LMFDB - Embedded newform 224.2.u.b.85.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(29,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("224.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.u (of order $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			85.8
Character	$\chi$	$=$	224.85
Dual form			224.2.u.b.29.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16944 + 0.795236i) q^{2} +(1.29558 - 0.536647i) q^{3} +(0.735199 + 1.85997i) q^{4} +(0.937867 - 2.26421i) q^{5} +(1.94187 + 0.402713i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.619339 + 2.75979i) q^{8} +(-0.730784 + 0.730784i) q^{9} +O(q^{10})$	\(q+(1.16944 + 0.795236i) q^{2} +(1.29558 - 0.536647i) q^{3} +(0.735199 + 1.85997i) q^{4} +(0.937867 - 2.26421i) q^{5} +(1.94187 + 0.402713i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.619339 + 2.75979i) q^{8} +(-0.730784 + 0.730784i) q^{9} +(2.89737 - 1.90204i) q^{10} +(-2.12310 - 0.879416i) q^{11} +(1.95065 + 2.01519i) q^{12} +(-0.267138 - 0.644928i) q^{13} +(-0.264605 - 1.38924i) q^{14} -3.43677i q^{15} +(-2.91896 + 2.73489i) q^{16} +2.83430i q^{17} +(-1.43576 + 0.273465i) q^{18} +(-0.445544 - 1.07564i) q^{19} +(4.90088 + 0.0797566i) q^{20} +(-1.29558 - 0.536647i) q^{21} +(-1.78350 - 2.71679i) q^{22} +(-4.15632 + 4.15632i) q^{23} +(0.678626 + 3.90789i) q^{24} +(-0.711525 - 0.711525i) q^{25} +(0.200467 - 0.966645i) q^{26} +(-2.16456 + 5.22570i) q^{27} +(0.795332 - 1.83506i) q^{28} +(3.37949 - 1.39983i) q^{29} +(2.73304 - 4.01911i) q^{30} +2.27603 q^{31} +(-5.58845 + 0.877041i) q^{32} -3.22258 q^{33} +(-2.25394 + 3.31456i) q^{34} +(-2.26421 + 0.937867i) q^{35} +(-1.89651 - 0.821963i) q^{36} +(3.59295 - 8.67415i) q^{37} +(0.334347 - 1.61221i) q^{38} +(-0.692197 - 0.692197i) q^{39} +(5.66788 + 3.99063i) q^{40} +(0.419720 - 0.419720i) q^{41} +(-1.08835 - 1.65787i) q^{42} +(-6.63049 - 2.74644i) q^{43} +(0.0747859 - 4.59544i) q^{44} +(0.969271 + 2.34003i) q^{45} +(-8.16585 + 1.55533i) q^{46} -12.0972i q^{47} +(-2.31408 + 5.10972i) q^{48} +1.00000i q^{49} +(-0.266258 - 1.39792i) q^{50} +(1.52102 + 3.67206i) q^{51} +(1.00315 - 0.971019i) q^{52} +(8.31047 + 3.44231i) q^{53} +(-6.68699 + 4.38983i) q^{54} +(-3.98237 + 3.98237i) q^{55} +(2.38940 - 1.51352i) q^{56} +(-1.15447 - 1.15447i) q^{57} +(5.06532 + 1.05047i) q^{58} +(-3.36630 + 8.12696i) q^{59} +(6.39228 - 2.52671i) q^{60} +(8.49805 - 3.52001i) q^{61} +(2.66168 + 1.80998i) q^{62} +1.03348 q^{63} +(-7.23284 - 3.41849i) q^{64} -1.71079 q^{65} +(-3.76862 - 2.56271i) q^{66} +(4.08688 - 1.69284i) q^{67} +(-5.27171 + 2.08378i) q^{68} +(-3.15437 + 7.61533i) q^{69} +(-3.39369 - 0.703799i) q^{70} +(-9.89815 - 9.89815i) q^{71} +(-1.56420 - 2.46941i) q^{72} +(1.37852 - 1.37852i) q^{73} +(11.0998 - 7.28669i) q^{74} +(-1.30367 - 0.540000i) q^{75} +(1.67309 - 1.61951i) q^{76} +(0.879416 + 2.12310i) q^{77} +(-0.259026 - 1.35995i) q^{78} +3.67858i q^{79} +(3.45478 + 9.17412i) q^{80} +4.83146i q^{81} +(0.824617 - 0.157063i) q^{82} +(2.34025 + 5.64986i) q^{83} +(0.0456366 - 2.80428i) q^{84} +(6.41746 + 2.65820i) q^{85} +(-5.56992 - 8.48461i) q^{86} +(3.62718 - 3.62718i) q^{87} +(3.74192 - 5.31464i) q^{88} +(-11.4830 - 11.4830i) q^{89} +(-0.727366 + 3.50733i) q^{90} +(-0.267138 + 0.644928i) q^{91} +(-10.7864 - 4.67491i) q^{92} +(2.94877 - 1.22142i) q^{93} +(9.62010 - 14.1470i) q^{94} -2.85333 q^{95} +(-6.76962 + 4.13530i) q^{96} +14.8956 q^{97} +(-0.795236 + 1.16944i) q^{98} +(2.19419 - 0.908863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} + 4 q^{3} + 8 q^{5} + 12 q^{6} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 40 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 + 12 * q^6 - 8 * q^8 + 8 * q^9	$ 40 q + 4 q^{2} + 4 q^{3} + 8 q^{5} + 12 q^{6} - 8 q^{8} + 8 q^{9} - 16 q^{10} + 12 q^{11} - 36 q^{12} + 8 q^{16} + 4 q^{19} - 4 q^{21} - 52 q^{22} + 16 q^{23} - 8 q^{24} - 16 q^{25} + 12 q^{26} - 32 q^{27} + 8 q^{28} + 16 q^{29} + 36 q^{30} + 24 q^{31} - 36 q^{32} + 8 q^{33} - 8 q^{34} - 8 q^{36} + 16 q^{37} - 12 q^{38} - 24 q^{39} + 36 q^{40} + 8 q^{41} + 52 q^{43} - 44 q^{44} - 64 q^{45} - 32 q^{46} - 36 q^{48} + 52 q^{50} + 16 q^{51} - 16 q^{52} - 32 q^{54} - 8 q^{55} + 12 q^{56} - 8 q^{57} + 40 q^{58} + 20 q^{59} + 52 q^{60} - 16 q^{61} - 12 q^{62} - 24 q^{63} - 48 q^{64} - 80 q^{65} - 40 q^{66} - 4 q^{67} - 4 q^{68} - 40 q^{69} + 32 q^{70} + 72 q^{72} - 24 q^{73} - 12 q^{74} + 20 q^{75} - 72 q^{76} + 4 q^{77} + 12 q^{78} + 60 q^{80} + 16 q^{82} + 4 q^{83} + 8 q^{84} - 64 q^{85} - 48 q^{86} - 32 q^{87} + 16 q^{88} + 32 q^{89} + 20 q^{90} + 108 q^{92} - 24 q^{93} + 68 q^{94} - 80 q^{95} - 40 q^{96} + 56 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 + 12 * q^6 - 8 * q^8 + 8 * q^9 - 16 * q^10 + 12 * q^11 - 36 * q^12 + 8 * q^16 + 4 * q^19 - 4 * q^21 - 52 * q^22 + 16 * q^23 - 8 * q^24 - 16 * q^25 + 12 * q^26 - 32 * q^27 + 8 * q^28 + 16 * q^29 + 36 * q^30 + 24 * q^31 - 36 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^36 + 16 * q^37 - 12 * q^38 - 24 * q^39 + 36 * q^40 + 8 * q^41 + 52 * q^43 - 44 * q^44 - 64 * q^45 - 32 * q^46 - 36 * q^48 + 52 * q^50 + 16 * q^51 - 16 * q^52 - 32 * q^54 - 8 * q^55 + 12 * q^56 - 8 * q^57 + 40 * q^58 + 20 * q^59 + 52 * q^60 - 16 * q^61 - 12 * q^62 - 24 * q^63 - 48 * q^64 - 80 * q^65 - 40 * q^66 - 4 * q^67 - 4 * q^68 - 40 * q^69 + 32 * q^70 + 72 * q^72 - 24 * q^73 - 12 * q^74 + 20 * q^75 - 72 * q^76 + 4 * q^77 + 12 * q^78 + 60 * q^80 + 16 * q^82 + 4 * q^83 + 8 * q^84 - 64 * q^85 - 48 * q^86 - 32 * q^87 + 16 * q^88 + 32 * q^89 + 20 * q^90 + 108 * q^92 - 24 * q^93 + 68 * q^94 - 80 * q^95 - 40 * q^96 + 56 * q^97 + 4 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	1.16944	+	0.795236i	0.826922	+	0.562317i
$2$	1.16944	+	0.795236i	0.826922	+	0.562317i
$3$	1.29558	−	0.536647i	0.748003	−	0.309833i	0.0240766	−	0.999710i	$-0.492335\pi$
$3$	1.29558	−	0.536647i	0.748003	−	0.309833i	0.723927	+	0.689877i	$0.242335\pi$
$4$	0.735199	+	1.85997i	0.367600	+	0.929984i
$5$	0.937867	−	2.26421i	0.419427	−	1.01259i	−0.563087	−	0.826398i	$-0.690386\pi$
$5$	0.937867	−	2.26421i	0.419427	−	1.01259i	0.982514	−	0.186189i	$-0.0596136\pi$
$6$	1.94187	+	0.402713i	0.792764	+	0.164407i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	−0.619339	+	2.75979i	−0.218970	+	0.975732i
$9$	−0.730784	+	0.730784i	−0.243595	+	0.243595i
$10$	2.89737	−	1.90204i	0.916228	−	0.601479i
$11$	−2.12310	−	0.879416i	−0.640138	−	0.265154i	0.0389155	−	0.999243i	$-0.487610\pi$
$11$	−2.12310	−	0.879416i	−0.640138	−	0.265154i	−0.679054	+	0.734089i	$0.737610\pi$
$12$	1.95065	+	2.01519i	0.563105	+	0.581737i
$13$	−0.267138	−	0.644928i	−0.0740907	−	0.178871i	0.882495	−	0.470322i	$-0.155862\pi$
$13$	−0.267138	−	0.644928i	−0.0740907	−	0.178871i	−0.956586	+	0.291451i	$0.905862\pi$
$14$	−0.264605	−	1.38924i	−0.0707187	−	0.371290i
$15$		−	3.43677i		−	0.887370i
$16$	−2.91896	+	2.73489i	−0.729741	+	0.683724i
$17$			2.83430i			0.687419i	0.939076	+	0.343709i	$0.111684\pi$
$17$			2.83430i			0.687419i	−0.939076	+	0.343709i	$0.888316\pi$
$18$	−1.43576	+	0.273465i	−0.338411	+	0.0644564i
$19$	−0.445544	−	1.07564i	−0.102215	−	0.246768i	0.864496	−	0.502639i	$-0.167638\pi$
$19$	−0.445544	−	1.07564i	−0.102215	−	0.246768i	−0.966711	+	0.255871i	$0.917638\pi$
$20$	4.90088	+	0.0797566i	1.09587	+	0.0178341i
$21$	−1.29558	−	0.536647i	−0.282719	−	0.117106i
$22$	−1.78350	−	2.71679i	−0.380244	−	0.579222i
$23$	−4.15632	+	4.15632i	−0.866654	+	0.866654i	−0.992100	−	0.125447i	$-0.959964\pi$
$23$	−4.15632	+	4.15632i	−0.866654	+	0.866654i	0.125447	+	0.992100i	$0.459964\pi$
$24$	0.678626	+	3.90789i	0.138524	+	0.797694i
$25$	−0.711525	−	0.711525i	−0.142305	−	0.142305i
$26$	0.200467	−	0.966645i	0.0393148	−	0.189575i
$27$	−2.16456	+	5.22570i	−0.416569	+	1.00569i
$28$	0.795332	−	1.83506i	0.150304	−	0.346794i
$29$	3.37949	−	1.39983i	0.627555	−	0.259942i	−0.0461587	−	0.998934i	$-0.514698\pi$
$29$	3.37949	−	1.39983i	0.627555	−	0.259942i	0.673714	+	0.738992i	$0.264698\pi$
$30$	2.73304	−	4.01911i	0.498983	−	0.733786i
$31$	2.27603			0.408786			0.204393	−	0.978889i	$-0.434478\pi$
$31$	2.27603			0.408786			0.204393	+	0.978889i	$0.434478\pi$
$32$	−5.58845	+	0.877041i	−0.987908	+	0.155040i
$33$	−3.22258			−0.560979
$34$	−2.25394	+	3.31456i	−0.386547	+	0.568442i
$35$	−2.26421	+	0.937867i	−0.382722	+	0.158528i
$36$	−1.89651	−	0.821963i	−0.316084	−	0.136994i
$37$	3.59295	−	8.67415i	0.590678	−	1.42602i	−0.292172	−	0.956366i	$-0.594378\pi$
$37$	3.59295	−	8.67415i	0.590678	−	1.42602i	0.882850	−	0.469656i	$-0.155622\pi$
$38$	0.334347	−	1.61221i	0.0542383	−	0.261535i
$39$	−0.692197	−	0.692197i	−0.110840	−	0.110840i
$40$	5.66788	+	3.99063i	0.896171	+	0.630974i
$41$	0.419720	−	0.419720i	0.0655493	−	0.0655493i	−0.673572	−	0.739121i	$-0.735241\pi$
$41$	0.419720	−	0.419720i	0.0655493	−	0.0655493i	0.739121	+	0.673572i	$0.235241\pi$
$42$	−1.08835	−	1.65787i	−0.167936	−	0.255815i
$43$	−6.63049	−	2.74644i	−1.01114	−	0.418828i	−0.185270	−	0.982688i	$-0.559316\pi$
$43$	−6.63049	−	2.74644i	−1.01114	−	0.418828i	−0.825871	+	0.563860i	$0.809316\pi$
$44$	0.0747859	−	4.59544i	0.0112744	−	0.692789i
$45$	0.969271	+	2.34003i	0.144490	+	0.348831i
$46$	−8.16585	+	1.55533i	−1.20399	+	0.229321i
$47$		−	12.0972i		−	1.76455i	−0.470732	−	0.882276i	$-0.656010\pi$
$47$		−	12.0972i		−	1.76455i	0.470732	−	0.882276i	$-0.343990\pi$
$48$	−2.31408	+	5.10972i	−0.334008	+	0.737525i
$49$			1.00000i			0.142857i
$50$	−0.266258	−	1.39792i	−0.0376546	−	0.197696i
$51$	1.52102	+	3.67206i	0.212985	+	0.514192i
$52$	1.00315	−	0.971019i	0.139111	−	0.134656i
$53$	8.31047	+	3.44231i	1.14153	+	0.472837i	0.871685	−	0.490066i	$-0.163027\pi$
$53$	8.31047	+	3.44231i	1.14153	+	0.472837i	0.269845	+	0.962904i	$0.413027\pi$
$54$	−6.68699	+	4.38983i	−0.909984	+	0.597380i
$55$	−3.98237	+	3.98237i	−0.536982	+	0.536982i
$56$	2.38940	−	1.51352i	0.319297	−	0.202253i
$57$	−1.15447	−	1.15447i	−0.152914	−	0.152914i
$58$	5.06532	+	1.05047i	0.665109	+	0.137933i
$59$	−3.36630	+	8.12696i	−0.438254	+	1.05804i	0.538297	+	0.842755i	$0.319068\pi$
$59$	−3.36630	+	8.12696i	−0.438254	+	1.05804i	−0.976551	+	0.215284i	$0.930932\pi$
$60$	6.39228	−	2.52671i	0.825240	−	0.326197i
$61$	8.49805	−	3.52001i	1.08806	−	0.450691i	0.234732	−	0.972060i	$-0.424579\pi$
$61$	8.49805	−	3.52001i	1.08806	−	0.450691i	0.853331	+	0.521370i	$0.174579\pi$
$62$	2.66168	+	1.80998i	0.338034	+	0.229867i
$63$	1.03348			0.130207
$64$	−7.23284	−	3.41849i	−0.904105	−	0.427311i
$65$	−1.71079			−0.212198
$66$	−3.76862	−	2.56271i	−0.463886	−	0.315448i
$67$	4.08688	−	1.69284i	0.499292	−	0.206813i	−0.118802	−	0.992918i	$-0.537905\pi$
$67$	4.08688	−	1.69284i	0.499292	−	0.206813i	0.618093	+	0.786105i	$0.287905\pi$
$68$	−5.27171	+	2.08378i	−0.639289	+	0.252695i
$69$	−3.15437	+	7.61533i	−0.379742	+	0.916778i
$70$	−3.39369	−	0.703799i	−0.405624	−	0.0841201i
$71$	−9.89815	−	9.89815i	−1.17469	−	1.17469i	−0.981077	−	0.193617i	$-0.937978\pi$
$71$	−9.89815	−	9.89815i	−1.17469	−	1.17469i	−0.193617	−	0.981077i	$-0.562022\pi$
$72$	−1.56420	−	2.46941i	−0.184343	−	0.291023i
$73$	1.37852	−	1.37852i	0.161343	−	0.161343i	−0.621818	−	0.783161i	$-0.713606\pi$
$73$	1.37852	−	1.37852i	0.161343	−	0.161343i	0.783161	+	0.621818i	$0.213606\pi$
$74$	11.0998	−	7.28669i	1.29032	−	0.847061i
$75$	−1.30367	−	0.540000i	−0.150535	−	0.0623538i
$76$	1.67309	−	1.61951i	0.191916	−	0.185770i
$77$	0.879416	+	2.12310i	0.100219	+	0.241949i
$78$	−0.259026	−	1.35995i	−0.0293289	−	0.153984i
$79$			3.67858i			0.413873i	0.978354	+	0.206936i	$0.0663493\pi$
$79$			3.67858i			0.413873i	−0.978354	+	0.206936i	$0.933651\pi$
$80$	3.45478	+	9.17412i	0.386256	+	1.02570i
$81$			4.83146i			0.536828i
$82$	0.824617	−	0.157063i	0.0910637	−	0.0173447i
$83$	2.34025	+	5.64986i	0.256876	+	0.620153i	0.998729	−	0.0504098i	$-0.0160527\pi$
$83$	2.34025	+	5.64986i	0.256876	+	0.620153i	−0.741853	+	0.670563i	$0.766053\pi$
$84$	0.0456366	−	2.80428i	0.00497937	−	0.305972i
$85$	6.41746	+	2.65820i	0.696071	+	0.288322i
$86$	−5.56992	−	8.48461i	−0.600620	−	0.914919i
$87$	3.62718	−	3.62718i	0.388875	−	0.388875i
$88$	3.74192	−	5.31464i	0.398890	−	0.566542i
$89$	−11.4830	−	11.4830i	−1.21719	−	1.21719i	−0.968611	−	0.248581i	$-0.920036\pi$
$89$	−11.4830	−	11.4830i	−1.21719	−	1.21719i	−0.248581	−	0.968611i	$-0.579964\pi$
$90$	−0.727366	+	3.50733i	−0.0766711	+	0.369705i
$91$	−0.267138	+	0.644928i	−0.0280037	+	0.0676068i
$92$	−10.7864	−	4.67491i	−1.12456	−	0.487393i
$93$	2.94877	−	1.22142i	0.305773	−	0.126655i
$94$	9.62010	−	14.1470i	0.992238	−	1.45915i
$95$	−2.85333			−0.292746
$96$	−6.76962	+	4.13530i	−0.690922	+	0.422057i
$97$	14.8956			1.51242			0.756210	−	0.654329i	$-0.227049\pi$
$97$	14.8956			1.51242			0.756210	+	0.654329i	$0.227049\pi$
$98$	−0.795236	+	1.16944i	−0.0803310	+	0.118132i
$99$	2.19419	−	0.908863i	0.220524	−	0.0913442i
$100$	0.800301	−	1.84653i	0.0800301	−	0.184653i
$101$	−2.83882	+	6.85351i	−0.282473	+	0.681950i	−0.999892	−	0.0146917i	$-0.995323\pi$
$101$	−2.83882	+	6.85351i	−0.282473	+	0.681950i	0.717419	+	0.696642i	$0.245323\pi$
$102$	−1.14141	+	5.50384i	−0.113016	+	0.544961i
$103$	8.13425	+	8.13425i	0.801492	+	0.801492i	0.983329	−	0.181837i	$-0.0582043\pi$
$103$	8.13425	+	8.13425i	0.801492	+	0.801492i	−0.181837	+	0.983329i	$0.558204\pi$
$104$	1.94531	−	0.337814i	0.190754	−	0.0331254i
$105$	−2.43016	+	2.43016i	−0.237160	+	0.237160i
$106$	6.98118	+	10.6344i	0.678072	+	1.03290i
$107$	−1.49059	−	0.617424i	−0.144101	−	0.0596886i	0.309467	−	0.950910i	$-0.399849\pi$
$107$	−1.49059	−	0.617424i	−0.144101	−	0.0596886i	−0.453568	+	0.891221i	$0.649849\pi$
$108$	−11.3110	−	0.184075i	−1.08840	−	0.0177126i
$109$	6.67150	+	16.1064i	0.639014	+	1.54272i	0.827995	+	0.560735i	$0.189481\pi$
$109$	6.67150	+	16.1064i	0.639014	+	1.54272i	−0.188981	+	0.981981i	$0.560519\pi$
$110$	−7.82408	+	1.49023i	−0.745997	+	0.142088i
$111$		−	13.1662i		−	1.24968i
$112$	3.99788	+	0.130157i	0.377764	+	0.0122987i
$113$			18.9873i			1.78617i	0.449885	+	0.893086i	$0.351465\pi$
$113$			18.9873i			1.78617i	−0.449885	+	0.893086i	$0.648535\pi$
$114$	−0.432014	−	2.26817i	−0.0404618	−	0.212434i
$115$	5.51272	+	13.3089i	0.514064	+	1.24106i
$116$	5.08824	+	5.25659i	0.472431	+	0.488062i
$117$	0.666523	+	0.276083i	0.0616201	+	0.0255239i
$118$	−10.3995	+	6.82702i	−0.957356	+	0.628478i
$119$	2.00415	−	2.00415i	0.183720	−	0.183720i
$120$	9.48475	+	2.12853i	0.865835	+	0.194307i
$121$	−4.04400	−	4.04400i	−0.367636	−	0.367636i
$122$	12.7372	+	2.64150i	1.15317	+	0.239150i
$123$	0.318540	−	0.769023i	0.0287218	−	0.0693404i
$124$	1.67333	+	4.23334i	0.150270	+	0.380165i
$125$	9.04270	−	3.74561i	0.808804	−	0.335017i
$126$	1.20860	+	0.821864i	0.107671	+	0.0732175i
$127$	1.32340			0.117433			0.0587164	−	0.998275i	$-0.481299\pi$
$127$	1.32340			0.117433			0.0587164	+	0.998275i	$0.481299\pi$
$128$	−5.73989	−	9.74954i	−0.507340	−	0.861746i
$129$	−10.0642			−0.886103
$130$	−2.00068	−	1.36048i	−0.175471	−	0.119322i
$131$	3.10303	−	1.28532i	0.271113	−	0.112299i	−0.242985	−	0.970030i	$-0.578127\pi$
$131$	3.10303	−	1.28532i	0.271113	−	0.112299i	0.514098	+	0.857731i	$0.328127\pi$
$132$	−2.36924	−	5.99389i	−0.206216	−	0.521701i
$133$	−0.445544	+	1.07564i	−0.0386335	+	0.0932696i
$134$	6.12558	+	1.27035i	0.529170	+	0.109742i
$135$	9.80202	+	9.80202i	0.843624	+	0.843624i
$136$	−7.82206	−	1.75539i	−0.670736	−	0.150524i
$137$	−4.33149	+	4.33149i	−0.370064	+	0.370064i	−0.867500	−	0.497436i	$-0.834275\pi$
$137$	−4.33149	+	4.33149i	−0.370064	+	0.370064i	0.497436	+	0.867500i	$0.334275\pi$
$138$	−9.74484	+	6.39723i	−0.829536	+	0.544568i
$139$	20.8542	+	8.63808i	1.76883	+	0.732672i	0.995068	+	0.0991918i	$0.0316257\pi$
$139$	20.8542	+	8.63808i	1.76883	+	0.732672i	0.773759	+	0.633480i	$0.218374\pi$
$140$	−3.40905	−	3.52184i	−0.288117	−	0.297650i
$141$	−6.49190	−	15.6728i	−0.546717	−	1.31989i
$142$	−3.70397	−	19.4467i	−0.310830	−	1.63193i
$143$			1.60417i			0.134148i
$144$	0.134515	−	4.13175i	0.0112096	−	0.344312i
$145$		−	8.96473i		−	0.744480i
$146$	2.70834	−	0.515851i	0.224144	−	0.0426922i
$147$	0.536647	+	1.29558i	0.0442619	+	0.106858i
$148$	18.7752	+	0.305546i	1.54331	+	0.0251157i
$149$	−18.0162	−	7.46256i	−1.47595	−	0.611357i	−0.507740	−	0.861511i	$-0.669519\pi$
$149$	−18.0162	−	7.46256i	−1.47595	−	0.611357i	−0.968206	+	0.250154i	$0.919519\pi$
$150$	−1.09515	−	1.66823i	−0.0894184	−	0.136210i
$151$	−9.22926	+	9.22926i	−0.751067	+	0.751067i	−0.974678	−	0.223612i	$-0.928215\pi$
$151$	−9.22926	+	9.22926i	−0.751067	+	0.751067i	0.223612	+	0.974678i	$0.428215\pi$
$152$	3.24447	−	0.563420i	0.263161	−	0.0456994i
$153$	−2.07126	−	2.07126i	−0.167452	−	0.167452i
$154$	−0.659936	+	3.18219i	−0.0531792	+	0.256428i
$155$	2.13461	−	5.15340i	0.171456	−	0.413931i
$156$	0.778562	−	1.79637i	0.0623348	−	0.143824i
$157$	−1.00290	+	0.415416i	−0.0800404	+	0.0331538i	−0.422344	−	0.906435i	$-0.638793\pi$
$157$	−1.00290	+	0.415416i	−0.0800404	+	0.0331538i	0.342304	+	0.939589i	$0.388793\pi$
$158$	−2.92534	+	4.30189i	−0.232728	+	0.342240i
$159$	12.6142			1.00037
$160$	−3.25542	+	13.4760i	−0.257364	+	1.06537i
$161$	5.87793			0.463246
$162$	−3.84215	+	5.65012i	−0.301868	+	0.443915i
$163$	9.23082	−	3.82353i	0.723014	−	0.299482i	0.00933617	−	0.999956i	$-0.497028\pi$
$163$	9.23082	−	3.82353i	0.723014	−	0.299482i	0.713678	+	0.700474i	$0.247028\pi$
$164$	1.08924	+	0.472089i	0.0850557	+	0.0368639i
$165$	−3.02235	+	7.29660i	−0.235290	+	0.568039i
$166$	−1.75618	+	8.46825i	−0.136306	+	0.657264i
$167$	−11.3582	−	11.3582i	−0.878923	−	0.878923i	0.114500	−	0.993423i	$-0.463473\pi$
$167$	−11.3582	−	11.3582i	−0.878923	−	0.878923i	−0.993423	+	0.114500i	$0.963473\pi$
$168$	2.28343	−	3.24316i	0.176171	−	0.250215i
$169$	8.84782	−	8.84782i	0.680601	−	0.680601i
$170$	5.39096	+	8.21201i	0.413468	+	0.629832i
$171$	1.11166	+	0.460463i	0.0850104	+	0.0352125i
$172$	0.233558	−	14.3517i	0.0178086	−	1.09431i
$173$	−4.39105	−	10.6009i	−0.333846	−	0.805975i	−0.998280	−	0.0586279i	$-0.981327\pi$
$173$	−4.39105	−	10.6009i	−0.333846	−	0.805975i	0.664434	−	0.747347i	$-0.268673\pi$
$174$	7.12625	−	1.35732i	0.540240	−	0.102898i
$175$			1.00625i			0.0760652i
$176$	8.60236	−	3.23947i	0.648427	−	0.244184i
$177$			12.3356i			0.927203i
$178$	−4.29702	−	22.5604i	−0.322075	−	1.69097i
$179$	6.33193	+	15.2866i	0.473271	+	1.14258i	0.962709	+	0.270539i	$0.0872018\pi$
$179$	6.33193	+	15.2866i	0.473271	+	1.14258i	−0.489439	+	0.872038i	$0.662798\pi$
$180$	−3.63977	+	3.52320i	−0.271292	+	0.262604i
$181$	−18.1200	−	7.50555i	−1.34685	−	0.557883i	−0.411435	−	0.911439i	$-0.634972\pi$
$181$	−18.1200	−	7.50555i	−1.34685	−	0.557883i	−0.935413	+	0.353556i	$0.884972\pi$
$182$	−0.825273	+	0.541770i	−0.0611733	+	0.0401586i
$183$	9.12089	−	9.12089i	0.674236	−	0.674236i
$184$	−8.89639	−	14.0447i	−0.655851	−	1.03539i
$185$	−16.2704	−	16.2704i	−1.19622	−	1.19622i
$186$	4.41974	+	0.916586i	0.324071	+	0.0672073i
$187$	2.49253	−	6.01750i	0.182272	−	0.440043i
$188$	22.5003	−	8.89383i	1.64101	−	0.648649i
$189$	5.22570	−	2.16456i	0.380114	−	0.157448i
$190$	−3.33681	−	2.26907i	−0.242078	−	0.164616i
$191$	−1.38255			−0.100038			−0.0500191	−	0.998748i	$-0.515928\pi$
$191$	−1.38255			−0.100038			−0.0500191	+	0.998748i	$0.515928\pi$
$192$	−11.2052	−	0.547446i	−0.808668	−	0.0395085i
$193$	−8.82532			−0.635261			−0.317630	−	0.948215i	$-0.602887\pi$
$193$	−8.82532			−0.635261			−0.317630	+	0.948215i	$0.602887\pi$
$194$	17.4196	+	11.8455i	1.25065	+	0.850459i
$195$	−2.21647	+	0.918092i	−0.158725	+	0.0657459i
$196$	−1.85997	+	0.735199i	−0.132855	+	0.0525142i
$197$	−6.52016	+	15.7411i	−0.464542	+	1.12150i	0.501970	+	0.864885i	$0.332609\pi$
$197$	−6.52016	+	15.7411i	−0.464542	+	1.12150i	−0.966513	+	0.256619i	$0.917391\pi$
$198$	3.28874	+	0.682034i	0.233721	+	0.0484700i
$199$	1.30551	+	1.30551i	0.0925451	+	0.0925451i	0.751864	−	0.659319i	$-0.229155\pi$
$199$	1.30551	+	1.30551i	0.0925451	+	0.0925451i	−0.659319	+	0.751864i	$0.729155\pi$
$200$	2.40433	−	1.52298i	0.170012	−	0.107691i
$201$	4.38642	−	4.38642i	0.309394	−	0.309394i
$202$	−8.77000	+	5.75727i	−0.617055	+	0.405080i
$203$	−3.37949	−	1.39983i	−0.237194	−	0.0982488i
$204$	−5.71167	+	5.52874i	−0.399897	+	0.387089i
$205$	−0.556694	−	1.34398i	−0.0388812	−	0.0938675i
$206$	3.04390	+	15.9812i	0.212079	+	1.11346i
$207$		−	6.07475i		−	0.422224i
$208$	2.54358	+	1.15193i	0.176365	+	0.0798718i
$209$			2.67550i			0.185068i
$210$	−4.77449	+	0.909386i	−0.329471	+	0.0627536i
$211$	−4.96178	−	11.9788i	−0.341583	−	0.824654i	−0.997556	−	0.0698698i	$-0.977742\pi$
$211$	−4.96178	−	11.9788i	−0.341583	−	0.824654i	0.655973	−	0.754784i	$-0.272258\pi$
$212$	−0.292735	+	17.9880i	−0.0201051	+	1.23542i
$213$	−18.1356	−	7.51203i	−1.24263	−	0.514716i
$214$	−1.25217	−	1.90742i	−0.0855964	−	0.130388i
$215$	−12.4370	+	12.4370i	−0.848199	+	0.848199i
$216$	−13.0812	−	9.21019i	−0.890064	−	0.626674i
$217$	−1.60939	−	1.60939i	−0.109253	−	0.109253i
$218$	−5.00647	+	24.1410i	−0.339081	+	1.63503i
$219$	1.04620	−	2.52575i	0.0706957	−	0.170674i
$220$	−10.3349	−	4.47924i	−0.696780	−	0.301991i
$221$	1.82792	−	0.757149i	0.122959	−	0.0509314i
$222$	10.4702	−	15.3971i	0.702716	−	1.03339i
$223$	−9.62710			−0.644678			−0.322339	−	0.946624i	$-0.604469\pi$
$223$	−9.62710			−0.644678			−0.322339	+	0.946624i	$0.604469\pi$
$224$	4.57179	+	3.33147i	0.305466	+	0.222593i
$225$	1.03994			0.0693295
$226$	−15.0994	+	22.2046i	−1.00439	+	1.47703i
$227$	7.62873	−	3.15992i	0.506336	−	0.209731i	−0.114867	−	0.993381i	$-0.536644\pi$
$227$	7.62873	−	3.15992i	0.506336	−	0.209731i	0.621203	+	0.783649i	$0.286644\pi$
$228$	1.29852	−	2.99605i	0.0859964	−	0.198419i
$229$	2.56102	−	6.18286i	0.169237	−	0.408575i	−0.816392	−	0.577498i	$-0.804029\pi$
$229$	2.56102	−	6.18286i	0.169237	−	0.408575i	0.985629	+	0.168923i	$0.0540291\pi$
$230$	−4.13688	+	19.9479i	−0.272778	+	1.31533i
$231$	2.27871	+	2.27871i	0.149928	+	0.149928i
$232$	1.77018	+	10.1936i	0.116218	+	0.669245i
$233$	−21.3157	+	21.3157i	−1.39644	+	1.39644i	−0.586467	+	0.809973i	$0.699482\pi$
$233$	−21.3157	+	21.3157i	−1.39644	+	1.39644i	−0.809973	+	0.586467i	$0.800518\pi$
$234$	0.559911	+	0.852907i	0.0366025	+	0.0557563i
$235$	−27.3905	−	11.3455i	−1.78676	−	0.740101i
$236$	−17.5908	−	0.286271i	−1.14506	−	0.0186347i
$237$	1.97410	+	4.76589i	0.128231	+	0.309578i
$238$	3.93752	−	0.749970i	0.255232	−	0.0486134i
$239$			4.55993i			0.294957i	0.989065	+	0.147479i	$0.0471158\pi$
$239$			4.55993i			0.294957i	−0.989065	+	0.147479i	$0.952884\pi$
$240$	9.39920	+	10.0318i	0.606716	+	0.647550i
$241$		−	9.26787i		−	0.596996i	−0.954410	−	0.298498i	$-0.903514\pi$
$241$		−	9.26787i		−	0.596996i	0.954410	−	0.298498i	$-0.0964856\pi$
$242$	−1.51330	−	7.94517i	−0.0972785	−	0.510735i
$243$	−3.90088	−	9.41756i	−0.250242	−	0.604137i
$244$	12.7949	+	13.2182i	0.819107	+	0.846208i
$245$	2.26421	+	0.937867i	0.144655	+	0.0599181i
$246$	0.984069	−	0.646015i	0.0627419	−	0.0411884i
$247$	−0.574687	+	0.574687i	−0.0365665	+	0.0365665i
$248$	−1.40963	+	6.28134i	−0.0895117	+	0.398866i
$249$	6.06396	+	6.06396i	0.384288	+	0.384288i
$250$	13.5536	+	2.81080i	0.857203	+	0.177771i
$251$	10.3872	−	25.0769i	0.655634	−	1.58284i	−0.148845	−	0.988861i	$-0.547556\pi$
$251$	10.3872	−	25.0769i	0.655634	−	1.58284i	0.804479	−	0.593981i	$-0.202444\pi$
$252$	0.759817	+	1.92225i	0.0478640	+	0.121090i
$253$	12.4794	−	5.16915i	0.784575	−	0.324981i
$254$	1.54764	+	1.05242i	0.0971078	+	0.0660345i
$255$	9.74084			0.609995
$256$	1.04070	−	15.9661i	0.0650440	−	0.997882i
$257$	−16.8628			−1.05187			−0.525935	−	0.850525i	$-0.676285\pi$
$257$	−16.8628			−1.05187			−0.525935	+	0.850525i	$0.676285\pi$
$258$	−11.7695	−	8.00341i	−0.732738	−	0.498270i
$259$	−8.67415	+	3.59295i	−0.538986	+	0.223255i
$260$	−1.25777	−	3.18202i	−0.0780038	−	0.197341i
$261$	−1.44670	+	3.49265i	−0.0895487	+	0.216190i
$262$	4.65095	+	0.964534i	0.287336	+	0.0595891i
$263$	−1.60993	−	1.60993i	−0.0992726	−	0.0992726i	0.655726	−	0.754999i	$-0.272363\pi$
$263$	−1.60993	−	1.60993i	−0.0992726	−	0.0992726i	−0.754999	+	0.655726i	$0.772363\pi$
$264$	1.99587	−	8.89362i	0.122837	−	0.547365i
$265$	15.5882	−	15.5882i	0.957577	−	0.957577i
$266$	−1.37642	+	0.903586i	−0.0843940	+	0.0554024i
$267$	−21.0394	−	8.71480i	−1.28759	−	0.533337i
$268$	6.15330	+	6.35689i	0.375873	+	0.388309i
$269$	−7.61243	−	18.3780i	−0.464138	−	1.12053i	−0.966683	−	0.255977i	$-0.917603\pi$
$269$	−7.61243	−	18.3780i	−0.464138	−	1.12053i	0.502545	−	0.864551i	$-0.332397\pi$
$270$	3.66800	+	19.2578i	0.223227	+	1.17199i
$271$		−	17.0922i		−	1.03828i	−0.854689	−	0.519140i	$-0.826252\pi$
$271$		−	17.0922i		−	1.03828i	0.854689	−	0.519140i	$-0.173748\pi$
$272$	−7.75151	−	8.27322i	−0.470005	−	0.501638i
$273$			0.978914i			0.0592466i
$274$	−8.50999	+	1.62088i	−0.514107	+	0.0979208i
$275$	0.884911	+	2.13636i	0.0533621	+	0.128828i
$276$	−16.4834	−	0.268249i	−0.992181	−	0.0161467i
$277$	−2.08377	−	0.863128i	−0.125202	−	0.0518603i	0.319203	−	0.947686i	$-0.396585\pi$
$277$	−2.08377	−	0.863128i	−0.125202	−	0.0518603i	−0.444405	+	0.895826i	$0.646585\pi$
$278$	17.5185	+	26.6857i	1.05069	+	1.60050i
$279$	−1.66328	+	1.66328i	−0.0995781	+	0.0995781i
$280$	−1.18600	−	6.82960i	−0.0708769	−	0.408147i
$281$	5.99919	+	5.99919i	0.357882	+	0.357882i	0.863032	−	0.505150i	$-0.168563\pi$
$281$	5.99919	+	5.99919i	0.357882	+	0.357882i	−0.505150	+	0.863032i	$0.668563\pi$
$282$	4.87169	−	23.4911i	0.290105	−	1.39887i
$283$	−2.20107	+	5.31384i	−0.130840	+	0.315875i	−0.975700	−	0.219113i	$-0.929684\pi$
$283$	−2.20107	+	5.31384i	−0.130840	+	0.315875i	0.844860	+	0.534988i	$0.179684\pi$
$284$	11.1331	−	25.6874i	0.660630	−	1.52426i
$285$	−3.69672	+	1.53123i	−0.218975	+	0.0907023i
$286$	−1.27569	+	1.87599i	−0.0754334	+	0.110930i
$287$	−0.593574			−0.0350376
$288$	3.44302	−	4.72488i	0.202882	−	0.278416i
$289$	8.96674			0.527455
$290$	7.12908	−	10.4838i	0.418634	−	0.615627i
$291$	19.2984	−	7.99368i	1.13129	−	0.468598i
$292$	3.57748	+	1.55051i	0.209356	+	0.0907368i
$293$	−7.31865	+	17.6688i	−0.427560	+	1.03222i	0.552499	+	0.833514i	$0.313674\pi$
$293$	−7.31865	+	17.6688i	−0.427560	+	1.03222i	−0.980059	+	0.198708i	$0.936326\pi$
$294$	−0.402713	+	1.94187i	−0.0234867	+	0.113252i
$295$	15.2440	+	15.2440i	0.887541	+	0.887541i
$296$	21.7135	+	15.2880i	1.26207	+	0.888598i
$297$	9.19113	−	9.19113i	0.533323	−	0.533323i
$298$	−15.1345	−	23.0542i	−0.876716	−	1.33549i
$299$	3.79084	+	1.57022i	0.219230	+	0.0908081i
$300$	0.0459218	−	2.82180i	0.00265130	−	0.162917i
$301$	2.74644	+	6.63049i	0.158302	+	0.382175i
$302$	−18.1326	+	3.45366i	−1.04341	+	0.198736i
$303$			10.4027i			0.597620i
$304$	4.24228	+	1.92123i	0.243312	+	0.110190i
$305$		−	22.5427i		−	1.29079i
$306$	−0.775083	−	4.06937i	−0.0443085	−	0.232630i
$307$	−3.30869	−	7.98788i	−0.188837	−	0.455893i	0.800899	−	0.598799i	$-0.204355\pi$
$307$	−3.30869	−	7.98788i	−0.188837	−	0.455893i	−0.989736	+	0.142906i	$0.954355\pi$
$308$	−3.30235	+	3.19659i	−0.188169	+	0.182142i
$309$	14.9038	+	6.17335i	0.847847	+	0.351190i
$310$	6.59448	−	4.32910i	0.374541	−	0.245876i
$311$	8.27891	−	8.27891i	0.469454	−	0.469454i	−0.432284	−	0.901738i	$-0.642292\pi$
$311$	8.27891	−	8.27891i	0.469454	−	0.469454i	0.901738	+	0.432284i	$0.142292\pi$
$312$	2.33902	−	1.48161i	0.132421	−	0.0838797i
$313$	23.1536	+	23.1536i	1.30872	+	1.30872i	0.922339	+	0.386381i	$0.126275\pi$
$313$	23.1536	+	23.1536i	1.30872	+	1.30872i	0.386381	+	0.922339i	$0.373725\pi$
$314$	−1.50319	−	0.311739i	−0.0848301	−	0.0175924i
$315$	0.969271	−	2.34003i	0.0546122	−	0.131846i
$316$	−6.84204	+	2.70449i	−0.384895	+	0.152139i
$317$	3.39235	−	1.40516i	0.190533	−	0.0789216i	−0.285377	−	0.958415i	$-0.592119\pi$
$317$	3.39235	−	1.40516i	0.190533	−	0.0789216i	0.475910	+	0.879494i	$0.342119\pi$
$318$	14.7516	+	10.0312i	0.827227	+	0.562524i
$319$	−8.40602			−0.470647
$320$	−14.5236	+	13.1706i	−0.811895	+	0.736258i
$321$	−2.26252			−0.126282
$322$	6.87391	+	4.67434i	0.383068	+	0.260491i
$323$	3.04868	−	1.26281i	0.169633	−	0.0702644i
$324$	−8.98635	+	3.55208i	−0.499242	+	0.197338i
$325$	−0.268807	+	0.648958i	−0.0149107	+	0.0359977i
$326$	13.8355	+	2.86928i	0.766280	+	0.158914i
$327$	17.2869	+	17.2869i	0.955969	+	0.955969i
$328$	0.898389	+	1.41829i	0.0496052	+	0.0783119i
$329$	−8.55399	+	8.55399i	−0.471597	+	0.471597i
$330$	−9.33699	+	6.12948i	−0.513984	+	0.337417i
$331$	−11.3873	−	4.71676i	−0.625901	−	0.259257i	0.0471094	−	0.998890i	$-0.484999\pi$
$331$	−11.3873	−	4.71676i	−0.625901	−	0.259257i	−0.673010	+	0.739633i	$0.734999\pi$
$332$	−8.78801	+	8.50656i	−0.482305	+	0.466858i
$333$	3.71326	+	8.96460i	0.203485	+	0.491257i
$334$	−4.25032	−	22.3152i	−0.232567	−	1.22103i
$335$		−	10.8412i		−	0.592319i
$336$	5.24942	−	1.97682i	0.286379	−	0.107844i
$337$			21.9214i			1.19414i	0.802191	+	0.597068i	$0.203668\pi$
$337$			21.9214i			1.19414i	−0.802191	+	0.597068i	$0.796332\pi$
$338$	17.3831	−	3.31093i	0.945518	−	0.180091i
$339$	10.1895	+	24.5995i	0.553415	+	1.33606i
$340$	−0.226054	+	13.8906i	−0.0122595	+	0.753322i
$341$	−4.83223	−	2.00157i	−0.261680	−	0.108391i
$342$	0.933842	+	1.42251i	0.0504964	+	0.0769207i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	11.6861	−	16.5978i	0.630073	−	0.894891i
$345$	14.2843	+	14.2843i	0.769042	+	0.769042i
$346$	3.29516	−	15.8891i	0.177149	−	0.854205i
$347$	−8.36418	+	20.1929i	−0.449013	+	1.08401i	0.523680	+	0.851915i	$0.324559\pi$
$347$	−8.36418	+	20.1929i	−0.449013	+	1.08401i	−0.972692	+	0.232098i	$0.925441\pi$
$348$	9.41314	+	4.07974i	0.504598	+	0.218697i
$349$	−21.0293	+	8.71064i	−1.12567	+	0.466270i	−0.866309	−	0.499509i	$-0.833514\pi$
$349$	−21.0293	+	8.71064i	−1.12567	+	0.466270i	−0.259366	+	0.965779i	$0.583514\pi$
$350$	−0.800205	+	1.17675i	−0.0427728	+	0.0629000i
$351$	3.94844			0.210752
$352$	12.6361	+	3.05253i	0.673507	+	0.162700i
$353$	22.2969			1.18674			0.593372	−	0.804928i	$-0.297796\pi$
$353$	22.2969			1.18674			0.593372	+	0.804928i	$0.297796\pi$
$354$	−9.80974	+	14.4258i	−0.521382	+	0.766724i
$355$	−31.6947	+	13.1284i	−1.68218	+	0.696781i
$356$	12.9157	−	29.8002i	0.684530	−	1.57941i
$357$	1.52102	−	3.67206i	0.0805008	−	0.194346i
$358$	−4.75164	+	22.9122i	−0.251132	+	1.21095i
$359$	15.1531	+	15.1531i	0.799750	+	0.799750i	0.983056	−	0.183306i	$-0.0586799\pi$
$359$	15.1531	+	15.1531i	0.799750	+	0.799750i	−0.183306	+	0.983056i	$0.558680\pi$
$360$	−7.05828	+	1.22571i	−0.372004	+	0.0646006i
$361$	12.4765	−	12.4765i	0.656660	−	0.656660i
$362$	−15.2216	−	23.1870i	−0.800032	−	1.21868i
$363$	−7.40952	−	3.06913i	−0.388899	−	0.161087i
$364$	−1.39595	−	0.0227175i	−0.0731674	−	0.00119072i
$365$	−1.82839	−	4.41411i	−0.0957021	−	0.231045i
$366$	17.9196	−	3.41311i	0.936675	−	0.178406i
$367$			33.7656i			1.76255i	0.472604	+	0.881275i	$0.343314\pi$
$367$			33.7656i			1.76255i	−0.472604	+	0.881275i	$0.656686\pi$
$368$	0.765054	−	23.4993i	0.0398812	−	1.22498i
$369$			0.613450i			0.0319349i
$370$	−6.08852	−	31.9661i	−0.316527	−	1.66184i
$371$	−3.44231	−	8.31047i	−0.178716	−	0.431458i
$372$	4.43974	+	4.58663i	0.230190	+	0.237806i
$373$	−0.411412	−	0.170413i	−0.0213021	−	0.00882363i	0.372007	−	0.928230i	$-0.378670\pi$
$373$	−0.411412	−	0.170413i	−0.0213021	−	0.00882363i	−0.393309	+	0.919406i	$0.628670\pi$
$374$	7.70021	−	5.05498i	0.398168	−	0.261387i
$375$	9.70547	−	9.70547i	0.501188	−	0.501188i
$376$	33.3856	+	7.49225i	1.72173	+	0.386383i
$377$	−1.80558	−	1.80558i	−0.0929921	−	0.0929921i
$378$	7.83250	+	1.62434i	0.402860	+	0.0835469i
$379$	1.18801	−	2.86811i	0.0610240	−	0.147325i	−0.890426	−	0.455128i	$-0.849594\pi$
$379$	1.18801	−	2.86811i	0.0610240	−	0.147325i	0.951450	+	0.307803i	$0.0995936\pi$
$380$	−2.09777	−	5.30711i	−0.107613	−	0.272249i
$381$	1.71457	−	0.710199i	0.0878402	−	0.0363846i
$382$	−1.61682	−	1.09946i	−0.0827237	−	0.0562531i
$383$	10.7444			0.549015			0.274508	−	0.961585i	$-0.411485\pi$
$383$	10.7444			0.549015			0.274508	+	0.961585i	$0.411485\pi$
$384$	−12.6685	−	9.55101i	−0.646489	−	0.487398i
$385$	5.63192			0.287029
$386$	−10.3207	−	7.01822i	−0.525311	−	0.357218i
$387$	6.85251	−	2.83840i	0.348333	−	0.144284i
$388$	10.9512	+	27.7054i	0.555965	+	1.40653i
$389$	3.78165	−	9.12972i	0.191737	−	0.462895i	−0.798550	−	0.601928i	$-0.794399\pi$
$389$	3.78165	−	9.12972i	0.191737	−	0.462895i	0.990288	+	0.139033i	$0.0443994\pi$
$390$	−3.32214	−	0.688959i	−0.168223	−	0.0348868i
$391$	−11.7803	−	11.7803i	−0.595754	−	0.595754i
$392$	−2.75979	−	0.619339i	−0.139390	−	0.0312814i
$393$	3.33046	−	3.33046i	0.167999	−	0.167999i
$394$	−20.1428	+	13.2232i	−1.01478	+	0.666176i
$395$	8.32909	+	3.45002i	0.419082	+	0.173589i
$396$	3.30362	+	3.41293i	0.166013	+	0.171506i
$397$	0.997948	+	2.40926i	0.0500856	+	0.120917i	0.946942	−	0.321404i	$-0.104155\pi$
$397$	0.997948	+	2.40926i	0.0500856	+	0.120917i	−0.896856	+	0.442322i	$0.854155\pi$
$398$	0.488532	+	2.56491i	0.0244879	+	0.128567i
$399$			1.63267i			0.0817359i
$400$	4.02286	+	0.130970i	0.201143	+	0.00654851i
$401$		−	2.79740i		−	0.139696i	−0.997558	−	0.0698478i	$-0.977749\pi$
$401$		−	2.79740i		−	0.139696i	0.997558	−	0.0698478i	$-0.0222514\pi$
$402$	8.61791	−	1.64143i	0.429822	−	0.0818672i
$403$	−0.608013	−	1.46787i	−0.0302873	−	0.0731200i
$404$	−14.8344	−	0.241414i	−0.738040	−	0.0120108i
$405$	10.9394	+	4.53126i	0.543585	+	0.225160i
$406$	−2.83893	−	4.32451i	−0.140894	−	0.214622i
$407$	−15.2564	+	15.2564i	−0.756231	+	0.756231i
$408$	−11.0761	+	1.92343i	−0.548350	+	0.0952240i
$409$	−13.6798	−	13.6798i	−0.676422	−	0.676422i	0.282767	−	0.959189i	$-0.408748\pi$
$409$	−13.6798	−	13.6798i	−0.676422	−	0.676422i	−0.959189	+	0.282767i	$0.908748\pi$
$410$	0.417757	−	2.01441i	0.0206316	−	0.0994846i
$411$	−3.28731	+	7.93627i	−0.162151	+	0.391467i
$412$	−9.14916	+	21.1098i	−0.450747	+	1.04000i
$413$	8.12696	−	3.36630i	0.399901	−	0.165645i
$414$	4.83086	−	7.10408i	0.237424	−	0.349147i
$415$	14.9873			0.735699
$416$	2.05852	+	3.36986i	0.100927	+	0.165221i
$417$	31.6538			1.55009
$418$	−2.12766	+	3.12885i	−0.104067	+	0.153037i
$419$	−0.289761	+	0.120023i	−0.0141558	+	0.00586351i	−0.389750	−	0.920921i	$-0.627439\pi$
$419$	−0.289761	+	0.120023i	−0.0141558	+	0.00586351i	0.375594	+	0.926784i	$0.377439\pi$
$420$	−6.30668	−	2.73337i	−0.307734	−	0.133375i
$421$	10.3046	−	24.8775i	0.502216	−	1.21246i	−0.446059	−	0.895004i	$-0.647173\pi$
$421$	10.3046	−	24.8775i	0.502216	−	1.21246i	0.948274	−	0.317452i	$-0.102827\pi$
$422$	3.72344	−	17.9543i	0.181254	−	0.874002i
$423$	8.84041	+	8.84041i	0.429836	+	0.429836i
$424$	−14.6470	+	20.8032i	−0.711323	+	1.01029i
$425$	2.01668	−	2.01668i	0.0978232	−	0.0978232i
$426$	−15.2348	−	23.2070i	−0.738128	−	1.12438i
$427$	−8.49805	−	3.52001i	−0.411249	−	0.170345i
$428$	0.0525060	−	3.22639i	0.00253797	−	0.155953i
$429$	0.860873	+	2.07833i	0.0415633	+	0.100343i
$430$	−24.4348	+	4.65404i	−1.17835	+	0.224438i
$431$		−	16.8246i		−	0.810413i	−0.914225	−	0.405206i	$-0.867200\pi$
$431$		−	16.8246i		−	0.810413i	0.914225	−	0.405206i	$-0.132800\pi$
$432$	−7.97348	−	21.1735i	−0.383624	−	1.01871i
$433$		−	21.7221i		−	1.04390i	−0.852977	−	0.521949i	$-0.825205\pi$
$433$		−	21.7221i		−	1.04390i	0.852977	−	0.521949i	$-0.174795\pi$
$434$	−0.602248	−	3.16194i	−0.0289088	−	0.151778i
$435$	−4.81089	−	11.6145i	−0.230665	−	0.556874i
$436$	−25.0526	+	24.2502i	−1.19980	+	1.16137i
$437$	6.32252	+	2.61888i	0.302447	+	0.125278i
$438$	3.23204	−	2.12175i	0.154433	−	0.101381i
$439$	−14.3142	+	14.3142i	−0.683180	+	0.683180i	−0.960715	−	0.277536i	$-0.910482\pi$
$439$	−14.3142	+	14.3142i	−0.683180	+	0.683180i	0.277536	+	0.960715i	$0.410482\pi$
$440$	−8.52405	−	13.4569i	−0.406368	−	0.641534i
$441$	−0.730784	−	0.730784i	−0.0347992	−	0.0347992i
$442$	2.73976	+	0.568184i	0.130317	+	0.0270258i
$443$	4.30186	−	10.3856i	0.204388	−	0.493436i	−0.788134	−	0.615504i	$-0.788953\pi$
$443$	4.30186	−	10.3856i	0.204388	−	0.493436i	0.992522	+	0.122068i	$0.0389526\pi$
$444$	24.4887	−	9.67978i	1.16218	−	0.459382i
$445$	−36.7694	+	15.2304i	−1.74304	+	0.721989i
$446$	−11.2584	−	7.65582i	−0.533099	−	0.362514i
$447$	−27.3462			−1.29343
$448$	2.69715	+	7.53162i	0.127428	+	0.355836i
$449$	−29.1788			−1.37703			−0.688516	−	0.725221i	$-0.741737\pi$
$449$	−29.1788			−1.37703			−0.688516	+	0.725221i	$0.741737\pi$
$450$	1.21615	+	0.827000i	0.0573301	+	0.0389851i
$451$	−1.26022	+	0.521999i	−0.0593413	+	0.0245800i
$452$	−35.3157	+	13.9594i	−1.66111	+	0.656596i
$453$	−7.00439	+	16.9101i	−0.329095	+	0.794506i
$454$	11.4343	+	2.37129i	0.536636	+	0.111290i
$455$	1.20971	+	1.20971i	0.0567123	+	0.0567123i
$456$	3.90111	−	2.47109i	0.182686	−	0.115719i
$457$	−2.00998	+	2.00998i	−0.0940230	+	0.0940230i	−0.752554	−	0.658531i	$-0.771178\pi$
$457$	−2.00998	+	2.00998i	−0.0940230	+	0.0940230i	0.658531	+	0.752554i	$0.271178\pi$
$458$	7.91181	−	5.19389i	0.369694	−	0.242695i
$459$	−14.8112	−	6.13500i	−0.691328	−	0.286357i
$460$	−20.7011	+	20.0382i	−0.965196	+	0.934284i
$461$	5.03881	+	12.1648i	0.234681	+	0.566570i	0.996717	−	0.0809649i	$-0.0258002\pi$
$461$	5.03881	+	12.1648i	0.234681	+	0.566570i	−0.762036	+	0.647534i	$0.775800\pi$
$462$	0.852710	+	4.47693i	0.0396717	+	0.208286i
$463$			28.9122i			1.34366i	0.740703	+	0.671832i	$0.234492\pi$
$463$			28.9122i			1.34366i	−0.740703	+	0.671832i	$0.765508\pi$
$464$	−6.03622	+	13.3286i	−0.280224	+	0.618765i
$465$		−	7.82217i		−	0.362745i
$466$	−41.8786	+	7.97652i	−1.93999	+	0.369505i
$467$	−7.03631	−	16.9872i	−0.325602	−	0.786072i	−0.998909	−	0.0467086i	$-0.985127\pi$
$467$	−7.03631	−	16.9872i	−0.325602	−	0.786072i	0.673307	−	0.739363i	$-0.264873\pi$
$468$	−0.0234782	+	1.44269i	−0.00108528	+	0.0666883i
$469$	−4.08688	−	1.69284i	−0.188714	−	0.0781681i
$470$	−23.0093	−	35.0499i	−1.06134	−	1.61673i
$471$	−1.07641	+	1.07641i	−0.0495983	+	0.0495983i
$472$	−20.3438	−	14.3236i	−0.936398	−	0.659297i
$473$	11.6619	+	11.6619i	0.536216	+	0.536216i
$474$	−1.48141	+	7.14332i	−0.0680436	+	0.328104i
$475$	−0.448328	+	1.08236i	−0.0205707	+	0.0496620i
$476$	5.20111	+	2.25421i	0.238393	+	0.103322i
$477$	−8.58874	+	3.55757i	−0.393251	+	0.162890i
$478$	−3.62622	+	5.33258i	−0.165859	+	0.243907i
$479$	−6.87875			−0.314298			−0.157149	−	0.987575i	$-0.550230\pi$
$479$	−6.87875			−0.314298			−0.157149	+	0.987575i	$0.550230\pi$
$480$	3.01419	+	19.2062i	0.137578	+	0.876640i
$481$	−6.55402			−0.298838
$482$	7.37014	−	10.8383i	0.335701	−	0.493669i
$483$	7.61533	−	3.15437i	0.346509	−	0.143529i
$484$	4.54857	−	10.4949i	0.206753	−	0.477039i
$485$	13.9701	−	33.7268i	0.634350	−	1.53146i
$486$	2.92732	−	14.1154i	0.132786	−	0.640289i
$487$	−13.4673	−	13.4673i	−0.610261	−	0.610261i	0.332753	−	0.943014i	$-0.392022\pi$
$487$	−13.4673	−	13.4673i	−0.610261	−	0.610261i	−0.943014	+	0.332753i	$0.892022\pi$
$488$	4.45129	+	25.6329i	0.201500	+	1.16035i
$489$	9.90738	−	9.90738i	0.448027	−	0.448027i
$490$	1.90204	+	2.89737i	0.0859256	+	0.130890i
$491$	24.4439	+	10.1250i	1.10314	+	0.456936i	0.858570	−	0.512696i	$-0.171353\pi$
$491$	24.4439	+	10.1250i	1.10314	+	0.456936i	0.244570	+	0.969632i	$0.421353\pi$
$492$	1.66455	+	0.0270887i	0.0750436	+	0.00122125i
$493$	3.96754	+	9.57849i	0.178689	+	0.431393i
$494$	−1.12908	+	0.215053i	−0.0507996	+	0.00967568i
$495$		−	5.82050i		−	0.261612i
$496$	−6.64364	+	6.22469i	−0.298308	+	0.279497i
$497$			13.9981i			0.627901i
$498$	2.26918	+	11.9137i	0.101684	+	0.533867i
$499$	−0.650253	−	1.56985i	−0.0291093	−	0.0702761i	0.908656	−	0.417545i	$-0.137109\pi$
$499$	−0.650253	−	1.56985i	−0.0291093	−	0.0702761i	−0.937766	+	0.347269i	$0.887109\pi$
$500$	13.6149	+	14.0654i	0.608877	+	0.629022i
$501$	−20.8108	−	8.62010i	−0.929756	−	0.385118i
$502$	32.0893	−	21.0658i	1.43222	−	0.940212i
$503$	−13.5604	+	13.5604i	−0.604627	+	0.604627i	−0.941537	−	0.336910i	$-0.890618\pi$
$503$	−13.5604	+	13.5604i	−0.604627	+	0.604627i	0.336910	+	0.941537i	$0.390618\pi$
$504$	−0.640078	+	2.85220i	−0.0285113	+	0.127047i
$505$	12.8554	+	12.8554i	0.572057	+	0.572057i
$506$	18.7047	+	3.87906i	0.831525	+	0.172445i
$507$	6.71490	−	16.2112i	0.298219	−	0.719965i
$508$	0.972964	+	2.46148i	0.0431683	+	0.109211i
$509$	−6.20772	+	2.57132i	−0.275153	+	0.113972i	−0.515993	−	0.856593i	$-0.672577\pi$
$509$	−6.20772	+	2.57132i	−0.275153	+	0.113972i	0.240840	+	0.970565i	$0.422577\pi$
$510$	11.3914	+	7.74627i	0.504418	+	0.343010i
$511$	−1.94951			−0.0862414
$512$	13.9139	−	17.8439i	0.614912	−	0.788595i
$513$	6.58536			0.290751
$514$	−19.7201	−	13.4099i	−0.869815	−	0.591485i
$515$	26.0465	−	10.7888i	1.14775	−	0.475412i
$516$	−7.39919	−	18.7191i	−0.325731	−	0.824061i
$517$	−10.6384	+	25.6835i	−0.467878	+	1.12956i
$518$	−13.0012	−	2.69624i	−0.571239	−	0.118466i
$519$	−11.3779	−	11.3779i	−0.499435	−	0.499435i
$520$	1.05956	−	4.72142i	0.0464649	−	0.207048i
$521$	−6.33736	+	6.33736i	−0.277645	+	0.277645i	−0.832168	−	0.554523i	$-0.812901\pi$
$521$	−6.33736	+	6.33736i	−0.277645	+	0.277645i	0.554523	+	0.832168i	$0.312901\pi$
$522$	−4.46932	+	2.93399i	−0.195617	+	0.128417i
$523$	36.2665	+	15.0221i	1.58583	+	0.656870i	0.989323	−	0.145741i	$-0.0465565\pi$
$523$	36.2665	+	15.0221i	1.58583	+	0.656870i	0.596503	+	0.802611i	$0.296557\pi$
$524$	4.67199	+	4.82657i	0.204097	+	0.210850i
$525$	0.540000	+	1.30367i	0.0235675	+	0.0568970i
$526$	−0.602449	−	3.16300i	−0.0262680	−	0.137913i
$527$			6.45094i			0.281007i
$528$	9.40659	−	8.81341i	0.409369	−	0.383554i
$529$		−	11.5501i		−	0.502177i
$530$	30.6259	−	5.83324i	1.33030	−	0.253380i
$531$	−3.47901	−	8.39909i	−0.150976	−	0.364489i
$532$	−2.32822	−	0.0378892i	−0.100941	−	0.00164271i
$533$	−0.382813	−	0.158566i	−0.0165815	−	0.00686827i
$534$	−17.6741	−	26.9228i	−0.764832	−	1.16506i
$535$	−2.79596	+	2.79596i	−0.120880	+	0.120880i
$536$	2.14071	+	12.3274i	0.0924647	+	0.532460i
$537$	16.4070	+	16.4070i	0.708016	+	0.708016i
$538$	5.71256	−	27.5458i	0.246286	−	1.18758i
$539$	0.879416	−	2.12310i	0.0378791	−	0.0914483i
$540$	−11.0250	+	25.4379i	−0.474441	+	1.09467i
$541$	1.86843	−	0.773930i	0.0803302	−	0.0332739i	−0.342157	−	0.939643i	$-0.611157\pi$
$541$	1.86843	−	0.773930i	0.0803302	−	0.0332739i	0.422487	+	0.906369i	$0.361157\pi$
$542$	13.5924	−	19.9884i	0.583842	−	0.858576i
$543$	−27.5037			−1.18030
$544$	−2.48580	−	15.8394i	−0.106578	−	0.679107i
$545$	42.7253			1.83015
$546$	−0.778468	+	1.14479i	−0.0333154	+	0.0489923i
$547$	−37.0577	+	15.3498i	−1.58447	+	0.656310i	−0.989114	−	0.147151i	$-0.952990\pi$
$547$	−37.0577	+	15.3498i	−1.58447	+	0.656310i	−0.595358	+	0.803461i	$0.702990\pi$
$548$	−11.2409	−	4.87193i	−0.480189	−	0.208118i
$549$	−3.63787	+	8.78260i	−0.155261	+	0.374832i
$550$	−0.664060	+	3.20207i	−0.0283156	+	0.136537i
$551$	−3.01142	−	3.01142i	−0.128291	−	0.128291i
$552$	−19.0630	−	13.4219i	−0.811377	−	0.571272i
$553$	2.60115	−	2.60115i	0.110612	−	0.110612i
$554$	−1.75047	−	2.66647i	−0.0743703	−	0.113288i
$555$	−29.8111	−	12.3481i	−1.26541	−	0.524149i
$556$	−0.734586	+	45.1388i	−0.0311534	+	1.91431i
$557$	2.86879	+	6.92586i	0.121554	+	0.293458i	0.972931	−	0.231097i	$-0.0742315\pi$
$557$	2.86879	+	6.92586i	0.121554	+	0.293458i	−0.851376	+	0.524555i	$0.824232\pi$
$558$	−3.26782	+	0.622414i	−0.138338	+	0.0263489i
$559$			5.00987i			0.211895i
$560$	4.04418	−	8.92998i	0.170898	−	0.377361i
$561$		−	9.13376i		−	0.385627i
$562$	2.24495	+	11.7865i	0.0946974	+	0.497183i
$563$	−11.8519	−	28.6131i	−0.499499	−	1.20590i	−0.949754	−	0.312997i	$-0.898667\pi$
$563$	−11.8519	−	28.6131i	−0.499499	−	1.20590i	0.450255	−	0.892900i	$-0.351333\pi$
$564$	24.3781	−	23.5974i	1.02650	−	0.993629i
$565$	42.9912	+	17.8075i	1.80865	+	0.749169i
$566$	−6.79978	+	4.46387i	−0.285816	+	0.187631i
$567$	3.41636	−	3.41636i	0.143473	−	0.143473i
$568$	33.4471	−	21.1865i	1.40341	−	0.888964i
$569$	−13.4490	−	13.4490i	−0.563812	−	0.563812i	0.366576	−	0.930388i	$-0.380530\pi$
$569$	−13.4490	−	13.4490i	−0.563812	−	0.563812i	−0.930388	+	0.366576i	$0.880530\pi$
$570$	−5.54080	−	1.14907i	−0.232078	−	0.0481294i
$571$	0.828679	−	2.00061i	0.0346791	−	0.0837228i	−0.905591	−	0.424152i	$-0.860572\pi$
$571$	0.828679	−	2.00061i	0.0346791	−	0.0837228i	0.940270	+	0.340429i	$0.110572\pi$
$572$	−2.98371	+	1.17939i	−0.124755	+	0.0493126i
$573$	−1.79121	+	0.741943i	−0.0748288	+	0.0309951i
$574$	−0.694152	−	0.472032i	−0.0289733	−	0.0197022i
$575$	5.91466			0.246658
$576$	7.78382	−	2.78746i	0.324326	−	0.116144i
$577$	−1.53610			−0.0639486			−0.0319743	−	0.999489i	$-0.510179\pi$
$577$	−1.53610			−0.0639486			−0.0319743	+	0.999489i	$0.510179\pi$
$578$	10.4861	+	7.13067i	0.436164	+	0.296597i
$579$	−11.4339	+	4.73608i	−0.475177	+	0.196825i
$580$	16.6741	−	6.59086i	0.692355	−	0.273671i
$581$	2.34025	−	5.64986i	0.0970899	−	0.234396i
$582$	28.9253	+	5.99866i	1.19899	+	0.248652i
$583$	−14.6167	−	14.6167i	−0.605363	−	0.605363i
$584$	2.95064	+	4.65818i	0.122098	+	0.192757i
$585$	1.25022	−	1.25022i	0.0516903	−	0.0516903i
$586$	−22.6096	+	14.8426i	−0.933994	+	0.613142i
$587$	39.4143	+	16.3260i	1.62680	+	0.673844i	0.994868	−	0.101177i	$-0.0322608\pi$
$587$	39.4143	+	16.3260i	1.62680	+	0.673844i	0.631935	+	0.775021i	$0.282261\pi$
$588$	−2.01519	+	1.95065i	−0.0831052	+	0.0804436i
$589$	−1.01407	−	2.44818i	−0.0417840	−	0.100875i
$590$	5.70443	+	29.9496i	0.234848	+	1.23301i
$591$			23.8928i			0.982819i
$592$	13.2352	+	35.1459i	0.543963	+	1.44449i
$593$			44.4798i			1.82657i	0.407324	+	0.913284i	$0.366462\pi$
$593$			44.4798i			1.82657i	−0.407324	+	0.913284i	$0.633538\pi$
$594$	18.0576	−	3.43939i	0.740913	−	0.141120i
$595$	−2.65820	−	6.41746i	−0.108975	−	0.263090i
$596$	0.634619	−	38.9961i	0.0259950	−	1.59734i
$597$	2.39199	+	0.990794i	0.0978975	+	0.0405505i
$598$	3.18448	+	4.85090i	0.130223	+	0.198368i
$599$	8.92455	−	8.92455i	0.364647	−	0.364647i	−0.500873	−	0.865521i	$-0.666988\pi$
$599$	8.92455	−	8.92455i	0.364647	−	0.364647i	0.865521	+	0.500873i	$0.166988\pi$
$600$	2.29770	−	3.26342i	0.0938033	−	0.133229i
$601$	−7.13660	−	7.13660i	−0.291108	−	0.291108i	0.546410	−	0.837518i	$-0.315994\pi$
$601$	−7.13660	−	7.13660i	−0.291108	−	0.291108i	−0.837518	+	0.546410i	$0.815994\pi$
$602$	−2.06100	+	9.93805i	−0.0840000	+	0.405045i
$603$	−1.74952	+	4.22373i	−0.0712461	+	0.172003i
$604$	−23.9515	−	10.3808i	−0.974572	−	0.422388i
$605$	−12.9492	+	5.36374i	−0.526460	+	0.218067i
$606$	−8.27261	+	12.1654i	−0.336052	+	0.494185i
$607$	15.7286			0.638403			0.319202	−	0.947687i	$-0.396585\pi$
$607$	15.7286			0.638403			0.319202	+	0.947687i	$0.396585\pi$
$608$	3.43328	+	5.62039i	0.139238	+	0.227937i
$609$	−5.12961			−0.207862
$610$	17.9267	−	26.3624i	0.725833	−	1.06738i
$611$	−7.80180	+	3.23161i	−0.315627	+	0.130737i
$612$	2.32969	−	5.37527i	0.0941722	−	0.217282i
$613$	15.3083	−	36.9574i	0.618295	−	1.49270i	−0.235388	−	0.971901i	$-0.575636\pi$
$613$	15.3083	−	36.9574i	0.618295	−	1.49270i	0.853683	−	0.520794i	$-0.174364\pi$
$614$	2.48293	−	11.9726i	0.100203	−	0.483174i
$615$	−1.44248	−	1.44248i	−0.0581665	−	0.0581665i
$616$	−6.40395	+	1.11208i	−0.258023	+	0.0448070i
$617$	−6.37638	+	6.37638i	−0.256703	+	0.256703i	−0.823712	−	0.567009i	$-0.808101\pi$
$617$	−6.37638	+	6.37638i	−0.256703	+	0.256703i	0.567009	+	0.823712i	$0.308101\pi$
$618$	12.5199	+	19.0714i	0.503623	+	0.767165i
$619$	12.3129	+	5.10015i	0.494895	+	0.204992i	0.616150	−	0.787629i	$-0.288692\pi$
$619$	12.3129	+	5.10015i	0.494895	+	0.204992i	−0.121254	+	0.992621i	$0.538692\pi$
$620$	11.1545	+	0.181528i	0.447977	+	0.00729034i
$621$	−12.7231	−	30.7163i	−0.510561	−	1.23260i
$622$	16.2654	−	3.09804i	0.652184	−	0.124220i
$623$			16.2394i			0.650617i
$624$	3.91358	+	0.127413i	0.156669	+	0.00510058i
$625$		−	29.0187i		−	1.16075i
$626$	8.66427	+	45.4895i	0.346294	+	1.81812i
$627$	1.43580	+	3.46633i	0.0573403	+	0.138432i
$628$	−1.50999	−	1.55995i	−0.0602554	−	0.0622490i
$629$	24.5852	+	10.1835i	0.980274	+	0.406043i
$630$	2.99438	−	1.96573i	0.119299	−	0.0783167i
$631$	−6.39133	+	6.39133i	−0.254435	+	0.254435i	−0.822786	−	0.568351i	$-0.807582\pi$
$631$	−6.39133	+	6.39133i	−0.254435	+	0.254435i	0.568351	+	0.822786i	$0.307582\pi$
$632$	−10.1521	−	2.27829i	−0.403829	−	0.0906255i
$633$	−12.8568	−	12.8568i	−0.511010	−	0.511010i
$634$	5.08460	+	1.05447i	0.201935	+	0.0418782i
$635$	1.24117	−	2.99646i	0.0492545	−	0.118911i
$636$	9.27393	+	23.4620i	0.367735	+	0.930327i
$637$	0.644928	−	0.267138i	0.0255530	−	0.0105844i
$638$	−9.83037	−	6.68477i	−0.389188	−	0.264653i
$639$	14.4668			0.572299
$640$	−27.4583	+	3.85256i	−1.08538	+	0.152286i
$641$	34.0027			1.34302			0.671512	−	0.740994i	$-0.265645\pi$
$641$	34.0027			1.34302			0.671512	+	0.740994i	$0.265645\pi$
$642$	−2.64589	−	1.79924i	−0.104425	−	0.0710103i
$643$	−3.51412	+	1.45560i	−0.138584	+	0.0574032i	−0.450897	−	0.892576i	$-0.648896\pi$
$643$	−3.51412	+	1.45560i	−0.138584	+	0.0574032i	0.312314	+	0.949979i	$0.398896\pi$
$644$	4.32145	+	10.9328i	0.170289	+	0.430811i
$645$	−9.43887	+	22.7875i	−0.371655	+	0.897255i
$646$	4.56949	+	0.947641i	0.179784	+	0.0372844i
$647$	−32.4776	−	32.4776i	−1.27682	−	1.27682i	−0.942435	−	0.334390i	$-0.891470\pi$
$647$	−32.4776	−	32.4776i	−1.27682	−	1.27682i	−0.334390	−	0.942435i	$-0.608530\pi$
$648$	−13.3338	−	2.99231i	−0.523800	−	0.117549i
$649$	14.2940	−	14.2940i	0.561087	−	0.561087i
$650$	−0.830430	+	0.545155i	−0.0325721	+	0.0213827i
$651$	−2.94877	−	1.22142i	−0.115571	−	0.0478713i
$652$	13.8981	+	14.3580i	0.544293	+	0.562302i
$653$	−5.54675	−	13.3910i	−0.217061	−	0.524032i	0.777416	−	0.628987i	$-0.216530\pi$
$653$	−5.54675	−	13.3910i	−0.217061	−	0.524032i	−0.994477	+	0.104955i	$0.966530\pi$
$654$	6.46890	+	33.9633i	0.252954	+	1.32807i
$655$		−	8.23137i		−	0.321626i
$656$	−0.0772579	+	2.37304i	−0.00301641	+	0.0926517i
$657$			2.01479i			0.0786046i
$658$	−16.8058	+	3.20097i	−0.655160	+	0.124787i
$659$	−4.31278	−	10.4120i	−0.168002	−	0.405593i	0.817346	−	0.576147i	$-0.195444\pi$
$659$	−4.31278	−	10.4120i	−0.168002	−	0.405593i	−0.985348	+	0.170554i	$0.945444\pi$
$660$	−15.7935	−	0.257022i	−0.614760	−	0.0100046i
$661$	−23.6876	−	9.81171i	−0.921339	−	0.381631i	−0.128953	−	0.991651i	$-0.541162\pi$
$661$	−23.6876	−	9.81171i	−0.921339	−	0.381631i	−0.792386	+	0.610019i	$0.791162\pi$
$662$	−9.56584	−	14.5716i	−0.371787	−	0.566340i
$663$	1.96189	−	1.96189i	0.0761937	−	0.0761937i
$664$	−17.0418	+	2.95940i	−0.661351	+	0.114847i
$665$	2.01761	+	2.01761i	0.0782396	+	0.0782396i
$666$	−2.78653	+	13.4365i	−0.107976	+	0.520655i
$667$	−8.22810	+	19.8644i	−0.318593	+	0.769153i
$668$	12.7753	−	29.4764i	0.494293	−	1.14048i
$669$	−12.4727	+	5.16635i	−0.482221	+	0.199743i
$670$	8.62133	−	12.6782i	0.333071	−	0.489801i
$671$	−21.1377			−0.816013
$672$	7.71094	+	1.86275i	0.297456	+	0.0718571i
$673$	−15.7894			−0.608637			−0.304318	−	0.952570i	$-0.598429\pi$
$673$	−15.7894			−0.608637			−0.304318	+	0.952570i	$0.598429\pi$
$674$	−17.4327	+	25.6359i	−0.671483	+	0.987457i
$675$	5.25835	−	2.17808i	0.202394	−	0.0838344i
$676$	22.9616	+	9.95175i	0.883137	+	0.382760i
$677$	−0.872998	+	2.10760i	−0.0335520	+	0.0810018i	−0.939767	−	0.341815i	$-0.888958\pi$
$677$	−0.872998	+	2.10760i	−0.0335520	+	0.0810018i	0.906215	+	0.422816i	$0.138958\pi$
$678$	−7.64643	+	36.8708i	−0.293659	+	1.41601i
$679$	−10.5328	−	10.5328i	−0.404211	−	0.404211i
$680$	−11.3106	+	16.0645i	−0.433743	+	0.616045i
$681$	8.18786	−	8.18786i	0.313759	−	0.313759i
$682$	−4.05929	−	6.18349i	−0.155438	−	0.236778i
$683$	21.1120	+	8.74487i	0.807828	+	0.334613i	0.748087	−	0.663601i	$-0.230973\pi$
$683$	21.1120	+	8.74487i	0.807828	+	0.334613i	0.0597409	+	0.998214i	$0.480973\pi$
$684$	−0.0391579	+	2.40617i	−0.00149724	+	0.0920024i
$685$	5.74505	+	13.8698i	0.219507	+	0.529937i
$686$	1.38924	−	0.264605i	0.0530414	−	0.0101027i
$687$		−	9.38475i		−	0.358050i
$688$	26.8654	−	10.1169i	1.02423	−	0.385704i
$689$		−	6.27923i		−	0.239219i
$690$	5.34531	+	28.0641i	0.203493	+	1.06838i
$691$	−1.67347	−	4.04011i	−0.0636617	−	0.153693i	0.888847	−	0.458204i	$-0.151507\pi$
$691$	−1.67347	−	4.04011i	−0.0636617	−	0.153693i	−0.952509	+	0.304511i	$0.901507\pi$
$692$	16.4891	−	15.9610i	0.626822	−	0.606747i
$693$	−2.19419	−	0.908863i	−0.0833504	−	0.0345248i
$694$	−25.8396	+	16.9630i	−0.980857	+	0.643907i
$695$	39.1169	−	39.1169i	1.48379	−	1.48379i
$696$	7.76379	+	12.2567i	0.294286	+	0.464589i
$697$	1.18961	+	1.18961i	0.0450599	+	0.0450599i
$698$	−31.5197	−	6.53669i	−1.19304	−	0.247417i
$699$	−16.1772	+	39.0552i	−0.611878	+	1.47720i
$700$	−1.87159	+	0.739793i	−0.0707395	+	0.0279616i
$701$	20.9962	−	8.69691i	0.793016	−	0.328478i	0.0508604	−	0.998706i	$-0.483804\pi$
$701$	20.9962	−	8.69691i	0.793016	−	0.328478i	0.742155	+	0.670228i	$0.233804\pi$
$702$	4.61748	+	3.13994i	0.174275	+	0.118509i
$703$	−10.9311			−0.412273
$704$	12.3497	+	13.6185i	0.465449	+	0.513265i
$705$	−41.5752			−1.56581
$706$	26.0750	+	17.7313i	0.981344	+	0.667326i
$707$	6.85351	−	2.83882i	0.257753	−	0.106765i
$708$	−22.9439	+	9.06914i	−0.862284	+	0.340839i
$709$	9.38638	−	22.6607i	0.352513	−	0.851041i	−0.643796	−	0.765197i	$-0.722641\pi$
$709$	9.38638	−	22.6607i	0.352513	−	0.851041i	0.996309	−	0.0858439i	$-0.0273586\pi$
$710$	−47.5053	−	9.85185i	−1.78284	−	0.369733i
$711$	−2.68825	−	2.68825i	−0.100817	−	0.100817i
$712$	38.8024	−	24.5787i	1.45418	−	0.921125i
$713$	−9.45990	+	9.45990i	−0.354276	+	0.354276i
$714$	4.69890	−	3.08470i	0.175852	−	0.115442i
$715$	3.63218	+	1.50450i	0.135836	+	0.0562651i
$716$	−23.7774	+	23.0159i	−0.888604	+	0.860145i
$717$	2.44707	+	5.90775i	0.0913875	+	0.220629i
$718$	5.67041	+	29.7710i	0.211618	+	1.11104i
$719$		−	8.85217i		−	0.330130i	−0.986283	−	0.165065i	$-0.947217\pi$
$719$		−	8.85217i		−	0.330130i	0.986283	−	0.165065i	$-0.0527834\pi$
$720$	−9.22900	−	4.17960i	−0.343944	−	0.155765i
$721$		−	11.5036i		−	0.428415i
$722$	24.5124	−	4.66882i	0.912258	−	0.173756i
$723$	−4.97357	−	12.0073i	−0.184969	−	0.446555i
$724$	0.638275	−	39.2207i	0.0237213	−	1.45763i
$725$	−3.40061	−	1.40858i	−0.126295	−	0.0523132i
$726$	−6.22435	−	9.48149i	−0.231007	−	0.351891i
$727$	20.0896	−	20.0896i	0.745081	−	0.745081i	−0.228470	−	0.973551i	$-0.573372\pi$
$727$	20.0896	−	20.0896i	0.745081	−	0.745081i	0.973551	+	0.228470i	$0.0733721\pi$
$728$	−1.61441	−	1.13667i	−0.0598342	−	0.0421279i
$729$	−20.3569	−	20.3569i	−0.753958	−	0.753958i
$730$	1.37207	−	6.61606i	0.0507825	−	0.244871i
$731$	7.78423	−	18.7928i	0.287910	−	0.695077i
$732$	23.6702	+	10.2589i	0.874877	+	0.379180i
$733$	−17.2564	+	7.14782i	−0.637378	+	0.264011i	−0.677884	−	0.735169i	$-0.737103\pi$
$733$	−17.2564	+	7.14782i	−0.637378	+	0.264011i	0.0405062	+	0.999179i	$0.487103\pi$
$734$	−26.8516	+	39.4870i	−0.991111	+	1.45749i
$735$	3.43677			0.126767
$736$	19.5822	−	26.8727i	0.721808	−	0.990540i
$737$	−10.1656			−0.374453
$738$	−0.487838	+	0.717396i	−0.0179575	+	0.0264077i
$739$	−6.98086	+	2.89157i	−0.256795	+	0.106368i	−0.507367	−	0.861730i	$-0.669381\pi$
$739$	−6.98086	+	2.89157i	−0.256795	+	0.106368i	0.250572	+	0.968098i	$0.419381\pi$
$740$	18.3004	−	42.2244i	0.672738	−	1.55220i
$741$	−0.436149	+	1.05296i	−0.0160223	+	0.0386813i
$742$	2.58320	−	12.4561i	0.0948321	−	0.457277i
$743$	32.1681	+	32.1681i	1.18013	+	1.18013i	0.979709	+	0.200425i	$0.0642323\pi$
$743$	32.1681	+	32.1681i	1.18013	+	1.18013i	0.200425	+	0.979709i	$0.435768\pi$
$744$	1.54457	+	8.89445i	0.0566267	+	0.326086i
$745$	−33.7936	+	33.7936i	−1.23810	+	1.23810i
$746$	−0.345605	−	0.526458i	−0.0126535	−	0.0192750i
$747$	−5.83905	−	2.41861i	−0.213639	−	0.0884924i
$748$	13.0249	+	0.211966i	0.476236	+	0.00775024i
$749$	0.617424	+	1.49059i	0.0225602	+	0.0544651i
$750$	19.0681	−	3.63186i	0.696270	−	0.132617i
$751$			32.5564i			1.18800i	0.804465	+	0.594000i	$0.202452\pi$
$751$			32.5564i			1.18800i	−0.804465	+	0.594000i	$0.797548\pi$
$752$	33.0845	+	35.3112i	1.20647	+	1.28767i
$753$		−	38.0634i		−	1.38711i
$754$	−0.675663	−	3.54739i	−0.0246062	−	0.129188i
$755$	12.2412	+	29.5528i	0.445502	+	1.07554i
$756$	7.86793	+	8.12826i	0.286154	+	0.295622i
$757$	22.4912	+	9.31618i	0.817458	+	0.338602i	0.751925	−	0.659248i	$-0.229125\pi$
$757$	22.4912	+	9.31618i	0.817458	+	0.338602i	0.0655327	+	0.997850i	$0.479125\pi$
$758$	3.67014	−	2.40935i	0.133305	−	0.0875115i
$759$	13.3941	−	13.3941i	0.486174	−	0.486174i
$760$	1.76718	−	7.87459i	0.0641024	−	0.285641i
$761$	−5.77118	−	5.77118i	−0.209205	−	0.209205i	0.594725	−	0.803930i	$-0.297261\pi$
$761$	−5.77118	−	5.77118i	−0.209205	−	0.209205i	−0.803930	+	0.594725i	$0.797261\pi$
$762$	2.56987	+	0.532951i	0.0930966	+	0.0193068i
$763$	6.67150	−	16.1064i	0.241525	−	0.583092i
$764$	−1.01645	−	2.57151i	−0.0367740	−	0.0930339i
$765$	−6.63234	+	2.74721i	−0.239793	+	0.0993255i
$766$	12.5650	+	8.54437i	0.453993	+	0.308721i
$767$	6.14057			0.221723
$768$	−7.21985	−	21.2439i	−0.260524	−	0.766572i
$769$	−52.8746			−1.90671			−0.953353	−	0.301856i	$-0.902394\pi$
$769$	−52.8746			−1.90671			−0.953353	+	0.301856i	$0.902394\pi$
$770$	6.58621	+	4.47870i	0.237351	+	0.161401i
$771$	−21.8471	+	9.04935i	−0.786803	+	0.325904i
$772$	−6.48837	−	16.4148i	−0.233522	−	0.590782i
$773$	10.6154	−	25.6279i	0.381810	−	0.921770i	−0.609806	−	0.792550i	$-0.708753\pi$
$773$	10.6154	−	25.6279i	0.381810	−	0.921770i	0.991616	−	0.129220i	$-0.0412472\pi$
$774$	10.2708	+	2.13001i	0.369177	+	0.0765616i
$775$	−1.61945	−	1.61945i	−0.0581723	−	0.0581723i
$776$	−9.22544	+	41.1087i	−0.331174	+	1.47572i
$777$	−9.30991	+	9.30991i	−0.333991	+	0.333991i
$778$	11.6827	−	7.66939i	0.418846	−	0.274961i
$779$	−0.638471	−	0.264463i	−0.0228756	−	0.00947538i
$780$	−3.33717	−	3.44758i	−0.119490	−	0.123443i
$781$	12.3102	+	29.7193i	0.440492	+	1.06344i
$782$	−4.40827	−	23.1445i	−0.157640	−	0.827645i
$783$			20.6902i			0.739408i
$784$	−2.73489	−	2.91896i	−0.0976748	−	0.104249i
$785$			2.66039i			0.0949534i
$786$	6.54328	−	1.24628i	0.233391	−	0.0444535i
$787$	−4.14760	−	10.0132i	−0.147846	−	0.356932i	0.832555	−	0.553942i	$-0.186877\pi$
$787$	−4.14760	−	10.0132i	−0.147846	−	0.356932i	−0.980402	+	0.197010i	$0.936877\pi$
$788$	−34.0715	−	0.554477i	−1.21375	−	0.0197524i
$789$	−2.94976	−	1.22183i	−0.105014	−	0.0434983i
$790$	6.99682	+	10.6582i	0.248936	+	0.379202i
$791$	13.4260	−	13.4260i	0.477375	−	0.477375i
$792$	1.14932	+	6.61839i	0.0408393	+	0.235174i
$793$	−4.54030	−	4.54030i	−0.161231	−	0.161231i
$794$	−0.748886	+	3.61110i	−0.0265770	+	0.128153i
$795$	11.8304	−	28.5612i	0.419582	−	1.01296i
$796$	−1.46840	+	3.38801i	−0.0520459	+	0.120085i
$797$	−4.22734	+	1.75102i	−0.149740	+	0.0620243i	−0.456295	−	0.889829i	$-0.650824\pi$
$797$	−4.22734	+	1.75102i	−0.149740	+	0.0620243i	0.306555	+	0.951853i	$0.400824\pi$
$798$	−1.29836	+	1.90932i	−0.0459615	+	0.0675892i
$799$	34.2870			1.21299
$800$	4.60036	+	3.35229i	0.162647	+	0.118521i
$801$	16.7831			0.593003
$802$	2.22460	−	3.27141i	0.0785532	−	0.115517i
$803$	−4.13901	+	1.71443i	−0.146063	+	0.0605011i
$804$	11.3835	+	4.93371i	0.401465	+	0.173998i
$805$	5.51272	−	13.3089i	0.194298	−	0.469076i
$806$	0.456268	−	2.20011i	0.0160714	−	0.0774955i
$807$	−19.7250	−	19.7250i	−0.694353	−	0.694353i
$808$	−17.1560	−	12.0792i	−0.603547	−	0.424944i
$809$	−14.2147	+	14.2147i	−0.499762	+	0.499762i	−0.911364	−	0.411602i	$-0.864969\pi$
$809$	−14.2147	+	14.2147i	−0.499762	+	0.499762i	0.411602	+	0.911364i	$0.364969\pi$
$810$	9.18964	+	13.9985i	0.322891	+	0.491857i
$811$	44.4462	+	18.4102i	1.56072	+	0.646470i	0.985214	−	0.171330i	$-0.0548066\pi$
$811$	44.4462	+	18.4102i	1.56072	+	0.646470i	0.575502	+	0.817800i	$0.304807\pi$
$812$	0.119042	−	7.31490i	0.00417756	−	0.256703i
$813$	−9.17249	−	22.1443i	−0.321693	−	0.776636i
$814$	−29.9739	+	5.70906i	−1.05058	+	0.200102i
$815$		−	24.4865i		−	0.857725i
$816$	−14.4825	−	6.55879i	−0.506989	−	0.229604i
$817$			8.35566i			0.292328i
$818$	−5.11908	−	26.8764i	−0.178985	−	0.939711i
$819$	−0.276083	−	0.666523i	−0.00964712	−	0.0232902i
$820$	2.09048	−	2.02352i	0.0730026	−	0.0706645i
$821$	1.92822	+	0.798696i	0.0672955	+	0.0278747i	0.416077	−	0.909329i	$-0.363405\pi$
$821$	1.92822	+	0.798696i	0.0672955	+	0.0278747i	−0.348782	+	0.937204i	$0.613405\pi$
$822$	−10.1555	+	6.66683i	−0.354215	+	0.232533i
$823$	36.1616	−	36.1616i	1.26051	−	1.26051i	0.309668	−	0.950845i	$-0.399782\pi$
$823$	36.1616	−	36.1616i	1.26051	−	1.26051i	0.950845	−	0.309668i	$-0.100218\pi$
$824$	−27.4867	+	17.4109i	−0.957543	+	0.606539i
$825$	2.29295	+	2.29295i	0.0798301	+	0.0798301i
$826$	12.1810	+	2.52615i	0.423832	+	0.0878962i
$827$	−12.8042	+	30.9120i	−0.445245	+	1.07492i	0.528838	+	0.848723i	$0.322628\pi$
$827$	−12.8042	+	30.9120i	−0.445245	+	1.07492i	−0.974083	+	0.226193i	$0.927372\pi$
$828$	11.2988	−	4.46615i	0.392662	−	0.155210i
$829$	12.2405	−	5.07016i	0.425129	−	0.176094i	−0.159853	−	0.987141i	$-0.551102\pi$
$829$	12.2405	−	5.07016i	0.425129	−	0.176094i	0.584981	+	0.811047i	$0.301102\pi$
$830$	17.5268	+	11.9185i	0.608365	+	0.413696i
$831$	−3.16289			−0.109719
$832$	−0.272514	+	5.57787i	−0.00944772	+	0.193378i
$833$	−2.83430			−0.0982027
$834$	37.0174	+	25.1723i	1.28181	+	0.871644i
$835$	−36.3698	+	15.0649i	−1.25863	+	0.521341i
$836$	−4.97635	+	1.96703i	−0.172111	+	0.0680311i
$837$	−4.92658	+	11.8938i	−0.170288	+	0.411111i
$838$	−0.434306	−	0.0900683i	−0.0150029	−	0.00311136i
$839$	−11.8794	−	11.8794i	−0.410122	−	0.410122i	0.471659	−	0.881781i	$-0.343655\pi$
$839$	−11.8794	−	11.8794i	−0.410122	−	0.410122i	−0.881781	+	0.471659i	$0.843655\pi$
$840$	−5.20163	−	8.21182i	−0.179473	−	0.283335i
$841$	−11.0447	+	11.0447i	−0.380851	+	0.380851i
$842$	31.8342	−	20.8983i	1.09708	−	0.720202i
$843$	10.9919	+	4.55299i	0.378580	+	0.156813i
$844$	18.6323	−	18.0355i	0.641349	−	0.620809i
$845$	−11.7353	−	28.3314i	−0.403705	−	0.974630i
$846$	3.30815	+	17.3686i	0.113737	+	0.597144i
$847$			5.71908i			0.196510i
$848$	−33.6723	+	12.6803i	−1.15631	+	0.435442i
$849$			8.06570i			0.276814i
$850$	3.96212	−	0.754657i	0.135900	−	0.0258845i
$851$	21.1191	+	50.9861i	0.723954	+	1.74778i
$852$	0.638826	−	39.2546i	0.0218858	−	1.34484i
$853$	−4.28076	−	1.77315i	−0.146571	−	0.0607115i	0.308192	−	0.951324i	$-0.400276\pi$
$853$	−4.28076	−	1.77315i	−0.146571	−	0.0607115i	−0.454763	+	0.890613i	$0.650276\pi$
$854$	−7.13875	−	10.8744i	−0.244283	−	0.372114i
$855$	2.08517	−	2.08517i	0.0713113	−	0.0713113i
$856$	2.62714	−	3.73132i	0.0897938	−	0.127534i
$857$	28.4535	+	28.4535i	0.971953	+	0.971953i	0.999617	−	0.0276642i	$-0.00880693\pi$
$857$	28.4535	+	28.4535i	0.971953	+	0.971953i	−0.0276642	+	0.999617i	$0.508807\pi$
$858$	−0.646021	+	3.11509i	−0.0220548	+	0.106347i
$859$	−14.8162	+	35.7694i	−0.505521	+	1.22044i	0.440916	+	0.897548i	$0.354654\pi$
$859$	−14.8162	+	35.7694i	−0.505521	+	1.22044i	−0.946437	+	0.322888i	$0.895346\pi$
$860$	−32.2762	−	13.9888i	−1.10061	−	0.477014i
$861$	−0.769023	+	0.318540i	−0.0262082	+	0.0108558i
$862$	13.3795	−	19.6754i	0.455709	−	0.670148i
$863$	−6.82864			−0.232450			−0.116225	−	0.993223i	$-0.537079\pi$
$863$	−6.82864			−0.232450			−0.116225	+	0.993223i	$0.537079\pi$
$864$	7.51336	−	31.1020i	0.255610	−	1.05811i
$865$	−28.1210			−0.956143
$866$	17.2742	−	25.4028i	0.587002	−	0.863222i
$867$	11.6171	−	4.81197i	0.394538	−	0.163423i
$868$	1.81020	−	4.17664i	0.0614420	−	0.141765i
$869$	3.23500	−	7.80999i	0.109740	−	0.264936i
$870$	3.61022	−	17.4083i	0.122398	−	0.590198i
$871$	−2.18352	−	2.18352i	−0.0739858	−	0.0739858i
$872$	−48.5822	+	8.43657i	−1.64520	+	0.285698i
$873$	−10.8855	+	10.8855i	−0.368417	+	0.368417i
$874$	5.31122	+	8.09053i	0.179655	+	0.273666i
$875$	−9.04270	−	3.74561i	−0.305699	−	0.126625i
$876$	5.46698	+	0.0889693i	0.184712	+	0.00300599i
$877$	12.0741	+	29.1495i	0.407714	+	0.984308i	0.985738	+	0.168288i	$0.0538240\pi$
$877$	12.0741	+	29.1495i	0.407714	+	0.984308i	−0.578024	+	0.816020i	$0.696176\pi$
$878$	−28.1228	+	5.35649i	−0.949100	+	0.180773i
$879$			26.8188i			0.904577i
$880$	0.733034	−	22.5157i	0.0247106	−	0.759006i
$881$		−	8.77861i		−	0.295759i	−0.989005	−	0.147880i	$-0.952755\pi$
$881$		−	8.77861i		−	0.295759i	0.989005	−	0.147880i	$-0.0472448\pi$
$882$	−0.273465	−	1.43576i	−0.00920805	−	0.0483444i
$883$	−14.9807	−	36.1666i	−0.504140	−	1.21710i	−0.947210	−	0.320614i	$-0.896111\pi$
$883$	−14.9807	−	36.1666i	−0.504140	−	1.21710i	0.443070	−	0.896487i	$-0.353889\pi$
$884$	2.75216	+	2.84322i	0.0925652	+	0.0956278i
$885$	27.9305	+	11.5692i	0.938873	+	0.388894i
$886$	13.2898	−	8.72440i	0.446480	−	0.293102i
$887$	−36.9463	+	36.9463i	−1.24054	+	1.24054i	−0.280757	+	0.959779i	$0.590585\pi$
$887$	−36.9463	+	36.9463i	−1.24054	+	1.24054i	−0.959779	+	0.280757i	$0.909415\pi$
$888$	36.3359	+	8.15435i	1.21935	+	0.273642i
$889$	−0.935786	−	0.935786i	−0.0313853	−	0.0313853i
$890$	−55.1115	−	11.4293i	−1.84734	−	0.383110i
$891$	4.24886	−	10.2577i	0.142342	−	0.343644i
$892$	−7.07784	−	17.9061i	−0.236984	−	0.599541i
$893$	−13.0122	+	5.38982i	−0.435436	+	0.180363i
$894$	−31.9798	−	21.7467i	−1.06957	−	0.727318i
$895$	40.5507			1.35546
$896$	−2.83525	+	10.9527i	−0.0947191	+	0.365904i
$897$	5.75399			0.192120
$898$	−34.1230	−	23.2040i	−1.13870	−	0.774328i
$899$	7.69180	−	3.18605i	0.256536	−	0.106261i
$900$	0.764565	+	1.93426i	0.0254855	+	0.0644753i
$901$	−9.75654	+	23.5544i	−0.325037	+	0.784710i
$902$	−1.88887	−	0.391721i	−0.0628923	−	0.0130429i
$903$	7.11646	+	7.11646i	0.236821	+	0.236821i
$904$	−52.4008	−	11.7596i	−1.74283	−	0.391117i
$905$	−33.9883	+	33.9883i	−1.12981	+	1.12981i
$906$	−21.6388	+	14.2053i	−0.718900	+	0.471938i
$907$	18.1974	+	7.53762i	0.604235	+	0.250283i	0.663762	−	0.747944i	$-0.268959\pi$
$907$	18.1974	+	7.53762i	0.604235	+	0.250283i	−0.0595261	+	0.998227i	$0.518959\pi$
$908$	11.4860	+	11.8660i	0.381176	+	0.393788i
$909$	−2.93388	−	7.08300i	−0.0973105	−	0.234928i
$910$	0.452685	+	2.37670i	0.0150064	+	0.0787869i
$911$		−	57.0276i		−	1.88941i	−0.327925	−	0.944704i	$-0.606349\pi$
$911$		−	57.0276i		−	1.88941i	0.327925	−	0.944704i	$-0.393651\pi$
$912$	6.52724	+	0.212504i	0.216138	+	0.00703671i
$913$		−	14.0533i		−	0.465095i
$914$	−3.94897	+	0.752152i	−0.130620	+	0.0248790i
$915$	−12.0974	−	29.2058i	−0.399929	−	0.965515i
$916$	13.3828	+	0.217791i	0.442180	+	0.00719600i
$917$	−3.10303	−	1.28532i	−0.102471	−	0.0424449i
$918$	−12.4421	−	18.9529i	−0.410651	−	0.625540i
$919$	31.2648	−	31.2648i	1.03133	−	1.03133i	0.0318377	−	0.999493i	$-0.489864\pi$
$919$	31.2648	−	31.2648i	1.03133	−	1.03133i	0.999493	−	0.0318377i	$-0.0101360\pi$
$920$	−40.1439	+	6.97121i	−1.32351	+	0.229834i
$921$	−8.57334	−	8.57334i	−0.282501	−	0.282501i
$922$	−3.78125	+	18.2331i	−0.124529	+	0.600474i
$923$	−3.73942	+	9.02777i	−0.123085	+	0.297153i
$924$	−2.56302	+	5.91363i	−0.0843171	+	0.194544i
$925$	−8.72835	+	3.61540i	−0.286986	+	0.118874i
$926$	−22.9920	+	33.8112i	−0.755565	+	1.11111i
$927$	−11.8888			−0.390478
$928$	−17.6584	+	10.7868i	−0.579666	+	0.354095i
$929$	−44.2482			−1.45174			−0.725868	−	0.687834i	$-0.758562\pi$
$929$	−44.2482			−1.45174			−0.725868	+	0.687834i	$0.758562\pi$
$930$	6.22047	−	9.14759i	0.203977	−	0.299961i
$931$	1.07564	−	0.445544i	0.0352526	−	0.0146021i
$932$	−55.3179	−	23.9753i	−1.81200	−	0.785336i
$933$	6.28314	−	15.1688i	0.205701	−	0.496606i
$934$	5.28023	−	25.4611i	0.172774	−	0.833111i
$935$	−11.2872	−	11.2872i	−0.369132	−	0.369132i
$936$	−1.17473	+	1.66847i	−0.0383974	+	0.0545357i
$937$	29.9652	−	29.9652i	0.978921	−	0.978921i	−0.0208609	−	0.999782i	$-0.506641\pi$
$937$	29.9652	−	29.9652i	0.978921	−	0.978921i	0.999782	+	0.0208609i	$0.00664071\pi$
$938$	−3.43317	−	5.22972i	−0.112097	−	0.170756i
$939$	42.4227	+	17.5720i	1.38441	+	0.573442i
$940$	0.964829	−	59.2868i	0.0314692	−	1.93372i
$941$	4.37900	+	10.5718i	0.142751	+	0.344632i	0.979043	−	0.203652i	$-0.0652812\pi$
$941$	4.37900	+	10.5718i	0.142751	+	0.344632i	−0.836292	+	0.548284i	$0.815281\pi$
$942$	−2.11480	+	0.402801i	−0.0689039	+	0.0131240i
$943$			3.48899i			0.113617i
$944$	−12.4003	−	32.9288i	−0.403594	−	1.07174i
$945$		−	13.8622i		−	0.450936i
$946$	4.36398	+	22.9119i	0.141885	+	0.744931i
$947$	−3.08144	−	7.43925i	−0.100133	−	0.241743i	0.865872	−	0.500266i	$-0.166764\pi$
$947$	−3.08144	−	7.43925i	−0.100133	−	0.241743i	−0.966005	+	0.258523i	$0.916764\pi$
$948$	−7.41306	+	7.17564i	−0.240765	+	0.233054i
$949$	−1.25730	−	0.520789i	−0.0408136	−	0.0169055i
$950$	−1.38503	+	0.909232i	−0.0449361	+	0.0294994i
$951$	3.64099	−	3.64099i	0.118067	−	0.118067i
$952$	4.28978	+	6.77229i	0.139033	+	0.219491i
$953$	24.0353	+	24.0353i	0.778579	+	0.778579i	0.979589	−	0.201010i	$-0.0644223\pi$
$953$	24.0353	+	24.0353i	0.778579	+	0.778579i	−0.201010	+	0.979589i	$0.564422\pi$
$954$	−12.8732	−	2.66969i	−0.416784	−	0.0864345i
$955$	−1.29665	+	3.13040i	−0.0419587	+	0.101297i
$956$	−8.48133	+	3.35246i	−0.274306	+	0.108426i
$957$	−10.8907	+	4.51106i	−0.352045	+	0.145822i
$958$	−8.04432	−	5.47023i	−0.259900	−	0.176735i
$959$	6.12565			0.197808
$960$	−11.7486	+	24.8576i	−0.379183	+	0.802275i
$961$	−25.8197			−0.832894
$962$	−7.66456	−	5.21199i	−0.247115	−	0.168041i
$963$	1.54051	−	0.638098i	0.0496421	−	0.0205624i
$964$	17.2379	−	6.81373i	0.555197	−	0.219455i
$965$	−8.27698	+	19.9824i	−0.266445	+	0.643256i
$966$	11.4142	+	2.36712i	0.367245	+	0.0761609i
$967$	5.87633	+	5.87633i	0.188970	+	0.188970i	0.795251	−	0.606281i	$-0.207339\pi$
$967$	5.87633	+	5.87633i	0.188970	+	0.188970i	−0.606281	+	0.795251i	$0.707339\pi$
$968$	13.6652	−	8.65597i	0.439216	−	0.278213i
$969$	3.27213	−	3.27213i	0.105116	−	0.105116i
$970$	43.1580	−	28.3321i	1.38572	−	0.909689i
$971$	25.6554	+	10.6268i	0.823320	+	0.341030i	0.754255	−	0.656582i	$-0.227998\pi$
$971$	25.6554	+	10.6268i	0.823320	+	0.341030i	0.0690654	+	0.997612i	$0.477998\pi$
$972$	14.6484	−	14.1793i	0.469849	−	0.454801i
$973$	−8.63808	−	20.8542i	−0.276924	−	0.668554i
$974$	−5.03957	−	26.4589i	−0.161478	−	0.847798i
$975$			0.985031i			0.0315462i
$976$	−15.1786	+	33.5160i	−0.485857	+	1.07282i
$977$			42.1569i			1.34872i	0.738403	+	0.674360i	$0.235580\pi$
$977$			42.1569i			1.34872i	−0.738403	+	0.674360i	$0.764420\pi$
$978$	19.4648	−	3.70742i	0.622417	−	0.118550i
$979$	14.2812	+	34.4778i	0.456428	+	1.10191i
$980$	−0.0797566	+	4.90088i	−0.00254773	+	0.156553i
$981$	−16.6457	−	6.89489i	−0.531458	−	0.220137i
$982$	20.5341	+	31.2793i	0.655268	+	0.998164i
$983$	−4.54892	+	4.54892i	−0.145088	+	0.145088i	−0.775920	−	0.630832i	$-0.782714\pi$
$983$	−4.54892	+	4.54892i	−0.145088	+	0.145088i	0.630832	+	0.775920i	$0.282714\pi$
$984$	1.92505	+	1.35539i	0.0613685	+	0.0432082i
$985$	29.5260	+	29.5260i	0.940778	+	0.940778i
$986$	−2.97734	+	14.3566i	−0.0948179	+	0.457209i
$987$	−6.49190	+	15.6728i	−0.206640	+	0.498872i
$988$	−1.49141	−	0.646391i	−0.0474481	−	0.0205644i
$989$	38.9736	−	16.1434i	1.23929	−	0.513329i
$990$	4.62867	−	6.80675i	0.147109	−	0.216333i
$991$	−7.21662			−0.229243			−0.114622	−	0.993409i	$-0.536566\pi$
$991$	−7.21662			−0.229243			−0.114622	+	0.993409i	$0.536566\pi$
$992$	−12.7195	+	1.99617i	−0.403843	+	0.0633784i
$993$	−17.2843			−0.548502
$994$	−11.1318	+	16.3700i	−0.353079	+	0.519225i
$995$	4.18034	−	1.73155i	0.132526	−	0.0548940i
$996$	−6.82055	+	15.7370i	−0.216117	+	0.498645i
$997$	14.6891	−	35.4626i	0.465208	−	1.12311i	−0.501024	−	0.865434i	$-0.667043\pi$
$997$	14.6891	−	35.4626i	0.465208	−	1.12311i	0.966231	−	0.257677i	$-0.0829570\pi$
$998$	0.487966	−	2.35296i	0.0154463	−	0.0744815i
$999$	37.5514	+	37.5514i	1.18807	+	1.18807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.u.b.85.8	yes	40
4.3	odd	2		896.2.u.b.561.4		40
32.3	odd	8		896.2.u.b.337.4		40
32.29	even	8	inner	224.2.u.b.29.8	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.b.29.8	✓	40	32.29	even	8	inner
224.2.u.b.85.8	yes	40	1.1	even	1	trivial
896.2.u.b.337.4		40	32.3	odd	8
896.2.u.b.561.4		40	4.3	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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16944 + 0.795236i) q^{2} +(1.29558 - 0.536647i) q^{3} +(0.735199 + 1.85997i) q^{4} +(0.937867 - 2.26421i) q^{5} +(1.94187 + 0.402713i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.619339 + 2.75979i) q^{8} +(-0.730784 + 0.730784i) q^{9} +O(q^{10})\)	\(q+(1.16944 + 0.795236i) q^{2} +(1.29558 - 0.536647i) q^{3} +(0.735199 + 1.85997i) q^{4} +(0.937867 - 2.26421i) q^{5} +(1.94187 + 0.402713i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.619339 + 2.75979i) q^{8} +(-0.730784 + 0.730784i) q^{9} +(2.89737 - 1.90204i) q^{10} +(-2.12310 - 0.879416i) q^{11} +(1.95065 + 2.01519i) q^{12} +(-0.267138 - 0.644928i) q^{13} +(-0.264605 - 1.38924i) q^{14} -3.43677i q^{15} +(-2.91896 + 2.73489i) q^{16} +2.83430i q^{17} +(-1.43576 + 0.273465i) q^{18} +(-0.445544 - 1.07564i) q^{19} +(4.90088 + 0.0797566i) q^{20} +(-1.29558 - 0.536647i) q^{21} +(-1.78350 - 2.71679i) q^{22} +(-4.15632 + 4.15632i) q^{23} +(0.678626 + 3.90789i) q^{24} +(-0.711525 - 0.711525i) q^{25} +(0.200467 - 0.966645i) q^{26} +(-2.16456 + 5.22570i) q^{27} +(0.795332 - 1.83506i) q^{28} +(3.37949 - 1.39983i) q^{29} +(2.73304 - 4.01911i) q^{30} +2.27603 q^{31} +(-5.58845 + 0.877041i) q^{32} -3.22258 q^{33} +(-2.25394 + 3.31456i) q^{34} +(-2.26421 + 0.937867i) q^{35} +(-1.89651 - 0.821963i) q^{36} +(3.59295 - 8.67415i) q^{37} +(0.334347 - 1.61221i) q^{38} +(-0.692197 - 0.692197i) q^{39} +(5.66788 + 3.99063i) q^{40} +(0.419720 - 0.419720i) q^{41} +(-1.08835 - 1.65787i) q^{42} +(-6.63049 - 2.74644i) q^{43} +(0.0747859 - 4.59544i) q^{44} +(0.969271 + 2.34003i) q^{45} +(-8.16585 + 1.55533i) q^{46} -12.0972i q^{47} +(-2.31408 + 5.10972i) q^{48} +1.00000i q^{49} +(-0.266258 - 1.39792i) q^{50} +(1.52102 + 3.67206i) q^{51} +(1.00315 - 0.971019i) q^{52} +(8.31047 + 3.44231i) q^{53} +(-6.68699 + 4.38983i) q^{54} +(-3.98237 + 3.98237i) q^{55} +(2.38940 - 1.51352i) q^{56} +(-1.15447 - 1.15447i) q^{57} +(5.06532 + 1.05047i) q^{58} +(-3.36630 + 8.12696i) q^{59} +(6.39228 - 2.52671i) q^{60} +(8.49805 - 3.52001i) q^{61} +(2.66168 + 1.80998i) q^{62} +1.03348 q^{63} +(-7.23284 - 3.41849i) q^{64} -1.71079 q^{65} +(-3.76862 - 2.56271i) q^{66} +(4.08688 - 1.69284i) q^{67} +(-5.27171 + 2.08378i) q^{68} +(-3.15437 + 7.61533i) q^{69} +(-3.39369 - 0.703799i) q^{70} +(-9.89815 - 9.89815i) q^{71} +(-1.56420 - 2.46941i) q^{72} +(1.37852 - 1.37852i) q^{73} +(11.0998 - 7.28669i) q^{74} +(-1.30367 - 0.540000i) q^{75} +(1.67309 - 1.61951i) q^{76} +(0.879416 + 2.12310i) q^{77} +(-0.259026 - 1.35995i) q^{78} +3.67858i q^{79} +(3.45478 + 9.17412i) q^{80} +4.83146i q^{81} +(0.824617 - 0.157063i) q^{82} +(2.34025 + 5.64986i) q^{83} +(0.0456366 - 2.80428i) q^{84} +(6.41746 + 2.65820i) q^{85} +(-5.56992 - 8.48461i) q^{86} +(3.62718 - 3.62718i) q^{87} +(3.74192 - 5.31464i) q^{88} +(-11.4830 - 11.4830i) q^{89} +(-0.727366 + 3.50733i) q^{90} +(-0.267138 + 0.644928i) q^{91} +(-10.7864 - 4.67491i) q^{92} +(2.94877 - 1.22142i) q^{93} +(9.62010 - 14.1470i) q^{94} -2.85333 q^{95} +(-6.76962 + 4.13530i) q^{96} +14.8956 q^{97} +(-0.795236 + 1.16944i) q^{98} +(2.19419 - 0.908863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} + 4 q^{3} + 8 q^{5} + 12 q^{6} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 40 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 + 12 * q^6 - 8 * q^8 + 8 * q^9	\( 40 q + 4 q^{2} + 4 q^{3} + 8 q^{5} + 12 q^{6} - 8 q^{8} + 8 q^{9} - 16 q^{10} + 12 q^{11} - 36 q^{12} + 8 q^{16} + 4 q^{19} - 4 q^{21} - 52 q^{22} + 16 q^{23} - 8 q^{24} - 16 q^{25} + 12 q^{26} - 32 q^{27} + 8 q^{28} + 16 q^{29} + 36 q^{30} + 24 q^{31} - 36 q^{32} + 8 q^{33} - 8 q^{34} - 8 q^{36} + 16 q^{37} - 12 q^{38} - 24 q^{39} + 36 q^{40} + 8 q^{41} + 52 q^{43} - 44 q^{44} - 64 q^{45} - 32 q^{46} - 36 q^{48} + 52 q^{50} + 16 q^{51} - 16 q^{52} - 32 q^{54} - 8 q^{55} + 12 q^{56} - 8 q^{57} + 40 q^{58} + 20 q^{59} + 52 q^{60} - 16 q^{61} - 12 q^{62} - 24 q^{63} - 48 q^{64} - 80 q^{65} - 40 q^{66} - 4 q^{67} - 4 q^{68} - 40 q^{69} + 32 q^{70} + 72 q^{72} - 24 q^{73} - 12 q^{74} + 20 q^{75} - 72 q^{76} + 4 q^{77} + 12 q^{78} + 60 q^{80} + 16 q^{82} + 4 q^{83} + 8 q^{84} - 64 q^{85} - 48 q^{86} - 32 q^{87} + 16 q^{88} + 32 q^{89} + 20 q^{90} + 108 q^{92} - 24 q^{93} + 68 q^{94} - 80 q^{95} - 40 q^{96} + 56 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 + 12 * q^6 - 8 * q^8 + 8 * q^9 - 16 * q^10 + 12 * q^11 - 36 * q^12 + 8 * q^16 + 4 * q^19 - 4 * q^21 - 52 * q^22 + 16 * q^23 - 8 * q^24 - 16 * q^25 + 12 * q^26 - 32 * q^27 + 8 * q^28 + 16 * q^29 + 36 * q^30 + 24 * q^31 - 36 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^36 + 16 * q^37 - 12 * q^38 - 24 * q^39 + 36 * q^40 + 8 * q^41 + 52 * q^43 - 44 * q^44 - 64 * q^45 - 32 * q^46 - 36 * q^48 + 52 * q^50 + 16 * q^51 - 16 * q^52 - 32 * q^54 - 8 * q^55 + 12 * q^56 - 8 * q^57 + 40 * q^58 + 20 * q^59 + 52 * q^60 - 16 * q^61 - 12 * q^62 - 24 * q^63 - 48 * q^64 - 80 * q^65 - 40 * q^66 - 4 * q^67 - 4 * q^68 - 40 * q^69 + 32 * q^70 + 72 * q^72 - 24 * q^73 - 12 * q^74 + 20 * q^75 - 72 * q^76 + 4 * q^77 + 12 * q^78 + 60 * q^80 + 16 * q^82 + 4 * q^83 + 8 * q^84 - 64 * q^85 - 48 * q^86 - 32 * q^87 + 16 * q^88 + 32 * q^89 + 20 * q^90 + 108 * q^92 - 24 * q^93 + 68 * q^94 - 80 * q^95 - 40 * q^96 + 56 * q^97 + 4 * q^98 - 60 * q^99

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