LMFDB - Embedded newform 418.2.j.c.111.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(23,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([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("418.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.j (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			111.5
Character	$\chi$	$=$	418.111
Dual form			418.2.j.c.177.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(2.69748 - 0.981803i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.218104 - 1.23693i) q^{5} +(-2.69748 - 0.981803i) q^{6} +(-0.789822 - 1.36801i) q^{7} +(0.500000 - 0.866025i) q^{8} +(4.01433 - 3.36842i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(2.69748 - 0.981803i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.218104 - 1.23693i) q^{5} +(-2.69748 - 0.981803i) q^{6} +(-0.789822 - 1.36801i) q^{7} +(0.500000 - 0.866025i) q^{8} +(4.01433 - 3.36842i) q^{9} +(-0.962162 + 0.807349i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.43530 + 2.48601i) q^{12} +(-0.183559 - 0.0668099i) q^{13} +(-0.274302 + 1.55564i) q^{14} +(-0.626090 - 3.55073i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-2.43575 - 2.04384i) q^{17} -5.24034 q^{18} +(1.65375 - 4.03300i) q^{19} +1.25601 q^{20} +(-3.47365 - 2.91473i) q^{21} +(0.939693 - 0.342020i) q^{22} +(0.901439 + 5.11231i) q^{23} +(0.498474 - 2.82699i) q^{24} +(3.21603 + 1.17054i) q^{25} +(0.0976695 + 0.169169i) q^{26} +(3.21556 - 5.56951i) q^{27} +(1.21008 - 1.01538i) q^{28} +(-0.582238 + 0.488555i) q^{29} +(-1.80275 + 3.12246i) q^{30} +(3.15603 + 5.46640i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.498474 + 2.82699i) q^{33} +(0.552141 + 3.13134i) q^{34} +(-1.86440 + 0.678586i) q^{35} +(4.01433 + 3.36842i) q^{36} -0.361281 q^{37} +(-3.85921 + 2.02645i) q^{38} -0.560740 q^{39} +(-0.962162 - 0.807349i) q^{40} +(-1.81879 + 0.661987i) q^{41} +(0.787411 + 4.46563i) q^{42} +(-0.148527 + 0.842340i) q^{43} +(-0.939693 - 0.342020i) q^{44} +(-3.29097 - 5.70012i) q^{45} +(2.59559 - 4.49569i) q^{46} +(-1.02167 + 0.857287i) q^{47} +(-2.19901 + 1.84519i) q^{48} +(2.25236 - 3.90121i) q^{49} +(-1.71122 - 2.96391i) q^{50} +(-8.57705 - 3.12179i) q^{51} +(0.0339203 - 0.192371i) q^{52} +(0.897526 + 5.09012i) q^{53} +(-6.04327 + 2.19957i) q^{54} +(0.962162 + 0.807349i) q^{55} -1.57964 q^{56} +(0.501359 - 12.5026i) q^{57} +0.760057 q^{58} +(-9.31674 - 7.81767i) q^{59} +(3.38807 - 1.23316i) q^{60} +(2.40656 + 13.6483i) q^{61} +(1.09608 - 6.21616i) q^{62} +(-7.77865 - 2.83120i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.122674 + 0.212478i) q^{65} +(2.19901 - 1.84519i) q^{66} +(9.11996 - 7.65255i) q^{67} +(1.58983 - 2.75366i) q^{68} +(7.45090 + 12.9053i) q^{69} +(1.86440 + 0.678586i) q^{70} +(0.408834 - 2.31861i) q^{71} +(-0.909975 - 5.16073i) q^{72} +(-3.92921 + 1.43012i) q^{73} +(0.276758 + 0.232227i) q^{74} +9.82443 q^{75} +(4.25890 + 0.928307i) q^{76} +1.57964 q^{77} +(0.429552 + 0.360437i) q^{78} +(-0.0451652 + 0.0164388i) q^{79} +(0.218104 + 1.23693i) q^{80} +(0.475819 - 2.69850i) q^{81} +(1.81879 + 0.661987i) q^{82} +(5.04988 + 8.74665i) q^{83} +(2.26726 - 3.92701i) q^{84} +(-3.05934 + 2.56709i) q^{85} +(0.655224 - 0.549798i) q^{86} +(-1.09091 + 1.88951i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-11.0026 - 4.00462i) q^{89} +(-1.14294 + 6.48194i) q^{90} +(0.0535819 + 0.303878i) q^{91} +(-4.87811 + 1.77549i) q^{92} +(13.8802 + 11.6469i) q^{93} +1.33370 q^{94} +(-4.62785 - 2.92519i) q^{95} +2.87060 q^{96} +(8.03546 + 6.74255i) q^{97} +(-4.23306 + 1.54071i) q^{98} +(0.909975 + 5.16073i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) $ 30 * q - 12 * q^7 + 15 * q^8	$ 30 q - 12 q^{7} + 15 q^{8} - 15 q^{11} + 3 q^{12} - 3 q^{13} + 9 q^{14} + 27 q^{15} - 36 q^{18} - 9 q^{19} + 18 q^{20} - 27 q^{21} - 3 q^{23} - 12 q^{25} + 3 q^{27} + 9 q^{28} + 3 q^{29} + 9 q^{30} + 30 q^{31} - 9 q^{34} + 15 q^{35} + 18 q^{37} + 6 q^{38} - 6 q^{41} - 45 q^{42} + 39 q^{43} - 18 q^{45} + 21 q^{46} + 45 q^{47} - 33 q^{49} + 36 q^{50} - 36 q^{51} + 6 q^{52} - 24 q^{53} + 45 q^{54} - 24 q^{56} - 24 q^{57} - 30 q^{58} + 3 q^{59} - 9 q^{60} - 27 q^{61} + 15 q^{62} - 93 q^{63} - 15 q^{64} + 18 q^{65} - 9 q^{67} - 21 q^{68} + 48 q^{69} - 15 q^{70} + 39 q^{73} + 3 q^{74} - 42 q^{75} - 15 q^{76} + 24 q^{77} + 6 q^{78} + 21 q^{79} + 84 q^{81} + 6 q^{82} - 36 q^{83} - 27 q^{84} + 63 q^{85} + 6 q^{86} - 21 q^{87} + 15 q^{88} + 54 q^{89} + 12 q^{90} + 3 q^{91} - 3 q^{92} + 51 q^{93} - 78 q^{94} + 6 q^{95} + 6 q^{96} - 18 q^{97} + 3 q^{98}+O(q^{100}) $ 30 * q - 12 * q^7 + 15 * q^8 - 15 * q^11 + 3 * q^12 - 3 * q^13 + 9 * q^14 + 27 * q^15 - 36 * q^18 - 9 * q^19 + 18 * q^20 - 27 * q^21 - 3 * q^23 - 12 * q^25 + 3 * q^27 + 9 * q^28 + 3 * q^29 + 9 * q^30 + 30 * q^31 - 9 * q^34 + 15 * q^35 + 18 * q^37 + 6 * q^38 - 6 * q^41 - 45 * q^42 + 39 * q^43 - 18 * q^45 + 21 * q^46 + 45 * q^47 - 33 * q^49 + 36 * q^50 - 36 * q^51 + 6 * q^52 - 24 * q^53 + 45 * q^54 - 24 * q^56 - 24 * q^57 - 30 * q^58 + 3 * q^59 - 9 * q^60 - 27 * q^61 + 15 * q^62 - 93 * q^63 - 15 * q^64 + 18 * q^65 - 9 * q^67 - 21 * q^68 + 48 * q^69 - 15 * q^70 + 39 * q^73 + 3 * q^74 - 42 * q^75 - 15 * q^76 + 24 * q^77 + 6 * q^78 + 21 * q^79 + 84 * q^81 + 6 * q^82 - 36 * q^83 - 27 * q^84 + 63 * q^85 + 6 * q^86 - 21 * q^87 + 15 * q^88 + 54 * q^89 + 12 * q^90 + 3 * q^91 - 3 * q^92 + 51 * q^93 - 78 * q^94 + 6 * q^95 + 6 * q^96 - 18 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	2.69748	−	0.981803i	1.55739	−	0.566844i	0.587254	−	0.809402i	$-0.300209\pi$
$3$	2.69748	−	0.981803i	1.55739	−	0.566844i	0.970137	+	0.242558i	$0.0779866\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.218104	−	1.23693i	0.0975392	−	0.553172i	−0.896400	−	0.443245i	$-0.853827\pi$
$5$	0.218104	−	1.23693i	0.0975392	−	0.553172i	0.993940	−	0.109927i	$-0.0350618\pi$
$6$	−2.69748	−	0.981803i	−1.10124	−	0.400819i
$7$	−0.789822	−	1.36801i	−0.298525	−	0.517060i	0.677274	−	0.735731i	$-0.263161\pi$
$7$	−0.789822	−	1.36801i	−0.298525	−	0.517060i	−0.975799	+	0.218671i	$0.929828\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	4.01433	−	3.36842i	1.33811	−	1.12281i
$10$	−0.962162	+	0.807349i	−0.304262	+	0.255306i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	1.43530	+	2.48601i	0.414335	+	0.717650i
$13$	−0.183559	−	0.0668099i	−0.0509100	−	0.0185297i	0.316440	−	0.948613i	$-0.397513\pi$
$13$	−0.183559	−	0.0668099i	−0.0509100	−	0.0185297i	−0.367350	+	0.930083i	$0.619735\pi$
$14$	−0.274302	+	1.55564i	−0.0733103	+	0.415764i
$15$	−0.626090	−	3.55073i	−0.161656	−	0.916795i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−2.43575	−	2.04384i	−0.590757	−	0.495704i	0.297703	−	0.954659i	$-0.403780\pi$
$17$	−2.43575	−	2.04384i	−0.590757	−	0.495704i	−0.888460	+	0.458955i	$0.848224\pi$
$18$	−5.24034			−1.23516
$19$	1.65375	−	4.03300i	0.379397	−	0.925234i
$19$	1.65375	−	4.03300i	0.379397	−	0.925234i
$20$	1.25601			0.280853
$21$	−3.47365	−	2.91473i	−0.758012	−	0.636047i
$22$	0.939693	−	0.342020i	0.200343	−	0.0729189i
$23$	0.901439	+	5.11231i	0.187963	+	1.06599i	0.922089	+	0.386978i	$0.126481\pi$
$23$	0.901439	+	5.11231i	0.187963	+	1.06599i	−0.734126	+	0.679013i	$0.762408\pi$
$24$	0.498474	−	2.82699i	0.101751	−	0.577057i
$25$	3.21603	+	1.17054i	0.643207	+	0.234108i
$26$	0.0976695	+	0.169169i	0.0191546	+	0.0331767i
$27$	3.21556	−	5.56951i	0.618834	−	1.07185i
$28$	1.21008	−	1.01538i	0.228683	−	0.191888i
$29$	−0.582238	+	0.488555i	−0.108119	+	0.0907225i	−0.695244	−	0.718773i	$-0.744704\pi$
$29$	−0.582238	+	0.488555i	−0.108119	+	0.0907225i	0.587126	+	0.809496i	$0.300259\pi$
$30$	−1.80275	+	3.12246i	−0.329136	+	0.570081i
$31$	3.15603	+	5.46640i	0.566839	+	0.981794i	0.996876	+	0.0789826i	$0.0251671\pi$
$31$	3.15603	+	5.46640i	0.566839	+	0.981794i	−0.430037	+	0.902811i	$0.641500\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	−0.498474	+	2.82699i	−0.0867732	+	0.492115i
$34$	0.552141	+	3.13134i	0.0946913	+	0.537021i
$35$	−1.86440	+	0.678586i	−0.315141	+	0.114702i
$36$	4.01433	+	3.36842i	0.669055	+	0.561404i
$37$	−0.361281			−0.0593943			−0.0296971	−	0.999559i	$-0.509454\pi$
$37$	−0.361281			−0.0593943			−0.0296971	+	0.999559i	$0.509454\pi$
$38$	−3.85921	+	2.02645i	−0.626047	+	0.328733i
$39$	−0.560740			−0.0897903
$40$	−0.962162	−	0.807349i	−0.152131	−	0.127653i
$41$	−1.81879	+	0.661987i	−0.284048	+	0.103385i	−0.480115	−	0.877206i	$-0.659405\pi$
$41$	−1.81879	+	0.661987i	−0.284048	+	0.103385i	0.196067	+	0.980590i	$0.437183\pi$
$42$	0.787411	+	4.46563i	0.121500	+	0.689062i
$43$	−0.148527	+	0.842340i	−0.0226502	+	0.128456i	−0.994036	−	0.109051i	$-0.965219\pi$
$43$	−0.148527	+	0.842340i	−0.0226502	+	0.128456i	0.971386	+	0.237506i	$0.0763300\pi$
$44$	−0.939693	−	0.342020i	−0.141664	−	0.0515615i
$45$	−3.29097	−	5.70012i	−0.490588	−	0.849724i
$46$	2.59559	−	4.49569i	0.382699	−	0.662854i
$47$	−1.02167	+	0.857287i	−0.149027	+	0.125048i	−0.714253	−	0.699888i	$-0.753233\pi$
$47$	−1.02167	+	0.857287i	−0.149027	+	0.125048i	0.565226	+	0.824936i	$0.308789\pi$
$48$	−2.19901	+	1.84519i	−0.317399	+	0.266330i
$49$	2.25236	−	3.90121i	0.321766	−	0.557315i
$50$	−1.71122	−	2.96391i	−0.242003	−	0.419161i
$51$	−8.57705	−	3.12179i	−1.20103	−	0.437138i
$52$	0.0339203	−	0.192371i	0.00470389	−	0.0266771i
$53$	0.897526	+	5.09012i	0.123285	+	0.699182i	0.982312	+	0.187252i	$0.0599581\pi$
$53$	0.897526	+	5.09012i	0.123285	+	0.699182i	−0.859027	+	0.511930i	$0.828931\pi$
$54$	−6.04327	+	2.19957i	−0.822385	+	0.299324i
$55$	0.962162	+	0.807349i	0.129738	+	0.108863i
$56$	−1.57964			−0.211089
$57$	0.501359	−	12.5026i	0.0664066	−	1.65601i
$58$	0.760057			0.0998004
$59$	−9.31674	−	7.81767i	−1.21294	−	1.01777i	−0.999164	−	0.0408912i	$-0.986980\pi$
$59$	−9.31674	−	7.81767i	−1.21294	−	1.01777i	−0.213773	−	0.976883i	$-0.568575\pi$
$60$	3.38807	−	1.23316i	0.437398	−	0.159200i
$61$	2.40656	+	13.6483i	0.308129	+	1.74749i	0.608398	+	0.793632i	$0.291812\pi$
$61$	2.40656	+	13.6483i	0.308129	+	1.74749i	−0.300269	+	0.953854i	$0.597077\pi$
$62$	1.09608	−	6.21616i	0.139202	−	0.789453i
$63$	−7.77865	−	2.83120i	−0.980018	−	0.356697i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.122674	+	0.212478i	−0.0152159	+	0.0263546i
$66$	2.19901	−	1.84519i	0.270679	−	0.227127i
$67$	9.11996	−	7.65255i	1.11418	−	0.934908i	0.115884	−	0.993263i	$-0.463030\pi$
$67$	9.11996	−	7.65255i	1.11418	−	0.934908i	0.998296	+	0.0583544i	$0.0185853\pi$
$68$	1.58983	−	2.75366i	0.192795	−	0.333930i
$69$	7.45090	+	12.9053i	0.896982	+	1.55362i
$70$	1.86440	+	0.678586i	0.222838	+	0.0811065i
$71$	0.408834	−	2.31861i	0.0485197	−	0.275169i	−0.950890	−	0.309530i	$-0.899828\pi$
$71$	0.408834	−	2.31861i	0.0485197	−	0.275169i	0.999409	+	0.0343609i	$0.0109396\pi$
$72$	−0.909975	−	5.16073i	−0.107242	−	0.608197i
$73$	−3.92921	+	1.43012i	−0.459880	+	0.167382i	−0.561562	−	0.827434i	$-0.689800\pi$
$73$	−3.92921	+	1.43012i	−0.459880	+	0.167382i	0.101683	+	0.994817i	$0.467577\pi$
$74$	0.276758	+	0.232227i	0.0321724	+	0.0269959i
$75$	9.82443			1.13443
$76$	4.25890	+	0.928307i	0.488530	+	0.106484i
$77$	1.57964			0.180017
$78$	0.429552	+	0.360437i	0.0486372	+	0.0408114i
$79$	−0.0451652	+	0.0164388i	−0.00508149	+	0.00184951i	−0.344560	−	0.938764i	$-0.611972\pi$
$79$	−0.0451652	+	0.0164388i	−0.00508149	+	0.00184951i	0.339478	+	0.940614i	$0.389750\pi$
$80$	0.218104	+	1.23693i	0.0243848	+	0.138293i
$81$	0.475819	−	2.69850i	0.0528687	−	0.299834i
$82$	1.81879	+	0.661987i	0.200852	+	0.0731042i
$83$	5.04988	+	8.74665i	0.554297	+	0.960070i	0.997958	+	0.0638754i	$0.0203460\pi$
$83$	5.04988	+	8.74665i	0.554297	+	0.960070i	−0.443661	+	0.896195i	$0.646321\pi$
$84$	2.26726	−	3.92701i	0.247378	−	0.428472i
$85$	−3.05934	+	2.56709i	−0.331832	+	0.278440i
$86$	0.655224	−	0.549798i	0.0706546	−	0.0592863i
$87$	−1.09091	+	1.88951i	−0.116958	+	0.202577i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−11.0026	−	4.00462i	−1.16628	−	0.424489i	−0.314940	−	0.949112i	$-0.601984\pi$
$89$	−11.0026	−	4.00462i	−1.16628	−	0.424489i	−0.851335	+	0.524622i	$0.824207\pi$
$90$	−1.14294	+	6.48194i	−0.120476	+	0.683256i
$91$	0.0535819	+	0.303878i	0.00561691	+	0.0318551i
$92$	−4.87811	+	1.77549i	−0.508578	+	0.185107i
$93$	13.8802	+	11.6469i	1.43931	+	1.20773i
$94$	1.33370			0.137561
$95$	−4.62785	−	2.92519i	−0.474808	−	0.300119i
$96$	2.87060			0.292979
$97$	8.03546	+	6.74255i	0.815877	+	0.684602i	0.952003	−	0.306090i	$-0.0990207\pi$
$97$	8.03546	+	6.74255i	0.815877	+	0.684602i	−0.136126	+	0.990692i	$0.543465\pi$
$98$	−4.23306	+	1.54071i	−0.427604	+	0.155635i
$99$	0.909975	+	5.16073i	0.0914559	+	0.518672i
$100$	−0.594299	+	3.37044i	−0.0594299	+	0.337044i
$101$	−14.2085	−	5.17149i	−1.41380	−	0.514582i	−0.481559	−	0.876414i	$-0.659929\pi$
$101$	−14.2085	−	5.17149i	−1.41380	−	0.514582i	−0.932244	+	0.361831i	$0.882152\pi$
$102$	4.56375	+	7.90465i	0.451879	+	0.782677i
$103$	−5.41987	+	9.38749i	−0.534036	+	0.924977i	0.465173	+	0.885220i	$0.345992\pi$
$103$	−5.41987	+	9.38749i	−0.534036	+	0.924977i	−0.999209	+	0.0397577i	$0.987341\pi$
$104$	−0.149638	+	0.125561i	−0.0146732	+	0.0123123i
$105$	−4.36294	+	3.66094i	−0.425780	+	0.357272i
$106$	2.58432	−	4.47618i	0.251012	−	0.434765i
$107$	5.79472	+	10.0368i	0.560197	+	0.970290i	0.997479	+	0.0709653i	$0.0226079\pi$
$107$	5.79472	+	10.0368i	0.560197	+	0.970290i	−0.437282	+	0.899325i	$0.644059\pi$
$108$	6.04327	+	2.19957i	0.581514	+	0.211654i
$109$	−2.48489	+	14.0925i	−0.238009	+	1.34982i	0.598174	+	0.801366i	$0.295893\pi$
$109$	−2.48489	+	14.0925i	−0.238009	+	1.34982i	−0.836183	+	0.548450i	$0.815218\pi$
$110$	−0.218104	−	1.23693i	−0.0207954	−	0.117937i
$111$	−0.974549	+	0.354707i	−0.0925001	+	0.0336673i
$112$	1.21008	+	1.01538i	0.114342	+	0.0959439i
$113$	11.5480			1.08634			0.543170	−	0.839623i	$-0.317224\pi$
$113$	11.5480			1.08634			0.543170	+	0.839623i	$0.317224\pi$
$114$	−8.42058	+	9.25528i	−0.788660	+	0.866837i
$115$	6.52019			0.608010
$116$	−0.582238	−	0.488555i	−0.0540594	−	0.0453612i
$117$	−0.961909	+	0.350106i	−0.0889285	+	0.0323673i
$118$	2.11193	+	11.9774i	0.194419	+	1.10261i
$119$	−0.872185	+	4.94641i	−0.0799531	+	0.453436i
$120$	−3.38807	−	1.23316i	−0.309287	−	0.112571i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	6.92943	−	12.0021i	0.627361	−	1.08662i
$123$	−4.25622	+	3.57139i	−0.383770	+	0.322022i
$124$	−4.83531	+	4.05731i	−0.434224	+	0.364357i
$125$	5.28934	−	9.16141i	0.473093	−	0.819421i
$126$	4.13893	+	7.16884i	0.368725	+	0.638651i
$127$	6.94745	+	2.52867i	0.616487	+	0.224383i	0.631339	−	0.775507i	$-0.282506\pi$
$127$	6.94745	+	2.52867i	0.616487	+	0.224383i	−0.0148525	+	0.999890i	$0.504728\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	0.426362	+	2.41802i	0.0375391	+	0.212895i
$130$	0.230552	−	0.0839140i	0.0202207	−	0.00735975i
$131$	5.07476	+	4.25823i	0.443384	+	0.372043i	0.836974	−	0.547243i	$-0.184323\pi$
$131$	5.07476	+	4.25823i	0.443384	+	0.372043i	−0.393590	+	0.919286i	$0.628767\pi$
$132$	−2.87060			−0.249854
$133$	−6.82336	+	0.922997i	−0.591660	+	0.0800340i
$134$	−11.9053			−1.02846
$135$	−6.18777	−	5.19215i	−0.532558	−	0.446870i
$136$	−2.98789	+	1.08750i	−0.256210	+	0.0932528i
$137$	−0.633790	−	3.59440i	−0.0541483	−	0.307090i	0.945690	−	0.325070i	$-0.105388\pi$
$137$	−0.633790	−	3.59440i	−0.0541483	−	0.307090i	−0.999838	+	0.0179794i	$0.994277\pi$
$138$	2.58767	−	14.6754i	0.220277	−	1.24925i
$139$	3.44844	+	1.25513i	0.292493	+	0.106459i	0.484099	−	0.875013i	$-0.339147\pi$
$139$	3.44844	+	1.25513i	0.292493	+	0.106459i	−0.191606	+	0.981472i	$0.561370\pi$
$140$	−0.992026	−	1.71824i	−0.0838415	−	0.145218i
$141$	−1.91426	+	3.31560i	−0.161210	+	0.279224i
$142$	−1.80356	+	1.51337i	−0.151351	+	0.126999i
$143$	0.149638	−	0.125561i	0.0125134	−	0.0105000i
$144$	−2.62017	+	4.53827i	−0.218347	+	0.378189i
$145$	0.477321	+	0.826744i	0.0396393	+	0.0686573i
$146$	3.92921	+	1.43012i	0.325184	+	0.118357i
$147$	2.24549	−	12.7348i	0.185205	−	1.05035i
$148$	−0.0627359	−	0.355793i	−0.00515686	−	0.0292460i
$149$	−6.36152	+	2.31540i	−0.521156	+	0.189685i	−0.589185	−	0.807998i	$-0.700551\pi$
$149$	−6.36152	+	2.31540i	−0.521156	+	0.189685i	0.0680292	+	0.997683i	$0.478329\pi$
$150$	−7.52595	−	6.31502i	−0.614491	−	0.515619i
$151$	21.8195			1.77564			0.887822	−	0.460187i	$-0.152218\pi$
$151$	21.8195			1.77564			0.887822	+	0.460187i	$0.152218\pi$
$152$	−2.66580	−	3.44869i	−0.216225	−	0.279726i
$153$	−16.6624			−1.34708
$154$	−1.21008	−	1.01538i	−0.0975108	−	0.0818213i
$155$	7.44990	−	2.71154i	0.598390	−	0.217796i
$156$	−0.0973715	−	0.552221i	−0.00779596	−	0.0442131i
$157$	2.54034	−	14.4070i	0.202741	−	1.14980i	−0.698214	−	0.715889i	$-0.746022\pi$
$157$	2.54034	−	14.4070i	0.202741	−	1.14980i	0.900955	−	0.433913i	$-0.142867\pi$
$158$	0.0451652	+	0.0164388i	0.00359315	+	0.00130780i
$159$	7.41855	+	12.8493i	0.588330	+	1.01902i
$160$	0.628006	−	1.08774i	0.0496483	−	0.0859933i
$161$	6.28172	−	5.27099i	0.495069	−	0.415412i
$162$	−2.09906	+	1.76132i	−0.164918	+	0.138383i
$163$	0.298366	−	0.516786i	0.0233699	−	0.0404778i	−0.854104	−	0.520102i	$-0.825894\pi$
$163$	0.298366	−	0.516786i	0.0233699	−	0.0404778i	0.877474	+	0.479625i	$0.159227\pi$
$164$	−0.967760	−	1.67621i	−0.0755693	−	0.130890i
$165$	3.38807	+	1.23316i	0.263761	+	0.0960011i
$166$	1.75381	−	9.94633i	0.136122	−	0.771985i
$167$	0.930580	+	5.27758i	0.0720105	+	0.408392i	0.999411	+	0.0343214i	$0.0109270\pi$
$167$	0.930580	+	5.27758i	0.0720105	+	0.408392i	−0.927400	+	0.374070i	$0.877962\pi$
$168$	−4.26106	+	1.55090i	−0.328748	+	0.119654i
$169$	−9.92935	−	8.33171i	−0.763796	−	0.640901i
$170$	3.99368			0.306301
$171$	−6.94614	−	21.7604i	−0.531185	−	1.66406i
$172$	−0.855334			−0.0652186
$173$	−13.8642	−	11.6335i	−1.05408	−	0.884476i	−0.0605614	−	0.998164i	$-0.519289\pi$
$173$	−13.8642	−	11.6335i	−1.05408	−	0.884476i	−0.993516	+	0.113688i	$0.963734\pi$
$174$	2.05024	−	0.746226i	0.155428	−	0.0565713i
$175$	−0.938781	−	5.32409i	−0.0709651	−	0.402463i
$176$	0.173648	−	0.984808i	0.0130892	−	0.0742327i
$177$	−32.8071	−	11.9408i	−2.46594	−	0.897527i
$178$	5.85437	+	10.1401i	0.438804	+	0.760030i
$179$	−7.35125	+	12.7327i	−0.549459	+	0.951690i	0.448853	+	0.893606i	$0.351833\pi$
$179$	−7.35125	+	12.7327i	−0.549459	+	0.951690i	−0.998312	+	0.0580846i	$0.981501\pi$
$180$	5.04205	−	4.23078i	0.375812	−	0.315344i
$181$	−11.3565	+	9.52921i	−0.844120	+	0.708300i	−0.958486	−	0.285138i	$-0.907961\pi$
$181$	−11.3565	+	9.52921i	−0.844120	+	0.708300i	0.114367	+	0.993439i	$0.463516\pi$
$182$	0.154283	−	0.267226i	0.0114362	−	0.0198081i
$183$	19.8916	+	34.4533i	1.47043	+	2.54686i
$184$	4.87811	+	1.77549i	0.359619	+	0.130891i
$185$	−0.0787970	+	0.446880i	−0.00579327	+	0.0328553i
$186$	−3.14640	−	17.8441i	−0.230705	−	1.30839i
$187$	2.98789	−	1.08750i	0.218496	−	0.0795262i
$188$	−1.02167	−	0.857287i	−0.0745133	−	0.0625240i
$189$	−10.1589			−0.738949
$190$	1.66486	+	5.21556i	0.120782	+	0.378376i
$191$	−21.9265			−1.58655			−0.793273	−	0.608866i	$-0.791625\pi$
$191$	−21.9265			−1.58655			−0.793273	+	0.608866i	$0.791625\pi$
$192$	−2.19901	−	1.84519i	−0.158700	−	0.133165i
$193$	9.03864	−	3.28980i	0.650615	−	0.236805i	0.00443595	−	0.999990i	$-0.498588\pi$
$193$	9.03864	−	3.28980i	0.650615	−	0.236805i	0.646179	+	0.763186i	$0.276366\pi$
$194$	−1.82149	−	10.3302i	−0.130775	−	0.741664i
$195$	−0.122300	+	0.693597i	−0.00875807	+	0.0496695i
$196$	4.23306	+	1.54071i	0.302361	+	0.110051i
$197$	−10.9926	−	19.0397i	−0.783188	−	1.35652i	−0.930075	−	0.367369i	$-0.880259\pi$
$197$	−10.9926	−	19.0397i	−0.783188	−	1.35652i	0.146887	−	0.989153i	$-0.453075\pi$
$198$	2.62017	−	4.53827i	0.186207	−	0.322521i
$199$	−0.177988	+	0.149349i	−0.0126172	+	0.0105871i	−0.649074	−	0.760725i	$-0.724844\pi$
$199$	−0.177988	+	0.149349i	−0.0126172	+	0.0105871i	0.636457	+	0.771312i	$0.280399\pi$
$200$	2.62174	−	2.19990i	0.185385	−	0.155556i
$201$	17.0876	−	29.5966i	1.20527	−	2.08758i
$202$	7.56021	+	13.0947i	0.531934	+	0.921337i
$203$	1.12821	+	0.410636i	0.0791850	+	0.0288210i
$204$	1.58497	−	8.98884i	0.110970	−	0.629344i
$205$	0.422145	+	2.39410i	0.0294839	+	0.167211i
$206$	10.1860	−	3.70741i	0.709694	−	0.258308i
$207$	20.8391	+	17.4861i	1.44842	+	1.21537i
$208$	0.195339			0.0135443
$209$	2.66580	+	3.44869i	0.184398	+	0.238551i
$210$	5.69542			0.393021
$211$	−15.0044	−	12.5902i	−1.03295	−	0.866745i	−0.0417475	−	0.999128i	$-0.513293\pi$
$211$	−15.0044	−	12.5902i	−1.03295	−	0.866745i	−0.991199	+	0.132384i	$0.957737\pi$
$212$	−4.85694	+	1.76778i	−0.333576	+	0.121412i
$213$	−1.17360	−	6.65581i	−0.0804136	−	0.456048i
$214$	2.01249	−	11.4134i	0.137571	−	0.780202i
$215$	1.00952	+	0.367436i	0.0688488	+	0.0250589i
$216$	−3.21556	−	5.56951i	−0.218791	−	0.378957i
$217$	4.98539	−	8.63496i	0.338431	−	0.586179i
$218$	10.9620	−	9.19822i	0.742441	−	0.622982i
$219$	−9.19488	+	7.71542i	−0.621333	+	0.521360i
$220$	−0.628006	+	1.08774i	−0.0423402	+	0.0733353i
$221$	0.310555	+	0.537897i	0.0208902	+	0.0361829i
$222$	0.974549	+	0.354707i	0.0654075	+	0.0238064i
$223$	2.59316	−	14.7065i	0.173651	−	0.984823i	−0.766039	−	0.642794i	$-0.777775\pi$
$223$	2.59316	−	14.7065i	0.173651	−	0.984823i	0.939690	−	0.342029i	$-0.111114\pi$
$224$	−0.274302	−	1.55564i	−0.0183276	−	0.103941i
$225$	16.8531	−	6.13403i	1.12354	−	0.408935i
$226$	−8.84625	−	7.42288i	−0.588444	−	0.493763i
$227$	18.1632			1.20554			0.602768	−	0.797916i	$-0.294064\pi$
$227$	18.1632			1.20554			0.602768	+	0.797916i	$0.294064\pi$
$228$	12.3997	−	1.67731i	0.821192	−	0.111083i
$229$	−23.0792			−1.52512			−0.762559	−	0.646919i	$-0.776057\pi$
$229$	−23.0792			−1.52512			−0.762559	+	0.646919i	$0.776057\pi$
$230$	−4.99475	−	4.19109i	−0.329344	−	0.276353i
$231$	4.26106	−	1.55090i	0.280357	−	0.102042i
$232$	0.131983	+	0.748510i	0.00866508	+	0.0491421i
$233$	2.83448	−	16.0751i	0.185693	−	1.05312i	−0.739370	−	0.673300i	$-0.764876\pi$
$233$	2.83448	−	16.0751i	0.185693	−	1.05312i	0.925062	−	0.379816i	$-0.124013\pi$
$234$	0.961909	+	0.350106i	0.0628820	+	0.0228872i
$235$	0.837573	+	1.45072i	0.0546372	+	0.0946344i
$236$	6.08107	−	10.5327i	0.395844	−	0.685622i
$237$	−0.105693	+	0.0886867i	−0.00686548	+	0.00576082i
$238$	3.84762	−	3.22854i	0.249404	−	0.209275i
$239$	9.08991	−	15.7442i	0.587978	−	1.01841i	−0.406519	−	0.913642i	$-0.633258\pi$
$239$	9.08991	−	15.7442i	0.587978	−	1.01841i	0.994497	−	0.104765i	$-0.0334090\pi$
$240$	1.80275	+	3.12246i	0.116367	+	0.201554i
$241$	−23.2648	−	8.46768i	−1.49862	−	0.545451i	−0.542913	−	0.839789i	$-0.682679\pi$
$241$	−23.2648	−	8.46768i	−1.49862	−	0.545451i	−0.955702	+	0.294337i	$0.904901\pi$
$242$	−0.173648	+	0.984808i	−0.0111625	+	0.0633058i
$243$	1.98437	+	11.2539i	0.127297	+	0.721939i
$244$	−13.0231	+	4.74001i	−0.833716	+	0.303448i
$245$	−4.33428	−	3.63689i	−0.276907	−	0.232352i
$246$	5.55610			0.354244
$247$	−0.573005	+	0.629805i	−0.0364594	+	0.0400735i
$248$	6.31205			0.400816
$249$	22.2095	+	18.6359i	1.40747	+	1.18100i
$250$	−9.94071	+	3.61812i	−0.628706	+	0.228830i
$251$	−2.73789	−	15.5273i	−0.172814	−	0.980076i	−0.940637	−	0.339414i	$-0.889771\pi$
$251$	−2.73789	−	15.5273i	−0.172814	−	0.980076i	0.767823	−	0.640662i	$-0.221340\pi$
$252$	1.43744	−	8.15211i	0.0905500	−	0.513534i
$253$	−4.87811	−	1.77549i	−0.306684	−	0.111624i
$254$	−3.69666	−	6.40281i	−0.231949	−	0.401748i
$255$	−5.73213	+	9.92834i	−0.358960	+	0.621737i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−11.4231	+	9.58510i	−0.712552	+	0.597902i	−0.925314	−	0.379202i	$-0.876199\pi$
$257$	−11.4231	+	9.58510i	−0.712552	+	0.597902i	0.212762	+	0.977104i	$0.431754\pi$
$258$	1.22766	−	2.12637i	0.0764308	−	0.132382i
$259$	0.285348	+	0.494237i	0.0177307	+	0.0307104i
$260$	−0.230552	−	0.0839140i	−0.0142982	−	0.00520413i
$261$	−0.691633	+	3.92245i	−0.0428110	+	0.242793i
$262$	−1.15036	−	6.52399i	−0.0710692	−	0.403053i
$263$	13.0221	−	4.73966i	0.802978	−	0.292260i	0.0922581	−	0.995735i	$-0.470592\pi$
$263$	13.0221	−	4.73966i	0.802978	−	0.292260i	0.710720	+	0.703475i	$0.248369\pi$
$264$	2.19901	+	1.84519i	0.135339	+	0.113563i
$265$	6.49188			0.398793
$266$	5.82029	+	3.67892i	0.356865	+	0.225569i
$267$	−33.6111			−2.05697
$268$	9.11996	+	7.65255i	0.557090	+	0.467454i
$269$	−20.1966	+	7.35095i	−1.23141	+	0.448195i	−0.874079	−	0.485784i	$-0.838534\pi$
$269$	−20.1966	+	7.35095i	−1.23141	+	0.448195i	−0.357327	+	0.933979i	$0.616312\pi$
$270$	1.40265	+	7.95484i	0.0853628	+	0.484116i
$271$	−0.254715	+	1.44456i	−0.0154728	+	0.0877507i	−0.991566	−	0.129600i	$-0.958631\pi$
$271$	−0.254715	+	1.44456i	−0.0154728	+	0.0877507i	0.976093	+	0.217351i	$0.0697417\pi$
$272$	2.98789	+	1.08750i	0.181168	+	0.0659397i
$273$	0.442885	+	0.767098i	0.0268046	+	0.0464269i
$274$	−1.82493	+	3.16086i	−0.110248	+	0.190955i
$275$	−2.62174	+	2.19990i	−0.158097	+	0.132659i
$276$	−11.4154	+	9.57869i	−0.687128	+	0.576569i
$277$	5.88330	−	10.1902i	0.353494	−	0.612269i	−0.633365	−	0.773853i	$-0.718327\pi$
$277$	5.88330	−	10.1902i	0.353494	−	0.612269i	0.986859	+	0.161584i	$0.0516603\pi$
$278$	−1.83488	−	3.17810i	−0.110049	−	0.190610i
$279$	31.0825	+	11.3131i	1.86086	+	0.677297i
$280$	−0.344527	+	1.95391i	−0.0205894	+	0.116768i
$281$	−2.08126	−	11.8034i	−0.124158	−	0.704134i	−0.981804	−	0.189895i	$-0.939185\pi$
$281$	−2.08126	−	11.8034i	−0.124158	−	0.704134i	0.857647	−	0.514240i	$-0.171926\pi$
$282$	3.59763	−	1.30943i	0.214236	−	0.0779755i
$283$	15.2226	+	12.7733i	0.904890	+	0.759293i	0.971140	−	0.238510i	$-0.0766589\pi$
$283$	15.2226	+	12.7733i	0.904890	+	0.759293i	−0.0662496	+	0.997803i	$0.521103\pi$
$284$	2.35438			0.139707
$285$	−15.3555	−	3.34702i	−0.909582	−	0.198260i
$286$	−0.195339			−0.0115506
$287$	2.34213	+	1.96528i	0.138251	+	0.116007i
$288$	4.92431	−	1.79230i	0.290168	−	0.105612i
$289$	−1.19640	−	6.78515i	−0.0703767	−	0.399126i
$290$	0.165772	−	0.940139i	0.00973445	−	0.0552068i
$291$	28.2953	+	10.2987i	1.65870	+	0.603718i
$292$	−2.09069	−	3.62118i	−0.122348	−	0.211914i
$293$	−15.3126	+	26.5222i	−0.894572	+	1.54944i	−0.0602384	+	0.998184i	$0.519186\pi$
$293$	−15.3126	+	26.5222i	−0.894572	+	1.54944i	−0.834334	+	0.551260i	$0.814147\pi$
$294$	−9.90592	+	8.31206i	−0.577725	+	0.484769i
$295$	−11.7019	+	9.81910i	−0.681314	+	0.571690i
$296$	−0.180641	+	0.312879i	−0.0104995	+	0.0181857i
$297$	3.21556	+	5.56951i	0.186586	+	0.323176i
$298$	6.36152	+	2.31540i	0.368513	+	0.134128i
$299$	0.176086	−	0.998634i	0.0101833	−	0.0577525i
$300$	1.70599	+	9.67518i	0.0984956	+	0.558596i
$301$	1.26964	−	0.462111i	0.0731808	−	0.0266356i
$302$	−16.7147	−	14.0253i	−0.961823	−	0.807065i
$303$	−43.4046			−2.49353
$304$	−0.174653	+	4.35540i	−0.0100170	+	0.249799i
$305$	17.4069			0.996716
$306$	12.7642	+	10.7104i	0.729679	+	0.612274i
$307$	−5.74740	+	2.09188i	−0.328021	+	0.119390i	−0.500781	−	0.865574i	$-0.666954\pi$
$307$	−5.74740	+	2.09188i	−0.328021	+	0.119390i	0.172760	+	0.984964i	$0.444732\pi$
$308$	0.274302	+	1.55564i	0.0156298	+	0.0886411i
$309$	−5.40333	+	30.6438i	−0.307385	+	1.74327i
$310$	−7.44990	−	2.71154i	−0.423126	−	0.154005i
$311$	1.72638	+	2.99018i	0.0978940	+	0.169557i	0.910813	−	0.412820i	$-0.135456\pi$
$311$	1.72638	+	2.99018i	0.0978940	+	0.169557i	−0.812919	+	0.582377i	$0.802123\pi$
$312$	−0.280370	+	0.485615i	−0.0158728	+	0.0274925i
$313$	−4.29845	+	3.60683i	−0.242963	+	0.203870i	−0.756135	−	0.654416i	$-0.772915\pi$
$313$	−4.29845	+	3.60683i	−0.242963	+	0.203870i	0.513172	+	0.858286i	$0.328470\pi$
$314$	−11.2066	+	9.40348i	−0.632427	+	0.530669i
$315$	−5.19855	+	9.00416i	−0.292905	+	0.507327i
$316$	−0.0240319	−	0.0416245i	−0.00135190	−	0.00234156i
$317$	7.09185	+	2.58122i	0.398318	+	0.144976i	0.533409	−	0.845857i	$-0.320911\pi$
$317$	7.09185	+	2.58122i	0.398318	+	0.144976i	−0.135091	+	0.990833i	$0.543133\pi$
$318$	2.57644	−	14.6117i	0.144479	−	0.819383i
$319$	−0.131983	−	0.748510i	−0.00738961	−	0.0419085i
$320$	−1.18027	+	0.429582i	−0.0659789	+	0.0240143i
$321$	25.4853	+	21.3847i	1.42245	+	1.19358i
$322$	−8.20021			−0.456980
$323$	−12.2709	+	6.44339i	−0.682774	+	0.358520i
$324$	2.74013			0.152229
$325$	−0.512127	−	0.429726i	−0.0284077	−	0.0238369i
$326$	−0.560746	+	0.204095i	−0.0310568	+	0.0113038i
$327$	7.13311	+	40.4539i	0.394462	+	2.23711i
$328$	−0.336099	+	1.90611i	−0.0185580	+	0.105248i
$329$	1.97972	+	0.720558i	0.109145	+	0.0397257i
$330$	−1.80275	−	3.12246i	−0.0992384	−	0.171886i
$331$	15.0647	−	26.0928i	0.828030	−	1.43419i	−0.0715520	−	0.997437i	$-0.522795\pi$
$331$	15.0647	−	26.0928i	0.828030	−	1.43419i	0.899582	−	0.436753i	$-0.143871\pi$
$332$	−7.73687	+	6.49200i	−0.424616	+	0.356295i
$333$	−1.45030	+	1.21695i	−0.0794761	+	0.0666884i
$334$	2.67950	−	4.64103i	0.146616	−	0.253946i
$335$	−7.47658	−	12.9498i	−0.408489	−	0.707524i
$336$	4.26106	+	1.55090i	0.232460	+	0.0846084i
$337$	−1.56289	+	8.86359i	−0.0851361	+	0.482831i	0.912191	+	0.409765i	$0.134389\pi$
$337$	−1.56289	+	8.86359i	−0.0851361	+	0.482831i	−0.997327	+	0.0730655i	$0.976722\pi$
$338$	2.25080	+	12.7649i	0.122427	+	0.694320i
$339$	31.1504	−	11.3378i	1.69186	−	0.615786i
$340$	−3.05934	−	2.56709i	−0.165916	−	0.139220i
$341$	−6.31205			−0.341817
$342$	−8.66623	+	21.1343i	−0.468616	+	1.14281i
$343$	−18.1734			−0.981269
$344$	0.655224	+	0.549798i	0.0353273	+	0.0296431i
$345$	17.5881	−	6.40154i	0.946910	−	0.344647i
$346$	3.14277	+	17.8235i	0.168956	+	0.958198i
$347$	1.25486	−	7.11668i	0.0673645	−	0.382043i	−0.932422	−	0.361372i	$-0.882309\pi$
$347$	1.25486	−	7.11668i	0.0673645	−	0.382043i	0.999786	−	0.0206714i	$-0.00658039\pi$
$348$	−2.05024	−	0.746226i	−0.109904	−	0.0400019i
$349$	−6.11086	−	10.5843i	−0.327107	−	0.566566i	0.654830	−	0.755776i	$-0.272740\pi$
$349$	−6.11086	−	10.5843i	−0.327107	−	0.566566i	−0.981936	+	0.189211i	$0.939407\pi$
$350$	−2.70311	+	4.68193i	−0.144487	+	0.250259i
$351$	−0.962341	+	0.807500i	−0.0513660	+	0.0431012i
$352$	−0.766044	+	0.642788i	−0.0408303	+	0.0342607i
$353$	−7.28649	+	12.6206i	−0.387821	+	0.671725i	−0.992156	−	0.125005i	$-0.960105\pi$
$353$	−7.28649	+	12.6206i	−0.387821	+	0.671725i	0.604336	+	0.796730i	$0.293439\pi$
$354$	17.4563	+	30.2352i	0.927793	+	1.60698i
$355$	−2.77879	−	1.01140i	−0.147483	−	0.0536795i
$356$	2.03320	−	11.5309i	0.107759	−	0.611134i
$357$	2.50369	+	14.1992i	0.132510	+	0.751499i
$358$	13.8158	−	5.02855i	0.730190	−	0.265767i
$359$	−2.52765	−	2.12095i	−0.133404	−	0.111939i	0.573644	−	0.819105i	$-0.305529\pi$
$359$	−2.52765	−	2.12095i	−0.133404	−	0.111939i	−0.707048	+	0.707165i	$0.749974\pi$
$360$	−6.58193			−0.346898
$361$	−13.5302	−	13.3392i	−0.712115	−	0.702062i
$362$	14.8248			0.779175
$363$	−2.19901	−	1.84519i	−0.115418	−	0.0968471i
$364$	−0.289957	+	0.105536i	−0.0151979	+	0.00553158i
$365$	0.911977	+	5.17208i	0.0477351	+	0.270719i
$366$	6.90828	−	39.1788i	0.361102	−	2.04791i
$367$	22.3362	+	8.12971i	1.16594	+	0.424367i	0.851216	−	0.524816i	$-0.175866\pi$
$367$	22.3362	+	8.12971i	1.16594	+	0.424367i	0.314724	+	0.949183i	$0.398088\pi$
$368$	−2.59559	−	4.49569i	−0.135304	−	0.234354i
$369$	−5.07139	+	8.78390i	−0.264006	+	0.457272i
$370$	0.347611	−	0.291680i	0.0180714	−	0.0151637i
$371$	6.25446	−	5.24811i	0.324715	−	0.272468i
$372$	−9.05968	+	15.6918i	−0.469723	+	0.813584i
$373$	−17.6509	−	30.5723i	−0.913930	−	1.58297i	−0.808461	−	0.588550i	$-0.799699\pi$
$373$	−17.6509	−	30.5723i	−0.913930	−	1.58297i	−0.105469	−	0.994423i	$-0.533634\pi$
$374$	−2.98789	−	1.08750i	−0.154500	−	0.0562335i
$375$	5.27320	−	29.9058i	0.272307	−	1.54433i
$376$	0.231595	+	1.31344i	0.0119436	+	0.0677355i
$377$	0.139515	−	0.0507793i	0.00718539	−	0.00261527i
$378$	7.78214	+	6.52999i	0.400270	+	0.335867i
$379$	−21.7022			−1.11477			−0.557385	−	0.830254i	$-0.688195\pi$
$379$	−21.7022			−1.11477			−0.557385	+	0.830254i	$0.688195\pi$
$380$	2.07714	−	5.06550i	0.106555	−	0.259855i
$381$	21.2233			1.08730
$382$	16.7967	+	14.0941i	0.859393	+	0.721116i
$383$	−2.98354	+	1.08592i	−0.152452	+	0.0554879i	−0.417119	−	0.908852i	$-0.636960\pi$
$383$	−2.98354	+	1.08592i	−0.152452	+	0.0554879i	0.264667	+	0.964340i	$0.414738\pi$
$384$	0.498474	+	2.82699i	0.0254377	+	0.144264i
$385$	0.344527	−	1.95391i	0.0175587	−	0.0995805i
$386$	−9.03864	−	3.28980i	−0.460055	−	0.167446i
$387$	2.24112	+	3.88173i	0.113923	+	0.197320i
$388$	−5.24477	+	9.08421i	−0.266263	+	0.461181i
$389$	17.9537	−	15.0649i	0.910289	−	0.763823i	−0.0618851	−	0.998083i	$-0.519711\pi$
$389$	17.9537	−	15.0649i	0.910289	−	0.763823i	0.972174	+	0.234260i	$0.0752668\pi$
$390$	0.539522	−	0.452713i	0.0273198	−	0.0229240i
$391$	8.25307	−	14.2947i	0.417376	−	0.722916i
$392$	−2.25236	−	3.90121i	−0.113762	−	0.197041i
$393$	17.8698	+	6.50408i	0.901413	+	0.328087i
$394$	−3.81768	+	21.6511i	−0.192332	+	1.09077i
$395$	0.0104829	+	0.0594517i	0.000527453	+	0.00299134i
$396$	−4.92431	+	1.79230i	−0.247456	+	0.0900665i
$397$	−2.69711	−	2.26315i	−0.135364	−	0.113584i	0.572592	−	0.819841i	$-0.305938\pi$
$397$	−2.69711	−	2.26315i	−0.135364	−	0.113584i	−0.707956	+	0.706257i	$0.750382\pi$
$398$	0.232346			0.0116465
$399$	−17.4997	+	9.18896i	−0.876080	+	0.460023i
$400$	−3.42243			−0.171122
$401$	9.80788	+	8.22979i	0.489782	+	0.410976i	0.853948	−	0.520358i	$-0.174201\pi$
$401$	9.80788	+	8.22979i	0.489782	+	0.410976i	−0.364166	+	0.931334i	$0.618646\pi$
$402$	−32.1142	+	11.6886i	−1.60171	+	0.582975i
$403$	−0.214106	−	1.21426i	−0.0106654	−	0.0604865i
$404$	2.62563	−	14.8907i	0.130630	−	0.740840i
$405$	−3.23408	−	1.17711i	−0.160703	−	0.0584911i
$406$	−0.600310	−	1.03977i	−0.0297929	−	0.0516028i
$407$	0.180641	−	0.312879i	0.00895403	−	0.0155088i
$408$	−6.99207	+	5.86705i	−0.346159	+	0.290462i
$409$	5.24189	−	4.39847i	0.259195	−	0.217490i	−0.503925	−	0.863748i	$-0.668111\pi$
$409$	5.24189	−	4.39847i	0.259195	−	0.217490i	0.763120	+	0.646257i	$0.223667\pi$
$410$	1.21552	−	2.10534i	0.0600302	−	0.103975i
$411$	−5.23863	−	9.07357i	−0.258402	−	0.447566i
$412$	−10.1860	−	3.70741i	−0.501830	−	0.182651i
$413$	−3.33610	+	18.9200i	−0.164159	+	0.930991i
$414$	−4.72384	−	26.7902i	−0.232164	−	1.31667i
$415$	11.9204	−	4.33867i	0.585150	−	0.212977i
$416$	−0.149638	−	0.125561i	−0.00733662	−	0.00615616i
$417$	10.5344			0.515871
$418$	0.174653	−	4.35540i	0.00854256	−	0.213030i
$419$	21.8760			1.06871			0.534356	−	0.845260i	$-0.320554\pi$
$419$	21.8760			1.06871			0.534356	+	0.845260i	$0.320554\pi$
$420$	−4.36294	−	3.66094i	−0.212890	−	0.178636i
$421$	25.5076	−	9.28402i	1.24317	−	0.452476i	0.365079	−	0.930976i	$-0.381042\pi$
$421$	25.5076	−	9.28402i	1.24317	−	0.452476i	0.878087	+	0.478501i	$0.158820\pi$
$422$	3.40122	+	19.2893i	0.165569	+	0.938988i
$423$	−1.21363	+	6.88287i	−0.0590089	+	0.334656i
$424$	4.85694	+	1.76778i	0.235874	+	0.0858510i
$425$	−5.44107	−	9.42421i	−0.263931	−	0.457141i
$426$	−3.37924	+	5.85302i	−0.163725	+	0.283580i
$427$	16.7703	−	14.0719i	0.811571	−	0.680989i
$428$	−8.87803	+	7.44955i	−0.429136	+	0.360088i
$429$	0.280370	−	0.485615i	0.0135364	−	0.0234457i
$430$	−0.537155	−	0.930380i	−0.0259039	−	0.0448669i
$431$	−2.34552	−	0.853698i	−0.112980	−	0.0411212i	0.284912	−	0.958554i	$-0.408036\pi$
$431$	−2.34552	−	0.853698i	−0.112980	−	0.0411212i	−0.397891	+	0.917433i	$0.630258\pi$
$432$	−1.11675	+	6.33341i	−0.0537297	+	0.304716i
$433$	2.53332	+	14.3671i	0.121743	+	0.690441i	0.983189	+	0.182591i	$0.0584484\pi$
$433$	2.53332	+	14.3671i	0.121743	+	0.690441i	−0.861446	+	0.507850i	$0.830440\pi$
$434$	−9.36948	+	3.41021i	−0.449749	+	0.163695i
$435$	2.09926	+	1.76149i	0.100652	+	0.0844570i
$436$	−14.3099			−0.685319
$437$	22.1087	+	4.81901i	1.05760	+	0.230524i
$438$	12.0031			0.573529
$439$	20.1123	+	16.8762i	0.959908	+	0.805458i	0.980938	−	0.194321i	$-0.0622502\pi$
$439$	20.1123	+	16.8762i	0.959908	+	0.805458i	−0.0210303	+	0.999779i	$0.506695\pi$
$440$	1.18027	−	0.429582i	0.0562670	−	0.0204795i
$441$	−4.09919	−	23.2477i	−0.195200	−	1.10703i
$442$	0.107855	−	0.611674i	0.00513012	−	0.0290944i
$443$	−25.8296	−	9.40122i	−1.22720	−	0.446665i	−0.354564	−	0.935032i	$-0.615371\pi$
$443$	−25.8296	−	9.40122i	−1.22720	−	0.446665i	−0.872639	+	0.488366i	$0.837593\pi$
$444$	−0.518547	−	0.898150i	−0.0246091	−	0.0426243i
$445$	−7.35316	+	12.7361i	−0.348573	+	0.603747i
$446$	−11.4397	+	9.59901i	−0.541684	+	0.454527i
$447$	−14.8868	+	12.4915i	−0.704122	+	0.590828i
$448$	−0.789822	+	1.36801i	−0.0373156	+	0.0646325i
$449$	−15.4171	−	26.7032i	−0.727577	−	1.26020i	−0.957904	−	0.287087i	$-0.907313\pi$
$449$	−15.4171	−	26.7032i	−0.727577	−	1.26020i	0.230327	−	0.973113i	$-0.426020\pi$
$450$	−16.8531	−	6.13403i	−0.794463	−	0.289161i
$451$	0.336099	−	1.90611i	0.0158263	−	0.0897554i
$452$	2.00528	+	11.3725i	0.0943205	+	0.534918i
$453$	58.8576	−	21.4224i	2.76537	−	1.00651i
$454$	−13.9139	−	11.6751i	−0.653009	−	0.547940i
$455$	0.387563			0.0181692
$456$	−10.5769	−	6.68549i	−0.495308	−	0.313077i
$457$	−4.28914			−0.200638			−0.100319	−	0.994955i	$-0.531986\pi$
$457$	−4.28914			−0.200638			−0.100319	+	0.994955i	$0.531986\pi$
$458$	17.6797	+	14.8350i	0.826118	+	0.693196i
$459$	−19.2155	+	6.99387i	−0.896902	+	0.326446i
$460$	1.13222	+	6.42113i	0.0527900	+	0.299387i
$461$	5.00273	−	28.3719i	0.233000	−	1.32141i	−0.613784	−	0.789474i	$-0.710354\pi$
$461$	5.00273	−	28.3719i	0.233000	−	1.32141i	0.846785	−	0.531936i	$-0.178535\pi$
$462$	−4.26106	−	1.55090i	−0.198242	−	0.0721543i
$463$	−16.2482	−	28.1428i	−0.755119	−	1.30791i	−0.945315	−	0.326159i	$-0.894246\pi$
$463$	−16.2482	−	28.1428i	−0.755119	−	1.30791i	0.190196	−	0.981746i	$-0.439088\pi$
$464$	0.380029	−	0.658229i	0.0176424	−	0.0305575i
$465$	17.4338	−	14.6287i	0.808471	−	0.678388i
$466$	−12.5042	+	10.4923i	−0.579247	+	0.486046i
$467$	−12.3081	+	21.3182i	−0.569550	+	0.986490i	0.427060	+	0.904223i	$0.359549\pi$
$467$	−12.3081	+	21.3182i	−0.569550	+	0.986490i	−0.996610	+	0.0822667i	$0.973784\pi$
$468$	−0.511821	−	0.886500i	−0.0236589	−	0.0409785i
$469$	−17.6719	−	6.43205i	−0.816013	−	0.297005i
$470$	0.290886	−	1.64970i	0.0134176	−	0.0760948i
$471$	−7.29229	−	41.3566i	−0.336011	−	1.90561i
$472$	−11.4287	+	4.15970i	−0.526047	+	0.191466i
$473$	−0.655224	−	0.549798i	−0.0301272	−	0.0252797i
$474$	0.137972			0.00633726
$475$	10.0393	−	11.0345i	0.460636	−	0.506297i
$476$	−5.02271			−0.230216
$477$	20.7487	+	17.4102i	0.950016	+	0.797158i
$478$	−17.0834	+	6.21787i	−0.781379	+	0.284399i
$479$	3.03506	+	17.2127i	0.138675	+	0.786467i	0.972230	+	0.234029i	$0.0751911\pi$
$479$	3.03506	+	17.2127i	0.138675	+	0.786467i	−0.833554	+	0.552438i	$0.813698\pi$
$480$	0.626090	−	3.55073i	0.0285770	−	0.162068i
$481$	0.0663163	+	0.0241372i	0.00302376	+	0.00110056i
$482$	12.3789	+	21.4409i	0.563844	+	0.976607i
$483$	11.7698	−	20.3858i	0.535542	−	0.927587i
$484$	0.766044	−	0.642788i	0.0348202	−	0.0292176i
$485$	10.0926	−	8.46873i	0.458283	−	0.384545i
$486$	5.71376	−	9.89652i	0.259181	−	0.448915i
$487$	16.8221	+	29.1367i	0.762282	+	1.32031i	0.941671	+	0.336534i	$0.109255\pi$
$487$	16.8221	+	29.1367i	0.762282	+	1.32031i	−0.179389	+	0.983778i	$0.557412\pi$
$488$	13.0231	+	4.74001i	0.589526	+	0.214570i
$489$	0.297456	−	1.68696i	0.0134514	−	0.0762868i
$490$	0.982500	+	5.57204i	0.0443848	+	0.251719i
$491$	12.9583	−	4.71643i	0.584799	−	0.212849i	−0.0326413	−	0.999467i	$-0.510392\pi$
$491$	12.9583	−	4.71643i	0.584799	−	0.212849i	0.617440	+	0.786618i	$0.288170\pi$
$492$	−4.25622	−	3.57139i	−0.191885	−	0.161011i
$493$	2.41672			0.108843
$494$	0.843778	−	0.114138i	0.0379634	−	0.00513531i
$495$	6.58193			0.295836
$496$	−4.83531	−	4.05731i	−0.217112	−	0.182179i
$497$	−3.49479	+	1.27200i	−0.156763	+	0.0570570i
$498$	−5.03447	−	28.5519i	−0.225600	−	1.27944i
$499$	4.24285	−	24.0624i	0.189936	−	1.07718i	−0.729511	−	0.683969i	$-0.760252\pi$
$499$	4.24285	−	24.0624i	0.189936	−	1.07718i	0.919447	−	0.393213i	$-0.128637\pi$
$500$	9.94071	+	3.61812i	0.444562	+	0.161807i
$501$	7.69177	+	13.3225i	0.343643	+	0.595207i
$502$	−7.88343	+	13.6545i	−0.351855	+	0.609430i
$503$	−19.3672	+	16.2510i	−0.863539	+	0.724596i	−0.962728	−	0.270473i	$-0.912820\pi$
$503$	−19.3672	+	16.2510i	−0.863539	+	0.724596i	0.0991882	+	0.995069i	$0.468375\pi$
$504$	−6.34121	+	5.32091i	−0.282460	+	0.237012i
$505$	−9.49572	+	16.4471i	−0.422554	+	0.731885i
$506$	2.59559	+	4.49569i	0.115388	+	0.199858i
$507$	−34.9643	−	12.7260i	−1.55282	−	0.565180i
$508$	−1.28384	+	7.28100i	−0.0569611	+	0.323042i
$509$	4.93587	+	27.9927i	0.218779	+	1.24076i	0.874228	+	0.485516i	$0.161368\pi$
$509$	4.93587	+	27.9927i	0.218779	+	1.24076i	−0.655449	+	0.755239i	$0.727521\pi$
$510$	10.7729	−	3.92101i	0.477031	−	0.173625i
$511$	5.05979	+	4.24567i	0.223832	+	0.187817i
$512$	−1.00000			−0.0441942
$513$	−17.1441	−	22.1789i	−0.756930	−	0.979224i
$514$	14.9118			0.657730
$515$	10.4296	+	8.75146i	0.459582	+	0.385635i
$516$	−2.30725	+	0.839769i	−0.101571	+	0.0369688i
$517$	−0.231595	−	1.31344i	−0.0101855	−	0.0577650i
$518$	0.0991003	−	0.562025i	0.00435422	−	0.0246940i
$519$	−48.8203	−	17.7691i	−2.14297	−	0.779978i
$520$	0.122674	+	0.212478i	0.00537962	+	0.00931777i
$521$	−17.6172	+	30.5138i	−0.771822	+	1.33684i	0.164741	+	0.986337i	$0.447321\pi$
$521$	−17.6172	+	30.5138i	−0.771822	+	1.33684i	−0.936563	+	0.350499i	$0.886012\pi$
$522$	3.05112	−	2.56020i	0.133544	−	0.112057i
$523$	−4.12654	+	3.46258i	−0.180441	+	0.151408i	−0.728535	−	0.685009i	$-0.759798\pi$
$523$	−4.12654	+	3.46258i	−0.180441	+	0.151408i	0.548094	+	0.836417i	$0.315354\pi$
$524$	−3.31232	+	5.73710i	−0.144699	+	0.250626i
$525$	−7.75955	−	13.4399i	−0.338654	−	0.586567i
$526$	−13.0221	−	4.73966i	−0.567791	−	0.206659i
$527$	3.48514	−	19.7652i	0.151815	−	0.860986i
$528$	−0.498474	−	2.82699i	−0.0216933	−	0.123029i
$529$	−3.71022	+	1.35041i	−0.161314	+	0.0587134i
$530$	−4.97307	−	4.17290i	−0.216016	−	0.181259i
$531$	−63.7337			−2.76581
$532$	−2.09384	−	6.55942i	−0.0907794	−	0.284387i
$533$	0.378082			0.0163766
$534$	25.7476	+	21.6048i	1.11421	+	0.934931i
$535$	13.6786	−	4.97861i	0.591379	−	0.215244i
$536$	−2.06733	−	11.7244i	−0.0892949	−	0.506417i
$537$	−7.32882	+	41.5638i	−0.316262	+	1.79361i
$538$	20.1966	+	7.35095i	0.870736	+	0.316922i
$539$	2.25236	+	3.90121i	0.0970162	+	0.168037i
$540$	4.03878	−	6.99537i	0.173801	−	0.301033i
$541$	−18.7674	+	15.7477i	−0.806873	+	0.677047i	−0.949859	−	0.312678i	$-0.898774\pi$
$541$	−18.7674	+	15.7477i	−0.806873	+	0.677047i	0.142986	+	0.989725i	$0.454329\pi$
$542$	1.12367	−	0.942869i	0.0482657	−	0.0404997i
$543$	−21.2780	+	36.8547i	−0.913129	+	1.58158i
$544$	−1.58983	−	2.75366i	−0.0681632	−	0.118062i
$545$	16.8895	+	6.14727i	0.723466	+	0.263320i
$546$	0.153812	−	0.872312i	0.00658255	−	0.0373315i
$547$	5.90356	+	33.4807i	0.252418	+	1.43153i	0.802615	+	0.596498i	$0.203442\pi$
$547$	5.90356	+	33.4807i	0.252418	+	1.43153i	−0.550197	+	0.835035i	$0.685447\pi$
$548$	3.42974	−	1.24832i	0.146511	−	0.0533257i
$549$	55.6340	+	46.6825i	2.37440	+	1.99236i
$550$	3.42243			0.145933
$551$	1.00747	+	3.15612i	0.0429195	+	0.134455i
$552$	14.9018			0.634262
$553$	0.0581609	+	0.0488028i	0.00247325	+	0.00207531i
$554$	−11.0570	+	4.02442i	−0.469767	+	0.170981i
$555$	0.226195	+	1.28281i	0.00960143	+	0.0544524i
$556$	−0.637246	+	3.61400i	−0.0270252	+	0.153268i
$557$	−0.0277960	−	0.0101169i	−0.00117775	−	0.000428667i	0.341431	−	0.939907i	$-0.389088\pi$
$557$	−0.0277960	−	0.0101169i	−0.00117775	−	0.000428667i	−0.342609	+	0.939478i	$0.611311\pi$
$558$	−16.5386	−	28.6458i	−0.700137	−	1.21267i
$559$	0.0835400	−	0.144696i	0.00353337	−	0.00611997i
$560$	1.51987	−	1.27532i	0.0642263	−	0.0538923i
$561$	6.99207	−	5.86705i	0.295206	−	0.247707i
$562$	−5.99276	+	10.3798i	−0.252789	+	0.437844i
$563$	7.71390	+	13.3609i	0.325102	+	0.563093i	0.981533	−	0.191293i	$-0.0612680\pi$
$563$	7.71390	+	13.3609i	0.325102	+	0.563093i	−0.656431	+	0.754386i	$0.727935\pi$
$564$	−3.59763	−	1.30943i	−0.151488	−	0.0551370i
$565$	2.51866	−	14.2840i	0.105961	−	0.600934i
$566$	−3.45069	−	19.5698i	−0.145043	−	0.822581i
$567$	−4.06739	+	1.48041i	−0.170814	+	0.0621714i
$568$	−1.80356	−	1.51337i	−0.0756757	−	0.0634994i
$569$	20.6201			0.864440			0.432220	−	0.901768i	$-0.357730\pi$
$569$	20.6201			0.864440			0.432220	+	0.901768i	$0.357730\pi$
$570$	9.61158	+	12.4343i	0.402585	+	0.520815i
$571$	−2.58294			−0.108093			−0.0540463	−	0.998538i	$-0.517212\pi$
$571$	−2.58294			−0.108093			−0.0540463	+	0.998538i	$0.517212\pi$
$572$	0.149638	+	0.125561i	0.00625669	+	0.00524999i
$573$	−59.1463	+	21.5275i	−2.47087	+	0.899325i
$574$	−0.530917	−	3.01098i	−0.0221601	−	0.125676i
$575$	−3.08511	+	17.4965i	−0.128658	+	0.729656i
$576$	−4.92431	−	1.79230i	−0.205179	−	0.0746792i
$577$	−19.3280	−	33.4770i	−0.804634	−	1.39367i	−0.916538	−	0.399947i	$-0.869028\pi$
$577$	−19.3280	−	33.4770i	−0.804634	−	1.39367i	0.111905	−	0.993719i	$-0.464305\pi$
$578$	−3.44491	+	5.96676i	−0.143289	+	0.248184i
$579$	21.1516	−	17.7483i	0.879031	−	0.737595i
$580$	−0.731298	+	0.613632i	−0.0303655	+	0.0254797i
$581$	7.97701	−	13.8166i	0.330942	−	0.573209i
$582$	−15.0556	−	26.0771i	−0.624076	−	1.08093i
$583$	−4.85694	−	1.76778i	−0.201154	−	0.0732140i
$584$	−0.726089	+	4.11786i	−0.0300458	+	0.170398i
$585$	0.223261	+	1.26618i	0.00923070	+	0.0523499i
$586$	28.7783	−	10.4744i	1.18882	−	0.432695i
$587$	−20.3468	−	17.0730i	−0.839804	−	0.704680i	0.117715	−	0.993047i	$-0.462443\pi$
$587$	−20.3468	−	17.0730i	−0.839804	−	0.704680i	−0.957520	+	0.288368i	$0.906887\pi$
$588$	12.9313			0.533276
$589$	27.2653	−	3.68818i	1.12345	−	0.151969i
$590$	15.2758			0.628895
$591$	−48.3455	−	40.5667i	−1.98867	−	1.66869i
$592$	0.339493	−	0.123566i	0.0139531	−	0.00507851i
$593$	6.59552	+	37.4051i	0.270846	+	1.53604i	0.751857	+	0.659327i	$0.229159\pi$
$593$	6.59552	+	37.4051i	0.270846	+	1.53604i	−0.481011	+	0.876715i	$0.659730\pi$
$594$	1.11675	−	6.33341i	0.0458208	−	0.259863i
$595$	5.92814	+	2.15767i	0.243030	+	0.0884557i
$596$	−3.38489	−	5.86281i	−0.138651	−	0.240150i
$597$	−0.333487	+	0.577616i	−0.0136487	+	0.0236402i
$598$	−0.776799	+	0.651812i	−0.0317657	+	0.0266546i
$599$	7.64699	−	6.41659i	0.312448	−	0.262175i	−0.473055	−	0.881033i	$-0.656849\pi$
$599$	7.64699	−	6.41659i	0.312448	−	0.262175i	0.785503	+	0.618858i	$0.212404\pi$
$600$	4.91222	−	8.50821i	0.200540	−	0.347346i
$601$	4.29537	+	7.43980i	0.175212	+	0.303476i	0.940235	−	0.340527i	$-0.110606\pi$
$601$	4.29537	+	7.43980i	0.175212	+	0.303476i	−0.765023	+	0.644003i	$0.777272\pi$
$602$	−1.26964	−	0.462111i	−0.0517467	−	0.0188342i
$603$	10.8335	−	61.4398i	0.441174	−	2.50202i
$604$	3.78891	+	21.4880i	0.154169	+	0.874334i
$605$	−1.18027	+	0.429582i	−0.0479846	+	0.0174650i
$606$	33.2499	+	27.9000i	1.35068	+	1.13336i
$607$	−27.4790			−1.11534			−0.557669	−	0.830063i	$-0.688304\pi$
$607$	−27.4790			−1.11534			−0.557669	+	0.830063i	$0.688304\pi$
$608$	2.93339	−	3.22416i	0.118965	−	0.130757i
$609$	3.44650			0.139659
$610$	−13.3345	−	11.1889i	−0.539896	−	0.453027i
$611$	0.244812	−	0.0891044i	0.00990405	−	0.00360478i
$612$	−2.89340	−	16.4093i	−0.116959	−	0.663307i
$613$	2.92694	−	16.5995i	0.118218	−	0.670448i	−0.866888	−	0.498502i	$-0.833884\pi$
$613$	2.92694	−	16.5995i	0.118218	−	0.670448i	0.985106	−	0.171946i	$-0.0550053\pi$
$614$	5.74740	+	2.09188i	0.231946	+	0.0844215i
$615$	3.48927	+	6.04358i	0.140701	+	0.243701i
$616$	0.789822	−	1.36801i	0.0318228	−	0.0551187i
$617$	22.2673	−	18.6845i	0.896449	−	0.752210i	−0.0730443	−	0.997329i	$-0.523271\pi$
$617$	22.2673	−	18.6845i	0.896449	−	0.752210i	0.969493	+	0.245119i	$0.0788270\pi$
$618$	23.8367	−	20.0013i	0.958851	−	0.804572i
$619$	1.07803	−	1.86720i	0.0433296	−	0.0750491i	−0.843547	−	0.537055i	$-0.819537\pi$
$619$	1.07803	−	1.86720i	0.0433296	−	0.0750491i	0.886877	+	0.462006i	$0.152870\pi$
$620$	3.96401	+	6.86586i	0.159198	+	0.275740i
$621$	31.3717	+	11.4184i	1.25890	+	0.458203i
$622$	0.599565	−	3.40030i	0.0240404	−	0.136340i
$623$	3.21173	+	18.2146i	0.128675	+	0.729754i
$624$	0.526923	−	0.191784i	0.0210938	−	0.00767752i
$625$	2.93028	+	2.45879i	0.117211	+	0.0983517i
$626$	5.61123			0.224270
$627$	10.5769	+	6.68549i	0.422400	+	0.266993i
$628$	14.6292			0.583770
$629$	0.879992	+	0.738401i	0.0350876	+	0.0294420i
$630$	9.77008	−	3.55602i	0.389249	−	0.141675i
$631$	−5.81249	−	32.9643i	−0.231392	−	1.31229i	−0.850081	−	0.526651i	$-0.823447\pi$
$631$	−5.81249	−	32.9643i	−0.231392	−	1.31229i	0.618690	−	0.785635i	$-0.287664\pi$
$632$	−0.00834620	+	0.0473336i	−0.000331994	+	0.00188283i
$633$	−52.8352	−	19.2304i	−2.10001	−	0.764341i
$634$	−3.77349	−	6.53588i	−0.149865	−	0.259573i
$635$	4.64305	−	8.04200i	0.184254	−	0.319137i
$636$	−11.3659	+	9.53711i	−0.450687	+	0.378171i
$637$	−0.674080	+	0.565620i	−0.0267080	+	0.0224107i
$638$	−0.380029	+	0.658229i	−0.0150455	+	0.0260595i
$639$	−6.16887	−	10.6848i	−0.244037	−	0.422684i
$640$	1.18027	+	0.429582i	0.0466541	+	0.0169807i
$641$	−8.20732	+	46.5460i	−0.324170	+	1.83846i	0.191278	+	0.981536i	$0.438737\pi$
$641$	−8.20732	+	46.5460i	−0.324170	+	1.83846i	−0.515447	+	0.856921i	$0.672374\pi$
$642$	−5.77704	−	32.7632i	−0.228002	−	1.29306i
$643$	41.0658	−	14.9467i	1.61948	−	0.589441i	0.636195	−	0.771529i	$-0.280508\pi$
$643$	41.0658	−	14.9467i	1.61948	−	0.589441i	0.983282	+	0.182087i	$0.0582853\pi$
$644$	6.28172	+	5.27099i	0.247535	+	0.207706i
$645$	3.08391			0.121429
$646$	13.5418	+	2.95169i	0.532796	+	0.116133i
$647$	17.3270			0.681196			0.340598	−	0.940209i	$-0.389370\pi$
$647$	17.3270			0.681196			0.340598	+	0.940209i	$0.389370\pi$
$648$	−2.09906	−	1.76132i	−0.0824589	−	0.0691913i
$649$	11.4287	−	4.15970i	0.448615	−	0.163282i
$650$	0.116090	+	0.658378i	0.00455342	+	0.0258237i
$651$	4.97018	−	28.1873i	0.194797	−	1.10475i
$652$	0.560746	+	0.204095i	0.0219605	+	0.00799297i
$653$	−10.9481	−	18.9627i	−0.428434	−	0.742069i	0.568301	−	0.822821i	$-0.307601\pi$
$653$	−10.9481	−	18.9627i	−0.428434	−	0.742069i	−0.996734	+	0.0807522i	$0.974268\pi$
$654$	20.5390	−	35.5746i	0.803138	−	1.39108i
$655$	6.37397	−	5.34839i	0.249051	−	0.208979i
$656$	1.48269	−	1.24413i	0.0578895	−	0.0485750i
$657$	−10.9559	+	18.9762i	−0.427431	+	0.740333i
$658$	−1.05339	−	1.82452i	−0.0410653	−	0.0711271i
$659$	15.5856	+	5.67271i	0.607130	+	0.220977i	0.627247	−	0.778820i	$-0.284182\pi$
$659$	15.5856	+	5.67271i	0.607130	+	0.220977i	−0.0201169	+	0.999798i	$0.506404\pi$
$660$	−0.626090	+	3.55073i	−0.0243705	+	0.138212i
$661$	5.95549	+	33.7753i	0.231642	+	1.31371i	0.849572	+	0.527473i	$0.176860\pi$
$661$	5.95549	+	33.7753i	0.231642	+	1.31371i	−0.617930	+	0.786233i	$0.712028\pi$
$662$	−28.3123	+	10.3048i	−1.10039	+	0.400509i
$663$	1.36582	+	1.14606i	0.0530442	+	0.0445094i
$664$	10.0998			0.391947
$665$	−0.346521	+	8.64134i	−0.0134375	+	0.335097i
$666$	1.89324			0.0733614
$667$	−3.02250	−	2.53618i	−0.117032	−	0.0982012i
$668$	−5.03581	+	1.83289i	−0.194841	+	0.0709165i
$669$	−7.44392	−	42.2166i	−0.287799	−	1.63219i
$670$	−2.59659	+	14.7260i	−0.100315	+	0.568914i
$671$	−13.0231	−	4.74001i	−0.502750	−	0.182986i
$672$	−2.26726	−	3.92701i	−0.0874615	−	0.151488i
$673$	−19.2071	+	33.2678i	−0.740381	+	1.28238i	0.211941	+	0.977283i	$0.432022\pi$
$673$	−19.2071	+	33.2678i	−0.740381	+	1.28238i	−0.952322	+	0.305095i	$0.901312\pi$
$674$	6.89465	−	5.78530i	0.265572	−	0.222841i
$675$	16.8607	−	14.1478i	0.648968	−	0.544549i
$676$	6.48092	−	11.2253i	0.249266	−	0.431742i
$677$	−12.5021	−	21.6543i	−0.480495	−	0.832242i	0.519255	−	0.854620i	$-0.326210\pi$
$677$	−12.5021	−	21.6543i	−0.480495	−	0.832242i	−0.999750	+	0.0223780i	$0.992876\pi$
$678$	−31.1504	−	11.3378i	−1.19632	−	0.435426i
$679$	2.87730	−	16.3180i	0.110421	−	0.626227i
$680$	0.693496	+	3.93301i	0.0265943	+	0.150824i
$681$	48.9950	−	17.8327i	1.87749	−	0.683351i
$682$	4.83531	+	4.05731i	0.185154	+	0.155362i
$683$	48.1934			1.84407			0.922034	−	0.387110i	$-0.126526\pi$
$683$	48.1934			1.84407			0.922034	+	0.387110i	$0.126526\pi$
$684$	20.2236	−	10.6193i	0.773268	−	0.406037i
$685$	−4.58426			−0.175155
$686$	13.9216	+	11.6816i	0.531529	+	0.446006i
$687$	−62.2557	+	22.6592i	−2.37520	+	0.864504i
$688$	−0.148527	−	0.842340i	−0.00566255	−	0.0321139i
$689$	0.175322	−	0.994299i	0.00667923	−	0.0378798i
$690$	−17.5881	−	6.40154i	−0.669567	−	0.243702i
$691$	−14.1254	−	24.4658i	−0.537354	−	0.930724i	−0.999045	−	0.0436836i	$-0.986091\pi$
$691$	−14.1254	−	24.4658i	−0.537354	−	0.930724i	0.461692	−	0.887041i	$-0.347243\pi$
$692$	9.04923	−	15.6737i	0.344000	−	0.595826i
$693$	6.34121	−	5.32091i	0.240883	−	0.202125i
$694$	−5.53579	+	4.64508i	−0.210136	+	0.176325i
$695$	2.30463	−	3.99173i	0.0874195	−	0.151415i
$696$	1.09091	+	1.88951i	0.0413508	+	0.0716217i
$697$	5.78313	+	2.10489i	0.219052	+	0.0797282i
$698$	−2.12228	+	12.0360i	−0.0803294	+	0.455571i
$699$	−8.13664	−	46.1452i	−0.307756	−	1.74537i
$700$	5.08019	−	1.84904i	0.192013	−	0.0698870i
$701$	10.9142	+	9.15806i	0.412222	+	0.345895i	0.825195	−	0.564848i	$-0.191065\pi$
$701$	10.9142	+	9.15806i	0.412222	+	0.345895i	−0.412973	+	0.910743i	$0.635510\pi$
$702$	1.25625			0.0474140
$703$	−0.597471	+	1.45705i	−0.0225340	+	0.0549536i
$704$	1.00000			0.0376889
$705$	3.68366	+	3.09095i	0.138734	+	0.116412i
$706$	13.6941	−	4.98425i	0.515385	−	0.187585i
$707$	4.14756	+	23.5220i	0.155985	+	0.884636i
$708$	6.06252	−	34.3822i	0.227843	−	1.29216i
$709$	9.42574	+	3.43069i	0.353991	+	0.128842i	0.512894	−	0.858452i	$-0.328573\pi$
$709$	9.42574	+	3.43069i	0.353991	+	0.128842i	−0.158903	+	0.987294i	$0.550796\pi$
$710$	1.47857	+	2.56095i	0.0554896	+	0.0961108i
$711$	−0.125935	+	0.218127i	−0.00472295	+	0.00818038i
$712$	−8.96942	+	7.52623i	−0.336143	+	0.282058i
$713$	−25.1010	+	21.0622i	−0.940038	+	0.788786i
$714$	7.20910	−	12.4865i	0.269794	−	0.467296i
$715$	−0.122674	−	0.212478i	−0.00458775	−	0.00794622i
$716$	−13.8158	−	5.02855i	−0.516322	−	0.187926i
$717$	9.06218	−	51.3941i	0.338433	−	1.91935i
$718$	0.572971	+	3.24948i	0.0213831	+	0.121270i
$719$	−10.9749	+	3.99455i	−0.409296	+	0.148971i	−0.538459	−	0.842652i	$-0.680993\pi$
$719$	−10.9749	+	3.99455i	−0.409296	+	0.148971i	0.129163	+	0.991623i	$0.458771\pi$
$720$	5.04205	+	4.23078i	0.187906	+	0.157672i
$721$	17.1229			0.637691
$722$	1.79047	+	18.9154i	0.0666343	+	0.703960i
$723$	−71.0698			−2.64312
$724$	−11.3565	−	9.52921i	−0.422060	−	0.354150i
$725$	−2.44437	+	0.889678i	−0.0907816	+	0.0330418i
$726$	0.498474	+	2.82699i	0.0185001	+	0.104919i
$727$	−6.14471	+	34.8484i	−0.227895	+	1.29246i	0.629179	+	0.777261i	$0.283391\pi$
$727$	−6.14471	+	34.8484i	−0.227895	+	1.29246i	−0.857073	+	0.515194i	$0.827720\pi$
$728$	0.289957	+	0.105536i	0.0107465	+	0.00391142i
$729$	20.5121	+	35.5280i	0.759708	+	1.31585i
$730$	2.62593	−	4.54825i	0.0971902	−	0.168338i
$731$	2.08338	−	1.74817i	0.0770567	−	0.0646583i
$732$	−30.4757	+	25.5722i	−1.12641	+	0.945174i
$733$	−6.21656	+	10.7674i	−0.229614	+	0.397703i	−0.957694	−	0.287789i	$-0.907080\pi$
$733$	−6.21656	+	10.7674i	−0.229614	+	0.397703i	0.728080	+	0.685492i	$0.240413\pi$
$734$	−11.8848	−	20.5851i	−0.438677	−	0.759811i
$735$	−15.2623	−	5.55503i	−0.562960	−	0.204901i
$736$	−0.901439	+	5.11231i	−0.0332275	+	0.188442i
$737$	2.06733	+	11.7244i	0.0761510	+	0.431874i
$738$	9.53109	−	3.46903i	0.350844	−	0.127697i
$739$	−24.9227	−	20.9126i	−0.916796	−	0.769283i	0.0566040	−	0.998397i	$-0.481973\pi$
$739$	−24.9227	−	20.9126i	−0.916796	−	0.769283i	−0.973400	+	0.229114i	$0.926417\pi$
$740$	−0.453774			−0.0166811
$741$	−0.927326	+	2.26146i	−0.0340662	+	0.0830770i
$742$	−8.16461			−0.299732
$743$	9.44886	+	7.92854i	0.346645	+	0.290870i	0.799441	−	0.600744i	$-0.205129\pi$
$743$	9.44886	+	7.92854i	0.346645	+	0.290870i	−0.452796	+	0.891614i	$0.649573\pi$
$744$	17.0266	−	6.19719i	0.624227	−	0.227200i
$745$	1.47652	+	8.37376i	0.0540955	+	0.306791i
$746$	−6.13010	+	34.7655i	−0.224439	+	1.27286i
$747$	49.7344	+	18.1018i	1.81968	+	0.662311i
$748$	1.58983	+	2.75366i	0.0581298	+	0.100684i
$749$	9.15360	−	15.8545i	0.334465	−	0.579311i
$750$	−23.2626	+	19.5196i	−0.849430	+	0.712756i
$751$	−19.2585	+	16.1598i	−0.702753	+	0.589680i	−0.922555	−	0.385865i	$-0.873903\pi$
$751$	−19.2585	+	16.1598i	−0.702753	+	0.589680i	0.219802	+	0.975544i	$0.429459\pi$
$752$	0.666851	−	1.15502i	0.0243175	−	0.0421192i
$753$	−22.6302	−	39.1966i	−0.824689	−	1.42840i
$754$	−0.139515	−	0.0507793i	−0.00508084	−	0.00184927i
$755$	4.75892	−	26.9892i	0.173195	−	0.982237i
$756$	−1.76407	−	10.0045i	−0.0641585	−	0.363861i
$757$	−45.4964	+	16.5593i	−1.65360	+	0.601860i	−0.989337	−	0.145643i	$-0.953475\pi$
$757$	−45.4964	+	16.5593i	−1.65360	+	0.601860i	−0.664258	+	0.747503i	$0.731253\pi$
$758$	16.6249	+	13.9499i	0.603843	+	0.506684i
$759$	−14.9018			−0.540901
$760$	−4.84722	+	2.54524i	−0.175827	+	0.0923256i
$761$	43.1742			1.56506			0.782532	−	0.622611i	$-0.213928\pi$
$761$	43.1742			1.56506			0.782532	+	0.622611i	$0.213928\pi$
$762$	−16.2580	−	13.6421i	−0.588964	−	0.494199i
$763$	21.2413	−	7.73120i	0.768987	−	0.279888i
$764$	−3.80750	−	21.5934i	−0.137750	−	0.781222i
$765$	−3.63415	+	20.6103i	−0.131393	+	0.745167i
$766$	2.98354	+	1.08592i	0.107800	+	0.0392359i
$767$	1.18787	+	2.05745i	0.0428915	+	0.0742903i
$768$	1.43530	−	2.48601i	0.0517919	−	0.0897062i
$769$	−28.0982	+	23.5772i	−1.01325	+	0.850215i	−0.988764	−	0.149486i	$-0.952238\pi$
$769$	−28.0982	+	23.5772i	−1.01325	+	0.850215i	−0.0244824	+	0.999700i	$0.507794\pi$
$770$	−1.51987	+	1.27532i	−0.0547724	+	0.0459595i
$771$	−21.4029	+	37.0708i	−0.770805	+	1.33507i
$772$	4.80936	+	8.33005i	0.173093	+	0.299805i
$773$	40.4308	+	14.7156i	1.45419	+	0.529283i	0.943759	−	0.330633i	$-0.107262\pi$
$773$	40.4308	+	14.7156i	1.45419	+	0.529283i	0.510434	+	0.859917i	$0.329485\pi$
$774$	0.778333	−	4.41414i	0.0279766	−	0.158663i
$775$	3.75125	+	21.2744i	0.134749	+	0.764198i
$776$	9.85695	−	3.58763i	0.353844	−	0.128789i
$777$	1.25496	+	1.05304i	0.0450216	+	0.0377776i
$778$	−23.4369			−0.840253
$779$	−0.338045	+	8.42996i	−0.0121117	+	0.302035i
$780$	−0.704296			−0.0252179
$781$	1.80356	+	1.51337i	0.0645364	+	0.0541525i
$782$	−15.5107	+	5.64543i	−0.554661	+	0.201880i
$783$	0.848795	+	4.81375i	0.0303335	+	0.172030i
$784$	−0.782238	+	4.43629i	−0.0279371	+	0.158439i
$785$	−17.2664	−	6.28445i	−0.616263	−	0.224302i
$786$	−9.50833	−	16.4689i	−0.339151	−	0.587427i
$787$	22.6228	−	39.1838i	0.806414	−	1.39675i	−0.108918	−	0.994051i	$-0.534738\pi$
$787$	22.6228	−	39.1838i	0.806414	−	1.39675i	0.915332	−	0.402700i	$-0.131928\pi$
$788$	16.8416	−	14.1318i	0.599957	−	0.503424i
$789$	30.4735	−	25.5703i	1.08489	−	0.910327i
$790$	0.0301844	−	0.0522809i	0.00107391	−	0.00186007i
$791$	−9.12083	−	15.7977i	−0.324299	−	0.561703i
$792$	4.92431	+	1.79230i	0.174978	+	0.0636867i
$793$	0.470096	−	2.66605i	0.0166936	−	0.0946741i
$794$	0.611386	+	3.46734i	0.0216973	+	0.123051i
$795$	17.5117	−	6.37375i	0.621077	−	0.226054i
$796$	−0.177988	−	0.149349i	−0.00630860	−	0.00529355i
$797$	14.0223			0.496695			0.248347	−	0.968671i	$-0.420113\pi$
$797$	14.0223			0.496695			0.248347	+	0.968671i	$0.420113\pi$
$798$	19.3121	+	4.20943i	0.683640	+	0.149012i
$799$	4.24070			0.150025
$800$	2.62174	+	2.19990i	0.0926923	+	0.0777781i
$801$	−57.6574	+	20.9856i	−2.03723	+	0.741489i
$802$	−2.22327	−	12.6088i	−0.0785063	−	0.445231i
$803$	0.726089	−	4.11786i	0.0256231	−	0.145316i
$804$	32.1142	+	11.6886i	1.13258	+	0.412226i
$805$	−5.14978	−	8.91969i	−0.181506	−	0.314378i
$806$	−0.616495	+	1.06780i	−0.0217151	+	0.0376117i
$807$	−47.2627	+	39.6581i	−1.66372	+	1.39603i
$808$	−11.5829	+	9.71922i	−0.407485	+	0.341921i
$809$	7.45619	−	12.9145i	0.262146	−	0.454050i	−0.704666	−	0.709539i	$-0.748903\pi$
$809$	7.45619	−	12.9145i	0.262146	−	0.454050i	0.966812	+	0.255489i	$0.0822366\pi$
$810$	1.72082	+	2.98055i	0.0604634	+	0.104726i
$811$	−44.0921	−	16.0482i	−1.54828	−	0.563529i	−0.580269	−	0.814425i	$-0.697053\pi$
$811$	−44.0921	−	16.0482i	−1.54828	−	0.563529i	−0.968014	+	0.250896i	$0.919275\pi$
$812$	−0.208485	+	1.18238i	−0.00731640	+	0.0414934i
$813$	0.731184	+	4.14675i	0.0256437	+	0.145433i
$814$	−0.339493	+	0.123566i	−0.0118992	+	0.00433097i
$815$	−0.574154	−	0.481772i	−0.0201117	−	0.0168757i
$816$	9.12750			0.319527
$817$	3.15153	+	1.99203i	0.110258	+	0.0696924i
$818$	−6.84281			−0.239253
$819$	1.23869	+	1.03938i	0.0432832	+	0.0363189i
$820$	−2.28443	+	0.831463i	−0.0797757	+	0.0290360i
$821$	1.30728	+	7.41395i	0.0456244	+	0.258749i	0.999085	−	0.0427688i	$-0.0136179\pi$
$821$	1.30728	+	7.41395i	0.0456244	+	0.258749i	−0.953461	+	0.301518i	$0.902507\pi$
$822$	−1.81936	+	10.3181i	−0.0634573	+	0.359884i
$823$	−6.01224	−	2.18828i	−0.209573	−	0.0762785i	0.235100	−	0.971971i	$-0.424458\pi$
$823$	−6.01224	−	2.18828i	−0.209573	−	0.0762785i	−0.444674	+	0.895693i	$0.646680\pi$
$824$	5.41987	+	9.38749i	0.188810	+	0.327029i
$825$	−4.91222	+	8.50821i	−0.171021	+	0.296218i
$826$	14.7171	−	12.3491i	0.512074	−	0.429681i
$827$	−34.8186	+	29.2163i	−1.21076	+	1.01595i	−0.211505	+	0.977377i	$0.567836\pi$
$827$	−34.8186	+	29.2163i	−1.21076	+	1.01595i	−0.999256	+	0.0385721i	$0.987719\pi$
$828$	−13.6018	+	23.5589i	−0.472694	+	0.818730i
$829$	−13.9187	−	24.1078i	−0.483415	−	0.837299i	0.516404	−	0.856345i	$-0.327270\pi$
$829$	−13.9187	−	24.1078i	−0.483415	−	0.837299i	−0.999819	+	0.0190462i	$0.993937\pi$
$830$	−11.9204	−	4.33867i	−0.413763	−	0.150598i
$831$	5.86535	−	33.2641i	0.203467	−	1.15392i
$832$	0.0339203	+	0.192371i	0.00117597	+	0.00666928i
$833$	−13.4597	+	4.89891i	−0.466349	+	0.169737i
$834$	−8.06981	−	6.77137i	−0.279435	−	0.234473i
$835$	6.73097			0.232935
$836$	−2.93339	+	3.22416i	−0.101453	+	0.111510i
$837$	40.5935			1.40312
$838$	−16.7580	−	14.0616i	−0.578895	−	0.485750i
$839$	22.1293	−	8.05442i	0.763990	−	0.278070i	0.0695095	−	0.997581i	$-0.477857\pi$
$839$	22.1293	−	8.05442i	0.763990	−	0.278070i	0.694480	+	0.719512i	$0.255634\pi$
$840$	0.988999	+	5.60889i	0.0341237	+	0.193525i
$841$	−4.93548	+	27.9905i	−0.170189	+	0.965190i
$842$	−25.5076	−	9.28402i	−0.879052	−	0.319949i
$843$	−17.2028	−	29.7962i	−0.592497	−	1.02623i
$844$	9.79343	−	16.9627i	0.337104	−	0.583881i
$845$	−12.4714	+	10.4647i	−0.429029	+	0.359998i
$846$	5.35392	−	4.49247i	0.184072	−	0.154454i
$847$	−0.789822	+	1.36801i	−0.0271386	+	0.0470054i
$848$	−2.58432	−	4.47618i	−0.0887460	−	0.153713i
$849$	53.6036	+	19.5101i	1.83967	+	0.669585i
$850$	−1.88966	+	10.7168i	−0.0648149	+	0.367584i
$851$	−0.325673	−	1.84698i	−0.0111639	−	0.0633138i
$852$	6.35090	−	2.31154i	0.217578	−	0.0791919i
$853$	12.2024	+	10.2390i	0.417801	+	0.350576i	0.827326	−	0.561723i	$-0.189861\pi$
$853$	12.2024	+	10.2390i	0.417801	+	0.350576i	−0.409525	+	0.912299i	$0.634306\pi$
$854$	−21.8920			−0.749130
$855$	−28.4310	+	3.84587i	−0.972321	+	0.131526i
$856$	11.5894			0.396119
$857$	33.9772	+	28.5102i	1.16064	+	0.973891i	0.999914	−	0.0131083i	$-0.00417262\pi$
$857$	33.9772	+	28.5102i	1.16064	+	0.973891i	0.160724	+	0.986999i	$0.448617\pi$
$858$	−0.526923	+	0.191784i	−0.0179889	+	0.00654741i
$859$	3.89241	+	22.0749i	0.132807	+	0.753187i	0.976362	+	0.216143i	$0.0693478\pi$
$859$	3.89241	+	22.0749i	0.132807	+	0.753187i	−0.843554	+	0.537044i	$0.819541\pi$
$860$	−0.186552	+	1.05799i	−0.00636137	+	0.0360771i
$861$	8.24736	+	3.00179i	0.281069	+	0.102301i
$862$	1.24802	+	2.16164i	0.0425078	+	0.0736257i
$863$	−8.35738	+	14.4754i	−0.284489	+	0.492749i	−0.972485	−	0.232965i	$-0.925157\pi$
$863$	−8.35738	+	14.4754i	−0.284489	+	0.492749i	0.687997	+	0.725714i	$0.258490\pi$
$864$	4.92652	−	4.13384i	0.167604	−	0.140636i
$865$	−17.4136	+	14.6118i	−0.592082	+	0.496816i
$866$	7.29439	−	12.6343i	0.247874	−	0.429330i
$867$	−9.88896	−	17.1282i	−0.335847	−	0.581703i
$868$	9.36948	+	3.41021i	0.318021	+	0.115750i
$869$	0.00834620	−	0.0473336i	0.000283125	−	0.00160568i
$870$	−0.475864	−	2.69876i	−0.0161333	−	0.0914966i
$871$	−2.18531	+	0.795389i	−0.0740465	+	0.0269507i
$872$	10.9620	+	9.19822i	0.371221	+	0.311491i
$873$	54.9687			1.86041
$874$	−13.8387	−	17.9028i	−0.468100	−	0.605571i
$875$	−16.7105			−0.564919
$876$	−9.19488	−	7.71542i	−0.310666	−	0.260680i
$877$	6.43068	−	2.34058i	0.217149	−	0.0790356i	−0.231155	−	0.972917i	$-0.574251\pi$
$877$	6.43068	−	2.34058i	0.217149	−	0.0790356i	0.448304	+	0.893881i	$0.352028\pi$
$878$	−4.55909	−	25.8559i	−0.153862	−	0.872594i
$879$	−15.2659	+	86.5771i	−0.514905	+	2.92017i
$880$	−1.18027	−	0.429582i	−0.0397868	−	0.0144812i
$881$	3.47249	+	6.01453i	0.116991	+	0.202635i	0.918574	−	0.395249i	$-0.129342\pi$
$881$	3.47249	+	6.01453i	0.116991	+	0.202635i	−0.801583	+	0.597884i	$0.796008\pi$
$882$	−11.8031	+	20.4437i	−0.397433	+	0.688374i
$883$	31.0027	−	26.0143i	1.04332	−	0.875452i	0.0509477	−	0.998701i	$-0.483776\pi$
$883$	31.0027	−	26.0143i	1.04332	−	0.875452i	0.992376	+	0.123249i	$0.0393314\pi$
$884$	−0.475798	+	0.399242i	−0.0160028	+	0.0134280i
$885$	−21.9254	+	37.9758i	−0.737013	+	1.27654i
$886$	13.7437	+	23.8047i	0.461727	+	0.799735i
$887$	17.8696	+	6.50399i	0.600001	+	0.218382i	0.624122	−	0.781327i	$-0.285457\pi$
$887$	17.8696	+	6.50399i	0.600001	+	0.218382i	−0.0241215	+	0.999709i	$0.507679\pi$
$888$	−0.180089	+	1.02134i	−0.00604341	+	0.0342739i
$889$	−2.02800	−	11.5014i	−0.0680171	−	0.385744i
$890$	13.8194	−	5.02986i	0.463228	−	0.168601i
$891$	2.09906	+	1.76132i	0.0703212	+	0.0590065i
$892$	14.9334			0.500008
$893$	1.76784	+	5.53815i	0.0591585	+	0.185327i
$894$	19.4333			0.649948
$895$	14.1462	+	11.8701i	0.472855	+	0.396772i
$896$	1.48438	−	0.540270i	0.0495896	−	0.0180491i
$897$	−0.505473	−	2.86668i	−0.0168772	−	0.0957156i
$898$	−5.35430	+	30.3657i	−0.178675	+	1.01332i
$899$	−4.50820	−	1.64085i	−0.150357	−	0.0547254i
$900$	8.96735	+	15.5319i	0.298912	+	0.517730i
$901$	8.21724	−	14.2327i	0.273756	−	0.474159i
$902$	−1.48269	+	1.24413i	−0.0493683	+	0.0414249i
$903$	2.97113	−	2.49307i	0.0988729	−	0.0829642i
$904$	5.77398	−	10.0008i	0.192040	−	0.332623i
$905$	9.31008	+	16.1255i	0.309477	+	0.536031i
$906$	−58.8576	−	21.4224i	−1.95541	−	0.711712i
$907$	−0.299948	+	1.70109i	−0.00995961	+	0.0564838i	−0.989383	−	0.145335i	$-0.953574\pi$
$907$	−0.299948	+	1.70109i	−0.00995961	+	0.0564838i	0.979423	+	0.201819i	$0.0646852\pi$
$908$	3.15401	+	17.8873i	0.104670	+	0.593611i
$909$	−74.4576	+	27.1003i	−2.46960	+	0.898862i
$910$	−0.296890	−	0.249121i	−0.00984182	−	0.00825826i
$911$	33.3550			1.10510			0.552551	−	0.833479i	$-0.313655\pi$
$911$	33.3550			1.10510			0.552551	+	0.833479i	$0.313655\pi$
$912$	3.80502	+	11.9201i	0.125997	+	0.394713i
$913$	−10.0998			−0.334253
$914$	3.28567	+	2.75701i	0.108680	+	0.0911937i
$915$	46.9548	−	17.0901i	1.55228	−	0.564982i
$916$	−4.00766	−	22.7286i	−0.132417	−	0.750974i
$917$	1.81715	−	10.3056i	0.0600076	−	0.340320i
$918$	19.2155	+	6.99387i	0.634206	+	0.230832i
$919$	27.7470	+	48.0592i	0.915290	+	1.58533i	0.806477	+	0.591266i	$0.201372\pi$
$919$	27.7470	+	48.0592i	0.915290	+	1.58533i	0.108813	+	0.994062i	$0.465295\pi$
$920$	3.26009	−	5.64665i	0.107482	−	0.186164i
$921$	−13.4497	+	11.2856i	−0.443182	+	0.371874i
$922$	−22.0694	+	18.5184i	−0.726817	+	0.609872i
$923$	−0.229951	+	0.398287i	−0.00756893	+	0.0131098i
$924$	2.26726	+	3.92701i	0.0745874	+	0.129189i
$925$	−1.16189	−	0.422895i	−0.0382028	−	0.0139047i
$926$	−5.64295	+	32.0028i	−0.185439	+	1.05168i
$927$	9.86390	+	55.9409i	0.323973	+	1.83734i
$928$	−0.714220	+	0.259955i	−0.0234454	+	0.00853344i
$929$	−21.6620	−	18.1766i	−0.710707	−	0.596354i	0.214091	−	0.976814i	$-0.431321\pi$
$929$	−21.6620	−	18.1766i	−0.710707	−	0.596354i	−0.924797	+	0.380460i	$0.875766\pi$
$930$	−22.7582			−0.746269
$931$	−12.0087	−	15.5354i	−0.393570	−	0.509153i
$932$	16.3231			0.534681
$933$	7.59264	+	6.37098i	0.248572	+	0.208577i
$934$	23.1316	−	8.41923i	0.756890	−	0.275485i
$935$	−0.693496	−	3.93301i	−0.0226797	−	0.128623i
$936$	−0.177754	+	1.00809i	−0.00581006	+	0.0329505i
$937$	−50.8567	−	18.5103i	−1.66142	−	0.604706i	−0.670832	−	0.741610i	$-0.734063\pi$
$937$	−50.8567	−	18.5103i	−1.66142	−	0.604706i	−0.990584	+	0.136903i	$0.956285\pi$
$938$	9.40303	+	16.2865i	0.307020	+	0.531774i
$939$	−8.05379	+	13.9496i	−0.262826	+	0.455227i
$940$	−1.28324	+	1.07676i	−0.0418545	+	0.0351201i
$941$	26.8753	−	22.5510i	0.876109	−	0.735143i	−0.0892663	−	0.996008i	$-0.528452\pi$
$941$	26.8753	−	22.5510i	0.876109	−	0.735143i	0.965375	+	0.260865i	$0.0840078\pi$
$942$	−20.9973	+	36.3684i	−0.684130	+	1.18495i
$943$	−5.02381	−	8.70150i	−0.163598	−	0.283360i
$944$	11.4287	+	4.15970i	0.371972	+	0.135387i
$945$	−2.21569	+	12.5658i	−0.0720765	+	0.408766i
$946$	0.148527	+	0.842340i	0.00482904	+	0.0273868i
$947$	−35.3703	+	12.8737i	−1.14938	+	0.418340i	−0.845292	−	0.534304i	$-0.820574\pi$
$947$	−35.3703	+	12.8737i	−1.14938	+	0.418340i	−0.304087	+	0.952644i	$0.598351\pi$
$948$	−0.105693	−	0.0886867i	−0.00343274	−	0.00288041i
$949$	0.816787			0.0265140
$950$	−14.7834	+	1.99975i	−0.479637	+	0.0648805i
$951$	21.6644			0.702516
$952$	3.84762	+	3.22854i	0.124702	+	0.104638i
$953$	5.91740	−	2.15376i	0.191683	−	0.0697671i	−0.244395	−	0.969676i	$-0.578589\pi$
$953$	5.91740	−	2.15376i	0.191683	−	0.0697671i	0.436078	+	0.899909i	$0.356367\pi$
$954$	−4.70334	−	26.6740i	−0.152276	−	0.863601i
$955$	−4.78227	+	27.1216i	−0.154751	+	0.877634i
$956$	17.0834	+	6.21787i	0.552518	+	0.201100i
$957$	−1.09091	−	1.88951i	−0.0352641	−	0.0610792i
$958$	8.73910	−	15.1366i	0.282347	−	0.489040i
$959$	−4.41660	+	3.70597i	−0.142619	+	0.119672i
$960$	−2.76198	+	2.31758i	−0.0891425	+	0.0747995i
$961$	−4.42099	+	7.65738i	−0.142613	+	0.247012i
$962$	−0.0352862	−	0.0611174i	−0.00113767	−	0.00197051i
$963$	57.0700	+	20.7718i	1.83906	+	0.669361i
$964$	4.29915	−	24.3817i	0.138466	−	0.785282i
$965$	−2.09788	−	11.8977i	−0.0675333	−	0.383000i
$966$	−22.1199	+	8.05099i	−0.711696	+	0.259036i
$967$	−7.38872	−	6.19988i	−0.237605	−	0.199375i	0.516208	−	0.856463i	$-0.327343\pi$
$967$	−7.38872	−	6.19988i	−0.237605	−	0.199375i	−0.753813	+	0.657089i	$0.771788\pi$
$968$	−1.00000			−0.0321412
$969$	−26.7745	+	29.4286i	−0.860121	+	0.945382i
$970$	−13.1750			−0.423024
$971$	−28.0271	−	23.5176i	−0.899434	−	0.754715i	0.0706459	−	0.997501i	$-0.477494\pi$
$971$	−28.0271	−	23.5176i	−0.899434	−	0.754715i	−0.970080	+	0.242787i	$0.921938\pi$
$972$	−10.7384	+	3.90844i	−0.344433	+	0.125363i
$973$	−1.00662	−	5.70883i	−0.0322708	−	0.183017i
$974$	5.84226	−	33.1331i	0.187198	−	1.06165i
$975$	−1.80336	−	0.656369i	−0.0577537	−	0.0210206i
$976$	−6.92943	−	12.0021i	−0.221806	−	0.384178i
$977$	14.1067	−	24.4335i	0.451313	−	0.781696i	−0.547155	−	0.837031i	$-0.684289\pi$
$977$	14.1067	−	24.4335i	0.451313	−	0.781696i	0.998468	+	0.0553347i	$0.0176226\pi$
$978$	−1.31222	+	1.10108i	−0.0419602	+	0.0352088i
$979$	8.96942	−	7.52623i	0.286664	−	0.240539i
$980$	2.82900	−	4.89997i	0.0903690	−	0.156524i
$981$	37.4943	+	64.9421i	1.19710	+	2.07344i
$982$	−12.9583	−	4.71643i	−0.413515	−	0.150507i
$983$	−1.02952	+	5.83871i	−0.0328367	+	0.186226i	−0.996814	−	0.0797573i	$-0.974585\pi$
$983$	−1.02952	+	5.83871i	−0.0328367	+	0.186226i	0.963978	+	0.265983i	$0.0856966\pi$
$984$	0.964806	+	5.47169i	0.0307569	+	0.174431i
$985$	−25.9483	+	9.44441i	−0.826782	+	0.300924i
$986$	−1.85131	−	1.55344i	−0.0589578	−	0.0494715i
$987$	6.04770			0.192500
$988$	−0.719738	−	0.454935i	−0.0228979	−	0.0144734i
$989$	−4.44019			−0.141190
$990$	−5.04205	−	4.23078i	−0.160247	−	0.134463i
$991$	26.2074	−	9.53872i	0.832506	−	0.303007i	0.109619	−	0.993974i	$-0.465037\pi$
$991$	26.2074	−	9.53872i	0.832506	−	0.303007i	0.722887	+	0.690966i	$0.242815\pi$
$992$	1.09608	+	6.21616i	0.0348005	+	0.197363i
$993$	15.0187	−	85.1753i	0.476604	−	2.70296i
$994$	3.49479	+	1.27200i	0.110848	+	0.0403454i
$995$	0.145915	+	0.252732i	0.00462582	+	0.00801215i
$996$	−14.4962	+	25.1081i	−0.459329	+	0.795582i
$997$	24.2793	−	20.3727i	0.768932	−	0.645210i	−0.171503	−	0.985184i	$-0.554862\pi$
$997$	24.2793	−	20.3727i	0.768932	−	0.645210i	0.940435	+	0.339973i	$0.110418\pi$
$998$	−18.7172	+	15.7056i	−0.592484	+	0.497153i
$999$	−1.16172	+	2.01216i	−0.0367552	+	0.0636619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.j.c.111.5	✓	30
19.5	even	9		7942.2.a.bz.1.2		15
19.6	even	9	inner	418.2.j.c.177.5	yes	30
19.14	odd	18		7942.2.a.cb.1.14		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.c.111.5	✓	30	1.1	even	1	trivial
418.2.j.c.177.5	yes	30	19.6	even	9	inner
7942.2.a.bz.1.2		15	19.5	even	9
7942.2.a.cb.1.14		15	19.14	odd	18

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.j (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(2.69748 - 0.981803i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.218104 - 1.23693i) q^{5} +(-2.69748 - 0.981803i) q^{6} +(-0.789822 - 1.36801i) q^{7} +(0.500000 - 0.866025i) q^{8} +(4.01433 - 3.36842i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(2.69748 - 0.981803i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.218104 - 1.23693i) q^{5} +(-2.69748 - 0.981803i) q^{6} +(-0.789822 - 1.36801i) q^{7} +(0.500000 - 0.866025i) q^{8} +(4.01433 - 3.36842i) q^{9} +(-0.962162 + 0.807349i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.43530 + 2.48601i) q^{12} +(-0.183559 - 0.0668099i) q^{13} +(-0.274302 + 1.55564i) q^{14} +(-0.626090 - 3.55073i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-2.43575 - 2.04384i) q^{17} -5.24034 q^{18} +(1.65375 - 4.03300i) q^{19} +1.25601 q^{20} +(-3.47365 - 2.91473i) q^{21} +(0.939693 - 0.342020i) q^{22} +(0.901439 + 5.11231i) q^{23} +(0.498474 - 2.82699i) q^{24} +(3.21603 + 1.17054i) q^{25} +(0.0976695 + 0.169169i) q^{26} +(3.21556 - 5.56951i) q^{27} +(1.21008 - 1.01538i) q^{28} +(-0.582238 + 0.488555i) q^{29} +(-1.80275 + 3.12246i) q^{30} +(3.15603 + 5.46640i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.498474 + 2.82699i) q^{33} +(0.552141 + 3.13134i) q^{34} +(-1.86440 + 0.678586i) q^{35} +(4.01433 + 3.36842i) q^{36} -0.361281 q^{37} +(-3.85921 + 2.02645i) q^{38} -0.560740 q^{39} +(-0.962162 - 0.807349i) q^{40} +(-1.81879 + 0.661987i) q^{41} +(0.787411 + 4.46563i) q^{42} +(-0.148527 + 0.842340i) q^{43} +(-0.939693 - 0.342020i) q^{44} +(-3.29097 - 5.70012i) q^{45} +(2.59559 - 4.49569i) q^{46} +(-1.02167 + 0.857287i) q^{47} +(-2.19901 + 1.84519i) q^{48} +(2.25236 - 3.90121i) q^{49} +(-1.71122 - 2.96391i) q^{50} +(-8.57705 - 3.12179i) q^{51} +(0.0339203 - 0.192371i) q^{52} +(0.897526 + 5.09012i) q^{53} +(-6.04327 + 2.19957i) q^{54} +(0.962162 + 0.807349i) q^{55} -1.57964 q^{56} +(0.501359 - 12.5026i) q^{57} +0.760057 q^{58} +(-9.31674 - 7.81767i) q^{59} +(3.38807 - 1.23316i) q^{60} +(2.40656 + 13.6483i) q^{61} +(1.09608 - 6.21616i) q^{62} +(-7.77865 - 2.83120i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.122674 + 0.212478i) q^{65} +(2.19901 - 1.84519i) q^{66} +(9.11996 - 7.65255i) q^{67} +(1.58983 - 2.75366i) q^{68} +(7.45090 + 12.9053i) q^{69} +(1.86440 + 0.678586i) q^{70} +(0.408834 - 2.31861i) q^{71} +(-0.909975 - 5.16073i) q^{72} +(-3.92921 + 1.43012i) q^{73} +(0.276758 + 0.232227i) q^{74} +9.82443 q^{75} +(4.25890 + 0.928307i) q^{76} +1.57964 q^{77} +(0.429552 + 0.360437i) q^{78} +(-0.0451652 + 0.0164388i) q^{79} +(0.218104 + 1.23693i) q^{80} +(0.475819 - 2.69850i) q^{81} +(1.81879 + 0.661987i) q^{82} +(5.04988 + 8.74665i) q^{83} +(2.26726 - 3.92701i) q^{84} +(-3.05934 + 2.56709i) q^{85} +(0.655224 - 0.549798i) q^{86} +(-1.09091 + 1.88951i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-11.0026 - 4.00462i) q^{89} +(-1.14294 + 6.48194i) q^{90} +(0.0535819 + 0.303878i) q^{91} +(-4.87811 + 1.77549i) q^{92} +(13.8802 + 11.6469i) q^{93} +1.33370 q^{94} +(-4.62785 - 2.92519i) q^{95} +2.87060 q^{96} +(8.03546 + 6.74255i) q^{97} +(-4.23306 + 1.54071i) q^{98} +(0.909975 + 5.16073i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) \) 30 * q - 12 * q^7 + 15 * q^8	\( 30 q - 12 q^{7} + 15 q^{8} - 15 q^{11} + 3 q^{12} - 3 q^{13} + 9 q^{14} + 27 q^{15} - 36 q^{18} - 9 q^{19} + 18 q^{20} - 27 q^{21} - 3 q^{23} - 12 q^{25} + 3 q^{27} + 9 q^{28} + 3 q^{29} + 9 q^{30} + 30 q^{31} - 9 q^{34} + 15 q^{35} + 18 q^{37} + 6 q^{38} - 6 q^{41} - 45 q^{42} + 39 q^{43} - 18 q^{45} + 21 q^{46} + 45 q^{47} - 33 q^{49} + 36 q^{50} - 36 q^{51} + 6 q^{52} - 24 q^{53} + 45 q^{54} - 24 q^{56} - 24 q^{57} - 30 q^{58} + 3 q^{59} - 9 q^{60} - 27 q^{61} + 15 q^{62} - 93 q^{63} - 15 q^{64} + 18 q^{65} - 9 q^{67} - 21 q^{68} + 48 q^{69} - 15 q^{70} + 39 q^{73} + 3 q^{74} - 42 q^{75} - 15 q^{76} + 24 q^{77} + 6 q^{78} + 21 q^{79} + 84 q^{81} + 6 q^{82} - 36 q^{83} - 27 q^{84} + 63 q^{85} + 6 q^{86} - 21 q^{87} + 15 q^{88} + 54 q^{89} + 12 q^{90} + 3 q^{91} - 3 q^{92} + 51 q^{93} - 78 q^{94} + 6 q^{95} + 6 q^{96} - 18 q^{97} + 3 q^{98}+O(q^{100}) \) 30 * q - 12 * q^7 + 15 * q^8 - 15 * q^11 + 3 * q^12 - 3 * q^13 + 9 * q^14 + 27 * q^15 - 36 * q^18 - 9 * q^19 + 18 * q^20 - 27 * q^21 - 3 * q^23 - 12 * q^25 + 3 * q^27 + 9 * q^28 + 3 * q^29 + 9 * q^30 + 30 * q^31 - 9 * q^34 + 15 * q^35 + 18 * q^37 + 6 * q^38 - 6 * q^41 - 45 * q^42 + 39 * q^43 - 18 * q^45 + 21 * q^46 + 45 * q^47 - 33 * q^49 + 36 * q^50 - 36 * q^51 + 6 * q^52 - 24 * q^53 + 45 * q^54 - 24 * q^56 - 24 * q^57 - 30 * q^58 + 3 * q^59 - 9 * q^60 - 27 * q^61 + 15 * q^62 - 93 * q^63 - 15 * q^64 + 18 * q^65 - 9 * q^67 - 21 * q^68 + 48 * q^69 - 15 * q^70 + 39 * q^73 + 3 * q^74 - 42 * q^75 - 15 * q^76 + 24 * q^77 + 6 * q^78 + 21 * q^79 + 84 * q^81 + 6 * q^82 - 36 * q^83 - 27 * q^84 + 63 * q^85 + 6 * q^86 - 21 * q^87 + 15 * q^88 + 54 * q^89 + 12 * q^90 + 3 * q^91 - 3 * q^92 + 51 * q^93 - 78 * q^94 + 6 * q^95 + 6 * q^96 - 18 * q^97 + 3 * q^98

Introduction

L-functions

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