LMFDB - Embedded newform 75.2.g.c.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,2,Mod(16,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("75.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.g (of order $5$, degree $4$, 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:	$0.598878015160$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 $ x^12 + 3x^10 - 2x^9 + 34x^8 - 22x^7 + 236x^6 - 179x^5 + 877x^4 - 409x^3 + 96x^2 - 11x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			16.2
Root			$0.0437845 + 0.134755i$ of defining polynomial
Character	$\chi$	$=$	75.16
Dual form			75.2.g.c.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.114629 + 0.0832830i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.611830 - 1.88302i) q^{4} +(2.14898 + 0.617963i) q^{5} +(0.0437845 - 0.134755i) q^{6} -0.858311 q^{7} +(0.174259 - 0.536314i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.114629 + 0.0832830i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.611830 - 1.88302i) q^{4} +(2.14898 + 0.617963i) q^{5} +(0.0437845 - 0.134755i) q^{6} -0.858311 q^{7} +(0.174259 - 0.536314i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.194870 + 0.249810i) q^{10} +(2.97713 + 2.16301i) q^{11} +(-1.60179 + 1.16377i) q^{12} +(-3.70638 + 2.69285i) q^{13} +(-0.0983875 - 0.0714827i) q^{14} +(-0.0763538 - 2.23476i) q^{15} +(-3.13894 + 2.28058i) q^{16} +(-1.63996 + 5.04728i) q^{17} -0.141689 q^{18} +(1.96804 - 6.05699i) q^{19} +(-0.151175 - 4.42466i) q^{20} +(0.265233 + 0.816302i) q^{21} +(0.161124 + 0.495888i) q^{22} +(-2.76990 - 2.01245i) q^{23} -0.563913 q^{24} +(4.23624 + 2.65598i) q^{25} -0.649128 q^{26} +(0.809017 + 0.587785i) q^{27} +(0.525140 + 1.61622i) q^{28} +(1.15388 + 3.55129i) q^{29} +(0.177365 - 0.262528i) q^{30} +(0.387167 - 1.19158i) q^{31} -1.67757 q^{32} +(1.13716 - 3.49982i) q^{33} +(-0.608340 + 0.441985i) q^{34} +(-1.84449 - 0.530404i) q^{35} +(1.60179 + 1.16377i) q^{36} +(6.02772 - 4.37939i) q^{37} +(0.730039 - 0.530404i) q^{38} +(3.70638 + 2.69285i) q^{39} +(0.705901 - 1.04484i) q^{40} +(2.04817 - 1.48808i) q^{41} +(-0.0375807 + 0.115661i) q^{42} -3.37972 q^{43} +(2.25149 - 6.92938i) q^{44} +(-2.10179 + 0.763197i) q^{45} +(-0.149909 - 0.461371i) q^{46} +(-2.62645 - 8.08338i) q^{47} +(3.13894 + 2.28058i) q^{48} -6.26330 q^{49} +(0.264399 + 0.657260i) q^{50} +5.30702 q^{51} +(7.33836 + 5.33163i) q^{52} +(-0.725656 - 2.23334i) q^{53} +(0.0437845 + 0.134755i) q^{54} +(5.06113 + 6.48802i) q^{55} +(-0.149568 + 0.460324i) q^{56} -6.36870 q^{57} +(-0.163493 + 0.503181i) q^{58} +(-10.6195 + 7.71550i) q^{59} +(-4.16139 + 1.51107i) q^{60} +(-8.37141 - 6.08218i) q^{61} +(0.143619 - 0.104345i) q^{62} +(0.694388 - 0.504502i) q^{63} +(6.08559 + 4.42144i) q^{64} +(-9.62903 + 3.49647i) q^{65} +(0.421827 - 0.306475i) q^{66} +(1.03412 - 3.18270i) q^{67} +10.5075 q^{68} +(-1.05801 + 3.25621i) q^{69} +(-0.167259 - 0.214415i) q^{70} +(-1.33585 - 4.11131i) q^{71} +(0.174259 + 0.536314i) q^{72} +(7.34593 + 5.33713i) q^{73} +1.05568 q^{74} +(1.21692 - 4.84965i) q^{75} -12.6095 q^{76} +(-2.55530 - 1.85653i) q^{77} +(0.200592 + 0.617357i) q^{78} +(-1.00347 - 3.08837i) q^{79} +(-8.15484 + 2.96116i) q^{80} +(0.309017 - 0.951057i) q^{81} +0.358712 q^{82} +(-2.28447 + 7.03087i) q^{83} +(1.37484 - 0.998876i) q^{84} +(-6.64327 + 9.83307i) q^{85} +(-0.387414 - 0.281473i) q^{86} +(3.02091 - 2.19482i) q^{87} +(1.67884 - 1.21975i) q^{88} +(12.5378 + 9.10921i) q^{89} +(-0.304488 - 0.0875589i) q^{90} +(3.18123 - 2.31130i) q^{91} +(-2.09478 + 6.44705i) q^{92} -1.25290 q^{93} +(0.372140 - 1.14533i) q^{94} +(7.97227 - 11.8002i) q^{95} +(0.518399 + 1.59547i) q^{96} +(-3.10209 - 9.54725i) q^{97} +(-0.717957 - 0.521627i) q^{98} -3.67993 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 10 q^{4} - 6 q^{5} - 12 q^{7} + 9 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 10 * q^4 - 6 * q^5 - 12 * q^7 + 9 * q^8 - 3 * q^9	\( 12 q + 3 q^{3} - 10 q^{4} - 6 q^{5} - 12 q^{7} + 9 q^{8} - 3 q^{9} - 9 q^{10} - 4 q^{11} - 2 q^{13} + 6 q^{14} - 9 q^{15} + 16 q^{16} - q^{17} + 7 q^{19} + 26 q^{20} - 3 q^{21} + 13 q^{22} + 19 q^{23} + 6 q^{24} + 4 q^{25} - 56 q^{26} + 3 q^{27} + q^{28} - q^{29} + 19 q^{30} + 13 q^{31} - 32 q^{32} - q^{33} - 25 q^{34} - 10 q^{35} + 8 q^{37} - 22 q^{38} + 2 q^{39} - 28 q^{40} + 8 q^{41} - 16 q^{42} - 4 q^{43} + 33 q^{44} - 6 q^{45} - 22 q^{46} - 13 q^{47} - 16 q^{48} - 28 q^{49} + 81 q^{50} + 26 q^{51} + 44 q^{52} + 44 q^{53} + 9 q^{55} + 45 q^{56} - 22 q^{57} + 41 q^{58} - 22 q^{59} + 14 q^{60} - 8 q^{61} + 41 q^{62} + 3 q^{63} + 49 q^{64} - 38 q^{65} - 3 q^{66} - 6 q^{67} - 100 q^{68} + 6 q^{69} - 45 q^{70} - 21 q^{71} + 9 q^{72} - 16 q^{73} - 44 q^{74} - 4 q^{75} - 52 q^{76} + q^{77} - 19 q^{78} + 10 q^{79} - 99 q^{80} - 3 q^{81} + 26 q^{82} - 10 q^{83} - 6 q^{84} + 23 q^{85} + 56 q^{86} - 4 q^{87} - 16 q^{88} + 57 q^{89} + 16 q^{90} - 7 q^{91} + 3 q^{92} + 22 q^{93} - 23 q^{94} + 21 q^{95} - 23 q^{96} + 4 q^{97} - 18 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 10 * q^4 - 6 * q^5 - 12 * q^7 + 9 * q^8 - 3 * q^9 - 9 * q^10 - 4 * q^11 - 2 * q^13 + 6 * q^14 - 9 * q^15 + 16 * q^16 - q^17 + 7 * q^19 + 26 * q^20 - 3 * q^21 + 13 * q^22 + 19 * q^23 + 6 * q^24 + 4 * q^25 - 56 * q^26 + 3 * q^27 + q^28 - q^29 + 19 * q^30 + 13 * q^31 - 32 * q^32 - q^33 - 25 * q^34 - 10 * q^35 + 8 * q^37 - 22 * q^38 + 2 * q^39 - 28 * q^40 + 8 * q^41 - 16 * q^42 - 4 * q^43 + 33 * q^44 - 6 * q^45 - 22 * q^46 - 13 * q^47 - 16 * q^48 - 28 * q^49 + 81 * q^50 + 26 * q^51 + 44 * q^52 + 44 * q^53 + 9 * q^55 + 45 * q^56 - 22 * q^57 + 41 * q^58 - 22 * q^59 + 14 * q^60 - 8 * q^61 + 41 * q^62 + 3 * q^63 + 49 * q^64 - 38 * q^65 - 3 * q^66 - 6 * q^67 - 100 * q^68 + 6 * q^69 - 45 * q^70 - 21 * q^71 + 9 * q^72 - 16 * q^73 - 44 * q^74 - 4 * q^75 - 52 * q^76 + q^77 - 19 * q^78 + 10 * q^79 - 99 * q^80 - 3 * q^81 + 26 * q^82 - 10 * q^83 - 6 * q^84 + 23 * q^85 + 56 * q^86 - 4 * q^87 - 16 * q^88 + 57 * q^89 + 16 * q^90 - 7 * q^91 + 3 * q^92 + 22 * q^93 - 23 * q^94 + 21 * q^95 - 23 * q^96 + 4 * q^97 - 18 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	0.114629	+	0.0832830i	0.0810551	+	0.0588900i	0.627575	−	0.778556i	$-0.284048\pi$
$2$	0.114629	+	0.0832830i	0.0810551	+	0.0588900i	−0.546520	+	0.837446i	$0.684048\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.611830	−	1.88302i	−0.305915	−	0.941510i
$5$	2.14898	+	0.617963i	0.961054	+	0.276362i
$5$	2.14898	+	0.617963i	0.961054	+	0.276362i
$6$	0.0437845	−	0.134755i	0.0178749	−	0.0550134i
$7$	−0.858311			−0.324411			−0.162205	−	0.986757i	$-0.551861\pi$
$7$	−0.858311			−0.324411			−0.162205	+	0.986757i	$0.551861\pi$
$8$	0.174259	−	0.536314i	0.0616098	−	0.189615i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	0.194870	+	0.249810i	0.0616234	+	0.0789969i
$11$	2.97713	+	2.16301i	0.897637	+	0.652171i	0.937858	−	0.347019i	$-0.112806\pi$
$11$	2.97713	+	2.16301i	0.897637	+	0.652171i	−0.0402210	+	0.999191i	$0.512806\pi$
$12$	−1.60179	+	1.16377i	−0.462398	+	0.335952i
$13$	−3.70638	+	2.69285i	−1.02797	+	0.746861i	−0.967901	−	0.251334i	$-0.919131\pi$
$13$	−3.70638	+	2.69285i	−1.02797	+	0.746861i	−0.0600653	+	0.998194i	$0.519131\pi$
$14$	−0.0983875	−	0.0714827i	−0.0262952	−	0.0191045i
$15$	−0.0763538	−	2.23476i	−0.0197145	−	0.577014i
$16$	−3.13894	+	2.28058i	−0.784736	+	0.570144i
$17$	−1.63996	+	5.04728i	−0.397749	+	1.22414i	0.529052	+	0.848590i	$0.322548\pi$
$17$	−1.63996	+	5.04728i	−0.397749	+	1.22414i	−0.926800	+	0.375555i	$0.877452\pi$
$18$	−0.141689			−0.0333965
$19$	1.96804	−	6.05699i	0.451499	−	1.38957i	−0.423699	−	0.905803i	$-0.639268\pi$
$19$	1.96804	−	6.05699i	0.451499	−	1.38957i	0.875197	−	0.483766i	$-0.160732\pi$
$20$	−0.151175	−	4.42466i	−0.0338037	−	0.989385i
$21$	0.265233	+	0.816302i	0.0578785	+	0.178132i
$22$	0.161124	+	0.495888i	0.0343517	+	0.105724i
$23$	−2.76990	−	2.01245i	−0.577564	−	0.419625i	0.260281	−	0.965533i	$-0.416185\pi$
$23$	−2.76990	−	2.01245i	−0.577564	−	0.419625i	−0.837845	+	0.545908i	$0.816185\pi$
$24$	−0.563913			−0.115108
$25$	4.23624	+	2.65598i	0.847249	+	0.531197i
$26$	−0.649128			−0.127304
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.525140	+	1.61622i	0.0992422	+	0.305436i
$29$	1.15388	+	3.55129i	0.214271	+	0.659458i	0.999205	+	0.0398784i	$0.0126971\pi$
$29$	1.15388	+	3.55129i	0.214271	+	0.659458i	−0.784934	+	0.619580i	$0.787303\pi$
$30$	0.177365	−	0.262528i	0.0323824	−	0.0479309i
$31$	0.387167	−	1.19158i	0.0695373	−	0.214014i	−0.910249	−	0.414062i	$-0.864110\pi$
$31$	0.387167	−	1.19158i	0.0695373	−	0.214014i	0.979786	+	0.200048i	$0.0641098\pi$
$32$	−1.67757			−0.296556
$33$	1.13716	−	3.49982i	0.197954	−	0.609241i
$34$	−0.608340	+	0.441985i	−0.104329	+	0.0757997i
$35$	−1.84449	−	0.530404i	−0.311776	−	0.0896547i
$36$	1.60179	+	1.16377i	0.266965	+	0.193962i
$37$	6.02772	−	4.37939i	0.990951	−	0.719968i	0.0308218	−	0.999525i	$-0.490188\pi$
$37$	6.02772	−	4.37939i	0.990951	−	0.719968i	0.960129	+	0.279557i	$0.0901876\pi$
$38$	0.730039	−	0.530404i	0.118428	−	0.0860430i
$39$	3.70638	+	2.69285i	0.593496	+	0.431200i
$40$	0.705901	−	1.04484i	0.111613	−	0.165204i
$41$	2.04817	−	1.48808i	0.319870	−	0.232399i	−0.416250	−	0.909250i	$-0.636656\pi$
$41$	2.04817	−	1.48808i	0.319870	−	0.232399i	0.736120	+	0.676851i	$0.236656\pi$
$42$	−0.0375807	+	0.115661i	−0.00579882	+	0.0178469i
$43$	−3.37972			−0.515402			−0.257701	−	0.966225i	$-0.582965\pi$
$43$	−3.37972			−0.515402			−0.257701	+	0.966225i	$0.582965\pi$
$44$	2.25149	−	6.92938i	0.339425	−	1.04464i
$45$	−2.10179	+	0.763197i	−0.313317	+	0.113771i
$46$	−0.149909	−	0.461371i	−0.0221028	−	0.0680255i
$47$	−2.62645	−	8.08338i	−0.383107	−	1.17908i	−0.937844	−	0.347057i	$-0.887181\pi$
$47$	−2.62645	−	8.08338i	−0.383107	−	1.17908i	0.554737	−	0.832026i	$-0.312819\pi$
$48$	3.13894	+	2.28058i	0.453067	+	0.329173i
$49$	−6.26330			−0.894758
$50$	0.264399	+	0.657260i	0.0373917	+	0.0929506i
$51$	5.30702			0.743132
$52$	7.33836	+	5.33163i	1.01765	+	0.739364i
$53$	−0.725656	−	2.23334i	−0.0996765	−	0.306773i	0.888768	−	0.458358i	$-0.151562\pi$
$53$	−0.725656	−	2.23334i	−0.0996765	−	0.306773i	−0.988444	+	0.151585i	$0.951562\pi$
$54$	0.0437845	+	0.134755i	0.00595831	+	0.0183378i
$55$	5.06113	+	6.48802i	0.682442	+	0.874844i
$56$	−0.149568	+	0.460324i	−0.0199869	+	0.0615133i
$57$	−6.36870			−0.843555
$58$	−0.163493	+	0.503181i	−0.0214677	+	0.0660709i
$59$	−10.6195	+	7.71550i	−1.38254	+	1.00447i	−0.385900	+	0.922541i	$0.626109\pi$
$59$	−10.6195	+	7.71550i	−1.38254	+	1.00447i	−0.996638	+	0.0819317i	$0.973891\pi$
$60$	−4.16139	+	1.51107i	−0.537233	+	0.195079i
$61$	−8.37141	−	6.08218i	−1.07185	−	0.778744i	−0.0956052	−	0.995419i	$-0.530479\pi$
$61$	−8.37141	−	6.08218i	−1.07185	−	0.778744i	−0.976244	+	0.216676i	$0.930479\pi$
$62$	0.143619	−	0.104345i	0.0182396	−	0.0132519i
$63$	0.694388	−	0.504502i	0.0874846	−	0.0635613i
$64$	6.08559	+	4.42144i	0.760698	+	0.552680i
$65$	−9.62903	+	3.49647i	−1.19433	+	0.433683i
$66$	0.421827	−	0.306475i	0.0519234	−	0.0377245i
$67$	1.03412	−	3.18270i	0.126338	−	0.388828i	−0.867805	−	0.496906i	$-0.834469\pi$
$67$	1.03412	−	3.18270i	0.126338	−	0.388828i	0.994142	+	0.108077i	$0.0344695\pi$
$68$	10.5075			1.27422
$69$	−1.05801	+	3.25621i	−0.127369	+	0.392002i
$70$	−0.167259	−	0.214415i	−0.0199913	−	0.0256275i
$71$	−1.33585	−	4.11131i	−0.158536	−	0.487923i	0.839966	−	0.542639i	$-0.182575\pi$
$71$	−1.33585	−	4.11131i	−0.158536	−	0.487923i	−0.998502	+	0.0547158i	$0.982575\pi$
$72$	0.174259	+	0.536314i	0.0205366	+	0.0632052i
$73$	7.34593	+	5.33713i	0.859776	+	0.624664i	0.927824	−	0.373018i	$-0.121677\pi$
$73$	7.34593	+	5.33713i	0.859776	+	0.624664i	−0.0680477	+	0.997682i	$0.521677\pi$
$74$	1.05568			0.122721
$75$	1.21692	−	4.84965i	0.140518	−	0.559989i
$76$	−12.6095			−1.44641
$77$	−2.55530	−	1.85653i	−0.291203	−	0.211572i
$78$	0.200592	+	0.617357i	0.0227125	+	0.0699020i
$79$	−1.00347	−	3.08837i	−0.112899	−	0.347469i	0.878604	−	0.477552i	$-0.158476\pi$
$79$	−1.00347	−	3.08837i	−0.112899	−	0.347469i	−0.991503	+	0.130083i	$0.958476\pi$
$80$	−8.15484	+	2.96116i	−0.911739	+	0.331068i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	0.358712			0.0396131
$83$	−2.28447	+	7.03087i	−0.250753	+	0.771738i	0.743884	+	0.668309i	$0.232981\pi$
$83$	−2.28447	+	7.03087i	−0.250753	+	0.771738i	−0.994637	+	0.103429i	$0.967019\pi$
$84$	1.37484	−	0.998876i	0.150007	−	0.108986i
$85$	−6.64327	+	9.83307i	−0.720564	+	1.06655i
$86$	−0.387414	−	0.281473i	−0.0417760	−	0.0303520i
$87$	3.02091	−	2.19482i	0.323875	−	0.235309i
$88$	1.67884	−	1.21975i	0.178965	−	0.130026i
$89$	12.5378	+	9.10921i	1.32900	+	0.965575i	0.999773	+	0.0213236i	$0.00678803\pi$
$89$	12.5378	+	9.10921i	1.32900	+	0.965575i	0.329227	+	0.944251i	$0.393212\pi$
$90$	−0.304488	−	0.0875589i	−0.0320959	−	0.00922952i
$91$	3.18123	−	2.31130i	0.333483	−	0.242290i
$92$	−2.09478	+	6.44705i	−0.218395	+	0.672152i
$93$	−1.25290			−0.129920
$94$	0.372140	−	1.14533i	0.0383833	−	0.118132i
$95$	7.97227	−	11.8002i	0.817938	−	1.21067i
$96$	0.518399	+	1.59547i	0.0529089	+	0.162837i
$97$	−3.10209	−	9.54725i	−0.314970	−	0.969377i	−0.975767	−	0.218812i	$-0.929782\pi$
$97$	−3.10209	−	9.54725i	−0.314970	−	0.969377i	0.660797	−	0.750564i	$-0.270218\pi$
$98$	−0.717957	−	0.521627i	−0.0725247	−	0.0526922i
$99$	−3.67993			−0.369847
$100$	2.40941	−	9.60194i	0.240941	−	0.960194i
$101$	−0.714616			−0.0711070			−0.0355535	−	0.999368i	$-0.511319\pi$
$101$	−0.714616			−0.0711070			−0.0355535	+	0.999368i	$0.511319\pi$
$102$	0.608340	+	0.441985i	0.0602346	+	0.0437630i
$103$	0.241269	+	0.742551i	0.0237730	+	0.0731657i	0.962239	−	0.272205i	$-0.0877530\pi$
$103$	0.241269	+	0.742551i	0.0237730	+	0.0731657i	−0.938466	+	0.345371i	$0.887753\pi$
$104$	0.798339	+	2.45704i	0.0782836	+	0.240932i
$105$	0.0655353	+	1.91812i	0.00639559	+	0.187189i
$106$	0.102818	−	0.316441i	0.00998655	−	0.0307354i
$107$	11.9601			1.15623			0.578113	−	0.815957i	$-0.303789\pi$
$107$	11.9601			1.15623			0.578113	+	0.815957i	$0.303789\pi$
$108$	0.611830	−	1.88302i	0.0588734	−	0.181194i
$109$	−1.96902	+	1.43057i	−0.188598	+	0.137024i	−0.678078	−	0.734990i	$-0.737187\pi$
$109$	−1.96902	+	1.43057i	−0.188598	+	0.137024i	0.489480	+	0.872015i	$0.337187\pi$
$110$	0.0398114	+	1.16522i	0.00379587	+	0.111100i
$111$	−6.02772	−	4.37939i	−0.572126	−	0.415674i
$112$	2.69419	−	1.95744i	0.254577	−	0.184961i
$113$	12.9729	−	9.42535i	1.22039	−	0.886662i	0.224254	−	0.974531i	$-0.428006\pi$
$113$	12.9729	−	9.42535i	1.22039	−	0.886662i	0.996132	+	0.0878685i	$0.0280055\pi$
$114$	−0.730039	−	0.530404i	−0.0683744	−	0.0496769i
$115$	−4.70884	−	6.03642i	−0.439102	−	0.562899i
$116$	5.98117	−	4.34558i	0.555338	−	0.403477i
$117$	1.41571	−	4.35712i	0.130883	−	0.402815i
$118$	−1.85987			−0.171215
$119$	1.40759	−	4.33213i	0.129034	−	0.397126i
$120$	−1.21184	−	0.348478i	−0.110625	−	0.0318115i
$121$	0.785483	+	2.41747i	0.0714076	+	0.219770i
$122$	−0.453065	−	1.39439i	−0.0410186	−	0.126242i
$123$	−2.04817	−	1.48808i	−0.184677	−	0.134176i
$124$	−2.48065			−0.222769
$125$	7.46231	+	8.32550i	0.667449	+	0.744655i
$126$	0.121614			0.0108342
$127$	3.10539	+	2.25620i	0.275559	+	0.200205i	0.716978	−	0.697096i	$-0.245525\pi$
$127$	3.10539	+	2.25620i	0.275559	+	0.200205i	−0.441419	+	0.897301i	$0.645525\pi$
$128$	1.36615	+	4.20459i	0.120752	+	0.371637i
$129$	1.04439	+	3.21430i	0.0919534	+	0.283004i
$130$	−1.39496	−	0.401137i	−0.122346	−	0.0351821i
$131$	−3.84709	+	11.8401i	−0.336122	+	1.03448i	0.630044	+	0.776559i	$0.283037\pi$
$131$	−3.84709	+	11.8401i	−0.336122	+	1.03448i	−0.966167	+	0.257919i	$0.916963\pi$
$132$	−7.28598			−0.634163
$133$	−1.68919	+	5.19878i	−0.146471	+	0.450791i
$134$	0.383605	−	0.278705i	0.0331384	−	0.0240765i
$135$	1.37533	+	1.76308i	0.118370	+	0.151742i
$136$	2.42115	+	1.75907i	0.207611	+	0.150839i
$137$	9.59406	−	6.97049i	0.819676	−	0.595529i	−0.0969439	−	0.995290i	$-0.530907\pi$
$137$	9.59406	−	6.97049i	0.819676	−	0.595529i	0.916620	+	0.399761i	$0.130907\pi$
$138$	−0.392466	+	0.285143i	−0.0334089	+	0.0242730i
$139$	3.77074	+	2.73960i	0.319830	+	0.232370i	0.736103	−	0.676870i	$-0.236664\pi$
$139$	3.77074	+	2.73960i	0.319830	+	0.232370i	−0.416273	+	0.909240i	$0.636664\pi$
$140$	0.129755	+	3.79773i	0.0109663	+	0.320967i
$141$	−6.87614	+	4.99580i	−0.579075	+	0.420723i
$142$	0.189275	−	0.582530i	0.0158836	−	0.0488848i
$143$	−16.8590			−1.40982
$144$	1.19897	−	3.69005i	0.0999141	−	0.307504i
$145$	0.285109	+	8.34472i	0.0236770	+	0.692991i
$146$	0.397566	+	1.22358i	0.0329028	+	0.101264i
$147$	1.93547	+	5.95676i	0.159635	+	0.491305i
$148$	−11.9344	−	8.67087i	−0.981004	−	0.712741i
$149$	−11.5480			−0.946053			−0.473026	−	0.881048i	$-0.656838\pi$
$149$	−11.5480			−0.946053			−0.473026	+	0.881048i	$0.656838\pi$
$150$	0.543388	−	0.454563i	0.0443674	−	0.0371149i
$151$	24.4694			1.99129			0.995646	−	0.0932103i	$-0.0297129\pi$
$151$	24.4694			1.99129			0.995646	+	0.0932103i	$0.0297129\pi$
$152$	−2.90550	−	2.11097i	−0.235667	−	0.171222i
$153$	−1.63996	−	5.04728i	−0.132583	−	0.408048i
$154$	−0.138294	−	0.425626i	−0.0111441	−	0.0342979i
$155$	1.56837	−	2.32143i	0.125974	−	0.186461i
$156$	2.80300	−	8.62676i	0.224420	−	0.690693i
$157$	−22.3660			−1.78500			−0.892501	−	0.451045i	$-0.851052\pi$
$157$	−22.3660			−1.78500			−0.892501	+	0.451045i	$0.851052\pi$
$158$	0.142181	−	0.437589i	0.0113113	−	0.0348127i
$159$	−1.89979	+	1.38028i	−0.150663	+	0.109463i
$160$	−3.60508	−	1.03668i	−0.285006	−	0.0819567i
$161$	2.37743	+	1.72731i	0.187368	+	0.136131i
$162$	0.114629	−	0.0832830i	0.00900612	−	0.00654333i
$163$	0.658095	−	0.478134i	0.0515460	−	0.0374503i	−0.561714	−	0.827332i	$-0.689858\pi$
$163$	0.658095	−	0.478134i	0.0515460	−	0.0374503i	0.613260	+	0.789881i	$0.289858\pi$
$164$	−4.05522	−	2.94629i	−0.316659	−	0.230067i
$165$	4.60650	−	6.81833i	0.358615	−	0.530806i
$166$	−0.847418	+	0.615685i	−0.0657724	+	0.0477865i
$167$	−7.77671	+	23.9343i	−0.601780	+	1.85209i	−0.0842082	+	0.996448i	$0.526836\pi$
$167$	−7.77671	+	23.9343i	−0.601780	+	1.85209i	−0.517572	+	0.855640i	$0.673164\pi$
$168$	0.484013			0.0373424
$169$	2.46864	−	7.59770i	0.189896	−	0.584438i
$170$	−1.58044	+	0.573885i	−0.121214	+	0.0440150i
$171$	1.96804	+	6.05699i	0.150500	+	0.463190i
$172$	2.06781	+	6.36408i	0.157669	+	0.485256i
$173$	−0.332462	−	0.241548i	−0.0252766	−	0.0183645i	0.575075	−	0.818101i	$-0.304973\pi$
$173$	−0.332462	−	0.241548i	−0.0252766	−	0.0183645i	−0.600352	+	0.799736i	$0.704973\pi$
$174$	0.529076			0.0401091
$175$	−3.63601	−	2.27966i	−0.274857	−	0.172326i
$176$	−14.2779			−1.07624
$177$	10.6195	+	7.71550i	0.798208	+	0.579932i
$178$	0.678550	+	2.08836i	0.0508595	+	0.156529i
$179$	−4.58896	−	14.1234i	−0.342995	−	1.05563i	−0.962648	−	0.270755i	$-0.912727\pi$
$179$	−4.58896	−	14.1234i	−0.342995	−	1.05563i	0.619653	−	0.784876i	$-0.287273\pi$
$180$	2.72305	+	3.49077i	0.202965	+	0.260187i
$181$	0.228432	−	0.703043i	0.0169792	−	0.0522568i	−0.942208	−	0.335029i	$-0.891254\pi$
$181$	0.228432	−	0.703043i	0.0169792	−	0.0522568i	0.959187	+	0.282772i	$0.0912540\pi$
$182$	0.557153			0.0412990
$183$	−3.19759	+	9.84118i	−0.236373	+	0.727481i
$184$	−1.56198	+	1.13485i	−0.115151	+	0.0836621i
$185$	15.6598	−	5.68633i	1.15133	−	0.418067i
$186$	−0.143619	−	0.104345i	−0.0105307	−	0.00765097i
$187$	−15.7997	+	11.4791i	−1.15539	+	0.839437i
$188$	−13.6142	+	9.89131i	−0.992920	+	0.721398i
$189$	−0.694388	−	0.504502i	−0.0505093	−	0.0366971i
$190$	1.89661	−	0.688692i	0.137595	−	0.0499630i
$191$	2.20462	−	1.60175i	0.159521	−	0.115899i	−0.505161	−	0.863025i	$-0.668567\pi$
$191$	2.20462	−	1.60175i	0.159521	−	0.115899i	0.664682	+	0.747126i	$0.268567\pi$
$192$	2.32449	−	7.15404i	0.167755	−	0.516298i
$193$	14.2040			1.02243			0.511215	−	0.859453i	$-0.329196\pi$
$193$	14.2040			1.02243			0.511215	+	0.859453i	$0.329196\pi$
$194$	0.439534	−	1.35275i	0.0315567	−	0.0971215i
$195$	6.30087	+	8.07728i	0.451215	+	0.578426i
$196$	3.83208	+	11.7939i	0.273720	+	0.842423i
$197$	−1.71378	−	5.27447i	−0.122102	−	0.375791i	0.871260	−	0.490821i	$-0.163303\pi$
$197$	−1.71378	−	5.27447i	−0.122102	−	0.375791i	−0.993362	+	0.115031i	$0.963303\pi$
$198$	−0.421827	−	0.306475i	−0.0299780	−	0.0217803i
$199$	5.96371			0.422756			0.211378	−	0.977404i	$-0.432205\pi$
$199$	5.96371			0.422756			0.211378	+	0.977404i	$0.432205\pi$
$200$	2.16264	−	1.80913i	0.152922	−	0.127925i
$201$	−3.34649			−0.236043
$202$	−0.0819159	−	0.0595154i	−0.00576358	−	0.00418749i
$203$	−0.990391	−	3.04811i	−0.0695119	−	0.213935i
$204$	−3.24700	−	9.99322i	−0.227335	−	0.699666i
$205$	5.32106	−	1.93217i	0.371639	−	0.134948i
$206$	−0.0341853	+	0.105212i	−0.00238181	+	0.00733044i
$207$	3.42379			0.237970
$208$	5.49289	−	16.9054i	0.380863	−	1.17218i
$209$	18.9604	−	13.7755i	1.31152	−	0.952875i
$210$	−0.152235	+	0.225331i	−0.0105052	+	0.0155493i
$211$	11.0983	+	8.06342i	0.764042	+	0.555109i	0.900147	−	0.435586i	$-0.143459\pi$
$211$	11.0983	+	8.06342i	0.764042	+	0.555109i	−0.136106	+	0.990694i	$0.543459\pi$
$212$	−3.76144	+	2.73285i	−0.258337	+	0.187693i
$213$	−3.49729	+	2.54093i	−0.239630	+	0.174102i
$214$	1.37098	+	0.996073i	0.0937180	+	0.0680901i
$215$	−7.26295	−	2.08854i	−0.495329	−	0.142437i
$216$	0.456216	−	0.331460i	0.0310415	−	0.0225530i
$217$	−0.332310	+	1.02274i	−0.0225587	+	0.0694284i
$218$	−0.344849			−0.0233561
$219$	2.80590	−	8.63566i	0.189605	−	0.583544i
$220$	9.12052	−	13.4998i	0.614905	−	0.910154i
$221$	−7.51322	−	23.1233i	−0.505394	−	1.55544i
$222$	−0.326224	−	1.00401i	−0.0218947	−	0.0673849i
$223$	−2.62259	−	1.90543i	−0.175622	−	0.127597i	0.496502	−	0.868036i	$-0.334618\pi$
$223$	−2.62259	−	1.90543i	−0.175622	−	0.127597i	−0.672124	+	0.740439i	$0.734618\pi$
$224$	1.43988			0.0962060
$225$	−4.98834	+	0.341265i	−0.332556	+	0.0227510i
$226$	2.27204			0.151134
$227$	−10.6627	−	7.74694i	−0.707711	−	0.514182i	0.174723	−	0.984618i	$-0.444097\pi$
$227$	−10.6627	−	7.74694i	−0.707711	−	0.514182i	−0.882434	+	0.470435i	$0.844097\pi$
$228$	3.89656	+	11.9924i	0.258056	+	0.794215i
$229$	1.80407	+	5.55236i	0.119216	+	0.366911i	0.992803	−	0.119758i	$-0.0382119\pi$
$229$	1.80407	+	5.55236i	0.119216	+	0.366911i	−0.873587	+	0.486669i	$0.838212\pi$
$230$	−0.0370403	−	1.08412i	−0.00244237	−	0.0714845i
$231$	−0.976037	+	3.00393i	−0.0642185	+	0.197644i
$232$	2.10568			0.138245
$233$	2.88453	−	8.87767i	0.188972	−	0.581595i	−0.811022	−	0.585015i	$-0.801089\pi$
$233$	2.88453	−	8.87767i	0.188972	−	0.581595i	0.999994	+	0.00341975i	$0.00108854\pi$
$234$	0.525156	−	0.381548i	0.0343305	−	0.0249426i
$235$	−0.648959	−	18.9941i	−0.0423334	−	1.23904i
$236$	21.0258	+	15.2761i	1.36866	+	0.994390i
$237$	−2.62712	+	1.90872i	−0.170650	+	0.123984i
$238$	0.522144	−	0.379360i	0.0338456	−	0.0245903i
$239$	−13.8748	−	10.0806i	−0.897485	−	0.652061i	0.0403340	−	0.999186i	$-0.487158\pi$
$239$	−13.8748	−	10.0806i	−0.897485	−	0.652061i	−0.937819	+	0.347125i	$0.887158\pi$
$240$	5.33622	+	6.84067i	0.344451	+	0.441563i
$241$	−5.84169	+	4.24424i	−0.376296	+	0.273395i	−0.759817	−	0.650137i	$-0.774711\pi$
$241$	−5.84169	+	4.24424i	−0.376296	+	0.273395i	0.383521	+	0.923532i	$0.374711\pi$
$242$	−0.111295	+	0.342530i	−0.00715430	+	0.0220187i
$243$	−1.00000			−0.0641500
$244$	−6.33099	+	19.4848i	−0.405300	+	1.24739i
$245$	−13.4597	−	3.87049i	−0.859910	−	0.247277i
$246$	−0.110848	−	0.341155i	−0.00706742	−	0.0217513i
$247$	9.01625	+	27.7492i	0.573690	+	1.76564i
$248$	−0.571593	−	0.415286i	−0.0362962	−	0.0263707i
$249$	7.39269			0.468493
$250$	0.162026	+	1.57583i	0.0102474	+	0.0996642i
$251$	−5.75708			−0.363383			−0.181692	−	0.983356i	$-0.558157\pi$
$251$	−5.75708			−0.363383			−0.181692	+	0.983356i	$0.558157\pi$
$252$	−1.37484	−	0.998876i	−0.0866065	−	0.0629233i
$253$	−3.89339	−	11.9826i	−0.244776	−	0.753342i
$254$	0.168066	+	0.517253i	0.0105454	+	0.0324553i
$255$	11.4047	+	3.27954i	0.714189	+	0.205373i
$256$	4.45541	−	13.7123i	0.278463	−	0.857021i
$257$	26.9602			1.68173			0.840867	−	0.541242i	$-0.182046\pi$
$257$	26.9602			1.68173			0.840867	+	0.541242i	$0.182046\pi$
$258$	−0.147979	+	0.455433i	−0.00921278	+	0.0283540i
$259$	−5.17365	+	3.75888i	−0.321475	+	0.233565i
$260$	12.4752	+	15.9924i	0.773682	+	0.991807i
$261$	−3.02091	−	2.19482i	−0.186990	−	0.135856i
$262$	−1.42707	+	1.03683i	−0.0881648	+	0.0640555i
$263$	−16.7202	+	12.1479i	−1.03101	+	0.749073i	−0.968511	−	0.248972i	$-0.919907\pi$
$263$	−16.7202	+	12.1479i	−1.03101	+	0.749073i	−0.0625002	+	0.998045i	$0.519907\pi$
$264$	−1.67884	−	1.21975i	−0.103326	−	0.0750704i
$265$	−0.179299	−	5.24783i	−0.0110143	−	0.322372i
$266$	−0.626600	+	0.455252i	−0.0384193	+	0.0279133i
$267$	4.78900	−	14.7390i	0.293082	−	0.902013i
$268$	−6.62579			−0.404734
$269$	−4.24699	+	13.0709i	−0.258943	+	0.796946i	0.734084	+	0.679059i	$0.237612\pi$
$269$	−4.24699	+	13.0709i	−0.258943	+	0.796946i	−0.993027	+	0.117887i	$0.962388\pi$
$270$	0.0108185	+	0.316643i	0.000658395	+	0.0192703i
$271$	1.03333	+	3.18025i	0.0627701	+	0.193187i	0.977524	−	0.210826i	$-0.0676153\pi$
$271$	1.03333	+	3.18025i	0.0627701	+	0.193187i	−0.914754	+	0.404012i	$0.867615\pi$
$272$	−6.36296	−	19.5832i	−0.385811	−	1.18740i
$273$	−3.18123	−	2.31130i	−0.192537	−	0.139886i
$274$	1.68028			0.101510
$275$	6.86691	+	17.0702i	0.414090	+	1.02937i
$276$	6.77883			0.408038
$277$	−7.20791	−	5.23685i	−0.433081	−	0.314652i	0.349799	−	0.936825i	$-0.386250\pi$
$277$	−7.20791	−	5.23685i	−0.433081	−	0.314652i	−0.782880	+	0.622173i	$0.786250\pi$
$278$	0.204075	+	0.628077i	0.0122396	+	0.0376696i
$279$	0.387167	+	1.19158i	0.0231791	+	0.0713380i
$280$	−0.605882	+	0.896799i	−0.0362084	+	0.0535940i
$281$	−6.95019	+	21.3905i	−0.414613	+	1.27605i	0.497983	+	0.867187i	$0.334074\pi$
$281$	−6.95019	+	21.3905i	−0.414613	+	1.27605i	−0.912596	+	0.408862i	$0.865926\pi$
$282$	−1.20427			−0.0717133
$283$	0.403866	−	1.24297i	0.0240073	−	0.0738870i	−0.938335	−	0.345727i	$-0.887632\pi$
$283$	0.403866	−	1.24297i	0.0240073	−	0.0738870i	0.962342	+	0.271840i	$0.0876322\pi$
$284$	−6.92437	+	5.03085i	−0.410886	+	0.298526i
$285$	−13.6862	−	3.93562i	−0.810702	−	0.233126i
$286$	−1.93254	−	1.40407i	−0.114273	−	0.0830243i
$287$	−1.75797	+	1.27724i	−0.103769	+	0.0753929i
$288$	1.35719	−	0.986054i	0.0799730	−	0.0581038i
$289$	−9.03225	−	6.56231i	−0.531309	−	0.386018i
$290$	−0.662291	+	0.980293i	−0.0388911	+	0.0575648i
$291$	−8.12138	+	5.90053i	−0.476084	+	0.345895i
$292$	5.55546	−	17.0980i	0.325109	−	1.00058i
$293$	1.97058			0.115123			0.0575613	−	0.998342i	$-0.481668\pi$
$293$	1.97058			0.115123			0.0575613	+	0.998342i	$0.481668\pi$
$294$	−0.274235	+	0.844010i	−0.0159937	+	0.0492236i
$295$	−27.5889	+	10.0180i	−1.60629	+	0.583272i
$296$	−1.29835	−	3.99590i	−0.0754648	−	0.232257i
$297$	1.13716	+	3.49982i	0.0659847	+	0.203080i
$298$	−1.32374	−	0.961756i	−0.0766824	−	0.0557130i
$299$	15.6855			0.907118
$300$	−9.87653	+	0.675680i	−0.570222	+	0.0390104i
$301$	2.90085			0.167202
$302$	2.80491	+	2.03789i	0.161404	+	0.117267i
$303$	0.220829	+	0.679640i	0.0126863	+	0.0390443i
$304$	7.63588	+	23.5008i	0.437948	+	1.34786i
$305$	−14.2314	−	18.2437i	−0.814889	−	1.04463i
$306$	0.232365	−	0.715146i	0.0132834	−	0.0408822i
$307$	−15.2544			−0.870617			−0.435308	−	0.900281i	$-0.643361\pi$
$307$	−15.2544			−0.870617			−0.435308	+	0.900281i	$0.643361\pi$
$308$	−1.93248	+	5.94756i	−0.110113	+	0.338894i
$309$	0.631652	−	0.458922i	0.0359334	−	0.0261071i
$310$	0.373116	−	0.135485i	0.0211916	−	0.00769502i
$311$	−14.3562	−	10.4304i	−0.814065	−	0.591453i	0.100941	−	0.994892i	$-0.467815\pi$
$311$	−14.3562	−	10.4304i	−0.814065	−	0.591453i	−0.915006	+	0.403439i	$0.867815\pi$
$312$	2.09008	−	1.51853i	0.118327	−	0.0859699i
$313$	22.1565	−	16.0976i	1.25236	−	0.909890i	0.254001	−	0.967204i	$-0.418253\pi$
$313$	22.1565	−	16.0976i	1.25236	−	0.909890i	0.998356	+	0.0573136i	$0.0182535\pi$
$314$	−2.56380	−	1.86271i	−0.144684	−	0.105119i
$315$	1.80399	−	0.655060i	0.101643	−	0.0369084i
$316$	−5.20150	+	3.77911i	−0.292607	+	0.212592i
$317$	2.67165	−	8.22248i	0.150055	−	0.461821i	−0.847572	−	0.530681i	$-0.821936\pi$
$317$	2.67165	−	8.22248i	0.150055	−	0.461821i	0.997626	+	0.0688603i	$0.0219363\pi$
$318$	−0.332725			−0.0186583
$319$	−4.24621	+	13.0685i	−0.237742	+	0.731696i
$320$	10.3455	+	13.2623i	0.578333	+	0.741383i
$321$	−3.69587	−	11.3747i	−0.206283	−	0.634875i
$322$	0.128668	+	0.396000i	0.00717039	+	0.0220682i
$323$	27.3438	+	19.8664i	1.52145	+	1.10540i
$324$	−1.97992			−0.109996
$325$	−22.8533	+	1.56345i	−1.26767	+	0.0867248i
$326$	0.115257			0.00638351
$327$	1.96902	+	1.43057i	0.108887	+	0.0791109i
$328$	−0.441167	−	1.35777i	−0.0243594	−	0.0749704i
$329$	2.25431	+	6.93805i	0.124284	+	0.382507i
$330$	1.09589	−	0.397936i	0.0603267	−	0.0219057i
$331$	1.53353	−	4.71971i	0.0842903	−	0.259419i	−0.900025	−	0.435839i	$-0.856452\pi$
$331$	1.53353	−	4.71971i	0.0842903	−	0.259419i	0.984315	+	0.176420i	$0.0564517\pi$
$332$	14.6370			0.803308
$333$	−2.30238	+	7.08601i	−0.126170	+	0.388311i
$334$	−2.88475	+	2.09590i	−0.157847	+	0.114682i
$335$	4.18910	−	6.20051i	0.228875	−	0.338770i
$336$	−2.69419	−	1.95744i	−0.146980	−	0.106787i
$337$	5.91011	−	4.29394i	0.321944	−	0.233906i	−0.415061	−	0.909794i	$-0.636240\pi$
$337$	5.91011	−	4.29394i	0.321944	−	0.233906i	0.737005	+	0.675888i	$0.236240\pi$
$338$	0.915738	−	0.665322i	0.0498096	−	0.0361888i
$339$	−12.9729	−	9.42535i	−0.704590	−	0.511915i
$340$	22.5804	+	6.49325i	1.22460	+	0.352146i
$341$	3.73004	−	2.71003i	0.201993	−	0.146757i
$342$	−0.278850	+	0.858212i	−0.0150785	+	0.0464068i
$343$	11.3840			0.614680
$344$	−0.588946	+	1.81259i	−0.0317538	+	0.0977282i
$345$	−4.28586	+	6.34373i	−0.230743	+	0.341535i
$346$	−0.0179930	−	0.0553768i	−0.000967311	−	0.00297708i
$347$	4.92493	+	15.1574i	0.264384	+	0.813691i	0.991835	+	0.127531i	$0.0407051\pi$
$347$	4.92493	+	15.1574i	0.264384	+	0.813691i	−0.727450	+	0.686160i	$0.759295\pi$
$348$	−5.98117	−	4.34558i	−0.320624	−	0.232947i
$349$	16.5844			0.887743			0.443871	−	0.896091i	$-0.353605\pi$
$349$	16.5844			0.887743			0.443871	+	0.896091i	$0.353605\pi$
$350$	−0.226936	−	0.564133i	−0.0121303	−	0.0301542i
$351$	−4.58134			−0.244534
$352$	−4.99435	−	3.62861i	−0.266200	−	0.193405i
$353$	4.00768	+	12.3344i	0.213307	+	0.656492i	0.999269	+	0.0382177i	$0.0121680\pi$
$353$	4.00768	+	12.3344i	0.213307	+	0.656492i	−0.785962	+	0.618275i	$0.787832\pi$
$354$	0.574732	+	1.76884i	0.0305467	+	0.0940129i
$355$	−0.330069	−	9.66063i	−0.0175182	−	0.512733i
$356$	9.48185	−	29.1821i	0.502537	−	1.54665i
$357$	−4.55507			−0.241080
$358$	0.650208	−	2.00113i	0.0343646	−	0.105763i
$359$	10.9153	−	7.93042i	0.576087	−	0.418551i	−0.261225	−	0.965278i	$-0.584126\pi$
$359$	10.9153	−	7.93042i	0.576087	−	0.418551i	0.837311	+	0.546727i	$0.184126\pi$
$360$	0.0430569	+	1.26021i	0.00226930	+	0.0664191i
$361$	−17.4427	−	12.6728i	−0.918036	−	0.666992i
$362$	0.0847365	−	0.0615647i	0.00445365	−	0.00323577i
$363$	2.05642	−	1.49408i	0.107934	−	0.0784188i
$364$	−6.29859	−	4.57619i	−0.330136	−	0.239858i
$365$	12.4881	+	16.0089i	0.653658	+	0.837945i
$366$	−1.18614	+	0.861781i	−0.0620006	+	0.0450460i
$367$	1.41364	−	4.35073i	0.0737913	−	0.227106i	−0.907358	−	0.420360i	$-0.861904\pi$
$367$	1.41364	−	4.35073i	0.0737913	−	0.227106i	0.981149	+	0.193253i	$0.0619039\pi$
$368$	13.2841			0.692482
$369$	−0.782331	+	2.40777i	−0.0407265	+	0.125343i
$370$	2.26864	+	0.652373i	0.117941	+	0.0339152i
$371$	0.622838	+	1.91690i	0.0323361	+	0.0995204i
$372$	0.766562	+	2.35924i	0.0397444	+	0.122321i
$373$	16.7841	+	12.1944i	0.869048	+	0.631401i	0.930331	−	0.366720i	$-0.119519\pi$
$373$	16.7841	+	12.1944i	0.869048	+	0.631401i	−0.0612830	+	0.998120i	$0.519519\pi$
$374$	−2.76712			−0.143084
$375$	5.61204	−	9.66980i	0.289805	−	0.499346i
$376$	−4.79291			−0.247175
$377$	−13.8398	−	10.0552i	−0.712787	−	0.517870i
$378$	−0.0375807	−	0.115661i	−0.00193294	−	0.00594898i
$379$	−1.78662	−	5.49865i	−0.0917725	−	0.282447i	0.894627	−	0.446815i	$-0.147442\pi$
$379$	−1.78662	−	5.49865i	−0.0917725	−	0.282447i	−0.986399	+	0.164368i	$0.947442\pi$
$380$	−27.0977	−	7.79223i	−1.39008	−	0.399733i
$381$	1.18615	−	3.65061i	0.0607686	−	0.187026i
$382$	0.386113			0.0197553
$383$	7.97647	−	24.5491i	0.407579	−	1.25440i	−0.511144	−	0.859495i	$-0.670778\pi$
$383$	7.97647	−	24.5491i	0.407579	−	1.25440i	0.918723	−	0.394903i	$-0.129222\pi$
$384$	3.57664	−	2.59858i	0.182519	−	0.132608i
$385$	−4.34402	−	5.56873i	−0.221392	−	0.283809i
$386$	1.62820	+	1.18295i	0.0828731	+	0.0602108i
$387$	2.73425	−	1.98655i	0.138990	−	0.100982i
$388$	−16.0797	+	11.6826i	−0.816324	+	0.593094i
$389$	12.7053	+	9.23092i	0.644183	+	0.468026i	0.861285	−	0.508123i	$-0.169660\pi$
$389$	12.7053	+	9.23092i	0.644183	+	0.468026i	−0.217102	+	0.976149i	$0.569660\pi$
$390$	0.0495634	+	1.45065i	0.00250974	+	0.0734564i
$391$	14.6999	−	10.6801i	0.743407	−	0.540117i
$392$	−1.09144	+	3.35909i	−0.0551258	+	0.169660i
$393$	12.4495			0.627992
$394$	0.242825	−	0.747337i	0.0122333	−	0.0376503i
$395$	−0.247944	−	7.25695i	−0.0124754	−	0.365137i
$396$	2.25149	+	6.92938i	0.113142	+	0.348214i
$397$	−6.05796	−	18.6445i	−0.304040	−	0.935740i	−0.980034	−	0.198832i	$-0.936285\pi$
$397$	−6.05796	−	18.6445i	−0.304040	−	0.935740i	0.675993	−	0.736908i	$-0.263715\pi$
$398$	0.683615	+	0.496675i	0.0342665	+	0.0248961i
$399$	5.46632			0.273658
$400$	−19.3545	+	1.32409i	−0.967725	+	0.0662046i
$401$	−14.4239			−0.720297			−0.360148	−	0.932895i	$-0.617274\pi$
$401$	−14.4239			−0.720297			−0.360148	+	0.932895i	$0.617274\pi$
$402$	−0.383605	−	0.278705i	−0.0191325	−	0.0139006i
$403$	1.77375	+	5.45903i	0.0883566	+	0.271934i
$404$	0.437224	+	1.34564i	0.0217527	+	0.0669479i
$405$	1.25179	−	1.85284i	0.0622019	−	0.0920684i
$406$	0.140328	−	0.431885i	0.00696436	−	0.0214341i
$407$	27.4179			1.35906
$408$	0.924795	−	2.84623i	0.0457842	−	0.140909i
$409$	22.5507	−	16.3841i	1.11506	−	0.810140i	0.131609	−	0.991302i	$-0.457986\pi$
$409$	22.5507	−	16.3841i	1.11506	−	0.810140i	0.983453	+	0.181162i	$0.0579858\pi$
$410$	0.770865	+	0.221671i	0.0380703	+	0.0109475i
$411$	−9.59406	−	6.97049i	−0.473240	−	0.343829i
$412$	1.25062	−	0.908630i	0.0616137	−	0.0447650i
$413$	9.11481	−	6.62229i	0.448510	−	0.325862i
$414$	0.392466	+	0.285143i	0.0192886	+	0.0140140i
$415$	−9.25410	+	13.6975i	−0.454266	+	0.672383i
$416$	6.21773	−	4.51745i	0.304850	−	0.221486i
$417$	1.44030	−	4.43277i	0.0705316	−	0.217074i
$418$	3.32069			0.162420
$419$	−11.2137	+	34.5121i	−0.547823	+	1.68603i	0.166359	+	0.986065i	$0.446799\pi$
$419$	−11.2137	+	34.5121i	−0.547823	+	1.68603i	−0.714182	+	0.699960i	$0.753201\pi$
$420$	3.57176	−	1.29697i	0.174284	−	0.0632856i
$421$	−1.04324	−	3.21077i	−0.0508445	−	0.156483i	0.922410	−	0.386211i	$-0.126216\pi$
$421$	−1.04324	−	3.21077i	−0.0508445	−	0.156483i	−0.973255	+	0.229728i	$0.926216\pi$
$422$	0.600649	+	1.84861i	0.0292391	+	0.0899888i
$423$	6.87614	+	4.99580i	0.334329	+	0.242904i
$424$	−1.32422			−0.0643099
$425$	−20.3527	+	17.0258i	−0.987253	+	0.825872i
$426$	−0.612508			−0.0296761
$427$	7.18527	+	5.22040i	0.347719	+	0.252633i
$428$	−7.31755	−	22.5211i	−0.353707	−	1.08860i
$429$	5.20972	+	16.0339i	0.251528	+	0.774123i
$430$	−0.658606	−	0.844288i	−0.0317608	−	0.0407152i
$431$	−7.93015	+	24.4065i	−0.381982	+	1.17562i	0.556665	+	0.830737i	$0.312081\pi$
$431$	−7.93015	+	24.4065i	−0.381982	+	1.17562i	−0.938646	+	0.344881i	$0.887919\pi$
$432$	−3.87995			−0.186674
$433$	−12.3010	+	37.8587i	−0.591150	+	1.81937i	−0.0181229	+	0.999836i	$0.505769\pi$
$433$	−12.3010	+	37.8587i	−0.591150	+	1.81937i	−0.573027	+	0.819536i	$0.694231\pi$
$434$	−0.123270	+	0.0895606i	−0.00591713	+	0.00429905i
$435$	7.84820	−	2.84981i	0.376292	−	0.136638i
$436$	3.89850	+	2.83243i	0.186704	+	0.135649i
$437$	−17.6407	+	12.8167i	−0.843867	+	0.613106i
$438$	1.04084	−	0.756216i	0.0497333	−	0.0361334i
$439$	−27.4402	−	19.9365i	−1.30965	−	0.951516i	−1.00000		0.000665125i	$-0.999788\pi$
$439$	−27.4402	−	19.9365i	−1.30965	−	0.951516i	−0.309649	−	0.950851i	$-0.600212\pi$
$440$	4.36156	−	1.58376i	0.207929	−	0.0755026i
$441$	5.06712	−	3.68148i	0.241291	−	0.175308i
$442$	1.06454	−	3.27633i	0.0506352	−	0.155839i
$443$	−28.9300			−1.37451			−0.687253	−	0.726418i	$-0.741184\pi$
$443$	−28.9300			−1.37451			−0.687253	+	0.726418i	$0.741184\pi$
$444$	−4.55855	+	14.0298i	−0.216339	+	0.665823i
$445$	21.3142	+	27.3234i	1.01039	+	1.29525i
$446$	−0.141936	−	0.436835i	−0.00672088	−	0.0206847i
$447$	3.56854	+	10.9828i	0.168786	+	0.519471i
$448$	−5.22332	−	3.79497i	−0.246779	−	0.179295i
$449$	−10.2089			−0.481788			−0.240894	−	0.970551i	$-0.577441\pi$
$449$	−10.2089			−0.481788			−0.240894	+	0.970551i	$0.577441\pi$
$450$	−0.600231	−	0.376325i	−0.0282952	−	0.0177401i
$451$	9.31639			0.438692
$452$	−25.6853	−	18.6615i	−1.20814	−	0.877762i
$453$	−7.56147	−	23.2718i	−0.355269	−	1.09340i
$454$	−0.577074	−	1.77605i	−0.0270834	−	0.0833542i
$455$	8.26470	−	3.00105i	0.387455	−	0.140692i
$456$	−1.10980	+	3.41562i	−0.0519712	+	0.159951i
$457$	32.4952			1.52006			0.760030	−	0.649888i	$-0.225184\pi$
$457$	32.4952			1.52006			0.760030	+	0.649888i	$0.225184\pi$
$458$	−0.255618	+	0.786712i	−0.0119442	+	0.0367606i
$459$	−4.29347	+	3.11939i	−0.200402	+	0.145601i
$460$	−8.48568	+	12.5601i	−0.395647	+	0.585618i
$461$	0.566772	+	0.411784i	0.0263972	+	0.0191787i	0.600906	−	0.799320i	$-0.294807\pi$
$461$	0.566772	+	0.411784i	0.0263972	+	0.0191787i	−0.574508	+	0.818499i	$0.694807\pi$
$462$	−0.362059	+	0.263051i	−0.0168445	+	0.0122382i
$463$	−1.75659	+	1.27623i	−0.0816355	+	0.0593117i	−0.627854	−	0.778331i	$-0.716067\pi$
$463$	−1.75659	+	1.27623i	−0.0816355	+	0.0593117i	0.546219	+	0.837642i	$0.316067\pi$
$464$	−11.7210	−	8.51578i	−0.544132	−	0.395335i
$465$	−2.69246	−	0.774246i	−0.124860	−	0.0359048i
$466$	1.07001	−	0.777408i	0.0495673	−	0.0360127i
$467$	−1.19809	+	3.68734i	−0.0554410	+	0.170630i	−0.974943	−	0.222456i	$-0.928593\pi$
$467$	−1.19809	+	3.68734i	−0.0554410	+	0.170630i	0.919502	+	0.393086i	$0.128593\pi$
$468$	−9.07071			−0.419294
$469$	−0.887597	+	2.73174i	−0.0409854	+	0.126140i
$470$	1.50749	−	2.23132i	0.0695356	−	0.102923i
$471$	6.91148	+	21.2714i	0.318464	+	0.980132i
$472$	2.28739	+	7.03986i	0.105286	+	0.324036i
$473$	−10.0618	−	7.31036i	−0.462644	−	0.336131i
$474$	−0.460109			−0.0211335
$475$	24.4244	−	20.4318i	1.12067	−	0.937476i
$476$	−9.01870			−0.413371
$477$	1.89979	+	1.38028i	0.0869855	+	0.0631986i
$478$	−0.750911	−	2.31107i	−0.0343459	−	0.105706i
$479$	−6.79817	−	20.9226i	−0.310617	−	0.955979i	−0.977521	−	0.210836i	$-0.932381\pi$
$479$	−6.79817	−	20.9226i	−0.310617	−	0.955979i	0.666905	−	0.745143i	$-0.267619\pi$
$480$	0.128089	+	3.74898i	0.00584645	+	0.171117i
$481$	−10.5480	+	32.4634i	−0.480948	+	1.48020i
$482$	−1.02310			−0.0466010
$483$	0.908099	−	2.79484i	0.0413199	−	0.127170i
$484$	4.07156	−	2.95816i	0.185071	−	0.134462i
$485$	−0.766483	−	22.4338i	−0.0348042	−	1.01867i
$486$	−0.114629	−	0.0832830i	−0.00519969	−	0.00377779i
$487$	−22.9759	+	16.6929i	−1.04114	+	0.756430i	−0.970507	−	0.241073i	$-0.922501\pi$
$487$	−22.9759	+	16.6929i	−1.04114	+	0.756430i	−0.0706291	+	0.997503i	$0.522501\pi$
$488$	−4.72075	+	3.42982i	−0.213698	+	0.155261i
$489$	−0.658095	−	0.478134i	−0.0297601	−	0.0216220i
$490$	−1.22053	−	1.56464i	−0.0551380	−	0.0706831i
$491$	11.3641	−	8.25653i	0.512856	−	0.372612i	−0.301050	−	0.953608i	$-0.597337\pi$
$491$	11.3641	−	8.25653i	0.512856	−	0.372612i	0.813906	+	0.580997i	$0.197337\pi$
$492$	−1.54896	+	4.76720i	−0.0698323	+	0.214922i
$493$	−19.8167			−0.892498
$494$	−1.27751	+	3.93176i	−0.0574778	+	0.176898i
$495$	−7.90810	−	2.27406i	−0.355443	−	0.102211i
$496$	1.50219	+	4.62326i	0.0674503	+	0.207591i
$497$	1.14657	+	3.52878i	0.0514307	+	0.158287i
$498$	0.847418	+	0.615685i	0.0379737	+	0.0275895i
$499$	13.0842			0.585731			0.292866	−	0.956154i	$-0.405391\pi$
$499$	13.0842			0.585731			0.292866	+	0.956154i	$0.405391\pi$
$500$	11.1114	−	19.1455i	0.496918	−	0.856211i
$501$	25.1660			1.12433
$502$	−0.659929	−	0.479467i	−0.0294541	−	0.0213996i
$503$	3.80226	+	11.7022i	0.169534	+	0.521773i	0.999342	−	0.0362767i	$-0.0115498\pi$
$503$	3.80226	+	11.7022i	0.169534	+	0.521773i	−0.829807	+	0.558050i	$0.811550\pi$
$504$	−0.149568	−	0.460324i	−0.00666230	−	0.0205044i
$505$	−1.53570	−	0.441607i	−0.0683376	−	0.0196512i
$506$	0.551653	−	1.69781i	0.0245240	−	0.0754770i
$507$	−7.98869			−0.354790
$508$	2.34850	−	7.22793i	0.104198	−	0.320688i
$509$	−0.0634186	+	0.0460763i	−0.00281098	+	0.00204230i	−0.589190	−	0.807995i	$-0.700553\pi$
$509$	−0.0634186	+	0.0460763i	−0.00281098	+	0.00204230i	0.586379	+	0.810037i	$0.300553\pi$
$510$	1.03418	+	1.32575i	0.0457943	+	0.0587051i
$511$	−6.30509	−	4.58092i	−0.278921	−	0.202648i
$512$	8.80600	−	6.39793i	0.389174	−	0.282751i
$513$	5.15239	−	3.74343i	0.227483	−	0.165276i
$514$	3.09043	+	2.24533i	0.136313	+	0.0990372i
$515$	0.0596143	+	1.74482i	0.00262692	+	0.0768861i
$516$	5.41361	−	3.93321i	0.238321	−	0.173150i
$517$	9.66515	−	29.7463i	0.425073	−	1.30824i
$518$	−0.906103			−0.0398119
$519$	−0.126989	+	0.390832i	−0.00557420	+	0.0171556i
$520$	0.197259	+	5.77347i	0.00865036	+	0.253183i
$521$	5.59919	+	17.2325i	0.245305	+	0.754971i	0.995586	+	0.0938524i	$0.0299182\pi$
$521$	5.59919	+	17.2325i	0.245305	+	0.754971i	−0.750281	+	0.661119i	$0.770082\pi$
$522$	−0.163493	−	0.503181i	−0.00715591	−	0.0220236i
$523$	−9.40913	−	6.83613i	−0.411432	−	0.298923i	0.362749	−	0.931887i	$-0.381838\pi$
$523$	−9.40913	−	6.83613i	−0.411432	−	0.298923i	−0.774181	+	0.632964i	$0.781838\pi$
$524$	24.6490			1.07680
$525$	−1.04449	+	4.16251i	−0.0455855	+	0.181667i
$526$	−2.92834			−0.127682
$527$	5.37929	+	3.90828i	0.234326	+	0.170247i
$528$	4.41212	+	13.5791i	0.192013	+	0.590955i
$529$	−3.48500	−	10.7257i	−0.151522	−	0.466336i
$530$	0.416502	−	0.616487i	0.0180917	−	0.0267785i
$531$	4.05628	−	12.4839i	0.176027	−	0.541757i
$532$	10.8229			0.469232
$533$	−3.58413	+	11.0308i	−0.155246	+	0.477797i
$534$	1.77647	−	1.29068i	0.0768753	−	0.0558532i
$535$	25.7020	+	7.39090i	1.11120	+	0.319536i
$536$	−1.52672	−	1.10923i	−0.0659442	−	0.0479113i
$537$	−12.0141	+	8.72873i	−0.518445	+	0.376672i
$538$	−1.57541	+	1.14460i	−0.0679208	+	0.0493473i
$539$	−18.6466	−	13.5476i	−0.803167	−	0.583535i
$540$	2.47845	−	3.66849i	0.106655	−	0.157866i
$541$	−23.6812	+	17.2054i	−1.01814	+	0.739719i	−0.965900	−	0.258916i	$-0.916635\pi$
$541$	−23.6812	+	17.2054i	−1.01814	+	0.739719i	−0.0522359	+	0.998635i	$0.516635\pi$
$542$	−0.146412	+	0.450608i	−0.00628891	+	0.0193553i
$543$	−0.739223			−0.0317231
$544$	2.75115	−	8.46718i	0.117955	−	0.363027i
$545$	−5.11542	+	1.85750i	−0.219121	+	0.0795665i
$546$	−0.172170	−	0.529884i	−0.00736819	−	0.0226770i
$547$	3.72908	+	11.4769i	0.159444	+	0.490717i	0.998584	−	0.0531977i	$-0.0169413\pi$
$547$	3.72908	+	11.4769i	0.159444	+	0.490717i	−0.839140	+	0.543915i	$0.816941\pi$
$548$	−18.9955	−	13.8010i	−0.811448	−	0.589551i
$549$	10.3476			0.441626
$550$	−0.634510	+	2.52864i	−0.0270556	+	0.107822i
$551$	23.7810			1.01311
$552$	1.56198	+	1.13485i	0.0664825	+	0.0483023i
$553$	0.861290	+	2.65078i	0.0366258	+	0.112723i
$554$	−0.390096	−	1.20059i	−0.0165736	−	0.0510083i
$555$	−10.2472	−	13.1361i	−0.434967	−	0.557598i
$556$	2.85168	−	8.77655i	0.120938	−	0.372209i
$557$	−41.4154			−1.75483			−0.877413	−	0.479737i	$-0.840732\pi$
$557$	−41.4154			−1.75483			−0.877413	+	0.479737i	$0.840732\pi$
$558$	−0.0548576	+	0.168834i	−0.00232231	+	0.00714732i
$559$	12.5265	−	9.10106i	0.529816	−	0.384934i
$560$	6.99939	−	2.54160i	0.295778	−	0.107402i
$561$	15.7997	+	11.4791i	0.667062	+	0.484649i
$562$	−2.57816	+	1.87314i	−0.108753	+	0.0790137i
$563$	26.0072	−	18.8954i	1.09607	−	0.796345i	0.115660	−	0.993289i	$-0.463102\pi$
$563$	26.0072	−	18.8954i	1.09607	−	0.796345i	0.980415	+	0.196944i	$0.0631018\pi$
$564$	13.6142	+	9.89131i	0.573262	+	0.416499i
$565$	33.7030	−	12.2381i	1.41790	−	0.514862i
$566$	0.149813	−	0.108846i	0.00629712	−	0.00457513i
$567$	−0.265233	+	0.816302i	−0.0111387	+	0.0342815i
$568$	−2.43773			−0.102285
$569$	6.52273	−	20.0749i	0.273447	−	0.841583i	−0.716179	−	0.697916i	$-0.754111\pi$
$569$	6.52273	−	20.0749i	0.273447	−	0.841583i	0.989626	−	0.143667i	$-0.0458893\pi$
$570$	−1.24107	−	1.59097i	−0.0519827	−	0.0666383i
$571$	−7.64795	−	23.5380i	−0.320057	−	0.985034i	−0.973623	−	0.228164i	$-0.926728\pi$
$571$	−7.64795	−	23.5380i	−0.320057	−	0.985034i	0.653566	−	0.756870i	$-0.273272\pi$
$572$	10.3149	+	31.7459i	0.431286	+	1.32736i
$573$	−2.20462	−	1.60175i	−0.0920994	−	0.0669142i
$574$	−0.307886			−0.0128509
$575$	−6.38894	−	15.8820i	−0.266437	−	0.662327i
$576$	−7.52220			−0.313425
$577$	15.1861	+	11.0333i	0.632205	+	0.459324i	0.857163	−	0.515045i	$-0.172225\pi$
$577$	15.1861	+	11.0333i	0.632205	+	0.459324i	−0.224959	+	0.974368i	$0.572225\pi$
$578$	−0.488830	−	1.50446i	−0.0203327	−	0.0625775i
$579$	−4.38929	−	13.5088i	−0.182413	−	0.561408i
$580$	15.5388	−	5.64242i	0.645215	−	0.234289i
$581$	1.96078	−	6.03467i	0.0813470	−	0.250360i
$582$	−1.42236			−0.0589587
$583$	2.67036	−	8.21853i	0.110595	−	0.340377i
$584$	4.14247	−	3.00968i	0.171417	−	0.124541i
$585$	5.73488	−	8.48850i	0.237108	−	0.350956i
$586$	0.225886	+	0.164116i	0.00933127	+	0.00677956i
$587$	−11.9388	+	8.67406i	−0.492768	+	0.358017i	−0.806248	−	0.591578i	$-0.798505\pi$
$587$	−11.9388	+	8.67406i	−0.492768	+	0.358017i	0.313480	+	0.949595i	$0.398505\pi$
$588$	10.0325	−	7.28905i	0.413734	−	0.300595i
$589$	−6.45543	−	4.69014i	−0.265991	−	0.193254i
$590$	−3.99683	−	1.14933i	−0.164547	−	0.0473173i
$591$	−4.48673	+	3.25980i	−0.184560	+	0.134090i
$592$	−8.93313	+	27.4933i	−0.367149	+	1.12997i
$593$	8.01859			0.329284			0.164642	−	0.986353i	$-0.447353\pi$
$593$	8.01859			0.329284			0.164642	+	0.986353i	$0.447353\pi$
$594$	−0.161124	+	0.495888i	−0.00661099	+	0.0203465i
$595$	5.70199	−	8.43983i	0.233759	−	0.345999i
$596$	7.06544	+	21.7452i	0.289412	+	0.890718i
$597$	−1.84289	−	5.67182i	−0.0754243	−	0.232132i
$598$	1.79802	+	1.30634i	0.0735265	+	0.0534201i
$599$	−1.28951			−0.0526878			−0.0263439	−	0.999653i	$-0.508386\pi$
$599$	−1.28951			−0.0526878			−0.0263439	+	0.999653i	$0.508386\pi$
$600$	−2.38887	−	1.49774i	−0.0975254	−	0.0611452i
$601$	−16.8813			−0.688603			−0.344302	−	0.938859i	$-0.611884\pi$
$601$	−16.8813			−0.688603			−0.344302	+	0.938859i	$0.611884\pi$
$602$	0.332522	+	0.241591i	0.0135526	+	0.00984652i
$603$	1.03412	+	3.18270i	0.0421127	+	0.129609i
$604$	−14.9711	−	46.0764i	−0.609167	−	1.87482i
$605$	0.194082	+	5.68050i	0.00789055	+	0.230945i
$606$	−0.0312891	+	0.0962979i	−0.00127103	+	0.00391184i
$607$	−0.499318			−0.0202667			−0.0101334	−	0.999949i	$-0.503226\pi$
$607$	−0.499318			−0.0202667			−0.0101334	+	0.999949i	$0.503226\pi$
$608$	−3.30153	+	10.1611i	−0.133895	+	0.412085i
$609$	−2.59288	+	1.88384i	−0.105069	+	0.0763369i
$610$	−0.111946	−	3.27650i	−0.00453257	−	0.132662i
$611$	31.5019	+	22.8875i	1.27443	+	0.925929i
$612$	−8.50074	+	6.17615i	−0.343622	+	0.249656i
$613$	−22.1866	+	16.1195i	−0.896108	+	0.651061i	−0.937463	−	0.348084i	$-0.886832\pi$
$613$	−22.1866	+	16.1195i	−0.896108	+	0.651061i	0.0413552	+	0.999145i	$0.486832\pi$
$614$	−1.74860	−	1.27043i	−0.0705679	−	0.0512706i
$615$	−3.48190	−	4.46355i	−0.140404	−	0.179988i
$616$	−1.44097	+	1.04692i	−0.0580582	+	0.0421818i
$617$	−8.75151	+	26.9344i	−0.352323	+	1.08434i	0.605223	+	0.796056i	$0.293084\pi$
$617$	−8.75151	+	26.9344i	−0.352323	+	1.08434i	−0.957546	+	0.288282i	$0.906916\pi$
$618$	0.110626			0.00445003
$619$	−0.114894	+	0.353606i	−0.00461796	+	0.0142126i	−0.953339	−	0.301902i	$-0.902378\pi$
$619$	−0.114894	+	0.353606i	−0.00461796	+	0.0142126i	0.948721	+	0.316115i	$0.102378\pi$
$620$	−5.33087	−	1.53295i	−0.214093	−	0.0615647i
$621$	−1.05801	−	3.25621i	−0.0424564	−	0.130667i
$622$	−0.776966	−	2.39125i	−0.0311535	−	0.0958806i
$623$	−10.7613	−	7.81853i	−0.431142	−	0.313243i
$624$	−17.7754			−0.711584
$625$	10.8915	+	22.5028i	0.435660	+	0.900111i
$626$	3.88043			0.155093
$627$	−18.9604	−	13.7755i	−0.757206	−	0.550142i
$628$	13.6842	+	42.1157i	0.546059	+	1.68060i
$629$	12.2188	+	37.6056i	0.487195	+	1.49943i
$630$	0.261345	+	0.0751527i	0.0104122	+	0.00299416i
$631$	5.08354	−	15.6455i	0.202373	−	0.622839i	−0.797438	−	0.603400i	$-0.793812\pi$
$631$	5.08354	−	15.6455i	0.202373	−	0.622839i	0.999811	−	0.0194386i	$-0.00618787\pi$
$632$	−1.83120			−0.0728411
$633$	4.23919	−	13.0469i	0.168493	−	0.518567i
$634$	0.991042	−	0.720034i	0.0393593	−	0.0285962i
$635$	5.27919	+	6.76755i	0.209498	+	0.268562i
$636$	3.76144	+	2.73285i	0.149151	+	0.108364i
$637$	23.2142	−	16.8661i	0.919780	−	0.668259i
$638$	−1.57512	+	1.14439i	−0.0623598	+	0.0453070i
$639$	3.49729	+	2.54093i	0.138351	+	0.100518i
$640$	0.337558	+	9.87982i	0.0133431	+	0.390534i
$641$	1.63910	−	1.19088i	0.0647407	−	0.0470368i	−0.554944	−	0.831888i	$-0.687260\pi$
$641$	1.63910	−	1.19088i	0.0647407	−	0.0470368i	0.619685	+	0.784851i	$0.287260\pi$
$642$	0.523666	−	1.61168i	0.0206675	−	0.0636079i
$643$	−33.2034			−1.30941			−0.654706	−	0.755883i	$-0.727208\pi$
$643$	−33.2034			−1.30941			−0.654706	+	0.755883i	$0.727208\pi$
$644$	1.79797	−	5.53357i	0.0708498	−	0.218053i
$645$	0.258054	+	7.55287i	0.0101609	+	0.297394i
$646$	1.47986	+	4.55455i	0.0582244	+	0.179196i
$647$	−12.5398	−	38.5936i	−0.492992	−	1.51727i	−0.820064	−	0.572273i	$-0.806062\pi$
$647$	−12.5398	−	38.5936i	−0.492992	−	1.51727i	0.327072	−	0.944999i	$-0.393938\pi$
$648$	−0.456216	−	0.331460i	−0.0179218	−	0.0130210i
$649$	−48.3042			−1.89611
$650$	−2.74986	−	1.72407i	−0.107859	−	0.0676237i
$651$	1.07538			0.0421474
$652$	−1.30298	−	0.946669i	−0.0510286	−	0.0370744i
$653$	−2.87297	−	8.84208i	−0.112428	−	0.346017i	0.878974	−	0.476870i	$-0.158229\pi$
$653$	−2.87297	−	8.84208i	−0.112428	−	0.346017i	−0.991402	+	0.130852i	$0.958229\pi$
$654$	0.106564	+	0.327971i	0.00416699	+	0.0128247i
$655$	−15.5841	+	23.0669i	−0.608921	+	0.901297i
$656$	−3.03540	+	9.34201i	−0.118513	+	0.364744i
$657$	−9.08007			−0.354247
$658$	−0.319412	+	0.983049i	−0.0124520	+	0.0383232i
$659$	2.81185	−	2.04293i	0.109534	−	0.0795811i	−0.531670	−	0.846952i	$-0.678435\pi$
$659$	2.81185	−	2.04293i	0.109534	−	0.0795811i	0.641204	+	0.767371i	$0.278435\pi$
$660$	−15.6574	−	4.50247i	−0.609465	−	0.175258i
$661$	−3.29515	−	2.39407i	−0.128166	−	0.0931184i	0.521855	−	0.853034i	$-0.325240\pi$
$661$	−3.29515	−	2.39407i	−0.128166	−	0.0931184i	−0.650022	+	0.759916i	$0.725240\pi$
$662$	0.568859	−	0.413300i	0.0221093	−	0.0160634i
$663$	−19.6699	+	14.2910i	−0.763914	+	0.555016i
$664$	3.37266	+	2.45038i	0.130885	+	0.0950932i
$665$	−6.84269	+	10.1282i	−0.265348	+	0.392756i
$666$	−0.854064	+	0.620514i	−0.0330943	+	0.0240444i
$667$	3.95065	−	12.1589i	0.152970	−	0.470793i
$668$	49.8267			1.92785
$669$	−1.00174	+	3.08304i	−0.0387296	+	0.119197i
$670$	0.996590	−	0.361879i	0.0385016	−	0.0139806i
$671$	−11.7669	−	36.2148i	−0.454257	−	1.39806i
$672$	−0.444947	−	1.36941i	−0.0171642	−	0.0528260i
$673$	−17.3003	−	12.5694i	−0.666877	−	0.484514i	0.202102	−	0.979365i	$-0.435223\pi$
$673$	−17.3003	−	12.5694i	−0.666877	−	0.484514i	−0.868978	+	0.494850i	$0.835223\pi$
$674$	1.03508			0.0398699
$675$	1.86604	+	4.63874i	0.0718241	+	0.178545i
$676$	−15.8170			−0.608346
$677$	16.4438	+	11.9472i	0.631988	+	0.459166i	0.857088	−	0.515169i	$-0.172271\pi$
$677$	16.4438	+	11.9472i	0.631988	+	0.459166i	−0.225100	+	0.974336i	$0.572271\pi$
$678$	−0.702100	−	2.16084i	−0.0269640	−	0.0829866i
$679$	2.66256	+	8.19451i	0.102180	+	0.314476i
$680$	4.11596	+	5.27638i	0.157840	+	0.202340i
$681$	−4.07281	+	12.5348i	−0.156070	+	0.480335i
$682$	0.653271			0.0250150
$683$	−5.85868	+	18.0312i	−0.224176	+	0.689943i	0.774198	+	0.632943i	$0.218153\pi$
$683$	−5.85868	+	18.0312i	−0.224176	+	0.689943i	−0.998374	+	0.0569998i	$0.981847\pi$
$684$	10.2013	−	7.41170i	0.390058	−	0.283394i
$685$	24.9250	−	9.05068i	0.952334	−	0.345809i
$686$	1.30494	+	0.948096i	0.0498229	+	0.0361985i
$687$	4.72312	−	3.43155i	0.180198	−	0.130922i
$688$	10.6087	−	7.70770i	0.404455	−	0.293853i
$689$	8.70359	+	6.32353i	0.331580	+	0.240907i
$690$	−1.01961	+	0.370238i	−0.0388159	+	0.0140947i
$691$	−11.9893	+	8.71071i	−0.456093	+	0.331371i	−0.791997	−	0.610525i	$-0.790958\pi$
$691$	−11.9893	+	8.71071i	−0.456093	+	0.331371i	0.335904	+	0.941896i	$0.390958\pi$
$692$	−0.251429	+	0.773818i	−0.00955789	+	0.0294162i
$693$	3.15852			0.119982
$694$	−0.697811	+	2.14764i	−0.0264885	+	0.0815234i
$695$	6.41028	+	8.21754i	0.243156	+	0.311709i
$696$	−0.650691	−	2.00262i	−0.0246644	−	0.0759092i
$697$	4.15185	+	12.7781i	0.157262	+	0.484004i
$698$	1.90106	+	1.38120i	0.0719560	+	0.0522791i
$699$	−9.33453			−0.353064
$700$	−2.06802	+	8.24145i	−0.0781638	+	0.311497i
$701$	31.3996			1.18595			0.592973	−	0.805222i	$-0.297954\pi$
$701$	31.3996			1.18595			0.592973	+	0.805222i	$0.297954\pi$
$702$	−0.525156	−	0.381548i	−0.0198207	−	0.0144006i
$703$	−14.6632	−	45.1287i	−0.553033	−	1.70206i
$704$	8.55395	+	26.3264i	0.322389	+	0.992212i
$705$	−17.8639	+	6.48669i	−0.672794	+	0.244303i
$706$	−0.567846	+	1.74765i	−0.0213712	+	0.0657737i
$707$	0.613363			0.0230679
$708$	8.03112	−	24.7173i	0.301828	−	0.928931i
$709$	−20.4944	+	14.8900i	−0.769682	+	0.559207i	−0.901865	−	0.432019i	$-0.857801\pi$
$709$	−20.4944	+	14.8900i	−0.769682	+	0.559207i	0.132183	+	0.991225i	$0.457801\pi$
$710$	0.766731	−	1.13488i	0.0287749	−	0.0425913i
$711$	2.62712	+	1.90872i	0.0985248	+	0.0715825i
$712$	7.07021	−	5.13681i	0.264967	−	0.192510i
$713$	−3.47041	+	2.52140i	−0.129968	+	0.0944272i
$714$	−0.522144	−	0.379360i	−0.0195408	−	0.0141972i
$715$	−36.2297	−	10.4183i	−1.35491	−	0.389620i
$716$	−23.7869	+	17.2822i	−0.888959	+	0.645867i
$717$	−5.29969	+	16.3108i	−0.197921	+	0.609137i
$718$	1.91168			0.0713432
$719$	−1.27535	+	3.92511i	−0.0475624	+	0.146382i	−0.972017	−	0.234910i	$-0.924521\pi$
$719$	−1.27535	+	3.92511i	−0.0475624	+	0.146382i	0.924455	+	0.381292i	$0.124521\pi$
$720$	4.85688	−	7.18893i	0.181005	−	0.267916i
$721$	−0.207084	−	0.637339i	−0.00771221	−	0.0237358i
$722$	−0.944008	−	2.90536i	−0.0351323	−	0.108126i
$723$	5.84169	+	4.24424i	0.217255	+	0.157845i
$724$	−1.46361			−0.0543945
$725$	−4.54404	+	18.1088i	−0.168761	+	0.672545i
$726$	0.360157			0.0133667
$727$	−18.6106	−	13.5214i	−0.690227	−	0.501479i	0.186508	−	0.982454i	$-0.440283\pi$
$727$	−18.6106	−	13.5214i	−0.690227	−	0.501479i	−0.876735	+	0.480974i	$0.840283\pi$
$728$	−0.685223	−	2.10890i	−0.0253961	−	0.0781610i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	0.0982330	+	2.87514i	0.00363577	+	0.106414i
$731$	5.54260	−	17.0584i	0.205000	−	0.630927i
$732$	20.4875			0.757240
$733$	−2.89145	+	8.89896i	−0.106798	+	0.328690i	−0.990148	−	0.140023i	$-0.955282\pi$
$733$	−2.89145	+	8.89896i	−0.106798	+	0.328690i	0.883350	+	0.468714i	$0.155282\pi$
$734$	0.524386	−	0.380989i	0.0193554	−	0.0140625i
$735$	0.478227	+	13.9970i	0.0176397	+	0.516287i
$736$	4.64671	+	3.37604i	0.171280	+	0.124442i
$737$	9.96291	−	7.23847i	0.366988	−	0.266633i
$738$	−0.290204	+	0.210846i	−0.0106826	+	0.00776133i
$739$	38.1657	+	27.7290i	1.40395	+	1.02003i	0.994168	+	0.107844i	$0.0343948\pi$
$739$	38.1657	+	27.7290i	1.40395	+	1.02003i	0.409781	+	0.912184i	$0.365605\pi$
$740$	−20.2886	−	26.0086i	−0.745823	−	0.956094i
$741$	23.6048	−	17.1499i	0.867146	−	0.630018i
$742$	−0.0882496	+	0.271604i	−0.00323974	+	0.00997091i
$743$	2.39450			0.0878455			0.0439228	−	0.999035i	$-0.486014\pi$
$743$	2.39450			0.0878455			0.0439228	+	0.999035i	$0.486014\pi$
$744$	−0.218329	+	0.671947i	−0.00800433	+	0.0246348i
$745$	−24.8165	−	7.13627i	−0.909208	−	0.261453i
$746$	0.908366	+	2.79566i	0.0332576	+	0.102356i
$747$	−2.28447	−	7.03087i	−0.0835843	−	0.257246i
$748$	31.2821	+	22.7278i	1.14379	+	0.831011i
$749$	−10.2655			−0.375092
$750$	1.44863	−	0.641053i	0.0528966	−	0.0234080i
$751$	−7.21632			−0.263327			−0.131664	−	0.991294i	$-0.542032\pi$
$751$	−7.21632			−0.263327			−0.131664	+	0.991294i	$0.542032\pi$
$752$	26.6790	+	19.3835i	0.972885	+	0.706842i
$753$	1.77903	+	5.47530i	0.0648316	+	0.199531i
$754$	−0.749019	−	2.30524i	−0.0272777	−	0.0839520i
$755$	52.5843	+	15.1212i	1.91374	+	0.550317i
$756$	−0.525140	+	1.61622i	−0.0190992	+	0.0587812i
$757$	13.3742			0.486094			0.243047	−	0.970015i	$-0.421853\pi$
$757$	13.3742			0.486094			0.243047	+	0.970015i	$0.421853\pi$
$758$	0.253145	−	0.779101i	0.00919465	−	0.0282982i
$759$	−10.1930	+	7.40567i	−0.369984	+	0.268809i
$760$	−4.93936	−	6.33193i	−0.179170	−	0.229683i
$761$	−17.5994	−	12.7867i	−0.637978	−	0.463518i	0.221177	−	0.975234i	$-0.429010\pi$
$761$	−17.5994	−	12.7867i	−0.637978	−	0.463518i	−0.859155	+	0.511716i	$0.829010\pi$
$762$	0.440002	−	0.319680i	0.0159396	−	0.0115808i
$763$	1.69003	−	1.22788i	0.0611831	−	0.0444521i
$764$	−4.36499	−	3.17135i	−0.157920	−	0.114735i
$765$	−0.405211	−	11.8599i	−0.0146504	−	0.428797i
$766$	2.95886	−	2.14973i	0.106908	−	0.0776730i
$767$	18.5832	−	57.1932i	0.671000	−	2.06513i
$768$	−14.4180			−0.520265
$769$	4.38814	−	13.5053i	0.158240	−	0.487014i	−0.840234	−	0.542223i	$-0.817583\pi$
$769$	4.38814	−	13.5053i	0.158240	−	0.487014i	0.998475	+	0.0552094i	$0.0175826\pi$
$770$	−0.0341706	−	1.00012i	−0.00123142	−	0.0360419i
$771$	−8.33117	−	25.6407i	−0.300040	−	0.923427i
$772$	−8.69046	−	26.7465i	−0.312777	−	0.962627i
$773$	−18.4752	−	13.4230i	−0.664505	−	0.482791i	0.203676	−	0.979038i	$-0.434711\pi$
$773$	−18.4752	−	13.4230i	−0.664505	−	0.482791i	−0.868181	+	0.496247i	$0.834711\pi$
$774$	0.478870			0.0172126
$775$	4.80495	−	4.01951i	0.172599	−	0.144385i
$776$	−5.66089			−0.203214
$777$	5.17365	+	3.75888i	0.185604	+	0.134849i
$778$	0.687616	+	2.11627i	0.0246522	+	0.0758718i
$779$	−4.98243	−	15.3343i	−0.178514	−	0.549410i
$780$	11.3546	−	16.8066i	0.406561	−	0.601772i
$781$	4.91582	−	15.1293i	0.175902	−	0.541370i
$782$	2.57451			0.0920644
$783$	−1.15388	+	3.55129i	−0.0412365	+	0.126913i
$784$	19.6602	−	14.2839i	0.702148	−	0.510141i
$785$	−48.0642	−	13.8214i	−1.71548	−	0.493306i
$786$	1.42707	+	1.03683i	0.0509020	+	0.0369824i
$787$	31.1279	−	22.6157i	1.10959	−	0.806163i	0.126990	−	0.991904i	$-0.459469\pi$
$787$	31.1279	−	22.6157i	1.10959	−	0.806163i	0.982599	+	0.185741i	$0.0594685\pi$
$788$	−8.88339	+	6.45416i	−0.316458	+	0.229920i
$789$	16.7202	+	12.1479i	0.595254	+	0.432478i
$790$	0.575959	−	0.852508i	0.0204917	−	0.0303309i
$791$	−11.1348	+	8.08988i	−0.395906	+	0.287643i
$792$	−0.641260	+	1.97360i	−0.0227862	+	0.0701287i
$793$	47.4060			1.68344
$794$	0.858349	−	2.64173i	0.0304617	−	0.0937514i
$795$	−4.93558	+	1.79219i	−0.175047	+	0.0635625i
$796$	−3.64878	−	11.2298i	−0.129327	−	0.398029i
$797$	−0.577055	−	1.77599i	−0.0204404	−	0.0629089i	0.940316	−	0.340302i	$-0.110529\pi$
$797$	−0.577055	−	1.77599i	−0.0204404	−	0.0629089i	−0.960756	+	0.277393i	$0.910529\pi$
$798$	0.626600	+	0.455252i	0.0221814	+	0.0161157i
$799$	45.1063			1.59575
$800$	−7.10661	−	4.45561i	−0.251257	−	0.157530i
$801$	−15.4975			−0.547578
$802$	−1.65340	−	1.20127i	−0.0583837	−	0.0424182i
$803$	10.3255	+	31.7786i	0.364379	+	1.12144i
$804$	2.04748	+	6.30150i	0.0722091	+	0.222237i
$805$	4.04165	+	5.18112i	0.142449	+	0.182610i
$806$	−0.251321	+	0.773487i	−0.00885241	+	0.0272449i
$807$	13.7435			0.483796
$808$	−0.124528	+	0.383258i	−0.00438089	+	0.0134830i
$809$	−28.4381	+	20.6615i	−0.999831	+	0.726420i	−0.962052	−	0.272866i	$-0.912028\pi$
$809$	−28.4381	+	20.6615i	−0.999831	+	0.726420i	−0.0377789	+	0.999286i	$0.512028\pi$
$810$	0.297802	−	0.108137i	0.0104637	−	0.00379955i
$811$	5.33270	+	3.87443i	0.187256	+	0.136050i	0.677464	−	0.735556i	$-0.263079\pi$
$811$	5.33270	+	3.87443i	0.187256	+	0.136050i	−0.490208	+	0.871606i	$0.663079\pi$
$812$	−5.13370	+	3.72985i	−0.180158	+	0.130892i
$813$	2.70528	−	1.96550i	0.0948785	−	0.0689332i
$814$	3.14290	+	2.28345i	0.110158	+	0.0800348i
$815$	1.70970	−	0.620822i	0.0598883	−	0.0217465i
$816$	−16.6584	+	12.1031i	−0.583162	+	0.423692i
$817$	−6.65141	+	20.4709i	−0.232703	+	0.716187i
$818$	3.94949			0.138091
$819$	−1.21512	+	3.73976i	−0.0424598	+	0.130678i
$820$	−6.89389	−	8.83750i	−0.240745	−	0.308619i
$821$	1.62463	+	5.00011i	0.0567001	+	0.174505i	0.975396	−	0.220461i	$-0.0707563\pi$
$821$	1.62463	+	5.00011i	0.0567001	+	0.174505i	−0.918696	+	0.394966i	$0.870756\pi$
$822$	−0.519236	−	1.59804i	−0.0181104	−	0.0557382i
$823$	17.9536	+	13.0440i	0.625823	+	0.454687i	0.854951	−	0.518709i	$-0.173587\pi$
$823$	17.9536	+	13.0440i	0.625823	+	0.454687i	−0.229128	+	0.973396i	$0.573587\pi$
$824$	0.440283			0.0153380
$825$	14.1128	−	11.8058i	0.491343	−	0.411026i
$826$	1.59635			0.0555440
$827$	5.30922	+	3.85738i	0.184620	+	0.134134i	0.676256	−	0.736666i	$-0.263601\pi$
$827$	5.30922	+	3.85738i	0.184620	+	0.134134i	−0.491637	+	0.870800i	$0.663601\pi$
$828$	−2.09478	−	6.44705i	−0.0727985	−	0.224051i
$829$	7.74316	+	23.8310i	0.268931	+	0.827685i	0.990762	+	0.135615i	$0.0433010\pi$
$829$	7.74316	+	23.8310i	0.268931	+	0.827685i	−0.721831	+	0.692070i	$0.756699\pi$
$830$	−2.20156	+	0.799423i	−0.0764172	+	0.0277484i
$831$	−2.75318	+	8.47340i	−0.0955066	+	0.293939i
$832$	−34.4618			−1.19475
$833$	10.2716	−	31.6126i	0.355889	−	1.09531i
$834$	0.534274	−	0.388173i	0.0185004	−	0.0134413i
$835$	−31.5025	+	46.6285i	−1.09019	+	1.61365i
$836$	−37.5402	−	27.2745i	−1.29835	−	0.943310i
$837$	1.01362	−	0.736436i	0.0350357	−	0.0254550i
$838$	−4.15968	+	3.02219i	−0.143694	+	0.104400i
$839$	34.0989	+	24.7743i	1.17722	+	0.855303i	0.991856	−	0.127366i	$-0.0406524\pi$
$839$	34.0989	+	24.7743i	1.17722	+	0.855303i	0.185368	+	0.982669i	$0.440652\pi$
$840$	1.04013	+	0.299102i	0.0358881	+	0.0103200i
$841$	12.1813	−	8.85021i	0.420044	−	0.305180i
$842$	0.147816	−	0.454932i	0.00509409	−	0.0156780i
$843$	22.4913			0.774641
$844$	8.39327	−	25.8318i	0.288908	−	0.889169i
$845$	10.0002	−	14.8018i	0.344016	−	0.509197i
$846$	0.372140	+	1.14533i	0.0127944	+	0.0393773i
$847$	−0.674189	−	2.07494i	−0.0231654	−	0.0712957i
$848$	7.37109	+	5.35541i	0.253124	+	0.183906i
$849$	−1.30694			−0.0448540
$850$	−3.75098	+	0.256614i	−0.128657	+	0.00880180i
$851$	−25.5095			−0.874454
$852$	6.92437	+	5.03085i	0.237225	+	0.172354i
$853$	13.3641	+	41.1306i	0.457580	+	1.40829i	0.868080	+	0.496425i	$0.165354\pi$
$853$	13.3641	+	41.1306i	0.457580	+	1.40829i	−0.410500	+	0.911861i	$0.634646\pi$
$854$	0.388871	+	1.19682i	0.0133069	+	0.0409544i
$855$	0.486274	+	14.2325i	0.0166302	+	0.486743i
$856$	2.08415	−	6.41436i	0.0712349	−	0.219238i
$857$	−39.2430			−1.34052			−0.670258	−	0.742128i	$-0.733817\pi$
$857$	−39.2430			−1.34052			−0.670258	+	0.742128i	$0.733817\pi$
$858$	−0.738163	+	2.27183i	−0.0252005	+	0.0775590i
$859$	−42.5617	+	30.9229i	−1.45219	+	1.05508i	−0.466872	+	0.884325i	$0.654619\pi$
$859$	−42.5617	+	30.9229i	−1.45219	+	1.05508i	−0.985314	+	0.170750i	$0.945381\pi$
$860$	0.510928	+	14.9541i	0.0174225	+	0.509931i
$861$	1.75797	+	1.27724i	0.0599113	+	0.0435281i
$862$	−2.94167	+	2.13725i	−0.100194	+	0.0727950i
$863$	34.6861	−	25.2009i	1.18073	−	0.857850i	0.188476	−	0.982078i	$-0.439645\pi$
$863$	34.6861	−	25.2009i	1.18073	−	0.857850i	0.992254	+	0.124228i	$0.0396454\pi$
$864$	−1.35719	−	0.986054i	−0.0461724	−	0.0335462i
$865$	−0.565187	−	0.724530i	−0.0192169	−	0.0246348i
$866$	−4.56304	+	3.31524i	−0.155058	+	0.112657i
$867$	−3.45001	+	10.6180i	−0.117169	+	0.360608i
$868$	2.12917			0.0722686
$869$	3.69270	−	11.3650i	0.125266	−	0.385530i
$870$	1.13697	+	0.326949i	0.0385470	+	0.0110846i
$871$	4.73766	+	14.5810i	0.160530	+	0.494059i
$872$	0.424118	+	1.30530i	0.0143624	+	0.0442031i
$873$	8.12138	+	5.90053i	0.274867	+	0.199703i
$874$	−3.08955			−0.104506
$875$	−6.40498	−	7.14587i	−0.216528	−	0.241574i
$876$	−17.9779			−0.607415
$877$	0.315771	+	0.229421i	0.0106628	+	0.00774700i	0.593104	−	0.805126i	$-0.297902\pi$
$877$	0.315771	+	0.229421i	0.0106628	+	0.00774700i	−0.582441	+	0.812873i	$0.697902\pi$
$878$	−1.48508	−	4.57060i	−0.0501190	−	0.154250i
$879$	−0.608943	−	1.87413i	−0.0205391	−	0.0632129i
$880$	−30.6830	−	8.82324i	−1.03432	−	0.297431i
$881$	13.8131	−	42.5124i	0.465376	−	1.43228i	−0.393133	−	0.919481i	$-0.628609\pi$
$881$	13.8131	−	42.5124i	0.465376	−	1.43228i	0.858509	−	0.512798i	$-0.171391\pi$
$882$	0.887444			0.0298818
$883$	10.1224	−	31.1534i	0.340645	−	1.04840i	−0.623230	−	0.782039i	$-0.714180\pi$
$883$	10.1224	−	31.1534i	0.340645	−	1.04840i	0.963874	−	0.266358i	$-0.0858202\pi$
$884$	−38.9448	+	28.2951i	−1.30986	+	0.951666i
$885$	18.0532	+	23.1429i	0.606850	+	0.777940i
$886$	−3.31622	−	2.40938i	−0.111411	−	0.0809446i
$887$	12.7121	−	9.23588i	0.426830	−	0.310110i	−0.353550	−	0.935416i	$-0.615026\pi$
$887$	12.7121	−	9.23588i	0.426830	−	0.310110i	0.780380	+	0.625305i	$0.215026\pi$
$888$	−3.39911	+	2.46960i	−0.114067	+	0.0828743i
$889$	−2.66539	−	1.93652i	−0.0893944	−	0.0649488i
$890$	0.167660	+	4.90717i	0.00561999	+	0.164489i
$891$	2.97713	−	2.16301i	0.0997374	−	0.0724635i
$892$	−1.98337	+	6.10419i	−0.0664082	+	0.204383i
$893$	−54.1299			−1.81139
$894$	−0.505625	+	1.55615i	−0.0169106	+	0.0520456i
$895$	−1.13387	−	33.1867i	−0.0379011	−	1.10931i
$896$	−1.17258	−	3.60884i	−0.0391733	−	0.120563i
$897$	−4.84710	−	14.9178i	−0.161840	−	0.498092i
$898$	−1.17024	−	0.850228i	−0.0390514	−	0.0283725i
$899$	4.67839			0.156033
$900$	3.69463	+	9.18435i	0.123154	+	0.306145i
$901$	12.4623			0.415180
$902$	1.06793	+	0.775897i	0.0355582	+	0.0258345i
$903$	−0.896411	−	2.75887i	−0.0298307	−	0.0918094i
$904$	−2.79430	−	8.59998i	−0.0929372	−	0.286031i
$905$	0.925352	−	1.36966i	0.0307597	−	0.0455291i
$906$	1.07138	−	3.29737i	0.0355942	−	0.109548i
$907$	−1.50466			−0.0499613			−0.0249806	−	0.999688i	$-0.507952\pi$
$907$	−1.50466			−0.0499613			−0.0249806	+	0.999688i	$0.507952\pi$
$908$	−8.06385	+	24.8180i	−0.267608	+	0.823613i
$909$	0.578137	−	0.420041i	0.0191756	−	0.0139319i
$910$	1.19731	+	0.344300i	0.0396905	+	0.0114134i
$911$	−9.26400	−	6.73069i	−0.306930	−	0.222998i	0.423648	−	0.905827i	$-0.360749\pi$
$911$	−9.26400	−	6.73069i	−0.306930	−	0.222998i	−0.730578	+	0.682829i	$0.760749\pi$
$912$	19.9910	−	14.5243i	0.661968	−	0.480948i
$913$	−22.0090	+	15.9904i	−0.728390	+	0.529207i
$914$	3.72489	+	2.70629i	0.123209	+	0.0895162i
$915$	−12.9531	+	19.1725i	−0.428215	+	0.633824i
$916$	9.35142	−	6.79421i	0.308980	−	0.224487i
$917$	3.30200	−	10.1625i	0.109042	−	0.335596i
$918$	−0.751949			−0.0248180
$919$	−6.73660	+	20.7331i	−0.222220	+	0.683923i	0.776342	+	0.630312i	$0.217073\pi$
$919$	−6.73660	+	20.7331i	−0.222220	+	0.683923i	−0.998562	+	0.0536108i	$0.982927\pi$
$920$	−4.05797	+	1.47352i	−0.133787	+	0.0485805i
$921$	4.71388	+	14.5078i	0.155328	+	0.478049i
$922$	0.0306740	+	0.0944049i	0.00101019	+	0.00310906i
$923$	16.0223	+	11.6409i	0.527380	+	0.383164i
$924$	6.25363			0.205729
$925$	37.1665	−	2.54266i	1.22203	−	0.0836020i
$926$	−0.307645			−0.0101098
$927$	−0.631652	−	0.458922i	−0.0207462	−	0.0150730i
$928$	−1.93573	−	5.95756i	−0.0635434	−	0.195566i
$929$	−9.50249	−	29.2457i	−0.311767	−	0.959519i	−0.977065	−	0.212941i	$-0.931696\pi$
$929$	−9.50249	−	29.2457i	−0.311767	−	0.959519i	0.665298	−	0.746578i	$-0.268304\pi$
$930$	−0.244153	−	0.312987i	−0.00800609	−	0.0102633i
$931$	−12.3264	+	37.9368i	−0.403982	+	1.24333i
$932$	−18.4817			−0.605387
$933$	−5.48358	+	16.8767i	−0.179524	+	0.552519i
$934$	−0.444429	+	0.322896i	−0.0145421	+	0.0105655i
$935$	−41.0469	+	14.9048i	−1.34238	+	0.487440i
$936$	−2.09008	−	1.51853i	−0.0683164	−	0.0496348i
$937$	3.08284	−	2.23982i	0.100712	−	0.0731716i	−0.536289	−	0.844034i	$-0.680174\pi$
$937$	3.08284	−	2.23982i	0.100712	−	0.0731716i	0.637002	+	0.770862i	$0.280174\pi$
$938$	−0.329252	+	0.239216i	−0.0107505	+	0.00781067i
$939$	−22.1565	−	16.0976i	−0.723049	−	0.525326i
$940$	−35.3692	+	12.8432i	−1.15362	+	0.418898i
$941$	16.7501	−	12.1697i	0.546037	−	0.396719i	−0.280285	−	0.959917i	$-0.590429\pi$
$941$	16.7501	−	12.1697i	0.546037	−	0.396719i	0.826322	+	0.563197i	$0.190429\pi$
$942$	−0.979284	+	3.01393i	−0.0319068	+	0.0981990i
$943$	−8.66792			−0.282266
$944$	15.7381	−	48.4370i	0.512233	−	1.57649i
$945$	−1.18046	−	1.51327i	−0.0384005	−	0.0492267i
$946$	−0.544553	−	1.67596i	−0.0177049	−	0.0544902i
$947$	4.84640	+	14.9157i	0.157487	+	0.484695i	0.998404	−	0.0564684i	$-0.0179840\pi$
$947$	4.84640	+	14.9157i	0.157487	+	0.484695i	−0.840917	+	0.541163i	$0.817984\pi$
$948$	5.20150	+	3.77911i	0.168937	+	0.122740i
$949$	−41.5989			−1.35036
$950$	4.50137	−	0.307950i	0.146044	−	0.00999123i
$951$	−8.64563			−0.280354
$952$	−2.07809	−	1.50982i	−0.0673514	−	0.0489337i
$953$	−2.39552	−	7.37266i	−0.0775985	−	0.238824i	0.904731	−	0.425983i	$-0.140072\pi$
$953$	−2.39552	−	7.37266i	−0.0775985	−	0.238824i	−0.982330	+	0.187160i	$0.940072\pi$
$954$	0.102818	+	0.316441i	0.00332885	+	0.0102451i
$955$	5.72752	−	2.07976i	0.185338	−	0.0672994i
$956$	−10.4930	+	32.2941i	−0.339368	+	1.04447i
$957$	13.7410			0.444185
$958$	0.963230	−	2.96452i	0.0311205	−	0.0957792i
$959$	−8.23468	+	5.98285i	−0.265912	+	0.193196i
$960$	9.41621	−	13.9374i	0.303907	−	0.449829i
$961$	23.8096	+	17.2987i	0.768050	+	0.558021i
$962$	−3.91276	+	2.84279i	−0.126152	+	0.0916551i
$963$	−9.67592	+	7.02997i	−0.311802	+	0.226538i
$964$	11.5661	+	8.40326i	0.372519	+	0.270651i
$965$	30.5242	+	8.77758i	0.982609	+	0.282560i
$966$	0.336857	−	0.244741i	0.0108382	−	0.00787442i
$967$	−14.9649	+	46.0571i	−0.481238	+	1.48110i	0.356119	+	0.934441i	$0.384100\pi$
$967$	−14.9649	+	46.0571i	−0.481238	+	1.48110i	−0.837357	+	0.546657i	$0.815900\pi$
$968$	1.43340			0.0460712
$969$	10.4444	−	32.1446i	0.335523	−	1.03263i
$970$	1.78050	−	2.63541i	0.0571683	−	0.0846179i
$971$	7.82895	+	24.0950i	0.251243	+	0.773246i	0.994547	+	0.104292i	$0.0332577\pi$
$971$	7.82895	+	24.0950i	0.251243	+	0.773246i	−0.743304	+	0.668954i	$0.766742\pi$
$972$	0.611830	+	1.88302i	0.0196245	+	0.0603979i
$973$	−3.23647	−	2.35143i	−0.103756	−	0.0753834i
$974$	−4.02394			−0.128936
$975$	8.54899	+	21.2516i	0.273787	+	0.680597i
$976$	40.1483			1.28511
$977$	0.945620	+	0.687033i	0.0302531	+	0.0219801i	0.602809	−	0.797885i	$-0.294048\pi$
$977$	0.945620	+	0.687033i	0.0302531	+	0.0219801i	−0.572556	+	0.819866i	$0.694048\pi$
$978$	−0.0356165	−	0.109616i	−0.00113889	−	0.00350514i
$979$	17.6232	+	54.2385i	0.563239	+	1.73347i
$980$	0.946853	+	27.7130i	0.0302461	+	0.885259i
$981$	0.752097	−	2.31472i	0.0240126	−	0.0739033i
$982$	1.99029			0.0635127
$983$	−7.41464	+	22.8199i	−0.236490	+	0.727842i	0.760430	+	0.649420i	$0.224988\pi$
$983$	−7.41464	+	22.8199i	−0.236490	+	0.727842i	−0.996920	+	0.0784223i	$0.975012\pi$
$984$	−1.15499	+	0.839150i	−0.0368197	+	0.0267511i
$985$	−0.423451	−	12.3938i	−0.0134923	−	0.394899i
$986$	−2.27157	−	1.65039i	−0.0723415	−	0.0525592i
$987$	5.90186	−	4.28795i	0.187858	−	0.136487i
$988$	46.7358	−	33.9555i	1.48686	−	1.08027i
$989$	9.36148	+	6.80151i	0.297678	+	0.216276i
$990$	−0.717109	−	0.919284i	−0.0227912	−	0.0292168i
$991$	29.6688	−	21.5556i	0.942459	−	0.684737i	−0.00655196	−	0.999979i	$-0.502086\pi$
$991$	29.6688	−	21.5556i	0.942459	−	0.684737i	0.949011	+	0.315242i	$0.102086\pi$
$992$	−0.649502	+	1.99896i	−0.0206217	+	0.0634671i
$993$	−4.96260			−0.157483
$994$	−0.162457	+	0.499991i	−0.00515282	+	0.0158588i
$995$	12.8159	+	3.68535i	0.406291	+	0.116834i
$996$	−4.52307	−	13.9206i	−0.143319	−	0.441091i
$997$	−17.6202	−	54.2295i	−0.558038	−	1.71747i	−0.687782	−	0.725918i	$-0.741415\pi$
$997$	−17.6202	−	54.2295i	−0.558038	−	1.71747i	0.129743	−	0.991548i	$-0.458585\pi$
$998$	1.49984	+	1.08970i	0.0474765	+	0.0344937i
$999$	7.45067			0.235729

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.g.c.16.2	✓	12
3.2	odd	2		225.2.h.d.91.2		12
5.2	odd	4		375.2.i.d.49.3		24
5.3	odd	4		375.2.i.d.49.4		24
5.4	even	2		375.2.g.c.76.2		12
25.2	odd	20		375.2.i.d.199.4		24
25.6	even	5		1875.2.a.j.1.3		6
25.8	odd	20		1875.2.b.f.1249.7		12
25.11	even	5	inner	75.2.g.c.61.2	yes	12
25.14	even	10		375.2.g.c.301.2		12
25.17	odd	20		1875.2.b.f.1249.6		12
25.19	even	10		1875.2.a.k.1.4		6
25.23	odd	20		375.2.i.d.199.3		24
75.11	odd	10		225.2.h.d.136.2		12
75.44	odd	10		5625.2.a.q.1.3		6
75.56	odd	10		5625.2.a.p.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.16.2	✓	12	1.1	even	1	trivial
75.2.g.c.61.2	yes	12	25.11	even	5	inner
225.2.h.d.91.2		12	3.2	odd	2
225.2.h.d.136.2		12	75.11	odd	10
375.2.g.c.76.2		12	5.4	even	2
375.2.g.c.301.2		12	25.14	even	10
375.2.i.d.49.3		24	5.2	odd	4
375.2.i.d.49.4		24	5.3	odd	4
375.2.i.d.199.3		24	25.23	odd	20
375.2.i.d.199.4		24	25.2	odd	20
1875.2.a.j.1.3		6	25.6	even	5
1875.2.a.k.1.4		6	25.19	even	10
1875.2.b.f.1249.6		12	25.17	odd	20
1875.2.b.f.1249.7		12	25.8	odd	20
5625.2.a.p.1.4		6	75.56	odd	10
5625.2.a.q.1.3		6	75.44	odd	10

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.114629 + 0.0832830i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.611830 - 1.88302i) q^{4} +(2.14898 + 0.617963i) q^{5} +(0.0437845 - 0.134755i) q^{6} -0.858311 q^{7} +(0.174259 - 0.536314i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.114629 + 0.0832830i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.611830 - 1.88302i) q^{4} +(2.14898 + 0.617963i) q^{5} +(0.0437845 - 0.134755i) q^{6} -0.858311 q^{7} +(0.174259 - 0.536314i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.194870 + 0.249810i) q^{10} +(2.97713 + 2.16301i) q^{11} +(-1.60179 + 1.16377i) q^{12} +(-3.70638 + 2.69285i) q^{13} +(-0.0983875 - 0.0714827i) q^{14} +(-0.0763538 - 2.23476i) q^{15} +(-3.13894 + 2.28058i) q^{16} +(-1.63996 + 5.04728i) q^{17} -0.141689 q^{18} +(1.96804 - 6.05699i) q^{19} +(-0.151175 - 4.42466i) q^{20} +(0.265233 + 0.816302i) q^{21} +(0.161124 + 0.495888i) q^{22} +(-2.76990 - 2.01245i) q^{23} -0.563913 q^{24} +(4.23624 + 2.65598i) q^{25} -0.649128 q^{26} +(0.809017 + 0.587785i) q^{27} +(0.525140 + 1.61622i) q^{28} +(1.15388 + 3.55129i) q^{29} +(0.177365 - 0.262528i) q^{30} +(0.387167 - 1.19158i) q^{31} -1.67757 q^{32} +(1.13716 - 3.49982i) q^{33} +(-0.608340 + 0.441985i) q^{34} +(-1.84449 - 0.530404i) q^{35} +(1.60179 + 1.16377i) q^{36} +(6.02772 - 4.37939i) q^{37} +(0.730039 - 0.530404i) q^{38} +(3.70638 + 2.69285i) q^{39} +(0.705901 - 1.04484i) q^{40} +(2.04817 - 1.48808i) q^{41} +(-0.0375807 + 0.115661i) q^{42} -3.37972 q^{43} +(2.25149 - 6.92938i) q^{44} +(-2.10179 + 0.763197i) q^{45} +(-0.149909 - 0.461371i) q^{46} +(-2.62645 - 8.08338i) q^{47} +(3.13894 + 2.28058i) q^{48} -6.26330 q^{49} +(0.264399 + 0.657260i) q^{50} +5.30702 q^{51} +(7.33836 + 5.33163i) q^{52} +(-0.725656 - 2.23334i) q^{53} +(0.0437845 + 0.134755i) q^{54} +(5.06113 + 6.48802i) q^{55} +(-0.149568 + 0.460324i) q^{56} -6.36870 q^{57} +(-0.163493 + 0.503181i) q^{58} +(-10.6195 + 7.71550i) q^{59} +(-4.16139 + 1.51107i) q^{60} +(-8.37141 - 6.08218i) q^{61} +(0.143619 - 0.104345i) q^{62} +(0.694388 - 0.504502i) q^{63} +(6.08559 + 4.42144i) q^{64} +(-9.62903 + 3.49647i) q^{65} +(0.421827 - 0.306475i) q^{66} +(1.03412 - 3.18270i) q^{67} +10.5075 q^{68} +(-1.05801 + 3.25621i) q^{69} +(-0.167259 - 0.214415i) q^{70} +(-1.33585 - 4.11131i) q^{71} +(0.174259 + 0.536314i) q^{72} +(7.34593 + 5.33713i) q^{73} +1.05568 q^{74} +(1.21692 - 4.84965i) q^{75} -12.6095 q^{76} +(-2.55530 - 1.85653i) q^{77} +(0.200592 + 0.617357i) q^{78} +(-1.00347 - 3.08837i) q^{79} +(-8.15484 + 2.96116i) q^{80} +(0.309017 - 0.951057i) q^{81} +0.358712 q^{82} +(-2.28447 + 7.03087i) q^{83} +(1.37484 - 0.998876i) q^{84} +(-6.64327 + 9.83307i) q^{85} +(-0.387414 - 0.281473i) q^{86} +(3.02091 - 2.19482i) q^{87} +(1.67884 - 1.21975i) q^{88} +(12.5378 + 9.10921i) q^{89} +(-0.304488 - 0.0875589i) q^{90} +(3.18123 - 2.31130i) q^{91} +(-2.09478 + 6.44705i) q^{92} -1.25290 q^{93} +(0.372140 - 1.14533i) q^{94} +(7.97227 - 11.8002i) q^{95} +(0.518399 + 1.59547i) q^{96} +(-3.10209 - 9.54725i) q^{97} +(-0.717957 - 0.521627i) q^{98} -3.67993 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 10 q^{4} - 6 q^{5} - 12 q^{7} + 9 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 10 * q^4 - 6 * q^5 - 12 * q^7 + 9 * q^8 - 3 * q^9	\( 12 q + 3 q^{3} - 10 q^{4} - 6 q^{5} - 12 q^{7} + 9 q^{8} - 3 q^{9} - 9 q^{10} - 4 q^{11} - 2 q^{13} + 6 q^{14} - 9 q^{15} + 16 q^{16} - q^{17} + 7 q^{19} + 26 q^{20} - 3 q^{21} + 13 q^{22} + 19 q^{23} + 6 q^{24} + 4 q^{25} - 56 q^{26} + 3 q^{27} + q^{28} - q^{29} + 19 q^{30} + 13 q^{31} - 32 q^{32} - q^{33} - 25 q^{34} - 10 q^{35} + 8 q^{37} - 22 q^{38} + 2 q^{39} - 28 q^{40} + 8 q^{41} - 16 q^{42} - 4 q^{43} + 33 q^{44} - 6 q^{45} - 22 q^{46} - 13 q^{47} - 16 q^{48} - 28 q^{49} + 81 q^{50} + 26 q^{51} + 44 q^{52} + 44 q^{53} + 9 q^{55} + 45 q^{56} - 22 q^{57} + 41 q^{58} - 22 q^{59} + 14 q^{60} - 8 q^{61} + 41 q^{62} + 3 q^{63} + 49 q^{64} - 38 q^{65} - 3 q^{66} - 6 q^{67} - 100 q^{68} + 6 q^{69} - 45 q^{70} - 21 q^{71} + 9 q^{72} - 16 q^{73} - 44 q^{74} - 4 q^{75} - 52 q^{76} + q^{77} - 19 q^{78} + 10 q^{79} - 99 q^{80} - 3 q^{81} + 26 q^{82} - 10 q^{83} - 6 q^{84} + 23 q^{85} + 56 q^{86} - 4 q^{87} - 16 q^{88} + 57 q^{89} + 16 q^{90} - 7 q^{91} + 3 q^{92} + 22 q^{93} - 23 q^{94} + 21 q^{95} - 23 q^{96} + 4 q^{97} - 18 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 10 * q^4 - 6 * q^5 - 12 * q^7 + 9 * q^8 - 3 * q^9 - 9 * q^10 - 4 * q^11 - 2 * q^13 + 6 * q^14 - 9 * q^15 + 16 * q^16 - q^17 + 7 * q^19 + 26 * q^20 - 3 * q^21 + 13 * q^22 + 19 * q^23 + 6 * q^24 + 4 * q^25 - 56 * q^26 + 3 * q^27 + q^28 - q^29 + 19 * q^30 + 13 * q^31 - 32 * q^32 - q^33 - 25 * q^34 - 10 * q^35 + 8 * q^37 - 22 * q^38 + 2 * q^39 - 28 * q^40 + 8 * q^41 - 16 * q^42 - 4 * q^43 + 33 * q^44 - 6 * q^45 - 22 * q^46 - 13 * q^47 - 16 * q^48 - 28 * q^49 + 81 * q^50 + 26 * q^51 + 44 * q^52 + 44 * q^53 + 9 * q^55 + 45 * q^56 - 22 * q^57 + 41 * q^58 - 22 * q^59 + 14 * q^60 - 8 * q^61 + 41 * q^62 + 3 * q^63 + 49 * q^64 - 38 * q^65 - 3 * q^66 - 6 * q^67 - 100 * q^68 + 6 * q^69 - 45 * q^70 - 21 * q^71 + 9 * q^72 - 16 * q^73 - 44 * q^74 - 4 * q^75 - 52 * q^76 + q^77 - 19 * q^78 + 10 * q^79 - 99 * q^80 - 3 * q^81 + 26 * q^82 - 10 * q^83 - 6 * q^84 + 23 * q^85 + 56 * q^86 - 4 * q^87 - 16 * q^88 + 57 * q^89 + 16 * q^90 - 7 * q^91 + 3 * q^92 + 22 * q^93 - 23 * q^94 + 21 * q^95 - 23 * q^96 + 4 * q^97 - 18 * q^98 + 6 * q^99

Introduction

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