LMFDB - Embedded newform 74.2.f.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	74.9
Dual form			74.2.f.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(0.266044 - 1.50881i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.79813 - 1.50881i) q^{5} -1.53209 q^{6} +(1.93969 + 1.62760i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.613341 + 0.223238i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(0.266044 - 1.50881i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.79813 - 1.50881i) q^{5} -1.53209 q^{6} +(1.93969 + 1.62760i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.613341 + 0.223238i) q^{9} +(-1.17365 + 2.03282i) q^{10} +(-0.560307 - 0.970481i) q^{11} +(0.266044 + 1.50881i) q^{12} +(1.70574 - 0.620838i) q^{13} +(1.26604 - 2.19285i) q^{14} +(-2.75490 + 2.31164i) q^{15} +(0.766044 - 0.642788i) q^{16} +(2.81908 + 1.02606i) q^{17} +(0.113341 - 0.642788i) q^{18} +(-0.971782 + 5.51125i) q^{19} +(2.20574 + 0.802823i) q^{20} +(2.97178 - 2.49362i) q^{21} +(-0.858441 + 0.720317i) q^{22} +(-4.55303 + 7.88609i) q^{23} +(1.43969 - 0.524005i) q^{24} +(0.0885259 + 0.502055i) q^{25} +(-0.907604 - 1.57202i) q^{26} +(2.79813 - 4.84651i) q^{27} +(-2.37939 - 0.866025i) q^{28} +(-4.52481 - 7.83721i) q^{29} +(2.75490 + 2.31164i) q^{30} -4.53209 q^{31} +(-0.766044 - 0.642788i) q^{32} +(-1.61334 + 0.587208i) q^{33} +(0.520945 - 2.95442i) q^{34} +(-1.03209 - 5.85327i) q^{35} -0.652704 q^{36} +(2.33750 + 5.61570i) q^{37} +5.59627 q^{38} +(-0.482926 - 2.73881i) q^{39} +(0.407604 - 2.31164i) q^{40} +(6.98545 - 2.54250i) q^{41} +(-2.97178 - 2.49362i) q^{42} -8.92902 q^{43} +(0.858441 + 0.720317i) q^{44} +(-0.766044 - 1.32683i) q^{45} +(8.55690 + 3.11446i) q^{46} +(0.194593 - 0.337044i) q^{47} +(-0.766044 - 1.32683i) q^{48} +(-0.102196 - 0.579585i) q^{49} +(0.479055 - 0.174362i) q^{50} +(2.29813 - 3.98048i) q^{51} +(-1.39053 + 1.16679i) q^{52} +(-9.23055 + 7.74535i) q^{53} +(-5.25877 - 1.91404i) q^{54} +(-0.456767 + 2.59045i) q^{55} +(-0.439693 + 2.49362i) q^{56} +(8.05690 + 2.93247i) q^{57} +(-6.93242 + 5.81699i) q^{58} +(6.41534 - 5.38311i) q^{59} +(1.79813 - 3.11446i) q^{60} +(2.45336 - 0.892951i) q^{61} +(0.786989 + 4.46324i) q^{62} +(0.826352 + 1.43128i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-4.00387 - 1.45729i) q^{65} +(0.858441 + 1.48686i) q^{66} +(5.62836 + 4.72275i) q^{67} -3.00000 q^{68} +(10.6873 + 8.96773i) q^{69} +(-5.58512 + 2.03282i) q^{70} +(-0.448311 + 2.54250i) q^{71} +(0.113341 + 0.642788i) q^{72} -0.709141 q^{73} +(5.12449 - 3.27714i) q^{74} +0.781059 q^{75} +(-0.971782 - 5.51125i) q^{76} +(0.492726 - 2.79439i) q^{77} +(-2.61334 + 0.951178i) q^{78} +(3.39646 + 2.84997i) q^{79} -2.34730 q^{80} +(-5.06805 - 4.25260i) q^{81} +(-3.71688 - 6.43783i) q^{82} +(6.81180 + 2.47929i) q^{83} +(-1.93969 + 3.35965i) q^{84} +(-3.52094 - 6.09845i) q^{85} +(1.55051 + 8.79336i) q^{86} +(-13.0287 + 4.74205i) q^{87} +(0.560307 - 0.970481i) q^{88} +(-9.95336 + 8.35186i) q^{89} +(-1.17365 + 0.984808i) q^{90} +(4.31908 + 1.57202i) q^{91} +(1.58125 - 8.96773i) q^{92} +(-1.20574 + 6.83807i) q^{93} +(-0.365715 - 0.133109i) q^{94} +(10.0628 - 8.44372i) q^{95} +(-1.17365 + 0.984808i) q^{96} +(7.34730 - 12.7259i) q^{97} +(-0.553033 + 0.201288i) q^{98} +(-0.127011 - 0.720317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + 3 q^{5} + 6 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 + 3 * q^5 + 6 * q^7 + 3 * q^8 - 3 * q^9	$ 6 q - 3 q^{3} + 3 q^{5} + 6 q^{7} + 3 q^{8} - 3 q^{9} - 6 q^{10} - 9 q^{11} - 3 q^{12} + 3 q^{14} - 18 q^{15} - 6 q^{18} + 9 q^{19} + 3 q^{20} + 3 q^{21} + 3 q^{22} - 15 q^{23} + 3 q^{24} + 21 q^{25} - 9 q^{26} + 3 q^{27} - 3 q^{28} + 18 q^{30} - 18 q^{31} - 3 q^{33} + 3 q^{35} - 6 q^{36} + 9 q^{37} + 6 q^{38} + 18 q^{39} + 6 q^{40} + 6 q^{41} - 3 q^{42} + 12 q^{43} - 3 q^{44} + 15 q^{46} - 3 q^{47} + 6 q^{50} + 9 q^{52} - 18 q^{53} - 9 q^{54} - 18 q^{55} + 3 q^{56} + 12 q^{57} - 18 q^{58} - 6 q^{59} - 3 q^{60} - 12 q^{61} - 3 q^{62} + 6 q^{63} - 3 q^{64} - 3 q^{66} - 3 q^{67} - 18 q^{68} + 42 q^{69} - 12 q^{70} - 6 q^{71} - 6 q^{72} - 36 q^{73} + 18 q^{74} - 30 q^{75} + 9 q^{76} - 15 q^{77} - 9 q^{78} + 30 q^{79} - 12 q^{80} + 12 q^{81} - 6 q^{82} + 6 q^{83} - 6 q^{84} - 18 q^{85} + 12 q^{86} - 27 q^{87} + 9 q^{88} - 33 q^{89} - 6 q^{90} + 9 q^{91} + 12 q^{92} + 3 q^{93} - 12 q^{94} + 51 q^{95} - 6 q^{96} + 42 q^{97} + 9 q^{98} + 27 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 + 3 * q^5 + 6 * q^7 + 3 * q^8 - 3 * q^9 - 6 * q^10 - 9 * q^11 - 3 * q^12 + 3 * q^14 - 18 * q^15 - 6 * q^18 + 9 * q^19 + 3 * q^20 + 3 * q^21 + 3 * q^22 - 15 * q^23 + 3 * q^24 + 21 * q^25 - 9 * q^26 + 3 * q^27 - 3 * q^28 + 18 * q^30 - 18 * q^31 - 3 * q^33 + 3 * q^35 - 6 * q^36 + 9 * q^37 + 6 * q^38 + 18 * q^39 + 6 * q^40 + 6 * q^41 - 3 * q^42 + 12 * q^43 - 3 * q^44 + 15 * q^46 - 3 * q^47 + 6 * q^50 + 9 * q^52 - 18 * q^53 - 9 * q^54 - 18 * q^55 + 3 * q^56 + 12 * q^57 - 18 * q^58 - 6 * q^59 - 3 * q^60 - 12 * q^61 - 3 * q^62 + 6 * q^63 - 3 * q^64 - 3 * q^66 - 3 * q^67 - 18 * q^68 + 42 * q^69 - 12 * q^70 - 6 * q^71 - 6 * q^72 - 36 * q^73 + 18 * q^74 - 30 * q^75 + 9 * q^76 - 15 * q^77 - 9 * q^78 + 30 * q^79 - 12 * q^80 + 12 * q^81 - 6 * q^82 + 6 * q^83 - 6 * q^84 - 18 * q^85 + 12 * q^86 - 27 * q^87 + 9 * q^88 - 33 * q^89 - 6 * q^90 + 9 * q^91 + 12 * q^92 + 3 * q^93 - 12 * q^94 + 51 * q^95 - 6 * q^96 + 42 * q^97 + 9 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	0.266044	−	1.50881i	0.153601	−	0.871114i	−0.806453	−	0.591298i	$-0.798616\pi$
$3$	0.266044	−	1.50881i	0.153601	−	0.871114i	0.960054	−	0.279815i	$-0.0902733\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−1.79813	−	1.50881i	−0.804150	−	0.674762i	0.145054	−	0.989424i	$-0.453664\pi$
$5$	−1.79813	−	1.50881i	−0.804150	−	0.674762i	−0.949204	+	0.314662i	$0.898109\pi$
$6$	−1.53209			−0.625473
$7$	1.93969	+	1.62760i	0.733135	+	0.615173i	0.930984	−	0.365059i	$-0.118951\pi$
$7$	1.93969	+	1.62760i	0.733135	+	0.615173i	−0.197849	+	0.980232i	$0.563396\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.613341	+	0.223238i	0.204447	+	0.0744126i
$10$	−1.17365	+	2.03282i	−0.371140	+	0.642834i
$11$	−0.560307	−	0.970481i	−0.168939	−	0.292611i	0.769108	−	0.639119i	$-0.220701\pi$
$11$	−0.560307	−	0.970481i	−0.168939	−	0.292611i	−0.938047	+	0.346508i	$0.887367\pi$
$12$	0.266044	+	1.50881i	0.0768004	+	0.435557i
$13$	1.70574	−	0.620838i	0.473086	−	0.172189i	−0.0944636	−	0.995528i	$-0.530114\pi$
$13$	1.70574	−	0.620838i	0.473086	−	0.172189i	0.567550	+	0.823339i	$0.307891\pi$
$14$	1.26604	−	2.19285i	0.338365	−	0.586065i
$15$	−2.75490	+	2.31164i	−0.711312	+	0.596862i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	2.81908	+	1.02606i	0.683727	+	0.248856i	0.660447	−	0.750873i	$-0.270367\pi$
$17$	2.81908	+	1.02606i	0.683727	+	0.248856i	0.0232799	+	0.999729i	$0.492589\pi$
$18$	0.113341	−	0.642788i	0.0267147	−	0.151506i
$19$	−0.971782	+	5.51125i	−0.222942	+	1.26437i	0.643639	+	0.765330i	$0.277424\pi$
$19$	−0.971782	+	5.51125i	−0.222942	+	1.26437i	−0.866581	+	0.499037i	$0.833687\pi$
$20$	2.20574	+	0.802823i	0.493218	+	0.179517i
$21$	2.97178	−	2.49362i	0.648496	−	0.544153i
$22$	−0.858441	+	0.720317i	−0.183020	+	0.153572i
$23$	−4.55303	+	7.88609i	−0.949373	+	1.64436i	−0.202624	+	0.979257i	$0.564947\pi$
$23$	−4.55303	+	7.88609i	−0.949373	+	1.64436i	−0.746749	+	0.665106i	$0.768386\pi$
$24$	1.43969	−	0.524005i	0.293876	−	0.106962i
$25$	0.0885259	+	0.502055i	0.0177052	+	0.100411i
$26$	−0.907604	−	1.57202i	−0.177996	−	0.308298i
$27$	2.79813	−	4.84651i	0.538501	−	0.932711i
$28$	−2.37939	−	0.866025i	−0.449662	−	0.163663i
$29$	−4.52481	−	7.83721i	−0.840237	−	1.45533i	−0.889694	−	0.456557i	$-0.849082\pi$
$29$	−4.52481	−	7.83721i	−0.840237	−	1.45533i	0.0494571	−	0.998776i	$-0.484251\pi$
$30$	2.75490	+	2.31164i	0.502974	+	0.422045i
$31$	−4.53209			−0.813987			−0.406994	−	0.913431i	$-0.633423\pi$
$31$	−4.53209			−0.813987			−0.406994	+	0.913431i	$0.633423\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	−1.61334	+	0.587208i	−0.280847	+	0.102220i
$34$	0.520945	−	2.95442i	0.0893413	−	0.506679i
$35$	−1.03209	−	5.85327i	−0.174455	−	0.989383i
$36$	−0.652704			−0.108784
$37$	2.33750	+	5.61570i	0.384282	+	0.923216i
$37$	2.33750	+	5.61570i	0.384282	+	0.923216i
$38$	5.59627			0.907834
$39$	−0.482926	−	2.73881i	−0.0773300	−	0.438560i
$40$	0.407604	−	2.31164i	0.0644478	−	0.365502i
$41$	6.98545	−	2.54250i	1.09094	−	0.397071i	0.266974	−	0.963704i	$-0.413976\pi$
$41$	6.98545	−	2.54250i	1.09094	−	0.397071i	0.823971	+	0.566633i	$0.191754\pi$
$42$	−2.97178	−	2.49362i	−0.458556	−	0.384774i
$43$	−8.92902			−1.36166			−0.680831	−	0.732441i	$-0.738381\pi$
$43$	−8.92902			−1.36166			−0.680831	+	0.732441i	$0.738381\pi$
$44$	0.858441	+	0.720317i	0.129415	+	0.108592i
$45$	−0.766044	−	1.32683i	−0.114195	−	0.197792i
$46$	8.55690	+	3.11446i	1.26165	+	0.459202i
$47$	0.194593	−	0.337044i	0.0283843	−	0.0491630i	−0.851484	−	0.524380i	$-0.824297\pi$
$47$	0.194593	−	0.337044i	0.0283843	−	0.0491630i	0.879869	+	0.475217i	$0.157630\pi$
$48$	−0.766044	−	1.32683i	−0.110569	−	0.191511i
$49$	−0.102196	−	0.579585i	−0.0145995	−	0.0827978i
$50$	0.479055	−	0.174362i	0.0677487	−	0.0246585i
$51$	2.29813	−	3.98048i	0.321803	−	0.557379i
$52$	−1.39053	+	1.16679i	−0.192832	+	0.161805i
$53$	−9.23055	+	7.74535i	−1.26791	+	1.06391i	−0.273122	+	0.961979i	$0.588056\pi$
$53$	−9.23055	+	7.74535i	−1.26791	+	1.06391i	−0.994792	+	0.101927i	$0.967499\pi$
$54$	−5.25877	−	1.91404i	−0.715628	−	0.260467i
$55$	−0.456767	+	2.59045i	−0.0615904	+	0.349297i
$56$	−0.439693	+	2.49362i	−0.0587564	+	0.333224i
$57$	8.05690	+	2.93247i	1.06716	+	0.388416i
$58$	−6.93242	+	5.81699i	−0.910271	+	0.763808i
$59$	6.41534	−	5.38311i	0.835207	−	0.700822i	−0.121273	−	0.992619i	$-0.538698\pi$
$59$	6.41534	−	5.38311i	0.835207	−	0.700822i	0.956480	+	0.291797i	$0.0942533\pi$
$60$	1.79813	−	3.11446i	0.232138	−	0.402075i
$61$	2.45336	−	0.892951i	0.314121	−	0.114331i	−0.180149	−	0.983639i	$-0.557658\pi$
$61$	2.45336	−	0.892951i	0.314121	−	0.114331i	0.494269	+	0.869309i	$0.335436\pi$
$62$	0.786989	+	4.46324i	0.0999477	+	0.566832i
$63$	0.826352	+	1.43128i	0.104111	+	0.180325i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−4.00387	−	1.45729i	−0.496619	−	0.180755i
$66$	0.858441	+	1.48686i	0.105667	+	0.183020i
$67$	5.62836	+	4.72275i	0.687613	+	0.576976i	0.918220	−	0.396071i	$-0.129627\pi$
$67$	5.62836	+	4.72275i	0.687613	+	0.576976i	−0.230607	+	0.973047i	$0.574071\pi$
$68$	−3.00000			−0.363803
$69$	10.6873	+	8.96773i	1.28660	+	1.07959i
$70$	−5.58512	+	2.03282i	−0.667550	+	0.242968i
$71$	−0.448311	+	2.54250i	−0.0532047	+	0.301739i	−0.999785	−	0.0207290i	$-0.993401\pi$
$71$	−0.448311	+	2.54250i	−0.0532047	+	0.301739i	0.946580	+	0.322468i	$0.104512\pi$
$72$	0.113341	+	0.642788i	0.0133573	+	0.0757532i
$73$	−0.709141			−0.0829986			−0.0414993	−	0.999139i	$-0.513213\pi$
$73$	−0.709141			−0.0829986			−0.0414993	+	0.999139i	$0.513213\pi$
$74$	5.12449	−	3.27714i	0.595709	−	0.380960i
$75$	0.781059			0.0901889
$76$	−0.971782	−	5.51125i	−0.111471	−	0.632183i
$77$	0.492726	−	2.79439i	0.0561513	−	0.318450i
$78$	−2.61334	+	0.951178i	−0.295903	+	0.107700i
$79$	3.39646	+	2.84997i	0.382132	+	0.320646i	0.813539	−	0.581511i	$-0.197538\pi$
$79$	3.39646	+	2.84997i	0.382132	+	0.320646i	−0.431407	+	0.902157i	$0.641983\pi$
$80$	−2.34730			−0.262436
$81$	−5.06805	−	4.25260i	−0.563116	−	0.472511i
$82$	−3.71688	−	6.43783i	−0.410461	−	0.710939i
$83$	6.81180	+	2.47929i	0.747693	+	0.272138i	0.687634	−	0.726057i	$-0.258649\pi$
$83$	6.81180	+	2.47929i	0.747693	+	0.272138i	0.0600581	+	0.998195i	$0.480871\pi$
$84$	−1.93969	+	3.35965i	−0.211638	+	0.366567i
$85$	−3.52094	−	6.09845i	−0.381900	−	0.661470i
$86$	1.55051	+	8.79336i	0.167195	+	0.948213i
$87$	−13.0287	+	4.74205i	−1.39682	+	0.508402i
$88$	0.560307	−	0.970481i	0.0597290	−	0.103454i
$89$	−9.95336	+	8.35186i	−1.05505	+	0.885296i	−0.993616	−	0.112815i	$-0.964013\pi$
$89$	−9.95336	+	8.35186i	−1.05505	+	0.885296i	−0.0614384	+	0.998111i	$0.519569\pi$
$90$	−1.17365	+	0.984808i	−0.123713	+	0.103808i
$91$	4.31908	+	1.57202i	0.452762	+	0.164792i
$92$	1.58125	−	8.96773i	0.164857	−	0.934950i
$93$	−1.20574	+	6.83807i	−0.125029	+	0.709075i
$94$	−0.365715	−	0.133109i	−0.0377206	−	0.0137292i
$95$	10.0628	−	8.44372i	1.03242	−	0.866307i
$96$	−1.17365	+	0.984808i	−0.119785	+	0.100512i
$97$	7.34730	−	12.7259i	0.746005	−	1.29212i	−0.203719	−	0.979029i	$-0.565303\pi$
$97$	7.34730	−	12.7259i	0.746005	−	1.29212i	0.949724	−	0.313089i	$-0.101364\pi$
$98$	−0.553033	+	0.201288i	−0.0558648	+	0.0203331i
$99$	−0.127011	−	0.720317i	−0.0127651	−	0.0723946i
$100$	−0.254900	−	0.441500i	−0.0254900	−	0.0441500i
$101$	−1.51367	+	2.62175i	−0.150616	+	0.260874i	−0.931454	−	0.363859i	$-0.881459\pi$
$101$	−1.51367	+	2.62175i	−0.150616	+	0.260874i	0.780838	+	0.624733i	$0.214792\pi$
$102$	−4.31908	−	1.57202i	−0.427652	−	0.155653i
$103$	−4.20826	−	7.28893i	−0.414653	−	0.718199i	0.580739	−	0.814090i	$-0.302764\pi$
$103$	−4.20826	−	7.28893i	−0.414653	−	0.718199i	−0.995392	+	0.0958903i	$0.969430\pi$
$104$	1.39053	+	1.16679i	0.136353	+	0.114413i
$105$	−9.10607			−0.888661
$106$	9.23055	+	7.74535i	0.896550	+	0.752295i
$107$	−5.67752	+	2.06645i	−0.548866	+	0.199771i	−0.601543	−	0.798841i	$-0.705447\pi$
$107$	−5.67752	+	2.06645i	−0.548866	+	0.199771i	0.0526763	+	0.998612i	$0.483225\pi$
$108$	−0.971782	+	5.51125i	−0.0935097	+	0.530320i
$109$	−3.47906	−	19.7307i	−0.333233	−	1.88986i	−0.444024	−	0.896015i	$-0.646449\pi$
$109$	−3.47906	−	19.7307i	−0.333233	−	1.88986i	0.110791	−	0.993844i	$-0.464662\pi$
$110$	2.63041			0.250800
$111$	9.09492	−	2.03282i	0.863252	−	0.192947i
$112$	2.53209			0.239260
$113$	−0.442219	−	2.50795i	−0.0416004	−	0.235928i	0.956917	−	0.290362i	$-0.0937757\pi$
$113$	−0.442219	−	2.50795i	−0.0416004	−	0.235928i	−0.998517	+	0.0544340i	$0.982665\pi$
$114$	1.48886	−	8.44372i	0.139444	−	0.790827i
$115$	20.0856	−	7.31056i	1.87299	−	0.681713i
$116$	6.93242	+	5.81699i	0.643659	+	0.540094i
$117$	1.18479			0.109534
$118$	−6.41534	−	5.38311i	−0.590580	−	0.495556i
$119$	3.79813	+	6.57856i	0.348174	+	0.603056i
$120$	−3.37939	−	1.23000i	−0.308494	−	0.112283i
$121$	4.87211	−	8.43874i	0.442919	−	0.767159i
$122$	−1.30541	−	2.26103i	−0.118186	−	0.204704i
$123$	−1.97771	−	11.2162i	−0.178324	−	1.01133i
$124$	4.25877	−	1.55007i	0.382449	−	0.139200i
$125$	−5.26991	+	9.12776i	−0.471356	+	0.816412i
$126$	1.26604	−	1.06234i	0.112788	−	0.0946405i
$127$	−5.38326	+	4.51709i	−0.477687	+	0.400827i	−0.849589	−	0.527445i	$-0.823150\pi$
$127$	−5.38326	+	4.51709i	−0.477687	+	0.400827i	0.371902	+	0.928272i	$0.378706\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	−2.37551	+	13.4722i	−0.209152	+	1.18616i
$130$	−0.739885	+	4.19610i	−0.0648922	+	0.368022i
$131$	0.852044	+	0.310119i	0.0744434	+	0.0270952i	0.378973	−	0.925408i	$-0.376277\pi$
$131$	0.852044	+	0.310119i	0.0744434	+	0.0270952i	−0.304530	+	0.952503i	$0.598499\pi$
$132$	1.31521	−	1.10359i	0.114474	−	0.0960552i
$133$	−10.8550	+	9.10846i	−0.941251	+	0.789803i
$134$	3.67365	−	6.36295i	0.317355	−	0.549675i
$135$	−12.3439	+	4.49281i	−1.06239	+	0.386679i
$136$	0.520945	+	2.95442i	0.0446706	+	0.253340i
$137$	−0.979055	−	1.69577i	−0.0836464	−	0.144880i	0.821167	−	0.570688i	$-0.193323\pi$
$137$	−0.979055	−	1.69577i	−0.0836464	−	0.144880i	−0.904814	+	0.425808i	$0.859990\pi$
$138$	6.97565	−	12.0822i	0.593807	−	1.02850i
$139$	−12.7811	−	4.65193i	−1.08408	−	0.394571i	−0.262652	−	0.964891i	$-0.584597\pi$
$139$	−12.7811	−	4.65193i	−1.08408	−	0.394571i	−0.821423	+	0.570319i	$0.806819\pi$
$140$	2.97178	+	5.14728i	0.251161	+	0.435024i
$141$	−0.456767	−	0.383273i	−0.0384667	−	0.0322774i
$142$	2.58172			0.216653
$143$	−1.55825	−	1.30753i	−0.130307	−	0.109341i
$144$	0.613341	−	0.223238i	0.0511117	−	0.0186031i
$145$	−3.68866	+	20.9194i	−0.306327	+	1.73727i
$146$	0.123141	+	0.698367i	0.0101912	+	0.0577973i
$147$	−0.901674			−0.0743688
$148$	−4.11721	−	4.47756i	−0.338433	−	0.368053i
$149$	−6.73648			−0.551874			−0.275937	−	0.961176i	$-0.588988\pi$
$149$	−6.73648			−0.551874			−0.275937	+	0.961176i	$0.588988\pi$
$150$	−0.135630	−	0.769193i	−0.0110741	−	0.0628044i
$151$	0.832748	−	4.72275i	0.0677681	−	0.384332i	−0.931993	−	0.362476i	$-0.881931\pi$
$151$	0.832748	−	4.72275i	0.0677681	−	0.384332i	0.999761	−	0.0218558i	$-0.00695748\pi$
$152$	−5.25877	+	1.91404i	−0.426543	+	0.155249i
$153$	1.50000	+	1.25865i	0.121268	+	0.101756i
$154$	−2.83750			−0.228652
$155$	8.14930	+	6.83807i	0.654568	+	0.549247i
$156$	1.39053	+	2.40847i	0.111331	+	0.192832i
$157$	13.5954	+	4.94832i	1.08503	+	0.394919i	0.821778	−	0.569808i	$-0.192983\pi$
$157$	13.5954	+	4.94832i	1.08503	+	0.394919i	0.263253	+	0.964727i	$0.415205\pi$
$158$	2.21688	−	3.83975i	0.176366	−	0.305474i
$159$	9.23055	+	15.9878i	0.732030	+	1.26791i
$160$	0.407604	+	2.31164i	0.0322239	+	0.182751i
$161$	−21.6668	+	7.88609i	−1.70759	+	0.621511i
$162$	−3.30793	+	5.72951i	−0.259896	+	0.450153i
$163$	7.69846	−	6.45978i	0.602990	−	0.505969i	−0.289415	−	0.957204i	$-0.593461\pi$
$163$	7.69846	−	6.45978i	0.602990	−	0.505969i	0.892405	+	0.451235i	$0.149016\pi$
$164$	−5.69459	+	4.77833i	−0.444673	+	0.373125i
$165$	3.78699	+	1.37835i	0.294817	+	0.107305i
$166$	1.25877	−	7.13884i	0.0976995	−	0.554082i
$167$	1.81315	−	10.2829i	0.140306	−	0.795713i	−0.830712	−	0.556703i	$-0.812066\pi$
$167$	1.81315	−	10.2829i	0.140306	−	0.795713i	0.971017	−	0.239010i	$-0.0768228\pi$
$168$	3.64543	+	1.32683i	0.281251	+	0.102367i
$169$	−7.43448	+	6.23827i	−0.571883	+	0.479867i
$170$	−5.39440	+	4.52644i	−0.413732	+	0.347162i
$171$	−1.82635	+	3.16333i	−0.139665	+	0.241906i
$172$	8.39053	−	3.05390i	0.639772	−	0.232858i
$173$	0.182266	+	1.03368i	0.0138575	+	0.0785895i	0.990952	−	0.134215i	$-0.0428513\pi$
$173$	0.182266	+	1.03368i	0.0138575	+	0.0785895i	−0.977095	+	0.212805i	$0.931740\pi$
$174$	6.93242	+	12.0073i	0.525545	+	0.910271i
$175$	−0.645430	+	1.11792i	−0.0487899	+	0.0845066i
$176$	−1.05303	−	0.383273i	−0.0793754	−	0.0288903i
$177$	−6.41534	−	11.1117i	−0.482207	−	0.835207i
$178$	9.95336	+	8.35186i	0.746036	+	0.625999i
$179$	9.15570			0.684329			0.342164	−	0.939640i	$-0.388840\pi$
$179$	9.15570			0.684329			0.342164	+	0.939640i	$0.388840\pi$
$180$	1.17365	+	0.984808i	0.0874786	+	0.0734032i
$181$	21.2408	−	7.73103i	1.57882	−	0.574643i	0.603871	−	0.797082i	$-0.293624\pi$
$181$	21.2408	−	7.73103i	1.57882	−	0.574643i	0.974947	+	0.222439i	$0.0714019\pi$
$182$	0.798133	−	4.52644i	0.0591616	−	0.335522i
$183$	−0.694593	−	3.93923i	−0.0513458	−	0.291196i
$184$	−9.10607			−0.671308
$185$	4.26991	−	13.6246i	0.313930	−	1.00170i
$186$	6.94356			0.509127
$187$	−0.583778	−	3.31077i	−0.0426901	−	0.242108i
$188$	−0.0675813	+	0.383273i	−0.00492888	+	0.0279530i
$189$	13.3157	−	4.84651i	0.968573	−	0.352532i
$190$	−10.0628	−	8.44372i	−0.730035	−	0.612572i
$191$	−19.1334			−1.38444			−0.692222	−	0.721684i	$-0.743368\pi$
$191$	−19.1334			−1.38444			−0.692222	+	0.721684i	$0.743368\pi$
$192$	1.17365	+	0.984808i	0.0847008	+	0.0710724i
$193$	9.50640	+	16.4656i	0.684285	+	1.18522i	0.973661	+	0.228001i	$0.0732191\pi$
$193$	9.50640	+	16.4656i	0.684285	+	1.18522i	−0.289375	+	0.957216i	$0.593448\pi$
$194$	−13.8084	−	5.02585i	−0.991385	−	0.360835i
$195$	−3.26399	+	5.65339i	−0.233739	+	0.404848i
$196$	0.294263	+	0.509678i	0.0210188	+	0.0364056i
$197$	3.20914	+	18.1999i	0.228642	+	1.29669i	0.855599	+	0.517639i	$0.173189\pi$
$197$	3.20914	+	18.1999i	0.228642	+	1.29669i	−0.626958	+	0.779053i	$0.715700\pi$
$198$	−0.687319	+	0.250164i	−0.0488456	+	0.0177784i
$199$	2.78699	−	4.82721i	0.197564	−	0.342192i	−0.750174	−	0.661241i	$-0.770030\pi$
$199$	2.78699	−	4.82721i	0.197564	−	0.342192i	0.947738	+	0.319049i	$0.103364\pi$
$200$	−0.390530	+	0.327693i	−0.0276146	+	0.0231714i
$201$	8.62314	−	7.23567i	0.608229	−	0.510365i
$202$	2.84477	+	1.03541i	0.200157	+	0.0728513i
$203$	3.97906	−	22.5663i	0.279275	−	1.58385i
$204$	−0.798133	+	4.52644i	−0.0558805	+	0.316914i
$205$	−16.3969	−	5.96799i	−1.14521	−	0.416823i
$206$	−6.44743	+	5.41004i	−0.449214	+	0.376935i
$207$	−4.55303	+	3.82045i	−0.316458	+	0.265540i
$208$	0.907604	−	1.57202i	0.0629310	−	0.109000i
$209$	5.89306	−	2.14490i	0.407631	−	0.148366i
$210$	1.58125	+	8.96773i	0.109117	+	0.618832i
$211$	−10.8550	−	18.8015i	−0.747292	−	1.29435i	−0.949116	−	0.314925i	$-0.898021\pi$
$211$	−10.8550	−	18.8015i	−0.747292	−	1.29435i	0.201825	−	0.979422i	$-0.435313\pi$
$212$	6.02481	−	10.4353i	0.413786	−	0.716698i
$213$	3.71688	+	1.35283i	0.254677	+	0.0926947i
$214$	3.02094	+	5.23243i	0.206508	+	0.357682i
$215$	16.0556	+	13.4722i	1.09498	+	0.918797i
$216$	5.59627			0.380778
$217$	−8.79086	−	7.37641i	−0.596762	−	0.500743i
$218$	−18.8268	+	6.85240i	−1.27511	+	0.464103i
$219$	−0.188663	+	1.06996i	−0.0127487	+	0.0723012i
$220$	−0.456767	−	2.59045i	−0.0307952	−	0.174648i
$221$	5.44562			0.366312
$222$	−3.58125	−	8.60375i	−0.240358	−	0.577446i
$223$	−10.1429			−0.679219			−0.339610	−	0.940567i	$-0.610295\pi$
$223$	−10.1429			−0.679219			−0.339610	+	0.940567i	$0.610295\pi$
$224$	−0.439693	−	2.49362i	−0.0293782	−	0.166612i
$225$	−0.0577812	+	0.327693i	−0.00385208	+	0.0218462i
$226$	−2.39306	+	0.871001i	−0.159184	+	0.0579381i
$227$	−3.34524	−	2.80699i	−0.222031	−	0.186306i	0.524986	−	0.851111i	$-0.324070\pi$
$227$	−3.34524	−	2.80699i	−0.222031	−	0.186306i	−0.747017	+	0.664804i	$0.768515\pi$
$228$	−8.57398			−0.567826
$229$	−9.01889	−	7.56774i	−0.595985	−	0.500091i	0.294167	−	0.955754i	$-0.404958\pi$
$229$	−9.01889	−	7.56774i	−0.595985	−	0.500091i	−0.890152	+	0.455663i	$0.849402\pi$
$230$	−10.6873	−	18.5110i	−0.704701	−	1.22058i
$231$	−4.08512	−	1.48686i	−0.268781	−	0.0978284i
$232$	4.52481	−	7.83721i	0.297069	−	0.514538i
$233$	−8.13816	−	14.0957i	−0.533148	−	0.923440i	−0.999251	−	0.0387091i	$-0.987675\pi$
$233$	−8.13816	−	14.0957i	−0.533148	−	0.923440i	0.466102	−	0.884731i	$-0.345658\pi$
$234$	−0.205737	−	1.16679i	−0.0134495	−	0.0762756i
$235$	−0.858441	+	0.312447i	−0.0559985	+	0.0203818i
$236$	−4.18732	+	7.25265i	−0.272571	+	0.472107i
$237$	5.20368	−	4.36640i	0.338015	−	0.283628i
$238$	5.81908	−	4.88279i	0.377195	−	0.316504i
$239$	14.6493	+	5.33191i	0.947584	+	0.344893i	0.769157	−	0.639060i	$-0.220677\pi$
$239$	14.6493	+	5.33191i	0.947584	+	0.344893i	0.178428	+	0.983953i	$0.442899\pi$
$240$	−0.624485	+	3.54163i	−0.0403103	+	0.228611i
$241$	−0.151826	+	0.861050i	−0.00977999	+	0.0554651i	−0.989307	−	0.145847i	$-0.953409\pi$
$241$	−0.151826	+	0.861050i	−0.00977999	+	0.0554651i	0.979527	+	0.201312i	$0.0645205\pi$
$242$	−9.15657	−	3.33272i	−0.588607	−	0.214235i
$243$	5.09627	−	4.27628i	0.326926	−	0.274323i
$244$	−2.00000	+	1.67820i	−0.128037	+	0.107436i
$245$	−0.690722	+	1.19637i	−0.0441286	+	0.0764330i
$246$	−10.7023	+	3.89533i	−0.682356	+	0.248357i
$247$	1.76399	+	10.0041i	0.112240	+	0.636543i
$248$	−2.26604	−	3.92490i	−0.143894	−	0.249232i
$249$	5.55303	−	9.61814i	0.351909	−	0.609525i
$250$	9.90420	+	3.60483i	0.626397	+	0.227990i
$251$	1.26991	+	2.19956i	0.0801563	+	0.138835i	0.903317	−	0.428974i	$-0.141125\pi$
$251$	1.26991	+	2.19956i	0.0801563	+	0.138835i	−0.823161	+	0.567809i	$0.807791\pi$
$252$	−1.26604	−	1.06234i	−0.0797533	−	0.0669210i
$253$	10.2044			0.641545
$254$	5.38326	+	4.51709i	0.337775	+	0.283427i
$255$	−10.1382	+	3.68999i	−0.634876	+	0.231076i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	2.89187	+	16.4006i	0.180390	+	1.02304i	0.931736	+	0.363135i	$0.118294\pi$
$257$	2.89187	+	16.4006i	0.180390	+	1.02304i	−0.751346	+	0.659908i	$0.770595\pi$
$258$	13.6800			0.851682
$259$	−4.60607	+	14.6972i	−0.286207	+	0.913242i
$260$	4.26083			0.264245
$261$	−1.02569	−	5.81699i	−0.0634888	−	0.360063i
$262$	0.157451	−	0.892951i	0.00972738	−	0.0551667i
$263$	6.14068	−	2.23503i	0.378651	−	0.137818i	−0.145681	−	0.989332i	$-0.546537\pi$
$263$	6.14068	−	2.23503i	0.378651	−	0.137818i	0.524332	+	0.851514i	$0.324315\pi$
$264$	−1.31521	−	1.10359i	−0.0809454	−	0.0679213i
$265$	28.2841			1.73748
$266$	10.8550	+	9.10846i	0.665565	+	0.558475i
$267$	9.95336	+	17.2397i	0.609136	+	1.05505i
$268$	−6.90420	−	2.51292i	−0.421741	−	0.153501i
$269$	4.42902	−	7.67128i	0.270042	−	0.467726i	−0.698830	−	0.715287i	$-0.746296\pi$
$269$	4.42902	−	7.67128i	0.270042	−	0.467726i	0.968872	+	0.247561i	$0.0796291\pi$
$270$	6.56805	+	11.3762i	0.399719	+	0.692333i
$271$	1.64930	+	9.35365i	0.100188	+	0.568194i	0.993034	+	0.117831i	$0.0375941\pi$
$271$	1.64930	+	9.35365i	0.100188	+	0.568194i	−0.892846	+	0.450362i	$0.851295\pi$
$272$	2.81908	−	1.02606i	0.170932	−	0.0622141i
$273$	3.52094	−	6.09845i	0.213097	−	0.369095i
$274$	−1.50000	+	1.25865i	−0.0906183	+	0.0760378i
$275$	0.437633	−	0.367218i	0.0263903	−	0.0221441i
$276$	−13.1099	−	4.77163i	−0.789125	−	0.287218i
$277$	−5.11040	+	28.9825i	−0.307054	+	1.74139i	0.306619	+	0.951832i	$0.400802\pi$
$277$	−5.11040	+	28.9825i	−0.307054	+	1.74139i	−0.613674	+	0.789560i	$0.710309\pi$
$278$	−2.36184	+	13.3947i	−0.141654	+	0.803360i
$279$	−2.77972	−	1.01173i	−0.166417	−	0.0605709i
$280$	4.55303	−	3.82045i	0.272096	−	0.228315i
$281$	4.54323	−	3.81223i	0.271027	−	0.227418i	−0.497137	−	0.867672i	$-0.665615\pi$
$281$	4.54323	−	3.81223i	0.271027	−	0.227418i	0.768163	+	0.640254i	$0.221171\pi$
$282$	−0.298133	+	0.516382i	−0.0177536	+	0.0307501i
$283$	−21.2062	+	7.71843i	−1.26058	+	0.458813i	−0.883963	−	0.467557i	$-0.845134\pi$
$283$	−21.2062	+	7.71843i	−1.26058	+	0.458813i	−0.376615	+	0.926370i	$0.622912\pi$
$284$	−0.448311	−	2.54250i	−0.0266023	−	0.150869i
$285$	−10.0628	−	17.4293i	−0.596071	−	1.03242i
$286$	−1.01707	+	1.76162i	−0.0601409	+	0.104167i
$287$	17.6878	+	6.43783i	1.04408	+	0.380013i
$288$	−0.326352	−	0.565258i	−0.0192305	−	0.0333081i
$289$	−6.12836	−	5.14230i	−0.360492	−	0.302488i
$290$	21.2422			1.24738
$291$	−17.2463	−	14.4713i	−1.01099	−	0.848325i
$292$	0.666374	−	0.242540i	0.0389966	−	0.0141936i
$293$	−0.705737	+	4.00243i	−0.0412296	+	0.233825i	−0.998458	−	0.0555078i	$-0.982322\pi$
$293$	−0.705737	+	4.00243i	−0.0412296	+	0.233825i	0.957229	+	0.289333i	$0.0934333\pi$
$294$	0.156574	+	0.887975i	0.00913158	+	0.0517878i
$295$	−19.6578			−1.14452
$296$	−3.69459	+	4.83218i	−0.214744	+	0.280865i
$297$	−6.27126			−0.363895
$298$	1.16978	+	6.63414i	0.0677634	+	0.384305i
$299$	−2.87030	+	16.2783i	−0.165994	+	0.941397i
$300$	−0.733956	+	0.267138i	−0.0423749	+	0.0154232i
$301$	−17.3195	−	14.5328i	−0.998282	−	0.837658i
$302$	−4.79561			−0.275956
$303$	3.55303	+	2.98135i	0.204116	+	0.171274i
$304$	2.79813	+	4.84651i	0.160484	+	0.277966i
$305$	−5.75877	−	2.09602i	−0.329746	−	0.120018i
$306$	0.979055	−	1.69577i	0.0559689	−	0.0969409i
$307$	5.59240	+	9.68631i	0.319175	+	0.552827i	0.980316	−	0.197434i	$-0.0632609\pi$
$307$	5.59240	+	9.68631i	0.319175	+	0.552827i	−0.661141	+	0.750261i	$0.729928\pi$
$308$	0.492726	+	2.79439i	0.0280757	+	0.159225i
$309$	−12.1172	+	4.41030i	−0.689324	+	0.250893i
$310$	5.31908	−	9.21291i	0.302103	−	0.523258i
$311$	6.32501	−	5.30731i	0.358658	−	0.300950i	−0.445597	−	0.895233i	$-0.647009\pi$
$311$	6.32501	−	5.30731i	0.358658	−	0.300950i	0.804256	+	0.594283i	$0.202564\pi$
$312$	2.13041	−	1.78763i	0.120611	−	0.101205i
$313$	11.0633	+	4.02671i	0.625335	+	0.227603i	0.635199	−	0.772348i	$-0.280918\pi$
$313$	11.0633	+	4.02671i	0.625335	+	0.227603i	−0.00986477	+	0.999951i	$0.503140\pi$
$314$	2.51233	−	14.2481i	0.141779	−	0.804067i
$315$	0.673648	−	3.82045i	0.0379558	−	0.215258i
$316$	−4.16637	−	1.51644i	−0.234377	−	0.0853062i
$317$	10.1441	−	8.51190i	0.569749	−	0.478076i	−0.311814	−	0.950143i	$-0.600937\pi$
$317$	10.1441	−	8.51190i	0.569749	−	0.478076i	0.881562	+	0.472067i	$0.156492\pi$
$318$	14.1420	−	11.8666i	0.793045	−	0.665444i
$319$	−5.07057	+	8.78249i	−0.283898	+	0.491725i
$320$	2.20574	−	0.802823i	0.123304	−	0.0448791i
$321$	1.60741	+	9.11608i	0.0897169	+	0.508810i
$322$	11.5287	+	19.9683i	0.642469	+	1.11279i
$323$	−8.39440	+	14.5395i	−0.467077	+	0.809001i
$324$	6.21688	+	2.26276i	0.345382	+	0.125709i
$325$	0.462697	+	0.801414i	0.0256658	+	0.0444544i
$326$	−7.69846	−	6.45978i	−0.426378	−	0.357774i
$327$	−30.6955			−1.69747
$328$	5.69459	+	4.77833i	0.314431	+	0.263839i
$329$	0.926022	−	0.337044i	0.0510532	−	0.0185819i
$330$	0.699807	−	3.96880i	0.0385231	−	0.218475i
$331$	4.26217	+	24.1720i	0.234270	+	1.32861i	0.844145	+	0.536115i	$0.180109\pi$
$331$	4.26217	+	24.1720i	0.234270	+	1.32861i	−0.609875	+	0.792498i	$0.708780\pi$
$332$	−7.24897			−0.397839
$333$	0.180045	+	3.96616i	0.00986639	+	0.217344i
$334$	−10.4415			−0.571334
$335$	−2.99479	−	16.9843i	−0.163623	−	0.927950i
$336$	0.673648	−	3.82045i	0.0367505	−	0.208423i
$337$	−11.3576	+	4.13381i	−0.618686	+	0.225183i	−0.632299	−	0.774724i	$-0.717889\pi$
$337$	−11.3576	+	4.13381i	−0.618686	+	0.225183i	0.0136136	+	0.999907i	$0.495667\pi$
$338$	7.43448	+	6.23827i	0.404382	+	0.339317i
$339$	−3.90167			−0.211910
$340$	5.39440	+	4.52644i	0.292552	+	0.245481i
$341$	2.53936	+	4.39831i	0.137514	+	0.238182i
$342$	3.43242	+	1.24930i	0.185604	+	0.0675543i
$343$	9.60741	−	16.6405i	0.518751	−	0.898504i
$344$	−4.46451	−	7.73275i	−0.240710	−	0.416922i
$345$	−5.68660	−	32.2503i	−0.306156	−	1.73630i
$346$	0.986329	−	0.358995i	0.0530254	−	0.0192997i
$347$	0.904200	−	1.56612i	0.0485400	−	0.0840738i	−0.840735	−	0.541447i	$-0.817876\pi$
$347$	0.904200	−	1.56612i	0.0485400	−	0.0840738i	0.889275	+	0.457374i	$0.151210\pi$
$348$	10.6211	−	8.91215i	0.569350	−	0.477741i
$349$	3.95677	−	3.32012i	0.211801	−	0.177722i	−0.530715	−	0.847550i	$-0.678077\pi$
$349$	3.95677	−	3.32012i	0.211801	−	0.177722i	0.742516	+	0.669828i	$0.233632\pi$
$350$	1.21301	+	0.441500i	0.0648382	+	0.0235992i
$351$	1.76399	−	10.0041i	0.0941546	−	0.533977i
$352$	−0.194593	+	1.10359i	−0.0103718	+	0.0588216i
$353$	29.1570	+	10.6123i	1.55187	+	0.564835i	0.968856	−	0.247625i	$-0.0796500\pi$
$353$	29.1570	+	10.6123i	1.55187	+	0.564835i	0.583017	+	0.812460i	$0.301872\pi$
$354$	−9.82888	+	8.24741i	−0.522399	+	0.438345i
$355$	4.64227	−	3.89533i	0.246386	−	0.206743i
$356$	6.49660	−	11.2524i	0.344319	−	0.596378i
$357$	10.9363	−	3.98048i	0.578810	−	0.210670i
$358$	−1.58987	−	9.01660i	−0.0840272	−	0.476542i
$359$	−1.51367	−	2.62175i	−0.0798885	−	0.138371i	0.823313	−	0.567587i	$-0.192123\pi$
$359$	−1.51367	−	2.62175i	−0.0798885	−	0.138371i	−0.903202	+	0.429216i	$0.858790\pi$
$360$	0.766044	−	1.32683i	0.0403741	−	0.0699300i
$361$	−11.5753	−	4.21307i	−0.609227	−	0.221741i
$362$	−11.3020	−	19.5756i	−0.594020	−	1.02887i
$363$	−11.4363	−	9.59619i	−0.600250	−	0.503669i
$364$	−4.59627			−0.240910
$365$	1.27513	+	1.06996i	0.0667433	+	0.0560043i
$366$	−3.75877	+	1.36808i	−0.196474	+	0.0715107i
$367$	4.82651	−	27.3725i	0.251942	−	1.42883i	−0.551860	−	0.833937i	$-0.686082\pi$
$367$	4.82651	−	27.3725i	0.251942	−	1.42883i	0.803802	−	0.594897i	$-0.202807\pi$
$368$	1.58125	+	8.96773i	0.0824285	+	0.467475i
$369$	4.85204			0.252587
$370$	−14.1591	−	1.83915i	−0.736097	−	0.0956131i
$371$	−30.5107			−1.58404
$372$	−1.20574	−	6.83807i	−0.0625146	−	0.354538i
$373$	0.898681	−	5.09667i	0.0465319	−	0.263896i	−0.952662	−	0.304030i	$-0.901668\pi$
$373$	0.898681	−	5.09667i	0.0465319	−	0.263896i	0.999194	+	0.0401346i	$0.0127787\pi$
$374$	−3.15910	+	1.14982i	−0.163353	+	0.0594557i
$375$	12.3701	+	10.3797i	0.638787	+	0.536006i
$376$	0.389185			0.0200707
$377$	−12.5838	−	10.5590i	−0.648098	−	0.543818i
$378$	−7.08512	−	12.2718i	−0.364419	−	0.631193i
$379$	19.8195	+	7.21372i	1.01806	+	0.370544i	0.796523	−	0.604608i	$-0.206670\pi$
$379$	19.8195	+	7.21372i	1.01806	+	0.370544i	0.221538	+	0.975152i	$0.428892\pi$
$380$	−6.56805	+	11.3762i	−0.336934	+	0.583586i
$381$	5.38326	+	9.32407i	0.275793	+	0.477687i
$382$	3.32248	+	18.8427i	0.169993	+	0.964078i
$383$	36.6771	−	13.3494i	1.87411	−	0.682121i	0.911455	−	0.411400i	$-0.134960\pi$
$383$	36.6771	−	13.3494i	1.87411	−	0.682121i	0.962658	−	0.270721i	$-0.0872621\pi$
$384$	0.766044	−	1.32683i	0.0390920	−	0.0677094i
$385$	−5.10220	+	4.28125i	−0.260032	+	0.218193i
$386$	14.5646	−	12.2212i	0.741321	−	0.622042i
$387$	−5.47653	−	1.99329i	−0.278388	−	0.101325i
$388$	−2.55169	+	14.4713i	−0.129542	+	0.734671i
$389$	2.78312	−	15.7838i	0.141110	−	0.800273i	−0.829299	−	0.558805i	$-0.811260\pi$
$389$	2.78312	−	15.7838i	0.141110	−	0.800273i	0.970409	−	0.241468i	$-0.0776289\pi$
$390$	6.13429	+	2.23270i	0.310622	+	0.113057i
$391$	−20.9270	+	17.5598i	−1.05832	+	0.888037i
$392$	0.450837	−	0.378297i	0.0227707	−	0.0191069i
$393$	0.694593	−	1.20307i	0.0350376	−	0.0606868i
$394$	17.3662	−	6.32077i	0.874896	−	0.318436i
$395$	−1.80722	−	10.2492i	−0.0909310	−	0.515695i
$396$	0.365715	+	0.633436i	0.0183779	+	0.0318314i
$397$	−7.32042	+	12.6793i	−0.367401	+	0.636358i	−0.989158	−	0.146852i	$-0.953086\pi$
$397$	−7.32042	+	12.6793i	−0.367401	+	0.636358i	0.621757	+	0.783210i	$0.286419\pi$
$398$	−5.23783	−	1.90641i	−0.262548	−	0.0955598i
$399$	10.8550	+	18.8015i	0.543432	+	0.941251i
$400$	0.390530	+	0.327693i	0.0195265	+	0.0163847i
$401$	11.8075			0.589637			0.294818	−	0.955553i	$-0.404741\pi$
$401$	11.8075			0.589637			0.294818	+	0.955553i	$0.404741\pi$
$402$	−8.62314	−	7.23567i	−0.430083	−	0.360883i
$403$	−7.73055	+	2.81369i	−0.385086	+	0.140160i
$404$	0.525692	−	2.98135i	0.0261542	−	0.148328i
$405$	2.69665	+	15.2935i	0.133998	+	0.759939i
$406$	−22.9145			−1.13723
$407$	4.14022	−	5.41501i	0.205223	−	0.268412i
$408$	4.59627			0.227549
$409$	0.975652	+	5.53320i	0.0482429	+	0.273599i	0.999382	−	0.0351652i	$-0.0111957\pi$
$409$	0.975652	+	5.53320i	0.0482429	+	0.273599i	−0.951139	+	0.308764i	$0.900085\pi$
$410$	−3.03003	+	17.1842i	−0.149642	+	0.848665i
$411$	−2.81908	+	1.02606i	−0.139055	+	0.0506118i
$412$	6.44743	+	5.41004i	0.317642	+	0.266533i
$413$	21.2053			1.04345
$414$	4.55303	+	3.82045i	0.223769	+	0.187765i
$415$	−8.50774	−	14.7358i	−0.417629	−	0.723354i
$416$	−1.70574	−	0.620838i	−0.0836306	−	0.0304391i
$417$	−10.4192	+	18.0466i	−0.510231	+	0.883746i
$418$	−3.13563	−	5.43107i	−0.153369	−	0.265642i
$419$	−1.76171	−	9.99114i	−0.0860650	−	0.488099i	−0.997122	−	0.0758179i	$-0.975843\pi$
$419$	−1.76171	−	9.99114i	−0.0860650	−	0.488099i	0.911057	−	0.412281i	$-0.135268\pi$
$420$	8.55690	−	3.11446i	0.417534	−	0.151970i
$421$	−5.48158	+	9.49438i	−0.267156	+	0.462728i	−0.968126	−	0.250463i	$-0.919417\pi$
$421$	−5.48158	+	9.49438i	−0.267156	+	0.462728i	0.700970	+	0.713190i	$0.252751\pi$
$422$	−16.6309	+	13.9550i	−0.809579	+	0.679317i
$423$	0.194593	−	0.163283i	0.00946142	−	0.00793908i
$424$	−11.3229	−	4.12122i	−0.549891	−	0.200144i
$425$	−0.265578	+	1.50617i	−0.0128824	+	0.0730598i
$426$	0.686852	−	3.89533i	0.0332781	−	0.188729i
$427$	6.21213	+	2.26103i	0.300626	+	0.109419i
$428$	4.62836	−	3.88365i	0.223720	−	0.187723i
$429$	−2.38737	+	2.00324i	−0.115264	+	0.0967176i
$430$	10.4795	−	18.1511i	0.505367	−	0.875322i
$431$	−4.80066	+	1.74730i	−0.231240	+	0.0841643i	−0.455041	−	0.890470i	$-0.650375\pi$
$431$	−4.80066	+	1.74730i	−0.231240	+	0.0841643i	0.223802	+	0.974635i	$0.428153\pi$
$432$	−0.971782	−	5.51125i	−0.0467549	−	0.265160i
$433$	13.8712	+	24.0257i	0.666609	+	1.15460i	0.978846	+	0.204596i	$0.0655882\pi$
$433$	13.8712	+	24.0257i	0.666609	+	1.15460i	−0.312237	+	0.950004i	$0.601078\pi$
$434$	−5.73783	+	9.93821i	−0.275424	+	0.477049i
$435$	30.5822	+	11.1310i	1.46630	+	0.533691i
$436$	10.0175	+	17.3509i	0.479753	+	0.830957i
$437$	−39.0376	−	32.7564i	−1.86742	−	1.56695i
$438$	1.08647			0.0519134
$439$	−22.3214	−	18.7298i	−1.06534	−	0.893927i	−0.0707180	−	0.997496i	$-0.522529\pi$
$439$	−22.3214	−	18.7298i	−1.06534	−	0.893927i	−0.994622	+	0.103570i	$0.966973\pi$
$440$	−2.47178	+	0.899655i	−0.117838	+	0.0428894i
$441$	0.0667040	−	0.378297i	0.00317638	−	0.0180141i
$442$	−0.945622	−	5.36289i	−0.0449787	−	0.255087i
$443$	6.97864			0.331565			0.165783	−	0.986162i	$-0.446985\pi$
$443$	6.97864			0.331565			0.165783	+	0.986162i	$0.446985\pi$
$444$	−7.85117	+	5.02087i	−0.372600	+	0.238280i
$445$	30.4989			1.44579
$446$	1.76130	+	9.98881i	0.0833998	+	0.472984i
$447$	−1.79220	+	10.1641i	−0.0847683	+	0.480745i
$448$	−2.37939	+	0.866025i	−0.112415	+	0.0409159i
$449$	13.9834	+	11.7335i	0.659917	+	0.553736i	0.910062	−	0.414472i	$-0.136034\pi$
$449$	13.9834	+	11.7335i	0.659917	+	0.553736i	−0.250145	+	0.968208i	$0.580478\pi$
$450$	0.332748			0.0156859
$451$	−6.38144	−	5.35467i	−0.300490	−	0.252141i
$452$	1.27332	+	2.20545i	0.0598919	+	0.103736i
$453$	−6.90420	−	2.51292i	−0.324388	−	0.118067i
$454$	−2.18345	+	3.78184i	−0.102474	+	0.177491i
$455$	−5.39440	−	9.34337i	−0.252893	−	0.438024i
$456$	1.48886	+	8.44372i	0.0697221	+	0.395413i
$457$	21.4209	−	7.79656i	1.00203	−	0.364708i	0.211660	−	0.977343i	$-0.432113\pi$
$457$	21.4209	−	7.79656i	1.00203	−	0.364708i	0.790365	+	0.612636i	$0.209891\pi$
$458$	−5.88666	+	10.1960i	−0.275066	+	0.476427i
$459$	12.8610	−	10.7916i	0.600299	−	0.503710i
$460$	−16.3739	+	13.7394i	−0.763438	+	0.640601i
$461$	−8.17277	−	2.97465i	−0.380644	−	0.138543i	0.144610	−	0.989489i	$-0.453807\pi$
$461$	−8.17277	−	2.97465i	−0.380644	−	0.138543i	−0.525254	+	0.850946i	$0.676030\pi$
$462$	−0.754900	+	4.28125i	−0.0351211	+	0.199182i
$463$	0.592701	−	3.36137i	0.0275451	−	0.156216i	−0.967933	−	0.251209i	$-0.919172\pi$
$463$	0.592701	−	3.36137i	0.0275451	−	0.156216i	0.995478	+	0.0949930i	$0.0302829\pi$
$464$	−8.50387	−	3.09516i	−0.394782	−	0.143689i
$465$	12.4855	−	10.4765i	0.578999	−	0.485838i
$466$	−12.4684	+	10.4622i	−0.577586	+	0.484653i
$467$	−18.3170	+	31.7260i	−0.847611	+	1.46810i	0.0357242	+	0.999362i	$0.488626\pi$
$467$	−18.3170	+	31.7260i	−0.847611	+	1.46810i	−0.883335	+	0.468743i	$0.844707\pi$
$468$	−1.11334	+	0.405223i	−0.0514642	+	0.0187314i
$469$	3.23055	+	18.3214i	0.149173	+	0.846002i
$470$	0.456767	+	0.791143i	0.0210691	+	0.0364927i
$471$	11.0831	−	19.1964i	0.510681	−	0.884525i
$472$	7.86959	+	2.86429i	0.362227	+	0.131840i
$473$	5.00299	+	8.66544i	0.230038	+	0.398437i
$474$	−5.20368	−	4.36640i	−0.239013	−	0.200556i
$475$	−2.85298			−0.130904
$476$	−5.81908	−	4.88279i	−0.266717	−	0.223802i
$477$	−7.39053	+	2.68993i	−0.338389	+	0.123164i
$478$	2.70708	−	15.3526i	0.123819	−	0.702213i
$479$	−3.57832	−	20.2936i	−0.163497	−	0.927240i	−0.950600	−	0.310418i	$-0.899531\pi$
$479$	−3.57832	−	20.2936i	−0.163497	−	0.927240i	0.787103	−	0.616822i	$-0.211580\pi$
$480$	3.59627			0.164146
$481$	7.47359	+	8.12771i	0.340766	+	0.370592i
$482$	0.874333			0.0398248
$483$	6.13429	+	34.7893i	0.279120	+	1.58297i
$484$	−1.69207	+	9.59619i	−0.0769121	+	0.436190i
$485$	−32.4124	+	11.7972i	−1.47177	+	0.535681i
$486$	−5.09627	−	4.27628i	−0.231171	−	0.193976i
$487$	42.2867			1.91620			0.958098	−	0.286442i	$-0.0924726\pi$
$487$	42.2867			1.91620			0.958098	+	0.286442i	$0.0924726\pi$
$488$	2.00000	+	1.67820i	0.0905357	+	0.0759685i
$489$	−7.69846	−	13.3341i	−0.348137	−	0.602990i
$490$	1.29813	+	0.472482i	0.0586437	+	0.0213446i
$491$	−16.5560	+	28.6759i	−0.747163	+	1.29412i	0.202014	+	0.979383i	$0.435251\pi$
$491$	−16.5560	+	28.6759i	−0.747163	+	1.29412i	−0.949177	+	0.314742i	$0.898082\pi$
$492$	5.69459	+	9.86332i	0.256732	+	0.444673i
$493$	−4.71436	−	26.7364i	−0.212324	−	1.20415i
$494$	9.54576	−	3.47437i	0.429484	−	0.156319i
$495$	−0.858441	+	1.48686i	−0.0385840	+	0.0668295i
$496$	−3.47178	+	2.91317i	−0.155888	+	0.130805i
$497$	−5.00774	+	4.20199i	−0.224628	+	0.188485i
$498$	−10.4363	−	3.79850i	−0.467661	−	0.170215i
$499$	−1.73577	+	9.84402i	−0.0777036	+	0.440679i	0.920990	+	0.389586i	$0.127382\pi$
$499$	−1.73577	+	9.84402i	−0.0777036	+	0.440679i	−0.998694	+	0.0510934i	$0.983729\pi$
$500$	1.83022	−	10.3797i	0.0818500	−	0.464195i
$501$	−15.0326	−	5.47140i	−0.671605	−	0.244444i
$502$	1.94562	−	1.63257i	0.0868374	−	0.0728652i
$503$	25.5023	−	21.3990i	1.13709	−	0.954132i	0.137751	−	0.990467i	$-0.456013\pi$
$503$	25.5023	−	21.3990i	1.13709	−	0.954132i	0.999340	+	0.0363348i	$0.0115683\pi$
$504$	−0.826352	+	1.43128i	−0.0368086	+	0.0637544i
$505$	6.67752	−	2.43042i	0.297146	−	0.108152i
$506$	−1.77197	−	10.0494i	−0.0787739	−	0.446749i
$507$	7.43448	+	12.8769i	0.330177	+	0.571883i
$508$	3.51367	−	6.08586i	0.155894	−	0.270016i
$509$	−19.3751	−	7.05196i	−0.858786	−	0.312573i	−0.125169	−	0.992135i	$-0.539947\pi$
$509$	−19.3751	−	7.05196i	−0.858786	−	0.312573i	−0.733617	+	0.679563i	$0.762170\pi$
$510$	5.39440	+	9.34337i	0.238868	+	0.413732i
$511$	−1.37551	−	1.15419i	−0.0608492	−	0.0510585i
$512$	−1.00000			−0.0441942
$513$	23.9911	+	20.1310i	1.05923	+	0.888803i
$514$	15.6493	−	5.69588i	0.690261	−	0.251234i
$515$	−3.43061	+	19.4559i	−0.151171	+	0.857331i
$516$	−2.37551	−	13.4722i	−0.104576	−	0.593081i
$517$	−0.436127			−0.0191808
$518$	15.2738	+	1.98394i	0.671092	+	0.0871694i
$519$	1.60813			0.0705889
$520$	−0.739885	−	4.19610i	−0.0324461	−	0.184011i
$521$	−4.53121	+	25.6978i	−0.198516	+	1.12584i	0.708806	+	0.705404i	$0.249234\pi$
$521$	−4.53121	+	25.6978i	−0.198516	+	1.12584i	−0.907322	+	0.420437i	$0.861877\pi$
$522$	−5.55051	+	2.02022i	−0.242939	+	0.0884226i
$523$	1.10535	+	0.927500i	0.0483337	+	0.0405567i	0.666634	−	0.745385i	$-0.267734\pi$
$523$	1.10535	+	0.927500i	0.0483337	+	0.0405567i	−0.618301	+	0.785942i	$0.712179\pi$
$524$	−0.906726			−0.0396105
$525$	1.51501	+	1.27125i	0.0661207	+	0.0554818i
$526$	−3.26739	−	5.65928i	−0.142465	−	0.246756i
$527$	−12.7763	−	4.65020i	−0.556545	−	0.202566i
$528$	−0.858441	+	1.48686i	−0.0373588	+	0.0647074i
$529$	−29.9602	−	51.8926i	−1.30262	−	2.25620i
$530$	−4.91147	−	27.8544i	−0.213341	−	1.20992i
$531$	5.13651	−	1.86954i	0.222905	−	0.0811309i
$532$	7.08512	−	12.2718i	0.307179	−	0.532050i
$533$	10.3369	−	8.67366i	0.447739	−	0.375698i
$534$	15.2494	−	12.7958i	0.659908	−	0.553728i
$535$	13.3268	+	4.85057i	0.576169	+	0.209708i
$536$	−1.27584	+	7.23567i	−0.0551081	+	0.312534i
$537$	2.43582	−	13.8142i	0.105113	−	0.596128i
$538$	−8.32383	−	3.02962i	−0.358866	−	0.130616i
$539$	−0.505215	+	0.423925i	−0.0217611	+	0.0182598i
$540$	10.0628	−	8.44372i	0.433035	−	0.363360i
$541$	2.72921	−	4.72713i	0.117338	−	0.203235i	−0.801374	−	0.598164i	$-0.795897\pi$
$541$	2.72921	−	4.72713i	0.117338	−	0.203235i	0.918712	+	0.394929i	$0.129231\pi$
$542$	8.92514	−	3.24849i	0.383368	−	0.139534i
$543$	−6.01367	−	34.1052i	−0.258071	−	1.46360i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	−23.5141	+	40.7277i	−1.00723	+	1.74458i
$546$	−6.61721	−	2.40847i	−0.283190	−	0.103073i
$547$	−20.1086	−	34.8291i	−0.859781	−	1.48918i	−0.872137	−	0.489261i	$-0.837266\pi$
$547$	−20.1086	−	34.8291i	−0.859781	−	1.48918i	0.0123559	−	0.999924i	$-0.496067\pi$
$548$	1.50000	+	1.25865i	0.0640768	+	0.0537668i
$549$	1.70409			0.0727287
$550$	−0.437633	−	0.367218i	−0.0186607	−	0.0156582i
$551$	47.5899	−	17.3213i	2.02740	−	0.737913i
$552$	−2.42262	+	13.7394i	−0.103113	+	0.584786i
$553$	1.94949	+	11.0561i	0.0829009	+	0.470154i
$554$	29.4296			1.25035
$555$	−19.4210	−	10.0673i	−0.824377	−	0.427331i
$556$	13.6013			0.576824
$557$	−3.06640	−	17.3904i	−0.129928	−	0.736856i	−0.978259	−	0.207389i	$-0.933503\pi$
$557$	−3.06640	−	17.3904i	−0.129928	−	0.736856i	0.848331	−	0.529466i	$-0.177608\pi$
$558$	−0.513671	+	2.91317i	−0.0217454	+	0.123324i
$559$	−15.2306	+	5.54347i	−0.644184	+	0.234464i
$560$	−4.55303	−	3.82045i	−0.192401	−	0.161443i
$561$	−5.15064			−0.217460
$562$	−4.54323	−	3.81223i	−0.191645	−	0.160809i
$563$	−1.15523	−	2.00092i	−0.0486871	−	0.0843286i	0.840655	−	0.541571i	$-0.182170\pi$
$563$	−1.15523	−	2.00092i	−0.0486871	−	0.0843286i	−0.889342	+	0.457243i	$0.848837\pi$
$564$	0.560307	+	0.203935i	0.0235932	+	0.00858722i
$565$	−2.98886	+	5.17685i	−0.125742	+	0.217792i
$566$	11.2836	+	19.5437i	0.474284	+	0.821485i
$567$	−2.90895	−	16.4975i	−0.122164	−	0.692828i
$568$	−2.42602	+	0.883000i	−0.101794	+	0.0370498i
$569$	0.141559	−	0.245188i	0.00593447	−	0.0102788i	−0.863043	−	0.505131i	$-0.831444\pi$
$569$	0.141559	−	0.245188i	0.00593447	−	0.0102788i	0.868977	+	0.494852i	$0.164778\pi$
$570$	−15.4172	+	12.9365i	−0.645754	+	0.541852i
$571$	−8.40420	+	7.05196i	−0.351705	+	0.295115i	−0.801474	−	0.598029i	$-0.795951\pi$
$571$	−8.40420	+	7.05196i	−0.351705	+	0.295115i	0.449769	+	0.893145i	$0.351506\pi$
$572$	1.91147	+	0.695720i	0.0799227	+	0.0290895i
$573$	−5.09034	+	28.8687i	−0.212652	+	1.20601i
$574$	3.26857	−	18.5370i	0.136428	−	0.773719i
$575$	−4.36231	−	1.58775i	−0.181921	−	0.0662138i
$576$	−0.500000	+	0.419550i	−0.0208333	+	0.0174812i
$577$	−12.1382	+	10.1851i	−0.505318	+	0.424012i	−0.859478	−	0.511173i	$-0.829211\pi$
$577$	−12.1382	+	10.1851i	−0.505318	+	0.424012i	0.354160	+	0.935185i	$0.384767\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	27.3726	−	9.96280i	1.13757	−	0.414040i
$580$	−3.68866	−	20.9194i	−0.153163	−	0.868633i
$581$	9.17752	+	15.8959i	0.380748	+	0.659474i
$582$	−11.2567	+	19.4972i	−0.466606	+	0.808185i
$583$	12.6887	+	4.61830i	0.525511	+	0.191270i
$584$	−0.354570	−	0.614134i	−0.0146722	−	0.0254130i
$585$	−2.13041	−	1.78763i	−0.0880818	−	0.0739094i
$586$	4.06418			0.167890
$587$	−14.2947	−	11.9947i	−0.590007	−	0.495074i	0.298209	−	0.954500i	$-0.403611\pi$
$587$	−14.2947	−	11.9947i	−0.590007	−	0.495074i	−0.888216	+	0.459426i	$0.848055\pi$
$588$	0.847296	−	0.308391i	0.0349419	−	0.0127178i
$589$	4.40420	−	24.9775i	0.181472	−	1.02918i
$590$	3.41353	+	19.3591i	0.140533	+	0.797002i
$591$	28.3141			1.16469
$592$	5.40033	+	2.79936i	0.221952	+	0.115053i
$593$	−39.4329			−1.61932			−0.809658	−	0.586901i	$-0.800348\pi$
$593$	−39.4329			−1.61932			−0.809658	+	0.586901i	$0.800348\pi$
$594$	1.08899	+	6.17598i	0.0446819	+	0.253404i
$595$	3.09627	−	17.5598i	0.126935	−	0.719882i
$596$	6.33022	−	2.30401i	0.259296	−	0.0943760i
$597$	−6.54189	−	5.48930i	−0.267742	−	0.224662i
$598$	16.5294			0.675937
$599$	5.35710	+	4.49514i	0.218885	+	0.183666i	0.745636	−	0.666353i	$-0.232146\pi$
$599$	5.35710	+	4.49514i	0.218885	+	0.183666i	−0.526751	+	0.850019i	$0.676590\pi$
$600$	0.390530	+	0.676417i	0.0159433	+	0.0276146i
$601$	−33.7301	−	12.2768i	−1.37588	−	0.500780i	−0.454954	−	0.890515i	$-0.650344\pi$
$601$	−33.7301	−	12.2768i	−1.37588	−	0.500780i	−0.920927	+	0.389735i	$0.872567\pi$
$602$	−11.3045	+	19.5800i	−0.460738	+	0.798022i
$603$	2.39780	+	4.15312i	0.0976461	+	0.169128i
$604$	0.832748	+	4.72275i	0.0338841	+	0.192166i
$605$	−21.4932	+	7.82288i	−0.873823	+	0.318045i
$606$	2.31908	−	4.01676i	0.0942061	−	0.163170i
$607$	8.60788	−	7.22287i	0.349383	−	0.293167i	−0.451159	−	0.892443i	$-0.648989\pi$
$607$	8.60788	−	7.22287i	0.349383	−	0.293167i	0.800542	+	0.599276i	$0.204545\pi$
$608$	4.28699	−	3.59721i	0.173860	−	0.145886i
$609$	−32.9898	−	12.0073i	−1.33681	−	0.486560i
$610$	−1.06418	+	6.03525i	−0.0430873	+	0.244360i
$611$	0.122674	−	0.695720i	0.00496286	−	0.0281458i
$612$	−1.84002	−	0.669713i	−0.0743785	−	0.0270716i
$613$	0.735767	−	0.617381i	0.0297173	−	0.0249358i	−0.627808	−	0.778368i	$-0.716048\pi$
$613$	0.735767	−	0.617381i	0.0297173	−	0.0249358i	0.657525	+	0.753432i	$0.271603\pi$
$614$	8.56805	−	7.18945i	0.345778	−	0.290142i
$615$	−13.3669	+	23.1521i	−0.539005	+	0.933585i
$616$	2.66637	−	0.970481i	0.107431	−	0.0391018i
$617$	−3.71641	−	21.0768i	−0.149617	−	0.848521i	−0.963543	−	0.267553i	$-0.913785\pi$
$617$	−3.71641	−	21.0768i	−0.149617	−	0.848521i	0.813926	−	0.580969i	$-0.197326\pi$
$618$	6.44743	+	11.1673i	0.259354	+	0.449214i
$619$	−5.72550	+	9.91686i	−0.230127	+	0.398592i	−0.957845	−	0.287284i	$-0.907248\pi$
$619$	−5.72550	+	9.91686i	−0.230127	+	0.398592i	0.727718	+	0.685876i	$0.240581\pi$
$620$	−9.99660	−	3.63846i	−0.401473	−	0.146124i
$621$	25.4800	+	44.1326i	1.02248	+	1.77098i
$622$	−6.32501	−	5.30731i	−0.253610	−	0.212804i
$623$	−32.8999			−1.31811
$624$	−2.13041	−	1.78763i	−0.0852849	−	0.0715625i
$625$	25.6434	−	9.33342i	1.02573	−	0.373337i
$626$	2.04442	−	11.5945i	0.0817113	−	0.463408i
$627$	−1.66843	−	9.46216i	−0.0666308	−	0.377882i
$628$	−14.4679			−0.577333
$629$	0.827534	+	18.2295i	0.0329959	+	0.726858i
$630$	−3.87939			−0.154558
$631$	8.35710	+	47.3954i	0.332691	+	1.88678i	0.448938	+	0.893563i	$0.351802\pi$
$631$	8.35710	+	47.3954i	0.332691	+	1.88678i	−0.116247	+	0.993220i	$0.537087\pi$
$632$	−0.769915	+	4.36640i	−0.0306256	+	0.173686i
$633$	−31.2558	+	11.3762i	−1.24231	+	0.452163i
$634$	−10.1441	−	8.51190i	−0.402873	−	0.338051i
$635$	16.4953			0.654594
$636$	−14.1420	−	11.8666i	−0.560768	−	0.470540i
$637$	−0.534148	−	0.925172i	−0.0211637	−	0.0366566i
$638$	9.52956	+	3.46848i	0.377279	+	0.137318i
$639$	−0.842549	+	1.45934i	−0.0333307	+	0.0577305i
$640$	−1.17365	−	2.03282i	−0.0463925	−	0.0803542i
$641$	5.53121	+	31.3691i	0.218470	+	1.23900i	0.874783	+	0.484515i	$0.161004\pi$
$641$	5.53121	+	31.3691i	0.218470	+	1.23900i	−0.656313	+	0.754488i	$0.727885\pi$
$642$	8.69846	−	3.16598i	0.343301	−	0.124951i
$643$	−11.2897	+	19.5543i	−0.445221	+	0.771146i	−0.998068	−	0.0621372i	$-0.980208\pi$
$643$	−11.2897	+	19.5543i	−0.445221	+	0.771146i	0.552846	+	0.833283i	$0.313542\pi$
$644$	17.6630	−	14.8210i	0.696019	−	0.584029i
$645$	24.5985	−	20.6406i	0.968567	−	0.812724i
$646$	15.7763	+	5.74211i	0.620711	+	0.225920i
$647$	5.12954	−	29.0911i	0.201663	−	1.14369i	−0.700942	−	0.713218i	$-0.747237\pi$
$647$	5.12954	−	29.0911i	0.201663	−	1.14369i	0.902605	−	0.430469i	$-0.141652\pi$
$648$	1.14883	−	6.51536i	0.0451304	−	0.255947i
$649$	−8.81877	−	3.20977i	−0.346167	−	0.125995i
$650$	0.708892	−	0.594831i	0.0278050	−	0.0233312i
$651$	−13.4684	+	11.3013i	−0.527867	+	0.442933i
$652$	−5.02481	+	8.70323i	−0.196787	+	0.340845i
$653$	8.71600	−	3.17237i	0.341084	−	0.124144i	−0.165799	−	0.986160i	$-0.553020\pi$
$653$	8.71600	−	3.17237i	0.341084	−	0.124144i	0.506882	+	0.862015i	$0.330798\pi$
$654$	5.33022	+	30.2292i	0.208428	+	1.18205i
$655$	−1.06418	−	1.84321i	−0.0415809	−	0.0720202i
$656$	3.71688	−	6.43783i	0.145120	−	0.251355i
$657$	−0.434945	−	0.158307i	−0.0169688	−	0.00617614i
$658$	−0.492726	−	0.853427i	−0.0192085	−	0.0332700i
$659$	20.8418	+	17.4884i	0.811883	+	0.681250i	0.951056	−	0.309018i	$-0.100000\pi$
$659$	20.8418	+	17.4884i	0.811883	+	0.681250i	−0.139174	+	0.990268i	$0.544445\pi$
$660$	−4.03003			−0.156869
$661$	8.43763	+	7.08001i	0.328186	+	0.275381i	0.791960	−	0.610573i	$-0.209061\pi$
$661$	8.43763	+	7.08001i	0.328186	+	0.275381i	−0.463774	+	0.885953i	$0.653505\pi$
$662$	23.0646	−	8.39484i	0.896433	−	0.326275i
$663$	1.44878	−	8.21643i	0.0562659	−	0.319100i
$664$	1.25877	+	7.13884i	0.0488498	+	0.277041i
$665$	33.2618			1.28984
$666$	3.87464	−	0.866025i	0.150139	−	0.0335578i
$667$	82.4065			3.19079
$668$	1.81315	+	10.2829i	0.0701528	+	0.397856i
$669$	−2.69846	+	15.3037i	−0.104329	+	0.591677i
$670$	−16.2062	+	5.89858i	−0.626100	+	0.227882i
$671$	−2.24123	−	1.88061i	−0.0865217	−	0.0726003i
$672$	−3.87939			−0.149651
$673$	10.1141	+	8.48670i	0.389868	+	0.327138i	0.816562	−	0.577258i	$-0.195877\pi$
$673$	10.1141	+	8.48670i	0.389868	+	0.327138i	−0.426694	+	0.904396i	$0.640322\pi$
$674$	6.04323	+	10.4672i	0.232777	+	0.403181i
$675$	2.68092	+	0.975776i	0.103189	+	0.0375576i
$676$	4.85251	−	8.40480i	0.186635	−	0.323261i
$677$	17.7763	+	30.7895i	0.683199	+	1.18334i	0.973999	+	0.226552i	$0.0727452\pi$
$677$	17.7763	+	30.7895i	0.683199	+	1.18334i	−0.290800	+	0.956784i	$0.593921\pi$
$678$	0.677519	+	3.84240i	0.0260199	+	0.147566i
$679$	34.9641	−	12.7259i	1.34180	−	0.488375i
$680$	3.52094	−	6.09845i	0.135022	−	0.233865i
$681$	−5.12520	+	4.30055i	−0.196398	+	0.164798i
$682$	3.89053	−	3.26454i	0.148976	−	0.125006i
$683$	−30.8756	−	11.2378i	−1.18142	−	0.430002i	−0.324717	−	0.945811i	$-0.605269\pi$
$683$	−30.8756	−	11.2378i	−1.18142	−	0.430002i	−0.856704	+	0.515809i	$0.827491\pi$
$684$	0.634285	−	3.59721i	0.0242525	−	0.137543i
$685$	−0.798133	+	4.52644i	−0.0304951	+	0.172946i
$686$	−18.0560	−	6.57186i	−0.689382	−	0.250915i
$687$	−13.8177	+	11.5945i	−0.527179	+	0.442356i
$688$	−6.84002	+	5.73946i	−0.260773	+	0.218815i
$689$	−10.9363	+	18.9422i	−0.416639	+	0.721641i
$690$	−30.7729	+	11.2004i	−1.17150	+	0.426393i
$691$	−7.38089	−	41.8591i	−0.280782	−	1.59240i	−0.719973	−	0.694002i	$-0.755846\pi$
$691$	−7.38089	−	41.8591i	−0.280782	−	1.59240i	0.439191	−	0.898394i	$-0.355265\pi$
$692$	−0.524815	−	0.909006i	−0.0199505	−	0.0345552i
$693$	0.926022	−	1.60392i	0.0351767	−	0.0609278i
$694$	−1.69934	−	0.618509i	−0.0645061	−	0.0234783i
$695$	15.9632	+	27.6490i	0.605517	+	1.04879i
$696$	−10.6211	−	8.91215i	−0.402591	−	0.337814i
$697$	22.3013			0.844722
$698$	−3.95677	−	3.32012i	−0.149766	−	0.125668i
$699$	−23.4329	+	8.52887i	−0.886313	+	0.322592i
$700$	0.224155	−	1.27125i	0.00847228	−	0.0480487i
$701$	−2.88161	−	16.3424i	−0.108837	−	0.617244i	−0.989618	−	0.143721i	$-0.954093\pi$
$701$	−2.88161	−	16.3424i	−0.108837	−	0.617244i	0.880781	−	0.473523i	$-0.157018\pi$
$702$	−10.1584			−0.383404
$703$	−33.2211	+	7.42528i	−1.25296	+	0.280050i
$704$	1.12061			0.0422348
$705$	0.243041	+	1.37835i	0.00915344	+	0.0519117i
$706$	5.38800	−	30.5569i	0.202780	−	1.15002i
$707$	−7.20321	+	2.62175i	−0.270905	+	0.0986012i
$708$	9.82888	+	8.24741i	0.369392	+	0.309957i
$709$	5.68779			0.213609			0.106805	−	0.994280i	$-0.465938\pi$
$709$	5.68779			0.213609			0.106805	+	0.994280i	$0.465938\pi$
$710$	−4.64227	−	3.89533i	−0.174221	−	0.146189i
$711$	1.44697	+	2.50622i	0.0542655	+	0.0939906i
$712$	−12.2096	−	4.44393i	−0.457574	−	0.166543i
$713$	20.6348	−	35.7404i	0.772778	−	1.33849i
$714$	−5.81908	−	10.0789i	−0.217774	−	0.377195i
$715$	0.829126	+	4.70221i	0.0310076	+	0.175853i
$716$	−8.60354	+	3.13143i	−0.321529	+	0.117027i
$717$	11.9422	−	20.6845i	0.445990	−	0.772478i
$718$	−2.31908	+	1.94594i	−0.0865472	+	0.0726217i
$719$	9.21735	−	7.73427i	0.343749	−	0.288440i	−0.454525	−	0.890734i	$-0.650191\pi$
$719$	9.21735	−	7.73427i	0.343749	−	0.288440i	0.798274	+	0.602294i	$0.205747\pi$
$720$	−1.43969	−	0.524005i	−0.0536542	−	0.0195285i
$721$	3.70068	−	20.9876i	0.137821	−	0.781620i
$722$	−2.13903	+	12.1311i	−0.0796066	+	0.451471i
$723$	1.25877	+	0.458155i	0.0468142	+	0.0170390i
$724$	−17.3157	+	14.5296i	−0.643532	+	0.539987i
$725$	3.53415	−	2.96550i	0.131255	−	0.110136i
$726$	−7.46451	+	12.9289i	−0.277034	+	0.479837i
$727$	−25.5898	+	9.31391i	−0.949072	+	0.345434i	−0.769742	−	0.638355i	$-0.779615\pi$
$727$	−25.5898	+	9.31391i	−0.949072	+	0.345434i	−0.179330	+	0.983789i	$0.557393\pi$
$728$	0.798133	+	4.52644i	0.0295808	+	0.167761i
$729$	−15.0201	−	26.0155i	−0.556299	−	0.963538i
$730$	0.832282	−	1.44155i	0.0308041	−	0.0533543i
$731$	−25.1716	−	9.16171i	−0.931005	−	0.338858i
$732$	2.00000	+	3.46410i	0.0739221	+	0.128037i
$733$	−16.2324	−	13.6206i	−0.599556	−	0.503087i	0.291747	−	0.956496i	$-0.405764\pi$
$733$	−16.2324	−	13.6206i	−0.599556	−	0.503087i	−0.891303	+	0.453408i	$0.850208\pi$
$734$	−27.7948			−1.02592
$735$	1.62133	+	1.36046i	0.0598037	+	0.0501812i
$736$	8.55690	−	3.11446i	0.315412	−	0.114800i
$737$	1.42973	−	8.10840i	0.0526648	−	0.298677i
$738$	−0.842549	−	4.77833i	−0.0310146	−	0.175893i
$739$	−30.6195			−1.12636			−0.563178	−	0.826336i	$-0.690421\pi$
$739$	−30.6195			−1.12636			−0.563178	+	0.826336i	$0.690421\pi$
$740$	0.647489	+	14.2634i	0.0238022	+	0.524331i
$741$	15.5635			0.571741
$742$	5.29813	+	30.0472i	0.194501	+	1.10307i
$743$	−2.98798	+	16.9457i	−0.109618	+	0.621676i	0.879656	+	0.475610i	$0.157772\pi$
$743$	−2.98798	+	16.9457i	−0.109618	+	0.621676i	−0.989275	+	0.146067i	$0.953339\pi$
$744$	−6.52481	+	2.37484i	−0.239211	+	0.0870658i
$745$	12.1131	+	10.1641i	0.443789	+	0.372383i
$746$	−5.17530			−0.189481
$747$	3.62449	+	3.04130i	0.132613	+	0.111275i
$748$	1.68092	+	2.91144i	0.0614606	+	0.106453i
$749$	−14.3760	−	5.23243i	−0.525287	−	0.191189i
$750$	8.07398	−	13.9845i	0.294820	−	0.510643i
$751$	13.7506	+	23.8168i	0.501767	+	0.869086i	0.999998	+	0.00204181i	$0.000649930\pi$
$751$	13.7506	+	23.8168i	0.501767	+	0.869086i	−0.498231	+	0.867045i	$0.666017\pi$
$752$	−0.0675813	−	0.383273i	−0.00246444	−	0.0139765i
$753$	3.65657	−	1.33088i	0.133253	−	0.0485001i
$754$	−8.21348	+	14.2262i	−0.299117	+	0.518086i
$755$	−8.62314	+	7.23567i	−0.313828	+	0.263333i
$756$	−10.8550	+	9.10846i	−0.394794	+	0.331271i
$757$	−18.0753	−	6.57888i	−0.656959	−	0.239113i	−0.00803598	−	0.999968i	$-0.502558\pi$
$757$	−18.0753	−	6.57888i	−0.656959	−	0.239113i	−0.648923	+	0.760854i	$0.724780\pi$
$758$	3.66250	−	20.7711i	0.133028	−	0.754440i
$759$	2.71482	−	15.3965i	0.0985418	−	0.558858i
$760$	12.3439	+	4.49281i	0.447760	+	0.162971i
$761$	30.1313	−	25.2832i	1.09226	−	0.916515i	0.0953800	−	0.995441i	$-0.469593\pi$
$761$	30.1313	−	25.2832i	1.09226	−	0.916515i	0.996881	+	0.0789255i	$0.0251489\pi$
$762$	8.24763	−	6.92058i	0.298780	−	0.250706i
$763$	25.3653	−	43.9340i	0.918286	−	1.59052i
$764$	17.9795	−	6.54401i	0.650476	−	0.236754i
$765$	−0.798133	−	4.52644i	−0.0288566	−	0.163654i
$766$	−19.5155	−	33.8018i	−0.705123	−	1.22131i
$767$	7.60085	−	13.1651i	0.274451	−	0.475363i
$768$	−1.43969	−	0.524005i	−0.0519504	−	0.0189084i
$769$	−6.48087	−	11.2252i	−0.233706	−	0.404791i	0.725190	−	0.688549i	$-0.241752\pi$
$769$	−6.48087	−	11.2252i	−0.233706	−	0.404791i	−0.958896	+	0.283758i	$0.908419\pi$
$770$	5.10220	+	4.28125i	0.183870	+	0.154286i
$771$	25.5149			0.918895
$772$	−14.5646	−	12.2212i	−0.524193	−	0.439850i
$773$	−11.1878	+	4.07202i	−0.402397	+	0.146460i	−0.535287	−	0.844670i	$-0.679796\pi$
$773$	−11.1878	+	4.07202i	−0.402397	+	0.146460i	0.132890	+	0.991131i	$0.457574\pi$
$774$	−1.01202	+	5.73946i	−0.0363764	+	0.206301i
$775$	−0.401207	−	2.27536i	−0.0144118	−	0.0817333i
$776$	14.6946			0.527505
$777$	20.9500	+	10.8598i	0.751576	+	0.389594i
$778$	−16.0273			−0.574608
$779$	7.22399	+	40.9693i	0.258826	+	1.46788i
$780$	1.13357	−	6.42880i	0.0405883	−	0.230188i
$781$	2.71864	−	0.989503i	0.0972804	−	0.0354072i
$782$	20.9270	+	17.5598i	0.748346	+	0.627937i
$783$	−50.6441			−1.80987
$784$	−0.450837	−	0.378297i	−0.0161013	−	0.0135106i
$785$	−16.9802	−	29.4106i	−0.606051	−	1.04971i
$786$	−1.30541	−	0.475129i	−0.0465623	−	0.0169473i
$787$	−10.4618	+	18.1204i	−0.372924	+	0.645923i	−0.990014	−	0.140970i	$-0.954978\pi$
$787$	−10.4618	+	18.1204i	−0.372924	+	0.645923i	0.617090	+	0.786892i	$0.288311\pi$
$788$	−9.24035	−	16.0048i	−0.329174	−	0.570146i
$789$	−1.73854	−	9.85976i	−0.0618937	−	0.351017i
$790$	−9.77972	+	3.55953i	−0.347947	+	0.126642i
$791$	3.22416	−	5.58440i	0.114638	−	0.198558i
$792$	0.560307	−	0.470154i	0.0199097	−	0.0167062i
$793$	3.63041	−	3.04628i	0.128920	−	0.108177i
$794$	13.7579	+	5.00746i	0.488249	+	0.177708i
$795$	7.52481	−	42.6753i	0.266878	−	1.51354i
$796$	−0.967911	+	5.48930i	−0.0343067	+	0.194563i
$797$	3.67752	+	1.33851i	0.130264	+	0.0474124i	0.406330	−	0.913726i	$-0.366808\pi$
$797$	3.67752	+	1.33851i	0.130264	+	0.0474124i	−0.276065	+	0.961139i	$0.589031\pi$
$798$	16.6309	−	13.9550i	0.588727	−	0.494000i
$799$	0.894400	−	0.750491i	0.0316416	−	0.0265505i
$800$	0.254900	−	0.441500i	0.00901208	−	0.0156094i
$801$	−7.96926	+	2.90057i	−0.281580	+	0.102487i
$802$	−2.05035	−	11.6281i	−0.0724002	−	0.410602i
$803$	0.397337	+	0.688207i	0.0140217	+	0.0242863i
$804$	−5.62836	+	9.74860i	−0.198497	+	0.343807i
$805$	50.8585	+	18.5110i	1.79253	+	0.652426i
$806$	4.11334	+	7.12452i	0.144886	+	0.250950i
$807$	−10.3962	−	8.72346i	−0.365964	−	0.307080i
$808$	−3.02734			−0.106501
$809$	11.5921	+	9.72697i	0.407558	+	0.341982i	0.823406	−	0.567452i	$-0.192071\pi$
$809$	11.5921	+	9.72697i	0.407558	+	0.341982i	−0.415848	+	0.909434i	$0.636515\pi$
$810$	14.5929	−	5.31137i	0.512741	−	0.186622i
$811$	6.99629	−	39.6779i	0.245673	−	1.39328i	−0.573251	−	0.819380i	$-0.694318\pi$
$811$	6.99629	−	39.6779i	0.245673	−	1.39328i	0.818924	−	0.573901i	$-0.194571\pi$
$812$	3.97906	+	22.5663i	0.139637	+	0.791923i
$813$	14.5517			0.510350
$814$	−6.05169	−	3.13701i	−0.212112	−	0.109952i
$815$	−23.5895			−0.826303
$816$	−0.798133	−	4.52644i	−0.0279403	−	0.158457i
$817$	8.67705	−	49.2100i	0.303572	−	1.72164i
$818$	5.27972	−	1.92166i	0.184601	−	0.0671892i
$819$	2.29813	+	1.92836i	0.0803033	+	0.0673825i
$820$	17.4492			0.609354
$821$	19.4008	+	16.2792i	0.677092	+	0.568148i	0.915155	−	0.403102i	$-0.132068\pi$
$821$	19.4008	+	16.2792i	0.677092	+	0.568148i	−0.238063	+	0.971250i	$0.576512\pi$
$822$	1.50000	+	2.59808i	0.0523185	+	0.0906183i
$823$	−26.7212	−	9.72573i	−0.931443	−	0.339018i	−0.168662	−	0.985674i	$-0.553945\pi$
$823$	−26.7212	−	9.72573i	−0.931443	−	0.339018i	−0.762781	+	0.646656i	$0.776167\pi$
$824$	4.20826	−	7.28893i	0.146602	−	0.253922i
$825$	−0.437633	−	0.758003i	−0.0152364	−	0.0263903i
$826$	−3.68227	−	20.8832i	−0.128122	−	0.726618i
$827$	−2.64068	+	0.961130i	−0.0918255	+	0.0334218i	−0.387524	−	0.921859i	$-0.626670\pi$
$827$	−2.64068	+	0.961130i	−0.0918255	+	0.0334218i	0.295699	+	0.955281i	$0.404447\pi$
$828$	2.97178	−	5.14728i	0.103277	−	0.178880i
$829$	−15.2585	+	12.8034i	−0.529950	+	0.444681i	−0.868084	−	0.496417i	$-0.834649\pi$
$829$	−15.2585	+	12.8034i	−0.529950	+	0.444681i	0.338134	+	0.941098i	$0.390204\pi$
$830$	−13.0346	+	10.9373i	−0.452438	+	0.379641i
$831$	42.3696	+	15.4213i	1.46979	+	0.534959i
$832$	−0.315207	+	1.78763i	−0.0109279	+	0.0619749i
$833$	0.306589	−	1.73875i	0.0106227	−	0.0602443i
$834$	19.5817	+	7.12716i	0.678059	+	0.246793i
$835$	−18.7752	+	15.7543i	−0.649743	+	0.545199i
$836$	−4.80406	+	4.03109i	−0.166152	+	0.139418i
$837$	−12.6814	+	21.9648i	−0.438333	+	0.759215i
$838$	−9.53343	+	3.46989i	−0.329327	+	0.119865i
$839$	6.48726	+	36.7911i	0.223965	+	1.27017i	0.864654	+	0.502369i	$0.167538\pi$
$839$	6.48726	+	36.7911i	0.223965	+	1.27017i	−0.640688	+	0.767801i	$0.721351\pi$
$840$	−4.55303	−	7.88609i	−0.157095	−	0.272096i
$841$	−26.4479	+	45.8091i	−0.911997	+	1.57962i
$842$	10.3020	+	3.74962i	0.355030	+	0.129221i
$843$	−4.54323	−	7.86911i	−0.156477	−	0.271027i
$844$	16.6309	+	13.9550i	0.572459	+	0.480350i
$845$	22.7806			0.783675
$846$	−0.194593	−	0.163283i	−0.00669024	−	0.00561377i
$847$	23.1853	−	8.43874i	0.796655	−	0.289959i
$848$	−2.09240	+	11.8666i	−0.0718532	+	0.407500i
$849$	6.00387	+	34.0496i	0.206052	+	1.16858i
$850$	1.52940			0.0524580
$851$	−54.9286	−	7.13479i	−1.88293	−	0.244577i
$852$	−3.95542			−0.135511
$853$	3.87227	+	21.9608i	0.132584	+	0.751922i	0.976512	+	0.215465i	$0.0691266\pi$
$853$	3.87227	+	21.9608i	0.132584	+	0.751922i	−0.843928	+	0.536457i	$0.819762\pi$
$854$	1.14796	−	6.51038i	0.0392822	−	0.222781i
$855$	8.05690	−	2.93247i	0.275540	−	0.100288i
$856$	−4.62836	−	3.88365i	−0.158194	−	0.132740i
$857$	−18.2817			−0.624491			−0.312245	−	0.950002i	$-0.601081\pi$
$857$	−18.2817			−0.624491			−0.312245	+	0.950002i	$0.601081\pi$
$858$	2.38737	+	2.00324i	0.0815036	+	0.0683897i
$859$	7.59358	+	13.1525i	0.259090	+	0.448756i	0.965998	−	0.258549i	$-0.0832442\pi$
$859$	7.59358	+	13.1525i	0.259090	+	0.448756i	−0.706909	+	0.707305i	$0.749911\pi$
$860$	−19.6951	−	7.16842i	−0.671596	−	0.244441i
$861$	14.4192	−	24.9748i	0.491406	−	0.851139i
$862$	2.55438	+	4.42431i	0.0870024	+	0.150693i
$863$	0.353855	+	2.00681i	0.0120454	+	0.0683127i	0.990238	−	0.139387i	$-0.0445133\pi$
$863$	0.353855	+	2.00681i	0.0120454	+	0.0683127i	−0.978193	+	0.207700i	$0.933402\pi$
$864$	−5.25877	+	1.91404i	−0.178907	+	0.0651168i
$865$	1.23190	−	2.13371i	0.0418857	−	0.0725482i
$866$	21.2520	−	17.8325i	0.722171	−	0.605974i
$867$	−9.38919	+	7.87846i	−0.318873	+	0.267567i
$868$	10.7836	+	3.92490i	0.366019	+	0.133220i
$869$	0.862778	−	4.89306i	0.0292677	−	0.165986i
$870$	5.65136	−	32.0505i	0.191599	−	1.08661i
$871$	12.5326	+	4.56148i	0.424649	+	0.154560i
$872$	15.3478	−	12.8783i	0.519741	−	0.436114i
$873$	7.34730	−	6.16511i	0.248668	−	0.208657i
$874$	−25.4800	+	44.1326i	−0.861873	+	1.49281i
$875$	−25.0783	+	9.12776i	−0.847802	+	0.308575i
$876$	−0.188663	−	1.06996i	−0.00637433	−	0.0361506i
$877$	−1.13445	−	1.96492i	−0.0383076	−	0.0663507i	0.846236	−	0.532808i	$-0.178863\pi$
$877$	−1.13445	−	1.96492i	−0.0383076	−	0.0663507i	−0.884544	+	0.466458i	$0.845530\pi$
$878$	−14.5692	+	25.2346i	−0.491688	+	0.851628i
$879$	5.85117	+	2.12965i	0.197355	+	0.0718313i
$880$	1.31521	+	2.27801i	0.0443356	+	0.0767916i
$881$	23.1616	+	19.4349i	0.780335	+	0.654779i	0.943333	−	0.331848i	$-0.107672\pi$
$881$	23.1616	+	19.4349i	0.780335	+	0.654779i	−0.162998	+	0.986626i	$0.552116\pi$
$882$	−0.384133			−0.0129344
$883$	−1.65136	−	1.38566i	−0.0555727	−	0.0466310i	0.614578	−	0.788856i	$-0.289326\pi$
$883$	−1.65136	−	1.38566i	−0.0555727	−	0.0466310i	−0.670151	+	0.742225i	$0.733771\pi$
$884$	−5.11721	+	1.86251i	−0.172110	+	0.0626431i
$885$	−5.22984	+	29.6599i	−0.175799	+	0.997006i
$886$	−1.21183	−	6.87262i	−0.0407122	−	0.230890i
$887$	−30.0387			−1.00860			−0.504300	−	0.863528i	$-0.668250\pi$
$887$	−30.0387			−1.00860			−0.504300	+	0.863528i	$0.668250\pi$
$888$	6.30793	+	6.86002i	0.211680	+	0.230207i
$889$	−17.7939			−0.596787
$890$	−5.29607	−	30.0355i	−0.177525	−	1.00679i
$891$	−1.28740	+	7.30121i	−0.0431295	+	0.244600i
$892$	9.53121	−	3.46908i	0.319129	−	0.116153i
$893$	1.66843	+	1.39998i	0.0558320	+	0.0468486i
$894$	10.3209			0.345182
$895$	−16.4632	−	13.8142i	−0.550303	−	0.461759i
$896$	1.26604	+	2.19285i	0.0422956	+	0.0732581i
$897$	23.7973	+	8.66149i	0.794567	+	0.289199i
$898$	9.12701	−	15.8084i	0.304572	−	0.527535i
$899$	20.5069	+	35.5189i	0.683942	+	1.18462i
$900$	−0.0577812	−	0.327693i	−0.00192604	−	0.0109231i
$901$	−33.9688	+	12.3636i	−1.13167	+	0.411893i
$902$	−4.16519	+	7.21432i	−0.138686	+	0.240211i
$903$	−26.5351	+	22.2656i	−0.883032	+	0.740952i
$904$	1.95084	−	1.63695i	0.0648839	−	0.0544440i
$905$	−49.8585	−	18.1470i	−1.65735	−	0.603227i
$906$	−1.27584	+	7.23567i	−0.0423871	+	0.240389i
$907$	−0.218474	+	1.23903i	−0.00725431	+	0.0411412i	−0.988220	−	0.153040i	$-0.951094\pi$
$907$	−0.218474	+	1.23903i	−0.00725431	+	0.0411412i	0.980966	+	0.194181i	$0.0622049\pi$
$908$	4.10354	+	1.49357i	0.136181	+	0.0495657i
$909$	−1.51367	+	1.27012i	−0.0502053	+	0.0421272i
$910$	−8.26470	+	6.93491i	−0.273972	+	0.229890i
$911$	22.8371	−	39.5550i	0.756626	−	1.31052i	−0.187935	−	0.982181i	$-0.560180\pi$
$911$	22.8371	−	39.5550i	0.756626	−	1.31052i	0.944562	−	0.328334i	$-0.106487\pi$
$912$	8.05690	−	2.93247i	0.266791	−	0.0971039i
$913$	−1.41060	−	7.99989i	−0.0466839	−	0.264758i
$914$	−11.3978	−	19.7416i	−0.377006	−	0.652993i
$915$	−4.69459	+	8.13127i	−0.155198	+	0.268812i
$916$	11.0633	+	4.02671i	0.365542	+	0.133046i
$917$	1.14796	+	1.98832i	0.0379088	+	0.0656600i
$918$	−12.8610	−	10.7916i	−0.424475	−	0.356177i
$919$	−12.5006			−0.412358			−0.206179	−	0.978514i	$-0.566103\pi$
$919$	−12.5006			−0.412358			−0.206179	+	0.978514i	$0.566103\pi$
$920$	16.3739	+	13.7394i	0.539832	+	0.452973i
$921$	16.1027	−	5.86089i	0.530601	−	0.193123i
$922$	−1.51027	+	8.56515i	−0.0497380	+	0.282078i
$923$	0.813777	+	4.61516i	0.0267858	+	0.151910i
$924$	4.34730			0.143016
$925$	−2.61246	+	1.67069i	−0.0858973	+	0.0549318i
$926$	−3.41323			−0.112166
$927$	−0.953936	−	5.41004i	−0.0313314	−	0.177689i
$928$	−1.57145	+	8.91215i	−0.0515854	+	0.292556i
$929$	−14.8769	+	5.41473i	−0.488094	+	0.177652i	−0.574331	−	0.818623i	$-0.694738\pi$
$929$	−14.8769	+	5.41473i	−0.488094	+	0.177652i	0.0862374	+	0.996275i	$0.472516\pi$
$930$	−12.4855	−	10.4765i	−0.409414	−	0.343539i
$931$	3.29355			0.107942
$932$	12.4684	+	10.4622i	0.408415	+	0.342701i
$933$	−6.32501	−	10.9552i	−0.207071	−	0.358658i
$934$	34.4247	+	12.5296i	1.12641	+	0.409980i
$935$	−3.94562	+	6.83402i	−0.129036	+	0.223496i
$936$	0.592396	+	1.02606i	0.0193631	+	0.0335378i
$937$	7.32454	+	41.5395i	0.239282	+	1.35704i	0.833405	+	0.552663i	$0.186388\pi$
$937$	7.32454	+	41.5395i	0.239282	+	1.35704i	−0.594123	+	0.804375i	$0.702501\pi$
$938$	17.4820	−	6.36295i	0.570809	−	0.207758i
$939$	9.01889	−	15.6212i	0.294320	−	0.509778i
$940$	0.699807	−	0.587208i	0.0228252	−	0.0191526i
$941$	40.3469	−	33.8551i	1.31527	−	1.10364i	0.327986	−	0.944683i	$-0.393630\pi$
$941$	40.3469	−	33.8551i	1.31527	−	1.10364i	0.987285	−	0.158961i	$-0.0508143\pi$
$942$	−20.8293	−	7.58126i	−0.678657	−	0.247011i
$943$	−11.7547	+	66.6639i	−0.382784	+	2.17088i
$944$	1.45424	−	8.24741i	0.0473315	−	0.268430i
$945$	−31.2558	−	11.3762i	−1.01675	−	0.370068i
$946$	7.66503	−	6.43172i	0.249212	−	0.209113i
$947$	3.45929	−	2.90269i	0.112412	−	0.0943248i	−0.584849	−	0.811142i	$-0.698846\pi$
$947$	3.45929	−	2.90269i	0.112412	−	0.0943248i	0.697261	+	0.716817i	$0.254402\pi$
$948$	−3.39646	+	5.88284i	−0.110312	+	0.191066i
$949$	−1.20961	+	0.440261i	−0.0392655	+	0.0142915i
$950$	0.495414	+	2.80963i	0.0160734	+	0.0911566i
$951$	−10.1441	−	17.5701i	−0.328945	−	0.569749i
$952$	−3.79813	+	6.57856i	−0.123098	+	0.213212i
$953$	−44.1715	−	16.0771i	−1.43085	−	0.520789i	−0.493678	−	0.869645i	$-0.664348\pi$
$953$	−44.1715	−	16.0771i	−1.43085	−	0.520789i	−0.937176	+	0.348856i	$0.886570\pi$
$954$	3.93242	+	6.81115i	0.127317	+	0.220519i
$955$	34.4044	+	28.8687i	1.11330	+	0.934170i
$956$	−15.5895			−0.504199
$957$	11.9021	+	9.98708i	0.384742	+	0.322837i
$958$	−19.3640	+	7.04791i	−0.625621	+	0.227707i
$959$	0.860967	−	4.88279i	0.0278021	−	0.157673i
$960$	−0.624485	−	3.54163i	−0.0201552	−	0.114306i
$961$	−10.4602			−0.337425
$962$	6.70645	−	8.77141i	0.216225	−	0.282802i
$963$	−3.94356			−0.127080
$964$	−0.151826	−	0.861050i	−0.00489000	−	0.0277325i
$965$	7.74969	−	43.9507i	0.249471	−	1.41482i
$966$	33.1955	−	12.0822i	1.06805	−	0.388738i
$967$	0.149548	+	0.125486i	0.00480915	+	0.00403536i	0.645189	−	0.764023i	$-0.276779\pi$
$967$	0.149548	+	0.125486i	0.00480915	+	0.00403536i	−0.640380	+	0.768058i	$0.721223\pi$
$968$	9.74422			0.313191
$969$	19.7041	+	16.5337i	0.632988	+	0.531140i
$970$	17.2463	+	29.8714i	0.553745	+	0.959114i
$971$	−0.752679	−	0.273953i	−0.0241546	−	0.00879156i	0.329915	−	0.944011i	$-0.392980\pi$
$971$	−0.752679	−	0.273953i	−0.0241546	−	0.00879156i	−0.354069	+	0.935219i	$0.615202\pi$
$972$	−3.32635	+	5.76141i	−0.106693	+	0.184797i
$973$	−17.2199	−	29.8257i	−0.552044	−	0.956168i
$974$	−7.34302	−	41.6443i	−0.235285	−	1.33437i
$975$	1.33228	−	0.484911i	0.0426672	−	0.0155296i
$976$	1.30541	−	2.26103i	0.0417851	−	0.0723739i
$977$	−12.6438	+	10.6094i	−0.404512	+	0.339426i	−0.822235	−	0.569149i	$-0.807273\pi$
$977$	−12.6438	+	10.6094i	−0.404512	+	0.339426i	0.417722	+	0.908575i	$0.362828\pi$
$978$	−11.7947	+	9.89695i	−0.377154	+	0.316470i
$979$	13.6823	+	4.97994i	0.437287	+	0.159159i
$980$	0.239885	−	1.36046i	0.00766286	−	0.0434582i
$981$	2.27079	−	12.8783i	0.0725008	−	0.411173i
$982$	31.1152	+	11.3250i	0.992924	+	0.361395i
$983$	−22.4466	+	18.8349i	−0.715934	+	0.600740i	−0.926257	−	0.376892i	$-0.876993\pi$
$983$	−22.4466	+	18.8349i	−0.715934	+	0.600740i	0.210323	+	0.977632i	$0.432548\pi$
$984$	8.72462	−	7.32083i	0.278131	−	0.233379i
$985$	21.6898	−	37.5679i	0.691096	−	1.19701i
$986$	−25.5116	+	9.28547i	−0.812455	+	0.295710i
$987$	−0.262174	−	1.48686i	−0.00834509	−	0.0473274i
$988$	−5.07919	−	8.79742i	−0.161591	−	0.279883i
$989$	40.6541	−	70.4150i	1.29273	−	2.23907i
$990$	1.61334	+	0.587208i	0.0512753	+	0.0186627i
$991$	6.89393	+	11.9406i	0.218993	+	0.379307i	0.954500	−	0.298210i	$-0.0963895\pi$
$991$	6.89393	+	11.9406i	0.218993	+	0.379307i	−0.735507	+	0.677517i	$0.763056\pi$
$992$	3.47178	+	2.91317i	0.110229	+	0.0924933i
$993$	37.6049			1.19336
$994$	5.00774	+	4.20199i	0.158836	+	0.133279i
$995$	−12.2947	+	4.47492i	−0.389769	+	0.141864i
$996$	−1.92855	+	10.9373i	−0.0611084	+	0.346563i
$997$	3.43170	+	19.4622i	0.108683	+	0.616373i	0.989685	+	0.143260i	$0.0457585\pi$
$997$	3.43170	+	19.4622i	0.108683	+	0.616373i	−0.881002	+	0.473113i	$0.843130\pi$
$998$	9.99588			0.316414
$999$	33.7572	+	4.38479i	1.06803	+	0.138729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.f.a.9.1	✓	6
3.2	odd	2		666.2.x.c.379.1		6
4.3	odd	2		592.2.bc.b.305.1		6
37.12	even	9		2738.2.a.m.1.3		3
37.25	even	18		2738.2.a.p.1.3		3
37.33	even	9	inner	74.2.f.a.33.1	yes	6
111.107	odd	18		666.2.x.c.181.1		6
148.107	odd	18		592.2.bc.b.33.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.a.9.1	✓	6	1.1	even	1	trivial
74.2.f.a.33.1	yes	6	37.33	even	9	inner
592.2.bc.b.33.1		6	148.107	odd	18
592.2.bc.b.305.1		6	4.3	odd	2
666.2.x.c.181.1		6	111.107	odd	18
666.2.x.c.379.1		6	3.2	odd	2
2738.2.a.m.1.3		3	37.12	even	9
2738.2.a.p.1.3		3	37.25	even	18

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(0.266044 - 1.50881i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.79813 - 1.50881i) q^{5} -1.53209 q^{6} +(1.93969 + 1.62760i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.613341 + 0.223238i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(0.266044 - 1.50881i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.79813 - 1.50881i) q^{5} -1.53209 q^{6} +(1.93969 + 1.62760i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.613341 + 0.223238i) q^{9} +(-1.17365 + 2.03282i) q^{10} +(-0.560307 - 0.970481i) q^{11} +(0.266044 + 1.50881i) q^{12} +(1.70574 - 0.620838i) q^{13} +(1.26604 - 2.19285i) q^{14} +(-2.75490 + 2.31164i) q^{15} +(0.766044 - 0.642788i) q^{16} +(2.81908 + 1.02606i) q^{17} +(0.113341 - 0.642788i) q^{18} +(-0.971782 + 5.51125i) q^{19} +(2.20574 + 0.802823i) q^{20} +(2.97178 - 2.49362i) q^{21} +(-0.858441 + 0.720317i) q^{22} +(-4.55303 + 7.88609i) q^{23} +(1.43969 - 0.524005i) q^{24} +(0.0885259 + 0.502055i) q^{25} +(-0.907604 - 1.57202i) q^{26} +(2.79813 - 4.84651i) q^{27} +(-2.37939 - 0.866025i) q^{28} +(-4.52481 - 7.83721i) q^{29} +(2.75490 + 2.31164i) q^{30} -4.53209 q^{31} +(-0.766044 - 0.642788i) q^{32} +(-1.61334 + 0.587208i) q^{33} +(0.520945 - 2.95442i) q^{34} +(-1.03209 - 5.85327i) q^{35} -0.652704 q^{36} +(2.33750 + 5.61570i) q^{37} +5.59627 q^{38} +(-0.482926 - 2.73881i) q^{39} +(0.407604 - 2.31164i) q^{40} +(6.98545 - 2.54250i) q^{41} +(-2.97178 - 2.49362i) q^{42} -8.92902 q^{43} +(0.858441 + 0.720317i) q^{44} +(-0.766044 - 1.32683i) q^{45} +(8.55690 + 3.11446i) q^{46} +(0.194593 - 0.337044i) q^{47} +(-0.766044 - 1.32683i) q^{48} +(-0.102196 - 0.579585i) q^{49} +(0.479055 - 0.174362i) q^{50} +(2.29813 - 3.98048i) q^{51} +(-1.39053 + 1.16679i) q^{52} +(-9.23055 + 7.74535i) q^{53} +(-5.25877 - 1.91404i) q^{54} +(-0.456767 + 2.59045i) q^{55} +(-0.439693 + 2.49362i) q^{56} +(8.05690 + 2.93247i) q^{57} +(-6.93242 + 5.81699i) q^{58} +(6.41534 - 5.38311i) q^{59} +(1.79813 - 3.11446i) q^{60} +(2.45336 - 0.892951i) q^{61} +(0.786989 + 4.46324i) q^{62} +(0.826352 + 1.43128i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-4.00387 - 1.45729i) q^{65} +(0.858441 + 1.48686i) q^{66} +(5.62836 + 4.72275i) q^{67} -3.00000 q^{68} +(10.6873 + 8.96773i) q^{69} +(-5.58512 + 2.03282i) q^{70} +(-0.448311 + 2.54250i) q^{71} +(0.113341 + 0.642788i) q^{72} -0.709141 q^{73} +(5.12449 - 3.27714i) q^{74} +0.781059 q^{75} +(-0.971782 - 5.51125i) q^{76} +(0.492726 - 2.79439i) q^{77} +(-2.61334 + 0.951178i) q^{78} +(3.39646 + 2.84997i) q^{79} -2.34730 q^{80} +(-5.06805 - 4.25260i) q^{81} +(-3.71688 - 6.43783i) q^{82} +(6.81180 + 2.47929i) q^{83} +(-1.93969 + 3.35965i) q^{84} +(-3.52094 - 6.09845i) q^{85} +(1.55051 + 8.79336i) q^{86} +(-13.0287 + 4.74205i) q^{87} +(0.560307 - 0.970481i) q^{88} +(-9.95336 + 8.35186i) q^{89} +(-1.17365 + 0.984808i) q^{90} +(4.31908 + 1.57202i) q^{91} +(1.58125 - 8.96773i) q^{92} +(-1.20574 + 6.83807i) q^{93} +(-0.365715 - 0.133109i) q^{94} +(10.0628 - 8.44372i) q^{95} +(-1.17365 + 0.984808i) q^{96} +(7.34730 - 12.7259i) q^{97} +(-0.553033 + 0.201288i) q^{98} +(-0.127011 - 0.720317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + 3 q^{5} + 6 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 + 3 * q^5 + 6 * q^7 + 3 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} + 3 q^{5} + 6 q^{7} + 3 q^{8} - 3 q^{9} - 6 q^{10} - 9 q^{11} - 3 q^{12} + 3 q^{14} - 18 q^{15} - 6 q^{18} + 9 q^{19} + 3 q^{20} + 3 q^{21} + 3 q^{22} - 15 q^{23} + 3 q^{24} + 21 q^{25} - 9 q^{26} + 3 q^{27} - 3 q^{28} + 18 q^{30} - 18 q^{31} - 3 q^{33} + 3 q^{35} - 6 q^{36} + 9 q^{37} + 6 q^{38} + 18 q^{39} + 6 q^{40} + 6 q^{41} - 3 q^{42} + 12 q^{43} - 3 q^{44} + 15 q^{46} - 3 q^{47} + 6 q^{50} + 9 q^{52} - 18 q^{53} - 9 q^{54} - 18 q^{55} + 3 q^{56} + 12 q^{57} - 18 q^{58} - 6 q^{59} - 3 q^{60} - 12 q^{61} - 3 q^{62} + 6 q^{63} - 3 q^{64} - 3 q^{66} - 3 q^{67} - 18 q^{68} + 42 q^{69} - 12 q^{70} - 6 q^{71} - 6 q^{72} - 36 q^{73} + 18 q^{74} - 30 q^{75} + 9 q^{76} - 15 q^{77} - 9 q^{78} + 30 q^{79} - 12 q^{80} + 12 q^{81} - 6 q^{82} + 6 q^{83} - 6 q^{84} - 18 q^{85} + 12 q^{86} - 27 q^{87} + 9 q^{88} - 33 q^{89} - 6 q^{90} + 9 q^{91} + 12 q^{92} + 3 q^{93} - 12 q^{94} + 51 q^{95} - 6 q^{96} + 42 q^{97} + 9 q^{98} + 27 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 + 3 * q^5 + 6 * q^7 + 3 * q^8 - 3 * q^9 - 6 * q^10 - 9 * q^11 - 3 * q^12 + 3 * q^14 - 18 * q^15 - 6 * q^18 + 9 * q^19 + 3 * q^20 + 3 * q^21 + 3 * q^22 - 15 * q^23 + 3 * q^24 + 21 * q^25 - 9 * q^26 + 3 * q^27 - 3 * q^28 + 18 * q^30 - 18 * q^31 - 3 * q^33 + 3 * q^35 - 6 * q^36 + 9 * q^37 + 6 * q^38 + 18 * q^39 + 6 * q^40 + 6 * q^41 - 3 * q^42 + 12 * q^43 - 3 * q^44 + 15 * q^46 - 3 * q^47 + 6 * q^50 + 9 * q^52 - 18 * q^53 - 9 * q^54 - 18 * q^55 + 3 * q^56 + 12 * q^57 - 18 * q^58 - 6 * q^59 - 3 * q^60 - 12 * q^61 - 3 * q^62 + 6 * q^63 - 3 * q^64 - 3 * q^66 - 3 * q^67 - 18 * q^68 + 42 * q^69 - 12 * q^70 - 6 * q^71 - 6 * q^72 - 36 * q^73 + 18 * q^74 - 30 * q^75 + 9 * q^76 - 15 * q^77 - 9 * q^78 + 30 * q^79 - 12 * q^80 + 12 * q^81 - 6 * q^82 + 6 * q^83 - 6 * q^84 - 18 * q^85 + 12 * q^86 - 27 * q^87 + 9 * q^88 - 33 * q^89 - 6 * q^90 + 9 * q^91 + 12 * q^92 + 3 * q^93 - 12 * q^94 + 51 * q^95 - 6 * q^96 + 42 * q^97 + 9 * q^98 + 27 * q^99

Introduction

L-functions

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