LMFDB - Embedded newform 370.2.q.f.103.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(97,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("370.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.q (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.6
Character	$\chi$	$=$	370.103
Dual form			370.2.q.f.97.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.0936541 + 0.349522i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.693098 + 2.12594i) q^{5} +(-0.255868 + 0.255868i) q^{6} +(0.0100267 + 0.0374200i) q^{7} -1.00000 q^{8} +(2.48468 - 1.43453i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.0936541 + 0.349522i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.693098 + 2.12594i) q^{5} +(-0.255868 + 0.255868i) q^{6} +(0.0100267 + 0.0374200i) q^{7} -1.00000 q^{8} +(2.48468 - 1.43453i) q^{9} +(-2.18767 + 0.462729i) q^{10} +3.45168i q^{11} +(-0.349522 - 0.0936541i) q^{12} +(-1.24424 + 2.15509i) q^{13} +(-0.0273933 + 0.0273933i) q^{14} +(-0.807974 - 0.0431499i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.63142 + 0.941903i) q^{17} +(2.48468 + 1.43453i) q^{18} +(-5.26026 + 1.40948i) q^{19} +(-1.49457 - 1.66321i) q^{20} +(-0.0121401 + 0.00700907i) q^{21} +(-2.98924 + 1.72584i) q^{22} +0.905777 q^{23} +(-0.0936541 - 0.349522i) q^{24} +(-4.03923 - 2.94697i) q^{25} -2.48848 q^{26} +(1.50170 + 1.50170i) q^{27} +(-0.0374200 - 0.0100267i) q^{28} +(6.45203 - 6.45203i) q^{29} +(-0.366618 - 0.721301i) q^{30} +(4.37609 + 4.37609i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.20644 + 0.323264i) q^{33} +(-1.63142 - 0.941903i) q^{34} +(-0.0865021 - 0.00461965i) q^{35} +2.86906i q^{36} +(-6.07501 - 0.307010i) q^{37} +(-3.85078 - 3.85078i) q^{38} +(-0.869779 - 0.233056i) q^{39} +(0.693098 - 2.12594i) q^{40} +(8.36534 + 4.82973i) q^{41} +(-0.0121401 - 0.00700907i) q^{42} +8.19202 q^{43} +(-2.98924 - 1.72584i) q^{44} +(1.32760 + 6.27655i) q^{45} +(0.452889 + 0.784426i) q^{46} +(5.31164 - 5.31164i) q^{47} +(0.255868 - 0.255868i) q^{48} +(6.06088 - 3.49925i) q^{49} +(0.532532 - 4.97156i) q^{50} +(-0.482005 - 0.482005i) q^{51} +(-1.24424 - 2.15509i) q^{52} +(0.879138 - 3.28099i) q^{53} +(-0.549662 + 2.05137i) q^{54} +(-7.33806 - 2.39235i) q^{55} +(-0.0100267 - 0.0374200i) q^{56} +(-0.985291 - 1.70657i) q^{57} +(8.81363 + 2.36161i) q^{58} +(-1.03235 + 3.85279i) q^{59} +(0.441356 - 0.678151i) q^{60} +(-0.0232515 + 0.00623022i) q^{61} +(-1.60176 + 5.97785i) q^{62} +(0.0785932 + 0.0785932i) q^{63} +1.00000 q^{64} +(-3.71920 - 4.13886i) q^{65} +(-0.883173 - 0.883173i) q^{66} +(-14.8563 + 3.98072i) q^{67} -1.88381i q^{68} +(0.0848298 + 0.316589i) q^{69} +(-0.0392503 - 0.0772228i) q^{70} +(6.17295 - 10.6919i) q^{71} +(-2.48468 + 1.43453i) q^{72} +(6.60939 - 6.60939i) q^{73} +(-2.77163 - 5.41462i) q^{74} +(0.651739 - 1.68780i) q^{75} +(1.40948 - 5.26026i) q^{76} +(-0.129162 + 0.0346088i) q^{77} +(-0.233056 - 0.869779i) q^{78} +(4.82122 - 1.29184i) q^{79} +(2.18767 - 0.462729i) q^{80} +(3.91936 - 6.78853i) q^{81} +9.65946i q^{82} +(-3.63463 + 13.5646i) q^{83} -0.0140181i q^{84} +(-0.871692 - 4.12114i) q^{85} +(4.09601 + 7.09449i) q^{86} +(2.85938 + 1.65087i) q^{87} -3.45168i q^{88} +(2.48871 + 0.666849i) q^{89} +(-4.77185 + 4.28801i) q^{90} +(-0.0931189 - 0.0249511i) q^{91} +(-0.452889 + 0.784426i) q^{92} +(-1.11970 + 1.93938i) q^{93} +(7.25584 + 1.94420i) q^{94} +(0.649401 - 12.1599i) q^{95} +(0.349522 + 0.0936541i) q^{96} +2.55804i q^{97} +(6.06088 + 3.49925i) q^{98} +(4.95154 + 8.57632i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 2 q^{3} - 16 q^{4} + 6 q^{5} + 8 q^{6} - 10 q^{7} - 32 q^{8} + 12 q^{9}+O(q^{10}) $ 32 * q + 16 * q^2 - 2 * q^3 - 16 * q^4 + 6 * q^5 + 8 * q^6 - 10 * q^7 - 32 * q^8 + 12 * q^9	\( 32 q + 16 q^{2} - 2 q^{3} - 16 q^{4} + 6 q^{5} + 8 q^{6} - 10 q^{7} - 32 q^{8} + 12 q^{9} + 6 q^{10} + 10 q^{12} + 10 q^{13} - 8 q^{14} - 8 q^{15} - 16 q^{16} - 12 q^{17} + 12 q^{18} + 2 q^{19} - 54 q^{21} + 6 q^{22} + 12 q^{23} + 2 q^{24} - 16 q^{25} + 20 q^{26} + 40 q^{27} + 2 q^{28} + 6 q^{29} + 8 q^{30} - 4 q^{31} + 16 q^{32} + 26 q^{33} - 12 q^{34} - 12 q^{35} + 20 q^{37} - 26 q^{38} - 58 q^{39} - 6 q^{40} + 18 q^{41} - 54 q^{42} - 32 q^{43} + 6 q^{44} + 56 q^{45} + 6 q^{46} + 18 q^{47} - 8 q^{48} - 12 q^{49} - 14 q^{50} - 4 q^{51} + 10 q^{52} - 24 q^{53} + 20 q^{54} - 32 q^{55} + 10 q^{56} + 8 q^{57} + 36 q^{58} + 42 q^{59} + 16 q^{60} - 46 q^{61} - 14 q^{62} + 32 q^{64} - 18 q^{65} + 4 q^{66} + 50 q^{67} - 66 q^{69} + 12 q^{70} - 12 q^{71} - 12 q^{72} - 28 q^{73} + 16 q^{74} - 20 q^{75} - 28 q^{76} + 12 q^{77} - 26 q^{78} + 38 q^{79} - 6 q^{80} + 56 q^{81} - 8 q^{85} - 16 q^{86} + 18 q^{87} + 18 q^{89} + 4 q^{90} + 4 q^{91} - 6 q^{92} + 32 q^{93} + 30 q^{94} + 96 q^{95} - 10 q^{96} - 12 q^{98} - 26 q^{99}+O(q^{100}) \) 32 * q + 16 * q^2 - 2 * q^3 - 16 * q^4 + 6 * q^5 + 8 * q^6 - 10 * q^7 - 32 * q^8 + 12 * q^9 + 6 * q^10 + 10 * q^12 + 10 * q^13 - 8 * q^14 - 8 * q^15 - 16 * q^16 - 12 * q^17 + 12 * q^18 + 2 * q^19 - 54 * q^21 + 6 * q^22 + 12 * q^23 + 2 * q^24 - 16 * q^25 + 20 * q^26 + 40 * q^27 + 2 * q^28 + 6 * q^29 + 8 * q^30 - 4 * q^31 + 16 * q^32 + 26 * q^33 - 12 * q^34 - 12 * q^35 + 20 * q^37 - 26 * q^38 - 58 * q^39 - 6 * q^40 + 18 * q^41 - 54 * q^42 - 32 * q^43 + 6 * q^44 + 56 * q^45 + 6 * q^46 + 18 * q^47 - 8 * q^48 - 12 * q^49 - 14 * q^50 - 4 * q^51 + 10 * q^52 - 24 * q^53 + 20 * q^54 - 32 * q^55 + 10 * q^56 + 8 * q^57 + 36 * q^58 + 42 * q^59 + 16 * q^60 - 46 * q^61 - 14 * q^62 + 32 * q^64 - 18 * q^65 + 4 * q^66 + 50 * q^67 - 66 * q^69 + 12 * q^70 - 12 * q^71 - 12 * q^72 - 28 * q^73 + 16 * q^74 - 20 * q^75 - 28 * q^76 + 12 * q^77 - 26 * q^78 + 38 * q^79 - 6 * q^80 + 56 * q^81 - 8 * q^85 - 16 * q^86 + 18 * q^87 + 18 * q^89 + 4 * q^90 + 4 * q^91 - 6 * q^92 + 32 * q^93 + 30 * q^94 + 96 * q^95 - 10 * q^96 - 12 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.0936541	+	0.349522i	0.0540712	+	0.201797i	0.987677	−	0.156505i	$-0.0500227\pi$
$3$	0.0936541	+	0.349522i	0.0540712	+	0.201797i	−0.933606	+	0.358301i	$0.883356\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.693098	+	2.12594i	−0.309963	+	0.950749i
$5$	−0.693098	+	2.12594i	−0.309963	+	0.950749i
$6$	−0.255868	+	0.255868i	−0.104458	+	0.104458i
$7$	0.0100267	+	0.0374200i	0.00378972	+	0.0141434i	0.967795	−	0.251740i	$-0.0810029\pi$
$7$	0.0100267	+	0.0374200i	0.00378972	+	0.0141434i	−0.964005	+	0.265884i	$0.914336\pi$
$8$	−1.00000			−0.353553
$9$	2.48468	−	1.43453i	0.828227	−	0.478177i
$10$	−2.18767	+	0.462729i	−0.691801	+	0.146328i
$11$			3.45168i			1.04072i	0.853947	+	0.520360i	$0.174202\pi$
$11$			3.45168i			1.04072i	−0.853947	+	0.520360i	$0.825798\pi$
$12$	−0.349522	−	0.0936541i	−0.100898	−	0.0270356i
$13$	−1.24424	+	2.15509i	−0.345090	+	0.597714i	−0.985370	−	0.170428i	$-0.945485\pi$
$13$	−1.24424	+	2.15509i	−0.345090	+	0.597714i	0.640280	+	0.768142i	$0.278818\pi$
$14$	−0.0273933	+	0.0273933i	−0.00732118	+	0.00732118i
$15$	−0.807974	−	0.0431499i	−0.208618	−	0.0111413i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.63142	+	0.941903i	−0.395678	+	0.228445i	−0.684618	−	0.728902i	$-0.740031\pi$
$17$	−1.63142	+	0.941903i	−0.395678	+	0.228445i	0.288939	+	0.957347i	$0.406697\pi$
$18$	2.48468	+	1.43453i	0.585645	+	0.338122i
$19$	−5.26026	+	1.40948i	−1.20679	+	0.323358i	−0.805501	−	0.592595i	$-0.798104\pi$
$19$	−5.26026	+	1.40948i	−1.20679	+	0.323358i	−0.401287	+	0.915952i	$0.631437\pi$
$20$	−1.49457	−	1.66321i	−0.334196	−	0.371905i
$21$	−0.0121401	+	0.00700907i	−0.00264918	+	0.00152951i
$22$	−2.98924	+	1.72584i	−0.637308	+	0.367950i
$23$	0.905777			0.188868			0.0944338	−	0.995531i	$-0.469896\pi$
$23$	0.905777			0.188868			0.0944338	+	0.995531i	$0.469896\pi$
$24$	−0.0936541	−	0.349522i	−0.0191171	−	0.0713459i
$25$	−4.03923	−	2.94697i	−0.807846	−	0.589393i
$26$	−2.48848			−0.488031
$27$	1.50170	+	1.50170i	0.289003	+	0.289003i
$28$	−0.0374200	−	0.0100267i	−0.00707171	−	0.00189486i
$29$	6.45203	−	6.45203i	1.19811	−	1.19811i	0.223380	−	0.974731i	$-0.428291\pi$
$29$	6.45203	−	6.45203i	1.19811	−	1.19811i	0.974731	−	0.223380i	$-0.0717091\pi$
$30$	−0.366618	−	0.721301i	−0.0669350	−	0.131691i
$31$	4.37609	+	4.37609i	0.785968	+	0.785968i	0.980831	−	0.194862i	$-0.0624260\pi$
$31$	4.37609	+	4.37609i	0.785968	+	0.785968i	−0.194862	+	0.980831i	$0.562426\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.20644	+	0.323264i	−0.210014	+	0.0562730i
$34$	−1.63142	−	0.941903i	−0.279787	−	0.161535i
$35$	−0.0865021	−	0.00461965i	−0.0146215	−	0.000780863i
$36$			2.86906i			0.478177i
$37$	−6.07501	−	0.307010i	−0.998725	−	0.0504721i
$37$	−6.07501	−	0.307010i	−0.998725	−	0.0504721i
$38$	−3.85078	−	3.85078i	−0.624679	−	0.624679i
$39$	−0.869779	−	0.233056i	−0.139276	−	0.0373189i
$40$	0.693098	−	2.12594i	0.109588	−	0.336140i
$41$	8.36534	+	4.82973i	1.30645	+	0.754277i	0.981501	−	0.191455i	$-0.0613207\pi$
$41$	8.36534	+	4.82973i	1.30645	+	0.754277i	0.324945	+	0.945733i	$0.394654\pi$
$42$	−0.0121401	−	0.00700907i	−0.00187325	−	0.00108152i
$43$	8.19202			1.24927			0.624635	−	0.780917i	$-0.285248\pi$
$43$	8.19202			1.24927			0.624635	+	0.780917i	$0.285248\pi$
$44$	−2.98924	−	1.72584i	−0.450645	−	0.260180i
$45$	1.32760	+	6.27655i	0.197907	+	0.935653i
$46$	0.452889	+	0.784426i	0.0667748	+	0.115657i
$47$	5.31164	−	5.31164i	0.774782	−	0.774782i	−0.204156	−	0.978938i	$-0.565445\pi$
$47$	5.31164	−	5.31164i	0.774782	−	0.774782i	0.978938	+	0.204156i	$0.0654450\pi$
$48$	0.255868	−	0.255868i	0.0369313	−	0.0369313i
$49$	6.06088	−	3.49925i	0.865840	−	0.499893i
$50$	0.532532	−	4.97156i	0.0753114	−	0.703085i
$51$	−0.482005	−	0.482005i	−0.0674942	−	0.0674942i
$52$	−1.24424	−	2.15509i	−0.172545	−	0.298857i
$53$	0.879138	−	3.28099i	0.120759	−	0.450678i	−0.878894	−	0.477017i	$-0.841718\pi$
$53$	0.879138	−	3.28099i	0.120759	−	0.450678i	0.999653	+	0.0263384i	$0.00838474\pi$
$54$	−0.549662	+	2.05137i	−0.0747995	+	0.279156i
$55$	−7.33806	−	2.39235i	−0.989463	−	0.322584i
$56$	−0.0100267	−	0.0374200i	−0.00133987	−	0.00500046i
$57$	−0.985291	−	1.70657i	−0.130505	−	0.226041i
$58$	8.81363	+	2.36161i	1.15729	+	0.310094i
$59$	−1.03235	+	3.85279i	−0.134401	+	0.501590i	0.865599	+	0.500738i	$0.166938\pi$
$59$	−1.03235	+	3.85279i	−0.134401	+	0.501590i	−1.00000		0.000852369i	$0.999729\pi$
$60$	0.441356	−	0.678151i	0.0569788	−	0.0875489i
$61$	−0.0232515	+	0.00623022i	−0.00297705	+	0.000797698i	−0.260307	−	0.965526i	$-0.583824\pi$
$61$	−0.0232515	+	0.00623022i	−0.00297705	+	0.000797698i	0.257330	+	0.966324i	$0.417157\pi$
$62$	−1.60176	+	5.97785i	−0.203424	+	0.759187i
$63$	0.0785932	+	0.0785932i	0.00990181	+	0.00990181i
$64$	1.00000			0.125000
$65$	−3.71920	−	4.13886i	−0.461310	−	0.513363i
$66$	−0.883173	−	0.883173i	−0.108711	−	0.108711i
$67$	−14.8563	+	3.98072i	−1.81498	+	0.486323i	−0.996146	−	0.0877072i	$-0.972046\pi$
$67$	−14.8563	+	3.98072i	−1.81498	+	0.486323i	−0.818834	+	0.574030i	$0.805379\pi$
$68$		−	1.88381i		−	0.228445i
$69$	0.0848298	+	0.316589i	0.0102123	+	0.0381128i
$70$	−0.0392503	−	0.0772228i	−0.00469131	−	0.00922989i
$71$	6.17295	−	10.6919i	0.732595	−	1.26889i	−0.223176	−	0.974778i	$-0.571642\pi$
$71$	6.17295	−	10.6919i	0.732595	−	1.26889i	0.955771	−	0.294113i	$-0.0950242\pi$
$72$	−2.48468	+	1.43453i	−0.292823	+	0.169061i
$73$	6.60939	−	6.60939i	0.773570	−	0.773570i	−0.205158	−	0.978729i	$-0.565771\pi$
$73$	6.60939	−	6.60939i	0.773570	−	0.773570i	0.978729	+	0.205158i	$0.0657710\pi$
$74$	−2.77163	−	5.41462i	−0.322195	−	0.629437i
$75$	0.651739	−	1.68780i	0.0752563	−	0.194890i
$76$	1.40948	−	5.26026i	0.161679	−	0.603394i
$77$	−0.129162	+	0.0346088i	−0.0147193	+	0.00394404i
$78$	−0.233056	−	0.869779i	−0.0263885	−	0.0984830i
$79$	4.82122	−	1.29184i	0.542429	−	0.145343i	0.0228074	−	0.999740i	$-0.492740\pi$
$79$	4.82122	−	1.29184i	0.542429	−	0.145343i	0.519622	+	0.854396i	$0.326073\pi$
$80$	2.18767	−	0.462729i	0.244588	−	0.0517347i
$81$	3.91936	−	6.78853i	0.435484	−	0.754281i
$82$			9.65946i			1.06671i
$83$	−3.63463	+	13.5646i	−0.398952	+	1.48891i	0.415991	+	0.909369i	$0.363435\pi$
$83$	−3.63463	+	13.5646i	−0.398952	+	1.48891i	−0.814943	+	0.579541i	$0.803232\pi$
$84$		−	0.0140181i		−	0.00152951i
$85$	−0.871692	−	4.12114i	−0.0945483	−	0.447000i
$86$	4.09601	+	7.09449i	0.441684	+	0.765019i
$87$	2.85938	+	1.65087i	0.306558	+	0.176991i
$88$		−	3.45168i		−	0.367950i
$89$	2.48871	+	0.666849i	0.263803	+	0.0706858i	0.388296	−	0.921535i	$-0.373064\pi$
$89$	2.48871	+	0.666849i	0.263803	+	0.0706858i	−0.124493	+	0.992220i	$0.539730\pi$
$90$	−4.77185	+	4.28801i	−0.502998	+	0.451996i
$91$	−0.0931189	−	0.0249511i	−0.00976152	−	0.00261559i
$92$	−0.452889	+	0.784426i	−0.0472169	+	0.0817821i
$93$	−1.11970	+	1.93938i	−0.116107	+	0.201104i
$94$	7.25584	+	1.94420i	0.748382	+	0.200528i
$95$	0.649401	−	12.1599i	0.0666271	−	1.24758i
$96$	0.349522	+	0.0936541i	0.0356729	+	0.00955853i
$97$			2.55804i			0.259729i	0.991532	+	0.129865i	$0.0414543\pi$
$97$			2.55804i			0.259729i	−0.991532	+	0.129865i	$0.958546\pi$
$98$	6.06088	+	3.49925i	0.612241	+	0.353478i
$99$	4.95154	+	8.57632i	0.497649	+	0.861953i
$100$	4.57176	−	2.02459i	0.457176	−	0.202459i
$101$		−	16.0383i		−	1.59587i	−0.602741	−	0.797937i	$-0.705925\pi$
$101$		−	16.0383i		−	1.59587i	0.602741	−	0.797937i	$-0.294075\pi$
$102$	0.176426	−	0.658431i	0.0174688	−	0.0651944i
$103$			4.28679i			0.422390i	0.977444	+	0.211195i	$0.0677355\pi$
$103$			4.28679i			0.422390i	−0.977444	+	0.211195i	$0.932264\pi$
$104$	1.24424	−	2.15509i	0.122008	−	0.211324i
$105$	−0.00648661	−	0.0306670i	−0.000633028	−	0.00299279i
$106$	3.28099	−	0.879138i	0.318678	−	0.0853894i
$107$	1.23738	+	4.61796i	0.119622	+	0.446435i	0.999591	−	0.0285960i	$-0.00910364\pi$
$107$	1.23738	+	4.61796i	0.119622	+	0.446435i	−0.879969	+	0.475031i	$0.842437\pi$
$108$	−2.05137	+	0.549662i	−0.197393	+	0.0528913i
$109$	−1.51602	+	5.65787i	−0.145209	+	0.541926i	0.854537	+	0.519390i	$0.173841\pi$
$109$	−1.51602	+	5.65787i	−0.145209	+	0.541926i	−0.999746	+	0.0225361i	$0.992826\pi$
$110$	−1.59719	−	7.55112i	−0.152286	−	0.719971i
$111$	−0.461643	−	2.15210i	−0.0438172	−	0.204268i
$112$	0.0273933	−	0.0273933i	0.00258843	−	0.00258843i
$113$	6.40021	−	3.69516i	0.602081	−	0.347612i	−0.167779	−	0.985825i	$-0.553659\pi$
$113$	6.40021	−	3.69516i	0.602081	−	0.347612i	0.769860	+	0.638213i	$0.220326\pi$
$114$	0.985291	−	1.70657i	0.0922810	−	0.159835i
$115$	−0.627792	+	1.92563i	−0.0585419	+	0.179566i
$116$	2.36161	+	8.81363i	0.219270	+	0.818325i
$117$			7.13961i			0.660057i
$118$	−3.85279	+	1.03235i	−0.354678	+	0.0950357i
$119$	−0.0516037	−	0.0516037i	−0.00473050	−	0.00473050i
$120$	0.807974	+	0.0431499i	0.0737576	+	0.00393903i
$121$	−0.914082			−0.0830983
$122$	−0.0170213	−	0.0170213i	−0.00154103	−	0.00154103i
$123$	−0.904649	+	3.37619i	−0.0815694	+	0.304421i
$124$	−5.97785	+	1.60176i	−0.536826	+	0.143842i
$125$	9.06465	−	6.54462i	0.810767	−	0.585369i
$126$	−0.0287671	+	0.107360i	−0.00256278	+	0.00956442i
$127$	−15.6289	−	4.18775i	−1.38684	−	0.371603i	−0.513240	−	0.858245i	$-0.671555\pi$
$127$	−15.6289	−	4.18775i	−1.38684	−	0.371603i	−0.873602	+	0.486642i	$0.838222\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	0.767216	+	2.86329i	0.0675496	+	0.252099i
$130$	1.72476	−	5.29036i	0.151271	−	0.463995i
$131$	−2.18373	+	8.14980i	−0.190794	+	0.712052i	0.802522	+	0.596622i	$0.203491\pi$
$131$	−2.18373	+	8.14980i	−0.190794	+	0.712052i	−0.993316	+	0.115429i	$0.963176\pi$
$132$	0.323264	−	1.20644i	0.0281365	−	0.105007i
$133$	−0.105486	−	0.182707i	−0.00914677	−	0.0158427i
$134$	−10.8755	−	10.8755i	−0.939503	−	0.939503i
$135$	−4.23336	+	2.15170i	−0.364350	+	0.185189i
$136$	1.63142	−	0.941903i	0.139893	−	0.0807675i
$137$	−5.52489	+	5.52489i	−0.472023	+	0.472023i	−0.902569	−	0.430546i	$-0.858321\pi$
$137$	−5.52489	+	5.52489i	−0.472023	+	0.472023i	0.430546	+	0.902569i	$0.358321\pi$
$138$	−0.231759	+	0.231759i	−0.0197287	+	0.0197287i
$139$	−4.60322	−	7.97300i	−0.390440	−	0.676261i	0.602068	−	0.798445i	$-0.294344\pi$
$139$	−4.60322	−	7.97300i	−0.390440	−	0.676261i	−0.992508	+	0.122184i	$0.961010\pi$
$140$	0.0472518	−	0.0726032i	0.00399350	−	0.00613609i
$141$	2.35399	+	1.35908i	0.198242	+	0.114455i
$142$	12.3459			1.03605
$143$	−7.43867	−	4.29472i	−0.622053	−	0.359142i
$144$	−2.48468	−	1.43453i	−0.207057	−	0.119544i
$145$	9.24473	+	18.1885i	0.767733	+	1.51047i
$146$	9.02859	+	2.41920i	0.747212	+	0.200215i
$147$	1.79069	+	1.79069i	0.147694	+	0.147694i
$148$	3.30338	−	5.10761i	0.271536	−	0.419843i
$149$		−	15.3857i		−	1.26044i	−0.776415	−	0.630222i	$-0.782964\pi$
$149$		−	15.3857i		−	1.26044i	0.776415	−	0.630222i	$-0.217036\pi$
$150$	1.78754	−	0.279476i	0.145952	−	0.0228191i
$151$	−6.97358	−	4.02620i	−0.567502	−	0.327647i	0.188649	−	0.982045i	$-0.439589\pi$
$151$	−6.97358	−	4.02620i	−0.567502	−	0.327647i	−0.756151	+	0.654397i	$0.772922\pi$
$152$	5.26026	−	1.40948i	0.426664	−	0.114324i
$153$	−2.70238	+	4.68066i	−0.218474	+	0.378409i
$154$	−0.0945530	−	0.0945530i	−0.00761930	−	0.00761930i
$155$	−12.3363	+	6.27024i	−0.990879	+	0.503638i
$156$	0.636722	−	0.636722i	0.0509786	−	0.0509786i
$157$	1.65798	+	0.444254i	0.132321	+	0.0354553i	0.324372	−	0.945930i	$-0.394847\pi$
$157$	1.65798	+	0.444254i	0.132321	+	0.0354553i	−0.192051	+	0.981385i	$0.561514\pi$
$158$	3.52938	+	3.52938i	0.280782	+	0.280782i
$159$	1.22911			0.0974750
$160$	1.49457	+	1.66321i	0.118156	+	0.131488i
$161$	0.00908192	+	0.0338942i	0.000715755	+	0.00267124i
$162$	7.83871			0.615868
$163$	−5.35241	+	3.09022i	−0.419233	+	0.242044i	−0.694749	−	0.719252i	$-0.744485\pi$
$163$	−5.35241	+	3.09022i	−0.419233	+	0.242044i	0.275516	+	0.961296i	$0.411151\pi$
$164$	−8.36534	+	4.82973i	−0.653223	+	0.377139i
$165$	0.148940	−	2.78887i	0.0115949	−	0.217113i
$166$	−13.5646	+	3.63463i	−1.05282	+	0.282102i
$167$	−13.9283	−	8.04153i	−1.07781	−	0.622273i	−0.147503	−	0.989062i	$-0.547124\pi$
$167$	−13.9283	−	8.04153i	−1.07781	−	0.622273i	−0.930304	+	0.366789i	$0.880457\pi$
$168$	0.0121401	−	0.00700907i	0.000936627	−	0.000540762i
$169$	3.40373	+	5.89544i	0.261826	+	0.453495i
$170$	3.13316	−	2.81548i	0.240303	−	0.215937i
$171$	−11.0481	+	11.0481i	−0.844872	+	0.844872i
$172$	−4.09601	+	7.09449i	−0.312318	+	0.540950i
$173$	−4.27166	−	1.14459i	−0.324768	−	0.0870214i	0.0927514	−	0.995689i	$-0.470434\pi$
$173$	−4.27166	−	1.14459i	−0.324768	−	0.0870214i	−0.417520	+	0.908668i	$0.637100\pi$
$174$			3.30173i			0.250304i
$175$	0.0697755	−	0.180696i	0.00527453	−	0.0136593i
$176$	2.98924	−	1.72584i	0.225323	−	0.130090i
$177$	−1.44332			−0.108486
$178$	0.666849	+	2.48871i	0.0499824	+	0.186537i
$179$	4.56704	−	4.56704i	0.341357	−	0.341357i	−0.515520	−	0.856877i	$-0.672401\pi$
$179$	4.56704	−	4.56704i	0.341357	−	0.341357i	0.856877	+	0.515520i	$0.172401\pi$
$180$	−6.09945	−	1.98854i	−0.454626	−	0.148217i
$181$	4.88795	−	8.46618i	0.363319	−	0.629286i	−0.625186	−	0.780476i	$-0.714977\pi$
$181$	4.88795	−	8.46618i	0.363319	−	0.629286i	0.988505	+	0.151189i	$0.0483103\pi$
$182$	−0.0249511	−	0.0931189i	−0.00184950	−	0.00690243i
$183$	−0.00435520	−	0.00754342i	−0.000321945	−	0.000557626i
$184$	−0.905777			−0.0667748
$185$	4.86326	−	12.7023i	0.357554	−	0.933892i
$186$	−2.23940			−0.164201
$187$	−3.25115	−	5.63115i	−0.237747	−	0.411790i
$188$	1.94420	+	7.25584i	0.141795	+	0.529186i
$189$	−0.0411367	+	0.0712508i	−0.00299225	+	0.00518274i
$190$	10.8555	−	5.51756i	0.787540	−	0.400286i
$191$	−6.50378	+	6.50378i	−0.470597	+	0.470597i	−0.902108	−	0.431511i	$-0.857981\pi$
$191$	−6.50378	+	6.50378i	−0.470597	+	0.470597i	0.431511	+	0.902108i	$0.357981\pi$
$192$	0.0936541	+	0.349522i	0.00675890	+	0.0252246i
$193$	−25.4877			−1.83465			−0.917324	−	0.398142i	$-0.869655\pi$
$193$	−25.4877			−1.83465			−0.917324	+	0.398142i	$0.869655\pi$
$194$	−2.21533	+	1.27902i	−0.159051	+	0.0918282i
$195$	1.09831	−	1.68757i	0.0786513	−	0.120849i
$196$			6.99850i			0.499893i
$197$	8.54797	+	2.29042i	0.609018	+	0.163186i	0.550130	−	0.835079i	$-0.314578\pi$
$197$	8.54797	+	2.29042i	0.609018	+	0.163186i	0.0588875	+	0.998265i	$0.481245\pi$
$198$	−4.95154	+	8.57632i	−0.351891	+	0.609493i
$199$	−11.2939	+	11.2939i	−0.800606	+	0.800606i	−0.983190	−	0.182585i	$-0.941554\pi$
$199$	−11.2939	+	11.2939i	−0.800606	+	0.800606i	0.182585	+	0.983190i	$0.441554\pi$
$200$	4.03923	+	2.94697i	0.285617	+	0.208382i
$201$	−2.78270	−	4.81978i	−0.196276	−	0.339961i
$202$	13.8896	−	8.01916i	0.977269	−	0.564226i
$203$	0.306127	+	0.176743i	0.0214859	+	0.0124049i
$204$	0.658431	−	0.176426i	0.0460994	−	0.0123523i
$205$	−16.0657	+	14.4367i	−1.12208	+	1.00830i
$206$	−3.71247	+	2.14340i	−0.258660	+	0.149337i
$207$	2.25057	−	1.29937i	0.156425	−	0.0903122i
$208$	2.48848			0.172545
$209$	−4.86508	−	18.1567i	−0.336525	−	1.25593i
$210$	0.0233151	−	0.0209511i	0.00160890	−	0.00144576i
$211$	5.60994			0.386204			0.193102	−	0.981179i	$-0.438145\pi$
$211$	5.60994			0.386204			0.193102	+	0.981179i	$0.438145\pi$
$212$	2.40185	+	2.40185i	0.164960	+	0.164960i
$213$	4.31516	+	1.15624i	0.295670	+	0.0792246i
$214$	−3.38058	+	3.38058i	−0.231092	+	0.231092i
$215$	−5.67787	+	17.4157i	−0.387227	+	1.18774i
$216$	−1.50170	−	1.50170i	−0.102178	−	0.102178i
$217$	−0.119876	+	0.207631i	−0.00813769	+	0.0140949i
$218$	−5.65787	+	1.51602i	−0.383200	+	0.102678i
$219$	2.92912	+	1.69113i	0.197932	+	0.114276i
$220$	5.74086	−	5.15877i	0.387049	−	0.347804i
$221$		−	4.68781i		−	0.315336i
$222$	1.63295	−	1.47585i	0.109597	−	0.0990523i
$223$	3.95959	+	3.95959i	0.265154	+	0.265154i	0.827144	−	0.561990i	$-0.189964\pi$
$223$	3.95959	+	3.95959i	0.265154	+	0.265154i	−0.561990	+	0.827144i	$0.689964\pi$
$224$	0.0374200	+	0.0100267i	0.00250023	+	0.000669934i
$225$	−14.2637	−	1.52787i	−0.950915	−	0.101858i
$226$	6.40021	+	3.69516i	0.425736	+	0.245799i
$227$	6.73621	+	3.88915i	0.447098	+	0.258132i	0.706604	−	0.707610i	$-0.250226\pi$
$227$	6.73621	+	3.88915i	0.447098	+	0.258132i	−0.259506	+	0.965742i	$0.583560\pi$
$228$	1.97058			0.130505
$229$	1.63172	+	0.942077i	0.107827	+	0.0622542i	0.552944	−	0.833219i	$-0.313504\pi$
$229$	1.63172	+	0.942077i	0.107827	+	0.0622542i	−0.445116	+	0.895473i	$0.646838\pi$
$230$	−1.98154	+	0.419130i	−0.130659	+	0.0276366i
$231$	−0.0241931	−	0.0419036i	−0.00159179	−	0.00275706i
$232$	−6.45203	+	6.45203i	−0.423596	+	0.423596i
$233$	6.70483	−	6.70483i	0.439248	−	0.439248i	−0.452511	−	0.891759i	$-0.649472\pi$
$233$	6.70483	−	6.70483i	0.439248	−	0.439248i	0.891759	+	0.452511i	$0.149472\pi$
$234$	−6.18308	+	3.56980i	−0.404201	+	0.233365i
$235$	7.61074	+	14.9737i	0.496470	+	0.976777i
$236$	−2.82044	−	2.82044i	−0.183595	−	0.183595i
$237$	0.903054	+	1.56413i	0.0586596	+	0.101601i
$238$	0.0188883	−	0.0704920i	0.00122434	−	0.00456932i
$239$	−1.59987	+	5.97079i	−0.103487	+	0.386218i	−0.998169	−	0.0604848i	$-0.980735\pi$
$239$	−1.59987	+	5.97079i	−0.103487	+	0.386218i	0.894682	+	0.446703i	$0.147402\pi$
$240$	0.366618	+	0.721301i	0.0236651	+	0.0465598i
$241$	2.30366	+	8.59737i	0.148392	+	0.553805i	0.999581	+	0.0289464i	$0.00921521\pi$
$241$	2.30366	+	8.59737i	0.148392	+	0.553805i	−0.851189	+	0.524859i	$0.824118\pi$
$242$	−0.457041	−	0.791618i	−0.0293797	−	0.0508871i
$243$	8.89390	+	2.38311i	0.570544	+	0.152877i
$244$	0.00623022	−	0.0232515i	0.000398849	−	0.00148852i
$245$	3.23841	+	15.3104i	0.206894	+	0.978144i
$246$	−3.37619	+	0.904649i	−0.215258	+	0.0576783i
$247$	3.50747	−	13.0901i	0.223175	−	0.832901i
$248$	−4.37609	−	4.37609i	−0.277882	−	0.277882i
$249$	−5.08153			−0.322029
$250$	10.2001	+	4.57791i	0.645113	+	0.289532i
$251$	−8.72161	−	8.72161i	−0.550503	−	0.550503i	0.376083	−	0.926586i	$-0.377271\pi$
$251$	−8.72161	−	8.72161i	−0.550503	−	0.550503i	−0.926586	+	0.376083i	$0.877271\pi$
$252$	−0.107360	+	0.0287671i	−0.00676306	+	0.00181216i
$253$			3.12645i			0.196558i
$254$	−4.18775	−	15.6289i	−0.262763	−	0.980645i
$255$	1.35879	−	0.690637i	0.0850907	−	0.0432494i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	25.9078	−	14.9579i	1.61608	−	0.933045i	0.628161	−	0.778083i	$-0.283808\pi$
$257$	25.9078	−	14.9579i	1.61608	−	0.933045i	0.987920	−	0.154962i	$-0.0495256\pi$
$258$	−2.09607	+	2.09607i	−0.130496	+	0.130496i
$259$	−0.0494237	−	0.230405i	−0.00307104	−	0.0143167i
$260$	5.44396	−	1.15149i	0.337620	−	0.0714126i
$261$	6.77560	−	25.2869i	0.419399	−	1.56522i
$262$	−8.14980	+	2.18373i	−0.503496	+	0.134911i
$263$	5.33763	+	19.9203i	0.329132	+	1.22834i	0.910092	+	0.414406i	$0.136011\pi$
$263$	5.33763	+	19.9203i	0.329132	+	1.22834i	−0.580960	+	0.813932i	$0.697323\pi$
$264$	1.20644	−	0.323264i	0.0742511	−	0.0198955i
$265$	6.36585	+	4.14304i	0.391051	+	0.254505i
$266$	0.105486	−	0.182707i	0.00646775	−	0.0112025i
$267$			0.932313i			0.0570566i
$268$	3.98072	−	14.8563i	0.243161	−	0.907490i
$269$			9.11261i			0.555606i	0.960638	+	0.277803i	$0.0896062\pi$
$269$			9.11261i			0.555606i	−0.960638	+	0.277803i	$0.910394\pi$
$270$	−3.98011	−	2.59034i	−0.242222	−	0.157643i
$271$	6.57499	+	11.3882i	0.399403	+	0.691785i	0.993652	−	0.112495i	$-0.0358843\pi$
$271$	6.57499	+	11.3882i	0.399403	+	0.691785i	−0.594250	+	0.804281i	$0.702551\pi$
$272$	1.63142	+	0.941903i	0.0989196	+	0.0571112i
$273$		−	0.0348839i		−	0.00211127i
$274$	−7.54713	−	2.02225i	−0.455939	−	0.122168i
$275$	10.1720	−	13.9421i	0.613393	−	0.840742i
$276$	−0.316589	−	0.0848298i	−0.0190564	−	0.00510615i
$277$	−8.30013	+	14.3762i	−0.498707	+	0.863785i	−0.999999	−	0.00149292i	$-0.999525\pi$
$277$	−8.30013	+	14.3762i	−0.498707	+	0.863785i	0.501292	+	0.865278i	$0.332858\pi$
$278$	4.60322	−	7.97300i	0.276083	−	0.478189i
$279$	17.1508	+	4.59555i	1.02679	+	0.275128i
$280$	0.0865021	+	0.00461965i	0.00516949	+	0.000276077i
$281$	−28.5145	−	7.64045i	−1.70103	−	0.455791i	−0.727835	−	0.685753i	$-0.759473\pi$
$281$	−28.5145	−	7.64045i	−1.70103	−	0.455791i	−0.973200	+	0.229962i	$0.926140\pi$
$282$			2.71816i			0.161864i
$283$	−12.9321	−	7.46633i	−0.768731	−	0.443827i	0.0636908	−	0.997970i	$-0.479713\pi$
$283$	−12.9321	−	7.46633i	−0.768731	−	0.443827i	−0.832422	+	0.554143i	$0.813046\pi$
$284$	6.17295	+	10.6919i	0.366297	+	0.634446i
$285$	4.31098	−	0.911846i	0.255360	−	0.0540131i
$286$		−	8.58943i		−	0.507904i
$287$	−0.0968521	+	0.361457i	−0.00571700	+	0.0213361i
$288$		−	2.86906i		−	0.169061i
$289$	−6.72564	+	11.6491i	−0.395626	+	0.685244i
$290$	−11.1293	+	17.1004i	−0.653537	+	1.00417i
$291$	−0.894090	+	0.239571i	−0.0524125	+	0.0140439i
$292$	2.41920	+	9.02859i	0.141573	+	0.528358i
$293$	−0.791535	+	0.212091i	−0.0462420	+	0.0123905i	−0.281866	−	0.959454i	$-0.590953\pi$
$293$	−0.791535	+	0.212091i	−0.0462420	+	0.0123905i	0.235624	+	0.971844i	$0.424287\pi$
$294$	−0.655438	+	2.44613i	−0.0382259	+	0.142661i
$295$	−7.47527	−	4.86507i	−0.435227	−	0.283256i
$296$	6.07501	+	0.307010i	0.353103	+	0.0178446i
$297$	−5.18340	+	5.18340i	−0.300771	+	0.300771i
$298$	13.3244	−	7.69284i	0.771861	−	0.445634i
$299$	−1.12700	+	1.95203i	−0.0651764	+	0.112889i
$300$	1.13580	+	1.40832i	0.0655757	+	0.0813094i
$301$	0.0821385	+	0.306545i	0.00473439	+	0.0176690i
$302$		−	8.05240i		−	0.463363i
$303$	5.60575	−	1.50206i	0.322042	−	0.0862908i
$304$	3.85078	+	3.85078i	0.220857	+	0.220857i
$305$	0.00287049	−	0.0537494i	0.000164364	−	0.00307768i
$306$	−5.40476			−0.308969
$307$	−4.35290	−	4.35290i	−0.248433	−	0.248433i	0.571894	−	0.820327i	$-0.306209\pi$
$307$	−4.35290	−	4.35290i	−0.248433	−	0.248433i	−0.820327	+	0.571894i	$0.806209\pi$
$308$	0.0346088	−	0.129162i	0.00197202	−	0.00735967i
$309$	−1.49833	+	0.401476i	−0.0852369	+	0.0228392i
$310$	−11.5984	−	7.54847i	−0.658743	−	0.428724i
$311$	4.57100	−	17.0592i	0.259198	−	0.967339i	−0.706509	−	0.707704i	$-0.749731\pi$
$311$	4.57100	−	17.0592i	0.259198	−	0.967339i	0.965707	−	0.259635i	$-0.0836022\pi$
$312$	0.869779	+	0.233056i	0.0492415	+	0.0131942i
$313$	−4.75598	−	8.23759i	−0.268824	−	0.465616i	0.699735	−	0.714403i	$-0.253302\pi$
$313$	−4.75598	−	8.23759i	−0.268824	−	0.465616i	−0.968558	+	0.248787i	$0.919968\pi$
$314$	0.444254	+	1.65798i	0.0250707	+	0.0935651i
$315$	−0.221557	+	0.112612i	−0.0124833	+	0.00634494i
$316$	−1.29184	+	4.82122i	−0.0726717	+	0.271215i
$317$	7.97887	−	29.7776i	0.448138	−	1.67247i	−0.259377	−	0.965776i	$-0.583517\pi$
$317$	7.97887	−	29.7776i	0.448138	−	1.67247i	0.707515	−	0.706698i	$-0.249816\pi$
$318$	0.614556	+	1.06444i	0.0344626	+	0.0596910i
$319$	22.2703	+	22.2703i	1.24690	+	1.24690i
$320$	−0.693098	+	2.12594i	−0.0387453	+	0.118844i
$321$	−1.49819	+	0.864981i	−0.0836209	+	0.0482785i
$322$	−0.0248123	+	0.0248123i	−0.00138273	+	0.00138273i
$323$	7.25412	−	7.25412i	0.403630	−	0.403630i
$324$	3.91936	+	6.78853i	0.217742	+	0.377140i
$325$	11.3767	−	5.03816i	0.631068	−	0.279467i
$326$	−5.35241	−	3.09022i	−0.296443	−	0.171151i
$327$	−2.11953			−0.117210
$328$	−8.36534	−	4.82973i	−0.461899	−	0.266677i
$329$	0.252020	+	0.145504i	0.0138943	+	0.00802187i
$330$	2.48970	−	1.26545i	0.137053	−	0.0696606i
$331$	30.5927	+	8.19729i	1.68153	+	0.450564i	0.968181	−	0.250249i	$-0.0805126\pi$
$331$	30.5927	+	8.19729i	1.68153	+	0.450564i	0.713345	+	0.700813i	$0.247179\pi$
$332$	−9.92998	−	9.92998i	−0.544979	−	0.544979i
$333$	−15.5349	+	7.95197i	−0.851306	+	0.435765i
$334$		−	16.0831i		−	0.880026i
$335$	1.83406	−	34.3425i	0.100206	−	1.87633i
$336$	0.0121401	+	0.00700907i	0.000662295	+	0.000382376i
$337$	16.7495	−	4.48800i	0.912401	−	0.244477i	0.228067	−	0.973646i	$-0.426760\pi$
$337$	16.7495	−	4.48800i	0.912401	−	0.244477i	0.684334	+	0.729168i	$0.260093\pi$
$338$	−3.40373	+	5.89544i	−0.185139	+	0.320669i
$339$	1.89095	+	1.89095i	0.102702	+	0.102702i
$340$	4.00486	+	1.30566i	0.217194	+	0.0708094i
$341$	−15.1048	+	15.1048i	−0.817973	+	0.817973i
$342$	−15.0920	−	4.04390i	−0.816084	−	0.218669i
$343$	0.383466	+	0.383466i	0.0207052	+	0.0207052i
$344$	−8.19202			−0.441684
$345$	−0.731844	−	0.0390842i	−0.0394012	−	0.00210422i
$346$	−1.14459	−	4.27166i	−0.0615334	−	0.229646i
$347$	18.6679			1.00215			0.501074	−	0.865405i	$-0.332939\pi$
$347$	18.6679			1.00215			0.501074	+	0.865405i	$0.332939\pi$
$348$	−2.85938	+	1.65087i	−0.153279	+	0.0884957i
$349$	−8.51145	+	4.91409i	−0.455608	+	0.263045i	−0.710196	−	0.704004i	$-0.751393\pi$
$349$	−8.51145	+	4.91409i	−0.455608	+	0.263045i	0.254588	+	0.967050i	$0.418060\pi$
$350$	0.191375	−	0.0299208i	0.0102294	−	0.00159933i
$351$	−5.10479	+	1.36782i	−0.272473	+	0.0730090i
$352$	2.98924	+	1.72584i	0.159327	+	0.0919875i
$353$	3.81914	−	2.20498i	0.203272	−	0.117359i	−0.394909	−	0.918720i	$-0.629224\pi$
$353$	3.81914	−	2.20498i	0.203272	−	0.117359i	0.598181	+	0.801361i	$0.295890\pi$
$354$	−0.721659	−	1.24995i	−0.0383557	−	0.0664341i
$355$	18.4518	+	20.5338i	0.979320	+	1.08982i
$356$	−1.82186	+	1.82186i	−0.0965586	+	0.0965586i
$357$	0.0132037	−	0.0228695i	0.000698815	−	0.00121038i
$358$	6.23870	+	1.67165i	0.329725	+	0.0883496i
$359$		−	15.6181i		−	0.824291i	−0.911118	−	0.412145i	$-0.864780\pi$
$359$		−	15.6181i		−	0.824291i	0.911118	−	0.412145i	$-0.135220\pi$
$360$	−1.32760	−	6.27655i	−0.0699706	−	0.330803i
$361$	9.22926	−	5.32852i	0.485751	−	0.280448i
$362$	9.77591			0.513810
$363$	−0.0856075	−	0.319492i	−0.00449323	−	0.0167690i
$364$	0.0681678	−	0.0681678i	0.00357296	−	0.00357296i
$365$	9.47020	+	18.6321i	0.495693	+	0.975249i
$366$	0.00435520	−	0.00754342i	0.000227650	−	0.000394301i
$367$	−6.32485	−	23.6047i	−0.330155	−	1.23215i	−0.909028	−	0.416736i	$-0.863174\pi$
$367$	−6.32485	−	23.6047i	−0.330155	−	1.23215i	0.578873	−	0.815418i	$-0.303493\pi$
$368$	−0.452889	−	0.784426i	−0.0236085	−	0.0408910i
$369$	27.7136			1.44271
$370$	13.4322	−	2.13945i	0.698304	−	0.111225i
$371$	0.131589			0.00683178
$372$	−1.11970	−	1.93938i	−0.0580537	−	0.100552i
$373$	−4.98465	−	18.6030i	−0.258096	−	0.963226i	−0.966342	−	0.257261i	$-0.917180\pi$
$373$	−4.98465	−	18.6030i	−0.258096	−	0.963226i	0.708246	−	0.705965i	$-0.249487\pi$
$374$	3.25115	−	5.63115i	0.168113	−	0.291180i
$375$	3.13643	+	2.55536i	0.161965	+	0.131958i
$376$	−5.31164	+	5.31164i	−0.273927	+	0.273927i
$377$	5.87681	+	21.9326i	0.302671	+	1.12958i
$378$	−0.0822734			−0.00423169
$379$	13.8986	−	8.02439i	0.713925	−	0.412185i	−0.0985873	−	0.995128i	$-0.531432\pi$
$379$	13.8986	−	8.02439i	0.713925	−	0.412185i	0.812513	+	0.582943i	$0.198099\pi$
$380$	10.2061	+	6.64235i	0.523561	+	0.340746i
$381$		−	5.85485i		−	0.299953i
$382$	−8.88432	−	2.38055i	−0.454562	−	0.121799i
$383$	1.35736	−	2.35102i	0.0693579	−	0.120131i	−0.829261	−	0.558862i	$-0.811238\pi$
$383$	1.35736	−	2.35102i	0.0693579	−	0.120131i	0.898619	+	0.438730i	$0.144572\pi$
$384$	−0.255868	+	0.255868i	−0.0130572	+	0.0130572i
$385$	0.0159455	−	0.298577i	0.000812660	−	0.0152169i
$386$	−12.7439	−	22.0730i	−0.648646	−	1.12349i
$387$	20.3546	−	11.7517i	1.03468	−	0.597373i
$388$	−2.21533	−	1.27902i	−0.112466	−	0.0649324i
$389$	11.6111	−	3.11119i	0.588708	−	0.157744i	0.0478451	−	0.998855i	$-0.484765\pi$
$389$	11.6111	−	3.11119i	0.588708	−	0.157744i	0.540862	+	0.841111i	$0.318098\pi$
$390$	2.01063	+	0.107378i	0.101812	+	0.00543728i
$391$	−1.47771	+	0.853154i	−0.0747308	+	0.0431459i
$392$	−6.06088	+	3.49925i	−0.306121	+	0.176739i
$393$	−3.05305			−0.154006
$394$	2.29042	+	8.54797i	0.115390	+	0.430641i
$395$	−0.595198	+	11.1450i	−0.0299477	+	0.560765i
$396$	−9.90308			−0.497649
$397$	−19.3447	−	19.3447i	−0.970884	−	0.970884i	0.0287044	−	0.999588i	$-0.490862\pi$
$397$	−19.3447	−	19.3447i	−0.970884	−	0.970884i	−0.999588	+	0.0287044i	$0.990862\pi$
$398$	−15.4278	−	4.13387i	−0.773326	−	0.207212i
$399$	0.0539808	−	0.0539808i	0.00270242	−	0.00270242i
$400$	−0.532532	+	4.97156i	−0.0266266	+	0.248578i
$401$	7.48958	+	7.48958i	0.374012	+	0.374012i	0.868936	−	0.494924i	$-0.164804\pi$
$401$	7.48958	+	7.48958i	0.374012	+	0.374012i	−0.494924	+	0.868936i	$0.664804\pi$
$402$	2.78270	−	4.81978i	0.138788	−	0.240389i
$403$	−14.8758	+	3.98595i	−0.741014	+	0.198554i
$404$	13.8896	+	8.01916i	0.691033	+	0.398968i
$405$	11.7155	+	13.0374i	0.582148	+	0.647835i
$406$			0.353485i			0.0175432i
$407$	1.05970	−	20.9690i	0.0525274	−	1.03939i
$408$	0.482005	+	0.482005i	0.0238628	+	0.0238628i
$409$	−25.2943	−	6.77759i	−1.25072	−	0.335130i	−0.428107	−	0.903728i	$-0.640819\pi$
$409$	−25.2943	−	6.77759i	−1.25072	−	0.335130i	−0.822616	+	0.568598i	$0.807486\pi$
$410$	−20.5354	−	6.69495i	−1.01417	−	0.330640i
$411$	−2.44850	−	1.41364i	−0.120775	−	0.0697297i
$412$	−3.71247	−	2.14340i	−0.182900	−	0.105598i
$413$	−0.154522			−0.00760355
$414$	2.25057	+	1.29937i	0.110609	+	0.0638604i
$415$	−26.3184	−	17.1286i	−1.29192	−	0.840809i
$416$	1.24424	+	2.15509i	0.0610039	+	0.105662i
$417$	2.35563	−	2.35563i	0.115356	−	0.115356i
$418$	13.2917	−	13.2917i	0.650116	−	0.650116i
$419$	6.62659	−	3.82586i	0.323730	−	0.186906i	−0.329324	−	0.944217i	$-0.606821\pi$
$419$	6.62659	−	3.82586i	0.323730	−	0.186906i	0.653054	+	0.757311i	$0.273487\pi$
$420$	0.0298017	+	0.00971594i	0.00145418	+	0.000474089i
$421$	1.38114	+	1.38114i	0.0673126	+	0.0673126i	0.739962	−	0.672649i	$-0.234844\pi$
$421$	1.38114	+	1.38114i	0.0673126	+	0.0673126i	−0.672649	+	0.739962i	$0.734844\pi$
$422$	2.80497	+	4.85835i	0.136544	+	0.236501i
$423$	5.57802	−	20.8175i	0.271213	−	1.01218i
$424$	−0.879138	+	3.28099i	−0.0426947	+	0.159339i
$425$	9.36545	+	1.00319i	0.454291	+	0.0486617i
$426$	1.15624	+	4.31516i	0.0560203	+	0.209070i
$427$	−0.000466269	0	0.000807602i	−2.25644e−5	0	3.90826e-5i
$428$	−4.61796	−	1.23738i	−0.223217	−	0.0598109i
$429$	0.804436	−	3.00220i	0.0388385	−	0.144947i
$430$	−17.9214	+	3.79069i	−0.864246	+	0.182803i
$431$	−37.4554	+	10.0361i	−1.80416	+	0.483424i	−0.994616	−	0.103630i	$-0.966954\pi$
$431$	−37.4554	+	10.0361i	−1.80416	+	0.483424i	−0.809547	+	0.587055i	$0.800287\pi$
$432$	0.549662	−	2.05137i	0.0264456	−	0.0986964i
$433$	−3.72069	−	3.72069i	−0.178805	−	0.178805i	0.612030	−	0.790835i	$-0.290353\pi$
$433$	−3.72069	−	3.72069i	−0.178805	−	0.178805i	−0.790835	+	0.612030i	$0.790353\pi$
$434$	−0.239751			−0.0115084
$435$	−5.49147	+	4.93467i	−0.263296	+	0.236599i
$436$	−4.14185	−	4.14185i	−0.198359	−	0.198359i
$437$	−4.76463	+	1.27668i	−0.227923	+	0.0610718i
$438$			3.38226i			0.161611i
$439$	4.30777	+	16.0768i	0.205599	+	0.767305i	0.989266	+	0.146124i	$0.0466799\pi$
$439$	4.30777	+	16.0768i	0.205599	+	0.767305i	−0.783668	+	0.621180i	$0.786653\pi$
$440$	7.33806	+	2.39235i	0.349828	+	0.114051i
$441$	10.0396	−	17.3890i	0.478075	−	0.828050i
$442$	4.05977	−	2.34391i	0.193103	−	0.111488i
$443$	10.2017	−	10.2017i	0.484695	−	0.484695i	−0.421932	−	0.906627i	$-0.638648\pi$
$443$	10.2017	−	10.2017i	0.484695	−	0.484695i	0.906627	+	0.421932i	$0.138648\pi$
$444$	2.09460	+	0.676256i	0.0994052	+	0.0320937i
$445$	−3.14260	+	4.82866i	−0.148974	+	0.228901i
$446$	−1.44931	+	5.40891i	−0.0686269	+	0.256119i
$447$	5.37763	−	1.44093i	0.254353	−	0.0681538i
$448$	0.0100267	+	0.0374200i	0.000473715	+	0.00176793i
$449$	−28.9067	+	7.74552i	−1.36419	+	0.365534i	−0.865353	−	0.501162i	$-0.832906\pi$
$449$	−28.9067	+	7.74552i	−1.36419	+	0.365534i	−0.498837	+	0.866696i	$0.666239\pi$
$450$	−5.80869	−	13.1167i	−0.273824	−	0.618326i
$451$	−16.6707	+	28.8745i	−0.784992	+	1.35965i
$452$			7.39033i			0.347612i
$453$	0.754140	−	2.81449i	0.0354326	−	0.132236i
$454$			7.77830i			0.365054i
$455$	0.117585	−	0.180672i	0.00551247	−	0.00847001i
$456$	0.985291	+	1.70657i	0.0461405	+	0.0799177i
$457$	18.7594	+	10.8307i	0.877525	+	0.506640i	0.869842	−	0.493331i	$-0.164221\pi$
$457$	18.7594	+	10.8307i	0.877525	+	0.506640i	0.00768374	+	0.999970i	$0.497554\pi$
$458$			1.88415i			0.0880407i
$459$	−3.86438	−	1.03546i	−0.180374	−	0.0483310i
$460$	−1.35375	−	1.50650i	−0.0631187	−	0.0702408i
$461$	33.2879	+	8.91947i	1.55037	+	0.415421i	0.929600	−	0.368570i	$-0.120152\pi$
$461$	33.2879	+	8.91947i	1.55037	+	0.415421i	0.620773	+	0.783991i	$0.286819\pi$
$462$	0.0241931	−	0.0419036i	0.00112556	−	0.00194953i
$463$	20.9835	−	36.3444i	0.975184	−	1.68907i	0.295858	−	0.955232i	$-0.404394\pi$
$463$	20.9835	−	36.3444i	0.975184	−	1.68907i	0.679326	−	0.733837i	$-0.262272\pi$
$464$	−8.81363	−	2.36161i	−0.409163	−	0.109635i
$465$	−3.34694	−	3.72459i	−0.155210	−	0.172724i
$466$	9.15897	+	2.45414i	0.424281	+	0.113686i
$467$			34.0379i			1.57509i	0.616259	+	0.787544i	$0.288647\pi$
$467$			34.0379i			1.57509i	−0.616259	+	0.787544i	$0.711353\pi$
$468$	−6.18308	−	3.56980i	−0.285813	−	0.165014i
$469$	−0.297917	−	0.516008i	−0.0137565	−	0.0238270i
$470$	−9.16224	+	14.0779i	−0.422623	+	0.649367i
$471$			0.621106i			0.0286190i
$472$	1.03235	−	3.85279i	0.0475178	−	0.177339i
$473$			28.2762i			1.30014i
$474$	−0.903054	+	1.56413i	−0.0414786	+	0.0718431i
$475$	25.4011	+	9.80859i	1.16548	+	0.450049i
$476$	0.0704920	−	0.0188883i	0.00323099	−	0.000865742i
$477$	−2.52230	−	9.41336i	−0.115488	−	0.431008i
$478$	−5.97079	+	1.59987i	−0.273098	+	0.0731763i
$479$	−1.43918	+	5.37111i	−0.0657580	+	0.245412i	−0.990979	−	0.134016i	$-0.957213\pi$
$479$	−1.43918	+	5.37111i	−0.0657580	+	0.245412i	0.925221	+	0.379428i	$0.123879\pi$
$480$	−0.441356	+	0.678151i	−0.0201450	+	0.0309532i
$481$	8.22041	−	12.7102i	0.374818	−	0.579534i
$482$	−6.29371	+	6.29371i	−0.286671	+	0.286671i
$483$	−0.0109962	+	0.00634866i	−0.000500344	+	0.000288874i
$484$	0.457041	−	0.791618i	0.0207746	−	0.0359826i
$485$	−5.43823	−	1.77297i	−0.246937	−	0.0805064i
$486$	2.38311	+	8.89390i	0.108100	+	0.403436i
$487$		−	22.8368i		−	1.03484i	−0.855733	−	0.517418i	$-0.826893\pi$
$487$		−	22.8368i		−	1.03484i	0.855733	−	0.517418i	$-0.173107\pi$
$488$	0.0232515	−	0.00623022i	0.00105255	−	0.000282029i
$489$	−1.58137	−	1.58137i	−0.0715122	−	0.0715122i
$490$	−11.6400	+	10.4597i	−0.525840	+	0.472523i
$491$	−30.9246			−1.39561			−0.697804	−	0.716288i	$-0.745839\pi$
$491$	−30.9246			−1.39561			−0.697804	+	0.716288i	$0.745839\pi$
$492$	−2.47155	−	2.47155i	−0.111426	−	0.111426i
$493$	−4.44881	+	16.6032i	−0.200364	+	0.747769i
$494$	13.0901	−	3.50747i	0.588950	−	0.157809i
$495$	−21.6646	+	4.58245i	−0.973753	+	0.205966i
$496$	1.60176	−	5.97785i	0.0719211	−	0.268413i
$497$	0.461984	+	0.123788i	0.0207228	+	0.00555266i
$498$	−2.54076	−	4.40073i	−0.113854	−	0.197201i
$499$	−7.78532	−	29.0552i	−0.348519	−	1.30069i	−0.888447	−	0.458979i	$-0.848215\pi$
$499$	−7.78532	−	29.0552i	−0.348519	−	1.30069i	0.539928	−	0.841711i	$-0.318451\pi$
$500$	1.13548	+	11.1225i	0.0507804	+	0.497415i
$501$	1.50625	−	5.62138i	0.0672941	−	0.251145i
$502$	3.19233	−	11.9139i	0.142481	−	0.531745i
$503$	−10.2683	−	17.7851i	−0.457839	−	0.793000i	0.541007	−	0.841018i	$-0.318043\pi$
$503$	−10.2683	−	17.7851i	−0.457839	−	0.793000i	−0.998847	+	0.0480173i	$0.984710\pi$
$504$	−0.0785932	−	0.0785932i	−0.00350082	−	0.00350082i
$505$	34.0965	+	11.1161i	1.51727	+	0.494661i
$506$	−2.70759	+	1.56323i	−0.120367	+	0.0694939i
$507$	−1.74181	+	1.74181i	−0.0773565	+	0.0773565i
$508$	11.4412	−	11.4412i	0.507619	−	0.507619i
$509$	3.81799	+	6.61296i	0.169230	+	0.293114i	0.938149	−	0.346231i	$-0.112539\pi$
$509$	3.81799	+	6.61296i	0.169230	+	0.293114i	−0.768920	+	0.639345i	$0.779205\pi$
$510$	1.27750	+	0.831428i	0.0565688	+	0.0368163i
$511$	0.313593	+	0.181053i	0.0138725	+	0.00800932i
$512$	−1.00000			−0.0441942
$513$	−10.0160	−	5.78274i	−0.442217	−	0.255314i
$514$	25.9078	+	14.9579i	1.14274	+	0.659763i
$515$	−9.11346	−	2.97117i	−0.401587	−	0.130925i
$516$	−2.86329	−	0.767216i	−0.126049	−	0.0337748i
$517$	18.3341	+	18.3341i	0.806332	+	0.806332i
$518$	0.174825	−	0.158005i	0.00768136	−	0.00694233i
$519$		−	1.60023i		−	0.0702424i
$520$	3.71920	+	4.13886i	0.163098	+	0.181501i
$521$	19.9246	+	11.5035i	0.872915	+	0.503977i	0.868316	−	0.496012i	$-0.165203\pi$
$521$	19.9246	+	11.5035i	0.872915	+	0.503977i	0.00459887	+	0.999989i	$0.498536\pi$
$522$	25.2869	−	6.77560i	1.10678	−	0.296560i
$523$	−4.20802	+	7.28850i	−0.184004	+	0.318704i	−0.943240	−	0.332111i	$-0.892239\pi$
$523$	−4.20802	+	7.28850i	−0.184004	+	0.318704i	0.759237	+	0.650815i	$0.225573\pi$
$524$	−5.96607	−	5.96607i	−0.260629	−	0.260629i
$525$	0.0696921	+	0.00746511i	0.00304161	+	0.000325804i
$526$	−14.5827	+	14.5827i	−0.635835	+	0.635835i
$527$	−11.2611	−	3.01740i	−0.490541	−	0.131440i
$528$	0.883173	+	0.883173i	0.0384352	+	0.0384352i
$529$	−22.1796			−0.964329
$530$	−0.405051	+	7.58451i	−0.0175943	+	0.329450i
$531$	2.96188	+	11.0539i	0.128535	+	0.479698i
$532$	0.210971			0.00914677
$533$	−20.8170	+	12.0187i	−0.901684	+	0.520587i
$534$	−0.807407	+	0.466157i	−0.0349399	+	0.0201726i
$535$	−10.6751	−	0.570105i	−0.461525	−	0.0246478i
$536$	14.8563	−	3.98072i	0.641693	−	0.171941i
$537$	2.02400	+	1.16856i	0.0873422	+	0.0504271i
$538$	−7.89176	+	4.55631i	−0.340238	+	0.196436i
$539$	12.0783	+	20.9202i	0.520248	+	0.901097i
$540$	0.253249	−	4.74205i	0.0108981	−	0.204065i
$541$	−26.2274	+	26.2274i	−1.12760	+	1.12760i	−0.137037	+	0.990566i	$0.543758\pi$
$541$	−26.2274	+	26.2274i	−1.12760	+	1.12760i	−0.990566	+	0.137037i	$0.956242\pi$
$542$	−6.57499	+	11.3882i	−0.282420	+	0.489166i
$543$	3.41689	+	0.915554i	0.146633	+	0.0392902i
$544$			1.88381i			0.0807675i
$545$	−10.9775	−	7.14443i	−0.470226	−	0.306034i
$546$	0.0302103	−	0.0174419i	0.00129288	−	0.000746446i
$547$	29.1061			1.24449			0.622244	−	0.782823i	$-0.286221\pi$
$547$	29.1061			1.24449			0.622244	+	0.782823i	$0.286221\pi$
$548$	−2.02225	−	7.54713i	−0.0863862	−	0.322398i
$549$	−0.0488351	+	0.0488351i	−0.00208423	+	0.00208423i
$550$	17.1602	+	1.83813i	0.731714	+	0.0783781i
$551$	−24.8453	+	43.0334i	−1.05845	+	1.83328i
$552$	−0.0848298	−	0.316589i	−0.00361059	−	0.0134749i
$553$	0.0966813	+	0.167457i	0.00411131	+	0.00712100i
$554$	−16.6003			−0.705278
$555$	4.89520	+	0.510192i	0.207790	+	0.0216564i
$556$	9.20643			0.390440
$557$	3.77101	+	6.53158i	0.159783	+	0.276752i	0.934790	−	0.355200i	$-0.115587\pi$
$557$	3.77101	+	6.53158i	0.159783	+	0.276752i	−0.775007	+	0.631952i	$0.782254\pi$
$558$	4.59555	+	17.1508i	0.194545	+	0.726052i
$559$	−10.1928	+	17.6545i	−0.431111	+	0.746706i
$560$	0.0392503	+	0.0772228i	0.00165863	+	0.00326326i
$561$	1.66373	−	1.66373i	0.0702426	−	0.0702426i
$562$	−7.64045	−	28.5145i	−0.322293	−	1.20281i
$563$	24.0624			1.01411			0.507054	−	0.861914i	$-0.330734\pi$
$563$	24.0624			1.01411			0.507054	+	0.861914i	$0.330734\pi$
$564$	−2.35399	+	1.35908i	−0.0991210	+	0.0572275i
$565$	3.41972	+	16.1676i	0.143869	+	0.680175i
$566$		−	14.9327i		−	0.627666i
$567$	0.293325	+	0.0785961i	0.0123185	+	0.00330073i
$568$	−6.17295	+	10.6919i	−0.259011	+	0.448621i
$569$	−12.1736	+	12.1736i	−0.510346	+	0.510346i	−0.914632	−	0.404286i	$-0.867520\pi$
$569$	−12.1736	+	12.1736i	−0.510346	+	0.510346i	0.404286	+	0.914632i	$0.367520\pi$
$570$	2.94517	+	3.27749i	0.123360	+	0.137279i
$571$	−11.8671	−	20.5543i	−0.496621	−	0.860172i	0.503372	−	0.864070i	$-0.332093\pi$
$571$	−11.8671	−	20.5543i	−0.496621	−	0.860172i	−0.999992	+	0.00389768i	$0.998759\pi$
$572$	7.43867	−	4.29472i	0.311026	−	0.179571i
$573$	−2.88232	−	1.66411i	−0.120411	−	0.0695191i
$574$	−0.361457	+	0.0968521i	−0.0150869	+	0.00404253i
$575$	−3.65864	−	2.66929i	−0.152576	−	0.111317i
$576$	2.48468	−	1.43453i	0.103528	−	0.0597722i
$577$	−38.2570	+	22.0877i	−1.59266	+	0.919523i	−0.599812	+	0.800141i	$0.704758\pi$
$577$	−38.2570	+	22.0877i	−1.59266	+	0.919523i	−0.992848	+	0.119382i	$0.961909\pi$
$578$	−13.4513			−0.559499
$579$	−2.38703	−	8.90852i	−0.0992017	−	0.370226i
$580$	−20.3741	−	1.08808i	−0.845987	−	0.0451800i
$581$	−0.544031			−0.0225702
$582$	−0.654520	−	0.654520i	−0.0271307	−	0.0271307i
$583$	11.3249	+	3.03450i	0.469030	+	0.125676i
$584$	−6.60939	+	6.60939i	−0.273498	+	0.273498i
$585$	−15.1784	−	4.94845i	−0.627548	−	0.204593i
$586$	−0.579444	−	0.579444i	−0.0239366	−	0.0239366i
$587$	−3.18681	+	5.51972i	−0.131534	+	0.227823i	−0.924268	−	0.381744i	$-0.875324\pi$
$587$	−3.18681	+	5.51972i	−0.131534	+	0.227823i	0.792734	+	0.609568i	$0.208657\pi$
$588$	−2.44613	+	0.655438i	−0.100877	+	0.0270298i
$589$	−29.1874	−	16.8514i	−1.20265	−	0.694348i
$590$	0.475642	−	8.90631i	0.0195819	−	0.366667i
$591$			3.20221i			0.131721i
$592$	2.77163	+	5.41462i	0.113913	+	0.222539i
$593$	2.13586	+	2.13586i	0.0877091	+	0.0877091i	0.749600	−	0.661891i	$-0.230246\pi$
$593$	2.13586	+	2.13586i	0.0877091	+	0.0877091i	−0.661891	+	0.749600i	$0.730246\pi$
$594$	−7.08066	−	1.89726i	−0.290523	−	0.0778454i
$595$	0.145473	−	0.0739399i	0.00596380	−	0.00303124i
$596$	13.3244	+	7.69284i	0.545788	+	0.315111i
$597$	−5.00520	−	2.88975i	−0.204849	−	0.118270i
$598$	−2.25401			−0.0921733
$599$	26.1788	+	15.1143i	1.06964	+	0.617554i	0.928082	−	0.372377i	$-0.121457\pi$
$599$	26.1788	+	15.1143i	1.06964	+	0.617554i	0.141553	+	0.989931i	$0.454790\pi$
$600$	−0.651739	+	1.68780i	−0.0266071	+	0.0689040i
$601$	23.7499	+	41.1361i	0.968780	+	1.67798i	0.699098	+	0.715026i	$0.253585\pi$
$601$	23.7499	+	41.1361i	0.968780	+	1.67798i	0.269682	+	0.962949i	$0.413081\pi$
$602$	−0.224407	+	0.224407i	−0.00914613	+	0.00914613i
$603$	−31.2026	+	31.2026i	−1.27067	+	1.27067i
$604$	6.97358	−	4.02620i	0.283751	−	0.163824i
$605$	0.633548	−	1.94328i	0.0257574	−	0.0790056i
$606$	4.10369	+	4.10369i	0.166701	+	0.166701i
$607$	−1.24940	−	2.16403i	−0.0507116	−	0.0878351i	0.839555	−	0.543274i	$-0.182816\pi$
$607$	−1.24940	−	2.16403i	−0.0507116	−	0.0878351i	−0.890267	+	0.455439i	$0.849482\pi$
$608$	−1.40948	+	5.26026i	−0.0571621	+	0.213332i
$609$	−0.0331053	+	0.123551i	−0.00134150	+	0.00500653i
$610$	0.0479836	−	0.0243888i	0.00194280	−	0.000987473i
$611$	4.83809	+	18.0560i	0.195728	+	0.730468i
$612$	−2.70238	−	4.68066i	−0.109237	−	0.189204i
$613$	11.4585	+	3.07030i	0.462805	+	0.124008i	0.482685	−	0.875794i	$-0.339662\pi$
$613$	11.4585	+	3.07030i	0.462805	+	0.124008i	−0.0198797	+	0.999802i	$0.506328\pi$
$614$	1.59327	−	5.94617i	0.0642992	−	0.239968i
$615$	−6.55057	−	4.26326i	−0.264145	−	0.171911i
$616$	0.129162	−	0.0346088i	0.00520408	−	0.00139443i
$617$	−6.07156	+	22.6594i	−0.244432	+	0.912231i	0.729237	+	0.684262i	$0.239875\pi$
$617$	−6.07156	+	22.6594i	−0.244432	+	0.912231i	−0.973668	+	0.227970i	$0.926791\pi$
$618$	−1.09685	−	1.09685i	−0.0441219	−	0.0441219i
$619$	20.4916			0.823627			0.411814	−	0.911268i	$-0.364895\pi$
$619$	20.4916			0.823627			0.411814	+	0.911268i	$0.364895\pi$
$620$	0.737989	−	13.8187i	0.0296384	−	0.554973i
$621$	1.36021	+	1.36021i	0.0545833	+	0.0545833i
$622$	17.0592	−	4.57100i	0.684012	−	0.183280i
$623$			0.0998139i			0.00399896i
$624$	0.233056	+	0.869779i	0.00932973	+	0.0348190i
$625$	7.63078	+	23.8070i	0.305231	+	0.952278i
$626$	4.75598	−	8.23759i	0.190087	−	0.329240i
$627$	5.89054	−	3.40091i	0.235246	−	0.135819i
$628$	−1.21372	+	1.21372i	−0.0484328	+	0.0484328i
$629$	10.2001	−	5.22121i	0.406704	−	0.208183i
$630$	−0.208303	−	0.135568i	−0.00829899	−	0.00540117i
$631$	12.1068	−	45.1831i	0.481963	−	1.79871i	−0.111401	−	0.993775i	$-0.535534\pi$
$631$	12.1068	−	45.1831i	0.481963	−	1.79871i	0.593364	−	0.804934i	$-0.297799\pi$
$632$	−4.82122	+	1.29184i	−0.191778	+	0.0513867i
$633$	0.525394	+	1.96080i	0.0208826	+	0.0779348i
$634$	29.7776	−	7.97887i	1.18262	−	0.316882i
$635$	19.7353	−	30.3236i	0.783170	−	1.20335i
$636$	−0.614556	+	1.06444i	−0.0243687	+	0.0422079i
$637$			17.4156i			0.690032i
$638$	−8.15150	+	30.4218i	−0.322721	+	1.20441i
$639$		−	35.4212i		−	1.40124i
$640$	−2.18767	+	0.462729i	−0.0864751	+	0.0182910i
$641$	−14.6814	−	25.4290i	−0.579882	−	1.00438i	−0.995492	−	0.0948421i	$-0.969765\pi$
$641$	−14.6814	−	25.4290i	−0.579882	−	1.00438i	0.415610	−	0.909543i	$-0.363568\pi$
$642$	−1.49819	−	0.864981i	−0.0591289	−	0.0341381i
$643$		−	48.3551i		−	1.90694i	−0.301489	−	0.953470i	$-0.597484\pi$
$643$		−	48.3551i		−	1.90694i	0.301489	−	0.953470i	$-0.402516\pi$
$644$	−0.0338942	−	0.00908192i	−0.00133562	−	0.000357878i
$645$	−6.61893	−	0.353485i	−0.260620	−	0.0139184i
$646$	9.90932	+	2.65519i	0.389877	+	0.104467i
$647$	−20.6475	+	35.7625i	−0.811737	+	1.40597i	0.0999100	+	0.994996i	$0.468145\pi$
$647$	−20.6475	+	35.7625i	−0.811737	+	1.40597i	−0.911647	+	0.410974i	$0.865189\pi$
$648$	−3.91936	+	6.78853i	−0.153967	+	0.266678i
$649$	−13.2986	−	3.56335i	−0.522015	−	0.139874i
$650$	10.0515	+	7.33347i	0.394254	+	0.287642i
$651$	−0.0837983	−	0.0224537i	−0.00328431	−	0.000880030i
$652$		−	6.18043i		−	0.242044i
$653$	−4.83500	−	2.79149i	−0.189208	−	0.109239i	0.402404	−	0.915462i	$-0.368175\pi$
$653$	−4.83500	−	2.79149i	−0.189208	−	0.109239i	−0.591612	+	0.806223i	$0.701508\pi$
$654$	−1.05977	−	1.83557i	−0.0414401	−	0.0717764i
$655$	−15.8124	−	10.2911i	−0.617843	−	0.402106i
$656$		−	9.65946i		−	0.377139i
$657$	6.94085	−	25.9036i	0.270788	−	1.01060i
$658$			0.291007i			0.0113446i
$659$	11.6925	−	20.2521i	0.455477	−	0.788909i	−0.543239	−	0.839578i	$-0.682802\pi$
$659$	11.6925	−	20.2521i	0.455477	−	0.788909i	0.998715	+	0.0506693i	$0.0161355\pi$
$660$	2.34076	+	1.52342i	0.0911139	+	0.0592990i
$661$	−23.1904	+	6.21386i	−0.902003	+	0.241691i	−0.679876	−	0.733327i	$-0.737967\pi$
$661$	−23.1904	+	6.21386i	−0.902003	+	0.241691i	−0.222127	+	0.975018i	$0.571300\pi$
$662$	8.19729	+	30.5927i	0.318597	+	1.18902i
$663$	1.63849	−	0.439033i	0.0636338	−	0.0170506i
$664$	3.63463	−	13.5646i	0.141051	−	0.526409i
$665$	0.461535	−	0.0976227i	0.0178976	−	0.00378564i
$666$	−14.6541	−	9.47762i	−0.567833	−	0.367250i
$667$	5.84410	−	5.84410i	0.226284	−	0.226284i
$668$	13.9283	−	8.04153i	0.538904	−	0.311136i
$669$	−1.01313	+	1.75480i	−0.0391700	+	0.0678444i
$670$	30.6585	−	15.5829i	1.18444	−	0.602021i
$671$	−0.0215047	−	0.0802567i	−0.000830180	−	0.00309827i
$672$			0.0140181i			0.000540762i
$673$	−19.9447	+	5.34416i	−0.768811	+	0.206002i	−0.621846	−	0.783140i	$-0.713617\pi$
$673$	−19.9447	+	5.34416i	−0.768811	+	0.206002i	−0.146965	+	0.989142i	$0.546950\pi$
$674$	12.2615	+	12.2615i	0.472293	+	0.472293i
$675$	−1.64026	−	10.4912i	−0.0631336	−	0.403807i
$676$	−6.80746			−0.261826
$677$	−23.8894	−	23.8894i	−0.918144	−	0.918144i	0.0787507	−	0.996894i	$-0.474907\pi$
$677$	−23.8894	−	23.8894i	−0.918144	−	0.918144i	−0.996894	+	0.0787507i	$0.974907\pi$
$678$	−0.692135	+	2.58308i	−0.0265813	+	0.0992026i
$679$	−0.0957218	+	0.0256486i	−0.00367346	+	0.000984302i
$680$	0.871692	+	4.12114i	0.0334279	+	0.158038i
$681$	−0.728470	+	2.71869i	−0.0279150	+	0.104180i
$682$	−20.6336	−	5.52876i	−0.790101	−	0.211707i
$683$	9.90437	+	17.1549i	0.378980	+	0.656413i	0.990914	−	0.134496i	$-0.0429415\pi$
$683$	9.90437	+	17.1549i	0.378980	+	0.656413i	−0.611934	+	0.790909i	$0.709608\pi$
$684$	−4.04390	−	15.0920i	−0.154622	−	0.577058i
$685$	−7.91628	−	15.5749i	−0.302466	−	0.595085i
$686$	−0.140358	+	0.523824i	−0.00535890	+	0.0199997i
$687$	−0.176459	+	0.658553i	−0.00673232	+	0.0251254i
$688$	−4.09601	−	7.09449i	−0.156159	−	0.270475i
$689$	5.97696	+	5.97696i	0.227704	+	0.227704i
$690$	−0.332074	−	0.653338i	−0.0126418	−	0.0248721i
$691$	−22.6779	+	13.0931i	−0.862709	+	0.498085i	−0.864919	−	0.501912i	$-0.832630\pi$
$691$	−22.6779	+	13.0931i	−0.862709	+	0.498085i	0.00220952	+	0.999998i	$0.499297\pi$
$692$	3.12707	−	3.12707i	0.118873	−	0.118873i
$693$	−0.271278	+	0.271278i	−0.0103050	+	0.0103050i
$694$	9.33397	+	16.1669i	0.354312	+	0.613687i
$695$	20.1406	−	4.26009i	0.763976	−	0.161594i
$696$	−2.85938	−	1.65087i	−0.108385	−	0.0625759i
$697$	−18.1966			−0.689243
$698$	−8.51145	−	4.91409i	−0.322163	−	0.186001i
$699$	2.97142	+	1.71555i	0.112389	+	0.0648881i
$700$	0.121600	+	0.150775i	0.00459604	+	0.00569878i
$701$	3.56684	+	0.955731i	0.134718	+	0.0360975i	0.325548	−	0.945526i	$-0.394451\pi$
$701$	3.56684	+	0.955731i	0.134718	+	0.0360975i	−0.190830	+	0.981623i	$0.561118\pi$
$702$	−3.73696	−	3.73696i	−0.141043	−	0.141043i
$703$	32.3889	−	6.94767i	1.22157	−	0.262036i
$704$			3.45168i			0.130090i
$705$	−4.52086	+	4.06247i	−0.170266	+	0.153001i
$706$	3.81914	+	2.20498i	0.143735	+	0.0829856i
$707$	0.600154	−	0.160811i	0.0225711	−	0.00604791i
$708$	0.721659	−	1.24995i	0.0271216	−	0.0469760i
$709$	−1.77322	−	1.77322i	−0.0665945	−	0.0665945i	0.673025	−	0.739620i	$-0.264995\pi$
$709$	−1.77322	−	1.77322i	−0.0665945	−	0.0665945i	−0.739620	+	0.673025i	$0.764995\pi$
$710$	−8.55692	+	26.2466i	−0.321135	+	0.985019i
$711$	10.1260	−	10.1260i	0.379755	−	0.379755i
$712$	−2.48871	−	0.666849i	−0.0932685	−	0.0249912i
$713$	3.96376	+	3.96376i	0.148444	+	0.148444i
$714$	0.0264075			0.000988274
$715$	14.2860	−	12.8375i	0.534267	−	0.480095i
$716$	1.67165	+	6.23870i	0.0624726	+	0.233151i
$717$	−2.23676			−0.0835332
$718$	13.5257	−	7.80904i	0.504773	−	0.291431i
$719$	−21.2320	+	12.2583i	−0.791819	+	0.457157i	−0.840602	−	0.541653i	$-0.817799\pi$
$719$	−21.2320	+	12.2583i	−0.791819	+	0.457157i	0.0487837	+	0.998809i	$0.484466\pi$
$720$	4.77185	−	4.28801i	0.177836	−	0.159805i
$721$	−0.160412	+	0.0429822i	−0.00597404	+	0.00160074i
$722$	9.22926	+	5.32852i	0.343478	+	0.198307i
$723$	−2.78922	+	1.61036i	−0.103732	+	0.0598899i
$724$	4.88795	+	8.46618i	0.181659	+	0.314643i
$725$	−45.0751	+	7.04733i	−1.67405	+	0.261731i
$726$	0.233884	−	0.233884i	0.00868025	−	0.00868025i
$727$	18.6931	−	32.3774i	0.693289	−	1.20081i	−0.277465	−	0.960736i	$-0.589494\pi$
$727$	18.6931	−	32.3774i	0.693289	−	1.20081i	0.970754	−	0.240076i	$-0.0771724\pi$
$728$	0.0931189	+	0.0249511i	0.00345122	+	0.000924751i
$729$		−	20.1843i		−	0.747568i
$730$	−11.4008	+	17.5175i	−0.421962	+	0.648351i
$731$	−13.3646	+	7.71608i	−0.494309	+	0.285390i
$732$	0.00871039			0.000321945
$733$	−4.82643	−	18.0125i	−0.178268	−	0.665306i	−0.995972	−	0.0896664i	$-0.971420\pi$
$733$	−4.82643	−	18.0125i	−0.178268	−	0.665306i	0.817704	−	0.575639i	$-0.195247\pi$
$734$	17.2798	−	17.2798i	0.637810	−	0.637810i
$735$	−5.04802	+	2.56578i	−0.186199	+	0.0946401i
$736$	0.452889	−	0.784426i	0.0166937	−	0.0289143i
$737$	−13.7402	−	51.2790i	−0.506126	−	1.88889i
$738$	13.8568	+	24.0007i	0.510076	+	0.883478i
$739$	−38.4904			−1.41589			−0.707946	−	0.706267i	$-0.750378\pi$
$739$	−38.4904			−1.41589			−0.707946	+	0.706267i	$0.750378\pi$
$740$	8.56889	+	10.5629i	0.314999	+	0.388299i
$741$	4.90376			0.180144
$742$	0.0657947	+	0.113960i	0.00241540	+	0.00418359i
$743$	−3.96390	−	14.7935i	−0.145421	−	0.542719i	−0.999736	−	0.0229639i	$-0.992690\pi$
$743$	−3.96390	−	14.7935i	−0.145421	−	0.542719i	0.854315	−	0.519755i	$-0.173977\pi$
$744$	1.11970	−	1.93938i	0.0410502	−	0.0711010i
$745$	32.7090	+	10.6638i	1.19837	+	0.390691i
$746$	13.6183	−	13.6183i	0.498602	−	0.498602i
$747$	10.4280	+	38.9177i	0.381540	+	1.42393i
$748$	6.50229			0.237747
$749$	−0.160397	+	0.0926053i	−0.00586078	+	0.00338372i
$750$	−0.644794	+	3.99391i	−0.0235445	+	0.145837i
$751$		−	43.8126i		−	1.59875i	−0.600835	−	0.799373i	$-0.705165\pi$
$751$		−	43.8126i		−	1.59875i	0.600835	−	0.799373i	$-0.294835\pi$
$752$	−7.25584	−	1.94420i	−0.264593	−	0.0708975i
$753$	2.23158	−	3.86521i	0.0813233	−	0.140856i
$754$	−16.0557	+	16.0557i	−0.584716	+	0.584716i
$755$	13.3928	−	12.0349i	0.487415	−	0.437993i
$756$	−0.0411367	−	0.0712508i	−0.00149613	−	0.00259137i
$757$	12.1669	−	7.02456i	0.442213	−	0.255312i	−0.262323	−	0.964980i	$-0.584488\pi$
$757$	12.1669	−	7.02456i	0.442213	−	0.255312i	0.704536	+	0.709668i	$0.251155\pi$
$758$	13.8986	+	8.02439i	0.504822	+	0.291459i
$759$	−1.09276	+	0.292805i	−0.0396648	+	0.0106282i
$760$	−0.649401	+	12.1599i	−0.0235562	+	0.441086i
$761$	15.2772	−	8.82031i	0.553799	−	0.319736i	−0.196854	−	0.980433i	$-0.563072\pi$
$761$	15.2772	−	8.82031i	0.553799	−	0.319736i	0.750653	+	0.660697i	$0.229739\pi$
$762$	5.07045	−	2.92742i	0.183683	−	0.106049i
$763$	−0.226918			−0.00821499
$764$	−2.38055	−	8.88432i	−0.0861252	−	0.321424i
$765$	−8.07778	−	8.98924i	−0.292053	−	0.325007i
$766$	2.71472			0.0980868
$767$	−7.01860	−	7.01860i	−0.253427	−	0.253427i
$768$	−0.349522	−	0.0936541i	−0.0126123	−	0.00337945i
$769$	8.23413	−	8.23413i	0.296930	−	0.296930i	−0.542880	−	0.839810i	$-0.682666\pi$
$769$	8.23413	−	8.23413i	0.296930	−	0.296930i	0.839810	+	0.542880i	$0.182666\pi$
$770$	0.266548	−	0.135479i	0.00960573	−	0.00488234i
$771$	7.65447	+	7.65447i	0.275669	+	0.275669i
$772$	12.7439	−	22.0730i	0.458662	−	0.794426i
$773$	47.6839	−	12.7769i	1.71507	−	0.459551i	0.738411	−	0.674351i	$-0.235576\pi$
$773$	47.6839	−	12.7769i	1.71507	−	0.459551i	0.976658	+	0.214800i	$0.0689098\pi$
$774$	20.3546	+	11.7517i	0.731629	+	0.422406i
$775$	−4.77985	−	30.5722i	−0.171697	−	1.09819i
$776$		−	2.55804i		−	0.0918282i
$777$	0.0759029	−	0.0388531i	0.00272300	−	0.00139385i
$778$	8.49994	+	8.49994i	0.304737	+	0.304737i
$779$	−50.8113	−	13.6149i	−1.82051	−	0.487803i
$780$	0.912322	+	1.79494i	0.0326664	+	0.0642693i
$781$	36.9049	+	21.3070i	1.32056	+	0.762426i
$782$	−1.47771	−	0.853154i	−0.0528427	−	0.0305087i
$783$	19.3781			0.692516
$784$	−6.06088	−	3.49925i	−0.216460	−	0.124973i
$785$	−2.09360	+	3.21685i	−0.0747237	+	0.114814i
$786$	−1.52653	−	2.64402i	−0.0544494	−	0.0943090i
$787$	−15.0937	+	15.0937i	−0.538031	+	0.538031i	−0.922950	−	0.384919i	$-0.874229\pi$
$787$	−15.0937	+	15.0937i	−0.538031	+	0.538031i	0.384919	+	0.922950i	$0.374229\pi$
$788$	−6.25755	+	6.25755i	−0.222916	+	0.222916i
$789$	−6.46269	+	3.73124i	−0.230078	+	0.132836i
$790$	−9.94944	+	5.05703i	−0.353985	+	0.179921i
$791$	0.202446	+	0.202446i	0.00719814	+	0.00719814i
$792$	−4.95154	−	8.57632i	−0.175945	−	0.304746i
$793$	0.0155038	−	0.0578609i	0.000550555	−	0.00205470i
$794$	7.08066	−	26.4254i	0.251283	−	0.937801i
$795$	−0.851895	+	2.61302i	−0.0302136	+	0.0926742i
$796$	−4.13387	−	15.4278i	−0.146521	−	0.546824i
$797$	18.4258	+	31.9144i	0.652675	+	1.13047i	0.982471	+	0.186414i	$0.0596867\pi$
$797$	18.4258	+	31.9144i	0.652675	+	1.13047i	−0.329796	+	0.944052i	$0.606980\pi$
$798$	0.0737392	+	0.0197583i	0.00261034	+	0.000699438i
$799$	−3.66249	+	13.6686i	−0.129569	+	0.483560i
$800$	−4.57176	+	2.02459i	−0.161636	+	0.0715802i
$801$	7.14028	−	1.91323i	0.252289	−	0.0676007i
$802$	−2.74138	+	10.2310i	−0.0968014	+	0.361268i
$803$	22.8135	+	22.8135i	0.805070	+	0.805070i
$804$	5.56540			0.196276
$805$	−0.0783516	−	0.00418437i	−0.00276153	−	0.000147480i
$806$	−10.8898	−	10.8898i	−0.383577	−	0.383577i
$807$	−3.18506	+	0.853434i	−0.112119	+	0.0300423i
$808$			16.0383i			0.564226i
$809$	2.06610	+	7.71081i	0.0726404	+	0.271098i	0.992688	−	0.120709i	$-0.0385169\pi$
$809$	2.06610	+	7.71081i	0.0726404	+	0.271098i	−0.920048	+	0.391807i	$0.871850\pi$
$810$	−5.43299	+	16.6646i	−0.190896	+	0.585535i
$811$	0.0222507	−	0.0385394i	0.000781329	−	0.00135330i	−0.865634	−	0.500676i	$-0.833085\pi$
$811$	0.0222507	−	0.0385394i	0.000781329	−	0.00135330i	0.866416	+	0.499323i	$0.166418\pi$
$812$	−0.306127	+	0.176743i	−0.0107430	+	0.00620245i
$813$	−3.36466	+	3.36466i	−0.118004	+	0.118004i
$814$	18.6895	−	9.56676i	0.655067	−	0.335315i
$815$	−2.85987	−	13.5207i	−0.100177	−	0.473610i
$816$	−0.176426	+	0.658431i	−0.00617615	+	0.0230497i
$817$	−43.0922	+	11.5465i	−1.50760	+	0.403961i
$818$	−6.77759	−	25.2943i	−0.236973	−	0.884394i
$819$	−0.267164	+	0.0715864i	−0.00933547	+	0.00250143i
$820$	−4.46972	−	21.1317i	−0.156089	−	0.737950i
$821$	15.5509	−	26.9349i	0.542729	−	0.940034i	−0.456017	−	0.889971i	$-0.650725\pi$
$821$	15.5509	−	26.9349i	0.542729	−	0.940034i	0.998746	−	0.0500628i	$-0.0159421\pi$
$822$		−	2.82728i		−	0.0986127i
$823$	12.4166	−	46.3393i	0.432815	−	1.61529i	−0.313428	−	0.949612i	$-0.601477\pi$
$823$	12.4166	−	46.3393i	0.432815	−	1.61529i	0.746242	−	0.665674i	$-0.231856\pi$
$824$		−	4.28679i		−	0.149337i
$825$	5.82573	+	2.24959i	0.202826	+	0.0783207i
$826$	−0.0772612	−	0.133820i	−0.00268826	−	0.00465620i
$827$	38.0406	+	21.9628i	1.32280	+	0.763720i	0.984175	−	0.177201i	$-0.0567042\pi$
$827$	38.0406	+	21.9628i	1.32280	+	0.763720i	0.338627	+	0.940921i	$0.390037\pi$
$828$			2.59873i			0.0903122i
$829$	−27.6032	−	7.39626i	−0.958700	−	0.256883i	−0.254650	−	0.967033i	$-0.581960\pi$
$829$	−27.6032	−	7.39626i	−0.958700	−	0.256883i	−0.704050	+	0.710151i	$0.748627\pi$
$830$	1.67461	−	31.3567i	0.0581264	−	1.08841i
$831$	−5.80216	−	1.55468i	−0.201275	−	0.0539314i
$832$	−1.24424	+	2.15509i	−0.0431363	+	0.0747142i
$833$	−6.59191	+	11.4175i	−0.228396	+	0.395593i
$834$	3.21785	+	0.862220i	0.111425	+	0.0298562i
$835$	26.7495	−	24.0372i	0.925705	−	0.831843i
$836$	18.1567	+	4.86508i	0.627964	+	0.168262i
$837$			13.1432i			0.454295i
$838$	6.62659	+	3.82586i	0.228912	+	0.132162i
$839$	10.9130	+	18.9019i	0.376759	+	0.652566i	0.990589	−	0.136873i	$-0.0437052\pi$
$839$	10.9130	+	18.9019i	0.376759	+	0.652566i	−0.613830	+	0.789439i	$0.710372\pi$
$840$	0.00648661	+	0.0306670i	0.000223809	+	0.00105811i
$841$		−	54.2573i		−	1.87094i
$842$	−0.505532	+	1.88667i	−0.0174218	+	0.0650189i
$843$		−	10.6820i		−	0.367908i
$844$	−2.80497	+	4.85835i	−0.0965511	+	0.167231i
$845$	−14.8925	+	3.15001i	−0.512316	+	0.108364i
$846$	20.8175	−	5.57802i	0.715719	−	0.191776i
$847$	−0.00916518	−	0.0342049i	−0.000314919	−	0.00117530i
$848$	−3.28099	+	0.879138i	−0.112670	+	0.0301897i
$849$	1.39850	−	5.21929i	0.0479966	−	0.179126i
$850$	3.81394	+	8.61231i	0.130817	+	0.295400i
$851$	−5.50261	−	0.278083i	−0.188627	−	0.00953255i
$852$	−3.15892	+	3.15892i	−0.108223	+	0.108223i
$853$	15.4731	−	8.93342i	0.529790	−	0.305874i	−0.211141	−	0.977456i	$-0.567718\pi$
$853$	15.4731	−	8.93342i	0.529790	−	0.305874i	0.740931	+	0.671581i	$0.234385\pi$
$854$	0.000466269	0	0.000807602i	1.59554e−5	0	2.76356e-5i
$855$	−15.8302	−	31.1451i	−0.541382	−	1.06514i
$856$	−1.23738	−	4.61796i	−0.0422927	−	0.157838i
$857$			52.3061i			1.78674i	0.449318	+	0.893372i	$0.351667\pi$
$857$			52.3061i			1.78674i	−0.449318	+	0.893372i	$0.648333\pi$
$858$	3.00220	−	0.804436i	0.102493	−	0.0274630i
$859$	−8.66774	−	8.66774i	−0.295739	−	0.295739i	0.543603	−	0.839342i	$-0.317060\pi$
$859$	−8.66774	−	8.66774i	−0.295739	−	0.295739i	−0.839342	+	0.543603i	$0.817060\pi$
$860$	−12.2435	−	13.6250i	−0.417501	−	0.464610i
$861$	−0.135408			−0.00461468
$862$	−27.4193	−	27.4193i	−0.933904	−	0.933904i
$863$	−8.63098	+	32.2113i	−0.293802	+	1.09648i	0.648362	+	0.761332i	$0.275454\pi$
$863$	−8.63098	+	32.2113i	−0.293802	+	1.09648i	−0.942164	+	0.335152i	$0.891212\pi$
$864$	2.05137	−	0.549662i	0.0697889	−	0.0186999i
$865$	5.39400	−	8.28797i	0.183401	−	0.281799i
$866$	1.36187	−	5.08256i	0.0462782	−	0.172712i
$867$	−4.70152	−	1.25977i	−0.159672	−	0.0427840i
$868$	−0.119876	−	0.207631i	−0.00406884	−	0.00704744i
$869$	4.45902	+	16.6413i	0.151262	+	0.564517i
$870$	−7.01928	−	2.28842i	−0.237976	−	0.0775848i
$871$	9.90595	−	36.9695i	0.335650	−	1.25266i
$872$	1.51602	−	5.65787i	0.0513390	−	0.191600i
$873$	3.66959	+	6.35591i	0.124197	+	0.215115i
$874$	−3.48795	−	3.48795i	−0.117982	−	0.117982i
$875$	0.335788	+	0.273578i	0.0113517	+	0.00924864i
$876$	−2.92912	+	1.69113i	−0.0989659	+	0.0571380i
$877$	−16.9359	+	16.9359i	−0.571884	+	0.571884i	−0.932655	−	0.360771i	$-0.882514\pi$
$877$	−16.9359	+	16.9359i	−0.571884	+	0.571884i	0.360771	+	0.932655i	$0.382514\pi$
$878$	−11.7690	+	11.7690i	−0.397186	+	0.397186i
$879$	−0.148261	−	0.256796i	−0.00500072	−	0.00866150i
$880$	1.59719	+	7.55112i	0.0538413	+	0.254548i
$881$	−33.7092	−	19.4620i	−1.13569	−	0.655692i	−0.190331	−	0.981720i	$-0.560956\pi$
$881$	−33.7092	−	19.4620i	−1.13569	−	0.655692i	−0.945360	+	0.326028i	$0.894290\pi$
$882$	20.0791			0.676100
$883$	31.0123	+	17.9049i	1.04365	+	0.602549i	0.920864	−	0.389885i	$-0.127485\pi$
$883$	31.0123	+	17.9049i	1.04365	+	0.602549i	0.122782	+	0.992434i	$0.460818\pi$
$884$	4.05977	+	2.34391i	0.136545	+	0.0788341i
$885$	1.00036	−	3.06841i	0.0336267	−	0.103143i
$886$	13.9357	+	3.73407i	0.468180	+	0.125448i
$887$	21.3968	+	21.3968i	0.718433	+	0.718433i	0.968284	−	0.249851i	$-0.0803817\pi$
$887$	21.3968	+	21.3968i	0.718433	+	0.718433i	−0.249851	+	0.968284i	$0.580382\pi$
$888$	0.461643	+	2.15210i	0.0154917	+	0.0722198i
$889$		−	0.626823i		−	0.0210230i
$890$	−5.75304	−	0.307242i	−0.192842	−	0.0102988i
$891$	23.4318	+	13.5284i	0.784995	+	0.453217i
$892$	−5.40891	+	1.44931i	−0.181104	+	0.0485266i
$893$	−20.4540	+	35.4273i	−0.684466	+	1.18553i
$894$	3.93670	+	3.93670i	0.131663	+	0.131663i
$895$	6.54385	+	12.8747i	0.218737	+	0.430352i
$896$	−0.0273933	+	0.0273933i	−0.000915147	+	0.000915147i
$897$	−0.787826	−	0.211097i	−0.0263047	−	0.00704833i
$898$	−21.1611	−	21.1611i	−0.706157	−	0.706157i
$899$	56.4693			1.88336
$900$	8.45503	−	11.5888i	0.281834	−	0.386294i
$901$	1.65613	+	6.18074i	0.0551735	+	0.205910i
$902$	−33.3414			−1.11015
$903$	−0.0994516	+	0.0574184i	−0.00330954	+	0.00191077i
$904$	−6.40021	+	3.69516i	−0.212868	+	0.122899i
$905$	14.6108	+	16.2594i	0.485678	+	0.540480i
$906$	2.81449	−	0.754140i	0.0935052	−	0.0250546i
$907$	−21.7517	−	12.5583i	−0.722252	−	0.416993i	0.0933288	−	0.995635i	$-0.470249\pi$
$907$	−21.7517	−	12.5583i	−0.722252	−	0.416993i	−0.815581	+	0.578643i	$0.803583\pi$
$908$	−6.73621	+	3.88915i	−0.223549	+	0.129066i
$909$	−23.0075	−	39.8501i	−0.763110	−	1.32175i
$910$	0.215259	+	0.0114959i	0.00713576	+	0.000381086i
$911$	−2.97654	+	2.97654i	−0.0986172	+	0.0986172i	−0.754694	−	0.656077i	$-0.772215\pi$
$911$	−2.97654	+	2.97654i	−0.0986172	+	0.0986172i	0.656077	+	0.754694i	$0.272215\pi$
$912$	−0.985291	+	1.70657i	−0.0326262	+	0.0565103i
$913$	−46.8207	−	12.5456i	−1.54954	−	0.415197i
$914$			21.6614i			0.716497i
$915$	0.0190554	−	0.00403055i	0.000629953	−	0.000133246i
$916$	−1.63172	+	0.942077i	−0.0539137	+	0.0311271i
$917$	−0.326861			−0.0107939
$918$	−1.03546	−	3.86438i	−0.0341751	−	0.127543i
$919$	−18.5055	+	18.5055i	−0.610439	+	0.610439i	−0.943060	−	0.332622i	$-0.892067\pi$
$919$	−18.5055	+	18.5055i	−0.610439	+	0.610439i	0.332622	+	0.943060i	$0.392067\pi$
$920$	0.627792	−	1.92563i	0.0206977	−	0.0634860i
$921$	1.11377	−	1.92910i	0.0366999	−	0.0635660i
$922$	8.91947	+	33.2879i	0.293747	+	1.09628i
$923$	15.3613	+	26.6065i	0.505622	+	0.875764i
$924$	0.0483861			0.00159179
$925$	23.6336	+	19.1429i	0.777069	+	0.629416i
$926$	41.9669			1.37912
$927$	6.14954	+	10.6513i	0.201977	+	0.349835i
$928$	−2.36161	−	8.81363i	−0.0775235	−	0.289322i
$929$	−17.0494	+	29.5304i	−0.559371	+	0.968859i	0.438178	+	0.898888i	$0.355624\pi$
$929$	−17.0494	+	29.5304i	−0.559371	+	0.968859i	−0.997549	+	0.0699711i	$0.977709\pi$
$930$	1.55212	−	4.76083i	0.0508961	−	0.156114i
$931$	−26.9497	+	26.9497i	−0.883240	+	0.883240i
$932$	2.45414	+	9.15897i	0.0803880	+	0.300012i
$933$	6.39066			0.209221
$934$	−29.4777	+	17.0190i	−0.964540	+	0.556877i
$935$	14.2248	−	3.00880i	0.465202	−	0.0983983i
$936$		−	7.13961i		−	0.233365i
$937$	29.4060	+	7.87932i	0.960653	+	0.257406i	0.704877	−	0.709330i	$-0.251002\pi$
$937$	29.4060	+	7.87932i	0.960653	+	0.257406i	0.255776	+	0.966736i	$0.417669\pi$
$938$	0.297917	−	0.516008i	0.00972734	−	0.0168482i
$939$	2.43380	−	2.43380i	0.0794242	−	0.0794242i
$940$	−16.7730	−	0.895762i	−0.547074	−	0.0292165i
$941$	−1.40860	−	2.43977i	−0.0459190	−	0.0795341i	0.842152	−	0.539240i	$-0.181288\pi$
$941$	−1.40860	−	2.43977i	−0.0459190	−	0.0795341i	−0.888071	+	0.459706i	$0.847955\pi$
$942$	−0.537893	+	0.310553i	−0.0175255	+	0.0101184i
$943$	7.57714	+	4.37466i	0.246745	+	0.142459i
$944$	3.85279	−	1.03235i	0.125398	−	0.0336002i
$945$	−0.122963	−	0.136838i	−0.00399999	−	0.00445134i
$946$	−24.4879	+	14.1381i	−0.796171	+	0.459669i
$947$	−8.09376	+	4.67293i	−0.263012	+	0.151850i	−0.625708	−	0.780058i	$-0.715190\pi$
$947$	−8.09376	+	4.67293i	−0.263012	+	0.151850i	0.362696	+	0.931908i	$0.381856\pi$
$948$	−1.80611			−0.0586596
$949$	6.02014	+	22.4675i	0.195422	+	0.729325i
$950$	4.20607	+	26.9023i	0.136463	+	0.872826i
$951$	11.1552			0.361731
$952$	0.0516037	+	0.0516037i	0.00167249	+	0.00167249i
$953$	17.3818	+	4.65744i	0.563052	+	0.150869i	0.529108	−	0.848554i	$-0.322527\pi$
$953$	17.3818	+	4.65744i	0.563052	+	0.150869i	0.0339440	+	0.999424i	$0.489193\pi$
$954$	6.89106	−	6.89106i	0.223106	−	0.223106i
$955$	−9.31888	−	18.3344i	−0.301552	−	0.593287i
$956$	−4.37092	−	4.37092i	−0.141366	−	0.141366i
$957$	−5.69826	+	9.86968i	−0.184199	+	0.319041i
$958$	−5.37111	+	1.43918i	−0.173533	+	0.0464979i
$959$	−0.262137	−	0.151345i	−0.00846485	−	0.00488719i
$960$	−0.807974	−	0.0431499i	−0.0260772	−	0.00139266i
$961$			7.30027i			0.235493i
$962$	15.1175	+	0.763988i	0.487409	+	0.0246320i
$963$	9.69909	+	9.69909i	0.312549	+	0.312549i
$964$	−8.59737	−	2.30366i	−0.276903	−	0.0741958i
$965$	17.6655	−	54.1854i	0.568672	−	1.74429i
$966$	−0.0109962	−	0.00634866i	−0.000353797	−	0.000204265i
$967$	−36.4193	−	21.0267i	−1.17117	−	0.676173i	−0.217212	−	0.976125i	$-0.569696\pi$
$967$	−36.4193	−	21.0267i	−1.17117	−	0.676173i	−0.953955	+	0.299951i	$0.903030\pi$
$968$	0.914082			0.0293797
$969$	3.21485	+	1.85610i	0.103276	+	0.0596264i
$970$	−1.18368	−	5.59613i	−0.0380056	−	0.179681i
$971$	9.41767	+	16.3119i	0.302227	+	0.523473i	0.976640	−	0.214881i	$-0.0689365\pi$
$971$	9.41767	+	16.3119i	0.302227	+	0.523473i	−0.674413	+	0.738355i	$0.735603\pi$
$972$	−6.51079	+	6.51079i	−0.208834	+	0.208834i
$973$	0.252195	−	0.252195i	0.00808500	−	0.00808500i
$974$	19.7773	−	11.4184i	0.633705	−	0.365870i
$975$	2.82643	+	3.50458i	0.0905181	+	0.112236i
$976$	0.0170213	+	0.0170213i	0.000544838	+	0.000544838i
$977$	1.42052	+	2.46041i	0.0454464	+	0.0787154i	0.887854	−	0.460126i	$-0.152196\pi$
$977$	1.42052	+	2.46041i	0.0454464	+	0.0787154i	−0.842407	+	0.538841i	$0.818862\pi$
$978$	0.578823	−	2.16020i	0.0185087	−	0.0690755i
$979$	−2.30175	+	8.59024i	−0.0735642	+	0.274545i
$980$	−14.8784	−	4.85064i	−0.475272	−	0.154948i
$981$	4.34956	+	16.2328i	0.138871	+	0.518273i
$982$	−15.4623	−	26.7815i	−0.493422	−	0.854632i
$983$	−10.4139	−	2.79039i	−0.332152	−	0.0889997i	0.0888891	−	0.996042i	$-0.471668\pi$
$983$	−10.4139	−	2.79039i	−0.332152	−	0.0889997i	−0.421041	+	0.907042i	$0.638335\pi$
$984$	0.904649	−	3.37619i	0.0288391	−	0.107629i
$985$	−10.7939	+	16.5850i	−0.343922	+	0.528442i
$986$	−16.6032	+	4.44881i	−0.528753	+	0.141679i
$987$	−0.0272540	+	0.101713i	−0.000867505	+	0.00323757i
$988$	9.58259	+	9.58259i	0.304863	+	0.304863i
$989$	7.42014			0.235947
$990$	−14.8008	−	16.4709i	−0.470401	−	0.523480i
$991$	27.4825	+	27.4825i	0.873009	+	0.873009i	0.992799	−	0.119790i	$-0.0382222\pi$
$991$	27.4825	+	27.4825i	0.873009	+	0.873009i	−0.119790	+	0.992799i	$0.538222\pi$
$992$	5.97785	−	1.60176i	0.189797	−	0.0508559i
$993$			11.4605i			0.363689i
$994$	0.123788	+	0.461984i	0.00392632	+	0.0146532i
$995$	−16.1824	−	31.8380i	−0.513017	−	1.00933i
$996$	2.54076	−	4.40073i	0.0805072	−	0.139443i
$997$	17.0304	−	9.83252i	0.539359	−	0.311399i	−0.205460	−	0.978665i	$-0.565869\pi$
$997$	17.0304	−	9.83252i	0.539359	−	0.311399i	0.744819	+	0.667267i	$0.232536\pi$
$998$	21.2699	−	21.2699i	0.673287	−	0.673287i
$999$	−8.66183	−	9.58391i	−0.274048	−	0.303221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.q.f.103.6	yes	32
5.2	odd	4		370.2.r.f.177.6	yes	32
37.23	odd	12		370.2.r.f.23.6	yes	32
185.97	even	12	inner	370.2.q.f.97.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.f.97.6	✓	32	185.97	even	12	inner
370.2.q.f.103.6	yes	32	1.1	even	1	trivial
370.2.r.f.23.6	yes	32	37.23	odd	12
370.2.r.f.177.6	yes	32	5.2	odd	4

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.0936541 + 0.349522i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.693098 + 2.12594i) q^{5} +(-0.255868 + 0.255868i) q^{6} +(0.0100267 + 0.0374200i) q^{7} -1.00000 q^{8} +(2.48468 - 1.43453i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.0936541 + 0.349522i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.693098 + 2.12594i) q^{5} +(-0.255868 + 0.255868i) q^{6} +(0.0100267 + 0.0374200i) q^{7} -1.00000 q^{8} +(2.48468 - 1.43453i) q^{9} +(-2.18767 + 0.462729i) q^{10} +3.45168i q^{11} +(-0.349522 - 0.0936541i) q^{12} +(-1.24424 + 2.15509i) q^{13} +(-0.0273933 + 0.0273933i) q^{14} +(-0.807974 - 0.0431499i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.63142 + 0.941903i) q^{17} +(2.48468 + 1.43453i) q^{18} +(-5.26026 + 1.40948i) q^{19} +(-1.49457 - 1.66321i) q^{20} +(-0.0121401 + 0.00700907i) q^{21} +(-2.98924 + 1.72584i) q^{22} +0.905777 q^{23} +(-0.0936541 - 0.349522i) q^{24} +(-4.03923 - 2.94697i) q^{25} -2.48848 q^{26} +(1.50170 + 1.50170i) q^{27} +(-0.0374200 - 0.0100267i) q^{28} +(6.45203 - 6.45203i) q^{29} +(-0.366618 - 0.721301i) q^{30} +(4.37609 + 4.37609i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.20644 + 0.323264i) q^{33} +(-1.63142 - 0.941903i) q^{34} +(-0.0865021 - 0.00461965i) q^{35} +2.86906i q^{36} +(-6.07501 - 0.307010i) q^{37} +(-3.85078 - 3.85078i) q^{38} +(-0.869779 - 0.233056i) q^{39} +(0.693098 - 2.12594i) q^{40} +(8.36534 + 4.82973i) q^{41} +(-0.0121401 - 0.00700907i) q^{42} +8.19202 q^{43} +(-2.98924 - 1.72584i) q^{44} +(1.32760 + 6.27655i) q^{45} +(0.452889 + 0.784426i) q^{46} +(5.31164 - 5.31164i) q^{47} +(0.255868 - 0.255868i) q^{48} +(6.06088 - 3.49925i) q^{49} +(0.532532 - 4.97156i) q^{50} +(-0.482005 - 0.482005i) q^{51} +(-1.24424 - 2.15509i) q^{52} +(0.879138 - 3.28099i) q^{53} +(-0.549662 + 2.05137i) q^{54} +(-7.33806 - 2.39235i) q^{55} +(-0.0100267 - 0.0374200i) q^{56} +(-0.985291 - 1.70657i) q^{57} +(8.81363 + 2.36161i) q^{58} +(-1.03235 + 3.85279i) q^{59} +(0.441356 - 0.678151i) q^{60} +(-0.0232515 + 0.00623022i) q^{61} +(-1.60176 + 5.97785i) q^{62} +(0.0785932 + 0.0785932i) q^{63} +1.00000 q^{64} +(-3.71920 - 4.13886i) q^{65} +(-0.883173 - 0.883173i) q^{66} +(-14.8563 + 3.98072i) q^{67} -1.88381i q^{68} +(0.0848298 + 0.316589i) q^{69} +(-0.0392503 - 0.0772228i) q^{70} +(6.17295 - 10.6919i) q^{71} +(-2.48468 + 1.43453i) q^{72} +(6.60939 - 6.60939i) q^{73} +(-2.77163 - 5.41462i) q^{74} +(0.651739 - 1.68780i) q^{75} +(1.40948 - 5.26026i) q^{76} +(-0.129162 + 0.0346088i) q^{77} +(-0.233056 - 0.869779i) q^{78} +(4.82122 - 1.29184i) q^{79} +(2.18767 - 0.462729i) q^{80} +(3.91936 - 6.78853i) q^{81} +9.65946i q^{82} +(-3.63463 + 13.5646i) q^{83} -0.0140181i q^{84} +(-0.871692 - 4.12114i) q^{85} +(4.09601 + 7.09449i) q^{86} +(2.85938 + 1.65087i) q^{87} -3.45168i q^{88} +(2.48871 + 0.666849i) q^{89} +(-4.77185 + 4.28801i) q^{90} +(-0.0931189 - 0.0249511i) q^{91} +(-0.452889 + 0.784426i) q^{92} +(-1.11970 + 1.93938i) q^{93} +(7.25584 + 1.94420i) q^{94} +(0.649401 - 12.1599i) q^{95} +(0.349522 + 0.0936541i) q^{96} +2.55804i q^{97} +(6.06088 + 3.49925i) q^{98} +(4.95154 + 8.57632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 2 q^{3} - 16 q^{4} + 6 q^{5} + 8 q^{6} - 10 q^{7} - 32 q^{8} + 12 q^{9}+O(q^{10}) \) 32 * q + 16 * q^2 - 2 * q^3 - 16 * q^4 + 6 * q^5 + 8 * q^6 - 10 * q^7 - 32 * q^8 + 12 * q^9	\( 32 q + 16 q^{2} - 2 q^{3} - 16 q^{4} + 6 q^{5} + 8 q^{6} - 10 q^{7} - 32 q^{8} + 12 q^{9} + 6 q^{10} + 10 q^{12} + 10 q^{13} - 8 q^{14} - 8 q^{15} - 16 q^{16} - 12 q^{17} + 12 q^{18} + 2 q^{19} - 54 q^{21} + 6 q^{22} + 12 q^{23} + 2 q^{24} - 16 q^{25} + 20 q^{26} + 40 q^{27} + 2 q^{28} + 6 q^{29} + 8 q^{30} - 4 q^{31} + 16 q^{32} + 26 q^{33} - 12 q^{34} - 12 q^{35} + 20 q^{37} - 26 q^{38} - 58 q^{39} - 6 q^{40} + 18 q^{41} - 54 q^{42} - 32 q^{43} + 6 q^{44} + 56 q^{45} + 6 q^{46} + 18 q^{47} - 8 q^{48} - 12 q^{49} - 14 q^{50} - 4 q^{51} + 10 q^{52} - 24 q^{53} + 20 q^{54} - 32 q^{55} + 10 q^{56} + 8 q^{57} + 36 q^{58} + 42 q^{59} + 16 q^{60} - 46 q^{61} - 14 q^{62} + 32 q^{64} - 18 q^{65} + 4 q^{66} + 50 q^{67} - 66 q^{69} + 12 q^{70} - 12 q^{71} - 12 q^{72} - 28 q^{73} + 16 q^{74} - 20 q^{75} - 28 q^{76} + 12 q^{77} - 26 q^{78} + 38 q^{79} - 6 q^{80} + 56 q^{81} - 8 q^{85} - 16 q^{86} + 18 q^{87} + 18 q^{89} + 4 q^{90} + 4 q^{91} - 6 q^{92} + 32 q^{93} + 30 q^{94} + 96 q^{95} - 10 q^{96} - 12 q^{98} - 26 q^{99}+O(q^{100}) \) 32 * q + 16 * q^2 - 2 * q^3 - 16 * q^4 + 6 * q^5 + 8 * q^6 - 10 * q^7 - 32 * q^8 + 12 * q^9 + 6 * q^10 + 10 * q^12 + 10 * q^13 - 8 * q^14 - 8 * q^15 - 16 * q^16 - 12 * q^17 + 12 * q^18 + 2 * q^19 - 54 * q^21 + 6 * q^22 + 12 * q^23 + 2 * q^24 - 16 * q^25 + 20 * q^26 + 40 * q^27 + 2 * q^28 + 6 * q^29 + 8 * q^30 - 4 * q^31 + 16 * q^32 + 26 * q^33 - 12 * q^34 - 12 * q^35 + 20 * q^37 - 26 * q^38 - 58 * q^39 - 6 * q^40 + 18 * q^41 - 54 * q^42 - 32 * q^43 + 6 * q^44 + 56 * q^45 + 6 * q^46 + 18 * q^47 - 8 * q^48 - 12 * q^49 - 14 * q^50 - 4 * q^51 + 10 * q^52 - 24 * q^53 + 20 * q^54 - 32 * q^55 + 10 * q^56 + 8 * q^57 + 36 * q^58 + 42 * q^59 + 16 * q^60 - 46 * q^61 - 14 * q^62 + 32 * q^64 - 18 * q^65 + 4 * q^66 + 50 * q^67 - 66 * q^69 + 12 * q^70 - 12 * q^71 - 12 * q^72 - 28 * q^73 + 16 * q^74 - 20 * q^75 - 28 * q^76 + 12 * q^77 - 26 * q^78 + 38 * q^79 - 6 * q^80 + 56 * q^81 - 8 * q^85 - 16 * q^86 + 18 * q^87 + 18 * q^89 + 4 * q^90 + 4 * q^91 - 6 * q^92 + 32 * q^93 + 30 * q^94 + 96 * q^95 - 10 * q^96 - 12 * q^98 - 26 * q^99

Introduction

L-functions

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