LMFDB - Embedded newform 75.2.g.b.31.2

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.26265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 $ x^8 - 3x^7 + 2x^6 + x^4 + 8x^2 - 24x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.2
Root			$-1.21700 - 0.720348i$ of defining polynomial
Character	$\chi$	$=$	75.31
Dual form			75.2.g.b.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.655837 + 2.01846i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-2.02602 + 1.47199i) q^{4} +(-2.21700 - 0.291365i) q^{5} +(-1.71700 - 1.24748i) q^{6} +4.35840 q^{7} +(-0.865884 - 0.629102i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.655837 + 2.01846i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-2.02602 + 1.47199i) q^{4} +(-2.21700 - 0.291365i) q^{5} +(-1.71700 - 1.24748i) q^{6} +4.35840 q^{7} +(-0.865884 - 0.629102i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.865884 - 4.66602i) q^{10} +(-0.488218 - 1.50258i) q^{11} +(0.773871 - 2.38173i) q^{12} +(0.370184 - 1.13931i) q^{13} +(2.85840 + 8.79726i) q^{14} +(1.96485 - 1.06740i) q^{15} +(-0.845805 + 2.60312i) q^{16} +(0.907987 + 0.659691i) q^{17} +2.12233 q^{18} +(-6.21218 - 4.51341i) q^{19} +(4.92058 - 2.67310i) q^{20} +(-3.52602 + 2.56180i) q^{21} +(2.71270 - 1.97090i) q^{22} +(-0.717004 - 2.20671i) q^{23} +1.07029 q^{24} +(4.83021 + 1.29192i) q^{25} +2.54243 q^{26} +(0.309017 + 0.951057i) q^{27} +(-8.83021 + 6.41552i) q^{28} +(4.45307 - 3.23535i) q^{29} +(3.44313 + 3.26594i) q^{30} +(-3.88495 - 2.82258i) q^{31} -7.94959 q^{32} +(1.27817 + 0.928645i) q^{33} +(-0.736068 + 2.26538i) q^{34} +(-9.66259 - 1.26989i) q^{35} +(0.773871 + 2.38173i) q^{36} +(-1.96915 + 6.06043i) q^{37} +(5.03596 - 15.4991i) q^{38} +(0.370184 + 1.13931i) q^{39} +(1.73637 + 1.64701i) q^{40} +(-2.30902 + 7.10642i) q^{41} +(-7.48339 - 5.43700i) q^{42} -1.24998 q^{43} +(3.20092 + 2.32561i) q^{44} +(-0.962197 + 2.01846i) q^{45} +(3.98392 - 2.89449i) q^{46} +(-3.33934 + 2.42617i) q^{47} +(-0.845805 - 2.60312i) q^{48} +11.9957 q^{49} +(0.560152 + 10.5969i) q^{50} -1.12233 q^{51} +(0.927051 + 2.85317i) q^{52} +(-3.03032 + 2.20166i) q^{53} +(-1.71700 + 1.24748i) q^{54} +(0.644581 + 3.47347i) q^{55} +(-3.77387 - 2.74188i) q^{56} +7.67867 q^{57} +(9.45090 + 6.86648i) q^{58} +(2.82940 - 8.70799i) q^{59} +(-2.40963 + 5.05483i) q^{60} +(0.431351 + 1.32756i) q^{61} +(3.14937 - 9.69276i) q^{62} +(1.34682 - 4.14509i) q^{63} +(-3.52202 - 10.8397i) q^{64} +(-1.15265 + 2.41799i) q^{65} +(-1.03616 + 3.18898i) q^{66} +(3.12499 + 2.27044i) q^{67} -2.81066 q^{68} +(1.87714 + 1.36382i) q^{69} +(-3.77387 - 20.3364i) q^{70} +(8.57970 - 6.23352i) q^{71} +(-0.865884 + 0.629102i) q^{72} +(1.54407 + 4.75216i) q^{73} -13.5242 q^{74} +(-4.66709 + 1.79395i) q^{75} +19.2297 q^{76} +(-2.12785 - 6.54885i) q^{77} +(-2.05687 + 1.49440i) q^{78} +(-11.7737 + 8.55407i) q^{79} +(2.63361 - 5.52469i) q^{80} +(-0.809017 - 0.587785i) q^{81} -15.8584 q^{82} +(7.06760 + 5.13491i) q^{83} +(3.37284 - 10.3805i) q^{84} +(-1.82080 - 1.72709i) q^{85} +(-0.819784 - 2.52304i) q^{86} +(-1.70092 + 5.23490i) q^{87} +(-0.522535 + 1.60820i) q^{88} +(-3.10195 - 9.54683i) q^{89} +(-4.70522 - 0.618375i) q^{90} +(1.61341 - 4.96556i) q^{91} +(4.70092 + 3.41542i) q^{92} +4.80206 q^{93} +(-7.08719 - 5.14914i) q^{94} +(12.4574 + 11.8163i) q^{95} +(6.43135 - 4.67265i) q^{96} +(6.06760 - 4.40837i) q^{97} +(7.86720 + 24.2128i) q^{98} -1.57991 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 2 q^{3} + q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q - q^2 - 2 * q^3 + q^4 - 5 * q^5 - q^6 + 4 * q^7 - 2 * q^9	\( 8 q - q^{2} - 2 q^{3} + q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 2 q^{9} + 16 q^{11} - 9 q^{12} - 8 q^{13} - 8 q^{14} + 5 q^{15} - 17 q^{16} - q^{17} + 4 q^{18} - 5 q^{19} - 10 q^{20} - 11 q^{21} + 13 q^{22} + 7 q^{23} + 30 q^{24} - 15 q^{25} + 6 q^{26} - 2 q^{27} - 17 q^{28} + 5 q^{29} + 30 q^{30} - 19 q^{31} + 24 q^{32} - 9 q^{33} + 12 q^{34} - 10 q^{35} - 9 q^{36} - q^{37} - 10 q^{38} - 8 q^{39} + 25 q^{40} - 14 q^{41} - 8 q^{42} + 32 q^{43} - 3 q^{44} - 5 q^{45} + 16 q^{46} - q^{47} - 17 q^{48} + 16 q^{49} + 10 q^{50} + 4 q^{51} - 6 q^{52} - 3 q^{53} - q^{54} + 15 q^{55} - 15 q^{56} + 10 q^{57} + 5 q^{58} + 30 q^{59} - 15 q^{60} - 14 q^{61} - 17 q^{62} + 9 q^{63} - 44 q^{64} + 25 q^{65} - 7 q^{66} + 4 q^{67} - 22 q^{68} - 8 q^{69} - 15 q^{70} + 21 q^{71} + 2 q^{73} - 38 q^{74} - 15 q^{75} + 80 q^{76} - 37 q^{77} - 14 q^{78} - 30 q^{79} - 50 q^{80} - 2 q^{81} - 12 q^{82} + 2 q^{83} + 8 q^{84} - 30 q^{85} - 34 q^{86} + 15 q^{87} + 70 q^{88} - 5 q^{90} + 21 q^{91} + 9 q^{92} + 46 q^{93} - 33 q^{94} + 65 q^{95} + 34 q^{96} - 6 q^{97} + 73 q^{98} - 14 q^{99}+O(q^{100}) \) 8 * q - q^2 - 2 * q^3 + q^4 - 5 * q^5 - q^6 + 4 * q^7 - 2 * q^9 + 16 * q^11 - 9 * q^12 - 8 * q^13 - 8 * q^14 + 5 * q^15 - 17 * q^16 - q^17 + 4 * q^18 - 5 * q^19 - 10 * q^20 - 11 * q^21 + 13 * q^22 + 7 * q^23 + 30 * q^24 - 15 * q^25 + 6 * q^26 - 2 * q^27 - 17 * q^28 + 5 * q^29 + 30 * q^30 - 19 * q^31 + 24 * q^32 - 9 * q^33 + 12 * q^34 - 10 * q^35 - 9 * q^36 - q^37 - 10 * q^38 - 8 * q^39 + 25 * q^40 - 14 * q^41 - 8 * q^42 + 32 * q^43 - 3 * q^44 - 5 * q^45 + 16 * q^46 - q^47 - 17 * q^48 + 16 * q^49 + 10 * q^50 + 4 * q^51 - 6 * q^52 - 3 * q^53 - q^54 + 15 * q^55 - 15 * q^56 + 10 * q^57 + 5 * q^58 + 30 * q^59 - 15 * q^60 - 14 * q^61 - 17 * q^62 + 9 * q^63 - 44 * q^64 + 25 * q^65 - 7 * q^66 + 4 * q^67 - 22 * q^68 - 8 * q^69 - 15 * q^70 + 21 * q^71 + 2 * q^73 - 38 * q^74 - 15 * q^75 + 80 * q^76 - 37 * q^77 - 14 * q^78 - 30 * q^79 - 50 * q^80 - 2 * q^81 - 12 * q^82 + 2 * q^83 + 8 * q^84 - 30 * q^85 - 34 * q^86 + 15 * q^87 + 70 * q^88 - 5 * q^90 + 21 * q^91 + 9 * q^92 + 46 * q^93 - 33 * q^94 + 65 * q^95 + 34 * q^96 - 6 * q^97 + 73 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.655837	+	2.01846i	0.463747	+	1.42727i	0.860552	+	0.509363i	$0.170119\pi$
$2$	0.655837	+	2.01846i	0.463747	+	1.42727i	−0.396805	+	0.917903i	$0.629881\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−2.02602	+	1.47199i	−1.01301	+	0.735995i
$5$	−2.21700	−	0.291365i	−0.991474	−	0.130303i
$5$	−2.21700	−	0.291365i	−0.991474	−	0.130303i
$6$	−1.71700	−	1.24748i	−0.700964	−	0.509280i
$7$	4.35840			1.64732			0.823660	−	0.567083i	$-0.191928\pi$
$7$	4.35840			1.64732			0.823660	+	0.567083i	$0.191928\pi$
$8$	−0.865884	−	0.629102i	−0.306136	−	0.222421i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−0.865884	−	4.66602i	−0.273817	−	1.47553i
$11$	−0.488218	−	1.50258i	−0.147203	−	0.453045i	0.850085	−	0.526646i	$-0.176551\pi$
$11$	−0.488218	−	1.50258i	−0.147203	−	0.453045i	−0.997288	+	0.0736014i	$0.976551\pi$
$12$	0.773871	−	2.38173i	0.223397	−	0.687546i
$13$	0.370184	−	1.13931i	0.102670	−	0.315987i	−0.886506	−	0.462717i	$-0.846875\pi$
$13$	0.370184	−	1.13931i	0.102670	−	0.315987i	0.989177	+	0.146729i	$0.0468747\pi$
$14$	2.85840	+	8.79726i	0.763940	+	2.35117i
$15$	1.96485	−	1.06740i	0.507323	−	0.275602i
$16$	−0.845805	+	2.60312i	−0.211451	+	0.650780i
$17$	0.907987	+	0.659691i	0.220219	+	0.159999i	0.692425	−	0.721490i	$-0.256542\pi$
$17$	0.907987	+	0.659691i	0.220219	+	0.159999i	−0.472206	+	0.881488i	$0.656542\pi$
$18$	2.12233			0.500239
$19$	−6.21218	−	4.51341i	−1.42517	−	1.03545i	−0.990890	−	0.134670i	$-0.957002\pi$
$19$	−6.21218	−	4.51341i	−1.42517	−	1.03545i	−0.434281	−	0.900777i	$-0.642998\pi$
$20$	4.92058	−	2.67310i	1.10028	−	0.597722i
$21$	−3.52602	+	2.56180i	−0.769441	+	0.559031i
$22$	2.71270	−	1.97090i	0.578351	−	0.420196i
$23$	−0.717004	−	2.20671i	−0.149506	−	0.460131i	0.848057	−	0.529905i	$-0.177772\pi$
$23$	−0.717004	−	2.20671i	−0.149506	−	0.460131i	−0.997563	+	0.0697736i	$0.977772\pi$
$24$	1.07029			0.218472
$25$	4.83021	+	1.29192i	0.966042	+	0.258383i
$26$	2.54243			0.498611
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−8.83021	+	6.41552i	−1.66875	+	1.21242i
$29$	4.45307	−	3.23535i	0.826915	−	0.600789i	−0.0917701	−	0.995780i	$-0.529252\pi$
$29$	4.45307	−	3.23535i	0.826915	−	0.600789i	0.918685	+	0.394992i	$0.129252\pi$
$30$	3.44313	+	3.26594i	0.628627	+	0.596276i
$31$	−3.88495	−	2.82258i	−0.697757	−	0.506950i	0.181444	−	0.983401i	$-0.441923\pi$
$31$	−3.88495	−	2.82258i	−0.697757	−	0.506950i	−0.879201	+	0.476451i	$0.841923\pi$
$32$	−7.94959			−1.40530
$33$	1.27817	+	0.928645i	0.222501	+	0.161656i
$34$	−0.736068	+	2.26538i	−0.126235	+	0.388510i
$35$	−9.66259	−	1.26989i	−1.63328	−	0.214650i
$36$	0.773871	+	2.38173i	0.128979	+	0.396955i
$37$	−1.96915	+	6.06043i	−0.323727	+	0.996329i	0.648285	+	0.761398i	$0.275486\pi$
$37$	−1.96915	+	6.06043i	−0.323727	+	0.996329i	−0.972012	+	0.234931i	$0.924514\pi$
$38$	5.03596	−	15.4991i	0.816941	−	2.51428i
$39$	0.370184	+	1.13931i	0.0592768	+	0.182435i
$40$	1.73637	+	1.64701i	0.274544	+	0.260415i
$41$	−2.30902	+	7.10642i	−0.360608	+	1.10984i	0.592078	+	0.805881i	$0.298308\pi$
$41$	−2.30902	+	7.10642i	−0.360608	+	1.10984i	−0.952686	+	0.303956i	$0.901692\pi$
$42$	−7.48339	−	5.43700i	−1.15471	−	0.838948i
$43$	−1.24998			−0.190620			−0.0953102	−	0.995448i	$-0.530384\pi$
$43$	−1.24998			−0.190620			−0.0953102	+	0.995448i	$0.530384\pi$
$44$	3.20092	+	2.32561i	0.482557	+	0.350598i
$45$	−0.962197	+	2.01846i	−0.143436	+	0.300894i
$46$	3.98392	−	2.89449i	0.587397	−	0.426769i
$47$	−3.33934	+	2.42617i	−0.487092	+	0.353893i	−0.804065	−	0.594541i	$-0.797334\pi$
$47$	−3.33934	+	2.42617i	−0.487092	+	0.353893i	0.316973	+	0.948435i	$0.397334\pi$
$48$	−0.845805	−	2.60312i	−0.122081	−	0.375728i
$49$	11.9957			1.71367
$50$	0.560152	+	10.5969i	0.0792174	+	1.49862i
$51$	−1.12233			−0.157158
$52$	0.927051	+	2.85317i	0.128559	+	0.395663i
$53$	−3.03032	+	2.20166i	−0.416247	+	0.302421i	−0.776126	−	0.630578i	$-0.782818\pi$
$53$	−3.03032	+	2.20166i	−0.416247	+	0.302421i	0.359879	+	0.932999i	$0.382818\pi$
$54$	−1.71700	+	1.24748i	−0.233655	+	0.169760i
$55$	0.644581	+	3.47347i	0.0869153	+	0.468363i
$56$	−3.77387	−	2.74188i	−0.504305	−	0.366399i
$57$	7.67867			1.01707
$58$	9.45090	+	6.86648i	1.24096	+	0.901613i
$59$	2.82940	−	8.70799i	0.368356	−	1.13368i	−0.579496	−	0.814975i	$-0.696751\pi$
$59$	2.82940	−	8.70799i	0.368356	−	1.13368i	0.947853	−	0.318709i	$-0.103249\pi$
$60$	−2.40963	+	5.05483i	−0.311082	+	0.652575i
$61$	0.431351	+	1.32756i	0.0552288	+	0.169977i	0.974866	−	0.222792i	$-0.0715172\pi$
$61$	0.431351	+	1.32756i	0.0552288	+	0.169977i	−0.919637	+	0.392769i	$0.871517\pi$
$62$	3.14937	−	9.69276i	0.399970	−	1.23098i
$63$	1.34682	−	4.14509i	0.169683	−	0.522232i
$64$	−3.52202	−	10.8397i	−0.440253	−	1.35496i
$65$	−1.15265	+	2.41799i	−0.142969	+	0.299915i
$66$	−1.03616	+	3.18898i	−0.127543	+	0.392536i
$67$	3.12499	+	2.27044i	0.381778	+	0.277378i	0.762078	−	0.647485i	$-0.224179\pi$
$67$	3.12499	+	2.27044i	0.381778	+	0.277378i	−0.380300	+	0.924863i	$0.624179\pi$
$68$	−2.81066			−0.340843
$69$	1.87714	+	1.36382i	0.225981	+	0.164185i
$70$	−3.77387	−	20.3364i	−0.451064	−	2.43066i
$71$	8.57970	−	6.23352i	1.01822	−	0.739783i	0.0523057	−	0.998631i	$-0.483343\pi$
$71$	8.57970	−	6.23352i	1.01822	−	0.739783i	0.965918	+	0.258848i	$0.0833430\pi$
$72$	−0.865884	+	0.629102i	−0.102045	+	0.0741403i
$73$	1.54407	+	4.75216i	0.180720	+	0.556198i	0.999848	−	0.0174117i	$-0.00554259\pi$
$73$	1.54407	+	4.75216i	0.180720	+	0.556198i	−0.819129	+	0.573610i	$0.805543\pi$
$74$	−13.5242			−1.57215
$75$	−4.66709	+	1.79395i	−0.538910	+	0.207147i
$76$	19.2297			2.20580
$77$	−2.12785	−	6.54885i	−0.242491	−	0.746310i
$78$	−2.05687	+	1.49440i	−0.232894	+	0.169208i
$79$	−11.7737	+	8.55407i	−1.32464	+	0.962408i	−0.324779	+	0.945790i	$0.605290\pi$
$79$	−11.7737	+	8.55407i	−1.32464	+	0.962408i	−0.999862	+	0.0166185i	$0.994710\pi$
$80$	2.63361	−	5.52469i	0.294447	−	0.617679i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−15.8584			−1.75126
$83$	7.06760	+	5.13491i	0.775770	+	0.563630i	0.903706	−	0.428153i	$-0.140835\pi$
$83$	7.06760	+	5.13491i	0.775770	+	0.563630i	−0.127937	+	0.991782i	$0.540835\pi$
$84$	3.37284	−	10.3805i	0.368007	−	1.13261i
$85$	−1.82080	−	1.72709i	−0.197493	−	0.187330i
$86$	−0.819784	−	2.52304i	−0.0883996	−	0.272066i
$87$	−1.70092	+	5.23490i	−0.182358	+	0.561240i
$88$	−0.522535	+	1.60820i	−0.0557025	+	0.171435i
$89$	−3.10195	−	9.54683i	−0.328806	−	1.01196i	−0.969693	−	0.244326i	$-0.921433\pi$
$89$	−3.10195	−	9.54683i	−0.328806	−	1.01196i	0.640887	−	0.767635i	$-0.278567\pi$
$90$	−4.70522	−	0.618375i	−0.495974	−	0.0651824i
$91$	1.61341	−	4.96556i	0.169131	−	0.520532i
$92$	4.70092	+	3.41542i	0.490105	+	0.356082i
$93$	4.80206			0.497950
$94$	−7.08719	−	5.14914i	−0.730988	−	0.531094i
$95$	12.4574	+	11.8163i	1.27810	+	1.21232i
$96$	6.43135	−	4.67265i	0.656397	−	0.476900i
$97$	6.06760	−	4.40837i	0.616071	−	0.447602i	−0.235476	−	0.971880i	$-0.575665\pi$
$97$	6.06760	−	4.40837i	0.616071	−	0.447602i	0.851547	+	0.524278i	$0.175665\pi$
$98$	7.86720	+	24.2128i	0.794707	+	2.44586i
$99$	−1.57991			−0.158787
$100$	−11.6878	+	4.49258i	−1.16878	+	0.449258i
$101$	−6.51821			−0.648586			−0.324293	−	0.945957i	$-0.605126\pi$
$101$	−6.51821			−0.648586			−0.324293	+	0.945957i	$0.605126\pi$
$102$	−0.736068	−	2.26538i	−0.0728816	−	0.224306i
$103$	−6.51158	+	4.73094i	−0.641605	+	0.466153i	−0.860401	−	0.509617i	$-0.829787\pi$
$103$	−6.51158	+	4.73094i	−0.641605	+	0.466153i	0.218796	+	0.975771i	$0.429787\pi$
$104$	−1.03728	+	0.753626i	−0.101713	+	0.0738991i
$105$	8.56362	−	4.65217i	0.835724	−	0.454005i
$106$	−6.43135	−	4.67265i	−0.624668	−	0.453848i
$107$	9.47745			0.916220			0.458110	−	0.888896i	$-0.348527\pi$
$107$	9.47745			0.916220			0.458110	+	0.888896i	$0.348527\pi$
$108$	−2.02602	−	1.47199i	−0.194954	−	0.141642i
$109$	−3.60491	+	11.0948i	−0.345288	+	1.06269i	0.616142	+	0.787635i	$0.288695\pi$
$109$	−3.60491	+	11.0948i	−0.345288	+	1.06269i	−0.961429	+	0.275052i	$0.911305\pi$
$110$	−6.58833	+	3.57909i	−0.628172	+	0.341253i
$111$	−1.96915	−	6.06043i	−0.186904	−	0.575231i
$112$	−3.68636	+	11.3454i	−0.348328	+	1.07204i
$113$	−4.61219	+	14.1949i	−0.433879	+	1.33534i	0.460353	+	0.887736i	$0.347723\pi$
$113$	−4.61219	+	14.1949i	−0.433879	+	1.33534i	−0.894231	+	0.447605i	$0.852277\pi$
$114$	5.03596	+	15.4991i	0.471661	+	1.45162i
$115$	0.946641	+	5.10120i	0.0882747	+	0.475689i
$116$	−4.25962	+	13.1098i	−0.395496	+	1.21721i
$117$	−0.969154	−	0.704131i	−0.0895983	−	0.0650970i
$118$	19.4324			1.78889
$119$	3.95737	+	2.87520i	0.362772	+	0.263569i
$120$	−2.37284	−	0.311846i	−0.216610	−	0.0284675i
$121$	6.87980	−	4.99847i	0.625436	−	0.454406i
$122$	−2.39673	+	1.74133i	−0.216990	+	0.157652i
$123$	−2.30902	−	7.10642i	−0.208197	−	0.640765i
$124$	12.0258			1.07995
$125$	−10.3322	−	4.27154i	−0.924138	−	0.382058i
$126$	9.24998			0.824054
$127$	−5.25195	−	16.1638i	−0.466035	−	1.43431i	−0.857676	−	0.514190i	$-0.828092\pi$
$127$	−5.25195	−	16.1638i	−0.466035	−	1.43431i	0.391641	−	0.920118i	$-0.371908\pi$
$128$	6.70686	−	4.87282i	0.592809	−	0.430701i
$129$	1.01126	−	0.734721i	0.0890362	−	0.0646886i
$130$	−5.63657	−	0.740776i	−0.494360	−	0.0649703i
$131$	0.266063	+	0.193306i	0.0232461	+	0.0168892i	0.599348	−	0.800489i	$-0.295427\pi$
$131$	0.266063	+	0.193306i	0.0232461	+	0.0168892i	−0.576102	+	0.817378i	$0.695427\pi$
$132$	−3.95656			−0.344374
$133$	−27.0752	−	19.6713i	−2.34771	−	1.70571i
$134$	−2.53330	+	7.79670i	−0.218844	+	0.673533i
$135$	−0.407987	−	2.19853i	−0.0351139	−	0.189220i
$136$	−0.371199	−	1.14243i	−0.0318300	−	0.0979628i
$137$	1.40995	−	4.33939i	0.120461	−	0.370739i	−0.872586	−	0.488460i	$-0.837559\pi$
$137$	1.40995	−	4.33939i	0.120461	−	0.370739i	0.993047	+	0.117721i	$0.0375588\pi$
$138$	−1.52172	+	4.68338i	−0.129538	+	0.398676i
$139$	−1.46289	−	4.50230i	−0.124080	−	0.381880i	0.869652	−	0.493665i	$-0.164343\pi$
$139$	−1.46289	−	4.50230i	−0.124080	−	0.381880i	−0.993732	+	0.111785i	$0.964343\pi$
$140$	21.4459	−	11.6504i	1.81251	−	0.984641i
$141$	1.27551	−	3.92563i	0.107418	−	0.330597i
$142$	18.2090	+	13.2296i	1.52806	+	1.11020i
$143$	−1.89263			−0.158270
$144$	2.21435	+	1.60882i	0.184529	+	0.134068i
$145$	−10.8151	+	5.87530i	−0.898149	+	0.487917i
$146$	−8.57938	+	6.23328i	−0.710035	+	0.515870i
$147$	−9.70470	+	7.05087i	−0.800430	+	0.581546i
$148$	−4.93135	−	15.1771i	−0.405355	−	1.24755i
$149$	4.67644			0.383109			0.191555	−	0.981482i	$-0.438647\pi$
$149$	4.67644			0.383109			0.191555	+	0.981482i	$0.438647\pi$
$150$	−6.68186	−	8.24380i	−0.545571	−	0.673104i
$151$	−6.54178			−0.532362			−0.266181	−	0.963923i	$-0.585762\pi$
$151$	−6.54178			−0.532362			−0.266181	+	0.963923i	$0.585762\pi$
$152$	2.53963	+	7.81618i	0.205991	+	0.633976i
$153$	0.907987	−	0.659691i	0.0734064	−	0.0533329i
$154$	11.8231	−	8.58995i	0.952729	−	0.692198i
$155$	7.79054	+	7.38961i	0.625751	+	0.593548i
$156$	−2.42705	−	1.76336i	−0.194320	−	0.141181i
$157$	3.99404			0.318759			0.159379	−	0.987217i	$-0.449051\pi$
$157$	3.99404			0.318759			0.159379	+	0.987217i	$0.449051\pi$
$158$	−24.9877	−	18.1546i	−1.98791	−	1.44430i
$159$	1.15748	−	3.56236i	0.0917941	−	0.282513i
$160$	17.6243	+	2.31623i	1.39332	+	0.183114i
$161$	−3.12499	−	9.61773i	−0.246284	−	0.757984i
$162$	0.655837	−	2.01846i	0.0515274	−	0.158585i
$163$	1.48372	−	4.56641i	0.116214	−	0.357669i	−0.875985	−	0.482339i	$-0.839787\pi$
$163$	1.48372	−	4.56641i	0.116214	−	0.357669i	0.992198	+	0.124670i	$0.0397873\pi$
$164$	−5.78247	−	17.7966i	−0.451535	−	1.38968i
$165$	−2.56313	−	2.43123i	−0.199540	−	0.189271i
$166$	−5.72941	+	17.6333i	−0.444689	+	1.36861i
$167$	−19.1414	−	13.9070i	−1.48120	−	1.07616i	−0.977167	−	0.212474i	$-0.931848\pi$
$167$	−19.1414	−	13.9070i	−1.48120	−	1.07616i	−0.504036	−	0.863682i	$-0.668152\pi$
$168$	4.66476			0.359894
$169$	9.35623	+	6.79770i	0.719710	+	0.522900i
$170$	2.29192	−	4.80790i	0.175782	−	0.368749i
$171$	−6.21218	+	4.51341i	−0.475057	+	0.345149i
$172$	2.53249	−	1.83996i	0.193100	−	0.140296i
$173$	4.48208	+	13.7944i	0.340766	+	1.04877i	0.963812	+	0.266584i	$0.0858950\pi$
$173$	4.48208	+	13.7944i	0.340766	+	1.04877i	−0.623046	+	0.782185i	$0.714105\pi$
$174$	−11.6820			−0.885607
$175$	21.0520	+	5.63069i	1.59138	+	0.425640i
$176$	4.32433			0.325959
$177$	2.82940	+	8.70799i	0.212671	+	0.654533i
$178$	17.2355	−	12.5223i	1.29186	−	0.938588i
$179$	−0.644581	+	0.468315i	−0.0481782	+	0.0350035i	−0.611614	−	0.791157i	$-0.709479\pi$
$179$	−0.644581	+	0.468315i	−0.0481782	+	0.0350035i	0.563436	+	0.826160i	$0.309479\pi$
$180$	−1.02172	−	5.50578i	−0.0761546	−	0.410377i
$181$	11.5030	+	8.35741i	0.855010	+	0.621201i	0.926523	−	0.376239i	$-0.122783\pi$
$181$	11.5030	+	8.35741i	0.855010	+	0.621201i	−0.0715129	+	0.997440i	$0.522783\pi$
$182$	11.0809			0.821372
$183$	−1.12929	−	0.820477i	−0.0834795	−	0.0606514i
$184$	−0.767403	+	2.36182i	−0.0565737	+	0.174116i
$185$	6.13142	−	12.8623i	0.450791	−	0.945652i
$186$	3.14937	+	9.69276i	0.230923	+	0.710708i
$187$	0.547943	−	1.68640i	0.0400696	−	0.123321i
$188$	3.19427	−	9.83094i	0.232966	−	0.716995i
$189$	1.34682	+	4.14509i	0.0979667	+	0.301511i
$190$	−15.6806	+	32.8942i	−1.13759	+	2.38640i
$191$	−3.20441	+	9.86215i	−0.231863	+	0.713600i	0.765659	+	0.643246i	$0.222413\pi$
$191$	−3.20441	+	9.86215i	−0.231863	+	0.713600i	−0.997522	+	0.0703540i	$0.977587\pi$
$192$	9.22078	+	6.69929i	0.665452	+	0.483479i
$193$	4.34712			0.312913			0.156456	−	0.987685i	$-0.449993\pi$
$193$	4.34712			0.312913			0.156456	+	0.987685i	$0.449993\pi$
$194$	12.8775	+	9.35603i	0.924548	+	0.671724i
$195$	−0.488744	−	2.63371i	−0.0349997	−	0.188604i
$196$	−24.3035	+	17.6575i	−1.73596	+	1.26125i
$197$	−1.52087	+	1.10498i	−0.108358	+	0.0787263i	−0.640644	−	0.767838i	$-0.721333\pi$
$197$	−1.52087	+	1.10498i	−0.108358	+	0.0787263i	0.532287	+	0.846564i	$0.321333\pi$
$198$	−1.03616	−	3.18898i	−0.0736367	−	0.226631i
$199$	4.26028			0.302003			0.151002	−	0.988534i	$-0.451750\pi$
$199$	4.26028			0.302003			0.151002	+	0.988534i	$0.451750\pi$
$200$	−3.36966	−	4.15735i	−0.238271	−	0.293969i
$201$	−3.86270			−0.272454
$202$	−4.27489	−	13.1567i	−0.300780	−	0.925705i
$203$	19.4083	−	14.1009i	1.36219	−	0.989692i
$204$	2.27387	−	1.65206i	0.159203	−	0.115668i
$205$	7.18967	−	15.0822i	0.502148	−	1.05339i
$206$	−13.8197	−	10.0406i	−0.962867	−	0.699564i
$207$	−2.32027			−0.161270
$208$	2.65265	+	1.92727i	0.183928	+	0.133632i
$209$	−3.74887	+	11.5378i	−0.259314	+	0.798088i
$210$	15.0066	+	14.2343i	1.03555	+	0.982257i
$211$	−2.87284	−	8.84170i	−0.197775	−	0.608687i	−0.999933	−	0.0115762i	$-0.996315\pi$
$211$	−2.87284	−	8.84170i	−0.197775	−	0.608687i	0.802158	−	0.597111i	$-0.203685\pi$
$212$	2.89868	−	8.92120i	0.199082	−	0.612711i
$213$	−3.27716	+	10.0860i	−0.224547	+	0.691085i
$214$	6.21566	+	19.1298i	0.424894	+	1.30769i
$215$	2.77121	+	0.364201i	0.188995	+	0.0248383i
$216$	0.330738	−	1.01791i	0.0225039	−	0.0692599i
$217$	−16.9322	−	12.3019i	−1.14943	−	0.835110i
$218$	−24.7586			−1.67686
$219$	−4.04243	−	2.93700i	−0.273162	−	0.198464i
$220$	−6.41886	−	6.08852i	−0.432759	−	0.410488i
$221$	1.08771	−	0.790270i	0.0731675	−	0.0531593i
$222$	10.9413	−	7.94931i	0.734331	−	0.533523i
$223$	−1.04991	−	3.23129i	−0.0703072	−	0.216383i	0.909729	−	0.415203i	$-0.136289\pi$
$223$	−1.04991	−	3.23129i	−0.0703072	−	0.216383i	−0.980036	+	0.198819i	$0.936289\pi$
$224$	−34.6475			−2.31498
$225$	2.72130	−	4.19458i	0.181420	−	0.279639i
$226$	−31.6766			−2.10710
$227$	8.28083	+	25.4858i	0.549618	+	1.69155i	0.709750	+	0.704454i	$0.248808\pi$
$227$	8.28083	+	25.4858i	0.549618	+	1.69155i	−0.160132	+	0.987096i	$0.551192\pi$
$228$	−15.5572	+	11.3029i	−1.03030	+	0.748555i
$229$	0.956255	−	0.694760i	0.0631911	−	0.0459110i	−0.555741	−	0.831355i	$-0.687565\pi$
$229$	0.956255	−	0.694760i	0.0631911	−	0.0459110i	0.618932	+	0.785444i	$0.287565\pi$
$230$	−9.67572	+	5.25631i	−0.637998	+	0.346591i
$231$	5.57078	+	4.04741i	0.366530	+	0.266300i
$232$	−5.89121			−0.386777
$233$	−5.73984	−	4.17024i	−0.376030	−	0.273201i	0.383677	−	0.923467i	$-0.374658\pi$
$233$	−5.73984	−	4.17024i	−0.376030	−	0.273201i	−0.759707	+	0.650266i	$0.774658\pi$
$234$	0.785653	−	2.41799i	0.0513598	−	0.158069i
$235$	8.11023	−	4.40586i	0.529053	−	0.287407i
$236$	7.08566	+	21.8074i	0.461237	+	1.41954i
$237$	4.49714	−	13.8408i	0.292121	−	0.899055i
$238$	−3.20808	+	9.87345i	−0.207949	+	0.640001i
$239$	0.0132236	+	0.0406981i	0.000855365	+	0.00263254i	0.951483	−	0.307700i	$-0.0995595\pi$
$239$	0.0132236	+	0.0406981i	0.000855365	+	0.00263254i	−0.950628	+	0.310333i	$0.899559\pi$
$240$	1.11669	+	6.01757i	0.0720823	+	0.388432i
$241$	−3.63746	+	11.1950i	−0.234310	+	0.721131i	0.762903	+	0.646513i	$0.223774\pi$
$241$	−3.63746	+	11.1950i	−0.234310	+	0.721131i	−0.997212	+	0.0746174i	$0.976226\pi$
$242$	14.6012	+	10.6084i	0.938602	+	0.681934i
$243$	1.00000			0.0641500
$244$	−2.82808	−	2.05472i	−0.181049	−	0.131540i
$245$	−26.5944	−	3.49512i	−1.69906	−	0.223295i
$246$	12.8297	−	9.32131i	0.817991	−	0.594305i
$247$	−7.44182	+	5.40680i	−0.473511	+	0.344026i
$248$	1.58823	+	4.88806i	0.100852	+	0.310392i
$249$	−8.73603			−0.553623
$250$	1.84570	−	23.6565i	0.116733	−	1.49617i
$251$	17.4764			1.10310			0.551550	−	0.834142i	$-0.314036\pi$
$251$	17.4764			1.10310			0.551550	+	0.834142i	$0.314036\pi$
$252$	3.37284	+	10.3805i	0.212469	+	0.653912i
$253$	−2.96571	+	2.15471i	−0.186452	+	0.135466i
$254$	29.1816	−	21.2017i	1.83102	−	1.33031i
$255$	2.48822	+	0.327009i	0.155818	+	0.0204781i
$256$	−4.20735	−	3.05682i	−0.262960	−	0.191051i
$257$	15.4671			0.964814			0.482407	−	0.875947i	$-0.339763\pi$
$257$	15.4671			0.964814			0.482407	+	0.875947i	$0.339763\pi$
$258$	2.14622	+	1.55932i	0.133618	+	0.0970792i
$259$	−8.58236	+	26.4138i	−0.533282	+	1.64127i
$260$	−1.22396	−	6.59560i	−0.0759068	−	0.409042i
$261$	−1.70092	−	5.23490i	−0.105284	−	0.324032i
$262$	−0.215687	+	0.663815i	−0.0133252	+	0.0410106i
$263$	0.447331	−	1.37674i	0.0275836	−	0.0848936i	−0.936317	−	0.351156i	$-0.885789\pi$
$263$	0.447331	−	1.37674i	0.0275836	−	0.0848936i	0.963901	+	0.266262i	$0.0857887\pi$
$264$	−0.522535	−	1.60820i	−0.0321598	−	0.0989778i
$265$	7.35972	−	3.99815i	0.452104	−	0.245604i
$266$	21.9487	−	67.5513i	1.34576	−	4.14183i
$267$	8.12102	+	5.90026i	0.496998	+	0.361090i
$268$	−9.67336			−0.590895
$269$	7.04344	+	5.11736i	0.429446	+	0.312011i	0.781427	−	0.623996i	$-0.214492\pi$
$269$	7.04344	+	5.11736i	0.429446	+	0.312011i	−0.351981	+	0.936007i	$0.614492\pi$
$270$	4.17008	−	2.26538i	0.253783	−	0.137867i
$271$	23.1652	−	16.8305i	1.40719	−	1.02238i	0.413462	−	0.910521i	$-0.364319\pi$
$271$	23.1652	−	16.8305i	1.40719	−	1.02238i	0.993724	−	0.111860i	$-0.0356807\pi$
$272$	−2.48524	+	1.80563i	−0.150690	+	0.109482i
$273$	1.61341	+	4.96556i	0.0976480	+	0.300530i
$274$	9.68359			0.585007
$275$	−0.416988	−	7.88852i	−0.0251453	−	0.475695i
$276$	−5.81066			−0.349761
$277$	1.63844	+	5.04259i	0.0984442	+	0.302980i	0.988136	−	0.153582i	$-0.0490808\pi$
$277$	1.63844	+	5.04259i	0.0984442	+	0.302980i	−0.889692	+	0.456562i	$0.849081\pi$
$278$	8.12830	−	5.90555i	0.487503	−	0.354192i
$279$	−3.88495	+	2.82258i	−0.232586	+	0.168983i
$280$	7.56780	+	7.17833i	0.452262	+	0.428987i
$281$	19.4837	+	14.1557i	1.16230	+	0.844461i	0.990067	−	0.140595i	$-0.0449015\pi$
$281$	19.4837	+	14.1557i	1.16230	+	0.844461i	0.172234	+	0.985056i	$0.444902\pi$
$282$	8.76025			0.521665
$283$	21.9359	+	15.9374i	1.30396	+	0.947380i	0.999986	−	0.00530192i	$-0.00168766\pi$
$283$	21.9359	+	15.9374i	1.30396	+	0.947380i	0.303970	+	0.952682i	$0.401688\pi$
$284$	−8.20698	+	25.2585i	−0.486995	+	1.49882i
$285$	−17.0237	−	2.23730i	−1.00839	−	0.132526i
$286$	−1.24126	−	3.82020i	−0.0733971	−	0.225893i
$287$	−10.0636	+	30.9726i	−0.594037	+	1.82826i
$288$	−2.45656	+	7.56051i	−0.144754	+	0.445507i
$289$	−4.86404	−	14.9700i	−0.286120	−	0.880587i
$290$	−18.9520	−	17.9767i	−1.11290	−	1.05563i
$291$	−2.31762	+	7.13289i	−0.135861	+	0.418137i
$292$	−10.1234	−	7.35512i	−0.592430	−	0.430426i
$293$	−20.3016			−1.18603			−0.593017	−	0.805190i	$-0.702063\pi$
$293$	−20.3016			−1.18603			−0.593017	+	0.805190i	$0.702063\pi$
$294$	−20.5966	−	14.9643i	−1.20122	−	0.872736i
$295$	−8.81000	+	18.4813i	−0.512938	+	1.07602i
$296$	5.51769	−	4.00883i	0.320709	−	0.233009i
$297$	1.27817	−	0.928645i	0.0741670	−	0.0538855i
$298$	3.06698	+	9.43921i	0.177666	+	0.546799i
$299$	−2.77955			−0.160745
$300$	6.81496	−	10.5045i	0.393462	−	0.606477i
$301$	−5.44792			−0.314013
$302$	−4.29034	−	13.2043i	−0.246881	−	0.759823i
$303$	5.27335	−	3.83131i	0.302946	−	0.220103i
$304$	17.0032	−	12.3536i	0.975203	−	0.708527i
$305$	−0.569501	−	3.06889i	−0.0326095	−	0.175724i
$306$	1.92705	+	1.40008i	0.110162	+	0.0800375i
$307$	−2.51330			−0.143442			−0.0717208	−	0.997425i	$-0.522849\pi$
$307$	−2.51330			−0.143442			−0.0717208	+	0.997425i	$0.522849\pi$
$308$	13.9509	+	10.1359i	0.794927	+	0.577548i
$309$	2.48720	−	7.65482i	0.141492	−	0.435468i
$310$	−9.80630	+	20.5713i	−0.556960	+	1.16837i
$311$	1.49075	+	4.58806i	0.0845327	+	0.260165i	0.984385	−	0.176030i	$-0.0563257\pi$
$311$	1.49075	+	4.58806i	0.0845327	+	0.260165i	−0.899852	+	0.436195i	$0.856326\pi$
$312$	0.396205	−	1.21939i	0.0224307	−	0.0690345i
$313$	−1.85043	+	5.69504i	−0.104592	+	0.321903i	−0.989635	−	0.143608i	$-0.954129\pi$
$313$	−1.85043	+	5.69504i	−0.104592	+	0.321903i	0.885042	+	0.465511i	$0.154129\pi$
$314$	2.61944	+	8.06180i	0.147823	+	0.454954i
$315$	−4.19364	+	8.79726i	−0.236285	+	0.495669i
$316$	11.2622	−	34.6615i	0.633548	−	1.94986i
$317$	−14.0389	−	10.1999i	−0.788506	−	0.572883i	0.119014	−	0.992893i	$-0.462027\pi$
$317$	−14.0389	−	10.1999i	−0.788506	−	0.572883i	−0.907520	+	0.420010i	$0.862027\pi$
$318$	7.94959			0.445791
$319$	−7.03543	−	5.11154i	−0.393909	−	0.286191i
$320$	4.65003	+	25.0578i	0.259945	+	1.40077i
$321$	−7.66742	+	5.57071i	−0.427954	+	0.310926i
$322$	17.3635	−	12.6153i	0.967631	−	0.703025i
$323$	−2.66312	−	8.19624i	−0.148180	−	0.456051i
$324$	2.50430			0.139128
$325$	3.25996	−	5.02486i	0.180830	−	0.278729i
$326$	10.1902			0.564383
$327$	−3.60491	−	11.0948i	−0.199352	−	0.613543i
$328$	6.47000	−	4.70073i	0.357246	−	0.259555i
$329$	−14.5542	+	10.5742i	−0.802398	+	0.582976i
$330$	3.22633	−	6.76807i	0.177604	−	0.372570i
$331$	−16.4518	−	11.9529i	−0.904270	−	0.656991i	0.0352890	−	0.999377i	$-0.488765\pi$
$331$	−16.4518	−	11.9529i	−0.904270	−	0.656991i	−0.939559	+	0.342386i	$0.888765\pi$
$332$	−21.8776			−1.20069
$333$	5.15531	+	3.74555i	0.282509	+	0.205255i
$334$	15.5171	−	47.7568i	0.849059	−	2.61314i
$335$	−6.26659	−	5.94409i	−0.342380	−	0.324760i
$336$	−3.68636	−	11.3454i	−0.201107	−	0.618945i
$337$	10.5860	−	32.5805i	0.576658	−	1.77477i	−0.0538048	−	0.998551i	$-0.517135\pi$
$337$	10.5860	−	32.5805i	0.576658	−	1.77477i	0.630463	−	0.776219i	$-0.282865\pi$
$338$	−7.58472	+	23.3434i	−0.412554	+	1.26971i
$339$	−4.61219	−	14.1949i	−0.250500	−	0.770960i
$340$	6.23124	+	0.818929i	0.337937	+	0.0444127i
$341$	−2.34445	+	7.21548i	−0.126959	+	0.390740i
$342$	−13.1843	−	9.57897i	−0.712926	−	0.517971i
$343$	21.7731			1.17564
$344$	1.08234	+	0.786366i	0.0583558	+	0.0423980i
$345$	−3.76426	−	3.57053i	−0.202661	−	0.192231i
$346$	−24.9039	+	18.0938i	−1.33884	+	0.972727i
$347$	0.0399344	−	0.0290140i	0.00214379	−	0.00155756i	−0.586713	−	0.809795i	$-0.699578\pi$
$347$	0.0399344	−	0.0290140i	0.00214379	−	0.00155756i	0.588857	+	0.808238i	$0.299578\pi$
$348$	−4.25962	−	13.1098i	−0.228340	−	0.702757i
$349$	−7.47437			−0.400094			−0.200047	−	0.979786i	$-0.564109\pi$
$349$	−7.47437			−0.400094			−0.200047	+	0.979786i	$0.564109\pi$
$350$	2.44137	+	46.1854i	0.130497	+	2.46871i
$351$	1.19794			0.0639413
$352$	3.88113	+	11.9449i	0.206865	+	0.636665i
$353$	15.0194	−	10.9122i	0.799401	−	0.580799i	−0.111337	−	0.993783i	$-0.535513\pi$
$353$	15.0194	−	10.9122i	0.799401	−	0.580799i	0.910738	+	0.412984i	$0.135513\pi$
$354$	−15.7211	+	11.4220i	−0.835567	+	0.607075i
$355$	−20.8375	+	11.3199i	−1.10594	+	0.600798i
$356$	20.3375	+	14.7760i	1.07788	+	0.783128i
$357$	−4.89158			−0.258890
$358$	−1.36802	−	0.993921i	−0.0723019	−	0.0525304i
$359$	3.27695	−	10.0854i	0.172951	−	0.532289i	−0.826583	−	0.562815i	$-0.809718\pi$
$359$	3.27695	−	10.0854i	0.172951	−	0.532289i	0.999534	+	0.0305264i	$0.00971835\pi$
$360$	2.10297	−	1.14243i	0.110836	−	0.0602115i
$361$	12.3490	+	38.0062i	0.649945	+	2.00032i
$362$	−9.32500	+	28.6994i	−0.490111	+	1.50841i
$363$	−2.62785	+	8.08769i	−0.137926	+	0.424493i
$364$	4.04046	+	12.4353i	0.211778	+	0.651785i
$365$	−2.03859	−	10.9854i	−0.106705	−	0.575004i
$366$	0.915470	−	2.81753i	0.0478524	−	0.147274i
$367$	9.39886	+	6.82867i	0.490617	+	0.356454i	0.805421	−	0.592703i	$-0.201939\pi$
$367$	9.39886	+	6.82867i	0.490617	+	0.356454i	−0.314805	+	0.949156i	$0.601939\pi$
$368$	6.35078			0.331057
$369$	6.04508	+	4.39201i	0.314695	+	0.228639i
$370$	29.9832	+	3.94048i	1.55875	+	0.204856i
$371$	−13.2074	+	9.59570i	−0.685692	+	0.498184i
$372$	−9.72907	+	7.06859i	−0.504429	+	0.366489i
$373$	−7.14671	−	21.9953i	−0.370043	−	1.13887i	−0.946763	−	0.321932i	$-0.895668\pi$
$373$	−7.14671	−	21.9953i	−0.370043	−	1.13887i	0.576720	−	0.816942i	$-0.304332\pi$
$374$	3.76328			0.194595
$375$	10.8697	−	2.61735i	0.561307	−	0.135160i
$376$	4.41779			0.227830
$377$	−2.03760	−	6.27109i	−0.104942	−	0.322978i
$378$	−7.48339	+	5.43700i	−0.384904	+	0.279649i
$379$	−20.1374	+	14.6307i	−1.03439	+	0.751527i	−0.969182	−	0.246345i	$-0.920770\pi$
$379$	−20.1374	+	14.6307i	−1.03439	+	0.751527i	−0.0652058	+	0.997872i	$0.520770\pi$
$380$	−42.6323	−	5.60287i	−2.18699	−	0.287421i
$381$	13.7498	+	9.98980i	0.704423	+	0.511793i
$382$	−22.0079			−1.12602
$383$	12.7195	+	9.24123i	0.649934	+	0.472205i	0.863249	−	0.504779i	$-0.168426\pi$
$383$	12.7195	+	9.24123i	0.649934	+	0.472205i	−0.213315	+	0.976984i	$0.568426\pi$
$384$	−2.56179	+	7.88439i	−0.130731	+	0.402349i
$385$	2.80934	+	15.1388i	0.143177	+	0.771545i
$386$	2.85100	+	8.77449i	0.145112	+	0.446610i
$387$	−0.386266	+	1.18880i	−0.0196350	+	0.0604303i
$388$	−5.80400	+	17.8629i	−0.294654	+	0.906851i
$389$	−2.62860	−	8.09000i	−0.133275	−	0.410179i	0.862042	−	0.506836i	$-0.169185\pi$
$389$	−2.62860	−	8.09000i	−0.133275	−	0.410179i	−0.995318	+	0.0966568i	$0.969185\pi$
$390$	4.99550	−	2.71379i	0.252957	−	0.137418i
$391$	0.804717	−	2.47667i	0.0406963	−	0.125250i
$392$	−10.3869	−	7.54649i	−0.524615	−	0.381155i
$393$	−0.328872			−0.0165894
$394$	−3.22779	−	2.34513i	−0.162614	−	0.118146i
$395$	28.5946	−	15.5340i	1.43875	−	0.781599i
$396$	3.20092	−	2.32561i	0.160852	−	0.116866i
$397$	−21.2407	+	15.4322i	−1.06604	+	0.774522i	−0.975196	−	0.221343i	$-0.928956\pi$
$397$	−21.2407	+	15.4322i	−1.06604	+	0.774522i	−0.0908420	+	0.995865i	$0.528956\pi$
$398$	2.79405	+	8.59921i	0.140053	+	0.431039i
$399$	33.4667			1.67543
$400$	−7.44843	+	11.4809i	−0.372422	+	0.574046i
$401$	−25.2815			−1.26250			−0.631250	−	0.775579i	$-0.717458\pi$
$401$	−25.2815			−1.26250			−0.631250	+	0.775579i	$0.717458\pi$
$402$	−2.53330	−	7.79670i	−0.126350	−	0.388864i
$403$	−4.65393	+	3.38128i	−0.231829	+	0.168434i
$404$	13.2060	−	9.59475i	0.657025	−	0.477356i
$405$	1.62233	+	1.53884i	0.0806144	+	0.0764657i
$406$	41.1908	+	29.9269i	2.04427	+	1.48525i
$407$	10.0677			0.499035
$408$	0.971811	+	0.706062i	0.0481118	+	0.0349553i
$409$	10.4427	−	32.1392i	0.516357	−	1.58918i	−0.264443	−	0.964401i	$-0.585188\pi$
$409$	10.4427	−	32.1392i	0.516357	−	1.58918i	0.780800	−	0.624781i	$-0.214812\pi$
$410$	35.1581	+	4.62058i	1.73633	+	0.228194i
$411$	1.40995	+	4.33939i	0.0695479	+	0.214046i
$412$	6.22870	−	19.1700i	0.306866	−	0.944437i
$413$	12.3317	−	37.9529i	0.606801	−	1.86754i
$414$	−1.52172	−	4.68338i	−0.0747885	−	0.230175i
$415$	−14.1728	−	13.4434i	−0.695713	−	0.659909i
$416$	−2.94281	+	9.05703i	−0.144283	+	0.444057i
$417$	3.82989	+	2.78258i	0.187550	+	0.136263i
$418$	−25.7473			−1.25934
$419$	−6.41819	−	4.66309i	−0.313549	−	0.227807i	0.419869	−	0.907585i	$-0.362076\pi$
$419$	−6.41819	−	4.66309i	−0.313549	−	0.227807i	−0.733418	+	0.679778i	$0.762076\pi$
$420$	−10.5021	+	22.0310i	−0.512452	+	1.07500i
$421$	−6.05788	+	4.40131i	−0.295243	+	0.214507i	−0.725539	−	0.688181i	$-0.758409\pi$
$421$	−6.05788	+	4.40131i	−0.295243	+	0.214507i	0.430296	+	0.902688i	$0.358409\pi$
$422$	15.9625	−	11.5974i	0.777042	−	0.564554i
$423$	1.27551	+	3.92563i	0.0620176	+	0.190870i
$424$	4.00897			0.194693
$425$	3.53350	+	4.35949i	0.171400	+	0.211466i
$426$	−22.5076			−1.09049
$427$	1.88000	+	5.78604i	0.0909795	+	0.280006i
$428$	−19.2015	+	13.9507i	−0.928140	+	0.674333i
$429$	1.53117	−	1.11246i	0.0739257	−	0.0537101i
$430$	1.08234	+	5.83244i	0.0521950	+	0.281265i
$431$	−18.8882	−	13.7231i	−0.909811	−	0.661016i	0.0311564	−	0.999515i	$-0.490081\pi$
$431$	−18.8882	−	13.7231i	−0.909811	−	0.661016i	−0.940967	+	0.338498i	$0.890081\pi$
$432$	−2.73708			−0.131688
$433$	2.71569	+	1.97306i	0.130508	+	0.0948193i	0.651124	−	0.758971i	$-0.274298\pi$
$433$	2.71569	+	1.97306i	0.130508	+	0.0948193i	−0.520616	+	0.853791i	$0.674298\pi$
$434$	13.7262	−	42.2449i	0.658879	−	2.02782i
$435$	5.29622	−	11.1102i	0.253934	−	0.532693i
$436$	−9.02778	−	27.7846i	−0.432352	−	1.33064i
$437$	−5.50564	+	16.9446i	−0.263370	+	0.810571i
$438$	3.27703	−	10.0857i	0.156583	−	0.481912i
$439$	−2.93072	−	9.01984i	−0.139876	−	0.430493i	0.856441	−	0.516245i	$-0.172671\pi$
$439$	−2.93072	−	9.01984i	−0.139876	−	0.430493i	−0.996317	+	0.0857520i	$0.972671\pi$
$440$	1.62704	−	3.41313i	0.0775659	−	0.162715i
$441$	3.70686	−	11.4086i	0.176517	−	0.543264i
$442$	2.30849	+	1.67722i	0.109804	+	0.0797771i
$443$	9.65446			0.458697			0.229349	−	0.973344i	$-0.426340\pi$
$443$	9.65446			0.458697			0.229349	+	0.973344i	$0.426340\pi$
$444$	12.9104	+	9.37999i	0.612703	+	0.445154i
$445$	4.09542	+	22.0692i	0.194142	+	1.04618i
$446$	5.83366	−	4.23840i	0.276232	−	0.200694i
$447$	−3.78332	+	2.74874i	−0.178945	+	0.130011i
$448$	−15.3504	−	47.2437i	−0.725238	−	2.23205i
$449$	31.5260			1.48780			0.743902	−	0.668289i	$-0.232973\pi$
$449$	31.5260			1.48780			0.743902	+	0.668289i	$0.232973\pi$
$450$	10.2513	+	2.74188i	0.483252	+	0.129253i
$451$	11.8053			0.555888
$452$	−11.5503	−	35.5482i	−0.543281	−	1.67205i
$453$	5.29241	−	3.84516i	0.248659	−	0.180661i
$454$	−46.0111	+	33.4290i	−2.15941	+	1.56890i
$455$	−5.02373	+	10.5386i	−0.235516	+	0.494056i
$456$	−6.64884	−	4.83067i	−0.311361	−	0.226217i
$457$	−9.94467			−0.465192			−0.232596	−	0.972573i	$-0.574722\pi$
$457$	−9.94467			−0.465192			−0.232596	+	0.972573i	$0.574722\pi$
$458$	2.02949	+	1.47451i	0.0948319	+	0.0688994i
$459$	−0.346820	+	1.06740i	−0.0161882	+	0.0498221i
$460$	−9.42683	−	8.94169i	−0.439528	−	0.416908i
$461$	−7.31863	−	22.5244i	−0.340863	−	1.04907i	−0.963762	−	0.266765i	$-0.914045\pi$
$461$	−7.31863	−	22.5244i	−0.340863	−	1.04907i	0.622899	−	0.782302i	$-0.285955\pi$
$462$	−4.51601	+	13.8988i	−0.210104	+	0.646632i
$463$	8.54443	−	26.2971i	0.397094	−	1.22213i	−0.530226	−	0.847857i	$-0.677893\pi$
$463$	8.54443	−	26.2971i	0.397094	−	1.22213i	0.927319	−	0.374272i	$-0.122107\pi$
$464$	4.65556	+	14.3284i	0.216129	+	0.665177i
$465$	−10.6462	−	1.39915i	−0.493705	−	0.0648842i
$466$	4.65306	−	14.3206i	0.215549	−	0.663391i
$467$	−3.52602	−	2.56180i	−0.163165	−	0.118546i	0.503207	−	0.864166i	$-0.332153\pi$
$467$	−3.52602	−	2.56180i	−0.163165	−	0.118546i	−0.666371	+	0.745620i	$0.732153\pi$
$468$	3.00000			0.138675
$469$	13.6200	+	9.89548i	0.628912	+	0.456931i
$470$	14.2120	+	13.4806i	0.655553	+	0.621815i
$471$	−3.23124	+	2.34764i	−0.148888	+	0.108173i
$472$	−7.92814	+	5.76013i	−0.364922	+	0.265132i
$473$	0.610263	+	1.87820i	0.0280599	+	0.0863596i
$474$	30.8864			1.41866
$475$	−24.1752	−	29.8264i	−1.10923	−	1.36853i
$476$	−12.2500			−0.561477
$477$	1.15748	+	3.56236i	0.0529973	+	0.163109i
$478$	−0.0734750	+	0.0533827i	−0.00336067	+	0.00244167i
$479$	−10.3670	+	7.53204i	−0.473679	+	0.344148i	−0.798873	−	0.601499i	$-0.794570\pi$
$479$	−10.3670	+	7.53204i	−0.473679	+	0.344148i	0.325195	+	0.945647i	$0.394570\pi$
$480$	−15.6198	+	8.48541i	−0.712942	+	0.387304i
$481$	6.17575	+	4.48695i	0.281590	+	0.204587i
$482$	−24.9822			−1.13791
$483$	8.18133	+	5.94409i	0.372263	+	0.270465i
$484$	−6.58092	+	20.2540i	−0.299133	+	0.920636i
$485$	−14.7363	+	8.00548i	−0.669142	+	0.363510i
$486$	0.655837	+	2.01846i	0.0297494	+	0.0915592i
$487$	−2.13904	+	6.58330i	−0.0969293	+	0.298318i	−0.987752	−	0.156034i	$-0.950129\pi$
$487$	−2.13904	+	6.58330i	−0.0969293	+	0.298318i	0.890822	+	0.454352i	$0.150129\pi$
$488$	0.461671	−	1.42088i	0.0208989	−	0.0643201i
$489$	1.48372	+	4.56641i	0.0670960	+	0.206500i
$490$	−10.3869	−	55.9720i	−0.469230	−	2.52856i
$491$	8.28665	−	25.5037i	0.373971	−	1.15096i	−0.570199	−	0.821507i	$-0.693134\pi$
$491$	8.28665	−	25.5037i	0.373971	−	1.15096i	0.944170	−	0.329458i	$-0.106866\pi$
$492$	15.1387	+	10.9989i	0.682505	+	0.495869i
$493$	6.17766			0.278228
$494$	−15.7940	−	11.4750i	−0.710606	−	0.516286i
$495$	3.50266	+	0.460330i	0.157433	+	0.0206903i
$496$	10.6334	−	7.72564i	0.477455	−	0.346891i
$497$	37.3938	−	27.1682i	1.67734	−	1.21866i
$498$	−5.72941	−	17.6333i	−0.256741	−	0.790168i
$499$	2.75460			0.123313			0.0616565	−	0.998097i	$-0.480362\pi$
$499$	2.75460			0.123313			0.0616565	+	0.998097i	$0.480362\pi$
$500$	27.2209	−	6.55464i	1.21735	−	0.293132i
$501$	23.6600			1.05705
$502$	11.4617	+	35.2754i	0.511559	+	1.57442i
$503$	−12.7098	+	9.23422i	−0.566702	+	0.411733i	−0.833906	−	0.551907i	$-0.813900\pi$
$503$	−12.7098	+	9.23422i	−0.566702	+	0.411733i	0.267203	+	0.963640i	$0.413900\pi$
$504$	−3.77387	+	2.74188i	−0.168102	+	0.122133i
$505$	14.4509	+	1.89918i	0.643057	+	0.0845125i
$506$	−6.29422	−	4.57302i	−0.279812	−	0.203295i
$507$	−11.5649			−0.513617
$508$	34.4336	+	25.0175i	1.52774	+	1.10997i
$509$	−12.6970	+	39.0774i	−0.562785	+	1.73207i	0.111657	+	0.993747i	$0.464384\pi$
$509$	−12.6970	+	39.0774i	−0.562785	+	1.73207i	−0.674442	+	0.738328i	$0.735616\pi$
$510$	0.971811	+	5.23683i	0.0430325	+	0.231891i
$511$	6.72968	+	20.7118i	0.297703	+	0.916237i
$512$	8.53432	−	26.2659i	0.377167	−	1.16080i
$513$	2.37284	−	7.30285i	0.104763	−	0.322429i
$514$	10.1439	+	31.2198i	0.447430	+	1.37705i
$515$	15.8146	−	8.59126i	0.696876	−	0.378576i
$516$	−0.967325	+	2.97712i	−0.0425841	+	0.131060i
$517$	5.27584	+	3.83312i	0.232031	+	0.168580i
$518$	−58.9438			−2.58984
$519$	−11.7342	−	8.52541i	−0.515075	−	0.374224i
$520$	2.51923	−	1.36856i	0.110475	−	0.0600155i
$521$	−29.2630	+	21.2608i	−1.28203	+	0.931452i	−0.999612	−	0.0278383i	$-0.991138\pi$
$521$	−29.2630	+	21.2608i	−1.28203	+	0.931452i	−0.282421	+	0.959290i	$0.591138\pi$
$522$	9.45090	−	6.86648i	0.413655	−	0.300538i
$523$	8.66761	+	26.6761i	0.379008	+	1.16647i	0.940735	+	0.339144i	$0.110137\pi$
$523$	8.66761	+	26.6761i	0.379008	+	1.16647i	−0.561727	+	0.827323i	$0.689863\pi$
$524$	−0.823595			−0.0359789
$525$	−20.3411	+	7.81873i	−0.887757	+	0.341237i
$526$	3.07228			0.133958
$527$	−1.66545	−	5.12573i	−0.0725482	−	0.223280i
$528$	−3.49846	+	2.54178i	−0.152251	+	0.110617i
$529$	14.2519	−	10.3546i	0.619648	−	0.450201i
$530$	12.8969	+	12.2332i	0.560205	+	0.531374i
$531$	−7.40746	−	5.38184i	−0.321456	−	0.233552i
$532$	83.8108			3.63366
$533$	7.24165	+	5.26137i	0.313671	+	0.227895i
$534$	−6.58338	+	20.2616i	−0.284891	+	0.876803i
$535$	−21.0115	−	2.76140i	−0.908408	−	0.119386i
$536$	−1.27754	−	3.93187i	−0.0551815	−	0.169831i
$537$	0.246208	−	0.757750i	0.0106247	−	0.0326993i
$538$	−5.70983	+	17.5731i	−0.246168	+	0.757628i
$539$	−5.85650	−	18.0244i	−0.252257	−	0.776368i
$540$	4.06281	+	3.85372i	0.174835	+	0.165838i
$541$	1.06865	−	3.28896i	0.0459448	−	0.141404i	−0.925452	−	0.378864i	$-0.876315\pi$
$541$	1.06865	−	3.28896i	0.0459448	−	0.141404i	0.971397	+	0.237460i	$0.0763149\pi$
$542$	49.1643	+	35.7200i	2.11179	+	1.53430i
$543$	−14.2185			−0.610173
$544$	−7.21812	−	5.24427i	−0.309474	−	0.224846i
$545$	11.2247	−	23.5468i	0.480815	−	1.00863i
$546$	−8.96465	+	6.51320i	−0.383652	+	0.278739i
$547$	−11.2967	+	8.20751i	−0.483011	+	0.350928i	−0.802490	−	0.596665i	$-0.796492\pi$
$547$	−11.2967	+	8.20751i	−0.483011	+	0.350928i	0.319479	+	0.947593i	$0.396492\pi$
$548$	3.53095	+	10.8671i	0.150835	+	0.464221i
$549$	1.39588			0.0595747
$550$	15.6492	−	6.01525i	0.667283	−	0.256491i
$551$	−42.2657			−1.80058
$552$	−0.767403	−	2.36182i	−0.0326629	−	0.100526i
$553$	−51.3144	+	37.2821i	−2.18211	+	1.58540i
$554$	−9.10372	+	6.61424i	−0.386780	+	0.281012i
$555$	2.59982	+	14.0097i	0.110356	+	0.594681i
$556$	9.59118	+	6.96840i	0.406757	+	0.295526i
$557$	−6.59585			−0.279475			−0.139738	−	0.990189i	$-0.544626\pi$
$557$	−6.59585			−0.279475			−0.139738	+	0.990189i	$0.544626\pi$
$558$	−8.24516	−	5.99046i	−0.349045	−	0.253596i
$559$	−0.462723	+	1.42411i	−0.0195711	+	0.0602336i
$560$	11.4783	−	24.0788i	0.485048	−	1.01752i
$561$	0.547943	+	1.68640i	0.0231342	+	0.0711997i
$562$	−15.7947	+	48.6110i	−0.666257	+	2.05053i
$563$	−4.95100	+	15.2376i	−0.208660	+	0.642189i	0.790883	+	0.611967i	$0.209621\pi$
$563$	−4.95100	+	15.2376i	−0.208660	+	0.642189i	−0.999543	+	0.0302222i	$0.990379\pi$
$564$	3.19427	+	9.83094i	0.134503	+	0.413957i
$565$	14.3611	−	30.1263i	0.604178	−	1.26742i
$566$	−17.7826	+	54.7291i	−0.747457	+	2.30044i
$567$	−3.52602	−	2.56180i	−0.148079	−	0.107586i
$568$	−11.3505			−0.476258
$569$	−18.6813	−	13.5728i	−0.783162	−	0.569001i	0.122764	−	0.992436i	$-0.460824\pi$
$569$	−18.6813	−	13.5728i	−0.783162	−	0.569001i	−0.905926	+	0.423435i	$0.860824\pi$
$570$	−6.64884	−	35.8288i	−0.278489	−	1.50071i
$571$	27.5148	−	19.9907i	1.15146	−	0.836583i	0.162784	−	0.986662i	$-0.447953\pi$
$571$	27.5148	−	19.9907i	1.15146	−	0.836583i	0.988674	+	0.150078i	$0.0479526\pi$
$572$	3.83451	−	2.78594i	0.160329	−	0.116486i
$573$	−3.20441	−	9.86215i	−0.133866	−	0.411997i
$574$	−69.1171			−2.88489
$575$	−0.612394	−	11.5852i	−0.0255386	−	0.483136i
$576$	−11.3975			−0.474896
$577$	−1.99850	−	6.15074i	−0.0831985	−	0.256059i	0.900800	−	0.434233i	$-0.142981\pi$
$577$	−1.99850	−	6.15074i	−0.0831985	−	0.256059i	−0.983999	+	0.178175i	$0.942981\pi$
$578$	27.0263	−	19.6357i	1.12414	−	0.816739i
$579$	−3.51690	+	2.55517i	−0.146157	+	0.106189i
$580$	13.2633	−	27.8233i	0.550729	−	1.15530i
$581$	30.8034	+	22.3800i	1.27794	+	0.928479i
$582$	−15.9174			−0.659798
$583$	4.78762	+	3.47841i	0.198283	+	0.144061i
$584$	1.65261	−	5.08620i	0.0683853	−	0.210468i
$585$	1.94346	+	1.84344i	0.0803521	+	0.0762169i
$586$	−13.3146	−	40.9780i	−0.550019	−	1.69279i
$587$	11.8975	−	36.6168i	0.491063	−	1.51134i	−0.331940	−	0.943301i	$-0.607703\pi$
$587$	11.8975	−	36.6168i	0.491063	−	1.51134i	0.823003	−	0.568037i	$-0.192297\pi$
$588$	9.28310	−	28.5704i	0.382828	−	1.17822i
$589$	11.3945	+	35.0687i	0.469503	+	1.44498i
$590$	−43.0816	−	5.66192i	−1.77364	−	0.233097i
$591$	0.580921	−	1.78789i	0.0238959	−	0.0735440i
$592$	−14.1105	−	10.2519i	−0.579939	−	0.421350i
$593$	4.93069			0.202479			0.101240	−	0.994862i	$-0.467719\pi$
$593$	4.93069			0.202479			0.101240	+	0.994862i	$0.467719\pi$
$594$	2.71270	+	1.97090i	0.111304	+	0.0808668i
$595$	−7.93577	−	7.52737i	−0.325335	−	0.308592i
$596$	−9.47457	+	6.88368i	−0.388093	+	0.281966i
$597$	−3.44664	+	2.50413i	−0.141062	+	0.102487i
$598$	−1.82293	−	5.61040i	−0.0745452	−	0.229426i
$599$	−35.0268			−1.43116			−0.715578	−	0.698533i	$-0.753836\pi$
$599$	−35.0268			−1.43116			−0.715578	+	0.698533i	$0.753836\pi$
$600$	5.16974	+	1.38273i	0.211054	+	0.0564496i
$601$	−4.90570			−0.200108			−0.100054	−	0.994982i	$-0.531901\pi$
$601$	−4.90570			−0.200108			−0.100054	+	0.994982i	$0.531901\pi$
$602$	−3.57295	−	10.9964i	−0.145623	−	0.448180i
$603$	3.12499	−	2.27044i	0.127259	−	0.0924594i
$604$	13.2538	−	9.62943i	0.539289	−	0.391816i
$605$	−16.7089	+	9.07708i	−0.679314	+	0.369036i
$606$	11.1918	+	8.13132i	0.454636	+	0.330312i
$607$	48.6955			1.97649			0.988244	−	0.152884i	$-0.0488562\pi$
$607$	48.6955			1.97649			0.988244	+	0.152884i	$0.0488562\pi$
$608$	49.3842	+	35.8798i	2.00280	+	1.45512i
$609$	−7.41330	+	22.8158i	−0.300402	+	0.924543i
$610$	5.82092	−	3.16220i	0.235682	−	0.128034i
$611$	1.52799	+	4.70266i	0.0618158	+	0.190249i
$612$	−0.868541	+	2.67310i	−0.0351087	+	0.108053i
$613$	5.31938	−	16.3714i	0.214848	−	0.661234i	−0.784317	−	0.620361i	$-0.786986\pi$
$613$	5.31938	−	16.3714i	0.214848	−	0.661234i	0.999164	−	0.0408728i	$-0.0130138\pi$
$614$	−1.64832	−	5.07299i	−0.0665206	−	0.204729i
$615$	3.04853	+	16.4277i	0.122929	+	0.662430i
$616$	−2.27742	+	7.00918i	−0.0917598	+	0.282408i
$617$	25.5723	+	18.5794i	1.02950	+	0.747978i	0.968209	−	0.250141i	$-0.0804771\pi$
$617$	25.5723	+	18.5794i	1.02950	+	0.747978i	0.0612947	+	0.998120i	$0.480477\pi$
$618$	17.0821			0.687145
$619$	18.4615	+	13.4130i	0.742029	+	0.539116i	0.893346	−	0.449370i	$-0.148351\pi$
$619$	18.4615	+	13.4130i	0.742029	+	0.539116i	−0.151317	+	0.988485i	$0.548351\pi$
$620$	−26.6612	−	3.50390i	−1.07074	−	0.140720i
$621$	1.87714	−	1.36382i	0.0753271	−	0.0547283i
$622$	−8.28312	+	6.01804i	−0.332123	+	0.241301i
$623$	−13.5196	−	41.6089i	−0.541649	−	1.66703i
$624$	−3.27886			−0.131259
$625$	21.6619	+	12.4805i	0.866476	+	0.499219i
$626$	−12.7088			−0.507945
$627$	−3.74887	−	11.5378i	−0.149715	−	0.460776i
$628$	−8.09200	+	5.87918i	−0.322906	+	0.234605i
$629$	−5.78598	+	4.20376i	−0.230702	+	0.167615i
$630$	−20.5072	−	2.69512i	−0.817028	−	0.107376i
$631$	−30.7830	−	22.3652i	−1.22545	−	0.890344i	−0.228913	−	0.973447i	$-0.573517\pi$
$631$	−30.7830	−	22.3652i	−1.22545	−	0.890344i	−0.996541	+	0.0831027i	$0.973517\pi$
$632$	15.5760			0.619581
$633$	7.52120	+	5.46447i	0.298941	+	0.217193i
$634$	11.3808	−	35.0265i	0.451989	−	1.39108i
$635$	6.93401	+	37.3655i	0.275168	+	1.48281i
$636$	2.89868	+	8.92120i	0.114940	+	0.353749i
$637$	4.44060	−	13.6668i	0.175943	−	0.541497i
$638$	5.70334	−	17.5531i	0.225797	−	0.694933i
$639$	−3.27716	−	10.0860i	−0.129642	−	0.398998i
$640$	−16.2889	+	8.84892i	−0.643876	+	0.349784i
$641$	8.19229	−	25.2133i	0.323576	−	0.995864i	−0.648504	−	0.761212i	$-0.724605\pi$
$641$	8.19229	−	25.2133i	0.323576	−	0.995864i	0.972079	−	0.234652i	$-0.0753952\pi$
$642$	−16.2728	−	11.8229i	−0.642237	−	0.466612i
$643$	−36.0014			−1.41976			−0.709879	−	0.704324i	$-0.751250\pi$
$643$	−36.0014			−1.41976			−0.709879	+	0.704324i	$0.751250\pi$
$644$	20.4885	+	14.8858i	0.807360	+	0.586582i
$645$	−2.45603	+	1.33423i	−0.0967061	+	0.0525354i
$646$	14.7972	−	10.7508i	0.582188	−	0.422984i
$647$	−33.8040	+	24.5600i	−1.32897	+	0.965554i	−0.329197	+	0.944261i	$0.606778\pi$
$647$	−33.8040	+	24.5600i	−1.32897	+	0.965554i	−0.999773	+	0.0212924i	$0.993222\pi$
$648$	0.330738	+	1.01791i	0.0129926	+	0.0399872i
$649$	−14.4658			−0.567833
$650$	12.2805	+	3.28460i	0.481679	+	0.128833i
$651$	20.9293			0.820284
$652$	3.71567	+	11.4357i	0.145517	+	0.447855i
$653$	−17.3456	+	12.6023i	−0.678787	+	0.493168i	−0.872955	−	0.487801i	$-0.837799\pi$
$653$	−17.3456	+	12.6023i	−0.678787	+	0.493168i	0.194168	+	0.980968i	$0.437799\pi$
$654$	20.0301	−	14.5527i	0.783240	−	0.569057i
$655$	−0.533541	−	0.506082i	−0.0208472	−	0.0197743i
$656$	−16.5459	−	12.0213i	−0.646009	−	0.469353i
$657$	4.99672			0.194940
$658$	−30.8888	−	22.4420i	−1.20417	−	0.874882i
$659$	−5.20135	+	16.0081i	−0.202616	+	0.623587i	0.797187	+	0.603732i	$0.206320\pi$
$659$	−5.20135	+	16.0081i	−0.202616	+	0.623587i	−0.999803	+	0.0198549i	$0.993680\pi$
$660$	8.77170	+	1.15280i	0.341438	+	0.0448728i
$661$	0.629918	+	1.93869i	0.0245010	+	0.0754062i	0.962559	−	0.271071i	$-0.0873778\pi$
$661$	0.629918	+	1.93869i	0.0245010	+	0.0754062i	−0.938058	+	0.346477i	$0.887378\pi$
$662$	13.3368	−	41.0463i	0.518348	−	1.59531i
$663$	−0.415470	+	1.27868i	−0.0161355	+	0.0496600i
$664$	−2.88934	−	8.89248i	−0.112128	−	0.345095i
$665$	54.2942	+	51.5000i	2.10544	+	1.99709i
$666$	−4.17920	+	12.8623i	−0.161941	+	0.498402i
$667$	−10.3323	−	7.50689i	−0.400070	−	0.290668i
$668$	59.2518			2.29252
$669$	2.74870	+	1.99705i	0.106271	+	0.0772104i
$670$	7.88803	−	16.5472i	0.304741	−	0.639274i
$671$	1.78417	−	1.29628i	0.0688772	−	0.0500422i
$672$	28.0304	−	20.3653i	1.08130	−	0.785608i
$673$	10.9323	+	33.6461i	0.421409	+	1.29696i	0.906391	+	0.422439i	$0.138826\pi$
$673$	10.9323	+	33.6461i	0.421409	+	1.29696i	−0.484983	+	0.874524i	$0.661174\pi$
$674$	72.7050			2.80049
$675$	0.263932	+	4.99303i	0.0101587	+	0.192182i
$676$	−28.9621			−1.11393
$677$	13.7257	+	42.2434i	0.527522	+	1.62354i	0.759275	+	0.650770i	$0.225554\pi$
$677$	13.7257	+	42.2434i	0.527522	+	1.62354i	−0.231753	+	0.972775i	$0.574446\pi$
$678$	25.6269	−	18.6190i	0.984196	−	0.715060i
$679$	26.4450	−	19.2134i	1.01487	−	0.737344i
$680$	0.490084	+	2.64093i	0.0187939	+	0.101275i
$681$	−21.6795	−	15.7511i	−0.830760	−	0.603582i
$682$	−16.1017			−0.616567
$683$	−34.3793	−	24.9780i	−1.31549	−	0.955758i	−0.999977	−	0.00683639i	$-0.997824\pi$
$683$	−34.3793	−	24.9780i	−1.31549	−	0.955758i	−0.315512	−	0.948922i	$-0.602176\pi$
$684$	5.94230	−	18.2885i	0.227210	−	0.699280i
$685$	−4.39022	+	9.20964i	−0.167742	+	0.351882i
$686$	14.2796	+	43.9481i	0.545198	+	1.67795i
$687$	−0.365257	+	1.12415i	−0.0139354	+	0.0428888i
$688$	1.05724	−	3.25385i	0.0403069	−	0.124052i
$689$	1.38659	+	4.26749i	0.0528249	+	0.162578i
$690$	4.73824	−	9.93969i	0.180382	−	0.378397i
$691$	8.67746	−	26.7065i	0.330106	−	1.01596i	−0.638977	−	0.769226i	$-0.720642\pi$
$691$	8.67746	−	26.7065i	0.330106	−	1.01596i	0.969083	−	0.246736i	$-0.0793580\pi$
$692$	−29.3860	−	21.3502i	−1.11709	−	0.811612i
$693$	−6.88586			−0.261572
$694$	0.0847541	+	0.0615775i	0.00321722	+	0.00233745i
$695$	1.93141	+	10.4079i	0.0732626	+	0.394793i
$696$	4.76609	−	3.46276i	0.180658	−	0.131256i
$697$	−6.78460	+	4.92930i	−0.256985	+	0.186711i
$698$	−4.90197	−	15.0867i	−0.185542	−	0.571040i
$699$	7.09483			0.268351
$700$	−50.9401	+	19.5804i	−1.92536	+	0.740071i
$701$	46.4314			1.75369			0.876845	−	0.480772i	$-0.159644\pi$
$701$	46.4314			1.75369			0.876845	+	0.480772i	$0.159644\pi$
$702$	0.785653	+	2.41799i	0.0296526	+	0.0912612i
$703$	39.5860	−	28.7609i	1.49301	−	1.08474i
$704$	−14.5680	+	10.5842i	−0.549051	+	0.398909i
$705$	−3.97161	+	8.33149i	−0.149579	+	0.313782i
$706$	31.8762	+	23.1594i	1.19967	+	0.871615i
$707$	−28.4090			−1.06843
$708$	−18.5505	−	13.4777i	−0.697171	−	0.506524i
$709$	15.0285	−	46.2529i	0.564406	−	1.73706i	−0.105305	−	0.994440i	$-0.533582\pi$
$709$	15.0285	−	46.2529i	0.564406	−	1.73706i	0.669710	−	0.742622i	$-0.266418\pi$
$710$	−36.5148	−	34.6356i	−1.37037	−	1.29985i
$711$	4.49714	+	13.8408i	0.168656	+	0.519070i
$712$	−3.31999	+	10.2179i	−0.124422	+	0.382932i
$713$	−3.44310	+	10.5968i	−0.128945	+	0.396852i
$714$	−3.20808	−	9.87345i	−0.120059	−	0.369505i
$715$	4.19597	+	0.551448i	0.156920	+	0.0206230i
$716$	0.616579	−	1.89763i	0.0230426	−	0.0709179i
$717$	−0.0346199	−	0.0251528i	−0.00129290	−	0.000939350i
$718$	22.5062			0.839923
$719$	17.1475	+	12.4584i	0.639493	+	0.464619i	0.859676	−	0.510840i	$-0.170666\pi$
$719$	17.1475	+	12.4584i	0.639493	+	0.464619i	−0.220183	+	0.975459i	$0.570666\pi$
$720$	−4.44046	−	4.21194i	−0.165486	−	0.156970i
$721$	−28.3801	+	20.6193i	−1.05693	+	0.767904i
$722$	−68.6150	+	49.8517i	−2.55359	+	1.85529i
$723$	−3.63746	−	11.1950i	−0.135279	−	0.416345i
$724$	−35.6073			−1.32333
$725$	25.6891	−	9.87441i	0.954068	−	0.366726i
$726$	−18.0481			−0.669828
$727$	4.19988	+	12.9259i	0.155765	+	0.479396i	0.998238	−	0.0593437i	$-0.0189008\pi$
$727$	4.19988	+	12.9259i	0.155765	+	0.479396i	−0.842473	+	0.538739i	$0.818901\pi$
$728$	−4.52087	+	3.28460i	−0.167555	+	0.121736i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	20.8367	−	11.3195i	0.771200	−	0.418953i
$731$	−1.13497	−	0.824602i	−0.0419783	−	0.0304990i
$732$	3.49570			0.129205
$733$	−15.0907	−	10.9640i	−0.557386	−	0.404965i	0.273115	−	0.961981i	$-0.411946\pi$
$733$	−15.0907	−	10.9640i	−0.557386	−	0.404965i	−0.830501	+	0.557017i	$0.811946\pi$
$734$	−7.61927	+	23.4497i	−0.281233	+	0.865545i
$735$	23.5697	−	12.8042i	0.869383	−	0.472290i
$736$	5.69988	+	17.5424i	0.210101	+	0.646623i
$737$	1.88584	−	5.80402i	0.0694658	−	0.213794i
$738$	−4.90050	+	15.0822i	−0.180390	+	0.555183i
$739$	8.17202	+	25.1509i	0.300613	+	0.925191i	0.981278	+	0.192596i	$0.0616907\pi$
$739$	8.17202	+	25.1509i	0.300613	+	0.925191i	−0.680665	+	0.732594i	$0.738309\pi$
$740$	6.51073	+	35.0846i	0.239339	+	1.28974i
$741$	2.84252	−	8.74838i	0.104423	−	0.321380i
$742$	−28.0304	−	20.3653i	−1.02903	−	0.747633i
$743$	−29.0191			−1.06461			−0.532304	−	0.846553i	$-0.678674\pi$
$743$	−29.0191			−1.06461			−0.532304	+	0.846553i	$0.678674\pi$
$744$	−4.15803	−	3.02098i	−0.152441	−	0.110755i
$745$	−10.3677	−	1.36255i	−0.379843	−	0.0499201i
$746$	39.7096	−	28.8507i	1.45387	−	1.05630i
$747$	7.06760	−	5.13491i	0.258590	−	0.187877i
$748$	1.37221	+	4.22324i	0.0501731	+	0.154417i
$749$	41.3065			1.50931
$750$	12.4117	+	20.2234i	0.453213	+	0.738454i
$751$	15.9489			0.581985			0.290992	−	0.956725i	$-0.406015\pi$
$751$	15.9489			0.581985			0.290992	+	0.956725i	$0.406015\pi$
$752$	−3.49119	−	10.7448i	−0.127310	−	0.391821i
$753$	−14.1387	+	10.2724i	−0.515243	+	0.374346i
$754$	11.3216	−	8.22563i	0.412309	−	0.299560i
$755$	14.5031	+	1.90605i	0.527824	+	0.0693682i
$756$	−8.83021	−	6.41552i	−0.321152	−	0.233330i
$757$	−16.4183			−0.596734			−0.298367	−	0.954451i	$-0.596442\pi$
$757$	−16.4183			−0.596734			−0.298367	+	0.954451i	$0.596442\pi$
$758$	−42.7382	−	31.0512i	−1.55232	−	1.12783i
$759$	1.13280	−	3.48640i	0.0411180	−	0.126548i
$760$	−3.35301	−	18.0685i	−0.121626	−	0.655412i
$761$	−15.2257	−	46.8600i	−0.551932	−	1.69867i	−0.703910	−	0.710289i	$-0.748564\pi$
$761$	−15.2257	−	46.8600i	−0.551932	−	1.69867i	0.151978	−	0.988384i	$-0.451436\pi$
$762$	−11.1464	+	34.3051i	−0.403791	+	1.24274i
$763$	−15.7117	+	48.3555i	−0.568800	+	1.75059i
$764$	−8.02480	−	24.6978i	−0.290327	−	0.893534i
$765$	−2.20522	+	1.19798i	−0.0797300	+	0.0433131i
$766$	−10.3111	+	31.7345i	−0.372557	+	1.14661i
$767$	−8.87369	−	6.44711i	−0.320410	−	0.232792i
$768$	5.20057			0.187660
$769$	−39.9845	−	29.0504i	−1.44188	−	1.04759i	−0.987646	−	0.156702i	$-0.949914\pi$
$769$	−39.9845	−	29.0504i	−1.44188	−	1.04759i	−0.454232	−	0.890884i	$-0.650086\pi$
$770$	−28.7146	+	15.5991i	−1.03480	+	0.562154i
$771$	−12.5132	+	9.09136i	−0.450651	+	0.327417i
$772$	−8.80736	+	6.39892i	−0.316984	+	0.230302i
$773$	8.00613	+	24.6403i	0.287960	+	0.886251i	0.985496	+	0.169701i	$0.0542801\pi$
$773$	8.00613	+	24.6403i	0.287960	+	0.886251i	−0.697535	+	0.716550i	$0.745720\pi$
$774$	−2.65288			−0.0953557
$775$	−15.1186	−	18.6527i	−0.543076	−	0.670024i
$776$	−8.02715			−0.288158
$777$	−8.58236	−	26.4138i	−0.307891	−	0.947590i
$778$	14.6054	−	10.6114i	0.523629	−	0.380439i
$779$	46.4182	−	33.7248i	1.66311	−	1.20832i
$780$	4.86700	+	4.61653i	0.174267	+	0.165298i
$781$	−13.5551	−	9.84838i	−0.485041	−	0.352403i
$782$	5.52681			0.197638
$783$	4.45307	+	3.23535i	0.159140	+	0.115622i
$784$	−10.1460	+	31.2262i	−0.362357	+	1.11522i
$785$	−8.85479	−	1.16372i	−0.316041	−	0.0415351i
$786$	−0.215687	−	0.663815i	−0.00769329	−	0.0236775i
$787$	9.49160	−	29.2122i	0.338339	−	1.04130i	−0.626715	−	0.779249i	$-0.715601\pi$
$787$	9.49160	−	29.2122i	0.338339	−	1.04130i	0.965054	−	0.262052i	$-0.0843992\pi$
$788$	1.45480	−	4.47741i	0.0518251	−	0.159501i
$789$	0.447331	+	1.37674i	0.0159254	+	0.0490134i
$790$	50.1081	+	47.5293i	1.78277	+	1.69102i
$791$	−20.1018	+	61.8670i	−0.714737	+	2.19974i
$792$	1.36802	+	0.993921i	0.0486103	+	0.0353175i
$793$	1.67218			0.0593808
$794$	−45.0798	−	32.7524i	−1.59982	−	1.16234i
$795$	−3.60408	+	7.56051i	−0.127824	+	0.268144i
$796$	−8.63142	+	6.27109i	−0.305933	+	0.222273i
$797$	27.2753	−	19.8166i	0.966140	−	0.701942i	0.0115713	−	0.999933i	$-0.496317\pi$
$797$	27.2753	−	19.8166i	0.966140	−	0.701942i	0.954569	+	0.297991i	$0.0963167\pi$
$798$	21.9487	+	67.5513i	0.776977	+	2.39129i
$799$	−4.63260			−0.163890
$800$	−38.3982	−	10.2702i	−1.35758	−	0.363106i
$801$	−10.0381			−0.354680
$802$	−16.5806	−	51.0298i	−0.585480	−	1.80192i
$803$	6.38665	−	4.64018i	0.225380	−	0.163748i
$804$	7.82591	−	5.68586i	0.275999	−	0.200525i
$805$	4.12584	+	22.2331i	0.145417	+	0.783613i
$806$	−9.87720	−	7.17621i	−0.347910	−	0.252771i
$807$	−8.70617			−0.306472
$808$	5.64402	+	4.10062i	0.198556	+	0.144259i
$809$	−0.285227	+	0.877838i	−0.0100280	+	0.0308632i	−0.955945	−	0.293545i	$-0.905165\pi$
$809$	−0.285227	+	0.877838i	−0.0100280	+	0.0308632i	0.945917	+	0.324408i	$0.105165\pi$
$810$	−2.04210	+	4.28384i	−0.0717522	+	0.150519i
$811$	8.27593	+	25.4707i	0.290607	+	0.894397i	0.984662	+	0.174474i	$0.0558226\pi$
$811$	8.27593	+	25.4707i	0.290607	+	0.894397i	−0.694055	+	0.719922i	$0.744177\pi$
$812$	−18.5651	+	57.1376i	−0.651508	+	2.00514i
$813$	−8.84832	+	27.2323i	−0.310324	+	0.955080i
$814$	6.60274	+	20.3212i	0.231426	+	0.712256i
$815$	−4.61990	+	9.69145i	−0.161828	+	0.339477i
$816$	0.949275	−	2.92157i	0.0332313	−	0.102275i
$817$	7.76511	+	5.64168i	0.271667	+	0.197377i
$818$	71.7204			2.50765
$819$	−4.22396	−	3.06889i	−0.147597	−	0.107236i
$820$	7.63444	+	41.1400i	0.266606	+	1.43667i
$821$	29.8114	−	21.6592i	1.04042	−	0.755912i	0.0700559	−	0.997543i	$-0.477682\pi$
$821$	29.8114	−	21.6592i	1.04042	−	0.755912i	0.970368	+	0.241631i	$0.0776822\pi$
$822$	−7.83419	+	5.69187i	−0.273249	+	0.198527i
$823$	6.31204	+	19.4265i	0.220024	+	0.677164i	0.998759	+	0.0498106i	$0.0158618\pi$
$823$	6.31204	+	19.4265i	0.220024	+	0.677164i	−0.778735	+	0.627353i	$0.784138\pi$
$824$	8.61452			0.300101
$825$	4.97410	+	6.13684i	0.173176	+	0.213657i
$826$	84.6940			2.94688
$827$	1.33810	+	4.11824i	0.0465302	+	0.143205i	0.971622	−	0.236537i	$-0.0760126\pi$
$827$	1.33810	+	4.11824i	0.0465302	+	0.143205i	−0.925092	+	0.379743i	$0.876013\pi$
$828$	4.70092	−	3.41542i	0.163368	−	0.118694i
$829$	0.497018	−	0.361104i	0.0172621	−	0.0125417i	−0.579121	−	0.815242i	$-0.696604\pi$
$829$	0.497018	−	0.361104i	0.0172621	−	0.0125417i	0.596383	+	0.802700i	$0.296604\pi$
$830$	17.8399	−	37.4238i	0.619231	−	1.29900i
$831$	−4.28949	−	3.11649i	−0.148801	−	0.108110i
$832$	−13.6535			−0.473351
$833$	10.8919	+	7.91343i	0.377382	+	0.274184i
$834$	−3.10473	+	9.55539i	−0.107508	+	0.330876i
$835$	38.3844	+	36.4090i	1.32835	+	1.25999i
$836$	−9.38828	−	28.8942i	−0.324701	−	0.999325i
$837$	1.48392	−	4.56703i	0.0512917	−	0.157860i
$838$	5.20297	−	16.0131i	0.179733	−	0.553163i
$839$	1.66863	+	5.13553i	0.0576077	+	0.177298i	0.975720	−	0.219023i	$-0.0702868\pi$
$839$	1.66863	+	5.13553i	0.0576077	+	0.177298i	−0.918112	+	0.396321i	$0.870287\pi$
$840$	−10.3418	−	1.35915i	−0.356826	−	0.0468951i
$841$	0.400892	−	1.23382i	0.0138239	−	0.0425455i
$842$	−12.8568	−	9.34105i	−0.443076	−	0.321914i
$843$	−24.0832			−0.829469
$844$	18.8353	+	13.6847i	0.648339	+	0.471046i
$845$	−18.7622	−	17.7966i	−0.645439	−	0.612222i
$846$	−7.08719	+	5.14914i	−0.243663	+	0.177031i
$847$	29.9849	−	21.7853i	1.03029	−	0.748552i
$848$	−3.16812	−	9.75046i	−0.108794	−	0.334832i
$849$	−27.1143			−0.930561
$850$	−6.48205	+	9.99135i	−0.222333	+	0.342700i
$851$	14.7855			0.506841
$852$	−8.20698	−	25.2585i	−0.281166	−	0.865341i
$853$	32.1936	−	23.3900i	1.10229	−	0.800860i	0.120857	−	0.992670i	$-0.461436\pi$
$853$	32.1936	−	23.3900i	1.10229	−	0.800860i	0.981432	+	0.191810i	$0.0614358\pi$
$854$	−10.4459	+	7.58940i	−0.357452	+	0.259704i
$855$	15.0875	−	8.19624i	0.515981	−	0.280305i
$856$	−8.20637	−	5.96228i	−0.280488	−	0.203787i
$857$	−42.8643			−1.46422			−0.732109	−	0.681188i	$-0.761464\pi$
$857$	−42.8643			−1.46422			−0.732109	+	0.681188i	$0.761464\pi$
$858$	3.24966	+	2.36101i	0.110941	+	0.0806037i
$859$	−1.41064	+	4.34152i	−0.0481306	+	0.148131i	−0.972233	−	0.234013i	$-0.924814\pi$
$859$	−1.41064	+	4.34152i	−0.0481306	+	0.148131i	0.924103	+	0.382144i	$0.124814\pi$
$860$	−6.15064	+	3.34132i	−0.209735	+	0.113938i
$861$	−10.0636	−	30.9726i	−0.342967	−	1.05554i
$862$	15.3119	−	47.1251i	0.521524	−	1.60509i
$863$	−11.6275	+	35.7857i	−0.395804	+	1.21816i	0.532530	+	0.846411i	$0.321241\pi$
$863$	−11.6275	+	35.7857i	−0.395804	+	1.21816i	−0.928334	+	0.371747i	$0.878759\pi$
$864$	−2.45656	−	7.56051i	−0.0835738	−	0.257214i
$865$	−5.91756	−	31.8882i	−0.201203	−	1.08423i
$866$	−2.20150	+	6.77551i	−0.0748099	+	0.230241i
$867$	12.7342	+	9.25196i	0.432477	+	0.314213i
$868$	52.4133			1.77902
$869$	18.6013	+	13.5146i	0.631006	+	0.458452i
$870$	25.8989	+	3.40372i	0.878057	+	0.115397i
$871$	3.74355	−	2.71985i	0.126845	−	0.0921586i
$872$	10.1012	−	7.33894i	0.342069	−	0.248528i
$873$	−2.31762	−	7.13289i	−0.0784394	−	0.241412i
$874$	−37.8128			−1.27904
$875$	−45.0318	−	18.6171i	−1.52235	−	0.629373i
$876$	12.5133			0.422784
$877$	16.1938	+	49.8393i	0.546825	+	1.68295i	0.716612	+	0.697472i	$0.245692\pi$
$877$	16.1938	+	49.8393i	0.546825	+	1.68295i	−0.169787	+	0.985481i	$0.554308\pi$
$878$	16.2841	−	11.8311i	0.549562	−	0.399280i
$879$	16.4244	−	11.9330i	0.553980	−	0.402490i
$880$	−9.58706	−	1.25996i	−0.323180	−	0.0424733i
$881$	6.42180	+	4.66571i	0.216356	+	0.157192i	0.690685	−	0.723156i	$-0.257309\pi$
$881$	6.42180	+	4.66571i	0.216356	+	0.157192i	−0.474329	+	0.880348i	$0.657309\pi$
$882$	25.4588			0.857242
$883$	−25.6393	−	18.6280i	−0.862831	−	0.626883i	0.0658227	−	0.997831i	$-0.479033\pi$
$883$	−25.6393	−	18.6280i	−0.862831	−	0.626883i	−0.928654	+	0.370948i	$0.879033\pi$
$884$	−1.04046	+	3.20221i	−0.0349945	+	0.107702i
$885$	−3.73558	−	20.1300i	−0.125570	−	0.676664i
$886$	6.33175	+	19.4871i	0.212719	+	0.654683i
$887$	0.871749	−	2.68297i	0.0292705	−	0.0900853i	−0.935354	−	0.353713i	$-0.884919\pi$
$887$	0.871749	−	2.68297i	0.0292705	−	0.0900853i	0.964625	+	0.263628i	$0.0849190\pi$
$888$	−2.10757	+	6.48643i	−0.0707254	+	0.217670i
$889$	−22.8901	−	70.4485i	−0.767709	−	2.36277i
$890$	−41.8598	+	22.7402i	−1.40314	+	0.762254i
$891$	−0.488218	+	1.50258i	−0.0163559	+	0.0503383i
$892$	6.88357	+	5.00121i	0.230479	+	0.167453i
$893$	31.6949			1.06063
$894$	−8.02947	−	5.83375i	−0.268546	−	0.195110i
$895$	1.56549	−	0.850448i	0.0523285	−	0.0284274i
$896$	29.2312	−	21.2377i	0.976546	−	0.709502i
$897$	2.24870	−	1.63378i	0.0750820	−	0.0545502i
$898$	20.6759	+	63.6340i	0.689965	+	2.12349i
$899$	−26.4320			−0.881556
$900$	0.660965	+	12.5040i	0.0220322	+	0.416801i
$901$	−4.20390			−0.140052
$902$	7.74233	+	23.8285i	0.257792	+	0.793401i
$903$	4.40746	−	3.20221i	0.146671	−	0.106563i
$904$	12.9236	−	9.38958i	0.429834	−	0.312293i
$905$	−23.0671	−	21.8800i	−0.766776	−	0.727315i
$906$	11.2323	+	8.16071i	0.373167	+	0.271122i
$907$	−44.1799			−1.46697			−0.733485	−	0.679705i	$-0.762108\pi$
$907$	−44.1799			−1.46697			−0.733485	+	0.679705i	$0.762108\pi$
$908$	−54.2919	−	39.4454i	−1.80174	−	1.30904i
$909$	−2.01424	+	6.19919i	−0.0668081	+	0.205614i
$910$	−24.5664	−	3.22860i	−0.814370	−	0.107027i
$911$	−10.6691	−	32.8362i	−0.353484	−	1.08791i	−0.956883	−	0.290472i	$-0.906188\pi$
$911$	−10.6691	−	32.8362i	−0.353484	−	1.08791i	0.603400	−	0.797439i	$-0.293812\pi$
$912$	−6.49466	+	19.9885i	−0.215060	+	0.661886i
$913$	4.26509	−	13.1266i	0.141154	−	0.434426i
$914$	−6.52209	−	20.0729i	−0.215731	−	0.663953i
$915$	2.26458	+	2.14804i	0.0748648	+	0.0710119i
$916$	−0.914713	+	2.81520i	−0.0302230	+	0.0930167i
$917$	1.15961	+	0.842506i	0.0382937	+	0.0278220i
$918$	−2.38197			−0.0786166
$919$	0.429648	+	0.312158i	0.0141728	+	0.0102971i	0.594849	−	0.803837i	$-0.297212\pi$
$919$	0.429648	+	0.312158i	0.0141728	+	0.0102971i	−0.580676	+	0.814135i	$0.697212\pi$
$920$	2.38949	−	5.01258i	0.0787792	−	0.165260i
$921$	2.03330	−	1.47728i	0.0669996	−	0.0486781i
$922$	40.6648	−	29.5447i	1.33922	−	0.973003i
$923$	−3.92584	−	12.0825i	−0.129220	−	0.397700i
$924$	−17.2443			−0.567295
$925$	−17.3410	+	26.7292i	−0.570169	+	0.878850i
$926$	58.6833			1.92845
$927$	2.48720	+	7.65482i	0.0816905	+	0.251417i
$928$	−35.4001	+	25.7197i	−1.16206	+	0.844289i
$929$	−37.3735	+	27.1534i	−1.22618	+	0.890874i	−0.996598	−	0.0824143i	$-0.973737\pi$
$929$	−37.3735	+	27.1534i	−1.22618	+	0.890874i	−0.229585	+	0.973289i	$0.573737\pi$
$930$	−4.15803	−	22.4065i	−0.136347	−	0.734738i
$931$	−74.5192	−	54.1414i	−2.44227	−	1.77441i
$932$	17.7676			0.581997
$933$	−3.90284	−	2.83558i	−0.127773	−	0.0928326i
$934$	2.85840	−	8.79726i	0.0935298	−	0.287855i
$935$	−1.70615	+	3.57909i	−0.0557971	+	0.117049i
$936$	0.396205	+	1.21939i	0.0129504	+	0.0398571i
$937$	−9.30820	+	28.6477i	−0.304086	+	0.935880i	0.675931	+	0.736965i	$0.263742\pi$
$937$	−9.30820	+	28.6477i	−0.304086	+	0.935880i	−0.980017	+	0.198915i	$0.936258\pi$
$938$	−11.0412	+	33.9812i	−0.360506	+	1.10952i
$939$	−1.85043	−	5.69504i	−0.0603865	−	0.185851i
$940$	−9.94610	+	20.8645i	−0.324406	+	0.680526i
$941$	17.6382	−	54.2847i	0.574988	−	1.76963i	−0.0612315	−	0.998124i	$-0.519503\pi$
$941$	17.6382	−	54.2847i	0.574988	−	1.76963i	0.636220	−	0.771508i	$-0.280497\pi$
$942$	−6.85777	−	4.98246i	−0.223438	−	0.162337i
$943$	17.3374			0.564583
$944$	20.2748	+	14.7305i	0.659890	+	0.479438i
$945$	−1.77817	−	9.58209i	−0.0578439	−	0.311705i
$946$	−3.39083	+	2.46358i	−0.110245	+	0.0800980i
$947$	33.2708	−	24.1727i	1.08116	−	0.785506i	0.103273	−	0.994653i	$-0.467069\pi$
$947$	33.2708	−	24.1727i	1.08116	−	0.785506i	0.977884	+	0.209147i	$0.0670686\pi$
$948$	11.2622	+	34.6615i	0.365779	+	1.12575i
$949$	5.98576			0.194306
$950$	44.3483	−	68.3579i	1.43885	−	2.21782i
$951$	17.3531			0.562712
$952$	−1.61783	−	4.97918i	−0.0524343	−	0.161376i
$953$	−28.1654	+	20.4633i	−0.912366	+	0.662873i	−0.941612	−	0.336700i	$-0.890689\pi$
$953$	−28.1654	+	20.4633i	−0.912366	+	0.662873i	0.0292462	+	0.999572i	$0.490689\pi$
$954$	−6.43135	+	4.67265i	−0.208223	+	0.151283i
$955$	9.97767	−	20.9308i	0.322870	−	0.677304i
$956$	−0.0866986	−	0.0629902i	−0.00280403	−	0.00203725i
$957$	8.69627			0.281111
$958$	−22.0022	−	15.9855i	−0.710857	−	0.516468i
$959$	6.14515	−	18.9128i	0.198437	−	0.610727i
$960$	−18.4906	−	17.5390i	−0.596780	−	0.566068i
$961$	−2.45366	−	7.55160i	−0.0791504	−	0.243600i
$962$	−5.00643	+	15.4082i	−0.161414	+	0.496781i
$963$	2.92869	−	9.01359i	0.0943758	−	0.290459i
$964$	−9.10930	−	28.0355i	−0.293391	−	0.902964i
$965$	−9.63759	−	1.26660i	−0.310245	−	0.0407733i
$966$	−6.63227	+	20.4120i	−0.213390	+	0.656746i
$967$	30.1519	+	21.9066i	0.969618	+	0.704469i	0.955365	−	0.295430i	$-0.0954628\pi$
$967$	30.1519	+	21.9066i	0.969618	+	0.704469i	0.0142537	+	0.999898i	$0.495463\pi$
$968$	−9.10165			−0.292538
$969$	6.97214	+	5.06555i	0.223977	+	0.162729i
$970$	−25.8234	−	24.4944i	−0.829138	−	0.786468i
$971$	21.0419	−	15.2879i	0.675267	−	0.490611i	−0.196517	−	0.980500i	$-0.562963\pi$
$971$	21.0419	−	15.2879i	0.675267	−	0.490611i	0.871784	+	0.489890i	$0.162963\pi$
$972$	−2.02602	+	1.47199i	−0.0649846	+	0.0472141i
$973$	−6.37585	−	19.6228i	−0.204400	−	0.629079i
$974$	−14.6910			−0.470729
$975$	0.316175	+	5.98135i	0.0101257	+	0.191556i
$976$	−3.82064			−0.122296
$977$	0.141709	+	0.436134i	0.00453366	+	0.0139532i	0.953298	−	0.302032i	$-0.0976650\pi$
$977$	0.141709	+	0.436134i	0.00453366	+	0.0139532i	−0.948764	+	0.315985i	$0.897665\pi$
$978$	−8.24404	+	5.98965i	−0.263615	+	0.191528i
$979$	−12.8304	+	9.32186i	−0.410063	+	0.297928i
$980$	59.0257	−	32.0656i	1.88551	−	1.02430i
$981$	9.43778	+	6.85695i	0.301325	+	0.218926i
$982$	56.9128			1.81616
$983$	−7.23718	−	5.25812i	−0.230830	−	0.167708i	0.466358	−	0.884596i	$-0.345566\pi$
$983$	−7.23718	−	5.25812i	−0.230830	−	0.167708i	−0.697188	+	0.716888i	$0.745566\pi$
$984$	−2.47132	+	7.60595i	−0.0787829	+	0.242469i
$985$	3.69373	−	2.00661i	0.117692	−	0.0639359i
$986$	4.05154	+	12.4694i	0.129027	+	0.397105i
$987$	5.55920	−	17.1095i	0.176951	−	0.544600i
$988$	7.11852	−	21.9086i	0.226470	−	0.697004i
$989$	0.896242	+	2.75835i	0.0284988	+	0.0877104i
$990$	1.36802	+	7.37187i	0.0434784	+	0.234293i
$991$	−17.4699	+	53.7667i	−0.554949	+	1.70796i	0.141130	+	0.989991i	$0.454926\pi$
$991$	−17.4699	+	53.7667i	−0.554949	+	1.70796i	−0.696079	+	0.717965i	$0.745074\pi$
$992$	30.8837	+	22.4383i	0.980559	+	0.712418i
$993$	20.3355			0.645327
$994$	79.3621	+	57.6599i	2.51721	+	1.82886i
$995$	−9.44506	−	1.24130i	−0.299429	−	0.0393518i
$996$	17.6994	−	12.8594i	0.560826	−	0.407464i
$997$	−32.0463	+	23.2830i	−1.01492	+	0.737380i	−0.965235	−	0.261385i	$-0.915821\pi$
$997$	−32.0463	+	23.2830i	−1.01492	+	0.737380i	−0.0496816	+	0.998765i	$0.515821\pi$
$998$	1.80657	+	5.56005i	0.0571860	+	0.176000i
$999$	−6.37232			−0.201611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.g.b.31.2	✓	8
3.2	odd	2		225.2.h.c.181.1		8
5.2	odd	4		375.2.i.b.349.1		16
5.3	odd	4		375.2.i.b.349.4		16
5.4	even	2		375.2.g.b.151.1		8
25.2	odd	20		1875.2.b.c.1249.7		8
25.3	odd	20		375.2.i.b.274.1		16
25.4	even	10		375.2.g.b.226.1		8
25.11	even	5		1875.2.a.h.1.3		4
25.14	even	10		1875.2.a.e.1.2		4
25.21	even	5	inner	75.2.g.b.46.2	yes	8
25.22	odd	20		375.2.i.b.274.4		16
25.23	odd	20		1875.2.b.c.1249.2		8
75.11	odd	10		5625.2.a.i.1.2		4
75.14	odd	10		5625.2.a.n.1.3		4
75.71	odd	10		225.2.h.c.46.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.b.31.2	✓	8	1.1	even	1	trivial
75.2.g.b.46.2	yes	8	25.21	even	5	inner
225.2.h.c.46.1		8	75.71	odd	10
225.2.h.c.181.1		8	3.2	odd	2
375.2.g.b.151.1		8	5.4	even	2
375.2.g.b.226.1		8	25.4	even	10
375.2.i.b.274.1		16	25.3	odd	20
375.2.i.b.274.4		16	25.22	odd	20
375.2.i.b.349.1		16	5.2	odd	4
375.2.i.b.349.4		16	5.3	odd	4
1875.2.a.e.1.2		4	25.14	even	10
1875.2.a.h.1.3		4	25.11	even	5
1875.2.b.c.1249.2		8	25.23	odd	20
1875.2.b.c.1249.7		8	25.2	odd	20
5625.2.a.i.1.2		4	75.11	odd	10
5625.2.a.n.1.3		4	75.14	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)

\(f(q)\)	\(=\)	\(q+(0.655837 + 2.01846i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-2.02602 + 1.47199i) q^{4} +(-2.21700 - 0.291365i) q^{5} +(-1.71700 - 1.24748i) q^{6} +4.35840 q^{7} +(-0.865884 - 0.629102i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.655837 + 2.01846i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-2.02602 + 1.47199i) q^{4} +(-2.21700 - 0.291365i) q^{5} +(-1.71700 - 1.24748i) q^{6} +4.35840 q^{7} +(-0.865884 - 0.629102i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.865884 - 4.66602i) q^{10} +(-0.488218 - 1.50258i) q^{11} +(0.773871 - 2.38173i) q^{12} +(0.370184 - 1.13931i) q^{13} +(2.85840 + 8.79726i) q^{14} +(1.96485 - 1.06740i) q^{15} +(-0.845805 + 2.60312i) q^{16} +(0.907987 + 0.659691i) q^{17} +2.12233 q^{18} +(-6.21218 - 4.51341i) q^{19} +(4.92058 - 2.67310i) q^{20} +(-3.52602 + 2.56180i) q^{21} +(2.71270 - 1.97090i) q^{22} +(-0.717004 - 2.20671i) q^{23} +1.07029 q^{24} +(4.83021 + 1.29192i) q^{25} +2.54243 q^{26} +(0.309017 + 0.951057i) q^{27} +(-8.83021 + 6.41552i) q^{28} +(4.45307 - 3.23535i) q^{29} +(3.44313 + 3.26594i) q^{30} +(-3.88495 - 2.82258i) q^{31} -7.94959 q^{32} +(1.27817 + 0.928645i) q^{33} +(-0.736068 + 2.26538i) q^{34} +(-9.66259 - 1.26989i) q^{35} +(0.773871 + 2.38173i) q^{36} +(-1.96915 + 6.06043i) q^{37} +(5.03596 - 15.4991i) q^{38} +(0.370184 + 1.13931i) q^{39} +(1.73637 + 1.64701i) q^{40} +(-2.30902 + 7.10642i) q^{41} +(-7.48339 - 5.43700i) q^{42} -1.24998 q^{43} +(3.20092 + 2.32561i) q^{44} +(-0.962197 + 2.01846i) q^{45} +(3.98392 - 2.89449i) q^{46} +(-3.33934 + 2.42617i) q^{47} +(-0.845805 - 2.60312i) q^{48} +11.9957 q^{49} +(0.560152 + 10.5969i) q^{50} -1.12233 q^{51} +(0.927051 + 2.85317i) q^{52} +(-3.03032 + 2.20166i) q^{53} +(-1.71700 + 1.24748i) q^{54} +(0.644581 + 3.47347i) q^{55} +(-3.77387 - 2.74188i) q^{56} +7.67867 q^{57} +(9.45090 + 6.86648i) q^{58} +(2.82940 - 8.70799i) q^{59} +(-2.40963 + 5.05483i) q^{60} +(0.431351 + 1.32756i) q^{61} +(3.14937 - 9.69276i) q^{62} +(1.34682 - 4.14509i) q^{63} +(-3.52202 - 10.8397i) q^{64} +(-1.15265 + 2.41799i) q^{65} +(-1.03616 + 3.18898i) q^{66} +(3.12499 + 2.27044i) q^{67} -2.81066 q^{68} +(1.87714 + 1.36382i) q^{69} +(-3.77387 - 20.3364i) q^{70} +(8.57970 - 6.23352i) q^{71} +(-0.865884 + 0.629102i) q^{72} +(1.54407 + 4.75216i) q^{73} -13.5242 q^{74} +(-4.66709 + 1.79395i) q^{75} +19.2297 q^{76} +(-2.12785 - 6.54885i) q^{77} +(-2.05687 + 1.49440i) q^{78} +(-11.7737 + 8.55407i) q^{79} +(2.63361 - 5.52469i) q^{80} +(-0.809017 - 0.587785i) q^{81} -15.8584 q^{82} +(7.06760 + 5.13491i) q^{83} +(3.37284 - 10.3805i) q^{84} +(-1.82080 - 1.72709i) q^{85} +(-0.819784 - 2.52304i) q^{86} +(-1.70092 + 5.23490i) q^{87} +(-0.522535 + 1.60820i) q^{88} +(-3.10195 - 9.54683i) q^{89} +(-4.70522 - 0.618375i) q^{90} +(1.61341 - 4.96556i) q^{91} +(4.70092 + 3.41542i) q^{92} +4.80206 q^{93} +(-7.08719 - 5.14914i) q^{94} +(12.4574 + 11.8163i) q^{95} +(6.43135 - 4.67265i) q^{96} +(6.06760 - 4.40837i) q^{97} +(7.86720 + 24.2128i) q^{98} -1.57991 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 2 q^{3} + q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q - q^2 - 2 * q^3 + q^4 - 5 * q^5 - q^6 + 4 * q^7 - 2 * q^9	\( 8 q - q^{2} - 2 q^{3} + q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 2 q^{9} + 16 q^{11} - 9 q^{12} - 8 q^{13} - 8 q^{14} + 5 q^{15} - 17 q^{16} - q^{17} + 4 q^{18} - 5 q^{19} - 10 q^{20} - 11 q^{21} + 13 q^{22} + 7 q^{23} + 30 q^{24} - 15 q^{25} + 6 q^{26} - 2 q^{27} - 17 q^{28} + 5 q^{29} + 30 q^{30} - 19 q^{31} + 24 q^{32} - 9 q^{33} + 12 q^{34} - 10 q^{35} - 9 q^{36} - q^{37} - 10 q^{38} - 8 q^{39} + 25 q^{40} - 14 q^{41} - 8 q^{42} + 32 q^{43} - 3 q^{44} - 5 q^{45} + 16 q^{46} - q^{47} - 17 q^{48} + 16 q^{49} + 10 q^{50} + 4 q^{51} - 6 q^{52} - 3 q^{53} - q^{54} + 15 q^{55} - 15 q^{56} + 10 q^{57} + 5 q^{58} + 30 q^{59} - 15 q^{60} - 14 q^{61} - 17 q^{62} + 9 q^{63} - 44 q^{64} + 25 q^{65} - 7 q^{66} + 4 q^{67} - 22 q^{68} - 8 q^{69} - 15 q^{70} + 21 q^{71} + 2 q^{73} - 38 q^{74} - 15 q^{75} + 80 q^{76} - 37 q^{77} - 14 q^{78} - 30 q^{79} - 50 q^{80} - 2 q^{81} - 12 q^{82} + 2 q^{83} + 8 q^{84} - 30 q^{85} - 34 q^{86} + 15 q^{87} + 70 q^{88} - 5 q^{90} + 21 q^{91} + 9 q^{92} + 46 q^{93} - 33 q^{94} + 65 q^{95} + 34 q^{96} - 6 q^{97} + 73 q^{98} - 14 q^{99}+O(q^{100}) \) 8 * q - q^2 - 2 * q^3 + q^4 - 5 * q^5 - q^6 + 4 * q^7 - 2 * q^9 + 16 * q^11 - 9 * q^12 - 8 * q^13 - 8 * q^14 + 5 * q^15 - 17 * q^16 - q^17 + 4 * q^18 - 5 * q^19 - 10 * q^20 - 11 * q^21 + 13 * q^22 + 7 * q^23 + 30 * q^24 - 15 * q^25 + 6 * q^26 - 2 * q^27 - 17 * q^28 + 5 * q^29 + 30 * q^30 - 19 * q^31 + 24 * q^32 - 9 * q^33 + 12 * q^34 - 10 * q^35 - 9 * q^36 - q^37 - 10 * q^38 - 8 * q^39 + 25 * q^40 - 14 * q^41 - 8 * q^42 + 32 * q^43 - 3 * q^44 - 5 * q^45 + 16 * q^46 - q^47 - 17 * q^48 + 16 * q^49 + 10 * q^50 + 4 * q^51 - 6 * q^52 - 3 * q^53 - q^54 + 15 * q^55 - 15 * q^56 + 10 * q^57 + 5 * q^58 + 30 * q^59 - 15 * q^60 - 14 * q^61 - 17 * q^62 + 9 * q^63 - 44 * q^64 + 25 * q^65 - 7 * q^66 + 4 * q^67 - 22 * q^68 - 8 * q^69 - 15 * q^70 + 21 * q^71 + 2 * q^73 - 38 * q^74 - 15 * q^75 + 80 * q^76 - 37 * q^77 - 14 * q^78 - 30 * q^79 - 50 * q^80 - 2 * q^81 - 12 * q^82 + 2 * q^83 + 8 * q^84 - 30 * q^85 - 34 * q^86 + 15 * q^87 + 70 * q^88 - 5 * q^90 + 21 * q^91 + 9 * q^92 + 46 * q^93 - 33 * q^94 + 65 * q^95 + 34 * q^96 - 6 * q^97 + 73 * q^98 - 14 * q^99

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