LMFDB - Embedded newform 88.2.o.a.69.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [88,2,Mod(5,88)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(88, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("88.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 88 = 2^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	88.o (of order $10$, degree $4$, 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:	$0.702683537787$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.10
Character	$\chi$	$=$	88.69
Dual form			88.2.o.a.37.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.37413 - 0.334310i) q^{2} +(-1.22337 + 0.397498i) q^{3} +(1.77647 - 0.918772i) q^{4} +(0.929834 - 1.27981i) q^{5} +(-1.54819 + 0.955200i) q^{6} +(-0.577320 + 1.77681i) q^{7} +(2.13395 - 1.85641i) q^{8} +(-1.08841 + 0.790780i) q^{9} +(0.849862 - 2.06948i) q^{10} +(-3.18123 + 0.937955i) q^{11} +(-1.80808 + 1.83015i) q^{12} +(0.189309 + 0.260562i) q^{13} +(-0.199308 + 2.63457i) q^{14} +(-0.628813 + 1.93529i) q^{15} +(2.31171 - 3.26435i) q^{16} +(-3.87722 - 2.81696i) q^{17} +(-1.23126 + 1.45050i) q^{18} +(-3.22055 + 1.04642i) q^{19} +(0.475974 - 3.12785i) q^{20} -2.40318i q^{21} +(-4.05786 + 2.35239i) q^{22} +3.08044 q^{23} +(-1.87270 + 3.11932i) q^{24} +(0.771771 + 2.37527i) q^{25} +(0.347245 + 0.294758i) q^{26} +(3.28546 - 4.52205i) q^{27} +(0.606889 + 3.68688i) q^{28} +(9.90342 + 3.21782i) q^{29} +(-0.217085 + 2.86956i) q^{30} +(2.28197 - 1.65795i) q^{31} +(2.08529 - 5.25847i) q^{32} +(3.51900 - 2.41200i) q^{33} +(-6.26955 - 2.57468i) q^{34} +(1.73716 + 2.39100i) q^{35} +(-1.20699 + 2.40480i) q^{36} +(-3.39741 - 1.10389i) q^{37} +(-4.07563 + 2.51458i) q^{38} +(-0.335169 - 0.243514i) q^{39} +(-0.391621 - 4.45720i) q^{40} +(-1.39036 - 4.27910i) q^{41} +(-0.803409 - 3.30229i) q^{42} +3.61796i q^{43} +(-4.78961 + 4.58908i) q^{44} +2.12826i q^{45} +(4.23293 - 1.02982i) q^{46} +(-3.93270 - 12.1036i) q^{47} +(-1.53052 + 4.91242i) q^{48} +(2.83937 + 2.06292i) q^{49} +(1.85459 + 3.00592i) q^{50} +(5.86302 + 1.90501i) q^{51} +(0.575700 + 0.288949i) q^{52} +(-3.32525 - 4.57681i) q^{53} +(3.00289 - 7.31225i) q^{54} +(-1.75762 + 4.94351i) q^{55} +(2.06651 + 4.86337i) q^{56} +(3.52398 - 2.56032i) q^{57} +(14.6843 + 1.11089i) q^{58} +(5.12075 + 1.66383i) q^{59} +(0.661019 + 4.01572i) q^{60} +(-6.42387 + 8.84170i) q^{61} +(2.58146 - 3.04112i) q^{62} +(-0.776701 - 2.39044i) q^{63} +(1.10750 - 7.92297i) q^{64} +0.509496 q^{65} +(4.02921 - 4.49084i) q^{66} -10.9885i q^{67} +(-9.47592 - 1.44198i) q^{68} +(-3.76852 + 1.22447i) q^{69} +(3.18642 + 2.70479i) q^{70} +(9.00915 + 6.54553i) q^{71} +(-0.854616 + 3.70803i) q^{72} +(-3.89653 + 11.9923i) q^{73} +(-5.03753 - 0.381094i) q^{74} +(-1.88833 - 2.59906i) q^{75} +(-4.75980 + 4.81789i) q^{76} +(0.170022 - 6.19394i) q^{77} +(-0.541975 - 0.222570i) q^{78} +(-4.83788 + 3.51492i) q^{79} +(-2.02823 - 5.99385i) q^{80} +(-0.974626 + 2.99959i) q^{81} +(-3.34109 - 5.41523i) q^{82} +(0.0820804 - 0.112974i) q^{83} +(-2.20798 - 4.26919i) q^{84} +(-7.21034 + 2.34278i) q^{85} +(1.20952 + 4.97155i) q^{86} -13.3946 q^{87} +(-5.04737 + 7.90721i) q^{88} +4.28990 q^{89} +(0.711498 + 2.92450i) q^{90} +(-0.572261 + 0.185939i) q^{91} +(5.47232 - 2.83022i) q^{92} +(-2.13267 + 2.93536i) q^{93} +(-9.45040 - 15.3172i) q^{94} +(-1.65536 + 5.09468i) q^{95} +(-0.460858 + 7.26197i) q^{96} +(-10.0271 + 7.28510i) q^{97} +(4.59132 + 1.88549i) q^{98} +(2.72078 - 3.53654i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} - q^{4} - 7 q^{6} - 10 q^{7} - 5 q^{8} - 20 q^{10} - 6 q^{12} + 2 q^{14} - 18 q^{15} + 15 q^{16} - 6 q^{17} - 20 q^{18} + 8 q^{20} - 35 q^{22} - 8 q^{23} + 25 q^{24} - 4 q^{25} - 10 q^{26}+ \cdots - 144 q^{98}+O(q^{100}) $ 40 * q - 5 * q^2 - q^4 - 7 * q^6 - 10 * q^7 - 5 * q^8 - 20 * q^10 - 6 * q^12 + 2 * q^14 - 18 * q^15 + 15 * q^16 - 6 * q^17 - 20 * q^18 + 8 * q^20 - 35 * q^22 - 8 * q^23 + 25 * q^24 - 4 * q^25 - 10 * q^26 + 32 * q^28 - 28 * q^30 - 6 * q^31 + 20 * q^32 - 10 * q^33 + 10 * q^34 + 18 * q^36 + 12 * q^38 - 34 * q^39 + 10 * q^40 - 14 * q^41 + 40 * q^42 + 26 * q^44 + 18 * q^46 - 6 * q^47 + 18 * q^48 - 4 * q^49 + 61 * q^50 + 20 * q^52 + 108 * q^54 - 2 * q^55 - 32 * q^56 - 26 * q^57 + 4 * q^58 - 46 * q^60 + 48 * q^62 + 60 * q^63 - 49 * q^64 - 36 * q^65 + 50 * q^66 - 42 * q^68 - 8 * q^70 + 22 * q^71 - 101 * q^72 - 6 * q^73 + 54 * q^74 - 134 * q^76 - 12 * q^78 + 74 * q^79 - 44 * q^80 - 4 * q^81 - 31 * q^82 - 28 * q^84 - 15 * q^86 + 68 * q^87 - 73 * q^88 - 16 * q^89 - 84 * q^90 - 4 * q^92 - 100 * q^94 + 66 * q^95 - 30 * q^96 + 10 * q^97 - 144 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$.

$n$	$23$	$45$	$57$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	1.37413	−	0.334310i	0.971658	−	0.236393i
$2$	1.37413	−	0.334310i	0.971658	−	0.236393i
$3$	−1.22337	+	0.397498i	−0.706315	+	0.229495i	−0.640080	−	0.768309i	$-0.721099\pi$
$3$	−1.22337	+	0.397498i	−0.706315	+	0.229495i	−0.0662349	+	0.997804i	$0.521099\pi$
$4$	1.77647	−	0.918772i	0.888237	−	0.459386i
$5$	0.929834	−	1.27981i	0.415835	−	0.572347i	−0.548795	−	0.835957i	$-0.684913\pi$
$5$	0.929834	−	1.27981i	0.415835	−	0.572347i	0.964629	+	0.263610i	$0.0849132\pi$
$6$	−1.54819	+	0.955200i	−0.632045	+	0.389959i
$7$	−0.577320	+	1.77681i	−0.218207	+	0.671571i	0.780704	+	0.624901i	$0.214861\pi$
$7$	−0.577320	+	1.77681i	−0.218207	+	0.671571i	−0.998910	+	0.0466696i	$0.985139\pi$
$8$	2.13395	−	1.85641i	0.754466	−	0.656339i
$9$	−1.08841	+	0.790780i	−0.362805	+	0.263593i
$10$	0.849862	−	2.06948i	0.268750	−	0.654426i
$11$	−3.18123	+	0.937955i	−0.959178	+	0.282804i
$11$	−3.18123	+	0.937955i	−0.959178	+	0.282804i
$12$	−1.80808	+	1.83015i	−0.521947	+	0.528317i
$13$	0.189309	+	0.260562i	0.0525050	+	0.0722669i	0.834462	−	0.551065i	$-0.185778\pi$
$13$	0.189309	+	0.260562i	0.0525050	+	0.0722669i	−0.781957	+	0.623332i	$0.785778\pi$
$14$	−0.199308	+	2.63457i	−0.0532674	+	0.704119i
$15$	−0.628813	+	1.93529i	−0.162359	+	0.499689i
$16$	2.31171	−	3.26435i	0.577929	−	0.816087i
$17$	−3.87722	−	2.81696i	−0.940363	−	0.683214i	0.00814475	−	0.999967i	$-0.497407\pi$
$17$	−3.87722	−	2.81696i	−0.940363	−	0.683214i	−0.948508	+	0.316753i	$0.897407\pi$
$18$	−1.23126	+	1.45050i	−0.290211	+	0.341887i
$19$	−3.22055	+	1.04642i	−0.738845	+	0.240065i	−0.654174	−	0.756344i	$-0.726984\pi$
$19$	−3.22055	+	1.04642i	−0.738845	+	0.240065i	−0.0846703	+	0.996409i	$0.526984\pi$
$20$	0.475974	−	3.12785i	0.106431	−	0.699408i
$21$		−	2.40318i		−	0.524418i
$22$	−4.05786	+	2.35239i	−0.865139	+	0.501532i
$23$	3.08044			0.642316			0.321158	−	0.947026i	$-0.395928\pi$
$23$	3.08044			0.642316			0.321158	+	0.947026i	$0.395928\pi$
$24$	−1.87270	+	3.11932i	−0.382263	+	0.636728i
$25$	0.771771	+	2.37527i	0.154354	+	0.475053i
$26$	0.347245	+	0.294758i	0.0681003	+	0.0578069i
$27$	3.28546	−	4.52205i	0.632287	−	0.870269i
$28$	0.606889	+	3.68688i	0.114691	+	0.696755i
$29$	9.90342	+	3.21782i	1.83902	+	0.597534i	0.998439	+	0.0558456i	$0.0177855\pi$
$29$	9.90342	+	3.21782i	1.83902	+	0.597534i	0.840580	+	0.541688i	$0.182215\pi$
$30$	−0.217085	+	2.86956i	−0.0396341	+	0.523907i
$31$	2.28197	−	1.65795i	0.409854	−	0.297776i	−0.363689	−	0.931520i	$-0.618483\pi$
$31$	2.28197	−	1.65795i	0.409854	−	0.297776i	0.773543	+	0.633744i	$0.218483\pi$
$32$	2.08529	−	5.25847i	0.368631	−	0.929576i
$33$	3.51900	−	2.41200i	0.612579	−	0.419876i
$34$	−6.26955	−	2.57468i	−1.07522	−	0.441555i
$35$	1.73716	+	2.39100i	0.293634	+	0.404152i
$36$	−1.20699	+	2.40480i	−0.201166	+	0.400801i
$37$	−3.39741	−	1.10389i	−0.558531	−	0.181478i	0.0161292	−	0.999870i	$-0.494866\pi$
$37$	−3.39741	−	1.10389i	−0.558531	−	0.181478i	−0.574660	+	0.818392i	$0.694866\pi$
$38$	−4.07563	+	2.51458i	−0.661154	+	0.407919i
$39$	−0.335169	−	0.243514i	−0.0536700	−	0.0389935i
$40$	−0.391621	−	4.45720i	−0.0619207	−	0.704745i
$41$	−1.39036	−	4.27910i	−0.217138	−	0.668283i	−0.998995	−	0.0448246i	$-0.985727\pi$
$41$	−1.39036	−	4.27910i	−0.217138	−	0.668283i	0.781857	−	0.623458i	$-0.214273\pi$
$42$	−0.803409	−	3.30229i	−0.123969	−	0.509554i
$43$			3.61796i			0.551734i	0.961196	+	0.275867i	$0.0889649\pi$
$43$			3.61796i			0.551734i	−0.961196	+	0.275867i	$0.911035\pi$
$44$	−4.78961	+	4.58908i	−0.722060	+	0.691830i
$45$			2.12826i			0.317262i
$46$	4.23293	−	1.02982i	0.624111	−	0.151839i
$47$	−3.93270	−	12.1036i	−0.573643	−	1.76549i	−0.640754	−	0.767746i	$-0.721378\pi$
$47$	−3.93270	−	12.1036i	−0.573643	−	1.76549i	0.0671113	−	0.997745i	$-0.478622\pi$
$48$	−1.53052	+	4.91242i	−0.220911	+	0.709046i
$49$	2.83937	+	2.06292i	0.405624	+	0.294703i
$50$	1.85459	+	3.00592i	0.262279	+	0.425101i
$51$	5.86302	+	1.90501i	0.820987	+	0.266755i
$52$	0.575700	+	0.288949i	0.0798353	+	0.0400701i
$53$	−3.32525	−	4.57681i	−0.456758	−	0.628673i	0.517075	−	0.855940i	$-0.327021\pi$
$53$	−3.32525	−	4.57681i	−0.456758	−	0.628673i	−0.973832	+	0.227267i	$0.927021\pi$
$54$	3.00289	−	7.31225i	0.408641	−	0.995072i
$55$	−1.75762	+	4.94351i	−0.236997	+	0.666582i
$56$	2.06651	+	4.86337i	0.276149	+	0.649895i
$57$	3.52398	−	2.56032i	0.466763	−	0.339123i
$58$	14.6843	+	1.11089i	1.92815	+	0.145867i
$59$	5.12075	+	1.66383i	0.666665	+	0.216613i	0.622748	−	0.782423i	$-0.286016\pi$
$59$	5.12075	+	1.66383i	0.666665	+	0.216613i	0.0439173	+	0.999035i	$0.486016\pi$
$60$	0.661019	+	4.01572i	0.0853372	+	0.518428i
$61$	−6.42387	+	8.84170i	−0.822492	+	1.13206i	0.166782	+	0.985994i	$0.446662\pi$
$61$	−6.42387	+	8.84170i	−0.822492	+	1.13206i	−0.989274	+	0.146070i	$0.953338\pi$
$62$	2.58146	−	3.04112i	0.327845	−	0.386223i
$63$	−0.776701	−	2.39044i	−0.0978551	−	0.301167i
$64$	1.10750	−	7.92297i	0.138438	−	0.990371i
$65$	0.509496			0.0631951
$66$	4.02921	−	4.49084i	0.495961	−	0.552785i
$67$		−	10.9885i		−	1.34246i	−0.741249	−	0.671230i	$-0.765766\pi$
$67$		−	10.9885i		−	1.34246i	0.741249	−	0.671230i	$-0.234234\pi$
$68$	−9.47592	−	1.44198i	−1.14912	−	0.174866i
$69$	−3.76852	+	1.22447i	−0.453677	+	0.147409i
$70$	3.18642	+	2.70479i	0.380850	+	0.323285i
$71$	9.00915	+	6.54553i	1.06919	+	0.776812i	0.975766	−	0.218815i	$-0.0702191\pi$
$71$	9.00915	+	6.54553i	1.06919	+	0.776812i	0.0934231	+	0.995626i	$0.470219\pi$
$72$	−0.854616	+	3.70803i	−0.100717	+	0.436995i
$73$	−3.89653	+	11.9923i	−0.456054	+	1.40359i	0.413838	+	0.910350i	$0.364188\pi$
$73$	−3.89653	+	11.9923i	−0.456054	+	1.40359i	−0.869893	+	0.493241i	$0.835812\pi$
$74$	−5.03753	−	0.381094i	−0.585601	−	0.0443013i
$75$	−1.88833	−	2.59906i	−0.218045	−	0.300113i
$76$	−4.75980	+	4.81789i	−0.545986	+	0.552650i
$77$	0.170022	−	6.19394i	0.0193758	−	0.705866i
$78$	−0.541975	−	0.222570i	−0.0613666	−	0.0252011i
$79$	−4.83788	+	3.51492i	−0.544304	+	0.395460i	−0.825681	−	0.564138i	$-0.809209\pi$
$79$	−4.83788	+	3.51492i	−0.544304	+	0.395460i	0.281377	+	0.959597i	$0.409209\pi$
$80$	−2.02823	−	5.99385i	−0.226763	−	0.670133i
$81$	−0.974626	+	2.99959i	−0.108292	+	0.333288i
$82$	−3.34109	−	5.41523i	−0.368962	−	0.598012i
$83$	0.0820804	−	0.112974i	0.00900949	−	0.0124005i	−0.804488	−	0.593968i	$-0.797560\pi$
$83$	0.0820804	−	0.112974i	0.00900949	−	0.0124005i	0.813498	+	0.581568i	$0.197560\pi$
$84$	−2.20798	−	4.26919i	−0.240910	−	0.465807i
$85$	−7.21034	+	2.34278i	−0.782071	+	0.254110i
$86$	1.20952	+	4.97155i	0.130426	+	0.536096i
$87$	−13.3946			−1.43606
$88$	−5.04737	+	7.90721i	−0.538052	+	0.842912i
$89$	4.28990			0.454729			0.227364	−	0.973810i	$-0.426989\pi$
$89$	4.28990			0.454729			0.227364	+	0.973810i	$0.426989\pi$
$90$	0.711498	+	2.92450i	0.0749984	+	0.308270i
$91$	−0.572261	+	0.185939i	−0.0599893	+	0.0194917i
$92$	5.47232	−	2.83022i	0.570528	−	0.295071i
$93$	−2.13267	+	2.93536i	−0.221147	+	0.304383i
$94$	−9.45040	−	15.3172i	−0.974734	−	1.57985i
$95$	−1.65536	+	5.09468i	−0.169836	+	0.522703i
$96$	−0.460858	+	7.26197i	−0.0470362	+	0.741172i
$97$	−10.0271	+	7.28510i	−1.01810	+	0.739690i	−0.965892	−	0.258947i	$-0.916625\pi$
$97$	−10.0271	+	7.28510i	−1.01810	+	0.739690i	−0.0522041	+	0.998636i	$0.516625\pi$
$98$	4.59132	+	1.88549i	0.463793	+	0.190464i
$99$	2.72078	−	3.53654i	0.273449	−	0.355436i
$100$	3.55336	+	3.51051i	0.355336	+	0.351051i
$101$	−9.02999	−	12.4287i	−0.898518	−	1.23670i	−0.970938	−	0.239330i	$-0.923072\pi$
$101$	−9.02999	−	12.4287i	−0.898518	−	1.23670i	0.0724206	−	0.997374i	$-0.476928\pi$
$102$	8.69342	+	0.657667i	0.860777	+	0.0651187i
$103$	2.52680	−	7.77671i	0.248973	−	0.766262i	−0.745984	−	0.665964i	$-0.768020\pi$
$103$	2.52680	−	7.77671i	0.248973	−	0.766262i	0.994957	−	0.100298i	$-0.0319795\pi$
$104$	0.887687	+	0.204592i	0.0870448	+	0.0200619i
$105$	−3.07561	−	2.23456i	−0.300149	−	0.218071i
$106$	−6.09940	−	5.17747i	−0.592426	−	0.502881i
$107$	−4.78604	+	1.55508i	−0.462684	+	0.150335i	−0.531077	−	0.847323i	$-0.678213\pi$
$107$	−4.78604	+	1.55508i	−0.462684	+	0.150335i	0.0683937	+	0.997658i	$0.478213\pi$
$108$	1.68180	−	11.0519i	0.161831	−	1.06347i
$109$			10.1839i			0.975439i	0.873000	+	0.487720i	$0.162171\pi$
$109$			10.1839i			0.975439i	−0.873000	+	0.487720i	$0.837829\pi$
$110$	−0.762531	+	7.38062i	−0.0727045	+	0.703714i
$111$	4.59509			0.436147
$112$	4.46553	+	5.99205i	0.421953	+	0.566196i
$113$	2.48818	+	7.65782i	0.234068	+	0.720387i	0.997244	+	0.0741959i	$0.0236390\pi$
$113$	2.48818	+	7.65782i	0.234068	+	0.720387i	−0.763176	+	0.646191i	$0.776361\pi$
$114$	3.98647	−	4.69632i	0.373367	−	0.439851i
$115$	2.86430	−	3.94237i	0.267097	−	0.367628i
$116$	20.5496	−	3.38263i	1.90798	−	0.314069i
$117$	−0.412094	−	0.133898i	−0.0380981	−	0.0123788i
$118$	7.59282	+	0.574405i	0.698976	+	0.0528783i
$119$	7.24360	−	5.26279i	0.664020	−	0.482439i
$120$	2.25083	+	5.29715i	0.205471	+	0.483561i
$121$	9.24048	−	5.96771i	0.840044	−	0.542519i
$122$	−5.87137	+	14.2972i	−0.531569	+	1.29441i
$123$	3.40187	+	4.68227i	0.306736	+	0.422186i
$124$	2.53058	−	5.04191i	0.227253	−	0.452777i
$125$	11.2800	+	3.66510i	1.00892	+	0.327816i
$126$	−1.86644	−	3.02512i	−0.166275	−	0.269499i
$127$	10.5546	+	7.66834i	0.936566	+	0.680455i	0.947592	−	0.319484i	$-0.103510\pi$
$127$	10.5546	+	7.66834i	0.936566	+	0.680455i	−0.0110254	+	0.999939i	$0.503510\pi$
$128$	−1.12687	−	11.2574i	−0.0996025	−	0.995027i
$129$	−1.43813	−	4.42611i	−0.126620	−	0.389698i
$130$	0.700114	−	0.170330i	0.0614040	−	0.0149389i
$131$			11.5519i			1.00930i	0.863325	+	0.504648i	$0.168378\pi$
$131$			11.5519i			1.00930i	−0.863325	+	0.504648i	$0.831622\pi$
$132$	4.03532	−	7.51802i	0.351230	−	0.654359i
$133$		−	6.32642i		−	0.548570i
$134$	−3.67357	−	15.0997i	−0.317348	−	1.30441i
$135$	−2.73242	−	8.40951i	−0.235169	−	0.723776i
$136$	−13.5032	+	1.18643i	−1.15789	+	0.101735i
$137$	−14.5778	−	10.5914i	−1.24547	−	0.904886i	−0.247519	−	0.968883i	$-0.579615\pi$
$137$	−14.5778	−	10.5914i	−1.24547	−	0.904886i	−0.997950	+	0.0639968i	$0.979615\pi$
$138$	−4.76909	+	2.94244i	−0.405972	+	0.250477i
$139$	−6.37674	−	2.07193i	−0.540868	−	0.175739i	0.0258270	−	0.999666i	$-0.491778\pi$
$139$	−6.37674	−	2.07193i	−0.540868	−	0.175739i	−0.566695	+	0.823928i	$0.691778\pi$
$140$	5.28280	+	2.65149i	0.446478	+	0.224092i
$141$	9.62231	+	13.2440i	0.810345	+	1.11534i
$142$	14.5680	+	5.98257i	1.22252	+	0.502046i
$143$	−0.846633	−	0.651345i	−0.0707990	−	0.0544682i
$144$	0.0652769	+	5.38102i	0.00543974	+	0.448419i
$145$	13.3267	−	9.68243i	1.10672	−	0.804082i
$146$	−1.34520	+	17.7816i	−0.111329	+	1.47162i
$147$	−4.29361	−	1.39508i	−0.354131	−	0.115064i
$148$	−7.04963	+	1.16042i	−0.579476	+	0.0953863i
$149$	2.35559	−	3.24219i	0.192977	−	0.265611i	−0.701553	−	0.712617i	$-0.747510\pi$
$149$	2.35559	−	3.24219i	0.192977	−	0.265611i	0.894531	+	0.447006i	$0.147510\pi$
$150$	−3.46370	−	2.94016i	−0.282810	−	0.240063i
$151$	−0.721284	−	2.21989i	−0.0586973	−	0.180652i	0.917409	−	0.397946i	$-0.130277\pi$
$151$	−0.721284	−	2.21989i	−0.0586973	−	0.180652i	−0.976106	+	0.217294i	$0.930277\pi$
$152$	−4.92992	+	8.21166i	−0.399869	+	0.666054i
$153$	6.44762			0.521259
$154$	−1.83707	−	8.56813i	−0.148035	−	0.690440i
$155$		−	4.46210i		−	0.358404i
$156$	−0.819153	−	0.124653i	−0.0655847	−	0.00998022i
$157$	7.55694	−	2.45540i	0.603109	−	0.195962i	0.00848265	−	0.999964i	$-0.497300\pi$
$157$	7.55694	−	2.45540i	0.603109	−	0.195962i	0.594627	+	0.804002i	$0.297300\pi$
$158$	−5.47280	+	6.44732i	−0.435393	+	0.512921i
$159$	5.88729	+	4.27737i	0.466892	+	0.339217i
$160$	−4.79086	−	7.55828i	−0.378750	−	0.597535i
$161$	−1.77840	+	5.47335i	−0.140158	+	0.431361i
$162$	−0.336470	+	4.44766i	−0.0264356	+	0.349441i
$163$	3.30058	+	4.54286i	0.258522	+	0.355825i	0.918473	−	0.395484i	$-0.129423\pi$
$163$	3.30058	+	4.54286i	0.258522	+	0.355825i	−0.659951	+	0.751308i	$0.729423\pi$
$164$	−6.40146	−	6.32428i	−0.499870	−	0.493843i
$165$	0.185187	−	6.74640i	0.0144168	−	0.525207i
$166$	0.0750208	−	0.182681i	0.00582275	−	0.0141788i
$167$	−14.5842	+	10.5961i	−1.12856	+	0.819948i	−0.985485	−	0.169764i	$-0.945700\pi$
$167$	−14.5842	+	10.5961i	−1.12856	+	0.819948i	−0.143077	+	0.989712i	$0.545700\pi$
$168$	−4.46129	−	5.12828i	−0.344196	−	0.395655i
$169$	3.98517	−	12.2651i	0.306551	−	0.943468i
$170$	−9.12474	+	5.62978i	−0.699835	+	0.431784i
$171$	2.67781	−	3.68568i	0.204777	−	0.281851i
$172$	3.32408	+	6.42721i	0.253459	+	0.490070i
$173$	14.3308	−	4.65634i	1.08955	−	0.354015i	0.291476	−	0.956578i	$-0.405854\pi$
$173$	14.3308	−	4.65634i	1.08955	−	0.354015i	0.798071	+	0.602563i	$0.205854\pi$
$174$	−18.4060	+	4.47797i	−1.39536	+	0.339474i
$175$	−4.66595			−0.352713
$176$	−4.29229	+	12.5529i	−0.323543	+	0.946213i
$177$	−6.92596			−0.520587
$178$	5.89489	−	1.43416i	0.441841	−	0.107495i
$179$	−21.1962	+	6.88705i	−1.58428	+	0.514762i	−0.963154	−	0.268952i	$-0.913323\pi$
$179$	−21.1962	+	6.88705i	−1.58428	+	0.514762i	−0.621122	+	0.783714i	$0.713323\pi$
$180$	1.95538	+	3.78079i	0.145746	+	0.281803i
$181$	6.76629	−	9.31300i	0.502934	−	0.692230i	−0.479773	−	0.877392i	$-0.659281\pi$
$181$	6.76629	−	9.31300i	0.502934	−	0.692230i	0.982708	+	0.185163i	$0.0592811\pi$
$182$	−0.724201	+	0.446817i	−0.0536813	+	0.0331203i
$183$	4.34423	−	13.3702i	0.321135	−	0.988351i
$184$	6.57351	−	5.71855i	0.484605	−	0.421577i
$185$	−4.57179	+	3.32160i	−0.336125	+	0.244209i
$186$	−1.94924	+	4.74655i	−0.142925	+	0.348034i
$187$	14.9765	+	5.32476i	1.09519	+	0.389385i
$188$	−18.1068	−	17.8885i	−1.32057	−	1.30465i
$189$	6.13806	+	8.44831i	0.446478	+	0.614524i
$190$	−0.571480	+	7.55416i	−0.0414595	+	0.548036i
$191$	−3.33654	+	10.2688i	−0.241423	+	0.743025i	0.754781	+	0.655977i	$0.227743\pi$
$191$	−3.33654	+	10.2688i	−0.241423	+	0.743025i	−0.996204	+	0.0870476i	$0.972257\pi$
$192$	1.79447	+	10.1330i	0.129505	+	0.731284i
$193$	−7.32690	−	5.32330i	−0.527402	−	0.383180i	0.291983	−	0.956423i	$-0.405685\pi$
$193$	−7.32690	−	5.32330i	−0.527402	−	0.383180i	−0.819385	+	0.573244i	$0.805685\pi$
$194$	−11.3430	+	13.3628i	−0.814383	+	0.959396i
$195$	−0.623303	+	0.202523i	−0.0446356	+	0.0145030i
$196$	6.93941	+	1.05599i	0.495672	+	0.0754279i
$197$		−	8.74114i		−	0.622780i	−0.950282	−	0.311390i	$-0.899205\pi$
$197$		−	8.74114i		−	0.622780i	0.950282	−	0.311390i	$-0.100795\pi$
$198$	2.55641	−	5.76925i	0.181676	−	0.410003i
$199$	2.55580			0.181176			0.0905878	−	0.995888i	$-0.471125\pi$
$199$	2.55580			0.181176			0.0905878	+	0.995888i	$0.471125\pi$
$200$	6.05638	+	3.63598i	0.428251	+	0.257103i
$201$	4.36791	+	13.4430i	0.308089	+	0.948200i
$202$	−16.5634	−	14.0599i	−1.16540	−	0.989249i
$203$	−11.4349	+	15.7388i	−0.802572	+	1.10465i
$204$	12.1658	−	2.00258i	0.851774	−	0.140209i
$205$	−6.76923	−	2.19946i	−0.472783	−	0.153617i
$206$	0.872329	−	11.5310i	0.0607780	−	0.803399i
$207$	−3.35279	+	2.43595i	−0.233035	+	0.169310i
$208$	1.28819	−	0.0156270i	0.0893202	−	0.00108354i
$209$	9.26382	−	6.34964i	0.640792	−	0.439214i
$210$	−4.97333	−	2.04237i	−0.343192	−	0.140937i
$211$	−1.94891	−	2.68244i	−0.134168	−	0.184667i	0.736647	−	0.676278i	$-0.236408\pi$
$211$	−1.94891	−	2.68244i	−0.134168	−	0.184667i	−0.870815	+	0.491611i	$0.836408\pi$
$212$	−10.1123	−	5.07544i	−0.694513	−	0.348582i
$213$	−13.6234	−	4.42651i	−0.933459	−	0.303299i
$214$	−6.05676	+	3.73690i	−0.414032	+	0.255449i
$215$	4.63029	+	3.36410i	0.315783	+	0.229430i
$216$	−1.38375	−	15.7490i	−0.0941521	−	1.07158i
$217$	1.62843	+	5.01179i	0.110545	+	0.340222i
$218$	3.40458	+	13.9940i	0.230587	+	0.947793i
$219$		−	16.2199i		−	1.09604i
$220$	1.41960	+	10.3969i	0.0957093	+	0.700956i
$221$		−	1.54353i		−	0.103829i
$222$	6.31426	−	1.53619i	0.423785	−	0.103102i
$223$	−4.60594	−	14.1756i	−0.308436	−	0.949270i	−0.978372	−	0.206851i	$-0.933678\pi$
$223$	−4.60594	−	14.1756i	−0.308436	−	0.949270i	0.669936	−	0.742419i	$-0.266322\pi$
$224$	8.13942	+	6.74099i	0.543838	+	0.450402i
$225$	−2.71832	−	1.97497i	−0.181221	−	0.131665i
$226$	5.97917	+	9.69102i	0.397728	+	0.644637i
$227$	1.25796	+	0.408735i	0.0834936	+	0.0271287i	0.350466	−	0.936575i	$-0.386023\pi$
$227$	1.25796	+	0.408735i	0.0834936	+	0.0271287i	−0.266972	+	0.963704i	$0.586023\pi$
$228$	3.90791	−	7.78608i	0.258807	−	0.515646i
$229$	13.8734	+	19.0951i	0.916782	+	1.26184i	0.964797	+	0.262995i	$0.0847103\pi$
$229$	13.8734	+	19.0951i	0.916782	+	1.26184i	−0.0480154	+	0.998847i	$0.515290\pi$
$230$	2.61795	−	6.37489i	0.172622	−	0.420348i
$231$	2.25408	+	7.64509i	0.148308	+	0.503010i
$232$	27.1070	−	11.5181i	1.77966	−	0.756201i
$233$	−1.99893	+	1.45231i	−0.130955	+	0.0951440i	−0.651334	−	0.758791i	$-0.725790\pi$
$233$	−1.99893	+	1.45231i	−0.130955	+	0.0951440i	0.520380	+	0.853935i	$0.325790\pi$
$234$	−0.611035	−	0.0462255i	−0.0399446	−	0.00302185i
$235$	−19.1470	−	6.22125i	−1.24901	−	0.405829i
$236$	10.6256	−	1.74905i	0.691665	−	0.113854i
$237$	4.52135	−	6.22310i	0.293693	−	0.404234i
$238$	8.19426	−	9.65337i	0.531155	−	0.625735i
$239$	4.88858	+	15.0455i	0.316216	+	0.973213i	0.975251	+	0.221101i	$0.0709649\pi$
$239$	4.88858	+	15.0455i	0.316216	+	0.973213i	−0.659035	+	0.752112i	$0.729035\pi$
$240$	4.86382	+	6.52650i	0.313958	+	0.421284i
$241$	−3.22511			−0.207748			−0.103874	−	0.994590i	$-0.533124\pi$
$241$	−3.22511			−0.207748			−0.103874	+	0.994590i	$0.533124\pi$
$242$	10.7026	−	11.2896i	0.687987	−	0.725723i
$243$			12.7117i			0.815453i
$244$	−3.28832	+	21.6091i	−0.210513	+	1.38338i
$245$	5.28028	−	1.71567i	0.337345	−	0.109610i
$246$	6.23994	+	5.29677i	0.397844	+	0.337710i
$247$	−0.882338	−	0.641056i	−0.0561418	−	0.0407894i
$248$	1.79179	−	7.77424i	0.113779	−	0.493665i
$249$	−0.0555080	+	0.170836i	−0.00351767	+	0.0108263i
$250$	16.7255	+	1.26530i	1.05781	+	0.0800247i
$251$	0.203282	+	0.279794i	0.0128311	+	0.0176604i	0.815384	−	0.578920i	$-0.196526\pi$
$251$	0.203282	+	0.279794i	0.0128311	+	0.0176604i	−0.802553	+	0.596580i	$0.796526\pi$
$252$	−3.57606	−	3.53294i	−0.225270	−	0.222554i
$253$	−9.79959	+	2.88931i	−0.616095	+	0.181650i
$254$	17.0670	+	7.00881i	1.07088	+	0.439772i
$255$	7.88968	−	5.73219i	0.494071	−	0.358964i
$256$	−5.31195	−	15.0925i	−0.331997	−	0.943280i
$257$	−0.130366	+	0.401224i	−0.00813199	+	0.0250277i	−0.955040	−	0.296476i	$-0.904188\pi$
$257$	−0.130366	+	0.401224i	−0.00813199	+	0.0250277i	0.946908	+	0.321504i	$0.104188\pi$
$258$	−3.45588	−	5.60128i	−0.215153	−	0.348720i
$259$	3.92279	−	5.39926i	0.243750	−	0.335493i
$260$	0.905105	−	0.468110i	0.0561322	−	0.0290310i
$261$	−13.3236	+	4.32911i	−0.824711	+	0.267965i
$262$	3.86192	+	15.8738i	0.238590	+	0.980689i
$263$	−2.35352			−0.145124			−0.0725621	−	0.997364i	$-0.523118\pi$
$263$	−2.35352			−0.145124			−0.0725621	+	0.997364i	$0.523118\pi$
$264$	3.03171	−	11.6798i	0.186589	−	0.718841i
$265$	−8.94936			−0.549755
$266$	−2.11499	−	8.69333i	−0.129678	−	0.533022i
$267$	−5.24815	+	1.70523i	−0.321182	+	0.104358i
$268$	−10.0959	−	19.5208i	−0.616708	−	1.19242i
$269$	−13.5525	+	18.6534i	−0.826310	+	1.13732i	0.162289	+	0.986743i	$0.448112\pi$
$269$	−13.5525	+	18.6534i	−0.826310	+	1.13732i	−0.988599	+	0.150575i	$0.951888\pi$
$270$	−6.56609	−	10.6423i	−0.399599	−	0.647670i
$271$	1.35239	−	4.16224i	0.0821520	−	0.252838i	−0.901541	−	0.432694i	$-0.857563\pi$
$271$	1.35239	−	4.16224i	0.0821520	−	0.252838i	0.983693	+	0.179856i	$0.0575631\pi$
$272$	−18.1586	+	6.14458i	−1.10103	+	0.372570i
$273$	0.626179	−	0.454945i	0.0378980	−	0.0275345i
$274$	−23.5727	−	9.68048i	−1.42408	−	0.584819i
$275$	−4.68308	−	6.83239i	−0.282400	−	0.412008i
$276$	−5.56967	+	5.63765i	−0.335255	+	0.339347i
$277$	−3.68342	−	5.06979i	−0.221315	−	0.304614i	0.683893	−	0.729582i	$-0.260285\pi$
$277$	−3.68342	−	5.06979i	−0.221315	−	0.304614i	−0.905208	+	0.424968i	$0.860285\pi$
$278$	−9.45514	−	0.715291i	−0.567081	−	0.0429003i
$279$	−1.17266	+	3.60907i	−0.0702052	+	0.216069i
$280$	8.14568	+	1.87740i	0.486798	+	0.112196i
$281$	−9.04898	−	6.57447i	−0.539817	−	0.392200i	0.284200	−	0.958765i	$-0.408272\pi$
$281$	−9.04898	−	6.57447i	−0.539817	−	0.392200i	−0.824017	+	0.566565i	$0.808272\pi$
$282$	17.6499	+	14.9821i	1.05104	+	0.892172i
$283$	30.4152	−	9.88251i	1.80800	−	0.587454i	0.807999	−	0.589184i	$-0.200551\pi$
$283$	30.4152	−	9.88251i	1.80800	−	0.587454i	0.999999	+	0.00172970i	$0.000550581\pi$
$284$	22.0184	+	3.35060i	1.30655	+	0.198822i
$285$		−	6.89069i		−	0.408169i
$286$	−1.38114	−	0.611995i	−0.0816683	−	0.0361880i
$287$	8.40583			0.496180
$288$	1.88863	+	7.37241i	0.111289	+	0.434423i
$289$	1.84424	+	5.67600i	0.108485	+	0.333882i
$290$	15.0757	−	17.7602i	0.885277	−	1.04291i
$291$	9.37104	−	12.8981i	0.549340	−	0.756102i
$292$	4.09610	+	24.8840i	0.239706	+	1.45623i
$293$	−7.28970	−	2.36857i	−0.425869	−	0.138373i	0.0882379	−	0.996099i	$-0.471876\pi$
$293$	−7.28970	−	2.36857i	−0.425869	−	0.138373i	−0.514107	+	0.857726i	$0.671876\pi$
$294$	−6.36637	−	0.481623i	−0.371294	−	0.0280888i
$295$	6.89084	−	5.00649i	0.401200	−	0.291489i
$296$	−9.29917	+	3.95134i	−0.540503	+	0.229667i
$297$	−6.21034	+	17.4673i	−0.360360	+	1.01356i
$298$	2.15299	−	5.24269i	0.124719	−	0.303701i
$299$	0.583156	+	0.802645i	0.0337248	+	0.0464182i
$300$	−5.74250	−	2.88221i	−0.331544	−	0.166405i
$301$	−6.42843	−	2.08872i	−0.370528	−	0.120392i
$302$	−1.73327	−	2.80928i	−0.0997385	−	0.161656i
$303$	15.9874	+	11.6156i	0.918454	+	0.667296i
$304$	−4.02911	+	12.9320i	−0.231085	+	0.741702i
$305$	5.34253	+	16.4426i	0.305913	+	0.941502i
$306$	8.85987	−	2.15551i	0.506485	−	0.123222i
$307$			3.57511i			0.204042i	0.994782	+	0.102021i	$0.0325309\pi$
$307$			3.57511i			0.204042i	−0.994782	+	0.102021i	$0.967469\pi$
$308$	−5.38879	−	11.1596i	−0.307055	−	0.635877i
$309$			10.5182i			0.598360i
$310$	−1.49172	−	6.13150i	−0.0847243	−	0.348246i
$311$	−0.0242025	−	0.0744877i	−0.00137240	−	0.00422381i	0.950368	−	0.311128i	$-0.100707\pi$
$311$	−0.0242025	−	0.0744877i	−0.00137240	−	0.00422381i	−0.951740	+	0.306904i	$0.900707\pi$
$312$	−1.16730	+	0.102562i	−0.0660851	+	0.00580641i
$313$	7.23887	+	5.25935i	0.409165	+	0.297276i	0.773264	−	0.634084i	$-0.218623\pi$
$313$	7.23887	+	5.25935i	0.409165	+	0.297276i	−0.364098	+	0.931360i	$0.618623\pi$
$314$	9.56336	−	5.90040i	0.539692	−	0.332979i
$315$	−3.78150	−	1.22869i	−0.213064	−	0.0692286i
$316$	−5.36494	+	10.6891i	−0.301802	+	0.601307i
$317$	−14.3909	−	19.8074i	−0.808273	−	1.11249i	−0.991588	−	0.129438i	$-0.958683\pi$
$317$	−14.3909	−	19.8074i	−0.808273	−	1.11249i	0.183314	−	0.983054i	$-0.441317\pi$
$318$	9.51987	+	3.90948i	0.533848	+	0.219233i
$319$	−34.5233	−	0.947655i	−1.93293	−	0.0530585i
$320$	−9.11008	−	8.78444i	−0.509269	−	0.491065i
$321$	5.23697	−	3.80488i	0.292299	−	0.212368i
$322$	−0.613957	+	8.11564i	−0.0342145	+	0.452267i
$323$	15.4345	+	5.01497i	0.858798	+	0.279040i
$324$	1.02454	+	6.22415i	0.0569191	+	0.345786i
$325$	−0.472801	+	0.650754i	−0.0262263	+	0.0360974i
$326$	6.05416	+	5.13907i	0.335309	+	0.284627i
$327$	−4.04807	−	12.4587i	−0.223859	−	0.688967i
$328$	−10.9107	−	6.55031i	−0.602444	−	0.361680i
$329$	23.7762			1.31083
$330$	−2.00092	−	9.33235i	−0.110147	−	0.513729i
$331$			24.2083i			1.33061i	0.746572	+	0.665305i	$0.231698\pi$
$331$			24.2083i			1.33061i	−0.746572	+	0.665305i	$0.768302\pi$
$332$	0.0420162	−	0.276108i	0.00230594	−	0.0151534i
$333$	4.57072	−	1.48512i	0.250474	−	0.0813840i
$334$	−16.4983	+	19.4360i	−0.902745	+	1.06349i
$335$	−14.0632	−	10.2175i	−0.768354	−	0.558242i
$336$	−7.84483	−	5.55547i	−0.427971	−	0.303076i
$337$	6.89251	−	21.2130i	0.375459	−	1.15554i	−0.567709	−	0.823229i	$-0.692170\pi$
$337$	6.89251	−	21.2130i	0.375459	−	1.15554i	0.943168	−	0.332315i	$-0.107830\pi$
$338$	1.37580	−	18.1861i	0.0748336	−	0.989194i
$339$	−6.08793	−	8.37932i	−0.330651	−	0.455102i
$340$	−10.6565	+	10.7865i	−0.577929	+	0.584983i
$341$	−5.70439	+	7.41470i	−0.308910	+	0.401529i
$342$	2.44749	−	5.95983i	0.132345	−	0.322271i
$343$	−15.8848	+	11.5409i	−0.857696	+	0.623153i
$344$	6.71641	+	7.72055i	0.362124	+	0.416264i
$345$	−1.93702	+	5.96153i	−0.104286	+	0.320958i
$346$	18.1357	−	11.1893i	0.974980	−	0.601543i
$347$	9.89801	−	13.6234i	0.531353	−	0.731344i	−0.455983	−	0.889988i	$-0.650712\pi$
$347$	9.89801	−	13.6234i	0.531353	−	0.731344i	0.987336	+	0.158644i	$0.0507122\pi$
$348$	−23.7952	+	12.3066i	−1.27556	+	0.659705i
$349$	5.68153	−	1.84604i	0.304126	−	0.0988164i	−0.152979	−	0.988229i	$-0.548887\pi$
$349$	5.68153	−	1.84604i	0.304126	−	0.0988164i	0.457104	+	0.889413i	$0.348887\pi$
$350$	−6.41163	+	1.55988i	−0.342716	+	0.0833789i
$351$	1.80024			0.0960899
$352$	−1.70159	+	18.6843i	−0.0906950	+	0.995879i
$353$	−6.69469			−0.356322			−0.178161	−	0.984001i	$-0.557015\pi$
$353$	−6.69469			−0.356322			−0.178161	+	0.984001i	$0.557015\pi$
$354$	−9.51718	+	2.31542i	−0.505832	+	0.123063i
$355$	16.7540	−	5.44372i	0.889212	−	0.288922i
$356$	7.62090	−	3.94145i	0.403907	−	0.208896i
$357$	−6.76968	+	9.31767i	−0.358290	+	0.493143i
$358$	−26.8239	+	16.5498i	−1.41769	+	0.874684i
$359$	6.21755	−	19.1356i	0.328149	−	1.00994i	−0.641849	−	0.766831i	$-0.721833\pi$
$359$	6.21755	−	19.1356i	0.328149	−	1.00994i	0.969999	−	0.243110i	$-0.0781674\pi$
$360$	3.95091	+	4.54159i	0.208231	+	0.239363i
$361$	−6.09438	+	4.42783i	−0.320757	+	0.233044i
$362$	6.18434	−	15.0593i	0.325042	−	0.791501i
$363$	−8.93240	+	10.9738i	−0.468829	+	0.575975i
$364$	−0.845771	+	0.856094i	−0.0443305	+	0.0448715i
$365$	11.7247	+	16.1376i	0.613698	+	0.844683i
$366$	1.49976	−	19.8247i	0.0783936	−	1.03625i
$367$	2.30509	−	7.09433i	0.120325	−	0.370321i	−0.872696	−	0.488264i	$-0.837630\pi$
$367$	2.30509	−	7.09433i	0.120325	−	0.370321i	0.993020	+	0.117943i	$0.0376302\pi$
$368$	7.12109	−	10.0556i	0.371213	−	0.524186i
$369$	4.89712	+	3.55796i	0.254934	+	0.185220i
$370$	−5.17179	+	6.09271i	−0.268869	+	0.316745i
$371$	10.0519	−	3.26604i	0.521866	−	0.169565i
$372$	−1.09169	+	7.17403i	−0.0566017	+	0.371956i
$373$			1.53907i			0.0796902i	0.999206	+	0.0398451i	$0.0126864\pi$
$373$			1.53907i			0.0796902i	−0.999206	+	0.0398451i	$0.987314\pi$
$374$	22.3598	+	2.31011i	1.15620	+	0.119453i
$375$	−15.2565			−0.787844
$376$	−30.8614	−	18.5278i	−1.59156	−	0.955499i
$377$	1.03637	+	3.18962i	0.0533758	+	0.164274i
$378$	11.2589	+	9.55707i	0.579093	+	0.491563i
$379$	3.14473	−	4.32834i	0.161534	−	0.222332i	−0.720576	−	0.693376i	$-0.756123\pi$
$379$	3.14473	−	4.32834i	0.161534	−	0.222332i	0.882110	+	0.471044i	$0.156123\pi$
$380$	1.74014	+	10.5715i	0.0892676	+	0.542304i
$381$	−15.9603	−	5.18582i	−0.817672	−	0.265678i
$382$	−1.15187	+	15.2261i	−0.0589349	+	0.779036i
$383$	7.76114	−	5.63880i	0.396576	−	0.288129i	−0.371569	−	0.928405i	$-0.621180\pi$
$383$	7.76114	−	5.63880i	0.396576	−	0.288129i	0.768145	+	0.640276i	$0.221180\pi$
$384$	5.85340	+	13.3241i	0.298705	+	0.679944i
$385$	−7.76896	−	5.97694i	−0.395943	−	0.304613i
$386$	−11.8478	−	4.86546i	−0.603035	−	0.247645i
$387$	−2.86101	−	3.93784i	−0.145433	−	0.200172i
$388$	−11.1195	+	22.1544i	−0.564507	+	1.12472i
$389$	10.6847	+	3.47166i	0.541735	+	0.176020i	0.567086	−	0.823658i	$-0.308071\pi$
$389$	10.6847	+	3.47166i	0.541735	+	0.176020i	−0.0253517	+	0.999679i	$0.508071\pi$
$390$	−0.788794	+	0.486670i	−0.0399422	+	0.0246435i
$391$	−11.9435	−	8.67748i	−0.604010	−	0.438839i
$392$	9.88869	−	0.868846i	0.499454	−	0.0438834i
$393$	−4.59186	−	14.1323i	−0.231629	−	0.712880i
$394$	−2.92225	−	12.0115i	−0.147221	−	0.605129i
$395$			9.45984i			0.475976i
$396$	1.58413	−	8.78235i	0.0796054	−	0.441330i
$397$		−	9.83583i		−	0.493646i	−0.969061	−	0.246823i	$-0.920613\pi$
$397$		−	9.83583i		−	0.493646i	0.969061	−	0.246823i	$-0.0793866\pi$
$398$	3.51200	−	0.854429i	0.176041	−	0.0428287i
$399$	2.51474	+	7.73957i	0.125894	+	0.387463i
$400$	9.53781	+	2.97161i	0.476891	+	0.148580i
$401$	−8.69507	−	6.31734i	−0.434211	−	0.315473i	0.349119	−	0.937078i	$-0.386481\pi$
$401$	−8.69507	−	6.31734i	−0.434211	−	0.315473i	−0.783331	+	0.621605i	$0.786481\pi$
$402$	10.4962	+	17.0123i	0.523505	+	0.848495i
$403$	0.863996	+	0.280729i	0.0430387	+	0.0139841i
$404$	−27.4607	−	13.7828i	−1.36622	−	0.685719i
$405$	2.93266	+	4.03645i	0.145725	+	0.200573i
$406$	−10.4514	+	25.4500i	−0.518695	+	1.26306i
$407$	11.8433	+	0.325097i	0.587053	+	0.0161145i
$408$	16.0479	−	6.81895i	0.794488	−	0.337588i
$409$	5.12153	−	3.72101i	0.253243	−	0.183992i	−0.453920	−	0.891043i	$-0.649975\pi$
$409$	5.12153	−	3.72101i	0.253243	−	0.183992i	0.707163	+	0.707051i	$0.249975\pi$
$410$	−10.0371	−	0.759318i	−0.495697	−	0.0375000i
$411$	22.0442	+	7.16260i	1.08736	+	0.353305i
$412$	−2.65622	−	16.1367i	−0.130863	−	0.794997i
$413$	−5.91263	+	8.13804i	−0.290942	+	0.400447i
$414$	−3.79282	+	4.46819i	−0.186407	+	0.219599i
$415$	−0.0682637	−	0.210094i	−0.00335093	−	0.0103131i
$416$	1.76492	−	0.452130i	0.0865325	−	0.0221675i
$417$	8.62471			0.422354
$418$	10.6070	−	11.8222i	0.518803	−	0.578244i
$419$		−	8.63496i		−	0.421846i	−0.977503	−	0.210923i	$-0.932353\pi$
$419$		−	8.63496i		−	0.421846i	0.977503	−	0.210923i	$-0.0676469\pi$
$420$	−7.51680	−	1.14385i	−0.366782	−	0.0558143i
$421$	28.0335	−	9.10864i	1.36627	−	0.443928i	0.468138	−	0.883655i	$-0.344925\pi$
$421$	28.0335	−	9.10864i	1.36627	−	0.443928i	0.898131	+	0.439727i	$0.144925\pi$
$422$	−3.57482	−	3.03449i	−0.174020	−	0.147716i
$423$	13.8517	+	10.0638i	0.673492	+	0.489321i
$424$	−15.5923	−	3.59368i	−0.757231	−	0.174525i
$425$	3.69871	−	11.3835i	0.179414	−	0.552179i
$426$	−20.2001	−	1.52816i	−0.978700	−	0.0740397i
$427$	−12.0014	−	16.5185i	−0.580788	−	0.799386i
$428$	−7.07350	+	7.15983i	−0.341911	+	0.346083i
$429$	1.29466	+	0.460303i	0.0625066	+	0.0222236i
$430$	7.48728	+	3.07477i	0.361069	+	0.148278i
$431$	17.5301	−	12.7363i	0.844394	−	0.613488i	−0.0792005	−	0.996859i	$-0.525237\pi$
$431$	17.5301	−	12.7363i	0.844394	−	0.613488i	0.923595	+	0.383370i	$0.125237\pi$
$432$	−7.16650	−	21.1786i	−0.344798	−	1.01895i
$433$	−3.55844	+	10.9517i	−0.171008	+	0.526307i	−0.999429	−	0.0337985i	$-0.989240\pi$
$433$	−3.55844	+	10.9517i	−0.171008	+	0.526307i	0.828421	+	0.560106i	$0.189240\pi$
$434$	3.91317	+	6.34246i	0.187838	+	0.304448i
$435$	−12.4548	+	17.1426i	−0.597162	+	0.821923i
$436$	9.35667	+	18.0914i	0.448103	+	0.866421i
$437$	−9.92070	+	3.22343i	−0.474572	+	0.154198i
$438$	−5.42248	−	22.2883i	−0.259096	−	1.06497i
$439$	35.9563			1.71610			0.858049	−	0.513567i	$-0.171676\pi$
$439$	35.9563			1.71610			0.858049	+	0.513567i	$0.171676\pi$
$440$	5.42649	+	13.8121i	0.258698	+	0.658464i
$441$	−4.72172			−0.224844
$442$	−0.516019	−	2.12102i	−0.0245445	−	0.100887i
$443$	26.4542	−	8.59548i	1.25688	−	0.408384i	0.396496	−	0.918037i	$-0.370226\pi$
$443$	26.4542	−	8.59548i	1.25688	−	0.408384i	0.860380	+	0.509653i	$0.170226\pi$
$444$	8.16306	−	4.22184i	0.387402	−	0.200360i
$445$	3.98890	−	5.49025i	0.189092	−	0.260263i
$446$	−11.0682	−	17.9393i	−0.524095	−	0.849453i
$447$	−1.59300	+	4.90275i	−0.0753463	+	0.231892i
$448$	13.4382	+	6.54192i	0.634896	+	0.309076i
$449$	10.5857	−	7.69100i	0.499572	−	0.362961i	−0.309281	−	0.950971i	$-0.600088\pi$
$449$	10.5857	−	7.69100i	0.499572	−	0.362961i	0.808854	+	0.588010i	$0.200088\pi$
$450$	−4.39558	−	1.80511i	−0.207210	−	0.0850938i
$451$	8.43667	+	12.3087i	0.397267	+	0.579594i
$452$	11.4560	+	11.3178i	0.538843	+	0.532346i
$453$	1.76480	+	2.42904i	0.0829175	+	0.114126i
$454$	1.86524	+	0.141108i	0.0875402	+	0.00662251i
$455$	−0.294142	+	0.905277i	−0.0137896	+	0.0424400i
$456$	2.76701	−	12.0056i	0.129577	−	0.562211i
$457$	5.36391	+	3.89711i	0.250913	+	0.182299i	0.706131	−	0.708081i	$-0.250439\pi$
$457$	5.36391	+	3.89711i	0.250913	+	0.182299i	−0.455218	+	0.890380i	$0.650439\pi$
$458$	25.4476	+	21.6012i	1.18909	+	1.00936i
$459$	−25.4769	+	8.27795i	−1.18916	+	0.386381i
$460$	1.46621	−	9.63515i	0.0683623	−	0.449241i
$461$		−	8.43029i		−	0.392638i	−0.980540	−	0.196319i	$-0.937101\pi$
$461$		−	8.43029i		−	0.392638i	0.980540	−	0.196319i	$-0.0628988\pi$
$462$	5.65323	+	9.75179i	0.263012	+	0.453694i
$463$	9.16056			0.425727			0.212864	−	0.977082i	$-0.431721\pi$
$463$	9.16056			0.425727			0.212864	+	0.977082i	$0.431721\pi$
$464$	33.3980	−	24.8896i	1.55046	−	1.15547i
$465$	1.77367	+	5.45881i	0.0822521	+	0.253146i
$466$	−2.26128	+	2.66393i	−0.104752	+	0.123404i
$467$	−6.80276	+	9.36320i	−0.314794	+	0.433277i	−0.936869	−	0.349681i	$-0.886290\pi$
$467$	−6.80276	+	9.36320i	−0.314794	+	0.433277i	0.622075	+	0.782958i	$0.286290\pi$
$468$	−0.855096	+	0.140756i	−0.0395268	+	0.00650643i
$469$	19.5245	+	6.34389i	0.901558	+	0.292934i
$470$	−28.3904	−	2.14776i	−1.30955	−	0.0990688i
$471$	−8.26894	+	6.00773i	−0.381012	+	0.276822i
$472$	14.0162	−	5.95566i	0.645148	−	0.274132i
$473$	−3.39349	−	11.5096i	−0.156033	−	0.529211i
$474$	4.13248	−	10.0629i	0.189811	−	0.462204i
$475$	−4.97105	−	6.84206i	−0.228087	−	0.313935i
$476$	8.03277	−	16.0044i	0.368181	−	0.733562i
$477$	7.23850	+	2.35193i	0.331428	+	0.107687i
$478$	11.7474	+	19.0402i	0.537314	+	0.870878i
$479$	−15.4993	−	11.2609i	−0.708181	−	0.514524i	0.174405	−	0.984674i	$-0.444200\pi$
$479$	−15.4993	−	11.2609i	−0.708181	−	0.514524i	−0.882586	+	0.470150i	$0.844200\pi$
$480$	8.86540	+	7.34224i	0.404648	+	0.335126i
$481$	−0.355531	−	1.09421i	−0.0162108	−	0.0498918i
$482$	−4.43173	+	1.07819i	−0.201860	+	0.0491102i
$483$		−	7.40286i		−	0.336842i
$484$	10.9325	−	19.0914i	0.496932	−	0.867790i
$485$			19.6067i			0.890293i
$486$	4.24964	+	17.4675i	0.192767	+	0.792341i
$487$	13.1143	+	40.3616i	0.594265	+	1.82896i	0.558353	+	0.829603i	$0.311433\pi$
$487$	13.1143	+	40.3616i	0.594265	+	1.82896i	0.0359111	+	0.999355i	$0.488567\pi$
$488$	2.70556	+	30.7931i	0.122475	+	1.39394i
$489$	−5.84362	−	4.24564i	−0.264258	−	0.191995i
$490$	6.68223	−	4.12280i	0.301872	−	0.186249i
$491$	−37.3377	−	12.1318i	−1.68503	−	0.547499i	−0.699152	−	0.714973i	$-0.746439\pi$
$491$	−37.3377	−	12.1318i	−1.68503	−	0.547499i	−0.985876	+	0.167475i	$0.946439\pi$
$492$	10.3453	+	5.19238i	0.466400	+	0.234091i
$493$	−29.3332	−	40.3737i	−1.32110	−	1.81834i
$494$	−1.42676	−	0.585920i	−0.0641929	−	0.0263618i
$495$	−1.99621	−	6.77047i	−0.0897229	−	0.304310i
$496$	−0.136859	−	11.2818i	−0.00614517	−	0.506570i
$497$	−16.8313	+	12.2287i	−0.754988	+	0.548531i
$498$	−0.0191630	+	0.253308i	−0.000858715	+	0.0113510i
$499$	−21.5545	−	7.00348i	−0.964912	−	0.313519i	−0.216152	−	0.976360i	$-0.569351\pi$
$499$	−21.5545	−	7.00348i	−0.964912	−	0.313519i	−0.748760	+	0.662841i	$0.769351\pi$
$500$	23.4060	−	3.85282i	1.04675	−	0.172303i
$501$	13.6300	−	18.7601i	0.608945	−	0.838141i
$502$	0.372874	+	0.316514i	0.0166422	+	0.0141267i
$503$	4.80180	+	14.7784i	0.214102	+	0.658937i	0.999216	+	0.0395862i	$0.0126040\pi$
$503$	4.80180	+	14.7784i	0.214102	+	0.658937i	−0.785115	+	0.619350i	$0.787396\pi$
$504$	−6.09507	−	3.65921i	−0.271496	−	0.162994i
$505$	−24.3028			−1.08146
$506$	−12.5000	+	7.24640i	−0.555693	+	0.322142i
$507$			16.5889i			0.736737i
$508$	25.7954	+	3.92536i	1.14448	+	0.174160i
$509$	−12.7916	+	4.15624i	−0.566978	+	0.184222i	−0.578459	−	0.815712i	$-0.696346\pi$
$509$	−12.7916	+	4.15624i	−0.566978	+	0.184222i	0.0114806	+	0.999934i	$0.496346\pi$
$510$	8.92513	−	10.5144i	0.395211	−	0.465585i
$511$	−19.0585	−	13.8468i	−0.843097	−	0.612546i
$512$	−12.3449	−	18.9632i	−0.545572	−	0.838064i
$513$	−5.84903	+	18.0015i	−0.258241	+	0.794784i
$514$	−0.0450061	+	0.594918i	−0.00198514	+	0.0262407i
$515$	−7.60317	−	10.4649i	−0.335036	−	0.461137i
$516$	−6.62139	−	6.54156i	−0.291491	−	0.287976i
$517$	23.8635	+	34.8157i	1.04951	+	1.53119i
$518$	3.58540	−	8.73071i	0.157533	−	0.383606i
$519$	−15.6810	+	11.3929i	−0.688318	+	0.500092i
$520$	1.08724	−	0.945831i	0.0476786	−	0.0414774i
$521$	−2.06824	+	6.36540i	−0.0906114	+	0.278873i	−0.986085	−	0.166241i	$-0.946837\pi$
$521$	−2.06824	+	6.36540i	−0.0906114	+	0.278873i	0.895474	+	0.445114i	$0.146837\pi$
$522$	−16.8611	+	10.4030i	−0.737992	+	0.455326i
$523$	−13.9650	+	19.2212i	−0.610647	+	0.840483i	−0.996630	−	0.0820226i	$-0.973862\pi$
$523$	−13.9650	+	19.2212i	−0.610647	+	0.840483i	0.385984	+	0.922506i	$0.373862\pi$
$524$	10.6136	+	20.5217i	0.463656	+	0.896493i
$525$	5.70820	−	1.85471i	0.249126	−	0.0809460i
$526$	−3.23404	+	0.786806i	−0.141011	+	0.0343064i
$527$	−13.5181			−0.588856
$528$	0.261300	−	17.0631i	0.0113716	−	0.742576i
$529$	−13.5109			−0.587431
$530$	−12.2976	+	2.99186i	−0.534174	+	0.129958i
$531$	−6.88923	+	2.23845i	−0.298967	+	0.0971403i
$532$	−5.81254	−	11.2387i	−0.252006	−	0.487260i
$533$	0.851762	−	1.17235i	0.0368939	−	0.0507801i
$534$	−6.64157	+	4.09772i	−0.287409	+	0.177326i
$535$	−2.46002	+	7.57117i	−0.106356	+	0.327330i
$536$	−20.3992	−	23.4490i	−0.881109	−	1.01284i
$537$	23.1932	−	16.8509i	1.00086	−	0.727168i
$538$	−12.3869	+	30.1630i	−0.534036	+	1.30042i
$539$	−10.9676	−	3.89943i	−0.472408	−	0.167960i
$540$	−12.5805	−	12.4288i	−0.541378	−	0.534851i
$541$	−16.7940	−	23.1150i	−0.722031	−	0.993791i	−0.999454	−	0.0330429i	$-0.989480\pi$
$541$	−16.7940	−	23.1150i	−0.722031	−	0.993791i	0.277423	−	0.960748i	$-0.410520\pi$
$542$	0.466886	−	6.17158i	0.0200545	−	0.265092i
$543$	−4.57580	+	14.0829i	−0.196366	+	0.604353i
$544$	−22.8981	+	14.5141i	−0.981746	+	0.622285i
$545$	13.0334	+	9.46932i	0.558290	+	0.405621i
$546$	0.708359	−	0.834493i	0.0303149	−	0.0357130i
$547$	−28.7471	+	9.34049i	−1.22914	+	0.399370i	−0.850401	−	0.526135i	$-0.823641\pi$
$547$	−28.7471	+	9.34049i	−1.22914	+	0.399370i	−0.378735	+	0.925505i	$0.623641\pi$
$548$	−35.6283	−	5.42166i	−1.52196	−	0.231602i
$549$		−	14.7033i		−	0.627522i
$550$	−8.71930	−	7.82299i	−0.371792	−	0.333574i
$551$	−35.2616			−1.50220
$552$	−5.76874	+	9.60887i	−0.245534	+	0.408981i
$553$	−3.45234	−	10.6252i	−0.146809	−	0.451830i
$554$	−6.75638	−	5.73515i	−0.287051	−	0.243663i
$555$	4.27267	−	5.88083i	0.181365	−	0.249627i
$556$	−13.2317	+	2.17805i	−0.561150	+	0.0923697i
$557$	7.55374	+	2.45436i	0.320062	+	0.103995i	0.464642	−	0.885499i	$-0.346183\pi$
$557$	7.55374	+	2.45436i	0.320062	+	0.103995i	−0.144580	+	0.989493i	$0.546183\pi$
$558$	−0.404836	+	5.35137i	−0.0171381	+	0.226541i
$559$	−0.942703	+	0.684914i	−0.0398721	+	0.0289688i
$560$	11.8209	−	0.143398i	0.499523	−	0.00605968i
$561$	−20.4384	−	0.561030i	−0.862912	−	0.0236867i
$562$	−14.6324	−	6.00901i	−0.617230	−	0.253475i
$563$	10.4467	+	14.3787i	0.440276	+	0.605988i	0.970273	−	0.242011i	$-0.0778070\pi$
$563$	10.4467	+	14.3787i	0.440276	+	0.605988i	−0.529997	+	0.847999i	$0.677807\pi$
$564$	29.2620	+	14.6869i	1.23215	+	0.618428i
$565$	12.1141	+	3.93612i	0.509645	+	0.165594i
$566$	38.4907	−	23.7480i	1.61788	−	0.998202i
$567$	−4.76703	−	3.46345i	−0.200196	−	0.145451i
$568$	31.3763	−	2.75680i	1.31652	−	0.115673i
$569$	8.76455	+	26.9745i	0.367429	+	1.13083i	0.948446	+	0.316939i	$0.102655\pi$
$569$	8.76455	+	26.9745i	0.367429	+	1.13083i	−0.581017	+	0.813892i	$0.697345\pi$
$570$	−2.30363	−	9.46872i	−0.0964884	−	0.396601i
$571$		−	11.9221i		−	0.498923i	−0.968385	−	0.249461i	$-0.919746\pi$
$571$		−	11.9221i		−	0.498923i	0.968385	−	0.249461i	$-0.0802535\pi$
$572$	−2.10246	−	0.379233i	−0.0879082	−	0.0158565i
$573$		−	13.8888i		−	0.580215i
$574$	11.5507	−	2.81016i	0.482117	−	0.117294i
$575$	2.37739	+	7.31686i	0.0991441	+	0.305134i
$576$	5.05990	+	9.49927i	0.210829	+	0.395803i
$577$	19.9017	+	14.4594i	0.828519	+	0.601955i	0.919140	−	0.393931i	$-0.128885\pi$
$577$	19.9017	+	14.4594i	0.828519	+	0.601955i	−0.0906207	+	0.995885i	$0.528885\pi$
$578$	4.43178	+	7.18302i	0.184338	+	0.298774i
$579$	11.0795	+	3.59996i	0.460450	+	0.149609i
$580$	14.7786	−	29.4448i	0.613649	−	1.22263i
$581$	0.153346	+	0.211063i	0.00636188	+	0.00875638i
$582$	8.56506	−	20.8566i	0.355033	−	0.864532i
$583$	14.8712	+	11.4410i	0.615903	+	0.473836i
$584$	13.9476	+	32.8245i	0.577154	+	1.35829i
$585$	−0.554543	+	0.402899i	−0.0229275	+	0.0166578i
$586$	−10.8088	−	0.817700i	−0.446509	−	0.0337789i
$587$	11.5034	+	3.73767i	0.474795	+	0.154270i	0.536633	−	0.843816i	$-0.319696\pi$
$587$	11.5034	+	3.73767i	0.474795	+	0.154270i	−0.0618378	+	0.998086i	$0.519696\pi$
$588$	−8.90924	+	1.46653i	−0.367411	+	0.0604787i
$589$	−5.61428	+	7.72740i	−0.231332	+	0.318402i
$590$	7.79519	−	9.18325i	0.320923	−	0.378068i
$591$	3.47458	+	10.6937i	0.142925	+	0.439879i
$592$	−11.4573	+	8.53847i	−0.470893	+	0.350929i
$593$	−1.77063			−0.0727109			−0.0363554	−	0.999339i	$-0.511575\pi$
$593$	−1.77063			−0.0727109			−0.0363554	+	0.999339i	$0.511575\pi$
$594$	−2.69431	+	26.0786i	−0.110549	+	1.07002i
$595$		−	14.1639i		−	0.580665i
$596$	1.20581	−	7.92392i	0.0493917	−	0.324576i
$597$	−3.12669	+	1.01592i	−0.127967	+	0.0415790i
$598$	1.06967	+	0.907985i	0.0437419	+	0.0371303i
$599$	11.5861	+	8.41779i	0.473395	+	0.343942i	0.798763	−	0.601646i	$-0.205488\pi$
$599$	11.5861	+	8.41779i	0.473395	+	0.343942i	−0.325368	+	0.945588i	$0.605488\pi$
$600$	−8.85451	−	2.04076i	−0.361484	−	0.0833138i
$601$	6.48697	−	19.9649i	0.264609	−	0.814383i	−0.727174	−	0.686453i	$-0.759167\pi$
$601$	6.48697	−	19.9649i	0.264609	−	0.814383i	0.991783	−	0.127930i	$-0.0408333\pi$
$602$	−9.53178	−	0.721089i	−0.388486	−	0.0293894i
$603$	8.68950	+	11.9601i	0.353864	+	0.487051i
$604$	−3.32091	−	3.28087i	−0.135126	−	0.133497i
$605$	0.954599	−	17.3750i	0.0388100	−	0.706395i
$606$	25.8520	+	10.6165i	1.05017	+	0.431267i
$607$	27.5066	−	19.9847i	1.11646	−	0.811155i	0.132790	−	0.991144i	$-0.457606\pi$
$607$	27.5066	−	19.9847i	1.11646	−	0.811155i	0.983669	+	0.179990i	$0.0576064\pi$
$608$	−1.21322	+	19.1173i	−0.0492025	+	0.775308i
$609$	7.73300	−	23.7997i	0.313357	−	0.964414i
$610$	12.8383	+	20.8083i	0.519807	+	0.842502i
$611$	2.40924	−	3.31604i	0.0974675	−	0.134153i
$612$	11.4540	−	5.92389i	0.463001	−	0.239459i
$613$	12.7425	−	4.14030i	0.514666	−	0.167225i	−0.0401574	−	0.999193i	$-0.512786\pi$
$613$	12.7425	−	4.14030i	0.514666	−	0.167225i	0.554823	+	0.831968i	$0.312786\pi$
$614$	1.19520	+	4.91267i	0.0482342	+	0.198259i
$615$	9.15557			0.369188
$616$	−11.1357	−	13.5332i	−0.448669	−	0.545269i
$617$	24.0930			0.969946			0.484973	−	0.874529i	$-0.338829\pi$
$617$	24.0930			0.969946			0.484973	+	0.874529i	$0.338829\pi$
$618$	3.51635	+	14.4534i	0.141448	+	0.581401i
$619$	−2.30077	+	0.747567i	−0.0924759	+	0.0300472i	−0.354890	−	0.934908i	$-0.615482\pi$
$619$	−2.30077	+	0.747567i	−0.0924759	+	0.0300472i	0.262414	+	0.964955i	$0.415482\pi$
$620$	−4.09965	−	7.92679i	−0.164646	−	0.318348i
$621$	10.1207	−	13.9299i	0.406128	−	0.558987i
$622$	−0.0581595	−	0.0942648i	−0.00233198	−	0.00377967i
$623$	−2.47665	+	7.62234i	−0.0992249	+	0.305383i
$624$	−1.56973	+	0.531172i	−0.0628395	+	0.0212639i
$625$	5.07656	−	3.68834i	0.203062	−	0.147533i
$626$	11.7054	+	4.80701i	0.467843	+	0.192127i
$627$	−8.80914	+	11.4503i	−0.351803	+	0.457282i
$628$	11.1687	−	11.3051i	0.445682	−	0.451121i
$629$	10.0629	+	13.8504i	0.401234	+	0.552251i
$630$	−5.60704	−	0.424179i	−0.223390	−	0.0168997i
$631$	12.5167	−	38.5223i	0.498280	−	1.53355i	−0.313502	−	0.949588i	$-0.601502\pi$
$631$	12.5167	−	38.5223i	0.498280	−	1.53355i	0.811782	−	0.583961i	$-0.198498\pi$
$632$	−3.79867	+	16.4817i	−0.151103	+	0.655609i
$633$	3.45050	+	2.50694i	0.137145	+	0.0996419i
$634$	−26.3968	−	22.4069i	−1.04835	−	0.889891i
$635$	19.6280	−	6.37752i	0.778913	−	0.253084i
$636$	14.3885	+	2.18955i	0.570543	+	0.0868212i
$637$			1.13036i			0.0447865i
$638$	−47.7563	+	10.2393i	−1.89069	+	0.405377i
$639$	−14.9818			−0.592670
$640$	−15.4552	−	9.02538i	−0.610919	−	0.356759i
$641$	−6.88190	−	21.1803i	−0.271819	−	0.836572i	−0.990044	−	0.140761i	$-0.955045\pi$
$641$	−6.88190	−	21.1803i	−0.271819	−	0.836572i	0.718225	−	0.695811i	$-0.244955\pi$
$642$	5.92427	−	6.97917i	0.233812	−	0.275446i
$643$	−14.6757	+	20.1994i	−0.578753	+	0.796585i	−0.993558	−	0.113325i	$-0.963850\pi$
$643$	−14.6757	+	20.1994i	−0.578753	+	0.796585i	0.414805	+	0.909910i	$0.363850\pi$
$644$	1.86949	+	11.3572i	0.0736680	+	0.447537i
$645$	−7.00180	−	2.27502i	−0.275695	−	0.0895789i
$646$	22.8856	+	1.73132i	0.900421	+	0.0681178i
$647$	9.99280	−	7.26020i	0.392858	−	0.285428i	−0.373768	−	0.927522i	$-0.621934\pi$
$647$	9.99280	−	7.26020i	0.392858	−	0.285428i	0.766626	+	0.642094i	$0.221934\pi$
$648$	3.48866	+	8.21028i	0.137047	+	0.322530i
$649$	−17.8509	−	0.490003i	−0.700709	−	0.0192343i
$650$	−0.432136	+	1.05228i	−0.0169498	+	0.0412740i
$651$	−3.98435	−	5.48399i	−0.156159	−	0.214935i
$652$	10.0373	+	5.03779i	0.393089	+	0.197295i
$653$	−4.54949	−	1.47822i	−0.178035	−	0.0578472i	0.218643	−	0.975805i	$-0.429837\pi$
$653$	−4.54949	−	1.47822i	−0.178035	−	0.0578472i	−0.396678	+	0.917958i	$0.629837\pi$
$654$	−9.72765	−	15.7666i	−0.380381	−	0.616521i
$655$	14.7842	+	10.7414i	0.577667	+	0.419700i
$656$	−17.1826	−	5.35342i	−0.670868	−	0.209016i
$657$	−5.24222	−	16.1339i	−0.204518	−	0.629443i
$658$	32.6716	−	7.94864i	1.27367	−	0.309870i
$659$		−	34.4552i		−	1.34219i	−0.741374	−	0.671093i	$-0.765825\pi$
$659$		−	34.4552i		−	1.34219i	0.741374	−	0.671093i	$-0.234175\pi$
$660$	−5.86943	−	12.1549i	−0.228467	−	0.473131i
$661$			39.9505i			1.55389i	0.629567	+	0.776947i	$0.283233\pi$
$661$			39.9505i			1.55389i	−0.629567	+	0.776947i	$0.716767\pi$
$662$	8.09309	+	33.2654i	0.314547	+	1.29290i
$663$	0.613551	+	1.88832i	0.0238284	+	0.0733361i
$664$	−0.0345700	−	0.393456i	−0.00134158	−	0.0152690i
$665$	−8.09660	−	5.88252i	−0.313973	−	0.228114i
$666$	5.78428	−	3.56879i	0.224136	−	0.138288i
$667$	30.5069	+	9.91228i	1.18123	+	0.383805i
$668$	−16.1731	+	32.2232i	−0.625757	+	1.24675i
$669$	11.2696	+	15.5112i	0.435706	+	0.599698i
$670$	−22.7405	−	9.33872i	−0.878541	−	0.360786i
$671$	12.1427	−	34.1528i	0.468764	−	1.31845i
$672$	−12.6371	−	5.01134i	−0.487486	−	0.193317i
$673$	−8.75188	+	6.35861i	−0.337360	+	0.245107i	−0.743547	−	0.668683i	$-0.766858\pi$
$673$	−8.75188	+	6.35861i	−0.337360	+	0.245107i	0.406187	+	0.913790i	$0.366858\pi$
$674$	2.37950	−	31.4536i	0.0916550	−	1.21155i
$675$	13.2767	+	4.31386i	0.511020	+	0.166041i
$676$	−4.18928	−	25.4500i	−0.161126	−	0.978848i
$677$	−21.9997	+	30.2800i	−0.845518	+	1.16376i	0.139314	+	0.990248i	$0.455510\pi$
$677$	−21.9997	+	30.2800i	−0.845518	+	1.16376i	−0.984832	+	0.173508i	$0.944490\pi$
$678$	−11.1669	−	9.47903i	−0.428863	−	0.364040i
$679$	−7.15540	−	22.0220i	−0.274599	−	0.845129i
$680$	−11.0374	+	18.3847i	−0.423264	+	0.705021i
$681$	−1.70142			−0.0651987
$682$	−5.35977	+	12.0958i	−0.205236	+	0.463172i
$683$		−	24.1362i		−	0.923545i	−0.886998	−	0.461772i	$-0.847214\pi$
$683$		−	24.1362i		−	0.923545i	0.886998	−	0.461772i	$-0.152786\pi$
$684$	1.37075	−	9.00781i	0.0524118	−	0.344422i
$685$	−27.1100	+	8.80856i	−1.03582	+	0.336558i
$686$	−17.9695	+	21.1692i	−0.686078	+	0.808244i
$687$	−24.5626	−	17.8458i	−0.937123	−	0.680860i
$688$	11.8103	+	8.36369i	0.450263	+	0.318863i
$689$	0.563042	−	1.73287i	0.0214502	−	0.0660170i
$690$	−0.668717	+	8.83950i	−0.0254576	+	0.336514i
$691$	26.3394	+	36.2531i	1.00200	+	1.37913i	0.924091	+	0.382174i	$0.124824\pi$
$691$	26.3394	+	36.2531i	1.00200	+	1.37913i	0.0779091	+	0.996960i	$0.475176\pi$
$692$	21.1801	−	21.4386i	0.805146	−	0.814972i
$693$	4.71299	+	6.87603i	0.179032	+	0.261199i
$694$	9.04670	−	22.0294i	0.343408	−	0.836224i
$695$	−8.58097	+	6.23444i	−0.325495	+	0.236486i
$696$	−28.5835	+	24.8659i	−1.08346	+	0.942540i
$697$	−6.66332	+	20.5076i	−0.252391	+	0.776781i
$698$	7.19002	−	4.43610i	0.272146	−	0.167909i
$699$	1.86815	−	2.57129i	0.0706599	−	0.0972551i
$700$	−8.28894	+	4.28695i	−0.313293	+	0.162031i
$701$	21.7906	−	7.08021i	0.823021	−	0.267416i	0.132918	−	0.991127i	$-0.457565\pi$
$701$	21.7906	−	7.08021i	0.823021	−	0.267416i	0.690103	+	0.723711i	$0.257565\pi$
$702$	2.47377	−	0.601840i	0.0933665	−	0.0227150i
$703$	12.0967			0.456234
$704$	3.90816	+	26.2436i	0.147294	+	0.989093i
$705$	25.8969			0.975333
$706$	−9.19938	+	2.23810i	−0.346223	+	0.0842321i
$707$	27.2967	−	8.86922i	1.02660	−	0.333562i
$708$	−12.3038	+	6.36338i	−0.462404	+	0.239150i
$709$	23.4355	−	32.2562i	0.880138	−	1.21141i	−0.0962447	−	0.995358i	$-0.530683\pi$
$709$	23.4355	−	32.2562i	0.880138	−	1.21141i	0.976383	−	0.216048i	$-0.0693169\pi$
$710$	21.2024	−	13.0814i	0.795710	−	0.490937i
$711$	2.48609	−	7.65139i	0.0932355	−	0.286949i
$712$	9.15445	−	7.96381i	0.343078	−	0.298456i
$713$	7.02946	−	5.10720i	0.263255	−	0.191266i
$714$	−6.18744	+	15.0669i	−0.231559	+	0.563863i
$715$	−1.62082	+	0.477884i	−0.0606154	+	0.0178719i
$716$	−31.3268	+	31.7091i	−1.17074	+	1.18502i
$717$	−11.9611	−	16.4631i	−0.446696	−	0.614824i
$718$	2.14648	−	28.3735i	0.0801060	−	1.05889i
$719$	−11.2065	+	34.4900i	−0.417931	+	1.28626i	0.491671	+	0.870781i	$0.336386\pi$
$719$	−11.2065	+	34.4900i	−0.417931	+	1.28626i	−0.909603	+	0.415479i	$0.863614\pi$
$720$	6.94737	+	4.91992i	0.258913	+	0.183355i
$721$	12.3589	+	8.97930i	0.460271	+	0.334407i
$722$	−6.89421	+	8.12183i	−0.256576	+	0.302263i
$723$	3.94552	−	1.28198i	0.146735	−	0.0476772i
$724$	3.46361	−	22.7610i	0.128724	−	0.845905i
$725$			26.0067i			0.965864i
$726$	−8.60563	+	18.0656i	−0.319385	+	0.670479i
$727$	4.42926			0.164272			0.0821360	−	0.996621i	$-0.473826\pi$
$727$	4.42926			0.164272			0.0821360	+	0.996621i	$0.473826\pi$
$728$	−0.876000	+	1.45914i	−0.0324667	+	0.0540791i
$729$	−7.97673	−	24.5499i	−0.295435	−	0.909254i
$730$	21.5062	+	18.2556i	0.795982	+	0.675669i
$731$	10.1917	−	14.0276i	0.376952	−	0.518830i
$732$	−4.56673	−	27.7431i	−0.168791	−	1.02541i
$733$	−25.9257	−	8.42378i	−0.957588	−	0.311139i	−0.211793	−	0.977315i	$-0.567930\pi$
$733$	−25.9257	−	8.42378i	−0.957588	−	0.311139i	−0.745795	+	0.666175i	$0.767930\pi$
$734$	0.795785	−	10.5192i	0.0293730	−	0.388269i
$735$	−5.77777	+	4.19780i	−0.213116	+	0.154838i
$736$	6.42362	−	16.1984i	0.236778	−	0.597081i
$737$	10.3067	+	34.9570i	0.379654	+	1.28766i
$738$	7.91875	+	3.25195i	0.291493	+	0.119706i
$739$	−0.687316	−	0.946010i	−0.0252833	−	0.0347995i	0.796188	−	0.605049i	$-0.206847\pi$
$739$	−0.687316	−	0.946010i	−0.0252833	−	0.0347995i	−0.821472	+	0.570250i	$0.806847\pi$
$740$	−5.06987	+	10.1012i	−0.186372	+	0.371326i
$741$	1.33425	+	0.433523i	0.0490147	+	0.0159259i
$742$	12.7207	−	7.84841i	0.466991	−	0.288124i
$743$	−32.0828	−	23.3095i	−1.17700	−	0.855144i	−0.185174	−	0.982706i	$-0.559285\pi$
$743$	−32.0828	−	23.3095i	−1.17700	−	0.855144i	−0.991831	+	0.127562i	$0.959285\pi$
$744$	0.898222	+	10.2230i	0.0329304	+	0.374794i
$745$	−1.95907	−	6.02940i	−0.0717748	−	0.220900i
$746$	0.514528	+	2.11489i	0.0188382	+	0.0774316i
$747$			0.187870i			0.00687380i
$748$	31.4976	−	4.30072i	1.15167	−	0.157250i
$749$		−	9.40165i		−	0.343529i
$750$	−20.9645	+	5.10042i	−0.765515	+	0.186241i
$751$	−2.04348	−	6.28918i	−0.0745676	−	0.229496i	0.906825	−	0.421507i	$-0.138499\pi$
$751$	−2.04348	−	6.28918i	−0.0745676	−	0.229496i	−0.981393	+	0.192012i	$0.938499\pi$
$752$	−48.6017	−	15.1424i	−1.77232	−	0.552185i
$753$	−0.359907	−	0.261488i	−0.0131158	−	0.00952915i
$754$	2.49043	+	4.03649i	0.0906961	+	0.147000i
$755$	−3.51170	−	1.14102i	−0.127804	−	0.0415260i
$756$	18.6662	+	9.36872i	0.678882	+	0.340737i
$757$	12.1575	+	16.7334i	0.441873	+	0.608186i	0.970627	−	0.240589i	$-0.0773406\pi$
$757$	12.1575	+	16.7334i	0.441873	+	0.608186i	−0.528754	+	0.848775i	$0.677341\pi$
$758$	2.87426	−	6.99903i	0.104398	−	0.254216i
$759$	10.8401	−	7.43002i	0.393469	−	0.269693i
$760$	5.92534	+	13.9448i	0.214935	+	0.505832i
$761$	−36.8499	+	26.7730i	−1.33581	+	0.970521i	−0.336221	+	0.941783i	$0.609149\pi$
$761$	−36.8499	+	26.7730i	−1.33581	+	0.970521i	−0.999587	+	0.0287383i	$0.990851\pi$
$762$	−23.6652	−	1.79030i	−0.857301	−	0.0648557i
$763$	−18.0948	−	5.87936i	−0.655077	−	0.212847i
$764$	3.50743	+	21.3078i	0.126894	+	0.770888i
$765$	5.99522	−	8.25171i	0.216758	−	0.298341i
$766$	8.77972	−	10.3431i	0.317224	−	0.373711i
$767$	0.535875	+	1.64925i	0.0193493	+	0.0595511i
$768$	12.4977	+	16.3522i	0.450973	+	0.590061i
$769$	−19.1817			−0.691711			−0.345856	−	0.938288i	$-0.612411\pi$
$769$	−19.1817			−0.691711			−0.345856	+	0.938288i	$0.612411\pi$
$770$	−12.6737	−	5.61585i	−0.456729	−	0.202381i
$771$		−	0.542667i		−	0.0195437i
$772$	−17.9069	−	2.72495i	−0.644485	−	0.0980732i
$773$	−47.6869	+	15.4944i	−1.71518	+	0.557296i	−0.991182	−	0.132507i	$-0.957697\pi$
$773$	−47.6869	+	15.4944i	−1.71518	+	0.557296i	−0.723998	+	0.689803i	$0.757697\pi$
$774$	−5.24786	−	4.45465i	−0.188631	−	0.160119i
$775$	5.69922	+	4.14073i	0.204722	+	0.148739i
$776$	−7.87320	+	34.1604i	−0.282631	+	1.22629i
$777$	−2.65284	+	8.16460i	−0.0951701	+	0.292903i
$778$	15.8428	+	1.19852i	0.567990	+	0.0429691i
$779$	8.95547	+	12.3261i	0.320863	+	0.441630i
$780$	−0.921208	+	0.932451i	−0.0329845	+	0.0333871i
$781$	−34.7996	−	12.3727i	−1.24523	−	0.442729i
$782$	−19.3129	−	7.93115i	−0.690630	−	0.283617i
$783$	47.0884	−	34.2117i	1.68280	−	1.22263i
$784$	13.2979	−	4.49980i	0.474925	−	0.160707i
$785$	3.88426	−	11.9545i	0.138635	−	0.426676i
$786$	−11.0344	−	17.8845i	−0.393584	−	0.637920i
$787$	13.4100	−	18.4572i	0.478014	−	0.657930i	−0.500108	−	0.865963i	$-0.666706\pi$
$787$	13.4100	−	18.4572i	0.478014	−	0.657930i	0.978122	+	0.208033i	$0.0667063\pi$
$788$	−8.03111	−	15.5284i	−0.286097	−	0.553176i
$789$	2.87923	−	0.935519i	0.102503	−	0.0333054i
$790$	3.16252	+	12.9991i	0.112518	+	0.462486i
$791$	−15.0430			−0.534866
$792$	−0.759231	−	12.5977i	−0.0269781	−	0.447639i
$793$	−3.51991			−0.124996
$794$	−3.28822	−	13.5157i	−0.116695	−	0.479655i
$795$	10.9484	−	3.55735i	0.388300	−	0.126166i
$796$	4.54030	−	2.34820i	0.160927	−	0.0832296i
$797$	−15.6746	+	21.5743i	−0.555224	+	0.764201i	−0.990709	−	0.135995i	$-0.956577\pi$
$797$	−15.6746	+	21.5743i	−0.555224	+	0.764201i	0.435485	+	0.900196i	$0.356577\pi$
$798$	6.04300	+	9.79448i	0.213920	+	0.346721i
$799$	−18.8475	+	58.0066i	−0.666776	+	2.05212i
$800$	14.0996	+	0.894790i	0.498498	+	0.0316356i
$801$	−4.66920	+	3.39237i	−0.164978	+	0.119863i
$802$	−14.0601	−	5.77400i	−0.496480	−	0.203887i
$803$	1.14754	−	41.8050i	0.0404957	−	1.47527i
$804$	20.1106	+	19.8681i	0.709246	+	0.700694i
$805$	5.35122	+	7.36532i	0.188606	+	0.259593i
$806$	1.28109	+	0.0969162i	0.0451246	+	0.00341373i
$807$	9.16506	−	28.2072i	0.322625	−	0.992939i
$808$	−42.3423	−	9.75895i	−1.48960	−	0.343319i
$809$	31.2009	+	22.6688i	1.09697	+	0.796993i	0.980562	−	0.196209i	$-0.0628632\pi$
$809$	31.2009	+	22.6688i	1.09697	+	0.796993i	0.116404	+	0.993202i	$0.462863\pi$
$810$	5.37928	+	4.56620i	0.189009	+	0.160440i
$811$	−16.0047	+	5.20024i	−0.562000	+	0.182605i	−0.576221	−	0.817294i	$-0.695473\pi$
$811$	−16.0047	+	5.20024i	−0.562000	+	0.182605i	0.0142207	+	0.999899i	$0.495473\pi$
$812$	−5.85342	+	38.4656i	−0.205415	+	1.34988i
$813$			5.62954i			0.197437i
$814$	16.3830	−	3.51263i	0.574224	−	0.123118i
$815$	8.88299			0.311157
$816$	19.7722	−	14.7351i	0.692167	−	0.515832i
$817$	−3.78591	−	11.6518i	−0.132452	−	0.407646i
$818$	5.79368	−	6.82533i	0.202571	−	0.238642i
$819$	0.475821	−	0.654911i	0.0166265	−	0.0228845i
$820$	−14.0462	+	2.31211i	−0.490513	+	0.0807423i
$821$	1.19308	+	0.387655i	0.0416388	+	0.0135293i	0.329762	−	0.944064i	$-0.393031\pi$
$821$	1.19308	+	0.387655i	0.0416388	+	0.0135293i	−0.288124	+	0.957593i	$0.593031\pi$
$822$	32.6862	+	2.47274i	1.14006	+	0.0862468i
$823$	−40.6599	+	29.5412i	−1.41732	+	1.02974i	−0.425110	+	0.905142i	$0.639764\pi$
$823$	−40.6599	+	29.5412i	−1.41732	+	1.02974i	−0.992207	+	0.124599i	$0.960236\pi$
$824$	−9.04465	−	21.2859i	−0.315085	−	0.741529i
$825$	8.44500	+	6.49704i	0.294017	+	0.226198i
$826$	−5.40410	+	13.1594i	−0.188033	+	0.457874i
$827$	13.9238	+	19.1644i	0.484177	+	0.666413i	0.979301	−	0.202410i	$-0.0648773\pi$
$827$	13.9238	+	19.1644i	0.484177	+	0.666413i	−0.495124	+	0.868822i	$0.664877\pi$
$828$	−3.71807	+	7.40785i	−0.129212	+	0.257441i
$829$	−31.7753	−	10.3244i	−1.10360	−	0.358583i	−0.300115	−	0.953903i	$-0.597025\pi$
$829$	−31.7753	−	10.3244i	−1.10360	−	0.358583i	−0.803488	+	0.595320i	$0.797025\pi$
$830$	−0.164040	−	0.265876i	−0.00569391	−	0.00922867i
$831$	6.52143	+	4.73809i	0.226226	+	0.164363i
$832$	2.27409	−	1.21132i	0.0788398	−	0.0419949i
$833$	−5.19767	−	15.9968i	−0.180089	−	0.554255i
$834$	11.8515	−	2.88333i	0.410383	−	0.0998415i
$835$			28.5176i			0.986892i
$836$	10.6231	−	19.7913i	0.367406	−	0.684496i
$837$		−	15.7663i		−	0.544963i
$838$	−2.88676	−	11.8656i	−0.0997214	−	0.409889i
$839$	5.81010	+	17.8817i	0.200587	+	0.617343i	0.999866	+	0.0163829i	$0.00521508\pi$
$839$	5.81010	+	17.8817i	0.200587	+	0.617343i	−0.799279	+	0.600960i	$0.794785\pi$
$840$	−10.7115	+	0.941138i	−0.369581	+	0.0324723i
$841$	64.2619	+	46.6890i	2.21593	+	1.60997i
$842$	35.4766	−	21.8884i	1.22260	−	0.754323i
$843$	13.6836	+	4.44607i	0.471289	+	0.153131i
$844$	−5.92674	−	2.97468i	−0.204007	−	0.102393i
$845$	−11.9914	−	16.5047i	−0.412516	−	0.567780i
$846$	22.3985	+	9.19828i	0.770076	+	0.316243i
$847$	5.26876	+	19.8639i	0.181037	+	0.682530i
$848$	−22.6273	+	0.274491i	−0.777026	+	0.00942605i
$849$	−33.2809	+	24.1800i	−1.14220	+	0.829855i
$850$	1.27691	−	16.8789i	0.0437975	−	0.578942i
$851$	−10.4655	−	3.40045i	−0.358753	−	0.116566i
$852$	−28.2685	+	4.65322i	−0.968464	+	0.159417i
$853$	25.8045	−	35.5169i	0.883530	−	1.21607i	−0.0919009	−	0.995768i	$-0.529294\pi$
$853$	25.8045	−	35.5169i	0.883530	−	1.21607i	0.975431	−	0.220306i	$-0.0707057\pi$
$854$	−22.0138	−	18.6864i	−0.753296	−	0.639435i
$855$	−2.22705	−	6.85415i	−0.0761634	−	0.234407i
$856$	−7.32632	+	12.2033i	−0.250408	+	0.417100i
$857$	−35.4141			−1.20972			−0.604861	−	0.796331i	$-0.706771\pi$
$857$	−35.4141			−1.20972			−0.604861	+	0.796331i	$0.706771\pi$
$858$	1.93291	+	0.199699i	0.0659885	+	0.00681762i
$859$		−	36.4697i		−	1.24433i	−0.782886	−	0.622165i	$-0.786253\pi$
$859$		−	36.4697i		−	1.24433i	0.782886	−	0.622165i	$-0.213747\pi$
$860$	11.3164	+	1.72206i	0.385887	+	0.0587216i
$861$	−10.2835	+	3.34130i	−0.350459	+	0.113871i
$862$	19.8307	−	23.3619i	0.675438	−	0.795709i
$863$	−19.4427	−	14.1259i	−0.661836	−	0.480852i	0.205446	−	0.978668i	$-0.434135\pi$
$863$	−19.4427	−	14.1259i	−0.661836	−	0.480852i	−0.867283	+	0.497816i	$0.834135\pi$
$864$	−16.9279	−	26.7063i	−0.575900	−	0.908567i
$865$	7.36600	−	22.6702i	0.250452	−	0.770811i
$866$	−1.22848	+	16.2388i	−0.0417454	+	0.551816i
$867$	−4.51239	−	6.21078i	−0.153249	−	0.210929i
$868$	7.49756	+	7.40716i	0.254484	+	0.251415i
$869$	12.0936	−	15.7195i	0.410246	−	0.533247i
$870$	−11.3836	+	27.7199i	−0.385940	+	0.939793i
$871$	2.86319	−	2.08023i	0.0970155	−	0.0704859i
$872$	18.9054	+	21.7319i	0.640219	+	0.735936i
$873$	5.15271	−	15.8584i	0.174393	−	0.536726i
$874$	−12.5547	+	7.74601i	−0.424670	+	0.262013i
$875$	−13.0244	+	17.9265i	−0.440304	+	0.606027i
$876$	−14.9024	−	28.8142i	−0.503505	−	0.973542i
$877$	−17.7411	+	5.76443i	−0.599074	+	0.194651i	−0.592827	−	0.805330i	$-0.701988\pi$
$877$	−17.7411	+	5.76443i	−0.599074	+	0.194651i	−0.00624654	+	0.999980i	$0.501988\pi$
$878$	49.4086	−	12.0205i	1.66746	−	0.405674i
$879$	9.85952			0.332553
$880$	12.0742	+	17.1655i	0.407022	+	0.578647i
$881$	32.4553			1.09345			0.546723	−	0.837314i	$-0.315875\pi$
$881$	32.4553			1.09345			0.546723	+	0.837314i	$0.315875\pi$
$882$	−6.48827	+	1.57852i	−0.218471	+	0.0531516i
$883$	−12.3827	+	4.02340i	−0.416712	+	0.135398i	−0.509866	−	0.860254i	$-0.670305\pi$
$883$	−12.3827	+	4.02340i	−0.416712	+	0.135398i	0.0931540	+	0.995652i	$0.470305\pi$
$884$	−1.41816	−	2.74205i	−0.0476977	−	0.0922250i
$885$	−6.43999	+	8.86389i	−0.216478	+	0.297956i
$886$	33.4780	−	20.6552i	1.12471	−	0.693926i
$887$	5.91629	−	18.2085i	0.198649	−	0.611380i	−0.801265	−	0.598309i	$-0.795839\pi$
$887$	5.91629	−	18.2085i	0.198649	−	0.611380i	0.999915	−	0.0130707i	$-0.00416064\pi$
$888$	9.80571	−	8.53036i	0.329058	−	0.286260i
$889$	−19.7185	+	14.3264i	−0.661339	+	0.480491i
$890$	3.64582	−	8.87785i	0.122208	−	0.297586i
$891$	0.287030	−	10.4565i	0.00961586	−	0.350308i
$892$	−21.2065	−	20.9508i	−0.710046	−	0.701485i
$893$	25.3309	+	34.8650i	0.847666	+	1.16671i
$894$	−0.549951	+	7.26958i	−0.0183931	+	0.243131i
$895$	−10.8948	+	33.5308i	−0.364174	+	1.12081i
$896$	20.6529	+	4.49692i	0.689965	+	0.150231i
$897$	−1.03247	−	0.750131i	−0.0344731	−	0.0250461i
$898$	11.9750	−	14.1074i	0.399612	−	0.470769i
$899$	27.9343	−	9.07639i	0.931660	−	0.302715i
$900$	−6.64357	−	1.01097i	−0.221452	−	0.0336991i
$901$			27.1124i			0.903245i
$902$	15.7080	+	14.0933i	0.523020	+	0.469256i
$903$	8.69462			0.289339
$904$	19.5257	+	11.7223i	0.649414	+	0.389880i
$905$	−5.62731	−	17.3191i	−0.187058	−	0.575706i
$906$	3.23712	+	2.74783i	0.107546	+	0.0912904i
$907$	−31.3432	+	43.1403i	−1.04073	+	1.43245i	−0.144161	+	0.989554i	$0.546048\pi$
$907$	−31.3432	+	43.1403i	−1.04073	+	1.43245i	−0.896574	+	0.442894i	$0.853952\pi$
$908$	2.61026	−	0.429670i	0.0866246	−	0.0142591i
$909$	19.6568	+	6.38687i	0.651973	+	0.211839i
$910$	−0.101547	+	1.34230i	−0.00336624	+	0.0444969i
$911$	−38.2880	+	27.8178i	−1.26854	+	0.921646i	−0.999143	−	0.0413837i	$-0.986823\pi$
$911$	−38.2880	+	27.8178i	−1.26854	+	0.921646i	−0.269394	+	0.963030i	$0.586823\pi$
$912$	−0.211348	−	17.4222i	−0.00699844	−	0.576908i
$913$	−0.155152	+	0.436384i	−0.00513479	+	0.0144422i
$914$	8.67355	+	3.56193i	0.286896	+	0.117818i
$915$	−13.0718	−	17.9918i	−0.432141	−	0.594791i
$916$	42.1898	+	21.1755i	1.39399	+	0.699657i
$917$	−20.5255	−	6.66915i	−0.677813	−	0.220235i
$918$	−32.2412	+	19.8922i	−1.06412	+	0.656540i
$919$	−45.2313	−	32.8624i	−1.49204	−	1.08403i	−0.973420	−	0.229029i	$-0.926445\pi$
$919$	−45.2313	−	32.8624i	−1.49204	−	1.08403i	−0.518622	−	0.855003i	$-0.673555\pi$
$920$	−1.20636	−	13.7301i	−0.0397727	−	0.452669i
$921$	−1.42110	−	4.37369i	−0.0468268	−	0.144118i
$922$	−2.81833	−	11.5843i	−0.0928168	−	0.381509i
$923$			3.58657i			0.118054i
$924$	11.0284	+	11.5103i	0.362808	+	0.378661i
$925$		−	8.92170i		−	0.293344i
$926$	12.5878	−	3.06247i	0.413661	−	0.100639i
$927$	3.39945	+	10.4624i	0.111653	+	0.343631i
$928$	37.5723	−	45.3668i	1.23337	−	1.48924i
$929$	−16.3830	−	11.9029i	−0.537507	−	0.390522i	0.285651	−	0.958334i	$-0.407790\pi$
$929$	−16.3830	−	11.9029i	−0.537507	−	0.390522i	−0.823158	+	0.567812i	$0.807790\pi$
$930$	4.26219	+	6.90816i	0.139763	+	0.226527i
$931$	−11.3030	−	3.67257i	−0.370441	−	0.120363i
$932$	−2.21671	+	4.41656i	−0.0726107	+	0.144669i
$933$	0.0592174	+	0.0815058i	0.00193869	+	0.00266838i
$934$	−6.21767	+	15.1405i	−0.203449	+	0.495412i
$935$	20.7403	−	14.2159i	0.678282	−	0.464910i
$936$	−1.12796	+	0.479284i	−0.0368685	+	0.0156659i
$937$	32.8987	−	23.9023i	1.07475	−	0.780855i	0.0979939	−	0.995187i	$-0.468757\pi$
$937$	32.8987	−	23.9023i	1.07475	−	0.780855i	0.976761	+	0.214332i	$0.0687574\pi$
$938$	28.9501	+	2.19010i	0.945253	+	0.0715094i
$939$	−10.9464	−	3.55671i	−0.357223	−	0.116069i
$940$	−39.7301	+	6.53988i	−1.29585	+	0.213308i
$941$	1.31659	−	1.81214i	0.0429197	−	0.0590739i	−0.787018	−	0.616930i	$-0.788376\pi$
$941$	1.31659	−	1.81214i	0.0429197	−	0.0590739i	0.829937	+	0.557856i	$0.188376\pi$
$942$	−9.35416	+	11.0198i	−0.304775	+	0.359045i
$943$	−4.28293	−	13.1815i	−0.139471	−	0.429249i
$944$	17.2691	−	12.8696i	0.562060	−	0.418870i
$945$	16.5196			0.537382
$946$	−8.51086	−	14.6812i	−0.276712	−	0.477327i
$947$			14.7173i			0.478247i	0.970989	+	0.239123i	$0.0768601\pi$
$947$			14.7173i			0.478247i	−0.970989	+	0.239123i	$0.923140\pi$
$948$	2.31444	−	15.2093i	0.0751695	−	0.493974i
$949$	−3.86239	+	1.25497i	−0.125378	+	0.0407379i
$950$	−9.11825	−	7.74002i	−0.295835	−	0.251119i
$951$	25.4788	+	18.5114i	0.826207	+	0.600275i
$952$	5.68763	−	24.6776i	0.184337	−	0.799806i
$953$	−5.65681	+	17.4099i	−0.183242	+	0.563961i	−0.999914	−	0.0131415i	$-0.995817\pi$
$953$	−5.65681	+	17.4099i	−0.183242	+	0.563961i	0.816672	+	0.577103i	$0.195817\pi$
$954$	10.7329	+	0.811957i	0.347491	+	0.0262881i
$955$	10.0397	+	13.8184i	0.324876	+	0.447153i
$956$	22.5078	+	22.2364i	0.727955	+	0.719178i
$957$	42.6115	−	12.5636i	1.37743	−	0.406123i
$958$	−25.0627	−	10.2924i	−0.809739	−	0.332532i
$959$	27.2350	−	19.7874i	0.879465	−	0.638969i
$960$	14.6368	+	7.12541i	0.472401	+	0.229972i
$961$	−7.12094	+	21.9160i	−0.229708	+	0.706967i
$962$	−0.854353	−	1.38473i	−0.0275454	−	0.0446456i
$963$	3.97947	−	5.47727i	0.128237	−	0.176503i
$964$	−5.72933	+	2.96315i	−0.184529	+	0.0954365i
$965$	−13.6256	+	4.42723i	−0.438624	+	0.142517i
$966$	−2.47485	−	10.1725i	−0.0796271	−	0.327295i
$967$	7.98210			0.256687			0.128343	−	0.991730i	$-0.459034\pi$
$967$	7.98210			0.256687			0.128343	+	0.991730i	$0.459034\pi$
$968$	8.64025	−	29.8889i	0.277708	−	0.960666i
$969$	−20.8756			−0.670620
$970$	6.55471	+	26.9421i	0.210459	+	0.865060i
$971$	−33.8405	+	10.9954i	−1.08599	+	0.352860i	−0.796697	−	0.604379i	$-0.793421\pi$
$971$	−33.8405	+	10.9954i	−1.08599	+	0.352860i	−0.289296	+	0.957240i	$0.593421\pi$
$972$	11.6791	+	22.5819i	0.374608	+	0.724315i
$973$	7.36284	−	10.1341i	0.236042	−	0.324884i
$974$	31.5140	+	51.0779i	1.00977	+	1.63664i
$975$	0.319738	−	0.984052i	0.0102398	−	0.0315149i
$976$	14.0122	+	41.4092i	0.448521	+	1.32548i
$977$	31.2139	−	22.6782i	0.998621	−	0.725540i	0.0368286	−	0.999322i	$-0.488274\pi$
$977$	31.2139	−	22.6782i	0.998621	−	0.725540i	0.961792	+	0.273781i	$0.0882744\pi$
$978$	−9.44927	−	3.88048i	−0.302154	−	0.124084i
$979$	−13.6472	+	4.02374i	−0.436166	+	0.128599i
$980$	7.80397	−	7.89921i	0.249289	−	0.252331i
$981$	−8.05321	−	11.0843i	−0.257119	−	0.353894i
$982$	−55.3627	−	4.18825i	−1.76670	−	0.133652i
$983$	10.3967	−	31.9976i	0.331602	−	1.02057i	−0.636770	−	0.771054i	$-0.719730\pi$
$983$	10.3967	−	31.9976i	0.331602	−	1.02057i	0.968372	−	0.249512i	$-0.0802702\pi$
$984$	15.9516	+	3.67648i	0.508519	+	0.117202i
$985$	−11.1870	−	8.12781i	−0.356446	−	0.258973i
$986$	−53.8051	−	45.6724i	−1.71350	−	1.45451i
$987$	−29.0872	+	9.45100i	−0.925855	+	0.300829i
$988$	−2.15643	−	0.328151i	−0.0686053	−	0.0104399i
$989$			11.1449i			0.354387i
$990$	−5.00649	−	8.63617i	−0.159117	−	0.274475i
$991$	34.6130			1.09952			0.549758	−	0.835324i	$-0.314720\pi$
$991$	34.6130			1.09952			0.549758	+	0.835324i	$0.314720\pi$
$992$	−3.95970	−	15.4570i	−0.125721	−	0.490760i
$993$	−9.62275	−	29.6158i	−0.305369	−	0.939829i
$994$	−19.0403	+	22.4307i	−0.603921	+	0.711458i
$995$	2.37647	−	3.27093i	0.0753391	−	0.103695i
$996$	0.0583510	+	0.354485i	0.00184892	+	0.0112323i
$997$	13.5735	+	4.41030i	0.429878	+	0.139676i	0.515961	−	0.856612i	$-0.327435\pi$
$997$	13.5735	+	4.41030i	0.429878	+	0.139676i	−0.0860831	+	0.996288i	$0.527435\pi$
$998$	−31.9601	−	2.41781i	−1.01168	−	0.0765345i
$999$	−16.1539	+	11.7365i	−0.511086	+	0.371326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.2.o.a.69.10	yes	40
3.2	odd	2		792.2.br.b.685.1		40
4.3	odd	2		352.2.w.a.113.8		40
8.3	odd	2		352.2.w.a.113.3		40
8.5	even	2	inner	88.2.o.a.69.8	yes	40
11.2	odd	10		968.2.c.i.485.18		20
11.3	even	5		968.2.o.j.269.5		40
11.4	even	5	inner	88.2.o.a.37.8	✓	40
11.5	even	5		968.2.o.j.493.3		40
11.6	odd	10		968.2.o.d.493.8		40
11.7	odd	10		968.2.o.i.565.3		40
11.8	odd	10		968.2.o.d.269.6		40
11.9	even	5		968.2.c.h.485.3		20
11.10	odd	2		968.2.o.i.245.1		40
24.5	odd	2		792.2.br.b.685.3		40
33.26	odd	10		792.2.br.b.37.3		40
44.15	odd	10		352.2.w.a.81.3		40
44.31	odd	10		3872.2.c.h.1937.6		20
44.35	even	10		3872.2.c.i.1937.6		20
88.5	even	10		968.2.o.j.493.5		40
88.13	odd	10		968.2.c.i.485.17		20
88.21	odd	2		968.2.o.i.245.3		40
88.29	odd	10		968.2.o.i.565.1		40
88.35	even	10		3872.2.c.i.1937.15		20
88.37	even	10	inner	88.2.o.a.37.10	yes	40
88.53	even	10		968.2.c.h.485.4		20
88.59	odd	10		352.2.w.a.81.8		40
88.61	odd	10		968.2.o.d.493.6		40
88.69	even	10		968.2.o.j.269.3		40
88.75	odd	10		3872.2.c.h.1937.15		20
88.85	odd	10		968.2.o.d.269.8		40
264.125	odd	10		792.2.br.b.37.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.37.8	✓	40	11.4	even	5	inner
88.2.o.a.37.10	yes	40	88.37	even	10	inner
88.2.o.a.69.8	yes	40	8.5	even	2	inner
88.2.o.a.69.10	yes	40	1.1	even	1	trivial
352.2.w.a.81.3		40	44.15	odd	10
352.2.w.a.81.8		40	88.59	odd	10
352.2.w.a.113.3		40	8.3	odd	2
352.2.w.a.113.8		40	4.3	odd	2
792.2.br.b.37.1		40	264.125	odd	10
792.2.br.b.37.3		40	33.26	odd	10
792.2.br.b.685.1		40	3.2	odd	2
792.2.br.b.685.3		40	24.5	odd	2
968.2.c.h.485.3		20	11.9	even	5
968.2.c.h.485.4		20	88.53	even	10
968.2.c.i.485.17		20	88.13	odd	10
968.2.c.i.485.18		20	11.2	odd	10
968.2.o.d.269.6		40	11.8	odd	10
968.2.o.d.269.8		40	88.85	odd	10
968.2.o.d.493.6		40	88.61	odd	10
968.2.o.d.493.8		40	11.6	odd	10
968.2.o.i.245.1		40	11.10	odd	2
968.2.o.i.245.3		40	88.21	odd	2
968.2.o.i.565.1		40	88.29	odd	10
968.2.o.i.565.3		40	11.7	odd	10
968.2.o.j.269.3		40	88.69	even	10
968.2.o.j.269.5		40	11.3	even	5
968.2.o.j.493.3		40	11.5	even	5
968.2.o.j.493.5		40	88.5	even	10
3872.2.c.h.1937.6		20	44.31	odd	10
3872.2.c.h.1937.15		20	88.75	odd	10
3872.2.c.i.1937.6		20	44.35	even	10
3872.2.c.i.1937.15		20	88.35	even	10

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:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	88.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37413 - 0.334310i) q^{2} +(-1.22337 + 0.397498i) q^{3} +(1.77647 - 0.918772i) q^{4} +(0.929834 - 1.27981i) q^{5} +(-1.54819 + 0.955200i) q^{6} +(-0.577320 + 1.77681i) q^{7} +(2.13395 - 1.85641i) q^{8} +(-1.08841 + 0.790780i) q^{9} +(0.849862 - 2.06948i) q^{10} +(-3.18123 + 0.937955i) q^{11} +(-1.80808 + 1.83015i) q^{12} +(0.189309 + 0.260562i) q^{13} +(-0.199308 + 2.63457i) q^{14} +(-0.628813 + 1.93529i) q^{15} +(2.31171 - 3.26435i) q^{16} +(-3.87722 - 2.81696i) q^{17} +(-1.23126 + 1.45050i) q^{18} +(-3.22055 + 1.04642i) q^{19} +(0.475974 - 3.12785i) q^{20} -2.40318i q^{21} +(-4.05786 + 2.35239i) q^{22} +3.08044 q^{23} +(-1.87270 + 3.11932i) q^{24} +(0.771771 + 2.37527i) q^{25} +(0.347245 + 0.294758i) q^{26} +(3.28546 - 4.52205i) q^{27} +(0.606889 + 3.68688i) q^{28} +(9.90342 + 3.21782i) q^{29} +(-0.217085 + 2.86956i) q^{30} +(2.28197 - 1.65795i) q^{31} +(2.08529 - 5.25847i) q^{32} +(3.51900 - 2.41200i) q^{33} +(-6.26955 - 2.57468i) q^{34} +(1.73716 + 2.39100i) q^{35} +(-1.20699 + 2.40480i) q^{36} +(-3.39741 - 1.10389i) q^{37} +(-4.07563 + 2.51458i) q^{38} +(-0.335169 - 0.243514i) q^{39} +(-0.391621 - 4.45720i) q^{40} +(-1.39036 - 4.27910i) q^{41} +(-0.803409 - 3.30229i) q^{42} +3.61796i q^{43} +(-4.78961 + 4.58908i) q^{44} +2.12826i q^{45} +(4.23293 - 1.02982i) q^{46} +(-3.93270 - 12.1036i) q^{47} +(-1.53052 + 4.91242i) q^{48} +(2.83937 + 2.06292i) q^{49} +(1.85459 + 3.00592i) q^{50} +(5.86302 + 1.90501i) q^{51} +(0.575700 + 0.288949i) q^{52} +(-3.32525 - 4.57681i) q^{53} +(3.00289 - 7.31225i) q^{54} +(-1.75762 + 4.94351i) q^{55} +(2.06651 + 4.86337i) q^{56} +(3.52398 - 2.56032i) q^{57} +(14.6843 + 1.11089i) q^{58} +(5.12075 + 1.66383i) q^{59} +(0.661019 + 4.01572i) q^{60} +(-6.42387 + 8.84170i) q^{61} +(2.58146 - 3.04112i) q^{62} +(-0.776701 - 2.39044i) q^{63} +(1.10750 - 7.92297i) q^{64} +0.509496 q^{65} +(4.02921 - 4.49084i) q^{66} -10.9885i q^{67} +(-9.47592 - 1.44198i) q^{68} +(-3.76852 + 1.22447i) q^{69} +(3.18642 + 2.70479i) q^{70} +(9.00915 + 6.54553i) q^{71} +(-0.854616 + 3.70803i) q^{72} +(-3.89653 + 11.9923i) q^{73} +(-5.03753 - 0.381094i) q^{74} +(-1.88833 - 2.59906i) q^{75} +(-4.75980 + 4.81789i) q^{76} +(0.170022 - 6.19394i) q^{77} +(-0.541975 - 0.222570i) q^{78} +(-4.83788 + 3.51492i) q^{79} +(-2.02823 - 5.99385i) q^{80} +(-0.974626 + 2.99959i) q^{81} +(-3.34109 - 5.41523i) q^{82} +(0.0820804 - 0.112974i) q^{83} +(-2.20798 - 4.26919i) q^{84} +(-7.21034 + 2.34278i) q^{85} +(1.20952 + 4.97155i) q^{86} -13.3946 q^{87} +(-5.04737 + 7.90721i) q^{88} +4.28990 q^{89} +(0.711498 + 2.92450i) q^{90} +(-0.572261 + 0.185939i) q^{91} +(5.47232 - 2.83022i) q^{92} +(-2.13267 + 2.93536i) q^{93} +(-9.45040 - 15.3172i) q^{94} +(-1.65536 + 5.09468i) q^{95} +(-0.460858 + 7.26197i) q^{96} +(-10.0271 + 7.28510i) q^{97} +(4.59132 + 1.88549i) q^{98} +(2.72078 - 3.53654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - q^{4} - 7 q^{6} - 10 q^{7} - 5 q^{8} - 20 q^{10} - 6 q^{12} + 2 q^{14} - 18 q^{15} + 15 q^{16} - 6 q^{17} - 20 q^{18} + 8 q^{20} - 35 q^{22} - 8 q^{23} + 25 q^{24} - 4 q^{25} - 10 q^{26}+ \cdots - 144 q^{98}+O(q^{100}) \) 40 * q - 5 * q^2 - q^4 - 7 * q^6 - 10 * q^7 - 5 * q^8 - 20 * q^10 - 6 * q^12 + 2 * q^14 - 18 * q^15 + 15 * q^16 - 6 * q^17 - 20 * q^18 + 8 * q^20 - 35 * q^22 - 8 * q^23 + 25 * q^24 - 4 * q^25 - 10 * q^26 + 32 * q^28 - 28 * q^30 - 6 * q^31 + 20 * q^32 - 10 * q^33 + 10 * q^34 + 18 * q^36 + 12 * q^38 - 34 * q^39 + 10 * q^40 - 14 * q^41 + 40 * q^42 + 26 * q^44 + 18 * q^46 - 6 * q^47 + 18 * q^48 - 4 * q^49 + 61 * q^50 + 20 * q^52 + 108 * q^54 - 2 * q^55 - 32 * q^56 - 26 * q^57 + 4 * q^58 - 46 * q^60 + 48 * q^62 + 60 * q^63 - 49 * q^64 - 36 * q^65 + 50 * q^66 - 42 * q^68 - 8 * q^70 + 22 * q^71 - 101 * q^72 - 6 * q^73 + 54 * q^74 - 134 * q^76 - 12 * q^78 + 74 * q^79 - 44 * q^80 - 4 * q^81 - 31 * q^82 - 28 * q^84 - 15 * q^86 + 68 * q^87 - 73 * q^88 - 16 * q^89 - 84 * q^90 - 4 * q^92 - 100 * q^94 + 66 * q^95 - 30 * q^96 + 10 * q^97 - 144 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more