LMFDB - Embedded newform 770.2.n.j.421.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 11 x^{10} - 11 x^{9} + 39 x^{8} - 43 x^{7} + 99 x^{6} + 36 x^{5} + 431 x^{4} + \cdots + 25 $ x^12 - 2x^11 + 11x^10 - 11x^9 + 39x^8 - 43x^7 + 99x^6 + 36x^5 + 431x^4 - 350x^3 + 510x^2 - 175*x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.2
Root			$0.198931 - 0.144532i$ of defining polynomial
Character	$\chi$	$=$	770.421
Dual form			770.2.n.j.631.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.0759851 + 0.233858i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.198931 + 0.144532i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.37814 - 1.72782i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.0759851 + 0.233858i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.198931 + 0.144532i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.37814 - 1.72782i) q^{9} -1.00000 q^{10} +(-3.31659 + 0.0151188i) q^{11} +0.245893 q^{12} +(0.931963 - 0.677111i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(0.0759851 - 0.233858i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.30007 - 3.85073i) q^{17} +(0.908367 - 2.79567i) q^{18} +(-1.06140 - 3.26666i) q^{19} +(-0.809017 + 0.587785i) q^{20} +0.245893 q^{21} +(-2.67429 + 1.96167i) q^{22} +8.30827 q^{23} +(0.198931 - 0.144532i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.355978 - 1.09559i) q^{26} +(1.18156 + 0.858454i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-0.906490 + 2.78989i) q^{29} +(-0.0759851 - 0.233858i) q^{30} +(5.12881 - 3.72630i) q^{31} -1.00000 q^{32} +(-0.255547 - 0.774462i) q^{33} -6.55125 q^{34} +(-0.809017 + 0.587785i) q^{35} +(-0.908367 - 2.79567i) q^{36} +(-1.19510 + 3.67814i) q^{37} +(-2.77879 - 2.01891i) q^{38} +(0.229163 + 0.166497i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(-3.26193 - 10.0392i) q^{41} +(0.198931 - 0.144532i) q^{42} -2.95752 q^{43} +(-1.01050 + 3.15894i) q^{44} -2.93954 q^{45} +(6.72153 - 4.88348i) q^{46} +(-1.90664 - 5.86805i) q^{47} +(0.0759851 - 0.233858i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(0.809017 + 0.587785i) q^{50} +(0.497797 - 1.53206i) q^{51} +(-0.355978 - 1.09559i) q^{52} +(-4.33374 + 3.14865i) q^{53} +1.46049 q^{54} +(2.69206 + 1.93721i) q^{55} -1.00000 q^{56} +(0.683283 - 0.496434i) q^{57} +(0.906490 + 2.78989i) q^{58} +(-0.692706 + 2.13193i) q^{59} +(-0.198931 - 0.144532i) q^{60} +(8.07842 + 5.86932i) q^{61} +(1.95903 - 6.02928i) q^{62} +(-0.908367 - 2.79567i) q^{63} +(-0.809017 + 0.587785i) q^{64} -1.15197 q^{65} +(-0.661959 - 0.476346i) q^{66} +14.2147 q^{67} +(-5.30007 + 3.85073i) q^{68} +(0.631304 + 1.94295i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(0.307605 + 0.223488i) q^{71} +(-2.37814 - 1.72782i) q^{72} +(-2.23486 + 6.87819i) q^{73} +(1.19510 + 3.67814i) q^{74} +(-0.198931 + 0.144532i) q^{75} -3.43477 q^{76} +(-1.01050 + 3.15894i) q^{77} +0.283261 q^{78} +(1.83955 - 1.33651i) q^{79} +(0.309017 + 0.951057i) q^{80} +(2.61413 - 8.04545i) q^{81} +(-8.53984 - 6.20456i) q^{82} +(9.16555 + 6.65916i) q^{83} +(0.0759851 - 0.233858i) q^{84} +(2.02445 + 6.23061i) q^{85} +(-2.39268 + 1.73839i) q^{86} -0.721318 q^{87} +(1.03926 + 3.14959i) q^{88} -4.48891 q^{89} +(-2.37814 + 1.72782i) q^{90} +(-0.355978 - 1.09559i) q^{91} +(2.56740 - 7.90163i) q^{92} +(1.26114 + 0.916271i) q^{93} +(-4.99166 - 3.62665i) q^{94} +(-1.06140 + 3.26666i) q^{95} +(-0.0759851 - 0.233858i) q^{96} +(-2.79473 + 2.03049i) q^{97} -1.00000 q^{98} +(-7.86118 + 5.76641i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 12 q^{10} - q^{11} - 2 q^{12} + 2 q^{13} + 3 q^{14} + 3 q^{15} - 3 q^{16} + 7 q^{17} + 9 q^{18} + 6 q^{19} - 3 q^{20} - 2 q^{21} + q^{22} + 8 q^{23} + 2 q^{24} - 3 q^{25} - 7 q^{26} - 3 q^{27} - 3 q^{28} + 20 q^{29} - 3 q^{30} + 6 q^{31} - 12 q^{32} - 12 q^{33} + 18 q^{34} - 3 q^{35} - 9 q^{36} + 22 q^{37} - 6 q^{38} + 23 q^{39} + 3 q^{40} + 2 q^{41} + 2 q^{42} - 60 q^{43} - 11 q^{44} + 6 q^{45} + 2 q^{46} - 4 q^{47} + 3 q^{48} - 3 q^{49} + 3 q^{50} + 13 q^{51} + 7 q^{52} + 18 q^{53} + 8 q^{54} + 14 q^{55} - 12 q^{56} + 8 q^{57} - 20 q^{58} - 32 q^{59} - 2 q^{60} + 8 q^{61} + 14 q^{62} - 9 q^{63} - 3 q^{64} - 18 q^{65} - 8 q^{66} + 36 q^{67} + 7 q^{68} + 50 q^{69} + 3 q^{70} - 34 q^{71} - 6 q^{72} + 14 q^{73} - 22 q^{74} - 2 q^{75} - 24 q^{76} - 11 q^{77} - 38 q^{78} - 12 q^{79} - 3 q^{80} + 4 q^{81} - 2 q^{82} + 30 q^{83} + 3 q^{84} + 2 q^{85} - 28 q^{87} + q^{88} - 36 q^{89} - 6 q^{90} + 7 q^{91} - 2 q^{92} + 12 q^{93} - 11 q^{94} + 6 q^{95} - 3 q^{96} + 39 q^{97} - 12 q^{98} - 15 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 - 12 * q^10 - q^11 - 2 * q^12 + 2 * q^13 + 3 * q^14 + 3 * q^15 - 3 * q^16 + 7 * q^17 + 9 * q^18 + 6 * q^19 - 3 * q^20 - 2 * q^21 + q^22 + 8 * q^23 + 2 * q^24 - 3 * q^25 - 7 * q^26 - 3 * q^27 - 3 * q^28 + 20 * q^29 - 3 * q^30 + 6 * q^31 - 12 * q^32 - 12 * q^33 + 18 * q^34 - 3 * q^35 - 9 * q^36 + 22 * q^37 - 6 * q^38 + 23 * q^39 + 3 * q^40 + 2 * q^41 + 2 * q^42 - 60 * q^43 - 11 * q^44 + 6 * q^45 + 2 * q^46 - 4 * q^47 + 3 * q^48 - 3 * q^49 + 3 * q^50 + 13 * q^51 + 7 * q^52 + 18 * q^53 + 8 * q^54 + 14 * q^55 - 12 * q^56 + 8 * q^57 - 20 * q^58 - 32 * q^59 - 2 * q^60 + 8 * q^61 + 14 * q^62 - 9 * q^63 - 3 * q^64 - 18 * q^65 - 8 * q^66 + 36 * q^67 + 7 * q^68 + 50 * q^69 + 3 * q^70 - 34 * q^71 - 6 * q^72 + 14 * q^73 - 22 * q^74 - 2 * q^75 - 24 * q^76 - 11 * q^77 - 38 * q^78 - 12 * q^79 - 3 * q^80 + 4 * q^81 - 2 * q^82 + 30 * q^83 + 3 * q^84 + 2 * q^85 - 28 * q^87 + q^88 - 36 * q^89 - 6 * q^90 + 7 * q^91 - 2 * q^92 + 12 * q^93 - 11 * q^94 + 6 * q^95 - 3 * q^96 + 39 * q^97 - 12 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.0759851	+	0.233858i	0.0438700	+	0.135018i	0.970592	−	0.240729i	$-0.0773863\pi$
$3$	0.0759851	+	0.233858i	0.0438700	+	0.135018i	−0.926722	+	0.375746i	$0.877386\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	0.198931	+	0.144532i	0.0812134	+	0.0590050i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	2.37814	−	1.72782i	0.792712	−	0.575939i
$10$	−1.00000			−0.316228
$11$	−3.31659	+	0.0151188i	−0.999990	+	0.00455850i
$11$	−3.31659	+	0.0151188i	−0.999990	+	0.00455850i
$12$	0.245893			0.0709831
$13$	0.931963	−	0.677111i	0.258480	−	0.187797i	−0.450997	−	0.892526i	$-0.648931\pi$
$13$	0.931963	−	0.677111i	0.258480	−	0.187797i	0.709477	+	0.704729i	$0.248931\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	0.0759851	−	0.233858i	0.0196193	−	0.0603819i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−5.30007	−	3.85073i	−1.28546	−	0.933938i	−0.285752	−	0.958303i	$-0.592244\pi$
$17$	−5.30007	−	3.85073i	−1.28546	−	0.933938i	−0.999703	+	0.0243653i	$0.992244\pi$
$18$	0.908367	−	2.79567i	0.214104	−	0.658945i
$19$	−1.06140	−	3.26666i	−0.243502	−	0.749423i	−0.995879	−	0.0906900i	$-0.971093\pi$
$19$	−1.06140	−	3.26666i	−0.243502	−	0.749423i	0.752377	−	0.658733i	$-0.228907\pi$
$20$	−0.809017	+	0.587785i	−0.180902	+	0.131433i
$21$	0.245893			0.0536582
$22$	−2.67429	+	1.96167i	−0.570161	+	0.418230i
$23$	8.30827			1.73239			0.866197	−	0.499703i	$-0.166558\pi$
$23$	8.30827			1.73239			0.866197	+	0.499703i	$0.166558\pi$
$24$	0.198931	−	0.144532i	0.0406067	−	0.0295025i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	0.355978	−	1.09559i	0.0698131	−	0.214863i
$27$	1.18156	+	0.858454i	0.227391	+	0.165210i
$28$	−0.809017	−	0.587785i	−0.152890	−	0.111081i
$29$	−0.906490	+	2.78989i	−0.168331	+	0.518070i	−0.999266	−	0.0382994i	$-0.987806\pi$
$29$	−0.906490	+	2.78989i	−0.168331	+	0.518070i	0.830935	+	0.556369i	$0.187806\pi$
$30$	−0.0759851	−	0.233858i	−0.0138729	−	0.0426964i
$31$	5.12881	−	3.72630i	0.921162	−	0.669264i	−0.0226508	−	0.999743i	$-0.507211\pi$
$31$	5.12881	−	3.72630i	0.921162	−	0.669264i	0.943813	+	0.330480i	$0.107211\pi$
$32$	−1.00000			−0.176777
$33$	−0.255547	−	0.774462i	−0.0444850	−	0.134817i
$34$	−6.55125			−1.12353
$35$	−0.809017	+	0.587785i	−0.136749	+	0.0993538i
$36$	−0.908367	−	2.79567i	−0.151394	−	0.465944i
$37$	−1.19510	+	3.67814i	−0.196473	+	0.604683i	0.803483	+	0.595328i	$0.202978\pi$
$37$	−1.19510	+	3.67814i	−0.196473	+	0.604683i	−0.999956	+	0.00935492i	$0.997022\pi$
$38$	−2.77879	−	2.01891i	−0.450779	−	0.327510i
$39$	0.229163	+	0.166497i	0.0366955	+	0.0266608i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	−3.26193	−	10.0392i	−0.509428	−	1.56786i	−0.793197	−	0.608965i	$-0.791585\pi$
$41$	−3.26193	−	10.0392i	−0.509428	−	1.56786i	0.283769	−	0.958893i	$-0.408415\pi$
$42$	0.198931	−	0.144532i	0.0306958	−	0.0223018i
$43$	−2.95752			−0.451018			−0.225509	−	0.974241i	$-0.572404\pi$
$43$	−2.95752			−0.451018			−0.225509	+	0.974241i	$0.572404\pi$
$44$	−1.01050	+	3.15894i	−0.152339	+	0.476228i
$45$	−2.93954			−0.438200
$46$	6.72153	−	4.88348i	0.991035	−	0.720029i
$47$	−1.90664	−	5.86805i	−0.278113	−	0.855943i	−0.988379	−	0.152010i	$-0.951426\pi$
$47$	−1.90664	−	5.86805i	−0.278113	−	0.855943i	0.710266	−	0.703933i	$-0.248574\pi$
$48$	0.0759851	−	0.233858i	0.0109675	−	0.0337545i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$	0.497797	−	1.53206i	0.0697055	−	0.214531i
$52$	−0.355978	−	1.09559i	−0.0493653	−	0.151931i
$53$	−4.33374	+	3.14865i	−0.595285	+	0.432500i	−0.844202	−	0.536025i	$-0.819925\pi$
$53$	−4.33374	+	3.14865i	−0.595285	+	0.432500i	0.248917	+	0.968525i	$0.419925\pi$
$54$	1.46049			0.198747
$55$	2.69206	+	1.93721i	0.362998	+	0.261214i
$56$	−1.00000			−0.133631
$57$	0.683283	−	0.496434i	0.0905031	−	0.0657543i
$58$	0.906490	+	2.78989i	0.119028	+	0.366331i
$59$	−0.692706	+	2.13193i	−0.0901826	+	0.277553i	−0.985968	−	0.166933i	$-0.946614\pi$
$59$	−0.692706	+	2.13193i	−0.0901826	+	0.277553i	0.895786	+	0.444486i	$0.146614\pi$
$60$	−0.198931	−	0.144532i	−0.0256819	−	0.0186590i
$61$	8.07842	+	5.86932i	1.03434	+	0.751489i	0.969172	−	0.246385i	$-0.0792429\pi$
$61$	8.07842	+	5.86932i	1.03434	+	0.751489i	0.0651643	+	0.997875i	$0.479243\pi$
$62$	1.95903	−	6.02928i	0.248797	−	0.765720i
$63$	−0.908367	−	2.79567i	−0.114443	−	0.352221i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−1.15197			−0.142884
$66$	−0.661959	−	0.476346i	−0.0814816	−	0.0586342i
$67$	14.2147			1.73660			0.868299	−	0.496041i	$-0.165213\pi$
$67$	14.2147			1.73660			0.868299	+	0.496041i	$0.165213\pi$
$68$	−5.30007	+	3.85073i	−0.642728	+	0.466969i
$69$	0.631304	+	1.94295i	0.0760001	+	0.233904i
$70$	−0.309017	+	0.951057i	−0.0369346	+	0.113673i
$71$	0.307605	+	0.223488i	0.0365060	+	0.0265231i	0.605889	−	0.795549i	$-0.292818\pi$
$71$	0.307605	+	0.223488i	0.0365060	+	0.0265231i	−0.569383	+	0.822073i	$0.692818\pi$
$72$	−2.37814	−	1.72782i	−0.280266	−	0.203625i
$73$	−2.23486	+	6.87819i	−0.261571	+	0.805031i	0.730893	+	0.682492i	$0.239104\pi$
$73$	−2.23486	+	6.87819i	−0.261571	+	0.805031i	−0.992464	+	0.122539i	$0.960896\pi$
$74$	1.19510	+	3.67814i	0.138928	+	0.427575i
$75$	−0.198931	+	0.144532i	−0.0229706	+	0.0166891i
$76$	−3.43477			−0.393995
$77$	−1.01050	+	3.15894i	−0.115158	+	0.359994i
$78$	0.283261			0.0320730
$79$	1.83955	−	1.33651i	0.206966	−	0.150369i	−0.479474	−	0.877556i	$-0.659173\pi$
$79$	1.83955	−	1.33651i	0.206966	−	0.150369i	0.686440	+	0.727187i	$0.259173\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$	2.61413	−	8.04545i	0.290458	−	0.893939i
$82$	−8.53984	−	6.20456i	−0.943068	−	0.685179i
$83$	9.16555	+	6.65916i	1.00605	+	0.730938i	0.963377	−	0.268151i	$-0.0864127\pi$
$83$	9.16555	+	6.65916i	1.00605	+	0.730938i	0.0426728	+	0.999089i	$0.486413\pi$
$84$	0.0759851	−	0.233858i	0.00829065	−	0.0255160i
$85$	2.02445	+	6.23061i	0.219582	+	0.675804i
$86$	−2.39268	+	1.73839i	−0.258010	+	0.187455i
$87$	−0.721318			−0.0773334
$88$	1.03926	+	3.14959i	0.110786	+	0.335748i
$89$	−4.48891			−0.475823			−0.237912	−	0.971287i	$-0.576463\pi$
$89$	−4.48891			−0.475823			−0.237912	+	0.971287i	$0.576463\pi$
$90$	−2.37814	+	1.72782i	−0.250677	+	0.182128i
$91$	−0.355978	−	1.09559i	−0.0373167	−	0.114849i
$92$	2.56740	−	7.90163i	0.267669	−	0.823802i
$93$	1.26114	+	0.916271i	0.130774	+	0.0950128i
$94$	−4.99166	−	3.62665i	−0.514850	−	0.374061i
$95$	−1.06140	+	3.26666i	−0.108898	+	0.335152i
$96$	−0.0759851	−	0.233858i	−0.00775519	−	0.0238680i
$97$	−2.79473	+	2.03049i	−0.283761	+	0.206165i	−0.720556	−	0.693396i	$-0.756114\pi$
$97$	−2.79473	+	2.03049i	−0.283761	+	0.206165i	0.436795	+	0.899561i	$0.356114\pi$
$98$	−1.00000			−0.101015
$99$	−7.86118	+	5.76641i	−0.790078	+	0.579546i
$100$	1.00000			0.100000
$101$	−2.19820	+	1.59708i	−0.218729	+	0.158916i	−0.691754	−	0.722133i	$-0.743162\pi$
$101$	−2.19820	+	1.59708i	−0.218729	+	0.158916i	0.473025	+	0.881049i	$0.343162\pi$
$102$	−0.497797	−	1.53206i	−0.0492892	−	0.151697i
$103$	−3.06218	+	9.42441i	−0.301725	+	0.928614i	0.679154	+	0.733996i	$0.262347\pi$
$103$	−3.06218	+	9.42441i	−0.301725	+	0.928614i	−0.980879	+	0.194619i	$0.937653\pi$
$104$	−0.931963	−	0.677111i	−0.0913865	−	0.0663962i
$105$	−0.198931	−	0.144532i	−0.0194137	−	0.0141049i
$106$	−1.65534	+	5.09462i	−0.160781	+	0.494833i
$107$	1.60283	+	4.93301i	0.154952	+	0.476892i	0.998156	−	0.0607010i	$-0.0193336\pi$
$107$	1.60283	+	4.93301i	0.154952	+	0.476892i	−0.843204	+	0.537593i	$0.819334\pi$
$108$	1.18156	−	0.858454i	0.113696	−	0.0826048i
$109$	12.1283			1.16168			0.580839	−	0.814018i	$-0.302725\pi$
$109$	12.1283			1.16168			0.580839	+	0.814018i	$0.302725\pi$
$110$	3.31659	−	0.0151188i	0.316224	−	0.00144153i
$111$	−0.950972			−0.0902623
$112$	−0.809017	+	0.587785i	−0.0764449	+	0.0555405i
$113$	4.48383	+	13.7998i	0.421804	+	1.29818i	0.906022	+	0.423231i	$0.139104\pi$
$113$	4.48383	+	13.7998i	0.421804	+	1.29818i	−0.484218	+	0.874947i	$0.660896\pi$
$114$	0.260991	−	0.803248i	0.0244440	−	0.0752310i
$115$	−6.72153	−	4.88348i	−0.626786	−	0.455387i
$116$	2.37322	+	1.72425i	0.220348	+	0.160092i
$117$	1.04641	−	3.22052i	0.0967408	−	0.297737i
$118$	0.692706	+	2.13193i	0.0637687	+	0.196260i
$119$	−5.30007	+	3.85073i	−0.485857	+	0.352995i
$120$	−0.245893			−0.0224468
$121$	10.9995	−	0.100286i	0.999958	−	0.00911691i
$122$	9.98548			0.904043
$123$	2.09989	−	1.52566i	0.189340	−	0.137564i
$124$	−1.95903	−	6.02928i	−0.175926	−	0.541446i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	−2.37814	−	1.72782i	−0.211861	−	0.153926i
$127$	0.662099	+	0.481043i	0.0587518	+	0.0426857i	0.616774	−	0.787141i	$-0.288439\pi$
$127$	0.662099	+	0.481043i	0.0587518	+	0.0426857i	−0.558022	+	0.829826i	$0.688439\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−0.224727	−	0.691640i	−0.0197861	−	0.0608955i
$130$	−0.931963	+	0.677111i	−0.0817386	+	0.0593866i
$131$	9.76900			0.853522			0.426761	−	0.904365i	$-0.359655\pi$
$131$	9.76900			0.853522			0.426761	+	0.904365i	$0.359655\pi$
$132$	−0.815526	+	0.00371762i	−0.0709824	+	0.000323577i
$133$	−3.43477			−0.297832
$134$	11.4999	−	8.35517i	0.993441	−	0.721777i
$135$	−0.451316	−	1.38901i	−0.0388431	−	0.119547i
$136$	−2.02445	+	6.23061i	−0.173595	+	0.534270i
$137$	5.41168	+	3.93181i	0.462351	+	0.335918i	0.794453	−	0.607326i	$-0.207758\pi$
$137$	5.41168	+	3.93181i	0.462351	+	0.335918i	−0.332102	+	0.943244i	$0.607758\pi$
$138$	1.65278	+	1.20081i	0.140694	+	0.102220i
$139$	−2.73588	+	8.42017i	−0.232054	+	0.714189i	0.765444	+	0.643502i	$0.222519\pi$
$139$	−2.73588	+	8.42017i	−0.232054	+	0.714189i	−0.997499	+	0.0706871i	$0.977481\pi$
$140$	0.309017	+	0.951057i	0.0261167	+	0.0803789i
$141$	1.22741	−	0.891768i	0.103367	−	0.0751004i
$142$	0.380220			0.0319074
$143$	−3.08070	+	2.25979i	−0.257621	+	0.188973i
$144$	−2.93954			−0.244961
$145$	2.37322	−	1.72425i	0.197085	−	0.143191i
$146$	2.23486	+	6.87819i	0.184958	+	0.569243i
$147$	0.0759851	−	0.233858i	0.00626714	−	0.0192883i
$148$	3.12881	+	2.27322i	0.257187	+	0.186857i
$149$	3.49896	+	2.54214i	0.286646	+	0.208260i	0.721811	−	0.692090i	$-0.243310\pi$
$149$	3.49896	+	2.54214i	0.286646	+	0.208260i	−0.435165	+	0.900351i	$0.643310\pi$
$150$	−0.0759851	+	0.233858i	−0.00620415	+	0.0190944i
$151$	−5.41219	−	16.6570i	−0.440438	−	1.35553i	−0.887410	−	0.460981i	$-0.847498\pi$
$151$	−5.41219	−	16.6570i	−0.440438	−	1.35553i	0.446972	−	0.894548i	$-0.352502\pi$
$152$	−2.77879	+	2.01891i	−0.225389	+	0.163755i
$153$	−19.2576			−1.55689
$154$	1.03926	+	3.14959i	0.0837461	+	0.253801i
$155$	−6.33956			−0.509206
$156$	0.229163	−	0.166497i	0.0183477	−	0.0133304i
$157$	2.53528	+	7.80280i	0.202338	+	0.622731i	0.999812	+	0.0193787i	$0.00616882\pi$
$157$	2.53528	+	7.80280i	0.202338	+	0.622731i	−0.797475	+	0.603353i	$0.793831\pi$
$158$	0.702647	−	2.16252i	0.0558996	−	0.172041i
$159$	−1.06564	−	0.774229i	−0.0845104	−	0.0614004i
$160$	0.809017	+	0.587785i	0.0639584	+	0.0464685i
$161$	2.56740	−	7.90163i	0.202339	−	0.622736i
$162$	−2.61413	−	8.04545i	−0.205385	−	0.632110i
$163$	9.27017	−	6.73517i	0.726096	−	0.527539i	−0.162230	−	0.986753i	$-0.551869\pi$
$163$	9.27017	−	6.73517i	0.726096	−	0.527539i	0.888326	+	0.459214i	$0.151869\pi$
$164$	−10.5558			−0.824271
$165$	−0.248476	+	0.776760i	−0.0193438	+	0.0604707i
$166$	11.3292			0.879320
$167$	0.617383	−	0.448555i	0.0477745	−	0.0347102i	−0.563642	−	0.826019i	$-0.690600\pi$
$167$	0.617383	−	0.448555i	0.0477745	−	0.0347102i	0.611416	+	0.791309i	$0.290600\pi$
$168$	−0.0759851	−	0.233858i	−0.00586237	−	0.0180425i
$169$	−3.60714	+	11.1016i	−0.277473	+	0.853973i
$170$	5.30007	+	3.85073i	0.406497	+	0.295337i
$171$	−8.16834	−	5.93465i	−0.624649	−	0.453834i
$172$	−0.913924	+	2.81277i	−0.0696861	+	0.214472i
$173$	−2.70931	−	8.33841i	−0.205985	−	0.633957i	−0.999671	−	0.0256300i	$-0.991841\pi$
$173$	−2.70931	−	8.33841i	−0.205985	−	0.633957i	0.793686	−	0.608327i	$-0.208159\pi$
$174$	−0.583558	+	0.423980i	−0.0442394	+	0.0321418i
$175$	1.00000			0.0755929
$176$	2.69206	+	1.93721i	0.202922	+	0.146023i
$177$	−0.551204			−0.0414310
$178$	−3.63160	+	2.63851i	−0.272200	+	0.197765i
$179$	4.64388	+	14.2924i	0.347100	+	1.06826i	0.960450	+	0.278452i	$0.0898214\pi$
$179$	4.64388	+	14.2924i	0.347100	+	1.06826i	−0.613350	+	0.789811i	$0.710179\pi$
$180$	−0.908367	+	2.79567i	−0.0677057	+	0.208377i
$181$	−17.1421	−	12.4544i	−1.27416	−	0.925731i	−0.274799	−	0.961502i	$-0.588611\pi$
$181$	−17.1421	−	12.4544i	−1.27416	−	0.925731i	−0.999360	+	0.0357706i	$0.988611\pi$
$182$	−0.931963	−	0.677111i	−0.0690817	−	0.0501908i
$183$	−0.758747	+	2.33518i	−0.0560882	+	0.172622i
$184$	−2.56740	−	7.90163i	−0.189271	−	0.582516i
$185$	3.12881	−	2.27322i	0.230035	−	0.167130i
$186$	1.55885			0.114301
$187$	17.6364	+	12.6911i	1.28970	+	0.928069i
$188$	−6.17003			−0.449996
$189$	1.18156	−	0.858454i	0.0859459	−	0.0624433i
$190$	1.06140	+	3.26666i	0.0770022	+	0.236988i
$191$	1.25214	−	3.85368i	0.0906014	−	0.278842i	−0.895481	−	0.445100i	$-0.853168\pi$
$191$	1.25214	−	3.85368i	0.0906014	−	0.278842i	0.986082	+	0.166257i	$0.0531682\pi$
$192$	−0.198931	−	0.144532i	−0.0143566	−	0.0104307i
$193$	16.5959	+	12.0576i	1.19460	+	0.867926i	0.993743	−	0.111694i	$-0.0356278\pi$
$193$	16.5959	+	12.0576i	1.19460	+	0.867926i	0.200856	+	0.979621i	$0.435628\pi$
$194$	−1.06749	+	3.28540i	−0.0766414	+	0.235878i
$195$	−0.0875325	−	0.269397i	−0.00626833	−	0.0192919i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	−20.4398			−1.45628			−0.728139	−	0.685429i	$-0.759614\pi$
$197$	−20.4398			−1.45628			−0.728139	+	0.685429i	$0.759614\pi$
$198$	−2.97041	+	9.28581i	−0.211098	+	0.659914i
$199$	−3.23576			−0.229377			−0.114688	−	0.993402i	$-0.536587\pi$
$199$	−3.23576			−0.229377			−0.114688	+	0.993402i	$0.536587\pi$
$200$	0.809017	−	0.587785i	0.0572061	−	0.0415627i
$201$	1.08010	+	3.32421i	0.0761846	+	0.234472i
$202$	−0.839637	+	2.58414i	−0.0590767	+	0.181819i
$203$	2.37322	+	1.72425i	0.166568	+	0.121018i
$204$	−1.30325	−	0.946866i	−0.0912457	−	0.0662939i
$205$	−3.26193	+	10.0392i	−0.227823	+	0.701167i
$206$	3.06218	+	9.42441i	0.213352	+	0.656630i
$207$	19.7582	−	14.3552i	1.37329	−	0.997752i
$208$	−1.15197			−0.0798748
$209$	3.56962	+	10.8181i	0.246916	+	0.748305i
$210$	−0.245893			−0.0169682
$211$	9.98966	−	7.25791i	0.687717	−	0.499655i	−0.188192	−	0.982132i	$-0.560263\pi$
$211$	9.98966	−	7.25791i	0.687717	−	0.499655i	0.875909	+	0.482477i	$0.160263\pi$
$212$	1.65534	+	5.09462i	0.113689	+	0.349900i
$213$	−0.0288911	+	0.0889175i	−0.00197958	+	0.00609253i
$214$	4.19627	+	3.04877i	0.286851	+	0.208410i
$215$	2.39268	+	1.73839i	0.163180	+	0.118557i
$216$	0.451316	−	1.38901i	0.0307082	−	0.0945100i
$217$	−1.95903	−	6.02928i	−0.132988	−	0.409294i
$218$	9.81198	−	7.12882i	0.664551	−	0.482825i
$219$	−1.77834			−0.120169
$220$	2.67429	−	1.96167i	0.180301	−	0.132256i
$221$	−7.54684			−0.507655
$222$	−0.769353	+	0.558968i	−0.0516356	+	0.0375154i
$223$	2.56746	+	7.90182i	0.171930	+	0.529145i	0.999480	−	0.0322466i	$-0.0102662\pi$
$223$	2.56746	+	7.90182i	0.171930	+	0.529145i	−0.827550	+	0.561392i	$0.810266\pi$
$224$	−0.309017	+	0.951057i	−0.0206471	+	0.0635451i
$225$	2.37814	+	1.72782i	0.158542	+	0.115188i
$226$	11.7388	+	8.52876i	0.780855	+	0.567325i
$227$	−4.86088	+	14.9603i	−0.322628	+	0.992948i	0.649872	+	0.760044i	$0.274823\pi$
$227$	−4.86088	+	14.9603i	−0.322628	+	0.992948i	−0.972500	+	0.232904i	$0.925177\pi$
$228$	−0.260991	−	0.803248i	−0.0172846	−	0.0531964i
$229$	19.1987	−	13.9487i	1.26868	−	0.921753i	0.269535	−	0.962991i	$-0.413130\pi$
$229$	19.1987	−	13.9487i	1.26868	−	0.921753i	0.999149	+	0.0412376i	$0.0131300\pi$
$230$	−8.30827			−0.547831
$231$	−0.815526	+	0.00371762i	−0.0536577	+	0.000244601i
$232$	2.93346			0.192591
$233$	−9.62916	+	6.99599i	−0.630827	+	0.458323i	−0.856687	−	0.515837i	$-0.827481\pi$
$233$	−9.62916	+	6.99599i	−0.630827	+	0.458323i	0.225860	+	0.974160i	$0.427481\pi$
$234$	−1.04641	−	3.22052i	−0.0684061	−	0.210532i
$235$	−1.90664	+	5.86805i	−0.124376	+	0.382789i
$236$	1.81353	+	1.31760i	0.118051	+	0.0857687i
$237$	0.452333	+	0.328639i	0.0293822	+	0.0213474i
$238$	−2.02445	+	6.23061i	−0.131225	+	0.403870i
$239$	−6.74227	−	20.7506i	−0.436121	−	1.34224i	−0.891933	−	0.452167i	$-0.850651\pi$
$239$	−6.74227	−	20.7506i	−0.436121	−	1.34224i	0.455812	−	0.890076i	$-0.349349\pi$
$240$	−0.198931	+	0.144532i	−0.0128410	+	0.00932951i
$241$	−14.7413			−0.949569			−0.474785	−	0.880102i	$-0.657474\pi$
$241$	−14.7413			−0.949569			−0.474785	+	0.880102i	$0.657474\pi$
$242$	8.83987	−	6.54650i	0.568248	−	0.420825i
$243$	6.46159			0.414511
$244$	8.07842	−	5.86932i	0.517168	−	0.375745i
$245$	0.309017	+	0.951057i	0.0197424	+	0.0607608i
$246$	0.802085	−	2.46856i	0.0511391	−	0.157390i
$247$	−3.20108	−	2.32572i	−0.203680	−	0.147982i
$248$	−5.12881	−	3.72630i	−0.325680	−	0.236620i
$249$	−0.860853	+	2.64943i	−0.0545543	+	0.167901i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	10.3886	−	7.54775i	0.655722	−	0.476410i	−0.209494	−	0.977810i	$-0.567182\pi$
$251$	10.3886	−	7.54775i	0.655722	−	0.476410i	0.865216	+	0.501400i	$0.167182\pi$
$252$	−2.93954			−0.185173
$253$	−27.5551	+	0.125611i	−1.73238	+	0.00789712i
$254$	0.818399			0.0513509
$255$	−1.30325	+	0.946866i	−0.0816126	+	0.0592950i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	1.76339	−	5.42717i	0.109998	−	0.338538i	−0.880873	−	0.473352i	$-0.843044\pi$
$257$	1.76339	−	5.42717i	0.109998	−	0.338538i	0.990871	+	0.134815i	$0.0430439\pi$
$258$	−0.588344	−	0.427457i	−0.0366287	−	0.0266123i
$259$	3.12881	+	2.27322i	0.194415	+	0.141251i
$260$	−0.355978	+	1.09559i	−0.0220768	+	0.0679455i
$261$	2.66466	+	8.20099i	0.164938	+	0.507628i
$262$	7.90329	−	5.74207i	0.488267	−	0.354747i
$263$	12.9095			0.796033			0.398016	−	0.917378i	$-0.369699\pi$
$263$	12.9095			0.796033			0.398016	+	0.917378i	$0.369699\pi$
$264$	−0.657589	+	0.482362i	−0.0404718	+	0.0296873i
$265$	5.35680			0.329065
$266$	−2.77879	+	2.01891i	−0.170378	+	0.123787i
$267$	−0.341090	−	1.04977i	−0.0208744	−	0.0642447i
$268$	4.39258	−	13.5190i	0.268319	−	0.825802i
$269$	−15.5857	−	11.3237i	−0.950277	−	0.690417i	0.000595243	−	1.00000i	$-0.499811\pi$
$269$	−15.5857	−	11.3237i	−0.950277	−	0.690417i	−0.950872	+	0.309583i	$0.899811\pi$
$270$	−1.18156	−	0.858454i	−0.0719075	−	0.0522439i
$271$	8.59629	−	26.4567i	0.522188	−	1.60713i	−0.247623	−	0.968856i	$-0.579649\pi$
$271$	8.59629	−	26.4567i	0.522188	−	1.60713i	0.769811	−	0.638272i	$-0.220351\pi$
$272$	2.02445	+	6.23061i	0.122750	+	0.377786i
$273$	0.229163	−	0.166497i	0.0138696	−	0.0100768i
$274$	6.68920			0.404110
$275$	−1.03926	−	3.14959i	−0.0626698	−	0.189928i
$276$	2.04294			0.122971
$277$	−10.0075	+	7.27089i	−0.601294	+	0.436866i	−0.846338	−	0.532646i	$-0.821198\pi$
$277$	−10.0075	+	7.27089i	−0.601294	+	0.436866i	0.245044	+	0.969512i	$0.421198\pi$
$278$	2.73588	+	8.42017i	0.164087	+	0.505008i
$279$	5.75865	−	17.7233i	0.344761	−	1.06107i
$280$	0.809017	+	0.587785i	0.0483480	+	0.0351269i
$281$	−17.7889	−	12.9244i	−1.06120	−	0.771005i	−0.0868878	−	0.996218i	$-0.527692\pi$
$281$	−17.7889	−	12.9244i	−1.06120	−	0.771005i	−0.974310	+	0.225213i	$0.927692\pi$
$282$	0.468830	−	1.44291i	0.0279184	−	0.0859241i
$283$	−4.27076	−	13.1441i	−0.253870	−	0.781333i	−0.994050	−	0.108924i	$-0.965260\pi$
$283$	−4.27076	−	13.1441i	−0.253870	−	0.781333i	0.740180	−	0.672409i	$-0.234740\pi$
$284$	0.307605	−	0.223488i	0.0182530	−	0.0132616i
$285$	−0.844585			−0.0500289
$286$	−1.16407	+	3.63900i	−0.0688329	+	0.215179i
$287$	−10.5558			−0.623091
$288$	−2.37814	+	1.72782i	−0.140133	+	0.101813i
$289$	8.00936	+	24.6503i	0.471139	+	1.45002i
$290$	0.906490	−	2.78989i	0.0532310	−	0.163828i
$291$	−0.687203	−	0.499282i	−0.0402846	−	0.0292684i
$292$	5.85094	+	4.25096i	0.342400	+	0.248768i
$293$	−5.62571	+	17.3142i	−0.328658	+	1.01150i	0.641105	+	0.767453i	$0.278476\pi$
$293$	−5.62571	+	17.3142i	−0.328658	+	1.01150i	−0.969762	+	0.244051i	$0.921524\pi$
$294$	−0.0759851	−	0.233858i	−0.00443154	−	0.0136389i
$295$	1.81353	−	1.31760i	0.105588	−	0.0767139i
$296$	3.86743			0.224790
$297$	−3.93173	−	2.82928i	−0.228142	−	0.164171i
$298$	4.32495			0.250538
$299$	7.74300	−	5.62562i	0.447789	−	0.325338i
$300$	0.0759851	+	0.233858i	0.00438700	+	0.0135018i
$301$	−0.913924	+	2.81277i	−0.0526777	+	0.162125i
$302$	−14.1693	−	10.2946i	−0.815352	−	0.592388i
$303$	−0.540521	−	0.392712i	−0.0310521	−	0.0225607i
$304$	−1.06140	+	3.26666i	−0.0608756	+	0.187356i
$305$	−3.08568	−	9.49676i	−0.176686	−	0.543783i
$306$	−15.5797	+	11.3193i	−0.890635	+	0.647084i
$307$	23.7729			1.35679			0.678395	−	0.734697i	$-0.262676\pi$
$307$	23.7729			1.35679			0.678395	+	0.734697i	$0.262676\pi$
$308$	2.69206	+	1.93721i	0.153395	+	0.110383i
$309$	−2.43665			−0.138616
$310$	−5.12881	+	3.72630i	−0.291297	+	0.211640i
$311$	−5.63985	−	17.3577i	−0.319806	−	0.984263i	−0.973731	−	0.227703i	$-0.926879\pi$
$311$	−5.63985	−	17.3577i	−0.319806	−	0.984263i	0.653924	−	0.756560i	$-0.273121\pi$
$312$	0.0875325	−	0.269397i	0.00495555	−	0.0152516i
$313$	13.2682	+	9.63989i	0.749961	+	0.544879i	0.895815	−	0.444427i	$-0.146593\pi$
$313$	13.2682	+	9.63989i	0.749961	+	0.544879i	−0.145854	+	0.989306i	$0.546593\pi$
$314$	6.63746	+	4.82240i	0.374573	+	0.272144i
$315$	−0.908367	+	2.79567i	−0.0511807	+	0.157518i
$316$	−0.702647	−	2.16252i	−0.0395270	−	0.121651i
$317$	21.2636	−	15.4489i	1.19428	−	0.867696i	0.200571	−	0.979679i	$-0.435720\pi$
$317$	21.2636	−	15.4489i	1.19428	−	0.867696i	0.993710	+	0.111983i	$0.0357203\pi$
$318$	−1.31720			−0.0738648
$319$	2.96428	−	9.26663i	0.165968	−	0.518832i
$320$	1.00000			0.0559017
$321$	−1.03183	+	0.749670i	−0.0575913	+	0.0418425i
$322$	−2.56740	−	7.90163i	−0.143075	−	0.440341i
$323$	−6.95350	+	21.4007i	−0.386903	+	1.19077i
$324$	−6.84387	−	4.97236i	−0.380215	−	0.276242i
$325$	0.931963	+	0.677111i	0.0516960	+	0.0375594i
$326$	3.54089	−	10.8977i	0.196112	−	0.603570i
$327$	0.921568	+	2.83629i	0.0509628	+	0.156847i
$328$	−8.53984	+	6.20456i	−0.471534	+	0.342589i
$329$	−6.17003			−0.340165
$330$	0.255547	+	0.774462i	0.0140674	+	0.0426327i
$331$	24.6604			1.35546			0.677729	−	0.735312i	$-0.262964\pi$
$331$	24.6604			1.35546			0.677729	+	0.735312i	$0.262964\pi$
$332$	9.16555	−	6.65916i	0.503025	−	0.365469i
$333$	3.51304	+	10.8120i	0.192514	+	0.592496i
$334$	0.235819	−	0.725777i	0.0129035	−	0.0397127i
$335$	−11.4999	−	8.35517i	−0.628307	−	0.456492i
$336$	−0.198931	−	0.144532i	−0.0108526	−	0.00788488i
$337$	−2.37268	+	7.30235i	−0.129248	+	0.397784i	−0.994651	−	0.103292i	$-0.967062\pi$
$337$	−2.37268	+	7.30235i	−0.129248	+	0.397784i	0.865403	+	0.501076i	$0.167062\pi$
$338$	3.60714	+	11.1016i	0.196203	+	0.603850i
$339$	−2.88649	+	2.09716i	−0.156773	+	0.113902i
$340$	6.55125			0.355291
$341$	−16.9538	+	12.4362i	−0.918102	+	0.673456i
$342$	−10.0966			−0.545963
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	0.913924	+	2.81277i	0.0492755	+	0.151654i
$345$	0.631304	−	1.94295i	0.0339883	−	0.104605i
$346$	−7.09307	−	5.15342i	−0.381326	−	0.277050i
$347$	−14.8317	−	10.7759i	−0.796209	−	0.578480i	0.113590	−	0.993528i	$-0.463765\pi$
$347$	−14.8317	−	10.7759i	−0.796209	−	0.578480i	−0.909800	+	0.415048i	$0.863765\pi$
$348$	−0.222899	+	0.686014i	−0.0119487	+	0.0367742i
$349$	−1.95440	−	6.01501i	−0.104616	−	0.321976i	0.885024	−	0.465546i	$-0.154142\pi$
$349$	−1.95440	−	6.01501i	−0.104616	−	0.321976i	−0.989640	+	0.143569i	$0.954142\pi$
$350$	0.809017	−	0.587785i	0.0432438	−	0.0314184i
$351$	1.68244			0.0898020
$352$	3.31659	−	0.0151188i	0.176775	−	0.000805837i
$353$	−18.7476			−0.997834			−0.498917	−	0.866650i	$-0.666269\pi$
$353$	−18.7476			−0.997834			−0.498917	+	0.866650i	$0.666269\pi$
$354$	−0.445933	+	0.323989i	−0.0237011	+	0.0172198i
$355$	−0.117495	−	0.361611i	−0.00623596	−	0.0191923i
$356$	−1.38715	+	4.26920i	−0.0735187	+	0.226267i
$357$	−1.30325	−	0.946866i	−0.0689752	−	0.0501134i
$358$	12.1578	+	8.83318i	0.642561	+	0.466848i
$359$	6.44017	−	19.8208i	0.339899	−	1.04610i	−0.624359	−	0.781137i	$-0.714640\pi$
$359$	6.44017	−	19.8208i	0.339899	−	1.04610i	0.964258	−	0.264964i	$-0.0853602\pi$
$360$	0.908367	+	2.79567i	0.0478751	+	0.147345i
$361$	5.82684	−	4.23345i	0.306676	−	0.222813i
$362$	−21.1888			−1.11366
$363$	0.859254	+	2.56471i	0.0450991	+	0.134612i
$364$	−1.15197			−0.0603796
$365$	5.85094	−	4.25096i	0.306252	−	0.222505i
$366$	0.758747	+	2.33518i	0.0396604	+	0.122062i
$367$	−7.92307	+	24.3847i	−0.413581	+	1.27287i	0.499934	+	0.866064i	$0.333358\pi$
$367$	−7.92307	+	24.3847i	−0.413581	+	1.27287i	−0.913514	+	0.406807i	$0.866642\pi$
$368$	−6.72153	−	4.88348i	−0.350384	−	0.254569i
$369$	−25.1032	−	18.2385i	−1.30682	−	0.949460i
$370$	1.19510	−	3.67814i	0.0621303	−	0.191217i
$371$	1.65534	+	5.09462i	0.0859410	+	0.264499i
$372$	1.26114	−	0.916271i	0.0653870	−	0.0475064i
$373$	−34.9239			−1.80829			−0.904146	−	0.427223i	$-0.859492\pi$
$373$	−34.9239			−1.80829			−0.904146	+	0.427223i	$0.859492\pi$
$374$	21.7278	−	0.0990473i	1.12352	−	0.00512161i
$375$	0.245893			0.0126978
$376$	−4.99166	+	3.62665i	−0.257425	+	0.187030i
$377$	1.04425	+	3.21387i	0.0537816	+	0.165523i
$378$	0.451316	−	1.38901i	0.0232132	−	0.0714429i
$379$	−1.07121	−	0.778279i	−0.0550243	−	0.0399775i	0.559933	−	0.828538i	$-0.310827\pi$
$379$	−1.07121	−	0.778279i	−0.0550243	−	0.0399775i	−0.614957	+	0.788560i	$0.710827\pi$
$380$	2.77879	+	2.01891i	0.142549	+	0.103568i
$381$	−0.0621861	+	0.191389i	−0.00318589	+	0.00980516i
$382$	−1.25214	−	3.85368i	−0.0640648	−	0.197171i
$383$	−1.95972	+	1.42382i	−0.100137	+	0.0727537i	−0.636727	−	0.771089i	$-0.719712\pi$
$383$	−1.95972	+	1.42382i	−0.100137	+	0.0727537i	0.536590	+	0.843843i	$0.319712\pi$
$384$	−0.245893			−0.0125482
$385$	2.67429	−	1.96167i	0.136295	−	0.0999762i
$386$	20.5136			1.04412
$387$	−7.03338	+	5.11005i	−0.357527	+	0.259759i
$388$	1.06749	+	3.28540i	0.0541936	+	0.166791i
$389$	−6.56806	+	20.2144i	−0.333014	+	1.02491i	0.634678	+	0.772777i	$0.281133\pi$
$389$	−6.56806	+	20.2144i	−0.333014	+	1.02491i	−0.967692	+	0.252135i	$0.918867\pi$
$390$	−0.229163	−	0.166497i	−0.0116041	−	0.00843089i
$391$	−44.0344	−	31.9929i	−2.22691	−	1.61795i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$	0.742298	+	2.28456i	0.0374440	+	0.115241i
$394$	−16.5362	+	12.0142i	−0.833080	+	0.605268i
$395$	−2.27381			−0.114408
$396$	3.05495	+	9.25834i	0.153517	+	0.465249i
$397$	12.8715			0.646003			0.323001	−	0.946398i	$-0.395308\pi$
$397$	12.8715			0.646003			0.323001	+	0.946398i	$0.395308\pi$
$398$	−2.61779	+	1.90193i	−0.131218	+	0.0953353i
$399$	−0.260991	−	0.803248i	−0.0130659	−	0.0402127i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	9.03882	+	6.56708i	0.451377	+	0.327945i	0.790139	−	0.612927i	$-0.210008\pi$
$401$	9.03882	+	6.56708i	0.451377	+	0.327945i	−0.338762	+	0.940872i	$0.610008\pi$
$402$	2.82775	+	2.05448i	0.141035	+	0.102468i
$403$	2.25675	−	6.94555i	0.112417	−	0.345983i
$404$	0.839637	+	2.58414i	0.0417735	+	0.128566i
$405$	−6.84387	+	4.97236i	−0.340075	+	0.247079i
$406$	2.93346			0.145585
$407$	3.90805	−	12.2170i	0.193715	−	0.605572i
$408$	−1.61090			−0.0797516
$409$	−11.9159	+	8.65742i	−0.589204	+	0.428082i	−0.842031	−	0.539430i	$-0.818640\pi$
$409$	−11.9159	+	8.65742i	−0.589204	+	0.428082i	0.252826	+	0.967512i	$0.418640\pi$
$410$	3.26193	+	10.0392i	0.161095	+	0.495800i
$411$	−0.508279	+	1.56432i	−0.0250716	+	0.0771624i
$412$	8.01688	+	5.82460i	0.394963	+	0.286958i
$413$	1.81353	+	1.31760i	0.0892378	+	0.0648351i
$414$	7.54695	−	23.2271i	0.370913	−	1.14155i
$415$	−3.50093	−	10.7747i	−0.171854	−	0.528912i
$416$	−0.931963	+	0.677111i	−0.0456933	+	0.0331981i
$417$	−2.17701			−0.106609
$418$	9.24662	+	6.65387i	0.452267	+	0.325451i
$419$	−14.1913			−0.693290			−0.346645	−	0.937996i	$-0.612679\pi$
$419$	−14.1913			−0.693290			−0.346645	+	0.937996i	$0.612679\pi$
$420$	−0.198931	+	0.144532i	−0.00970686	+	0.00705245i
$421$	−8.05282	−	24.7840i	−0.392470	−	1.20790i	−0.930914	−	0.365238i	$-0.880988\pi$
$421$	−8.05282	−	24.7840i	−0.392470	−	1.20790i	0.538444	−	0.842661i	$-0.319012\pi$
$422$	3.81571	−	11.7435i	0.185746	−	0.571667i
$423$	−14.6732	−	10.6607i	−0.713434	−	0.518340i
$424$	4.33374	+	3.14865i	0.210465	+	0.152912i
$425$	2.02445	−	6.23061i	0.0982001	−	0.302229i
$426$	0.0288911	+	0.0889175i	0.00139978	+	0.00430807i
$427$	8.07842	−	5.86932i	0.390942	−	0.284036i
$428$	5.18688			0.250717
$429$	−0.762557	−	0.548737i	−0.0368166	−	0.0264933i
$430$	2.95752			0.142624
$431$	15.2214	−	11.0590i	0.733188	−	0.532692i	−0.157383	−	0.987538i	$-0.550306\pi$
$431$	15.2214	−	11.0590i	0.733188	−	0.532692i	0.890570	+	0.454846i	$0.150306\pi$
$432$	−0.451316	−	1.38901i	−0.0217140	−	0.0668287i
$433$	6.30482	−	19.4042i	0.302990	−	0.932508i	−0.677429	−	0.735588i	$-0.736906\pi$
$433$	6.30482	−	19.4042i	0.302990	−	0.932508i	0.980420	−	0.196920i	$-0.0630939\pi$
$434$	−5.12881	−	3.72630i	−0.246191	−	0.178868i
$435$	0.583558	+	0.423980i	0.0279795	+	0.0203283i
$436$	3.74784	−	11.5347i	0.179489	−	0.552411i
$437$	−8.81841	−	27.1403i	−0.421842	−	1.29829i
$438$	−1.43870	+	1.04528i	−0.0687439	+	0.0499454i
$439$	17.5292			0.836621			0.418311	−	0.908304i	$-0.362622\pi$
$439$	17.5292			0.836621			0.418311	+	0.908304i	$0.362622\pi$
$440$	1.01050	−	3.15894i	0.0481739	−	0.150596i
$441$	−2.93954			−0.139978
$442$	−6.10552	+	4.43592i	−0.290410	+	0.210995i
$443$	−8.09469	−	24.9129i	−0.384591	−	1.18365i	−0.936777	−	0.349927i	$-0.886206\pi$
$443$	−8.09469	−	24.9129i	−0.384591	−	1.18365i	0.552186	−	0.833721i	$-0.313794\pi$
$444$	−0.293867	+	0.904429i	−0.0139463	+	0.0429223i
$445$	3.63160	+	2.63851i	0.172154	+	0.125078i
$446$	6.72169	+	4.88359i	0.318281	+	0.231245i
$447$	−0.328631	+	1.01142i	−0.0155437	+	0.0478387i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	7.68323	−	5.58219i	0.362594	−	0.263440i	−0.391539	−	0.920161i	$-0.628057\pi$
$449$	7.68323	−	5.58219i	0.362594	−	0.263440i	0.754133	+	0.656721i	$0.228057\pi$
$450$	2.93954			0.138571
$451$	10.9703	+	33.2466i	0.516570	+	1.56552i
$452$	14.5100			0.682493
$453$	3.48413	−	2.53137i	0.163699	−	0.118934i
$454$	4.86088	+	14.9603i	0.228133	+	0.702120i
$455$	−0.355978	+	1.09559i	−0.0166885	+	0.0513620i
$456$	−0.683283	−	0.496434i	−0.0319977	−	0.0232477i
$457$	−14.1912	−	10.3105i	−0.663835	−	0.482304i	0.204121	−	0.978946i	$-0.434566\pi$
$457$	−14.1912	−	10.3105i	−0.663835	−	0.482304i	−0.867956	+	0.496641i	$0.834566\pi$
$458$	7.33324	−	22.5694i	0.342660	−	1.05460i
$459$	−2.95668	−	9.09973i	−0.138006	−	0.424739i
$460$	−6.72153	+	4.88348i	−0.313393	+	0.227693i
$461$	−22.6720			−1.05594			−0.527970	−	0.849263i	$-0.677047\pi$
$461$	−22.6720			−1.05594			−0.527970	+	0.849263i	$0.677047\pi$
$462$	−0.657589	+	0.482362i	−0.0305938	+	0.0224415i
$463$	−26.9554			−1.25272			−0.626362	−	0.779532i	$-0.715457\pi$
$463$	−26.9554			−1.25272			−0.626362	+	0.779532i	$0.715457\pi$
$464$	2.37322	−	1.72425i	0.110174	−	0.0800462i
$465$	−0.481712	−	1.48256i	−0.0223389	−	0.0687519i
$466$	−3.67801	+	11.3198i	−0.170381	+	0.524377i
$467$	−11.9506	−	8.68264i	−0.553009	−	0.401785i	0.275885	−	0.961191i	$-0.411029\pi$
$467$	−11.9506	−	8.68264i	−0.553009	−	0.401785i	−0.828894	+	0.559406i	$0.811029\pi$
$468$	−2.73954	−	1.99039i	−0.126635	−	0.0920059i
$469$	4.39258	−	13.5190i	0.202830	−	0.624247i
$470$	1.90664	+	5.86805i	0.0879469	+	0.270673i
$471$	−1.63210	+	1.18579i	−0.0752034	+	0.0546384i
$472$	2.24164			0.103180
$473$	9.80888	−	0.0447143i	0.451013	−	0.00205597i
$474$	0.559114			0.0256810
$475$	2.77879	−	2.01891i	0.127499	−	0.0926337i
$476$	2.02445	+	6.23061i	0.0927903	+	0.285579i
$477$	−4.86594	+	14.9758i	−0.222796	+	0.685695i
$478$	−17.6515	−	12.8246i	−0.807361	−	0.586582i
$479$	25.7445	+	18.7045i	1.17630	+	0.854630i	0.991749	−	0.128194i	$-0.0409179\pi$
$479$	25.7445	+	18.7045i	1.17630	+	0.854630i	0.184548	+	0.982824i	$0.440918\pi$
$480$	−0.0759851	+	0.233858i	−0.00346823	+	0.0106741i
$481$	1.37672	+	4.23711i	0.0627730	+	0.193196i
$482$	−11.9259	+	8.66470i	−0.543212	+	0.394666i
$483$	2.04294			0.0929571
$484$	3.30367	−	10.4922i	0.150167	−	0.476917i
$485$	3.45447			0.156859
$486$	5.22754	−	3.79803i	0.237126	−	0.172282i
$487$	7.68415	+	23.6494i	0.348202	+	1.07166i	0.959847	+	0.280524i	$0.0905081\pi$
$487$	7.68415	+	23.6494i	0.348202	+	1.07166i	−0.611645	+	0.791132i	$0.709492\pi$
$488$	3.08568	−	9.49676i	0.139682	−	0.429898i
$489$	2.27947	+	1.65613i	0.103081	+	0.0748928i
$490$	0.809017	+	0.587785i	0.0365477	+	0.0265534i
$491$	−12.9322	+	39.8013i	−0.583623	+	1.79621i	0.0211073	+	0.999777i	$0.493281\pi$
$491$	−12.9322	+	39.8013i	−0.583623	+	1.79621i	−0.604730	+	0.796430i	$0.706719\pi$
$492$	−0.802085	−	2.46856i	−0.0361608	−	0.111291i
$493$	15.5476	−	11.2960i	0.700227	−	0.508745i
$494$	−3.95675			−0.178023
$495$	9.74924	−	0.0444424i	0.438196	−	0.00199754i
$496$	−6.33956			−0.284655
$497$	0.307605	−	0.223488i	0.0137980	−	0.0100248i
$498$	0.860853	+	2.64943i	0.0385757	+	0.118724i
$499$	7.67446	−	23.6195i	0.343556	−	1.05736i	−0.618797	−	0.785551i	$-0.712379\pi$
$499$	7.67446	−	23.6195i	0.343556	−	1.05736i	0.962352	−	0.271805i	$-0.0876205\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	0.151810	+	0.110296i	0.00678237	+	0.00492768i
$502$	3.96809	−	12.2125i	0.177104	−	0.545071i
$503$	2.75924	+	8.49207i	0.123028	+	0.378643i	0.993537	−	0.113511i	$-0.0362098\pi$
$503$	2.75924	+	8.49207i	0.123028	+	0.378643i	−0.870508	+	0.492154i	$0.836210\pi$
$504$	−2.37814	+	1.72782i	−0.105931	+	0.0769631i
$505$	2.71712			0.120910
$506$	−22.2187	+	16.2981i	−0.987743	+	0.724539i
$507$	−2.87030			−0.127474
$508$	0.662099	−	0.481043i	0.0293759	−	0.0213428i
$509$	7.06674	+	21.7492i	0.313228	+	0.964016i	0.976478	+	0.215618i	$0.0691767\pi$
$509$	7.06674	+	21.7492i	0.313228	+	0.964016i	−0.663250	+	0.748398i	$0.730823\pi$
$510$	−0.497797	+	1.53206i	−0.0220428	+	0.0678408i
$511$	5.85094	+	4.25096i	0.258830	+	0.188051i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	1.55017	−	4.77092i	0.0684415	−	0.210641i
$514$	−1.76339	−	5.42717i	−0.0777800	−	0.239382i
$515$	8.01688	−	5.82460i	0.353266	−	0.256663i
$516$	−0.727233			−0.0320147
$517$	6.41228	+	19.4331i	0.282012	+	0.854666i
$518$	3.86743			0.169925
$519$	1.74414	−	1.26719i	0.0765591	−	0.0556234i
$520$	0.355978	+	1.09559i	0.0156107	+	0.0480447i
$521$	−10.6342	+	32.7288i	−0.465895	+	1.43388i	0.391960	+	0.919982i	$0.371797\pi$
$521$	−10.6342	+	32.7288i	−0.465895	+	1.43388i	−0.857854	+	0.513893i	$0.828203\pi$
$522$	6.97618	+	5.06849i	0.305339	+	0.221842i
$523$	5.42297	+	3.94002i	0.237130	+	0.172285i	0.700004	−	0.714139i	$-0.253182\pi$
$523$	5.42297	+	3.94002i	0.237130	+	0.172285i	−0.462874	+	0.886424i	$0.653182\pi$
$524$	3.01879	−	9.29087i	0.131876	−	0.405874i
$525$	0.0759851	+	0.233858i	0.00331626	+	0.0102064i
$526$	10.4440	−	7.58800i	0.455380	−	0.330853i
$527$	−41.5320			−1.80916
$528$	−0.248476	+	0.776760i	−0.0108135	+	0.0338041i
$529$	46.0273			2.00119
$530$	4.33374	−	3.14865i	0.188246	−	0.136768i
$531$	2.03623	+	6.26688i	0.0883650	+	0.271960i
$532$	−1.06140	+	3.26666i	−0.0460176	+	0.141628i
$533$	−9.83764	−	7.14747i	−0.426116	−	0.309591i
$534$	−0.892985	−	0.648791i	−0.0386432	−	0.0280759i
$535$	1.60283	−	4.93301i	0.0692965	−	0.213273i
$536$	−4.39258	−	13.5190i	−0.189730	−	0.583930i
$537$	−2.98952	+	2.17202i	−0.129007	+	0.0937294i
$538$	−19.2650			−0.830573
$539$	2.69206	+	1.93721i	0.115955	+	0.0834416i
$540$	−1.46049			−0.0628495
$541$	13.2696	−	9.64090i	0.570503	−	0.414495i	−0.264785	−	0.964308i	$-0.585301\pi$
$541$	13.2696	−	9.64090i	0.570503	−	0.414495i	0.835288	+	0.549813i	$0.185301\pi$
$542$	−8.59629	−	26.4567i	−0.369242	−	1.13641i
$543$	1.61003	−	4.95516i	0.0690929	−	0.212646i
$544$	5.30007	+	3.85073i	0.227239	+	0.165099i
$545$	−9.81198	−	7.12882i	−0.420299	−	0.305365i
$546$	0.0875325	−	0.269397i	0.00374605	−	0.0115291i
$547$	−2.16266	−	6.65599i	−0.0924688	−	0.284590i	0.894117	−	0.447834i	$-0.147804\pi$
$547$	−2.16266	−	6.65599i	−0.0924688	−	0.284590i	−0.986586	+	0.163244i	$0.947804\pi$
$548$	5.41168	−	3.93181i	0.231175	−	0.167959i
$549$	29.3527			1.25274
$550$	−2.69206	−	1.93721i	−0.114790	−	0.0826030i
$551$	10.0758			0.429242
$552$	1.65278	−	1.20081i	0.0703468	−	0.0511099i
$553$	−0.702647	−	2.16252i	−0.0298796	−	0.0919599i
$554$	−3.82254	+	11.7646i	−0.162404	+	0.499828i
$555$	0.769353	+	0.558968i	0.0326572	+	0.0237269i
$556$	7.16262	+	5.20395i	0.303763	+	0.220697i
$557$	4.38325	−	13.4902i	0.185724	−	0.571600i	−0.814236	−	0.580534i	$-0.802844\pi$
$557$	4.38325	−	13.4902i	0.185724	−	0.571600i	0.999960	+	0.00893401i	$0.00284382\pi$
$558$	−5.75865	−	17.7233i	−0.243783	−	0.750287i
$559$	−2.75630	+	2.00257i	−0.116579	+	0.0846997i
$560$	1.00000			0.0422577
$561$	−1.62782	+	5.08874i	−0.0687268	+	0.214847i
$562$	−21.9883			−0.927520
$563$	21.5403	−	15.6500i	0.907817	−	0.659568i	−0.0326445	−	0.999467i	$-0.510393\pi$
$563$	21.5403	−	15.6500i	0.907817	−	0.659568i	0.940462	+	0.339899i	$0.110393\pi$
$564$	−0.468830	−	1.44291i	−0.0197413	−	0.0607575i
$565$	4.48383	−	13.7998i	0.188636	−	0.580563i
$566$	−11.1810	−	8.12347i	−0.469972	−	0.341455i
$567$	−6.84387	−	4.97236i	−0.287415	−	0.208820i
$568$	0.117495	−	0.361611i	0.00492996	−	0.0151729i
$569$	−0.401649	−	1.23615i	−0.0168380	−	0.0518220i	0.942284	−	0.334813i	$-0.108673\pi$
$569$	−0.401649	−	1.23615i	−0.0168380	−	0.0518220i	−0.959122	+	0.282991i	$0.908673\pi$
$570$	−0.683283	+	0.496434i	−0.0286196	+	0.0207933i
$571$	−24.2338			−1.01415			−0.507076	−	0.861901i	$-0.669274\pi$
$571$	−24.2338			−1.01415			−0.507076	+	0.861901i	$0.669274\pi$
$572$	1.19720	+	3.62824i	0.0500574	+	0.151704i
$573$	0.996357			0.0416234
$574$	−8.53984	+	6.20456i	−0.356446	+	0.258973i
$575$	2.56740	+	7.90163i	0.107068	+	0.329521i
$576$	−0.908367	+	2.79567i	−0.0378486	+	0.116486i
$577$	30.7400	+	22.3339i	1.27972	+	0.929774i	0.999545	−	0.0301741i	$-0.00960619\pi$
$577$	30.7400	+	22.3339i	1.27972	+	0.929774i	0.280179	+	0.959948i	$0.409606\pi$
$578$	20.9688	+	15.2347i	0.872186	+	0.633680i
$579$	−1.55873	+	4.79728i	−0.0647786	+	0.199368i
$580$	−0.906490	−	2.78989i	−0.0376400	−	0.115844i
$581$	9.16555	−	6.65916i	0.380251	−	0.276269i
$582$	−0.849430			−0.0352100
$583$	14.3256	−	10.5083i	0.593307	−	0.435209i
$584$	7.23216			0.299269
$585$	−2.73954	+	1.99039i	−0.113266	+	0.0822926i
$586$	5.62571	+	17.3142i	0.232396	+	0.715241i
$587$	1.71351	−	5.27363i	0.0707240	−	0.217666i	−0.909447	−	0.415820i	$-0.863495\pi$
$587$	1.71351	−	5.27363i	0.0707240	−	0.217666i	0.980171	+	0.198154i	$0.0634946\pi$
$588$	−0.198931	−	0.144532i	−0.00820379	−	0.00596041i
$589$	−17.6163	−	12.7990i	−0.725866	−	0.527373i
$590$	0.692706	−	2.13193i	0.0285182	−	0.0877701i
$591$	−1.55312	−	4.78002i	−0.0638869	−	0.196624i
$592$	3.12881	−	2.27322i	0.128593	−	0.0934286i
$593$	−45.5378			−1.87001			−0.935006	−	0.354633i	$-0.884606\pi$
$593$	−45.5378			−1.87001			−0.935006	+	0.354633i	$0.884606\pi$
$594$	−4.84384	+	0.0220809i	−0.198745	+	0.000905991i
$595$	6.55125			0.268575
$596$	3.49896	−	2.54214i	0.143323	−	0.104130i
$597$	−0.245869	−	0.756708i	−0.0100628	−	0.0309700i
$598$	2.95756	−	9.10244i	0.120944	−	0.372227i
$599$	−30.9358	−	22.4762i	−1.26400	−	0.918353i	−0.265057	−	0.964233i	$-0.585391\pi$
$599$	−30.9358	−	22.4762i	−1.26400	−	0.918353i	−0.998947	+	0.0458796i	$0.985391\pi$
$600$	0.198931	+	0.144532i	0.00812134	+	0.00590050i
$601$	12.9397	−	39.8243i	0.527821	−	1.62447i	−0.230847	−	0.972990i	$-0.574150\pi$
$601$	12.9397	−	39.8243i	0.527821	−	1.62447i	0.758669	−	0.651477i	$-0.225850\pi$
$602$	0.913924	+	2.81277i	0.0372488	+	0.114640i
$603$	33.8044	−	24.5603i	1.37662	−	1.00017i
$604$	−17.5142			−0.712644
$605$	−8.95776	−	6.38424i	−0.364185	−	0.259556i
$606$	−0.668121			−0.0271406
$607$	−5.55804	+	4.03816i	−0.225594	+	0.163904i	−0.694841	−	0.719163i	$-0.744525\pi$
$607$	−5.55804	+	4.03816i	−0.225594	+	0.163904i	0.469247	+	0.883067i	$0.344525\pi$
$608$	1.06140	+	3.26666i	0.0430455	+	0.132480i
$609$	−0.222899	+	0.686014i	−0.00903234	+	0.0277987i
$610$	−8.07842	−	5.86932i	−0.327086	−	0.237642i
$611$	−5.75024	−	4.17780i	−0.232630	−	0.169016i
$612$	−5.95093	+	18.3151i	−0.240552	+	0.740344i
$613$	11.7082	+	36.0343i	0.472892	+	1.45541i	0.848780	+	0.528746i	$0.177337\pi$
$613$	11.7082	+	36.0343i	0.472892	+	1.45541i	−0.375889	+	0.926665i	$0.622663\pi$
$614$	19.2327	−	13.9734i	0.776167	−	0.563919i
$615$	−2.59560			−0.104665
$616$	3.31659	−	0.0151188i	0.133629	−	0.000609156i
$617$	19.7135			0.793636			0.396818	−	0.917897i	$-0.370114\pi$
$617$	19.7135			0.793636			0.396818	+	0.917897i	$0.370114\pi$
$618$	−1.97129	+	1.43223i	−0.0792970	+	0.0576127i
$619$	14.0046	+	43.1019i	0.562894	+	1.73241i	0.674127	+	0.738615i	$0.264520\pi$
$619$	14.0046	+	43.1019i	0.562894	+	1.73241i	−0.111233	+	0.993794i	$0.535480\pi$
$620$	−1.95903	+	6.02928i	−0.0786766	+	0.242142i
$621$	9.81672	+	7.13227i	0.393931	+	0.286208i
$622$	−14.7653	−	10.7276i	−0.592035	−	0.430139i
$623$	−1.38715	+	4.26920i	−0.0555749	+	0.171042i
$624$	−0.0875325	−	0.269397i	−0.00350410	−	0.0107845i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	16.4004			0.655490
$627$	−2.25867	+	1.65680i	−0.0902024	+	0.0661662i
$628$	8.20435			0.327389
$629$	20.4976	−	14.8924i	0.817294	−	0.593799i
$630$	0.908367	+	2.79567i	0.0361902	+	0.111382i
$631$	−9.05893	+	27.8805i	−0.360630	+	1.10991i	0.592042	+	0.805907i	$0.298322\pi$
$631$	−9.05893	+	27.8805i	−0.360630	+	1.10991i	−0.952672	+	0.303999i	$0.901678\pi$
$632$	−1.83955	−	1.33651i	−0.0731735	−	0.0531636i
$633$	2.45639	+	1.78467i	0.0976326	+	0.0709342i
$634$	8.12196	−	24.9968i	0.322564	−	0.992751i
$635$	−0.252899	−	0.778344i	−0.0100360	−	0.0308876i
$636$	−1.06564	+	0.774229i	−0.0422552	+	0.0307002i
$637$	−1.15197			−0.0456427
$638$	−3.04864	−	9.23922i	−0.120697	−	0.365784i
$639$	1.11767			0.0442144
$640$	0.809017	−	0.587785i	0.0319792	−	0.0232343i
$641$	−6.79035	−	20.8986i	−0.268203	−	0.825443i	−0.990938	−	0.134319i	$-0.957115\pi$
$641$	−6.79035	−	20.8986i	−0.268203	−	0.825443i	0.722735	−	0.691125i	$-0.242885\pi$
$642$	−0.394125	+	1.21299i	−0.0155549	+	0.0478730i
$643$	37.5979	+	27.3165i	1.48272	+	1.07726i	0.976668	+	0.214753i	$0.0688948\pi$
$643$	37.5979	+	27.3165i	1.48272	+	1.07726i	0.506050	+	0.862504i	$0.331105\pi$
$644$	−6.72153	−	4.88348i	−0.264865	−	0.192436i
$645$	−0.224727	+	0.691640i	−0.00884863	+	0.0272333i
$646$	6.95350	+	21.4007i	0.273582	+	0.841999i
$647$	−15.6531	+	11.3726i	−0.615387	+	0.447105i	−0.851307	−	0.524668i	$-0.824190\pi$
$647$	−15.6531	+	11.3726i	−0.615387	+	0.447105i	0.235920	+	0.971772i	$0.424190\pi$
$648$	−8.45949			−0.332320
$649$	2.26519	−	7.08121i	0.0889164	−	0.277962i
$650$	1.15197			0.0451840
$651$	1.26114	−	0.916271i	0.0494279	−	0.0359115i
$652$	−3.54089	−	10.8977i	−0.138672	−	0.426788i
$653$	11.4067	−	35.1063i	0.446380	−	1.37382i	−0.434584	−	0.900631i	$-0.643105\pi$
$653$	11.4067	−	35.1063i	0.446380	−	1.37382i	0.880964	−	0.473184i	$-0.156895\pi$
$654$	2.41270	+	1.75293i	0.0943439	+	0.0685448i
$655$	−7.90329	−	5.74207i	−0.308807	−	0.224361i
$656$	−3.26193	+	10.0392i	−0.127357	+	0.391964i
$657$	6.56945	+	20.2187i	0.256299	+	0.788807i
$658$	−4.99166	+	3.62665i	−0.194595	+	0.141382i
$659$	−24.3913			−0.950151			−0.475075	−	0.879945i	$-0.657579\pi$
$659$	−24.3913			−0.950151			−0.475075	+	0.879945i	$0.657579\pi$
$660$	0.661959	+	0.476346i	0.0257667	+	0.0185418i
$661$	−5.60864			−0.218151			−0.109075	−	0.994033i	$-0.534789\pi$
$661$	−5.60864			−0.218151			−0.109075	+	0.994033i	$0.534789\pi$
$662$	19.9507	−	14.4950i	0.775405	−	0.563365i
$663$	−0.573447	−	1.76489i	−0.0222708	−	0.0685426i
$664$	3.50093	−	10.7747i	0.135862	−	0.418141i
$665$	2.77879	+	2.01891i	0.107757	+	0.0782898i
$666$	9.19726	+	6.68220i	0.356387	+	0.258930i
$667$	−7.53136	+	23.1792i	−0.291616	+	0.897500i
$668$	−0.235819	−	0.725777i	−0.00912412	−	0.0280812i
$669$	−1.65281	+	1.20084i	−0.0639015	+	0.0464272i
$670$	−14.2147			−0.549161
$671$	−26.8816	−	19.3440i	−1.03775	−	0.746766i
$672$	−0.245893			−0.00948552
$673$	−22.3745	+	16.2560i	−0.862474	+	0.626624i	−0.928557	−	0.371190i	$-0.878950\pi$
$673$	−22.3745	+	16.2560i	−0.862474	+	0.626624i	0.0660828	+	0.997814i	$0.478950\pi$
$674$	2.37268	+	7.30235i	0.0913921	+	0.281276i
$675$	−0.451316	+	1.38901i	−0.0173712	+	0.0534629i
$676$	9.44363	+	6.86120i	0.363216	+	0.263892i
$677$	23.2034	+	16.8582i	0.891778	+	0.647915i	0.936341	−	0.351092i	$-0.114189\pi$
$677$	23.2034	+	16.8582i	0.891778	+	0.647915i	−0.0445628	+	0.999007i	$0.514189\pi$
$678$	−1.10254	+	3.39328i	−0.0423429	+	0.130318i
$679$	1.06749	+	3.28540i	0.0409665	+	0.126082i
$680$	5.30007	−	3.85073i	0.203248	−	0.147669i
$681$	−3.86793			−0.148219
$682$	−6.40615	+	20.0263i	−0.245304	+	0.766846i
$683$	−38.9631			−1.49088			−0.745440	−	0.666572i	$-0.767761\pi$
$683$	−38.9631			−1.49088			−0.745440	+	0.666572i	$0.767761\pi$
$684$	−8.16834	+	5.93465i	−0.312324	+	0.226917i
$685$	−2.06708	−	6.36181i	−0.0789790	−	0.243072i
$686$	−0.309017	+	0.951057i	−0.0117983	+	0.0363115i
$687$	4.72082	+	3.42987i	0.180110	+	0.130858i
$688$	2.39268	+	1.73839i	0.0912202	+	0.0662754i
$689$	−1.90690	+	5.86885i	−0.0726472	+	0.223585i
$690$	−0.631304	−	1.94295i	−0.0240333	−	0.0739670i
$691$	12.1733	−	8.84445i	0.463096	−	0.336459i	−0.331649	−	0.943403i	$-0.607605\pi$
$691$	12.1733	−	8.84445i	0.463096	−	0.336459i	0.794745	+	0.606944i	$0.207605\pi$
$692$	−8.76752			−0.333291
$693$	3.05495	+	9.25834i	0.116048	+	0.351695i
$694$	−18.3330			−0.695912
$695$	7.16262	−	5.20395i	0.271694	−	0.197397i
$696$	0.222899	+	0.686014i	0.00844898	+	0.0260033i
$697$	−21.3697	+	65.7692i	−0.809435	+	2.49119i
$698$	−5.11668	−	3.71748i	−0.193669	−	0.140709i
$699$	−2.36774	−	1.72026i	−0.0895561	−	0.0650663i
$700$	0.309017	−	0.951057i	0.0116797	−	0.0359466i
$701$	8.32792	+	25.6307i	0.314541	+	0.968058i	0.975943	+	0.218026i	$0.0699619\pi$
$701$	8.32792	+	25.6307i	0.314541	+	0.968058i	−0.661402	+	0.750032i	$0.730038\pi$
$702$	1.36112	−	0.988913i	0.0513723	−	0.0373241i
$703$	13.2837			0.501005
$704$	2.67429	−	1.96167i	0.100791	−	0.0739334i
$705$	−1.51717			−0.0571398
$706$	−15.1671	+	11.0196i	−0.570823	+	0.414727i
$707$	0.839637	+	2.58414i	0.0315778	+	0.0971865i
$708$	−0.170331	+	0.524226i	−0.00640144	+	0.0197016i
$709$	22.7327	+	16.5163i	0.853745	+	0.620282i	0.926176	−	0.377091i	$-0.123076\pi$
$709$	22.7327	+	16.5163i	0.853745	+	0.620282i	−0.0724308	+	0.997373i	$0.523076\pi$
$710$	−0.307605	−	0.223488i	−0.0115442	−	0.00838735i
$711$	2.06546	−	6.35682i	0.0774606	−	0.238399i
$712$	1.38715	+	4.26920i	0.0519856	+	0.159995i
$713$	42.6116	−	30.9591i	1.59582	−	1.15943i
$714$	−1.61090			−0.0602866
$715$	3.82061	−	0.0174165i	0.142883	−	0.000651339i
$716$	15.0279			0.561619
$717$	4.34038	−	3.15347i	0.162094	−	0.117768i
$718$	−6.44017	−	19.8208i	−0.240345	−	0.739706i
$719$	−10.5649	+	32.5154i	−0.394004	+	1.21262i	0.535731	+	0.844389i	$0.320036\pi$
$719$	−10.5649	+	32.5154i	−0.394004	+	1.21262i	−0.929735	+	0.368230i	$0.879964\pi$
$720$	2.37814	+	1.72782i	0.0886279	+	0.0643919i
$721$	8.01688	+	5.82460i	0.298564	+	0.216920i
$722$	2.22566	−	6.84986i	0.0828303	−	0.254925i
$723$	−1.12012	−	3.44736i	−0.0416576	−	0.128209i
$724$	−17.1421	+	12.4544i	−0.637080	+	0.462865i
$725$	−2.93346			−0.108946
$726$	2.20265	+	1.56984i	0.0817480	+	0.0582621i
$727$	46.8368			1.73708			0.868541	−	0.495618i	$-0.165058\pi$
$727$	46.8368			1.73708			0.868541	+	0.495618i	$0.165058\pi$
$728$	−0.931963	+	0.677111i	−0.0345409	+	0.0250954i
$729$	−7.35139	−	22.6253i	−0.272274	−	0.837972i
$730$	2.23486	−	6.87819i	0.0827159	−	0.254573i
$731$	15.6751	+	11.3886i	0.579763	+	0.421223i
$732$	1.98643	+	1.44322i	0.0734204	+	0.0533431i
$733$	−1.48607	+	4.57365i	−0.0548893	+	0.168932i	−0.974743	−	0.223330i	$-0.928307\pi$
$733$	−1.48607	+	4.57365i	−0.0548893	+	0.168932i	0.919854	+	0.392262i	$0.128307\pi$
$734$	7.92307	+	24.3847i	0.292446	+	0.900055i
$735$	−0.198931	+	0.144532i	−0.00733770	+	0.00533115i
$736$	−8.30827			−0.306247
$737$	−47.1442	+	0.214909i	−1.73658	+	0.00791629i
$738$	−31.0292			−1.14220
$739$	−6.14866	+	4.46727i	−0.226182	+	0.164331i	−0.695105	−	0.718908i	$-0.744642\pi$
$739$	−6.14866	+	4.46727i	−0.226182	+	0.164331i	0.468923	+	0.883239i	$0.344642\pi$
$740$	−1.19510	−	3.67814i	−0.0439328	−	0.135211i
$741$	0.300654	−	0.925317i	0.0110448	−	0.0339924i
$742$	4.33374	+	3.14865i	0.159097	+	0.115590i
$743$	41.7437	+	30.3286i	1.53143	+	1.11265i	0.955438	+	0.295192i	$0.0953837\pi$
$743$	41.7437	+	30.3286i	1.53143	+	1.11265i	0.575991	+	0.817456i	$0.304616\pi$
$744$	0.481712	−	1.48256i	0.0176604	−	0.0543532i
$745$	−1.33648	−	4.11327i	−0.0489649	−	0.150699i
$746$	−28.2541	+	20.5278i	−1.03445	+	0.751575i
$747$	33.3027			1.21848
$748$	17.5199	−	12.8514i	0.640592	−	0.469894i
$749$	5.18688			0.189524
$750$	0.198931	−	0.144532i	0.00726395	−	0.00527757i
$751$	14.0081	+	43.1126i	0.511164	+	1.57320i	0.790154	+	0.612908i	$0.210000\pi$
$751$	14.0081	+	43.1126i	0.511164	+	1.57320i	−0.278990	+	0.960294i	$0.590000\pi$
$752$	−1.90664	+	5.86805i	−0.0695282	+	0.213986i
$753$	2.55448	+	1.85594i	0.0930904	+	0.0676341i
$754$	2.73388	+	1.98628i	0.0995621	+	0.0723361i
$755$	−5.41219	+	16.6570i	−0.196970	+	0.606211i
$756$	−0.451316	−	1.38901i	−0.0164142	−	0.0505177i
$757$	−31.9741	+	23.2305i	−1.16212	+	0.844327i	−0.990044	−	0.140757i	$-0.955046\pi$
$757$	−31.9741	+	23.2305i	−1.16212	+	0.844327i	−0.172073	+	0.985084i	$0.555046\pi$
$758$	−1.32409			−0.0480930
$759$	−2.12315	−	6.43444i	−0.0770655	−	0.233555i
$760$	3.43477			0.124592
$761$	−21.9343	+	15.9362i	−0.795116	+	0.577686i	−0.909477	−	0.415754i	$-0.863518\pi$
$761$	−21.9343	+	15.9362i	−0.795116	+	0.577686i	0.114361	+	0.993439i	$0.463518\pi$
$762$	0.0621861	+	0.191389i	0.00225277	+	0.00693330i
$763$	3.74784	−	11.5347i	0.135681	−	0.417583i
$764$	−3.27813	−	2.38170i	−0.118599	−	0.0861670i
$765$	15.5797	+	11.3193i	0.563287	+	0.409252i
$766$	−0.748546	+	2.30379i	−0.0270461	+	0.0832392i
$767$	0.797976	+	2.45592i	0.0288133	+	0.0886781i
$768$	−0.198931	+	0.144532i	−0.00717832	+	0.00521536i
$769$	18.0791			0.651948			0.325974	−	0.945379i	$-0.394308\pi$
$769$	18.0791			0.651948			0.325974	+	0.945379i	$0.394308\pi$
$770$	1.01050	−	3.15894i	0.0364160	−	0.113840i
$771$	1.40318			0.0505342
$772$	16.5959	−	12.0576i	0.597299	−	0.433963i
$773$	−11.6525	−	35.8628i	−0.419112	−	1.28989i	−0.908521	−	0.417840i	$-0.862787\pi$
$773$	−11.6525	−	35.8628i	−0.419112	−	1.28989i	0.489408	−	0.872055i	$-0.337213\pi$
$774$	−2.68651	+	8.26824i	−0.0965647	+	0.297196i
$775$	5.12881	+	3.72630i	0.184232	+	0.133853i
$776$	2.79473	+	2.03049i	0.100325	+	0.0728903i
$777$	−0.293867	+	0.904429i	−0.0105424	+	0.0324462i
$778$	6.56806	+	20.2144i	0.235477	+	0.724722i
$779$	−29.3324	+	21.3112i	−1.05094	+	0.763554i
$780$	−0.283261			−0.0101424
$781$	−1.02358	−	0.736567i	−0.0366265	−	0.0263564i
$782$	−54.4295			−1.94639
$783$	−3.46607	+	2.51824i	−0.123867	+	0.0899947i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	2.53528	−	7.80280i	0.0904882	−	0.278494i
$786$	1.94336	+	1.41193i	0.0693174	+	0.0503620i
$787$	−3.84001	−	2.78993i	−0.136882	−	0.0994502i	0.517237	−	0.855842i	$-0.326960\pi$
$787$	−3.84001	−	2.78993i	−0.136882	−	0.0994502i	−0.654119	+	0.756392i	$0.726960\pi$
$788$	−6.31626	+	19.4394i	−0.225007	+	0.692501i
$789$	0.980928	+	3.01899i	0.0349220	+	0.107479i
$790$	−1.83955	+	1.33651i	−0.0654483	+	0.0475510i
$791$	14.5100			0.515916
$792$	7.91342	+	5.69450i	0.281191	+	0.202345i
$793$	11.5030			0.408483
$794$	10.4133	−	7.56569i	0.369553	−	0.268496i
$795$	0.407036	+	1.25273i	0.0144361	+	0.0444297i
$796$	−0.999905	+	3.07739i	−0.0354407	+	0.109075i
$797$	20.6172	+	14.9793i	0.730300	+	0.530594i	0.889658	−	0.456627i	$-0.150942\pi$
$797$	20.6172	+	14.9793i	0.730300	+	0.530594i	−0.159358	+	0.987221i	$0.550942\pi$
$798$	−0.683283	−	0.496434i	−0.0241880	−	0.0175736i
$799$	−12.4909	+	38.4430i	−0.441896	+	1.36002i
$800$	−0.309017	−	0.951057i	−0.0109254	−	0.0336249i
$801$	−10.6752	+	7.75601i	−0.377191	+	0.274045i
$802$	11.1726			0.394518
$803$	7.30812	−	22.8459i	0.257898	−	0.806215i
$804$	3.49529			0.123269
$805$	−6.72153	+	4.88348i	−0.236903	+	0.172120i
$806$	−2.25675	−	6.94555i	−0.0794905	−	0.244647i
$807$	1.46385	−	4.50527i	0.0515300	−	0.158593i
$808$	2.19820	+	1.59708i	0.0773323	+	0.0561852i
$809$	5.85807	+	4.25613i	0.205959	+	0.149638i	0.685983	−	0.727617i	$-0.259372\pi$
$809$	5.85807	+	4.25613i	0.205959	+	0.149638i	−0.480025	+	0.877255i	$0.659372\pi$
$810$	−2.61413	+	8.04545i	−0.0918510	+	0.282688i
$811$	3.84816	+	11.8434i	0.135127	+	0.415879i	0.995610	−	0.0936012i	$-0.0298379\pi$
$811$	3.84816	+	11.8434i	0.135127	+	0.415879i	−0.860483	+	0.509480i	$0.829838\pi$
$812$	2.37322	−	1.72425i	0.0832838	−	0.0605092i
$813$	6.84029			0.239900
$814$	−4.01927	−	12.1808i	−0.140875	−	0.426938i
$815$	−11.4586			−0.401376
$816$	−1.30325	+	0.946866i	−0.0456228	+	0.0331469i
$817$	3.13912	+	9.66121i	0.109824	+	0.338003i
$818$	−4.55148	+	14.0080i	−0.159139	+	0.489778i
$819$	−2.73954	−	1.99039i	−0.0957273	−	0.0695500i
$820$	8.53984	+	6.20456i	0.298224	+	0.216673i
$821$	−5.11984	+	15.7573i	−0.178684	+	0.549932i	−0.999783	−	0.0208541i	$-0.993361\pi$
$821$	−5.11984	+	15.7573i	−0.178684	+	0.549932i	0.821099	+	0.570786i	$0.193361\pi$
$822$	0.508279	+	1.56432i	0.0177283	+	0.0545620i
$823$	23.3785	−	16.9855i	0.814924	−	0.592077i	−0.100330	−	0.994954i	$-0.531990\pi$
$823$	23.3785	−	16.9855i	0.814924	−	0.592077i	0.915254	+	0.402877i	$0.131990\pi$
$824$	9.90941			0.345211
$825$	0.657589	−	0.482362i	0.0228943	−	0.0167937i
$826$	2.24164			0.0779967
$827$	18.2141	−	13.2333i	0.633367	−	0.460168i	−0.224198	−	0.974544i	$-0.571976\pi$
$827$	18.2141	−	13.2333i	0.633367	−	0.460168i	0.857565	+	0.514376i	$0.171976\pi$
$828$	−7.54695	−	23.2271i	−0.262275	−	0.807199i
$829$	−8.61415	+	26.5116i	−0.299182	+	0.920787i	0.682603	+	0.730790i	$0.260848\pi$
$829$	−8.61415	+	26.5116i	−0.299182	+	0.920787i	−0.981785	+	0.189997i	$0.939152\pi$
$830$	−9.16555	−	6.65916i	−0.318141	−	0.231143i
$831$	−2.46078	−	1.78786i	−0.0853635	−	0.0620202i
$832$	−0.355978	+	1.09559i	−0.0123413	+	0.0379827i
$833$	2.02445	+	6.23061i	0.0701429	+	0.215878i
$834$	−1.76124	+	1.27961i	−0.0609866	+	0.0443094i
$835$	−0.763127			−0.0264091
$836$	11.3917	−	0.0519297i	0.393991	−	0.00179603i
$837$	9.25886			0.320033
$838$	−11.4810	+	8.34143i	−0.396604	+	0.288150i
$839$	9.89965	+	30.4680i	0.341774	+	1.05187i	0.963288	+	0.268469i	$0.0865177\pi$
$839$	9.89965	+	30.4680i	0.341774	+	1.05187i	−0.621515	+	0.783403i	$0.713482\pi$
$840$	−0.0759851	+	0.233858i	−0.00262173	+	0.00806887i
$841$	16.4997	+	11.9878i	0.568956	+	0.413371i
$842$	−21.0825	−	15.3174i	−0.726553	−	0.527871i
$843$	1.67078	−	5.14214i	0.0575448	−	0.177105i
$844$	−3.81571	−	11.7435i	−0.131342	−	0.404230i
$845$	9.44363	−	6.86120i	0.324871	−	0.236032i
$846$	−18.1370			−0.623564
$847$	3.30367	−	10.4922i	0.113515	−	0.360515i
$848$	5.35680			0.183953
$849$	2.74933	−	1.99750i	0.0943567	−	0.0685541i
$850$	−2.02445	−	6.23061i	−0.0694379	−	0.213708i
$851$	−9.92921	+	30.5590i	−0.340369	+	1.04755i
$852$	0.0756378	+	0.0549541i	0.00259131	+	0.00188269i
$853$	−16.4527	−	11.9536i	−0.563329	−	0.409282i	0.269347	−	0.963043i	$-0.413192\pi$
$853$	−16.4527	−	11.9536i	−0.563329	−	0.409282i	−0.832676	+	0.553761i	$0.813192\pi$
$854$	3.08568	−	9.49676i	0.105590	−	0.324972i
$855$	3.12003	+	9.60246i	0.106703	+	0.328397i
$856$	4.19627	−	3.04877i	0.143426	−	0.104205i
$857$	52.8958			1.80689			0.903444	−	0.428706i	$-0.141031\pi$
$857$	52.8958			1.80689			0.903444	+	0.428706i	$0.141031\pi$
$858$	−0.939461	+	0.00428258i	−0.0320727	+	0.000146205i
$859$	−56.9360			−1.94263			−0.971315	−	0.237797i	$-0.923575\pi$
$859$	−56.9360			−1.94263			−0.971315	+	0.237797i	$0.923575\pi$
$860$	2.39268	−	1.73839i	0.0815899	−	0.0592785i
$861$	−0.802085	−	2.46856i	−0.0273350	−	0.0841284i
$862$	5.81405	−	17.8938i	0.198027	−	0.609465i
$863$	13.3892	+	9.72782i	0.455773	+	0.331139i	0.791871	−	0.610688i	$-0.209107\pi$
$863$	13.3892	+	9.72782i	0.455773	+	0.331139i	−0.336098	+	0.941827i	$0.609107\pi$
$864$	−1.18156	−	0.858454i	−0.0401975	−	0.0292052i
$865$	−2.70931	+	8.33841i	−0.0921194	+	0.283514i
$866$	−6.30482	−	19.4042i	−0.214246	−	0.659382i
$867$	−5.15607	+	3.74610i	−0.175109	+	0.127224i
$868$	−6.33956			−0.215179
$869$	−6.08084	+	4.46048i	−0.206278	+	0.151311i
$870$	0.721318			0.0244550
$871$	13.2476	−	9.62491i	0.448876	−	0.326128i
$872$	−3.74784	−	11.5347i	−0.126918	−	0.390613i
$873$	−3.13793	+	9.65755i	−0.106203	+	0.326858i
$874$	−23.0869	−	16.7736i	−0.780926	−	0.567376i
$875$	−0.809017	−	0.587785i	−0.0273498	−	0.0198708i
$876$	−0.549536	+	1.69130i	−0.0185671	+	0.0571437i
$877$	−14.8895	−	45.8253i	−0.502784	−	1.54741i	−0.804465	−	0.594000i	$-0.797548\pi$
$877$	−14.8895	−	45.8253i	−0.502784	−	1.54741i	0.301681	−	0.953409i	$-0.402452\pi$
$878$	14.1814	−	10.3034i	0.478599	−	0.347722i
$879$	−4.47652			−0.150989
$880$	−1.03926	−	3.14959i	−0.0350335	−	0.106173i
$881$	−42.1700			−1.42074			−0.710372	−	0.703827i	$-0.751473\pi$
$881$	−42.1700			−1.42074			−0.710372	+	0.703827i	$0.751473\pi$
$882$	−2.37814	+	1.72782i	−0.0800760	+	0.0581786i
$883$	12.1167	+	37.2914i	0.407760	+	1.25496i	0.918569	+	0.395261i	$0.129346\pi$
$883$	12.1167	+	37.2914i	0.407760	+	1.25496i	−0.510809	+	0.859694i	$0.670654\pi$
$884$	−2.33210	+	7.17747i	−0.0784371	+	0.241404i
$885$	0.445933	+	0.323989i	0.0149899	+	0.0108908i
$886$	−21.1922	−	15.3970i	−0.711965	−	0.517273i
$887$	13.9204	−	42.8425i	0.467401	−	1.43851i	−0.388538	−	0.921433i	$-0.627020\pi$
$887$	13.9204	−	42.8425i	0.467401	−	1.43851i	0.855938	−	0.517078i	$-0.172980\pi$
$888$	0.293867	+	0.904429i	0.00986152	+	0.0303506i
$889$	0.662099	−	0.481043i	0.0222061	−	0.0161337i
$890$	4.48891			0.150468
$891$	−8.54834	+	26.7230i	−0.286380	+	0.895254i
$892$	8.30846			0.278188
$893$	−17.1452	+	12.4567i	−0.573742	+	0.416848i
$894$	0.328631	+	1.01142i	0.0109911	+	0.0338271i
$895$	4.64388	−	14.2924i	0.155228	−	0.477742i
$896$	0.809017	+	0.587785i	0.0270274	+	0.0196365i
$897$	1.90395	+	1.38330i	0.0635710	+	0.0461870i
$898$	2.93473	−	9.03218i	0.0979333	−	0.301408i
$899$	5.74675	+	17.6867i	0.191665	+	0.589884i
$900$	2.37814	−	1.72782i	0.0792712	−	0.0575939i
$901$	35.0937			1.16914
$902$	28.4170	+	20.4489i	0.946181	+	0.680873i
$903$	−0.727233			−0.0242008
$904$	11.7388	−	8.52876i	0.390428	−	0.283662i
$905$	6.54768	+	20.1517i	0.217652	+	0.669865i
$906$	1.33082	−	4.09584i	0.0442135	−	0.136075i
$907$	−29.8450	−	21.6836i	−0.990986	−	0.719993i	−0.0308489	−	0.999524i	$-0.509821\pi$
$907$	−29.8450	−	21.6836i	−0.990986	−	0.719993i	−0.960137	+	0.279531i	$0.909821\pi$
$908$	12.7260	+	9.24595i	0.422326	+	0.306838i
$909$	−2.46814	+	7.59617i	−0.0818632	+	0.251949i
$910$	0.355978	+	1.09559i	0.0118006	+	0.0363184i
$911$	16.7136	−	12.1431i	0.553746	−	0.402320i	−0.275419	−	0.961324i	$-0.588817\pi$
$911$	16.7136	−	12.1431i	0.553746	−	0.402320i	0.829165	+	0.559004i	$0.188817\pi$
$912$	−0.844585			−0.0279670
$913$	−30.4990	−	21.9471i	−1.00937	−	0.726344i
$914$	−17.5412			−0.580213
$915$	1.98643	−	1.44322i	0.0656692	−	0.0477115i
$916$	−7.33324	−	22.5694i	−0.242297	−	0.745714i
$917$	3.01879	−	9.29087i	0.0996891	−	0.306812i
$918$	−7.74069	−	5.62394i	−0.255481	−	0.185618i
$919$	−32.6043	−	23.6884i	−1.07552	−	0.781409i	−0.0986215	−	0.995125i	$-0.531443\pi$
$919$	−32.6043	−	23.6884i	−1.07552	−	0.781409i	−0.976896	+	0.213716i	$0.931443\pi$
$920$	−2.56740	+	7.90163i	−0.0846445	+	0.260509i
$921$	1.80638	+	5.55948i	0.0595224	+	0.183191i
$922$	−18.3420	+	13.3263i	−0.604063	+	0.438877i
$923$	0.438002			0.0144170
$924$	−0.248476	+	0.776760i	−0.00817425	+	0.0255535i
$925$	−3.86743			−0.127160
$926$	−21.8074	+	15.8440i	−0.716635	+	0.520666i
$927$	9.00138	+	27.7034i	0.295644	+	0.909899i
$928$	0.906490	−	2.78989i	0.0297570	−	0.0915826i
$929$	6.04153	+	4.38943i	0.198216	+	0.144013i	0.682466	−	0.730917i	$-0.260907\pi$
$929$	6.04153	+	4.38943i	0.198216	+	0.144013i	−0.484250	+	0.874930i	$0.660907\pi$
$930$	−1.26114	−	0.916271i	−0.0413544	−	0.0300457i
$931$	−1.06140	+	3.26666i	−0.0347860	+	0.107060i
$932$	3.67801	+	11.3198i	0.120477	+	0.370791i
$933$	3.63068	−	2.63785i	0.118863	−	0.0863592i
$934$	−14.7718			−0.483348
$935$	−6.80846	−	20.6338i	−0.222660	−	0.674796i
$936$	−3.38626			−0.110683
$937$	19.1343	−	13.9019i	0.625091	−	0.454156i	−0.229605	−	0.973284i	$-0.573743\pi$
$937$	19.1343	−	13.9019i	0.625091	−	0.454156i	0.854696	+	0.519128i	$0.173743\pi$
$938$	−4.39258	−	13.5190i	−0.143423	−	0.441410i
$939$	−1.24618	+	3.83535i	−0.0406676	+	0.125162i
$940$	4.99166	+	3.62665i	0.162810	+	0.118288i
$941$	27.5249	+	19.9980i	0.897286	+	0.651916i	0.937767	−	0.347264i	$-0.112889\pi$
$941$	27.5249	+	19.9980i	0.897286	+	0.651916i	−0.0404818	+	0.999180i	$0.512889\pi$
$942$	−0.623408	+	1.91865i	−0.0203117	+	0.0625131i
$943$	−27.1010	−	83.4082i	−0.882529	−	2.71615i
$944$	1.81353	−	1.31760i	0.0590253	−	0.0428844i
$945$	−1.46049			−0.0475097
$946$	7.90927	−	5.80169i	0.257153	−	0.188629i
$947$	16.1828			0.525871			0.262935	−	0.964813i	$-0.415309\pi$
$947$	16.1828			0.525871			0.262935	+	0.964813i	$0.415309\pi$
$948$	0.452333	−	0.328639i	0.0146911	−	0.0106737i
$949$	2.57449	+	7.92347i	0.0835715	+	0.257207i
$950$	1.06140	−	3.26666i	0.0344364	−	0.105984i
$951$	5.22856	+	3.79877i	0.169548	+	0.123184i
$952$	5.30007	+	3.85073i	0.171776	+	0.124803i
$953$	17.0540	−	52.4868i	0.552433	−	1.70021i	−0.150196	−	0.988656i	$-0.547990\pi$
$953$	17.0540	−	52.4868i	0.552433	−	1.70021i	0.702628	−	0.711557i	$-0.252010\pi$
$954$	4.86594	+	14.9758i	0.157541	+	0.484860i
$955$	−3.27813	+	2.38170i	−0.106078	+	0.0770701i
$956$	−21.8184			−0.705659
$957$	2.39232	−	0.0109055i	0.0773326	−	0.000352525i
$958$	31.8220			1.02812
$959$	5.41168	−	3.93181i	0.174752	−	0.126965i
$960$	0.0759851	+	0.233858i	0.00245241	+	0.00754773i
$961$	2.83988	−	8.74026i	0.0916091	−	0.281944i
$962$	3.60430	+	2.61868i	0.116207	+	0.0844295i
$963$	12.3351	+	8.96197i	0.397493	+	0.288795i
$964$	−4.55530	+	14.0198i	−0.146716	+	0.451547i
$965$	−6.33907	−	19.5096i	−0.204062	−	0.628037i
$966$	1.65278	−	1.20081i	0.0531772	−	0.0386355i
$967$	−48.0059			−1.54376			−0.771882	−	0.635765i	$-0.780685\pi$
$967$	−48.0059			−1.54376			−0.771882	+	0.635765i	$0.780685\pi$
$968$	−3.49442	−	10.4302i	−0.112315	−	0.335239i
$969$	−5.53308			−0.177748
$970$	2.79473	−	2.03049i	0.0897333	−	0.0651950i
$971$	2.60097	+	8.00498i	0.0834693	+	0.256892i	0.984078	−	0.177740i	$-0.0568785\pi$
$971$	2.60097	+	8.00498i	0.0834693	+	0.256892i	−0.900608	+	0.434632i	$0.856879\pi$
$972$	1.99674	−	6.14534i	0.0640455	−	0.197112i
$973$	7.16262	+	5.20395i	0.229623	+	0.166831i
$974$	20.1174	+	14.6161i	0.644602	+	0.468331i
$975$	−0.0875325	+	0.269397i	−0.00280328	+	0.00862762i
$976$	−3.08568	−	9.49676i	−0.0987703	−	0.303984i
$977$	−27.2819	+	19.8214i	−0.872824	+	0.634144i	−0.931343	−	0.364142i	$-0.881362\pi$
$977$	−27.2819	+	19.8214i	−0.872824	+	0.634144i	0.0585190	+	0.998286i	$0.481362\pi$
$978$	2.81758			0.0900962
$979$	14.8879	−	0.0678671i	0.475818	−	0.00216904i
$980$	1.00000			0.0319438
$981$	28.8427	−	20.9554i	0.920876	−	0.669056i
$982$	12.9322	+	39.8013i	0.412684	+	1.27011i
$983$	5.04004	−	15.5116i	0.160752	−	0.494744i	−0.837946	−	0.545753i	$-0.816244\pi$
$983$	5.04004	−	15.5116i	0.160752	−	0.494744i	0.998698	+	0.0510088i	$0.0162437\pi$
$984$	−2.09989	−	1.52566i	−0.0669419	−	0.0486361i
$985$	16.5362	+	12.0142i	0.526886	+	0.382805i
$986$	5.93864	−	18.2773i	0.189125	−	0.582067i
$987$	−0.468830	−	1.44291i	−0.0149230	−	0.0459284i
$988$	−3.20108	+	2.32572i	−0.101840	+	0.0739910i
$989$	−24.5719			−0.781340
$990$	7.86118	−	5.76641i	0.249845	−	0.183269i
$991$	1.23518			0.0392367			0.0196183	−	0.999808i	$-0.493755\pi$
$991$	1.23518			0.0392367			0.0196183	+	0.999808i	$0.493755\pi$
$992$	−5.12881	+	3.72630i	−0.162840	+	0.118310i
$993$	1.87382	+	5.76703i	0.0594639	+	0.183011i
$994$	0.117495	−	0.361611i	0.00372670	−	0.0114696i
$995$	2.61779	+	1.90193i	0.0829894	+	0.0602953i
$996$	2.25374	+	1.63744i	0.0714126	+	0.0518843i
$997$	−2.61319	+	8.04258i	−0.0827606	+	0.254711i	−0.983871	−	0.178878i	$-0.942753\pi$
$997$	−2.61319	+	8.04258i	−0.0827606	+	0.254711i	0.901111	+	0.433589i	$0.142753\pi$
$998$	−7.67446	−	23.6195i	−0.242931	−	0.747664i
$999$	−4.56960	+	3.32001i	−0.144576	+	0.105040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.j.421.2	✓	12
11.2	odd	10		8470.2.a.dc.1.4		6
11.4	even	5	inner	770.2.n.j.631.2	yes	12
11.9	even	5		8470.2.a.cw.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.j.421.2	✓	12	1.1	even	1	trivial
770.2.n.j.631.2	yes	12	11.4	even	5	inner
8470.2.a.cw.1.4		6	11.9	even	5
8470.2.a.dc.1.4		6	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.0759851 + 0.233858i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.198931 + 0.144532i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.37814 - 1.72782i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.0759851 + 0.233858i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.198931 + 0.144532i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.37814 - 1.72782i) q^{9} -1.00000 q^{10} +(-3.31659 + 0.0151188i) q^{11} +0.245893 q^{12} +(0.931963 - 0.677111i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(0.0759851 - 0.233858i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.30007 - 3.85073i) q^{17} +(0.908367 - 2.79567i) q^{18} +(-1.06140 - 3.26666i) q^{19} +(-0.809017 + 0.587785i) q^{20} +0.245893 q^{21} +(-2.67429 + 1.96167i) q^{22} +8.30827 q^{23} +(0.198931 - 0.144532i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.355978 - 1.09559i) q^{26} +(1.18156 + 0.858454i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-0.906490 + 2.78989i) q^{29} +(-0.0759851 - 0.233858i) q^{30} +(5.12881 - 3.72630i) q^{31} -1.00000 q^{32} +(-0.255547 - 0.774462i) q^{33} -6.55125 q^{34} +(-0.809017 + 0.587785i) q^{35} +(-0.908367 - 2.79567i) q^{36} +(-1.19510 + 3.67814i) q^{37} +(-2.77879 - 2.01891i) q^{38} +(0.229163 + 0.166497i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(-3.26193 - 10.0392i) q^{41} +(0.198931 - 0.144532i) q^{42} -2.95752 q^{43} +(-1.01050 + 3.15894i) q^{44} -2.93954 q^{45} +(6.72153 - 4.88348i) q^{46} +(-1.90664 - 5.86805i) q^{47} +(0.0759851 - 0.233858i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(0.809017 + 0.587785i) q^{50} +(0.497797 - 1.53206i) q^{51} +(-0.355978 - 1.09559i) q^{52} +(-4.33374 + 3.14865i) q^{53} +1.46049 q^{54} +(2.69206 + 1.93721i) q^{55} -1.00000 q^{56} +(0.683283 - 0.496434i) q^{57} +(0.906490 + 2.78989i) q^{58} +(-0.692706 + 2.13193i) q^{59} +(-0.198931 - 0.144532i) q^{60} +(8.07842 + 5.86932i) q^{61} +(1.95903 - 6.02928i) q^{62} +(-0.908367 - 2.79567i) q^{63} +(-0.809017 + 0.587785i) q^{64} -1.15197 q^{65} +(-0.661959 - 0.476346i) q^{66} +14.2147 q^{67} +(-5.30007 + 3.85073i) q^{68} +(0.631304 + 1.94295i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(0.307605 + 0.223488i) q^{71} +(-2.37814 - 1.72782i) q^{72} +(-2.23486 + 6.87819i) q^{73} +(1.19510 + 3.67814i) q^{74} +(-0.198931 + 0.144532i) q^{75} -3.43477 q^{76} +(-1.01050 + 3.15894i) q^{77} +0.283261 q^{78} +(1.83955 - 1.33651i) q^{79} +(0.309017 + 0.951057i) q^{80} +(2.61413 - 8.04545i) q^{81} +(-8.53984 - 6.20456i) q^{82} +(9.16555 + 6.65916i) q^{83} +(0.0759851 - 0.233858i) q^{84} +(2.02445 + 6.23061i) q^{85} +(-2.39268 + 1.73839i) q^{86} -0.721318 q^{87} +(1.03926 + 3.14959i) q^{88} -4.48891 q^{89} +(-2.37814 + 1.72782i) q^{90} +(-0.355978 - 1.09559i) q^{91} +(2.56740 - 7.90163i) q^{92} +(1.26114 + 0.916271i) q^{93} +(-4.99166 - 3.62665i) q^{94} +(-1.06140 + 3.26666i) q^{95} +(-0.0759851 - 0.233858i) q^{96} +(-2.79473 + 2.03049i) q^{97} -1.00000 q^{98} +(-7.86118 + 5.76641i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 12 q^{10} - q^{11} - 2 q^{12} + 2 q^{13} + 3 q^{14} + 3 q^{15} - 3 q^{16} + 7 q^{17} + 9 q^{18} + 6 q^{19} - 3 q^{20} - 2 q^{21} + q^{22} + 8 q^{23} + 2 q^{24} - 3 q^{25} - 7 q^{26} - 3 q^{27} - 3 q^{28} + 20 q^{29} - 3 q^{30} + 6 q^{31} - 12 q^{32} - 12 q^{33} + 18 q^{34} - 3 q^{35} - 9 q^{36} + 22 q^{37} - 6 q^{38} + 23 q^{39} + 3 q^{40} + 2 q^{41} + 2 q^{42} - 60 q^{43} - 11 q^{44} + 6 q^{45} + 2 q^{46} - 4 q^{47} + 3 q^{48} - 3 q^{49} + 3 q^{50} + 13 q^{51} + 7 q^{52} + 18 q^{53} + 8 q^{54} + 14 q^{55} - 12 q^{56} + 8 q^{57} - 20 q^{58} - 32 q^{59} - 2 q^{60} + 8 q^{61} + 14 q^{62} - 9 q^{63} - 3 q^{64} - 18 q^{65} - 8 q^{66} + 36 q^{67} + 7 q^{68} + 50 q^{69} + 3 q^{70} - 34 q^{71} - 6 q^{72} + 14 q^{73} - 22 q^{74} - 2 q^{75} - 24 q^{76} - 11 q^{77} - 38 q^{78} - 12 q^{79} - 3 q^{80} + 4 q^{81} - 2 q^{82} + 30 q^{83} + 3 q^{84} + 2 q^{85} - 28 q^{87} + q^{88} - 36 q^{89} - 6 q^{90} + 7 q^{91} - 2 q^{92} + 12 q^{93} - 11 q^{94} + 6 q^{95} - 3 q^{96} + 39 q^{97} - 12 q^{98} - 15 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 - 12 * q^10 - q^11 - 2 * q^12 + 2 * q^13 + 3 * q^14 + 3 * q^15 - 3 * q^16 + 7 * q^17 + 9 * q^18 + 6 * q^19 - 3 * q^20 - 2 * q^21 + q^22 + 8 * q^23 + 2 * q^24 - 3 * q^25 - 7 * q^26 - 3 * q^27 - 3 * q^28 + 20 * q^29 - 3 * q^30 + 6 * q^31 - 12 * q^32 - 12 * q^33 + 18 * q^34 - 3 * q^35 - 9 * q^36 + 22 * q^37 - 6 * q^38 + 23 * q^39 + 3 * q^40 + 2 * q^41 + 2 * q^42 - 60 * q^43 - 11 * q^44 + 6 * q^45 + 2 * q^46 - 4 * q^47 + 3 * q^48 - 3 * q^49 + 3 * q^50 + 13 * q^51 + 7 * q^52 + 18 * q^53 + 8 * q^54 + 14 * q^55 - 12 * q^56 + 8 * q^57 - 20 * q^58 - 32 * q^59 - 2 * q^60 + 8 * q^61 + 14 * q^62 - 9 * q^63 - 3 * q^64 - 18 * q^65 - 8 * q^66 + 36 * q^67 + 7 * q^68 + 50 * q^69 + 3 * q^70 - 34 * q^71 - 6 * q^72 + 14 * q^73 - 22 * q^74 - 2 * q^75 - 24 * q^76 - 11 * q^77 - 38 * q^78 - 12 * q^79 - 3 * q^80 + 4 * q^81 - 2 * q^82 + 30 * q^83 + 3 * q^84 + 2 * q^85 - 28 * q^87 + q^88 - 36 * q^89 - 6 * q^90 + 7 * q^91 - 2 * q^92 + 12 * q^93 - 11 * q^94 + 6 * q^95 - 3 * q^96 + 39 * q^97 - 12 * q^98 - 15 * q^99

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