LMFDB - Embedded newform 690.2.m.c.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (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:	$5.50967773947$
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} - 4 x^{19} - 3 x^{18} + 66 x^{17} - 163 x^{16} - 52 x^{15} + 1567 x^{14} - 6182 x^{13} + \cdots + 529 $ x^20 - 4x^19 - 3x^18 + 66x^17 - 163x^16 - 52x^15 + 1567x^14 - 6182x^13 + 17043x^12 - 35832x^11 + 60906x^10 - 87666x^9 + 106197x^8 - 102542x^7 + 92618x^6 - 8374x^5 + 38352x^4 + 60038x^3 + 32919x^2 + 5681*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.1
Root			$0.180562 - 1.25584i$ of defining polynomial
Character	$\chi$	$=$	690.31
Dual form			690.2.m.c.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.654861 - 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-1.32376 - 0.850727i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.654861 - 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-1.32376 - 0.850727i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(0.841254 - 0.540641i) q^{10} +(0.308448 + 2.14530i) q^{11} +(0.142315 + 0.989821i) q^{12} +(-0.178324 + 0.114602i) q^{13} +(1.03046 - 1.18921i) q^{14} +(-0.415415 + 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-2.86530 + 0.841327i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(0.700061 + 0.205556i) q^{19} +(0.415415 + 0.909632i) q^{20} +(-0.223940 + 1.55754i) q^{21} -2.16736 q^{22} +(-2.44401 + 4.12636i) q^{23} -1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(-0.0880575 - 0.192819i) q^{26} +(0.959493 + 0.281733i) q^{27} +(1.03046 + 1.18921i) q^{28} +(-5.97820 + 1.75536i) q^{29} +(-0.841254 - 0.540641i) q^{30} +(-1.76017 + 3.85423i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(1.82330 - 1.17177i) q^{33} +(-0.424989 - 2.95586i) q^{34} +(0.223940 + 1.55754i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-6.99603 + 8.07385i) q^{37} +(-0.303093 + 0.663682i) q^{38} +(0.178324 + 0.114602i) q^{39} +(-0.959493 + 0.281733i) q^{40} +(6.89281 + 7.95473i) q^{41} +(-1.50981 - 0.443321i) q^{42} +(-3.95589 - 8.66219i) q^{43} +(0.308448 - 2.14530i) q^{44} +1.00000 q^{45} +(-3.73654 - 3.00637i) q^{46} -5.12157 q^{47} +(0.142315 - 0.989821i) q^{48} +(-1.87931 - 4.11511i) q^{49} +(-0.959493 - 0.281733i) q^{50} +(1.95558 + 2.25686i) q^{51} +(0.203388 - 0.0597202i) q^{52} +(6.72208 + 4.32002i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(1.41932 - 1.63798i) q^{55} +(-1.32376 + 0.850727i) q^{56} +(-0.103835 - 0.722189i) q^{57} +(-0.886704 - 6.16716i) q^{58} +(-6.90331 + 4.43649i) q^{59} +(0.654861 - 0.755750i) q^{60} +(-2.36875 + 5.18683i) q^{61} +(-3.56450 - 2.29077i) q^{62} +(1.50981 - 0.443321i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(0.203388 + 0.0597202i) q^{65} +(0.900355 + 1.97150i) q^{66} +(2.17625 - 15.1361i) q^{67} +2.98626 q^{68} +(4.76874 + 0.508997i) q^{69} -1.57355 q^{70} +(0.286605 - 1.99338i) q^{71} +(0.415415 + 0.909632i) q^{72} +(-1.77683 - 0.521724i) q^{73} +(-6.99603 - 8.07385i) q^{74} +(0.959493 - 0.281733i) q^{75} +(-0.613792 - 0.394460i) q^{76} +(1.41676 - 3.10227i) q^{77} +(-0.138814 + 0.160200i) q^{78} +(2.50585 - 1.61041i) q^{79} +(-0.142315 - 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-8.85471 + 5.69058i) q^{82} +(-3.99455 + 4.60995i) q^{83} +(0.653678 - 1.43135i) q^{84} +(2.51220 + 1.61449i) q^{85} +(9.13700 - 2.68287i) q^{86} +(4.08016 + 4.70876i) q^{87} +(2.07957 + 0.610617i) q^{88} +(5.73900 + 12.5667i) q^{89} +(-0.142315 + 0.989821i) q^{90} +0.333553 q^{91} +(3.50754 - 3.27065i) q^{92} +4.23713 q^{93} +(0.728876 - 5.06944i) q^{94} +(-0.303093 - 0.663682i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-5.45096 - 6.29074i) q^{97} +(4.34068 - 1.27454i) q^{98} +(-1.82330 - 1.17177i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * 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 $

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	−0.654861	−	0.755750i	−0.292863	−	0.337981i
$5$	−0.654861	−	0.755750i	−0.292863	−	0.337981i
$6$	0.959493	−	0.281733i	0.391711	−	0.115017i
$7$	−1.32376	−	0.850727i	−0.500333	−	0.321545i	0.266016	−	0.963969i	$-0.414293\pi$
$7$	−1.32376	−	0.850727i	−0.500333	−	0.321545i	−0.766350	+	0.642424i	$0.777929\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	0.841254	−	0.540641i	0.266028	−	0.170966i
$11$	0.308448	+	2.14530i	0.0930006	+	0.646833i	0.981994	+	0.188913i	$0.0604964\pi$
$11$	0.308448	+	2.14530i	0.0930006	+	0.646833i	−0.888993	+	0.457920i	$0.848595\pi$
$12$	0.142315	+	0.989821i	0.0410828	+	0.285737i
$13$	−0.178324	+	0.114602i	−0.0494583	+	0.0317849i	−0.565136	−	0.824998i	$-0.691176\pi$
$13$	−0.178324	+	0.114602i	−0.0494583	+	0.0317849i	0.515678	+	0.856782i	$0.327540\pi$
$14$	1.03046	−	1.18921i	0.275402	−	0.317830i
$15$	−0.415415	+	0.909632i	−0.107260	+	0.234866i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−2.86530	+	0.841327i	−0.694936	+	0.204052i	−0.610078	−	0.792341i	$-0.708862\pi$
$17$	−2.86530	+	0.841327i	−0.694936	+	0.204052i	−0.0848583	+	0.996393i	$0.527044\pi$
$18$	−0.654861	−	0.755750i	−0.154352	−	0.178132i
$19$	0.700061	+	0.205556i	0.160605	+	0.0471579i	0.361047	−	0.932548i	$-0.382420\pi$
$19$	0.700061	+	0.205556i	0.160605	+	0.0471579i	−0.200442	+	0.979706i	$0.564238\pi$
$20$	0.415415	+	0.909632i	0.0928896	+	0.203400i
$21$	−0.223940	+	1.55754i	−0.0488677	+	0.339882i
$22$	−2.16736			−0.462083
$23$	−2.44401	+	4.12636i	−0.509611	+	0.860405i
$23$	−2.44401	+	4.12636i	−0.509611	+	0.860405i
$24$	−1.00000			−0.204124
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$	−0.0880575	−	0.192819i	−0.0172695	−	0.0378149i
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$	1.03046	+	1.18921i	0.194738	+	0.224740i
$29$	−5.97820	+	1.75536i	−1.11012	+	0.325962i	−0.784867	−	0.619664i	$-0.787269\pi$
$29$	−5.97820	+	1.75536i	−1.11012	+	0.325962i	−0.325257	+	0.945626i	$0.605451\pi$
$30$	−0.841254	−	0.540641i	−0.153591	−	0.0987071i
$31$	−1.76017	+	3.85423i	−0.316135	+	0.692240i	−0.999276	−	0.0380469i	$-0.987886\pi$
$31$	−1.76017	+	3.85423i	−0.316135	+	0.692240i	0.683141	+	0.730287i	$0.260614\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	1.82330	−	1.17177i	0.317396	−	0.203978i
$34$	−0.424989	−	2.95586i	−0.0728850	−	0.506927i
$35$	0.223940	+	1.55754i	0.0378528	+	0.263272i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	−6.99603	+	8.07385i	−1.15014	+	1.32733i	−0.213540	+	0.976934i	$0.568500\pi$
$37$	−6.99603	+	8.07385i	−1.15014	+	1.32733i	−0.936600	+	0.350399i	$0.886046\pi$
$38$	−0.303093	+	0.663682i	−0.0491682	+	0.107663i
$39$	0.178324	+	0.114602i	0.0285548	+	0.0183510i
$40$	−0.959493	+	0.281733i	−0.151709	+	0.0445458i
$41$	6.89281	+	7.95473i	1.07648	+	1.24232i	0.968724	+	0.248142i	$0.0798200\pi$
$41$	6.89281	+	7.95473i	1.07648	+	1.24232i	0.107753	+	0.994178i	$0.465635\pi$
$42$	−1.50981	−	0.443321i	−0.232969	−	0.0684060i
$43$	−3.95589	−	8.66219i	−0.603268	−	1.32097i	−0.927085	−	0.374852i	$-0.877693\pi$
$43$	−3.95589	−	8.66219i	−0.603268	−	1.32097i	0.323817	−	0.946120i	$-0.395034\pi$
$44$	0.308448	−	2.14530i	0.0465003	−	0.323417i
$45$	1.00000			0.149071
$46$	−3.73654	−	3.00637i	−0.550923	−	0.443266i
$47$	−5.12157			−0.747058			−0.373529	−	0.927619i	$-0.621852\pi$
$47$	−5.12157			−0.747058			−0.373529	+	0.927619i	$0.621852\pi$
$48$	0.142315	−	0.989821i	0.0205414	−	0.142868i
$49$	−1.87931	−	4.11511i	−0.268473	−	0.587873i
$50$	−0.959493	−	0.281733i	−0.135693	−	0.0398430i
$51$	1.95558	+	2.25686i	0.273837	+	0.316024i
$52$	0.203388	−	0.0597202i	0.0282049	−	0.00828170i
$53$	6.72208	+	4.32002i	0.923348	+	0.593400i	0.913627	−	0.406553i	$-0.133269\pi$
$53$	6.72208	+	4.32002i	0.923348	+	0.593400i	0.00972097	+	0.999953i	$0.496906\pi$
$54$	−0.415415	+	0.909632i	−0.0565308	+	0.123785i
$55$	1.41932	−	1.63798i	0.191381	−	0.220866i
$56$	−1.32376	+	0.850727i	−0.176895	+	0.113683i
$57$	−0.103835	−	0.722189i	−0.0137533	−	0.0956563i
$58$	−0.886704	−	6.16716i	−0.116430	−	0.809788i
$59$	−6.90331	+	4.43649i	−0.898734	+	0.577582i	−0.906415	−	0.422389i	$-0.861192\pi$
$59$	−6.90331	+	4.43649i	−0.898734	+	0.577582i	0.00768030	+	0.999971i	$0.497555\pi$
$60$	0.654861	−	0.755750i	0.0845422	−	0.0975669i
$61$	−2.36875	+	5.18683i	−0.303287	+	0.664105i	−0.998503	−	0.0546951i	$-0.982581\pi$
$61$	−2.36875	+	5.18683i	−0.303287	+	0.664105i	0.695216	+	0.718801i	$0.255309\pi$
$62$	−3.56450	−	2.29077i	−0.452692	−	0.290928i
$63$	1.50981	−	0.443321i	0.190219	−	0.0558532i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	0.203388	+	0.0597202i	0.0252272	+	0.00740737i
$66$	0.900355	+	1.97150i	0.110826	+	0.242675i
$67$	2.17625	−	15.1361i	0.265871	−	1.84917i	−0.220458	−	0.975396i	$-0.570755\pi$
$67$	2.17625	−	15.1361i	0.265871	−	1.84917i	0.486329	−	0.873776i	$-0.338336\pi$
$68$	2.98626			0.362137
$69$	4.76874	+	0.508997i	0.574089	+	0.0612760i
$70$	−1.57355			−0.188076
$71$	0.286605	−	1.99338i	0.0340138	−	0.236571i	−0.965721	−	0.259580i	$-0.916416\pi$
$71$	0.286605	−	1.99338i	0.0340138	−	0.236571i	0.999735	+	0.0230096i	$0.00732481\pi$
$72$	0.415415	+	0.909632i	0.0489571	+	0.107201i
$73$	−1.77683	−	0.521724i	−0.207962	−	0.0610632i	0.176092	−	0.984374i	$-0.443654\pi$
$73$	−1.77683	−	0.521724i	−0.207962	−	0.0610632i	−0.384054	+	0.923310i	$0.625472\pi$
$74$	−6.99603	−	8.07385i	−0.813272	−	0.938566i
$75$	0.959493	−	0.281733i	0.110793	−	0.0325317i
$76$	−0.613792	−	0.394460i	−0.0704067	−	0.0452477i
$77$	1.41676	−	3.10227i	0.161454	−	0.353536i
$78$	−0.138814	+	0.160200i	−0.0157176	+	0.0181390i
$79$	2.50585	−	1.61041i	0.281930	−	0.181186i	−0.392032	−	0.919952i	$-0.628228\pi$
$79$	2.50585	−	1.61041i	0.281930	−	0.181186i	0.673962	+	0.738766i	$0.264591\pi$
$80$	−0.142315	−	0.989821i	−0.0159113	−	0.110665i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	−8.85471	+	5.69058i	−0.977839	+	0.628419i
$83$	−3.99455	+	4.60995i	−0.438459	+	0.506008i	−0.931371	−	0.364070i	$-0.881387\pi$
$83$	−3.99455	+	4.60995i	−0.438459	+	0.506008i	0.492913	+	0.870079i	$0.335932\pi$
$84$	0.653678	−	1.43135i	0.0713221	−	0.156174i
$85$	2.51220	+	1.61449i	0.272487	+	0.175116i
$86$	9.13700	−	2.68287i	0.985269	−	0.289301i
$87$	4.08016	+	4.70876i	0.437439	+	0.504832i
$88$	2.07957	+	0.610617i	0.221683	+	0.0650920i
$89$	5.73900	+	12.5667i	0.608333	+	1.33206i	0.923709	+	0.383096i	$0.125142\pi$
$89$	5.73900	+	12.5667i	0.608333	+	1.33206i	−0.315376	+	0.948967i	$0.602131\pi$
$90$	−0.142315	+	0.989821i	−0.0150013	+	0.104336i
$91$	0.333553			0.0349659
$92$	3.50754	−	3.27065i	0.365686	−	0.340989i
$93$	4.23713			0.439370
$94$	0.728876	−	5.06944i	0.0751778	−	0.522873i
$95$	−0.303093	−	0.663682i	−0.0310967	−	0.0680923i
$96$	0.959493	+	0.281733i	0.0979278	+	0.0287542i
$97$	−5.45096	−	6.29074i	−0.553461	−	0.638728i	0.408225	−	0.912881i	$-0.366148\pi$
$97$	−5.45096	−	6.29074i	−0.553461	−	0.638728i	−0.961686	+	0.274153i	$0.911602\pi$
$98$	4.34068	−	1.27454i	0.438475	−	0.128748i
$99$	−1.82330	−	1.17177i	−0.183249	−	0.117767i
$100$	0.415415	−	0.909632i	0.0415415	−	0.0909632i
$101$	−2.14739	+	2.47822i	−0.213673	+	0.246592i	−0.852461	−	0.522791i	$-0.824891\pi$
$101$	−2.14739	+	2.47822i	−0.213673	+	0.246592i	0.638788	+	0.769383i	$0.279436\pi$
$102$	−2.51220	+	1.61449i	−0.248745	+	0.159859i
$103$	−1.82014	−	12.6594i	−0.179344	−	1.24736i	−0.858286	−	0.513171i	$-0.828471\pi$
$103$	−1.82014	−	12.6594i	−0.179344	−	1.24736i	0.678942	−	0.734191i	$-0.262439\pi$
$104$	0.0301671	+	0.209817i	0.00295813	+	0.0205743i
$105$	1.32376	−	0.850727i	0.129185	−	0.0830225i
$106$	−5.23270	+	6.03885i	−0.508244	+	0.586545i
$107$	−0.258616	+	0.566291i	−0.0250014	+	0.0547454i	−0.921721	−	0.387854i	$-0.873216\pi$
$107$	−0.258616	+	0.566291i	−0.0250014	+	0.0547454i	0.896719	+	0.442600i	$0.145944\pi$
$108$	−0.841254	−	0.540641i	−0.0809497	−	0.0520232i
$109$	5.63387	−	1.65425i	0.539627	−	0.158449i	−0.000550814	−	1.00000i	$-0.500175\pi$
$109$	5.63387	−	1.65425i	0.539627	−	0.158449i	0.540177	+	0.841551i	$0.318357\pi$
$110$	1.41932	+	1.63798i	0.135327	+	0.156176i
$111$	10.2505	+	3.00982i	0.972934	+	0.285679i
$112$	−0.653678	−	1.43135i	−0.0617667	−	0.135250i
$113$	1.01353	−	7.04928i	0.0953451	−	0.663140i	−0.884962	−	0.465663i	$-0.845816\pi$
$113$	1.01353	−	7.04928i	0.0953451	−	0.663140i	0.980307	−	0.197477i	$-0.0632749\pi$
$114$	0.729615			0.0683347
$115$	4.71898	−	0.855132i	0.440047	−	0.0797414i
$116$	6.23058			0.578495
$117$	0.0301671	−	0.209817i	0.00278895	−	0.0193976i
$118$	−3.40889	−	7.46442i	−0.313814	−	0.687156i
$119$	4.50870	+	1.32387i	0.413312	+	0.121359i
$120$	0.654861	+	0.755750i	0.0597803	+	0.0689902i
$121$	6.04724	−	1.77563i	0.549749	−	0.161421i
$122$	−4.79693	−	3.08280i	−0.434293	−	0.279103i
$123$	4.37250	−	9.57443i	0.394255	−	0.863298i
$124$	2.77473	−	3.20221i	0.249178	−	0.287567i
$125$	0.841254	−	0.540641i	0.0752440	−	0.0483564i
$126$	0.223940	+	1.55754i	0.0199502	+	0.138756i
$127$	−0.0743873	−	0.517375i	−0.00660080	−	0.0459096i	0.986255	−	0.165231i	$-0.0528371\pi$
$127$	−0.0743873	−	0.517375i	−0.00660080	−	0.0459096i	−0.992856	+	0.119322i	$0.961928\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	−6.23607	+	7.19681i	−0.549055	+	0.633644i
$130$	−0.0880575	+	0.192819i	−0.00772315	+	0.0169113i
$131$	1.35345	+	0.869809i	0.118251	+	0.0759956i	0.598430	−	0.801175i	$-0.295792\pi$
$131$	1.35345	+	0.869809i	0.118251	+	0.0759956i	−0.480178	+	0.877171i	$0.659428\pi$
$132$	−2.07957	+	0.610617i	−0.181003	+	0.0531474i
$133$	−0.751838	−	0.867668i	−0.0651927	−	0.0752363i
$134$	14.6723	+	4.30819i	1.26750	+	0.372171i
$135$	−0.415415	−	0.909632i	−0.0357532	−	0.0782887i
$136$	−0.424989	+	2.95586i	−0.0364425	+	0.253463i
$137$	−7.50760			−0.641418			−0.320709	−	0.947178i	$-0.603921\pi$
$137$	−7.50760			−0.641418			−0.320709	+	0.947178i	$0.603921\pi$
$138$	−1.18248	+	4.64777i	−0.100659	+	0.395644i
$139$	−8.39251			−0.711843			−0.355922	−	0.934516i	$-0.615833\pi$
$139$	−8.39251			−0.711843			−0.355922	+	0.934516i	$0.615833\pi$
$140$	0.223940	−	1.55754i	0.0189264	−	0.131636i
$141$	2.12758	+	4.65874i	0.179174	+	0.392337i
$142$	1.93230	+	0.567376i	0.162155	+	0.0476131i
$143$	−0.300860	−	0.347211i	−0.0251592	−	0.0290353i
$144$	−0.959493	+	0.281733i	−0.0799577	+	0.0234777i
$145$	5.24150	+	3.36851i	0.435283	+	0.279739i
$146$	0.769283	−	1.68450i	0.0636663	−	0.139410i
$147$	−2.96254	+	3.41896i	−0.244346	+	0.281991i
$148$	8.98731	−	5.77580i	0.738753	−	0.474767i
$149$	−0.834859	−	5.80657i	−0.0683943	−	0.475693i	−0.995017	−	0.0997014i	$-0.968211\pi$
$149$	−0.834859	−	5.80657i	−0.0683943	−	0.475693i	0.926623	−	0.375992i	$-0.122698\pi$
$150$	0.142315	+	0.989821i	0.0116200	+	0.0808186i
$151$	8.78863	−	5.64811i	0.715209	−	0.459637i	−0.131758	−	0.991282i	$-0.542062\pi$
$151$	8.78863	−	5.64811i	0.715209	−	0.459637i	0.846967	+	0.531645i	$0.178426\pi$
$152$	0.477796	−	0.551407i	0.0387544	−	0.0447250i
$153$	1.24054	−	2.71640i	0.100292	−	0.219608i
$154$	2.86906	+	1.84384i	0.231196	+	0.148580i
$155$	4.06550	−	1.19374i	0.326549	−	0.0958833i
$156$	−0.138814	−	0.160200i	−0.0111140	−	0.0128262i
$157$	2.48623	+	0.730022i	0.198423	+	0.0582621i	0.379434	−	0.925219i	$-0.376119\pi$
$157$	2.48623	+	0.730022i	0.198423	+	0.0582621i	−0.181011	+	0.983481i	$0.557937\pi$
$158$	1.23740	+	2.70953i	0.0984424	+	0.215559i
$159$	1.13717	−	7.90922i	0.0901837	−	0.627242i
$160$	1.00000			0.0790569
$161$	6.74568	−	3.38311i	0.531634	−	0.266627i
$162$	1.00000			0.0785674
$163$	−0.379070	+	2.63649i	−0.0296911	+	0.206506i	−0.999267	−	0.0382854i	$-0.987810\pi$
$163$	−0.379070	+	2.63649i	−0.0296911	+	0.206506i	0.969576	+	0.244791i	$0.0787195\pi$
$164$	−4.37250	−	9.57443i	−0.341435	−	0.747638i
$165$	−2.07957	−	0.610617i	−0.161894	−	0.0475365i
$166$	−3.99455	−	4.60995i	−0.310037	−	0.357802i
$167$	5.13997	−	1.50923i	0.397743	−	0.116788i	−0.0767430	−	0.997051i	$-0.524452\pi$
$167$	5.13997	−	1.50923i	0.397743	−	0.116788i	0.474486	+	0.880263i	$0.342634\pi$
$168$	1.32376	+	0.850727i	0.102130	+	0.0656350i
$169$	−5.38173	+	11.7843i	−0.413979	+	0.906488i
$170$	−1.95558	+	2.25686i	−0.149986	+	0.173094i
$171$	−0.613792	+	0.394460i	−0.0469378	+	0.0301651i
$172$	1.35523	+	9.42582i	0.103335	+	0.718712i
$173$	3.23370	+	22.4909i	0.245854	+	1.70995i	0.621689	+	0.783264i	$0.286447\pi$
$173$	3.23370	+	22.4909i	0.245854	+	1.70995i	−0.375835	+	0.926687i	$0.622644\pi$
$174$	−5.24150	+	3.36851i	−0.397357	+	0.255366i
$175$	1.03046	−	1.18921i	0.0778953	−	0.0898960i
$176$	−0.900355	+	1.97150i	−0.0678668	+	0.148608i
$177$	6.90331	+	4.43649i	0.518885	+	0.333467i
$178$	−13.2555	+	3.89216i	−0.993541	+	0.291730i
$179$	−5.61516	−	6.48024i	−0.419697	−	0.484356i	0.506048	−	0.862505i	$-0.331106\pi$
$179$	−5.61516	−	6.48024i	−0.419697	−	0.484356i	−0.925744	+	0.378150i	$0.876560\pi$
$180$	−0.959493	−	0.281733i	−0.0715164	−	0.0209991i
$181$	2.45971	+	5.38602i	0.182829	+	0.400340i	0.978749	−	0.205062i	$-0.0657396\pi$
$181$	2.45971	+	5.38602i	0.182829	+	0.400340i	−0.795920	+	0.605402i	$0.793012\pi$
$182$	−0.0474696	+	0.330158i	−0.00351868	+	0.0244730i
$183$	5.70212			0.421513
$184$	2.73819	+	3.93730i	0.201862	+	0.290261i
$185$	10.6832			0.785447
$186$	−0.603007	+	4.19400i	−0.0442146	+	0.307519i
$187$	−2.68870	−	5.88742i	−0.196617	−	0.430531i
$188$	4.91411	+	1.44291i	0.358398	+	0.105235i
$189$	−1.03046	−	1.18921i	−0.0749548	−	0.0865025i
$190$	0.700061	−	0.205556i	0.0507878	−	0.0149126i
$191$	1.80760	+	1.16167i	0.130793	+	0.0840557i	0.604401	−	0.796680i	$-0.293412\pi$
$191$	1.80760	+	1.16167i	0.130793	+	0.0840557i	−0.473608	+	0.880736i	$0.657049\pi$
$192$	−0.415415	+	0.909632i	−0.0299800	+	0.0656470i
$193$	−9.51150	+	10.9769i	−0.684653	+	0.790131i	−0.986594	−	0.163195i	$-0.947820\pi$
$193$	−9.51150	+	10.9769i	−0.684653	+	0.790131i	0.301941	+	0.953327i	$0.402365\pi$
$194$	7.00246	−	4.50021i	0.502748	−	0.323096i
$195$	−0.0301671	−	0.209817i	−0.00216031	−	0.0150253i
$196$	0.643822	+	4.47788i	0.0459873	+	0.319849i
$197$	14.3473	−	9.22045i	1.02220	−	0.656930i	0.0816797	−	0.996659i	$-0.473972\pi$
$197$	14.3473	−	9.22045i	1.02220	−	0.656930i	0.940524	+	0.339729i	$0.110335\pi$
$198$	1.41932	−	1.63798i	0.100867	−	0.116406i
$199$	−2.65786	+	5.81990i	−0.188411	+	0.412562i	−0.980139	−	0.198311i	$-0.936454\pi$
$199$	−2.65786	+	5.81990i	−0.188411	+	0.412562i	0.791728	+	0.610873i	$0.209182\pi$
$200$	0.841254	+	0.540641i	0.0594856	+	0.0382291i
$201$	−14.6723	+	4.30819i	−1.03491	+	0.303876i
$202$	−2.14739	−	2.47822i	−0.151090	−	0.174367i
$203$	9.40702	+	2.76215i	0.660243	+	0.193865i
$204$	−1.24054	−	2.71640i	−0.0868550	−	0.190186i
$205$	1.49795	−	10.4185i	0.104621	−	0.727658i
$206$	12.7895			0.891089
$207$	−1.51801	−	4.54925i	−0.105509	−	0.316195i
$208$	−0.211975			−0.0146978
$209$	−0.225048	+	1.56525i	−0.0155669	+	0.108270i
$210$	0.653678	+	1.43135i	0.0451080	+	0.0987729i
$211$	13.0873	+	3.84277i	0.900965	+	0.264547i	0.699233	−	0.714893i	$-0.253525\pi$
$211$	13.0873	+	3.84277i	0.900965	+	0.264547i	0.201732	+	0.979441i	$0.435343\pi$
$212$	−5.23270	−	6.03885i	−0.359383	−	0.414750i
$213$	−1.93230	+	0.567376i	−0.132399	+	0.0388759i
$214$	−0.523722	−	0.336576i	−0.0358009	−	0.0230078i
$215$	−3.95589	+	8.66219i	−0.269789	+	0.590757i
$216$	0.654861	−	0.755750i	0.0445576	−	0.0514222i
$217$	5.60893	−	3.60464i	0.380759	−	0.244699i
$218$	0.835632	+	5.81195i	0.0565961	+	0.393635i
$219$	0.263545	+	1.83299i	0.0178087	+	0.123862i
$220$	−1.82330	+	1.17177i	−0.122927	+	0.0790004i
$221$	0.414534	−	0.478398i	0.0278846	−	0.0321805i
$222$	−4.43798	+	9.71782i	−0.297858	+	0.652217i
$223$	−12.6168	−	8.10833i	−0.844884	−	0.542974i	0.0450914	−	0.998983i	$-0.485642\pi$
$223$	−12.6168	−	8.10833i	−0.844884	−	0.542974i	−0.889975	+	0.456009i	$0.849278\pi$
$224$	1.50981	−	0.443321i	0.100879	−	0.0296206i
$225$	−0.654861	−	0.755750i	−0.0436574	−	0.0503833i
$226$	6.83328	+	2.00643i	0.454543	+	0.133466i
$227$	−10.9363	−	23.9472i	−0.725870	−	1.58943i	−0.805490	−	0.592609i	$-0.798098\pi$
$227$	−10.9363	−	23.9472i	−0.725870	−	1.58943i	0.0796200	−	0.996825i	$-0.474629\pi$
$228$	−0.103835	+	0.722189i	−0.00687665	+	0.0478281i
$229$	8.48699			0.560836			0.280418	−	0.959878i	$-0.409527\pi$
$229$	8.48699			0.560836			0.280418	+	0.959878i	$0.409527\pi$
$230$	0.174847	+	4.79264i	0.0115291	+	0.316018i
$231$	−3.41046			−0.224392
$232$	−0.886704	+	6.16716i	−0.0582150	+	0.404894i
$233$	−1.55914	−	3.41405i	−0.102143	−	0.223662i	0.851660	−	0.524095i	$-0.175596\pi$
$233$	−1.55914	−	3.41405i	−0.102143	−	0.223662i	−0.953803	+	0.300433i	$0.902869\pi$
$234$	0.203388	+	0.0597202i	0.0132959	+	0.00390403i
$235$	3.35392	+	3.87063i	0.218785	+	0.252492i
$236$	7.87358	−	2.31189i	0.512526	−	0.150491i
$237$	−2.50585	−	1.61041i	−0.162773	−	0.104608i
$238$	−1.95205	+	4.27440i	−0.126533	+	0.277068i
$239$	−12.5834	+	14.5221i	−0.813955	+	0.939354i	−0.999059	−	0.0433647i	$-0.986192\pi$
$239$	−12.5834	+	14.5221i	−0.813955	+	0.939354i	0.185104	+	0.982719i	$0.440738\pi$
$240$	−0.841254	+	0.540641i	−0.0543027	+	0.0348982i
$241$	1.01041	+	7.02757i	0.0650864	+	0.452686i	0.996138	+	0.0877988i	$0.0279833\pi$
$241$	1.01041	+	7.02757i	0.0650864	+	0.452686i	−0.931052	+	0.364887i	$0.881108\pi$
$242$	0.896944	+	6.23838i	0.0576578	+	0.401019i
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$	3.73409	−	4.30937i	0.239051	−	0.275879i
$245$	−1.87931	+	4.11511i	−0.120065	+	0.262905i
$246$	8.85471	+	5.69058i	0.564556	+	0.362818i
$247$	−0.148395	+	0.0435728i	−0.00944216	+	0.00277247i
$248$	2.77473	+	3.20221i	0.176196	+	0.203341i
$249$	5.85276	+	1.71852i	0.370903	+	0.108907i
$250$	0.415415	+	0.909632i	0.0262732	+	0.0575302i
$251$	3.76561	−	26.1904i	0.237683	−	1.65312i	−0.425716	−	0.904857i	$-0.639978\pi$
$251$	3.76561	−	26.1904i	0.237683	−	1.65312i	0.663399	−	0.748266i	$-0.269113\pi$
$252$	−1.57355			−0.0991246
$253$	−9.60614	−	3.97037i	−0.603933	−	0.249615i
$254$	0.522695			0.0327968
$255$	0.424989	−	2.95586i	0.0266139	−	0.185103i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	6.12308	+	1.79790i	0.381947	+	0.112150i	0.467069	−	0.884221i	$-0.345310\pi$
$257$	6.12308	+	1.79790i	0.381947	+	0.112150i	−0.0851221	+	0.996371i	$0.527128\pi$
$258$	−6.23607	−	7.19681i	−0.388241	−	0.448054i
$259$	16.1297	−	4.73611i	1.00225	−	0.294287i
$260$	−0.178324	−	0.114602i	−0.0110592	−	0.00710732i
$261$	2.58828	−	5.66754i	0.160210	−	0.350812i
$262$	−1.05357	+	1.21589i	−0.0650899	+	0.0751177i
$263$	−12.4799	+	8.02037i	−0.769546	+	0.494557i	−0.865549	−	0.500824i	$-0.833030\pi$
$263$	−12.4799	+	8.02037i	−0.769546	+	0.494557i	0.0960034	+	0.995381i	$0.469394\pi$
$264$	−0.308448	−	2.14530i	−0.0189837	−	0.132034i
$265$	−1.13717	−	7.90922i	−0.0698560	−	0.485859i
$266$	0.965834	−	0.620704i	0.0592191	−	0.0380578i
$267$	9.04696	−	10.4408i	0.553665	−	0.638964i
$268$	−6.35243	+	13.9099i	−0.388037	+	0.849682i
$269$	−16.3597	−	10.5138i	−0.997470	−	0.641035i	−0.0633491	−	0.997991i	$-0.520178\pi$
$269$	−16.3597	−	10.5138i	−0.997470	−	0.641035i	−0.934121	+	0.356956i	$0.883815\pi$
$270$	0.959493	−	0.281733i	0.0583929	−	0.0171457i
$271$	16.9935	+	19.6116i	1.03228	+	1.19132i	0.981274	+	0.192619i	$0.0616983\pi$
$271$	16.9935	+	19.6116i	1.03228	+	1.19132i	0.0510090	+	0.998698i	$0.483756\pi$
$272$	−2.86530	−	0.841327i	−0.173734	−	0.0510129i
$273$	−0.138563	−	0.303411i	−0.00838622	−	0.0183633i
$274$	1.06844	−	7.43118i	0.0645470	−	0.448934i
$275$	−2.16736			−0.130697
$276$	−4.43218	−	1.83189i	−0.266786	−	0.110267i
$277$	−15.3274			−0.920933			−0.460467	−	0.887677i	$-0.652318\pi$
$277$	−15.3274			−0.920933			−0.460467	+	0.887677i	$0.652318\pi$
$278$	1.19438	−	8.30708i	0.0716340	−	0.498226i
$279$	−1.76017	−	3.85423i	−0.105378	−	0.230747i
$280$	1.50981	+	0.443321i	0.0902286	+	0.0264935i
$281$	−13.5955	−	15.6901i	−0.811042	−	0.935992i	0.187890	−	0.982190i	$-0.439835\pi$
$281$	−13.5955	−	15.6901i	−0.811042	−	0.935992i	−0.998932	+	0.0461978i	$0.985290\pi$
$282$	−4.91411	+	1.44291i	−0.292631	+	0.0859242i
$283$	−18.6624	−	11.9936i	−1.10936	−	0.712945i	−0.148209	−	0.988956i	$-0.547351\pi$
$283$	−18.6624	−	11.9936i	−1.10936	−	0.712945i	−0.961154	+	0.276011i	$0.910987\pi$
$284$	−0.836596	+	1.83189i	−0.0496428	+	0.108703i
$285$	−0.477796	+	0.551407i	−0.0283022	+	0.0326625i
$286$	0.386494	−	0.248385i	0.0228539	−	0.0146873i
$287$	−2.35711	−	16.3940i	−0.139136	−	0.967709i
$288$	−0.142315	−	0.989821i	−0.00838598	−	0.0583258i
$289$	−6.79922	+	4.36959i	−0.399954	+	0.257035i
$290$	−4.08016	+	4.70876i	−0.239595	+	0.276508i
$291$	−3.45785	+	7.57164i	−0.202703	+	0.443857i
$292$	1.55787	+	1.00118i	0.0911674	+	0.0585897i
$293$	−13.2236	+	3.88279i	−0.772529	+	0.226835i	−0.644159	−	0.764891i	$-0.722793\pi$
$293$	−13.2236	+	3.88279i	−0.772529	+	0.226835i	−0.128370	+	0.991726i	$0.540974\pi$
$294$	−2.96254	−	3.41896i	−0.172779	−	0.199398i
$295$	7.87358	+	2.31189i	0.458418	+	0.134604i
$296$	4.43798	+	9.71782i	0.257952	+	0.564837i
$297$	−0.308448	+	2.14530i	−0.0178980	+	0.124483i
$298$	5.86628			0.339825
$299$	−0.0370632	−	1.01592i	−0.00214342	−	0.0587521i
$300$	−1.00000			−0.0577350
$301$	−2.13252	+	14.8320i	−0.122917	+	0.854904i
$302$	4.33987	+	9.50299i	0.249731	+	0.546836i
$303$	3.14632	+	0.923844i	0.180752	+	0.0530734i
$304$	0.477796	+	0.551407i	0.0274035	+	0.0316253i
$305$	5.47114	−	1.60647i	0.313277	−	0.0919863i
$306$	2.51220	+	1.61449i	0.143613	+	0.0922945i
$307$	6.23946	−	13.6625i	0.356105	−	0.779761i	−0.643789	−	0.765203i	$-0.722639\pi$
$307$	6.23946	−	13.6625i	0.356105	−	0.779761i	0.999894	−	0.0145582i	$-0.00463420\pi$
$308$	−2.23338	+	2.57746i	−0.127259	+	0.146864i
$309$	−10.7592	+	6.91454i	−0.612072	+	0.393355i
$310$	0.603007	+	4.19400i	0.0342485	+	0.238203i
$311$	−0.400583	−	2.78612i	−0.0227150	−	0.157986i	0.975307	−	0.220854i	$-0.0708844\pi$
$311$	−0.400583	−	2.78612i	−0.0227150	−	0.157986i	−0.998022	+	0.0628678i	$0.979975\pi$
$312$	0.178324	−	0.114602i	0.0100956	−	0.00648807i
$313$	2.29458	−	2.64808i	0.129697	−	0.149678i	−0.687186	−	0.726481i	$-0.741154\pi$
$313$	2.29458	−	2.64808i	0.129697	−	0.149678i	0.816883	+	0.576803i	$0.195700\pi$
$314$	−1.07642	+	2.35703i	−0.0607458	+	0.133015i
$315$	−1.32376	−	0.850727i	−0.0745853	−	0.0479331i
$316$	−2.85805	+	0.839200i	−0.160778	+	0.0472087i
$317$	3.09921	+	3.57668i	0.174069	+	0.200887i	0.836080	−	0.548608i	$-0.184842\pi$
$317$	3.09921	+	3.57668i	0.174069	+	0.200887i	−0.662011	+	0.749495i	$0.730297\pi$
$318$	7.66687	+	2.25120i	0.429937	+	0.126241i
$319$	−5.60974	−	12.2836i	−0.314085	−	0.687750i
$320$	−0.142315	+	0.989821i	−0.00795564	+	0.0553327i
$321$	0.622550			0.0347473
$322$	2.38867	+	7.15848i	0.133115	+	0.398927i
$323$	−2.17882			−0.121233
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	−0.0880575	−	0.192819i	−0.00488455	−	0.0106957i
$326$	−2.55571	−	0.750424i	−0.141548	−	0.0415621i
$327$	−3.84515	−	4.43754i	−0.212637	−	0.245397i
$328$	10.0993	−	2.96541i	0.557638	−	0.163737i
$329$	6.77972	+	4.35706i	0.373778	+	0.240213i
$330$	0.900355	−	1.97150i	0.0495629	−	0.108528i
$331$	12.6958	−	14.6517i	0.697825	−	0.805332i	−0.290632	−	0.956835i	$-0.593866\pi$
$331$	12.6958	−	14.6517i	0.697825	−	0.805332i	0.988457	+	0.151502i	$0.0484111\pi$
$332$	5.13152	−	3.29782i	0.281629	−	0.180992i
$333$	−1.52038	−	10.5745i	−0.0833165	−	0.579479i
$334$	0.762376	+	5.30244i	0.0417154	+	0.290137i
$335$	−12.8643	+	8.26736i	−0.702850	+	0.451694i
$336$	−1.03046	+	1.18921i	−0.0562161	+	0.0648769i
$337$	−7.10835	+	15.5651i	−0.387216	+	0.847885i	0.611192	+	0.791482i	$0.290690\pi$
$337$	−7.10835	+	15.5651i	−0.387216	+	0.847885i	−0.998408	+	0.0564028i	$0.982037\pi$
$338$	−10.8985	−	7.00404i	−0.592800	−	0.380969i
$339$	−6.83328	+	2.00643i	−0.371133	+	0.108974i
$340$	−1.95558	−	2.25686i	−0.106056	−	0.122396i
$341$	−8.81141	−	2.58726i	−0.477165	−	0.140108i
$342$	−0.303093	−	0.663682i	−0.0163894	−	0.0358878i
$343$	−2.58067	+	17.9489i	−0.139343	+	0.969152i
$344$	−9.52274			−0.513432
$345$	−2.73819	−	3.93730i	−0.147419	−	0.211977i
$346$	−22.7222			−1.22155
$347$	4.12557	−	28.6940i	0.221472	−	1.54037i	−0.511002	−	0.859579i	$-0.670726\pi$
$347$	4.12557	−	28.6940i	0.221472	−	1.54037i	0.732475	−	0.680794i	$-0.238365\pi$
$348$	−2.58828	−	5.66754i	−0.138746	−	0.303812i
$349$	−18.6674	−	5.48124i	−0.999242	−	0.293404i	−0.259097	−	0.965851i	$-0.583425\pi$
$349$	−18.6674	−	5.48124i	−0.999242	−	0.293404i	−0.740145	+	0.672447i	$0.765243\pi$
$350$	1.03046	+	1.18921i	0.0550803	+	0.0635661i
$351$	−0.203388	+	0.0597202i	−0.0108561	+	0.00318763i
$352$	−1.82330	−	1.17177i	−0.0971823	−	0.0624553i
$353$	−10.5894	+	23.1876i	−0.563619	+	1.23415i	0.386506	+	0.922287i	$0.373682\pi$
$353$	−10.5894	+	23.1876i	−0.563619	+	1.23415i	−0.950126	+	0.311867i	$0.899046\pi$
$354$	−5.37377	+	6.20167i	−0.285613	+	0.329615i
$355$	−1.69418	+	1.08879i	−0.0899179	+	0.0577868i
$356$	−1.96609	−	13.6745i	−0.104203	−	0.724746i
$357$	−0.668743	−	4.65121i	−0.0353936	−	0.246168i
$358$	7.21340	−	4.63577i	0.381240	−	0.245008i
$359$	−13.6098	+	15.7066i	−0.718300	+	0.828963i	−0.991102	−	0.133108i	$-0.957504\pi$
$359$	−13.6098	+	15.7066i	−0.718300	+	0.828963i	0.272801	+	0.962070i	$0.412050\pi$
$360$	0.415415	−	0.909632i	0.0218943	−	0.0479418i
$361$	−15.5360	−	9.98437i	−0.817683	−	0.525493i
$362$	−5.68125	+	1.66817i	−0.298600	+	0.0876769i
$363$	−4.12728	−	4.76314i	−0.216626	−	0.250000i
$364$	−0.320042	−	0.0939729i	−0.0167748	−	0.00492552i
$365$	0.769283	+	1.68450i	0.0402661	+	0.0881705i
$366$	−0.811496	+	5.64408i	−0.0424176	+	0.295021i
$367$	−9.83949			−0.513617			−0.256809	−	0.966462i	$-0.582671\pi$
$367$	−9.83949			−0.513617			−0.256809	+	0.966462i	$0.582671\pi$
$368$	−4.28691	+	2.14998i	−0.223470	+	0.112076i
$369$	−10.5256			−0.547942
$370$	−1.52038	+	10.5745i	−0.0790410	+	0.549742i
$371$	−5.22324	−	11.4373i	−0.271177	−	0.593795i
$372$	−4.06550	−	1.19374i	−0.210786	−	0.0618924i
$373$	7.12236	+	8.21964i	0.368782	+	0.425597i	0.909563	−	0.415567i	$-0.136417\pi$
$373$	7.12236	+	8.21964i	0.368782	+	0.425597i	−0.540781	+	0.841163i	$0.681871\pi$
$374$	6.21014	−	1.82346i	0.321119	−	0.0942889i
$375$	−0.841254	−	0.540641i	−0.0434421	−	0.0279186i
$376$	−2.12758	+	4.65874i	−0.109721	+	0.240256i
$377$	0.864891	−	0.998138i	0.0445442	−	0.0514067i
$378$	1.32376	−	0.850727i	0.0680867	−	0.0437567i
$379$	−3.50519	−	24.3792i	−0.180050	−	1.25227i	−0.856641	−	0.515914i	$-0.827452\pi$
$379$	−3.50519	−	24.3792i	−0.180050	−	1.25227i	0.676591	−	0.736359i	$-0.263457\pi$
$380$	0.103835	+	0.722189i	0.00532663	+	0.0370475i
$381$	−0.439719	+	0.282590i	−0.0225275	+	0.0144775i
$382$	−1.40710	+	1.62388i	−0.0719934	+	0.0830848i
$383$	−11.5087	+	25.2006i	−0.588068	+	1.28769i	0.348535	+	0.937296i	$0.386679\pi$
$383$	−11.5087	+	25.2006i	−0.588068	+	1.28769i	−0.936603	+	0.350393i	$0.886048\pi$
$384$	−0.841254	−	0.540641i	−0.0429300	−	0.0275895i
$385$	−3.27231	+	0.960838i	−0.166773	+	0.0489689i
$386$	−9.51150	−	10.9769i	−0.484123	−	0.558707i
$387$	9.13700	+	2.68287i	0.464460	+	0.136378i
$388$	3.45785	+	7.57164i	0.175546	+	0.384392i
$389$	2.21897	−	15.4333i	0.112506	−	0.782499i	−0.852961	−	0.521975i	$-0.825195\pi$
$389$	2.21897	−	15.4333i	0.112506	−	0.782499i	0.965467	−	0.260524i	$-0.0838954\pi$
$390$	0.211975			0.0107338
$391$	3.53119	−	13.8794i	0.178580	−	0.701914i
$392$	−4.52393			−0.228493
$393$	0.228963	−	1.59247i	0.0115497	−	0.0803297i
$394$	7.08477	+	15.5135i	0.356925	+	0.781558i
$395$	−2.85805	−	0.839200i	−0.143804	−	0.0422247i
$396$	1.41932	+	1.63798i	0.0713236	+	0.0823118i
$397$	−0.00241068		0.000707840i	−0.000120989		3.55255e-5i	−0.281793	−	0.959475i	$-0.590929\pi$
$397$	−0.00241068		0.000707840i	−0.000120989		3.55255e-5i	0.281672	+	0.959511i	$0.409111\pi$
$398$	−5.38241	−	3.45907i	−0.269796	−	0.173387i
$399$	−0.476933	+	1.04434i	−0.0238765	+	0.0522823i
$400$	−0.654861	+	0.755750i	−0.0327430	+	0.0377875i
$401$	14.2313	−	9.14592i	0.710679	−	0.456725i	−0.134705	−	0.990886i	$-0.543009\pi$
$401$	14.2313	−	9.14592i	0.710679	−	0.456725i	0.845383	+	0.534160i	$0.179372\pi$
$402$	−2.17625	−	15.1361i	−0.108541	−	0.754921i
$403$	−0.127822	−	0.889022i	−0.00636727	−	0.0442854i
$404$	2.75860	−	1.77284i	0.137245	−	0.0882022i
$405$	−0.654861	+	0.755750i	−0.0325403	+	0.0375535i
$406$	−4.07279	+	8.91817i	−0.202129	+	0.442602i
$407$	−19.4788	−	12.5182i	−0.965527	−	0.620507i
$408$	2.86530	−	0.841327i	0.141853	−	0.0416519i
$409$	21.7941	+	25.1518i	1.07765	+	1.24367i	0.968332	+	0.249668i	$0.0803214\pi$
$409$	21.7941	+	25.1518i	1.07765	+	1.24367i	0.109319	+	0.994007i	$0.465133\pi$
$410$	10.0993	+	2.96541i	0.498767	+	0.146451i
$411$	3.11877	+	6.82915i	0.153838	+	0.336857i
$412$	−1.82014	+	12.6594i	−0.0896719	+	0.623681i
$413$	12.9125			0.635385
$414$	4.71898	−	0.855132i	0.231925	−	0.0420274i
$415$	6.09984			0.299430
$416$	0.0301671	−	0.209817i	0.00147907	−	0.0102871i
$417$	3.48637	+	7.63409i	0.170728	+	0.373843i
$418$	−1.51729	−	0.445515i	−0.0742129	−	0.0217909i
$419$	−14.4029	−	16.6218i	−0.703626	−	0.812028i	0.285612	−	0.958345i	$-0.407803\pi$
$419$	−14.4029	−	16.6218i	−0.703626	−	0.812028i	−0.989238	+	0.146318i	$0.953258\pi$
$420$	−1.50981	+	0.443321i	−0.0736714	+	0.0216319i
$421$	13.8880	+	8.92529i	0.676861	+	0.434992i	0.833393	−	0.552681i	$-0.186395\pi$
$421$	13.8880	+	8.92529i	0.676861	+	0.434992i	−0.156532	+	0.987673i	$0.550032\pi$
$422$	−5.66617	+	12.4072i	−0.275825	+	0.603972i
$423$	3.35392	−	3.87063i	0.163073	−	0.188196i
$424$	6.72208	−	4.32002i	0.326453	−	0.209799i
$425$	−0.424989	−	2.95586i	−0.0206150	−	0.143380i
$426$	−0.286605	−	1.99338i	−0.0138861	−	0.0965797i
$427$	7.54822	−	4.85095i	0.365284	−	0.234754i
$428$	0.407683	−	0.470492i	0.0197061	−	0.0227421i
$429$	−0.190853	+	0.417909i	−0.00921445	+	0.0201768i
$430$	−8.01104	−	5.14838i	−0.386327	−	0.248277i
$431$	3.12324	−	0.917067i	0.150441	−	0.0441736i	−0.205645	−	0.978627i	$-0.565929\pi$
$431$	3.12324	−	0.917067i	0.150441	−	0.0441736i	0.356086	+	0.934453i	$0.384111\pi$
$432$	0.654861	+	0.755750i	0.0315070	+	0.0363610i
$433$	33.5771	+	9.85913i	1.61361	+	0.473800i	0.959292	−	0.282417i	$-0.0911362\pi$
$433$	33.5771	+	9.85913i	1.61361	+	0.473800i	0.654321	+	0.756217i	$0.272954\pi$
$434$	2.76972	+	6.06484i	0.132951	+	0.291121i
$435$	0.886704	−	6.16716i	0.0425142	−	0.295693i
$436$	−5.87171			−0.281204
$437$	−2.55915	+	2.38632i	−0.122421	+	0.114153i
$438$	−1.85184			−0.0884844
$439$	−3.06140	+	21.2925i	−0.146112	+	1.01623i	0.776393	+	0.630250i	$0.217047\pi$
$439$	−3.06140	+	21.2925i	−0.146112	+	1.01623i	−0.922505	+	0.385985i	$0.873862\pi$
$440$	−0.900355	−	1.97150i	−0.0429228	−	0.0939877i
$441$	4.34068	+	1.27454i	0.206699	+	0.0606923i
$442$	0.414534	+	0.478398i	0.0197174	+	0.0227551i
$443$	−5.24561	+	1.54025i	−0.249227	+	0.0731795i	−0.403960	−	0.914777i	$-0.632366\pi$
$443$	−5.24561	+	1.54025i	−0.249227	+	0.0731795i	0.154733	+	0.987956i	$0.450548\pi$
$444$	−8.98731	−	5.77580i	−0.426519	−	0.274107i
$445$	5.73900	−	12.5667i	0.272055	−	0.595717i
$446$	9.82135	−	11.3344i	0.465055	−	0.536702i
$447$	−4.93503	+	3.17155i	−0.233419	+	0.150009i
$448$	0.223940	+	1.55754i	0.0105802	+	0.0735867i
$449$	2.97157	+	20.6677i	0.140237	+	0.975371i	0.931460	+	0.363843i	$0.118536\pi$
$449$	2.97157	+	20.6677i	0.140237	+	0.975371i	−0.791223	+	0.611528i	$0.790555\pi$
$450$	0.841254	−	0.540641i	0.0396571	−	0.0254861i
$451$	−14.9392	+	17.2408i	−0.703461	+	0.811837i
$452$	−2.95849	+	6.47819i	−0.139156	+	0.304708i
$453$	−8.78863	−	5.64811i	−0.412926	−	0.265371i
$454$	25.2599	−	7.41697i	1.18551	−	0.348096i
$455$	−0.218431	−	0.252083i	−0.0102402	−	0.0118178i
$456$	−0.700061	−	0.205556i	−0.0327834	−	0.00962606i
$457$	−7.70442	−	16.8703i	−0.360397	−	0.789160i	−0.999794	−	0.0202834i	$-0.993543\pi$
$457$	−7.70442	−	16.8703i	−0.360397	−	0.789160i	0.639397	−	0.768877i	$-0.279184\pi$
$458$	−1.20782	+	8.40061i	−0.0564379	+	0.392534i
$459$	−2.98626			−0.139387
$460$	−4.76874	−	0.508997i	−0.222344	−	0.0237321i
$461$	−37.2038			−1.73275			−0.866376	−	0.499393i	$-0.833557\pi$
$461$	−37.2038			−1.73275			−0.866376	+	0.499393i	$0.833557\pi$
$462$	0.485359	−	3.37575i	0.0225810	−	0.157054i
$463$	6.84882	+	14.9968i	0.318292	+	0.696962i	0.999379	−	0.0352407i	$-0.0112198\pi$
$463$	6.84882	+	14.9968i	0.318292	+	0.696962i	−0.681087	+	0.732202i	$0.738493\pi$
$464$	−5.97820	−	1.75536i	−0.277531	−	0.0814904i
$465$	−2.77473	−	3.20221i	−0.128675	−	0.148499i
$466$	3.60119	−	1.05740i	0.166822	−	0.0489833i
$467$	30.6845	+	19.7197i	1.41991	+	0.912520i	0.999988	+	0.00495867i	$0.00157840\pi$
$467$	30.6845	+	19.7197i	1.41991	+	0.912520i	0.419920	+	0.907561i	$0.362058\pi$
$468$	−0.0880575	+	0.192819i	−0.00407046	+	0.00891306i
$469$	−15.7575	+	18.1852i	−0.727615	+	0.839713i
$470$	−4.30854	+	2.76893i	−0.198738	+	0.127721i
$471$	−0.368765	−	2.56481i	−0.0169918	−	0.118180i
$472$	1.16783	+	8.12245i	0.0537539	+	0.373866i
$473$	17.3628	−	11.1584i	0.798344	−	0.513065i
$474$	1.95064	−	2.25116i	0.0895959	−	0.103399i
$475$	−0.303093	+	0.663682i	−0.0139069	+	0.0304518i
$476$	−3.95308	−	2.54049i	−0.181189	−	0.116443i
$477$	−7.66687	+	2.25120i	−0.351042	+	0.103075i
$478$	−12.5834	−	14.5221i	−0.575553	−	0.664224i
$479$	−15.6755	−	4.60275i	−0.716234	−	0.210305i	−0.0967432	−	0.995309i	$-0.530843\pi$
$479$	−15.6755	−	4.60275i	−0.716234	−	0.210305i	−0.619490	+	0.785004i	$0.712661\pi$
$480$	−0.415415	−	0.909632i	−0.0189610	−	0.0415188i
$481$	0.322283	−	2.24153i	0.0146948	−	0.102205i
$482$	−7.09984			−0.323389
$483$	−5.87964	−	4.73069i	−0.267533	−	0.215254i
$484$	−6.30254			−0.286479
$485$	−1.18461	+	8.23912i	−0.0537902	+	0.374119i
$486$	−0.415415	−	0.909632i	−0.0188436	−	0.0412617i
$487$	33.1026	+	9.71979i	1.50002	+	0.440446i	0.925723	−	0.378202i	$-0.123457\pi$
$487$	33.1026	+	9.71979i	1.50002	+	0.440446i	0.574297	+	0.818647i	$0.305276\pi$
$488$	3.73409	+	4.30937i	0.169034	+	0.195076i
$489$	2.55571	−	0.750424i	0.115573	−	0.0339353i
$490$	−3.80577	−	2.44582i	−0.171927	−	0.110491i
$491$	5.98515	−	13.1057i	0.270106	−	0.591450i	−0.725166	−	0.688574i	$-0.758237\pi$
$491$	5.98515	−	13.1057i	0.270106	−	0.591450i	0.995272	+	0.0971240i	$0.0309643\pi$
$492$	−6.89281	+	7.95473i	−0.310752	+	0.358627i
$493$	15.6525	−	10.0592i	0.704952	−	0.453045i
$494$	−0.0220104	−	0.153086i	−0.000990295	−	0.00688765i
$495$	0.308448	+	2.14530i	0.0138637	+	0.0964242i
$496$	−3.56450	+	2.29077i	−0.160051	+	0.102858i
$497$	−2.07522	+	2.39493i	−0.0930863	+	0.107427i
$498$	−2.53397	+	5.54861i	−0.113550	+	0.248639i
$499$	28.2070	+	18.1276i	1.26272	+	0.811501i	0.988654	−	0.150210i	$-0.0479950\pi$
$499$	28.2070	+	18.1276i	1.26272	+	0.811501i	0.274066	+	0.961711i	$0.411631\pi$
$500$	−0.959493	+	0.281733i	−0.0429098	+	0.0125995i
$501$	−3.50807	−	4.04853i	−0.156729	−	0.180875i
$502$	25.3879	+	7.45456i	1.13312	+	0.332713i
$503$	9.52974	+	20.8672i	0.424910	+	0.930423i	0.994125	+	0.108235i	$0.0345198\pi$
$503$	9.52974	+	20.8672i	0.424910	+	0.930423i	−0.569215	+	0.822188i	$0.692753\pi$
$504$	0.223940	−	1.55754i	0.00997508	−	0.0693782i
$505$	3.27915			0.145920
$506$	5.29705	−	8.94332i	0.235483	−	0.397579i
$507$	12.9551			0.575355
$508$	−0.0743873	+	0.517375i	−0.00330040	+	0.0229548i
$509$	1.25324	+	2.74421i	0.0555489	+	0.121635i	0.935371	−	0.353668i	$-0.115066\pi$
$509$	1.25324	+	2.74421i	0.0555489	+	0.121635i	−0.879822	+	0.475303i	$0.842338\pi$
$510$	2.86530	+	0.841327i	0.126877	+	0.0372546i
$511$	1.90825	+	2.20223i	0.0844159	+	0.0974211i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	0.613792	+	0.394460i	0.0270996	+	0.0174158i
$514$	−2.65100	+	5.80489i	−0.116931	+	0.256043i
$515$	−8.37536	+	9.66568i	−0.369062	+	0.425921i
$516$	8.01104	−	5.14838i	0.352666	−	0.226645i
$517$	−1.57974	−	10.9873i	−0.0694768	−	0.483222i
$518$	2.39240	+	16.6395i	0.105116	+	0.731099i
$519$	19.1151	−	12.2845i	0.839060	−	0.539231i
$520$	0.138814	−	0.160200i	0.00608739	−	0.00702522i
$521$	−7.56431	+	16.5635i	−0.331399	+	0.725662i	−0.999836	−	0.0181066i	$-0.994236\pi$
$521$	−7.56431	+	16.5635i	−0.331399	+	0.725662i	0.668437	+	0.743768i	$0.266963\pi$
$522$	5.24150	+	3.36851i	0.229414	+	0.147436i
$523$	−6.04591	+	1.77524i	−0.264369	+	0.0776257i	−0.411231	−	0.911531i	$-0.634901\pi$
$523$	−6.04591	+	1.77524i	−0.264369	+	0.0776257i	0.146862	+	0.989157i	$0.453083\pi$
$524$	−1.05357	−	1.21589i	−0.0460255	−	0.0531163i
$525$	−1.50981	−	0.443321i	−0.0658937	−	0.0193481i
$526$	−6.16265	−	13.4943i	−0.268704	−	0.588381i
$527$	1.80073	−	12.5244i	0.0784412	−	0.545571i
$528$	2.16736			0.0943224
$529$	−11.0537	−	20.1697i	−0.480594	−	0.876943i
$530$	7.99055			0.347087
$531$	1.16783	−	8.12245i	0.0506796	−	0.352485i
$532$	0.476933	+	1.04434i	0.0206777	+	0.0452778i
$533$	−2.14079	−	0.628591i	−0.0927277	−	0.0272273i
$534$	9.04696	+	10.4408i	0.391500	+	0.451816i
$535$	0.597332	−	0.175392i	0.0258249	−	0.00758288i
$536$	−12.8643	−	8.26736i	−0.555651	−	0.357095i
$537$	−3.56201	+	7.79971i	−0.153712	+	0.336582i
$538$	12.7350	−	14.6969i	0.549044	−	0.633630i
$539$	8.24849	−	5.30098i	0.355288	−	0.228329i
$540$	0.142315	+	0.989821i	0.00612426	+	0.0425951i
$541$	1.01424	+	7.05422i	0.0436057	+	0.303285i	0.999939	+	0.0110075i	$0.00350386\pi$
$541$	1.01424	+	7.05422i	0.0436057	+	0.303285i	−0.956334	+	0.292277i	$0.905587\pi$
$542$	−21.8304	+	14.0295i	−0.937695	+	0.602620i
$543$	3.87750	−	4.47487i	0.166399	−	0.192035i
$544$	1.24054	−	2.71640i	0.0531876	−	0.116465i
$545$	−4.93960	−	3.17449i	−0.211589	−	0.135980i
$546$	0.320042	−	0.0939729i	0.0136965	−	0.00402167i
$547$	18.1803	+	20.9812i	0.777335	+	0.897092i	0.996914	−	0.0785028i	$-0.0250139\pi$
$547$	18.1803	+	20.9812i	0.777335	+	0.897092i	−0.219579	+	0.975595i	$0.570468\pi$
$548$	7.20349	+	2.11514i	0.307718	+	0.0903541i
$549$	−2.36875	−	5.18683i	−0.101096	−	0.221368i
$550$	0.308448	−	2.14530i	0.0131523	−	0.0914760i
$551$	−4.54593			−0.193663
$552$	2.44401	−	4.12636i	0.104024	−	0.175629i
$553$	−4.68716			−0.199318
$554$	2.18131	−	15.1714i	0.0926751	−	0.644570i
$555$	−4.43798	−	9.71782i	−0.188382	−	0.412498i
$556$	8.05255	+	2.36444i	0.341504	+	0.100275i
$557$	9.12359	+	10.5292i	0.386579	+	0.446136i	0.915369	−	0.402617i	$-0.131899\pi$
$557$	9.12359	+	10.5292i	0.386579	+	0.446136i	−0.528789	+	0.848753i	$0.677354\pi$
$558$	4.06550	−	1.19374i	0.172106	−	0.0505349i
$559$	1.69814	+	1.09133i	0.0718236	+	0.0461582i
$560$	−0.653678	+	1.43135i	−0.0276229	+	0.0604858i
$561$	−4.23846	+	4.89145i	−0.178948	+	0.206517i
$562$	17.4652	−	11.2242i	0.736726	−	0.473465i
$563$	4.26600	+	29.6707i	0.179791	+	1.25047i	0.857246	+	0.514907i	$0.172174\pi$
$563$	4.26600	+	29.6707i	0.179791	+	1.25047i	−0.677456	+	0.735564i	$0.736917\pi$
$564$	−0.728876	−	5.06944i	−0.0306912	−	0.213462i
$565$	−5.99121	+	3.85032i	−0.252052	+	0.161984i
$566$	14.5274	−	16.7656i	0.610634	−	0.704709i
$567$	−0.653678	+	1.43135i	−0.0274519	+	0.0601112i
$568$	−1.69418	−	1.08879i	−0.0710864	−	0.0456844i
$569$	18.9571	−	5.56632i	0.794724	−	0.233352i	0.140925	−	0.990020i	$-0.454992\pi$
$569$	18.9571	−	5.56632i	0.794724	−	0.233352i	0.653799	+	0.756668i	$0.273174\pi$
$570$	−0.477796	−	0.551407i	−0.0200127	−	0.0230959i
$571$	−16.2296	−	4.76543i	−0.679186	−	0.199427i	−0.0760964	−	0.997100i	$-0.524246\pi$
$571$	−16.2296	−	4.76543i	−0.679186	−	0.199427i	−0.603090	+	0.797673i	$0.706064\pi$
$572$	0.190853	+	0.417909i	0.00797994	+	0.0174736i
$573$	0.305791	−	2.12683i	0.0127746	−	0.0888494i
$574$	16.5626			0.691310
$575$	−3.73654	−	3.00637i	−0.155824	−	0.125374i
$576$	1.00000			0.0416667
$577$	−3.69235	+	25.6809i	−0.153715	+	1.06911i	0.756208	+	0.654331i	$0.227050\pi$
$577$	−3.69235	+	25.6809i	−0.153715	+	1.06911i	−0.909923	+	0.414778i	$0.863859\pi$
$578$	−3.35749	−	7.35187i	−0.139653	−	0.305798i
$579$	13.9361	+	4.09201i	0.579165	+	0.170058i
$580$	−4.08016	−	4.70876i	−0.169420	−	0.195521i
$581$	9.20963	−	2.70419i	0.382080	−	0.112189i
$582$	−7.00246	−	4.50021i	−0.290262	−	0.186540i
$583$	−7.19433	+	15.7534i	−0.297959	+	0.652439i
$584$	−1.21270	+	1.39953i	−0.0501818	+	0.0579129i
$585$	−0.178324	+	0.114602i	−0.00737281	+	0.00473822i
$586$	−1.96136	−	13.6415i	−0.0810230	−	0.563527i
$587$	4.95472	+	34.4609i	0.204503	+	1.42235i	0.790710	+	0.612191i	$0.209711\pi$
$587$	4.95472	+	34.4609i	0.204503	+	1.42235i	−0.586207	+	0.810161i	$0.699379\pi$
$588$	3.80577	−	2.44582i	0.156947	−	0.100864i
$589$	−2.02449	+	2.33638i	−0.0834175	+	0.0962689i
$590$	−3.40889	+	7.46442i	−0.140342	+	0.307305i
$591$	−14.3473	−	9.22045i	−0.590169	−	0.379279i
$592$	−10.2505	+	3.00982i	−0.421293	+	0.123703i
$593$	11.2510	+	12.9843i	0.462022	+	0.533201i	0.938175	−	0.346161i	$-0.112515\pi$
$593$	11.2510	+	12.9843i	0.462022	+	0.533201i	−0.476154	+	0.879362i	$0.657969\pi$
$594$	−2.07957	−	0.610617i	−0.0853258	−	0.0250539i
$595$	−1.95205	−	4.27440i	−0.0800263	−	0.175233i
$596$	−0.834859	+	5.80657i	−0.0341972	+	0.237846i
$597$	6.39809			0.261856
$598$	1.01085	+	0.107894i	0.0413368	+	0.00441213i
$599$	16.5166			0.674848			0.337424	−	0.941353i	$-0.390444\pi$
$599$	16.5166			0.674848			0.337424	+	0.941353i	$0.390444\pi$
$600$	0.142315	−	0.989821i	0.00580998	−	0.0404093i
$601$	5.74327	+	12.5760i	0.234273	+	0.512986i	0.989857	−	0.142065i	$-0.0453743\pi$
$601$	5.74327	+	12.5760i	0.234273	+	0.512986i	−0.755584	+	0.655051i	$0.772647\pi$
$602$	−14.3776	−	4.22163i	−0.585986	−	0.172061i
$603$	10.0140	+	11.5568i	0.407801	+	0.470627i
$604$	−10.0239	+	2.94328i	−0.407866	+	0.119760i
$605$	−5.30203	−	3.40741i	−0.215558	−	0.138531i
$606$	−1.36221	+	2.98282i	−0.0553360	+	0.121169i
$607$	−11.9103	+	13.7452i	−0.483425	+	0.557902i	−0.944097	−	0.329669i	$-0.893063\pi$
$607$	−11.9103	+	13.7452i	−0.483425	+	0.557902i	0.460672	+	0.887570i	$0.347608\pi$
$608$	−0.613792	+	0.394460i	−0.0248925	+	0.0159975i
$609$	−1.39528	−	9.70436i	−0.0565395	−	0.393241i
$610$	0.811496	+	5.64408i	0.0328565	+	0.228522i
$611$	0.913301	−	0.586943i	0.0369482	−	0.0237452i
$612$	−1.95558	+	2.25686i	−0.0790498	+	0.0912284i
$613$	13.0064	−	28.4800i	0.525323	−	1.15030i	−0.442062	−	0.896984i	$-0.645753\pi$
$613$	13.0064	−	28.4800i	0.525323	−	1.15030i	0.967385	−	0.253312i	$-0.0815198\pi$
$614$	12.6355	+	8.12034i	0.509927	+	0.327710i
$615$	−10.0993	+	2.96541i	−0.407241	+	0.119577i
$616$	−2.23338	−	2.57746i	−0.0899854	−	0.103849i
$617$	31.5185	+	9.25465i	1.26889	+	0.372578i	0.845794	−	0.533509i	$-0.179127\pi$
$617$	31.5185	+	9.25465i	1.26889	+	0.372578i	0.423091	+	0.906087i	$0.360945\pi$
$618$	−5.31296	−	11.6338i	−0.213719	−	0.467979i
$619$	3.73050	−	25.9462i	0.149941	−	1.04286i	−0.766370	−	0.642399i	$-0.777939\pi$
$619$	3.73050	−	25.9462i	0.149941	−	1.04286i	0.916312	−	0.400466i	$-0.131152\pi$
$620$	−4.23713			−0.170167
$621$	−3.50754	+	3.27065i	−0.140753	+	0.131247i
$622$	2.81477			0.112862
$623$	3.09375	−	21.5175i	0.123949	−	0.862081i
$624$	0.0880575	+	0.192819i	0.00352512	+	0.00771893i
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$	2.29458	+	2.64808i	0.0917097	+	0.105839i
$627$	1.51729	−	0.445515i	0.0605946	−	0.0177922i
$628$	−2.17985	−	1.40090i	−0.0869854	−	0.0559021i
$629$	13.2530	−	29.0199i	0.528430	−	1.15710i
$630$	1.03046	−	1.18921i	0.0410544	−	0.0473794i
$631$	15.9385	−	10.2430i	0.634500	−	0.407769i	−0.183473	−	0.983025i	$-0.558734\pi$
$631$	15.9385	−	10.2430i	0.634500	−	0.407769i	0.817973	+	0.575256i	$0.195098\pi$
$632$	−0.423915	−	2.94839i	−0.0168624	−	0.117281i
$633$	−1.94114	−	13.5010i	−0.0771535	−	0.536615i
$634$	−3.98134	+	2.55865i	−0.158119	+	0.101617i
$635$	−0.342293	+	0.395027i	−0.0135835	+	0.0156762i
$636$	−3.31939	+	7.26846i	−0.131623	+	0.288213i
$637$	0.806727	+	0.518452i	0.0319637	+	0.0205418i
$638$	12.9569	−	3.80450i	0.512970	−	0.150622i
$639$	1.31881	+	1.52199i	0.0521714	+	0.0602090i
$640$	−0.959493	−	0.281733i	−0.0379273	−	0.0111365i
$641$	−2.63936	−	5.77939i	−0.104248	−	0.228272i	0.850319	−	0.526268i	$-0.176409\pi$
$641$	−2.63936	−	5.77939i	−0.104248	−	0.228272i	−0.954567	+	0.297996i	$0.903682\pi$
$642$	−0.0885980	+	0.616213i	−0.00349669	+	0.0243200i
$643$	20.4018			0.804568			0.402284	−	0.915515i	$-0.368217\pi$
$643$	20.4018			0.804568			0.402284	+	0.915515i	$0.368217\pi$
$644$	−7.42556	+	1.34560i	−0.292608	+	0.0530239i
$645$	9.52274			0.374958
$646$	0.310079	−	2.15664i	0.0121999	−	0.0848520i
$647$	1.07443	+	2.35268i	0.0422404	+	0.0924935i	0.929576	−	0.368631i	$-0.120173\pi$
$647$	1.07443	+	2.35268i	0.0422404	+	0.0924935i	−0.887335	+	0.461125i	$0.847446\pi$
$648$	−0.959493	−	0.281733i	−0.0376924	−	0.0110675i
$649$	−11.6469	−	13.4413i	−0.457182	−	0.527616i
$650$	0.203388	−	0.0597202i	0.00797754	−	0.00234242i
$651$	−5.60893	−	3.60464i	−0.219831	−	0.141277i
$652$	1.10650	−	2.42290i	0.0433339	−	0.0948880i
$653$	−28.7076	+	33.1303i	−1.12342	+	1.29649i	−0.173203	+	0.984886i	$0.555412\pi$
$653$	−28.7076	+	33.1303i	−1.12342	+	1.29649i	−0.950212	+	0.311604i	$0.899134\pi$
$654$	4.93960	−	3.17449i	0.193154	−	0.124132i
$655$	−0.228963	−	1.59247i	−0.00894633	−	0.0622231i
$656$	1.49795	+	10.4185i	0.0584852	+	0.406773i
$657$	1.55787	−	1.00118i	0.0607783	−	0.0390598i
$658$	−5.27757	+	6.09064i	−0.205741	+	0.237438i
$659$	2.20816	−	4.83520i	0.0860177	−	0.188353i	−0.861735	−	0.507359i	$-0.830622\pi$
$659$	2.20816	−	4.83520i	0.0860177	−	0.188353i	0.947753	+	0.319006i	$0.103349\pi$
$660$	1.82330	+	1.17177i	0.0709719	+	0.0456109i
$661$	−17.0979	+	5.02038i	−0.665030	+	0.195270i	−0.596789	−	0.802399i	$-0.703557\pi$
$661$	−17.0979	+	5.02038i	−0.665030	+	0.195270i	−0.0682411	+	0.997669i	$0.521739\pi$
$662$	12.6958	+	14.6517i	0.493436	+	0.569456i
$663$	−0.607370	−	0.178340i	−0.0235883	−	0.00692615i
$664$	2.53397	+	5.54861i	0.0983370	+	0.215328i
$665$	−0.163390	+	1.13640i	−0.00633600	+	0.0440678i
$666$	10.6832			0.413967
$667$	7.36753	−	28.9583i	0.285272	−	1.12127i
$668$	−5.35697			−0.207267
$669$	−2.13438	+	14.8450i	−0.0825201	+	0.573940i
$670$	−6.35243	−	13.9099i	−0.245416	−	0.537386i
$671$	−11.8580	−	3.48181i	−0.457771	−	0.134414i
$672$	−1.03046	−	1.18921i	−0.0397508	−	0.0458749i
$673$	34.9140	−	10.2517i	1.34584	−	0.395173i	0.472088	−	0.881551i	$-0.343500\pi$
$673$	34.9140	−	10.2517i	1.34584	−	0.395173i	0.873748	+	0.486378i	$0.161682\pi$
$674$	−14.3951	−	9.25114i	−0.554477	−	0.356341i
$675$	−0.415415	+	0.909632i	−0.0159893	+	0.0350118i
$676$	8.48376	−	9.79079i	0.326299	−	0.376569i
$677$	21.4069	−	13.7574i	0.822735	−	0.528740i	−0.0602267	−	0.998185i	$-0.519182\pi$
$677$	21.4069	−	13.7574i	0.822735	−	0.528740i	0.882962	+	0.469445i	$0.155546\pi$
$678$	−1.01353	−	7.04928i	−0.0389245	−	0.270726i
$679$	1.86404	+	12.9647i	0.0715354	+	0.497539i
$680$	2.51220	−	1.61449i	0.0963386	−	0.0619130i
$681$	−17.2401	+	19.8961i	−0.660640	+	0.762420i
$682$	3.81492	−	8.35352i	0.146081	−	0.319873i
$683$	−33.2503	−	21.3686i	−1.27229	−	0.817649i	−0.282370	−	0.959306i	$-0.591121\pi$
$683$	−33.2503	−	21.3686i	−1.27229	−	0.817649i	−0.989916	+	0.141657i	$0.954757\pi$
$684$	0.700061	−	0.205556i	0.0267675	−	0.00785965i
$685$	4.91643	+	5.67387i	0.187847	+	0.216787i
$686$	−17.3990	−	5.10880i	−0.664296	−	0.195055i
$687$	−3.52562	−	7.72004i	−0.134511	−	0.294538i
$688$	1.35523	−	9.42582i	0.0516676	−	0.359356i
$689$	−1.69379			−0.0645284
$690$	4.28691	−	2.14998i	0.163200	−	0.0818484i
$691$	6.48084			0.246543			0.123271	−	0.992373i	$-0.460661\pi$
$691$	6.48084			0.246543			0.123271	+	0.992373i	$0.460661\pi$
$692$	3.23370	−	22.4909i	0.122927	−	0.854975i
$693$	1.41676	+	3.10227i	0.0538182	+	0.117845i
$694$	27.8148	+	8.16716i	1.05583	+	0.310021i
$695$	5.49592	+	6.34263i	0.208472	+	0.240590i
$696$	5.97820	−	1.75536i	0.226603	−	0.0665367i
$697$	−26.4425	−	16.9935i	−1.00158	−	0.643676i
$698$	8.08209	−	17.6973i	0.305912	−	0.669853i
$699$	−2.45784	+	2.83649i	−0.0929639	+	0.107286i
$700$	−1.32376	+	0.850727i	−0.0500333	+	0.0321545i
$701$	−6.16570	−	42.8834i	−0.232875	−	1.61968i	−0.685563	−	0.728013i	$-0.740444\pi$
$701$	−6.16570	−	42.8834i	−0.232875	−	1.61968i	0.452688	−	0.891669i	$-0.350465\pi$
$702$	−0.0301671	−	0.209817i	−0.00113859	−	0.00791903i
$703$	−6.55728	+	4.21411i	−0.247313	+	0.158938i
$704$	1.41932	−	1.63798i	0.0534927	−	0.0617338i
$705$	2.12758	−	4.65874i	0.0801292	−	0.175458i
$706$	−21.4446	−	13.7816i	−0.807078	−	0.518678i
$707$	4.95091	−	1.45372i	0.186198	−	0.0546727i
$708$	−5.37377	−	6.20167i	−0.201959	−	0.233073i
$709$	38.7329	+	11.3730i	1.45464	+	0.427122i	0.911075	−	0.412242i	$-0.135254\pi$
$709$	38.7329	+	11.3730i	1.45464	+	0.427122i	0.543570	+	0.839364i	$0.317072\pi$
$710$	−0.836596	−	1.83189i	−0.0313969	−	0.0687496i
$711$	−0.423915	+	2.94839i	−0.0158980	+	0.110573i
$712$	13.8151			0.517743
$713$	−11.6021	−	16.6828i	−0.434501	−	0.624778i
$714$	4.69904			0.175857
$715$	−0.0653832	+	0.454750i	−0.00244519	+	0.0170067i
$716$	3.56201	+	7.79971i	0.133119	+	0.291489i
$717$	18.4371	+	5.41362i	0.688545	+	0.202175i
$718$	−13.6098	−	15.7066i	−0.507915	−	0.586165i
$719$	17.4442	−	5.12207i	0.650557	−	0.191021i	0.0602295	−	0.998185i	$-0.480817\pi$
$719$	17.4442	−	5.12207i	0.650557	−	0.191021i	0.590328	+	0.807164i	$0.298999\pi$
$720$	0.841254	+	0.540641i	0.0313517	+	0.0201485i
$721$	−8.36023	+	18.3064i	−0.311351	+	0.681764i
$722$	12.0937	−	13.9569i	0.450083	−	0.519423i
$723$	5.97276	−	3.83846i	0.222129	−	0.142754i
$724$	−0.842660	−	5.86083i	−0.0313172	−	0.217816i
$725$	−0.886704	−	6.16716i	−0.0329314	−	0.229043i
$726$	5.30203	−	3.40741i	0.196777	−	0.126461i
$727$	2.51415	−	2.90148i	0.0932445	−	0.107610i	−0.707210	−	0.707004i	$-0.750046\pi$
$727$	2.51415	−	2.90148i	0.0932445	−	0.107610i	0.800454	+	0.599394i	$0.204592\pi$
$728$	0.138563	−	0.303411i	0.00513549	−	0.0112452i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	−1.77683	+	0.521724i	−0.0657634	+	0.0193099i
$731$	18.6225	+	21.4915i	0.688779	+	0.794893i
$732$	−5.47114	−	1.60647i	−0.202219	−	0.0593769i
$733$	−17.2848	−	37.8485i	−0.638429	−	1.39796i	−0.901326	−	0.433141i	$-0.857405\pi$
$733$	−17.2848	−	37.8485i	−0.638429	−	1.39796i	0.262897	−	0.964824i	$-0.415322\pi$
$734$	1.40031	−	9.73934i	0.0516862	−	0.359486i
$735$	4.52393			0.166868
$736$	−1.51801	−	4.54925i	−0.0559545	−	0.167687i
$737$	33.1428			1.22083
$738$	1.49795	−	10.4185i	0.0551403	−	0.383509i
$739$	6.09060	+	13.3365i	0.224046	+	0.490593i	0.987957	−	0.154729i	$-0.0494505\pi$
$739$	6.09060	+	13.3365i	0.224046	+	0.490593i	−0.763911	+	0.645322i	$0.776723\pi$
$740$	−10.2505	−	3.00982i	−0.376816	−	0.110643i
$741$	0.101281	+	0.116884i	0.00372064	+	0.00429385i
$742$	12.0642	−	3.54238i	0.442892	−	0.130045i
$743$	19.4748	+	12.5157i	0.714460	+	0.459155i	0.846706	−	0.532061i	$-0.178582\pi$
$743$	19.4748	+	12.5157i	0.714460	+	0.459155i	−0.132246	+	0.991217i	$0.542219\pi$
$744$	1.76017	−	3.85423i	0.0645309	−	0.141303i
$745$	−3.84160	+	4.43344i	−0.140745	+	0.162429i
$746$	−9.14959	+	5.88009i	−0.334990	+	0.215285i
$747$	−0.868098	−	6.03776i	−0.0317621	−	0.220910i
$748$	0.921106	+	6.40643i	0.0336790	+	0.234242i
$749$	0.824105	−	0.529620i	0.0301121	−	0.0193519i
$750$	0.654861	−	0.755750i	0.0239121	−	0.0275961i
$751$	−5.98831	+	13.1126i	−0.218517	+	0.478484i	−0.986865	−	0.161547i	$-0.948352\pi$
$751$	−5.98831	+	13.1126i	−0.218517	+	0.478484i	0.768348	+	0.640032i	$0.221079\pi$
$752$	−4.30854	−	2.76893i	−0.157116	−	0.100973i
$753$	−25.3879	+	7.45456i	−0.925187	+	0.271659i
$754$	0.864891	+	0.998138i	0.0314975	+	0.0363500i
$755$	−10.0239	−	2.94328i	−0.364807	−	0.107117i
$756$	0.653678	+	1.43135i	0.0237740	+	0.0520579i
$757$	−7.18900	+	50.0006i	−0.261288	+	1.81730i	0.261912	+	0.965092i	$0.415647\pi$
$757$	−7.18900	+	50.0006i	−0.261288	+	1.81730i	−0.523201	+	0.852210i	$0.675262\pi$
$758$	24.6298			0.894596
$759$	0.378957	+	10.3874i	0.0137553	+	0.377039i
$760$	−0.729615			−0.0264659
$761$	5.82441	−	40.5097i	0.211135	−	1.46848i	−0.558241	−	0.829679i	$-0.688524\pi$
$761$	5.82441	−	40.5097i	0.211135	−	1.46848i	0.769376	−	0.638796i	$-0.220567\pi$
$762$	−0.217135	−	0.475460i	−0.00786599	−	0.0172241i
$763$	−8.86519	−	2.60305i	−0.320941	−	0.0942369i
$764$	−1.40710	−	1.62388i	−0.0509070	−	0.0587498i
$765$	−2.86530	+	0.841327i	−0.103595	+	0.0304182i
$766$	−23.3062	−	14.9780i	−0.842087	−	0.541177i
$767$	0.722598	−	1.58227i	0.0260915	−	0.0571324i
$768$	0.654861	−	0.755750i	0.0236303	−	0.0272708i
$769$	−33.4945	+	21.5256i	−1.20784	+	0.776233i	−0.980296	−	0.197535i	$-0.936707\pi$
$769$	−33.4945	+	21.5256i	−1.20784	+	0.776233i	−0.227546	+	0.973767i	$0.573070\pi$
$770$	−0.485359	−	3.37575i	−0.0174911	−	0.121654i
$771$	−0.908193	−	6.31662i	−0.0327078	−	0.227488i
$772$	12.2188	−	7.85252i	0.439763	−	0.282618i
$773$	22.4831	−	25.9469i	0.808661	−	0.933245i	−0.190162	−	0.981753i	$-0.560901\pi$
$773$	22.4831	−	25.9469i	0.808661	−	0.933245i	0.998823	+	0.0485081i	$0.0154467\pi$
$774$	−3.95589	+	8.66219i	−0.142192	+	0.311356i
$775$	−3.56450	−	2.29077i	−0.128041	−	0.0822867i
$776$	−7.98667	+	2.34510i	−0.286705	+	0.0841841i
$777$	−11.0086	−	12.7046i	−0.394933	−	0.455776i
$778$	14.9604	+	4.39277i	0.536357	+	0.157489i
$779$	3.19024	+	6.98566i	0.114302	+	0.250287i
$780$	−0.0301671	+	0.209817i	−0.00108016	+	0.00751266i
$781$	4.36481			0.156185
$782$	13.2356	+	5.47050i	0.473305	+	0.195625i
$783$	−6.23058			−0.222663
$784$	0.643822	−	4.47788i	0.0229937	−	0.159924i
$785$	−1.07642	−	2.35703i	−0.0384190	−	0.0841260i
$786$	1.54368	+	0.453265i	0.0550612	+	0.0161674i
$787$	6.32380	+	7.29806i	0.225419	+	0.260148i	0.857181	−	0.515015i	$-0.172214\pi$
$787$	6.32380	+	7.29806i	0.225419	+	0.260148i	−0.631762	+	0.775162i	$0.717668\pi$
$788$	−16.3638	+	4.80486i	−0.582938	+	0.171166i
$789$	12.4799	+	8.02037i	0.444297	+	0.285533i
$790$	1.23740	−	2.70953i	0.0440248	−	0.0964008i
$791$	−7.33868	+	8.46929i	−0.260934	+	0.301133i
$792$	−1.82330	+	1.17177i	−0.0647882	+	0.0416369i
$793$	−0.172017	−	1.19640i	−0.00610849	−	0.0424855i
$794$	−0.000357559	−	0.00248688i	−1.26893e−5	−	8.82561e-5i
$795$	−6.72208	+	4.32002i	−0.238407	+	0.153215i
$796$	4.18986	−	4.83535i	0.148506	−	0.171384i
$797$	−4.78666	+	10.4813i	−0.169552	+	0.371268i	−0.975265	−	0.221039i	$-0.929055\pi$
$797$	−4.78666	+	10.4813i	−0.169552	+	0.371268i	0.805713	+	0.592307i	$0.201783\pi$
$798$	−0.965834	−	0.620704i	−0.0341901	−	0.0219727i
$799$	14.6748	−	4.30891i	0.519158	−	0.152438i
$800$	−0.654861	−	0.755750i	−0.0231528	−	0.0267198i
$801$	−13.2555	−	3.89216i	−0.468360	−	0.137523i
$802$	7.02750	+	15.3881i	0.248150	+	0.543372i
$803$	0.571197	−	3.97276i	0.0201571	−	0.140196i
$804$	15.2918			0.539299
$805$	−6.97427	−	2.88258i	−0.245811	−	0.101597i
$806$	0.898164			0.0316365
$807$	−2.76757	+	19.2489i	−0.0974232	+	0.677594i
$808$	1.36221	+	2.98282i	0.0479223	+	0.104935i
$809$	40.5238	+	11.8988i	1.42474	+	0.418341i	0.901105	−	0.433602i	$-0.142757\pi$
$809$	40.5238	+	11.8988i	1.42474	+	0.418341i	0.523635	+	0.851943i	$0.324576\pi$
$810$	−0.654861	−	0.755750i	−0.0230095	−	0.0265543i
$811$	0.522292	−	0.153359i	0.0183401	−	0.00538515i	−0.272550	−	0.962142i	$-0.587867\pi$
$811$	0.522292	−	0.153359i	0.0183401	−	0.00538515i	0.290890	+	0.956757i	$0.406049\pi$
$812$	−8.24778	−	5.30053i	−0.289440	−	0.186012i
$813$	10.7799	−	23.6048i	0.378069	−	0.827856i
$814$	15.1629	−	17.4990i	0.531461	−	0.613339i
$815$	2.24077	−	1.44005i	0.0784906	−	0.0504428i
$816$	0.424989	+	2.95586i	0.0148776	+	0.103476i
$817$	−0.988795	−	6.87722i	−0.0345936	−	0.240603i
$818$	−27.9974	+	17.9928i	−0.978905	+	0.629104i
$819$	−0.218431	+	0.252083i	−0.00763260	+	0.00880849i
$820$	−4.37250	+	9.57443i	−0.152694	+	0.334354i
$821$	−28.6208	−	18.3935i	−0.998873	−	0.641937i	−0.0643828	−	0.997925i	$-0.520508\pi$
$821$	−28.6208	−	18.3935i	−0.998873	−	0.641937i	−0.934490	+	0.355989i	$0.884144\pi$
$822$	−7.20349	+	2.11514i	−0.251251	+	0.0737738i
$823$	9.75934	+	11.2629i	0.340189	+	0.392599i	0.899905	−	0.436085i	$-0.143635\pi$
$823$	9.75934	+	11.2629i	0.340189	+	0.392599i	−0.559716	+	0.828684i	$0.689090\pi$
$824$	−12.2715	−	3.60323i	−0.427497	−	0.125524i
$825$	0.900355	+	1.97150i	0.0313463	+	0.0686389i
$826$	−1.83765	+	12.7811i	−0.0639399	+	0.444712i
$827$	−2.72839			−0.0948753			−0.0474376	−	0.998874i	$-0.515106\pi$
$827$	−2.72839			−0.0948753			−0.0474376	+	0.998874i	$0.515106\pi$
$828$	0.174847	+	4.79264i	0.00607636	+	0.166556i
$829$	−33.7708			−1.17291			−0.586455	−	0.809982i	$-0.699477\pi$
$829$	−33.7708			−1.17291			−0.586455	+	0.809982i	$0.699477\pi$
$830$	−0.868098	+	6.03776i	−0.0301321	+	0.209574i
$831$	6.36722	+	13.9423i	0.220877	+	0.483652i
$832$	0.203388	+	0.0597202i	0.00705122	+	0.00207042i
$833$	8.84693	+	10.2099i	0.306528	+	0.353752i
$834$	−8.05255	+	2.36444i	−0.278837	+	0.0818739i
$835$	−4.50657	−	2.89620i	−0.155956	−	0.100227i
$836$	0.656913	−	1.43844i	0.0227198	−	0.0497495i
$837$	−2.77473	+	3.20221i	−0.0959087	+	0.110685i
$838$	18.5023	−	11.8907i	0.639153	−	0.410759i
$839$	−1.36485	−	9.49276i	−0.0471200	−	0.327727i	−0.999724	−	0.0235122i	$-0.992515\pi$
$839$	−1.36485	−	9.49276i	−0.0471200	−	0.327727i	0.952604	−	0.304214i	$-0.0983939\pi$
$840$	−0.223940	−	1.55754i	−0.00772666	−	0.0537401i
$841$	8.26124	−	5.30918i	0.284870	−	0.183075i
$842$	−10.8109	+	12.4765i	−0.372569	+	0.429967i
$843$	−8.62442	+	18.8848i	−0.297041	+	0.650428i
$844$	−11.4745	−	7.37422i	−0.394969	−	0.253831i
$845$	12.4303	−	3.64986i	0.427615	−	0.125559i
$846$	3.35392	+	3.87063i	0.115310	+	0.133075i
$847$	−9.51565	−	2.79405i	−0.326962	−	0.0960046i
$848$	3.31939	+	7.26846i	0.113988	+	0.249600i
$849$	−3.15711	+	21.9582i	−0.108352	+	0.753604i
$850$	2.98626			0.102428
$851$	−16.2172	−	48.6007i	−0.555920	−	1.66601i
$852$	2.01388			0.0689944
$853$	3.06929	−	21.3473i	0.105090	−	0.730919i	−0.867338	−	0.497719i	$-0.834171\pi$
$853$	3.06929	−	21.3473i	0.105090	−	0.730919i	0.972429	−	0.233200i	$-0.0749198\pi$
$854$	3.72735	+	8.16175i	0.127547	+	0.279289i
$855$	0.700061	+	0.205556i	0.0239416	+	0.00702988i
$856$	0.407683	+	0.470492i	0.0139343	+	0.0160811i
$857$	−13.2987	+	3.90485i	−0.454275	+	0.133387i	−0.500862	−	0.865527i	$-0.666984\pi$
$857$	−13.2987	+	3.90485i	−0.454275	+	0.133387i	0.0465872	+	0.998914i	$0.485165\pi$
$858$	−0.386494	−	0.248385i	−0.0131947	−	0.00847971i
$859$	−6.02096	+	13.1841i	−0.205433	+	0.449835i	−0.984103	−	0.177599i	$-0.943167\pi$
$859$	−6.02096	+	13.1841i	−0.205433	+	0.449835i	0.778670	+	0.627433i	$0.215894\pi$
$860$	6.23607	−	7.19681i	0.212648	−	0.245409i
$861$	−13.9334	+	8.95443i	−0.474848	+	0.305166i
$862$	0.463249	+	3.22197i	0.0157783	+	0.109741i
$863$	4.97576	+	34.6072i	0.169377	+	1.17804i	0.880176	+	0.474647i	$0.157424\pi$
$863$	4.97576	+	34.6072i	0.169377	+	1.17804i	−0.710799	+	0.703395i	$0.751666\pi$
$864$	−0.841254	+	0.540641i	−0.0286200	+	0.0183930i
$865$	14.8799	−	17.1723i	0.505930	−	0.583875i
$866$	−14.5373	+	31.8322i	−0.493998	+	1.08170i
$867$	6.79922	+	4.36959i	0.230914	+	0.148399i
$868$	−6.39728	+	1.87841i	−0.217138	+	0.0637574i
$869$	4.22775	+	4.87908i	0.143417	+	0.165511i
$870$	5.97820	+	1.75536i	0.202680	+	0.0595122i
$871$	1.34655	+	2.94854i	0.0456263	+	0.0999076i
$872$	0.835632	−	5.81195i	0.0282981	−	0.196817i
$873$	8.32385			0.281720
$874$	−1.99783	−	2.87271i	−0.0675774	−	0.0971710i
$875$	−1.57355			−0.0531958
$876$	0.263545	−	1.83299i	0.00890435	−	0.0619311i
$877$	13.3038	+	29.1313i	0.449238	+	0.983694i	0.989810	+	0.142396i	$0.0454807\pi$
$877$	13.3038	+	29.1313i	0.449238	+	0.983694i	−0.540572	+	0.841298i	$0.681792\pi$
$878$	−20.6401	−	6.06047i	−0.696569	−	0.204531i
$879$	9.02518	+	10.4156i	0.304412	+	0.351310i
$880$	2.07957	−	0.610617i	0.0701023	−	0.0205839i
$881$	24.1108	+	15.4951i	0.812313	+	0.522042i	0.879612	−	0.475691i	$-0.157802\pi$
$881$	24.1108	+	15.4951i	0.812313	+	0.522042i	−0.0672995	+	0.997733i	$0.521438\pi$
$882$	−1.87931	+	4.11511i	−0.0632796	+	0.138563i
$883$	−7.39240	+	8.53128i	−0.248774	+	0.287101i	−0.866378	−	0.499389i	$-0.833558\pi$
$883$	−7.39240	+	8.53128i	−0.248774	+	0.287101i	0.617604	+	0.786489i	$0.288103\pi$
$884$	−0.532523	+	0.342232i	−0.0179107	+	0.0115105i
$885$	−1.16783	−	8.12245i	−0.0392563	−	0.273033i
$886$	−0.778045	−	5.41142i	−0.0261389	−	0.181800i
$887$	−37.1808	+	23.8947i	−1.24841	+	0.802304i	−0.986654	−	0.162830i	$-0.947938\pi$
$887$	−37.1808	+	23.8947i	−1.24841	+	0.802304i	−0.261756	+	0.965134i	$0.584302\pi$
$888$	6.99603	−	8.07385i	0.234772	−	0.270941i
$889$	−0.341674	+	0.748162i	−0.0114594	+	0.0250926i
$890$	11.6220	+	7.46901i	0.389570	+	0.250362i
$891$	2.07957	−	0.610617i	0.0696682	−	0.0204564i
$892$	9.82135	+	11.3344i	0.328843	+	0.379505i
$893$	−3.58541	−	1.05277i	−0.119981	−	0.0352297i
$894$	−2.43694	−	5.33616i	−0.0815035	−	0.178468i
$895$	−1.22029	+	8.48730i	−0.0407898	+	0.283699i
$896$	−1.57355			−0.0525687
$897$	−0.908716	+	0.455742i	−0.0303411	+	0.0152168i
$898$	−20.8803			−0.696784
$899$	3.75708	−	26.1311i	0.125306	−	0.871520i
$900$	0.415415	+	0.909632i	0.0138472	+	0.0303211i
$901$	−22.8953	−	6.72266i	−0.762752	−	0.223964i
$902$	−14.9392	−	17.2408i	−0.497422	−	0.574055i
$903$	14.3776	−	4.22163i	0.478455	−	0.140487i
$904$	−5.99121	−	3.85032i	−0.199265	−	0.128060i
$905$	2.45971	−	5.38602i	0.0817636	−	0.179037i
$906$	6.84138	−	7.89537i	0.227289	−	0.262306i
$907$	−2.04705	+	1.31556i	−0.0679711	+	0.0436824i	−0.574185	−	0.818726i	$-0.694681\pi$
$907$	−2.04705	+	1.31556i	−0.0679711	+	0.0436824i	0.506214	+	0.862408i	$0.331045\pi$
$908$	3.74662	+	26.0583i	0.124336	+	0.864776i
$909$	−0.466672	−	3.24577i	−0.0154785	−	0.107656i
$910$	0.280603	−	0.180333i	0.00930190	−	0.00597797i
$911$	−33.9714	+	39.2050i	−1.12552	+	1.29892i	−0.176291	+	0.984338i	$0.556410\pi$
$911$	−33.9714	+	39.2050i	−1.12552	+	1.29892i	−0.949230	+	0.314583i	$0.898135\pi$
$912$	0.303093	−	0.663682i	0.0100364	−	0.0219767i
$913$	−11.1219	−	7.14759i	−0.368080	−	0.236551i
$914$	17.7951	−	5.22510i	0.588608	−	0.172831i
$915$	−3.73409	−	4.30937i	−0.123445	−	0.142463i
$916$	−8.14321	−	2.39106i	−0.269059	−	0.0790029i
$917$	−1.05167	−	2.30283i	−0.0347292	−	0.0760463i
$918$	0.424989	−	2.95586i	0.0140267	−	0.0975581i
$919$	−15.5282			−0.512228			−0.256114	−	0.966647i	$-0.582442\pi$
$919$	−15.5282			−0.512228			−0.256114	+	0.966647i	$0.582442\pi$
$920$	1.18248	−	4.64777i	0.0389852	−	0.153232i
$921$	−15.0198			−0.494920
$922$	5.29465	−	36.8251i	0.174370	−	1.21277i
$923$	0.177337	+	0.388314i	0.00583712	+	0.0127815i
$924$	3.27231	+	0.960838i	0.107651	+	0.0316093i
$925$	−6.99603	−	8.07385i	−0.230028	−	0.265467i
$926$	−15.8189	+	4.64484i	−0.519840	+	0.152639i
$927$	10.7592	+	6.91454i	0.353380	+	0.227103i
$928$	2.58828	−	5.66754i	0.0849644	−	0.186046i
$929$	−24.7747	+	28.5916i	−0.812833	+	0.938059i	−0.999011	−	0.0444569i	$-0.985844\pi$
$929$	−24.7747	+	28.5916i	−0.812833	+	0.938059i	0.186179	+	0.982516i	$0.440390\pi$
$930$	3.56450	−	2.29077i	0.116885	−	0.0751172i
$931$	−0.469743	−	3.26713i	−0.0153952	−	0.107076i
$932$	0.534139	+	3.71502i	0.0174963	+	0.121689i
$933$	−2.36793	+	1.52178i	−0.0775226	+	0.0498208i
$934$	−23.8859	+	27.5657i	−0.781569	+	0.901979i
$935$	−2.68870	+	5.88742i	−0.0879297	+	0.192539i
$936$	−0.178324	−	0.114602i	−0.00582872	−	0.00374589i
$937$	13.3715	−	3.92624i	0.436829	−	0.128265i	−0.0559215	−	0.998435i	$-0.517810\pi$
$937$	13.3715	−	3.92624i	0.436829	−	0.128265i	0.492751	+	0.870171i	$0.335991\pi$
$938$	−15.7575	−	18.1852i	−0.514502	−	0.593767i
$939$	−3.36198	−	0.987167i	−0.109714	−	0.0322150i
$940$	−2.12758	−	4.65874i	−0.0693939	−	0.151952i
$941$	−0.534073	+	3.71456i	−0.0174103	+	0.121091i	−0.996673	−	0.0815028i	$-0.974028\pi$
$941$	−0.534073	+	3.71456i	−0.0174103	+	0.121091i	0.979263	+	0.202594i	$0.0649371\pi$
$942$	2.59119			0.0844255
$943$	−49.6701	+	9.00079i	−1.61748	+	0.293106i
$944$	−8.20598			−0.267082
$945$	−0.223940	+	1.55754i	−0.00728477	+	0.0506667i
$946$	8.57385	+	18.7741i	0.278760	+	0.610399i
$947$	29.3374	+	8.61423i	0.953337	+	0.279925i	0.721175	−	0.692752i	$-0.243602\pi$
$947$	29.3374	+	8.61423i	0.953337	+	0.279925i	0.232161	+	0.972677i	$0.425420\pi$
$948$	1.95064	+	2.25116i	0.0633539	+	0.0731143i
$949$	0.376643	−	0.110592i	0.0122263	−	0.00358998i
$950$	−0.613792	−	0.394460i	−0.0199140	−	0.0127980i
$951$	1.96601	−	4.30495i	0.0637521	−	0.139598i
$952$	3.07722	−	3.55130i	0.0997332	−	0.115098i
$953$	45.6360	−	29.3285i	1.47830	−	0.950043i	0.480987	−	0.876728i	$-0.340278\pi$
$953$	45.6360	−	29.3285i	1.47830	−	0.950043i	0.997309	−	0.0733151i	$-0.0233579\pi$
$954$	−1.13717	−	7.90922i	−0.0368174	−	0.256070i
$955$	−0.305791	−	2.12683i	−0.00989518	−	0.0688225i
$956$	16.1651	−	10.3887i	0.522815	−	0.335993i
$957$	−8.84320	+	10.2056i	−0.285860	+	0.329900i
$958$	6.78677	−	14.8609i	0.219270	−	0.480135i
$959$	9.93824	+	6.38692i	0.320923	+	0.206244i
$960$	0.959493	−	0.281733i	0.0309675	−	0.00909288i
$961$	8.54379	+	9.86006i	0.275606	+	0.318066i
$962$	2.17284	+	0.638005i	0.0700553	+	0.0205701i
$963$	−0.258616	−	0.566291i	−0.00833380	−	0.0182485i
$964$	1.01041	−	7.02757i	0.0325432	−	0.226343i
$965$	14.5245			0.467559
$966$	5.51930	−	5.14655i	0.177580	−	0.165588i
$967$	−28.2890			−0.909712			−0.454856	−	0.890565i	$-0.650309\pi$
$967$	−28.2890			−0.909712			−0.454856	+	0.890565i	$0.650309\pi$
$968$	0.896944	−	6.23838i	0.0288289	−	0.200509i
$969$	0.905115	+	1.98193i	0.0290765	+	0.0636686i
$970$	−7.98667	−	2.34510i	−0.256437	−	0.0752966i
$971$	8.85494	+	10.2191i	0.284168	+	0.327948i	0.879831	−	0.475287i	$-0.157656\pi$
$971$	8.85494	+	10.2191i	0.284168	+	0.327948i	−0.595662	+	0.803235i	$0.703110\pi$
$972$	0.959493	−	0.281733i	0.0307758	−	0.00903658i
$973$	11.1096	+	7.13973i	0.356159	+	0.228889i
$974$	−14.3318	+	31.3823i	−0.459222	+	1.00556i
$975$	−0.138814	+	0.160200i	−0.00444560	+	0.00513050i
$976$	−4.79693	+	3.08280i	−0.153546	+	0.0986780i
$977$	2.81864	+	19.6041i	0.0901763	+	0.627190i	0.983920	+	0.178611i	$0.0571605\pi$
$977$	2.81864	+	19.6041i	0.0901763	+	0.627190i	−0.893743	+	0.448579i	$0.851930\pi$
$978$	0.379070	+	2.63649i	0.0121213	+	0.0843057i
$979$	−25.1891	+	16.1880i	−0.805047	+	0.517372i
$980$	2.96254	−	3.41896i	0.0946350	−	0.109215i
$981$	−2.43920	+	5.34110i	−0.0778776	+	0.170528i
$982$	12.1205	+	7.78936i	0.386780	+	0.248569i
$983$	−39.6971	+	11.6561i	−1.26614	+	0.371772i	−0.844776	−	0.535120i	$-0.820267\pi$
$983$	−39.6971	+	11.6561i	−1.26614	+	0.371772i	−0.421364	+	0.906892i	$0.638448\pi$
$984$	−6.89281	−	7.95473i	−0.219735	−	0.253587i
$985$	−16.3638	−	4.80486i	−0.521395	−	0.153095i
$986$	7.72927	+	16.9247i	0.246150	+	0.538994i
$987$	1.14692	−	7.97704i	0.0365070	−	0.253912i
$988$	0.154660			0.00492039
$989$	45.4115	+	4.84705i	1.44400	+	0.154127i
$990$	−2.16736			−0.0688833
$991$	−3.53801	+	24.6074i	−0.112389	+	0.781680i	0.853196	+	0.521591i	$0.174661\pi$
$991$	−3.53801	+	24.6074i	−0.112389	+	0.781680i	−0.965585	+	0.260089i	$0.916248\pi$
$992$	−1.76017	−	3.85423i	−0.0558854	−	0.122372i
$993$	−18.6017	−	5.46196i	−0.590308	−	0.173330i
$994$	−2.07522	−	2.39493i	−0.0658220	−	0.0759626i
$995$	6.13892	−	1.80255i	0.194617	−	0.0571447i
$996$	−5.13152	−	3.29782i	−0.162598	−	0.104496i
$997$	6.95280	−	15.2245i	0.220197	−	0.482165i	−0.767004	−	0.641642i	$-0.778253\pi$
$997$	6.95280	−	15.2245i	0.220197	−	0.482165i	0.987202	+	0.159477i	$0.0509807\pi$
$998$	−21.9573	+	25.3401i	−0.695047	+	0.802127i
$999$	−8.98731	+	5.77580i	−0.284346	+	0.182738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.c.31.1	✓	20
23.3	even	11	inner	690.2.m.c.601.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.c.31.1	✓	20	1.1	even	1	trivial
690.2.m.c.601.1	yes	20	23.3	even	11	inner

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.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.654861 - 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-1.32376 - 0.850727i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.654861 - 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-1.32376 - 0.850727i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(0.841254 - 0.540641i) q^{10} +(0.308448 + 2.14530i) q^{11} +(0.142315 + 0.989821i) q^{12} +(-0.178324 + 0.114602i) q^{13} +(1.03046 - 1.18921i) q^{14} +(-0.415415 + 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-2.86530 + 0.841327i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(0.700061 + 0.205556i) q^{19} +(0.415415 + 0.909632i) q^{20} +(-0.223940 + 1.55754i) q^{21} -2.16736 q^{22} +(-2.44401 + 4.12636i) q^{23} -1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(-0.0880575 - 0.192819i) q^{26} +(0.959493 + 0.281733i) q^{27} +(1.03046 + 1.18921i) q^{28} +(-5.97820 + 1.75536i) q^{29} +(-0.841254 - 0.540641i) q^{30} +(-1.76017 + 3.85423i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(1.82330 - 1.17177i) q^{33} +(-0.424989 - 2.95586i) q^{34} +(0.223940 + 1.55754i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-6.99603 + 8.07385i) q^{37} +(-0.303093 + 0.663682i) q^{38} +(0.178324 + 0.114602i) q^{39} +(-0.959493 + 0.281733i) q^{40} +(6.89281 + 7.95473i) q^{41} +(-1.50981 - 0.443321i) q^{42} +(-3.95589 - 8.66219i) q^{43} +(0.308448 - 2.14530i) q^{44} +1.00000 q^{45} +(-3.73654 - 3.00637i) q^{46} -5.12157 q^{47} +(0.142315 - 0.989821i) q^{48} +(-1.87931 - 4.11511i) q^{49} +(-0.959493 - 0.281733i) q^{50} +(1.95558 + 2.25686i) q^{51} +(0.203388 - 0.0597202i) q^{52} +(6.72208 + 4.32002i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(1.41932 - 1.63798i) q^{55} +(-1.32376 + 0.850727i) q^{56} +(-0.103835 - 0.722189i) q^{57} +(-0.886704 - 6.16716i) q^{58} +(-6.90331 + 4.43649i) q^{59} +(0.654861 - 0.755750i) q^{60} +(-2.36875 + 5.18683i) q^{61} +(-3.56450 - 2.29077i) q^{62} +(1.50981 - 0.443321i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(0.203388 + 0.0597202i) q^{65} +(0.900355 + 1.97150i) q^{66} +(2.17625 - 15.1361i) q^{67} +2.98626 q^{68} +(4.76874 + 0.508997i) q^{69} -1.57355 q^{70} +(0.286605 - 1.99338i) q^{71} +(0.415415 + 0.909632i) q^{72} +(-1.77683 - 0.521724i) q^{73} +(-6.99603 - 8.07385i) q^{74} +(0.959493 - 0.281733i) q^{75} +(-0.613792 - 0.394460i) q^{76} +(1.41676 - 3.10227i) q^{77} +(-0.138814 + 0.160200i) q^{78} +(2.50585 - 1.61041i) q^{79} +(-0.142315 - 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-8.85471 + 5.69058i) q^{82} +(-3.99455 + 4.60995i) q^{83} +(0.653678 - 1.43135i) q^{84} +(2.51220 + 1.61449i) q^{85} +(9.13700 - 2.68287i) q^{86} +(4.08016 + 4.70876i) q^{87} +(2.07957 + 0.610617i) q^{88} +(5.73900 + 12.5667i) q^{89} +(-0.142315 + 0.989821i) q^{90} +0.333553 q^{91} +(3.50754 - 3.27065i) q^{92} +4.23713 q^{93} +(0.728876 - 5.06944i) q^{94} +(-0.303093 - 0.663682i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-5.45096 - 6.29074i) q^{97} +(4.34068 - 1.27454i) q^{98} +(-1.82330 - 1.17177i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Introduction

L-functions

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