LMFDB - Embedded newform 690.2.r.b.169.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(49,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 16]))

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

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

chi := DirichletCharacter("690.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.r (of order $22$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			169.11
Character	$\chi$	$=$	690.169
Dual form			690.2.r.b.49.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.989821 + 0.142315i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(1.08184 - 1.95694i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.378014 - 0.588202i) q^{7} +(0.909632 + 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.989821 + 0.142315i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(1.08184 - 1.95694i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.378014 - 0.588202i) q^{7} +(0.909632 + 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +(1.34933 - 1.78306i) q^{10} +(-0.745698 - 5.18645i) q^{11} +(-0.989821 + 0.142315i) q^{12} +(-1.92796 - 2.99996i) q^{13} +(0.457877 - 0.528418i) q^{14} +(-0.171128 + 2.22951i) q^{15} +(0.841254 + 0.540641i) q^{16} +(0.765463 + 2.60693i) q^{17} +(0.755750 - 0.654861i) q^{18} +(-3.73394 - 1.09638i) q^{19} +(1.58935 - 1.57289i) q^{20} +(-0.0995061 + 0.692080i) q^{21} -5.23978i q^{22} +(0.308327 + 4.78591i) q^{23} -1.00000 q^{24} +(-2.65926 - 4.23418i) q^{25} +(-1.48140 - 3.24380i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(0.528418 - 0.457877i) q^{28} +(8.22773 - 2.41588i) q^{29} +(-0.486678 + 2.18246i) q^{30} +(2.66056 - 5.82581i) q^{31} +(0.755750 + 0.654861i) q^{32} +(2.83284 + 4.40798i) q^{33} +(0.386667 + 2.68933i) q^{34} +(-0.742129 - 1.37609i) q^{35} +(0.841254 - 0.540641i) q^{36} +(4.34838 + 3.76789i) q^{37} +(-3.53991 - 1.61662i) q^{38} +(2.99996 + 1.92796i) q^{39} +(1.79702 - 1.33069i) q^{40} +(-1.31526 - 1.51789i) q^{41} +(-0.196987 + 0.670875i) q^{42} +(4.36540 - 1.99361i) q^{43} +(0.745698 - 5.18645i) q^{44} +(-0.770509 - 2.09912i) q^{45} +(-0.375917 + 4.78108i) q^{46} +5.47253i q^{47} +(-0.989821 - 0.142315i) q^{48} +(2.70482 + 5.92273i) q^{49} +(-2.02961 - 4.56954i) q^{50} +(-1.77925 - 2.05336i) q^{51} +(-1.00468 - 3.42161i) q^{52} +(1.05405 - 1.64013i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(-10.9563 - 4.15159i) q^{55} +(0.588202 - 0.378014i) q^{56} +(3.85197 - 0.553830i) q^{57} +(8.48780 - 1.22036i) q^{58} +(-9.17993 + 5.89959i) q^{59} +(-0.792321 + 2.09099i) q^{60} +(5.71509 - 12.5143i) q^{61} +(3.46258 - 5.38788i) q^{62} +(-0.196987 - 0.670875i) q^{63} +(0.654861 + 0.755750i) q^{64} +(-7.95649 + 0.527443i) q^{65} +(2.17668 + 4.76627i) q^{66} +(-3.44525 - 0.495352i) q^{67} +2.71699i q^{68} +(-2.26860 - 4.22533i) q^{69} +(-0.538737 - 1.46770i) q^{70} +(-0.0479933 + 0.333800i) q^{71} +(0.909632 - 0.415415i) q^{72} +(-3.65477 + 12.4470i) q^{73} +(3.76789 + 4.34838i) q^{74} +(4.17790 + 2.74685i) q^{75} +(-3.27381 - 2.10395i) q^{76} +(-3.33256 - 1.52193i) q^{77} +(2.69505 + 2.33527i) q^{78} +(-3.98251 + 2.55940i) q^{79} +(1.96810 - 1.06140i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-1.08585 - 1.68962i) q^{82} +(12.2644 + 10.6272i) q^{83} +(-0.290457 + 0.636012i) q^{84} +(5.92972 + 1.32230i) q^{85} +(4.60469 - 1.35206i) q^{86} +(-6.48061 + 5.61548i) q^{87} +(1.47622 - 5.02753i) q^{88} +(3.75816 + 8.22923i) q^{89} +(-0.463930 - 2.18741i) q^{90} -2.49338 q^{91} +(-1.05251 + 4.67891i) q^{92} +6.40458i q^{93} +(-0.778822 + 5.41682i) q^{94} +(-6.18508 + 6.12101i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(5.51857 - 4.78187i) q^{97} +(1.83440 + 6.24738i) q^{98} +(-4.40798 - 2.83284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9	$ 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9} - 18 q^{10} - 8 q^{11} - 4 q^{15} - 12 q^{16} + 16 q^{19} + 14 q^{20} - 22 q^{21} - 120 q^{24} + 28 q^{25} + 8 q^{26} + 8 q^{29} + 8 q^{30} + 8 q^{31} + 44 q^{34} + 58 q^{35} - 12 q^{36} + 14 q^{39} - 4 q^{40} + 8 q^{44} - 8 q^{45} + 12 q^{49} - 4 q^{50} + 12 q^{54} + 92 q^{55} - 94 q^{59} + 4 q^{60} - 60 q^{61} + 12 q^{64} - 44 q^{65} - 8 q^{66} + 16 q^{70} - 16 q^{74} + 4 q^{75} - 16 q^{76} + 172 q^{79} + 8 q^{80} - 12 q^{81} - 32 q^{85} - 40 q^{86} + 48 q^{89} - 4 q^{90} + 288 q^{91} + 24 q^{94} - 78 q^{95} - 12 q^{96} - 36 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9 - 18 * q^10 - 8 * q^11 - 4 * q^15 - 12 * q^16 + 16 * q^19 + 14 * q^20 - 22 * q^21 - 120 * q^24 + 28 * q^25 + 8 * q^26 + 8 * q^29 + 8 * q^30 + 8 * q^31 + 44 * q^34 + 58 * q^35 - 12 * q^36 + 14 * q^39 - 4 * q^40 + 8 * q^44 - 8 * q^45 + 12 * q^49 - 4 * q^50 + 12 * q^54 + 92 * q^55 - 94 * q^59 + 4 * q^60 - 60 * q^61 + 12 * q^64 - 44 * q^65 - 8 * q^66 + 16 * q^70 - 16 * q^74 + 4 * q^75 - 16 * q^76 + 172 * q^79 + 8 * q^80 - 12 * q^81 - 32 * q^85 - 40 * q^86 + 48 * q^89 - 4 * q^90 + 288 * q^91 + 24 * q^94 - 78 * q^95 - 12 * q^96 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	0.989821	+	0.142315i	0.699909	+	0.100632i
$2$	0.989821	+	0.142315i	0.699909	+	0.100632i
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$4$	0.959493	+	0.281733i	0.479746	+	0.140866i
$5$	1.08184	−	1.95694i	0.483811	−	0.875172i
$5$	1.08184	−	1.95694i	0.483811	−	0.875172i
$6$	−0.959493	+	0.281733i	−0.391711	+	0.115017i
$7$	0.378014	−	0.588202i	0.142876	−	0.222319i	−0.762439	−	0.647060i	$-0.775998\pi$
$7$	0.378014	−	0.588202i	0.142876	−	0.222319i	0.905315	+	0.424741i	$0.139635\pi$
$8$	0.909632	+	0.415415i	0.321603	+	0.146871i
$9$	0.654861	−	0.755750i	0.218287	−	0.251917i
$10$	1.34933	−	1.78306i	0.426694	−	0.563855i
$11$	−0.745698	−	5.18645i	−0.224837	−	1.56377i	−0.719378	−	0.694619i	$-0.755573\pi$
$11$	−0.745698	−	5.18645i	−0.224837	−	1.56377i	0.494542	−	0.869154i	$-0.335336\pi$
$12$	−0.989821	+	0.142315i	−0.285737	+	0.0410828i
$13$	−1.92796	−	2.99996i	−0.534719	−	0.832040i	0.463828	−	0.885925i	$-0.346476\pi$
$13$	−1.92796	−	2.99996i	−0.534719	−	0.832040i	−0.998547	+	0.0538857i	$0.982839\pi$
$14$	0.457877	−	0.528418i	0.122373	−	0.141226i
$15$	−0.171128	+	2.22951i	−0.0441850	+	0.575657i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	0.765463	+	2.60693i	0.185652	+	0.632273i	0.998742	+	0.0501355i	$0.0159653\pi$
$17$	0.765463	+	2.60693i	0.185652	+	0.632273i	−0.813090	+	0.582138i	$0.802217\pi$
$18$	0.755750	−	0.654861i	0.178132	−	0.154352i
$19$	−3.73394	−	1.09638i	−0.856625	−	0.251528i	−0.176208	−	0.984353i	$-0.556383\pi$
$19$	−3.73394	−	1.09638i	−0.856625	−	0.251528i	−0.680417	+	0.732825i	$0.738201\pi$
$20$	1.58935	−	1.57289i	0.355389	−	0.351708i
$21$	−0.0995061	+	0.692080i	−0.0217140	+	0.151024i
$22$		−	5.23978i		−	1.11712i
$23$	0.308327	+	4.78591i	0.0642907	+	0.997931i
$23$	0.308327	+	4.78591i	0.0642907	+	0.997931i
$24$	−1.00000			−0.204124
$25$	−2.65926	−	4.23418i	−0.531853	−	0.846837i
$26$	−1.48140	−	3.24380i	−0.290526	−	0.636162i
$27$	−0.281733	+	0.959493i	−0.0542195	+	0.184655i
$28$	0.528418	−	0.457877i	0.0998616	−	0.0865305i
$29$	8.22773	−	2.41588i	1.52785	−	0.448617i	0.593459	−	0.804864i	$-0.297762\pi$
$29$	8.22773	−	2.41588i	1.52785	−	0.448617i	0.934392	+	0.356247i	$0.115944\pi$
$30$	−0.486678	+	2.18246i	−0.0888549	+	0.398461i
$31$	2.66056	−	5.82581i	0.477851	−	1.04635i	−0.505198	−	0.863003i	$-0.668581\pi$
$31$	2.66056	−	5.82581i	0.477851	−	1.04635i	0.983049	−	0.183344i	$-0.0586922\pi$
$32$	0.755750	+	0.654861i	0.133599	+	0.115764i
$33$	2.83284	+	4.40798i	0.493134	+	0.767331i
$34$	0.386667	+	2.68933i	0.0663129	+	0.461216i
$35$	−0.742129	−	1.37609i	−0.125443	−	0.232602i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	4.34838	+	3.76789i	0.714870	+	0.619438i	0.934424	−	0.356162i	$-0.115915\pi$
$37$	4.34838	+	3.76789i	0.714870	+	0.619438i	−0.219555	+	0.975600i	$0.570460\pi$
$38$	−3.53991	−	1.61662i	−0.574249	−	0.262251i
$39$	2.99996	+	1.92796i	0.480378	+	0.308720i
$40$	1.79702	−	1.33069i	0.284133	−	0.210400i
$41$	−1.31526	−	1.51789i	−0.205408	−	0.237054i	0.643693	−	0.765284i	$-0.277401\pi$
$41$	−1.31526	−	1.51789i	−0.205408	−	0.237054i	−0.849101	+	0.528230i	$0.822856\pi$
$42$	−0.196987	+	0.670875i	−0.0303957	+	0.103518i
$43$	4.36540	−	1.99361i	0.665718	−	0.304023i	−0.0537443	−	0.998555i	$-0.517116\pi$
$43$	4.36540	−	1.99361i	0.665718	−	0.304023i	0.719462	+	0.694532i	$0.244388\pi$
$44$	0.745698	−	5.18645i	0.112418	−	0.781886i
$45$	−0.770509	−	2.09912i	−0.114861	−	0.312919i
$46$	−0.375917	+	4.78108i	−0.0554259	+	0.704931i
$47$			5.47253i			0.798250i	0.916896	+	0.399125i	$0.130686\pi$
$47$			5.47253i			0.798250i	−0.916896	+	0.399125i	$0.869314\pi$
$48$	−0.989821	−	0.142315i	−0.142868	−	0.0205414i
$49$	2.70482	+	5.92273i	0.386403	+	0.846104i
$50$	−2.02961	−	4.56954i	−0.287030	−	0.646230i
$51$	−1.77925	−	2.05336i	−0.249144	−	0.287528i
$52$	−1.00468	−	3.42161i	−0.139323	−	0.474492i
$53$	1.05405	−	1.64013i	0.144784	−	0.225289i	−0.761286	−	0.648417i	$-0.775431\pi$
$53$	1.05405	−	1.64013i	0.144784	−	0.225289i	0.906070	+	0.423128i	$0.139068\pi$
$54$	−0.415415	+	0.909632i	−0.0565308	+	0.123785i
$55$	−10.9563	−	4.15159i	−1.47735	−	0.559800i
$56$	0.588202	−	0.378014i	0.0786018	−	0.0505143i
$57$	3.85197	−	0.553830i	0.510206	−	0.0733565i
$58$	8.48780	−	1.22036i	1.11450	−	0.160241i
$59$	−9.17993	+	5.89959i	−1.19513	+	0.768061i	−0.978106	−	0.208107i	$-0.933270\pi$
$59$	−9.17993	+	5.89959i	−1.19513	+	0.768061i	−0.217020	+	0.976167i	$0.569634\pi$
$60$	−0.792321	+	2.09099i	−0.102288	+	0.269945i
$61$	5.71509	−	12.5143i	0.731742	−	1.60229i	−0.0649364	−	0.997889i	$-0.520684\pi$
$61$	5.71509	−	12.5143i	0.731742	−	1.60229i	0.796679	−	0.604403i	$-0.206588\pi$
$62$	3.46258	−	5.38788i	0.439748	−	0.684261i
$63$	−0.196987	−	0.670875i	−0.0248180	−	0.0845222i
$64$	0.654861	+	0.755750i	0.0818576	+	0.0944687i
$65$	−7.95649	+	0.527443i	−0.986882	+	0.0654213i
$66$	2.17668	+	4.76627i	0.267931	+	0.586687i
$67$	−3.44525	−	0.495352i	−0.420904	−	0.0605169i	−0.0713911	−	0.997448i	$-0.522744\pi$
$67$	−3.44525	−	0.495352i	−0.420904	−	0.0605169i	−0.349513	+	0.936932i	$0.613653\pi$
$68$			2.71699i			0.329483i
$69$	−2.26860	−	4.22533i	−0.273108	−	0.508670i
$70$	−0.538737	−	1.46770i	−0.0643914	−	0.175424i
$71$	−0.0479933	+	0.333800i	−0.00569575	+	0.0396148i	−0.992471	−	0.122479i	$-0.960916\pi$
$71$	−0.0479933	+	0.333800i	−0.00569575	+	0.0396148i	0.986775	+	0.162094i	$0.0518247\pi$
$72$	0.909632	−	0.415415i	0.107201	−	0.0489571i
$73$	−3.65477	+	12.4470i	−0.427759	+	1.45681i	0.410662	+	0.911788i	$0.365298\pi$
$73$	−3.65477	+	12.4470i	−0.427759	+	1.45681i	−0.838420	+	0.545024i	$0.816521\pi$
$74$	3.76789	+	4.34838i	0.438009	+	0.505489i
$75$	4.17790	+	2.74685i	0.482422	+	0.317179i
$76$	−3.27381	−	2.10395i	−0.375531	−	0.241339i
$77$	−3.33256	−	1.52193i	−0.379781	−	0.173440i
$78$	2.69505	+	2.33527i	0.305154	+	0.264418i
$79$	−3.98251	+	2.55940i	−0.448067	+	0.287955i	−0.745151	−	0.666896i	$-0.767622\pi$
$79$	−3.98251	+	2.55940i	−0.448067	+	0.287955i	0.297083	+	0.954852i	$0.403986\pi$
$80$	1.96810	−	1.06140i	0.220040	−	0.118668i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	−1.08585	−	1.68962i	−0.119912	−	0.186587i
$83$	12.2644	+	10.6272i	1.34620	+	1.16649i	0.970874	+	0.239592i	$0.0770137\pi$
$83$	12.2644	+	10.6272i	1.34620	+	1.16649i	0.375323	+	0.926894i	$0.377532\pi$
$84$	−0.290457	+	0.636012i	−0.0316914	+	0.0693946i
$85$	5.92972	+	1.32230i	0.643168	+	0.143423i
$86$	4.60469	−	1.35206i	0.496537	−	0.145796i
$87$	−6.48061	+	5.61548i	−0.694794	+	0.602043i
$88$	1.47622	−	5.02753i	0.157365	−	0.535937i
$89$	3.75816	+	8.22923i	0.398364	+	0.872296i	0.997433	+	0.0715990i	$0.0228102\pi$
$89$	3.75816	+	8.22923i	0.398364	+	0.872296i	−0.599069	+	0.800697i	$0.704463\pi$
$90$	−0.463930	−	2.18741i	−0.0489025	−	0.230573i
$91$	−2.49338			−0.261377
$92$	−1.05251	+	4.67891i	−0.109732	+	0.487810i
$93$			6.40458i			0.664124i
$94$	−0.778822	+	5.41682i	−0.0803293	+	0.558703i
$95$	−6.18508	+	6.12101i	−0.634575	+	0.628003i
$96$	−0.959493	−	0.281733i	−0.0979278	−	0.0287542i
$97$	5.51857	−	4.78187i	0.560326	−	0.485525i	−0.328038	−	0.944664i	$-0.606387\pi$
$97$	5.51857	−	4.78187i	0.560326	−	0.485525i	0.888364	+	0.459139i	$0.151842\pi$
$98$	1.83440	+	6.24738i	0.185302	+	0.631080i
$99$	−4.40798	−	2.83284i	−0.443019	−	0.284711i
$100$	−1.35864	−	4.81187i	−0.135864	−	0.481187i
$101$	−7.49296	+	8.64734i	−0.745578	+	0.860442i	−0.994132	−	0.108176i	$-0.965499\pi$
$101$	−7.49296	+	8.64734i	−0.745578	+	0.860442i	0.248554	+	0.968618i	$0.420045\pi$
$102$	−1.46891	−	2.28567i	−0.145444	−	0.226315i
$103$	−0.662661	+	0.0952763i	−0.0652940	+	0.00938786i	−0.174884	−	0.984589i	$-0.555955\pi$
$103$	−0.662661	+	0.0952763i	−0.0652940	+	0.00938786i	0.109590	+	0.993977i	$0.465046\pi$
$104$	−0.507504	−	3.52976i	−0.0497648	−	0.346122i
$105$	1.24671	+	0.943445i	0.121667	+	0.0920708i
$106$	1.27673	−	1.47343i	0.124007	−	0.143112i
$107$	−16.0338	−	7.32238i	−1.55004	−	0.707881i	−0.557546	−	0.830146i	$-0.688257\pi$
$107$	−16.0338	−	7.32238i	−1.55004	−	0.707881i	−0.992498	+	0.122265i	$0.960984\pi$
$108$	−0.540641	+	0.841254i	−0.0520232	+	0.0809497i
$109$	18.5700	−	5.45265i	1.77869	−	0.522269i	0.783598	−	0.621269i	$-0.213382\pi$
$109$	18.5700	−	5.45265i	1.77869	−	0.522269i	0.995087	+	0.0989994i	$0.0315642\pi$
$110$	−10.2540	−	5.66858i	−0.977677	−	0.540478i
$111$	−5.52067	−	1.62101i	−0.523998	−	0.153860i
$112$	0.636012	−	0.290457i	0.0600975	−	0.0274456i
$113$	8.26542	+	1.18839i	0.777546	+	0.111794i	0.519651	−	0.854379i	$-0.326062\pi$
$113$	8.26542	+	1.18839i	0.777546	+	0.111794i	0.257895	+	0.966173i	$0.416971\pi$
$114$	3.89158			0.364480
$115$	9.69932	+	4.57419i	0.904466	+	0.426545i
$116$	8.57508			0.796176
$117$	−3.52976	−	0.507504i	−0.326327	−	0.0469187i
$118$	−9.92609	+	4.53310i	−0.913771	+	0.417305i
$119$	1.82276	+	0.535210i	0.167092	+	0.0490626i
$120$	−1.08184	+	1.95694i	−0.0987576	+	0.178644i
$121$	−15.7887	+	4.63599i	−1.43534	+	0.421454i
$122$	7.43789	−	11.5736i	0.673395	−	1.04782i
$123$	1.82695	+	0.834341i	0.164731	+	0.0752300i
$124$	4.19411	−	4.84026i	0.376642	−	0.434668i
$125$	−11.1629	+	0.623345i	−0.998445	+	0.0557537i
$126$	−0.0995061	−	0.692080i	−0.00886471	−	0.0616554i
$127$	−10.1325	+	1.45683i	−0.899110	+	0.129273i	−0.576345	−	0.817206i	$-0.695522\pi$
$127$	−10.1325	+	1.45683i	−0.899110	+	0.129273i	−0.322765	+	0.946479i	$0.604612\pi$
$128$	0.540641	+	0.841254i	0.0477863	+	0.0743570i
$129$	−3.14273	+	3.62691i	−0.276702	+	0.319332i
$130$	−7.95057	−	0.610252i	−0.697311	−	0.0535227i
$131$	−9.08296	−	5.83726i	−0.793582	−	0.510004i	0.0799340	−	0.996800i	$-0.474529\pi$
$131$	−9.08296	−	5.83726i	−0.793582	−	0.510004i	−0.873516	+	0.486796i	$0.838165\pi$
$132$	1.47622	+	5.02753i	0.128488	+	0.437590i
$133$	−2.05638	+	1.78186i	−0.178311	+	0.154507i
$134$	−3.33968	−	0.980620i	−0.288505	−	0.0847126i
$135$	1.57289	+	1.58935i	0.135373	+	0.136789i
$136$	−0.386667	+	2.68933i	−0.0331565	+	0.230608i
$137$			5.08329i			0.434295i	0.976139	+	0.217148i	$0.0696753\pi$
$137$			5.08329i			0.434295i	−0.976139	+	0.217148i	$0.930325\pi$
$138$	−1.64418	−	4.50518i	−0.139962	−	0.383506i
$139$	−7.27060			−0.616684			−0.308342	−	0.951276i	$-0.599774\pi$
$139$	−7.27060			−0.616684			−0.308342	+	0.951276i	$0.599774\pi$
$140$	−0.324378	−	1.52943i	−0.0274150	−	0.129261i
$141$	−2.27337	−	4.97799i	−0.191452	−	0.419222i
$142$	−0.0950095	+	0.323573i	−0.00797302	+	0.0271536i
$143$	−14.1215	+	12.2363i	−1.18090	+	1.02325i
$144$	0.959493	−	0.281733i	0.0799577	−	0.0234777i
$145$	4.17330	−	18.7148i	0.346574	−	1.55418i
$146$	−5.38896	+	11.8002i	−0.445994	+	0.976590i
$147$	−4.92078	−	4.26388i	−0.405859	−	0.351679i
$148$	3.11070	+	4.84035i	0.255698	+	0.397874i
$149$	3.26584	+	22.7144i	0.267548	+	1.86084i	0.471514	+	0.881859i	$0.343708\pi$
$149$	3.26584	+	22.7144i	0.267548	+	1.86084i	−0.203966	+	0.978978i	$0.565383\pi$
$150$	3.74445	+	3.31347i	0.305733	+	0.270544i
$151$	−8.86234	+	5.69548i	−0.721207	+	0.463492i	−0.849057	−	0.528302i	$-0.822829\pi$
$151$	−8.86234	+	5.69548i	−0.721207	+	0.463492i	0.127849	+	0.991794i	$0.459193\pi$
$152$	−2.94106	−	2.54844i	−0.238551	−	0.206706i
$153$	2.47146	+	1.12868i	0.199805	+	0.0912481i
$154$	−3.08205	−	1.98071i	−0.248359	−	0.159610i
$155$	−8.52251	−	11.5091i	−0.684544	−	0.924436i
$156$	2.33527	+	2.69505i	0.186972	+	0.215777i
$157$	2.99734	−	10.2080i	0.239214	−	0.814688i	−0.749126	−	0.662427i	$-0.769526\pi$
$157$	2.99734	−	10.2080i	0.239214	−	0.814688i	0.988340	−	0.152261i	$-0.0486554\pi$
$158$	−4.30621	+	1.96658i	−0.342584	+	0.156453i
$159$	−0.277461	+	1.92978i	−0.0220041	+	0.153042i
$160$	2.09912	−	0.770509i	0.165950	−	0.0609141i
$161$	2.93163	+	1.62778i	0.231045	+	0.128287i
$162$		−	1.00000i		−	0.0785674i
$163$	0.652108	+	0.0937589i	0.0510770	+	0.00734377i	0.167806	−	0.985820i	$-0.446332\pi$
$163$	0.652108	+	0.0937589i	0.0510770	+	0.00734377i	−0.116729	+	0.993164i	$0.537241\pi$
$164$	−0.834341	−	1.82695i	−0.0651511	−	0.142661i
$165$	11.6908	−	0.774997i	0.910131	−	0.0603334i
$166$	10.6272	+	12.2644i	0.824830	+	0.951905i
$167$	2.60631	+	8.87626i	0.201682	+	0.686866i	0.996765	+	0.0803657i	$0.0256088\pi$
$167$	2.60631	+	8.87626i	0.201682	+	0.686866i	−0.795083	+	0.606500i	$0.792573\pi$
$168$	−0.378014	+	0.588202i	−0.0291644	+	0.0453808i
$169$	0.117647	−	0.257611i	0.00904977	−	0.0198162i
$170$	5.68118	+	2.15273i	0.435727	+	0.165107i
$171$	−3.27381	+	2.10395i	−0.250354	+	0.160893i
$172$	4.75024	−	0.682982i	0.362202	−	0.0520769i
$173$	−2.41967	+	0.347896i	−0.183964	+	0.0264501i	−0.233681	−	0.972313i	$-0.575077\pi$
$173$	−2.41967	+	0.347896i	−0.183964	+	0.0264501i	0.0497169	+	0.998763i	$0.484168\pi$
$174$	−7.21381	+	4.63604i	−0.546878	+	0.351457i
$175$	−3.49580	−	0.0363977i	−0.264257	−	0.00275141i
$176$	2.17668	−	4.76627i	0.164074	−	0.359271i
$177$	5.89959	−	9.17993i	0.443440	−	0.690006i
$178$	2.54877	+	8.68031i	0.191038	+	0.650617i
$179$	8.61580	+	9.94317i	0.643975	+	0.743187i	0.980072	−	0.198640i	$-0.0636525\pi$
$179$	8.61580	+	9.94317i	0.643975	+	0.743187i	−0.336097	+	0.941827i	$0.609107\pi$
$180$	−0.147906	−	2.23117i	−0.0110243	−	0.166302i
$181$	3.70354	+	8.10962i	0.275282	+	0.602783i	0.995891	−	0.0905581i	$-0.0288651\pi$
$181$	3.70354	+	8.10962i	0.275282	+	0.602783i	−0.720609	+	0.693341i	$0.756138\pi$
$182$	−2.46800	−	0.354845i	−0.182940	−	0.0263029i
$183$			13.7575i			1.01699i
$184$	−1.70767	+	4.48150i	−0.125891	+	0.330381i
$185$	12.0778	−	4.43330i	0.887977	−	0.325943i
$186$	−0.911467	+	6.33939i	−0.0668320	+	0.464827i
$187$	12.9499	−	5.91402i	0.946990	−	0.432476i
$188$	−1.54179	+	5.25085i	−0.112447	+	0.382958i
$189$	0.457877	+	0.528418i	0.0333056	+	0.0384367i
$190$	−6.99323	+	5.17848i	−0.507342	+	0.375687i
$191$	11.2683	+	7.24171i	0.815347	+	0.523991i	0.880591	−	0.473878i	$-0.157146\pi$
$191$	11.2683	+	7.24171i	0.815347	+	0.523991i	−0.0652440	+	0.997869i	$0.520783\pi$
$192$	−0.909632	−	0.415415i	−0.0656470	−	0.0299800i
$193$	−14.6648	−	12.7071i	−1.05560	−	0.914679i	−0.0590945	−	0.998252i	$-0.518821\pi$
$193$	−14.6648	−	12.7071i	−1.05560	−	0.914679i	−0.996502	+	0.0835731i	$0.973367\pi$
$194$	6.14293	−	3.94782i	0.441037	−	0.283437i
$195$	7.01837	−	3.78503i	0.502596	−	0.271051i
$196$	0.926630	+	6.44485i	0.0661878	+	0.460346i
$197$	−9.87333	−	15.3632i	−0.703446	−	1.09458i	−0.990612	−	0.136702i	$-0.956350\pi$
$197$	−9.87333	−	15.3632i	−0.703446	−	1.09458i	0.287166	−	0.957881i	$-0.407287\pi$
$198$	−3.95996	−	3.43133i	−0.281422	−	0.243854i
$199$	5.07810	−	11.1195i	0.359977	−	0.788240i	−0.639828	−	0.768518i	$-0.720995\pi$
$199$	5.07810	−	11.1195i	0.359977	−	0.788240i	0.999806	−	0.0197220i	$-0.00627811\pi$
$200$	−0.660009	−	4.95625i	−0.0466697	−	0.350460i
$201$	3.33968	−	0.980620i	0.235563	−	0.0691676i
$202$	−8.64734	+	7.49296i	−0.608425	+	0.527203i
$203$	1.68917	−	5.75280i	0.118557	−	0.403768i
$204$	−1.12868	−	2.47146i	−0.0790232	−	0.173037i
$205$	−4.39331	+	0.931780i	−0.306842	+	0.0650784i
$206$	−0.669476			−0.0466446
$207$	3.81886	+	2.90109i	0.265429	+	0.201639i
$208$		−	3.56606i		−	0.247262i
$209$	−2.90194	+	20.1835i	−0.200732	+	1.39612i
$210$	1.09976	+	1.11127i	0.0758905	+	0.0766847i
$211$	17.9165	+	5.26076i	1.23342	+	0.362166i	0.832541	−	0.553964i	$-0.186885\pi$
$211$	17.9165	+	5.26076i	1.23342	+	0.362166i	0.400883	+	0.916129i	$0.368704\pi$
$212$	1.47343	−	1.27673i	0.101195	−	0.0876864i
$213$	−0.0950095	−	0.323573i	−0.00650994	−	0.0221708i
$214$	−14.8285	−	9.52969i	−1.01365	−	0.651436i
$215$	0.821257	−	10.6996i	0.0560093	−	0.729708i
$216$	−0.654861	+	0.755750i	−0.0445576	+	0.0514222i
$217$	−2.42103	−	3.76719i	−0.164350	−	0.255733i
$218$	19.1570	−	2.75436i	1.29748	−	0.186549i
$219$	−1.84618	−	12.8404i	−0.124753	−	0.867677i
$220$	−9.34287	−	7.07017i	−0.629896	−	0.476671i
$221$	6.34491	−	7.32241i	0.426805	−	0.492559i
$222$	−5.23378	−	2.39019i	−0.351268	−	0.160419i
$223$	4.19821	−	6.53253i	0.281133	−	0.437451i	−0.671755	−	0.740773i	$-0.734459\pi$
$223$	4.19821	−	6.53253i	0.281133	−	0.437451i	0.952888	+	0.303322i	$0.0980958\pi$
$224$	0.670875	−	0.196987i	0.0448247	−	0.0131617i
$225$	−4.94143	−	0.763062i	−0.329429	−	0.0508708i
$226$	8.01217	+	2.35259i	0.532962	+	0.156492i
$227$	−0.0690392	+	0.0315291i	−0.00458229	+	0.00209266i	−0.417705	−	0.908583i	$-0.637165\pi$
$227$	−0.0690392	+	0.0315291i	−0.00458229	+	0.00209266i	0.413123	+	0.910675i	$0.364438\pi$
$228$	3.85197	+	0.553830i	0.255103	+	0.0366783i
$229$	−14.6648			−0.969081			−0.484540	−	0.874769i	$-0.661013\pi$
$229$	−14.6648			−0.969081			−0.484540	+	0.874769i	$0.661013\pi$
$230$	8.94962	+	5.90799i	0.590121	+	0.389561i
$231$	3.66364			0.241050
$232$	8.48780	+	1.22036i	0.557251	+	0.0801206i
$233$	15.6535	−	7.14871i	1.02549	−	0.468328i	0.169619	−	0.985510i	$-0.445746\pi$
$233$	15.6535	−	7.14871i	1.02549	−	0.468328i	0.855875	+	0.517182i	$0.173019\pi$
$234$	−3.42161	−	1.00468i	−0.223678	−	0.0656777i
$235$	10.7094	+	5.92037i	0.698606	+	0.386203i
$236$	−10.4702	+	3.07432i	−0.681551	+	0.200121i
$237$	2.55940	−	3.98251i	0.166251	−	0.258692i
$238$	1.72804	+	0.789167i	0.112012	+	0.0511541i
$239$	2.66870	−	3.07985i	0.172624	−	0.199219i	−0.662844	−	0.748757i	$-0.730651\pi$
$239$	2.66870	−	3.07985i	0.172624	−	0.199219i	0.835468	+	0.549538i	$0.185196\pi$
$240$	−1.34933	+	1.78306i	−0.0870986	+	0.115096i
$241$	−3.41098	−	23.7239i	−0.219720	−	1.52819i	−0.739071	−	0.673627i	$-0.764735\pi$
$241$	−3.41098	−	23.7239i	−0.219720	−	1.52819i	0.519351	−	0.854561i	$-0.326174\pi$
$242$	−16.2878	+	2.34183i	−1.04702	+	0.150539i
$243$	0.540641	+	0.841254i	0.0346821	+	0.0539664i
$244$	9.00928	−	10.3973i	0.576760	−	0.665616i
$245$	14.5166	+	1.11423i	0.927433	+	0.0711858i
$246$	1.68962	+	1.08585i	0.107726	+	0.0692313i
$247$	3.90978	+	13.3155i	0.248773	+	0.847243i
$248$	4.84026	−	4.19411i	0.307357	−	0.266326i
$249$	−15.5708	−	4.57201i	−0.986761	−	0.289739i
$250$	−11.1380	−	0.971653i	−0.704431	−	0.0614527i
$251$	−0.237575	+	1.65237i	−0.0149956	+	0.104297i	−0.995945	−	0.0899689i	$-0.971323\pi$
$251$	−0.237575	+	1.65237i	−0.0149956	+	0.104297i	0.980949	+	0.194265i	$0.0622323\pi$
$252$		−	0.699197i		−	0.0440453i
$253$	24.5919	−	5.16797i	1.54608	−	0.324907i
$254$	−10.2367			−0.642305
$255$	−5.94317	+	1.26049i	−0.372175	+	0.0789350i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	2.45152	−	8.34913i	0.152922	−	0.520804i	−0.847020	−	0.531561i	$-0.821606\pi$
$257$	2.45152	−	8.34913i	0.152922	−	0.520804i	0.999942	+	0.0107565i	$0.00342396\pi$
$258$	−3.62691	+	3.14273i	−0.225801	+	0.195658i
$259$	3.86003	−	1.13341i	0.239851	−	0.0704265i
$260$	−7.78280	−	1.73552i	−0.482669	−	0.107633i
$261$	3.56222	−	7.80017i	0.220496	−	0.482818i
$262$	−8.15978	−	7.07049i	−0.504113	−	0.436816i
$263$	9.90143	+	15.4069i	0.610548	+	0.950032i	0.999585	+	0.0288094i	$0.00917159\pi$
$263$	9.90143	+	15.4069i	0.610548	+	0.950032i	−0.389037	+	0.921222i	$0.627192\pi$
$264$	0.745698	+	5.18645i	0.0458946	+	0.319204i
$265$	−2.06934	−	3.83706i	−0.127118	−	0.235709i
$266$	−2.28903	+	1.47107i	−0.140350	+	0.0901973i
$267$	−6.83709	−	5.92437i	−0.418423	−	0.362566i
$268$	−3.16613	−	1.44593i	−0.193402	−	0.0883239i
$269$	11.1820	+	7.18625i	0.681780	+	0.438153i	0.835155	−	0.550015i	$-0.185378\pi$
$269$	11.1820	+	7.18625i	0.681780	+	0.438153i	−0.153375	+	0.988168i	$0.549014\pi$
$270$	1.33069	+	1.79702i	0.0809831	+	0.109363i
$271$	−1.23019	−	1.41971i	−0.0747286	−	0.0862414i	0.717154	−	0.696915i	$-0.245444\pi$
$271$	−1.23019	−	1.41971i	−0.0747286	−	0.0862414i	−0.791883	+	0.610673i	$0.790899\pi$
$272$	−0.765463	+	2.60693i	−0.0464130	+	0.158068i
$273$	2.26806	−	1.03579i	0.137269	−	0.0626887i
$274$	−0.723428	+	5.03155i	−0.0437039	+	0.303967i
$275$	−19.9774	+	16.9496i	−1.20468	+	1.02210i
$276$	−0.986295	−	4.69332i	−0.0593680	−	0.282504i
$277$		−	15.2176i		−	0.914338i	−0.889380	−	0.457169i	$-0.848863\pi$
$277$		−	15.2176i		−	0.914338i	0.889380	−	0.457169i	$-0.151137\pi$
$278$	−7.19659	−	1.03471i	−0.431623	−	0.0620580i
$279$	−2.66056	−	5.82581i	−0.159284	−	0.348782i
$280$	−0.103416	−	1.56003i	−0.00618027	−	0.0932295i
$281$	11.4483	+	13.2120i	0.682947	+	0.788163i	0.986343	−	0.164702i	$-0.0526661\pi$
$281$	11.4483	+	13.2120i	0.682947	+	0.788163i	−0.303397	+	0.952864i	$0.598121\pi$
$282$	−1.54179	−	5.25085i	−0.0918122	−	0.312684i
$283$	−10.4488	+	16.2587i	−0.621118	+	0.966479i	0.378054	+	0.925784i	$0.376594\pi$
$283$	−10.4488	+	16.2587i	−0.621118	+	0.966479i	−0.999172	+	0.0406948i	$0.987043\pi$
$284$	−0.140092	+	0.306758i	−0.00831291	+	0.0182027i
$285$	3.08338	−	8.13724i	0.182644	−	0.482009i
$286$	−15.7191	+	10.1021i	−0.929492	+	0.597348i
$287$	−1.39001	+	0.199853i	−0.0820496	+	0.0117970i
$288$	0.989821	−	0.142315i	0.0583258	−	0.00838598i
$289$	8.09117	−	5.19988i	0.475951	−	0.305875i
$290$	6.79422	−	17.9304i	0.398970	−	1.05291i
$291$	−3.03341	+	6.64224i	−0.177822	+	0.389375i
$292$	−7.01345	+	10.9131i	−0.410431	+	0.638644i
$293$	8.18543	+	27.8770i	0.478198	+	1.62859i	0.746591	+	0.665283i	$0.231689\pi$
$293$	8.18543	+	27.8770i	0.478198	+	1.62859i	−0.268394	+	0.963309i	$0.586493\pi$
$294$	−4.26388	−	4.92078i	−0.248674	−	0.286986i
$295$	1.61399	+	24.3470i	0.0939699	+	1.41754i
$296$	2.39019	+	5.23378i	0.138927	+	0.304207i
$297$	5.18645	+	0.745698i	0.300948	+	0.0432698i
$298$			22.9480i			1.32934i
$299$	13.7631	−	10.1520i	0.795941	−	0.587106i
$300$	3.23478	+	3.81263i	0.186760	+	0.220122i
$301$	0.477539	−	3.32135i	0.0275249	−	0.191440i
$302$	−9.58269	+	4.37627i	−0.551422	+	0.251826i
$303$	3.22360	−	10.9786i	0.185191	−	0.630703i
$304$	−2.54844	−	2.94106i	−0.146163	−	0.168681i
$305$	−18.3070	−	24.7225i	−1.04826	−	1.41561i
$306$	2.28567	+	1.46891i	0.130663	+	0.0839722i
$307$	15.5716	+	7.11132i	0.888719	+	0.405864i	0.806835	−	0.590778i	$-0.201179\pi$
$307$	15.5716	+	7.11132i	0.888719	+	0.405864i	0.0818844	+	0.996642i	$0.473906\pi$
$308$	−2.76879	−	2.39917i	−0.157767	−	0.136706i
$309$	0.563199	−	0.361946i	0.0320393	−	0.0205904i
$310$	−6.79784	−	12.6049i	−0.386091	−	0.715909i
$311$	−2.93809	−	20.4349i	−0.166604	−	1.15876i	−0.885840	−	0.463991i	$-0.846417\pi$
$311$	−2.93809	−	20.4349i	−0.166604	−	1.15876i	0.719236	−	0.694766i	$-0.244492\pi$
$312$	1.92796	+	2.99996i	0.109149	+	0.169839i
$313$	−10.1029	−	8.75417i	−0.571047	−	0.494815i	0.320803	−	0.947146i	$-0.396047\pi$
$313$	−10.1029	−	8.75417i	−0.571047	−	0.494815i	−0.891850	+	0.452331i	$0.850593\pi$
$314$	4.41959	−	9.67754i	0.249412	−	0.546135i
$315$	−1.52597	−	0.340284i	−0.0859787	−	0.0191728i
$316$	−4.54226	+	1.33373i	−0.255522	+	0.0750280i
$317$	−2.29903	+	1.99212i	−0.129126	+	0.111888i	−0.717030	−	0.697043i	$-0.754499\pi$
$317$	−2.29903	+	1.99212i	−0.129126	+	0.111888i	0.587904	+	0.808931i	$0.299953\pi$
$318$	−0.549273	+	1.87065i	−0.0308017	+	0.104901i
$319$	−18.6652	−	40.8711i	−1.04505	−	2.28834i
$320$	2.18741	−	0.463930i	0.122280	−	0.0259345i
$321$	17.6267			0.983824
$322$	2.67014	+	2.02843i	0.148801	+	0.113040i
$323$		−	10.5734i		−	0.588318i
$324$	0.142315	−	0.989821i	0.00790638	−	0.0549901i
$325$	−7.57544	+	16.1410i	−0.420210	+	0.895343i
$326$	0.632127	+	0.185609i	0.0350103	+	0.0102799i
$327$	−14.6268	+	12.6742i	−0.808862	+	0.700883i
$328$	−0.565846	−	1.92709i	−0.0312436	−	0.106406i
$329$	3.21895	+	2.06869i	0.177467	+	0.114051i
$330$	11.6821	+	0.896672i	0.643081	+	0.0493602i
$331$	9.23796	−	10.6612i	0.507764	−	0.585991i	−0.442760	−	0.896640i	$-0.646001\pi$
$331$	9.23796	−	10.6612i	0.507764	−	0.585991i	0.950525	+	0.310649i	$0.100546\pi$
$332$	8.77361	+	13.6520i	0.481515	+	0.749251i
$333$	5.69517	−	0.818842i	0.312093	−	0.0448722i
$334$	1.31655	+	9.15683i	0.0720386	+	0.501039i
$335$	−4.69657	+	6.20627i	−0.256601	+	0.339085i
$336$	−0.457877	+	0.528418i	−0.0249792	+	0.0288276i
$337$	16.3025	+	7.44512i	0.888056	+	0.405562i	0.806588	−	0.591114i	$-0.201312\pi$
$337$	16.3025	+	7.44512i	0.888056	+	0.405562i	0.0814681	+	0.996676i	$0.474039\pi$
$338$	0.153111	−	0.238246i	0.00832816	−	0.0129589i
$339$	−8.01217	+	2.35259i	−0.435161	+	0.127775i
$340$	5.31699	+	2.93933i	0.288354	+	0.159408i
$341$	−32.1993	−	9.45455i	−1.74369	−	0.511993i
$342$	−3.53991	+	1.61662i	−0.191416	+	0.0874168i
$343$	9.35078	+	1.34444i	0.504895	+	0.0725929i
$344$	4.79909			0.258750
$345$	−10.7230	−	0.131583i	−0.577307	−	0.00708420i
$346$	−2.44455			−0.131420
$347$	6.59279	+	0.947901i	0.353920	+	0.0508860i	0.316982	−	0.948432i	$-0.397331\pi$
$347$	6.59279	+	0.947901i	0.353920	+	0.0508860i	0.0369378	+	0.999318i	$0.488240\pi$
$348$	−7.80017	+	3.56222i	−0.418133	+	0.190955i
$349$	−15.3854	−	4.51755i	−0.823559	−	0.241819i	−0.157311	−	0.987549i	$-0.550283\pi$
$349$	−15.3854	−	4.51755i	−0.823559	−	0.241819i	−0.666248	+	0.745730i	$0.732101\pi$
$350$	−3.45503	−	0.533531i	−0.184679	−	0.0285184i
$351$	3.42161	−	1.00468i	0.182632	−	0.0536256i
$352$	2.83284	−	4.40798i	0.150991	−	0.234946i
$353$	−6.70203	−	3.06071i	−0.356713	−	0.162905i	0.228995	−	0.973428i	$-0.426456\pi$
$353$	−6.70203	−	3.06071i	−0.356713	−	0.162905i	−0.585708	+	0.810522i	$0.699183\pi$
$354$	7.14598	−	8.24690i	0.379804	−	0.438318i
$355$	0.601308	+	0.455037i	0.0319141	+	0.0241509i
$356$	1.28749	+	8.95468i	0.0682368	+	0.474597i
$357$	−1.88037	+	0.270357i	−0.0995198	+	0.0143088i
$358$	7.11305	+	11.0681i	0.375936	+	0.584968i
$359$	16.4979	−	19.0396i	0.870725	−	1.00487i	−0.129187	−	0.991620i	$-0.541237\pi$
$359$	16.4979	−	19.0396i	0.870725	−	1.00487i	0.999912	−	0.0132499i	$-0.00421770\pi$
$360$	0.171128	−	2.22951i	0.00901923	−	0.117505i
$361$	−3.24354	−	2.08450i	−0.170713	−	0.109710i
$362$	2.51172	+	8.55414i	0.132013	+	0.449596i
$363$	12.4361	−	10.7759i	0.652725	−	0.565589i
$364$	−2.39238	−	0.702466i	−0.125395	−	0.0368192i
$365$	20.4042	+	20.6178i	1.06801	+	1.07918i
$366$	−1.95790	+	13.6175i	−0.102341	+	0.711799i
$367$			24.9237i			1.30100i	0.759505	+	0.650502i	$0.225441\pi$
$367$			24.9237i			1.30100i	−0.759505	+	0.650502i	$0.774559\pi$
$368$	−2.32808	+	4.19286i	−0.121359	+	0.218568i
$369$	−2.00845			−0.104556
$370$	12.5858	−	2.66933i	0.654304	−	0.138772i
$371$	−0.566282	−	1.23998i	−0.0293999	−	0.0643768i
$372$	−1.80438	+	6.14515i	−0.0935527	+	0.318611i
$373$	8.54253	−	7.40214i	0.442315	−	0.383268i	−0.405036	−	0.914301i	$-0.632741\pi$
$373$	8.54253	−	7.40214i	0.442315	−	0.383268i	0.847352	+	0.531032i	$0.178196\pi$
$374$	13.6597	−	4.01086i	0.706328	−	0.207397i
$375$	9.89523	−	5.20427i	0.510987	−	0.268747i
$376$	−2.27337	+	4.97799i	−0.117240	+	0.256720i
$377$	−23.1103	−	20.0252i	−1.19024	−	1.03135i
$378$	0.378014	+	0.588202i	0.0194430	+	0.0302538i
$379$	3.30677	+	22.9991i	0.169857	+	1.18138i	0.879177	+	0.476496i	$0.158093\pi$
$379$	3.30677	+	22.9991i	0.169857	+	1.18138i	−0.709319	+	0.704887i	$0.750998\pi$
$380$	−7.65903	+	4.13053i	−0.392900	+	0.211892i
$381$	8.61162	−	5.53435i	0.441187	−	0.283533i
$382$	10.1230	+	8.77164i	0.517939	+	0.448796i
$383$	−32.8631	−	15.0081i	−1.67923	−	0.766877i	−0.999440	−	0.0334683i	$-0.989345\pi$
$383$	−32.8631	−	15.0081i	−1.67923	−	0.766877i	−0.679788	−	0.733409i	$-0.737928\pi$
$384$	−0.841254	−	0.540641i	−0.0429300	−	0.0275895i
$385$	−6.58362	+	4.87516i	−0.335532	+	0.248461i
$386$	−12.7071	−	14.6648i	−0.646776	−	0.746419i
$387$	1.35206	−	4.60469i	0.0687290	−	0.234070i
$388$	6.64224	−	3.03341i	0.337209	−	0.153998i
$389$	0.329297	−	2.29031i	0.0166960	−	0.116123i	−0.979769	−	0.200132i	$-0.935863\pi$
$389$	0.329297	−	2.29031i	0.0166960	−	0.116123i	0.996465	+	0.0840081i	$0.0267721\pi$
$390$	7.48560	−	2.74768i	0.379048	−	0.139134i
$391$	−12.2405	+	4.46723i	−0.619029	+	0.225917i
$392$			6.51112i			0.328861i
$393$	10.6870	+	1.53656i	0.539090	+	0.0775094i
$394$	−7.58642	−	16.6119i	−0.382198	−	0.836898i
$395$	0.700192	+	10.5624i	0.0352305	+	0.531452i
$396$	−3.43133	−	3.95996i	−0.172431	−	0.198996i
$397$	9.32110	+	31.7448i	0.467813	+	1.59322i	0.768730	+	0.639574i	$0.220889\pi$
$397$	9.32110	+	31.7448i	0.467813	+	1.59322i	−0.300917	+	0.953650i	$0.597293\pi$
$398$	6.60888	−	10.2836i	0.331273	−	0.515471i
$399$	1.13034	−	2.47509i	0.0565876	−	0.123910i
$400$	0.0520564	−	4.99973i	0.00260282	−	0.249986i
$401$	−5.41843	+	3.48222i	−0.270584	+	0.173894i	−0.668895	−	0.743357i	$-0.733233\pi$
$401$	−5.41843	+	3.48222i	−0.270584	+	0.173894i	0.398312	+	0.917250i	$0.369596\pi$
$402$	3.44525	−	0.495352i	0.171833	−	0.0247059i
$403$	−22.6067	+	3.25035i	−1.12612	+	0.161911i
$404$	−9.62568	+	6.18605i	−0.478896	+	0.307767i
$405$	−2.09099	−	0.792321i	−0.103902	−	0.0393708i
$406$	2.49069	−	5.45385i	0.123611	−	0.270670i
$407$	16.2994	−	25.3624i	0.807931	−	1.25717i
$408$	−0.765463	−	2.60693i	−0.0378961	−	0.129062i
$409$	−13.1488	−	15.1745i	−0.650166	−	0.750332i	0.330972	−	0.943641i	$-0.392623\pi$
$409$	−13.1488	−	15.1745i	−0.650166	−	0.750332i	−0.981138	+	0.193309i	$0.938078\pi$
$410$	−4.48120	+	0.297063i	−0.221311	+	0.0146709i
$411$	−2.11168	−	4.62393i	−0.104161	−	0.228082i
$412$	−0.662661	−	0.0952763i	−0.0326470	−	0.00469393i
$413$			7.62978i			0.375437i
$414$	3.36712	+	3.41504i	0.165485	+	0.167840i
$415$	34.0649	−	12.5040i	1.67218	−	0.613795i
$416$	0.507504	−	3.52976i	0.0248824	−	0.173061i
$417$	6.61357	−	3.02031i	0.323868	−	0.147905i
$418$	−5.74481	+	19.5650i	−0.280988	+	0.956957i
$419$	−3.11298	−	3.59257i	−0.152079	−	0.175509i	0.674598	−	0.738185i	$-0.264317\pi$
$419$	−3.11298	−	3.59257i	−0.152079	−	0.175509i	−0.826677	+	0.562677i	$0.809772\pi$
$420$	0.930414	+	1.25647i	0.0453995	+	0.0613094i
$421$	7.03159	+	4.51893i	0.342699	+	0.220239i	0.700657	−	0.713499i	$-0.252890\pi$
$421$	7.03159	+	4.51893i	0.342699	+	0.220239i	−0.357958	+	0.933738i	$0.616527\pi$
$422$	16.9855	+	7.75700i	0.826839	+	0.377605i
$423$	4.13586	+	3.58374i	0.201092	+	0.174248i
$424$	1.64013	−	1.05405i	0.0796517	−	0.0511890i
$425$	9.00264	−	10.1736i	0.436692	−	0.493493i
$426$	−0.0479933	−	0.333800i	−0.00232528	−	0.0161727i
$427$	−5.20055	−	8.09221i	−0.251672	−	0.391610i
$428$	−13.3213	−	11.5430i	−0.643911	−	0.557952i
$429$	7.76219	−	16.9968i	0.374762	−	0.820614i
$430$	2.33561	−	10.4738i	0.112633	−	0.505093i
$431$	12.5236	−	3.67727i	0.603242	−	0.177128i	0.0341706	−	0.999416i	$-0.489121\pi$
$431$	12.5236	−	3.67727i	0.603242	−	0.177128i	0.569071	+	0.822288i	$0.307303\pi$
$432$	−0.755750	+	0.654861i	−0.0363610	+	0.0315070i
$433$	−0.235621	+	0.802452i	−0.0113232	+	0.0385634i	−0.964961	−	0.262394i	$-0.915488\pi$
$433$	−0.235621	+	0.802452i	−0.0113232	+	0.0385634i	0.953638	+	0.300957i	$0.0973062\pi$
$434$	−1.86026	−	4.07339i	−0.0892951	−	0.195529i
$435$	3.97823	+	18.7572i	0.190742	+	0.899340i
$436$	19.3540			0.926888
$437$	4.09592	−	18.2084i	0.195935	−	0.871024i
$438$		−	12.9725i		−	0.619849i
$439$	−2.32546	+	16.1739i	−0.110988	+	0.771940i	0.855974	+	0.517020i	$0.172959\pi$
$439$	−2.32546	+	16.1739i	−0.110988	+	0.771940i	−0.966962	+	0.254921i	$0.917951\pi$
$440$	−8.24158	−	8.32784i	−0.392902	−	0.397014i
$441$	6.24738	+	1.83440i	0.297494	+	0.0873522i
$442$	7.32241	−	6.34491i	0.348292	−	0.301796i
$443$	−1.27270	−	4.33442i	−0.0604678	−	0.205935i	0.923718	−	0.383073i	$-0.125134\pi$
$443$	−1.27270	−	4.33442i	−0.0604678	−	0.205935i	−0.984186	+	0.177138i	$0.943316\pi$
$444$	−4.84035	−	3.11070i	−0.229713	−	0.147627i
$445$	20.1699	+	1.54815i	0.956143	+	0.0733895i
$446$	5.08515	−	5.86858i	0.240789	−	0.277885i
$447$	−12.4066	−	19.3051i	−0.586813	−	0.913099i
$448$	0.692080	−	0.0995061i	0.0326977	−	0.00470122i
$449$	1.69888	+	11.8159i	0.0801749	+	0.557628i	0.989829	+	0.142262i	$0.0454376\pi$
$449$	1.69888	+	11.8159i	0.0801749	+	0.557628i	−0.909654	+	0.415366i	$0.863653\pi$
$450$	−4.78254	−	1.45853i	−0.225451	−	0.0687560i
$451$	−6.89165	+	7.95339i	−0.324515	+	0.374510i
$452$	7.59581	+	3.46889i	0.357277	+	0.163163i
$453$	5.69548	−	8.86234i	0.267597	−	0.416389i
$454$	−0.0728235	+	0.0213829i	−0.00341778	+	0.00100355i
$455$	−2.69743	+	4.87941i	−0.126457	+	0.228750i
$456$	3.73394	+	1.09638i	0.174858	+	0.0513429i
$457$	11.1120	−	5.07468i	0.519797	−	0.237383i	−0.138199	−	0.990404i	$-0.544131\pi$
$457$	11.1120	−	5.07468i	0.519797	−	0.237383i	0.657996	+	0.753021i	$0.271404\pi$
$458$	−14.5156	−	2.08703i	−0.678269	−	0.0975203i
$459$	−2.71699			−0.126818
$460$	8.01773	+	7.12151i	0.373829	+	0.332042i
$461$	−26.9976			−1.25740			−0.628701	−	0.777647i	$-0.716413\pi$
$461$	−26.9976			−1.25740			−0.628701	+	0.777647i	$0.716413\pi$
$462$	3.62635	+	0.521390i	0.168713	+	0.0242573i
$463$	−10.4920	+	4.79156i	−0.487607	+	0.222683i	−0.644019	−	0.765009i	$-0.722734\pi$
$463$	−10.4920	+	4.79156i	−0.487607	+	0.222683i	0.156413	+	0.987692i	$0.450007\pi$
$464$	8.22773	+	2.41588i	0.381963	+	0.112154i
$465$	12.5334	+	6.92871i	0.581223	+	0.321311i
$466$	16.5115	−	4.84822i	0.764882	−	0.224590i
$467$	9.48329	−	14.7563i	0.438834	−	0.682839i	−0.549439	−	0.835534i	$-0.685159\pi$
$467$	9.48329	−	14.7563i	0.438834	−	0.682839i	0.988273	+	0.152694i	$0.0487950\pi$
$468$	−3.24380	−	1.48140i	−0.149945	−	0.0684775i
$469$	−1.59372	+	1.83925i	−0.0735912	+	0.0849287i
$470$	9.75787	+	7.38422i	0.450097	+	0.340609i
$471$	1.51408	+	10.5307i	0.0697652	+	0.485228i
$472$	−10.8011	+	1.55297i	−0.497163	+	0.0714812i
$473$	−13.5950	−	21.1543i	−0.625101	−	0.972676i
$474$	3.10012	−	3.57773i	0.142393	−	0.164331i
$475$	5.28725	+	18.7258i	0.242596	+	0.859198i
$476$	1.59814	+	1.02706i	0.0732504	+	0.0470752i
$477$	−0.549273	−	1.87065i	−0.0251495	−	0.0856512i
$478$	3.07985	−	2.66870i	0.140869	−	0.122064i
$479$	−6.31947	−	1.85556i	−0.288744	−	0.0847829i	0.134153	−	0.990961i	$-0.457169\pi$
$479$	−6.31947	−	1.85556i	−0.288744	−	0.0847829i	−0.422897	+	0.906178i	$0.638987\pi$
$480$	−1.58935	+	1.57289i	−0.0725435	+	0.0717921i
$481$	2.92004	−	20.3093i	0.133142	−	0.926025i
$482$		−	23.9678i		−	1.09170i
$483$	−3.34291	−	0.262840i	−0.152108	−	0.0119596i
$484$	−16.4553			−0.747968
$485$	−3.38767	−	15.9727i	−0.153826	−	0.725285i
$486$	0.415415	+	0.909632i	0.0188436	+	0.0412617i
$487$	−10.8847	+	37.0698i	−0.493232	+	1.67979i	0.217281	+	0.976109i	$0.430281\pi$
$487$	−10.8847	+	37.0698i	−0.493232	+	1.67979i	−0.710513	+	0.703684i	$0.751537\pi$
$488$	10.3973	−	9.00928i	0.470662	−	0.407831i
$489$	−0.632127	+	0.185609i	−0.0285858	+	0.00839354i
$490$	14.2103	+	3.16882i	0.641955	+	0.143153i
$491$	12.1731	−	26.6554i	0.549365	−	1.20294i	−0.407713	−	0.913110i	$-0.633674\pi$
$491$	12.1731	−	26.6554i	0.549365	−	1.20294i	0.957078	−	0.289831i	$-0.0935992\pi$
$492$	1.51789	+	1.31526i	0.0684316	+	0.0592963i
$493$	12.5960	+	19.5998i	0.567297	+	0.882732i
$494$	1.97499	+	13.7364i	0.0888590	+	0.618028i
$495$	−10.3124	+	5.56151i	−0.463509	+	0.249971i
$496$	5.38788	−	3.46258i	0.241923	−	0.155474i
$497$	0.178200	+	0.154411i	0.00799336	+	0.00692628i
$498$	−14.7617	−	6.74143i	−0.661486	−	0.302091i
$499$	−3.82672	−	2.45928i	−0.171307	−	0.110093i	0.452177	−	0.891928i	$-0.350647\pi$
$499$	−3.82672	−	2.45928i	−0.171307	−	0.110093i	−0.623485	+	0.781835i	$0.714284\pi$
$500$	−10.8864	−	2.54687i	−0.486854	−	0.113900i
$501$	−6.05811	−	6.99143i	−0.270656	−	0.312354i
$502$	−0.470313	+	1.60174i	−0.0209911	+	0.0714891i
$503$	6.79778	−	3.10444i	0.303098	−	0.138420i	−0.258060	−	0.966129i	$-0.583083\pi$
$503$	6.79778	−	3.10444i	0.303098	−	0.138420i	0.561158	+	0.827709i	$0.310356\pi$
$504$	0.0995061	−	0.692080i	0.00443235	−	0.0308277i
$505$	8.81621	+	24.0183i	0.392316	+	1.06880i
$506$	25.0771	−	1.61557i	1.11481	−	0.0718207i
$507$			0.283203i			0.0125775i
$508$	−10.1325	−	1.45683i	−0.449555	−	0.0646363i
$509$	18.7127	+	40.9751i	0.829426	+	1.81619i	0.467580	+	0.883951i	$0.345126\pi$
$509$	18.7127	+	40.9751i	0.829426	+	1.81619i	0.361846	+	0.932238i	$0.382147\pi$
$510$	−6.06206	+	0.401860i	−0.268432	+	0.0177946i
$511$	5.93980	+	6.85489i	0.262761	+	0.303242i
$512$	0.281733	+	0.959493i	0.0124509	+	0.0424040i
$513$	2.10395	−	3.27381i	0.0928915	−	0.144542i
$514$	3.61478	−	7.91526i	0.159441	−	0.349127i
$515$	−0.530440	+	1.39986i	−0.0233740	+	0.0616854i
$516$	−4.03725	+	2.59458i	−0.177730	+	0.114220i
$517$	28.3830	−	4.08085i	1.24828	−	0.179476i
$518$	3.98204	−	0.572532i	0.174961	−	0.0251556i
$519$	2.05649	−	1.32163i	0.0902698	−	0.0580129i
$520$	−7.45659	−	2.82547i	−0.326993	−	0.123905i
$521$	8.96959	−	19.6407i	0.392965	−	0.860473i	−0.604970	−	0.796248i	$-0.706815\pi$
$521$	8.96959	−	19.6407i	0.392965	−	0.860473i	0.997935	−	0.0642254i	$-0.0204577\pi$
$522$	4.63604	−	7.21381i	0.202914	−	0.315740i
$523$	−10.1525	−	34.5763i	−0.443938	−	1.51191i	−0.812863	−	0.582455i	$-0.802092\pi$
$523$	−10.1525	−	34.5763i	−0.443938	−	1.51191i	0.368924	−	0.929459i	$-0.379726\pi$
$524$	−7.07049	−	8.15978i	−0.308876	−	0.356461i
$525$	3.19501	−	1.41910i	0.139442	−	0.0619345i
$526$	7.60801	+	16.6592i	0.331725	+	0.726377i
$527$	17.2240	+	2.47644i	0.750291	+	0.107876i
$528$			5.23978i			0.228032i
$529$	−22.8099	+	2.95125i	−0.991733	+	0.128315i
$530$	−1.50220	−	4.09250i	−0.0652515	−	0.177767i
$531$	−1.55297	+	10.8011i	−0.0673931	+	0.468729i
$532$	−2.47509	+	1.13034i	−0.107309	+	0.0490063i
$533$	−2.01784	+	6.87214i	−0.0874024	+	0.297665i
$534$	−5.92437	−	6.83709i	−0.256373	−	0.295870i
$535$	−31.6754	+	23.4556i	−1.36945	+	1.01407i
$536$	−2.92813	−	1.88180i	−0.126476	−	0.0812812i
$537$	−11.9678	−	5.46549i	−0.516447	−	0.235853i
$538$	10.0455	+	8.70447i	0.433092	+	0.375276i
$539$	28.7009	−	18.4450i	1.23624	−	0.794481i
$540$	1.06140	+	1.96810i	0.0456755	+	0.0846936i
$541$	−0.764317	−	5.31594i	−0.0328606	−	0.228550i	0.966772	−	0.255638i	$-0.0822856\pi$
$541$	−0.764317	−	5.31594i	−0.0328606	−	0.228550i	−0.999633	+	0.0270881i	$0.991377\pi$
$542$	−1.01562	−	1.58034i	−0.0436246	−	0.0678812i
$543$	−6.73772	−	5.83826i	−0.289143	−	0.250544i
$544$	−1.12868	+	2.47146i	−0.0483916	+	0.105963i
$545$	9.41917	−	42.2394i	0.403473	−	1.80934i
$546$	2.39238	−	0.702466i	0.102384	−	0.0300628i
$547$	−14.8188	+	12.8406i	−0.633608	+	0.549024i	−0.911351	−	0.411631i	$-0.864959\pi$
$547$	−14.8188	+	12.8406i	−0.633608	+	0.549024i	0.277743	+	0.960656i	$0.410414\pi$
$548$	−1.43213	+	4.87739i	−0.0611775	+	0.208352i
$549$	−5.71509	−	12.5143i	−0.243914	−	0.534097i
$550$	−22.1862	+	13.9340i	−0.946022	+	0.594146i
$551$	−33.3706			−1.42164
$552$	−0.308327	−	4.78591i	−0.0131233	−	0.203702i
$553$			3.31001i			0.140756i
$554$	2.16569	−	15.0627i	0.0920115	−	0.639954i
$555$	−9.14469	+	9.04997i	−0.388170	+	0.384150i
$556$	−6.97609	−	2.04836i	−0.295852	−	0.0868700i
$557$	−5.70848	+	4.94643i	−0.241876	+	0.209587i	−0.767360	−	0.641217i	$-0.778430\pi$
$557$	−5.70848	+	4.94643i	−0.241876	+	0.209587i	0.525484	+	0.850804i	$0.323884\pi$
$558$	−1.80438	−	6.14515i	−0.0763855	−	0.260145i
$559$	−14.3971	−	9.25244i	−0.608932	−	0.391337i
$560$	0.119652	−	1.55887i	0.00505622	−	0.0658741i
$561$	−9.32286	+	10.7592i	−0.393612	+	0.454252i
$562$	9.45148	+	14.7068i	0.398687	+	0.620369i
$563$	9.00327	−	1.29448i	0.379443	−	0.0545556i	0.0500452	−	0.998747i	$-0.484063\pi$
$563$	9.00327	−	1.29448i	0.379443	−	0.0545556i	0.329398	+	0.944191i	$0.393154\pi$
$564$	−0.778822	−	5.41682i	−0.0327943	−	0.228089i
$565$	11.2674	−	14.8893i	0.474025	−	0.626399i
$566$	−12.6563	+	14.6062i	−0.531985	+	0.613943i
$567$	−0.636012	−	0.290457i	−0.0267100	−	0.0121980i
$568$	−0.182322	+	0.283698i	−0.00765006	+	0.0119037i
$569$	−1.36234	+	0.400018i	−0.0571121	+	0.0167696i	−0.310164	−	0.950683i	$-0.600384\pi$
$569$	−1.36234	+	0.400018i	−0.0571121	+	0.0167696i	0.253052	+	0.967453i	$0.418566\pi$
$570$	4.21005	−	7.61561i	0.176340	−	0.318983i
$571$	−34.9130	−	10.2514i	−1.46106	−	0.429007i	−0.547880	−	0.836557i	$-0.684565\pi$
$571$	−34.9130	−	10.2514i	−1.46106	−	0.429007i	−0.913183	+	0.407550i	$0.866383\pi$
$572$	−16.9968	+	7.76219i	−0.710673	+	0.324553i
$573$	−13.2583	−	1.90626i	−0.553875	−	0.0796352i
$574$	−1.40430			−0.0586145
$575$	19.4445	−	14.0325i	0.810892	−	0.585196i
$576$	1.00000			0.0416667
$577$	−37.8576	−	5.44311i	−1.57603	−	0.226600i	−0.701897	−	0.712278i	$-0.747663\pi$
$577$	−37.8576	−	5.44311i	−1.57603	−	0.226600i	−0.874137	+	0.485679i	$0.838572\pi$
$578$	8.74883	−	3.99546i	0.363903	−	0.166189i
$579$	18.6183	+	5.46683i	0.773751	+	0.227194i
$580$	9.27682	−	16.7810i	0.385199	−	0.696791i
$581$	10.8871	−	3.19673i	0.451672	−	0.132623i
$582$	−3.94782	+	6.14293i	−0.163643	+	0.254633i
$583$	−9.29244	−	4.24372i	−0.384854	−	0.175757i
$584$	−8.49517	+	9.80395i	−0.351533	+	0.405690i
$585$	−4.81178	+	6.35852i	−0.198943	+	0.262892i
$586$	4.13480	+	28.7582i	0.170807	+	1.18799i
$587$	23.8886	−	3.43466i	0.985988	−	0.141764i	0.369587	−	0.929196i	$-0.379499\pi$
$587$	23.8886	−	3.43466i	0.985988	−	0.141764i	0.616401	+	0.787432i	$0.288590\pi$
$588$	−3.52018	−	5.47751i	−0.145170	−	0.225889i
$589$	−16.3217	+	18.8363i	−0.672525	+	0.776135i
$590$	−1.86738	+	24.3289i	−0.0768789	+	1.00160i
$591$	15.3632	+	9.87333i	0.631958	+	0.406135i
$592$	1.62101	+	5.52067i	0.0666233	+	0.226898i
$593$	−11.9524	+	10.3568i	−0.490828	+	0.425305i	−0.864786	−	0.502141i	$-0.832546\pi$
$593$	−11.9524	+	10.3568i	−0.490828	+	0.425305i	0.373958	+	0.927446i	$0.378000\pi$
$594$	5.02753	+	1.47622i	0.206282	+	0.0605699i
$595$	3.01930	−	2.98803i	0.123779	−	0.122497i
$596$	−3.26584	+	22.7144i	−0.133774	+	0.930418i
$597$			12.2242i			0.500302i
$598$	15.0678	−	8.08998i	0.616168	−	0.330824i
$599$	17.9876			0.734955			0.367478	−	0.930032i	$-0.380221\pi$
$599$	17.9876			0.734955			0.367478	+	0.930032i	$0.380221\pi$
$600$	2.65926	+	4.23418i	0.108564	+	0.172860i
$601$	18.5179	+	40.5485i	0.755361	+	1.65401i	0.756486	+	0.654010i	$0.226915\pi$
$601$	18.5179	+	40.5485i	0.755361	+	1.65401i	−0.00112508	+	0.999999i	$0.500358\pi$
$602$	0.945356	−	3.21959i	0.0385298	−	0.131221i
$603$	−2.63052	+	2.27936i	−0.107123	+	0.0928226i
$604$	−10.1080	+	2.96796i	−0.411287	+	0.120765i
$605$	−8.00843	+	35.9131i	−0.325589	+	1.46007i
$606$	4.75321	−	10.4081i	0.193086	−	0.422799i
$607$	−18.7469	−	16.2443i	−0.760912	−	0.659334i	0.185373	−	0.982668i	$-0.440651\pi$
$607$	−18.7469	−	16.2443i	−0.760912	−	0.659334i	−0.946285	+	0.323334i	$0.895196\pi$
$608$	−2.10395	−	3.27381i	−0.0853263	−	0.132770i
$609$	0.853273	+	5.93464i	0.0345763	+	0.240484i
$610$	−14.6023	−	27.0763i	−0.591229	−	1.09629i
$611$	16.4174	−	10.5508i	0.664176	−	0.426840i
$612$	2.05336	+	1.77925i	0.0830022	+	0.0719218i
$613$	−18.2522	−	8.33551i	−0.737201	−	0.336668i	0.0111803	−	0.999937i	$-0.496441\pi$
$613$	−18.2522	−	8.33551i	−0.737201	−	0.336668i	−0.748381	+	0.663269i	$0.769168\pi$
$614$	14.4011	+	9.25501i	0.581180	+	0.373502i
$615$	3.60922	−	2.67262i	0.145538	−	0.107771i
$616$	−2.39917	−	2.76879i	−0.0966654	−	0.111558i
$617$	−12.8572	+	43.7876i	−0.517611	+	1.76282i	0.120326	+	0.992734i	$0.461606\pi$
$617$	−12.8572	+	43.7876i	−0.517611	+	1.76282i	−0.637938	+	0.770088i	$0.720212\pi$
$618$	0.608977	−	0.278110i	0.0244966	−	0.0111872i
$619$	−3.39385	+	23.6047i	−0.136410	+	0.948755i	0.800537	+	0.599284i	$0.204548\pi$
$619$	−3.39385	+	23.6047i	−0.136410	+	0.948755i	−0.936947	+	0.349471i	$0.886361\pi$
$620$	−4.93479	−	13.4440i	−0.198186	−	0.539924i
$621$	−4.67891	−	1.05251i	−0.187758	−	0.0422357i
$622$		−	20.6450i		−	0.827790i
$623$	6.26109	+	0.900208i	0.250845	+	0.0360661i
$624$	1.48140	+	3.24380i	0.0593033	+	0.129856i
$625$	−10.8566	+	22.5196i	−0.434265	+	0.900785i
$626$	−8.75417	−	10.1029i	−0.349887	−	0.403791i
$627$	−5.74481	−	19.5650i	−0.229426	−	0.781353i
$628$	5.75186	−	8.95007i	0.229524	−	0.357147i
$629$	−6.49410	+	14.2201i	−0.258937	+	0.566993i
$630$	−1.46201	−	0.553989i	−0.0582479	−	0.0220714i
$631$	2.84185	−	1.82635i	0.113132	−	0.0727057i	−0.482851	−	0.875702i	$-0.660399\pi$
$631$	2.84185	−	1.82635i	0.113132	−	0.0727057i	0.595983	+	0.802997i	$0.296762\pi$
$632$	−4.68583	+	0.673721i	−0.186392	+	0.0267992i
$633$	−18.4828	+	2.65743i	−0.734627	+	0.105623i
$634$	−2.55913	+	1.64465i	−0.101636	+	0.0653176i
$635$	−8.11072	+	21.4047i	−0.321864	+	0.849420i
$636$	−0.809903	+	1.77344i	−0.0321148	+	0.0703215i
$637$	12.5532	−	19.5331i	0.497375	−	0.773931i
$638$	−12.6587	−	43.1115i	−0.501162	−	1.70680i
$639$	0.220841	+	0.254864i	0.00873632	+	0.0100823i
$640$	2.23117	−	0.147906i	0.0881948	−	0.00584652i
$641$	5.74361	+	12.5768i	0.226859	+	0.496752i	0.988495	−	0.151253i	$-0.0483308\pi$
$641$	5.74361	+	12.5768i	0.226859	+	0.496752i	−0.761636	+	0.648005i	$0.775604\pi$
$642$	17.4472	+	2.50854i	0.688588	+	0.0990040i
$643$		−	24.0953i		−	0.950224i	−0.879925	−	0.475112i	$-0.842408\pi$
$643$		−	24.0953i		−	0.950224i	0.879925	−	0.475112i	$-0.157592\pi$
$644$	2.35428	+	2.38778i	0.0927717	+	0.0940919i
$645$	3.69774	+	10.0739i	0.145598	+	0.396658i
$646$	1.50475	−	10.4657i	0.0592035	−	0.411769i
$647$	−41.9590	+	19.1620i	−1.64958	+	0.753337i	−0.999976	−	0.00693652i	$-0.997792\pi$
$647$	−41.9590	+	19.1620i	−1.64958	+	0.753337i	−0.649603	+	0.760274i	$0.725065\pi$
$648$	0.281733	−	0.959493i	0.0110675	−	0.0376924i
$649$	37.4433	+	43.2119i	1.46978	+	1.69622i
$650$	−9.79544	+	14.8986i	−0.384209	+	0.584373i
$651$	3.76719	+	2.42103i	0.147648	+	0.0948875i
$652$	0.599278	+	0.273681i	0.0234695	+	0.0107182i
$653$	−8.60115	−	7.45294i	−0.336589	−	0.291656i	0.470123	−	0.882601i	$-0.344210\pi$
$653$	−8.60115	−	7.45294i	−0.336589	−	0.291656i	−0.806712	+	0.590945i	$0.798755\pi$
$654$	−16.2816	+	10.4636i	−0.636661	+	0.409157i
$655$	−21.2495	+	11.4599i	−0.830285	+	0.447775i
$656$	−0.285832	−	1.98801i	−0.0111599	−	0.0776187i
$657$	7.01345	+	10.9131i	0.273621	+	0.425762i
$658$	2.89178	+	2.50574i	0.112733	+	0.0976840i
$659$	10.4342	−	22.8477i	0.406459	−	0.890021i	−0.590115	−	0.807319i	$-0.700918\pi$
$659$	10.4342	−	22.8477i	0.406459	−	0.890021i	0.996574	−	0.0827023i	$-0.0263551\pi$
$660$	11.4356	+	2.55009i	0.445131	+	0.0992620i
$661$	−2.43097	+	0.713797i	−0.0945538	+	0.0277635i	−0.328667	−	0.944446i	$-0.606599\pi$
$661$	−2.43097	+	0.713797i	−0.0945538	+	0.0277635i	0.234113	+	0.972209i	$0.424781\pi$
$662$	10.6612	−	9.23796i	0.414358	−	0.359044i
$663$	−2.72969	+	9.29647i	−0.106012	+	0.361045i
$664$	6.74143	+	14.7617i	0.261618	+	0.572864i
$665$	1.26234	+	5.95190i	0.0489516	+	0.230805i
$666$	5.75373			0.222953
$667$	14.0990	+	38.6323i	0.545916	+	1.49585i
$668$			9.25099i			0.357932i
$669$	−1.10511	+	7.68620i	−0.0427260	+	0.297166i
$670$	−5.53201	+	5.47471i	−0.213720	+	0.211506i
$671$	−69.1665	−	20.3091i	−2.67014	−	0.784025i
$672$	−0.528418	+	0.457877i	−0.0203842	+	0.0176630i
$673$	7.08131	+	24.1167i	0.272965	+	0.929632i	0.975871	+	0.218349i	$0.0700672\pi$
$673$	7.08131	+	24.1167i	0.272965	+	0.929632i	−0.702906	+	0.711283i	$0.748115\pi$
$674$	15.0771	+	9.68943i	0.580746	+	0.373223i
$675$	4.81187	−	1.35864i	0.185209	−	0.0522940i
$676$	0.185459	−	0.214031i	0.00713303	−	0.00823196i
$677$	11.8284	+	18.4054i	0.454603	+	0.707376i	0.990592	−	0.136849i	$-0.0436975\pi$
$677$	11.8284	+	18.4054i	0.454603	+	0.707376i	−0.535989	+	0.844225i	$0.680061\pi$
$678$	−8.26542	+	1.18839i	−0.317432	+	0.0456398i
$679$	−0.726605	−	5.05365i	−0.0278846	−	0.193941i
$680$	4.84456	+	3.66610i	0.185780	+	0.140588i
$681$	0.0497026	−	0.0573598i	0.00190461	−	0.00219803i
$682$	−30.5260	−	13.9408i	−1.16890	−	0.533819i
$683$	25.8187	−	40.1747i	0.987926	−	1.53724i	0.152014	−	0.988378i	$-0.451424\pi$
$683$	25.8187	−	40.1747i	0.987926	−	1.53724i	0.835912	−	0.548864i	$-0.184939\pi$
$684$	−3.73394	+	1.09638i	−0.142771	+	0.0419213i
$685$	9.94773	+	5.49929i	0.380083	+	0.210117i
$686$	9.06427	+	2.66151i	0.346075	+	0.101617i
$687$	13.3396	−	6.09200i	0.508938	−	0.232424i
$688$	4.75024	+	0.682982i	0.181101	+	0.0260384i
$689$	−6.95248			−0.264868
$690$	−10.5951	−	1.65629i	−0.403350	−	0.0630537i
$691$	23.0171			0.875612			0.437806	−	0.899069i	$-0.355756\pi$
$691$	23.0171			0.875612			0.437806	+	0.899069i	$0.355756\pi$
$692$	−2.41967	−	0.347896i	−0.0919821	−	0.0132250i
$693$	−3.33256	+	1.52193i	−0.126594	+	0.0578133i
$694$	6.39079	+	1.87650i	0.242591	+	0.0712311i
$695$	−7.86559	+	14.2282i	−0.298359	+	0.539705i
$696$	−8.22773	+	2.41588i	−0.311871	+	0.0915736i
$697$	2.95024	−	4.59066i	0.111748	−	0.173884i
$698$	−14.5858	−	6.66113i	−0.552082	−	0.252127i
$699$	−11.2692	+	13.0054i	−0.426242	+	0.491909i
$700$	−3.34394	−	1.01980i	−0.126389	−	0.0385449i
$701$	1.18616	+	8.24992i	0.0448006	+	0.311595i	0.999884	+	0.0152567i	$0.00485655\pi$
$701$	1.18616	+	8.24992i	0.0448006	+	0.311595i	−0.955083	+	0.296338i	$0.904234\pi$
$702$	3.52976	−	0.507504i	0.133222	−	0.0191545i
$703$	−12.1056	−	18.8366i	−0.456569	−	0.710436i
$704$	3.43133	−	3.95996i	0.129323	−	0.149247i
$705$	−12.2011	−	0.936501i	−0.459518	−	0.0352707i
$706$	−6.19823	−	3.98336i	−0.233273	−	0.149916i
$707$	2.25393	+	7.67619i	0.0847679	+	0.288693i
$708$	8.24690	−	7.14598i	0.309937	−	0.268562i
$709$	8.07302	+	2.37045i	0.303189	+	0.0890242i	0.429788	−	0.902930i	$-0.358588\pi$
$709$	8.07302	+	2.37045i	0.303189	+	0.0890242i	−0.126600	+	0.991954i	$0.540406\pi$
$710$	0.530429	+	0.535981i	0.0199067	+	0.0201150i
$711$	−0.673721	+	4.68583i	−0.0252665	+	0.175732i
$712$			9.04677i			0.339042i
$713$	28.7021	+	10.9369i	1.07490	+	0.409592i
$714$	−1.89971			−0.0710948
$715$	8.66870	+	40.8726i	0.324191	+	1.52855i
$716$	5.46549	+	11.9678i	0.204255	+	0.447256i
$717$	−1.14812	+	3.91015i	−0.0428774	+	0.146027i
$718$	19.0396	−	16.4979i	0.710550	−	0.615695i
$719$	−3.52071	+	1.03377i	−0.131300	+	0.0385533i	−0.346723	−	0.937968i	$-0.612705\pi$
$719$	−3.52071	+	1.03377i	−0.131300	+	0.0385533i	0.215422	+	0.976521i	$0.430887\pi$
$720$	0.486678	−	2.18246i	0.0181374	−	0.0813356i
$721$	−0.194454	+	0.425795i	−0.00724184	+	0.0158574i
$722$	−2.91387	−	2.52488i	−0.108443	−	0.0939665i
$723$	12.9580	+	20.1630i	0.481913	+	0.749871i
$724$	1.26878	+	8.82453i	0.0471537	+	0.327961i
$725$	−32.1090	−	28.4132i	−1.19250	−	1.05524i
$726$	13.8431	−	8.89640i	0.513765	−	0.330176i
$727$	−9.73748	−	8.43757i	−0.361143	−	0.312932i	0.455322	−	0.890327i	$-0.349524\pi$
$727$	−9.73748	−	8.43757i	−0.361143	−	0.312932i	−0.816465	+	0.577394i	$0.804069\pi$
$728$	−2.26806	−	1.03579i	−0.0840598	−	0.0383888i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	17.2623	+	23.3118i	0.638908	+	0.862807i
$731$	8.53876	+	9.85426i	0.315818	+	0.364473i
$732$	−3.87595	+	13.2003i	−0.143259	+	0.487896i
$733$	−4.85548	+	2.21742i	−0.179341	+	0.0819023i	−0.503062	−	0.864250i	$-0.667793\pi$
$733$	−4.85548	+	2.21742i	−0.179341	+	0.0819023i	0.323721	+	0.946153i	$0.395066\pi$
$734$	−3.54701	+	24.6700i	−0.130922	+	0.910585i
$735$	−13.6676	+	5.01688i	−0.504139	+	0.185050i
$736$	−2.90109	+	3.81886i	−0.106935	+	0.140765i
$737$			18.2380i			0.671804i
$738$	−1.98801	−	0.285832i	−0.0731796	−	0.0105216i
$739$	−12.1432	−	26.5898i	−0.446693	−	0.978122i	−0.990321	−	0.138795i	$-0.955677\pi$
$739$	−12.1432	−	26.5898i	−0.446693	−	0.978122i	0.543628	−	0.839326i	$-0.317050\pi$
$740$	12.8376	−	0.851014i	0.471918	−	0.0312839i
$741$	−9.08791	−	10.4880i	−0.333853	−	0.385286i
$742$	−0.384050	−	1.30795i	−0.0140989	−	0.0480165i
$743$	−14.5834	+	22.6923i	−0.535015	+	0.832499i	−0.998564	−	0.0535721i	$-0.982939\pi$
$743$	−14.5834	+	22.6923i	−0.535015	+	0.832499i	0.463549	+	0.886071i	$0.346576\pi$
$744$	−2.66056	+	5.82581i	−0.0975409	+	0.213585i
$745$	47.9839	+	18.1822i	1.75800	+	0.666144i
$746$	9.50901	−	6.11107i	0.348150	−	0.223742i
$747$	16.0630	−	2.30951i	0.587714	−	0.0845006i
$748$	14.0915	−	2.02605i	0.515236	−	0.0740798i
$749$	−10.3680	+	6.66313i	−0.378840	+	0.243466i
$750$	10.5352	−	3.74306i	0.384689	−	0.136677i
$751$	−0.511459	+	1.11994i	−0.0186634	+	0.0408672i	−0.918734	−	0.394877i	$-0.870787\pi$
$751$	−0.511459	+	1.11994i	−0.0186634	+	0.0408672i	0.900071	+	0.435744i	$0.143515\pi$
$752$	−2.95867	+	4.60378i	−0.107892	+	0.167883i
$753$	−0.470313	−	1.60174i	−0.0171392	−	0.0583706i
$754$	−20.0252	−	23.1103i	−0.729273	−	0.841626i
$755$	1.55815	+	23.5047i	0.0567068	+	0.855423i
$756$	0.290457	+	0.636012i	0.0105638	+	0.0231315i
$757$	4.19318	+	0.602888i	0.152404	+	0.0219123i	0.218094	−	0.975928i	$-0.430016\pi$
$757$	4.19318	+	0.602888i	0.152404	+	0.0219123i	−0.0656907	+	0.997840i	$0.520925\pi$
$758$			23.2356i			0.843954i
$759$	−20.2228	+	14.9168i	−0.734040	+	0.541446i
$760$	−8.16890	+	2.99850i	−0.296317	+	0.108767i
$761$	5.56522	−	38.7069i	0.201739	−	1.40313i	−0.597383	−	0.801956i	$-0.703793\pi$
$761$	5.56522	−	38.7069i	0.201739	−	1.40313i	0.799122	−	0.601169i	$-0.205298\pi$
$762$	9.31159	−	4.25246i	0.337323	−	0.154050i
$763$	3.81248	−	12.9841i	0.138021	−	0.470056i
$764$	8.77164	+	10.1230i	0.317347	+	0.366238i
$765$	4.88247	−	3.61546i	0.176526	−	0.130717i
$766$	−30.3928	−	19.5322i	−1.09813	−	0.705728i
$767$	35.3971	+	16.1653i	1.27811	+	0.583695i
$768$	−0.755750	−	0.654861i	−0.0272708	−	0.0236303i
$769$	−11.2721	+	7.24413i	−0.406482	+	0.261230i	−0.727867	−	0.685719i	$-0.759488\pi$
$769$	−11.2721	+	7.24413i	−0.406482	+	0.261230i	0.321385	+	0.946949i	$0.395852\pi$
$770$	−7.21041	+	3.88859i	−0.259845	+	0.140135i
$771$	1.23837	+	8.61303i	0.0445987	+	0.310191i
$772$	−10.4908	−	16.3240i	−0.377571	−	0.587512i
$773$	−36.8187	−	31.9036i	−1.32428	−	1.14749i	−0.977824	−	0.209426i	$-0.932840\pi$
$773$	−36.8187	−	31.9036i	−1.32428	−	1.14749i	−0.346454	−	0.938067i	$-0.612614\pi$
$774$	1.99361	−	4.36540i	0.0716590	−	0.156911i
$775$	−31.7427	+	4.22708i	−1.14023	+	0.151841i
$776$	7.00633	−	2.05724i	0.251513	−	0.0738508i
$777$	−3.04038	+	2.63450i	−0.109073	+	0.0945122i
$778$	0.651891	−	2.22014i	0.0233714	−	0.0795957i
$779$	3.24690	+	7.10973i	0.116332	+	0.254732i
$780$	7.80044	−	1.65440i	0.279301	−	0.0592371i
$781$	1.76703			0.0632292
$782$	−12.7517	+	2.67975i	−0.455999	+	0.0958276i
$783$			8.57508i			0.306448i
$784$	−0.926630	+	6.44485i	−0.0330939	+	0.230173i
$785$	−16.7339	−	16.9090i	−0.597258	−	0.603509i
$786$	10.3596	+	3.04185i	0.369514	+	0.108499i
$787$	8.79069	−	7.61718i	0.313354	−	0.271523i	−0.483956	−	0.875092i	$-0.660801\pi$
$787$	8.79069	−	7.61718i	0.313354	−	0.271523i	0.797311	+	0.603569i	$0.206255\pi$
$788$	−5.14508	−	17.5225i	−0.183286	−	0.624214i
$789$	−15.4069	−	9.90143i	−0.548501	−	0.352500i
$790$	−0.810122	+	10.5545i	−0.0288228	+	0.375514i
$791$	3.82346	−	4.41251i	0.135947	−	0.156891i
$792$	−2.83284	−	4.40798i	−0.100661	−	0.156631i
$793$	−48.5609	+	6.98200i	−1.72445	+	0.247938i
$794$	4.70848	+	32.7482i	0.167098	+	1.16219i
$795$	3.47631	+	2.63068i	0.123292	+	0.0933006i
$796$	8.00512	−	9.23841i	0.283734	−	0.327447i
$797$	−45.4841	−	20.7719i	−1.61113	−	0.735778i	−0.612620	−	0.790377i	$-0.709884\pi$
$797$	−45.4841	−	20.7719i	−1.61113	−	0.735778i	−0.998508	+	0.0545996i	$0.982612\pi$
$798$	1.47107	−	2.28903i	0.0520754	−	0.0810310i
$799$	−14.2665	+	4.18902i	−0.504712	+	0.148197i
$800$	0.763062	−	4.94143i	0.0269783	−	0.174706i
$801$	8.68031	+	2.54877i	0.306704	+	0.0900563i
$802$	−5.85885	+	2.67565i	−0.206883	+	0.0944804i
$803$	67.2811	+	9.67356i	2.37430	+	0.341372i
$804$	3.48068			0.122754
$805$	6.35703	−	3.97605i	0.224056	−	0.140137i
$806$	−22.8391			−0.804474
$807$	−13.1568	−	1.89166i	−0.463141	−	0.0665897i
$808$	−10.4081	+	4.75321i	−0.366155	+	0.167217i
$809$	−31.2777	−	9.18396i	−1.09967	−	0.322891i	−0.318946	−	0.947773i	$-0.603329\pi$
$809$	−31.2777	−	9.18396i	−1.09967	−	0.322891i	−0.780719	+	0.624882i	$0.785147\pi$
$810$	−1.95694	−	1.08184i	−0.0687600	−	0.0380118i
$811$	−25.5222	+	7.49401i	−0.896207	+	0.263150i	−0.697224	−	0.716853i	$-0.745582\pi$
$811$	−25.5222	+	7.49401i	−0.896207	+	0.263150i	−0.198983	+	0.980003i	$0.563764\pi$
$812$	3.24150	−	5.04388i	0.113754	−	0.177005i
$813$	1.70879	+	0.780377i	0.0599298	+	0.0273690i
$814$	19.7429	−	22.7846i	0.691989	−	0.798598i
$815$	0.888954	−	1.17471i	0.0311387	−	0.0411482i
$816$	−0.386667	−	2.68933i	−0.0135361	−	0.0941454i
$817$	−18.4859	+	2.65788i	−0.646741	+	0.0929874i
$818$	−10.8554	−	16.8913i	−0.379550	−	0.590592i
$819$	−1.63282	+	1.88437i	−0.0570552	+	0.0658452i
$820$	−4.47786	−	0.343702i	−0.156374	−	0.0120026i
$821$	−25.0451	−	16.0955i	−0.874078	−	0.561736i	0.0249193	−	0.999689i	$-0.492067\pi$
$821$	−25.0451	−	16.0955i	−0.874078	−	0.561736i	−0.898998	+	0.437953i	$0.855703\pi$
$822$	−1.43213	−	4.87739i	−0.0499513	−	0.170118i
$823$	5.44243	−	4.71589i	0.189711	−	0.164386i	−0.554827	−	0.831966i	$-0.687215\pi$
$823$	5.44243	−	4.71589i	0.189711	−	0.164386i	0.744538	+	0.667580i	$0.232670\pi$
$824$	−0.642357	−	0.188613i	−0.0223776	−	0.00657065i
$825$	11.1309	−	23.7168i	0.387530	−	0.825711i
$826$	−1.08583	+	7.55212i	−0.0377809	+	0.262772i
$827$		−	22.9928i		−	0.799538i	−0.916616	−	0.399769i	$-0.869090\pi$
$827$		−	22.9928i		−	0.799538i	0.916616	−	0.399769i	$-0.130910\pi$
$828$	2.84684	+	3.85947i	0.0989345	+	0.134126i
$829$	18.4944			0.642336			0.321168	−	0.947022i	$-0.395925\pi$
$829$	18.4944			0.642336			0.321168	+	0.947022i	$0.395925\pi$
$830$	35.4977	−	7.52873i	1.23214	−	0.261326i
$831$	6.32163	+	13.8424i	0.219295	+	0.480189i
$832$	1.00468	−	3.42161i	0.0348309	−	0.118623i
$833$	−13.3697	+	11.5849i	−0.463232	+	0.401393i
$834$	6.97609	−	2.04836i	0.241562	−	0.0709290i
$835$	20.1899	+	4.50226i	0.698702	+	0.155807i
$836$	−8.47074	+	18.5483i	−0.292967	+	0.641507i
$837$	4.84026	+	4.19411i	0.167304	+	0.144970i
$838$	−2.57002	−	3.99903i	−0.0887799	−	0.138144i
$839$	7.80746	+	54.3021i	0.269544	+	1.87472i	0.452744	+	0.891641i	$0.350445\pi$
$839$	7.80746	+	54.3021i	0.269544	+	1.87472i	−0.183200	+	0.983076i	$0.558646\pi$
$840$	0.742129	+	1.37609i	0.0256059	+	0.0474796i
$841$	37.4627	−	24.0758i	1.29182	−	0.830200i
$842$	6.31691	+	5.47364i	0.217695	+	0.188634i
$843$	−15.9022	−	7.26229i	−0.547700	−	0.250126i
$844$	15.7086	+	10.0953i	0.540714	+	0.347496i
$845$	−0.376856	−	0.508921i	−0.0129642	−	0.0175074i
$846$	3.58374	+	4.13586i	0.123212	+	0.142194i
$847$	−3.24147	+	11.0394i	−0.111378	+	0.379320i
$848$	1.77344	−	0.809903i	0.0609002	−	0.0278122i
$849$	2.75048	−	19.1300i	0.0943963	−	0.656541i
$850$	10.3589	−	8.78886i	0.355306	−	0.301456i
$851$	−16.6921	+	21.9727i	−0.572197	+	0.753215i
$852$		−	0.337233i		−	0.0115534i
$853$	−44.3081	−	6.37054i	−1.51708	−	0.218123i	−0.667112	−	0.744958i	$-0.732470\pi$
$853$	−44.3081	−	6.37054i	−1.51708	−	0.218123i	−0.849968	+	0.526835i	$0.823379\pi$
$854$	−3.99597	−	8.74996i	−0.136739	−	0.299418i
$855$	0.575590	+	8.68278i	0.0196848	+	0.296945i
$856$	−11.5430	−	13.3213i	−0.394532	−	0.455314i
$857$	8.53776	+	29.0769i	0.291644	+	0.993250i	0.966791	+	0.255566i	$0.0822620\pi$
$857$	8.53776	+	29.0769i	0.291644	+	0.993250i	−0.675147	+	0.737683i	$0.735920\pi$
$858$	10.1021	−	15.7191i	0.344879	−	0.536643i
$859$	12.8822	−	28.2081i	0.439535	−	0.962447i	−0.552148	−	0.833746i	$-0.686192\pi$
$859$	12.8822	−	28.2081i	0.439535	−	0.962447i	0.991683	−	0.128702i	$-0.0410809\pi$
$860$	3.80242	−	10.0348i	0.129661	−	0.342185i
$861$	1.18137	−	0.759224i	0.0402611	−	0.0258743i
$862$	12.9195	−	1.85754i	0.440039	−	0.0632681i
$863$	−42.9696	+	6.17810i	−1.46270	+	0.210305i	−0.827250	−	0.561834i	$-0.810096\pi$
$863$	−42.9696	+	6.17810i	−1.46270	+	0.210305i	−0.635454	+	0.772139i	$0.719187\pi$
$864$	−0.841254	+	0.540641i	−0.0286200	+	0.0183930i
$865$	−1.93687	+	5.11153i	−0.0658556	+	0.173797i
$866$	−0.347424	+	0.760752i	−0.0118059	+	0.0258514i
$867$	−5.19988	+	8.09117i	−0.176597	+	0.274790i
$868$	−1.26162	−	4.29667i	−0.0428221	−	0.145839i
$869$	16.2440	+	18.7465i	0.551038	+	0.635932i
$870$	1.26831	+	19.1325i	0.0429997	+	0.648651i
$871$	5.15626	+	11.2906i	0.174713	+	0.382568i
$872$	19.1570	+	2.75436i	0.648738	+	0.0932744i
$873$		−	7.30212i		−	0.247139i
$874$	6.64555	−	17.4401i	0.224789	−	0.589921i
$875$	−3.85310	+	6.80170i	−0.130259	+	0.229939i
$876$	1.84618	−	12.8404i	0.0623765	−	0.433838i
$877$	17.7560	−	8.10889i	0.599577	−	0.273818i	−0.0924175	−	0.995720i	$-0.529459\pi$
$877$	17.7560	−	8.10889i	0.599577	−	0.273818i	0.691995	+	0.721903i	$0.256732\pi$
$878$	−4.60359	+	15.6784i	−0.155363	+	0.529119i
$879$	−19.0263	−	21.9575i	−0.641740	−	0.740607i
$880$	−6.97252	−	9.41597i	−0.235043	−	0.317412i
$881$	18.6660	+	11.9959i	0.628874	+	0.404153i	0.815893	−	0.578203i	$-0.196246\pi$
$881$	18.6660	+	11.9959i	0.628874	+	0.404153i	−0.187018	+	0.982356i	$0.559882\pi$
$882$	5.92273	+	2.70482i	0.199429	+	0.0910760i
$883$	−8.90304	−	7.71453i	−0.299611	−	0.259614i	0.492061	−	0.870561i	$-0.336244\pi$
$883$	−8.90304	−	7.71453i	−0.299611	−	0.259614i	−0.791672	+	0.610946i	$0.790789\pi$
$884$	8.15085	−	5.23824i	0.274143	−	0.176181i
$885$	−11.5822	−	21.4763i	−0.389333	−	0.721919i
$886$	−0.642894	−	4.47143i	−0.0215985	−	0.150221i
$887$	0.647473	+	1.00749i	0.0217400	+	0.0338281i	0.851953	−	0.523617i	$-0.175418\pi$
$887$	0.647473	+	1.00749i	0.0217400	+	0.0338281i	−0.830213	+	0.557446i	$0.811782\pi$
$888$	−4.34838	−	3.76789i	−0.145922	−	0.126442i
$889$	−2.97331	+	6.51063i	−0.0997215	+	0.218360i
$890$	19.7442	+	4.40286i	0.661828	+	0.147584i
$891$	−5.02753	+	1.47622i	−0.168429	+	0.0494551i
$892$	5.86858	−	5.08515i	0.196494	−	0.170263i
$893$	6.00000	−	20.4341i	0.200782	−	0.683801i
$894$	−9.53294	−	20.8742i	−0.318829	−	0.698138i
$895$	28.7791	−	6.10378i	0.961979	−	0.204027i
$896$	0.699197			0.0233585
$897$	−8.30207	+	14.9520i	−0.277198	+	0.499232i
$898$			11.9374i			0.398358i
$899$	7.81590	−	54.3608i	0.260675	−	1.81303i
$900$	−4.52629	−	2.12431i	−0.150876	−	0.0708105i
$901$	5.08253	+	1.49237i	0.169324	+	0.0497179i
$902$	−7.95339	+	6.89165i	−0.264819	+	0.229467i
$903$	0.945356	+	3.21959i	0.0314595	+	0.107141i
$904$	7.02482	+	4.51458i	0.233642	+	0.150153i
$905$	19.8767	+	1.52565i	0.660724	+	0.0507144i
$906$	6.89875	−	7.96158i	0.229196	−	0.264506i
$907$	7.92354	+	12.3293i	0.263097	+	0.409387i	0.947519	−	0.319699i	$-0.103582\pi$
$907$	7.92354	+	12.3293i	0.263097	+	0.409387i	−0.684422	+	0.729086i	$0.739945\pi$
$908$	−0.0751254	+	0.0108014i	−0.00249312	+	0.000358457i
$909$	1.62838	+	11.3256i	0.0540098	+	0.375647i
$910$	−3.36438	+	4.44586i	−0.111528	+	0.147379i
$911$	−14.9183	+	17.2167i	−0.494267	+	0.570414i	−0.947001	−	0.321231i	$-0.895903\pi$
$911$	−14.9183	+	17.2167i	−0.494267	+	0.570414i	0.452734	+	0.891646i	$0.350449\pi$
$912$	3.53991	+	1.61662i	0.117218	+	0.0535317i
$913$	45.9718	−	71.5335i	1.52144	−	2.36741i
$914$	11.7211	−	3.44162i	0.387699	−	0.113839i
$915$	26.9228	+	14.8834i	0.890039	+	0.492030i
$916$	−14.0708	−	4.13157i	−0.464913	−	0.136511i
$917$	−6.86698	+	3.13604i	−0.226768	+	0.103561i
$918$	−2.68933	−	0.386667i	−0.0887611	−	0.0127619i
$919$	39.6564			1.30814			0.654072	−	0.756433i	$-0.273060\pi$
$919$	39.6564			1.30814			0.654072	+	0.756433i	$0.273060\pi$
$920$	6.92263	+	8.19007i	0.228232	+	0.270019i
$921$	−17.1186			−0.564077
$922$	−26.7228	−	3.84216i	−0.880068	−	0.126535i
$923$	1.09392	−	0.499575i	0.0360067	−	0.0164437i
$924$	3.51523	+	1.03217i	0.115643	+	0.0339558i
$925$	4.39046	−	28.4317i	0.144357	−	0.934828i
$926$	−11.0672	+	3.24961i	−0.363690	+	0.106789i
$927$	−0.361946	+	0.563199i	−0.0118879	+	0.0184979i
$928$	7.80017	+	3.56222i	0.256053	+	0.116935i
$929$	−32.4419	+	37.4399i	−1.06438	+	1.22836i	−0.0918071	+	0.995777i	$0.529264\pi$
$929$	−32.4419	+	37.4399i	−1.06438	+	1.22836i	−0.972576	+	0.232586i	$0.925281\pi$
$930$	11.4198	+	8.64187i	0.374470	+	0.283378i
$931$	−3.60605	−	25.0806i	−0.118184	−	0.821985i
$932$	17.0334	−	2.44904i	0.557949	−	0.0802209i
$933$	11.1615	+	17.3677i	0.365413	+	0.568593i
$934$	11.4868	−	13.2565i	0.375860	−	0.433765i
$935$	2.43624	−	31.7402i	0.0796737	−	1.03802i
$936$	−2.99996	−	1.92796i	−0.0980568	−	0.0630173i
$937$	−9.94120	−	33.8566i	−0.324765	−	1.10605i	−0.946469	−	0.322795i	$-0.895377\pi$
$937$	−9.94120	−	33.8566i	−0.324765	−	1.10605i	0.621704	−	0.783252i	$-0.286441\pi$
$938$	−1.83925	+	1.59372i	−0.0600537	+	0.0520368i
$939$	12.8265	+	3.76620i	0.418577	+	0.122905i
$940$	8.60766	+	8.69775i	0.280751	+	0.283689i
$941$	3.56718	−	24.8102i	0.116287	−	0.808791i	−0.845301	−	0.534291i	$-0.820579\pi$
$941$	3.56718	−	24.8102i	0.116287	−	0.808791i	0.961587	−	0.274500i	$-0.0885123\pi$
$942$			10.6390i			0.346636i
$943$	6.85894	−	6.76270i	0.223358	−	0.220224i
$944$	−10.9122			−0.355162
$945$	1.52943	−	0.324378i	0.0497524	−	0.0105520i
$946$	−10.4461	−	22.8738i	−0.339632	−	0.743690i
$947$	−1.94658	+	6.62943i	−0.0632552	+	0.215427i	−0.985055	−	0.172238i	$-0.944900\pi$
$947$	−1.94658	+	6.62943i	−0.0632552	+	0.215427i	0.921800	+	0.387665i	$0.126718\pi$
$948$	3.57773	−	3.10012i	0.116199	−	0.100687i
$949$	44.3868	−	13.0331i	1.44086	−	0.423074i
$950$	2.56848	+	19.2876i	0.0833324	+	0.625773i
$951$	1.26371	−	2.76714i	0.0409787	−	0.0897308i
$952$	1.43570	+	1.24404i	0.0465314	+	0.0403197i
$953$	−3.57940	−	5.56966i	−0.115948	−	0.180419i	0.778429	−	0.627733i	$-0.216017\pi$
$953$	−3.57940	−	5.56966i	−0.115948	−	0.180419i	−0.894377	+	0.447314i	$0.852381\pi$
$954$	−0.277461	−	1.92978i	−0.00898312	−	0.0624789i
$955$	26.3621	−	14.2171i	0.853057	−	0.460056i
$956$	3.42829	−	2.20323i	0.110879	−	0.0712576i
$957$	33.9570	+	29.4239i	1.09767	+	0.951139i
$958$	−5.99107	−	2.73603i	−0.193563	−	0.0883972i
$959$	2.99000	+	1.92156i	0.0965522	+	0.0620504i
$960$	−1.79702	+	1.33069i	−0.0579984	+	0.0429478i
$961$	−6.56085	−	7.57163i	−0.211640	−	0.244246i
$962$	5.78064	−	19.6870i	0.186375	−	0.634736i
$963$	−16.0338	+	7.32238i	−0.516681	+	0.235960i
$964$	3.41098	−	23.7239i	0.109860	−	0.764094i
$965$	−40.7321	+	14.9512i	−1.31121	+	0.481296i
$966$	−3.27148	−	0.735911i	−0.105258	−	0.0236775i
$967$		−	60.2686i		−	1.93811i	−0.246850	−	0.969054i	$-0.579395\pi$
$967$		−	60.2686i		−	1.93811i	0.246850	−	0.969054i	$-0.420605\pi$
$968$	−16.2878	−	2.34183i	−0.523510	−	0.0752693i
$969$	4.39234	+	9.61787i	0.141102	+	0.308971i
$970$	−1.08003	−	16.2923i	−0.0346777	−	0.523113i
$971$	−4.91137	−	5.66802i	−0.157613	−	0.181895i	0.671451	−	0.741049i	$-0.265672\pi$
$971$	−4.91137	−	5.66802i	−0.157613	−	0.181895i	−0.829064	+	0.559154i	$0.811126\pi$
$972$	0.281733	+	0.959493i	0.00903658	+	0.0307758i
$973$	−2.74839	+	4.27658i	−0.0881093	+	0.137101i
$974$	−16.0495	+	35.1434i	−0.514258	+	1.12607i
$975$	0.185636	−	17.8293i	0.00594512	−	0.570996i
$976$	11.5736	−	7.43789i	0.370461	−	0.238081i
$977$	48.2484	−	6.93707i	1.54360	−	0.221936i	0.682697	−	0.730702i	$-0.260807\pi$
$977$	48.2484	−	6.93707i	1.54360	−	0.221936i	0.860905	+	0.508766i	$0.169898\pi$
$978$	−0.652108	+	0.0937589i	−0.0208521	+	0.00299808i
$979$	39.8780	−	25.6280i	1.27451	−	0.819075i
$980$	13.6147	+	5.15890i	0.434905	+	0.164795i
$981$	8.03994	−	17.6050i	0.256695	−	0.562085i
$982$	15.8427	−	24.6517i	0.505560	−	0.786667i
$983$	−10.0778	−	34.3217i	−0.321431	−	1.09469i	−0.948775	−	0.315951i	$-0.897676\pi$
$983$	−10.0778	−	34.3217i	−0.321431	−	1.09469i	0.627345	−	0.778742i	$-0.284142\pi$
$984$	1.31526	+	1.51789i	0.0419288	+	0.0483884i
$985$	−40.7463	+	2.70111i	−1.29828	+	0.0860645i
$986$	9.67849	+	21.1929i	0.308226	+	0.674921i
$987$	−3.78743	−	0.544550i	−0.120555	−	0.0173332i
$988$			13.8776i			0.441506i
$989$	10.8872	+	20.2777i	0.346194	+	0.644795i
$990$	−10.9989	+	4.03730i	−0.349569	+	0.128314i
$991$	−6.47209	+	45.0144i	−0.205593	+	1.42993i	0.581727	+	0.813384i	$0.302377\pi$
$991$	−6.47209	+	45.0144i	−0.205593	+	1.42993i	−0.787319	+	0.616545i	$0.788532\pi$
$992$	5.82581	−	2.66056i	0.184970	−	0.0844729i
$993$	−3.97433	+	13.5353i	−0.126122	+	0.429531i
$994$	0.154411	+	0.178200i	0.00489762	+	0.00565216i
$995$	−16.2666	−	21.9670i	−0.515685	−	0.696401i
$996$	−13.6520	−	8.77361i	−0.432580	−	0.278003i
$997$	−29.9179	−	13.6630i	−0.947508	−	0.432712i	−0.119128	−	0.992879i	$-0.538010\pi$
$997$	−29.9179	−	13.6630i	−0.947508	−	0.432712i	−0.828380	+	0.560166i	$0.810737\pi$
$998$	−3.43778	−	2.97885i	−0.108821	−	0.0942938i
$999$	−4.84035	+	3.11070i	−0.153142	+	0.0984183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.r.b.169.11	yes	120
5.4	even	2	inner	690.2.r.b.169.1	yes	120
23.3	even	11	inner	690.2.r.b.49.1	✓	120
115.49	even	22	inner	690.2.r.b.49.11	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.r.b.49.1	✓	120	23.3	even	11	inner
690.2.r.b.49.11	yes	120	115.49	even	22	inner
690.2.r.b.169.1	yes	120	5.4	even	2	inner
690.2.r.b.169.11	yes	120	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.989821 + 0.142315i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(1.08184 - 1.95694i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.378014 - 0.588202i) q^{7} +(0.909632 + 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.989821 + 0.142315i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(1.08184 - 1.95694i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.378014 - 0.588202i) q^{7} +(0.909632 + 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +(1.34933 - 1.78306i) q^{10} +(-0.745698 - 5.18645i) q^{11} +(-0.989821 + 0.142315i) q^{12} +(-1.92796 - 2.99996i) q^{13} +(0.457877 - 0.528418i) q^{14} +(-0.171128 + 2.22951i) q^{15} +(0.841254 + 0.540641i) q^{16} +(0.765463 + 2.60693i) q^{17} +(0.755750 - 0.654861i) q^{18} +(-3.73394 - 1.09638i) q^{19} +(1.58935 - 1.57289i) q^{20} +(-0.0995061 + 0.692080i) q^{21} -5.23978i q^{22} +(0.308327 + 4.78591i) q^{23} -1.00000 q^{24} +(-2.65926 - 4.23418i) q^{25} +(-1.48140 - 3.24380i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(0.528418 - 0.457877i) q^{28} +(8.22773 - 2.41588i) q^{29} +(-0.486678 + 2.18246i) q^{30} +(2.66056 - 5.82581i) q^{31} +(0.755750 + 0.654861i) q^{32} +(2.83284 + 4.40798i) q^{33} +(0.386667 + 2.68933i) q^{34} +(-0.742129 - 1.37609i) q^{35} +(0.841254 - 0.540641i) q^{36} +(4.34838 + 3.76789i) q^{37} +(-3.53991 - 1.61662i) q^{38} +(2.99996 + 1.92796i) q^{39} +(1.79702 - 1.33069i) q^{40} +(-1.31526 - 1.51789i) q^{41} +(-0.196987 + 0.670875i) q^{42} +(4.36540 - 1.99361i) q^{43} +(0.745698 - 5.18645i) q^{44} +(-0.770509 - 2.09912i) q^{45} +(-0.375917 + 4.78108i) q^{46} +5.47253i q^{47} +(-0.989821 - 0.142315i) q^{48} +(2.70482 + 5.92273i) q^{49} +(-2.02961 - 4.56954i) q^{50} +(-1.77925 - 2.05336i) q^{51} +(-1.00468 - 3.42161i) q^{52} +(1.05405 - 1.64013i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(-10.9563 - 4.15159i) q^{55} +(0.588202 - 0.378014i) q^{56} +(3.85197 - 0.553830i) q^{57} +(8.48780 - 1.22036i) q^{58} +(-9.17993 + 5.89959i) q^{59} +(-0.792321 + 2.09099i) q^{60} +(5.71509 - 12.5143i) q^{61} +(3.46258 - 5.38788i) q^{62} +(-0.196987 - 0.670875i) q^{63} +(0.654861 + 0.755750i) q^{64} +(-7.95649 + 0.527443i) q^{65} +(2.17668 + 4.76627i) q^{66} +(-3.44525 - 0.495352i) q^{67} +2.71699i q^{68} +(-2.26860 - 4.22533i) q^{69} +(-0.538737 - 1.46770i) q^{70} +(-0.0479933 + 0.333800i) q^{71} +(0.909632 - 0.415415i) q^{72} +(-3.65477 + 12.4470i) q^{73} +(3.76789 + 4.34838i) q^{74} +(4.17790 + 2.74685i) q^{75} +(-3.27381 - 2.10395i) q^{76} +(-3.33256 - 1.52193i) q^{77} +(2.69505 + 2.33527i) q^{78} +(-3.98251 + 2.55940i) q^{79} +(1.96810 - 1.06140i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-1.08585 - 1.68962i) q^{82} +(12.2644 + 10.6272i) q^{83} +(-0.290457 + 0.636012i) q^{84} +(5.92972 + 1.32230i) q^{85} +(4.60469 - 1.35206i) q^{86} +(-6.48061 + 5.61548i) q^{87} +(1.47622 - 5.02753i) q^{88} +(3.75816 + 8.22923i) q^{89} +(-0.463930 - 2.18741i) q^{90} -2.49338 q^{91} +(-1.05251 + 4.67891i) q^{92} +6.40458i q^{93} +(-0.778822 + 5.41682i) q^{94} +(-6.18508 + 6.12101i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(5.51857 - 4.78187i) q^{97} +(1.83440 + 6.24738i) q^{98} +(-4.40798 - 2.83284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9	\( 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9} - 18 q^{10} - 8 q^{11} - 4 q^{15} - 12 q^{16} + 16 q^{19} + 14 q^{20} - 22 q^{21} - 120 q^{24} + 28 q^{25} + 8 q^{26} + 8 q^{29} + 8 q^{30} + 8 q^{31} + 44 q^{34} + 58 q^{35} - 12 q^{36} + 14 q^{39} - 4 q^{40} + 8 q^{44} - 8 q^{45} + 12 q^{49} - 4 q^{50} + 12 q^{54} + 92 q^{55} - 94 q^{59} + 4 q^{60} - 60 q^{61} + 12 q^{64} - 44 q^{65} - 8 q^{66} + 16 q^{70} - 16 q^{74} + 4 q^{75} - 16 q^{76} + 172 q^{79} + 8 q^{80} - 12 q^{81} - 32 q^{85} - 40 q^{86} + 48 q^{89} - 4 q^{90} + 288 q^{91} + 24 q^{94} - 78 q^{95} - 12 q^{96} - 36 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9 - 18 * q^10 - 8 * q^11 - 4 * q^15 - 12 * q^16 + 16 * q^19 + 14 * q^20 - 22 * q^21 - 120 * q^24 + 28 * q^25 + 8 * q^26 + 8 * q^29 + 8 * q^30 + 8 * q^31 + 44 * q^34 + 58 * q^35 - 12 * q^36 + 14 * q^39 - 4 * q^40 + 8 * q^44 - 8 * q^45 + 12 * q^49 - 4 * q^50 + 12 * q^54 + 92 * q^55 - 94 * q^59 + 4 * q^60 - 60 * q^61 + 12 * q^64 - 44 * q^65 - 8 * q^66 + 16 * q^70 - 16 * q^74 + 4 * q^75 - 16 * q^76 + 172 * q^79 + 8 * q^80 - 12 * q^81 - 32 * q^85 - 40 * q^86 + 48 * q^89 - 4 * q^90 + 288 * q^91 + 24 * q^94 - 78 * q^95 - 12 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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