.1748	−	5.33661i	−1.63215	−	0.479242i
$125$	−6.40639	+	7.39337i	−0.573005	+	0.661283i
$126$	1.84770	+	1.18744i	0.164606	+	0.105786i
$127$	−13.0283	−	8.37278i	−1.15607	−	0.742964i	−0.185235	−	0.982694i	$-0.559305\pi$
$127$	−13.0283	−	8.37278i	−1.15607	−	0.742964i	−0.970839	+	0.239731i	$0.922941\pi$
$128$	8.67684	−	10.0136i	0.766931	−	0.885086i
$129$	0.456889	+	0.134155i	0.0402268	+	0.0118117i
$130$	2.22419	+	15.4696i	0.195074	+	1.35677i
$131$	−11.8086	−	13.6279i	−1.03172	−	1.19067i	−0.981407	−	0.191939i	$-0.938522\pi$
$131$	−11.8086	−	13.6279i	−1.03172	−	1.19067i	−0.0503168	−	0.998733i	$-0.516023\pi$
$132$	1.20467	+	2.63786i	0.104853	+	0.229596i
$133$	4.18587	−	1.22908i	0.362961	−	0.106575i
$134$	5.51492	−	12.0760i	0.476417	−	1.04321i
$135$	−0.348867	+	2.42643i	−0.0300257	+	0.208834i
$136$	1.83318	−	1.17812i	0.157194	−	0.101023i
$137$	−14.5483			−1.24295			−0.621474	−	0.783435i	$-0.713466\pi$
$137$	−14.5483			−1.24295			−0.621474	+	0.783435i	$0.713466\pi$
$138$	−6.66236	−	8.15876i	−0.567138	−	0.694520i
$139$	7.49546			0.635756			0.317878	−	0.948132i	$-0.397030\pi$
$139$	7.49546			0.635756			0.317878	+	0.948132i	$0.397030\pi$
$140$	−5.82378	+	3.74272i	−0.492199	+	0.316317i
$141$	−0.705869	+	4.90943i	−0.0594449	+	0.413448i
$142$	12.2520	−	26.8281i	1.02816	−	2.25137i
$143$	2.86000	−	0.839773i	0.239165	−	0.0702253i
$144$	−0.694968	−	1.52177i	−0.0579140	−	0.126814i
$145$	−0.671064	−	0.774449i	−0.0557288	−	0.0643145i
$146$	−2.20331	−	15.3243i	−0.182347	−	1.26825i
$147$	0.959493	+	0.281733i	0.0791376	+	0.0232369i
$148$	−5.17640	+	5.97389i	−0.425498	+	0.491050i
$149$	1.25781	+	0.808344i	0.103044	+	0.0662221i	0.591148	−	0.806563i	$-0.298675\pi$
$149$	1.25781	+	0.808344i	0.103044	+	0.0662221i	−0.488104	+	0.872785i	$0.662311\pi$
$150$	−1.86480	−	1.19843i	−0.152260	−	0.0978517i
$151$	−8.91036	+	10.2831i	−0.725115	+	0.836827i	−0.991912	−	0.126925i	$-0.959489\pi$
$151$	−8.91036	+	10.2831i	−0.725115	+	0.836827i	0.266797	+	0.963753i	$0.414035\pi$
$152$	7.57580	+	2.22446i	0.614479	+	0.180427i
$153$	−0.171351	−	1.19177i	−0.0138529	−	0.0963491i
$154$	1.47697	+	1.70452i	0.119018	+	0.137354i
$155$	−6.83051	−	14.9567i	−0.548640	−	1.20135i
$156$	7.86531	−	2.30946i	0.629729	−	0.184905i
$157$	3.60886	−	7.90230i	0.288018	−	0.630672i	−0.709216	−	0.704991i	$-0.750951\pi$
$157$	3.60886	−	7.90230i	0.288018	−	0.630672i	0.997235	+	0.0743190i	$0.0236783\pi$
$158$	4.10580	−	28.5564i	0.326640	−	2.27183i
$159$	5.93736	−	3.81571i	0.470863	−	0.302605i
$160$	17.8806			1.41359
$161$	−3.95703	−	2.70960i	−0.311857	−	0.213546i
$162$	2.19637			0.172563
$163$	2.70390	−	1.73769i	0.211785	−	0.136106i	−0.430448	−	0.902615i	$-0.641644\pi$
$163$	2.70390	−	1.73769i	0.211785	−	0.136106i	0.642233	+	0.766509i	$0.278008\pi$
$164$	−2.46935	+	17.1747i	−0.192824	+	1.34112i
$165$	−1.04571	+	2.28978i	−0.0814084	+	0.178259i
$166$	−13.1477	+	3.86051i	−1.02046	+	0.299634i
$167$	−6.32181	−	13.8428i	−0.489197	−	1.07119i	−0.979831	−	0.199826i	$-0.935962\pi$
$167$	−6.32181	−	13.8428i	−0.489197	−	1.07119i	0.490635	−	0.871365i	$-0.336765\pi$
$168$	1.18520	+	1.36779i	0.0914402	+	0.105528i
$169$	0.650974	+	4.52762i	0.0500749	+	0.348279i
$170$	6.22004	+	1.82637i	0.477055	+	0.140076i
$171$	2.85689	−	3.29702i	0.218472	−	0.252130i
$172$	1.13126	+	0.727018i	0.0862580	+	0.0554346i
$173$	−2.14518	−	1.37862i	−0.163095	−	0.104815i	0.456547	−	0.889699i	$-0.349086\pi$
$173$	−2.14518	−	1.37862i	−0.163095	−	0.104815i	−0.619642	+	0.784884i	$0.712722\pi$
$174$	−0.601254	+	0.693885i	−0.0455810	+	0.0526033i
$175$	−0.968373	−	0.284340i	−0.0732021	−	0.0214941i
$176$	−0.244484	−	1.70043i	−0.0184287	−	0.128174i
$177$	3.11116	+	3.59046i	0.233849	+	0.269876i
$178$	16.1149	+	35.2867i	1.20786	+	2.64485i
$179$	−16.3085	+	4.78861i	−1.21896	+	0.357918i	−0.827071	−	0.562097i	$-0.809995\pi$
$179$	−16.3085	+	4.78861i	−1.21896	+	0.357918i	−0.391884	+	0.920015i	$0.628177\pi$
$180$	−2.87581	+	6.29715i	−0.214350	+	0.469362i
$181$	0.530037	−	3.68649i	0.0393973	−	0.274015i	−0.960595	−	0.277952i	$-0.910344\pi$
$181$	0.530037	−	3.68649i	0.0393973	−	0.274015i	0.999992	+	0.00393766i	$0.00125340\pi$
$182$	5.36337	−	3.44683i	0.397559	−	0.255496i
$183$	9.10480			0.673046
$184$	−3.37346	−	7.99735i	−0.248695	−	0.589573i
$185$	−6.86154			−0.504470
$186$	−12.3935	+	7.96479i	−0.908732	+	0.584007i
$187$	0.175956	−	1.22380i	0.0128672	−	0.0894934i
$188$	−5.81867	+	12.7411i	−0.424370	+	0.929241i
$189$	0.959493	−	0.281733i	0.0697928	−	0.0204930i
$190$	9.75756	+	21.3661i	0.707888	+	1.55006i
$191$	1.68725	+	1.94719i	0.122085	+	0.140894i	0.813502	−	0.581563i	$-0.197558\pi$
$191$	1.68725	+	1.94719i	0.122085	+	0.140894i	−0.691417	+	0.722456i	$0.743013\pi$
$192$	−1.80379	−	12.5456i	−0.130177	−	0.905402i
$193$	−8.53198	−	2.50521i	−0.614145	−	0.180329i	−0.0401577	−	0.999193i	$-0.512786\pi$
$193$	−8.53198	−	2.50521i	−0.614145	−	0.180329i	−0.573988	+	0.818864i	$0.694604\pi$
$194$	3.13430	−	3.61717i	0.225030	−	0.259698i
$195$	5.98609	+	3.84703i	0.428673	+	0.275491i
$196$	2.37572	+	1.52678i	0.169694	+	0.109056i
$197$	−9.22433	+	10.6454i	−0.657206	+	0.758456i	−0.982318	−	0.187219i	$-0.940052\pi$
$197$	−9.22433	+	10.6454i	−0.657206	+	0.758456i	0.325112	+	0.945675i	$0.394598\pi$
$198$	2.16404	+	0.635419i	0.153792	+	0.0451573i
$199$	−1.35690	−	9.43742i	−0.0961878	−	0.669001i	−0.979682	−	0.200558i	$-0.935724\pi$
$199$	−1.35690	−	9.43742i	−0.0961878	−	0.669001i	0.883494	−	0.468443i	$-0.155185\pi$
$200$	−1.19617	−	1.38045i	−0.0845819	−	0.0976127i
$201$	−2.51093	−	5.49817i	−0.177107	−	0.387811i
$202$	−26.6712	+	7.83136i	−1.87658	+	0.551013i
$203$	−0.173655	+	0.380251i	−0.0121882	+	0.0266884i
$204$	0.483899	−	3.36559i	0.0338797	−	0.235638i
$205$	−12.6708	+	8.14300i	−0.884964	+	0.568732i
$206$	3.75193			0.261409
$207$	−4.79378	−	0.140129i	−0.333191	−	0.00973967i
$208$	−4.85611			−0.336711
$209$	3.76868	−	2.42199i	0.260685	−	0.167532i
$210$	−0.766240	+	5.32932i	−0.0528756	+	0.367758i
$211$	8.11757	−	17.7750i	0.558837	−	1.22368i	−0.393694	−	0.919241i	$-0.628803\pi$
$211$	8.11757	−	17.7750i	0.558837	−	1.22368i	0.952531	−	0.304441i	$-0.0984696\pi$
$212$	19.1239	−	5.61528i	1.31343	−	0.385659i
$213$	−5.57830	−	12.2148i	−0.382219	−	0.836943i
$214$	11.6251	+	13.4160i	0.794674	+	0.917102i
$215$	0.166123	+	1.15541i	0.0113295	+	0.0787983i
$216$	1.73654	+	0.509894i	0.118157	+	0.0346939i
$217$	−4.39248	+	5.06919i	−0.298181	+	0.344119i
$218$	4.63099	+	2.97615i	0.313650	+	0.201571i
$219$	−5.92990	−	3.81091i	−0.400705	−	0.257518i
$220$	−4.65528	+	5.37248i	−0.313859	+	0.362212i
$221$	−3.35339	−	0.984645i	−0.225574	−	0.0662344i
$222$	0.874915	+	6.08517i	0.0587205	+	0.408410i
$223$	11.6957	+	13.4975i	0.783200	+	0.903861i	0.997336	−	0.0729429i	$-0.0232391\pi$
$223$	11.6957	+	13.4975i	0.783200	+	0.903861i	−0.214136	+	0.976804i	$0.568694\pi$
$224$	−3.03008	−	6.63495i	−0.202456	−	0.443316i
$225$	−0.968373	+	0.284340i	−0.0645582	+	0.0189560i
$226$	8.73817	−	19.1339i	0.581254	−	1.27277i
$227$	−2.44176	+	16.9828i	−0.162065	+	1.12719i	0.732668	+	0.680586i	$0.238275\pi$
$227$	−2.44176	+	16.9828i	−0.162065	+	1.12719i	−0.894733	+	0.446601i	$0.852634\pi$
$228$	10.3643	−	6.66071i	0.686391	−	0.441117i
$229$	24.6023			1.62577			0.812883	−	0.582427i	$-0.197897\pi$
$229$	24.6023			1.62577			0.812883	+	0.582427i	$0.197897\pi$
$230$	11.4083	−	23.1645i	0.752240	−	1.52742i
$231$	1.02688			0.0675636
$232$	−0.636465	+	0.409031i	−0.0417860	+	0.0268542i
$233$	−2.97386	+	20.6836i	−0.194824	+	1.35503i	0.624198	+	0.781266i	$0.285426\pi$
$233$	−2.97386	+	20.6836i	−0.194824	+	1.35503i	−0.819022	+	0.573763i	$0.805483\pi$
$234$	2.64846	−	5.79931i	0.173135	−	0.379113i
$235$	−11.6661	+	3.42548i	−0.761013	+	0.223454i
$236$	5.57343	+	12.2041i	0.362800	+	0.794420i
$237$	−8.60185	−	9.92706i	−0.558750	−	0.644832i
$238$	−0.376349	−	2.61757i	−0.0243951	−	0.169672i
$239$	−25.6698	−	7.53734i	−1.66044	−	0.487550i	−0.688988	−	0.724773i	$-0.741945\pi$
$239$	−25.6698	−	7.53734i	−1.66044	−	0.487550i	−0.971455	+	0.237222i	$0.923763\pi$
$240$	2.68560	−	3.09935i	0.173355	−	0.200062i
$241$	−11.7813	−	7.57138i	−0.758900	−	0.487715i	0.103070	−	0.994674i	$-0.467133\pi$
$241$	−11.7813	−	7.57138i	−0.758900	−	0.487715i	−0.861970	+	0.506959i	$0.830770\pi$
$242$	−18.3763	−	11.8098i	−1.18128	−	0.759160i
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$	24.6706	+	7.24395i	1.57937	+	0.463746i
$245$	0.348867	+	2.42643i	0.0222883	+	0.155019i
$246$	8.83728	+	10.1988i	0.563445	+	0.650250i
$247$	−5.26056	−	11.5190i	−0.334722	−	0.732938i
$248$	−11.6478	+	3.42011i	−0.739638	+	0.217177i
$249$	−2.59170	+	5.67504i	−0.164243	+	0.359641i
$250$	−3.05787	+	21.2680i	−0.193397	+	1.34510i
$251$	25.0372	−	16.0905i	1.58034	−	1.01562i	0.604639	−	0.796500i	$-0.293317\pi$
$251$	25.0372	−	16.0905i	1.58034	−	1.01562i	0.975698	−	0.219121i	$-0.0703189\pi$
$252$	2.82402			0.177897
$253$	−4.68269	−	1.52493i	−0.294398	−	0.0958716i
$254$	−34.0146			−2.13427
$255$	2.48298	−	1.59572i	0.155490	−	0.0999276i
$256$	0.534017	−	3.71417i	0.0333761	−	0.232136i
$257$	−0.388334	+	0.850334i	−0.0242236	+	0.0530424i	−0.921357	−	0.388717i	$-0.872918\pi$
$257$	−0.388334	+	0.850334i	−0.0242236	+	0.0530424i	0.897133	+	0.441760i	$0.145646\pi$
$258$	1.00349	−	0.294653i	0.0624748	−	0.0183443i
$259$	1.16277	+	2.54611i	0.0722509	+	0.158207i
$260$	13.1593	+	15.1867i	0.816106	+	0.941836i
$261$	0.0594915	+	0.413772i	0.00368243	+	0.0256119i
$262$	−38.0011	−	11.1581i	−2.34772	−	0.689352i
$263$	−0.550862	+	0.635729i	−0.0339676	+	0.0392007i	−0.772479	−	0.635040i	$-0.780984\pi$
$263$	−0.550862	+	0.635729i	−0.0339676	+	0.0392007i	0.738512	+	0.674241i	$0.235529\pi$
$264$	1.56347	+	1.00478i	0.0962246	+	0.0618398i
$265$	14.5547	+	9.35375i	0.894089	+	0.574596i
$266$	6.27477	−	7.24147i	0.384731	−	0.444003i
$267$	16.9466	+	4.97596i	1.03711	+	0.304524i
$268$	−2.42924	−	16.8957i	−0.148390	−	1.03207i
$269$	−3.08166	−	3.55643i	−0.187892	−	0.216839i	0.653986	−	0.756506i	$-0.273095\pi$
$269$	−3.08166	−	3.55643i	−0.187892	−	0.216839i	−0.841878	+	0.539667i	$0.818550\pi$
$270$	2.23665	+	4.89757i	0.136118	+	0.298057i
$271$	−11.9907	+	3.52078i	−0.728382	+	0.213872i	−0.624840	−	0.780753i	$-0.714836\pi$
$271$	−11.9907	+	3.52078i	−0.728382	+	0.213872i	−0.103542	+	0.994625i	$0.533018\pi$
$272$	−0.836760	+	1.83225i	−0.0507360	+	0.111096i
$273$	0.413101	−	2.87318i	0.0250020	−	0.173893i
$274$	−26.8810	+	17.2753i	−1.62394	+	1.04364i
$275$	−1.03638			−0.0624961
$276$	−12.8779	−	4.19372i	−0.775157	−	0.252432i
$277$	−11.8950			−0.714700			−0.357350	−	0.933971i	$-0.616320\pi$
$277$	−11.8950			−0.714700			−0.357350	+	0.933971i	$0.616320\pi$
$278$	13.8494	−	8.90044i	0.830629	−	0.533813i
$279$	−0.954577	+	6.63923i	−0.0571490	+	0.397480i
$280$	−1.84304	+	4.03570i	−0.110143	+	0.241179i
$281$	6.88319	−	2.02109i	0.410617	−	0.120568i	−0.0698988	−	0.997554i	$-0.522268\pi$
$281$	6.88319	−	2.02109i	0.410617	−	0.120568i	0.480516	+	0.876986i	$0.340449\pi$
$282$	4.52544	+	9.90933i	0.269486	+	0.590092i
$283$	−10.0352	−	11.5813i	−0.596532	−	0.688435i	0.374543	−	0.927210i	$-0.377800\pi$
$283$	−10.0352	−	11.5813i	−0.596532	−	0.688435i	−0.971075	+	0.238775i	$0.923254\pi$
$284$	−5.39682	−	37.5357i	−0.320243	−	2.22734i
$285$	10.2612	+	3.01295i	0.607818	+	0.178472i
$286$	4.28724	−	4.94774i	0.253510	−	0.292566i
$287$	5.16883	+	3.32180i	0.305106	+	0.196080i
$288$	−6.13619	−	3.94349i	−0.361579	−	0.232372i
$289$	10.1833	−	11.7521i	0.599017	−	0.691303i
$290$	−2.15954	−	0.634098i	−0.126813	−	0.0372355i
$291$	−0.310125	−	2.15697i	−0.0181799	−	0.126444i
$292$	−13.0358	−	15.0441i	−0.762861	−	0.880389i
$293$	0.640822	+	1.40320i	0.0374372	+	0.0819760i	0.927427	−	0.374005i	$-0.122016\pi$
$293$	0.640822	+	1.40320i	0.0374372	+	0.0819760i	−0.889989	+	0.455981i	$0.849288\pi$
$294$	2.10740	−	0.618788i	0.122906	−	0.0360884i
$295$	−4.83799	+	10.5937i	−0.281679	+	0.616791i
$296$	−0.720948	+	5.01431i	−0.0419043	+	0.291451i
$297$	0.863864	−	0.555172i	0.0501265	−	0.0322143i
$298$	3.28392			0.190232
$299$	−6.15052	+	12.4886i	−0.355694	+	0.722234i
$300$	−2.85016			−0.164554
$301$	0.400586	−	0.257441i	0.0230894	−	0.0148386i
$302$	−4.25306	+	29.5807i	−0.244736	+	1.70218i
$303$	−5.25748	+	11.5123i	−0.302034	+	0.661363i
$304$	−7.00274	+	2.05619i	−0.401635	+	0.117931i
$305$	9.27177	+	20.3023i	0.530900	+	1.16251i
$306$	−1.73177	−	1.99857i	−0.0989987	−	0.114251i
$307$	−3.73398	−	25.9704i	−0.213110	−	1.48221i	−0.762687	−	0.646767i	$-0.776120\pi$
$307$	−3.73398	−	25.9704i	−0.213110	−	1.48221i	0.549578	−	0.835443i	$-0.314789\pi$
$308$	2.78246	+	0.817003i	0.158545	+	0.0465531i
$309$	1.11866	−	1.29101i	0.0636385	−	0.0734428i
$310$	−30.3810	−	19.5247i	−1.72553	−	1.10893i
$311$	12.6036	+	8.09987i	0.714687	+	0.459301i	0.846785	−	0.531935i	$-0.178535\pi$
$311$	12.6036	+	8.09987i	0.714687	+	0.459301i	−0.132098	+	0.991237i	$0.542171\pi$
$312$	3.44031	−	3.97033i	0.194769	−	0.224776i
$313$	16.2561	+	4.77323i	0.918851	+	0.269799i	0.706762	−	0.707451i	$-0.250155\pi$
$313$	16.2561	+	4.77323i	0.918851	+	0.269799i	0.212089	+	0.977250i	$0.431973\pi$
$314$	−2.71545	−	18.8864i	−0.153242	−	1.06582i
$315$	1.60531	+	1.85263i	0.0904490	+	0.104384i
$316$	−15.4096	−	33.7424i	−0.866861	−	1.89816i
$317$	15.5422	−	4.56359i	0.872935	−	0.256317i	0.185572	−	0.982631i	$-0.440586\pi$
$317$	15.5422	−	4.56359i	0.872935	−	0.256317i	0.687363	+	0.726314i	$0.258768\pi$
$318$	6.43952	−	14.1006i	0.361110	−	0.790721i
$319$	−0.0610905	+	0.424894i	−0.00342041	+	0.0237895i
$320$	26.1380	−	16.7979i	1.46116	−	0.939030i
$321$	8.08243			0.451117
$322$	−10.5289	−	0.307775i	−0.586753	−	0.0171517i
$323$	−5.25268			−0.292267
$324$	2.37572	−	1.52678i	0.131984	−	0.0848212i
$325$	−0.416924	+	2.89977i	−0.0231268	+	0.160850i
$326$	2.93258	−	6.42145i	0.162421	−	0.355651i
$327$	2.40483	−	0.706121i	0.132987	−	0.0390486i
$328$	4.61945	+	10.1152i	0.255066	+	0.558517i
$329$	3.24805	+	3.74845i	0.179071	+	0.206659i
$330$	0.786835	+	5.47256i	0.0433138	+	0.301254i
$331$	14.6917	+	4.31388i	0.807531	+	0.237113i	0.659339	−	0.751846i	$-0.270836\pi$
$331$	14.6917	+	4.31388i	0.807531	+	0.237113i	0.148192	+	0.988959i	$0.452654\pi$
$332$	−11.5377	+	13.3152i	−0.633215	+	0.730769i
$333$	2.35471	+	1.51328i	0.129038	+	0.0829274i
$334$	−28.1184	−	18.0706i	−1.53857	−	0.988780i
$335$	9.70313	−	11.1980i	0.530139	−	0.611813i
$336$	−1.60518	−	0.471324i	−0.0875698	−	0.0257128i
$337$	−4.09936	−	28.5117i	−0.223306	−	1.55313i	−0.725407	−	0.688321i	$-0.758348\pi$
$337$	−4.09936	−	28.5117i	−0.223306	−	1.55313i	0.502100	−	0.864809i	$-0.332561\pi$
$338$	6.57911	+	7.59269i	0.357856	+	0.412988i
$339$	−3.97847	−	8.71163i	−0.216081	−	0.473151i
$340$	7.99754	−	2.34829i	0.433728	−	0.127354i
$341$	−2.86129	+	6.26535i	−0.154947	+	0.339288i
$342$	1.36364	−	9.48430i	0.0737371	−	0.512852i
$343$	0.841254	−	0.540641i	0.0454234	−	0.0291919i
$344$	0.861810			0.0464657
$345$	−4.56923	−	10.8321i	−0.245999	−	0.583182i
$346$	−5.60068			−0.301094
$347$	25.8712	−	16.6264i	1.38884	−	0.892554i	0.389250	−	0.921132i	$-0.372734\pi$
$347$	25.8712	−	16.6264i	1.38884	−	0.892554i	0.999592	+	0.0285780i	$0.00909790\pi$
$348$	−0.168005	+	1.16850i	−0.00900603	+	0.0626383i
$349$	9.79394	−	21.4457i	0.524257	−	1.14796i	−0.443545	−	0.896252i	$-0.646279\pi$
$349$	9.79394	−	21.4457i	0.524257	−	1.14796i	0.967802	−	0.251712i	$-0.0809934\pi$
$350$	−2.12690	+	0.624514i	−0.113688	+	0.0333817i
$351$	−1.20584	−	2.64041i	−0.0643628	−	0.140935i
$352$	−4.90501	−	5.66068i	−0.261438	−	0.301715i
$353$	3.15820	+	21.9657i	0.168094	+	1.16912i	0.882819	+	0.469713i	$0.155643\pi$
$353$	3.15820	+	21.9657i	0.168094	+	1.16912i	−0.714725	+	0.699405i	$0.753448\pi$
$354$	10.0120	+	2.93978i	0.532130	+	0.156247i
$355$	21.5566	−	24.8776i	1.14410	−	1.32037i
$356$	41.9599	+	26.9660i	2.22387	+	1.42920i
$357$	−1.01289	−	0.650947i	−0.0536080	−	0.0344517i
$358$	−24.4470	+	28.2134i	−1.29207	+	1.49112i
$359$	24.1404	+	7.08827i	1.27408	+	0.374104i	0.847718	−	0.530447i	$-0.177976\pi$
$359$	24.1404	+	7.08827i	1.27408	+	0.374104i	0.426365	+	0.904551i	$0.359794\pi$
$360$	0.631398	+	4.39147i	0.0332776	+	0.231451i
$361$	−0.0210617	−	0.0243065i	−0.00110851	−	0.00127929i
$362$	−3.39815	−	7.44092i	−0.178603	−	0.391086i
$363$	−9.54266	+	2.80198i	−0.500860	+	0.147066i
$364$	3.40531	−	7.45658i	0.178487	−	0.390831i
$365$	2.45913	−	17.1036i	0.128717	−	0.895243i
$366$	16.8229	−	10.8114i	0.879349	−	0.565123i
$367$	−24.8041			−1.29476			−0.647382	−	0.762166i	$-0.724136\pi$
$367$	−24.8041			−1.29476			−0.647382	+	0.762166i	$0.724136\pi$
$368$	6.61990	+	4.53302i	0.345086	+	0.236300i
$369$	6.14420			0.319854
$370$	−12.6781	+	8.14770i	−0.659101	+	0.423579i
$371$	1.00442	−	6.98591i	0.0521470	−	0.362691i
$372$	−7.86884	+	17.2304i	−0.407980	+	0.893353i
$373$	−15.1132	+	4.43764i	−0.782532	+	0.229772i	−0.648510	−	0.761206i	$-0.724608\pi$
$373$	−15.1132	+	4.43764i	−0.782532	+	0.229772i	−0.134022	+	0.990978i	$0.542789\pi$
$374$	−1.12809	−	2.47016i	−0.0583319	−	0.127729i
$375$	6.40639	+	7.39337i	0.330824	+	0.381792i
$376$	1.27752	+	8.88533i	0.0658829	+	0.458226i
$377$	1.16427	+	0.341860i	0.0599628	+	0.0176067i
$378$	1.43831	−	1.65990i	0.0739789	−	0.0853762i
$379$	−26.3577	−	16.9390i	−1.35390	−	0.870100i	−0.355977	−	0.934495i	$-0.615852\pi$
$379$	−26.3577	−	16.9390i	−1.35390	−	0.870100i	−0.997925	+	0.0643945i	$0.979488\pi$
$380$	25.4068	+	16.3279i	1.30334	+	0.837605i
$381$	−10.1417	+	11.7041i	−0.519574	+	0.599620i
$382$	5.42971	+	1.59431i	0.277808	+	0.0815718i
$383$	2.65315	+	18.4531i	0.135570	+	0.942907i	0.938117	+	0.346319i	$0.112568\pi$
$383$	2.65315	+	18.4531i	0.135570	+	0.942907i	−0.802547	+	0.596589i	$0.796522\pi$
$384$	−8.67684	−	10.0136i	−0.442788	−	0.511005i
$385$	1.04571	+	2.28978i	0.0532943	+	0.116698i
$386$	−18.7393	+	5.50237i	−0.953807	+	0.280063i
$387$	0.197811	−	0.433146i	0.0100553	−	0.0220181i
$388$	0.875800	−	6.09133i	0.0444620	−	0.309240i
$389$	29.4534	−	18.9286i	1.49335	−	0.959716i	0.497618	−	0.867396i	$-0.334208\pi$
$389$	29.4534	−	18.9286i	1.49335	−	0.959716i	0.995729	−	0.0923196i	$-0.0294281\pi$
$390$	15.6286			0.791387
$391$	3.65225	+	4.47256i	0.184702	+	0.226187i
$392$	1.80985			0.0914113
$393$	−15.1697	+	9.74897i	−0.765210	+	0.491771i
$394$	−4.40292	+	30.6230i	−0.221816	+	1.54276i
$395$	13.3763	−	29.2900i	0.673033	−	1.47374i
$396$	2.78246	−	0.817003i	0.139824	−	0.0410559i
$397$	2.53959	+	5.56093i	0.127458	+	0.279095i	0.962593	−	0.270950i	$-0.0873378\pi$
$397$	2.53959	+	5.56093i	0.127458	+	0.279095i	−0.835135	+	0.550045i	$0.814611\pi$
$398$	−13.7136	−	15.8263i	−0.687398	−	0.793300i
$399$	−0.620861	−	4.31818i	−0.0310819	−	0.216179i
$400$	1.62004	+	0.475686i	0.0810018	+	0.0237843i
$401$	1.22482	−	1.41352i	0.0611648	−	0.0705879i	−0.724343	−	0.689440i	$-0.757857\pi$
$401$	1.22482	−	1.41352i	0.0611648	−	0.0705879i	0.785507	+	0.618852i	$0.212402\pi$
$402$	−11.1682	−	7.17738i	−0.557020	−	0.357975i
$403$	16.3792	+	10.5263i	0.815908	+	0.524352i
$404$	−23.4052	+	27.0110i	−1.16445	+	1.34385i
$405$	2.35208	+	0.690633i	0.116876	+	0.0343178i
$406$	0.130665	+	0.908795i	0.00648480	+	0.0451028i
$407$	1.88226	+	2.17224i	0.0933000	+	0.107674i
$408$	−0.905235	−	1.98219i	−0.0448158	−	0.0981330i
$409$	28.3619	−	8.32781i	1.40241	−	0.411783i	0.508896	−	0.860828i	$-0.330054\pi$
$409$	28.3619	−	8.32781i	1.40241	−	0.411783i	0.893509	+	0.449044i	$0.148235\pi$
$410$	−13.7424	+	30.0916i	−0.678688	+	1.48612i
$411$	−2.07044	+	14.4003i	−0.102127	+	0.710312i
$412$	4.05831	−	2.60812i	0.199939	−	0.128493i
$413$	4.75087			0.233775
$414$	−9.02387	+	5.43344i	−0.443499	+	0.267039i
$415$	−15.2937			−0.750740
$416$	−17.8117	+	11.4469i	−0.873290	+	0.561229i
$417$	1.06671	−	7.41916i	0.0522373	−	0.363318i
$418$	4.08742	−	8.95020i	0.199922	−	0.437769i
$419$	6.35488	−	1.86596i	0.310456	−	0.0911582i	−0.122793	−	0.992432i	$-0.539185\pi$
$419$	6.35488	−	1.86596i	0.310456	−	0.0911582i	0.433249	+	0.901274i	$0.357367\pi$
$420$	2.87581	+	6.29715i	0.140325	+	0.307269i
$421$	7.52515	+	8.68448i	0.366753	+	0.423256i	0.908891	−	0.417034i	$-0.136930\pi$
$421$	7.52515	+	8.68448i	0.366753	+	0.423256i	−0.542138	+	0.840290i	$0.682385\pi$
$422$	−6.10800	−	42.4821i	−0.297333	−	2.06799i
$423$	4.75900	+	1.39737i	0.231390	+	0.0679424i
$424$	8.36485	−	9.65355i	0.406233	−	0.468818i
$425$	1.02227	+	0.656971i	0.0495872	+	0.0318678i
$426$	−24.8114	−	15.9453i	−1.20212	−	0.772554i
$427$	5.96237	−	6.88095i	0.288539	−	0.332992i
$428$	21.9004	+	6.43053i	1.05860	+	0.310832i
$429$	−0.424204	−	2.95040i	−0.0204808	−	0.142447i
$430$	1.67893	+	1.93759i	0.0809652	+	0.0934388i
$431$	8.43402	+	18.4679i	0.406252	+	0.889568i	0.996598	+	0.0824178i	$0.0262642\pi$
$431$	8.43402	+	18.4679i	0.406252	+	0.889568i	−0.590346	+	0.807151i	$0.701009\pi$
$432$	−1.60518	+	0.471324i	−0.0772293	+	0.0226766i
$433$	−13.8581	+	30.3450i	−0.665979	+	1.45829i	0.210866	+	0.977515i	$0.432372\pi$
$433$	−13.8581	+	30.3450i	−0.665979	+	1.45829i	−0.876844	+	0.480775i	$0.840356\pi$
$434$	−2.09660	+	14.5822i	−0.100640	+	0.699967i
$435$	−0.862069	+	0.554018i	−0.0413330	+	0.0265631i
$436$	7.07799			0.338974
$437$	−3.58138	+	20.6134i	−0.171320	+	0.986074i
$438$	−15.4819			−0.739755
$439$	12.2084	−	7.84589i	0.582677	−	0.374464i	−0.215846	−	0.976427i	$-0.569251\pi$
$439$	12.2084	−	7.84589i	0.582677	−	0.374464i	0.798524	+	0.601963i	$0.205615\pi$
$440$	−0.648368	+	4.50950i	−0.0309098	+	0.214982i
$441$	0.415415	−	0.909632i	0.0197817	−	0.0433158i
$442$	−7.36527	+	2.16264i	−0.350330	+	0.102866i
$443$	5.75476	+	12.6012i	0.273417	+	0.598699i	0.995673	−	0.0929265i	$-0.0296221\pi$
$443$	5.75476	+	12.6012i	0.273417	+	0.598699i	−0.722256	+	0.691626i	$0.756895\pi$
$444$	5.17640	+	5.97389i	0.245661	+	0.283508i
$445$	6.16170	+	42.8556i	0.292093	+	2.03155i
$446$	37.6377	+	11.0514i	1.78219	+	0.523300i
$447$	0.979121	−	1.12997i	0.0463108	−	0.0534456i
$448$	−10.6626	−	6.85242i	−0.503759	−	0.323746i
$449$	−25.2402	−	16.2209i	−1.19116	−	0.765510i	−0.213752	−	0.976888i	$-0.568568\pi$
$449$	−25.2402	−	16.2209i	−1.19116	−	0.765510i	−0.977404	+	0.211378i	$0.932205\pi$
$450$	−1.45162	+	1.67526i	−0.0684302	+	0.0789727i
$451$	6.05376	+	1.77755i	0.285061	+	0.0837014i
$452$	−3.84903	−	26.7706i	−0.181043	−	1.25918i
$453$	8.91036	+	10.2831i	0.418645	+	0.483142i
$454$	15.6545	+	34.2786i	0.734702	+	1.60877i
$455$	6.82744	−	2.00472i	0.320076	−	0.0939827i
$456$	3.27996	−	7.18212i	0.153598	−	0.336334i
$457$	−5.65661	+	39.3426i	−0.264605	+	1.84037i	0.232398	+	0.972621i	$0.425343\pi$
$457$	−5.65661	+	39.3426i	−0.264605	+	1.84037i	−0.497003	+	0.867749i	$0.665566\pi$
$458$	45.4577	−	29.2139i	2.12410	−	1.36507i
$459$	−1.20403			−0.0561992
$460$	−3.76267	−	32.9864i	−0.175436	−	1.53800i
$461$	2.26230			0.105366			0.0526829	−	0.998611i	$-0.483223\pi$
$461$	2.26230			0.105366			0.0526829	+	0.998611i	$0.483223\pi$
$462$	1.89736	−	1.21936i	0.0882732	−	0.0567298i
$463$	3.13011	−	21.7704i	0.145469	−	1.01176i	−0.778050	−	0.628203i	$-0.783791\pi$
$463$	3.13011	−	21.7704i	0.145469	−	1.01176i	0.923518	−	0.383554i	$-0.125300\pi$
$464$	0.290515	−	0.636140i	0.0134868	−	0.0295321i
$465$	−15.7766	+	4.63242i	−0.731621	+	0.214823i
$466$	19.0659	+	41.7484i	0.883209	+	1.93396i
$467$	−4.11198	−	4.74548i	−0.190280	−	0.219595i	0.652591	−	0.757710i	$-0.273682\pi$
$467$	−4.11198	−	4.74548i	−0.190280	−	0.219595i	−0.842871	+	0.538115i	$0.819136\pi$
$468$	−1.16661	−	8.11392i	−0.0539264	−	0.375066i
$469$	−5.79955	−	1.70290i	−0.267798	−	0.0786327i
$470$	−17.4879	+	20.1821i	−0.806657	+	0.930931i
$471$	−7.30827	−	4.69674i	−0.336747	−	0.216414i
$472$	7.23340	+	4.64862i	0.332944	+	0.213970i
$473$	0.320211	−	0.369543i	0.0147233	−	0.0169916i
$474$	−27.6815	−	8.12801i	−1.27145	−	0.373332i
$475$	0.626607	+	4.35814i	0.0287507	+	0.199965i
$476$	−2.22666	−	2.56970i	−0.102059	−	0.117782i
$477$	−2.93190	−	6.41996i	−0.134242	−	0.293950i
$478$	−56.3803	+	16.5548i	−2.57878	+	0.757197i
$479$	−11.0320	+	24.1567i	−0.504064	+	1.10375i	0.471063	+	0.882100i	$0.343871\pi$
$479$	−11.0320	+	24.1567i	−0.504064	+	1.10375i	−0.975127	+	0.221647i	$0.928857\pi$
$480$	2.54468	−	17.6986i	0.116148	−	0.807828i
$481$	6.83509	−	4.39264i	0.311653	−	0.200287i
$482$	−30.7589			−1.40103
$483$	−3.24516	+	3.53113i	−0.147660	+	0.160672i
$484$	−28.0864			−1.27665
$485$	4.49391	−	2.88806i	0.204058	−	0.131140i
$486$	0.312575	−	2.17401i	0.0141787	−	0.0986151i
$487$	2.50489	−	5.48493i	0.113507	−	0.248546i	−0.844349	−	0.535793i	$-0.820013\pi$
$487$	2.50489	−	5.48493i	0.113507	−	0.248546i	0.957857	+	0.287247i	$0.0927400\pi$
$488$	15.8108	−	4.64248i	0.715723	−	0.210155i
$489$	−1.33520	−	2.92367i	−0.0603797	−	0.132213i
$490$	3.52585	+	4.06905i	0.159282	+	0.183821i
$491$	3.80199	+	26.4434i	0.171582	+	1.19338i	0.875544	+	0.483139i	$0.160503\pi$
$491$	3.80199	+	26.4434i	0.171582	+	1.19338i	−0.703962	+	0.710237i	$0.748588\pi$
$492$	16.6485	+	4.88844i	0.750572	+	0.220388i
$493$	0.329602	−	0.380381i	0.0148445	−	0.0171315i
$494$	−23.3982	−	15.0371i	−1.05273	−	0.676550i
$495$	2.11766	+	1.36094i	0.0951816	+	0.0611695i
$496$	7.34839	−	8.48049i	0.329952	−	0.380785i
$497$	−12.8843	−	3.78318i	−0.577941	−	0.169699i
$498$	1.95010	+	13.5633i	0.0873863	+	0.607785i
$499$	15.2877	+	17.6429i	0.684370	+	0.789805i	0.986552	−	0.163445i	$-0.0522607\pi$
$499$	15.2877	+	17.6429i	0.684370	+	0.789805i	−0.302183	+	0.953250i	$0.597715\pi$
$500$	11.4766	+	25.1303i	0.513251	+	1.12386i
$501$	−14.6016	+	4.28743i	−0.652353	+	0.191548i
$502$	27.1548	−	59.4607i	1.21198	−	2.65386i
$503$	−2.25286	+	15.6690i	−0.100450	+	0.698645i	0.875907	+	0.482480i	$0.160264\pi$
$503$	−2.25286	+	15.6690i	−0.100450	+	0.698645i	−0.976357	+	0.216165i	$0.930645\pi$
$504$	1.52254	−	0.978479i	0.0678195	−	0.0435849i
$505$	−31.0246			−1.38058
$506$	−10.4630	+	2.74282i	−0.465136	+	0.121933i
$507$	4.57418			0.203146
$508$	−36.7922	+	23.6449i	−1.63239	+	1.04907i
$509$	−1.24645	+	8.66922i	−0.0552477	+	0.384256i	0.943372	+	0.331736i	$0.107634\pi$
$509$	−1.24645	+	8.66922i	−0.0552477	+	0.384256i	−0.998620	+	0.0525200i	$0.983275\pi$
$510$	2.69298	−	5.89681i	0.119247	−	0.261115i
$511$	−6.76335	+	1.98590i	−0.299193	+	0.0878510i
$512$	7.58474	+	16.6083i	0.335201	+	0.733989i
$513$	−2.85689	−	3.29702i	−0.126135	−	0.145567i
$514$	0.292199	+	2.03229i	0.0128883	+	0.0896404i
$515$	4.01793	+	1.17977i	0.177051	+	0.0519869i
$516$	0.880614	−	1.01628i	0.0387669	−	0.0447393i
$517$	4.28469	+	2.75360i	0.188440	+	0.121103i
$518$	5.17181	+	3.32372i	0.227236	+	0.146036i
$519$	−1.66988	+	1.92714i	−0.0732996	+	0.0845922i
$520$	12.3567	+	3.62824i	0.541875	+	0.159109i
$521$	−4.20367	−	29.2372i	−0.184166	−	1.28091i	−0.846780	−	0.531944i	$-0.821462\pi$
$521$	−4.20367	−	29.2372i	−0.184166	−	1.28091i	0.662613	−	0.748962i	$-0.269447\pi$
$522$	0.601254	+	0.693885i	0.0263162	+	0.0303705i
$523$	15.6713	+	34.3153i	0.685258	+	1.50050i	0.856975	+	0.515358i	$0.172341\pi$
$523$	15.6713	+	34.3153i	0.685258	+	1.50050i	−0.171717	+	0.985146i	$0.554932\pi$
$524$	−48.8607	+	14.3468i	−2.13449	+	0.626743i
$525$	−0.419259	+	0.918050i	−0.0182980	+	0.0400670i
$526$	−0.262935	+	1.82875i	−0.0114645	+	0.0797375i
$527$	6.79398	−	4.36622i	0.295950	−	0.190196i
$528$	−1.71791			−0.0747625
$529$	20.0421	−	11.2833i	0.871398	−	0.490577i
$530$	37.9998			1.65061
$531$	3.99668	−	2.56851i	0.173441	−	0.111464i
$532$	1.75332	−	12.1946i	0.0760162	−	0.528705i
$533$	7.40889	−	16.2232i	0.320915	−	0.702706i
$534$	37.2209	−	10.9290i	1.61070	−	0.472946i
$535$	8.23066	+	18.0226i	0.355842	+	0.779186i
$536$	−7.16381	−	8.26748i	−0.309430	−	0.357101i
$537$	2.41893	+	16.8240i	0.104384	+	0.726009i
$538$	−9.91704	−	2.91191i	−0.427554	−	0.125541i
$539$	0.672462	−	0.776062i	0.0289650	−	0.0334274i
$540$	5.82378	+	3.74272i	0.250616	+	0.161061i
$541$	30.7520	+	19.7631i	1.32213	+	0.849683i	0.995435	−	0.0954456i	$-0.0304276\pi$
$541$	30.7520	+	19.7631i	1.32213	+	0.849683i	0.326698	+	0.945129i	$0.394064\pi$
$542$	−17.9744	+	20.7436i	−0.772068	+	0.891014i
$543$	−3.57353	−	1.04928i	−0.153355	−	0.0450291i
$544$	1.24985	+	8.69292i	0.0535870	+	0.372706i
$545$	4.02347	+	4.64334i	0.172347	+	0.198899i
$546$	−2.64846	−	5.79931i	−0.113343	−	0.248188i
$547$	−6.73876	+	1.97868i	−0.288129	+	0.0846022i	−0.422603	−	0.906315i	$-0.638884\pi$
$547$	−6.73876	+	1.97868i	−0.288129	+	0.0846022i	0.134474	+	0.990917i	$0.457065\pi$
$548$	−17.0672	+	37.3720i	−0.729076	+	1.59645i
$549$	1.29575	−	9.01212i	0.0553012	−	0.384628i
$550$	−1.91492	+	1.23064i	−0.0816525	+	0.0524749i
$551$	1.82368			0.0776914
$552$	−8.39604	+	2.20098i	−0.357359	+	0.0936800i
$553$	−13.1354			−0.558573
$554$	−21.9784	+	14.1246i	−0.933771	+	0.600098i
$555$	−0.976499	+	6.79170i	−0.0414501	+	0.288291i
$556$	8.79323	−	19.2545i	0.372916	−	0.816572i
$557$	−31.2256	+	9.16865i	−1.32307	+	0.388488i	−0.865599	−	0.500737i	$-0.833062\pi$
$557$	−31.2256	+	9.16865i	−1.32307	+	0.388488i	−0.457470	+	0.889225i	$0.651244\pi$
$558$	6.11994	+	13.4008i	0.259078	+	0.567302i
$559$	−0.905157	−	1.04461i	−0.0382840	−	0.0441821i
$560$	−0.583637	−	4.05929i	−0.0246632	−	0.171536i
$561$	−1.18631	−	0.348331i	−0.0500859	−	0.0147065i
$562$	10.3181	−	11.9078i	0.435245	−	0.502299i
$563$	32.9976	+	21.2063i	1.39068	+	0.893737i	0.999645	−	0.0266379i	$-0.00848012\pi$
$563$	32.9976	+	21.2063i	1.39068	+	0.893737i	0.391037	+	0.920375i	$0.372116\pi$
$564$	11.7833	+	7.57270i	0.496168	+	0.318868i
$565$	15.3742	−	17.7428i	0.646798	−	0.746445i
$566$	−32.2942	−	9.48243i	−1.35743	−	0.398576i
$567$	−0.142315	−	0.989821i	−0.00597666	−	0.0415686i
$568$	−15.9152	−	18.3671i	−0.667787	−	0.770667i
$569$	−3.84241	−	8.41370i	−0.161082	−	0.352721i	0.811831	−	0.583893i	$-0.198471\pi$
$569$	−3.84241	−	8.41370i	−0.161082	−	0.352721i	−0.972913	+	0.231172i	$0.925744\pi$
$570$	22.5372	−	6.61753i	0.943981	−	0.277178i
$571$	−10.5011	+	22.9943i	−0.439459	+	0.962281i	0.552238	+	0.833687i	$0.313774\pi$
$571$	−10.5011	+	22.9943i	−0.439459	+	0.962281i	−0.991697	+	0.128595i	$0.958953\pi$
$572$	1.19796	−	8.33200i	0.0500893	−	0.348379i
$573$	2.16749	−	1.39296i	0.0905482	−	0.0581918i
$574$	13.4949			0.563266
$575$	3.27520	−	3.56381i	0.136585	−	0.148621i
$576$	−12.6746			−0.528109
$577$	−26.1876	+	16.8298i	−1.09021	+	0.700633i	−0.956893	−	0.290441i	$-0.906198\pi$
$577$	−26.1876	+	16.8298i	−1.09021	+	0.700633i	−0.133313	+	0.991074i	$0.542562\pi$
$578$	4.86065	−	33.8065i	0.202176	−	1.40617i
$579$	−3.69394	+	8.08861i	−0.153515	+	0.336151i
$580$	−2.77667	+	0.815305i	−0.115295	+	0.0338537i
$581$	2.59170	+	5.67504i	0.107522	+	0.235440i
$582$	−3.13430	−	3.61717i	−0.129921	−	0.149937i
$583$	−1.03142	−	7.17368i	−0.0427170	−	0.297103i
$584$	−12.2407	−	3.59418i	−0.506522	−	0.148728i
$585$	4.65978	−	5.37767i	0.192658	−	0.222339i
$586$	2.85027	+	1.83176i	0.117744	+	0.0756693i
$587$	−2.10491	−	1.35274i	−0.0868789	−	0.0558337i	0.496480	−	0.868048i	$-0.334626\pi$
$587$	−2.10491	−	1.35274i	−0.0868789	−	0.0558337i	−0.583359	+	0.812214i	$0.698262\pi$
$588$	1.84934	−	2.13425i	0.0762655	−	0.0880151i
$589$	28.0767	+	8.24407i	1.15688	+	0.339691i
$590$	3.64031	+	25.3189i	0.149869	+	1.04236i
$591$	9.22433	+	10.6454i	0.379438	+	0.437895i
$592$	−1.94525	−	4.25951i	−0.0799493	−	0.175065i
$593$	−2.71726	+	0.797859i	−0.111584	+	0.0327641i	−0.337048	−	0.941487i	$-0.609428\pi$
$593$	−2.71726	+	0.797859i	−0.111584	+	0.0327641i	0.225464	+	0.974252i	$0.427610\pi$
$594$	0.936926	−	2.05158i	0.0384425	−	0.0841774i
$595$	0.420046	−	2.92148i	0.0172202	−	0.119769i
$596$	3.55208	−	2.28278i	0.145499	−	0.0935064i
$597$	−9.53447			−0.390220
$598$	3.46521	+	30.3786i	0.141703	+	1.24227i
$599$	24.5032			1.00118			0.500588	−	0.865686i	$-0.333117\pi$
$599$	24.5032			1.00118			0.500588	+	0.865686i	$0.333117\pi$
$600$	−1.53663	+	0.987535i	−0.0627328	+	0.0403159i
$601$	1.02003	−	7.09444i	0.0416077	−	0.289388i	−0.958385	−	0.285480i	$-0.907847\pi$
$601$	1.02003	−	7.09444i	0.0416077	−	0.289388i	0.999992	−	0.00390800i	$-0.00124396\pi$
$602$	0.434466	−	0.951347i	0.0177075	−	0.0387740i
$603$	−5.79955	+	1.70290i	−0.236176	+	0.0693475i
$604$	15.9623	+	34.9526i	0.649498	+	1.42220i
$605$	−15.9657	−	18.4254i	−0.649096	−	0.749097i
$606$	3.95595	+	27.5142i	0.160699	+	1.11769i
$607$	−10.3598	−	3.04192i	−0.420492	−	0.123468i	0.0646396	−	0.997909i	$-0.479410\pi$
$607$	−10.3598	−	3.04192i	−0.420492	−	0.123468i	−0.485132	+	0.874441i	$0.661228\pi$
$608$	−20.8384	+	24.0488i	−0.845110	+	0.975309i
$609$	0.351667	+	0.226003i	0.0142503	+	0.00915809i
$610$	41.2394	+	26.5029i	1.66973	+	1.07307i
$611$	9.42820	−	10.8807i	0.381424	−	0.440187i
$612$	−3.26247	−	0.957947i	−0.131877	−	0.0387227i
$613$	2.60586	+	18.1241i	0.105250	+	0.732027i	0.972288	+	0.233786i	$0.0751115\pi$
$613$	2.60586	+	18.1241i	0.105250	+	0.732027i	−0.867038	+	0.498241i	$0.833979\pi$
$614$	−37.7377	−	43.5517i	−1.52297	−	1.75760i
$615$	6.25688	+	13.7007i	0.252302	+	0.552464i
$616$	1.78321	−	0.523599i	0.0718477	−	0.0210964i
$617$	2.95542	−	6.47146i	0.118981	−	0.260531i	−0.840766	−	0.541399i	$-0.817895\pi$
$617$	2.95542	−	6.47146i	0.118981	−	0.260531i	0.959746	+	0.280868i	$0.0906222\pi$
$618$	0.533956	−	3.71374i	0.0214788	−	0.149389i
$619$	41.5792	−	26.7214i	1.67121	−	1.07402i	0.773061	−	0.634332i	$-0.218725\pi$
$619$	41.5792	−	26.7214i	1.67121	−	1.07402i	0.898150	−	0.439690i	$-0.144912\pi$
$620$	−46.4343			−1.86485
$621$	−0.820930	+	4.72505i	−0.0329428	+	0.189610i
$622$	32.9059			1.31941
$623$	14.8582	−	9.54880i	0.595282	−	0.382565i
$624$	−0.691096	+	4.80668i	−0.0276660	+	0.192421i
$625$	−12.0585	+	26.4045i	−0.482341	+	1.05618i
$626$	35.7044	−	10.4838i	1.42704	−	0.419015i
$627$	−1.86099	−	4.07501i	−0.0743209	−	0.162740i
$628$	−16.0659	−	18.5410i	−0.641098	−	0.739867i
$629$	−0.479621	−	3.33583i	−0.0191237	−	0.133008i
$630$	5.16603	+	1.51688i	0.205819	+	0.0604340i
$631$	13.9510	−	16.1003i	0.555381	−	0.640944i	−0.406747	−	0.913541i	$-0.633337\pi$
$631$	13.9510	−	16.1003i	0.555381	−	0.640944i	0.962128	+	0.272597i	$0.0878824\pi$
$632$	−19.9992	−	12.8527i	−0.795525	−	0.511253i
$633$	−16.4388	−	10.5646i	−0.653385	−	0.419905i
$634$	23.2982	−	26.8876i	0.925291	−	1.06784i
$635$	−36.4261	−	10.6957i	−1.44553	−	0.424445i
$636$	−2.83651	−	19.7284i	−0.112475	−	0.782281i
$637$	−1.90088	−	2.19373i	−0.0753157	−	0.0869189i
$638$	0.391661	+	0.857617i	0.0155060	+	0.0339534i
$639$	−12.8843	+	3.78318i	−0.509696	+	0.149660i
$640$	13.4929	−	29.5453i	0.533353	−	1.16788i
$641$	2.15581	−	14.9940i	0.0851494	−	0.592227i	−0.901916	−	0.431911i	$-0.857839\pi$
$641$	2.15581	−	14.9940i	0.0851494	−	0.592227i	0.987066	−	0.160316i	$-0.0512515\pi$
$642$	14.9339	−	9.59744i	0.589394	−	0.378781i
$643$	22.3313			0.880659			0.440329	−	0.897836i	$-0.354862\pi$
$643$	22.3313			0.880659			0.440329	+	0.897836i	$0.354862\pi$
$644$	−11.6026	+	6.98615i	−0.457207	+	0.275293i
$645$	1.16729			0.0459620
$646$	−9.70537	+	6.23726i	−0.381853	+	0.245402i
$647$	6.34303	−	44.1167i	0.249370	−	1.73441i	−0.352498	−	0.935813i	$-0.614668\pi$
$647$	6.34303	−	44.1167i	0.249370	−	1.73441i	0.601868	−	0.798595i	$-0.294423\pi$
$648$	0.751839	−	1.64630i	0.0295350	−	0.0646727i
$649$	4.68094	−	1.37445i	0.183743	−	0.0539518i
$650$	2.67297	+	5.85298i	0.104842	+	0.229573i
$651$	4.39248	+	5.06919i	0.172155	+	0.198677i
$652$	−1.29176	−	8.98437i	−0.0505891	−	0.351855i
$653$	20.3410	+	5.97267i	0.796006	+	0.233729i	0.654354	−	0.756188i	$-0.272940\pi$
$653$	20.3410	+	5.97267i	0.796006	+	0.233729i	0.141652	+	0.989917i	$0.454759\pi$
$654$	3.60492	−	4.16030i	0.140964	−	0.162681i
$655$	−37.1867	−	23.8984i	−1.45300	−	0.933789i
$656$	−8.64718	−	5.55720i	−0.337616	−	0.216972i
$657$	−4.61604	+	5.32719i	−0.180089	+	0.207833i
$658$	10.4525	+	3.06913i	0.407481	+	0.119647i
$659$	−4.04058	−	28.1028i	−0.157399	−	1.09473i	−0.903404	−	0.428791i	$-0.858940\pi$
$659$	−4.04058	−	28.1028i	−0.157399	−	1.09473i	0.746005	−	0.665940i	$-0.231969\pi$
$660$	4.65528	+	5.37248i	0.181207	+	0.209123i
$661$	−4.87118	−	10.6664i	−0.189467	−	0.414875i	0.790930	−	0.611906i	$-0.209597\pi$
$661$	−4.87118	−	10.6664i	−0.189467	−	0.414875i	−0.980397	+	0.197032i	$0.936870\pi$
$662$	32.2684	−	9.47487i	1.25415	−	0.368251i
$663$	−1.45186	+	3.17913i	−0.0563856	+	0.123467i
$664$	−1.60693	+	11.1764i	−0.0623608	+	0.433729i
$665$	8.99666	−	5.78180i	0.348875	−	0.224209i
$666$	6.14774			0.238220
$667$	−1.26803	−	1.55283i	−0.0490982	−	0.0601259i
$668$	−42.9761			−1.66280
$669$	15.0246	−	9.65573i	0.580885	−	0.373312i
$670$	4.63146	−	32.2125i	0.178929	−	1.24448i
$671$	3.88393	−	8.50461i	0.149937	−	0.328317i
$672$	−6.99864	+	2.05499i	−0.269979	+	0.0792729i
$673$	13.4725	+	29.5006i	0.519326	+	1.13716i	0.969694	+	0.244322i	$0.0785654\pi$
$673$	13.4725	+	29.5006i	0.519326	+	1.13716i	−0.450368	+	0.892843i	$0.648707\pi$
$674$	−41.4304	−	47.8133i	−1.59584	−	1.84170i
$675$	0.143632	+	0.998982i	0.00552839	+	0.0384508i
$676$	12.3943	+	3.63930i	0.476705	+	0.139973i
$677$	−16.3501	+	18.8690i	−0.628386	+	0.725196i	−0.977277	−	0.211967i	$-0.932013\pi$
$677$	−16.3501	+	18.8690i	−0.628386	+	0.725196i	0.348891	+	0.937163i	$0.386558\pi$
$678$	−17.6956	−	11.3723i	−0.679595	−	0.436749i
$679$	−1.83322	−	1.17814i	−0.0703524	−	0.0452128i
$680$	3.49815	−	4.03708i	0.134148	−	0.154815i
$681$	16.4624	+	4.83381i	0.630842	+	0.185232i
$682$	2.15295	+	14.9741i	0.0824407	+	0.573388i
$683$	−10.1734	−	11.7407i	−0.389273	−	0.449245i	0.526960	−	0.849890i	$-0.323332\pi$
$683$	−10.1734	−	11.7407i	−0.389273	−	0.449245i	−0.916234	+	0.400645i	$0.868786\pi$
$684$	−5.11793	−	11.2067i	−0.195689	−	0.428499i
$685$	−34.2188	+	10.0476i	−1.30743	+	0.383897i
$686$	0.912403	−	1.99788i	0.0348357	−	0.0762796i
$687$	3.50127	−	24.3519i	0.133582	−	0.929082i
$688$	−0.670159	+	0.430685i	−0.0255496	+	0.0164197i
$689$	−20.4867			−0.780482
$690$	−21.3051	−	14.5888i	−0.811072	−	0.555387i
$691$	−33.1187			−1.25990			−0.629948	−	0.776637i	$-0.716924\pi$
$691$	−33.1187			−1.25990			−0.629948	+	0.776637i	$0.716924\pi$
$692$	−6.05802	+	3.89326i	−0.230292	+	0.147999i
$693$	0.146140	−	1.01643i	0.00555140	−	0.0386108i
$694$	28.0593	−	61.4414i	1.06512	−	2.33228i
$695$	17.6299	−	5.17661i	0.668741	−	0.196360i
$696$	0.314289	+	0.688198i	0.0119131	+	0.0260861i
$697$	−4.84452	−	5.59087i	−0.183499	−	0.211769i
$698$	−7.36936	−	51.2550i	−0.278934	−	1.94003i
$699$	20.0499	+	5.88717i	0.758356	+	0.222673i
$700$	−1.86646	+	2.15400i	−0.0705454	+	0.0814137i
$701$	−9.25091	−	5.94520i	−0.349402	−	0.224547i	0.354154	−	0.935187i	$-0.384769\pi$
$701$	−9.25091	−	5.94520i	−0.349402	−	0.224547i	−0.703556	+	0.710640i	$0.748405\pi$
$702$	−5.36337	−	3.44683i	−0.202427	−	0.130092i
$703$	7.99658	−	9.22854i	0.301597	−	0.348061i
$704$	−12.4881	−	3.66683i	−0.470662	−	0.138199i
$705$	1.73035	+	12.0349i	0.0651688	+	0.453259i
$706$	31.9185	+	36.8359i	1.20127	+	1.38634i
$707$	5.25748	+	11.5123i	0.197728	+	0.432964i
$708$	12.8731	−	3.77988i	0.483800	−	0.142056i
$709$	−12.2391	+	26.7998i	−0.459648	+	1.00649i	0.527919	+	0.849295i	$0.322972\pi$
$709$	−12.2391	+	26.7998i	−0.459648	+	1.00649i	−0.987568	+	0.157195i	$0.949755\pi$
$710$	10.2893	−	71.5635i	0.386150	−	2.68573i
$711$	−11.0502	+	7.10152i	−0.414414	+	0.266328i
$712$	31.9656			1.19796
$713$	−12.5024	−	29.6390i	−0.468219	−	1.10999i
$714$	−2.64448			−0.0989674
$715$	6.14698	−	3.95042i	0.229884	−	0.147738i
$716$	−6.83110	+	47.5113i	−0.255290	+	1.77558i
$717$	−11.1138	+	24.3359i	−0.415053	+	0.908840i
$718$	53.0212	−	15.5684i	1.97873	−	0.581008i
$719$	−4.99233	−	10.9317i	−0.186182	−	0.407683i	0.793407	−	0.608691i	$-0.208305\pi$
$719$	−4.99233	−	10.9317i	−0.186182	−	0.407683i	−0.979589	+	0.201009i	$0.935578\pi$
$720$	−2.68560	−	3.09935i	−0.100086	−	0.115506i
$721$	−0.243109	−	1.69086i	−0.00905384	−	0.0629709i
$722$	−0.0677783	−	0.0199015i	−0.00252245	−	0.000740658i
$723$	−9.17096	+	10.5839i	−0.341072	+	0.393618i
$724$	−8.84812	−	5.68634i	−0.328838	−	0.211331i
$725$	−0.354921	−	0.228094i	−0.0131815	−	0.00847121i
$726$	−14.3048	+	16.5086i	−0.530900	+	0.612691i
$727$	7.25644	+	2.13068i	0.269126	+	0.0790226i	0.413511	−	0.910499i	$-0.364302\pi$
$727$	7.25644	+	2.13068i	0.269126	+	0.0790226i	−0.144385	+	0.989522i	$0.546120\pi$
$728$	−0.747651	−	5.20003i	−0.0277098	−	0.192726i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	−15.7658	−	34.5224i	−0.583520	−	1.27773i
$731$	−0.550107	+	0.161526i	−0.0203464	+	0.00597425i
$732$	10.6812	−	23.3886i	0.394789	−	0.864467i
$733$	−0.828863	+	5.76487i	−0.0306148	+	0.212930i	−0.999386	−	0.0350240i	$-0.988849\pi$
$733$	−0.828863	+	5.76487i	−0.0306148	+	0.212930i	0.968772	+	0.247954i	$0.0797583\pi$
$734$	−45.8306	+	29.4535i	−1.69164	+	1.08715i
$735$	2.45138			0.0904204
$736$	34.9664	+	1.02212i	1.28888	+	0.0376758i
$737$	−6.20685			−0.228632
$738$	11.3526	−	7.29590i	0.417896	−	0.268566i
$739$	6.19623	−	43.0957i	0.227932	−	1.58530i	−0.478866	−	0.877888i	$-0.658952\pi$
$739$	6.19623	−	43.0957i	0.227932	−	1.58530i	0.706799	−	0.707415i	$-0.250139\pi$
$740$	−8.04955	+	17.6261i	−0.295907	+	0.647947i
$741$	−12.1504	+	3.56769i	−0.446357	+	0.131062i
$742$	−6.43952	−	14.1006i	−0.236402	−	0.517648i
$743$	17.6949	+	20.4210i	0.649164	+	0.749175i	0.980967	−	0.194174i	$-0.0622025\pi$
$743$	17.6949	+	20.4210i	0.649164	+	0.749175i	−0.331803	+	0.943349i	$0.607657\pi$
$744$	1.72764	+	12.0160i	0.0633384	+	0.440528i
$745$	3.51673	+	1.03261i	0.128843	+	0.0378318i
$746$	−22.6552	+	26.1455i	−0.829467	+	0.957256i
$747$	5.24844	+	3.37297i	0.192030	+	0.123410i
$748$	−2.93731	−	1.88769i	−0.107399	−	0.0690210i
$749$	5.29287	−	6.10829i	0.193397	−	0.223192i
$750$	20.6163	+	6.05349i	0.752801	+	0.221042i
$751$	−5.33528	−	37.1077i	−0.194687	−	1.35408i	−0.819399	−	0.573224i	$-0.805693\pi$
$751$	−5.33528	−	37.1077i	−0.194687	−	1.35408i	0.624712	−	0.780855i	$-0.285216\pi$
$752$	−5.43382	−	6.27096i	−0.198151	−	0.228678i
$753$	−12.3635	−	27.0723i	−0.450551	−	0.986570i
$754$	2.55716	−	0.750849i	0.0931261	−	0.0273443i
$755$	−13.8560	+	30.3405i	−0.504273	+	1.10420i
$756$	0.401900	−	2.79528i	0.0146170	−	0.101663i
$757$	−30.4410	+	19.5632i	−1.10640	+	0.711038i	−0.960505	−	0.278263i	$-0.910241\pi$
$757$	−30.4410	+	19.5632i	−1.10640	+	0.711038i	−0.145891	+	0.989301i	$0.546605\pi$
$758$	−68.8152			−2.49948
$759$	−2.17583	+	4.41800i	−0.0789775	+	0.160363i
$760$	19.3552			0.702086
$761$	−0.865543	+	0.556251i	−0.0313759	+	0.0201641i	−0.556235	−	0.831025i	$-0.687754\pi$
$761$	−0.865543	+	0.556251i	−0.0313759	+	0.0201641i	0.524859	+	0.851189i	$0.324118\pi$
$762$	−4.84078	+	33.6684i	−0.175363	+	1.21968i
$763$	1.04118	−	2.27986i	0.0376931	−	0.0825364i
$764$	6.98136	−	2.04991i	0.252577	−	0.0741632i
$765$	−1.22611	−	2.68480i	−0.0443301	−	0.0970693i
$766$	26.8142	+	30.9453i	0.968837	+	1.11810i
$767$	−1.96259	−	13.6501i	−0.0708649	−	0.492876i
$768$	−3.60037	−	1.05716i	−0.129917	−	0.0381471i
$769$	10.4313	−	12.0383i	0.376161	−	0.434113i	−0.535828	−	0.844327i	$-0.680001\pi$
$769$	10.4313	−	12.0383i	0.376161	−	0.434113i	0.911989	+	0.410214i	$0.134546\pi$
$770$	4.65115	+	2.98911i	0.167616	+	0.107720i
$771$	0.786413	+	0.505397i	0.0283220	+	0.0182014i
$772$	−16.4447	+	18.9781i	−0.591856	+	0.683038i
$773$	22.6337	+	6.64587i	0.814079	+	0.239035i	0.662165	−	0.749358i	$-0.269638\pi$
$773$	22.6337	+	6.64587i	0.814079	+	0.239035i	0.151915	+	0.988394i	$0.451456\pi$
$774$	−0.148841	−	1.03521i	−0.00534999	−	0.0372100i
$775$	−4.43313	−	5.11610i	−0.159243	−	0.183776i
$776$	−1.63837	−	3.58753i	−0.0588141	−	0.128785i
$777$	2.68567	−	0.788584i	0.0963479	−	0.0282903i
$778$	31.9445	−	69.9486i	1.14526	−	2.50778i
$779$	3.81469	−	26.5318i	0.136676	−	0.950599i
$780$	16.9048	−	10.8641i	0.605291	−	0.388997i
$781$	−13.7892			−0.493416
$782$	12.0592	+	3.92711i	0.431235	+	0.140433i
$783$	0.418027			0.0149391
$784$	−1.40737	+	0.904464i	−0.0502633	+	0.0323023i
$785$	3.03074	−	21.0792i	0.108172	−	0.752350i
$786$	−16.4527	+	36.0264i	−0.586848	+	1.28502i
$787$	2.05032	−	0.602029i	0.0730860	−	0.0214600i	−0.244985	−	0.969527i	$-0.578783\pi$
$787$	2.05032	−	0.602029i	0.0730860	−	0.0214600i	0.318071	+	0.948067i	$0.396965\pi$
$788$	16.5248	+	36.1842i	0.588671	+	1.28901i
$789$	0.550862	+	0.635729i	0.0196112	+	0.0226325i
$790$	−10.0649	−	70.0026i	−0.358092	−	2.49058i
$791$	−9.18915	−	2.69818i	−0.326729	−	0.0959362i
$792$	1.21706	−	1.40456i	0.0432462	−	0.0499088i
$793$	−22.2333	−	14.2885i	−0.789526	−	0.507398i
$794$	11.2957	+	7.25931i	0.400869	+	0.257623i
$795$	11.3299	−	13.0754i	0.401830	−	0.463736i
$796$	−25.8349	−	7.58580i	−0.915693	−	0.268872i
$797$	2.31228	+	16.0823i	0.0819051	+	0.569663i	0.988907	+	0.148536i	$0.0474561\pi$
$797$	2.31228	+	16.0823i	0.0819051	+	0.569663i	−0.907002	+	0.421127i	$0.861635\pi$
$798$	−6.27477	−	7.24147i	−0.222124	−	0.256345i
$799$	−2.48080	−	5.43220i	−0.0877645	−	0.192178i
$800$	7.06341	−	2.07401i	0.249729	−	0.0733272i
$801$	7.33706	−	16.0659i	0.259242	−	0.567662i
$802$	0.584628	−	4.06618i	0.0206439	−	0.143582i
$803$	−6.08928	+	3.91334i	−0.214886	+	0.138099i
$804$	−17.0695			−0.601994
$805$	−11.1786	−	3.64034i	−0.393993	−	0.128305i
$806$	42.7633			1.50627
$807$	−3.95879	+	2.54416i	−0.139356	+	0.0895587i
$808$	−3.25978	+	22.6723i	−0.114679	+	0.797608i
$809$	10.2348	−	22.4112i	0.359837	−	0.787934i	−0.639972	−	0.768398i	$-0.721054\pi$
$809$	10.2348	−	22.4112i	0.359837	−	0.787934i	0.999809	−	0.0195356i	$-0.00621879\pi$
$810$	5.16603	−	1.51688i	0.181516	−	0.0532978i
$811$	12.8931	+	28.2320i	0.452739	+	0.991360i	0.989083	+	0.147361i	$0.0470778\pi$
$811$	12.8931	+	28.2320i	0.452739	+	0.991360i	−0.536344	+	0.844000i	$0.680195\pi$
$812$	0.773075	+	0.892176i	0.0271296	+	0.0313092i
$813$	1.77849	+	12.3697i	0.0623745	+	0.433824i
$814$	6.05726	+	1.77857i	0.212307	+	0.0623389i
$815$	5.15967	−	5.95458i	0.180736	−	0.208580i
$816$	1.69452	+	1.08900i	0.0593199	+	0.0381226i
$817$	−1.74759	−	1.12311i	−0.0611404	−	0.0392926i
$818$	42.5155	−	49.0655i	1.48652	−	1.71553i
$819$	−2.78515	−	0.817792i	−0.0973209	−	0.0285760i
$820$	6.05332	+	42.1018i	0.211391	+	1.47026i
$821$	22.1602	+	25.5743i	0.773398	+	0.892549i	0.996614	−	0.0822204i	$-0.0262011\pi$
$821$	22.1602	+	25.5743i	0.773398	+	0.892549i	−0.223216	+	0.974769i	$0.571656\pi$
$822$	13.2739	+	29.0659i	0.462982	+	1.01379i
$823$	−20.0761	+	5.89488i	−0.699809	+	0.205482i	−0.612235	−	0.790676i	$-0.709729\pi$
$823$	−20.0761	+	5.89488i	−0.699809	+	0.205482i	−0.0875737	+	0.996158i	$0.527911\pi$
$824$	1.28433	−	2.81228i	0.0447416	−	0.0979705i
$825$	−0.147492	+	1.02583i	−0.00513502	+	0.0357149i
$826$	8.77817	−	5.64139i	0.305432	−	0.196289i
$827$	−19.8510			−0.690288			−0.345144	−	0.938550i	$-0.612170\pi$
$827$	−19.8510			−0.690288			−0.345144	+	0.938550i	$0.612170\pi$
$828$	−5.98375	+	12.1500i	−0.207950	+	0.422241i
$829$	50.2154			1.74405			0.872027	−	0.489458i	$-0.162805\pi$
$829$	50.2154			1.74405			0.872027	+	0.489458i	$0.162805\pi$
$830$	−28.2582	+	18.1605i	−0.980857	+	0.630359i
$831$	−1.69283	+	11.7739i	−0.0587237	+	0.408432i
$832$	−15.2835	+	33.4662i	−0.529861	+	1.16023i
$833$	−1.15526	+	0.339214i	−0.0400273	+	0.0117531i
$834$	−6.83888	−	14.9751i	−0.236811	−	0.518544i
$835$	−24.4297	−	28.1934i	−0.845426	−	0.975673i
$836$	−1.80045	−	12.5224i	−0.0622698	−	0.433096i
$837$	6.43580	+	1.88972i	0.222454	+	0.0653183i
$838$	9.52619	−	10.9938i	0.329077	−	0.379775i
$839$	37.5385	+	24.1245i	1.29597	+	0.832870i	0.992767	−	0.120055i	$-0.0383071\pi$
$839$	37.5385	+	24.1245i	1.29597	+	0.832870i	0.303205	+	0.952926i	$0.401943\pi$
$840$	3.73233	+	2.39862i	0.128778	+	0.0827603i
$841$	18.8765	−	21.7847i	0.650915	−	0.751196i
$842$	24.2166	+	7.11062i	0.834558	+	0.245048i
$843$	−1.02094	−	7.10076i	−0.0351629	−	0.244563i
$844$	−36.1377	−	41.7052i	−1.24391	−	1.43555i
$845$	4.65807	+	10.1997i	0.160242	+	0.350882i
$846$	10.4525	−	3.06913i	0.359364	−	0.105519i
$847$	−4.13152	+	9.04677i	−0.141961	+	0.310851i
$848$	−1.68035	+	11.6871i	−0.0577034	+	0.401336i
$849$	−12.8915	+	8.28489i	−0.442437	+	0.284337i
$850$	2.66896			0.0915445
$851$	−13.4181	−	0.392230i	−0.459965	−	0.0134455i
$852$	−37.9217			−1.29918
$853$	−28.4458	+	18.2810i	−0.973965	+	0.625929i	−0.927829	−	0.373006i	$-0.878327\pi$
$853$	−28.4458	+	18.2810i	−0.973965	+	0.625929i	−0.0461362	+	0.998935i	$0.514691\pi$
$854$	2.84594	−	19.7939i	0.0973859	−	0.677334i
$855$	4.44259	−	9.72792i	0.151933	−	0.332688i
$856$	14.0355	−	4.12118i	0.479722	−	0.140859i
$857$	−20.7430	−	45.4208i	−0.708566	−	1.55154i	−0.829266	−	0.558855i	$-0.811241\pi$
$857$	−20.7430	−	45.4208i	−0.708566	−	1.55154i	0.120699	−	0.992689i	$-0.461486\pi$
$858$	−4.28724	−	4.94774i	−0.146364	−	0.168913i
$859$	−0.917181	−	6.37914i	−0.0312938	−	0.217653i	0.968174	−	0.250279i	$-0.0805223\pi$
$859$	−0.917181	−	6.37914i	−0.0312938	−	0.217653i	−0.999468	+	0.0326254i	$0.989613\pi$
$860$	3.16292	+	0.928718i	0.107855	+	0.0316690i
$861$	4.02359	−	4.64347i	0.137124	−	0.158249i
$862$	37.5132	+	24.1082i	1.27770	+	0.821130i
$863$	−22.8142	−	14.6618i	−0.776605	−	0.499094i	0.0913000	−	0.995823i	$-0.470898\pi$
$863$	−22.8142	−	14.6618i	−0.776605	−	0.499094i	−0.867905	+	0.496729i	$0.834534\pi$
$864$	−4.77662	+	5.51252i	−0.162504	+	0.187540i
$865$	−5.99775	−	1.76110i	−0.203930	−	0.0598791i
$866$	10.4274	+	72.5243i	0.354338	+	2.46448i
$867$	−10.1833	−	11.7521i	−0.345843	−	0.399124i
$868$	7.86884	+	17.2304i	0.267086	+	0.584837i
$869$	−12.9420	+	3.80013i	−0.439029	+	0.128911i
$870$	−0.934979	+	2.04732i	−0.0316988	+	0.0694106i
$871$	−2.49694	+	17.3666i	−0.0846057	+	0.588446i
$872$	3.81603	−	2.45241i	0.129227	−	0.0830492i
$873$	−2.17915			−0.0737530
$874$	17.8600	+	42.3401i	0.604123	+	1.43218i
$875$	9.78283			0.330720
$876$	−16.7462	+	10.7621i	−0.565800	+	0.363618i
$877$	3.98934	−	27.7464i	0.134710	−	0.936931i	−0.804589	−	0.593832i	$-0.797614\pi$
$877$	3.98934	−	27.7464i	0.134710	−	0.936931i	0.939299	−	0.343099i	$-0.111477\pi$
$878$	13.2410	−	28.9937i	0.446862	−	0.978490i
$879$	1.48012	−	0.434602i	0.0499232	−	0.0146588i
$880$	−1.74942	−	3.83069i	−0.0589729	−	0.129133i
$881$	−3.03683	−	3.50469i	−0.102313	−	0.118076i	0.702283	−	0.711897i	$-0.252164\pi$
$881$	−3.03683	−	3.50469i	−0.102313	−	0.118076i	−0.804597	+	0.593822i	$0.797618\pi$
$882$	−0.312575	−	2.17401i	−0.0105250	−	0.0732027i
$883$	−34.1780	−	10.0356i	−1.15018	−	0.337724i	−0.349571	−	0.936910i	$-0.613673\pi$
$883$	−34.1780	−	10.0356i	−1.15018	−	0.337724i	−0.800610	+	0.599186i	$0.795491\pi$
$884$	−6.46338	+	7.45913i	−0.217387	+	0.250878i
$885$	9.79738	+	6.29639i	0.329335	+	0.211651i
$886$	25.5962	+	16.4497i	0.859923	+	0.552639i
$887$	2.89857	−	3.34513i	0.0973245	−	0.112318i	−0.704998	−	0.709209i	$-0.749052\pi$
$887$	2.89857	−	3.34513i	0.0973245	−	0.112318i	0.802322	+	0.596891i	$0.203598\pi$
$888$	4.86067	+	1.42722i	0.163113	+	0.0478944i
$889$	2.20400	+	15.3291i	0.0739197	+	0.514123i
$890$	62.2736	+	71.8676i	2.08742	+	2.40901i
$891$	−0.426580	−	0.934081i	−0.0142910	−	0.0312929i
$892$	48.3934	−	14.2096i	1.62033	−	0.475772i
$893$	8.98877	−	19.6827i	0.300798	−	0.658655i
$894$	0.467350	−	3.25049i	0.0156305	−	0.108713i
$895$	−35.0517	+	22.5264i	−1.17165	+	0.752974i
$896$	−13.2499			−0.442648
$897$	11.4862	+	7.86523i	0.383512	+	0.262612i
$898$	−65.8976			−2.19903
$899$	−2.35881	+	1.51591i	−0.0786706	+	0.0505585i
$900$	−0.405619	+	2.82115i	−0.0135206	+	0.0940382i
$901$	−3.53008	+	7.72981i	−0.117604	+	0.257517i
$902$	13.2963	−	3.90414i	0.442718	−	0.129994i
$903$	−0.197811	−	0.433146i	−0.00658274	−	0.0144142i
$904$	−11.3508	−	13.0995i	−0.377521	−	0.435683i
$905$	−1.29932	−	9.03698i	−0.0431909	−	0.300399i
$906$	28.6743	+	8.41953i	0.952640	+	0.279720i
$907$	20.0645	−	23.1556i	0.666229	−	0.768870i	−0.317552	−	0.948241i	$-0.602861\pi$
$907$	20.0645	−	23.1556i	0.666229	−	0.768870i	0.983781	+	0.179371i	$0.0574063\pi$
$908$	40.7612	+	26.1956i	1.35271	+	0.869333i
$909$	10.6469	+	6.84234i	0.353135	+	0.226946i
$910$	10.2346	−	11.8113i	0.339273	−	0.391542i
$911$	38.1106	+	11.1903i	1.26266	+	0.370750i	0.843484	−	0.537155i	$-0.180501\pi$
$911$	38.1106	+	11.1903i	1.26266	+	0.370750i	0.419176	+	0.907905i	$0.362319\pi$
$912$	1.03867	+	7.22409i	0.0343937	+	0.239214i
$913$	4.19537	+	4.84172i	0.138847	+	0.160238i
$914$	36.2655	+	79.4103i	1.19955	+	2.62666i
$915$	21.4152	−	6.28807i	0.707965	−	0.207877i
$916$	28.8620	−	63.1989i	0.953626	−	2.08815i
$917$	−2.56626	+	17.8487i	−0.0847453	+	0.589416i
$918$	−2.22468	+	1.42972i	−0.0734255	+	0.0471877i
$919$	1.40621			0.0463865			0.0231932	−	0.999731i	$-0.492617\pi$
$919$	1.40621			0.0463865			0.0231932	+	0.999731i	$0.492617\pi$
$920$	−13.4579	−	16.4806i	−0.443693	−	0.543349i
$921$	−26.2375			−0.864554
$922$	4.18005	−	2.68635i	0.137663	−	0.0884704i
$923$	−5.54723	+	38.5818i	−0.182589	+	1.26994i
$924$	1.20467	−	2.63786i	0.0396308	−	0.0867793i
$925$	−2.71053	+	0.795882i	−0.0891216	+	0.0261685i
$926$	−20.0676	−	43.9420i	−0.659464	−	1.44402i
$927$	−1.11866	−	1.29101i	−0.0367417	−	0.0424022i
$928$	−0.433937	−	3.01810i	−0.0142447	−	0.0990740i
$929$	−10.4737	−	3.07536i	−0.343632	−	0.100899i	0.105363	−	0.994434i	$-0.466400\pi$
$929$	−10.4737	−	3.07536i	−0.343632	−	0.100899i	−0.448995	+	0.893534i	$0.648218\pi$
$930$	−23.6496	+	27.2931i	−0.775502	+	0.894977i
$931$	−3.67004	−	2.35859i	−0.120281	−	0.0772997i
$932$	49.6437	+	31.9041i	1.62613	+	1.04505i
$933$	9.81111	−	11.3226i	0.321201	−	0.370686i
$934$	−13.2327	−	3.88547i	−0.432988	−	0.127137i
$935$	−0.431336	−	3.00001i	−0.0141062	−	0.0981107i
$936$	−3.44031	−	3.97033i	−0.112450	−	0.129774i
$937$	−23.4995	−	51.4567i	−0.767695	−	1.68102i	−0.731663	−	0.681667i	$-0.761255\pi$
$937$	−23.4995	−	51.4567i	−0.767695	−	1.68102i	−0.0360319	−	0.999351i	$-0.511472\pi$
$938$	−12.7379	+	3.74019i	−0.415908	+	0.122122i
$939$	7.03814	−	15.4114i	0.229681	−	0.502931i
$940$	−4.88655	+	33.9867i	−0.159382	+	1.10852i
$941$	22.6309	−	14.5440i	0.737745	−	0.474120i	−0.117024	−	0.993129i	$-0.537335\pi$
$941$	22.6309	−	14.5440i	0.737745	−	0.474120i	0.854769	+	0.519009i	$0.173699\pi$
$942$	−19.0806			−0.621680
$943$	−25.2437	+	15.1997i	−0.822049	+	0.494970i
$944$	−7.94795			−0.258684
$945$	2.06223	−	1.32532i	0.0670844	−	0.0431125i
$946$	0.152842	−	1.06304i	0.00496931	−	0.0345623i
$947$	−23.2012	+	50.8036i	−0.753939	+	1.65090i	0.00521566	+	0.999986i	$0.498340\pi$
$947$	−23.2012	+	50.8036i	−0.753939	+	1.65090i	−0.759155	+	0.650910i	$0.774387\pi$
$948$	−35.5920	+	10.4508i	−1.15597	+	0.339425i
$949$	8.49980	+	18.6120i	0.275915	+	0.604170i
$950$	6.33284	+	7.30848i	0.205464	+	0.237119i
$951$	−2.30526	−	16.0334i	−0.0747532	−	0.519920i
$952$	−2.09084	−	0.613926i	−0.0677646	−	0.0198975i
$953$	−19.7586	+	22.8026i	−0.640043	+	0.738649i	−0.979382	−	0.202015i	$-0.935251\pi$
$953$	−19.7586	+	22.8026i	−0.640043	+	0.738649i	0.339340	+	0.940664i	$0.389796\pi$
$954$	−13.0406	−	8.38069i	−0.422205	−	0.271335i
$955$	5.31334	+	3.41467i	0.171936	+	0.110496i
$956$	−49.4764	+	57.0988i	−1.60018	+	1.84671i
$957$	0.411875	+	0.120937i	0.0133140	+	0.00390935i
$958$	8.30092	+	57.7342i	0.268191	+	1.86531i
$959$	9.52713	+	10.9949i	0.307647	+	0.355044i
$960$	−12.9071	−	28.2625i	−0.416574	−	0.912170i
$961$	−13.4239	+	3.94160i	−0.433027	+	0.127148i
$962$	7.41317	−	16.2326i	0.239010	−	0.523359i
$963$	1.15025	−	8.00016i	0.0370663	−	0.257802i
$964$	−33.2706	+	21.3817i	−1.07157	+	0.688659i
$965$	−21.7981			−0.701705
$966$	−1.80306	+	10.3779i	−0.0580126	+	0.333904i
$967$	15.0523			0.484048			0.242024	−	0.970270i	$-0.422189\pi$
$967$	15.0523			0.484048			0.242024	+	0.970270i	$0.422189\pi$
$968$	−15.1425	+	9.73149i	−0.486698	+	0.312782i
$969$	−0.747534	+	5.19921i	−0.0240142	+	0.167023i
$970$	4.87398	−	10.6725i	0.156494	−	0.342674i
$971$	−41.0209	+	12.0448i	−1.31642	+	0.386537i	−0.863201	−	0.504860i	$-0.831544\pi$
$971$	−41.0209	+	12.0448i	−1.31642	+	0.386537i	−0.453223	+	0.891397i	$0.649726\pi$
$972$	−1.17314	−	2.56882i	−0.0376285	−	0.0823949i
$973$	−4.90848	−	5.66469i	−0.157359	−	0.181602i
$974$	−1.88478	−	13.1089i	−0.0603922	−	0.420037i
$975$	2.81092	+	0.825361i	0.0900215	+	0.0264327i
$976$	−9.97474	+	11.5115i	−0.319284	+	0.368473i
$977$	−2.45201	−	1.57581i	−0.0784467	−	0.0504146i	0.500830	−	0.865546i	$-0.333028\pi$
$977$	−2.45201	−	1.57581i	−0.0784467	−	0.0504146i	−0.579276	+	0.815131i	$0.696665\pi$
$978$	−5.93874	−	3.81660i	−0.189900	−	0.122041i
$979$	11.8770	−	13.7068i	0.379591	−	0.438072i
$980$	6.64232	+	1.95036i	0.212181	+	0.0623020i
$981$	−0.356691	−	2.48084i	−0.0113883	−	0.0792071i
$982$	38.4251	+	44.3449i	1.22619	+	1.41510i
$983$	−11.0857	−	24.2743i	−0.353579	−	0.774230i	−0.999937	−	0.0111961i	$-0.996436\pi$
$983$	−11.0857	−	24.2743i	−0.353579	−	0.774230i	0.646358	−	0.763034i	$-0.276291\pi$
$984$	10.6696	−	3.13289i	0.340136	−	0.0998729i
$985$	−14.3443	+	31.4095i	−0.457046	+	1.00079i
$986$	0.157324	−	1.09421i	0.00501023	−	0.0348469i
$987$	4.17254	−	2.68153i	0.132813	−	0.0853540i
$988$	−35.7617			−1.13773
$989$	0.258814	+	2.26895i	0.00822979	+	0.0721485i
$990$	5.52883			0.175718
$991$	−49.7722	+	31.9867i	−1.58107	+	1.01609i	−0.605647	+	0.795733i	$0.707086\pi$
$991$	−49.7722	+	31.9867i	−1.58107	+	1.01609i	−0.975419	+	0.220357i	$0.929278\pi$
$992$	6.96279	−	48.4272i	0.221069	−	1.53757i
$993$	6.36083	−	13.9283i	0.201855	−	0.442000i
$994$	−28.2987	+	8.30925i	−0.897580	+	0.263553i
$995$	−9.70933	−	21.2605i	−0.307806	−	0.674002i
$996$	11.5377	+	13.3152i	0.365587	+	0.421909i
$997$	5.66595	+	39.4076i	0.179443	+	1.24805i	0.858056	+	0.513555i	$0.171672\pi$
$997$	5.66595	+	39.4076i	0.179443	+	1.24805i	−0.678614	+	0.734495i	$0.737419\pi$
$998$	49.1970	+	14.4455i	1.55730	+	0.457265i
$999$	1.83299	−	2.11538i	0.0579932	−	0.0669278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.d.127.5	✓	60
23.2	even	11	inner	483.2.q.d.232.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.d.127.5	✓	60	1.1	even	1	trivial
483.2.q.d.232.5	yes	60	23.2	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.84770 - 1.18744i) q^{2} +(0.142315 - 0.989821i) q^{3} +(1.17314 - 2.56882i) q^{4} +(2.35208 - 0.690633i) q^{5} +(-0.912403 - 1.99788i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.257569 - 1.79143i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(1.84770 - 1.18744i) q^{2} +(0.142315 - 0.989821i) q^{3} +(1.17314 - 2.56882i) q^{4} +(2.35208 - 0.690633i) q^{5} +(-0.912403 - 1.99788i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.257569 - 1.79143i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(3.52585 - 4.06905i) q^{10} +(-0.863864 - 0.555172i) q^{11} +(-2.37572 - 1.52678i) q^{12} +(-1.90088 + 2.19373i) q^{13} +(-2.10740 - 0.618788i) q^{14} +(-0.348867 - 2.42643i) q^{15} +(1.09555 + 1.26433i) q^{16} +(0.500171 + 1.09522i) q^{17} +(-2.10740 + 0.618788i) q^{18} +(-1.81228 + 3.96835i) q^{19} +(0.985209 - 6.85228i) q^{20} +(-0.841254 + 0.540641i) q^{21} -2.25540 q^{22} +(4.63908 - 1.21611i) q^{23} -1.80985 q^{24} +(0.849039 - 0.545644i) q^{25} +(-0.907321 + 6.31055i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-2.70963 + 0.795619i) q^{28} +(-0.173655 - 0.380251i) q^{29} +(-3.52585 - 4.06905i) q^{30} +(-0.954577 - 6.63923i) q^{31} +(6.99864 + 2.05499i) q^{32} +(-0.672462 + 0.776062i) q^{33} +(2.22468 + 1.42972i) q^{34} +(-2.06223 - 1.32532i) q^{35} +(-1.84934 + 2.13425i) q^{36} +(-2.68567 - 0.788584i) q^{37} +(1.36364 + 9.48430i) q^{38} +(1.90088 + 2.19373i) q^{39} +(-1.84304 - 4.03570i) q^{40} +(-5.89531 + 1.73102i) q^{41} +(-0.912403 + 1.99788i) q^{42} +(-0.0677671 + 0.471330i) q^{43} +(-2.43957 + 1.56782i) q^{44} -2.45138 q^{45} +(7.12756 - 7.75566i) q^{46} -4.95991 q^{47} +(1.40737 - 0.904464i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(0.920847 - 2.01637i) q^{50} +(1.15526 - 0.339214i) q^{51} +(3.40531 + 7.45658i) q^{52} +(4.62185 + 5.33389i) q^{53} +(0.312575 + 2.17401i) q^{54} +(-2.41530 - 0.709195i) q^{55} +(-1.18520 + 1.36779i) q^{56} +(3.67004 + 2.35859i) q^{57} +(-0.772389 - 0.496384i) q^{58} +(-3.11116 + 3.59046i) q^{59} +(-6.64232 - 1.95036i) q^{60} +(1.29575 + 9.01212i) q^{61} +(-9.64749 - 11.1338i) q^{62} +(0.415415 + 0.909632i) q^{63} +(12.1612 - 3.57086i) q^{64} +(-2.95596 + 6.47265i) q^{65} +(-0.320977 + 2.23244i) q^{66} +(5.08487 - 3.26784i) q^{67} +3.40020 q^{68} +(-0.543523 - 4.76493i) q^{69} -5.38412 q^{70} +(11.2966 - 7.25987i) q^{71} +(-0.257569 + 1.79143i) q^{72} +(2.92821 - 6.41189i) q^{73} +(-5.89872 + 1.73202i) q^{74} +(-0.419259 - 0.918050i) q^{75} +(8.06791 + 9.31086i) q^{76} +(0.146140 + 1.01643i) q^{77} +(6.11720 + 1.79617i) q^{78} +(8.60185 - 9.92706i) q^{79} +(3.45000 + 2.21718i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-8.83728 + 10.1988i) q^{82} +(-5.98611 - 1.75768i) q^{83} +(0.401900 + 2.79528i) q^{84} +(1.93284 + 2.23062i) q^{85} +(0.434466 + 0.951347i) q^{86} +(-0.401094 + 0.117772i) q^{87} +(-0.772047 + 1.69055i) q^{88} +(-2.51357 + 17.4822i) q^{89} +(-4.52941 + 2.91088i) q^{90} +2.90273 q^{91} +(2.31832 - 13.3436i) q^{92} -6.70750 q^{93} +(-9.16443 + 5.88962i) q^{94} +(-1.52196 + 10.5855i) q^{95} +(3.03008 - 6.63495i) q^{96} +(2.09088 - 0.613937i) q^{97} +(0.912403 + 1.99788i) q^{98} +(0.672462 + 0.776062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * q^99

Introduction

L-functions

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