LMFDB - Embedded newform 171.2.x.a.110.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(14,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([15, 7]))

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

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

chi := DirichletCharacter("171.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.x (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			110.4
Character	$\chi$	$=$	171.110
Dual form			171.2.x.a.14.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50803 + 1.26539i) q^{2} +(-1.01330 + 1.40472i) q^{3} +(0.325651 - 1.84686i) q^{4} +(1.48603 - 4.08283i) q^{5} +(-0.249426 - 3.40056i) q^{6} +(-0.0709257 - 0.122847i) q^{7} +(-0.122694 - 0.212511i) q^{8} +(-0.946454 - 2.84679i) q^{9} +O(q^{10})$	\(q+(-1.50803 + 1.26539i) q^{2} +(-1.01330 + 1.40472i) q^{3} +(0.325651 - 1.84686i) q^{4} +(1.48603 - 4.08283i) q^{5} +(-0.249426 - 3.40056i) q^{6} +(-0.0709257 - 0.122847i) q^{7} +(-0.122694 - 0.212511i) q^{8} +(-0.946454 - 2.84679i) q^{9} +(2.92538 + 8.03742i) q^{10} -3.16400i q^{11} +(2.26433 + 2.32886i) q^{12} +(-0.419951 - 1.15381i) q^{13} +(0.262407 + 0.0955082i) q^{14} +(4.22943 + 6.22457i) q^{15} +(3.97844 + 1.44803i) q^{16} +(-0.619138 + 1.70107i) q^{17} +(5.02957 + 3.09541i) q^{18} +(3.16043 + 3.00195i) q^{19} +(-7.05648 - 4.07406i) q^{20} +(0.244434 + 0.0248501i) q^{21} +(4.00369 + 4.77141i) q^{22} +(-2.14224 - 0.377734i) q^{23} +(0.422843 + 0.0429878i) q^{24} +(-10.6310 - 8.92047i) q^{25} +(2.09331 + 1.20857i) q^{26} +(4.95797 + 1.55515i) q^{27} +(-0.249978 + 0.0909845i) q^{28} +(0.884375 - 5.01554i) q^{29} +(-14.2546 - 4.03497i) q^{30} -8.26801i q^{31} +(-7.37074 + 2.68273i) q^{32} +(4.44453 + 3.20608i) q^{33} +(-1.21883 - 3.34871i) q^{34} +(-0.606961 + 0.107024i) q^{35} +(-5.56583 + 0.820907i) q^{36} -0.413061i q^{37} +(-8.56464 - 0.527860i) q^{38} +(2.04631 + 0.579238i) q^{39} +(-1.04997 + 0.185139i) q^{40} +(-3.55993 + 2.98714i) q^{41} +(-0.400058 + 0.271829i) q^{42} +(1.32771 + 7.52984i) q^{43} +(-5.84347 - 1.03036i) q^{44} +(-13.0294 - 0.366202i) q^{45} +(3.70853 - 2.14112i) q^{46} +(12.2375 + 2.15781i) q^{47} +(-6.06542 + 4.12129i) q^{48} +(3.48994 - 6.04475i) q^{49} +27.3197 q^{50} +(-1.76215 - 2.59340i) q^{51} +(-2.26767 + 0.399852i) q^{52} +(-0.614881 - 0.515946i) q^{53} +(-9.44463 + 3.92854i) q^{54} +(-12.9181 - 4.70180i) q^{55} +(-0.0174042 + 0.0301450i) q^{56} +(-7.41934 + 1.39764i) q^{57} +(5.01293 + 8.68265i) q^{58} +(0.650462 + 3.68895i) q^{59} +(12.8732 - 5.78412i) q^{60} +(6.52236 - 2.37394i) q^{61} +(10.4622 + 12.4684i) q^{62} +(-0.282592 + 0.318180i) q^{63} +(3.48683 - 6.03936i) q^{64} -5.33486 q^{65} +(-10.7594 + 0.789185i) q^{66} +(-2.01606 + 2.40265i) q^{67} +(2.94001 + 1.69742i) q^{68} +(2.70133 - 2.62648i) q^{69} +(0.779888 - 0.929434i) q^{70} +(-5.89164 + 4.94368i) q^{71} +(-0.488852 + 0.550415i) q^{72} +(-0.787319 - 4.46511i) q^{73} +(0.522681 + 0.622907i) q^{74} +(23.3031 - 5.89445i) q^{75} +(6.57337 - 4.85928i) q^{76} +(-0.388688 + 0.224409i) q^{77} +(-3.81885 + 1.71586i) q^{78} +(0.163949 - 0.450445i) q^{79} +(11.8241 - 14.0915i) q^{80} +(-7.20845 + 5.38872i) q^{81} +(1.58859 - 9.00937i) q^{82} +(-7.22014 + 4.16855i) q^{83} +(0.125495 - 0.443342i) q^{84} +(6.02512 + 5.05567i) q^{85} +(-11.5304 - 9.67514i) q^{86} +(6.14928 + 6.32453i) q^{87} +(-0.672387 + 0.388203i) q^{88} +(-0.225886 + 1.28106i) q^{89} +(20.1121 - 15.9350i) q^{90} +(-0.111956 + 0.133424i) q^{91} +(-1.39524 + 3.83340i) q^{92} +(11.6142 + 8.37796i) q^{93} +(-21.1850 + 12.2312i) q^{94} +(16.9529 - 8.44251i) q^{95} +(3.70028 - 13.0722i) q^{96} +(6.74465 + 8.03796i) q^{97} +(2.38602 + 13.5318i) q^{98} +(-9.00726 + 2.99459i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) $ 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−1.50803	+	1.26539i	−1.06634	+	0.894763i	−0.994716	−	0.102669i	$-0.967262\pi$
$2$	−1.50803	+	1.26539i	−1.06634	+	0.894763i	−0.0716212	+	0.997432i	$0.522817\pi$
$3$	−1.01330	+	1.40472i	−0.585028	+	0.811013i
$3$	−1.01330	+	1.40472i	−0.585028	+	0.811013i
$4$	0.325651	−	1.84686i	0.162825	−	0.923429i
$5$	1.48603	−	4.08283i	0.664572	−	1.82590i	0.109695	−	0.993965i	$-0.465013\pi$
$5$	1.48603	−	4.08283i	0.664572	−	1.82590i	0.554877	−	0.831932i	$-0.312765\pi$
$6$	−0.249426	−	3.40056i	−0.101828	−	1.38827i
$7$	−0.0709257	−	0.122847i	−0.0268074	−	0.0464318i	0.852310	−	0.523036i	$-0.175201\pi$
$7$	−0.0709257	−	0.122847i	−0.0268074	−	0.0464318i	−0.879118	+	0.476604i	$0.841867\pi$
$8$	−0.122694	−	0.212511i	−0.0433787	−	0.0751342i
$9$	−0.946454	−	2.84679i	−0.315485	−	0.948931i
$10$	2.92538	+	8.03742i	0.925087	+	2.54166i
$11$		−	3.16400i		−	0.953983i	−0.878908	−	0.476992i	$-0.841727\pi$
$11$		−	3.16400i		−	0.953983i	0.878908	−	0.476992i	$-0.158273\pi$
$12$	2.26433	+	2.32886i	0.653656	+	0.672285i
$13$	−0.419951	−	1.15381i	−0.116474	−	0.320008i	0.867733	−	0.497030i	$-0.165576\pi$
$13$	−0.419951	−	1.15381i	−0.116474	−	0.320008i	−0.984207	+	0.177021i	$0.943354\pi$
$14$	0.262407	+	0.0955082i	0.0701311	+	0.0255256i
$15$	4.22943	+	6.22457i	1.09203	+	1.60718i
$16$	3.97844	+	1.44803i	0.994609	+	0.362008i
$17$	−0.619138	+	1.70107i	−0.150163	+	0.412570i	−0.991852	−	0.127392i	$-0.959339\pi$
$17$	−0.619138	+	1.70107i	−0.150163	+	0.412570i	0.841689	+	0.539962i	$0.181561\pi$
$18$	5.02957	+	3.09541i	1.18548	+	0.729596i
$19$	3.16043	+	3.00195i	0.725052	+	0.688694i
$19$	3.16043	+	3.00195i	0.725052	+	0.688694i
$20$	−7.05648	−	4.07406i	−1.57788	−	0.910988i
$21$	0.244434	+	0.0248501i	0.0533398	+	0.00542273i
$22$	4.00369	+	4.77141i	0.853589	+	1.01727i
$23$	−2.14224	−	0.377734i	−0.446687	−	0.0787630i	−0.0542200	−	0.998529i	$-0.517267\pi$
$23$	−2.14224	−	0.377734i	−0.446687	−	0.0787630i	−0.392467	+	0.919766i	$0.628378\pi$
$24$	0.422843	+	0.0429878i	0.0863126	+	0.00877486i
$25$	−10.6310	−	8.92047i	−2.12620	−	1.78409i
$26$	2.09331	+	1.20857i	0.410532	+	0.237021i
$27$	4.95797	+	1.55515i	0.954163	+	0.299289i
$28$	−0.249978	+	0.0909845i	−0.0472414	+	0.0171944i
$29$	0.884375	−	5.01554i	0.164224	−	0.931363i	−0.785636	−	0.618689i	$-0.787664\pi$
$29$	0.884375	−	5.01554i	0.164224	−	0.931363i	0.949861	−	0.312674i	$-0.101225\pi$
$30$	−14.2546	−	4.03497i	−2.60252	−	0.736682i
$31$		−	8.26801i		−	1.48498i	−0.669858	−	0.742489i	$-0.733645\pi$
$31$		−	8.26801i		−	1.48498i	0.669858	−	0.742489i	$-0.266355\pi$
$32$	−7.37074	+	2.68273i	−1.30297	+	0.474244i
$33$	4.44453	+	3.20608i	0.773693	+	0.558107i
$34$	−1.21883	−	3.34871i	−0.209028	−	0.574299i
$35$	−0.606961	+	0.107024i	−0.102595	+	0.0180903i
$36$	−5.56583	+	0.820907i	−0.927639	+	0.136818i
$37$		−	0.413061i		−	0.0679068i	−0.999423	−	0.0339534i	$-0.989190\pi$
$37$		−	0.413061i		−	0.0679068i	0.999423	−	0.0339534i	$-0.0108098\pi$
$38$	−8.56464	−	0.527860i	−1.38937	−	0.0856302i
$39$	2.04631	+	0.579238i	0.327671	+	0.0927523i
$40$	−1.04997	+	0.185139i	−0.166016	+	0.0292730i
$41$	−3.55993	+	2.98714i	−0.555968	+	0.466512i	−0.876956	−	0.480571i	$-0.840429\pi$
$41$	−3.55993	+	2.98714i	−0.555968	+	0.466512i	0.320988	+	0.947083i	$0.395985\pi$
$42$	−0.400058	+	0.271829i	−0.0617303	+	0.0419440i
$43$	1.32771	+	7.52984i	0.202474	+	1.14829i	0.901365	+	0.433061i	$0.142566\pi$
$43$	1.32771	+	7.52984i	0.202474	+	1.14829i	−0.698890	+	0.715229i	$0.746322\pi$
$44$	−5.84347	−	1.03036i	−0.880936	−	0.155333i
$45$	−13.0294	−	0.366202i	−1.94231	−	0.0545901i
$46$	3.70853	−	2.14112i	0.546793	−	0.315691i
$47$	12.2375	+	2.15781i	1.78503	+	0.314749i	0.965911	−	0.258876i	$-0.0833521\pi$
$47$	12.2375	+	2.15781i	1.78503	+	0.314749i	0.819118	+	0.573625i	$0.194463\pi$
$48$	−6.06542	+	4.12129i	−0.875468	+	0.594856i
$49$	3.48994	−	6.04475i	0.498563	−	0.863536i
$50$	27.3197			3.86359
$51$	−1.76215	−	2.59340i	−0.246750	−	0.363149i
$52$	−2.26767	+	0.399852i	−0.314470	+	0.0554495i
$53$	−0.614881	−	0.515946i	−0.0844604	−	0.0708707i	0.599580	−	0.800315i	$-0.295334\pi$
$53$	−0.614881	−	0.515946i	−0.0844604	−	0.0708707i	−0.684040	+	0.729444i	$0.739779\pi$
$54$	−9.44463	+	3.92854i	−1.28525	+	0.534607i
$55$	−12.9181	−	4.70180i	−1.74188	−	0.633991i
$56$	−0.0174042	+	0.0301450i	−0.00232574	+	0.00402830i
$57$	−7.41934	+	1.39764i	−0.982716	+	0.185122i
$58$	5.01293	+	8.68265i	0.658230	+	1.14009i
$59$	0.650462	+	3.68895i	0.0846829	+	0.480261i	0.997425	+	0.0717235i	$0.0228499\pi$
$59$	0.650462	+	3.68895i	0.0846829	+	0.480261i	−0.912742	+	0.408537i	$0.866039\pi$
$60$	12.8732	−	5.78412i	1.66193	−	0.746726i
$61$	6.52236	−	2.37394i	0.835103	−	0.303952i	0.111151	−	0.993804i	$-0.464546\pi$
$61$	6.52236	−	2.37394i	0.835103	−	0.303952i	0.723951	+	0.689851i	$0.242324\pi$
$62$	10.4622	+	12.4684i	1.32870	+	1.58349i
$63$	−0.282592	+	0.318180i	−0.0356032	+	0.0400869i
$64$	3.48683	−	6.03936i	0.435853	−	0.754920i
$65$	−5.33486			−0.661708
$66$	−10.7594	+	0.789185i	−1.32439	+	0.0971419i
$67$	−2.01606	+	2.40265i	−0.246301	+	0.293530i	−0.875004	−	0.484115i	$-0.839142\pi$
$67$	−2.01606	+	2.40265i	−0.246301	+	0.293530i	0.628703	+	0.777645i	$0.283586\pi$
$68$	2.94001	+	1.69742i	0.356528	+	0.205842i
$69$	2.70133	−	2.62648i	0.325202	−	0.316191i
$70$	0.779888	−	0.929434i	0.0932144	−	0.111089i
$71$	−5.89164	+	4.94368i	−0.699210	+	0.586706i	−0.921549	−	0.388263i	$-0.873075\pi$
$71$	−5.89164	+	4.94368i	−0.699210	+	0.586706i	0.222339	+	0.974969i	$0.428631\pi$
$72$	−0.488852	+	0.550415i	−0.0576118	+	0.0648671i
$73$	−0.787319	−	4.46511i	−0.0921488	−	0.522602i	−0.995584	−	0.0938766i	$-0.970074\pi$
$73$	−0.787319	−	4.46511i	−0.0921488	−	0.522602i	0.903435	−	0.428725i	$-0.141037\pi$
$74$	0.522681	+	0.622907i	0.0607604	+	0.0724115i
$75$	23.3031	−	5.89445i	2.69081	−	0.680632i
$76$	6.57337	−	4.85928i	0.754017	−	0.557397i
$77$	−0.388688	+	0.224409i	−0.0442951	+	0.0255738i
$78$	−3.81885	+	1.71586i	−0.432399	+	0.194283i
$79$	0.163949	−	0.450445i	0.0184457	−	0.0506790i	−0.930128	−	0.367235i	$-0.880304\pi$
$79$	0.163949	−	0.450445i	0.0184457	−	0.0506790i	0.948574	+	0.316556i	$0.102527\pi$
$80$	11.8241	−	14.0915i	1.32198	−	1.57547i
$81$	−7.20845	+	5.38872i	−0.800939	+	0.598746i
$82$	1.58859	−	9.00937i	0.175431	−	0.994918i
$83$	−7.22014	+	4.16855i	−0.792513	+	0.457558i	−0.840847	−	0.541273i	$-0.817942\pi$
$83$	−7.22014	+	4.16855i	−0.792513	+	0.457558i	0.0483332	+	0.998831i	$0.484609\pi$
$84$	0.125495	−	0.443342i	0.0136926	−	0.0483726i
$85$	6.02512	+	5.05567i	0.653516	+	0.548365i
$86$	−11.5304	−	9.67514i	−1.24335	−	1.04330i
$87$	6.14928	+	6.32453i	0.659272	+	0.678061i
$88$	−0.672387	+	0.388203i	−0.0716767	+	0.0413826i
$89$	−0.225886	+	1.28106i	−0.0239438	+	0.135792i	−0.994436	−	0.105339i	$-0.966407\pi$
$89$	−0.225886	+	1.28106i	−0.0239438	+	0.135792i	0.970493	+	0.241131i	$0.0775184\pi$
$90$	20.1121	−	15.9350i	2.12000	−	1.67970i
$91$	−0.111956	+	0.133424i	−0.0117362	+	0.0139867i
$92$	−1.39524	+	3.83340i	−0.145464	+	0.399659i
$93$	11.6142	+	8.37796i	1.20434	+	0.868754i
$94$	−21.1850	+	12.2312i	−2.18507	+	1.26155i
$95$	16.9529	−	8.44251i	1.73933	−	0.866184i
$96$	3.70028	−	13.0722i	0.377658	−	1.33418i
$97$	6.74465	+	8.03796i	0.684816	+	0.816132i	0.990718	−	0.135931i	$-0.0434026\pi$
$97$	6.74465	+	8.03796i	0.684816	+	0.816132i	−0.305903	+	0.952063i	$0.598958\pi$
$98$	2.38602	+	13.5318i	0.241024	+	1.36692i
$99$	−9.00726	+	2.99459i	−0.905264	+	0.300967i
$100$	−19.9368	+	16.7290i	−1.99368	+	1.67290i
$101$	−2.35427	+	2.80571i	−0.234259	+	0.279179i	−0.870348	−	0.492437i	$-0.836106\pi$
$101$	−2.35427	+	2.80571i	−0.234259	+	0.279179i	0.636090	+	0.771615i	$0.280551\pi$
$102$	5.93902	+	1.68113i	0.588051	+	0.166457i
$103$	−9.65468	−	5.57413i	−0.951304	−	0.549236i	−0.0578182	−	0.998327i	$-0.518414\pi$
$103$	−9.65468	−	5.57413i	−0.951304	−	0.549236i	−0.893486	+	0.449092i	$0.851748\pi$
$104$	−0.193672	+	0.230809i	−0.0189911	+	0.0226327i
$105$	0.464694	−	0.961054i	0.0453495	−	0.0937893i
$106$	1.58013			0.153476
$107$	2.98126	−	5.16370i	0.288210	−	0.499194i	−0.685173	−	0.728381i	$-0.740273\pi$
$107$	2.98126	−	5.16370i	0.288210	−	0.499194i	0.973382	+	0.229187i	$0.0736067\pi$
$108$	4.48671	−	8.65024i	0.431734	−	0.832370i
$109$	9.10817	+	10.8547i	0.872404	+	1.03969i	0.998861	+	0.0477190i	$0.0151952\pi$
$109$	9.10817	+	10.8547i	0.872404	+	1.03969i	−0.126456	+	0.991972i	$0.540360\pi$
$110$	25.4304	−	9.25592i	2.42470	−	0.882518i
$111$	0.580233	+	0.418554i	0.0550733	+	0.0397273i
$112$	−0.104287	−	0.591441i	−0.00985420	−	0.0558860i
$113$	−5.79498	−	10.0372i	−0.545146	−	0.944220i	−0.998598	−	0.0529396i	$-0.983141\pi$
$113$	−5.79498	−	10.0372i	−0.545146	−	0.944220i	0.453452	−	0.891281i	$-0.350192\pi$
$114$	9.42002	−	11.4960i	0.882266	−	1.07670i
$115$	−4.72565	+	8.18506i	−0.440669	+	0.763261i
$116$	−8.97499	−	3.26663i	−0.833307	−	0.303299i
$117$	−2.88718	+	2.28754i	−0.266920	+	0.211483i
$118$	−5.64886	−	4.73996i	−0.520020	−	0.436349i
$119$	0.252884	−	0.0445902i	0.0231818	−	0.00408758i
$120$	0.803870	−	1.66252i	0.0733829	−	0.151766i
$121$	0.989076			0.0899160
$122$	−6.83194	+	11.8333i	−0.618535	+	1.07133i
$123$	−0.588808	−	8.02755i	−0.0530910	−	0.723820i
$124$	−15.2698	−	2.69248i	−1.37127	−	0.241792i
$125$	−33.4050	+	19.2864i	−2.98783	+	1.72502i
$126$	0.0235361	−	0.837411i	0.00209676	−	0.0746025i
$127$	15.1084	+	2.66403i	1.34066	+	0.236394i	0.797542	−	0.603264i	$-0.206133\pi$
$127$	15.1084	+	2.66403i	1.34066	+	0.236394i	0.543116	+	0.839658i	$0.317245\pi$
$128$	−0.340226	−	1.92952i	−0.0300720	−	0.170547i
$129$	−11.9227	−	5.76491i	−1.04973	−	0.507572i
$130$	8.04511	−	6.75065i	0.705603	−	0.592071i
$131$	−2.36813	+	0.417565i	−0.206905	+	0.0364829i	−0.276140	−	0.961118i	$-0.589055\pi$
$131$	−2.36813	+	0.417565i	−0.206905	+	0.0364829i	0.0692351	+	0.997600i	$0.477944\pi$
$132$	7.36854	−	7.16435i	0.641349	−	0.623577i
$133$	0.144624	−	0.601164i	0.0125405	−	0.0521275i
$134$		−	6.17436i		−	0.533384i
$135$	13.7171	−	17.9316i	1.18058	−	1.54330i
$136$	0.437461	−	0.0771362i	0.0375120	−	0.00661437i
$137$	3.91642	+	10.7603i	0.334602	+	0.919312i	0.986898	+	0.161347i	$0.0515840\pi$
$137$	3.91642	+	10.7603i	0.334602	+	0.919312i	−0.652295	+	0.757965i	$0.726194\pi$
$138$	−0.750179	+	7.37903i	−0.0638595	+	0.628144i
$139$	−14.0807	+	5.12497i	−1.19431	+	0.434694i	−0.861236	−	0.508206i	$-0.830309\pi$
$139$	−14.0807	+	5.12497i	−1.19431	+	0.434694i	−0.333076	+	0.942900i	$0.608087\pi$
$140$			1.15582i			0.0976848i
$141$	−15.4314	+	15.0038i	−1.29956	+	1.26355i
$142$	2.62911	−	14.9104i	0.220630	−	1.25125i
$143$	−3.65065	+	1.32873i	−0.305283	+	0.111114i
$144$	0.356838	−	12.6963i	0.0297365	−	1.05802i
$145$	−19.1634	−	11.0640i	−1.59143	−	0.918815i
$146$	6.83738	+	5.73725i	0.565866	+	0.474818i
$147$	4.95481	+	11.0275i	0.408666	+	0.909534i
$148$	−0.762864	−	0.134514i	−0.0627071	−	0.0110569i
$149$	11.3574	+	13.5352i	0.930435	+	1.10885i	0.993836	+	0.110861i	$0.0353607\pi$
$149$	11.3574	+	13.5352i	0.930435	+	1.10885i	−0.0634013	+	0.997988i	$0.520195\pi$
$150$	−27.6830	+	38.3764i	−2.26031	+	3.13342i
$151$	4.67744	+	2.70052i	0.380645	+	0.219765i	0.678099	−	0.734971i	$-0.262804\pi$
$151$	4.67744	+	2.70052i	0.380645	+	0.219765i	−0.297454	+	0.954736i	$0.596137\pi$
$152$	0.250184	−	1.03995i	0.0202926	−	0.0843508i
$153$	5.42857	+	0.152574i	0.438874	+	0.0123349i
$154$	0.302188	−	0.830256i	0.0243510	−	0.0669039i
$155$	−33.7569	−	12.2865i	−2.71142	−	0.986875i
$156$	1.73615	−	3.59061i	0.139003	−	0.287479i
$157$	−0.679787	−	0.247422i	−0.0542529	−	0.0197465i	0.314751	−	0.949174i	$-0.398079\pi$
$157$	−0.679787	−	0.247422i	−0.0542529	−	0.0197465i	−0.369004	+	0.929428i	$0.620301\pi$
$158$	0.322748	+	0.886742i	0.0256764	+	0.0705454i
$159$	1.34782	−	0.340926i	0.106889	−	0.0270372i
$160$			34.0801i			2.69427i
$161$	0.105536	+	0.289958i	0.00831741	+	0.0228519i
$162$	4.05173	−	17.2478i	0.318334	−	1.35512i
$163$	−6.23499	−	10.7993i	−0.488362	−	0.845868i	0.511549	−	0.859254i	$-0.329072\pi$
$163$	−6.23499	−	10.7993i	−0.488362	−	0.845868i	−0.999910	+	0.0133868i	$0.995739\pi$
$164$	4.35752	+	7.54745i	0.340265	+	0.589357i
$165$	19.6946	−	13.3819i	1.53322	−	1.04178i
$166$	5.61335	−	15.4226i	0.435680	−	1.19702i
$167$	0.935142	−	5.30345i	0.0723635	−	0.410394i	−0.927011	−	0.375034i	$-0.877631\pi$
$167$	0.935142	−	5.30345i	0.0723635	−	0.410394i	0.999375	−	0.0353599i	$-0.0112577\pi$
$168$	−0.0247095	−	0.0549939i	−0.00190638	−	0.00424287i
$169$	8.80367	−	7.38715i	0.677205	−	0.568243i
$170$	−15.4834			−1.18752
$171$	5.55472	−	11.8383i	0.424780	−	0.905297i
$172$	14.3389			1.09333
$173$	9.19911	−	7.71897i	0.699396	−	0.586863i	−0.222206	−	0.975000i	$-0.571326\pi$
$173$	9.19911	−	7.71897i	0.699396	−	0.586863i	0.921602	+	0.388137i	$0.126881\pi$
$174$	−17.2763	−	1.75637i	−1.30971	−	0.133150i
$175$	−0.341841	+	1.93868i	−0.0258407	+	0.146550i
$176$	4.58158	−	12.5878i	0.345350	−	0.948841i
$177$	−5.84104	−	2.82429i	−0.439040	−	0.212287i
$178$	−1.28040	−	2.21771i	−0.0959697	−	0.166224i
$179$	6.49431	+	11.2485i	0.485408	+	0.840751i	0.999859	−	0.0167685i	$-0.00533783\pi$
$179$	6.49431	+	11.2485i	0.485408	+	0.840751i	−0.514452	+	0.857519i	$0.672004\pi$
$180$	−4.91937	+	23.9443i	−0.366668	+	1.78470i
$181$	−3.80245	−	10.4472i	−0.282634	−	0.776531i	−0.997046	−	0.0768057i	$-0.975528\pi$
$181$	−3.80245	−	10.4472i	−0.282634	−	0.776531i	0.714412	−	0.699725i	$-0.246694\pi$
$182$		−	0.342875i		−	0.0254156i
$183$	−3.27438	+	11.5676i	−0.242049	+	0.855100i
$184$	0.182566	+	0.501595i	0.0134589	+	0.0369781i
$185$	−1.68646	−	0.613820i	−0.123991	−	0.0451289i
$186$	−28.1159	+	2.06226i	−2.06156	+	0.151212i
$187$	5.38219	+	1.95896i	0.393585	+	0.143253i
$188$	7.97033	−	21.8983i	0.581296	−	1.59710i
$189$	−0.160603	−	0.719372i	−0.0116821	−	0.0523266i
$190$	−14.8825	+	34.1835i	−1.07969	+	2.47993i
$191$	13.0070	+	7.50960i	0.941154	+	0.543375i	0.890322	−	0.455332i	$-0.150479\pi$
$191$	13.0070	+	7.50960i	0.941154	+	0.543375i	0.0508320	+	0.998707i	$0.483813\pi$
$192$	4.95039	+	11.0177i	0.357264	+	0.795132i
$193$	15.1001	+	17.9955i	1.08693	+	1.29535i	0.952538	+	0.304418i	$0.0984621\pi$
$193$	15.1001	+	17.9955i	1.08693	+	1.29535i	0.134387	+	0.990929i	$0.457093\pi$
$194$	−20.3422	−	3.58689i	−1.46049	−	0.257523i
$195$	5.40580	−	7.49396i	0.387117	−	0.536654i
$196$	−10.0273	−	8.41390i	−0.716235	−	0.600993i
$197$	17.9775	+	10.3793i	1.28085	+	0.739496i	0.977003	−	0.213226i	$-0.0683970\pi$
$197$	17.9775	+	10.3793i	1.28085	+	0.739496i	0.303842	+	0.952722i	$0.401730\pi$
$198$	9.79390	−	15.9136i	0.696022	−	1.13093i
$199$	12.9905	−	4.72814i	0.920870	−	0.335169i	0.162285	−	0.986744i	$-0.448113\pi$
$199$	12.9905	−	4.72814i	0.920870	−	0.335169i	0.758585	+	0.651575i	$0.225891\pi$
$200$	−0.591347	+	3.35369i	−0.0418145	+	0.237142i
$201$	−1.33217	−	5.26660i	−0.0939640	−	0.371477i
$202$		−	7.21015i		−	0.507304i
$203$	−0.678869	+	0.247088i	−0.0476472	+	0.0173422i
$204$	−5.36349	+	2.40989i	−0.375520	+	0.168726i
$205$	6.90581	+	18.9736i	0.482323	+	1.32517i
$206$	21.6130	−	3.81095i	1.50585	−	0.265521i
$207$	0.952199	+	6.45601i	0.0661824	+	0.448724i
$208$		−	5.19845i		−	0.360448i
$209$	9.49818	−	9.99961i	0.657003	−	0.691687i
$210$	0.515332	+	2.03731i	0.0355613	+	0.140588i
$211$	−8.37720	+	1.47713i	−0.576710	+	0.101690i	−0.454393	−	0.890801i	$-0.650144\pi$
$211$	−8.37720	+	1.47713i	−0.576710	+	0.101690i	−0.122317	+	0.992491i	$0.539033\pi$
$212$	−1.15312	+	0.967580i	−0.0791964	+	0.0664536i
$213$	−0.974471	−	13.2855i	−0.0667696	−	0.910308i
$214$	2.03824	+	11.5595i	0.139331	+	0.790188i
$215$	32.7161	+	5.76873i	2.23122	+	0.393424i
$216$	−0.277825	−	1.24443i	−0.0189036	−	0.0846730i
$217$	−1.01570	+	0.586414i	−0.0689501	+	0.0398084i
$218$	−27.4707	−	4.84383i	−1.86055	−	0.328066i
$219$	7.07000	+	3.41853i	0.477746	+	0.231003i
$220$	−12.8903	+	22.3267i	−0.869067	+	1.50527i
$221$	2.22271			0.149516
$222$	−1.40464	+	0.103028i	−0.0942732	+	0.00691479i
$223$	−11.8636	+	2.09188i	−0.794447	+	0.140082i	−0.556119	−	0.831102i	$-0.687710\pi$
$223$	−11.8636	+	2.09188i	−0.794447	+	0.140082i	−0.238327	+	0.971185i	$0.576599\pi$
$224$	0.852339	+	0.715198i	0.0569493	+	0.0477862i
$225$	−15.3330	+	38.7071i	−1.02220	+	2.58047i
$226$	21.4399	+	7.80349i	1.42616	+	0.519081i
$227$	−5.44666	+	9.43389i	−0.361508	+	0.626149i	−0.988209	−	0.153110i	$-0.951071\pi$
$227$	−5.44666	+	9.43389i	−0.361508	+	0.626149i	0.626702	+	0.779259i	$0.284404\pi$
$228$	0.165123	+	14.1576i	0.0109355	+	0.937611i
$229$	−5.55758	−	9.62602i	−0.367256	−	0.636105i	0.621880	−	0.783113i	$-0.286369\pi$
$229$	−5.55758	−	9.62602i	−0.367256	−	0.636105i	−0.989135	+	0.147007i	$0.953036\pi$
$230$	−3.23085	−	18.3231i	−0.213036	−	1.20819i
$231$	0.0786257	−	0.773390i	0.00517319	−	0.0508853i
$232$	−1.17437	+	0.427435i	−0.0771010	+	0.0280625i
$233$	−18.9999	−	22.6432i	−1.24473	−	1.48341i	−0.813936	−	0.580955i	$-0.802679\pi$
$233$	−18.9999	−	22.6432i	−1.24473	−	1.48341i	−0.430791	−	0.902452i	$-0.641765\pi$
$234$	1.45933	−	7.10307i	0.0953996	−	0.464342i
$235$	26.9953	−	46.7572i	1.76098	−	3.05011i
$236$	7.02480			0.457275
$237$	0.466619	+	0.686736i	0.0303101	+	0.0446083i
$238$	−0.324932	+	0.387239i	−0.0210622	+	0.0251010i
$239$	11.5036	+	6.64162i	0.744107	+	0.429610i	0.823561	−	0.567228i	$-0.191984\pi$
$239$	11.5036	+	6.64162i	0.744107	+	0.429610i	−0.0794536	+	0.996839i	$0.525318\pi$
$240$	7.81313	+	30.8884i	0.504335	+	1.99384i
$241$	10.2024	−	12.1587i	0.657192	−	0.783211i	−0.329788	−	0.944055i	$-0.606977\pi$
$241$	10.2024	−	12.1587i	0.657192	−	0.783211i	0.986980	+	0.160844i	$0.0514216\pi$
$242$	−1.49155	+	1.25156i	−0.0958808	+	0.0804535i
$243$	−0.265312	−	15.5862i	−0.0170198	−	0.999855i
$244$	−2.26033	−	12.8189i	−0.144703	−	0.820649i
$245$	−19.4935	−	23.2315i	−1.24540	−	1.48421i
$246$	11.0459	+	11.3607i	0.704260	+	0.724332i
$247$	2.13644	−	4.90720i	0.135939	−	0.312237i
$248$	−1.75705	+	1.01443i	−0.111573	+	0.0644165i
$249$	1.46052	−	14.3662i	0.0925570	−	0.910423i
$250$	25.9709	−	71.3545i	1.64255	−	4.51286i
$251$	−1.32102	+	1.57433i	−0.0833822	+	0.0993710i	−0.806123	−	0.591749i	$-0.798438\pi$
$251$	−1.32102	+	1.57433i	−0.0833822	+	0.0993710i	0.722740	+	0.691120i	$0.242882\pi$
$252$	0.495606	+	0.625522i	0.0312203	+	0.0394042i
$253$	−1.19515	+	6.77804i	−0.0751386	+	0.426132i
$254$	−26.1550	+	15.1006i	−1.64111	+	0.947494i
$255$	−13.2070	+	3.34068i	−0.827056	+	0.209201i
$256$	13.6389	+	11.4444i	0.852432	+	0.715275i
$257$	8.31231	+	6.97485i	0.518507	+	0.435079i	0.864111	−	0.503301i	$-0.167881\pi$
$257$	8.31231	+	6.97485i	0.518507	+	0.435079i	−0.345604	+	0.938381i	$0.612326\pi$
$258$	25.2745	−	6.39311i	1.57352	−	0.398018i
$259$	−0.0507432	+	0.0292966i	−0.00315303	+	0.00182040i
$260$	−1.73730	+	9.85272i	−0.107743	+	0.611040i
$261$	−15.1152	+	2.22935i	−0.935609	+	0.137993i
$262$	3.04283	−	3.62630i	0.187986	−	0.224034i
$263$	−0.0210578	+	0.0578557i	−0.00129848	+	0.00356754i	−0.940340	−	0.340236i	$-0.889493\pi$
$263$	−0.0210578	+	0.0578557i	−0.00129848	+	0.00356754i	0.939042	+	0.343803i	$0.111715\pi$
$264$	0.136014	−	1.33788i	0.00837107	−	0.0823407i
$265$	−3.02025	+	1.74374i	−0.185533	+	0.107117i
$266$	0.542607	+	1.08958i	0.0332694	+	0.0668063i
$267$	−1.57064	−	1.61540i	−0.0961215	−	0.0988610i
$268$	3.78082	+	4.50581i	0.230950	+	0.275236i
$269$	−2.38329	−	13.5163i	−0.145312	−	0.824104i	−0.967116	−	0.254334i	$-0.918144\pi$
$269$	−2.38329	−	13.5163i	−0.145312	−	0.824104i	0.821805	−	0.569769i	$-0.192967\pi$
$270$	2.00458	+	44.3987i	0.121995	+	2.70202i
$271$	−8.44378	+	7.08518i	−0.512923	+	0.430394i	−0.862156	−	0.506642i	$-0.830887\pi$
$271$	−8.44378	+	7.08518i	−0.512923	+	0.430394i	0.349233	+	0.937036i	$0.386442\pi$
$272$	−4.92641	+	5.87106i	−0.298707	+	0.355985i
$273$	−0.0739781	−	0.292465i	−0.00447736	−	0.0177008i
$274$	−19.5220	−	11.2710i	−1.17937	−	0.680907i
$275$	−28.2244	+	33.6365i	−1.70200	+	2.02836i
$276$	−3.97104	−	5.84429i	−0.239028	−	0.351785i
$277$	−8.97968			−0.539537			−0.269768	−	0.962925i	$-0.586947\pi$
$277$	−8.97968			−0.539537			−0.269768	+	0.962925i	$0.586947\pi$
$278$	14.7491	−	25.5461i	0.884591	−	1.53216i
$279$	−23.5373	+	7.82529i	−1.40914	+	0.468488i
$280$	0.0972139	+	0.115855i	0.00580964	+	0.00692366i
$281$	7.11182	−	2.58849i	0.424256	−	0.154416i	−0.121064	−	0.992645i	$-0.538631\pi$
$281$	7.11182	−	2.58849i	0.424256	−	0.154416i	0.545320	+	0.838228i	$0.316408\pi$
$282$	4.28541	−	42.1528i	0.255192	−	2.51016i
$283$	0.570468	+	3.23528i	0.0339108	+	0.192318i	0.997057	−	0.0766596i	$-0.0244255\pi$
$283$	0.570468	+	3.23528i	0.0339108	+	0.192318i	−0.963147	+	0.268977i	$0.913314\pi$
$284$	7.21165	+	12.4909i	0.427933	+	0.741201i
$285$	−5.31904	+	32.3688i	−0.315073	+	1.91736i
$286$	3.82393	−	6.62324i	0.226114	−	0.391640i
$287$	0.619451	+	0.225462i	0.0365650	+	0.0133086i
$288$	14.6132	+	18.4439i	0.861093	+	1.08682i
$289$	10.5125	+	8.82100i	0.618380	+	0.518882i
$290$	42.8992	−	7.56428i	2.51913	−	0.444190i
$291$	−18.1254	+	1.32947i	−1.06253	+	0.0779349i
$292$	−8.50281			−0.497590
$293$	4.12597	−	7.14639i	0.241042	−	0.417497i	−0.719969	−	0.694006i	$-0.755844\pi$
$293$	4.12597	−	7.14639i	0.241042	−	0.417497i	0.961011	+	0.276509i	$0.0891776\pi$
$294$	−21.4260	−	10.3600i	−1.24959	−	0.604210i
$295$	16.0280	+	2.82617i	0.933185	+	0.164546i
$296$	−0.0877801	+	0.0506799i	−0.00510212	+	0.00294571i
$297$	4.92050	−	15.6871i	0.285516	−	0.910255i
$298$	−34.2546	−	6.04000i	−1.98431	−	0.349888i
$299$	0.463803	+	2.63036i	0.0268224	+	0.152117i
$300$	−3.29753	−	44.9571i	−0.190383	−	2.59560i
$301$	0.830848	−	0.697164i	0.0478893	−	0.0401839i
$302$	−10.4709	+	1.84631i	−0.602534	+	0.106243i
$303$	−1.55565	−	6.15010i	−0.0893697	−	0.353314i
$304$	8.22665	+	16.5195i	0.471831	+	0.947456i
$305$		−	30.1574i		−	1.72681i
$306$	−8.37951	+	6.63915i	−0.479024	+	0.379535i
$307$	0.768855	−	0.135570i	0.0438809	−	0.00773738i	−0.151665	−	0.988432i	$-0.548463\pi$
$307$	0.768855	−	0.135570i	0.0438809	−	0.00773738i	0.195546	+	0.980695i	$0.437352\pi$
$308$	0.287875	+	0.790931i	0.0164032	+	0.0450675i
$309$	17.6131	−	7.91383i	1.00198	−	0.450202i
$310$	66.4535	−	24.1871i	3.77430	−	1.37373i
$311$			16.5673i			0.939445i	0.882814	+	0.469723i	$0.155646\pi$
$311$			16.5673i			0.939445i	−0.882814	+	0.469723i	$0.844354\pi$
$312$	−0.127974	−	0.505932i	−0.00724510	−	0.0286428i
$313$	1.06588	−	6.04493i	0.0602473	−	0.341680i	−0.939753	−	0.341855i	$-0.888945\pi$
$313$	1.06588	−	6.04493i	0.0602473	−	0.341680i	1.00000		0.000175612i	$5.58992e-5\pi$
$314$	1.33822	−	0.487073i	0.0755203	−	0.0274871i
$315$	0.879134	+	1.62660i	0.0495336	+	0.0916484i
$316$	−0.778518	−	0.449478i	−0.0437951	−	0.0252851i
$317$	4.67927	+	3.92638i	0.262814	+	0.220527i	0.764667	−	0.644426i	$-0.222904\pi$
$317$	4.67927	+	3.92638i	0.262814	+	0.220527i	−0.501853	+	0.864953i	$0.667348\pi$
$318$	−1.60114	+	2.21963i	−0.0897876	+	0.124471i
$319$	−15.8692	−	2.79817i	−0.888504	−	0.156667i
$320$	−19.4762	−	23.2108i	−1.08875	−	1.29752i
$321$	4.23262	+	9.42020i	0.236242	+	0.525784i
$322$	−0.526060	−	0.303721i	−0.0293162	−	0.0169257i
$323$	−7.06326	+	3.51748i	−0.393010	+	0.195718i
$324$	7.60476	+	15.0678i	0.422487	+	0.837101i
$325$	−5.82800	+	16.0123i	−0.323279	+	0.888202i
$326$	23.0678	+	8.39600i	1.27761	+	0.465012i
$327$	−24.4771	+	1.79535i	−1.35358	+	0.0992832i
$328$	1.07158	+	0.390024i	0.0591682	+	0.0215355i
$329$	−0.602876	−	1.65639i	−0.0332376	−	0.0913196i
$330$	−12.7667	+	45.1016i	−0.702782	+	2.48276i
$331$			12.4912i			0.686579i	0.939230	+	0.343290i	$0.111541\pi$
$331$			12.4912i			0.686579i	−0.939230	+	0.343290i	$0.888459\pi$
$332$	5.34748	+	14.6921i	0.293481	+	0.806332i
$333$	−1.17590	+	0.390943i	−0.0644388	+	0.0214235i
$334$	5.30069	+	9.18107i	0.290041	+	0.502366i
$335$	6.81369	+	11.8017i	0.372272	+	0.644793i
$336$	0.936481	+	0.452813i	0.0510892	+	0.0247030i
$337$	3.28508	−	9.02568i	0.178950	−	0.491660i	−0.817493	−	0.575939i	$-0.804637\pi$
$337$	3.28508	−	9.02568i	0.178950	−	0.491660i	0.996442	+	0.0842792i	$0.0268588\pi$
$338$	−3.92858	+	22.2801i	−0.213686	+	1.21188i
$339$	19.9715	+	2.03037i	1.08470	+	0.110275i
$340$	11.2992	−	9.48115i	0.612785	−	0.514188i
$341$	−26.1600			−1.41664
$342$	6.60333	+	24.8813i	0.357067	+	1.34543i
$343$	−1.98306			−0.107075
$344$	1.43728	−	1.20602i	0.0774927	−	0.0650241i
$345$	−6.70920	−	14.9321i	−0.361211	−	0.803917i
$346$	−4.10504	+	23.2808i	−0.220688	+	1.25159i
$347$	−6.33474	+	17.4046i	−0.340067	+	0.934326i	0.645308	+	0.763923i	$0.276729\pi$
$347$	−6.33474	+	17.4046i	−0.340067	+	0.934326i	−0.985374	+	0.170403i	$0.945493\pi$
$348$	13.6830	−	9.29725i	0.733488	−	0.498385i
$349$	9.06510	+	15.7012i	0.485243	+	0.840466i	0.999856	−	0.0169564i	$-0.00539765\pi$
$349$	9.06510	+	15.7012i	0.485243	+	0.840466i	−0.514613	+	0.857423i	$0.672064\pi$
$350$	−1.93767	−	3.35614i	−0.103573	−	0.179393i
$351$	−0.287767	−	6.37363i	−0.0153599	−	0.340199i
$352$	8.48817	+	23.3210i	0.452421	+	1.24302i
$353$		−	14.1091i		−	0.750949i	−0.926833	−	0.375475i	$-0.877480\pi$
$353$		−	14.1091i		−	0.750949i	0.926833	−	0.375475i	$-0.122520\pi$
$354$	12.3823	−	3.13206i	0.658111	−	0.166467i
$355$	11.4290	+	31.4010i	0.606591	+	1.66659i
$356$	2.29238	+	0.834358i	0.121496	+	0.0442209i
$357$	−0.193610	+	0.400413i	−0.0102469	+	0.0211921i
$358$	−24.0273	−	8.74521i	−1.26988	−	0.462199i
$359$	7.48602	−	20.5677i	0.395097	−	1.08552i	−0.569546	−	0.821959i	$-0.692881\pi$
$359$	7.48602	−	20.5677i	0.395097	−	1.08552i	0.964643	−	0.263560i	$-0.0848968\pi$
$360$	1.52080	+	2.81383i	0.0801535	+	0.148302i
$361$	0.976618	+	18.9749i	0.0514010	+	0.998678i
$362$	18.9539	+	10.9430i	0.996194	+	0.575153i
$363$	−1.00223	+	1.38937i	−0.0526034	+	0.0729231i
$364$	0.209957	+	0.250217i	0.0110047	+	0.0131149i
$365$	−19.4003	−	3.42079i	−1.01546	−	0.179052i
$366$	−9.69960	−	21.5876i	−0.507006	−	1.12840i
$367$	−12.0897	−	10.1445i	−0.631080	−	0.529539i	0.270185	−	0.962809i	$-0.412915\pi$
$367$	−12.0897	−	10.1445i	−0.631080	−	0.529539i	−0.901264	+	0.433270i	$0.857360\pi$
$368$	−7.97578	−	4.60482i	−0.415766	−	0.240043i
$369$	11.8731	+	7.30719i	0.618087	+	0.380397i
$370$	3.31994	−	1.20836i	0.172596	−	0.0628197i
$371$	−0.0197716	+	0.112130i	−0.00102649	+	0.00582150i
$372$	19.2551	−	18.7215i	0.998329	−	0.970664i
$373$			11.2133i			0.580604i	0.956935	+	0.290302i	$0.0937558\pi$
$373$			11.2133i			0.580604i	−0.956935	+	0.290302i	$0.906244\pi$
$374$	−10.5953	+	3.85638i	−0.547871	+	0.199409i
$375$	6.75732	−	66.4673i	0.348946	−	3.43236i
$376$	−1.04291	−	2.86537i	−0.0537839	−	0.147770i
$377$	−6.15836	+	1.08588i	−0.317172	+	0.0559259i
$378$	1.15248	+	0.881608i	0.0592770	+	0.0453450i
$379$			5.06956i			0.260406i	0.991487	+	0.130203i	$0.0415629\pi$
$379$			5.06956i			0.260406i	−0.991487	+	0.130203i	$0.958437\pi$
$380$	−10.0714	−	34.0590i	−0.516651	−	1.74719i
$381$	−19.0515	+	18.5236i	−0.976040	+	0.948994i
$382$	−29.1175	+	5.13419i	−1.48978	+	0.262688i
$383$	18.8351	−	15.8045i	0.962427	−	0.807572i	−0.0189195	−	0.999821i	$-0.506023\pi$
$383$	18.8351	−	15.8045i	0.962427	−	0.807572i	0.981346	+	0.192249i	$0.0615782\pi$
$384$	3.05518	+	1.47726i	0.155909	+	0.0753859i
$385$	0.338623	+	1.92043i	0.0172578	+	0.0978740i
$386$	−45.5426	−	8.03039i	−2.31806	−	0.408736i
$387$	20.1793	−	10.9064i	1.02577	−	0.554402i
$388$	17.0414	−	9.83885i	0.865145	−	0.499492i
$389$	−4.68862	−	0.826730i	−0.237723	−	0.0419169i	0.0535175	−	0.998567i	$-0.482957\pi$
$389$	−4.68862	−	0.826730i	−0.237723	−	0.0419169i	−0.291240	+	0.956650i	$0.594068\pi$
$390$	1.33065	+	18.1415i	0.0673802	+	0.918632i
$391$	1.96889	−	3.41022i	0.0995711	−	0.172462i
$392$	−1.71277			−0.0865081
$393$	1.81306	−	3.74967i	0.0914569	−	0.189146i
$394$	−40.2445	+	7.09618i	−2.02749	+	0.357501i
$395$	−1.59546	−	1.33875i	−0.0802763	−	0.0673598i
$396$	2.59735	+	17.6103i	0.130522	+	0.884952i
$397$	−19.4539	−	7.08065i	−0.976365	−	0.355368i	−0.195939	−	0.980616i	$-0.562775\pi$
$397$	−19.4539	−	7.08065i	−0.976365	−	0.355368i	−0.780426	+	0.625248i	$0.784998\pi$
$398$	−13.6071	+	23.5681i	−0.682060	+	1.18136i
$399$	0.697917	+	0.812314i	0.0349396	+	0.0406666i
$400$	−29.3776	−	50.8836i	−1.46888	−	2.54418i
$401$	−6.69397	−	37.9634i	−0.334281	−	1.89580i	−0.434220	−	0.900807i	$-0.642976\pi$
$401$	−6.69397	−	37.9634i	−0.334281	−	1.89580i	0.0999397	−	0.994993i	$-0.468135\pi$
$402$	8.67322	+	6.25647i	0.432581	+	0.312044i
$403$	−9.53968	+	3.47216i	−0.475205	+	0.172961i
$404$	4.41508	+	5.26168i	0.219658	+	0.261779i
$405$	11.2893	+	37.4387i	0.560968	+	1.86034i
$406$	0.711091	−	1.23165i	0.0352909	−	0.0611256i
$407$	−1.30693			−0.0647819
$408$	−0.334924	+	0.692670i	−0.0165812	+	0.0342923i
$409$	17.2014	−	20.4999i	0.850557	−	1.01365i	−0.149135	−	0.988817i	$-0.547649\pi$
$409$	17.2014	−	20.4999i	0.850557	−	1.01365i	0.999692	−	0.0248371i	$-0.00790672\pi$
$410$	−34.4230	−	19.8741i	−1.70003	−	0.981514i
$411$	−19.0836	−	5.40191i	−0.941326	−	0.266456i
$412$	−13.4387	+	16.0156i	−0.662077	+	0.789032i
$413$	0.407042	−	0.341549i	0.0200292	−	0.0168065i
$414$	−9.60528	−	8.53094i	−0.472074	−	0.419273i
$415$	6.29015	+	35.6732i	0.308771	+	1.75113i
$416$	6.19070	+	7.37779i	0.303524	+	0.361726i
$417$	7.06885	−	24.9725i	0.346163	−	1.22291i
$418$	−1.67015	+	27.0985i	−0.0816898	+	1.32543i
$419$	−2.82454	+	1.63075i	−0.137988	+	0.0796674i	−0.567405	−	0.823439i	$-0.692052\pi$
$419$	−2.82454	+	1.63075i	−0.137988	+	0.0796674i	0.429417	+	0.903106i	$0.358719\pi$
$420$	−1.62360	−	1.17119i	−0.0792237	−	0.0571483i
$421$	−11.9632	+	32.8687i	−0.583053	+	1.60192i	0.199881	+	0.979820i	$0.435944\pi$
$421$	−11.9632	+	32.8687i	−0.583053	+	1.60192i	−0.782934	+	0.622104i	$0.786278\pi$
$422$	10.7639	−	12.8279i	0.523979	−	0.624454i
$423$	−5.43944	−	36.8800i	−0.264475	−	1.79317i
$424$	−0.0342026	+	0.193973i	−0.00166103	+	0.00942014i
$425$	21.7564	−	12.5611i	1.05534	−	0.609301i
$426$	18.2808	+	18.8018i	0.885708	+	0.910952i
$427$	−0.754235	−	0.632878i	−0.0365000	−	0.0306271i
$428$	−8.56577	−	7.18754i	−0.414042	−	0.347423i
$429$	1.83271	−	6.47452i	0.0884841	−	0.312593i
$430$	−56.6364	+	32.6991i	−2.73125	+	1.57689i
$431$	−4.75962	+	26.9932i	−0.229263	+	1.30021i	0.625103	+	0.780542i	$0.285057\pi$
$431$	−4.75962	+	26.9932i	−0.229263	+	1.30021i	−0.854366	+	0.519672i	$0.826054\pi$
$432$	17.4731	+	13.3664i	0.840674	+	0.643090i
$433$	−6.85106	+	8.16477i	−0.329241	+	0.392374i	−0.905117	−	0.425163i	$-0.860217\pi$
$433$	−6.85106	+	8.16477i	−0.329241	+	0.392374i	0.575876	+	0.817537i	$0.304661\pi$
$434$	0.789662	−	2.16958i	0.0379050	−	0.104143i
$435$	34.9600	−	15.7080i	1.67620	−	0.753141i
$436$	23.0132	−	13.2867i	1.10213	−	0.636315i
$437$	−5.63645	−	7.62468i	−0.269628	−	0.364738i
$438$	−14.9875	+	3.79104i	−0.716131	+	0.181143i
$439$	−12.5522	−	14.9591i	−0.599084	−	0.713961i	0.378240	−	0.925707i	$-0.376529\pi$
$439$	−12.5522	−	14.9591i	−0.599084	−	0.713961i	−0.977325	+	0.211747i	$0.932085\pi$
$440$	0.585780	+	3.32212i	0.0279260	+	0.158376i
$441$	−20.5112	−	4.21405i	−0.976725	−	0.200669i
$442$	−3.35191	+	2.81259i	−0.159434	+	0.133781i
$443$	6.99009	−	8.33046i	0.332109	−	0.395792i	−0.573987	−	0.818865i	$-0.694604\pi$
$443$	6.99009	−	8.33046i	0.332109	−	0.395792i	0.906096	+	0.423072i	$0.139048\pi$
$444$	0.961962	−	0.935306i	0.0456527	−	0.0443876i
$445$	4.89469	+	2.82595i	0.232030	+	0.133963i
$446$	15.2436	−	18.1667i	0.721807	−	0.860216i
$447$	−30.5216	+	2.23871i	−1.44362	+	0.105887i
$448$	−0.989222			−0.0467363
$449$	−16.0502	+	27.7997i	−0.757454	+	1.31195i	0.186691	+	0.982419i	$0.440224\pi$
$449$	−16.0502	+	27.7997i	−0.757454	+	1.31195i	−0.944145	+	0.329530i	$0.893110\pi$
$450$	−25.8568	−	77.7735i	−1.21890	−	3.66628i
$451$	9.45131	+	11.2636i	0.445045	+	0.530384i
$452$	−20.4244	+	7.43388i	−0.960684	+	0.349660i
$453$	−8.53311	+	3.83405i	−0.400921	+	0.180139i
$454$	−3.72380	−	21.1187i	−0.174766	−	0.991150i
$455$	0.378378	+	0.655371i	0.0177387	+	0.0307242i
$456$	1.20732	+	1.40521i	0.0565379	+	0.0658052i
$457$	9.04691	−	15.6697i	0.423197	−	0.732998i	−0.573053	−	0.819518i	$-0.694241\pi$
$457$	9.04691	−	15.6697i	0.423197	−	0.732998i	0.996250	+	0.0865198i	$0.0275746\pi$
$458$	20.5616	+	7.48382i	0.960781	+	0.349696i
$459$	−5.71509	+	7.47100i	−0.266757	+	0.348717i
$460$	13.5777	+	11.3931i	0.633065	+	0.531205i
$461$	21.7322	−	3.83198i	1.01217	−	0.178473i	0.357120	−	0.934058i	$-0.383759\pi$
$461$	21.7322	−	3.83198i	1.01217	−	0.178473i	0.655050	+	0.755585i	$0.272647\pi$
$462$	0.860067	+	1.26579i	0.0400139	+	0.0588897i
$463$	−23.4137			−1.08813			−0.544063	−	0.839044i	$-0.683115\pi$
$463$	−23.4137			−1.08813			−0.544063	+	0.839044i	$0.683115\pi$
$464$	10.7811	−	18.6734i	0.500500	−	0.866891i
$465$	51.4648	−	34.9689i	2.38662	−	1.62165i
$466$	57.3048	+	10.1044i	2.65459	+	0.468077i
$467$	27.2373	−	15.7254i	1.26039	−	0.727687i	0.287240	−	0.957858i	$-0.407262\pi$
$467$	27.2373	−	15.7254i	1.26039	−	0.727687i	0.973150	+	0.230172i	$0.0739288\pi$
$468$	3.28455	+	6.07716i	0.151828	+	0.280917i
$469$	0.438149	+	0.0772575i	0.0202318	+	0.00356742i
$470$	18.4563	+	104.671i	0.851324	+	4.82810i
$471$	1.03639	−	0.704195i	0.0477541	−	0.0324476i
$472$	0.704137	−	0.590842i	0.0324106	−	0.0271957i
$473$	23.8244	−	4.20089i	1.09545	−	0.193157i
$474$	−1.57266	−	0.445165i	−0.0722347	−	0.0204471i
$475$	−6.81974	−	60.1062i	−0.312911	−	2.75786i
$476$		−	0.481561i		−	0.0220723i
$477$	−0.886835	+	2.23876i	−0.0406054	+	0.102506i
$478$	−25.7520	+	4.54077i	−1.17787	+	0.207690i
$479$	−2.63618	−	7.24285i	−0.120450	−	0.330934i	0.864784	−	0.502143i	$-0.167455\pi$
$479$	−2.63618	−	7.24285i	−0.120450	−	0.330934i	−0.985235	+	0.171209i	$0.945233\pi$
$480$	−47.8728	−	34.5333i	−2.18509	−	1.57622i
$481$	−0.476592	+	0.173465i	−0.0217307	+	0.00790934i
$482$			31.2456i			1.42320i
$483$	−0.514248	−	0.145566i	−0.0233991	−	0.00662347i
$484$	0.322094	−	1.82668i	0.0146406	−	0.0830311i
$485$	42.8404	−	15.5926i	1.94528	−	0.708025i
$486$	20.1227	+	23.1687i	0.912782	+	1.05095i
$487$	−27.1014	−	15.6470i	−1.22808	−	0.709033i	−0.261453	−	0.965216i	$-0.584202\pi$
$487$	−27.1014	−	15.6470i	−1.22808	−	0.709033i	−0.966628	+	0.256183i	$0.917535\pi$
$488$	−1.30474	−	1.09481i	−0.0590629	−	0.0495597i
$489$	21.4879	+	2.18454i	0.971715	+	0.0987882i
$490$	58.7936	+	10.3669i	2.65603	+	0.468329i
$491$	11.4692	+	13.6684i	0.517596	+	0.616846i	0.960010	−	0.279964i	$-0.0903226\pi$
$491$	11.4692	+	13.6684i	0.517596	+	0.616846i	−0.442415	+	0.896810i	$0.645878\pi$
$492$	−15.0175	−	1.52673i	−0.677041	−	0.0688305i
$493$	7.98423	+	4.60970i	0.359592	+	0.207610i
$494$	2.98768	+	10.1036i	0.134422	+	0.454583i
$495$	−1.15866	+	41.2252i	−0.0520781	+	1.85293i
$496$	11.9723	−	32.8938i	0.537574	−	1.47697i
$497$	1.02518	+	0.373137i	0.0459858	+	0.0167375i
$498$	15.9763	+	23.5128i	0.715916	+	1.05363i
$499$	8.74426	+	3.18265i	0.391447	+	0.142475i	0.530242	−	0.847846i	$-0.322101\pi$
$499$	8.74426	+	3.18265i	0.391447	+	0.142475i	−0.138796	+	0.990321i	$0.544323\pi$
$500$	24.7408	+	67.9749i	1.10644	+	3.03993i
$501$	6.50227	+	6.68759i	0.290500	+	0.298779i
$502$		−	4.04574i		−	0.180570i
$503$	1.23674	+	3.39791i	0.0551433	+	0.151505i	0.964206	−	0.265154i	$-0.0854229\pi$
$503$	1.23674	+	3.39791i	0.0551433	+	0.151505i	−0.909063	+	0.416660i	$0.863201\pi$
$504$	0.102289	+	0.0210154i	0.00455631	+	0.000936099i
$505$	7.95672	+	13.7815i	0.354070	+	0.613267i
$506$	−6.77452	−	11.7338i	−0.301164	−	0.521631i
$507$	1.45612	+	19.8520i	0.0646684	+	0.881660i
$508$	9.84015	−	27.0356i	0.436586	−	1.19951i
$509$	−3.17272	+	17.9934i	−0.140628	+	0.797543i	0.830145	+	0.557547i	$0.188257\pi$
$509$	−3.17272	+	17.9934i	−0.140628	+	0.797543i	−0.970774	+	0.239996i	$0.922854\pi$
$510$	15.6893	−	21.7498i	0.694735	−	0.963098i
$511$	−0.492684	+	0.413411i	−0.0217950	+	0.0182882i
$512$	−31.1309			−1.37580
$513$	11.0008	+	19.7985i	0.485699	+	0.874126i
$514$	−21.3611			−0.942196
$515$	−37.1054	+	31.1351i	−1.63506	+	1.37198i
$516$	−14.5296	+	20.1421i	−0.639630	+	0.886707i
$517$	6.82732	−	38.7196i	0.300265	−	1.70289i
$518$	0.0394507	−	0.108390i	0.00173336	−	0.00476238i
$519$	1.52152	+	20.7438i	0.0667874	+	0.910550i
$520$	0.654553	+	1.13372i	0.0287040	+	0.0497168i
$521$	13.8636	+	24.0124i	0.607374	+	1.05200i	0.991672	+	0.128793i	$0.0411103\pi$
$521$	13.8636	+	24.0124i	0.607374	+	1.05200i	−0.384298	+	0.923209i	$0.625556\pi$
$522$	19.9732	−	22.4885i	0.874203	−	0.984295i
$523$	7.30987	+	20.0837i	0.319638	+	0.878199i	0.990610	+	0.136716i	$0.0436549\pi$
$523$	7.30987	+	20.0837i	0.319638	+	0.878199i	−0.670972	+	0.741483i	$0.734123\pi$
$524$			4.50958i			0.197002i
$525$	−2.37690	−	2.44465i	−0.103737	−	0.106693i
$526$	−0.0414541	−	0.113894i	−0.00180749	−	0.00496603i
$527$	14.0644	+	5.11904i	0.612657	+	0.222989i
$528$	13.0398	+	19.1910i	0.567483	+	0.835181i
$529$	−17.1664	−	6.24807i	−0.746367	−	0.271655i
$530$	2.34812	−	6.45140i	0.101996	−	0.280231i
$531$	9.88605	−	5.34316i	0.429018	−	0.231873i
$532$	−1.06317	−	0.462870i	−0.0460942	−	0.0200680i
$533$	4.94158	+	2.85302i	0.214043	+	0.123578i
$534$	4.41267	+	0.448609i	0.190955	+	0.0194132i
$535$	−16.6523	−	19.8454i	−0.719941	−	0.857992i
$536$	0.757949	+	0.133647i	0.0327384	+	0.00577266i
$537$	−22.3816	−	2.27540i	−0.965837	−	0.0981906i
$538$	20.6974	+	17.3672i	0.892328	+	0.748752i
$539$	−19.1256	−	11.0422i	−0.823799	−	0.475620i
$540$	−28.6501	−	31.1730i	−1.23290	−	1.34147i
$541$	14.6001	−	5.31399i	0.627706	−	0.228466i	−0.00852673	−	0.999964i	$-0.502714\pi$
$541$	14.6001	−	5.31399i	0.627706	−	0.228466i	0.636232	+	0.771497i	$0.280492\pi$
$542$	3.76798	−	21.3693i	0.161849	−	0.917889i
$543$	18.5283	+	5.24471i	0.795126	+	0.225072i
$544$		−	14.1991i		−	0.608782i
$545$	57.8529	−	21.0567i	2.47815	−	0.901971i
$546$	0.481642	+	0.347435i	0.0206124	+	0.0148688i
$547$	−11.6651	−	32.0496i	−0.498763	−	1.37034i	−0.892471	−	0.451105i	$-0.851030\pi$
$547$	−11.6651	−	32.0496i	−0.498763	−	1.37034i	0.393708	−	0.919236i	$-0.371192\pi$
$548$	21.1481	−	3.72898i	0.903401	−	0.159294i
$549$	−12.9312	−	16.3210i	−0.551892	−	0.696562i
$550$		−	86.4396i		−	3.68580i
$551$	17.8514	−	13.1964i	0.760495	−	0.562186i
$552$	−0.889592	−	0.251812i	−0.0378636	−	0.0107178i
$553$	−0.0669640	+	0.0118076i	−0.00284760	+	0.000502108i
$554$	13.5416	−	11.3628i	0.575328	−	0.482757i
$555$	2.57113	−	1.74701i	0.109138	−	0.0741565i
$556$	4.87968	+	27.6741i	0.206945	+	1.17364i
$557$	−0.657872	−	0.116001i	−0.0278749	−	0.00491510i	0.159693	−	0.987167i	$-0.448949\pi$
$557$	−0.657872	−	0.116001i	−0.0278749	−	0.00491510i	−0.187568	+	0.982252i	$0.560061\pi$
$558$	25.5929	−	41.5845i	1.08343	−	1.76041i
$559$	8.13040	−	4.69409i	0.343879	−	0.198539i
$560$	−2.56973	−	0.453112i	−0.108591	−	0.0191475i
$561$	−8.20554	+	5.57544i	−0.346438	+	0.235395i
$562$	−7.44939	+	12.9027i	−0.314233	+	0.544268i
$563$	−10.8375			−0.456746			−0.228373	−	0.973574i	$-0.573341\pi$
$563$	−10.8375			−0.456746			−0.228373	+	0.973574i	$0.573341\pi$
$564$	22.6846	+	33.3856i	0.955193	+	1.40579i
$565$	−49.5917	+	8.74435i	−2.08634	+	0.367878i
$566$	−4.95416	−	4.15704i	−0.208239	−	0.174733i
$567$	1.17325	+	0.503337i	0.0492719	+	0.0211382i
$568$	1.77345	+	0.645485i	0.0744125	+	0.0270839i
$569$	5.00006	−	8.66036i	0.209613	−	0.363061i	−0.741979	−	0.670423i	$-0.766113\pi$
$569$	5.00006	−	8.66036i	0.209613	−	0.363061i	0.951593	+	0.307362i	$0.0994461\pi$
$570$	−32.9378	−	55.5437i	−1.37961	−	2.32647i
$571$	13.4961	+	23.3759i	0.564794	+	0.978251i	0.997069	+	0.0765095i	$0.0243776\pi$
$571$	13.4961	+	23.3759i	0.564794	+	0.978251i	−0.432275	+	0.901742i	$0.642289\pi$
$572$	1.26513	+	7.17493i	0.0528979	+	0.299999i
$573$	−23.7288	+	10.6617i	−0.991286	+	0.445398i
$574$	−1.21945	+	0.443842i	−0.0508987	+	0.0185256i
$575$	19.4046	+	23.1254i	0.809226	+	0.964398i
$576$	−20.4929	−	4.21029i	−0.853872	−	0.175429i
$577$	1.40602	−	2.43529i	0.0585332	−	0.101383i	−0.835274	−	0.549834i	$-0.814691\pi$
$577$	1.40602	−	2.43529i	0.0585332	−	0.101383i	0.893807	+	0.448451i	$0.148024\pi$
$578$	−27.0150			−1.12368
$579$	−40.5795	+	2.97644i	−1.68643	+	0.123697i
$580$	−26.6742	+	31.7891i	−1.10759	+	1.31997i
$581$	1.02419	+	0.591315i	0.0424904	+	0.0245319i
$582$	25.6513	−	24.9405i	1.06328	−	1.03382i
$583$	−1.63246	+	1.94549i	−0.0676095	+	0.0805738i
$584$	−0.852288	+	0.715155i	−0.0352679	+	0.0295933i
$585$	5.04920	+	15.1872i	0.208759	+	0.627915i
$586$	2.82086	+	15.9979i	0.116529	+	0.660867i
$587$	−5.73880	−	6.83924i	−0.236866	−	0.282285i	0.634497	−	0.772926i	$-0.281207\pi$
$587$	−5.73880	−	6.83924i	−0.236866	−	0.282285i	−0.871362	+	0.490640i	$0.836763\pi$
$588$	21.9798	−	5.55972i	0.906431	−	0.229279i
$589$	24.8201	−	26.1304i	1.02270	−	1.07669i
$590$	−27.7468	+	16.0196i	−1.14232	+	0.659518i
$591$	−32.7966	+	14.7360i	−1.34907	+	0.606157i
$592$	0.598125	−	1.64334i	0.0245828	−	0.0675407i
$593$	−1.32702	+	1.58148i	−0.0544942	+	0.0649436i	−0.792603	−	0.609738i	$-0.791275\pi$
$593$	−1.32702	+	1.58148i	−0.0544942	+	0.0649436i	0.738109	+	0.674682i	$0.235719\pi$
$594$	12.4299	+	29.8828i	0.510006	+	1.22611i
$595$	0.193738	−	1.09874i	0.00794249	−	0.0450441i
$596$	28.6962	−	16.5678i	1.17544	−	0.678642i
$597$	−6.52152	+	23.0389i	−0.266908	+	0.942921i
$598$	−4.02784	−	3.37976i	−0.164711	−	0.138209i
$599$	−7.09300	−	5.95174i	−0.289812	−	0.243181i	0.486277	−	0.873805i	$-0.338355\pi$
$599$	−7.09300	−	5.95174i	−0.289812	−	0.243181i	−0.776089	+	0.630624i	$0.782799\pi$
$600$	−4.11178	−	4.22897i	−0.167863	−	0.172647i
$601$	16.4352	−	9.48885i	0.670405	−	0.387058i	−0.125825	−	0.992052i	$-0.540158\pi$
$601$	16.4352	−	9.48885i	0.670405	−	0.387058i	0.796230	+	0.604994i	$0.206825\pi$
$602$	−0.370760	+	2.10269i	−0.0151111	+	0.0856991i
$603$	8.74796	+	3.46531i	0.356244	+	0.141118i
$604$	6.51070	−	7.75915i	0.264917	−	0.315715i
$605$	1.46980	−	4.03823i	0.0597557	−	0.164177i
$606$	10.1282	+	7.30603i	0.411430	+	0.296787i
$607$	−19.5396	+	11.2812i	−0.793089	+	0.457890i	−0.841049	−	0.540959i	$-0.818061\pi$
$607$	−19.5396	+	11.2812i	−0.793089	+	0.457890i	0.0479597	+	0.998849i	$0.484728\pi$
$608$	−31.3481	−	13.6480i	−1.27133	−	0.553499i
$609$	0.340808	−	1.20399i	0.0138102	−	0.0487882i
$610$	38.1608	+	45.4783i	1.54509	+	1.84136i
$611$	−2.64948	−	15.0259i	−0.107186	−	0.607884i
$612$	2.04960	−	9.97612i	0.0828503	−	0.403261i
$613$	−32.9592	+	27.6560i	−1.33121	+	1.11702i	−0.347414	+	0.937712i	$0.612940\pi$
$613$	−32.9592	+	27.6560i	−1.33121	+	1.11702i	−0.983794	+	0.179304i	$0.942615\pi$
$614$	−0.987907	+	1.17734i	−0.0398687	+	0.0475136i
$615$	−33.6501	−	9.52517i	−1.35690	−	0.384092i
$616$	0.0953790	+	0.0550671i	0.00384293	+	0.00221872i
$617$	2.10193	−	2.50498i	0.0846205	−	0.100847i	−0.722073	−	0.691817i	$-0.756810\pi$
$617$	2.10193	−	2.50498i	0.0846205	−	0.100847i	0.806693	+	0.590970i	$0.201255\pi$
$618$	−16.5471	+	34.2217i	−0.665621	+	1.37660i
$619$	−1.49343			−0.0600258			−0.0300129	−	0.999550i	$-0.509555\pi$
$619$	−1.49343			−0.0600258			−0.0300129	+	0.999550i	$0.509555\pi$
$620$	−33.6844	+	58.3431i	−1.35280	+	2.34311i
$621$	−10.0337	−	5.20429i	−0.402639	−	0.208841i
$622$	−20.9640	−	24.9839i	−0.840581	−	1.00176i
$623$	0.173396	−	0.0631108i	0.00694695	−	0.00252848i
$624$	7.30235	+	5.26758i	0.292328	+	0.210872i
$625$	17.0530	+	96.7121i	0.682118	+	3.86849i
$626$	6.04178	+	10.4647i	0.241478	+	0.418252i
$627$	4.42213	+	23.4748i	0.176603	+	0.937494i
$628$	−0.678327	+	1.17490i	−0.0270682	+	0.0468835i
$629$	0.702644	+	0.255742i	0.0280163	+	0.0101971i
$630$	−3.38403	−	1.34051i	−0.134823	−	0.0534072i
$631$	−24.8633	−	20.8627i	−0.989791	−	0.830533i	−0.00425316	−	0.999991i	$-0.501354\pi$
$631$	−24.8633	−	20.8627i	−0.989791	−	0.830533i	−0.985537	+	0.169458i	$0.945798\pi$
$632$	−0.115840	+	0.0204258i	−0.00460788	+	0.000812493i
$633$	6.41366	−	13.2644i	0.254920	−	0.527211i
$634$	−12.0249			−0.477568
$635$	33.3283	−	57.7264i	1.32259	−	2.29080i
$636$	−0.190724	−	2.60025i	−0.00756270	−	0.103107i
$637$	−8.44008	−	1.48821i	−0.334408	−	0.0589652i
$638$	27.4719	−	15.8609i	1.08762	−	0.627940i
$639$	19.6498	+	12.0933i	0.777334	+	0.478404i
$640$	−8.38348	−	1.47823i	−0.331386	−	0.0584323i
$641$	−4.64858	−	26.3634i	−0.183608	−	1.04129i	−0.927731	−	0.373250i	$-0.878243\pi$
$641$	−4.64858	−	26.3634i	−0.183608	−	1.04129i	0.744123	−	0.668043i	$-0.232868\pi$
$642$	−18.3031	−	8.85002i	−0.722366	−	0.349282i
$643$	−16.8790	+	14.1632i	−0.665642	+	0.558540i	−0.911772	−	0.410697i	$-0.865286\pi$
$643$	−16.8790	+	14.1632i	−0.665642	+	0.558540i	0.246130	+	0.969237i	$0.420841\pi$
$644$	0.569879	−	0.100485i	0.0224564	−	0.00395967i
$645$	−41.2546	+	40.1114i	−1.62440	+	1.57938i
$646$	6.20062	−	14.2422i	0.243960	−	0.560352i
$647$		−	12.4108i		−	0.487921i	−0.969785	−	0.243960i	$-0.921553\pi$
$647$		−	12.4108i		−	0.487921i	0.969785	−	0.243960i	$-0.0784467\pi$
$648$	2.02959	+	0.870717i	0.0797300	+	0.0342050i
$649$	11.6719	−	2.05806i	0.458161	−	0.0807861i
$650$	−11.4729	−	31.5216i	−0.450006	−	1.23638i
$651$	0.205460	−	2.02098i	0.00805263	−	0.0792085i
$652$	−21.9752	+	7.99833i	−0.860616	+	0.313239i
$653$			18.2285i			0.713338i	0.934231	+	0.356669i	$0.116088\pi$
$653$			18.2285i			0.713338i	−0.934231	+	0.356669i	$0.883912\pi$
$654$	34.6403	−	33.6804i	1.35454	−	1.31701i
$655$	−1.81426	+	10.2892i	−0.0708891	+	0.402032i
$656$	−18.4884	+	6.72924i	−0.721852	+	0.262733i
$657$	−11.9661	+	6.46736i	−0.466841	+	0.252316i
$658$	3.00512	+	1.73501i	0.117152	+	0.0676377i
$659$	−4.93695	−	4.14259i	−0.192316	−	0.161373i	0.541545	−	0.840672i	$-0.317839\pi$
$659$	−4.93695	−	4.14259i	−0.192316	−	0.161373i	−0.733862	+	0.679299i	$0.762284\pi$
$660$	−18.3010	−	40.7309i	−0.712364	−	1.58545i
$661$	−10.2308	−	1.80397i	−0.397932	−	0.0701661i	−0.0288987	−	0.999582i	$-0.509200\pi$
$661$	−10.2308	−	1.80397i	−0.397932	−	0.0701661i	−0.369033	+	0.929416i	$0.620311\pi$
$662$	−15.8062	−	18.8371i	−0.614326	−	0.732125i
$663$	−2.25227	+	3.12228i	−0.0874709	+	0.121259i
$664$	1.77173	+	1.02291i	0.0687564	+	0.0396965i
$665$	−2.23953	−	1.48382i	−0.0868454	−	0.0575402i
$666$	1.27859	−	2.07752i	0.0495445	−	0.0805022i
$667$	−3.78908	+	10.4104i	−0.146714	+	0.403093i
$668$	−9.49020	−	3.45415i	−0.367187	−	0.133645i
$669$	9.08289	−	18.7847i	0.351165	−	0.726259i
$670$	−25.2089	−	9.17528i	−0.973904	−	0.354472i
$671$	−7.51117	−	20.6368i	−0.289966	−	0.796674i
$672$	−1.86832	+	0.472587i	−0.0720721	+	0.0182304i
$673$		−	22.4529i		−	0.865496i	−0.901515	−	0.432748i	$-0.857544\pi$
$673$		−	22.4529i		−	0.865496i	0.901515	−	0.432748i	$-0.142456\pi$
$674$	6.46697	+	17.7679i	0.249098	+	0.684392i
$675$	−38.8356	−	60.7603i	−1.49478	−	2.33866i
$676$	−10.7761	−	18.6648i	−0.414465	−	0.717875i
$677$	−20.3793	−	35.2979i	−0.783239	−	1.35661i	−0.930046	−	0.367444i	$-0.880233\pi$
$677$	−20.3793	−	35.2979i	−0.783239	−	1.35661i	0.146807	−	0.989165i	$-0.453100\pi$
$678$	−32.6867	+	22.2097i	−1.25533	+	0.852960i
$679$	0.509070	−	1.39866i	0.0195363	−	0.0536756i
$680$	0.335146	−	1.90071i	0.0128522	−	0.0728887i
$681$	−7.73285	−	17.2104i	−0.296323	−	0.659502i
$682$	39.4500	−	33.1025i	1.51062	−	1.26756i
$683$	37.0207			1.41656			0.708278	−	0.705933i	$-0.249472\pi$
$683$	37.0207			1.41656			0.708278	+	0.705933i	$0.249472\pi$
$684$	−20.0547	−	14.1139i	−0.766812	−	0.539660i
$685$	49.7523			1.90094
$686$	2.99052	−	2.50934i	0.114178	−	0.0958071i
$687$	19.1533	+	1.94720i	0.730744	+	0.0742902i
$688$	−5.62123	+	31.8796i	−0.214307	+	1.21540i
$689$	−0.337082	+	0.926126i	−0.0128418	+	0.0352826i
$690$	29.0125	+	14.0283i	1.10449	+	0.534048i
$691$	0.410516	+	0.711035i	0.0156168	+	0.0270490i	0.873728	−	0.486415i	$-0.161695\pi$
$691$	0.410516	+	0.711035i	0.0156168	+	0.0270490i	−0.858111	+	0.513464i	$0.828362\pi$
$692$	−11.2601	−	19.5031i	−0.428047	−	0.741398i
$693$	1.00672	+	0.894121i	0.0382422	+	0.0339648i
$694$	−12.4705	−	34.2625i	−0.473374	−	1.30059i
$695$			65.1051i			2.46958i
$696$	0.589560	−	2.08277i	0.0223472	−	0.0789472i
$697$	−2.87723	−	7.90514i	−0.108983	−	0.299428i
$698$	−33.5385	−	12.2070i	−1.26945	−	0.462042i
$699$	51.0599	−	3.74516i	1.93126	−	0.141655i
$700$	3.46914	+	1.26266i	0.131121	+	0.0477242i
$701$	−11.7782	+	32.3604i	−0.444857	+	1.22224i	0.491404	+	0.870932i	$0.336484\pi$
$701$	−11.7782	+	32.3604i	−0.444857	+	1.22224i	−0.936261	+	0.351304i	$0.885738\pi$
$702$	8.49906	+	9.24748i	0.320776	+	0.349024i
$703$	1.23999	−	1.30545i	0.0467670	−	0.0492359i
$704$	−19.1086	−	11.0323i	−0.720181	−	0.415797i
$705$	38.3264	+	85.2998i	1.44345	+	3.21257i
$706$	17.8534	+	21.2769i	0.671922	+	0.800765i
$707$	0.511651	+	0.0902179i	0.0192426	+	0.00339299i
$708$	−7.11821	+	9.86785i	−0.267519	+	0.370856i
$709$	13.2380	+	11.1080i	0.497165	+	0.417171i	0.856586	−	0.516005i	$-0.172581\pi$
$709$	13.2380	+	11.1080i	0.497165	+	0.417171i	−0.359421	+	0.933176i	$0.617026\pi$
$710$	−56.9697	−	32.8915i	−2.13804	−	1.23440i
$711$	−1.43749	−	0.0404018i	−0.0539102	−	0.00151519i
$712$	0.299955	−	0.109175i	0.0112413	−	0.00409149i
$713$	−3.12311	+	17.7120i	−0.116961	+	0.663321i
$714$	−0.214708	−	0.848825i	−0.00803523	−	0.0317665i
$715$			16.8795i			0.631258i
$716$	22.8892	−	8.33100i	0.855411	−	0.311344i
$717$	−20.9862	+	9.42938i	−0.783743	+	0.352147i
$718$	14.7369	+	40.4893i	0.549976	+	1.51105i
$719$	−36.6533	+	6.46297i	−1.36694	+	0.241028i	−0.808490	−	0.588511i	$-0.799715\pi$
$719$	−36.6533	+	6.46297i	−1.36694	+	0.241028i	−0.558449	+	0.829539i	$0.688603\pi$
$720$	−51.3065	−	20.3239i	−1.91208	−	0.757429i
$721$			1.58140i			0.0588943i
$722$	−25.4833	−	27.3789i	−0.948391	−	1.01894i
$723$	6.74149	+	26.6518i	0.250719	+	0.991192i
$724$	−20.5327	+	3.62047i	−0.763091	+	0.134554i
$725$	−54.1428	+	45.4312i	−2.01081	+	1.68727i
$726$	−0.246701	−	3.36342i	−0.00915594	−	0.124828i
$727$	1.75918	+	9.97679i	0.0652443	+	0.370019i	0.999896	+	0.0144529i	$0.00460067\pi$
$727$	1.75918	+	9.97679i	0.0652443	+	0.370019i	−0.934651	+	0.355566i	$0.884288\pi$
$728$	0.0420905	+	0.00742169i	0.00155998	+	0.000275066i
$729$	22.1630	+	15.4208i	0.820853	+	0.571140i
$730$	33.5848	−	19.3902i	1.24303	−	0.717662i
$731$	−13.6308	−	2.40348i	−0.504154	−	0.0888959i
$732$	20.2974	+	9.81430i	0.750212	+	0.362747i
$733$	13.2906	−	23.0200i	0.490900	−	0.850264i	−0.509045	−	0.860740i	$-0.670001\pi$
$733$	13.2906	−	23.0200i	0.490900	−	0.850264i	0.999945	+	0.0104759i	$0.00333466\pi$
$734$	31.0684			1.14676
$735$	52.3864	−	3.84246i	1.93230	−	0.141731i
$736$	16.8032	−	2.96286i	0.619375	−	0.109212i
$737$	7.60200	+	6.37883i	0.280023	+	0.234967i
$738$	−27.1513	+	4.00456i	−0.999454	+	0.147410i
$739$	20.9400	+	7.62155i	0.770291	+	0.280363i	0.697118	−	0.716956i	$-0.254465\pi$
$739$	20.9400	+	7.62155i	0.770291	+	0.280363i	0.0731731	+	0.997319i	$0.476687\pi$
$740$	−1.68283	+	2.91476i	−0.0618622	+	0.107149i
$741$	4.72836	+	7.97354i	0.173701	+	0.292915i
$742$	−0.112072	−	0.194114i	−0.00411428	−	0.00712615i
$743$	−0.610971	−	3.46499i	−0.0224144	−	0.127118i	0.971547	−	0.236845i	$-0.0761134\pi$
$743$	−0.610971	−	3.46499i	−0.0224144	−	0.127118i	−0.993962	+	0.109727i	$0.965002\pi$
$744$	0.355424	−	3.49607i	0.0130305	−	0.128172i
$745$	72.1395	−	26.2566i	2.64299	−	0.961968i
$746$	−14.1892	−	16.9100i	−0.519503	−	0.619120i
$747$	18.7005	+	16.6089i	0.684217	+	0.607688i
$748$	5.37063	−	9.30220i	0.196370	−	0.340122i
$749$	−0.845793			−0.0309046
$750$	73.9166	+	108.785i	2.69905	+	3.97227i
$751$	1.12702	−	1.34313i	0.0411256	−	0.0490116i	−0.745090	−	0.666964i	$-0.767593\pi$
$751$	1.12702	−	1.34313i	0.0411256	−	0.0490116i	0.786215	+	0.617953i	$0.212038\pi$
$752$	45.5617	+	26.3051i	1.66146	+	0.959247i
$753$	−0.872901	−	3.45093i	−0.0318103	−	0.125759i
$754$	7.91291	−	9.43024i	0.288171	−	0.343429i
$755$	17.9766	−	15.0842i	0.654235	−	0.548969i
$756$	−1.38088	+	0.0623461i	−0.0502220	+	0.00226750i
$757$	−6.00805	−	34.0734i	−0.218366	−	1.23842i	−0.874968	−	0.484180i	$-0.839118\pi$
$757$	−6.00805	−	34.0734i	−0.218366	−	1.23842i	0.656602	−	0.754237i	$-0.271993\pi$
$758$	−6.41495	−	7.64503i	−0.233001	−	0.277680i
$759$	−8.31018	−	8.54703i	−0.301641	−	0.310237i
$760$	−3.87415	−	2.56685i	−0.140530	−	0.0931095i
$761$	0.764305	−	0.441272i	0.0277060	−	0.0159961i	−0.486083	−	0.873913i	$-0.661575\pi$
$761$	0.764305	−	0.441272i	0.0277060	−	0.0159961i	0.513789	+	0.857917i	$0.328241\pi$
$762$	5.29075	−	52.0417i	0.191664	−	1.88527i
$763$	0.687462	−	1.88879i	0.0248878	−	0.0683787i
$764$	18.1049	−	21.5766i	0.655012	−	0.780613i
$765$	8.68995	−	21.9372i	0.314186	−	0.793142i
$766$	−8.40502	+	47.6672i	−0.303686	+	1.72229i
$767$	3.98318	−	2.29969i	0.143824	−	0.0830369i
$768$	−29.8964	+	7.56220i	−1.07879	+	0.272878i
$769$	−22.9977	−	19.2974i	−0.829319	−	0.695882i	0.125815	−	0.992054i	$-0.459845\pi$
$769$	−22.9977	−	19.2974i	−0.829319	−	0.695882i	−0.955135	+	0.296172i	$0.904290\pi$
$770$	−2.94073	−	2.46757i	−0.105977	−	0.0889250i
$771$	−18.2205	+	4.60883i	−0.656196	+	0.165983i
$772$	38.1526	−	22.0274i	1.37314	−	0.792783i
$773$	−3.04841	+	17.2884i	−0.109644	+	0.621821i	0.879620	+	0.475678i	$0.157797\pi$
$773$	−3.04841	+	17.2884i	−0.109644	+	0.621821i	−0.989263	+	0.146143i	$0.953314\pi$
$774$	−16.6301	+	41.9817i	−0.597757	+	1.50900i
$775$	−73.7545	+	87.8972i	−2.64934	+	3.15736i
$776$	0.880634	−	2.41952i	0.0316129	−	0.0868558i
$777$	0.0102646	−	0.100966i	0.000368240	−	0.00362214i
$778$	8.11670	−	4.68618i	0.290998	−	0.168008i
$779$	−20.2181	−	1.24609i	−0.724390	−	0.0446460i
$780$	−12.0799	−	12.4242i	−0.432529	−	0.444856i
$781$	15.6418	+	18.6412i	0.559708	+	0.667034i
$782$	1.34610	+	7.63412i	0.0481365	+	0.272995i
$783$	12.1846	−	23.4916i	0.435443	−	0.839521i
$784$	22.6375	−	18.9951i	0.808482	−	0.678397i
$785$	−2.02037	+	2.40778i	−0.0721100	+	0.0859373i
$786$	2.01063	+	7.94883i	0.0717168	+	0.283525i
$787$	−33.0360	−	19.0733i	−1.17761	−	0.679891i	−0.222147	−	0.975013i	$-0.571306\pi$
$787$	−33.0360	−	19.0733i	−1.17761	−	0.679891i	−0.955460	+	0.295122i	$0.904640\pi$
$788$	25.0235	−	29.8219i	0.891427	−	1.06236i
$789$	−0.0599331	−	0.0882053i	−0.00213367	−	0.00314019i
$790$	4.10003			0.145873
$791$	−0.822026	+	1.42379i	−0.0292279	+	0.0506242i
$792$	1.74152	+	1.54673i	0.0618821	+	0.0549607i
$793$	−5.47815	−	6.52860i	−0.194535	−	0.231837i
$794$	38.2968	−	13.9389i	1.35910	−	0.494673i
$795$	0.610951	−	6.00953i	0.0216682	−	0.213136i
$796$	−4.50185	−	25.5313i	−0.159564	−	0.904932i
$797$	13.4869	+	23.3601i	0.477732	+	0.827456i	0.999674	−	0.0255245i	$-0.00812559\pi$
$797$	13.4869	+	23.3601i	0.477732	+	0.827456i	−0.521942	+	0.852981i	$0.674792\pi$
$798$	−2.08037	−	0.341859i	−0.0736443	−	0.0121017i
$799$	−11.2473	+	19.4809i	−0.397901	+	0.689185i
$800$	102.290	+	37.2303i	3.61648	+	1.31629i
$801$	3.86071	−	0.569417i	0.136411	−	0.0201194i
$802$	58.1330	+	48.7794i	2.05275	+	1.72246i
$803$	−14.1276	+	2.49108i	−0.498553	+	0.0879084i
$804$	−10.1605	+	0.745255i	−0.358332	+	0.0262831i
$805$	1.34068			0.0472527
$806$	9.99249	−	17.3075i	0.351970	−	0.609630i
$807$	21.4015	+	10.3482i	0.753370	+	0.364274i
$808$	0.885099	+	0.156067i	0.0311377	+	0.00549041i
$809$	−18.7347	+	10.8165i	−0.658676	+	0.380287i	−0.791772	−	0.610817i	$-0.790841\pi$
$809$	−18.7347	+	10.8165i	−0.658676	+	0.380287i	0.133097	+	0.991103i	$0.457508\pi$
$810$	−64.3989	−	42.1733i	−2.26275	−	1.48182i
$811$	−43.7775	−	7.71915i	−1.53724	−	0.271056i	−0.660055	−	0.751217i	$-0.729467\pi$
$811$	−43.7775	−	7.71915i	−1.53724	−	0.271056i	−0.877180	+	0.480161i	$0.840578\pi$
$812$	0.235262	+	1.33424i	0.00825608	+	0.0468226i
$813$	−1.39659	−	19.0405i	−0.0489806	−	0.667780i
$814$	1.97088	−	1.65377i	0.0690793	−	0.0579644i
$815$	−53.3571	+	9.40830i	−1.86902	+	0.329559i
$816$	−3.25526	−	12.8693i	−0.113957	−	0.450517i
$817$	−18.4080	+	27.7832i	−0.644016	+	0.972013i
$818$			52.6809i			1.84194i
$819$	0.485792	+	0.192436i	0.0169750	+	0.00672426i
$820$	37.2904	−	6.57530i	1.30224	−	0.229619i
$821$	3.30575	+	9.08246i	0.115371	+	0.316980i	0.983916	−	0.178630i	$-0.0571666\pi$
$821$	3.30575	+	9.08246i	0.115371	+	0.316980i	−0.868545	+	0.495610i	$0.834944\pi$
$822$	35.6141	−	16.0019i	1.24219	−	0.558131i
$823$	28.8576	−	10.5033i	1.00591	−	0.366122i	0.214050	−	0.976823i	$-0.431334\pi$
$823$	28.8576	−	10.5033i	1.00591	−	0.366122i	0.791861	+	0.610701i	$0.209112\pi$
$824$			2.73564i			0.0953005i
$825$	−18.6501	−	73.7311i	−0.649311	−	2.56699i
$826$	−0.181640	+	1.03013i	−0.00632006	+	0.0358428i
$827$	−6.21829	+	2.26327i	−0.216231	+	0.0787017i	−0.447864	−	0.894101i	$-0.647815\pi$
$827$	−6.21829	+	2.26327i	−0.216231	+	0.0787017i	0.231633	+	0.972803i	$0.425593\pi$
$828$	12.2334	+	0.343829i	0.425141	+	0.0119489i
$829$	47.8115	+	27.6040i	1.66056	+	0.958727i	0.972446	+	0.233127i	$0.0748959\pi$
$829$	47.8115	+	27.6040i	1.66056	+	0.958727i	0.688117	+	0.725599i	$0.258437\pi$
$830$	−54.6261	−	45.8367i	−1.89610	−	1.59102i
$831$	9.09909	−	12.6139i	0.315644	−	0.437571i
$832$	−8.43255	−	1.48689i	−0.292346	−	0.0515485i
$833$	8.12178	+	9.67916i	0.281403	+	0.335363i
$834$	20.9399	+	46.6041i	0.725088	+	1.61377i
$835$	−20.2635	−	11.6991i	−0.701246	−	0.404864i
$836$	−15.3748	−	20.7982i	−0.531748	−	0.719320i
$837$	12.8580	−	40.9926i	0.444437	−	1.41691i
$838$	2.19596	−	6.03336i	0.0758582	−	0.208419i
$839$	−19.1363	−	6.96503i	−0.660657	−	0.240459i	−0.0101370	−	0.999949i	$-0.503227\pi$
$839$	−19.1363	−	6.96503i	−0.660657	−	0.240459i	−0.650520	+	0.759489i	$0.725449\pi$
$840$	−0.261250	+	0.0191623i	−0.00901398	+	0.000661161i
$841$	2.87755	+	1.04734i	0.0992260	+	0.0361153i
$842$	−23.5507	−	64.7051i	−0.811612	−	2.22988i
$843$	−3.57030	+	12.6130i	−0.122968	+	0.434415i
$844$			15.9525i			0.549109i
$845$	−17.0780	−	46.9214i	−0.587501	−	1.61415i
$846$	54.8703	+	48.7331i	1.88648	+	1.67548i
$847$	−0.0701509	−	0.121505i	−0.00241041	−	0.00417496i
$848$	−1.69916	−	2.94303i	−0.0583493	−	0.101064i
$849$	−5.12271	−	2.47696i	−0.175811	−	0.0850091i
$850$	−16.9147	+	46.4727i	−0.580168	+	1.59400i
$851$	−0.156027	+	0.884873i	−0.00534854	+	0.0303331i
$852$	−24.8538	−	2.52673i	−0.851476	−	0.0865643i
$853$	27.6323	−	23.1863i	0.946113	−	0.793883i	−0.0325257	−	0.999471i	$-0.510355\pi$
$853$	27.6323	−	23.1863i	0.946113	−	0.793883i	0.978639	+	0.205588i	$0.0659106\pi$
$854$	1.93824			0.0663253
$855$	−40.0793	−	40.2710i	−1.37068	−	1.37724i
$856$	−1.46313			−0.0500087
$857$	−13.1054	+	10.9968i	−0.447673	+	0.375642i	−0.838572	−	0.544791i	$-0.816609\pi$
$857$	−13.1054	+	10.9968i	−0.447673	+	0.375642i	0.390898	+	0.920434i	$0.372164\pi$
$858$	5.42899	+	12.0828i	0.185343	+	0.412502i
$859$	2.83100	−	16.0554i	0.0965924	−	0.547803i	−0.897655	−	0.440698i	$-0.854731\pi$
$859$	2.83100	−	16.0554i	0.0965924	−	0.547803i	0.994248	−	0.107105i	$-0.0341580\pi$
$860$	21.3080	−	58.5434i	0.726598	−	1.99631i
$861$	−0.944398	+	0.641693i	−0.0321850	+	0.0218688i
$862$	−26.9791	−	46.7292i	−0.918912	−	1.59160i
$863$	2.35883	+	4.08562i	0.0802956	+	0.139076i	0.903377	−	0.428848i	$-0.141080\pi$
$863$	2.35883	+	4.08562i	0.0802956	+	0.139076i	−0.823081	+	0.567924i	$0.807747\pi$
$864$	−40.7160	+	1.83831i	−1.38519	+	0.0625405i
$865$	−17.8451	−	49.0290i	−0.606752	−	1.66704i
$866$		−	20.9819i		−	0.712995i
$867$	−23.0432	+	5.82872i	−0.782590	+	0.197954i
$868$	0.752260	+	2.06682i	0.0255334	+	0.0701524i
$869$	−1.42521	−	0.518734i	−0.0483470	−	0.0175969i
$870$	−32.8440	+	67.9260i	−1.11351	+	2.30291i
$871$	3.61884	+	1.31715i	0.122620	+	0.0446300i
$872$	1.18923	−	3.26739i	0.0402725	−	0.110648i
$873$	16.4989	−	26.8082i	0.558403	−	0.907320i
$874$	18.1481	+	4.36596i	0.613868	+	0.147681i
$875$	4.73854	+	2.73580i	0.160192	+	0.0924868i
$876$	8.61588	−	11.9440i	0.291104	−	0.403552i
$877$	−1.74121	−	2.07509i	−0.0587964	−	0.0700708i	0.735845	−	0.677150i	$-0.236785\pi$
$877$	−1.74121	−	2.07509i	−0.0587964	−	0.0700708i	−0.794641	+	0.607080i	$0.792341\pi$
$878$	37.8582	+	6.67541i	1.27765	+	0.225284i
$879$	5.85781	+	13.0372i	0.197579	+	0.439735i
$880$	−44.5855	−	37.4116i	−1.50298	−	1.26115i
$881$	−39.2832	−	22.6802i	−1.32348	−	0.764114i	−0.339202	−	0.940714i	$-0.610157\pi$
$881$	−39.2832	−	22.6802i	−1.32348	−	0.764114i	−0.984283	+	0.176599i	$0.943490\pi$
$882$	36.2639	−	19.5997i	1.22107	−	0.659956i
$883$	23.8546	−	8.68236i	0.802771	−	0.292185i	0.0921369	−	0.995746i	$-0.470630\pi$
$883$	23.8546	−	8.68236i	0.802771	−	0.292185i	0.710634	+	0.703562i	$0.248408\pi$
$884$	0.723828	−	4.10503i	0.0243450	−	0.138067i
$885$	−20.2111	+	19.6510i	−0.679388	+	0.660562i
$886$			21.4077i			0.719207i
$887$	30.1035	−	10.9568i	1.01078	−	0.367893i	0.217046	−	0.976161i	$-0.430358\pi$
$887$	30.1035	−	10.9568i	1.01078	−	0.367893i	0.793731	+	0.608269i	$0.208136\pi$
$888$	0.0177566	−	0.174660i	0.000595872	−	0.00586121i
$889$	−0.744309	−	2.04497i	−0.0249633	−	0.0685862i
$890$	−10.9572	+	1.93206i	−0.367287	+	0.0647627i
$891$	17.0499	+	22.8076i	0.571194	+	0.764082i
$892$			22.5916i			0.756424i
$893$	32.1982	+	43.5561i	1.07747	+	1.45755i
$894$	43.1946	−	41.9976i	1.44464	−	1.40461i
$895$	55.5764	−	9.79961i	1.85771	−	0.327565i
$896$	−0.212905	+	0.178648i	−0.00711264	+	0.00596821i
$897$	−4.16487	−	2.01382i	−0.139061	−	0.0672396i
$898$	−10.9732	−	62.2324i	−0.366182	−	2.07672i
$899$	−41.4685	−	7.31202i	−1.38305	−	0.243870i
$900$	66.4933	+	40.9228i	2.21644	+	1.36409i
$901$	1.25836	−	0.726513i	0.0419219	−	0.0242036i
$902$	−28.5057	−	5.02632i	−0.949135	−	0.167358i
$903$	0.137421	+	1.87354i	0.00457309	+	0.0623476i
$904$	−1.42201	+	2.46300i	−0.0472955	+	0.0819182i
$905$	−48.3045			−1.60570
$906$	8.01663	−	16.5795i	0.266335	−	0.550818i
$907$	12.7375	−	2.24596i	0.422941	−	0.0745759i	0.0418731	−	0.999123i	$-0.486667\pi$
$907$	12.7375	−	2.24596i	0.422941	−	0.0745759i	0.381068	+	0.924547i	$0.375556\pi$
$908$	15.6494	+	13.1314i	0.519342	+	0.435780i
$909$	10.2155	+	4.04664i	0.338826	+	0.134219i
$910$	−1.39990	−	0.509523i	−0.0464063	−	0.0168905i
$911$	13.5776	−	23.5171i	0.449845	−	0.779155i	−0.548530	−	0.836131i	$-0.684812\pi$
$911$	13.5776	−	23.5171i	0.449845	−	0.779155i	0.998376	+	0.0569757i	$0.0181457\pi$
$912$	−31.5412	−	5.18304i	−1.04443	−	0.171627i
$913$	13.1893	+	22.8446i	0.436502	+	0.756044i
$914$	6.18523	+	35.0782i	0.204589	+	1.16028i
$915$	42.3626	+	30.5585i	1.40047	+	1.01023i
$916$	−19.5877	+	7.12935i	−0.647197	+	0.235560i
$917$	0.219258	+	0.261301i	0.00724053	+	0.00862893i
$918$	−0.835189	−	18.4983i	−0.0275653	−	0.610534i
$919$	−2.36075	+	4.08895i	−0.0778741	+	0.134882i	−0.902333	−	0.431041i	$-0.858147\pi$
$919$	−2.36075	+	4.08895i	−0.0778741	+	0.134882i	0.824458	+	0.565923i	$0.191480\pi$
$920$	2.31923			0.0764626
$921$	−0.588642	+	1.21740i	−0.0193964	+	0.0401146i
$922$	−27.9239	+	33.2784i	−0.919624	+	1.09596i
$923$	8.17825	+	4.72172i	0.269190	+	0.155417i
$924$	−1.40274	−	0.397066i	−0.0461466	−	0.0130625i
$925$	−3.68470	+	4.39125i	−0.121152	+	0.144383i
$926$	35.3085	−	29.6273i	1.16031	−	0.973615i
$927$	−6.73068	+	32.7605i	−0.221065	+	1.07600i
$928$	6.93684	+	39.3408i	0.227713	+	1.29142i
$929$	−23.3011	−	27.7692i	−0.764485	−	0.911078i	0.233638	−	0.972324i	$-0.424937\pi$
$929$	−23.3011	−	27.7692i	−0.764485	−	0.911078i	−0.998123	+	0.0612460i	$0.980493\pi$
$930$	−33.3612	+	117.857i	−1.09396	+	3.86468i
$931$	29.1757	−	8.62739i	0.956196	−	0.282751i
$932$	−48.0062	+	27.7164i	−1.57249	+	0.907880i
$933$	−23.2723	−	16.7876i	−0.761902	−	0.549602i
$934$	−21.1758	+	58.1801i	−0.692894	+	1.90371i
$935$	15.9962	−	19.0635i	0.523131	−	0.623443i
$936$	0.840367	+	0.332893i	0.0274683	+	0.0108810i
$937$	−1.68081	+	9.53233i	−0.0549096	+	0.311408i	−0.999876	−	0.0157602i	$-0.994983\pi$
$937$	−1.68081	+	9.53233i	−0.0549096	+	0.311408i	0.944966	+	0.327168i	$0.106094\pi$
$938$	−0.758501	+	0.437921i	−0.0247659	+	0.0142986i
$939$	7.41135	+	7.62258i	0.241860	+	0.248753i
$940$	−77.5629	−	65.0830i	−2.52982	−	2.12277i
$941$	38.5627	+	32.3579i	1.25711	+	1.05484i	0.995984	+	0.0895326i	$0.0285373\pi$
$941$	38.5627	+	32.3579i	1.25711	+	1.05484i	0.261123	+	0.965305i	$0.415907\pi$
$942$	−0.671819	+	2.37337i	−0.0218890	+	0.0773287i
$943$	8.75455	−	5.05444i	0.285088	−	0.164595i
$944$	−2.75390	+	15.6182i	−0.0896319	+	0.508328i
$945$	−3.17573	−	0.413294i	−0.103307	−	0.0134445i
$946$	−30.6122	+	36.4822i	−0.995288	+	1.18614i
$947$	−15.6222	+	42.9217i	−0.507653	+	1.39477i	0.375998	+	0.926621i	$0.377300\pi$
$947$	−15.6222	+	42.9217i	−0.507653	+	1.39477i	−0.883651	+	0.468146i	$0.844922\pi$
$948$	1.42026	−	0.638142i	0.0461279	−	0.0207259i
$949$	−4.82124	+	2.78354i	−0.156504	+	0.0903576i
$950$	86.3419	+	82.0123i	2.80130	+	2.66083i
$951$	−10.2569	+	2.59446i	−0.332604	+	0.0841312i
$952$	−0.0405031	−	0.0482698i	−0.00131271	−	0.00156443i
$953$	2.59880	+	14.7385i	0.0841835	+	0.477428i	0.997530	+	0.0702446i	$0.0223780\pi$
$953$	2.59880	+	14.7385i	0.0841835	+	0.477428i	−0.913346	+	0.407184i	$0.866511\pi$
$954$	−1.49552	−	4.49830i	−0.0484193	−	0.145638i
$955$	49.9892	−	41.9459i	1.61761	−	1.35734i
$956$	16.0123	−	19.0827i	0.517874	−	0.617179i
$957$	20.0109	−	19.4563i	0.646859	−	0.628934i
$958$	13.1404	+	7.58664i	0.424548	+	0.245113i
$959$	1.04409	−	1.24430i	0.0337155	−	0.0401805i
$960$	52.3397	−	3.83903i	1.68926	−	0.123904i
$961$	−37.3600			−1.20516
$962$	0.499214	−	0.864663i	0.0160953	−	0.0278779i
$963$	−17.5216	−	3.59983i	−0.564626	−	0.116003i
$964$	−19.1330	−	22.8018i	−0.616232	−	0.734397i
$965$	95.9119	−	34.9091i	3.08751	−	1.12376i
$966$	0.959697	−	0.431205i	0.0308778	−	0.0138738i
$967$	6.17436	+	35.0165i	0.198554	+	1.12606i	0.907266	+	0.420558i	$0.138166\pi$
$967$	6.17436	+	35.0165i	0.198554	+	1.12606i	−0.708712	+	0.705498i	$0.750723\pi$
$968$	−0.121353	−	0.210190i	−0.00390044	−	0.00675577i
$969$	2.21612	−	13.4861i	0.0711921	−	0.433237i
$970$	−44.8738	+	77.7237i	−1.44081	+	2.49556i
$971$	−32.6746	−	11.8926i	−1.04858	−	0.381651i	−0.240451	−	0.970661i	$-0.577295\pi$
$971$	−32.6746	−	11.8926i	−1.04858	−	0.381651i	−0.808125	+	0.589011i	$0.799518\pi$
$972$	−28.8719	−	4.58567i	−0.926067	−	0.147085i
$973$	1.62827	+	1.36628i	0.0522000	+	0.0438010i
$974$	60.6691	−	10.6976i	1.94396	−	0.342773i
$975$	−16.5872	−	24.4119i	−0.531216	−	0.781806i
$976$	29.3863			0.940634
$977$	−18.0719	+	31.3014i	−0.578170	+	1.00142i	0.417519	+	0.908668i	$0.362900\pi$
$977$	−18.0719	+	31.3014i	−0.578170	+	1.00142i	−0.995689	+	0.0927515i	$0.970434\pi$
$978$	−35.1686	+	23.8961i	−1.12457	+	0.764113i
$979$	4.05328	+	0.714703i	0.129544	+	0.0228420i
$980$	−49.2534	+	28.4365i	−1.57334	+	0.908369i
$981$	22.2806	−	36.2025i	0.711364	−	1.15586i
$982$	−34.5916	−	6.09943i	−1.10386	−	0.194641i
$983$	−8.97963	−	50.9260i	−0.286406	−	1.62429i	−0.700221	−	0.713926i	$-0.746915\pi$
$983$	−8.97963	−	50.9260i	−0.286406	−	1.62429i	0.413816	−	0.910361i	$-0.364196\pi$
$984$	−1.63370	+	1.11006i	−0.0520806	+	0.0353873i
$985$	69.0922	−	57.9752i	2.20146	−	1.84724i
$986$	−17.8735	+	3.15158i	−0.569208	+	0.100367i
$987$	2.93765	+	0.831545i	0.0935064	+	0.0264684i
$988$	−8.36716	−	5.54374i	−0.266195	−	0.176370i
$989$		−	16.6322i		−	0.528874i
$990$	−50.4184	−	63.6349i	−1.60240	−	2.02245i
$991$	−10.9402	+	1.92906i	−0.347528	+	0.0612786i	−0.344688	−	0.938717i	$-0.612015\pi$
$991$	−10.9402	+	1.92906i	−0.347528	+	0.0612786i	−0.00284032	+	0.999996i	$0.500904\pi$
$992$	22.1808	+	60.9413i	0.704242	+	1.93489i
$993$	−17.5466	−	12.6573i	−0.556825	−	0.401668i
$994$	−2.01817	+	0.734553i	−0.0640124	+	0.0232986i
$995$		−	60.0640i		−	1.90416i
$996$	−26.0568	−	7.37576i	−0.825640	−	0.233710i
$997$	−9.97313	+	56.5604i	−0.315852	+	1.79129i	0.251549	+	0.967845i	$0.419060\pi$
$997$	−9.97313	+	56.5604i	−0.315852	+	1.79129i	−0.567401	+	0.823442i	$0.692051\pi$
$998$	−17.2139	+	6.26533i	−0.544895	+	0.198326i
$999$	0.642371	−	2.04794i	0.0203237	−	0.0647941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.110.4	yes	108
3.2	odd	2		513.2.bo.a.224.15		108
9.4	even	3		513.2.cd.a.395.4		108
9.5	odd	6		171.2.bd.a.167.15	yes	108
19.14	odd	18		171.2.bd.a.128.15	yes	108
57.14	even	18		513.2.cd.a.413.4		108
171.14	even	18	inner	171.2.x.a.14.4	✓	108
171.166	odd	18		513.2.bo.a.71.15		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.4	✓	108	171.14	even	18	inner
171.2.x.a.110.4	yes	108	1.1	even	1	trivial
171.2.bd.a.128.15	yes	108	19.14	odd	18
171.2.bd.a.167.15	yes	108	9.5	odd	6
513.2.bo.a.71.15		108	171.166	odd	18
513.2.bo.a.224.15		108	3.2	odd	2
513.2.cd.a.395.4		108	9.4	even	3
513.2.cd.a.413.4		108	57.14	even	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50803 + 1.26539i) q^{2} +(-1.01330 + 1.40472i) q^{3} +(0.325651 - 1.84686i) q^{4} +(1.48603 - 4.08283i) q^{5} +(-0.249426 - 3.40056i) q^{6} +(-0.0709257 - 0.122847i) q^{7} +(-0.122694 - 0.212511i) q^{8} +(-0.946454 - 2.84679i) q^{9} +O(q^{10})\)	\(q+(-1.50803 + 1.26539i) q^{2} +(-1.01330 + 1.40472i) q^{3} +(0.325651 - 1.84686i) q^{4} +(1.48603 - 4.08283i) q^{5} +(-0.249426 - 3.40056i) q^{6} +(-0.0709257 - 0.122847i) q^{7} +(-0.122694 - 0.212511i) q^{8} +(-0.946454 - 2.84679i) q^{9} +(2.92538 + 8.03742i) q^{10} -3.16400i q^{11} +(2.26433 + 2.32886i) q^{12} +(-0.419951 - 1.15381i) q^{13} +(0.262407 + 0.0955082i) q^{14} +(4.22943 + 6.22457i) q^{15} +(3.97844 + 1.44803i) q^{16} +(-0.619138 + 1.70107i) q^{17} +(5.02957 + 3.09541i) q^{18} +(3.16043 + 3.00195i) q^{19} +(-7.05648 - 4.07406i) q^{20} +(0.244434 + 0.0248501i) q^{21} +(4.00369 + 4.77141i) q^{22} +(-2.14224 - 0.377734i) q^{23} +(0.422843 + 0.0429878i) q^{24} +(-10.6310 - 8.92047i) q^{25} +(2.09331 + 1.20857i) q^{26} +(4.95797 + 1.55515i) q^{27} +(-0.249978 + 0.0909845i) q^{28} +(0.884375 - 5.01554i) q^{29} +(-14.2546 - 4.03497i) q^{30} -8.26801i q^{31} +(-7.37074 + 2.68273i) q^{32} +(4.44453 + 3.20608i) q^{33} +(-1.21883 - 3.34871i) q^{34} +(-0.606961 + 0.107024i) q^{35} +(-5.56583 + 0.820907i) q^{36} -0.413061i q^{37} +(-8.56464 - 0.527860i) q^{38} +(2.04631 + 0.579238i) q^{39} +(-1.04997 + 0.185139i) q^{40} +(-3.55993 + 2.98714i) q^{41} +(-0.400058 + 0.271829i) q^{42} +(1.32771 + 7.52984i) q^{43} +(-5.84347 - 1.03036i) q^{44} +(-13.0294 - 0.366202i) q^{45} +(3.70853 - 2.14112i) q^{46} +(12.2375 + 2.15781i) q^{47} +(-6.06542 + 4.12129i) q^{48} +(3.48994 - 6.04475i) q^{49} +27.3197 q^{50} +(-1.76215 - 2.59340i) q^{51} +(-2.26767 + 0.399852i) q^{52} +(-0.614881 - 0.515946i) q^{53} +(-9.44463 + 3.92854i) q^{54} +(-12.9181 - 4.70180i) q^{55} +(-0.0174042 + 0.0301450i) q^{56} +(-7.41934 + 1.39764i) q^{57} +(5.01293 + 8.68265i) q^{58} +(0.650462 + 3.68895i) q^{59} +(12.8732 - 5.78412i) q^{60} +(6.52236 - 2.37394i) q^{61} +(10.4622 + 12.4684i) q^{62} +(-0.282592 + 0.318180i) q^{63} +(3.48683 - 6.03936i) q^{64} -5.33486 q^{65} +(-10.7594 + 0.789185i) q^{66} +(-2.01606 + 2.40265i) q^{67} +(2.94001 + 1.69742i) q^{68} +(2.70133 - 2.62648i) q^{69} +(0.779888 - 0.929434i) q^{70} +(-5.89164 + 4.94368i) q^{71} +(-0.488852 + 0.550415i) q^{72} +(-0.787319 - 4.46511i) q^{73} +(0.522681 + 0.622907i) q^{74} +(23.3031 - 5.89445i) q^{75} +(6.57337 - 4.85928i) q^{76} +(-0.388688 + 0.224409i) q^{77} +(-3.81885 + 1.71586i) q^{78} +(0.163949 - 0.450445i) q^{79} +(11.8241 - 14.0915i) q^{80} +(-7.20845 + 5.38872i) q^{81} +(1.58859 - 9.00937i) q^{82} +(-7.22014 + 4.16855i) q^{83} +(0.125495 - 0.443342i) q^{84} +(6.02512 + 5.05567i) q^{85} +(-11.5304 - 9.67514i) q^{86} +(6.14928 + 6.32453i) q^{87} +(-0.672387 + 0.388203i) q^{88} +(-0.225886 + 1.28106i) q^{89} +(20.1121 - 15.9350i) q^{90} +(-0.111956 + 0.133424i) q^{91} +(-1.39524 + 3.83340i) q^{92} +(11.6142 + 8.37796i) q^{93} +(-21.1850 + 12.2312i) q^{94} +(16.9529 - 8.44251i) q^{95} +(3.70028 - 13.0722i) q^{96} +(6.74465 + 8.03796i) q^{97} +(2.38602 + 13.5318i) q^{98} +(-9.00726 + 2.99459i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

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