LMFDB - Embedded newform 507.2.m.b.40.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

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("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			40.14
Character	$\chi$	$=$	507.40
Dual form			507.2.m.b.469.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45113 + 0.357672i) q^{2} +(0.120537 - 0.992709i) q^{3} +(0.206949 + 0.108615i) q^{4} +(0.974467 - 1.41176i) q^{5} +(0.529980 - 1.39744i) q^{6} +(2.67610 + 2.37082i) q^{7} +(-1.97593 - 1.75052i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})$	\(q+(1.45113 + 0.357672i) q^{2} +(0.120537 - 0.992709i) q^{3} +(0.206949 + 0.108615i) q^{4} +(0.974467 - 1.41176i) q^{5} +(0.529980 - 1.39744i) q^{6} +(2.67610 + 2.37082i) q^{7} +(-1.97593 - 1.75052i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(1.91903 - 1.70011i) q^{10} +(5.93239 - 1.46220i) q^{11} +(0.132768 - 0.192348i) q^{12} +(-3.60482 - 0.0723678i) q^{13} +(3.03541 + 4.39755i) q^{14} +(-1.28401 - 1.13753i) q^{15} +(-2.50676 - 3.63168i) q^{16} +(-2.19665 - 1.94606i) q^{17} +(-1.32337 - 0.694558i) q^{18} -3.84341 q^{19} +(0.355004 - 0.186320i) q^{20} +(2.67610 - 2.37082i) q^{21} +9.13168 q^{22} +5.36473 q^{23} +(-1.97593 + 1.75052i) q^{24} +(0.729546 + 1.92366i) q^{25} +(-5.20520 - 1.39436i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(0.296310 + 0.781305i) q^{28} +(3.76521 + 0.928040i) q^{29} +(-1.45640 - 2.10996i) q^{30} +(2.86345 - 7.55030i) q^{31} +(-0.466518 - 1.23011i) q^{32} +(-0.736471 - 6.06538i) q^{33} +(-2.49158 - 3.60968i) q^{34} +(5.95480 - 1.46773i) q^{35} +(-0.174942 - 0.154985i) q^{36} +(-0.990644 + 2.61211i) q^{37} +(-5.57731 - 1.37468i) q^{38} +(-0.506354 + 3.56982i) q^{39} +(-4.39680 + 1.08371i) q^{40} +(-1.46167 + 12.0379i) q^{41} +(4.73136 - 2.48321i) q^{42} +(1.68516 + 4.44340i) q^{43} +(1.38652 + 0.341746i) q^{44} +(-1.28401 + 1.13753i) q^{45} +(7.78494 + 1.91881i) q^{46} +(-7.01907 + 3.68389i) q^{47} +(-3.90735 + 2.05074i) q^{48} +(0.696981 + 5.74016i) q^{49} +(0.370631 + 3.05242i) q^{50} +(-2.19665 + 1.94606i) q^{51} +(-0.738155 - 0.406515i) q^{52} +(-10.1963 - 9.03313i) q^{53} +(-0.849009 + 1.23000i) q^{54} +(3.71664 - 9.79997i) q^{55} +(-1.13762 - 9.36916i) q^{56} +(-0.463272 + 3.81539i) q^{57} +(5.13188 + 2.69342i) q^{58} +(-6.36831 + 9.22609i) q^{59} +(-0.142171 - 0.374874i) q^{60} +(-0.471721 + 0.417909i) q^{61} +(6.85578 - 9.93232i) q^{62} +(-2.03097 - 2.94236i) q^{63} +(0.826808 + 6.80937i) q^{64} +(-3.61495 + 5.01862i) q^{65} +(1.10070 - 9.06510i) q^{66} +(3.30688 - 1.73559i) q^{67} +(-0.243223 - 0.641325i) q^{68} +(0.646646 - 5.32561i) q^{69} +9.16618 q^{70} +(-1.51955 + 12.5146i) q^{71} +(1.49959 + 2.17253i) q^{72} +(-5.31937 + 1.31111i) q^{73} +(-2.37184 + 3.43620i) q^{74} +(1.99757 - 0.492356i) q^{75} +(-0.795390 - 0.417453i) q^{76} +(19.3423 + 10.1516i) q^{77} +(-2.01161 + 4.99918i) q^{78} +(1.05904 - 0.555825i) q^{79} -7.56981 q^{80} +(0.885456 + 0.464723i) q^{81} +(-6.42672 + 16.9459i) q^{82} +(0.0124589 + 0.102609i) q^{83} +(0.811324 - 0.199973i) q^{84} +(-4.88793 + 1.20477i) q^{85} +(0.856110 + 7.05070i) q^{86} +(1.37512 - 3.62589i) q^{87} +(-14.2816 - 7.49557i) q^{88} +3.73430 q^{89} +(-2.27013 + 1.19146i) q^{90} +(-9.47531 - 8.74006i) q^{91} +(1.11022 + 0.582691i) q^{92} +(-7.15009 - 3.75266i) q^{93} +(-11.5032 + 2.83529i) q^{94} +(-3.74528 + 5.42597i) q^{95} +(-1.27737 + 0.314843i) q^{96} +(-3.70967 - 5.37438i) q^{97} +(-1.04168 + 8.57903i) q^{98} -6.10993 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) $ 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{13}\right)$

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 $

$2$	1.45113	+	0.357672i	1.02611	+	0.252913i	0.716230	−	0.697864i	$-0.245866\pi$
$2$	1.45113	+	0.357672i	1.02611	+	0.252913i	0.309877	+	0.950777i	$0.399712\pi$
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$4$	0.206949	+	0.108615i	0.103475	+	0.0543076i
$5$	0.974467	−	1.41176i	0.435795	−	0.631358i	−0.542135	−	0.840291i	$-0.682384\pi$
$5$	0.974467	−	1.41176i	0.435795	−	0.631358i	0.977930	+	0.208934i	$0.0669992\pi$
$6$	0.529980	−	1.39744i	0.216363	−	0.570503i
$7$	2.67610	+	2.37082i	1.01147	+	0.896086i	0.994601	−	0.103772i	$-0.0330911\pi$
$7$	2.67610	+	2.37082i	1.01147	+	0.896086i	0.0168708	+	0.999858i	$0.494630\pi$
$8$	−1.97593	−	1.75052i	−0.698597	−	0.618903i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	1.91903	−	1.70011i	0.606851	−	0.537623i
$11$	5.93239	−	1.46220i	1.78868	−	0.440871i	0.801173	−	0.598432i	$-0.204209\pi$
$11$	5.93239	−	1.46220i	1.78868	−	0.440871i	0.987509	+	0.157562i	$0.0503633\pi$
$12$	0.132768	−	0.192348i	0.0383269	−	0.0555261i
$13$	−3.60482	−	0.0723678i	−0.999799	−	0.0200712i
$13$	−3.60482	−	0.0723678i	−0.999799	−	0.0200712i
$14$	3.03541	+	4.39755i	0.811247	+	1.17529i
$15$	−1.28401	−	1.13753i	−0.331529	−	0.293709i
$16$	−2.50676	−	3.63168i	−0.626691	−	0.907919i
$17$	−2.19665	−	1.94606i	−0.532766	−	0.471989i	0.353325	−	0.935501i	$-0.385051\pi$
$17$	−2.19665	−	1.94606i	−0.532766	−	0.471989i	−0.886091	+	0.463511i	$0.846589\pi$
$18$	−1.32337	−	0.694558i	−0.311921	−	0.163709i
$19$	−3.84341			−0.881739			−0.440870	−	0.897571i	$-0.645330\pi$
$19$	−3.84341			−0.881739			−0.440870	+	0.897571i	$0.645330\pi$
$20$	0.355004	−	0.186320i	0.0793812	−	0.0416625i
$21$	2.67610	−	2.37082i	0.583974	−	0.517355i
$22$	9.13168			1.94688
$23$	5.36473			1.11862			0.559311	−	0.828958i	$-0.311066\pi$
$23$	5.36473			1.11862			0.559311	+	0.828958i	$0.311066\pi$
$24$	−1.97593	+	1.75052i	−0.403335	+	0.357324i
$25$	0.729546	+	1.92366i	0.145909	+	0.384731i
$26$	−5.20520	−	1.39436i	−1.02082	−	0.273457i
$27$	−0.354605	+	0.935016i	−0.0682437	+	0.179944i
$28$	0.296310	+	0.781305i	0.0559973	+	0.147653i
$29$	3.76521	+	0.928040i	0.699181	+	0.172333i	0.572856	−	0.819656i	$-0.305836\pi$
$29$	3.76521	+	0.928040i	0.699181	+	0.172333i	0.126325	+	0.991989i	$0.459682\pi$
$30$	−1.45640	−	2.10996i	−0.265902	−	0.385225i
$31$	2.86345	−	7.55030i	0.514291	−	1.35607i	−0.386688	−	0.922210i	$-0.626381\pi$
$31$	2.86345	−	7.55030i	0.514291	−	1.35607i	0.900979	−	0.433863i	$-0.142850\pi$
$32$	−0.466518	−	1.23011i	−0.0824694	−	0.217454i
$33$	−0.736471	−	6.06538i	−0.128203	−	1.05585i
$34$	−2.49158	−	3.60968i	−0.427303	−	0.619055i
$35$	5.95480	−	1.46773i	1.00655	−	0.248091i
$36$	−0.174942	−	0.154985i	−0.0291570	−	0.0258309i
$37$	−0.990644	+	2.61211i	−0.162861	+	0.429429i	−0.991460	−	0.130414i	$-0.958369\pi$
$37$	−0.990644	+	2.61211i	−0.162861	+	0.429429i	0.828599	+	0.559843i	$0.189139\pi$
$38$	−5.57731	−	1.37468i	−0.904759	−	0.223003i
$39$	−0.506354	+	3.56982i	−0.0810815	+	0.571628i
$40$	−4.39680	+	1.08371i	−0.695195	+	0.171350i
$41$	−1.46167	+	12.0379i	−0.228275	+	1.88001i	0.205018	+	0.978758i	$0.434275\pi$
$41$	−1.46167	+	12.0379i	−0.228275	+	1.88001i	−0.433293	+	0.901253i	$0.642648\pi$
$42$	4.73136	−	2.48321i	0.730065	−	0.383168i
$43$	1.68516	+	4.44340i	0.256984	+	0.677612i	0.999966	+	0.00829950i	$0.00264184\pi$
$43$	1.68516	+	4.44340i	0.256984	+	0.677612i	−0.742981	+	0.669312i	$0.766589\pi$
$44$	1.38652	+	0.341746i	0.209026	+	0.0515202i
$45$	−1.28401	+	1.13753i	−0.191408	+	0.169573i
$46$	7.78494	+	1.91881i	1.14783	+	0.282914i
$47$	−7.01907	+	3.68389i	−1.02384	+	0.537351i	−0.891103	−	0.453801i	$-0.850068\pi$
$47$	−7.01907	+	3.68389i	−1.02384	+	0.537351i	−0.132733	+	0.991152i	$0.542375\pi$
$48$	−3.90735	+	2.05074i	−0.563978	+	0.295998i
$49$	0.696981	+	5.74016i	0.0995688	+	0.820023i
$50$	0.370631	+	3.05242i	0.0524151	+	0.431678i
$51$	−2.19665	+	1.94606i	−0.307593	+	0.272503i
$52$	−0.738155	−	0.406515i	−0.102364	−	0.0563735i
$53$	−10.1963	−	9.03313i	−1.40057	−	1.24080i	−0.934460	−	0.356069i	$-0.884117\pi$
$53$	−10.1963	−	9.03313i	−1.40057	−	1.24080i	−0.466110	−	0.884727i	$-0.654345\pi$
$54$	−0.849009	+	1.23000i	−0.115535	+	0.167382i
$55$	3.71664	−	9.79997i	0.501152	−	1.32143i
$56$	−1.13762	−	9.36916i	−0.152021	−	1.25201i
$57$	−0.463272	+	3.81539i	−0.0613619	+	0.505361i
$58$	5.13188	+	2.69342i	0.673849	+	0.353663i
$59$	−6.36831	+	9.22609i	−0.829083	+	1.20113i	0.148150	+	0.988965i	$0.452668\pi$
$59$	−6.36831	+	9.22609i	−0.829083	+	1.20113i	−0.977233	+	0.212169i	$0.931947\pi$
$60$	−0.142171	−	0.374874i	−0.0183542	−	0.0483960i
$61$	−0.471721	+	0.417909i	−0.0603977	+	0.0535077i	−0.692782	−	0.721147i	$-0.743615\pi$
$61$	−0.471721	+	0.417909i	−0.0603977	+	0.0535077i	0.632384	+	0.774655i	$0.282077\pi$
$62$	6.85578	−	9.93232i	0.870685	−	1.26141i
$63$	−2.03097	−	2.94236i	−0.255878	−	0.370703i
$64$	0.826808	+	6.80937i	0.103351	+	0.851172i
$65$	−3.61495	+	5.01862i	−0.448379	+	0.622484i
$66$	1.10070	−	9.06510i	0.135487	−	1.11584i
$67$	3.30688	−	1.73559i	0.404000	−	0.212035i	−0.250469	−	0.968125i	$-0.580585\pi$
$67$	3.30688	−	1.73559i	0.404000	−	0.212035i	0.654469	+	0.756089i	$0.272892\pi$
$68$	−0.243223	−	0.641325i	−0.0294951	−	0.0777721i
$69$	0.646646	−	5.32561i	0.0778471	−	0.641128i
$70$	9.16618			1.09557
$71$	−1.51955	+	12.5146i	−0.180338	+	1.48521i	0.568622	+	0.822599i	$0.307477\pi$
$71$	−1.51955	+	12.5146i	−0.180338	+	1.48521i	−0.748960	+	0.662616i	$0.769446\pi$
$72$	1.49959	+	2.17253i	0.176728	+	0.256035i
$73$	−5.31937	+	1.31111i	−0.622585	+	0.153453i	−0.537975	−	0.842961i	$-0.680811\pi$
$73$	−5.31937	+	1.31111i	−0.622585	+	0.153453i	−0.0846098	+	0.996414i	$0.526964\pi$
$74$	−2.37184	+	3.43620i	−0.275721	+	0.399450i
$75$	1.99757	−	0.492356i	0.230659	−	0.0568524i
$76$	−0.795390	−	0.417453i	−0.0912375	−	0.0478852i
$77$	19.3423	+	10.1516i	2.20426	+	1.15689i
$78$	−2.01161	+	4.99918i	−0.227770	+	0.566045i
$79$	1.05904	−	0.555825i	0.119151	−	0.0625351i	−0.404095	−	0.914717i	$-0.632413\pi$
$79$	1.05904	−	0.555825i	0.119151	−	0.0625351i	0.523245	+	0.852182i	$0.324721\pi$
$80$	−7.56981			−0.846331
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	−6.42672	+	16.9459i	−0.709713	+	1.87136i
$83$	0.0124589	+	0.102609i	0.00136755	+	0.0112628i	0.993377	−	0.114903i	$-0.0366558\pi$
$83$	0.0124589	+	0.102609i	0.00136755	+	0.0112628i	−0.992009	+	0.126166i	$0.959733\pi$
$84$	0.811324	−	0.199973i	0.0885227	−	0.0218189i
$85$	−4.88793	+	1.20477i	−0.530171	+	0.130675i
$86$	0.856110	+	7.05070i	0.0923167	+	0.760296i
$87$	1.37512	−	3.62589i	0.147428	−	0.388736i
$88$	−14.2816	−	7.49557i	−1.52243	−	0.799030i
$89$	3.73430			0.395835			0.197918	−	0.980219i	$-0.436582\pi$
$89$	3.73430			0.395835			0.197918	+	0.980219i	$0.436582\pi$
$90$	−2.27013	+	1.19146i	−0.239293	+	0.125590i
$91$	−9.47531	−	8.74006i	−0.993283	−	0.916207i
$92$	1.11022	+	0.582691i	0.115749	+	0.0607497i
$93$	−7.15009	−	3.75266i	−0.741430	−	0.389133i
$94$	−11.5032	+	2.83529i	−1.18647	+	0.292438i
$95$	−3.74528	+	5.42597i	−0.384257	+	0.556693i
$96$	−1.27737	+	0.314843i	−0.130371	+	0.0321336i
$97$	−3.70967	−	5.37438i	−0.376660	−	0.545686i	0.588110	−	0.808781i	$-0.299872\pi$
$97$	−3.70967	−	5.37438i	−0.376660	−	0.545686i	−0.964770	+	0.263095i	$0.915257\pi$
$98$	−1.04168	+	8.57903i	−0.105226	+	0.866613i
$99$	−6.10993			−0.614071
$100$	−0.0579594	+	0.477339i	−0.00579594	+	0.0477339i
$101$	6.46246	+	17.0401i	0.643039	+	1.69556i	0.715891	+	0.698212i	$0.246021\pi$
$101$	6.46246	+	17.0401i	0.643039	+	1.69556i	−0.0728515	+	0.997343i	$0.523210\pi$
$102$	−3.88369	+	2.03832i	−0.384542	+	0.201823i
$103$	−1.13929	+	9.38290i	−0.112258	+	0.924524i	0.822384	+	0.568933i	$0.192644\pi$
$103$	−1.13929	+	9.38290i	−0.112258	+	0.924524i	−0.934642	+	0.355591i	$0.884280\pi$
$104$	6.99621	+	6.45332i	0.686034	+	0.632800i
$105$	−0.739253	−	6.08830i	−0.0721437	−	0.594157i
$106$	−11.5653	−	16.7552i	−1.12332	−	1.62741i
$107$	5.29529	−	7.67155i	0.511915	−	0.741636i	−0.478751	−	0.877951i	$-0.658910\pi$
$107$	5.29529	−	7.67155i	0.511915	−	0.741636i	0.990666	+	0.136314i	$0.0435257\pi$
$108$	−0.174942	+	0.154985i	−0.0168338	+	0.0149135i
$109$	−0.674581	−	1.77872i	−0.0646131	−	0.170371i	0.898821	−	0.438316i	$-0.144425\pi$
$109$	−0.674581	−	1.77872i	−0.0646131	−	0.170371i	−0.963434	+	0.267945i	$0.913656\pi$
$110$	8.89852	−	12.8917i	0.848441	−	1.22918i
$111$	2.47366	+	1.29828i	0.234789	+	0.123227i
$112$	1.90169	−	15.6618i	0.179693	−	1.47990i
$113$	−1.08792	−	8.95984i	−0.102343	−	0.842871i	−0.949984	−	0.312300i	$-0.898901\pi$
$113$	−1.08792	−	8.95984i	−0.102343	−	0.842871i	0.847640	−	0.530571i	$-0.178022\pi$
$114$	−2.03693	+	5.37094i	−0.190776	+	0.503035i
$115$	5.22775	−	7.57370i	0.487490	−	0.706251i
$116$	0.678406	+	0.601016i	0.0629884	+	0.0558029i
$117$	3.48276	+	0.932956i	0.321981	+	0.0862518i
$118$	−12.5412	+	11.1105i	−1.15451	+	1.02281i
$119$	−1.26470	−	10.4157i	−0.115935	−	0.954808i
$120$	0.545836	+	4.49537i	0.0498278	+	0.410369i
$121$	23.3152	−	12.2368i	2.11956	−	1.11243i
$122$	−0.834006	+	0.437720i	−0.0755073	+	0.0396293i
$123$	11.7740	+	2.90203i	1.06162	+	0.261667i
$124$	1.41267	−	1.25151i	0.126861	−	0.112389i
$125$	11.7545	+	2.89722i	1.05135	+	0.259136i
$126$	−1.89480	−	4.99618i	−0.168802	−	0.445095i
$127$	−6.05758	+	3.17926i	−0.537523	+	0.282114i	−0.711560	−	0.702625i	$-0.752011\pi$
$127$	−6.05758	+	3.17926i	−0.537523	+	0.282114i	0.174037	+	0.984739i	$0.444319\pi$
$128$	−1.55287	+	12.7891i	−0.137256	+	1.13040i
$129$	4.61412	−	1.13728i	0.406251	−	0.100132i
$130$	−7.04080	+	5.98973i	−0.617519	+	0.525334i
$131$	−0.253811	−	0.0625589i	−0.0221756	−	0.00546579i	0.228212	−	0.973611i	$-0.426712\pi$
$131$	−0.253811	−	0.0625589i	−0.0221756	−	0.00546579i	−0.250388	+	0.968146i	$0.580558\pi$
$132$	0.506381	−	1.33522i	0.0440748	−	0.116216i
$133$	−10.2854	−	9.11204i	−0.891854	−	0.790114i
$134$	5.41950	−	1.33579i	0.468173	−	0.115394i
$135$	0.974467	+	1.41176i	0.0838688	+	0.121505i
$136$	0.933804	+	7.69057i	0.0800731	+	0.659461i
$137$	−2.34934	−	6.19471i	−0.200718	−	0.529249i	0.796429	−	0.604732i	$-0.206720\pi$
$137$	−2.34934	−	6.19471i	−0.200718	−	0.529249i	−0.997147	+	0.0754822i	$0.975950\pi$
$138$	2.84319	−	7.49689i	0.242029	−	0.638178i
$139$	−6.96342	−	10.0883i	−0.590630	−	0.855675i	0.407720	−	0.913107i	$-0.366324\pi$
$139$	−6.96342	−	10.0883i	−0.590630	−	0.855675i	−0.998349	+	0.0574323i	$0.981709\pi$
$140$	1.39176	+	0.343038i	0.117625	+	0.0289920i
$141$	2.81098	+	7.41194i	0.236727	+	0.624198i
$142$	−6.68122	+	17.6169i	−0.560675	+	1.47838i
$143$	−21.4910	+	4.84167i	−1.79717	+	0.404881i
$144$	1.56481	+	4.12605i	0.130400	+	0.343838i
$145$	4.97924	−	4.41122i	0.413503	−	0.366332i
$146$	−8.18806			−0.677649
$147$	5.78232			0.476918
$148$	−0.488728	+	0.432975i	−0.0401732	+	0.0355903i
$149$	9.46038	−	4.96519i	0.775025	−	0.406764i	−0.0303432	−	0.999540i	$-0.509660\pi$
$149$	9.46038	−	4.96519i	0.775025	−	0.406764i	0.805368	+	0.592775i	$0.201968\pi$
$150$	3.07484			0.251060
$151$	−6.78304	−	3.56001i	−0.551996	−	0.289710i	0.165573	−	0.986198i	$-0.447053\pi$
$151$	−6.78304	−	3.56001i	−0.551996	−	0.289710i	−0.717569	+	0.696488i	$0.754745\pi$
$152$	7.59432	+	6.72798i	0.615981	+	0.545711i
$153$	1.66710	+	2.41521i	0.134777	+	0.195258i
$154$	24.4373	+	21.6496i	1.96922	+	1.74457i
$155$	−7.86886	−	11.4000i	−0.632042	−	0.915671i
$156$	−0.492526	+	0.683773i	−0.0394336	+	0.0547456i
$157$	11.6179	−	16.8314i	0.927209	−	1.34329i	−0.0119924	−	0.999928i	$-0.503817\pi$
$157$	11.6179	−	16.8314i	0.927209	−	1.34329i	0.939202	−	0.343366i	$-0.111567\pi$
$158$	1.73561	−	0.427788i	0.138077	−	0.0340330i
$159$	−10.1963	+	9.03313i	−0.808619	+	0.716374i
$160$	−2.19122	−	0.540087i	−0.173231	−	0.0426976i
$161$	14.3566	+	12.7188i	1.13146	+	1.00238i
$162$	1.11870	+	0.991079i	0.0878931	+	0.0778665i
$163$	5.87842	−	15.5001i	0.460433	−	1.21406i	−0.480957	−	0.876744i	$-0.659711\pi$
$163$	5.87842	−	15.5001i	0.460433	−	1.21406i	0.941391	−	0.337319i	$-0.109520\pi$
$164$	−1.61000	+	2.33248i	−0.125720	+	0.182136i
$165$	−9.28053	−	4.87080i	−0.722488	−	0.379191i
$166$	−0.0186207	+	0.153355i	−0.00144524	+	0.0119027i
$167$	2.25642	+	0.556157i	0.174607	+	0.0430368i	0.325650	−	0.945490i	$-0.394417\pi$
$167$	2.25642	+	0.556157i	0.174607	+	0.0430368i	−0.151043	+	0.988527i	$0.548263\pi$
$168$	−9.43797			−0.728155
$169$	12.9895	+	0.521747i	0.999194	+	0.0401344i
$170$	−7.52396			−0.577061
$171$	3.73173	+	0.919789i	0.285372	+	0.0703380i
$172$	−0.133879	+	1.10259i	−0.0102082	+	0.0840717i
$173$	8.22960	+	4.31923i	0.625685	+	0.328385i	0.747594	−	0.664157i	$-0.231209\pi$
$173$	8.22960	+	4.31923i	0.625685	+	0.328385i	−0.121909	+	0.992541i	$0.538901\pi$
$174$	3.29236	−	4.76981i	0.249593	−	0.361598i
$175$	−2.60830	+	6.87752i	−0.197169	+	0.519892i
$176$	−20.1814	−	17.8791i	−1.52123	−	1.34769i
$177$	8.39121	+	7.43396i	0.630722	+	0.558771i
$178$	5.41897	+	1.33566i	0.406169	+	0.100112i
$179$	3.70913	−	3.28600i	0.277233	−	0.245607i	−0.513036	−	0.858367i	$-0.671479\pi$
$179$	3.70913	−	3.28600i	0.277233	−	0.245607i	0.790269	+	0.612760i	$0.209941\pi$
$180$	−0.389277	+	0.0959482i	−0.0290150	+	0.00715156i
$181$	−13.7271	+	19.8871i	−1.02033	+	1.47820i	−0.148176	+	0.988961i	$0.547340\pi$
$181$	−13.7271	+	19.8871i	−1.02033	+	1.47820i	−0.872151	+	0.489237i	$0.837275\pi$
$182$	−10.6239	−	16.0721i	−0.787494	−	1.19134i
$183$	0.358002	+	0.518655i	0.0264643	+	0.0383401i
$184$	−10.6003	−	9.39107i	−0.781467	−	0.692319i
$185$	2.72232	+	3.94397i	0.200149	+	0.289966i
$186$	−9.03352	−	8.00300i	−0.662370	−	0.586809i
$187$	−15.8769	−	8.33285i	−1.16104	−	0.609358i
$188$	−1.85272			−0.135123
$189$	−3.16571	+	1.66150i	−0.230272	+	0.120856i
$190$	−7.37562	+	6.53423i	−0.535084	+	0.474043i
$191$	−6.40448			−0.463412			−0.231706	−	0.972786i	$-0.574431\pi$
$191$	−6.40448			−0.463412			−0.231706	+	0.972786i	$0.574431\pi$
$192$	6.85939			0.495033
$193$	1.15744	−	1.02540i	0.0833142	−	0.0738099i	−0.620438	−	0.784256i	$-0.713045\pi$
$193$	1.15744	−	1.02540i	0.0833142	−	0.0738099i	0.703752	+	0.710446i	$0.251507\pi$
$194$	−3.46096	−	9.12580i	−0.248482	−	0.655194i
$195$	4.54630	+	4.19352i	0.325567	+	0.300304i
$196$	−0.479229	+	1.26362i	−0.0342306	+	0.0902588i
$197$	−5.35450	−	14.1187i	−0.381493	−	1.00591i	−0.978966	−	0.204024i	$-0.934598\pi$
$197$	−5.35450	−	14.1187i	−0.381493	−	1.00591i	0.597473	−	0.801889i	$-0.296171\pi$
$198$	−8.86633	−	2.18535i	−0.630103	−	0.155306i
$199$	−14.7369	−	21.3501i	−1.04467	−	1.51347i	−0.845840	−	0.533437i	$-0.820900\pi$
$199$	−14.7369	−	21.3501i	−1.04467	−	1.51347i	−0.198833	−	0.980033i	$-0.563715\pi$
$200$	1.92587	−	5.07810i	0.136180	−	0.359076i
$201$	−1.32433	−	3.49197i	−0.0934111	−	0.246305i
$202$	3.28312	+	27.0389i	0.231000	+	1.90245i
$203$	7.87586	+	11.4102i	0.552777	+	0.800836i
$204$	−0.665967	+	0.164146i	−0.0466270	+	0.0114925i
$205$	15.5703	+	13.7941i	1.08748	+	0.963422i
$206$	−5.00927	+	13.2083i	−0.349012	+	0.920269i
$207$	−5.20884	−	1.28386i	−0.362039	−	0.0892346i
$208$	8.77363	+	13.2730i	0.608342	+	0.920315i
$209$	−22.8006	+	5.61985i	−1.57715	+	0.388733i
$210$	1.10486	−	9.09935i	0.0762427	−	0.627915i
$211$	−7.42187	+	3.89530i	−0.510943	+	0.268164i	−0.700432	−	0.713719i	$-0.747009\pi$
$211$	−7.42187	+	3.89530i	−0.510943	+	0.268164i	0.189489	+	0.981883i	$0.439317\pi$
$212$	−1.12898	−	2.97687i	−0.0775386	−	0.204452i
$213$	12.2402	+	3.01695i	0.838687	+	0.206718i
$214$	10.4281	−	9.23847i	0.712848	−	0.631529i
$215$	7.91514	+	1.95091i	0.539808	+	0.133051i
$216$	2.33744	−	1.22678i	0.159043	−	0.0834721i
$217$	25.5633	−	13.4166i	1.73535	−	0.910781i
$218$	−0.342707	−	2.82244i	−0.0232110	−	0.191160i
$219$	0.660368	+	5.43862i	0.0446235	+	0.367508i
$220$	1.83358	−	1.62441i	0.123620	−	0.109518i
$221$	7.77771	+	7.17418i	0.523185	+	0.482588i
$222$	3.12525	+	2.76873i	0.209753	+	0.185825i
$223$	−13.8539	+	20.0709i	−0.927729	+	1.34405i	0.0112003	+	0.999937i	$0.496435\pi$
$223$	−13.8539	+	20.0709i	−0.927729	+	1.34405i	−0.938929	+	0.344110i	$0.888181\pi$
$224$	1.66791	−	4.39792i	0.111442	−	0.293848i
$225$	−0.247986	−	2.04235i	−0.0165324	−	0.136157i
$226$	1.62597	−	13.3911i	0.108158	−	0.890760i
$227$	−4.02454	−	2.11224i	−0.267118	−	0.140194i	0.325847	−	0.945422i	$-0.394351\pi$
$227$	−4.02454	−	2.11224i	−0.267118	−	0.140194i	−0.592965	+	0.805228i	$0.702043\pi$
$228$	−0.510283	+	0.739273i	−0.0337943	+	0.0489595i
$229$	−5.35946	−	14.1317i	−0.354163	−	0.933852i	−0.987165	−	0.159702i	$-0.948947\pi$
$229$	−5.35946	−	14.1317i	−0.354163	−	0.933852i	0.633002	−	0.774150i	$-0.281822\pi$
$230$	10.2951	−	9.12064i	0.678837	−	0.601397i
$231$	12.4091	−	17.9776i	0.816457	−	1.18284i
$232$	−5.81523	−	8.42482i	−0.381789	−	0.553117i
$233$	−0.145918	−	1.20174i	−0.00955939	−	0.0787286i	0.987148	−	0.159806i	$-0.0510869\pi$
$233$	−0.145918	−	1.20174i	−0.00955939	−	0.0787286i	−0.996708	+	0.0810776i	$0.974164\pi$
$234$	4.72025	+	2.59953i	0.308573	+	0.169937i
$235$	−1.63908	+	13.4991i	−0.106922	+	0.880582i
$236$	−2.32001	+	1.21763i	−0.151020	+	0.0792613i
$237$	−0.424119	−	1.11831i	−0.0275495	−	0.0726421i
$238$	1.89017	−	15.5670i	0.122522	−	1.00906i
$239$	−1.24968			−0.0808354			−0.0404177	−	0.999183i	$-0.512869\pi$
$239$	−1.24968			−0.0808354			−0.0404177	+	0.999183i	$0.512869\pi$
$240$	−0.912440	+	7.51462i	−0.0588977	+	0.485067i
$241$	−0.854514	−	1.23798i	−0.0550441	−	0.0797451i	0.794495	−	0.607270i	$-0.207735\pi$
$241$	−0.854514	−	1.23798i	−0.0550441	−	0.0797451i	−0.849539	+	0.527525i	$0.823120\pi$
$242$	38.2102	−	9.41797i	2.45625	−	0.605410i
$243$	0.568065	−	0.822984i	0.0364414	−	0.0527944i
$244$	−0.143014	+	0.0352497i	−0.00915550	+	0.00225663i
$245$	8.78291	+	4.60963i	0.561119	+	0.294498i
$246$	16.0477	+	8.42246i	1.02316	+	0.536997i
$247$	13.8548	+	0.278139i	0.881562	+	0.0176976i
$248$	−18.8749	+	9.90633i	−1.19856	+	0.629053i
$249$	0.103362			0.00655031
$250$	16.0211	+	8.40852i	1.01326	+	0.531802i
$251$	8.68645	−	22.9043i	0.548284	−	1.44571i	−0.318933	−	0.947777i	$-0.603325\pi$
$251$	8.68645	−	22.9043i	0.548284	−	1.44571i	0.867218	−	0.497929i	$-0.165906\pi$
$252$	−0.100721	−	0.829513i	−0.00634483	−	0.0522544i
$253$	31.8256	−	7.84432i	2.00086	−	0.493168i
$254$	−9.92750	+	2.44691i	−0.622907	+	0.153533i
$255$	0.606808	+	4.99751i	0.0379998	+	0.312956i
$256$	−1.96298	+	5.17594i	−0.122686	+	0.323496i
$257$	15.1810	+	7.96759i	0.946964	+	0.497005i	0.866183	−	0.499727i	$-0.166566\pi$
$257$	15.1810	+	7.96759i	0.946964	+	0.497005i	0.0807807	+	0.996732i	$0.474259\pi$
$258$	7.10248			0.442181
$259$	−8.84392	+	4.64165i	−0.549534	+	0.288418i
$260$	−1.29321	+	0.645961i	−0.0802014	+	0.0400608i
$261$	−3.43370	−	1.80215i	−0.212541	−	0.111550i
$262$	−0.345939	−	0.181563i	−0.0213722	−	0.0112170i
$263$	−10.3515	+	2.55142i	−0.638303	+	0.157328i	−0.545169	−	0.838326i	$-0.683535\pi$
$263$	−10.3515	+	2.55142i	−0.638303	+	0.157328i	−0.0931339	+	0.995654i	$0.529688\pi$
$264$	−9.16238	+	13.2740i	−0.563905	+	0.816958i
$265$	−22.6886	+	5.59223i	−1.39375	+	0.343528i
$266$	−11.6663	−	16.9016i	−0.715308	−	1.03630i
$267$	0.450120	−	3.70708i	0.0275469	−	0.226869i
$268$	0.872867			0.0533188
$269$	−0.420641	+	3.46429i	−0.0256469	+	0.211221i	−0.999899	−	0.0142419i	$-0.995467\pi$
$269$	−0.420641	+	3.46429i	−0.0256469	+	0.211221i	0.974252	+	0.225463i	$0.0723896\pi$
$270$	0.909135	+	2.39719i	0.0553282	+	0.145888i
$271$	−0.993314	+	0.521331i	−0.0603395	+	0.0316686i	−0.494623	−	0.869108i	$-0.664694\pi$
$271$	−0.993314	+	0.521331i	−0.0603395	+	0.0316686i	0.434284	+	0.900776i	$0.357002\pi$
$272$	−1.56098	+	12.8558i	−0.0946484	+	0.779500i
$273$	−9.81845	+	8.35273i	−0.594240	+	0.505530i
$274$	−1.19353	−	9.82964i	−0.0721041	−	0.593830i
$275$	7.14073	+	10.3451i	0.430602	+	0.623835i
$276$	0.712265	−	1.03189i	0.0428733	−	0.0621127i
$277$	6.15556	−	5.45335i	0.369852	−	0.327660i	−0.457640	−	0.889137i	$-0.651305\pi$
$277$	6.15556	−	5.45335i	0.369852	−	0.327660i	0.827492	+	0.561477i	$0.189767\pi$
$278$	−6.49657	−	17.1300i	−0.389638	−	1.02739i
$279$	−4.58715	+	6.64563i	−0.274625	+	0.397863i
$280$	−14.3356	−	7.52389i	−0.856714	−	0.449638i
$281$	−1.98302	+	16.3317i	−0.118297	+	0.974266i	0.805821	+	0.592159i	$0.201724\pi$
$281$	−1.98302	+	16.3317i	−0.118297	+	0.974266i	−0.924118	+	0.382107i	$0.875199\pi$
$282$	1.42806	+	11.7611i	0.0850397	+	0.700365i
$283$	1.42169	−	3.74868i	0.0845105	−	0.222836i	−0.886099	−	0.463496i	$-0.846595\pi$
$283$	1.42169	−	3.74868i	0.0845105	−	0.222836i	0.970609	+	0.240660i	$0.0773640\pi$
$284$	−1.67375	+	2.42485i	−0.0993188	+	0.143888i
$285$	4.93497	+	4.37200i	0.292322	+	0.258975i
$286$	−32.9181	−	0.660840i	−1.94649	−	0.0390763i
$287$	−32.4514	+	28.7494i	−1.91555	+	1.69702i
$288$	0.158578	+	1.30601i	0.00934429	+	0.0769572i
$289$	−1.01101	−	8.32642i	−0.0594712	−	0.489789i
$290$	8.80331	−	4.62033i	0.516948	−	0.271315i
$291$	−5.78235	+	3.03481i	−0.338967	+	0.177904i
$292$	−1.24324	−	0.306432i	−0.0727554	−	0.0179326i
$293$	17.1257	−	15.1721i	1.00049	−	0.886361i	0.00696986	−	0.999976i	$-0.497781\pi$
$293$	17.1257	−	15.1721i	1.00049	−	0.886361i	0.993525	+	0.113615i	$0.0362429\pi$
$294$	8.39092	+	2.06818i	0.489368	+	0.120618i
$295$	6.81931	+	17.9810i	0.397035	+	1.04690i
$296$	6.53001	−	3.42721i	0.379549	−	0.199203i
$297$	−0.736471	+	6.06538i	−0.0427344	+	0.351949i
$298$	15.5042	−	3.82144i	0.898134	−	0.221370i
$299$	−19.3389	−	0.388234i	−1.11840	−	0.0224521i
$300$	0.466872	+	0.115074i	0.0269549	+	0.00664378i
$301$	−6.02484	+	15.8862i	−0.347266	+	0.915665i
$302$	−8.56978	−	7.59216i	−0.493135	−	0.436880i
$303$	17.6948	−	4.36139i	1.01654	−	0.250555i
$304$	9.63453	+	13.9580i	0.552578	+	0.800548i
$305$	0.130309	+	1.07320i	0.00746150	+	0.0614510i
$306$	1.55533	+	4.10106i	0.0889122	+	0.234442i
$307$	3.65430	−	9.63561i	0.208562	−	0.549933i	−0.789390	−	0.613891i	$-0.789603\pi$
$307$	3.65430	−	9.63561i	0.208562	−	0.549933i	0.997953	+	0.0639583i	$0.0203725\pi$
$308$	2.90025	+	4.20174i	0.165257	+	0.239416i
$309$	9.17716	+	2.26197i	0.522070	+	0.128679i
$310$	−7.34130	−	19.3574i	−0.416958	−	1.09943i
$311$	−0.284283	+	0.749592i	−0.0161202	+	0.0425055i	−0.942835	−	0.333261i	$-0.891851\pi$
$311$	−0.284283	+	0.749592i	−0.0161202	+	0.0425055i	0.926715	+	0.375766i	$0.122620\pi$
$312$	7.24957	−	6.16733i	0.410426	−	0.349157i
$313$	3.64642	+	9.61483i	0.206108	+	0.543462i	0.997715	−	0.0675688i	$-0.0215242\pi$
$313$	3.64642	+	9.61483i	0.206108	+	0.543462i	−0.791607	+	0.611031i	$0.790755\pi$
$314$	22.8793	−	20.2693i	1.29115	−	1.14386i
$315$	−6.13302			−0.345556
$316$	0.279537			0.0157252
$317$	9.99782	−	8.85730i	0.561534	−	0.497475i	−0.333937	−	0.942595i	$-0.608377\pi$
$317$	9.99782	−	8.85730i	0.561534	−	0.497475i	0.895471	+	0.445120i	$0.146839\pi$
$318$	−18.0271	+	9.46135i	−1.01091	+	0.530566i
$319$	23.6936			1.32659
$320$	10.4189	+	5.46826i	0.582434	+	0.305685i
$321$	−6.97734	−	6.18138i	−0.389437	−	0.345011i
$322$	16.2841	+	23.5916i	0.907479	+	1.31471i
$323$	8.44263	+	7.47952i	0.469761	+	0.416172i
$324$	0.132768	+	0.192348i	0.00737601	+	0.0106860i
$325$	−2.49068	−	6.98724i	−0.138158	−	0.387582i
$326$	14.0743	−	20.3902i	0.779505	−	1.12931i
$327$	−1.84707	+	0.455261i	−0.102143	+	0.0251760i
$328$	23.9609	−	21.2275i	1.32302	−	1.17209i
$329$	−27.5176	−	6.78248i	−1.51709	−	0.373930i
$330$	−11.7251	−	10.3876i	−0.645448	−	0.571817i
$331$	1.52292	+	1.34919i	0.0837072	+	0.0741581i	0.703939	−	0.710261i	$-0.251423\pi$
$331$	1.52292	+	1.34919i	0.0837072	+	0.0741581i	−0.620232	+	0.784419i	$0.712961\pi$
$332$	−0.00856649	+	0.0225880i	−0.000470147	+	0.00123968i
$333$	1.58698	−	2.29913i	0.0869658	−	0.125992i
$334$	3.07545	+	1.61412i	0.168281	+	0.0883206i
$335$	0.772218	−	6.35979i	0.0421908	−	0.347472i
$336$	−15.3184	−	3.77565i	−0.835688	−	0.205979i
$337$	−32.2312			−1.75575			−0.877874	−	0.478892i	$-0.841038\pi$
$337$	−32.2312			−1.75575			−0.877874	+	0.478892i	$0.841038\pi$
$338$	18.6629	+	5.40312i	1.01513	+	0.293891i
$339$	−9.02565			−0.490206
$340$	−1.14241	−	0.281579i	−0.0619558	−	0.0152707i
$341$	5.94703	−	48.9782i	0.322050	−	2.65232i
$342$	5.08626	+	2.66947i	0.275033	+	0.144349i
$343$	2.47307	−	3.58286i	0.133533	−	0.193456i
$344$	4.44851	−	11.7298i	0.239848	−	0.632426i
$345$	−6.88834	−	6.10254i	−0.370856	−	0.328550i
$346$	10.3974	+	9.21128i	0.558967	+	0.495201i
$347$	16.9596	+	4.18016i	0.910438	+	0.224403i	0.666602	−	0.745414i	$-0.267748\pi$
$347$	16.9596	+	4.18016i	0.910438	+	0.224403i	0.243836	+	0.969816i	$0.421594\pi$
$348$	0.678406	−	0.601016i	0.0363664	−	0.0322178i
$349$	31.5858	−	7.78519i	1.69075	−	0.416732i	0.727663	−	0.685935i	$-0.240606\pi$
$349$	31.5858	−	7.78519i	1.69075	−	0.416732i	0.963083	+	0.269203i	$0.0867603\pi$
$350$	−6.24490	+	9.04729i	−0.333804	+	0.483598i
$351$	1.34595	−	3.34491i	0.0718417	−	0.178538i
$352$	−4.56623	−	6.61532i	−0.243381	−	0.352598i
$353$	−4.75418	−	4.21183i	−0.253039	−	0.224173i	0.527061	−	0.849827i	$-0.323294\pi$
$353$	−4.75418	−	4.21183i	−0.253039	−	0.224173i	−0.780101	+	0.625654i	$0.784832\pi$
$354$	9.51784	+	13.7890i	0.505868	+	0.732876i
$355$	16.1869	+	14.3403i	0.859112	+	0.761107i
$356$	0.772810	+	0.405602i	0.0409589	+	0.0214969i
$357$	−10.4922			−0.555308
$358$	6.55775	−	3.44177i	0.346588	−	0.181903i
$359$	−18.8122	+	16.6662i	−0.992871	+	0.879607i	−0.992726	−	0.120393i	$-0.961584\pi$
$359$	−18.8122	+	16.6662i	−0.992871	+	0.879607i	−0.000144545		1.00000i	$0.500046\pi$
$360$	4.52838			0.238667
$361$	−4.22818			−0.222536
$362$	−27.0329	+	23.9491i	−1.42082	+	1.25874i
$363$	−9.33720	−	24.6202i	−0.490076	−	1.29222i
$364$	−1.01160	−	2.83791i	−0.0530224	−	0.148747i
$365$	−3.33258	+	8.78730i	−0.174435	+	0.459948i
$366$	0.334000	+	0.880686i	0.0174585	+	0.0460342i
$367$	6.34621	+	1.56420i	0.331269	+	0.0816506i	0.401442	−	0.915884i	$-0.368509\pi$
$367$	6.34621	+	1.56420i	0.331269	+	0.0816506i	−0.0701731	+	0.997535i	$0.522355\pi$
$368$	−13.4481	−	19.4829i	−0.701031	−	1.01562i
$369$	4.30007	−	11.3383i	0.223853	−	0.590251i
$370$	2.53981	+	6.69693i	0.132038	+	0.348157i
$371$	−5.87041	−	48.3472i	−0.304777	−	2.51006i
$372$	−1.07211	−	1.55322i	−0.0555863	−	0.0805306i
$373$	−20.6398	+	5.08725i	−1.06869	+	0.263408i	−0.734159	−	0.678978i	$-0.762423\pi$
$373$	−20.6398	+	5.08725i	−1.06869	+	0.263408i	−0.334529	+	0.942385i	$0.608577\pi$
$374$	−20.0591	−	17.7708i	−1.03723	−	0.918907i
$375$	4.29295	−	11.3196i	0.221687	−	0.584540i
$376$	20.3179	+	5.00792i	1.04782	+	0.258264i
$377$	−13.5057	−	3.61790i	−0.695581	−	0.186331i
$378$	−5.18815	+	1.27876i	−0.266850	+	0.0657725i
$379$	−0.905487	+	7.45736i	−0.0465117	+	0.383059i	0.950801	+	0.309801i	$0.100263\pi$
$379$	−0.905487	+	7.45736i	−0.0465117	+	0.383059i	−0.997313	+	0.0732574i	$0.976661\pi$
$380$	−1.36442	+	0.716105i	−0.0699935	+	0.0367354i
$381$	2.42592	+	6.39663i	0.124284	+	0.327709i
$382$	−9.29377	−	2.29071i	−0.475510	−	0.117203i
$383$	9.41671	−	8.34248i	0.481172	−	0.426281i	−0.387350	−	0.921933i	$-0.626609\pi$
$383$	9.41671	−	8.34248i	0.481172	−	0.426281i	0.868521	+	0.495652i	$0.165071\pi$
$384$	12.5086	+	3.08310i	0.638328	+	0.157334i
$385$	33.1801	−	17.4143i	1.69101	−	0.887513i
$386$	2.04636	−	1.07401i	0.104157	−	0.0546657i
$387$	−0.572816	−	4.71756i	−0.0291179	−	0.239807i
$388$	−0.183973	−	1.51515i	−0.00933979	−	0.0769201i
$389$	15.6921	−	13.9020i	0.795622	−	0.704860i	−0.163905	−	0.986476i	$-0.552409\pi$
$389$	15.6921	−	13.9020i	0.795622	−	0.704860i	0.959527	+	0.281617i	$0.0908706\pi$
$390$	5.09738	+	7.71145i	0.258116	+	0.390484i
$391$	−11.7844	−	10.4401i	−0.595964	−	0.527978i
$392$	8.67109	−	12.5622i	0.437956	−	0.634489i
$393$	−0.0926963	+	0.244420i	−0.00467591	+	0.0123294i
$394$	−2.72025	−	22.4032i	−0.137044	−	1.12866i
$395$	0.247304	−	2.03674i	0.0124432	−	0.102479i
$396$	−1.26444	−	0.663632i	−0.0635407	−	0.0333487i
$397$	−14.3148	+	20.7385i	−0.718438	+	1.04084i	0.278329	+	0.960486i	$0.410219\pi$
$397$	−14.3148	+	20.7385i	−0.718438	+	1.04084i	−0.996767	+	0.0803507i	$0.974396\pi$
$398$	−13.7489	−	36.2529i	−0.689171	−	1.81719i
$399$	−10.2854	+	9.11204i	−0.514912	+	0.456173i
$400$	5.15729	−	7.47163i	0.257865	−	0.373581i
$401$	−13.9501	−	20.2103i	−0.696637	−	1.00925i	−0.998437	−	0.0558817i	$-0.982203\pi$
$401$	−13.9501	−	20.2103i	−0.696637	−	1.00925i	0.301801	−	0.953371i	$-0.402412\pi$
$402$	−0.672799	−	5.54100i	−0.0335562	−	0.276360i
$403$	−10.8686	+	27.0103i	−0.541405	+	1.34548i
$404$	−0.513416	+	4.22836i	−0.0255434	+	0.210369i
$405$	1.51892	−	0.797193i	0.0754760	−	0.0396129i
$406$	7.34783	+	19.3746i	0.364667	+	0.961548i
$407$	−2.05745	+	16.9446i	−0.101984	+	0.839912i
$408$	7.74706			0.383536
$409$	1.74039	−	14.3334i	0.0860567	−	0.708741i	−0.884275	−	0.466966i	$-0.845347\pi$
$409$	1.74039	−	14.3334i	0.0860567	−	0.708741i	0.970332	−	0.241775i	$-0.0777297\pi$
$410$	17.6609	+	25.5862i	0.872208	+	1.26361i
$411$	−6.43272	+	1.58552i	−0.317303	+	0.0782081i
$412$	−1.25490	+	1.81804i	−0.0618245	+	0.0895682i
$413$	−38.9157	+	9.59185i	−1.91491	+	0.471984i
$414$	−7.09952	−	3.72611i	−0.348922	−	0.183129i
$415$	0.156999	+	0.0823997i	0.00770680	+	0.00404484i
$416$	1.59269	+	4.46808i	0.0780883	+	0.219066i
$417$	−10.8540	+	5.69664i	−0.531525	+	0.278966i
$418$	−35.0968			−1.71664
$419$	−2.73418	−	1.43501i	−0.133573	−	0.0701047i	0.396613	−	0.917986i	$-0.370186\pi$
$419$	−2.73418	−	1.43501i	−0.133573	−	0.0701047i	−0.530186	+	0.847881i	$0.677878\pi$
$420$	0.508294	−	1.34026i	0.0248022	−	0.0653981i
$421$	3.67899	+	30.2992i	0.179303	+	1.47669i	0.753214	+	0.657776i	$0.228502\pi$
$421$	3.67899	+	30.2992i	0.179303	+	1.47669i	−0.573911	+	0.818918i	$0.694574\pi$
$422$	−12.1634	+	2.99800i	−0.592104	+	0.145941i
$423$	7.69672	−	1.89707i	0.374227	−	0.0922388i
$424$	4.33449	+	35.6977i	0.210501	+	1.73363i
$425$	2.14100	−	5.64534i	0.103854	−	0.273839i
$426$	16.6831	+	8.75599i	0.808301	+	0.424229i
$427$	−2.25316			−0.109038
$428$	1.92910	−	1.01247i	0.0932466	−	0.0489396i
$429$	2.21591	+	21.9179i	0.106985	+	1.05821i
$430$	10.7881	+	5.66205i	0.520250	+	0.273048i
$431$	17.8343	+	9.36014i	0.859046	+	0.450862i	0.835908	−	0.548870i	$-0.184942\pi$
$431$	17.8343	+	9.36014i	0.859046	+	0.450862i	0.0231385	+	0.999732i	$0.492634\pi$
$432$	4.28459	−	1.05606i	0.206142	−	0.0508095i
$433$	−20.1227	+	29.1528i	−0.967035	+	1.40099i	−0.0515362	+	0.998671i	$0.516412\pi$
$433$	−20.1227	+	29.1528i	−0.967035	+	1.40099i	−0.915499	+	0.402321i	$0.868204\pi$
$434$	41.8945	−	10.3261i	2.01100	−	0.495667i
$435$	−3.77888	−	5.47465i	−0.181183	−	0.262489i
$436$	0.0535926	−	0.441375i	0.00256662	−	0.0211380i
$437$	−20.6189			−0.986333
$438$	−0.986962	+	8.12836i	−0.0471589	+	0.388388i
$439$	1.90728	+	5.02908i	0.0910294	+	0.240025i	0.972797	−	0.231659i	$-0.0744155\pi$
$439$	1.90728	+	5.02908i	0.0910294	+	0.240025i	−0.881768	+	0.471684i	$0.843646\pi$
$440$	−24.4989	+	12.8580i	−1.16794	+	0.612982i
$441$	0.696981	−	5.74016i	0.0331896	−	0.273341i
$442$	8.72049	+	13.1926i	0.414791	+	0.627507i
$443$	−0.182869	−	1.50606i	−0.00868836	−	0.0715551i	0.987720	−	0.156236i	$-0.0499360\pi$
$443$	−0.182869	−	1.50606i	−0.00868836	−	0.0715551i	−0.996408	+	0.0846808i	$0.973013\pi$
$444$	0.370909	+	0.537354i	0.0176025	+	0.0255017i
$445$	3.63895	−	5.27194i	0.172503	−	0.249914i
$446$	−27.2828	+	24.1704i	−1.29188	+	1.14450i
$447$	−3.78867	−	9.98989i	−0.179198	−	0.472506i
$448$	−13.9312	+	20.1828i	−0.658186	+	0.953547i
$449$	27.1040	+	14.2253i	1.27912	+	0.671332i	0.960955	−	0.276705i	$-0.0892423\pi$
$449$	27.1040	+	14.2253i	1.27912	+	0.671332i	0.318161	+	0.948037i	$0.396935\pi$
$450$	0.370631	−	3.05242i	0.0174717	−	0.143893i
$451$	8.93071	+	73.5510i	0.420531	+	3.46338i
$452$	0.748031	−	1.97240i	0.0351844	−	0.0927737i
$453$	−4.35166	+	6.30447i	−0.204459	+	0.296210i
$454$	−5.08465	−	4.50461i	−0.238635	−	0.211412i
$455$	−21.5722	+	4.85996i	−1.01132	+	0.227839i
$456$	7.59432	−	6.72798i	0.355637	−	0.315067i
$457$	−4.42539	−	36.4464i	−0.207011	−	1.70489i	−0.612238	−	0.790674i	$-0.709730\pi$
$457$	−4.42539	−	36.4464i	−0.207011	−	1.70489i	0.405227	−	0.914216i	$-0.367193\pi$
$458$	−2.72277	−	22.4240i	−0.127226	−	1.04780i
$459$	2.59854	−	1.36382i	0.121290	−	0.0636577i
$460$	1.90450	−	0.999557i	0.0887976	−	0.0466046i
$461$	−15.5670	−	3.83693i	−0.725030	−	0.178704i	−0.140505	−	0.990080i	$-0.544873\pi$
$461$	−15.5670	−	3.83693i	−0.725030	−	0.178704i	−0.584524	+	0.811376i	$0.698719\pi$
$462$	24.4373	−	21.6496i	1.13693	−	1.00723i
$463$	−16.5904	−	4.08916i	−0.771020	−	0.190039i	−0.165867	−	0.986148i	$-0.553042\pi$
$463$	−16.5904	−	4.08916i	−0.771020	−	0.190039i	−0.605154	+	0.796109i	$0.706888\pi$
$464$	−6.06814	−	16.0004i	−0.281707	−	0.742799i
$465$	−12.2654	+	6.43737i	−0.568793	+	0.298526i
$466$	0.218083	−	1.79608i	0.0101025	−	0.0832017i
$467$	−24.1156	+	5.94397i	−1.11594	+	0.275054i	−0.753822	−	0.657079i	$-0.771792\pi$
$467$	−24.1156	+	5.94397i	−1.11594	+	0.275054i	−0.362116	+	0.932133i	$0.617946\pi$
$468$	0.619420	+	0.571355i	0.0286327	+	0.0264109i
$469$	12.9643	+	3.19542i	0.598637	+	0.147551i
$470$	−7.20678	+	19.0027i	−0.332424	+	0.876529i
$471$	−15.3083	−	13.5620i	−0.705371	−	0.624904i
$472$	28.7338	−	7.08225i	1.32258	−	0.325987i
$473$	16.4942	+	23.8959i	0.758402	+	1.09874i
$474$	−0.215465	−	1.77452i	−0.00989664	−	0.0815062i
$475$	−2.80395	−	7.39340i	−0.128654	−	0.339233i
$476$	0.869578	−	2.29289i	0.0398571	−	0.105094i
$477$	7.73824	+	11.2108i	0.354310	+	0.513306i
$478$	−1.81346	−	0.446978i	−0.0829457	−	0.0204443i
$479$	9.84449	+	25.9578i	0.449806	+	1.18604i	0.947801	+	0.318862i	$0.103301\pi$
$479$	9.84449	+	25.9578i	0.449806	+	1.18604i	−0.497995	+	0.867180i	$0.665930\pi$
$480$	−0.800272	+	2.11014i	−0.0365272	+	0.0963144i
$481$	3.76013	−	9.34452i	0.171447	−	0.426073i
$482$	−0.797224	−	2.10211i	−0.0363126	−	0.0957484i
$483$	14.3566	−	12.7188i	0.653246	−	0.578726i
$484$	6.15415			0.279734
$485$	−11.2023			−0.508670
$486$	1.11870	−	0.991079i	0.0507451	−	0.0449563i
$487$	20.2609	−	10.6338i	0.918110	−	0.481861i	0.0616636	−	0.998097i	$-0.480359\pi$
$487$	20.2609	−	10.6338i	0.918110	−	0.481861i	0.856447	+	0.516236i	$0.172667\pi$
$488$	1.66365			0.0753098
$489$	−14.6785	−	7.70389i	−0.663786	−	0.348382i
$490$	11.0964	+	9.83059i	0.501286	+	0.444101i
$491$	1.68471	+	2.44072i	0.0760299	+	0.110148i	0.859154	−	0.511717i	$-0.170990\pi$
$491$	1.68471	+	2.44072i	0.0760299	+	0.110148i	−0.783124	+	0.621865i	$0.786375\pi$
$492$	2.12141	+	1.87941i	0.0956406	+	0.0847302i
$493$	−6.46482	−	9.36590i	−0.291161	−	0.421819i
$494$	20.0057	+	5.35911i	0.900100	+	0.241118i
$495$	−5.95393	+	8.62575i	−0.267609	+	0.387699i
$496$	−34.5982	+	8.52770i	−1.55351	+	0.382905i
$497$	−33.7364	+	29.8879i	−1.51329	+	1.34065i
$498$	0.149992	+	0.0369698i	0.00672132	+	0.00165666i
$499$	−19.3357	−	17.1300i	−0.865587	−	0.766843i	0.108242	−	0.994125i	$-0.465478\pi$
$499$	−19.3357	−	17.1300i	−0.865587	−	0.766843i	−0.973829	+	0.227282i	$0.927016\pi$
$500$	2.11790	+	1.87630i	0.0947154	+	0.0839105i
$501$	0.824084	−	2.17293i	0.0368173	−	0.0970794i
$502$	20.7974	−	30.1303i	0.928236	−	1.34478i
$503$	−31.0562	−	16.2995i	−1.38473	−	0.726761i	−0.402670	−	0.915345i	$-0.631918\pi$
$503$	−31.0562	−	16.2995i	−1.38473	−	0.726761i	−0.982057	+	0.188585i	$0.939610\pi$
$504$	−1.13762	+	9.36916i	−0.0506737	+	0.417335i
$505$	30.3540	+	7.48159i	1.35074	+	0.332926i
$506$	48.9890			2.17783
$507$	2.08366	−	12.8319i	0.0925385	−	0.569886i
$508$	−1.59893			−0.0709409
$509$	13.9889	+	3.44794i	0.620045	+	0.152827i	0.536811	−	0.843703i	$-0.319629\pi$
$509$	13.9889	+	3.44794i	0.620045	+	0.152827i	0.0832343	+	0.996530i	$0.473475\pi$
$510$	−0.906913	+	7.46910i	−0.0401588	+	0.330737i
$511$	−17.3436	−	9.10261i	−0.767235	−	0.402676i
$512$	9.93691	−	14.3961i	0.439153	−	0.636224i
$513$	1.36289	−	3.59365i	0.0601732	−	0.158664i
$514$	19.1799	+	16.9919i	0.845987	+	0.749479i
$515$	12.1362	+	10.7517i	0.534784	+	0.473778i
$516$	1.07841	+	0.265805i	0.0474745	+	0.0117014i
$517$	−36.2533	+	32.1176i	−1.59442	+	1.41253i
$518$	−14.4939	+	3.57243i	−0.636825	+	0.156963i
$519$	5.27970	−	7.64897i	0.231753	−	0.335753i
$520$	15.9281	−	3.58841i	0.698494	−	0.157362i
$521$	10.0298	+	14.5306i	0.439412	+	0.636599i	0.978645	−	0.205558i	$-0.0659010\pi$
$521$	10.0298	+	14.5306i	0.439412	+	0.636599i	−0.539233	+	0.842157i	$0.681286\pi$
$522$	−4.33818	−	3.84329i	−0.189877	−	0.168216i
$523$	−17.3623	−	25.1537i	−0.759201	−	1.09989i	−0.991860	−	0.127334i	$-0.959358\pi$
$523$	−17.3623	−	25.1537i	−0.759201	−	1.09989i	0.232659	−	0.972558i	$-0.425257\pi$
$524$	−0.0457312	−	0.0405143i	−0.00199778	−	0.00176987i
$525$	6.51298	+	3.41828i	0.284250	+	0.149186i
$526$	−15.9340			−0.694757
$527$	−20.9833	+	11.0129i	−0.914049	+	0.479730i
$528$	−20.1814	+	17.8791i	−0.878281	+	0.778089i
$529$	5.78028			0.251317
$530$	−34.9243			−1.51702
$531$	8.39121	−	7.43396i	0.364147	−	0.322606i
$532$	−1.13884	−	3.00288i	−0.0493750	−	0.130191i
$533$	6.14023	−	43.2889i	0.265963	−	1.87505i
$534$	1.97910	−	5.21847i	0.0856442	−	0.225825i
$535$	−5.67029	−	14.9513i	−0.245148	−	0.646403i
$536$	−9.57235	−	2.35937i	−0.413463	−	0.101909i
$537$	−2.81495	−	4.07817i	−0.121474	−	0.175986i
$538$	−1.84949	+	4.87670i	−0.0797371	+	0.210249i
$539$	12.5280	+	33.0337i	0.539621	+	1.42286i
$540$	0.0483265	+	0.398004i	0.00207964	+	0.0171274i
$541$	14.1590	+	20.5129i	0.608743	+	0.881917i	0.999252	−	0.0386823i	$-0.0123160\pi$
$541$	14.1590	+	20.5129i	0.608743	+	0.881917i	−0.390508	+	0.920599i	$0.627701\pi$
$542$	−1.62790	+	0.401241i	−0.0699242	+	0.0172348i
$543$	18.0875	+	16.0241i	0.776209	+	0.687661i
$544$	−1.36909	+	3.60998i	−0.0586991	+	0.154777i
$545$	−3.16849	−	0.780961i	−0.135723	−	0.0334527i
$546$	−17.2354	+	8.60914i	−0.737609	+	0.368437i
$547$	15.6039	−	3.84603i	0.667177	−	0.164444i	0.108841	−	0.994059i	$-0.465286\pi$
$547$	15.6039	−	3.84603i	0.667177	−	0.164444i	0.558336	+	0.829615i	$0.311440\pi$
$548$	0.186645	−	1.53716i	0.00797309	−	0.0656643i
$549$	0.558026	−	0.292875i	0.0238160	−	0.0124996i
$550$	6.66199	+	17.5662i	0.284068	+	0.749026i
$551$	−14.4712	−	3.56684i	−0.616495	−	0.151952i
$552$	−10.6003	+	9.39107i	−0.451180	+	0.399711i
$553$	4.15185	+	1.02334i	0.176555	+	0.0435168i
$554$	10.8831	−	5.71187i	0.462377	−	0.242674i
$555$	4.24335	−	2.22708i	0.180120	−	0.0945344i
$556$	−0.345335	−	2.84409i	−0.0146455	−	0.120616i
$557$	5.03098	+	41.4338i	0.213169	+	1.75561i	0.570192	+	0.821511i	$0.306869\pi$
$557$	5.03098	+	41.4338i	0.213169	+	1.75561i	−0.357023	+	0.934096i	$0.616208\pi$
$558$	−9.03352	+	8.00300i	−0.382420	+	0.338794i
$559$	−5.75314	−	16.1396i	−0.243332	−	0.682633i
$560$	−20.2576	−	17.9467i	−0.856040	−	0.758385i
$561$	−10.1858	+	14.7567i	−0.430047	+	0.623030i
$562$	−8.71903	+	22.9902i	−0.367790	+	0.969782i
$563$	0.665458	+	5.48054i	0.0280457	+	0.230977i	0.999991	−	0.00422959i	$-0.00134633\pi$
$563$	0.665458	+	5.48054i	0.0280457	+	0.230977i	−0.971945	+	0.235207i	$0.924423\pi$
$564$	−0.223320	+	1.83921i	−0.00940348	+	0.0774446i
$565$	−13.7093	−	7.19519i	−0.576754	−	0.302704i
$566$	3.40386	−	4.93134i	0.143075	−	0.207280i
$567$	1.26780	+	3.34290i	0.0532424	+	0.140389i
$568$	24.9097	−	22.0681i	1.04519	−	0.925955i
$569$	6.76285	−	9.79768i	0.283514	−	0.410740i	−0.655191	−	0.755463i	$-0.727412\pi$
$569$	6.76285	−	9.79768i	0.283514	−	0.410740i	0.938704	+	0.344723i	$0.112027\pi$
$570$	5.59756	+	8.10946i	0.234456	+	0.339668i
$571$	−0.722804	−	5.95283i	−0.0302484	−	0.249118i	−0.999988	−	0.00497503i	$-0.998416\pi$
$571$	−0.722804	−	5.95283i	−0.0302484	−	0.249118i	0.969739	−	0.244143i	$-0.0785067\pi$
$572$	−4.97343	−	1.33228i	−0.207950	−	0.0557052i
$573$	−0.771975	+	6.35779i	−0.0322497	+	0.265600i
$574$	−57.3742	+	30.1123i	−2.39475	+	1.25686i
$575$	3.91382	+	10.3199i	0.163217	+	0.430369i
$576$	0.826808	−	6.80937i	0.0344503	−	0.283724i
$577$	−14.7229			−0.612923			−0.306461	−	0.951883i	$-0.599145\pi$
$577$	−14.7229			−0.612923			−0.306461	+	0.951883i	$0.599145\pi$
$578$	1.51102	−	12.4444i	0.0628501	−	0.517617i
$579$	−0.878410	−	1.27260i	−0.0365055	−	0.0528873i
$580$	1.50957	−	0.372076i	0.0626816	−	0.0154496i
$581$	−0.209925	+	0.304129i	−0.00870916	+	0.0126174i
$582$	−9.47643	+	2.33573i	−0.392811	+	0.0968192i
$583$	−73.6967	−	38.6790i	−3.05220	−	1.60192i
$584$	12.8058	+	6.72102i	0.529909	+	0.278118i
$585$	4.71094	−	4.00768i	0.194773	−	0.165697i
$586$	30.2783	−	15.8913i	1.25079	−	0.656463i
$587$	4.92361			0.203219			0.101610	−	0.994824i	$-0.467601\pi$
$587$	4.92361			0.203219			0.101610	+	0.994824i	$0.467601\pi$
$588$	1.19665	+	0.628048i	0.0493488	+	0.0259003i
$589$	−11.0054	+	29.0189i	−0.453470	+	1.19570i
$590$	3.46441	+	28.5320i	0.142627	+	1.17464i
$591$	−14.6611	+	3.61365i	−0.603079	+	0.148646i
$592$	11.9697	−	2.95026i	0.491950	−	0.121255i
$593$	2.33160	+	19.2025i	0.0957475	+	0.788551i	0.958927	+	0.283654i	$0.0915467\pi$
$593$	2.33160	+	19.2025i	0.0957475	+	0.788551i	−0.863179	+	0.504898i	$0.831530\pi$
$594$	−3.23814	+	8.53827i	−0.132862	+	0.350330i
$595$	−15.9369	−	8.36433i	−0.653349	−	0.342904i
$596$	2.49711			0.102286
$597$	−22.9708	+	12.0560i	−0.940132	+	0.493419i
$598$	−27.9245	−	7.48037i	−1.14192	−	0.305895i
$599$	16.8476	+	8.84233i	0.688376	+	0.361288i	0.772365	−	0.635179i	$-0.219074\pi$
$599$	16.8476	+	8.84233i	0.688376	+	0.361288i	−0.0839888	+	0.996467i	$0.526766\pi$
$600$	−4.80894	−	2.52392i	−0.196324	−	0.103039i
$601$	−5.00993	+	1.23484i	−0.204359	+	0.0503701i	−0.340166	−	0.940365i	$-0.610483\pi$
$601$	−5.00993	+	1.23484i	−0.204359	+	0.0503701i	0.135807	+	0.990735i	$0.456637\pi$
$602$	−14.4249	+	20.8981i	−0.587915	+	0.851742i
$603$	−3.62614	+	0.893764i	−0.147668	+	0.0363969i
$604$	−1.01707	−	1.47348i	−0.0413840	−	0.0599551i
$605$	5.44453	−	44.8397i	0.221352	−	1.82299i
$606$	27.2375			1.10645
$607$	0.285777	−	2.35359i	0.0115993	−	0.0955292i	−0.985759	−	0.168162i	$-0.946217\pi$
$607$	0.285777	−	2.35359i	0.0115993	−	0.0955292i	0.997359	+	0.0726325i	$0.0231400\pi$
$608$	1.79302	+	4.72780i	0.0727165	+	0.191738i
$609$	12.2763	−	6.44310i	0.497460	−	0.261087i
$610$	−0.194756	+	1.60396i	−0.00788543	+	0.0649424i
$611$	25.5691	−	12.7718i	1.03442	−	0.516693i
$612$	0.0826758	+	0.680897i	0.00334197	+	0.0275236i
$613$	21.0484	+	30.4938i	0.850135	+	1.23163i	0.971027	+	0.238968i	$0.0768091\pi$
$613$	21.0484	+	30.4938i	0.850135	+	1.23163i	−0.120892	+	0.992666i	$0.538575\pi$
$614$	8.74928	−	12.6755i	0.353092	−	0.511542i
$615$	15.5703	−	13.7941i	0.627856	−	0.556232i
$616$	−20.4484	−	53.9181i	−0.823890	−	2.17242i
$617$	17.0350	−	24.6794i	0.685802	−	0.993556i	−0.313234	−	0.949676i	$-0.601413\pi$
$617$	17.0350	−	24.6794i	0.685802	−	0.993556i	0.999037	−	0.0438803i	$-0.0139720\pi$
$618$	12.5082	+	6.56483i	0.503155	+	0.264076i
$619$	1.41124	−	11.6226i	0.0567227	−	0.467153i	−0.936477	−	0.350729i	$-0.885934\pi$
$619$	1.41124	−	11.6226i	0.0567227	−	0.467153i	0.993200	−	0.116424i	$-0.0371432\pi$
$620$	−0.390238	−	3.21390i	−0.0156723	−	0.129073i
$621$	−1.90236	+	5.01611i	−0.0763390	+	0.201289i
$622$	−0.680641	+	0.986079i	−0.0272912	+	0.0395382i
$623$	9.99338	+	8.85336i	0.400376	+	0.354702i
$624$	14.2337	−	7.10978i	0.569805	−	0.284619i
$625$	7.84481	−	6.94990i	0.313792	−	0.277996i
$626$	1.85249	+	15.2566i	0.0740404	+	0.609778i
$627$	2.83056	+	23.3118i	0.113042	+	0.930982i
$628$	4.23246	−	2.22137i	0.168894	−	0.0886422i
$629$	7.25943	−	3.81004i	0.289453	−	0.151916i
$630$	−8.89983	−	2.19361i	−0.354578	−	0.0873956i
$631$	−14.5440	+	12.8848i	−0.578986	+	0.512937i	−0.901012	−	0.433794i	$-0.857175\pi$
$631$	−14.5440	+	12.8848i	−0.578986	+	0.512937i	0.322026	+	0.946731i	$0.395636\pi$
$632$	−3.06556	−	0.755594i	−0.121942	−	0.0300559i
$633$	2.97229	+	7.83729i	0.118138	+	0.311504i
$634$	17.6762	−	9.27718i	0.702011	−	0.368444i
$635$	−1.41456	+	11.6499i	−0.0561350	+	0.462313i
$636$	−3.09125	+	0.761925i	−0.122576	+	0.0302123i
$637$	−2.09709	−	20.7427i	−0.0830899	−	0.821856i
$638$	34.3827	+	8.47456i	1.36122	+	0.335511i
$639$	4.47035	−	11.7873i	0.176844	−	0.466300i
$640$	16.5418	+	14.6548i	0.653874	+	0.579281i
$641$	−22.8798	+	5.63936i	−0.903697	+	0.222741i	−0.663670	−	0.748025i	$-0.731002\pi$
$641$	−22.8798	+	5.63936i	−0.903697	+	0.222741i	−0.240026	+	0.970766i	$0.577156\pi$
$642$	−7.91414	−	11.4656i	−0.312346	−	0.452512i
$643$	−5.55121	−	45.7183i	−0.218918	−	1.80295i	−0.525163	−	0.851001i	$-0.675996\pi$
$643$	−5.55121	−	45.7183i	−0.218918	−	1.80295i	0.306245	−	0.951953i	$-0.400927\pi$
$644$	1.58962	+	4.19148i	0.0626398	+	0.165168i
$645$	2.89075	−	7.62227i	0.113823	−	0.300127i
$646$	9.57617	+	13.8735i	0.376770	+	0.545845i
$647$	−0.997359	−	0.245827i	−0.0392102	−	0.00966445i	0.219662	−	0.975576i	$-0.429505\pi$
$647$	−0.997359	−	0.245827i	−0.0392102	−	0.00966445i	−0.258872	+	0.965912i	$0.583351\pi$
$648$	−0.936092	−	2.46827i	−0.0367732	−	0.0969629i
$649$	−24.2889	+	64.0445i	−0.953422	+	2.51397i
$650$	−1.11516	−	11.0303i	−0.0437403	−	0.432643i
$651$	−10.2375	−	26.9941i	−0.401240	−	1.05798i
$652$	2.90008	−	2.56925i	0.113576	−	0.100620i
$653$	−14.1873			−0.555191			−0.277596	−	0.960698i	$-0.589538\pi$
$653$	−14.1873			−0.555191			−0.277596	+	0.960698i	$0.589538\pi$
$654$	−2.84317			−0.111177
$655$	−0.335649	+	0.297359i	−0.0131149	+	0.0116188i
$656$	47.3820	−	24.8680i	1.84996	−	0.970932i
$657$	5.47856			0.213739
$658$	−37.5058	−	19.6846i	−1.46213	−	0.767385i
$659$	9.80222	+	8.68401i	0.381840	+	0.338281i	0.832109	−	0.554612i	$-0.187133\pi$
$659$	9.80222	+	8.68401i	0.381840	+	0.338281i	−0.450269	+	0.892893i	$0.648672\pi$
$660$	−1.39155	−	2.01601i	−0.0541662	−	0.0784732i
$661$	3.50553	+	3.10563i	0.136349	+	0.120795i	0.728541	−	0.685002i	$-0.240199\pi$
$661$	3.50553	+	3.10563i	0.136349	+	0.120795i	−0.592192	+	0.805797i	$0.701737\pi$
$662$	1.72739	+	2.50256i	0.0671370	+	0.0972647i
$663$	8.05937	−	6.85625i	0.313000	−	0.266275i
$664$	0.155001	−	0.224557i	0.00601519	−	0.00871451i
$665$	−22.8868	+	5.64108i	−0.887510	+	0.218752i
$666$	3.12525	−	2.76873i	0.121101	−	0.107286i
$667$	20.1993	+	4.97868i	0.782120	+	0.192775i
$668$	0.406557	+	0.360178i	0.0157301	+	0.0139357i
$669$	18.2547	+	16.1722i	0.705766	+	0.625254i
$670$	3.39531	−	8.95271i	0.131172	−	0.345873i
$671$	−2.18737	+	3.16895i	−0.0844424	+	0.122336i
$672$	−4.16481	−	2.18586i	−0.160661	−	0.0843214i
$673$	−3.45995	+	28.4953i	−0.133371	+	1.09841i	0.760262	+	0.649616i	$0.225070\pi$
$673$	−3.45995	+	28.4953i	−0.133371	+	1.09841i	−0.893634	+	0.448797i	$0.851853\pi$
$674$	−46.7718	−	11.5282i	−1.80158	−	0.444051i
$675$	−2.05735			−0.0791874
$676$	2.63150	+	1.51884i	0.101212	+	0.0584167i
$677$	19.1740			0.736918			0.368459	−	0.929644i	$-0.379885\pi$
$677$	19.1740			0.736918			0.368459	+	0.929644i	$0.379885\pi$
$678$	−13.0974	−	3.22823i	−0.503004	−	0.123979i
$679$	2.81424	−	23.1774i	0.108001	−	0.889466i
$680$	11.7672	+	6.17590i	0.451251	+	0.236835i
$681$	−2.58194	+	3.74059i	−0.0989403	+	0.143340i
$682$	26.1481	−	68.9469i	1.00126	−	2.64011i
$683$	−3.76279	−	3.33354i	−0.143979	−	0.127554i	0.588059	−	0.808818i	$-0.299892\pi$
$683$	−3.76279	−	3.33354i	−0.143979	−	0.127554i	−0.732038	+	0.681264i	$0.761431\pi$
$684$	0.672375	+	0.595672i	0.0257089	+	0.0227761i
$685$	−11.0348	−	2.71983i	−0.421618	−	0.103919i
$686$	4.87025	−	4.31466i	0.185947	−	0.164735i
$687$	−14.6747	+	3.61699i	−0.559875	+	0.137997i
$688$	11.9127	−	17.2585i	0.454167	−	0.657974i
$689$	36.1022	+	33.3007i	1.37538	+	1.26866i
$690$	−7.81320	−	11.3194i	−0.297444	−	0.430921i
$691$	−2.59086	−	2.29530i	−0.0985608	−	0.0873173i	0.612403	−	0.790545i	$-0.290203\pi$
$691$	−2.59086	−	2.29530i	−0.0985608	−	0.0873173i	−0.710964	+	0.703228i	$0.751741\pi$
$692$	1.23397	+	1.78772i	0.0469086	+	0.0679589i
$693$	−16.3508	−	14.4856i	−0.621116	−	0.550261i
$694$	23.1155	+	12.1320i	0.877453	+	0.460523i
$695$	−21.0278			−0.797630
$696$	−9.06434	+	4.75733i	−0.343583	+	0.180326i
$697$	26.6374	−	23.5987i	1.00896	−	0.893863i
$698$	48.6197			1.84028
$699$	−1.21057			−0.0457878
$700$	−1.28679	+	1.14000i	−0.0486361	+	0.0430878i
$701$	5.74444	+	15.1468i	0.216965	+	0.572089i	0.998670	−	0.0515594i	$-0.0164191\pi$
$701$	5.74444	+	15.1468i	0.216965	+	0.572089i	−0.781705	+	0.623648i	$0.785650\pi$
$702$	3.14954	−	4.37250i	0.118872	−	0.165029i
$703$	3.80745	−	10.0394i	0.143601	−	0.378644i
$704$	14.8616	+	39.1869i	0.560119	+	1.47691i
$705$	13.2031	+	3.25427i	0.497257	+	0.122563i
$706$	−5.39249	−	7.81237i	−0.202949	−	0.294022i
$707$	−23.1048	+	60.9225i	−0.868947	+	2.29122i
$708$	0.929111	+	2.44986i	0.0349181	+	0.0920715i
$709$	−2.02454	−	16.6736i	−0.0760333	−	0.626190i	−0.980058	−	0.198711i	$-0.936325\pi$
$709$	−2.02454	−	16.6736i	−0.0760333	−	0.626190i	0.904025	−	0.427480i	$-0.140598\pi$
$710$	18.3602	+	26.5994i	0.689047	+	0.998257i
$711$	−1.16128	+	0.286230i	−0.0435514	+	0.0107344i
$712$	−7.37873	−	6.53698i	−0.276529	−	0.244984i
$713$	15.3616	−	40.5053i	0.575297	−	1.51693i
$714$	−15.2256	−	3.75278i	−0.569805	−	0.140444i
$715$	−14.1070	+	35.0582i	−0.527573	+	1.31110i
$716$	1.12451	−	0.277167i	0.0420249	−	0.0103582i
$717$	−0.150633	+	1.24057i	−0.00562549	+	0.0463300i
$718$	−33.2601	+	17.4562i	−1.24126	+	0.651461i
$719$	−12.3139	−	32.4691i	−0.459231	−	1.21089i	−0.942139	−	0.335222i	$-0.891189\pi$
$719$	−12.3139	−	32.4691i	−0.459231	−	1.21089i	0.482908	−	0.875671i	$-0.339581\pi$
$720$	7.34985	+	1.81157i	0.273913	+	0.0675134i
$721$	−25.2940	+	22.4085i	−0.941998	+	0.834538i
$722$	−6.13566	−	1.51230i	−0.228346	−	0.0562822i
$723$	−1.33195	+	0.699062i	−0.0495358	+	0.0259984i
$724$	−5.00085	+	2.62465i	−0.185855	+	0.0975443i
$725$	0.961663	+	7.92001i	0.0357153	+	0.294142i
$726$	−4.74357	−	39.0668i	−0.176050	−	1.44991i
$727$	39.1159	−	34.6536i	1.45073	−	1.28523i	0.561730	−	0.827321i	$-0.310136\pi$
$727$	39.1159	−	34.6536i	1.45073	−	1.28523i	0.888998	−	0.457911i	$-0.151402\pi$
$728$	3.42290	+	33.8565i	0.126861	+	1.25481i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	−7.97900	+	11.5596i	−0.295316	+	0.427839i
$731$	4.94542	−	13.0400i	0.182913	−	0.482302i
$732$	0.0177543	+	0.146220i	0.000656217	+	0.00540443i
$733$	3.96694	−	32.6707i	0.146522	−	1.20672i	−0.715047	−	0.699077i	$-0.753595\pi$
$733$	3.96694	−	32.6707i	0.146522	−	1.20672i	0.861569	−	0.507641i	$-0.169482\pi$
$734$	8.64973	+	4.53973i	0.319267	+	0.167564i
$735$	5.63468	−	8.16324i	0.207838	−	0.301106i
$736$	−2.50274	−	6.59918i	−0.0922522	−	0.243249i
$737$	17.0799	−	15.1315i	0.629147	−	0.557376i
$738$	10.2954	−	14.9154i	0.378978	−	0.549045i
$739$	6.65866	+	9.64674i	0.244943	+	0.354861i	0.926101	−	0.377275i	$-0.123139\pi$
$739$	6.65866	+	9.64674i	0.244943	+	0.354861i	−0.681158	+	0.732136i	$0.738524\pi$
$740$	0.135007	+	1.11189i	0.00496297	+	0.0408738i
$741$	1.94613	−	13.7203i	0.0714927	−	0.504027i
$742$	8.77370	−	72.2580i	0.322093	−	2.65267i
$743$	−12.1013	+	6.35127i	−0.443955	+	0.233005i	−0.671860	−	0.740678i	$-0.734505\pi$
$743$	−12.1013	+	6.35127i	−0.443955	+	0.233005i	0.227906	+	0.973683i	$0.426812\pi$
$744$	7.55898	+	19.9314i	0.277126	+	0.730721i
$745$	2.20918	−	18.1942i	0.0809379	−	0.666584i
$746$	−31.7707			−1.16321
$747$	0.0124589	−	0.102609i	0.000455849	−	0.00375425i
$748$	−2.38064	−	3.44895i	−0.0870448	−	0.126106i
$749$	32.3586	−	7.97568i	1.18236	−	0.291425i
$750$	10.2783	−	14.8908i	0.375312	−	0.543733i
$751$	1.29037	−	0.318047i	0.0470862	−	0.0116057i	−0.215702	−	0.976459i	$-0.569204\pi$
$751$	1.29037	−	0.318047i	0.0470862	−	0.0116057i	0.262788	+	0.964853i	$0.415358\pi$
$752$	30.9739	+	16.2563i	1.12950	+	0.592808i
$753$	−21.6903	−	11.3839i	−0.790437	−	0.414853i
$754$	−18.3046	−	10.0807i	−0.666615	−	0.367117i
$755$	−11.6357	+	6.10690i	−0.423467	+	0.222253i
$756$	−0.835605			−0.0303907
$757$	−14.8458	−	7.79166i	−0.539578	−	0.283193i	0.172837	−	0.984950i	$-0.444707\pi$
$757$	−14.8458	−	7.79166i	−0.539578	−	0.283193i	−0.712416	+	0.701758i	$0.752399\pi$
$758$	−3.98127	+	10.4978i	−0.144606	+	0.381296i
$759$	−3.95096	−	32.5391i	−0.143411	−	1.18110i
$760$	16.8987	−	4.16516i	0.612980	−	0.151086i
$761$	14.2089	−	3.50217i	0.515070	−	0.126953i	0.0267914	−	0.999641i	$-0.491471\pi$
$761$	14.2089	−	3.50217i	0.515070	−	0.126953i	0.488279	+	0.872688i	$0.337625\pi$
$762$	1.23244	+	10.1501i	0.0446466	+	0.367698i
$763$	2.41179	−	6.35936i	0.0873125	−	0.230224i
$764$	−1.32540	−	0.695624i	−0.0479513	−	0.0251668i
$765$	5.03422			0.182013
$766$	16.6488	−	8.73796i	0.601545	−	0.315715i
$767$	23.6243	−	32.7976i	0.853024	−	1.18425i
$768$	4.90159	+	2.57255i	0.176871	+	0.0928290i
$769$	31.1681	+	16.3583i	1.12395	+	0.589894i	0.921104	−	0.389316i	$-0.127289\pi$
$769$	31.1681	+	16.3583i	1.12395	+	0.589894i	0.202846	+	0.979211i	$0.434981\pi$
$770$	54.3774	−	13.4028i	1.95962	−	0.483004i
$771$	9.73937	−	14.1099i	0.350755	−	0.508156i
$772$	0.350905	−	0.0864902i	0.0126293	−	0.00311285i
$773$	−0.712911	−	1.03283i	−0.0256416	−	0.0371483i	0.809953	−	0.586494i	$-0.199492\pi$
$773$	−0.712911	−	1.03283i	−0.0256416	−	0.0371483i	−0.835595	+	0.549346i	$0.814877\pi$
$774$	0.856110	−	7.05070i	0.0307722	−	0.253432i
$775$	16.6132			0.596763
$776$	−2.07793	+	17.1133i	−0.0745933	+	0.614331i
$777$	3.54179	+	9.33892i	0.127061	+	0.335032i
$778$	27.7437	−	14.5610i	0.994661	−	0.522038i
$779$	5.61781	−	46.2668i	0.201279	−	1.65768i
$780$	0.485372	+	1.36164i	0.0173791	+	0.0487546i
$781$	9.28436	+	76.4636i	0.332221	+	2.73608i
$782$	−13.3667	−	19.3649i	−0.477990	−	0.692489i
$783$	−2.20289	+	3.19144i	−0.0787249	+	0.114053i
$784$	19.0992	−	16.9204i	0.682115	−	0.604301i
$785$	−12.4407	−	32.8033i	−0.444027	−	1.17080i
$786$	−0.221937	+	0.321531i	−0.00791624	+	0.0114686i
$787$	7.40705	+	3.88752i	0.264033	+	0.138575i	0.591545	−	0.806272i	$-0.298518\pi$
$787$	7.40705	+	3.88752i	0.264033	+	0.138575i	−0.327513	+	0.944847i	$0.606210\pi$
$788$	0.425393	−	3.50342i	0.0151540	−	0.124804i
$789$	1.28508	+	10.5836i	0.0457501	+	0.376786i
$790$	1.08736	−	2.86712i	0.0386864	−	0.102008i
$791$	18.3308	−	26.5567i	0.651768	−	0.944249i
$792$	12.0728	+	10.6956i	0.428989	+	0.380051i
$793$	1.73072	−	1.47235i	0.0614595	−	0.0522847i
$794$	−28.1902	+	24.9744i	−1.00043	+	0.886308i
$795$	2.81665	+	23.1972i	0.0998963	+	0.822720i
$796$	−0.730844	−	6.01904i	−0.0259041	−	0.213339i
$797$	−28.4587	+	14.9363i	−1.00806	+	0.529070i	−0.886114	−	0.463467i	$-0.846605\pi$
$797$	−28.4587	+	14.9363i	−1.00806	+	0.529070i	−0.121944	+	0.992537i	$0.538913\pi$
$798$	−18.1846	+	9.54400i	−0.643727	+	0.337854i
$799$	22.5875	+	5.56732i	0.799089	+	0.196958i
$800$	2.02595	−	1.79484i	0.0716283	−	0.0634571i
$801$	−3.62579	−	0.893677i	−0.128111	−	0.0315765i
$802$	−13.0149	−	34.3174i	−0.459571	−	1.21179i
$803$	−29.6395	+	15.5560i	−1.04595	+	0.548959i
$804$	0.105212	−	0.866503i	0.00371056	−	0.0305592i
$805$	31.9459	−	7.87395i	1.12594	−	0.277520i
$806$	−25.4327	+	35.3081i	−0.895828	+	1.24368i
$807$	3.38833	+	0.835148i	0.119275	+	0.0293986i
$808$	17.0597	−	44.9828i	0.600159	−	1.58249i
$809$	−2.80759	−	2.48731i	−0.0987095	−	0.0874490i	0.612325	−	0.790606i	$-0.290234\pi$
$809$	−2.80759	−	2.48731i	−0.0987095	−	0.0874490i	−0.711034	+	0.703157i	$0.751773\pi$
$810$	2.48930	−	0.613557i	0.0874650	−	0.0215582i
$811$	−28.7501	−	41.6516i	−1.00955	−	1.46259i	−0.882284	−	0.470718i	$-0.843995\pi$
$811$	−28.7501	−	41.6516i	−1.00955	−	1.46259i	−0.127267	−	0.991868i	$-0.540621\pi$
$812$	0.390585	+	3.21676i	0.0137069	+	0.112886i
$813$	0.397800	+	1.04891i	0.0139514	+	0.0367869i
$814$	−9.04625	+	23.8530i	−0.317071	+	0.836047i
$815$	−16.1541	−	23.4033i	−0.565854	−	0.819780i
$816$	12.5740	+	3.09920i	0.440176	+	0.108494i
$817$	−6.47676	−	17.0778i	−0.226593	−	0.597477i
$818$	7.65220	−	20.1772i	0.267553	−	0.705479i
$819$	7.10834	+	10.7537i	0.248386	+	0.375764i
$820$	1.72401	+	4.54585i	0.0602052	+	0.158748i
$821$	38.6297	−	34.2229i	1.34819	−	1.19439i	0.385839	−	0.922566i	$-0.373912\pi$
$821$	38.6297	−	34.2229i	1.34819	−	1.19439i	0.962347	−	0.271822i	$-0.0876263\pi$
$822$	−9.90184			−0.345366
$823$	−15.2985			−0.533270			−0.266635	−	0.963798i	$-0.585912\pi$
$823$	−15.2985			−0.533270			−0.266635	+	0.963798i	$0.585912\pi$
$824$	18.6761	−	16.5456i	0.650614	−	0.576394i
$825$	11.1304	−	5.84170i	0.387512	−	0.203382i
$826$	−59.9026			−2.08428
$827$	37.3185	+	19.5863i	1.29769	+	0.681082i	0.965073	−	0.261979i	$-0.0843752\pi$
$827$	37.3185	+	19.5863i	1.29769	+	0.681082i	0.332619	+	0.943061i	$0.392068\pi$
$828$	−0.938517	−	0.831453i	−0.0326157	−	0.0288950i
$829$	8.02751	+	11.6298i	0.278807	+	0.403921i	0.937222	−	0.348734i	$-0.113388\pi$
$829$	8.02751	+	11.6298i	0.278807	+	0.403921i	−0.658415	+	0.752655i	$0.728773\pi$
$830$	0.198355	+	0.175727i	0.00688501	+	0.00609959i
$831$	−4.67162	−	6.76801i	−0.162057	−	0.234780i
$832$	−2.48772	−	24.6064i	−0.0862461	−	0.853074i
$833$	9.63968	−	13.9655i	0.333995	−	0.483876i
$834$	−17.7882	+	4.38440i	−0.615956	+	0.151819i
$835$	2.98397	−	2.64356i	0.103264	−	0.0914843i
$836$	−5.32897	−	1.31347i	−0.184306	−	0.0454274i
$837$	6.04426	+	5.35474i	0.208920	+	0.185087i
$838$	−3.45440	−	3.06033i	−0.119330	−	0.105717i
$839$	2.50757	−	6.61191i	0.0865708	−	0.228268i	−0.884739	−	0.466087i	$-0.845663\pi$
$839$	2.50757	−	6.61191i	0.0865708	−	0.228268i	0.971310	+	0.237819i	$0.0764325\pi$
$840$	−9.19699	+	13.3241i	−0.317326	+	0.459727i
$841$	−12.3627	−	6.48845i	−0.426300	−	0.223740i
$842$	−5.49848	+	45.2841i	−0.189490	+	1.56059i
$843$	15.9736	+	3.93713i	0.550159	+	0.135602i
$844$	−1.95904			−0.0674329
$845$	13.3944	−	17.8297i	0.460783	−	0.613359i
$846$	11.8475			0.407326
$847$	91.4050	+	22.5293i	3.14071	+	0.774116i
$848$	−7.24569	+	59.6736i	−0.248818	+	2.04920i
$849$	−3.54998	−	1.86317i	−0.121835	−	0.0639439i
$850$	5.12606	−	7.42637i	0.175822	−	0.254722i
$851$	−5.31453	+	14.0133i	−0.182180	+	0.480369i
$852$	2.20542	+	1.95383i	0.0755564	+	0.0669371i
$853$	−4.10979	−	3.64095i	−0.140716	−	0.124664i	0.589828	−	0.807529i	$-0.299195\pi$
$853$	−4.10979	−	3.64095i	−0.140716	−	0.124664i	−0.730545	+	0.682865i	$0.760734\pi$
$854$	−3.26964	−	0.805894i	−0.111885	−	0.0275771i
$855$	4.93497	−	4.37200i	0.168772	−	0.149519i
$856$	−23.8923	+	5.88893i	−0.816623	+	0.201280i
$857$	17.9893	−	26.0620i	0.614502	−	0.890260i	−0.384964	−	0.922932i	$-0.625786\pi$
$857$	17.9893	−	26.0620i	0.614502	−	0.890260i	0.999466	+	0.0326713i	$0.0104015\pi$
$858$	−4.62386	+	32.5985i	−0.157856	+	1.11289i
$859$	21.6766	+	31.4040i	0.739597	+	1.07149i	0.994522	+	0.104530i	$0.0333339\pi$
$859$	21.6766	+	31.4040i	0.739597	+	1.07149i	−0.254925	+	0.966961i	$0.582051\pi$
$860$	1.42613	+	1.26344i	0.0486307	+	0.0430830i
$861$	24.6282	+	35.6801i	0.839328	+	1.21598i
$862$	22.5320	+	19.9617i	0.767445	+	0.679897i
$863$	−11.5239	−	6.04820i	−0.392278	−	0.205883i	0.257039	−	0.966401i	$-0.417253\pi$
$863$	−11.5239	−	6.04820i	−0.392278	−	0.205883i	−0.649317	+	0.760518i	$0.724945\pi$
$864$	1.31560			0.0447576
$865$	14.1172	−	7.40927i	0.479999	−	0.251923i
$866$	−39.6279	+	35.1072i	−1.34661	+	1.19299i
$867$	−8.38757			−0.284857
$868$	6.74755			0.229027
$869$	5.46988	−	4.84589i	0.185553	−	0.164386i
$870$	−3.52553	−	9.29605i	−0.119527	−	0.315165i
$871$	−12.0463	+	6.01717i	−0.408174	+	0.203884i
$872$	−1.78077	+	4.69550i	−0.0603045	+	0.159010i
$873$	2.31570	+	6.10600i	0.0783745	+	0.206657i
$874$	−29.9207	−	7.37480i	−1.01208	−	0.249456i
$875$	24.5875	+	35.6211i	0.831208	+	1.20421i
$876$	−0.454054	+	1.19724i	−0.0153411	+	0.0404511i
$877$	19.4052	+	51.1673i	0.655266	+	1.72780i	0.685314	+	0.728247i	$0.259665\pi$
$877$	19.4052	+	51.1673i	0.655266	+	1.72780i	−0.0300480	+	0.999548i	$0.509566\pi$
$878$	0.968953	+	7.98005i	0.0327006	+	0.269314i
$879$	−12.9972	−	18.8296i	−0.438383	−	0.635108i
$880$	−44.9071	+	11.0686i	−1.51382	+	0.373122i
$881$	−28.1909	−	24.9750i	−0.949776	−	0.841428i	0.0376849	−	0.999290i	$-0.488002\pi$
$881$	−28.1909	−	24.9750i	−0.949776	−	0.841428i	−0.987461	+	0.157861i	$0.949540\pi$
$882$	3.06451	−	8.08045i	0.103187	−	0.272083i
$883$	−44.6466	−	11.0044i	−1.50248	−	0.370327i	−0.599626	−	0.800280i	$-0.704684\pi$
$883$	−44.6466	−	11.0044i	−1.50248	−	0.370327i	−0.902851	+	0.429953i	$0.858530\pi$
$884$	0.830364	+	2.32947i	0.0279282	+	0.0783485i
$885$	18.6719	−	4.60221i	0.627649	−	0.154702i
$886$	0.273309	−	2.25090i	0.00918200	−	0.0756206i
$887$	−20.5113	+	10.7652i	−0.688703	+	0.361459i	−0.772492	−	0.635024i	$-0.780990\pi$
$887$	−20.5113	+	10.7652i	−0.688703	+	0.361459i	0.0837893	+	0.996483i	$0.473298\pi$
$888$	−2.61512	−	6.89550i	−0.0877576	−	0.231398i
$889$	−23.7482	−	5.85340i	−0.796488	−	0.196317i
$890$	7.16624	−	6.34873i	0.240213	−	0.212810i
$891$	5.93239	+	1.46220i	0.198743	+	0.0489856i
$892$	−5.04707	+	2.64891i	−0.168988	+	0.0886919i
$893$	26.9772	−	14.1587i	0.902757	−	0.473803i
$894$	−1.92475	−	15.8518i	−0.0643734	−	0.530163i
$895$	−1.02462	−	8.43849i	−0.0342492	−	0.282068i
$896$	−34.4762	+	30.5432i	−1.15177	+	1.02038i
$897$	−2.71645	+	19.1511i	−0.0906996	+	0.639437i
$898$	34.2435	+	30.3371i	1.14272	+	1.01236i
$899$	17.7884	−	25.7710i	0.593278	−	0.859511i
$900$	0.170510	−	0.449597i	0.00568366	−	0.0149866i
$901$	4.81866	+	39.6853i	0.160533	+	1.32211i
$902$	−13.3475	+	109.927i	−0.444424	+	3.66016i
$903$	15.0442	+	7.89578i	0.500638	+	0.262755i
$904$	−13.5347	+	19.6085i	−0.450159	+	0.652168i
$905$	14.6992	+	38.7587i	0.488619	+	1.28838i
$906$	−8.56978	+	7.59216i	−0.284712	+	0.252233i
$907$	16.1853	−	23.4484i	0.537424	−	0.778593i	−0.456375	−	0.889788i	$-0.650852\pi$
$907$	16.1853	−	23.4484i	0.537424	−	0.778593i	0.993799	+	0.111195i	$0.0354678\pi$
$908$	−0.603453	−	0.874252i	−0.0200263	−	0.0290131i
$909$	−2.19671	−	18.0915i	−0.0728603	−	0.600058i
$910$	−33.0425	−	0.663337i	−1.09535	−	0.0219894i
$911$	−1.12645	+	9.27713i	−0.0373209	+	0.307365i	0.962080	+	0.272766i	$0.0879385\pi$
$911$	−1.12645	+	9.27713i	−0.0373209	+	0.307365i	−0.999401	+	0.0345990i	$0.988985\pi$
$912$	15.0176	−	7.88183i	0.497281	−	0.260993i
$913$	0.223946	+	0.590497i	0.00741152	+	0.0195426i
$914$	6.61403	−	54.4714i	0.218773	−	1.80176i
$915$	1.08108			0.0357393
$916$	0.425787	−	3.50667i	0.0140684	−	0.115864i
$917$	−0.530909	−	0.769155i	−0.0175322	−	0.0253997i
$918$	4.25864	−	1.04966i	0.140556	−	0.0346439i
$919$	−11.7089	+	16.9633i	−0.386242	+	0.559569i	−0.967087	−	0.254446i	$-0.918107\pi$
$919$	−11.7089	+	16.9633i	−0.386242	+	0.559569i	0.580845	+	0.814014i	$0.302722\pi$
$920$	−23.5876	+	5.81382i	−0.777660	+	0.191676i
$921$	−9.12488	−	4.78910i	−0.300675	−	0.157806i
$922$	−21.2175	−	11.1358i	−0.698761	−	0.366738i
$923$	6.38338	−	45.0031i	0.210111	−	1.48130i
$924$	4.52069	−	2.37264i	0.148720	−	0.0780541i
$925$	−5.74753			−0.188978
$926$	−22.6123	−	11.8678i	−0.743086	−	0.390002i
$927$	3.35166	−	8.83760i	0.110083	−	0.290265i
$928$	−0.614947	−	5.06455i	−0.0201866	−	0.166252i
$929$	0.267604	−	0.0659584i	0.00877979	−	0.00216402i	−0.234923	−	0.972014i	$-0.575484\pi$
$929$	0.267604	−	0.0659584i	0.00877979	−	0.00216402i	0.243703	+	0.969850i	$0.421638\pi$
$930$	−20.1012	+	4.95450i	−0.659144	+	0.162464i
$931$	−2.67879	−	22.0618i	−0.0877937	−	0.723046i
$932$	0.100330	−	0.264548i	0.00328641	−	0.00866556i
$933$	0.709860	+	0.372564i	0.0232398	+	0.0121972i
$934$	−37.1210			−1.21464
$935$	−27.2355	+	14.2943i	−0.890697	+	0.467474i
$936$	−5.24853	−	7.94010i	−0.171554	−	0.259530i
$937$	−34.8605	−	18.2962i	−1.13884	−	0.597711i	−0.213538	−	0.976935i	$-0.568499\pi$
$937$	−34.8605	−	18.2962i	−1.13884	−	0.597711i	−0.925305	+	0.379224i	$0.876191\pi$
$938$	17.6701	+	9.27396i	0.576948	+	0.302805i
$939$	9.98426	−	2.46090i	0.325824	−	0.0803084i
$940$	−1.80541	+	2.61559i	−0.0588860	+	0.0853111i
$941$	25.5615	−	6.30033i	0.833280	−	0.205385i	0.200477	−	0.979698i	$-0.435751\pi$
$941$	25.5615	−	6.30033i	0.833280	−	0.205385i	0.632802	+	0.774313i	$0.281905\pi$
$942$	−17.3637	−	25.1556i	−0.565739	−	0.819615i
$943$	−7.84147	+	64.5803i	−0.255353	+	2.10302i
$944$	49.4700			1.61011
$945$	−0.739253	+	6.08830i	−0.0240479	+	0.198052i
$946$	15.3883	+	40.5757i	0.500318	+	1.31923i
$947$	3.54554	−	1.86084i	0.115215	−	0.0604693i	−0.406131	−	0.913815i	$-0.633122\pi$
$947$	3.54554	−	1.86084i	0.115215	−	0.0604693i	0.521346	+	0.853345i	$0.325430\pi$
$948$	0.0336945	−	0.277499i	0.00109435	−	0.00901275i
$949$	19.2703	−	4.34136i	0.625539	−	0.140926i
$950$	−1.42449	−	11.7317i	−0.0462165	−	0.380627i
$951$	−7.58761	−	10.9926i	−0.246045	−	0.356458i
$952$	−15.7340	+	22.7946i	−0.509942	+	0.738779i
$953$	−8.46722	+	7.50130i	−0.274280	+	0.242991i	−0.789038	−	0.614345i	$-0.789420\pi$
$953$	−8.46722	+	7.50130i	−0.274280	+	0.242991i	0.514758	+	0.857336i	$0.327882\pi$
$954$	7.21944	+	19.0361i	0.233738	+	0.616317i
$955$	−6.24096	+	9.04159i	−0.201953	+	0.292579i
$956$	−0.258621	−	0.135735i	−0.00836440	−	0.00438998i
$957$	2.85595	−	23.5209i	0.0923199	−	0.760322i
$958$	5.00129	+	41.1894i	0.161584	+	1.33077i
$959$	8.39945	−	22.1475i	0.271232	−	0.715181i
$960$	6.68424	−	9.68380i	0.215733	−	0.312543i
$961$	−25.6038	−	22.6830i	−0.825929	−	0.731709i
$962$	8.79873	−	12.2153i	0.283682	−	0.393836i
$963$	−6.97734	+	6.18138i	−0.224842	+	0.199192i
$964$	−0.0423777	−	0.349011i	−0.00136489	−	0.0112409i
$965$	−0.319733	−	2.63324i	−0.0102926	−	0.0847671i
$966$	25.3825	−	13.3217i	0.816667	−	0.428620i
$967$	4.33175	−	2.27348i	0.139300	−	0.0731101i	−0.393633	−	0.919268i	$-0.628782\pi$
$967$	4.33175	−	2.27348i	0.139300	−	0.0731101i	0.532933	+	0.846157i	$0.321090\pi$
$968$	−67.4899	−	16.6348i	−2.16921	−	0.534662i
$969$	8.44263	−	7.47952i	0.271216	−	0.240277i
$970$	−16.2560	−	4.00675i	−0.521949	−	0.128649i
$971$	11.4387	+	30.1615i	0.367087	+	0.967929i	0.983565	+	0.180556i	$0.0577898\pi$
$971$	11.4387	+	30.1615i	0.367087	+	0.967929i	−0.616478	+	0.787372i	$0.711441\pi$
$972$	0.206949	−	0.108615i	0.00663789	−	0.00348384i
$973$	5.28261	−	43.5062i	0.169353	−	1.39475i
$974$	33.2047	−	8.18423i	1.06395	−	0.262240i
$975$	−7.23651	+	1.63030i	−0.231754	+	0.0522113i
$976$	2.70020	+	0.665540i	0.0864314	+	0.0213034i
$977$	12.3945	−	32.6816i	0.396535	−	1.04558i	−0.576940	−	0.816787i	$-0.695753\pi$
$977$	12.3945	−	32.6816i	0.396535	−	1.04558i	0.973475	−	0.228792i	$-0.0734774\pi$
$978$	−18.5451	−	16.4295i	−0.593006	−	0.525357i
$979$	22.1533	−	5.46031i	0.708024	−	0.174512i
$980$	1.31694	+	1.90791i	0.0420681	+	0.0609461i
$981$	0.229302	+	1.88847i	0.00732106	+	0.0602943i
$982$	1.57176	+	4.14439i	0.0501569	+	0.132253i
$983$	1.36599	−	3.60183i	0.0435684	−	0.114881i	−0.911466	−	0.411375i	$-0.865049\pi$
$983$	1.36599	−	3.60183i	0.0435684	−	0.114881i	0.955034	+	0.296495i	$0.0958178\pi$
$984$	−18.1845	−	26.3448i	−0.579702	−	0.839843i
$985$	−25.1499	−	6.19890i	−0.801344	−	0.197513i
$986$	−6.03139	−	15.9035i	−0.192079	−	0.506470i
$987$	−10.0499	+	26.4994i	−0.319892	+	0.843486i
$988$	2.83703	+	1.56241i	0.0902580	+	0.0497068i
$989$	9.04041	+	23.8376i	0.287468	+	0.757992i
$990$	−11.7251	+	10.3876i	−0.372650	+	0.330139i
$991$	41.1143			1.30604			0.653019	−	0.757342i	$-0.273502\pi$
$991$	41.1143			1.30604			0.653019	+	0.757342i	$0.273502\pi$
$992$	−10.6235			−0.337297
$993$	1.52292	−	1.34919i	0.0483284	−	0.0428152i
$994$	−59.6462	+	31.3047i	−1.89186	+	0.992926i
$995$	−44.5019			−1.41080
$996$	0.0213907	+	0.0112267i	0.000677791	+	0.000355732i
$997$	−16.0039	−	14.1782i	−0.506847	−	0.449027i	0.370536	−	0.928818i	$-0.379174\pi$
$997$	−16.0039	−	14.1782i	−0.506847	−	0.449027i	−0.877383	+	0.479791i	$0.840713\pi$
$998$	−21.9318	−	31.7738i	−0.694240	−	1.00578i
$999$	−2.09108	−	1.85254i	−0.0661589	−	0.0586116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.b.40.14	✓	204
169.131	even	13	inner	507.2.m.b.469.14	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.b.40.14	✓	204	1.1	even	1	trivial
507.2.m.b.469.14	yes	204	169.131	even	13	inner

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.45113 + 0.357672i) q^{2} +(0.120537 - 0.992709i) q^{3} +(0.206949 + 0.108615i) q^{4} +(0.974467 - 1.41176i) q^{5} +(0.529980 - 1.39744i) q^{6} +(2.67610 + 2.37082i) q^{7} +(-1.97593 - 1.75052i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})\)	\(q+(1.45113 + 0.357672i) q^{2} +(0.120537 - 0.992709i) q^{3} +(0.206949 + 0.108615i) q^{4} +(0.974467 - 1.41176i) q^{5} +(0.529980 - 1.39744i) q^{6} +(2.67610 + 2.37082i) q^{7} +(-1.97593 - 1.75052i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(1.91903 - 1.70011i) q^{10} +(5.93239 - 1.46220i) q^{11} +(0.132768 - 0.192348i) q^{12} +(-3.60482 - 0.0723678i) q^{13} +(3.03541 + 4.39755i) q^{14} +(-1.28401 - 1.13753i) q^{15} +(-2.50676 - 3.63168i) q^{16} +(-2.19665 - 1.94606i) q^{17} +(-1.32337 - 0.694558i) q^{18} -3.84341 q^{19} +(0.355004 - 0.186320i) q^{20} +(2.67610 - 2.37082i) q^{21} +9.13168 q^{22} +5.36473 q^{23} +(-1.97593 + 1.75052i) q^{24} +(0.729546 + 1.92366i) q^{25} +(-5.20520 - 1.39436i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(0.296310 + 0.781305i) q^{28} +(3.76521 + 0.928040i) q^{29} +(-1.45640 - 2.10996i) q^{30} +(2.86345 - 7.55030i) q^{31} +(-0.466518 - 1.23011i) q^{32} +(-0.736471 - 6.06538i) q^{33} +(-2.49158 - 3.60968i) q^{34} +(5.95480 - 1.46773i) q^{35} +(-0.174942 - 0.154985i) q^{36} +(-0.990644 + 2.61211i) q^{37} +(-5.57731 - 1.37468i) q^{38} +(-0.506354 + 3.56982i) q^{39} +(-4.39680 + 1.08371i) q^{40} +(-1.46167 + 12.0379i) q^{41} +(4.73136 - 2.48321i) q^{42} +(1.68516 + 4.44340i) q^{43} +(1.38652 + 0.341746i) q^{44} +(-1.28401 + 1.13753i) q^{45} +(7.78494 + 1.91881i) q^{46} +(-7.01907 + 3.68389i) q^{47} +(-3.90735 + 2.05074i) q^{48} +(0.696981 + 5.74016i) q^{49} +(0.370631 + 3.05242i) q^{50} +(-2.19665 + 1.94606i) q^{51} +(-0.738155 - 0.406515i) q^{52} +(-10.1963 - 9.03313i) q^{53} +(-0.849009 + 1.23000i) q^{54} +(3.71664 - 9.79997i) q^{55} +(-1.13762 - 9.36916i) q^{56} +(-0.463272 + 3.81539i) q^{57} +(5.13188 + 2.69342i) q^{58} +(-6.36831 + 9.22609i) q^{59} +(-0.142171 - 0.374874i) q^{60} +(-0.471721 + 0.417909i) q^{61} +(6.85578 - 9.93232i) q^{62} +(-2.03097 - 2.94236i) q^{63} +(0.826808 + 6.80937i) q^{64} +(-3.61495 + 5.01862i) q^{65} +(1.10070 - 9.06510i) q^{66} +(3.30688 - 1.73559i) q^{67} +(-0.243223 - 0.641325i) q^{68} +(0.646646 - 5.32561i) q^{69} +9.16618 q^{70} +(-1.51955 + 12.5146i) q^{71} +(1.49959 + 2.17253i) q^{72} +(-5.31937 + 1.31111i) q^{73} +(-2.37184 + 3.43620i) q^{74} +(1.99757 - 0.492356i) q^{75} +(-0.795390 - 0.417453i) q^{76} +(19.3423 + 10.1516i) q^{77} +(-2.01161 + 4.99918i) q^{78} +(1.05904 - 0.555825i) q^{79} -7.56981 q^{80} +(0.885456 + 0.464723i) q^{81} +(-6.42672 + 16.9459i) q^{82} +(0.0124589 + 0.102609i) q^{83} +(0.811324 - 0.199973i) q^{84} +(-4.88793 + 1.20477i) q^{85} +(0.856110 + 7.05070i) q^{86} +(1.37512 - 3.62589i) q^{87} +(-14.2816 - 7.49557i) q^{88} +3.73430 q^{89} +(-2.27013 + 1.19146i) q^{90} +(-9.47531 - 8.74006i) q^{91} +(1.11022 + 0.582691i) q^{92} +(-7.15009 - 3.75266i) q^{93} +(-11.5032 + 2.83529i) q^{94} +(-3.74528 + 5.42597i) q^{95} +(-1.27737 + 0.314843i) q^{96} +(-3.70967 - 5.37438i) q^{97} +(-1.04168 + 8.57903i) q^{98} -6.10993 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Introduction

L-functions

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