LMFDB - Embedded newform 690.2.m.f.31.2

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} - 6 x^{19} + 36 x^{18} - 172 x^{17} + 691 x^{16} - 2342 x^{15} + 7870 x^{14} - 23240 x^{13} + \cdots + 123904 $ x^20 - 6x^19 + 36x^18 - 172x^17 + 691x^16 - 2342x^15 + 7870x^14 - 23240x^13 + 63837x^12 - 154607x^11 + 334467x^10 - 664202x^9 + 1099560x^8 - 1331000x^7 + 1218096x^6 + 395648x^5 - 588544x^4 + 665984x^3 + 2323200x^2 + 991232*x + 123904
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			31.2
Root			$-1.91971 - 2.21546i$ of defining polynomial
Character	$\chi$	$=$	690.31
Dual form			690.2.m.f.601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 - 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(1.55070 + 0.996574i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(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} +(1.55070 + 0.996574i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(0.841254 - 0.540641i) q^{10} +(0.0871226 + 0.605951i) q^{11} +(0.142315 + 0.989821i) q^{12} +(4.39743 - 2.82606i) q^{13} +(1.20712 - 1.39309i) q^{14} +(0.415415 - 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(0.716207 - 0.210297i) q^{17} +(0.654861 + 0.755750i) q^{18} +(0.112406 + 0.0330053i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(0.262332 - 1.82456i) q^{21} +0.612182 q^{22} +(4.77332 - 0.464120i) q^{23} +1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(-2.17147 - 4.75486i) q^{26} +(0.959493 + 0.281733i) q^{27} +(-1.20712 - 1.39309i) q^{28} +(1.21541 - 0.356875i) q^{29} +(-0.841254 - 0.540641i) q^{30} +(3.68368 - 8.06613i) q^{31} +(0.654861 - 0.755750i) q^{32} +(0.515001 - 0.330971i) q^{33} +(-0.106230 - 0.738845i) q^{34} +(0.262332 + 1.82456i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-1.14301 + 1.31910i) q^{37} +(0.0486663 - 0.106564i) q^{38} +(-4.39743 - 2.82606i) q^{39} +(-0.959493 + 0.281733i) q^{40} +(3.17364 + 3.66258i) q^{41} +(-1.76865 - 0.519323i) q^{42} +(-1.41381 - 3.09582i) q^{43} +(0.0871226 - 0.605951i) q^{44} -1.00000 q^{45} +(0.219918 - 4.79079i) q^{46} -11.0065 q^{47} +(0.142315 - 0.989821i) q^{48} +(-1.49640 - 3.27665i) q^{49} +(0.959493 + 0.281733i) q^{50} +(-0.488816 - 0.564124i) q^{51} +(-5.01549 + 1.47268i) q^{52} +(2.36926 + 1.52263i) q^{53} +(0.415415 - 0.909632i) q^{54} +(-0.400894 + 0.462657i) q^{55} +(-1.55070 + 0.996574i) q^{56} +(-0.0166723 - 0.115959i) q^{57} +(-0.180273 - 1.25382i) q^{58} +(-2.82619 + 1.81629i) q^{59} +(-0.654861 + 0.755750i) q^{60} +(1.89805 - 4.15614i) q^{61} +(-7.45978 - 4.79411i) q^{62} +(-1.76865 + 0.519323i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(5.01549 + 1.47268i) q^{65} +(-0.254310 - 0.556861i) q^{66} +(-0.108339 + 0.753513i) q^{67} -0.746443 q^{68} +(-2.40509 - 4.14916i) q^{69} +1.84332 q^{70} +(-0.0729397 + 0.507307i) q^{71} +(-0.415415 - 0.909632i) q^{72} +(13.6625 + 4.01168i) q^{73} +(1.14301 + 1.31910i) q^{74} +(0.959493 - 0.281733i) q^{75} +(-0.0985537 - 0.0633366i) q^{76} +(-0.468774 + 1.02647i) q^{77} +(-3.42311 + 3.95048i) q^{78} +(-0.228674 + 0.146960i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(4.07695 - 2.62010i) q^{82} +(-5.55705 + 6.41318i) q^{83} +(-0.765742 + 1.67674i) q^{84} +(0.627948 + 0.403558i) q^{85} +(-3.26552 + 0.958843i) q^{86} +(-0.829523 - 0.957321i) q^{87} +(-0.587385 - 0.172472i) q^{88} +(-3.22000 - 7.05081i) q^{89} +(-0.142315 + 0.989821i) q^{90} +9.63546 q^{91} +(-4.71073 - 0.899480i) q^{92} -8.86746 q^{93} +(-1.56638 + 10.8944i) q^{94} +(0.0486663 + 0.106564i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(5.14880 + 5.94204i) q^{97} +(-3.45626 + 1.01485i) q^{98} +(-0.515001 - 0.330971i) 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	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + 18 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 13 q^{21} + 26 q^{22} + 20 q^{24} - 2 q^{25} + 9 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} + 8 q^{31} + 2 q^{32} + 4 q^{33} + 13 q^{34} + 13 q^{35} - 2 q^{36} + 16 q^{37} - 15 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} + 9 q^{42} - 16 q^{43} + 18 q^{44} - 20 q^{45} - 34 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} - 9 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 7 q^{55} + 2 q^{56} + 29 q^{57} + 16 q^{58} + 25 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 9 q^{63} - 2 q^{64} - 2 q^{65} - 15 q^{66} + 20 q^{67} - 2 q^{68} - 22 q^{69} - 2 q^{70} - q^{71} + 2 q^{72} - q^{73} - 16 q^{74} + 2 q^{75} + 4 q^{76} + 53 q^{77} + 2 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} - 25 q^{82} + 9 q^{83} - 9 q^{84} - 9 q^{85} - 28 q^{86} - 6 q^{87} - 7 q^{88} - 31 q^{89} - 2 q^{90} - 26 q^{91} + 11 q^{92} - 30 q^{93} + q^{94} - 15 q^{95} - 2 q^{96} - 35 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 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 + 18 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 13 * q^21 + 26 * q^22 + 20 * q^24 - 2 * q^25 + 9 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 + 8 * q^31 + 2 * q^32 + 4 * q^33 + 13 * q^34 + 13 * q^35 - 2 * q^36 + 16 * q^37 - 15 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 + 9 * q^42 - 16 * q^43 + 18 * q^44 - 20 * q^45 - 34 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 - 9 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 7 * q^55 + 2 * q^56 + 29 * q^57 + 16 * q^58 + 25 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 9 * q^63 - 2 * q^64 - 2 * q^65 - 15 * q^66 + 20 * q^67 - 2 * q^68 - 22 * q^69 - 2 * q^70 - q^71 + 2 * q^72 - q^73 - 16 * q^74 + 2 * q^75 + 4 * q^76 + 53 * q^77 + 2 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 - 25 * q^82 + 9 * q^83 - 9 * q^84 - 9 * q^85 - 28 * q^86 - 6 * q^87 - 7 * q^88 - 31 * q^89 - 2 * q^90 - 26 * q^91 + 11 * q^92 - 30 * q^93 + q^94 - 15 * q^95 - 2 * q^96 - 35 * q^97 - 5 * q^98 - 4 * 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
$7$	1.55070	+	0.996574i	0.586109	+	0.376669i	0.799831	−	0.600225i	$-0.204922\pi$
$7$	1.55070	+	0.996574i	0.586109	+	0.376669i	−0.213722	+	0.976895i	$0.568559\pi$
$8$	−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
$11$	0.0871226	+	0.605951i	0.0262685	+	0.182701i	0.998731	−	0.0503569i	$-0.0160359\pi$
$11$	0.0871226	+	0.605951i	0.0262685	+	0.182701i	−0.972463	+	0.233058i	$0.925127\pi$
$12$	0.142315	+	0.989821i	0.0410828	+	0.285737i
$13$	4.39743	−	2.82606i	1.21963	−	0.783807i	0.237384	−	0.971416i	$-0.423710\pi$
$13$	4.39743	−	2.82606i	1.21963	−	0.783807i	0.982244	+	0.187609i	$0.0600738\pi$
$14$	1.20712	−	1.39309i	0.322616	−	0.372318i
$15$	0.415415	−	0.909632i	0.107260	−	0.234866i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	0.716207	−	0.210297i	0.173706	−	0.0510046i	−0.193723	−	0.981056i	$-0.562056\pi$
$17$	0.716207	−	0.210297i	0.173706	−	0.0510046i	0.367429	+	0.930052i	$0.380238\pi$
$18$	0.654861	+	0.755750i	0.154352	+	0.178132i
$19$	0.112406	+	0.0330053i	0.0257876	+	0.00757193i	0.294601	−	0.955620i	$-0.404813\pi$
$19$	0.112406	+	0.0330053i	0.0257876	+	0.00757193i	−0.268813	+	0.963192i	$0.586631\pi$
$20$	−0.415415	−	0.909632i	−0.0928896	−	0.203400i
$21$	0.262332	−	1.82456i	0.0572455	−	0.398151i
$22$	0.612182			0.130518
$23$	4.77332	−	0.464120i	0.995306	−	0.0967757i
$23$	4.77332	−	0.464120i	0.995306	−	0.0967757i
$24$	1.00000			0.204124
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$	−2.17147	−	4.75486i	−0.425861	−	0.932505i
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$	−1.20712	−	1.39309i	−0.228124	−	0.263269i
$29$	1.21541	−	0.356875i	0.225695	−	0.0662701i	−0.166930	−	0.985969i	$-0.553385\pi$
$29$	1.21541	−	0.356875i	0.225695	−	0.0662701i	0.392625	+	0.919699i	$0.371567\pi$
$30$	−0.841254	−	0.540641i	−0.153591	−	0.0987071i
$31$	3.68368	−	8.06613i	0.661608	−	1.44872i	−0.219408	−	0.975633i	$-0.570413\pi$
$31$	3.68368	−	8.06613i	0.661608	−	1.44872i	0.881016	−	0.473086i	$-0.156860\pi$
$32$	0.654861	−	0.755750i	0.115764	−	0.133599i
$33$	0.515001	−	0.330971i	0.0896501	−	0.0576146i
$34$	−0.106230	−	0.738845i	−0.0182183	−	0.126711i
$35$	0.262332	+	1.82456i	0.0443421	+	0.308406i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	−1.14301	+	1.31910i	−0.187909	+	0.216859i	−0.841885	−	0.539656i	$-0.818554\pi$
$37$	−1.14301	+	1.31910i	−0.187909	+	0.216859i	0.653976	+	0.756515i	$0.273100\pi$
$38$	0.0486663	−	0.106564i	0.00789472	−	0.0172870i
$39$	−4.39743	−	2.82606i	−0.704152	−	0.452531i
$40$	−0.959493	+	0.281733i	−0.151709	+	0.0445458i
$41$	3.17364	+	3.66258i	0.495639	+	0.571998i	0.947364	−	0.320159i	$-0.103736\pi$
$41$	3.17364	+	3.66258i	0.495639	+	0.571998i	−0.451724	+	0.892157i	$0.649191\pi$
$42$	−1.76865	−	0.519323i	−0.272909	−	0.0801333i
$43$	−1.41381	−	3.09582i	−0.215605	−	0.472108i	0.770667	−	0.637238i	$-0.219923\pi$
$43$	−1.41381	−	3.09582i	−0.215605	−	0.472108i	−0.986272	+	0.165129i	$0.947196\pi$
$44$	0.0871226	−	0.605951i	0.0131342	−	0.0913506i
$45$	−1.00000			−0.149071
$46$	0.219918	−	4.79079i	0.0324252	−	0.706363i
$47$	−11.0065			−1.60546			−0.802728	−	0.596345i	$-0.796619\pi$
$47$	−11.0065			−1.60546			−0.802728	+	0.596345i	$0.796619\pi$
$48$	0.142315	−	0.989821i	0.0205414	−	0.142868i
$49$	−1.49640	−	3.27665i	−0.213771	−	0.468093i
$50$	0.959493	+	0.281733i	0.135693	+	0.0398430i
$51$	−0.488816	−	0.564124i	−0.0684480	−	0.0789932i
$52$	−5.01549	+	1.47268i	−0.695524	+	0.204224i
$53$	2.36926	+	1.52263i	0.325443	+	0.209150i	0.693152	−	0.720791i	$-0.256221\pi$
$53$	2.36926	+	1.52263i	0.325443	+	0.209150i	−0.367709	+	0.929941i	$0.619858\pi$
$54$	0.415415	−	0.909632i	0.0565308	−	0.123785i
$55$	−0.400894	+	0.462657i	−0.0540566	+	0.0623846i
$56$	−1.55070	+	0.996574i	−0.207221	+	0.133173i
$57$	−0.0166723	−	0.115959i	−0.00220830	−	0.0153591i
$58$	−0.180273	−	1.25382i	−0.0236710	−	0.164635i
$59$	−2.82619	+	1.81629i	−0.367939	+	0.236460i	−0.711524	−	0.702661i	$-0.751995\pi$
$59$	−2.82619	+	1.81629i	−0.367939	+	0.236460i	0.343585	+	0.939121i	$0.388359\pi$
$60$	−0.654861	+	0.755750i	−0.0845422	+	0.0975669i
$61$	1.89805	−	4.15614i	0.243020	−	0.532139i	−0.748339	−	0.663316i	$-0.769148\pi$
$61$	1.89805	−	4.15614i	0.243020	−	0.532139i	0.991359	+	0.131177i	$0.0418756\pi$
$62$	−7.45978	−	4.79411i	−0.947393	−	0.608853i
$63$	−1.76865	+	0.519323i	−0.222829	+	0.0654286i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	5.01549	+	1.47268i	0.622095	+	0.182664i
$66$	−0.254310	−	0.556861i	−0.0313034	−	0.0685448i
$67$	−0.108339	+	0.753513i	−0.0132357	+	0.0920563i	−0.995369	−	0.0961327i	$-0.969353\pi$
$67$	−0.108339	+	0.753513i	−0.0132357	+	0.0920563i	0.982133	+	0.188189i	$0.0602618\pi$
$68$	−0.746443			−0.0905195
$69$	−2.40509	−	4.14916i	−0.289539	−	0.499501i
$70$	1.84332			0.220319
$71$	−0.0729397	+	0.507307i	−0.00865635	+	0.0602062i	−0.993692	−	0.112146i	$-0.964228\pi$
$71$	−0.0729397	+	0.507307i	−0.00865635	+	0.0602062i	0.985035	+	0.172352i	$0.0551367\pi$
$72$	−0.415415	−	0.909632i	−0.0489571	−	0.107201i
$73$	13.6625	+	4.01168i	1.59908	+	0.469531i	0.955289	−	0.295673i	$-0.0955437\pi$
$73$	13.6625	+	4.01168i	1.59908	+	0.469531i	0.643788	+	0.765204i	$0.277362\pi$
$74$	1.14301	+	1.31910i	0.132872	+	0.153342i
$75$	0.959493	−	0.281733i	0.110793	−	0.0325317i
$76$	−0.0985537	−	0.0633366i	−0.0113049	−	0.00726521i
$77$	−0.468774	+	1.02647i	−0.0534218	+	0.116977i
$78$	−3.42311	+	3.95048i	−0.387591	+	0.447304i
$79$	−0.228674	+	0.146960i	−0.0257279	+	0.0165343i	−0.553442	−	0.832888i	$-0.686686\pi$
$79$	−0.228674	+	0.146960i	−0.0257279	+	0.0165343i	0.527714	+	0.849422i	$0.323049\pi$
$80$	0.142315	+	0.989821i	0.0159113	+	0.110665i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	4.07695	−	2.62010i	0.450224	−	0.289341i
$83$	−5.55705	+	6.41318i	−0.609966	+	0.703938i	−0.973769	−	0.227538i	$-0.926932\pi$
$83$	−5.55705	+	6.41318i	−0.609966	+	0.703938i	0.363804	+	0.931476i	$0.381478\pi$
$84$	−0.765742	+	1.67674i	−0.0835494	+	0.182948i
$85$	0.627948	+	0.403558i	0.0681105	+	0.0437720i
$86$	−3.26552	+	0.958843i	−0.352130	+	0.103395i
$87$	−0.829523	−	0.957321i	−0.0889342	−	0.102636i
$88$	−0.587385	−	0.172472i	−0.0626154	−	0.0183855i
$89$	−3.22000	−	7.05081i	−0.341319	−	0.747384i	0.658668	−	0.752433i	$-0.271120\pi$
$89$	−3.22000	−	7.05081i	−0.341319	−	0.747384i	−0.999987	+	0.00504920i	$0.998393\pi$
$90$	−0.142315	+	0.989821i	−0.0150013	+	0.104336i
$91$	9.63546			1.01007
$92$	−4.71073	−	0.899480i	−0.491127	−	0.0937773i
$93$	−8.86746			−0.919513
$94$	−1.56638	+	10.8944i	−0.161560	+	1.12367i
$95$	0.0486663	+	0.106564i	0.00499306	+	0.0109333i
$96$	−0.959493	−	0.281733i	−0.0979278	−	0.0287542i
$97$	5.14880	+	5.94204i	0.522782	+	0.603322i	0.954325	−	0.298770i	$-0.0965763\pi$
$97$	5.14880	+	5.94204i	0.522782	+	0.603322i	−0.431543	+	0.902092i	$0.642031\pi$
$98$	−3.45626	+	1.01485i	−0.349135	+	0.102515i
$99$	−0.515001	−	0.330971i	−0.0517595	−	0.0332638i
$100$	0.415415	−	0.909632i	0.0415415	−	0.0909632i
$101$	8.57508	−	9.89617i	0.853253	−	0.984706i	−0.146737	−	0.989175i	$-0.546877\pi$
$101$	8.57508	−	9.89617i	0.853253	−	0.984706i	0.999990	+	0.00446957i	$0.00142271\pi$
$102$	−0.627948	+	0.403558i	−0.0621761	+	0.0399582i
$103$	−0.00469252	−	0.0326372i	−0.000462367	−	0.00321584i	0.989589	−	0.143923i	$-0.0459716\pi$
$103$	−0.00469252	−	0.0326372i	−0.000462367	−	0.00321584i	−0.990051	+	0.140707i	$0.955063\pi$
$104$	0.743913	+	5.17403i	0.0729467	+	0.507355i
$105$	1.55070	−	0.996574i	0.151333	−	0.0972556i
$106$	1.84432	−	2.12845i	0.179136	−	0.206734i
$107$	−8.52100	+	18.6584i	−0.823757	+	1.80378i	−0.293434	+	0.955979i	$0.594798\pi$
$107$	−8.52100	+	18.6584i	−0.823757	+	1.80378i	−0.530322	+	0.847796i	$0.677929\pi$
$108$	−0.841254	−	0.540641i	−0.0809497	−	0.0520232i
$109$	−1.45356	+	0.426804i	−0.139226	+	0.0408804i	−0.350603	−	0.936524i	$-0.614023\pi$
$109$	−1.45356	+	0.426804i	−0.139226	+	0.0408804i	0.211377	+	0.977405i	$0.432205\pi$
$110$	0.400894	+	0.462657i	0.0382238	+	0.0441126i
$111$	1.67472	+	0.491741i	0.158957	+	0.0466740i
$112$	0.765742	+	1.67674i	0.0723559	+	0.158437i
$113$	−2.81430	+	19.5739i	−0.264747	+	1.84135i	0.231082	+	0.972934i	$0.425774\pi$
$113$	−2.81430	+	19.5739i	−0.264747	+	1.84135i	−0.495829	+	0.868420i	$0.665136\pi$
$114$	−0.117151			−0.0109722
$115$	3.47662	+	3.30350i	0.324196	+	0.308053i
$116$	−1.26672			−0.117612
$117$	−0.743913	+	5.17403i	−0.0687748	+	0.478339i
$118$	1.39559	+	3.05591i	0.128474	+	0.281320i
$119$	1.32020	+	0.387645i	0.121022	+	0.0355354i
$120$	0.654861	+	0.755750i	0.0597803	+	0.0689902i
$121$	10.1948	−	2.99347i	0.926803	−	0.272134i
$122$	−3.84372	−	2.47021i	−0.347994	−	0.223642i
$123$	2.01322	−	4.40833i	0.181526	−	0.397486i
$124$	−5.80695	+	6.70158i	−0.521480	+	0.601820i
$125$	−0.841254	+	0.540641i	−0.0752440	+	0.0483564i
$126$	0.262332	+	1.82456i	0.0233704	+	0.162544i
$127$	0.610338	+	4.24499i	0.0541587	+	0.376682i	0.998817	+	0.0486263i	$0.0154844\pi$
$127$	0.610338	+	4.24499i	0.0541587	+	0.376682i	−0.944658	+	0.328056i	$0.893607\pi$
$128$	−0.841254	+	0.540641i	−0.0743570	+	0.0477863i
$129$	−2.22874	+	2.57210i	−0.196230	+	0.226461i
$130$	2.17147	−	4.75486i	0.190451	−	0.417029i
$131$	−13.9540	−	8.96771i	−1.21917	−	0.783512i	−0.237000	−	0.971510i	$-0.576164\pi$
$131$	−13.9540	−	8.96771i	−1.21917	−	0.783512i	−0.982170	+	0.187997i	$0.939800\pi$
$132$	−0.587385	+	0.172472i	−0.0511253	+	0.0150117i
$133$	0.141415	+	0.163202i	0.0122622	+	0.0141514i
$134$	0.730425	+	0.214472i	0.0630991	+	0.0185276i
$135$	0.415415	+	0.909632i	0.0357532	+	0.0782887i
$136$	−0.106230	+	0.738845i	−0.00910914	+	0.0633555i
$137$	7.62967			0.651846			0.325923	−	0.945396i	$-0.394325\pi$
$137$	7.62967			0.651846			0.325923	+	0.945396i	$0.394325\pi$
$138$	−4.44921	+	1.79012i	−0.378742	+	0.152385i
$139$	−1.57397			−0.133502			−0.0667512	−	0.997770i	$-0.521263\pi$
$139$	−1.57397			−0.133502			−0.0667512	+	0.997770i	$0.521263\pi$
$140$	0.262332	−	1.82456i	0.0221711	−	0.154203i
$141$	4.57225	+	10.0118i	0.385053	+	0.843148i
$142$	0.491763	+	0.144395i	0.0412678	+	0.0121173i
$143$	2.09557	+	2.41841i	0.175240	+	0.202238i
$144$	−0.959493	+	0.281733i	−0.0799577	+	0.0234777i
$145$	1.06563	+	0.684839i	0.0884957	+	0.0568728i
$146$	5.91523	−	12.9525i	0.489548	−	1.07196i
$147$	−2.35892	+	2.72234i	−0.194561	+	0.224535i
$148$	1.46834	−	0.943645i	0.120697	−	0.0775671i
$149$	2.12060	+	14.7491i	0.173727	+	1.20829i	0.870925	+	0.491416i	$0.163521\pi$
$149$	2.12060	+	14.7491i	0.173727	+	1.20829i	−0.697198	+	0.716878i	$0.745570\pi$
$150$	−0.142315	−	0.989821i	−0.0116200	−	0.0808186i
$151$	9.89381	−	6.35836i	0.805147	−	0.517436i	−0.0721449	−	0.997394i	$-0.522984\pi$
$151$	9.89381	−	6.35836i	0.805147	−	0.517436i	0.877292	+	0.479958i	$0.159348\pi$
$152$	−0.0767176	+	0.0885368i	−0.00622262	+	0.00718129i
$153$	−0.310084	+	0.678988i	−0.0250688	+	0.0548930i
$154$	0.949310	+	0.610085i	0.0764976	+	0.0491620i
$155$	8.50827	−	2.49825i	0.683400	−	0.200664i
$156$	3.42311	+	3.95048i	0.274068	+	0.316291i
$157$	−8.07841	−	2.37204i	−0.644727	−	0.189309i	−0.0570077	−	0.998374i	$-0.518156\pi$
$157$	−8.07841	−	2.37204i	−0.644727	−	0.189309i	−0.587720	+	0.809065i	$0.699974\pi$
$158$	0.112920	+	0.247261i	0.00898346	+	0.0196710i
$159$	0.400808	−	2.78768i	0.0317862	−	0.221078i
$160$	1.00000			0.0790569
$161$	7.86451	+	4.03725i	0.619810	+	0.318180i
$162$	−1.00000			−0.0785674
$163$	1.21104	−	8.42296i	0.0948559	−	0.659737i	−0.885810	−	0.464048i	$-0.846397\pi$
$163$	1.21104	−	8.42296i	0.0948559	−	0.659737i	0.980666	−	0.195689i	$-0.0626944\pi$
$164$	−2.01322	−	4.40833i	−0.157206	−	0.344233i
$165$	0.587385	+	0.172472i	0.0457278	+	0.0134269i
$166$	5.55705	+	6.41318i	0.431311	+	0.497759i
$167$	−10.5823	+	3.10725i	−0.818884	+	0.240446i	−0.664235	−	0.747524i	$-0.731243\pi$
$167$	−10.5823	+	3.10725i	−0.818884	+	0.240446i	−0.154648	+	0.987970i	$0.549425\pi$
$168$	1.55070	+	0.996574i	0.119639	+	0.0768873i
$169$	5.95039	−	13.0295i	0.457722	−	1.00227i
$170$	0.488816	−	0.564124i	0.0374905	−	0.0432663i
$171$	−0.0985537	+	0.0633366i	−0.00753659	+	0.00484347i
$172$	0.484351	+	3.36874i	0.0369314	+	0.256864i
$173$	1.22387	+	8.51220i	0.0930490	+	0.647170i	0.981960	+	0.189090i	$0.0605537\pi$
$173$	1.22387	+	8.51220i	0.0930490	+	0.647170i	−0.888911	+	0.458080i	$0.848537\pi$
$174$	−1.06563	+	0.684839i	−0.0807852	+	0.0519175i
$175$	−1.20712	+	1.39309i	−0.0912495	+	0.105308i
$176$	−0.254310	+	0.556861i	−0.0191693	+	0.0419749i
$177$	2.82619	+	1.81629i	0.212430	+	0.136520i
$178$	−7.43729	+	2.18379i	−0.557449	+	0.163682i
$179$	−8.69866	−	10.0388i	−0.650169	−	0.750335i	0.330970	−	0.943641i	$-0.392624\pi$
$179$	−8.69866	−	10.0388i	−0.650169	−	0.750335i	−0.981138	+	0.193307i	$0.938079\pi$
$180$	0.959493	+	0.281733i	0.0715164	+	0.0209991i
$181$	6.21080	+	13.5998i	0.461645	+	1.01086i	0.987110	+	0.160046i	$0.0511644\pi$
$181$	6.21080	+	13.5998i	0.461645	+	1.01086i	−0.525464	+	0.850816i	$0.676108\pi$
$182$	1.37127	−	9.53738i	0.101645	−	0.706958i
$183$	−4.56904			−0.337753
$184$	−1.56073	+	4.53477i	−0.115059	+	0.334308i
$185$	−1.74542			−0.128326
$186$	−1.26197	+	8.77720i	−0.0925322	+	0.643576i
$187$	0.189828	+	0.415665i	0.0138816	+	0.0303964i
$188$	10.5606	+	3.10088i	0.770212	+	0.226155i
$189$	1.20712	+	1.39309i	0.0878049	+	0.101332i
$190$	0.112406	−	0.0330053i	0.00815476	−	0.00239445i
$191$	−12.1287	−	7.79466i	−0.877604	−	0.564002i	0.0224659	−	0.999748i	$-0.492848\pi$
$191$	−12.1287	−	7.79466i	−0.877604	−	0.564002i	−0.900070	+	0.435746i	$0.856485\pi$
$192$	−0.415415	+	0.909632i	−0.0299800	+	0.0656470i
$193$	−4.47634	+	5.16597i	−0.322214	+	0.371855i	−0.893629	−	0.448806i	$-0.851849\pi$
$193$	−4.47634	+	5.16597i	−0.322214	+	0.371855i	0.571415	+	0.820661i	$0.306395\pi$
$194$	6.61431	−	4.25076i	0.474879	−	0.305187i
$195$	−0.743913	−	5.17403i	−0.0532727	−	0.370520i
$196$	0.512643	+	3.56551i	0.0366173	+	0.254679i
$197$	−12.8348	+	8.24842i	−0.914441	+	0.587675i	−0.911040	−	0.412319i	$-0.864719\pi$
$197$	−12.8348	+	8.24842i	−0.914441	+	0.587675i	−0.00340114	+	0.999994i	$0.501083\pi$
$198$	−0.400894	+	0.462657i	−0.0284903	+	0.0328796i
$199$	−8.83026	+	19.3356i	−0.625961	+	1.37066i	0.285143	+	0.958485i	$0.407959\pi$
$199$	−8.83026	+	19.3356i	−0.625961	+	1.37066i	−0.911104	+	0.412177i	$0.864768\pi$
$200$	−0.841254	−	0.540641i	−0.0594856	−	0.0382291i
$201$	0.730425	−	0.214472i	0.0515202	−	0.0151277i
$202$	−8.57508	−	9.89617i	−0.603341	−	0.696292i
$203$	2.24038	+	0.657835i	0.157244	+	0.0461710i
$204$	0.310084	+	0.678988i	0.0217102	+	0.0475387i
$205$	−0.689698	+	4.79695i	−0.0481706	+	0.335034i
$206$	−0.0329728			−0.00229732
$207$	−2.77510	+	3.91137i	−0.192883	+	0.271859i
$208$	5.22723			0.362443
$209$	−0.0102065	+	0.0709878i	−0.000705999	+	0.00491033i
$210$	−0.765742	−	1.67674i	−0.0528412	−	0.115706i
$211$	−8.00931	−	2.35175i	−0.551384	−	0.161901i	−0.00583945	−	0.999983i	$-0.501859\pi$
$211$	−8.00931	−	2.35175i	−0.551384	−	0.161901i	−0.545544	+	0.838082i	$0.683677\pi$
$212$	−1.84432	−	2.12845i	−0.126668	−	0.146183i
$213$	0.491763	−	0.144395i	0.0336950	−	0.00989375i
$214$	17.2558	+	11.0896i	1.17958	+	0.758072i
$215$	1.41381	−	3.09582i	0.0964213	−	0.211133i
$216$	−0.654861	+	0.755750i	−0.0445576	+	0.0514222i
$217$	13.7508	−	8.83708i	0.933462	−	0.599900i
$218$	0.215597	+	1.49951i	0.0146020	+	0.101559i
$219$	−2.02647	−	14.0944i	−0.136936	−	0.952410i
$220$	0.515001	−	0.330971i	0.0347213	−	0.0223140i
$221$	2.55516	−	2.94881i	0.171878	−	0.198358i
$222$	0.725073	−	1.58769i	0.0486637	−	0.106559i
$223$	−20.9821	−	13.4844i	−1.40506	−	0.902980i	−0.405128	−	0.914260i	$-0.632773\pi$
$223$	−20.9821	−	13.4844i	−1.40506	−	0.902980i	−0.999936	+	0.0112796i	$0.996410\pi$
$224$	1.76865	−	0.519323i	0.118173	−	0.0346987i
$225$	−0.654861	−	0.755750i	−0.0436574	−	0.0503833i
$226$	18.9741	+	5.57130i	1.26214	+	0.370598i
$227$	0.0601815	+	0.131779i	0.00399439	+	0.00874649i	0.911619	−	0.411037i	$-0.134833\pi$
$227$	0.0601815	+	0.131779i	0.00399439	+	0.00874649i	−0.907624	+	0.419783i	$0.862106\pi$
$228$	−0.0166723	+	0.115959i	−0.00110415	+	0.00767955i
$229$	−9.67719			−0.639487			−0.319743	−	0.947504i	$-0.603597\pi$
$229$	−9.67719			−0.639487			−0.319743	+	0.947504i	$0.603597\pi$
$230$	3.76465	−	2.97109i	0.248234	−	0.195908i
$231$	1.12845			0.0742464
$232$	−0.180273	+	1.25382i	−0.0118355	+	0.0823175i
$233$	1.75471	+	3.84229i	0.114955	+	0.251717i	0.958360	−	0.285561i	$-0.0921800\pi$
$233$	1.75471	+	3.84229i	0.114955	+	0.251717i	−0.843405	+	0.537278i	$0.819453\pi$
$234$	5.01549	+	1.47268i	0.327873	+	0.0962722i
$235$	−7.20770	−	8.31812i	−0.470178	−	0.542615i
$236$	3.22342	−	0.946482i	0.209827	−	0.0616107i
$237$	0.228674	+	0.146960i	0.0148540	+	0.00954607i
$238$	0.571583	−	1.25159i	0.0370502	−	0.0811287i
$239$	−7.21153	+	8.32255i	−0.466475	+	0.538341i	−0.939428	−	0.342747i	$-0.888643\pi$
$239$	−7.21153	+	8.32255i	−0.466475	+	0.538341i	0.472953	+	0.881088i	$0.343188\pi$
$240$	0.841254	−	0.540641i	0.0543027	−	0.0348982i
$241$	1.36014	+	9.46000i	0.0876145	+	0.609372i	0.985568	+	0.169281i	$0.0541446\pi$
$241$	1.36014	+	9.46000i	0.0876145	+	0.609372i	−0.897953	+	0.440091i	$0.854946\pi$
$242$	−1.51213	−	10.5171i	−0.0972033	−	0.676064i
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$	−2.99208	+	3.45305i	−0.191548	+	0.221059i
$245$	1.49640	−	3.27665i	0.0956013	−	0.209338i
$246$	−4.07695	−	2.62010i	−0.259937	−	0.167051i
$247$	0.587570	−	0.172526i	0.0373862	−	0.0109776i
$248$	5.80695	+	6.70158i	0.368742	+	0.425551i
$249$	8.14211	+	2.39074i	0.515986	+	0.151507i
$250$	0.415415	+	0.909632i	0.0262732	+	0.0575302i
$251$	0.891121	−	6.19788i	0.0562470	−	0.391207i	−0.942178	−	0.335112i	$-0.891226\pi$
$251$	0.891121	−	6.19788i	0.0562470	−	0.391207i	0.998425	−	0.0560950i	$-0.0178650\pi$
$252$	1.84332			0.116118
$253$	0.697098	+	2.85196i	0.0438262	+	0.179301i
$254$	4.28865			0.269094
$255$	0.106230	−	0.738845i	0.00665238	−	0.0462683i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−4.51379	−	1.32537i	−0.281563	−	0.0826742i	0.137902	−	0.990446i	$-0.455964\pi$
$257$	−4.51379	−	1.32537i	−0.281563	−	0.0826742i	−0.419465	+	0.907772i	$0.637782\pi$
$258$	2.22874	+	2.57210i	0.138755	+	0.160132i
$259$	−3.08704	+	0.906436i	−0.191819	+	0.0563232i
$260$	−4.39743	−	2.82606i	−0.272717	−	0.175265i
$261$	−0.526213	+	1.15225i	−0.0325718	+	0.0713222i
$262$	−10.8623	+	12.5358i	−0.671075	+	0.774462i
$263$	26.7195	−	17.1716i	1.64760	−	1.05885i	0.714237	−	0.699904i	$-0.246774\pi$
$263$	26.7195	−	17.1716i	1.64760	−	1.05885i	0.933360	−	0.358943i	$-0.116863\pi$
$264$	0.0871226	+	0.605951i	0.00536203	+	0.0372937i
$265$	0.400808	+	2.78768i	0.0246214	+	0.171246i
$266$	0.181666	−	0.116750i	0.0111387	−	0.00715838i
$267$	−5.07601	+	5.85802i	−0.310647	+	0.358505i
$268$	0.316240	−	0.692468i	0.0193174	−	0.0422992i
$269$	−4.03945	−	2.59599i	−0.246289	−	0.158281i	0.411672	−	0.911332i	$-0.364945\pi$
$269$	−4.03945	−	2.59599i	−0.246289	−	0.158281i	−0.657962	+	0.753051i	$0.728581\pi$
$270$	0.959493	−	0.281733i	0.0583929	−	0.0171457i
$271$	0.124314	+	0.143466i	0.00755156	+	0.00871496i	0.759513	−	0.650492i	$-0.225437\pi$
$271$	0.124314	+	0.143466i	0.00755156	+	0.00871496i	−0.751961	+	0.659207i	$0.770892\pi$
$272$	0.716207	+	0.210297i	0.0434264	+	0.0127511i
$273$	−4.00271	−	8.76472i	−0.242255	−	0.530465i
$274$	1.08581	−	7.55201i	0.0655965	−	0.456234i
$275$	−0.612182			−0.0369160
$276$	1.13871	+	4.65868i	0.0685423	+	0.280420i
$277$	−15.3878			−0.924563			−0.462282	−	0.886733i	$-0.652969\pi$
$277$	−15.3878			−0.924563			−0.462282	+	0.886733i	$0.652969\pi$
$278$	−0.223999	+	1.55795i	−0.0134346	+	0.0934395i
$279$	3.68368	+	8.06613i	0.220536	+	0.482906i
$280$	−1.76865	−	0.519323i	−0.105697	−	0.0310355i
$281$	−14.1357	−	16.3135i	−0.843267	−	0.973182i	0.156628	−	0.987658i	$-0.449938\pi$
$281$	−14.1357	−	16.3135i	−0.843267	−	0.973182i	−0.999895	+	0.0144753i	$0.995392\pi$
$282$	10.5606	−	3.10088i	0.628876	−	0.184655i
$283$	−15.2172	−	9.77953i	−0.904571	−	0.581332i	0.00357159	−	0.999994i	$-0.498863\pi$
$283$	−15.2172	−	9.77953i	−0.904571	−	0.581332i	−0.908143	+	0.418661i	$0.862499\pi$
$284$	0.212910	−	0.466208i	0.0126339	−	0.0276643i
$285$	0.0767176	−	0.0885368i	0.00454436	−	0.00524447i
$286$	2.69203	−	1.73006i	0.159183	−	0.102301i
$287$	1.27133	+	8.84232i	0.0750444	+	0.521945i
$288$	0.142315	+	0.989821i	0.00838598	+	0.0583258i
$289$	−13.8326	+	8.88966i	−0.813681	+	0.522921i
$290$	0.829523	−	0.957321i	0.0487113	−	0.0562158i
$291$	3.26618	−	7.15193i	0.191467	−	0.419253i
$292$	−11.9789	−	7.69835i	−0.701011	−	0.450512i
$293$	4.78417	−	1.40476i	0.279494	−	0.0820670i	−0.138981	−	0.990295i	$-0.544383\pi$
$293$	4.78417	−	1.40476i	0.279494	−	0.0820670i	0.418476	+	0.908228i	$0.362565\pi$
$294$	2.35892	+	2.72234i	0.137575	+	0.158770i
$295$	−3.22342	−	0.946482i	−0.187675	−	0.0551063i
$296$	−0.725073	−	1.58769i	−0.0421440	−	0.0922825i
$297$	−0.0871226	+	0.605951i	−0.00505537	+	0.0351609i
$298$	14.9008			0.863179
$299$	19.6787	−	15.5306i	1.13805	−	0.898158i
$300$	−1.00000			−0.0577350
$301$	0.892814	−	6.20966i	0.0514609	−	0.357919i
$302$	−4.88561	−	10.6980i	−0.281135	−	0.615600i
$303$	−12.5641	−	3.68915i	−0.721788	−	0.211936i
$304$	0.0767176	+	0.0885368i	0.00440006	+	0.00507794i
$305$	4.38396	−	1.28725i	0.251025	−	0.0737075i
$306$	0.627948	+	0.403558i	0.0358974	+	0.0230699i
$307$	4.18750	−	9.16934i	0.238993	−	0.523322i	−0.751689	−	0.659518i	$-0.770760\pi$
$307$	4.18750	−	9.16934i	0.238993	−	0.523322i	0.990682	+	0.136196i	$0.0434878\pi$
$308$	0.738976	−	0.852824i	0.0421071	−	0.0485941i
$309$	−0.0277385	+	0.0178264i	−0.00157799	+	0.00101411i
$310$	−1.26197	−	8.77720i	−0.0716752	−	0.498512i
$311$	2.27228	+	15.8040i	0.128849	+	0.896164i	0.947017	+	0.321185i	$0.104081\pi$
$311$	2.27228	+	15.8040i	0.128849	+	0.896164i	−0.818168	+	0.574980i	$0.805010\pi$
$312$	4.39743	−	2.82606i	0.248955	−	0.159994i
$313$	−3.21934	+	3.71532i	−0.181968	+	0.210002i	−0.839404	−	0.543508i	$-0.817096\pi$
$313$	−3.21934	+	3.71532i	−0.181968	+	0.210002i	0.657436	+	0.753510i	$0.271641\pi$
$314$	−3.49757	+	7.65861i	−0.197379	+	0.432200i
$315$	−1.55070	−	0.996574i	−0.0873720	−	0.0561506i
$316$	0.260815	−	0.0765821i	0.0146720	−	0.00430808i
$317$	−4.71256	−	5.43859i	−0.264684	−	0.305462i	0.607814	−	0.794079i	$-0.292047\pi$
$317$	−4.71256	−	5.43859i	−0.264684	−	0.305462i	−0.872498	+	0.488618i	$0.837501\pi$
$318$	−2.70227	−	0.793457i	−0.151536	−	0.0444949i
$319$	0.322138	+	0.705385i	0.0180363	+	0.0394940i
$320$	0.142315	−	0.989821i	0.00795564	−	0.0553327i
$321$	20.5120			1.14487
$322$	5.11540	−	7.20990i	0.285070	−	0.401792i
$323$	0.0874466			0.00486566
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	2.17147	+	4.75486i	0.120452	+	0.263752i
$326$	−8.16488	−	2.39742i	−0.452211	−	0.132781i
$327$	0.992066	+	1.14491i	0.0548614	+	0.0633134i
$328$	−4.64997	+	1.36536i	−0.256752	+	0.0753891i
$329$	−17.0677	−	10.9687i	−0.940973	−	0.604726i
$330$	0.254310	−	0.556861i	0.0139993	−	0.0306542i
$331$	−18.7397	+	21.6268i	−1.03003	+	1.18871i	−0.0482190	+	0.998837i	$0.515355\pi$
$331$	−18.7397	+	21.6268i	−1.03003	+	1.18871i	−0.981808	+	0.189878i	$0.939191\pi$
$332$	7.13875	−	4.58780i	0.391790	−	0.251788i
$333$	−0.248399	−	1.72765i	−0.0136122	−	0.0946748i
$334$	1.56960	+	10.9168i	0.0858847	+	0.597341i
$335$	−0.640414	+	0.411569i	−0.0349896	+	0.0224864i
$336$	1.20712	−	1.39309i	0.0658536	−	0.0759992i
$337$	−10.0458	+	21.9972i	−0.547228	+	1.19826i	0.410836	+	0.911709i	$0.365237\pi$
$337$	−10.0458	+	21.9972i	−0.547228	+	1.19826i	−0.958064	+	0.286554i	$0.907490\pi$
$338$	−12.0501	−	7.74412i	−0.655439	−	0.421225i
$339$	18.9741	−	5.57130i	1.03053	−	0.302592i
$340$	−0.488816	−	0.564124i	−0.0265098	−	0.0305939i
$341$	5.20861	+	1.52939i	0.282062	+	0.0828209i
$342$	0.0486663	+	0.106564i	0.00263157	+	0.00576234i
$343$	2.78129	−	19.3443i	0.150175	−	1.04449i
$344$	3.40338			0.183498
$345$	1.56073	−	4.53477i	0.0840269	−	0.244144i
$346$	8.59973			0.462324
$347$	1.24160	−	8.63555i	0.0666528	−	0.463580i	−0.928973	−	0.370148i	$-0.879307\pi$
$347$	1.24160	−	8.63555i	0.0666528	−	0.463580i	0.995626	−	0.0934325i	$-0.0297839\pi$
$348$	0.526213	+	1.15225i	0.0282080	+	0.0617669i
$349$	10.7224	+	3.14837i	0.573955	+	0.168528i	0.555813	−	0.831307i	$-0.312407\pi$
$349$	10.7224	+	3.14837i	0.573955	+	0.168528i	0.0181416	+	0.999835i	$0.494225\pi$
$350$	1.20712	+	1.39309i	0.0645231	+	0.0744637i
$351$	5.01549	−	1.47268i	0.267707	−	0.0786059i
$352$	0.515001	+	0.330971i	0.0274496	+	0.0176408i
$353$	6.49698	−	14.2264i	0.345799	−	0.757195i	−0.654200	−	0.756321i	$-0.726995\pi$
$353$	6.49698	−	14.2264i	0.345799	−	0.757195i	1.00000		0.000873370i	$-0.000278002\pi$
$354$	2.20001	−	2.53894i	0.116929	−	0.134943i
$355$	−0.431162	+	0.277091i	−0.0228837	+	0.0147065i
$356$	1.10312	+	7.67238i	0.0584653	+	0.406635i
$357$	−0.195816	−	1.36193i	−0.0103637	−	0.0720809i
$358$	−11.1746	+	7.18145i	−0.590594	+	0.379552i
$359$	−8.45871	+	9.76187i	−0.446433	+	0.515212i	−0.933707	−	0.358038i	$-0.883446\pi$
$359$	−8.45871	+	9.76187i	−0.446433	+	0.515212i	0.487274	+	0.873249i	$0.337991\pi$
$360$	0.415415	−	0.909632i	0.0218943	−	0.0479418i
$361$	−15.9723	−	10.2648i	−0.840646	−	0.540250i
$362$	14.3452	−	4.21214i	0.753968	−	0.221385i
$363$	−6.95805	−	8.03002i	−0.365203	−	0.421466i
$364$	−9.24516	−	2.71462i	−0.484578	−	0.142285i
$365$	5.91523	+	12.9525i	0.309617	+	0.677967i
$366$	−0.650242	+	4.52253i	−0.0339887	+	0.236396i
$367$	28.4211			1.48357			0.741786	−	0.670637i	$-0.233979\pi$
$367$	28.4211			1.48357			0.741786	+	0.670637i	$0.233979\pi$
$368$	4.26650	+	2.19021i	0.222406	+	0.114173i
$369$	−4.84628			−0.252287
$370$	−0.248399	+	1.72765i	−0.0129136	+	0.0898164i
$371$	2.15660	+	4.72229i	0.111965	+	0.245169i
$372$	8.50827	+	2.49825i	0.441133	+	0.129528i
$373$	−16.1318	−	18.6170i	−0.835271	−	0.963954i	0.164478	−	0.986381i	$-0.447406\pi$
$373$	−16.1318	−	18.6170i	−0.835271	−	0.963954i	−0.999748	+	0.0224271i	$0.992861\pi$
$374$	0.438449	−	0.128740i	0.0226717	−	0.00665700i
$375$	0.841254	+	0.540641i	0.0434421	+	0.0279186i
$376$	4.57225	−	10.0118i	0.235796	−	0.516320i
$377$	4.33611	−	5.00414i	0.223321	−	0.257726i
$378$	1.55070	−	0.996574i	0.0797593	−	0.0512582i
$379$	−4.89701	−	34.0594i	−0.251542	−	1.74952i	−0.588962	−	0.808161i	$-0.700463\pi$
$379$	−4.89701	−	34.0594i	−0.251542	−	1.74952i	0.337419	−	0.941354i	$-0.390446\pi$
$380$	−0.0166723	−	0.115959i	−0.000855272	−	0.00594855i
$381$	3.60784	−	2.31862i	0.184835	−	0.118786i
$382$	−9.44142	+	10.8960i	−0.483065	+	0.557487i
$383$	−9.37653	+	20.5317i	−0.479118	+	1.04912i	0.503586	+	0.863945i	$0.332014\pi$
$383$	−9.37653	+	20.5317i	−0.479118	+	1.04912i	−0.982705	+	0.185178i	$0.940714\pi$
$384$	0.841254	+	0.540641i	0.0429300	+	0.0275895i
$385$	−1.08274	+	0.317920i	−0.0551814	+	0.0162027i
$386$	4.47634	+	5.16597i	0.227840	+	0.262941i
$387$	3.26552	+	0.958843i	0.165996	+	0.0487407i
$388$	−3.26618	−	7.15193i	−0.165815	−	0.363084i
$389$	2.81409	−	19.5725i	0.142680	−	0.992363i	−0.785135	−	0.619324i	$-0.787407\pi$
$389$	2.81409	−	19.5725i	0.142680	−	0.992363i	0.927816	−	0.373039i	$-0.121684\pi$
$390$	−5.22723			−0.264691
$391$	3.32108	−	1.33622i	0.167954	−	0.0675757i
$392$	3.60217			0.181937
$393$	−2.36060	+	16.4184i	−0.119077	+	0.828196i
$394$	6.33788	+	13.8780i	0.319298	+	0.699165i
$395$	−0.260815	−	0.0765821i	−0.0131230	−	0.00385326i
$396$	0.400894	+	0.462657i	0.0201457	+	0.0232494i
$397$	9.78406	−	2.87286i	0.491048	−	0.144185i	−0.0268286	−	0.999640i	$-0.508541\pi$
$397$	9.78406	−	2.87286i	0.491048	−	0.144185i	0.517877	+	0.855455i	$0.326723\pi$
$398$	17.8821	+	11.4921i	0.896348	+	0.576048i
$399$	0.0897075	−	0.196432i	0.00449099	−	0.00983390i
$400$	−0.654861	+	0.755750i	−0.0327430	+	0.0377875i
$401$	19.0604	−	12.2494i	0.951833	−	0.611706i	0.0301066	−	0.999547i	$-0.490415\pi$
$401$	19.0604	−	12.2494i	0.951833	−	0.611706i	0.921726	+	0.387841i	$0.126779\pi$
$402$	−0.108339	−	0.753513i	−0.00540345	−	0.0375818i
$403$	−6.59662	−	45.8805i	−0.328601	−	2.28547i
$404$	−11.0158	+	7.07943i	−0.548057	+	0.352215i
$405$	0.654861	−	0.755750i	0.0325403	−	0.0375535i
$406$	0.969979	−	2.12396i	0.0481392	−	0.105410i
$407$	−0.898891	−	0.577682i	−0.0445564	−	0.0286347i
$408$	0.716207	−	0.210297i	0.0354575	−	0.0104113i
$409$	−3.92315	−	4.52756i	−0.193987	−	0.223873i	0.650420	−	0.759575i	$-0.274593\pi$
$409$	−3.92315	−	4.52756i	−0.193987	−	0.223873i	−0.844408	+	0.535701i	$0.820047\pi$
$410$	4.64997	+	1.36536i	0.229646	+	0.0674301i
$411$	−3.16948	−	6.94019i	−0.156339	−	0.342334i
$412$	−0.00469252	+	0.0326372i	−0.000231184	+	0.00160792i
$413$	−6.19264			−0.304720
$414$	3.47662	+	3.30350i	0.170867	+	0.162358i
$415$	−8.48585			−0.416554
$416$	0.743913	−	5.17403i	0.0364733	−	0.253678i
$417$	0.653850	+	1.43173i	0.0320192	+	0.0701123i
$418$	0.0688127	+	0.0202052i	0.00336574	+	0.000988270i
$419$	−2.62097	−	3.02477i	−0.128043	−	0.147769i	0.688108	−	0.725608i	$-0.258442\pi$
$419$	−2.62097	−	3.02477i	−0.128043	−	0.147769i	−0.816151	+	0.577839i	$0.803896\pi$
$420$	−1.76865	+	0.519323i	−0.0863014	+	0.0253404i
$421$	−29.9622	−	19.2555i	−1.46027	−	0.938456i	−0.998680	−	0.0513609i	$-0.983644\pi$
$421$	−29.9622	−	19.2555i	−1.46027	−	0.938456i	−0.461586	−	0.887095i	$-0.652720\pi$
$422$	−3.46765	+	7.59310i	−0.168803	+	0.369626i
$423$	7.20770	−	8.31812i	0.350450	−	0.404441i
$424$	−2.36926	+	1.52263i	−0.115062	+	0.0739456i
$425$	0.106230	+	0.738845i	0.00515291	+	0.0358393i
$426$	−0.0729397	−	0.507307i	−0.00353394	−	0.0245791i
$427$	7.08520	−	4.55338i	0.342877	−	0.220354i
$428$	13.4325	−	15.5020i	0.649285	−	0.749315i
$429$	1.32934	−	2.91084i	0.0641810	−	0.140537i
$430$	−2.86310	−	1.84001i	−0.138071	−	0.0887329i
$431$	−8.42494	+	2.47378i	−0.405815	+	0.119158i	−0.478268	−	0.878214i	$-0.658735\pi$
$431$	−8.42494	+	2.47378i	−0.405815	+	0.119158i	0.0724534	+	0.997372i	$0.476917\pi$
$432$	0.654861	+	0.755750i	0.0315070	+	0.0363610i
$433$	4.50220	+	1.32197i	0.216362	+	0.0635296i	0.388117	−	0.921610i	$-0.373126\pi$
$433$	4.50220	+	1.32197i	0.216362	+	0.0635296i	−0.171755	+	0.985140i	$0.554944\pi$
$434$	−6.79019	−	14.8684i	−0.325940	−	0.713708i
$435$	0.180273	−	1.25382i	0.00864341	−	0.0601162i
$436$	1.51493			0.0725518
$437$	0.551866	+	0.105375i	0.0263993	+	0.00504077i
$438$	−14.2393			−0.680381
$439$	−2.04240	+	14.2052i	−0.0974786	+	0.677979i	0.881224	+	0.472698i	$0.156720\pi$
$439$	−2.04240	+	14.2052i	−0.0974786	+	0.677979i	−0.978703	+	0.205281i	$0.934189\pi$
$440$	−0.254310	−	0.556861i	−0.0121237	−	0.0265473i
$441$	3.45626	+	1.01485i	0.164584	+	0.0483262i
$442$	−2.55516	−	2.94881i	−0.121536	−	0.140260i
$443$	−9.53856	+	2.80077i	−0.453191	+	0.133069i	−0.500359	−	0.865818i	$-0.666799\pi$
$443$	−9.53856	+	2.80077i	−0.453191	+	0.133069i	0.0471680	+	0.998887i	$0.484980\pi$
$444$	−1.46834	−	0.943645i	−0.0696843	−	0.0447834i
$445$	3.22000	−	7.05081i	0.152642	−	0.334240i
$446$	−16.3332	+	18.8495i	−0.773399	+	0.892550i
$447$	12.5353	−	8.05597i	0.592901	−	0.381034i
$448$	−0.262332	−	1.82456i	−0.0123940	−	0.0862022i
$449$	1.38603	+	9.64005i	0.0654108	+	0.454942i	0.996035	+	0.0889651i	$0.0283560\pi$
$449$	1.38603	+	9.64005i	0.0654108	+	0.454942i	−0.930624	+	0.365977i	$0.880735\pi$
$450$	−0.841254	+	0.540641i	−0.0396571	+	0.0254861i
$451$	−1.94285	+	2.24216i	−0.0914850	+	0.105579i
$452$	8.21490	−	17.9881i	0.386396	−	0.846090i
$453$	−9.89381	−	6.35836i	−0.464852	−	0.298742i
$454$	0.139002	−	0.0408148i	0.00652371	−	0.00191553i
$455$	6.30988	+	7.28199i	0.295812	+	0.341385i
$456$	0.112406	+	0.0330053i	0.00526387	+	0.00154561i
$457$	9.72738	+	21.3000i	0.455028	+	0.996372i	0.988593	+	0.150613i	$0.0481246\pi$
$457$	9.72738	+	21.3000i	0.455028	+	0.996372i	−0.533565	+	0.845759i	$0.679148\pi$
$458$	−1.37721	+	9.57869i	−0.0643527	+	0.447583i
$459$	0.746443			0.0348410
$460$	−2.40509	−	4.14916i	−0.112138	−	0.193456i
$461$	2.26684			0.105577			0.0527885	−	0.998606i	$-0.483189\pi$
$461$	2.26684			0.105577			0.0527885	+	0.998606i	$0.483189\pi$
$462$	0.160595	−	1.11696i	0.00747155	−	0.0519657i
$463$	0.710309	+	1.55536i	0.0330109	+	0.0722837i	0.925419	−	0.378945i	$-0.123713\pi$
$463$	0.710309	+	1.55536i	0.0330109	+	0.0722837i	−0.892408	+	0.451229i	$0.850986\pi$
$464$	1.21541	+	0.356875i	0.0564238	+	0.0165675i
$465$	−5.80695	−	6.70158i	−0.269291	−	0.310778i
$466$	4.05290	−	1.19004i	0.187747	−	0.0551275i
$467$	10.4863	+	6.73915i	0.485249	+	0.311851i	0.760292	−	0.649581i	$-0.225056\pi$
$467$	10.4863	+	6.73915i	0.485249	+	0.311851i	−0.275043	+	0.961432i	$0.588692\pi$
$468$	2.17147	−	4.75486i	0.100376	−	0.219793i
$469$	−0.918932	+	1.06050i	−0.0424323	+	0.0489695i
$470$	−9.25922	+	5.95054i	−0.427096	+	0.274478i
$471$	1.19821	+	8.33376i	0.0552108	+	0.383999i
$472$	−0.478107	−	3.32531i	−0.0220067	−	0.153060i
$473$	1.75274	−	1.12642i	0.0805911	−	0.0517928i
$474$	0.178008	−	0.205432i	0.00817617	−	0.00943580i
$475$	−0.0486663	+	0.106564i	−0.00223296	+	0.00488951i
$476$	−1.15751	−	0.743885i	−0.0530543	−	0.0340959i
$477$	−2.70227	+	0.793457i	−0.123728	+	0.0363299i
$478$	7.21153	+	8.32255i	0.329848	+	0.380664i
$479$	−6.72557	−	1.97481i	−0.307299	−	0.0902312i	0.124447	−	0.992226i	$-0.460284\pi$
$479$	−6.72557	−	1.97481i	−0.307299	−	0.0902312i	−0.431746	+	0.901995i	$0.642102\pi$
$480$	−0.415415	−	0.909632i	−0.0189610	−	0.0415188i
$481$	−1.29844	+	9.03084i	−0.0592037	+	0.411771i
$482$	9.55728			0.435322
$483$	0.405380	−	8.83095i	0.0184454	−	0.401822i
$484$	−10.6252			−0.482965
$485$	−1.11894	+	7.78241i	−0.0508085	+	0.353381i
$486$	0.415415	+	0.909632i	0.0188436	+	0.0412617i
$487$	30.3602	+	8.91455i	1.37575	+	0.403957i	0.884288	−	0.466941i	$-0.154644\pi$
$487$	30.3602	+	8.91455i	1.37575	+	0.403957i	0.491463	+	0.870898i	$0.336462\pi$
$488$	2.99208	+	3.45305i	0.135445	+	0.156312i
$489$	−8.16488	+	2.39742i	−0.369228	+	0.108415i
$490$	−3.03034	−	1.94748i	−0.136897	−	0.0879783i
$491$	0.854124	−	1.87027i	0.0385461	−	0.0844041i	−0.889379	−	0.457170i	$-0.848863\pi$
$491$	0.854124	−	1.87027i	0.0385461	−	0.0844041i	0.927926	+	0.372766i	$0.121590\pi$
$492$	−3.17364	+	3.66258i	−0.143079	+	0.165122i
$493$	0.795432	−	0.511193i	0.0358245	−	0.0230230i
$494$	−0.0871502	−	0.606143i	−0.00392107	−	0.0272716i
$495$	−0.0871226	−	0.605951i	−0.00391587	−	0.0272355i
$496$	7.45978	−	4.79411i	0.334954	−	0.215262i
$497$	−0.618676	+	0.713990i	−0.0277514	+	0.0320268i
$498$	3.52515	−	7.71900i	0.157966	−	0.345897i
$499$	7.00666	+	4.50291i	0.313661	+	0.201578i	0.687993	−	0.725717i	$-0.258492\pi$
$499$	7.00666	+	4.50291i	0.313661	+	0.201578i	−0.374332	+	0.927295i	$0.622128\pi$
$500$	0.959493	−	0.281733i	0.0429098	−	0.0125995i
$501$	7.22250	+	8.33521i	0.322678	+	0.372390i
$502$	−6.00798	−	1.76410i	−0.268149	−	0.0787357i
$503$	9.14963	+	20.0349i	0.407962	+	0.893312i	0.996401	+	0.0847698i	$0.0270155\pi$
$503$	9.14963	+	20.0349i	0.407962	+	0.893312i	−0.588439	+	0.808542i	$0.700257\pi$
$504$	0.262332	−	1.82456i	0.0116852	−	0.0812722i
$505$	13.0945			0.582698
$506$	2.92214	−	0.284126i	0.129905	−	0.0126309i
$507$	−14.3240			−0.636150
$508$	0.610338	−	4.24499i	0.0270794	−	0.188341i
$509$	−8.45134	−	18.5058i	−0.374599	−	0.820257i	−0.999226	−	0.0393341i	$-0.987476\pi$
$509$	−8.45134	−	18.5058i	−0.374599	−	0.820257i	0.624627	−	0.780923i	$-0.285251\pi$
$510$	−0.716207	−	0.210297i	−0.0317142	−	0.00931212i
$511$	17.1885	+	19.8366i	0.760376	+	0.877520i
$512$	0.959493	−	0.281733i	0.0424040	−	0.0124509i
$513$	0.0985537	+	0.0633366i	0.00435125	+	0.00279638i
$514$	−1.95426	+	4.27923i	−0.0861986	+	0.188749i
$515$	0.0215926	−	0.0249192i	0.000951483	−	0.00109807i
$516$	2.86310	−	1.84001i	0.126041	−	0.0810017i
$517$	−0.958911	−	6.66937i	−0.0421729	−	0.293319i
$518$	0.457879	+	3.18462i	0.0201180	+	0.139924i
$519$	7.23455	−	4.64936i	0.317562	−	0.204084i
$520$	−3.42311	+	3.95048i	−0.150113	+	0.173240i
$521$	7.72860	−	16.9233i	0.338596	−	0.741422i	−0.661367	−	0.750063i	$-0.730023\pi$
$521$	7.72860	−	16.9233i	0.338596	−	0.741422i	0.999963	+	0.00864104i	$0.00275056\pi$
$522$	1.06563	+	0.684839i	0.0466414	+	0.0299746i
$523$	−20.7227	+	6.08473i	−0.906140	+	0.266067i	−0.701415	−	0.712753i	$-0.747448\pi$
$523$	−20.7227	+	6.08473i	−0.906140	+	0.266067i	−0.204725	+	0.978820i	$0.565630\pi$
$524$	10.8623	+	12.5358i	0.474522	+	0.547627i
$525$	1.76865	+	0.519323i	0.0771903	+	0.0226651i
$526$	−13.1942	−	28.8913i	−0.575296	−	1.25972i
$527$	0.941990	−	6.55168i	0.0410337	−	0.285396i
$528$	0.612182			0.0266418
$529$	22.5692	−	4.43079i	0.981269	−	0.192643i
$530$	2.81635			0.122334
$531$	0.478107	−	3.32531i	0.0207481	−	0.144306i
$532$	−0.0897075	−	0.196432i	−0.00388931	−	0.00851641i
$533$	24.3065	+	7.13703i	1.05283	+	0.309139i
$534$	5.07601	+	5.85802i	0.219660	+	0.253501i
$535$	−19.6811	+	5.77891i	−0.850890	+	0.249844i
$536$	−0.640414	−	0.411569i	−0.0276617	−	0.0177771i
$537$	−5.51805	+	12.0828i	−0.238122	+	0.521413i
$538$	−3.14444	+	3.62888i	−0.135567	+	0.156452i
$539$	1.85512	−	1.19221i	0.0799057	−	0.0513523i
$540$	−0.142315	−	0.989821i	−0.00612426	−	0.0425951i
$541$	5.29365	+	36.8181i	0.227592	+	1.58294i	0.708208	+	0.706004i	$0.249504\pi$
$541$	5.29365	+	36.8181i	0.227592	+	1.58294i	−0.480616	+	0.876931i	$0.659587\pi$
$542$	0.159698	−	0.102632i	0.00685961	−	0.00440841i
$543$	9.79071	−	11.2991i	0.420160	−	0.484890i
$544$	0.310084	−	0.678988i	0.0132947	−	0.0291114i
$545$	−1.27444	−	0.819031i	−0.0545909	−	0.0350834i
$546$	−9.24516	+	2.71462i	−0.395656	+	0.116175i
$547$	−28.1505	−	32.4875i	−1.20363	−	1.38906i	−0.899780	−	0.436343i	$-0.856273\pi$
$547$	−28.1505	−	32.4875i	−1.20363	−	1.38906i	−0.303850	−	0.952720i	$-0.598272\pi$
$548$	−7.32061	−	2.14953i	−0.312721	−	0.0918232i
$549$	1.89805	+	4.15614i	0.0810066	+	0.177380i
$550$	−0.0871226	+	0.605951i	−0.00371492	+	0.0258378i
$551$	0.148397			0.00632193
$552$	4.77332	−	0.464120i	0.203166	−	0.0197543i
$553$	−0.501061			−0.0213073
$554$	−2.18991	+	15.2312i	−0.0930405	+	0.647111i
$555$	0.725073	+	1.58769i	0.0307776	+	0.0673936i
$556$	1.51021	+	0.443438i	0.0640473	+	0.0188060i
$557$	4.81988	+	5.56244i	0.204225	+	0.235688i	0.848618	−	0.529007i	$-0.177435\pi$
$557$	4.81988	+	5.56244i	0.204225	+	0.235688i	−0.644393	+	0.764695i	$0.722890\pi$
$558$	8.50827	−	2.49825i	0.360184	−	0.105759i
$559$	−14.9661	−	9.61814i	−0.632999	−	0.406804i
$560$	−0.765742	+	1.67674i	−0.0323585	+	0.0708553i
$561$	0.299245	−	0.345347i	0.0126341	−	0.0145806i
$562$	−18.1592	+	11.6702i	−0.765999	+	0.492278i
$563$	0.131925	+	0.917560i	0.00555998	+	0.0386705i	0.992413	−	0.122952i	$-0.0392363\pi$
$563$	0.131925	+	0.917560i	0.00555998	+	0.0386705i	−0.986853	+	0.161623i	$0.948327\pi$
$564$	−1.56638	−	10.8944i	−0.0659566	−	0.458738i
$565$	−16.6359	+	10.6913i	−0.699878	+	0.449784i
$566$	−11.8456	+	13.6706i	−0.497909	+	0.574617i
$567$	0.765742	−	1.67674i	0.0321582	−	0.0704165i
$568$	−0.431162	−	0.277091i	−0.0180912	−	0.0116265i
$569$	35.8751	−	10.5339i	1.50396	−	0.441603i	0.576996	−	0.816747i	$-0.304225\pi$
$569$	35.8751	−	10.5339i	1.50396	−	0.441603i	0.926966	+	0.375144i	$0.122407\pi$
$570$	−0.0767176	−	0.0885368i	−0.00321335	−	0.00370840i
$571$	20.8021	+	6.10804i	0.870540	+	0.255614i	0.686345	−	0.727276i	$-0.259214\pi$
$571$	20.8021	+	6.10804i	0.870540	+	0.255614i	0.184195	+	0.982890i	$0.441032\pi$
$572$	−1.32934	−	2.91084i	−0.0555823	−	0.121708i
$573$	−2.05182	+	14.2707i	−0.0857159	+	0.596167i
$574$	8.93324			0.372866
$575$	−0.219918	+	4.79079i	−0.00917123	+	0.199790i
$576$	1.00000			0.0416667
$577$	−2.87918	+	20.0251i	−0.119862	+	0.833657i	0.837844	+	0.545909i	$0.183816\pi$
$577$	−2.87918	+	20.0251i	−0.119862	+	0.833657i	−0.957706	+	0.287748i	$0.907093\pi$
$578$	6.83060	+	14.9569i	0.284115	+	0.622126i
$579$	6.55867	+	1.92580i	0.272569	+	0.0800335i
$580$	−0.829523	−	0.957321i	−0.0344441	−	0.0397506i
$581$	−15.0085	+	4.40690i	−0.622658	+	0.182829i
$582$	−6.61431	−	4.25076i	−0.274172	−	0.176200i
$583$	−0.716225	+	1.56831i	−0.0296630	+	0.0649529i
$584$	−9.32477	+	10.7614i	−0.385862	+	0.445308i
$585$	−4.39743	+	2.82606i	−0.181811	+	0.116843i
$586$	−0.709603	−	4.93540i	−0.0293134	−	0.203879i
$587$	5.69768	+	39.6283i	0.235169	+	1.63563i	0.675189	+	0.737645i	$0.264062\pi$
$587$	5.69768	+	39.6283i	0.235169	+	1.63563i	−0.440020	+	0.897988i	$0.645029\pi$
$588$	3.03034	−	1.94748i	0.124969	−	0.0803128i
$589$	0.680290	−	0.785097i	0.0280309	−	0.0323494i
$590$	−1.39559	+	3.05591i	−0.0574555	+	0.125810i
$591$	12.8348	+	8.24842i	0.527953	+	0.339295i
$592$	−1.67472	+	0.491741i	−0.0688304	+	0.0202104i
$593$	31.6162	+	36.4871i	1.29832	+	1.49834i	0.748651	+	0.662964i	$0.230702\pi$
$593$	31.6162	+	36.4871i	1.29832	+	1.49834i	0.549672	+	0.835381i	$0.314753\pi$
$594$	0.587385	+	0.172472i	0.0241007	+	0.00707660i
$595$	0.571583	+	1.25159i	0.0234326	+	0.0513103i
$596$	2.12060	−	14.7491i	0.0868633	−	0.604147i
$597$	21.2565			0.869970
$598$	−12.5720	−	21.6886i	−0.514105	−	0.886915i
$599$	22.4569			0.917563			0.458782	−	0.888549i	$-0.348286\pi$
$599$	22.4569			0.917563			0.458782	+	0.888549i	$0.348286\pi$
$600$	−0.142315	+	0.989821i	−0.00580998	+	0.0404093i
$601$	7.35498	+	16.1051i	0.300016	+	0.656943i	0.998263	−	0.0589138i	$-0.0187637\pi$
$601$	7.35498	+	16.1051i	0.300016	+	0.656943i	−0.698247	+	0.715857i	$0.746036\pi$
$602$	−6.01939	−	1.76745i	−0.245332	−	0.0720360i
$603$	−0.498520	−	0.575323i	−0.0203013	−	0.0234290i
$604$	−11.2844	+	3.31340i	−0.459156	+	0.134820i
$605$	8.93851	+	5.74443i	0.363402	+	0.233544i
$606$	−5.43966	+	11.9112i	−0.220971	+	0.483859i
$607$	−18.4927	+	21.3418i	−0.750597	+	0.866235i	−0.994626	−	0.103533i	$-0.966985\pi$
$607$	−18.4927	+	21.3418i	−0.750597	+	0.866235i	0.244029	+	0.969768i	$0.421531\pi$
$608$	0.0985537	−	0.0633366i	0.00399688	−	0.00256864i
$609$	−0.332300	−	2.31120i	−0.0134655	−	0.0936544i
$610$	−0.650242	−	4.52253i	−0.0263275	−	0.183112i
$611$	−48.4001	+	31.1049i	−1.95806	+	1.25837i
$612$	0.488816	−	0.564124i	0.0197592	−	0.0228034i
$613$	−9.53331	+	20.8750i	−0.385047	+	0.843135i	0.613523	+	0.789677i	$0.289752\pi$
$613$	−9.53331	+	20.8750i	−0.385047	+	0.843135i	−0.998570	+	0.0534581i	$0.982976\pi$
$614$	−8.48006	−	5.44981i	−0.342228	−	0.219936i
$615$	4.64997	−	1.36536i	0.187505	−	0.0550564i
$616$	−0.738976	−	0.852824i	−0.0297742	−	0.0343612i
$617$	−28.7400	−	8.43882i	−1.15703	−	0.339734i	−0.353751	−	0.935340i	$-0.615094\pi$
$617$	−28.7400	−	8.43882i	−1.15703	−	0.339734i	−0.803277	+	0.595605i	$0.796912\pi$
$618$	0.0136974	+	0.0299931i	0.000550990	+	0.00120650i
$619$	1.76833	−	12.2990i	0.0710753	−	0.494340i	−0.922926	−	0.384976i	$-0.874210\pi$
$619$	1.76833	−	12.2990i	0.0710753	−	0.494340i	0.994002	−	0.109364i	$-0.0348813\pi$
$620$	−8.86746			−0.356126
$621$	4.71073	+	0.899480i	0.189035	+	0.0360949i
$622$	15.9665			0.640200
$623$	2.03341	−	14.1426i	0.0814667	−	0.566613i
$624$	−2.17147	−	4.75486i	−0.0869284	−	0.190347i
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$	3.21934	+	3.71532i	0.128671	+	0.148494i
$627$	0.0688127	−	0.0202052i	0.00274811	−	0.000806919i
$628$	7.08290	+	4.55190i	0.282638	+	0.181641i
$629$	−0.541226	+	1.18512i	−0.0215801	+	0.0472538i
$630$	−1.20712	+	1.39309i	−0.0480927	+	0.0555019i
$631$	−32.0765	+	20.6143i	−1.27694	+	0.820642i	−0.990508	−	0.137458i	$-0.956107\pi$
$631$	−32.0765	+	20.6143i	−1.27694	+	0.820642i	−0.286436	+	0.958099i	$0.592470\pi$
$632$	−0.0386848	−	0.269059i	−0.00153880	−	0.0107026i
$633$	1.18796	+	8.26247i	0.0472173	+	0.328404i
$634$	−6.05390	+	3.89060i	−0.240431	+	0.154516i
$635$	−2.80847	+	3.24114i	−0.111451	+	0.128621i
$636$	−1.16995	+	2.56184i	−0.0463917	+	0.101584i
$637$	−15.8403	−	10.1799i	−0.627616	−	0.403344i
$638$	0.744050	−	0.218473i	0.0294572	−	0.00864942i
$639$	−0.335632	−	0.387339i	−0.0132774	−	0.0153229i
$640$	−0.959493	−	0.281733i	−0.0379273	−	0.0111365i
$641$	−17.7833	−	38.9399i	−0.702397	−	1.53803i	−0.837041	−	0.547140i	$-0.815716\pi$
$641$	−17.7833	−	38.9399i	−0.702397	−	1.53803i	0.134644	−	0.990894i	$-0.457011\pi$
$642$	2.91917	−	20.3032i	0.115210	−	0.801305i
$643$	46.1831			1.82128			0.910642	−	0.413196i	$-0.135588\pi$
$643$	46.1831			1.82128			0.910642	+	0.413196i	$0.135588\pi$
$644$	−6.40852	−	6.08941i	−0.252531	−	0.239956i
$645$	−3.40338			−0.134008
$646$	0.0124449	−	0.0865565i	0.000489640	−	0.00340552i
$647$	8.00273	+	17.5235i	0.314620	+	0.688921i	0.999199	−	0.0400173i	$-0.0127413\pi$
$647$	8.00273	+	17.5235i	0.314620	+	0.688921i	−0.684579	+	0.728938i	$0.740014\pi$
$648$	0.959493	+	0.281733i	0.0376924	+	0.0110675i
$649$	−1.34681	−	1.55430i	−0.0528667	−	0.0610115i
$650$	5.01549	−	1.47268i	0.196724	−	0.0577633i
$651$	−13.7508	−	8.83708i	−0.538935	−	0.346352i
$652$	−3.53500	+	7.74058i	−0.138441	+	0.303145i
$653$	4.26441	−	4.92139i	0.166879	−	0.192589i	−0.666150	−	0.745818i	$-0.732059\pi$
$653$	4.26441	−	4.92139i	0.166879	−	0.192589i	0.833029	+	0.553229i	$0.186604\pi$
$654$	1.27444	−	0.819031i	0.0498344	−	0.0320266i
$655$	−2.36060	−	16.4184i	−0.0922364	−	0.641518i
$656$	0.689698	+	4.79695i	0.0269282	+	0.187290i
$657$	−11.9789	+	7.69835i	−0.467340	+	0.300341i
$658$	−13.2861	+	15.3330i	−0.517945	+	0.597741i
$659$	−5.52873	+	12.1062i	−0.215369	+	0.471591i	−0.986223	−	0.165420i	$-0.947102\pi$
$659$	−5.52873	+	12.1062i	−0.215369	+	0.471591i	0.770855	+	0.637011i	$0.219829\pi$
$660$	−0.515001	−	0.330971i	−0.0200464	−	0.0128830i
$661$	−2.92604	+	0.859164i	−0.113810	+	0.0334176i	−0.338142	−	0.941095i	$-0.609798\pi$
$661$	−2.92604	+	0.859164i	−0.113810	+	0.0334176i	0.224332	+	0.974513i	$0.427980\pi$
$662$	18.7397	+	21.6268i	0.728339	+	0.840548i
$663$	−3.74378	−	1.09927i	−0.145396	−	0.0426922i
$664$	−3.52515	−	7.71900i	−0.136802	−	0.299555i
$665$	−0.0307324	+	0.213749i	−0.00119175	+	0.00828882i
$666$	−1.74542			−0.0676336
$667$	5.63589	−	2.26757i	0.218222	−	0.0878008i
$668$	11.0291			0.426727
$669$	−3.54954	+	24.6876i	−0.137233	+	0.954477i
$670$	0.316240	+	0.692468i	0.0122174	+	0.0267524i
$671$	2.68378	+	0.788029i	0.103606	+	0.0304215i
$672$	−1.20712	−	1.39309i	−0.0465656	−	0.0537395i
$673$	−42.9529	+	12.6121i	−1.65571	+	0.486161i	−0.970282	−	0.241976i	$-0.922204\pi$
$673$	−42.9529	+	12.6121i	−1.65571	+	0.486161i	−0.685431	+	0.728138i	$0.740386\pi$
$674$	20.3436	+	13.0741i	0.783607	+	0.503594i
$675$	−0.415415	+	0.909632i	−0.0159893	+	0.0350118i
$676$	−9.38021	+	10.8253i	−0.360777	+	0.416359i
$677$	35.4995	−	22.8142i	1.36436	−	0.876820i	0.365810	−	0.930690i	$-0.380792\pi$
$677$	35.4995	−	22.8142i	1.36436	−	0.876820i	0.998548	+	0.0538700i	$0.0171557\pi$
$678$	−2.81430	−	19.5739i	−0.108082	−	0.751730i
$679$	2.06257	+	14.3455i	0.0791541	+	0.550529i
$680$	−0.627948	+	0.403558i	−0.0240807	+	0.0154757i
$681$	0.0948702	−	0.109486i	0.00363543	−	0.00419551i
$682$	2.25508	−	4.93794i	0.0863515	−	0.189083i
$683$	−24.1133	−	15.4967i	−0.922670	−	0.592964i	−0.00923909	−	0.999957i	$-0.502941\pi$
$683$	−24.1133	−	15.4967i	−0.922670	−	0.592964i	−0.913431	+	0.406993i	$0.866577\pi$
$684$	0.112406	−	0.0330053i	0.00429794	−	0.00126199i
$685$	4.99637	+	5.76612i	0.190901	+	0.220312i
$686$	−18.7516	−	5.50595i	−0.715938	−	0.210218i
$687$	4.02005	+	8.80269i	0.153375	+	0.335843i
$688$	0.484351	−	3.36874i	0.0184657	−	0.128432i
$689$	14.7217			0.560852
$690$	−4.26650	−	2.19021i	−0.162423	−	0.0833798i
$691$	−34.4330			−1.30989			−0.654947	−	0.755675i	$-0.727309\pi$
$691$	−34.4330			−1.30989			−0.654947	+	0.755675i	$0.727309\pi$
$692$	1.22387	−	8.51220i	0.0465245	−	0.323585i
$693$	−0.468774	−	1.02647i	−0.0178073	−	0.0389924i
$694$	−8.37095	−	2.45793i	−0.317757	−	0.0933018i
$695$	−1.03073	−	1.18953i	−0.0390978	−	0.0451213i
$696$	1.21541	−	0.356875i	0.0460698	−	0.0135273i
$697$	3.04321	+	1.95575i	0.115270	+	0.0740795i
$698$	4.64228	−	10.1652i	0.175713	−	0.384757i
$699$	2.76613	−	3.19229i	0.104625	−	0.120743i
$700$	1.55070	−	0.996574i	0.0586109	−	0.0376669i
$701$	−0.800642	−	5.56859i	−0.0302398	−	0.210323i	0.969099	−	0.246671i	$-0.0793366\pi$
$701$	−0.800642	−	5.56859i	−0.0302398	−	0.210323i	−0.999339	+	0.0363481i	$0.988427\pi$
$702$	−0.743913	−	5.17403i	−0.0280772	−	0.195281i
$703$	−0.172017	+	0.110549i	−0.00648776	+	0.00416943i
$704$	0.400894	−	0.462657i	0.0151093	−	0.0174370i
$705$	−4.57225	+	10.0118i	−0.172201	+	0.377067i
$706$	−13.1570	−	8.45547i	−0.495169	−	0.318226i
$707$	23.1596	−	6.80028i	0.871008	−	0.255751i
$708$	−2.20001	−	2.53894i	−0.0826813	−	0.0954194i
$709$	29.0159	+	8.51982i	1.08971	+	0.319969i	0.776758	−	0.629799i	$-0.216863\pi$
$709$	29.0159	+	8.51982i	1.08971	+	0.319969i	0.312955	+	0.949768i	$0.398681\pi$
$710$	0.212910	+	0.466208i	0.00799037	+	0.0174965i
$711$	0.0386848	−	0.269059i	0.00145079	−	0.0100905i
$712$	7.75128			0.290491
$713$	13.8397	−	40.2119i	0.518302	−	1.50595i
$714$	−1.37593			−0.0514930
$715$	−0.455410	+	3.16745i	−0.0170314	+	0.118456i
$716$	5.51805	+	12.0828i	0.206219	+	0.451557i
$717$	10.5662	+	3.10252i	0.394603	+	0.115866i
$718$	8.45871	+	9.76187i	0.315676	+	0.364310i
$719$	13.1253	−	3.85393i	0.489490	−	0.143727i	−0.0276680	−	0.999617i	$-0.508808\pi$
$719$	13.1253	−	3.85393i	0.489490	−	0.143727i	0.517158	+	0.855890i	$0.326990\pi$
$720$	−0.841254	−	0.540641i	−0.0313517	−	0.0201485i
$721$	0.0252487	−	0.0552869i	0.000940309	−	0.00205899i
$722$	−12.4334	+	14.3489i	−0.462722	+	0.534010i
$723$	8.04009	−	5.16705i	0.299014	−	0.192165i
$724$	−2.12773	−	14.7987i	−0.0790763	−	0.549988i
$725$	0.180273	+	1.25382i	0.00669516	+	0.0465658i
$726$	−8.93851	+	5.74443i	−0.331739	+	0.213196i
$727$	32.6889	−	37.7250i	1.21236	−	1.39914i	0.320250	−	0.947333i	$-0.396233\pi$
$727$	32.6889	−	37.7250i	1.21236	−	1.39914i	0.892114	−	0.451810i	$-0.149222\pi$
$728$	−4.00271	+	8.76472i	−0.148350	+	0.324842i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	13.6625	−	4.01168i	0.505673	−	0.148479i
$731$	−1.66363	−	1.91993i	−0.0615315	−	0.0710111i
$732$	4.38396	+	1.28725i	0.162036	+	0.0475780i
$733$	16.4623	+	36.0475i	0.608051	+	1.33145i	0.923899	+	0.382636i	$0.124984\pi$
$733$	16.4623	+	36.0475i	0.608051	+	1.33145i	−0.315849	+	0.948810i	$0.602289\pi$
$734$	4.04475	−	28.1318i	0.149294	−	1.03837i
$735$	−3.60217			−0.132868
$736$	2.77510	−	3.91137i	0.102292	−	0.144175i
$737$	−0.466031			−0.0171665
$738$	−0.689698	+	4.79695i	−0.0253881	+	0.176578i
$739$	−9.61820	−	21.0609i	−0.353811	−	0.774738i	−0.999934	−	0.0115047i	$-0.996338\pi$
$739$	−9.61820	−	21.0609i	−0.353811	−	0.774738i	0.646123	−	0.763234i	$-0.276389\pi$
$740$	1.67472	+	0.491741i	0.0615638	+	0.0180768i
$741$	−0.401021	−	0.462803i	−0.0147319	−	0.0170015i
$742$	4.98114	−	1.46259i	0.182863	−	0.0536935i
$743$	4.96492	+	3.19076i	0.182145	+	0.117058i	0.628536	−	0.777780i	$-0.283654\pi$
$743$	4.96492	+	3.19076i	0.182145	+	0.117058i	−0.446391	+	0.894838i	$0.647291\pi$
$744$	3.68368	−	8.06613i	0.135050	−	0.295719i
$745$	−9.75794	+	11.2613i	−0.357503	+	0.412581i
$746$	−20.7233	+	13.3181i	−0.758735	+	0.487609i
$747$	−1.20766	−	8.39948i	−0.0441861	−	0.307321i
$748$	−0.0650321	−	0.452308i	−0.00237781	−	0.0165380i
$749$	−31.8080	+	20.4417i	−1.16224	+	0.746925i
$750$	0.654861	−	0.755750i	0.0239121	−	0.0275961i
$751$	−18.7333	+	41.0202i	−0.683588	+	1.49685i	0.175207	+	0.984532i	$0.443940\pi$
$751$	−18.7333	+	41.0202i	−0.683588	+	1.49685i	−0.858796	+	0.512318i	$0.828787\pi$
$752$	−9.25922	−	5.95054i	−0.337649	−	0.216994i
$753$	−6.00798	+	1.76410i	−0.218943	+	0.0642874i
$754$	−4.33611	−	5.00414i	−0.157912	−	0.182240i
$755$	11.2844	+	3.31340i	0.410681	+	0.120587i
$756$	−0.765742	−	1.67674i	−0.0278498	−	0.0609825i
$757$	0.122361	−	0.851038i	0.00444728	−	0.0309315i	−0.987477	−	0.157763i	$-0.949572\pi$
$757$	0.122361	−	0.851038i	0.00444728	−	0.0309315i	0.991924	+	0.126832i	$0.0404808\pi$
$758$	−34.4097			−1.24982
$759$	2.30465	−	1.81885i	0.0836536	−	0.0660201i
$760$	−0.117151			−0.00424951
$761$	4.86134	−	33.8113i	0.176223	−	1.22566i	−0.689182	−	0.724588i	$-0.742030\pi$
$761$	4.86134	−	33.8113i	0.176223	−	1.22566i	0.865406	−	0.501072i	$-0.167061\pi$
$762$	−1.78157	−	3.90109i	−0.0645394	−	0.141322i
$763$	−2.67938	−	0.786736i	−0.0970000	−	0.0284818i
$764$	9.44142	+	10.8960i	0.341579	+	0.394203i
$765$	−0.716207	+	0.210297i	−0.0258945	+	0.00760332i
$766$	18.9883	+	12.2031i	0.686077	+	0.440915i
$767$	−7.29507	+	15.9740i	−0.263410	+	0.576787i
$768$	0.654861	−	0.755750i	0.0236303	−	0.0272708i
$769$	5.68376	−	3.65273i	0.204962	−	0.131721i	−0.434133	−	0.900849i	$-0.642945\pi$
$769$	5.68376	−	3.65273i	0.204962	−	0.131721i	0.639095	+	0.769128i	$0.279309\pi$
$770$	0.160595	+	1.11696i	0.00578743	+	0.0402525i
$771$	0.669499	+	4.65647i	0.0241114	+	0.167699i
$772$	5.75044	−	3.69558i	0.206963	−	0.133007i
$773$	−30.6224	+	35.3402i	−1.10141	+	1.27110i	−0.141762	+	0.989901i	$0.545277\pi$
$773$	−30.6224	+	35.3402i	−1.10141	+	1.27110i	−0.959650	+	0.281196i	$0.909269\pi$
$774$	1.41381	−	3.09582i	0.0508185	−	0.111277i
$775$	7.45978	+	4.79411i	0.267963	+	0.172210i
$776$	−7.54396	+	2.21511i	−0.270812	+	0.0795177i
$777$	2.10693	+	2.43152i	0.0755855	+	0.0872303i
$778$	−18.9727	−	5.57090i	−0.680206	−	0.199727i
$779$	0.235851	+	0.516441i	0.00845022	+	0.0185034i
$780$	−0.743913	+	5.17403i	−0.0266364	+	0.185260i
$781$	−0.313758			−0.0112271
$782$	−0.849983	−	3.47744i	−0.0303953	−	0.124353i
$783$	1.26672			0.0452688
$784$	0.512643	−	3.56551i	0.0183087	−	0.127340i
$785$	−3.49757	−	7.65861i	−0.124834	−	0.273347i
$786$	15.9153	+	4.67315i	0.567680	+	0.166686i
$787$	10.1797	+	11.7480i	0.362867	+	0.418771i	0.907598	−	0.419840i	$-0.137914\pi$
$787$	10.1797	+	11.7480i	0.362867	+	0.418771i	−0.544731	+	0.838611i	$0.683368\pi$
$788$	14.6387	−	4.29832i	0.521483	−	0.153121i
$789$	−26.7195	−	17.1716i	−0.951241	−	0.611325i
$790$	−0.112920	+	0.247261i	−0.00401753	+	0.00879716i
$791$	−23.8709	+	27.5485i	−0.848753	+	0.979513i
$792$	0.515001	−	0.330971i	0.0182997	−	0.0117605i
$793$	−3.39897	−	23.6403i	−0.120701	−	0.839492i
$794$	−1.45120	−	10.0933i	−0.0515012	−	0.358199i
$795$	2.36926	−	1.52263i	0.0840291	−	0.0540022i
$796$	13.9200	−	16.0646i	0.493383	−	0.569394i
$797$	2.98085	−	6.52714i	0.105587	−	0.231203i	−0.849463	−	0.527648i	$-0.823074\pi$
$797$	2.98085	−	6.52714i	0.105587	−	0.231203i	0.955050	+	0.296445i	$0.0958012\pi$
$798$	−0.181666	−	0.116750i	−0.00643091	−	0.00413289i
$799$	−7.88290	+	2.31463i	−0.278877	+	0.0818856i
$800$	0.654861	+	0.755750i	0.0231528	+	0.0267198i
$801$	7.43729	+	2.18379i	0.262784	+	0.0771603i
$802$	−9.41214	−	20.6097i	−0.332354	−	0.727754i
$803$	−1.24057	+	8.62833i	−0.0437786	+	0.304487i
$804$	−0.761262			−0.0268476
$805$	2.09901	+	8.58744i	0.0739803	+	0.302668i
$806$	−46.3523			−1.63269
$807$	−0.683353	+	4.75282i	−0.0240552	+	0.167307i
$808$	5.43966	+	11.9112i	0.191366	+	0.419034i
$809$	−16.2252	−	4.76416i	−0.570449	−	0.167499i	−0.0162279	−	0.999868i	$-0.505166\pi$
$809$	−16.2252	−	4.76416i	−0.570449	−	0.167499i	−0.554221	+	0.832369i	$0.686984\pi$
$810$	−0.654861	−	0.755750i	−0.0230095	−	0.0265543i
$811$	−13.2891	+	3.90204i	−0.466645	+	0.137019i	−0.506598	−	0.862182i	$-0.669097\pi$
$811$	−13.2891	+	3.90204i	−0.466645	+	0.137019i	0.0399534	+	0.999202i	$0.487279\pi$
$812$	−1.96430	−	1.26238i	−0.0689333	−	0.0443007i
$813$	0.0788596	−	0.172678i	0.00276573	−	0.00605610i
$814$	−0.699728	+	0.807529i	−0.0245255	+	0.0283039i
$815$	7.15871	−	4.60062i	0.250759	−	0.161153i
$816$	−0.106230	−	0.738845i	−0.00371879	−	0.0258648i
$817$	−0.0567422	−	0.394651i	−0.00198516	−	0.0138071i
$818$	−5.03980	+	3.23888i	−0.176212	+	0.113245i
$819$	−6.30988	+	7.28199i	−0.220485	+	0.254453i
$820$	2.01322	−	4.40833i	0.0703046	−	0.153946i
$821$	−36.1690	−	23.2444i	−1.26231	−	0.811236i	−0.273710	−	0.961812i	$-0.588251\pi$
$821$	−36.1690	−	23.2444i	−1.26231	−	0.811236i	−0.988598	+	0.150576i	$0.951887\pi$
$822$	−7.32061	+	2.14953i	−0.255336	+	0.0749733i
$823$	22.1669	+	25.5820i	0.772690	+	0.891732i	0.996559	−	0.0828874i	$-0.0264142\pi$
$823$	22.1669	+	25.5820i	0.772690	+	0.891732i	−0.223869	+	0.974619i	$0.571869\pi$
$824$	0.0316372	+	0.00928951i	0.00110213	+	0.000323615i
$825$	0.254310	+	0.556861i	0.00885393	+	0.0193874i
$826$	−0.881304	+	6.12961i	−0.0306645	+	0.213276i
$827$	6.51116			0.226415			0.113208	−	0.993571i	$-0.463888\pi$
$827$	6.51116			0.226415			0.113208	+	0.993571i	$0.463888\pi$
$828$	3.76465	−	2.97109i	0.130831	−	0.103253i
$829$	49.4371			1.71702			0.858511	−	0.512795i	$-0.171390\pi$
$829$	49.4371			1.71702			0.858511	+	0.512795i	$0.171390\pi$
$830$	−1.20766	+	8.39948i	−0.0419186	+	0.291550i
$831$	6.39232	+	13.9972i	0.221747	+	0.485559i
$832$	−5.01549	−	1.47268i	−0.173881	−	0.0510561i
$833$	−1.76080	−	2.03207i	−0.0610082	−	0.0704072i
$834$	1.51021	−	0.443438i	0.0522944	−	0.0153550i
$835$	−9.27824	−	5.96276i	−0.321087	−	0.206350i
$836$	0.0297926	−	0.0652368i	0.00103040	−	0.00225626i
$837$	5.80695	−	6.70158i	0.200718	−	0.231640i
$838$	−3.36698	+	2.16383i	−0.116310	+	0.0747482i
$839$	0.817359	+	5.68486i	0.0282184	+	0.196263i	0.999054	−	0.0434822i	$-0.0138452\pi$
$839$	0.817359	+	5.68486i	0.0282184	+	0.196263i	−0.970836	+	0.239745i	$0.922936\pi$
$840$	0.262332	+	1.82456i	0.00905130	+	0.0629532i
$841$	−23.0465	+	14.8111i	−0.794707	+	0.510727i
$842$	−23.3236	+	26.9168i	−0.803784	+	0.927616i
$843$	−8.96709	+	19.6352i	−0.308843	+	0.676272i
$844$	7.02231	+	4.51297i	0.241718	+	0.155343i
$845$	13.7437	−	4.03553i	0.472799	−	0.138826i
$846$	−7.20770	−	8.31812i	−0.247806	−	0.285983i
$847$	18.7923	+	5.51793i	0.645712	+	0.189598i
$848$	1.16995	+	2.56184i	0.0401764	+	0.0879740i
$849$	−2.57430	+	17.9046i	−0.0883497	+	0.614486i
$850$	0.746443			0.0256028
$851$	−4.84371	+	6.82698i	−0.166040	+	0.234026i
$852$	−0.512524			−0.0175588
$853$	2.57549	−	17.9130i	0.0881832	−	0.613328i	−0.897027	−	0.441976i	$-0.854278\pi$
$853$	2.57549	−	17.9130i	0.0881832	−	0.613328i	0.985210	−	0.171352i	$-0.0548134\pi$
$854$	−3.49871	−	7.66110i	−0.119723	−	0.262157i
$855$	−0.112406	−	0.0330053i	−0.00384419	−	0.00112876i
$856$	−13.4325	−	15.5020i	−0.459114	−	0.529846i
$857$	49.7782	−	14.6162i	1.70039	−	0.499280i	0.719608	−	0.694380i	$-0.244321\pi$
$857$	49.7782	−	14.6162i	1.70039	−	0.499280i	0.980783	+	0.195100i	$0.0625031\pi$
$858$	−2.69203	−	1.73006i	−0.0919043	−	0.0590633i
$859$	−3.65866	+	8.01136i	−0.124832	+	0.273344i	−0.961722	−	0.274027i	$-0.911644\pi$
$859$	−3.65866	+	8.01136i	−0.124832	+	0.273344i	0.836890	+	0.547371i	$0.184371\pi$
$860$	−2.22874	+	2.57210i	−0.0759994	+	0.0877079i
$861$	7.51512	−	4.82968i	0.256115	−	0.164595i
$862$	1.24961	+	8.69124i	0.0425619	+	0.296025i
$863$	2.76079	+	19.2017i	0.0939785	+	0.653634i	0.981300	+	0.192484i	$0.0616542\pi$
$863$	2.76079	+	19.2017i	0.0939785	+	0.653634i	−0.887322	+	0.461151i	$0.847437\pi$
$864$	0.841254	−	0.540641i	0.0286200	−	0.0183930i
$865$	−5.63162	+	6.49924i	−0.191481	+	0.220981i
$866$	1.94924	−	4.26824i	0.0662379	−	0.145041i
$867$	13.8326	+	8.88966i	0.469779	+	0.301909i
$868$	−15.6835	+	4.60508i	−0.532331	+	0.156306i
$869$	−0.108973	−	0.125762i	−0.00369666	−	0.00426618i
$870$	−1.21541	−	0.356875i	−0.0412061	−	0.0120992i
$871$	1.65306	+	3.61969i	0.0560117	+	0.122649i
$872$	0.215597	−	1.49951i	0.00730102	−	0.0507797i
$873$	−7.86244			−0.266103
$874$	0.182841	−	0.531253i	0.00618470	−	0.0179699i
$875$	−1.84332			−0.0623156
$876$	−2.02647	+	14.0944i	−0.0684679	+	0.476205i
$877$	−5.14583	−	11.2678i	−0.173762	−	0.380486i	0.802634	−	0.596471i	$-0.203431\pi$
$877$	−5.14583	−	11.2678i	−0.173762	−	0.380486i	−0.976397	+	0.215985i	$0.930704\pi$
$878$	13.7700	+	4.04323i	0.464714	+	0.136452i
$879$	−3.26523	−	3.76828i	−0.110134	−	0.127101i
$880$	−0.587385	+	0.172472i	−0.0198007	+	0.00581402i
$881$	−16.5178	−	10.6154i	−0.556500	−	0.357641i	0.231961	−	0.972725i	$-0.425486\pi$
$881$	−16.5178	−	10.6154i	−0.556500	−	0.357641i	−0.788461	+	0.615084i	$0.789122\pi$
$882$	1.49640	−	3.27665i	0.0503863	−	0.110331i
$883$	34.0761	−	39.3259i	1.14675	−	1.32342i	0.208278	−	0.978070i	$-0.433214\pi$
$883$	34.0761	−	39.3259i	1.14675	−	1.32342i	0.938473	−	0.345352i	$-0.112240\pi$
$884$	−3.28243	+	2.10949i	−0.110400	+	0.0709498i
$885$	0.478107	+	3.32531i	0.0160714	+	0.111779i
$886$	1.41479	+	9.84007i	0.0475307	+	0.330583i
$887$	14.4386	−	9.27911i	0.484800	−	0.311562i	−0.275311	−	0.961355i	$-0.588781\pi$
$887$	14.4386	−	9.27911i	0.484800	−	0.311562i	0.760111	+	0.649793i	$0.225144\pi$
$888$	−1.14301	+	1.31910i	−0.0383568	+	0.0442661i
$889$	−3.28400	+	7.19095i	−0.110142	+	0.241177i
$890$	−6.52079	−	4.19066i	−0.218577	−	0.140471i
$891$	0.587385	−	0.172472i	0.0196781	−	0.00577802i
$892$	16.3332	+	18.8495i	0.546875	+	0.631128i
$893$	−1.23719	−	0.363271i	−0.0414009	−	0.0121564i
$894$	−6.19001	−	13.5542i	−0.207025	−	0.453321i
$895$	1.89040	−	13.1480i	0.0631891	−	0.439490i
$896$	−1.84332			−0.0615810
$897$	−22.3020	−	11.4487i	−0.744641	−	0.382262i
$898$	9.73918			0.325001
$899$	1.59856	−	11.1182i	0.0533150	−	0.370814i
$900$	0.415415	+	0.909632i	0.0138472	+	0.0303211i
$901$	2.01709	+	0.592270i	0.0671989	+	0.0197314i
$902$	1.94285	+	2.24216i	0.0646897	+	0.0746559i
$903$	−6.01939	+	1.76745i	−0.200313	+	0.0588171i
$904$	−16.6359	−	10.6913i	−0.553302	−	0.355586i
$905$	−6.21080	+	13.5998i	−0.206454	+	0.452071i
$906$	−7.70168	+	8.88821i	−0.255871	+	0.295291i
$907$	−14.9348	+	9.59800i	−0.495901	+	0.318697i	−0.764575	−	0.644535i	$-0.777051\pi$
$907$	−14.9348	+	9.59800i	−0.495901	+	0.318697i	0.268674	+	0.963231i	$0.413415\pi$
$908$	−0.0206173	−	0.143396i	−0.000684208	−	0.00475877i
$909$	1.86354	+	12.9612i	0.0618098	+	0.429897i
$910$	8.10586	−	5.20932i	0.268707	−	0.172687i
$911$	20.8220	−	24.0298i	0.689863	−	0.796144i	−0.297483	−	0.954727i	$-0.596147\pi$
$911$	20.8220	−	24.0298i	0.689863	−	0.796144i	0.987346	+	0.158583i	$0.0506926\pi$
$912$	0.0486663	−	0.106564i	0.00161150	−	0.00352870i
$913$	−4.37022	−	2.80857i	−0.144633	−	0.0929501i
$914$	22.4675	−	6.59706i	0.743160	−	0.218212i
$915$	−2.99208	−	3.45305i	−0.0989152	−	0.114154i
$916$	9.28520	+	2.72638i	0.306792	+	0.0900821i
$917$	−12.7015	−	27.8124i	−0.419441	−	0.918447i
$918$	0.106230	−	0.738845i	0.00350611	−	0.0243855i
$919$	19.7462			0.651368			0.325684	−	0.945479i	$-0.394405\pi$
$919$	19.7462			0.651368			0.325684	+	0.945479i	$0.394405\pi$
$920$	−4.44921	+	1.79012i	−0.146686	+	0.0590185i
$921$	−10.0803			−0.332156
$922$	0.322604	−	2.24376i	0.0106244	−	0.0738944i
$923$	1.11293	+	2.43698i	0.0366325	+	0.0802141i
$924$	−1.08274	−	0.317920i	−0.0356194	−	0.0104588i
$925$	−1.14301	−	1.31910i	−0.0375818	−	0.0433717i
$926$	1.64062	−	0.481729i	0.0539140	−	0.0158306i
$927$	0.0277385	+	0.0178264i	0.000911051	+	0.000585497i
$928$	0.526213	−	1.15225i	0.0172738	−	0.0378243i
$929$	−13.3386	+	15.3936i	−0.437625	+	0.505046i	−0.931125	−	0.364699i	$-0.881172\pi$
$929$	−13.3386	+	15.3936i	−0.437625	+	0.505046i	0.493500	+	0.869746i	$0.335717\pi$
$930$	−7.45978	+	4.79411i	−0.244616	+	0.157205i
$931$	−0.0600566	−	0.417703i	−0.00196828	−	0.0136897i
$932$	−0.601138	−	4.18101i	−0.0196909	−	0.136953i
$933$	13.4319	−	8.63217i	0.439741	−	0.282604i
$934$	8.16291	−	9.42050i	0.267099	−	0.308248i
$935$	−0.189828	+	0.415665i	−0.00620803	+	0.0135937i
$936$	−4.39743	−	2.82606i	−0.143734	−	0.0923725i
$937$	40.6838	−	11.9458i	1.32908	−	0.390253i	0.461319	−	0.887234i	$-0.347376\pi$
$937$	40.6838	−	11.9458i	1.32908	−	0.390253i	0.867762	+	0.496981i	$0.165558\pi$
$938$	0.918932	+	1.06050i	0.0300042	+	0.0346267i
$939$	4.71693	+	1.38502i	0.153931	+	0.0451983i
$940$	4.57225	+	10.0118i	0.149130	+	0.326550i
$941$	2.48209	−	17.2633i	0.0809139	−	0.562769i	−0.908526	−	0.417828i	$-0.862792\pi$
$941$	2.48209	−	17.2633i	0.0809139	−	0.562769i	0.989440	−	0.144941i	$-0.0462993\pi$
$942$	8.41946			0.274321
$943$	16.8487	+	16.0097i	0.548668	+	0.521347i
$944$	−3.35950			−0.109343
$945$	−0.262332	+	1.82456i	−0.00853365	+	0.0593528i
$946$	−0.865512	−	1.89521i	−0.0281402	−	0.0616185i
$947$	−52.8833	−	15.5279i	−1.71848	−	0.504590i	−0.733856	−	0.679305i	$-0.762281\pi$
$947$	−52.8833	−	15.5279i	−1.71848	−	0.504590i	−0.984619	+	0.174715i	$0.944100\pi$
$948$	−0.178008	−	0.205432i	−0.00578143	−	0.00667212i
$949$	71.4172	−	20.9700i	2.31830	−	0.680714i
$950$	0.0985537	+	0.0633366i	0.00319750	+	0.00205491i
$951$	−2.98944	+	6.54597i	−0.0969394	+	0.212268i
$952$	−0.901044	+	1.03986i	−0.0292030	+	0.0337021i
$953$	22.7087	−	14.5940i	0.735607	−	0.472746i	−0.118427	−	0.992963i	$-0.537785\pi$
$953$	22.7087	−	14.5940i	0.735607	−	0.472746i	0.854034	+	0.520217i	$0.174149\pi$
$954$	0.400808	+	2.78768i	0.0129766	+	0.0902545i
$955$	−2.05182	−	14.2707i	−0.0663952	−	0.461789i
$956$	9.26414	−	5.95370i	0.299624	−	0.192556i
$957$	0.507819	−	0.586055i	0.0164155	−	0.0189445i
$958$	−2.91185	+	6.37607i	−0.0940778	+	0.206002i
$959$	11.8313	+	7.60352i	0.382053	+	0.245531i
$960$	−0.959493	+	0.281733i	−0.0309675	+	0.00909288i
$961$	−31.1922	−	35.9978i	−1.00620	−	1.16122i
$962$	8.75414	+	2.57045i	0.282245	+	0.0828745i
$963$	−8.52100	−	18.6584i	−0.274586	−	0.601258i
$964$	1.36014	−	9.46000i	0.0438072	−	0.304686i
$965$	−6.83556			−0.220045
$966$	−8.68337	−	1.65803i	−0.279383	−	0.0533462i
$967$	18.5663			0.597052			0.298526	−	0.954401i	$-0.403505\pi$
$967$	18.5663			0.597052			0.298526	+	0.954401i	$0.403505\pi$
$968$	−1.51213	+	10.5171i	−0.0486016	+	0.338032i
$969$	−0.0363266	−	0.0795442i	−0.00116698	−	0.00255533i
$970$	7.54396	+	2.21511i	0.242222	+	0.0711227i
$971$	−13.4556	−	15.5286i	−0.431811	−	0.498336i	0.497588	−	0.867414i	$-0.334219\pi$
$971$	−13.4556	−	15.5286i	−0.431811	−	0.498336i	−0.929399	+	0.369077i	$0.879674\pi$
$972$	0.959493	−	0.281733i	0.0307758	−	0.00903658i
$973$	−2.44075	−	1.56858i	−0.0782469	−	0.0502862i
$974$	13.1445	−	28.7825i	0.421178	−	0.922250i
$975$	3.42311	−	3.95048i	0.109627	−	0.126517i
$976$	3.84372	−	2.47021i	0.123034	−	0.0790694i
$977$	−7.98878	−	55.5632i	−0.255584	−	1.77762i	−0.563407	−	0.826180i	$-0.690510\pi$
$977$	−7.98878	−	55.5632i	−0.255584	−	1.77762i	0.307823	−	0.951444i	$-0.400400\pi$
$978$	1.21104	+	8.42296i	0.0387247	+	0.269337i
$979$	3.99191	−	2.56545i	0.127582	−	0.0819920i
$980$	−2.35892	+	2.72234i	−0.0753530	+	0.0869620i
$981$	0.629323	−	1.37803i	0.0200927	−	0.0439970i
$982$	−1.72968	−	1.11160i	−0.0551963	−	0.0354725i
$983$	31.2159	−	9.16580i	0.995631	−	0.292344i	0.256969	−	0.966420i	$-0.417276\pi$
$983$	31.2159	−	9.16580i	0.995631	−	0.292344i	0.738662	+	0.674076i	$0.235458\pi$
$984$	3.17364	+	3.66258i	0.101172	+	0.116759i
$985$	−14.6387	−	4.29832i	−0.466429	−	0.136956i
$986$	−0.392788	−	0.860086i	−0.0125089	−	0.0273907i
$987$	−2.88734	+	20.0819i	−0.0919051	+	0.639214i
$988$	−0.612376			−0.0194823
$989$	−8.18542	−	14.1212i	−0.260281	−	0.449027i
$990$	−0.612182			−0.0194564
$991$	4.47339	−	31.1131i	0.142102	−	0.988340i	−0.786587	−	0.617480i	$-0.788154\pi$
$991$	4.47339	−	31.1131i	0.142102	−	0.988340i	0.928689	−	0.370860i	$-0.120937\pi$
$992$	−3.68368	−	8.06613i	−0.116957	−	0.256100i
$993$	27.4571	+	8.06215i	0.871326	+	0.255844i
$994$	0.618676	+	0.713990i	0.0196232	+	0.0226464i
$995$	−20.3954	+	5.98864i	−0.646579	+	0.189853i
$996$	−7.13875	−	4.58780i	−0.226200	−	0.145370i
$997$	23.0075	−	50.3793i	0.728654	−	1.59553i	−0.0727101	−	0.997353i	$-0.523165\pi$
$997$	23.0075	−	50.3793i	0.728654	−	1.59553i	0.801364	−	0.598177i	$-0.204108\pi$
$998$	5.45422	−	6.29451i	0.172650	−	0.199249i
$999$	−1.46834	+	0.943645i	−0.0464562	+	0.0298556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.f.31.2	✓	20
23.3	even	11	inner	690.2.m.f.601.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.f.31.2	✓	20	1.1	even	1	trivial
690.2.m.f.601.2	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)

\(f(q)\)	\(=\)	\(q+(0.142315 - 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(1.55070 + 0.996574i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(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} +(1.55070 + 0.996574i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(0.841254 - 0.540641i) q^{10} +(0.0871226 + 0.605951i) q^{11} +(0.142315 + 0.989821i) q^{12} +(4.39743 - 2.82606i) q^{13} +(1.20712 - 1.39309i) q^{14} +(0.415415 - 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(0.716207 - 0.210297i) q^{17} +(0.654861 + 0.755750i) q^{18} +(0.112406 + 0.0330053i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(0.262332 - 1.82456i) q^{21} +0.612182 q^{22} +(4.77332 - 0.464120i) q^{23} +1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(-2.17147 - 4.75486i) q^{26} +(0.959493 + 0.281733i) q^{27} +(-1.20712 - 1.39309i) q^{28} +(1.21541 - 0.356875i) q^{29} +(-0.841254 - 0.540641i) q^{30} +(3.68368 - 8.06613i) q^{31} +(0.654861 - 0.755750i) q^{32} +(0.515001 - 0.330971i) q^{33} +(-0.106230 - 0.738845i) q^{34} +(0.262332 + 1.82456i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-1.14301 + 1.31910i) q^{37} +(0.0486663 - 0.106564i) q^{38} +(-4.39743 - 2.82606i) q^{39} +(-0.959493 + 0.281733i) q^{40} +(3.17364 + 3.66258i) q^{41} +(-1.76865 - 0.519323i) q^{42} +(-1.41381 - 3.09582i) q^{43} +(0.0871226 - 0.605951i) q^{44} -1.00000 q^{45} +(0.219918 - 4.79079i) q^{46} -11.0065 q^{47} +(0.142315 - 0.989821i) q^{48} +(-1.49640 - 3.27665i) q^{49} +(0.959493 + 0.281733i) q^{50} +(-0.488816 - 0.564124i) q^{51} +(-5.01549 + 1.47268i) q^{52} +(2.36926 + 1.52263i) q^{53} +(0.415415 - 0.909632i) q^{54} +(-0.400894 + 0.462657i) q^{55} +(-1.55070 + 0.996574i) q^{56} +(-0.0166723 - 0.115959i) q^{57} +(-0.180273 - 1.25382i) q^{58} +(-2.82619 + 1.81629i) q^{59} +(-0.654861 + 0.755750i) q^{60} +(1.89805 - 4.15614i) q^{61} +(-7.45978 - 4.79411i) q^{62} +(-1.76865 + 0.519323i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(5.01549 + 1.47268i) q^{65} +(-0.254310 - 0.556861i) q^{66} +(-0.108339 + 0.753513i) q^{67} -0.746443 q^{68} +(-2.40509 - 4.14916i) q^{69} +1.84332 q^{70} +(-0.0729397 + 0.507307i) q^{71} +(-0.415415 - 0.909632i) q^{72} +(13.6625 + 4.01168i) q^{73} +(1.14301 + 1.31910i) q^{74} +(0.959493 - 0.281733i) q^{75} +(-0.0985537 - 0.0633366i) q^{76} +(-0.468774 + 1.02647i) q^{77} +(-3.42311 + 3.95048i) q^{78} +(-0.228674 + 0.146960i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(4.07695 - 2.62010i) q^{82} +(-5.55705 + 6.41318i) q^{83} +(-0.765742 + 1.67674i) q^{84} +(0.627948 + 0.403558i) q^{85} +(-3.26552 + 0.958843i) q^{86} +(-0.829523 - 0.957321i) q^{87} +(-0.587385 - 0.172472i) q^{88} +(-3.22000 - 7.05081i) q^{89} +(-0.142315 + 0.989821i) q^{90} +9.63546 q^{91} +(-4.71073 - 0.899480i) q^{92} -8.86746 q^{93} +(-1.56638 + 10.8944i) q^{94} +(0.0486663 + 0.106564i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(5.14880 + 5.94204i) q^{97} +(-3.45626 + 1.01485i) q^{98} +(-0.515001 - 0.330971i) 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	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + 18 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 13 q^{21} + 26 q^{22} + 20 q^{24} - 2 q^{25} + 9 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} + 8 q^{31} + 2 q^{32} + 4 q^{33} + 13 q^{34} + 13 q^{35} - 2 q^{36} + 16 q^{37} - 15 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} + 9 q^{42} - 16 q^{43} + 18 q^{44} - 20 q^{45} - 34 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} - 9 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 7 q^{55} + 2 q^{56} + 29 q^{57} + 16 q^{58} + 25 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 9 q^{63} - 2 q^{64} - 2 q^{65} - 15 q^{66} + 20 q^{67} - 2 q^{68} - 22 q^{69} - 2 q^{70} - q^{71} + 2 q^{72} - q^{73} - 16 q^{74} + 2 q^{75} + 4 q^{76} + 53 q^{77} + 2 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} - 25 q^{82} + 9 q^{83} - 9 q^{84} - 9 q^{85} - 28 q^{86} - 6 q^{87} - 7 q^{88} - 31 q^{89} - 2 q^{90} - 26 q^{91} + 11 q^{92} - 30 q^{93} + q^{94} - 15 q^{95} - 2 q^{96} - 35 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 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 + 18 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 13 * q^21 + 26 * q^22 + 20 * q^24 - 2 * q^25 + 9 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 + 8 * q^31 + 2 * q^32 + 4 * q^33 + 13 * q^34 + 13 * q^35 - 2 * q^36 + 16 * q^37 - 15 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 + 9 * q^42 - 16 * q^43 + 18 * q^44 - 20 * q^45 - 34 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 - 9 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 7 * q^55 + 2 * q^56 + 29 * q^57 + 16 * q^58 + 25 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 9 * q^63 - 2 * q^64 - 2 * q^65 - 15 * q^66 + 20 * q^67 - 2 * q^68 - 22 * q^69 - 2 * q^70 - q^71 + 2 * q^72 - q^73 - 16 * q^74 + 2 * q^75 + 4 * q^76 + 53 * q^77 + 2 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 - 25 * q^82 + 9 * q^83 - 9 * q^84 - 9 * q^85 - 28 * q^86 - 6 * q^87 - 7 * q^88 - 31 * q^89 - 2 * q^90 - 26 * q^91 + 11 * q^92 - 30 * q^93 + q^94 - 15 * q^95 - 2 * q^96 - 35 * q^97 - 5 * q^98 - 4 * q^99

Introduction

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