LMFDB - Embedded newform 525.2.n.b.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.n (of order $5$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 31 x^{18} - 74 x^{17} + 109 x^{16} - 72 x^{15} - 51 x^{14} + 9 x^{13} + 866 x^{12} + \cdots + 3125 $ x^20 - 8x^19 + 31x^18 - 74x^17 + 109x^16 - 72x^15 - 51x^14 + 9x^13 + 866x^12 - 3240x^11 + 6385x^10 - 6775x^9 + 330x^8 + 11325x^7 - 18525x^6 + 12000x^5 + 5875x^4 - 21250x^3 + 22500x^2 - 12500*x + 3125
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.1
Root			$1.14677 - 0.258633i$ of defining polynomial
Character	$\chi$	$=$	525.421
Dual form			525.2.n.b.106.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.724838 + 2.23082i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-2.83314 - 2.05840i) q^{4} +(0.884129 - 2.05385i) q^{5} +(-1.89765 + 1.37872i) q^{6} -1.00000 q^{7} +(2.85019 - 2.07078i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.724838 + 2.23082i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-2.83314 - 2.05840i) q^{4} +(0.884129 - 2.05385i) q^{5} +(-1.89765 + 1.37872i) q^{6} -1.00000 q^{7} +(2.85019 - 2.07078i) q^{8} +(0.309017 + 0.951057i) q^{9} +(3.94093 + 3.46105i) q^{10} +(-0.733310 + 2.25690i) q^{11} +(-1.08216 - 3.33056i) q^{12} +(2.06160 + 6.34497i) q^{13} +(0.724838 - 2.23082i) q^{14} +(1.92250 - 1.14192i) q^{15} +(0.389294 + 1.19812i) q^{16} +(-5.57125 + 4.04775i) q^{17} -2.34562 q^{18} +(0.145282 - 0.105554i) q^{19} +(-6.73251 + 3.99897i) q^{20} +(-0.809017 - 0.587785i) q^{21} +(-4.50320 - 3.27177i) q^{22} +(-2.19964 + 6.76981i) q^{23} +3.52302 q^{24} +(-3.43663 - 3.63174i) q^{25} -15.6488 q^{26} +(-0.309017 + 0.951057i) q^{27} +(2.83314 + 2.05840i) q^{28} +(2.78482 + 2.02329i) q^{29} +(1.15393 + 5.11647i) q^{30} +(2.34858 - 1.70635i) q^{31} +4.09107 q^{32} +(-1.91983 + 1.39484i) q^{33} +(-4.99156 - 15.3624i) q^{34} +(-0.884129 + 2.05385i) q^{35} +(1.08216 - 3.33056i) q^{36} +(0.00316176 + 0.00973088i) q^{37} +(0.130166 + 0.400608i) q^{38} +(-2.06160 + 6.34497i) q^{39} +(-1.73315 - 7.68470i) q^{40} +(2.49666 + 7.68393i) q^{41} +(1.89765 - 1.37872i) q^{42} +8.29474 q^{43} +(6.72316 - 4.88466i) q^{44} +(2.22654 + 0.206181i) q^{45} +(-13.5078 - 9.81403i) q^{46} +(-1.46115 - 1.06159i) q^{47} +(-0.389294 + 1.19812i) q^{48} +1.00000 q^{49} +(10.5928 - 5.03408i) q^{50} -6.88645 q^{51} +(7.21965 - 22.2198i) q^{52} +(0.764121 + 0.555166i) q^{53} +(-1.89765 - 1.37872i) q^{54} +(3.98699 + 3.50150i) q^{55} +(-2.85019 + 2.07078i) q^{56} +0.179579 q^{57} +(-6.53215 + 4.74588i) q^{58} +(-3.67251 - 11.3028i) q^{59} +(-7.79725 - 0.722038i) q^{60} +(0.945379 - 2.90958i) q^{61} +(2.10421 + 6.47609i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(-3.74395 + 11.5227i) q^{64} +(14.8544 + 1.37554i) q^{65} +(-1.72007 - 5.29383i) q^{66} +(9.67145 - 7.02672i) q^{67} +24.1160 q^{68} +(-5.75874 + 4.18397i) q^{69} +(-3.94093 - 3.46105i) q^{70} +(-3.55634 - 2.58383i) q^{71} +(2.85019 + 2.07078i) q^{72} +(2.51112 - 7.72843i) q^{73} -0.0239996 q^{74} +(-0.645607 - 4.95814i) q^{75} -0.628877 q^{76} +(0.733310 - 2.25690i) q^{77} +(-12.6602 - 9.19814i) q^{78} +(-1.52385 - 1.10714i) q^{79} +(2.80496 + 0.259743i) q^{80} +(-0.809017 + 0.587785i) q^{81} -18.9512 q^{82} +(10.4788 - 7.61326i) q^{83} +(1.08216 + 3.33056i) q^{84} +(3.38778 + 15.0213i) q^{85} +(-6.01234 + 18.5041i) q^{86} +(1.06371 + 3.27375i) q^{87} +(2.58347 + 7.95110i) q^{88} +(-3.58739 + 11.0409i) q^{89} +(-2.07384 + 4.81757i) q^{90} +(-2.06160 - 6.34497i) q^{91} +(20.1669 - 14.6521i) q^{92} +2.90301 q^{93} +(3.42732 - 2.49009i) q^{94} +(-0.0883437 - 0.391712i) q^{95} +(3.30975 + 2.40467i) q^{96} +(-8.48646 - 6.16577i) q^{97} +(-0.724838 + 2.23082i) q^{98} -2.37304 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9	\( 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9} - 15 q^{10} + 12 q^{11} + 5 q^{12} - 17 q^{13} + 2 q^{14} + 15 q^{15} - 28 q^{16} - 9 q^{17} - 2 q^{18} - 9 q^{19} - 20 q^{20} - 5 q^{21} - 21 q^{22} + 7 q^{23} + 6 q^{24} - 15 q^{25} - 20 q^{26} + 5 q^{27} + 28 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{33} - 5 q^{35} - 5 q^{36} - 5 q^{37} - 6 q^{38} + 17 q^{39} - 10 q^{40} + 11 q^{41} + 3 q^{42} + 28 q^{43} - 17 q^{44} + 5 q^{45} - 43 q^{46} - 24 q^{47} + 28 q^{48} + 20 q^{49} + 10 q^{50} - 36 q^{51} - 9 q^{52} - 26 q^{53} - 3 q^{54} - 25 q^{55} - 4 q^{56} + 24 q^{57} - 16 q^{58} + 64 q^{59} + 5 q^{60} + 8 q^{61} + 27 q^{62} + 5 q^{63} + 26 q^{64} + 25 q^{65} - 4 q^{66} - 3 q^{67} + 80 q^{68} - 2 q^{69} + 15 q^{70} + 19 q^{71} + 4 q^{72} + 31 q^{73} + 8 q^{74} - 5 q^{75} - 72 q^{76} - 12 q^{77} - 30 q^{78} + 43 q^{79} - 25 q^{80} - 5 q^{81} - 6 q^{82} + 32 q^{83} - 5 q^{84} + 35 q^{85} + 53 q^{86} + 17 q^{87} - 61 q^{88} - 47 q^{89} + 10 q^{90} + 17 q^{91} + 41 q^{92} + 4 q^{93} + 12 q^{94} - 40 q^{95} - 6 q^{96} - 45 q^{97} - 2 q^{98} - 18 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9 - 15 * q^10 + 12 * q^11 + 5 * q^12 - 17 * q^13 + 2 * q^14 + 15 * q^15 - 28 * q^16 - 9 * q^17 - 2 * q^18 - 9 * q^19 - 20 * q^20 - 5 * q^21 - 21 * q^22 + 7 * q^23 + 6 * q^24 - 15 * q^25 - 20 * q^26 + 5 * q^27 + 28 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^33 - 5 * q^35 - 5 * q^36 - 5 * q^37 - 6 * q^38 + 17 * q^39 - 10 * q^40 + 11 * q^41 + 3 * q^42 + 28 * q^43 - 17 * q^44 + 5 * q^45 - 43 * q^46 - 24 * q^47 + 28 * q^48 + 20 * q^49 + 10 * q^50 - 36 * q^51 - 9 * q^52 - 26 * q^53 - 3 * q^54 - 25 * q^55 - 4 * q^56 + 24 * q^57 - 16 * q^58 + 64 * q^59 + 5 * q^60 + 8 * q^61 + 27 * q^62 + 5 * q^63 + 26 * q^64 + 25 * q^65 - 4 * q^66 - 3 * q^67 + 80 * q^68 - 2 * q^69 + 15 * q^70 + 19 * q^71 + 4 * q^72 + 31 * q^73 + 8 * q^74 - 5 * q^75 - 72 * q^76 - 12 * q^77 - 30 * q^78 + 43 * q^79 - 25 * q^80 - 5 * q^81 - 6 * q^82 + 32 * q^83 - 5 * q^84 + 35 * q^85 + 53 * q^86 + 17 * q^87 - 61 * q^88 - 47 * q^89 + 10 * q^90 + 17 * q^91 + 41 * q^92 + 4 * q^93 + 12 * q^94 - 40 * q^95 - 6 * q^96 - 45 * q^97 - 2 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.724838	+	2.23082i	−0.512538	+	1.57743i	0.275180	+	0.961393i	$0.411263\pi$
$2$	−0.724838	+	2.23082i	−0.512538	+	1.57743i	−0.787718	+	0.616036i	$0.788737\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	−2.83314	−	2.05840i	−1.41657	−	1.02920i
$5$	0.884129	−	2.05385i	0.395395	−	0.918511i
$5$	0.884129	−	2.05385i	0.395395	−	0.918511i
$6$	−1.89765	+	1.37872i	−0.774712	+	0.562862i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	2.85019	−	2.07078i	1.00769	−	0.732132i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	3.94093	+	3.46105i	1.24623	+	1.09448i
$11$	−0.733310	+	2.25690i	−0.221101	+	0.680480i	0.777563	+	0.628805i	$0.216456\pi$
$11$	−0.733310	+	2.25690i	−0.221101	+	0.680480i	−0.998664	+	0.0516743i	$0.983544\pi$
$12$	−1.08216	−	3.33056i	−0.312394	−	0.961449i
$13$	2.06160	+	6.34497i	0.571786	+	1.75978i	0.646871	+	0.762600i	$0.276077\pi$
$13$	2.06160	+	6.34497i	0.571786	+	1.75978i	−0.0750847	+	0.997177i	$0.523923\pi$
$14$	0.724838	−	2.23082i	0.193721	−	0.596212i
$15$	1.92250	−	1.14192i	0.496388	−	0.294844i
$16$	0.389294	+	1.19812i	0.0973235	+	0.299531i
$17$	−5.57125	+	4.04775i	−1.35123	+	0.981724i	−0.352278	+	0.935895i	$0.614593\pi$
$17$	−5.57125	+	4.04775i	−1.35123	+	0.981724i	−0.998949	+	0.0458288i	$0.985407\pi$
$18$	−2.34562			−0.552869
$19$	0.145282	−	0.105554i	0.0333301	−	0.0242157i	−0.570996	−	0.820953i	$-0.693443\pi$
$19$	0.145282	−	0.105554i	0.0333301	−	0.0242157i	0.604326	+	0.796737i	$0.293443\pi$
$20$	−6.73251	+	3.99897i	−1.50544	+	0.894197i
$21$	−0.809017	−	0.587785i	−0.176542	−	0.128265i
$22$	−4.50320	−	3.27177i	−0.960086	−	0.697543i
$23$	−2.19964	+	6.76981i	−0.458657	+	1.41160i	0.408130	+	0.912924i	$0.366181\pi$
$23$	−2.19964	+	6.76981i	−0.458657	+	1.41160i	−0.866787	+	0.498679i	$0.833819\pi$
$24$	3.52302			0.719134
$25$	−3.43663	−	3.63174i	−0.687326	−	0.726349i
$26$	−15.6488			−3.06899
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	2.83314	+	2.05840i	0.535413	+	0.389001i
$29$	2.78482	+	2.02329i	0.517128	+	0.375716i	0.815521	−	0.578727i	$-0.196450\pi$
$29$	2.78482	+	2.02329i	0.517128	+	0.375716i	−0.298393	+	0.954443i	$0.596450\pi$
$30$	1.15393	+	5.11647i	0.210678	+	0.934135i
$31$	2.34858	−	1.70635i	0.421818	−	0.306469i	−0.356551	−	0.934276i	$-0.616047\pi$
$31$	2.34858	−	1.70635i	0.421818	−	0.306469i	0.778369	+	0.627807i	$0.216047\pi$
$32$	4.09107			0.723206
$33$	−1.91983	+	1.39484i	−0.334200	+	0.242810i
$34$	−4.99156	−	15.3624i	−0.856045	−	2.63464i
$35$	−0.884129	+	2.05385i	−0.149445	+	0.347165i
$36$	1.08216	−	3.33056i	0.180361	−	0.555093i
$37$	0.00316176	+	0.00973088i	0.000519789	+	0.00159975i	0.951316	−	0.308217i	$-0.0997323\pi$
$37$	0.00316176	+	0.00973088i	0.000519789	+	0.00159975i	−0.950796	+	0.309817i	$0.899732\pi$
$38$	0.130166	+	0.400608i	0.0211156	+	0.0649873i
$39$	−2.06160	+	6.34497i	−0.330121	+	1.01601i
$40$	−1.73315	−	7.68470i	−0.274035	−	1.21506i
$41$	2.49666	+	7.68393i	0.389913	+	1.20003i	0.932853	+	0.360257i	$0.117311\pi$
$41$	2.49666	+	7.68393i	0.389913	+	1.20003i	−0.542940	+	0.839771i	$0.682689\pi$
$42$	1.89765	−	1.37872i	0.292814	−	0.212742i
$43$	8.29474			1.26494			0.632468	−	0.774586i	$-0.282042\pi$
$43$	8.29474			1.26494			0.632468	+	0.774586i	$0.282042\pi$
$44$	6.72316	−	4.88466i	1.01355	−	0.736390i
$45$	2.22654	+	0.206181i	0.331913	+	0.0307357i
$46$	−13.5078	−	9.81403i	−1.99162	−	1.44700i
$47$	−1.46115	−	1.06159i	−0.213131	−	0.154849i	0.476098	−	0.879392i	$-0.342051\pi$
$47$	−1.46115	−	1.06159i	−0.213131	−	0.154849i	−0.689229	+	0.724543i	$0.742051\pi$
$48$	−0.389294	+	1.19812i	−0.0561897	+	0.172934i
$49$	1.00000			0.142857
$50$	10.5928	−	5.03408i	1.49804	−	0.711927i
$51$	−6.88645			−0.964296
$52$	7.21965	−	22.2198i	1.00118	−	3.08133i
$53$	0.764121	+	0.555166i	0.104960	+	0.0762580i	0.639027	−	0.769184i	$-0.279337\pi$
$53$	0.764121	+	0.555166i	0.104960	+	0.0762580i	−0.534067	+	0.845442i	$0.679337\pi$
$54$	−1.89765	−	1.37872i	−0.258237	−	0.187621i
$55$	3.98699	+	3.50150i	0.537606	+	0.472142i
$56$	−2.85019	+	2.07078i	−0.380872	+	0.276720i
$57$	0.179579			0.0237858
$58$	−6.53215	+	4.74588i	−0.857713	+	0.623165i
$59$	−3.67251	−	11.3028i	−0.478121	−	1.47150i	−0.841702	−	0.539942i	$-0.818446\pi$
$59$	−3.67251	−	11.3028i	−0.478121	−	1.47150i	0.363582	−	0.931562i	$-0.381554\pi$
$60$	−7.79725	−	0.722038i	−1.00662	−	0.0932146i
$61$	0.945379	−	2.90958i	0.121043	−	0.372533i	−0.872116	−	0.489299i	$-0.837253\pi$
$61$	0.945379	−	2.90958i	0.121043	−	0.372533i	0.993159	+	0.116766i	$0.0372527\pi$
$62$	2.10421	+	6.47609i	0.267235	+	0.822465i
$63$	−0.309017	−	0.951057i	−0.0389325	−	0.119822i
$64$	−3.74395	+	11.5227i	−0.467994	+	1.44034i
$65$	14.8544	+	1.37554i	1.84246	+	0.170614i
$66$	−1.72007	−	5.29383i	−0.211726	−	0.651625i
$67$	9.67145	−	7.02672i	1.18156	−	0.858451i	0.189209	−	0.981937i	$-0.439407\pi$
$67$	9.67145	−	7.02672i	1.18156	−	0.858451i	0.992346	+	0.123486i	$0.0394075\pi$
$68$	24.1160			2.92450
$69$	−5.75874	+	4.18397i	−0.693271	+	0.503691i
$70$	−3.94093	−	3.46105i	−0.471031	−	0.413674i
$71$	−3.55634	−	2.58383i	−0.422060	−	0.306644i	0.356406	−	0.934331i	$-0.384002\pi$
$71$	−3.55634	−	2.58383i	−0.422060	−	0.306644i	−0.778466	+	0.627687i	$0.784002\pi$
$72$	2.85019	+	2.07078i	0.335898	+	0.244044i
$73$	2.51112	−	7.72843i	0.293904	−	0.904544i	−0.689683	−	0.724111i	$-0.742250\pi$
$73$	2.51112	−	7.72843i	0.293904	−	0.904544i	0.983587	−	0.180433i	$-0.0577498\pi$
$74$	−0.0239996			−0.00278990
$75$	−0.645607	−	4.95814i	−0.0745482	−	0.572517i
$76$	−0.628877			−0.0721372
$77$	0.733310	−	2.25690i	0.0835684	−	0.257197i
$78$	−12.6602	−	9.19814i	−1.43348	−	1.04148i
$79$	−1.52385	−	1.10714i	−0.171447	−	0.124563i	0.498753	−	0.866744i	$-0.333792\pi$
$79$	−1.52385	−	1.10714i	−0.171447	−	0.124563i	−0.670200	+	0.742181i	$0.733792\pi$
$80$	2.80496	+	0.259743i	0.313604	+	0.0290402i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−18.9512			−2.09280
$83$	10.4788	−	7.61326i	1.15019	−	0.835664i	0.161686	−	0.986842i	$-0.448307\pi$
$83$	10.4788	−	7.61326i	1.15019	−	0.835664i	0.988506	+	0.151178i	$0.0483068\pi$
$84$	1.08216	+	3.33056i	0.118074	+	0.363394i
$85$	3.38778	+	15.0213i	0.367457	+	1.62929i
$86$	−6.01234	+	18.5041i	−0.648328	+	1.99535i
$87$	1.06371	+	3.27375i	0.114041	+	0.350983i
$88$	2.58347	+	7.95110i	0.275399	+	0.847590i
$89$	−3.58739	+	11.0409i	−0.380263	+	1.17033i	0.559596	+	0.828766i	$0.310956\pi$
$89$	−3.58739	+	11.0409i	−0.380263	+	1.17033i	−0.939859	+	0.341563i	$0.889044\pi$
$90$	−2.07384	+	4.81757i	−0.218601	+	0.507816i
$91$	−2.06160	−	6.34497i	−0.216115	−	0.665133i
$92$	20.1669	−	14.6521i	2.10254	−	1.52759i
$93$	2.90301			0.301028
$94$	3.42732	−	2.49009i	0.353501	−	0.256833i
$95$	−0.0883437	−	0.391712i	−0.00906387	−	0.0401888i
$96$	3.30975	+	2.40467i	0.337800	+	0.245426i
$97$	−8.48646	−	6.16577i	−0.861669	−	0.626039i	0.0666694	−	0.997775i	$-0.478763\pi$
$97$	−8.48646	−	6.16577i	−0.861669	−	0.626039i	−0.928339	+	0.371736i	$0.878763\pi$
$98$	−0.724838	+	2.23082i	−0.0732197	+	0.225347i
$99$	−2.37304			−0.238500
$100$	2.26089	+	17.3632i	0.226089	+	1.73632i
$101$	−16.3450			−1.62639			−0.813193	−	0.581994i	$-0.802273\pi$
$101$	−16.3450			−1.62639			−0.813193	+	0.581994i	$0.802273\pi$
$102$	4.99156	−	15.3624i	0.494238	−	1.52111i
$103$	1.24903	+	0.907475i	0.123071	+	0.0894162i	0.647618	−	0.761965i	$-0.275765\pi$
$103$	1.24903	+	0.907475i	0.123071	+	0.0894162i	−0.524547	+	0.851381i	$0.675765\pi$
$104$	19.0150	+	13.8152i	1.86457	+	1.35469i
$105$	−1.92250	+	1.14192i	−0.187617	+	0.111440i
$106$	−1.79234	+	1.30221i	−0.174088	+	0.126482i
$107$	−3.29647			−0.318682			−0.159341	−	0.987224i	$-0.550937\pi$
$107$	−3.29647			−0.318682			−0.159341	+	0.987224i	$0.550937\pi$
$108$	2.83314	−	2.05840i	0.272619	−	0.198069i
$109$	−3.60250	−	11.0873i	−0.345057	−	1.06197i	−0.961554	−	0.274618i	$-0.911449\pi$
$109$	−3.60250	−	11.0873i	−0.345057	−	1.06197i	0.616497	−	0.787357i	$-0.288551\pi$
$110$	−10.7011	+	6.35625i	−1.02031	+	0.606045i
$111$	−0.00316176	+	0.00973088i	−0.000300101	+	0.000923614i
$112$	−0.389294	−	1.19812i	−0.0367848	−	0.113212i
$113$	3.43522	+	10.5725i	0.323158	+	0.994579i	0.972265	+	0.233882i	$0.0751429\pi$
$113$	3.43522	+	10.5725i	0.323158	+	0.994579i	−0.649107	+	0.760697i	$0.724857\pi$
$114$	−0.130166	+	0.400608i	−0.0121911	+	0.0375204i
$115$	11.9594	+	10.5031i	1.11522	+	0.979422i
$116$	−3.72506	−	11.4645i	−0.345863	−	1.06446i
$117$	−5.39735	+	3.92140i	−0.498985	+	0.362534i
$118$	27.8766			2.56625
$119$	5.57125	−	4.04775i	0.510716	−	0.371057i
$120$	3.11481	−	7.23578i	0.284342	−	0.660533i
$121$	4.34335	+	3.15563i	0.394850	+	0.286875i
$122$	5.80550	+	4.21795i	0.525606	+	0.381875i
$123$	−2.49666	+	7.68393i	−0.225116	+	0.692837i
$124$	−10.1662			−0.912952
$125$	−10.4975	+	3.84740i	−0.938925	+	0.344122i
$126$	2.34562			0.208965
$127$	−1.81415	+	5.58337i	−0.160979	+	0.495444i	−0.998718	−	0.0506285i	$-0.983878\pi$
$127$	−1.81415	+	5.58337i	−0.160979	+	0.495444i	0.837738	+	0.546072i	$0.183878\pi$
$128$	−16.3718	−	11.8948i	−1.44708	−	1.05137i
$129$	6.71059	+	4.87553i	0.590834	+	0.429266i
$130$	−13.8356	+	32.1404i	−1.21346	+	2.81890i
$131$	17.0865	−	12.4141i	1.49285	−	1.08462i	0.519732	−	0.854329i	$-0.326032\pi$
$131$	17.0865	−	12.4141i	1.49285	−	1.08462i	0.973121	−	0.230293i	$-0.0739683\pi$
$132$	8.31028			0.723317
$133$	−0.145282	+	0.105554i	−0.0125976	+	0.00915268i
$134$	8.66513	+	26.6685i	0.748553	+	2.30381i
$135$	1.68012	+	1.47553i	0.144602	+	0.126994i
$136$	−7.49710	+	23.0737i	−0.642871	+	1.97855i
$137$	4.69781	+	14.4584i	0.401361	+	1.23526i	0.923896	+	0.382644i	$0.124986\pi$
$137$	4.69781	+	14.4584i	0.401361	+	1.23526i	−0.522535	+	0.852618i	$0.675014\pi$
$138$	−5.15954	−	15.8794i	−0.439209	−	1.35175i
$139$	−2.12580	+	6.54254i	−0.180308	+	0.554931i	−0.999836	−	0.0181080i	$-0.994236\pi$
$139$	−2.12580	+	6.54254i	−0.180308	+	0.554931i	0.819528	+	0.573039i	$0.194236\pi$
$140$	6.73251	−	3.99897i	0.569001	−	0.337975i
$141$	−0.558111	−	1.71769i	−0.0470014	−	0.144656i
$142$	8.34183	−	6.06070i	0.700031	−	0.508602i
$143$	−15.8317			−1.32391
$144$	−1.01918	+	0.740481i	−0.0849321	+	0.0617067i
$145$	6.61769	−	3.93077i	0.549569	−	0.326432i
$146$	15.4206	+	11.2037i	1.27622	+	0.927226i
$147$	0.809017	+	0.587785i	0.0667266	+	0.0484797i
$148$	0.0110723	−	0.0340771i	0.000910140	−	0.00280112i
$149$	−0.433080			−0.0354793			−0.0177397	−	0.999843i	$-0.505647\pi$
$149$	−0.433080			−0.0354793			−0.0177397	+	0.999843i	$0.505647\pi$
$150$	11.5287	+	2.15362i	0.941314	+	0.175842i
$151$	15.6555			1.27403			0.637014	−	0.770852i	$-0.280169\pi$
$151$	15.6555			1.27403			0.637014	+	0.770852i	$0.280169\pi$
$152$	0.195503	−	0.601696i	0.0158574	−	0.0488040i
$153$	−5.57125	−	4.04775i	−0.450409	−	0.327241i
$154$	4.50320	+	3.27177i	0.362878	+	0.263647i
$155$	−1.42813	−	6.33228i	−0.114710	−	0.508621i
$156$	18.9013	−	13.7326i	1.51331	−	1.09949i
$157$	−8.57741			−0.684551			−0.342276	−	0.939600i	$-0.611198\pi$
$157$	−8.57741			−0.684551			−0.342276	+	0.939600i	$0.611198\pi$
$158$	3.57439	−	2.59694i	0.284363	−	0.206602i
$159$	0.291868	+	0.898278i	0.0231467	+	0.0712381i
$160$	3.61704	−	8.40247i	0.285952	−	0.664273i
$161$	2.19964	−	6.76981i	0.173356	−	0.533536i
$162$	−0.724838	−	2.23082i	−0.0569486	−	0.175270i
$163$	4.78383	+	14.7231i	0.374699	+	1.15320i	0.943682	+	0.330855i	$0.107337\pi$
$163$	4.78383	+	14.7231i	0.374699	+	1.15320i	−0.568983	+	0.822349i	$0.692663\pi$
$164$	8.74319	−	26.9088i	0.682729	−	2.10122i
$165$	1.16742	+	5.17627i	0.0908832	+	0.402972i
$166$	9.38843	+	28.8946i	0.728683	+	2.24266i
$167$	4.81457	−	3.49799i	0.372563	−	0.270683i	−0.385710	−	0.922620i	$-0.626043\pi$
$167$	4.81457	−	3.49799i	0.372563	−	0.270683i	0.758273	+	0.651937i	$0.226043\pi$
$168$	−3.52302			−0.271807
$169$	−25.4912	+	18.5204i	−1.96086	+	1.42465i
$170$	−35.9654	−	3.33045i	−2.75842	−	0.255434i
$171$	0.145282	+	0.105554i	0.0111100	+	0.00807190i
$172$	−23.5002	−	17.0739i	−1.79187	−	1.30187i
$173$	1.47651	−	4.54424i	0.112257	−	0.345492i	−0.879108	−	0.476623i	$-0.841861\pi$
$173$	1.47651	−	4.54424i	0.112257	−	0.345492i	0.991365	+	0.131131i	$0.0418608\pi$
$174$	−8.07418			−0.612102
$175$	3.43663	+	3.63174i	0.259785	+	0.274534i
$176$	−2.98951			−0.225343
$177$	3.67251	−	11.3028i	0.276043	−	0.849573i
$178$	−22.0299	−	16.0057i	−1.65121	−	1.19968i
$179$	−14.3839	−	10.4505i	−1.07511	−	0.781110i	−0.0982823	−	0.995159i	$-0.531335\pi$
$179$	−14.3839	−	10.4505i	−1.07511	−	0.781110i	−0.976823	+	0.214049i	$0.931335\pi$
$180$	−5.88371	−	5.16725i	−0.438546	−	0.385144i
$181$	11.3896	−	8.27505i	0.846585	−	0.615080i	−0.0776177	−	0.996983i	$-0.524731\pi$
$181$	11.3896	−	8.27505i	0.846585	−	0.615080i	0.924202	+	0.381904i	$0.124731\pi$
$182$	15.6488			1.15997
$183$	2.47504	−	1.79822i	0.182960	−	0.132928i
$184$	7.74940	+	23.8502i	0.571293	+	1.75826i
$185$	0.0227812	+	0.00210958i	0.00167491	+	0.000155099i
$186$	−2.10421	+	6.47609i	−0.154288	+	0.474850i
$187$	−5.04990	−	15.5420i	−0.369285	−	1.13654i
$188$	1.95448	+	6.01527i	0.142545	+	0.438709i
$189$	0.309017	−	0.951057i	0.0224777	−	0.0691792i
$190$	0.937874	+	0.0868486i	0.0680406	+	0.00630066i
$191$	−5.48865	−	16.8923i	−0.397145	−	1.22229i	−0.927279	−	0.374372i	$-0.877858\pi$
$191$	−5.48865	−	16.8923i	−0.397145	−	1.22229i	0.530134	−	0.847914i	$-0.322142\pi$
$192$	−9.80180	+	7.12142i	−0.707384	+	0.513944i
$193$	−9.23745			−0.664926			−0.332463	−	0.943116i	$-0.607880\pi$
$193$	−9.23745			−0.664926			−0.332463	+	0.943116i	$0.607880\pi$
$194$	19.9060	−	14.4626i	1.42917	−	1.03835i
$195$	11.2089	+	9.84400i	0.802686	+	0.704944i
$196$	−2.83314	−	2.05840i	−0.202367	−	0.147028i
$197$	5.82383	+	4.23126i	0.414931	+	0.301465i	0.775595	−	0.631231i	$-0.217450\pi$
$197$	5.82383	+	4.23126i	0.414931	+	0.301465i	−0.360664	+	0.932696i	$0.617450\pi$
$198$	1.72007	−	5.29383i	0.122240	−	0.376216i
$199$	15.6819			1.11166			0.555829	−	0.831297i	$-0.312401\pi$
$199$	15.6819			1.11166			0.555829	+	0.831297i	$0.312401\pi$
$200$	−17.3156	−	3.23464i	−1.22440	−	0.228723i
$201$	11.9546			0.843210
$202$	11.8475	−	36.4627i	0.833584	−	2.56551i
$203$	−2.78482	−	2.02329i	−0.195456	−	0.142007i
$204$	19.5103	+	14.1750i	1.36599	+	0.992452i
$205$	17.9890	+	1.66581i	1.25641	+	0.116345i
$206$	−2.92976	+	2.12860i	−0.204126	+	0.148306i
$207$	−7.11820			−0.494749
$208$	−6.79948	+	4.94011i	−0.471459	+	0.342535i
$209$	0.131687	+	0.405291i	0.00910898	+	0.0280345i
$210$	−1.15393	−	5.11647i	−0.0796286	−	0.353070i
$211$	−1.68739	+	5.19326i	−0.116165	+	0.357518i	−0.992188	−	0.124750i	$-0.960187\pi$
$211$	−1.68739	+	5.19326i	−0.116165	+	0.357518i	0.876023	+	0.482269i	$0.160187\pi$
$212$	−1.02211	−	3.14573i	−0.0701988	−	0.216050i
$213$	−1.35840	−	4.18073i	−0.0930760	−	0.286459i
$214$	2.38941	−	7.35384i	0.163337	−	0.502698i
$215$	7.33363	−	17.0362i	0.500149	−	1.16186i
$216$	1.08867	+	3.35059i	0.0740749	+	0.227979i
$217$	−2.34858	+	1.70635i	−0.159432	+	0.115834i
$218$	27.3451			1.85204
$219$	6.57419	−	4.77643i	0.444243	−	0.322761i
$220$	−4.08824	−	18.1271i	−0.275629	−	1.22213i
$221$	−37.1686	−	27.0045i	−2.50023	−	1.81652i
$222$	−0.0194161	−	0.0141066i	−0.00130312	−	0.000946775i
$223$	4.53735	−	13.9645i	0.303843	−	0.935134i	−0.676263	−	0.736660i	$-0.736402\pi$
$223$	4.53735	−	13.9645i	0.303843	−	0.935134i	0.980106	−	0.198473i	$-0.0635984\pi$
$224$	−4.09107			−0.273346
$225$	2.39202	−	4.39070i	0.159468	−	0.292713i
$226$	−26.0754			−1.73451
$227$	−6.56490	+	20.2047i	−0.435728	+	1.34103i	0.456611	+	0.889666i	$0.349063\pi$
$227$	−6.56490	+	20.2047i	−0.435728	+	1.34103i	−0.892339	+	0.451366i	$0.850937\pi$
$228$	−0.508772	−	0.369645i	−0.0336943	−	0.0244803i
$229$	21.9686	+	15.9611i	1.45173	+	1.05474i	0.985424	+	0.170116i	$0.0544142\pi$
$229$	21.9686	+	15.9611i	1.45173	+	1.05474i	0.466303	+	0.884625i	$0.345586\pi$
$230$	−32.0993	+	19.0663i	−2.11656	+	1.25719i
$231$	1.91983	−	1.39484i	0.126316	−	0.0917736i
$232$	12.1271			0.796180
$233$	13.1700	−	9.56853i	0.862792	−	0.626855i	−0.0658509	−	0.997829i	$-0.520976\pi$
$233$	13.1700	−	9.56853i	0.862792	−	0.626855i	0.928643	+	0.370974i	$0.120976\pi$
$234$	−4.83575	−	14.8829i	−0.316123	−	0.972926i
$235$	−3.47220	+	2.06241i	−0.226501	+	0.134537i
$236$	−12.8610	+	39.5820i	−0.837179	+	2.57657i
$237$	−0.582060	−	1.79140i	−0.0378089	−	0.116364i
$238$	4.99156	+	15.3624i	0.323555	+	0.995799i
$239$	−3.93178	+	12.1008i	−0.254326	+	0.782735i	0.739636	+	0.673007i	$0.234998\pi$
$239$	−3.93178	+	12.1008i	−0.254326	+	0.782735i	−0.993962	+	0.109727i	$0.965002\pi$
$240$	2.11658	+	1.85885i	0.136625	+	0.119988i
$241$	7.02123	+	21.6091i	0.452277	+	1.39197i	0.874302	+	0.485382i	$0.161320\pi$
$241$	7.02123	+	21.6091i	0.452277	+	1.39197i	−0.422025	+	0.906584i	$0.638680\pi$
$242$	−10.1879	+	7.40192i	−0.654901	+	0.475814i
$243$	−1.00000			−0.0641500
$244$	−8.66746	+	6.29728i	−0.554878	+	0.403142i
$245$	0.884129	−	2.05385i	0.0564850	−	0.131216i
$246$	−15.3318	−	11.1392i	−0.977520	−	0.710210i
$247$	0.969250	+	0.704201i	0.0616719	+	0.0448073i
$248$	3.16043	−	9.72681i	0.200688	−	0.617653i
$249$	12.9525			0.820828
$250$	−0.973889	−	26.2068i	−0.0615942	−	1.65746i
$251$	13.1000			0.826862			0.413431	−	0.910535i	$-0.364330\pi$
$251$	13.1000			0.826862			0.413431	+	0.910535i	$0.364330\pi$
$252$	−1.08216	+	3.33056i	−0.0681699	+	0.209805i
$253$	−13.6657	−	9.92873i	−0.859157	−	0.624214i
$254$	−11.1405	−	8.09407i	−0.699019	−	0.507867i
$255$	−6.08851	+	14.1438i	−0.381277	+	0.885716i
$256$	18.7986	−	13.6580i	1.17491	−	0.853624i
$257$	−14.4201			−0.899500			−0.449750	−	0.893155i	$-0.648487\pi$
$257$	−14.4201			−0.899500			−0.449750	+	0.893155i	$0.648487\pi$
$258$	−15.7405	+	11.4362i	−0.979962	+	0.711984i
$259$	−0.00316176	−	0.00973088i	−0.000196462	−	0.000604648i
$260$	−39.2531	−	34.4733i	−2.43437	−	2.13794i
$261$	−1.06371	+	3.27375i	−0.0658418	+	0.202640i
$262$	15.3086	+	47.1151i	0.945770	+	2.91078i
$263$	0.686680	+	2.11338i	0.0423425	+	0.130317i	0.969993	−	0.243133i	$-0.0781750\pi$
$263$	0.686680	+	2.11338i	0.0423425	+	0.130317i	−0.927651	+	0.373449i	$0.878175\pi$
$264$	−2.58347	+	7.95110i	−0.159001	+	0.489356i
$265$	1.81581	−	1.07855i	0.111544	−	0.0662550i
$266$	−0.130166	−	0.400608i	−0.00798096	−	0.0245629i
$267$	−9.39192	+	6.82363i	−0.574776	+	0.417599i
$268$	−41.8644			−2.55727
$269$	15.6025	−	11.3359i	0.951304	−	0.691163i	0.000188956	−	1.00000i	$-0.499940\pi$
$269$	15.6025	−	11.3359i	0.951304	−	0.691163i	0.951115	+	0.308837i	$0.0999399\pi$
$270$	−4.50947	+	2.67853i	−0.274437	+	0.163010i
$271$	−14.2907	−	10.3828i	−0.868096	−	0.630709i	0.0619795	−	0.998077i	$-0.480259\pi$
$271$	−14.2907	−	10.3828i	−0.868096	−	0.630709i	−0.930075	+	0.367369i	$0.880259\pi$
$272$	−7.01856	−	5.09928i	−0.425563	−	0.309189i
$273$	2.06160	−	6.34497i	0.124774	−	0.384015i
$274$	−35.6592			−2.15425
$275$	10.7166	−	5.09292i	0.646234	−	0.307115i
$276$	24.9276			1.50047
$277$	−4.92397	+	15.1544i	−0.295853	+	0.910540i	0.687081	+	0.726581i	$0.258892\pi$
$277$	−4.92397	+	15.1544i	−0.295853	+	0.910540i	−0.982934	+	0.183960i	$0.941108\pi$
$278$	−13.0544	−	9.48456i	−0.782950	−	0.568846i
$279$	2.34858	+	1.70635i	0.140606	+	0.102156i
$280$	1.73315	+	7.68470i	0.103575	+	0.459249i
$281$	0.837519	−	0.608493i	0.0499622	−	0.0362997i	−0.562524	−	0.826781i	$-0.690170\pi$
$281$	0.837519	−	0.608493i	0.0499622	−	0.0362997i	0.612486	+	0.790481i	$0.290170\pi$
$282$	4.23640			0.252274
$283$	13.0105	−	9.45265i	0.773392	−	0.561902i	−0.129597	−	0.991567i	$-0.541368\pi$
$283$	13.0105	−	9.45265i	0.773392	−	0.561902i	0.902988	+	0.429665i	$0.141368\pi$
$284$	4.75706	+	14.6407i	0.282279	+	0.868767i
$285$	0.158771	−	0.368829i	0.00940478	−	0.0218475i
$286$	11.4754	−	35.3177i	0.678556	−	2.08838i
$287$	−2.49666	−	7.68393i	−0.147373	−	0.453568i
$288$	1.26421	+	3.89084i	0.0744944	+	0.229270i
$289$	9.40127	−	28.9341i	0.553016	−	1.70201i
$290$	3.97209	+	17.6120i	0.233249	+	1.03422i
$291$	−3.24154	−	9.97643i	−0.190022	−	0.584829i
$292$	−23.0225	+	16.7268i	−1.34729	+	0.978865i
$293$	24.8634			1.45253			0.726267	−	0.687413i	$-0.241254\pi$
$293$	24.8634			1.45253			0.726267	+	0.687413i	$0.241254\pi$
$294$	−1.89765	+	1.37872i	−0.110673	+	0.0804088i
$295$	−26.4614	−	2.45036i	−1.54064	−	0.142666i
$296$	0.0291621	+	0.0211875i	0.00169501	+	0.00123150i
$297$	−1.91983	−	1.39484i	−0.111400	−	0.0809367i
$298$	0.313913	−	0.966125i	0.0181845	−	0.0559661i
$299$	−47.4890			−2.74636
$300$	−8.37674	+	15.3760i	−0.483631	+	0.887736i
$301$	−8.29474			−0.478101
$302$	−11.3477	+	34.9247i	−0.652988	+	2.00969i
$303$	−13.2234	−	9.60734i	−0.759662	−	0.551927i
$304$	0.183024	+	0.132975i	0.0104971	+	0.00762662i
$305$	−5.14001	−	4.51412i	−0.294316	−	0.258477i
$306$	13.0681	−	9.49451i	0.747052	−	0.542765i
$307$	−18.8210			−1.07417			−0.537085	−	0.843528i	$-0.680474\pi$
$307$	−18.8210			−1.07417			−0.537085	+	0.843528i	$0.680474\pi$
$308$	−6.72316	+	4.88466i	−0.383088	+	0.278329i
$309$	0.477088	+	1.46833i	0.0271406	+	0.0835301i
$310$	15.1613	+	1.40396i	0.861107	+	0.0797398i
$311$	4.16086	−	12.8058i	0.235940	−	0.726150i	−0.761055	−	0.648688i	$-0.775318\pi$
$311$	4.16086	−	12.8058i	0.235940	−	0.726150i	0.996995	−	0.0774625i	$-0.0246818\pi$
$312$	7.26308	+	22.3535i	0.411191	+	1.26552i
$313$	−0.760050	−	2.33919i	−0.0429605	−	0.132219i	0.927276	−	0.374379i	$-0.122144\pi$
$313$	−0.760050	−	2.33919i	−0.0429605	−	0.132219i	−0.970236	+	0.242160i	$0.922144\pi$
$314$	6.21723	−	19.1347i	0.350859	−	1.07983i
$315$	−2.22654	−	0.206181i	−0.125451	−	0.0116170i
$316$	2.03835	+	6.27339i	0.114666	+	0.352906i
$317$	−6.44850	+	4.68511i	−0.362184	+	0.263142i	−0.753962	−	0.656918i	$-0.771860\pi$
$317$	−6.44850	+	4.68511i	−0.362184	+	0.263142i	0.391779	+	0.920060i	$0.371860\pi$
$318$	−2.21545			−0.124237
$319$	−6.60849	+	4.80135i	−0.370005	+	0.268824i
$320$	20.3558	+	17.8771i	1.13792	+	0.999360i
$321$	−2.66690	−	1.93762i	−0.148852	−	0.108147i
$322$	13.5078	+	9.81403i	0.752763	+	0.546914i
$323$	−0.382149	+	1.17613i	−0.0212633	+	0.0654418i
$324$	3.50196			0.194553
$325$	15.9583	−	29.2925i	0.885208	−	1.62486i
$326$	−36.3122			−2.01114
$327$	3.60250	−	11.0873i	0.199219	−	0.613132i
$328$	23.0277	+	16.7306i	1.27149	+	0.923793i
$329$	1.46115	+	1.06159i	0.0805560	+	0.0585274i
$330$	−12.3935	−	1.14766i	−0.682241	−	0.0631765i
$331$	−6.25084	+	4.54150i	−0.343577	+	0.249624i	−0.746170	−	0.665756i	$-0.768109\pi$
$331$	−6.25084	+	4.54150i	−0.343577	+	0.249624i	0.402592	+	0.915379i	$0.368109\pi$
$332$	−45.3589			−2.48939
$333$	−0.00827758	+	0.00601402i	−0.000453609	+	0.000329566i
$334$	4.31361	+	13.2759i	0.236030	+	0.726427i
$335$	−5.88104	−	26.0763i	−0.321316	−	1.42470i
$336$	0.389294	−	1.19812i	0.0212377	−	0.0653630i
$337$	−0.394506	−	1.21416i	−0.0214901	−	0.0661397i	0.939736	−	0.341900i	$-0.111070\pi$
$337$	−0.394506	−	1.21416i	−0.0214901	−	0.0661397i	−0.961226	+	0.275760i	$0.911070\pi$
$338$	−22.8388	−	70.2905i	−1.24227	−	3.82330i
$339$	−3.43522	+	10.5725i	−0.186576	+	0.574221i
$340$	21.3217	−	49.5308i	1.15633	−	2.68619i
$341$	2.12880	+	6.55179i	0.115281	+	0.354799i
$342$	−0.340778	+	0.247590i	−0.0184272	+	0.0133881i
$343$	−1.00000			−0.0539949
$344$	23.6416	−	17.1766i	1.27467	−	0.926100i
$345$	3.50179	+	15.5268i	0.188530	+	0.835934i
$346$	9.06715	+	6.58767i	0.487453	+	0.354155i
$347$	20.3851	+	14.8106i	1.09433	+	0.795075i	0.980125	−	0.198382i	$-0.0635687\pi$
$347$	20.3851	+	14.8106i	1.09433	+	0.795075i	0.114203	+	0.993457i	$0.463569\pi$
$348$	3.72506	−	11.4645i	0.199684	−	0.614564i
$349$	22.2577			1.19143			0.595713	−	0.803197i	$-0.296870\pi$
$349$	22.2577			1.19143			0.595713	+	0.803197i	$0.296870\pi$
$350$	−10.5928	+	5.03408i	−0.566208	+	0.269083i
$351$	−6.67149			−0.356098
$352$	−3.00002	+	9.23313i	−0.159902	+	0.492127i
$353$	15.3604	+	11.1600i	0.817553	+	0.593987i	0.916010	−	0.401154i	$-0.131391\pi$
$353$	15.3604	+	11.1600i	0.817553	+	0.593987i	−0.0984577	+	0.995141i	$0.531391\pi$
$354$	22.5526	+	16.3855i	1.19866	+	0.870877i
$355$	−8.45107	+	5.01976i	−0.448536	+	0.266421i
$356$	32.8901	−	23.8960i	1.74317	−	1.26649i
$357$	6.88645			0.364469
$358$	33.7393	−	24.5130i	1.78318	−	1.29555i
$359$	4.91676	+	15.1322i	0.259497	+	0.798649i	0.992910	+	0.118866i	$0.0379259\pi$
$359$	4.91676	+	15.1322i	0.259497	+	0.798649i	−0.733414	+	0.679783i	$0.762074\pi$
$360$	6.77302	−	4.02303i	0.356969	−	0.212032i
$361$	−5.86136	+	18.0394i	−0.308493	+	0.949442i
$362$	10.2045	+	31.4063i	0.536338	+	1.65068i
$363$	1.65901	+	5.10592i	0.0870756	+	0.267991i
$364$	−7.21965	+	22.2198i	−0.378412	+	1.16463i
$365$	−13.6529	−	11.9904i	−0.714626	−	0.627606i
$366$	2.21751	+	6.82478i	0.115911	+	0.356737i
$367$	−0.434194	+	0.315460i	−0.0226647	+	0.0164669i	−0.599060	−	0.800704i	$-0.704459\pi$
$367$	−0.434194	+	0.315460i	−0.0226647	+	0.0164669i	0.576395	+	0.817171i	$0.304459\pi$
$368$	−8.96737			−0.467457
$369$	−6.53634	+	4.74893i	−0.340268	+	0.247219i
$370$	−0.0212188	+	0.0492917i	−0.00110311	+	0.00256255i
$371$	−0.764121	−	0.555166i	−0.0396712	−	0.0288228i
$372$	−8.22463	−	5.97555i	−0.426427	−	0.309818i
$373$	−1.14848	+	3.53465i	−0.0594659	+	0.183017i	−0.976377	−	0.216075i	$-0.930675\pi$
$373$	−1.14848	+	3.53465i	−0.0594659	+	0.183017i	0.916911	+	0.399092i	$0.130675\pi$
$374$	38.3318			1.98209
$375$	−10.7541	−	3.05766i	−0.555339	−	0.157897i
$376$	−6.36288			−0.328141
$377$	−7.09651	+	21.8408i	−0.365489	+	1.12486i
$378$	1.89765	+	1.37872i	0.0976046	+	0.0709139i
$379$	4.17616	+	3.03416i	0.214515	+	0.155854i	0.689854	−	0.723948i	$-0.257675\pi$
$379$	4.17616	+	3.03416i	0.214515	+	0.155854i	−0.475339	+	0.879803i	$0.657675\pi$
$380$	−0.556009	+	1.29162i	−0.0285226	+	0.0662588i
$381$	−4.74949	+	3.45071i	−0.243324	+	0.176785i
$382$	41.6621			2.13162
$383$	4.40980	−	3.20391i	0.225330	−	0.163712i	−0.469392	−	0.882990i	$-0.655527\pi$
$383$	4.40980	−	3.20391i	0.225330	−	0.163712i	0.694723	+	0.719278i	$0.255527\pi$
$384$	−6.25349	−	19.2463i	−0.319122	−	0.982156i
$385$	−3.98699	−	3.50150i	−0.203196	−	0.178453i
$386$	6.69565	−	20.6071i	0.340800	−	1.04887i
$387$	2.56322	+	7.88877i	0.130296	+	0.401009i
$388$	11.3517	+	34.9370i	0.576296	+	1.77366i
$389$	0.436463	−	1.34329i	0.0221295	−	0.0681077i	−0.939382	−	0.342873i	$-0.888600\pi$
$389$	0.436463	−	1.34329i	0.0221295	−	0.0681077i	0.961511	+	0.274765i	$0.0886001\pi$
$390$	−30.0849	+	17.8698i	−1.52341	+	0.904871i
$391$	−15.1477	−	46.6199i	−0.766054	−	2.35767i
$392$	2.85019	−	2.07078i	0.143956	−	0.104590i
$393$	21.1201			1.06537
$394$	−13.6605	+	9.92496i	−0.688208	+	0.500012i
$395$	−3.62119	+	2.15091i	−0.182202	+	0.108224i
$396$	6.72316	+	4.88466i	0.337851	+	0.245463i
$397$	−14.9931	−	10.8931i	−0.752480	−	0.546709i	0.144115	−	0.989561i	$-0.453967\pi$
$397$	−14.9931	−	10.8931i	−0.752480	−	0.546709i	−0.896595	+	0.442852i	$0.853967\pi$
$398$	−11.3668	+	34.9834i	−0.569767	+	1.75356i
$399$	−0.179579			−0.00899019
$400$	3.01342	−	5.53132i	0.150671	−	0.276566i
$401$	14.0048			0.699367			0.349684	−	0.936868i	$-0.386289\pi$
$401$	14.0048			0.699367			0.349684	+	0.936868i	$0.386289\pi$
$402$	−8.66513	+	26.6685i	−0.432177	+	1.33010i
$403$	15.6686	+	11.3839i	0.780506	+	0.567071i
$404$	46.3076	+	33.6445i	2.30389	+	1.67387i
$405$	0.491949	+	2.18128i	0.0244452	+	0.108389i
$406$	6.53215	−	4.74588i	0.324185	−	0.235534i
$407$	−0.0242801			−0.00120352
$408$	−19.6277	+	14.2603i	−0.971714	+	0.705992i
$409$	−3.00653	−	9.25315i	−0.148663	−	0.457539i	0.848801	−	0.528713i	$-0.177325\pi$
$409$	−3.00653	−	9.25315i	−0.148663	−	0.457539i	−0.997464	+	0.0711745i	$0.977325\pi$
$410$	−16.7553	+	38.9229i	−0.827484	+	1.92226i
$411$	−4.69781	+	14.4584i	−0.231726	+	0.713179i
$412$	−1.67074	−	5.14201i	−0.0823115	−	0.253329i
$413$	3.67251	+	11.3028i	0.180713	+	0.556176i
$414$	5.15954	−	15.8794i	0.253578	−	0.780431i
$415$	−6.37195	−	28.2529i	−0.312787	−	1.38688i
$416$	8.43417	+	25.9577i	0.413519	+	1.27268i
$417$	−5.56542	+	4.04351i	−0.272540	+	0.198012i
$418$	−0.999583			−0.0488912
$419$	1.86250	−	1.35318i	0.0909889	−	0.0661073i	−0.541361	−	0.840790i	$-0.682091\pi$
$419$	1.86250	−	1.35318i	0.0909889	−	0.0661073i	0.632350	+	0.774683i	$0.282091\pi$
$420$	7.79725	+	0.722038i	0.380467	+	0.0352318i
$421$	13.4669	+	9.78424i	0.656334	+	0.476855i	0.865423	−	0.501042i	$-0.167050\pi$
$421$	13.4669	+	9.78424i	0.656334	+	0.476855i	−0.209089	+	0.977897i	$0.567050\pi$
$422$	−10.3621	−	7.52854i	−0.504421	−	0.366483i
$423$	0.558111	−	1.71769i	0.0271363	−	0.0835169i
$424$	3.32751			0.161598
$425$	33.8467	+	6.32274i	1.64181	+	0.306698i
$426$	10.3111			0.499573
$427$	−0.945379	+	2.90958i	−0.0457501	+	0.140804i
$428$	9.33938	+	6.78545i	0.451436	+	0.327987i
$429$	−12.8081	−	9.30565i	−0.618382	−	0.449281i
$430$	32.6890	+	28.7085i	1.57640	+	1.38445i
$431$	23.3682	−	16.9780i	1.12561	−	0.817800i	0.140556	−	0.990073i	$-0.455111\pi$
$431$	23.3682	−	16.9780i	1.12561	−	0.817800i	0.985049	+	0.172272i	$0.0551109\pi$
$432$	−1.25978			−0.0606113
$433$	−25.3315	+	18.4044i	−1.21736	+	0.884461i	−0.995878	−	0.0907046i	$-0.971088\pi$
$433$	−25.3315	+	18.4044i	−1.21736	+	0.884461i	−0.221478	+	0.975165i	$0.571088\pi$
$434$	−2.10421	−	6.47609i	−0.101005	−	0.310862i
$435$	7.66427	+	0.709723i	0.367473	+	0.0340286i
$436$	−12.6158	+	38.8274i	−0.604186	+	1.85949i
$437$	0.395010	+	1.21571i	0.0188959	+	0.0581555i
$438$	5.89014	+	18.1280i	0.281442	+	0.866189i
$439$	1.16331	−	3.58029i	0.0555216	−	0.170878i	−0.919450	−	0.393207i	$-0.871366\pi$
$439$	1.16331	−	3.58029i	0.0555216	−	0.170878i	0.974972	+	0.222328i	$0.0713657\pi$
$440$	18.6145	+	1.72373i	0.887412	+	0.0821757i
$441$	0.309017	+	0.951057i	0.0147151	+	0.0452884i
$442$	87.1835	−	63.3425i	4.14690	−	3.01290i
$443$	21.6482			1.02854			0.514268	−	0.857630i	$-0.328064\pi$
$443$	21.6482			1.02854			0.514268	+	0.857630i	$0.328064\pi$
$444$	0.0289877	−	0.0210608i	0.00137570	−	0.000999502i
$445$	19.5046	+	17.1295i	0.924606	+	0.812018i
$446$	27.8635	+	20.2440i	1.31938	+	0.958583i
$447$	−0.350369	−	0.254558i	−0.0165719	−	0.0120402i
$448$	3.74395	−	11.5227i	0.176885	−	0.544397i
$449$	14.1660			0.668533			0.334266	−	0.942479i	$-0.391511\pi$
$449$	14.1660			0.668533			0.334266	+	0.942479i	$0.391511\pi$
$450$	8.06105	+	8.51871i	0.380001	+	0.401576i
$451$	−19.1727			−0.902805
$452$	12.0300	−	37.0245i	0.565843	−	1.74149i
$453$	12.6656	+	9.20208i	0.595081	+	0.432352i
$454$	−40.3146	−	29.2903i	−1.89206	−	1.37466i
$455$	−14.8544	−	1.37554i	−0.696383	−	0.0644861i
$456$	0.511833	−	0.371869i	0.0239688	−	0.0174143i
$457$	14.2988			0.668868			0.334434	−	0.942419i	$-0.391455\pi$
$457$	14.2988			0.668868			0.334434	+	0.942419i	$0.391455\pi$
$458$	−51.5301	+	37.4388i	−2.40784	+	1.74940i
$459$	−2.12803	−	6.54940i	−0.0993279	−	0.305700i
$460$	−12.2631	−	54.3741i	−0.571771	−	2.53521i
$461$	5.62261	−	17.3046i	0.261871	−	0.805956i	−0.730527	−	0.682884i	$-0.760725\pi$
$461$	5.62261	−	17.3046i	0.261871	−	0.805956i	0.992398	−	0.123072i	$-0.0392746\pi$
$462$	1.72007	+	5.29383i	0.0800249	+	0.246291i
$463$	−1.71484	−	5.27774i	−0.0796955	−	0.245277i	0.903268	−	0.429076i	$-0.141161\pi$
$463$	−1.71484	−	5.27774i	−0.0796955	−	0.245277i	−0.982964	+	0.183798i	$0.941161\pi$
$464$	−1.34004	+	4.12421i	−0.0622097	+	0.191462i
$465$	2.56663	−	5.96235i	0.119025	−	0.276498i
$466$	11.7996	+	36.3154i	0.546606	+	1.68228i
$467$	9.52080	−	6.91726i	0.440570	−	0.320093i	−0.345291	−	0.938496i	$-0.612220\pi$
$467$	9.52080	−	6.91726i	0.440570	−	0.320093i	0.785861	+	0.618403i	$0.212220\pi$
$468$	23.3633			1.07997
$469$	−9.67145	+	7.02672i	−0.446586	+	0.324464i
$470$	−2.08409	−	9.24078i	−0.0961321	−	0.426245i
$471$	−6.93927	−	5.04167i	−0.319745	−	0.232308i
$472$	−33.8731	−	24.6102i	−1.55913	−	1.13278i
$473$	−6.08262	+	18.7204i	−0.279679	+	0.860764i
$474$	4.41818			0.202934
$475$	−0.882626	−	0.164879i	−0.0404977	−	0.00756517i
$476$	−24.1160			−1.10536
$477$	−0.291868	+	0.898278i	−0.0133637	+	0.0411293i
$478$	−24.1448	−	17.5422i	−1.10436	−	0.802362i
$479$	−26.3064	−	19.1128i	−1.20197	−	0.873284i	−0.207495	−	0.978236i	$-0.566531\pi$
$479$	−26.3064	−	19.1128i	−1.20197	−	0.873284i	−0.994477	+	0.104952i	$0.966531\pi$
$480$	7.86509	−	4.67170i	0.358991	−	0.213233i
$481$	−0.0552238	+	0.0401225i	−0.00251799	+	0.00182943i
$482$	−53.2954			−2.42754
$483$	5.75874	−	4.18397i	0.262032	−	0.190377i
$484$	−5.80979	−	17.8807i	−0.264081	−	0.812759i
$485$	−20.1667	+	11.9786i	−0.915724	+	0.543920i
$486$	0.724838	−	2.23082i	0.0328793	−	0.101192i
$487$	1.84414	+	5.67568i	0.0835659	+	0.257189i	0.984106	−	0.177584i	$-0.0568283\pi$
$487$	1.84414	+	5.67568i	0.0835659	+	0.257189i	−0.900540	+	0.434774i	$0.856828\pi$
$488$	−3.33059	−	10.2505i	−0.150769	−	0.464019i
$489$	−4.78383	+	14.7231i	−0.216332	+	0.665803i
$490$	3.94093	+	3.46105i	0.178033	+	0.156354i
$491$	−0.784510	−	2.41447i	−0.0354045	−	0.108964i	0.931792	−	0.362991i	$-0.118245\pi$
$491$	−0.784510	−	2.41447i	−0.0354045	−	0.108964i	−0.967197	+	0.254028i	$0.918245\pi$
$492$	22.8900	−	16.6305i	1.03196	−	0.749763i
$493$	−23.7047			−1.06761
$494$	−2.27350	+	1.65179i	−0.102289	+	0.0743176i
$495$	−2.09807	+	4.87388i	−0.0943014	+	0.219065i
$496$	2.95870	+	2.14962i	0.132850	+	0.0965209i
$497$	3.55634	+	2.58383i	0.159524	+	0.115901i
$498$	−9.38843	+	28.8946i	−0.420706	+	1.29480i
$499$	31.0837			1.39150			0.695748	−	0.718286i	$-0.255073\pi$
$499$	31.0837			1.39150			0.695748	+	0.718286i	$0.255073\pi$
$500$	37.6604	+	10.7078i	1.68422	+	0.478867i
$501$	5.95114			0.265877
$502$	−9.49535	+	29.2237i	−0.423798	+	1.30432i
$503$	−29.3444	−	21.3200i	−1.30840	−	0.950611i	−0.308404	−	0.951255i	$-0.599795\pi$
$503$	−29.3444	−	21.3200i	−1.30840	−	0.950611i	−1.00000		0.000644197i	$0.999795\pi$
$504$	−2.85019	−	2.07078i	−0.126957	−	0.0922399i
$505$	−14.4511	+	33.5702i	−0.643064	+	1.49385i
$506$	32.0547	−	23.2891i	1.42500	−	1.03533i
$507$	−31.5088			−1.39935
$508$	16.6325	−	12.0842i	0.737949	−	0.536151i
$509$	−9.23095	−	28.4099i	−0.409155	−	1.25925i	−0.917376	−	0.398022i	$-0.869697\pi$
$509$	−9.23095	−	28.4099i	−0.409155	−	1.25925i	0.508221	−	0.861227i	$-0.330303\pi$
$510$	−27.1390	−	23.8343i	−1.20174	−	1.05540i
$511$	−2.51112	+	7.72843i	−0.111085	+	0.341885i
$512$	4.33561	+	13.3436i	0.191609	+	0.589711i
$513$	0.0554929	+	0.170790i	0.00245007	+	0.00754055i
$514$	10.4522	−	32.1686i	0.461028	−	1.41890i
$515$	2.96813	−	1.76300i	0.130791	−	0.0776872i
$516$	−8.97627	−	27.6261i	−0.395158	−	1.21617i
$517$	3.46738	−	2.51920i	0.152495	−	0.110794i
$518$	0.0239996			0.00105448
$519$	3.86556	−	2.80849i	0.169679	−	0.123279i
$520$	45.1861	−	26.8396i	1.98154	−	1.17699i
$521$	18.2598	+	13.2666i	0.799978	+	0.581218i	0.910908	−	0.412610i	$-0.135383\pi$
$521$	18.2598	+	13.2666i	0.799978	+	0.581218i	−0.110930	+	0.993828i	$0.535383\pi$
$522$	−6.53215	−	4.74588i	−0.285904	−	0.207722i
$523$	1.64662	−	5.06776i	0.0720015	−	0.221598i	−0.908580	−	0.417712i	$-0.862832\pi$
$523$	1.64662	−	5.06776i	0.0720015	−	0.221598i	0.980581	+	0.196114i	$0.0628322\pi$
$524$	−73.9615			−3.23102
$525$	0.645607	+	4.95814i	0.0281766	+	0.216391i
$526$	−5.21231			−0.227268
$527$	−6.17769	+	19.0130i	−0.269104	+	0.828218i
$528$	−2.41857	−	1.75719i	−0.105255	−	0.0764719i
$529$	−22.3845	−	16.2633i	−0.973238	−	0.707099i
$530$	1.08989	+	4.83253i	0.0473419	+	0.209912i
$531$	9.61477	−	6.98554i	0.417245	−	0.303147i
$532$	0.628877			0.0272653
$533$	−43.6071	+	31.6824i	−1.88884	+	1.37232i
$534$	−8.41468	−	25.8977i	−0.364139	−	1.12070i
$535$	−2.91451	+	6.77047i	−0.126005	+	0.292713i
$536$	13.0146	−	40.0549i	0.562147	−	1.73011i
$537$	−5.49417	−	16.9093i	−0.237091	−	0.729691i
$538$	13.9791	+	43.0232i	0.602681	+	1.85486i
$539$	−0.733310	+	2.25690i	−0.0315859	+	0.0972114i
$540$	−1.72278	−	7.63875i	−0.0741368	−	0.328719i
$541$	7.26584	+	22.3620i	0.312383	+	0.961416i	0.976818	+	0.214070i	$0.0686721\pi$
$541$	7.26584	+	22.3620i	0.312383	+	0.961416i	−0.664435	+	0.747346i	$0.731328\pi$
$542$	33.5205	−	24.3541i	1.43983	−	1.04610i
$543$	14.0784			0.604160
$544$	−22.7924	+	16.5597i	−0.977216	+	0.709989i
$545$	−25.9569	−	2.40365i	−1.11187	−	0.102961i
$546$	12.6602	+	9.19814i	0.541805	+	0.393644i
$547$	4.10830	+	2.98486i	0.175658	+	0.127623i	0.672140	−	0.740424i	$-0.265375\pi$
$547$	4.10830	+	2.98486i	0.175658	+	0.127623i	−0.496482	+	0.868047i	$0.665375\pi$
$548$	16.4515	−	50.6326i	0.702774	−	2.16292i
$549$	3.05931			0.130568
$550$	3.59362	+	27.5983i	0.153232	+	1.17680i
$551$	0.618152			0.0263341
$552$	−7.74940	+	23.8502i	−0.329836	+	1.01513i
$553$	1.52385	+	1.10714i	0.0648008	+	0.0470805i
$554$	−30.2377	−	21.9690i	−1.28468	−	0.933373i
$555$	0.0171904	+	0.0150971i	0.000729692	+	0.000640838i
$556$	19.4898	−	14.1602i	0.826554	−	0.600526i
$557$	−29.1969			−1.23711			−0.618556	−	0.785741i	$-0.712282\pi$
$557$	−29.1969			−1.23711			−0.618556	+	0.785741i	$0.712282\pi$
$558$	−5.50889	+	4.00245i	−0.233210	+	0.169437i
$559$	17.1005	+	52.6299i	0.723273	+	2.22601i
$560$	−2.80496	−	0.259743i	−0.118531	−	0.0109762i
$561$	5.04990	−	15.5420i	0.213207	−	0.656184i
$562$	0.750375	+	2.30942i	0.0316526	+	0.0974168i
$563$	0.534740	+	1.64576i	0.0225366	+	0.0693606i	0.961692	−	0.274131i	$-0.0883903\pi$
$563$	0.534740	+	1.64576i	0.0225366	+	0.0693606i	−0.939156	+	0.343492i	$0.888390\pi$
$564$	−1.95448	+	6.01527i	−0.0822985	+	0.253289i
$565$	24.7516	+	2.29204i	1.04131	+	0.0964267i
$566$	11.6567	+	35.8757i	0.489968	+	1.50797i
$567$	0.809017	−	0.587785i	0.0339755	−	0.0246847i
$568$	−15.4868			−0.649811
$569$	−22.9631	+	16.6837i	−0.962665	+	0.699417i	−0.953768	−	0.300543i	$-0.902832\pi$
$569$	−22.9631	+	16.6837i	−0.962665	+	0.699417i	−0.00889704	+	0.999960i	$0.502832\pi$
$570$	0.707708	+	0.621531i	0.0296426	+	0.0260331i
$571$	−26.0053	−	18.8939i	−1.08829	−	0.790687i	−0.109178	−	0.994022i	$-0.534822\pi$
$571$	−26.0053	−	18.8939i	−1.08829	−	0.790687i	−0.979109	+	0.203335i	$0.934822\pi$
$572$	44.8535	+	32.5880i	1.87542	+	1.36257i
$573$	5.48865	−	16.8923i	0.229292	−	0.705687i
$574$	18.9512			0.791006
$575$	32.1456	−	15.2768i	1.34056	−	0.637086i
$576$	−12.1157			−0.504820
$577$	−1.44927	+	4.46041i	−0.0603341	+	0.185689i	−0.976681	−	0.214696i	$-0.931124\pi$
$577$	−1.44927	+	4.46041i	−0.0603341	+	0.185689i	0.916347	+	0.400386i	$0.131124\pi$
$578$	57.7325	+	41.9451i	2.40136	+	1.74469i
$579$	−7.47325	−	5.42964i	−0.310578	−	0.225648i
$580$	−26.8399	−	2.48542i	−1.11447	−	0.103201i
$581$	−10.4788	+	7.61326i	−0.434732	+	0.315851i
$582$	24.6052			1.01992
$583$	−1.81329	+	1.31743i	−0.0750988	+	0.0545625i
$584$	−8.84673	−	27.2274i	−0.366080	−	1.12668i
$585$	3.28204	+	14.5524i	0.135695	+	0.601668i
$586$	−18.0219	+	55.4658i	−0.744479	+	2.29127i
$587$	−12.0909	−	37.2121i	−0.499046	−	1.53591i	−0.810554	−	0.585663i	$-0.800834\pi$
$587$	−12.0909	−	37.2121i	−0.499046	−	1.53591i	0.311508	−	0.950244i	$-0.399166\pi$
$588$	−1.08216	−	3.33056i	−0.0446277	−	0.137350i
$589$	0.161096	−	0.495804i	0.00663786	−	0.0204292i
$590$	24.6465	−	57.2544i	1.01468	−	2.35713i
$591$	2.22451	+	6.84633i	0.0915040	+	0.281620i
$592$	−0.0104279	+	0.00757635i	−0.000428586	+	0.000311386i
$593$	−46.7848			−1.92122			−0.960612	−	0.277895i	$-0.910363\pi$
$593$	−46.7848			−1.92122			−0.960612	+	0.277895i	$0.910363\pi$
$594$	4.50320	−	3.27177i	0.184769	−	0.134242i
$595$	−3.38778	−	15.0213i	−0.138886	−	0.615812i
$596$	1.22698	+	0.891452i	0.0502590	+	0.0365153i
$597$	12.6869	+	9.21757i	0.519240	+	0.377250i
$598$	34.4218	−	105.939i	1.40761	−	4.33219i
$599$	−10.3975			−0.424829			−0.212415	−	0.977180i	$-0.568133\pi$
$599$	−10.3975			−0.424829			−0.212415	+	0.977180i	$0.568133\pi$
$600$	−12.1073	−	12.7947i	−0.494280	−	0.522342i
$601$	−21.9492			−0.895327			−0.447663	−	0.894202i	$-0.647744\pi$
$601$	−21.9492			−0.895327			−0.447663	+	0.894202i	$0.647744\pi$
$602$	6.01234	−	18.5041i	0.245045	−	0.754171i
$603$	9.67145	+	7.02672i	0.393852	+	0.286150i
$604$	−44.3543	−	32.2253i	−1.80475	−	1.31123i
$605$	10.3213	−	6.13063i	0.419620	−	0.249245i
$606$	31.0171	−	22.5352i	1.25998	−	0.915430i
$607$	11.9790			0.486212			0.243106	−	0.970000i	$-0.421834\pi$
$607$	11.9790			0.486212			0.243106	+	0.970000i	$0.421834\pi$
$608$	0.594361	−	0.431828i	0.0241045	−	0.0175130i
$609$	−1.06371	−	3.27375i	−0.0431036	−	0.132659i
$610$	13.7959	−	8.19445i	0.558578	−	0.331783i
$611$	3.72343	−	11.4596i	0.150634	−	0.463604i
$612$	7.45226	+	22.9357i	0.301240	+	0.927121i
$613$	12.7440	+	39.2219i	0.514725	+	1.58416i	0.783783	+	0.621035i	$0.213288\pi$
$613$	12.7440	+	39.2219i	0.514725	+	1.58416i	−0.269058	+	0.963124i	$0.586712\pi$
$614$	13.6422	−	41.9862i	0.550552	−	1.69443i
$615$	13.5743	+	11.9214i	0.547369	+	0.480716i
$616$	−2.58347	−	7.95110i	−0.104091	−	0.320359i
$617$	8.44895	−	6.13852i	0.340142	−	0.247127i	−0.404580	−	0.914503i	$-0.632582\pi$
$617$	8.44895	−	6.13852i	0.340142	−	0.247127i	0.744722	+	0.667375i	$0.232582\pi$
$618$	−3.62138			−0.145673
$619$	−22.5958	+	16.4168i	−0.908203	+	0.659848i	−0.940560	−	0.339628i	$-0.889699\pi$
$619$	−22.5958	+	16.4168i	−0.908203	+	0.659848i	0.0323567	+	0.999476i	$0.489699\pi$
$620$	−8.98824	+	20.8799i	−0.360976	+	0.838557i
$621$	−5.75874	−	4.18397i	−0.231090	−	0.167897i
$622$	25.5515	+	18.5643i	1.02452	+	0.744359i
$623$	3.58739	−	11.0409i	0.143726	−	0.442343i
$624$	−8.40462			−0.336454
$625$	−1.37914	+	24.9619i	−0.0551656	+	0.998477i
$626$	5.76923			0.230585
$627$	−0.131687	+	0.405291i	−0.00525907	+	0.0161858i
$628$	24.3010	+	17.6557i	0.969716	+	0.704540i
$629$	−0.0570031	−	0.0414152i	−0.00227286	−	0.00165133i
$630$	2.07384	−	4.81757i	0.0826236	−	0.191937i
$631$	−6.76437	+	4.91460i	−0.269285	+	0.195647i	−0.714231	−	0.699911i	$-0.753223\pi$
$631$	−6.76437	+	4.91460i	−0.269285	+	0.195647i	0.444945	+	0.895558i	$0.353223\pi$
$632$	−6.63592			−0.263963
$633$	−4.41765	+	3.20961i	−0.175586	+	0.127570i
$634$	−5.77753	−	17.7814i	−0.229455	−	0.706189i
$635$	9.86348	+	8.66241i	0.391420	+	0.343757i
$636$	1.02211	−	3.14573i	0.0405293	−	0.124736i
$637$	2.06160	+	6.34497i	0.0816837	+	0.251397i
$638$	−5.92087	−	18.2226i	−0.234410	−	0.721439i
$639$	1.35840	−	4.18073i	0.0537375	−	0.165387i
$640$	−38.9051	+	23.1088i	−1.53786	+	0.913455i
$641$	1.49611	+	4.60454i	0.0590926	+	0.181868i	0.976246	−	0.216667i	$-0.0695186\pi$
$641$	1.49611	+	4.60454i	0.0590926	+	0.181868i	−0.917153	+	0.398535i	$0.869519\pi$
$642$	6.25555	−	4.54493i	0.246887	−	0.179374i
$643$	−7.83613			−0.309027			−0.154513	−	0.987991i	$-0.549381\pi$
$643$	−7.83613			−0.309027			−0.154513	+	0.987991i	$0.549381\pi$
$644$	−20.1669	+	14.6521i	−0.794686	+	0.577373i
$645$	15.9466	−	9.47197i	0.627899	−	0.372958i
$646$	−2.34675	−	1.70501i	−0.0923316	−	0.0670828i
$647$	−14.2329	−	10.3408i	−0.559553	−	0.406539i	0.271742	−	0.962370i	$-0.412400\pi$
$647$	−14.2329	−	10.3408i	−0.559553	−	0.406539i	−0.831295	+	0.555831i	$0.812400\pi$
$648$	−1.08867	+	3.35059i	−0.0427672	+	0.131624i
$649$	28.2024			1.10704
$650$	53.7792	+	56.8325i	2.10939	+	2.22915i
$651$	−2.90301			−0.113778
$652$	16.7528	−	51.5597i	0.656089	−	2.01923i
$653$	−22.5923	−	16.4143i	−0.884104	−	0.642339i	0.0502298	−	0.998738i	$-0.484005\pi$
$653$	−22.5923	−	16.4143i	−0.884104	−	0.642339i	−0.934334	+	0.356398i	$0.884005\pi$
$654$	22.1227	+	16.0731i	0.865065	+	0.628506i
$655$	−10.3900	−	46.0688i	−0.405971	−	1.80006i
$656$	−8.23436	+	5.98261i	−0.321498	+	0.233582i
$657$	8.12615			0.317031
$658$	−3.42732	+	2.49009i	−0.133611	+	0.0970739i
$659$	10.2523	+	31.5534i	0.399374	+	1.22915i	0.925502	+	0.378742i	$0.123643\pi$
$659$	10.2523	+	31.5534i	0.399374	+	1.22915i	−0.526129	+	0.850405i	$0.676357\pi$
$660$	7.34736	−	17.0681i	0.285996	−	0.664375i
$661$	2.60730	−	8.02445i	0.101412	−	0.312115i	−0.887459	−	0.460886i	$-0.847532\pi$
$661$	2.60730	−	8.02445i	0.101412	−	0.312115i	0.988872	+	0.148771i	$0.0475317\pi$
$662$	−5.60044	−	17.2364i	−0.217667	−	0.669910i
$663$	−14.1971	−	43.6943i	−0.551371	−	1.69694i
$664$	14.1010	−	43.3984i	0.547225	−	1.68419i
$665$	0.0883437	+	0.391712i	0.00342582	+	0.0151899i
$666$	−0.00741629	−	0.0228250i	−0.000287375	−	0.000884451i
$667$	−19.8229	+	14.4022i	−0.767546	+	0.557655i
$668$	−20.8406			−0.806348
$669$	11.8789	−	8.63055i	0.459266	−	0.333676i
$670$	62.4343	+	5.78152i	2.41205	+	0.223359i
$671$	5.87336	+	4.26725i	0.226739	+	0.164735i
$672$	−3.30975	−	2.40467i	−0.127676	−	0.0927623i
$673$	2.56708	−	7.90066i	0.0989536	−	0.304548i	−0.889310	−	0.457304i	$-0.848815\pi$
$673$	2.56708	−	7.90066i	0.0989536	−	0.304548i	0.988264	+	0.152756i	$0.0488150\pi$
$674$	2.99454			0.115345
$675$	4.51597	−	2.14616i	0.173820	−	0.0826057i
$676$	110.342			4.24394
$677$	7.19325	−	22.1385i	0.276459	−	0.850854i	−0.712371	−	0.701804i	$-0.752378\pi$
$677$	7.19325	−	22.1385i	0.276459	−	0.850854i	0.988830	−	0.149050i	$-0.0476216\pi$
$678$	−21.0954	−	15.3267i	−0.810165	−	0.588619i
$679$	8.48646	+	6.16577i	0.325680	+	0.236621i
$680$	40.7616	+	35.7981i	1.56314	+	1.37279i
$681$	−17.1871	+	12.4872i	−0.658613	+	0.478510i
$682$	−16.1589			−0.618757
$683$	−7.43798	+	5.40401i	−0.284606	+	0.206779i	−0.720924	−	0.693014i	$-0.756282\pi$
$683$	−7.43798	+	5.40401i	−0.284606	+	0.206779i	0.436318	+	0.899793i	$0.356282\pi$
$684$	−0.194334	−	0.598098i	−0.00743054	−	0.0228688i
$685$	33.8489	+	3.13446i	1.29330	+	0.119761i
$686$	0.724838	−	2.23082i	0.0276744	−	0.0851732i
$687$	8.39126	+	25.8256i	0.320147	+	0.985310i
$688$	3.22909	+	9.93813i	0.123108	+	0.378888i
$689$	−1.94720	+	5.99285i	−0.0741823	+	0.228310i
$690$	−37.1757	−	3.44253i	−1.41526	−	0.131055i
$691$	−8.26429	−	25.4349i	−0.314388	−	0.967588i	−0.976005	−	0.217746i	$-0.930129\pi$
$691$	−8.26429	−	25.4349i	−0.314388	−	0.967588i	0.661617	−	0.749842i	$-0.269871\pi$
$692$	−13.5370	+	9.83522i	−0.514600	+	0.373879i
$693$	2.37304			0.0901444
$694$	−47.8157	+	34.7401i	−1.81506	+	1.31872i
$695$	11.5579	+	10.1505i	0.438418	+	0.385032i
$696$	9.81099	+	7.12810i	0.371885	+	0.270190i
$697$	−45.0122	−	32.7033i	−1.70496	−	1.23872i
$698$	−16.1332	+	49.6529i	−0.610651	+	1.87939i
$699$	16.2790			0.615727
$700$	−2.26089	−	17.3632i	−0.0854534	−	0.656267i
$701$	44.2821			1.67251			0.836256	−	0.548339i	$-0.184740\pi$
$701$	44.2821			1.67251			0.836256	+	0.548339i	$0.184740\pi$
$702$	4.83575	−	14.8829i	0.182514	−	0.561719i
$703$	0.00148648	+	0.00107999i	5.60636e−5	+	4.07326e-5i
$704$	−23.2601	−	16.8994i	−0.876646	−	0.636921i
$705$	−4.02133	−	0.372381i	−0.151452	−	0.0140247i
$706$	−36.0298	+	26.1772i	−1.35600	+	0.985191i
$707$	16.3450			0.614716
$708$	−33.6705	+	24.4630i	−1.26541	+	0.919377i
$709$	−8.37359	−	25.7713i	−0.314477	−	0.967861i	−0.975969	−	0.217909i	$-0.930077\pi$
$709$	−8.37359	−	25.7713i	−0.314477	−	0.967861i	0.661492	−	0.749952i	$-0.269923\pi$
$710$	−5.07252	−	22.4913i	−0.190368	−	0.844085i
$711$	0.582060	−	1.79140i	0.0218290	−	0.0671826i
$712$	12.6385	+	38.8972i	0.473647	+	1.45773i
$713$	6.38559	+	19.6528i	0.239142	+	0.736004i
$714$	−4.99156	+	15.3624i	−0.186804	+	0.574925i
$715$	−13.9973	+	32.5160i	−0.523469	+	1.21603i
$716$	19.2403	+	59.2157i	0.719045	+	2.21299i
$717$	−10.2935	+	7.47870i	−0.384419	+	0.279297i
$718$	−37.3212			−1.39281
$719$	−0.572103	+	0.415657i	−0.0213359	+	0.0155014i	−0.598402	−	0.801196i	$-0.704197\pi$
$719$	−0.572103	+	0.415657i	−0.0213359	+	0.0155014i	0.577066	+	0.816697i	$0.304197\pi$
$720$	0.619749	+	2.74794i	0.0230967	+	0.102410i
$721$	−1.24903	−	0.907475i	−0.0465164	−	0.0337961i
$722$	−35.9942	−	26.1513i	−1.33956	−	0.973250i
$723$	−7.02123	+	21.6091i	−0.261122	+	0.803652i
$724$	−49.3018			−1.83229
$725$	−2.22233	−	17.0671i	−0.0825351	−	0.633855i
$726$	−12.5929			−0.467367
$727$	−1.53512	+	4.72462i	−0.0569345	+	0.175226i	−0.975480	−	0.220090i	$-0.929365\pi$
$727$	−1.53512	+	4.72462i	−0.0569345	+	0.175226i	0.918545	+	0.395316i	$0.129365\pi$
$728$	−19.0150	−	13.8152i	−0.704743	−	0.512025i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	36.6446	−	21.7661i	1.35628	−	0.805600i
$731$	−46.2121	+	33.5751i	−1.70922	+	1.24182i
$732$	−10.7136			−0.395985
$733$	−26.9317	+	19.5670i	−0.994745	+	0.722724i	−0.960955	−	0.276705i	$-0.910758\pi$
$733$	−26.9317	+	19.5670i	−0.994745	+	0.722724i	−0.0337897	+	0.999429i	$0.510758\pi$
$734$	−0.389016	−	1.19727i	−0.0143588	−	0.0441919i
$735$	1.92250	−	1.14192i	0.0709125	−	0.0421205i
$736$	−8.99891	+	27.6958i	−0.331704	+	1.02088i
$737$	8.76640	+	26.9802i	0.322915	+	0.993829i
$738$	−5.85623	−	18.0236i	−0.215571	−	0.663459i
$739$	−14.2743	+	43.9318i	−0.525089	+	1.61606i	0.239051	+	0.971007i	$0.423164\pi$
$739$	−14.2743	+	43.9318i	−0.525089	+	1.61606i	−0.764140	+	0.645051i	$0.776836\pi$
$740$	−0.0602000	−	0.0528695i	−0.00221300	−	0.00194352i
$741$	0.370221	+	1.13942i	0.0136004	+	0.0418577i
$742$	1.79234	−	1.30221i	0.0657989	−	0.0478057i
$743$	−41.2531			−1.51343			−0.756715	−	0.653744i	$-0.773197\pi$
$743$	−41.2531			−1.51343			−0.756715	+	0.653744i	$0.773197\pi$
$744$	8.27412	−	6.01150i	0.303344	−	0.220392i
$745$	−0.382899	+	0.889484i	−0.0140283	+	0.0325882i
$746$	−7.05272	−	5.12410i	−0.258218	−	0.187607i
$747$	10.4788	+	7.61326i	0.383398	+	0.278555i
$748$	−17.6845	+	54.4274i	−0.646610	+	1.99006i
$749$	3.29647			0.120451
$750$	14.6161	−	21.7742i	0.533704	−	0.795081i
$751$	−28.3581			−1.03480			−0.517402	−	0.855743i	$-0.673101\pi$
$751$	−28.3581			−1.03480			−0.517402	+	0.855743i	$0.673101\pi$
$752$	0.703098	−	2.16391i	0.0256393	−	0.0789098i
$753$	10.5981	+	7.69996i	0.386216	+	0.280602i
$754$	−43.5792	−	31.6621i	−1.58706	−	1.15307i
$755$	13.8415	−	32.1542i	0.503744	−	1.17021i
$756$	−2.83314	+	2.05840i	−0.103040	+	0.0748632i
$757$	−3.66239			−0.133112			−0.0665560	−	0.997783i	$-0.521201\pi$
$757$	−3.66239			−0.133112			−0.0665560	+	0.997783i	$0.521201\pi$
$758$	−9.79571	+	7.11700i	−0.355796	+	0.258501i
$759$	−5.21984	−	16.0650i	−0.189468	−	0.583124i
$760$	−1.06295	−	0.933511i	−0.0385571	−	0.0338620i
$761$	2.68973	−	8.27813i	0.0975025	−	0.300082i	−0.890395	−	0.455188i	$-0.849572\pi$
$761$	2.68973	−	8.27813i	0.0975025	−	0.300082i	0.987898	+	0.155106i	$0.0495720\pi$
$762$	−4.25530	−	13.0965i	−0.154153	−	0.474435i
$763$	3.60250	+	11.0873i	0.130419	+	0.401389i
$764$	−19.2210	+	59.1562i	−0.695392	+	2.14020i
$765$	−13.2392	+	7.86380i	−0.478664	+	0.284316i
$766$	3.95096	+	12.1598i	0.142754	+	0.439351i
$767$	64.1448	−	46.6040i	2.31614	−	1.68277i
$768$	23.2363			0.838469
$769$	42.5766	−	30.9337i	1.53535	−	1.11550i	0.582184	−	0.813057i	$-0.302198\pi$
$769$	42.5766	−	30.9337i	1.53535	−	1.11550i	0.953168	−	0.302442i	$-0.0978018\pi$
$770$	10.7011	−	6.35625i	0.385642	−	0.229063i
$771$	−11.6661	−	8.47591i	−0.420144	−	0.305252i
$772$	26.1710	+	19.0143i	0.941915	+	0.684341i
$773$	−2.85746	+	8.79436i	−0.102776	+	0.316311i	−0.989202	−	0.146559i	$-0.953180\pi$
$773$	−2.85746	+	8.79436i	−0.102776	+	0.316311i	0.886426	+	0.462870i	$0.153180\pi$
$774$	−19.4564			−0.699344
$775$	−14.2682	−	2.66538i	−0.512530	−	0.0957431i
$776$	−36.9560			−1.32664
$777$	0.00316176	−	0.00973088i	0.000113427	−	0.000349093i
$778$	2.68028	+	1.94734i	0.0960928	+	0.0698155i
$779$	1.17379	+	0.852807i	0.0420553	+	0.0305550i
$780$	−11.4935	−	50.9618i	−0.411535	−	1.82473i
$781$	8.43933	−	6.13153i	0.301983	−	0.219404i
$782$	114.980			4.11169
$783$	−2.78482	+	2.02329i	−0.0995214	+	0.0723065i
$784$	0.389294	+	1.19812i	0.0139034	+	0.0427901i
$785$	−7.58354	+	17.6167i	−0.270668	+	0.628768i
$786$	−15.3086	+	47.1151i	−0.546041	+	1.68054i
$787$	−10.4282	−	32.0948i	−0.371726	−	1.14406i	−0.945661	−	0.325154i	$-0.894584\pi$
$787$	−10.4282	−	32.0948i	−0.371726	−	1.14406i	0.573935	−	0.818901i	$-0.305416\pi$
$788$	−7.79012	−	23.9755i	−0.277512	−	0.854093i
$789$	−0.686680	+	2.11338i	−0.0244464	+	0.0752384i
$790$	−2.17352	−	9.63730i	−0.0773305	−	0.342880i
$791$	−3.43522	−	10.5725i	−0.122142	−	0.375916i
$792$	−6.76361	+	4.91405i	−0.240334	+	0.174613i
$793$	20.4102			0.724787
$794$	35.1681	−	25.5511i	1.24807	−	0.906775i
$795$	2.10298	+	0.194739i	0.0745850	+	0.00690669i
$796$	−44.4289	−	32.2795i	−1.57474	−	1.14412i
$797$	27.3052	+	19.8384i	0.967199	+	0.702711i	0.954811	−	0.297212i	$-0.0960569\pi$
$797$	27.3052	+	19.8384i	0.967199	+	0.702711i	0.0123873	+	0.999923i	$0.496057\pi$
$798$	0.130166	−	0.400608i	0.00460781	−	0.0141814i
$799$	12.4375			0.440008
$800$	−14.0595	−	14.8577i	−0.497079	−	0.525300i
$801$	−11.6090			−0.410186
$802$	−10.1512	+	31.2422i	−0.358452	+	1.10320i
$803$	15.6008	+	11.3347i	0.550541	+	0.399992i
$804$	−33.8690	−	24.6073i	−1.19447	−	0.867831i
$805$	−11.9594	−	10.5031i	−0.421514	−	0.370187i
$806$	−36.7525	+	26.7023i	−1.29455	+	0.940548i
$807$	19.2858			0.678892
$808$	−46.5862	+	33.8469i	−1.63890	+	1.19073i
$809$	−2.92017	−	8.98737i	−0.102668	−	0.315979i	0.886508	−	0.462713i	$-0.153124\pi$
$809$	−2.92017	−	8.98737i	−0.102668	−	0.315979i	−0.989176	+	0.146734i	$0.953124\pi$
$810$	−5.22263	−	0.483624i	−0.183505	−	0.0169928i
$811$	−12.3880	+	38.1265i	−0.435003	+	1.33880i	0.458081	+	0.888910i	$0.348537\pi$
$811$	−12.3880	+	38.1265i	−0.435003	+	1.33880i	−0.893084	+	0.449890i	$0.851463\pi$
$812$	3.72506	+	11.4645i	0.130724	+	0.402327i
$813$	−5.45855	−	16.7997i	−0.191440	−	0.589190i
$814$	0.0175992	−	0.0541646i	0.000616850	−	0.00189847i
$815$	34.4687	+	3.19185i	1.20738	+	0.111806i
$816$	−2.68085	−	8.25081i	−0.0938486	−	0.288836i
$817$	1.20508	−	0.875542i	0.0421604	−	0.0306313i
$818$	22.8214			0.797930
$819$	5.39735	−	3.92140i	0.188599	−	0.137025i
$820$	−47.5366	−	41.7481i	−1.66005	−	1.45791i
$821$	37.5862	+	27.3080i	1.31177	+	0.953056i	0.999996	+	0.00289886i	$0.000922738\pi$
$821$	37.5862	+	27.3080i	1.31177	+	0.953056i	0.311773	+	0.950157i	$0.399077\pi$
$822$	−28.8489	−	20.9600i	−1.00622	−	0.731062i
$823$	2.21729	−	6.82413i	0.0772900	−	0.237874i	−0.904945	−	0.425528i	$-0.860088\pi$
$823$	2.21729	−	6.82413i	0.0772900	−	0.237874i	0.982235	+	0.187654i	$0.0600884\pi$
$824$	5.43916			0.189482
$825$	11.6634	+	2.17879i	0.406069	+	0.0758557i
$826$	−27.8766			−0.969951
$827$	−2.63484	+	8.10921i	−0.0916224	+	0.281985i	−0.986359	−	0.164610i	$-0.947363\pi$
$827$	−2.63484	+	8.10921i	−0.0916224	+	0.281985i	0.894736	+	0.446595i	$0.147363\pi$
$828$	20.1669	+	14.6521i	0.700847	+	0.509195i
$829$	−22.1672	−	16.1054i	−0.769897	−	0.559363i	0.132033	−	0.991245i	$-0.457850\pi$
$829$	−22.1672	−	16.1054i	−0.769897	−	0.559363i	−0.901930	+	0.431882i	$0.857850\pi$
$830$	67.6459	+	6.26411i	2.34802	+	0.217431i
$831$	−12.8911	+	9.36594i	−0.447188	+	0.324901i
$832$	−80.8297			−2.80227
$833$	−5.57125	+	4.04775i	−0.193032	+	0.140246i
$834$	−4.98633	−	15.3463i	−0.172663	−	0.531401i
$835$	−2.92766	−	12.9811i	−0.101316	−	0.449230i
$836$	0.461162	−	1.41931i	0.0159496	−	0.0490879i
$837$	0.897079	+	2.76093i	0.0310076	+	0.0954315i
$838$	1.66870	+	5.13574i	0.0576444	+	0.177411i
$839$	0.316357	−	0.973645i	0.0109218	−	0.0336140i	−0.945447	−	0.325776i	$-0.894375\pi$
$839$	0.316357	−	0.973645i	0.0109218	−	0.0336140i	0.956369	+	0.292162i	$0.0943746\pi$
$840$	−3.11481	+	7.23578i	−0.107471	+	0.249658i
$841$	−5.29997	−	16.3116i	−0.182758	−	0.562470i
$842$	−31.5882	+	22.9502i	−1.08860	+	0.790915i
$843$	1.03523			0.0356552
$844$	15.4704	−	11.2399i	0.532513	−	0.386894i
$845$	15.5007	+	68.7295i	0.533241	+	2.36437i
$846$	3.42732	+	2.49009i	0.117834	+	0.0856112i
$847$	−4.34335	−	3.15563i	−0.149239	−	0.108429i
$848$	−0.367690	+	1.13163i	−0.0126265	+	0.0388605i
$849$	16.0818			0.551926
$850$	−38.6383	+	70.9231i	−1.32528	+	2.43264i
$851$	−0.0728309			−0.00249661
$852$	−4.75706	+	14.6407i	−0.162974	+	0.501583i
$853$	20.6962	+	15.0366i	0.708623	+	0.514845i	0.882729	−	0.469882i	$-0.155704\pi$
$853$	20.6962	+	15.0366i	0.708623	+	0.514845i	−0.174106	+	0.984727i	$0.555704\pi$
$854$	−5.80550	−	4.21795i	−0.198660	−	0.144335i
$855$	0.345240	−	0.205065i	0.0118070	−	0.00701309i
$856$	−9.39556	+	6.82628i	−0.321134	+	0.233317i
$857$	11.1407			0.380557			0.190279	−	0.981730i	$-0.439061\pi$
$857$	11.1407			0.380557			0.190279	+	0.981730i	$0.439061\pi$
$858$	30.0431	−	21.8276i	1.02565	−	0.745181i
$859$	−2.75032	−	8.46462i	−0.0938397	−	0.288809i	0.893110	−	0.449839i	$-0.148519\pi$
$859$	−2.75032	−	8.46462i	−0.0938397	−	0.288809i	−0.986950	+	0.161030i	$0.948519\pi$
$860$	−55.8445	+	33.1704i	−1.90428	+	1.13110i
$861$	2.49666	−	7.68393i	0.0850860	−	0.261868i
$862$	20.9367	+	64.4365i	0.713107	+	2.19472i
$863$	0.914872	+	2.81569i	0.0311426	+	0.0958471i	0.965420	−	0.260701i	$-0.0839536\pi$
$863$	0.914872	+	2.81569i	0.0311426	+	0.0958471i	−0.934277	+	0.356548i	$0.883954\pi$
$864$	−1.26421	+	3.89084i	−0.0430093	+	0.132369i
$865$	−8.02777	−	7.05023i	−0.272952	−	0.239715i
$866$	−22.6958	−	69.8504i	−0.771233	−	2.37361i
$867$	24.6129	−	17.8823i	0.835896	−	0.607314i
$868$	10.1662			0.345064
$869$	3.61616	−	2.62730i	0.122670	−	0.0891249i
$870$	−7.13862	+	16.5832i	−0.242022	+	0.562222i
$871$	64.5230	+	46.8787i	2.18628	+	1.58842i
$872$	−33.2273	−	24.1410i	−1.12522	−	0.817518i
$873$	3.24154	−	9.97643i	0.109709	−	0.337651i
$874$	−2.99836			−0.101421
$875$	10.4975	−	3.84740i	0.354880	−	0.130066i
$876$	−28.4574			−0.961487
$877$	10.5896	−	32.5913i	0.357584	−	1.10053i	−0.596912	−	0.802307i	$-0.703606\pi$
$877$	10.5896	−	32.5913i	0.357584	−	1.10053i	0.954496	−	0.298224i	$-0.0963943\pi$
$878$	7.14379	+	5.19026i	0.241091	+	0.175163i
$879$	20.1149	+	14.6143i	0.678459	+	0.492929i
$880$	−2.64312	+	6.14002i	−0.0890994	+	0.206980i
$881$	30.9094	−	22.4570i	1.04137	−	0.756596i	0.0708139	−	0.997490i	$-0.477440\pi$
$881$	30.9094	−	22.4570i	1.04137	−	0.756596i	0.970552	+	0.240893i	$0.0774403\pi$
$882$	−2.34562			−0.0789813
$883$	−41.2468	+	29.9675i	−1.38806	+	1.00849i	−0.391989	+	0.919970i	$0.628213\pi$
$883$	−41.2468	+	29.9675i	−1.38806	+	1.00849i	−0.996075	+	0.0885179i	$0.971787\pi$
$884$	49.7177	+	153.015i	1.67219	+	5.14646i
$885$	−19.9674	−	17.5360i	−0.671197	−	0.589465i
$886$	−15.6914	+	48.2932i	−0.527163	+	1.62244i
$887$	−14.9924	−	46.1420i	−0.503397	−	1.54930i	−0.803449	−	0.595373i	$-0.797004\pi$
$887$	−14.9924	−	46.1420i	−0.503397	−	1.54930i	0.300053	−	0.953923i	$-0.402996\pi$
$888$	0.0111389	+	0.0342821i	0.000373798	+	0.00115043i
$889$	1.81415	−	5.58337i	0.0608445	−	0.187260i
$890$	−52.3506	+	31.0951i	−1.75480	+	1.04231i
$891$	−0.733310	−	2.25690i	−0.0245668	−	0.0756088i
$892$	−41.5995	+	30.2238i	−1.39285	+	1.01197i
$893$	−0.324335			−0.0108534
$894$	0.821835	−	0.597098i	0.0274863	−	0.0199699i
$895$	−34.1811	+	20.3029i	−1.14255	+	0.678650i
$896$	16.3718	+	11.8948i	0.546945	+	0.397379i
$897$	−38.4194	−	27.9133i	−1.28279	−	0.931999i
$898$	−10.2680	+	31.6017i	−0.342648	+	1.05456i
$899$	9.99282			0.333279
$900$	−15.8147	+	7.51575i	−0.527158	+	0.250525i
$901$	−6.50429			−0.216689
$902$	13.8971	−	42.7708i	0.462722	−	1.42411i
$903$	−6.71059	−	4.87553i	−0.223314	−	0.162247i
$904$	31.6844	+	23.0201i	1.05381	+	0.765636i
$905$	−6.92584	−	30.7088i	−0.230223	−	1.02080i
$906$	−29.7087	+	21.5846i	−0.987006	+	0.717102i
$907$	8.93453			0.296666			0.148333	−	0.988937i	$-0.452609\pi$
$907$	8.93453			0.296666			0.148333	+	0.988937i	$0.452609\pi$
$908$	60.1886	−	43.7296i	1.99743	−	1.45122i
$909$	−5.05088	−	15.5450i	−0.167527	−	0.515595i
$910$	13.8356	−	32.1404i	0.458645	−	1.06544i
$911$	16.9686	−	52.2240i	0.562195	−	1.73026i	−0.113948	−	0.993487i	$-0.536350\pi$
$911$	16.9686	−	52.2240i	0.562195	−	1.73026i	0.676143	−	0.736771i	$-0.263650\pi$
$912$	0.0699090	+	0.215158i	0.00231492	+	0.00712458i
$913$	9.49816	+	29.2323i	0.314343	+	0.967449i
$914$	−10.3643	+	31.8980i	−0.342820	+	1.05509i
$915$	−1.50503	−	6.67322i	−0.0497546	−	0.220610i
$916$	−29.3858	−	90.4403i	−0.970935	−	2.98823i
$917$	−17.0865	+	12.4141i	−0.564246	+	0.409948i
$918$	16.1530			0.533129
$919$	18.6667	−	13.5621i	0.615756	−	0.447373i	−0.235680	−	0.971831i	$-0.575732\pi$
$919$	18.6667	−	13.5621i	0.615756	−	0.447373i	0.851437	+	0.524458i	$0.175732\pi$
$920$	55.8363	+	5.17053i	1.84087	+	0.170467i
$921$	−15.2265	−	11.0627i	−0.501730	−	0.364528i
$922$	34.5280	+	25.0861i	1.13712	+	0.826166i
$923$	9.06255	−	27.8917i	0.298298	−	0.918066i
$924$	−8.31028			−0.273388
$925$	0.0244743	−	0.0449241i	0.000804710	−	0.00147710i
$926$	13.0167			0.427755
$927$	−0.477088	+	1.46833i	−0.0156696	+	0.0482261i
$928$	11.3929	+	8.27743i	0.373991	+	0.271720i
$929$	17.0669	+	12.3998i	0.559945	+	0.406824i	0.831439	−	0.555616i	$-0.187518\pi$
$929$	17.0669	+	12.3998i	0.559945	+	0.406824i	−0.271494	+	0.962440i	$0.587518\pi$
$930$	11.4406	+	10.0474i	0.375151	+	0.329469i
$931$	0.145282	−	0.105554i	0.00476144	−	0.00345939i
$932$	−57.0082			−1.86737
$933$	10.8933	−	7.91442i	0.356629	−	0.259106i
$934$	8.53015	+	26.2531i	0.279115	+	0.859028i
$935$	−36.3857	−	3.36938i	−1.18994	−	0.110190i
$936$	−7.26308	+	22.3535i	−0.237401	+	0.730646i
$937$	3.17997	+	9.78695i	0.103885	+	0.319726i	0.989467	−	0.144757i	$-0.0462402\pi$
$937$	3.17997	+	9.78695i	0.103885	+	0.319726i	−0.885582	+	0.464483i	$0.846240\pi$
$938$	−8.66513	−	26.6685i	−0.282926	−	0.870758i
$939$	0.760050	−	2.33919i	0.0248033	−	0.0763367i
$940$	14.0825	+	1.30406i	0.459321	+	0.0425338i
$941$	−15.8116	−	48.6630i	−0.515442	−	1.58637i	−0.782476	−	0.622680i	$-0.786044\pi$
$941$	−15.8116	−	48.6630i	−0.515442	−	1.58637i	0.267034	−	0.963687i	$-0.413956\pi$
$942$	16.2769	−	11.8259i	0.530331	−	0.385308i
$943$	−57.5105			−1.87280
$944$	12.1125	−	8.80025i	0.394229	−	0.286424i
$945$	−1.68012	−	1.47553i	−0.0546543	−	0.0479991i
$946$	−37.3529	−	27.1385i	−1.21445	−	0.882348i
$947$	28.1279	+	20.4361i	0.914034	+	0.664085i	0.942032	−	0.335523i	$-0.108913\pi$
$947$	28.1279	+	20.4361i	0.914034	+	0.664085i	−0.0279978	+	0.999608i	$0.508913\pi$
$948$	−2.03835	+	6.27339i	−0.0662025	+	0.203750i
$949$	54.2135			1.75985
$950$	1.00758	−	1.84947i	0.0326901	−	0.0600048i
$951$	−7.97078			−0.258470
$952$	7.49710	−	23.0737i	0.242982	−	0.747823i
$953$	−11.1733	−	8.11784i	−0.361937	−	0.262963i	0.391922	−	0.919998i	$-0.371810\pi$
$953$	−11.1733	−	8.11784i	−0.361937	−	0.262963i	−0.753860	+	0.657036i	$0.771810\pi$
$954$	−1.79234	−	1.30221i	−0.0580292	−	0.0421607i
$955$	−39.5470	−	3.66212i	−1.27971	−	0.118503i
$956$	36.0475	−	26.1901i	1.16586	−	0.847047i
$957$	−8.16855			−0.264052
$958$	61.7051	−	44.8313i	1.99360	−	1.44844i
$959$	−4.69781	−	14.4584i	−0.151700	−	0.466885i
$960$	5.96030	+	26.4277i	0.192368	+	0.852951i
$961$	−6.97530	+	21.4678i	−0.225010	+	0.692508i
$962$	−0.0494777	−	0.152277i	−0.00159523	−	0.00490960i
$963$	−1.01867	−	3.13513i	−0.0328261	−	0.101028i
$964$	24.5880	−	75.6742i	0.791928	−	2.43730i
$965$	−8.16710	+	18.9724i	−0.262908	+	0.610742i
$966$	5.15954	+	15.8794i	0.166005	+	0.510912i
$967$	30.9976	−	22.5211i	0.996816	−	0.724229i	0.0354126	−	0.999373i	$-0.488725\pi$
$967$	30.9976	−	22.5211i	0.996816	−	0.724229i	0.961403	+	0.275144i	$0.0887255\pi$
$968$	18.9140			0.607918
$969$	−1.00048	+	0.726891i	−0.0321400	+	0.0233511i
$970$	−12.1045	−	53.6709i	−0.388653	−	1.72327i
$971$	−10.6289	−	7.72234i	−0.341097	−	0.247822i	0.404027	−	0.914747i	$-0.367610\pi$
$971$	−10.6289	−	7.72234i	−0.341097	−	0.247822i	−0.745125	+	0.666925i	$0.767610\pi$
$972$	2.83314	+	2.05840i	0.0908731	+	0.0660231i
$973$	2.12580	−	6.54254i	0.0681500	−	0.209744i
$974$	−13.9981			−0.448529
$975$	30.1283	−	14.3181i	0.964877	−	0.458546i
$976$	3.85406			0.123366
$977$	2.03029	−	6.24858i	0.0649546	−	0.199910i	−0.913312	−	0.407260i	$-0.866484\pi$
$977$	2.03029	−	6.24858i	0.0649546	−	0.199910i	0.978267	+	0.207351i	$0.0664841\pi$
$978$	−29.3772	−	21.3438i	−0.939378	−	0.682498i
$979$	−22.2874	−	16.1927i	−0.712308	−	0.517522i
$980$	−6.73251	+	3.99897i	−0.215062	+	0.127742i
$981$	9.43146	−	6.85236i	0.301123	−	0.218779i
$982$	5.95490			0.190029
$983$	−22.1927	+	16.1239i	−0.707837	+	0.514274i	−0.882475	−	0.470359i	$-0.844125\pi$
$983$	−22.1927	+	16.1239i	−0.707837	+	0.514274i	0.174638	+	0.984633i	$0.444125\pi$
$984$	8.79579	+	27.0707i	0.280400	+	0.862982i
$985$	13.8394	−	8.22032i	0.440961	−	0.261921i
$986$	17.1821	−	52.8810i	0.547189	−	1.68407i
$987$	0.558111	+	1.71769i	0.0177649	+	0.0546747i
$988$	−1.29650	−	3.99020i	−0.0412470	−	0.126945i
$989$	−18.2455	+	56.1538i	−0.580173	+	1.78559i
$990$	−9.35199	−	8.21320i	−0.297226	−	0.261033i
$991$	3.84376	+	11.8299i	0.122101	+	0.375788i	0.993362	−	0.115032i	$-0.0366972\pi$
$991$	3.84376	+	11.8299i	0.122101	+	0.375788i	−0.871261	+	0.490820i	$0.836697\pi$
$992$	9.60823	−	6.98079i	0.305061	−	0.221640i
$993$	−7.72647			−0.245192
$994$	−8.34183	+	6.06070i	−0.264587	+	0.192234i
$995$	13.8648	−	32.2083i	0.439544	−	1.02107i
$996$	−36.6961	−	26.6613i	−1.16276	−	0.844796i
$997$	−35.2958	−	25.6439i	−1.11783	−	0.812151i	−0.133951	−	0.990988i	$-0.542767\pi$
$997$	−35.2958	−	25.6439i	−1.11783	−	0.812151i	−0.983879	+	0.178837i	$0.942767\pi$
$998$	−22.5306	+	69.3421i	−0.713194	+	2.19499i
$999$	−0.0102317			−0.000323715

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.b.421.1	yes	20
25.6	even	5	inner	525.2.n.b.106.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.b.106.1	✓	20	25.6	even	5	inner
525.2.n.b.421.1	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.724838 + 2.23082i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-2.83314 - 2.05840i) q^{4} +(0.884129 - 2.05385i) q^{5} +(-1.89765 + 1.37872i) q^{6} -1.00000 q^{7} +(2.85019 - 2.07078i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.724838 + 2.23082i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-2.83314 - 2.05840i) q^{4} +(0.884129 - 2.05385i) q^{5} +(-1.89765 + 1.37872i) q^{6} -1.00000 q^{7} +(2.85019 - 2.07078i) q^{8} +(0.309017 + 0.951057i) q^{9} +(3.94093 + 3.46105i) q^{10} +(-0.733310 + 2.25690i) q^{11} +(-1.08216 - 3.33056i) q^{12} +(2.06160 + 6.34497i) q^{13} +(0.724838 - 2.23082i) q^{14} +(1.92250 - 1.14192i) q^{15} +(0.389294 + 1.19812i) q^{16} +(-5.57125 + 4.04775i) q^{17} -2.34562 q^{18} +(0.145282 - 0.105554i) q^{19} +(-6.73251 + 3.99897i) q^{20} +(-0.809017 - 0.587785i) q^{21} +(-4.50320 - 3.27177i) q^{22} +(-2.19964 + 6.76981i) q^{23} +3.52302 q^{24} +(-3.43663 - 3.63174i) q^{25} -15.6488 q^{26} +(-0.309017 + 0.951057i) q^{27} +(2.83314 + 2.05840i) q^{28} +(2.78482 + 2.02329i) q^{29} +(1.15393 + 5.11647i) q^{30} +(2.34858 - 1.70635i) q^{31} +4.09107 q^{32} +(-1.91983 + 1.39484i) q^{33} +(-4.99156 - 15.3624i) q^{34} +(-0.884129 + 2.05385i) q^{35} +(1.08216 - 3.33056i) q^{36} +(0.00316176 + 0.00973088i) q^{37} +(0.130166 + 0.400608i) q^{38} +(-2.06160 + 6.34497i) q^{39} +(-1.73315 - 7.68470i) q^{40} +(2.49666 + 7.68393i) q^{41} +(1.89765 - 1.37872i) q^{42} +8.29474 q^{43} +(6.72316 - 4.88466i) q^{44} +(2.22654 + 0.206181i) q^{45} +(-13.5078 - 9.81403i) q^{46} +(-1.46115 - 1.06159i) q^{47} +(-0.389294 + 1.19812i) q^{48} +1.00000 q^{49} +(10.5928 - 5.03408i) q^{50} -6.88645 q^{51} +(7.21965 - 22.2198i) q^{52} +(0.764121 + 0.555166i) q^{53} +(-1.89765 - 1.37872i) q^{54} +(3.98699 + 3.50150i) q^{55} +(-2.85019 + 2.07078i) q^{56} +0.179579 q^{57} +(-6.53215 + 4.74588i) q^{58} +(-3.67251 - 11.3028i) q^{59} +(-7.79725 - 0.722038i) q^{60} +(0.945379 - 2.90958i) q^{61} +(2.10421 + 6.47609i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(-3.74395 + 11.5227i) q^{64} +(14.8544 + 1.37554i) q^{65} +(-1.72007 - 5.29383i) q^{66} +(9.67145 - 7.02672i) q^{67} +24.1160 q^{68} +(-5.75874 + 4.18397i) q^{69} +(-3.94093 - 3.46105i) q^{70} +(-3.55634 - 2.58383i) q^{71} +(2.85019 + 2.07078i) q^{72} +(2.51112 - 7.72843i) q^{73} -0.0239996 q^{74} +(-0.645607 - 4.95814i) q^{75} -0.628877 q^{76} +(0.733310 - 2.25690i) q^{77} +(-12.6602 - 9.19814i) q^{78} +(-1.52385 - 1.10714i) q^{79} +(2.80496 + 0.259743i) q^{80} +(-0.809017 + 0.587785i) q^{81} -18.9512 q^{82} +(10.4788 - 7.61326i) q^{83} +(1.08216 + 3.33056i) q^{84} +(3.38778 + 15.0213i) q^{85} +(-6.01234 + 18.5041i) q^{86} +(1.06371 + 3.27375i) q^{87} +(2.58347 + 7.95110i) q^{88} +(-3.58739 + 11.0409i) q^{89} +(-2.07384 + 4.81757i) q^{90} +(-2.06160 - 6.34497i) q^{91} +(20.1669 - 14.6521i) q^{92} +2.90301 q^{93} +(3.42732 - 2.49009i) q^{94} +(-0.0883437 - 0.391712i) q^{95} +(3.30975 + 2.40467i) q^{96} +(-8.48646 - 6.16577i) q^{97} +(-0.724838 + 2.23082i) q^{98} -2.37304 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9	\( 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9} - 15 q^{10} + 12 q^{11} + 5 q^{12} - 17 q^{13} + 2 q^{14} + 15 q^{15} - 28 q^{16} - 9 q^{17} - 2 q^{18} - 9 q^{19} - 20 q^{20} - 5 q^{21} - 21 q^{22} + 7 q^{23} + 6 q^{24} - 15 q^{25} - 20 q^{26} + 5 q^{27} + 28 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{33} - 5 q^{35} - 5 q^{36} - 5 q^{37} - 6 q^{38} + 17 q^{39} - 10 q^{40} + 11 q^{41} + 3 q^{42} + 28 q^{43} - 17 q^{44} + 5 q^{45} - 43 q^{46} - 24 q^{47} + 28 q^{48} + 20 q^{49} + 10 q^{50} - 36 q^{51} - 9 q^{52} - 26 q^{53} - 3 q^{54} - 25 q^{55} - 4 q^{56} + 24 q^{57} - 16 q^{58} + 64 q^{59} + 5 q^{60} + 8 q^{61} + 27 q^{62} + 5 q^{63} + 26 q^{64} + 25 q^{65} - 4 q^{66} - 3 q^{67} + 80 q^{68} - 2 q^{69} + 15 q^{70} + 19 q^{71} + 4 q^{72} + 31 q^{73} + 8 q^{74} - 5 q^{75} - 72 q^{76} - 12 q^{77} - 30 q^{78} + 43 q^{79} - 25 q^{80} - 5 q^{81} - 6 q^{82} + 32 q^{83} - 5 q^{84} + 35 q^{85} + 53 q^{86} + 17 q^{87} - 61 q^{88} - 47 q^{89} + 10 q^{90} + 17 q^{91} + 41 q^{92} + 4 q^{93} + 12 q^{94} - 40 q^{95} - 6 q^{96} - 45 q^{97} - 2 q^{98} - 18 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9 - 15 * q^10 + 12 * q^11 + 5 * q^12 - 17 * q^13 + 2 * q^14 + 15 * q^15 - 28 * q^16 - 9 * q^17 - 2 * q^18 - 9 * q^19 - 20 * q^20 - 5 * q^21 - 21 * q^22 + 7 * q^23 + 6 * q^24 - 15 * q^25 - 20 * q^26 + 5 * q^27 + 28 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^33 - 5 * q^35 - 5 * q^36 - 5 * q^37 - 6 * q^38 + 17 * q^39 - 10 * q^40 + 11 * q^41 + 3 * q^42 + 28 * q^43 - 17 * q^44 + 5 * q^45 - 43 * q^46 - 24 * q^47 + 28 * q^48 + 20 * q^49 + 10 * q^50 - 36 * q^51 - 9 * q^52 - 26 * q^53 - 3 * q^54 - 25 * q^55 - 4 * q^56 + 24 * q^57 - 16 * q^58 + 64 * q^59 + 5 * q^60 + 8 * q^61 + 27 * q^62 + 5 * q^63 + 26 * q^64 + 25 * q^65 - 4 * q^66 - 3 * q^67 + 80 * q^68 - 2 * q^69 + 15 * q^70 + 19 * q^71 + 4 * q^72 + 31 * q^73 + 8 * q^74 - 5 * q^75 - 72 * q^76 - 12 * q^77 - 30 * q^78 + 43 * q^79 - 25 * q^80 - 5 * q^81 - 6 * q^82 + 32 * q^83 - 5 * q^84 + 35 * q^85 + 53 * q^86 + 17 * q^87 - 61 * q^88 - 47 * q^89 + 10 * q^90 + 17 * q^91 + 41 * q^92 + 4 * q^93 + 12 * q^94 - 40 * q^95 - 6 * q^96 - 45 * q^97 - 2 * q^98 - 18 * q^99

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