LMFDB - Embedded newform 345.2.m.a.256.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,2,Mod(16,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("345.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.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:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			256.1
Character	$\chi$	$=$	345.256
Dual form			345.2.m.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.353423 - 2.45811i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-3.99842 + 1.17404i) q^{4} +(0.654861 - 0.755750i) q^{5} +(2.38279 + 0.699652i) q^{6} +(2.47922 - 1.59330i) q^{7} +(2.23579 + 4.89569i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.353423 - 2.45811i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-3.99842 + 1.17404i) q^{4} +(0.654861 - 0.755750i) q^{5} +(2.38279 + 0.699652i) q^{6} +(2.47922 - 1.59330i) q^{7} +(2.23579 + 4.89569i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-2.08916 - 1.34262i) q^{10} +(0.448469 - 3.11917i) q^{11} +(0.593058 - 4.12481i) q^{12} +(-5.66800 - 3.64260i) q^{13} +(-4.79272 - 5.53109i) q^{14} +(0.415415 + 0.909632i) q^{15} +(4.23260 - 2.72013i) q^{16} +(3.21040 + 0.942659i) q^{17} +(-1.62627 + 1.87682i) q^{18} +(-5.44333 + 1.59831i) q^{19} +(-1.73113 + 3.79064i) q^{20} +(0.419409 + 2.91706i) q^{21} -7.82577 q^{22} +(4.79578 + 0.0223496i) q^{23} -5.38206 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-6.95072 + 15.2200i) q^{26} +(0.959493 - 0.281733i) q^{27} +(-8.04236 + 9.28138i) q^{28} +(-3.40493 - 0.999777i) q^{29} +(2.08916 - 1.34262i) q^{30} +(-3.88796 - 8.51344i) q^{31} +(-1.13328 - 1.30787i) q^{32} +(2.65100 + 1.70369i) q^{33} +(1.18253 - 8.22468i) q^{34} +(0.419409 - 2.91706i) q^{35} +(3.50569 + 2.25297i) q^{36} +(3.34392 + 3.85909i) q^{37} +(5.85261 + 12.8154i) q^{38} +(5.66800 - 3.64260i) q^{39} +(5.16405 + 1.51630i) q^{40} +(5.34095 - 6.16379i) q^{41} +(7.02222 - 2.06191i) q^{42} +(0.765035 - 1.67519i) q^{43} +(1.86887 + 12.9983i) q^{44} -1.00000 q^{45} +(-1.64000 - 11.7965i) q^{46} -5.82461 q^{47} +(0.716029 + 4.98009i) q^{48} +(0.700024 - 1.53284i) q^{49} +(-2.38279 + 0.699652i) q^{50} +(-2.19112 + 2.52869i) q^{51} +(26.9396 + 7.91019i) q^{52} +(4.46523 - 2.86963i) q^{53} +(-1.03164 - 2.25897i) q^{54} +(-2.06363 - 2.38155i) q^{55} +(13.3433 + 8.57522i) q^{56} +(0.807371 - 5.61539i) q^{57} +(-1.25418 + 8.72304i) q^{58} +(2.44571 + 1.57176i) q^{59} +(-2.72895 - 3.14938i) q^{60} +(2.86267 + 6.26837i) q^{61} +(-19.5529 + 12.5659i) q^{62} +(-2.82768 - 0.830281i) q^{63} +(3.77523 - 4.35685i) q^{64} +(-6.46465 + 1.89819i) q^{65} +(3.25094 - 7.11857i) q^{66} +(1.93776 + 13.4774i) q^{67} -13.9433 q^{68} +(-2.01257 + 4.35311i) q^{69} -7.31868 q^{70} +(-0.754903 - 5.25046i) q^{71} +(2.23579 - 4.89569i) q^{72} +(8.24134 - 2.41988i) q^{73} +(8.30426 - 9.58363i) q^{74} +(0.959493 + 0.281733i) q^{75} +(19.8882 - 12.7814i) q^{76} +(-3.85791 - 8.44765i) q^{77} +(-10.9571 - 12.6452i) q^{78} +(4.06233 + 2.61070i) q^{79} +(0.716029 - 4.98009i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-17.0389 - 10.9502i) q^{82} +(5.78608 + 6.67749i) q^{83} +(-5.10172 - 11.1712i) q^{84} +(2.81478 - 1.80895i) q^{85} +(-4.38819 - 1.28849i) q^{86} +(2.32389 - 2.68191i) q^{87} +(16.2732 - 4.77824i) q^{88} +(4.68328 - 10.2550i) q^{89} +(0.353423 + 2.45811i) q^{90} -19.8560 q^{91} +(-19.2018 + 5.54109i) q^{92} +9.35921 q^{93} +(2.05855 + 14.3175i) q^{94} +(-2.35670 + 5.16046i) q^{95} +(1.66046 - 0.487556i) q^{96} +(6.93359 - 8.00179i) q^{97} +(-4.01529 - 1.17900i) q^{98} +(-2.65100 + 1.70369i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9} - 7 q^{11} - 2 q^{12} + 7 q^{13} - 47 q^{14} - 3 q^{15} + 26 q^{16} + 15 q^{17} - 7 q^{19} - 2 q^{20} - 12 q^{21} - 18 q^{22} + 12 q^{23} - 3 q^{25} - 18 q^{26} + 3 q^{27} + 2 q^{28} - 6 q^{29} + 22 q^{31} + 33 q^{32} - 4 q^{33} - 53 q^{34} - 12 q^{35} - 9 q^{36} - 23 q^{37} + 21 q^{38} - 7 q^{39} + 11 q^{40} + 26 q^{41} + 3 q^{42} - 19 q^{43} - 47 q^{44} - 30 q^{45} - 44 q^{46} + 14 q^{47} + 7 q^{48} + 2 q^{49} - 11 q^{50} - 15 q^{51} + 55 q^{52} - 14 q^{53} - 11 q^{54} - 4 q^{55} + 6 q^{56} - 26 q^{57} - 18 q^{58} + 40 q^{59} - 9 q^{60} + 37 q^{61} + 19 q^{62} - 10 q^{63} + 14 q^{64} + 4 q^{65} - 4 q^{66} - 108 q^{67} + 54 q^{68} + 21 q^{69} - 30 q^{70} + 39 q^{71} + 22 q^{72} + 57 q^{73} - 11 q^{74} + 3 q^{75} + 22 q^{76} + 2 q^{77} + 7 q^{78} + 55 q^{79} + 7 q^{80} - 3 q^{81} - 26 q^{82} - 79 q^{83} - 2 q^{84} + 18 q^{85} - 44 q^{86} - 5 q^{87} - 8 q^{88} - 30 q^{89} + 40 q^{91} + 35 q^{92} + 44 q^{93} - 29 q^{94} + 7 q^{95} + 22 q^{96} - 52 q^{97} + 28 q^{98} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9 - 7 * q^11 - 2 * q^12 + 7 * q^13 - 47 * q^14 - 3 * q^15 + 26 * q^16 + 15 * q^17 - 7 * q^19 - 2 * q^20 - 12 * q^21 - 18 * q^22 + 12 * q^23 - 3 * q^25 - 18 * q^26 + 3 * q^27 + 2 * q^28 - 6 * q^29 + 22 * q^31 + 33 * q^32 - 4 * q^33 - 53 * q^34 - 12 * q^35 - 9 * q^36 - 23 * q^37 + 21 * q^38 - 7 * q^39 + 11 * q^40 + 26 * q^41 + 3 * q^42 - 19 * q^43 - 47 * q^44 - 30 * q^45 - 44 * q^46 + 14 * q^47 + 7 * q^48 + 2 * q^49 - 11 * q^50 - 15 * q^51 + 55 * q^52 - 14 * q^53 - 11 * q^54 - 4 * q^55 + 6 * q^56 - 26 * q^57 - 18 * q^58 + 40 * q^59 - 9 * q^60 + 37 * q^61 + 19 * q^62 - 10 * q^63 + 14 * q^64 + 4 * q^65 - 4 * q^66 - 108 * q^67 + 54 * q^68 + 21 * q^69 - 30 * q^70 + 39 * q^71 + 22 * q^72 + 57 * q^73 - 11 * q^74 + 3 * q^75 + 22 * q^76 + 2 * q^77 + 7 * q^78 + 55 * q^79 + 7 * q^80 - 3 * q^81 - 26 * q^82 - 79 * q^83 - 2 * q^84 + 18 * q^85 - 44 * q^86 - 5 * q^87 - 8 * q^88 - 30 * q^89 + 40 * q^91 + 35 * q^92 + 44 * q^93 - 29 * q^94 + 7 * q^95 + 22 * q^96 - 52 * q^97 + 28 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.353423	−	2.45811i	−0.249908	−	1.73815i	−0.598723	−	0.800956i	$-0.704325\pi$
$2$	−0.353423	−	2.45811i	−0.249908	−	1.73815i	0.348815	−	0.937192i	$-0.386584\pi$
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$4$	−3.99842	+	1.17404i	−1.99921	+	0.587021i
$5$	0.654861	−	0.755750i	0.292863	−	0.337981i
$5$	0.654861	−	0.755750i	0.292863	−	0.337981i
$6$	2.38279	+	0.699652i	0.972772	+	0.285632i
$7$	2.47922	−	1.59330i	0.937056	−	0.602210i	0.0194977	−	0.999810i	$-0.493793\pi$
$7$	2.47922	−	1.59330i	0.937056	−	0.602210i	0.917559	+	0.397600i	$0.130157\pi$
$8$	2.23579	+	4.89569i	0.790470	+	1.73089i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	−2.08916	−	1.34262i	−0.660650	−	0.424574i
$11$	0.448469	−	3.11917i	0.135218	−	0.940465i	−0.803383	−	0.595462i	$-0.796969\pi$
$11$	0.448469	−	3.11917i	0.135218	−	0.940465i	0.938602	−	0.345003i	$-0.112122\pi$
$12$	0.593058	−	4.12481i	0.171201	−	1.19073i
$13$	−5.66800	−	3.64260i	−1.57202	−	1.01028i	−0.978696	−	0.205313i	$-0.934179\pi$
$13$	−5.66800	−	3.64260i	−1.57202	−	1.01028i	−0.593324	−	0.804964i	$-0.702185\pi$
$14$	−4.79272	−	5.53109i	−1.28091	−	1.47825i
$15$	0.415415	+	0.909632i	0.107260	+	0.234866i
$16$	4.23260	−	2.72013i	1.05815	−	0.680032i
$17$	3.21040	+	0.942659i	0.778637	+	0.228628i	0.646817	−	0.762645i	$-0.276100\pi$
$17$	3.21040	+	0.942659i	0.778637	+	0.228628i	0.131820	+	0.991274i	$0.457918\pi$
$18$	−1.62627	+	1.87682i	−0.383317	+	0.442371i
$19$	−5.44333	+	1.59831i	−1.24879	+	0.366676i	−0.838309	−	0.545195i	$-0.816456\pi$
$19$	−5.44333	+	1.59831i	−1.24879	+	0.366676i	−0.410476	+	0.911871i	$0.634637\pi$
$20$	−1.73113	+	3.79064i	−0.387092	+	0.847613i
$21$	0.419409	+	2.91706i	0.0915226	+	0.636554i
$22$	−7.82577			−1.66846
$23$	4.79578	+	0.0223496i	0.999989	+	0.00466022i
$23$	4.79578	+	0.0223496i	0.999989	+	0.00466022i
$24$	−5.38206			−1.09861
$25$	−0.142315	−	0.989821i	−0.0284630	−	0.197964i
$26$	−6.95072	+	15.2200i	−1.36315	+	2.98488i
$27$	0.959493	−	0.281733i	0.184655	−	0.0542195i
$28$	−8.04236	+	9.28138i	−1.51986	+	1.75402i
$29$	−3.40493	−	0.999777i	−0.632279	−	0.185654i	−0.0501389	−	0.998742i	$-0.515966\pi$
$29$	−3.40493	−	0.999777i	−0.632279	−	0.185654i	−0.582140	+	0.813088i	$0.697785\pi$
$30$	2.08916	−	1.34262i	0.381427	−	0.245128i
$31$	−3.88796	−	8.51344i	−0.698298	−	1.52906i	−0.842023	−	0.539441i	$-0.818636\pi$
$31$	−3.88796	−	8.51344i	−0.698298	−	1.52906i	0.143726	−	0.989618i	$-0.454092\pi$
$32$	−1.13328	−	1.30787i	−0.200337	−	0.231202i
$33$	2.65100	+	1.70369i	0.461479	+	0.296575i
$34$	1.18253	−	8.22468i	0.202802	−	1.41052i
$35$	0.419409	−	2.91706i	0.0708931	−	0.493072i
$36$	3.50569	+	2.25297i	0.584282	+	0.375495i
$37$	3.34392	+	3.85909i	0.549738	+	0.634431i	0.960822	−	0.277166i	$-0.0893953\pi$
$37$	3.34392	+	3.85909i	0.549738	+	0.634431i	−0.411084	+	0.911597i	$0.634850\pi$
$38$	5.85261	+	12.8154i	0.949419	+	2.07894i
$39$	5.66800	−	3.64260i	0.907607	−	0.583283i
$40$	5.16405	+	1.51630i	0.816508	+	0.239748i
$41$	5.34095	−	6.16379i	0.834116	−	0.962621i	−0.165606	−	0.986192i	$-0.552958\pi$
$41$	5.34095	−	6.16379i	0.834116	−	0.962621i	0.999722	+	0.0235705i	$0.00750342\pi$
$42$	7.02222	−	2.06191i	1.08355	−	0.318160i
$43$	0.765035	−	1.67519i	0.116667	−	0.255464i	−0.842286	−	0.539031i	$-0.818790\pi$
$43$	0.765035	−	1.67519i	0.116667	−	0.255464i	0.958953	+	0.283567i	$0.0915178\pi$
$44$	1.86887	+	12.9983i	0.281743	+	1.95956i
$45$	−1.00000			−0.149071
$46$	−1.64000	−	11.7965i	−0.241805	−	1.73929i
$47$	−5.82461			−0.849607			−0.424803	−	0.905286i	$-0.639657\pi$
$47$	−5.82461			−0.849607			−0.424803	+	0.905286i	$0.639657\pi$
$48$	0.716029	+	4.98009i	0.103350	+	0.718814i
$49$	0.700024	−	1.53284i	0.100003	−	0.218977i
$50$	−2.38279	+	0.699652i	−0.336978	+	0.0989457i
$51$	−2.19112	+	2.52869i	−0.306818	+	0.354087i
$52$	26.9396	+	7.91019i	3.73585	+	1.09695i
$53$	4.46523	−	2.86963i	0.613347	−	0.394174i	−0.196764	−	0.980451i	$-0.563043\pi$
$53$	4.46523	−	2.86963i	0.613347	−	0.394174i	0.810111	+	0.586277i	$0.199407\pi$
$54$	−1.03164	−	2.25897i	−0.140388	−	0.307407i
$55$	−2.06363	−	2.38155i	−0.278259	−	0.321128i
$56$	13.3433	+	8.57522i	1.78307	+	1.14591i
$57$	0.807371	−	5.61539i	0.106939	−	0.743776i
$58$	−1.25418	+	8.72304i	−0.164682	+	1.14539i
$59$	2.44571	+	1.57176i	0.318404	+	0.204626i	0.690073	−	0.723739i	$-0.257578\pi$
$59$	2.44571	+	1.57176i	0.318404	+	0.204626i	−0.371670	+	0.928365i	$0.621215\pi$
$60$	−2.72895	−	3.14938i	−0.352306	−	0.406583i
$61$	2.86267	+	6.26837i	0.366527	+	0.802582i	0.999594	+	0.0284852i	$0.00906835\pi$
$61$	2.86267	+	6.26837i	0.366527	+	0.802582i	−0.633067	+	0.774097i	$0.718204\pi$
$62$	−19.5529	+	12.5659i	−2.48322	+	1.59587i
$63$	−2.82768	−	0.830281i	−0.356254	−	0.104606i
$64$	3.77523	−	4.35685i	0.471904	−	0.544606i
$65$	−6.46465	+	1.89819i	−0.801841	+	0.235442i
$66$	3.25094	−	7.11857i	0.400163	−	0.876236i
$67$	1.93776	+	13.4774i	0.236736	+	1.64653i	0.667895	+	0.744256i	$0.267196\pi$
$67$	1.93776	+	13.4774i	0.236736	+	1.64653i	−0.431159	+	0.902276i	$0.641895\pi$
$68$	−13.9433			−1.69087
$69$	−2.01257	+	4.35311i	−0.242285	+	0.524053i
$70$	−7.31868			−0.874749
$71$	−0.754903	−	5.25046i	−0.0895905	−	0.623115i	−0.984305	−	0.176477i	$-0.943530\pi$
$71$	−0.754903	−	5.25046i	−0.0895905	−	0.623115i	0.894714	−	0.446639i	$-0.147379\pi$
$72$	2.23579	−	4.89569i	0.263490	−	0.576963i
$73$	8.24134	−	2.41988i	0.964576	−	0.283225i	0.238733	−	0.971085i	$-0.423268\pi$
$73$	8.24134	−	2.41988i	0.964576	−	0.283225i	0.725843	+	0.687860i	$0.241450\pi$
$74$	8.30426	−	9.58363i	0.965351	−	1.11407i
$75$	0.959493	+	0.281733i	0.110793	+	0.0325317i
$76$	19.8882	−	12.7814i	2.28134	−	1.46613i
$77$	−3.85791	−	8.44765i	−0.439650	−	0.962699i
$78$	−10.9571	−	12.6452i	−1.24065	−	1.43179i
$79$	4.06233	+	2.61070i	0.457048	+	0.293727i	0.748835	−	0.662756i	$-0.230614\pi$
$79$	4.06233	+	2.61070i	0.457048	+	0.293727i	−0.291787	+	0.956483i	$0.594250\pi$
$80$	0.716029	−	4.98009i	0.0800545	−	0.556791i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−17.0389	−	10.9502i	−1.88163	−	1.20925i
$83$	5.78608	+	6.67749i	0.635105	+	0.732950i	0.978501	−	0.206241i	$-0.0661230\pi$
$83$	5.78608	+	6.67749i	0.635105	+	0.732950i	−0.343397	+	0.939190i	$0.611578\pi$
$84$	−5.10172	−	11.1712i	−0.556644	−	1.21888i
$85$	2.81478	−	1.80895i	0.305306	−	0.196208i
$86$	−4.38819	−	1.28849i	−0.473191	−	0.138941i
$87$	2.32389	−	2.68191i	0.249147	−	0.287531i
$88$	16.2732	−	4.77824i	1.73473	−	0.509362i
$89$	4.68328	−	10.2550i	0.496427	−	1.08702i	−0.481187	−	0.876618i	$-0.659794\pi$
$89$	4.68328	−	10.2550i	0.496427	−	1.08702i	0.977614	−	0.210406i	$-0.0674785\pi$
$90$	0.353423	+	2.45811i	0.0372541	+	0.259108i
$91$	−19.8560			−2.08147
$92$	−19.2018	+	5.54109i	−2.00192	+	0.577698i
$93$	9.35921			0.970505
$94$	2.05855	+	14.3175i	0.212323	+	1.47674i
$95$	−2.35670	+	5.16046i	−0.241793	+	0.529452i
$96$	1.66046	−	0.487556i	0.169470	−	0.0497610i
$97$	6.93359	−	8.00179i	0.703999	−	0.812459i	−0.285288	−	0.958442i	$-0.592089\pi$
$97$	6.93359	−	8.00179i	0.703999	−	0.812459i	0.989287	+	0.145983i	$0.0466346\pi$
$98$	−4.01529	−	1.17900i	−0.405606	−	0.119097i
$99$	−2.65100	+	1.70369i	−0.266435	+	0.171227i
$100$	1.73113	+	3.79064i	0.173113	+	0.379064i
$101$	7.98186	+	9.21156i	0.794225	+	0.916585i	0.998050	−	0.0624226i	$-0.0198827\pi$
$101$	7.98186	+	9.21156i	0.794225	+	0.916585i	−0.203825	+	0.979007i	$0.565337\pi$
$102$	6.99020	+	4.49233i	0.692132	+	0.444807i
$103$	0.887743	−	6.17439i	0.0874720	−	0.608381i	−0.898185	−	0.439618i	$-0.855114\pi$
$103$	0.887743	−	6.17439i	0.0874720	−	0.608381i	0.985657	−	0.168763i	$-0.0539771\pi$
$104$	5.16062	−	35.8929i	0.506040	−	3.51959i
$105$	2.47922	+	1.59330i	0.241947	+	0.155490i
$106$	−8.63199	−	9.96184i	−0.838413	−	0.967580i
$107$	2.24304	+	4.91157i	0.216843	+	0.474820i	0.986526	−	0.163607i	$-0.0523129\pi$
$107$	2.24304	+	4.91157i	0.216843	+	0.474820i	−0.769683	+	0.638427i	$0.779586\pi$
$108$	−3.50569	+	2.25297i	−0.337335	+	0.216792i
$109$	−5.04277	−	1.48069i	−0.483009	−	0.141824i	0.0311575	−	0.999514i	$-0.490081\pi$
$109$	−5.04277	−	1.48069i	−0.483009	−	0.141824i	−0.514167	+	0.857690i	$0.671899\pi$
$110$	−5.12479	+	5.91432i	−0.488630	+	0.563909i
$111$	−4.89947	+	1.43861i	−0.465037	+	0.136547i
$112$	6.15957	−	13.4876i	0.582025	−	1.27446i
$113$	0.261593	+	1.81942i	0.0246086	+	0.171157i	0.998419	−	0.0562036i	$-0.0178996\pi$
$113$	0.261593	+	1.81942i	0.0246086	+	0.171157i	−0.973811	+	0.227360i	$0.926990\pi$
$114$	−14.0886			−1.31952
$115$	3.15746	−	3.60977i	0.294435	−	0.336613i
$116$	14.7881			1.37304
$117$	0.958856	+	6.66899i	0.0886462	+	0.616548i
$118$	2.99919	−	6.56731i	0.276098	−	0.604570i
$119$	9.46122	−	2.77807i	0.867309	−	0.254665i
$120$	−3.52450	+	4.06749i	−0.321741	+	0.371309i
$121$	1.02632	+	0.301355i	0.0933020	+	0.0273959i
$122$	14.3966	−	9.25214i	1.30341	−	0.837649i
$123$	3.38807	+	7.41883i	0.305492	+	0.668933i
$124$	25.5408	+	29.4757i	2.29363	+	2.64699i
$125$	−0.841254	−	0.540641i	−0.0752440	−	0.0483564i
$126$	−1.04156	+	7.24419i	−0.0927892	+	0.645363i
$127$	−1.63892	+	11.3990i	−0.145431	+	1.01149i	0.778147	+	0.628083i	$0.216160\pi$
$127$	−1.63892	+	11.3990i	−0.145431	+	1.01149i	−0.923578	+	0.383412i	$0.874749\pi$
$128$	−14.9556	−	9.61136i	−1.32190	−	0.849532i
$129$	1.20600	+	1.39180i	0.106183	+	0.122541i
$130$	6.95072	+	15.2200i	0.609619	+	1.33488i
$131$	4.05973	−	2.60903i	0.354700	−	0.227952i	−0.351140	−	0.936323i	$-0.614206\pi$
$131$	4.05973	−	2.60903i	0.354700	−	0.227952i	0.705840	+	0.708371i	$0.250570\pi$
$132$	−12.6000	−	3.69970i	−1.09669	−	0.322017i
$133$	−10.9486	+	12.6354i	−0.949366	+	1.09563i
$134$	32.4442	−	9.52648i	2.80275	−	0.822963i
$135$	0.415415	−	0.909632i	0.0357532	−	0.0782887i
$136$	2.56281	+	17.8247i	0.219759	+	1.52846i
$137$	18.8262			1.60843			0.804216	−	0.594337i	$-0.202586\pi$
$137$	18.8262			1.60843			0.804216	+	0.594337i	$0.202586\pi$
$138$	11.4117	+	3.40863i	0.971430	+	0.290162i
$139$	−11.4713			−0.972983			−0.486492	−	0.873685i	$-0.661724\pi$
$139$	−11.4713			−0.972983			−0.486492	+	0.873685i	$0.661724\pi$
$140$	1.74777	+	12.1560i	0.147714	+	1.02737i
$141$	2.41963	−	5.29825i	0.203770	−	0.446193i
$142$	−12.6394	+	3.71127i	−1.06068	+	0.311443i
$143$	−13.9038	+	16.0459i	−1.16270	+	1.34182i
$144$	−4.82750	−	1.41748i	−0.402292	−	0.118123i
$145$	−2.98533	+	1.91856i	−0.247919	+	0.159328i
$146$	−8.86101	−	19.4029i	−0.733343	−	1.60580i
$147$	1.10352	+	1.27353i	0.0910166	+	0.105039i
$148$	−17.9012	−	11.5044i	−1.47147	−	0.945653i
$149$	−1.29670	+	9.01873i	−0.106230	+	0.738843i	0.865185	+	0.501453i	$0.167201\pi$
$149$	−1.29670	+	9.01873i	−0.106230	+	0.738843i	−0.971414	+	0.237390i	$0.923708\pi$
$150$	0.353423	−	2.45811i	0.0288569	−	0.200704i
$151$	−12.4989	−	8.03253i	−1.01714	−	0.653678i	−0.0779107	−	0.996960i	$-0.524825\pi$
$151$	−12.4989	−	8.03253i	−1.01714	−	0.653678i	−0.939232	+	0.343282i	$0.888461\pi$
$152$	−19.9949	−	23.0754i	−1.62180	−	1.87166i
$153$	−1.38995	−	3.04357i	−0.112371	−	0.246058i
$154$	−19.4018	+	12.4688i	−1.56344	+	1.00476i
$155$	−8.98010	−	2.63679i	−0.721299	−	0.211792i
$156$	−18.3865	+	21.2191i	−1.47210	+	1.69889i
$157$	12.2032	−	3.58319i	0.973923	−	0.285970i	0.244210	−	0.969722i	$-0.421472\pi$
$157$	12.2032	−	3.58319i	0.973923	−	0.285970i	0.729714	+	0.683753i	$0.239653\pi$
$158$	4.98167	−	10.9083i	0.396321	−	0.867821i
$159$	0.755383	+	5.25380i	0.0599058	+	0.416654i
$160$	−1.73056			−0.136813
$161$	11.9254	−	7.58569i	0.939853	−	0.597836i
$162$	2.48339			0.195114
$163$	2.87010	+	19.9620i	0.224804	+	1.56354i	0.719509	+	0.694483i	$0.244367\pi$
$163$	2.87010	+	19.9620i	0.224804	+	1.56354i	−0.494706	+	0.869061i	$0.664724\pi$
$164$	−14.1188	+	30.9159i	−1.10249	+	2.41413i
$165$	3.02360	−	0.887809i	0.235387	−	0.0691158i
$166$	14.3691	−	16.5828i	1.11526	−	1.28708i
$167$	−10.5182	−	3.08842i	−0.813923	−	0.238989i	−0.151826	−	0.988407i	$-0.548515\pi$
$167$	−10.5182	−	3.08842i	−0.813923	−	0.238989i	−0.662097	+	0.749418i	$0.730333\pi$
$168$	−13.3433	+	8.57522i	−1.02946	+	0.661592i
$169$	13.4573	+	29.4673i	1.03518	+	2.26672i
$170$	−5.44141	−	6.27972i	−0.417337	−	0.481633i
$171$	4.77254	+	3.06713i	0.364965	+	0.234549i
$172$	−1.09218	+	7.59631i	−0.0832783	+	0.579213i
$173$	2.29723	−	15.9776i	0.174655	−	1.21475i	−0.694235	−	0.719749i	$-0.744257\pi$
$173$	2.29723	−	15.9776i	0.174655	−	1.21475i	0.868890	−	0.495005i	$-0.164834\pi$
$174$	−7.41375	−	4.76453i	−0.562035	−	0.361198i
$175$	−1.92991	−	2.22723i	−0.145887	−	0.168363i
$176$	−6.58635	−	14.4221i	−0.496465	−	1.08711i
$177$	−2.44571	+	1.57176i	−0.183830	+	0.118141i
$178$	−26.8630	−	7.88770i	−2.01347	−	0.591208i
$179$	−2.52744	+	2.91682i	−0.188909	+	0.218013i	−0.842302	−	0.539007i	$-0.818800\pi$
$179$	−2.52744	+	2.91682i	−0.188909	+	0.218013i	0.653392	+	0.757020i	$0.273345\pi$
$180$	3.99842	−	1.17404i	0.298025	−	0.0875080i
$181$	−0.0100441	+	0.0219935i	−0.000746572	+	0.00163476i	−0.910005	−	0.414597i	$-0.863922\pi$
$181$	−0.0100441	+	0.0219935i	−0.000746572	+	0.00163476i	0.909258	+	0.416232i	$0.136650\pi$
$182$	7.01756	+	48.8082i	0.520176	+	3.61790i
$183$	−6.89110			−0.509405
$184$	10.6129	+	23.5286i	0.782396	+	1.73455i
$185$	5.10631			0.375423
$186$	−3.30776	−	23.0060i	−0.242537	−	1.68688i
$187$	4.38008	−	9.59104i	0.320303	−	0.701366i
$188$	23.2893	−	6.83834i	1.69854	−	0.498737i
$189$	1.92991	−	2.22723i	0.140380	−	0.162007i
$190$	13.5179	+	3.96922i	0.980692	+	0.287957i
$191$	−16.7863	+	10.7879i	−1.21461	+	0.780583i	−0.981424	−	0.191849i	$-0.938552\pi$
$191$	−16.7863	+	10.7879i	−1.21461	+	0.780583i	−0.233186	+	0.972432i	$0.574915\pi$
$192$	2.39484	+	5.24397i	0.172833	+	0.378451i
$193$	−1.73442	−	2.00163i	−0.124846	−	0.144080i	0.689885	−	0.723919i	$-0.257661\pi$
$193$	−1.73442	−	2.00163i	−0.124846	−	0.144080i	−0.814731	+	0.579839i	$0.803116\pi$
$194$	−22.1198	−	14.2155i	−1.58811	−	1.02062i
$195$	0.958856	−	6.66899i	0.0686651	−	0.477576i
$196$	−0.999373	+	6.95079i	−0.0713838	+	0.496485i
$197$	6.45704	+	4.14968i	0.460045	+	0.295653i	0.750061	−	0.661369i	$-0.230024\pi$
$197$	6.45704	+	4.14968i	0.460045	+	0.295653i	−0.290016	+	0.957022i	$0.593661\pi$
$198$	5.12479	+	5.91432i	0.364203	+	0.420313i
$199$	−0.179234	−	0.392468i	−0.0127056	−	0.0278213i	0.903173	−	0.429277i	$-0.141232\pi$
$199$	−0.179234	−	0.392468i	−0.0127056	−	0.0278213i	−0.915878	+	0.401456i	$0.868504\pi$
$200$	4.52768	−	2.90976i	0.320155	−	0.205751i
$201$	−13.0645	−	3.83608i	−0.921498	−	0.270576i
$202$	19.8221	−	22.8759i	1.39468	−	1.60954i
$203$	−10.0345	+	2.94640i	−0.704284	+	0.206796i
$204$	5.79224	−	12.6832i	0.405538	−	0.888004i
$205$	−1.16070	−	8.07284i	−0.0810668	−	0.563832i
$206$	−15.4911			−1.07932
$207$	−3.12368	−	3.63904i	−0.217111	−	0.252931i
$208$	−33.8987			−2.35045
$209$	2.54422	+	17.6955i	0.175988	+	1.22402i
$210$	3.04029	−	6.65730i	0.209800	−	0.459398i
$211$	−18.2118	+	5.34748i	−1.25376	+	0.368136i	−0.840167	−	0.542328i	$-0.817543\pi$
$211$	−18.2118	+	5.34748i	−1.25376	+	0.368136i	−0.413588	+	0.910464i	$0.635725\pi$
$212$	−14.4848	+	16.7164i	−0.994821	+	1.14808i
$213$	5.08959	+	1.49444i	0.348733	+	0.102397i
$214$	11.2805	−	7.24951i	0.771116	−	0.495566i
$215$	−0.765035	−	1.67519i	−0.0521749	−	0.114247i
$216$	3.52450	+	4.06749i	0.239812	+	0.276758i
$217$	−23.2035	−	14.9120i	−1.57516	−	1.01229i
$218$	−1.85747	+	12.9190i	−0.125804	+	0.874985i
$219$	−1.22238	+	8.50184i	−0.0826008	+	0.574501i
$220$	11.0473	+	7.09966i	0.744808	+	0.478659i
$221$	−14.7628	−	17.0372i	−0.993055	−	1.14605i
$222$	5.26786	+	11.5350i	0.353556	+	0.774179i
$223$	15.3691	−	9.87712i	1.02919	−	0.661421i	0.0869003	−	0.996217i	$-0.472304\pi$
$223$	15.3691	−	9.87712i	1.02919	−	0.661421i	0.942291	+	0.334796i	$0.108667\pi$
$224$	−4.89348	−	1.43685i	−0.326959	−	0.0960039i
$225$	−0.654861	+	0.755750i	−0.0436574	+	0.0503833i
$226$	4.37989	−	1.28605i	0.291346	−	0.0855468i
$227$	11.1316	−	24.3747i	0.738828	−	1.61781i	−0.0466453	−	0.998912i	$-0.514853\pi$
$227$	11.1316	−	24.3747i	0.738828	−	1.61781i	0.785473	−	0.618896i	$-0.212420\pi$
$228$	3.36449	+	23.4006i	0.222819	+	1.54974i
$229$	−8.46771			−0.559562			−0.279781	−	0.960064i	$-0.590262\pi$
$229$	−8.46771			−0.559562			−0.279781	+	0.960064i	$0.590262\pi$
$230$	−9.98914	−	6.48561i	−0.658665	−	0.427648i
$231$	9.28689			0.611032
$232$	−2.71810	−	18.9048i	−0.178452	−	1.24116i
$233$	−3.78770	+	8.29390i	−0.248140	+	0.543351i	−0.992185	−	0.124779i	$-0.960178\pi$
$233$	−3.78770	+	8.29390i	−0.248140	+	0.543351i	0.744044	+	0.668130i	$0.232905\pi$
$234$	16.0542	−	4.71395i	1.04950	−	0.308160i
$235$	−3.81431	+	4.40195i	−0.248818	+	0.287151i
$236$	−11.6243	−	3.41319i	−0.756676	−	0.222180i
$237$	−4.06233	+	2.61070i	−0.263877	+	0.169583i
$238$	−10.1726	−	22.2749i	−0.659392	−	1.44387i
$239$	8.82668	+	10.1865i	0.570951	+	0.658912i	0.965634	−	0.259905i	$-0.0836912\pi$
$239$	8.82668	+	10.1865i	0.570951	+	0.658912i	−0.394683	+	0.918817i	$0.629146\pi$
$240$	4.23260	+	2.72013i	0.273213	+	0.175583i
$241$	−1.18522	+	8.24340i	−0.0763469	+	0.531004i	0.915375	+	0.402602i	$0.131894\pi$
$241$	−1.18522	+	8.24340i	−0.0763469	+	0.531004i	−0.991722	+	0.128403i	$0.959015\pi$
$242$	0.378039	−	2.62932i	0.0243013	−	0.169019i
$243$	−0.841254	−	0.540641i	−0.0539664	−	0.0346821i
$244$	−18.8055	−	21.7027i	−1.20390	−	1.38937i
$245$	−0.700024	−	1.53284i	−0.0447229	−	0.0979294i
$246$	17.0389	−	10.9502i	1.08636	−	0.698161i
$247$	36.6748	+	10.7687i	2.33356	+	0.685195i
$248$	32.9865	−	38.0685i	2.09465	−	2.41735i
$249$	−8.47768	+	2.48927i	−0.537251	+	0.157751i
$250$	−1.03164	+	2.25897i	−0.0652465	+	0.142870i
$251$	−1.04339	−	7.25697i	−0.0658585	−	0.458056i	−0.995890	−	0.0905751i	$-0.971129\pi$
$251$	−1.04339	−	7.25697i	−0.0658585	−	0.458056i	0.930031	−	0.367481i	$-0.119780\pi$
$252$	12.2810			0.773632
$253$	2.22047	−	14.9488i	0.139600	−	0.939825i
$254$	28.5992			1.79447
$255$	0.476176	+	3.31188i	0.0298193	+	0.207398i
$256$	−13.5505	+	29.6714i	−0.846904	+	1.85446i
$257$	16.3838	−	4.81072i	1.02199	−	0.300084i	0.272542	−	0.962144i	$-0.412136\pi$
$257$	16.3838	−	4.81072i	1.02199	−	0.300084i	0.749451	+	0.662060i	$0.230317\pi$
$258$	2.99497	−	3.45638i	0.186459	−	0.215185i
$259$	14.4390	+	4.23967i	0.897196	+	0.263440i
$260$	23.6198	−	15.1795i	1.46484	−	0.941395i
$261$	1.47417	+	3.22799i	0.0912490	+	0.199807i
$262$	−7.84808	−	9.05717i	−0.484856	−	0.559554i
$263$	−20.2609	−	13.0209i	−1.24934	−	0.802902i	−0.262552	−	0.964918i	$-0.584564\pi$
$263$	−20.2609	−	13.0209i	−1.24934	−	0.802902i	−0.986788	+	0.162016i	$0.948200\pi$
$264$	−2.41369	+	16.7876i	−0.148552	+	1.03320i
$265$	0.755383	−	5.25380i	0.0464028	−	0.322739i
$266$	34.9287	+	22.4473i	2.14162	+	1.37633i
$267$	7.38274	+	8.52013i	0.451816	+	0.521424i
$268$	−23.5711	−	51.6135i	−1.43983	−	3.15279i
$269$	12.1014	−	7.77710i	0.737836	−	0.474178i	−0.116964	−	0.993136i	$-0.537316\pi$
$269$	12.1014	−	7.77710i	0.737836	−	0.474178i	0.854800	+	0.518958i	$0.173680\pi$
$270$	−2.38279	−	0.699652i	−0.145012	−	0.0425794i
$271$	−12.7739	+	14.7418i	−0.775956	+	0.895502i	−0.996810	−	0.0798054i	$-0.974570\pi$
$271$	−12.7739	+	14.7418i	−0.775956	+	0.895502i	0.220854	+	0.975307i	$0.429116\pi$
$272$	16.1525	−	4.74280i	0.979389	−	0.287575i
$273$	8.24846	−	18.0616i	0.499220	−	1.09314i
$274$	−6.65362	−	46.2769i	−0.401960	−	2.79569i
$275$	−3.15125			−0.190027
$276$	2.93636	−	19.7684i	0.176748	−	1.18992i
$277$	−9.24815			−0.555667			−0.277834	−	0.960629i	$-0.589616\pi$
$277$	−9.24815			−0.555667			−0.277834	+	0.960629i	$0.589616\pi$
$278$	4.05422	+	28.1977i	0.243156	+	1.69119i
$279$	−3.88796	+	8.51344i	−0.232766	+	0.509686i
$280$	15.2187	−	4.46862i	0.909492	−	0.267051i
$281$	1.48813	−	1.71740i	0.0887746	−	0.102451i	−0.709624	−	0.704580i	$-0.751135\pi$
$281$	1.48813	−	1.71740i	0.0887746	−	0.102451i	0.798399	+	0.602129i	$0.205681\pi$
$282$	−13.8789	−	4.07520i	−0.826474	−	0.242675i
$283$	3.39993	−	2.18500i	0.202105	−	0.129885i	−0.435674	−	0.900105i	$-0.643490\pi$
$283$	3.39993	−	2.18500i	0.202105	−	0.129885i	0.637779	+	0.770220i	$0.279853\pi$
$284$	9.18269	+	20.1073i	0.544892	+	1.19315i
$285$	−3.71511	−	4.28747i	−0.220064	−	0.253968i
$286$	44.3565	+	28.5062i	2.62285	+	1.68561i
$287$	3.42064	−	23.7911i	0.201914	−	1.40434i
$288$	−0.246285	+	1.71295i	−0.0145125	+	0.100937i
$289$	−4.88324	−	3.13827i	−0.287249	−	0.184604i
$290$	5.77112	+	6.66022i	0.338892	+	0.391102i
$291$	4.39837	+	9.63108i	0.257837	+	0.564584i
$292$	−30.1113	+	19.3514i	−1.76213	+	1.13245i
$293$	−11.2231	−	3.29539i	−0.655658	−	0.192519i	−0.0630510	−	0.998010i	$-0.520083\pi$
$293$	−11.2231	−	3.29539i	−0.655658	−	0.192519i	−0.592607	+	0.805492i	$0.701901\pi$
$294$	2.74047	−	3.16267i	0.159827	−	0.184450i
$295$	2.78945	−	0.819057i	0.162408	−	0.0476874i
$296$	−11.4166	+	24.9989i	−0.663578	+	1.45303i
$297$	−0.448469	−	3.11917i	−0.0260228	−	0.180993i
$298$	22.6273			1.31077
$299$	−27.1011	−	17.5958i	−1.56730	−	1.01759i
$300$	−4.16722			−0.240595
$301$	−0.772391	−	5.37210i	−0.0445199	−	0.309642i
$302$	−15.3275	+	33.5625i	−0.881997	+	1.93130i
$303$	−11.6949	+	3.43394i	−0.671856	+	0.197275i
$304$	−18.6918	+	21.5715i	−1.07205	+	1.23721i
$305$	6.61196	+	1.94145i	0.378600	+	0.111167i
$306$	−6.99020	+	4.49233i	−0.399603	+	0.256809i
$307$	−6.22061	−	13.6212i	−0.355029	−	0.777406i	−0.999914	−	0.0131257i	$-0.995822\pi$
$307$	−6.22061	−	13.6212i	−0.355029	−	0.777406i	0.644885	−	0.764280i	$-0.276905\pi$
$308$	25.3435	+	29.2479i	1.44408	+	1.66655i
$309$	5.24764	+	3.37245i	0.298528	+	0.191852i
$310$	−3.30776	+	23.0060i	−0.187868	+	1.30665i
$311$	2.52757	−	17.5796i	0.143325	−	0.996849i	−0.783510	−	0.621380i	$-0.786572\pi$
$311$	2.52757	−	17.5796i	0.143325	−	0.996849i	0.926835	−	0.375469i	$-0.122518\pi$
$312$	30.5055	+	19.6047i	1.72703	+	1.10990i
$313$	−16.3873	−	18.9120i	−0.926267	−	1.06897i	−0.997440	−	0.0715053i	$-0.977220\pi$
$313$	−16.3873	−	18.9120i	−0.926267	−	1.06897i	0.0711731	−	0.997464i	$-0.477326\pi$
$314$	−13.1208	−	28.7305i	−0.740449	−	1.62136i
$315$	−2.47922	+	1.59330i	−0.139688	+	0.0897721i
$316$	−19.3080	−	5.66933i	−1.08616	−	0.318925i
$317$	−12.7563	+	14.7216i	−0.716466	+	0.826846i	−0.990877	−	0.134767i	$-0.956972\pi$
$317$	−12.7563	+	14.7216i	−0.716466	+	0.826846i	0.274411	+	0.961612i	$0.411517\pi$
$318$	12.6475	−	3.71363i	0.709235	−	0.208250i
$319$	−4.64548	+	10.1722i	−0.260097	+	0.569533i
$320$	−0.820436	−	5.70626i	−0.0458638	−	0.318990i
$321$	−5.39952			−0.301372
$322$	−22.8612	−	26.6330i	−1.27400	−	1.48420i
$323$	−18.9819			−1.05618
$324$	−0.593058	−	4.12481i	−0.0329476	−	0.229156i
$325$	−2.79889	+	6.12871i	−0.155254	+	0.339959i
$326$	48.0544	−	14.1101i	2.66149	−	0.781484i
$327$	3.44172	−	3.97196i	0.190328	−	0.219650i
$328$	42.1172	+	12.3667i	2.32554	+	0.682839i
$329$	−14.4405	+	9.28034i	−0.796130	+	0.511641i
$330$	−3.25094	−	7.11857i	−0.178958	−	0.391864i
$331$	20.8420	+	24.0529i	1.14558	+	1.32207i	0.939110	+	0.343616i	$0.111652\pi$
$331$	20.8420	+	24.0529i	1.14558	+	1.32207i	0.206469	+	0.978453i	$0.433803\pi$
$332$	−30.9748	−	19.9063i	−1.69996	−	1.09250i
$333$	0.726704	−	5.05434i	0.0398231	−	0.276976i
$334$	−3.87431	+	26.9464i	−0.211993	+	1.47444i
$335$	11.4545	+	7.36138i	0.625828	+	0.402195i
$336$	9.70995	+	11.2059i	0.529721	+	0.611331i
$337$	−1.41084	−	3.08932i	−0.0768535	−	0.168286i	0.867305	−	0.497777i	$-0.165850\pi$
$337$	−1.41084	−	3.08932i	−0.0768535	−	0.168286i	−0.944159	+	0.329491i	$0.893123\pi$
$338$	67.6779	−	43.4939i	3.68119	−	2.36576i
$339$	−1.76367	−	0.517861i	−0.0957896	−	0.0281264i
$340$	−9.13089	+	10.5376i	−0.495192	+	0.571482i
$341$	−28.2985	+	8.30919i	−1.53245	+	0.449968i
$342$	5.85261	−	12.8154i	0.316473	−	0.692979i
$343$	2.22911	+	15.5038i	0.120361	+	0.837127i
$344$	9.91168			0.534402
$345$	1.97191	+	4.37168i	0.106164	+	0.235363i
$346$	−40.0866			−2.15507
$347$	−3.00044	−	20.8685i	−0.161072	−	1.12028i	−0.896618	−	0.442805i	$-0.853983\pi$
$347$	−3.00044	−	20.8685i	−0.161072	−	1.12028i	0.735546	−	0.677475i	$-0.236926\pi$
$348$	−6.14321	+	13.4517i	−0.329310	+	0.721089i
$349$	−16.4595	+	4.83295i	−0.881057	+	0.258702i	−0.690812	−	0.723035i	$-0.742747\pi$
$349$	−16.4595	+	4.83295i	−0.881057	+	0.258702i	−0.190246	+	0.981736i	$0.560928\pi$
$350$	−4.79272	+	5.53109i	−0.256181	+	0.295649i
$351$	−6.46465	−	1.89819i	−0.345057	−	0.101318i
$352$	−4.58772	+	2.94835i	−0.244526	+	0.157148i
$353$	11.8186	+	25.8792i	0.629043	+	1.37741i	0.908756	+	0.417328i	$0.137033\pi$
$353$	11.8186	+	25.8792i	0.629043	+	1.37741i	−0.279713	+	0.960084i	$0.590239\pi$
$354$	4.72793	+	5.45632i	0.251287	+	0.290000i
$355$	−4.46239	−	2.86781i	−0.236839	−	0.152207i
$356$	−6.68598	+	46.5020i	−0.354356	+	2.46460i
$357$	−1.40332	+	9.76028i	−0.0742714	+	0.516569i
$358$	8.06311	+	5.18185i	0.426149	+	0.273869i
$359$	14.5527	+	16.7947i	0.768060	+	0.886388i	0.996187	−	0.0872432i	$-0.0278057\pi$
$359$	14.5527	+	16.7947i	0.768060	+	0.886388i	−0.228127	+	0.973631i	$0.573260\pi$
$360$	−2.23579	−	4.89569i	−0.117836	−	0.258026i
$361$	11.0914	−	7.12803i	0.583760	−	0.375159i
$362$	0.0576123	+	0.0169165i	0.00302803	+	0.000889111i
$363$	−0.700472	+	0.808388i	−0.0367652	+	0.0424294i
$364$	79.3925	−	23.3117i	4.16130	−	1.22187i
$365$	3.56811	−	7.81308i	0.186764	−	0.408955i
$366$	2.43547	+	16.9391i	0.127304	+	0.885421i
$367$	−36.3329			−1.89656			−0.948282	−	0.317430i	$-0.897180\pi$
$367$	−36.3329			−1.89656			−0.948282	+	0.317430i	$0.897180\pi$
$368$	20.3594	−	12.9505i	1.06131	−	0.675093i
$369$	−8.15586			−0.424577
$370$	−1.80469	−	12.5519i	−0.0938213	−	0.652541i
$371$	6.49811	−	14.2289i	0.337365	−	0.738726i
$372$	−37.4221	+	10.9881i	−1.94024	+	0.569707i
$373$	12.2362	−	14.1213i	0.633567	−	0.731176i	−0.344656	−	0.938729i	$-0.612005\pi$
$373$	12.2362	−	14.1213i	0.633567	−	0.731176i	0.978224	+	0.207553i	$0.0665500\pi$
$374$	−25.1239	−	7.37703i	−1.29912	−	0.381457i
$375$	0.841254	−	0.540641i	0.0434421	−	0.0279186i
$376$	−13.0226	−	28.5155i	−0.671589	−	1.47058i
$377$	15.6573	+	18.0695i	0.806394	+	0.930628i
$378$	−6.15686	−	3.95678i	−0.316675	−	0.203515i
$379$	0.264115	−	1.83696i	0.0135667	−	0.0943584i	−0.981913	−	0.189332i	$-0.939368\pi$
$379$	0.264115	−	1.83696i	0.0135667	−	0.0943584i	0.995480	+	0.0949739i	$0.0302768\pi$
$380$	3.36449	−	23.4006i	0.172595	−	1.20042i
$381$	−9.68803	−	6.22612i	−0.496333	−	0.318974i
$382$	32.4504	+	37.4498i	1.66031	+	1.91610i
$383$	0.990424	+	2.16873i	0.0506083	+	0.110817i	0.933247	−	0.359235i	$-0.116962\pi$
$383$	0.990424	+	2.16873i	0.0506083	+	0.110817i	−0.882639	+	0.470052i	$0.844235\pi$
$384$	14.9556	−	9.61136i	0.763198	−	0.490478i
$385$	−8.91070	−	2.61642i	−0.454131	−	0.133345i
$386$	−4.30724	+	4.97082i	−0.219233	+	0.253008i
$387$	−1.76702	+	0.518843i	−0.0898225	+	0.0263743i
$388$	−18.3290	+	40.1349i	−0.930513	+	2.03754i
$389$	−5.48429	−	38.1441i	−0.278065	−	1.93398i	−0.350395	−	0.936602i	$-0.613953\pi$
$389$	−5.48429	−	38.1441i	−0.278065	−	1.93398i	0.0723304	−	0.997381i	$-0.476956\pi$
$390$	−16.7320			−0.847258
$391$	15.3753	+	4.59254i	0.777563	+	0.232255i
$392$	9.06941			0.458074
$393$	0.686784	+	4.77668i	0.0346437	+	0.240952i
$394$	7.91832	−	17.3387i	0.398919	−	0.873512i
$395$	4.63330	−	1.36046i	0.233126	−	0.0684521i
$396$	8.59959	−	9.92446i	0.432146	−	0.498723i
$397$	6.64868	+	1.95223i	0.333687	+	0.0979795i	0.444284	−	0.895886i	$-0.353458\pi$
$397$	6.64868	+	1.95223i	0.333687	+	0.0979795i	−0.110597	+	0.993865i	$0.535276\pi$
$398$	−0.901385	+	0.579285i	−0.0451823	+	0.0290369i
$399$	−6.94533	−	15.2082i	−0.347701	−	0.761360i
$400$	−3.29480	−	3.80240i	−0.164740	−	0.190120i
$401$	8.42112	+	5.41193i	0.420531	+	0.270259i	0.733747	−	0.679423i	$-0.237770\pi$
$401$	8.42112	+	5.41193i	0.420531	+	0.270259i	−0.313216	+	0.949682i	$0.601406\pi$
$402$	−4.81222	+	33.4697i	−0.240012	+	1.66932i
$403$	−8.97413	+	62.4164i	−0.447033	+	3.10918i
$404$	−42.7296	−	27.4607i	−2.12588	−	1.36622i
$405$	0.654861	+	0.755750i	0.0325403	+	0.0375535i
$406$	10.7890	+	23.6246i	0.535449	+	1.17247i
$407$	13.5368	−	8.69958i	0.670995	−	0.431222i
$408$	−17.2786	−	5.07345i	−0.855417	−	0.251173i
$409$	11.0025	−	12.6976i	0.544041	−	0.627856i	−0.415444	−	0.909619i	$-0.636374\pi$
$409$	11.0025	−	12.6976i	0.544041	−	0.627856i	0.959484	+	0.281763i	$0.0909191\pi$
$410$	−19.4337	+	5.70626i	−0.959764	+	0.281812i
$411$	−7.82069	+	17.1249i	−0.385766	+	0.844710i
$412$	3.69943	+	25.7301i	0.182258	+	1.26763i
$413$	8.56772			0.421590
$414$	−7.84120	+	8.96447i	−0.385374	+	0.440580i
$415$	8.83559			0.433722
$416$	1.65936	+	11.5411i	0.0813569	+	0.565850i
$417$	4.76535	−	10.4347i	0.233360	−	0.510988i
$418$	42.5982	−	12.5080i	2.08355	−	0.611785i
$419$	−3.09064	+	3.56679i	−0.150988	+	0.174249i	−0.826205	−	0.563370i	$-0.809505\pi$
$419$	−3.09064	+	3.56679i	−0.150988	+	0.174249i	0.675217	+	0.737619i	$0.264050\pi$
$420$	−11.7836	−	3.45996i	−0.574979	−	0.168829i
$421$	1.90414	−	1.22371i	0.0928019	−	0.0596402i	−0.493417	−	0.869793i	$-0.664252\pi$
$421$	1.90414	−	1.22371i	0.0928019	−	0.0596402i	0.586219	+	0.810153i	$0.300616\pi$
$422$	19.5812	+	42.8768i	0.953198	+	2.08721i
$423$	3.81431	+	4.40195i	0.185458	+	0.214030i
$424$	24.0321	+	15.4445i	1.16710	+	0.750052i
$425$	0.476176	−	3.31188i	0.0230979	−	0.160650i
$426$	1.87472	−	13.0389i	0.0908304	−	0.631739i
$427$	17.0845	+	10.9796i	0.826779	+	0.531339i
$428$	−14.7350	−	17.0051i	−0.712244	−	0.821973i
$429$	−8.81998	−	19.3131i	−0.425833	−	0.932443i
$430$	−3.84743	+	2.47259i	−0.185540	+	0.119239i
$431$	7.87724	+	2.31297i	0.379433	+	0.111412i	0.465887	−	0.884844i	$-0.345735\pi$
$431$	7.87724	+	2.31297i	0.379433	+	0.111412i	−0.0864537	+	0.996256i	$0.527553\pi$
$432$	3.29480	−	3.80240i	0.158521	−	0.182943i
$433$	34.8369	−	10.2290i	1.67415	−	0.491576i	0.699376	−	0.714754i	$-0.253461\pi$
$433$	34.8369	−	10.2290i	1.67415	−	0.491576i	0.974778	+	0.223178i	$0.0716431\pi$
$434$	−28.4547	+	62.3071i	−1.36587	+	2.99084i
$435$	−0.505029	−	3.51255i	−0.0242143	−	0.168414i
$436$	21.9015			1.04889
$437$	−26.1407	+	7.54346i	−1.25048	+	0.360853i
$438$	21.3305			1.01921
$439$	−4.92784	−	34.2739i	−0.235193	−	1.63580i	−0.675076	−	0.737749i	$-0.735889\pi$
$439$	−4.92784	−	34.2739i	−0.235193	−	1.63580i	0.439882	−	0.898055i	$-0.355020\pi$
$440$	7.04552	−	15.4275i	0.335882	−	0.735479i
$441$	−1.61686	+	0.474753i	−0.0769933	+	0.0226073i
$442$	−36.6618	+	42.3100i	−1.74383	+	2.01248i
$443$	3.22681	+	0.947477i	0.153310	+	0.0450160i	0.357487	−	0.933918i	$-0.383634\pi$
$443$	3.22681	+	0.947477i	0.153310	+	0.0450160i	−0.204177	+	0.978934i	$0.565452\pi$
$444$	17.9012	−	11.5044i	0.849551	−	0.545973i
$445$	−4.68328	−	10.2550i	−0.222009	−	0.486132i
$446$	−29.7109	−	34.2882i	−1.40685	−	1.62359i
$447$	−7.66506	−	4.92603i	−0.362545	−	0.232993i
$448$	2.41787	−	16.8166i	0.114234	−	0.794512i
$449$	−2.00683	+	13.9578i	−0.0947080	+	0.658708i	0.886066	+	0.463560i	$0.153428\pi$
$449$	−2.00683	+	13.9578i	−0.0947080	+	0.658708i	−0.980774	+	0.195149i	$0.937481\pi$
$450$	2.08916	+	1.34262i	0.0984840	+	0.0632918i
$451$	−16.8306	−	19.4236i	−0.792524	−	0.914622i
$452$	−3.18204	−	6.96769i	−0.149670	−	0.327733i
$453$	12.4989	−	8.03253i	0.587248	−	0.377401i
$454$	−63.8500	−	18.7480i	−2.99663	−	0.879889i
$455$	−13.0029	+	15.0061i	−0.609585	+	0.703498i
$456$	29.2963	−	8.60217i	1.37193	−	0.402834i
$457$	3.51580	−	7.69852i	0.164462	−	0.360122i	−0.809401	−	0.587256i	$-0.800208\pi$
$457$	3.51580	−	7.69852i	0.164462	−	0.360122i	0.973863	+	0.227134i	$0.0729356\pi$
$458$	2.99269	+	20.8146i	0.139839	+	0.972602i
$459$	3.34594			0.156175
$460$	−8.38682	+	18.1404i	−0.391038	+	0.845800i
$461$	23.1443			1.07794			0.538968	−	0.842326i	$-0.318814\pi$
$461$	23.1443			1.07794			0.538968	+	0.842326i	$0.318814\pi$
$462$	−3.28220	−	22.8282i	−0.152702	−	1.06206i
$463$	2.82584	−	6.18774i	0.131328	−	0.287568i	−0.832532	−	0.553977i	$-0.813110\pi$
$463$	2.82584	−	6.18774i	0.131328	−	0.287568i	0.963860	+	0.266408i	$0.0858369\pi$
$464$	−17.1312	+	5.03018i	−0.795297	+	0.233520i
$465$	6.12898	−	7.07322i	0.284225	−	0.328013i
$466$	21.7260	+	6.37932i	1.00644	+	0.295516i
$467$	−6.72584	+	4.32244i	−0.311235	+	0.200018i	−0.686928	−	0.726726i	$-0.741041\pi$
$467$	−6.72584	+	4.32244i	−0.311235	+	0.200018i	0.375693	+	0.926744i	$0.377405\pi$
$468$	−11.6636	−	25.5397i	−0.539149	−	1.18057i
$469$	26.2777	+	30.3261i	1.21339	+	1.40033i
$470$	12.1685	+	7.82025i	0.561293	+	0.360721i
$471$	−1.81002	+	12.5890i	−0.0834012	+	0.580068i
$472$	−2.22677	+	15.4875i	−0.102496	+	0.712872i
$473$	−4.88212	−	3.13755i	−0.224480	−	0.144265i
$474$	7.85312	+	9.06298i	0.360706	+	0.416276i
$475$	2.35670	+	5.16046i	0.108133	+	0.236778i
$476$	−34.5684	+	22.2158i	−1.58444	+	1.01826i
$477$	−5.09283	−	1.49539i	−0.233184	−	0.0684691i
$478$	21.9201	−	25.2971i	1.00260	−	1.15706i
$479$	1.95684	−	0.574581i	0.0894105	−	0.0262533i	−0.236721	−	0.971578i	$-0.576073\pi$
$479$	1.95684	−	0.574581i	0.0894105	−	0.0262533i	0.326132	+	0.945324i	$0.394255\pi$
$480$	0.718902	−	1.57418i	0.0328133	−	0.0718510i
$481$	−4.89622	−	34.0539i	−0.223248	−	1.55273i
$482$	20.6821			0.942043
$483$	1.94620	+	13.9989i	0.0885551	+	0.636973i
$484$	−4.45747			−0.202612
$485$	−1.50681	−	10.4801i	−0.0684209	−	0.475878i
$486$	−1.03164	+	2.25897i	−0.0467960	+	0.102469i
$487$	5.89815	−	1.73185i	0.267271	−	0.0784778i	−0.145351	−	0.989380i	$-0.546431\pi$
$487$	5.89815	−	1.73185i	0.267271	−	0.0784778i	0.412622	+	0.910902i	$0.364613\pi$
$488$	−24.2877	+	28.0295i	−1.09945	+	1.26883i
$489$	−19.3503	−	5.68177i	−0.875053	−	0.256939i
$490$	−3.52048	+	2.26248i	−0.159039	+	0.102208i
$491$	−10.3926	−	22.7565i	−0.469009	−	1.02699i	−0.985341	−	0.170599i	$-0.945430\pi$
$491$	−10.3926	−	22.7565i	−0.469009	−	1.02699i	0.516331	−	0.856389i	$-0.327297\pi$
$492$	−22.2569	−	25.6859i	−1.00342	−	1.15801i
$493$	−9.98874	−	6.41937i	−0.449870	−	0.289114i
$494$	13.5089	−	93.9566i	0.607795	−	4.22731i
$495$	−0.448469	+	3.11917i	−0.0201572	+	0.140196i
$496$	−39.6138	−	25.4582i	−1.77871	−	1.14311i
$497$	−10.2371	−	11.8143i	−0.459197	−	0.529942i
$498$	9.11512	+	19.9593i	0.408458	+	0.894399i
$499$	2.22810	−	1.43191i	0.0997435	−	0.0641012i	−0.489818	−	0.871825i	$-0.662937\pi$
$499$	2.22810	−	1.43191i	0.0997435	−	0.0641012i	0.589562	+	0.807723i	$0.299300\pi$
$500$	3.99842	+	1.17404i	0.178815	+	0.0525048i
$501$	7.17875	−	8.28472i	0.320723	−	0.370134i
$502$	−17.4697	+	5.12956i	−0.779710	+	0.228944i
$503$	−12.5386	+	27.4556i	−0.559067	+	1.22419i	0.393350	+	0.919389i	$0.371316\pi$
$503$	−12.5386	+	27.4556i	−0.559067	+	1.22419i	−0.952417	+	0.304797i	$0.901411\pi$
$504$	−2.25729	−	15.6998i	−0.100547	−	0.699323i
$505$	12.1886			0.542388
$506$	−37.5307	−	0.174903i	−1.66844	−	0.00777539i
$507$	−32.3948			−1.43870
$508$	−6.82976	−	47.5020i	−0.303022	−	2.10756i
$509$	2.56159	−	5.60909i	0.113540	−	0.248619i	−0.844328	−	0.535827i	$-0.820000\pi$
$509$	2.56159	−	5.60909i	0.113540	−	0.248619i	0.957868	+	0.287208i	$0.0927272\pi$
$510$	7.97268	−	2.34099i	0.353036	−	0.103661i
$511$	16.5765	−	19.1303i	0.733302	−	0.846275i
$512$	43.6095	+	12.8049i	1.92728	+	0.565902i
$513$	−4.77254	+	3.06713i	−0.210713	+	0.135417i
$514$	−17.6157	−	38.5730i	−0.776995	−	1.70138i
$515$	−4.08495	−	4.71428i	−0.180004	−	0.207736i
$516$	−6.45614	−	4.14911i	−0.284216	−	0.182654i
$517$	−2.61216	+	18.1680i	−0.114883	+	0.799026i
$518$	5.31851	−	36.9911i	0.233682	−	1.62529i
$519$	13.5794	+	8.72697i	0.596071	+	0.383071i
$520$	−23.7465	−	27.4050i	−1.04135	−	1.20179i
$521$	18.0774	+	39.5841i	0.791987	+	1.73421i	0.670874	+	0.741571i	$0.265919\pi$
$521$	18.0774	+	39.5841i	0.791987	+	1.73421i	0.121113	+	0.992639i	$0.461354\pi$
$522$	7.41375	−	4.76453i	0.324491	−	0.208538i
$523$	22.7169	+	6.67029i	0.993341	+	0.291671i	0.737721	−	0.675106i	$-0.235902\pi$
$523$	22.7169	+	6.67029i	0.993341	+	0.291671i	0.255620	+	0.966777i	$0.417720\pi$
$524$	−13.1694	+	15.1983i	−0.575307	+	0.663940i
$525$	2.82768	−	0.830281i	0.123410	−	0.0362364i
$526$	−24.8461	+	54.4054i	−1.08334	+	2.37219i
$527$	−4.45663	−	30.9966i	−0.194134	−	1.35023i
$528$	15.8549			0.689995
$529$	22.9990	+	0.214368i	0.999957	+	0.00932034i
$530$	−13.1814			−0.572564
$531$	−0.413740	−	2.87762i	−0.0179548	−	0.124878i
$532$	28.9427	−	63.3758i	1.25483	−	2.74769i
$533$	−52.7247	+	15.4814i	−2.28376	+	0.670573i
$534$	18.3342	−	21.1588i	0.793399	−	0.915631i
$535$	5.18080	+	1.52122i	0.223985	+	0.0657680i
$536$	−61.6490	+	39.6194i	−2.66283	+	1.71130i
$537$	−1.60329	−	3.51072i	−0.0691873	−	0.151499i
$538$	−23.3939	−	26.9980i	−1.00858	−	1.16397i
$539$	−4.46724	−	2.87092i	−0.192418	−	0.123659i
$540$	−0.593058	+	4.12481i	−0.0255211	+	0.177503i
$541$	4.37444	−	30.4249i	0.188072	−	1.30807i	−0.648921	−	0.760855i	$-0.724780\pi$
$541$	4.37444	−	30.4249i	0.188072	−	1.30807i	0.836993	−	0.547213i	$-0.184311\pi$
$542$	40.7516	+	26.1895i	1.75043	+	1.12493i
$543$	−0.0158335	−	0.0182729i	−0.000679481	−	0.000784163i
$544$	−2.40540	−	5.26709i	−0.103131	−	0.225825i
$545$	−4.42134	+	2.84142i	−0.189389	+	0.121713i
$546$	−47.3127	−	13.8923i	−2.02480	−	0.594534i
$547$	0.415504	−	0.479517i	0.0177657	−	0.0205027i	−0.746797	−	0.665052i	$-0.768409\pi$
$547$	0.415504	−	0.479517i	0.0177657	−	0.0205027i	0.764563	+	0.644549i	$0.222955\pi$
$548$	−75.2751	+	22.1028i	−3.21559	+	0.944184i
$549$	2.86267	−	6.26837i	0.122176	−	0.267527i
$550$	1.11372	+	7.74612i	0.0474893	+	0.330295i
$551$	20.1321			0.857656
$552$	−25.8112	−	0.120287i	−1.09860	−	0.00511976i
$553$	14.2310			0.605165
$554$	3.26851	+	22.7330i	0.138866	+	0.965832i
$555$	−2.12124	+	4.64486i	−0.0900416	+	0.197164i
$556$	45.8671	−	13.4678i	1.94520	−	0.571162i
$557$	−7.08952	+	8.18174i	−0.300392	+	0.346671i	−0.885799	−	0.464068i	$-0.846389\pi$
$557$	−7.08952	+	8.18174i	−0.300392	+	0.346671i	0.585407	+	0.810740i	$0.300935\pi$
$558$	22.3011	+	6.54819i	0.944080	+	0.277207i
$559$	−10.4383	+	6.70827i	−0.441492	+	0.283730i
$560$	−6.15957	−	13.4876i	−0.260289	−	0.569954i
$561$	6.90476	+	7.96852i	0.291519	+	0.336431i
$562$	−4.74750	−	3.05103i	−0.200261	−	0.128700i
$563$	−1.28485	+	8.93633i	−0.0541500	+	0.376621i	0.944669	+	0.328026i	$0.106383\pi$
$563$	−1.28485	+	8.93633i	−0.0541500	+	0.376621i	−0.998819	+	0.0485951i	$0.984526\pi$
$564$	−3.45433	+	24.0254i	−0.145454	+	1.01165i
$565$	1.54633	+	0.993768i	0.0650548	+	0.0418082i
$566$	−6.57260	−	7.58518i	−0.276267	−	0.318829i
$567$	1.22425	+	2.68073i	0.0514137	+	0.112580i
$568$	24.0169	−	15.4347i	1.00772	−	0.647626i
$569$	−12.9721	−	3.80895i	−0.543819	−	0.159680i	−0.00172629	−	0.999999i	$-0.500549\pi$
$569$	−12.9721	−	3.80895i	−0.543819	−	0.159680i	−0.542092	+	0.840319i	$0.682368\pi$
$570$	−9.22607	+	10.6474i	−0.386437	+	0.445973i
$571$	−28.3379	+	8.32077i	−1.18591	+	0.348213i	−0.814448	−	0.580236i	$-0.802960\pi$
$571$	−28.3379	+	8.32077i	−1.18591	+	0.348213i	−0.371458	+	0.928450i	$0.621142\pi$
$572$	36.7548	−	80.4818i	1.53680	−	3.36511i
$573$	−2.83973	−	19.7508i	−0.118631	−	0.825100i
$574$	−59.6901			−2.49142
$575$	−0.660388	−	4.75015i	−0.0275401	−	0.198095i
$576$	−5.76494			−0.240206
$577$	2.87278	+	19.9806i	0.119595	+	0.831803i	0.958003	+	0.286759i	$0.0925779\pi$
$577$	2.87278	+	19.9806i	0.119595	+	0.831803i	−0.838408	+	0.545044i	$0.816513\pi$
$578$	−5.98836	+	13.1127i	−0.249083	+	0.545416i
$579$	2.54125	−	0.746178i	0.105611	−	0.0310101i
$580$	9.68416	−	11.1761i	0.402113	−	0.464063i
$581$	24.9842	+	7.33602i	1.03652	+	0.304349i
$582$	22.1198	−	14.2155i	0.916895	−	0.589252i
$583$	−6.94835	−	15.2148i	−0.287771	−	0.630131i
$584$	30.2729	+	34.9368i	1.25270	+	1.44569i
$585$	5.66800	+	3.64260i	0.234343	+	0.150603i
$586$	−4.13394	+	28.7522i	−0.170772	+	1.18774i
$587$	−3.75117	+	26.0900i	−0.154827	+	1.07685i	0.753156	+	0.657842i	$0.228530\pi$
$587$	−3.75117	+	26.0900i	−0.154827	+	1.07685i	−0.907983	+	0.419006i	$0.862379\pi$
$588$	−5.90751	−	3.79652i	−0.243621	−	0.156566i
$589$	34.7705	+	40.1273i	1.43269	+	1.65342i
$590$	−2.99919	−	6.56731i	−0.123475	−	0.270372i
$591$	−6.45704	+	4.14968i	−0.265607	+	0.170695i
$592$	24.6507	+	7.23810i	1.01314	+	0.297484i
$593$	−15.3530	+	17.7183i	−0.630474	+	0.727605i	−0.977660	−	0.210191i	$-0.932592\pi$
$593$	−15.3530	+	17.7183i	−0.630474	+	0.727605i	0.347187	+	0.937796i	$0.387137\pi$
$594$	−7.50877	+	2.20477i	−0.308089	+	0.0904630i
$595$	4.09626	−	8.96956i	0.167930	−	0.367716i
$596$	−5.40363	−	37.5831i	−0.221341	−	1.53946i
$597$	0.431458			0.0176584
$598$	−33.6743	+	72.8362i	−1.37704	+	2.97850i
$599$	−10.6944			−0.436960			−0.218480	−	0.975841i	$-0.570110\pi$
$599$	−10.6944			−0.436960			−0.218480	+	0.975841i	$0.570110\pi$
$600$	0.765947	+	5.32728i	0.0312696	+	0.217485i
$601$	−19.3330	+	42.3334i	−0.788611	+	1.72682i	−0.108026	+	0.994148i	$0.534453\pi$
$601$	−19.3330	+	42.3334i	−0.788611	+	1.72682i	−0.680585	+	0.732669i	$0.738274\pi$
$602$	−12.9322	+	3.79725i	−0.527078	+	0.154764i
$603$	8.91661	−	10.2903i	0.363112	−	0.419054i
$604$	59.4062	+	17.4432i	2.41721	+	0.709756i
$605$	0.899847	−	0.578297i	0.0365840	−	0.0235111i
$606$	12.5743	+	27.5338i	0.510794	+	1.11848i
$607$	11.1119	+	12.8238i	0.451019	+	0.520504i	0.935035	−	0.354556i	$-0.115368\pi$
$607$	11.1119	+	12.8238i	0.451019	+	0.520504i	−0.484016	+	0.875059i	$0.660822\pi$
$608$	8.25919	+	5.30786i	0.334954	+	0.215262i
$609$	1.48835	−	10.3517i	0.0603109	−	0.419471i
$610$	2.43547	−	16.9391i	0.0986095	−	0.685844i
$611$	33.0139	+	21.2167i	1.33560	+	0.858338i
$612$	9.13089	+	10.5376i	0.369094	+	0.425958i
$613$	7.63140	+	16.7104i	0.308229	+	0.674928i	0.998833	−	0.0483057i	$-0.0153822\pi$
$613$	7.63140	+	16.7104i	0.308229	+	0.674928i	−0.690603	+	0.723234i	$0.742655\pi$
$614$	−31.2840	+	20.1050i	−1.26252	+	0.811373i
$615$	7.82549	+	2.29777i	0.315554	+	0.0926550i
$616$	32.7316	−	37.7743i	1.31879	−	1.52197i
$617$	15.8117	−	4.64272i	0.636554	−	0.186909i	0.0524960	−	0.998621i	$-0.483282\pi$
$617$	15.8117	−	4.64272i	0.636554	−	0.186909i	0.584058	+	0.811712i	$0.301464\pi$
$618$	6.43523	−	14.0912i	0.258863	−	0.566831i
$619$	−0.411489	−	2.86197i	−0.0165391	−	0.115032i	0.979879	−	0.199591i	$-0.0639612\pi$
$619$	−0.411489	−	2.86197i	−0.0165391	−	0.115032i	−0.996419	+	0.0845582i	$0.973052\pi$
$620$	39.0019			1.56635
$621$	4.60781	−	1.32968i	0.184905	−	0.0533583i
$622$	−44.1060			−1.76849
$623$	−4.72832	−	32.8862i	−0.189436	−	1.31756i
$624$	14.0820	−	30.8354i	0.563733	−	1.23440i
$625$	−0.959493	+	0.281733i	−0.0383797	+	0.0112693i
$626$	−40.6961	+	46.9659i	−1.62654	+	1.87713i
$627$	−17.1533	−	5.03665i	−0.685036	−	0.201145i
$628$	−44.5868	+	28.6542i	−1.77921	+	1.14343i
$629$	7.09753	+	15.5414i	0.282997	+	0.619677i
$630$	4.79272	+	5.53109i	0.190946	+	0.220364i
$631$	36.8600	+	23.6885i	1.46737	+	0.943023i	0.998203	+	0.0599148i	$0.0190829\pi$
$631$	36.8600	+	23.6885i	1.46737	+	0.943023i	0.469169	+	0.883108i	$0.344553\pi$
$632$	−3.69868	+	25.7249i	−0.147126	+	1.02328i
$633$	2.70124	−	18.7875i	0.107364	−	0.746736i
$634$	40.6956	+	26.1535i	1.61623	+	1.03869i
$635$	7.54149	+	8.70335i	0.299275	+	0.345382i
$636$	−9.18853	−	20.1201i	−0.364349	−	0.797813i
$637$	−9.55126	+	6.13822i	−0.378435	+	0.243205i
$638$	26.6462	+	7.82403i	1.05493	+	0.309756i
$639$	−3.47368	+	4.00884i	−0.137417	+	0.158587i
$640$	−17.0576	+	5.00856i	−0.674261	+	0.197981i
$641$	−9.81433	+	21.4904i	−0.387643	+	0.848820i	0.610732	+	0.791837i	$0.290875\pi$
$641$	−9.81433	+	21.4904i	−0.387643	+	0.848820i	−0.998375	+	0.0569824i	$0.981852\pi$
$642$	1.90831	+	13.2726i	0.0753151	+	0.523828i
$643$	33.1886			1.30883			0.654415	−	0.756135i	$-0.272915\pi$
$643$	33.1886			1.30883			0.654415	+	0.756135i	$0.272915\pi$
$644$	−38.7768	+	44.3317i	−1.52802	+	1.74691i
$645$	1.84162			0.0725135
$646$	6.70865	+	46.6597i	0.263948	+	1.83580i
$647$	14.3339	−	31.3869i	0.563524	−	1.23394i	−0.386651	−	0.922226i	$-0.626368\pi$
$647$	14.3339	−	31.3869i	0.563524	−	1.23394i	0.950175	−	0.311718i	$-0.100905\pi$
$648$	−5.16405	+	1.51630i	−0.202863	+	0.0595659i
$649$	5.99941	−	6.92369i	0.235497	−	0.271778i
$650$	16.0542	+	4.71395i	0.629699	+	0.184896i
$651$	23.2035	−	14.9120i	0.909418	−	0.584447i
$652$	−34.9121	−	76.4468i	−1.36726	−	2.99389i
$653$	18.6084	+	21.4753i	0.728204	+	0.840392i	0.992268	−	0.124113i	$-0.0396086\pi$
$653$	18.6084	+	21.4753i	0.728204	+	0.840392i	−0.264064	+	0.964505i	$0.585063\pi$
$654$	−10.9799	−	7.05636i	−0.429348	−	0.275925i
$655$	0.686784	−	4.77668i	0.0268349	−	0.186641i
$656$	5.83983	−	40.6169i	0.228007	−	1.58582i
$657$	−7.22575	−	4.64371i	−0.281904	−	0.181168i
$658$	27.9157	+	32.2164i	1.08827	+	1.25593i
$659$	−11.2160	−	24.5596i	−0.436912	−	0.956705i	−0.992155	−	0.125016i	$-0.960102\pi$
$659$	−11.2160	−	24.5596i	−0.436912	−	0.956705i	0.555242	−	0.831689i	$-0.312625\pi$
$660$	−11.0473	+	7.09966i	−0.430015	+	0.276354i
$661$	17.7280	+	5.20540i	0.689538	+	0.202467i	0.607685	−	0.794178i	$-0.292098\pi$
$661$	17.7280	+	5.20540i	0.689538	+	0.202467i	0.0818526	+	0.996644i	$0.473916\pi$
$662$	51.7588	−	59.7328i	2.01166	−	2.32158i
$663$	21.6303	−	6.35123i	0.840051	−	0.246661i
$664$	−19.7545	+	43.2563i	−0.766623	+	1.67867i
$665$	2.37936	+	16.5488i	0.0922678	+	0.641736i
$666$	−12.6810			−0.491377
$667$	−16.3069	−	4.87081i	−0.631407	−	0.188598i
$668$	45.6822			1.76750
$669$	2.59999	+	18.0833i	0.100521	+	0.699142i
$670$	14.0468	−	30.7582i	0.542676	−	1.18829i
$671$	20.8359	−	6.11798i	0.804362	−	0.236182i
$672$	3.33983	−	3.85437i	0.128837	−	0.148686i
$673$	−24.4402	−	7.17630i	−0.942102	−	0.276626i	−0.225607	−	0.974218i	$-0.572436\pi$
$673$	−24.4402	−	7.17630i	−0.942102	−	0.276626i	−0.716495	+	0.697592i	$0.754255\pi$
$674$	−7.09526	+	4.55985i	−0.273299	+	0.175639i
$675$	−0.415415	−	0.909632i	−0.0159893	−	0.0350118i
$676$	−88.4038	−	102.023i	−3.40015	−	3.92398i
$677$	−36.1809	−	23.2520i	−1.39054	−	0.893649i	−0.390903	−	0.920432i	$-0.627837\pi$
$677$	−36.1809	−	23.2520i	−1.39054	−	0.893649i	−0.999641	+	0.0267834i	$0.991474\pi$
$678$	−0.649638	+	4.51833i	−0.0249492	+	0.173525i
$679$	4.44066	−	30.8854i	0.170417	−	1.18527i
$680$	15.1493	+	9.73587i	0.580950	+	0.373354i
$681$	17.5478	+	20.2513i	0.672434	+	0.776030i
$682$	30.4263	+	66.6242i	1.16508	+	2.55117i
$683$	−22.3921	+	14.3906i	−0.856812	+	0.550639i	−0.893692	−	0.448680i	$-0.851894\pi$
$683$	−22.3921	+	14.3906i	−0.856812	+	0.550639i	0.0368806	+	0.999320i	$0.488258\pi$
$684$	−22.6836	−	6.66050i	−0.867328	−	0.254670i
$685$	12.3285	−	14.2279i	0.471050	−	0.543620i
$686$	37.3223	−	10.9588i	1.42497	−	0.418409i
$687$	3.51761	−	7.70250i	0.134205	−	0.293869i
$688$	−1.31865	−	9.17141i	−0.0502731	−	0.349657i
$689$	−35.7619			−1.36242
$690$	10.0492	−	6.39223i	0.382565	−	0.243348i
$691$	−24.0301			−0.914149			−0.457075	−	0.889428i	$-0.651103\pi$
$691$	−24.0301			−0.914149			−0.457075	+	0.889428i	$0.651103\pi$
$692$	9.57308	+	66.5822i	0.363914	+	2.53108i
$693$	−3.85791	+	8.44765i	−0.146550	+	0.320900i
$694$	−50.2367	+	14.7508i	−1.90696	+	0.559934i
$695$	−7.51211	+	8.66943i	−0.284950	+	0.328850i
$696$	18.3255	+	5.38086i	0.694627	+	0.203961i
$697$	22.9569	−	14.7535i	0.869556	−	0.558830i
$698$	17.6971	+	38.7512i	0.669845	+	1.46676i
$699$	−5.97093	−	6.89082i	−0.225841	−	0.260635i
$700$	10.3315	+	6.63962i	0.390492	+	0.250954i
$701$	−2.67286	+	18.5902i	−0.100953	+	0.702140i	0.874995	+	0.484133i	$0.160865\pi$
$701$	−2.67286	+	18.5902i	−0.100953	+	0.702140i	−0.975947	+	0.218008i	$0.930044\pi$
$702$	−2.38121	+	16.5617i	−0.0898730	+	0.625081i
$703$	−24.3701	−	15.6617i	−0.919135	−	0.590692i
$704$	−11.8967	−	13.7295i	−0.448373	−	0.517450i
$705$	−2.41963	−	5.29825i	−0.0911286	−	0.199544i
$706$	59.4370	−	38.1979i	2.23694	−	1.43760i
$707$	34.4655	+	10.1200i	1.29621	+	0.380602i
$708$	7.93365	−	9.15592i	0.298165	−	0.344100i
$709$	−10.3806	+	3.04801i	−0.389850	+	0.114470i	−0.470783	−	0.882249i	$-0.656028\pi$
$709$	−10.3806	+	3.04801i	−0.389850	+	0.114470i	0.0809325	+	0.996720i	$0.474210\pi$
$710$	−5.47227	+	11.9826i	−0.205371	+	0.449699i
$711$	−0.687224	−	4.77975i	−0.0257729	−	0.179255i
$712$	60.6760			2.27393
$713$	−18.4555	−	40.9155i	−0.691164	−	1.53230i
$714$	24.4878			0.916434
$715$	3.02159	+	21.0156i	0.113001	+	0.785940i
$716$	6.68128	−	14.6300i	0.249691	−	0.546748i
$717$	−12.9327	+	3.79739i	−0.482982	+	0.141816i
$718$	36.1399	−	41.7077i	1.34873	−	1.55652i
$719$	13.7771	+	4.04532i	0.513799	+	0.150865i	0.528346	−	0.849029i	$-0.322812\pi$
$719$	13.7771	+	4.04532i	0.513799	+	0.150865i	−0.0145469	+	0.999894i	$0.504631\pi$
$720$	−4.23260	+	2.72013i	−0.157740	+	0.101373i
$721$	−7.63673	−	16.7221i	−0.284407	−	0.622764i
$722$	−21.4415	−	24.7448i	−0.797969	−	0.920905i
$723$	−7.00610	−	4.50255i	−0.260560	−	0.167452i
$724$	0.0143392	−	0.0997314i	0.000532913	−	0.00370649i
$725$	−0.505029	+	3.51255i	−0.0187563	+	0.130453i
$726$	2.23467	+	1.43614i	0.0829364	+	0.0533000i
$727$	17.7954	+	20.5370i	0.659994	+	0.761674i	0.982776	−	0.184799i	$-0.0591636\pi$
$727$	17.7954	+	20.5370i	0.659994	+	0.761674i	−0.322782	+	0.946473i	$0.604618\pi$
$728$	−44.3937	−	97.2087i	−1.64534	−	3.60279i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	−20.4665	−	6.00950i	−0.757498	−	0.222421i
$731$	4.03520	−	4.65687i	0.149247	−	0.172241i
$732$	27.5535	−	8.09044i	1.01841	−	0.299031i
$733$	−12.3293	+	26.9974i	−0.455392	+	0.997170i	0.533121	+	0.846039i	$0.321019\pi$
$733$	−12.3293	+	26.9974i	−0.455392	+	0.997170i	−0.988514	+	0.151131i	$0.951708\pi$
$734$	12.8409	+	89.3104i	0.473966	+	3.29651i
$735$	1.68512			0.0621565
$736$	−5.40572	−	6.29760i	−0.199258	−	0.232133i
$737$	42.9075			1.58052
$738$	2.88247	+	20.0480i	0.106105	+	0.737977i
$739$	−12.7439	+	27.9052i	−0.468791	+	1.02651i	0.516604	+	0.856224i	$0.327196\pi$
$739$	−12.7439	+	27.9052i	−0.468791	+	1.02651i	−0.985395	+	0.170284i	$0.945531\pi$
$740$	−20.4172	+	5.99503i	−0.750551	+	0.220382i
$741$	−25.0308	+	28.8871i	−0.919529	+	1.06119i
$742$	−37.2728	−	10.9443i	−1.36833	−	0.401777i
$743$	30.6012	−	19.6662i	1.12265	−	0.721482i	0.158635	−	0.987337i	$-0.449291\pi$
$743$	30.6012	−	19.6662i	1.12265	−	0.721482i	0.964013	+	0.265855i	$0.0856543\pi$
$744$	20.9252	+	45.8198i	0.767155	+	1.67984i
$745$	5.96674	+	6.88599i	0.218605	+	0.252283i
$746$	−39.0364	−	25.0872i	−1.42922	−	0.918507i
$747$	1.25744	−	8.74565i	0.0460071	−	0.319987i
$748$	−6.25312	+	43.4914i	−0.228637	+	1.59020i
$749$	13.3866	+	8.60303i	0.489135	+	0.314348i
$750$	−1.62627	−	1.87682i	−0.0593831	−	0.0685318i
$751$	−12.7489	−	27.9161i	−0.465213	−	1.01867i	−0.986268	−	0.165151i	$-0.947189\pi$
$751$	−12.7489	−	27.9161i	−0.465213	−	1.01867i	0.521055	−	0.853523i	$-0.325538\pi$
$752$	−24.6533	+	15.8437i	−0.899012	+	0.577760i
$753$	7.03461	+	2.06555i	0.256356	+	0.0752728i
$754$	38.8833	−	44.8737i	1.41605	−	1.63420i
$755$	−14.2556	+	4.18582i	−0.518814	+	0.152338i
$756$	−5.10172	+	11.1712i	−0.185548	+	0.406293i
$757$	−2.27500	−	15.8230i	−0.0826862	−	0.575095i	−0.988477	−	0.151370i	$-0.951631\pi$
$757$	−2.27500	−	15.8230i	−0.0826862	−	0.575095i	0.905791	−	0.423725i	$-0.139278\pi$
$758$	−4.60880			−0.167399
$759$	12.6755	+	8.22978i	0.460092	+	0.298722i
$760$	−30.5331			−1.10755
$761$	5.14198	+	35.7633i	0.186397	+	1.29642i	0.841244	+	0.540656i	$0.181824\pi$
$761$	5.14198	+	35.7633i	0.186397	+	1.29642i	−0.654847	+	0.755761i	$0.727267\pi$
$762$	−11.8805	+	26.0147i	−0.430386	+	0.942414i
$763$	−14.8613	+	4.36367i	−0.538015	+	0.157975i
$764$	54.4531	−	62.8422i	1.97004	−	2.27355i
$765$	−3.21040	−	0.942659i	−0.116072	−	0.0340819i
$766$	4.98093	−	3.20105i	0.179968	−	0.115659i
$767$	−8.13696	−	17.8175i	−0.293809	−	0.643351i
$768$	−21.3610	−	24.6519i	−0.770798	−	0.889548i
$769$	−43.8217	−	28.1625i	−1.58025	−	1.01557i	−0.975730	−	0.218977i	$-0.929728\pi$
$769$	−43.8217	−	28.1625i	−1.58025	−	1.01557i	−0.604521	−	0.796589i	$-0.706635\pi$
$770$	−3.28220	+	22.8282i	−0.118282	+	0.822672i
$771$	−2.43009	+	16.9017i	−0.0875177	+	0.608699i
$772$	9.28494	+	5.96707i	0.334172	+	0.214759i
$773$	13.1916	+	15.2239i	0.474468	+	0.547566i	0.941649	−	0.336596i	$-0.109276\pi$
$773$	13.1916	+	15.2239i	0.474468	+	0.547566i	−0.467181	+	0.884162i	$0.654730\pi$
$774$	1.89988	+	4.16016i	0.0682898	+	0.149534i
$775$	−7.87347	+	5.05997i	−0.282823	+	0.181760i
$776$	54.6763	+	16.0544i	1.96277	+	0.576320i
$777$	−9.85472	+	11.3729i	−0.353536	+	0.408002i
$778$	−91.8242	+	26.9620i	−3.29206	+	0.966635i
$779$	−19.2209	+	42.0880i	−0.688662	+	1.50796i
$780$	3.99577	+	27.7912i	0.143071	+	0.995083i
$781$	−16.7156			−0.598133
$782$	5.85498	−	39.4173i	0.209374	−	1.40956i
$783$	−3.54867			−0.126819
$784$	−1.20659	−	8.39204i	−0.0430926	−	0.299716i
$785$	5.28342	−	11.5691i	0.188573	−	0.412918i
$786$	11.4989	−	3.37638i	0.410152	−	0.120432i
$787$	−18.4807	+	21.3278i	−0.658765	+	0.760256i	−0.982575	−	0.185867i	$-0.940491\pi$
$787$	−18.4807	+	21.3278i	−0.658765	+	0.760256i	0.323810	+	0.946122i	$0.395036\pi$
$788$	−30.6899	−	9.01135i	−1.09328	−	0.321016i
$789$	20.2609	−	13.0209i	0.721307	−	0.463556i
$790$	−4.98167	−	10.9083i	−0.177240	−	0.388102i
$791$	3.54742	+	4.09395i	0.126132	+	0.145564i
$792$	−14.2678	−	9.16937i	−0.506985	−	0.325819i
$793$	6.60757	−	45.9567i	0.234642	−	1.63197i
$794$	2.44900	−	17.0332i	0.0869117	−	0.604484i
$795$	4.46523	+	2.86963i	0.158365	+	0.101775i
$796$	1.17743	+	1.35882i	0.0417328	+	0.0481622i
$797$	5.69838	+	12.4777i	0.201847	+	0.441983i	0.983303	−	0.181977i	$-0.0582498\pi$
$797$	5.69838	+	12.4777i	0.201847	+	0.441983i	−0.781456	+	0.623961i	$0.785523\pi$
$798$	−34.9287	+	22.4473i	−1.23646	+	0.794626i
$799$	−18.6993	−	5.49062i	−0.661535	−	0.194244i
$800$	−1.13328	+	1.30787i	−0.0400675	+	0.0462403i
$801$	−10.8171	+	3.17618i	−0.382203	+	0.112225i
$802$	10.3269	−	22.6128i	0.364656	−	0.798485i
$803$	−3.85202	−	26.7914i	−0.135935	−	0.945448i
$804$	56.7410			2.00110
$805$	2.07659	−	13.9802i	0.0731902	−	0.492737i
$806$	156.598			5.51594
$807$	2.04719	+	14.2385i	0.0720647	+	0.501221i
$808$	−27.2512	+	59.6719i	−0.958695	+	2.09925i
$809$	−13.7846	+	4.04754i	−0.484642	+	0.142304i	−0.514921	−	0.857238i	$-0.672179\pi$
$809$	−13.7846	+	4.04754i	−0.484642	+	0.142304i	0.0302787	+	0.999541i	$0.490361\pi$
$810$	1.62627	−	1.87682i	0.0571415	−	0.0659448i
$811$	−31.9111	−	9.36996i	−1.12055	−	0.329024i	−0.331564	−	0.943433i	$-0.607576\pi$
$811$	−31.9111	−	9.36996i	−1.12055	−	0.329024i	−0.788988	+	0.614409i	$0.789395\pi$
$812$	36.6630	−	23.5619i	1.28662	−	0.826859i
$813$	−8.10318	−	17.7435i	−0.284191	−	0.622291i
$814$	−26.1688	−	30.2004i	−0.917215	−	1.05852i
$815$	16.9658	+	10.9032i	0.594285	+	0.381924i
$816$	−2.39579	+	16.6631i	−0.0838693	+	0.583324i
$817$	−1.48687	+	10.3414i	−0.0520189	+	0.361799i
$818$	−35.1007	−	22.5578i	−1.22727	−	0.788717i
$819$	13.0029	+	15.0061i	0.454358	+	0.524357i
$820$	14.1188	+	30.9159i	0.493051	+	1.07963i
$821$	37.6642	−	24.2053i	1.31449	−	0.844771i	0.319779	−	0.947492i	$-0.396391\pi$
$821$	37.6642	−	24.2053i	1.31449	−	0.844771i	0.994710	+	0.102722i	$0.0327550\pi$
$822$	44.8590	+	13.1718i	1.56464	+	0.459419i
$823$	−20.7781	+	23.9792i	−0.724278	+	0.835861i	−0.991815	−	0.127686i	$-0.959245\pi$
$823$	−20.7781	+	23.9792i	−0.724278	+	0.835861i	0.267537	+	0.963548i	$0.413790\pi$
$824$	32.2127	−	9.45851i	1.12218	−	0.329503i
$825$	1.30907	−	2.86647i	0.0455761	−	0.0997978i
$826$	−3.02803	−	21.0604i	−0.105359	−	0.732785i
$827$	−18.4921			−0.643032			−0.321516	−	0.946904i	$-0.604192\pi$
$827$	−18.4921			−0.643032			−0.321516	+	0.946904i	$0.604192\pi$
$828$	16.7622	+	10.8831i	0.582526	+	0.378214i
$829$	47.3101			1.64315			0.821574	−	0.570101i	$-0.193096\pi$
$829$	47.3101			1.64315			0.821574	+	0.570101i	$0.193096\pi$
$830$	−3.12270	−	21.7189i	−0.108391	−	0.753873i
$831$	3.84182	−	8.41241i	0.133271	−	0.291823i
$832$	−37.2683	+	10.9430i	−1.29205	+	0.379379i
$833$	3.69230	−	4.26114i	0.127931	−	0.147640i
$834$	−27.3338	−	8.02592i	−0.946491	−	0.277915i
$835$	−9.22203	+	5.92664i	−0.319142	+	0.205100i
$836$	−30.9481	−	67.7669i	−1.07036	−	2.34377i
$837$	−6.12898	−	7.07322i	−0.211849	−	0.244486i
$838$	9.85988	+	6.33656i	0.340604	+	0.218893i
$839$	3.80394	−	26.4570i	0.131327	−	0.913396i	−0.812502	−	0.582959i	$-0.801895\pi$
$839$	3.80394	−	26.4570i	0.131327	−	0.913396i	0.943828	−	0.330437i	$-0.107196\pi$
$840$	−2.25729	+	15.6998i	−0.0778838	+	0.541693i
$841$	−13.8024	−	8.87025i	−0.475944	−	0.305871i
$842$	−3.68099	−	4.24809i	−0.126855	−	0.146399i
$843$	0.944007	+	2.06709i	0.0325133	+	0.0711942i
$844$	66.5405	−	42.7630i	2.29042	−	1.47196i
$845$	31.0826	+	9.12667i	1.06927	+	0.313967i
$846$	9.47242	−	10.9318i	0.325668	−	0.375841i
$847$	3.02462	−	0.888110i	0.103927	−	0.0305158i
$848$	11.0938	−	24.2920i	0.380962	−	0.834190i
$849$	0.575166	+	4.00037i	0.0197397	+	0.137292i
$850$	−8.30926			−0.285005
$851$	15.9505	+	18.5821i	0.546775	+	0.636986i
$852$	−22.1049			−0.757300
$853$	−4.75589	−	33.0779i	−0.162838	−	1.13257i	−0.893250	−	0.449560i	$-0.851581\pi$
$853$	−4.75589	−	33.0779i	−0.162838	−	1.13257i	0.730412	−	0.683007i	$-0.239328\pi$
$854$	20.9509	−	45.8762i	0.716926	−	1.56985i
$855$	5.44333	−	1.59831i	0.186158	−	0.0546609i
$856$	−19.0306	+	21.9625i	−0.650452	+	0.750662i
$857$	−32.6022	−	9.57288i	−1.11367	−	0.327003i	−0.327400	−	0.944886i	$-0.606173\pi$
$857$	−32.6022	−	9.57288i	−1.11367	−	0.327003i	−0.786271	+	0.617882i	$0.787991\pi$
$858$	−44.3565	+	28.5062i	−1.51431	+	0.973185i
$859$	13.5601	+	29.6926i	0.462666	+	1.01310i	0.986872	+	0.161505i	$0.0516349\pi$
$859$	13.5601	+	29.6926i	0.462666	+	1.01310i	−0.524206	+	0.851591i	$0.675638\pi$
$860$	5.02568	+	5.79994i	0.171374	+	0.197776i
$861$	20.2201	+	12.9947i	0.689101	+	0.442858i
$862$	2.90153	−	20.1806i	0.0988266	−	0.687354i
$863$	3.15279	−	21.9282i	0.107322	−	0.746443i	−0.863101	−	0.505032i	$-0.831481\pi$
$863$	3.15279	−	21.9282i	0.107322	−	0.746443i	0.970423	−	0.241411i	$-0.0776102\pi$
$864$	−1.45584	−	0.935614i	−0.0495288	−	0.0318302i
$865$	−10.5707	−	12.1992i	−0.359414	−	0.414786i
$866$	−37.4563	−	82.0178i	−1.27282	−	2.78708i
$867$	4.88324	−	3.13827i	0.165843	−	0.106581i
$868$	110.285	+	32.3825i	3.74331	+	1.09913i
$869$	9.96505	−	11.5003i	0.338041	−	0.390120i
$870$	−8.45576	+	2.48284i	−0.286677	+	0.0841760i
$871$	38.1097	−	83.4487i	1.29130	−	2.82755i
$872$	−4.02555	−	27.9983i	−0.136322	−	0.948144i
$873$	−10.5879			−0.358346
$874$	27.7814	+	61.5908i	0.939721	+	2.08334i
$875$	−2.94705			−0.0996286
$876$	−5.09393	−	35.4291i	−0.172108	−	1.19704i
$877$	6.45989	−	14.1452i	0.218135	−	0.477649i	−0.768653	−	0.639666i	$-0.779073\pi$
$877$	6.45989	−	14.1452i	0.218135	−	0.477649i	0.986788	+	0.162017i	$0.0518000\pi$
$878$	−82.5075	+	24.2264i	−2.78449	+	0.817601i
$879$	7.65982	−	8.83990i	0.258359	−	0.298162i
$880$	−15.2126	−	4.46683i	−0.512818	−	0.150577i
$881$	−4.05126	+	2.60358i	−0.136490	+	0.0877170i	−0.607104	−	0.794622i	$-0.707669\pi$
$881$	−4.05126	+	2.60358i	−0.136490	+	0.0877170i	0.470614	+	0.882339i	$0.344033\pi$
$882$	1.73843	+	3.80663i	0.0585360	+	0.128176i
$883$	−2.52572	−	2.91484i	−0.0849974	−	0.0980922i	0.711658	−	0.702526i	$-0.247945\pi$
$883$	−2.52572	−	2.91484i	−0.0849974	−	0.0980922i	−0.796655	+	0.604434i	$0.793399\pi$
$884$	79.0304	+	50.7898i	2.65808	+	1.70824i
$885$	−0.413740	+	2.87762i	−0.0139077	+	0.0967303i
$886$	1.18858	−	8.26672i	0.0399310	−	0.277726i
$887$	19.9952	+	12.8501i	0.671372	+	0.431465i	0.831420	−	0.555644i	$-0.187528\pi$
$887$	19.9952	+	12.8501i	0.671372	+	0.431465i	−0.160048	+	0.987109i	$0.551165\pi$
$888$	−17.9972	−	20.7699i	−0.603946	−	0.696991i
$889$	14.0987	+	30.8718i	0.472855	+	1.03541i
$890$	−23.5527	+	15.1364i	−0.789487	+	0.507373i
$891$	3.02360	+	0.887809i	0.101294	+	0.0297427i
$892$	−49.8560	+	57.5369i	−1.66930	+	1.92648i
$893$	31.7053	−	9.30951i	1.06098	−	0.311531i
$894$	−9.39973	+	20.5825i	−0.314374	+	0.688383i
$895$	0.549264	+	3.82022i	0.0183599	+	0.127696i
$896$	−52.3919			−1.75029
$897$	27.2639	−	17.3424i	0.910315	−	0.579047i
$898$	35.0190			1.16860
$899$	4.72667	+	32.8747i	0.157643	+	1.09643i
$900$	1.73113	−	3.79064i	0.0577042	−	0.126355i
$901$	17.0403	−	5.00347i	0.567694	−	0.166690i
$902$	−41.7970	+	48.2364i	−1.39169	+	1.60610i
$903$	5.20749	+	1.52906i	0.173295	+	0.0508839i
$904$	−8.32246	+	5.34852i	−0.276801	+	0.177889i
$905$	0.0100441	+	0.0219935i	0.000333877	+	0.000731088i
$906$	−24.1622	−	27.8847i	−0.802737	−	0.926408i
$907$	9.00887	+	5.78965i	0.299135	+	0.192242i	0.681595	−	0.731730i	$-0.261287\pi$
$907$	9.00887	+	5.78965i	0.299135	+	0.192242i	−0.382460	+	0.923972i	$0.624923\pi$
$908$	−15.8917	+	110.529i	−0.527385	+	3.66805i
$909$	1.73463	−	12.0646i	0.0575339	−	0.400157i
$910$	41.4823	+	26.6590i	1.37512	+	0.883739i
$911$	−17.4845	−	20.1782i	−0.579289	−	0.668535i	0.388163	−	0.921591i	$-0.373110\pi$
$911$	−17.4845	−	20.1782i	−0.579289	−	0.668535i	−0.967452	+	0.253056i	$0.918564\pi$
$912$	−11.8573	−	25.9638i	−0.392634	−	0.859749i
$913$	23.4231	−	15.0531i	0.775192	−	0.498185i
$914$	−20.1664	−	5.92139i	−0.667045	−	0.195862i
$915$	−4.51271	+	5.20795i	−0.149186	+	0.172169i
$916$	33.8575	−	9.94145i	1.11868	−	0.328475i
$917$	5.90799	−	12.9367i	0.195099	−	0.427207i
$918$	−1.18253	−	8.22468i	−0.0390293	−	0.271455i
$919$	18.6204			0.614231			0.307115	−	0.951672i	$-0.400636\pi$
$919$	18.6204			0.614231			0.307115	+	0.951672i	$0.400636\pi$
$920$	24.7317	+	7.38726i	0.815381	+	0.243551i
$921$	14.9745			0.493425
$922$	−8.17972	−	56.8912i	−0.269385	−	1.87361i
$923$	−14.8466	+	32.5094i	−0.488681	+	1.07006i
$924$	−37.1329	+	10.9032i	−1.22158	+	0.358689i
$925$	3.34392	−	3.85909i	0.109948	−	0.126886i
$926$	−16.2089	−	4.75935i	−0.532656	−	0.156402i
$927$	−5.24764	+	3.37245i	−0.172355	+	0.110766i
$928$	2.55115	+	5.58624i	0.0837456	+	0.183377i
$929$	8.55052	+	9.86783i	0.280533	+	0.323753i	0.878476	−	0.477786i	$-0.158561\pi$
$929$	8.55052	+	9.86783i	0.280533	+	0.323753i	−0.597943	+	0.801539i	$0.704015\pi$
$930$	−19.5529	−	12.5659i	−0.641164	−	0.412051i
$931$	−1.36052	+	9.46259i	−0.0445891	+	0.310124i
$932$	5.40742	−	37.6094i	0.177126	−	1.23194i
$933$	14.9410	+	9.60200i	0.489146	+	0.314355i
$934$	13.0021	+	15.0052i	0.425442	+	0.490986i
$935$	−4.38008	−	9.59104i	−0.143244	−	0.313660i
$936$	−30.5055	+	19.6047i	−0.997104	+	0.640800i
$937$	−38.4382	−	11.2865i	−1.25572	−	0.368713i	−0.414821	−	0.909903i	$-0.636156\pi$
$937$	−38.4382	−	11.2865i	−1.25572	−	0.368713i	−0.840900	+	0.541190i	$0.817974\pi$
$938$	65.2578	−	75.3115i	2.13074	−	2.45901i
$939$	24.0105	−	7.05012i	0.783553	−	0.230072i
$940$	10.0831	−	22.0790i	0.328876	−	0.720138i
$941$	1.87338	+	13.0296i	0.0610704	+	0.424754i	0.997304	+	0.0733765i	$0.0233775\pi$
$941$	1.87338	+	13.0296i	0.0610704	+	0.424754i	−0.936234	+	0.351377i	$0.885713\pi$
$942$	31.5848			1.02909
$943$	25.7518	−	29.4408i	0.838593	−	0.958724i
$944$	14.6271			0.476071
$945$	−0.419409	−	2.91706i	−0.0136434	−	0.0948918i
$946$	−5.98699	+	13.1097i	−0.194654	+	0.426232i
$947$	−3.92796	+	1.15335i	−0.127642	+	0.0374789i	−0.344929	−	0.938629i	$-0.612097\pi$
$947$	−3.92796	+	1.15335i	−0.127642	+	0.0374789i	0.217288	+	0.976108i	$0.430279\pi$
$948$	13.1778	−	15.2080i	0.427996	−	0.493934i
$949$	−55.5266	−	16.3041i	−1.80247	−	0.529253i
$950$	11.8521	−	7.61687i	0.384532	−	0.247124i
$951$	−8.09205	−	17.7191i	−0.262403	−	0.574582i
$952$	34.7538	+	40.1081i	1.12638	+	1.29991i
$953$	35.8403	+	23.0332i	1.16098	+	0.746117i	0.971796	−	0.235824i	$-0.0757789\pi$
$953$	35.8403	+	23.0332i	1.16098	+	0.746117i	0.189185	+	0.981941i	$0.439415\pi$
$954$	−1.87591	+	13.0472i	−0.0607348	+	0.422420i
$955$	−2.83973	+	19.7508i	−0.0918915	+	0.639119i
$956$	−47.2522	−	30.3672i	−1.52825	−	0.982144i
$957$	−7.32314	−	8.45135i	−0.236723	−	0.273193i
$958$	−2.10398	−	4.60707i	−0.0679765	−	0.148848i
$959$	46.6743	−	29.9957i	1.50719	−	0.968613i
$960$	5.53142	+	1.62417i	0.178526	+	0.0524199i
$961$	−37.0617	+	42.7715i	−1.19554	+	1.37973i
$962$	−81.9779	+	24.0709i	−2.64307	+	0.776077i
$963$	2.24304	−	4.91157i	0.0722809	−	0.158273i
$964$	−4.93909	−	34.3521i	−0.159077	−	1.10641i
$965$	−2.64853			−0.0852593
$966$	33.7231	−	9.73152i	1.08502	−	0.313107i
$967$	0.716943			0.0230553			0.0115277	−	0.999934i	$-0.496331\pi$
$967$	0.716943			0.0230553			0.0115277	+	0.999934i	$0.496331\pi$
$968$	0.819295	+	5.69832i	0.0263331	+	0.183151i
$969$	7.88538	−	17.2666i	0.253315	−	0.554682i
$970$	−25.2288	+	7.40783i	−0.810046	+	0.237851i
$971$	13.4879	−	15.5659i	0.432848	−	0.499533i	−0.496860	−	0.867831i	$-0.665514\pi$
$971$	13.4879	−	15.5659i	0.432848	−	0.499533i	0.929708	+	0.368297i	$0.120059\pi$
$972$	3.99842	+	1.17404i	0.128249	+	0.0376574i
$973$	−28.4399	+	18.2772i	−0.911740	+	0.585940i
$974$	−6.34163	−	13.8862i	−0.203199	−	0.444944i
$975$	−4.41217	−	5.09191i	−0.141302	−	0.163072i
$976$	29.1673	+	18.7447i	0.933622	+	0.600002i
$977$	−3.87595	+	26.9578i	−0.124003	+	0.862457i	0.828947	+	0.559328i	$0.188941\pi$
$977$	−3.87595	+	26.9578i	−0.124003	+	0.862457i	−0.952949	+	0.303130i	$0.901968\pi$
$978$	−7.12758	+	49.5734i	−0.227915	+	1.58518i
$979$	−29.8867	−	19.2070i	−0.955182	−	0.613858i
$980$	4.59861	+	5.30707i	0.146897	+	0.169528i
$981$	2.18328	+	4.78071i	0.0697067	+	0.152636i
$982$	−52.2651	+	33.5888i	−1.66785	+	1.07186i
$983$	−27.6915	−	8.13096i	−0.883222	−	0.259337i	−0.191492	−	0.981494i	$-0.561333\pi$
$983$	−27.6915	−	8.13096i	−0.883222	−	0.259337i	−0.691729	+	0.722157i	$0.743151\pi$
$984$	−28.7453	+	33.1739i	−0.916367	+	1.05754i
$985$	7.36458	−	2.16244i	0.234655	−	0.0689010i
$986$	−12.2493	+	26.8222i	−0.390097	+	0.854193i
$987$	−2.44290	−	16.9907i	−0.0777582	−	0.540820i
$988$	−159.284			−5.06750
$989$	3.70638	−	8.01676i	0.117856	−	0.254918i
$990$	7.82577			0.248719
$991$	1.56932	+	10.9149i	0.0498512	+	0.346723i	0.999447	+	0.0332464i	$0.0105846\pi$
$991$	1.56932	+	10.9149i	0.0498512	+	0.346723i	−0.949596	+	0.313477i	$0.898506\pi$
$992$	−6.72836	+	14.7331i	−0.213626	+	0.467775i
$993$	−30.5374	+	8.96659i	−0.969075	+	0.284546i
$994$	−25.4227	+	29.3394i	−0.806361	+	0.930590i
$995$	−0.413981	−	0.121556i	−0.0131241	−	0.00385358i
$996$	30.9748	−	19.9063i	0.981475	−	0.630756i
$997$	−5.22174	−	11.4340i	−0.165374	−	0.362119i	0.808743	−	0.588162i	$-0.200148\pi$
$997$	−5.22174	−	11.4340i	−0.165374	−	0.362119i	−0.974117	+	0.226043i	$0.927421\pi$
$998$	−4.30727	−	4.97085i	−0.136344	−	0.157349i
$999$	4.29570	+	2.76068i	0.135910	+	0.0873441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.m.a.256.1	yes	30
23.8	even	11	inner	345.2.m.a.31.1	✓	30
23.10	odd	22		7935.2.a.bq.1.15		15
23.13	even	11		7935.2.a.bp.1.15		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.a.31.1	✓	30	23.8	even	11	inner
345.2.m.a.256.1	yes	30	1.1	even	1	trivial
7935.2.a.bp.1.15		15	23.13	even	11
7935.2.a.bq.1.15		15	23.10	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.353423 - 2.45811i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-3.99842 + 1.17404i) q^{4} +(0.654861 - 0.755750i) q^{5} +(2.38279 + 0.699652i) q^{6} +(2.47922 - 1.59330i) q^{7} +(2.23579 + 4.89569i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.353423 - 2.45811i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-3.99842 + 1.17404i) q^{4} +(0.654861 - 0.755750i) q^{5} +(2.38279 + 0.699652i) q^{6} +(2.47922 - 1.59330i) q^{7} +(2.23579 + 4.89569i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-2.08916 - 1.34262i) q^{10} +(0.448469 - 3.11917i) q^{11} +(0.593058 - 4.12481i) q^{12} +(-5.66800 - 3.64260i) q^{13} +(-4.79272 - 5.53109i) q^{14} +(0.415415 + 0.909632i) q^{15} +(4.23260 - 2.72013i) q^{16} +(3.21040 + 0.942659i) q^{17} +(-1.62627 + 1.87682i) q^{18} +(-5.44333 + 1.59831i) q^{19} +(-1.73113 + 3.79064i) q^{20} +(0.419409 + 2.91706i) q^{21} -7.82577 q^{22} +(4.79578 + 0.0223496i) q^{23} -5.38206 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-6.95072 + 15.2200i) q^{26} +(0.959493 - 0.281733i) q^{27} +(-8.04236 + 9.28138i) q^{28} +(-3.40493 - 0.999777i) q^{29} +(2.08916 - 1.34262i) q^{30} +(-3.88796 - 8.51344i) q^{31} +(-1.13328 - 1.30787i) q^{32} +(2.65100 + 1.70369i) q^{33} +(1.18253 - 8.22468i) q^{34} +(0.419409 - 2.91706i) q^{35} +(3.50569 + 2.25297i) q^{36} +(3.34392 + 3.85909i) q^{37} +(5.85261 + 12.8154i) q^{38} +(5.66800 - 3.64260i) q^{39} +(5.16405 + 1.51630i) q^{40} +(5.34095 - 6.16379i) q^{41} +(7.02222 - 2.06191i) q^{42} +(0.765035 - 1.67519i) q^{43} +(1.86887 + 12.9983i) q^{44} -1.00000 q^{45} +(-1.64000 - 11.7965i) q^{46} -5.82461 q^{47} +(0.716029 + 4.98009i) q^{48} +(0.700024 - 1.53284i) q^{49} +(-2.38279 + 0.699652i) q^{50} +(-2.19112 + 2.52869i) q^{51} +(26.9396 + 7.91019i) q^{52} +(4.46523 - 2.86963i) q^{53} +(-1.03164 - 2.25897i) q^{54} +(-2.06363 - 2.38155i) q^{55} +(13.3433 + 8.57522i) q^{56} +(0.807371 - 5.61539i) q^{57} +(-1.25418 + 8.72304i) q^{58} +(2.44571 + 1.57176i) q^{59} +(-2.72895 - 3.14938i) q^{60} +(2.86267 + 6.26837i) q^{61} +(-19.5529 + 12.5659i) q^{62} +(-2.82768 - 0.830281i) q^{63} +(3.77523 - 4.35685i) q^{64} +(-6.46465 + 1.89819i) q^{65} +(3.25094 - 7.11857i) q^{66} +(1.93776 + 13.4774i) q^{67} -13.9433 q^{68} +(-2.01257 + 4.35311i) q^{69} -7.31868 q^{70} +(-0.754903 - 5.25046i) q^{71} +(2.23579 - 4.89569i) q^{72} +(8.24134 - 2.41988i) q^{73} +(8.30426 - 9.58363i) q^{74} +(0.959493 + 0.281733i) q^{75} +(19.8882 - 12.7814i) q^{76} +(-3.85791 - 8.44765i) q^{77} +(-10.9571 - 12.6452i) q^{78} +(4.06233 + 2.61070i) q^{79} +(0.716029 - 4.98009i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-17.0389 - 10.9502i) q^{82} +(5.78608 + 6.67749i) q^{83} +(-5.10172 - 11.1712i) q^{84} +(2.81478 - 1.80895i) q^{85} +(-4.38819 - 1.28849i) q^{86} +(2.32389 - 2.68191i) q^{87} +(16.2732 - 4.77824i) q^{88} +(4.68328 - 10.2550i) q^{89} +(0.353423 + 2.45811i) q^{90} -19.8560 q^{91} +(-19.2018 + 5.54109i) q^{92} +9.35921 q^{93} +(2.05855 + 14.3175i) q^{94} +(-2.35670 + 5.16046i) q^{95} +(1.66046 - 0.487556i) q^{96} +(6.93359 - 8.00179i) q^{97} +(-4.01529 - 1.17900i) q^{98} +(-2.65100 + 1.70369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9} - 7 q^{11} - 2 q^{12} + 7 q^{13} - 47 q^{14} - 3 q^{15} + 26 q^{16} + 15 q^{17} - 7 q^{19} - 2 q^{20} - 12 q^{21} - 18 q^{22} + 12 q^{23} - 3 q^{25} - 18 q^{26} + 3 q^{27} + 2 q^{28} - 6 q^{29} + 22 q^{31} + 33 q^{32} - 4 q^{33} - 53 q^{34} - 12 q^{35} - 9 q^{36} - 23 q^{37} + 21 q^{38} - 7 q^{39} + 11 q^{40} + 26 q^{41} + 3 q^{42} - 19 q^{43} - 47 q^{44} - 30 q^{45} - 44 q^{46} + 14 q^{47} + 7 q^{48} + 2 q^{49} - 11 q^{50} - 15 q^{51} + 55 q^{52} - 14 q^{53} - 11 q^{54} - 4 q^{55} + 6 q^{56} - 26 q^{57} - 18 q^{58} + 40 q^{59} - 9 q^{60} + 37 q^{61} + 19 q^{62} - 10 q^{63} + 14 q^{64} + 4 q^{65} - 4 q^{66} - 108 q^{67} + 54 q^{68} + 21 q^{69} - 30 q^{70} + 39 q^{71} + 22 q^{72} + 57 q^{73} - 11 q^{74} + 3 q^{75} + 22 q^{76} + 2 q^{77} + 7 q^{78} + 55 q^{79} + 7 q^{80} - 3 q^{81} - 26 q^{82} - 79 q^{83} - 2 q^{84} + 18 q^{85} - 44 q^{86} - 5 q^{87} - 8 q^{88} - 30 q^{89} + 40 q^{91} + 35 q^{92} + 44 q^{93} - 29 q^{94} + 7 q^{95} + 22 q^{96} - 52 q^{97} + 28 q^{98} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9 - 7 * q^11 - 2 * q^12 + 7 * q^13 - 47 * q^14 - 3 * q^15 + 26 * q^16 + 15 * q^17 - 7 * q^19 - 2 * q^20 - 12 * q^21 - 18 * q^22 + 12 * q^23 - 3 * q^25 - 18 * q^26 + 3 * q^27 + 2 * q^28 - 6 * q^29 + 22 * q^31 + 33 * q^32 - 4 * q^33 - 53 * q^34 - 12 * q^35 - 9 * q^36 - 23 * q^37 + 21 * q^38 - 7 * q^39 + 11 * q^40 + 26 * q^41 + 3 * q^42 - 19 * q^43 - 47 * q^44 - 30 * q^45 - 44 * q^46 + 14 * q^47 + 7 * q^48 + 2 * q^49 - 11 * q^50 - 15 * q^51 + 55 * q^52 - 14 * q^53 - 11 * q^54 - 4 * q^55 + 6 * q^56 - 26 * q^57 - 18 * q^58 + 40 * q^59 - 9 * q^60 + 37 * q^61 + 19 * q^62 - 10 * q^63 + 14 * q^64 + 4 * q^65 - 4 * q^66 - 108 * q^67 + 54 * q^68 + 21 * q^69 - 30 * q^70 + 39 * q^71 + 22 * q^72 + 57 * q^73 - 11 * q^74 + 3 * q^75 + 22 * q^76 + 2 * q^77 + 7 * q^78 + 55 * q^79 + 7 * q^80 - 3 * q^81 - 26 * q^82 - 79 * q^83 - 2 * q^84 + 18 * q^85 - 44 * q^86 - 5 * q^87 - 8 * q^88 - 30 * q^89 + 40 * q^91 + 35 * q^92 + 44 * q^93 - 29 * q^94 + 7 * q^95 + 22 * q^96 - 52 * q^97 + 28 * q^98 + 4 * q^99

Introduction

L-functions

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