LMFDB - Embedded newform 273.2.by.c.202.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(76,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("273.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.by (of order $12$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			202.6
Character	$\chi$	$=$	273.202
Dual form			273.2.by.c.223.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34112 - 0.359352i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.0625832 + 0.0361324i) q^{4} +(-2.52867 + 2.52867i) q^{5} +(-1.34112 - 0.359352i) q^{6} +(-1.59355 + 2.11202i) q^{7} +(-2.03448 + 2.03448i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.34112 - 0.359352i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.0625832 + 0.0361324i) q^{4} +(-2.52867 + 2.52867i) q^{5} +(-1.34112 - 0.359352i) q^{6} +(-1.59355 + 2.11202i) q^{7} +(-2.03448 + 2.03448i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.48257 + 4.29993i) q^{10} +(0.0529715 + 0.197692i) q^{11} +0.0722649 q^{12} +(2.07540 - 2.94834i) q^{13} +(-1.37818 + 3.40511i) q^{14} +(3.45423 - 0.925558i) q^{15} +(-1.92512 + 3.33441i) q^{16} +(-1.13739 - 1.97002i) q^{17} +(0.981768 + 0.981768i) q^{18} +(1.50152 + 0.402330i) q^{19} +(0.0668853 - 0.249619i) q^{20} +(2.43606 - 1.03229i) q^{21} +(0.142082 + 0.246094i) q^{22} +(2.59661 + 1.49915i) q^{23} +(2.77915 - 0.744672i) q^{24} -7.78835i q^{25} +(1.72386 - 4.69988i) q^{26} -1.00000i q^{27} +(0.0234170 - 0.189755i) q^{28} +(-4.75430 + 8.23469i) q^{29} +(4.29993 - 2.48257i) q^{30} +(-2.75209 + 2.75209i) q^{31} +(0.105751 - 0.394667i) q^{32} +(0.0529715 - 0.197692i) q^{33} +(-2.23331 - 2.23331i) q^{34} +(-1.31104 - 9.37014i) q^{35} +(-0.0625832 - 0.0361324i) q^{36} +(1.17697 + 4.39250i) q^{37} +2.15829 q^{38} +(-3.27152 + 1.51564i) q^{39} -10.2891i q^{40} +(1.36054 + 5.07760i) q^{41} +(2.89609 - 2.25982i) q^{42} +(1.76513 - 1.01910i) q^{43} +(-0.0104582 - 0.0104582i) q^{44} +(-3.45423 - 0.925558i) q^{45} +(4.02109 + 1.07745i) q^{46} +(9.42358 + 9.42358i) q^{47} +(3.33441 - 1.92512i) q^{48} +(-1.92122 - 6.73119i) q^{49} +(-2.79876 - 10.4451i) q^{50} +2.27478i q^{51} +(-0.0233541 + 0.259506i) q^{52} -12.6997 q^{53} +(-0.359352 - 1.34112i) q^{54} +(-0.633846 - 0.365951i) q^{55} +(-1.05481 - 7.53890i) q^{56} +(-1.09919 - 1.09919i) q^{57} +(-3.41693 + 12.7522i) q^{58} +(0.510631 - 1.90570i) q^{59} +(-0.182734 + 0.182734i) q^{60} +(0.850570 - 0.491077i) q^{61} +(-2.70191 + 4.67985i) q^{62} +(-2.62583 - 0.324044i) q^{63} -8.26779i q^{64} +(2.20740 + 12.7034i) q^{65} -0.284164i q^{66} +(15.1633 - 4.06300i) q^{67} +(0.142363 + 0.0821934i) q^{68} +(-1.49915 - 2.59661i) q^{69} +(-5.12543 - 12.0954i) q^{70} +(0.00355777 - 0.0132778i) q^{71} +(-2.77915 - 0.744672i) q^{72} +(-2.24560 - 2.24560i) q^{73} +(3.15691 + 5.46792i) q^{74} +(-3.89417 + 6.74490i) q^{75} +(-0.108507 + 0.0290743i) q^{76} +(-0.501942 - 0.203155i) q^{77} +(-3.84285 + 3.20828i) q^{78} +12.7231 q^{79} +(-3.56363 - 13.2996i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.64929 + 6.32076i) q^{82} +(-3.37812 + 3.37812i) q^{83} +(-0.115157 + 0.152625i) q^{84} +(7.85762 + 2.10544i) q^{85} +(2.00104 - 2.00104i) q^{86} +(8.23469 - 4.75430i) q^{87} +(-0.509971 - 0.294432i) q^{88} +(-11.8364 + 3.17155i) q^{89} -4.96513 q^{90} +(2.91971 + 9.08159i) q^{91} -0.216672 q^{92} +(3.75943 - 1.00734i) q^{93} +(16.0245 + 9.25177i) q^{94} +(-4.81420 + 2.77948i) q^{95} +(-0.288916 + 0.288916i) q^{96} +(7.85674 + 2.10521i) q^{97} +(-4.99545 - 8.33694i) q^{98} +(-0.144721 + 0.144721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9	$ 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9} - 2 q^{10} - 4 q^{11} - 32 q^{12} - 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} + 8 q^{17} + 2 q^{18} - 2 q^{19} - 44 q^{20} + 2 q^{21} - 4 q^{22} - 18 q^{23} - 4 q^{24} + 28 q^{26} - 18 q^{28} - 18 q^{29} + 14 q^{31} - 8 q^{32} - 4 q^{33} + 66 q^{34} - 20 q^{35} + 6 q^{36} - 24 q^{37} - 24 q^{38} + 8 q^{39} + 16 q^{42} - 6 q^{43} - 20 q^{44} - 4 q^{45} - 58 q^{46} + 28 q^{47} + 60 q^{48} + 10 q^{49} + 70 q^{50} - 28 q^{52} - 80 q^{53} + 4 q^{54} - 60 q^{55} - 120 q^{56} + 16 q^{57} - 4 q^{58} + 42 q^{59} - 58 q^{60} - 36 q^{61} - 52 q^{62} + 2 q^{63} + 14 q^{65} + 26 q^{67} + 72 q^{68} - 2 q^{69} + 68 q^{70} - 4 q^{71} + 4 q^{72} - 12 q^{73} - 18 q^{74} - 16 q^{75} + 48 q^{76} - 28 q^{77} - 14 q^{78} - 4 q^{79} + 98 q^{80} - 16 q^{81} - 20 q^{82} + 36 q^{83} + 32 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} + 54 q^{89} - 4 q^{90} - 54 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} - 22 q^{96} + 40 q^{97} + 4 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9 - 2 * q^10 - 4 * q^11 - 32 * q^12 - 6 * q^13 + 34 * q^14 + 4 * q^15 + 14 * q^16 + 8 * q^17 + 2 * q^18 - 2 * q^19 - 44 * q^20 + 2 * q^21 - 4 * q^22 - 18 * q^23 - 4 * q^24 + 28 * q^26 - 18 * q^28 - 18 * q^29 + 14 * q^31 - 8 * q^32 - 4 * q^33 + 66 * q^34 - 20 * q^35 + 6 * q^36 - 24 * q^37 - 24 * q^38 + 8 * q^39 + 16 * q^42 - 6 * q^43 - 20 * q^44 - 4 * q^45 - 58 * q^46 + 28 * q^47 + 60 * q^48 + 10 * q^49 + 70 * q^50 - 28 * q^52 - 80 * q^53 + 4 * q^54 - 60 * q^55 - 120 * q^56 + 16 * q^57 - 4 * q^58 + 42 * q^59 - 58 * q^60 - 36 * q^61 - 52 * q^62 + 2 * q^63 + 14 * q^65 + 26 * q^67 + 72 * q^68 - 2 * q^69 + 68 * q^70 - 4 * q^71 + 4 * q^72 - 12 * q^73 - 18 * q^74 - 16 * q^75 + 48 * q^76 - 28 * q^77 - 14 * q^78 - 4 * q^79 + 98 * q^80 - 16 * q^81 - 20 * q^82 + 36 * q^83 + 32 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 + 54 * q^89 - 4 * q^90 - 54 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 - 22 * q^96 + 40 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$-1$

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 $

$2$	1.34112	−	0.359352i	0.948315	−	0.254100i	0.248668	−	0.968589i	$-0.420007\pi$
$2$	1.34112	−	0.359352i	0.948315	−	0.254100i	0.699647	+	0.714489i	$0.253341\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.0625832	+	0.0361324i	−0.0312916	+	0.0180662i
$5$	−2.52867	+	2.52867i	−1.13086	+	1.13086i	−0.140821	+	0.990035i	$0.544974\pi$
$5$	−2.52867	+	2.52867i	−1.13086	+	1.13086i	−0.990035	+	0.140821i	$0.955026\pi$
$6$	−1.34112	−	0.359352i	−0.547510	−	0.146705i
$7$	−1.59355	+	2.11202i	−0.602304	+	0.798267i
$7$	−1.59355	+	2.11202i	−0.602304	+	0.798267i
$8$	−2.03448	+	2.03448i	−0.719298	+	0.719298i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.48257	+	4.29993i	−0.785056	+	1.35976i
$11$	0.0529715	+	0.197692i	0.0159715	+	0.0596065i	0.973452	−	0.228893i	$-0.0735105\pi$
$11$	0.0529715	+	0.197692i	0.0159715	+	0.0596065i	−0.957480	+	0.288499i	$0.906844\pi$
$12$	0.0722649			0.0208611
$13$	2.07540	−	2.94834i	0.575611	−	0.817724i
$13$	2.07540	−	2.94834i	0.575611	−	0.817724i
$14$	−1.37818	+	3.40511i	−0.368334	+	0.910054i
$15$	3.45423	−	0.925558i	0.891878	−	0.238978i
$16$	−1.92512	+	3.33441i	−0.481281	+	0.833603i
$17$	−1.13739	−	1.97002i	−0.275858	−	0.477800i	0.694493	−	0.719499i	$-0.255629\pi$
$17$	−1.13739	−	1.97002i	−0.275858	−	0.477800i	−0.970351	+	0.241699i	$0.922295\pi$
$18$	0.981768	+	0.981768i	0.231405	+	0.231405i
$19$	1.50152	+	0.402330i	0.344472	+	0.0923009i	0.426907	−	0.904296i	$-0.359603\pi$
$19$	1.50152	+	0.402330i	0.344472	+	0.0923009i	−0.0824354	+	0.996596i	$0.526270\pi$
$20$	0.0668853	−	0.249619i	0.0149560	−	0.0558166i
$21$	2.43606	−	1.03229i	0.531592	−	0.225263i
$22$	0.142082	+	0.246094i	0.0302920	+	0.0524673i
$23$	2.59661	+	1.49915i	0.541430	+	0.312595i	0.745658	−	0.666328i	$-0.232135\pi$
$23$	2.59661	+	1.49915i	0.541430	+	0.312595i	−0.204228	+	0.978923i	$0.565468\pi$
$24$	2.77915	−	0.744672i	0.567293	−	0.152006i
$25$		−	7.78835i		−	1.55767i
$26$	1.72386	−	4.69988i	0.338077	−	0.921722i
$27$		−	1.00000i		−	0.192450i
$28$	0.0234170	−	0.189755i	0.00442540	−	0.0358604i
$29$	−4.75430	+	8.23469i	−0.882852	+	1.52914i	−0.0346955	+	0.999398i	$0.511046\pi$
$29$	−4.75430	+	8.23469i	−0.882852	+	1.52914i	−0.848156	+	0.529746i	$0.822287\pi$
$30$	4.29993	−	2.48257i	0.785056	−	0.453253i
$31$	−2.75209	+	2.75209i	−0.494290	+	0.494290i	−0.909655	−	0.415365i	$-0.863654\pi$
$31$	−2.75209	+	2.75209i	−0.494290	+	0.494290i	0.415365	+	0.909655i	$0.363654\pi$
$32$	0.105751	−	0.394667i	0.0186943	−	0.0697679i
$33$	0.0529715	−	0.197692i	0.00922115	−	0.0344138i
$34$	−2.23331	−	2.23331i	−0.383009	−	0.383009i
$35$	−1.31104	−	9.37014i	−0.221605	−	1.58384i
$36$	−0.0625832	−	0.0361324i	−0.0104305	−	0.00602207i
$37$	1.17697	+	4.39250i	0.193492	+	0.722122i	0.992652	+	0.121004i	$0.0386114\pi$
$37$	1.17697	+	4.39250i	0.193492	+	0.722122i	−0.799160	+	0.601119i	$0.794722\pi$
$38$	2.15829			0.350121
$39$	−3.27152	+	1.51564i	−0.523862	+	0.242697i
$40$		−	10.2891i		−	1.62684i
$41$	1.36054	+	5.07760i	0.212480	+	0.792988i	0.987038	+	0.160485i	$0.0513058\pi$
$41$	1.36054	+	5.07760i	0.212480	+	0.792988i	−0.774558	+	0.632503i	$0.782028\pi$
$42$	2.89609	−	2.25982i	0.446877	−	0.348698i
$43$	1.76513	−	1.01910i	0.269180	−	0.155411i	−0.359335	−	0.933209i	$-0.616996\pi$
$43$	1.76513	−	1.01910i	0.269180	−	0.155411i	0.628515	+	0.777798i	$0.283663\pi$
$44$	−0.0104582	−	0.0104582i	−0.00157664	−	0.00157664i
$45$	−3.45423	−	0.925558i	−0.514926	−	0.137974i
$46$	4.02109	+	1.07745i	0.592877	+	0.158861i
$47$	9.42358	+	9.42358i	1.37457	+	1.37457i	0.853535	+	0.521036i	$0.174454\pi$
$47$	9.42358	+	9.42358i	1.37457	+	1.37457i	0.521036	+	0.853535i	$0.325546\pi$
$48$	3.33441	−	1.92512i	0.481281	−	0.277868i
$49$	−1.92122	−	6.73119i	−0.274460	−	0.961599i
$50$	−2.79876	−	10.4451i	−0.395804	−	1.47716i
$51$			2.27478i			0.318533i
$52$	−0.0233541	+	0.259506i	−0.00323863	+	0.0359870i
$53$	−12.6997			−1.74444			−0.872218	−	0.489117i	$-0.837319\pi$
$53$	−12.6997			−1.74444			−0.872218	+	0.489117i	$0.837319\pi$
$54$	−0.359352	−	1.34112i	−0.0489016	−	0.182503i
$55$	−0.633846	−	0.365951i	−0.0854678	−	0.0493449i
$56$	−1.05481	−	7.53890i	−0.140956	−	1.00743i
$57$	−1.09919	−	1.09919i	−0.145591	−	0.145591i
$58$	−3.41693	+	12.7522i	−0.448666	+	1.67444i
$59$	0.510631	−	1.90570i	0.0664785	−	0.248101i	−0.924688	−	0.380726i	$-0.875674\pi$
$59$	0.510631	−	1.90570i	0.0664785	−	0.248101i	0.991166	+	0.132625i	$0.0423407\pi$
$60$	−0.182734	+	0.182734i	−0.0235909	+	0.0235909i
$61$	0.850570	−	0.491077i	0.108904	−	0.0628760i	−0.444558	−	0.895750i	$-0.646639\pi$
$61$	0.850570	−	0.491077i	0.108904	−	0.0628760i	0.553463	+	0.832874i	$0.313306\pi$
$62$	−2.70191	+	4.67985i	−0.343143	+	0.594342i
$63$	−2.62583	−	0.324044i	−0.330824	−	0.0408258i
$64$		−	8.26779i		−	1.03347i
$65$	2.20740	+	12.7034i	0.273794	+	1.57566i
$66$		−	0.284164i		−	0.0349782i
$67$	15.1633	−	4.06300i	1.85249	−	0.496374i	0.852828	−	0.522192i	$-0.174885\pi$
$67$	15.1633	−	4.06300i	1.85249	−	0.496374i	0.999667	+	0.0258173i	$0.00821883\pi$
$68$	0.142363	+	0.0821934i	0.0172641	+	0.00996742i
$69$	−1.49915	−	2.59661i	−0.180477	−	0.312595i
$70$	−5.12543	−	12.0954i	−0.612607	−	1.44567i
$71$	0.00355777	−	0.0132778i	0.000422230	−	0.00157578i	−0.965714	−	0.259607i	$-0.916407\pi$
$71$	0.00355777	−	0.0132778i	0.000422230	−	0.00157578i	0.966137	+	0.258031i	$0.0830737\pi$
$72$	−2.77915	−	0.744672i	−0.327527	−	0.0877605i
$73$	−2.24560	−	2.24560i	−0.262827	−	0.262827i	0.563374	−	0.826202i	$-0.309503\pi$
$73$	−2.24560	−	2.24560i	−0.262827	−	0.262827i	−0.826202	+	0.563374i	$0.809503\pi$
$74$	3.15691	+	5.46792i	0.366983	+	0.635633i
$75$	−3.89417	+	6.74490i	−0.449660	+	0.778835i
$76$	−0.108507	+	0.0290743i	−0.0124466	+	0.00333506i
$77$	−0.501942	−	0.203155i	−0.0572016	−	0.0231517i
$78$	−3.84285	+	3.20828i	−0.435117	+	0.363267i
$79$	12.7231			1.43146			0.715732	−	0.698375i	$-0.246093\pi$
$79$	12.7231			1.43146			0.715732	+	0.698375i	$0.246093\pi$
$80$	−3.56363	−	13.2996i	−0.398425	−	1.48694i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.64929	+	6.32076i	0.402997	+	0.698011i
$83$	−3.37812	+	3.37812i	−0.370797	+	0.370797i	−0.867767	−	0.496971i	$-0.834446\pi$
$83$	−3.37812	+	3.37812i	−0.370797	+	0.370797i	0.496971	+	0.867767i	$0.334446\pi$
$84$	−0.115157	+	0.152625i	−0.0125647	+	0.0166527i
$85$	7.85762	+	2.10544i	0.852278	+	0.228367i
$86$	2.00104	−	2.00104i	0.215777	−	0.215777i
$87$	8.23469	−	4.75430i	0.882852	−	0.509715i
$88$	−0.509971	−	0.294432i	−0.0543631	−	0.0313866i
$89$	−11.8364	+	3.17155i	−1.25466	+	0.336184i	−0.824133	−	0.566396i	$-0.808337\pi$
$89$	−11.8364	+	3.17155i	−1.25466	+	0.336184i	−0.430523	+	0.902580i	$0.641671\pi$
$90$	−4.96513			−0.523371
$91$	2.91971	+	9.08159i	0.306069	+	0.952009i
$92$	−0.216672			−0.0225896
$93$	3.75943	−	1.00734i	0.389834	−	0.104456i
$94$	16.0245	+	9.25177i	1.65280	+	0.954247i
$95$	−4.81420	+	2.77948i	−0.493927	+	0.285169i
$96$	−0.288916	+	0.288916i	−0.0294874	+	0.0294874i
$97$	7.85674	+	2.10521i	0.797731	+	0.213751i	0.634587	−	0.772851i	$-0.281170\pi$
$97$	7.85674	+	2.10521i	0.797731	+	0.213751i	0.163143	+	0.986602i	$0.447837\pi$
$98$	−4.99545	−	8.33694i	−0.504616	−	0.842158i
$99$	−0.144721	+	0.144721i	−0.0145450	+	0.0145450i
$100$	0.281412	+	0.487420i	0.0281412	+	0.0487420i
$101$	5.41672	−	9.38204i	0.538984	−	0.933548i	−0.459975	−	0.887932i	$-0.652142\pi$
$101$	5.41672	−	9.38204i	0.538984	−	0.933548i	0.998959	−	0.0456161i	$-0.0145251\pi$
$102$	0.817447	+	3.05075i	0.0809393	+	0.302070i
$103$	−2.40912			−0.237378			−0.118689	−	0.992931i	$-0.537869\pi$
$103$	−2.40912			−0.237378			−0.118689	+	0.992931i	$0.537869\pi$
$104$	1.77600	+	10.2207i	0.174151	+	1.00222i
$105$	−3.54968	+	8.77030i	−0.346414	+	0.855894i
$106$	−17.0318	+	4.56366i	−1.65428	+	0.443262i
$107$	−2.22804	+	3.85907i	−0.215392	+	0.373071i	−0.953394	−	0.301728i	$-0.902436\pi$
$107$	−2.22804	+	3.85907i	−0.215392	+	0.373071i	0.738001	+	0.674799i	$0.235770\pi$
$108$	0.0361324	+	0.0625832i	0.00347685	+	0.00602207i
$109$	−11.9987	−	11.9987i	−1.14927	−	1.14927i	−0.986697	−	0.162570i	$-0.948022\pi$
$109$	−11.9987	−	11.9987i	−1.14927	−	1.14927i	−0.162570	−	0.986697i	$-0.551978\pi$
$110$	−0.981569	−	0.263010i	−0.0935889	−	0.0250771i
$111$	1.17697	−	4.39250i	0.111713	−	0.416918i
$112$	−3.97455	−	9.37943i	−0.375560	−	0.886273i
$113$	0.238333	+	0.412805i	0.0224205	+	0.0388334i	0.877018	−	0.480458i	$-0.159529\pi$
$113$	0.238333	+	0.412805i	0.0224205	+	0.0388334i	−0.854597	+	0.519291i	$0.826196\pi$
$114$	−1.86914	−	1.07915i	−0.175061	−	0.101071i
$115$	−10.3568	+	2.77510i	−0.965780	+	0.258780i
$116$		−	0.687138i		−	0.0637992i
$117$	3.59104	+	0.323173i	0.331992	+	0.0298774i
$118$		−	2.73927i		−	0.252170i
$119$	5.97320	+	0.737131i	0.547562	+	0.0675727i
$120$	−5.14454	+	8.91060i	−0.469630	+	0.813422i
$121$	9.49000	−	5.47906i	0.862728	−	0.498096i
$122$	0.964247	−	0.964247i	0.0872988	−	0.0872988i
$123$	1.36054	−	5.07760i	0.122676	−	0.457832i
$124$	0.0727950	−	0.271675i	0.00653718	−	0.0243971i
$125$	7.05081	+	7.05081i	0.630643	+	0.630643i
$126$	−3.63800	+	0.509015i	−0.324099	+	0.0453467i
$127$	−1.88759	−	1.08980i	−0.167496	−	0.0967041i	0.413908	−	0.910319i	$-0.364163\pi$
$127$	−1.88759	−	1.08980i	−0.167496	−	0.0967041i	−0.581405	+	0.813614i	$0.697497\pi$
$128$	−2.75955	−	10.2988i	−0.243912	−	0.910291i
$129$	−2.03820			−0.179453
$130$	7.52537	+	16.2435i	0.660019	+	1.42465i
$131$			7.17276i			0.626687i	0.949640	+	0.313344i	$0.101449\pi$
$131$			7.17276i			0.626687i	−0.949640	+	0.313344i	$0.898551\pi$
$132$	0.00382798	+	0.0142862i	0.000333183	+	0.00124346i
$133$	−3.24246	+	2.53009i	−0.281157	+	0.219387i
$134$	18.8758	−	10.8979i	1.63062	−	0.941438i
$135$	2.52867	+	2.52867i	0.217633	+	0.217633i
$136$	6.32197	+	1.69397i	0.542105	+	0.145257i
$137$	12.1825	+	3.26430i	1.04082	+	0.278888i	0.738455	−	0.674303i	$-0.235556\pi$
$137$	12.1825	+	3.26430i	1.04082	+	0.278888i	0.302369	+	0.953191i	$0.402222\pi$
$138$	−2.94364	−	2.94364i	−0.250579	−	0.250579i
$139$	−17.5612	+	10.1390i	−1.48952	+	0.859975i	−0.999928	−	0.0119768i	$-0.996188\pi$
$139$	−17.5612	+	10.1390i	−1.48952	+	0.859975i	−0.489592	+	0.871952i	$0.662854\pi$
$140$	0.420615	+	0.539043i	0.0355485	+	0.0455574i
$141$	−3.44927	−	12.8729i	−0.290481	−	1.08409i
$142$		−	0.0190856i		−	0.00160163i
$143$	0.692802	+	0.254112i	0.0579350	+	0.0212499i
$144$	−3.85025			−0.320854
$145$	−8.80076	−	32.8449i	−0.730863	−	2.72762i
$146$	−3.81857	−	2.20465i	−0.316027	−	0.182459i
$147$	−1.70177	+	6.78999i	−0.140360	+	0.560029i
$148$	−0.232370	−	0.232370i	−0.0191007	−	0.0191007i
$149$	−2.91147	+	10.8658i	−0.238517	+	0.890157i	0.738015	+	0.674784i	$0.235763\pi$
$149$	−2.91147	+	10.8658i	−0.238517	+	0.890157i	−0.976532	+	0.215373i	$0.930903\pi$
$150$	−2.79876	+	10.4451i	−0.228518	+	0.852839i
$151$	−9.18076	+	9.18076i	−0.747120	+	0.747120i	−0.973937	−	0.226818i	$-0.927168\pi$
$151$	−9.18076	+	9.18076i	−0.747120	+	0.747120i	0.226818	+	0.973937i	$0.427168\pi$
$152$	−3.87334	+	2.23628i	−0.314170	+	0.181386i
$153$	1.13739	−	1.97002i	0.0919526	−	0.159267i
$154$	−0.746168	−	0.0920819i	−0.0601279	−	0.00742017i
$155$		−	13.9183i		−	1.11794i
$156$	0.149978	−	0.213062i	0.0120079	−	0.0170586i
$157$			20.3277i			1.62232i	0.584821	+	0.811162i	$0.301165\pi$
$157$			20.3277i			1.62232i	−0.584821	+	0.811162i	$0.698835\pi$
$158$	17.0632	−	4.57208i	1.35748	−	0.363735i
$159$	10.9983	+	6.34985i	0.872218	+	0.503576i
$160$	0.730574	+	1.26539i	0.0577569	+	0.100038i
$161$	−7.30405	+	3.09511i	−0.575640	+	0.243929i
$162$	−0.359352	+	1.34112i	−0.0282333	+	0.105368i
$163$	0.193660	+	0.0518911i	0.0151686	+	0.00406442i	0.266395	−	0.963864i	$-0.414167\pi$
$163$	0.193660	+	0.0518911i	0.0151686	+	0.00406442i	−0.251227	+	0.967928i	$0.580834\pi$
$164$	−0.268613	−	0.268613i	−0.0209752	−	0.0209752i
$165$	0.365951	+	0.633846i	0.0284893	+	0.0493449i
$166$	−3.31653	+	5.74439i	−0.257412	+	0.445852i
$167$	13.5813	−	3.63909i	1.05095	−	0.281602i	0.308306	−	0.951287i	$-0.400238\pi$
$167$	13.5813	−	3.63909i	1.05095	−	0.281602i	0.742645	+	0.669686i	$0.233571\pi$
$168$	−2.85595	+	7.05629i	−0.220342	+	0.544404i
$169$	−4.38547	−	12.2380i	−0.337344	−	0.941382i
$170$	11.2946			0.866256
$171$	0.402330	+	1.50152i	0.0307670	+	0.114824i
$172$	−0.0736451	+	0.127557i	−0.00561538	+	0.00972613i
$173$	−6.32817	−	10.9607i	−0.481122	−	0.833328i	0.518643	−	0.854991i	$-0.326437\pi$
$173$	−6.32817	−	10.9607i	−0.481122	−	0.833328i	−0.999765	+	0.0216628i	$0.993104\pi$
$174$	9.33524	−	9.33524i	0.707703	−	0.707703i
$175$	16.4491	+	12.4111i	1.24344	+	0.938190i
$176$	−0.761164	−	0.203953i	−0.0573749	−	0.0153736i
$177$	−1.39507	+	1.39507i	−0.104860	+	0.104860i
$178$	−14.7343	+	8.50687i	−1.10438	+	0.637617i
$179$	−8.90908	−	5.14366i	−0.665896	−	0.384455i	0.128624	−	0.991693i	$-0.458944\pi$
$179$	−8.90908	−	5.14366i	−0.665896	−	0.384455i	−0.794520	+	0.607238i	$0.792277\pi$
$180$	0.249619	−	0.0668853i	0.0186055	−	0.00498534i
$181$	−8.60644			−0.639711			−0.319856	−	0.947466i	$-0.603634\pi$
$181$	−8.60644			−0.639711			−0.319856	+	0.947466i	$0.603634\pi$
$182$	7.17916	+	11.1303i	0.532155	+	0.825032i
$183$	−0.982154			−0.0726029
$184$	−8.33276	+	2.23276i	−0.614299	+	0.164601i
$185$	−14.0833	−	8.13102i	−1.03543	−	0.597805i
$186$	4.67985	−	2.70191i	0.343143	−	0.198114i
$187$	0.329208	−	0.329208i	0.0240741	−	0.0240741i
$188$	−0.930255	−	0.249261i	−0.0678458	−	0.0181792i
$189$	2.11202	+	1.59355i	0.153627	+	0.115913i
$190$	−5.45761	+	5.45761i	−0.395936	+	0.395936i
$191$	8.10759	+	14.0428i	0.586645	+	1.01610i	0.994668	+	0.103127i	$0.0328848\pi$
$191$	8.10759	+	14.0428i	0.586645	+	1.01610i	−0.408023	+	0.912971i	$0.633782\pi$
$192$	−4.13390	+	7.16012i	−0.298338	+	0.516737i
$193$	5.21705	+	19.4703i	0.375531	+	1.40150i	0.852567	+	0.522618i	$0.175045\pi$
$193$	5.21705	+	19.4703i	0.375531	+	1.40150i	−0.477035	+	0.878884i	$0.658289\pi$
$194$	11.2933			0.810814
$195$	4.44003	−	12.1051i	0.317957	−	0.866868i
$196$	0.363450	+	0.351841i	0.0259607	+	0.0251315i
$197$	2.43284	−	0.651878i	0.173333	−	0.0464444i	−0.171109	−	0.985252i	$-0.554735\pi$
$197$	2.43284	−	0.651878i	0.173333	−	0.0464444i	0.344442	+	0.938808i	$0.388068\pi$
$198$	−0.142082	+	0.246094i	−0.0100973	+	0.0174891i
$199$	8.23179	+	14.2579i	0.583536	+	1.01071i	0.995056	+	0.0993137i	$0.0316647\pi$
$199$	8.23179	+	14.2579i	0.583536	+	1.01071i	−0.411520	+	0.911401i	$0.635002\pi$
$200$	15.8453	+	15.8453i	1.12043	+	1.12043i
$201$	−15.1633	−	4.06300i	−1.06954	−	0.286582i
$202$	3.89302	−	14.5289i	0.273912	−	1.02225i
$203$	−9.81559	−	23.1635i	−0.688920	−	1.62576i
$204$	−0.0821934	−	0.142363i	−0.00575469	−	0.00996742i
$205$	−16.2799	−	9.39922i	−1.13704	−	0.656470i
$206$	−3.23092	+	0.865723i	−0.225109	+	0.0603178i
$207$			2.99831i			0.208397i
$208$	5.83560	+	12.5962i	0.404626	+	0.873386i
$209$			0.318150i			0.0220069i
$210$	−1.60892	+	13.0376i	−0.111026	+	0.899680i
$211$	−3.66647	+	6.35051i	−0.252410	+	0.437187i	−0.964189	−	0.265217i	$-0.914557\pi$
$211$	−3.66647	+	6.35051i	−0.252410	+	0.437187i	0.711779	+	0.702404i	$0.247890\pi$
$212$	0.794788	−	0.458871i	0.0545862	−	0.0315154i
$213$	−0.00972001	+	0.00972001i	−0.000666004	+	0.000666004i
$214$	−1.60130	+	5.97613i	−0.109463	+	0.408520i
$215$	−1.88647	+	7.04040i	−0.128656	+	0.480151i
$216$	2.03448	+	2.03448i	0.138429	+	0.138429i
$217$	−1.42687	−	10.1980i	−0.0968624	−	0.692288i
$218$	−20.4034	−	11.7799i	−1.38190	−	0.797838i
$219$	0.821946	+	3.06754i	0.0555419	+	0.207285i
$220$	0.0528908			0.00356590
$221$	−8.16883	−	0.735149i	−0.549495	−	0.0494515i
$222$		−	6.31381i		−	0.423755i
$223$	0.683979	+	2.55265i	0.0458026	+	0.170938i	0.985038	−	0.172335i	$-0.0551311\pi$
$223$	0.683979	+	2.55265i	0.0458026	+	0.170938i	−0.939236	+	0.343273i	$0.888464\pi$
$224$	0.665024	+	0.852267i	0.0444338	+	0.0569445i
$225$	6.74490	−	3.89417i	0.449660	−	0.259612i
$226$	0.467975	+	0.467975i	0.0311293	+	0.0311293i
$227$	17.7461	+	4.75506i	1.17785	+	0.315604i	0.794074	−	0.607821i	$-0.207956\pi$
$227$	17.7461	+	4.75506i	1.17785	+	0.315604i	0.383777	+	0.923426i	$0.374623\pi$
$228$	0.108507	+	0.0290743i	0.00718605	+	0.00192550i
$229$	−5.79771	−	5.79771i	−0.383124	−	0.383124i	0.489103	−	0.872226i	$-0.337324\pi$
$229$	−5.79771	−	5.79771i	−0.383124	−	0.383124i	−0.872226	+	0.489103i	$0.837324\pi$
$230$	−12.8925	+	7.44349i	−0.850107	+	0.490809i
$231$	0.333117	+	0.426909i	0.0219175	+	0.0280885i
$232$	−7.08079	−	26.4259i	−0.464877	−	1.73494i
$233$		−	21.0210i		−	1.37713i	−0.725173	−	0.688567i	$-0.758240\pi$
$233$		−	21.0210i		−	1.37713i	0.725173	−	0.688567i	$-0.241760\pi$
$234$	4.93214	−	0.857033i	0.322424	−	0.0560260i
$235$	−47.6583			−3.10888
$236$	0.0369007	+	0.137715i	0.00240203	+	0.00896450i
$237$	−11.0186	−	6.36156i	−0.715732	−	0.413228i
$238$	8.27566	−	1.15790i	0.536431	−	0.0750555i
$239$	10.3794	+	10.3794i	0.671386	+	0.671386i	0.958036	−	0.286650i	$-0.0925415\pi$
$239$	10.3794	+	10.3794i	0.671386	+	0.671386i	−0.286650	+	0.958036i	$0.592542\pi$
$240$	−3.56363	+	13.2996i	−0.230031	+	0.858488i
$241$	0.355487	−	1.32670i	0.0228989	−	0.0854600i	−0.953531	−	0.301296i	$-0.902581\pi$
$241$	0.355487	−	1.32670i	0.0228989	−	0.0854600i	0.976430	+	0.215836i	$0.0692476\pi$
$242$	10.7583	−	10.7583i	0.691571	−	0.691571i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−0.0354876	+	0.0614664i	−0.00227186	+	0.00393498i
$245$	21.8791	+	12.1628i	1.39780	+	0.777055i
$246$		−	7.29858i		−	0.465341i
$247$	4.30245	−	3.59199i	0.273758	−	0.228553i
$248$		−	11.1982i		−	0.711084i
$249$	4.61460	−	1.23648i	0.292438	−	0.0783586i
$250$	11.9897	+	6.92225i	0.758295	+	0.437802i
$251$	−1.76834	−	3.06285i	−0.111616	−	0.193325i	0.804806	−	0.593538i	$-0.202269\pi$
$251$	−1.76834	−	3.06285i	−0.111616	−	0.193325i	−0.916422	+	0.400213i	$0.868936\pi$
$252$	0.176042	−	0.0745980i	0.0110896	−	0.00469923i
$253$	−0.158825	+	0.592742i	−0.00998523	+	0.0372654i
$254$	−2.92310	−	0.783243i	−0.183412	−	0.0491451i
$255$	−5.75217	−	5.75217i	−0.360215	−	0.360215i
$256$	0.866033	+	1.50001i	0.0541271	+	0.0937508i
$257$	10.0381	−	17.3866i	0.626163	−	1.08455i	−0.362152	−	0.932119i	$-0.617958\pi$
$257$	10.0381	−	17.3866i	0.626163	−	1.08455i	0.988315	−	0.152426i	$-0.0487087\pi$
$258$	−2.73347	+	0.732430i	−0.170178	+	0.0455991i
$259$	−11.1526	−	4.51388i	−0.692987	−	0.280479i
$260$	−0.597150	−	0.715260i	−0.0370337	−	0.0443585i
$261$	−9.50860			−0.588568
$262$	2.57755	+	9.61953i	0.159241	+	0.594297i
$263$	10.5381	−	18.2526i	0.649809	−	1.12550i	−0.333360	−	0.942800i	$-0.608182\pi$
$263$	10.5381	−	18.2526i	0.649809	−	1.12550i	0.983168	−	0.182702i	$-0.0584843\pi$
$264$	0.294432	+	0.509971i	0.0181210	+	0.0313866i
$265$	32.1133	−	32.1133i	1.97271	−	1.97271i
$266$	−3.43934	+	4.55834i	−0.210879	+	0.279490i
$267$	11.8364	+	3.17155i	0.724376	+	0.194096i
$268$	−0.802164	+	0.802164i	−0.0489999	+	0.0489999i
$269$	21.4982	−	12.4120i	1.31077	−	0.756773i	0.328546	−	0.944488i	$-0.393441\pi$
$269$	21.4982	−	12.4120i	1.31077	−	0.756773i	0.982224	+	0.187715i	$0.0601081\pi$
$270$	4.29993	+	2.48257i	0.261685	+	0.151084i
$271$	12.1049	−	3.24351i	0.735323	−	0.197029i	0.128325	−	0.991732i	$-0.459040\pi$
$271$	12.1049	−	3.24351i	0.735323	−	0.197029i	0.606999	+	0.794703i	$0.292373\pi$
$272$	8.75848			0.531061
$273$	2.01225	−	9.32474i	0.121787	−	0.564359i
$274$	17.5113			1.05789
$275$	1.53970	−	0.412560i	0.0928472	−	0.0248783i
$276$	0.187644	+	0.108336i	0.0112948	+	0.00652107i
$277$	14.3673	−	8.29496i	0.863247	−	0.498396i	−0.00185106	−	0.999998i	$-0.500589\pi$
$277$	14.3673	−	8.29496i	0.863247	−	0.498396i	0.865098	+	0.501602i	$0.167256\pi$
$278$	−19.9082	+	19.9082i	−1.19401	+	1.19401i
$279$	−3.75943	−	1.00734i	−0.225071	−	0.0603076i
$280$	21.7307	+	16.3961i	1.29866	+	0.979855i
$281$	−5.40004	+	5.40004i	−0.322140	+	0.322140i	−0.849587	−	0.527448i	$-0.823149\pi$
$281$	−5.40004	+	5.40004i	−0.322140	+	0.322140i	0.527448	+	0.849587i	$0.323149\pi$
$282$	−9.25177	−	16.0245i	−0.550935	−	0.954247i
$283$	12.4721	−	21.6023i	0.741390	−	1.28412i	−0.210473	−	0.977600i	$-0.567500\pi$
$283$	12.4721	−	21.6023i	0.741390	−	1.28412i	0.951863	−	0.306525i	$-0.0991663\pi$
$284$	0.000257102	0	0.000959517i	1.52562e−5	0	5.69369e-5i
$285$	5.55896			0.329284
$286$	1.02045	+	0.0918343i	0.0603402	+	0.00543028i
$287$	−12.8921	−	5.21792i	−0.760994	−	0.308004i
$288$	0.394667	−	0.105751i	0.0232560	−	0.00623142i
$289$	5.91268	−	10.2411i	0.347805	−	0.602416i
$290$	−23.6057	−	40.8863i	−1.38618	−	2.40093i
$291$	−5.75153	−	5.75153i	−0.337161	−	0.337161i
$292$	0.221676	+	0.0593978i	0.0129726	+	0.00347599i
$293$	3.65015	−	13.6225i	0.213244	−	0.795838i	−0.773533	−	0.633756i	$-0.781512\pi$
$293$	3.65015	−	13.6225i	0.213244	−	0.795838i	0.986777	−	0.162082i	$-0.0518209\pi$
$294$	0.157715	+	9.71772i	0.00919814	+	0.566749i
$295$	3.52767	+	6.11011i	0.205389	+	0.355744i
$296$	−11.3310	−	6.54195i	−0.658600	−	0.380243i
$297$	0.197692	−	0.0529715i	0.0114713	−	0.00307372i
$298$			15.6185i			0.904756i
$299$	9.80901	−	4.54436i	0.567270	−	0.262807i
$300$		−	0.562824i		−	0.0324947i
$301$	−0.660467	+	5.35197i	−0.0380687	+	0.308482i
$302$	−9.01337	+	15.6116i	−0.518661	+	0.898348i
$303$	−9.38204	+	5.41672i	−0.538984	+	0.311183i
$304$	−4.23214	+	4.23214i	−0.242730	+	0.242730i
$305$	−0.909040	+	3.39258i	−0.0520515	+	0.194259i
$306$	0.817447	−	3.05075i	0.0467304	−	0.174400i
$307$	6.57661	+	6.57661i	0.375347	+	0.375347i	0.869420	−	0.494073i	$-0.164493\pi$
$307$	6.57661	+	6.57661i	0.375347	+	0.375347i	−0.494073	+	0.869420i	$0.664493\pi$
$308$	0.0387536	−	0.00542226i	0.00220819	−	0.000308962i
$309$	2.08636	+	1.20456i	0.118689	+	0.0685251i
$310$	−5.00155	−	18.6660i	−0.284069	−	1.06016i
$311$	−6.01960			−0.341340			−0.170670	−	0.985328i	$-0.554593\pi$
$311$	−6.01960			−0.341340			−0.170670	+	0.985328i	$0.554593\pi$
$312$	3.57230	−	9.73939i	0.202241	−	0.551385i
$313$		−	4.19182i		−	0.236935i	−0.992958	−	0.118468i	$-0.962202\pi$
$313$		−	4.19182i		−	0.236935i	0.992958	−	0.118468i	$-0.0377982\pi$
$314$	7.30479	+	27.2618i	0.412233	+	1.53847i
$315$	7.45927	−	5.82046i	0.420282	−	0.327946i
$316$	−0.796254	+	0.459718i	−0.0447928	+	0.0258611i
$317$	−10.1411	−	10.1411i	−0.569578	−	0.569578i	0.362432	−	0.932010i	$-0.381946\pi$
$317$	−10.1411	−	10.1411i	−0.569578	−	0.569578i	−0.932010	+	0.362432i	$0.881946\pi$
$318$	17.0318	+	4.56366i	0.955096	+	0.255917i
$319$	−1.87978	−	0.503685i	−0.105247	−	0.0282009i
$320$	20.9065	+	20.9065i	1.16871	+	1.16871i
$321$	3.85907	−	2.22804i	0.215392	−	0.124357i
$322$	−8.68337	+	6.77563i	−0.483906	+	0.377591i
$323$	−0.915214	−	3.41562i	−0.0509239	−	0.190050i
$324$		−	0.0722649i		−	0.00401472i
$325$	−22.9627	−	16.1639i	−1.27374	−	0.896612i
$326$	0.278368			0.0154174
$327$	4.39183	+	16.3905i	0.242869	+	0.906399i
$328$	−13.0983	−	7.56230i	−0.723232	−	0.417558i
$329$	−34.9197	+	4.88583i	−1.92518	+	0.269364i
$330$	0.718558	+	0.718558i	0.0395553	+	0.0395553i
$331$	3.99969	−	14.9270i	0.219843	−	0.820465i	−0.764563	−	0.644550i	$-0.777045\pi$
$331$	3.99969	−	14.9270i	0.219843	−	0.820465i	0.984405	−	0.175915i	$-0.0562884\pi$
$332$	0.0893539	−	0.333473i	0.00490393	−	0.0183017i
$333$	−3.21553	+	3.21553i	−0.176210	+	0.176210i
$334$	16.9064	−	9.76092i	0.925077	−	0.534094i
$335$	−28.0691	+	48.6170i	−1.53358	+	2.65623i
$336$	−1.24765	+	10.1101i	−0.0680650	+	0.551551i
$337$			32.5729i			1.77436i	0.461427	+	0.887178i	$0.347338\pi$
$337$			32.5729i			1.77436i	−0.461427	+	0.887178i	$0.652662\pi$
$338$	−10.2792	−	14.8366i	−0.559113	−	0.807007i
$339$		−	0.476666i		−	0.0258890i
$340$	−0.567830	+	0.152150i	−0.0307949	+	0.00825147i
$341$	−0.689850	−	0.398285i	−0.0373574	−	0.0215683i
$342$	1.07915	+	1.86914i	0.0583535	+	0.101071i
$343$	17.2779	+	6.66883i	0.932920	+	0.360083i
$344$	−1.51779	+	5.66447i	−0.0818337	+	0.305408i
$345$	10.3568	+	2.77510i	0.557593	+	0.149407i
$346$	−12.4256	−	12.4256i	−0.668004	−	0.668004i
$347$	−11.6943	−	20.2551i	−0.627783	−	1.08735i	−0.987996	−	0.154481i	$-0.950629\pi$
$347$	−11.6943	−	20.2551i	−0.627783	−	1.08735i	0.360213	−	0.932870i	$-0.382704\pi$
$348$	−0.343569	+	0.595079i	−0.0184172	+	0.0318996i
$349$	−21.3942	+	5.73255i	−1.14520	+	0.306856i	−0.781041	−	0.624479i	$-0.785311\pi$
$349$	−21.3942	+	5.73255i	−1.14520	+	0.306856i	−0.364162	+	0.931336i	$0.618644\pi$
$350$	26.5202	+	10.7337i	1.41756	+	0.573743i
$351$	−2.94834	−	2.07540i	−0.157371	−	0.110776i
$352$	0.0836244			0.00445720
$353$	3.15762	+	11.7844i	0.168063	+	0.627220i	0.997630	+	0.0688124i	$0.0219210\pi$
$353$	3.15762	+	11.7844i	0.168063	+	0.627220i	−0.829566	+	0.558408i	$0.811412\pi$
$354$	−1.36963	+	2.37228i	−0.0727953	+	0.126085i
$355$	0.0245787	+	0.0425715i	0.00130450	+	0.00225946i
$356$	0.626164	−	0.626164i	0.0331866	−	0.0331866i
$357$	−4.80438	−	3.62497i	−0.254274	−	0.191854i
$358$	−13.7965	−	3.69677i	−0.729169	−	0.195380i
$359$	7.63230	−	7.63230i	0.402818	−	0.402818i	−0.476407	−	0.879225i	$-0.658061\pi$
$359$	7.63230	−	7.63230i	0.402818	−	0.402818i	0.879225	+	0.476407i	$0.158061\pi$
$360$	8.91060	−	5.14454i	0.469630	−	0.271141i
$361$	−14.3618	−	8.29179i	−0.755884	−	0.436410i
$362$	−11.5423	+	3.09274i	−0.606648	+	0.162551i
$363$	−10.9581			−0.575152
$364$	−0.510865	−	0.462859i	−0.0267766	−	0.0242604i
$365$	11.3568			0.594440
$366$	−1.31719	+	0.352939i	−0.0688504	+	0.0184484i
$367$	29.9667	+	17.3013i	1.56425	+	0.903118i	0.996819	+	0.0796947i	$0.0253946\pi$
$367$	29.9667	+	17.3013i	1.56425	+	0.903118i	0.567427	+	0.823423i	$0.307939\pi$
$368$	−9.99759	+	5.77211i	−0.521160	+	0.300892i
$369$	−3.71706	+	3.71706i	−0.193503	+	0.193503i
$370$	−21.8093	−	5.84380i	−1.13381	−	0.303804i
$371$	20.2376	−	26.8219i	1.05068	−	1.39253i
$372$	−0.198880	+	0.198880i	−0.0103114	+	0.0103114i
$373$	7.12384	+	12.3388i	0.368858	+	0.638881i	0.989387	−	0.145302i	$-0.0464154\pi$
$373$	7.12384	+	12.3388i	0.368858	+	0.638881i	−0.620529	+	0.784183i	$0.713082\pi$
$374$	0.323206	−	0.559809i	0.0167126	−	0.0289471i
$375$	−2.58077	−	9.63158i	−0.133271	−	0.497373i
$376$	−38.3442			−1.97745
$377$	14.4117	+	31.1076i	0.742238	+	1.60212i
$378$	3.40511	+	1.37818i	0.175140	+	0.0708859i
$379$	21.6859	−	5.81071i	1.11393	−	0.298476i	0.345504	−	0.938417i	$-0.387708\pi$
$379$	21.6859	−	5.81071i	1.11393	−	0.298476i	0.768424	+	0.639941i	$0.221041\pi$
$380$	0.200859	−	0.347898i	0.0103038	−	0.0178468i
$381$	1.08980	+	1.88759i	0.0558322	+	0.0967041i
$382$	15.9195	+	15.9195i	0.814515	+	0.814515i
$383$	13.1230	+	3.51630i	0.670554	+	0.179674i	0.578004	−	0.816034i	$-0.303832\pi$
$383$	13.1230	+	3.51630i	0.670554	+	0.179674i	0.0925494	+	0.995708i	$0.470498\pi$
$384$	−2.75955	+	10.2988i	−0.140822	+	0.525557i
$385$	1.78296	−	0.755532i	0.0908680	−	0.0385055i
$386$	13.9934	+	24.2372i	0.712244	+	1.23364i
$387$	1.76513	+	1.01910i	0.0897267	+	0.0518037i
$388$	−0.567766	+	0.152132i	−0.0288240	+	0.00772336i
$389$			20.6138i			1.04516i	0.852590	+	0.522581i	$0.175031\pi$
$389$			20.6138i			1.04516i	−0.852590	+	0.522581i	$0.824969\pi$
$390$	1.60460	−	17.8300i	0.0812520	−	0.902856i
$391$		−	6.82049i		−	0.344927i
$392$	17.6032	+	9.78581i	0.889094	+	0.494258i
$393$	3.58638	−	6.21180i	0.180909	−	0.313344i
$394$	3.02848	−	1.74849i	0.152572	−	0.0880877i
$395$	−32.1726	+	32.1726i	−1.61878	+	1.61878i
$396$	0.00382798	−	0.0142862i	0.000192363	−	0.000717909i
$397$	−4.36581	+	16.2934i	−0.219114	+	0.817743i	0.765564	+	0.643360i	$0.222460\pi$
$397$	−4.36581	+	16.2934i	−0.219114	+	0.817743i	−0.984678	+	0.174384i	$0.944207\pi$
$398$	16.1634	+	16.1634i	0.810199	+	0.810199i
$399$	4.07310	−	0.569893i	0.203910	−	0.0285304i
$400$	25.9696	+	14.9935i	1.29848	+	0.749677i
$401$	3.52338	+	13.1494i	0.175949	+	0.656652i	0.996388	+	0.0849175i	$0.0270627\pi$
$401$	3.52338	+	13.1494i	0.175949	+	0.656652i	−0.820439	+	0.571735i	$0.806271\pi$
$402$	−21.7959			−1.08708
$403$	2.40243	+	13.8258i	0.119674	+	0.688712i
$404$			0.782878i			0.0389496i
$405$	−0.925558	−	3.45423i	−0.0459913	−	0.171642i
$406$	−21.4877	−	27.5378i	−1.06642	−	1.36668i
$407$	−0.806018	+	0.465355i	−0.0399528	+	0.0230668i
$408$	−4.62800	−	4.62800i	−0.229120	−	0.229120i
$409$	−30.8141	−	8.25662i	−1.52366	−	0.408263i	−0.602715	−	0.797956i	$-0.705914\pi$
$409$	−30.8141	−	8.25662i	−1.52366	−	0.408263i	−0.920945	+	0.389693i	$0.872581\pi$
$410$	−25.2110	−	6.75526i	−1.24508	−	0.333618i
$411$	−8.91824	−	8.91824i	−0.439904	−	0.439904i
$412$	0.150771	−	0.0870475i	0.00742794	−	0.00428852i
$413$	3.21116	+	4.11529i	0.158011	+	0.202500i
$414$	1.07745	+	4.02109i	0.0529536	+	0.197626i
$415$		−	17.0843i		−	0.838635i
$416$	−0.944140	−	1.13088i	−0.0462903	−	0.0554459i
$417$	20.2779			0.993013
$418$	0.114328	+	0.426678i	0.00559196	+	0.0208695i
$419$	−25.3302	−	14.6244i	−1.23746	−	0.714449i	−0.268888	−	0.963172i	$-0.586656\pi$
$419$	−25.3302	−	14.6244i	−1.23746	−	0.714449i	−0.968575	+	0.248722i	$0.919989\pi$
$420$	−0.0947418	−	0.677132i	−0.00462293	−	0.0330407i
$421$	19.1090	+	19.1090i	0.931318	+	0.931318i	0.997788	−	0.0664703i	$-0.0211738\pi$
$421$	19.1090	+	19.1090i	0.931318	+	0.931318i	−0.0664703	+	0.997788i	$0.521174\pi$
$422$	−2.63510	+	9.83434i	−0.128275	+	0.478728i
$423$	−3.44927	+	12.8729i	−0.167709	+	0.625899i
$424$	25.8373	−	25.8373i	1.25477	−	1.25477i
$425$	−15.3432	+	8.85840i	−0.744254	+	0.429695i
$426$	−0.00954279	+	0.0165286i	−0.000462350	+	0.000800813i
$427$	−0.318262	+	2.57897i	−0.0154018	+	0.124805i
$428$		−	0.322018i		−	0.0155653i
$429$	−0.472928	−	0.566468i	−0.0228332	−	0.0273493i
$430$			10.1199i			0.488026i
$431$	−26.6643	+	7.14467i	−1.28437	+	0.344147i	−0.835520	−	0.549460i	$-0.814834\pi$
$431$	−26.6643	+	7.14467i	−1.28437	+	0.344147i	−0.448852	+	0.893606i	$0.648167\pi$
$432$	3.33441	+	1.92512i	0.160427	+	0.0926226i
$433$	11.9677	+	20.7287i	0.575132	+	0.996157i	0.996027	+	0.0890483i	$0.0283825\pi$
$433$	11.9677	+	20.7287i	0.575132	+	0.996157i	−0.420896	+	0.907109i	$0.638284\pi$
$434$	−5.57829	−	13.1640i	−0.267767	−	0.631894i
$435$	−8.80076	+	32.8449i	−0.421964	+	1.57479i
$436$	1.18446	+	0.317375i	0.0567253	+	0.0151995i
$437$	3.29570	+	3.29570i	0.157655	+	0.157655i
$438$	2.20465	+	3.81857i	0.105342	+	0.182459i
$439$	−5.23894	+	9.07411i	−0.250041	+	0.433083i	−0.963537	−	0.267576i	$-0.913777\pi$
$439$	−5.23894	+	9.07411i	−0.250041	+	0.433083i	0.713496	+	0.700659i	$0.247111\pi$
$440$	2.03407	−	0.545027i	0.0969705	−	0.0259832i
$441$	4.86877	−	5.02942i	0.231846	−	0.239496i
$442$	−11.2196	+	1.94956i	−0.533660	+	0.0927312i
$443$	−19.7645			−0.939041			−0.469521	−	0.882922i	$-0.655573\pi$
$443$	−19.7645			−0.939041			−0.469521	+	0.882922i	$0.655573\pi$
$444$	0.0850534	+	0.317423i	0.00403645	+	0.0150643i
$445$	21.9105	−	37.9502i	1.03866	−	1.79901i
$446$	1.83460	+	3.17761i	0.0868706	+	0.150464i
$447$	7.95428	−	7.95428i	0.376225	−	0.376225i
$448$	17.4617	+	13.1751i	0.824988	+	0.622466i
$449$	27.2909	+	7.31258i	1.28794	+	0.345102i	0.836877	−	0.547391i	$-0.184379\pi$
$449$	27.2909	+	7.31258i	1.28794	+	0.345102i	0.451061	+	0.892493i	$0.351046\pi$
$450$	7.64634	−	7.64634i	0.360452	−	0.360452i
$451$	−0.931733	+	0.537936i	−0.0438736	+	0.0253304i
$452$	−0.0298313	−	0.0172231i	−0.00140315	−	0.000810107i
$453$	12.5412	−	3.36039i	0.589235	−	0.157885i
$454$	25.5084			1.19717
$455$	−30.3473	−	15.5814i	−1.42270	−	0.730466i
$456$	4.47255			0.209446
$457$	−18.9311	+	5.07256i	−0.885558	+	0.237285i	−0.672804	−	0.739821i	$-0.734910\pi$
$457$	−18.9311	+	5.07256i	−0.885558	+	0.237285i	−0.212754	+	0.977106i	$0.568243\pi$
$458$	−9.85884	−	5.69201i	−0.460673	−	0.265970i
$459$	−1.97002	+	1.13739i	−0.0919526	+	0.0530889i
$460$	0.547893	−	0.547893i	0.0255456	−	0.0255456i
$461$	−14.1139	−	3.78182i	−0.657351	−	0.176137i	−0.0853010	−	0.996355i	$-0.527185\pi$
$461$	−14.1139	−	3.78182i	−0.657351	−	0.176137i	−0.572050	+	0.820218i	$0.693852\pi$
$462$	0.600160	+	0.452829i	0.0279219	+	0.0210675i
$463$	0.639781	−	0.639781i	0.0297332	−	0.0297332i	−0.692084	−	0.721817i	$-0.743307\pi$
$463$	0.639781	−	0.639781i	0.0297332	−	0.0297332i	0.721817	+	0.692084i	$0.243307\pi$
$464$	−18.3052	−	31.7056i	−0.849800	−	1.47190i
$465$	−6.95913	+	12.0536i	−0.322722	+	0.558971i
$466$	−7.55395	−	28.1917i	−0.349930	−	1.30596i
$467$	−18.2232			−0.843268			−0.421634	−	0.906766i	$-0.638543\pi$
$467$	−18.2232			−0.843268			−0.421634	+	0.906766i	$0.638543\pi$
$468$	−0.236416	+	0.109528i	−0.0109283	+	0.00506292i
$469$	−15.5823	+	38.4998i	−0.719526	+	1.77775i
$470$	−63.9154	+	17.1261i	−2.94820	+	0.789967i
$471$	10.1638	−	17.6043i	0.468325	−	0.811162i
$472$	2.83825	+	4.91599i	0.130641	+	0.226277i
$473$	0.294970	+	0.294970i	0.0135627	+	0.0135627i
$474$	−17.0632	−	4.57208i	−0.783740	−	0.210003i
$475$	3.13349	−	11.6943i	0.143774	−	0.536573i
$476$	−0.400456	+	0.169694i	−0.0183549	+	0.00777792i
$477$	−6.34985	−	10.9983i	−0.290739	−	0.503576i
$478$	17.6498	+	10.1901i	0.807284	+	0.466086i
$479$	37.9467	−	10.1678i	1.73383	−	0.464578i	0.752770	−	0.658284i	$-0.228717\pi$
$479$	37.9467	−	10.1678i	1.73383	−	0.464578i	0.981060	+	0.193706i	$0.0620507\pi$
$480$		−	1.46115i		−	0.0666920i
$481$	15.3933	+	5.64607i	0.701873	+	0.257439i
$482$		−	1.90700i		−	0.0868616i
$483$	7.87305	+	0.971585i	0.358236	+	0.0442086i
$484$	−0.395943	+	0.685794i	−0.0179974	+	0.0311725i
$485$	−25.1905	+	14.5437i	−1.14384	+	0.660396i
$486$	0.981768	−	0.981768i	0.0445339	−	0.0445339i
$487$	5.80987	−	21.6827i	0.263270	−	0.982538i	−0.700030	−	0.714113i	$-0.746830\pi$
$487$	5.80987	−	21.6827i	0.263270	−	0.982538i	0.963301	−	0.268425i	$-0.0865031\pi$
$488$	−0.731383	+	2.72956i	−0.0331081	+	0.123561i
$489$	−0.141769	−	0.141769i	−0.00641102	−	0.00641102i
$490$	33.7132	+	8.44953i	1.52301	+	0.381711i
$491$	5.46145	+	3.15317i	0.246472	+	0.142301i	0.618148	−	0.786062i	$-0.287883\pi$
$491$	5.46145	+	3.15317i	0.246472	+	0.142301i	−0.371676	+	0.928363i	$0.621217\pi$
$492$	0.0983192	+	0.366932i	0.00443257	+	0.0165426i
$493$	21.6300			0.974166
$494$	4.47931	−	6.36339i	0.201534	−	0.286302i
$495$		−	0.731902i		−	0.0328966i
$496$	−3.87849	−	14.4747i	−0.174149	−	0.649934i
$497$	0.0223734	+	0.0286728i	0.00100358	+	0.00128615i
$498$	5.74439	−	3.31653i	0.257412	−	0.148617i
$499$	−0.186545	−	0.186545i	−0.00835090	−	0.00835090i	0.702919	−	0.711270i	$-0.251880\pi$
$499$	−0.186545	−	0.186545i	−0.00835090	−	0.00835090i	−0.711270	+	0.702919i	$0.751880\pi$
$500$	−0.696025	−	0.186499i	−0.0311272	−	0.00834050i
$501$	−13.5813	−	3.63909i	−0.606767	−	0.162583i
$502$	−3.47219	−	3.47219i	−0.154971	−	0.154971i
$503$	−14.8498	+	8.57353i	−0.662119	+	0.382275i	−0.793084	−	0.609112i	$-0.791526\pi$
$503$	−14.8498	+	8.57353i	−0.662119	+	0.382275i	0.130965	+	0.991387i	$0.458193\pi$
$504$	6.00147	−	4.68295i	0.267327	−	0.208595i
$505$	10.0270	+	37.4212i	0.446195	+	1.66522i
$506$			0.852012i			0.0378765i
$507$	−2.32106	+	12.7911i	−0.103082	+	0.568073i
$508$	0.157509			0.00698831
$509$	−4.12567	−	15.3972i	−0.182867	−	0.682470i	−0.995077	−	0.0991045i	$-0.968402\pi$
$509$	−4.12567	−	15.3972i	−0.182867	−	0.682470i	0.812210	−	0.583366i	$-0.198264\pi$
$510$	−9.78141	−	5.64730i	−0.433128	−	0.250067i
$511$	8.32120	−	1.16427i	0.368108	−	0.0515043i
$512$	16.7789	+	16.7789i	0.741531	+	0.741531i
$513$	0.402330	−	1.50152i	0.0177633	−	0.0662936i
$514$	7.21446	−	26.9247i	0.318216	−	1.18760i
$515$	6.09188	−	6.09188i	0.268440	−	0.268440i
$516$	0.127557	−	0.0736451i	0.00561538	−	0.00324204i
$517$	−1.36379	+	2.36215i	−0.0599793	+	0.103887i
$518$	−16.5790	−	2.04596i	−0.728440	−	0.0898941i
$519$			12.6563i			0.555552i
$520$	−30.3357	−	21.3539i	−1.33031	−	0.936430i
$521$			5.95318i			0.260814i	0.991461	+	0.130407i	$0.0416283\pi$
$521$			5.95318i			0.260814i	−0.991461	+	0.130407i	$0.958372\pi$
$522$	−12.7522	+	3.41693i	−0.558147	+	0.149555i
$523$	7.98659	+	4.61106i	0.349229	+	0.201628i	0.664346	−	0.747425i	$-0.268710\pi$
$523$	7.98659	+	4.61106i	0.349229	+	0.201628i	−0.315116	+	0.949053i	$0.602044\pi$
$524$	−0.259170	−	0.448895i	−0.0113219	−	0.0196101i
$525$	−8.03980	−	18.9729i	−0.350885	−	0.828044i
$526$	7.57379	−	28.2658i	0.330233	−	1.23245i
$527$	8.55188	+	2.29147i	0.372526	+	0.0998179i
$528$	0.557211	+	0.557211i	0.0242495	+	0.0242495i
$529$	−7.00508	−	12.1332i	−0.304569	−	0.527528i
$530$	31.5278	−	54.6078i	1.36948	−	2.37201i
$531$	1.90570	−	0.510631i	0.0827004	−	0.0221595i
$532$	0.111505	−	0.275500i	0.00483437	−	0.0119444i
$533$	17.7942	+	6.52669i	0.770751	+	0.282702i
$534$	17.0137			0.736256
$535$	−4.12435	−	15.3923i	−0.178311	−	0.665467i
$536$	−22.5834	+	39.1156i	−0.975455	+	1.68954i
$537$	5.14366	+	8.90908i	0.221965	+	0.384455i
$538$	24.3714	−	24.3714i	1.05073	−	1.05073i
$539$	1.22893	−	0.736371i	0.0529340	−	0.0317177i
$540$	−0.249619	−	0.0668853i	−0.0107419	−	0.00287829i
$541$	−18.1277	+	18.1277i	−0.779369	+	0.779369i	−0.979723	−	0.200354i	$-0.935791\pi$
$541$	−18.1277	+	18.1277i	−0.779369	+	0.779369i	0.200354	+	0.979723i	$0.435791\pi$
$542$	15.0686	−	8.69987i	0.647253	−	0.373691i
$543$	7.45339	+	4.30322i	0.319856	+	0.184669i
$544$	−0.897782	+	0.240560i	−0.0384921	+	0.0103139i
$545$	60.6815			2.59931
$546$	−0.652190	−	13.2287i	−0.0279111	−	0.566136i
$547$	−9.47939			−0.405309			−0.202655	−	0.979250i	$-0.564957\pi$
$547$	−9.47939			−0.405309			−0.202655	+	0.979250i	$0.564957\pi$
$548$	−0.880370	+	0.235894i	−0.0376075	+	0.0100769i
$549$	0.850570	+	0.491077i	0.0363015	+	0.0209587i
$550$	1.91666	−	1.10659i	0.0817267	−	0.0471850i
$551$	−10.4517	+	10.4517i	−0.445259	+	0.445259i
$552$	8.33276	+	2.23276i	0.354666	+	0.0950324i
$553$	−20.2749	+	26.8714i	−0.862177	+	1.14269i
$554$	16.2875	−	16.2875i	0.691988	−	0.691988i
$555$	8.13102	+	14.0833i	0.345143	+	0.597805i
$556$	0.732690	−	1.26906i	0.0310730	−	0.0538200i
$557$	−4.20935	−	15.7095i	−0.178356	−	0.665633i	−0.995956	−	0.0898459i	$-0.971363\pi$
$557$	−4.20935	−	15.7095i	−0.178356	−	0.665633i	0.817600	−	0.575787i	$-0.195304\pi$
$558$	−5.40383			−0.228762
$559$	0.658691	−	7.31925i	0.0278597	−	0.309571i
$560$	33.7678	+	13.6672i	1.42695	+	0.577543i
$561$	−0.449707	+	0.120499i	−0.0189866	+	0.00508746i
$562$	−5.30159	+	9.18262i	−0.223634	+	0.387345i
$563$	8.25217	+	14.2932i	0.347788	+	0.602386i	0.985856	−	0.167594i	$-0.0535997\pi$
$563$	8.25217	+	14.2932i	0.347788	+	0.602386i	−0.638068	+	0.769980i	$0.720266\pi$
$564$	0.680994	+	0.680994i	0.0286750	+	0.0286750i
$565$	−1.64651	−	0.441182i	−0.0692693	−	0.0185607i
$566$	8.96375	−	33.4532i	0.376774	−	1.40614i
$567$	−1.03229	−	2.43606i	−0.0433519	−	0.102305i
$568$	0.0197752	+	0.0342516i	0.000829748	+	0.00143717i
$569$	−17.3607	−	10.0232i	−0.727797	−	0.420194i	0.0898186	−	0.995958i	$-0.471371\pi$
$569$	−17.3607	−	10.0232i	−0.727797	−	0.420194i	−0.817616	+	0.575764i	$0.804705\pi$
$570$	7.45523	−	1.99762i	0.312265	−	0.0836712i
$571$			37.7943i			1.58164i	0.612046	+	0.790822i	$0.290347\pi$
$571$			37.7943i			1.58164i	−0.612046	+	0.790822i	$0.709653\pi$
$572$	−0.0525394	+	0.00912950i	−0.00219678	+	0.000381724i
$573$		−	16.2152i		−	0.677399i
$574$	−19.1649	−	2.36506i	−0.799925	−	0.0987159i
$575$	11.6759	−	20.2233i	0.486920	−	0.843370i
$576$	7.16012	−	4.13390i	0.298338	−	0.172246i
$577$	7.30060	−	7.30060i	0.303928	−	0.303928i	−0.538621	−	0.842548i	$-0.681054\pi$
$577$	7.30060	−	7.30060i	0.303928	−	0.303928i	0.842548	+	0.538621i	$0.181054\pi$
$578$	4.24947	−	15.8592i	0.176755	−	0.659657i
$579$	5.21705	−	19.4703i	0.216813	−	0.809158i
$580$	1.73755	+	1.73755i	0.0721477	+	0.0721477i
$581$	−1.75145	−	12.5178i	−0.0726623	−	0.519327i
$582$	−9.78031	−	5.64667i	−0.405407	−	0.234062i
$583$	−0.672722	−	2.51063i	−0.0278613	−	0.103980i
$584$	9.13726			0.378102
$585$	−9.89775	+	8.26335i	−0.409222	+	0.341648i
$586$		−	19.5812i		−	0.808890i
$587$	−5.01367	−	18.7113i	−0.206936	−	0.772296i	−0.988851	−	0.148911i	$-0.952423\pi$
$587$	−5.01367	−	18.7113i	−0.206936	−	0.772296i	0.781915	−	0.623386i	$-0.214243\pi$
$588$	−0.138837	−	0.486429i	−0.00572552	−	0.0200600i
$589$	−5.23956	+	3.02506i	−0.215892	+	0.124645i
$590$	6.92671	+	6.92671i	0.285168	+	0.285168i
$591$	−2.43284	−	0.651878i	−0.100074	−	0.0268147i
$592$	−16.9122	−	4.53161i	−0.695088	−	0.186248i
$593$	11.9510	+	11.9510i	0.490769	+	0.490769i	0.908548	−	0.417780i	$-0.137192\pi$
$593$	11.9510	+	11.9510i	0.490769	+	0.490769i	−0.417780	+	0.908548i	$0.637192\pi$
$594$	0.246094	−	0.142082i	0.0100973	−	0.00582970i
$595$	−16.9682	+	13.2403i	−0.695629	+	0.542799i
$596$	−0.210397	−	0.785213i	−0.00861820	−	0.0321636i
$597$		−	16.4636i		−	0.673810i
$598$	11.5220	−	9.61942i	0.471171	−	0.393367i
$599$	14.2777			0.583372			0.291686	−	0.956514i	$-0.405784\pi$
$599$	14.2777			0.583372			0.291686	+	0.956514i	$0.405784\pi$
$600$	−5.79976	−	21.6450i	−0.236774	−	0.883654i
$601$	−20.5084	−	11.8405i	−0.836556	−	0.482986i	0.0195364	−	0.999809i	$-0.493781\pi$
$601$	−20.5084	−	11.8405i	−0.836556	−	0.482986i	−0.856092	+	0.516824i	$0.827114\pi$
$602$	1.03747	+	7.41497i	0.0422843	+	0.302211i
$603$	11.1003	+	11.1003i	0.452040	+	0.452040i
$604$	0.242838	−	0.906285i	0.00988095	−	0.0368762i
$605$	−10.1424	+	37.8518i	−0.412346	+	1.53890i
$606$	−10.6359	+	10.6359i	−0.432055	+	0.432055i
$607$	−12.8523	+	7.42026i	−0.521657	+	0.301179i	−0.737612	−	0.675224i	$-0.764047\pi$
$607$	−12.8523	+	7.42026i	−0.521657	+	0.301179i	0.215955	+	0.976403i	$0.430713\pi$
$608$	0.317573	−	0.550052i	0.0128793	−	0.0223076i
$609$	−3.08121	+	24.9680i	−0.124857	+	1.01175i
$610$			4.87652i			0.197445i
$611$	47.3416	−	8.22630i	1.91524	−	0.332801i
$612$			0.164387i			0.00664495i
$613$	15.9485	−	4.27337i	0.644152	−	0.172600i	0.0780686	−	0.996948i	$-0.475125\pi$
$613$	15.9485	−	4.27337i	0.644152	−	0.172600i	0.566083	+	0.824348i	$0.308458\pi$
$614$	11.1833	+	6.45671i	0.451323	+	0.260571i
$615$	9.39922	+	16.2799i	0.379013	+	0.656470i
$616$	1.43451	−	0.607876i	0.0577980	−	0.0244920i
$617$	1.60910	−	6.00524i	0.0647799	−	0.241762i	−0.925942	−	0.377665i	$-0.876727\pi$
$617$	1.60910	−	6.00524i	0.0647799	−	0.241762i	0.990722	+	0.135903i	$0.0433937\pi$
$618$	3.23092	+	0.865723i	0.129967	+	0.0348245i
$619$	−19.0180	−	19.0180i	−0.764399	−	0.764399i	0.212715	−	0.977114i	$-0.431769\pi$
$619$	−19.0180	−	19.0180i	−0.764399	−	0.764399i	−0.977114	+	0.212715i	$0.931769\pi$
$620$	0.502901	+	0.871050i	0.0201970	+	0.0349822i
$621$	1.49915	−	2.59661i	0.0601589	−	0.104198i
$622$	−8.07300	+	2.16316i	−0.323698	+	0.0867346i
$623$	12.1635	−	30.0527i	0.487320	−	1.20404i
$624$	1.24430	−	13.8264i	0.0498118	−	0.553499i
$625$	3.28341			0.131336
$626$	−1.50634	−	5.62173i	−0.0602053	−	0.224689i
$627$	0.159075	−	0.275526i	0.00635285	−	0.0110035i
$628$	−0.734488	−	1.27217i	−0.0293093	−	0.0507652i
$629$	7.31464	−	7.31464i	0.291654	−	0.291654i
$630$	7.91217	−	10.4864i	0.315228	−	0.417790i
$631$	−31.4581	−	8.42917i	−1.25233	−	0.335560i	−0.429092	−	0.903261i	$-0.641166\pi$
$631$	−31.4581	−	8.42917i	−1.25233	−	0.335560i	−0.823235	+	0.567701i	$0.807833\pi$
$632$	−25.8850	+	25.8850i	−1.02965	+	1.02965i
$633$	6.35051	−	3.66647i	0.252410	−	0.145729i
$634$	−17.2446	−	9.95615i	−0.684869	−	0.395409i
$635$	7.52884	−	2.01735i	0.298773	−	0.0800559i
$636$	−0.917742			−0.0363908
$637$	−23.8332	−	8.30548i	−0.944304	−	0.329075i
$638$	−2.70201			−0.106973
$639$	0.0132778	−	0.00355777i	0.000525261	−	0.000140743i
$640$	33.0202	+	19.0642i	1.30524	+	0.753579i
$641$	10.6137	−	6.12780i	0.419214	−	0.242034i	−0.275527	−	0.961293i	$-0.588852\pi$
$641$	10.6137	−	6.12780i	0.419214	−	0.242034i	0.694741	+	0.719260i	$0.255519\pi$
$642$	4.37483	−	4.37483i	0.172661	−	0.172661i
$643$	10.2233	+	2.73933i	0.403169	+	0.108029i	0.454704	−	0.890642i	$-0.349745\pi$
$643$	10.2233	+	2.73933i	0.403169	+	0.108029i	−0.0515356	+	0.998671i	$0.516412\pi$
$644$	0.345277	−	0.457615i	0.0136058	−	0.0180326i
$645$	5.15393	−	5.15393i	0.202936	−	0.202936i
$646$	−2.45482	−	4.25188i	−0.0965837	−	0.167288i
$647$	12.5880	−	21.8030i	0.494884	−	0.857164i	−0.505099	−	0.863061i	$-0.668544\pi$
$647$	12.5880	−	21.8030i	0.494884	−	0.857164i	0.999983	+	0.00589775i	$0.00187732\pi$
$648$	−0.744672	−	2.77915i	−0.0292535	−	0.109176i
$649$	0.403791			0.0158502
$650$	−36.6043	−	13.4260i	−1.43574	−	0.526612i
$651$	−3.86331	+	9.54520i	−0.151415	+	0.374106i
$652$	−0.0139948	+	0.00374990i	−0.000548080	+	0.000146857i
$653$	5.72589	−	9.91753i	0.224071	−	0.388103i	−0.731969	−	0.681338i	$-0.761398\pi$
$653$	5.72589	−	9.91753i	0.224071	−	0.388103i	0.956040	+	0.293235i	$0.0947318\pi$
$654$	11.7799	+	20.4034i	0.460632	+	0.797838i
$655$	−18.1376	−	18.1376i	−0.708693	−	0.708693i
$656$	−19.5500	−	5.23841i	−0.763300	−	0.204526i
$657$	0.821946	−	3.06754i	0.0320672	−	0.119676i
$658$	−45.0757	+	19.1009i	−1.75723	+	0.744632i
$659$	10.2755	+	17.7977i	0.400276	+	0.693298i	0.993759	−	0.111548i	$-0.0355809\pi$
$659$	10.2755	+	17.7977i	0.400276	+	0.693298i	−0.593483	+	0.804846i	$0.702248\pi$
$660$	−0.0458048	−	0.0264454i	−0.00178295	−	0.00102939i
$661$	0.197372	−	0.0528857i	0.00767689	−	0.00205702i	−0.254979	−	0.966947i	$-0.582068\pi$
$661$	0.197372	−	0.0528857i	0.00767689	−	0.00205702i	0.262655	+	0.964890i	$0.415402\pi$
$662$		−	21.4562i		−	0.833921i
$663$	6.70684	+	4.72107i	0.260472	+	0.183351i
$664$		−	13.7454i		−	0.533427i
$665$	1.80135	−	14.5969i	0.0698534	−	0.566043i
$666$	−3.15691	+	5.46792i	−0.122328	+	0.211878i
$667$	−24.6901	+	14.2549i	−0.956006	+	0.551950i
$668$	−0.718471	+	0.718471i	−0.0277985	+	0.0277985i
$669$	0.683979	−	2.55265i	0.0264442	−	0.0986910i
$670$	−20.1733	+	75.2879i	−0.779364	+	2.90863i
$671$	0.142138	+	0.142138i	0.00548718	+	0.00548718i
$672$	−0.149794	−	1.07060i	−0.00577843	−	0.0412992i
$673$	22.6738	+	13.0907i	0.874010	+	0.504610i	0.868679	−	0.495376i	$-0.164970\pi$
$673$	22.6738	+	13.0907i	0.874010	+	0.504610i	0.00533138	+	0.999986i	$0.498303\pi$
$674$	11.7051	+	43.6841i	0.450864	+	1.68265i
$675$	−7.78835			−0.299774
$676$	0.716644	+	0.607434i	0.0275632	+	0.0233628i
$677$		−	17.3226i		−	0.665762i	−0.942969	−	0.332881i	$-0.891979\pi$
$677$		−	17.3226i		−	0.665762i	0.942969	−	0.332881i	$-0.108021\pi$
$678$	−0.171291	−	0.639266i	−0.00657839	−	0.0245509i
$679$	−16.9663	+	13.2388i	−0.651107	+	0.508059i
$680$	−20.2697	+	11.7027i	−0.777306	+	0.448778i
$681$	−12.9911	−	12.9911i	−0.497819	−	0.497819i
$682$	−1.06830	−	0.286249i	−0.0409071	−	0.0109610i
$683$	−33.8713	−	9.07578i	−1.29605	−	0.347275i	−0.456094	−	0.889932i	$-0.650752\pi$
$683$	−33.8713	−	9.07578i	−1.29605	−	0.347275i	−0.839954	+	0.542657i	$0.817418\pi$
$684$	−0.0794326	−	0.0794326i	−0.00303718	−	0.00303718i
$685$	−39.0600	+	22.5513i	−1.49240	+	0.861640i
$686$	25.5682	+	2.73484i	0.976199	+	0.104417i
$687$	2.12211	+	7.91982i	0.0809635	+	0.302160i
$688$			7.84757i			0.299186i
$689$	−26.3569	+	37.4431i	−1.00412	+	1.42647i
$690$	14.8870			0.566738
$691$	−4.51121	−	16.8361i	−0.171614	−	0.640474i	−0.997104	−	0.0760557i	$-0.975767\pi$
$691$	−4.51121	−	16.8361i	−0.171614	−	0.640474i	0.825489	−	0.564418i	$-0.190899\pi$
$692$	0.792075	+	0.457305i	0.0301102	+	0.0173841i
$693$	−0.0750332	−	0.536272i	−0.00285027	−	0.0203713i
$694$	−22.9622	−	22.9622i	−0.871631	−	0.871631i
$695$	18.7684	−	70.0445i	0.711925	−	2.65694i
$696$	−7.08079	+	26.4259i	−0.268397	+	1.00167i
$697$	8.45551	−	8.45551i	0.320275	−	0.320275i
$698$	−26.6321	+	15.3761i	−1.00804	+	0.581993i
$699$	−10.5105	+	18.2048i	−0.397544	+	0.688567i
$700$	−1.47788	−	0.182380i	−0.0558587	−	0.00689331i
$701$			18.7752i			0.709130i	0.935031	+	0.354565i	$0.115371\pi$
$701$			18.7752i			0.709130i	−0.935031	+	0.354565i	$0.884629\pi$
$702$	−4.69988	−	1.72386i	−0.177385	−	0.0650629i
$703$			7.06894i			0.266610i
$704$	1.63448	−	0.437957i	0.0616018	−	0.0165061i
$705$	41.2733	+	23.8291i	1.55444	+	0.897457i
$706$	8.46949	+	14.6696i	0.318754	+	0.552097i
$707$	11.1832	+	26.3909i	0.420588	+	0.992533i
$708$	0.0369007	−	0.137715i	0.00138681	−	0.00517566i
$709$	−0.672100	−	0.180089i	−0.0252412	−	0.00676337i	0.246176	−	0.969225i	$-0.420826\pi$
$709$	−0.672100	−	0.180089i	−0.0252412	−	0.00676337i	−0.271418	+	0.962462i	$0.587492\pi$
$710$	0.0482611	+	0.0482611i	0.00181121	+	0.00181121i
$711$	6.36156	+	11.0186i	0.238577	+	0.413228i
$712$	17.6285	−	30.5334i	0.660655	−	1.14429i
$713$	−11.2719	+	3.02030i	−0.422136	+	0.113111i
$714$	−7.74588	−	3.13506i	−0.289882	−	0.117327i
$715$	−2.39443	+	1.10930i	−0.0895467	+	0.0414856i
$716$	0.743412			0.0277826
$717$	−3.79912	−	14.1785i	−0.141881	−	0.529505i
$718$	7.49315	−	12.9785i	0.279642	−	0.484354i
$719$	−15.1031	−	26.1593i	−0.563249	−	0.975576i	−0.997210	−	0.0746442i	$-0.976218\pi$
$719$	−15.1031	−	26.1593i	−0.563249	−	0.975576i	0.433961	−	0.900931i	$-0.357115\pi$
$720$	9.73601	−	9.73601i	0.362840	−	0.362840i
$721$	3.83905	−	5.08810i	0.142974	−	0.189491i
$722$	−22.2406	−	5.95934i	−0.827708	−	0.221784i
$723$	−0.971208	+	0.971208i	−0.0361196	+	0.0361196i
$724$	0.538619	−	0.310972i	0.0200176	−	0.0115572i
$725$	64.1346	+	37.0281i	2.38190	+	1.37519i
$726$	−14.6961	+	3.93782i	−0.545425	+	0.146146i
$727$	8.42295			0.312390			0.156195	−	0.987726i	$-0.450077\pi$
$727$	8.42295			0.312390			0.156195	+	0.987726i	$0.450077\pi$
$728$	−24.4164	−	12.5362i	−0.904933	−	0.464624i
$729$	−1.00000			−0.0370370
$730$	15.2308	−	4.08107i	0.563716	−	0.151047i
$731$	−4.01529	−	2.31823i	−0.148511	−	0.0857428i
$732$	0.0614664	−	0.0354876i	0.00227186	−	0.00131166i
$733$	−22.1020	+	22.1020i	−0.816357	+	0.816357i	−0.985578	−	0.169221i	$-0.945875\pi$
$733$	−22.1020	+	22.1020i	−0.816357	+	0.816357i	0.169221	+	0.985578i	$0.445875\pi$
$734$	46.4061	+	12.4345i	1.71288	+	0.458965i
$735$	−12.8664	−	21.4729i	−0.474585	−	0.792039i
$736$	0.866260	−	0.866260i	0.0319308	−	0.0319308i
$737$	1.60645	+	2.78245i	0.0591743	+	0.102493i
$738$	−3.64929	+	6.32076i	−0.134332	+	0.232670i
$739$	13.4932	+	50.3573i	0.496356	+	1.85242i	0.522301	+	0.852761i	$0.325074\pi$
$739$	13.4932	+	50.3573i	0.496356	+	1.85242i	−0.0259454	+	0.999663i	$0.508260\pi$
$740$	1.17517			0.0432003
$741$	−5.52203	+	0.959533i	−0.202857	+	0.0352493i
$742$	17.5025	−	43.2438i	0.642536	−	1.58753i
$743$	39.2722	−	10.5230i	1.44076	−	0.386050i	0.547958	−	0.836506i	$-0.315405\pi$
$743$	39.2722	−	10.5230i	1.44076	−	0.386050i	0.892799	+	0.450456i	$0.148739\pi$
$744$	−5.59908	+	9.69789i	−0.205272	+	0.355542i
$745$	−20.1138	−	34.8381i	−0.736911	−	1.27637i
$746$	13.9879	+	13.9879i	0.512134	+	0.512134i
$747$	−4.61460	−	1.23648i	−0.168839	−	0.0452403i
$748$	−0.00870782	+	0.0324980i	−0.000318389	+	0.00118825i
$749$	−4.59994	−	10.8553i	−0.168078	−	0.396643i
$750$	−6.92225	−	11.9897i	−0.252765	−	0.437802i
$751$	34.2507	+	19.7747i	1.24983	+	0.721588i	0.971075	−	0.238775i	$-0.0767459\pi$
$751$	34.2507	+	19.7747i	1.24983	+	0.721588i	0.278752	+	0.960363i	$0.410079\pi$
$752$	−49.5637	+	13.2805i	−1.80740	+	0.484292i
$753$			3.53667i			0.128884i
$754$	30.5063	+	36.5401i	1.11097	+	1.33071i
$755$		−	46.4302i		−	1.68977i
$756$	−0.189755	−	0.0234170i	−0.00690134	−	0.000851669i
$757$	10.7369	−	18.5969i	0.390241	−	0.675917i	−0.602240	−	0.798315i	$-0.705725\pi$
$757$	10.7369	−	18.5969i	0.390241	−	0.675917i	0.992481	+	0.122398i	$0.0390584\pi$
$758$	26.9953	−	15.5857i	0.980512	−	0.566099i
$759$	0.433917	−	0.433917i	0.0157502	−	0.0157502i
$760$	4.13960	−	15.4492i	0.150159	−	0.560402i
$761$	5.26977	−	19.6670i	0.191029	−	0.712930i	−0.802230	−	0.597015i	$-0.796353\pi$
$761$	5.26977	−	19.6670i	0.191029	−	0.712930i	0.993259	−	0.115915i	$-0.0369800\pi$
$762$	2.13986	+	2.13986i	0.0775190	+	0.0775190i
$763$	44.4619	−	6.22095i	1.60963	−	0.225213i
$764$	−1.01480	−	0.585894i	−0.0367141	−	0.0211969i
$765$	2.10544	+	7.85762i	0.0761224	+	0.284093i
$766$	18.8631			0.681551
$767$	−4.55890	−	5.46060i	−0.164612	−	0.197171i
$768$		−	1.73207i		−	0.0625005i
$769$	11.7253	+	43.7592i	0.422823	+	1.57800i	0.768631	+	0.639693i	$0.220938\pi$
$769$	11.7253	+	43.7592i	0.422823	+	1.57800i	−0.345807	+	0.938306i	$0.612395\pi$
$770$	2.11966	−	1.65397i	0.0763872	−	0.0596049i
$771$	−17.3866	+	10.0381i	−0.626163	+	0.361515i
$772$	−1.03001	−	1.03001i	−0.0370708	−	0.0370708i
$773$	19.0521	+	5.10499i	0.685256	+	0.183614i	0.584617	−	0.811309i	$-0.301245\pi$
$773$	19.0521	+	5.10499i	0.685256	+	0.183614i	0.100638	+	0.994923i	$0.467911\pi$
$774$	2.73347	+	0.732430i	0.0982524	+	0.0263267i
$775$	21.4342	+	21.4342i	0.769940	+	0.769940i
$776$	−20.2674	+	11.7014i	−0.727557	+	0.420055i
$777$	7.40147	+	9.48543i	0.265526	+	0.340288i
$778$	7.40762	+	27.6456i	0.265576	+	0.991143i
$779$			8.17149i			0.292774i
$780$	0.159517	+	0.918008i	0.00571164	+	0.0328700i
$781$	0.00281338			0.000100670
$782$	−2.45096	−	9.14710i	−0.0876461	−	0.327100i
$783$	8.23469	+	4.75430i	0.294284	+	0.169905i
$784$	26.1431	+	6.55225i	0.933684	+	0.234009i
$785$	−51.4020	−	51.4020i	−1.83461	−	1.83461i
$786$	2.57755	−	9.61953i	0.0919380	−	0.343117i
$787$	6.36046	−	23.7376i	0.226726	−	0.846153i	−0.754980	−	0.655748i	$-0.772353\pi$
$787$	6.36046	−	23.7376i	0.226726	−	0.846153i	0.981706	−	0.190405i	$-0.0609800\pi$
$788$	−0.128701	+	0.128701i	−0.00458479	+	0.00458479i
$789$	−18.2526	+	10.5381i	−0.649809	+	0.375167i
$790$	−31.5860	+	54.7086i	−1.12378	+	1.94644i
$791$	−1.25165	−	0.154461i	−0.0445034	−	0.00549200i
$792$		−	0.588864i		−	0.0209244i
$793$	0.317406	−	3.52695i	0.0112714	−	0.125246i
$794$			23.4203i			0.831155i
$795$	−43.8676	+	11.7543i	−1.55582	+	0.416882i
$796$	−1.03034	−	0.594870i	−0.0365196	−	0.0210846i
$797$	10.4117	+	18.0336i	0.368802	+	0.638783i	0.989378	−	0.145362i	$-0.0464348\pi$
$797$	10.4117	+	18.0336i	0.368802	+	0.638783i	−0.620577	+	0.784146i	$0.713102\pi$
$798$	5.25773	−	2.22797i	0.186122	−	0.0788694i
$799$	7.84634	−	29.2829i	0.277584	−	1.03596i
$800$	−3.07380	−	0.823623i	−0.108675	−	0.0291195i
$801$	−8.66485	−	8.66485i	−0.306157	−	0.306157i
$802$	9.45056	+	16.3688i	0.333711	+	0.578004i
$803$	0.324985	−	0.562890i	0.0114685	−	0.0198640i
$804$	1.09578	−	0.293612i	0.0386450	−	0.0103549i
$805$	10.6430	−	26.2960i	0.375118	−	0.926814i
$806$	8.19027	+	17.6787i	0.288490	+	0.622706i
$807$	−24.8240			−0.873846
$808$	8.06737	+	30.1078i	0.283809	+	1.05919i
$809$	−8.68330	+	15.0399i	−0.305289	+	0.528776i	−0.977326	−	0.211742i	$-0.932086\pi$
$809$	−8.68330	+	15.0399i	−0.305289	+	0.528776i	0.672037	+	0.740518i	$0.265420\pi$
$810$	−2.48257	−	4.29993i	−0.0872285	−	0.151084i
$811$	−9.89362	+	9.89362i	−0.347412	+	0.347412i	−0.859145	−	0.511733i	$-0.829004\pi$
$811$	−9.89362	+	9.89362i	−0.347412	+	0.347412i	0.511733	+	0.859145i	$0.329004\pi$
$812$	1.45125	+	1.09499i	0.0509288	+	0.0384265i
$813$	−12.1049	−	3.24351i	−0.424539	−	0.113755i
$814$	−0.913740	+	0.913740i	−0.0320266	+	0.0320266i
$815$	−0.620918	+	0.358487i	−0.0217498	+	0.0125573i
$816$	−7.58506	−	4.37924i	−0.265530	−	0.153304i
$817$	3.06039	−	0.820029i	0.107069	−	0.0286892i
$818$	−44.2924			−1.54865
$819$	−6.40504	+	7.06934i	−0.223810	+	0.247023i
$820$	1.35847			0.0474397
$821$	1.09064	−	0.292235i	0.0380635	−	0.0101991i	−0.239737	−	0.970838i	$-0.577061\pi$
$821$	1.09064	−	0.292235i	0.0380635	−	0.0101991i	0.277801	+	0.960639i	$0.410395\pi$
$822$	−15.1652	−	8.75563i	−0.528947	−	0.305388i
$823$	−18.7452	+	10.8226i	−0.653417	+	0.377250i	−0.789764	−	0.613411i	$-0.789797\pi$
$823$	−18.7452	+	10.8226i	−0.653417	+	0.377250i	0.136347	+	0.990661i	$0.456464\pi$
$824$	4.90132	−	4.90132i	0.170746	−	0.170746i
$825$	−1.53970	−	0.412560i	−0.0536053	−	0.0143635i
$826$	5.78538	+	4.36515i	0.201299	+	0.151883i
$827$	−22.8457	+	22.8457i	−0.794421	+	0.794421i	−0.982210	−	0.187788i	$-0.939868\pi$
$827$	−22.8457	+	22.8457i	−0.794421	+	0.794421i	0.187788	+	0.982210i	$0.439868\pi$
$828$	−0.108336	−	0.187644i	−0.00376494	−	0.00652107i
$829$	23.5978	−	40.8725i	0.819585	−	1.41956i	−0.0864042	−	0.996260i	$-0.527538\pi$
$829$	23.5978	−	40.8725i	0.819585	−	1.41956i	0.905989	−	0.423302i	$-0.139129\pi$
$830$	−6.13927	−	22.9121i	−0.213097	−	0.795290i
$831$	−16.5899			−0.575498
$832$	−24.3763	−	17.1589i	−0.845096	−	0.594879i
$833$	−11.0754	+	11.4408i	−0.383740	+	0.396401i
$834$	27.1951	−	7.28690i	0.941689	−	0.252325i
$835$	−25.1405	+	43.5446i	−0.870023	+	1.50692i
$836$	−0.0114956	−	0.0199109i	−0.000397582	−	0.000688632i
$837$	2.75209	+	2.75209i	0.0951262	+	0.0951262i
$838$	−39.2262	−	10.5106i	−1.35505	−	0.363083i
$839$	−6.00349	+	22.4053i	−0.207263	+	0.773518i	0.781484	+	0.623925i	$0.214463\pi$
$839$	−6.00349	+	22.4053i	−0.207263	+	0.773518i	−0.988748	+	0.149593i	$0.952204\pi$
$840$	−10.6213	−	25.0648i	−0.366468	−	0.864817i
$841$	−30.7068	−	53.1857i	−1.05885	−	1.83399i
$842$	32.4944	+	18.7606i	1.11983	+	0.646535i
$843$	7.37660	−	1.97655i	0.254063	−	0.0680761i
$844$		−	0.529914i		−	0.0182404i
$845$	42.0352	+	19.8564i	1.44605	+	0.683080i
$846$			18.5035i			0.636165i
$847$	−3.55092	+	28.7742i	−0.122011	+	0.988692i
$848$	24.4485	−	42.3460i	0.839564	−	1.45417i
$849$	−21.6023	+	12.4721i	−0.741390	+	0.428042i
$850$	−17.3938	+	17.3938i	−0.596601	+	0.596601i
$851$	−3.52891	+	13.1701i	−0.120969	+	0.451464i
$852$	0.000257102	0	0.000959517i	8.80816e−6	0	3.28725e-5i
$853$	11.1326	+	11.1326i	0.381173	+	0.381173i	0.871525	−	0.490352i	$-0.163132\pi$
$853$	11.1326	+	11.1326i	0.381173	+	0.381173i	−0.490352	+	0.871525i	$0.663132\pi$
$854$	0.499932	+	3.57308i	0.0171073	+	0.122268i
$855$	−4.81420	−	2.77948i	−0.164642	−	0.0950562i
$856$	−3.31831	−	12.3841i	−0.113418	−	0.423281i
$857$	−13.9305			−0.475858			−0.237929	−	0.971283i	$-0.576469\pi$
$857$	−13.9305			−0.475858			−0.237929	+	0.971283i	$0.576469\pi$
$858$	−0.837814	−	0.589754i	−0.0286025	−	0.0201339i
$859$		−	39.1906i		−	1.33717i	−0.743638	−	0.668583i	$-0.766901\pi$
$859$		−	39.1906i		−	1.33717i	0.743638	−	0.668583i	$-0.233099\pi$
$860$	−0.136326	−	0.508774i	−0.00464866	−	0.0173490i
$861$	8.55589	+	10.9649i	0.291584	+	0.373682i
$862$	−33.1925	+	19.1637i	−1.13054	+	0.652718i
$863$	13.9862	+	13.9862i	0.476097	+	0.476097i	0.903881	−	0.427784i	$-0.140706\pi$
$863$	13.9862	+	13.9862i	0.476097	+	0.476097i	−0.427784	+	0.903881i	$0.640706\pi$
$864$	−0.394667	−	0.105751i	−0.0134268	−	0.00359771i
$865$	43.7179	+	11.7142i	1.48645	+	0.398294i
$866$	23.4990	+	23.4990i	0.798530	+	0.798530i
$867$	−10.2411	+	5.91268i	−0.347805	+	0.200805i
$868$	0.457779	+	0.586670i	0.0155380	+	0.0199129i
$869$	0.673963	+	2.51526i	0.0228626	+	0.0853245i
$870$			47.2115i			1.60062i
$871$	19.4908	−	53.1390i	0.660420	−	1.80055i
$872$	48.8223			1.65333
$873$	2.10521	+	7.85674i	0.0712504	+	0.265910i
$874$	5.60424	+	3.23561i	0.189566	+	0.109446i
$875$	−26.1272	+	3.65562i	−0.883260	+	0.123582i
$876$	−0.162278	−	0.162278i	−0.00548286	−	0.00548286i
$877$	−3.66574	+	13.6807i	−0.123783	+	0.461965i	−0.999793	−	0.0203276i	$-0.993529\pi$
$877$	−3.66574	+	13.6807i	−0.123783	+	0.461965i	0.876010	+	0.482292i	$0.160196\pi$
$878$	−3.76524	+	14.0521i	−0.127071	+	0.474235i
$879$	−9.97240	+	9.97240i	−0.336361	+	0.336361i
$880$	2.44046	−	1.40900i	0.0822680	−	0.0474975i
$881$	12.7604	−	22.1016i	0.429908	−	0.744623i	−0.566957	−	0.823748i	$-0.691879\pi$
$881$	12.7604	−	22.1016i	0.429908	−	0.744623i	0.996865	+	0.0791249i	$0.0252126\pi$
$882$	4.72228	−	8.49465i	0.159007	−	0.286030i
$883$		−	24.3281i		−	0.818705i	−0.912376	−	0.409352i	$-0.865755\pi$
$883$		−	24.3281i		−	0.818705i	0.912376	−	0.409352i	$-0.134245\pi$
$884$	0.537795	−	0.249152i	0.0180880	−	0.00837988i
$885$		−	7.05534i		−	0.237163i
$886$	−26.5066	+	7.10242i	−0.890506	+	0.238610i
$887$	11.5771	+	6.68405i	0.388722	+	0.224429i	0.681606	−	0.731719i	$-0.261282\pi$
$887$	11.5771	+	6.68405i	0.388722	+	0.224429i	−0.292884	+	0.956148i	$0.594615\pi$
$888$	6.54195	+	11.3310i	0.219533	+	0.380243i
$889$	5.30964	−	2.24997i	0.178079	−	0.0754616i
$890$	15.7472	−	58.7693i	0.527847	−	1.96995i
$891$	−0.197692	−	0.0529715i	−0.00662294	−	0.00177461i
$892$	−0.135039	−	0.135039i	−0.00452144	−	0.00452144i
$893$	10.3583	+	17.9411i	0.346626	+	0.600375i
$894$	7.80926	−	13.5260i	0.261181	−	0.452378i
$895$	35.5347	−	9.52150i	1.18780	−	0.318269i
$896$	26.1486	+	10.5834i	0.873564	+	0.353565i
$897$	−10.7670	−	0.968972i	−0.359501	−	0.0323530i
$898$	39.2282			1.30906
$899$	−9.57835	−	35.7469i	−0.319456	−	1.19223i
$900$	−0.281412	+	0.487420i	−0.00938040	+	0.0162473i
$901$	14.4445	+	25.0186i	0.481217	+	0.833492i
$902$	−1.05626	+	1.05626i	−0.0351695	+	0.0351695i
$903$	3.24796	−	4.30471i	0.108085	−	0.143252i
$904$	−1.32473	−	0.354960i	−0.0440598	−	0.0118058i
$905$	21.7628	−	21.7628i	0.723421	−	0.723421i
$906$	15.6116	−	9.01337i	0.518661	−	0.299449i
$907$	31.5715	+	18.2278i	1.04831	+	0.605244i	0.922177	−	0.386769i	$-0.126409\pi$
$907$	31.5715	+	18.2278i	1.04831	+	0.605244i	0.126137	+	0.992013i	$0.459742\pi$
$908$	−1.28242	+	0.343624i	−0.0425586	+	0.0114036i
$909$	10.8334			0.359323
$910$	−46.2986	−	9.99111i	−1.53478	−	0.331202i
$911$	−23.9100			−0.792174			−0.396087	−	0.918213i	$-0.629632\pi$
$911$	−23.9100			−0.792174			−0.396087	+	0.918213i	$0.629632\pi$
$912$	5.78121	−	1.54907i	0.191435	−	0.0512949i
$913$	−0.846772	−	0.488884i	−0.0280241	−	0.0161797i
$914$	−23.5660	+	13.6058i	−0.779494	+	0.450041i
$915$	2.48354	−	2.48354i	0.0821034	−	0.0821034i
$916$	0.572325	+	0.153354i	0.0189102	+	0.00506696i
$917$	−15.1490	−	11.4301i	−0.500264	−	0.377456i
$918$	−2.23331	+	2.23331i	−0.0737101	+	0.0737101i
$919$	−5.06332	−	8.76993i	−0.167024	−	0.289293i	0.770348	−	0.637623i	$-0.220082\pi$
$919$	−5.06332	−	8.76993i	−0.167024	−	0.289293i	−0.937372	+	0.348330i	$0.886749\pi$
$920$	15.4249	−	26.7167i	0.508544	−	0.880823i
$921$	−2.40721	−	8.98382i	−0.0793202	−	0.296027i
$922$	−20.2875			−0.668132
$923$	−0.0317637	−	0.0380462i	−0.00104551	−	0.00125231i
$924$	−0.0362728	−	0.0146810i	−0.00119329	−	0.000482969i
$925$	34.2103	−	9.16662i	1.12483	−	0.301397i
$926$	0.628116	−	1.08793i	0.0206412	−	0.0357516i
$927$	−1.20456	−	2.08636i	−0.0395630	−	0.0685251i
$928$	2.74719	+	2.74719i	0.0901810	+	0.0901810i
$929$	−38.8295	−	10.4043i	−1.27396	−	0.341355i	−0.442411	−	0.896813i	$-0.645877\pi$
$929$	−38.8295	−	10.4043i	−1.27396	−	0.341355i	−0.831545	+	0.555457i	$0.812543\pi$
$930$	−5.00155	+	18.6660i	−0.164007	+	0.612084i
$931$	−0.176578	−	10.8800i	−0.00578711	−	0.356576i
$932$	0.759542	+	1.31556i	0.0248796	+	0.0430928i
$933$	5.21313	+	3.00980i	0.170670	+	0.0985365i
$934$	−24.4394	+	6.54853i	−0.799683	+	0.214274i
$935$			1.66492i			0.0544487i
$936$	−7.96340	+	6.64841i	−0.260292	+	0.217310i
$937$			0.991729i			0.0323984i	0.999869	+	0.0161992i	$0.00515658\pi$
$937$			0.991729i			0.0323984i	−0.999869	+	0.0161992i	$0.994843\pi$
$938$	−7.06283	+	57.2323i	−0.230610	+	1.86870i
$939$	−2.09591	+	3.63022i	−0.0683974	+	0.118468i
$940$	2.98261	−	1.72201i	0.0972819	−	0.0561658i
$941$	−10.1768	+	10.1768i	−0.331753	+	0.331753i	−0.853252	−	0.521499i	$-0.825373\pi$
$941$	−10.1768	+	10.1768i	−0.331753	+	0.331753i	0.521499	+	0.853252i	$0.325373\pi$
$942$	7.30479	−	27.2618i	0.238003	−	0.888238i
$943$	−4.07931	+	15.2242i	−0.132841	+	0.495768i
$944$	5.37137	+	5.37137i	0.174823	+	0.174823i
$945$	−9.37014	+	1.31104i	−0.304811	+	0.0426480i
$946$	0.501587	+	0.289592i	0.0163080	+	0.00941544i
$947$	2.29842	+	8.57781i	0.0746885	+	0.278741i	0.993163	−	0.116740i	$-0.0372444\pi$
$947$	2.29842	+	8.57781i	0.0746885	+	0.278741i	−0.918474	+	0.395481i	$0.870578\pi$
$948$	0.919435			0.0298619
$949$	−11.2813	+	1.96029i	−0.366206	+	0.0636337i
$950$		−	16.8095i		−	0.545373i
$951$	3.71188	+	13.8529i	0.120366	+	0.449212i
$952$	−13.6520	+	10.6527i	−0.442465	+	0.345256i
$953$	13.1520	−	7.59333i	0.426036	−	0.245972i	−0.271620	−	0.962404i	$-0.587560\pi$
$953$	13.1520	−	7.59333i	0.426036	−	0.245972i	0.697657	+	0.716432i	$0.254226\pi$
$954$	−12.4681	−	12.4681i	−0.403671	−	0.403671i
$955$	−56.0109	−	15.0081i	−1.81247	−	0.485650i
$956$	−1.02461	−	0.274543i	−0.0331382	−	0.00887934i
$957$	1.37609	+	1.37609i	0.0444828	+	0.0444828i
$958$	47.2373	−	27.2724i	1.52617	−	0.881133i
$959$	−26.3077	+	20.5279i	−0.849520	+	0.662880i
$960$	−7.65232	−	28.5588i	−0.246978	−	0.921733i
$961$			15.8520i			0.511355i
$962$	22.6731	+	2.04046i	0.731011	+	0.0657869i
$963$	−4.45607			−0.143595
$964$	0.0256892	+	0.0958735i	0.000827394	+	0.00308788i
$965$	−62.4262	−	36.0418i	−2.00957	−	1.16023i
$966$	10.9078	−	1.52618i	0.350954	−	0.0491042i
$967$	−31.1019	−	31.1019i	−1.00017	−	1.00017i	−1.00000		0.000170581i	$-0.999946\pi$
$967$	−31.1019	−	31.1019i	−1.00017	−	1.00017i	−0.000170581	−	1.00000i	$-0.500054\pi$
$968$	−8.16020	+	30.4543i	−0.262279	+	0.978838i
$969$	−0.915214	+	3.41562i	−0.0294009	+	0.109726i
$970$	−28.5571	+	28.5571i	−0.916914	+	0.916914i
$971$	5.28808	−	3.05308i	0.169703	−	0.0979778i	−0.412743	−	0.910848i	$-0.635429\pi$
$971$	5.28808	−	3.05308i	0.169703	−	0.0979778i	0.582446	+	0.812870i	$0.302096\pi$
$972$	−0.0361324	+	0.0625832i	−0.00115895	+	0.00200736i
$973$	6.57094	−	53.2464i	0.210655	−	1.70700i
$974$		−	31.1669i		−	0.998652i
$975$	11.8044	+	25.4797i	0.378042	+	0.816004i
$976$			3.78154i			0.121044i
$977$	45.5205	−	12.1972i	1.45633	−	0.390222i	0.558109	−	0.829767i	$-0.311527\pi$
$977$	45.5205	−	12.1972i	1.45633	−	0.390222i	0.898221	+	0.439545i	$0.144860\pi$
$978$	−0.241074	−	0.139184i	−0.00770870	−	0.00445062i
$979$	−1.25398	−	2.17196i	−0.0400775	−	0.0694163i
$980$	−1.80874	+	0.0293552i	−0.0577780	+	0.000937716i
$981$	4.39183	−	16.3905i	0.140220	−	0.523309i
$982$	8.45756	+	2.26620i	0.269891	+	0.0723172i
$983$	11.6944	+	11.6944i	0.372994	+	0.372994i	0.868567	−	0.495572i	$-0.165042\pi$
$983$	11.6944	+	11.6944i	0.372994	+	0.372994i	−0.495572	+	0.868567i	$0.665042\pi$
$984$	7.56230	+	13.0983i	0.241077	+	0.417558i
$985$	−4.50347	+	7.80024i	−0.143492	+	0.248536i
$986$	29.0084	−	7.77278i	0.923816	−	0.247536i
$987$	32.6842	+	13.2286i	1.04035	+	0.421070i
$988$	−0.139474	+	0.380257i	−0.00443725	+	0.0120976i
$989$	6.11114			0.194323
$990$	−0.263010	−	0.981569i	−0.00835902	−	0.0311963i
$991$	−10.3485	+	17.9242i	−0.328732	+	0.569381i	−0.982261	−	0.187521i	$-0.939955\pi$
$991$	−10.3485	+	17.9242i	−0.328732	+	0.569381i	0.653529	+	0.756902i	$0.273288\pi$
$992$	0.795124	+	1.37720i	0.0252452	+	0.0437260i
$993$	−10.9274	+	10.9274i	−0.346769	+	0.346769i
$994$	0.0403090	+	0.0304138i	0.00127852	+	0.000964666i
$995$	−56.8690	−	15.2380i	−1.80287	−	0.483077i
$996$	−0.244119	+	0.244119i	−0.00773522	+	0.00773522i
$997$	1.20776	−	0.697298i	0.0382500	−	0.0220836i	−0.480753	−	0.876856i	$-0.659637\pi$
$997$	1.20776	−	0.697298i	0.0382500	−	0.0220836i	0.519003	+	0.854772i	$0.326303\pi$
$998$	−0.317214	−	0.183144i	−0.0100412	−	0.00579731i
$999$	4.39250	−	1.17697i	0.138973	−	0.0372376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.by.c.202.6	✓	32
3.2	odd	2		819.2.fm.f.748.3		32
7.6	odd	2		273.2.by.d.202.6	yes	32
13.2	odd	12		273.2.by.d.223.6	yes	32
21.20	even	2		819.2.fm.e.748.3		32
39.2	even	12		819.2.fm.e.496.3		32
91.41	even	12	inner	273.2.by.c.223.6	yes	32
273.41	odd	12		819.2.fm.f.496.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.6	✓	32	1.1	even	1	trivial
273.2.by.c.223.6	yes	32	91.41	even	12	inner
273.2.by.d.202.6	yes	32	7.6	odd	2
273.2.by.d.223.6	yes	32	13.2	odd	12
819.2.fm.e.496.3		32	39.2	even	12
819.2.fm.e.748.3		32	21.20	even	2
819.2.fm.f.496.3		32	273.41	odd	12
819.2.fm.f.748.3		32	3.2	odd	2

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34112 - 0.359352i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.0625832 + 0.0361324i) q^{4} +(-2.52867 + 2.52867i) q^{5} +(-1.34112 - 0.359352i) q^{6} +(-1.59355 + 2.11202i) q^{7} +(-2.03448 + 2.03448i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.34112 - 0.359352i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.0625832 + 0.0361324i) q^{4} +(-2.52867 + 2.52867i) q^{5} +(-1.34112 - 0.359352i) q^{6} +(-1.59355 + 2.11202i) q^{7} +(-2.03448 + 2.03448i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.48257 + 4.29993i) q^{10} +(0.0529715 + 0.197692i) q^{11} +0.0722649 q^{12} +(2.07540 - 2.94834i) q^{13} +(-1.37818 + 3.40511i) q^{14} +(3.45423 - 0.925558i) q^{15} +(-1.92512 + 3.33441i) q^{16} +(-1.13739 - 1.97002i) q^{17} +(0.981768 + 0.981768i) q^{18} +(1.50152 + 0.402330i) q^{19} +(0.0668853 - 0.249619i) q^{20} +(2.43606 - 1.03229i) q^{21} +(0.142082 + 0.246094i) q^{22} +(2.59661 + 1.49915i) q^{23} +(2.77915 - 0.744672i) q^{24} -7.78835i q^{25} +(1.72386 - 4.69988i) q^{26} -1.00000i q^{27} +(0.0234170 - 0.189755i) q^{28} +(-4.75430 + 8.23469i) q^{29} +(4.29993 - 2.48257i) q^{30} +(-2.75209 + 2.75209i) q^{31} +(0.105751 - 0.394667i) q^{32} +(0.0529715 - 0.197692i) q^{33} +(-2.23331 - 2.23331i) q^{34} +(-1.31104 - 9.37014i) q^{35} +(-0.0625832 - 0.0361324i) q^{36} +(1.17697 + 4.39250i) q^{37} +2.15829 q^{38} +(-3.27152 + 1.51564i) q^{39} -10.2891i q^{40} +(1.36054 + 5.07760i) q^{41} +(2.89609 - 2.25982i) q^{42} +(1.76513 - 1.01910i) q^{43} +(-0.0104582 - 0.0104582i) q^{44} +(-3.45423 - 0.925558i) q^{45} +(4.02109 + 1.07745i) q^{46} +(9.42358 + 9.42358i) q^{47} +(3.33441 - 1.92512i) q^{48} +(-1.92122 - 6.73119i) q^{49} +(-2.79876 - 10.4451i) q^{50} +2.27478i q^{51} +(-0.0233541 + 0.259506i) q^{52} -12.6997 q^{53} +(-0.359352 - 1.34112i) q^{54} +(-0.633846 - 0.365951i) q^{55} +(-1.05481 - 7.53890i) q^{56} +(-1.09919 - 1.09919i) q^{57} +(-3.41693 + 12.7522i) q^{58} +(0.510631 - 1.90570i) q^{59} +(-0.182734 + 0.182734i) q^{60} +(0.850570 - 0.491077i) q^{61} +(-2.70191 + 4.67985i) q^{62} +(-2.62583 - 0.324044i) q^{63} -8.26779i q^{64} +(2.20740 + 12.7034i) q^{65} -0.284164i q^{66} +(15.1633 - 4.06300i) q^{67} +(0.142363 + 0.0821934i) q^{68} +(-1.49915 - 2.59661i) q^{69} +(-5.12543 - 12.0954i) q^{70} +(0.00355777 - 0.0132778i) q^{71} +(-2.77915 - 0.744672i) q^{72} +(-2.24560 - 2.24560i) q^{73} +(3.15691 + 5.46792i) q^{74} +(-3.89417 + 6.74490i) q^{75} +(-0.108507 + 0.0290743i) q^{76} +(-0.501942 - 0.203155i) q^{77} +(-3.84285 + 3.20828i) q^{78} +12.7231 q^{79} +(-3.56363 - 13.2996i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.64929 + 6.32076i) q^{82} +(-3.37812 + 3.37812i) q^{83} +(-0.115157 + 0.152625i) q^{84} +(7.85762 + 2.10544i) q^{85} +(2.00104 - 2.00104i) q^{86} +(8.23469 - 4.75430i) q^{87} +(-0.509971 - 0.294432i) q^{88} +(-11.8364 + 3.17155i) q^{89} -4.96513 q^{90} +(2.91971 + 9.08159i) q^{91} -0.216672 q^{92} +(3.75943 - 1.00734i) q^{93} +(16.0245 + 9.25177i) q^{94} +(-4.81420 + 2.77948i) q^{95} +(-0.288916 + 0.288916i) q^{96} +(7.85674 + 2.10521i) q^{97} +(-4.99545 - 8.33694i) q^{98} +(-0.144721 + 0.144721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9	\( 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9} - 2 q^{10} - 4 q^{11} - 32 q^{12} - 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} + 8 q^{17} + 2 q^{18} - 2 q^{19} - 44 q^{20} + 2 q^{21} - 4 q^{22} - 18 q^{23} - 4 q^{24} + 28 q^{26} - 18 q^{28} - 18 q^{29} + 14 q^{31} - 8 q^{32} - 4 q^{33} + 66 q^{34} - 20 q^{35} + 6 q^{36} - 24 q^{37} - 24 q^{38} + 8 q^{39} + 16 q^{42} - 6 q^{43} - 20 q^{44} - 4 q^{45} - 58 q^{46} + 28 q^{47} + 60 q^{48} + 10 q^{49} + 70 q^{50} - 28 q^{52} - 80 q^{53} + 4 q^{54} - 60 q^{55} - 120 q^{56} + 16 q^{57} - 4 q^{58} + 42 q^{59} - 58 q^{60} - 36 q^{61} - 52 q^{62} + 2 q^{63} + 14 q^{65} + 26 q^{67} + 72 q^{68} - 2 q^{69} + 68 q^{70} - 4 q^{71} + 4 q^{72} - 12 q^{73} - 18 q^{74} - 16 q^{75} + 48 q^{76} - 28 q^{77} - 14 q^{78} - 4 q^{79} + 98 q^{80} - 16 q^{81} - 20 q^{82} + 36 q^{83} + 32 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} + 54 q^{89} - 4 q^{90} - 54 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} - 22 q^{96} + 40 q^{97} + 4 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9 - 2 * q^10 - 4 * q^11 - 32 * q^12 - 6 * q^13 + 34 * q^14 + 4 * q^15 + 14 * q^16 + 8 * q^17 + 2 * q^18 - 2 * q^19 - 44 * q^20 + 2 * q^21 - 4 * q^22 - 18 * q^23 - 4 * q^24 + 28 * q^26 - 18 * q^28 - 18 * q^29 + 14 * q^31 - 8 * q^32 - 4 * q^33 + 66 * q^34 - 20 * q^35 + 6 * q^36 - 24 * q^37 - 24 * q^38 + 8 * q^39 + 16 * q^42 - 6 * q^43 - 20 * q^44 - 4 * q^45 - 58 * q^46 + 28 * q^47 + 60 * q^48 + 10 * q^49 + 70 * q^50 - 28 * q^52 - 80 * q^53 + 4 * q^54 - 60 * q^55 - 120 * q^56 + 16 * q^57 - 4 * q^58 + 42 * q^59 - 58 * q^60 - 36 * q^61 - 52 * q^62 + 2 * q^63 + 14 * q^65 + 26 * q^67 + 72 * q^68 - 2 * q^69 + 68 * q^70 - 4 * q^71 + 4 * q^72 - 12 * q^73 - 18 * q^74 - 16 * q^75 + 48 * q^76 - 28 * q^77 - 14 * q^78 - 4 * q^79 + 98 * q^80 - 16 * q^81 - 20 * q^82 + 36 * q^83 + 32 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 + 54 * q^89 - 4 * q^90 - 54 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 - 22 * q^96 + 40 * q^97 + 4 * q^99

Introduction

L-functions

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