LMFDB - Embedded newform 76.2.k.a.3.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, 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:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.7
Character	$\chi$	$=$	76.3
Dual form			76.2.k.a.51.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.947064 + 1.05027i) q^{2} +(-2.80443 + 1.02073i) q^{3} +(-0.206140 + 1.98935i) q^{4} +(-0.165124 + 0.936467i) q^{5} +(-3.72802 - 1.97872i) q^{6} +(2.67390 - 1.54378i) q^{7} +(-2.28458 + 1.66754i) q^{8} +(4.52481 - 3.79677i) q^{9} +O(q^{10})$	\(q+(0.947064 + 1.05027i) q^{2} +(-2.80443 + 1.02073i) q^{3} +(-0.206140 + 1.98935i) q^{4} +(-0.165124 + 0.936467i) q^{5} +(-3.72802 - 1.97872i) q^{6} +(2.67390 - 1.54378i) q^{7} +(-2.28458 + 1.66754i) q^{8} +(4.52481 - 3.79677i) q^{9} +(-1.13993 + 0.713469i) q^{10} +(3.39303 + 1.95897i) q^{11} +(-1.45248 - 5.78940i) q^{12} +(-0.284588 + 0.781900i) q^{13} +(4.15373 + 1.34626i) q^{14} +(-0.492800 - 2.79481i) q^{15} +(-3.91501 - 0.820168i) q^{16} +(-3.14351 - 2.63772i) q^{17} +(8.27293 + 1.15650i) q^{18} +(0.473541 - 4.33310i) q^{19} +(-1.82892 - 0.521533i) q^{20} +(-5.92298 + 7.05874i) q^{21} +(1.15597 + 5.41887i) q^{22} +(-2.45271 + 0.432479i) q^{23} +(4.70485 - 7.00844i) q^{24} +(3.84876 + 1.40083i) q^{25} +(-1.09073 + 0.441614i) q^{26} +(-4.33744 + 7.51266i) q^{27} +(2.51991 + 5.63755i) q^{28} +(1.95130 + 2.32547i) q^{29} +(2.46859 - 3.16443i) q^{30} +(-0.560318 - 0.970499i) q^{31} +(-2.84637 - 4.88858i) q^{32} +(-11.5151 - 2.03042i) q^{33} +(-0.206785 - 5.79963i) q^{34} +(1.00417 + 2.75893i) q^{35} +(6.62035 + 9.78410i) q^{36} -11.0692i q^{37} +(4.99940 - 3.60638i) q^{38} -2.48327i q^{39} +(-1.18435 - 2.41479i) q^{40} +(1.74742 + 4.80099i) q^{41} +(-13.0230 + 0.464335i) q^{42} +(-2.92630 - 0.515985i) q^{43} +(-4.59650 + 6.34610i) q^{44} +(2.80839 + 4.86428i) q^{45} +(-2.77709 - 2.16642i) q^{46} +(2.23924 + 2.66862i) q^{47} +(11.8166 - 1.69607i) q^{48} +(1.26648 - 2.19361i) q^{49} +(2.17376 + 5.36892i) q^{50} +(11.5082 + 4.18863i) q^{51} +(-1.49681 - 0.727326i) q^{52} +(-4.27071 + 0.753042i) q^{53} +(-11.9982 + 2.55948i) q^{54} +(-2.39478 + 2.85399i) q^{55} +(-3.53444 + 7.98571i) q^{56} +(3.09491 + 12.6352i) q^{57} +(-0.594368 + 4.25176i) q^{58} +(0.677042 + 0.568105i) q^{59} +(5.66143 - 0.404230i) q^{60} +(-1.74615 - 9.90290i) q^{61} +(0.488630 - 1.50761i) q^{62} +(6.23753 - 17.1375i) q^{63} +(2.43864 - 7.61925i) q^{64} +(-0.685231 - 0.395618i) q^{65} +(-8.77304 - 14.0169i) q^{66} +(-6.32640 + 5.30848i) q^{67} +(5.89535 - 5.70980i) q^{68} +(6.43701 - 3.71641i) q^{69} +(-1.94662 + 3.66754i) q^{70} +(1.66114 - 9.42079i) q^{71} +(-4.00606 + 16.2193i) q^{72} +(2.43877 - 0.887641i) q^{73} +(11.6257 - 10.4832i) q^{74} -12.2235 q^{75} +(8.52243 + 1.83526i) q^{76} +12.0968 q^{77} +(2.60811 - 2.35182i) q^{78} +(3.07726 - 1.12003i) q^{79} +(1.41452 - 3.53085i) q^{80} +(1.41857 - 8.04512i) q^{81} +(-3.38743 + 6.38210i) q^{82} +(-10.7084 + 6.18250i) q^{83} +(-12.8213 - 13.2380i) q^{84} +(2.98921 - 2.50824i) q^{85} +(-2.22947 - 3.56208i) q^{86} +(-7.84597 - 4.52987i) q^{87} +(-11.0183 + 1.18258i) q^{88} +(-0.254375 + 0.698890i) q^{89} +(-2.44909 + 7.55636i) q^{90} +(0.446118 + 2.53006i) q^{91} +(-0.354750 - 4.96844i) q^{92} +(2.56199 + 2.14976i) q^{93} +(-0.682075 + 4.87917i) q^{94} +(3.97961 + 1.15896i) q^{95} +(12.9724 + 10.8043i) q^{96} +(-6.10468 + 7.27528i) q^{97} +(3.50333 - 0.747341i) q^{98} +(22.7906 - 4.01859i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	0.947064	+	1.05027i	0.669675	+	0.742654i
$2$	0.947064	+	1.05027i	0.669675	+	0.742654i
$3$	−2.80443	+	1.02073i	−1.61914	+	0.589319i	−0.983218	−	0.182435i	$-0.941602\pi$
$3$	−2.80443	+	1.02073i	−1.61914	+	0.589319i	−0.635921	+	0.771754i	$0.719380\pi$
$4$	−0.206140	+	1.98935i	−0.103070	+	0.994674i
$5$	−0.165124	+	0.936467i	−0.0738459	+	0.418801i	0.925365	+	0.379078i	$0.123759\pi$
$5$	−0.165124	+	0.936467i	−0.0738459	+	0.418801i	−0.999211	+	0.0397232i	$0.987352\pi$
$6$	−3.72802	−	1.97872i	−1.52196	−	0.807808i
$7$	2.67390	−	1.54378i	1.01064	−	0.583492i	0.0992597	−	0.995062i	$-0.468353\pi$
$7$	2.67390	−	1.54378i	1.01064	−	0.583492i	0.911378	+	0.411569i	$0.135019\pi$
$8$	−2.28458	+	1.66754i	−0.807722	+	0.589563i
$9$	4.52481	−	3.79677i	1.50827	−	1.26559i
$10$	−1.13993	+	0.713469i	−0.360477	+	0.225619i
$11$	3.39303	+	1.95897i	1.02304	+	0.590651i	0.914982	−	0.403494i	$-0.132205\pi$
$11$	3.39303	+	1.95897i	1.02304	+	0.590651i	0.108055	+	0.994145i	$0.465538\pi$
$12$	−1.45248	−	5.78940i	−0.419295	−	1.67126i
$13$	−0.284588	+	0.781900i	−0.0789306	+	0.216860i	−0.972881	−	0.231306i	$-0.925700\pi$
$13$	−0.284588	+	0.781900i	−0.0789306	+	0.216860i	0.893951	+	0.448166i	$0.147922\pi$
$14$	4.15373	+	1.34626i	1.11013	+	0.359804i
$15$	−0.492800	−	2.79481i	−0.127240	−	0.721616i
$16$	−3.91501	−	0.820168i	−0.978753	−	0.205042i
$17$	−3.14351	−	2.63772i	−0.762414	−	0.639741i	0.176340	−	0.984329i	$-0.443574\pi$
$17$	−3.14351	−	2.63772i	−0.762414	−	0.639741i	−0.938754	+	0.344588i	$0.888019\pi$
$18$	8.27293	+	1.15650i	1.94995	+	0.272589i
$19$	0.473541	−	4.33310i	0.108638	−	0.994081i
$19$	0.473541	−	4.33310i	0.108638	−	0.994081i
$20$	−1.82892	−	0.521533i	−0.408959	−	0.116618i
$21$	−5.92298	+	7.05874i	−1.29250	+	1.54034i
$22$	1.15597	+	5.41887i	0.246454	+	1.15531i
$23$	−2.45271	+	0.432479i	−0.511425	+	0.0901780i	−0.423405	−	0.905941i	$-0.639165\pi$
$23$	−2.45271	+	0.432479i	−0.511425	+	0.0901780i	−0.0880203	+	0.996119i	$0.528054\pi$
$24$	4.70485	−	7.00844i	0.960374	−	1.43059i
$25$	3.84876	+	1.40083i	0.769752	+	0.280167i
$26$	−1.09073	+	0.441614i	−0.213910	+	0.0866076i
$27$	−4.33744	+	7.51266i	−0.834740	+	1.44581i
$28$	2.51991	+	5.63755i	0.476218	+	1.06540i
$29$	1.95130	+	2.32547i	0.362347	+	0.431829i	0.916160	−	0.400812i	$-0.131272\pi$
$29$	1.95130	+	2.32547i	0.362347	+	0.431829i	−0.553813	+	0.832641i	$0.686828\pi$
$30$	2.46859	−	3.16443i	0.450701	−	0.577744i
$31$	−0.560318	−	0.970499i	−0.100636	−	0.174307i	0.811311	−	0.584615i	$-0.198754\pi$
$31$	−0.560318	−	0.970499i	−0.100636	−	0.174307i	−0.911947	+	0.410308i	$0.865421\pi$
$32$	−2.84637	−	4.88858i	−0.503172	−	0.864186i
$33$	−11.5151	−	2.03042i	−2.00452	−	0.353451i
$34$	−0.206785	−	5.79963i	−0.0354634	−	0.994628i
$35$	1.00417	+	2.75893i	0.169736	+	0.466345i
$36$	6.62035	+	9.78410i	1.10339	+	1.63068i
$37$		−	11.0692i		−	1.81976i	−0.414866	−	0.909882i	$-0.636172\pi$
$37$		−	11.0692i		−	1.81976i	0.414866	−	0.909882i	$-0.363828\pi$
$38$	4.99940	−	3.60638i	0.811011	−	0.585032i
$39$		−	2.48327i		−	0.397642i
$40$	−1.18435	−	2.41479i	−0.187263	−	0.381812i
$41$	1.74742	+	4.80099i	0.272901	+	0.749788i	0.998121	+	0.0612717i	$0.0195156\pi$
$41$	1.74742	+	4.80099i	0.272901	+	0.749788i	−0.725220	+	0.688517i	$0.758262\pi$
$42$	−13.0230	+	0.464335i	−2.00950	+	0.0716485i
$43$	−2.92630	−	0.515985i	−0.446256	−	0.0786870i	−0.0539956	−	0.998541i	$-0.517196\pi$
$43$	−2.92630	−	0.515985i	−0.446256	−	0.0786870i	−0.392260	+	0.919854i	$0.628307\pi$
$44$	−4.59650	+	6.34610i	−0.692949	+	0.956710i
$45$	2.80839	+	4.86428i	0.418651	+	0.725124i
$46$	−2.77709	−	2.16642i	−0.409460	−	0.319422i
$47$	2.23924	+	2.66862i	0.326627	+	0.389259i	0.904221	−	0.427066i	$-0.140453\pi$
$47$	2.23924	+	2.66862i	0.326627	+	0.389259i	−0.577594	+	0.816324i	$0.696008\pi$
$48$	11.8166	−	1.69607i	1.70557	−	0.244806i
$49$	1.26648	−	2.19361i	0.180926	−	0.313373i
$50$	2.17376	+	5.36892i	0.307417	+	0.759280i
$51$	11.5082	+	4.18863i	1.61147	+	0.586525i
$52$	−1.49681	−	0.727326i	−0.207570	−	0.100862i
$53$	−4.27071	+	0.753042i	−0.586627	+	0.103438i	−0.459081	−	0.888394i	$-0.651821\pi$
$53$	−4.27071	+	0.753042i	−0.586627	+	0.103438i	−0.127546	+	0.991833i	$0.540710\pi$
$54$	−11.9982	+	2.55948i	−1.63274	+	0.348302i
$55$	−2.39478	+	2.85399i	−0.322912	+	0.384832i
$56$	−3.53444	+	7.98571i	−0.472309	+	1.06713i
$57$	3.09491	+	12.6352i	0.409931	+	1.67358i
$58$	−0.594368	+	4.25176i	−0.0780443	+	0.558284i
$59$	0.677042	+	0.568105i	0.0881433	+	0.0739610i	0.685795	−	0.727795i	$-0.259455\pi$
$59$	0.677042	+	0.568105i	0.0881433	+	0.0739610i	−0.597651	+	0.801756i	$0.703899\pi$
$60$	5.66143	−	0.404230i	0.730887	−	0.0521858i
$61$	−1.74615	−	9.90290i	−0.223571	−	1.26794i	−0.865398	−	0.501086i	$-0.832934\pi$
$61$	−1.74615	−	9.90290i	−0.223571	−	1.26794i	0.641826	−	0.766850i	$-0.278177\pi$
$62$	0.488630	−	1.50761i	0.0620561	−	0.191467i
$63$	6.23753	−	17.1375i	0.785855	−	2.15912i
$64$	2.43864	−	7.61925i	0.304830	−	0.952407i
$65$	−0.685231	−	0.395618i	−0.0849924	−	0.0490704i
$66$	−8.77304	−	14.0169i	−1.07989	−	1.72536i
$67$	−6.32640	+	5.30848i	−0.772893	+	0.648535i	−0.941448	−	0.337158i	$-0.890534\pi$
$67$	−6.32640	+	5.30848i	−0.772893	+	0.648535i	0.168555	+	0.985692i	$0.446090\pi$
$68$	5.89535	−	5.70980i	0.714916	−	0.692415i
$69$	6.43701	−	3.71641i	0.774925	−	0.447403i
$70$	−1.94662	+	3.66754i	−0.232665	+	0.438354i
$71$	1.66114	−	9.42079i	0.197141	−	1.11804i	−0.712195	−	0.701981i	$-0.752299\pi$
$71$	1.66114	−	9.42079i	0.197141	−	1.11804i	0.909337	−	0.416061i	$-0.136590\pi$
$72$	−4.00606	+	16.2193i	−0.472119	+	1.91147i
$73$	2.43877	−	0.887641i	0.285437	−	0.103891i	−0.195334	−	0.980737i	$-0.562579\pi$
$73$	2.43877	−	0.887641i	0.285437	−	0.103891i	0.480771	+	0.876846i	$0.340357\pi$
$74$	11.6257	−	10.4832i	1.35146	−	1.21865i
$75$	−12.2235			−1.41144
$76$	8.52243	+	1.83526i	0.977590	+	0.210519i
$77$	12.0968			1.37856
$78$	2.60811	−	2.35182i	0.295310	−	0.266291i
$79$	3.07726	−	1.12003i	0.346219	−	0.126013i	−0.163057	−	0.986617i	$-0.552135\pi$
$79$	3.07726	−	1.12003i	0.346219	−	0.126013i	0.509276	+	0.860603i	$0.329913\pi$
$80$	1.41452	−	3.53085i	0.158149	−	0.394761i
$81$	1.41857	−	8.04512i	0.157619	−	0.893903i
$82$	−3.38743	+	6.38210i	−0.374079	+	0.704786i
$83$	−10.7084	+	6.18250i	−1.17540	+	0.678618i	−0.954946	−	0.296779i	$-0.904087\pi$
$83$	−10.7084	+	6.18250i	−1.17540	+	0.678618i	−0.220455	+	0.975397i	$0.570754\pi$
$84$	−12.8213	−	13.2380i	−1.39892	−	1.44438i
$85$	2.98921	−	2.50824i	0.324225	−	0.272057i
$86$	−2.22947	−	3.56208i	−0.240409	−	0.384109i
$87$	−7.84597	−	4.52987i	−0.841176	−	0.485653i
$88$	−11.0183	+	1.18258i	−1.17456	+	0.126064i
$89$	−0.254375	+	0.698890i	−0.0269637	+	0.0740822i	−0.952444	−	0.304713i	$-0.901439\pi$
$89$	−0.254375	+	0.698890i	−0.0269637	+	0.0740822i	0.925480	+	0.378795i	$0.123662\pi$
$90$	−2.44909	+	7.55636i	−0.258156	+	0.796510i
$91$	0.446118	+	2.53006i	0.0467658	+	0.265222i
$92$	−0.354750	−	4.96844i	−0.0369852	−	0.517996i
$93$	2.56199	+	2.14976i	0.265666	+	0.222920i
$94$	−0.682075	+	4.87917i	−0.0703506	+	0.503248i
$95$	3.97961	+	1.15896i	0.408300	+	0.118906i
$96$	12.9724	+	10.8043i	1.32399	+	1.10271i
$97$	−6.10468	+	7.27528i	−0.619837	+	0.738693i	−0.981042	−	0.193794i	$-0.937921\pi$
$97$	−6.10468	+	7.27528i	−0.619837	+	0.738693i	0.361206	+	0.932486i	$0.382365\pi$
$98$	3.50333	−	0.747341i	0.353890	−	0.0754929i
$99$	22.7906	−	4.01859i	2.29054	−	0.403884i
$100$	−3.58013	+	7.36775i	−0.358013	+	0.736775i
$101$	−9.25142	−	3.36724i	−0.920550	−	0.335053i	−0.162093	−	0.986776i	$-0.551824\pi$
$101$	−9.25142	−	3.36724i	−0.920550	−	0.335053i	−0.758457	+	0.651723i	$0.774047\pi$
$102$	6.49977	+	16.0536i	0.643573	+	1.58954i
$103$	0.981169	−	1.69943i	0.0966774	−	0.167450i	−0.813630	−	0.581383i	$-0.802512\pi$
$103$	0.981169	−	1.69943i	0.0966774	−	0.167450i	0.910307	+	0.413933i	$0.135845\pi$
$104$	−0.653681	−	2.26088i	−0.0640987	−	0.221697i
$105$	−5.63225	−	6.71225i	−0.549651	−	0.655049i
$106$	−4.83554	−	3.77223i	−0.469669	−	0.366391i
$107$	1.49933	+	2.59691i	0.144945	+	0.251053i	0.929353	−	0.369193i	$-0.120366\pi$
$107$	1.49933	+	2.59691i	0.144945	+	0.251053i	−0.784407	+	0.620246i	$0.787033\pi$
$108$	−14.0512	−	10.1773i	−1.35208	−	0.979314i
$109$	9.12021	+	1.60814i	0.873558	+	0.154032i	0.592414	−	0.805634i	$-0.298175\pi$
$109$	9.12021	+	1.60814i	0.873558	+	0.154032i	0.281144	+	0.959666i	$0.409286\pi$
$110$	−5.26547	+	0.187740i	−0.502043	+	0.0179003i
$111$	11.2987	+	31.0428i	1.07242	+	2.94645i
$112$	−11.7345	+	3.85086i	−1.10881	+	0.363872i
$113$			10.5830i			0.995568i	0.867301	+	0.497784i	$0.165853\pi$
$113$			10.5830i			0.995568i	−0.867301	+	0.497784i	$0.834147\pi$
$114$	−10.3394	+	15.2169i	−0.968369	+	1.42519i
$115$		−	2.36829i		−	0.220845i
$116$	−5.02841	+	3.40245i	−0.466876	+	0.315909i
$117$	1.68098	+	4.61847i	0.155407	+	0.426977i
$118$	0.0445369	+	1.24911i	0.00409996	+	0.114990i
$119$	−12.4775	−	2.20012i	−1.14381	−	0.201684i
$120$	5.78629	+	5.56321i	0.528213	+	0.507849i
$121$	2.17510	+	3.76738i	0.197736	+	0.342489i
$122$	8.74701	−	11.2126i	0.791917	−	1.01514i
$123$	−9.80102	−	11.6804i	−0.883728	−	1.05319i
$124$	2.04616	−	0.914609i	0.183751	−	0.0821343i
$125$	−4.32464	+	7.49050i	−0.386808	+	0.669971i
$126$	23.9063	−	9.67918i	2.12975	−	0.862290i
$127$	1.50832	+	0.548984i	0.133842	+	0.0487144i	0.408073	−	0.912949i	$-0.366201\pi$
$127$	1.50832	+	0.548984i	0.133842	+	0.0487144i	−0.274231	+	0.961664i	$0.588423\pi$
$128$	10.3118	−	4.65469i	0.911446	−	0.411420i
$129$	8.73328	−	1.53991i	0.768922	−	0.135582i
$130$	−0.233451	−	1.09435i	−0.0204750	−	0.0959812i
$131$	6.30386	−	7.51265i	0.550771	−	0.656383i	−0.416795	−	0.909000i	$-0.636847\pi$
$131$	6.30386	−	7.51265i	0.550771	−	0.656383i	0.967566	+	0.252617i	$0.0812913\pi$
$132$	6.41293	−	22.4890i	0.558174	−	1.95741i
$133$	−5.42313	−	12.3173i	−0.470245	−	1.06805i
$134$	−11.5669	−	1.61697i	−0.999224	−	0.139685i
$135$	−6.31914	−	5.30239i	−0.543865	−	0.456357i
$136$	11.5801	+	0.784166i	0.992986	+	0.0672417i
$137$	−0.959987	−	5.44436i	−0.0820172	−	0.465143i	−0.997960	−	0.0638350i	$-0.979667\pi$
$137$	−0.959987	−	5.44436i	−0.0820172	−	0.465143i	0.915943	−	0.401308i	$-0.131444\pi$
$138$	9.99950	+	3.24093i	0.851214	+	0.275886i
$139$	−3.12444	+	8.58433i	−0.265012	+	0.728113i	0.733800	+	0.679366i	$0.237745\pi$
$139$	−3.12444	+	8.58433i	−0.265012	+	0.728113i	−0.998811	+	0.0487473i	$0.984477\pi$
$140$	−5.69548	+	1.42892i	−0.481356	+	0.120766i
$141$	−9.00374	−	5.19831i	−0.758252	−	0.437777i
$142$	11.4676	−	7.17745i	0.962339	−	0.602318i
$143$	−2.49733	+	2.09551i	−0.208837	+	0.175235i
$144$	−20.8287	+	11.1533i	−1.73572	+	0.929441i
$145$	−2.49993	+	1.44334i	−0.207608	+	0.119863i
$146$	3.24194	+	1.72072i	0.268305	+	0.142408i
$147$	−1.31268	+	7.44458i	−0.108268	+	0.614018i
$148$	22.0205	+	2.28180i	1.81007	+	0.187563i
$149$	−17.4242	+	6.34187i	−1.42744	+	0.519547i	−0.936197	−	0.351475i	$-0.885680\pi$
$149$	−17.4242	+	6.34187i	−1.42744	+	0.519547i	−0.491245	+	0.871021i	$0.663458\pi$
$150$	−11.5764	−	12.8379i	−0.945208	−	1.04821i
$151$	−19.1746			−1.56040			−0.780202	−	0.625527i	$-0.784884\pi$
$151$	−19.1746			−1.56040			−0.780202	+	0.625527i	$0.784884\pi$
$152$	6.14376	+	10.6890i	0.498325	+	0.866990i
$153$	−24.2386			−1.95958
$154$	11.4565	+	12.7049i	0.923188	+	1.02379i
$155$	1.00136	−	0.364466i	0.0804314	−	0.0292746i
$156$	4.94009	+	0.511901i	0.395524	+	0.0409849i
$157$	−1.38284	+	7.84250i	−0.110363	+	0.625899i	0.878579	+	0.477597i	$0.158492\pi$
$157$	−1.38284	+	7.84250i	−0.110363	+	0.625899i	−0.988942	+	0.148303i	$0.952619\pi$
$158$	4.09070	+	2.17122i	0.325439	+	0.172733i
$159$	11.2083	−	6.47110i	0.888874	−	0.513191i
$160$	5.04800	−	1.85831i	0.399079	−	0.146912i
$161$	−5.89064	+	4.94283i	−0.464247	+	0.389550i
$162$	9.79304	−	6.12936i	0.769414	−	0.481568i
$163$	14.7556	+	8.51913i	1.15574	+	0.667269i	0.950281	−	0.311395i	$-0.100796\pi$
$163$	14.7556	+	8.51913i	1.15574	+	0.667269i	0.205464	+	0.978665i	$0.434130\pi$
$164$	−9.91105	+	2.48655i	−0.773923	+	0.194167i
$165$	3.80285	−	10.4482i	0.296051	−	0.813394i
$166$	−16.6349	−	5.39151i	−1.29112	−	0.418462i
$167$	−2.11555	−	11.9979i	−0.163706	−	0.928422i	−0.950389	−	0.311065i	$-0.899314\pi$
$167$	−2.11555	−	11.9979i	−0.163706	−	0.928422i	0.786683	−	0.617357i	$-0.211797\pi$
$168$	1.76084	−	26.0031i	0.135852	−	2.00618i
$169$	9.42820	+	7.91120i	0.725246	+	0.608554i
$170$	5.46531	+	0.764013i	0.419170	+	0.0585971i
$171$	−14.3091	−	21.4044i	−1.09424	−	1.63684i
$172$	1.62970	−	5.71506i	0.124263	−	0.435769i
$173$	14.0933	−	16.7958i	1.07150	−	1.27696i	0.112465	−	0.993656i	$-0.464125\pi$
$173$	14.0933	−	16.7958i	1.07150	−	1.27696i	0.959030	−	0.283303i	$-0.0914303\pi$
$174$	−2.67304	−	12.5305i	−0.202642	−	0.949932i
$175$	12.4538	−	2.19593i	0.941415	−	0.165997i
$176$	−11.6771	−	10.4522i	−0.880192	−	0.787867i
$177$	−2.47860	−	0.902136i	−0.186303	−	0.0678087i
$178$	−0.974933	+	0.394730i	−0.0730743	+	0.0295863i
$179$	−0.183973	+	0.318651i	−0.0137508	+	0.0238171i	−0.872819	−	0.488044i	$-0.837710\pi$
$179$	−0.183973	+	0.318651i	−0.0137508	+	0.0238171i	0.859068	+	0.511861i	$0.171044\pi$
$180$	−10.2557	+	4.58415i	−0.764413	+	0.341683i
$181$	12.1366	+	14.4639i	0.902109	+	1.07509i	0.996828	+	0.0795875i	$0.0253603\pi$
$181$	12.1366	+	14.4639i	0.902109	+	1.07509i	−0.0947190	+	0.995504i	$0.530195\pi$
$182$	−2.23475	+	2.86467i	−0.165650	+	0.212344i
$183$	15.0051	+	25.9896i	1.10921	+	1.92121i
$184$	4.88224	−	5.07802i	0.359924	−	0.374356i
$185$	10.3659	+	1.82780i	0.762119	+	0.134382i
$186$	0.168532	+	4.72675i	0.0123574	+	0.346582i
$187$	−5.49882	−	15.1079i	−0.402114	−	1.10480i
$188$	−5.77042	+	3.90452i	−0.420851	+	0.284767i
$189$			26.7841i			1.94826i
$190$	2.55173	+	5.27728i	0.185122	+	0.382854i
$191$		−	14.9125i		−	1.07903i	−0.841975	−	0.539516i	$-0.818607\pi$
$191$		−	14.9125i		−	1.07903i	0.841975	−	0.539516i	$-0.181393\pi$
$192$	0.938203	+	23.8569i	0.0677090	+	1.72172i
$193$	−2.55696	−	7.02519i	−0.184054	−	0.505684i	0.813011	−	0.582249i	$-0.197827\pi$
$193$	−2.55696	−	7.02519i	−0.184054	−	0.505684i	−0.997065	+	0.0765647i	$0.975605\pi$
$194$	−13.4225	+	0.478580i	−0.963682	+	0.0343600i
$195$	2.32550	+	0.410049i	0.166533	+	0.0293642i
$196$	4.10279	+	2.97167i	0.293056	+	0.212262i
$197$	−10.7161	−	18.5607i	−0.763487	−	1.32240i	−0.941043	−	0.338288i	$-0.890152\pi$
$197$	−10.7161	−	18.5607i	−0.763487	−	1.32240i	0.177556	−	0.984111i	$-0.443181\pi$
$198$	25.8047	+	20.1304i	1.83386	+	1.43061i
$199$	16.4631	+	19.6199i	1.16704	+	1.39082i	0.904812	+	0.425812i	$0.140012\pi$
$199$	16.4631	+	19.6199i	1.16704	+	1.39082i	0.262224	+	0.965007i	$0.415544\pi$
$200$	−11.1287	+	3.21763i	−0.786921	+	0.227521i
$201$	12.3234	−	21.3448i	0.869229	−	1.50555i
$202$	−5.22517	−	12.9055i	−0.367641	−	0.908027i
$203$	8.80758	+	3.20570i	0.618171	+	0.224996i
$204$	−10.7049	+	22.0303i	−0.749495	+	1.54243i
$205$	−4.78451	+	0.843638i	−0.334165	+	0.0589223i
$206$	2.71410	−	0.578979i	0.189100	−	0.0403394i
$207$	−9.45603	+	11.2693i	−0.657239	+	0.783267i
$208$	1.75546	−	2.82774i	0.121719	−	0.196068i
$209$	10.0951	−	13.7747i	0.698295	−	0.952815i
$210$	1.71559	−	12.2723i	0.118387	−	0.846871i
$211$	−2.40668	−	2.01944i	−0.165682	−	0.139024i	0.556177	−	0.831064i	$-0.312268\pi$
$211$	−2.40668	−	2.01944i	−0.165682	−	0.139024i	−0.721859	+	0.692040i	$0.756712\pi$
$212$	−0.617699	−	8.65117i	−0.0424237	−	0.594165i
$213$	4.95753	+	28.1155i	0.339684	+	1.92645i
$214$	−1.30750	+	4.03414i	−0.0893790	+	0.275768i
$215$	0.966406	−	2.65518i	0.0659084	−	0.181082i
$216$	−2.61841	−	24.3961i	−0.178160	−	1.65995i
$217$	−2.99646	−	1.73001i	−0.203413	−	0.117441i
$218$	6.94844	+	11.1017i	0.470608	+	0.751902i
$219$	−5.93333	+	4.97866i	−0.400938	+	0.336427i
$220$	−5.18392	−	5.35237i	−0.349500	−	0.360857i
$221$	2.95704	−	1.70725i	0.198912	−	0.114842i
$222$	−21.9028	+	41.2662i	−1.47002	+	2.76960i
$223$	0.648948	−	3.68036i	0.0434567	−	0.246455i	−0.955339	−	0.295511i	$-0.904510\pi$
$223$	0.648948	−	3.68036i	0.0434567	−	0.246455i	0.998796	+	0.0490557i	$0.0156212\pi$
$224$	−15.1578	−	8.67740i	−1.01277	−	0.579783i
$225$	22.7336	−	8.27434i	1.51557	−	0.551623i
$226$	−11.1151	+	10.0228i	−0.739363	+	0.666707i
$227$	14.1806			0.941200			0.470600	−	0.882347i	$-0.344037\pi$
$227$	14.1806			0.941200			0.470600	+	0.882347i	$0.344037\pi$
$228$	−25.7739	+	3.55223i	−1.70692	+	0.235252i
$229$	−7.84295			−0.518276			−0.259138	−	0.965840i	$-0.583439\pi$
$229$	−7.84295			−0.518276			−0.259138	+	0.965840i	$0.583439\pi$
$230$	2.48735	−	2.24293i	0.164011	−	0.147894i
$231$	−33.9247	+	12.3476i	−2.23208	+	0.812411i
$232$	−8.33572	−	2.05886i	−0.547267	−	0.135171i
$233$	0.355231	−	2.01461i	0.0232719	−	0.131982i	−0.970958	−	0.239249i	$-0.923099\pi$
$233$	0.355231	−	2.01461i	0.0232719	−	0.131982i	0.994230	+	0.107267i	$0.0342100\pi$
$234$	−3.25864	+	6.13947i	−0.213024	+	0.401350i
$235$	−2.86883	+	1.65632i	−0.187142	+	0.108047i
$236$	−1.26972	+	1.22976i	−0.0826520	+	0.0800507i
$237$	−7.48672	+	6.28210i	−0.486315	+	0.408067i
$238$	−9.50625	−	15.1884i	−0.616199	−	0.984517i
$239$	−19.1085	−	11.0323i	−1.23603	−	0.713621i	−0.267749	−	0.963489i	$-0.586280\pi$
$239$	−19.1085	−	11.0323i	−1.23603	−	0.713621i	−0.968280	+	0.249867i	$0.919613\pi$
$240$	−0.362892	+	11.3459i	−0.0234246	+	0.732373i
$241$	−3.29430	+	9.05100i	−0.212204	+	0.583026i	−0.999434	−	0.0336331i	$-0.989292\pi$
$241$	−3.29430	+	9.05100i	−0.212204	+	0.583026i	0.787230	+	0.616659i	$0.211514\pi$
$242$	−1.89682	+	5.85239i	−0.121932	+	0.376206i
$243$	−0.285520	−	1.61927i	−0.0183161	−	0.103876i
$244$	20.0603	−	1.43232i	1.28423	−	0.0916946i
$245$	1.84512	+	1.54824i	0.117880	+	0.0989134i
$246$	2.98540	−	21.3558i	0.190342	−	1.36160i
$247$	3.25329	+	1.60341i	0.207002	+	0.102023i
$248$	2.89844	+	1.28283i	0.184051	+	0.0814601i
$249$	23.7203	−	28.2688i	1.50322	−	1.79146i
$250$	−11.9628	+	2.55194i	−0.756592	+	0.161399i
$251$	−1.62834	+	0.287120i	−0.102780	+	0.0181229i	−0.224802	−	0.974405i	$-0.572173\pi$
$251$	−1.62834	+	0.287120i	−0.102780	+	0.0181229i	0.122022	+	0.992527i	$0.461062\pi$
$252$	32.8066	+	15.9413i	2.06662	+	1.00421i
$253$	−9.16932	−	3.33736i	−0.576470	−	0.209818i
$254$	0.851894	+	2.10407i	0.0534526	+	0.132021i
$255$	−5.82279	+	10.0854i	−0.364638	+	0.631571i
$256$	14.6547	+	6.42193i	0.915916	+	0.401371i
$257$	13.2973	+	15.8471i	0.829460	+	0.988512i	0.999995	+	0.00316078i	$0.00100611\pi$
$257$	13.2973	+	15.8471i	0.829460	+	0.988512i	−0.170535	+	0.985352i	$0.554549\pi$
$258$	9.88830	+	7.71392i	0.615619	+	0.480247i
$259$	−17.0884	−	29.5979i	−1.06182	−	1.83912i
$260$	0.928276	−	1.28161i	0.0575692	−	0.0794821i
$261$	17.6585	+	3.11368i	1.09304	+	0.192732i
$262$	13.8605	−	0.494194i	0.856303	−	0.0305314i
$263$	5.04518	+	13.8615i	0.311099	+	0.854738i	0.992435	+	0.122767i	$0.0391769\pi$
$263$	5.04518	+	13.8615i	0.311099	+	0.854738i	−0.681336	+	0.731970i	$0.738601\pi$
$264$	29.6930	−	14.5632i	1.82748	−	0.896302i
$265$		−	4.12373i		−	0.253319i
$266$	7.80046	−	17.3610i	0.478277	−	1.06447i
$267$		−	2.21964i		−	0.135840i
$268$	−9.25630	−	13.6797i	−0.565418	−	0.835621i
$269$	−2.61291	−	7.17890i	−0.159312	−	0.437705i	0.834196	−	0.551468i	$-0.185932\pi$
$269$	−2.61291	−	7.17890i	−0.159312	−	0.437705i	−0.993508	+	0.113762i	$0.963710\pi$
$270$	−0.415684	−	11.6585i	−0.0252977	−	0.709515i
$271$	−1.47921	−	0.260825i	−0.0898557	−	0.0158440i	0.128540	−	0.991704i	$-0.458971\pi$
$271$	−1.47921	−	0.260825i	−0.0898557	−	0.0158440i	−0.218395	+	0.975860i	$0.570082\pi$
$272$	10.1435	+	12.9049i	0.615041	+	0.782475i
$273$	−3.83361	−	6.64001i	−0.232021	−	0.401872i
$274$	4.80888	−	6.16440i	0.290515	−	0.372405i
$275$	10.3148	+	12.2927i	0.622004	+	0.741275i
$276$	6.06631	+	13.5716i	0.365149	+	0.816911i
$277$	−5.63204	+	9.75498i	−0.338397	+	0.586120i	−0.984131	−	0.177442i	$-0.943218\pi$
$277$	−5.63204	+	9.75498i	−0.338397	+	0.586120i	0.645735	+	0.763562i	$0.276551\pi$
$278$	−11.9749	+	4.84840i	−0.718208	+	0.290788i
$279$	−6.22009	−	2.26393i	−0.372387	−	0.135538i
$280$	−6.89473	−	4.62852i	−0.412039	−	0.276607i
$281$	−22.5573	+	3.97746i	−1.34566	+	0.237275i	−0.799630	−	0.600493i	$-0.794971\pi$
$281$	−22.5573	+	3.97746i	−1.34566	+	0.237275i	−0.546026	+	0.837769i	$0.683860\pi$
$282$	−3.06748	−	14.3795i	−0.182666	−	0.856287i
$283$	11.9630	−	14.2570i	0.711128	−	0.847490i	−0.282608	−	0.959235i	$-0.591200\pi$
$283$	11.9630	−	14.2570i	0.711128	−	0.847490i	0.993737	+	0.111746i	$0.0356441\pi$
$284$	18.3988	+	5.24659i	1.09177	+	0.311328i
$285$	−12.3435	+	0.811895i	−0.731168	+	0.0480925i
$286$	−4.56599	−	0.638294i	−0.269992	−	0.0377431i
$287$	12.0841	+	10.1397i	0.713299	+	0.598529i
$288$	−31.4401	−	11.3129i	−1.85263	−	0.666619i
$289$	−0.0279168	−	0.158324i	−0.00164216	−	0.00931317i
$290$	−3.88349	−	1.25868i	−0.228047	−	0.0739120i
$291$	9.69408	−	26.6343i	0.568277	−	1.56133i
$292$	1.26310	+	5.03455i	0.0739173	+	0.294625i
$293$	17.6564	+	10.1939i	1.03150	+	0.595536i	0.917414	−	0.397934i	$-0.130273\pi$
$293$	17.6564	+	10.1939i	1.03150	+	0.595536i	0.114086	+	0.993471i	$0.463606\pi$
$294$	−9.06202	+	5.67182i	−0.528508	+	0.330787i
$295$	−0.643808	+	0.540219i	−0.0374840	+	0.0314528i
$296$	18.4583	+	25.2885i	1.07287	+	1.46986i
$297$	−29.4341	+	16.9938i	−1.70794	+	0.986079i
$298$	−23.1625	−	12.2939i	−1.34177	−	0.712168i
$299$	0.359857	−	2.04085i	0.0208111	−	0.118025i
$300$	2.51974	−	24.3167i	0.145477	−	1.40393i
$301$	−8.62118	+	3.13785i	−0.496917	+	0.180863i
$302$	−18.1595	−	20.1385i	−1.04496	−	1.15884i
$303$	29.3820			1.68795
$304$	−5.40779	+	16.5758i	−0.310158	+	0.950685i
$305$	9.56207			0.547523
$306$	−22.9555	−	25.4571i	−1.31228	−	1.45529i
$307$	27.2216	−	9.90786i	1.55362	−	0.565472i	0.584357	−	0.811497i	$-0.301347\pi$
$307$	27.2216	−	9.90786i	1.55362	−	0.565472i	0.969263	+	0.246025i	$0.0791246\pi$
$308$	−2.49363	+	24.0648i	−0.142088	+	1.37122i
$309$	−1.01696	+	5.76746i	−0.0578527	+	0.328099i
$310$	1.33114	+	0.706530i	0.0756038	+	0.0401282i
$311$	8.00357	−	4.62086i	0.453841	−	0.262025i	−0.255610	−	0.966780i	$-0.582276\pi$
$311$	8.00357	−	4.62086i	0.453841	−	0.262025i	0.709451	+	0.704755i	$0.248943\pi$
$312$	4.14095	+	5.67324i	0.234435	+	0.321184i
$313$	−19.3111	+	16.2039i	−1.09153	+	0.915898i	−0.996826	−	0.0796075i	$-0.974633\pi$
$313$	−19.3111	+	16.2039i	−1.09153	+	0.915898i	−0.0946990	+	0.995506i	$0.530189\pi$
$314$	−9.54639	+	5.97499i	−0.538734	+	0.337188i
$315$	15.0187	+	8.67106i	0.846209	+	0.488559i
$316$	1.59379	+	6.35263i	0.0896575	+	0.357363i
$317$	10.3833	−	28.5279i	0.583185	−	1.60229i	−0.199518	−	0.979894i	$-0.563938\pi$
$317$	10.3833	−	28.5279i	0.583185	−	1.60229i	0.782703	−	0.622395i	$-0.213840\pi$
$318$	17.4114	+	5.64318i	0.976380	+	0.316454i
$319$	2.06530	+	11.7129i	0.115635	+	0.655798i
$320$	6.73250	+	3.54183i	0.376358	+	0.197994i
$321$	−6.85550	−	5.75245i	−0.382637	−	0.321071i
$322$	−10.7701	−	1.50559i	−0.600196	−	0.0839033i
$323$	−12.9181	+	12.3721i	−0.718782	+	0.688401i
$324$	15.7121	+	4.48045i	0.872896	+	0.248914i
$325$	−2.19062	+	2.61068i	−0.121514	+	0.144815i
$326$	5.02706	+	23.5655i	0.278423	+	1.30517i
$327$	−27.2185	+	4.79935i	−1.50519	+	0.265405i
$328$	−11.9979	−	8.05437i	−0.662476	−	0.444728i
$329$	10.1073	+	3.67874i	0.557231	+	0.202816i
$330$	14.5750	−	5.90113i	0.802329	−	0.324846i
$331$	−10.1102	+	17.5114i	−0.555707	+	0.962514i	0.442141	+	0.896946i	$0.354219\pi$
$331$	−10.1102	+	17.5114i	−0.555707	+	0.962514i	−0.997848	+	0.0655678i	$0.979114\pi$
$332$	−10.0917	−	22.5772i	−0.553855	−	1.23909i
$333$	−42.0272	−	50.0861i	−2.30308	−	2.74470i
$334$	10.5974	−	13.5846i	0.579867	−	0.743318i
$335$	−3.92658	−	6.80103i	−0.214532	−	0.371580i
$336$	28.9779	−	22.7772i	1.58087	−	1.24260i
$337$	−12.9142	−	2.27711i	−0.703479	−	0.124042i	−0.189545	−	0.981872i	$-0.560701\pi$
$337$	−12.9142	−	2.27711i	−0.703479	−	0.124042i	−0.513934	+	0.857830i	$0.671812\pi$
$338$	0.620203	+	17.3946i	0.0337346	+	0.946141i
$339$	−10.8024	−	29.6794i	−0.586707	−	1.61196i
$340$	4.37358	+	6.46363i	0.237191	+	0.350539i
$341$		−	4.39057i		−	0.237763i
$342$	8.92880	−	35.2998i	0.482814	−	1.90879i
$343$			13.7922i			0.744708i
$344$	7.54579	−	3.70090i	0.406842	−	0.199539i
$345$	2.41739	+	6.64172i	0.130148	+	0.357578i
$346$	30.9874	−	1.10485i	1.66589	−	0.0593973i
$347$	4.62735	+	0.815927i	0.248409	+	0.0438013i	0.296466	−	0.955043i	$-0.404192\pi$
$347$	4.62735	+	0.815927i	0.248409	+	0.0438013i	−0.0480569	+	0.998845i	$0.515303\pi$
$348$	10.6289	−	14.6746i	0.569766	−	0.786640i
$349$	10.8285	+	18.7555i	0.579636	+	1.00396i	0.995521	+	0.0945424i	$0.0301388\pi$
$349$	10.8285	+	18.7555i	0.579636	+	1.00396i	−0.415884	+	0.909418i	$0.636528\pi$
$350$	14.1008	+	11.0001i	0.753721	+	0.587982i
$351$	−4.63976	−	5.52945i	−0.247652	−	0.295140i
$352$	−0.0812553	−	22.1630i	−0.00433092	−	1.18129i
$353$	−12.4664	+	21.5924i	−0.663519	+	1.14925i	0.316166	+	0.948704i	$0.397604\pi$
$353$	−12.4664	+	21.5924i	−0.663519	+	1.14925i	−0.979685	+	0.200544i	$0.935729\pi$
$354$	−1.39990	−	3.45758i	−0.0744041	−	0.183768i
$355$	8.54797	+	3.11121i	0.453679	+	0.165126i
$356$	−1.33790	−	0.650110i	−0.0709085	−	0.0344557i
$357$	37.2379	−	6.56605i	1.97084	−	0.347512i
$358$	−0.508904	+	0.108561i	−0.0268964	+	0.00573763i
$359$	−15.4763	+	18.4439i	−0.816807	+	0.973433i	−0.999953	−	0.00965302i	$-0.996927\pi$
$359$	−15.4763	+	18.4439i	−0.816807	+	0.973433i	0.183146	+	0.983086i	$0.441372\pi$
$360$	−14.5274	−	6.42975i	−0.765660	−	0.338878i
$361$	−18.5515	−	4.10380i	−0.976396	−	0.215990i
$362$	−3.69683	+	26.4450i	−0.194301	+	1.38992i
$363$	−9.94539	−	8.34518i	−0.521998	−	0.438008i
$364$	−5.12513	+	0.365938i	−0.268630	+	0.0191803i
$365$	0.428546	+	2.43040i	0.0224311	+	0.127213i
$366$	−13.0854	+	40.3733i	−0.683983	+	2.11035i
$367$	−3.55314	+	9.76216i	−0.185472	+	0.509581i	−0.997227	−	0.0744174i	$-0.976290\pi$
$367$	−3.55314	+	9.76216i	−0.185472	+	0.509581i	0.811755	+	0.583998i	$0.198513\pi$
$368$	9.95709	+	0.318472i	0.519049	+	0.0166015i
$369$	26.1350	+	15.0890i	1.36053	+	0.785504i
$370$	7.89753	+	12.6181i	0.410573	+	0.655983i
$371$	−10.2569	+	8.60658i	−0.532513	+	0.446831i
$372$	−4.80476	+	4.65354i	−0.249115	+	0.241275i
$373$	7.05267	−	4.07186i	0.365173	−	0.210833i	−0.306174	−	0.951975i	$-0.599049\pi$
$373$	7.05267	−	4.07186i	0.365173	−	0.210833i	0.671348	+	0.741143i	$0.265716\pi$
$374$	10.6597	−	20.0834i	0.551197	−	1.03849i
$375$	4.48239	−	25.4209i	0.231470	−	1.31273i
$376$	−9.56576	−	2.36267i	−0.493317	−	0.121846i
$377$	−2.37360	+	0.863920i	−0.122247	+	0.0444941i
$378$	−28.1306	+	25.3663i	−1.44688	+	1.30470i
$379$	−26.6265			−1.36771			−0.683856	−	0.729617i	$-0.739698\pi$
$379$	−26.6265			−1.36771			−0.683856	+	0.729617i	$0.739698\pi$
$380$	−3.12593	+	7.67793i	−0.160357	+	0.393870i
$381$	−4.79035			−0.245417
$382$	15.6622	−	14.1231i	0.801348	−	0.722602i
$383$	−17.2405	+	6.27503i	−0.880948	+	0.320639i	−0.742592	−	0.669744i	$-0.766404\pi$
$383$	−17.2405	+	6.27503i	−0.880948	+	0.320639i	−0.138356	+	0.990383i	$0.544182\pi$
$384$	−24.1676	+	23.5793i	−1.23330	+	1.20328i
$385$	−1.99748	+	11.3283i	−0.101801	+	0.577342i
$386$	4.95675	−	9.33880i	0.252292	−	0.475333i
$387$	−15.2000	+	8.77574i	−0.772661	+	0.446096i
$388$	−13.2146	−	13.6441i	−0.670872	−	0.692673i
$389$	13.8384	−	11.6118i	0.701634	−	0.588741i	−0.220604	−	0.975364i	$-0.570803\pi$
$389$	13.8384	−	11.6118i	0.701634	−	0.588741i	0.922238	+	0.386622i	$0.126358\pi$
$390$	1.77174	+	2.83075i	0.0897154	+	0.143341i
$391$	8.85088	+	5.11006i	0.447608	+	0.258427i
$392$	0.764546	+	7.12340i	0.0386154	+	0.359786i
$393$	−10.0104	+	27.5033i	−0.504956	+	1.38736i
$394$	9.34503	−	28.8330i	0.470796	−	1.45258i
$395$	0.540742	+	3.06670i	0.0272077	+	0.154302i
$396$	3.29634	+	46.1668i	0.165647	+	2.31997i
$397$	0.378892	+	0.317928i	0.0190160	+	0.0159564i	0.652246	−	0.758007i	$-0.273827\pi$
$397$	0.378892	+	0.317928i	0.0190160	+	0.0159564i	−0.633230	+	0.773964i	$0.718271\pi$
$398$	−5.01466	+	35.8720i	−0.251362	+	1.79810i
$399$	27.7814	+	29.0075i	1.39081	+	1.45219i
$400$	−13.9190	−	8.64091i	−0.695951	−	0.432045i
$401$	−18.6318	+	22.2046i	−0.930430	+	1.10884i	0.0634064	+	0.997988i	$0.479804\pi$
$401$	−18.6318	+	22.2046i	−0.930430	+	1.10884i	−0.993837	+	0.110856i	$0.964641\pi$
$402$	34.0890	−	7.27196i	1.70020	−	0.362692i
$403$	0.918292	−	0.161920i	0.0457434	−	0.00806580i
$404$	8.60570	−	17.7102i	0.428149	−	0.881114i
$405$	7.29976	+	2.65689i	0.362728	+	0.132022i
$406$	4.97449	+	12.2863i	0.246880	+	0.609761i
$407$	21.6842	−	37.5581i	1.07485	−	1.86169i
$408$	−33.2760	+	9.62102i	−1.64741	+	0.476312i
$409$	4.45901	+	5.31404i	0.220484	+	0.262762i	0.864936	−	0.501882i	$-0.167359\pi$
$409$	4.45901	+	5.31404i	0.220484	+	0.262762i	−0.644452	+	0.764645i	$0.722914\pi$
$410$	−5.41729	−	4.22606i	−0.267541	−	0.208710i
$411$	8.24944	+	14.2884i	0.406915	+	0.704797i
$412$	3.17851	+	2.30221i	0.156594	+	0.113422i
$413$	2.68737	+	0.473855i	0.132237	+	0.0233169i
$414$	−20.7912	+	0.741310i	−1.02183	+	0.0364334i
$415$	−4.02149	−	11.0490i	−0.197407	−	0.542372i
$416$	4.63242	−	0.834343i	0.227123	−	0.0409071i
$417$		−	27.2634i		−	1.33509i
$418$	24.0279	−	2.44288i	1.17524	−	0.119485i
$419$			25.1365i			1.22800i	0.789307	+	0.613999i	$0.210440\pi$
$419$			25.1365i			1.22800i	−0.789307	+	0.613999i	$0.789560\pi$
$420$	14.5140	−	9.82084i	0.708213	−	0.479208i
$421$	−8.13950	−	22.3631i	−0.396695	−	1.08991i	−0.963884	−	0.266323i	$-0.914191\pi$
$421$	−8.13950	−	22.3631i	−0.396695	−	1.08991i	0.567189	−	0.823588i	$-0.308031\pi$
$422$	−0.158315	−	4.44020i	−0.00770666	−	0.216146i
$423$	20.2643	+	3.57314i	0.985284	+	0.173732i
$424$	8.50107	−	8.84196i	0.412849	−	0.429403i
$425$	−8.40361	−	14.5555i	−0.407635	−	0.706045i
$426$	−24.8339	+	31.8340i	−1.20320	+	1.54236i
$427$	−19.9569	−	23.7837i	−0.965780	−	1.15097i
$428$	−5.47523	+	2.44736i	−0.264655	+	0.118297i
$429$	4.86465	−	8.42581i	0.234867	−	0.406802i
$430$	3.70391	−	1.49964i	0.178618	−	0.0723189i
$431$	−3.86038	−	1.40506i	−0.185948	−	0.0676795i	0.247368	−	0.968922i	$-0.420434\pi$
$431$	−3.86038	−	1.40506i	−0.185948	−	0.0676795i	−0.433316	+	0.901242i	$0.642657\pi$
$432$	23.1428	−	25.8547i	1.11346	−	1.24394i
$433$	11.0190	−	1.94295i	0.529540	−	0.0933721i	0.0975153	−	0.995234i	$-0.468911\pi$
$433$	11.0190	−	1.94295i	0.529540	−	0.0933721i	0.432024	+	0.901862i	$0.357799\pi$
$434$	−1.02086	−	4.78553i	−0.0490030	−	0.229713i
$435$	5.53764	−	6.59950i	0.265509	−	0.316422i
$436$	−5.07919	+	17.8118i	−0.243249	+	0.853029i
$437$	0.712515	+	10.8326i	0.0340842	+	0.518195i
$438$	−10.8482	−	1.51650i	−0.518347	−	0.0724613i
$439$	−18.6381	−	15.6392i	−0.889549	−	0.746420i	0.0785707	−	0.996909i	$-0.474964\pi$
$439$	−18.6381	−	15.6392i	−0.889549	−	0.746420i	−0.968120	+	0.250488i	$0.919409\pi$
$440$	0.711943	−	10.5136i	0.0339405	−	0.501214i
$441$	−2.59804	−	14.7342i	−0.123716	−	0.701631i
$442$	4.59358	+	1.48882i	0.218494	+	0.0708160i
$443$	−5.10633	+	14.0295i	−0.242609	+	0.666563i	0.757300	+	0.653068i	$0.226518\pi$
$443$	−5.10633	+	14.0295i	−0.242609	+	0.666563i	−0.999909	+	0.0134959i	$0.995704\pi$
$444$	−64.0841	+	16.0778i	−3.04129	+	0.763019i
$445$	−0.612484	−	0.353618i	−0.0290345	−	0.0167631i
$446$	4.47998	−	2.80397i	0.212133	−	0.132772i
$447$	42.3915	−	35.5707i	2.00505	−	1.68244i
$448$	−5.24175	−	24.1378i	−0.247649	−	1.14040i
$449$	29.1082	−	16.8057i	1.37370	−	0.793108i	0.382311	−	0.924034i	$-0.375128\pi$
$449$	29.1082	−	16.8057i	1.37370	−	0.793108i	0.991392	+	0.130926i	$0.0417950\pi$
$450$	30.2204	+	16.0401i	1.42460	+	0.756136i
$451$	−3.47594	+	19.7130i	−0.163676	+	0.928250i
$452$	−21.0533	−	2.18158i	−0.990266	−	0.102613i
$453$	53.7738	−	19.5721i	2.52651	−	0.919576i
$454$	13.4299	+	14.8935i	0.630298	+	0.698986i
$455$	−2.44298			−0.114529
$456$	−28.1403	−	23.7054i	−1.31779	−	1.11011i
$457$	42.0825			1.96853			0.984267	−	0.176687i	$-0.0565381\pi$
$457$	42.0825			1.96853			0.984267	+	0.176687i	$0.0565381\pi$
$458$	−7.42777	−	8.23722i	−0.347077	−	0.384900i
$459$	33.4511	−	12.1752i	1.56136	−	0.568289i
$460$	4.71136	+	0.488200i	0.219668	+	0.0227624i
$461$	1.07453	−	6.09398i	0.0500460	−	0.283825i	−0.949506	−	0.313748i	$-0.898415\pi$
$461$	1.07453	−	6.09398i	0.0500460	−	0.283825i	0.999552	+	0.0299234i	$0.00952635\pi$
$462$	−45.0972	−	23.9362i	−2.09811	−	1.11361i
$463$	−10.3129	+	5.95417i	−0.479282	+	0.276714i	−0.720117	−	0.693852i	$-0.755912\pi$
$463$	−10.3129	+	5.95417i	−0.479282	+	0.276714i	0.240835	+	0.970566i	$0.422579\pi$
$464$	−5.73209	−	10.7046i	−0.266106	−	0.496950i
$465$	−2.43623	+	2.04424i	−0.112978	+	0.0947994i
$466$	2.45232	−	1.53488i	0.113601	−	0.0711019i
$467$	13.8551	+	7.99927i	0.641139	+	0.370162i	0.785053	−	0.619428i	$-0.212636\pi$
$467$	13.8551	+	7.99927i	0.641139	+	0.370162i	−0.143914	+	0.989590i	$0.545969\pi$
$468$	−9.53426	+	2.39201i	−0.440721	+	0.110571i
$469$	−8.72105	+	23.9609i	−0.402701	+	1.10641i
$470$	−4.45656	−	1.44441i	−0.205566	−	0.0666257i
$471$	−4.12698	−	23.4053i	−0.190161	−	1.07846i
$472$	−2.49409	−	0.168892i	−0.114800	−	0.00777387i
$473$	−8.91821	−	7.48327i	−0.410060	−	0.344081i
$474$	−13.6883	−	1.91353i	−0.628725	−	0.0878915i
$475$	7.89250	−	16.0137i	0.362133	−	0.734759i
$476$	6.94890	−	24.3685i	0.318502	−	1.11693i
$477$	−16.4651	+	19.6223i	−0.753883	+	0.898443i
$478$	−6.51008	−	30.5175i	−0.297764	−	1.39584i
$479$	−12.1768	+	2.14710i	−0.556372	+	0.0981034i	−0.444762	−	0.895649i	$-0.646712\pi$
$479$	−12.1768	+	2.14710i	−0.556372	+	0.0981034i	−0.111610	+	0.993752i	$0.535601\pi$
$480$	−12.2599	+	10.3641i	−0.559587	+	0.473056i
$481$	8.65500	+	3.15016i	0.394634	+	0.143635i
$482$	−12.6259	+	5.11197i	−0.575095	+	0.232844i
$483$	11.4746	−	19.8746i	0.522112	−	0.904325i
$484$	−7.94301	+	3.55042i	−0.361046	+	0.161383i
$485$	−5.80503	−	6.91816i	−0.263593	−	0.314138i
$486$	1.43026	−	1.83342i	0.0648781	−	0.0831658i
$487$	5.21271	+	9.02868i	0.236210	+	0.409128i	0.959624	−	0.281287i	$-0.0907612\pi$
$487$	5.21271	+	9.02868i	0.236210	+	0.409128i	−0.723413	+	0.690415i	$0.757428\pi$
$488$	20.5027	+	19.7122i	0.928112	+	0.892330i
$489$	−50.0767	−	8.82987i	−2.26455	−	0.399301i
$490$	0.121375	+	3.40416i	0.00548317	+	0.153784i
$491$	5.18753	+	14.2526i	0.234110	+	0.643212i	1.00000		0.000240450i	$7.65377e-5\pi$
$491$	5.18753	+	14.2526i	0.234110	+	0.643212i	−0.765890	+	0.642972i	$0.777701\pi$
$492$	25.2568	−	17.0899i	1.13866	−	0.770470i
$493$		−	12.4571i		−	0.561041i
$494$	1.39705	+	4.93536i	0.0628564	+	0.222053i
$495$			22.0062i			0.989105i
$496$	1.39768	+	4.25907i	0.0627577	+	0.191238i
$497$	−10.1019	−	27.7547i	−0.453131	−	1.24497i
$498$	52.1546	−	1.85957i	2.33710	−	0.0833292i
$499$	8.46511	+	1.49263i	0.378950	+	0.0668192i	0.359879	−	0.932999i	$-0.382818\pi$
$499$	8.46511	+	1.49263i	0.378950	+	0.0668192i	0.0190713	+	0.999818i	$0.493929\pi$
$500$	−14.0097	−	10.1473i	−0.626535	−	0.453802i
$501$	18.1795	+	31.4878i	0.812199	+	1.40677i
$502$	−1.84370	−	1.43828i	−0.0822882	−	0.0641935i
$503$	−21.2815	−	25.3623i	−0.948895	−	1.13085i	−0.991283	−	0.131748i	$-0.957941\pi$
$503$	−21.2815	−	25.3623i	−0.948895	−	1.13085i	0.0423882	−	0.999101i	$-0.486503\pi$
$504$	14.3272	+	49.5533i	0.638185	+	2.20728i
$505$	4.68095	−	8.10764i	0.208299	−	0.360785i
$506$	−5.17880	−	12.7910i	−0.230226	−	0.568628i
$507$	−34.5159	−	12.5628i	−1.53291	−	0.557932i
$508$	−1.40304	+	2.88741i	−0.0622500	+	0.128108i
$509$	−30.6280	+	5.40055i	−1.35756	+	0.239375i	−0.804593	−	0.593826i	$-0.797617\pi$
$509$	−30.6280	+	5.40055i	−1.35756	+	0.239375i	−0.552970	+	0.833201i	$0.686506\pi$
$510$	−16.1069	+	3.43598i	−0.713227	+	0.152148i
$511$	5.15071	−	6.13838i	0.227854	−	0.271546i
$512$	7.13412	+	21.4733i	0.315286	+	0.948997i
$513$	30.4992	+	22.3521i	1.34657	+	0.986869i
$514$	−4.05036	+	28.9739i	−0.178654	+	1.27798i
$515$	1.42945	+	1.19945i	0.0629891	+	0.0528541i
$516$	1.26315	+	17.6910i	0.0556069	+	0.778802i
$517$	2.37007	+	13.4413i	0.104235	+	0.591149i
$518$	14.9021	−	45.9785i	0.654759	−	2.02018i
$519$	−22.3798	+	61.4881i	−0.982365	+	2.69903i
$520$	2.22518	−	0.238825i	0.0975804	−	0.0104732i
$521$	23.9923	+	13.8520i	1.05112	+	0.606866i	0.922964	−	0.384887i	$-0.125760\pi$
$521$	23.9923	+	13.8520i	1.05112	+	0.606866i	0.128160	+	0.991754i	$0.459093\pi$
$522$	13.4536	+	21.4951i	0.588847	+	0.940816i
$523$	−0.617244	+	0.517929i	−0.0269902	+	0.0226474i	−0.656183	−	0.754602i	$-0.727830\pi$
$523$	−0.617244	+	0.517929i	−0.0269902	+	0.0226474i	0.629193	+	0.777249i	$0.283386\pi$
$524$	13.6458	+	14.0892i	0.596120	+	0.615491i
$525$	−32.6842	+	18.8703i	−1.42646	+	0.823566i
$526$	−9.78024	+	18.4265i	−0.426439	+	0.803436i
$527$	−0.798538	+	4.52874i	−0.0347849	+	0.197275i
$528$	43.4165	+	17.3934i	1.88946	+	0.756952i
$529$	−15.7842	+	5.74498i	−0.686269	+	0.249782i
$530$	4.33103	−	3.90544i	0.188128	−	0.169641i
$531$	5.22045			0.226548
$532$	25.6213	−	8.24941i	1.11083	−	0.357657i
$533$	−4.25118			−0.184139
$534$	2.33122	−	2.10214i	0.100882	−	0.0909684i
$535$	−2.67950	+	0.975258i	−0.115845	+	0.0421641i
$536$	5.60110	−	22.6772i	0.241931	−	0.979505i
$537$	0.190684	−	1.08142i	0.00822861	−	0.0466668i
$538$	5.06520	−	9.54314i	0.218376	−	0.411434i
$539$	8.59443	−	4.96200i	0.370188	−	0.213728i
$540$	11.8509	−	11.4779i	0.509983	−	0.493932i
$541$	21.0196	−	17.6376i	0.903705	−	0.758299i	−0.0672060	−	0.997739i	$-0.521408\pi$
$541$	21.0196	−	17.6376i	0.903705	−	0.758299i	0.970911	+	0.239441i	$0.0769640\pi$
$542$	−1.12697	−	1.80059i	−0.0484075	−	0.0773420i
$543$	−48.8001	−	28.1747i	−2.09421	−	1.20909i
$544$	−3.94710	+	22.8752i	−0.169231	+	0.980767i
$545$	−3.01194	+	8.27524i	−0.129017	+	0.354472i
$546$	3.34314	−	10.3148i	0.143073	−	0.441435i
$547$	6.63465	+	37.6270i	0.283677	+	1.60881i	0.709972	+	0.704229i	$0.248707\pi$
$547$	6.63465	+	37.6270i	0.283677	+	1.60881i	−0.426295	+	0.904584i	$0.640182\pi$
$548$	11.0286	−	0.787450i	0.471119	−	0.0336382i
$549$	−45.5000	−	38.1790i	−1.94189	−	1.62944i
$550$	−3.14188	+	22.4752i	−0.133970	+	0.958347i
$551$	11.0005	−	7.35398i	0.468638	−	0.313290i
$552$	−8.50863	+	19.2244i	−0.362151	+	0.818245i
$553$	6.49920	−	7.74545i	0.276374	−	0.329370i
$554$	−15.5793	+	3.32342i	−0.661900	+	0.141199i
$555$	−30.9363	+	5.45490i	−1.31317	+	0.231548i
$556$	−16.4332	−	7.98517i	−0.696921	−	0.338647i
$557$	33.4845	+	12.1874i	1.41878	+	0.516395i	0.933695	−	0.358069i	$-0.116565\pi$
$557$	33.4845	+	12.1874i	1.41878	+	0.516395i	0.485089	+	0.874465i	$0.338787\pi$
$558$	−3.51309	−	8.67687i	−0.148721	−	0.367321i
$559$	1.23624	−	2.14123i	0.0522873	−	0.0905642i
$560$	−1.66855	−	11.6248i	−0.0705090	−	0.491239i
$561$	30.8422	+	36.7562i	1.30216	+	1.55185i
$562$	−25.5406	−	19.9244i	−1.07737	−	0.840459i
$563$	−2.01778	−	3.49489i	−0.0850391	−	0.147292i	0.820369	−	0.571835i	$-0.193768\pi$
$563$	−2.01778	−	3.49489i	−0.0850391	−	0.147292i	−0.905408	+	0.424543i	$0.860435\pi$
$564$	12.1973	−	16.8400i	0.513598	−	0.709092i
$565$	−9.91067	−	1.74752i	−0.416945	−	0.0735186i
$566$	26.3035	−	0.937848i	1.10562	−	0.0394207i
$567$	−8.62675	−	23.7018i	−0.362289	−	0.995382i
$568$	11.9145	+	24.2926i	0.499922	+	1.01929i
$569$		−	22.5123i		−	0.943765i	−0.881661	−	0.471883i	$-0.843575\pi$
$569$		−	22.5123i		−	0.943765i	0.881661	−	0.471883i	$-0.156425\pi$
$570$	−12.5428	−	12.1951i	−0.525361	−	0.510798i
$571$			2.03284i			0.0850718i	0.999095	+	0.0425359i	$0.0135437\pi$
$571$			2.03284i			0.0850718i	−0.999095	+	0.0425359i	$0.986456\pi$
$572$	−3.65390	−	5.40003i	−0.152777	−	0.225787i
$573$	15.2217	+	41.8212i	0.635894	+	1.74710i
$574$	0.794909	+	22.2945i	0.0331789	+	0.930555i
$575$	−10.0457	−	1.77133i	−0.418935	−	0.0738696i
$576$	−17.8942	−	43.7347i	−0.745590	−	1.82228i
$577$	−21.0040	−	36.3800i	−0.874409	−	1.51452i	−0.857391	−	0.514665i	$-0.827916\pi$
$577$	−21.0040	−	36.3800i	−0.874409	−	1.51452i	−0.0170172	−	0.999855i	$-0.505417\pi$
$578$	0.139844	−	0.179263i	0.00581674	−	0.00745636i
$579$	14.3416	+	17.0917i	0.596018	+	0.710307i
$580$	−2.35597	−	5.27077i	−0.0978261	−	0.218857i
$581$	−19.0888	+	33.0628i	−0.791936	+	1.37167i
$582$	37.1541	−	15.0429i	1.54009	−	0.623550i
$583$	−15.9658	−	5.81109i	−0.661237	−	0.240671i
$584$	−4.09141	+	6.09464i	−0.169304	+	0.252198i
$585$	−4.60262	+	0.811565i	−0.190295	+	0.0335541i
$586$	6.01536	+	28.1984i	0.248492	+	1.16486i
$587$	0.130312	−	0.155300i	0.00537856	−	0.00640992i	−0.763348	−	0.645987i	$-0.776446\pi$
$587$	0.130312	−	0.155300i	0.00537856	−	0.00640992i	0.768727	+	0.639577i	$0.220890\pi$
$588$	−14.5393	−	4.14600i	−0.599589	−	0.170978i
$589$	−4.47060	+	1.96834i	−0.184208	+	0.0811041i
$590$	−1.17710	−	0.164551i	−0.0484606	−	0.00677447i
$591$	48.9979	+	41.1142i	2.01551	+	1.69121i
$592$	−9.07860	+	43.3361i	−0.373128	+	1.78110i
$593$	−3.92427	−	22.2556i	−0.161150	−	0.913930i	−0.952945	−	0.303143i	$-0.901964\pi$
$593$	−3.92427	−	22.2556i	−0.161150	−	0.913930i	0.791795	−	0.610787i	$-0.209147\pi$
$594$	−45.7241	−	14.8196i	−1.87608	−	0.608055i
$595$	4.12067	−	11.3215i	0.168931	−	0.464134i
$596$	−9.02438	−	35.9700i	−0.369653	−	1.47339i
$597$	−66.1962	−	38.2184i	−2.70923	−	1.56417i
$598$	2.48425	−	1.55487i	0.101589	−	0.0635833i
$599$	24.7817	−	20.7943i	1.01255	−	0.849632i	0.0238789	−	0.999715i	$-0.492398\pi$
$599$	24.7817	−	20.7943i	1.01255	−	0.849632i	0.988673	+	0.150083i	$0.0479539\pi$
$600$	27.9255	−	20.3831i	1.14005	−	0.832135i
$601$	30.9510	−	17.8696i	1.26252	−	0.728915i	0.288957	−	0.957342i	$-0.406692\pi$
$601$	30.9510	−	17.8696i	1.26252	−	0.728915i	0.973561	+	0.228427i	$0.0733583\pi$
$602$	−11.4604	−	6.08283i	−0.467091	−	0.247918i
$603$	−8.47071	+	48.0398i	−0.344954	+	1.95633i
$604$	3.95264	−	38.1449i	0.160831	−	1.55209i
$605$	−3.88719	+	1.41482i	−0.158037	+	0.0575207i
$606$	27.8266	+	30.8591i	1.13038	+	1.25356i
$607$	35.8454			1.45492			0.727460	−	0.686150i	$-0.240701\pi$
$607$	35.8454			1.45492			0.727460	+	0.686150i	$0.240701\pi$
$608$	−22.5306	+	10.0187i	−0.913735	+	0.406310i
$609$	−27.9724			−1.13350
$610$	9.05589	+	10.0428i	0.366662	+	0.406620i
$611$	−2.72386	+	0.991403i	−0.110196	+	0.0401079i
$612$	4.99654	−	48.2191i	0.201973	−	1.94914i
$613$	−2.07723	+	11.7805i	−0.0838984	+	0.475812i	0.913690	+	0.406411i	$0.133220\pi$
$613$	−2.07723	+	11.7805i	−0.0838984	+	0.475812i	−0.997589	+	0.0694008i	$0.977891\pi$
$614$	36.1866	+	19.2067i	1.46037	+	0.775120i
$615$	12.5567	−	7.24962i	0.506335	−	0.292333i
$616$	−27.6362	+	20.1719i	−1.11349	+	0.812749i
$617$	−12.3624	+	10.3733i	−0.497691	+	0.417612i	−0.856773	−	0.515694i	$-0.827534\pi$
$617$	−12.3624	+	10.3733i	−0.497691	+	0.417612i	0.359082	+	0.933306i	$0.383090\pi$
$618$	−7.02052	+	4.39407i	−0.282407	+	0.176755i
$619$	21.6900	+	12.5227i	0.871796	+	0.503332i	0.867945	−	0.496661i	$-0.165441\pi$
$619$	21.6900	+	12.5227i	0.871796	+	0.503332i	0.00385145	+	0.999993i	$0.498774\pi$
$620$	0.518630	+	2.06719i	0.0208287	+	0.0830203i
$621$	7.38940	−	20.3022i	0.296526	−	0.814700i
$622$	12.4331	+	4.02967i	0.498520	+	0.161575i
$623$	0.398756	+	2.26146i	0.0159758	+	0.0906034i
$624$	−2.03670	+	9.72204i	−0.0815332	+	0.389193i
$625$	9.38717	+	7.87677i	0.375487	+	0.315071i
$626$	−35.3073	−	4.93572i	−1.41116	−	0.197271i
$627$	−14.2509	+	48.9346i	−0.569126	+	1.95426i
$628$	−15.3164	−	4.36761i	−0.611191	−	0.174287i
$629$	−29.1974	+	34.7962i	−1.16418	+	1.38741i
$630$	5.11672	+	23.9858i	0.203855	+	0.955616i
$631$	33.3599	−	5.88225i	1.32804	−	0.234169i	0.535781	−	0.844357i	$-0.320017\pi$
$631$	33.3599	−	5.88225i	1.32804	−	0.234169i	0.792257	+	0.610188i	$0.208906\pi$
$632$	−5.16257	+	7.69025i	−0.205356	+	0.305902i
$633$	8.81066	+	3.20682i	0.350192	+	0.127460i
$634$	39.7958	−	16.1125i	1.58049	−	0.639908i
$635$	−0.763166	+	1.32184i	−0.0302853	+	0.0524557i
$636$	10.5628	+	23.6311i	0.418842	+	0.937034i
$637$	1.35476	+	1.61454i	0.0536775	+	0.0639704i
$638$	−10.3458	+	13.2620i	−0.409593	+	0.525048i
$639$	−28.2522	−	48.9343i	−1.11764	−	1.93581i
$640$	2.65623	+	10.4253i	0.104997	+	0.412096i
$641$	−7.27625	−	1.28300i	−0.287395	−	0.0506755i	0.0280923	−	0.999605i	$-0.491057\pi$
$641$	−7.27625	−	1.28300i	−0.287395	−	0.0506755i	−0.315487	+	0.948930i	$0.602168\pi$
$642$	−0.450966	−	12.6481i	−0.0177982	−	0.499180i
$643$	−15.7177	−	43.1840i	−0.619845	−	1.70301i	−0.707366	−	0.706847i	$-0.750117\pi$
$643$	−15.7177	−	43.1840i	−0.619845	−	1.70301i	0.0875217	−	0.996163i	$-0.472105\pi$
$644$	−8.61872	−	12.7374i	−0.339625	−	0.501926i
$645$			8.43271i			0.332038i
$646$	−25.2283	−	1.85034i	−0.992594	−	0.0728007i
$647$		−	41.8157i		−	1.64394i	−0.569529	−	0.821971i	$-0.692874\pi$
$647$		−	41.8157i		−	1.64394i	0.569529	−	0.821971i	$-0.307126\pi$
$648$	10.1747	+	20.7453i	0.399700	+	0.814951i
$649$	1.18432	+	3.25390i	0.0464887	+	0.127727i
$650$	−4.81658	+	0.171735i	−0.188922	+	0.00673600i
$651$	10.1692	+	1.79311i	0.398564	+	0.0702776i
$652$	−19.9892	+	27.5978i	−0.782838	+	1.08081i
$653$	12.8848	+	22.3172i	0.504223	+	0.873339i	0.999988	+	0.00488267i	$0.00155421\pi$
$653$	12.8848	+	22.3172i	0.504223	+	0.873339i	−0.495766	+	0.868456i	$0.665112\pi$
$654$	−30.8183	−	24.0415i	−1.20509	−	0.940097i
$655$	5.99443	+	7.14388i	0.234222	+	0.279135i
$656$	−2.90354	−	20.2291i	−0.113364	−	0.789814i
$657$	7.66483	−	13.2759i	0.299034	−	0.517941i
$658$	5.70854	+	14.0994i	0.222542	+	0.549651i
$659$	−20.9947	−	7.64146i	−0.817839	−	0.297669i	−0.100981	−	0.994888i	$-0.532198\pi$
$659$	−20.9947	−	7.64146i	−0.817839	−	0.297669i	−0.716858	+	0.697219i	$0.754420\pi$
$660$	20.0013	+	9.71899i	0.778548	+	0.378311i
$661$	29.7635	−	5.24811i	1.15767	−	0.204128i	0.438346	−	0.898807i	$-0.355565\pi$
$661$	29.7635	−	5.24811i	1.15767	−	0.204128i	0.719320	+	0.694679i	$0.244454\pi$
$662$	−27.9667	+	5.96595i	−1.08696	+	0.231873i
$663$	−6.55017	+	7.80619i	−0.254388	+	0.303167i
$664$	14.1547	−	31.9811i	0.549309	−	1.24111i
$665$	12.4302	−	3.04470i	0.482024	−	0.118068i
$666$	12.8015	−	91.5747i	0.496049	−	3.54845i
$667$	−5.79169	−	4.85980i	−0.224255	−	0.188172i
$668$	24.3040	−	1.73532i	0.940350	−	0.0671416i
$669$	1.93673	+	10.9837i	0.0748782	+	0.424656i
$670$	3.42421	−	10.5650i	0.132289	−	0.408161i
$671$	13.4747	−	37.0215i	0.520185	−	1.42920i
$672$	51.3662	+	8.86319i	1.98149	+	0.341905i
$673$	−13.8432	−	7.99236i	−0.533615	−	0.308083i	0.208872	−	0.977943i	$-0.433021\pi$
$673$	−13.8432	−	7.99236i	−0.533615	−	0.308083i	−0.742487	+	0.669860i	$0.766354\pi$
$674$	−9.83894	−	15.7199i	−0.378982	−	0.605509i
$675$	−27.2177	+	22.8384i	−1.04761	+	0.879050i
$676$	−17.6817	+	17.1252i	−0.680064	+	0.658660i
$677$	−15.2731	+	8.81795i	−0.586994	+	0.338901i	−0.763908	−	0.645325i	$-0.776722\pi$
$677$	−15.2731	+	8.81795i	−0.586994	+	0.338901i	0.176914	+	0.984226i	$0.443389\pi$
$678$	20.9408	−	39.4538i	0.804228	−	1.51521i
$679$	−5.09190	+	28.8776i	−0.195409	+	1.10822i
$680$	−2.64651	+	10.7149i	−0.101489	+	0.410898i
$681$	−39.7685	+	14.4746i	−1.52393	+	0.554667i
$682$	4.61129	−	4.15815i	0.176576	−	0.159224i
$683$	28.6039			1.09450			0.547249	−	0.836970i	$-0.315675\pi$
$683$	28.6039			1.09450			0.547249	+	0.836970i	$0.315675\pi$
$684$	45.5305	−	24.0535i	1.74090	−	0.919708i
$685$	5.25698			0.200859
$686$	−14.4855	+	13.0621i	−0.553061	+	0.498713i
$687$	21.9950	−	8.00553i	0.839162	−	0.305430i
$688$	11.0333	+	4.42014i	0.420640	+	0.168516i
$689$	0.626591	−	3.55358i	0.0238712	−	0.135380i
$690$	−4.68619	+	8.82905i	−0.178400	+	0.336116i
$691$	−4.66323	+	2.69231i	−0.177397	+	0.102420i	−0.586069	−	0.810261i	$-0.699325\pi$
$691$	−4.66323	+	2.69231i	−0.177397	+	0.102420i	0.408672	+	0.912681i	$0.365992\pi$
$692$	30.5074	+	31.4988i	1.15972	+	1.19741i
$693$	54.7358	−	45.9288i	2.07924	−	1.74469i
$694$	3.52545	+	5.63271i	0.133824	+	0.213815i
$695$	−7.52302	−	4.34342i	−0.285365	−	0.164755i
$696$	25.4785	−	2.73458i	0.965760	−	0.103654i
$697$	7.17064	−	19.7012i	0.271607	−	0.746235i
$698$	−9.44310	+	29.1355i	−0.357427	+	1.10280i
$699$	1.06016	+	6.01244i	0.0400988	+	0.227411i
$700$	1.80126	+	25.2275i	0.0680813	+	0.953511i
$701$	4.35970	+	3.65823i	0.164664	+	0.138169i	0.721396	−	0.692523i	$-0.243501\pi$
$701$	4.35970	+	3.65823i	0.164664	+	0.138169i	−0.556732	+	0.830692i	$0.687945\pi$
$702$	1.41327	−	10.1098i	0.0533406	−	0.381568i
$703$	−47.9639	−	5.24172i	−1.80899	−	0.197695i
$704$	23.2002	−	21.0751i	0.874392	−	0.794299i
$705$	6.35479	−	7.57335i	0.239335	−	0.285229i
$706$	−34.4844	+	7.35631i	−1.29784	+	0.276858i
$707$	−29.9356	+	5.27845i	−1.12584	+	0.198517i
$708$	2.30560	−	4.74483i	0.0866498	−	0.178322i
$709$	−28.6122	−	10.4140i	−1.07455	−	0.391105i	−0.256675	−	0.966498i	$-0.582627\pi$
$709$	−28.6122	−	10.4140i	−1.07455	−	0.391105i	−0.817877	+	0.575393i	$0.804849\pi$
$710$	4.82786	+	11.9242i	0.181187	+	0.447507i
$711$	9.67154	−	16.7516i	0.362711	−	0.628234i
$712$	−0.584284	−	2.02085i	−0.0218970	−	0.0757346i
$713$	1.79402	+	2.13802i	0.0671864	+	0.0800697i
$714$	42.1629	+	32.8915i	1.57791	+	1.23093i
$715$	−1.55001	−	2.68469i	−0.0579669	−	0.100402i
$716$	−0.595983	−	0.431673i	−0.0222729	−	0.0161324i
$717$	64.8496	+	11.4347i	2.42185	+	0.427038i
$718$	−34.0281	+	1.21327i	−1.26992	+	0.0452789i
$719$	−2.98701	−	8.20674i	−0.111397	−	0.306060i	0.871450	−	0.490484i	$-0.163180\pi$
$719$	−2.98701	−	8.20674i	−0.111397	−	0.306060i	−0.982847	+	0.184425i	$0.940958\pi$
$720$	−7.00537	−	21.3471i	−0.261075	−	0.795559i
$721$		−	6.05882i		−	0.225642i
$722$	−13.2594	−	23.3707i	−0.493463	−	0.869767i
$723$		−	28.7455i		−	1.06906i
$724$	−31.2755	+	21.1624i	−1.16235	+	0.786495i
$725$	4.25249	+	11.6836i	0.157933	+	0.433919i
$726$	−0.654224	−	18.3488i	−0.0242805	−	0.680987i
$727$	21.6522	+	3.81787i	0.803036	+	0.141597i	0.560078	−	0.828440i	$-0.310771\pi$
$727$	21.6522	+	3.81787i	0.803036	+	0.141597i	0.242958	+	0.970037i	$0.421882\pi$
$728$	−5.23816	−	5.03621i	−0.194139	−	0.186654i
$729$	14.7074	+	25.4740i	0.544719	+	0.943481i
$730$	−2.14672	+	2.75184i	−0.0794538	+	0.101850i
$731$	7.83782	+	9.34075i	0.289892	+	0.345480i
$732$	−54.7956	+	24.4929i	−2.02530	+	0.905285i
$733$	10.4654	−	18.1267i	0.386549	−	0.669523i	−0.605433	−	0.795896i	$-0.707000\pi$
$733$	10.4654	−	18.1267i	0.386549	−	0.669523i	0.991983	+	0.126373i	$0.0403335\pi$
$734$	−13.6180	+	5.51364i	−0.502648	+	0.203512i
$735$	−6.75485	−	2.45856i	−0.249156	−	0.0906855i
$736$	9.09552	+	10.7593i	0.335265	+	0.396592i
$737$	−31.8648	+	5.61863i	−1.17376	+	0.206965i
$738$	8.90392	+	41.7391i	0.327758	+	1.53644i
$739$	9.03080	−	10.7625i	0.332203	−	0.395905i	−0.573925	−	0.818908i	$-0.694580\pi$
$739$	9.03080	−	10.7625i	0.332203	−	0.395905i	0.906128	+	0.423003i	$0.139024\pi$
$740$	−5.77296	+	20.2447i	−0.212218	+	0.744210i
$741$	−10.7603	−	1.17593i	−0.395288	−	0.0431989i
$742$	−18.7532	−	2.62157i	−0.688452	−	0.0962408i
$743$	15.7144	+	13.1860i	0.576506	+	0.483746i	0.883798	−	0.467869i	$-0.154978\pi$
$743$	15.7144	+	13.1860i	0.576506	+	0.483746i	−0.307291	+	0.951615i	$0.599423\pi$
$744$	−9.43789	−	0.639102i	−0.346010	−	0.0234306i
$745$	−3.06180	−	17.3644i	−0.112176	−	0.636181i
$746$	10.9559	+	3.55090i	0.401123	+	0.130008i
$747$	−24.9800	+	68.6321i	−0.913971	+	2.51112i
$748$	31.1884	−	7.82474i	1.14036	−	0.286101i
$749$	8.01809	+	4.62925i	0.292975	+	0.169149i
$750$	30.9439	−	19.3675i	1.12991	−	0.707201i
$751$	−25.9874	+	21.8061i	−0.948295	+	0.795714i	−0.979010	−	0.203814i	$-0.934666\pi$
$751$	−25.9874	+	21.8061i	−0.948295	+	0.795714i	0.0307144	+	0.999528i	$0.490222\pi$
$752$	−6.57794	−	12.2843i	−0.239873	−	0.447961i
$753$	4.27350	−	2.46731i	0.155735	−	0.0899136i
$754$	−3.15530	−	1.67474i	−0.114909	−	0.0609903i
$755$	3.16619	−	17.9564i	0.115230	−	0.653499i
$756$	−53.2829	−	5.52127i	−1.93788	−	0.200807i
$757$	−26.8038	+	9.75577i	−0.974199	+	0.354580i	−0.779582	−	0.626300i	$-0.784569\pi$
$757$	−26.8038	+	9.75577i	−0.974199	+	0.354580i	−0.194617	+	0.980879i	$0.562346\pi$
$758$	−25.2170	−	27.9651i	−0.915923	−	1.01574i
$759$	29.1213			1.05704
$760$	−11.0244	+	3.98842i	−0.399896	+	0.144675i
$761$	16.4874			0.597667			0.298834	−	0.954305i	$-0.403402\pi$
$761$	16.4874			0.597667			0.298834	+	0.954305i	$0.403402\pi$
$762$	−4.53676	−	5.03116i	−0.164350	−	0.182260i
$763$	26.8691	−	9.77956i	0.972727	−	0.354044i
$764$	29.6662	+	3.07407i	1.07329	+	0.111216i
$765$	4.00239	−	22.6987i	0.144707	−	0.820673i
$766$	−22.9183	−	12.1643i	−0.828073	−	0.439516i
$767$	−0.636879	+	0.367702i	−0.0229964	+	0.0132770i
$768$	−47.6530	−	3.05144i	−1.71953	−	0.110109i
$769$	1.90875	−	1.60163i	0.0688314	−	0.0577564i	−0.607723	−	0.794149i	$-0.707917\pi$
$769$	1.90875	−	1.60163i	0.0688314	−	0.0577564i	0.676554	+	0.736393i	$0.263472\pi$
$770$	−13.7895	+	8.63070i	−0.496939	+	0.311029i
$771$	−53.4668	−	30.8691i	−1.92556	−	1.11172i
$772$	14.5026	−	3.63851i	0.521961	−	0.130953i
$773$	−0.00136352	+	0.00374623i	−4.90422e−5	+	0.000134742i	−0.939717	−	0.341953i	$-0.888912\pi$
$773$	−0.00136352	+	0.00374623i	−4.90422e−5	+	0.000134742i	0.939668	+	0.342088i	$0.111134\pi$
$774$	−23.6123	−	7.65296i	−0.848727	−	0.275080i
$775$	−0.797020	−	4.52013i	−0.0286298	−	0.162368i
$776$	1.81486	−	26.8008i	0.0651496	−	0.962092i
$777$	78.1346	+	65.5627i	2.80306	+	2.35205i
$778$	25.3014	+	3.53696i	0.907098	+	0.126806i
$779$	21.6306	−	5.29827i	0.774998	−	0.189830i
$780$	−1.29511	+	4.54171i	−0.0463723	+	0.162619i
$781$	24.0913	−	28.7109i	0.862055	−	1.02736i
$782$	3.01540	+	14.1354i	0.107830	+	0.505480i
$783$	−25.9341	+	4.57288i	−0.926809	+	0.163422i
$784$	−6.75743	+	7.54930i	−0.241337	+	0.269618i
$785$	−7.11590	−	2.58998i	−0.253977	−	0.0924402i
$786$	−38.3663	+	15.5337i	−1.36848	+	0.554070i
$787$	−14.7870	+	25.6119i	−0.527100	+	0.912964i	0.472401	+	0.881384i	$0.343387\pi$
$787$	−14.7870	+	25.6119i	−0.527100	+	0.912964i	−0.999501	+	0.0315805i	$0.989946\pi$
$788$	39.1328	−	17.4919i	1.39405	−	0.623121i
$789$	−28.2977	−	33.7239i	−1.00743	−	1.20060i
$790$	−2.70875	+	3.47229i	−0.0963730	+	0.123538i
$791$	16.3378	+	28.2979i	0.580906	+	1.00616i
$792$	−45.3658	+	47.1849i	−1.61200	+	1.67664i
$793$	8.24000	+	1.45293i	0.292611	+	0.0515952i
$794$	0.0249241	+	0.699038i	0.000884525	+	0.0248079i
$795$	4.20921	+	11.5647i	0.149285	+	0.410158i
$796$	−42.4245	+	28.7063i	−1.50370	+	1.01747i
$797$			23.5686i			0.834844i	0.908713	+	0.417422i	$0.137066\pi$
$797$			23.5686i			0.834844i	−0.908713	+	0.417422i	$0.862934\pi$
$798$	−4.15493	+	56.6500i	−0.147083	+	2.00539i
$799$		−	14.2953i		−	0.505733i
$800$	−4.10690	−	22.8022i	−0.145201	−	0.806181i
$801$	1.50252	+	4.12815i	0.0530891	+	0.145861i
$802$	−40.9664	+	1.46065i	−1.44657	+	0.0515775i
$803$	10.0137	+	1.76568i	0.353376	+	0.0623096i
$804$	39.9219	+	28.9156i	1.40794	+	1.01978i
$805$	−3.65611	−	6.33257i	−0.128861	−	0.223194i
$806$	1.03974	+	0.811108i	0.0366233	+	0.0285701i
$807$	14.6554	+	17.4657i	0.515896	+	0.614820i
$808$	26.7506	−	7.73434i	0.941084	−	0.272093i
$809$	9.96738	−	17.2640i	0.350434	−	0.606970i	−0.635891	−	0.771779i	$-0.719367\pi$
$809$	9.96738	−	17.2640i	0.350434	−	0.606970i	0.986326	+	0.164809i	$0.0527006\pi$
$810$	4.12288	+	10.1830i	0.144863	+	0.357793i
$811$	−7.15270	−	2.60337i	−0.251165	−	0.0914167i	0.213369	−	0.976972i	$-0.431556\pi$
$811$	−7.15270	−	2.60337i	−0.251165	−	0.0914167i	−0.464535	+	0.885555i	$0.653778\pi$
$812$	−8.19284	+	16.8605i	−0.287512	+	0.591688i
$813$	4.41458	−	0.778409i	0.154826	−	0.0273000i
$814$	59.9825	−	12.7957i	2.10239	−	0.448487i
$815$	−10.4144	+	12.4114i	−0.364800	+	0.434752i
$816$	−41.6192	−	25.8372i	−1.45696	−	0.904481i
$817$	−3.62154	+	12.4356i	−0.126702	+	0.435066i
$818$	−1.35822	+	9.71591i	−0.0474890	+	0.339709i
$819$	11.6247	+	9.75424i	0.406198	+	0.340841i
$820$	−0.692012	−	9.69197i	−0.0241661	−	0.338458i
$821$	−3.47380	−	19.7009i	−0.121237	−	0.687567i	−0.983472	−	0.181059i	$-0.942047\pi$
$821$	−3.47380	−	19.7009i	−0.121237	−	0.687567i	0.862236	−	0.506507i	$-0.169064\pi$
$822$	−7.19400	+	22.1962i	−0.250919	+	0.774182i
$823$	−4.87923	+	13.4056i	−0.170079	+	0.467289i	−0.995222	−	0.0976351i	$-0.968872\pi$
$823$	−4.87923	+	13.4056i	−0.170079	+	0.467289i	0.825143	+	0.564924i	$0.191094\pi$
$824$	0.592308	+	5.51863i	0.0206340	+	0.192251i
$825$	−41.4745	−	23.9453i	−1.44396	−	0.833669i
$826$	2.04743	+	3.27124i	0.0712393	+	0.113821i
$827$	38.9790	−	32.7073i	1.35543	−	1.13734i	0.378071	−	0.925777i	$-0.376588\pi$
$827$	38.9790	−	32.7073i	1.35543	−	1.13734i	0.977363	−	0.211568i	$-0.0678568\pi$
$828$	−20.4692	−	21.1344i	−0.711354	−	0.734470i
$829$	17.8100	−	10.2826i	0.618567	−	0.357130i	−0.157744	−	0.987480i	$-0.550422\pi$
$829$	17.8100	−	10.2826i	0.618567	−	0.357130i	0.776311	+	0.630350i	$0.217089\pi$
$830$	7.79580	−	14.6877i	0.270596	−	0.509819i
$831$	5.83748	−	33.1060i	0.202500	−	1.14843i
$832$	5.26348	+	4.07512i	0.182478	+	0.141279i
$833$	−9.76734	+	3.55502i	−0.338418	+	0.123174i
$834$	28.6339	−	25.8202i	0.991512	−	0.894079i
$835$	11.5849			0.400913
$836$	25.3216	+	22.9223i	0.875767	+	0.792783i
$837$	9.72137			0.336020
$838$	−26.4001	+	23.8059i	−0.911977	+	0.822360i
$839$	−17.8217	+	6.48656i	−0.615272	+	0.223941i	−0.630809	−	0.775939i	$-0.717277\pi$
$839$	−17.8217	+	6.48656i	−0.615272	+	0.223941i	0.0155363	+	0.999879i	$0.495054\pi$
$840$	24.0603	+	5.94271i	0.830158	+	0.205043i
$841$	3.43556	−	19.4840i	0.118468	−	0.671864i
$842$	15.7787	−	29.7280i	0.543769	−	1.02449i
$843$	59.2005	−	34.1794i	2.03897	−	1.17720i
$844$	4.51348	−	4.37143i	0.155360	−	0.150471i
$845$	−8.96541	+	7.52287i	−0.308419	+	0.258795i
$846$	15.4388	+	24.6670i	0.530798	+	0.848070i
$847$	11.6320	+	6.71573i	0.399680	+	0.230755i
$848$	17.3375	+	0.554532i	0.595373	+	0.0190427i
$849$	−18.9970	+	52.1938i	−0.651975	+	1.79129i
$850$	7.32845	−	22.6110i	0.251364	−	0.775552i
$851$	4.78719	+	27.1495i	0.164103	+	0.930673i
$852$	−56.9536	+	4.06652i	−1.95120	+	0.139317i
$853$	5.99511	+	5.03049i	0.205269	+	0.172241i	0.739627	−	0.673017i	$-0.235002\pi$
$853$	5.99511	+	5.03049i	0.205269	+	0.172241i	−0.534358	+	0.845258i	$0.679447\pi$
$854$	6.07887	−	43.4848i	0.208015	−	1.48802i
$855$	22.4073	−	9.86562i	0.766314	−	0.337397i
$856$	−7.75578	−	3.43267i	−0.265087	−	0.117326i
$857$	19.4931	−	23.2309i	0.665871	−	0.793554i	−0.322345	−	0.946622i	$-0.604471\pi$
$857$	19.4931	−	23.2309i	0.665871	−	0.793554i	0.988216	+	0.153068i	$0.0489154\pi$
$858$	13.4565	−	2.87059i	0.459398	−	0.0980002i
$859$	−38.2799	+	6.74979i	−1.30609	+	0.230300i	−0.783025	−	0.621990i	$-0.786324\pi$
$859$	−38.2799	+	6.74979i	−1.30609	+	0.230300i	−0.523070	+	0.852290i	$0.675213\pi$
$860$	5.08286	+	2.46986i	0.173324	+	0.0842214i
$861$	−44.2388	−	16.1016i	−1.50766	−	0.548742i
$862$	−2.18033	−	5.38513i	−0.0742622	−	0.183418i
$863$	−14.7302	+	25.5135i	−0.501423	+	0.868490i	0.498576	+	0.866846i	$0.333857\pi$
$863$	−14.7302	+	25.5135i	−0.501423	+	0.868490i	−0.999999	+	0.00164372i	$0.999477\pi$
$864$	49.0722	−	0.179911i	1.66947	−	0.00612070i
$865$	13.4015	+	15.9713i	0.455666	+	0.543042i
$866$	12.4763	+	9.73285i	0.423963	+	0.330736i
$867$	0.239896	+	0.415513i	0.00814731	+	0.0141116i
$868$	4.05928	−	5.60439i	0.137781	−	0.190225i
$869$	12.6353	+	2.22795i	0.428625	+	0.0755781i
$870$	12.1758	−	0.434126i	0.412797	−	0.0147182i
$871$	−2.35028	−	6.45734i	−0.0796362	−	0.218799i
$872$	−23.5175	+	11.5344i	−0.796403	+	0.390603i
$873$			56.0974i			1.89861i
$874$	−10.7024	+	11.0075i	−0.362014	+	0.372335i
$875$			26.7051i			0.902798i
$876$	−8.68119	−	12.8298i	−0.293310	−	0.433478i
$877$	11.5291	+	31.6760i	0.389311	+	1.06962i	0.967313	+	0.253587i	$0.0816103\pi$
$877$	11.5291	+	31.6760i	0.389311	+	1.06962i	−0.578002	+	0.816035i	$0.696167\pi$
$878$	−1.22605	−	34.3864i	−0.0413771	−	1.16049i
$879$	−59.9215	−	10.5658i	−2.02110	−	0.356375i
$880$	11.7163	−	9.20928i	0.394958	−	0.310445i
$881$	−13.9103	−	24.0933i	−0.468649	−	0.811724i	0.530709	−	0.847554i	$-0.321926\pi$
$881$	−13.9103	−	24.0933i	−0.468649	−	0.811724i	−0.999358	+	0.0358302i	$0.988592\pi$
$882$	13.0144	−	16.6829i	0.438219	−	0.561743i
$883$	−22.1282	−	26.3714i	−0.744673	−	0.887467i	0.252103	−	0.967700i	$-0.418878\pi$
$883$	−22.1282	−	26.3714i	−0.744673	−	0.887467i	−0.996776	+	0.0802332i	$0.974433\pi$
$884$	2.78675	+	6.23451i	0.0937284	+	0.209689i
$885$	1.25410	−	2.17216i	0.0421561	−	0.0730164i
$886$	−19.5708	+	7.92383i	−0.657495	+	0.266206i
$887$	−16.7427	−	6.09383i	−0.562163	−	0.204611i	0.0452791	−	0.998974i	$-0.485582\pi$
$887$	−16.7427	−	6.09383i	−0.562163	−	0.204611i	−0.607443	+	0.794364i	$0.707805\pi$
$888$	−77.5778	−	52.0789i	−2.60334	−	1.74765i
$889$	4.88060	−	0.860582i	0.163690	−	0.0288630i
$890$	−0.208667	−	0.978173i	−0.00699453	−	0.0327884i
$891$	20.5734	−	24.5184i	0.689234	−	0.821397i
$892$	7.18775	+	2.04965i	0.240664	+	0.0686274i
$893$	12.6238	−	8.43916i	0.422439	−	0.282406i
$894$	77.5064	+	10.8349i	2.59220	+	0.362372i
$895$	−0.268028	−	0.224902i	−0.00895918	−	0.00751764i
$896$	20.3870	−	28.3653i	0.681081	−	0.947618i
$897$	1.07396	+	6.09074i	0.0358585	+	0.203364i
$898$	45.2179	+	14.6555i	1.50894	+	0.489061i
$899$	1.16352	−	3.19674i	0.0388055	−	0.106617i
$900$	11.7742	+	46.9306i	0.392475	+	1.56435i
$901$	15.4114	+	8.89775i	0.513427	+	0.296427i
$902$	−23.9960	+	15.0188i	−0.798978	+	0.500072i
$903$	20.9746	−	17.5998i	0.697991	−	0.585684i
$904$	−17.6476	−	24.1778i	−0.586951	−	0.804142i
$905$	−15.5490	+	8.97722i	−0.516866	+	0.298413i
$906$	71.4832	+	37.9411i	2.37487	+	1.26051i
$907$	−2.92970	+	16.6152i	−0.0972792	+	0.551698i	0.896746	+	0.442546i	$0.145925\pi$
$907$	−2.92970	+	16.6152i	−0.0972792	+	0.551698i	−0.994025	+	0.109152i	$0.965186\pi$
$908$	−2.92319	+	28.2102i	−0.0970094	+	0.936187i
$909$	−54.6456	+	19.8894i	−1.81248	+	0.659689i
$910$	−2.31366	−	2.56579i	−0.0766971	−	0.0850553i
$911$	−43.3664			−1.43679			−0.718396	−	0.695635i	$-0.755123\pi$
$911$	−43.3664			−1.43679			−0.718396	+	0.695635i	$0.755123\pi$
$912$	−1.75360	−	52.0055i	−0.0580674	−	1.72207i
$913$	−48.4453			−1.60330
$914$	39.8548	+	44.1980i	1.31828	+	1.46194i
$915$	−26.8162	+	9.76029i	−0.886515	+	0.322665i
$916$	1.61674	−	15.6024i	0.0534187	−	0.515516i
$917$	5.25803	−	29.8198i	0.173636	−	0.984736i
$918$	44.4676	+	23.6020i	1.46765	+	0.778983i
$919$	−10.4580	+	6.03794i	−0.344978	+	0.199173i	−0.662471	−	0.749087i	$-0.730492\pi$
$919$	−10.4580	+	6.03794i	−0.344978	+	0.199173i	0.317493	+	0.948261i	$0.397159\pi$
$920$	3.94922	+	5.41056i	0.130202	+	0.178381i
$921$	−66.2279	+	55.5718i	−2.18228	+	1.83115i
$922$	7.41798	−	4.64283i	0.244298	−	0.152904i
$923$	6.89337	+	3.97989i	0.226898	+	0.131000i
$924$	−17.5704	−	70.0333i	−0.578024	−	2.30393i
$925$	15.5061	−	42.6027i	0.509837	−	1.40077i
$926$	−16.0205	−	5.19239i	−0.526466	−	0.170633i
$927$	−2.01275	−	11.4149i	−0.0661075	−	0.374914i
$928$	5.81412	−	16.1582i	0.190858	−	0.530420i
$929$	−17.9287	−	15.0439i	−0.588220	−	0.493575i	0.299415	−	0.954123i	$-0.403209\pi$
$929$	−17.9287	−	15.0439i	−0.588220	−	0.493575i	−0.887635	+	0.460548i	$0.847653\pi$
$930$	−4.45428	−	0.622677i	−0.146061	−	0.0204184i
$931$	−8.90542	−	6.52657i	−0.291863	−	0.213900i
$932$	3.93454	+	1.12197i	0.128880	+	0.0367514i
$933$	−17.7288	+	21.1284i	−0.580415	+	0.691712i
$934$	4.72030	+	22.1275i	0.154453	+	0.724033i
$935$	15.0560	−	2.65479i	0.492385	−	0.0868208i
$936$	−11.5418	−	7.74817i	−0.377256	−	0.253257i
$937$	−26.6320	−	9.69324i	−0.870028	−	0.316664i	−0.131849	−	0.991270i	$-0.542092\pi$
$937$	−26.6320	−	9.69324i	−0.870028	−	0.316664i	−0.738178	+	0.674605i	$0.764314\pi$
$938$	−33.4248	+	13.5330i	−1.09136	+	0.441869i
$939$	37.6167	−	65.1541i	1.22758	−	2.12622i
$940$	−2.70362	−	6.04854i	−0.0881824	−	0.197282i
$941$	0.258229	+	0.307745i	0.00841802	+	0.0100322i	0.770237	−	0.637758i	$-0.220138\pi$
$941$	0.258229	+	0.307745i	0.00841802	+	0.0100322i	−0.761819	+	0.647790i	$0.775693\pi$
$942$	20.6734	−	26.5007i	0.673574	−	0.863440i
$943$	−6.36223	−	11.0197i	−0.207183	−	0.358851i
$944$	−2.18469	−	2.77943i	−0.0711054	−	0.0904627i
$945$	−25.0824	−	4.42271i	−0.815932	−	0.143871i
$946$	−0.586655	−	16.4537i	−0.0190738	−	0.534955i
$947$	1.37169	+	3.76869i	0.0445739	+	0.122466i	0.959982	−	0.280060i	$-0.0903545\pi$
$947$	1.37169	+	3.76869i	0.0445739	+	0.122466i	−0.915408	+	0.402526i	$0.868132\pi$
$948$	−10.9540	−	16.1887i	−0.355769	−	0.525784i
$949$			2.15949i			0.0701000i
$950$	24.2934	−	6.87674i	0.788183	−	0.223111i
$951$			90.6032i			2.93801i
$952$	32.1746	−	15.7803i	1.04278	−	0.511443i
$953$	12.2206	+	33.5757i	0.395863	+	1.08762i	0.964280	+	0.264884i	$0.0853336\pi$
$953$	12.2206	+	33.5757i	0.395863	+	1.08762i	−0.568417	+	0.822740i	$0.692444\pi$
$954$	−36.2022	+	1.29079i	−1.17209	+	0.0417908i
$955$	13.9651	+	2.46242i	0.451900	+	0.0796821i
$956$	25.8862	−	35.7393i	0.837218	−	1.15589i
$957$	−17.7477	−	30.7400i	−0.573703	−	0.993682i
$958$	−13.7872	−	10.7555i	−0.445445	−	0.347494i
$959$	−10.9718	−	13.0756i	−0.354297	−	0.422235i
$960$	−22.4961	−	3.06076i	−0.726059	−	0.0987855i
$961$	14.8721	−	25.7592i	0.479745	−	0.830942i
$962$	4.88831	+	12.0735i	0.157606	+	0.389265i
$963$	16.6441	+	6.05794i	0.536347	+	0.195214i
$964$	−17.3265	−	8.41927i	−0.558049	−	0.271167i
$965$	7.00108	−	1.23448i	0.225373	−	0.0397393i
$966$	31.7409	−	6.77106i	1.02125	−	0.217855i
$967$	30.5866	−	36.4517i	0.983598	−	1.17221i	−0.00146235	−	0.999999i	$-0.500465\pi$
$967$	30.5866	−	36.4517i	0.983598	−	1.17221i	0.985061	−	0.172208i	$-0.0550901\pi$
$968$	−11.2514	−	4.97984i	−0.361635	−	0.160058i
$969$	23.5993	−	47.8825i	0.758120	−	1.53821i
$970$	1.76822	−	12.6488i	0.0567740	−	0.406129i
$971$	−38.0365	−	31.9164i	−1.22065	−	1.02425i	−0.998791	−	0.0491676i	$-0.984343\pi$
$971$	−38.0365	−	31.9164i	−1.22065	−	1.02425i	−0.221859	−	0.975079i	$-0.571212\pi$
$972$	3.28014	−	0.234204i	0.105211	−	0.00751211i
$973$	4.89784	+	27.7770i	0.157018	+	0.890491i
$974$	−4.54579	+	14.0255i	−0.145657	+	0.449406i
$975$	3.47865	−	9.55751i	0.111406	−	0.306085i
$976$	−1.28584	+	40.2021i	−0.0411589	+	1.28684i
$977$	−0.637676	−	0.368162i	−0.0204011	−	0.0117786i	0.489765	−	0.871855i	$-0.337083\pi$
$977$	−0.637676	−	0.368162i	−0.0204011	−	0.0117786i	−0.510166	+	0.860076i	$0.670416\pi$
$978$	−38.1521	−	60.9566i	−1.21997	−	1.94918i
$979$	−2.23220	+	1.87304i	−0.0713415	+	0.0598627i
$980$	−3.46034	+	3.35143i	−0.110537	+	0.107058i
$981$	47.3730	−	27.3508i	1.51250	−	0.873244i
$982$	−10.0562	+	18.9465i	−0.320906	+	0.604606i
$983$	−3.73409	+	21.1771i	−0.119099	+	0.675444i	0.865540	+	0.500840i	$0.166976\pi$
$983$	−3.73409	+	21.1771i	−0.119099	+	0.675444i	−0.984639	+	0.174604i	$0.944136\pi$
$984$	41.8688	+	10.3413i	1.33473	+	0.329668i
$985$	19.1510	−	6.97040i	0.610202	−	0.222095i
$986$	13.0834	−	11.7977i	0.416659	−	0.375715i
$987$	−32.1001			−1.02176
$988$	−3.86037	+	6.14139i	−0.122815	+	0.195384i
$989$	7.40050			0.235322
$990$	−23.1125	+	20.8413i	−0.734563	+	0.662379i
$991$	37.2349	−	13.5524i	1.18281	−	0.430506i	0.325614	−	0.945503i	$-0.394429\pi$
$991$	37.2349	−	13.5524i	1.18281	−	0.430506i	0.857192	+	0.514996i	$0.172207\pi$
$992$	−3.14949	+	5.50155i	−0.0999963	+	0.174675i
$993$	10.4790	−	59.4293i	0.332541	−	1.88593i
$994$	19.5828	−	36.8951i	0.621129	−	1.17024i
$995$	−21.0919	+	12.1774i	−0.668657	+	0.386049i
$996$	51.3468	+	53.0153i	1.62699	+	1.67986i
$997$	−45.3533	+	38.0559i	−1.43635	+	1.20524i	−0.494518	+	0.869167i	$0.664656\pi$
$997$	−45.3533	+	38.0559i	−1.43635	+	1.20524i	−0.941835	+	0.336076i	$0.890900\pi$
$998$	6.44934	+	10.3043i	0.204150	+	0.326176i
$999$	83.1591	+	48.0119i	2.63104	+	1.51903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.3.7	yes	48
3.2	odd	2		684.2.cf.a.307.2		48
4.3	odd	2	inner	76.2.k.a.3.3	✓	48
12.11	even	2		684.2.cf.a.307.6		48
19.13	odd	18	inner	76.2.k.a.51.3	yes	48
57.32	even	18		684.2.cf.a.127.6		48
76.51	even	18	inner	76.2.k.a.51.7	yes	48
228.203	odd	18		684.2.cf.a.127.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.3.3	✓	48	4.3	odd	2	inner
76.2.k.a.3.7	yes	48	1.1	even	1	trivial
76.2.k.a.51.3	yes	48	19.13	odd	18	inner
76.2.k.a.51.7	yes	48	76.51	even	18	inner
684.2.cf.a.127.2		48	228.203	odd	18
684.2.cf.a.127.6		48	57.32	even	18
684.2.cf.a.307.2		48	3.2	odd	2
684.2.cf.a.307.6		48	12.11	even	2

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.947064 + 1.05027i) q^{2} +(-2.80443 + 1.02073i) q^{3} +(-0.206140 + 1.98935i) q^{4} +(-0.165124 + 0.936467i) q^{5} +(-3.72802 - 1.97872i) q^{6} +(2.67390 - 1.54378i) q^{7} +(-2.28458 + 1.66754i) q^{8} +(4.52481 - 3.79677i) q^{9} +O(q^{10})\)	\(q+(0.947064 + 1.05027i) q^{2} +(-2.80443 + 1.02073i) q^{3} +(-0.206140 + 1.98935i) q^{4} +(-0.165124 + 0.936467i) q^{5} +(-3.72802 - 1.97872i) q^{6} +(2.67390 - 1.54378i) q^{7} +(-2.28458 + 1.66754i) q^{8} +(4.52481 - 3.79677i) q^{9} +(-1.13993 + 0.713469i) q^{10} +(3.39303 + 1.95897i) q^{11} +(-1.45248 - 5.78940i) q^{12} +(-0.284588 + 0.781900i) q^{13} +(4.15373 + 1.34626i) q^{14} +(-0.492800 - 2.79481i) q^{15} +(-3.91501 - 0.820168i) q^{16} +(-3.14351 - 2.63772i) q^{17} +(8.27293 + 1.15650i) q^{18} +(0.473541 - 4.33310i) q^{19} +(-1.82892 - 0.521533i) q^{20} +(-5.92298 + 7.05874i) q^{21} +(1.15597 + 5.41887i) q^{22} +(-2.45271 + 0.432479i) q^{23} +(4.70485 - 7.00844i) q^{24} +(3.84876 + 1.40083i) q^{25} +(-1.09073 + 0.441614i) q^{26} +(-4.33744 + 7.51266i) q^{27} +(2.51991 + 5.63755i) q^{28} +(1.95130 + 2.32547i) q^{29} +(2.46859 - 3.16443i) q^{30} +(-0.560318 - 0.970499i) q^{31} +(-2.84637 - 4.88858i) q^{32} +(-11.5151 - 2.03042i) q^{33} +(-0.206785 - 5.79963i) q^{34} +(1.00417 + 2.75893i) q^{35} +(6.62035 + 9.78410i) q^{36} -11.0692i q^{37} +(4.99940 - 3.60638i) q^{38} -2.48327i q^{39} +(-1.18435 - 2.41479i) q^{40} +(1.74742 + 4.80099i) q^{41} +(-13.0230 + 0.464335i) q^{42} +(-2.92630 - 0.515985i) q^{43} +(-4.59650 + 6.34610i) q^{44} +(2.80839 + 4.86428i) q^{45} +(-2.77709 - 2.16642i) q^{46} +(2.23924 + 2.66862i) q^{47} +(11.8166 - 1.69607i) q^{48} +(1.26648 - 2.19361i) q^{49} +(2.17376 + 5.36892i) q^{50} +(11.5082 + 4.18863i) q^{51} +(-1.49681 - 0.727326i) q^{52} +(-4.27071 + 0.753042i) q^{53} +(-11.9982 + 2.55948i) q^{54} +(-2.39478 + 2.85399i) q^{55} +(-3.53444 + 7.98571i) q^{56} +(3.09491 + 12.6352i) q^{57} +(-0.594368 + 4.25176i) q^{58} +(0.677042 + 0.568105i) q^{59} +(5.66143 - 0.404230i) q^{60} +(-1.74615 - 9.90290i) q^{61} +(0.488630 - 1.50761i) q^{62} +(6.23753 - 17.1375i) q^{63} +(2.43864 - 7.61925i) q^{64} +(-0.685231 - 0.395618i) q^{65} +(-8.77304 - 14.0169i) q^{66} +(-6.32640 + 5.30848i) q^{67} +(5.89535 - 5.70980i) q^{68} +(6.43701 - 3.71641i) q^{69} +(-1.94662 + 3.66754i) q^{70} +(1.66114 - 9.42079i) q^{71} +(-4.00606 + 16.2193i) q^{72} +(2.43877 - 0.887641i) q^{73} +(11.6257 - 10.4832i) q^{74} -12.2235 q^{75} +(8.52243 + 1.83526i) q^{76} +12.0968 q^{77} +(2.60811 - 2.35182i) q^{78} +(3.07726 - 1.12003i) q^{79} +(1.41452 - 3.53085i) q^{80} +(1.41857 - 8.04512i) q^{81} +(-3.38743 + 6.38210i) q^{82} +(-10.7084 + 6.18250i) q^{83} +(-12.8213 - 13.2380i) q^{84} +(2.98921 - 2.50824i) q^{85} +(-2.22947 - 3.56208i) q^{86} +(-7.84597 - 4.52987i) q^{87} +(-11.0183 + 1.18258i) q^{88} +(-0.254375 + 0.698890i) q^{89} +(-2.44909 + 7.55636i) q^{90} +(0.446118 + 2.53006i) q^{91} +(-0.354750 - 4.96844i) q^{92} +(2.56199 + 2.14976i) q^{93} +(-0.682075 + 4.87917i) q^{94} +(3.97961 + 1.15896i) q^{95} +(12.9724 + 10.8043i) q^{96} +(-6.10468 + 7.27528i) q^{97} +(3.50333 - 0.747341i) q^{98} +(22.7906 - 4.01859i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Introduction

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