LMFDB - Embedded newform 670.2.k.c.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(81,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("670.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.k (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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	670.81
Dual form			670.2.k.c.91.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{2} +(-0.628511 - 0.403919i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-0.106325 + 0.739508i) q^{6} +(1.26092 + 2.76102i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-1.01437 - 2.22116i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{2} +(-0.628511 - 0.403919i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-0.106325 + 0.739508i) q^{6} +(1.26092 + 2.76102i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-1.01437 - 2.22116i) q^{9} +(-0.841254 + 0.540641i) q^{10} +(0.533051 + 3.70745i) q^{11} +(0.716849 - 0.210486i) q^{12} +(0.290278 - 0.0852333i) q^{13} +(1.98771 - 2.29394i) q^{14} +(-0.310362 + 0.679597i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(1.20641 + 1.39227i) q^{17} +(-1.59905 + 1.84541i) q^{18} +(-2.37502 + 5.20057i) q^{19} +(0.841254 + 0.540641i) q^{20} +(0.322730 - 2.24464i) q^{21} +(3.15098 - 2.02501i) q^{22} +(0.632137 + 0.406250i) q^{23} +(-0.489254 - 0.564630i) q^{24} +(-0.959493 + 0.281733i) q^{25} +(-0.198117 - 0.228639i) q^{26} +(-0.578603 + 4.02427i) q^{27} +(-2.91236 - 0.855147i) q^{28} +7.59281 q^{29} +0.747112 q^{30} +(8.69985 + 2.55451i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(1.16248 - 2.54548i) q^{33} +(0.765294 - 1.67576i) q^{34} +(2.55347 - 1.64102i) q^{35} +(2.34291 + 0.687941i) q^{36} +0.755318 q^{37} +5.71722 q^{38} +(-0.216870 - 0.0636788i) q^{39} +(0.142315 - 0.989821i) q^{40} +(1.04054 + 1.20085i) q^{41} +(-2.17586 + 0.638891i) q^{42} +(-6.67378 - 7.70195i) q^{43} +(-3.15098 - 2.02501i) q^{44} +(-2.05419 + 1.32015i) q^{45} +(0.106939 - 0.743774i) q^{46} +(1.73003 + 1.11182i) q^{47} +(-0.310362 + 0.679597i) q^{48} +(-1.44930 + 1.67258i) q^{49} +(0.654861 + 0.755750i) q^{50} +(-0.195876 - 1.36235i) q^{51} +(-0.125677 + 0.275193i) q^{52} +(5.65239 - 6.52321i) q^{53} +(3.90097 - 1.14543i) q^{54} +(3.59385 - 1.05525i) q^{55} +(0.431970 + 3.00442i) q^{56} +(3.59334 - 2.30930i) q^{57} +(-3.15417 - 6.90666i) q^{58} +(13.9494 + 4.09593i) q^{59} +(-0.310362 - 0.679597i) q^{60} +(-1.21575 + 8.45571i) q^{61} +(-1.29039 - 8.97484i) q^{62} +(4.85363 - 5.60139i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-0.125677 - 0.275193i) q^{65} -2.79836 q^{66} +(-5.77369 + 5.80211i) q^{67} -1.84224 q^{68} +(-0.233213 - 0.510665i) q^{69} +(-2.55347 - 1.64102i) q^{70} +(-0.263582 + 0.304189i) q^{71} +(-0.347508 - 2.41697i) q^{72} +(-0.0846669 + 0.588871i) q^{73} +(-0.313770 - 0.687062i) q^{74} +(0.716849 + 0.210486i) q^{75} +(-2.37502 - 5.20057i) q^{76} +(-9.56420 + 6.14654i) q^{77} +(0.0321668 + 0.223725i) q^{78} +(4.91747 - 1.44390i) q^{79} +(-0.959493 + 0.281733i) q^{80} +(-2.80802 + 3.24063i) q^{81} +(0.660075 - 1.44536i) q^{82} +(0.0360398 + 0.250663i) q^{83} +(1.48504 + 1.71383i) q^{84} +(1.20641 - 1.39227i) q^{85} +(-4.23355 + 9.27019i) q^{86} +(-4.77216 - 3.06688i) q^{87} +(-0.533051 + 3.70745i) q^{88} +(3.52590 - 2.26596i) q^{89} +(2.05419 + 1.32015i) q^{90} +(0.601347 + 0.693991i) q^{91} +(-0.720985 + 0.211700i) q^{92} +(-4.43613 - 5.11957i) q^{93} +(0.292669 - 2.03556i) q^{94} +(5.48563 + 1.61073i) q^{95} +0.747112 q^{96} -11.7146 q^{97} +(2.12349 + 0.623513i) q^{98} +(7.69413 - 4.94471i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9	\( 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9} + 5 q^{10} - 12 q^{11} - 2 q^{12} + 24 q^{13} + 23 q^{14} - 2 q^{15} - 5 q^{16} + 31 q^{17} + q^{18} + 4 q^{19} - 5 q^{20} + 12 q^{21} + q^{22} + 27 q^{23} - 9 q^{24} - 5 q^{25} - 2 q^{26} - 14 q^{27} + 10 q^{28} - 36 q^{29} + 2 q^{30} - 13 q^{31} + 5 q^{32} - 42 q^{33} + 2 q^{34} + 21 q^{35} - q^{36} - 50 q^{37} - 26 q^{38} - 31 q^{39} + 5 q^{40} - 10 q^{41} + 21 q^{42} + 16 q^{43} - q^{44} - q^{45} + 17 q^{46} - 13 q^{47} - 2 q^{48} - 40 q^{49} + 5 q^{50} - 19 q^{51} - 20 q^{52} - 5 q^{53} + 47 q^{54} + 10 q^{55} + 12 q^{56} - 90 q^{57} - 8 q^{58} - 20 q^{59} - 2 q^{60} + 12 q^{61} + 13 q^{62} - 15 q^{63} - 5 q^{64} - 20 q^{65} + 20 q^{66} - 21 q^{67} - 24 q^{68} + 77 q^{69} - 21 q^{70} + 24 q^{71} + 12 q^{72} - 68 q^{73} - 16 q^{74} - 2 q^{75} + 4 q^{76} + 7 q^{77} + 53 q^{78} - 26 q^{79} - 5 q^{80} - 21 q^{81} + 21 q^{82} - 10 q^{83} + 12 q^{84} + 31 q^{85} - 27 q^{86} + 61 q^{87} + 12 q^{88} + 51 q^{89} + q^{90} - 10 q^{91} - 6 q^{92} - 38 q^{93} - 9 q^{94} + 15 q^{95} + 2 q^{96} + 72 q^{97} - 37 q^{98} - 32 q^{99}+O(q^{100}) \) 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9 + 5 * q^10 - 12 * q^11 - 2 * q^12 + 24 * q^13 + 23 * q^14 - 2 * q^15 - 5 * q^16 + 31 * q^17 + q^18 + 4 * q^19 - 5 * q^20 + 12 * q^21 + q^22 + 27 * q^23 - 9 * q^24 - 5 * q^25 - 2 * q^26 - 14 * q^27 + 10 * q^28 - 36 * q^29 + 2 * q^30 - 13 * q^31 + 5 * q^32 - 42 * q^33 + 2 * q^34 + 21 * q^35 - q^36 - 50 * q^37 - 26 * q^38 - 31 * q^39 + 5 * q^40 - 10 * q^41 + 21 * q^42 + 16 * q^43 - q^44 - q^45 + 17 * q^46 - 13 * q^47 - 2 * q^48 - 40 * q^49 + 5 * q^50 - 19 * q^51 - 20 * q^52 - 5 * q^53 + 47 * q^54 + 10 * q^55 + 12 * q^56 - 90 * q^57 - 8 * q^58 - 20 * q^59 - 2 * q^60 + 12 * q^61 + 13 * q^62 - 15 * q^63 - 5 * q^64 - 20 * q^65 + 20 * q^66 - 21 * q^67 - 24 * q^68 + 77 * q^69 - 21 * q^70 + 24 * q^71 + 12 * q^72 - 68 * q^73 - 16 * q^74 - 2 * q^75 + 4 * q^76 + 7 * q^77 + 53 * q^78 - 26 * q^79 - 5 * q^80 - 21 * q^81 + 21 * q^82 - 10 * q^83 + 12 * q^84 + 31 * q^85 - 27 * q^86 + 61 * q^87 + 12 * q^88 + 51 * q^89 + q^90 - 10 * q^91 - 6 * q^92 - 38 * q^93 - 9 * q^94 + 15 * q^95 + 2 * q^96 + 72 * q^97 - 37 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$

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 $

$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$3$	−0.628511	−	0.403919i	−0.362871	−	0.233203i	0.346482	−	0.938057i	$-0.387376\pi$
$3$	−0.628511	−	0.403919i	−0.362871	−	0.233203i	−0.709353	+	0.704854i	$0.751013\pi$
$4$	−0.654861	+	0.755750i	−0.327430	+	0.377875i
$5$	−0.142315	−	0.989821i	−0.0636451	−	0.442662i
$5$	−0.142315	−	0.989821i	−0.0636451	−	0.442662i
$6$	−0.106325	+	0.739508i	−0.0434071	+	0.301903i
$7$	1.26092	+	2.76102i	0.476581	+	1.04357i	0.983389	+	0.181508i	$0.0580980\pi$
$7$	1.26092	+	2.76102i	0.476581	+	1.04357i	−0.506808	+	0.862059i	$0.669175\pi$
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$	−1.01437	−	2.22116i	−0.338123	−	0.740387i
$10$	−0.841254	+	0.540641i	−0.266028	+	0.170966i
$11$	0.533051	+	3.70745i	0.160721	+	1.11784i	0.897279	+	0.441464i	$0.145541\pi$
$11$	0.533051	+	3.70745i	0.160721	+	1.11784i	−0.736558	+	0.676374i	$0.763550\pi$
$12$	0.716849	−	0.210486i	0.206936	−	0.0607620i
$13$	0.290278	−	0.0852333i	0.0805086	−	0.0236395i	−0.241230	−	0.970468i	$-0.577551\pi$
$13$	0.290278	−	0.0852333i	0.0805086	−	0.0236395i	0.321739	+	0.946828i	$0.395733\pi$
$14$	1.98771	−	2.29394i	0.531237	−	0.613081i
$15$	−0.310362	+	0.679597i	−0.0801350	+	0.175471i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	1.20641	+	1.39227i	0.292597	+	0.337675i	0.882947	−	0.469472i	$-0.155556\pi$
$17$	1.20641	+	1.39227i	0.292597	+	0.337675i	−0.590350	+	0.807147i	$0.701010\pi$
$18$	−1.59905	+	1.84541i	−0.376901	+	0.434967i
$19$	−2.37502	+	5.20057i	−0.544867	+	1.19309i	0.414271	+	0.910153i	$0.364036\pi$
$19$	−2.37502	+	5.20057i	−0.544867	+	1.19309i	−0.959138	+	0.282938i	$0.908691\pi$
$20$	0.841254	+	0.540641i	0.188110	+	0.120891i
$21$	0.322730	−	2.24464i	0.0704255	−	0.489820i
$22$	3.15098	−	2.02501i	0.671790	−	0.431733i
$23$	0.632137	+	0.406250i	0.131810	+	0.0847089i	0.604884	−	0.796314i	$-0.293219\pi$
$23$	0.632137	+	0.406250i	0.131810	+	0.0847089i	−0.473074	+	0.881022i	$0.656856\pi$
$24$	−0.489254	−	0.564630i	−0.0998687	−	0.115255i
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$	−0.198117	−	0.228639i	−0.0388539	−	0.0448398i
$27$	−0.578603	+	4.02427i	−0.111352	+	0.774471i
$28$	−2.91236	−	0.855147i	−0.550385	−	0.161608i
$29$	7.59281			1.40995			0.704974	−	0.709233i	$-0.250959\pi$
$29$	7.59281			1.40995			0.704974	+	0.709233i	$0.250959\pi$
$30$	0.747112			0.136403
$31$	8.69985	+	2.55451i	1.56254	+	0.458803i	0.944818	−	0.327595i	$-0.106238\pi$
$31$	8.69985	+	2.55451i	1.56254	+	0.458803i	0.617721	+	0.786398i	$0.288056\pi$
$32$	−0.841254	+	0.540641i	−0.148714	+	0.0955727i
$33$	1.16248	−	2.54548i	0.202362	−	0.443111i
$34$	0.765294	−	1.67576i	0.131247	−	0.287390i
$35$	2.55347	−	1.64102i	0.431615	−	0.277382i
$36$	2.34291	+	0.687941i	0.390485	+	0.114657i
$37$	0.755318			0.124174			0.0620868	−	0.998071i	$-0.480224\pi$
$37$	0.755318			0.124174			0.0620868	+	0.998071i	$0.480224\pi$
$38$	5.71722			0.927456
$39$	−0.216870	−	0.0636788i	−0.0347270	−	0.0101968i
$40$	0.142315	−	0.989821i	0.0225020	−	0.156505i
$41$	1.04054	+	1.20085i	0.162506	+	0.187541i	0.831162	−	0.556030i	$-0.187676\pi$
$41$	1.04054	+	1.20085i	0.162506	+	0.187541i	−0.668657	+	0.743571i	$0.733130\pi$
$42$	−2.17586	+	0.638891i	−0.335743	+	0.0985830i
$43$	−6.67378	−	7.70195i	−1.01774	−	1.17454i	−0.984553	−	0.175087i	$-0.943979\pi$
$43$	−6.67378	−	7.70195i	−1.01774	−	1.17454i	−0.0331889	−	0.999449i	$-0.510566\pi$
$44$	−3.15098	−	2.02501i	−0.475028	−	0.305282i
$45$	−2.05419	+	1.32015i	−0.306221	+	0.196796i
$46$	0.106939	−	0.743774i	0.0157672	−	0.109664i
$47$	1.73003	+	1.11182i	0.252351	+	0.162176i	0.660701	−	0.750649i	$-0.270259\pi$
$47$	1.73003	+	1.11182i	0.252351	+	0.162176i	−0.408350	+	0.912826i	$0.633896\pi$
$48$	−0.310362	+	0.679597i	−0.0447968	+	0.0980914i
$49$	−1.44930	+	1.67258i	−0.207042	+	0.238940i
$50$	0.654861	+	0.755750i	0.0926113	+	0.106879i
$51$	−0.195876	−	1.36235i	−0.0274282	−	0.190767i
$52$	−0.125677	+	0.275193i	−0.0174282	+	0.0381624i
$53$	5.65239	−	6.52321i	0.776416	−	0.896031i	−0.220429	−	0.975403i	$-0.570746\pi$
$53$	5.65239	−	6.52321i	0.776416	−	0.896031i	0.996845	+	0.0793715i	$0.0252913\pi$
$54$	3.90097	−	1.14543i	0.530854	−	0.155873i
$55$	3.59385	−	1.05525i	0.484595	−	0.142290i
$56$	0.431970	+	3.00442i	0.0577245	+	0.401482i
$57$	3.59334	−	2.30930i	0.475949	−	0.305874i
$58$	−3.15417	−	6.90666i	−0.414162	−	0.906889i
$59$	13.9494	+	4.09593i	1.81606	+	0.533244i	0.999058	−	0.0433864i	$-0.0138147\pi$
$59$	13.9494	+	4.09593i	1.81606	+	0.533244i	0.817005	+	0.576631i	$0.195633\pi$
$60$	−0.310362	−	0.679597i	−0.0400675	−	0.0877356i
$61$	−1.21575	+	8.45571i	−0.155661	+	1.08264i	0.750854	+	0.660468i	$0.229642\pi$
$61$	−1.21575	+	8.45571i	−0.155661	+	1.08264i	−0.906514	+	0.422175i	$0.861267\pi$
$62$	−1.29039	−	8.97484i	−0.163879	−	1.13981i
$63$	4.85363	−	5.60139i	0.611500	−	0.705709i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−0.125677	−	0.275193i	−0.0155883	−	0.0341335i
$66$	−2.79836			−0.344455
$67$	−5.77369	+	5.80211i	−0.705369	+	0.708840i
$67$	−5.77369	+	5.80211i	−0.705369	+	0.708840i
$68$	−1.84224			−0.223404
$69$	−0.233213	−	0.510665i	−0.0280755	−	0.0614768i
$70$	−2.55347	−	1.64102i	−0.305198	−	0.196139i
$71$	−0.263582	+	0.304189i	−0.0312814	+	0.0361006i	−0.771175	−	0.636624i	$-0.780331\pi$
$71$	−0.263582	+	0.304189i	−0.0312814	+	0.0361006i	0.739893	+	0.672724i	$0.234876\pi$
$72$	−0.347508	−	2.41697i	−0.0409542	−	0.284843i
$73$	−0.0846669	+	0.588871i	−0.00990951	+	0.0689222i	−0.994176	−	0.107767i	$-0.965630\pi$
$73$	−0.0846669	+	0.588871i	−0.00990951	+	0.0689222i	0.984267	+	0.176690i	$0.0565389\pi$
$74$	−0.313770	−	0.687062i	−0.0364751	−	0.0798693i
$75$	0.716849	+	0.210486i	0.0827746	+	0.0243048i
$76$	−2.37502	−	5.20057i	−0.272433	−	0.596546i
$77$	−9.56420	+	6.14654i	−1.08994	+	0.700463i
$78$	0.0321668	+	0.223725i	0.00364218	+	0.0253319i
$79$	4.91747	−	1.44390i	0.553258	−	0.162451i	0.00685962	−	0.999976i	$-0.497816\pi$
$79$	4.91747	−	1.44390i	0.553258	−	0.162451i	0.546399	+	0.837525i	$0.315998\pi$
$80$	−0.959493	+	0.281733i	−0.107275	+	0.0314987i
$81$	−2.80802	+	3.24063i	−0.312003	+	0.360070i
$82$	0.660075	−	1.44536i	0.0728931	−	0.159614i
$83$	0.0360398	+	0.250663i	0.00395589	+	0.0275138i	0.991704	−	0.128544i	$-0.0410304\pi$
$83$	0.0360398	+	0.250663i	0.00395589	+	0.0275138i	−0.987748	+	0.156058i	$0.950121\pi$
$84$	1.48504	+	1.71383i	0.162031	+	0.186994i
$85$	1.20641	−	1.39227i	0.130854	−	0.151013i
$86$	−4.23355	+	9.27019i	−0.456516	+	0.999630i
$87$	−4.77216	−	3.06688i	−0.511629	−	0.328804i
$88$	−0.533051	+	3.70745i	−0.0568234	+	0.395215i
$89$	3.52590	−	2.26596i	0.373744	−	0.240191i	−0.340261	−	0.940331i	$-0.610515\pi$
$89$	3.52590	−	2.26596i	0.373744	−	0.240191i	0.714006	+	0.700140i	$0.246879\pi$
$90$	2.05419	+	1.32015i	0.216531	+	0.139156i
$91$	0.601347	+	0.693991i	0.0630383	+	0.0727500i
$92$	−0.720985	+	0.211700i	−0.0751678	+	0.0220713i
$93$	−4.43613	−	5.11957i	−0.460006	−	0.530875i
$94$	0.292669	−	2.03556i	0.0301865	−	0.209952i
$95$	5.48563	+	1.61073i	0.562814	+	0.165257i
$96$	0.747112			0.0762518
$97$	−11.7146			−1.18944			−0.594718	−	0.803934i	$-0.702736\pi$
$97$	−11.7146			−1.18944			−0.594718	+	0.803934i	$0.702736\pi$
$98$	2.12349	+	0.623513i	0.214505	+	0.0629843i
$99$	7.69413	−	4.94471i	0.773289	−	0.496963i
$100$	0.415415	−	0.909632i	0.0415415	−	0.0909632i
$101$	−1.98548	+	4.34760i	−0.197563	+	0.432603i	−0.982322	−	0.187198i	$-0.940059\pi$
$101$	−1.98548	+	4.34760i	−0.197563	+	0.432603i	0.784759	+	0.619801i	$0.212787\pi$
$102$	−1.15787	+	0.744116i	−0.114646	+	0.0736785i
$103$	−13.0968	−	3.84558i	−1.29047	−	0.378916i	−0.436719	−	0.899598i	$-0.643859\pi$
$103$	−13.0968	−	3.84558i	−1.29047	−	0.378916i	−0.853751	+	0.520682i	$0.825678\pi$
$104$	0.302533			0.0296658
$105$	−2.26772			−0.221307
$106$	−8.28181	−	2.43176i	−0.804400	−	0.236193i
$107$	−0.481457	+	3.34861i	−0.0465443	+	0.323722i	0.953225	+	0.302260i	$0.0977412\pi$
$107$	−0.481457	+	3.34861i	−0.0465443	+	0.323722i	−0.999770	+	0.0214620i	$0.993168\pi$
$108$	−2.66244	−	3.07262i	−0.256193	−	0.295663i
$109$	−5.58993	+	1.64135i	−0.535418	+	0.157213i	−0.538253	−	0.842783i	$-0.680916\pi$
$109$	−5.58993	+	1.64135i	−0.535418	+	0.157213i	0.00283526	+	0.999996i	$0.499098\pi$
$110$	−2.45283	−	2.83071i	−0.233868	−	0.269898i
$111$	−0.474726	−	0.305088i	−0.0450590	−	0.0289576i
$112$	2.55347	−	1.64102i	0.241280	−	0.155061i
$113$	−0.175561	+	1.22105i	−0.0165154	+	0.114867i	−0.996411	−	0.0846416i	$-0.973025\pi$
$113$	−0.175561	+	1.22105i	−0.0165154	+	0.114867i	0.979896	+	0.199509i	$0.0639346\pi$
$114$	−3.59334	−	2.30930i	−0.336547	−	0.216285i
$115$	0.312152	−	0.683518i	0.0291083	−	0.0637384i
$116$	−4.97223	+	5.73826i	−0.461660	+	0.532784i
$117$	−0.483766	−	0.558296i	−0.0447242	−	0.0516145i
$118$	−2.06902	−	14.3904i	−0.190469	−	1.32474i
$119$	−2.32291	+	5.08646i	−0.212941	+	0.466275i
$120$	−0.489254	+	0.564630i	−0.0446626	+	0.0515434i
$121$	−2.90660	+	0.853456i	−0.264237	+	0.0775869i
$122$	8.19663	−	2.40675i	0.742088	−	0.217897i
$123$	−0.168946	−	1.17504i	−0.0152333	−	0.105950i
$124$	−7.62776	+	4.90206i	−0.684993	+	0.440218i
$125$	0.415415	+	0.909632i	0.0371558	+	0.0813600i
$126$	−7.11148	−	2.08812i	−0.633541	−	0.186024i
$127$	5.77908	+	12.6544i	0.512811	+	1.12290i	0.972090	+	0.234607i	$0.0753802\pi$
$127$	5.77908	+	12.6544i	0.512811	+	1.12290i	−0.459280	+	0.888292i	$0.651892\pi$
$128$	0.142315	−	0.989821i	0.0125790	−	0.0874887i
$129$	1.08357	+	7.53643i	0.0954034	+	0.663546i
$130$	−0.198117	+	0.228639i	−0.0173760	+	0.0200530i
$131$	7.89249	+	5.07220i	0.689570	+	0.443160i	0.837933	−	0.545773i	$-0.183764\pi$
$131$	7.89249	+	5.07220i	0.689570	+	0.443160i	−0.148363	+	0.988933i	$0.547400\pi$
$132$	1.16248	+	2.54548i	0.101181	+	0.221556i
$133$	−17.3536			−1.50474
$134$	7.67626	+	2.84165i	0.663128	+	0.245481i
$135$	4.06565			0.349916
$136$	0.765294	+	1.67576i	0.0656234	+	0.143695i
$137$	−4.03692	−	2.59437i	−0.344898	−	0.221652i	0.356711	−	0.934215i	$-0.383898\pi$
$137$	−4.03692	−	2.59437i	−0.344898	−	0.221652i	−0.701609	+	0.712563i	$0.747534\pi$
$138$	−0.367637	+	0.424275i	−0.0312953	+	0.0361167i
$139$	−1.54913	−	10.7744i	−0.131395	−	0.913874i	−0.943738	−	0.330694i	$-0.892717\pi$
$139$	−1.54913	−	10.7744i	−0.131395	−	0.913874i	0.812343	−	0.583180i	$-0.198192\pi$
$140$	−0.431970	+	3.00442i	−0.0365082	+	0.253920i
$141$	−0.638256	−	1.39759i	−0.0537509	−	0.117698i
$142$	0.386196	+	0.113397i	0.0324089	+	0.00951610i
$143$	0.470731	+	1.03076i	0.0393645	+	0.0861962i
$144$	−2.05419	+	1.32015i	−0.171183	+	0.110012i
$145$	−1.08057	−	7.51552i	−0.0897364	−	0.624130i
$146$	0.570828	−	0.167610i	0.0472421	−	0.0138715i
$147$	1.58648	−	0.465834i	0.130851	−	0.0384213i
$148$	−0.494628	+	0.570831i	−0.0406582	+	0.0469220i
$149$	−7.30089	+	15.9867i	−0.598112	+	1.30968i	0.332302	+	0.943173i	$0.392175\pi$
$149$	−7.30089	+	15.9867i	−0.598112	+	1.30968i	−0.930414	+	0.366510i	$0.880552\pi$
$150$	−0.106325	−	0.739508i	−0.00868141	−	0.0603806i
$151$	9.98073	+	11.5184i	0.812220	+	0.937352i	0.998985	−	0.0450525i	$-0.0143455\pi$
$151$	9.98073	+	11.5184i	0.812220	+	0.937352i	−0.186764	+	0.982405i	$0.559800\pi$
$152$	−3.74398	+	4.32079i	−0.303677	+	0.350462i
$153$	1.86871	−	4.09191i	0.151076	−	0.330811i
$154$	9.56420	+	6.14654i	0.770706	+	0.495302i
$155$	1.29039	−	8.97484i	0.103646	−	0.720877i
$156$	0.190145	−	0.122199i	0.0152238	−	0.00978373i
$157$	6.86316	+	4.41068i	0.547739	+	0.352011i	0.785059	−	0.619421i	$-0.212633\pi$
$157$	6.86316	+	4.41068i	0.547739	+	0.352011i	−0.237320	+	0.971432i	$0.576269\pi$
$158$	−3.35621	−	3.87327i	−0.267005	−	0.308141i
$159$	−6.18744	+	1.81680i	−0.490696	+	0.144081i
$160$	0.654861	+	0.755750i	0.0517713	+	0.0597472i
$161$	−0.324592	+	2.25759i	−0.0255815	+	0.177923i
$162$	4.11428	+	1.20806i	0.323248	+	0.0949142i
$163$	−15.2760			−1.19651			−0.598255	−	0.801305i	$-0.704139\pi$
$163$	−15.2760			−1.19651			−0.598255	+	0.801305i	$0.704139\pi$
$164$	−1.58895			−0.124076
$165$	−2.68501	−	0.788390i	−0.209028	−	0.0613761i
$166$	0.213039	−	0.136912i	0.0165350	−	0.0106264i
$167$	9.39101	−	20.5634i	0.726698	−	1.59125i	−0.0775743	−	0.996987i	$-0.524717\pi$
$167$	9.39101	−	20.5634i	0.726698	−	1.59125i	0.804273	−	0.594261i	$-0.202555\pi$
$168$	0.942045	−	2.06279i	0.0726804	−	0.159148i
$169$	−10.8593	+	6.97885i	−0.835331	+	0.536834i
$170$	−1.76762	−	0.519019i	−0.135570	−	0.0398069i
$171$	13.9604			1.06758
$172$	10.1911			0.777067
$173$	−18.5625	−	5.45044i	−1.41128	−	0.414390i	−0.514739	−	0.857347i	$-0.672111\pi$
$173$	−18.5625	−	5.45044i	−1.41128	−	0.414390i	−0.896543	+	0.442958i	$0.853929\pi$
$174$	−0.807306	+	5.61494i	−0.0612017	+	0.425667i
$175$	−1.98771	−	2.29394i	−0.150257	−	0.173405i
$176$	3.59385	−	1.05525i	0.270897	−	0.0795424i
$177$	−7.11295	−	8.20879i	−0.534642	−	0.617010i
$178$	−3.52590	−	2.26596i	−0.264277	−	0.169841i
$179$	1.92267	−	1.23562i	0.143707	−	0.0923549i	−0.466812	−	0.884357i	$-0.654597\pi$
$179$	1.92267	−	1.23562i	0.143707	−	0.0923549i	0.610519	+	0.792002i	$0.290961\pi$
$180$	0.347508	−	2.41697i	0.0259017	−	0.180150i
$181$	−15.8305	−	10.1737i	−1.17667	−	0.756202i	−0.201902	−	0.979406i	$-0.564712\pi$
$181$	−15.8305	−	10.1737i	−1.17667	−	0.756202i	−0.974772	+	0.223204i	$0.928349\pi$
$182$	0.381468	−	0.835298i	0.0282763	−	0.0619164i
$183$	4.17954	−	4.82344i	0.308960	−	0.356559i
$184$	0.492077	+	0.567887i	0.0362764	+	0.0418652i
$185$	−0.107493	−	0.747630i	−0.00790304	−	0.0549669i
$186$	−2.81409	+	6.16200i	−0.206339	+	0.451820i
$187$	−4.51870	+	5.21485i	−0.330440	+	0.381348i
$188$	−1.97319	+	0.579381i	−0.143910	+	0.0422557i
$189$	−11.8407	+	3.47673i	−0.861281	+	0.252895i
$190$	−0.813645	−	5.65903i	−0.0590280	−	0.410549i
$191$	−4.97282	+	3.19583i	−0.359820	+	0.231242i	−0.708043	−	0.706169i	$-0.750422\pi$
$191$	−4.97282	+	3.19583i	−0.359820	+	0.231242i	0.348223	+	0.937412i	$0.386785\pi$
$192$	−0.310362	−	0.679597i	−0.0223984	−	0.0490457i
$193$	11.3054	+	3.31958i	0.813784	+	0.238949i	0.662037	−	0.749471i	$-0.269692\pi$
$193$	11.3054	+	3.31958i	0.813784	+	0.238949i	0.151747	+	0.988419i	$0.451510\pi$
$194$	4.86641	+	10.6560i	0.349388	+	0.765053i
$195$	−0.0321668	+	0.223725i	−0.00230351	+	0.0160213i
$196$	−0.314962	−	2.19061i	−0.0224973	−	0.156472i
$197$	−10.1736	+	11.7410i	−0.724840	+	0.836510i	−0.991880	−	0.127175i	$-0.959409\pi$
$197$	−10.1736	+	11.7410i	−0.724840	+	0.836510i	0.267040	+	0.963685i	$0.413954\pi$
$198$	−7.69413	−	4.94471i	−0.546798	−	0.351406i
$199$	−10.9867	−	24.0575i	−0.778827	−	1.70539i	−0.706177	−	0.708035i	$-0.749582\pi$
$199$	−10.9867	−	24.0575i	−0.778827	−	1.70539i	−0.0726497	−	0.997358i	$-0.523146\pi$
$200$	−1.00000			−0.0707107
$201$	5.97241	−	1.31458i	0.421262	−	0.0927235i
$202$	4.77952			0.336286
$203$	9.57389	+	20.9639i	0.671955	+	1.47138i
$204$	1.15787	+	0.744116i	0.0810669	+	0.0520985i
$205$	1.04054	−	1.20085i	0.0726747	−	0.0838711i
$206$	1.94256	+	13.5108i	0.135345	+	0.941343i
$207$	0.261125	−	1.81616i	0.0181494	−	0.126232i
$208$	−0.125677	−	0.275193i	−0.00871410	−	0.0190812i
$209$	−20.5468	−	6.03310i	−1.42125	−	0.417318i
$210$	0.942045	+	2.06279i	0.0650073	+	0.142346i
$211$	−11.5777	+	7.44055i	−0.797043	+	0.512228i	−0.874650	−	0.484756i	$-0.838909\pi$
$211$	−11.5777	+	7.44055i	−0.797043	+	0.512228i	0.0776066	+	0.996984i	$0.475272\pi$
$212$	1.22838	+	8.54358i	0.0843656	+	0.586776i
$213$	0.288532	−	0.0847206i	0.0197699	−	0.00580496i
$214$	3.24601	−	0.953114i	0.221893	−	0.0651535i
$215$	−6.67378	+	7.70195i	−0.455148	+	0.525269i
$216$	−1.68893	+	3.69825i	−0.114917	+	0.251634i
$217$	3.91673	+	27.2415i	0.265885	+	1.84927i
$218$	3.81517	+	4.40294i	0.258396	+	0.298205i
$219$	0.291071	−	0.335913i	0.0196687	−	0.0226989i
$220$	−1.55597	+	3.40709i	−0.104903	+	0.229706i
$221$	0.468862	+	0.301319i	0.0315391	+	0.0202689i
$222$	−0.0803093	+	0.558564i	−0.00539001	+	0.0374883i
$223$	12.3474	−	7.93518i	0.826841	−	0.531379i	−0.0574314	−	0.998349i	$-0.518291\pi$
$223$	12.3474	−	7.93518i	0.826841	−	0.531379i	0.884273	+	0.466971i	$0.154655\pi$
$224$	−2.55347	−	1.64102i	−0.170611	−	0.109645i
$225$	1.59905	+	1.84541i	0.106604	+	0.123027i
$226$	1.18364	−	0.347548i	0.0787345	−	0.0231185i
$227$	9.30859	+	10.7427i	0.617833	+	0.713017i	0.975294	−	0.220911i	$-0.0709030\pi$
$227$	9.30859	+	10.7427i	0.617833	+	0.713017i	−0.357461	+	0.933928i	$0.616358\pi$
$228$	−0.607884	+	4.22793i	−0.0402581	+	0.280001i
$229$	15.2698	+	4.48361i	1.00905	+	0.296285i	0.744167	−	0.667994i	$-0.232847\pi$
$229$	15.2698	+	4.48361i	1.00905	+	0.296285i	0.264888	+	0.964279i	$0.414665\pi$
$230$	−0.751422			−0.0495473
$231$	8.49391			0.558858
$232$	7.28524	+	2.13914i	0.478300	+	0.140441i
$233$	7.82670	−	5.02991i	0.512744	−	0.329521i	−0.258552	−	0.965997i	$-0.583245\pi$
$233$	7.82670	−	5.02991i	0.512744	−	0.329521i	0.771296	+	0.636477i	$0.219609\pi$
$234$	−0.306880	+	0.671973i	−0.0200614	+	0.0439283i
$235$	0.854297	−	1.87065i	0.0557282	−	0.122028i
$236$	−12.2304	+	7.86003i	−0.796134	+	0.511644i
$237$	−3.67390	−	1.07875i	−0.238645	−	0.0700726i
$238$	5.59177			0.362461
$239$	−12.6063			−0.815434			−0.407717	−	0.913108i	$-0.633675\pi$
$239$	−12.6063			−0.815434			−0.407717	+	0.913108i	$0.633675\pi$
$240$	0.716849	+	0.210486i	0.0462724	+	0.0135868i
$241$	3.32343	−	23.1150i	0.214081	−	1.48897i	−0.545256	−	0.838270i	$-0.683568\pi$
$241$	3.32343	−	23.1150i	0.214081	−	1.48897i	0.759337	−	0.650697i	$-0.225523\pi$
$242$	1.98378	+	2.28940i	0.127522	+	0.147168i
$243$	14.7767	−	4.33884i	0.947927	−	0.278337i
$244$	−5.59426	−	6.45612i	−0.358136	−	0.413311i
$245$	1.86181	+	1.19651i	0.118947	+	0.0764423i
$246$	−0.998675	+	0.641809i	−0.0636732	+	0.0409203i
$247$	−0.246154	+	1.71204i	−0.0156624	+	0.108935i
$248$	7.62776	+	4.90206i	0.484363	+	0.311281i
$249$	0.0785960	−	0.172101i	0.00498082	−	0.0109065i
$250$	0.654861	−	0.755750i	0.0414170	−	0.0477978i
$251$	3.28519	+	3.79131i	0.207359	+	0.239305i	0.849897	−	0.526949i	$-0.176664\pi$
$251$	3.28519	+	3.79131i	0.207359	+	0.239305i	−0.642538	+	0.766254i	$0.722119\pi$
$252$	1.05480	+	7.33626i	0.0664459	+	0.462141i
$253$	−1.16919	+	2.56017i	−0.0735063	+	0.160956i
$254$	9.11015	−	10.5137i	0.571622	−	0.659687i
$255$	−1.32061	+	0.387765i	−0.0826996	+	0.0242828i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	−1.46632	−	10.1985i	−0.0914666	−	0.636164i	−0.983054	−	0.183316i	$-0.941317\pi$
$257$	−1.46632	−	10.1985i	−0.0914666	−	0.636164i	0.891587	−	0.452848i	$-0.149592\pi$
$258$	6.40524	−	4.11640i	0.398773	−	0.256276i
$259$	0.952392	+	2.08545i	0.0591788	+	0.129583i
$260$	0.290278	+	0.0852333i	0.0180023	+	0.00528594i
$261$	−7.70191	−	16.8648i	−0.476737	−	1.04391i
$262$	1.33517	−	9.28633i	0.0824872	−	0.573711i
$263$	−3.51824	−	24.4699i	−0.216944	−	1.50888i	−0.749228	−	0.662313i	$-0.769575\pi$
$263$	−3.51824	−	24.4699i	−0.216944	−	1.50888i	0.532283	−	0.846566i	$-0.321334\pi$
$264$	1.83254	−	2.11486i	0.112785	−	0.130161i
$265$	−7.26123	−	4.66651i	−0.446054	−	0.286661i
$266$	7.20893	+	15.7854i	0.442008	+	0.967862i
$267$	−3.13133			−0.191634
$268$	−0.603977	−	8.16304i	−0.0368938	−	0.498637i
$269$	9.58103			0.584166			0.292083	−	0.956393i	$-0.405652\pi$
$269$	9.58103			0.584166			0.292083	+	0.956393i	$0.405652\pi$
$270$	−1.68893	−	3.69825i	−0.102785	−	0.225068i
$271$	−7.41577	−	4.76582i	−0.450476	−	0.289503i	0.295665	−	0.955292i	$-0.404459\pi$
$271$	−7.41577	−	4.76582i	−0.450476	−	0.289503i	−0.746140	+	0.665789i	$0.768095\pi$
$272$	1.20641	−	1.39227i	0.0731493	−	0.0844188i
$273$	−0.0976364	−	0.679076i	−0.00590923	−	0.0410996i
$274$	−0.682926	+	4.74986i	−0.0412571	+	0.286949i
$275$	−1.55597	−	3.40709i	−0.0938283	−	0.205455i
$276$	0.538656	+	0.158164i	0.0324233	+	0.00952034i
$277$	−5.22464	−	11.4404i	−0.313918	−	0.687385i	0.685244	−	0.728314i	$-0.259696\pi$
$277$	−5.22464	−	11.4404i	−0.313918	−	0.687385i	−0.999162	+	0.0409287i	$0.986968\pi$
$278$	−9.15722	+	5.88499i	−0.549213	+	0.352958i
$279$	−3.15090	−	21.9150i	−0.188639	−	1.31202i
$280$	2.91236	−	0.855147i	0.174047	−	0.0511048i
$281$	20.9706	−	6.15754i	1.25100	−	0.367328i	0.411865	−	0.911245i	$-0.364878\pi$
$281$	20.9706	−	6.15754i	1.25100	−	0.367328i	0.839139	+	0.543917i	$0.183059\pi$
$282$	−1.00615	+	1.16116i	−0.0599152	+	0.0691458i
$283$	−7.40460	+	16.2138i	−0.440158	+	0.963811i	0.551411	+	0.834234i	$0.314089\pi$
$283$	−7.40460	+	16.2138i	−0.440158	+	0.963811i	−0.991569	+	0.129578i	$0.958638\pi$
$284$	−0.0572818	−	0.398403i	−0.00339905	−	0.0236409i
$285$	−2.79718	−	3.22811i	−0.165690	−	0.191217i
$286$	0.742060	−	0.856383i	0.0438790	−	0.0506390i
$287$	−2.00354	+	4.38713i	−0.118265	+	0.258964i
$288$	2.05419	+	1.32015i	0.121044	+	0.0777905i
$289$	1.93636	−	13.4677i	0.113903	−	0.792216i
$290$	−6.38747	+	4.10498i	−0.375085	+	0.241053i
$291$	7.36274	+	4.73175i	0.431612	+	0.277380i
$292$	−0.389594	−	0.449616i	−0.0227993	−	0.0263118i
$293$	16.8742	−	4.95470i	0.985799	−	0.289457i	0.251183	−	0.967940i	$-0.419181\pi$
$293$	16.8742	−	4.95470i	0.985799	−	0.289457i	0.734616	+	0.678483i	$0.237362\pi$
$294$	−1.08279	−	1.24960i	−0.0631494	−	0.0728783i
$295$	2.06902	−	14.3904i	0.120463	−	0.837840i
$296$	0.724722	+	0.212798i	0.0421236	+	0.0123686i
$297$	−15.2282			−0.883630
$298$	17.5749			1.01809
$299$	0.218121	+	0.0640462i	0.0126143	+	0.00370389i
$300$	−0.628511	+	0.403919i	−0.0362871	+	0.0233203i
$301$	12.8502	−	28.1379i	0.740671	−	1.62184i
$302$	6.33134	−	13.8637i	0.364328	−	0.797766i
$303$	3.00398	−	1.93054i	0.172574	−	0.110907i
$304$	5.48563	+	1.61073i	0.314623	+	0.0923815i
$305$	8.54267			0.489152
$306$	−4.49842			−0.257158
$307$	29.1812	+	8.56837i	1.66546	+	0.489023i	0.972684	−	0.232132i	$-0.0745701\pi$
$307$	29.1812	+	8.56837i	1.66546	+	0.489023i	0.692774	+	0.721155i	$0.256388\pi$
$308$	1.61798	−	11.2533i	0.0921927	−	0.641215i
$309$	6.67820	+	7.70705i	0.379909	+	0.438439i
$310$	−8.69985	+	2.55451i	−0.494118	+	0.145086i
$311$	−5.70046	−	6.57868i	−0.323243	−	0.373043i	0.570749	−	0.821124i	$-0.306653\pi$
$311$	−5.70046	−	6.57868i	−0.323243	−	0.373043i	−0.893993	+	0.448082i	$0.852107\pi$
$312$	−0.190145	−	0.122199i	−0.0107648	−	0.00691814i
$313$	26.8090	−	17.2291i	1.51534	−	0.973848i	0.522727	−	0.852500i	$-0.324915\pi$
$313$	26.8090	−	17.2291i	1.51534	−	0.973848i	0.992610	−	0.121348i	$-0.0387217\pi$
$314$	1.16104	−	8.07521i	0.0655213	−	0.455710i
$315$	−6.23512	−	4.00707i	−0.351309	−	0.225773i
$316$	−2.12903	+	4.66193i	−0.119767	+	0.262254i
$317$	3.23875	−	3.73772i	0.181907	−	0.209931i	−0.657471	−	0.753479i	$-0.728374\pi$
$317$	3.23875	−	3.73772i	0.181907	−	0.209931i	0.839378	+	0.543548i	$0.182919\pi$
$318$	4.22297	+	4.87357i	0.236812	+	0.273296i
$319$	4.04735	+	28.1499i	0.226608	+	1.57609i
$320$	0.415415	−	0.909632i	0.0232224	−	0.0508500i
$321$	1.65517	−	1.91017i	0.0923826	−	0.106615i
$322$	2.18842	−	0.642577i	0.121956	−	0.0358094i
$323$	−10.1058	+	2.96734i	−0.562304	+	0.165107i
$324$	−0.610242	−	4.24433i	−0.0339023	−	0.235796i
$325$	−0.254507	+	0.163561i	−0.0141175	+	0.00907276i
$326$	6.34589	+	13.8956i	0.351466	+	0.769604i
$327$	4.17631	+	1.22627i	0.230950	+	0.0678131i
$328$	0.660075	+	1.44536i	0.0364466	+	0.0798068i
$329$	−0.888343	+	6.17856i	−0.0489760	+	0.340635i
$330$	0.398249	+	2.76988i	0.0219229	+	0.152477i
$331$	6.75723	−	7.79826i	0.371411	−	0.428631i	−0.539019	−	0.842293i	$-0.681205\pi$
$331$	6.75723	−	7.79826i	0.371411	−	0.428631i	0.910431	+	0.413662i	$0.135750\pi$
$332$	−0.213039	−	0.136912i	−0.0116920	−	0.00751402i
$333$	−0.766172	−	1.67768i	−0.0419860	−	0.0919365i
$334$	−22.6063			−1.23696
$335$	6.56473	+	4.88920i	0.358670	+	0.267125i
$336$	−2.26772			−0.123714
$337$	−6.63943	−	14.5383i	−0.361673	−	0.791953i	−0.999758	−	0.0219877i	$-0.993001\pi$
$337$	−6.63943	−	14.5383i	−0.361673	−	0.791953i	0.638085	−	0.769966i	$-0.279727\pi$
$338$	10.8593	+	6.97885i	0.590668	+	0.379599i
$339$	0.603549	−	0.696532i	0.0327803	−	0.0378304i
$340$	0.262178	+	1.82349i	0.0142186	+	0.0988925i
$341$	−4.83324	+	33.6159i	−0.261735	+	1.82040i
$342$	−5.79938	−	12.6989i	−0.313594	−	0.686676i
$343$	13.9411	+	4.09347i	0.752748	+	0.221027i
$344$	−4.23355	−	9.27019i	−0.228258	−	0.499815i
$345$	−0.472277	+	0.303514i	−0.0254265	+	0.0163406i
$346$	2.75325	+	19.1492i	0.148015	+	1.02947i
$347$	−9.58388	+	2.81408i	−0.514490	+	0.151068i	−0.528663	−	0.848832i	$-0.677307\pi$
$347$	−9.58388	+	2.81408i	−0.514490	+	0.151068i	0.0141734	+	0.999900i	$0.495488\pi$
$348$	5.44289	−	1.59818i	0.291770	−	0.0856713i
$349$	−13.8862	+	16.0256i	−0.743313	+	0.857829i	−0.993902	−	0.110265i	$-0.964830\pi$
$349$	−13.8862	+	16.0256i	−0.743313	+	0.857829i	0.250589	+	0.968093i	$0.419376\pi$
$350$	−1.26092	+	2.76102i	−0.0673988	+	0.147583i
$351$	0.175046	+	1.21747i	0.00934327	+	0.0649839i
$352$	−2.45283	−	2.83071i	−0.130736	−	0.150878i
$353$	−6.51174	+	7.51495i	−0.346585	+	0.399981i	−0.902101	−	0.431526i	$-0.857975\pi$
$353$	−6.51174	+	7.51495i	−0.346585	+	0.399981i	0.555516	+	0.831506i	$0.312521\pi$
$354$	−4.51215	+	9.88022i	−0.239818	+	0.525128i
$355$	0.338605	+	0.217608i	0.0179713	+	0.0115494i
$356$	−0.596476	+	4.14858i	−0.0316132	+	0.219874i
$357$	3.51449	−	2.25863i	0.186007	−	0.119539i
$358$	−1.92267	−	1.23562i	−0.101616	−	0.0653048i
$359$	1.12215	+	1.29503i	0.0592246	+	0.0683489i	0.784589	−	0.620016i	$-0.212874\pi$
$359$	1.12215	+	1.29503i	0.0592246	+	0.0683489i	−0.725364	+	0.688365i	$0.758329\pi$
$360$	−2.34291	+	0.687941i	−0.123482	+	0.0362577i
$361$	−8.96282	−	10.3437i	−0.471728	−	0.544403i
$362$	−2.67805	+	18.6262i	−0.140755	+	0.978974i
$363$	2.17156	+	0.637627i	0.113977	+	0.0334668i
$364$	−0.918282			−0.0481310
$365$	0.594927			0.0311399
$366$	−6.12380	−	1.79811i	−0.320096	−	0.0939887i
$367$	16.3361	−	10.4985i	0.852735	−	0.548019i	−0.0396917	−	0.999212i	$-0.512638\pi$
$367$	16.3361	−	10.4985i	0.852735	−	0.548019i	0.892427	+	0.451193i	$0.149001\pi$
$368$	0.312152	−	0.683518i	0.0162721	−	0.0356308i
$369$	1.61179	−	3.52932i	0.0839063	−	0.183729i
$370$	−0.635414	+	0.408356i	−0.0330336	+	0.0212294i
$371$	25.1379	+	7.38115i	1.30509	+	0.383210i
$372$	6.77417			0.351224
$373$	−20.8550			−1.07983			−0.539916	−	0.841719i	$-0.681544\pi$
$373$	−20.8550			−1.07983			−0.539916	+	0.841719i	$0.681544\pi$
$374$	6.62073	+	1.94402i	0.342350	+	0.100523i
$375$	0.106325	−	0.739508i	0.00549061	−	0.0381880i
$376$	1.34672	+	1.55419i	0.0694515	+	0.0801514i
$377$	2.20402	−	0.647160i	0.113513	−	0.0333304i
$378$	8.08133	+	9.32636i	0.415659	+	0.479696i
$379$	−13.1866	−	8.47448i	−0.677348	−	0.435305i	0.156220	−	0.987722i	$-0.450069\pi$
$379$	−13.1866	−	8.47448i	−0.677348	−	0.435305i	−0.833568	+	0.552417i	$0.813706\pi$
$380$	−4.80963	+	3.09096i	−0.246729	+	0.158563i
$381$	1.47915	−	10.2877i	0.0757792	−	0.527056i
$382$	4.97282	+	3.19583i	0.254431	+	0.163513i
$383$	−2.22193	+	4.86535i	−0.113535	+	0.248608i	−0.957866	−	0.287214i	$-0.907271\pi$
$383$	−2.22193	+	4.86535i	−0.113535	+	0.248608i	0.844331	+	0.535822i	$0.179998\pi$
$384$	−0.489254	+	0.564630i	−0.0249672	+	0.0288136i
$385$	7.44511	+	8.59211i	0.379438	+	0.437894i
$386$	−1.67686	−	11.6628i	−0.0853498	−	0.593621i
$387$	−10.3376	+	22.6362i	−0.525489	+	1.15066i
$388$	7.67142	−	8.85329i	0.389457	−	0.449458i
$389$	16.0876	−	4.72375i	0.815675	−	0.239504i	0.152822	−	0.988254i	$-0.451164\pi$
$389$	16.0876	−	4.72375i	0.815675	−	0.239504i	0.662853	+	0.748750i	$0.269346\pi$
$390$	0.216870	−	0.0636788i	0.0109816	−	0.00322450i
$391$	0.197006	+	1.37021i	0.00996304	+	0.0692945i
$392$	−1.86181	+	1.19651i	−0.0940355	+	0.0604330i
$393$	−2.91176	−	6.37586i	−0.146879	−	0.321620i
$394$	14.9062	+	4.37687i	0.750966	+	0.220503i
$395$	−2.12903	−	4.66193i	−0.107123	−	0.234567i
$396$	−1.30162	+	9.05293i	−0.0654086	+	0.454927i
$397$	−3.19808	−	22.2432i	−0.160507	−	1.11635i	−0.897680	−	0.440648i	$-0.854749\pi$
$397$	−3.19808	−	22.2432i	−0.160507	−	1.11635i	0.737173	−	0.675704i	$-0.236160\pi$
$398$	−17.3195	+	19.9877i	−0.868146	+	1.00189i
$399$	10.9069	+	7.00944i	0.546028	+	0.350911i
$400$	0.415415	+	0.909632i	0.0207708	+	0.0454816i
$401$	32.7896			1.63743			0.818717	−	0.574197i	$-0.194686\pi$
$401$	32.7896			1.63743			0.818717	+	0.574197i	$0.194686\pi$
$402$	−3.67682	−	4.88660i	−0.183383	−	0.243721i
$403$	2.74310			0.136644
$404$	−1.98548	−	4.34760i	−0.0987815	−	0.216301i
$405$	3.60727	+	2.31825i	0.179247	+	0.115195i
$406$	15.0923	−	17.4174i	0.749017	−	0.864412i
$407$	0.402623	+	2.80030i	0.0199573	+	0.138806i
$408$	0.195876	−	1.36235i	0.00969732	−	0.0674464i
$409$	7.62804	+	16.7031i	0.377183	+	0.825914i	0.999083	+	0.0428181i	$0.0136336\pi$
$409$	7.62804	+	16.7031i	0.377183	+	0.825914i	−0.621900	+	0.783096i	$0.713639\pi$
$410$	−1.52459	−	0.447660i	−0.0752941	−	0.0221084i
$411$	1.48933	+	3.26118i	0.0734634	+	0.160862i
$412$	11.4829	−	7.37961i	0.565722	−	0.363567i
$413$	6.28014	+	43.6793i	0.309025	+	2.14932i
$414$	−1.76052	+	0.516934i	−0.0865247	+	0.0254059i
$415$	0.242982	−	0.0713460i	0.0119275	−	0.00350224i
$416$	−0.198117	+	0.228639i	−0.00971347	+	0.0112099i
$417$	−3.37835	+	7.39756i	−0.165439	+	0.362260i
$418$	3.04757	+	21.1963i	0.149061	+	1.03674i
$419$	−3.18280	−	3.67315i	−0.155490	−	0.179445i	0.672660	−	0.739952i	$-0.265152\pi$
$419$	−3.18280	−	3.67315i	−0.155490	−	0.179445i	−0.828150	+	0.560507i	$0.810606\pi$
$420$	1.48504	−	1.71383i	0.0724626	−	0.0836263i
$421$	2.51147	−	5.49936i	0.122402	−	0.268022i	−0.838505	−	0.544893i	$-0.816570\pi$
$421$	2.51147	−	5.49936i	0.122402	−	0.268022i	0.960907	+	0.276871i	$0.0892975\pi$
$422$	11.5777	+	7.44055i	0.563595	+	0.362200i
$423$	0.714647	−	4.97048i	0.0347473	−	0.241673i
$424$	7.26123	−	4.66651i	0.352636	−	0.226626i
$425$	−1.54979	−	0.995989i	−0.0751758	−	0.0483126i
$426$	−0.196925	−	0.227264i	−0.00954105	−	0.0110110i
$427$	−24.8793	+	7.30524i	−1.20400	+	0.353525i
$428$	−2.21542	−	2.55673i	−0.107087	−	0.123584i
$429$	0.120483	−	0.837979i	0.00581698	−	0.0404580i
$430$	9.77833	+	2.87118i	0.471553	+	0.138460i
$431$	−20.7812			−1.00100			−0.500498	−	0.865737i	$-0.666850\pi$
$431$	−20.7812			−1.00100			−0.500498	+	0.865737i	$0.666850\pi$
$432$	4.06565			0.195609
$433$	−29.7474	−	8.73464i	−1.42957	−	0.419760i	−0.526839	−	0.849965i	$-0.676623\pi$
$433$	−29.7474	−	8.73464i	−1.42957	−	0.419760i	−0.902731	+	0.430205i	$0.858441\pi$
$434$	23.1526	−	14.8793i	1.11136	−	0.714229i
$435$	−2.35652	+	5.16005i	−0.112986	+	0.247405i
$436$	2.42018	−	5.29944i	0.115905	−	0.253797i
$437$	−3.61407	+	2.32262i	−0.172884	+	0.111106i
$438$	−0.426473	−	0.125224i	−0.0203777	−	0.00598342i
$439$	3.75710			0.179316			0.0896582	−	0.995973i	$-0.471423\pi$
$439$	3.75710			0.179316			0.0896582	+	0.995973i	$0.471423\pi$
$440$	3.74557			0.178563
$441$	5.18518	+	1.52251i	0.246914	+	0.0725004i
$442$	0.0793174	−	0.551664i	0.00377274	−	0.0262400i
$443$	−2.96444	−	3.42115i	−0.140845	−	0.162544i	0.680944	−	0.732335i	$-0.261569\pi$
$443$	−2.96444	−	3.42115i	−0.140845	−	0.162544i	−0.821789	+	0.569791i	$0.807024\pi$
$444$	0.541449	−	0.158984i	0.0256960	−	0.00754504i
$445$	−2.74468	−	3.16753i	−0.130110	−	0.150155i
$446$	−12.3474	−	7.93518i	−0.584665	−	0.375741i
$447$	11.0460	−	7.09886i	0.522460	−	0.335764i
$448$	−0.431970	+	3.00442i	−0.0204087	+	0.141945i
$449$	−9.03537	−	5.80668i	−0.426406	−	0.274034i	0.309787	−	0.950806i	$-0.399742\pi$
$449$	−9.03537	−	5.80668i	−0.426406	−	0.274034i	−0.736193	+	0.676772i	$0.763378\pi$
$450$	1.01437	−	2.22116i	0.0478179	−	0.104707i
$451$	−3.89743	+	4.49788i	−0.183523	+	0.211797i
$452$	−0.807842	−	0.932299i	−0.0379977	−	0.0438517i
$453$	−1.62050	−	11.2708i	−0.0761378	−	0.529550i
$454$	5.90496	−	12.9301i	0.277134	−	0.606838i
$455$	0.601347	−	0.693991i	0.0281916	−	0.0325348i
$456$	4.09838	−	1.20339i	0.191924	−	0.0563541i
$457$	20.1484	−	5.91610i	0.942502	−	0.276744i	0.225840	−	0.974164i	$-0.427487\pi$
$457$	20.1484	−	5.91610i	0.942502	−	0.276744i	0.716662	+	0.697421i	$0.245669\pi$
$458$	−2.26486	−	15.7524i	−0.105830	−	0.736063i
$459$	−6.30091	+	4.04935i	−0.294101	+	0.189007i
$460$	0.312152	+	0.683518i	0.0145542	+	0.0318692i
$461$	−1.97526	−	0.579988i	−0.0919969	−	0.0270127i	0.235410	−	0.971896i	$-0.424357\pi$
$461$	−1.97526	−	0.579988i	−0.0919969	−	0.0270127i	−0.327407	+	0.944883i	$0.606175\pi$
$462$	−3.52850	−	7.72633i	−0.164161	−	0.359462i
$463$	−2.10449	+	14.6371i	−0.0978040	+	0.680242i	0.880649	+	0.473770i	$0.157107\pi$
$463$	−2.10449	+	14.6371i	−0.0978040	+	0.680242i	−0.978453	+	0.206472i	$0.933802\pi$
$464$	−1.08057	−	7.51552i	−0.0501642	−	0.348899i
$465$	−4.43613	+	5.11957i	−0.205721	+	0.237414i
$466$	−7.82670	−	5.02991i	−0.362565	−	0.233006i
$467$	−0.214334	−	0.469325i	−0.00991818	−	0.0217178i	0.904608	−	0.426244i	$-0.140164\pi$
$467$	−0.214334	−	0.469325i	−0.00991818	−	0.0217178i	−0.914526	+	0.404527i	$0.867436\pi$
$468$	0.738731			0.0341479
$469$	−23.2999	−	8.62531i	−1.07589	−	0.398280i
$470$	−2.05649			−0.0948589
$471$	−2.53201	−	5.54432i	−0.116669	−	0.255469i
$472$	12.2304	+	7.86003i	0.562952	+	0.361787i
$473$	24.9971	−	28.8482i	1.14937	−	1.32644i
$474$	0.544924	+	3.79003i	0.0250292	+	0.174082i
$475$	0.813645	−	5.65903i	0.0373326	−	0.259654i
$476$	−2.32291	−	5.08646i	−0.106470	−	0.233137i
$477$	−20.2227	−	5.93792i	−0.925934	−	0.271879i
$478$	5.23685	+	11.4671i	0.239528	+	0.524493i
$479$	30.6642	−	19.7067i	1.40109	−	0.900423i	0.401206	−	0.915988i	$-0.368591\pi$
$479$	30.6642	−	19.7067i	1.40109	−	0.900423i	0.999879	+	0.0155649i	$0.00495468\pi$
$480$	−0.106325	−	0.739508i	−0.00485306	−	0.0337538i
$481$	0.219252	−	0.0643782i	0.00999704	−	0.00293540i
$482$	−22.4067	+	6.57921i	−1.02060	+	0.299675i
$483$	1.11589	−	1.28781i	0.0507749	−	0.0585974i
$484$	1.25842	−	2.75556i	0.0572010	−	0.125253i
$485$	1.66716	+	11.5953i	0.0757018	+	0.526518i
$486$	−10.0852	−	11.6390i	−0.457475	−	0.527954i
$487$	−25.2021	+	29.0847i	−1.14202	+	1.31796i	−0.201000	+	0.979591i	$0.564419\pi$
$487$	−25.2021	+	29.0847i	−1.14202	+	1.31796i	−0.941015	+	0.338364i	$0.890126\pi$
$488$	−3.54875	+	7.77068i	−0.160644	+	0.351762i
$489$	9.60115	+	6.17028i	0.434179	+	0.279030i
$490$	0.314962	−	2.19061i	0.0142285	−	0.0989617i
$491$	28.1333	−	18.0802i	1.26964	−	0.815948i	0.280067	−	0.959980i	$-0.409643\pi$
$491$	28.1333	−	18.0802i	1.26964	−	0.815948i	0.989573	+	0.144032i	$0.0460070\pi$
$492$	0.998675	+	0.641809i	0.0450237	+	0.0289350i
$493$	9.16004	+	10.5712i	0.412547	+	0.476105i
$494$	1.65958	−	0.487297i	0.0746682	−	0.0219245i
$495$	−5.98937	−	6.91211i	−0.269202	−	0.310676i
$496$	1.29039	−	8.97484i	0.0579401	−	0.402982i
$497$	−1.17223	−	0.344197i	−0.0525816	−	0.0154393i
$498$	−0.189199			−0.00847820
$499$	−21.1277			−0.945804			−0.472902	−	0.881115i	$-0.656793\pi$
$499$	−21.1277			−0.945804			−0.472902	+	0.881115i	$0.656793\pi$
$500$	−0.959493	−	0.281733i	−0.0429098	−	0.0125995i
$501$	−14.2083	+	9.13114i	−0.634781	+	0.407949i
$502$	2.08398	−	4.56328i	0.0930126	−	0.203669i
$503$	3.76042	−	8.23417i	0.167669	−	0.367143i	−0.807082	−	0.590440i	$-0.798954\pi$
$503$	3.76042	−	8.23417i	0.167669	−	0.367143i	0.974751	+	0.223296i	$0.0716817\pi$
$504$	6.23512	−	4.00707i	0.277734	−	0.178489i
$505$	4.58591	+	1.34655i	0.204071	+	0.0599205i
$506$	2.81451			0.125120
$507$	9.64408			0.428309
$508$	−13.3481	−	3.91935i	−0.592225	−	0.173893i
$509$	2.34091	−	16.2814i	0.103759	−	0.721660i	−0.869830	−	0.493352i	$-0.835772\pi$
$509$	2.34091	−	16.2814i	0.103759	−	0.721660i	0.973589	−	0.228308i	$-0.0733193\pi$
$510$	0.901324	+	1.04018i	0.0399113	+	0.0460601i
$511$	−1.73264	+	0.508750i	−0.0766476	+	0.0225058i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	−19.5543	−	12.5668i	−0.863343	−	0.554837i
$514$	−8.66774	+	5.57042i	−0.382318	+	0.245701i
$515$	−1.94256	+	13.5108i	−0.0855995	+	0.595357i
$516$	−6.40524	−	4.11640i	−0.281975	−	0.181214i
$517$	−3.19983	+	7.00666i	−0.140728	+	0.308152i
$518$	1.50135	−	1.73265i	0.0659656	−	0.0761284i
$519$	9.46520	+	10.9234i	0.415476	+	0.479485i
$520$	−0.0430549	−	0.299453i	−0.00188808	−	0.0131319i
$521$	−4.44819	+	9.74019i	−0.194879	+	0.426725i	−0.981694	−	0.190463i	$-0.939001\pi$
$521$	−4.44819	+	9.74019i	−0.194879	+	0.426725i	0.786815	+	0.617188i	$0.211728\pi$
$522$	−12.1413	+	14.0118i	−0.531411	+	0.613281i
$523$	−20.4990	+	6.01905i	−0.896358	+	0.263194i	−0.697288	−	0.716791i	$-0.745610\pi$
$523$	−20.4990	+	6.01905i	−0.896358	+	0.263194i	−0.199070	+	0.979985i	$0.563792\pi$
$524$	−9.00179	+	2.64317i	−0.393245	+	0.115467i
$525$	0.322730	+	2.24464i	0.0140851	+	0.0979641i
$526$	−20.7971	+	13.3655i	−0.906796	+	0.582762i
$527$	6.93902	+	15.1943i	0.302268	+	0.661875i
$528$	−2.68501	−	0.788390i	−0.116850	−	0.0343103i
$529$	−9.31999	−	20.4079i	−0.405217	−	0.887301i
$530$	−1.22838	+	8.54358i	−0.0533575	+	0.371110i
$531$	−5.05219	−	35.1387i	−0.219246	−	1.52489i
$532$	11.3642	−	13.1149i	0.492699	−	0.568605i
$533$	0.404399	+	0.259892i	0.0175165	+	0.0112572i
$534$	1.30080	+	2.84836i	0.0562912	+	0.123260i
$535$	3.38304			0.146262
$536$	−7.17446	+	3.94045i	−0.309890	+	0.170201i
$537$	−1.70751			−0.0736845
$538$	−3.98010	−	8.71521i	−0.171594	−	0.375739i
$539$	−6.97354	−	4.48162i	−0.300372	−	0.193037i
$540$	−2.66244	+	3.07262i	−0.114573	+	0.132224i
$541$	6.15123	+	42.7828i	0.264462	+	1.83937i	0.498184	+	0.867071i	$0.334000\pi$
$541$	6.15123	+	42.7828i	0.264462	+	1.83937i	−0.233722	+	0.972304i	$0.575091\pi$
$542$	−1.25452	+	8.72541i	−0.0538865	+	0.374789i
$543$	5.84032	+	12.7885i	0.250632	+	0.548808i
$544$	−1.76762	−	0.519019i	−0.0757859	−	0.0222527i
$545$	2.42018	+	5.29944i	0.103669	+	0.227003i
$546$	−0.577150	+	0.370912i	−0.0246997	+	0.0158736i
$547$	−4.03522	−	28.0656i	−0.172534	−	1.20000i	−0.873508	−	0.486810i	$-0.838160\pi$
$547$	−4.03522	−	28.0656i	−0.172534	−	1.20000i	0.700974	−	0.713187i	$-0.252749\pi$
$548$	4.60432	−	1.35195i	0.196687	−	0.0577524i
$549$	20.0147	−	5.87685i	0.854207	−	0.250818i
$550$	−2.45283	+	2.83071i	−0.104589	+	0.120702i
$551$	−18.0331	+	39.4869i	−0.768234	+	1.68220i
$552$	−0.0798951	−	0.555683i	−0.00340056	−	0.0236514i
$553$	10.1871	+	11.7566i	0.433201	+	0.499941i
$554$	−8.23613	+	9.50500i	−0.349920	+	0.403829i
$555$	−0.234422	+	0.513312i	−0.00995065	+	0.0217889i
$556$	9.15722	+	5.88499i	0.388353	+	0.249579i
$557$	−2.29801	+	15.9830i	−0.0973697	+	0.677221i	0.881417	+	0.472339i	$0.156590\pi$
$557$	−2.29801	+	15.9830i	−0.0973697	+	0.677221i	−0.978787	+	0.204882i	$0.934319\pi$
$558$	−18.6256	+	11.9700i	−0.788486	+	0.506729i
$559$	−2.59371	−	1.66688i	−0.109702	−	0.0705014i
$560$	−1.98771	−	2.29394i	−0.0839960	−	0.0969366i
$561$	4.94643	−	1.45240i	0.208838	−	0.0613205i
$562$	−14.3126	−	16.5176i	−0.603741	−	0.696754i
$563$	−3.13232	+	21.7857i	−0.132011	+	0.918159i	0.810916	+	0.585162i	$0.198969\pi$
$563$	−3.13232	+	21.7857i	−0.132011	+	0.918159i	−0.942928	+	0.332997i	$0.891940\pi$
$564$	1.47419	+	0.432862i	0.0620748	+	0.0182268i
$565$	1.23361			0.0518983
$566$	17.8246			0.749223
$567$	−12.4881	−	3.66685i	−0.524452	−	0.153993i
$568$	−0.338605	+	0.217608i	−0.0142075	+	0.00913063i
$569$	−6.81330	+	14.9190i	−0.285628	+	0.625439i	−0.997002	−	0.0773751i	$-0.975346\pi$
$569$	−6.81330	+	14.9190i	−0.285628	+	0.625439i	0.711374	+	0.702814i	$0.248073\pi$
$570$	−1.77441	+	3.88541i	−0.0743217	+	0.162742i
$571$	14.3469	−	9.22020i	0.600400	−	0.385853i	−0.204847	−	0.978794i	$-0.565670\pi$
$571$	14.3469	−	9.22020i	0.600400	−	0.385853i	0.805246	+	0.592941i	$0.202033\pi$
$572$	−1.08726	−	0.319247i	−0.0454605	−	0.0133484i
$573$	4.41633			0.184495
$574$	4.82298			0.201307
$575$	−0.720985	−	0.211700i	−0.0300671	−	0.00882851i
$576$	0.347508	−	2.41697i	0.0144795	−	0.100707i
$577$	−18.1620	−	20.9601i	−0.756095	−	0.872580i	0.239049	−	0.971007i	$-0.423164\pi$
$577$	−18.1620	−	20.9601i	−0.756095	−	0.872580i	−0.995144	+	0.0984271i	$0.968619\pi$
$578$	−13.0550	+	3.83330i	−0.543017	+	0.159444i
$579$	−5.76475	−	6.65288i	−0.239575	−	0.276484i
$580$	6.38747	+	4.10498i	0.265225	+	0.170450i
$581$	−0.646641	+	0.415571i	−0.0268272	+	0.0172408i
$582$	1.24556	−	8.66303i	0.0516299	−	0.359094i
$583$	27.1975	+	17.4787i	1.12640	+	0.723896i
$584$	−0.247142	+	0.541164i	−0.0102268	+	0.0223935i
$585$	−0.483766	+	0.558296i	−0.0200013	+	0.0230827i
$586$	−11.5167	−	13.2910i	−0.475752	−	0.549047i
$587$	−4.45547	−	30.9885i	−0.183897	−	1.27903i	−0.847439	−	0.530892i	$-0.821857\pi$
$587$	−4.45547	−	30.9885i	−0.183897	−	1.27903i	0.663542	−	0.748139i	$-0.269052\pi$
$588$	−0.686873	+	1.50404i	−0.0283261	+	0.0620256i
$589$	−33.9472	+	39.1771i	−1.39877	+	1.61427i
$590$	−13.9494	+	4.09593i	−0.574290	+	0.168627i
$591$	11.1366	−	3.27001i	0.458100	−	0.134510i
$592$	−0.107493	−	0.747630i	−0.00441793	−	0.0307274i
$593$	10.7563	−	6.91264i	0.441707	−	0.283868i	−0.300824	−	0.953680i	$-0.597262\pi$
$593$	10.7563	−	6.91264i	0.441707	−	0.283868i	0.742531	+	0.669812i	$0.233625\pi$
$594$	6.32602	+	13.8521i	0.259560	+	0.568357i
$595$	5.36527	+	1.57538i	0.219955	+	0.0645845i
$596$	−7.30089	−	15.9867i	−0.299056	−	0.654842i
$597$	−2.81204	+	19.5582i	−0.115089	+	0.800462i
$598$	−0.0323524	−	0.225016i	−0.00132299	−	0.00920158i
$599$	−24.4117	+	28.1726i	−0.997436	+	1.15110i	−0.00892394	+	0.999960i	$0.502841\pi$
$599$	−24.4117	+	28.1726i	−0.997436	+	1.15110i	−0.988512	+	0.151142i	$0.951705\pi$
$600$	0.628511	+	0.403919i	0.0256588	+	0.0164899i
$601$	−0.172296	−	0.377276i	−0.00702812	−	0.0153894i	0.906085	−	0.423095i	$-0.139056\pi$
$601$	−0.172296	−	0.377276i	−0.00702812	−	0.0153894i	−0.913114	+	0.407705i	$0.866329\pi$
$602$	−30.9333			−1.26075
$603$	18.7441	+	6.93881i	0.763318	+	0.282570i
$604$	−15.2410			−0.620147
$605$	1.25842	+	2.75556i	0.0511621	+	0.112029i
$606$	−3.00398	−	1.93054i	−0.122028	−	0.0784228i
$607$	11.8006	−	13.6186i	0.478970	−	0.552761i	−0.463915	−	0.885880i	$-0.653556\pi$
$607$	11.8006	−	13.6186i	0.478970	−	0.552761i	0.942885	+	0.333119i	$0.108101\pi$
$608$	−0.813645	−	5.65903i	−0.0329977	−	0.229504i
$609$	2.45043	−	17.0431i	0.0992964	−	0.690622i
$610$	−3.54875	−	7.77068i	−0.143685	−	0.314626i
$611$	0.596954	+	0.175282i	0.0241502	+	0.00709113i
$612$	1.86871	+	4.09191i	0.0755382	+	0.165406i
$613$	−26.9768	+	17.3370i	−1.08958	+	0.700233i	−0.956752	−	0.290905i	$-0.906044\pi$
$613$	−26.9768	+	17.3370i	−1.08958	+	0.700233i	−0.132832	+	0.991139i	$0.542407\pi$
$614$	−4.32824	−	30.1036i	−0.174674	−	1.21488i
$615$	−1.13904	+	0.334452i	−0.0459305	+	0.0134864i
$616$	−10.9085	+	3.20302i	−0.439515	+	0.129053i
$617$	19.7810	−	22.8285i	0.796354	−	0.919042i	−0.201821	−	0.979422i	$-0.564686\pi$
$617$	19.7810	−	22.8285i	0.796354	−	0.919042i	0.998175	+	0.0603806i	$0.0192315\pi$
$618$	4.23636	−	9.27633i	0.170411	−	0.373149i
$619$	−1.45855	−	10.1444i	−0.0586240	−	0.407739i	−0.997911	−	0.0646060i	$-0.979421\pi$
$619$	−1.45855	−	10.1444i	−0.0586240	−	0.407739i	0.939287	−	0.343133i	$-0.111488\pi$
$620$	5.93771	+	6.85248i	0.238464	+	0.275202i
$621$	−2.00061	+	2.30883i	−0.0802819	+	0.0926502i
$622$	−3.61612	+	7.91820i	−0.144993	+	0.317491i
$623$	10.7022	+	6.87789i	0.428775	+	0.275557i
$624$	−0.0321668	+	0.223725i	−0.00128770	+	0.00895618i
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$	−26.8090	−	17.2291i	−1.07151	−	0.688615i
$627$	10.4770	+	12.0911i	0.418412	+	0.482873i
$628$	−7.82778	+	2.29844i	−0.312363	+	0.0917179i
$629$	0.911223	+	1.05161i	0.0363328	+	0.0419303i
$630$	−1.05480	+	7.33626i	−0.0420240	+	0.292284i
$631$	3.61773	+	1.06226i	0.144020	+	0.0422879i	0.352948	−	0.935643i	$-0.385179\pi$
$631$	3.61773	+	1.06226i	0.144020	+	0.0422879i	−0.208928	+	0.977931i	$0.566998\pi$
$632$	5.12507			0.203864
$633$	10.2821			0.408677
$634$	−4.74538	−	1.39337i	−0.188463	−	0.0553377i
$635$	11.7032	−	7.52117i	0.464426	−	0.298469i
$636$	2.67887	−	5.86590i	0.106224	−	0.232598i
$637$	−0.278139	+	0.609040i	−0.0110203	+	0.0241311i
$638$	23.9247	−	15.3755i	0.947190	−	0.608722i
$639$	0.943023	+	0.276897i	0.0373054	+	0.0109539i
$640$	−1.00000			−0.0395285
$641$	−12.9669			−0.512163			−0.256081	−	0.966655i	$-0.582432\pi$
$641$	−12.9669			−0.512163			−0.256081	+	0.966655i	$0.582432\pi$
$642$	−2.42513	−	0.712083i	−0.0957123	−	0.0281037i
$643$	−6.03878	+	42.0006i	−0.238146	+	1.65634i	0.423032	+	0.906115i	$0.360966\pi$
$643$	−6.03878	+	42.0006i	−0.238146	+	1.65634i	−0.661178	+	0.750229i	$0.729943\pi$
$644$	−1.49361	−	1.72372i	−0.0588564	−	0.0679239i
$645$	7.30551	−	2.14509i	0.287654	−	0.0844629i
$646$	6.89731	+	7.95992i	0.271371	+	0.313179i
$647$	−13.0235	−	8.36967i	−0.512005	−	0.329046i	0.258997	−	0.965878i	$-0.416608\pi$
$647$	−13.0235	−	8.36967i	−0.512005	−	0.329046i	−0.771002	+	0.636832i	$0.780244\pi$
$648$	−3.60727	+	2.31825i	−0.141707	+	0.0910695i
$649$	−7.74968	+	53.9002i	−0.304201	+	2.11577i
$650$	0.254507	+	0.163561i	0.00998257	+	0.00641541i
$651$	8.54165	−	18.7036i	0.334774	−	0.733052i
$652$	10.0037	−	11.5449i	0.391774	−	0.452131i
$653$	−19.6218	−	22.6448i	−0.767860	−	0.886158i	0.228311	−	0.973588i	$-0.426680\pi$
$653$	−19.6218	−	22.6448i	−0.767860	−	0.886158i	−0.996171	+	0.0874306i	$0.972134\pi$
$654$	−0.619442	−	4.30831i	−0.0242221	−	0.168468i
$655$	3.89735	−	8.53401i	0.152282	−	0.333451i
$656$	1.04054	−	1.20085i	0.0406264	−	0.0468854i
$657$	1.39386	−	0.409275i	0.0543797	−	0.0159673i
$658$	5.98925	−	1.75860i	0.233485	−	0.0685575i
$659$	−5.64423	−	39.2565i	−0.219868	−	1.52921i	−0.738521	−	0.674230i	$-0.764476\pi$
$659$	−5.64423	−	39.2565i	−0.219868	−	1.52921i	0.518653	−	0.854985i	$-0.326433\pi$
$660$	2.35413	−	1.51291i	0.0916345	−	0.0588899i
$661$	−20.5555	−	45.0103i	−0.799517	−	1.75070i	−0.647134	−	0.762376i	$-0.724033\pi$
$661$	−20.5555	−	45.0103i	−0.799517	−	1.75070i	−0.152383	−	0.988322i	$-0.548695\pi$
$662$	−9.90061	−	2.90708i	−0.384798	−	0.112987i
$663$	−0.172976	−	0.378765i	−0.00671784	−	0.0147100i
$664$	−0.0360398	+	0.250663i	−0.00139862	+	0.00972759i
$665$	2.46967	+	17.1769i	0.0957697	+	0.666093i
$666$	−1.20779	+	1.39387i	−0.0468011	+	0.0540113i
$667$	4.79969	+	3.08457i	0.185845	+	0.119435i
$668$	9.39101	+	20.5634i	0.363349	+	0.795624i
$669$	−10.9656			−0.423956
$670$	1.72028	−	8.00254i	0.0664603	−	0.309165i
$671$	−31.9972			−1.23524
$672$	0.942045	+	2.06279i	0.0363402	+	0.0795739i
$673$	10.7355	+	6.89928i	0.413823	+	0.265948i	0.730944	−	0.682437i	$-0.239080\pi$
$673$	10.7355	+	6.89928i	0.413823	+	0.265948i	−0.317121	+	0.948385i	$0.602716\pi$
$674$	−10.4664	+	12.0789i	−0.403151	+	0.465261i
$675$	−0.578603	−	4.02427i	−0.0222704	−	0.154894i
$676$	1.83707	−	12.7771i	0.0706564	−	0.491426i
$677$	11.6920	+	25.6020i	0.449361	+	0.983963i	0.989785	+	0.142570i	$0.0455366\pi$
$677$	11.6920	+	25.6020i	0.449361	+	0.983963i	−0.540424	+	0.841393i	$0.681736\pi$
$678$	−0.884311	−	0.259657i	−0.0339618	−	0.00997207i
$679$	−14.7711	−	32.3442i	−0.566863	−	1.24126i
$680$	1.54979	−	0.995989i	0.0594317	−	0.0381945i
$681$	−1.51137	−	10.5118i	−0.0579159	−	0.402814i
$682$	32.5859	−	9.56809i	1.24778	−	0.366381i
$683$	−24.0861	+	7.07231i	−0.921628	+	0.270614i	−0.707928	−	0.706285i	$-0.750370\pi$
$683$	−24.0861	+	7.07231i	−0.921628	+	0.270614i	−0.213700	+	0.976899i	$0.568552\pi$
$684$	−9.14215	+	10.5506i	−0.349559	+	0.403412i
$685$	−1.99345	+	4.36505i	−0.0761659	+	0.166780i
$686$	−2.06778	−	14.3817i	−0.0789483	−	0.549098i
$687$	−7.78620	−	8.98575i	−0.297062	−	0.342828i
$688$	−6.67378	+	7.70195i	−0.254435	+	0.293634i
$689$	1.08477	−	2.37531i	0.0413264	−	0.0904923i
$690$	0.472277	+	0.303514i	0.0179793	+	0.0115546i
$691$	−4.55122	+	31.6544i	−0.173137	+	1.20419i	0.699070	+	0.715053i	$0.253598\pi$
$691$	−4.55122	+	31.6544i	−0.173137	+	1.20419i	−0.872207	+	0.489138i	$0.837312\pi$
$692$	16.2750	−	10.4593i	0.618684	−	0.397604i
$693$	23.3541	+	15.0088i	0.887149	+	0.570136i
$694$	6.54107	+	7.54879i	0.248296	+	0.286548i
$695$	−10.4443	+	3.06672i	−0.396174	+	0.116327i
$696$	−3.71481	−	4.28712i	−0.140810	−	0.162503i
$697$	−0.416589	+	2.89744i	−0.0157794	+	0.109748i
$698$	20.3459	+	5.97410i	0.770104	+	0.226123i
$699$	−6.95085			−0.262905
$700$	3.03531			0.114724
$701$	4.40779	+	1.29424i	0.166480	+	0.0488829i	0.363910	−	0.931434i	$-0.381441\pi$
$701$	4.40779	+	1.29424i	0.166480	+	0.0488829i	−0.197430	+	0.980317i	$0.563260\pi$
$702$	1.03474	−	0.664984i	0.0390536	−	0.0250982i
$703$	−1.79390	+	3.92808i	−0.0676580	+	0.148150i
$704$	−1.55597	+	3.40709i	−0.0586427	+	0.128410i
$705$	−1.29253	+	0.830657i	−0.0486794	+	0.0312843i
$706$	9.54092	+	2.80147i	0.359077	+	0.105435i
$707$	−14.5073			−0.545605
$708$	10.8618			0.408211
$709$	13.8304	+	4.06099i	0.519413	+	0.152513i	0.530923	−	0.847420i	$-0.321845\pi$
$709$	13.8304	+	4.06099i	0.519413	+	0.152513i	−0.0115094	+	0.999934i	$0.503664\pi$
$710$	0.0572818	−	0.398403i	0.00214975	−	0.0149518i
$711$	−8.19526	−	9.45784i	−0.307346	−	0.354697i
$712$	4.02147	−	1.18081i	0.150711	−	0.0442527i
$713$	4.46173	+	5.14911i	0.167093	+	0.192836i
$714$	−3.51449	−	2.25863i	−0.131527	−	0.0845270i
$715$	0.953273	−	0.612631i	0.0356504	−	0.0229111i
$716$	−0.325258	+	2.26222i	−0.0121555	+	0.0845430i
$717$	7.92320	+	5.09193i	0.295897	+	0.190162i
$718$	0.711841	−	1.55871i	0.0265657	−	0.0581707i
$719$	4.03801	−	4.66011i	0.150592	−	0.173793i	−0.675441	−	0.737414i	$-0.736047\pi$
$719$	4.03801	−	4.66011i	0.150592	−	0.173793i	0.826033	+	0.563621i	$0.190592\pi$
$720$	1.59905	+	1.84541i	0.0595932	+	0.0687743i
$721$	−5.89628	−	41.0096i	−0.219589	−	1.52728i
$722$	−5.68562	+	12.4498i	−0.211597	+	0.463333i
$723$	−11.4254	+	13.1856i	−0.424915	+	0.490378i
$724$	18.0555	−	5.30158i	0.671028	−	0.197032i
$725$	−7.28524	+	2.13914i	−0.270567	+	0.0794457i
$726$	−0.322092	−	2.24020i	−0.0119540	−	0.0831416i
$727$	0.00324928	−	0.00208819i	0.000120509	−	7.74465e-5i	−0.540581	−	0.841292i	$-0.681795\pi$
$727$	0.00324928	−	0.00208819i	0.000120509	−	7.74465e-5i	0.540701	+	0.841215i	$0.318159\pi$
$728$	0.381468	+	0.835298i	0.0141381	+	0.0309582i
$729$	1.30296	+	0.382584i	0.0482579	+	0.0141698i
$730$	−0.247142	−	0.541164i	−0.00914712	−	0.0200294i
$731$	2.67189	−	18.5834i	0.0988235	−	0.687333i
$732$	0.908300	+	6.31737i	0.0335717	+	0.233497i
$733$	−18.8160	+	21.7148i	−0.694985	+	0.802055i	−0.988066	−	0.154032i	$-0.950774\pi$
$733$	−18.8160	+	21.7148i	−0.694985	+	0.802055i	0.293081	+	0.956088i	$0.405319\pi$
$734$	−16.3361	−	10.4985i	−0.602975	−	0.387508i
$735$	−0.686873	−	1.50404i	−0.0253357	−	0.0554774i
$736$	−0.751422			−0.0276978
$737$	−24.5887	−	18.3128i	−0.905736	−	0.674562i
$738$	−3.87994			−0.142823
$739$	14.1359	+	30.9532i	0.519996	+	1.13863i	0.969441	+	0.245325i	$0.0788946\pi$
$739$	14.1359	+	30.9532i	0.519996	+	1.13863i	−0.449445	+	0.893308i	$0.648378\pi$
$740$	0.635414	+	0.408356i	0.0233583	+	0.0150115i
$741$	0.846237	−	0.976609i	0.0310873	−	0.0358766i
$742$	−3.72853	−	25.9325i	−0.136879	−	0.952011i
$743$	−1.04130	+	7.24243i	−0.0382017	+	0.265699i	−0.999967	−	0.00817771i	$-0.997397\pi$
$743$	−1.04130	+	7.24243i	−0.0382017	+	0.265699i	0.961765	+	0.273877i	$0.0883060\pi$
$744$	−2.81409	−	6.16200i	−0.103170	−	0.225910i
$745$	16.8630	+	4.95143i	0.617814	+	0.181406i
$746$	8.66349	+	18.9704i	0.317193	+	0.694555i
$747$	0.520204	−	0.334315i	0.0190333	−	0.0122319i
$748$	−0.982006	−	6.83000i	−0.0359057	−	0.249730i
$749$	−9.85266	+	2.89300i	−0.360008	+	0.105708i
$750$	−0.716849	+	0.210486i	−0.0261756	+	0.00768586i
$751$	−4.69953	+	5.42355i	−0.171488	+	0.197908i	−0.834987	−	0.550269i	$-0.814525\pi$
$751$	−4.69953	+	5.42355i	−0.171488	+	0.197908i	0.663499	+	0.748177i	$0.269071\pi$
$752$	0.854297	−	1.87065i	0.0311530	−	0.0682156i
$753$	−0.533393	−	3.70983i	−0.0194379	−	0.135194i
$754$	−1.50426	−	1.73601i	−0.0547820	−	0.0632218i
$755$	9.98073	−	11.5184i	0.363236	−	0.419197i
$756$	5.12644	−	11.2253i	0.186447	−	0.408262i
$757$	16.2190	+	10.4233i	0.589488	+	0.378841i	0.801116	−	0.598509i	$-0.204240\pi$
$757$	16.2190	+	10.4233i	0.589488	+	0.378841i	−0.211628	+	0.977350i	$0.567876\pi$
$758$	−2.23077	+	15.5153i	−0.0810252	+	0.563543i
$759$	1.76895	−	1.13683i	0.0642088	−	0.0412645i
$760$	4.80963	+	3.09096i	0.174464	+	0.112121i
$761$	5.29938	+	6.11581i	0.192103	+	0.221698i	0.843627	−	0.536929i	$-0.180416\pi$
$761$	5.29938	+	6.11581i	0.192103	+	0.221698i	−0.651525	+	0.758627i	$0.725870\pi$
$762$	−9.97250	+	2.92819i	−0.361266	+	0.106077i
$763$	−11.5802	−	13.3643i	−0.419233	−	0.483820i
$764$	0.841251	−	5.85103i	0.0304354	−	0.211683i
$765$	−4.31620	−	1.26735i	−0.156053	−	0.0458212i
$766$	5.34870			0.193257
$767$	4.39833			0.158814
$768$	0.716849	+	0.210486i	0.0258671	+	0.00759525i
$769$	39.4232	−	25.3358i	1.42164	−	0.913631i	0.421661	−	0.906754i	$-0.361447\pi$
$769$	39.4232	−	25.3358i	1.42164	−	0.913631i	0.999976	−	0.00687693i	$-0.00218901\pi$
$770$	4.72285	−	10.3416i	0.170200	−	0.372685i
$771$	−3.19777	+	7.00214i	−0.115165	+	0.252176i
$772$	−9.91227	+	6.37023i	−0.356750	+	0.229269i
$773$	−33.5514	−	9.85157i	−1.20676	−	0.354336i	−0.384325	−	0.923198i	$-0.625566\pi$
$773$	−33.5514	−	9.85157i	−1.20676	−	0.354336i	−0.822433	+	0.568861i	$0.807384\pi$
$774$	24.8850			0.894472
$775$	−9.06713			−0.325701
$776$	−11.2401	−	3.30038i	−0.403495	−	0.118477i
$777$	0.243764	−	1.69542i	0.00874499	−	0.0608227i
$778$	−10.9799	−	12.6715i	−0.393649	−	0.454295i
$779$	−8.71642	+	2.55937i	−0.312298	+	0.0916990i
$780$	−0.148015	−	0.170819i	−0.00529980	−	0.00611630i
$781$	−1.26827	−	0.815067i	−0.0453822	−	0.0291654i
$782$	1.16455	−	0.748409i	0.0416441	−	0.0267630i
$783$	−4.39322	+	30.5555i	−0.157001	+	1.09196i
$784$	1.86181	+	1.19651i	0.0664932	+	0.0427326i
$785$	3.38906	−	7.42100i	0.120961	−	0.264867i
$786$	−4.59010	+	5.29726i	−0.163723	+	0.188947i
$787$	−22.4946	−	25.9602i	−0.801847	−	0.925380i	0.196634	−	0.980477i	$-0.436999\pi$
$787$	−22.4946	−	25.9602i	−0.801847	−	0.925380i	−0.998481	+	0.0550964i	$0.982453\pi$
$788$	−2.21094	−	15.3774i	−0.0787614	−	0.547798i
$789$	−7.67262	+	16.8007i	−0.273152	+	0.598120i
$790$	−3.35621	+	3.87327i	−0.119408	+	0.137805i
$791$	−3.59272	+	1.05492i	−0.127742	+	0.0375085i
$792$	8.77555	−	2.57673i	0.311826	−	0.0915602i
$793$	0.367803	+	2.55813i	0.0130611	+	0.0908418i
$794$	−18.9046	+	12.1492i	−0.670898	+	0.431160i
$795$	2.67887	+	5.86590i	0.0950097	+	0.208042i
$796$	25.3762	+	7.45113i	0.899436	+	0.264098i
$797$	−9.37213	−	20.5221i	−0.331978	−	0.726930i	0.667872	−	0.744277i	$-0.267206\pi$
$797$	−9.37213	−	20.5221i	−0.331978	−	0.726930i	−0.999850	+	0.0173462i	$0.994478\pi$
$798$	1.84512	−	12.8331i	0.0653166	−	0.454287i
$799$	0.539167	+	3.74999i	0.0190743	+	0.132665i
$800$	0.654861	−	0.755750i	0.0231528	−	0.0267198i
$801$	−8.60962	−	5.53307i	−0.304206	−	0.195501i
$802$	−13.6213	−	29.8265i	−0.480984	−	1.05321i
$803$	−2.22834			−0.0786365
$804$	−2.91760	+	5.37452i	−0.102896	+	0.189545i
$805$	2.28080			0.0803878
$806$	−1.13953	−	2.49521i	−0.0401381	−	0.0878902i
$807$	−6.02178	−	3.86996i	−0.211977	−	0.136229i
$808$	−3.12992	+	3.61212i	−0.110110	+	0.127074i
$809$	−0.0379949	−	0.264261i	−0.00133583	−	0.00929091i	0.989143	−	0.146959i	$-0.0469485\pi$
$809$	−0.0379949	−	0.264261i	−0.00133583	−	0.00929091i	−0.990478	+	0.137668i	$0.956039\pi$
$810$	0.610242	−	4.24433i	0.0214417	−	0.149130i
$811$	17.2472	+	37.7662i	0.605633	+	1.32615i	0.925521	+	0.378696i	$0.123627\pi$
$811$	17.2472	+	37.7662i	0.605633	+	1.32615i	−0.319888	+	0.947455i	$0.603645\pi$
$812$	−22.1130	−	6.49297i	−0.776014	−	0.227858i
$813$	2.73588	+	5.99074i	0.0959515	+	0.210105i
$814$	2.37999	−	1.52953i	0.0834186	−	0.0536099i
$815$	2.17401	+	15.1205i	0.0761521	+	0.529649i
$816$	−1.32061	+	0.387765i	−0.0462305	+	0.0135745i
$817$	55.9049	−	16.4152i	1.95586	−	0.574293i
$818$	12.0249	−	13.8774i	0.420439	−	0.485213i
$819$	0.931477	−	2.03965i	0.0325485	−	0.0712712i
$820$	0.226132	+	1.57278i	0.00789686	+	0.0549239i
$821$	−32.9127	−	37.9832i	−1.14866	−	1.32562i	−0.937424	−	0.348189i	$-0.886797\pi$
$821$	−32.9127	−	37.9832i	−1.14866	−	1.32562i	−0.211236	−	0.977435i	$-0.567749\pi$
$822$	2.34779	−	2.70949i	0.0818884	−	0.0945043i
$823$	−9.56944	+	20.9541i	−0.333570	+	0.730416i	−0.999884	−	0.0152556i	$-0.995144\pi$
$823$	−9.56944	+	20.9541i	−0.333570	+	0.730416i	0.666314	+	0.745671i	$0.267871\pi$
$824$	−11.4829	−	7.37961i	−0.400026	−	0.257081i
$825$	−0.398249	+	2.76988i	−0.0138652	+	0.0964348i
$826$	37.1232	−	23.8577i	1.29168	−	0.830114i
$827$	−16.9768	−	10.9103i	−0.590341	−	0.379389i	0.211099	−	0.977465i	$-0.432296\pi$
$827$	−16.9768	−	10.9103i	−0.590341	−	0.379389i	−0.801440	+	0.598076i	$0.795932\pi$
$828$	1.20157	+	1.38668i	0.0417573	+	0.0481905i
$829$	−1.94711	+	0.571724i	−0.0676260	+	0.0198568i	−0.315371	−	0.948969i	$-0.602129\pi$
$829$	−1.94711	+	0.571724i	−0.0676260	+	0.0198568i	0.247745	+	0.968825i	$0.420311\pi$
$830$	−0.165837	−	0.191386i	−0.00575629	−	0.00664311i
$831$	−1.33724	+	9.30073i	−0.0463884	+	0.322639i
$832$	0.290278	+	0.0852333i	0.0100636	+	0.00295493i
$833$	−4.07713			−0.141264
$834$	8.13247			0.281604
$835$	−21.6906	−	6.36894i	−0.750635	−	0.220406i
$836$	18.0148	−	11.5774i	0.623056	−	0.400414i
$837$	−15.3138	+	33.5325i	−0.529322	+	1.15905i
$838$	−2.01903	+	4.42106i	−0.0697462	+	0.152723i
$839$	39.5885	−	25.4420i	1.36675	−	0.878354i	0.368070	−	0.929798i	$-0.380019\pi$
$839$	39.5885	−	25.4420i	1.36675	−	0.878354i	0.998676	+	0.0514439i	$0.0163823\pi$
$840$	−2.17586	−	0.638891i	−0.0750744	−	0.0220438i
$841$	28.6507			0.987955
$842$	−6.04569			−0.208348
$843$	−15.6674	−	4.60037i	−0.539615	−	0.158445i
$844$	1.95860	−	13.6224i	0.0674179	−	0.468902i
$845$	8.45325	+	9.75557i	0.290801	+	0.335602i
$846$	−4.81818	+	1.41474i	−0.165652	+	0.0486399i
$847$	−6.02139	−	6.94905i	−0.206897	−	0.238772i
$848$	−7.26123	−	4.66651i	−0.249352	−	0.160249i
$849$	11.2029	−	7.19970i	0.384484	−	0.247093i
$850$	−0.262178	+	1.82349i	−0.00899263	+	0.0625451i
$851$	0.477464	+	0.306848i	0.0163673	+	0.0105186i
$852$	−0.124921	+	0.273538i	−0.00427971	+	0.00937126i
$853$	15.5163	−	17.9068i	0.531269	−	0.613118i	−0.425147	−	0.905124i	$-0.639778\pi$
$853$	15.5163	−	17.9068i	0.531269	−	0.613118i	0.956416	+	0.292007i	$0.0943230\pi$
$854$	16.9803	+	19.5963i	0.581055	+	0.670573i
$855$	−1.98678	−	13.8183i	−0.0679464	−	0.472577i
$856$	−1.40537	+	3.07733i	−0.0480345	+	0.105181i
$857$	28.7562	−	33.1864i	0.982292	−	1.13363i	−0.00873477	−	0.999962i	$-0.502780\pi$
$857$	28.7562	−	33.1864i	0.982292	−	1.13363i	0.991027	−	0.133664i	$-0.0426741\pi$
$858$	−0.812303	+	0.238514i	−0.0277316	+	0.00814272i
$859$	50.4115	−	14.8022i	1.72002	−	0.505043i	0.735086	−	0.677974i	$-0.237142\pi$
$859$	50.4115	−	14.8022i	1.72002	−	0.505043i	0.984934	+	0.172931i	$0.0553237\pi$
$860$	−1.45035	−	10.0874i	−0.0494566	−	0.343978i
$861$	3.03129	−	1.94809i	0.103306	−	0.0663908i
$862$	8.63284	+	18.9033i	0.294036	+	0.643848i
$863$	52.4485	+	15.4003i	1.78537	+	0.524232i	0.995973	−	0.0896532i	$-0.0285759\pi$
$863$	52.4485	+	15.4003i	1.78537	+	0.524232i	0.789396	+	0.613885i	$0.210394\pi$
$864$	−1.68893	−	3.69825i	−0.0574587	−	0.125817i
$865$	−2.75325	+	19.1492i	−0.0936132	+	0.651094i
$866$	4.41223	+	30.6877i	0.149934	+	1.04281i
$867$	−6.65687	+	7.68244i	−0.226079	+	0.260909i
$868$	−23.1526	−	14.8793i	−0.785852	−	0.505036i
$869$	7.97444	+	17.4616i	0.270514	+	0.592344i
$870$	5.67268			0.192322
$871$	−1.18144	+	2.17633i	−0.0400317	+	0.0737423i
$872$	−5.82592			−0.197291
$873$	11.8829	+	26.0200i	0.402176	+	0.880643i
$874$	3.61407	+	2.32262i	0.122248	+	0.0785638i
$875$	−1.98771	+	2.29394i	−0.0671968	+	0.0775493i
$876$	0.0632557	+	0.439953i	0.00213721	+	0.0148646i
$877$	2.48857	−	17.3084i	0.0840329	−	0.584462i	−0.903683	−	0.428202i	$-0.859147\pi$
$877$	2.48857	−	17.3084i	0.0840329	−	0.584462i	0.987716	−	0.156260i	$-0.0499437\pi$
$878$	−1.56075	−	3.41757i	−0.0526729	−	0.115338i
$879$	−12.6069	−	3.70172i	−0.425220	−	0.124856i
$880$	−1.55597	−	3.40709i	−0.0524516	−	0.114853i
$881$	22.0459	−	14.1680i	0.742744	−	0.477333i	−0.113737	−	0.993511i	$-0.536282\pi$
$881$	22.0459	−	14.1680i	0.742744	−	0.477333i	0.856481	+	0.516178i	$0.172646\pi$
$882$	−0.769082	−	5.34908i	−0.0258963	−	0.180113i
$883$	22.5354	−	6.61700i	0.758378	−	0.222680i	0.120390	−	0.992727i	$-0.461585\pi$
$883$	22.5354	−	6.61700i	0.758378	−	0.222680i	0.637987	+	0.770047i	$0.279767\pi$
$884$	−0.534761	+	0.157020i	−0.0179860	+	0.00528116i
$885$	−7.11295	+	8.20879i	−0.239099	+	0.275935i
$886$	−1.88051	+	4.11775i	−0.0631771	+	0.138339i
$887$	0.632788	+	4.40114i	0.0212469	+	0.147776i	0.997683	−	0.0680299i	$-0.0216713\pi$
$887$	0.632788	+	4.40114i	0.0212469	+	0.147776i	−0.976436	+	0.215806i	$0.930762\pi$
$888$	−0.369543	−	0.426475i	−0.0124010	−	0.0143116i
$889$	−27.6522	+	31.9123i	−0.927424	+	1.07030i
$890$	−1.74111	+	3.81249i	−0.0583620	+	0.127795i
$891$	−13.5113	−	8.68318i	−0.452645	−	0.290898i
$892$	−2.08880	+	14.5280i	−0.0699384	+	0.486432i
$893$	−9.89097	+	6.35654i	−0.330989	+	0.212713i
$894$	−11.0460	−	7.09886i	−0.369435	−	0.237421i
$895$	−1.49667	−	1.72725i	−0.0500282	−	0.0577356i
$896$	2.91236	−	0.855147i	0.0972952	−	0.0285685i
$897$	−0.111222	−	0.128357i	−0.00371360	−	0.00428572i
$898$	−1.52851	+	10.6310i	−0.0510072	+	0.354763i
$899$	66.0563	+	19.3959i	2.20310	+	0.646888i
$900$	−2.44182			−0.0813941
$901$	15.9012			0.529745
$902$	5.71046	+	1.67674i	0.190138	+	0.0558294i
$903$	−19.4419	+	12.4946i	−0.646987	+	0.415793i
$904$	−0.512460	+	1.12213i	−0.0170442	+	0.0373215i
$905$	−7.81719	+	17.1173i	−0.259852	+	0.568997i
$906$	−9.57913	+	6.15613i	−0.318245	+	0.204524i
$907$	10.2512	+	3.01001i	0.340384	+	0.0999458i	0.447457	−	0.894305i	$-0.352330\pi$
$907$	10.2512	+	3.01001i	0.340384	+	0.0999458i	−0.107073	+	0.994251i	$0.534148\pi$
$908$	−14.2146			−0.471728
$909$	11.6707			0.387094
$910$	−0.881085	−	0.258710i	−0.0292077	−	0.00857615i
$911$	7.08796	−	49.2978i	0.234835	−	1.63331i	−0.441887	−	0.897071i	$-0.645691\pi$
$911$	7.08796	−	49.2978i	0.234835	−	1.63331i	0.676721	−	0.736239i	$-0.263400\pi$
$912$	−2.79718	−	3.22811i	−0.0926237	−	0.106894i
$913$	−0.910107	+	0.267232i	−0.0301202	+	0.00884408i
$914$	−13.7514	−	15.8700i	−0.454857	−	0.524933i
$915$	−5.36916	−	3.45055i	−0.177499	−	0.114072i
$916$	−13.3881	+	8.60398i	−0.442354	+	0.284284i
$917$	−4.05267	+	28.1869i	−0.133831	+	0.930815i
$918$	6.30091	+	4.04935i	0.207961	+	0.133648i
$919$	15.6377	−	34.2417i	0.515839	−	1.12953i	−0.455152	−	0.890414i	$-0.650415\pi$
$919$	15.6377	−	34.2417i	0.515839	−	1.12953i	0.970991	−	0.239116i	$-0.0768575\pi$
$920$	0.492077	−	0.567887i	0.0162233	−	0.0187227i
$921$	−14.8798	−	17.1722i	−0.490305	−	0.565842i
$922$	0.292976	+	2.03769i	0.00964865	+	0.0671078i
$923$	−0.0505849	+	0.110765i	−0.00166502	+	0.00364589i
$924$	−5.56233	+	6.41927i	−0.182987	+	0.211179i
$925$	−0.724722	+	0.212798i	−0.0238287	+	0.00699675i
$926$	14.1886	−	4.16614i	0.466266	−	0.136908i
$927$	4.74339	+	32.9910i	0.155793	+	1.08357i
$928$	−6.38747	+	4.10498i	−0.209679	+	0.134753i
$929$	14.4902	+	31.7291i	0.475408	+	1.04100i	0.983701	+	0.179814i	$0.0575495\pi$
$929$	14.4902	+	31.7291i	0.475408	+	1.04100i	−0.508293	+	0.861184i	$0.669723\pi$
$930$	6.49976	+	1.90850i	0.213136	+	0.0625823i
$931$	−5.25624	−	11.5096i	−0.172266	−	0.377211i
$932$	−1.32404	+	9.20892i	−0.0433705	+	0.301648i
$933$	0.925544	+	6.43730i	0.0303009	+	0.210748i
$934$	−0.337876	+	0.389930i	−0.0110556	+	0.0127589i
$935$	5.80485	+	3.73055i	0.189839	+	0.122002i
$936$	−0.306880	−	0.671973i	−0.0100307	−	0.0219641i
$937$	47.9315			1.56585			0.782926	−	0.622115i	$-0.213726\pi$
$937$	47.9315			1.56585			0.782926	+	0.622115i	$0.213726\pi$
$938$	1.83326	+	24.7774i	0.0598581	+	0.809011i
$939$	−23.8090			−0.776976
$940$	0.854297	+	1.87065i	0.0278641	+	0.0610139i
$941$	−32.0837	−	20.6189i	−1.04590	−	0.672158i	−0.0994598	−	0.995042i	$-0.531711\pi$
$941$	−32.0837	−	20.6189i	−1.04590	−	0.672158i	−0.946439	+	0.322883i	$0.895348\pi$
$942$	−3.99146	+	4.60639i	−0.130049	+	0.150084i
$943$	0.169920	+	1.18182i	0.00553337	+	0.0384854i
$944$	2.06902	−	14.3904i	0.0673410	−	0.468367i
$945$	5.12644	+	11.2253i	0.166763	+	0.365161i
$946$	−36.6254	−	10.7542i	−1.19080	−	0.349649i
$947$	−21.7228	−	47.5663i	−0.705896	−	1.54570i	−0.832673	−	0.553765i	$-0.813191\pi$
$947$	−21.7228	−	47.5663i	−0.705896	−	1.54570i	0.126777	−	0.991931i	$-0.459537\pi$
$948$	3.22116	−	2.07011i	0.104618	−	0.0672342i
$949$	0.0256145	+	0.178153i	0.000831482	+	0.00578308i
$950$	−5.48563	+	1.61073i	−0.177977	+	0.0522589i
$951$	−3.54533	+	1.04100i	−0.114965	+	0.0337568i
$952$	−3.66183	+	4.22598i	−0.118681	+	0.136965i
$953$	2.62725	−	5.75288i	0.0851050	−	0.186354i	−0.862295	−	0.506407i	$-0.830973\pi$
$953$	2.62725	−	5.75288i	0.0851050	−	0.186354i	0.947400	+	0.320053i	$0.103701\pi$
$954$	2.99949	+	20.8619i	0.0971121	+	0.675430i
$955$	3.87101	+	4.46739i	0.125263	+	0.144561i
$956$	8.25537	−	9.52721i	0.266998	−	0.308132i
$957$	8.82650	−	19.3273i	0.285320	−	0.624764i
$958$	−30.6642	−	19.7067i	−0.990717	−	0.636695i
$959$	2.07290	−	14.4173i	0.0669373	−	0.465559i
$960$	−0.628511	+	0.403919i	−0.0202851	+	0.0130364i
$961$	43.0830	+	27.6878i	1.38977	+	0.893154i
$962$	−0.149641	−	0.172695i	−0.00482462	−	0.00556791i
$963$	7.92618	−	2.32734i	0.255418	−	0.0749973i
$964$	15.2928	+	17.6488i	0.492546	+	0.568429i
$965$	1.67686	−	11.6628i	0.0539800	−	0.375439i
$966$	−1.63499	−	0.480077i	−0.0526050	−	0.0154462i
$967$	25.5391			0.821283			0.410642	−	0.911797i	$-0.365305\pi$
$967$	25.5391			0.821283			0.410642	+	0.911797i	$0.365305\pi$
$968$	−3.02931			−0.0973658
$969$	7.55020	+	2.21694i	0.242547	+	0.0712183i
$970$	9.85494	−	6.33338i	0.316423	−	0.203353i
$971$	15.4714	−	33.8777i	0.496502	−	1.08719i	−0.481089	−	0.876672i	$-0.659758\pi$
$971$	15.4714	−	33.8777i	0.496502	−	1.08719i	0.977590	−	0.210516i	$-0.0675143\pi$
$972$	−6.39762	+	14.0088i	−0.205204	+	0.449334i
$973$	27.7950	−	17.8628i	0.891068	−	0.572655i
$974$	36.9257	+	10.8424i	1.18318	+	0.347412i
$975$	0.226026			0.00723862
$976$	8.54267			0.273444
$977$	−1.87595	−	0.550829i	−0.0600170	−	0.0176226i	0.251586	−	0.967835i	$-0.419048\pi$
$977$	−1.87595	−	0.550829i	−0.0600170	−	0.0176226i	−0.311603	+	0.950212i	$0.600866\pi$
$978$	1.62423	−	11.2967i	0.0519370	−	0.361230i
$979$	10.2804	+	11.8642i	0.328563	+	0.379182i
$980$	−2.12349	+	0.623513i	−0.0678324	+	0.0199174i
$981$	9.31596	+	10.7512i	0.297436	+	0.343259i
$982$	−28.1333	−	18.0802i	−0.897771	−	0.576962i
$983$	−29.8876	+	19.2076i	−0.953267	+	0.612627i	−0.922127	−	0.386888i	$-0.873550\pi$
$983$	−29.8876	+	19.2076i	−0.953267	+	0.612627i	−0.0311400	+	0.999515i	$0.509914\pi$
$984$	0.168946	−	1.17504i	0.00538580	−	0.0374590i
$985$	13.0693	+	8.39915i	0.416424	+	0.267619i
$986$	5.81073	−	12.7237i	0.185051	−	0.405206i
$987$	3.05397	−	3.52447i	0.0972091	−	0.112185i
$988$	−1.13268	−	1.30718i	−0.0360353	−	0.0415869i
$989$	−1.08983	−	7.57991i	−0.0346545	−	0.241027i
$990$	−3.79940	+	8.31952i	−0.120753	+	0.264412i
$991$	−35.6786	+	41.1753i	−1.13337	+	1.30798i	−0.187926	+	0.982183i	$0.560176\pi$
$991$	−35.6786	+	41.1753i	−1.13337	+	1.30798i	−0.945441	+	0.325792i	$0.894369\pi$
$992$	−8.69985	+	2.55451i	−0.276220	+	0.0811057i
$993$	−7.39686	+	2.17192i	−0.234732	+	0.0689237i
$994$	0.173868	+	1.20928i	0.00551476	+	0.0383560i
$995$	−22.2491	+	14.2986i	−0.705343	+	0.453297i
$996$	0.0785960	+	0.172101i	0.00249041	+	0.00545324i
$997$	35.7252	+	10.4899i	1.13143	+	0.332217i	0.793269	−	0.608871i	$-0.208377\pi$
$997$	35.7252	+	10.4899i	1.13143	+	0.332217i	0.338160	+	0.941089i	$0.390196\pi$
$998$	8.77674	+	19.2184i	0.277823	+	0.608347i
$999$	−0.437029	+	3.03960i	−0.0138270	+	0.0961688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.k.c.81.3	✓	50
67.24	even	11	inner	670.2.k.c.91.3	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.k.c.81.3	✓	50	1.1	even	1	trivial
670.2.k.c.91.3	yes	50	67.24	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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{2} +(-0.628511 - 0.403919i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-0.106325 + 0.739508i) q^{6} +(1.26092 + 2.76102i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-1.01437 - 2.22116i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{2} +(-0.628511 - 0.403919i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-0.106325 + 0.739508i) q^{6} +(1.26092 + 2.76102i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-1.01437 - 2.22116i) q^{9} +(-0.841254 + 0.540641i) q^{10} +(0.533051 + 3.70745i) q^{11} +(0.716849 - 0.210486i) q^{12} +(0.290278 - 0.0852333i) q^{13} +(1.98771 - 2.29394i) q^{14} +(-0.310362 + 0.679597i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(1.20641 + 1.39227i) q^{17} +(-1.59905 + 1.84541i) q^{18} +(-2.37502 + 5.20057i) q^{19} +(0.841254 + 0.540641i) q^{20} +(0.322730 - 2.24464i) q^{21} +(3.15098 - 2.02501i) q^{22} +(0.632137 + 0.406250i) q^{23} +(-0.489254 - 0.564630i) q^{24} +(-0.959493 + 0.281733i) q^{25} +(-0.198117 - 0.228639i) q^{26} +(-0.578603 + 4.02427i) q^{27} +(-2.91236 - 0.855147i) q^{28} +7.59281 q^{29} +0.747112 q^{30} +(8.69985 + 2.55451i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(1.16248 - 2.54548i) q^{33} +(0.765294 - 1.67576i) q^{34} +(2.55347 - 1.64102i) q^{35} +(2.34291 + 0.687941i) q^{36} +0.755318 q^{37} +5.71722 q^{38} +(-0.216870 - 0.0636788i) q^{39} +(0.142315 - 0.989821i) q^{40} +(1.04054 + 1.20085i) q^{41} +(-2.17586 + 0.638891i) q^{42} +(-6.67378 - 7.70195i) q^{43} +(-3.15098 - 2.02501i) q^{44} +(-2.05419 + 1.32015i) q^{45} +(0.106939 - 0.743774i) q^{46} +(1.73003 + 1.11182i) q^{47} +(-0.310362 + 0.679597i) q^{48} +(-1.44930 + 1.67258i) q^{49} +(0.654861 + 0.755750i) q^{50} +(-0.195876 - 1.36235i) q^{51} +(-0.125677 + 0.275193i) q^{52} +(5.65239 - 6.52321i) q^{53} +(3.90097 - 1.14543i) q^{54} +(3.59385 - 1.05525i) q^{55} +(0.431970 + 3.00442i) q^{56} +(3.59334 - 2.30930i) q^{57} +(-3.15417 - 6.90666i) q^{58} +(13.9494 + 4.09593i) q^{59} +(-0.310362 - 0.679597i) q^{60} +(-1.21575 + 8.45571i) q^{61} +(-1.29039 - 8.97484i) q^{62} +(4.85363 - 5.60139i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-0.125677 - 0.275193i) q^{65} -2.79836 q^{66} +(-5.77369 + 5.80211i) q^{67} -1.84224 q^{68} +(-0.233213 - 0.510665i) q^{69} +(-2.55347 - 1.64102i) q^{70} +(-0.263582 + 0.304189i) q^{71} +(-0.347508 - 2.41697i) q^{72} +(-0.0846669 + 0.588871i) q^{73} +(-0.313770 - 0.687062i) q^{74} +(0.716849 + 0.210486i) q^{75} +(-2.37502 - 5.20057i) q^{76} +(-9.56420 + 6.14654i) q^{77} +(0.0321668 + 0.223725i) q^{78} +(4.91747 - 1.44390i) q^{79} +(-0.959493 + 0.281733i) q^{80} +(-2.80802 + 3.24063i) q^{81} +(0.660075 - 1.44536i) q^{82} +(0.0360398 + 0.250663i) q^{83} +(1.48504 + 1.71383i) q^{84} +(1.20641 - 1.39227i) q^{85} +(-4.23355 + 9.27019i) q^{86} +(-4.77216 - 3.06688i) q^{87} +(-0.533051 + 3.70745i) q^{88} +(3.52590 - 2.26596i) q^{89} +(2.05419 + 1.32015i) q^{90} +(0.601347 + 0.693991i) q^{91} +(-0.720985 + 0.211700i) q^{92} +(-4.43613 - 5.11957i) q^{93} +(0.292669 - 2.03556i) q^{94} +(5.48563 + 1.61073i) q^{95} +0.747112 q^{96} -11.7146 q^{97} +(2.12349 + 0.623513i) q^{98} +(7.69413 - 4.94471i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9	\( 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9} + 5 q^{10} - 12 q^{11} - 2 q^{12} + 24 q^{13} + 23 q^{14} - 2 q^{15} - 5 q^{16} + 31 q^{17} + q^{18} + 4 q^{19} - 5 q^{20} + 12 q^{21} + q^{22} + 27 q^{23} - 9 q^{24} - 5 q^{25} - 2 q^{26} - 14 q^{27} + 10 q^{28} - 36 q^{29} + 2 q^{30} - 13 q^{31} + 5 q^{32} - 42 q^{33} + 2 q^{34} + 21 q^{35} - q^{36} - 50 q^{37} - 26 q^{38} - 31 q^{39} + 5 q^{40} - 10 q^{41} + 21 q^{42} + 16 q^{43} - q^{44} - q^{45} + 17 q^{46} - 13 q^{47} - 2 q^{48} - 40 q^{49} + 5 q^{50} - 19 q^{51} - 20 q^{52} - 5 q^{53} + 47 q^{54} + 10 q^{55} + 12 q^{56} - 90 q^{57} - 8 q^{58} - 20 q^{59} - 2 q^{60} + 12 q^{61} + 13 q^{62} - 15 q^{63} - 5 q^{64} - 20 q^{65} + 20 q^{66} - 21 q^{67} - 24 q^{68} + 77 q^{69} - 21 q^{70} + 24 q^{71} + 12 q^{72} - 68 q^{73} - 16 q^{74} - 2 q^{75} + 4 q^{76} + 7 q^{77} + 53 q^{78} - 26 q^{79} - 5 q^{80} - 21 q^{81} + 21 q^{82} - 10 q^{83} + 12 q^{84} + 31 q^{85} - 27 q^{86} + 61 q^{87} + 12 q^{88} + 51 q^{89} + q^{90} - 10 q^{91} - 6 q^{92} - 38 q^{93} - 9 q^{94} + 15 q^{95} + 2 q^{96} + 72 q^{97} - 37 q^{98} - 32 q^{99}+O(q^{100}) \) 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9 + 5 * q^10 - 12 * q^11 - 2 * q^12 + 24 * q^13 + 23 * q^14 - 2 * q^15 - 5 * q^16 + 31 * q^17 + q^18 + 4 * q^19 - 5 * q^20 + 12 * q^21 + q^22 + 27 * q^23 - 9 * q^24 - 5 * q^25 - 2 * q^26 - 14 * q^27 + 10 * q^28 - 36 * q^29 + 2 * q^30 - 13 * q^31 + 5 * q^32 - 42 * q^33 + 2 * q^34 + 21 * q^35 - q^36 - 50 * q^37 - 26 * q^38 - 31 * q^39 + 5 * q^40 - 10 * q^41 + 21 * q^42 + 16 * q^43 - q^44 - q^45 + 17 * q^46 - 13 * q^47 - 2 * q^48 - 40 * q^49 + 5 * q^50 - 19 * q^51 - 20 * q^52 - 5 * q^53 + 47 * q^54 + 10 * q^55 + 12 * q^56 - 90 * q^57 - 8 * q^58 - 20 * q^59 - 2 * q^60 + 12 * q^61 + 13 * q^62 - 15 * q^63 - 5 * q^64 - 20 * q^65 + 20 * q^66 - 21 * q^67 - 24 * q^68 + 77 * q^69 - 21 * q^70 + 24 * q^71 + 12 * q^72 - 68 * q^73 - 16 * q^74 - 2 * q^75 + 4 * q^76 + 7 * q^77 + 53 * q^78 - 26 * q^79 - 5 * q^80 - 21 * q^81 + 21 * q^82 - 10 * q^83 + 12 * q^84 + 31 * q^85 - 27 * q^86 + 61 * q^87 + 12 * q^88 + 51 * q^89 + q^90 - 10 * q^91 - 6 * q^92 - 38 * q^93 - 9 * q^94 + 15 * q^95 + 2 * q^96 + 72 * q^97 - 37 * q^98 - 32 * q^99

Introduction

L-functions

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