LMFDB - Embedded newform 370.2.o.a.201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([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("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (of order $9$, degree $6$, 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:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 21 x^{16} - 20 x^{15} + 180 x^{14} - 126 x^{13} + 1002 x^{12} - 270 x^{11} + \cdots + 81 $ x^18 - 3x^17 + 21x^16 - 20x^15 + 180x^14 - 126x^13 + 1002x^12 - 270x^11 + 3294x^10 - 1172x^9 + 6585x^8 - 1464x^7 + 8092x^6 - 2088x^5 + 5598x^4 + 180x^3 + 972x^2 - 162*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			201.2
Root			$1.87438 - 3.24652i$ of defining polynomial
Character	$\chi$	$=$	370.201
Dual form			370.2.o.a.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(0.528795 - 0.192466i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.173648 - 0.984808i) q^{5} -0.562732 q^{6} +(-0.553248 + 3.13762i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.05555 + 1.72481i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(0.528795 - 0.192466i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.173648 - 0.984808i) q^{5} -0.562732 q^{6} +(-0.553248 + 3.13762i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.05555 + 1.72481i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.58682 + 2.74846i) q^{11} +(0.528795 + 0.192466i) q^{12} +(3.63368 + 3.04902i) q^{13} +(1.59301 - 2.75918i) q^{14} +(-0.0977173 - 0.554183i) q^{15} +(0.173648 + 0.984808i) q^{16} +(2.70668 - 2.27118i) q^{17} +(2.52151 - 0.917754i) q^{18} +(-5.64743 + 2.05550i) q^{19} +(0.766044 - 0.642788i) q^{20} +(0.311330 + 1.76564i) q^{21} +(-0.551098 - 3.12543i) q^{22} +(3.08028 - 5.33520i) q^{23} +(-0.431077 - 0.361717i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(-2.37171 - 4.10793i) q^{26} +(-1.59910 + 2.76972i) q^{27} +(-2.44064 + 2.04794i) q^{28} +(4.50884 + 7.80955i) q^{29} +(-0.0977173 + 0.554183i) q^{30} +0.673963 q^{31} +(0.173648 - 0.984808i) q^{32} +(1.36809 + 1.14796i) q^{33} +(-3.32024 + 1.20847i) q^{34} +(2.99388 + 1.08968i) q^{35} -2.68333 q^{36} +(1.14364 - 5.97429i) q^{37} +6.00987 q^{38} +(2.50830 + 0.912947i) q^{39} +(-0.939693 + 0.342020i) q^{40} +(4.45175 + 3.73546i) q^{41} +(0.311330 - 1.76564i) q^{42} +4.01520 q^{43} +(-0.551098 + 3.12543i) q^{44} +(1.34167 + 2.32383i) q^{45} +(-4.71926 + 3.95993i) q^{46} +(-3.66819 + 6.35349i) q^{47} +(0.281366 + 0.487340i) q^{48} +(-2.96074 - 1.07762i) q^{49} +(0.766044 + 0.642788i) q^{50} +(0.994156 - 1.72193i) q^{51} +(0.823688 + 4.67137i) q^{52} +(-1.88180 - 10.6722i) q^{53} +(2.44996 - 2.05576i) q^{54} +(2.98225 - 1.08545i) q^{55} +(2.99388 - 1.08968i) q^{56} +(-2.59072 + 2.17387i) q^{57} +(-1.56590 - 8.88069i) q^{58} +(0.132294 + 0.750274i) q^{59} +(0.281366 - 0.487340i) q^{60} +(-6.44154 - 5.40509i) q^{61} +(-0.633318 - 0.230509i) q^{62} +(-4.27458 - 7.40380i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(3.63368 - 3.04902i) q^{65} +(-0.892955 - 1.54664i) q^{66} +(-1.21616 + 6.89720i) q^{67} +3.53332 q^{68} +(0.601993 - 3.41407i) q^{69} +(-2.44064 - 2.04794i) q^{70} +(-6.37947 + 2.32194i) q^{71} +(2.52151 + 0.917754i) q^{72} -4.38099 q^{73} +(-3.11800 + 5.22284i) q^{74} -0.562732 q^{75} +(-5.64743 - 2.05550i) q^{76} +(-9.50153 + 3.45827i) q^{77} +(-2.04479 - 1.71578i) q^{78} +(-1.42681 + 8.09184i) q^{79} +1.00000 q^{80} +(1.08535 - 6.15532i) q^{81} +(-2.90567 - 5.03277i) q^{82} +(9.24781 - 7.75983i) q^{83} +(-0.896439 + 1.55268i) q^{84} +(-1.76666 - 3.05995i) q^{85} +(-3.77305 - 1.37328i) q^{86} +(3.88732 + 3.26185i) q^{87} +(1.58682 - 2.74846i) q^{88} +(-2.04916 - 11.6214i) q^{89} +(-0.465956 - 2.64257i) q^{90} +(-11.5770 + 9.71425i) q^{91} +(5.78903 - 2.10703i) q^{92} +(0.356388 - 0.129715i) q^{93} +(5.61999 - 4.71574i) q^{94} +(1.04360 + 5.91857i) q^{95} +(-0.0977173 - 0.554183i) q^{96} +(4.04892 - 7.01294i) q^{97} +(2.41362 + 2.02527i) q^{98} +(-8.00237 - 2.91262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9	$ 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9} - 9 q^{10} + 3 q^{11} + 9 q^{13} - 6 q^{17} + 6 q^{18} + 9 q^{19} - 6 q^{21} + 21 q^{23} + 6 q^{26} + 12 q^{27} - 3 q^{28} + 6 q^{29} - 30 q^{31} - 45 q^{33} - 15 q^{34} + 6 q^{35} + 24 q^{36} + 6 q^{37} - 12 q^{38} + 24 q^{39} + 15 q^{41} - 6 q^{42} - 12 q^{43} - 12 q^{45} + 24 q^{47} + 3 q^{48} + 33 q^{49} - 42 q^{51} - 12 q^{53} + 27 q^{54} + 6 q^{56} + 51 q^{57} - 15 q^{58} - 15 q^{59} + 3 q^{60} + 72 q^{61} - 57 q^{62} - 30 q^{63} - 9 q^{64} + 9 q^{65} - 3 q^{66} + 18 q^{67} + 24 q^{69} - 3 q^{70} + 6 q^{72} - 66 q^{73} - 24 q^{74} - 6 q^{75} + 9 q^{76} - 66 q^{77} + 6 q^{78} - 12 q^{79} + 18 q^{80} + 66 q^{81} + 45 q^{82} + 9 q^{83} + 42 q^{84} + 12 q^{86} + 48 q^{87} + 3 q^{88} + 6 q^{90} - 78 q^{91} + 18 q^{92} + 24 q^{94} - 3 q^{97} - 48 q^{98} - 96 q^{99}+O(q^{100}) $ 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9 - 9 * q^10 + 3 * q^11 + 9 * q^13 - 6 * q^17 + 6 * q^18 + 9 * q^19 - 6 * q^21 + 21 * q^23 + 6 * q^26 + 12 * q^27 - 3 * q^28 + 6 * q^29 - 30 * q^31 - 45 * q^33 - 15 * q^34 + 6 * q^35 + 24 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^39 + 15 * q^41 - 6 * q^42 - 12 * q^43 - 12 * q^45 + 24 * q^47 + 3 * q^48 + 33 * q^49 - 42 * q^51 - 12 * q^53 + 27 * q^54 + 6 * q^56 + 51 * q^57 - 15 * q^58 - 15 * q^59 + 3 * q^60 + 72 * q^61 - 57 * q^62 - 30 * q^63 - 9 * q^64 + 9 * q^65 - 3 * q^66 + 18 * q^67 + 24 * q^69 - 3 * q^70 + 6 * q^72 - 66 * q^73 - 24 * q^74 - 6 * q^75 + 9 * q^76 - 66 * q^77 + 6 * q^78 - 12 * q^79 + 18 * q^80 + 66 * q^81 + 45 * q^82 + 9 * q^83 + 42 * q^84 + 12 * q^86 + 48 * q^87 + 3 * q^88 + 6 * q^90 - 78 * q^91 + 18 * q^92 + 24 * q^94 - 3 * q^97 - 48 * q^98 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	0.528795	−	0.192466i	0.305300	−	0.111120i	−0.184827	−	0.982771i	$-0.559173\pi$
$3$	0.528795	−	0.192466i	0.305300	−	0.111120i	0.490127	+	0.871651i	$0.336950\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$6$	−0.562732			−0.229734
$7$	−0.553248	+	3.13762i	−0.209108	+	1.18591i	0.681735	+	0.731599i	$0.261226\pi$
$7$	−0.553248	+	3.13762i	−0.209108	+	1.18591i	−0.890843	+	0.454311i	$0.849886\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−2.05555	+	1.72481i	−0.685184	+	0.574938i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	1.58682	+	2.74846i	0.478445	+	0.828691i	0.999695	−	0.0247133i	$-0.00786729\pi$
$11$	1.58682	+	2.74846i	0.478445	+	0.828691i	−0.521250	+	0.853404i	$0.674534\pi$
$12$	0.528795	+	0.192466i	0.152650	+	0.0555600i
$13$	3.63368	+	3.04902i	1.00780	+	0.845645i	0.988046	−	0.154160i	$-0.0492670\pi$
$13$	3.63368	+	3.04902i	1.00780	+	0.845645i	0.0197548	+	0.999805i	$0.493711\pi$
$14$	1.59301	−	2.75918i	0.425751	−	0.737422i
$15$	−0.0977173	−	0.554183i	−0.0252305	−	0.143089i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	2.70668	−	2.27118i	0.656467	−	0.550841i	−0.252559	−	0.967582i	$-0.581272\pi$
$17$	2.70668	−	2.27118i	0.656467	−	0.550841i	0.909025	+	0.416741i	$0.136828\pi$
$18$	2.52151	−	0.917754i	0.594325	−	0.216317i
$19$	−5.64743	+	2.05550i	−1.29561	+	0.471564i	−0.895564	−	0.444932i	$-0.853228\pi$
$19$	−5.64743	+	2.05550i	−1.29561	+	0.471564i	−0.400046	+	0.916495i	$0.631006\pi$
$20$	0.766044	−	0.642788i	0.171293	−	0.143732i
$21$	0.311330	+	1.76564i	0.0679378	+	0.385294i
$22$	−0.551098	−	3.12543i	−0.117494	−	0.666344i
$23$	3.08028	−	5.33520i	0.642282	−	1.11247i	−0.342640	−	0.939467i	$-0.611321\pi$
$23$	3.08028	−	5.33520i	0.642282	−	1.11247i	0.984922	−	0.172998i	$-0.0553455\pi$
$24$	−0.431077	−	0.361717i	−0.0879933	−	0.0738352i
$25$	−0.939693	−	0.342020i	−0.187939	−	0.0684040i
$26$	−2.37171	−	4.10793i	−0.465131	−	0.805631i
$27$	−1.59910	+	2.76972i	−0.307746	+	0.533032i
$28$	−2.44064	+	2.04794i	−0.461237	+	0.387024i
$29$	4.50884	+	7.80955i	0.837271	+	1.45020i	0.892168	+	0.451704i	$0.149184\pi$
$29$	4.50884	+	7.80955i	0.837271	+	1.45020i	−0.0548965	+	0.998492i	$0.517483\pi$
$30$	−0.0977173	+	0.554183i	−0.0178407	+	0.101179i
$31$	0.673963			0.121047			0.0605237	−	0.998167i	$-0.480723\pi$
$31$	0.673963			0.121047			0.0605237	+	0.998167i	$0.480723\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	1.36809	+	1.14796i	0.238153	+	0.199834i
$34$	−3.32024	+	1.20847i	−0.569416	+	0.207250i
$35$	2.99388	+	1.08968i	0.506059	+	0.184190i
$36$	−2.68333			−0.447222
$37$	1.14364	−	5.97429i	0.188013	−	0.982167i
$37$	1.14364	−	5.97429i	0.188013	−	0.982167i
$38$	6.00987			0.974930
$39$	2.50830	+	0.912947i	0.401650	+	0.146188i
$40$	−0.939693	+	0.342020i	−0.148578	+	0.0540781i
$41$	4.45175	+	3.73546i	0.695246	+	0.583381i	0.920417	−	0.390938i	$-0.127849\pi$
$41$	4.45175	+	3.73546i	0.695246	+	0.583381i	−0.225170	+	0.974319i	$0.572294\pi$
$42$	0.311330	−	1.76564i	0.0480392	−	0.272444i
$43$	4.01520			0.612312			0.306156	−	0.951981i	$-0.400957\pi$
$43$	4.01520			0.612312			0.306156	+	0.951981i	$0.400957\pi$
$44$	−0.551098	+	3.12543i	−0.0830811	+	0.471176i
$45$	1.34167	+	2.32383i	0.200004	+	0.346417i
$46$	−4.71926	+	3.95993i	−0.695817	+	0.583859i
$47$	−3.66819	+	6.35349i	−0.535061	+	0.926752i	0.464100	+	0.885783i	$0.346378\pi$
$47$	−3.66819	+	6.35349i	−0.535061	+	0.926752i	−0.999160	+	0.0409693i	$0.986955\pi$
$48$	0.281366	+	0.487340i	0.0406117	+	0.0703415i
$49$	−2.96074	−	1.07762i	−0.422963	−	0.153946i
$50$	0.766044	+	0.642788i	0.108335	+	0.0909039i
$51$	0.994156	−	1.72193i	0.139210	−	0.241118i
$52$	0.823688	+	4.67137i	0.114225	+	0.647802i
$53$	−1.88180	−	10.6722i	−0.258485	−	1.46594i	−0.786967	−	0.616995i	$-0.788350\pi$
$53$	−1.88180	−	10.6722i	−0.258485	−	1.46594i	0.528483	−	0.848944i	$-0.322761\pi$
$54$	2.44996	−	2.05576i	0.333397	−	0.279753i
$55$	2.98225	−	1.08545i	0.402127	−	0.146362i
$56$	2.99388	−	1.08968i	0.400075	−	0.145615i
$57$	−2.59072	+	2.17387i	−0.343149	+	0.287937i
$58$	−1.56590	−	8.88069i	−0.205613	−	1.16609i
$59$	0.132294	+	0.750274i	0.0172232	+	0.0976774i	0.992208	−	0.124596i	$-0.0397634\pi$
$59$	0.132294	+	0.750274i	0.0172232	+	0.0976774i	−0.974984	+	0.222273i	$0.928652\pi$
$60$	0.281366	−	0.487340i	0.0363242	−	0.0629153i
$61$	−6.44154	−	5.40509i	−0.824754	−	0.692051i	0.129326	−	0.991602i	$-0.458719\pi$
$61$	−6.44154	−	5.40509i	−0.824754	−	0.692051i	−0.954080	+	0.299551i	$0.903163\pi$
$62$	−0.633318	−	0.230509i	−0.0804315	−	0.0292747i
$63$	−4.27458	−	7.40380i	−0.538547	−	0.932791i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	3.63368	−	3.04902i	0.450702	−	0.378184i
$66$	−0.892955	−	1.54664i	−0.109915	−	0.190379i
$67$	−1.21616	+	6.89720i	−0.148578	+	0.842627i	0.815846	+	0.578269i	$0.196271\pi$
$67$	−1.21616	+	6.89720i	−0.148578	+	0.842627i	−0.964424	+	0.264359i	$0.914840\pi$
$68$	3.53332			0.428478
$69$	0.601993	−	3.41407i	0.0724714	−	0.411006i
$70$	−2.44064	−	2.04794i	−0.291712	−	0.244775i
$71$	−6.37947	+	2.32194i	−0.757104	+	0.275563i	−0.691592	−	0.722289i	$-0.743090\pi$
$71$	−6.37947	+	2.32194i	−0.757104	+	0.275563i	−0.0655119	+	0.997852i	$0.520868\pi$
$72$	2.52151	+	0.917754i	0.297163	+	0.108158i
$73$	−4.38099			−0.512756			−0.256378	−	0.966577i	$-0.582529\pi$
$73$	−4.38099			−0.512756			−0.256378	+	0.966577i	$0.582529\pi$
$74$	−3.11800	+	5.22284i	−0.362460	+	0.607143i
$75$	−0.562732			−0.0649787
$76$	−5.64743	−	2.05550i	−0.647805	−	0.235782i
$77$	−9.50153	+	3.45827i	−1.08280	+	0.394107i
$78$	−2.04479	−	1.71578i	−0.231526	−	0.194274i
$79$	−1.42681	+	8.09184i	−0.160529	+	0.910403i	0.793027	+	0.609186i	$0.208504\pi$
$79$	−1.42681	+	8.09184i	−0.160529	+	0.910403i	−0.953556	+	0.301217i	$0.902607\pi$
$80$	1.00000			0.111803
$81$	1.08535	−	6.15532i	0.120594	−	0.683924i
$82$	−2.90567	−	5.03277i	−0.320878	−	0.555777i
$83$	9.24781	−	7.75983i	1.01508	−	0.851753i	0.0260779	−	0.999660i	$-0.491698\pi$
$83$	9.24781	−	7.75983i	1.01508	−	0.851753i	0.989001	+	0.147907i	$0.0472538\pi$
$84$	−0.896439	+	1.55268i	−0.0978095	+	0.169411i
$85$	−1.76666	−	3.05995i	−0.191621	−	0.331898i
$86$	−3.77305	−	1.37328i	−0.406859	−	0.148085i
$87$	3.88732	+	3.26185i	0.416765	+	0.349707i
$88$	1.58682	−	2.74846i	0.169156	−	0.292986i
$89$	−2.04916	−	11.6214i	−0.217210	−	1.23186i	−0.877030	−	0.480436i	$-0.840478\pi$
$89$	−2.04916	−	11.6214i	−0.217210	−	1.23186i	0.659819	−	0.751424i	$-0.270633\pi$
$90$	−0.465956	−	2.64257i	−0.0491161	−	0.278551i
$91$	−11.5770	+	9.71425i	−1.21360	+	1.01833i
$92$	5.78903	−	2.10703i	0.603548	−	0.219673i
$93$	0.356388	−	0.129715i	0.0369557	−	0.0134508i
$94$	5.61999	−	4.71574i	0.579658	−	0.486391i
$95$	1.04360	+	5.91857i	0.107071	+	0.607232i
$96$	−0.0977173	−	0.554183i	−0.00997323	−	0.0565610i
$97$	4.04892	−	7.01294i	0.411106	−	0.712056i	−0.583905	−	0.811822i	$-0.698476\pi$
$97$	4.04892	−	7.01294i	0.411106	−	0.712056i	0.995011	+	0.0997660i	$0.0318094\pi$
$98$	2.41362	+	2.02527i	0.243812	+	0.204583i
$99$	−8.00237	−	2.91262i	−0.804269	−	0.292730i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−1.11299	+	1.92775i	−0.110746	+	0.191818i	−0.916071	−	0.401015i	$-0.868657\pi$
$101$	−1.11299	+	1.92775i	−0.110746	+	0.191818i	0.805325	+	0.592833i	$0.201991\pi$
$102$	−1.52314	+	1.27806i	−0.150813	+	0.126547i
$103$	0.342093	+	0.592522i	0.0337074	+	0.0583829i	0.882387	−	0.470524i	$-0.155935\pi$
$103$	0.342093	+	0.592522i	0.0337074	+	0.0583829i	−0.848680	+	0.528907i	$0.822602\pi$
$104$	0.823688	−	4.67137i	0.0807692	−	0.458065i
$105$	1.79288			0.174967
$106$	−1.88180	+	10.6722i	−0.182776	+	1.03658i
$107$	−15.1560	−	12.7174i	−1.46519	−	1.22944i	−0.920465	−	0.390825i	$-0.872190\pi$
$107$	−15.1560	−	12.7174i	−1.46519	−	1.22944i	−0.544725	−	0.838615i	$-0.683366\pi$
$108$	−3.00532	+	1.09385i	−0.289187	+	0.105255i
$109$	−19.0875	−	6.94728i	−1.82825	−	0.665429i	−0.993365	−	0.115005i	$-0.963312\pi$
$109$	−19.0875	−	6.94728i	−1.82825	−	0.665429i	−0.834885	−	0.550424i	$-0.814466\pi$
$110$	−3.17364			−0.302595
$111$	−0.545094	−	3.37928i	−0.0517380	−	0.320747i
$112$	−3.18603			−0.301051
$113$	15.8823	+	5.78068i	1.49408	+	0.543801i	0.954520	−	0.298147i	$-0.0963685\pi$
$113$	15.8823	+	5.78068i	1.49408	+	0.543801i	0.539560	+	0.841947i	$0.318591\pi$
$114$	3.17799	−	1.15669i	0.297646	−	0.108334i
$115$	−4.71926	−	3.95993i	−0.440073	−	0.369265i
$116$	−1.56590	+	8.88069i	−0.145391	+	0.824551i
$117$	−12.7282			−1.17672
$118$	0.132294	−	0.750274i	0.0121786	−	0.0690684i
$119$	5.62863	+	9.74907i	0.515975	+	0.893695i
$120$	−0.431077	+	0.361717i	−0.0393518	+	0.0330201i
$121$	0.463990	−	0.803654i	0.0421809	−	0.0730594i
$122$	4.20442	+	7.28226i	0.380650	+	0.659305i
$123$	3.07301	+	1.11848i	0.277084	+	0.100850i
$124$	0.516286	+	0.433215i	0.0463638	+	0.0389039i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$	1.48455	+	8.41929i	0.132254	+	0.750050i
$127$	2.10224	+	11.9224i	0.186544	+	1.05794i	0.923956	+	0.382499i	$0.124936\pi$
$127$	2.10224	+	11.9224i	0.186544	+	1.05794i	−0.737413	+	0.675443i	$0.763953\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	2.12322	−	0.772788i	0.186939	−	0.0680402i
$130$	−4.45737	+	1.62235i	−0.390937	+	0.142289i
$131$	7.29228	−	6.11895i	0.637130	−	0.534615i	−0.266006	−	0.963971i	$-0.585704\pi$
$131$	7.29228	−	6.11895i	0.637130	−	0.534615i	0.903135	+	0.429356i	$0.141260\pi$
$132$	0.310120	+	1.75878i	0.0269925	+	0.153082i
$133$	−3.32495	−	18.8567i	−0.288309	−	1.63508i
$134$	3.50180	−	6.06530i	0.302510	−	0.523962i
$135$	2.44996	+	2.05576i	0.210859	+	0.176931i
$136$	−3.32024	−	1.20847i	−0.284708	−	0.103625i
$137$	−5.48935	−	9.50783i	−0.468986	−	0.812308i	0.530385	−	0.847757i	$-0.322047\pi$
$137$	−5.48935	−	9.50783i	−0.468986	−	0.812308i	−0.999372	+	0.0354485i	$0.988714\pi$
$138$	−1.73337	+	3.00228i	−0.147554	+	0.255571i
$139$	13.9652	−	11.7182i	1.18451	−	0.993925i	0.184575	−	0.982818i	$-0.440909\pi$
$139$	13.9652	−	11.7182i	1.18451	−	0.993925i	0.999938	−	0.0111062i	$-0.00353529\pi$
$140$	1.59301	+	2.75918i	0.134634	+	0.233193i
$141$	−0.716892	+	4.06569i	−0.0603732	+	0.342393i
$142$	6.78889			0.569711
$143$	−2.61409	+	14.8253i	−0.218601	+	1.23975i
$144$	−2.05555	−	1.72481i	−0.171296	−	0.143734i
$145$	8.47385	−	3.08423i	0.703715	−	0.256131i
$146$	4.11678	+	1.49839i	0.340707	+	0.124007i
$147$	−1.77303			−0.146237
$148$	4.71628	−	3.84145i	0.387675	−	0.315765i
$149$	5.81003			0.475976			0.237988	−	0.971268i	$-0.423512\pi$
$149$	5.81003			0.475976			0.237988	+	0.971268i	$0.423512\pi$
$150$	0.528795	+	0.192466i	0.0431759	+	0.0157147i
$151$	−0.713237	+	0.259597i	−0.0580424	+	0.0211257i	−0.370878	−	0.928682i	$-0.620943\pi$
$151$	−0.713237	+	0.259597i	−0.0580424	+	0.0211257i	0.312836	+	0.949807i	$0.398721\pi$
$152$	4.60383	+	3.86307i	0.373420	+	0.313337i
$153$	−1.64637	+	9.33704i	−0.133101	+	0.754855i
$154$	10.1113			0.814793
$155$	0.117032	−	0.663724i	0.00940028	−	0.0533116i
$156$	1.33464	+	2.31166i	0.106857	+	0.185081i
$157$	2.53671	−	2.12855i	0.202451	−	0.169877i	−0.535925	−	0.844265i	$-0.680037\pi$
$157$	2.53671	−	2.12855i	0.202451	−	0.169877i	0.738377	+	0.674389i	$0.235593\pi$
$158$	4.10833	−	7.11584i	0.326842	−	0.566106i
$159$	−3.04911	−	5.28122i	−0.241811	−	0.418828i
$160$	−0.939693	−	0.342020i	−0.0742892	−	0.0270391i
$161$	15.0357	+	12.6164i	1.18498	+	0.994314i
$162$	−3.12514	+	5.41290i	−0.245534	+	0.425277i
$163$	2.02082	+	11.4607i	0.158283	+	0.897668i	0.955723	+	0.294269i	$0.0950762\pi$
$163$	2.02082	+	11.4607i	0.158283	+	0.897668i	−0.797440	+	0.603399i	$0.793813\pi$
$164$	1.00913	+	5.72306i	0.0787998	+	0.446896i
$165$	1.36809	−	1.14796i	0.106505	−	0.0893687i
$166$	−11.3441	+	4.12892i	−0.880474	+	0.320466i
$167$	7.87448	−	2.86608i	0.609346	−	0.221784i	−0.0188713	−	0.999822i	$-0.506007\pi$
$167$	7.87448	−	2.86608i	0.609346	−	0.221784i	0.628217	+	0.778038i	$0.283785\pi$
$168$	1.37342	−	1.15244i	0.105962	−	0.0889126i
$169$	1.64968	+	9.35579i	0.126898	+	0.719676i
$170$	0.613555	+	3.47964i	0.0470575	+	0.266876i
$171$	8.06325	−	13.9660i	0.616612	−	1.06800i
$172$	3.07582	+	2.58092i	0.234529	+	0.196793i
$173$	17.7156	+	6.44794i	1.34689	+	0.490228i	0.911976	−	0.410244i	$-0.134556\pi$
$173$	17.7156	+	6.44794i	1.34689	+	0.490228i	0.434914	+	0.900472i	$0.356779\pi$
$174$	−2.53727	−	4.39468i	−0.192350	−	0.333160i
$175$	1.59301	−	2.75918i	0.120420	−	0.208574i
$176$	−2.43115	+	2.03998i	−0.183255	+	0.153769i
$177$	0.214358	+	0.371279i	0.0161121	+	0.0279071i
$178$	−2.04916	+	11.6214i	−0.153591	+	0.871057i
$179$	16.0870			1.20240			0.601199	−	0.799099i	$-0.294690\pi$
$179$	16.0870			1.20240			0.601199	+	0.799099i	$0.294690\pi$
$180$	−0.465956	+	2.64257i	−0.0347303	+	0.196965i
$181$	−7.73619	−	6.49144i	−0.575027	−	0.482505i	0.308283	−	0.951295i	$-0.400246\pi$
$181$	−7.73619	−	6.49144i	−0.575027	−	0.482505i	−0.883310	+	0.468790i	$0.844690\pi$
$182$	14.2013	−	5.16884i	1.05267	−	0.383140i
$183$	−4.44655	−	1.61841i	−0.328698	−	0.119636i
$184$	−6.16055			−0.454162
$185$	−5.68493	−	2.16369i	−0.417965	−	0.159078i
$186$	−0.379261			−0.0278087
$187$	10.5373	+	3.83525i	0.770560	+	0.280461i
$188$	−6.89394	+	2.50919i	−0.502793	+	0.183002i
$189$	−7.80563	−	6.54970i	−0.567776	−	0.476420i
$190$	1.04360	−	5.91857i	0.0757110	−	0.429378i
$191$	−9.50698			−0.687901			−0.343950	−	0.938988i	$-0.611765\pi$
$191$	−9.50698			−0.687901			−0.343950	+	0.938988i	$0.611765\pi$
$192$	−0.0977173	+	0.554183i	−0.00705214	+	0.0399947i
$193$	1.31206	+	2.27255i	0.0944439	+	0.163582i	0.909376	−	0.415974i	$-0.136559\pi$
$193$	1.31206	+	2.27255i	0.0944439	+	0.163582i	−0.814932	+	0.579556i	$0.803226\pi$
$194$	−6.20331	+	5.20519i	−0.445371	+	0.373711i
$195$	1.33464	−	2.31166i	0.0955755	−	0.165542i
$196$	−1.57538	−	2.72864i	−0.112527	−	0.194903i
$197$	10.0008	+	3.63998i	0.712524	+	0.259338i	0.672749	−	0.739871i	$-0.265114\pi$
$197$	10.0008	+	3.63998i	0.712524	+	0.259338i	0.0397754	+	0.999209i	$0.487336\pi$
$198$	6.52359	+	5.47394i	0.463612	+	0.389016i
$199$	−3.19548	+	5.53473i	−0.226521	+	0.392347i	−0.956775	−	0.290830i	$-0.906069\pi$
$199$	−3.19548	+	5.53473i	−0.226521	+	0.392347i	0.730253	+	0.683176i	$0.239402\pi$
$200$	0.173648	+	0.984808i	0.0122788	+	0.0696364i
$201$	0.684373	+	3.88127i	0.0482720	+	0.273764i
$202$	1.70519	−	1.43083i	0.119977	−	0.100673i
$203$	−26.9979	+	9.82644i	−1.89488	+	0.689681i
$204$	1.86840	−	0.680043i	0.130814	−	0.0476125i
$205$	4.45175	−	3.73546i	0.310924	−	0.260896i
$206$	−0.118808	−	0.673791i	−0.00827771	−	0.0469452i
$207$	2.87055	+	16.2797i	0.199517	+	1.13152i
$208$	−2.37171	+	4.10793i	−0.164449	+	0.284834i
$209$	−14.6109	−	12.2600i	−1.01066	−	0.848043i
$210$	−1.68475	−	0.613200i	−0.116259	−	0.0423148i
$211$	4.12493	+	7.14459i	0.283972	+	0.491854i	0.972359	−	0.233489i	$-0.0750144\pi$
$211$	4.12493	+	7.14459i	0.283972	+	0.491854i	−0.688387	+	0.725343i	$0.741681\pi$
$212$	5.41842	−	9.38497i	0.372138	−	0.644563i
$213$	−2.92654	+	2.45566i	−0.200523	+	0.168259i
$214$	9.89240	+	17.1341i	0.676231	+	1.17127i
$215$	0.697232	−	3.95420i	0.0475509	−	0.269674i
$216$	3.19819			0.217609
$217$	−0.372869	+	2.11464i	−0.0253120	+	0.143551i
$218$	15.5603	+	13.0566i	1.05387	+	0.884306i
$219$	−2.31664	+	0.843190i	−0.156544	+	0.0569775i
$220$	2.98225	+	1.08545i	0.201063	+	0.0731811i
$221$	16.7601			1.12740
$222$	−0.643562	+	3.36192i	−0.0431930	+	0.225637i
$223$	−14.6189			−0.978955			−0.489478	−	0.872016i	$-0.662812\pi$
$223$	−14.6189			−0.978955			−0.489478	+	0.872016i	$0.662812\pi$
$224$	2.99388	+	1.08968i	0.200037	+	0.0728076i
$225$	2.52151	−	0.917754i	0.168101	−	0.0611836i
$226$	−12.9474	−	10.8641i	−0.861245	−	0.722671i
$227$	−1.52375	+	8.64162i	−0.101135	+	0.573565i	0.891559	+	0.452905i	$0.149612\pi$
$227$	−1.52375	+	8.64162i	−0.101135	+	0.573565i	−0.992694	+	0.120660i	$0.961499\pi$
$228$	−3.38195			−0.223975
$229$	−3.65463	+	20.7264i	−0.241505	+	1.36964i	0.586967	+	0.809611i	$0.300322\pi$
$229$	−3.65463	+	20.7264i	−0.241505	+	1.36964i	−0.828472	+	0.560030i	$0.810789\pi$
$230$	3.08028	+	5.33520i	0.203107	+	0.351792i
$231$	−4.35876	+	3.65743i	−0.286785	+	0.240641i
$232$	4.50884	−	7.80955i	0.296020	−	0.512722i
$233$	−5.78323	−	10.0168i	−0.378872	−	0.656226i	0.612026	−	0.790837i	$-0.290355\pi$
$233$	−5.78323	−	10.0168i	−0.378872	−	0.656226i	−0.990898	+	0.134612i	$0.957021\pi$
$234$	11.9606	+	4.35330i	0.781889	+	0.284584i
$235$	5.61999	+	4.71574i	0.366608	+	0.307621i
$236$	−0.380924	+	0.659780i	−0.0247961	+	0.0429480i
$237$	0.802911	+	4.55353i	0.0521547	+	0.295784i
$238$	−1.95480	−	11.0862i	−0.126711	−	0.718614i
$239$	−8.99786	+	7.55010i	−0.582023	+	0.488376i	−0.885611	−	0.464428i	$-0.846260\pi$
$239$	−8.99786	+	7.55010i	−0.582023	+	0.488376i	0.303588	+	0.952804i	$0.401816\pi$
$240$	0.528795	−	0.192466i	0.0341336	−	0.0124236i
$241$	24.8126	−	9.03106i	1.59832	−	0.581741i	0.619238	−	0.785203i	$-0.287441\pi$
$241$	24.8126	−	9.03106i	1.59832	−	0.581741i	0.979083	+	0.203462i	$0.0652192\pi$
$242$	−0.710874	+	0.596494i	−0.0456967	+	0.0383441i
$243$	−2.27684	−	12.9126i	−0.146059	−	0.828344i
$244$	−1.46018	−	8.28108i	−0.0934783	−	0.530142i
$245$	−1.57538	+	2.72864i	−0.100647	+	0.174326i
$246$	−2.50514	−	2.10206i	−0.159722	−	0.134023i
$247$	−26.7882	−	9.75011i	−1.70449	−	0.620384i
$248$	−0.336982	−	0.583669i	−0.0213984	−	0.0370630i
$249$	3.39669	−	5.88325i	0.215257	−	0.372836i
$250$	0.766044	−	0.642788i	0.0484489	−	0.0406535i
$251$	2.00625	+	3.47492i	0.126633	+	0.219335i	0.922370	−	0.386307i	$-0.126250\pi$
$251$	2.00625	+	3.47492i	0.126633	+	0.219335i	−0.795737	+	0.605642i	$0.792916\pi$
$252$	1.48455	−	8.41929i	0.0935177	−	0.530365i
$253$	19.5514			1.22919
$254$	2.10224	−	11.9224i	0.131906	−	0.748077i
$255$	−1.52314	−	1.27806i	−0.0953824	−	0.0800354i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−4.83384	−	1.75938i	−0.301527	−	0.109747i	0.186826	−	0.982393i	$-0.440180\pi$
$257$	−4.83384	−	1.75938i	−0.301527	−	0.109747i	−0.488353	+	0.872646i	$0.662402\pi$
$258$	−2.25948			−0.140669
$259$	18.1123	+	6.89357i	1.12545	+	0.428345i
$260$	4.74343			0.294175
$261$	−22.7382	−	8.27602i	−1.40746	−	0.512273i
$262$	−8.94531	+	3.25583i	−0.552643	+	0.201146i
$263$	−24.3139	−	20.4018i	−1.49926	−	1.25803i	−0.881986	−	0.471275i	$-0.843794\pi$
$263$	−24.3139	−	20.4018i	−1.49926	−	1.25803i	−0.617271	−	0.786751i	$-0.711762\pi$
$264$	0.310120	−	1.75878i	0.0190866	−	0.108245i
$265$	−10.8368			−0.665701
$266$	−3.32495	+	18.8567i	−0.203866	+	1.15618i
$267$	−3.32029	−	5.75092i	−0.203199	−	0.351950i
$268$	−5.36507	+	4.50183i	−0.327724	+	0.274993i
$269$	14.5891	−	25.2690i	0.889510	−	1.54068i	0.0490551	−	0.998796i	$-0.484379\pi$
$269$	14.5891	−	25.2690i	0.889510	−	1.54068i	0.840455	−	0.541881i	$-0.182288\pi$
$270$	−1.59910	−	2.76972i	−0.0973179	−	0.168560i
$271$	27.8486	+	10.1361i	1.69168	+	0.615722i	0.994836	−	0.101499i	$-0.0323638\pi$
$271$	27.8486	+	10.1361i	1.69168	+	0.615722i	0.696846	+	0.717221i	$0.254586\pi$
$272$	2.70668	+	2.27118i	0.164117	+	0.137710i
$273$	−4.25219	+	7.36502i	−0.257354	+	0.445751i
$274$	1.90643	+	10.8119i	0.115172	+	0.653171i
$275$	−0.551098	−	3.12543i	−0.0332324	−	0.188471i
$276$	2.65568	−	2.22838i	0.159853	−	0.134133i
$277$	12.4238	−	4.52188i	0.746472	−	0.271693i	0.0593514	−	0.998237i	$-0.481097\pi$
$277$	12.4238	−	4.52188i	0.746472	−	0.271693i	0.687120	+	0.726544i	$0.258875\pi$
$278$	−17.1309	+	6.23512i	−1.02744	+	0.373958i
$279$	−1.38537	+	1.16246i	−0.0829397	+	0.0695947i
$280$	−0.553248	−	3.13762i	−0.0330629	−	0.187509i
$281$	−4.00787	−	22.7298i	−0.239090	−	1.35595i	−0.833827	−	0.552025i	$-0.813855\pi$
$281$	−4.00787	−	22.7298i	−0.239090	−	1.35595i	0.594738	−	0.803920i	$-0.297256\pi$
$282$	2.06421	−	3.57531i	0.122922	−	0.212907i
$283$	0.134985	+	0.113266i	0.00802400	+	0.00673294i	0.646791	−	0.762667i	$-0.276111\pi$
$283$	0.134985	+	0.113266i	0.00802400	+	0.00673294i	−0.638767	+	0.769400i	$0.720555\pi$
$284$	−6.37947	−	2.32194i	−0.378552	−	0.137782i
$285$	1.69097	+	2.92885i	0.100165	+	0.173490i
$286$	7.52698	−	13.0371i	0.445080	−	0.770900i
$287$	−14.1834	+	11.9013i	−0.837219	+	0.702510i
$288$	1.34167	+	2.32383i	0.0790585	+	0.136933i
$289$	−0.784132	+	4.44703i	−0.0461254	+	0.261590i
$290$	−9.01769			−0.529537
$291$	0.791299	−	4.48768i	0.0463868	−	0.263073i
$292$	−3.35603	−	2.81605i	−0.196397	−	0.164797i
$293$	20.0608	−	7.30152i	1.17196	−	0.426559i	0.318606	−	0.947887i	$-0.396785\pi$
$293$	20.0608	−	7.30152i	1.17196	−	0.426559i	0.853356	+	0.521328i	$0.174563\pi$
$294$	1.66610	+	0.606412i	0.0971692	+	0.0353667i
$295$	0.761849			0.0443565
$296$	−5.74570	+	1.99672i	−0.333962	+	0.116057i
$297$	−10.1499			−0.588958
$298$	−5.45964	−	1.98715i	−0.316268	−	0.115112i
$299$	27.4598	−	9.99456i	1.58804	−	0.578000i
$300$	−0.431077	−	0.361717i	−0.0248883	−	0.0208837i
$301$	−2.22140	+	12.5982i	−0.128039	+	0.726147i
$302$	0.759011			0.0436762
$303$	−0.217516	+	1.23360i	−0.0124960	+	0.0708682i
$304$	−3.00494	−	5.20470i	−0.172345	−	0.298510i
$305$	−6.44154	+	5.40509i	−0.368841	+	0.309495i
$306$	4.74054	−	8.21086i	0.270999	−	0.469383i
$307$	−11.2614	−	19.5053i	−0.642721	−	1.11323i	−0.984823	−	0.173562i	$-0.944472\pi$
$307$	−11.2614	−	19.5053i	−0.642721	−	1.11323i	0.342102	−	0.939663i	$-0.388861\pi$
$308$	−9.50153	−	3.45827i	−0.541400	−	0.197053i
$309$	0.294937	+	0.247481i	0.0167784	+	0.0140787i
$310$	−0.336982	+	0.583669i	−0.0191393	+	0.0331502i
$311$	1.83992	+	10.4347i	0.104333	+	0.591699i	0.991485	+	0.130223i	$0.0415692\pi$
$311$	1.83992	+	10.4347i	0.104333	+	0.591699i	−0.887152	+	0.461477i	$0.847320\pi$
$312$	−0.463515	−	2.62873i	−0.0262414	−	0.148822i
$313$	0.597616	−	0.501459i	0.0337793	−	0.0283442i	−0.625742	−	0.780030i	$-0.715204\pi$
$313$	0.597616	−	0.501459i	0.0337793	−	0.0283442i	0.659521	+	0.751686i	$0.270759\pi$
$314$	−3.11173	+	1.13258i	−0.175605	+	0.0639150i
$315$	−8.03359	+	2.92399i	−0.452641	+	0.164748i
$316$	−6.29433	+	5.28157i	−0.354084	+	0.297112i
$317$	−3.22905	−	18.3128i	−0.181361	−	1.02855i	−0.930542	−	0.366186i	$-0.880664\pi$
$317$	−3.22905	−	18.3128i	−0.181361	−	1.02855i	0.749180	−	0.662366i	$-0.230448\pi$
$318$	1.05895	+	6.00558i	0.0593828	+	0.336776i
$319$	−14.3095	+	24.7847i	−0.801176	+	1.38768i
$320$	0.766044	+	0.642788i	0.0428232	+	0.0359329i
$321$	−10.4621	−	3.80789i	−0.583938	−	0.212536i
$322$	−9.81384	−	16.9981i	−0.546904	−	0.947265i
$323$	−10.6174	+	18.3899i	−0.590768	+	1.02324i
$324$	4.78799	−	4.01760i	0.265999	−	0.223200i
$325$	−2.37171	−	4.10793i	−0.131559	−	0.227867i
$326$	2.02082	−	11.4607i	0.111923	−	0.634747i
$327$	−11.4305			−0.632107
$328$	1.00913	−	5.72306i	0.0557199	−	0.316003i
$329$	−17.9054	−	15.0245i	−0.987159	−	0.828325i
$330$	−1.67821	+	0.610817i	−0.0923822	+	0.0336244i
$331$	8.85618	+	3.22339i	0.486780	+	0.177173i	0.573738	−	0.819039i	$-0.305493\pi$
$331$	8.85618	+	3.22339i	0.486780	+	0.177173i	−0.0869587	+	0.996212i	$0.527715\pi$
$332$	12.0722			0.662546
$333$	7.95372	+	14.2530i	0.435861	+	0.781061i
$334$	−8.37985			−0.458525
$335$	6.58123	+	2.39537i	0.359571	+	0.130873i
$336$	−1.68475	+	0.613200i	−0.0919109	+	0.0334528i
$337$	3.81134	+	3.19809i	0.207617	+	0.174211i	0.740667	−	0.671873i	$-0.234510\pi$
$337$	3.81134	+	3.19809i	0.207617	+	0.174211i	−0.533050	+	0.846084i	$0.678954\pi$
$338$	1.64968	−	9.35579i	0.0897307	−	0.508888i
$339$	9.51105			0.516569
$340$	0.613555	−	3.47964i	0.0332747	−	0.188710i
$341$	1.06946	+	1.85236i	0.0579145	+	0.100311i
$342$	−12.3536	+	10.3659i	−0.668007	+	0.560524i
$343$	−6.13189	+	10.6207i	−0.331091	+	0.573466i
$344$	−2.00760	−	3.47727i	−0.108243	−	0.187482i
$345$	−3.25767	−	1.18569i	−0.175387	−	0.0638356i
$346$	−14.4419	−	12.1182i	−0.776400	−	0.651477i
$347$	14.0536	−	24.3416i	0.754437	−	1.30672i	−0.191217	−	0.981548i	$-0.561243\pi$
$347$	14.0536	−	24.3416i	0.754437	−	1.30672i	0.945654	−	0.325175i	$-0.105423\pi$
$348$	0.881184	+	4.99744i	0.0472364	+	0.267891i
$349$	2.61460	+	14.8281i	0.139956	+	0.793732i	0.971279	+	0.237942i	$0.0764729\pi$
$349$	2.61460	+	14.8281i	0.139956	+	0.793732i	−0.831323	+	0.555790i	$0.812416\pi$
$350$	−2.44064	+	2.04794i	−0.130458	+	0.109467i
$351$	−14.2555	+	5.18858i	−0.760903	+	0.276946i
$352$	2.98225	−	1.08545i	0.158954	−	0.0578547i
$353$	−16.4953	+	13.8412i	−0.877958	+	0.736694i	−0.965758	−	0.259444i	$-0.916461\pi$
$353$	−16.4953	+	13.8412i	−0.877958	+	0.736694i	0.0878005	+	0.996138i	$0.472016\pi$
$354$	−0.0744458	−	0.422203i	−0.00395675	−	0.0224398i
$355$	1.17888	+	6.68575i	0.0625684	+	0.354843i
$356$	5.90031	−	10.2196i	0.312716	−	0.541640i
$357$	4.85275	+	4.07194i	0.256835	+	0.215510i
$358$	−15.1168	−	5.50207i	−0.798949	−	0.290794i
$359$	−11.6634	−	20.2016i	−0.615572	−	1.06620i	−0.990284	−	0.139061i	$-0.955592\pi$
$359$	−11.6634	−	20.2016i	−0.615572	−	1.06620i	0.374712	−	0.927141i	$-0.377742\pi$
$360$	1.34167	−	2.32383i	0.0707120	−	0.122477i
$361$	13.1136	−	11.0036i	0.690189	−	0.579137i
$362$	5.04944	+	8.74589i	0.265393	+	0.459674i
$363$	0.0906797	−	0.514270i	0.00475945	−	0.0269922i
$364$	−15.1127			−0.792120
$365$	−0.760751	+	4.31443i	−0.0398195	+	0.225828i
$366$	3.62486	+	3.04162i	0.189474	+	0.158988i
$367$	22.3500	−	8.13474i	1.16666	−	0.424630i	0.315189	−	0.949029i	$-0.397932\pi$
$367$	22.3500	−	8.13474i	1.16666	−	0.424630i	0.851473	+	0.524399i	$0.175710\pi$
$368$	5.78903	+	2.10703i	0.301774	+	0.109837i
$369$	−15.5938			−0.811780
$370$	4.60206	+	3.97756i	0.239250	+	0.206784i
$371$	34.5264			1.79252
$372$	0.356388	+	0.129715i	0.0184779	+	0.00672540i
$373$	−23.6925	+	8.62338i	−1.22675	+	0.446502i	−0.872484	−	0.488642i	$-0.837492\pi$
$373$	−23.6925	+	8.62338i	−1.22675	+	0.446502i	−0.354269	+	0.935144i	$0.615270\pi$
$374$	−8.59005	−	7.20790i	−0.444181	−	0.372712i
$375$	−0.0977173	+	0.554183i	−0.00504610	+	0.0286179i
$376$	7.33638			0.378345
$377$	−7.42776	+	42.1249i	−0.382549	+	2.16954i
$378$	5.09476	+	8.82438i	0.262046	+	0.453877i
$379$	8.20272	−	6.88290i	0.421345	−	0.353551i	−0.407329	−	0.913281i	$-0.633540\pi$
$379$	8.20272	−	6.88290i	0.421345	−	0.353551i	0.828675	+	0.559731i	$0.189095\pi$
$380$	−3.00494	+	5.20470i	−0.154150	+	0.266996i
$381$	3.40630	+	5.89989i	0.174510	+	0.302261i
$382$	8.93364	+	3.25158i	0.457085	+	0.166365i
$383$	4.34423	+	3.64524i	0.221980	+	0.186263i	0.746995	−	0.664830i	$-0.231496\pi$
$383$	4.34423	+	3.64524i	0.221980	+	0.186263i	−0.525015	+	0.851093i	$0.675940\pi$
$384$	0.281366	−	0.487340i	0.0143584	−	0.0248695i
$385$	1.75581	+	9.95770i	0.0894844	+	0.507491i
$386$	−0.455672	−	2.58425i	−0.0231931	−	0.131535i
$387$	−8.25346	+	6.92547i	−0.419547	+	0.352042i
$388$	7.60948	−	2.76962i	0.386313	−	0.140606i
$389$	−10.4964	+	3.82039i	−0.532191	+	0.193702i	−0.594116	−	0.804379i	$-0.702498\pi$
$389$	−10.4964	+	3.82039i	−0.532191	+	0.193702i	0.0619256	+	0.998081i	$0.480276\pi$
$390$	−2.04479	+	1.71578i	−0.103542	+	0.0868818i
$391$	−3.77984	−	21.4365i	−0.191155	−	1.08409i
$392$	0.547123	+	3.10289i	0.0276339	+	0.156720i
$393$	2.67843	−	4.63918i	0.135109	−	0.234016i
$394$	−8.15269	−	6.84092i	−0.410726	−	0.344640i
$395$	7.72114	+	2.81027i	0.388493	+	0.141400i
$396$	−4.25797	−	7.37503i	−0.213971	−	0.370609i
$397$	2.93638	−	5.08596i	0.147373	−	0.255257i	−0.782883	−	0.622169i	$-0.786252\pi$
$397$	2.93638	−	5.08596i	0.147373	−	0.255257i	0.930256	+	0.366912i	$0.119585\pi$
$398$	4.89576	−	4.10803i	0.245402	−	0.205917i
$399$	−5.38748	−	9.33139i	−0.269712	−	0.467154i
$400$	0.173648	−	0.984808i	0.00868241	−	0.0492404i
$401$	7.59493			0.379273			0.189636	−	0.981854i	$-0.439269\pi$
$401$	7.59493			0.379273			0.189636	+	0.981854i	$0.439269\pi$
$402$	0.684373	−	3.88127i	0.0341334	−	0.193580i
$403$	2.44897	+	2.05493i	0.121992	+	0.102363i
$404$	−2.09173	+	0.761328i	−0.104068	+	0.0378775i
$405$	−5.87334	−	2.13772i	−0.291848	−	0.106224i
$406$	28.7306			1.42587
$407$	18.2348	−	6.33689i	0.903866	−	0.314108i
$408$	−1.98831			−0.0984361
$409$	13.1079	+	4.77089i	0.648144	+	0.235905i	0.645110	−	0.764090i	$-0.276812\pi$
$409$	13.1079	+	4.77089i	0.648144	+	0.235905i	0.00303492	+	0.999995i	$0.499034\pi$
$410$	−5.46088	+	1.98760i	−0.269694	+	0.0981604i
$411$	−4.73267	−	3.97118i	−0.233445	−	0.195884i
$412$	−0.118808	+	0.673791i	−0.00585323	+	0.0331953i
$413$	−2.42727			−0.119438
$414$	2.87055	−	16.2797i	0.141080	−	0.800102i
$415$	−6.03608	−	10.4548i	−0.296300	−	0.513206i
$416$	3.63368	−	3.04902i	0.178156	−	0.149490i
$417$	5.12938	−	8.88434i	0.251187	−	0.435068i
$418$	9.53660	+	16.5179i	0.466450	+	0.807916i
$419$	−6.39031	−	2.32588i	−0.312187	−	0.113627i	0.181175	−	0.983451i	$-0.442010\pi$
$419$	−6.39031	−	2.32588i	−0.312187	−	0.113627i	−0.493362	+	0.869824i	$0.664232\pi$
$420$	1.37342	+	1.15244i	0.0670162	+	0.0562333i
$421$	16.1243	−	27.9280i	0.785849	−	1.36113i	−0.142642	−	0.989774i	$-0.545560\pi$
$421$	16.1243	−	27.9280i	0.785849	−	1.36113i	0.928491	−	0.371355i	$-0.121107\pi$
$422$	−1.43257	−	8.12453i	−0.0697366	−	0.395496i
$423$	−3.41843	−	19.3869i	−0.166210	−	0.942623i
$424$	−8.30150	+	6.96578i	−0.403156	+	0.338288i
$425$	−3.32024	+	1.20847i	−0.161055	+	0.0586193i
$426$	3.58993	−	1.30663i	0.173933	−	0.0633063i
$427$	20.5229	−	17.2208i	0.993173	−	0.833371i
$428$	−3.43560	−	19.4842i	−0.166066	−	0.941806i
$429$	1.47103	+	8.34264i	0.0710221	+	0.402786i
$430$	−2.00760	+	3.47727i	−0.0968151	+	0.167689i
$431$	−4.18063	−	3.50797i	−0.201374	−	0.168973i	0.536524	−	0.843885i	$-0.319737\pi$
$431$	−4.18063	−	3.50797i	−0.201374	−	0.168973i	−0.737898	+	0.674912i	$0.764181\pi$
$432$	−3.00532	−	1.09385i	−0.144593	−	0.0526277i
$433$	7.18721	+	12.4486i	0.345395	+	0.598243i	0.985426	−	0.170107i	$-0.0544114\pi$
$433$	7.18721	+	12.4486i	0.345395	+	0.598243i	−0.640030	+	0.768350i	$0.721078\pi$
$434$	1.07363	−	1.85959i	0.0515360	−	0.0892630i
$435$	3.88732	−	3.26185i	0.186383	−	0.156394i
$436$	−10.1562	−	17.5911i	−0.486396	−	0.842462i
$437$	−6.42917	+	36.4617i	−0.307549	+	1.74420i
$438$	2.46532			0.117798
$439$	−4.77357	+	27.0723i	−0.227830	+	1.29209i	0.629370	+	0.777106i	$0.283313\pi$
$439$	−4.77357	+	27.0723i	−0.227830	+	1.29209i	−0.857200	+	0.514984i	$0.827798\pi$
$440$	−2.43115	−	2.03998i	−0.115901	−	0.0972522i
$441$	7.94466	−	2.89162i	0.378317	−	0.137696i
$442$	−15.7493	−	5.73228i	−0.749118	−	0.272657i
$443$	−21.2054			−1.00750			−0.503750	−	0.863850i	$-0.668047\pi$
$443$	−21.2054			−1.00750			−0.503750	+	0.863850i	$0.668047\pi$
$444$	1.75459	−	2.93906i	0.0832694	−	0.139482i
$445$	−11.8006			−0.559403
$446$	13.7373	+	4.99996i	0.650479	+	0.236755i
$447$	3.07231	−	1.11823i	0.145315	−	0.0528905i
$448$	−2.44064	−	2.04794i	−0.115309	−	0.0967560i
$449$	−0.830899	+	4.71226i	−0.0392125	+	0.222385i	−0.998117	−	0.0613451i	$-0.980461\pi$
$449$	−0.830899	+	4.71226i	−0.0392125	+	0.222385i	0.958904	+	0.283730i	$0.0915721\pi$
$450$	−2.68333			−0.126494
$451$	−3.20262	+	18.1630i	−0.150805	+	0.855260i
$452$	8.45079	+	14.6372i	0.397492	+	0.688476i
$453$	−0.327193	+	0.274547i	−0.0153728	+	0.0128993i
$454$	4.38747	−	7.59932i	0.205914	−	0.356654i
$455$	7.55634	+	13.0880i	0.354247	+	0.613573i
$456$	3.17799	+	1.15669i	0.148823	+	0.0541671i
$457$	6.92025	+	5.80678i	0.323716	+	0.271630i	0.790133	−	0.612935i	$-0.210011\pi$
$457$	6.92025	+	5.80678i	0.323716	+	0.271630i	−0.466418	+	0.884565i	$0.654456\pi$
$458$	10.5231	−	18.2265i	0.491711	−	0.851669i
$459$	1.96227	+	11.1286i	0.0915907	+	0.519437i
$460$	−1.06977	−	6.06696i	−0.0498782	−	0.282873i
$461$	−27.4929	+	23.0693i	−1.28047	+	1.07444i	−0.287293	+	0.957843i	$0.592755\pi$
$461$	−27.4929	+	23.0693i	−1.28047	+	1.07444i	−0.993179	+	0.116601i	$0.962800\pi$
$462$	5.34681	−	1.94608i	0.248756	−	0.0905398i
$463$	−27.1325	+	9.87541i	−1.26095	+	0.458949i	−0.884089	−	0.467319i	$-0.845220\pi$
$463$	−27.1325	+	9.87541i	−1.26095	+	0.458949i	−0.376864	+	0.926269i	$0.622998\pi$
$464$	−6.90795	+	5.79646i	−0.320693	+	0.269094i
$465$	−0.0658579	−	0.373499i	−0.00305409	−	0.0173206i
$466$	2.00849	+	11.3907i	0.0930417	+	0.527666i
$467$	0.661683	−	1.14607i	0.0306190	−	0.0530337i	−0.850310	−	0.526282i	$-0.823585\pi$
$467$	0.661683	−	1.14607i	0.0306190	−	0.0530337i	0.880929	+	0.473249i	$0.156919\pi$
$468$	−9.75037	−	8.18153i	−0.450711	−	0.378191i
$469$	−20.9680	−	7.63172i	−0.968211	−	0.352400i
$470$	−3.66819	−	6.35349i	−0.169201	−	0.293065i
$471$	0.931724	−	1.61379i	0.0429316	−	0.0743597i
$472$	0.583610	−	0.489707i	0.0268628	−	0.0225406i
$473$	6.37141	+	11.0356i	0.292958	+	0.507418i
$474$	0.802911	−	4.55353i	0.0368789	−	0.209151i
$475$	6.00987			0.275752
$476$	−1.95480	+	11.0862i	−0.0895982	+	0.508137i
$477$	22.2757	+	18.6915i	1.01993	+	0.855826i
$478$	11.0375	−	4.01733i	0.504844	−	0.183748i
$479$	14.5189	+	5.28445i	0.663386	+	0.241453i	0.651697	−	0.758479i	$-0.274057\pi$
$479$	14.5189	+	5.28445i	0.663386	+	0.241453i	0.0116883	+	0.999932i	$0.496279\pi$
$480$	−0.562732			−0.0256851
$481$	22.3713	−	18.2217i	1.02004	−	0.830836i
$482$	−26.4050			−1.20272
$483$	10.3790	+	3.77765i	0.472262	+	0.171889i
$484$	0.872016	−	0.317388i	0.0396371	−	0.0144267i
$485$	−6.20331	−	5.20519i	−0.281678	−	0.236356i
$486$	−2.27684	+	12.9126i	−0.103280	+	0.585728i
$487$	7.71991			0.349823			0.174911	−	0.984584i	$-0.444036\pi$
$487$	7.71991			0.349823			0.174911	+	0.984584i	$0.444036\pi$
$488$	−1.46018	+	8.28108i	−0.0660992	+	0.374867i
$489$	3.27438	+	5.67140i	0.148073	+	0.256469i
$490$	2.41362	−	2.02527i	0.109036	−	0.0914923i
$491$	14.0065	−	24.2599i	0.632103	−	1.09484i	−0.355018	−	0.934860i	$-0.615525\pi$
$491$	14.0065	−	24.2599i	0.632103	−	1.09484i	0.987121	−	0.159976i	$-0.0511416\pi$
$492$	1.63511	+	2.83210i	0.0737166	+	0.127681i
$493$	29.9409	+	10.8976i	1.34847	+	0.490802i
$494$	21.8379	+	18.3242i	0.982535	+	0.824445i
$495$	−4.25797	+	7.37503i	−0.191382	+	0.331483i
$496$	0.117032	+	0.663724i	0.00525491	+	0.0298021i
$497$	−3.75594	−	21.3010i	−0.168477	−	0.955479i
$498$	−5.20404	+	4.36670i	−0.233198	+	0.195677i
$499$	33.2363	−	12.0970i	1.48786	−	0.541537i	0.534974	−	0.844868i	$-0.320321\pi$
$499$	33.2363	−	12.0970i	1.48786	−	0.541537i	0.952885	+	0.303332i	$0.0980990\pi$
$500$	−0.939693	+	0.342020i	−0.0420243	+	0.0152956i
$501$	3.61236	−	3.03113i	0.161388	−	0.135421i
$502$	−0.696762	−	3.95154i	−0.0310980	−	0.176366i
$503$	0.811504	+	4.60227i	0.0361832	+	0.205205i	0.997540	−	0.0701006i	$-0.0223320\pi$
$503$	0.811504	+	4.60227i	0.0361832	+	0.205205i	−0.961357	+	0.275306i	$0.911221\pi$
$504$	−4.27458	+	7.40380i	−0.190405	+	0.329791i
$505$	1.70519	+	1.43083i	0.0758802	+	0.0636710i
$506$	−18.3723	−	6.68697i	−0.816749	−	0.297272i
$507$	2.67301	+	4.62979i	0.118713	+	0.205616i
$508$	−6.05316	+	10.4844i	−0.268565	+	0.465169i
$509$	−25.0946	+	21.0569i	−1.11230	+	0.933330i	−0.998190	−	0.0601376i	$-0.980846\pi$
$509$	−25.0946	+	21.0569i	−1.11230	+	0.933330i	−0.114110	+	0.993468i	$0.536402\pi$
$510$	0.994156	+	1.72193i	0.0440220	+	0.0762483i
$511$	2.42377	−	13.7459i	0.107221	−	0.608082i
$512$	1.00000			0.0441942
$513$	3.33764	−	18.9287i	0.147361	−	0.835723i
$514$	3.94059	+	3.30654i	0.173812	+	0.145845i
$515$	0.642924	−	0.234005i	0.0283306	−	0.0103115i
$516$	2.12322	+	0.772788i	0.0934694	+	0.0340201i
$517$	−23.2831			−1.02399
$518$	−14.6623	−	12.6726i	−0.644224	−	0.556803i
$519$	10.6089			0.465680
$520$	−4.45737	−	1.62235i	−0.195468	−	0.0711447i
$521$	−31.1001	+	11.3195i	−1.36252	+	0.495917i	−0.916833	−	0.399271i	$-0.869263\pi$
$521$	−31.1001	+	11.3195i	−1.36252	+	0.495917i	−0.445688	+	0.895188i	$0.647041\pi$
$522$	18.5363	+	15.5538i	0.811313	+	0.680772i
$523$	4.33496	−	24.5848i	0.189554	−	1.07502i	−0.730408	−	0.683011i	$-0.760670\pi$
$523$	4.33496	−	24.5848i	0.189554	−	1.07502i	0.919963	−	0.392006i	$-0.128219\pi$
$524$	9.51940			0.415857
$525$	0.311330	−	1.76564i	0.0135876	−	0.0770588i
$526$	15.8697	+	27.4872i	0.691954	+	1.19850i
$527$	1.82420	−	1.53069i	0.0794636	−	0.0666779i
$528$	−0.892955	+	1.54664i	−0.0388609	+	0.0673090i
$529$	−7.47621	−	12.9492i	−0.325052	−	0.563007i
$530$	10.1833	+	3.70642i	0.442334	+	0.160996i
$531$	−1.56602	−	1.31405i	−0.0679595	−	0.0570248i
$532$	9.57380	−	16.5823i	0.415077	−	0.718935i
$533$	4.78673	+	27.1469i	0.207337	+	1.17586i
$534$	1.15313	+	6.53970i	0.0499006	+	0.283001i
$535$	−15.1560	+	12.7174i	−0.655253	+	0.549822i
$536$	6.58123	−	2.39537i	0.284266	−	0.103464i
$537$	8.50671	−	3.09619i	0.367092	−	0.133610i
$538$	−22.3517	+	18.7553i	−0.963651	+	0.808600i
$539$	−1.73638	−	9.84747i	−0.0747910	−	0.424161i
$540$	0.555360	+	3.14960i	0.0238989	+	0.135537i
$541$	11.0639	−	19.1632i	0.475673	−	0.823890i	−0.523939	−	0.851756i	$-0.675538\pi$
$541$	11.0639	−	19.1632i	0.475673	−	0.823890i	0.999612	+	0.0278661i	$0.00887120\pi$
$542$	−22.7024	−	19.0496i	−0.975151	−	0.818249i
$543$	−5.34024	−	1.94369i	−0.229171	−	0.0834116i
$544$	−1.76666	−	3.05995i	−0.0757450	−	0.131194i
$545$	−10.1562	+	17.5911i	−0.435046	+	0.753521i
$546$	6.51474	−	5.46651i	0.278805	−	0.233945i
$547$	−14.5447	−	25.1922i	−0.621887	−	1.07714i	−0.989134	−	0.147017i	$-0.953033\pi$
$547$	−14.5447	−	25.1922i	−0.621887	−	1.07714i	0.367247	−	0.930124i	$-0.380301\pi$
$548$	1.90643	−	10.8119i	0.0814386	−	0.461862i
$549$	22.5637			0.962995
$550$	−0.551098	+	3.12543i	−0.0234989	+	0.133269i
$551$	−41.5159	−	34.8360i	−1.76864	−	1.48406i
$552$	−3.25767	+	1.18569i	−0.138656	+	0.0504665i
$553$	−24.5998	−	8.95358i	−1.04609	−	0.380745i
$554$	−13.2211			−0.561711
$555$	−3.42260	−	0.0499935i	−0.145281	−	0.00212210i
$556$	18.2303			0.773136
$557$	13.5863	+	4.94502i	0.575672	+	0.209527i	0.613416	−	0.789760i	$-0.289795\pi$
$557$	13.5863	+	4.94502i	0.575672	+	0.209527i	−0.0377441	+	0.999287i	$0.512017\pi$
$558$	1.69940	−	0.618532i	0.0719415	−	0.0261846i
$559$	14.5899	+	12.2424i	0.617089	+	0.517799i
$560$	−0.553248	+	3.13762i	−0.0233790	+	0.132589i
$561$	6.31020			0.266417
$562$	−4.00787	+	22.7298i	−0.169062	+	0.958798i
$563$	−0.752545	−	1.30345i	−0.0317160	−	0.0549337i	0.849732	−	0.527215i	$-0.176764\pi$
$563$	−0.752545	−	1.30345i	−0.0317160	−	0.0549337i	−0.881448	+	0.472282i	$0.843431\pi$
$564$	−3.16255	+	2.65369i	−0.133167	+	0.111741i
$565$	8.45079	−	14.6372i	0.355527	−	0.615791i
$566$	−0.0881049	−	0.152602i	−0.00370333	−	0.00641435i
$567$	18.7126	+	6.81083i	0.785855	+	0.286028i
$568$	5.20059	+	4.36381i	0.218212	+	0.183102i
$569$	1.94587	−	3.37034i	0.0815750	−	0.141292i	−0.822352	−	0.568980i	$-0.807338\pi$
$569$	1.94587	−	3.37034i	0.0815750	−	0.141292i	0.903927	+	0.427688i	$0.140672\pi$
$570$	−0.587269	−	3.33057i	−0.0245980	−	0.139502i
$571$	6.82532	+	38.7083i	0.285631	+	1.61989i	0.703023	+	0.711167i	$0.251833\pi$
$571$	6.82532	+	38.7083i	0.285631	+	1.61989i	−0.417392	+	0.908727i	$0.637056\pi$
$572$	−11.5320	+	9.67650i	−0.482177	+	0.404595i
$573$	−5.02724	+	1.82977i	−0.210016	+	0.0764396i
$574$	17.3985	−	6.33254i	0.726199	−	0.264315i
$575$	−4.71926	+	3.95993i	−0.196807	+	0.165140i
$576$	−0.465956	−	2.64257i	−0.0194148	−	0.110107i
$577$	3.13045	+	17.7537i	0.130322	+	0.739095i	0.978003	+	0.208589i	$0.0668871\pi$
$577$	3.13045	+	17.7537i	0.130322	+	0.739095i	−0.847681	+	0.530506i	$0.822002\pi$
$578$	2.25782	−	3.91066i	0.0939129	−	0.162662i
$579$	1.13120	+	0.949186i	0.0470109	+	0.0394468i
$580$	8.47385	+	3.08423i	0.351858	+	0.128066i
$581$	19.2311	+	33.3092i	0.797841	+	1.38190i
$582$	−2.27846	+	3.94640i	−0.0944450	+	0.163584i
$583$	26.3460	−	22.1069i	1.09114	−	0.915575i
$584$	2.19049	+	3.79405i	0.0906433	+	0.156999i
$585$	−2.21023	+	12.5348i	−0.0913817	+	0.518251i
$586$	−21.3482			−0.881886
$587$	3.11790	−	17.6825i	0.128690	−	0.729835i	−0.850358	−	0.526204i	$-0.823615\pi$
$587$	3.11790	−	17.6825i	0.128690	−	0.729835i	0.979048	−	0.203631i	$-0.0652742\pi$
$588$	−1.35822	−	1.13968i	−0.0560121	−	0.0469997i
$589$	−3.80616	+	1.38533i	−0.156830	+	0.0570815i
$590$	−0.715904	−	0.260568i	−0.0294733	−	0.0107274i
$591$	5.98892			0.246351
$592$	6.08211	+	0.0888407i	0.249973	+	0.00365133i
$593$	−4.67650			−0.192041			−0.0960205	−	0.995379i	$-0.530611\pi$
$593$	−4.67650			−0.192041			−0.0960205	+	0.995379i	$0.530611\pi$
$594$	9.53781	+	3.47148i	0.391341	+	0.142436i
$595$	10.5784	−	3.85021i	0.433670	−	0.157843i
$596$	4.45074	+	3.73461i	0.182309	+	0.152976i
$597$	−0.624507	+	3.54176i	−0.0255594	+	0.144954i
$598$	−29.2221			−1.19498
$599$	−1.26147	+	7.15413i	−0.0515421	+	0.292310i	−0.999673	−	0.0255703i	$-0.991860\pi$
$599$	−1.26147	+	7.15413i	−0.0515421	+	0.292310i	0.948131	+	0.317880i	$0.102971\pi$
$600$	0.281366	+	0.487340i	0.0114867	+	0.0198956i
$601$	5.15286	−	4.32376i	0.210190	−	0.176370i	−0.531615	−	0.846986i	$-0.678415\pi$
$601$	5.15286	−	4.32376i	0.210190	−	0.176370i	0.741805	+	0.670616i	$0.233970\pi$
$602$	6.39627	−	11.0787i	0.260692	−	0.451532i
$603$	−9.39650	−	16.2752i	−0.382655	−	0.662778i
$604$	−0.713237	−	0.259597i	−0.0290212	−	0.0105629i
$605$	−0.710874	−	0.596494i	−0.0289011	−	0.0242509i
$606$	0.626313	−	1.08481i	0.0254422	−	0.0440672i
$607$	−3.78274	−	21.4530i	−0.153537	−	0.870750i	−0.960111	−	0.279618i	$-0.909792\pi$
$607$	−3.78274	−	21.4530i	−0.153537	−	0.870750i	0.806575	−	0.591132i	$-0.201319\pi$
$608$	1.04360	+	5.91857i	0.0423237	+	0.240030i
$609$	−12.3851	+	10.3923i	−0.501870	+	0.421119i
$610$	7.90172	−	2.87599i	0.319931	−	0.116445i
$611$	−32.7009	+	11.9022i	−1.32294	+	0.481510i
$612$	−7.26293	+	6.09432i	−0.293586	+	0.246348i
$613$	2.75313	+	15.6138i	0.111198	+	0.630635i	0.988563	+	0.150811i	$0.0481884\pi$
$613$	2.75313	+	15.6138i	0.111198	+	0.630635i	−0.877365	+	0.479824i	$0.840701\pi$
$614$	3.91104	+	22.1806i	0.157837	+	0.895136i
$615$	1.63511	−	2.83210i	0.0659342	−	0.114201i
$616$	7.74571	+	6.49943i	0.312084	+	0.261869i
$617$	11.5123	+	4.19014i	0.463469	+	0.168689i	0.563191	−	0.826326i	$-0.309573\pi$
$617$	11.5123	+	4.19014i	0.463469	+	0.168689i	−0.0997228	+	0.995015i	$0.531796\pi$
$618$	−0.192506	−	0.333431i	−0.00774374	−	0.0134126i
$619$	−12.9787	+	22.4798i	−0.521659	+	0.903540i	0.478023	+	0.878347i	$0.341353\pi$
$619$	−12.9787	+	22.4798i	−0.521659	+	0.903540i	−0.999683	+	0.0251932i	$0.991980\pi$
$620$	0.516286	−	0.433215i	0.0207345	−	0.0173983i
$621$	9.85131	+	17.0630i	0.395320	+	0.684714i
$622$	1.83992	−	10.4347i	0.0737743	−	0.418395i
$623$	37.5971			1.50630
$624$	−0.463515	+	2.62873i	−0.0185555	+	0.105233i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	−0.733085	+	0.266821i	−0.0293000	+	0.0106643i
$627$	−10.0858	−	3.67093i	−0.402788	−	0.146603i
$628$	3.31143			0.132141
$629$	−10.4732	−	18.7679i	−0.417593	−	0.748325i
$630$	8.54917			0.340607
$631$	−27.9453	−	10.1712i	−1.11248	−	0.404911i	−0.280579	−	0.959831i	$-0.590527\pi$
$631$	−27.9453	−	10.1712i	−1.11248	−	0.404911i	−0.831904	+	0.554920i	$0.812749\pi$
$632$	7.72114	−	2.81027i	0.307131	−	0.111786i
$633$	3.55633	+	2.98412i	0.141351	+	0.118608i
$634$	−3.22905	+	18.3128i	−0.128242	+	0.727296i
$635$	12.1063			0.480424
$636$	1.05895	−	6.00558i	0.0419900	−	0.238137i
$637$	−7.47270	−	12.9431i	−0.296079	−	0.512824i
$638$	21.9234	−	18.3959i	0.867955	−	0.728301i
$639$	9.10843	−	15.7763i	0.360324	−	0.624099i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−10.3230	−	3.75725i	−0.407732	−	0.148402i	0.130008	−	0.991513i	$-0.458500\pi$
$641$	−10.3230	−	3.75725i	−0.407732	−	0.148402i	−0.537740	+	0.843111i	$0.680722\pi$
$642$	8.52878	+	7.15650i	0.336604	+	0.282445i
$643$	−0.377740	+	0.654266i	−0.0148966	+	0.0258017i	−0.873378	−	0.487044i	$-0.838075\pi$
$643$	−0.377740	+	0.654266i	−0.0148966	+	0.0258017i	0.858481	+	0.512845i	$0.171409\pi$
$644$	3.40831	+	19.3295i	0.134306	+	0.761689i
$645$	−0.392355	−	2.22515i	−0.0154490	−	0.0876154i
$646$	16.2668	−	13.6495i	0.640009	−	0.537031i
$647$	−27.0373	+	9.84077i	−1.06295	+	0.386881i	−0.813534	−	0.581517i	$-0.802459\pi$
$647$	−27.0373	+	9.84077i	−1.06295	+	0.386881i	−0.249412	+	0.968398i	$0.580237\pi$
$648$	−5.87334	+	2.13772i	−0.230726	+	0.0839776i
$649$	−1.85217	+	1.55416i	−0.0727040	+	0.0610059i
$650$	0.823688	+	4.67137i	0.0323077	+	0.183226i
$651$	0.209825	+	1.18998i	0.00822369	+	0.0466388i
$652$	−5.81873	+	10.0783i	−0.227879	+	0.394698i
$653$	−15.4821	−	12.9910i	−0.605863	−	0.508379i	0.287461	−	0.957792i	$-0.407189\pi$
$653$	−15.4821	−	12.9910i	−0.605863	−	0.508379i	−0.893324	+	0.449413i	$0.851633\pi$
$654$	10.7411	+	3.90945i	0.420012	+	0.152872i
$655$	−4.75970	−	8.24404i	−0.185977	−	0.322121i
$656$	−2.90567	+	5.03277i	−0.113447	+	0.196497i
$657$	9.00535	−	7.55639i	0.351332	−	0.294803i
$658$	11.6870	+	20.2424i	0.455605	+	0.789131i
$659$	0.953433	−	5.40719i	0.0371405	−	0.210634i	−0.960590	−	0.277969i	$-0.910339\pi$
$659$	0.953433	−	5.40719i	0.0371405	−	0.210634i	0.997730	+	0.0673352i	$0.0214497\pi$
$660$	1.78591			0.0695165
$661$	−7.58609	+	43.0228i	−0.295065	+	1.67339i	0.371875	+	0.928283i	$0.378715\pi$
$661$	−7.58609	+	43.0228i	−0.295065	+	1.67339i	−0.666940	+	0.745112i	$0.732396\pi$
$662$	−7.21962	−	6.05798i	−0.280599	−	0.235450i
$663$	8.86263	−	3.22573i	0.344196	−	0.125277i
$664$	−11.3441	−	4.12892i	−0.440237	−	0.160233i
$665$	−19.1476			−0.742512
$666$	−2.59923	−	16.1138i	−0.100718	−	0.624397i
$667$	55.5539			2.15106
$668$	7.87448	+	2.86608i	0.304673	+	0.110892i
$669$	−7.73041	+	2.81364i	−0.298875	+	0.108782i
$670$	−5.36507	−	4.50183i	−0.207271	−	0.173921i
$671$	4.63409	−	26.2812i	0.178897	−	1.01457i
$672$	1.79288			0.0691618
$673$	−5.55537	+	31.5061i	−0.214144	+	1.21447i	0.668242	+	0.743944i	$0.267047\pi$
$673$	−5.55537	+	31.5061i	−0.214144	+	1.21447i	−0.882386	+	0.470527i	$0.844064\pi$
$674$	−2.48767	−	4.30878i	−0.0958216	−	0.165968i
$675$	2.44996	−	2.05576i	0.0942989	−	0.0791262i
$676$	−4.75006	+	8.22734i	−0.182695	+	0.316436i
$677$	−14.6543	−	25.3819i	−0.563209	−	0.975506i	−0.997214	−	0.0745959i	$-0.976233\pi$
$677$	−14.6543	−	25.3819i	−0.563209	−	0.975506i	0.434005	−	0.900910i	$-0.357100\pi$
$678$	−8.93747	−	3.25297i	−0.343241	−	0.124930i
$679$	19.7639	+	16.5839i	0.758468	+	0.636431i
$680$	−1.76666	+	3.05995i	−0.0677484	+	0.117344i
$681$	0.857463	+	4.86292i	0.0328581	+	0.186347i
$682$	−0.371420	−	2.10642i	−0.0142224	−	0.0806592i
$683$	−9.28446	+	7.79059i	−0.355260	+	0.298099i	−0.802898	−	0.596116i	$-0.796710\pi$
$683$	−9.28446	+	7.79059i	−0.355260	+	0.298099i	0.447638	+	0.894215i	$0.352265\pi$
$684$	15.1539	−	5.51558i	0.579426	−	0.210894i
$685$	−10.3166	+	3.75493i	−0.394177	+	0.143469i
$686$	9.39460	−	7.88301i	0.358688	−	0.300975i
$687$	2.05658	+	11.6634i	0.0784632	+	0.444987i
$688$	0.697232	+	3.95420i	0.0265817	+	0.150753i
$689$	25.7019	−	44.5170i	0.979163	−	1.69596i
$690$	2.65568	+	2.22838i	0.101100	+	0.0848328i
$691$	−22.8745	−	8.32565i	−0.870188	−	0.316722i	−0.131945	−	0.991257i	$-0.542122\pi$
$691$	−22.8745	−	8.32565i	−0.870188	−	0.316722i	−0.738243	+	0.674535i	$0.764344\pi$
$692$	9.42626	+	16.3268i	0.358333	+	0.620650i
$693$	13.5660	−	23.4970i	0.515330	−	0.892578i
$694$	−21.5314	+	18.0670i	−0.817320	+	0.685813i
$695$	−9.11514	−	15.7879i	−0.345757	−	0.598869i
$696$	0.881184	−	4.99744i	0.0334012	−	0.189428i
$697$	20.5334			0.777756
$698$	2.61460	−	14.8281i	0.0989641	−	0.561253i
$699$	−4.98604	−	4.18378i	−0.188589	−	0.158245i
$700$	2.99388	−	1.08968i	0.113158	−	0.0411862i
$701$	−9.73910	−	3.54474i	−0.367841	−	0.133883i	0.151485	−	0.988460i	$-0.451595\pi$
$701$	−9.73910	−	3.54474i	−0.367841	−	0.133883i	−0.519326	+	0.854577i	$0.673817\pi$
$702$	15.1704			0.572570
$703$	5.82151	+	36.0901i	0.219562	+	1.36116i
$704$	−3.17364			−0.119611
$705$	3.87944	+	1.41200i	0.146108	+	0.0531790i
$706$	20.2345	−	7.36476i	0.761536	−	0.277176i
$707$	−5.43279	−	4.55865i	−0.204321	−	0.171446i
$708$	−0.0744458	+	0.422203i	−0.00279785	+	0.0158674i
$709$	−22.2713			−0.836416			−0.418208	−	0.908351i	$-0.637342\pi$
$709$	−22.2713			−0.836416			−0.418208	+	0.908351i	$0.637342\pi$
$710$	1.17888	−	6.68575i	0.0442425	−	0.250912i
$711$	−11.0240	−	19.0942i	−0.413433	−	0.716088i
$712$	−9.03981	+	7.58530i	−0.338781	+	0.284271i
$713$	2.07599	−	3.59573i	0.0777466	−	0.134661i
$714$	−3.16741	−	5.48611i	−0.118537	−	0.205312i
$715$	14.1461	+	5.14876i	0.529034	+	0.192553i
$716$	12.3233	+	10.3405i	0.460545	+	0.386443i
$717$	−3.30489	+	5.72423i	−0.123423	+	0.213775i
$718$	4.05066	+	22.9725i	0.151169	+	0.857325i
$719$	0.882478	+	5.00478i	0.0329109	+	0.186647i	0.996831	−	0.0795434i	$-0.0253462\pi$
$719$	0.882478	+	5.00478i	0.0329109	+	0.186647i	−0.963921	+	0.266190i	$0.914235\pi$
$720$	−2.05555	+	1.72481i	−0.0766059	+	0.0642800i
$721$	−2.04837	+	0.745546i	−0.0762853	+	0.0277656i
$722$	−16.0862	+	5.85490i	−0.598666	+	0.217897i
$723$	11.3826	−	9.55115i	0.423324	−	0.355211i
$724$	−1.75365	−	9.94546i	−0.0651740	−	0.369620i
$725$	−1.56590	−	8.88069i	−0.0581562	−	0.329820i
$726$	−0.261102	+	0.452242i	−0.00969040	+	0.0167843i
$727$	−10.7862	−	9.05067i	−0.400037	−	0.335671i	0.420471	−	0.907306i	$-0.361865\pi$
$727$	−10.7862	−	9.05067i	−0.400037	−	0.335671i	−0.820508	+	0.571635i	$0.806309\pi$
$728$	14.2013	+	5.16884i	0.526334	+	0.191570i
$729$	5.68620	+	9.84879i	0.210600	+	0.364770i
$730$	2.19049	−	3.79405i	0.0810738	−	0.140424i
$731$	10.8679	−	9.11923i	0.401963	−	0.337287i
$732$	−2.36596	−	4.09796i	−0.0874483	−	0.151465i
$733$	−1.04067	+	5.90192i	−0.0384379	+	0.217992i	−0.997976	−	0.0635852i	$-0.979747\pi$
$733$	−1.04067	+	5.90192i	−0.0384379	+	0.217992i	0.959539	+	0.281577i	$0.0908576\pi$
$734$	−23.7844			−0.877898
$735$	−0.307884	+	1.74609i	−0.0113565	+	0.0644057i
$736$	−4.71926	−	3.95993i	−0.173954	−	0.145965i
$737$	−20.8865	+	7.60206i	−0.769364	+	0.280026i
$738$	14.6534	+	5.33339i	0.539398	+	0.196325i
$739$	−29.1927			−1.07387			−0.536936	−	0.843623i	$-0.680418\pi$
$739$	−29.1927			−1.07387			−0.536936	+	0.843623i	$0.680418\pi$
$740$	−2.96412	−	5.31169i	−0.108963	−	0.195261i
$741$	−16.0420			−0.589318
$742$	−32.4442	−	11.8087i	−1.19106	−	0.433512i
$743$	−0.822709	+	0.299441i	−0.0301823	+	0.0109854i	−0.357067	−	0.934079i	$-0.616223\pi$
$743$	−0.822709	+	0.299441i	−0.0301823	+	0.0109854i	0.326885	+	0.945064i	$0.394001\pi$
$744$	−0.290530	−	0.243784i	−0.0106514	−	0.00893755i
$745$	1.00890	−	5.72176i	0.0369633	−	0.209629i
$746$	25.2131			0.923116
$747$	−5.62509	+	31.9015i	−0.205811	+	1.16721i
$748$	5.60675	+	9.71118i	0.205003	+	0.355076i
$749$	48.2875	−	40.5180i	1.76439	−	1.48050i
$750$	0.281366	−	0.487340i	0.0102740	−	0.0177951i
$751$	−9.00831	−	15.6029i	−0.328718	−	0.569356i	0.653540	−	0.756892i	$-0.273283\pi$
$751$	−9.00831	−	15.6029i	−0.328718	−	0.569356i	−0.982258	+	0.187536i	$0.939950\pi$
$752$	−6.89394	−	2.50919i	−0.251396	−	0.0915008i
$753$	1.72970	+	1.45139i	0.0630336	+	0.0528915i
$754$	21.3874	−	37.0440i	0.778882	−	1.34906i
$755$	0.131801	+	0.747480i	0.00479672	+	0.0272036i
$756$	−1.76939	−	10.0347i	−0.0643521	−	0.364959i
$757$	23.8543	−	20.0161i	0.867000	−	0.727499i	−0.0964645	−	0.995336i	$-0.530753\pi$
$757$	23.8543	−	20.0161i	0.867000	−	0.727499i	0.963464	+	0.267837i	$0.0863090\pi$
$758$	−10.0621	+	3.66231i	−0.365473	+	0.133021i
$759$	10.3387	−	3.76297i	0.375270	−	0.136587i
$760$	4.60383	−	3.86307i	0.166998	−	0.140128i
$761$	6.16957	+	34.9894i	0.223647	+	1.26836i	0.865255	+	0.501331i	$0.167156\pi$
$761$	6.16957	+	34.9894i	0.223647	+	1.26836i	−0.641609	+	0.767032i	$0.721733\pi$
$762$	−1.18300	−	6.70911i	−0.0428554	−	0.243045i
$763$	32.3581	−	56.0458i	1.17144	−	2.02899i
$764$	−7.28277	−	6.11097i	−0.263481	−	0.221087i
$765$	8.90930	+	3.24272i	0.322116	+	0.117241i
$766$	−2.83549	−	4.91122i	−0.102451	−	0.177450i
$767$	−1.80689	+	3.12962i	−0.0652429	+	0.113004i
$768$	−0.431077	+	0.361717i	−0.0155552	+	0.0130523i
$769$	−11.1357	−	19.2876i	−0.401564	−	0.695528i	0.592351	−	0.805680i	$-0.298200\pi$
$769$	−11.1357	−	19.2876i	−0.401564	−	0.695528i	−0.993915	+	0.110151i	$0.964866\pi$
$770$	1.75581	−	9.95770i	0.0632750	−	0.358851i
$771$	−2.89473			−0.104251
$772$	−0.455672	+	2.58425i	−0.0164000	+	0.0930091i
$773$	−3.58292	−	3.00643i	−0.128869	−	0.108134i	0.576075	−	0.817397i	$-0.304583\pi$
$773$	−3.58292	−	3.00643i	−0.128869	−	0.108134i	−0.704944	+	0.709263i	$0.749028\pi$
$774$	10.1244	−	3.68497i	0.363913	−	0.132453i
$775$	−0.633318	−	0.230509i	−0.0227495	−	0.00828013i
$776$	−8.09784			−0.290696
$777$	10.9045	+	0.159280i	0.391196	+	0.00571415i
$778$	11.1701			0.400467
$779$	−32.8192	−	11.9452i	−1.17587	−	0.427982i
$780$	2.50830	−	0.912947i	0.0898116	−	0.0326887i
$781$	−16.5048	−	13.8492i	−0.590589	−	0.495563i
$782$	−3.77984	+	21.4365i	−0.135167	+	0.766569i
$783$	−28.8403			−1.03067
$784$	0.547123	−	3.10289i	0.0195401	−	0.110818i
$785$	−1.65572	−	2.86779i	−0.0590951	−	0.102356i
$786$	−4.10360	+	3.44333i	−0.146370	+	0.122819i
$787$	−5.03252	+	8.71658i	−0.179390	+	0.310712i	−0.941672	−	0.336533i	$-0.890746\pi$
$787$	−5.03252	+	8.71658i	−0.179390	+	0.310712i	0.762282	+	0.647245i	$0.224079\pi$
$788$	5.32129	+	9.21674i	0.189563	+	0.328333i
$789$	−16.7837	−	6.10876i	−0.597515	−	0.217478i
$790$	−6.29433	−	5.28157i	−0.223942	−	0.187910i
$791$	−26.9244	+	46.6345i	−0.957322	+	1.65813i
$792$	1.47878	+	8.38657i	0.0525461	+	0.298004i
$793$	−6.92625	−	39.2807i	−0.245958	−	1.39490i
$794$	−4.49879	+	3.77494i	−0.159656	+	0.133967i
$795$	−5.73046	+	2.08572i	−0.203239	+	0.0739728i
$796$	−6.00553	+	2.18584i	−0.212861	+	0.0774749i
$797$	19.1849	−	16.0980i	0.679563	−	0.570221i	−0.236316	−	0.971676i	$-0.575940\pi$
$797$	19.1849	−	16.0980i	0.679563	−	0.570221i	0.915879	+	0.401455i	$0.131496\pi$
$798$	1.87105	+	10.6113i	0.0662346	+	0.375635i
$799$	4.50127	+	25.5280i	0.159244	+	0.903115i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	24.2568	+	20.3539i	0.857072	+	0.719169i
$802$	−7.13690	−	2.59762i	−0.252013	−	0.0917251i
$803$	−6.95185	−	12.0410i	−0.245325	−	0.424916i
$804$	−1.97057	+	3.41314i	−0.0694968	+	0.120372i
$805$	15.0357	−	12.6164i	0.529938	−	0.444671i
$806$	−1.59845	−	2.76859i	−0.0563029	−	0.0975196i
$807$	2.85121	−	16.1700i	0.100367	−	0.569211i
$808$	2.22597			0.0783095
$809$	−1.05864	+	6.00387i	−0.0372200	+	0.211085i	−0.997746	−	0.0671056i	$-0.978624\pi$
$809$	−1.05864	+	6.00387i	−0.0372200	+	0.211085i	0.960526	+	0.278191i	$0.0897347\pi$
$810$	4.78799	+	4.01760i	0.168233	+	0.141164i
$811$	−1.96640	+	0.715713i	−0.0690498	+	0.0251321i	−0.376314	−	0.926492i	$-0.622809\pi$
$811$	−1.96640	+	0.715713i	−0.0690498	+	0.0251321i	0.307264	+	0.951624i	$0.400586\pi$
$812$	−26.9979	−	9.82644i	−0.947441	−	0.344840i
$813$	16.6770			0.584889
$814$	−19.3025	−	0.281949i	−0.676551	−	0.00988230i
$815$	11.6375			0.407642
$816$	1.86840	+	0.680043i	0.0654072	+	0.0238063i
$817$	−22.6756	+	8.25324i	−0.793318	+	0.288744i
$818$	−10.6857	−	8.96634i	−0.373616	−	0.313501i
$819$	7.04184	−	39.9363i	0.246062	−	1.39549i
$820$	5.81135			0.202941
$821$	−8.47858	+	48.0844i	−0.295905	+	1.67816i	0.367598	+	0.929985i	$0.380180\pi$
$821$	−8.47858	+	48.0844i	−0.295905	+	1.67816i	−0.663503	+	0.748174i	$0.730931\pi$
$822$	3.08903	+	5.35036i	0.107742	+	0.186615i
$823$	−34.5184	+	28.9644i	−1.20324	+	1.00964i	−0.203705	+	0.979032i	$0.565298\pi$
$823$	−34.5184	+	28.9644i	−1.20324	+	1.00964i	−0.999532	+	0.0306035i	$0.990257\pi$
$824$	0.342093	−	0.592522i	0.0119174	−	0.0206415i
$825$	−0.892955	−	1.54664i	−0.0310887	−	0.0538472i
$826$	2.28089	+	0.830175i	0.0793622	+	0.0288855i
$827$	−22.0396	−	18.4934i	−0.766392	−	0.643079i	0.173390	−	0.984853i	$-0.444528\pi$
$827$	−22.0396	−	18.4934i	−0.766392	−	0.643079i	−0.939782	+	0.341774i	$0.888972\pi$
$828$	−8.26541	+	14.3161i	−0.287243	+	0.497519i
$829$	1.18790	+	6.73693i	0.0412576	+	0.233983i	0.998463	−	0.0554269i	$-0.0176520\pi$
$829$	1.18790	+	6.73693i	0.0412576	+	0.233983i	−0.957205	+	0.289410i	$0.906541\pi$
$830$	2.09631	+	11.8888i	0.0727639	+	0.412665i
$831$	5.69932	−	4.78229i	0.197707	−	0.165896i
$832$	−4.45737	+	1.62235i	−0.154531	+	0.0562448i
$833$	−10.4613	+	3.80759i	−0.362461	+	0.131925i
$834$	−7.85866	+	6.59420i	−0.272123	+	0.228339i
$835$	−1.45515	−	8.25254i	−0.0503574	−	0.285591i
$836$	−3.31203	−	18.7834i	−0.114549	−	0.649639i
$837$	−1.07773	+	1.86669i	−0.0372519	+	0.0645221i
$838$	5.20942	+	4.37123i	0.179957	+	0.151001i
$839$	−17.6191	−	6.41285i	−0.608281	−	0.221396i	0.0194702	−	0.999810i	$-0.493802\pi$
$839$	−17.6191	−	6.41285i	−0.608281	−	0.221396i	−0.627751	+	0.778414i	$0.716024\pi$
$840$	−0.896439	−	1.55268i	−0.0309301	−	0.0535725i
$841$	−26.1593	+	45.3093i	−0.902046	+	1.56239i
$842$	−24.7038	+	20.7290i	−0.851349	+	0.714367i
$843$	−6.49404	−	11.2480i	−0.223667	−	0.387402i
$844$	−1.43257	+	8.12453i	−0.0493112	+	0.279658i
$845$	9.50012			0.326814
$846$	−3.41843	+	19.3869i	−0.117528	+	0.666535i
$847$	2.26486	+	1.90044i	0.0778216	+	0.0653000i
$848$	10.1833	−	3.70642i	0.349696	−	0.127279i
$849$	0.0931789	+	0.0339143i	0.00319789	+	0.00116394i
$850$	3.53332			0.121192
$851$	−28.3513	−	24.5040i	−0.971869	−	0.839986i
$852$	−3.82032			−0.130882
$853$	−4.18716	−	1.52400i	−0.143366	−	0.0521808i	0.269341	−	0.963045i	$-0.413194\pi$
$853$	−4.18716	−	1.52400i	−0.143366	−	0.0521808i	−0.412706	+	0.910864i	$0.635416\pi$
$854$	−25.1751	+	9.16297i	−0.861473	+	0.313551i
$855$	−12.3536	−	10.3659i	−0.422485	−	0.354507i
$856$	−3.43560	+	19.4842i	−0.117426	+	0.665957i
$857$	23.3982			0.799266			0.399633	−	0.916675i	$-0.369138\pi$
$857$	23.3982			0.799266			0.399633	+	0.916675i	$0.369138\pi$
$858$	1.47103	−	8.34264i	0.0502202	−	0.284813i
$859$	12.1098	+	20.9748i	0.413182	+	0.715652i	0.995236	−	0.0974985i	$-0.0310841\pi$
$859$	12.1098	+	20.9748i	0.413182	+	0.715652i	−0.582054	+	0.813150i	$0.697751\pi$
$860$	3.07582	−	2.58092i	0.104885	−	0.0880087i
$861$	−5.20952	+	9.02315i	−0.177540	+	0.307508i
$862$	2.72871	+	4.72627i	0.0929403	+	0.160977i
$863$	−45.3171	−	16.4941i	−1.54261	−	0.561465i	−0.575942	−	0.817490i	$-0.695365\pi$
$863$	−45.3171	−	16.4941i	−1.54261	−	0.561465i	−0.966670	+	0.256025i	$0.917587\pi$
$864$	2.44996	+	2.05576i	0.0833492	+	0.0699383i
$865$	9.42626	−	16.3268i	0.320502	−	0.555127i
$866$	−2.49609	−	14.1560i	−0.0848207	−	0.481042i
$867$	0.441256	+	2.50249i	0.0149858	+	0.0849889i
$868$	−1.64490	+	1.38023i	−0.0558315	+	0.0468482i
$869$	−24.5042	+	8.91879i	−0.831247	+	0.302549i
$870$	−4.76851	+	1.73559i	−0.161668	+	0.0588422i
$871$	−25.4488	+	21.3541i	−0.862301	+	0.723556i
$872$	3.52723	+	20.0039i	0.119447	+	0.677417i
$873$	3.77324	+	21.3991i	0.127705	+	0.724249i
$874$	18.5121	−	32.0638i	0.626180	−	1.08458i
$875$	−2.44064	−	2.04794i	−0.0825086	−	0.0692329i
$876$	−2.31664	−	0.843190i	−0.0782722	−	0.0284887i
$877$	−14.7055	−	25.4707i	−0.496570	−	0.860084i	0.503422	−	0.864040i	$-0.332074\pi$
$877$	−14.7055	−	25.4707i	−0.496570	−	0.860084i	−0.999992	+	0.00395646i	$0.998741\pi$
$878$	13.7450	−	23.8070i	0.463870	−	0.803446i
$879$	9.20273	−	7.72201i	0.310400	−	0.260457i
$880$	1.58682	+	2.74846i	0.0534918	+	0.0926505i
$881$	3.87864	−	21.9968i	0.130675	−	0.741092i	−0.847100	−	0.531433i	$-0.821654\pi$
$881$	3.87864	−	21.9968i	0.130675	−	0.741092i	0.977775	−	0.209659i	$-0.0672353\pi$
$882$	−8.45453			−0.284679
$883$	6.83225	−	38.7476i	0.229924	−	1.30396i	−0.623122	−	0.782125i	$-0.714136\pi$
$883$	6.83225	−	38.7476i	0.229924	−	1.30396i	0.853045	−	0.521837i	$-0.174753\pi$
$884$	12.8390	+	10.7732i	0.431821	+	0.362341i
$885$	0.402862	−	0.146630i	0.0135420	−	0.00492890i
$886$	19.9266	+	7.25268i	0.669446	+	0.243658i
$887$	−19.3658			−0.650239			−0.325120	−	0.945673i	$-0.605405\pi$
$887$	−19.3658			−0.650239			−0.325120	+	0.945673i	$0.605405\pi$
$888$	−2.65400	+	2.16171i	−0.0890623	+	0.0725421i
$889$	−38.5710			−1.29363
$890$	11.0890	+	4.03605i	0.371703	+	0.135289i
$891$	18.6399	−	6.78436i	0.624460	−	0.227285i
$892$	−11.1987	−	9.39686i	−0.374962	−	0.314630i
$893$	7.65627	−	43.4209i	0.256207	−	1.45302i
$894$	−3.26949			−0.109348
$895$	2.79348	−	15.8426i	0.0933756	−	0.529559i
$896$	1.59301	+	2.75918i	0.0532188	+	0.0921777i
$897$	12.5970	−	10.5701i	0.420602	−	0.352927i
$898$	2.39248	−	4.14389i	0.0798380	−	0.138284i
$899$	3.03879	+	5.26335i	0.101349	+	0.175542i
$900$	2.52151	+	0.917754i	0.0840503	+	0.0305918i
$901$	−29.3319	−	24.6123i	−0.977186	−	0.819956i
$902$	9.22157	−	15.9722i	0.307045	−	0.531817i
$903$	1.25005	+	7.08940i	0.0415991	+	0.235920i
$904$	−2.93493	−	16.6448i	−0.0976142	−	0.553598i
$905$	−7.73619	+	6.49144i	−0.257160	+	0.215783i
$906$	0.401361	−	0.146083i	0.0133343	−	0.00485330i
$907$	52.7691	−	19.2064i	1.75217	−	0.637738i	0.752391	−	0.658717i	$-0.228901\pi$
$907$	52.7691	−	19.2064i	1.75217	−	0.637738i	0.999780	+	0.0209795i	$0.00667846\pi$
$908$	−6.72199	+	5.64042i	−0.223077	+	0.187184i
$909$	−1.03721	−	5.88228i	−0.0344019	−	0.195103i
$910$	−2.62429	−	14.8831i	−0.0869944	−	0.493370i
$911$	8.31783	−	14.4069i	0.275582	−	0.477322i	−0.694700	−	0.719300i	$-0.744463\pi$
$911$	8.31783	−	14.4069i	0.275582	−	0.477322i	0.970282	+	0.241978i	$0.0777962\pi$
$912$	−2.59072	−	2.17387i	−0.0857873	−	0.0719841i
$913$	36.0022	+	13.1037i	1.19150	+	0.433670i
$914$	−4.51687	−	7.82345i	−0.149405	−	0.258777i
$915$	−2.36596	+	4.09796i	−0.0782161	+	0.135474i
$916$	−16.1223	+	13.5282i	−0.532696	+	0.446985i
$917$	15.1645	+	26.2657i	0.500777	+	0.867370i
$918$	1.96227	−	11.1286i	0.0647644	−	0.367297i
$919$	54.2166			1.78844			0.894220	−	0.447627i	$-0.147731\pi$
$919$	54.2166			1.78844			0.894220	+	0.447627i	$0.147731\pi$
$920$	−1.06977	+	6.06696i	−0.0352692	+	0.200022i
$921$	−9.70906	−	8.14686i	−0.319924	−	0.268448i
$922$	33.7250	−	12.2749i	1.11067	−	0.404253i
$923$	−30.2606	−	11.0139i	−0.996038	−	0.362528i
$924$	−5.68996			−0.187186
$925$	−3.11800	+	5.22284i	−0.102519	+	0.171726i
$926$	28.8738			0.948851
$927$	−1.72518	−	0.627914i	−0.0566623	−	0.0206234i
$928$	8.47385	−	3.08423i	0.278168	−	0.101245i
$929$	15.3922	+	12.9156i	0.505000	+	0.423745i	0.859366	−	0.511362i	$-0.170859\pi$
$929$	15.3922	+	12.9156i	0.505000	+	0.423745i	−0.354365	+	0.935107i	$0.615303\pi$
$930$	−0.0658579	+	0.373499i	−0.00215957	+	0.0122475i
$931$	18.9357			0.620591
$932$	2.00849	−	11.3907i	0.0657904	−	0.373116i
$933$	2.98127	+	5.16371i	0.0976024	+	0.169052i
$934$	−1.01376	+	0.850643i	−0.0331712	+	0.0278339i
$935$	5.60675	−	9.71118i	0.183360	−	0.317590i
$936$	6.36410	+	11.0229i	0.208017	+	0.360296i
$937$	−18.3678	−	6.68532i	−0.600049	−	0.218400i	0.0240945	−	0.999710i	$-0.492330\pi$
$937$	−18.3678	−	6.68532i	−0.600049	−	0.218400i	−0.624144	+	0.781310i	$0.714552\pi$
$938$	17.0933	+	14.3429i	0.558114	+	0.468314i
$939$	0.219503	−	0.380190i	0.00716320	−	0.0124070i
$940$	1.27395	+	7.22493i	0.0415516	+	0.235651i
$941$	8.13341	+	46.1269i	0.265142	+	1.50369i	0.768631	+	0.639692i	$0.220938\pi$
$941$	8.13341	+	46.1269i	0.265142	+	1.50369i	−0.503489	+	0.864001i	$0.667951\pi$
$942$	−1.42748	+	1.19780i	−0.0465100	+	0.0390265i
$943$	33.6420	−	12.2447i	1.09554	−	0.398742i
$944$	−0.715904	+	0.260568i	−0.0233007	+	0.00848075i
$945$	−7.80563	+	6.54970i	−0.253917	+	0.213062i
$946$	−2.21277	−	12.5492i	−0.0719433	−	0.408011i
$947$	−0.664860	−	3.77061i	−0.0216050	−	0.122528i	0.972098	−	0.234576i	$-0.0753702\pi$
$947$	−0.664860	−	3.77061i	−0.0216050	−	0.122528i	−0.993703	+	0.112048i	$0.964259\pi$
$948$	−2.31189	+	4.00431i	−0.0750867	+	0.130054i
$949$	−15.9191	−	13.3577i	−0.516756	−	0.433610i
$950$	−5.64743	−	2.05550i	−0.183227	−	0.0666892i
$951$	−5.23209	−	9.06225i	−0.169662	−	0.293864i
$952$	5.62863	−	9.74907i	0.182425	−	0.315969i
$953$	−4.42345	+	3.71171i	−0.143290	+	0.120234i	−0.711615	−	0.702570i	$-0.752036\pi$
$953$	−4.42345	+	3.71171i	−0.143290	+	0.120234i	0.568325	+	0.822804i	$0.307591\pi$
$954$	−14.5394	−	25.1830i	−0.470731	−	0.815330i
$955$	−1.65087	+	9.36255i	−0.0534209	+	0.302965i
$956$	−11.7459			−0.379889
$957$	−2.79657	+	15.8601i	−0.0904001	+	0.512685i
$958$	−11.8359	−	9.93152i	−0.382401	−	0.320873i
$959$	32.8689	−	11.9633i	1.06139	−	0.386316i
$960$	0.528795	+	0.192466i	0.0170668	+	0.00621180i
$961$	−30.5458			−0.985348
$962$	−27.2543	+	9.47131i	−0.878715	+	0.305367i
$963$	53.0892			1.71078
$964$	24.8126	+	9.03106i	0.799161	+	0.290871i
$965$	2.46586	−	0.897499i	0.0793788	−	0.0288915i
$966$	−8.46105	−	7.09966i	−0.272230	−	0.228428i
$967$	−7.71421	+	43.7494i	−0.248072	+	1.40689i	0.565176	+	0.824970i	$0.308808\pi$
$967$	−7.71421	+	43.7494i	−0.248072	+	1.40689i	−0.813248	+	0.581917i	$0.802303\pi$
$968$	−0.927980			−0.0298264
$969$	−2.07501	+	11.7680i	−0.0666589	+	0.378041i
$970$	4.04892	+	7.01294i	0.130003	+	0.225172i
$971$	−35.3611	+	29.6715i	−1.13479	+	0.952203i	−0.999256	−	0.0385700i	$-0.987720\pi$
$971$	−35.3611	+	29.6715i	−1.13479	+	0.952203i	−0.135535	+	0.990773i	$0.543275\pi$
$972$	6.55590	−	11.3552i	0.210281	−	0.364217i
$973$	29.0411	+	50.3006i	0.931014	+	1.61256i
$974$	−7.25435	−	2.64037i	−0.232444	−	0.0846028i
$975$	−2.04479	−	1.71578i	−0.0654855	−	0.0549489i
$976$	4.20442	−	7.28226i	0.134580	−	0.233099i
$977$	9.64471	+	54.6978i	0.308561	+	1.74994i	0.606248	+	0.795275i	$0.292674\pi$
$977$	9.64471	+	54.6978i	0.308561	+	1.74994i	−0.297687	+	0.954664i	$0.596215\pi$
$978$	−1.13718	−	6.44927i	−0.0363630	−	0.206225i
$979$	28.6891	−	24.0730i	0.916909	−	0.769378i
$980$	−2.96074	+	1.07762i	−0.0945775	+	0.0344234i
$981$	51.2181	−	18.6419i	1.63527	−	0.595189i
$982$	−21.4592	+	18.0064i	−0.684790	+	0.574607i
$983$	4.92402	+	27.9255i	0.157052	+	0.890686i	0.956886	+	0.290464i	$0.0938098\pi$
$983$	4.92402	+	27.9255i	0.157052	+	0.890686i	−0.799834	+	0.600221i	$0.795079\pi$
$984$	−0.567869	−	3.22055i	−0.0181030	−	0.102667i
$985$	5.32129	−	9.21674i	0.169550	−	0.293670i
$986$	−24.4080	−	20.4807i	−0.777309	−	0.652240i
$987$	−12.3600	−	4.49867i	−0.393423	−	0.143194i
$988$	−14.2537	−	24.6881i	−0.453471	−	0.785434i
$989$	12.3679	−	21.4219i	0.393277	−	0.681176i
$990$	6.52359	−	5.47394i	0.207333	−	0.173973i
$991$	2.52327	+	4.37044i	0.0801544	+	0.138832i	0.903316	−	0.428975i	$-0.141125\pi$
$991$	2.52327	+	4.37044i	0.0801544	+	0.138832i	−0.823162	+	0.567807i	$0.807792\pi$
$992$	0.117032	−	0.663724i	0.00371579	−	0.0210733i
$993$	5.30349			0.168301
$994$	−3.75594	+	21.3010i	−0.119131	+	0.675626i
$995$	4.89576	+	4.10803i	0.155206	+	0.130233i
$996$	6.38370	−	2.32348i	0.202275	−	0.0736221i
$997$	−52.9630	−	19.2770i	−1.67735	−	0.610507i	−0.684412	−	0.729096i	$-0.739941\pi$
$997$	−52.9630	−	19.2770i	−1.67735	−	0.610507i	−0.992943	+	0.118589i	$0.962163\pi$
$998$	−35.3693			−1.11960
$999$	14.7183	+	12.7210i	0.465666	+	0.402475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.a.201.2	yes	18
37.7	even	9	inner	370.2.o.a.81.2	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.a.81.2	✓	18	37.7	even	9	inner
370.2.o.a.201.2	yes	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.528795 - 0.192466i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.173648 - 0.984808i) q^{5} -0.562732 q^{6} +(-0.553248 + 3.13762i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.05555 + 1.72481i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.528795 - 0.192466i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.173648 - 0.984808i) q^{5} -0.562732 q^{6} +(-0.553248 + 3.13762i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.05555 + 1.72481i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.58682 + 2.74846i) q^{11} +(0.528795 + 0.192466i) q^{12} +(3.63368 + 3.04902i) q^{13} +(1.59301 - 2.75918i) q^{14} +(-0.0977173 - 0.554183i) q^{15} +(0.173648 + 0.984808i) q^{16} +(2.70668 - 2.27118i) q^{17} +(2.52151 - 0.917754i) q^{18} +(-5.64743 + 2.05550i) q^{19} +(0.766044 - 0.642788i) q^{20} +(0.311330 + 1.76564i) q^{21} +(-0.551098 - 3.12543i) q^{22} +(3.08028 - 5.33520i) q^{23} +(-0.431077 - 0.361717i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(-2.37171 - 4.10793i) q^{26} +(-1.59910 + 2.76972i) q^{27} +(-2.44064 + 2.04794i) q^{28} +(4.50884 + 7.80955i) q^{29} +(-0.0977173 + 0.554183i) q^{30} +0.673963 q^{31} +(0.173648 - 0.984808i) q^{32} +(1.36809 + 1.14796i) q^{33} +(-3.32024 + 1.20847i) q^{34} +(2.99388 + 1.08968i) q^{35} -2.68333 q^{36} +(1.14364 - 5.97429i) q^{37} +6.00987 q^{38} +(2.50830 + 0.912947i) q^{39} +(-0.939693 + 0.342020i) q^{40} +(4.45175 + 3.73546i) q^{41} +(0.311330 - 1.76564i) q^{42} +4.01520 q^{43} +(-0.551098 + 3.12543i) q^{44} +(1.34167 + 2.32383i) q^{45} +(-4.71926 + 3.95993i) q^{46} +(-3.66819 + 6.35349i) q^{47} +(0.281366 + 0.487340i) q^{48} +(-2.96074 - 1.07762i) q^{49} +(0.766044 + 0.642788i) q^{50} +(0.994156 - 1.72193i) q^{51} +(0.823688 + 4.67137i) q^{52} +(-1.88180 - 10.6722i) q^{53} +(2.44996 - 2.05576i) q^{54} +(2.98225 - 1.08545i) q^{55} +(2.99388 - 1.08968i) q^{56} +(-2.59072 + 2.17387i) q^{57} +(-1.56590 - 8.88069i) q^{58} +(0.132294 + 0.750274i) q^{59} +(0.281366 - 0.487340i) q^{60} +(-6.44154 - 5.40509i) q^{61} +(-0.633318 - 0.230509i) q^{62} +(-4.27458 - 7.40380i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(3.63368 - 3.04902i) q^{65} +(-0.892955 - 1.54664i) q^{66} +(-1.21616 + 6.89720i) q^{67} +3.53332 q^{68} +(0.601993 - 3.41407i) q^{69} +(-2.44064 - 2.04794i) q^{70} +(-6.37947 + 2.32194i) q^{71} +(2.52151 + 0.917754i) q^{72} -4.38099 q^{73} +(-3.11800 + 5.22284i) q^{74} -0.562732 q^{75} +(-5.64743 - 2.05550i) q^{76} +(-9.50153 + 3.45827i) q^{77} +(-2.04479 - 1.71578i) q^{78} +(-1.42681 + 8.09184i) q^{79} +1.00000 q^{80} +(1.08535 - 6.15532i) q^{81} +(-2.90567 - 5.03277i) q^{82} +(9.24781 - 7.75983i) q^{83} +(-0.896439 + 1.55268i) q^{84} +(-1.76666 - 3.05995i) q^{85} +(-3.77305 - 1.37328i) q^{86} +(3.88732 + 3.26185i) q^{87} +(1.58682 - 2.74846i) q^{88} +(-2.04916 - 11.6214i) q^{89} +(-0.465956 - 2.64257i) q^{90} +(-11.5770 + 9.71425i) q^{91} +(5.78903 - 2.10703i) q^{92} +(0.356388 - 0.129715i) q^{93} +(5.61999 - 4.71574i) q^{94} +(1.04360 + 5.91857i) q^{95} +(-0.0977173 - 0.554183i) q^{96} +(4.04892 - 7.01294i) q^{97} +(2.41362 + 2.02527i) q^{98} +(-8.00237 - 2.91262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9	\( 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9} - 9 q^{10} + 3 q^{11} + 9 q^{13} - 6 q^{17} + 6 q^{18} + 9 q^{19} - 6 q^{21} + 21 q^{23} + 6 q^{26} + 12 q^{27} - 3 q^{28} + 6 q^{29} - 30 q^{31} - 45 q^{33} - 15 q^{34} + 6 q^{35} + 24 q^{36} + 6 q^{37} - 12 q^{38} + 24 q^{39} + 15 q^{41} - 6 q^{42} - 12 q^{43} - 12 q^{45} + 24 q^{47} + 3 q^{48} + 33 q^{49} - 42 q^{51} - 12 q^{53} + 27 q^{54} + 6 q^{56} + 51 q^{57} - 15 q^{58} - 15 q^{59} + 3 q^{60} + 72 q^{61} - 57 q^{62} - 30 q^{63} - 9 q^{64} + 9 q^{65} - 3 q^{66} + 18 q^{67} + 24 q^{69} - 3 q^{70} + 6 q^{72} - 66 q^{73} - 24 q^{74} - 6 q^{75} + 9 q^{76} - 66 q^{77} + 6 q^{78} - 12 q^{79} + 18 q^{80} + 66 q^{81} + 45 q^{82} + 9 q^{83} + 42 q^{84} + 12 q^{86} + 48 q^{87} + 3 q^{88} + 6 q^{90} - 78 q^{91} + 18 q^{92} + 24 q^{94} - 3 q^{97} - 48 q^{98} - 96 q^{99}+O(q^{100}) \) 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9 - 9 * q^10 + 3 * q^11 + 9 * q^13 - 6 * q^17 + 6 * q^18 + 9 * q^19 - 6 * q^21 + 21 * q^23 + 6 * q^26 + 12 * q^27 - 3 * q^28 + 6 * q^29 - 30 * q^31 - 45 * q^33 - 15 * q^34 + 6 * q^35 + 24 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^39 + 15 * q^41 - 6 * q^42 - 12 * q^43 - 12 * q^45 + 24 * q^47 + 3 * q^48 + 33 * q^49 - 42 * q^51 - 12 * q^53 + 27 * q^54 + 6 * q^56 + 51 * q^57 - 15 * q^58 - 15 * q^59 + 3 * q^60 + 72 * q^61 - 57 * q^62 - 30 * q^63 - 9 * q^64 + 9 * q^65 - 3 * q^66 + 18 * q^67 + 24 * q^69 - 3 * q^70 + 6 * q^72 - 66 * q^73 - 24 * q^74 - 6 * q^75 + 9 * q^76 - 66 * q^77 + 6 * q^78 - 12 * q^79 + 18 * q^80 + 66 * q^81 + 45 * q^82 + 9 * q^83 + 42 * q^84 + 12 * q^86 + 48 * q^87 + 3 * q^88 + 6 * q^90 - 78 * q^91 + 18 * q^92 + 24 * q^94 - 3 * q^97 - 48 * q^98 - 96 * q^99

Introduction

L-functions

Modular forms

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