LMFDB - Embedded newform 69.2.e.c.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

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("69.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, 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:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 $ x^20 - 7x^19 + 24x^18 - 70x^17 + 209x^16 - 527x^15 + 1115x^14 - 2187x^13 + 4165x^12 - 7040x^11 + 10649x^10 - 13519x^9 + 15111x^8 - 12101x^7 + 8244x^6 - 2837x^5 + 1859x^4 - 1730x^3 + 1957x^2 - 1656*x + 529
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			25.2
Root			$0.124087 - 0.863041i$ of defining polynomial
Character	$\chi$	$=$	69.25
Dual form			69.2.e.c.58.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19300 + 0.766692i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.00459227 + 0.0100557i) q^{4} +(0.815022 + 0.239312i) q^{5} +(0.589107 - 1.28996i) q^{6} +(-3.31578 + 3.82661i) q^{7} +(0.401407 - 2.79185i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(1.19300 + 0.766692i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.00459227 + 0.0100557i) q^{4} +(0.815022 + 0.239312i) q^{5} +(0.589107 - 1.28996i) q^{6} +(-3.31578 + 3.82661i) q^{7} +(0.401407 - 2.79185i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(0.788839 + 0.910368i) q^{10} +(-1.24362 + 0.799227i) q^{11} +(0.00929977 - 0.00597660i) q^{12} +(-0.666743 - 0.769463i) q^{13} +(-6.88954 + 2.02295i) q^{14} +(0.120886 - 0.840784i) q^{15} +(2.63384 - 3.03962i) q^{16} +(2.37590 - 5.20249i) q^{17} +(-1.36067 - 0.399530i) q^{18} +(1.89731 + 4.15452i) q^{19} +(0.00133636 + 0.00929457i) q^{20} +(4.25955 + 2.73745i) q^{21} -2.09640 q^{22} +(4.33154 - 2.05857i) q^{23} -2.82056 q^{24} +(-3.59928 - 2.31312i) q^{25} +(-0.205481 - 1.42915i) q^{26} +(0.415415 + 0.909632i) q^{27} +(-0.0537061 - 0.0157695i) q^{28} +(-1.19571 + 2.61825i) q^{29} +(0.788839 - 0.910368i) q^{30} +(-0.751167 + 5.22448i) q^{31} +(0.0600008 - 0.0176178i) q^{32} +(0.968078 + 1.11722i) q^{33} +(6.82314 - 4.38497i) q^{34} +(-3.61819 + 2.32527i) q^{35} +(-0.00723926 - 0.00835455i) q^{36} +(0.443467 - 0.130214i) q^{37} +(-0.921759 + 6.41098i) q^{38} +(-0.666743 + 0.769463i) q^{39} +(0.995278 - 2.17935i) q^{40} +(6.61755 + 1.94309i) q^{41} +(2.98285 + 6.53152i) q^{42} +(-0.690297 - 4.80112i) q^{43} +(-0.0137478 - 0.00883519i) q^{44} -0.849430 q^{45} +(6.74580 + 0.865089i) q^{46} +4.11922 q^{47} +(-3.38351 - 2.17445i) q^{48} +(-2.65237 - 18.4477i) q^{49} +(-2.52048 - 5.51907i) q^{50} +(-5.48766 - 1.61132i) q^{51} +(0.00467560 - 0.0102381i) q^{52} +(-1.84980 + 2.13478i) q^{53} +(-0.201819 + 1.40368i) q^{54} +(-1.20484 + 0.353774i) q^{55} +(9.35234 + 10.7932i) q^{56} +(3.84222 - 2.46925i) q^{57} +(-3.43387 + 2.20681i) q^{58} +(-1.38652 - 1.60013i) q^{59} +(0.00900979 - 0.00264551i) q^{60} +(-1.39065 + 9.67215i) q^{61} +(-4.90170 + 5.65687i) q^{62} +(2.10339 - 4.60577i) q^{63} +(-7.63305 - 2.24127i) q^{64} +(-0.359269 - 0.786689i) q^{65} +(0.298348 + 2.07506i) q^{66} +(-4.61302 - 2.96461i) q^{67} +0.0632253 q^{68} +(-2.65406 - 3.99449i) q^{69} -6.09924 q^{70} +(-10.6456 - 6.84151i) q^{71} +(0.401407 + 2.79185i) q^{72} +(0.730756 + 1.60013i) q^{73} +(0.628889 + 0.184658i) q^{74} +(-1.77734 + 3.89183i) q^{75} +(-0.0330636 + 0.0381574i) q^{76} +(1.06524 - 7.40892i) q^{77} +(-1.38536 + 0.406779i) q^{78} +(1.53299 + 1.76917i) q^{79} +(2.87405 - 1.84704i) q^{80} +(0.841254 - 0.540641i) q^{81} +(6.40496 + 7.39172i) q^{82} +(-15.7737 + 4.63157i) q^{83} +(-0.00796585 + 0.0554037i) q^{84} +(3.18143 - 3.67156i) q^{85} +(2.85746 - 6.25696i) q^{86} +(2.76177 + 0.810928i) q^{87} +(1.73212 + 3.79282i) q^{88} +(1.44953 + 10.0817i) q^{89} +(-1.01337 - 0.651251i) q^{90} +5.15521 q^{91} +(0.0405920 + 0.0341030i) q^{92} +5.27820 q^{93} +(4.91421 + 3.15817i) q^{94} +(0.552119 + 3.84008i) q^{95} +(-0.0259775 - 0.0568828i) q^{96} +(10.8134 + 3.17511i) q^{97} +(10.9794 - 24.0415i) q^{98} +(0.968078 - 1.11722i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{1}{11}\right)$	$1$

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 $

$2$	1.19300	+	0.766692i	0.843575	+	0.542133i	0.889565	−	0.456809i	$-0.151008\pi$
$2$	1.19300	+	0.766692i	0.843575	+	0.542133i	−0.0459895	+	0.998942i	$0.514644\pi$
$3$	−0.142315	−	0.989821i	−0.0821655	−	0.571474i
$3$	−0.142315	−	0.989821i	−0.0821655	−	0.571474i
$4$	0.00459227	+	0.0100557i	0.00229614	+	0.00502784i
$5$	0.815022	+	0.239312i	0.364489	+	0.107024i	0.458848	−	0.888515i	$-0.348262\pi$
$5$	0.815022	+	0.239312i	0.364489	+	0.107024i	−0.0943595	+	0.995538i	$0.530080\pi$
$6$	0.589107	−	1.28996i	0.240502	−	0.526626i
$7$	−3.31578	+	3.82661i	−1.25325	+	1.44632i	−0.407092	+	0.913387i	$0.633457\pi$
$7$	−3.31578	+	3.82661i	−1.25325	+	1.44632i	−0.846155	+	0.532937i	$0.821088\pi$
$8$	0.401407	−	2.79185i	0.141919	−	0.987067i
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$	0.788839	+	0.910368i	0.249453	+	0.287884i
$11$	−1.24362	+	0.799227i	−0.374966	+	0.240976i	−0.714527	−	0.699608i	$-0.753358\pi$
$11$	−1.24362	+	0.799227i	−0.374966	+	0.240976i	0.339561	+	0.940584i	$0.389722\pi$
$12$	0.00929977	−	0.00597660i	0.00268461	−	0.00172530i
$13$	−0.666743	−	0.769463i	−0.184921	−	0.213411i	0.655718	−	0.755006i	$-0.272366\pi$
$13$	−0.666743	−	0.769463i	−0.184921	−	0.213411i	−0.840639	+	0.541595i	$0.817821\pi$
$14$	−6.88954	+	2.02295i	−1.84131	+	0.540657i
$15$	0.120886	−	0.840784i	0.0312127	−	0.217089i
$16$	2.63384	−	3.03962i	0.658460	−	0.759904i
$17$	2.37590	−	5.20249i	0.576240	−	1.26179i	−0.367168	−	0.930155i	$-0.619673\pi$
$17$	2.37590	−	5.20249i	0.576240	−	1.26179i	0.943408	−	0.331635i	$-0.107600\pi$
$18$	−1.36067	−	0.399530i	−0.320714	−	0.0941700i
$19$	1.89731	+	4.15452i	0.435272	+	0.953113i	0.992442	+	0.122715i	$0.0391599\pi$
$19$	1.89731	+	4.15452i	0.435272	+	0.953113i	−0.557170	+	0.830399i	$0.688113\pi$
$20$	0.00133636	+	0.00929457i	0.000298819	+	0.00207833i
$21$	4.25955	+	2.73745i	0.929510	+	0.597360i
$22$	−2.09640			−0.446953
$23$	4.33154	−	2.05857i	0.903189	−	0.429242i
$23$	4.33154	−	2.05857i	0.903189	−	0.429242i
$24$	−2.82056			−0.575744
$25$	−3.59928	−	2.31312i	−0.719856	−	0.462623i
$26$	−0.205481	−	1.42915i	−0.0402982	−	0.280280i
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$	−0.0537061	−	0.0157695i	−0.0101495	−	0.00298016i
$29$	−1.19571	+	2.61825i	−0.222039	+	0.486197i	−0.987566	−	0.157207i	$-0.949751\pi$
$29$	−1.19571	+	2.61825i	−0.222039	+	0.486197i	0.765527	+	0.643404i	$0.222478\pi$
$30$	0.788839	−	0.910368i	0.144022	−	0.166210i
$31$	−0.751167	+	5.22448i	−0.134913	+	0.938344i	0.804107	+	0.594484i	$0.202644\pi$
$31$	−0.751167	+	5.22448i	−0.134913	+	0.938344i	−0.939021	+	0.343860i	$0.888265\pi$
$32$	0.0600008	−	0.0176178i	0.0106067	−	0.00311442i
$33$	0.968078	+	1.11722i	0.168521	+	0.194483i
$34$	6.82314	−	4.38497i	1.17016	−	0.752016i
$35$	−3.61819	+	2.32527i	−0.611585	+	0.393042i
$36$	−0.00723926	−	0.00835455i	−0.00120654	−	0.00139243i
$37$	0.443467	−	0.130214i	0.0729056	−	0.0214070i	−0.245076	−	0.969504i	$-0.578813\pi$
$37$	0.443467	−	0.130214i	0.0729056	−	0.0214070i	0.317982	+	0.948097i	$0.396995\pi$
$38$	−0.921759	+	6.41098i	−0.149529	+	1.04000i
$39$	−0.666743	+	0.769463i	−0.106764	+	0.123213i
$40$	0.995278	−	2.17935i	0.157367	−	0.344586i
$41$	6.61755	+	1.94309i	1.03349	+	0.303460i	0.754128	−	0.656727i	$-0.228060\pi$
$41$	6.61755	+	1.94309i	1.03349	+	0.303460i	0.279360	+	0.960186i	$0.409878\pi$
$42$	2.98285	+	6.53152i	0.460263	+	1.00784i
$43$	−0.690297	−	4.80112i	−0.105269	−	0.732164i	−0.972271	−	0.233859i	$-0.924865\pi$
$43$	−0.690297	−	4.80112i	−0.105269	−	0.732164i	0.867001	−	0.498306i	$-0.166044\pi$
$44$	−0.0137478	−	0.00883519i	−0.00207256	−	0.00133195i
$45$	−0.849430			−0.126625
$46$	6.74580	+	0.865089i	0.994615	+	0.127550i
$47$	4.11922			0.600850			0.300425	−	0.953805i	$-0.402871\pi$
$47$	4.11922			0.600850			0.300425	+	0.953805i	$0.402871\pi$
$48$	−3.38351	−	2.17445i	−0.488368	−	0.313855i
$49$	−2.65237	−	18.4477i	−0.378911	−	2.63538i
$50$	−2.52048	−	5.51907i	−0.356449	−	0.780515i
$51$	−5.48766	−	1.61132i	−0.768426	−	0.225630i
$52$	0.00467560	−	0.0102381i	0.000648389	−	0.00141977i
$53$	−1.84980	+	2.13478i	−0.254090	+	0.293235i	−0.868436	−	0.495801i	$-0.834874\pi$
$53$	−1.84980	+	2.13478i	−0.254090	+	0.293235i	0.614346	+	0.789037i	$0.289420\pi$
$54$	−0.201819	+	1.40368i	−0.0274641	+	0.191017i
$55$	−1.20484	+	0.353774i	−0.162461	+	0.0477029i
$56$	9.35234	+	10.7932i	1.24976	+	1.44230i
$57$	3.84222	−	2.46925i	0.508915	−	0.327060i
$58$	−3.43387	+	2.20681i	−0.450889	+	0.289769i
$59$	−1.38652	−	1.60013i	−0.180510	−	0.208320i	0.658282	−	0.752771i	$-0.271283\pi$
$59$	−1.38652	−	1.60013i	−0.180510	−	0.208320i	−0.838792	+	0.544452i	$0.816738\pi$
$60$	0.00900979	−	0.00264551i	0.00116316	−	0.000341534i
$61$	−1.39065	+	9.67215i	−0.178054	+	1.23839i	0.683205	+	0.730226i	$0.260585\pi$
$61$	−1.39065	+	9.67215i	−0.178054	+	1.23839i	−0.861259	+	0.508166i	$0.830324\pi$
$62$	−4.90170	+	5.65687i	−0.622517	+	0.718423i
$63$	2.10339	−	4.60577i	0.265002	−	0.580273i
$64$	−7.63305	−	2.24127i	−0.954131	−	0.280158i
$65$	−0.359269	−	0.786689i	−0.0445618	−	0.0975767i
$66$	0.298348	+	2.07506i	0.0367241	+	0.255422i
$67$	−4.61302	−	2.96461i	−0.563571	−	0.362185i	0.227624	−	0.973749i	$-0.426904\pi$
$67$	−4.61302	−	2.96461i	−0.563571	−	0.362185i	−0.791195	+	0.611564i	$0.790541\pi$
$68$	0.0632253			0.00766719
$69$	−2.65406	−	3.99449i	−0.319512	−	0.480880i
$70$	−6.09924			−0.728999
$71$	−10.6456	−	6.84151i	−1.26340	−	0.811938i	−0.274654	−	0.961543i	$-0.588563\pi$
$71$	−10.6456	−	6.84151i	−1.26340	−	0.811938i	−0.988746	+	0.149606i	$0.952200\pi$
$72$	0.401407	+	2.79185i	0.0473063	+	0.329022i
$73$	0.730756	+	1.60013i	0.0855285	+	0.187281i	0.947564	−	0.319567i	$-0.103538\pi$
$73$	0.730756	+	1.60013i	0.0855285	+	0.187281i	−0.862035	+	0.506849i	$0.830810\pi$
$74$	0.628889	+	0.184658i	0.0731068	+	0.0214661i
$75$	−1.77734	+	3.89183i	−0.205230	+	0.449390i
$76$	−0.0330636	+	0.0381574i	−0.00379265	+	0.00437695i
$77$	1.06524	−	7.40892i	0.121396	−	0.844325i
$78$	−1.38536	+	0.406779i	−0.156861	+	0.0460587i
$79$	1.53299	+	1.76917i	0.172475	+	0.199047i	0.835405	−	0.549634i	$-0.185233\pi$
$79$	1.53299	+	1.76917i	0.172475	+	0.199047i	−0.662930	+	0.748681i	$0.730687\pi$
$80$	2.87405	−	1.84704i	0.321329	−	0.206506i
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$	6.40496	+	7.39172i	0.707310	+	0.816279i
$83$	−15.7737	+	4.63157i	−1.73139	+	0.508381i	−0.987186	−	0.159576i	$-0.948987\pi$
$83$	−15.7737	+	4.63157i	−1.73139	+	0.508381i	−0.744200	+	0.667957i	$0.767169\pi$
$84$	−0.00796585	+	0.0554037i	−0.000869146	+	0.00604504i
$85$	3.18143	−	3.67156i	0.345074	−	0.398237i
$86$	2.85746	−	6.25696i	0.308128	−	0.674706i
$87$	2.76177	+	0.810928i	0.296092	+	0.0869406i
$88$	1.73212	+	3.79282i	0.184645	+	0.404316i
$89$	1.44953	+	10.0817i	0.153650	+	1.06866i	0.910035	+	0.414531i	$0.136054\pi$
$89$	1.44953	+	10.0817i	0.153650	+	1.06866i	−0.756386	+	0.654126i	$0.773037\pi$
$90$	−1.01337	−	0.651251i	−0.106818	−	0.0686478i
$91$	5.15521			0.540413
$92$	0.0405920	+	0.0341030i	0.00423200	+	0.00355549i
$93$	5.27820			0.547324
$94$	4.91421	+	3.15817i	0.506862	+	0.325741i
$95$	0.552119	+	3.84008i	0.0566463	+	0.393983i
$96$	−0.0259775	−	0.0568828i	−0.00265132	−	0.00580558i
$97$	10.8134	+	3.17511i	1.09794	+	0.322384i	0.780033	−	0.625739i	$-0.215202\pi$
$97$	10.8134	+	3.17511i	1.09794	+	0.322384i	0.317905	+	0.948122i	$0.397021\pi$
$98$	10.9794	−	24.0415i	1.10909	−	2.42856i
$99$	0.968078	−	1.11722i	0.0972955	−	0.112285i
$100$	0.00673107	−	0.0468156i	0.000673107	−	0.00468156i
$101$	14.5621	−	4.27583i	1.44899	−	0.425461i	0.539781	−	0.841806i	$-0.318507\pi$
$101$	14.5621	−	4.27583i	1.44899	−	0.425461i	0.909207	+	0.416344i	$0.136689\pi$
$102$	−5.31137	−	6.12965i	−0.525904	−	0.606925i
$103$	−4.99950	+	3.21299i	−0.492616	+	0.316585i	−0.763257	−	0.646095i	$-0.776401\pi$
$103$	−4.99950	+	3.21299i	−0.492616	+	0.316585i	0.270641	+	0.962680i	$0.412764\pi$
$104$	−2.41586	+	1.55258i	−0.236894	+	0.152243i
$105$	2.81652	+	3.25044i	0.274864	+	0.317210i
$106$	−3.84353	+	1.12856i	−0.373316	+	0.109616i
$107$	2.71431	−	18.8784i	0.262402	−	1.82505i	−0.252265	−	0.967658i	$-0.581175\pi$
$107$	2.71431	−	18.8784i	0.262402	−	1.82505i	0.514667	−	0.857390i	$-0.327915\pi$
$108$	−0.00723926	+	0.00835455i	−0.000696598	+	0.000803917i
$109$	−2.74559	+	6.01201i	−0.262980	+	0.575846i	−0.994352	−	0.106133i	$-0.966153\pi$
$109$	−2.74559	+	6.01201i	−0.262980	+	0.575846i	0.731372	+	0.681979i	$0.238880\pi$
$110$	−1.70861	−	0.501693i	−0.162909	−	0.0478345i
$111$	−0.192000	−	0.420422i	−0.0182239	−	0.0399047i
$112$	2.89819	+	20.1574i	0.273854	+	1.90469i
$113$	−0.827237	−	0.531633i	−0.0778199	−	0.0500118i	0.501152	−	0.865359i	$-0.332910\pi$
$113$	−0.827237	−	0.531633i	−0.0778199	−	0.0500118i	−0.578972	+	0.815347i	$0.696546\pi$
$114$	6.47690			0.606618
$115$	4.02294	−	0.641192i	0.375141	−	0.0597915i
$116$	−0.0318193			−0.00295435
$117$	0.856518	+	0.550451i	0.0791852	+	0.0508892i
$118$	−0.427307	−	2.97199i	−0.0393368	−	0.273594i
$119$	12.0300	+	26.3420i	1.10279	+	2.41476i
$120$	−2.29881	−	0.674993i	−0.209852	−	0.0616181i
$121$	−3.66173	+	8.01808i	−0.332885	+	0.728916i
$122$	−9.07460	+	10.4726i	−0.821575	+	0.948148i
$123$	0.981535	−	6.82673i	0.0885020	−	0.615545i
$124$	−0.0559852	+	0.0164387i	−0.00502762	+	0.00147624i
$125$	−5.16122	−	5.95637i	−0.461634	−	0.532754i
$126$	6.04054	−	3.88202i	0.538134	−	0.345838i
$127$	4.50364	−	2.89432i	0.399634	−	0.256829i	−0.325352	−	0.945593i	$-0.605483\pi$
$127$	4.50364	−	2.89432i	0.399634	−	0.256829i	0.724986	+	0.688764i	$0.241846\pi$
$128$	−7.46974	−	8.62053i	−0.660238	−	0.761955i
$129$	−4.65402	+	1.36654i	−0.409763	+	0.120317i
$130$	0.174542	−	1.21396i	0.0153083	−	0.106472i
$131$	−5.98133	+	6.90282i	−0.522591	+	0.603102i	−0.954278	−	0.298922i	$-0.903373\pi$
$131$	−5.98133	+	6.90282i	−0.522591	+	0.603102i	0.431687	+	0.902024i	$0.357919\pi$
$132$	−0.00678874	+	0.0148653i	−0.000590884	+	0.00129386i
$133$	−22.1888	−	6.51522i	−1.92401	−	0.564941i
$134$	−3.23037	−	7.07353i	−0.279062	−	0.611060i
$135$	0.120886	+	0.840784i	0.0104042	+	0.0723631i
$136$	−13.5709	−	8.72146i	−1.16369	−	0.747859i
$137$	−5.65456			−0.483102			−0.241551	−	0.970388i	$-0.577656\pi$
$137$	−5.65456			−0.483102			−0.241551	+	0.970388i	$0.577656\pi$
$138$	−0.103744	−	6.80026i	−0.00883131	−	0.578876i
$139$	15.8561			1.34490			0.672448	−	0.740144i	$-0.265243\pi$
$139$	15.8561			1.34490			0.672448	+	0.740144i	$0.265243\pi$
$140$	−0.0399978	−	0.0257050i	−0.00338043	−	0.00217247i
$141$	−0.586226	−	4.07729i	−0.0493692	−	0.343370i
$142$	−7.45482	−	16.3238i	−0.625594	−	1.36986i
$143$	1.44415	+	0.424042i	0.120766	+	0.0354601i
$144$	−1.67079	+	3.65853i	−0.139233	+	0.304877i
$145$	−1.60111	+	1.84778i	−0.132965	+	0.153450i
$146$	−0.355020	+	2.46922i	−0.0293816	+	0.204354i
$147$	−17.8824	+	5.25075i	−1.47492	+	0.433075i
$148$	0.00334591	+	0.00386139i	0.000275032	+	0.000317404i
$149$	0.354287	−	0.227686i	0.0290243	−	0.0186528i	−0.526048	−	0.850455i	$-0.676327\pi$
$149$	0.354287	−	0.227686i	0.0290243	−	0.0186528i	0.555073	+	0.831802i	$0.312691\pi$
$150$	−5.10420	+	3.28027i	−0.416756	+	0.267833i
$151$	14.1704	+	16.3535i	1.15317	+	1.33083i	0.934888	+	0.354943i	$0.115500\pi$
$151$	14.1704	+	16.3535i	1.15317	+	1.33083i	0.218282	+	0.975886i	$0.429955\pi$
$152$	12.3604	−	3.62934i	1.00256	−	0.294378i
$153$	−0.813946	+	5.66112i	−0.0658037	+	0.457674i
$154$	6.95119	−	8.02210i	0.560143	−	0.646439i
$155$	−1.86250	+	4.07830i	−0.149599	+	0.327577i
$156$	−0.0107993	−	0.00317097i	−0.000864639	−	0.000253881i
$157$	0.748985	+	1.64005i	0.0597755	+	0.130890i	0.937162	−	0.348893i	$-0.113442\pi$
$157$	0.748985	+	1.64005i	0.0597755	+	0.130890i	−0.877387	+	0.479784i	$0.840715\pi$
$158$	0.472447	+	3.28594i	0.0375859	+	0.261415i
$159$	2.37631	+	1.52716i	0.188454	+	0.121112i
$160$	0.0531181			0.00419936
$161$	−6.48508	+	23.4009i	−0.511096	+	1.84425i
$162$	1.41812			0.111418
$163$	−10.3871	−	6.67541i	−0.813584	−	0.522859i	0.0664385	−	0.997791i	$-0.478836\pi$
$163$	−10.3871	−	6.67541i	−0.813584	−	0.522859i	−0.880023	+	0.474932i	$0.842473\pi$
$164$	0.0108505	+	0.0754671i	0.000847284	+	0.00589299i
$165$	0.521640	+	1.14223i	0.0406096	+	0.0889227i
$166$	−22.3689	−	6.56810i	−1.73616	−	0.509784i
$167$	5.59891	−	12.2599i	0.433257	−	0.948700i	−0.559531	−	0.828810i	$-0.689019\pi$
$167$	5.59891	−	12.2599i	0.433257	−	0.948700i	0.992787	−	0.119890i	$-0.0382542\pi$
$168$	9.35234	−	10.7932i	0.721549	−	0.832712i
$169$	1.70257	−	11.8416i	0.130967	−	0.910893i
$170$	6.61038	−	1.94098i	0.506993	−	0.148867i
$171$	−2.99092	−	3.45170i	−0.228721	−	0.263958i
$172$	0.0451085	−	0.0289895i	0.00343949	−	0.00221043i
$173$	−2.37257	+	1.52476i	−0.180383	+	0.115925i	−0.627716	−	0.778442i	$-0.716010\pi$
$173$	−2.37257	+	1.52476i	−0.180383	+	0.115925i	0.447333	+	0.894367i	$0.352374\pi$
$174$	2.67304	+	3.08486i	0.202643	+	0.233862i
$175$	20.7858	−	6.10326i	1.57126	−	0.461363i
$176$	−0.846160	+	5.88517i	−0.0637817	+	0.443611i
$177$	−1.38652	+	1.60013i	−0.104217	+	0.120273i
$178$	−6.00027	+	13.1388i	−0.449739	+	0.984791i
$179$	−5.30129	−	1.55660i	−0.396237	−	0.116346i	0.0775429	−	0.996989i	$-0.475293\pi$
$179$	−5.30129	−	1.55660i	−0.396237	−	0.116346i	−0.473780	+	0.880643i	$0.657111\pi$
$180$	−0.00390081	−	0.00854158i	−0.000290749	−	0.000636652i
$181$	−1.69164	−	11.7656i	−0.125739	−	0.874532i	−0.950870	−	0.309591i	$-0.899808\pi$
$181$	−1.69164	−	11.7656i	−0.125739	−	0.874532i	0.825131	−	0.564941i	$-0.191101\pi$
$182$	6.15014	+	3.95246i	0.455879	+	0.292976i
$183$	9.77162			0.722339
$184$	−4.00851	−	12.9193i	−0.295511	−	0.952426i
$185$	0.392597			0.0288643
$186$	6.29687	+	4.04675i	0.461709	+	0.296722i
$187$	1.20325	+	8.36881i	0.0879906	+	0.611988i
$188$	0.0189166	+	0.0414215i	0.00137963	+	0.00302098i
$189$	−4.85823	−	1.42651i	−0.353385	−	0.103763i
$190$	−2.28548	+	5.00450i	−0.165806	+	0.363064i
$191$	11.3856	−	13.1397i	0.823833	−	0.950754i	−0.175599	−	0.984462i	$-0.556186\pi$
$191$	11.3856	−	13.1397i	0.823833	−	0.950754i	0.999432	+	0.0337081i	$0.0107317\pi$
$192$	−1.13216	+	7.87432i	−0.0817063	+	0.568280i
$193$	9.99854	−	2.93584i	0.719711	−	0.211326i	0.0986878	−	0.995118i	$-0.468535\pi$
$193$	9.99854	−	2.93584i	0.719711	−	0.211326i	0.621023	+	0.783792i	$0.286717\pi$
$194$	10.4661	+	12.0785i	0.751419	+	0.867183i
$195$	−0.727552	+	0.467569i	−0.0521011	+	0.0334833i
$196$	0.173323	−	0.111388i	0.0123802	−	0.00795629i
$197$	6.83086	+	7.88323i	0.486679	+	0.561657i	0.944975	−	0.327142i	$-0.106086\pi$
$197$	6.83086	+	7.88323i	0.486679	+	0.561657i	−0.458296	+	0.888799i	$0.651540\pi$
$198$	2.01148	−	0.590623i	0.142950	−	0.0419738i
$199$	−0.654831	+	4.55445i	−0.0464197	+	0.322856i	0.953359	+	0.301838i	$0.0976000\pi$
$199$	−0.654831	+	4.55445i	−0.0464197	+	0.322856i	−0.999779	+	0.0210186i	$0.993309\pi$
$200$	−7.90264	+	9.12013i	−0.558801	+	0.644891i
$201$	−2.27793	+	4.98798i	−0.160673	+	0.351825i
$202$	20.6508	+	6.06363i	1.45299	+	0.426635i
$203$	−6.05430	−	13.2571i	−0.424929	−	0.930464i
$204$	−0.00899790	−	0.0625817i	−0.000629979	−	0.00438160i
$205$	4.92845	+	3.16732i	0.344218	+	0.221215i
$206$	−8.42776			−0.587190
$207$	−3.57612	+	3.19552i	−0.248557	+	0.222104i
$208$	−4.09497			−0.283935
$209$	−5.67994	−	3.65028i	−0.392890	−	0.252495i
$210$	0.868013	+	6.03716i	0.0598986	+	0.416604i
$211$	−0.220488	−	0.482801i	−0.0151790	−	0.0332374i	0.901891	−	0.431964i	$-0.142179\pi$
$211$	−0.220488	−	0.482801i	−0.0151790	−	0.0332374i	−0.917070	+	0.398727i	$0.869452\pi$
$212$	−0.0299615	−	0.00879748i	−0.00205776	−	0.000604214i
$213$	−5.25684	+	11.5109i	−0.360193	+	0.788713i
$214$	17.7121	−	20.4409i	1.21077	−	1.39731i
$215$	0.586359	−	4.07822i	0.0399893	−	0.278132i
$216$	2.70630	−	0.794643i	0.184141	−	0.0540686i
$217$	−17.5014	−	20.1976i	−1.18807	−	1.37111i
$218$	−7.88484	+	5.06728i	−0.534029	+	0.343199i
$219$	1.47985	−	0.951041i	0.0999989	−	0.0642654i
$220$	−0.00909040	−	0.0104909i	−0.000612875	−	0.000707295i
$221$	−5.58724	+	1.64056i	−0.375838	+	0.110356i
$222$	0.0932786	−	0.648767i	0.00626045	−	0.0435424i
$223$	2.15754	−	2.48993i	0.144479	−	0.166738i	−0.678897	−	0.734233i	$-0.737542\pi$
$223$	2.15754	−	2.48993i	0.144479	−	0.166738i	0.823377	+	0.567495i	$0.192087\pi$
$224$	−0.131533	+	0.288017i	−0.00878841	+	0.0192439i
$225$	4.10516	+	1.20538i	0.273677	+	0.0803589i
$226$	−0.579291	−	1.26847i	−0.0385339	−	0.0843774i
$227$	−1.85262	−	12.8852i	−0.122963	−	0.855224i	−0.954171	−	0.299263i	$-0.903259\pi$
$227$	−1.85262	−	12.8852i	−0.122963	−	0.855224i	0.831208	−	0.555961i	$-0.187650\pi$
$228$	0.0424744	+	0.0272967i	0.00281294	+	0.00180777i
$229$	−4.91857			−0.325028			−0.162514	−	0.986706i	$-0.551960\pi$
$229$	−4.91857			−0.325028			−0.162514	+	0.986706i	$0.551960\pi$
$230$	5.29095	+	2.31942i	0.348875	+	0.152938i
$231$	−7.48511			−0.492484
$232$	6.82978	+	4.38923i	0.448397	+	0.288167i
$233$	2.36668	+	16.4606i	0.155047	+	1.07837i	0.907598	+	0.419839i	$0.137914\pi$
$233$	2.36668	+	16.4606i	0.155047	+	1.07837i	−0.752552	+	0.658533i	$0.771177\pi$
$234$	0.599796	+	1.31337i	0.0392099	+	0.0858578i
$235$	3.35725	+	0.985779i	0.219003	+	0.0643051i
$236$	0.00972312	−	0.0212907i	0.000632921	−	0.00138590i
$237$	1.53299	−	1.76917i	0.0995786	−	0.114920i
$238$	−5.84446	+	40.6491i	−0.378840	+	2.63489i
$239$	8.83233	−	2.59341i	0.571316	−	0.167753i	0.0167008	−	0.999861i	$-0.494684\pi$
$239$	8.83233	−	2.59341i	0.571316	−	0.167753i	0.554615	+	0.832107i	$0.312866\pi$
$240$	−2.23726	−	2.58194i	−0.144415	−	0.166663i
$241$	2.27184	−	1.46002i	0.146342	−	0.0940482i	−0.465421	−	0.885089i	$-0.654097\pi$
$241$	2.27184	−	1.46002i	0.146342	−	0.0940482i	0.611763	+	0.791041i	$0.290461\pi$
$242$	−10.5158	+	6.75811i	−0.675983	+	0.434428i
$243$	−0.654861	−	0.755750i	−0.0420093	−	0.0484814i
$244$	−0.103646	+	0.0304333i	−0.00663527	+	0.00194829i
$245$	2.25300	−	15.6700i	0.143939	−	1.00112i
$246$	6.40496	−	7.39172i	0.408365	−	0.471279i
$247$	1.93173	−	4.22991i	0.122913	−	0.269143i
$248$	14.2844	+	4.19428i	0.907062	+	0.266337i
$249$	6.82925	+	14.9540i	0.432786	+	0.947670i
$250$	−1.59062	−	11.0630i	−0.100600	−	0.699685i
$251$	−7.62163	−	4.89812i	−0.481073	−	0.309167i	0.277533	−	0.960716i	$-0.410483\pi$
$251$	−7.62163	−	4.89812i	−0.481073	−	0.309167i	−0.758606	+	0.651549i	$0.774119\pi$
$252$	0.0559734			0.00352600
$253$	−3.74154	+	6.02198i	−0.235228	+	0.378598i
$254$	7.59188			0.476357
$255$	−4.08695	−	2.62653i	−0.255935	−	0.164479i
$256$	−0.0377567	−	0.262603i	−0.00235979	−	0.0164127i
$257$	−8.48884	−	18.5880i	−0.529519	−	1.15949i	−0.965708	−	0.259630i	$-0.916399\pi$
$257$	−8.48884	−	18.5880i	−0.529519	−	1.15949i	0.436189	−	0.899855i	$-0.356328\pi$
$258$	−6.59994	−	1.93792i	−0.410894	−	0.120649i
$259$	−0.972162	+	2.12874i	−0.0604072	+	0.132273i
$260$	0.00626082	−	0.00722537i	0.000388280	−	0.000448099i
$261$	0.409633	−	2.84906i	0.0253557	−	0.176353i
$262$	−12.4280	+	3.64920i	−0.767806	+	0.225448i
$263$	2.03326	+	2.34650i	0.125376	+	0.144692i	0.814967	−	0.579508i	$-0.196755\pi$
$263$	2.03326	+	2.34650i	0.125376	+	0.144692i	−0.689591	+	0.724199i	$0.742210\pi$
$264$	3.50771	−	2.25427i	0.215884	−	0.138740i
$265$	−2.01851	+	1.29722i	−0.123996	+	0.0796873i
$266$	−21.4760	−	24.7846i	−1.31678	−	1.51964i
$267$	9.77278	−	2.86955i	0.598085	−	0.175613i
$268$	0.00862689	−	0.0600013i	0.000526971	−	0.00366516i
$269$	−2.49938	+	2.88444i	−0.152390	+	0.175868i	−0.826812	−	0.562479i	$-0.809848\pi$
$269$	−2.49938	+	2.88444i	−0.152390	+	0.175868i	0.674421	+	0.738347i	$0.264393\pi$
$270$	−0.500405	+	1.09573i	−0.0304537	+	0.0666842i
$271$	1.90222	+	0.558543i	0.115552	+	0.0339291i	0.338997	−	0.940787i	$-0.389912\pi$
$271$	1.90222	+	0.558543i	0.115552	+	0.0339291i	−0.223445	+	0.974716i	$0.571730\pi$
$272$	−9.55583	−	20.9243i	−0.579407	−	1.26872i
$273$	−0.733663	−	5.10274i	−0.0444033	−	0.308832i
$274$	−6.74587	−	4.33531i	−0.407533	−	0.261905i
$275$	6.32485			0.381403
$276$	0.0279791	−	0.0450322i	0.00168414	−	0.00271062i
$277$	−14.5994			−0.877195			−0.438598	−	0.898684i	$-0.644525\pi$
$277$	−14.5994			−0.877195			−0.438598	+	0.898684i	$0.644525\pi$
$278$	18.9163	+	12.1567i	1.13452	+	0.729113i
$279$	−0.751167	−	5.22448i	−0.0449712	−	0.312781i
$280$	5.03943	+	11.0348i	0.301163	+	0.659456i
$281$	13.8332	+	4.06180i	0.825221	+	0.242307i	0.666963	−	0.745091i	$-0.267594\pi$
$281$	13.8332	+	4.06180i	0.825221	+	0.242307i	0.158258	+	0.987398i	$0.449412\pi$
$282$	2.42666	−	5.31365i	0.144506	−	0.316423i
$283$	−9.70517	+	11.2004i	−0.576913	+	0.665793i	−0.966938	−	0.255011i	$-0.917921\pi$
$283$	−9.70517	+	11.2004i	−0.576913	+	0.665793i	0.390025	+	0.920804i	$0.372466\pi$
$284$	0.0199085	−	0.138467i	0.00118135	−	0.00821648i
$285$	3.72241	−	1.09300i	0.220497	−	0.0647437i
$286$	1.39776	+	1.61310i	0.0826512	+	0.0953846i
$287$	−29.3778	+	18.8800i	−1.73412	+	1.11445i
$288$	−0.0526068	+	0.0338084i	−0.00309989	+	0.00199218i
$289$	−10.2884	−	11.8734i	−0.605199	−	0.698437i
$290$	−3.32680	+	0.976836i	−0.195356	+	0.0573618i
$291$	1.60388	−	11.1552i	0.0940212	−	0.653932i
$292$	−0.0127346	+	0.0146965i	−0.000745235	+	0.000860047i
$293$	−4.54987	+	9.96282i	−0.265806	+	0.582034i	−0.994726	−	0.102564i	$-0.967295\pi$
$293$	−4.54987	+	9.96282i	−0.265806	+	0.582034i	0.728920	+	0.684599i	$0.240023\pi$
$294$	−25.3594	−	7.44618i	−1.47899	−	0.434270i
$295$	−0.747116	−	1.63595i	−0.0434987	−	0.0952490i
$296$	−0.185526	−	1.29036i	−0.0107835	−	0.0750008i
$297$	−1.24362	−	0.799227i	−0.0721623	−	0.0463759i
$298$	0.597228			0.0345965
$299$	−4.47202	−	1.96042i	−0.258624	−	0.113374i
$300$	−0.0472970			−0.00273069
$301$	20.6609	+	13.2780i	1.19088	+	0.765329i
$302$	4.36712	+	30.3740i	0.251299	+	1.74783i
$303$	−6.30472	−	13.8054i	−0.362197	−	0.793100i
$304$	17.6254	+	5.17527i	1.01088	+	0.296822i
$305$	−3.44807	+	7.55022i	−0.197436	+	0.432324i
$306$	−5.31137	+	6.12965i	−0.303631	+	0.350409i
$307$	1.79661	−	12.4957i	0.102538	−	0.713166i	−0.872092	−	0.489342i	$-0.837237\pi$
$307$	1.79661	−	12.4957i	0.102538	−	0.713166i	0.974630	−	0.223824i	$-0.0718539\pi$
$308$	0.0793936	−	0.0233121i	0.00452387	−	0.00132833i
$309$	3.89179	+	4.49136i	0.221396	+	0.255505i
$310$	−5.34875	+	3.43743i	−0.303789	+	0.195233i
$311$	24.9256	−	16.0187i	1.41340	−	0.908336i	0.413401	−	0.910549i	$-0.364341\pi$
$311$	24.9256	−	16.0187i	1.41340	−	0.908336i	0.999998	+	0.00221286i	$0.000704376\pi$
$312$	1.88059	+	2.17031i	0.106467	+	0.122870i
$313$	1.44883	−	0.425416i	0.0818929	−	0.0240459i	−0.240529	−	0.970642i	$-0.577321\pi$
$313$	1.44883	−	0.425416i	0.0818929	−	0.0240459i	0.322422	+	0.946596i	$0.395503\pi$
$314$	−0.363876	+	2.53081i	−0.0205347	+	0.142822i
$315$	2.81652	−	3.25044i	0.158693	−	0.183141i
$316$	−0.0107502	+	0.0235398i	−0.000604749	+	0.00132422i
$317$	12.6824	+	3.72389i	0.712314	+	0.209154i	0.617761	−	0.786366i	$-0.288040\pi$
$317$	12.6824	+	3.72389i	0.712314	+	0.209154i	0.0945527	+	0.995520i	$0.469858\pi$
$318$	1.66406	+	3.64379i	0.0933161	+	0.204334i
$319$	−0.605560	−	4.21176i	−0.0339048	−	0.235813i
$320$	−5.68474	−	3.65336i	−0.317787	−	0.204229i
$321$	−19.0726			−1.06453
$322$	−25.6780	+	22.9451i	−1.43098	+	1.27868i
$323$	26.1217			1.45345
$324$	0.00929977	+	0.00597660i	0.000516654	+	0.000332033i
$325$	0.619938	+	4.31176i	0.0343880	+	0.239174i
$326$	−7.27384	−	15.9275i	−0.402860	−	0.882141i
$327$	6.34156	+	1.86205i	0.350689	+	0.102972i
$328$	8.08114	−	17.6952i	0.446206	−	0.977056i
$329$	−13.6584	+	15.7627i	−0.753014	+	0.869024i
$330$	−0.253426	+	1.76262i	−0.0139506	+	0.0970288i
$331$	−29.1836	+	8.56908i	−1.60408	+	0.470999i	−0.956677	−	0.291153i	$-0.905961\pi$
$331$	−29.1836	+	8.56908i	−1.60408	+	0.470999i	−0.647399	+	0.762152i	$0.724143\pi$
$332$	−0.119011	−	0.137345i	−0.00653155	−	0.00753781i
$333$	−0.388818	+	0.249878i	−0.0213071	+	0.0136933i
$334$	16.0790	−	10.3334i	0.879806	−	0.565417i
$335$	−3.05025	−	3.52017i	−0.166653	−	0.192328i
$336$	19.5398	−	5.73739i	1.06598	−	0.313000i
$337$	−0.133717	+	0.930023i	−0.00728403	+	0.0506616i	−0.993139	−	0.116937i	$-0.962692\pi$
$337$	−0.133717	+	0.930023i	−0.00728403	+	0.0506616i	0.985855	+	0.167599i	$0.0536014\pi$
$338$	11.1100	−	12.8216i	0.604305	−	0.697406i
$339$	−0.408493	+	0.894476i	−0.0221863	+	0.0485813i
$340$	0.0515300	+	0.0151306i	0.00279461	+	0.000820570i
$341$	−3.24138	−	7.09763i	−0.175531	−	0.384358i
$342$	−0.921759	−	6.41098i	−0.0498430	−	0.346666i
$343$	49.5699	+	31.8567i	2.67653	+	1.72010i
$344$	−13.6811			−0.737635
$345$	−1.20719	−	3.89074i	−0.0649929	−	0.209471i
$346$	−3.99948			−0.215013
$347$	23.4665	+	15.0810i	1.25975	+	0.809589i	0.988249	−	0.152850i	$-0.0488451\pi$
$347$	23.4665	+	15.0810i	1.25975	+	0.809589i	0.271496	+	0.962439i	$0.412481\pi$
$348$	0.00452836	+	0.0314954i	0.000242745	+	0.00168833i
$349$	9.10101	+	19.9284i	0.487166	+	1.06674i	0.980431	+	0.196865i	$0.0630761\pi$
$349$	9.10101	+	19.9284i	0.487166	+	1.06674i	−0.493265	+	0.869879i	$0.664197\pi$
$350$	29.4767	+	8.65514i	1.57560	+	0.462637i
$351$	0.422953	−	0.926138i	0.0225756	−	0.0494336i
$352$	−0.0605377	+	0.0698642i	−0.00322667	+	0.00372378i
$353$	2.48373	−	17.2747i	0.132195	−	0.919440i	−0.810489	−	0.585754i	$-0.800799\pi$
$353$	2.48373	−	17.2747i	0.132195	−	0.919440i	0.942684	−	0.333686i	$-0.108292\pi$
$354$	−2.88092	+	0.845916i	−0.153119	+	0.0449599i
$355$	−7.03913	−	8.12359i	−0.373598	−	0.431156i
$356$	−0.0947215	+	0.0608738i	−0.00502023	+	0.00322631i
$357$	24.3618	−	15.6564i	1.28936	−	0.828623i
$358$	−5.13098	−	5.92147i	−0.271181	−	0.312959i
$359$	−15.4036	+	4.52289i	−0.812968	+	0.238709i	−0.661686	−	0.749781i	$-0.730159\pi$
$359$	−15.4036	+	4.52289i	−0.812968	+	0.238709i	−0.151283	+	0.988491i	$0.548340\pi$
$360$	−0.340967	+	2.37148i	−0.0179705	+	0.124988i
$361$	−1.21794	+	1.40557i	−0.0641019	+	0.0739775i
$362$	7.00249	−	15.3333i	0.368043	−	0.805901i
$363$	8.45758	+	2.48337i	0.443908	+	0.130343i
$364$	0.0236741	+	0.0518391i	0.00124086	+	0.00271711i
$365$	0.212651	+	1.47902i	0.0111307	+	0.0774155i
$366$	11.6575	+	7.49182i	0.609347	+	0.391604i
$367$	12.0449			0.628736			0.314368	−	0.949301i	$-0.398207\pi$
$367$	12.0449			0.628736			0.314368	+	0.949301i	$0.398207\pi$
$368$	5.15133	−	18.5882i	0.268531	−	0.968976i
$369$	−6.89693			−0.359040
$370$	0.468367	+	0.301001i	0.0243492	+	0.0156483i
$371$	−2.03546	−	14.1569i	−0.105676	−	0.734992i
$372$	0.0242389	+	0.0530759i	0.00125673	+	0.00275186i
$373$	−16.2747	−	4.77868i	−0.842671	−	0.247431i	−0.168220	−	0.985750i	$-0.553802\pi$
$373$	−16.2747	−	4.77868i	−0.842671	−	0.247431i	−0.674452	+	0.738319i	$0.735620\pi$
$374$	−4.98082	+	10.9065i	−0.257552	+	0.563961i
$375$	−5.16122	+	5.95637i	−0.266524	+	0.307586i
$376$	1.65348	−	11.5002i	0.0852719	−	0.593079i
$377$	2.81188	−	0.825642i	0.144819	−	0.0425227i
$378$	−4.70216	−	5.42658i	−0.241853	−	0.279113i
$379$	−5.55732	+	3.57147i	−0.285460	+	0.183454i	−0.675533	−	0.737330i	$-0.736086\pi$
$379$	−5.55732	+	3.57147i	−0.285460	+	0.183454i	0.390072	+	0.920784i	$0.372450\pi$
$380$	−0.0360790	+	0.0231866i	−0.00185082	+	0.00118945i
$381$	−3.50579	−	4.04590i	−0.179607	−	0.207278i
$382$	23.6570	−	6.94634i	1.21040	−	0.355405i
$383$	−1.65497	+	11.5106i	−0.0845650	+	0.588163i	0.902843	+	0.429970i	$0.141476\pi$
$383$	−1.65497	+	11.5106i	−0.0845650	+	0.588163i	−0.987408	+	0.158193i	$0.949433\pi$
$384$	−7.46974	+	8.62053i	−0.381188	+	0.439915i
$385$	2.64124	−	5.78351i	0.134610	−	0.294755i
$386$	14.1791	+	4.16336i	0.721697	+	0.211909i
$387$	2.01497	+	4.41216i	0.102427	+	0.224283i
$388$	0.0177304	+	0.123317i	0.000900122	+	0.00626049i
$389$	−14.0012	−	8.99802i	−0.709889	−	0.456218i	0.135218	−	0.990816i	$-0.456827\pi$
$389$	−14.0012	−	8.99802i	−0.709889	−	0.456218i	−0.845106	+	0.534598i	$0.820463\pi$
$390$	−1.22645			−0.0621036
$391$	−0.418406	−	27.4258i	−0.0211597	−	1.38698i
$392$	−52.5677			−2.65507
$393$	7.68379	+	4.93807i	0.387596	+	0.249093i
$394$	2.10518	+	14.6418i	0.106057	+	0.737645i
$395$	0.826039	+	1.80877i	0.0415625	+	0.0910093i
$396$	0.0156801	+	0.00460409i	0.000787954	+	0.000231364i
$397$	−12.9047	+	28.2572i	−0.647666	+	1.41819i	0.245916	+	0.969291i	$0.420911\pi$
$397$	−12.9047	+	28.2572i	−0.647666	+	1.41819i	−0.893582	+	0.448899i	$0.851816\pi$
$398$	−4.27307	+	4.93138i	−0.214189	+	0.247188i
$399$	−3.29111	+	22.8902i	−0.164762	+	1.14594i
$400$	−16.5109	+	4.84804i	−0.825545	+	0.242402i
$401$	−10.6369	−	12.2757i	−0.531183	−	0.613018i	0.425212	−	0.905094i	$-0.360199\pi$
$401$	−10.6369	−	12.2757i	−0.531183	−	0.613018i	−0.956395	+	0.292076i	$0.905654\pi$
$402$	−6.54181	+	4.20416i	−0.326276	+	0.209685i
$403$	4.52088	−	2.90539i	0.225201	−	0.144728i
$404$	0.109870	+	0.126796i	0.00546622	+	0.00630836i
$405$	0.815022	−	0.239312i	0.0404988	−	0.0118915i
$406$	2.94133	−	20.4574i	0.145976	−	1.01528i
$407$	−0.447436	+	0.516368i	−0.0221786	+	0.0255954i
$408$	−6.70135	+	14.6739i	−0.331766	+	0.726467i
$409$	5.43103	+	1.59469i	0.268547	+	0.0788525i	0.413234	−	0.910625i	$-0.364399\pi$
$409$	5.43103	+	1.59469i	0.268547	+	0.0788525i	−0.144687	+	0.989478i	$0.546217\pi$
$410$	3.45126	+	7.55720i	0.170445	+	0.373223i
$411$	0.804728	+	5.59701i	0.0396943	+	0.276080i
$412$	−0.0552678	−	0.0355185i	−0.00272285	−	0.00174987i
$413$	10.7205			0.527521
$414$	−6.71628	+	1.07047i	−0.330087	+	0.0526105i
$415$	−13.9643			−0.685479
$416$	−0.0535614	−	0.0344218i	−0.00262606	−	0.00168767i
$417$	−2.25656	−	15.6947i	−0.110504	−	0.768573i
$418$	−3.97751	−	8.70953i	−0.194546	−	0.425997i
$419$	−15.7427	−	4.62248i	−0.769083	−	0.225823i	−0.126425	−	0.991976i	$-0.540350\pi$
$419$	−15.7427	−	4.62248i	−0.769083	−	0.225823i	−0.642658	+	0.766153i	$0.722168\pi$
$420$	−0.0197511	+	0.0432489i	−0.000963756	+	0.00211033i
$421$	−2.07761	+	2.39769i	−0.101256	+	0.116856i	−0.804116	−	0.594473i	$-0.797361\pi$
$421$	−2.07761	+	2.39769i	−0.101256	+	0.116856i	0.702859	+	0.711329i	$0.251906\pi$
$422$	0.107118	−	0.745025i	0.00521444	−	0.0362672i
$423$	−3.95236	+	1.16052i	−0.192170	+	0.0564263i
$424$	5.21747	+	6.02128i	0.253383	+	0.292419i
$425$	−20.5855	+	13.2295i	−0.998542	+	0.641724i
$426$	−15.0967	+	9.70205i	−0.731437	+	0.470066i
$427$	−32.4005	−	37.3922i	−1.56797	−	1.80954i
$428$	0.202300	−	0.0594007i	0.00977855	−	0.00287124i
$429$	0.214201	−	1.48980i	0.0103417	−	0.0719283i
$430$	3.82626	−	4.41574i	0.184519	−	0.212946i
$431$	−10.3239	+	22.6063i	−0.497286	+	1.08891i	0.480055	+	0.877238i	$0.340617\pi$
$431$	−10.3239	+	22.6063i	−0.497286	+	1.08891i	−0.977342	+	0.211667i	$0.932111\pi$
$432$	3.85907	+	1.13312i	0.185670	+	0.0545175i
$433$	6.37355	+	13.9561i	0.306293	+	0.670689i	0.998708	−	0.0508108i	$-0.0161805\pi$
$433$	6.37355	+	13.9561i	0.306293	+	0.670689i	−0.692415	+	0.721499i	$0.743453\pi$
$434$	−5.39368	−	37.5138i	−0.258905	−	1.80072i
$435$	2.05683	+	1.32185i	0.0986177	+	0.0633777i
$436$	−0.0730633			−0.00349910
$437$	16.7707	+	14.0898i	0.802250	+	0.674004i
$438$	2.49461			0.119197
$439$	−21.5080	−	13.8224i	−1.02652	−	0.659705i	−0.0849034	−	0.996389i	$-0.527058\pi$
$439$	−21.5080	−	13.8224i	−1.02652	−	0.659705i	−0.941618	+	0.336684i	$0.890695\pi$
$440$	0.504050	+	3.50575i	0.0240297	+	0.167130i
$441$	7.74224	+	16.9531i	0.368678	+	0.807293i
$442$	−7.92335	−	2.32651i	−0.376876	−	0.110661i
$443$	−9.94096	+	21.7677i	−0.472309	+	1.03421i	0.512198	+	0.858867i	$0.328831\pi$
$443$	−9.94096	+	21.7677i	−0.472309	+	1.03421i	−0.984507	+	0.175345i	$0.943896\pi$
$444$	0.00334591	−	0.00386139i	0.000158790	−	0.000183253i
$445$	−1.23127	+	8.56369i	−0.0583679	+	0.405958i
$446$	4.48294	−	1.31631i	0.212273	−	0.0623291i
$447$	−0.275789	−	0.318277i	−0.0130444	−	0.0150540i
$448$	33.8860	−	21.7772i	1.60096	−	1.02888i
$449$	6.80003	−	4.37012i	0.320913	−	0.206239i	−0.370259	−	0.928929i	$-0.620731\pi$
$449$	6.80003	−	4.37012i	0.320913	−	0.206239i	0.691172	+	0.722690i	$0.257095\pi$
$450$	3.97328	+	4.58541i	0.187302	+	0.216158i
$451$	−9.78271	+	2.87246i	−0.460650	+	0.135259i
$452$	0.00154703	−	0.0107598i	7.27661e−5	−	0.000506099i
$453$	14.1704	−	16.3535i	0.665783	−	0.768354i
$454$	7.66885	−	16.7924i	0.359917	−	0.788108i
$455$	4.20161	+	1.23370i	0.196974	+	0.0578369i
$456$	−5.35146	−	11.7181i	−0.250605	−	0.548749i
$457$	−3.23464	−	22.4974i	−0.151310	−	1.05238i	−0.914027	−	0.405653i	$-0.867044\pi$
$457$	−3.23464	−	22.4974i	−0.151310	−	1.05238i	0.762717	−	0.646732i	$-0.223865\pi$
$458$	−5.86783	−	3.77102i	−0.274186	−	0.176208i
$459$	5.71934			0.266956
$460$	0.0249221	+	0.0375089i	0.00116200	+	0.00174886i
$461$	−7.53588			−0.350981			−0.175490	−	0.984481i	$-0.556151\pi$
$461$	−7.53588			−0.350981			−0.175490	+	0.984481i	$0.556151\pi$
$462$	−8.92971	−	5.73877i	−0.415447	−	0.266992i
$463$	3.26986	+	22.7424i	0.151963	+	1.05693i	0.912924	+	0.408129i	$0.133819\pi$
$463$	3.26986	+	22.7424i	0.151963	+	1.05693i	−0.760961	+	0.648798i	$0.775272\pi$
$464$	4.80915	+	10.5306i	0.223259	+	0.488869i
$465$	4.30185	+	1.26314i	0.199493	+	0.0585766i
$466$	−9.79679	+	21.4520i	−0.453828	+	0.993744i
$467$	7.33848	−	8.46906i	0.339584	−	0.391901i	−0.560112	−	0.828417i	$-0.689242\pi$
$467$	7.33848	−	8.46906i	0.339584	−	0.391901i	0.899697	+	0.436515i	$0.143788\pi$
$468$	−0.00160179	+	0.0111407i	−7.40427e−5	+	0.000514978i
$469$	26.6402	−	7.82226i	1.23013	−	0.361199i
$470$	3.24940	+	3.75001i	0.149884	+	0.172975i
$471$	1.51676	−	0.974765i	0.0698888	−	0.0449148i
$472$	−5.02389	+	3.22866i	−0.231243	+	0.148611i
$473$	4.69566	+	5.41908i	0.215907	+	0.249170i
$474$	3.18526	−	0.935276i	0.146304	−	0.0429587i
$475$	2.78096	−	19.3420i	0.127599	−	0.887471i
$476$	−0.209641	+	0.241939i	−0.00960889	+	0.0110892i
$477$	1.17343	−	2.56946i	0.0537278	−	0.117647i
$478$	12.5253	+	3.67775i	0.572893	+	0.168216i
$479$	−8.61197	−	18.8576i	−0.393491	−	0.861625i	−0.997889	−	0.0649427i	$-0.979314\pi$
$479$	−8.61197	−	18.8576i	−0.393491	−	0.861625i	0.604398	−	0.796683i	$-0.293414\pi$
$480$	−0.00755950	−	0.0525775i	−0.000345042	−	0.00239982i
$481$	−0.395874	−	0.254413i	−0.0180503	−	0.0116002i
$482$	3.82968			0.174437
$483$	24.0857	+	3.08877i	1.09594	+	0.140544i
$484$	−0.0974428			−0.00442922
$485$	8.05334	+	5.17557i	0.365683	+	0.235010i
$486$	−0.201819	−	1.40368i	−0.00915470	−	0.0636723i
$487$	−10.4365	−	22.8528i	−0.472924	−	1.03556i	−0.984349	−	0.176231i	$-0.943609\pi$
$487$	−10.4365	−	22.8528i	−0.472924	−	1.03556i	0.511425	−	0.859328i	$-0.329118\pi$
$488$	26.4450	+	7.76494i	1.19711	+	0.351502i
$489$	−5.12922	+	11.2314i	−0.231951	+	0.507903i
$490$	14.7019	−	16.9669i	0.664163	−	0.766485i
$491$	−2.46426	+	17.1393i	−0.111211	+	0.773486i	0.855535	+	0.517745i	$0.173229\pi$
$491$	−2.46426	+	17.1393i	−0.111211	+	0.773486i	−0.966745	+	0.255741i	$0.917681\pi$
$492$	0.0731548	−	0.0214802i	0.00329807	−	0.000968401i
$493$	10.7805	+	12.4414i	0.485530	+	0.560332i
$494$	5.54759	−	3.56522i	0.249598	−	0.160407i
$495$	1.05637	−	0.678887i	0.0474803	−	0.0305137i
$496$	13.9019	+	16.0437i	0.624216	+	0.720384i
$497$	61.4782	−	18.0516i	2.75768	−	0.809727i
$498$	−3.31782	+	23.0760i	−0.148675	+	1.03406i
$499$	−25.3979	+	29.3107i	−1.13697	+	1.31213i	−0.193334	+	0.981133i	$0.561930\pi$
$499$	−25.3979	+	29.3107i	−1.13697	+	1.31213i	−0.943632	+	0.330996i	$0.892615\pi$
$500$	0.0361936	−	0.0792528i	0.00161862	−	0.00354429i
$501$	−12.9319	−	3.79715i	−0.577756	−	0.169644i
$502$	−5.33722	−	11.6869i	−0.238212	−	0.521611i
$503$	2.39704	+	16.6718i	0.106879	+	0.743357i	0.970828	+	0.239778i	$0.0770746\pi$
$503$	2.39704	+	16.6718i	0.106879	+	0.743357i	−0.863949	+	0.503579i	$0.832016\pi$
$504$	−12.0143	−	7.72112i	−0.535159	−	0.343926i
$505$	12.8917			0.573674
$506$	−9.08064	+	4.31559i	−0.403683	+	0.191851i
$507$	−11.9634			−0.531312
$508$	0.0497862	+	0.0319957i	0.00220891	+	0.00141958i
$509$	−3.46573	−	24.1047i	−0.153616	−	1.06842i	−0.910094	−	0.414403i	$-0.863990\pi$
$509$	−3.46573	−	24.1047i	−0.153616	−	1.06842i	0.756478	−	0.654020i	$-0.226919\pi$
$510$	−2.86198	−	6.26687i	−0.126731	−	0.277502i
$511$	−8.54612	−	2.50937i	−0.378058	−	0.111008i
$512$	−9.32066	+	20.4094i	−0.411919	+	0.901976i
$513$	−2.99092	+	3.45170i	−0.132052	+	0.152396i
$514$	4.12409	−	28.6837i	0.181906	−	1.26518i
$515$	−4.84361	+	1.42221i	−0.213435	+	0.0626702i
$516$	−0.0351140	−	0.0405237i	−0.00154581	−	0.00178396i
$517$	−5.12275	+	3.29219i	−0.225299	+	0.144791i
$518$	−2.79187	+	1.79423i	−0.122668	+	0.0788338i
$519$	1.84689	+	2.13142i	0.0810693	+	0.0935590i
$520$	−2.34053	+	0.687241i	−0.102639	+	0.0301375i
$521$	−3.92388	+	27.2912i	−0.171908	+	1.19565i	0.702940	+	0.711249i	$0.251870\pi$
$521$	−3.92388	+	27.2912i	−0.171908	+	1.19565i	−0.874848	+	0.484398i	$0.839039\pi$
$522$	2.67304	−	3.08486i	0.116996	−	0.135021i
$523$	−8.81501	+	19.3022i	−0.385454	+	0.844026i	0.613087	+	0.790016i	$0.289928\pi$
$523$	−8.81501	+	19.3022i	−0.385454	+	0.844026i	−0.998540	+	0.0540101i	$0.982800\pi$
$524$	−0.0968803	−	0.0284466i	−0.00423224	−	0.00124270i
$525$	−8.99927	−	19.7057i	−0.392760	−	0.860025i
$526$	0.626622	+	4.35825i	0.0273220	+	0.190029i
$527$	25.3956	+	16.3208i	1.10625	+	0.710944i
$528$	5.94569			0.258753
$529$	14.5245	−	17.8336i	0.631502	−	0.775374i
$530$	−3.40264			−0.147801
$531$	1.78117	+	1.14469i	0.0772961	+	0.0496752i
$532$	−0.0363821	−	0.253043i	−0.00157736	−	0.0109708i
$533$	−2.91708	−	6.38750i	−0.126353	−	0.276673i
$534$	13.8589	+	4.06935i	0.599735	+	0.176098i
$535$	6.73006	−	14.7368i	0.290966	−	0.637126i
$536$	−10.1284	+	11.6888i	−0.437482	+	0.504881i
$537$	−0.786302	+	5.46885i	−0.0339315	+	0.235998i
$538$	−5.19323	+	1.52487i	−0.223896	+	0.0657418i
$539$	18.0424	+	20.8221i	0.777143	+	0.896870i
$540$	−0.00789950	+	0.00507670i	−0.000339940	+	0.000218466i
$541$	10.7003	−	6.87668i	0.460043	−	0.295652i	−0.290017	−	0.957022i	$-0.593661\pi$
$541$	10.7003	−	6.87668i	0.460043	−	0.295652i	0.750060	+	0.661370i	$0.230025\pi$
$542$	1.84111	+	2.12476i	0.0790826	+	0.0912661i
$543$	−11.4051	+	3.34885i	−0.489441	+	0.143713i
$544$	0.0508992	−	0.354012i	0.00218229	−	0.0151781i
$545$	−3.67646	+	4.24287i	−0.157482	+	0.181744i
$546$	3.03697	−	6.65004i	0.129970	−	0.284595i
$547$	24.5840	+	7.21851i	1.05114	+	0.308641i	0.761276	−	0.648428i	$-0.224573\pi$
$547$	24.5840	+	7.21851i	1.05114	+	0.308641i	0.289860	+	0.957069i	$0.406391\pi$
$548$	−0.0259673	−	0.0568604i	−0.00110927	−	0.00242896i
$549$	−1.39065	−	9.67215i	−0.0593513	−	0.412798i
$550$	7.54551	+	4.84921i	0.321742	+	0.206771i
$551$	−13.1462			−0.560047
$552$	−12.2174	+	5.80632i	−0.520006	+	0.247134i
$553$	−11.8530			−0.504040
$554$	−17.4171	−	11.1933i	−0.739980	−	0.475556i
$555$	−0.0558724	−	0.388601i	−0.00237165	−	0.0164952i
$556$	0.0728155	+	0.159444i	0.00308806	+	0.00676192i
$557$	−31.1901	−	9.15824i	−1.32157	−	0.388047i	−0.456509	−	0.889719i	$-0.650900\pi$
$557$	−31.1901	−	9.15824i	−1.32157	−	0.388047i	−0.865058	+	0.501672i	$0.832719\pi$
$558$	3.10943	−	6.80869i	0.131632	−	0.288235i
$559$	−3.23404	+	3.73228i	−0.136785	+	0.157858i
$560$	−2.46181	+	17.1223i	−0.104031	+	0.723548i
$561$	8.11239	−	2.38201i	0.342505	−	0.100569i
$562$	13.3888	+	15.4515i	0.564774	+	0.651784i
$563$	25.9719	−	16.6911i	1.09458	−	0.703446i	0.136703	−	0.990612i	$-0.456350\pi$
$563$	25.9719	−	16.6911i	1.09458	−	0.703446i	0.957881	+	0.287166i	$0.0927132\pi$
$564$	0.0383078	−	0.0246189i	0.00161305	−	0.00103664i
$565$	−0.546990	−	0.631260i	−0.0230120	−	0.0265573i
$566$	−20.1655	+	5.92111i	−0.847618	+	0.248883i
$567$	−0.720588	+	5.01180i	−0.0302618	+	0.210476i
$568$	−23.3737	+	26.9746i	−0.980737	+	1.13183i
$569$	9.52698	−	20.8612i	0.399392	−	0.874546i	−0.597940	−	0.801541i	$-0.704014\pi$
$569$	9.52698	−	20.8612i	0.399392	−	0.874546i	0.997332	−	0.0730050i	$-0.0232589\pi$
$570$	5.27882	+	1.55000i	0.221105	+	0.0649224i
$571$	5.27646	+	11.5538i	0.220813	+	0.483513i	0.987324	−	0.158718i	$-0.0507362\pi$
$571$	5.27646	+	11.5538i	0.220813	+	0.483513i	−0.766511	+	0.642231i	$0.778009\pi$
$572$	0.00236792	+	0.0164692i	9.90077e−5	+	0.000688613i
$573$	−14.6263	−	9.39973i	−0.611021	−	0.392680i
$574$	−49.5227			−2.06704
$575$	−20.3521	−	2.60998i	−0.848743	−	0.108844i
$576$	7.95529			0.331471
$577$	9.24594	+	5.94200i	0.384913	+	0.247369i	0.718760	−	0.695259i	$-0.244710\pi$
$577$	9.24594	+	5.94200i	0.384913	+	0.247369i	−0.333846	+	0.942628i	$0.608347\pi$
$578$	−3.17074	−	22.0530i	−0.131885	−	0.917282i
$579$	−4.32890	−	9.47896i	−0.179903	−	0.393932i
$580$	−0.0259334	−	0.00761474i	−0.00107683	−	0.000316185i
$581$	34.5788	−	75.7170i	1.43457	−	3.14127i
$582$	10.4661	−	12.0785i	0.433832	−	0.500669i
$583$	0.594276	−	4.13328i	0.0246124	−	0.171183i
$584$	4.76066	−	1.39786i	0.196997	−	0.0578437i
$585$	0.566352	+	0.653605i	0.0234158	+	0.0270232i
$586$	−13.0664	+	8.39726i	−0.539768	+	0.346888i
$587$	−17.4816	+	11.2348i	−0.721544	+	0.463708i	−0.849174	−	0.528114i	$-0.822899\pi$
$587$	−17.4816	+	11.2348i	−0.721544	+	0.463708i	0.127630	+	0.991822i	$0.459263\pi$
$588$	−0.134921	−	0.155707i	−0.00556404	−	0.00642124i
$589$	−23.1304	+	6.79170i	−0.953072	+	0.279847i
$590$	0.362967	−	2.52449i	0.0149431	−	0.103932i
$591$	6.83086	−	7.88323i	0.280984	−	0.324273i
$592$	0.772223	−	1.69093i	0.0317382	−	0.0694969i
$593$	−30.3177	−	8.90209i	−1.24500	−	0.365565i	−0.408109	−	0.912933i	$-0.633812\pi$
$593$	−30.3177	−	8.90209i	−1.24500	−	0.365565i	−0.836892	+	0.547368i	$0.815630\pi$
$594$	−0.870875	−	1.90695i	−0.0357324	−	0.0782431i
$595$	3.50074	+	24.3482i	0.143516	+	0.998178i
$596$	0.00391652	+	0.00251699i	0.000160427	+	0.000103100i
$597$	4.60128			0.188318
$598$	−3.83207	−	5.76744i	−0.156705	−	0.235848i
$599$	21.9650			0.897466			0.448733	−	0.893666i	$-0.351875\pi$
$599$	21.9650			0.897466			0.448733	+	0.893666i	$0.351875\pi$
$600$	10.1520	+	6.52427i	0.414452	+	0.266352i
$601$	3.04007	+	21.1441i	0.124007	+	0.862487i	0.952944	+	0.303146i	$0.0980369\pi$
$601$	3.04007	+	21.1441i	0.124007	+	0.862487i	−0.828937	+	0.559342i	$0.811054\pi$
$602$	14.4683	+	31.6811i	0.589683	+	1.29123i
$603$	5.26139	+	1.54488i	0.214260	+	0.0629125i
$604$	−0.0993711	+	0.217592i	−0.00404335	+	0.00885371i
$605$	−4.90321	+	5.65861i	−0.199344	+	0.230055i
$606$	3.06299	−	21.3036i	0.124426	−	0.865399i
$607$	5.65071	−	1.65920i	0.229355	−	0.0673448i	−0.165035	−	0.986288i	$-0.552774\pi$
$607$	5.65071	−	1.65920i	0.229355	−	0.0673448i	0.394391	+	0.918943i	$0.370956\pi$
$608$	0.187034	+	0.215848i	0.00758522	+	0.00875381i
$609$	−12.2605	+	7.87936i	−0.496821	+	0.319288i
$610$	−9.90222	+	6.36377i	−0.400929	+	0.257662i
$611$	−2.74646	−	3.16959i	−0.111110	−	0.128228i
$612$	−0.0606642	+	0.0178126i	−0.00245221	+	0.000720033i
$613$	−0.720390	+	5.01042i	−0.0290963	+	0.202369i	−0.999184	−	0.0403847i	$-0.987142\pi$
$613$	−0.720390	+	5.01042i	−0.0290963	+	0.202369i	0.970088	+	0.242754i	$0.0780507\pi$
$614$	11.7237	−	13.5298i	0.473129	−	0.546020i
$615$	2.43369	−	5.32904i	0.0981358	−	0.214888i
$616$	−20.2570	−	5.94799i	−0.816177	−	0.239651i
$617$	−3.34228	−	7.31857i	−0.134555	−	0.294634i	0.830346	−	0.557248i	$-0.188143\pi$
$617$	−3.34228	−	7.31857i	−0.134555	−	0.294634i	−0.964901	+	0.262614i	$0.915416\pi$
$618$	1.19939	+	8.34197i	0.0482467	+	0.335563i
$619$	−6.01077	−	3.86289i	−0.241593	−	0.155263i	0.414242	−	0.910167i	$-0.364047\pi$
$619$	−6.01077	−	3.86289i	−0.241593	−	0.155263i	−0.655835	+	0.754904i	$0.727683\pi$
$620$	−0.0495631			−0.00199050
$621$	3.67193	+	3.08495i	0.147350	+	0.123795i
$622$	42.0175			1.68475
$623$	−43.3850	−	27.8819i	−1.73819	−	1.11706i
$624$	0.582775	+	4.05329i	0.0233297	+	0.162261i
$625$	6.10562	+	13.3695i	0.244225	+	0.534778i
$626$	2.05461	+	0.603289i	0.0821189	+	0.0241123i
$627$	−2.80478	+	6.14162i	−0.112012	+	0.245273i
$628$	−0.0130522	+	0.0150631i	−0.000520841	+	0.000601083i
$629$	0.376197	−	2.61651i	0.0150000	−	0.104327i
$630$	5.85218	−	1.71836i	0.233157	−	0.0684609i
$631$	−25.0399	−	28.8976i	−0.996823	−	1.15040i	−0.988621	−	0.150429i	$-0.951934\pi$
$631$	−25.0399	−	28.8976i	−0.996823	−	1.15040i	−0.00820264	−	0.999966i	$-0.502611\pi$
$632$	5.55460	−	3.56972i	0.220950	−	0.141996i
$633$	−0.446508	+	0.286953i	−0.0177471	+	0.0114054i
$634$	12.2750	+	14.1661i	0.487501	+	0.562606i
$635$	4.36321	−	1.28115i	0.173149	−	0.0508411i
$636$	−0.00444397	+	0.0309085i	−0.000176215	+	0.00122560i
$637$	−12.4263	+	14.3408i	−0.492350	+	0.568202i
$638$	2.50669	−	5.48889i	0.0992409	−	0.217307i
$639$	12.1418	+	3.56517i	0.480324	+	0.141036i
$640$	−4.02500	−	8.81352i	−0.159102	−	0.348385i
$641$	4.60792	+	32.0488i	0.182002	+	1.26585i	0.852021	+	0.523507i	$0.175377\pi$
$641$	4.60792	+	32.0488i	0.182002	+	1.26585i	−0.670020	+	0.742343i	$0.733714\pi$
$642$	−22.7535	−	14.6228i	−0.898009	−	0.577115i
$643$	35.7909			1.41146			0.705728	−	0.708483i	$-0.250620\pi$
$643$	35.7909			1.41146			0.705728	+	0.708483i	$0.250620\pi$
$644$	−0.265093	+	0.0422516i	−0.0104461	+	0.00166495i
$645$	−4.12015			−0.162231
$646$	31.1630	+	20.0273i	1.22609	+	0.787962i
$647$	0.635729	+	4.42159i	0.0249931	+	0.173831i	0.998495	−	0.0548497i	$-0.0174680\pi$
$647$	0.635729	+	4.42159i	0.0249931	+	0.173831i	−0.973502	+	0.228681i	$0.926559\pi$
$648$	−1.17170	−	2.56567i	−0.0460288	−	0.100789i
$649$	3.00318	+	0.881814i	0.117885	+	0.0346142i
$650$	−2.56621	+	5.61922i	−0.100655	+	0.220404i
$651$	−17.5014	+	20.1976i	−0.685932	+	0.791608i
$652$	0.0194252	−	0.135105i	0.000760748	−	0.00529112i
$653$	−20.4224	+	5.99656i	−0.799191	+	0.234664i	−0.655733	−	0.754993i	$-0.727640\pi$
$653$	−20.4224	+	5.99656i	−0.799191	+	0.234664i	−0.143458	+	0.989656i	$0.545822\pi$
$654$	6.13783	+	7.08343i	0.240008	+	0.276984i
$655$	−6.52684	+	4.19454i	−0.255025	+	0.163894i
$656$	23.3358	−	14.9970i	0.911111	−	0.585536i
$657$	−1.15197	−	1.32944i	−0.0449424	−	0.0518663i
$658$	−28.3796	+	8.33299i	−1.10635	+	0.324854i
$659$	6.55101	−	45.5632i	0.255191	−	1.77489i	−0.310795	−	0.950477i	$-0.600595\pi$
$659$	6.55101	−	45.5632i	0.255191	−	1.77489i	0.565986	−	0.824415i	$-0.308496\pi$
$660$	−0.00909040	+	0.0104909i	−0.000353843	+	0.000408357i
$661$	13.7426	−	30.0922i	0.534527	−	1.17045i	−0.429114	−	0.903250i	$-0.641174\pi$
$661$	13.7426	−	30.0922i	0.534527	−	1.17045i	0.963641	−	0.267200i	$-0.0860986\pi$
$662$	−41.3857	−	12.1519i	−1.60850	−	0.472299i
$663$	2.41901	+	5.29689i	0.0939465	+	0.205714i
$664$	6.59897	+	45.8968i	0.256090	+	1.78114i
$665$	−16.5252	−	10.6201i	−0.640819	−	0.411830i
$666$	−0.655438			−0.0253977
$667$	0.210571	+	13.8025i	0.00815333	+	0.534436i
$668$	0.148993			0.00576472
$669$	−2.77164	−	1.78122i	−0.107158	−	0.0688661i
$670$	−0.940044	−	6.53815i	−0.0363171	−	0.252591i
$671$	−6.00081	−	13.1399i	−0.231659	−	0.507262i
$672$	0.303804	+	0.0892050i	0.0117195	+	0.00344116i
$673$	17.1613	−	37.5779i	0.661518	−	1.44852i	−0.219583	−	0.975594i	$-0.570470\pi$
$673$	17.1613	−	37.5779i	0.661518	−	1.44852i	0.881101	−	0.472928i	$-0.156803\pi$
$674$	−0.872565	+	1.00699i	−0.0336099	+	0.0387879i
$675$	0.608890	−	4.23492i	0.0234362	−	0.163002i
$676$	0.126894	−	0.0372594i	0.00488054	−	0.00143306i
$677$	−19.6629	−	22.6922i	−0.755707	−	0.872132i	0.239402	−	0.970921i	$-0.423049\pi$
$677$	−19.6629	−	22.6922i	−0.755707	−	0.872132i	−0.995108	+	0.0987884i	$0.968503\pi$
$678$	−1.17312	+	0.753917i	−0.0450533	+	0.0289540i
$679$	−48.0049	+	30.8509i	−1.84226	+	1.18395i
$680$	−8.97339	−	10.3558i	−0.344114	−	0.397129i
$681$	−12.4904	+	3.66752i	−0.478635	+	0.140540i
$682$	1.57474	−	10.9526i	0.0603000	−	0.419396i
$683$	26.4965	−	30.5786i	1.01386	−	1.17006i	0.0284968	−	0.999594i	$-0.490928\pi$
$683$	26.4965	−	30.5786i	1.01386	−	1.17006i	0.985364	−	0.170464i	$-0.0545266\pi$
$684$	0.0209741	−	0.0459268i	0.000801964	−	0.00175606i
$685$	−4.60859	−	1.35320i	−0.176085	−	0.0517033i
$686$	34.7125	+	76.0097i	1.32533	+	2.90206i
$687$	0.699985	+	4.86850i	0.0267061	+	0.185745i
$688$	−16.4117	−	10.5472i	−0.625690	−	0.402107i
$689$	2.87598			0.109566
$690$	1.54283	−	5.56718i	0.0587345	−	0.211939i
$691$	3.24119			0.123301			0.0616503	−	0.998098i	$-0.480364\pi$
$691$	3.24119			0.123301			0.0616503	+	0.998098i	$0.480364\pi$
$692$	−0.0262279	−	0.0168556i	−0.000997035	−	0.000640756i
$693$	1.06524	+	7.40892i	0.0404652	+	0.281442i
$694$	16.4329	+	35.9831i	0.623785	+	1.36590i
$695$	12.9231	+	3.79455i	0.490200	+	0.143936i
$696$	3.37258	−	7.38492i	0.127837	−	0.279925i
$697$	25.8315	−	29.8112i	0.978439	−	1.12918i
$698$	−4.42150	+	30.7522i	−0.167356	+	1.16399i
$699$	15.9563	−	4.68519i	0.603522	−	0.177210i
$700$	0.156826	+	0.180987i	0.00592748	+	0.00684068i
$701$	25.0443	−	16.0950i	0.945909	−	0.607899i	0.0258443	−	0.999666i	$-0.491773\pi$
$701$	25.0443	−	16.0950i	0.945909	−	0.607899i	0.920064	+	0.391767i	$0.128136\pi$
$702$	1.21464	−	0.780604i	0.0458437	−	0.0294620i
$703$	1.38237	+	1.59534i	0.0521371	+	0.0601694i
$704$	11.2839	−	3.31325i	0.425278	−	0.124873i
$705$	0.497958	−	3.46337i	0.0187542	−	0.130438i
$706$	16.2074	−	18.7044i	0.609975	−	0.703949i
$707$	−31.9229	+	69.9014i	−1.20058	+	2.62891i
$708$	−0.0224577	−	0.00659418i	−0.000844012	−	0.000247824i
$709$	13.2698	+	29.0568i	0.498357	+	1.09125i	0.977000	+	0.213240i	$0.0684016\pi$
$709$	13.2698	+	29.0568i	0.498357	+	1.09125i	−0.478643	+	0.878010i	$0.658871\pi$
$710$	−2.16936	−	15.0883i	−0.0814148	−	0.566252i
$711$	−1.96933	−	1.26561i	−0.0738556	−	0.0474641i
$712$	28.7284			1.07664
$713$	7.50126	+	24.1764i	0.280925	+	0.905413i
$714$	41.0671			1.53690
$715$	1.07554	+	0.691206i	0.0402228	+	0.0258496i
$716$	−0.00869230	−	0.0604563i	−0.000324847	−	0.00225936i
$717$	−3.82398	−	8.37335i	−0.142809	−	0.312708i
$718$	−21.8440	−	6.41399i	−0.815212	−	0.239368i
$719$	−4.83459	+	10.5863i	−0.180300	+	0.394801i	−0.978104	−	0.208115i	$-0.933267\pi$
$719$	−4.83459	+	10.5863i	−0.180300	+	0.394801i	0.797805	+	0.602916i	$0.205995\pi$
$720$	−2.23726	+	2.58194i	−0.0833779	+	0.0962232i
$721$	4.28240	−	29.7847i	0.159485	−	1.10924i
$722$	−2.53063	+	0.743061i	−0.0941804	+	0.0276539i
$723$	−1.76848	−	2.04093i	−0.0657703	−	0.0759030i
$724$	0.110543	−	0.0710416i	0.00410829	−	0.00264024i
$725$	10.3600	−	6.65798i	0.384761	−	0.247271i
$726$	8.18588	+	9.44701i	0.303807	+	0.350611i
$727$	−34.5960	+	10.1583i	−1.28309	+	0.376751i	−0.851042	−	0.525098i	$-0.824029\pi$
$727$	−34.5960	+	10.1583i	−1.28309	+	0.376751i	−0.432053	+	0.901848i	$0.642211\pi$
$728$	2.06934	−	14.3926i	0.0766948	−	0.533424i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	−0.880262	+	1.92750i	−0.0325799	+	0.0713401i
$731$	−26.6179	−	7.81571i	−0.984498	−	0.289075i
$732$	0.0448739	+	0.0982601i	0.00165859	+	0.00363180i
$733$	−0.233177	−	1.62178i	−0.00861260	−	0.0599019i	0.985062	−	0.172201i	$-0.0550877\pi$
$733$	−0.233177	−	1.62178i	−0.00861260	−	0.0599019i	−0.993674	+	0.112299i	$0.964179\pi$
$734$	14.3695	+	9.23469i	0.530387	+	0.340859i
$735$	−15.8311			−0.583940
$736$	0.223629	−	0.199829i	0.00824306	−	0.00736578i
$737$	8.10626			0.298598
$738$	−8.22800	−	5.28782i	−0.302877	−	0.194647i
$739$	−5.12916	−	35.6741i	−0.188679	−	1.31229i	−0.835432	−	0.549594i	$-0.814782\pi$
$739$	−5.12916	−	35.6741i	−0.188679	−	1.31229i	0.646753	−	0.762700i	$-0.276127\pi$
$740$	0.00180291	+	0.00394783i	6.62764e−5	+	0.000145125i
$741$	−4.46177	−	1.31009i	−0.163907	−	0.0481275i
$742$	8.42572	−	18.4497i	0.309318	−	0.677312i
$743$	17.4000	−	20.0806i	0.638343	−	0.736687i	−0.340738	−	0.940158i	$-0.610677\pi$
$743$	17.4000	−	20.0806i	0.638343	−	0.736687i	0.979081	+	0.203471i	$0.0652222\pi$
$744$	2.11871	−	14.7359i	0.0776756	−	0.540246i
$745$	0.343239	−	0.100784i	0.0125753	−	0.00369245i
$746$	−15.7519	−	18.1786i	−0.576716	−	0.665566i
$747$	13.8299	−	8.88791i	0.506008	−	0.325192i
$748$	−0.0786284	+	0.0505314i	−0.00287494	+	0.00184761i
$749$	63.2405	+	72.9834i	2.31076	+	2.66675i
$750$	−10.7240	+	3.14886i	−0.391586	+	0.114980i
$751$	−4.41579	+	30.7125i	−0.161134	+	1.12071i	0.735366	+	0.677671i	$0.237010\pi$
$751$	−4.41579	+	30.7125i	−0.161134	+	1.12071i	−0.896500	+	0.443044i	$0.853899\pi$
$752$	10.8494	−	12.5208i	0.395636	−	0.456588i
$753$	−3.76360	+	8.24113i	−0.137153	+	0.300323i
$754$	3.98757	+	1.17086i	0.145219	+	0.0426401i
$755$	7.63559	+	16.7196i	0.277887	+	0.608489i
$756$	−0.00796585	−	0.0554037i	−0.000289715	−	0.00201501i
$757$	−9.14398	−	5.87648i	−0.332344	−	0.213584i	0.363817	−	0.931471i	$-0.381473\pi$
$757$	−9.14398	−	5.87648i	−0.332344	−	0.213584i	−0.696160	+	0.717886i	$0.745110\pi$
$758$	−9.36808			−0.340264
$759$	6.49316	+	2.84644i	0.235687	+	0.103319i
$760$	10.9425			0.396927
$761$	14.3975	+	9.25274i	0.521911	+	0.335412i	0.774927	−	0.632050i	$-0.217786\pi$
$761$	14.3975	+	9.25274i	0.521911	+	0.335412i	−0.253017	+	0.967462i	$0.581423\pi$
$762$	−1.08044	−	7.51460i	−0.0391401	−	0.272225i
$763$	−13.9019	−	30.4408i	−0.503281	−	1.10203i
$764$	0.184414	+	0.0541488i	0.00667186	+	0.00195904i
$765$	−2.01816	+	4.41915i	−0.0729666	+	0.159775i
$766$	−10.7994	+	12.4632i	−0.390199	+	0.450314i
$767$	−0.306788	+	2.13376i	−0.0110775	+	0.0770455i
$768$	−0.254557	+	0.0747447i	−0.00918554	+	0.00269712i
$769$	18.3252	+	21.1484i	0.660823	+	0.762630i	0.982911	−	0.184079i	$-0.0589303\pi$
$769$	18.3252	+	21.1484i	0.660823	+	0.762630i	−0.322088	+	0.946710i	$0.604385\pi$
$770$	7.58516	−	4.87468i	0.273350	−	0.175671i
$771$	−17.1907	+	11.0478i	−0.619107	+	0.397876i
$772$	0.0754378	+	0.0870599i	0.00271507	+	0.00313335i
$773$	−10.3412	+	3.03645i	−0.371947	+	0.109213i	−0.462363	−	0.886691i	$-0.652998\pi$
$773$	−10.3412	+	3.03645i	−0.371947	+	0.109213i	0.0904164	+	0.995904i	$0.471180\pi$
$774$	−0.978922	+	6.80855i	−0.0351866	+	0.244728i
$775$	14.7885	−	17.0668i	0.531218	−	0.613058i
$776$	13.2050	−	28.9149i	0.474032	−	1.03799i
$777$	2.24542	+	0.659316i	0.0805542	+	0.0236528i
$778$	−9.80465	−	21.4692i	−0.351514	−	0.769708i
$779$	4.48292	+	31.1794i	0.160617	+	1.11712i
$780$	−0.00804284	−	0.00516882i	−0.000287980	−	0.000185073i
$781$	18.7070			0.669390
$782$	20.5280	−	33.0396i	0.734078	−	1.18149i
$783$	−2.87836			−0.102864
$784$	−63.0597	−	40.5260i	−2.25213	−	1.44736i
$785$	0.217956	+	1.51592i	0.00777918	+	0.0541054i
$786$	5.38075	+	11.7822i	0.191925	+	0.420257i
$787$	31.6859	+	9.30382i	1.12948	+	0.331646i	0.792504	−	0.609867i	$-0.208777\pi$
$787$	31.6859	+	9.30382i	1.12948	+	0.331646i	0.336977	+	0.941513i	$0.390595\pi$
$788$	−0.0479020	+	0.104891i	−0.00170644	+	0.00373658i
$789$	2.03326	−	2.34650i	0.0723859	−	0.0835378i
$790$	−0.401311	+	2.79118i	−0.0142780	+	0.0993056i
$791$	4.77729	−	1.40274i	0.169861	−	0.0498756i
$792$	−2.73052	−	3.15119i	−0.0970248	−	0.111973i
$793$	8.36957	−	5.37879i	0.297212	−	0.191007i
$794$	−37.0598	+	23.8169i	−1.31520	+	0.845229i
$795$	1.57128	+	1.81335i	0.0557274	+	0.0643129i
$796$	−0.0488052	+	0.0143305i	−0.00172985	+	0.000507931i
$797$	−7.33853	+	51.0406i	−0.259944	+	1.80795i	0.273233	+	0.961948i	$0.411907\pi$
$797$	−7.33853	+	51.0406i	−0.259944	+	1.80795i	−0.533177	+	0.846004i	$0.679002\pi$
$798$	−21.4760	+	24.7846i	−0.760242	+	0.877366i
$799$	9.78685	−	21.4302i	0.346234	−	0.758146i
$800$	−0.256712	−	0.0753773i	−0.00907613	−	0.00266499i
$801$	−4.23115	−	9.26493i	−0.149500	−	0.327360i
$802$	−3.27815	−	22.8001i	−0.115756	−	0.805098i
$803$	−2.18765	−	1.40592i	−0.0772007	−	0.0496139i
$804$	−0.0606183			−0.00213784
$805$	−10.8856	+	17.5203i	−0.383667	+	0.617510i
$806$	7.62093			0.268436
$807$	3.21078	+	2.06344i	0.113025	+	0.0726367i
$808$	−6.09212	−	42.3716i	−0.214320	−	1.49063i
$809$	−2.73121	−	5.98051i	−0.0960241	−	0.210263i	0.855524	−	0.517763i	$-0.173235\pi$
$809$	−2.73121	−	5.98051i	−0.0960241	−	0.210263i	−0.951548	+	0.307499i	$0.900508\pi$
$810$	1.15580	+	0.339372i	0.0406105	+	0.0119243i
$811$	3.36425	−	7.36668i	0.118135	−	0.258679i	−0.841322	−	0.540534i	$-0.818222\pi$
$811$	3.36425	−	7.36668i	0.118135	−	0.258679i	0.959457	+	0.281855i	$0.0909496\pi$
$812$	0.105506	−	0.121760i	0.00370253	−	0.00427294i
$813$	0.282143	−	1.96235i	0.00989520	−	0.0688226i
$814$	−0.929684	+	0.272980i	−0.0325854	+	0.00956794i
$815$	−6.86824	−	7.92638i	−0.240584	−	0.277649i
$816$	−19.3514	+	12.4364i	−0.677436	+	0.435361i
$817$	18.6367	−	11.9771i	0.652015	−	0.419024i
$818$	5.25655	+	6.06639i	0.183791	+	0.212106i
$819$	−4.94639	+	1.45239i	−0.172841	+	0.0507506i
$820$	−0.00921676	+	0.0641040i	−0.000321863	+	0.00223861i
$821$	−34.3452	+	39.6365i	−1.19866	+	1.38332i	−0.294759	+	0.955572i	$0.595239\pi$
$821$	−34.3452	+	39.6365i	−1.19866	+	1.38332i	−0.903897	+	0.427751i	$0.859306\pi$
$822$	−3.33114	+	7.29418i	−0.116187	+	0.254414i
$823$	−7.33469	−	2.15366i	−0.255671	−	0.0750718i	0.151385	−	0.988475i	$-0.451627\pi$
$823$	−7.33469	−	2.15366i	−0.255671	−	0.0750718i	−0.407056	+	0.913403i	$0.633445\pi$
$824$	6.96333	+	15.2476i	0.242579	+	0.531174i
$825$	−0.900120	−	6.26047i	−0.0313381	−	0.217962i
$826$	12.7895	+	8.21932i	0.445004	+	0.285987i
$827$	−10.4045			−0.361800			−0.180900	−	0.983501i	$-0.557901\pi$
$827$	−10.4045			−0.361800			−0.180900	+	0.983501i	$0.557901\pi$
$828$	−0.0485556	−	0.0212856i	−0.00168743	−	0.000739724i
$829$	35.0711			1.21807			0.609035	−	0.793144i	$-0.291557\pi$
$829$	35.0711			1.21807			0.609035	+	0.793144i	$0.291557\pi$
$830$	−16.6593	−	10.7063i	−0.578253	−	0.371621i
$831$	2.07772	+	14.4508i	0.0720752	+	0.501294i
$832$	3.36471	+	7.36770i	0.116650	+	0.255429i
$833$	−102.276	−	30.0308i	−3.54364	−	1.04051i
$834$	9.34094	−	20.4538i	0.323450	−	0.708257i
$835$	7.49717	−	8.65220i	0.259450	−	0.299422i
$836$	0.0106222	−	0.0738787i	0.000367375	−	0.00255515i
$837$	−5.06440	+	1.48704i	−0.175051	+	0.0513997i
$838$	−15.2370	−	17.5844i	−0.526353	−	0.607444i
$839$	13.9538	−	8.96757i	0.481739	−	0.309595i	−0.277137	−	0.960831i	$-0.589385\pi$
$839$	13.9538	−	8.96757i	0.481739	−	0.309595i	0.758875	+	0.651236i	$0.225749\pi$
$840$	10.2053	−	6.55855i	0.352116	−	0.226291i
$841$	13.5655	+	15.6554i	0.467775	+	0.539841i
$842$	−4.31686	+	1.26754i	−0.148769	+	0.0436825i
$843$	2.05179	−	14.2705i	0.0706672	−	0.491501i
$844$	0.00384234	−	0.00443430i	0.000132259	−	0.000152635i
$845$	4.22147	−	9.24372i	0.145223	−	0.317994i
$846$	−5.60491	−	1.64575i	−0.192701	−	0.0565821i
$847$	−18.5406	−	40.5982i	−0.637062	−	1.39497i
$848$	1.61684	+	11.2454i	0.0555225	+	0.386167i
$849$	12.4676	+	8.01241i	0.427885	+	0.274985i
$850$	−34.7013			−1.19025
$851$	1.65284	−	1.47694i	0.0566588	−	0.0506288i
$852$	−0.139891			−0.00479257
$853$	−22.8625	−	14.6928i	−0.782798	−	0.503073i	0.0871634	−	0.996194i	$-0.472220\pi$
$853$	−22.8625	−	14.6928i	−0.782798	−	0.503073i	−0.869961	+	0.493121i	$0.835856\pi$
$854$	−9.98539	−	69.4499i	−0.341693	−	2.37653i
$855$	−1.61163	−	3.52898i	−0.0551165	−	0.120688i
$856$	−51.6162	−	15.1559i	−1.76421	−	0.518017i
$857$	−8.47480	+	18.5572i	−0.289494	+	0.633903i	−0.997373	−	0.0724301i	$-0.976925\pi$
$857$	−8.47480	+	18.5572i	−0.289494	+	0.633903i	0.707880	+	0.706333i	$0.249652\pi$
$858$	1.39776	−	1.61310i	0.0477187	−	0.0550703i
$859$	−1.36466	+	9.49141i	−0.0465616	+	0.323843i	0.953207	+	0.302319i	$0.0977608\pi$
$859$	−1.36466	+	9.49141i	−0.0465616	+	0.323843i	−0.999768	+	0.0215237i	$0.993148\pi$
$860$	0.0437019	−	0.0128320i	0.00149022	−	0.000437569i
$861$	22.8687	+	26.3919i	0.779363	+	0.899433i
$862$	−29.6484	+	19.0539i	−1.00983	+	0.648978i
$863$	−17.3869	+	11.1739i	−0.591858	+	0.380364i	−0.802015	−	0.597303i	$-0.796239\pi$
$863$	−17.3869	+	11.1739i	−0.591858	+	0.380364i	0.210157	+	0.977668i	$0.432602\pi$
$864$	0.0409510	+	0.0472599i	0.00139318	+	0.00160782i
$865$	−2.29858	+	0.674925i	−0.0781542	+	0.0229481i
$866$	−3.09643	+	21.5361i	−0.105221	+	0.731828i
$867$	−10.2884	+	11.8734i	−0.349412	+	0.403243i
$868$	0.122730	−	0.268741i	0.00416572	−	0.00912166i
$869$	−3.32043	−	0.974966i	−0.112638	−	0.0330735i
$870$	1.44035	+	3.15392i	0.0488323	+	0.106928i
$871$	0.794545	+	5.52618i	0.0269221	+	0.187248i
$872$	15.6825	+	10.0785i	0.531077	+	0.341302i
$873$	−11.2699			−0.381430
$874$	9.20483	+	29.6669i	0.311358	+	1.00350i
$875$	39.9062			1.34908
$876$	0.0163592	+	0.0105134i	0.000552727	+	0.000355216i
$877$	7.02177	+	48.8375i	0.237108	+	1.64912i	0.666134	+	0.745832i	$0.267948\pi$
$877$	7.02177	+	48.8375i	0.237108	+	1.64912i	−0.429026	+	0.903292i	$0.641143\pi$
$878$	−15.0615	−	32.9800i	−0.508300	−	1.11302i
$879$	10.5089	+	3.08570i	0.354457	+	0.104078i
$880$	−2.09803	+	4.59405i	−0.0707246	+	0.154865i
$881$	18.2842	−	21.1011i	0.616012	−	0.710916i	−0.358933	−	0.933363i	$-0.616859\pi$
$881$	18.2842	−	21.1011i	0.616012	−	0.710916i	0.974945	+	0.222448i	$0.0714047\pi$
$882$	−3.76138	+	26.1609i	−0.126652	+	0.880885i
$883$	5.40832	−	1.58802i	0.182004	−	0.0534413i	−0.189460	−	0.981888i	$-0.560674\pi$
$883$	5.40832	−	1.58802i	0.182004	−	0.0534413i	0.371465	+	0.928447i	$0.378856\pi$
$884$	−0.0421550	−	0.0486495i	−0.00141783	−	0.00163626i
$885$	−1.51298	+	0.972332i	−0.0508582	+	0.0326846i
$886$	−28.5486	+	18.3471i	−0.959109	+	0.616382i
$887$	11.4361	+	13.1979i	0.383986	+	0.443143i	0.914532	−	0.404513i	$-0.132559\pi$
$887$	11.4361	+	13.1979i	0.383986	+	0.443143i	−0.530547	+	0.847656i	$0.678013\pi$
$888$	−1.25082	+	0.367275i	−0.0419749	+	0.0123250i
$889$	−3.85766	+	26.8306i	−0.129382	+	0.899870i
$890$	−8.03461	+	9.27243i	−0.269321	+	0.310813i
$891$	−0.614107	+	1.34471i	−0.0205733	+	0.0450493i
$892$	0.0349459	+	0.0102610i	0.00117008	+	0.000343565i
$893$	7.81543	+	17.1134i	0.261533	+	0.572678i
$894$	−0.0849943	−	0.591149i	−0.00284264	−	0.0197710i
$895$	−3.94815	−	2.53732i	−0.131972	−	0.0848133i
$896$	57.7555			1.92947
$897$	−1.30403	+	4.70550i	−0.0435404	+	0.157112i
$898$	11.4629			0.382523
$899$	−12.7808	−	8.21372i	−0.426264	−	0.273943i
$900$	0.00673107	+	0.0468156i	0.000224369	+	0.00156052i
$901$	6.71126	+	14.6956i	0.223584	+	0.489581i
$902$	−13.8730	−	4.07349i	−0.461921	−	0.135632i
$903$	10.2025	−	22.3403i	0.339517	−	0.743438i
$904$	−1.81630	+	2.09612i	−0.0604091	+	0.0697158i
$905$	1.43693	−	9.99408i	0.0477652	−	0.332214i
$906$	29.4433	−	8.64533i	0.978188	−	0.287222i
$907$	24.0798	+	27.7896i	0.799558	+	0.922739i	0.998357	−	0.0573012i	$-0.0182495\pi$
$907$	24.0798	+	27.7896i	0.799558	+	0.922739i	−0.198799	+	0.980040i	$0.563704\pi$
$908$	0.121062	−	0.0778019i	0.00401759	−	0.00258195i
$909$	−12.7676	+	8.20526i	−0.423476	+	0.272151i
$910$	4.06663	+	4.69314i	0.134808	+	0.155576i
$911$	−13.1586	+	3.86373i	−0.435965	+	0.128011i	−0.492348	−	0.870398i	$-0.663861\pi$
$911$	−13.1586	+	3.86373i	−0.435965	+	0.128011i	0.0563831	+	0.998409i	$0.482043\pi$
$912$	2.61425	−	18.1825i	0.0865663	−	0.602082i
$913$	15.9148	−	18.3667i	0.526703	−	0.607848i
$914$	13.3897	−	29.3193i	0.442891	−	0.969796i
$915$	7.96408	+	2.33846i	0.263284	+	0.0773073i
$916$	−0.0225874	−	0.0494595i	−0.000746308	−	0.00163419i
$917$	−6.58166	−	45.7764i	−0.217346	−	1.51167i
$918$	6.82314	+	4.38497i	0.225197	+	0.144725i
$919$	−14.1731			−0.467528			−0.233764	−	0.972293i	$-0.575104\pi$
$919$	−14.1731			−0.467528			−0.233764	+	0.972293i	$0.575104\pi$
$920$	−0.175273	−	11.4888i	−0.00577858	−	0.378775i
$921$	−12.6242			−0.415980
$922$	−8.99027	−	5.77770i	−0.296079	−	0.190278i
$923$	1.83359	+	12.7529i	0.0603534	+	0.419767i
$924$	−0.0343737	−	0.0752678i	−0.00113081	−	0.00247613i
$925$	−1.89736	−	0.557116i	−0.0623849	−	0.0183179i
$926$	−13.5355	+	29.6385i	−0.444803	+	0.973982i
$927$	3.89179	−	4.49136i	0.127823	−	0.147516i
$928$	−0.0256160	+	0.178163i	−0.000840885	+	0.00584848i
$929$	−13.2089	+	3.87848i	−0.433370	+	0.127249i	−0.491139	−	0.871081i	$-0.663419\pi$
$929$	−13.2089	+	3.87848i	−0.433370	+	0.127249i	0.0577694	+	0.998330i	$0.481601\pi$
$930$	4.16365	+	4.80511i	0.136531	+	0.157566i
$931$	71.6089	−	46.0202i	2.34689	−	1.50825i
$932$	−0.154654	+	0.0993903i	−0.00506587	+	0.00325564i
$933$	−19.4029	−	22.3922i	−0.635223	−	0.733086i
$934$	15.2479	−	4.47720i	0.498928	−	0.146498i
$935$	−1.02208	+	7.10872i	−0.0334256	+	0.232480i
$936$	1.88059	−	2.17031i	0.0614689	−	0.0709389i
$937$	−0.974836	+	2.13459i	−0.0318465	+	0.0697341i	−0.924887	−	0.380243i	$-0.875840\pi$
$937$	−0.974836	+	2.13459i	−0.0318465	+	0.0697341i	0.893040	+	0.449977i	$0.148568\pi$
$938$	37.7789	+	11.0929i	1.23352	+	0.362195i
$939$	−0.627276	−	1.37354i	−0.0204704	−	0.0448239i
$940$	0.00550475	+	0.0382864i	0.000179545	+	0.00124876i
$941$	−43.2829	−	27.8162i	−1.41098	−	0.906783i	−0.410993	−	0.911638i	$-0.634818\pi$
$941$	−43.2829	−	27.8162i	−1.41098	−	0.906783i	−0.999988	+	0.00485554i	$0.998454\pi$
$942$	2.55684			0.0833062
$943$	32.6642	−	5.20615i	1.06369	−	0.169536i
$944$	−8.51567			−0.277161
$945$	−3.61819	−	2.32527i	−0.117700	−	0.0756410i
$946$	1.44714	+	10.0651i	0.0470505	+	0.327243i
$947$	14.6846	+	32.1547i	0.477184	+	1.04489i	0.983228	+	0.182380i	$0.0583802\pi$
$947$	14.6846	+	32.1547i	0.477184	+	1.04489i	−0.506044	+	0.862508i	$0.668893\pi$
$948$	0.0248301	+	0.00729077i	0.000806444	+	0.000236793i
$949$	0.744016	−	1.62917i	0.0241518	−	0.0528850i
$950$	18.1470	−	20.9428i	0.588766	−	0.679473i
$951$	1.88109	−	13.0833i	0.0609985	−	0.424254i
$952$	78.3716	−	23.0120i	2.54004	−	0.745823i
$953$	7.01592	+	8.09680i	0.227268	+	0.262281i	0.857919	−	0.513786i	$-0.171757\pi$
$953$	7.01592	+	8.09680i	0.227268	+	0.262281i	−0.630651	+	0.776067i	$0.717212\pi$
$954$	3.36988	−	2.16569i	0.109104	−	0.0701169i
$955$	12.4240	−	7.98441i	0.402031	−	0.258370i
$956$	0.0666389	+	0.0769054i	0.00215526	+	0.00248730i
$957$	−4.08271	+	1.19879i	−0.131975	+	0.0387514i
$958$	4.18391	−	29.0997i	0.135176	−	0.940170i
$959$	18.7493	−	21.6378i	0.605446	−	0.698722i
$960$	−2.80715	+	6.14680i	−0.0906004	+	0.198387i
$961$	3.01336	+	0.884803i	0.0972053	+	0.0285420i
$962$	−0.277220	−	0.607026i	−0.00893792	−	0.0195713i
$963$	2.71431	+	18.8784i	0.0874674	+	0.608349i
$964$	0.0251144	+	0.0161400i	0.000808880	+	0.000519835i
$965$	8.85161			0.284943
$966$	26.3660	+	22.1512i	0.848311	+	0.712702i
$967$	−44.9115			−1.44426			−0.722128	−	0.691759i	$-0.756836\pi$
$967$	−44.9115			−1.44426			−0.722128	+	0.691759i	$0.756836\pi$
$968$	20.9154	+	13.4415i	0.672247	+	0.432027i
$969$	−3.71750	−	25.8558i	−0.119423	−	0.830608i
$970$	5.63954	+	12.3489i	0.181075	+	0.396498i
$971$	27.5680	+	8.09469i	0.884699	+	0.259771i	0.692355	−	0.721557i	$-0.256573\pi$
$971$	27.5680	+	8.09469i	0.884699	+	0.259771i	0.192343	+	0.981328i	$0.438391\pi$
$972$	0.00459227	−	0.0100557i	0.000147297	−	0.000322536i
$973$	−52.5753	+	60.6752i	−1.68549	+	1.94516i
$974$	5.07033	−	35.2649i	0.162464	−	1.12996i
$975$	4.17965	−	1.22726i	0.133856	−	0.0393037i
$976$	25.7369	+	29.7019i	0.823818	+	0.950736i
$977$	35.7057	−	22.9466i	1.14233	−	0.734128i	0.174229	−	0.984705i	$-0.444257\pi$
$977$	35.7057	−	22.9466i	1.14233	−	0.734128i	0.968097	+	0.250577i	$0.0806204\pi$
$978$	−14.7302	+	9.46651i	−0.471019	+	0.302706i
$979$	−9.86023	−	11.3793i	−0.315134	−	0.363684i
$980$	0.167919	−	0.0493054i	0.00536397	−	0.00157500i
$981$	0.940598	−	6.54201i	0.0300310	−	0.208870i
$982$	−16.0804	+	18.5578i	−0.513147	+	0.592203i
$983$	0.256325	−	0.561274i	0.00817550	−	0.0179018i	−0.905500	−	0.424346i	$-0.860504\pi$
$983$	0.256325	−	0.561274i	0.00817550	−	0.0179018i	0.913676	+	0.406444i	$0.133231\pi$
$984$	−18.6652	−	5.48059i	−0.595024	−	0.174715i
$985$	3.68075	+	8.05971i	0.117278	+	0.256804i
$986$	3.32241	+	23.1078i	0.105807	+	0.735904i
$987$	17.5460	+	11.2761i	0.558496	+	0.358924i
$988$	0.0514056			0.00163543
$989$	−12.8735	−	19.3752i	−0.409354	−	0.616097i
$990$	1.78074			0.0565957
$991$	−11.8686	−	7.62752i	−0.377020	−	0.242296i	0.338382	−	0.941009i	$-0.390120\pi$
$991$	−11.8686	−	7.62752i	−0.377020	−	0.242296i	−0.715402	+	0.698713i	$0.753757\pi$
$992$	0.0469734	+	0.326707i	0.00149141	+	0.0103730i
$993$	12.6351	+	27.6670i	0.400963	+	0.877987i
$994$	87.1833	+	25.5993i	2.76529	+	0.811962i
$995$	−1.62363	+	3.55526i	−0.0514727	+	0.112709i
$996$	−0.119011	+	0.137345i	−0.00377099	+	0.00435196i
$997$	−7.79322	+	54.2030i	−0.246814	+	1.71663i	0.369589	+	0.929195i	$0.379498\pi$
$997$	−7.79322	+	54.2030i	−0.246814	+	1.71663i	−0.616403	+	0.787431i	$0.711411\pi$
$998$	−52.7719	+	15.4952i	−1.67047	+	0.490493i
$999$	0.302670	+	0.349299i	0.00957604	+	0.0110513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.c.25.2	✓	20
3.2	odd	2		207.2.i.d.163.1		20
23.9	even	11		1587.2.a.u.1.8		10
23.12	even	11	inner	69.2.e.c.58.2	yes	20
23.14	odd	22		1587.2.a.t.1.8		10
69.14	even	22		4761.2.a.bu.1.3		10
69.32	odd	22		4761.2.a.bt.1.3		10
69.35	odd	22		207.2.i.d.127.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.25.2	✓	20	1.1	even	1	trivial
69.2.e.c.58.2	yes	20	23.12	even	11	inner
207.2.i.d.127.1		20	69.35	odd	22
207.2.i.d.163.1		20	3.2	odd	2
1587.2.a.t.1.8		10	23.14	odd	22
1587.2.a.u.1.8		10	23.9	even	11
4761.2.a.bt.1.3		10	69.32	odd	22
4761.2.a.bu.1.3		10	69.14	even	22

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19300 + 0.766692i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.00459227 + 0.0100557i) q^{4} +(0.815022 + 0.239312i) q^{5} +(0.589107 - 1.28996i) q^{6} +(-3.31578 + 3.82661i) q^{7} +(0.401407 - 2.79185i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(1.19300 + 0.766692i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.00459227 + 0.0100557i) q^{4} +(0.815022 + 0.239312i) q^{5} +(0.589107 - 1.28996i) q^{6} +(-3.31578 + 3.82661i) q^{7} +(0.401407 - 2.79185i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(0.788839 + 0.910368i) q^{10} +(-1.24362 + 0.799227i) q^{11} +(0.00929977 - 0.00597660i) q^{12} +(-0.666743 - 0.769463i) q^{13} +(-6.88954 + 2.02295i) q^{14} +(0.120886 - 0.840784i) q^{15} +(2.63384 - 3.03962i) q^{16} +(2.37590 - 5.20249i) q^{17} +(-1.36067 - 0.399530i) q^{18} +(1.89731 + 4.15452i) q^{19} +(0.00133636 + 0.00929457i) q^{20} +(4.25955 + 2.73745i) q^{21} -2.09640 q^{22} +(4.33154 - 2.05857i) q^{23} -2.82056 q^{24} +(-3.59928 - 2.31312i) q^{25} +(-0.205481 - 1.42915i) q^{26} +(0.415415 + 0.909632i) q^{27} +(-0.0537061 - 0.0157695i) q^{28} +(-1.19571 + 2.61825i) q^{29} +(0.788839 - 0.910368i) q^{30} +(-0.751167 + 5.22448i) q^{31} +(0.0600008 - 0.0176178i) q^{32} +(0.968078 + 1.11722i) q^{33} +(6.82314 - 4.38497i) q^{34} +(-3.61819 + 2.32527i) q^{35} +(-0.00723926 - 0.00835455i) q^{36} +(0.443467 - 0.130214i) q^{37} +(-0.921759 + 6.41098i) q^{38} +(-0.666743 + 0.769463i) q^{39} +(0.995278 - 2.17935i) q^{40} +(6.61755 + 1.94309i) q^{41} +(2.98285 + 6.53152i) q^{42} +(-0.690297 - 4.80112i) q^{43} +(-0.0137478 - 0.00883519i) q^{44} -0.849430 q^{45} +(6.74580 + 0.865089i) q^{46} +4.11922 q^{47} +(-3.38351 - 2.17445i) q^{48} +(-2.65237 - 18.4477i) q^{49} +(-2.52048 - 5.51907i) q^{50} +(-5.48766 - 1.61132i) q^{51} +(0.00467560 - 0.0102381i) q^{52} +(-1.84980 + 2.13478i) q^{53} +(-0.201819 + 1.40368i) q^{54} +(-1.20484 + 0.353774i) q^{55} +(9.35234 + 10.7932i) q^{56} +(3.84222 - 2.46925i) q^{57} +(-3.43387 + 2.20681i) q^{58} +(-1.38652 - 1.60013i) q^{59} +(0.00900979 - 0.00264551i) q^{60} +(-1.39065 + 9.67215i) q^{61} +(-4.90170 + 5.65687i) q^{62} +(2.10339 - 4.60577i) q^{63} +(-7.63305 - 2.24127i) q^{64} +(-0.359269 - 0.786689i) q^{65} +(0.298348 + 2.07506i) q^{66} +(-4.61302 - 2.96461i) q^{67} +0.0632253 q^{68} +(-2.65406 - 3.99449i) q^{69} -6.09924 q^{70} +(-10.6456 - 6.84151i) q^{71} +(0.401407 + 2.79185i) q^{72} +(0.730756 + 1.60013i) q^{73} +(0.628889 + 0.184658i) q^{74} +(-1.77734 + 3.89183i) q^{75} +(-0.0330636 + 0.0381574i) q^{76} +(1.06524 - 7.40892i) q^{77} +(-1.38536 + 0.406779i) q^{78} +(1.53299 + 1.76917i) q^{79} +(2.87405 - 1.84704i) q^{80} +(0.841254 - 0.540641i) q^{81} +(6.40496 + 7.39172i) q^{82} +(-15.7737 + 4.63157i) q^{83} +(-0.00796585 + 0.0554037i) q^{84} +(3.18143 - 3.67156i) q^{85} +(2.85746 - 6.25696i) q^{86} +(2.76177 + 0.810928i) q^{87} +(1.73212 + 3.79282i) q^{88} +(1.44953 + 10.0817i) q^{89} +(-1.01337 - 0.651251i) q^{90} +5.15521 q^{91} +(0.0405920 + 0.0341030i) q^{92} +5.27820 q^{93} +(4.91421 + 3.15817i) q^{94} +(0.552119 + 3.84008i) q^{95} +(-0.0259775 - 0.0568828i) q^{96} +(10.8134 + 3.17511i) q^{97} +(10.9794 - 24.0415i) q^{98} +(0.968078 - 1.11722i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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