LMFDB - Embedded newform 69.2.g.a.14.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(5,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

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

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

chi := DirichletCharacter("69.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.g (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			14.3
Character	$\chi$	$=$	69.14
Dual form			69.2.g.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.298617 - 1.01700i) q^{2} +(-1.66399 - 0.480761i) q^{3} +(0.737395 - 0.473895i) q^{4} +(-0.228939 - 1.59231i) q^{5} +(0.00796426 + 1.83584i) q^{6} +(-1.28446 - 0.586593i) q^{7} +(-2.30424 - 1.99663i) q^{8} +(2.53774 + 1.59996i) q^{9} +O(q^{10})$	\(q+(-0.298617 - 1.01700i) q^{2} +(-1.66399 - 0.480761i) q^{3} +(0.737395 - 0.473895i) q^{4} +(-0.228939 - 1.59231i) q^{5} +(0.00796426 + 1.83584i) q^{6} +(-1.28446 - 0.586593i) q^{7} +(-2.30424 - 1.99663i) q^{8} +(2.53774 + 1.59996i) q^{9} +(-1.55101 + 0.708322i) q^{10} +(4.31116 + 1.26587i) q^{11} +(-1.45485 + 0.434047i) q^{12} +(1.54864 + 3.39104i) q^{13} +(-0.213002 + 1.48146i) q^{14} +(-0.384567 + 2.75965i) q^{15} +(-0.614226 + 1.34497i) q^{16} +(3.34349 + 2.14873i) q^{17} +(0.869347 - 3.05865i) q^{18} +(-1.74911 - 2.72167i) q^{19} +(-0.923407 - 1.06567i) q^{20} +(1.85532 + 1.59360i) q^{21} -4.76245i q^{22} +(-4.78334 + 0.345872i) q^{23} +(2.87433 + 4.43017i) q^{24} +(2.31443 - 0.679578i) q^{25} +(2.98623 - 2.58758i) q^{26} +(-3.45357 - 3.88237i) q^{27} +(-1.22514 + 0.176148i) q^{28} +(0.915281 - 1.42420i) q^{29} +(2.92140 - 0.432978i) q^{30} +(-5.36145 + 6.18744i) q^{31} +(-4.48457 - 0.644784i) q^{32} +(-6.56515 - 4.17904i) q^{33} +(1.18683 - 4.04197i) q^{34} +(-0.639974 + 2.17955i) q^{35} +(2.62953 - 0.0228154i) q^{36} +(3.88889 + 0.559137i) q^{37} +(-2.24562 + 2.59158i) q^{38} +(-0.946638 - 6.38718i) q^{39} +(-2.65172 + 4.12616i) q^{40} +(-1.40816 + 0.202463i) q^{41} +(1.06666 - 2.36273i) q^{42} +(7.30732 - 6.33183i) q^{43} +(3.77892 - 1.10959i) q^{44} +(1.96665 - 4.40716i) q^{45} +(1.78014 + 4.76136i) q^{46} +9.42076i q^{47} +(1.66867 - 1.94272i) q^{48} +(-3.27828 - 3.78334i) q^{49} +(-1.38226 - 2.15084i) q^{50} +(-4.53051 - 5.18288i) q^{51} +(2.74895 + 1.76665i) q^{52} +(-0.748661 + 1.63934i) q^{53} +(-2.91707 + 4.67162i) q^{54} +(1.02866 - 7.15451i) q^{55} +(1.78849 + 3.91624i) q^{56} +(1.60203 + 5.36974i) q^{57} +(-1.72173 - 0.505546i) q^{58} +(-5.57035 + 2.54389i) q^{59} +(1.02421 + 2.21720i) q^{60} +(-1.67433 - 1.45081i) q^{61} +(7.89364 + 3.60490i) q^{62} +(-2.32109 - 3.54371i) q^{63} +(1.10428 + 7.68041i) q^{64} +(5.04504 - 3.24225i) q^{65} +(-2.28960 + 7.92468i) q^{66} +(3.35387 + 11.4222i) q^{67} +3.48374 q^{68} +(8.12573 + 1.72412i) q^{69} +2.40771 q^{70} +(1.99326 + 6.78844i) q^{71} +(-2.65301 - 8.75362i) q^{72} +(-8.24368 + 5.29789i) q^{73} +(-0.592648 - 4.12196i) q^{74} +(-4.17791 + 0.0181246i) q^{75} +(-2.57957 - 1.17805i) q^{76} +(-4.79496 - 4.15486i) q^{77} +(-6.21307 + 2.87005i) q^{78} +(-3.41100 + 1.55775i) q^{79} +(2.28222 + 0.670121i) q^{80} +(3.88023 + 8.12058i) q^{81} +(0.626405 + 1.37163i) q^{82} +(2.14609 - 14.9264i) q^{83} +(2.12331 + 0.295889i) q^{84} +(2.65598 - 5.81579i) q^{85} +(-8.62155 - 5.54073i) q^{86} +(-2.20772 + 1.92983i) q^{87} +(-7.40645 - 11.5247i) q^{88} +(-0.298008 - 0.343919i) q^{89} +(-5.06934 - 0.684024i) q^{90} -5.26407i q^{91} +(-3.36331 + 2.52185i) q^{92} +(11.8961 - 7.71828i) q^{93} +(9.58089 - 2.81320i) q^{94} +(-3.93330 + 3.40822i) q^{95} +(7.15230 + 3.22892i) q^{96} +(-8.23456 + 1.18395i) q^{97} +(-2.86869 + 4.46377i) q^{98} +(8.91524 + 10.1102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 11 q^{3} - 10 q^{4} - 14 q^{6} - 22 q^{7} - 11 q^{9}+O(q^{10}) $ 60 * q - 11 * q^3 - 10 * q^4 - 14 * q^6 - 22 * q^7 - 11 * q^9	$ 60 q - 11 q^{3} - 10 q^{4} - 14 q^{6} - 22 q^{7} - 11 q^{9} - 22 q^{10} + 4 q^{12} - 22 q^{13} - 46 q^{16} + 12 q^{18} - 22 q^{19} + 22 q^{21} + 50 q^{24} + 8 q^{25} + 10 q^{27} - 22 q^{28} + 33 q^{30} - 22 q^{31} + 22 q^{36} + 22 q^{37} + 13 q^{39} + 132 q^{40} - 11 q^{42} + 22 q^{43} + 66 q^{46} - 58 q^{48} + 68 q^{49} - 11 q^{51} + 94 q^{52} - 33 q^{54} - 44 q^{57} - 8 q^{58} - 121 q^{60} - 66 q^{61} - 66 q^{63} - 20 q^{64} - 66 q^{66} - 44 q^{67} - 66 q^{69} - 132 q^{70} - 101 q^{72} - 44 q^{73} - 44 q^{75} - 110 q^{76} + 84 q^{78} - 66 q^{79} + 77 q^{81} - 132 q^{82} + 77 q^{84} - 44 q^{85} + 73 q^{87} + 66 q^{88} + 176 q^{90} + 116 q^{93} + 100 q^{94} + 85 q^{96} + 44 q^{97} + 121 q^{99}+O(q^{100}) $ 60 * q - 11 * q^3 - 10 * q^4 - 14 * q^6 - 22 * q^7 - 11 * q^9 - 22 * q^10 + 4 * q^12 - 22 * q^13 - 46 * q^16 + 12 * q^18 - 22 * q^19 + 22 * q^21 + 50 * q^24 + 8 * q^25 + 10 * q^27 - 22 * q^28 + 33 * q^30 - 22 * q^31 + 22 * q^36 + 22 * q^37 + 13 * q^39 + 132 * q^40 - 11 * q^42 + 22 * q^43 + 66 * q^46 - 58 * q^48 + 68 * q^49 - 11 * q^51 + 94 * q^52 - 33 * q^54 - 44 * q^57 - 8 * q^58 - 121 * q^60 - 66 * q^61 - 66 * q^63 - 20 * q^64 - 66 * q^66 - 44 * q^67 - 66 * q^69 - 132 * q^70 - 101 * q^72 - 44 * q^73 - 44 * q^75 - 110 * q^76 + 84 * q^78 - 66 * q^79 + 77 * q^81 - 132 * q^82 + 77 * q^84 - 44 * q^85 + 73 * q^87 + 66 * q^88 + 176 * q^90 + 116 * q^93 + 100 * q^94 + 85 * q^96 + 44 * q^97 + 121 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{21}{22}\right)$	$-1$

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 $

$2$	−0.298617	−	1.01700i	−0.211154	−	0.719126i	−0.995151	−	0.0983605i	$-0.968640\pi$
$2$	−0.298617	−	1.01700i	−0.211154	−	0.719126i	0.783996	−	0.620765i	$-0.213178\pi$
$3$	−1.66399	−	0.480761i	−0.960706	−	0.277567i
$3$	−1.66399	−	0.480761i	−0.960706	−	0.277567i
$4$	0.737395	−	0.473895i	0.368698	−	0.236948i
$5$	−0.228939	−	1.59231i	−0.102385	−	0.712102i	−0.974758	−	0.223262i	$-0.928329\pi$
$5$	−0.228939	−	1.59231i	−0.102385	−	0.712102i	0.872374	−	0.488840i	$-0.162580\pi$
$6$	0.00796426	+	1.83584i	0.00325140	+	0.749478i
$7$	−1.28446	−	0.586593i	−0.485480	−	0.221711i	0.157611	−	0.987501i	$-0.449621\pi$
$7$	−1.28446	−	0.586593i	−0.485480	−	0.221711i	−0.643091	+	0.765790i	$0.722348\pi$
$8$	−2.30424	−	1.99663i	−0.814670	−	0.705916i
$9$	2.53774	+	1.59996i	0.845913	+	0.533322i
$10$	−1.55101	+	0.708322i	−0.490472	+	0.223991i
$11$	4.31116	+	1.26587i	1.29986	+	0.381674i	0.857186	−	0.515007i	$-0.172211\pi$
$11$	4.31116	+	1.26587i	1.29986	+	0.381674i	0.442677	+	0.896681i	$0.354029\pi$
$12$	−1.45485	+	0.434047i	−0.419979	+	0.125299i
$13$	1.54864	+	3.39104i	0.429514	+	0.940505i	0.993405	+	0.114656i	$0.0365765\pi$
$13$	1.54864	+	3.39104i	0.429514	+	0.940505i	−0.563891	+	0.825849i	$0.690696\pi$
$14$	−0.213002	+	1.48146i	−0.0569271	+	0.395937i
$15$	−0.384567	+	2.75965i	−0.0992947	+	0.712540i
$16$	−0.614226	+	1.34497i	−0.153556	+	0.336242i
$17$	3.34349	+	2.14873i	0.810915	+	0.521143i	0.879161	−	0.476525i	$-0.158104\pi$
$17$	3.34349	+	2.14873i	0.810915	+	0.521143i	−0.0682462	+	0.997669i	$0.521740\pi$
$18$	0.869347	−	3.05865i	0.204907	−	0.720931i
$19$	−1.74911	−	2.72167i	−0.401273	−	0.624394i	0.580542	−	0.814230i	$-0.302841\pi$
$19$	−1.74911	−	2.72167i	−0.401273	−	0.624394i	−0.981816	+	0.189836i	$0.939204\pi$
$20$	−0.923407	−	1.06567i	−0.206480	−	0.238291i
$21$	1.85532	+	1.59360i	0.404864	+	0.347753i
$22$		−	4.76245i		−	1.01536i
$23$	−4.78334	+	0.345872i	−0.997396	+	0.0721194i
$23$	−4.78334	+	0.345872i	−0.997396	+	0.0721194i
$24$	2.87433	+	4.43017i	0.586720	+	0.904304i
$25$	2.31443	−	0.679578i	0.462886	−	0.135916i
$26$	2.98623	−	2.58758i	0.585648	−	0.507466i
$27$	−3.45357	−	3.88237i	−0.664641	−	0.747163i
$28$	−1.22514	+	0.176148i	−0.231529	+	0.0332889i
$29$	0.915281	−	1.42420i	0.169963	−	0.264468i	−0.745814	−	0.666154i	$-0.767939\pi$
$29$	0.915281	−	1.42420i	0.169963	−	0.264468i	0.915777	+	0.401686i	$0.131576\pi$
$30$	2.92140	−	0.432978i	0.533372	−	0.0790505i
$31$	−5.36145	+	6.18744i	−0.962945	+	1.11130i	0.0307889	+	0.999526i	$0.490198\pi$
$31$	−5.36145	+	6.18744i	−0.962945	+	1.11130i	−0.993734	+	0.111772i	$0.964347\pi$
$32$	−4.48457	−	0.644784i	−0.792767	−	0.113983i
$33$	−6.56515	−	4.17904i	−1.14285	−	0.727477i
$34$	1.18683	−	4.04197i	0.203539	−	0.693191i
$35$	−0.639974	+	2.17955i	−0.108175	+	0.368411i
$36$	2.62953	−	0.0228154i	0.438255	−	0.00380256i
$37$	3.88889	+	0.559137i	0.639329	+	0.0919216i	0.454353	−	0.890822i	$-0.349870\pi$
$37$	3.88889	+	0.559137i	0.639329	+	0.0919216i	0.184975	+	0.982743i	$0.440779\pi$
$38$	−2.24562	+	2.59158i	−0.364287	+	0.420410i
$39$	−0.946638	−	6.38718i	−0.151583	−	1.02277i
$40$	−2.65172	+	4.12616i	−0.419274	+	0.652404i
$41$	−1.40816	+	0.202463i	−0.219917	+	0.0316193i	−0.251393	−	0.967885i	$-0.580889\pi$
$41$	−1.40816	+	0.202463i	−0.219917	+	0.0316193i	0.0314753	+	0.999505i	$0.489979\pi$
$42$	1.06666	−	2.36273i	0.164589	−	0.364578i
$43$	7.30732	−	6.33183i	1.11436	−	0.965595i	0.114742	−	0.993395i	$-0.463396\pi$
$43$	7.30732	−	6.33183i	1.11436	−	0.965595i	0.999613	+	0.0278003i	$0.00885026\pi$
$44$	3.77892	−	1.10959i	0.569694	−	0.167277i
$45$	1.96665	−	4.40716i	0.293171	−	0.656980i
$46$	1.78014	+	4.76136i	0.262467	+	0.702025i
$47$			9.42076i			1.37416i	0.726582	+	0.687080i	$0.241108\pi$
$47$			9.42076i			1.37416i	−0.726582	+	0.687080i	$0.758892\pi$
$48$	1.66867	−	1.94272i	0.240852	−	0.280407i
$49$	−3.27828	−	3.78334i	−0.468326	−	0.540477i
$50$	−1.38226	−	2.15084i	−0.195481	−	0.304174i
$51$	−4.53051	−	5.18288i	−0.634398	−	0.725749i
$52$	2.74895	+	1.76665i	0.381211	+	0.244990i
$53$	−0.748661	+	1.63934i	−0.102837	+	0.225181i	−0.954055	−	0.299630i	$-0.903137\pi$
$53$	−0.748661	+	1.63934i	−0.102837	+	0.225181i	0.851219	+	0.524811i	$0.175864\pi$
$54$	−2.91707	+	4.67162i	−0.396962	+	0.635727i
$55$	1.02866	−	7.15451i	0.138705	−	0.964713i
$56$	1.78849	+	3.91624i	0.238997	+	0.523330i
$57$	1.60203	+	5.36974i	0.212194	+	0.711239i
$58$	−1.72173	−	0.505546i	−0.226074	−	0.0663814i
$59$	−5.57035	+	2.54389i	−0.725198	+	0.331187i	−0.743582	−	0.668644i	$-0.766875\pi$
$59$	−5.57035	+	2.54389i	−0.725198	+	0.331187i	0.0183847	+	0.999831i	$0.494148\pi$
$60$	1.02421	+	2.21720i	0.132225	+	0.286239i
$61$	−1.67433	−	1.45081i	−0.214376	−	0.185758i	0.541053	−	0.840989i	$-0.318026\pi$
$61$	−1.67433	−	1.45081i	−0.214376	−	0.185758i	−0.755429	+	0.655231i	$0.772571\pi$
$62$	7.89364	+	3.60490i	1.00249	+	0.457823i
$63$	−2.32109	−	3.54371i	−0.292430	−	0.446466i
$64$	1.10428	+	7.68041i	0.138034	+	0.960051i
$65$	5.04504	−	3.24225i	0.625760	−	0.402151i
$66$	−2.28960	+	7.92468i	−0.281830	+	0.975460i
$67$	3.35387	+	11.4222i	0.409741	+	1.39545i	0.863511	+	0.504331i	$0.168261\pi$
$67$	3.35387	+	11.4222i	0.409741	+	1.39545i	−0.453770	+	0.891119i	$0.649921\pi$
$68$	3.48374			0.422466
$69$	8.12573	+	1.72412i	0.978222	+	0.207559i
$70$	2.40771			0.287776
$71$	1.99326	+	6.78844i	0.236557	+	0.805639i	0.989119	+	0.147118i	$0.0469996\pi$
$71$	1.99326	+	6.78844i	0.236557	+	0.805639i	−0.752562	+	0.658521i	$0.771182\pi$
$72$	−2.65301	−	8.75362i	−0.312660	−	1.03162i
$73$	−8.24368	+	5.29789i	−0.964850	+	0.620072i	−0.925336	−	0.379147i	$-0.876217\pi$
$73$	−8.24368	+	5.29789i	−0.964850	+	0.620072i	−0.0395139	+	0.999219i	$0.512581\pi$
$74$	−0.592648	−	4.12196i	−0.0688939	−	0.479168i
$75$	−4.17791	+	0.0181246i	−0.482423	+	0.00209285i
$76$	−2.57957	−	1.17805i	−0.295897	−	0.135132i
$77$	−4.79496	−	4.15486i	−0.546436	−	0.473490i
$78$	−6.21307	+	2.87005i	−0.703491	+	0.324969i
$79$	−3.41100	+	1.55775i	−0.383767	+	0.175261i	−0.597951	−	0.801533i	$-0.704018\pi$
$79$	−3.41100	+	1.55775i	−0.383767	+	0.175261i	0.214184	+	0.976793i	$0.431291\pi$
$80$	2.28222	+	0.670121i	0.255160	+	0.0749218i
$81$	3.88023	+	8.12058i	0.431136	+	0.902287i
$82$	0.626405	+	1.37163i	0.0691748	+	0.151472i
$83$	2.14609	−	14.9264i	0.235564	−	1.63838i	−0.437800	−	0.899073i	$-0.644242\pi$
$83$	2.14609	−	14.9264i	0.235564	−	1.63838i	0.673364	−	0.739311i	$-0.264849\pi$
$84$	2.12331	+	0.295889i	0.231672	+	0.0322842i
$85$	2.65598	−	5.81579i	0.288082	−	0.630811i
$86$	−8.62155	−	5.54073i	−0.929685	−	0.597473i
$87$	−2.20772	+	1.92983i	−0.236693	+	0.206900i
$88$	−7.40645	−	11.5247i	−0.789530	−	1.22853i
$89$	−0.298008	−	0.343919i	−0.0315887	−	0.0364554i	0.739735	−	0.672898i	$-0.234951\pi$
$89$	−0.298008	−	0.343919i	−0.0315887	−	0.0364554i	−0.771324	+	0.636443i	$0.780405\pi$
$90$	−5.06934	−	0.684024i	−0.534356	−	0.0721024i
$91$		−	5.26407i		−	0.551825i
$92$	−3.36331	+	2.52185i	−0.350649	+	0.262921i
$93$	11.8961	−	7.71828i	1.23357	−	0.800348i
$94$	9.58089	−	2.81320i	0.988194	−	0.290160i
$95$	−3.93330	+	3.40822i	−0.403548	+	0.349676i
$96$	7.15230	+	3.22892i	0.729978	+	0.329550i
$97$	−8.23456	+	1.18395i	−0.836093	+	0.120212i	−0.547045	−	0.837103i	$-0.684248\pi$
$97$	−8.23456	+	1.18395i	−0.836093	+	0.120212i	−0.289047	+	0.957315i	$0.593338\pi$
$98$	−2.86869	+	4.46377i	−0.289782	+	0.450909i
$99$	8.91524	+	10.1102i	0.896016	+	1.01611i
$100$	1.38460	−	1.59792i	0.138460	−	0.159792i
$101$	6.96023	+	1.00073i	0.692569	+	0.0995763i	0.479606	−	0.877484i	$-0.340780\pi$
$101$	6.96023	+	1.00073i	0.692569	+	0.0995763i	0.212963	+	0.977060i	$0.431689\pi$
$102$	−3.91809	+	6.15522i	−0.387949	+	0.609457i
$103$	3.32222	−	11.3144i	0.327348	−	1.11484i	−0.617292	−	0.786734i	$-0.711770\pi$
$103$	3.32222	−	11.3144i	0.327348	−	1.11484i	0.944640	−	0.328109i	$-0.106411\pi$
$104$	3.20223	−	10.9058i	0.314005	−	1.06940i
$105$	2.11275	−	3.31908i	0.206184	−	0.323909i
$106$	1.89077	+	0.271851i	0.183648	+	0.0264045i
$107$	11.8206	−	13.6417i	1.14274	−	1.31879i	0.202103	−	0.979364i	$-0.435222\pi$
$107$	11.8206	−	13.6417i	1.14274	−	1.31879i	0.940633	−	0.339424i	$-0.110232\pi$
$108$	−4.38649	−	1.22621i	−0.422090	−	0.117992i
$109$	−4.16074	+	6.47424i	−0.398527	+	0.620120i	−0.981293	−	0.192520i	$-0.938334\pi$
$109$	−4.16074	+	6.47424i	−0.398527	+	0.620120i	0.582766	+	0.812640i	$0.301970\pi$
$110$	−7.58329	+	1.09031i	−0.723038	+	0.103957i
$111$	−6.20226	−	2.80002i	−0.588693	−	0.265767i
$112$	1.57790	−	1.36726i	0.149097	−	0.129194i
$113$	−13.5081	+	3.96634i	−1.27074	+	0.373121i	−0.846480	−	0.532421i	$-0.821282\pi$
$113$	−13.5081	+	3.96634i	−1.27074	+	0.373121i	−0.424255	+	0.905543i	$0.639464\pi$
$114$	4.98262	−	3.23276i	0.466665	−	0.302776i
$115$	1.64583	+	7.53738i	0.153475	+	0.702864i
$116$		−	1.48395i		−	0.137781i
$117$	−1.49551	+	11.0833i	−0.138260	+	1.02465i
$118$	4.25054	+	4.90538i	0.391294	+	0.451577i
$119$	−3.03415	−	4.72122i	−0.278140	−	0.432794i
$120$	6.39615	−	5.59106i	0.583886	−	0.510391i
$121$	7.72988	+	4.96769i	0.702716	+	0.451608i
$122$	−0.975490	+	2.13603i	−0.0883167	+	0.193387i
$123$	2.44050	+	0.340091i	0.220052	+	0.0306650i
$124$	−1.02131	+	7.10336i	−0.0917163	+	0.637901i
$125$	−4.95332	−	10.8463i	−0.443038	−	0.970118i
$126$	−2.91083	+	3.41876i	−0.259317	+	0.304567i
$127$	−1.24954	−	0.366898i	−0.110879	−	0.0325570i	0.225822	−	0.974168i	$-0.427493\pi$
$127$	−1.24954	−	0.366898i	−0.110879	−	0.0325570i	−0.336701	+	0.941612i	$0.609311\pi$
$128$	−0.761312	+	0.347680i	−0.0672912	+	0.0307308i
$129$	−15.2034	+	7.02304i	−1.33859	+	0.618344i
$130$	−4.80389	−	4.16260i	−0.421329	−	0.365084i
$131$	7.54331	+	3.44491i	0.659062	+	0.300984i	0.716729	−	0.697352i	$-0.245639\pi$
$131$	7.54331	+	3.44491i	0.659062	+	0.300984i	−0.0576663	+	0.998336i	$0.518366\pi$
$132$	−6.82154	+	0.0295933i	−0.593739	+	0.00257576i
$133$	0.650150	+	4.52189i	0.0563751	+	0.392098i
$134$	10.6149	−	6.82176i	0.916985	−	0.589311i
$135$	−5.39128	+	6.38799i	−0.464007	+	0.549790i
$136$	−3.41396	−	11.6269i	−0.292745	−	0.996998i
$137$	5.82629			0.497773			0.248887	−	0.968533i	$-0.419935\pi$
$137$	5.82629			0.497773			0.248887	+	0.968533i	$0.419935\pi$
$138$	−0.673062	−	8.77869i	−0.0572948	−	0.747292i
$139$	−9.61035			−0.815139			−0.407569	−	0.913174i	$-0.633624\pi$
$139$	−9.61035			−0.815139			−0.407569	+	0.913174i	$0.633624\pi$
$140$	0.560965	+	1.91047i	0.0474102	+	0.161464i
$141$	4.52913	−	15.6761i	0.381422	−	1.32016i
$142$	6.30860	−	4.05429i	0.529406	−	0.340229i
$143$	2.38380	+	16.5797i	0.199343	+	1.38646i
$144$	−3.71064	+	2.43043i	−0.309220	+	0.202536i
$145$	−2.47732	−	1.13135i	−0.205730	−	0.0939538i
$146$	7.84965	+	6.80176i	0.649642	+	0.562918i
$147$	3.63615	+	7.87151i	0.299905	+	0.649231i
$148$	3.13262	−	1.43062i	0.257500	−	0.117596i
$149$	−19.1223	−	5.61482i	−1.56656	−	0.459984i	−0.620564	−	0.784155i	$-0.713096\pi$
$149$	−19.1223	−	5.61482i	−1.56656	−	0.459984i	−0.945998	+	0.324171i	$0.894915\pi$
$150$	1.26603	+	4.24351i	0.103371	+	0.346481i
$151$	0.585077	+	1.28114i	0.0476129	+	0.104258i	0.931944	−	0.362603i	$-0.118112\pi$
$151$	0.585077	+	1.28114i	0.0476129	+	0.104258i	−0.884331	+	0.466861i	$0.845385\pi$
$152$	−1.40381	+	9.76370i	−0.113864	+	0.791940i
$153$	5.04700	+	10.8024i	0.408026	+	0.873320i
$154$	−2.79362	+	6.11718i	−0.225116	+	0.492936i
$155$	11.0798	+	7.12054i	0.889949	+	0.571935i
$156$	−3.72490	−	4.26127i	−0.298231	−	0.341175i
$157$	6.23984	+	9.70938i	0.497994	+	0.774893i	0.995718	−	0.0924420i	$-0.0294673\pi$
$157$	6.23984	+	9.70938i	0.497994	+	0.774893i	−0.497724	+	0.867335i	$0.665831\pi$
$158$	2.60281	+	3.00381i	0.207069	+	0.238970i
$159$	2.03390	−	2.36792i	0.161299	−	0.187788i
$160$			7.28843i			0.576201i
$161$	6.34690	+	2.36162i	0.500206	+	0.186122i
$162$	7.09991	−	6.37113i	0.557821	−	0.500563i
$163$	3.75567	−	1.10276i	0.294167	−	0.0863751i	−0.131319	−	0.991340i	$-0.541921\pi$
$163$	3.75567	−	1.10276i	0.294167	−	0.0863751i	0.425486	+	0.904965i	$0.360103\pi$
$164$	−0.942423	+	0.816615i	−0.0735909	+	0.0637669i
$165$	−5.15129	+	11.4105i	−0.401028	+	0.888306i
$166$	−15.8210	+	2.27471i	−1.22794	+	0.176552i
$167$	5.44450	−	8.47181i	0.421308	−	0.655568i	−0.564114	−	0.825697i	$-0.690782\pi$
$167$	5.44450	−	8.47181i	0.421308	−	0.655568i	0.985422	+	0.170129i	$0.0544184\pi$
$168$	−1.09325	−	7.37643i	−0.0843463	−	0.569104i
$169$	−0.587680	+	0.678219i	−0.0452062	+	0.0521707i
$170$	−6.70777	−	0.964432i	−0.514462	−	0.0739685i
$171$	−0.0842097	−	9.70540i	−0.00643968	−	0.742190i
$172$	2.38776	−	8.13197i	0.182065	−	0.620057i
$173$	−0.652717	+	2.22295i	−0.0496252	+	0.169008i	−0.980577	−	0.196134i	$-0.937161\pi$
$173$	−0.652717	+	2.22295i	−0.0496252	+	0.169008i	0.930952	+	0.365142i	$0.118979\pi$
$174$	2.62190	+	1.66897i	0.198766	+	0.126524i
$175$	−3.37143	−	0.484738i	−0.254856	−	0.0366428i
$176$	−4.35058	+	5.02084i	−0.327937	+	0.378460i
$177$	10.4920	−	1.55501i	0.788629	−	0.116882i
$178$	−0.260775	+	0.405773i	−0.0195459	+	0.0304140i
$179$	4.76707	−	0.685402i	0.356308	−	0.0512293i	0.0381632	−	0.999272i	$-0.487849\pi$
$179$	4.76707	−	0.685402i	0.356308	−	0.0512293i	0.318145	+	0.948042i	$0.396940\pi$
$180$	−0.638333	−	4.18180i	−0.0475785	−	0.311693i
$181$	13.1782	−	11.4190i	0.979527	−	0.848765i	−0.00897721	−	0.999960i	$-0.502858\pi$
$181$	13.1782	−	11.4190i	0.979527	−	0.848765i	0.988504	+	0.151195i	$0.0483121\pi$
$182$	−5.35355	+	1.57194i	−0.396831	+	0.116520i
$183$	2.08857	+	3.21909i	0.154392	+	0.237962i
$184$	11.7125	+	8.75360i	0.863459	+	0.645324i
$185$		−	6.32032i		−	0.464679i
$186$	−11.4019	−	9.79348i	−0.836024	−	0.718093i
$187$	11.6943	+	13.4959i	0.855171	+	0.986920i
$188$	4.46446	+	6.94683i	0.325604	+	0.506649i
$189$	2.15860	+	7.01260i	0.157015	+	0.510091i
$190$	4.64070	+	2.98240i	0.336672	+	0.216366i
$191$	−1.17349	+	2.56958i	−0.0849105	+	0.185928i	−0.947324	−	0.320276i	$-0.896224\pi$
$191$	−1.17349	+	2.56958i	−0.0849105	+	0.185928i	0.862414	+	0.506204i	$0.168952\pi$
$192$	1.85493	−	13.3110i	0.133868	−	0.960641i
$193$	2.77756	−	19.3183i	0.199933	−	1.39056i	−0.604540	−	0.796575i	$-0.706643\pi$
$193$	2.77756	−	19.3183i	0.199933	−	1.39056i	0.804473	−	0.593990i	$-0.202448\pi$
$194$	3.66306	+	8.02098i	0.262992	+	0.575873i
$195$	−9.95365	+	2.96962i	−0.712795	+	0.212659i
$196$	−4.21029	−	1.23625i	−0.300735	−	0.0883038i
$197$	−12.3272	+	5.62965i	−0.878278	+	0.401096i	−0.802939	−	0.596062i	$-0.796731\pi$
$197$	−12.3272	+	5.62965i	−0.878278	+	0.401096i	−0.0753397	+	0.997158i	$0.524004\pi$
$198$	7.61975	−	12.0858i	0.541512	−	0.858904i
$199$	−11.0680	−	9.59051i	−0.784592	−	0.679853i	0.167429	−	0.985884i	$-0.446453\pi$
$199$	−11.0680	−	9.59051i	−0.784592	−	0.679853i	−0.952022	+	0.306031i	$0.900999\pi$
$200$	−6.68986	−	3.05516i	−0.473045	−	0.216032i
$201$	−0.0894493	−	20.6189i	−0.00630927	−	1.45435i
$202$	−1.06071	−	7.37737i	−0.0746310	−	0.519070i
$203$	−2.01107	+	1.29244i	−0.141149	+	0.0907113i
$204$	−5.79692	−	1.67485i	−0.405866	−	0.117263i
$205$	0.644766	+	2.19587i	0.0450324	+	0.153366i
$206$	−12.4988			−0.870834
$207$	−12.6923	−	6.77545i	−0.882173	−	0.470926i
$208$	−5.51205			−0.382192
$209$	−4.09541	−	13.9477i	−0.283286	−	0.964782i
$210$	−4.00640	−	1.15753i	−0.276468	−	0.0798772i
$211$	−9.49791	+	6.10393i	−0.653863	+	0.420212i	−0.825076	−	0.565022i	$-0.808868\pi$
$211$	−9.49791	+	6.10393i	−0.653863	+	0.420212i	0.171213	+	0.985234i	$0.445231\pi$
$212$	0.224816	+	1.56363i	0.0154404	+	0.107390i
$213$	−0.0531613	−	12.2542i	−0.00364255	−	0.839643i
$214$	−17.4034	−	7.94785i	−1.18967	−	0.543304i
$215$	−11.7552	−	10.1859i	−0.801695	−	0.694673i
$216$	0.206181	+	15.8414i	0.0140288	+	1.07787i
$217$	10.5161	−	4.80253i	0.713878	−	0.326017i
$218$	7.82676	+	2.29814i	0.530095	+	0.155650i
$219$	16.2644	−	4.85241i	1.09905	−	0.327896i
$220$	−2.63196	−	5.76318i	−0.177446	−	0.388553i
$221$	−2.10858	+	14.6655i	−0.141838	+	0.986507i
$222$	−0.995514	+	7.14382i	−0.0668145	+	0.479462i
$223$	−4.76293	+	10.4294i	−0.318949	+	0.698402i	−0.999409	−	0.0343841i	$-0.989053\pi$
$223$	−4.76293	+	10.4294i	−0.318949	+	0.698402i	0.680459	+	0.732786i	$0.261780\pi$
$224$	5.38202	+	3.45882i	0.359602	+	0.231102i
$225$	6.96072	+	1.97842i	0.464048	+	0.131894i
$226$	8.06751	+	12.5533i	0.536643	+	0.835032i
$227$	−0.308514	−	0.356044i	−0.0204768	−	0.0236315i	0.745419	−	0.666596i	$-0.232250\pi$
$227$	−0.308514	−	0.356044i	−0.0204768	−	0.0236315i	−0.765896	+	0.642965i	$0.777704\pi$
$228$	3.72603	+	3.20042i	0.246762	+	0.211953i
$229$		−	1.12917i		−	0.0746174i	−0.999304	−	0.0373087i	$-0.988122\pi$
$229$		−	1.12917i		−	0.0746174i	0.999304	−	0.0373087i	$-0.0118785\pi$
$230$	7.17402	−	3.92460i	0.473041	−	0.258780i
$231$	5.98128	+	9.21888i	0.393539	+	0.606558i
$232$	−4.95264	+	1.45422i	−0.325156	+	0.0954745i
$233$	−2.56406	+	2.22177i	−0.167977	+	0.145553i	−0.734793	−	0.678292i	$-0.762721\pi$
$233$	−2.56406	+	2.22177i	−0.167977	+	0.145553i	0.566816	+	0.823845i	$0.308175\pi$
$234$	11.7183	−	1.78874i	0.766049	−	0.116934i
$235$	15.0008	−	2.15678i	0.978542	−	0.140693i
$236$	−2.90201	+	4.51562i	−0.188905	+	0.293942i
$237$	6.42478	−	0.952210i	0.417334	−	0.0618527i
$238$	−3.89542	+	4.49556i	−0.252503	+	0.291404i
$239$	2.87786	+	0.413774i	0.186153	+	0.0267648i	0.234761	−	0.972053i	$-0.424569\pi$
$239$	2.87786	+	0.413774i	0.186153	+	0.0267648i	−0.0486076	+	0.998818i	$0.515478\pi$
$240$	−3.47543	−	2.21228i	−0.224338	−	0.142802i
$241$	0.629154	−	2.14270i	0.0405274	−	0.138023i	−0.936744	−	0.350015i	$-0.886177\pi$
$241$	0.629154	−	2.14270i	0.0405274	−	0.138023i	0.977272	+	0.211991i	$0.0679948\pi$
$242$	2.74385	−	9.34471i	0.176382	−	0.600700i
$243$	−2.55261	−	15.3780i	−0.163750	−	0.986502i
$244$	−1.92218	−	0.276367i	−0.123055	−	0.0176926i
$245$	−5.27371	+	6.08619i	−0.336925	+	0.388832i
$246$	−0.382904	−	2.58354i	−0.0244130	−	0.164720i
$247$	6.52055	−	10.1462i	0.414893	−	0.645585i
$248$	24.7081	−	3.55249i	1.56897	−	0.225583i
$249$	−10.7471	+	23.8056i	−0.681070	+	1.50862i
$250$	−9.55147	+	8.27639i	−0.604088	+	0.523445i
$251$	11.1678	−	3.27916i	0.704904	−	0.206978i	0.0904154	−	0.995904i	$-0.471181\pi$
$251$	11.1678	−	3.27916i	0.704904	−	0.206978i	0.614489	+	0.788926i	$0.289362\pi$
$252$	−3.39091	−	1.51316i	−0.213607	−	0.0953201i
$253$	−21.0596	−	4.56398i	−1.32400	−	0.286935i
$254$			1.38034i			0.0866104i
$255$	−7.21554	+	8.40054i	−0.451855	+	0.526062i
$256$	10.7436	+	12.3987i	0.671473	+	0.774921i
$257$	1.38747	+	2.15894i	0.0865477	+	0.134671i	0.881828	−	0.471571i	$-0.156313\pi$
$257$	1.38747	+	2.15894i	0.0865477	+	0.134671i	−0.795281	+	0.606242i	$0.792676\pi$
$258$	11.6824	+	13.3646i	0.727316	+	0.832046i
$259$	−4.66713	−	2.99938i	−0.290001	−	0.186373i
$260$	2.18370	−	4.78164i	0.135427	−	0.296545i
$261$	4.60142	−	2.14984i	0.284821	−	0.133072i
$262$	1.25091	−	8.70024i	0.0772812	−	0.537503i
$263$	8.69346	+	19.0360i	0.536062	+	1.17381i	0.962993	+	0.269528i	$0.0868676\pi$
$263$	8.69346	+	19.0360i	0.536062	+	1.17381i	−0.426931	+	0.904284i	$0.640405\pi$
$264$	6.78367	+	22.7377i	0.417506	+	1.39941i
$265$	2.78173	+	0.816791i	0.170881	+	0.0501750i
$266$	4.40461	−	2.01152i	0.270064	−	0.123334i
$267$	0.330539	+	0.715549i	0.0202287	+	0.0437909i
$268$	7.88608	+	6.83333i	0.481719	+	0.417412i
$269$	−25.9223	−	11.8383i	−1.58051	−	0.721795i	−0.584531	−	0.811372i	$-0.698721\pi$
$269$	−25.9223	−	11.8383i	−1.58051	−	0.721795i	−0.995980	+	0.0895767i	$0.971449\pi$
$270$	8.10650	+	3.57535i	0.493346	+	0.217589i
$271$	0.00475284	+	0.0330567i	0.000288715	+	0.00200805i	0.989965	−	0.141311i	$-0.0451317\pi$
$271$	0.00475284	+	0.0330567i	0.000288715	+	0.00200805i	−0.989677	+	0.143319i	$0.954223\pi$
$272$	−4.94362	+	3.17707i	−0.299751	+	0.192638i
$273$	−2.53076	+	8.75937i	−0.153169	+	0.530141i
$274$	−1.73983	−	5.92532i	−0.105107	−	0.357962i
$275$	10.8381			0.653564
$276$	6.80892	−	2.57939i	0.409849	−	0.155261i
$277$	−30.3604			−1.82418			−0.912091	−	0.409987i	$-0.865533\pi$
$277$	−30.3604			−1.82418			−0.912091	+	0.409987i	$0.865533\pi$
$278$	2.86982	+	9.77370i	0.172120	+	0.586187i
$279$	−23.5056	+	7.12398i	−1.40725	+	0.426501i
$280$	5.82641	−	3.74441i	0.348195	−	0.223771i
$281$	−3.30204	−	22.9662i	−0.196983	−	1.37005i	−0.812976	−	0.582298i	$-0.802154\pi$
$281$	−3.30204	−	22.9662i	−0.196983	−	1.37005i	0.615992	−	0.787752i	$-0.288755\pi$
$282$	−17.2950	+	0.0750294i	−1.02990	+	0.00446794i
$283$	15.1659	+	6.92603i	0.901519	+	0.411710i	0.811583	−	0.584238i	$-0.198606\pi$
$283$	15.1659	+	6.92603i	0.901519	+	0.411710i	0.0899361	+	0.995948i	$0.471334\pi$
$284$	4.68683	+	4.06116i	0.278112	+	0.240986i
$285$	8.18351	−	3.78028i	0.484750	−	0.223924i
$286$	16.1496	−	7.37530i	0.954949	−	0.436110i
$287$	1.92749	+	0.565961i	0.113776	+	0.0334076i
$288$	−10.3490	−	8.81144i	−0.609822	−	0.519219i
$289$	−0.500187	−	1.09526i	−0.0294228	−	0.0644269i
$290$	−0.410813	+	2.85727i	−0.0241238	+	0.167785i
$291$	14.2714	+	1.98877i	0.836606	+	0.116584i
$292$	−3.56821	+	7.81329i	−0.208814	+	0.457238i
$293$	6.12390	+	3.93559i	0.357762	+	0.229920i	0.707158	−	0.707055i	$-0.249977\pi$
$293$	6.12390	+	3.93559i	0.357762	+	0.229920i	−0.349396	+	0.936975i	$0.613613\pi$
$294$	6.91949	−	6.04852i	0.403553	−	0.352757i
$295$	5.32594	+	8.28732i	0.310088	+	0.482506i
$296$	−7.84452	−	9.05306i	−0.455953	−	0.526198i
$297$	−9.97433	−	21.1093i	−0.578769	−	1.22489i
$298$			21.1241i			1.22368i
$299$	−8.58052	−	15.6849i	−0.496224	−	0.907079i
$300$	−3.07218	+	1.99326i	−0.177372	+	0.115081i
$301$	−13.1002	+	3.84656i	−0.755081	+	0.221712i
$302$	1.12820	−	0.977593i	0.0649208	−	0.0562542i
$303$	−11.1007	−	5.01141i	−0.637716	−	0.287898i
$304$	4.73490	−	0.680776i	0.271565	−	0.0390452i
$305$	−1.92682	+	2.99820i	−0.110330	+	0.171676i
$306$	9.47886	−	8.35856i	0.541870	−	0.477827i
$307$	0.473561	−	0.546519i	0.0270276	−	0.0311915i	−0.742075	−	0.670317i	$-0.766158\pi$
$307$	0.473561	−	0.546519i	0.0270276	−	0.0311915i	0.769102	+	0.639126i	$0.220704\pi$
$308$	−5.50475	−	0.791464i	−0.313662	−	0.0450978i
$309$	−10.9677	+	17.2299i	−0.623929	+	0.980176i
$310$	3.93296	−	13.3944i	0.223377	−	0.760752i
$311$	−0.566562	+	1.92953i	−0.0321268	+	0.109414i	−0.973996	−	0.226567i	$-0.927250\pi$
$311$	−0.566562	+	1.92953i	−0.0321268	+	0.109414i	0.941869	+	0.335981i	$0.109068\pi$
$312$	−10.5716	+	16.6077i	−0.598498	+	0.940224i
$313$	13.5345	+	1.94597i	0.765015	+	0.109993i	0.513767	−	0.857930i	$-0.328250\pi$
$313$	13.5345	+	1.94597i	0.765015	+	0.109993i	0.251249	+	0.967923i	$0.419159\pi$
$314$	8.01109	−	9.24530i	0.452092	−	0.521742i
$315$	−5.11129	+	4.50719i	−0.287989	+	0.253952i
$316$	−1.77704	+	2.76513i	−0.0999665	+	0.155551i
$317$	−8.43499	+	1.21277i	−0.473756	+	0.0681159i	−0.375058	−	0.927002i	$-0.622377\pi$
$317$	−8.43499	+	1.21277i	−0.473756	+	0.0681159i	−0.0986986	+	0.995117i	$0.531468\pi$
$318$	−3.01553	−	1.36137i	−0.169102	−	0.0763416i
$319$	5.74878	−	4.98135i	0.321870	−	0.278902i
$320$	11.9768	−	3.51670i	0.669522	−	0.196589i
$321$	−26.2277	+	17.0167i	−1.46389	+	0.949782i
$322$	0.506464	−	7.16000i	0.0282242	−	0.399011i
$323$		−	12.8582i		−	0.715451i
$324$	6.70957	+	4.14926i	0.372754	+	0.230514i
$325$	5.88868	+	6.79590i	0.326645	+	0.376969i
$326$	−2.24302	−	3.49020i	−0.124229	−	0.193304i
$327$	10.0360	−	8.77276i	0.554992	−	0.485135i
$328$	3.64897	+	2.34505i	0.201481	+	0.129484i
$329$	5.52616	−	12.1006i	0.304667	−	0.667127i
$330$	13.1427	+	1.83148i	0.723483	+	0.100820i
$331$	0.444763	−	3.09339i	0.0244464	−	0.170028i	−0.973941	−	0.226803i	$-0.927173\pi$
$331$	0.444763	−	3.09339i	0.0244464	−	0.170028i	0.998387	+	0.0567748i	$0.0180817\pi$
$332$	−5.49103	−	12.0237i	−0.301359	−	0.659885i
$333$	8.97437	+	7.64102i	0.491793	+	0.418726i
$334$	−10.2416	−	3.00722i	−0.560397	−	0.164547i
$335$	17.4199	−	7.95541i	0.951751	−	0.434650i
$336$	−3.28293	+	1.51651i	−0.179099	+	0.0827325i
$337$	−9.14689	−	7.92582i	−0.498263	−	0.431747i	0.369125	−	0.929380i	$-0.379657\pi$
$337$	−9.14689	−	7.92582i	−0.498263	−	0.431747i	−0.867388	+	0.497633i	$0.834203\pi$
$338$	0.865239	+	0.395141i	0.0470628	+	0.0214929i
$339$	24.3842	−	0.105784i	1.32437	−	0.00574539i
$340$	−0.797566	−	5.54720i	−0.0432541	−	0.300839i
$341$	−30.9466	+	19.8882i	−1.67585	+	1.07700i
$342$	−9.84522	+	2.98384i	−0.532368	+	0.161348i
$343$	4.77631	+	16.2666i	0.257897	+	0.878315i
$344$	−29.4801			−1.58946
$345$	0.885026	−	13.3334i	0.0476482	−	0.717845i
$346$	2.45565			0.132016
$347$	−4.63661	−	15.7908i	−0.248906	−	0.847696i	−0.985255	−	0.171094i	$-0.945270\pi$
$347$	−4.63661	−	15.7908i	−0.248906	−	0.847696i	0.736349	−	0.676602i	$-0.236548\pi$
$348$	−0.713425	+	2.46928i	−0.0382436	+	0.132367i
$349$	26.2501	−	16.8699i	1.40514	−	0.903026i	0.405198	−	0.914229i	$-0.367203\pi$
$349$	26.2501	−	16.8699i	1.40514	−	0.903026i	0.999937	+	0.0112031i	$0.00356614\pi$
$350$	0.513790	+	3.57349i	0.0274632	+	0.191011i
$351$	7.81695	−	17.7236i	0.417238	−	0.946015i
$352$	−18.5175	−	8.45665i	−0.986985	−	0.450741i
$353$	15.9800	+	13.8468i	0.850531	+	0.736989i	0.966610	−	0.256251i	$-0.0824873\pi$
$353$	15.9800	+	13.8468i	0.850531	+	0.736989i	−0.116080	+	0.993240i	$0.537033\pi$
$354$	−4.71454	−	10.2060i	−0.250575	−	0.542443i
$355$	10.3530	−	4.72803i	0.549478	−	0.250938i
$356$	−0.382731	−	0.112380i	−0.0202847	−	0.00595613i
$357$	2.77901	+	9.31477i	0.147081	+	0.492990i
$358$	−2.12058	−	4.64343i	−0.112076	−	0.245413i
$359$	0.608756	−	4.23399i	0.0321289	−	0.223462i	−0.967431	−	0.253136i	$-0.918538\pi$
$359$	0.608756	−	4.23399i	0.0321289	−	0.223462i	0.999560	+	0.0296745i	$0.00944706\pi$
$360$	−13.3311	+	6.22846i	−0.702610	+	0.328268i
$361$	3.54479	−	7.76201i	0.186568	−	0.408527i
$362$	−15.5483	−	9.99228i	−0.817200	−	0.525183i
$363$	−10.4742	−	11.9824i	−0.549752	−	0.628914i
$364$	−2.49462	−	3.88170i	−0.130754	−	0.203457i
$365$	10.3232	+	11.9136i	0.540340	+	0.623586i
$366$	2.65012	−	3.08535i	0.138524	−	0.161274i
$367$			11.2014i			0.584709i	0.956310	+	0.292354i	$0.0944387\pi$
$367$			11.2014i			0.584709i	−0.956310	+	0.292354i	$0.905561\pi$
$368$	2.47287	−	6.64588i	0.128907	−	0.346441i
$369$	−3.89747	−	1.73921i	−0.202894	−	0.0905395i
$370$	−6.42775	+	1.88736i	−0.334163	+	0.0981190i
$371$	1.92325	−	1.66651i	0.0998502	−	0.0865207i
$372$	5.11447	−	11.3289i	0.265173	−	0.587378i
$373$	−3.22490	+	0.463670i	−0.166979	+	0.0240079i	−0.225297	−	0.974290i	$-0.572335\pi$
$373$	−3.22490	+	0.463670i	−0.166979	+	0.0240079i	0.0583183	+	0.998298i	$0.481426\pi$
$374$	10.2332	−	15.9232i	0.529147	−	0.823368i
$375$	3.02783	+	20.4294i	0.156356	+	1.05497i
$376$	18.8098	−	21.7077i	0.970041	−	1.11949i
$377$	6.24697	+	0.898178i	0.321735	+	0.0462585i
$378$	6.48720	−	4.28938i	0.333665	−	0.220622i
$379$	−6.15345	+	20.9567i	−0.316081	+	1.07647i	0.636269	+	0.771467i	$0.280477\pi$
$379$	−6.15345	+	20.9567i	−0.316081	+	1.07647i	−0.952350	+	0.305007i	$0.901341\pi$
$380$	−1.28526	+	4.37718i	−0.0659322	+	0.224544i
$381$	1.90284	+	1.21125i	0.0974852	+	0.0620540i
$382$	2.96368	+	0.426113i	0.151635	+	0.0218018i
$383$	−9.92748	+	11.4569i	−0.507270	+	0.585421i	−0.950398	−	0.311038i	$-0.899324\pi$
$383$	−9.92748	+	11.4569i	−0.507270	+	0.585421i	0.443127	+	0.896459i	$0.353869\pi$
$384$	1.43397	−	0.212527i	0.0731769	−	0.0108455i
$385$	−5.51806	+	8.58627i	−0.281226	+	0.437597i
$386$	−20.4761	+	2.94402i	−1.04221	+	0.149847i
$387$	28.6748	−	4.37707i	1.45762	−	0.222499i
$388$	−5.51106	+	4.77536i	−0.279782	+	0.242432i
$389$	24.9651	−	7.33041i	1.26578	−	0.371667i	0.421137	−	0.906997i	$-0.361631\pi$
$389$	24.9651	−	7.33041i	1.26578	−	0.371667i	0.844643	+	0.535330i	$0.179813\pi$
$390$	5.99243	+	9.23605i	0.303438	+	0.467686i
$391$	−16.7362	−	9.12169i	−0.846387	−	0.461303i
$392$			15.2632i			0.770909i
$393$	−10.8958	−	9.35884i	−0.549622	−	0.472091i
$394$	9.40647	+	10.8556i	0.473891	+	0.546899i
$395$	3.26133	+	5.07473i	0.164095	+	0.255338i
$396$	11.3652	+	3.23029i	0.571123	+	0.162328i
$397$	−0.819795	−	0.526850i	−0.0411443	−	0.0264418i	0.519907	−	0.854223i	$-0.325967\pi$
$397$	−0.819795	−	0.526850i	−0.0411443	−	0.0264418i	−0.561051	+	0.827781i	$0.689603\pi$
$398$	−6.44841	+	14.1201i	−0.323230	+	0.707774i
$399$	1.09210	−	7.83696i	0.0546736	−	0.392339i
$400$	−0.507573	+	3.53025i	−0.0253786	+	0.176512i
$401$	5.62068	+	12.3076i	0.280684	+	0.614611i	0.996492	−	0.0836852i	$-0.0266690\pi$
$401$	5.62068	+	12.3076i	0.280684	+	0.614611i	−0.715809	+	0.698296i	$0.753942\pi$
$402$	−20.9427	+	6.24814i	−1.04453	+	0.311629i
$403$	−29.2848	−	8.59879i	−1.45878	−	0.428336i
$404$	5.60668	−	2.56049i	0.278943	−	0.127389i
$405$	12.0421	−	8.03764i	0.598379	−	0.399394i
$406$	1.91495	+	1.65931i	0.0950371	+	0.0823501i
$407$	16.0578	+	7.33336i	0.795956	+	0.363501i
$408$	0.0910519	+	20.9883i	0.00450774	+	1.03908i
$409$	2.19405	+	15.2599i	0.108489	+	0.754555i	0.969344	+	0.245706i	$0.0790199\pi$
$409$	2.19405	+	15.2599i	0.108489	+	0.754555i	−0.860856	+	0.508849i	$0.830071\pi$
$410$	2.04066	−	1.31145i	0.100781	−	0.0647679i
$411$	−9.69489	−	2.80105i	−0.478214	−	0.138166i
$412$	−2.91207	−	9.91759i	−0.143467	−	0.488605i
$413$	8.64712			0.425497
$414$	−3.10048	+	14.9313i	−0.152380	+	0.733831i
$415$	−24.2587			−1.19081
$416$	−4.75848	−	16.2059i	−0.233303	−	0.794559i
$417$	15.9915	+	4.62028i	0.783109	+	0.226256i
$418$	−12.9618	+	8.33005i	−0.633983	+	0.407436i
$419$	3.62086	+	25.1837i	0.176891	+	1.23030i	0.863904	+	0.503657i	$0.168012\pi$
$419$	3.62086	+	25.1837i	0.176891	+	1.23030i	−0.687013	+	0.726645i	$0.741078\pi$
$420$	−0.0149612	−	3.44870i	−0.000730031	−	0.168279i
$421$	−24.4417	−	11.1622i	−1.19122	−	0.544010i	−0.281629	−	0.959523i	$-0.590875\pi$
$421$	−24.4417	−	11.1622i	−1.19122	−	0.544010i	−0.909587	+	0.415513i	$0.863602\pi$
$422$	9.04393	+	7.83661i	0.440251	+	0.381480i
$423$	−15.0729	+	23.9074i	−0.732869	+	1.16242i
$424$	4.99825	−	2.28262i	0.242736	−	0.110854i
$425$	9.19850	+	2.70092i	0.446193	+	0.131014i
$426$	−12.4466	+	3.71338i	−0.603040	+	0.179914i
$427$	1.29957	+	2.84566i	0.0628906	+	0.137711i
$428$	2.25171	−	15.6610i	0.108841	−	0.757003i
$429$	4.00424	−	28.7345i	0.193327	−	1.38731i
$430$	−6.84875	+	14.9967i	−0.330276	+	0.723203i
$431$	−1.84035	−	1.18272i	−0.0886465	−	0.0569697i	0.495567	−	0.868570i	$-0.334960\pi$
$431$	−1.84035	−	1.18272i	−0.0886465	−	0.0569697i	−0.584213	+	0.811600i	$0.698597\pi$
$432$	7.34294	−	2.26029i	0.353287	−	0.108748i
$433$	12.7704	+	19.8711i	0.613704	+	0.954942i	0.999477	+	0.0323485i	$0.0102986\pi$
$433$	12.7704	+	19.8711i	0.613704	+	0.954942i	−0.385772	+	0.922594i	$0.626065\pi$
$434$	−8.02445	−	9.26071i	−0.385186	−	0.444528i
$435$	3.57833	+	3.07356i	0.171568	+	0.147366i
$436$			6.74583i			0.323067i
$437$	9.30794	+	12.4137i	0.445259	+	0.593828i
$438$	−9.79174	−	15.0919i	−0.467867	−	0.721118i
$439$	30.6380	−	8.99614i	1.46227	−	0.429362i	0.548694	−	0.836023i	$-0.315125\pi$
$439$	30.6380	−	8.99614i	1.46227	−	0.429362i	0.913579	+	0.406661i	$0.133307\pi$
$440$	−16.6552	+	14.4318i	−0.794005	+	0.688009i
$441$	−2.26621	−	14.8462i	−0.107915	−	0.706964i
$442$	15.5444	−	2.23495i	0.739373	−	0.106306i
$443$	−14.2088	+	22.1093i	−0.675078	+	1.05044i	0.319614	+	0.947548i	$0.396447\pi$
$443$	−14.2088	+	22.1093i	−0.675078	+	1.05044i	−0.994692	+	0.102895i	$0.967190\pi$
$444$	−5.90044	+	0.874498i	−0.280022	+	0.0415018i
$445$	−0.479400	+	0.553257i	−0.0227257	+	0.0262269i
$446$	12.0289	+	1.72950i	0.569586	+	0.0818941i
$447$	29.1200	+	18.5363i	1.37733	+	0.876737i
$448$	3.08688	−	10.5129i	0.145841	−	0.496689i
$449$	−10.7313	+	36.5474i	−0.506440	+	1.72478i	0.167390	+	0.985891i	$0.446466\pi$
$449$	−10.7313	+	36.5474i	−0.506440	+	1.72478i	−0.673830	+	0.738886i	$0.735352\pi$
$450$	−0.0665479	−	7.66982i	−0.00313710	−	0.361559i
$451$	−6.32709	−	0.909698i	−0.297931	−	0.0428360i
$452$	−8.08118	+	9.32618i	−0.380107	+	0.438667i
$453$	−0.357641	−	2.41309i	−0.0168035	−	0.113377i
$454$	−0.269968	+	0.420079i	−0.0126702	+	0.0197153i
$455$	−8.38203	+	1.20515i	−0.392956	+	0.0564985i
$456$	7.02993	−	15.5718i	0.329207	−	0.729217i
$457$	3.07782	−	2.66694i	0.143974	−	0.124754i	−0.579896	−	0.814690i	$-0.696907\pi$
$457$	3.07782	−	2.66694i	0.143974	−	0.124754i	0.723870	+	0.689936i	$0.242361\pi$
$458$	−1.14836	+	0.337189i	−0.0536593	+	0.0157558i
$459$	−3.20481	−	20.4015i	−0.149588	−	0.952258i
$460$	4.78556	+	4.77808i	0.223128	+	0.222779i
$461$		−	21.2506i		−	0.989741i	−0.868967	−	0.494871i	$-0.835215\pi$
$461$		−	21.2506i		−	0.989741i	0.868967	−	0.494871i	$-0.164785\pi$
$462$	7.58946	−	8.83587i	0.353094	−	0.411082i
$463$	−8.61186	−	9.93861i	−0.400227	−	0.461887i	0.519485	−	0.854479i	$-0.326124\pi$
$463$	−8.61186	−	9.93861i	−0.400227	−	0.461887i	−0.919712	+	0.392593i	$0.871578\pi$
$464$	1.35332	+	2.10581i	0.0628263	+	0.0977596i
$465$	−15.0134	−	17.1752i	−0.696228	−	0.796482i
$466$	3.02521	+	1.94418i	0.140140	+	0.0900625i
$467$	−5.23053	+	11.4533i	−0.242040	+	0.529994i	−0.991196	−	0.132399i	$-0.957732\pi$
$467$	−5.23053	+	11.4533i	−0.242040	+	0.529994i	0.749156	+	0.662393i	$0.230459\pi$
$468$	4.14955	+	8.88151i	0.191813	+	0.410548i
$469$	2.39230	−	16.6388i	0.110466	−	0.768307i
$470$	−6.67293	−	14.6117i	−0.307799	−	0.673987i
$471$	−5.71515	−	19.1562i	−0.263340	−	0.882672i
$472$	17.9146	+	5.26021i	0.824587	+	0.242121i
$473$	39.5183	−	18.0474i	1.81705	−	0.829820i
$474$	−2.88695	−	6.24964i	−0.132602	−	0.287055i
$475$	−5.89778	−	5.11046i	−0.270609	−	0.234484i
$476$	−4.47473	−	2.04354i	−0.205099	−	0.0936655i
$477$	−4.52279	+	2.96238i	−0.207084	+	0.135638i
$478$	−0.438572	−	3.05034i	−0.0200598	−	0.139519i
$479$	−9.44493	+	6.06989i	−0.431550	+	0.277340i	−0.738329	−	0.674440i	$-0.764385\pi$
$479$	−9.44493	+	6.06989i	−0.431550	+	0.277340i	0.306779	+	0.951781i	$0.400749\pi$
$480$	3.50399	−	12.1279i	0.159935	−	0.553560i
$481$	4.12641	+	14.0533i	0.188148	+	0.640774i
$482$	−2.36700			−0.107814
$483$	−9.42582	−	6.98105i	−0.428889	−	0.317649i
$484$	8.05414			0.366097
$485$	3.77043	+	12.8409i	0.171206	+	0.583076i
$486$	−14.8772	+	7.18815i	−0.674843	+	0.326061i
$487$	6.86912	−	4.41452i	0.311270	−	0.200041i	−0.375673	−	0.926752i	$-0.622589\pi$
$487$	6.86912	−	4.41452i	0.311270	−	0.200041i	0.686943	+	0.726711i	$0.258952\pi$
$488$	0.961306	+	6.68603i	0.0435163	+	0.302662i
$489$	−6.77957	+	0.0294112i	−0.306583	+	0.00133002i
$490$	7.76446	+	3.54591i	0.350763	+	0.160188i
$491$	2.83742	+	2.45864i	0.128051	+	0.110957i	0.716532	−	0.697554i	$-0.245728\pi$
$491$	2.83742	+	2.45864i	0.128051	+	0.110957i	−0.588481	+	0.808511i	$0.700274\pi$
$492$	1.96078	−	0.905760i	0.0883989	−	0.0408348i
$493$	6.12046	−	2.79512i	0.275652	−	0.125886i
$494$	−12.2658	−	3.60156i	−0.551864	−	0.162042i
$495$	14.0574	−	16.5104i	0.631835	−	0.742089i
$496$	−5.02877	−	11.0115i	−0.225798	−	0.494429i
$497$	1.42178	−	9.88871i	0.0637756	−	0.443569i
$498$	27.4195	+	3.82100i	1.22870	+	0.171223i
$499$	−5.68350	+	12.4451i	−0.254428	+	0.557120i	−0.993144	−	0.116897i	$-0.962705\pi$
$499$	−5.68350	+	12.4451i	−0.254428	+	0.557120i	0.738716	+	0.674017i	$0.235433\pi$
$500$	−8.79254	−	5.65062i	−0.393214	−	0.252704i
$501$	−13.1325	+	11.4795i	−0.586718	+	0.512867i
$502$	−6.66979	−	10.3784i	−0.297687	−	0.463210i
$503$	−12.7240	−	14.6842i	−0.567334	−	0.654738i	0.397499	−	0.917603i	$-0.369878\pi$
$503$	−12.7240	−	14.6842i	−0.567334	−	0.654738i	−0.964833	+	0.262864i	$0.915333\pi$
$504$	−1.72714	+	12.7999i	−0.0769328	+	0.570154i
$505$		−	11.3119i		−	0.503375i
$506$	1.64720	+	22.7804i	0.0732270	+	1.01271i
$507$	1.30396	−	0.846018i	0.0579107	−	0.0375730i
$508$	−1.09528	+	0.321603i	−0.0485951	+	0.0142688i
$509$	10.1882	−	8.82816i	0.451586	−	0.391301i	−0.399158	−	0.916882i	$-0.630697\pi$
$509$	10.1882	−	8.82816i	0.451586	−	0.391301i	0.850744	+	0.525581i	$0.176152\pi$
$510$	10.6980	+	4.82964i	0.473716	+	0.213860i
$511$	13.6964	−	1.96924i	0.605893	−	0.0871142i
$512$	8.49629	−	13.2205i	0.375487	−	0.584269i
$513$	−4.52585	+	16.1902i	−0.199821	+	0.714814i
$514$	1.78131	−	2.05575i	0.0785704	−	0.0906751i
$515$	−18.7766	−	2.69967i	−0.827398	−	0.118962i
$516$	−7.88275	+	12.3836i	−0.347019	+	0.545157i
$517$	−11.9255	+	40.6144i	−0.524481	+	1.78622i
$518$	−1.65668	+	5.64213i	−0.0727903	+	0.247901i
$519$	2.15482	−	3.38517i	0.0945863	−	0.148593i
$520$	−18.0985	−	2.60218i	−0.793673	−	0.114113i
$521$	4.39954	−	5.07734i	0.192747	−	0.222442i	−0.651147	−	0.758952i	$-0.725712\pi$
$521$	4.39954	−	5.07734i	0.192747	−	0.222442i	0.843894	+	0.536509i	$0.180257\pi$
$522$	−3.56045	−	4.03765i	−0.155837	−	0.176723i
$523$	6.99787	−	10.8889i	0.305996	−	0.476138i	−0.653867	−	0.756610i	$-0.726854\pi$
$523$	6.99787	−	10.8889i	0.305996	−	0.476138i	0.959862	+	0.280471i	$0.0904907\pi$
$524$	7.19493	−	1.03448i	0.314312	−	0.0451913i
$525$	5.37699	+	2.42745i	0.234671	+	0.105943i
$526$	16.7636	−	14.5257i	0.730927	−	0.633352i
$527$	−31.2211	+	9.16733i	−1.36001	+	0.399335i
$528$	9.65315	−	6.26304i	0.420100	−	0.272564i
$529$	22.7607	−	3.30885i	0.989598	−	0.143863i
$530$		−	3.07292i		−	0.133479i
$531$	−18.2062	−	2.45663i	−0.790083	−	0.106609i
$532$	2.62232	+	3.02632i	0.113692	+	0.131208i
$533$	−2.86728	−	4.46158i	−0.124196	−	0.193252i
$534$	0.629007	−	0.549833i	0.0272198	−	0.0237936i
$535$	−24.4279	−	15.6989i	−1.05611	−	0.678721i
$536$	15.0779	−	33.0160i	0.651266	−	1.42607i
$537$	−8.26189	−	1.15132i	−0.356527	−	0.0496831i
$538$	−4.29869	+	29.8980i	−0.185330	+	1.28900i
$539$	−9.34397	−	20.4604i	−0.402473	−	0.881294i
$540$	−0.948268	+	7.26537i	−0.0408069	+	0.312652i
$541$	16.4836	+	4.84001i	0.708684	+	0.208088i	0.616159	−	0.787622i	$-0.288688\pi$
$541$	16.4836	+	4.84001i	0.708684	+	0.208088i	0.0925251	+	0.995710i	$0.470506\pi$
$542$	0.0321993	−	0.0147049i	0.00138308	−	0.000631632i
$543$	−27.4182	+	12.6655i	−1.17663	+	0.543529i
$544$	−13.6086	−	11.7919i	−0.583465	−	0.505575i
$545$	11.2615	+	5.14298i	0.482392	+	0.220301i
$546$	9.66399	−	0.0419244i	0.413581	−	0.00179420i
$547$	−2.06388	−	14.3546i	−0.0882449	−	0.613757i	−0.985171	−	0.171576i	$-0.945114\pi$
$547$	−2.06388	−	14.3546i	−0.0882449	−	0.613757i	0.896926	−	0.442181i	$-0.145795\pi$
$548$	4.29628	−	2.76105i	0.183528	−	0.117946i
$549$	−1.92775	−	6.36065i	−0.0822746	−	0.271466i
$550$	−3.23646	−	11.0224i	−0.138003	−	0.469995i
$551$	−5.47714			−0.233334
$552$	−15.2812	−	20.1969i	−0.650410	−	0.859635i
$553$	5.29506			0.225169
$554$	9.06616	+	30.8765i	0.385184	+	1.31182i
$555$	−3.03856	+	10.5170i	−0.128980	+	0.446420i
$556$	−7.08663	+	4.55430i	−0.300540	+	0.193145i
$557$	−4.48426	−	31.1887i	−0.190004	−	1.32151i	−0.831989	−	0.554792i	$-0.812798\pi$
$557$	−4.48426	−	31.1887i	−0.190004	−	1.32151i	0.641985	−	0.766717i	$-0.278111\pi$
$558$	14.2643	+	21.7778i	0.603855	+	0.921930i
$559$	32.7879	+	14.9737i	1.38678	+	0.633320i
$560$	−2.53834	−	2.19948i	−0.107264	−	0.0929450i
$561$	−12.9709	−	28.0793i	−0.547631	−	1.18551i
$562$	−22.3705	+	10.2163i	−0.943644	+	0.430948i
$563$	5.54381	+	1.62781i	0.233644	+	0.0686041i	0.396459	−	0.918053i	$-0.370239\pi$
$563$	5.54381	+	1.62781i	0.233644	+	0.0686041i	−0.162815	+	0.986657i	$0.552057\pi$
$564$	−4.08905	−	13.7058i	−0.172180	−	0.577118i
$565$	9.40817	+	20.6010i	0.395805	+	0.866691i
$566$	2.51496	−	17.4919i	0.105712	−	0.735240i
$567$	−0.220518	−	12.7067i	−0.00926088	−	0.533630i
$568$	8.96106	−	19.6220i	0.375998	−	0.823320i
$569$	−5.87229	−	3.77389i	−0.246179	−	0.158210i	0.411733	−	0.911305i	$-0.364924\pi$
$569$	−5.87229	−	3.77389i	−0.246179	−	0.158210i	−0.657912	+	0.753095i	$0.728560\pi$
$570$	−6.28827	−	7.19376i	−0.263387	−	0.301313i
$571$	−1.26613	−	1.97013i	−0.0529857	−	0.0824474i	0.813750	−	0.581215i	$-0.197422\pi$
$571$	−1.26613	−	1.97013i	−0.0529857	−	0.0824474i	−0.866736	+	0.498768i	$0.833786\pi$
$572$	9.61483	+	11.0961i	0.402016	+	0.463952i
$573$	3.18803	−	3.71159i	0.133182	−	0.155054i
$574$		−	2.12925i		−	0.0888734i
$575$	−10.8357	+	4.05115i	−0.451879	+	0.168945i
$576$	−9.48602	+	21.2577i	−0.395251	+	0.885736i
$577$	−23.0132	+	6.75728i	−0.958051	+	0.281309i	−0.723135	−	0.690706i	$-0.757300\pi$
$577$	−23.0132	+	6.75728i	−0.958051	+	0.281309i	−0.234916	+	0.972016i	$0.575482\pi$
$578$	−0.964509	+	0.835752i	−0.0401183	+	0.0347627i
$579$	−13.9093	+	30.8102i	−0.578052	+	1.28043i
$580$	−2.36291	+	0.339735i	−0.0981143	+	0.0141067i
$581$	−11.5123	+	17.9135i	−0.477610	+	0.743176i
$582$	−2.23913	−	15.1079i	−0.0928147	−	0.626242i
$583$	−5.30279	+	6.11975i	−0.219619	+	0.253454i
$584$	29.5733	+	4.25200i	1.22375	+	0.175949i
$585$	17.9905	−	0.156096i	0.743814	−	0.00645377i
$586$	2.17379	−	7.40323i	0.0897982	−	0.305825i
$587$	1.66435	−	5.66827i	0.0686953	−	0.233955i	−0.917988	−	0.396608i	$-0.870187\pi$
$587$	1.66435	−	5.66827i	0.0686953	−	0.233955i	0.986683	+	0.162654i	$0.0520053\pi$
$588$	6.41155	+	4.08126i	0.264408	+	0.168308i
$589$	26.2179	+	3.76957i	1.08029	+	0.155322i
$590$	6.83777	−	7.89120i	0.281506	−	0.324876i
$591$	23.2189	−	3.44125i	0.955099	−	0.141554i
$592$	−3.14068	+	4.88699i	−0.129081	+	0.200854i
$593$	11.6702	−	1.67792i	0.479238	−	0.0689040i	0.101537	−	0.994832i	$-0.467624\pi$
$593$	11.6702	−	1.67792i	0.479238	−	0.0689040i	0.377701	+	0.925928i	$0.376715\pi$
$594$	−18.4896	+	16.4475i	−0.758638	+	0.674848i
$595$	−6.82301	+	5.91217i	−0.279716	+	0.242375i
$596$	−16.7616	+	4.92164i	−0.686580	+	0.201598i
$597$	13.8064	+	21.2796i	0.565057	+	0.870916i
$598$	−13.3892	+	13.4101i	−0.547524	+	0.548382i
$599$		−	27.3519i		−	1.11757i	−0.829313	−	0.558784i	$-0.811268\pi$
$599$		−	27.3519i		−	1.11757i	0.829313	−	0.558784i	$-0.188732\pi$
$600$	9.66307	+	8.29998i	0.394493	+	0.338845i
$601$	−14.9084	−	17.2052i	−0.608125	−	0.701813i	0.365282	−	0.930897i	$-0.380973\pi$
$601$	−14.9084	−	17.2052i	−0.608125	−	0.701813i	−0.973407	+	0.229084i	$0.926427\pi$
$602$	7.82388	+	12.1742i	0.318877	+	0.496183i
$603$	−9.76394	+	34.3527i	−0.397618	+	1.39895i
$604$	1.03856	+	0.667442i	0.0422584	+	0.0271578i
$605$	6.14042	−	13.4457i	0.249644	−	0.546644i
$606$	−1.78175	+	12.7858i	−0.0723785	+	0.519389i
$607$	0.491879	−	3.42109i	0.0199647	−	0.138858i	−0.977401	−	0.211393i	$-0.932200\pi$
$607$	0.491879	−	3.42109i	0.0199647	−	0.138858i	0.997366	+	0.0725354i	$0.0231090\pi$
$608$	6.08912	+	13.3333i	0.246946	+	0.540737i
$609$	3.96776	−	1.18376i	0.160782	−	0.0479684i
$610$	3.62454	+	1.06426i	0.146753	+	0.0430907i
$611$	−31.9462	+	14.5893i	−1.29240	+	0.590221i
$612$	8.84083	+	5.57387i	0.357369	+	0.225310i
$613$	5.90988	+	5.12094i	0.238698	+	0.206833i	0.765992	−	0.642850i	$-0.222248\pi$
$613$	5.90988	+	5.12094i	0.238698	+	0.206833i	−0.527295	+	0.849683i	$0.676794\pi$
$614$	−0.697222	−	0.318411i	−0.0281376	−	0.0128500i
$615$	−0.0171962	−	3.96389i	−0.000693418	−	0.159839i
$616$	2.75300	+	19.1475i	0.110922	+	0.771477i
$617$	11.0304	−	7.08879i	0.444066	−	0.285384i	−0.299437	−	0.954116i	$-0.596799\pi$
$617$	11.0304	−	7.08879i	0.444066	−	0.285384i	0.743504	+	0.668732i	$0.233163\pi$
$618$	20.7979	+	6.00894i	0.836615	+	0.241715i
$619$	−8.27724	−	28.1897i	−0.332690	−	1.13304i	−0.940737	−	0.339138i	$-0.889865\pi$
$619$	−8.27724	−	28.1897i	−0.332690	−	1.13304i	0.608046	−	0.793902i	$-0.291954\pi$
$620$	11.5446			0.463641
$621$	17.8624	+	17.3762i	0.716795	+	0.697284i
$622$	2.13152			0.0854660
$623$	0.181038	+	0.616560i	0.00725314	+	0.0247019i
$624$	9.17200	+	2.64998i	0.367174	+	0.106084i
$625$	−5.99047	+	3.84984i	−0.239619	+	0.153994i
$626$	−2.06259	−	14.3457i	−0.0824378	−	0.573368i
$627$	0.109226	+	25.1778i	0.00436209	+	1.00550i
$628$	9.20246	+	4.20262i	0.367218	+	0.167703i
$629$	11.8010	+	10.2256i	0.470537	+	0.407722i
$630$	6.11013	+	3.85224i	0.243433	+	0.153477i
$631$	−24.9917	+	11.4133i	−0.994902	+	0.454357i	−0.845244	−	0.534381i	$-0.820545\pi$
$631$	−24.9917	+	11.4133i	−0.994902	+	0.454357i	−0.149659	+	0.988738i	$0.547817\pi$
$632$	10.9700	+	3.22108i	0.436363	+	0.128128i
$633$	18.7390	−	5.59067i	0.744807	−	0.222209i
$634$	3.75222	+	8.21621i	0.149020	+	0.326307i
$635$	−0.298146	+	2.07365i	−0.0118316	+	0.0822904i
$636$	0.377640	−	2.70995i	0.0149744	−	0.107456i
$637$	7.75258	−	16.9758i	0.307168	−	0.672605i
$638$	−6.78270	−	4.35898i	−0.268530	−	0.172574i
$639$	−5.80288	+	20.4164i	−0.229558	+	0.807661i
$640$	0.727908	+	1.13265i	0.0287731	+	0.0447718i
$641$	29.5322	+	34.0820i	1.16645	+	1.34616i	0.926916	+	0.375270i	$0.122450\pi$
$641$	29.5322	+	34.0820i	1.16645	+	1.34616i	0.239536	+	0.970887i	$0.423005\pi$
$642$	25.1380	+	21.5920i	0.992119	+	0.852168i
$643$		−	40.9797i		−	1.61608i	−0.589126	−	0.808041i	$-0.700528\pi$
$643$		−	40.9797i		−	1.61608i	0.589126	−	0.808041i	$-0.299472\pi$
$644$	5.79933	−	1.26632i	0.228526	−	0.0499000i
$645$	14.6635	+	22.6007i	0.577375	+	0.889901i
$646$	−13.0768	+	3.83969i	−0.514499	+	0.151071i
$647$	22.7458	−	19.7094i	0.894231	−	0.774855i	−0.0808452	−	0.996727i	$-0.525762\pi$
$647$	22.7458	−	19.7094i	0.894231	−	0.774855i	0.975076	+	0.221871i	$0.0712165\pi$
$648$	7.27285	−	26.4591i	0.285705	−	1.03941i
$649$	−27.2349	+	3.91579i	−1.06906	+	0.153708i
$650$	5.15295	−	8.01815i	0.202115	−	0.314498i
$651$	−19.8075	+	2.93566i	−0.776319	+	0.115057i
$652$	2.24682	−	2.59297i	0.0879922	−	0.101548i
$653$	−16.3778	−	2.35477i	−0.640913	−	0.0921494i	−0.185807	−	0.982586i	$-0.559490\pi$
$653$	−16.3778	−	2.35477i	−0.640913	−	0.0921494i	−0.455107	+	0.890437i	$0.650399\pi$
$654$	−11.9188	−	7.58689i	−0.466062	−	0.296671i
$655$	3.75841	−	12.8000i	0.146853	−	0.500136i
$656$	0.592622	−	2.01828i	0.0231380	−	0.0788008i
$657$	−29.3968	+	0.255063i	−1.14688	+	0.00995097i
$658$	−13.9565	−	2.00664i	−0.544080	−	0.0782269i
$659$	−11.7423	+	13.5514i	−0.457416	+	0.527886i	−0.936869	−	0.349682i	$-0.886290\pi$
$659$	−11.7423	+	13.5514i	−0.457416	+	0.527886i	0.479453	+	0.877568i	$0.340835\pi$
$660$	1.60884	+	10.8552i	0.0626241	+	0.422539i
$661$	3.11846	−	4.85242i	0.121294	−	0.188737i	−0.775297	−	0.631597i	$-0.782400\pi$
$661$	3.11846	−	4.85242i	0.121294	−	0.188737i	0.896591	+	0.442860i	$0.146036\pi$
$662$	−3.27879	+	0.471418i	−0.127434	+	0.0183222i
$663$	10.5593	−	23.3895i	0.410087	−	0.908374i
$664$	−34.7476	+	30.1090i	−1.34847	+	1.16845i
$665$	7.05140	−	2.07048i	0.273442	−	0.0802897i
$666$	5.09100	−	11.4087i	0.197272	−	0.442076i
$667$	−3.88551	+	7.12903i	−0.150448	+	0.276037i
$668$		−	8.82720i		−	0.341535i
$669$	12.9395	−	15.0645i	0.500270	−	0.582429i
$670$	−13.2925	−	15.3404i	−0.513535	−	0.592651i
$671$	−5.38175	−	8.37417i	−0.207760	−	0.323281i
$672$	−7.29278	−	8.34291i	−0.281325	−	0.321835i
$673$	18.4088	+	11.8306i	0.709606	+	0.456036i	0.845007	−	0.534755i	$-0.179596\pi$
$673$	18.4088	+	11.8306i	0.709606	+	0.456036i	−0.135402	+	0.990791i	$0.543232\pi$
$674$	−5.32912	+	11.6692i	−0.205270	+	0.449479i
$675$	−10.6314	−	6.63851i	−0.409204	−	0.255516i
$676$	−0.111948	+	0.778615i	−0.00430569	+	0.0299467i
$677$	−16.0670	−	35.1818i	−0.617505	−	1.35215i	−0.917320	−	0.398151i	$-0.869652\pi$
$677$	−16.0670	−	35.1818i	−0.617505	−	1.35215i	0.299815	−	0.953997i	$-0.403075\pi$
$678$	−7.38914	−	24.7671i	−0.283778	−	0.951175i
$679$	11.2715	+	3.30960i	0.432559	+	0.127011i
$680$	−17.7320	+	8.09794i	−0.679991	+	0.310542i
$681$	0.342193	+	0.740776i	0.0131128	+	0.0283866i
$682$	29.4674	+	25.5336i	1.12836	+	0.977734i
$683$	−40.2698	−	18.3906i	−1.54088	−	0.703697i	−0.549596	−	0.835431i	$-0.685218\pi$
$683$	−40.2698	−	18.3906i	−1.54088	−	0.703697i	−0.991285	+	0.131734i	$0.957945\pi$
$684$	−4.66144	−	7.11681i	−0.178235	−	0.272118i
$685$	−1.33387	−	9.27725i	−0.0509644	−	0.354465i
$686$	15.1168	−	9.71500i	0.577163	−	0.370920i
$687$	−0.542859	+	1.87892i	−0.0207114	+	0.0716854i
$688$	4.02776	+	13.7173i	0.153557	+	0.522966i
$689$	−6.71847			−0.255953
$690$	−13.8243	+	3.08151i	−0.526282	+	0.117311i
$691$	32.7374			1.24539			0.622694	−	0.782465i	$-0.286038\pi$
$691$	32.7374			1.24539			0.622694	+	0.782465i	$0.286038\pi$
$692$	0.572135	+	1.94851i	0.0217493	+	0.0740714i
$693$	−5.52073	−	18.2157i	−0.209715	−	0.691957i
$694$	−14.6747	+	9.43083i	−0.557043	+	0.357990i
$695$	2.20019	+	15.3026i	0.0834579	+	0.580462i
$696$	8.94028	−	0.0387848i	0.338880	−	0.00147014i
$697$	−5.14320	−	2.34882i	−0.194812	−	0.0889678i
$698$	−24.9954	−	21.6586i	−0.946090	−	0.819791i
$699$	5.33471	−	2.46431i	0.201777	−	0.0932087i
$700$	−2.71579	+	1.24026i	−0.102647	+	0.0468774i
$701$	−10.5436	−	3.09589i	−0.398228	−	0.116930i	0.0764857	−	0.997071i	$-0.475630\pi$
$701$	−10.5436	−	3.09589i	−0.398228	−	0.116930i	−0.474713	+	0.880141i	$0.657448\pi$
$702$	−20.3591	−	2.65725i	−0.768405	−	0.100291i
$703$	−5.28030	−	11.5623i	−0.199150	−	0.436079i
$704$	−4.96169	+	34.5093i	−0.187001	+	1.30062i
$705$	−25.9980	−	3.62291i	−0.979143	−	0.136447i
$706$	9.31021	−	20.3865i	0.350395	−	0.767257i
$707$	−8.35311	−	5.36822i	−0.314151	−	0.201893i
$708$	6.99986	−	6.11878i	0.263071	−	0.229958i
$709$	−22.5622	−	35.1075i	−0.847342	−	1.31849i	−0.946264	−	0.323395i	$-0.895176\pi$
$709$	−22.5622	−	35.1075i	−0.847342	−	1.31849i	0.0989220	−	0.995095i	$-0.468461\pi$
$710$	−7.89997	−	9.11705i	−0.296481	−	0.342157i
$711$	−11.1486	−	1.50431i	−0.418104	−	0.0564162i
$712$			1.38748i			0.0519981i
$713$	23.5056	−	31.4510i	0.880291	−	1.17785i
$714$	8.64324	−	5.60780i	0.323465	−	0.209867i
$715$	25.8542	−	7.59149i	0.966893	−	0.283905i
$716$	3.19041	−	2.76451i	0.119231	−	0.103314i
$717$	−4.58981	−	2.07208i	−0.171410	−	0.0773832i
$718$	−4.48775	+	0.645240i	−0.167481	+	0.0240802i
$719$	19.7432	−	30.7211i	0.736299	−	1.14570i	−0.247926	−	0.968779i	$-0.579749\pi$
$719$	19.7432	−	30.7211i	0.736299	−	1.14570i	0.984224	−	0.176924i	$-0.0566147\pi$
$720$	4.71951	+	5.35207i	0.175886	+	0.199460i
$721$	−10.9042	+	12.5841i	−0.406094	+	0.468658i
$722$	−8.95248	−	1.28717i	−0.333177	−	0.0479036i
$723$	−2.07703	+	3.26296i	−0.0772457	+	0.121351i
$724$	4.30614	−	14.6654i	0.160036	−	0.545034i
$725$	1.15050	−	3.91823i	0.0427283	−	0.145519i
$726$	−9.05832	+	14.2304i	−0.336186	+	0.528139i
$727$	3.85722	+	0.554585i	0.143057	+	0.0205684i	0.213471	−	0.976949i	$-0.431523\pi$
$727$	3.85722	+	0.554585i	0.143057	+	0.0205684i	−0.0704145	+	0.997518i	$0.522432\pi$
$728$	−10.5104	+	12.1297i	−0.389542	+	0.449555i
$729$	−3.14565	+	26.8161i	−0.116505	+	0.993190i
$730$	9.03341	−	14.0563i	0.334342	−	0.520246i
$731$	38.0373	−	5.46894i	1.40686	−	0.202276i
$732$	3.06562	+	1.38398i	0.113308	+	0.0511533i
$733$	22.5664	−	19.5539i	0.833509	−	0.722240i	−0.129538	−	0.991575i	$-0.541349\pi$
$733$	22.5664	−	19.5539i	0.833509	−	0.722240i	0.963047	+	0.269335i	$0.0868038\pi$
$734$	11.3918	−	3.34494i	0.420479	−	0.123464i
$735$	11.7014	−	7.59197i	0.431613	−	0.280034i
$736$	21.6742	+	1.53313i	0.798923	+	0.0565120i
$737$			53.4887i			1.97028i
$738$	−0.604916	+	4.48307i	−0.0222673	+	0.165024i
$739$	3.35207	+	3.86850i	0.123308	+	0.142305i	0.814047	−	0.580799i	$-0.197260\pi$
$739$	3.35207	+	3.86850i	0.123308	+	0.142305i	−0.690739	+	0.723104i	$0.742715\pi$
$740$	−2.99517	−	4.66057i	−0.110105	−	0.171326i
$741$	−15.7280	+	13.7483i	−0.577783	+	0.505057i
$742$	−2.26915	−	1.45829i	−0.0833031	−	0.0535356i
$743$	−12.0053	+	26.2880i	−0.440433	+	0.964413i	0.551086	+	0.834449i	$0.314214\pi$
$743$	−12.0053	+	26.2880i	−0.440433	+	0.964413i	−0.991519	+	0.129965i	$0.958514\pi$
$744$	−42.8220	−	5.96738i	−1.56993	−	0.218775i
$745$	−4.56268	+	31.7341i	−0.167164	+	1.16265i
$746$	1.43456	+	3.14125i	0.0525230	+	0.115009i
$747$	29.3279	−	34.4456i	1.07305	−	1.26030i
$748$	15.0190	+	4.40997i	0.549148	+	0.161244i
$749$	−23.1851	+	10.5883i	−0.847167	+	0.386888i
$750$	19.8725	−	9.17988i	0.725642	−	0.335202i
$751$	25.7822	+	22.3404i	0.940807	+	0.815214i	0.982945	−	0.183898i	$-0.0588717\pi$
$751$	25.7822	+	22.3404i	0.940807	+	0.815214i	−0.0421386	+	0.999112i	$0.513417\pi$
$752$	−12.6706	−	5.78648i	−0.462050	−	0.211011i
$753$	−20.1596	+	0.0874565i	−0.734656	+	0.00318709i
$754$	−0.952008	−	6.62136i	−0.0346701	−	0.241136i
$755$	1.90602	−	1.22493i	0.0693673	−	0.0445797i
$756$	4.91498	+	4.14810i	0.178756	+	0.150865i
$757$	2.92187	+	9.95098i	0.106197	+	0.361674i	0.995396	−	0.0958464i	$-0.0305557\pi$
$757$	2.92187	+	9.95098i	0.106197	+	0.361674i	−0.889199	+	0.457521i	$0.848738\pi$
$758$	23.1505			0.840862
$759$	32.8488	+	17.7191i	1.19234	+	0.643161i
$760$	15.8682			0.575600
$761$	−7.97071	−	27.1457i	−0.288938	−	0.984033i	−0.968209	−	0.250145i	$-0.919522\pi$
$761$	−7.97071	−	27.1457i	−0.288938	−	0.984033i	0.679271	−	0.733888i	$-0.262296\pi$
$762$	0.663615	−	2.29688i	0.0240402	−	0.0832071i
$763$	9.14205	−	5.87524i	0.330965	−	0.212698i
$764$	0.352387	+	2.45091i	0.0127489	+	0.0886706i
$765$	16.0453	−	10.5095i	0.580117	−	0.379971i
$766$	14.6162	+	6.67498i	0.528104	+	0.241177i
$767$	−17.2529	−	14.9497i	−0.622965	−	0.539803i
$768$	−11.9164	−	25.7965i	−0.429995	−	0.930850i
$769$	−40.0709	+	18.2998i	−1.44500	+	0.659907i	−0.974887	−	0.222701i	$-0.928513\pi$
$769$	−40.0709	+	18.2998i	−1.44500	+	0.659907i	−0.470109	+	0.882609i	$0.655785\pi$
$770$	10.3800	+	3.04784i	0.374069	+	0.109837i
$771$	−1.27080	−	4.25950i	−0.0457667	−	0.153402i
$772$	−7.10671	−	15.5615i	−0.255776	−	0.560072i
$773$	−3.68503	+	25.6300i	−0.132541	+	0.921846i	0.809684	+	0.586866i	$0.199639\pi$
$773$	−3.68503	+	25.6300i	−0.132541	+	0.921846i	−0.942225	+	0.334980i	$0.891271\pi$
$774$	−13.0143	−	27.8551i	−0.467788	−	1.00123i
$775$	−8.20385	+	17.9639i	−0.294691	+	0.645284i
$776$	21.3383	+	13.7133i	0.766000	+	0.492278i
$777$	6.32408	+	7.23472i	0.226875	+	0.259544i
$778$	−14.9100	−	23.2004i	−0.534550	−	0.831776i
$779$	3.01406	+	3.47841i	0.107990	+	0.124627i
$780$	−5.93249	+	6.90677i	−0.212417	+	0.247302i
$781$			31.7892i			1.13751i
$782$	−4.27900	+	19.7446i	−0.153017	+	0.706065i
$783$	−8.69028	+	1.36514i	−0.310565	+	0.0487860i
$784$	7.10207	−	2.08535i	0.253645	−	0.0744770i
$785$	14.0318	−	12.1586i	0.500816	−	0.433960i
$786$	−6.26423	+	13.8757i	−0.223438	+	0.494931i
$787$	24.6361	−	3.54214i	0.878182	−	0.126264i	0.311546	−	0.950231i	$-0.399153\pi$
$787$	24.6361	−	3.54214i	0.878182	−	0.126264i	0.566637	+	0.823968i	$0.308244\pi$
$788$	−6.42217	+	9.99310i	−0.228780	+	0.355989i
$789$	−5.31407	−	35.8553i	−0.189186	−	1.27648i
$790$	4.18710	−	4.83217i	0.148970	−	0.171921i
$791$	19.6772	+	2.82916i	0.699642	+	0.100593i
$792$	−0.356579	−	41.0966i	−0.0126705	−	1.46031i
$793$	2.32684	−	7.92449i	0.0826285	−	0.281407i
$794$	−0.291000	+	0.991056i	−0.0103272	+	0.0351712i
$795$	−4.23610	−	2.69648i	−0.150239	−	0.0956343i
$796$	−12.7064	−	1.82691i	−0.450367	−	0.0647530i
$797$	−12.1916	+	14.0699i	−0.431849	+	0.498380i	−0.929410	−	0.369049i	$-0.879684\pi$
$797$	−12.1916	+	14.0699i	−0.431849	+	0.498380i	0.497561	+	0.867429i	$0.334229\pi$
$798$	−8.29629	+	1.22958i	−0.293685	+	0.0435268i
$799$	−20.2427	+	31.4982i	−0.716134	+	1.11433i
$800$	−10.8174	+	1.55531i	−0.382453	+	0.0549884i
$801$	−0.206007	−	1.34958i	−0.00727889	−	0.0476850i
$802$	10.8383	−	9.39148i	0.382715	−	0.331625i
$803$	−42.2463	+	12.4046i	−1.49084	+	0.437750i
$804$	−9.83718	−	15.1619i	−0.346930	−	0.534720i
$805$	2.30737	−	10.6469i	0.0813241	−	0.375254i
$806$			32.3503i			1.13949i
$807$	37.4431	+	32.1613i	1.31806	+	1.13213i
$808$	−14.0399	−	16.2029i	−0.493923	−	0.570017i
$809$	20.6545	+	32.1390i	0.726174	+	1.12995i	0.986394	+	0.164399i	$0.0525684\pi$
$809$	20.6545	+	32.1390i	0.726174	+	1.12995i	−0.260220	+	0.965549i	$0.583795\pi$
$810$	−11.7703	−	9.84664i	−0.413565	−	0.345976i
$811$	−6.36974	−	4.09358i	−0.223672	−	0.143745i	0.424006	−	0.905659i	$-0.360623\pi$
$811$	−6.36974	−	4.09358i	−0.223672	−	0.143745i	−0.647678	+	0.761914i	$0.724260\pi$
$812$	−0.870475	+	1.90607i	−0.0305477	+	0.0668901i
$813$	0.00798370	−	0.0572911i	0.000280001	−	0.00200929i
$814$	2.66286	−	18.5206i	0.0933333	−	0.649147i
$815$	−2.61576	−	5.72772i	−0.0916261	−	0.200633i
$816$	9.75356	−	2.90992i	0.341443	−	0.101868i
$817$	−30.0145	−	8.81304i	−1.05007	−	0.308329i
$818$	14.8641	−	6.78823i	0.519712	−	0.237345i
$819$	8.42233	−	13.3588i	0.294300	−	0.466795i
$820$	1.51606	+	1.31367i	0.0529431	+	0.0458755i
$821$	48.0854	+	21.9599i	1.67819	+	0.766405i	0.999488	+	0.0319923i	$0.0101852\pi$
$821$	48.0854	+	21.9599i	1.67819	+	0.766405i	0.678704	+	0.734412i	$0.262542\pi$
$822$	0.0464021	+	10.6961i	0.00161846	+	0.373070i
$823$	1.34935	+	9.38492i	0.0470353	+	0.327138i	0.999731	+	0.0232106i	$0.00738884\pi$
$823$	1.34935	+	9.38492i	0.0470353	+	0.327138i	−0.952695	+	0.303927i	$0.901702\pi$
$824$	−30.2459	+	19.4379i	−1.05367	+	0.677150i
$825$	−18.0346	−	5.21055i	−0.627883	−	0.181408i
$826$	−2.58218	−	8.79410i	−0.0898456	−	0.305986i
$827$	49.1675			1.70972			0.854860	−	0.518859i	$-0.173643\pi$
$827$	49.1675			1.70972			0.854860	+	0.518859i	$0.173643\pi$
$828$	−12.5701	+	1.01862i	−0.436840	+	0.0353994i
$829$	57.2339			1.98782			0.993908	−	0.110215i	$-0.0351539\pi$
$829$	57.2339			1.98782			0.993908	+	0.110215i	$0.0351539\pi$
$830$	7.24408	+	24.6711i	0.251446	+	0.856346i
$831$	50.5195	+	14.5961i	1.75250	+	0.506334i
$832$	−24.3344	+	15.6388i	−0.843645	+	0.542177i
$833$	−2.83152	−	19.6937i	−0.0981064	−	0.682345i
$834$	−0.0765393	−	17.6431i	−0.00265034	−	0.610929i
$835$	−14.7362	−	6.72980i	−0.509967	−	0.232894i
$836$	−9.62969	−	8.34417i	−0.333050	−	0.288589i
$837$	42.5381	−	0.553646i	1.47033	−	0.0191368i
$838$	24.5305	−	11.2027i	0.847391	−	0.386990i
$839$	−6.50174	−	1.90908i	−0.224465	−	0.0659089i	0.167566	−	0.985861i	$-0.446409\pi$
$839$	−6.50174	−	1.90908i	−0.224465	−	0.0659089i	−0.392031	+	0.919952i	$0.628227\pi$
$840$	−11.4953	+	3.42955i	−0.396624	+	0.118331i
$841$	10.8564	+	23.7722i	0.374359	+	0.819732i
$842$	−4.05317	+	28.1904i	−0.139681	+	0.971505i
$843$	−5.54669	+	39.8031i	−0.191038	+	1.37089i
$844$	−4.11109	+	9.00203i	−0.141509	+	0.309863i
$845$	1.21448	+	0.780497i	0.0417793	+	0.0268499i
$846$	28.8148	+	8.18991i	0.990674	+	0.281575i
$847$	−7.01471	−	10.9151i	−0.241028	−	0.375047i
$848$	−1.74501	−	2.01385i	−0.0599239	−	0.0691559i
$849$	−21.9062	−	18.8160i	−0.751817	−	0.645764i
$850$		−	10.1614i		−	0.348533i
$851$	−18.7953	−	1.32949i	−0.644293	−	0.0455743i
$852$	−5.84640	−	9.01099i	−0.200294	−	0.308711i
$853$	−25.2839	+	7.42402i	−0.865704	+	0.254194i	−0.684287	−	0.729213i	$-0.739886\pi$
$853$	−25.2839	+	7.42402i	−0.865704	+	0.254194i	−0.181417	+	0.983406i	$0.558068\pi$
$854$	2.50596	−	2.17142i	0.0857520	−	0.0743046i
$855$	−15.4347	+	2.35604i	−0.527856	+	0.0805747i
$856$	−54.4747	+	7.83228i	−1.86191	+	0.267702i
$857$	−23.4245	+	36.4493i	−0.800166	+	1.24508i	0.165735	+	0.986170i	$0.447001\pi$
$857$	−23.4245	+	36.4493i	−0.800166	+	1.24508i	−0.965901	+	0.258913i	$0.916636\pi$
$858$	−30.4186	+	4.50831i	−1.03848	+	0.153911i
$859$	−33.6570	+	38.8423i	−1.14836	+	1.32528i	−0.210775	+	0.977535i	$0.567599\pi$
$859$	−33.6570	+	38.8423i	−1.14836	+	1.32528i	−0.937588	+	0.347747i	$0.886947\pi$
$860$	−13.4953	−	1.94033i	−0.460184	−	0.0661645i
$861$	−2.93523	−	1.86841i	−0.100032	−	0.0636754i
$862$	−0.653264	+	2.22481i	−0.0222503	+	0.0757774i
$863$	13.6113	−	46.3557i	0.463333	−	1.57797i	−0.314349	−	0.949308i	$-0.601786\pi$
$863$	13.6113	−	46.3557i	0.463333	−	1.57797i	0.777681	−	0.628659i	$-0.216396\pi$
$864$	12.9845	+	19.6376i	0.441742	+	0.668084i
$865$	3.68906	+	0.530406i	0.125432	+	0.0180344i
$866$	16.3954	−	18.9213i	0.557137	−	0.642971i
$867$	0.305750	+	2.06297i	0.0103838	+	0.0700621i
$868$	5.47861	−	8.52489i	0.185956	−	0.289354i
$869$	−16.6773	+	2.39783i	−0.565738	+	0.0813408i
$870$	2.05725	−	4.55697i	0.0697474	−	0.154496i
$871$	−33.5393	+	29.0620i	−1.13644	+	0.984729i
$872$	22.5140	−	6.61071i	0.762421	−	0.223867i
$873$	−22.7914	−	10.1704i	−0.771373	−	0.344217i
$874$	9.84519	−	13.1731i	0.333019	−	0.445587i
$875$			16.8372i			0.569200i
$876$	9.69379	−	11.2858i	0.327523	−	0.381311i
$877$	−28.6924	−	33.1128i	−0.968873	−	1.11814i	−0.992962	−	0.118429i	$-0.962214\pi$
$877$	−28.6924	−	33.1128i	−0.968873	−	1.11814i	0.0240894	−	0.999710i	$-0.492331\pi$
$878$	−18.2981	−	28.4724i	−0.617531	−	0.960897i
$879$	−8.29805	−	9.49293i	−0.279886	−	0.320189i
$880$	8.99074	+	5.77800i	0.303078	+	0.194776i
$881$	4.94883	−	10.8364i	0.166730	−	0.365089i	−0.807762	−	0.589508i	$-0.799321\pi$
$881$	4.94883	−	10.8364i	0.166730	−	0.365089i	0.974493	+	0.224420i	$0.0720487\pi$
$882$	−14.4219	+	6.73808i	−0.485609	+	0.226883i
$883$	−4.97510	+	34.6026i	−0.167425	+	1.16447i	0.716755	+	0.697325i	$0.245626\pi$
$883$	−4.97510	+	34.6026i	−0.167425	+	1.16447i	−0.884181	+	0.467145i	$0.845283\pi$
$884$	5.39505	+	11.8135i	0.181455	+	0.397331i
$885$	−4.87810	−	16.3505i	−0.163975	−	0.549617i
$886$	26.7280	+	7.84806i	0.897946	+	0.263661i
$887$	12.5334	−	5.72381i	0.420830	−	0.192187i	−0.193733	−	0.981054i	$-0.562060\pi$
$887$	12.5334	−	5.72381i	0.420830	−	0.192187i	0.614563	+	0.788868i	$0.289332\pi$
$888$	8.70086	+	18.8356i	0.291982	+	0.632080i
$889$	1.38977	+	1.20424i	0.0466112	+	0.0403889i
$890$	0.705818	+	0.322336i	0.0236591	+	0.0108047i
$891$	6.44867	+	39.9210i	0.216039	+	1.33740i
$892$	1.43026	+	9.94769i	0.0478887	+	0.333073i
$893$	25.6402	−	16.4780i	0.858016	−	0.551414i
$894$	10.1556	−	35.1503i	0.339655	−	1.17560i
$895$	−2.18274	−	7.43374i	−0.0729611	−	0.248483i
$896$	1.18182			0.0394819
$897$	6.73724	+	30.2247i	0.224950	+	1.00917i
$898$	40.3731			1.34727
$899$	3.90495	+	13.2991i	0.130238	+	0.443548i
$900$	6.07036	−	1.83978i	0.202345	−	0.0613259i
$901$	−6.02563	+	3.87244i	−0.200743	+	0.129010i
$902$	0.964218	+	6.70628i	0.0321049	+	0.223295i
$903$	23.6478	−	0.102589i	0.786951	−	0.00341396i
$904$	39.0452	+	17.8313i	1.29862	+	0.593061i
$905$	−21.1995	−	18.3695i	−0.704696	−	0.610623i
$906$	−2.34731	+	1.08431i	−0.0779841	+	0.0360238i
$907$	−10.2997	+	4.70372i	−0.341997	+	0.156185i	−0.579007	−	0.815322i	$-0.696560\pi$
$907$	−10.2997	+	4.70372i	−0.341997	+	0.156185i	0.237011	+	0.971507i	$0.423832\pi$
$908$	−0.396224	−	0.116342i	−0.0131492	−	0.00386094i
$909$	16.0621	+	13.6757i	0.532746	+	0.453595i
$910$	3.72866	+	8.16462i	0.123604	+	0.270655i
$911$	−1.37642	+	9.57320i	−0.0456028	+	0.317174i	0.954233	+	0.299064i	$0.0966743\pi$
$911$	−1.37642	+	9.57320i	−0.0456028	+	0.317174i	−0.999836	+	0.0181108i	$0.994235\pi$
$912$	−8.20613	−	1.14355i	−0.271732	−	0.0378667i
$913$	28.1470	−	61.6334i	0.931530	−	2.03977i
$914$	−3.63136	−	2.33374i	−0.120115	−	0.0771931i
$915$	4.64763	−	4.06263i	0.153646	−	0.134306i
$916$	−0.535107	−	0.832642i	−0.0176804	−	0.0275113i
$917$	−7.66832	−	8.84971i	−0.253230	−	0.292243i
$918$	−19.7912	+	9.35152i	−0.653207	+	0.308646i
$919$		−	48.2925i		−	1.59302i	−0.604623	−	0.796512i	$-0.706676\pi$
$919$		−	48.2925i		−	1.59302i	0.604623	−	0.796512i	$-0.293324\pi$
$920$	11.2570	−	20.6540i	0.371132	−	0.680943i
$921$	−1.05075	+	0.681733i	−0.0346233	+	0.0224639i
$922$	−21.6119	+	6.34581i	−0.711749	+	0.208988i
$923$	−19.9330	+	17.2721i	−0.656103	+	0.568516i
$924$	8.77935	+	3.96346i	0.288820	+	0.130388i
$925$	9.38053	−	1.34872i	0.308430	−	0.0443455i
$926$	−7.53589	+	11.7261i	−0.247645	+	0.385343i
$927$	26.5336	−	23.3976i	0.871478	−	0.768479i
$928$	−5.02294	+	5.79678i	−0.164886	+	0.190289i
$929$	12.3923	+	1.78174i	0.406577	+	0.0584569i	0.342570	−	0.939492i	$-0.388703\pi$
$929$	12.3923	+	1.78174i	0.406577	+	0.0584569i	0.0640075	+	0.997949i	$0.479612\pi$
$930$	−12.9839	+	20.3974i	−0.425759	+	0.668857i
$931$	−4.56292	+	15.5399i	−0.149544	+	0.509298i
$932$	−0.837839	+	2.85342i	−0.0274443	+	0.0934668i
$933$	1.87040	−	2.93835i	0.0612341	−	0.0961972i
$934$	13.2099	+	1.89929i	0.432240	+	0.0621468i
$935$	18.8124	−	21.7107i	0.615231	−	0.710015i
$936$	25.5753	−	22.5526i	0.835956	−	0.737155i
$937$	9.87548	−	15.3665i	0.322618	−	0.502003i	−0.641627	−	0.767017i	$-0.721740\pi$
$937$	9.87548	−	15.3665i	0.322618	−	0.502003i	0.964245	+	0.265014i	$0.0853765\pi$
$938$	−17.6360	+	2.53567i	−0.575835	+	0.0827926i
$939$	−21.5858	−	9.74494i	−0.704425	−	0.318014i
$940$	10.0394	−	8.69919i	0.327449	−	0.283736i
$941$	10.7847	−	3.16668i	0.351572	−	0.103231i	−0.101178	−	0.994868i	$-0.532261\pi$
$941$	10.7847	−	3.16668i	0.351572	−	0.103231i	0.452750	+	0.891638i	$0.350443\pi$
$942$	−17.7752	+	11.5327i	−0.579146	+	0.375755i
$943$	6.66568	−	1.45549i	0.217064	−	0.0473973i
$944$		−	9.05446i		−	0.294698i
$945$	10.6720	−	5.04263i	0.347161	−	0.164037i
$946$	−30.1550	−	34.8007i	−0.980424	−	1.13147i
$947$	−13.4195	−	20.8811i	−0.436075	−	0.678546i	0.551768	−	0.833997i	$-0.313953\pi$
$947$	−13.4195	−	20.8811i	−0.436075	−	0.678546i	−0.987844	+	0.155451i	$0.950317\pi$
$948$	4.28636	−	3.74683i	0.139214	−	0.121691i
$949$	−30.7318	−	19.7501i	−0.997597	−	0.641117i
$950$	−3.43614	+	7.52410i	−0.111483	+	0.244114i
$951$	14.6188	+	2.03718i	0.474047	+	0.0660600i
$952$	−2.43516	+	16.9369i	−0.0789239	+	0.548927i
$953$	1.10582	+	2.42141i	0.0358210	+	0.0784370i	0.926697	−	0.375810i	$-0.122636\pi$
$953$	1.10582	+	2.42141i	0.0358210	+	0.0784370i	−0.890876	+	0.454247i	$0.849908\pi$
$954$	4.36332	+	3.71505i	0.141268	+	0.120279i
$955$	4.36022	+	1.28028i	0.141093	+	0.0414288i
$956$	2.31821	−	1.05869i	0.0749762	−	0.0342405i
$957$	−11.9608	+	5.52513i	−0.386636	+	0.178602i
$958$	8.99348	+	7.79289i	0.290566	+	0.251777i
$959$	−7.48363	−	3.41766i	−0.241659	−	0.110362i
$960$	−21.6199	+	0.0937918i	−0.697780	+	0.00302712i
$961$	−5.12755	−	35.6629i	−0.165405	−	1.15042i
$962$	13.0599	−	8.39310i	0.421069	−	0.270604i
$963$	51.8236	−	15.7065i	1.66999	−	0.506134i
$964$	−0.551481	−	1.87817i	−0.0177620	−	0.0604918i
$965$	−31.3967			−1.01069
$966$	−4.28500	+	11.6707i	−0.137868	+	0.375498i
$967$	1.99729			0.0642286			0.0321143	−	0.999484i	$-0.489776\pi$
$967$	1.99729			0.0642286			0.0321143	+	0.999484i	$0.489776\pi$
$968$	−7.89281	−	26.8805i	−0.253685	−	0.863971i
$969$	−6.18173	+	21.3960i	−0.198586	+	0.687338i
$970$	11.9333	−	7.66904i	0.383154	−	0.246238i
$971$	−3.09698	−	21.5400i	−0.0993869	−	0.691251i	−0.977211	−	0.212269i	$-0.931915\pi$
$971$	−3.09698	−	21.5400i	−0.0993869	−	0.691251i	0.877824	−	0.478983i	$-0.158994\pi$
$972$	−9.16986	−	10.1300i	−0.294123	−	0.324921i
$973$	12.3441	+	5.63736i	0.395734	+	0.180726i
$974$	−6.54079	−	5.66763i	−0.209580	−	0.181603i
$975$	−6.53152	−	14.1394i	−0.209176	−	0.452822i
$976$	2.97971	−	1.36079i	0.0953782	−	0.0435578i
$977$	1.03752	+	0.304644i	0.0331933	+	0.00974644i	0.298287	−	0.954476i	$-0.403585\pi$
$977$	1.03752	+	0.304644i	0.0331933	+	0.00974644i	−0.265094	+	0.964223i	$0.585403\pi$
$978$	2.05441	+	6.88602i	0.0656927	+	0.220191i
$979$	−0.849401	−	1.85993i	−0.0271470	−	0.0594436i
$980$	−1.00460	+	6.98712i	−0.0320906	+	0.223195i
$981$	−20.9174	+	9.77289i	−0.667842	+	0.312024i
$982$	1.65313	−	3.61984i	0.0527533	−	0.115514i
$983$	−33.3880	−	21.4572i	−1.06491	−	0.684378i	−0.113889	−	0.993494i	$-0.536331\pi$
$983$	−33.3880	−	21.4572i	−1.06491	−	0.684378i	−0.951025	+	0.309115i	$0.899967\pi$
$984$	−4.94445	−	5.65643i	−0.157623	−	0.180320i
$985$	11.7863	+	18.3399i	0.375544	+	0.584358i
$986$	−4.67030	−	5.38982i	−0.148733	−	0.171647i
$987$	−15.0130	+	17.4785i	−0.477868	+	0.556348i
$988$		−	10.5718i		−	0.336334i
$989$	−32.7634	+	32.8147i	−1.04182	+	1.04345i
$990$	−20.9889	−	9.36607i	−0.667070	−	0.297673i
$991$	45.2455	−	13.2853i	1.43727	−	0.422020i	0.531959	−	0.846770i	$-0.321456\pi$
$991$	45.2455	−	13.2853i	1.43727	−	0.422020i	0.905311	+	0.424750i	$0.139638\pi$
$992$	28.0334	−	24.2910i	0.890060	−	0.771241i
$993$	−2.22726	+	4.93356i	−0.0706801	+	0.156562i
$994$	−10.4814	+	1.50699i	−0.332449	+	0.0477989i
$995$	−12.7371	+	19.8194i	−0.403794	+	0.628316i
$996$	3.35651	+	22.6472i	0.106355	+	0.717603i
$997$	26.3103	−	30.3637i	0.833256	−	0.961628i	−0.166446	−	0.986051i	$-0.553229\pi$
$997$	26.3103	−	30.3637i	0.833256	−	0.961628i	0.999702	+	0.0244223i	$0.00777463\pi$
$998$	14.3539	+	2.06377i	0.454363	+	0.0653276i
$999$	−11.2598	−	17.0291i	−0.356244	−	0.538778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.g.a.14.3	yes	60
3.2	odd	2	inner	69.2.g.a.14.4	yes	60
23.5	odd	22	inner	69.2.g.a.5.4	yes	60
69.5	even	22	inner	69.2.g.a.5.3	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.g.a.5.3	✓	60	69.5	even	22	inner
69.2.g.a.5.4	yes	60	23.5	odd	22	inner
69.2.g.a.14.3	yes	60	1.1	even	1	trivial
69.2.g.a.14.4	yes	60	3.2	odd	2	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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.g (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.298617 - 1.01700i) q^{2} +(-1.66399 - 0.480761i) q^{3} +(0.737395 - 0.473895i) q^{4} +(-0.228939 - 1.59231i) q^{5} +(0.00796426 + 1.83584i) q^{6} +(-1.28446 - 0.586593i) q^{7} +(-2.30424 - 1.99663i) q^{8} +(2.53774 + 1.59996i) q^{9} +O(q^{10})\)	\(q+(-0.298617 - 1.01700i) q^{2} +(-1.66399 - 0.480761i) q^{3} +(0.737395 - 0.473895i) q^{4} +(-0.228939 - 1.59231i) q^{5} +(0.00796426 + 1.83584i) q^{6} +(-1.28446 - 0.586593i) q^{7} +(-2.30424 - 1.99663i) q^{8} +(2.53774 + 1.59996i) q^{9} +(-1.55101 + 0.708322i) q^{10} +(4.31116 + 1.26587i) q^{11} +(-1.45485 + 0.434047i) q^{12} +(1.54864 + 3.39104i) q^{13} +(-0.213002 + 1.48146i) q^{14} +(-0.384567 + 2.75965i) q^{15} +(-0.614226 + 1.34497i) q^{16} +(3.34349 + 2.14873i) q^{17} +(0.869347 - 3.05865i) q^{18} +(-1.74911 - 2.72167i) q^{19} +(-0.923407 - 1.06567i) q^{20} +(1.85532 + 1.59360i) q^{21} -4.76245i q^{22} +(-4.78334 + 0.345872i) q^{23} +(2.87433 + 4.43017i) q^{24} +(2.31443 - 0.679578i) q^{25} +(2.98623 - 2.58758i) q^{26} +(-3.45357 - 3.88237i) q^{27} +(-1.22514 + 0.176148i) q^{28} +(0.915281 - 1.42420i) q^{29} +(2.92140 - 0.432978i) q^{30} +(-5.36145 + 6.18744i) q^{31} +(-4.48457 - 0.644784i) q^{32} +(-6.56515 - 4.17904i) q^{33} +(1.18683 - 4.04197i) q^{34} +(-0.639974 + 2.17955i) q^{35} +(2.62953 - 0.0228154i) q^{36} +(3.88889 + 0.559137i) q^{37} +(-2.24562 + 2.59158i) q^{38} +(-0.946638 - 6.38718i) q^{39} +(-2.65172 + 4.12616i) q^{40} +(-1.40816 + 0.202463i) q^{41} +(1.06666 - 2.36273i) q^{42} +(7.30732 - 6.33183i) q^{43} +(3.77892 - 1.10959i) q^{44} +(1.96665 - 4.40716i) q^{45} +(1.78014 + 4.76136i) q^{46} +9.42076i q^{47} +(1.66867 - 1.94272i) q^{48} +(-3.27828 - 3.78334i) q^{49} +(-1.38226 - 2.15084i) q^{50} +(-4.53051 - 5.18288i) q^{51} +(2.74895 + 1.76665i) q^{52} +(-0.748661 + 1.63934i) q^{53} +(-2.91707 + 4.67162i) q^{54} +(1.02866 - 7.15451i) q^{55} +(1.78849 + 3.91624i) q^{56} +(1.60203 + 5.36974i) q^{57} +(-1.72173 - 0.505546i) q^{58} +(-5.57035 + 2.54389i) q^{59} +(1.02421 + 2.21720i) q^{60} +(-1.67433 - 1.45081i) q^{61} +(7.89364 + 3.60490i) q^{62} +(-2.32109 - 3.54371i) q^{63} +(1.10428 + 7.68041i) q^{64} +(5.04504 - 3.24225i) q^{65} +(-2.28960 + 7.92468i) q^{66} +(3.35387 + 11.4222i) q^{67} +3.48374 q^{68} +(8.12573 + 1.72412i) q^{69} +2.40771 q^{70} +(1.99326 + 6.78844i) q^{71} +(-2.65301 - 8.75362i) q^{72} +(-8.24368 + 5.29789i) q^{73} +(-0.592648 - 4.12196i) q^{74} +(-4.17791 + 0.0181246i) q^{75} +(-2.57957 - 1.17805i) q^{76} +(-4.79496 - 4.15486i) q^{77} +(-6.21307 + 2.87005i) q^{78} +(-3.41100 + 1.55775i) q^{79} +(2.28222 + 0.670121i) q^{80} +(3.88023 + 8.12058i) q^{81} +(0.626405 + 1.37163i) q^{82} +(2.14609 - 14.9264i) q^{83} +(2.12331 + 0.295889i) q^{84} +(2.65598 - 5.81579i) q^{85} +(-8.62155 - 5.54073i) q^{86} +(-2.20772 + 1.92983i) q^{87} +(-7.40645 - 11.5247i) q^{88} +(-0.298008 - 0.343919i) q^{89} +(-5.06934 - 0.684024i) q^{90} -5.26407i q^{91} +(-3.36331 + 2.52185i) q^{92} +(11.8961 - 7.71828i) q^{93} +(9.58089 - 2.81320i) q^{94} +(-3.93330 + 3.40822i) q^{95} +(7.15230 + 3.22892i) q^{96} +(-8.23456 + 1.18395i) q^{97} +(-2.86869 + 4.46377i) q^{98} +(8.91524 + 10.1102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 11 q^{3} - 10 q^{4} - 14 q^{6} - 22 q^{7} - 11 q^{9}+O(q^{10}) \) 60 * q - 11 * q^3 - 10 * q^4 - 14 * q^6 - 22 * q^7 - 11 * q^9	\( 60 q - 11 q^{3} - 10 q^{4} - 14 q^{6} - 22 q^{7} - 11 q^{9} - 22 q^{10} + 4 q^{12} - 22 q^{13} - 46 q^{16} + 12 q^{18} - 22 q^{19} + 22 q^{21} + 50 q^{24} + 8 q^{25} + 10 q^{27} - 22 q^{28} + 33 q^{30} - 22 q^{31} + 22 q^{36} + 22 q^{37} + 13 q^{39} + 132 q^{40} - 11 q^{42} + 22 q^{43} + 66 q^{46} - 58 q^{48} + 68 q^{49} - 11 q^{51} + 94 q^{52} - 33 q^{54} - 44 q^{57} - 8 q^{58} - 121 q^{60} - 66 q^{61} - 66 q^{63} - 20 q^{64} - 66 q^{66} - 44 q^{67} - 66 q^{69} - 132 q^{70} - 101 q^{72} - 44 q^{73} - 44 q^{75} - 110 q^{76} + 84 q^{78} - 66 q^{79} + 77 q^{81} - 132 q^{82} + 77 q^{84} - 44 q^{85} + 73 q^{87} + 66 q^{88} + 176 q^{90} + 116 q^{93} + 100 q^{94} + 85 q^{96} + 44 q^{97} + 121 q^{99}+O(q^{100}) \) 60 * q - 11 * q^3 - 10 * q^4 - 14 * q^6 - 22 * q^7 - 11 * q^9 - 22 * q^10 + 4 * q^12 - 22 * q^13 - 46 * q^16 + 12 * q^18 - 22 * q^19 + 22 * q^21 + 50 * q^24 + 8 * q^25 + 10 * q^27 - 22 * q^28 + 33 * q^30 - 22 * q^31 + 22 * q^36 + 22 * q^37 + 13 * q^39 + 132 * q^40 - 11 * q^42 + 22 * q^43 + 66 * q^46 - 58 * q^48 + 68 * q^49 - 11 * q^51 + 94 * q^52 - 33 * q^54 - 44 * q^57 - 8 * q^58 - 121 * q^60 - 66 * q^61 - 66 * q^63 - 20 * q^64 - 66 * q^66 - 44 * q^67 - 66 * q^69 - 132 * q^70 - 101 * q^72 - 44 * q^73 - 44 * q^75 - 110 * q^76 + 84 * q^78 - 66 * q^79 + 77 * q^81 - 132 * q^82 + 77 * q^84 - 44 * q^85 + 73 * q^87 + 66 * q^88 + 176 * q^90 + 116 * q^93 + 100 * q^94 + 85 * q^96 + 44 * q^97 + 121 * q^99

Introduction

L-functions

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