LMFDB - Embedded newform 680.2.f.e.341.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(341,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.341"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [30,0,0,-2,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			341.4
Character	$\chi$	$=$	680.341
Dual form			680.2.f.e.341.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25557 + 0.650807i) q^{2} +2.99039i q^{3} +(1.15290 - 1.63426i) q^{4} +1.00000i q^{5} +(-1.94617 - 3.75464i) q^{6} +4.36351 q^{7} +(-0.383952 + 2.80225i) q^{8} -5.94243 q^{9} +(-0.650807 - 1.25557i) q^{10} -4.18839i q^{11} +(4.88709 + 3.44762i) q^{12} +4.81117i q^{13} +(-5.47868 + 2.83980i) q^{14} -2.99039 q^{15} +(-1.34164 - 3.76829i) q^{16} +1.00000 q^{17} +(7.46112 - 3.86737i) q^{18} +7.77516i q^{19} +(1.63426 + 1.15290i) q^{20} +13.0486i q^{21} +(2.72584 + 5.25881i) q^{22} -4.68001 q^{23} +(-8.37980 - 1.14817i) q^{24} -1.00000 q^{25} +(-3.13114 - 6.04075i) q^{26} -8.79900i q^{27} +(5.03069 - 7.13113i) q^{28} +2.81555i q^{29} +(3.75464 - 1.94617i) q^{30} +0.493346 q^{31} +(4.13695 + 3.85819i) q^{32} +12.5249 q^{33} +(-1.25557 + 0.650807i) q^{34} +4.36351i q^{35} +(-6.85102 + 9.71150i) q^{36} -3.31941i q^{37} +(-5.06013 - 9.76224i) q^{38} -14.3873 q^{39} +(-2.80225 - 0.383952i) q^{40} +3.11630 q^{41} +(-8.49212 - 16.3834i) q^{42} +11.3358i q^{43} +(-6.84494 - 4.82880i) q^{44} -5.94243i q^{45} +(5.87607 - 3.04579i) q^{46} -4.84720 q^{47} +(11.2686 - 4.01204i) q^{48} +12.0402 q^{49} +(1.25557 - 0.650807i) q^{50} +2.99039i q^{51} +(7.86273 + 5.54680i) q^{52} -6.60759i q^{53} +(5.72645 + 11.0477i) q^{54} +4.18839 q^{55} +(-1.67538 + 12.2276i) q^{56} -23.2508 q^{57} +(-1.83238 - 3.53511i) q^{58} -13.5676i q^{59} +(-3.44762 + 4.88709i) q^{60} -6.61720i q^{61} +(-0.619430 + 0.321073i) q^{62} -25.9298 q^{63} +(-7.70516 - 2.15186i) q^{64} -4.81117 q^{65} +(-15.7259 + 8.15131i) q^{66} +0.623932i q^{67} +(1.15290 - 1.63426i) q^{68} -13.9951i q^{69} +(-2.83980 - 5.47868i) q^{70} -1.10092 q^{71} +(2.28161 - 16.6521i) q^{72} +1.75123 q^{73} +(2.16030 + 4.16774i) q^{74} -2.99039i q^{75} +(12.7067 + 8.96398i) q^{76} -18.2761i q^{77} +(18.0642 - 9.36334i) q^{78} -3.27909 q^{79} +(3.76829 - 1.34164i) q^{80} +8.48515 q^{81} +(-3.91272 + 2.02811i) q^{82} -3.08423i q^{83} +(21.3249 + 15.0437i) q^{84} +1.00000i q^{85} +(-7.37739 - 14.2328i) q^{86} -8.41957 q^{87} +(11.7369 + 1.60814i) q^{88} +4.89985 q^{89} +(3.86737 + 7.46112i) q^{90} +20.9936i q^{91} +(-5.39559 + 7.64838i) q^{92} +1.47530i q^{93} +(6.08599 - 3.15460i) q^{94} -7.77516 q^{95} +(-11.5375 + 12.3711i) q^{96} +15.8455 q^{97} +(-15.1173 + 7.83586i) q^{98} +24.8892i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{4} - 8 q^{6} + 12 q^{7} + 6 q^{8} - 36 q^{9} + 2 q^{10} + 8 q^{12} - 10 q^{14} - 14 q^{15} - 2 q^{16} + 30 q^{17} + 6 q^{18} + 4 q^{20} - 6 q^{22} + 12 q^{23} - 46 q^{24} - 30 q^{25} + 4 q^{26}+ \cdots - 16 q^{98}+O(q^{100}) $ 30 * q - 2 * q^4 - 8 * q^6 + 12 * q^7 + 6 * q^8 - 36 * q^9 + 2 * q^10 + 8 * q^12 - 10 * q^14 - 14 * q^15 - 2 * q^16 + 30 * q^17 + 6 * q^18 + 4 * q^20 - 6 * q^22 + 12 * q^23 - 46 * q^24 - 30 * q^25 + 4 * q^26 + 22 * q^28 + 6 * q^30 - 26 * q^31 - 10 * q^32 + 12 * q^33 + 32 * q^36 + 6 * q^38 + 2 * q^39 + 4 * q^40 - 20 * q^41 + 48 * q^42 + 22 * q^44 + 38 * q^46 - 22 * q^47 + 24 * q^48 + 30 * q^49 + 48 * q^52 - 66 * q^54 + 32 * q^55 - 6 * q^56 - 26 * q^57 - 32 * q^58 - 14 * q^60 - 46 * q^62 - 4 * q^63 - 50 * q^64 + 6 * q^65 - 44 * q^66 - 2 * q^68 - 2 * q^70 + 58 * q^71 - 14 * q^72 - 18 * q^73 + 56 * q^74 - 6 * q^76 + 12 * q^78 - 60 * q^79 - 42 * q^81 - 24 * q^82 + 72 * q^84 + 48 * q^86 + 6 * q^87 + 18 * q^88 + 6 * q^89 - 14 * q^90 + 74 * q^92 - 16 * q^94 - 30 * q^95 + 22 * q^96 + 38 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	−1.25557	+	0.650807i	−0.887820	+	0.460190i
$2$	−1.25557	+	0.650807i	−0.887820	+	0.460190i
$3$			2.99039i			1.72650i	0.504775	+	0.863251i	$0.331575\pi$
$3$			2.99039i			1.72650i	−0.504775	+	0.863251i	$0.668425\pi$
$4$	1.15290	−	1.63426i	0.576450	−	0.817132i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−1.94617	−	3.75464i	−0.794519	−	1.53282i
$7$	4.36351			1.64925			0.824626	−	0.565678i	$-0.191386\pi$
$7$	4.36351			1.64925			0.824626	+	0.565678i	$0.191386\pi$
$8$	−0.383952	+	2.80225i	−0.135748	+	0.990743i
$9$	−5.94243			−1.98081
$10$	−0.650807	−	1.25557i	−0.205803	−	0.397045i
$11$		−	4.18839i		−	1.26285i	−0.775438	−	0.631424i	$-0.782471\pi$
$11$		−	4.18839i		−	1.26285i	0.775438	−	0.631424i	$-0.217529\pi$
$12$	4.88709	+	3.44762i	1.41078	+	0.995242i
$13$			4.81117i			1.33438i	0.744888	+	0.667189i	$0.232503\pi$
$13$			4.81117i			1.33438i	−0.744888	+	0.667189i	$0.767497\pi$
$14$	−5.47868	+	2.83980i	−1.46424	+	0.758970i
$15$	−2.99039			−0.772115
$16$	−1.34164	−	3.76829i	−0.335411	−	0.942072i
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	7.46112	−	3.86737i	1.75860	−	0.911549i
$19$			7.77516i			1.78374i	0.452288	+	0.891872i	$0.350608\pi$
$19$			7.77516i			1.78374i	−0.452288	+	0.891872i	$0.649392\pi$
$20$	1.63426	+	1.15290i	0.365433	+	0.257796i
$21$			13.0486i			2.84744i
$22$	2.72584	+	5.25881i	0.581150	+	1.12118i
$23$	−4.68001			−0.975851			−0.487925	−	0.872885i	$-0.662246\pi$
$23$	−4.68001			−0.975851			−0.487925	+	0.872885i	$0.662246\pi$
$24$	−8.37980	−	1.14817i	−1.71052	−	0.234368i
$25$	−1.00000			−0.200000
$26$	−3.13114	−	6.04075i	−0.614068	−	1.18469i
$27$		−	8.79900i		−	1.69337i
$28$	5.03069	−	7.13113i	0.950711	−	1.34766i
$29$			2.81555i			0.522834i	0.965226	+	0.261417i	$0.0841897\pi$
$29$			2.81555i			0.522834i	−0.965226	+	0.261417i	$0.915810\pi$
$30$	3.75464	−	1.94617i	0.685499	−	0.355320i
$31$	0.493346			0.0886076			0.0443038	−	0.999018i	$-0.485893\pi$
$31$	0.493346			0.0886076			0.0443038	+	0.999018i	$0.485893\pi$
$32$	4.13695	+	3.85819i	0.731317	+	0.682038i
$33$	12.5249			2.18031
$34$	−1.25557	+	0.650807i	−0.215328	+	0.111613i
$35$			4.36351i			0.737568i
$36$	−6.85102	+	9.71150i	−1.14184	+	1.61858i
$37$		−	3.31941i		−	0.545707i	−0.962056	−	0.272854i	$-0.912032\pi$
$37$		−	3.31941i		−	0.545707i	0.962056	−	0.272854i	$-0.0879675\pi$
$38$	−5.06013	−	9.76224i	−0.820862	−	1.58364i
$39$	−14.3873			−2.30381
$40$	−2.80225	−	0.383952i	−0.443074	−	0.0607082i
$41$	3.11630			0.486684			0.243342	−	0.969941i	$-0.421756\pi$
$41$	3.11630			0.486684			0.243342	+	0.969941i	$0.421756\pi$
$42$	−8.49212	−	16.3834i	−1.31036	−	2.52801i
$43$			11.3358i			1.72869i	0.502903	+	0.864343i	$0.332265\pi$
$43$			11.3358i			1.72869i	−0.502903	+	0.864343i	$0.667735\pi$
$44$	−6.84494	−	4.82880i	−1.03191	−	0.727969i
$45$		−	5.94243i		−	0.885845i
$46$	5.87607	−	3.04579i	0.866380	−	0.449077i
$47$	−4.84720			−0.707037			−0.353519	−	0.935427i	$-0.615015\pi$
$47$	−4.84720			−0.707037			−0.353519	+	0.935427i	$0.615015\pi$
$48$	11.2686	−	4.01204i	1.62649	−	0.579088i
$49$	12.0402			1.72003
$50$	1.25557	−	0.650807i	0.177564	−	0.0920380i
$51$			2.99039i			0.418738i
$52$	7.86273	+	5.54680i	1.09036	+	0.769202i
$53$		−	6.60759i		−	0.907622i	−0.891098	−	0.453811i	$-0.850064\pi$
$53$		−	6.60759i		−	0.907622i	0.891098	−	0.453811i	$-0.149936\pi$
$54$	5.72645	+	11.0477i	0.779271	+	1.50341i
$55$	4.18839			0.564763
$56$	−1.67538	+	12.2276i	−0.223882	+	1.63399i
$57$	−23.2508			−3.07964
$58$	−1.83238	−	3.53511i	−0.240603	−	0.464182i
$59$		−	13.5676i		−	1.76636i	−0.469037	−	0.883178i	$-0.655399\pi$
$59$		−	13.5676i		−	1.76636i	0.469037	−	0.883178i	$-0.344601\pi$
$60$	−3.44762	+	4.88709i	−0.445086	+	0.630920i
$61$		−	6.61720i		−	0.847246i	−0.905839	−	0.423623i	$-0.860758\pi$
$61$		−	6.61720i		−	0.847246i	0.905839	−	0.423623i	$-0.139242\pi$
$62$	−0.619430	+	0.321073i	−0.0786677	+	0.0407764i
$63$	−25.9298			−3.26685
$64$	−7.70516	−	2.15186i	−0.963145	−	0.268982i
$65$	−4.81117			−0.596752
$66$	−15.7259	+	8.15131i	−1.93572	+	1.00336i
$67$			0.623932i			0.0762254i	0.999273	+	0.0381127i	$0.0121346\pi$
$67$			0.623932i			0.0762254i	−0.999273	+	0.0381127i	$0.987865\pi$
$68$	1.15290	−	1.63426i	0.139810	−	0.198184i
$69$		−	13.9951i		−	1.68481i
$70$	−2.83980	−	5.47868i	−0.339422	−	0.654828i
$71$	−1.10092			−0.130655			−0.0653277	−	0.997864i	$-0.520809\pi$
$71$	−1.10092			−0.130655			−0.0653277	+	0.997864i	$0.520809\pi$
$72$	2.28161	−	16.6521i	0.268890	−	1.96247i
$73$	1.75123			0.204965			0.102483	−	0.994735i	$-0.467321\pi$
$73$	1.75123			0.204965			0.102483	+	0.994735i	$0.467321\pi$
$74$	2.16030	+	4.16774i	0.251129	+	0.484490i
$75$		−	2.99039i		−	0.345300i
$76$	12.7067	+	8.96398i	1.45756	+	1.02824i
$77$		−	18.2761i		−	2.08275i
$78$	18.0642	−	9.36334i	2.04537	−	1.06019i
$79$	−3.27909			−0.368927			−0.184463	−	0.982839i	$-0.559055\pi$
$79$	−3.27909			−0.368927			−0.184463	+	0.982839i	$0.559055\pi$
$80$	3.76829	−	1.34164i	0.421307	−	0.150000i
$81$	8.48515			0.942794
$82$	−3.91272	+	2.02811i	−0.432088	+	0.223967i
$83$		−	3.08423i		−	0.338539i	−0.985570	−	0.169269i	$-0.945859\pi$
$83$		−	3.08423i		−	0.338539i	0.985570	−	0.169269i	$-0.0541408\pi$
$84$	21.3249	+	15.0437i	2.32673	+	1.64140i
$85$			1.00000i			0.108465i
$86$	−7.37739	−	14.2328i	−0.795524	−	1.53476i
$87$	−8.41957			−0.902673
$88$	11.7369	+	1.60814i	1.25116	+	0.171429i
$89$	4.89985			0.519383			0.259691	−	0.965692i	$-0.416379\pi$
$89$	4.89985			0.519383			0.259691	+	0.965692i	$0.416379\pi$
$90$	3.86737	+	7.46112i	0.407657	+	0.786471i
$91$			20.9936i			2.20073i
$92$	−5.39559	+	7.64838i	−0.562529	+	0.797399i
$93$			1.47530i			0.152981i
$94$	6.08599	−	3.15460i	0.627722	−	0.325372i
$95$	−7.77516			−0.797715
$96$	−11.5375	+	12.3711i	−1.17754	+	1.26262i
$97$	15.8455			1.60887			0.804434	−	0.594042i	$-0.202469\pi$
$97$	15.8455			1.60887			0.804434	+	0.594042i	$0.202469\pi$
$98$	−15.1173	+	7.83586i	−1.52708	+	0.791542i
$99$			24.8892i			2.50146i
$100$	−1.15290	+	1.63426i	−0.115290	+	0.163426i
$101$			15.4817i			1.54048i	0.637753	+	0.770241i	$0.279864\pi$
$101$			15.4817i			1.54048i	−0.637753	+	0.770241i	$0.720136\pi$
$102$	−1.94617	−	3.75464i	−0.192699	−	0.371764i
$103$	−13.9708			−1.37658			−0.688291	−	0.725435i	$-0.741639\pi$
$103$	−13.9708			−1.37658			−0.688291	+	0.725435i	$0.741639\pi$
$104$	−13.4821	−	1.84726i	−1.32203	−	0.181139i
$105$	−13.0486			−1.27341
$106$	4.30027	+	8.29627i	0.417679	+	0.805805i
$107$			2.65718i			0.256879i	0.991717	+	0.128440i	$0.0409968\pi$
$107$			2.65718i			0.256879i	−0.991717	+	0.128440i	$0.959003\pi$
$108$	−14.3799	−	10.1444i	−1.38371	−	0.976142i
$109$		−	1.67198i		−	0.160147i	−0.996789	−	0.0800734i	$-0.974485\pi$
$109$		−	1.67198i		−	0.160147i	0.996789	−	0.0800734i	$-0.0255155\pi$
$110$	−5.25881	+	2.72584i	−0.501408	+	0.259898i
$111$	9.92632			0.942165
$112$	−5.85428	−	16.4430i	−0.553177	−	1.55371i
$113$	14.1116			1.32750			0.663752	−	0.747952i	$-0.268963\pi$
$113$	14.1116			1.32750			0.663752	+	0.747952i	$0.268963\pi$
$114$	29.1929	−	15.1318i	2.73417	−	1.41722i
$115$		−	4.68001i		−	0.436414i
$116$	4.60135	+	3.24604i	0.427224	+	0.301387i
$117$		−	28.5900i		−	2.64315i
$118$	8.82992	+	17.0351i	0.812860	+	1.56821i
$119$	4.36351			0.400002
$120$	1.14817	−	8.37980i	0.104813	−	0.764968i
$121$	−6.54263			−0.594785
$122$	4.30652	+	8.30834i	0.389894	+	0.752202i
$123$			9.31894i			0.840260i
$124$	0.568779	−	0.806259i	0.0510779	−	0.0724042i
$125$		−	1.00000i		−	0.0894427i
$126$	32.5567	−	16.8753i	2.90038	−	1.50337i
$127$	5.77442			0.512397			0.256198	−	0.966624i	$-0.417530\pi$
$127$	5.77442			0.512397			0.256198	+	0.966624i	$0.417530\pi$
$128$	11.0748	−	2.31277i	0.978883	−	0.204422i
$129$	−33.8983			−2.98458
$130$	6.04075	−	3.13114i	0.529809	−	0.274619i
$131$		−	6.58384i		−	0.575232i	−0.957746	−	0.287616i	$-0.907137\pi$
$131$		−	6.58384i		−	0.575232i	0.957746	−	0.287616i	$-0.0928628\pi$
$132$	14.4400	−	20.4690i	1.25684	−	1.78160i
$133$			33.9270i			2.94184i
$134$	−0.406059	−	0.783389i	−0.0350782	−	0.0676745i
$135$	8.79900			0.757297
$136$	−0.383952	+	2.80225i	−0.0329236	+	0.240291i
$137$	10.4560			0.893314			0.446657	−	0.894705i	$-0.352614\pi$
$137$	10.4560			0.893314			0.446657	+	0.894705i	$0.352614\pi$
$138$	9.10809	+	17.5717i	0.775332	+	1.49581i
$139$		−	10.0894i		−	0.855770i	−0.903833	−	0.427885i	$-0.859259\pi$
$139$		−	10.0894i		−	0.855770i	0.903833	−	0.427885i	$-0.140741\pi$
$140$	7.13113	+	5.03069i	0.602691	+	0.425171i
$141$		−	14.4950i		−	1.22070i
$142$	1.38228	−	0.716488i	0.115999	−	0.0601263i
$143$	20.1511			1.68512
$144$	7.97262	+	22.3928i	0.664385	+	1.86606i
$145$	−2.81555			−0.233818
$146$	−2.19878	+	1.13971i	−0.181972	+	0.0943231i
$147$			36.0049i			2.96964i
$148$	−5.42479	−	3.82695i	−0.445915	−	0.314573i
$149$			18.8017i			1.54029i	0.637866	+	0.770147i	$0.279817\pi$
$149$			18.8017i			1.54029i	−0.637866	+	0.770147i	$0.720183\pi$
$150$	1.94617	+	3.75464i	0.158904	+	0.306565i
$151$	17.1539			1.39596			0.697980	−	0.716117i	$-0.254082\pi$
$151$	17.1539			1.39596			0.697980	+	0.716117i	$0.254082\pi$
$152$	−21.7879	−	2.98529i	−1.76723	−	0.242139i
$153$	−5.94243			−0.480417
$154$	11.8942	+	22.9469i	0.958463	+	1.84911i
$155$			0.493346i			0.0396265i
$156$	−16.5871	+	23.5126i	−1.32803	+	1.88252i
$157$		−	17.1493i		−	1.36866i	−0.729170	−	0.684332i	$-0.760094\pi$
$157$		−	17.1493i		−	1.36866i	0.729170	−	0.684332i	$-0.239906\pi$
$158$	4.11712	−	2.13406i	0.327541	−	0.169777i
$159$	19.7593			1.56701
$160$	−3.85819	+	4.13695i	−0.305017	+	0.327055i
$161$	−20.4213			−1.60942
$162$	−10.6537	+	5.52220i	−0.837032	+	0.433865i
$163$		−	9.99860i		−	0.783151i	−0.920146	−	0.391575i	$-0.871930\pi$
$163$		−	9.99860i		−	0.783151i	0.920146	−	0.391575i	$-0.128070\pi$
$164$	3.59278	−	5.09285i	0.280549	−	0.397685i
$165$			12.5249i			0.975064i
$166$	2.00724	+	3.87247i	0.155792	+	0.300562i
$167$	3.26637			0.252759			0.126380	−	0.991982i	$-0.459664\pi$
$167$	3.26637			0.252759			0.126380	+	0.991982i	$0.459664\pi$
$168$	−36.5654	−	5.01004i	−2.82108	−	0.386533i
$169$	−10.1473			−0.780565
$170$	−0.650807	−	1.25557i	−0.0499146	−	0.0962976i
$171$		−	46.2033i		−	3.53326i
$172$	18.5256	+	13.0690i	1.41257	+	0.996501i
$173$			8.32496i			0.632935i	0.948603	+	0.316468i	$0.102497\pi$
$173$			8.32496i			0.632935i	−0.948603	+	0.316468i	$0.897503\pi$
$174$	10.5713	−	5.47952i	0.801412	−	0.415401i
$175$	−4.36351			−0.329850
$176$	−15.7831	+	5.61933i	−1.18969	+	0.423573i
$177$	40.5725			3.04962
$178$	−6.15209	+	3.18886i	−0.461119	+	0.239015i
$179$			15.9643i			1.19323i	0.802528	+	0.596614i	$0.203488\pi$
$179$			15.9643i			1.19323i	−0.802528	+	0.596614i	$0.796512\pi$
$180$	−9.71150	−	6.85102i	−0.723852	−	0.510645i
$181$		−	7.10280i		−	0.527947i	−0.964530	−	0.263974i	$-0.914967\pi$
$181$		−	7.10280i		−	0.527947i	0.964530	−	0.263974i	$-0.0850332\pi$
$182$	−13.6628	−	26.3589i	−1.01275	−	1.95385i
$183$	19.7880			1.46277
$184$	1.79690	−	13.1146i	0.132469	−	0.966818i
$185$	3.31941			0.244048
$186$	−0.960134	−	1.85234i	−0.0704005	−	0.135820i
$187$		−	4.18839i		−	0.306286i
$188$	−5.58834	+	7.92162i	−0.407572	+	0.577743i
$189$		−	38.3945i		−	2.79279i
$190$	9.76224	−	5.06013i	0.708227	−	0.367100i
$191$	−6.67502			−0.482987			−0.241494	−	0.970402i	$-0.577637\pi$
$191$	−6.67502			−0.482987			−0.241494	+	0.970402i	$0.577637\pi$
$192$	6.43489	−	23.0414i	0.464398	−	1.66287i
$193$	9.52535			0.685650			0.342825	−	0.939399i	$-0.388616\pi$
$193$	9.52535			0.685650			0.342825	+	0.939399i	$0.388616\pi$
$194$	−19.8951	+	10.3124i	−1.42839	+	0.740385i
$195$		−	14.3873i		−	1.03029i
$196$	13.8812	−	19.6769i	0.991512	−	1.40549i
$197$			9.72890i			0.693156i	0.938021	+	0.346578i	$0.112656\pi$
$197$			9.72890i			0.693156i	−0.938021	+	0.346578i	$0.887344\pi$
$198$	−16.1981	−	31.2501i	−1.15115	−	2.22085i
$199$	−5.98787			−0.424469			−0.212234	−	0.977219i	$-0.568074\pi$
$199$	−5.98787			−0.424469			−0.212234	+	0.977219i	$0.568074\pi$
$200$	0.383952	−	2.80225i	0.0271495	−	0.198149i
$201$	−1.86580			−0.131603
$202$	−10.0756	−	19.4383i	−0.708915	−	1.36767i
$203$			12.2857i			0.862284i
$204$	4.88709	+	3.44762i	0.342165	+	0.241382i
$205$			3.11630i			0.217652i
$206$	17.5413	−	9.09229i	1.22216	−	0.633490i
$207$	27.8106			1.93297
$208$	18.1299	−	6.45488i	1.25708	−	0.447565i
$209$	32.5654			2.25260
$210$	16.3834	−	8.49212i	1.13056	−	0.586012i
$211$		−	6.99229i		−	0.481369i	−0.970603	−	0.240685i	$-0.922628\pi$
$211$		−	6.99229i		−	0.481369i	0.970603	−	0.240685i	$-0.0773719\pi$
$212$	−10.7986	−	7.61789i	−0.741648	−	0.523199i
$213$		−	3.29218i		−	0.225577i
$214$	−1.72931	−	3.33627i	−0.118213	−	0.228063i
$215$	−11.3358			−0.773092
$216$	24.6570	+	3.37839i	1.67769	+	0.229871i
$217$	2.15272			0.146136
$218$	1.08814	+	2.09929i	0.0736980	+	0.142182i
$219$			5.23685i			0.353873i
$220$	4.82880	−	6.84494i	0.325557	−	0.461486i
$221$			4.81117i			0.323634i
$222$	−12.4632	+	6.46012i	−0.836473	+	0.433575i
$223$	3.00057			0.200933			0.100467	−	0.994940i	$-0.467966\pi$
$223$	3.00057			0.200933			0.100467	+	0.994940i	$0.467966\pi$
$224$	18.0516	+	16.8352i	1.20613	+	1.12485i
$225$	5.94243			0.396162
$226$	−17.7180	+	9.18391i	−1.17859	+	0.610905i
$227$			9.76049i			0.647826i	0.946087	+	0.323913i	$0.104999\pi$
$227$			9.76049i			0.647826i	−0.946087	+	0.323913i	$0.895001\pi$
$228$	−26.8058	+	37.9979i	−1.77526	+	2.51647i
$229$		−	7.46158i		−	0.493075i	−0.969133	−	0.246537i	$-0.920707\pi$
$229$		−	7.46158i		−	0.493075i	0.969133	−	0.246537i	$-0.0792928\pi$
$230$	3.04579	+	5.87607i	0.200833	+	0.387457i
$231$	54.6526			3.59588
$232$	−7.88985	−	1.08103i	−0.517994	−	0.0709734i
$233$	8.79729			0.576330			0.288165	−	0.957581i	$-0.406955\pi$
$233$	8.79729			0.576330			0.288165	+	0.957581i	$0.406955\pi$
$234$	18.6066	+	35.8967i	1.21635	+	2.34664i
$235$		−	4.84720i		−	0.316197i
$236$	−22.1731	−	15.6421i	−1.44335	−	1.01822i
$237$		−	9.80577i		−	0.636953i
$238$	−5.47868	+	2.83980i	−0.355130	+	0.184077i
$239$	8.87913			0.574343			0.287172	−	0.957879i	$-0.407285\pi$
$239$	8.87913			0.574343			0.287172	+	0.957879i	$0.407285\pi$
$240$	4.01204	+	11.2686i	0.258976	+	0.727388i
$241$	−1.28824			−0.0829830			−0.0414915	−	0.999139i	$-0.513211\pi$
$241$	−1.28824			−0.0829830			−0.0414915	+	0.999139i	$0.513211\pi$
$242$	8.21471	−	4.25799i	0.528062	−	0.273714i
$243$		−	1.02310i		−	0.0656319i
$244$	−10.8143	−	7.62897i	−0.692312	−	0.488395i
$245$			12.0402i			0.769222i
$246$	−6.06483	−	11.7006i	−0.386680	−	0.746000i
$247$	−37.4076			−2.38019
$248$	−0.189421	+	1.38248i	−0.0120283	+	0.0877874i
$249$	9.22306			0.584488
$250$	0.650807	+	1.25557i	0.0411607	+	0.0794091i
$251$		−	2.81168i		−	0.177472i	−0.996055	−	0.0887358i	$-0.971717\pi$
$251$		−	2.81168i		−	0.177472i	0.996055	−	0.0887358i	$-0.0282827\pi$
$252$	−29.8945	+	42.3762i	−1.88318	+	2.66945i
$253$			19.6017i			1.23235i
$254$	−7.25017	+	3.75803i	−0.454916	+	0.235800i
$255$	−2.99039			−0.187265
$256$	−12.4000	+	10.1114i	−0.774999	+	0.631962i
$257$	−7.05348			−0.439984			−0.219992	−	0.975502i	$-0.570603\pi$
$257$	−7.05348			−0.439984			−0.219992	+	0.975502i	$0.570603\pi$
$258$	42.5616	−	22.0613i	2.64977	−	1.37347i
$259$		−	14.4843i		−	0.900009i
$260$	−5.54680	+	7.86273i	−0.343998	+	0.487626i
$261$		−	16.7312i		−	1.03563i
$262$	4.28481	+	8.26645i	0.264716	+	0.510703i
$263$	−27.9727			−1.72487			−0.862434	−	0.506169i	$-0.831061\pi$
$263$	−27.9727			−1.72487			−0.862434	+	0.506169i	$0.831061\pi$
$264$	−4.80897	+	35.0979i	−0.295972	+	2.16013i
$265$	6.60759			0.405901
$266$	−22.0799	−	42.5976i	−1.35381	−	2.61183i
$267$			14.6525i			0.896716i
$268$	1.01967	+	0.719331i	0.0622863	+	0.0439401i
$269$		−	3.16241i		−	0.192815i	−0.995342	−	0.0964077i	$-0.969265\pi$
$269$		−	3.16241i		−	0.192815i	0.995342	−	0.0964077i	$-0.0307353\pi$
$270$	−11.0477	+	5.72645i	−0.672344	+	0.348501i
$271$	−11.8882			−0.722158			−0.361079	−	0.932535i	$-0.617592\pi$
$271$	−11.8882			−0.722158			−0.361079	+	0.932535i	$0.617592\pi$
$272$	−1.34164	−	3.76829i	−0.0813491	−	0.228486i
$273$	−62.7790			−3.79956
$274$	−13.1282	+	6.80482i	−0.793102	+	0.411094i
$275$			4.18839i			0.252570i
$276$	−22.8716	−	16.1349i	−1.37671	−	0.971207i
$277$		−	5.65931i		−	0.340035i	−0.985441	−	0.170018i	$-0.945618\pi$
$277$		−	5.65931i		−	0.340035i	0.985441	−	0.170018i	$-0.0543825\pi$
$278$	6.56624	+	12.6679i	0.393817	+	0.759770i
$279$	−2.93167			−0.175515
$280$	−12.2276	−	1.67538i	−0.730741	−	0.100123i
$281$	7.47960			0.446196			0.223098	−	0.974796i	$-0.428383\pi$
$281$	7.47960			0.446196			0.223098	+	0.974796i	$0.428383\pi$
$282$	9.43347	+	18.1995i	0.561755	+	1.08376i
$283$			23.5049i			1.39722i	0.715502	+	0.698611i	$0.246198\pi$
$283$			23.5049i			1.39722i	−0.715502	+	0.698611i	$0.753802\pi$
$284$	−1.26925	+	1.79920i	−0.0753163	+	0.106763i
$285$		−	23.2508i		−	1.37726i
$286$	−25.3010	+	13.1145i	−1.49608	+	0.775474i
$287$	13.5980			0.802664
$288$	−24.5835	−	22.9270i	−1.44860	−	1.35099i
$289$	1.00000			0.0588235
$290$	3.53511	−	1.83238i	0.207589	−	0.107601i
$291$			47.3842i			2.77771i
$292$	2.01899	−	2.86197i	0.118152	−	0.167484i
$293$		−	21.4042i		−	1.25045i	−0.780445	−	0.625224i	$-0.785007\pi$
$293$		−	21.4042i		−	1.25045i	0.780445	−	0.625224i	$-0.214993\pi$
$294$	−23.4323	−	45.2066i	−1.36660	−	2.63651i
$295$	13.5676			0.789939
$296$	9.30180	+	1.27449i	0.540656	+	0.0740785i
$297$	−36.8537			−2.13847
$298$	−12.2363	−	23.6068i	−0.708828	−	1.36750i
$299$		−	22.5163i		−	1.30215i
$300$	−4.88709	−	3.44762i	−0.282156	−	0.199048i
$301$			49.4637i			2.85104i
$302$	−21.5378	+	11.1639i	−1.23936	+	0.642407i
$303$	−46.2962			−2.65965
$304$	29.2990	−	10.4315i	1.68042	−	0.598287i
$305$	6.61720			0.378900
$306$	7.46112	−	3.86737i	0.426524	−	0.221083i
$307$			19.5375i			1.11507i	0.830155	+	0.557533i	$0.188252\pi$
$307$			19.5375i			1.11507i	−0.830155	+	0.557533i	$0.811748\pi$
$308$	−29.8680	−	21.0705i	−1.70189	−	1.20060i
$309$		−	41.7781i		−	2.37667i
$310$	−0.321073	−	0.619430i	−0.0182357	−	0.0351812i
$311$	−17.4418			−0.989032			−0.494516	−	0.869168i	$-0.664655\pi$
$311$	−17.4418			−0.989032			−0.494516	+	0.869168i	$0.664655\pi$
$312$	5.52402	−	40.3167i	0.312736	−	2.28248i
$313$	20.1621			1.13963			0.569813	−	0.821774i	$-0.307016\pi$
$313$	20.1621			1.13963			0.569813	+	0.821774i	$0.307016\pi$
$314$	11.1609	+	21.5321i	0.629846	+	1.21513i
$315$		−	25.9298i		−	1.46098i
$316$	−3.78047	+	5.35891i	−0.212668	+	0.301462i
$317$			9.04681i			0.508119i	0.967189	+	0.254060i	$0.0817660\pi$
$317$			9.04681i			0.508119i	−0.967189	+	0.254060i	$0.918234\pi$
$318$	−24.8091	+	12.8595i	−1.39122	+	0.721123i
$319$	11.7926			0.660259
$320$	2.15186	−	7.70516i	0.120292	−	0.430732i
$321$	−7.94600			−0.443502
$322$	25.6403	−	13.2903i	1.42888	−	0.740641i
$323$			7.77516i			0.432622i
$324$	9.78253	−	13.8670i	0.543474	−	0.770388i
$325$		−	4.81117i		−	0.266876i
$326$	6.50716	+	12.5539i	0.360398	+	0.695297i
$327$	4.99987			0.276494
$328$	−1.19651	+	8.73263i	−0.0660662	+	0.482179i
$329$	−21.1508			−1.16608
$330$	−8.15131	−	15.7259i	−0.448715	−	0.865682i
$331$		−	13.8518i		−	0.761365i	−0.924706	−	0.380683i	$-0.875689\pi$
$331$		−	13.8518i		−	0.761365i	0.924706	−	0.380683i	$-0.124311\pi$
$332$	−5.04046	−	3.55581i	−0.276631	−	0.195151i
$333$			19.7253i			1.08094i
$334$	−4.10115	+	2.12578i	−0.224405	+	0.116317i
$335$	−0.623932			−0.0340890
$336$	49.1709	−	17.5066i	2.68249	−	0.955061i
$337$	13.4344			0.731817			0.365908	−	0.930651i	$-0.380758\pi$
$337$	13.4344			0.731817			0.365908	+	0.930651i	$0.380758\pi$
$338$	12.7407	−	6.60397i	0.693002	−	0.359208i
$339$			42.1991i			2.29194i
$340$	1.63426	+	1.15290i	0.0886305	+	0.0625248i
$341$		−	2.06633i		−	0.111898i
$342$	30.0695	+	58.0114i	1.62597	+	3.13690i
$343$	21.9931			1.18751
$344$	−31.7656	−	4.35239i	−1.71268	−	0.234665i
$345$	13.9951			0.753469
$346$	−5.41795	−	10.4526i	−0.291271	−	0.561933i
$347$			35.7242i			1.91778i	0.283784	+	0.958888i	$0.408410\pi$
$347$			35.7242i			1.91778i	−0.283784	+	0.958888i	$0.591590\pi$
$348$	−9.70693	+	13.7598i	−0.520346	+	0.737604i
$349$		−	31.2387i		−	1.67217i	−0.548600	−	0.836085i	$-0.684839\pi$
$349$		−	31.2387i		−	1.67217i	0.548600	−	0.836085i	$-0.315161\pi$
$350$	5.47868	−	2.83980i	0.292848	−	0.151794i
$351$	42.3335			2.25959
$352$	16.1596	−	17.3272i	0.861310	−	0.923542i
$353$	17.1251			0.911480			0.455740	−	0.890113i	$-0.349375\pi$
$353$	17.1251			0.911480			0.455740	+	0.890113i	$0.349375\pi$
$354$	−50.9416	+	26.4049i	−2.70751	+	1.40340i
$355$		−	1.10092i		−	0.0584309i
$356$	5.64903	−	8.00765i	0.299398	−	0.424405i
$357$			13.0486i			0.690605i
$358$	−10.3897	−	20.0443i	−0.549112	−	1.05937i
$359$	3.17882			0.167772			0.0838859	−	0.996475i	$-0.473267\pi$
$359$	3.17882			0.167772			0.0838859	+	0.996475i	$0.473267\pi$
$360$	16.6521	+	2.28161i	0.877645	+	0.120251i
$361$	−41.4531			−2.18174
$362$	4.62255	+	8.91805i	0.242956	+	0.468722i
$363$		−	19.5650i		−	1.02690i
$364$	34.3091	+	24.2035i	1.79828	+	1.26861i
$365$			1.75123i			0.0916633i
$366$	−24.8452	+	12.8782i	−1.29868	+	0.673153i
$367$	2.79725			0.146015			0.0730076	−	0.997331i	$-0.476740\pi$
$367$	2.79725			0.146015			0.0730076	+	0.997331i	$0.476740\pi$
$368$	6.27891	+	17.6356i	0.327311	+	0.919321i
$369$	−18.5184			−0.964027
$370$	−4.16774	+	2.16030i	−0.216671	+	0.112308i
$371$		−	28.8323i		−	1.49690i
$372$	2.41103	+	1.70087i	0.125006	+	0.0881860i
$373$		−	23.0371i		−	1.19282i	−0.802681	−	0.596409i	$-0.796594\pi$
$373$		−	23.0371i		−	1.19282i	0.802681	−	0.596409i	$-0.203406\pi$
$374$	2.72584	+	5.25881i	0.140950	+	0.271927i
$375$	2.99039			0.154423
$376$	1.86109	−	13.5831i	0.0959786	−	0.700493i
$377$	−13.5461			−0.697658
$378$	24.9874	+	48.2069i	1.28521	+	2.47950i
$379$		−	9.09953i		−	0.467411i	−0.972307	−	0.233706i	$-0.924915\pi$
$379$		−	9.09953i		−	0.467411i	0.972307	−	0.233706i	$-0.0750852\pi$
$380$	−8.96398	+	12.7067i	−0.459843	+	0.651839i
$381$			17.2678i			0.884654i
$382$	8.38093	−	4.34415i	0.428806	−	0.222266i
$383$	11.4168			0.583373			0.291687	−	0.956514i	$-0.405784\pi$
$383$	11.4168			0.583373			0.291687	+	0.956514i	$0.405784\pi$
$384$	6.91609	+	33.1179i	0.352935	+	1.69004i
$385$	18.2761			0.931436
$386$	−11.9597	+	6.19917i	−0.608734	+	0.315529i
$387$		−	67.3619i		−	3.42420i
$388$	18.2683	−	25.8958i	0.927432	−	1.31466i
$389$			12.0723i			0.612090i	0.952017	+	0.306045i	$0.0990058\pi$
$389$			12.0723i			0.612090i	−0.952017	+	0.306045i	$0.900994\pi$
$390$	9.36334	+	18.0642i	0.474131	+	0.914716i
$391$	−4.68001			−0.236679
$392$	−4.62287	+	33.7397i	−0.233490	+	1.70411i
$393$	19.6882			0.993140
$394$	−6.33164	−	12.2153i	−0.318983	−	0.615398i
$395$		−	3.27909i		−	0.164989i
$396$	40.6756	+	28.6948i	2.04402	+	1.44197i
$397$			28.8479i			1.44783i	0.689887	+	0.723917i	$0.257660\pi$
$397$			28.8479i			1.44783i	−0.689887	+	0.723917i	$0.742340\pi$
$398$	7.51817	−	3.89695i	0.376852	−	0.195336i
$399$	−101.455			−5.07910
$400$	1.34164	+	3.76829i	0.0670822	+	0.188414i
$401$	19.8245			0.989988			0.494994	−	0.868896i	$-0.335170\pi$
$401$	19.8245			0.989988			0.494994	+	0.868896i	$0.335170\pi$
$402$	2.34264	−	1.21428i	0.116840	−	0.0605626i
$403$			2.37357i			0.118236i
$404$	25.3011	+	17.8488i	1.25878	+	0.888011i
$405$			8.48515i			0.421630i
$406$	−7.99560	−	15.4255i	−0.396815	−	0.765554i
$407$	−13.9030			−0.689145
$408$	−8.37980	−	1.14817i	−0.414862	−	0.0568427i
$409$	23.2671			1.15049			0.575243	−	0.817983i	$-0.304908\pi$
$409$	23.2671			1.15049			0.575243	+	0.817983i	$0.304908\pi$
$410$	−2.02811	−	3.91272i	−0.100161	−	0.193236i
$411$			31.2674i			1.54231i
$412$	−16.1069	+	22.8320i	−0.793531	+	1.12485i
$413$		−	59.2026i		−	2.91317i
$414$	−34.9181	+	18.0994i	−1.71613	+	0.889535i
$415$	3.08423			0.151399
$416$	−18.5624	+	19.9036i	−0.910096	+	0.975853i
$417$	30.1712			1.47749
$418$	−40.8881	+	21.1938i	−1.99990	+	1.03662i
$419$		−	21.0274i		−	1.02726i	−0.858013	−	0.513628i	$-0.828301\pi$
$419$		−	21.0274i		−	1.02726i	0.858013	−	0.513628i	$-0.171699\pi$
$420$	−15.0437	+	21.3249i	−0.734058	+	1.04055i
$421$		−	15.0832i		−	0.735112i	−0.930001	−	0.367556i	$-0.880195\pi$
$421$		−	15.0832i		−	0.735112i	0.930001	−	0.367556i	$-0.119805\pi$
$422$	4.55063	+	8.77930i	0.221521	+	0.427369i
$423$	28.8042			1.40051
$424$	18.5161	+	2.53700i	0.899221	+	0.123208i
$425$	−1.00000			−0.0485071
$426$	2.14258	+	4.13356i	0.103808	+	0.200272i
$427$		−	28.8742i		−	1.39732i
$428$	4.34253	+	3.06346i	0.209904	+	0.148078i
$429$			60.2595i			2.90936i
$430$	14.2328	−	7.37739i	0.686367	−	0.355769i
$431$	−25.1632			−1.21207			−0.606034	−	0.795439i	$-0.707240\pi$
$431$	−25.1632			−1.21207			−0.606034	+	0.795439i	$0.707240\pi$
$432$	−33.1572	+	11.8051i	−1.59527	+	0.567974i
$433$	21.0944			1.01373			0.506867	−	0.862024i	$-0.330803\pi$
$433$	21.0944			1.01373			0.506867	+	0.862024i	$0.330803\pi$
$434$	−2.70289	+	1.40101i	−0.129743	+	0.0672505i
$435$		−	8.41957i		−	0.403688i
$436$	−2.73246	−	1.92763i	−0.130861	−	0.0923166i
$437$		−	36.3879i		−	1.74067i
$438$	−3.40818	−	6.57521i	−0.162849	−	0.314176i
$439$	24.7840			1.18287			0.591437	−	0.806351i	$-0.298561\pi$
$439$	24.7840			1.18287			0.591437	+	0.806351i	$0.298561\pi$
$440$	−1.60814	+	11.7369i	−0.0766652	+	0.559535i
$441$	−71.5481			−3.40705
$442$	−3.13114	−	6.04075i	−0.148933	−	0.287329i
$443$		−	5.21163i		−	0.247612i	−0.992306	−	0.123806i	$-0.960490\pi$
$443$		−	5.21163i		−	0.247612i	0.992306	−	0.123806i	$-0.0395101\pi$
$444$	11.4441	−	16.2222i	0.543111	−	0.769874i
$445$			4.89985i			0.232275i
$446$	−3.76742	+	1.95279i	−0.178392	+	0.0924674i
$447$	−56.2244			−2.65932
$448$	−33.6216	−	9.38965i	−1.58847	−	0.443619i
$449$	−11.0633			−0.522107			−0.261054	−	0.965324i	$-0.584070\pi$
$449$	−11.0633			−0.522107			−0.261054	+	0.965324i	$0.584070\pi$
$450$	−7.46112	+	3.86737i	−0.351720	+	0.182310i
$451$		−	13.0523i		−	0.614608i
$452$	16.2692	−	23.0620i	0.765240	−	1.08475i
$453$			51.2967i			2.41013i
$454$	−6.35220	−	12.2550i	−0.298123	−	0.575153i
$455$	−20.9936			−0.984195
$456$	8.92718	−	65.1543i	0.418053	−	3.05113i
$457$	−1.42217			−0.0665261			−0.0332631	−	0.999447i	$-0.510590\pi$
$457$	−1.42217			−0.0665261			−0.0332631	+	0.999447i	$0.510590\pi$
$458$	4.85605	+	9.36851i	0.226908	+	0.437762i
$459$		−	8.79900i		−	0.410702i
$460$	−7.64838	−	5.39559i	−0.356608	−	0.251571i
$461$		−	14.2774i		−	0.664966i	−0.943109	−	0.332483i	$-0.892114\pi$
$461$		−	14.2774i		−	0.664966i	0.943109	−	0.332483i	$-0.107886\pi$
$462$	−68.6201	+	35.5683i	−3.19249	+	1.65479i
$463$	36.4219			1.69267			0.846334	−	0.532652i	$-0.178805\pi$
$463$	36.4219			1.69267			0.846334	+	0.532652i	$0.178805\pi$
$464$	10.6098	−	3.77746i	0.492547	−	0.175364i
$465$	−1.47530			−0.0684153
$466$	−11.0456	+	5.72534i	−0.511677	+	0.265221i
$467$		−	24.4402i		−	1.13096i	−0.824762	−	0.565480i	$-0.808691\pi$
$467$		−	24.4402i		−	1.13096i	0.824762	−	0.565480i	$-0.191309\pi$
$468$	−46.7237	−	32.9614i	−2.15980	−	1.52364i
$469$			2.72253i			0.125715i
$470$	3.15460	+	6.08599i	0.145511	+	0.280726i
$471$	51.2831			2.36300
$472$	38.0199	+	5.20933i	1.75001	+	0.239779i
$473$	47.4786			2.18307
$474$	6.38166	+	12.3118i	0.293120	+	0.565500i
$475$		−	7.77516i		−	0.356749i
$476$	5.03069	−	7.13113i	0.230581	−	0.326855i
$477$			39.2651i			1.79783i
$478$	−11.1484	+	5.77860i	−0.509914	+	0.264307i
$479$	32.1022			1.46679			0.733393	−	0.679805i	$-0.237935\pi$
$479$	32.1022			1.46679			0.733393	+	0.679805i	$0.237935\pi$
$480$	−12.3711	−	11.5375i	−0.564661	−	0.526612i
$481$	15.9702			0.728180
$482$	1.61748	−	0.838398i	0.0736740	−	0.0381880i
$483$		−	61.0676i		−	2.77867i
$484$	−7.54300	+	10.6924i	−0.342864	+	0.486018i
$485$			15.8455i			0.719508i
$486$	0.665841	+	1.28457i	0.0302032	+	0.0582693i
$487$	−38.1693			−1.72962			−0.864808	−	0.502102i	$-0.832560\pi$
$487$	−38.1693			−1.72962			−0.864808	+	0.502102i	$0.832560\pi$
$488$	18.5430	+	2.54069i	0.839403	+	0.115012i
$489$	29.8997			1.35211
$490$	−7.83586	−	15.1173i	−0.353988	−	0.682931i
$491$			5.15051i			0.232439i	0.993224	+	0.116220i	$0.0370777\pi$
$491$			5.15051i			0.232439i	−0.993224	+	0.116220i	$0.962922\pi$
$492$	15.2296	+	10.7438i	0.686604	+	0.484368i
$493$			2.81555i			0.126806i
$494$	46.9678	−	24.3451i	2.11318	−	1.09534i
$495$	−24.8892			−1.11869
$496$	−0.661895	−	1.85907i	−0.0297200	−	0.0834748i
$497$	−4.80388			−0.215484
$498$	−11.5802	+	6.00244i	−0.518920	+	0.268976i
$499$		−	42.4590i		−	1.90073i	−0.311141	−	0.950364i	$-0.600711\pi$
$499$		−	42.4590i		−	1.90073i	0.311141	−	0.950364i	$-0.399289\pi$
$500$	−1.63426	−	1.15290i	−0.0730866	−	0.0515592i
$501$			9.76772i			0.436390i
$502$	1.82986	+	3.53025i	0.0816707	+	0.157563i
$503$	7.86424			0.350649			0.175324	−	0.984511i	$-0.443903\pi$
$503$	7.86424			0.350649			0.175324	+	0.984511i	$0.443903\pi$
$504$	9.95582	−	72.6618i	0.443467	−	3.23661i
$505$	−15.4817			−0.688925
$506$	−12.7570	−	24.6113i	−0.567116	−	1.09411i
$507$		−	30.3445i		−	1.34765i
$508$	6.65733	−	9.43693i	0.295371	−	0.418696i
$509$			5.49453i			0.243541i	0.992558	+	0.121770i	$0.0388571\pi$
$509$			5.49453i			0.243541i	−0.992558	+	0.121770i	$0.961143\pi$
$510$	3.75464	−	1.94617i	0.166258	−	0.0861777i
$511$	7.64149			0.338040
$512$	8.98845	−	20.7655i	0.397237	−	0.917716i
$513$	68.4136			3.02054
$514$	8.85612	−	4.59045i	0.390627	−	0.202476i
$515$		−	13.9708i		−	0.615626i
$516$	−39.0814	+	55.3988i	−1.72046	+	2.43880i
$517$			20.3020i			0.892881i
$518$	9.42647	+	18.1860i	0.414175	+	0.799046i
$519$	−24.8949			−1.09276
$520$	1.84726	−	13.4821i	0.0810077	−	0.591228i
$521$	−23.7341			−1.03981			−0.519904	−	0.854224i	$-0.674032\pi$
$521$	−23.7341			−1.03981			−0.519904	+	0.854224i	$0.674032\pi$
$522$	10.8888	+	21.0071i	0.476588	+	0.919456i
$523$		−	12.8950i		−	0.563861i	−0.959435	−	0.281930i	$-0.909025\pi$
$523$		−	12.8950i		−	0.563861i	0.959435	−	0.281930i	$-0.0909747\pi$
$524$	−10.7597	−	7.59050i	−0.470041	−	0.331593i
$525$		−	13.0486i		−	0.569487i
$526$	35.1216	−	18.2048i	1.53137	−	0.793768i
$527$	0.493346			0.0214905
$528$	−16.8040	−	47.1975i	−0.731300	−	2.05401i
$529$	−1.09746			−0.0477157
$530$	−8.29627	+	4.30027i	−0.360367	+	0.186792i
$531$			80.6247i			3.49882i
$532$	55.4457	+	39.1144i	2.40388	+	1.69583i
$533$			14.9930i			0.649420i
$534$	−9.53592	−	18.3971i	−0.412660	−	0.796122i
$535$	−2.65718			−0.114880
$536$	−1.74841	−	0.239560i	−0.0755198	−	0.0103474i
$537$	−47.7395			−2.06011
$538$	2.05812	+	3.97062i	0.0887318	+	0.171185i
$539$		−	50.4292i		−	2.17214i
$540$	10.1444	−	14.3799i	0.436544	−	0.618812i
$541$			10.4515i			0.449346i	0.974434	+	0.224673i	$0.0721314\pi$
$541$			10.4515i			0.449346i	−0.974434	+	0.224673i	$0.927869\pi$
$542$	14.9265	−	7.73694i	0.641147	−	0.332330i
$543$	21.2401			0.911502
$544$	4.13695	+	3.85819i	0.177370	+	0.165418i
$545$	1.67198			0.0716198
$546$	78.8233	−	40.8570i	3.37332	−	1.74852i
$547$		−	12.3993i		−	0.530157i	−0.964227	−	0.265079i	$-0.914602\pi$
$547$		−	12.3993i		−	0.530157i	0.964227	−	0.265079i	$-0.0853979\pi$
$548$	12.0547	−	17.0878i	0.514951	−	0.729956i
$549$			39.3222i			1.67823i
$550$	−2.72584	−	5.25881i	−0.116230	−	0.224236i
$551$	−21.8913			−0.932601
$552$	39.2176	+	5.37344i	1.66921	+	0.228709i
$553$	−14.3084			−0.608453
$554$	3.68312	+	7.10565i	0.156481	+	0.301890i
$555$			9.92632i			0.421349i
$556$	−16.4887	−	11.6320i	−0.699277	−	0.493308i
$557$		−	5.87623i		−	0.248984i	−0.992221	−	0.124492i	$-0.960270\pi$
$557$		−	5.87623i		−	0.248984i	0.992221	−	0.124492i	$-0.0397301\pi$
$558$	3.68092	−	1.90796i	0.155826	−	0.0807702i
$559$	−54.5382			−2.30672
$560$	16.4430	−	5.85428i	0.694842	−	0.247388i
$561$	12.5249			0.528803
$562$	−9.39115	+	4.86778i	−0.396142	+	0.205335i
$563$			31.4028i			1.32347i	0.749738	+	0.661734i	$0.230179\pi$
$563$			31.4028i			1.32347i	−0.749738	+	0.661734i	$0.769821\pi$
$564$	−23.6887	−	16.7113i	−0.997475	−	0.703673i
$565$			14.1116i			0.593678i
$566$	−15.2972	−	29.5120i	−0.642988	−	1.24048i
$567$	37.0250			1.55491
$568$	0.422701	−	3.08505i	0.0177362	−	0.129446i
$569$	−17.6943			−0.741785			−0.370892	−	0.928676i	$-0.620948\pi$
$569$	−17.6943			−0.741785			−0.370892	+	0.928676i	$0.620948\pi$
$570$	15.1318	+	29.1929i	0.633800	+	1.22276i
$571$			5.08576i			0.212832i	0.994322	+	0.106416i	$0.0339376\pi$
$571$			5.08576i			0.212832i	−0.994322	+	0.106416i	$0.966062\pi$
$572$	23.2322	−	32.9322i	0.971385	−	1.37696i
$573$		−	19.9609i		−	0.833878i
$574$	−17.0732	+	8.84967i	−0.712622	+	0.369378i
$575$	4.68001			0.195170
$576$	45.7874	+	12.7873i	1.90781	+	0.532802i
$577$	−40.4597			−1.68436			−0.842179	−	0.539198i	$-0.818727\pi$
$577$	−40.4597			−1.68436			−0.842179	+	0.539198i	$0.818727\pi$
$578$	−1.25557	+	0.650807i	−0.0522247	+	0.0270700i
$579$			28.4845i			1.18378i
$580$	−3.24604	+	4.60135i	−0.134785	+	0.191061i
$581$		−	13.4581i		−	0.558336i
$582$	−30.8380	−	59.4941i	−1.27828	−	2.46611i
$583$	−27.6752			−1.14619
$584$	−0.672387	+	4.90736i	−0.0278236	+	0.203068i
$585$	28.5900			1.18205
$586$	13.9300	+	26.8745i	0.575444	+	1.11017i
$587$			10.2955i			0.424940i	0.977168	+	0.212470i	$0.0681508\pi$
$587$			10.2955i			0.424940i	−0.977168	+	0.212470i	$0.931849\pi$
$588$	58.8416	+	41.5101i	2.42659	+	1.71185i
$589$			3.83585i			0.158053i
$590$	−17.0351	+	8.82992i	−0.701324	+	0.363522i
$591$	−29.0932			−1.19673
$592$	−12.5085	+	4.45346i	−0.514096	+	0.183036i
$593$	5.15631			0.211744			0.105872	−	0.994380i	$-0.466237\pi$
$593$	5.15631			0.211744			0.105872	+	0.994380i	$0.466237\pi$
$594$	46.2723	−	23.9846i	1.89857	−	0.984101i
$595$			4.36351i			0.178886i
$596$	30.7269	+	21.6765i	1.25862	+	0.887902i
$597$		−	17.9061i		−	0.732846i
$598$	14.6538	+	28.2708i	0.599238	+	1.15608i
$599$	13.2051			0.539546			0.269773	−	0.962924i	$-0.413051\pi$
$599$	13.2051			0.539546			0.269773	+	0.962924i	$0.413051\pi$
$600$	8.37980	+	1.14817i	0.342104	+	0.0468737i
$601$	37.1371			1.51486			0.757428	−	0.652919i	$-0.226456\pi$
$601$	37.1371			1.51486			0.757428	+	0.652919i	$0.226456\pi$
$602$	−32.1913	−	62.1050i	−1.31202	−	2.53121i
$603$		−	3.70767i		−	0.150988i
$604$	19.7767	−	28.0339i	0.804701	−	1.14068i
$605$		−	6.54263i		−	0.265996i
$606$	58.1280	−	30.1299i	2.36129	−	1.22394i
$607$	46.4987			1.88732			0.943662	−	0.330911i	$-0.107356\pi$
$607$	46.4987			1.88732			0.943662	+	0.330911i	$0.107356\pi$
$608$	−29.9980	+	32.1655i	−1.21658	+	1.30448i
$609$	−36.7389			−1.48874
$610$	−8.30834	+	4.30652i	−0.336395	+	0.174366i
$611$		−	23.3207i		−	0.943455i
$612$	−6.85102	+	9.71150i	−0.276936	+	0.392564i
$613$		−	5.63462i		−	0.227580i	−0.993505	−	0.113790i	$-0.963701\pi$
$613$		−	5.63462i		−	0.227580i	0.993505	−	0.113790i	$-0.0362991\pi$
$614$	−12.7152	−	24.5307i	−0.513143	−	0.989979i
$615$	−9.31894			−0.375776
$616$	51.2141	+	7.01715i	2.06347	+	0.282729i
$617$	−11.2965			−0.454781			−0.227390	−	0.973804i	$-0.573019\pi$
$617$	−11.2965			−0.454781			−0.227390	+	0.973804i	$0.573019\pi$
$618$	27.1895	+	52.4552i	1.09372	+	2.11006i
$619$			9.48152i			0.381094i	0.981678	+	0.190547i	$0.0610262\pi$
$619$			9.48152i			0.381094i	−0.981678	+	0.190547i	$0.938974\pi$
$620$	0.806259	+	0.568779i	0.0323801	+	0.0228427i
$621$			41.1794i			1.65247i
$622$	21.8993	−	11.3512i	0.878083	−	0.455143i
$623$	21.3805			0.856593
$624$	19.3026	+	54.2154i	0.772722	+	2.17035i
$625$	1.00000			0.0400000
$626$	−25.3148	+	13.1216i	−1.01178	+	0.524445i
$627$			97.3833i			3.88911i
$628$	−28.0265	−	19.7714i	−1.11838	−	0.788966i
$629$		−	3.31941i		−	0.132354i
$630$	16.8753	+	32.5567i	0.672329	+	1.29709i
$631$	2.50157			0.0995859			0.0497929	−	0.998760i	$-0.484144\pi$
$631$	2.50157			0.0995859			0.0497929	+	0.998760i	$0.484144\pi$
$632$	1.25902	−	9.18883i	0.0500809	−	0.365512i
$633$	20.9097			0.831085
$634$	−5.88773	−	11.3589i	−0.233832	−	0.451119i
$635$			5.77442i			0.229151i
$636$	22.7804	−	32.2919i	0.903304	−	1.28046i
$637$			57.9275i			2.29517i
$638$	−14.8064	+	7.67471i	−0.586192	+	0.303845i
$639$	6.54215			0.258803
$640$	2.31277	+	11.0748i	0.0914204	+	0.437770i
$641$	38.7534			1.53067			0.765334	−	0.643634i	$-0.222574\pi$
$641$	38.7534			1.53067			0.765334	+	0.643634i	$0.222574\pi$
$642$	9.97674	−	5.17131i	0.393750	−	0.204095i
$643$		−	36.5250i		−	1.44041i	−0.693763	−	0.720203i	$-0.744049\pi$
$643$		−	36.5250i		−	1.44041i	0.693763	−	0.720203i	$-0.255951\pi$
$644$	−23.5437	+	33.3738i	−0.927752	+	1.31511i
$645$		−	33.8983i		−	1.33474i
$646$	−5.06013	−	9.76224i	−0.199088	−	0.384090i
$647$	28.9267			1.13723			0.568613	−	0.822605i	$-0.307480\pi$
$647$	28.9267			1.13723			0.568613	+	0.822605i	$0.307480\pi$
$648$	−3.25789	+	23.7775i	−0.127982	+	0.934067i
$649$	−56.8266			−2.23064
$650$	3.13114	+	6.04075i	0.122814	+	0.236938i
$651$			6.43748i			0.252305i
$652$	−16.3404	−	11.5274i	−0.639938	−	0.451447i
$653$			12.3145i			0.481905i	0.970537	+	0.240953i	$0.0774599\pi$
$653$			12.3145i			0.481905i	−0.970537	+	0.240953i	$0.922540\pi$
$654$	−6.27768	+	3.25395i	−0.245477	+	0.127240i
$655$	6.58384			0.257252
$656$	−4.18096	−	11.7431i	−0.163239	−	0.458491i
$657$	−10.4065			−0.405997
$658$	26.5563	−	13.7651i	1.03527	−	0.536620i
$659$		−	29.6750i		−	1.15597i	−0.816046	−	0.577987i	$-0.803839\pi$
$659$		−	29.6750i		−	1.15597i	0.816046	−	0.577987i	$-0.196161\pi$
$660$	20.4690	+	14.4400i	0.796756	+	0.562075i
$661$		−	7.97630i		−	0.310242i	−0.987895	−	0.155121i	$-0.950423\pi$
$661$		−	7.97630i		−	0.310242i	0.987895	−	0.155121i	$-0.0495768\pi$
$662$	9.01487	+	17.3919i	0.350373	+	0.675955i
$663$	−14.3873			−0.558755
$664$	8.64278	+	1.18420i	0.335405	+	0.0459558i
$665$	−33.9270			−1.31563
$666$	−12.8374	−	24.7665i	−0.497439	−	0.959682i
$667$		−	13.1768i		−	0.510207i
$668$	3.76580	−	5.33812i	0.145703	−	0.206538i
$669$			8.97287i			0.346911i
$670$	0.783389	−	0.406059i	0.0302649	−	0.0156874i
$671$	−27.7154			−1.06994
$672$	−50.3439	+	53.9814i	−1.94206	+	2.08238i
$673$	−30.0834			−1.15963			−0.579815	−	0.814748i	$-0.696875\pi$
$673$	−30.0834			−1.15963			−0.579815	+	0.814748i	$0.696875\pi$
$674$	−16.8678	+	8.74319i	−0.649722	+	0.336775i
$675$			8.79900i			0.338674i
$676$	−11.6989	+	16.5835i	−0.449957	+	0.637825i
$677$		−	6.43558i		−	0.247339i	−0.992323	−	0.123670i	$-0.960534\pi$
$677$		−	6.43558i		−	0.247339i	0.992323	−	0.123670i	$-0.0394663\pi$
$678$	−27.4635	−	52.9838i	−1.05473	−	2.03483i
$679$	69.1420			2.65343
$680$	−2.80225	−	0.383952i	−0.107461	−	0.0147239i
$681$	−29.1877			−1.11847
$682$	1.34478	+	2.59442i	0.0514943	+	0.0993453i
$683$		−	30.2865i		−	1.15888i	−0.815014	−	0.579441i	$-0.803271\pi$
$683$		−	30.2865i		−	1.15888i	0.815014	−	0.579441i	$-0.196729\pi$
$684$	−75.5085	−	53.2678i	−2.88714	−	2.03675i
$685$			10.4560i			0.399502i
$686$	−27.6138	+	14.3132i	−1.05430	+	0.546482i
$687$	22.3130			0.851295
$688$	42.7164	−	15.2085i	1.62855	−	0.579820i
$689$	31.7902			1.21111
$690$	−17.5717	+	9.10809i	−0.668945	+	0.346739i
$691$			8.46436i			0.321999i	0.986954	+	0.161000i	$0.0514718\pi$
$691$			8.46436i			0.321999i	−0.986954	+	0.161000i	$0.948528\pi$
$692$	13.6052	+	9.59785i	0.517192	+	0.364856i
$693$			108.604i			4.12554i
$694$	−23.2496	−	44.8542i	−0.882542	−	1.70264i
$695$	10.0894			0.382712
$696$	3.23271	−	23.5937i	0.122536	−	0.894318i
$697$	3.11630			0.118038
$698$	20.3304	+	39.2223i	0.769517	+	1.48459i
$699$			26.3073i			0.995035i
$700$	−5.03069	+	7.13113i	−0.190142	+	0.269531i
$701$		−	31.1857i		−	1.17787i	−0.808181	−	0.588934i	$-0.799548\pi$
$701$		−	31.1857i		−	1.17787i	0.808181	−	0.588934i	$-0.200452\pi$
$702$	−53.1525	+	27.5509i	−2.00611	+	1.03984i
$703$	25.8089			0.973403
$704$	−9.01282	+	32.2722i	−0.339683	+	1.21631i
$705$	14.4950			0.545914
$706$	−21.5018	+	11.1452i	−0.809230	+	0.419454i
$707$			67.5544i			2.54064i
$708$	46.7761	−	66.3063i	1.75795	−	2.49194i
$709$			48.2214i			1.81099i	0.424355	+	0.905496i	$0.360501\pi$
$709$			48.2214i			1.81099i	−0.424355	+	0.905496i	$0.639499\pi$
$710$	0.716488	+	1.38228i	0.0268893	+	0.0518761i
$711$	19.4858			0.730774
$712$	−1.88131	+	13.7306i	−0.0705050	+	0.514575i
$713$	−2.30887			−0.0864678
$714$	−8.49212	−	16.3834i	−0.317810	−	0.613133i
$715$			20.1511i			0.753607i
$716$	26.0899	+	18.4052i	0.975026	+	0.687836i
$717$			26.5521i			0.991605i
$718$	−3.99123	+	2.06880i	−0.148951	+	0.0772069i
$719$	14.5842			0.543899			0.271949	−	0.962312i	$-0.412332\pi$
$719$	14.5842			0.543899			0.271949	+	0.962312i	$0.412332\pi$
$720$	−22.3928	+	7.97262i	−0.834529	+	0.297122i
$721$	−60.9616			−2.27033
$722$	52.0472	−	26.9780i	1.93700	−	1.00402i
$723$		−	3.85235i		−	0.143270i
$724$	−11.6079	−	8.18882i	−0.431403	−	0.304335i
$725$		−	2.81555i		−	0.104567i
$726$	12.7330	+	24.5652i	0.472568	+	0.911700i
$727$	32.8618			1.21878			0.609389	−	0.792872i	$-0.291415\pi$
$727$	32.8618			1.21878			0.609389	+	0.792872i	$0.291415\pi$
$728$	−58.8292	−	8.06053i	−2.18035	−	0.298743i
$729$	28.5149			1.05611
$730$	−1.13971	−	2.19878i	−0.0421826	−	0.0813806i
$731$			11.3358i			0.419268i
$732$	22.8136	−	32.3388i	0.843214	−	1.19528i
$733$			27.0533i			0.999236i	0.866246	+	0.499618i	$0.166526\pi$
$733$			27.0533i			0.999236i	−0.866246	+	0.499618i	$0.833474\pi$
$734$	−3.51213	+	1.82047i	−0.129635	+	0.0671947i
$735$	−36.0049			−1.32806
$736$	−19.3610	−	18.0564i	−0.713656	−	0.665567i
$737$	2.61327			0.0962611
$738$	23.2511	−	12.0519i	0.855883	−	0.443636i
$739$			42.9847i			1.58122i	0.612322	+	0.790608i	$0.290235\pi$
$739$			42.9847i			1.58122i	−0.612322	+	0.790608i	$0.709765\pi$
$740$	3.82695	−	5.42479i	0.140681	−	0.199419i
$741$		−	111.863i		−	4.10940i
$742$	18.7643	+	36.2009i	0.688858	+	1.32898i
$743$	−53.6886			−1.96964			−0.984822	−	0.173568i	$-0.944470\pi$
$743$	−53.6886			−1.96964			−0.984822	+	0.173568i	$0.944470\pi$
$744$	−4.13415	−	0.566444i	−0.151565	−	0.0207668i
$745$	−18.8017			−0.688840
$746$	14.9927	+	28.9247i	0.548923	+	1.05901i
$747$			18.3278i			0.670581i
$748$	−6.84494	−	4.82880i	−0.250276	−	0.176558i
$749$			11.5946i			0.423658i
$750$	−3.75464	+	1.94617i	−0.137100	+	0.0710640i
$751$	−23.1731			−0.845598			−0.422799	−	0.906223i	$-0.638952\pi$
$751$	−23.1731			−0.845598			−0.422799	+	0.906223i	$0.638952\pi$
$752$	6.50322	+	18.2657i	0.237148	+	0.666080i
$753$	8.40801			0.306405
$754$	17.0080	−	8.81588i	0.619395	−	0.321055i
$755$			17.1539i			0.624293i
$756$	−62.7468	−	44.2650i	−2.28208	−	1.60990i
$757$		−	5.88004i		−	0.213714i	−0.994274	−	0.106857i	$-0.965921\pi$
$757$		−	5.88004i		−	0.213714i	0.994274	−	0.106857i	$-0.0340787\pi$
$758$	5.92204	+	11.4251i	0.215098	+	0.414977i
$759$	−58.6168			−2.12766
$760$	2.98529	−	21.7879i	0.108288	−	0.790331i
$761$	35.5088			1.28719			0.643597	−	0.765365i	$-0.277441\pi$
$761$	35.5088			1.28719			0.643597	+	0.765365i	$0.277441\pi$
$762$	−11.2380	−	21.6808i	−0.407109	−	0.785414i
$763$		−	7.29571i		−	0.264122i
$764$	−7.69563	+	10.9087i	−0.278418	+	0.394665i
$765$		−	5.94243i		−	0.214849i
$766$	−14.3346	+	7.43016i	−0.517931	+	0.268463i
$767$	65.2762			2.35699
$768$	−30.2370	−	37.0808i	−1.09108	−	1.33804i
$769$	−12.0101			−0.433096			−0.216548	−	0.976272i	$-0.569480\pi$
$769$	−12.0101			−0.433096			−0.216548	+	0.976272i	$0.569480\pi$
$770$	−22.9469	+	11.8942i	−0.826948	+	0.428638i
$771$		−	21.0926i		−	0.759633i
$772$	10.9818	−	15.5669i	0.395243	−	0.560267i
$773$			18.5951i			0.668819i	0.942428	+	0.334409i	$0.108537\pi$
$773$			18.5951i			0.668819i	−0.942428	+	0.334409i	$0.891463\pi$
$774$	43.8396	+	84.5774i	1.57578	+	3.04007i
$775$	−0.493346			−0.0177215
$776$	−6.08392	+	44.4030i	−0.218400	+	1.59398i
$777$	43.3136			1.55387
$778$	−7.85674	−	15.1576i	−0.281678	−	0.543426i
$779$			24.2297i			0.868119i
$780$	−23.5126	−	16.5871i	−0.841886	−	0.593913i
$781$			4.61109i			0.164998i
$782$	5.87607	−	3.04579i	0.210128	−	0.108917i
$783$	24.7740			0.885350
$784$	−16.1537	−	45.3710i	−0.576918	−	1.62039i
$785$	17.1493			0.612085
$786$	−24.7199	+	12.8132i	−0.881730	+	0.457033i
$787$		−	29.8970i		−	1.06571i	−0.846206	−	0.532856i	$-0.821119\pi$
$787$		−	29.8970i		−	1.06571i	0.846206	−	0.532856i	$-0.178881\pi$
$788$	15.8996	+	11.2165i	0.566400	+	0.399570i
$789$		−	83.6491i		−	2.97799i
$790$	2.13406	+	4.11712i	0.0759264	+	0.146481i
$791$	61.5760			2.18939
$792$	−69.7457	−	9.55627i	−2.47830	−	0.339567i
$793$	31.8365			1.13055
$794$	−18.7744	−	36.2205i	−0.666279	−	1.28542i
$795$			19.7593i			0.700789i
$796$	−6.90341	+	9.78577i	−0.244685	+	0.346847i
$797$		−	2.37255i		−	0.0840399i	−0.999117	−	0.0420200i	$-0.986621\pi$
$797$		−	2.37255i		−	0.0840399i	0.999117	−	0.0420200i	$-0.0133793\pi$
$798$	127.383	−	66.0276i	4.50933	−	2.33735i
$799$	−4.84720			−0.171482
$800$	−4.13695	−	3.85819i	−0.146263	−	0.136408i
$801$	−29.1170			−1.02880
$802$	−24.8910	+	12.9019i	−0.878932	+	0.455583i
$803$		−	7.33482i		−	0.258840i
$804$	−2.15108	+	3.04921i	−0.0758627	+	0.107537i
$805$		−	20.4213i		−	0.719756i
$806$	−1.54474	−	2.98018i	−0.0544111	−	0.104972i
$807$	9.45683			0.332896
$808$	−43.3834	−	5.94422i	−1.52622	−	0.209117i
$809$	37.4156			1.31546			0.657731	−	0.753253i	$-0.271517\pi$
$809$	37.4156			1.31546			0.657731	+	0.753253i	$0.271517\pi$
$810$	−5.52220	−	10.6537i	−0.194030	−	0.374332i
$811$		−	32.9857i		−	1.15829i	−0.815226	−	0.579143i	$-0.803387\pi$
$811$		−	32.9857i		−	1.15829i	0.815226	−	0.579143i	$-0.196613\pi$
$812$	20.0780	+	14.1641i	0.704600	+	0.497064i
$813$		−	35.5504i		−	1.24681i
$814$	17.4561	−	9.04816i	0.611837	−	0.317138i
$815$	9.99860			0.350236
$816$	11.2686	−	4.01204i	0.394482	−	0.140449i
$817$	−88.1373			−3.08353
$818$	−29.2134	+	15.1424i	−1.02142	+	0.529442i
$819$		−	124.753i		−	4.35922i
$820$	5.09285	+	3.59278i	0.177850	+	0.125465i
$821$		−	8.03032i		−	0.280260i	−0.990133	−	0.140130i	$-0.955248\pi$
$821$		−	8.03032i		−	0.280260i	0.990133	−	0.140130i	$-0.0447521\pi$
$822$	−20.3491	−	39.2584i	−0.709755	−	1.36929i
$823$	−42.6045			−1.48510			−0.742550	−	0.669790i	$-0.766384\pi$
$823$	−42.6045			−1.48510			−0.742550	+	0.669790i	$0.766384\pi$
$824$	5.36411	−	39.1496i	0.186868	−	1.36384i
$825$	−12.5249			−0.436062
$826$	38.5295	+	74.3328i	1.34061	+	2.58637i
$827$			15.4169i			0.536098i	0.963405	+	0.268049i	$0.0863790\pi$
$827$			15.4169i			0.536098i	−0.963405	+	0.268049i	$0.913621\pi$
$828$	32.0629	−	45.4500i	1.11426	−	1.57950i
$829$			6.68865i			0.232306i	0.993231	+	0.116153i	$0.0370564\pi$
$829$			6.68865i			0.232306i	−0.993231	+	0.116153i	$0.962944\pi$
$830$	−3.87247	+	2.00724i	−0.134415	+	0.0696724i
$831$	16.9236			0.587072
$832$	10.3529	−	37.0708i	0.358924	−	1.28520i
$833$	12.0402			0.417169
$834$	−37.8819	+	19.6356i	−1.31174	+	0.679926i
$835$			3.26637i			0.113037i
$836$	37.5447	−	53.2205i	1.29851	−	1.84067i
$837$		−	4.34095i		−	0.150045i
$838$	13.6848	+	26.4013i	0.472733	+	0.912018i
$839$	−11.8447			−0.408924			−0.204462	−	0.978874i	$-0.565545\pi$
$839$	−11.8447			−0.408924			−0.204462	+	0.978874i	$0.565545\pi$
$840$	5.01004	−	36.5654i	0.172863	−	1.26162i
$841$	21.0727			0.726645
$842$	9.81628	+	18.9380i	0.338291	+	0.652648i
$843$			22.3669i			0.770358i
$844$	−11.4273	−	8.06141i	−0.393342	−	0.277485i
$845$		−	10.1473i		−	0.349079i
$846$	−36.1656	+	18.7460i	−1.24340	+	0.644499i
$847$	−28.5488			−0.980950
$848$	−24.8993	+	8.86503i	−0.855045	+	0.304426i
$849$	−70.2888			−2.41231
$850$	1.25557	−	0.650807i	0.0430656	−	0.0223225i
$851$			15.5349i			0.532529i
$852$	−5.38030	−	3.79556i	−0.184326	−	0.130034i
$853$		−	12.3374i		−	0.422424i	−0.977440	−	0.211212i	$-0.932259\pi$
$853$		−	12.3374i		−	0.422424i	0.977440	−	0.211212i	$-0.0677410\pi$
$854$	18.7915	+	36.2535i	0.643034	+	1.24057i
$855$	46.2033			1.58012
$856$	−7.44607	−	1.02023i	−0.254501	−	0.0348707i
$857$	15.4580			0.528034			0.264017	−	0.964518i	$-0.414953\pi$
$857$	15.4580			0.528034			0.264017	+	0.964518i	$0.414953\pi$
$858$	−39.2173	−	75.6599i	−1.33886	−	2.58299i
$859$		−	40.0837i		−	1.36764i	−0.729652	−	0.683819i	$-0.760318\pi$
$859$		−	40.0837i		−	1.36764i	0.729652	−	0.683819i	$-0.239682\pi$
$860$	−13.0690	+	18.5256i	−0.445649	+	0.631719i
$861$			40.6633i			1.38580i
$862$	31.5941	−	16.3764i	1.07610	−	0.557781i
$863$	−54.5943			−1.85841			−0.929206	−	0.369561i	$-0.879508\pi$
$863$	−54.5943			−1.85841			−0.929206	+	0.369561i	$0.879508\pi$
$864$	33.9482	−	36.4010i	1.15494	−	1.23839i
$865$	−8.32496			−0.283057
$866$	−26.4855	+	13.7284i	−0.900014	+	0.466511i
$867$			2.99039i			0.101559i
$868$	2.48187	−	3.51812i	0.0842403	−	0.119413i
$869$			13.7341i			0.465899i
$870$	5.47952	+	10.5713i	0.185773	+	0.358402i
$871$	−3.00184			−0.101714
$872$	4.68530	+	0.641961i	0.158664	+	0.0217395i
$873$	−94.1608			−3.18686
$874$	23.6815	+	45.6874i	0.801038	+	1.54540i
$875$		−	4.36351i		−	0.147514i
$876$	8.55839	+	6.03756i	0.289161	+	0.203990i
$877$			45.4591i			1.53504i	0.641022	+	0.767522i	$0.278511\pi$
$877$			45.4591i			1.53504i	−0.641022	+	0.767522i	$0.721489\pi$
$878$	−31.1179	+	16.1296i	−1.05018	+	0.544347i
$879$	64.0070			2.15890
$880$	−5.61933	−	15.7831i	−0.189428	−	0.532047i
$881$	−27.1739			−0.915510			−0.457755	−	0.889078i	$-0.651346\pi$
$881$	−27.1739			−0.915510			−0.457755	+	0.889078i	$0.651346\pi$
$882$	89.8335	−	46.5640i	3.02485	−	1.56789i
$883$			25.0675i			0.843588i	0.906692	+	0.421794i	$0.138599\pi$
$883$			25.0675i			0.843588i	−0.906692	+	0.421794i	$0.861401\pi$
$884$	7.86273	+	5.54680i	0.264452	+	0.186559i
$885$			40.5725i			1.36383i
$886$	3.39177	+	6.54355i	0.113949	+	0.219835i
$887$	−13.7944			−0.463170			−0.231585	−	0.972815i	$-0.574391\pi$
$887$	−13.7944			−0.463170			−0.231585	+	0.972815i	$0.574391\pi$
$888$	−3.81123	+	27.8160i	−0.127897	+	0.933444i
$889$	25.1967			0.845071
$890$	−3.18886	−	6.15209i	−0.106891	−	0.206219i
$891$		−	35.5391i		−	1.19061i
$892$	3.45936	−	4.90373i	0.115828	−	0.164189i
$893$		−	37.6878i		−	1.26117i
$894$	70.5935	−	36.5912i	2.36100	−	1.22379i
$895$	−15.9643			−0.533628
$896$	48.3250	−	10.0918i	1.61442	−	0.337144i
$897$	67.3326			2.24817
$898$	13.8907	−	7.20004i	0.463537	−	0.240269i
$899$			1.38904i			0.0463271i
$900$	6.85102	−	9.71150i	0.228367	−	0.323717i
$901$		−	6.60759i		−	0.220131i
$902$	8.49451	+	16.3880i	0.282836	+	0.545661i
$903$	−147.916			−4.92232
$904$	−5.41817	+	39.5441i	−0.180206	+	1.31522i
$905$	7.10280			0.236105
$906$	−33.3843	−	64.4065i	−1.10912	−	2.13976i
$907$		−	56.0451i		−	1.86095i	−0.366361	−	0.930473i	$-0.619396\pi$
$907$		−	56.0451i		−	1.86095i	0.366361	−	0.930473i	$-0.380604\pi$
$908$	15.9512	+	11.2529i	0.529360	+	0.373439i
$909$		−	91.9986i		−	3.05140i
$910$	26.3589	−	13.6628i	0.873788	−	0.452917i
$911$	31.0576			1.02898			0.514491	−	0.857496i	$-0.327981\pi$
$911$	31.0576			1.02898			0.514491	+	0.857496i	$0.327981\pi$
$912$	31.1942	+	87.6155i	1.03294	+	2.90124i
$913$	−12.9180			−0.427523
$914$	1.78563	−	0.925556i	0.0590633	−	0.0306147i
$915$			19.7880i			0.654171i
$916$	−12.1942	−	8.60245i	−0.402907	−	0.284233i
$917$		−	28.7286i		−	0.948703i
$918$	5.72645	+	11.0477i	0.189001	+	0.364630i
$919$	−39.0215			−1.28720			−0.643601	−	0.765361i	$-0.722560\pi$
$919$	−39.0215			−1.28720			−0.643601	+	0.765361i	$0.722560\pi$
$920$	13.1146	+	1.79690i	0.432374	+	0.0592421i
$921$	−58.4249			−1.92516
$922$	9.29185	+	17.9263i	0.306011	+	0.590370i
$923$		−	5.29672i		−	0.174344i
$924$	63.0090	−	89.3169i	2.07284	−	2.93831i
$925$			3.31941i			0.109141i
$926$	−45.7301	+	23.7036i	−1.50279	+	0.778950i
$927$	83.0203			2.72675
$928$	−10.8629	+	11.6478i	−0.356592	+	0.382357i
$929$	−52.7041			−1.72917			−0.864583	−	0.502490i	$-0.832417\pi$
$929$	−52.7041			−1.72917			−0.864583	+	0.502490i	$0.832417\pi$
$930$	1.85234	−	0.960134i	0.0607405	−	0.0314841i
$931$			93.6147i			3.06810i
$932$	10.1424	−	14.3771i	0.332225	−	0.470938i
$933$		−	52.1577i		−	1.70757i
$934$	15.9059	+	30.6864i	0.520457	+	1.00409i
$935$	4.18839			0.136975
$936$	80.1162	+	10.9772i	2.61868	+	0.358801i
$937$	−41.2115			−1.34632			−0.673161	−	0.739496i	$-0.735064\pi$
$937$	−41.2115			−1.34632			−0.673161	+	0.739496i	$0.735064\pi$
$938$	−1.77184	−	3.41832i	−0.0578528	−	0.111612i
$939$			60.2924i			1.96757i
$940$	−7.92162	−	5.58834i	−0.258375	−	0.182272i
$941$		−	11.4803i		−	0.374248i	−0.982336	−	0.187124i	$-0.940083\pi$
$941$		−	11.4803i		−	0.374248i	0.982336	−	0.187124i	$-0.0599166\pi$
$942$	−64.3894	+	33.3754i	−2.09792	+	1.08743i
$943$	−14.5843			−0.474931
$944$	−51.1268	+	18.2029i	−1.66404	+	0.592455i
$945$	38.3945			1.24897
$946$	−59.6126	+	30.8994i	−1.93817	+	1.00463i
$947$			59.7360i			1.94116i	0.240781	+	0.970580i	$0.422597\pi$
$947$			59.7360i			1.94116i	−0.240781	+	0.970580i	$0.577403\pi$
$948$	−16.0252	−	11.3051i	−0.520475	−	0.367172i
$949$			8.42544i			0.273501i
$950$	5.06013	+	9.76224i	0.164172	+	0.316729i
$951$	−27.0535			−0.877269
$952$	−1.67538	+	12.2276i	−0.0542994	+	0.396300i
$953$	−48.5108			−1.57142			−0.785709	−	0.618596i	$-0.787702\pi$
$953$	−48.5108			−1.57142			−0.785709	+	0.618596i	$0.787702\pi$
$954$	−25.5540	−	49.3000i	−0.827342	−	1.59615i
$955$		−	6.67502i		−	0.215998i
$956$	10.2368	−	14.5109i	0.331080	−	0.469315i
$957$			35.2645i			1.13994i
$958$	−40.3065	+	20.8923i	−1.30224	+	0.675001i
$959$	45.6247			1.47330
$960$	23.0414	+	6.43489i	0.743659	+	0.207685i
$961$	−30.7566			−0.992149
$962$	−20.0517	+	10.3935i	−0.646493	+	0.335101i
$963$		−	15.7901i		−	0.508828i
$964$	−1.48522	+	2.10533i	−0.0478356	+	0.0678081i
$965$			9.52535i			0.306632i
$966$	39.7432	+	76.6745i	1.27872	+	2.46696i
$967$	−51.1732			−1.64562			−0.822809	−	0.568318i	$-0.807594\pi$
$967$	−51.1732			−1.64562			−0.822809	+	0.568318i	$0.807594\pi$
$968$	2.51206	−	18.3341i	0.0807406	−	0.589279i
$969$	−23.2508			−0.746922
$970$	−10.3124	−	19.8951i	−0.331110	−	0.638793i
$971$		−	23.6865i		−	0.760137i	−0.924958	−	0.380069i	$-0.875900\pi$
$971$		−	23.6865i		−	0.760137i	0.924958	−	0.380069i	$-0.124100\pi$
$972$	−1.67202	−	1.17953i	−0.0536299	−	0.0378335i
$973$		−	44.0251i		−	1.41138i
$974$	47.9241	−	24.8409i	1.53559	−	0.795953i
$975$	14.3873			0.460761
$976$	−24.9355	+	8.87792i	−0.798166	+	0.284175i
$977$	−26.1676			−0.837174			−0.418587	−	0.908177i	$-0.637475\pi$
$977$	−26.1676			−0.837174			−0.418587	+	0.908177i	$0.637475\pi$
$978$	−37.5411	+	19.4589i	−1.20043	+	0.622228i
$979$		−	20.5225i		−	0.655902i
$980$	19.6769	+	13.8812i	0.628556	+	0.443418i
$981$			9.93562i			0.317220i
$982$	−3.35199	−	6.46682i	−0.106966	−	0.206364i
$983$	4.28167			0.136564			0.0682821	−	0.997666i	$-0.478248\pi$
$983$	4.28167			0.136564			0.0682821	+	0.997666i	$0.478248\pi$
$984$	−26.1140	−	3.57803i	−0.832483	−	0.114063i
$985$	−9.72890			−0.309989
$986$	−1.83238	−	3.53511i	−0.0583548	−	0.112581i
$987$		−	63.2492i		−	2.01324i
$988$	−43.1272	+	61.1340i	−1.37206	+	1.94493i
$989$		−	53.0515i		−	1.68694i
$990$	31.2501	−	16.1981i	0.993193	−	0.514809i
$991$	−11.6019			−0.368547			−0.184274	−	0.982875i	$-0.558993\pi$
$991$	−11.6019			−0.368547			−0.184274	+	0.982875i	$0.558993\pi$
$992$	2.04095	+	1.90342i	0.0648003	+	0.0604338i
$993$	41.4223			1.31450
$994$	6.03160	−	3.12640i	0.191311	−	0.0991635i
$995$		−	5.98787i		−	0.189828i
$996$	10.6333	−	15.0729i	0.336928	−	0.477604i
$997$			24.9376i			0.789783i	0.918728	+	0.394891i	$0.129218\pi$
$997$			24.9376i			0.789783i	−0.918728	+	0.394891i	$0.870782\pi$
$998$	27.6327	+	53.3102i	0.874696	+	1.68750i
$999$	−29.2075			−0.924084

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.f.e.341.4	yes	30
4.3	odd	2		2720.2.f.e.1361.2		30
8.3	odd	2		2720.2.f.e.1361.29		30
8.5	even	2	inner	680.2.f.e.341.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.f.e.341.3	✓	30	8.5	even	2	inner
680.2.f.e.341.4	yes	30	1.1	even	1	trivial
2720.2.f.e.1361.2		30	4.3	odd	2
2720.2.f.e.1361.29		30	8.3	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25557 + 0.650807i) q^{2} +2.99039i q^{3} +(1.15290 - 1.63426i) q^{4} +1.00000i q^{5} +(-1.94617 - 3.75464i) q^{6} +4.36351 q^{7} +(-0.383952 + 2.80225i) q^{8} -5.94243 q^{9} +(-0.650807 - 1.25557i) q^{10} -4.18839i q^{11} +(4.88709 + 3.44762i) q^{12} +4.81117i q^{13} +(-5.47868 + 2.83980i) q^{14} -2.99039 q^{15} +(-1.34164 - 3.76829i) q^{16} +1.00000 q^{17} +(7.46112 - 3.86737i) q^{18} +7.77516i q^{19} +(1.63426 + 1.15290i) q^{20} +13.0486i q^{21} +(2.72584 + 5.25881i) q^{22} -4.68001 q^{23} +(-8.37980 - 1.14817i) q^{24} -1.00000 q^{25} +(-3.13114 - 6.04075i) q^{26} -8.79900i q^{27} +(5.03069 - 7.13113i) q^{28} +2.81555i q^{29} +(3.75464 - 1.94617i) q^{30} +0.493346 q^{31} +(4.13695 + 3.85819i) q^{32} +12.5249 q^{33} +(-1.25557 + 0.650807i) q^{34} +4.36351i q^{35} +(-6.85102 + 9.71150i) q^{36} -3.31941i q^{37} +(-5.06013 - 9.76224i) q^{38} -14.3873 q^{39} +(-2.80225 - 0.383952i) q^{40} +3.11630 q^{41} +(-8.49212 - 16.3834i) q^{42} +11.3358i q^{43} +(-6.84494 - 4.82880i) q^{44} -5.94243i q^{45} +(5.87607 - 3.04579i) q^{46} -4.84720 q^{47} +(11.2686 - 4.01204i) q^{48} +12.0402 q^{49} +(1.25557 - 0.650807i) q^{50} +2.99039i q^{51} +(7.86273 + 5.54680i) q^{52} -6.60759i q^{53} +(5.72645 + 11.0477i) q^{54} +4.18839 q^{55} +(-1.67538 + 12.2276i) q^{56} -23.2508 q^{57} +(-1.83238 - 3.53511i) q^{58} -13.5676i q^{59} +(-3.44762 + 4.88709i) q^{60} -6.61720i q^{61} +(-0.619430 + 0.321073i) q^{62} -25.9298 q^{63} +(-7.70516 - 2.15186i) q^{64} -4.81117 q^{65} +(-15.7259 + 8.15131i) q^{66} +0.623932i q^{67} +(1.15290 - 1.63426i) q^{68} -13.9951i q^{69} +(-2.83980 - 5.47868i) q^{70} -1.10092 q^{71} +(2.28161 - 16.6521i) q^{72} +1.75123 q^{73} +(2.16030 + 4.16774i) q^{74} -2.99039i q^{75} +(12.7067 + 8.96398i) q^{76} -18.2761i q^{77} +(18.0642 - 9.36334i) q^{78} -3.27909 q^{79} +(3.76829 - 1.34164i) q^{80} +8.48515 q^{81} +(-3.91272 + 2.02811i) q^{82} -3.08423i q^{83} +(21.3249 + 15.0437i) q^{84} +1.00000i q^{85} +(-7.37739 - 14.2328i) q^{86} -8.41957 q^{87} +(11.7369 + 1.60814i) q^{88} +4.89985 q^{89} +(3.86737 + 7.46112i) q^{90} +20.9936i q^{91} +(-5.39559 + 7.64838i) q^{92} +1.47530i q^{93} +(6.08599 - 3.15460i) q^{94} -7.77516 q^{95} +(-11.5375 + 12.3711i) q^{96} +15.8455 q^{97} +(-15.1173 + 7.83586i) q^{98} +24.8892i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{4} - 8 q^{6} + 12 q^{7} + 6 q^{8} - 36 q^{9} + 2 q^{10} + 8 q^{12} - 10 q^{14} - 14 q^{15} - 2 q^{16} + 30 q^{17} + 6 q^{18} + 4 q^{20} - 6 q^{22} + 12 q^{23} - 46 q^{24} - 30 q^{25} + 4 q^{26}+ \cdots - 16 q^{98}+O(q^{100}) \) 30 * q - 2 * q^4 - 8 * q^6 + 12 * q^7 + 6 * q^8 - 36 * q^9 + 2 * q^10 + 8 * q^12 - 10 * q^14 - 14 * q^15 - 2 * q^16 + 30 * q^17 + 6 * q^18 + 4 * q^20 - 6 * q^22 + 12 * q^23 - 46 * q^24 - 30 * q^25 + 4 * q^26 + 22 * q^28 + 6 * q^30 - 26 * q^31 - 10 * q^32 + 12 * q^33 + 32 * q^36 + 6 * q^38 + 2 * q^39 + 4 * q^40 - 20 * q^41 + 48 * q^42 + 22 * q^44 + 38 * q^46 - 22 * q^47 + 24 * q^48 + 30 * q^49 + 48 * q^52 - 66 * q^54 + 32 * q^55 - 6 * q^56 - 26 * q^57 - 32 * q^58 - 14 * q^60 - 46 * q^62 - 4 * q^63 - 50 * q^64 + 6 * q^65 - 44 * q^66 - 2 * q^68 - 2 * q^70 + 58 * q^71 - 14 * q^72 - 18 * q^73 + 56 * q^74 - 6 * q^76 + 12 * q^78 - 60 * q^79 - 42 * q^81 - 24 * q^82 + 72 * q^84 + 48 * q^86 + 6 * q^87 + 18 * q^88 + 6 * q^89 - 14 * q^90 + 74 * q^92 - 16 * q^94 - 30 * q^95 + 22 * q^96 + 38 * q^97 - 16 * q^98

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