LMFDB - Embedded newform 805.2.u.d.36.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(36,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("805.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.u (of order $11$, degree $10$, 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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$130$
Relative dimension:	$13$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			36.3
Character	$\chi$	$=$	805.36
Dual form			805.2.u.d.246.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26899 - 1.46449i) q^{2} +(1.73669 + 1.11610i) q^{3} +(-0.249772 + 1.73720i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.569318 - 3.95969i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-0.399286 + 0.256605i) q^{8} +(0.524163 + 1.14776i) q^{9} +O(q^{10})$	\(q+(-1.26899 - 1.46449i) q^{2} +(1.73669 + 1.11610i) q^{3} +(-0.249772 + 1.73720i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.569318 - 3.95969i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-0.399286 + 0.256605i) q^{8} +(0.524163 + 1.14776i) q^{9} +(-1.85930 + 0.545941i) q^{10} +(0.0852326 - 0.0983636i) q^{11} +(-2.37267 + 2.73821i) q^{12} +(-1.33946 + 0.393300i) q^{13} +(-0.804991 - 1.76268i) q^{14} +(1.73669 - 1.11610i) q^{15} +(4.25043 + 1.24804i) q^{16} +(-0.930096 - 6.46896i) q^{17} +(1.01572 - 2.22412i) q^{18} +(0.801004 - 5.57111i) q^{19} +(1.47646 + 0.948861i) q^{20} +(1.35190 + 1.56018i) q^{21} -0.252212 q^{22} +(3.55936 - 3.21418i) q^{23} -0.979834 q^{24} +(-0.654861 - 0.755750i) q^{25} +(2.27574 + 1.46253i) q^{26} +(0.510681 - 3.55187i) q^{27} +(-0.729081 + 1.59646i) q^{28} +(0.999037 + 6.94845i) q^{29} +(-3.83836 - 1.12705i) q^{30} +(2.90793 - 1.86881i) q^{31} +(-3.17167 - 6.94499i) q^{32} +(0.257807 - 0.0756989i) q^{33} +(-8.29345 + 9.57115i) q^{34} +(0.654861 - 0.755750i) q^{35} +(-2.12481 + 0.623900i) q^{36} +(3.49874 + 7.66117i) q^{37} +(-9.17530 + 5.89661i) q^{38} +(-2.76519 - 0.811932i) q^{39} +(0.0675472 + 0.469801i) q^{40} +(4.52017 - 9.89780i) q^{41} +(0.569318 - 3.95969i) q^{42} +(7.94044 + 5.10301i) q^{43} +(0.149589 + 0.172635i) q^{44} +1.26178 q^{45} +(-9.22393 - 1.13389i) q^{46} +3.24857 q^{47} +(5.98875 + 6.91138i) q^{48} +(0.841254 + 0.540641i) q^{49} +(-0.275778 + 1.91808i) q^{50} +(5.60474 - 12.2727i) q^{51} +(-0.348683 - 2.42514i) q^{52} +(-9.76527 - 2.86734i) q^{53} +(-5.84973 + 3.75939i) q^{54} +(-0.0540678 - 0.118392i) q^{55} +(-0.455406 + 0.133719i) q^{56} +(7.60903 - 8.78129i) q^{57} +(8.90818 - 10.2806i) q^{58} +(-0.175414 + 0.0515063i) q^{59} +(1.50512 + 3.29576i) q^{60} +(7.06456 - 4.54012i) q^{61} +(-6.42699 - 1.88714i) q^{62} +(0.179570 + 1.24894i) q^{63} +(-2.46559 + 5.39889i) q^{64} +(-0.198672 + 1.38180i) q^{65} +(-0.438014 - 0.281494i) q^{66} +(-5.85748 - 6.75989i) q^{67} +11.4702 q^{68} +(9.76887 - 1.60943i) q^{69} -1.93780 q^{70} +(7.60760 + 8.77964i) q^{71} +(-0.503812 - 0.323780i) q^{72} +(-1.75464 + 12.2038i) q^{73} +(6.77986 - 14.8458i) q^{74} +(-0.293796 - 2.04340i) q^{75} +(9.47807 + 2.78301i) q^{76} +(0.109492 - 0.0703664i) q^{77} +(2.31992 + 5.07992i) q^{78} +(-10.6746 + 3.13435i) q^{79} +(2.90095 - 3.34788i) q^{80} +(7.33002 - 8.45930i) q^{81} +(-20.2313 + 5.94044i) q^{82} +(-6.03810 - 13.2216i) q^{83} +(-3.04801 + 1.95884i) q^{84} +(-6.27075 - 1.84126i) q^{85} +(-2.60302 - 18.1044i) q^{86} +(-6.02018 + 13.1823i) q^{87} +(-0.00879152 + 0.0611463i) q^{88} +(7.70110 + 4.94920i) q^{89} +(-1.60119 - 1.84787i) q^{90} -1.39601 q^{91} +(4.69466 + 6.98614i) q^{92} +7.13597 q^{93} +(-4.12240 - 4.75750i) q^{94} +(-4.73491 - 3.04294i) q^{95} +(2.24312 - 15.6012i) q^{96} +(-7.10610 + 15.5602i) q^{97} +(-0.275778 - 1.91808i) q^{98} +(0.157573 + 0.0462677i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9}+O(q^{10}) $ 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9} + 2 q^{10} + 2 q^{11} - 5 q^{12} + 13 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} - 51 q^{17} + q^{18} - 9 q^{19} - 16 q^{20} - 2 q^{21} + 34 q^{22} - 10 q^{23} - 76 q^{24} - 13 q^{25} - 31 q^{26} + 14 q^{27} + 27 q^{28} + 3 q^{29} + 5 q^{30} + 6 q^{31} + 22 q^{32} - 58 q^{33} + q^{34} + 13 q^{35} + 193 q^{36} - 36 q^{37} + 4 q^{38} - 2 q^{39} - 29 q^{40} - 34 q^{41} - 5 q^{42} - 22 q^{43} + 8 q^{44} + 170 q^{45} - 198 q^{46} - 14 q^{47} - 120 q^{48} - 13 q^{49} + 2 q^{50} - 6 q^{51} + 33 q^{52} - 18 q^{53} + 188 q^{54} - 31 q^{55} - 15 q^{56} - 9 q^{57} + 114 q^{58} + 46 q^{59} - 16 q^{60} - 56 q^{61} - 146 q^{62} + 17 q^{63} - 109 q^{64} + 2 q^{65} - 14 q^{66} - 10 q^{67} + 86 q^{68} - 6 q^{69} - 2 q^{70} - 25 q^{72} + 64 q^{73} + 79 q^{74} + 2 q^{75} + 32 q^{76} - 13 q^{77} - 64 q^{78} - 118 q^{79} - 17 q^{80} + 23 q^{81} + 129 q^{82} - 117 q^{83} - 72 q^{84} - 7 q^{85} + 74 q^{86} - 51 q^{87} - 40 q^{88} - 35 q^{89} + 100 q^{90} + 42 q^{91} + 76 q^{92} - 90 q^{93} - 7 q^{94} + 2 q^{95} + 393 q^{96} - 4 q^{97} + 2 q^{98} - 40 q^{99}+O(q^{100}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9 + 2 * q^10 + 2 * q^11 - 5 * q^12 + 13 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 - 51 * q^17 + q^18 - 9 * q^19 - 16 * q^20 - 2 * q^21 + 34 * q^22 - 10 * q^23 - 76 * q^24 - 13 * q^25 - 31 * q^26 + 14 * q^27 + 27 * q^28 + 3 * q^29 + 5 * q^30 + 6 * q^31 + 22 * q^32 - 58 * q^33 + q^34 + 13 * q^35 + 193 * q^36 - 36 * q^37 + 4 * q^38 - 2 * q^39 - 29 * q^40 - 34 * q^41 - 5 * q^42 - 22 * q^43 + 8 * q^44 + 170 * q^45 - 198 * q^46 - 14 * q^47 - 120 * q^48 - 13 * q^49 + 2 * q^50 - 6 * q^51 + 33 * q^52 - 18 * q^53 + 188 * q^54 - 31 * q^55 - 15 * q^56 - 9 * q^57 + 114 * q^58 + 46 * q^59 - 16 * q^60 - 56 * q^61 - 146 * q^62 + 17 * q^63 - 109 * q^64 + 2 * q^65 - 14 * q^66 - 10 * q^67 + 86 * q^68 - 6 * q^69 - 2 * q^70 - 25 * q^72 + 64 * q^73 + 79 * q^74 + 2 * q^75 + 32 * q^76 - 13 * q^77 - 64 * q^78 - 118 * q^79 - 17 * q^80 + 23 * q^81 + 129 * q^82 - 117 * q^83 - 72 * q^84 - 7 * q^85 + 74 * q^86 - 51 * q^87 - 40 * q^88 - 35 * q^89 + 100 * q^90 + 42 * q^91 + 76 * q^92 - 90 * q^93 - 7 * q^94 + 2 * q^95 + 393 * q^96 - 4 * q^97 + 2 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.26899	−	1.46449i	−0.897311	−	1.03555i	−0.999169	−	0.0407527i	$-0.987024\pi$
$2$	−1.26899	−	1.46449i	−0.897311	−	1.03555i	0.101859	−	0.994799i	$-0.467521\pi$
$3$	1.73669	+	1.11610i	1.00268	+	0.644383i	0.935488	−	0.353358i	$-0.114960\pi$
$3$	1.73669	+	1.11610i	1.00268	+	0.644383i	0.0671906	+	0.997740i	$0.478596\pi$
$4$	−0.249772	+	1.73720i	−0.124886	+	0.868601i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$6$	−0.569318	−	3.95969i	−0.232423	−	1.61654i
$7$	0.959493	+	0.281733i	0.362654	+	0.106485i
$7$	0.959493	+	0.281733i	0.362654	+	0.106485i
$8$	−0.399286	+	0.256605i	−0.141169	+	0.0907237i
$9$	0.524163	+	1.14776i	0.174721	+	0.382586i
$10$	−1.85930	+	0.545941i	−0.587964	+	0.172642i
$11$	0.0852326	−	0.0983636i	0.0256986	−	0.0296577i	−0.742755	−	0.669564i	$-0.766481\pi$
$11$	0.0852326	−	0.0983636i	0.0256986	−	0.0296577i	0.768453	+	0.639906i	$0.221027\pi$
$12$	−2.37267	+	2.73821i	−0.684932	+	0.790454i
$13$	−1.33946	+	0.393300i	−0.371499	+	0.109082i	−0.462152	−	0.886801i	$-0.652923\pi$
$13$	−1.33946	+	0.393300i	−0.371499	+	0.109082i	0.0906536	+	0.995882i	$0.471104\pi$
$14$	−0.804991	−	1.76268i	−0.215143	−	0.471097i
$15$	1.73669	−	1.11610i	0.448412	−	0.288177i
$16$	4.25043	+	1.24804i	1.06261	+	0.312010i
$17$	−0.930096	−	6.46896i	−0.225581	−	1.56895i	−0.716399	−	0.697691i	$-0.754211\pi$
$17$	−0.930096	−	6.46896i	−0.225581	−	1.56895i	0.490818	−	0.871262i	$-0.336698\pi$
$18$	1.01572	−	2.22412i	0.239408	−	0.524231i
$19$	0.801004	−	5.57111i	0.183763	−	1.27810i	−0.664003	−	0.747730i	$-0.731144\pi$
$19$	0.801004	−	5.57111i	0.183763	−	1.27810i	0.847766	−	0.530370i	$-0.177947\pi$
$20$	1.47646	+	0.948861i	0.330146	+	0.212172i
$21$	1.35190	+	1.56018i	0.295009	+	0.340458i
$22$	−0.252212			−0.0537717
$23$	3.55936	−	3.21418i	0.742178	−	0.670203i
$23$	3.55936	−	3.21418i	0.742178	−	0.670203i
$24$	−0.979834			−0.200008
$25$	−0.654861	−	0.755750i	−0.130972	−	0.151150i
$26$	2.27574	+	1.46253i	0.446309	+	0.286826i
$27$	0.510681	−	3.55187i	0.0982807	−	0.683557i
$28$	−0.729081	+	1.59646i	−0.137783	+	0.301703i
$29$	0.999037	+	6.94845i	0.185517	+	1.29030i	0.843445	+	0.537215i	$0.180524\pi$
$29$	0.999037	+	6.94845i	0.185517	+	1.29030i	−0.657929	+	0.753080i	$0.728567\pi$
$30$	−3.83836	−	1.12705i	−0.700786	−	0.205769i
$31$	2.90793	−	1.86881i	0.522280	−	0.335649i	−0.252793	−	0.967520i	$-0.581349\pi$
$31$	2.90793	−	1.86881i	0.522280	−	0.335649i	0.775073	+	0.631871i	$0.217713\pi$
$32$	−3.17167	−	6.94499i	−0.560677	−	1.22771i
$33$	0.257807	−	0.0756989i	0.0448784	−	0.0131775i
$34$	−8.29345	+	9.57115i	−1.42232	+	1.64144i
$35$	0.654861	−	0.755750i	0.110692	−	0.127745i
$36$	−2.12481	+	0.623900i	−0.354135	+	0.103983i
$37$	3.49874	+	7.66117i	0.575189	+	1.25949i	0.943988	+	0.329980i	$0.107042\pi$
$37$	3.49874	+	7.66117i	0.575189	+	1.25949i	−0.368799	+	0.929509i	$0.620231\pi$
$38$	−9.17530	+	5.89661i	−1.48843	+	0.956556i
$39$	−2.76519	−	0.811932i	−0.442784	−	0.130013i
$40$	0.0675472	+	0.469801i	0.0106801	+	0.0742820i
$41$	4.52017	−	9.89780i	0.705932	−	1.54578i	−0.126694	−	0.991942i	$-0.540437\pi$
$41$	4.52017	−	9.89780i	0.705932	−	1.54578i	0.832627	−	0.553835i	$-0.186836\pi$
$42$	0.569318	−	3.95969i	0.0878476	−	0.610994i
$43$	7.94044	+	5.10301i	1.21091	+	0.778202i	0.980810	−	0.194966i	$-0.0624596\pi$
$43$	7.94044	+	5.10301i	1.21091	+	0.778202i	0.230096	+	0.973168i	$0.426096\pi$
$44$	0.149589	+	0.172635i	0.0225514	+	0.0260257i
$45$	1.26178			0.188095
$46$	−9.22393	−	1.13389i	−1.35999	−	0.167183i
$47$	3.24857			0.473853			0.236926	−	0.971528i	$-0.423860\pi$
$47$	3.24857			0.473853			0.236926	+	0.971528i	$0.423860\pi$
$48$	5.98875	+	6.91138i	0.864401	+	0.997572i
$49$	0.841254	+	0.540641i	0.120179	+	0.0772344i
$50$	−0.275778	+	1.91808i	−0.0390008	+	0.271257i
$51$	5.60474	−	12.2727i	0.784820	−	1.71852i
$52$	−0.348683	−	2.42514i	−0.0483536	−	0.336307i
$53$	−9.76527	−	2.86734i	−1.34136	−	0.393860i	−0.469207	−	0.883088i	$-0.655460\pi$
$53$	−9.76527	−	2.86734i	−1.34136	−	0.393860i	−0.872156	+	0.489228i	$0.837279\pi$
$54$	−5.84973	+	3.75939i	−0.796047	+	0.511588i
$55$	−0.0540678	−	0.118392i	−0.00729050	−	0.0159640i
$56$	−0.455406	+	0.133719i	−0.0608562	+	0.0178690i
$57$	7.60903	−	8.78129i	1.00784	−	1.16311i
$58$	8.90818	−	10.2806i	1.16970	−	1.34991i
$59$	−0.175414	+	0.0515063i	−0.0228370	+	0.00670555i	−0.293131	−	0.956072i	$-0.594697\pi$
$59$	−0.175414	+	0.0515063i	−0.0228370	+	0.00670555i	0.270294	+	0.962778i	$0.412879\pi$
$60$	1.50512	+	3.29576i	0.194310	+	0.425480i
$61$	7.06456	−	4.54012i	0.904524	−	0.581302i	−0.00360443	−	0.999994i	$-0.501147\pi$
$61$	7.06456	−	4.54012i	0.904524	−	0.581302i	0.908129	+	0.418691i	$0.137511\pi$
$62$	−6.42699	−	1.88714i	−0.816229	−	0.239666i
$63$	0.179570	+	1.24894i	0.0226237	+	0.157352i
$64$	−2.46559	+	5.39889i	−0.308199	+	0.674861i
$65$	−0.198672	+	1.38180i	−0.0246423	+	0.171391i
$66$	−0.438014	−	0.281494i	−0.0539158	−	0.0346496i
$67$	−5.85748	−	6.75989i	−0.715605	−	0.825853i	0.275166	−	0.961397i	$-0.411267\pi$
$67$	−5.85748	−	6.75989i	−0.715605	−	0.825853i	−0.990771	+	0.135544i	$0.956722\pi$
$68$	11.4702			1.39097
$69$	9.76887	−	1.60943i	1.17603	−	0.193752i
$70$	−1.93780			−0.231611
$71$	7.60760	+	8.77964i	0.902856	+	1.04195i	0.998915	+	0.0465755i	$0.0148308\pi$
$71$	7.60760	+	8.77964i	0.902856	+	1.04195i	−0.0960589	+	0.995376i	$0.530624\pi$
$72$	−0.503812	−	0.323780i	−0.0593748	−	0.0381579i
$73$	−1.75464	+	12.2038i	−0.205365	+	1.42835i	0.582666	+	0.812712i	$0.302010\pi$
$73$	−1.75464	+	12.2038i	−0.205365	+	1.42835i	−0.788031	+	0.615635i	$0.788899\pi$
$74$	6.77986	−	14.8458i	0.788142	−	1.72579i
$75$	−0.293796	−	2.04340i	−0.0339246	−	0.235951i
$76$	9.47807	+	2.78301i	1.08721	+	0.319234i
$77$	0.109492	−	0.0703664i	0.0124778	−	0.00801900i
$78$	2.31992	+	5.07992i	0.262680	+	0.575188i
$79$	−10.6746	+	3.13435i	−1.20099	+	0.352642i	−0.820231	−	0.572032i	$-0.806155\pi$
$79$	−10.6746	+	3.13435i	−1.20099	+	0.352642i	−0.380759	+	0.924674i	$0.624337\pi$
$80$	2.90095	−	3.34788i	0.324336	−	0.374304i
$81$	7.33002	−	8.45930i	0.814447	−	0.939922i
$82$	−20.2313	+	5.94044i	−2.23417	+	0.656012i
$83$	−6.03810	−	13.2216i	−0.662768	−	1.45126i	−0.879920	−	0.475122i	$-0.842404\pi$
$83$	−6.03810	−	13.2216i	−0.662768	−	1.45126i	0.217152	−	0.976138i	$-0.430323\pi$
$84$	−3.04801	+	1.95884i	−0.332565	+	0.213727i
$85$	−6.27075	−	1.84126i	−0.680158	−	0.199712i
$86$	−2.60302	−	18.1044i	−0.280690	−	1.95224i
$87$	−6.02018	+	13.1823i	−0.645431	+	1.41330i
$88$	−0.00879152	+	0.0611463i	−0.000937179	+	0.00651822i
$89$	7.70110	+	4.94920i	0.816315	+	0.524614i	0.880902	−	0.473298i	$-0.156937\pi$
$89$	7.70110	+	4.94920i	0.816315	+	0.524614i	−0.0645871	+	0.997912i	$0.520573\pi$
$90$	−1.60119	−	1.84787i	−0.168780	−	0.194783i
$91$	−1.39601			−0.146341
$92$	4.69466	+	6.98614i	0.489452	+	0.728355i
$93$	7.13597			0.739965
$94$	−4.12240	−	4.75750i	−0.425193	−	0.490699i
$95$	−4.73491	−	3.04294i	−0.485791	−	0.312199i
$96$	2.24312	−	15.6012i	0.228937	−	1.59229i
$97$	−7.10610	+	15.5602i	−0.721515	+	1.57990i	0.0902539	+	0.995919i	$0.471232\pi$
$97$	−7.10610	+	15.5602i	−0.721515	+	1.57990i	−0.811769	+	0.583979i	$0.801495\pi$
$98$	−0.275778	−	1.91808i	−0.0278577	−	0.193755i
$99$	0.157573	+	0.0462677i	0.0158367	+	0.00465008i
$100$	1.47646	−	0.948861i	0.147646	−	0.0948861i
$101$	−0.416046	−	0.911013i	−0.0413981	−	0.0906492i	0.887803	−	0.460224i	$-0.152231\pi$
$101$	−0.416046	−	0.911013i	−0.0413981	−	0.0906492i	−0.929201	+	0.369574i	$0.879503\pi$
$102$	−25.0856	+	7.36578i	−2.48384	+	0.729321i
$103$	−7.65593	+	8.83542i	−0.754361	+	0.870579i	−0.994983	−	0.100039i	$-0.968103\pi$
$103$	−7.65593	+	8.83542i	−0.754361	+	0.870579i	0.240622	+	0.970619i	$0.422649\pi$
$104$	0.433903	−	0.500751i	0.0425477	−	0.0491027i
$105$	1.98079	−	0.581611i	0.193305	−	0.0567594i
$106$	8.19282	+	17.9398i	0.795757	+	1.74247i
$107$	−10.4562	+	6.71981i	−1.01084	+	0.649629i	−0.937611	−	0.347686i	$-0.886967\pi$
$107$	−10.4562	+	6.71981i	−1.01084	+	0.649629i	−0.0732311	+	0.997315i	$0.523331\pi$
$108$	6.04276	+	1.77431i	0.581465	+	0.170733i
$109$	−2.57332	−	17.8978i	−0.246479	−	1.71430i	−0.618253	−	0.785979i	$-0.712159\pi$
$109$	−2.57332	−	17.8978i	−0.246479	−	1.71430i	0.371774	−	0.928323i	$-0.378750\pi$
$110$	−0.104773	+	0.229420i	−0.00998967	+	0.0218743i
$111$	−2.47443	+	17.2100i	−0.234863	+	1.63350i
$112$	3.72665	+	2.39497i	0.352135	+	0.226303i
$113$	−6.61499	−	7.63411i	−0.622286	−	0.718156i	0.353853	−	0.935301i	$-0.384871\pi$
$113$	−6.61499	−	7.63411i	−0.622286	−	0.718156i	−0.976139	+	0.217145i	$0.930326\pi$
$114$	−22.5159			−2.10881
$115$	−1.44511	−	4.57293i	−0.134757	−	0.426428i
$116$	−12.3204			−1.14392
$117$	−1.15351	−	1.33122i	−0.106642	−	0.123071i
$118$	0.298029	+	0.191532i	0.0274358	+	0.0176319i
$119$	0.930096	−	6.46896i	0.0852617	−	0.593008i
$120$	−0.407038	+	0.891289i	−0.0371573	+	0.0813631i
$121$	1.56305	+	10.8713i	0.142096	+	0.988297i
$122$	−15.6138	−	4.58463i	−1.41361	−	0.415073i
$123$	18.8971	−	12.1444i	1.70390	−	1.09503i
$124$	2.52019	+	5.51844i	0.226320	+	0.495571i
$125$	−0.959493	+	0.281733i	−0.0858197	+	0.0251989i
$126$	1.60119	−	1.84787i	0.142645	−	0.164621i
$127$	2.69309	−	3.10799i	0.238973	−	0.275790i	−0.623576	−	0.781763i	$-0.714321\pi$
$127$	2.69309	−	3.10799i	0.238973	−	0.275790i	0.862549	+	0.505973i	$0.168866\pi$
$128$	−3.61593	+	1.06173i	−0.319606	+	0.0938447i
$129$	8.09460	+	17.7247i	0.712690	+	1.56057i
$130$	2.27574	−	1.46253i	0.199596	−	0.128272i
$131$	−15.0290	−	4.41293i	−1.31309	−	0.385559i	−0.451098	−	0.892474i	$-0.648968\pi$
$131$	−15.0290	−	4.41293i	−1.31309	−	0.385559i	−0.861996	+	0.506915i	$0.830786\pi$
$132$	0.0671114	+	0.466770i	0.00584129	+	0.0406271i
$133$	2.33812	−	5.11977i	0.202741	−	0.443940i
$134$	−2.46673	+	17.1565i	−0.213093	+	1.48209i
$135$	−3.01875	−	1.94003i	−0.259812	−	0.166971i
$136$	2.03134	+	2.34430i	0.174186	+	0.201022i
$137$	−12.5025			−1.06816			−0.534080	−	0.845434i	$-0.679342\pi$
$137$	−12.5025			−1.06816			−0.534080	+	0.845434i	$0.679342\pi$
$138$	−14.7536	−	12.2641i	−1.25591	−	1.04399i
$139$	14.8871			1.26271			0.631356	−	0.775494i	$-0.282499\pi$
$139$	14.8871			1.26271			0.631356	+	0.775494i	$0.282499\pi$
$140$	1.14932	+	1.32639i	0.0971356	+	0.112100i
$141$	5.64176	+	3.62574i	0.475122	+	0.305342i
$142$	3.20374	−	22.2825i	0.268852	−	1.86991i
$143$	−0.0754789	+	0.165276i	−0.00631187	+	0.0138211i
$144$	0.795474	+	5.53264i	0.0662895	+	0.461054i
$145$	6.73555	+	1.97774i	0.559357	+	0.164242i
$146$	20.0990	−	12.9168i	1.66340	−	1.06900i
$147$	0.857586	+	1.87785i	0.0707325	+	0.154883i
$148$	−14.1829	+	4.16447i	−1.16583	+	0.342318i
$149$	10.4006	−	12.0029i	0.852051	−	0.983320i	−0.147933	−	0.988997i	$-0.547262\pi$
$149$	10.4006	−	12.0029i	0.852051	−	0.983320i	0.999984	+	0.00567785i	$0.00180732\pi$
$150$	−2.61971	+	3.02331i	−0.213899	+	0.246852i
$151$	−4.93985	+	1.45047i	−0.402000	+	0.118038i	−0.476481	−	0.879185i	$-0.658088\pi$
$151$	−4.93985	+	1.45047i	−0.402000	+	0.118038i	0.0744817	+	0.997222i	$0.476270\pi$
$152$	1.10975	+	2.43001i	0.0900124	+	0.197100i
$153$	6.93728	−	4.45832i	0.560845	−	0.360433i
$154$	−0.241995	−	0.0710563i	−0.0195006	−	0.00572588i
$155$	−0.491935	−	3.42148i	−0.0395131	−	0.274820i
$156$	2.10116	−	4.60089i	0.168227	−	0.368366i
$157$	−1.52707	+	10.6210i	−0.121873	+	0.847648i	0.833557	+	0.552433i	$0.186300\pi$
$157$	−1.52707	+	10.6210i	−0.121873	+	0.847648i	−0.955431	+	0.295215i	$0.904609\pi$
$158$	18.1362	+	11.6554i	1.44284	+	0.927257i
$159$	−13.7590	−	15.8787i	−1.09116	−	1.25927i
$160$	−7.63494			−0.603595
$161$	4.32072	−	2.08120i	0.340520	−	0.164021i
$162$	−21.6903			−1.70415
$163$	−0.832598	−	0.960869i	−0.0652141	−	0.0752611i	0.722205	−	0.691679i	$-0.243129\pi$
$163$	−0.832598	−	0.960869i	−0.0652141	−	0.0752611i	−0.787419	+	0.616418i	$0.788583\pi$
$164$	16.0655	+	10.3246i	1.25450	+	0.806220i
$165$	0.0382386	−	0.265956i	0.00297687	−	0.0207046i
$166$	−11.7006	+	25.6208i	−0.908145	+	1.98856i
$167$	1.78643	+	12.4249i	0.138238	+	0.961466i	0.934360	+	0.356330i	$0.115972\pi$
$167$	1.78643	+	12.4249i	0.138238	+	0.961466i	−0.796122	+	0.605136i	$0.793119\pi$
$168$	−0.940144	−	0.276051i	−0.0725337	−	0.0212978i
$169$	−9.29684	+	5.97471i	−0.715141	+	0.459593i
$170$	5.26100	+	11.5200i	0.403501	+	0.883543i
$171$	6.81414	−	2.00081i	0.521090	−	0.153006i
$172$	−10.8483	+	12.5196i	−0.827173	+	0.954608i
$173$	2.59531	−	2.99515i	0.197318	−	0.227717i	−0.648465	−	0.761245i	$-0.724589\pi$
$173$	2.59531	−	2.99515i	0.197318	−	0.227717i	0.845783	+	0.533528i	$0.179134\pi$
$174$	26.9450	−	7.91176i	2.04269	−	0.599789i
$175$	−0.415415	−	0.909632i	−0.0314024	−	0.0687617i
$176$	0.485037	−	0.311714i	0.0365610	−	0.0234964i
$177$	−0.362127	−	0.106330i	−0.0272191	−	0.00799225i
$178$	−2.52456	−	17.5587i	−0.189223	−	1.31608i
$179$	−5.22994	+	11.4520i	−0.390904	+	0.855961i	0.607208	+	0.794543i	$0.292290\pi$
$179$	−5.22994	+	11.4520i	−0.390904	+	0.855961i	−0.998112	+	0.0614180i	$0.980438\pi$
$180$	−0.315158	+	2.19197i	−0.0234905	+	0.163380i
$181$	12.3336	+	7.92630i	0.916747	+	0.589157i	0.911712	−	0.410830i	$-0.134761\pi$
$181$	12.3336	+	7.92630i	0.916747	+	0.589157i	0.00503487	+	0.999987i	$0.498397\pi$
$182$	1.77151	+	2.04444i	0.131313	+	0.151544i
$183$	17.3362			1.28153
$184$	−0.596425	+	2.19673i	−0.0439690	+	0.161945i
$185$	8.42228			0.619218
$186$	−9.05546	−	10.4506i	−0.663979	−	0.766272i
$187$	−0.715585	−	0.459878i	−0.0523287	−	0.0336296i
$188$	−0.811402	+	5.64342i	−0.0591775	+	0.411589i
$189$	1.49067	−	3.26412i	0.108430	−	0.237429i
$190$	1.55219	+	10.7957i	0.112607	+	0.783202i
$191$	11.3513	+	3.33304i	0.821351	+	0.241171i	0.665298	−	0.746578i	$-0.268305\pi$
$191$	11.3513	+	3.33304i	0.821351	+	0.241171i	0.156054	+	0.987749i	$0.450123\pi$
$192$	−10.3077	+	6.62434i	−0.743893	+	0.478071i
$193$	6.03131	+	13.2067i	0.434143	+	0.950641i	0.992636	+	0.121132i	$0.0386524\pi$
$193$	6.03131	+	13.2067i	0.434143	+	0.950641i	−0.558493	+	0.829509i	$0.688620\pi$
$194$	31.8053	−	9.33888i	2.28349	−	0.670493i
$195$	−1.88726	+	2.17801i	−0.135149	+	0.155971i
$196$	−1.14932	+	1.32639i	−0.0820946	+	0.0947422i
$197$	6.52021	−	1.91451i	0.464546	−	0.136403i	−0.0410799	−	0.999156i	$-0.513080\pi$
$197$	6.52021	−	1.91451i	0.464546	−	0.136403i	0.505626	+	0.862753i	$0.331262\pi$
$198$	−0.132200	−	0.289478i	−0.00939506	−	0.0205723i
$199$	4.92972	−	3.16814i	0.349459	−	0.224584i	−0.354121	−	0.935200i	$-0.615220\pi$
$199$	4.92972	−	3.16814i	0.349459	−	0.224584i	0.703580	+	0.710616i	$0.251584\pi$
$200$	0.455406	+	0.133719i	0.0322021	+	0.00945538i
$201$	−2.62789	−	18.2774i	−0.185357	−	1.28919i
$202$	−0.806213	+	1.76536i	−0.0567250	+	0.124210i
$203$	−0.999037	+	6.94845i	−0.0701187	+	0.487686i
$204$	19.9202	+	12.8019i	1.39469	+	0.896315i
$205$	−7.12561	−	8.22339i	−0.497674	−	0.574346i
$206$	22.6547			1.57843
$207$	5.55479	+	2.40052i	0.386084	+	0.166848i
$208$	−6.18413			−0.428792
$209$	−0.479723	−	0.553630i	−0.0331831	−	0.0382954i
$210$	−3.36536	−	2.16278i	−0.232232	−	0.149246i
$211$	−3.19824	+	22.2443i	−0.220176	+	1.53136i	0.517193	+	0.855869i	$0.326977\pi$
$211$	−3.19824	+	22.2443i	−0.220176	+	1.53136i	−0.737369	+	0.675490i	$0.763932\pi$
$212$	7.42025	−	16.2481i	0.509625	−	1.11592i
$213$	3.41306	+	23.7384i	0.233859	+	1.62653i
$214$	23.1099	+	6.78569i	1.57976	+	0.463860i
$215$	7.94044	−	5.10301i	0.541534	−	0.348023i
$216$	0.707520	+	1.54925i	0.0481407	+	0.105413i
$217$	3.31665	−	0.973855i	0.225149	−	0.0661096i
$218$	−22.9457	+	26.4808i	−1.55408	+	1.79350i
$219$	−16.6680	+	19.2359i	−1.12632	+	1.29984i
$220$	0.219175	−	0.0643557i	0.0147768	−	0.00433886i
$221$	3.79007	+	8.29909i	0.254947	+	0.558257i
$222$	28.3440	−	18.2156i	1.90232	−	1.22255i
$223$	−0.858964	−	0.252215i	−0.0575205	−	0.0168895i	0.252846	−	0.967507i	$-0.418633\pi$
$223$	−0.858964	−	0.252215i	−0.0575205	−	0.0168895i	−0.310366	+	0.950617i	$0.600452\pi$
$224$	−1.08657	−	7.55723i	−0.0725992	−	0.504939i
$225$	0.524163	−	1.14776i	0.0349442	−	0.0765172i
$226$	−2.78573	+	19.3752i	−0.185304	+	1.28882i
$227$	16.1708	+	10.3923i	1.07329	+	0.689762i	0.952998	−	0.302976i	$-0.0979803\pi$
$227$	16.1708	+	10.3923i	1.07329	+	0.689762i	0.120293	+	0.992738i	$0.461617\pi$
$228$	13.3544	+	15.4117i	0.884414	+	1.02067i
$229$	11.6516			0.769959			0.384980	−	0.922925i	$-0.374208\pi$
$229$	11.6516			0.769959			0.384980	+	0.922925i	$0.374208\pi$
$230$	−4.86318	+	7.91934i	−0.320668	+	0.522186i
$231$	0.268690			0.0176785
$232$	−2.18191	−	2.51806i	−0.143250	−	0.165319i
$233$	−6.69657	−	4.30363i	−0.438707	−	0.281940i	0.302585	−	0.953122i	$-0.402150\pi$
$233$	−6.69657	−	4.30363i	−0.438707	−	0.281940i	−0.741292	+	0.671182i	$0.765787\pi$
$234$	−0.485770	+	3.37860i	−0.0317558	+	0.220866i
$235$	1.34950	−	2.95500i	0.0880320	−	0.192763i
$236$	−0.0456633	−	0.317595i	−0.00297243	−	0.0206737i
$237$	−22.0368	−	6.47059i	−1.43144	−	0.420310i
$238$	−10.6540	+	6.84692i	−0.690597	+	0.443820i
$239$	−5.43639	−	11.9040i	−0.351651	−	0.770008i	−0.999963	−	0.00863315i	$-0.997252\pi$
$239$	−5.43639	−	11.9040i	−0.351651	−	0.770008i	0.648312	−	0.761375i	$-0.275475\pi$
$240$	8.77463	−	2.57646i	0.566400	−	0.166310i
$241$	10.2055	−	11.7778i	0.657395	−	0.758674i	−0.324954	−	0.945730i	$-0.605349\pi$
$241$	10.2055	−	11.7778i	0.657395	−	0.758674i	0.982349	+	0.187055i	$0.0598944\pi$
$242$	13.9374	−	16.0846i	0.895929	−	1.03396i
$243$	11.8423	−	3.47722i	0.759685	−	0.223064i
$244$	6.12257	+	13.4066i	0.391958	+	0.858267i
$245$	0.841254	−	0.540641i	0.0537457	−	0.0345403i
$246$	−41.7656	−	12.2635i	−2.66288	−	0.781892i
$247$	1.11821	+	7.77730i	0.0711498	+	0.494857i
$248$	−0.681548	+	1.49238i	−0.0432783	+	0.0947663i
$249$	4.27036	−	29.7010i	0.270623	−	1.88222i
$250$	1.63018	+	1.04765i	0.103102	+	0.0662594i
$251$	8.32789	+	9.61090i	0.525652	+	0.606634i	0.955037	−	0.296487i	$-0.0958152\pi$
$251$	8.32789	+	9.61090i	0.525652	+	0.606634i	−0.429385	+	0.903121i	$0.641270\pi$
$252$	−2.21451			−0.139501
$253$	−0.0127853	−	0.624064i	−0.000803807	−	0.0392346i
$254$	−7.96913			−0.500028
$255$	−8.83532	−	10.1965i	−0.553289	−	0.638530i
$256$	16.1296	+	10.3658i	1.00810	+	0.647865i
$257$	−2.99063	+	20.8003i	−0.186551	+	1.29749i	0.654306	+	0.756230i	$0.272961\pi$
$257$	−2.99063	+	20.8003i	−0.186551	+	1.29749i	−0.840857	+	0.541258i	$0.817948\pi$
$258$	15.6857	−	34.3469i	0.976550	−	2.13835i
$259$	1.19861	+	8.33655i	0.0744783	+	0.518008i
$260$	−2.35084	−	0.690268i	−0.145793	−	0.0428086i
$261$	−7.45148	+	4.78878i	−0.461235	+	0.296418i
$262$	12.6090	+	27.6099i	0.778987	+	1.70574i
$263$	10.8724	−	3.19241i	0.670419	−	0.196853i	0.0712293	−	0.997460i	$-0.477308\pi$
$263$	10.8724	−	3.19241i	0.670419	−	0.196853i	0.599189	+	0.800607i	$0.295490\pi$
$264$	−0.0835138	+	0.0963801i	−0.00513992	+	0.00593178i
$265$	−6.66487	+	7.69167i	−0.409420	+	0.472495i
$266$	−10.4649	+	3.07277i	−0.641645	+	0.188404i
$267$	7.85062	+	17.1905i	0.480450	+	1.05204i
$268$	13.2063	−	8.48720i	0.806706	−	0.518438i
$269$	13.9409	+	4.09341i	0.849990	+	0.249579i	0.677583	−	0.735446i	$-0.263027\pi$
$269$	13.9409	+	4.09341i	0.849990	+	0.249579i	0.172407	+	0.985026i	$0.444846\pi$
$270$	0.989598	+	6.88280i	0.0602250	+	0.418874i
$271$	−3.64995	+	7.99228i	−0.221719	+	0.485496i	−0.987503	−	0.157601i	$-0.949624\pi$
$271$	−3.64995	+	7.99228i	−0.221719	+	0.485496i	0.765784	+	0.643098i	$0.222351\pi$
$272$	4.12021	−	28.6567i	0.249824	−	1.73757i
$273$	−2.42443	−	1.55809i	−0.146733	−	0.0942997i
$274$	15.8655	+	18.3098i	0.958471	+	1.10613i
$275$	−0.130154			−0.00784857
$276$	0.355914	+	17.3725i	0.0214235	+	1.04570i
$277$	−20.6972			−1.24357			−0.621787	−	0.783186i	$-0.713593\pi$
$277$	−20.6972			−1.24357			−0.621787	+	0.783186i	$0.713593\pi$
$278$	−18.8916	−	21.8021i	−1.13304	−	1.30760i
$279$	3.66918	+	2.35804i	0.219668	+	0.141172i
$280$	−0.0675472	+	0.469801i	−0.00403672	+	0.0280760i
$281$	−1.76507	+	3.86496i	−0.105295	+	0.230564i	−0.954945	−	0.296783i	$-0.904086\pi$
$281$	−1.76507	+	3.86496i	−0.105295	+	0.230564i	0.849650	+	0.527347i	$0.176813\pi$
$282$	−1.84947	−	12.8633i	−0.110134	−	0.766000i
$283$	−13.6018	−	3.99384i	−0.808542	−	0.237409i	−0.148767	−	0.988872i	$-0.547530\pi$
$283$	−13.6018	−	3.99384i	−0.808542	−	0.237409i	−0.659775	+	0.751463i	$0.729348\pi$
$284$	−17.1522	+	11.0230i	−1.01779	+	0.654097i
$285$	−4.82684	−	10.5693i	−0.285917	−	0.626071i
$286$	0.337827	−	0.0991949i	0.0199761	−	0.00586552i
$287$	7.12561	−	8.22339i	0.420611	−	0.485411i
$288$	6.30869	−	7.28062i	0.371743	−	0.429015i
$289$	−24.6710	+	7.24405i	−1.45123	+	0.426121i
$290$	−5.65096	−	12.3739i	−0.331836	−	0.726619i
$291$	−29.7079	+	19.0921i	−1.74151	+	1.11920i
$292$	−20.7622	−	6.09634i	−1.21502	−	0.356761i
$293$	−2.06282	−	14.3472i	−0.120511	−	0.838175i	−0.956979	−	0.290158i	$-0.906292\pi$
$293$	−2.06282	−	14.3472i	−0.120511	−	0.838175i	0.836467	−	0.548017i	$-0.184617\pi$
$294$	1.66183	−	3.63890i	0.0969199	−	0.212225i
$295$	−0.0260180	+	0.180959i	−0.00151482	+	0.0105358i
$296$	−3.36290	−	2.16120i	−0.195464	−	0.125617i
$297$	−0.305848	−	0.352967i	−0.0177471	−	0.0204812i
$298$	−30.7765			−1.78283
$299$	−3.50347	+	5.70515i	−0.202611	+	0.329938i
$300$	3.62317			0.209184
$301$	6.18111	+	7.13339i	0.356273	+	0.411162i
$302$	8.39282	+	5.39374i	0.482953	+	0.310375i
$303$	0.294242	−	2.04650i	0.0169038	−	0.117568i
$304$	10.3576	−	22.6799i	0.594048	−	1.30078i
$305$	−1.19511	−	8.31218i	−0.0684319	−	0.475954i
$306$	−15.3325	−	4.50202i	−0.876500	−	0.257364i
$307$	−13.4457	+	8.64105i	−0.767389	+	0.493171i	−0.864827	−	0.502071i	$-0.832572\pi$
$307$	−13.4457	+	8.64105i	−0.767389	+	0.493171i	0.0974377	+	0.995242i	$0.468935\pi$
$308$	0.0948926	+	0.207786i	0.00540701	+	0.0118397i
$309$	−23.1572	+	6.79957i	−1.31737	+	0.386814i
$310$	−4.38647	+	5.06225i	−0.249135	+	0.287517i
$311$	4.25331	−	4.90858i	0.241183	−	0.278340i	−0.622233	−	0.782832i	$-0.713775\pi$
$311$	4.25331	−	4.90858i	0.241183	−	0.278340i	0.863417	+	0.504491i	$0.168320\pi$
$312$	1.31245	−	0.385369i	0.0743026	−	0.0218172i
$313$	11.0315	+	24.1557i	0.623540	+	1.36536i	0.912917	+	0.408146i	$0.133825\pi$
$313$	11.0315	+	24.1557i	0.623540	+	1.36536i	−0.289377	+	0.957215i	$0.593448\pi$
$314$	17.4922	−	11.2415i	0.987141	−	0.634397i
$315$	1.21067	+	0.355485i	0.0682136	+	0.0200293i
$316$	−2.77878	−	19.3269i	−0.156319	−	1.08722i
$317$	−1.54631	+	3.38594i	−0.0868492	+	0.190173i	−0.948073	−	0.318053i	$-0.896971\pi$
$317$	−1.54631	+	3.38594i	−0.0868492	+	0.190173i	0.861224	+	0.508226i	$0.169698\pi$
$318$	−5.79425	+	40.2999i	−0.324925	+	2.25991i
$319$	0.768626	+	0.493966i	0.0430348	+	0.0276568i
$320$	3.88676	+	4.48556i	0.217276	+	0.250750i
$321$	−25.6592			−1.43216
$322$	−8.53084	−	3.68664i	−0.475405	−	0.205448i
$323$	−36.7843			−2.04673
$324$	12.8647	+	14.8466i	0.714704	+	0.824813i
$325$	1.17439	+	0.754737i	0.0651437	+	0.0418653i
$326$	−0.350627	+	2.43866i	−0.0194194	+	0.135065i
$327$	15.5068	−	33.9551i	0.857527	−	1.87772i
$328$	0.734988	+	5.11195i	0.0405829	+	0.282260i
$329$	3.11698	+	0.915228i	0.171845	+	0.0504581i
$330$	−0.438014	+	0.281494i	−0.0241119	+	0.0154958i
$331$	−12.7308	−	27.8766i	−0.699749	−	1.53224i	−0.840275	−	0.542160i	$-0.817607\pi$
$331$	−12.7308	−	27.8766i	−0.699749	−	1.53224i	0.140526	−	0.990077i	$-0.455120\pi$
$332$	24.4767	−	7.18702i	1.34334	−	0.394439i
$333$	−6.95926	+	8.03141i	−0.381365	+	0.440119i
$334$	15.9292	−	18.3832i	0.871605	−	1.00589i
$335$	−8.58230	+	2.51999i	−0.468901	+	0.137682i
$336$	3.79900	+	8.31865i	0.207252	+	0.453820i
$337$	12.5314	−	8.05346i	0.682630	−	0.438700i	−0.152829	−	0.988253i	$-0.548838\pi$
$337$	12.5314	−	8.05346i	0.682630	−	0.438700i	0.835459	+	0.549553i	$0.185202\pi$
$338$	20.5475	+	6.03329i	1.11764	+	0.328168i
$339$	−2.96774	−	20.6411i	−0.161186	−	1.12107i
$340$	4.76489	−	10.4337i	0.258413	−	0.565845i
$341$	0.0640271	−	0.445318i	0.00346726	−	0.0241153i
$342$	−11.5772	−	7.44024i	−0.626025	−	0.402322i
$343$	0.654861	+	0.755750i	0.0353592	+	0.0408066i
$344$	−4.47997			−0.241544
$345$	2.59415	−	9.55465i	0.139664	−	0.514405i
$346$	−7.67979			−0.412868
$347$	1.99594	+	2.30344i	0.107148	+	0.123655i	0.806790	−	0.590838i	$-0.201203\pi$
$347$	1.99594	+	2.30344i	0.107148	+	0.123655i	−0.699643	+	0.714493i	$0.746657\pi$
$348$	−21.3967	−	13.7508i	−1.14699	−	0.737123i
$349$	−0.317890	+	2.21098i	−0.0170163	+	0.118351i	−0.996559	−	0.0828849i	$-0.973587\pi$
$349$	−0.317890	+	2.21098i	−0.0170163	+	0.118351i	0.979543	+	0.201236i	$0.0644957\pi$
$350$	−0.804991	+	1.76268i	−0.0430286	+	0.0942194i
$351$	0.712914	+	4.95842i	0.0380525	+	0.264661i
$352$	−0.953464	−	0.279962i	−0.0508198	−	0.0149220i
$353$	10.1655	−	6.53298i	0.541056	−	0.347715i	−0.241396	−	0.970427i	$-0.577605\pi$
$353$	10.1655	−	6.53298i	0.541056	−	0.347715i	0.782452	+	0.622711i	$0.213969\pi$
$354$	0.303815	+	0.665263i	0.0161476	+	0.0353583i
$355$	11.1465	−	3.27292i	0.591597	−	0.173709i
$356$	−10.5213	+	12.1422i	−0.557627	+	0.643535i
$357$	8.83532	−	10.1965i	0.467615	−	0.539656i
$358$	23.4081	−	6.87323i	1.23715	−	0.363261i
$359$	3.06491	+	6.71123i	0.161760	+	0.354205i	0.973105	−	0.230363i	$-0.0739913\pi$
$359$	3.06491	+	6.71123i	0.161760	+	0.354205i	−0.811345	+	0.584568i	$0.801264\pi$
$360$	−0.503812	+	0.323780i	−0.0265532	+	0.0170647i
$361$	−12.1653	−	3.57205i	−0.640278	−	0.188002i
$362$	−4.04316	−	28.1208i	−0.212504	−	1.47800i
$363$	−9.41892	+	20.6246i	−0.494365	+	1.08251i
$364$	0.348683	−	2.42514i	0.0182760	−	0.127112i
$365$	10.3721	+	6.66572i	0.542899	+	0.348900i
$366$	−21.9994	−	25.3887i	−1.14993	−	1.32709i
$367$	−29.9066			−1.56111			−0.780556	−	0.625085i	$-0.785064\pi$
$367$	−29.9066			−1.56111			−0.780556	+	0.625085i	$0.785064\pi$
$368$	19.1402	−	9.21945i	0.997754	−	0.480597i
$369$	13.7296			0.714734
$370$	−10.6878	−	12.3343i	−0.555631	−	0.641232i
$371$	−8.56189	−	5.50239i	−0.444511	−	0.285670i
$372$	−1.78236	+	12.3966i	−0.0924113	+	0.642735i
$373$	2.03422	−	4.45431i	0.105328	−	0.230636i	−0.849629	−	0.527381i	$-0.823174\pi$
$373$	2.03422	−	4.45431i	0.105328	−	0.230636i	0.954957	+	0.296745i	$0.0959013\pi$
$374$	0.234581	+	1.63155i	0.0121299	+	0.0843653i
$375$	−1.98079	−	0.581611i	−0.102287	−	0.0300343i
$376$	−1.29711	+	0.833600i	−0.0668932	+	0.0429897i
$377$	−4.07099	−	8.91424i	−0.209667	−	0.459106i
$378$	−6.67191	+	1.95905i	−0.343166	+	0.100763i
$379$	15.2619	−	17.6132i	0.783954	−	0.904731i	−0.213435	−	0.976957i	$-0.568465\pi$
$379$	15.2619	−	17.6132i	0.783954	−	0.904731i	0.997388	+	0.0722266i	$0.0230105\pi$
$380$	6.46885	−	7.46545i	0.331845	−	0.382970i
$381$	8.14591	−	2.39185i	0.417328	−	0.122538i
$382$	−9.52346	−	20.8535i	−0.487263	−	1.06696i
$383$	9.16130	−	5.88761i	0.468121	−	0.300843i	−0.285233	−	0.958458i	$-0.592071\pi$
$383$	9.16130	−	5.88761i	0.468121	−	0.300843i	0.753354	+	0.657615i	$0.228435\pi$
$384$	−7.46475	−	2.19185i	−0.380934	−	0.111852i
$385$	−0.0185228	−	0.128829i	−0.000944010	−	0.00656573i
$386$	11.6875	−	25.5920i	0.594876	−	1.30260i
$387$	−1.69493	+	11.7885i	−0.0861583	+	0.599244i
$388$	−25.2563	−	16.2312i	−1.28219	−	0.824016i
$389$	17.3391	+	20.0103i	0.879125	+	1.01456i	0.999761	+	0.0218675i	$0.00696119\pi$
$389$	17.3391	+	20.0103i	0.879125	+	1.01456i	−0.120636	+	0.992697i	$0.538493\pi$
$390$	5.58459			0.282787
$391$	−24.1030	−	20.0358i	−1.21894	−	1.01326i
$392$	−0.474632			−0.0239725
$393$	−21.1755	−	24.4379i	−1.06816	−	1.23273i
$394$	−11.0779	−	7.11931i	−0.558094	−	0.358665i
$395$	−1.58329	+	11.0120i	−0.0796641	+	0.554076i
$396$	−0.119734	+	0.262181i	−0.00601685	+	0.0131751i
$397$	−1.89354	−	13.1699i	−0.0950340	−	0.660976i	−0.980536	−	0.196340i	$-0.937094\pi$
$397$	−1.89354	−	13.1699i	−0.0950340	−	0.660976i	0.885502	−	0.464636i	$-0.153815\pi$
$398$	−10.8955	−	3.19920i	−0.546141	−	0.160361i
$399$	9.77479	−	6.28187i	0.489351	−	0.314487i
$400$	−1.84024	−	4.02956i	−0.0920118	−	0.201478i
$401$	−16.0706	+	4.71875i	−0.802527	+	0.235643i	−0.657176	−	0.753737i	$-0.728249\pi$
$401$	−16.0706	+	4.71875i	−0.802527	+	0.235643i	−0.145351	+	0.989380i	$0.546431\pi$
$402$	−23.4323	+	27.0423i	−1.16870	+	1.34875i
$403$	−3.16004	+	3.64689i	−0.157413	+	0.181664i
$404$	1.68653	−	0.495210i	0.0839080	−	0.0246376i
$405$	−4.64985	−	10.1817i	−0.231053	−	0.505935i
$406$	11.4437	−	7.35443i	0.567942	−	0.364994i
$407$	1.05179	+	0.308833i	0.0521352	+	0.0153083i
$408$	0.911340	+	6.33851i	0.0451180	+	0.313803i
$409$	−7.03570	+	15.4060i	−0.347893	+	0.761779i	0.652100	+	0.758133i	$0.273888\pi$
$409$	−7.03570	+	15.4060i	−0.347893	+	0.761779i	−0.999993	+	0.00364672i	$0.998839\pi$
$410$	−3.00076	+	20.8708i	−0.148197	+	1.03073i
$411$	−21.7130	−	13.9541i	−1.07102	−	0.688303i
$412$	−13.4367	−	15.5067i	−0.661977	−	0.763962i
$413$	−0.182820			−0.00899597
$414$	−3.53342	−	11.1812i	−0.173658	−	0.549525i
$415$	−14.5351			−0.713501
$416$	6.97978	+	8.05510i	0.342212	+	0.394934i
$417$	25.8544	+	16.6156i	1.26609	+	0.813669i
$418$	−0.202023	+	1.40510i	−0.00988126	+	0.0687257i
$419$	−3.69576	+	8.09258i	−0.180550	+	0.395349i	−0.978169	−	0.207813i	$-0.933365\pi$
$419$	−3.69576	+	8.09258i	−0.180550	+	0.395349i	0.797619	+	0.603162i	$0.206093\pi$
$420$	0.515631	+	3.58630i	0.0251602	+	0.174993i
$421$	19.7848	+	5.80933i	0.964250	+	0.283129i	0.725708	−	0.688003i	$-0.241512\pi$
$421$	19.7848	+	5.80933i	0.964250	+	0.283129i	0.238542	+	0.971132i	$0.423331\pi$
$422$	36.6351	−	23.5439i	1.78337	−	1.14610i
$423$	1.70278	+	3.72857i	0.0827920	+	0.181289i
$424$	4.63491	−	1.36093i	0.225091	−	0.0660927i
$425$	−4.27983	+	4.93919i	−0.207602	+	0.239586i
$426$	30.4335	−	35.1221i	1.47451	−	1.70167i
$427$	8.05750	−	2.36589i	0.389930	−	0.114494i
$428$	−9.06200	−	19.8430i	−0.438028	−	0.959148i
$429$	−0.315549	+	0.202791i	−0.0152348	+	0.00979083i
$430$	−17.5496	−	5.15304i	−0.846319	−	0.248502i
$431$	4.91458	+	34.1817i	0.236727	+	1.64647i	0.667934	+	0.744221i	$0.267179\pi$
$431$	4.91458	+	34.1817i	0.236727	+	1.64647i	−0.431207	+	0.902253i	$0.641912\pi$
$432$	6.60349	−	14.4596i	0.317710	−	0.695689i
$433$	2.29004	−	15.9276i	0.110052	−	0.765431i	−0.857813	−	0.513962i	$-0.828177\pi$
$433$	2.29004	−	15.9276i	0.110052	−	0.765431i	0.967865	−	0.251469i	$-0.0809136\pi$
$434$	−5.63499	−	3.62139i	−0.270488	−	0.173832i
$435$	9.49021	+	10.9523i	0.455021	+	0.525122i
$436$	31.7349			1.51983
$437$	−15.0555	−	22.4041i	−0.720202	−	1.07174i
$438$	49.3222			2.35671
$439$	−4.37619	−	5.05039i	−0.208864	−	0.241042i	0.641646	−	0.767001i	$-0.278252\pi$
$439$	−4.37619	−	5.05039i	−0.208864	−	0.241042i	−0.850510	+	0.525959i	$0.823707\pi$
$440$	0.0519685	+	0.0333982i	0.00247750	+	0.00159219i
$441$	−0.179570	+	1.24894i	−0.00855097	+	0.0594733i
$442$	7.34439	−	16.0820i	0.349337	−	0.764941i
$443$	1.09709	+	7.63043i	0.0521243	+	0.362533i	0.999144	+	0.0413583i	$0.0131685\pi$
$443$	1.09709	+	7.63043i	0.0521243	+	0.362533i	−0.947020	+	0.321175i	$0.895922\pi$
$444$	−29.2793	−	8.59717i	−1.38953	−	0.408004i
$445$	7.70110	−	4.94920i	0.365067	−	0.234614i
$446$	0.720650	+	1.57800i	0.0341237	+	0.0747206i
$447$	31.4592	−	9.23725i	1.48797	−	0.436907i
$448$	−3.88676	+	4.48556i	−0.183632	+	0.211923i
$449$	7.97094	−	9.19896i	0.376172	−	0.434126i	−0.535821	−	0.844332i	$-0.679998\pi$
$449$	7.97094	−	9.19896i	0.376172	−	0.434126i	0.911993	+	0.410206i	$0.134543\pi$
$450$	−2.34604	+	0.688859i	−0.110593	+	0.0324731i
$451$	−0.588317	−	1.28824i	−0.0277028	−	0.0606606i
$452$	14.9142	−	9.58479i	0.701506	−	0.450831i
$453$	−10.1979	−	2.99437i	−0.479138	−	0.140688i
$454$	−5.30106	−	36.8697i	−0.248791	−	1.73038i
$455$	−0.579921	+	1.26985i	−0.0271871	+	0.0595315i
$456$	−0.784852	+	5.45876i	−0.0367540	+	0.255630i
$457$	19.2361	+	12.3623i	0.899828	+	0.578284i	0.906739	−	0.421692i	$-0.138564\pi$
$457$	19.2361	+	12.3623i	0.899828	+	0.578284i	−0.00691150	+	0.999976i	$0.502200\pi$
$458$	−14.7857	−	17.0637i	−0.690893	−	0.797333i
$459$	−23.4519			−1.09464
$460$	8.30505	−	1.36826i	0.387225	−	0.0637956i
$461$	−23.1502			−1.07821			−0.539105	−	0.842238i	$-0.681237\pi$
$461$	−23.1502			−1.07821			−0.539105	+	0.842238i	$0.681237\pi$
$462$	−0.340965	−	0.393495i	−0.0158631	−	0.0183070i
$463$	21.0547	+	13.5310i	0.978494	+	0.628840i	0.929057	−	0.369937i	$-0.120621\pi$
$463$	21.0547	+	13.5310i	0.978494	+	0.628840i	0.0494373	+	0.998777i	$0.484257\pi$
$464$	−4.42561	+	30.7808i	−0.205454	+	1.42896i
$465$	2.96439	−	6.49110i	0.137470	−	0.301018i
$466$	2.19525	+	15.2683i	0.101693	+	0.707292i
$467$	17.5141	+	5.14259i	0.810454	+	0.237971i	0.660601	−	0.750737i	$-0.270302\pi$
$467$	17.5141	+	5.14259i	0.810454	+	0.237971i	0.149853	+	0.988708i	$0.452120\pi$
$468$	2.60071	−	1.67137i	0.120218	−	0.0772593i
$469$	−3.71573	−	8.13631i	−0.171576	−	0.375700i
$470$	−6.04008	+	1.77353i	−0.278608	+	0.0818067i
$471$	−14.5062	+	16.7410i	−0.668409	+	0.771386i
$472$	0.0568237	−	0.0655780i	0.00261552	−	0.00301847i
$473$	1.17874	−	0.346108i	0.0541983	−	0.0159141i
$474$	18.4883	+	40.4838i	0.849197	+	1.85948i
$475$	−4.73491	+	3.04294i	−0.217253	+	0.139620i
$476$	11.0056	+	3.23153i	0.504440	+	0.148117i
$477$	−1.82758	−	12.7111i	−0.0836793	−	0.582002i
$478$	−10.5346	+	23.0676i	−0.481843	+	1.05509i
$479$	2.80897	−	19.5368i	0.128345	−	0.892658i	−0.819307	−	0.573354i	$-0.805642\pi$
$479$	2.80897	−	19.5368i	0.128345	−	0.892658i	0.947652	−	0.319304i	$-0.103449\pi$
$480$	−13.2595	−	8.52139i	−0.605212	−	0.388946i
$481$	−7.69955	−	8.88575i	−0.351069	−	0.405156i
$482$	−30.1992			−1.37553
$483$	9.82659	+	1.20797i	0.447125	+	0.0549646i
$484$	−19.2760			−0.876182
$485$	11.2021	+	12.9279i	0.508659	+	0.587024i
$486$	−20.1201	−	12.9304i	−0.912668	−	0.586536i
$487$	2.10044	−	14.6089i	0.0951800	−	0.661991i	−0.885249	−	0.465118i	$-0.846012\pi$
$487$	2.10044	−	14.6089i	0.0951800	−	0.661991i	0.980429	−	0.196874i	$-0.0630789\pi$
$488$	−1.65576	+	3.62561i	−0.0749527	+	0.164124i
$489$	−0.373536	−	2.59800i	−0.0168919	−	0.117486i
$490$	−1.85930	−	0.545941i	−0.0839948	−	0.0246631i
$491$	−16.5224	+	10.6183i	−0.745645	+	0.479197i	−0.857472	−	0.514531i	$-0.827966\pi$
$491$	−16.5224	+	10.6183i	−0.745645	+	0.479197i	0.111827	+	0.993728i	$0.464330\pi$
$492$	16.3774	+	35.8614i	0.738349	+	1.61676i
$493$	44.0201	−	12.9255i	1.98256	−	0.582133i
$494$	9.97079	−	11.5069i	0.448607	−	0.517720i
$495$	0.107545	−	0.124113i	0.00483379	−	0.00557849i
$496$	14.6923	−	4.31405i	0.659705	−	0.193707i
$497$	4.82593	+	10.5673i	0.216472	+	0.474009i
$498$	−48.9159	+	31.4363i	−2.19197	+	1.40869i
$499$	−6.08022	−	1.78531i	−0.272188	−	0.0799216i	0.142790	−	0.989753i	$-0.454393\pi$
$499$	−6.08022	−	1.78531i	−0.272188	−	0.0799216i	−0.414978	+	0.909831i	$0.636211\pi$
$500$	−0.249772	−	1.73720i	−0.0111701	−	0.0776901i
$501$	−10.7650	+	23.5720i	−0.480944	+	1.05312i
$502$	3.50707	−	24.3922i	0.156528	−	1.08868i
$503$	6.23248	+	4.00537i	0.277892	+	0.178591i	0.672162	−	0.740404i	$-0.265366\pi$
$503$	6.23248	+	4.00537i	0.277892	+	0.178591i	−0.394269	+	0.918995i	$0.629002\pi$
$504$	−0.392184	−	0.452605i	−0.0174693	−	0.0201606i
$505$	−1.00152			−0.0445670
$506$	−0.897712	+	0.810655i	−0.0399082	+	0.0360380i
$507$	−22.8141			−1.01321
$508$	4.72655	+	5.45473i	0.209707	+	0.242015i
$509$	−8.82349	−	5.67051i	−0.391094	−	0.251341i	0.330285	−	0.943881i	$-0.392855\pi$
$509$	−8.82349	−	5.67051i	−0.391094	−	0.251341i	−0.721379	+	0.692540i	$0.756492\pi$
$510$	−3.72076	+	25.8785i	−0.164758	+	1.14592i
$511$	−5.12178	+	11.2151i	−0.226574	+	0.496128i
$512$	−4.21490	−	29.3153i	−0.186274	−	1.29556i
$513$	−19.3788	−	5.69012i	−0.855594	−	0.251225i
$514$	34.2569	−	22.0156i	1.51101	−	0.971067i
$515$	4.85659	+	10.6344i	0.214007	+	0.468610i
$516$	−32.8132	+	9.63483i	−1.44452	+	0.424150i
$517$	0.276884	−	0.319541i	0.0121773	−	0.0140534i
$518$	10.6878	−	12.3343i	0.469594	−	0.541940i
$519$	7.85015	−	2.30501i	0.344583	−	0.101179i
$520$	−0.275249	−	0.602712i	−0.0120705	−	0.0264307i
$521$	−24.2325	+	15.5733i	−1.06164	+	0.682277i	−0.950246	−	0.311499i	$-0.899169\pi$
$521$	−24.2325	+	15.5733i	−1.06164	+	0.682277i	−0.111397	+	0.993776i	$0.535532\pi$
$522$	16.4690	+	4.83573i	0.720827	+	0.211654i
$523$	−1.65149	−	11.4863i	−0.0722144	−	0.502263i	−0.993541	−	0.113473i	$-0.963802\pi$
$523$	−1.65149	−	11.4863i	−0.0722144	−	0.502263i	0.921327	−	0.388789i	$-0.127107\pi$
$524$	11.4200	−	25.0063i	0.498884	−	1.09240i
$525$	0.293796	−	2.04340i	0.0128223	−	0.0891811i
$526$	−18.4722	−	11.8713i	−0.805425	−	0.517615i
$527$	−14.7939	−	17.0731i	−0.644434	−	0.743716i
$528$	1.19027			0.0517996
$529$	2.33807	−	22.8809i	0.101655	−	0.994820i
$530$	19.7220			0.856670
$531$	−0.151062	−	0.174335i	−0.00655555	−	0.00756551i
$532$	8.31008	+	5.34056i	0.360288	+	0.231543i
$533$	−2.16177	+	15.0355i	−0.0936368	+	0.651258i
$534$	15.2129	−	33.3116i	0.658327	−	1.44154i
$535$	1.76888	+	12.3028i	0.0764754	+	0.531898i
$536$	4.07344	+	1.19607i	0.175946	+	0.0516623i
$537$	−21.8644	+	14.0514i	−0.943518	+	0.606362i
$538$	−11.6960	−	25.6108i	−0.504252	−	1.10416i
$539$	0.124882	−	0.0366685i	0.00537903	−	0.00157943i
$540$	4.12422	−	4.75961i	0.177478	−	0.204821i
$541$	23.5270	−	27.1516i	1.01151	−	1.16734i	0.0256620	−	0.999671i	$-0.491831\pi$
$541$	23.5270	−	27.1516i	1.01151	−	1.16734i	0.985843	−	0.167669i	$-0.0536239\pi$
$542$	16.3364	−	4.79679i	0.701707	−	0.206040i
$543$	12.5730	+	27.5311i	0.539560	+	1.18147i
$544$	−41.9769	+	26.9769i	−1.79974	+	1.15663i
$545$	−17.3494	−	5.09426i	−0.743169	−	0.218214i
$546$	0.794770	+	5.52775i	0.0340130	+	0.236566i
$547$	−8.07377	+	17.6791i	−0.345210	+	0.755904i	0.654790	+	0.755811i	$0.272757\pi$
$547$	−8.07377	+	17.6791i	−0.345210	+	0.755904i	−1.00000		9.31037e-5i	$0.999970\pi$
$548$	3.12277	−	21.7193i	0.133398	−	0.927805i
$549$	8.91394	+	5.72864i	0.380438	+	0.244492i
$550$	0.165164	+	0.190609i	0.00704260	+	0.00812759i
$551$	39.5108			1.68322
$552$	−3.48758	+	3.14937i	−0.148441	+	0.134046i
$553$	−11.1253			−0.473095
$554$	26.2645	+	30.3109i	1.11587	+	1.28778i
$555$	14.6269	+	9.40013i	0.620877	+	0.399013i
$556$	−3.71839	+	25.8620i	−0.157695	+	1.09679i
$557$	6.01855	−	13.1788i	0.255014	−	0.558403i	−0.738216	−	0.674564i	$-0.764332\pi$
$557$	6.01855	−	13.1788i	0.255014	−	0.558403i	0.993230	+	0.116161i	$0.0370589\pi$
$558$	−1.20282	−	8.36580i	−0.0509194	−	0.354152i
$559$	−12.6429	−	3.71229i	−0.534738	−	0.157013i
$560$	3.72665	−	2.39497i	0.157480	−	0.101206i
$561$	−0.729478	−	1.59733i	−0.0307986	−	0.0674395i
$562$	7.90005	−	2.31967i	0.333244	−	0.0978492i
$563$	−4.06949	+	4.69644i	−0.171509	+	0.197931i	−0.834996	−	0.550256i	$-0.814530\pi$
$563$	−4.06949	+	4.69644i	−0.171509	+	0.197931i	0.663487	+	0.748187i	$0.269076\pi$
$564$	−7.70780	+	8.89527i	−0.324557	+	0.374559i
$565$	−9.69219	+	2.84588i	−0.407754	+	0.119727i
$566$	11.4116	+	24.9878i	0.479663	+	1.05032i
$567$	9.41636	−	6.05153i	0.395450	−	0.254140i
$568$	−5.29051	−	1.55343i	−0.221985	−	0.0651806i
$569$	−0.353773	−	2.46055i	−0.0148309	−	0.103151i	0.981061	−	0.193697i	$-0.0620479\pi$
$569$	−0.353773	−	2.46055i	−0.0148309	−	0.103151i	−0.995892	+	0.0905458i	$0.971139\pi$
$570$	−9.35344	+	20.4812i	−0.391773	+	0.857862i
$571$	−0.205953	+	1.43244i	−0.00861887	+	0.0599456i	−0.993677	−	0.112277i	$-0.964186\pi$
$571$	−0.205953	+	1.43244i	−0.00861887	+	0.0599456i	0.985058	+	0.172222i	$0.0550948\pi$
$572$	−0.268265	−	0.172403i	−0.0112167	−	0.00720855i
$573$	15.9937	+	18.4577i	0.668146	+	0.771081i
$574$	−21.0854			−0.880087
$575$	−4.76000	−	0.585142i	−0.198506	−	0.0244021i
$576$	−7.48898			−0.312041
$577$	5.31035	+	6.12847i	0.221073	+	0.255131i	0.855442	−	0.517899i	$-0.173286\pi$
$577$	5.31035	+	6.12847i	0.221073	+	0.255131i	−0.634369	+	0.773030i	$0.718740\pi$
$578$	41.9160	+	26.9378i	1.74348	+	1.12046i
$579$	−4.26555	+	29.6676i	−0.177270	+	1.23294i
$580$	−5.11808	+	11.2070i	−0.212517	+	0.465347i
$581$	−2.06856	−	14.3872i	−0.0858184	−	0.596880i
$582$	65.6592	+	19.2793i	2.72166	+	0.799151i
$583$	−1.11436	+	0.716157i	−0.0461521	+	0.0296602i
$584$	−2.43096	−	5.32306i	−0.100594	−	0.220270i
$585$	−1.69010	+	0.496259i	−0.0698772	+	0.0205178i
$586$	−18.3937	+	21.2275i	−0.759837	+	0.876899i
$587$	−17.3520	+	20.0252i	−0.716193	+	0.826530i	−0.990844	−	0.135014i	$-0.956892\pi$
$587$	−17.3520	+	20.0252i	−0.716193	+	0.826530i	0.274651	+	0.961544i	$0.411438\pi$
$588$	−3.47641	+	1.02077i	−0.143365	+	0.0420957i
$589$	−8.08210	−	17.6973i	−0.333017	−	0.729206i
$590$	0.298029	−	0.191532i	0.0122697	−	0.00788524i
$591$	13.4604	+	3.95233i	0.553686	+	0.162577i
$592$	5.30971	+	36.9299i	0.218228	+	1.51781i
$593$	9.25677	−	20.2695i	0.380130	−	0.832369i	−0.618774	−	0.785569i	$-0.712370\pi$
$593$	9.25677	−	20.2695i	0.380130	−	0.832369i	0.998904	−	0.0467998i	$-0.0149023\pi$
$594$	−0.128800	+	0.895823i	−0.00528472	+	0.0367561i
$595$	−5.49800	−	3.53335i	−0.225396	−	0.144853i
$596$	18.2538	+	21.0660i	0.747703	+	0.862896i
$597$	12.0974			0.495113
$598$	12.8010	−	2.10898i	0.523472	−	0.0862425i
$599$	−29.9166			−1.22236			−0.611180	−	0.791492i	$-0.709305\pi$
$599$	−29.9166			−1.22236			−0.611180	+	0.791492i	$0.709305\pi$
$600$	0.641655	+	0.740509i	0.0261955	+	0.0302312i
$601$	−6.78999	−	4.36366i	−0.276969	−	0.177997i	0.394780	−	0.918775i	$-0.370821\pi$
$601$	−6.78999	−	4.36366i	−0.276969	−	0.177997i	−0.671750	+	0.740778i	$0.734457\pi$
$602$	2.60302	−	18.1044i	0.106091	−	0.737879i
$603$	4.68844	−	10.2663i	0.190928	−	0.418074i
$604$	−1.28593	−	8.94381i	−0.0523236	−	0.363919i
$605$	10.5382	+	3.09429i	0.428437	+	0.125801i
$606$	−3.37047	+	2.16607i	−0.136916	+	0.0879905i
$607$	17.9909	+	39.3945i	0.730228	+	1.59898i	0.798991	+	0.601342i	$0.205367\pi$
$607$	17.9909	+	39.3945i	0.730228	+	1.59898i	−0.0687639	+	0.997633i	$0.521906\pi$
$608$	−41.2318	+	12.1068i	−1.67217	+	0.490994i
$609$	−9.49021	+	10.9523i	−0.384563	+	0.443809i
$610$	−10.6565	+	12.2983i	−0.431471	+	0.497944i
$611$	−4.35132	+	1.27766i	−0.176036	+	0.0516887i
$612$	6.01226	+	13.1650i	0.243031	+	0.532164i
$613$	34.1164	−	21.9253i	1.37795	−	0.885555i	0.378748	−	0.925500i	$-0.376355\pi$
$613$	34.1164	−	21.9253i	1.37795	−	0.885555i	0.999202	+	0.0399450i	$0.0127183\pi$
$614$	29.7172	+	8.72577i	1.19929	+	0.352143i
$615$	−3.19682	−	22.2344i	−0.128908	−	0.896577i
$616$	−0.0256623	+	0.0561926i	−0.00103396	+	0.00226407i
$617$	0.109455	−	0.761276i	0.00440649	−	0.0306478i	−0.987500	−	0.157622i	$-0.949617\pi$
$617$	0.109455	−	0.761276i	0.00440649	−	0.0306478i	0.991906	+	0.126974i	$0.0405264\pi$
$618$	39.3442	+	25.2850i	1.58265	+	1.01711i
$619$	−8.68206	−	10.0196i	−0.348961	−	0.402723i	0.553950	−	0.832550i	$-0.313120\pi$
$619$	−8.68206	−	10.0196i	−0.348961	−	0.402723i	−0.902911	+	0.429827i	$0.858574\pi$
$620$	6.06668			0.243644
$621$	−9.59865	−	14.2838i	−0.385180	−	0.573189i
$622$	−12.5860			−0.504652
$623$	5.99480	+	6.91837i	0.240177	+	0.277179i
$624$	−10.7399	−	6.90213i	−0.429941	−	0.276306i
$625$	−0.142315	+	0.989821i	−0.00569259	+	0.0395929i
$626$	21.3769	−	46.8089i	0.854393	−	1.87086i
$627$	−0.215222	−	1.49690i	−0.00859515	−	0.0597806i
$628$	−18.0694	−	5.30566i	−0.721048	−	0.211719i
$629$	46.3056	−	29.7588i	1.84633	−	1.18656i
$630$	−1.01572	−	2.22412i	−0.0404674	−	0.0886112i
$631$	17.3205	−	5.08576i	0.689518	−	0.202461i	0.0818417	−	0.996645i	$-0.473920\pi$
$631$	17.3205	−	5.08576i	0.689518	−	0.202461i	0.607677	+	0.794184i	$0.292102\pi$
$632$	3.45794	−	3.99067i	0.137549	−	0.158740i
$633$	−30.3813	+	35.0619i	−1.20755	+	1.39358i
$634$	6.92092	−	2.03217i	0.274865	−	0.0807076i
$635$	−1.70838	−	3.74083i	−0.0677950	−	0.148450i
$636$	31.0212	−	19.9361i	1.23007	−	0.790519i
$637$	−1.33946	−	0.393300i	−0.0530712	−	0.0155831i
$638$	−0.251969	−	1.75248i	−0.00997555	−	0.0693814i
$639$	−6.08927	+	13.3336i	−0.240888	+	0.527471i
$640$	−0.536325	+	3.73022i	−0.0212001	+	0.147450i
$641$	−23.2020	−	14.9110i	−0.916423	−	0.588949i	−0.00480525	−	0.999988i	$-0.501530\pi$
$641$	−23.2020	−	14.9110i	−0.916423	−	0.588949i	−0.911618	+	0.411039i	$0.865166\pi$
$642$	32.5613	+	37.5777i	1.28509	+	1.48308i
$643$	8.49019			0.334820			0.167410	−	0.985887i	$-0.446460\pi$
$643$	8.49019			0.334820			0.167410	+	0.985887i	$0.446460\pi$
$644$	2.53627	+	8.02579i	0.0999429	+	0.316260i
$645$	19.4856			0.767244
$646$	46.6788	+	53.8703i	1.83655	+	2.11950i
$647$	10.9104	+	7.01170i	0.428933	+	0.275658i	0.737243	−	0.675627i	$-0.236127\pi$
$647$	10.9104	+	7.01170i	0.428933	+	0.275658i	−0.308310	+	0.951286i	$0.599764\pi$
$648$	−0.756073	+	5.25860i	−0.0297013	+	0.206577i
$649$	−0.00988467	+	0.0216444i	−0.000388007	+	0.000849617i
$650$	−0.384987	−	2.67764i	−0.0151004	−	0.105026i
$651$	6.84691	+	2.01043i	0.268352	+	0.0787951i
$652$	1.87718	−	1.20639i	0.0735162	−	0.0472460i
$653$	7.75254	+	16.9757i	0.303380	+	0.664310i	0.998510	−	0.0545745i	$-0.0173802\pi$
$653$	7.75254	+	16.9757i	0.303380	+	0.664310i	−0.695129	+	0.718885i	$0.744653\pi$
$654$	−69.4049	+	20.3791i	−2.71395	+	0.796886i
$655$	−10.2574	+	11.8377i	−0.400791	+	0.462538i
$656$	31.5655	−	36.4286i	1.23243	−	1.42230i
$657$	−14.9267	+	4.38288i	−0.582347	+	0.170993i
$658$	−2.61507	−	5.72620i	−0.101946	−	0.223231i
$659$	−23.2253	+	14.9260i	−0.904730	+	0.581435i	−0.908190	−	0.418559i	$-0.862535\pi$
$659$	−23.2253	+	14.9260i	−0.904730	+	0.581435i	0.00345926	+	0.999994i	$0.498899\pi$
$660$	0.452468	+	0.132857i	0.0176123	+	0.00517143i
$661$	2.37718	+	16.5337i	0.0924617	+	0.643086i	0.982370	+	0.186946i	$0.0598590\pi$
$661$	2.37718	+	16.5337i	0.0924617	+	0.643086i	−0.889908	+	0.456139i	$0.849232\pi$
$662$	−24.6698	+	54.0193i	−0.958818	+	2.09952i
$663$	−2.68047	+	18.6431i	−0.104101	+	0.724036i
$664$	5.80366	+	3.72979i	0.225226	+	0.144744i
$665$	−3.68582	−	4.25366i	−0.142930	−	0.164950i
$666$	20.5931			0.797968
$667$	25.8895	+	21.5210i	1.00245	+	0.833295i
$668$	−22.0307			−0.852395
$669$	−1.21026	−	1.39671i	−0.0467913	−	0.0540000i
$670$	14.5814	+	9.37086i	0.563327	+	0.362028i
$671$	0.155548	−	1.08186i	0.00600487	−	0.0417648i
$672$	6.54762	−	14.3373i	0.252580	−	0.553073i
$673$	−5.66055	−	39.3700i	−0.218198	−	1.51760i	−0.744683	−	0.667418i	$-0.767399\pi$
$673$	−5.66055	−	39.3700i	−0.218198	−	1.51760i	0.526485	−	0.850184i	$-0.323510\pi$
$674$	−27.6965	−	8.13241i	−1.06683	−	0.313249i
$675$	−3.01875	+	1.94003i	−0.116192	+	0.0746718i
$676$	−8.05720	−	17.6428i	−0.309892	−	0.678569i
$677$	−18.1535	+	5.33036i	−0.697697	+	0.204862i	−0.611301	−	0.791398i	$-0.709353\pi$
$677$	−18.1535	+	5.33036i	−0.697697	+	0.204862i	−0.0863966	+	0.996261i	$0.527535\pi$
$678$	−26.4627	+	30.5396i	−1.01629	+	1.17286i
$679$	−11.2021	+	12.9279i	−0.429896	+	0.496126i
$680$	2.97630	−	0.873920i	0.114136	−	0.0335133i
$681$	16.4847	+	36.0965i	0.631695	+	1.38322i
$682$	−0.733415	+	0.471337i	−0.0280839	+	0.0180484i
$683$	19.4649	+	5.71542i	0.744805	+	0.218694i	0.632049	−	0.774928i	$-0.282214\pi$
$683$	19.4649	+	5.71542i	0.744805	+	0.218694i	0.112756	+	0.993623i	$0.464032\pi$
$684$	1.77383	+	12.3373i	0.0678242	+	0.471728i
$685$	−5.19372	+	11.3727i	−0.198442	+	0.434527i
$686$	0.275778	−	1.91808i	0.0105292	−	0.0732325i
$687$	20.2352	+	13.0044i	0.772022	+	0.496148i
$688$	27.3816	+	31.6000i	1.04391	+	1.20474i
$689$	14.2079			0.541277
$690$	−17.2846	+	8.32564i	−0.658015	+	0.316952i
$691$	19.7511			0.751366			0.375683	−	0.926748i	$-0.377408\pi$
$691$	19.7511			0.751366			0.375683	+	0.926748i	$0.377408\pi$
$692$	4.55494	+	5.25669i	0.173153	+	0.199829i
$693$	0.138155	+	0.0887871i	0.00524809	+	0.00337274i
$694$	0.840538	−	5.84607i	0.0319064	−	0.221914i
$695$	6.18434	−	13.5418i	0.234585	−	0.513671i
$696$	−0.978891	−	6.80833i	−0.0371048	−	0.258069i
$697$	−68.2326	−	20.0349i	−2.58450	−	0.758876i
$698$	3.64135	−	2.34016i	0.137827	−	0.0885762i
$699$	−6.82659	−	14.9481i	−0.258205	−	0.565391i
$700$	1.68397	−	0.494459i	0.0636482	−	0.0186888i
$701$	−1.84310	+	2.12705i	−0.0696128	+	0.0803375i	−0.789488	−	0.613766i	$-0.789654\pi$
$701$	−1.84310	+	2.12705i	−0.0696128	+	0.0803375i	0.719875	+	0.694104i	$0.244199\pi$
$702$	6.35689	−	7.33624i	0.239925	−	0.276889i
$703$	45.4837	−	13.3552i	1.71545	−	0.503702i
$704$	0.320906	+	0.702685i	0.0120946	+	0.0264834i
$705$	5.64176	−	3.62574i	0.212481	−	0.136553i
$706$	−22.4674	−	6.59703i	−0.845572	−	0.248282i
$707$	−0.142531	−	0.991324i	−0.00536043	−	0.0372826i
$708$	0.275166	−	0.602529i	0.0103414	−	0.0226444i
$709$	5.85266	−	40.7062i	0.219801	−	1.52875i	−0.518968	−	0.854794i	$-0.673684\pi$
$709$	5.85266	−	40.7062i	0.219801	−	1.52875i	0.738769	−	0.673959i	$-0.235407\pi$
$710$	−18.9380	−	12.1707i	−0.710731	−	0.456759i
$711$	−9.19273	−	10.6090i	−0.344754	−	0.397868i
$712$	−4.34493			−0.162833
$713$	4.34366	−	15.9984i	0.162671	−	0.599145i
$714$	−26.1446			−0.978437
$715$	0.118985	+	0.137316i	0.00444979	+	0.00513533i
$716$	−18.5881	−	11.9459i	−0.694670	−	0.446437i
$717$	3.84481	−	26.7412i	0.143587	−	0.998669i
$718$	5.93919	−	13.0050i	0.221649	−	0.485343i
$719$	1.70832	+	11.8816i	0.0637096	+	0.443110i	0.996562	+	0.0828511i	$0.0264026\pi$
$719$	1.70832	+	11.8816i	0.0637096	+	0.443110i	−0.932852	+	0.360259i	$0.882688\pi$
$720$	5.36312	+	1.57475i	0.199872	+	0.0586876i
$721$	−9.83504	+	6.32059i	−0.366276	+	0.235391i
$722$	10.2064	+	22.3488i	0.379842	+	0.831737i
$723$	30.8691	−	9.06397i	1.14803	−	0.337093i
$724$	−16.8502	+	19.4461i	−0.626232	+	0.722710i
$725$	4.59706	−	5.30529i	0.170731	−	0.197034i
$726$	42.1570	−	12.3784i	1.56459	−	0.459406i
$727$	9.77560	+	21.4056i	0.362557	+	0.793889i	0.999732	+	0.0231693i	$0.00737567\pi$
$727$	9.77560	+	21.4056i	0.362557	+	0.793889i	−0.637175	+	0.770719i	$0.719897\pi$
$728$	0.557405	−	0.358222i	0.0206588	−	0.0132766i
$729$	−7.77215	−	2.28211i	−0.287857	−	0.0845225i
$730$	−3.40014	−	23.6485i	−0.125845	−	0.875271i
$731$	25.6258	−	56.1127i	0.947805	−	2.07540i
$732$	−4.33010	+	30.1165i	−0.160045	+	1.11314i
$733$	−23.2038	−	14.9122i	−0.857053	−	0.550795i	0.0367139	−	0.999326i	$-0.488311\pi$
$733$	−23.2038	−	14.9122i	−0.857053	−	0.550795i	−0.893767	+	0.448531i	$0.851947\pi$
$734$	37.9512	+	43.7980i	1.40080	+	1.61661i
$735$	2.06441			0.0761469
$736$	−33.6116	−	14.5254i	−1.23894	−	0.535413i
$737$	−1.16418			−0.0428830
$738$	−17.4227	−	20.1069i	−0.641338	−	0.740143i
$739$	14.5363	+	9.34193i	0.534727	+	0.343648i	0.779974	−	0.625812i	$-0.215232\pi$
$739$	14.5363	+	9.34193i	0.534727	+	0.343648i	−0.245246	+	0.969461i	$0.578869\pi$
$740$	−2.10365	+	14.6312i	−0.0773317	+	0.537854i
$741$	−6.73829	+	14.7548i	−0.247537	+	0.542031i
$742$	2.80674	+	19.5213i	0.103039	+	0.716649i
$743$	−18.5221	−	5.43859i	−0.679511	−	0.199522i	−0.0762769	−	0.997087i	$-0.524303\pi$
$743$	−18.5221	−	5.43859i	−0.679511	−	0.199522i	−0.603234	+	0.797564i	$0.706121\pi$
$744$	−2.84929	+	1.83113i	−0.104460	+	0.0671324i
$745$	−6.59769	−	14.4469i	−0.241721	−	0.529295i
$746$	−9.10470	+	2.67338i	−0.333347	+	0.0978794i
$747$	12.0102	−	13.8606i	0.439432	−	0.507131i
$748$	0.977635	−	1.12825i	0.0357459	−	0.0412529i
$749$	−11.9259	+	3.50175i	−0.435762	+	0.127951i
$750$	1.66183	+	3.63890i	0.0606815	+	0.132874i
$751$	23.0550	−	14.8165i	0.841287	−	0.540662i	−0.0475588	−	0.998868i	$-0.515144\pi$
$751$	23.0550	−	14.8165i	0.841287	−	0.540662i	0.888846	+	0.458206i	$0.151508\pi$
$752$	13.8078	+	4.05434i	0.503520	+	0.147847i
$753$	3.73621	+	25.9859i	0.136155	+	0.946980i
$754$	−7.88877	+	17.2740i	−0.287292	+	0.629082i
$755$	−0.732694	+	5.09600i	−0.0266654	+	0.185462i
$756$	5.29810	+	3.40488i	0.192690	+	0.123834i
$757$	−9.13132	−	10.5381i	−0.331884	−	0.383014i	0.565141	−	0.824994i	$-0.308822\pi$
$757$	−9.13132	−	10.5381i	−0.331884	−	0.383014i	−0.897025	+	0.441980i	$0.854276\pi$
$758$	−45.1617			−1.64035
$759$	0.674316	−	1.09808i	0.0244761	−	0.0398577i
$760$	2.67142			0.0969025
$761$	−27.6185	−	31.8735i	−1.00117	−	1.15541i	−0.987836	−	0.155502i	$-0.950300\pi$
$761$	−27.6185	−	31.8735i	−1.00117	−	1.15541i	−0.0133357	−	0.999911i	$-0.504245\pi$
$762$	−13.8399	−	8.89437i	−0.501367	−	0.322209i
$763$	2.57332	−	17.8978i	0.0931605	−	0.647945i
$764$	−8.62541	+	18.8870i	−0.312056	+	0.683308i
$765$	−1.17358	−	8.16242i	−0.0424308	−	0.295113i
$766$	−20.2479	−	5.94533i	−0.731588	−	0.214814i
$767$	0.214703	−	0.137981i	0.00775246	−	0.00498220i
$768$	16.4427	+	36.0045i	0.593325	+	1.29920i
$769$	46.8094	−	13.7445i	1.68799	−	0.495639i	0.709985	−	0.704217i	$-0.248702\pi$
$769$	46.8094	−	13.7445i	1.68799	−	0.495639i	0.978006	+	0.208578i	$0.0668836\pi$
$770$	−0.165164	+	0.190609i	−0.00595208	+	0.00686907i
$771$	−28.4091	+	32.7859i	−1.02313	+	1.18075i
$772$	−24.4492	+	7.17894i	−0.879946	+	0.258376i
$773$	−19.4113	−	42.5049i	−0.698177	−	1.52879i	−0.842168	−	0.539215i	$-0.818721\pi$
$773$	−19.4113	−	42.5049i	−0.698177	−	1.52879i	0.143991	−	0.989579i	$-0.454006\pi$
$774$	19.4150	−	12.4773i	0.697859	−	0.448487i
$775$	−3.31665	−	0.973855i	−0.119137	−	0.0349819i
$776$	−1.15546	−	8.03643i	−0.0414787	−	0.288491i
$777$	−7.22283	+	15.8158i	−0.259117	+	0.567388i
$778$	7.30189	−	50.7858i	0.261786	−	1.82076i
$779$	−51.5210	−	33.1106i	−1.84593	−	1.18631i
$780$	−3.31227	−	3.82256i	−0.118598	−	0.136870i
$781$	1.51201			0.0541040
$782$	1.24406	+	60.7238i	0.0444876	+	2.17148i
$783$	25.1902			0.900223
$784$	2.90095	+	3.34788i	0.103605	+	0.119567i
$785$	9.02683	+	5.80119i	0.322181	+	0.207053i
$786$	−8.91753	+	62.0228i	−0.318078	+	2.21228i
$787$	20.7920	−	45.5280i	0.741153	−	1.62290i	−0.0404952	−	0.999180i	$-0.512894\pi$
$787$	20.7920	−	45.5280i	0.741153	−	1.62290i	0.781648	−	0.623719i	$-0.214379\pi$
$788$	1.69732	+	11.8051i	0.0604645	+	0.420540i
$789$	22.4450	+	6.59045i	0.799063	+	0.234626i
$790$	18.1362	−	11.6554i	0.645258	−	0.414682i
$791$	−4.19626	−	9.18853i	−0.149202	−	0.326706i
$792$	−0.0747894	+	0.0219601i	−0.00265752	+	0.000780320i
$793$	−7.67705	+	8.85978i	−0.272620	+	0.314620i
$794$	−16.8843	+	19.4855i	−0.599200	+	0.691513i
$795$	−20.1595	+	5.91937i	−0.714984	+	0.209938i
$796$	4.27240	+	9.35524i	0.151431	+	0.331588i
$797$	18.7480	−	12.0486i	0.664089	−	0.426784i	−0.164701	−	0.986343i	$-0.552666\pi$
$797$	18.7480	−	12.0486i	0.664089	−	0.426784i	0.828790	+	0.559560i	$0.189030\pi$
$798$	−21.6038	−	6.34346i	−0.764768	−	0.224556i
$799$	−3.02148	−	21.0149i	−0.106892	−	0.743452i
$800$	−3.17167	+	6.94499i	−0.112135	+	0.245542i
$801$	−1.64384	+	11.4332i	−0.0580824	+	0.403972i
$802$	27.3040	+	17.5472i	0.964137	+	0.619613i
$803$	1.05086	+	1.21275i	0.0370840	+	0.0427972i
$804$	32.4079			1.14294
$805$	−0.0982326	−	4.79483i	−0.00346224	−	0.168995i
$806$	9.35089			0.329371
$807$	19.6423	+	22.6684i	0.691442	+	0.797967i
$808$	0.399892	+	0.256995i	0.0140682	+	0.00904105i
$809$	−3.20371	+	22.2823i	−0.112636	+	0.783403i	0.852701	+	0.522399i	$0.174963\pi$
$809$	−3.20371	+	22.2823i	−0.112636	+	0.783403i	−0.965338	+	0.261004i	$0.915946\pi$
$810$	−9.01047	+	19.7302i	−0.316596	+	0.693248i
$811$	4.00849	+	27.8797i	0.140757	+	0.978988i	0.930694	+	0.365799i	$0.119204\pi$
$811$	4.00849	+	27.8797i	0.140757	+	0.978988i	−0.789937	+	0.613189i	$0.789887\pi$
$812$	−11.8213	−	3.47106i	−0.414848	−	0.121810i
$813$	−15.2590	+	9.80640i	−0.535158	+	0.343925i
$814$	−0.882423	−	1.93224i	−0.0309289	−	0.0677249i
$815$	−1.21991	+	0.358198i	−0.0427316	+	0.0125471i
$816$	39.1393	−	45.1692i	1.37015	−	1.58124i
$817$	34.7898	−	40.1495i	1.21714	−	1.40465i
$818$	31.4902	−	9.24636i	1.10103	−	0.323292i
$819$	−0.731735	−	1.60228i	−0.0255689	−	0.0559880i
$820$	16.0655	−	10.3246i	0.561030	−	0.360552i
$821$	−51.3090	−	15.0657i	−1.79070	−	0.525796i	−0.794067	−	0.607831i	$-0.792040\pi$
$821$	−51.3090	−	15.0657i	−1.79070	−	0.525796i	−0.996629	+	0.0820346i	$0.973858\pi$
$822$	7.11789	+	49.5060i	0.248265	+	1.72672i
$823$	12.1240	−	26.5479i	0.422617	−	0.925401i	−0.571851	−	0.820358i	$-0.693774\pi$
$823$	12.1240	−	26.5479i	0.422617	−	0.925401i	0.994468	−	0.105044i	$-0.0334983\pi$
$824$	0.789689	−	5.49241i	0.0275101	−	0.191337i
$825$	−0.226037	−	0.145265i	−0.00786959	−	0.00505748i
$826$	0.231996	+	0.267738i	0.00807218	+	0.00931580i
$827$	2.02806			0.0705227			0.0352614	−	0.999378i	$-0.488774\pi$
$827$	2.02806			0.0705227			0.0352614	+	0.999378i	$0.488774\pi$
$828$	−5.55763	+	9.05021i	−0.193141	+	0.314516i
$829$	−13.0305			−0.452567			−0.226284	−	0.974061i	$-0.572658\pi$
$829$	−13.0305			−0.452567			−0.226284	+	0.974061i	$0.572658\pi$
$830$	18.4449	+	21.2865i	0.640232	+	0.738867i
$831$	−35.9446	−	23.1002i	−1.24691	−	0.801337i
$832$	1.17917	−	8.20129i	0.0408803	−	0.284329i
$833$	2.71494	−	5.94488i	0.0940670	−	0.205978i
$834$	−8.47551	−	58.9485i	−0.293483	−	2.04122i
$835$	12.0442	+	3.53649i	0.416806	+	0.122385i
$836$	1.08159	−	0.695094i	0.0374075	−	0.0240403i
$837$	−5.15275	−	11.2830i	−0.178105	−	0.389996i
$838$	16.5414	−	4.85699i	0.571413	−	0.167782i
$839$	−24.5703	+	28.3556i	−0.848261	+	0.978945i	−0.999955	−	0.00948235i	$-0.996982\pi$
$839$	−24.5703	+	28.3556i	−0.848261	+	0.978945i	0.151694	+	0.988427i	$0.451527\pi$
$840$	−0.641655	+	0.740509i	−0.0221392	+	0.0255500i
$841$	−19.4577	+	5.71328i	−0.670954	+	0.197010i
$842$	−16.5989	−	36.3466i	−0.572037	−	1.25259i
$843$	−7.37908	+	4.74224i	−0.254149	+	0.163332i
$844$	−37.8440	−	11.1120i	−1.30264	−	0.382491i
$845$	1.57275	+	10.9387i	0.0541041	+	0.376302i
$846$	3.29965	−	7.22522i	0.113444	−	0.248408i
$847$	−1.56305	+	10.8713i	−0.0537071	+	0.373541i
$848$	−37.9281	−	24.3749i	−1.30246	−	0.837037i
$849$	−19.1645	−	22.1171i	−0.657725	−	0.759055i
$850$	12.6645			0.434387
$851$	37.0777	+	16.0233i	1.27101	+	0.549271i
$852$	−42.0909			−1.44201
$853$	6.01479	+	6.94143i	0.205942	+	0.237670i	0.849319	−	0.527879i	$-0.177013\pi$
$853$	6.01479	+	6.94143i	0.205942	+	0.237670i	−0.643377	+	0.765549i	$0.722467\pi$
$854$	−13.6897	−	8.79784i	−0.468452	−	0.301056i
$855$	1.01069	−	7.02953i	0.0345650	−	0.240405i
$856$	2.45068	−	5.36625i	0.0837627	−	0.183415i
$857$	−3.16780	−	22.0325i	−0.108210	−	0.752617i	−0.969604	−	0.244680i	$-0.921317\pi$
$857$	−3.16780	−	22.0325i	−0.108210	−	0.752617i	0.861394	−	0.507937i	$-0.169592\pi$
$858$	0.697413	+	0.204779i	0.0238093	+	0.00699103i
$859$	−41.1252	+	26.4296i	−1.40318	+	0.901766i	−0.999911	−	0.0133178i	$-0.995761\pi$
$859$	−41.1252	+	26.4296i	−1.40318	+	0.901766i	−0.403264	+	0.915084i	$0.632124\pi$
$860$	6.88167	+	15.0687i	0.234663	+	0.513840i
$861$	21.5531	−	6.32857i	0.734529	−	0.215677i
$862$	43.8222	−	50.5735i	1.49259	−	1.72254i
$863$	−28.9689	+	33.4319i	−0.986113	+	1.13804i	0.00431275	+	0.999991i	$0.498627\pi$
$863$	−28.9689	+	33.4319i	−0.986113	+	1.13804i	−0.990426	+	0.138045i	$0.955918\pi$
$864$	−26.2874	+	7.71867i	−0.894315	+	0.262595i
$865$	−1.64635	−	3.60501i	−0.0559777	−	0.122574i
$866$	−26.2318	+	16.8582i	−0.891394	+	0.572864i
$867$	−50.9310	−	14.9547i	−1.72971	−	0.507888i
$868$	0.863378	+	6.00493i	0.0293050	+	0.203820i
$869$	−0.601520	+	1.31714i	−0.0204052	+	0.0446811i
$870$	3.99656	−	27.7967i	0.135496	−	0.942395i
$871$	10.5045	+	6.75084i	0.355932	+	0.228743i
$872$	5.62017	+	6.48603i	0.190323	+	0.219645i
$873$	−21.5841			−0.730510
$874$	−13.7054	+	50.4792i	−0.463593	+	1.70749i
$875$	−1.00000			−0.0338062
$876$	−29.2534	−	33.7602i	−0.988381	−	1.14065i
$877$	−18.5262	−	11.9060i	−0.625584	−	0.402038i	0.189088	−	0.981960i	$-0.439447\pi$
$877$	−18.5262	−	11.9060i	−0.625584	−	0.402038i	−0.814672	+	0.579922i	$0.803083\pi$
$878$	−1.84292	+	12.8178i	−0.0621955	+	0.432579i
$879$	12.4305	−	27.2190i	0.419271	−	0.918075i
$880$	−0.0820537	−	0.570696i	−0.00276603	−	0.0192382i
$881$	44.9067	+	13.1858i	1.51294	+	0.444241i	0.929781	−	0.368114i	$-0.119996\pi$
$881$	44.9067	+	13.1858i	1.51294	+	0.444241i	0.583164	+	0.812354i	$0.301814\pi$
$882$	2.05693	−	1.32191i	0.0692605	−	0.0445111i
$883$	−1.23511	−	2.70451i	−0.0415647	−	0.0910141i	0.887711	−	0.460402i	$-0.152295\pi$
$883$	−1.23511	−	2.70451i	−0.0415647	−	0.0910141i	−0.929275	+	0.369388i	$0.879567\pi$
$884$	−15.3638	+	4.51123i	−0.516742	+	0.151729i
$885$	−0.247154	+	0.285231i	−0.00830799	+	0.00958794i
$886$	9.78251	−	11.2896i	0.328650	−	0.379282i
$887$	−8.33236	+	2.44660i	−0.279773	+	0.0821489i	−0.418609	−	0.908167i	$-0.637482\pi$
$887$	−8.33236	+	2.44660i	−0.279773	+	0.0821489i	0.138836	+	0.990315i	$0.455664\pi$
$888$	−3.42818	−	7.50668i	−0.115042	−	0.251908i
$889$	3.45962	−	2.22337i	0.116032	−	0.0745693i
$890$	−17.0207	−	4.99772i	−0.570534	−	0.167524i
$891$	−0.207330	−	1.44202i	−0.00694583	−	0.0483093i
$892$	0.652693	−	1.42920i	0.0218538	−	0.0478531i
$893$	2.60212	−	18.0981i	0.0870766	−	0.605631i
$894$	−53.4492	−	34.3497i	−1.78761	−	1.14883i
$895$	8.24449	+	9.51465i	0.275583	+	0.318040i
$896$	−3.76858			−0.125899
$897$	−12.4520	+	5.99786i	−0.415760	+	0.200263i
$898$	−23.5868			−0.787103
$899$	15.8905	+	18.3386i	0.529978	+	0.611627i
$900$	1.86297	+	1.19726i	0.0620989	+	0.0399085i
$901$	−9.46608	+	65.8380i	−0.315361	+	2.19338i
$902$	−1.14004	+	2.49634i	−0.0379592	+	0.0831191i
$903$	2.77309	+	19.2872i	0.0922826	+	0.641839i
$904$	4.60022	+	1.35075i	0.153001	+	0.0449252i
$905$	12.3336	−	7.92630i	0.409982	−	0.263479i
$906$	8.55576	+	18.7345i	0.284246	+	0.622412i
$907$	−42.4445	+	12.4628i	−1.40935	+	0.413822i	−0.895883	−	0.444290i	$-0.853456\pi$
$907$	−42.4445	+	12.4628i	−1.40935	+	0.413822i	−0.513464	+	0.858111i	$0.671638\pi$
$908$	−22.0926	+	25.4962i	−0.733167	+	0.846120i
$909$	0.827546	−	0.955039i	0.0274480	−	0.0316767i
$910$	2.59560	−	0.762137i	0.0860433	−	0.0252646i
$911$	15.3998	+	33.7208i	0.510218	+	1.11722i	0.973012	+	0.230755i	$0.0741196\pi$
$911$	15.3998	+	33.7208i	0.510218	+	1.11722i	−0.462794	+	0.886466i	$0.653153\pi$
$912$	43.3011	−	27.8279i	1.43384	−	0.921474i
$913$	−1.81517	−	0.532981i	−0.0600733	−	0.0176391i
$914$	−6.30594	−	43.8587i	−0.208582	−	1.45072i
$915$	7.20172	−	15.7696i	0.238081	−	0.521326i
$916$	−2.91024	+	20.2412i	−0.0961571	+	0.668788i
$917$	−13.1770	−	8.46835i	−0.435143	−	0.279649i
$918$	29.7601	+	34.3450i	0.982231	+	1.13356i
$919$	−52.7015			−1.73846			−0.869231	−	0.494406i	$-0.835386\pi$
$919$	−52.7015			−1.73846			−0.869231	+	0.494406i	$0.835386\pi$
$920$	1.75045	+	1.45508i	0.0577106	+	0.0479726i
$921$	−32.9954			−1.08724
$922$	29.3773	+	33.9032i	0.967490	+	1.11654i
$923$	−13.6431	−	8.76788i	−0.449068	−	0.288598i
$924$	−0.0671114	+	0.466770i	−0.00220780	+	0.0153556i
$925$	3.49874	−	7.66117i	0.115038	−	0.251898i
$926$	−6.90209	−	48.0051i	−0.226817	−	1.57755i
$927$	−14.1539	−	4.15595i	−0.464874	−	0.136499i
$928$	45.0883	−	28.9765i	1.48010	−	0.951201i
$929$	16.2171	+	35.5104i	0.532065	+	1.16506i	0.964666	+	0.263474i	$0.0848683\pi$
$929$	16.2171	+	35.5104i	0.532065	+	1.16506i	−0.432602	+	0.901585i	$0.642404\pi$
$930$	−13.2679	+	3.89582i	−0.435073	+	0.127749i
$931$	3.68582	−	4.25366i	0.120798	−	0.139408i
$932$	9.14889	−	10.5584i	0.299682	−	0.345851i
$933$	12.8652	−	3.77756i	0.421187	−	0.123672i
$934$	−14.6939	−	32.1751i	−0.480798	−	1.05280i
$935$	−0.715585	+	0.459878i	−0.0234021	+	0.0150396i
$936$	0.802177	+	0.235540i	0.0262200	+	0.00769888i
$937$	1.23871	+	8.61542i	0.0404669	+	0.281454i	1.00000		0.000142381i	$-4.53213e-5\pi$
$937$	1.23871	+	8.61542i	0.0404669	+	0.281454i	−0.959533	+	0.281596i	$0.909136\pi$
$938$	−7.20034	+	15.7665i	−0.235099	+	0.514796i
$939$	−7.80189	+	54.2633i	−0.254605	+	1.77082i
$940$	4.79637	+	3.08244i	0.156440	+	0.100538i
$941$	−9.20905	−	10.6278i	−0.300206	−	0.346457i	0.585525	−	0.810654i	$-0.300888\pi$
$941$	−9.20905	−	10.6278i	−0.300206	−	0.346457i	−0.885732	+	0.464197i	$0.846343\pi$
$942$	42.9253			1.39858
$943$	−15.7244	−	49.7585i	−0.512057	−	1.62036i
$944$	−0.809869			−0.0263590
$945$	−2.34990	−	2.71193i	−0.0764421	−	0.0882189i
$946$	−2.00267	−	1.28704i	−0.0651125	−	0.0418453i
$947$	−2.87490	+	19.9954i	−0.0934217	+	0.649762i	0.888275	+	0.459312i	$0.151904\pi$
$947$	−2.87490	+	19.9954i	−0.0934217	+	0.649762i	−0.981697	+	0.190450i	$0.939005\pi$
$948$	16.7449	−	36.6662i	0.543849	−	1.19086i
$949$	−2.44949	−	17.0366i	−0.0795138	−	0.553031i
$950$	10.4649	+	3.07277i	0.339526	+	0.0996940i
$951$	−6.46451	+	4.15449i	−0.209626	+	0.134719i
$952$	1.28860	+	2.82163i	0.0417636	+	0.0914496i
$953$	28.0772	−	8.24421i	0.909510	−	0.267056i	0.206675	−	0.978410i	$-0.433736\pi$
$953$	28.0772	−	8.24421i	0.909510	−	0.267056i	0.702834	+	0.711353i	$0.251917\pi$
$954$	−16.2961	+	18.8068i	−0.527607	+	0.608891i
$955$	7.74734	−	8.94091i	0.250698	−	0.289321i
$956$	22.0376	−	6.47082i	0.712746	−	0.209281i
$957$	0.783548	+	1.71573i	0.0253285	+	0.0554617i
$958$	−32.1760	+	20.6783i	−1.03956	+	0.668084i
$959$	−11.9960	−	3.52236i	−0.387373	−	0.113743i
$960$	1.74375	+	12.1280i	0.0562793	+	0.391431i
$961$	−7.91427	+	17.3298i	−0.255299	+	0.559027i
$962$	−3.24247	+	22.5518i	−0.104541	+	0.727101i
$963$	−13.1935	−	8.47894i	−0.425154	−	0.273230i
$964$	17.9114	+	20.6708i	0.576886	+	0.665762i
$965$	14.5188			0.467375
$966$	−10.7008	−	15.9239i	−0.344291	−	0.512342i
$967$	−15.5085			−0.498721			−0.249360	−	0.968411i	$-0.580220\pi$
$967$	−15.5085			−0.498721			−0.249360	+	0.968411i	$0.580220\pi$
$968$	−3.41373	−	3.93966i	−0.109721	−	0.126625i
$969$	−63.8829	−	41.0551i	−2.05222	−	1.31888i
$970$	4.71746	−	32.8106i	0.151468	−	1.05349i
$971$	−8.83950	+	19.3558i	−0.283673	+	0.621157i	−0.996805	−	0.0798724i	$-0.974549\pi$
$971$	−8.83950	+	19.3558i	−0.283673	+	0.621157i	0.713132	+	0.701030i	$0.247276\pi$
$972$	3.08275	+	21.4410i	0.0988794	+	0.687721i
$973$	14.2841	+	4.19419i	0.457928	+	0.134460i
$974$	−24.0600	+	15.4624i	−0.770932	+	0.495448i
$975$	1.19719	+	2.62149i	0.0383409	+	0.0839549i
$976$	35.6937	−	10.4806i	1.14253	−	0.335476i
$977$	−4.02447	+	4.64449i	−0.128754	+	0.148590i	−0.816466	−	0.577393i	$-0.804070\pi$
$977$	−4.02447	+	4.64449i	−0.128754	+	0.148590i	0.687712	+	0.725984i	$0.258615\pi$
$978$	−3.33073	+	3.84387i	−0.106505	+	0.122913i
$979$	1.14321	−	0.335675i	0.0365370	−	0.0107282i
$980$	0.729081	+	1.59646i	0.0232896	+	0.0509972i
$981$	19.1935	−	12.3349i	0.612803	−	0.393824i
$982$	36.5171	+	10.7224i	1.16531	+	0.342165i
$983$	1.78657	+	12.4259i	0.0569827	+	0.396323i	0.998274	+	0.0587279i	$0.0187044\pi$
$983$	1.78657	+	12.4259i	0.0569827	+	0.396323i	−0.941291	+	0.337595i	$0.890386\pi$
$984$	−4.42902	+	9.69820i	−0.141192	+	0.309167i
$985$	0.967097	−	6.72631i	0.0308143	−	0.214318i
$986$	−74.7902	−	48.0647i	−2.38180	−	1.53069i
$987$	4.39174	+	5.06834i	0.139791	+	0.161327i
$988$	−13.7900			−0.438719
$989$	44.6649	−	7.35858i	1.42026	−	0.233989i
$990$	−0.318236			−0.0101142
$991$	13.7499	+	15.8682i	0.436779	+	0.504069i	0.930875	−	0.365338i	$-0.119046\pi$
$991$	13.7499	+	15.8682i	0.436779	+	0.504069i	−0.494096	+	0.869407i	$0.664501\pi$
$992$	−22.2019	−	14.2683i	−0.704911	−	0.453019i
$993$	9.00368	−	62.6220i	0.285723	−	1.98725i
$994$	9.35168	−	20.4773i	0.296617	−	0.649501i
$995$	−0.833961	−	5.80033i	−0.0264384	−	0.183883i
$996$	50.5300	+	14.8369i	1.60110	+	0.470127i
$997$	33.8166	−	21.7326i	1.07098	−	0.688279i	0.118526	−	0.992951i	$-0.462183\pi$
$997$	33.8166	−	21.7326i	1.07098	−	0.688279i	0.952457	+	0.304672i	$0.0985468\pi$
$998$	5.10115	+	11.1700i	0.161474	+	0.353579i
$999$	28.9982	−	8.51464i	0.917462	−	0.269391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.u.d.36.3	✓	130
23.16	even	11	inner	805.2.u.d.246.3	yes	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.u.d.36.3	✓	130	1.1	even	1	trivial
805.2.u.d.246.3	yes	130	23.16	even	11	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:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.u (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26899 - 1.46449i) q^{2} +(1.73669 + 1.11610i) q^{3} +(-0.249772 + 1.73720i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.569318 - 3.95969i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-0.399286 + 0.256605i) q^{8} +(0.524163 + 1.14776i) q^{9} +O(q^{10})\)	\(q+(-1.26899 - 1.46449i) q^{2} +(1.73669 + 1.11610i) q^{3} +(-0.249772 + 1.73720i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.569318 - 3.95969i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-0.399286 + 0.256605i) q^{8} +(0.524163 + 1.14776i) q^{9} +(-1.85930 + 0.545941i) q^{10} +(0.0852326 - 0.0983636i) q^{11} +(-2.37267 + 2.73821i) q^{12} +(-1.33946 + 0.393300i) q^{13} +(-0.804991 - 1.76268i) q^{14} +(1.73669 - 1.11610i) q^{15} +(4.25043 + 1.24804i) q^{16} +(-0.930096 - 6.46896i) q^{17} +(1.01572 - 2.22412i) q^{18} +(0.801004 - 5.57111i) q^{19} +(1.47646 + 0.948861i) q^{20} +(1.35190 + 1.56018i) q^{21} -0.252212 q^{22} +(3.55936 - 3.21418i) q^{23} -0.979834 q^{24} +(-0.654861 - 0.755750i) q^{25} +(2.27574 + 1.46253i) q^{26} +(0.510681 - 3.55187i) q^{27} +(-0.729081 + 1.59646i) q^{28} +(0.999037 + 6.94845i) q^{29} +(-3.83836 - 1.12705i) q^{30} +(2.90793 - 1.86881i) q^{31} +(-3.17167 - 6.94499i) q^{32} +(0.257807 - 0.0756989i) q^{33} +(-8.29345 + 9.57115i) q^{34} +(0.654861 - 0.755750i) q^{35} +(-2.12481 + 0.623900i) q^{36} +(3.49874 + 7.66117i) q^{37} +(-9.17530 + 5.89661i) q^{38} +(-2.76519 - 0.811932i) q^{39} +(0.0675472 + 0.469801i) q^{40} +(4.52017 - 9.89780i) q^{41} +(0.569318 - 3.95969i) q^{42} +(7.94044 + 5.10301i) q^{43} +(0.149589 + 0.172635i) q^{44} +1.26178 q^{45} +(-9.22393 - 1.13389i) q^{46} +3.24857 q^{47} +(5.98875 + 6.91138i) q^{48} +(0.841254 + 0.540641i) q^{49} +(-0.275778 + 1.91808i) q^{50} +(5.60474 - 12.2727i) q^{51} +(-0.348683 - 2.42514i) q^{52} +(-9.76527 - 2.86734i) q^{53} +(-5.84973 + 3.75939i) q^{54} +(-0.0540678 - 0.118392i) q^{55} +(-0.455406 + 0.133719i) q^{56} +(7.60903 - 8.78129i) q^{57} +(8.90818 - 10.2806i) q^{58} +(-0.175414 + 0.0515063i) q^{59} +(1.50512 + 3.29576i) q^{60} +(7.06456 - 4.54012i) q^{61} +(-6.42699 - 1.88714i) q^{62} +(0.179570 + 1.24894i) q^{63} +(-2.46559 + 5.39889i) q^{64} +(-0.198672 + 1.38180i) q^{65} +(-0.438014 - 0.281494i) q^{66} +(-5.85748 - 6.75989i) q^{67} +11.4702 q^{68} +(9.76887 - 1.60943i) q^{69} -1.93780 q^{70} +(7.60760 + 8.77964i) q^{71} +(-0.503812 - 0.323780i) q^{72} +(-1.75464 + 12.2038i) q^{73} +(6.77986 - 14.8458i) q^{74} +(-0.293796 - 2.04340i) q^{75} +(9.47807 + 2.78301i) q^{76} +(0.109492 - 0.0703664i) q^{77} +(2.31992 + 5.07992i) q^{78} +(-10.6746 + 3.13435i) q^{79} +(2.90095 - 3.34788i) q^{80} +(7.33002 - 8.45930i) q^{81} +(-20.2313 + 5.94044i) q^{82} +(-6.03810 - 13.2216i) q^{83} +(-3.04801 + 1.95884i) q^{84} +(-6.27075 - 1.84126i) q^{85} +(-2.60302 - 18.1044i) q^{86} +(-6.02018 + 13.1823i) q^{87} +(-0.00879152 + 0.0611463i) q^{88} +(7.70110 + 4.94920i) q^{89} +(-1.60119 - 1.84787i) q^{90} -1.39601 q^{91} +(4.69466 + 6.98614i) q^{92} +7.13597 q^{93} +(-4.12240 - 4.75750i) q^{94} +(-4.73491 - 3.04294i) q^{95} +(2.24312 - 15.6012i) q^{96} +(-7.10610 + 15.5602i) q^{97} +(-0.275778 - 1.91808i) q^{98} +(0.157573 + 0.0462677i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9}+O(q^{10}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9} + 2 q^{10} + 2 q^{11} - 5 q^{12} + 13 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} - 51 q^{17} + q^{18} - 9 q^{19} - 16 q^{20} - 2 q^{21} + 34 q^{22} - 10 q^{23} - 76 q^{24} - 13 q^{25} - 31 q^{26} + 14 q^{27} + 27 q^{28} + 3 q^{29} + 5 q^{30} + 6 q^{31} + 22 q^{32} - 58 q^{33} + q^{34} + 13 q^{35} + 193 q^{36} - 36 q^{37} + 4 q^{38} - 2 q^{39} - 29 q^{40} - 34 q^{41} - 5 q^{42} - 22 q^{43} + 8 q^{44} + 170 q^{45} - 198 q^{46} - 14 q^{47} - 120 q^{48} - 13 q^{49} + 2 q^{50} - 6 q^{51} + 33 q^{52} - 18 q^{53} + 188 q^{54} - 31 q^{55} - 15 q^{56} - 9 q^{57} + 114 q^{58} + 46 q^{59} - 16 q^{60} - 56 q^{61} - 146 q^{62} + 17 q^{63} - 109 q^{64} + 2 q^{65} - 14 q^{66} - 10 q^{67} + 86 q^{68} - 6 q^{69} - 2 q^{70} - 25 q^{72} + 64 q^{73} + 79 q^{74} + 2 q^{75} + 32 q^{76} - 13 q^{77} - 64 q^{78} - 118 q^{79} - 17 q^{80} + 23 q^{81} + 129 q^{82} - 117 q^{83} - 72 q^{84} - 7 q^{85} + 74 q^{86} - 51 q^{87} - 40 q^{88} - 35 q^{89} + 100 q^{90} + 42 q^{91} + 76 q^{92} - 90 q^{93} - 7 q^{94} + 2 q^{95} + 393 q^{96} - 4 q^{97} + 2 q^{98} - 40 q^{99}+O(q^{100}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9 + 2 * q^10 + 2 * q^11 - 5 * q^12 + 13 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 - 51 * q^17 + q^18 - 9 * q^19 - 16 * q^20 - 2 * q^21 + 34 * q^22 - 10 * q^23 - 76 * q^24 - 13 * q^25 - 31 * q^26 + 14 * q^27 + 27 * q^28 + 3 * q^29 + 5 * q^30 + 6 * q^31 + 22 * q^32 - 58 * q^33 + q^34 + 13 * q^35 + 193 * q^36 - 36 * q^37 + 4 * q^38 - 2 * q^39 - 29 * q^40 - 34 * q^41 - 5 * q^42 - 22 * q^43 + 8 * q^44 + 170 * q^45 - 198 * q^46 - 14 * q^47 - 120 * q^48 - 13 * q^49 + 2 * q^50 - 6 * q^51 + 33 * q^52 - 18 * q^53 + 188 * q^54 - 31 * q^55 - 15 * q^56 - 9 * q^57 + 114 * q^58 + 46 * q^59 - 16 * q^60 - 56 * q^61 - 146 * q^62 + 17 * q^63 - 109 * q^64 + 2 * q^65 - 14 * q^66 - 10 * q^67 + 86 * q^68 - 6 * q^69 - 2 * q^70 - 25 * q^72 + 64 * q^73 + 79 * q^74 + 2 * q^75 + 32 * q^76 - 13 * q^77 - 64 * q^78 - 118 * q^79 - 17 * q^80 + 23 * q^81 + 129 * q^82 - 117 * q^83 - 72 * q^84 - 7 * q^85 + 74 * q^86 - 51 * q^87 - 40 * q^88 - 35 * q^89 + 100 * q^90 + 42 * q^91 + 76 * q^92 - 90 * q^93 - 7 * q^94 + 2 * q^95 + 393 * q^96 - 4 * q^97 + 2 * q^98 - 40 * q^99

Introduction

L-functions

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