LMFDB - Embedded newform 570.2.u.h.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	570.61
Dual form			570.2.u.h.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(2.43969 - 4.22567i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(2.43969 - 4.22567i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(0.939693 - 0.342020i) q^{10} +(-2.26604 - 3.92490i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.205737 + 1.16679i) q^{13} +(-3.73783 + 3.13641i) q^{14} +(-0.766044 - 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.32635 - 0.482753i) q^{17} +1.00000 q^{18} +(-4.21688 - 1.10359i) q^{19} -1.00000 q^{20} +(4.58512 + 1.66885i) q^{21} +(0.786989 + 4.46324i) q^{22} +(-2.73783 - 2.29731i) q^{23} +(0.766044 - 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(0.592396 - 1.02606i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(4.58512 - 1.66885i) q^{28} +(-0.0393628 + 0.0143269i) q^{29} +(0.500000 + 0.866025i) q^{30} +(4.95084 - 8.57510i) q^{31} +(0.173648 - 0.984808i) q^{32} +(3.47178 - 2.91317i) q^{33} +(1.08125 + 0.907278i) q^{34} +(0.847296 + 4.80526i) q^{35} +(-0.939693 - 0.342020i) q^{36} +7.35504 q^{37} +(3.58512 + 2.47929i) q^{38} -1.18479 q^{39} +(0.939693 + 0.342020i) q^{40} +(-0.928548 - 5.26606i) q^{41} +(-3.73783 - 3.13641i) q^{42} +(-0.748970 + 0.628461i) q^{43} +(0.786989 - 4.46324i) q^{44} +(0.500000 - 0.866025i) q^{45} +(1.78699 + 3.09516i) q^{46} +(1.70574 - 0.620838i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(-8.40420 - 14.5565i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.245100 - 1.39003i) q^{51} +(-0.907604 + 0.761570i) q^{52} +(8.99660 + 7.54904i) q^{53} +(0.173648 + 0.984808i) q^{54} +(4.25877 + 1.55007i) q^{55} -4.87939 q^{56} +(0.354570 - 4.34445i) q^{57} +0.0418891 q^{58} +(1.15270 + 0.419550i) q^{59} +(-0.173648 - 0.984808i) q^{60} +(-5.20961 - 4.37138i) q^{61} +(-7.58512 + 6.36467i) q^{62} +(-0.847296 + 4.80526i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.592396 - 1.02606i) q^{65} +(-4.25877 + 1.55007i) q^{66} +(5.13176 - 1.86781i) q^{67} +(-0.705737 - 1.22237i) q^{68} +(1.78699 - 3.09516i) q^{69} +(0.847296 - 4.80526i) q^{70} +(-7.63429 + 6.40593i) q^{71} +(0.766044 + 0.642788i) q^{72} +(2.52956 + 14.3459i) q^{73} +(-6.91147 - 2.51557i) q^{74} +1.00000 q^{75} +(-2.52094 - 3.55596i) q^{76} -22.1138 q^{77} +(1.11334 + 0.405223i) q^{78} +(-1.25490 - 7.11689i) q^{79} +(-0.766044 - 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-0.928548 + 5.26606i) q^{82} +(4.26991 - 7.39571i) q^{83} +(2.43969 + 4.22567i) q^{84} +(1.32635 - 0.482753i) q^{85} +(0.918748 - 0.334397i) q^{86} +(-0.0209445 - 0.0362770i) q^{87} +(-2.26604 + 3.92490i) q^{88} +(0.295607 - 1.67647i) q^{89} +(-0.766044 + 0.642788i) q^{90} +(4.42855 + 3.71599i) q^{91} +(-0.620615 - 3.51968i) q^{92} +(9.30453 + 3.38657i) q^{93} -1.81521 q^{94} +(3.93969 - 1.86516i) q^{95} +1.00000 q^{96} +(-6.57785 - 2.39414i) q^{97} +(2.91875 + 16.5530i) q^{98} +(3.47178 + 2.91317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q + 9 * q^7 - 3 * q^8	$ 6 q + 9 q^{7} - 3 q^{8} - 9 q^{11} - 3 q^{12} + 9 q^{13} - 3 q^{14} - 9 q^{17} + 6 q^{18} - 9 q^{19} - 6 q^{20} + 6 q^{21} - 3 q^{22} + 3 q^{23} - 3 q^{27} + 6 q^{28} - 9 q^{29} + 3 q^{30} + 18 q^{31} + 6 q^{33} + 9 q^{34} + 3 q^{35} - 6 q^{37} - 6 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 3 q^{45} + 3 q^{46} - 12 q^{49} - 3 q^{50} - 9 q^{52} + 12 q^{53} + 3 q^{55} - 18 q^{56} + 18 q^{57} - 6 q^{58} + 9 q^{59} + 3 q^{61} - 24 q^{62} - 3 q^{63} - 3 q^{64} - 3 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} + 3 q^{70} - 36 q^{71} + 21 q^{73} - 21 q^{74} + 6 q^{75} - 12 q^{76} - 60 q^{77} - 9 q^{79} - 6 q^{82} - 3 q^{83} + 9 q^{84} + 9 q^{85} + 3 q^{86} + 3 q^{87} - 9 q^{88} + 3 q^{89} + 27 q^{91} - 15 q^{92} + 3 q^{93} - 18 q^{94} + 18 q^{95} + 6 q^{96} + 15 q^{98} + 6 q^{99}+O(q^{100}) $ 6 * q + 9 * q^7 - 3 * q^8 - 9 * q^11 - 3 * q^12 + 9 * q^13 - 3 * q^14 - 9 * q^17 + 6 * q^18 - 9 * q^19 - 6 * q^20 + 6 * q^21 - 3 * q^22 + 3 * q^23 - 3 * q^27 + 6 * q^28 - 9 * q^29 + 3 * q^30 + 18 * q^31 + 6 * q^33 + 9 * q^34 + 3 * q^35 - 6 * q^37 - 6 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 3 * q^45 + 3 * q^46 - 12 * q^49 - 3 * q^50 - 9 * q^52 + 12 * q^53 + 3 * q^55 - 18 * q^56 + 18 * q^57 - 6 * q^58 + 9 * q^59 + 3 * q^61 - 24 * q^62 - 3 * q^63 - 3 * q^64 - 3 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 + 3 * q^70 - 36 * q^71 + 21 * q^73 - 21 * q^74 + 6 * q^75 - 12 * q^76 - 60 * q^77 - 9 * q^79 - 6 * q^82 - 3 * q^83 + 9 * q^84 + 9 * q^85 + 3 * q^86 + 3 * q^87 - 9 * q^88 + 3 * q^89 + 27 * q^91 - 15 * q^92 + 3 * q^93 - 18 * q^94 + 18 * q^95 + 6 * q^96 + 15 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$6$	0.173648	−	0.984808i	0.0708916	−	0.402046i
$7$	2.43969	−	4.22567i	0.922117	−	1.59715i	0.125984	−	0.992032i	$-0.459791\pi$
$7$	2.43969	−	4.22567i	0.922117	−	1.59715i	0.796133	−	0.605121i	$-0.206875\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	0.939693	−	0.342020i	0.297157	−	0.108156i
$11$	−2.26604	−	3.92490i	−0.683238	−	1.18340i	−0.973987	−	0.226604i	$-0.927238\pi$
$11$	−2.26604	−	3.92490i	−0.683238	−	1.18340i	0.290749	−	0.956799i	$-0.406096\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−0.205737	+	1.16679i	−0.0570612	+	0.323610i	−0.999955	−	0.00948328i	$-0.996981\pi$
$13$	−0.205737	+	1.16679i	−0.0570612	+	0.323610i	0.942894	+	0.333093i	$0.108092\pi$
$14$	−3.73783	+	3.13641i	−0.998976	+	0.838240i
$15$	−0.766044	−	0.642788i	−0.197792	−	0.165967i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−1.32635	−	0.482753i	−0.321688	−	0.117085i	0.176129	−	0.984367i	$-0.443642\pi$
$17$	−1.32635	−	0.482753i	−0.321688	−	0.117085i	−0.497816	+	0.867282i	$0.665865\pi$
$18$	1.00000			0.235702
$19$	−4.21688	−	1.10359i	−0.967419	−	0.253181i
$19$	−4.21688	−	1.10359i	−0.967419	−	0.253181i
$20$	−1.00000			−0.223607
$21$	4.58512	+	1.66885i	1.00056	+	0.364172i
$22$	0.786989	+	4.46324i	0.167787	+	0.951565i
$23$	−2.73783	−	2.29731i	−0.570876	−	0.479022i	0.311060	−	0.950390i	$-0.399316\pi$
$23$	−2.73783	−	2.29731i	−0.570876	−	0.479022i	−0.881937	+	0.471368i	$0.843760\pi$
$24$	0.766044	−	0.642788i	0.156368	−	0.131208i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	0.592396	−	1.02606i	0.116178	−	0.201227i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	4.58512	−	1.66885i	0.866507	−	0.315383i
$29$	−0.0393628	+	0.0143269i	−0.00730950	+	0.00266044i	−0.345672	−	0.938355i	$-0.612349\pi$
$29$	−0.0393628	+	0.0143269i	−0.00730950	+	0.00266044i	0.338363	+	0.941016i	$0.390127\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	4.95084	−	8.57510i	0.889197	−	1.54013i	0.0483697	−	0.998830i	$-0.484597\pi$
$31$	4.95084	−	8.57510i	0.889197	−	1.54013i	0.840827	−	0.541304i	$-0.182069\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	3.47178	−	2.91317i	0.604360	−	0.507118i
$34$	1.08125	+	0.907278i	0.185433	+	0.155597i
$35$	0.847296	+	4.80526i	0.143219	+	0.812237i
$36$	−0.939693	−	0.342020i	−0.156615	−	0.0570034i
$37$	7.35504			1.20916			0.604580	−	0.796544i	$-0.293341\pi$
$37$	7.35504			1.20916			0.604580	+	0.796544i	$0.293341\pi$
$38$	3.58512	+	2.47929i	0.581584	+	0.402195i
$39$	−1.18479			−0.189719
$40$	0.939693	+	0.342020i	0.148578	+	0.0540781i
$41$	−0.928548	−	5.26606i	−0.145015	−	0.822420i	−0.967355	−	0.253424i	$-0.918443\pi$
$41$	−0.928548	−	5.26606i	−0.145015	−	0.822420i	0.822340	−	0.568996i	$-0.192668\pi$
$42$	−3.73783	−	3.13641i	−0.576759	−	0.483958i
$43$	−0.748970	+	0.628461i	−0.114217	+	0.0958394i	−0.698107	−	0.715993i	$-0.745974\pi$
$43$	−0.748970	+	0.628461i	−0.114217	+	0.0958394i	0.583890	+	0.811832i	$0.301530\pi$
$44$	0.786989	−	4.46324i	0.118643	−	0.672858i
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	1.78699	+	3.09516i	0.263477	+	0.456356i
$47$	1.70574	−	0.620838i	0.248807	−	0.0905585i	−0.214606	−	0.976701i	$-0.568847\pi$
$47$	1.70574	−	0.620838i	0.248807	−	0.0905585i	0.463413	+	0.886142i	$0.346625\pi$
$48$	−0.939693	+	0.342020i	−0.135633	+	0.0493664i
$49$	−8.40420	−	14.5565i	−1.20060	−	2.07950i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	0.245100	−	1.39003i	0.0343209	−	0.194643i
$52$	−0.907604	+	0.761570i	−0.125862	+	0.105611i
$53$	8.99660	+	7.54904i	1.23578	+	1.03694i	0.997842	+	0.0656595i	$0.0209151\pi$
$53$	8.99660	+	7.54904i	1.23578	+	1.03694i	0.237935	+	0.971281i	$0.423529\pi$
$54$	0.173648	+	0.984808i	0.0236305	+	0.134015i
$55$	4.25877	+	1.55007i	0.574252	+	0.209011i
$56$	−4.87939			−0.652035
$57$	0.354570	−	4.34445i	0.0469640	−	0.575437i
$58$	0.0418891			0.00550030
$59$	1.15270	+	0.419550i	0.150069	+	0.0546207i	0.415963	−	0.909382i	$-0.363445\pi$
$59$	1.15270	+	0.419550i	0.150069	+	0.0546207i	−0.265893	+	0.964002i	$0.585667\pi$
$60$	−0.173648	−	0.984808i	−0.0224179	−	0.127138i
$61$	−5.20961	−	4.37138i	−0.667022	−	0.559698i	0.245160	−	0.969483i	$-0.421159\pi$
$61$	−5.20961	−	4.37138i	−0.667022	−	0.559698i	−0.912182	+	0.409785i	$0.865604\pi$
$62$	−7.58512	+	6.36467i	−0.963311	+	0.808314i
$63$	−0.847296	+	4.80526i	−0.106749	+	0.605405i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.592396	−	1.02606i	−0.0734777	−	0.127267i
$66$	−4.25877	+	1.55007i	−0.524218	+	0.190800i
$67$	5.13176	−	1.86781i	0.626944	−	0.228189i	−0.00895655	−	0.999960i	$-0.502851\pi$
$67$	5.13176	−	1.86781i	0.626944	−	0.228189i	0.635901	+	0.771771i	$0.280629\pi$
$68$	−0.705737	−	1.22237i	−0.0855832	−	0.148234i
$69$	1.78699	−	3.09516i	0.215128	−	0.372613i
$70$	0.847296	−	4.80526i	0.101271	−	0.574338i
$71$	−7.63429	+	6.40593i	−0.906023	+	0.760244i	−0.971358	−	0.237620i	$-0.923633\pi$
$71$	−7.63429	+	6.40593i	−0.906023	+	0.760244i	0.0653353	+	0.997863i	$0.479188\pi$
$72$	0.766044	+	0.642788i	0.0902792	+	0.0757532i
$73$	2.52956	+	14.3459i	0.296063	+	1.67906i	0.662851	+	0.748752i	$0.269346\pi$
$73$	2.52956	+	14.3459i	0.296063	+	1.67906i	−0.366788	+	0.930305i	$0.619542\pi$
$74$	−6.91147	−	2.51557i	−0.803443	−	0.292429i
$75$	1.00000			0.115470
$76$	−2.52094	−	3.55596i	−0.289172	−	0.407896i
$77$	−22.1138			−2.52010
$78$	1.11334	+	0.405223i	0.126061	+	0.0458825i
$79$	−1.25490	−	7.11689i	−0.141187	−	0.800713i	−0.970350	−	0.241705i	$-0.922293\pi$
$79$	−1.25490	−	7.11689i	−0.141187	−	0.800713i	0.829162	−	0.559008i	$-0.188818\pi$
$80$	−0.766044	−	0.642788i	−0.0856464	−	0.0718658i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−0.928548	+	5.26606i	−0.102541	+	0.581539i
$83$	4.26991	−	7.39571i	0.468684	−	0.811785i	−0.530675	−	0.847575i	$-0.678062\pi$
$83$	4.26991	−	7.39571i	0.468684	−	0.811785i	0.999359	+	0.0357907i	$0.0113950\pi$
$84$	2.43969	+	4.22567i	0.266192	+	0.461059i
$85$	1.32635	−	0.482753i	0.143863	−	0.0523619i
$86$	0.918748	−	0.334397i	0.0990712	−	0.0360590i
$87$	−0.0209445	−	0.0362770i	−0.00224549	−	0.00388930i
$88$	−2.26604	+	3.92490i	−0.241561	+	0.418396i
$89$	0.295607	−	1.67647i	0.0313343	−	0.177706i	−0.965124	−	0.261793i	$-0.915686\pi$
$89$	0.295607	−	1.67647i	0.0313343	−	0.177706i	0.996458	+	0.0840872i	$0.0267974\pi$
$90$	−0.766044	+	0.642788i	−0.0807482	+	0.0677558i
$91$	4.42855	+	3.71599i	0.464238	+	0.389542i
$92$	−0.620615	−	3.51968i	−0.0647036	−	0.366952i
$93$	9.30453	+	3.38657i	0.964835	+	0.351171i
$94$	−1.81521			−0.187224
$95$	3.93969	−	1.86516i	0.404204	−	0.191361i
$96$	1.00000			0.102062
$97$	−6.57785	−	2.39414i	−0.667879	−	0.243088i	−0.0142448	−	0.999899i	$-0.504534\pi$
$97$	−6.57785	−	2.39414i	−0.667879	−	0.243088i	−0.653635	+	0.756810i	$0.726757\pi$
$98$	2.91875	+	16.5530i	0.294838	+	1.67211i
$99$	3.47178	+	2.91317i	0.348927	+	0.292785i
$100$	0.766044	−	0.642788i	0.0766044	−	0.0642788i
$101$	−0.243756	+	1.38241i	−0.0242546	+	0.137555i	−0.994530	−	0.104447i	$-0.966693\pi$
$101$	−0.243756	+	1.38241i	−0.0242546	+	0.137555i	0.970276	+	0.242002i	$0.0778039\pi$
$102$	−0.705737	+	1.22237i	−0.0698784	+	0.121033i
$103$	5.55303	+	9.61814i	0.547157	+	0.947703i	0.998468	+	0.0553364i	$0.0176231\pi$
$103$	5.55303	+	9.61814i	0.547157	+	0.947703i	−0.451311	+	0.892367i	$0.649044\pi$
$104$	1.11334	−	0.405223i	0.109172	−	0.0397354i
$105$	−4.58512	+	1.66885i	−0.447462	+	0.162863i
$106$	−5.87211	−	10.1708i	−0.570350	−	0.987875i
$107$	2.92262	−	5.06212i	0.282540	−	0.489374i	−0.689470	−	0.724315i	$-0.742156\pi$
$107$	2.92262	−	5.06212i	0.282540	−	0.489374i	0.972010	+	0.234941i	$0.0754896\pi$
$108$	0.173648	−	0.984808i	0.0167093	−	0.0947632i
$109$	2.21688	−	1.86018i	0.212339	−	0.178173i	−0.530415	−	0.847738i	$-0.677964\pi$
$109$	2.21688	−	1.86018i	0.212339	−	0.178173i	0.742754	+	0.669565i	$0.233519\pi$
$110$	−3.47178	−	2.91317i	−0.331021	−	0.277760i
$111$	1.27719	+	7.24330i	0.121225	+	0.687503i
$112$	4.58512	+	1.66885i	0.433253	+	0.157691i
$113$	−12.3696			−1.16363			−0.581816	−	0.813320i	$-0.697658\pi$
$113$	−12.3696			−1.16363			−0.581816	+	0.813320i	$0.697658\pi$
$114$	−1.81908	+	3.96118i	−0.170372	+	0.370999i
$115$	3.57398			0.333275
$116$	−0.0393628	−	0.0143269i	−0.00365475	−	0.00133022i
$117$	−0.205737	−	1.16679i	−0.0190204	−	0.107870i
$118$	−0.939693	−	0.788496i	−0.0865057	−	0.0725869i
$119$	−5.27584	+	4.42696i	−0.483636	+	0.405819i
$120$	−0.173648	+	0.984808i	−0.0158518	+	0.0899002i
$121$	−4.76991	+	8.26173i	−0.433629	+	0.751067i
$122$	3.40033	+	5.88954i	0.307851	+	0.533214i
$123$	5.02481	−	1.82888i	0.453072	−	0.164905i
$124$	9.30453	−	3.38657i	0.835571	−	0.304123i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	2.43969	−	4.22567i	0.217345	−	0.376453i
$127$	0.195470	−	1.10857i	0.0173452	−	0.0983693i	−0.974906	−	0.222616i	$-0.928540\pi$
$127$	0.195470	−	1.10857i	0.0173452	−	0.0983693i	0.992251	+	0.124247i	$0.0396515\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	−0.748970	−	0.628461i	−0.0659432	−	0.0553329i
$130$	0.205737	+	1.16679i	0.0180443	+	0.102335i
$131$	20.7246	+	7.54315i	1.81072	+	0.659048i	0.996966	+	0.0778361i	$0.0248011\pi$
$131$	20.7246	+	7.54315i	1.81072	+	0.659048i	0.813752	+	0.581212i	$0.197421\pi$
$132$	4.53209			0.394468
$133$	−14.9513	+	15.1267i	−1.29644	+	1.31165i
$134$	−5.46110			−0.471768
$135$	0.939693	+	0.342020i	0.0808759	+	0.0294364i
$136$	0.245100	+	1.39003i	0.0210171	+	0.119194i
$137$	1.45471	+	1.22064i	0.124284	+	0.104287i	0.702811	−	0.711376i	$-0.251928\pi$
$137$	1.45471	+	1.22064i	0.124284	+	0.104287i	−0.578527	+	0.815663i	$0.696372\pi$
$138$	−2.73783	+	2.29731i	−0.233059	+	0.195560i
$139$	−4.00727	+	22.7264i	−0.339893	+	1.92763i	0.0323170	+	0.999478i	$0.489711\pi$
$139$	−4.00727	+	22.7264i	−0.339893	+	1.92763i	−0.372210	+	0.928149i	$0.621400\pi$
$140$	−2.43969	+	4.22567i	−0.206192	+	0.357134i
$141$	0.907604	+	1.57202i	0.0764340	+	0.132388i
$142$	9.36484	−	3.40852i	0.785880	−	0.286037i
$143$	5.04576	−	1.83651i	0.421948	−	0.153576i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.0209445	−	0.0362770i	0.00173935	−	0.00301264i
$146$	2.52956	−	14.3459i	0.209348	−	1.18727i
$147$	12.8760	−	10.8042i	1.06199	−	0.891118i
$148$	5.63429	+	4.72773i	0.463135	+	0.388617i
$149$	−3.02481	−	17.1546i	−0.247802	−	1.40536i	−0.813893	−	0.581015i	$-0.802656\pi$
$149$	−3.02481	−	17.1546i	−0.247802	−	1.40536i	0.566091	−	0.824343i	$-0.308455\pi$
$150$	−0.939693	−	0.342020i	−0.0767256	−	0.0279258i
$151$	−0.487511			−0.0396731			−0.0198366	−	0.999803i	$-0.506315\pi$
$151$	−0.487511			−0.0396731			−0.0198366	+	0.999803i	$0.506315\pi$
$152$	1.15270	+	4.20372i	0.0934966	+	0.340967i
$153$	1.41147			0.114111
$154$	20.7802	+	7.56337i	1.67451	+	0.609474i
$155$	1.71941	+	9.75125i	0.138106	+	0.783239i
$156$	−0.907604	−	0.761570i	−0.0726665	−	0.0609744i
$157$	−15.3858	+	12.9102i	−1.22792	+	1.03035i	−0.229548	+	0.973297i	$0.573725\pi$
$157$	−15.3858	+	12.9102i	−1.22792	+	1.03035i	−0.998371	+	0.0570490i	$0.981831\pi$
$158$	−1.25490	+	7.11689i	−0.0998345	+	0.566190i
$159$	−5.87211	+	10.1708i	−0.465689	+	0.806597i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−16.3871	+	5.96443i	−1.29149	+	0.470063i
$162$	−0.939693	+	0.342020i	−0.0738292	+	0.0268716i
$163$	4.35844	+	7.54904i	0.341379	+	0.591287i	0.984689	−	0.174320i	$-0.0557726\pi$
$163$	4.35844	+	7.54904i	0.341379	+	0.591287i	−0.643310	+	0.765606i	$0.722439\pi$
$164$	2.67365	−	4.63089i	0.208777	−	0.361612i
$165$	−0.786989	+	4.46324i	−0.0612670	+	0.347462i
$166$	−6.54189	+	5.48930i	−0.507749	+	0.426052i
$167$	−4.61721	−	3.87430i	−0.357291	−	0.299802i	0.446419	−	0.894824i	$-0.352699\pi$
$167$	−4.61721	−	3.87430i	−0.357291	−	0.299802i	−0.803710	+	0.595022i	$0.797143\pi$
$168$	−0.847296	−	4.80526i	−0.0653703	−	0.370734i
$169$	10.8969	+	3.96616i	0.838225	+	0.305089i
$170$	−1.41147			−0.108255
$171$	4.34002	−	0.405223i	0.331890	−	0.0309882i
$172$	−0.977711			−0.0745498
$173$	20.5744	+	7.48849i	1.56425	+	0.569339i	0.971704	−	0.236201i	$-0.0759023\pi$
$173$	20.5744	+	7.48849i	1.56425	+	0.569339i	0.592542	+	0.805540i	$0.298125\pi$
$174$	0.00727396	+	0.0412527i	0.000551437	+	0.00312736i
$175$	−3.73783	−	3.13641i	−0.282553	−	0.237090i
$176$	3.47178	−	2.91317i	0.261695	−	0.219588i
$177$	−0.213011	+	1.20805i	−0.0160109	+	0.0908023i
$178$	−0.851167	+	1.47426i	−0.0637976	+	0.110501i
$179$	−3.67499	−	6.36527i	−0.274682	−	0.475763i	0.695373	−	0.718649i	$-0.255239\pi$
$179$	−3.67499	−	6.36527i	−0.274682	−	0.475763i	−0.970055	+	0.242886i	$0.921906\pi$
$180$	0.939693	−	0.342020i	0.0700406	−	0.0254927i
$181$	−20.0792	+	7.30823i	−1.49247	+	0.543216i	−0.954100	−	0.299489i	$-0.903184\pi$
$181$	−20.0792	+	7.30823i	−1.49247	+	0.543216i	−0.538375	+	0.842705i	$0.680962\pi$
$182$	−2.89053	−	5.00654i	−0.214260	−	0.371110i
$183$	3.40033	−	5.88954i	0.251360	−	0.435368i
$184$	−0.620615	+	3.51968i	−0.0457523	+	0.259474i
$185$	−5.63429	+	4.72773i	−0.414241	+	0.347589i
$186$	−7.58512	−	6.36467i	−0.556168	−	0.466680i
$187$	1.11081	+	6.29974i	0.0812308	+	0.460683i
$188$	1.70574	+	0.620838i	0.124404	+	0.0452792i
$189$	−4.87939			−0.354923
$190$	−4.34002	+	0.405223i	−0.314858	+	0.0293980i
$191$	−9.73917			−0.704702			−0.352351	−	0.935868i	$-0.614618\pi$
$191$	−9.73917			−0.704702			−0.352351	+	0.935868i	$0.614618\pi$
$192$	−0.939693	−	0.342020i	−0.0678165	−	0.0246832i
$193$	−2.61721	−	14.8429i	−0.188391	−	1.06842i	−0.921521	−	0.388329i	$-0.873052\pi$
$193$	−2.61721	−	14.8429i	−0.188391	−	1.06842i	0.733130	−	0.680089i	$-0.238059\pi$
$194$	5.36231	+	4.49951i	0.384992	+	0.323046i
$195$	0.907604	−	0.761570i	0.0649949	−	0.0545372i
$196$	2.91875	−	16.5530i	0.208482	−	1.18236i
$197$	−9.87598	+	17.1057i	−0.703635	+	1.21873i	0.263547	+	0.964646i	$0.415107\pi$
$197$	−9.87598	+	17.1057i	−0.703635	+	1.21873i	−0.967182	+	0.254084i	$0.918226\pi$
$198$	−2.26604	−	3.92490i	−0.161041	−	0.278931i
$199$	9.16297	−	3.33505i	0.649546	−	0.236415i	0.00382939	−	0.999993i	$-0.498781\pi$
$199$	9.16297	−	3.33505i	0.649546	−	0.236415i	0.645716	+	0.763577i	$0.276559\pi$
$200$	−0.939693	+	0.342020i	−0.0664463	+	0.0241845i
$201$	2.73055	+	4.72945i	0.192598	+	0.333590i
$202$	0.701867	−	1.21567i	0.0493832	−	0.0855342i
$203$	−0.0354925	+	0.201288i	−0.00249108	+	0.0141276i
$204$	1.08125	−	0.907278i	0.0757028	−	0.0635222i
$205$	4.09627	+	3.43718i	0.286096	+	0.240063i
$206$	−1.92855	−	10.9373i	−0.134368	−	0.762041i
$207$	3.35844	+	1.22237i	0.233428	+	0.0849608i
$208$	−1.18479			−0.0821506
$209$	5.22416	+	19.0516i	0.361362	+	1.31783i
$210$	4.87939			0.336710
$211$	−21.3935	−	7.78661i	−1.47279	−	0.536052i	−0.523934	−	0.851759i	$-0.675536\pi$
$211$	−21.3935	−	7.78661i	−1.47279	−	0.536052i	−0.948857	+	0.315707i	$0.897758\pi$
$212$	2.03936	+	11.5658i	0.140064	+	0.794343i
$213$	−7.63429	−	6.40593i	−0.523093	−	0.438927i
$214$	−4.47771	+	3.75725i	−0.306090	+	0.256840i
$215$	0.169778	−	0.962858i	0.0115787	−	0.0656663i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	−24.1570	−	41.8412i	−1.63989	−	2.84037i
$218$	−2.71941	+	0.989783i	−0.184182	+	0.0670366i
$219$	−13.6887	+	4.98227i	−0.924994	+	0.336670i
$220$	2.26604	+	3.92490i	0.152777	+	0.264617i
$221$	0.836152	−	1.44826i	0.0562457	−	0.0974204i
$222$	1.27719	−	7.24330i	0.0857193	−	0.486138i
$223$	13.1650	−	11.0468i	0.881596	−	0.739747i	−0.0849109	−	0.996389i	$-0.527061\pi$
$223$	13.1650	−	11.0468i	0.881596	−	0.739747i	0.966507	+	0.256642i	$0.0826161\pi$
$224$	−3.73783	−	3.13641i	−0.249744	−	0.209560i
$225$	0.173648	+	0.984808i	0.0115765	+	0.0656539i
$226$	11.6236	+	4.23065i	0.773191	+	0.281418i
$227$	23.3455			1.54950			0.774749	−	0.632269i	$-0.217876\pi$
$227$	23.3455			1.54950			0.774749	+	0.632269i	$0.217876\pi$
$228$	3.06418	−	3.10013i	0.202930	−	0.205311i
$229$	6.41921			0.424194			0.212097	−	0.977249i	$-0.431971\pi$
$229$	6.41921			0.424194			0.212097	+	0.977249i	$0.431971\pi$
$230$	−3.35844	−	1.22237i	−0.221449	−	0.0806009i
$231$	−3.84002	−	21.7778i	−0.252655	−	1.43288i
$232$	0.0320889	+	0.0269258i	0.00210674	+	0.00176776i
$233$	17.4311	−	14.6264i	1.14195	−	0.958208i	0.142447	−	0.989802i	$-0.454503\pi$
$233$	17.4311	−	14.6264i	1.14195	−	0.958208i	0.999501	+	0.0315946i	$0.0100585\pi$
$234$	−0.205737	+	1.16679i	−0.0134495	+	0.0762756i
$235$	−0.907604	+	1.57202i	−0.0592055	+	0.102547i
$236$	0.613341	+	1.06234i	0.0399251	+	0.0691523i
$237$	6.79086	−	2.47167i	0.441114	−	0.160552i
$238$	6.47178	−	2.35554i	0.419503	−	0.152687i
$239$	0.964041	+	1.66977i	0.0623586	+	0.108008i	0.895519	−	0.445023i	$-0.146804\pi$
$239$	0.964041	+	1.66977i	0.0623586	+	0.108008i	−0.833161	+	0.553031i	$0.813471\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−1.10085	+	6.24324i	−0.0709121	+	0.402163i	0.928604	+	0.371071i	$0.121009\pi$
$241$	−1.10085	+	6.24324i	−0.0709121	+	0.402163i	−0.999517	+	0.0310915i	$0.990102\pi$
$242$	7.30793	−	6.13208i	0.469772	−	0.394185i
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$	−1.18092	−	6.69734i	−0.0756008	−	0.428753i
$245$	15.7947	+	5.74881i	1.00909	+	0.367278i
$246$	−5.34730			−0.340931
$247$	2.15523	−	4.69318i	0.137134	−	0.298620i
$248$	−9.90167			−0.628757
$249$	8.02481	+	2.92079i	0.508552	+	0.185098i
$250$	−0.173648	−	0.984808i	−0.0109825	−	0.0622847i
$251$	−1.57011	−	1.31748i	−0.0991043	−	0.0831584i	0.591889	−	0.806019i	$-0.298382\pi$
$251$	−1.57011	−	1.31748i	−0.0991043	−	0.0831584i	−0.690994	+	0.722861i	$0.742827\pi$
$252$	−3.73783	+	3.13641i	−0.235461	+	0.197575i
$253$	−2.81268	+	15.9515i	−0.176832	+	1.00286i
$254$	−0.562834	+	0.974856i	−0.0353153	+	0.0611679i
$255$	0.705737	+	1.22237i	0.0441950	+	0.0765479i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	28.6707	−	10.4353i	1.78843	−	0.650935i	0.789103	−	0.614261i	$-0.210546\pi$
$257$	28.6707	−	10.4353i	1.78843	−	0.650935i	0.999327	−	0.0366737i	$-0.0116762\pi$
$258$	0.488856	+	0.846723i	0.0304348	+	0.0527147i
$259$	17.9440	−	31.0800i	1.11499	−	1.93122i
$260$	0.205737	−	1.16679i	0.0127593	−	0.0723614i
$261$	0.0320889	−	0.0269258i	0.00198625	−	0.00166666i
$262$	−16.8949	−	14.1765i	−1.04377	−	0.875826i
$263$	−5.03849	−	28.5747i	−0.310686	−	1.76199i	−0.595450	−	0.803392i	$-0.703026\pi$
$263$	−5.03849	−	28.5747i	−0.310686	−	1.76199i	0.284764	−	0.958598i	$-0.408085\pi$
$264$	−4.25877	−	1.55007i	−0.262109	−	0.0953999i
$265$	−11.7442			−0.721442
$266$	19.2233	−	9.10083i	1.17865	−	0.558008i
$267$	1.70233			0.104181
$268$	5.13176	+	1.86781i	0.313472	+	0.114095i
$269$	2.10694	+	11.9491i	0.128463	+	0.728548i	0.979191	+	0.202942i	$0.0650503\pi$
$269$	2.10694	+	11.9491i	0.128463	+	0.728548i	−0.850728	+	0.525606i	$0.823839\pi$
$270$	−0.766044	−	0.642788i	−0.0466200	−	0.0391188i
$271$	4.58718	−	3.84910i	0.278651	−	0.233816i	−0.492741	−	0.870176i	$-0.664005\pi$
$271$	4.58718	−	3.84910i	0.278651	−	0.233816i	0.771392	+	0.636360i	$0.219561\pi$
$272$	0.245100	−	1.39003i	0.0148614	−	0.0842830i
$273$	−2.89053	+	5.00654i	−0.174943	+	0.303010i
$274$	−0.949493	−	1.64457i	−0.0573610	−	0.0993521i
$275$	−4.25877	+	1.55007i	−0.256814	+	0.0934725i
$276$	3.35844	−	1.22237i	0.202154	−	0.0735782i
$277$	−14.7986	−	25.6319i	−0.889162	−	1.54007i	−0.840868	−	0.541240i	$-0.817955\pi$
$277$	−14.7986	−	25.6319i	−0.889162	−	1.54007i	−0.0482936	−	0.998833i	$-0.515378\pi$
$278$	11.5385	−	19.9852i	0.692032	−	1.19864i
$279$	−1.71941	+	9.75125i	−0.102938	+	0.583792i
$280$	3.73783	−	3.13641i	0.223378	−	0.187436i
$281$	−4.50000	−	3.77595i	−0.268447	−	0.225254i	0.498620	−	0.866821i	$-0.333840\pi$
$281$	−4.50000	−	3.77595i	−0.268447	−	0.225254i	−0.767067	+	0.641567i	$0.778285\pi$
$282$	−0.315207	−	1.78763i	−0.0187703	−	0.106452i
$283$	−16.9941	−	6.18534i	−1.01019	−	0.367680i	−0.216686	−	0.976241i	$-0.569525\pi$
$283$	−16.9941	−	6.18534i	−1.01019	−	0.367680i	−0.793507	+	0.608561i	$0.791747\pi$
$284$	−9.96585			−0.591365
$285$	2.52094	+	3.55596i	0.149328	+	0.210637i
$286$	−5.36959			−0.317510
$287$	−24.5180	−	8.92383i	−1.44725	−	0.526757i
$288$	0.173648	+	0.984808i	0.0102323	+	0.0580304i
$289$	−11.4966	−	9.64679i	−0.676270	−	0.567458i
$290$	−0.0320889	+	0.0269258i	−0.00188432	+	0.00158114i
$291$	1.21554	−	6.89365i	0.0712561	−	0.404113i
$292$	−7.28359	+	12.6155i	−0.426240	+	0.738269i
$293$	7.50253	+	12.9948i	0.438302	+	0.759162i	0.997559	−	0.0698329i	$-0.0222466\pi$
$293$	7.50253	+	12.9948i	0.438302	+	0.759162i	−0.559256	+	0.828995i	$0.688913\pi$
$294$	−15.7947	+	5.74881i	−0.921167	+	0.335277i
$295$	−1.15270	+	0.419550i	−0.0671130	+	0.0244271i
$296$	−3.67752	−	6.36965i	−0.213751	−	0.370228i
$297$	−2.26604	+	3.92490i	−0.131489	+	0.227746i
$298$	−3.02481	+	17.1546i	−0.175223	+	0.993738i
$299$	3.24376	−	2.72183i	0.187591	−	0.157408i
$300$	0.766044	+	0.642788i	0.0442276	+	0.0371114i
$301$	0.828411	+	4.69815i	0.0477488	+	0.270797i
$302$	0.458111	+	0.166739i	0.0263613	+	0.00959474i
$303$	−1.40373			−0.0806424
$304$	0.354570	−	4.34445i	0.0203360	−	0.249172i
$305$	6.80066			0.389405
$306$	−1.32635	−	0.482753i	−0.0758225	−	0.0275971i
$307$	2.30706	+	13.0840i	0.131671	+	0.746741i	0.977120	+	0.212687i	$0.0682213\pi$
$307$	2.30706	+	13.0840i	0.131671	+	0.746741i	−0.845450	+	0.534055i	$0.820668\pi$
$308$	−16.9402	−	14.2145i	−0.965255	−	0.809945i
$309$	−8.50774	+	7.13884i	−0.483988	+	0.406115i
$310$	1.71941	−	9.75125i	0.0976558	−	0.553834i
$311$	−6.10741	+	10.5783i	−0.346320	+	0.599843i	−0.985593	−	0.169137i	$-0.945902\pi$
$311$	−6.10741	+	10.5783i	−0.346320	+	0.599843i	0.639273	+	0.768980i	$0.279235\pi$
$312$	0.592396	+	1.02606i	0.0335378	+	0.0580892i
$313$	−15.4731	+	5.63176i	−0.874593	+	0.318326i	−0.740026	−	0.672579i	$-0.765187\pi$
$313$	−15.4731	+	5.63176i	−0.874593	+	0.318326i	−0.134567	+	0.990904i	$0.542964\pi$
$314$	18.8735	−	6.86938i	1.06509	−	0.387661i
$315$	−2.43969	−	4.22567i	−0.137461	−	0.238090i
$316$	3.61334	−	6.25849i	0.203266	−	0.352068i
$317$	−5.41622	+	30.7169i	−0.304205	+	1.72523i	0.323016	+	0.946393i	$0.395303\pi$
$317$	−5.41622	+	30.7169i	−0.304205	+	1.72523i	−0.627222	+	0.778841i	$0.715808\pi$
$318$	8.99660	−	7.54904i	0.504504	−	0.423329i
$319$	0.145430	+	0.122030i	0.00814250	+	0.00683237i
$320$	−0.173648	−	0.984808i	−0.00970723	−	0.0550524i
$321$	5.49273	+	1.99919i	0.306574	+	0.111584i
$322$	17.4388			0.971827
$323$	5.06031	+	3.49946i	0.281563	+	0.194715i
$324$	1.00000			0.0555556
$325$	1.11334	+	0.405223i	0.0617570	+	0.0224777i
$326$	−1.51367	−	8.58445i	−0.0838345	−	0.475449i
$327$	2.21688	+	1.86018i	0.122594	+	0.102868i
$328$	−4.09627	+	3.43718i	−0.226178	+	0.189786i
$329$	1.53802	−	8.72254i	0.0847937	−	0.480889i
$330$	2.26604	−	3.92490i	0.124742	−	0.216059i
$331$	15.7750	+	27.3230i	0.867071	+	1.50181i	0.864976	+	0.501813i	$0.167333\pi$
$331$	15.7750	+	27.3230i	0.867071	+	1.50181i	0.00209423	+	0.999998i	$0.499333\pi$
$332$	8.02481	−	2.92079i	0.440419	−	0.160299i
$333$	−6.91147	+	2.51557i	−0.378746	+	0.137852i
$334$	3.01367	+	5.21983i	0.164901	+	0.285616i
$335$	−2.73055	+	4.72945i	−0.149186	+	0.258398i
$336$	−0.847296	+	4.80526i	−0.0462238	+	0.262148i
$337$	8.90941	−	7.47589i	0.485327	−	0.407237i	−0.367021	−	0.930213i	$-0.619622\pi$
$337$	8.90941	−	7.47589i	0.485327	−	0.407237i	0.852348	+	0.522975i	$0.175178\pi$
$338$	−8.88326	−	7.45394i	−0.483185	−	0.405441i
$339$	−2.14796	−	12.1817i	−0.116661	−	0.661617i
$340$	1.32635	+	0.482753i	0.0719315	+	0.0261809i
$341$	−44.8753			−2.43013
$342$	−4.21688	−	1.10359i	−0.228023	−	0.0596753i
$343$	−47.8590			−2.58414
$344$	0.918748	+	0.334397i	0.0495356	+	0.0180295i
$345$	0.620615	+	3.51968i	0.0334128	+	0.189493i
$346$	−16.7724	−	14.0737i	−0.901692	−	0.756609i
$347$	18.5096	−	15.5314i	0.993645	−	0.833767i	0.00755349	−	0.999971i	$-0.497596\pi$
$347$	18.5096	−	15.5314i	0.993645	−	0.833767i	0.986091	+	0.166204i	$0.0531512\pi$
$348$	0.00727396	−	0.0412527i	0.000389925	−	0.00221138i
$349$	2.36706	−	4.09987i	0.126706	−	0.219461i	−0.795693	−	0.605701i	$-0.792893\pi$
$349$	2.36706	−	4.09987i	0.126706	−	0.219461i	0.922398	+	0.386240i	$0.126226\pi$
$350$	2.43969	+	4.22567i	0.130407	+	0.225872i
$351$	1.11334	−	0.405223i	0.0594257	−	0.0216292i
$352$	−4.25877	+	1.55007i	−0.226993	+	0.0826188i
$353$	−2.80066	−	4.85088i	−0.149064	−	0.258187i	0.781818	−	0.623507i	$-0.214293\pi$
$353$	−2.80066	−	4.85088i	−0.149064	−	0.258187i	−0.930882	+	0.365321i	$0.880959\pi$
$354$	0.613341	−	1.06234i	0.0325987	−	0.0564626i
$355$	1.73055	−	9.81445i	0.0918482	−	0.520897i
$356$	1.30406	−	1.09424i	0.0691152	−	0.0579945i
$357$	−5.27584	−	4.42696i	−0.279227	−	0.234300i
$358$	1.27631	+	7.23832i	0.0674552	+	0.382557i
$359$	−4.41400	−	1.60656i	−0.232962	−	0.0847912i	0.222901	−	0.974841i	$-0.428447\pi$
$359$	−4.41400	−	1.60656i	−0.232962	−	0.0847912i	−0.455863	+	0.890050i	$0.650669\pi$
$360$	−1.00000			−0.0527046
$361$	16.5642	+	9.30742i	0.871799	+	0.489864i
$362$	21.3678			1.12307
$363$	−8.96451	−	3.26281i	−0.470515	−	0.171253i
$364$	1.00387	+	5.69323i	0.0526171	+	0.298406i
$365$	−11.1591	−	9.36360i	−0.584094	−	0.490113i
$366$	−5.20961	+	4.37138i	−0.272311	+	0.228496i
$367$	−4.57579	+	25.9506i	−0.238854	+	1.35461i	0.595489	+	0.803364i	$0.296959\pi$
$367$	−4.57579	+	25.9506i	−0.238854	+	1.35461i	−0.834343	+	0.551246i	$0.814153\pi$
$368$	1.78699	−	3.09516i	0.0931532	−	0.161346i
$369$	2.67365	+	4.63089i	0.139185	+	0.241075i
$370$	6.91147	−	2.51557i	0.359310	−	0.130778i
$371$	53.8487	−	19.5993i	2.79569	−	1.01755i
$372$	4.95084	+	8.57510i	0.256689	+	0.444598i
$373$	−4.27837	+	7.41036i	−0.221526	+	0.383694i	−0.955271	−	0.295730i	$-0.904437\pi$
$373$	−4.27837	+	7.41036i	−0.221526	+	0.383694i	0.733746	+	0.679424i	$0.237770\pi$
$374$	1.11081	−	6.29974i	0.0574389	−	0.325752i
$375$	−0.766044	+	0.642788i	−0.0395584	+	0.0331934i
$376$	−1.39053	−	1.16679i	−0.0717111	−	0.0601727i
$377$	−0.00861813	−	0.0488759i	−0.000443856	−	0.00251724i
$378$	4.58512	+	1.66885i	0.235833	+	0.0858363i
$379$	16.1489			0.829513			0.414756	−	0.909932i	$-0.363867\pi$
$379$	16.1489			0.829513			0.414756	+	0.909932i	$0.363867\pi$
$380$	4.21688	+	1.10359i	0.216321	+	0.0566130i
$381$	1.12567			0.0576697
$382$	9.15183	+	3.33099i	0.468248	+	0.170428i
$383$	−0.515730	−	2.92485i	−0.0263526	−	0.149453i	0.968792	−	0.247874i	$-0.0797319\pi$
$383$	−0.515730	−	2.92485i	−0.0263526	−	0.149453i	−0.995145	+	0.0984211i	$0.968621\pi$
$384$	0.766044	+	0.642788i	0.0390920	+	0.0328021i
$385$	16.9402	−	14.2145i	0.863350	−	0.724437i
$386$	−2.61721	+	14.8429i	−0.133213	+	0.755486i
$387$	0.488856	−	0.846723i	0.0248499	−	0.0430413i
$388$	−3.50000	−	6.06218i	−0.177686	−	0.307760i
$389$	15.4966	−	5.64030i	0.785709	−	0.285975i	0.0821577	−	0.996619i	$-0.473819\pi$
$389$	15.4966	−	5.64030i	0.785709	−	0.285975i	0.703551	+	0.710645i	$0.251597\pi$
$390$	−1.11334	+	0.405223i	−0.0563762	+	0.0205193i
$391$	2.52229	+	4.36873i	0.127558	+	0.220936i
$392$	−8.40420	+	14.5565i	−0.424476	+	0.735214i
$393$	−3.82976	+	21.7196i	−0.193186	+	1.09561i
$394$	15.1309	−	12.6963i	0.762283	−	0.639631i
$395$	5.53596	+	4.64522i	0.278544	+	0.233726i
$396$	0.786989	+	4.46324i	0.0395477	+	0.224286i
$397$	15.8919	+	5.78417i	0.797590	+	0.290299i	0.708488	−	0.705723i	$-0.249378\pi$
$397$	15.8919	+	5.78417i	0.797590	+	0.290299i	0.0891027	+	0.996022i	$0.471600\pi$
$398$	−9.75103			−0.488775
$399$	−17.4932	−	12.0974i	−0.875755	−	0.605629i
$400$	1.00000			0.0500000
$401$	26.9577	+	9.81180i	1.34620	+	0.489978i	0.911761	−	0.410722i	$-0.134723\pi$
$401$	26.9577	+	9.81180i	1.34620	+	0.489978i	0.434443	+	0.900700i	$0.356945\pi$
$402$	−0.948311	−	5.37814i	−0.0472974	−	0.268237i
$403$	8.98680	+	7.54082i	0.447664	+	0.375635i
$404$	−1.07532	+	0.902302i	−0.0534993	+	0.0448912i
$405$	−0.173648	+	0.984808i	−0.00862865	+	0.0489355i
$406$	0.102196	−	0.177009i	0.00507192	−	0.00878483i
$407$	−16.6668	−	28.8678i	−0.826145	−	1.43092i
$408$	−1.32635	+	0.482753i	−0.0656642	+	0.0238998i
$409$	25.0881	−	9.13133i	1.24053	−	0.451515i	0.363337	−	0.931658i	$-0.381637\pi$
$409$	25.0881	−	9.13133i	1.24053	−	0.451515i	0.877190	+	0.480143i	$0.159415\pi$
$410$	−2.67365	−	4.63089i	−0.132042	−	0.228704i
$411$	−0.949493	+	1.64457i	−0.0468350	+	0.0811206i
$412$	−1.92855	+	10.9373i	−0.0950128	+	0.538844i
$413$	4.58512	−	3.84737i	0.225619	−	0.189317i
$414$	−2.73783	−	2.29731i	−0.134557	−	0.112907i
$415$	1.48293	+	8.41009i	0.0727940	+	0.412835i
$416$	1.11334	+	0.405223i	0.0545860	+	0.0198677i
$417$	−23.0770			−1.13008
$418$	1.60694	−	19.6895i	0.0785982	−	0.963043i
$419$	6.34224			0.309839			0.154919	−	0.987927i	$-0.450488\pi$
$419$	6.34224			0.309839			0.154919	+	0.987927i	$0.450488\pi$
$420$	−4.58512	−	1.66885i	−0.223731	−	0.0814314i
$421$	−1.89053	−	10.7217i	−0.0921388	−	0.522545i	−0.995587	−	0.0938470i	$-0.970084\pi$
$421$	−1.89053	−	10.7217i	−0.0921388	−	0.522545i	0.903448	−	0.428698i	$-0.141028\pi$
$422$	17.4402	+	14.6340i	0.848974	+	0.712374i
$423$	−1.39053	+	1.16679i	−0.0676099	+	0.0567314i
$424$	2.03936	−	11.5658i	0.0990402	−	0.561685i
$425$	−0.705737	+	1.22237i	−0.0342333	+	0.0592938i
$426$	4.98293	+	8.63068i	0.241424	+	0.418158i
$427$	−31.1819	+	11.3493i	−1.50900	+	0.549230i
$428$	5.49273	−	1.99919i	0.265501	−	0.0966344i
$429$	2.68479	+	4.65020i	0.129623	+	0.224514i
$430$	−0.488856	+	0.846723i	−0.0235747	+	0.0408326i
$431$	−0.815207	+	4.62327i	−0.0392672	+	0.222695i	−0.998126	−	0.0611871i	$-0.980511\pi$
$431$	−0.815207	+	4.62327i	−0.0392672	+	0.222695i	0.958859	+	0.283882i	$0.0916225\pi$
$432$	0.766044	−	0.642788i	0.0368563	−	0.0309261i
$433$	−14.5364	−	12.1975i	−0.698576	−	0.586175i	0.222792	−	0.974866i	$-0.428483\pi$
$433$	−14.5364	−	12.1975i	−0.698576	−	0.586175i	−0.921368	+	0.388691i	$0.872927\pi$
$434$	8.38965	+	47.5801i	0.402716	+	2.28392i
$435$	0.0393628	+	0.0143269i	0.00188730	+	0.000686922i
$436$	2.89393			0.138594
$437$	9.00980	+	12.7089i	0.430997	+	0.607950i
$438$	14.5672			0.696046
$439$	22.6830	+	8.25595i	1.08260	+	0.394035i	0.820876	−	0.571107i	$-0.193486\pi$
$439$	22.6830	+	8.25595i	1.08260	+	0.394035i	0.261727	+	0.965142i	$0.415708\pi$
$440$	−0.786989	−	4.46324i	−0.0375182	−	0.212776i
$441$	12.8760	+	10.8042i	0.613142	+	0.514487i
$442$	−1.28106	+	1.07494i	−0.0609338	+	0.0511295i
$443$	0.839145	−	4.75903i	0.0398690	−	0.226108i	−0.958363	−	0.285554i	$-0.907822\pi$
$443$	0.839145	−	4.75903i	0.0398690	−	0.226108i	0.998232	+	0.0594460i	$0.0189334\pi$
$444$	−3.67752	+	6.36965i	−0.174527	+	0.302290i
$445$	0.851167	+	1.47426i	0.0403492	+	0.0698868i
$446$	−16.1493	+	5.87786i	−0.764692	+	0.278325i
$447$	16.3687	−	5.95772i	0.774213	−	0.281791i
$448$	2.43969	+	4.22567i	0.115265	+	0.199644i
$449$	−1.18866	+	2.05882i	−0.0560965	+	0.0971619i	−0.892710	−	0.450632i	$-0.851199\pi$
$449$	−1.18866	+	2.05882i	−0.0560965	+	0.0971619i	0.836613	+	0.547794i	$0.184532\pi$
$450$	0.173648	−	0.984808i	0.00818585	−	0.0464243i
$451$	−18.5646	+	15.5776i	−0.874175	+	0.733520i
$452$	−9.47565	−	7.95102i	−0.445697	−	0.373984i
$453$	−0.0846555	−	0.480105i	−0.00397746	−	0.0225573i
$454$	−21.9376	−	7.98465i	−1.02958	−	0.374738i
$455$	−5.78106			−0.271020
$456$	−3.93969	+	1.86516i	−0.184493	+	0.0873441i
$457$	14.2422			0.666220			0.333110	−	0.942888i	$-0.391902\pi$
$457$	14.2422			0.666220			0.333110	+	0.942888i	$0.391902\pi$
$458$	−6.03209	−	2.19550i	−0.281861	−	0.102589i
$459$	0.245100	+	1.39003i	0.0114403	+	0.0648811i
$460$	2.73783	+	2.29731i	0.127652	+	0.107113i
$461$	25.1498	−	21.1032i	1.17134	−	0.982872i	0.171344	−	0.985211i	$-0.445189\pi$
$461$	25.1498	−	21.1032i	1.17134	−	0.982872i	0.999997	+	0.00233908i	$0.000744553\pi$
$462$	−3.84002	+	21.7778i	−0.178654	+	1.01320i
$463$	−18.1400	+	31.4193i	−0.843036	+	1.46018i	0.0442804	+	0.999019i	$0.485900\pi$
$463$	−18.1400	+	31.4193i	−0.843036	+	1.46018i	−0.887316	+	0.461162i	$0.847433\pi$
$464$	−0.0209445	−	0.0362770i	−0.000972326	−	0.00168412i
$465$	−9.30453	+	3.38657i	−0.431487	+	0.157049i
$466$	−21.3824	+	7.78255i	−0.990520	+	0.360520i
$467$	−7.69372	−	13.3259i	−0.356023	−	0.616649i	0.631270	−	0.775563i	$-0.282534\pi$
$467$	−7.69372	−	13.3259i	−0.356023	−	0.616649i	−0.987292	+	0.158914i	$0.949201\pi$
$468$	0.592396	−	1.02606i	0.0273835	−	0.0474297i
$469$	4.62717	−	26.2420i	0.213663	−	1.21174i
$470$	1.39053	−	1.16679i	0.0641403	−	0.0538201i
$471$	−15.3858	−	12.9102i	−0.708939	−	0.594871i
$472$	−0.213011	−	1.20805i	−0.00980463	−	0.0556048i
$473$	4.16385	+	1.51552i	0.191454	+	0.0696835i
$474$	−7.22668			−0.331932
$475$	−1.81908	+	3.96118i	−0.0834650	+	0.181751i
$476$	−6.88713			−0.315671
$477$	−11.0360	−	4.01676i	−0.505302	−	0.183915i
$478$	−0.334808	−	1.89879i	−0.0153138	−	0.0868486i
$479$	−13.8118	−	11.5895i	−0.631077	−	0.529537i	0.270186	−	0.962808i	$-0.412915\pi$
$479$	−13.8118	−	11.5895i	−0.631077	−	0.529537i	−0.901264	+	0.433271i	$0.857359\pi$
$480$	−0.766044	+	0.642788i	−0.0349650	+	0.0293391i
$481$	−1.51320	+	8.58180i	−0.0689962	+	0.391297i
$482$	3.16978	−	5.49022i	0.144379	−	0.250072i
$483$	−8.71941	−	15.1025i	−0.396747	−	0.687186i
$484$	−8.96451	+	3.26281i	−0.407478	+	0.148310i
$485$	6.57785	−	2.39414i	0.298685	−	0.108712i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	6.68139	−	11.5725i	0.302763	−	0.524400i	−0.673998	−	0.738733i	$-0.735424\pi$
$487$	6.68139	−	11.5725i	0.302763	−	0.524400i	0.976761	+	0.214333i	$0.0687577\pi$
$488$	−1.18092	+	6.69734i	−0.0534578	+	0.303174i
$489$	−6.67752	+	5.60310i	−0.301968	+	0.253381i
$490$	−12.8760	−	10.8042i	−0.581678	−	0.488085i
$491$	5.19800	+	29.4793i	0.234582	+	1.33038i	0.843492	+	0.537142i	$0.180496\pi$
$491$	5.19800	+	29.4793i	0.234582	+	1.33038i	−0.608909	+	0.793240i	$0.708393\pi$
$492$	5.02481	+	1.82888i	0.226536	+	0.0824524i
$493$	0.0591253			0.00266287
$494$	−3.63041	+	3.67301i	−0.163340	+	0.165257i
$495$	−4.53209			−0.203702
$496$	9.30453	+	3.38657i	0.417786	+	0.152062i
$497$	8.44403	+	47.8885i	0.378767	+	2.14809i
$498$	−6.54189	−	5.48930i	−0.293149	−	0.245981i
$499$	−6.36097	+	5.33749i	−0.284756	+	0.238939i	−0.773966	−	0.633228i	$-0.781730\pi$
$499$	−6.36097	+	5.33749i	−0.284756	+	0.238939i	0.489210	+	0.872166i	$0.337285\pi$
$500$	−0.173648	+	0.984808i	−0.00776578	+	0.0440419i
$501$	3.01367	−	5.21983i	0.134641	−	0.233205i
$502$	1.02481	+	1.77503i	0.0457397	+	0.0792235i
$503$	29.5228	−	10.7454i	1.31635	−	0.479114i	0.414066	−	0.910247i	$-0.364108\pi$
$503$	29.5228	−	10.7454i	1.31635	−	0.479114i	0.902288	+	0.431133i	$0.141886\pi$
$504$	4.58512	−	1.66885i	0.204238	−	0.0743364i
$505$	−0.701867	−	1.21567i	−0.0312327	−	0.0540965i
$506$	8.09879	−	14.0275i	0.360035	−	0.623599i
$507$	−2.01367	+	11.4201i	−0.0894302	+	0.507184i
$508$	0.862311	−	0.723565i	0.0382589	−	0.0321030i
$509$	−11.2790	−	9.46420i	−0.499933	−	0.419493i	0.357637	−	0.933861i	$-0.383582\pi$
$509$	−11.2790	−	9.46420i	−0.499933	−	0.419493i	−0.857570	+	0.514367i	$0.828027\pi$
$510$	−0.245100	−	1.39003i	−0.0108532	−	0.0615516i
$511$	66.7923	+	24.3104i	2.95472	+	1.07543i
$512$	1.00000			0.0441942
$513$	1.15270	+	4.20372i	0.0508931	+	0.185599i
$514$	−30.5107			−1.34577
$515$	−10.4363	−	3.79850i	−0.459878	−	0.167382i
$516$	−0.169778	−	0.962858i	−0.00747405	−	0.0423874i
$517$	−6.30200	−	5.28801i	−0.277162	−	0.232566i
$518$	−27.4918	+	23.0684i	−1.20792	+	1.01357i
$519$	−3.80200	+	21.5622i	−0.166889	+	0.946477i
$520$	−0.592396	+	1.02606i	−0.0259783	+	0.0449957i
$521$	19.0175	+	32.9393i	0.833174	+	1.44310i	0.895509	+	0.445044i	$0.146812\pi$
$521$	19.0175	+	32.9393i	0.833174	+	1.44310i	−0.0623352	+	0.998055i	$0.519855\pi$
$522$	−0.0393628	+	0.0143269i	−0.00172286	+	0.000627072i
$523$	34.8097	−	12.6697i	1.52212	−	0.554008i	0.560446	−	0.828191i	$-0.310630\pi$
$523$	34.8097	−	12.6697i	1.52212	−	0.554008i	0.961678	+	0.274183i	$0.0884074\pi$
$524$	11.0273	+	19.0999i	0.481732	+	0.834384i
$525$	2.43969	−	4.22567i	0.106477	−	0.184423i
$526$	−5.03849	+	28.5747i	−0.219688	+	1.24591i
$527$	−10.7062	+	8.98357i	−0.466370	+	0.391331i
$528$	3.47178	+	2.91317i	0.151090	+	0.126779i
$529$	−1.77584	−	10.0713i	−0.0772106	−	0.437883i
$530$	11.0360	+	4.01676i	0.479371	+	0.174477i
$531$	−1.22668			−0.0532334
$532$	−21.1766	+	1.97724i	−0.918124	+	0.0857242i
$533$	6.33544			0.274418
$534$	−1.59967	−	0.582232i	−0.0692245	−	0.0251957i
$535$	1.01501	+	5.75643i	0.0438829	+	0.248872i
$536$	−4.18345	−	3.51033i	−0.180697	−	0.151623i
$537$	5.63041	−	4.72448i	0.242970	−	0.203876i
$538$	2.10694	−	11.9491i	0.0908368	−	0.515161i
$539$	−38.0886	+	65.9714i	−1.64059	+	2.84159i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	−4.13176	+	1.50384i	−0.177638	+	0.0646550i	−0.429308	−	0.903158i	$-0.641243\pi$
$541$	−4.13176	+	1.50384i	−0.177638	+	0.0646550i	0.251670	+	0.967813i	$0.419020\pi$
$542$	−5.62701	+	2.04806i	−0.241701	+	0.0879719i
$543$	−10.6839	−	18.5051i	−0.458491	−	0.794129i
$544$	−0.705737	+	1.22237i	−0.0302582	+	0.0524088i
$545$	−0.502526	+	2.84997i	−0.0215259	+	0.122079i
$546$	4.42855	−	3.71599i	0.189524	−	0.159030i
$547$	18.5326	+	15.5507i	0.792395	+	0.664898i	0.946337	−	0.323182i	$-0.104752\pi$
$547$	18.5326	+	15.5507i	0.792395	+	0.664898i	−0.153942	+	0.988080i	$0.549197\pi$
$548$	0.329755	+	1.87014i	0.0140865	+	0.0798882i
$549$	6.39053	+	2.32596i	0.272741	+	0.0992697i
$550$	4.53209			0.193249
$551$	0.181799	−	0.0169744i	0.00774492	−	0.000723134i
$552$	−3.57398			−0.152119
$553$	−33.1352	−	12.0602i	−1.40905	−	0.512853i
$554$	5.13950	+	29.1476i	0.218356	+	1.23836i
$555$	−5.63429	−	4.72773i	−0.239162	−	0.200681i
$556$	−17.6780	+	14.8336i	−0.749714	+	0.629084i
$557$	0.995252	−	5.64436i	0.0421702	−	0.239159i	−0.956436	−	0.291943i	$-0.905698\pi$
$557$	0.995252	−	5.64436i	0.0421702	−	0.239159i	0.998606	+	0.0527838i	$0.0168094\pi$
$558$	4.95084	−	8.57510i	0.209586	−	0.363013i
$559$	−0.579193	−	1.00319i	−0.0244972	−	0.0424305i
$560$	−4.58512	+	1.66885i	−0.193757	+	0.0705217i
$561$	−6.01114	+	2.18788i	−0.253791	+	0.0923723i
$562$	2.93717	+	5.08732i	0.123897	+	0.214596i
$563$	14.4470	−	25.0229i	0.608867	−	1.05459i	−0.382560	−	0.923930i	$-0.624958\pi$
$563$	14.4470	−	25.0229i	0.608867	−	1.05459i	0.991427	−	0.130658i	$-0.0417090\pi$
$564$	−0.315207	+	1.78763i	−0.0132726	+	0.0752728i
$565$	9.47565	−	7.95102i	0.398644	−	0.334502i
$566$	13.8537	+	11.6246i	0.582314	+	0.488620i
$567$	−0.847296	−	4.80526i	−0.0355831	−	0.201802i
$568$	9.36484	+	3.40852i	0.392940	+	0.143018i
$569$	−13.2540			−0.555638			−0.277819	−	0.960634i	$-0.589611\pi$
$569$	−13.2540			−0.555638			−0.277819	+	0.960634i	$0.589611\pi$
$570$	−1.15270	−	4.20372i	−0.0482814	−	0.176075i
$571$	−2.62536			−0.109868			−0.0549340	−	0.998490i	$-0.517495\pi$
$571$	−2.62536			−0.109868			−0.0549340	+	0.998490i	$0.517495\pi$
$572$	5.04576	+	1.83651i	0.210974	+	0.0767882i
$573$	−1.69119	−	9.59121i	−0.0706504	−	0.400679i
$574$	19.9873	+	16.7713i	0.834252	+	0.700021i
$575$	−2.73783	+	2.29731i	−0.114175	+	0.0958044i
$576$	0.173648	−	0.984808i	0.00723534	−	0.0410337i
$577$	4.12314	−	7.14149i	0.171649	−	0.297304i	−0.767348	−	0.641231i	$-0.778424\pi$
$577$	4.12314	−	7.14149i	0.171649	−	0.297304i	0.938996	+	0.343927i	$0.111757\pi$
$578$	7.50387	+	12.9971i	0.312120	+	0.540607i
$579$	14.1630	−	5.15490i	0.588593	−	0.214230i
$580$	0.0393628	−	0.0143269i	0.00163445	−	0.000594892i
$581$	−20.8346	−	36.0865i	−0.864363	−	1.49712i
$582$	−3.50000	+	6.06218i	−0.145080	+	0.251285i
$583$	9.24257	−	52.4172i	0.382788	−	2.17090i
$584$	11.1591	−	9.36360i	0.461767	−	0.387468i
$585$	0.907604	+	0.761570i	0.0375248	+	0.0314870i
$586$	−2.60560	−	14.7771i	−0.107636	−	0.610436i
$587$	−40.6737	−	14.8040i	−1.67878	−	0.611027i	−0.685641	−	0.727940i	$-0.740478\pi$
$587$	−40.6737	−	14.8040i	−1.67878	−	0.611027i	−0.993142	+	0.116912i	$0.962700\pi$
$588$	16.8084			0.693167
$589$	−30.3405	+	30.6965i	−1.25016	+	1.26483i
$590$	1.22668			0.0505017
$591$	−18.5608	−	6.75557i	−0.763488	−	0.277887i
$592$	1.27719	+	7.24330i	0.0524921	+	0.297698i
$593$	−20.0260	−	16.8038i	−0.822369	−	0.690050i	0.131156	−	0.991362i	$-0.458131\pi$
$593$	−20.0260	−	16.8038i	−0.822369	−	0.690050i	−0.953526	+	0.301312i	$0.902575\pi$
$594$	3.47178	−	2.91317i	0.142449	−	0.119529i
$595$	1.19594	−	6.78250i	0.0490286	−	0.278055i
$596$	8.70961	−	15.0855i	0.356759	−	0.617925i
$597$	4.87551	+	8.44464i	0.199542	+	0.345616i
$598$	−3.97906	+	1.44826i	−0.162716	+	0.0592237i
$599$	22.3567	−	8.13717i	0.913469	−	0.332476i	0.157832	−	0.987466i	$-0.449550\pi$
$599$	22.3567	−	8.13717i	0.913469	−	0.332476i	0.755637	+	0.654990i	$0.227327\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	−10.8883	+	18.8591i	−0.444143	+	0.769279i	−0.997992	−	0.0633384i	$-0.979825\pi$
$601$	−10.8883	+	18.8591i	−0.444143	+	0.769279i	0.553849	+	0.832617i	$0.313159\pi$
$602$	0.828411	−	4.69815i	0.0337635	−	0.191482i
$603$	−4.18345	+	3.51033i	−0.170363	+	0.142952i
$604$	−0.373455	−	0.313366i	−0.0151957	−	0.0127507i
$605$	−1.65657	−	9.39490i	−0.0673493	−	0.381957i
$606$	1.31908	+	0.480105i	0.0535839	+	0.0195029i
$607$	36.0360			1.46266			0.731328	−	0.682026i	$-0.238901\pi$
$607$	36.0360			1.46266			0.731328	+	0.682026i	$0.238901\pi$
$608$	−1.81908	+	3.96118i	−0.0737733	+	0.160647i
$609$	−0.204393			−0.00828242
$610$	−6.39053	−	2.32596i	−0.258745	−	0.0941755i
$611$	0.373455	+	2.11797i	0.0151084	+	0.0856839i
$612$	1.08125	+	0.907278i	0.0437070	+	0.0366745i
$613$	−1.10426	+	0.926581i	−0.0446005	+	0.0374242i	−0.664815	−	0.747008i	$-0.731490\pi$
$613$	−1.10426	+	0.926581i	−0.0446005	+	0.0374242i	0.620215	+	0.784432i	$0.287045\pi$
$614$	2.30706	−	13.0840i	0.0931052	−	0.528026i
$615$	−2.67365	+	4.63089i	−0.107812	+	0.186736i
$616$	11.0569	+	19.1511i	0.445495	+	0.771621i
$617$	−0.991849	+	0.361003i	−0.0399303	+	0.0145334i	−0.361908	−	0.932214i	$-0.617875\pi$
$617$	−0.991849	+	0.361003i	−0.0399303	+	0.0145334i	0.321978	+	0.946747i	$0.395652\pi$
$618$	10.4363	−	3.79850i	0.419809	−	0.152798i
$619$	4.20233	+	7.27866i	0.168906	+	0.292554i	0.938036	−	0.346539i	$-0.112643\pi$
$619$	4.20233	+	7.27866i	0.168906	+	0.292554i	−0.769129	+	0.639093i	$0.779310\pi$
$620$	−4.95084	+	8.57510i	−0.198830	+	0.344384i
$621$	−0.620615	+	3.51968i	−0.0249044	+	0.141240i
$622$	9.35710	−	7.85154i	0.375185	−	0.314818i
$623$	−6.36303	−	5.33921i	−0.254929	−	0.213911i
$624$	−0.205737	−	1.16679i	−0.00823607	−	0.0467091i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	16.4662			0.658120
$627$	−17.8550	+	8.45307i	−0.713061	+	0.337583i
$628$	−20.0847			−0.801467
$629$	−9.75537	−	3.55066i	−0.388972	−	0.141574i
$630$	0.847296	+	4.80526i	0.0337571	+	0.191446i
$631$	−24.0908	−	20.2146i	−0.959040	−	0.804730i	0.0217569	−	0.999763i	$-0.493074\pi$
$631$	−24.0908	−	20.2146i	−0.959040	−	0.804730i	−0.980797	+	0.195033i	$0.937518\pi$
$632$	−5.53596	+	4.64522i	−0.220209	+	0.184777i
$633$	3.95336	−	22.4206i	0.157132	−	0.891140i
$634$	15.5954	−	27.0120i	0.619372	−	1.07278i
$635$	0.562834	+	0.974856i	0.0223354	+	0.0386860i
$636$	−11.0360	+	4.01676i	−0.437604	+	0.159275i
$637$	18.7135	−	6.81115i	0.741455	−	0.269868i
$638$	−0.0949225	−	0.164411i	−0.00375802	−	0.00650908i
$639$	4.98293	−	8.63068i	0.197122	−	0.341424i
$640$	−0.173648	+	0.984808i	−0.00686405	+	0.0389279i
$641$	−2.43242	+	2.04104i	−0.0960748	+	0.0806163i	−0.689560	−	0.724229i	$-0.742196\pi$
$641$	−2.43242	+	2.04104i	−0.0960748	+	0.0806163i	0.593485	+	0.804845i	$0.297752\pi$
$642$	−4.47771	−	3.75725i	−0.176721	−	0.148287i
$643$	5.85797	+	33.2222i	0.231016	+	1.31016i	0.850844	+	0.525419i	$0.176091\pi$
$643$	5.85797	+	33.2222i	0.231016	+	1.31016i	−0.619828	+	0.784738i	$0.712798\pi$
$644$	−16.3871	−	5.96443i	−0.645743	−	0.235031i
$645$	0.977711			0.0384973
$646$	−3.55825	−	5.01914i	−0.139997	−	0.197476i
$647$	−14.6628			−0.576454			−0.288227	−	0.957562i	$-0.593066\pi$
$647$	−14.6628			−0.576454			−0.288227	+	0.957562i	$0.593066\pi$
$648$	−0.939693	−	0.342020i	−0.0369146	−	0.0134358i
$649$	−0.965385	−	5.47497i	−0.0378947	−	0.214911i
$650$	−0.907604	−	0.761570i	−0.0355991	−	0.0298712i
$651$	37.0107	−	31.0557i	1.45057	−	1.21717i
$652$	−1.51367	+	8.58445i	−0.0592799	+	0.336193i
$653$	−5.60813	+	9.71356i	−0.219463	+	0.380121i	−0.954644	−	0.297750i	$-0.903764\pi$
$653$	−5.60813	+	9.71356i	−0.219463	+	0.380121i	0.735181	+	0.677871i	$0.237097\pi$
$654$	−1.44697	−	2.50622i	−0.0565809	−	0.0980009i
$655$	−20.7246	+	7.54315i	−0.809778	+	0.294735i
$656$	5.02481	−	1.82888i	0.196186	−	0.0714059i
$657$	−7.28359	−	12.6155i	−0.284160	−	0.492179i
$658$	−4.42855	+	7.67047i	−0.172643	+	0.299026i
$659$	2.55468	−	14.4883i	0.0995163	−	0.564385i	−0.893753	−	0.448559i	$-0.851937\pi$
$659$	2.55468	−	14.4883i	0.0995163	−	0.564385i	0.993270	−	0.115826i	$-0.0369515\pi$
$660$	−3.47178	+	2.91317i	−0.135139	+	0.113395i
$661$	−19.6480	−	16.4866i	−0.764217	−	0.641254i	0.175004	−	0.984568i	$-0.444006\pi$
$661$	−19.6480	−	16.4866i	−0.764217	−	0.641254i	−0.939221	+	0.343314i	$0.888451\pi$
$662$	−5.47859	−	31.0706i	−0.212931	−	1.20759i
$663$	1.57145	+	0.571962i	0.0610301	+	0.0222132i
$664$	−8.53983			−0.331410
$665$	1.73009	−	21.1983i	0.0670898	−	0.822033i
$666$	7.35504			0.285002
$667$	0.140682	+	0.0512040i	0.00544723	+	0.00198263i
$668$	−1.04664	−	5.93577i	−0.0404956	−	0.229662i
$669$	13.1650	+	11.0468i	0.508989	+	0.427093i
$670$	4.18345	−	3.51033i	0.161621	−	0.135616i
$671$	−5.35204	+	30.3530i	−0.206613	+	1.17176i
$672$	2.43969	−	4.22567i	0.0941132	−	0.163009i
$673$	8.74557	+	15.1478i	0.337117	+	0.583903i	0.983889	−	0.178780i	$-0.0572149\pi$
$673$	8.74557	+	15.1478i	0.337117	+	0.583903i	−0.646772	+	0.762683i	$0.723882\pi$
$674$	−10.9290	+	3.97784i	−0.420970	+	0.153221i
$675$	−0.939693	+	0.342020i	−0.0361688	+	0.0131644i
$676$	5.79813	+	10.0427i	0.223005	+	0.386256i
$677$	−1.31227	+	2.27292i	−0.0504347	+	0.0873554i	−0.890141	−	0.455686i	$-0.849394\pi$
$677$	−1.31227	+	2.27292i	−0.0504347	+	0.0873554i	0.839706	+	0.543041i	$0.182727\pi$
$678$	−2.14796	+	12.1817i	−0.0824917	+	0.467834i
$679$	−26.1648	+	21.9549i	−1.00411	+	0.842550i
$680$	−1.08125	−	0.907278i	−0.0414641	−	0.0347925i
$681$	4.05391	+	22.9909i	0.155346	+	0.881012i
$682$	42.1690	+	15.3482i	1.61473	+	0.587715i
$683$	42.2354			1.61609			0.808045	−	0.589120i	$-0.200526\pi$
$683$	42.2354			1.61609			0.808045	+	0.589120i	$0.200526\pi$
$684$	3.58512	+	2.47929i	0.137081	+	0.0947982i
$685$	−1.89899			−0.0725565
$686$	44.9727	+	16.3687i	1.71707	+	0.624961i
$687$	1.11468	+	6.32169i	0.0425279	+	0.241188i
$688$	−0.748970	−	0.628461i	−0.0285542	−	0.0239598i
$689$	−10.6591	+	8.94405i	−0.406079	+	0.340741i
$690$	0.620615	−	3.51968i	0.0236264	−	0.133992i
$691$	23.9957	−	41.5618i	0.912840	−	1.58109i	0.102807	−	0.994701i	$-0.467218\pi$
$691$	23.9957	−	41.5618i	0.912840	−	1.58109i	0.810033	−	0.586384i	$-0.199449\pi$
$692$	10.9474	+	18.9615i	0.416159	+	0.720808i
$693$	20.7802	−	7.56337i	0.789374	−	0.287309i
$694$	−22.7053	+	8.26406i	−0.861882	+	0.313700i
$695$	−11.5385	−	19.9852i	−0.437680	−	0.758083i
$696$	−0.0209445	+	0.0362770i	−0.000793900	+	0.00137508i
$697$	−1.31062	+	7.43291i	−0.0496433	+	0.281541i
$698$	−3.62654	+	3.04303i	−0.137267	+	0.115180i
$699$	17.4311	+	14.6264i	0.659304	+	0.553222i
$700$	−0.847296	−	4.80526i	−0.0320248	−	0.181622i
$701$	−36.4334	−	13.2607i	−1.37607	−	0.500848i	−0.455085	−	0.890448i	$-0.650391\pi$
$701$	−36.4334	−	13.2607i	−1.37607	−	0.500848i	−0.920984	+	0.389600i	$0.872613\pi$
$702$	−1.18479			−0.0447171
$703$	−31.0153	−	8.11695i	−1.16976	−	0.306136i
$704$	4.53209			0.170810
$705$	−1.70574	−	0.620838i	−0.0642418	−	0.0233821i
$706$	0.972659	+	5.51622i	0.0366065	+	0.207606i
$707$	5.24691	+	4.40268i	0.197330	+	0.165580i
$708$	−0.939693	+	0.788496i	−0.0353158	+	0.0296335i
$709$	8.31109	−	47.1345i	0.312129	−	1.77017i	−0.275754	−	0.961228i	$-0.588927\pi$
$709$	8.31109	−	47.1345i	0.312129	−	1.77017i	0.587883	−	0.808946i	$-0.299962\pi$
$710$	−4.98293	+	8.63068i	−0.187006	+	0.323904i
$711$	3.61334	+	6.25849i	0.135511	+	0.234712i
$712$	−1.59967	+	0.582232i	−0.0599502	+	0.0218201i
$713$	−33.2542	+	12.1035i	−1.24538	+	0.453281i
$714$	3.44356	+	5.96443i	0.128872	+	0.223213i
$715$	−2.68479	+	4.65020i	−0.100406	+	0.173908i
$716$	1.27631	−	7.23832i	0.0476980	−	0.270509i
$717$	−1.47700	+	1.23935i	−0.0551594	+	0.0462843i
$718$	3.59833	+	3.01935i	0.134288	+	0.112681i
$719$	3.15317	+	17.8825i	0.117593	+	0.666905i	0.985433	+	0.170062i	$0.0543967\pi$
$719$	3.15317	+	17.8825i	0.117593	+	0.666905i	−0.867840	+	0.496844i	$0.834492\pi$
$720$	0.939693	+	0.342020i	0.0350203	+	0.0127463i
$721$	54.1908			2.01817
$722$	−12.3819	−	14.4114i	−0.460807	−	0.536337i
$723$	−6.33956			−0.235771
$724$	−20.0792	−	7.30823i	−0.746237	−	0.271608i
$725$	0.00727396	+	0.0412527i	0.000270148	+	0.00153209i
$726$	7.30793	+	6.13208i	0.271223	+	0.227583i
$727$	17.7672	−	14.9085i	0.658950	−	0.552925i	−0.250822	−	0.968033i	$-0.580701\pi$
$727$	17.7672	−	14.9085i	0.658950	−	0.552925i	0.909772	+	0.415109i	$0.136256\pi$
$728$	1.00387	−	5.69323i	0.0372059	−	0.211005i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	7.28359	+	12.6155i	0.269578	+	0.466922i
$731$	1.29679	−	0.471993i	0.0479635	−	0.0174573i
$732$	6.39053	−	2.32596i	0.236201	−	0.0859700i
$733$	−13.5025	−	23.3871i	−0.498727	−	0.863821i	0.501272	−	0.865290i	$-0.332866\pi$
$733$	−13.5025	−	23.3871i	−0.498727	−	0.863821i	−0.999999	+	0.00146910i	$0.999532\pi$
$734$	13.1755	−	22.8206i	0.486315	−	0.842322i
$735$	−2.91875	+	16.5530i	−0.107660	+	0.610568i
$736$	−2.73783	+	2.29731i	−0.100918	+	0.0846799i
$737$	−18.9598	−	15.9091i	−0.698392	−	0.586020i
$738$	−0.928548	−	5.26606i	−0.0341803	−	0.193846i
$739$	12.8383	+	4.67275i	0.472263	+	0.171890i	0.567177	−	0.823596i	$-0.308035\pi$
$739$	12.8383	+	4.67275i	0.472263	+	0.171890i	−0.0949140	+	0.995485i	$0.530258\pi$
$740$	−7.35504			−0.270377
$741$	4.99613	+	1.30753i	0.183537	+	0.0480331i
$742$	−57.3046			−2.10372
$743$	−5.26769	−	1.91728i	−0.193253	−	0.0703383i	0.243581	−	0.969881i	$-0.421678\pi$
$743$	−5.26769	−	1.91728i	−0.193253	−	0.0703383i	−0.436834	+	0.899542i	$0.643900\pi$
$744$	−1.71941	−	9.75125i	−0.0630365	−	0.357498i
$745$	13.3439	+	11.1969i	0.488882	+	0.410221i
$746$	6.55484	−	5.50017i	0.239990	−	0.201375i
$747$	−1.48293	+	8.41009i	−0.0542574	+	0.307709i
$748$	−3.19846	+	5.53990i	−0.116947	+	0.202559i
$749$	−14.2606	−	24.7001i	−0.521070	−	0.902520i
$750$	0.939693	−	0.342020i	0.0343127	−	0.0124888i
$751$	−28.4136	+	10.3417i	−1.03683	+	0.377374i	−0.803676	−	0.595067i	$-0.797126\pi$
$751$	−28.4136	+	10.3417i	−1.03683	+	0.377374i	−0.233150	+	0.972441i	$0.574903\pi$
$752$	0.907604	+	1.57202i	0.0330969	+	0.0573255i
$753$	1.02481	−	1.77503i	0.0373463	−	0.0646857i
$754$	−0.00861813	+	0.0488759i	−0.000313854	+	0.00177995i
$755$	0.373455	−	0.313366i	0.0135914	−	0.0114046i
$756$	−3.73783	−	3.13641i	−0.135943	−	0.114070i
$757$	−0.331566	−	1.88041i	−0.0120510	−	0.0683445i	0.978189	−	0.207716i	$-0.0666029\pi$
$757$	−0.331566	−	1.88041i	−0.0120510	−	0.0683445i	−0.990240	+	0.139371i	$0.955492\pi$
$758$	−15.1750	−	5.52325i	−0.551181	−	0.200613i
$759$	−16.1976			−0.587935
$760$	−3.58512	−	2.47929i	−0.130046	−	0.0899334i
$761$	43.7124			1.58457			0.792287	−	0.610148i	$-0.208890\pi$
$761$	43.7124			1.58457			0.792287	+	0.610148i	$0.208890\pi$
$762$	−1.05778	−	0.385001i	−0.0383194	−	0.0139471i
$763$	−2.45202	−	13.9061i	−0.0887690	−	0.503434i
$764$	−7.46064	−	6.26022i	−0.269916	−	0.226487i
$765$	−1.08125	+	0.907278i	−0.0390927	+	0.0328027i
$766$	−0.515730	+	2.92485i	−0.0186341	+	0.105679i
$767$	−0.726682	+	1.25865i	−0.0262390	+	0.0454472i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	37.1193	−	13.5103i	1.33856	−	0.487195i	0.429199	−	0.903210i	$-0.358796\pi$
$769$	37.1193	−	13.5103i	1.33856	−	0.487195i	0.909358	+	0.416015i	$0.136574\pi$
$770$	−20.7802	+	7.56337i	−0.748866	+	0.272565i
$771$	15.2554	+	26.4231i	0.549409	+	0.951604i
$772$	7.53596	−	13.0527i	0.271225	−	0.469776i
$773$	−0.00820761	+	0.0465477i	−0.000295207	+	0.00167420i	−0.984955	−	0.172811i	$-0.944715\pi$
$773$	−0.00820761	+	0.0465477i	−0.000295207	+	0.00167420i	0.984660	+	0.174485i	$0.0558261\pi$
$774$	−0.748970	+	0.628461i	−0.0269212	+	0.0225896i
$775$	−7.58512	−	6.36467i	−0.272466	−	0.228626i
$776$	1.21554	+	6.89365i	0.0436352	+	0.247468i
$777$	33.7237	+	12.2744i	1.20983	+	0.440343i
$778$	−16.4911			−0.591236
$779$	−1.89599	+	23.2311i	−0.0679310	+	0.832340i
$780$	1.18479			0.0424224
$781$	42.4423	+	15.4477i	1.51870	+	0.552763i
$782$	−0.875982	−	4.96794i	−0.0313250	−	0.177653i
$783$	0.0320889	+	0.0269258i	0.00114676	+	0.000962249i
$784$	12.8760	−	10.8042i	0.459856	−	0.385865i
$785$	3.48767	−	19.7796i	0.124480	−	0.705963i
$786$	11.0273	−	19.0999i	0.393332	−	0.681271i
$787$	5.33409	+	9.23892i	0.190140	+	0.329332i	0.945296	−	0.326213i	$-0.105773\pi$
$787$	5.33409	+	9.23892i	0.190140	+	0.329332i	−0.755157	+	0.655544i	$0.772439\pi$
$788$	−18.5608	+	6.75557i	−0.661200	+	0.240657i
$789$	27.2656	−	9.92388i	0.970682	−	0.353299i
$790$	−3.61334	−	6.25849i	−0.128557	−	0.222667i
$791$	−30.1780	+	52.2698i	−1.07301	+	1.85850i
$792$	0.786989	−	4.46324i	0.0279644	−	0.158594i
$793$	6.17230	−	5.17918i	0.219185	−	0.183918i
$794$	−12.9552	−	10.8707i	−0.459762	−	0.385786i
$795$	−2.03936	−	11.5658i	−0.0723287	−	0.410197i
$796$	9.16297	+	3.33505i	0.324773	+	0.118208i
$797$	50.0384			1.77245			0.886225	−	0.463255i	$-0.153318\pi$
$797$	50.0384			1.77245			0.886225	+	0.463255i	$0.153318\pi$
$798$	12.3007	+	17.3509i	0.435439	+	0.614215i
$799$	−2.56212			−0.0906412
$800$	−0.939693	−	0.342020i	−0.0332232	−	0.0120922i
$801$	0.295607	+	1.67647i	0.0104448	+	0.0592352i
$802$	−21.9761	−	18.4402i	−0.776004	−	0.651144i
$803$	50.5740	−	42.4367i	1.78472	−	1.49756i
$804$	−0.948311	+	5.37814i	−0.0334443	+	0.189672i
$805$	8.71941	−	15.1025i	0.307319	−	0.532292i
$806$	−5.86571	−	10.1597i	−0.206611	−	0.357861i
$807$	−11.4017	+	4.14987i	−0.401358	+	0.146082i
$808$	1.31908	−	0.480105i	0.0464050	−	0.0168900i
$809$	−24.4042	−	42.2693i	−0.858006	−	1.48611i	−0.873828	−	0.486235i	$-0.838370\pi$
$809$	−24.4042	−	42.2693i	−0.858006	−	1.48611i	0.0158220	−	0.999875i	$-0.494963\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	1.81908	−	10.3165i	0.0638765	−	0.362261i	−0.936069	−	0.351817i	$-0.885564\pi$
$811$	1.81908	−	10.3165i	0.0638765	−	0.362261i	0.999945	−	0.0104449i	$-0.00332478\pi$
$812$	−0.156574	+	0.131381i	−0.00549467	+	0.00461058i
$813$	4.58718	+	3.84910i	0.160879	+	0.134994i
$814$	5.78833	+	32.8273i	0.202881	+	1.15060i
$815$	−8.19119	−	2.98135i	−0.286925	−	0.104432i
$816$	1.41147			0.0494115
$817$	3.85188	−	1.82359i	0.134760	−	0.0637993i
$818$	−26.6982			−0.933481
$819$	−5.43242	−	1.97724i	−0.189824	−	0.0690903i
$820$	0.928548	+	5.26606i	0.0324263	+	0.183899i
$821$	−5.16116	−	4.33073i	−0.180126	−	0.151143i	0.548267	−	0.836303i	$-0.315288\pi$
$821$	−5.16116	−	4.33073i	−0.180126	−	0.151143i	−0.728393	+	0.685160i	$0.759732\pi$
$822$	1.45471	−	1.22064i	0.0507387	−	0.0425749i
$823$	−2.99448	+	16.9825i	−0.104381	+	0.591974i	0.887085	+	0.461607i	$0.152727\pi$
$823$	−2.99448	+	16.9825i	−0.104381	+	0.591974i	−0.991466	+	0.130368i	$0.958384\pi$
$824$	5.55303	−	9.61814i	0.193449	−	0.335064i
$825$	−2.26604	−	3.92490i	−0.0788935	−	0.136648i
$826$	−5.62449	+	2.04715i	−0.195701	+	0.0712293i
$827$	−43.0522	+	15.6697i	−1.49707	+	0.544890i	−0.955301	−	0.295636i	$-0.904468\pi$
$827$	−43.0522	+	15.6697i	−1.49707	+	0.544890i	−0.541771	+	0.840526i	$0.682246\pi$
$828$	1.78699	+	3.09516i	0.0621022	+	0.107564i
$829$	25.0942	−	43.4644i	0.871558	−	1.50958i	0.0111730	−	0.999938i	$-0.496443\pi$
$829$	25.0942	−	43.4644i	0.871558	−	1.50958i	0.860385	−	0.509645i	$-0.170223\pi$
$830$	1.48293	−	8.41009i	0.0514731	−	0.291919i
$831$	22.6728	−	19.0247i	0.786510	−	0.659960i
$832$	−0.907604	−	0.761570i	−0.0314655	−	0.0264027i
$833$	4.11974	+	23.3642i	0.142740	+	0.809521i
$834$	21.6853	+	7.89279i	0.750899	+	0.273305i
$835$	6.02734			0.208585
$836$	−8.24422	+	17.9524i	−0.285132	+	0.620898i
$837$	−9.90167			−0.342252
$838$	−5.95976	−	2.16918i	−0.205876	−	0.0749329i
$839$	−4.26368	−	24.1805i	−0.147199	−	0.834805i	−0.965576	−	0.260123i	$-0.916237\pi$
$839$	−4.26368	−	24.1805i	−0.147199	−	0.834805i	0.818377	−	0.574682i	$-0.194874\pi$
$840$	3.73783	+	3.13641i	0.128967	+	0.108216i
$841$	−22.2139	+	18.6397i	−0.765998	+	0.642749i
$842$	−1.89053	+	10.7217i	−0.0651520	+	0.369495i
$843$	2.93717	−	5.08732i	0.101161	−	0.175217i
$844$	−11.3833	−	19.7164i	−0.391828	−	0.678666i
$845$	−10.8969	+	3.96616i	−0.374866	+	0.136440i
$846$	1.70574	−	0.620838i	0.0586444	−	0.0213448i
$847$	23.2743	+	40.3122i	0.799713	+	1.38514i
$848$	−5.87211	+	10.1708i	−0.201649	+	0.349267i
$849$	3.14038	−	17.8100i	0.107777	−	0.611236i
$850$	1.08125	−	0.907278i	0.0370866	−	0.0311194i
$851$	−20.1368	−	16.8968i	−0.690281	−	0.579215i
$852$	−1.73055	−	9.81445i	−0.0592877	−	0.336237i
$853$	5.78699	+	2.10629i	0.198143	+	0.0721181i	0.439185	−	0.898396i	$-0.355267\pi$
$853$	5.78699	+	2.10629i	0.198143	+	0.0721181i	−0.241043	+	0.970515i	$0.577489\pi$
$854$	33.1830			1.13550
$855$	−3.06418	+	3.10013i	−0.104793	+	0.106022i
$856$	−5.84524			−0.199786
$857$	29.1428	+	10.6071i	0.995499	+	0.362332i	0.787847	−	0.615871i	$-0.211196\pi$
$857$	29.1428	+	10.6071i	0.995499	+	0.362332i	0.207652	+	0.978203i	$0.433418\pi$
$858$	−0.932419	−	5.28801i	−0.0318322	−	0.180530i
$859$	−4.46766	−	3.74881i	−0.152435	−	0.127908i	0.563381	−	0.826197i	$-0.309500\pi$
$859$	−4.46766	−	3.74881i	−0.152435	−	0.127908i	−0.715816	+	0.698289i	$0.753945\pi$
$860$	0.748970	−	0.628461i	0.0255397	−	0.0214303i
$861$	4.53074	−	25.6951i	0.154407	−	0.875688i
$862$	2.34730	−	4.06564i	0.0799492	−	0.138476i
$863$	14.0051	+	24.2575i	0.476738	+	0.825734i	0.999645	−	0.0266560i	$-0.00848588\pi$
$863$	14.0051	+	24.2575i	0.476738	+	0.825734i	−0.522907	+	0.852390i	$0.675153\pi$
$864$	−0.939693	+	0.342020i	−0.0319690	+	0.0116358i
$865$	−20.5744	+	7.48849i	−0.699552	+	0.254616i
$866$	9.48798	+	16.4337i	0.322415	+	0.558439i
$867$	7.50387	−	12.9971i	0.254845	−	0.441404i
$868$	8.38965	−	47.5801i	0.284763	−	1.61497i
$869$	−25.0895	+	21.0526i	−0.851102	+	0.714159i
$870$	−0.0320889	−	0.0269258i	−0.00108792	−	0.000912869i
$871$	1.12355	+	6.37198i	0.0380701	+	0.215906i
$872$	−2.71941	−	0.989783i	−0.0920908	−	0.0335183i
$873$	7.00000			0.236914
$874$	−4.11974	−	15.0240i	−0.139352	−	0.508195i
$875$	4.87939			0.164953
$876$	−13.6887	−	4.98227i	−0.462497	−	0.168335i
$877$	8.35937	+	47.4084i	0.282276	+	1.60087i	0.714856	+	0.699271i	$0.246492\pi$
$877$	8.35937	+	47.4084i	0.282276	+	1.60087i	−0.432580	+	0.901595i	$0.642397\pi$
$878$	−18.4914	−	15.5161i	−0.624054	−	0.523643i
$879$	−11.4945	+	9.64506i	−0.387701	+	0.325320i
$880$	−0.786989	+	4.46324i	−0.0265294	+	0.150456i
$881$	−21.4632	+	37.1753i	−0.723112	+	1.25247i	0.236634	+	0.971599i	$0.423956\pi$
$881$	−21.4632	+	37.1753i	−0.723112	+	1.25247i	−0.959746	+	0.280868i	$0.909378\pi$
$882$	−8.40420	−	14.5565i	−0.282984	−	0.490143i
$883$	7.29339	−	2.65458i	0.245442	−	0.0893336i	−0.216370	−	0.976311i	$-0.569422\pi$
$883$	7.29339	−	2.65458i	0.245442	−	0.0893336i	0.461812	+	0.886978i	$0.347200\pi$
$884$	1.57145	−	0.571962i	0.0528536	−	0.0192372i
$885$	−0.613341	−	1.06234i	−0.0206172	−	0.0357101i
$886$	−2.41622	+	4.18502i	−0.0811746	+	0.140598i
$887$	3.40667	−	19.3202i	0.114385	−	0.648708i	−0.872668	−	0.488314i	$-0.837612\pi$
$887$	3.40667	−	19.3202i	0.114385	−	0.648708i	0.987053	−	0.160395i	$-0.0512767\pi$
$888$	5.63429	−	4.72773i	0.189074	−	0.158652i
$889$	−4.20755	−	3.53055i	−0.141117	−	0.118411i
$890$	−0.295607	−	1.67647i	−0.00990877	−	0.0561954i
$891$	−4.25877	−	1.55007i	−0.142674	−	0.0519292i
$892$	17.1857			0.575421
$893$	−7.87804	+	0.735564i	−0.263629	+	0.0246147i
$894$	−17.4192			−0.582586
$895$	6.90673	+	2.51384i	0.230866	+	0.0840285i
$896$	−0.847296	−	4.80526i	−0.0283062	−	0.160532i
$897$	3.24376	+	2.72183i	0.108306	+	0.0908794i
$898$	1.82114	−	1.52812i	0.0607721	−	0.0509939i
$899$	−0.0720244	+	0.408471i	−0.00240215	+	0.0136233i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−8.28833	−	14.3558i	−0.276124	−	0.478262i
$902$	22.7729	−	8.28866i	0.758255	−	0.275982i
$903$	−4.48293	+	1.63165i	−0.149182	+	0.0542980i
$904$	6.18479	+	10.7124i	0.205703	+	0.356288i
$905$	10.6839	−	18.5051i	0.355145	−	0.615130i
$906$	−0.0846555	+	0.480105i	−0.00281249	+	0.0159504i
$907$	−15.9953	+	13.4216i	−0.531114	+	0.445657i	−0.868486	−	0.495714i	$-0.834906\pi$
$907$	−15.9953	+	13.4216i	−0.531114	+	0.445657i	0.337372	+	0.941371i	$0.390462\pi$
$908$	17.8837	+	15.0062i	0.593492	+	0.497999i
$909$	−0.243756	−	1.38241i	−0.00808487	−	0.0458516i
$910$	5.43242	+	1.97724i	0.180083	+	0.0655448i
$911$	−35.6509			−1.18117			−0.590584	−	0.806976i	$-0.701103\pi$
$911$	−35.6509			−1.18117			−0.590584	+	0.806976i	$0.701103\pi$
$912$	4.34002	−	0.405223i	0.143713	−	0.0134183i
$913$	−38.7033			−1.28089
$914$	−13.3833	−	4.87111i	−0.442679	−	0.161122i
$915$	1.18092	+	6.69734i	0.0390401	+	0.221407i
$916$	4.91740	+	4.12619i	0.162476	+	0.136333i
$917$	82.4366	−	69.1725i	2.72230	−	2.28428i
$918$	0.245100	−	1.39003i	0.00808950	−	0.0458778i
$919$	5.31908	−	9.21291i	0.175460	−	0.303906i	−0.764860	−	0.644196i	$-0.777192\pi$
$919$	5.31908	−	9.21291i	0.175460	−	0.303906i	0.940320	+	0.340290i	$0.110525\pi$
$920$	−1.78699	−	3.09516i	−0.0589153	−	0.102044i
$921$	−12.4846	+	4.54401i	−0.411381	+	0.149730i
$922$	−30.8508	+	11.2288i	−1.01602	+	0.369799i
$923$	−5.90373	−	10.2256i	−0.194324	−	0.336579i
$924$	11.0569	−	19.1511i	0.363745	−	0.630026i
$925$	1.27719	−	7.24330i	0.0419937	−	0.238158i
$926$	27.7920	−	23.3203i	0.913303	−	0.766352i
$927$	−8.50774	−	7.13884i	−0.279431	−	0.234470i
$928$	0.00727396	+	0.0412527i	0.000238779	+	0.00135419i
$929$	13.0625	+	4.75437i	0.428568	+	0.155986i	0.547293	−	0.836941i	$-0.315658\pi$
$929$	13.0625	+	4.75437i	0.428568	+	0.155986i	−0.118725	+	0.992927i	$0.537881\pi$
$930$	9.90167			0.324689
$931$	19.3751	+	70.6578i	0.634993	+	2.31572i
$932$	22.7547			0.745353
$933$	−11.4782	−	4.17772i	−0.375779	−	0.136772i
$934$	2.67200	+	15.1537i	0.0874305	+	0.495843i
$935$	−4.90033	−	4.11186i	−0.160258	−	0.134472i
$936$	−0.907604	+	0.761570i	−0.0296660	+	0.0248927i
$937$	−0.553967	+	3.14170i	−0.0180973	+	0.102635i	−0.992518	−	0.122095i	$-0.961039\pi$
$937$	−0.553967	+	3.14170i	−0.0180973	+	0.102635i	0.974421	+	0.224730i	$0.0721499\pi$
$938$	−13.3234	+	23.0768i	−0.435025	+	0.753485i
$939$	−8.23308	−	14.2601i	−0.268676	−	0.465361i
$940$	−1.70574	+	0.620838i	−0.0556350	+	0.0202495i
$941$	−25.6917	+	9.35100i	−0.837524	+	0.304834i	−0.724943	−	0.688809i	$-0.758134\pi$
$941$	−25.6917	+	9.35100i	−0.837524	+	0.304834i	−0.112581	+	0.993643i	$0.535912\pi$
$942$	10.0424	+	17.3939i	0.327198	+	0.566723i
$943$	−9.55556	+	16.5507i	−0.311172	+	0.538965i
$944$	−0.213011	+	1.20805i	−0.00693292	+	0.0393185i
$945$	3.73783	−	3.13641i	0.121591	−	0.102027i
$946$	−3.39440	−	2.84824i	−0.110361	−	0.0926043i
$947$	6.65166	+	37.7235i	0.216150	+	1.22585i	0.878900	+	0.477007i	$0.158278\pi$
$947$	6.65166	+	37.7235i	0.216150	+	1.22585i	−0.662750	+	0.748841i	$0.730611\pi$
$948$	6.79086	+	2.47167i	0.220557	+	0.0802761i
$949$	−17.2591			−0.560253
$950$	3.06418	−	3.10013i	0.0994151	−	0.100582i
$951$	−31.1908			−1.01143
$952$	6.47178	+	2.35554i	0.209752	+	0.0763434i
$953$	−0.555970	−	3.15306i	−0.0180096	−	0.102138i	0.974478	−	0.224483i	$-0.0720695\pi$
$953$	−0.555970	−	3.15306i	−0.0180096	−	0.102138i	−0.992488	+	0.122346i	$0.960958\pi$
$954$	8.99660	+	7.54904i	0.291276	+	0.244409i
$955$	7.46064	−	6.26022i	0.241421	−	0.202576i
$956$	−0.334808	+	1.89879i	−0.0108285	+	0.0614112i
$957$	−0.0949225	+	0.164411i	−0.00306841	+	0.00531464i
$958$	9.01501	+	15.6145i	0.291262	+	0.504480i
$959$	8.70708	−	3.16912i	0.281166	−	0.102336i
$960$	0.939693	−	0.342020i	0.0303284	−	0.0110387i
$961$	−33.5216	−	58.0611i	−1.08134	−	1.87294i
$962$	4.35710	−	7.54671i	0.140478	−	0.243316i
$963$	−1.01501	+	5.75643i	−0.0327084	+	0.185499i
$964$	−4.85638	+	4.07499i	−0.156414	+	0.131247i
$965$	11.5458	+	9.68804i	0.371671	+	0.311869i
$966$	3.02822	+	17.1739i	0.0974313	+	0.552561i
$967$	−16.3953	−	5.96739i	−0.527237	−	0.191898i	0.0646675	−	0.997907i	$-0.479401\pi$
$967$	−16.3953	−	5.96739i	−0.527237	−	0.191898i	−0.591904	+	0.806008i	$0.701624\pi$
$968$	9.53983			0.306622
$969$	−2.56758	+	5.59110i	−0.0824826	+	0.179612i
$970$	−7.00000			−0.224756
$971$	−24.9393	−	9.07716i	−0.800340	−	0.291300i	−0.0907124	−	0.995877i	$-0.528914\pi$
$971$	−24.9393	−	9.07716i	−0.800340	−	0.291300i	−0.709627	+	0.704577i	$0.751137\pi$
$972$	0.173648	+	0.984808i	0.00556977	+	0.0315877i
$973$	86.2577	+	72.3788i	2.76529	+	2.32036i
$974$	−10.2365	+	8.58943i	−0.327998	+	0.275223i
$975$	−0.205737	+	1.16679i	−0.00658886	+	0.0373673i
$976$	3.40033	−	5.88954i	0.108842	−	0.188520i
$977$	−11.1900	−	19.3817i	−0.358000	−	0.620074i	0.629627	−	0.776898i	$-0.283208\pi$
$977$	−11.1900	−	19.3817i	−0.358000	−	0.620074i	−0.987627	+	0.156824i	$0.949875\pi$
$978$	8.19119	−	2.98135i	0.261925	−	0.0953330i
$979$	−7.24985	+	2.63873i	−0.231706	+	0.0843341i
$980$	8.40420	+	14.5565i	0.268462	+	0.464990i
$981$	−1.44697	+	2.50622i	−0.0461981	+	0.0800174i
$982$	5.19800	−	29.4793i	0.165875	−	0.940722i
$983$	−21.5159	+	18.0540i	−0.686252	+	0.575834i	−0.917826	−	0.396983i	$-0.870057\pi$
$983$	−21.5159	+	18.0540i	−0.686252	+	0.575834i	0.231574	+	0.972817i	$0.425613\pi$
$984$	−4.09627	−	3.43718i	−0.130584	−	0.109573i
$985$	−3.42989	−	19.4519i	−0.109285	−	0.619789i
$986$	−0.0555596	−	0.0202221i	−0.00176938	−	0.000644001i
$987$	8.85710			0.281924
$988$	4.66772	−	2.20983i	0.148500	−	0.0703040i
$989$	3.49432			0.111113
$990$	4.25877	+	1.55007i	0.135353	+	0.0492643i
$991$	−5.87645	−	33.3270i	−0.186672	−	1.05867i	−0.923789	−	0.382902i	$-0.874925\pi$
$991$	−5.87645	−	33.3270i	−0.186672	−	1.05867i	0.737117	−	0.675765i	$-0.236186\pi$
$992$	−7.58512	−	6.36467i	−0.240828	−	0.202079i
$993$	−24.1687	+	20.2799i	−0.766969	+	0.643563i
$994$	8.44403	−	47.8885i	0.267828	−	1.51893i
$995$	−4.87551	+	8.44464i	−0.154564	+	0.267713i
$996$	4.26991	+	7.39571i	0.135297	+	0.234342i
$997$	−40.9350	+	14.8991i	−1.29642	+	0.471860i	−0.895831	−	0.444396i	$-0.853418\pi$
$997$	−40.9350	+	14.8991i	−1.29642	+	0.471860i	−0.400594	+	0.916256i	$0.631196\pi$
$998$	7.80288	−	2.84002i	0.246996	−	0.0898991i
$999$	−3.67752	−	6.36965i	−0.116352	−	0.201527i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.h.61.1	✓	6
19.5	even	9	inner	570.2.u.h.271.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.h.61.1	✓	6	1.1	even	1	trivial
570.2.u.h.271.1	yes	6	19.5	even	9	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(2.43969 - 4.22567i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(2.43969 - 4.22567i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(0.939693 - 0.342020i) q^{10} +(-2.26604 - 3.92490i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.205737 + 1.16679i) q^{13} +(-3.73783 + 3.13641i) q^{14} +(-0.766044 - 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.32635 - 0.482753i) q^{17} +1.00000 q^{18} +(-4.21688 - 1.10359i) q^{19} -1.00000 q^{20} +(4.58512 + 1.66885i) q^{21} +(0.786989 + 4.46324i) q^{22} +(-2.73783 - 2.29731i) q^{23} +(0.766044 - 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(0.592396 - 1.02606i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(4.58512 - 1.66885i) q^{28} +(-0.0393628 + 0.0143269i) q^{29} +(0.500000 + 0.866025i) q^{30} +(4.95084 - 8.57510i) q^{31} +(0.173648 - 0.984808i) q^{32} +(3.47178 - 2.91317i) q^{33} +(1.08125 + 0.907278i) q^{34} +(0.847296 + 4.80526i) q^{35} +(-0.939693 - 0.342020i) q^{36} +7.35504 q^{37} +(3.58512 + 2.47929i) q^{38} -1.18479 q^{39} +(0.939693 + 0.342020i) q^{40} +(-0.928548 - 5.26606i) q^{41} +(-3.73783 - 3.13641i) q^{42} +(-0.748970 + 0.628461i) q^{43} +(0.786989 - 4.46324i) q^{44} +(0.500000 - 0.866025i) q^{45} +(1.78699 + 3.09516i) q^{46} +(1.70574 - 0.620838i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(-8.40420 - 14.5565i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.245100 - 1.39003i) q^{51} +(-0.907604 + 0.761570i) q^{52} +(8.99660 + 7.54904i) q^{53} +(0.173648 + 0.984808i) q^{54} +(4.25877 + 1.55007i) q^{55} -4.87939 q^{56} +(0.354570 - 4.34445i) q^{57} +0.0418891 q^{58} +(1.15270 + 0.419550i) q^{59} +(-0.173648 - 0.984808i) q^{60} +(-5.20961 - 4.37138i) q^{61} +(-7.58512 + 6.36467i) q^{62} +(-0.847296 + 4.80526i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.592396 - 1.02606i) q^{65} +(-4.25877 + 1.55007i) q^{66} +(5.13176 - 1.86781i) q^{67} +(-0.705737 - 1.22237i) q^{68} +(1.78699 - 3.09516i) q^{69} +(0.847296 - 4.80526i) q^{70} +(-7.63429 + 6.40593i) q^{71} +(0.766044 + 0.642788i) q^{72} +(2.52956 + 14.3459i) q^{73} +(-6.91147 - 2.51557i) q^{74} +1.00000 q^{75} +(-2.52094 - 3.55596i) q^{76} -22.1138 q^{77} +(1.11334 + 0.405223i) q^{78} +(-1.25490 - 7.11689i) q^{79} +(-0.766044 - 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-0.928548 + 5.26606i) q^{82} +(4.26991 - 7.39571i) q^{83} +(2.43969 + 4.22567i) q^{84} +(1.32635 - 0.482753i) q^{85} +(0.918748 - 0.334397i) q^{86} +(-0.0209445 - 0.0362770i) q^{87} +(-2.26604 + 3.92490i) q^{88} +(0.295607 - 1.67647i) q^{89} +(-0.766044 + 0.642788i) q^{90} +(4.42855 + 3.71599i) q^{91} +(-0.620615 - 3.51968i) q^{92} +(9.30453 + 3.38657i) q^{93} -1.81521 q^{94} +(3.93969 - 1.86516i) q^{95} +1.00000 q^{96} +(-6.57785 - 2.39414i) q^{97} +(2.91875 + 16.5530i) q^{98} +(3.47178 + 2.91317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q + 9 * q^7 - 3 * q^8	\( 6 q + 9 q^{7} - 3 q^{8} - 9 q^{11} - 3 q^{12} + 9 q^{13} - 3 q^{14} - 9 q^{17} + 6 q^{18} - 9 q^{19} - 6 q^{20} + 6 q^{21} - 3 q^{22} + 3 q^{23} - 3 q^{27} + 6 q^{28} - 9 q^{29} + 3 q^{30} + 18 q^{31} + 6 q^{33} + 9 q^{34} + 3 q^{35} - 6 q^{37} - 6 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 3 q^{45} + 3 q^{46} - 12 q^{49} - 3 q^{50} - 9 q^{52} + 12 q^{53} + 3 q^{55} - 18 q^{56} + 18 q^{57} - 6 q^{58} + 9 q^{59} + 3 q^{61} - 24 q^{62} - 3 q^{63} - 3 q^{64} - 3 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} + 3 q^{70} - 36 q^{71} + 21 q^{73} - 21 q^{74} + 6 q^{75} - 12 q^{76} - 60 q^{77} - 9 q^{79} - 6 q^{82} - 3 q^{83} + 9 q^{84} + 9 q^{85} + 3 q^{86} + 3 q^{87} - 9 q^{88} + 3 q^{89} + 27 q^{91} - 15 q^{92} + 3 q^{93} - 18 q^{94} + 18 q^{95} + 6 q^{96} + 15 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q + 9 * q^7 - 3 * q^8 - 9 * q^11 - 3 * q^12 + 9 * q^13 - 3 * q^14 - 9 * q^17 + 6 * q^18 - 9 * q^19 - 6 * q^20 + 6 * q^21 - 3 * q^22 + 3 * q^23 - 3 * q^27 + 6 * q^28 - 9 * q^29 + 3 * q^30 + 18 * q^31 + 6 * q^33 + 9 * q^34 + 3 * q^35 - 6 * q^37 - 6 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 3 * q^45 + 3 * q^46 - 12 * q^49 - 3 * q^50 - 9 * q^52 + 12 * q^53 + 3 * q^55 - 18 * q^56 + 18 * q^57 - 6 * q^58 + 9 * q^59 + 3 * q^61 - 24 * q^62 - 3 * q^63 - 3 * q^64 - 3 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 + 3 * q^70 - 36 * q^71 + 21 * q^73 - 21 * q^74 + 6 * q^75 - 12 * q^76 - 60 * q^77 - 9 * q^79 - 6 * q^82 - 3 * q^83 + 9 * q^84 + 9 * q^85 + 3 * q^86 + 3 * q^87 - 9 * q^88 + 3 * q^89 + 27 * q^91 - 15 * q^92 + 3 * q^93 - 18 * q^94 + 18 * q^95 + 6 * q^96 + 15 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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