LMFDB - Embedded newform 322.2.i.d.239.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			239.3
Character	$\chi$	$=$	322.239
Dual form			322.2.i.d.225.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 + 0.281733i) q^{2} +(0.868196 + 1.00195i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.397385 - 2.76387i) q^{5} +(-1.11531 - 0.716766i) q^{6} +(-0.415415 + 0.909632i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.176802 - 1.22968i) q^{9} +O(q^{10})$	\(q+(-0.959493 + 0.281733i) q^{2} +(0.868196 + 1.00195i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.397385 - 2.76387i) q^{5} +(-1.11531 - 0.716766i) q^{6} +(-0.415415 + 0.909632i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.176802 - 1.22968i) q^{9} +(1.15996 + 2.53996i) q^{10} +(5.62974 + 1.65304i) q^{11} +(1.27207 + 0.373513i) q^{12} +(-2.66173 - 5.82838i) q^{13} +(0.142315 - 0.989821i) q^{14} +(2.42426 - 2.79775i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-0.167110 - 0.107395i) q^{17} +(0.176802 + 1.22968i) q^{18} +(3.30475 - 2.12383i) q^{19} +(-1.82857 - 2.11028i) q^{20} +(-1.27207 + 0.373513i) q^{21} -5.86741 q^{22} +(-1.51266 + 4.55103i) q^{23} -1.32577 q^{24} +(-2.68362 + 0.787983i) q^{25} +(4.19596 + 4.84239i) q^{26} +(4.73151 - 3.04076i) q^{27} +(0.142315 + 0.989821i) q^{28} +(4.01087 + 2.57763i) q^{29} +(-1.53784 + 3.36741i) q^{30} +(0.141345 - 0.163121i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(3.23145 + 7.07589i) q^{33} +(0.190598 + 0.0559646i) q^{34} +(2.67919 + 0.786681i) q^{35} +(-0.516082 - 1.13006i) q^{36} +(0.164549 - 1.14446i) q^{37} +(-2.57253 + 2.96886i) q^{38} +(3.52885 - 7.72710i) q^{39} +(2.34903 + 1.50963i) q^{40} +(0.668992 + 4.65294i) q^{41} +(1.11531 - 0.716766i) q^{42} +(-1.00790 - 1.16318i) q^{43} +(5.62974 - 1.65304i) q^{44} -3.46895 q^{45} +(0.169209 - 4.79285i) q^{46} -6.79783 q^{47} +(1.27207 - 0.373513i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(2.35292 - 1.51213i) q^{50} +(-0.0374797 - 0.260677i) q^{51} +(-5.39025 - 3.46411i) q^{52} +(2.78971 - 6.10862i) q^{53} +(-3.68317 + 4.25061i) q^{54} +(2.33162 - 16.2168i) q^{55} +(-0.415415 - 0.909632i) q^{56} +(4.99715 + 1.46729i) q^{57} +(-4.57460 - 1.34322i) q^{58} +(4.10096 + 8.97986i) q^{59} +(0.526842 - 3.66427i) q^{60} +(-3.44894 + 3.98029i) q^{61} +(-0.0896632 + 0.196335i) q^{62} +(1.04511 + 0.671654i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-15.0512 + 9.67281i) q^{65} +(-5.09406 - 5.87886i) q^{66} +(-10.4122 + 3.05731i) q^{67} -0.198645 q^{68} +(-5.87319 + 2.43558i) q^{69} -2.79230 q^{70} +(-14.6847 + 4.31183i) q^{71} +(0.813552 + 0.938890i) q^{72} +(6.06131 - 3.89537i) q^{73} +(0.164549 + 1.14446i) q^{74} +(-3.11943 - 2.00474i) q^{75} +(1.63190 - 3.57336i) q^{76} +(-3.84234 + 4.43429i) q^{77} +(-1.20893 + 8.40829i) q^{78} +(2.79084 + 6.11108i) q^{79} +(-2.67919 - 0.786681i) q^{80} +(3.57856 + 1.05076i) q^{81} +(-1.95278 - 4.27599i) q^{82} +(0.912329 - 6.34538i) q^{83} +(-0.868196 + 1.00195i) q^{84} +(-0.230420 + 0.504550i) q^{85} +(1.29478 + 0.832107i) q^{86} +(0.899560 + 6.25658i) q^{87} +(-4.93598 + 3.17216i) q^{88} +(-0.409412 - 0.472486i) q^{89} +(3.32843 - 0.977316i) q^{90} +6.40741 q^{91} +(1.18795 + 4.64637i) q^{92} +0.286155 q^{93} +(6.52247 - 1.91517i) q^{94} +(-7.18327 - 8.28993i) q^{95} +(-1.11531 + 0.716766i) q^{96} +(-1.02532 - 7.13128i) q^{97} +(0.841254 + 0.540641i) q^{98} +(3.02807 - 6.63054i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{11}\right)$

Coefficient data

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

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

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

$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$3$	0.868196	+	1.00195i	0.501253	+	0.578477i	0.948838	−	0.315765i	$-0.102261\pi$
$3$	0.868196	+	1.00195i	0.501253	+	0.578477i	−0.447584	+	0.894242i	$0.647716\pi$
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	−0.397385	−	2.76387i	−0.177716	−	1.23604i	−0.862031	−	0.506856i	$-0.830808\pi$
$5$	−0.397385	−	2.76387i	−0.177716	−	1.23604i	0.684315	−	0.729187i	$-0.260101\pi$
$6$	−1.11531	−	0.716766i	−0.455324	−	0.292619i
$7$	−0.415415	+	0.909632i	−0.157012	+	0.343809i
$7$	−0.415415	+	0.909632i	−0.157012	+	0.343809i
$8$	−0.654861	+	0.755750i	−0.231528	+	0.267198i
$9$	0.176802	−	1.22968i	0.0589340	−	0.409895i
$10$	1.15996	+	2.53996i	0.366812	+	0.803206i
$11$	5.62974	+	1.65304i	1.69743	+	0.498411i	0.980131	−	0.198353i	$-0.0635594\pi$
$11$	5.62974	+	1.65304i	1.69743	+	0.498411i	0.717300	+	0.696764i	$0.245378\pi$
$12$	1.27207	+	0.373513i	0.367215	+	0.107824i
$13$	−2.66173	−	5.82838i	−0.738232	−	1.61650i	−0.786441	−	0.617665i	$-0.788079\pi$
$13$	−2.66173	−	5.82838i	−0.738232	−	1.61650i	0.0482094	−	0.998837i	$-0.484649\pi$
$14$	0.142315	−	0.989821i	0.0380352	−	0.264541i
$15$	2.42426	−	2.79775i	0.625941	−	0.722375i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	−0.167110	−	0.107395i	−0.0405302	−	0.0260472i	0.520219	−	0.854033i	$-0.325850\pi$
$17$	−0.167110	−	0.107395i	−0.0405302	−	0.0260472i	−0.560749	+	0.827986i	$0.689487\pi$
$18$	0.176802	+	1.22968i	0.0416726	+	0.289839i
$19$	3.30475	−	2.12383i	0.758161	−	0.487241i	−0.103560	−	0.994623i	$-0.533023\pi$
$19$	3.30475	−	2.12383i	0.758161	−	0.487241i	0.861721	+	0.507383i	$0.169387\pi$
$20$	−1.82857	−	2.11028i	−0.408880	−	0.471872i
$21$	−1.27207	+	0.373513i	−0.277588	+	0.0815072i
$22$	−5.86741			−1.25094
$23$	−1.51266	+	4.55103i	−0.315410	+	0.948955i
$23$	−1.51266	+	4.55103i	−0.315410	+	0.948955i
$24$	−1.32577			−0.270622
$25$	−2.68362	+	0.787983i	−0.536725	+	0.157597i
$26$	4.19596	+	4.84239i	0.822895	+	0.949672i
$27$	4.73151	−	3.04076i	0.910580	−	0.585194i
$28$	0.142315	+	0.989821i	0.0268950	+	0.187059i
$29$	4.01087	+	2.57763i	0.744799	+	0.478653i	0.857183	−	0.515011i	$-0.172212\pi$
$29$	4.01087	+	2.57763i	0.744799	+	0.478653i	−0.112384	+	0.993665i	$0.535849\pi$
$30$	−1.53784	+	3.36741i	−0.280771	+	0.614802i
$31$	0.141345	−	0.163121i	0.0253863	−	0.0292974i	−0.742914	−	0.669386i	$-0.766557\pi$
$31$	0.141345	−	0.163121i	0.0253863	−	0.0292974i	0.768301	+	0.640089i	$0.221103\pi$
$32$	−0.142315	+	0.989821i	−0.0251579	+	0.174977i
$33$	3.23145	+	7.07589i	0.562523	+	1.23175i
$34$	0.190598	+	0.0559646i	0.0326873	+	0.00959786i
$35$	2.67919	+	0.786681i	0.452866	+	0.132973i
$36$	−0.516082	−	1.13006i	−0.0860137	−	0.188344i
$37$	0.164549	−	1.14446i	0.0270516	−	0.188148i	−0.971815	−	0.235745i	$-0.924247\pi$
$37$	0.164549	−	1.14446i	0.0270516	−	0.188148i	0.998867	+	0.0475966i	$0.0151562\pi$
$38$	−2.57253	+	2.96886i	−0.417319	+	0.481612i
$39$	3.52885	−	7.72710i	0.565068	−	1.23733i
$40$	2.34903	+	1.50963i	0.371414	+	0.238693i
$41$	0.668992	+	4.65294i	0.104479	+	0.726668i	0.972965	+	0.230953i	$0.0741845\pi$
$41$	0.668992	+	4.65294i	0.104479	+	0.726668i	−0.868486	+	0.495714i	$0.834906\pi$
$42$	1.11531	−	0.716766i	0.172096	−	0.110599i
$43$	−1.00790	−	1.16318i	−0.153704	−	0.177384i	0.673675	−	0.739028i	$-0.264715\pi$
$43$	−1.00790	−	1.16318i	−0.153704	−	0.177384i	−0.827379	+	0.561644i	$0.810169\pi$
$44$	5.62974	−	1.65304i	0.848715	−	0.249205i
$45$	−3.46895			−0.517121
$46$	0.169209	−	4.79285i	0.0249485	−	0.706667i
$47$	−6.79783			−0.991566			−0.495783	−	0.868446i	$-0.665119\pi$
$47$	−6.79783			−0.991566			−0.495783	+	0.868446i	$0.665119\pi$
$48$	1.27207	−	0.373513i	0.183607	−	0.0539120i
$49$	−0.654861	−	0.755750i	−0.0935515	−	0.107964i
$50$	2.35292	−	1.51213i	0.332753	−	0.213847i
$51$	−0.0374797	−	0.260677i	−0.00524820	−	0.0365020i
$52$	−5.39025	−	3.46411i	−0.747494	−	0.480385i
$53$	2.78971	−	6.10862i	0.383196	−	0.839083i	−0.615505	−	0.788133i	$-0.711048\pi$
$53$	2.78971	−	6.10862i	0.383196	−	0.839083i	0.998701	−	0.0509500i	$-0.0162249\pi$
$54$	−3.68317	+	4.25061i	−0.501216	+	0.578434i
$55$	2.33162	−	16.2168i	0.314396	−	2.18667i
$56$	−0.415415	−	0.909632i	−0.0555122	−	0.121555i
$57$	4.99715	+	1.46729i	0.661888	+	0.194348i
$58$	−4.57460	−	1.34322i	−0.600674	−	0.176374i
$59$	4.10096	+	8.97986i	0.533900	+	1.16908i	0.963904	+	0.266251i	$0.0857849\pi$
$59$	4.10096	+	8.97986i	0.533900	+	1.16908i	−0.430004	+	0.902827i	$0.641488\pi$
$60$	0.526842	−	3.66427i	0.0680150	−	0.473055i
$61$	−3.44894	+	3.98029i	−0.441592	+	0.509624i	−0.932293	−	0.361704i	$-0.882195\pi$
$61$	−3.44894	+	3.98029i	−0.441592	+	0.509624i	0.490701	+	0.871328i	$0.336741\pi$
$62$	−0.0896632	+	0.196335i	−0.0113872	+	0.0249346i
$63$	1.04511	+	0.671654i	0.131672	+	0.0846204i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	−15.0512	+	9.67281i	−1.86687	+	1.19976i
$66$	−5.09406	−	5.87886i	−0.627036	−	0.723638i
$67$	−10.4122	+	3.05731i	−1.27206	+	0.373510i	−0.846969	−	0.531642i	$-0.821575\pi$
$67$	−10.4122	+	3.05731i	−1.27206	+	0.373510i	−0.425089	+	0.905152i	$0.639757\pi$
$68$	−0.198645			−0.0240892
$69$	−5.87319	+	2.43558i	−0.707049	+	0.293209i
$70$	−2.79230			−0.333743
$71$	−14.6847	+	4.31183i	−1.74276	+	0.511720i	−0.989315	−	0.145793i	$-0.953427\pi$
$71$	−14.6847	+	4.31183i	−1.74276	+	0.511720i	−0.753443	+	0.657513i	$0.771609\pi$
$72$	0.813552	+	0.938890i	0.0958781	+	0.110649i
$73$	6.06131	−	3.89537i	0.709422	−	0.455918i	−0.135521	−	0.990775i	$-0.543271\pi$
$73$	6.06131	−	3.89537i	0.709422	−	0.455918i	0.844943	+	0.534856i	$0.179634\pi$
$74$	0.164549	+	1.14446i	0.0191284	+	0.133041i
$75$	−3.11943	−	2.00474i	−0.360201	−	0.231487i
$76$	1.63190	−	3.57336i	0.187192	−	0.409893i
$77$	−3.84234	+	4.43429i	−0.437875	+	0.505335i
$78$	−1.20893	+	8.40829i	−0.136884	+	0.952052i
$79$	2.79084	+	6.11108i	0.313994	+	0.687550i	0.999166	−	0.0408308i	$-0.0130005\pi$
$79$	2.79084	+	6.11108i	0.313994	+	0.687550i	−0.685172	+	0.728381i	$0.740273\pi$
$80$	−2.67919	−	0.786681i	−0.299542	−	0.0879536i
$81$	3.57856	+	1.05076i	0.397617	+	0.116751i
$82$	−1.95278	−	4.27599i	−0.215648	−	0.472204i
$83$	0.912329	−	6.34538i	0.100141	−	0.696496i	−0.876466	−	0.481464i	$-0.840105\pi$
$83$	0.912329	−	6.34538i	0.100141	−	0.696496i	0.976607	−	0.215032i	$-0.0689857\pi$
$84$	−0.868196	+	1.00195i	−0.0947279	+	0.109322i
$85$	−0.230420	+	0.504550i	−0.0249926	+	0.0547261i
$86$	1.29478	+	0.832107i	0.139620	+	0.0897285i
$87$	0.899560	+	6.25658i	0.0964430	+	0.670776i
$88$	−4.93598	+	3.17216i	−0.526177	+	0.338154i
$89$	−0.409412	−	0.472486i	−0.0433975	−	0.0500834i	0.733636	−	0.679543i	$-0.237822\pi$
$89$	−0.409412	−	0.472486i	−0.0433975	−	0.0500834i	−0.777033	+	0.629459i	$0.783276\pi$
$90$	3.32843	−	0.977316i	0.350848	−	0.103018i
$91$	6.40741			0.671679
$92$	1.18795	+	4.64637i	0.123852	+	0.484418i
$93$	0.286155			0.0296728
$94$	6.52247	−	1.91517i	0.672742	−	0.197535i
$95$	−7.18327	−	8.28993i	−0.736987	−	0.850529i
$96$	−1.11531	+	0.716766i	−0.113831	+	0.0731547i
$97$	−1.02532	−	7.13128i	−0.104106	−	0.724072i	−0.973289	−	0.229582i	$-0.926264\pi$
$97$	−1.02532	−	7.13128i	−0.104106	−	0.724072i	0.869183	−	0.494490i	$-0.164645\pi$
$98$	0.841254	+	0.540641i	0.0849794	+	0.0546130i
$99$	3.02807	−	6.63054i	0.304332	−	0.666395i
$100$	−1.83159	+	2.11377i	−0.183159	+	0.211377i
$101$	−2.24690	+	15.6275i	−0.223575	+	1.55500i	0.500782	+	0.865573i	$0.333046\pi$
$101$	−2.24690	+	15.6275i	−0.223575	+	1.55500i	−0.724357	+	0.689425i	$0.757863\pi$
$102$	0.109403	+	0.239558i	0.0108325	+	0.0237198i
$103$	−12.1753	−	3.57500i	−1.19967	−	0.352255i	−0.379944	−	0.925009i	$-0.624057\pi$
$103$	−12.1753	−	3.57500i	−1.19967	−	0.352255i	−0.819727	+	0.572754i	$0.805875\pi$
$104$	6.14786	+	1.80517i	0.602847	+	0.177012i
$105$	1.53784	+	3.36741i	0.150078	+	0.328626i
$106$	−0.955713	+	6.64713i	−0.0928270	+	0.645626i
$107$	−10.1496	+	11.7133i	−0.981203	+	1.13237i	0.00999141	+	0.999950i	$0.496820\pi$
$107$	−10.1496	+	11.7133i	−0.981203	+	1.13237i	−0.991194	+	0.132418i	$0.957726\pi$
$108$	2.33644	−	5.11610i	0.224824	−	0.492297i
$109$	−9.14123	−	5.87471i	−0.875571	−	0.562695i	0.0238812	−	0.999715i	$-0.492398\pi$
$109$	−9.14123	−	5.87471i	−0.875571	−	0.562695i	−0.899452	+	0.437020i	$0.856034\pi$
$110$	2.33162	+	16.2168i	0.222312	+	1.54621i
$111$	1.28955	−	0.828746i	0.122399	−	0.0786611i
$112$	0.654861	+	0.755750i	0.0618785	+	0.0714116i
$113$	6.60843	−	1.94041i	0.621668	−	0.182538i	0.0442950	−	0.999018i	$-0.485896\pi$
$113$	6.60843	−	1.94041i	0.621668	−	0.182538i	0.577373	+	0.816480i	$0.304078\pi$
$114$	−5.20811			−0.487784
$115$	13.1796	+	2.37228i	1.22900	+	0.221216i
$116$	4.76773			0.442672
$117$	−7.63767	+	2.24262i	−0.706103	+	0.207330i
$118$	−6.46476	−	7.46073i	−0.595130	−	0.686816i
$119$	0.167110	−	0.107395i	0.0153190	−	0.00984492i
$120$	0.526842	+	3.66427i	0.0480939	+	0.334500i
$121$	19.7077	+	12.6653i	1.79161	+	1.15139i
$122$	2.18786	−	4.79074i	0.198079	−	0.433734i
$123$	−4.08121	+	4.70996i	−0.367990	+	0.424683i
$124$	0.0307172	−	0.213643i	0.00275849	−	0.0191857i
$125$	−2.55549	−	5.59574i	−0.228570	−	0.500499i
$126$	−1.19201	−	0.350005i	−0.106192	−	0.0311809i
$127$	8.27434	+	2.42957i	0.734229	+	0.215589i	0.627410	−	0.778689i	$-0.284115\pi$
$127$	8.27434	+	2.42957i	0.734229	+	0.215589i	0.106819	+	0.994278i	$0.465933\pi$
$128$	0.415415	+	0.909632i	0.0367178	+	0.0804009i
$129$	0.290395	−	2.01974i	0.0255679	−	0.177829i
$130$	11.7164	−	13.5214i	1.02759	−	1.18591i
$131$	2.53567	−	5.55235i	0.221543	−	0.485111i	−0.765925	−	0.642930i	$-0.777719\pi$
$131$	2.53567	−	5.55235i	0.221543	−	0.485111i	0.987468	+	0.157818i	$0.0504460\pi$
$132$	6.54399	+	4.20556i	0.569581	+	0.366047i
$133$	0.559064	+	3.88838i	0.0484770	+	0.337165i
$134$	9.12913	−	5.86694i	0.788637	−	0.506826i
$135$	−10.2845	−	11.8690i	−0.885150	−	1.02152i
$136$	0.190598	−	0.0559646i	0.0163436	−	0.00479893i
$137$	−8.47009			−0.723648			−0.361824	−	0.932246i	$-0.617846\pi$
$137$	−8.47009			−0.723648			−0.361824	+	0.932246i	$0.617846\pi$
$138$	4.94911	−	3.99159i	0.421296	−	0.339787i
$139$	2.71390			0.230190			0.115095	−	0.993355i	$-0.463283\pi$
$139$	2.71390			0.230190			0.115095	+	0.993355i	$0.463283\pi$
$140$	2.67919	−	0.786681i	0.226433	−	0.0664867i
$141$	−5.90185	−	6.81110i	−0.497026	−	0.573598i
$142$	12.8751	−	8.27434i	1.08046	−	0.694367i
$143$	−5.35031	−	37.2122i	−0.447416	−	3.11184i
$144$	−1.04511	−	0.671654i	−0.0870928	−	0.0559711i
$145$	5.53038	−	12.1098i	0.459273	−	1.00567i
$146$	−4.71833	+	5.44524i	−0.390492	+	0.450652i
$147$	0.188677	−	1.31228i	0.0155618	−	0.108235i
$148$	−0.480315	−	1.05174i	−0.0394816	−	0.0864527i
$149$	16.3113	+	4.78944i	1.33628	+	0.392366i	0.870340	−	0.492451i	$-0.163899\pi$
$149$	16.3113	+	4.78944i	1.33628	+	0.392366i	0.465937	+	0.884818i	$0.345717\pi$
$150$	3.55787	+	1.04469i	0.290499	+	0.0852982i
$151$	6.29168	+	13.7768i	0.512009	+	1.12114i	0.972377	+	0.233416i	$0.0749903\pi$
$151$	6.29168	+	13.7768i	0.512009	+	1.12114i	−0.460368	+	0.887728i	$0.652282\pi$
$152$	−0.559064	+	3.88838i	−0.0453461	+	0.315389i
$153$	−0.161608	+	0.186505i	−0.0130652	+	0.0150781i
$154$	2.43741	−	5.33719i	0.196412	−	0.430083i
$155$	−0.507014	−	0.325838i	−0.0407244	−	0.0261720i
$156$	−1.20893	−	8.40829i	−0.0967919	−	0.673202i
$157$	−14.3064	+	9.19417i	−1.14178	+	0.733775i	−0.967985	−	0.251008i	$-0.919238\pi$
$157$	−14.3064	+	9.19417i	−1.14178	+	0.733775i	−0.173791	+	0.984783i	$0.555602\pi$
$158$	−4.39948	−	5.07727i	−0.350004	−	0.403926i
$159$	8.54256	−	2.50832i	0.677469	−	0.198923i
$160$	2.79230			0.220750
$161$	−3.51138	−	3.26653i	−0.276736	−	0.257438i
$162$	−3.72963			−0.293028
$163$	18.5306	−	5.44106i	1.45142	−	0.426177i	0.541412	−	0.840757i	$-0.317890\pi$
$163$	18.5306	−	5.44106i	1.45142	−	0.426177i	0.910013	+	0.414580i	$0.136072\pi$
$164$	3.07836	+	3.55262i	0.240380	+	0.277413i
$165$	18.2727	−	11.7432i	1.42253	−	0.914205i
$166$	0.912329	+	6.34538i	0.0708104	+	0.492497i
$167$	20.2657	+	13.0240i	1.56821	+	1.00783i	0.979971	+	0.199141i	$0.0638153\pi$
$167$	20.2657	+	13.0240i	1.56821	+	1.00783i	0.588240	+	0.808687i	$0.299821\pi$
$168$	0.550746	−	1.20596i	0.0424909	−	0.0930422i
$169$	−18.3720	+	21.2024i	−1.41323	+	1.63096i
$170$	0.0789384	−	0.549029i	0.00605430	−	0.0421086i
$171$	−2.02736	−	4.43929i	−0.155036	−	0.339481i
$172$	−1.47677	−	0.433618i	−0.112603	−	0.0330631i
$173$	20.3914	+	5.98746i	1.55033	+	0.455218i	0.941199	−	0.337852i	$-0.109700\pi$
$173$	20.3914	+	5.98746i	1.55033	+	0.455218i	0.609130	+	0.793070i	$0.291519\pi$
$174$	−2.62580	−	5.74971i	−0.199062	−	0.435884i
$175$	0.398043	−	2.76845i	0.0300892	−	0.209275i
$176$	3.84234	−	4.43429i	0.289627	−	0.334248i
$177$	−5.43694	+	11.9052i	−0.408665	+	0.894853i
$178$	0.525942	+	0.338003i	0.0394210	+	0.0253344i
$179$	−0.726446	−	5.05254i	−0.0542971	−	0.377645i	−0.998793	−	0.0491209i	$-0.984358\pi$
$179$	−0.726446	−	5.05254i	−0.0542971	−	0.377645i	0.944496	−	0.328524i	$-0.106551\pi$
$180$	−2.91827	+	1.87546i	−0.217515	+	0.139788i
$181$	2.45645	+	2.83489i	0.182586	+	0.210716i	0.839663	−	0.543108i	$-0.182753\pi$
$181$	2.45645	+	2.83489i	0.182586	+	0.210716i	−0.657076	+	0.753824i	$0.728207\pi$
$182$	−6.14786	+	1.80517i	−0.455710	+	0.133808i
$183$	−6.98242			−0.516155
$184$	−2.44886	−	4.12348i	−0.180532	−	0.303987i
$185$	−3.22853			−0.237367
$186$	−0.274563	+	0.0806190i	−0.0201320	+	0.00591128i
$187$	−0.763260	−	0.880848i	−0.0558151	−	0.0644140i
$188$	−5.71870	+	3.67519i	−0.417079	+	0.268040i
$189$	0.800430	+	5.56711i	0.0582227	+	0.404948i
$190$	9.22784	+	5.93037i	0.669458	+	0.430234i
$191$	−2.70489	+	5.92289i	−0.195719	+	0.428565i	−0.981892	−	0.189442i	$-0.939332\pi$
$191$	−2.70489	+	5.92289i	−0.195719	+	0.428565i	0.786173	+	0.618007i	$0.212060\pi$
$192$	0.868196	−	1.00195i	0.0626566	−	0.0723096i
$193$	−2.23527	+	15.5467i	−0.160898	+	1.11907i	0.736046	+	0.676931i	$0.236691\pi$
$193$	−2.23527	+	15.5467i	−0.160898	+	1.11907i	−0.896945	+	0.442142i	$0.854219\pi$
$194$	2.99291	+	6.55355i	0.214878	+	0.470517i
$195$	−22.7591	−	6.68266i	−1.62981	−	0.478555i
$196$	−0.959493	−	0.281733i	−0.0685352	−	0.0201238i
$197$	8.41360	+	18.4232i	0.599444	+	1.31260i	0.929564	+	0.368661i	$0.120184\pi$
$197$	8.41360	+	18.4232i	0.599444	+	1.31260i	−0.330119	+	0.943939i	$0.607089\pi$
$198$	−1.03737	+	7.21506i	−0.0737226	+	0.512752i
$199$	8.24674	−	9.51725i	0.584596	−	0.674660i	−0.383990	−	0.923337i	$-0.625450\pi$
$199$	8.24674	−	9.51725i	0.584596	−	0.674660i	0.968586	+	0.248677i	$0.0799959\pi$
$200$	1.16188	−	2.54417i	0.0821574	−	0.179900i
$201$	−12.1031	−	7.77822i	−0.853690	−	0.548633i
$202$	−2.24690	−	15.6275i	−0.158091	−	1.09955i
$203$	−4.01087	+	2.57763i	−0.281508	+	0.180914i
$204$	−0.172462	−	0.199032i	−0.0120748	−	0.0139350i
$205$	12.5943	−	3.69802i	0.879624	−	0.258281i
$206$	12.6893			0.884109
$207$	5.32889	+	2.66472i	0.370383	+	0.185211i
$208$	−6.40741			−0.444274
$209$	22.1157	−	6.49374i	1.52977	−	0.449182i
$210$	−2.42426	−	2.79775i	−0.167290	−	0.193063i
$211$	−5.35633	+	3.44231i	−0.368745	+	0.236978i	−0.711869	−	0.702312i	$-0.752151\pi$
$211$	−5.35633	+	3.44231i	−0.368745	+	0.236978i	0.343124	+	0.939290i	$0.388515\pi$
$212$	−0.955713	−	6.64713i	−0.0656386	−	0.456527i
$213$	−17.0695	−	10.9699i	−1.16958	−	0.751644i
$214$	6.43849	−	14.0983i	0.440126	−	0.963741i
$215$	−2.81437	+	3.24795i	−0.191938	+	0.221509i
$216$	−0.800430	+	5.56711i	−0.0544624	+	0.378794i
$217$	0.0896632	+	0.196335i	0.00608673	+	0.0133281i
$218$	10.4260	+	3.06136i	0.706141	+	0.207342i
$219$	9.16537	+	2.69120i	0.619338	+	0.181854i
$220$	−6.80597	−	14.9030i	−0.458859	−	1.00476i
$221$	−0.181138	+	1.25984i	−0.0121846	+	0.0847461i
$222$	−1.00383	+	1.15849i	−0.0673729	+	0.0777524i
$223$	5.21897	−	11.4280i	0.349488	−	0.765273i	−0.650495	−	0.759511i	$-0.725439\pi$
$223$	5.21897	−	11.4280i	0.349488	−	0.765273i	0.999983	−	0.00576229i	$-0.00183421\pi$
$224$	−0.841254	−	0.540641i	−0.0562086	−	0.0361231i
$225$	0.494500	+	3.43932i	0.0329667	+	0.229288i
$226$	−5.79406	+	3.72362i	−0.385415	+	0.247691i
$227$	5.73067	+	6.61355i	0.380358	+	0.438956i	0.913357	−	0.407159i	$-0.133481\pi$
$227$	5.73067	+	6.61355i	0.380358	+	0.438956i	−0.532999	+	0.846116i	$0.678935\pi$
$228$	4.99715	−	1.46729i	0.330944	−	0.0971740i
$229$	−4.65669			−0.307723			−0.153861	−	0.988092i	$-0.549171\pi$
$229$	−4.65669			−0.307723			−0.153861	+	0.988092i	$0.549171\pi$
$230$	−13.3141	+	1.43693i	−0.877903	+	0.0947486i
$231$	−7.77885			−0.511811
$232$	−4.57460	+	1.34322i	−0.300337	+	0.0881870i
$233$	14.5816	+	16.8281i	0.955273	+	1.10244i	0.994659	+	0.103219i	$0.0329144\pi$
$233$	14.5816	+	16.8281i	0.955273	+	1.10244i	−0.0393859	+	0.999224i	$0.512540\pi$
$234$	6.69647	−	4.30356i	0.437762	−	0.281332i
$235$	2.70136	+	18.7884i	0.176217	+	1.22562i
$236$	8.30483	+	5.33719i	0.540598	+	0.347421i
$237$	−3.70001	+	8.10190i	−0.240342	+	0.526275i
$238$	−0.130085	+	0.150126i	−0.00843213	+	0.00973119i
$239$	2.24421	−	15.6088i	0.145166	−	1.00965i	−0.778826	−	0.627240i	$-0.784184\pi$
$239$	2.24421	−	15.6088i	0.145166	−	1.00965i	0.923992	−	0.382412i	$-0.124907\pi$
$240$	−1.53784	−	3.36741i	−0.0992674	−	0.217365i
$241$	−23.6542	−	6.94549i	−1.52370	−	0.447398i	−0.590584	−	0.806976i	$-0.701103\pi$
$241$	−23.6542	−	6.94549i	−1.52370	−	0.447398i	−0.933115	+	0.359578i	$0.882921\pi$
$242$	−22.4776	−	6.60002i	−1.44491	−	0.424265i
$243$	−4.95525	−	10.8505i	−0.317880	−	0.696059i
$244$	−0.749527	+	5.21308i	−0.0479836	+	0.333733i
$245$	−1.82857	+	2.11028i	−0.116823	+	0.134821i
$246$	2.58894	−	5.66899i	0.165065	−	0.361441i
$247$	−21.1749	−	13.6083i	−1.34732	−	0.865873i
$248$	0.0307172	+	0.213643i	0.00195055	+	0.0135663i
$249$	7.14985	−	4.59493i	0.453103	−	0.291192i
$250$	4.02848	+	4.64911i	0.254783	+	0.294036i
$251$	2.16995	−	0.637155i	0.136966	−	0.0402169i	−0.212531	−	0.977154i	$-0.568171\pi$
$251$	2.16995	−	0.637155i	0.136966	−	0.0402169i	0.349497	+	0.936937i	$0.386352\pi$
$252$	1.24233			0.0782594
$253$	−16.0389	+	23.1206i	−1.00836	+	1.45358i
$254$	−8.62366			−0.541097
$255$	−0.705584	+	0.207178i	−0.0441854	+	0.0129740i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−8.97369	+	5.76704i	−0.559764	+	0.359738i	−0.789725	−	0.613462i	$-0.789777\pi$
$257$	−8.97369	+	5.76704i	−0.559764	+	0.359738i	0.229961	+	0.973200i	$0.426140\pi$
$258$	0.290395	+	2.01974i	0.0180792	+	0.125744i
$259$	0.972682	+	0.625105i	0.0604395	+	0.0388421i
$260$	−7.43235	+	16.2746i	−0.460935	+	1.00931i
$261$	3.87880	−	4.47637i	0.240091	−	0.277080i
$262$	−0.868683	+	6.04183i	−0.0536674	+	0.373265i
$263$	8.85842	+	19.3972i	0.546233	+	1.19608i	0.958519	+	0.285030i	$0.0920034\pi$
$263$	8.85842	+	19.3972i	0.546233	+	1.19608i	−0.412285	+	0.911055i	$0.635269\pi$
$264$	−7.46375	−	2.19156i	−0.459362	−	0.134881i
$265$	−17.9920	−	5.28294i	−1.10524	−	0.324528i
$266$	−1.63190	−	3.57336i	−0.100058	−	0.219097i
$267$	0.117959	−	0.820421i	0.00721896	−	0.0502089i
$268$	−7.10643	+	8.20126i	−0.434094	+	0.500971i
$269$	1.92474	−	4.21458i	0.117353	−	0.256968i	−0.841836	−	0.539734i	$-0.818525\pi$
$269$	1.92474	−	4.21458i	0.117353	−	0.256968i	0.959189	+	0.282766i	$0.0912521\pi$
$270$	13.2118	+	8.49070i	0.804044	+	0.516727i
$271$	−1.84360	−	12.8225i	−0.111991	−	0.778912i	−0.965979	−	0.258620i	$-0.916732\pi$
$271$	−1.84360	−	12.8225i	−0.111991	−	0.778912i	0.853988	−	0.520292i	$-0.174177\pi$
$272$	−0.167110	+	0.107395i	−0.0101326	+	0.00651180i
$273$	5.56288	+	6.41991i	0.336681	+	0.388551i
$274$	8.12699	−	2.38630i	0.490969	−	0.144162i
$275$	−16.4107			−0.989601
$276$	−3.62407	+	5.22423i	−0.218143	+	0.314461i
$277$	−12.3212			−0.740311			−0.370155	−	0.928970i	$-0.620696\pi$
$277$	−12.3212			−0.740311			−0.370155	+	0.928970i	$0.620696\pi$
$278$	−2.60396	+	0.764593i	−0.156175	+	0.0458572i
$279$	−0.175597	−	0.202650i	−0.0105127	−	0.0121323i
$280$	−2.34903	+	1.50963i	−0.140381	+	0.0902176i
$281$	−3.04160	−	21.1548i	−0.181446	−	1.26199i	−0.853346	−	0.521345i	$-0.825430\pi$
$281$	−3.04160	−	21.1548i	−0.181446	−	1.26199i	0.671899	−	0.740642i	$-0.265479\pi$
$282$	7.58169	+	4.87246i	0.451483	+	0.290151i
$283$	−8.77974	+	19.2250i	−0.521902	+	1.14281i	0.446813	+	0.894627i	$0.352559\pi$
$283$	−8.77974	+	19.2250i	−0.521902	+	1.14281i	−0.968715	+	0.248178i	$0.920168\pi$
$284$	−10.0224	+	11.5665i	−0.594723	+	0.686346i
$285$	2.06963	−	14.3946i	0.122594	−	0.852661i
$286$	15.6175	+	34.1975i	0.923481	+	2.02214i
$287$	−4.51038	−	1.32437i	−0.266239	−	0.0781748i
$288$	1.19201	+	0.350005i	0.0702396	+	0.0206242i
$289$	−7.04566	−	15.4279i	−0.414451	−	0.907521i
$290$	−1.89462	+	13.1774i	−0.111256	+	0.773804i
$291$	6.25502	−	7.21867i	0.366676	−	0.423166i
$292$	2.99310	−	6.55398i	0.175158	−	0.383543i
$293$	−17.7762	−	11.4241i	−1.03850	−	0.667401i	−0.0938817	−	0.995583i	$-0.529928\pi$
$293$	−17.7762	−	11.4241i	−1.03850	−	0.667401i	−0.944614	+	0.328182i	$0.893564\pi$
$294$	0.188677	+	1.31228i	0.0110039	+	0.0765336i
$295$	23.1895	−	14.9030i	1.35015	−	0.867687i
$296$	0.757169	+	0.873819i	0.0440095	+	0.0507897i
$297$	31.6637	−	9.29730i	1.83731	−	0.539484i
$298$	−17.0000			−0.984781
$299$	30.5514	−	3.29729i	1.76683	−	0.190687i
$300$	−3.70807			−0.214086
$301$	1.47677	−	0.433618i	0.0851195	−	0.0249933i
$302$	−9.91821	−	11.4462i	−0.570729	−	0.658656i
$303$	−17.6088	+	11.3165i	−1.01160	+	0.650115i
$304$	−0.559064	−	3.88838i	−0.0320645	−	0.223014i
$305$	12.3716	+	7.95074i	0.708395	+	0.455258i
$306$	0.102517	−	0.224481i	0.00586050	−	0.0128327i
$307$	−13.0635	+	15.0761i	−0.745572	+	0.860437i	−0.994131	−	0.108180i	$-0.965498\pi$
$307$	−13.0635	+	15.0761i	−0.745572	+	0.860437i	0.248559	+	0.968617i	$0.420043\pi$
$308$	−0.835020	+	5.80769i	−0.0475797	+	0.330924i
$309$	−6.98860	−	15.3029i	−0.397568	−	0.870552i
$310$	0.578276	+	0.169797i	0.0328439	+	0.00964383i
$311$	−4.24324	−	1.24593i	−0.240612	−	0.0706500i	0.159203	−	0.987246i	$-0.449107\pi$
$311$	−4.24324	−	1.24593i	−0.240612	−	0.0706500i	−0.399815	+	0.916596i	$0.630926\pi$
$312$	3.52885	+	7.72710i	0.199782	+	0.437461i
$313$	3.54253	−	24.6389i	0.200236	−	1.39267i	−0.603347	−	0.797479i	$-0.706167\pi$
$313$	3.54253	−	24.6389i	0.200236	−	1.39267i	0.803583	−	0.595193i	$-0.202924\pi$
$314$	11.1366	−	12.8523i	0.628475	−	0.725299i
$315$	1.44105	−	3.15547i	0.0811942	−	0.177791i
$316$	5.65170	+	3.63213i	0.317933	+	0.204323i
$317$	−4.77263	−	33.1944i	−0.268058	−	1.86438i	−0.466846	−	0.884339i	$-0.654610\pi$
$317$	−4.77263	−	33.1944i	−0.268058	−	1.86438i	0.198788	−	0.980042i	$-0.436299\pi$
$318$	−7.48985	+	4.81343i	−0.420010	+	0.269924i
$319$	18.3192	+	21.1415i	1.02568	+	1.18370i
$320$	−2.67919	+	0.786681i	−0.149771	+	0.0439768i
$321$	−20.5480			−1.14688
$322$	4.28943	+	2.14494i	0.239041	+	0.119533i
$323$	−0.780348			−0.0434197
$324$	3.57856	−	1.05076i	0.198809	−	0.0583755i
$325$	11.7358	+	13.5438i	0.650982	+	0.751274i
$326$	−16.2470	+	10.4413i	−0.899839	+	0.578291i
$327$	−2.05020	−	14.2595i	−0.113376	−	0.788550i
$328$	−3.95456	−	2.54144i	−0.218354	−	0.140327i
$329$	2.82392	−	6.18353i	0.155688	−	0.340909i
$330$	−14.2241	+	16.4155i	−0.783013	+	0.903645i
$331$	−0.383230	+	2.66542i	−0.0210642	+	0.146505i	−0.997639	−	0.0686721i	$-0.978124\pi$
$331$	−0.383230	+	2.66542i	−0.0210642	+	0.146505i	0.976575	+	0.215177i	$0.0690329\pi$
$332$	−2.66307	−	5.83132i	−0.146155	−	0.320035i
$333$	−1.37823	−	0.404685i	−0.0755266	−	0.0221766i
$334$	−23.1141	−	6.78692i	−1.26475	−	0.371364i
$335$	12.5877	+	27.5632i	0.687739	+	1.50594i
$336$	−0.188677	+	1.31228i	−0.0102932	+	0.0715906i
$337$	6.43444	−	7.42574i	0.350507	−	0.404506i	−0.552930	−	0.833228i	$-0.686490\pi$
$337$	6.43444	−	7.42574i	0.350507	−	0.404506i	0.903437	+	0.428722i	$0.141036\pi$
$338$	11.6544	−	25.5196i	0.633916	−	1.38808i
$339$	7.68160	+	4.93667i	0.417207	+	0.268123i
$340$	0.0789384	+	0.549029i	0.00428104	+	0.0297753i
$341$	1.06538	−	0.684680i	0.0576937	−	0.0370775i
$342$	3.19593	+	3.68830i	0.172816	+	0.199440i
$343$	0.959493	−	0.281733i	0.0518078	−	0.0152121i
$344$	1.53911			0.0829834
$345$	9.06555	+	15.2649i	0.488073	+	0.821835i
$346$	−21.2523			−1.14253
$347$	−20.6067	+	6.05069i	−1.10623	+	0.324818i	−0.783324	−	0.621614i	$-0.786477\pi$
$347$	−20.6067	+	6.05069i	−1.10623	+	0.324818i	−0.322904	+	0.946432i	$0.604659\pi$
$348$	4.13932	+	4.77703i	0.221891	+	0.256076i
$349$	2.55968	−	1.64501i	0.137016	−	0.0880551i	−0.470337	−	0.882487i	$-0.655868\pi$
$349$	2.55968	−	1.64501i	0.137016	−	0.0880551i	0.607353	+	0.794432i	$0.292231\pi$
$350$	0.398043	+	2.76845i	0.0212763	+	0.147980i
$351$	−30.3167	−	19.4834i	−1.61819	−	1.03995i
$352$	−2.43741	+	5.33719i	−0.129914	+	0.284473i
$353$	−10.1508	+	11.7147i	−0.540274	+	0.623509i	−0.958589	−	0.284792i	$-0.908075\pi$
$353$	−10.1508	+	11.7147i	−0.540274	+	0.623509i	0.418315	+	0.908302i	$0.362621\pi$
$354$	1.86261	−	12.9548i	0.0989968	−	0.688538i
$355$	17.7529	+	38.8733i	0.942224	+	2.06318i
$356$	−0.599864	−	0.176136i	−0.0317927	−	0.00933519i
$357$	0.252690	+	0.0741963i	0.0133737	+	0.00392689i
$358$	2.12048	+	4.64321i	0.112071	+	0.245401i
$359$	4.35804	−	30.3108i	0.230009	−	1.59975i	−0.468048	−	0.883703i	$-0.655043\pi$
$359$	4.35804	−	30.3108i	0.230009	−	1.59975i	0.698057	−	0.716042i	$-0.254048\pi$
$360$	2.27168	−	2.62166i	0.119728	−	0.138174i
$361$	−1.48219	+	3.24554i	−0.0780100	+	0.170818i
$362$	−3.15563	−	2.02800i	−0.165856	−	0.106589i
$363$	4.42005	+	30.7421i	0.231992	+	1.61354i
$364$	5.39025	−	3.46411i	0.282526	−	0.181568i
$365$	−13.1750	−	15.2047i	−0.689610	−	0.795852i
$366$	6.69958	−	1.96718i	0.350193	−	0.102826i
$367$	26.3500			1.37546			0.687730	−	0.725966i	$-0.258607\pi$
$367$	26.3500			1.37546			0.687730	+	0.725966i	$0.258607\pi$
$368$	3.51138	+	3.26653i	0.183043	+	0.170279i
$369$	5.83993			0.304015
$370$	3.09776	−	0.909583i	0.161045	−	0.0472870i
$371$	4.39771	+	5.07522i	0.228318	+	0.263492i
$372$	0.240729	−	0.154707i	0.0124812	−	0.00802118i
$373$	4.35061	+	30.2592i	0.225266	+	1.56676i	0.717664	+	0.696390i	$0.245212\pi$
$373$	4.35061	+	30.2592i	0.225266	+	1.56676i	−0.492397	+	0.870370i	$0.663879\pi$
$374$	0.980506	+	0.630133i	0.0507008	+	0.0325834i
$375$	3.38800	−	7.41868i	0.174955	−	0.383099i
$376$	4.45163	−	5.13746i	0.229575	−	0.264944i
$377$	4.34754	−	30.2378i	0.223910	−	1.55733i
$378$	−2.33644	−	5.11610i	−0.120174	−	0.263144i
$379$	2.82385	+	0.829158i	0.145052	+	0.0425910i	0.353452	−	0.935453i	$-0.385008\pi$
$379$	2.82385	+	0.829158i	0.145052	+	0.0425910i	−0.208401	+	0.978044i	$0.566826\pi$
$380$	−10.5248	−	3.09037i	−0.539912	−	0.158532i
$381$	4.74944	+	10.3998i	0.243321	+	0.532799i
$382$	0.926655	−	6.44502i	0.0474118	−	0.329756i
$383$	−1.94700	+	2.24696i	−0.0994870	+	0.114814i	−0.803310	−	0.595562i	$-0.796930\pi$
$383$	−1.94700	+	2.24696i	−0.0994870	+	0.114814i	0.703823	+	0.710376i	$0.251475\pi$
$384$	−0.550746	+	1.20596i	−0.0281051	+	0.0615416i
$385$	13.7827	+	8.85762i	0.702433	+	0.451426i
$386$	−2.23527	−	15.5467i	−0.113772	−	0.791305i
$387$	−1.60855	+	1.03375i	−0.0817671	+	0.0525485i
$388$	−4.71802	−	5.44488i	−0.239521	−	0.276422i
$389$	−5.64916	+	1.65874i	−0.286424	+	0.0841016i	−0.421789	−	0.906694i	$-0.638598\pi$
$389$	−5.64916	+	1.65874i	−0.286424	+	0.0841016i	0.135365	+	0.990796i	$0.456779\pi$
$390$	23.7199			1.20110
$391$	0.741540	−	0.598072i	0.0375013	−	0.0302458i
$392$	1.00000			0.0505076
$393$	7.76465	−	2.27991i	0.391675	−	0.115006i
$394$	−13.2632	−	15.3066i	−0.668191	−	0.771134i
$395$	15.7812	−	10.1420i	0.794039	−	0.510298i
$396$	−1.03737	−	7.21506i	−0.0521298	−	0.362571i
$397$	15.2088	+	9.77411i	0.763309	+	0.490549i	0.863456	−	0.504424i	$-0.168295\pi$
$397$	15.2088	+	9.77411i	0.763309	+	0.490549i	−0.100147	+	0.994973i	$0.531931\pi$
$398$	−5.23137	+	11.4551i	−0.262225	+	0.574193i
$399$	−3.41059	+	3.93603i	−0.170743	+	0.197048i
$400$	−0.398043	+	2.76845i	−0.0199021	+	0.138422i
$401$	−0.724769	−	1.58702i	−0.0361932	−	0.0792521i	0.890672	−	0.454647i	$-0.150234\pi$
$401$	−0.724769	−	1.58702i	−0.0361932	−	0.0792521i	−0.926865	+	0.375395i	$0.877507\pi$
$402$	13.8043	+	4.05330i	0.688494	+	0.202160i
$403$	−1.32695	−	0.389629i	−0.0661003	−	0.0194088i
$404$	6.55867	+	14.3615i	0.326306	+	0.714511i
$405$	1.48210	−	10.3082i	0.0736462	−	0.512220i
$406$	3.12220	−	3.60321i	0.154952	−	0.178824i
$407$	2.81821	−	6.17101i	0.139693	−	0.305886i
$408$	0.221550	+	0.142382i	0.0109684	+	0.00704895i
$409$	−3.98081	−	27.6872i	−0.196839	−	1.36904i	−0.813386	−	0.581724i	$-0.802378\pi$
$409$	−3.98081	−	27.6872i	−0.196839	−	1.36904i	0.616547	−	0.787318i	$-0.288531\pi$
$410$	−11.0423	+	7.09645i	−0.545340	+	0.350469i
$411$	−7.35369	−	8.48662i	−0.362731	−	0.418614i
$412$	−12.1753	+	3.57500i	−0.599836	+	0.176128i
$413$	−9.87197			−0.485768
$414$	−5.86377	−	1.05546i	−0.288188	−	0.0518729i
$415$	−17.9004			−0.878696
$416$	6.14786	−	1.80517i	0.301424	−	0.0885060i
$417$	2.35619	+	2.71919i	0.115383	+	0.133159i
$418$	−19.3903	+	12.4614i	−0.948412	+	0.609507i
$419$	3.30300	+	22.9729i	0.161362	+	1.12230i	0.896069	+	0.443915i	$0.146411\pi$
$419$	3.30300	+	22.9729i	0.161362	+	1.12230i	−0.734707	+	0.678385i	$0.762680\pi$
$420$	3.11428	+	2.00142i	0.151961	+	0.0976595i
$421$	3.33348	−	7.29930i	0.162464	−	0.355746i	−0.810840	−	0.585269i	$-0.800989\pi$
$421$	3.33348	−	7.29930i	0.162464	−	0.355746i	0.973303	+	0.229522i	$0.0737164\pi$
$422$	4.16956	−	4.81192i	0.202971	−	0.234241i
$423$	−1.20187	+	8.35919i	−0.0584369	+	0.406438i
$424$	2.78971	+	6.10862i	0.135480	+	0.296661i
$425$	0.533087	+	0.156528i	0.0258585	+	0.00759275i
$426$	19.4686	+	5.71650i	0.943258	+	0.276965i
$427$	−2.18786	−	4.79074i	−0.105878	−	0.231840i
$428$	−2.20573	+	15.3412i	−0.106618	+	0.741543i
$429$	32.6397	−	37.6683i	1.57586	−	1.81864i
$430$	1.78531	−	3.90929i	0.0860954	−	0.188523i
$431$	−28.8096	−	18.5148i	−1.38771	−	0.891825i	−0.388151	−	0.921596i	$-0.626886\pi$
$431$	−28.8096	−	18.5148i	−1.38771	−	0.891825i	−0.999557	+	0.0297704i	$0.990522\pi$
$432$	−0.800430	−	5.56711i	−0.0385107	−	0.267848i
$433$	−4.77402	+	3.06808i	−0.229425	+	0.147442i	−0.650303	−	0.759675i	$-0.725358\pi$
$433$	−4.77402	+	3.06808i	−0.229425	+	0.147442i	0.420879	+	0.907117i	$0.361722\pi$
$434$	−0.141345	−	0.163121i	−0.00678478	−	0.00783006i
$435$	16.9349	−	4.97254i	0.811968	−	0.238415i
$436$	−10.8662			−0.520396
$437$	4.66668	+	18.2526i	0.223238	+	0.873142i
$438$	−9.55231			−0.456427
$439$	−13.5616	+	3.98206i	−0.647261	+	0.190053i	−0.588854	−	0.808240i	$-0.700421\pi$
$439$	−13.5616	+	3.98206i	−0.647261	+	0.190053i	−0.0584078	+	0.998293i	$0.518602\pi$
$440$	10.7289	+	12.3819i	0.511482	+	0.590282i
$441$	−1.04511	+	0.671654i	−0.0497673	+	0.0319835i
$442$	−0.181138	−	1.25984i	−0.00861585	−	0.0599245i
$443$	−11.8529	−	7.61738i	−0.563147	−	0.361912i	0.227884	−	0.973688i	$-0.426819\pi$
$443$	−11.8529	−	7.61738i	−0.563147	−	0.361912i	−0.791031	+	0.611776i	$0.790456\pi$
$444$	0.636788	−	1.39437i	0.0302206	−	0.0661739i
$445$	−1.14320	+	1.31932i	−0.0541928	+	0.0625418i
$446$	−1.78794	+	12.4354i	−0.0846615	+	0.588833i
$447$	9.36265	+	20.5013i	0.442838	+	0.969681i
$448$	0.959493	+	0.281733i	0.0453318	+	0.0133106i
$449$	23.3607	+	6.85933i	1.10246	+	0.323712i	0.781830	−	0.623492i	$-0.214287\pi$
$449$	23.3607	+	6.85933i	1.10246	+	0.323712i	0.320631	+	0.947204i	$0.396105\pi$
$450$	−1.44344	−	3.16069i	−0.0680444	−	0.148996i
$451$	−3.92525	+	27.3007i	−0.184833	+	1.28554i
$452$	4.51030	−	5.20516i	0.212147	−	0.244830i
$453$	−8.34133	+	18.2650i	−0.391910	+	0.858163i
$454$	−7.36179	−	4.73113i	−0.345506	−	0.222043i
$455$	−2.54621	−	17.7093i	−0.119368	−	0.830223i
$456$	−4.38134	+	2.81572i	−0.205175	+	0.131858i
$457$	14.2973	+	16.5000i	0.668799	+	0.771836i	0.984188	−	0.177127i	$-0.0566803\pi$
$457$	14.2973	+	16.5000i	0.668799	+	0.771836i	−0.315389	+	0.948963i	$0.602135\pi$
$458$	4.46806	−	1.31194i	0.208779	−	0.0613030i
$459$	−1.11725			−0.0521487
$460$	12.3699	−	5.12973i	0.576751	−	0.239175i
$461$	18.4447			0.859053			0.429527	−	0.903054i	$-0.358680\pi$
$461$	18.4447			0.859053			0.429527	+	0.903054i	$0.358680\pi$
$462$	7.46375	−	2.19156i	0.347245	−	0.101960i
$463$	−2.39258	−	2.76118i	−0.111193	−	0.128323i	0.697425	−	0.716658i	$-0.254329\pi$
$463$	−2.39258	−	2.76118i	−0.111193	−	0.128323i	−0.808617	+	0.588335i	$0.799784\pi$
$464$	4.01087	−	2.57763i	0.186200	−	0.119663i
$465$	−0.113714	−	0.790895i	−0.00527334	−	0.0366769i
$466$	−18.7320	−	12.0383i	−0.867741	−	0.557664i
$467$	−3.39757	+	7.43965i	−0.157221	+	0.344266i	−0.971807	−	0.235776i	$-0.924237\pi$
$467$	−3.39757	+	7.43965i	−0.157221	+	0.344266i	0.814586	+	0.580042i	$0.196964\pi$
$468$	−5.21276	+	6.01585i	−0.240960	+	0.278083i
$469$	1.54437	−	10.7414i	0.0713126	−	0.495990i
$470$	−7.88523	−	17.2662i	−0.363718	−	0.796432i
$471$	−21.6329	−	6.35199i	−0.996791	−	0.292684i
$472$	−9.47208	−	2.78125i	−0.435988	−	0.128018i
$473$	−3.75145	−	8.21454i	−0.172492	−	0.377705i
$474$	1.26757	−	8.81613i	0.0582213	−	0.404938i
$475$	−7.19515	+	8.30365i	−0.330136	+	0.380998i
$476$	0.0825199	−	0.180693i	0.00378229	−	0.00828207i
$477$	−7.01844	−	4.51048i	−0.321352	−	0.206521i
$478$	2.24421	+	15.6088i	0.102648	+	0.713932i
$479$	7.75823	−	4.98591i	0.354483	−	0.227812i	−0.351264	−	0.936276i	$-0.614248\pi$
$479$	7.75823	−	4.98591i	0.354483	−	0.227812i	0.705747	+	0.708464i	$0.250612\pi$
$480$	2.42426	+	2.79775i	0.110652	+	0.127699i
$481$	−7.10833	+	2.08720i	−0.324112	+	0.0951679i
$482$	24.6528			1.12290
$483$	0.224332	−	6.35422i	0.0102075	−	0.289127i
$484$	23.4265			1.06484
$485$	−19.3025	+	5.66773i	−0.876482	+	0.257358i
$486$	7.81147	+	9.01491i	0.354335	+	0.408925i
$487$	32.3306	−	20.7776i	1.46504	−	0.941524i	0.466671	−	0.884431i	$-0.345453\pi$
$487$	32.3306	−	20.7776i	1.46504	−	0.941524i	0.998369	−	0.0570925i	$-0.0181830\pi$
$488$	−0.749527	−	5.21308i	−0.0339295	−	0.235985i
$489$	21.5398	+	13.8428i	0.974065	+	0.625993i
$490$	1.15996	−	2.53996i	0.0524017	−	0.114744i
$491$	−2.61955	+	3.02312i	−0.118219	+	0.136432i	−0.811774	−	0.583972i	$-0.801498\pi$
$491$	−2.61955	+	3.02312i	−0.118219	+	0.136432i	0.693555	+	0.720403i	$0.256043\pi$
$492$	−0.886931	+	6.16874i	−0.0399859	+	0.278108i
$493$	−0.393432	−	0.861497i	−0.0177193	−	0.0387999i
$494$	24.1510	+	7.09138i	1.08661	+	0.319056i
$495$	−19.5293	−	5.73432i	−0.877777	−	0.257738i
$496$	−0.0896632	−	0.196335i	−0.00402599	−	0.00881570i
$497$	2.17808	−	15.1489i	0.0977005	−	0.679522i
$498$	−5.56569	+	6.42315i	−0.249404	+	0.287828i
$499$	8.44574	−	18.4936i	0.378083	−	0.827887i	−0.620947	−	0.783853i	$-0.713252\pi$
$499$	8.44574	−	18.4936i	0.378083	−	0.827887i	0.999030	−	0.0440340i	$-0.0140210\pi$
$500$	−5.17510	−	3.32584i	−0.231438	−	0.148736i
$501$	4.54522	+	31.6127i	0.203065	+	1.41235i
$502$	−1.90255	+	1.22269i	−0.0849148	+	0.0545714i
$503$	−6.16118	−	7.11038i	−0.274713	−	0.317036i	0.601581	−	0.798812i	$-0.294538\pi$
$503$	−6.16118	−	7.11038i	−0.274713	−	0.317036i	−0.876295	+	0.481775i	$0.839992\pi$
$504$	−1.19201	+	0.350005i	−0.0530962	+	0.0155904i
$505$	44.0854			1.96178
$506$	8.87537	−	26.7028i	0.394558	−	1.18708i
$507$	−37.1943			−1.65186
$508$	8.27434	−	2.42957i	0.367115	−	0.107795i
$509$	−27.7296	−	32.0017i	−1.22909	−	1.41845i	−0.875616	−	0.483008i	$-0.839544\pi$
$509$	−27.7296	−	32.0017i	−1.22909	−	1.41845i	−0.353479	−	0.935443i	$-0.615001\pi$
$510$	0.618634	−	0.397572i	0.0273936	−	0.0176048i
$511$	1.02539	+	7.13175i	0.0453606	+	0.315490i
$512$	0.841254	+	0.540641i	0.0371785	+	0.0238932i
$513$	9.17840	−	20.0979i	0.405236	−	0.887343i
$514$	6.98543	−	8.06162i	0.308114	−	0.355583i
$515$	−5.04256	+	35.0718i	−0.222202	+	1.54545i
$516$	−0.847660	−	1.85612i	−0.0373161	−	0.0817110i
$517$	−38.2700	−	11.2371i	−1.68311	−	0.494207i
$518$	−1.10939	−	0.325747i	−0.0487440	−	0.0143125i
$519$	11.7046	+	25.6295i	0.513775	+	1.12501i
$520$	2.54621	−	17.7093i	0.111659	−	0.776603i
$521$	−16.7770	+	19.3617i	−0.735016	+	0.848253i	−0.993027	−	0.117888i	$-0.962387\pi$
$521$	−16.7770	+	19.3617i	−0.735016	+	0.848253i	0.258011	+	0.966142i	$0.416933\pi$
$522$	−2.46054	+	5.38783i	−0.107695	+	0.235819i
$523$	−3.39620	−	2.18260i	−0.148505	−	0.0954386i	0.464278	−	0.885689i	$-0.346314\pi$
$523$	−3.39620	−	2.18260i	−0.148505	−	0.0954386i	−0.612783	+	0.790251i	$0.709950\pi$
$524$	−0.868683	−	6.04183i	−0.0379486	−	0.263938i
$525$	3.11943	−	2.00474i	0.136143	−	0.0874939i
$526$	−13.9644	−	16.1158i	−0.608878	−	0.702682i
$527$	−0.0411387	+	0.0120794i	−0.00179203	+	0.000526187i
$528$	7.77885			0.338531
$529$	−18.4237	−	13.7683i	−0.801033	−	0.598621i
$530$	18.7516			0.814518
$531$	11.7674	−	3.45523i	0.510663	−	0.149944i
$532$	2.57253	+	2.96886i	0.111533	+	0.128716i
$533$	25.3385	−	16.2840i	1.09753	−	0.705340i
$534$	0.117959	+	0.820421i	0.00510457	+	0.0355031i
$535$	36.4074	+	23.3976i	1.57403	+	1.01157i
$536$	4.50801	−	9.87116i	0.194716	−	0.426369i
$537$	4.43170	−	5.11446i	0.191242	−	0.220705i
$538$	−0.659385	+	4.58613i	−0.0284281	+	0.197722i
$539$	−2.43741	−	5.33719i	−0.104987	−	0.229889i
$540$	−15.0687	−	4.42458i	−0.648455	−	0.190403i
$541$	12.0943	+	3.55121i	0.519975	+	0.152678i	0.531180	−	0.847259i	$-0.321749\pi$
$541$	12.0943	+	3.55121i	0.519975	+	0.152678i	−0.0112053	+	0.999937i	$0.503567\pi$
$542$	5.38144	+	11.7837i	0.231153	+	0.506154i
$543$	−0.707746	+	4.92248i	−0.0303723	+	0.211244i
$544$	0.130085	−	0.150126i	0.00557733	−	0.00643658i
$545$	−12.6044	+	27.5997i	−0.539912	+	1.18224i
$546$	−7.14625	−	4.59261i	−0.305831	−	0.196546i
$547$	0.709975	+	4.93799i	0.0303563	+	0.211133i	0.999354	−	0.0359366i	$-0.0114414\pi$
$547$	0.709975	+	4.93799i	0.0303563	+	0.211133i	−0.968998	+	0.247070i	$0.920532\pi$
$548$	−7.12549	+	4.57927i	−0.304386	+	0.195617i
$549$	4.28472	+	4.94483i	0.182868	+	0.211040i
$550$	15.7459	−	4.62342i	0.671408	−	0.197143i
$551$	18.7294			0.797897
$552$	2.00544	−	6.03363i	0.0853570	−	0.256808i
$553$	−6.71819			−0.285686
$554$	11.8221	−	3.47129i	0.502274	−	0.147481i
$555$	−2.80300	−	3.23483i	−0.118981	−	0.137311i
$556$	2.28307	−	1.46724i	0.0968239	−	0.0622250i
$557$	−1.68049	−	11.6881i	−0.0712046	−	0.495239i	−0.993950	−	0.109830i	$-0.964969\pi$
$557$	−1.68049	−	11.6881i	−0.0712046	−	0.495239i	0.922746	−	0.385409i	$-0.125940\pi$
$558$	0.225577	+	0.144970i	0.00954945	+	0.00613706i
$559$	−4.09671	+	8.97054i	−0.173272	+	0.379413i
$560$	1.82857	−	2.11028i	0.0772710	−	0.0891755i
$561$	0.219909	−	1.52950i	0.00928455	−	0.0645755i
$562$	8.87838	+	19.4409i	0.374512	+	0.820066i
$563$	−24.0881	−	7.07291i	−1.01519	−	0.298088i	−0.268517	−	0.963275i	$-0.586533\pi$
$563$	−24.0881	−	7.07291i	−1.01519	−	0.298088i	−0.746677	+	0.665187i	$0.768352\pi$
$564$	−8.64731	−	2.53908i	−0.364117	−	0.106915i
$565$	−7.98914	−	17.4938i	−0.336106	−	0.735969i
$566$	3.00781	−	20.9198i	0.126428	−	0.879323i
$567$	−2.44239	+	2.81867i	−0.102571	+	0.118373i
$568$	6.35780	−	13.9216i	0.266767	−	0.584139i
$569$	−16.8743	−	10.8444i	−0.707407	−	0.454623i	0.136829	−	0.990595i	$-0.456309\pi$
$569$	−16.8743	−	10.8444i	−0.707407	−	0.454623i	−0.844236	+	0.535972i	$0.819945\pi$
$570$	2.06963	+	14.3946i	0.0866871	+	0.602922i
$571$	26.7369	−	17.1827i	1.11890	−	0.719075i	0.155687	−	0.987806i	$-0.450241\pi$
$571$	26.7369	−	17.1827i	1.11890	−	0.719075i	0.963215	+	0.268731i	$0.0866044\pi$
$572$	−24.6194	−	28.4123i	−1.02939	−	1.18798i
$573$	−8.28282	+	2.43206i	−0.346020	+	0.101601i
$574$	4.70079			0.196207
$575$	0.473263	−	13.4052i	0.0197364	−	0.559035i
$576$	−1.24233			−0.0517637
$577$	−19.1448	+	5.62143i	−0.797010	+	0.234023i	−0.654789	−	0.755812i	$-0.727242\pi$
$577$	−19.1448	+	5.62143i	−0.797010	+	0.234023i	−0.142221	+	0.989835i	$0.545424\pi$
$578$	11.1068	+	12.8179i	0.461982	+	0.533155i
$579$	−17.5177	+	11.2579i	−0.728009	+	0.467863i
$580$	−1.89462	−	13.1774i	−0.0786700	−	0.547162i
$581$	5.39297	+	3.46585i	0.223738	+	0.143788i
$582$	−3.96791	+	8.68851i	−0.164475	+	0.360150i
$583$	25.8032	−	29.7784i	1.06866	−	1.23330i
$584$	−1.02539	+	7.13175i	−0.0424310	+	0.295114i
$585$	9.23342	+	20.2184i	0.381755	+	0.835927i
$586$	20.2747	+	5.95318i	0.837538	+	0.245923i
$587$	−24.0674	−	7.06684i	−0.993370	−	0.291680i	−0.255637	−	0.966773i	$-0.582285\pi$
$587$	−24.0674	−	7.06684i	−0.993370	−	0.291680i	−0.737733	+	0.675093i	$0.764103\pi$
$588$	−0.550746	−	1.20596i	−0.0227124	−	0.0497331i
$589$	0.120668	−	0.839267i	0.00497205	−	0.0345814i
$590$	−18.0515	+	20.8326i	−0.743170	+	0.857664i
$591$	−11.1545	+	24.4250i	−0.458836	+	1.00471i
$592$	−0.972682	−	0.625105i	−0.0399770	−	0.0256916i
$593$	−4.71520	−	32.7949i	−0.193630	−	1.34673i	−0.822300	−	0.569054i	$-0.807309\pi$
$593$	−4.71520	−	32.7949i	−0.193630	−	1.34673i	0.628670	−	0.777672i	$-0.283600\pi$
$594$	−27.7617	+	17.8414i	−1.13908	+	0.732041i
$595$	−0.363234	−	0.419195i	−0.0148912	−	0.0171853i
$596$	16.3113	−	4.78944i	0.668139	−	0.196183i
$597$	16.6956			0.683306
$598$	−28.3849	+	11.7711i	−1.16075	+	0.481354i
$599$	−13.4456			−0.549373			−0.274686	−	0.961534i	$-0.588574\pi$
$599$	−13.4456			−0.549373			−0.274686	+	0.961534i	$0.588574\pi$
$600$	3.55787	−	1.04469i	0.145250	−	0.0426491i
$601$	9.94749	+	11.4800i	0.405767	+	0.468280i	0.921449	−	0.388501i	$-0.127007\pi$
$601$	9.94749	+	11.4800i	0.405767	+	0.468280i	−0.515682	+	0.856780i	$0.672461\pi$
$602$	−1.29478	+	0.832107i	−0.0527715	+	0.0339142i
$603$	1.91862	+	13.3443i	0.0781323	+	0.543422i
$604$	12.7412	+	8.18829i	0.518433	+	0.333177i
$605$	27.1739	−	59.5025i	1.10478	−	2.41912i
$606$	13.7073	−	15.8190i	0.556820	−	0.642605i
$607$	1.74600	−	12.1437i	0.0708680	−	0.492898i	−0.923216	−	0.384282i	$-0.874449\pi$
$607$	1.74600	−	12.1437i	0.0708680	−	0.492898i	0.994084	−	0.108616i	$-0.0346419\pi$
$608$	1.63190	+	3.57336i	0.0661823	+	0.144919i
$609$	−6.06488	−	1.78081i	−0.245761	−	0.0721620i
$610$	−14.1104	−	4.14320i	−0.571315	−	0.167753i
$611$	18.0940	+	39.6204i	0.732006	+	1.60287i
$612$	−0.0351207	+	0.244270i	−0.00141967	+	0.00987403i
$613$	16.4947	−	19.0360i	0.666217	−	0.768855i	−0.317563	−	0.948237i	$-0.602864\pi$
$613$	16.4947	−	19.0360i	0.666217	−	0.768855i	0.983779	+	0.179382i	$0.0574099\pi$
$614$	8.28690	−	18.1458i	0.334432	−	0.732304i
$615$	14.6396	+	9.40827i	0.590324	+	0.379378i
$616$	−0.835020	−	5.80769i	−0.0336439	−	0.233999i
$617$	−7.45007	+	4.78787i	−0.299928	+	0.192752i	−0.681946	−	0.731403i	$-0.738866\pi$
$617$	−7.45007	+	4.78787i	−0.299928	+	0.192752i	0.382017	+	0.924155i	$0.375230\pi$
$618$	11.0168	+	12.7141i	0.443162	+	0.511437i
$619$	−15.1572	+	4.45056i	−0.609220	+	0.178883i	−0.571768	−	0.820415i	$-0.693742\pi$
$619$	−15.1572	+	4.45056i	−0.609220	+	0.178883i	−0.0374521	+	0.999298i	$0.511924\pi$
$620$	−0.602689			−0.0242046
$621$	6.68144	+	26.1329i	0.268117	+	1.04868i
$622$	4.42237			0.177321
$623$	0.599864	−	0.176136i	0.0240330	−	0.00705674i
$624$	−5.56288	−	6.41991i	−0.222694	−	0.257002i
$625$	−26.2150	+	16.8474i	−1.04860	+	0.673895i
$626$	3.54253	+	24.6389i	0.141588	+	0.984767i
$627$	25.7071	+	16.5210i	1.02664	+	0.659784i
$628$	−7.06457	+	15.4693i	−0.281907	+	0.617291i
$629$	−0.150407	+	0.173579i	−0.00599714	+	0.00692107i
$630$	−0.493683	+	3.43364i	−0.0196688	+	0.136800i
$631$	−8.03784	−	17.6004i	−0.319981	−	0.700661i	0.679473	−	0.733701i	$-0.262209\pi$
$631$	−8.03784	−	17.6004i	−0.319981	−	0.700661i	−0.999454	+	0.0330394i	$0.989481\pi$
$632$	−6.44605	−	1.89273i	−0.256410	−	0.0752888i
$633$	−8.09937	−	2.37819i	−0.321921	−	0.0945246i
$634$	13.9312	+	30.5052i	0.553280	+	1.21151i
$635$	3.42691	−	23.8347i	0.135993	−	0.945852i
$636$	5.83035	−	6.72859i	0.231189	−	0.266806i
$637$	−2.66173	+	5.82838i	−0.105462	+	0.230929i
$638$	−23.5334	−	15.1240i	−0.931697	−	0.598765i
$639$	2.70590	+	18.8199i	0.107044	+	0.744505i
$640$	2.34903	−	1.50963i	0.0928535	−	0.0596733i
$641$	−23.2660	−	26.8504i	−0.918951	−	1.06053i	−0.997972	−	0.0636528i	$-0.979725\pi$
$641$	−23.2660	−	26.8504i	−0.918951	−	1.06053i	0.0790213	−	0.996873i	$-0.474820\pi$
$642$	19.7157	−	5.78905i	0.778117	−	0.228476i
$643$	29.6484			1.16922			0.584610	−	0.811315i	$-0.301248\pi$
$643$	29.6484			1.16922			0.584610	+	0.811315i	$0.301248\pi$
$644$	−4.71998	−	0.849580i	−0.185993	−	0.0334781i
$645$	−5.69772			−0.224347
$646$	0.748738	−	0.219849i	0.0294587	−	0.00864986i
$647$	2.09014	+	2.41215i	0.0821719	+	0.0948315i	0.795347	−	0.606155i	$-0.207289\pi$
$647$	2.09014	+	2.41215i	0.0821719	+	0.0948315i	−0.713175	+	0.700986i	$0.752743\pi$
$648$	−3.13757	+	2.01639i	−0.123255	+	0.0792113i
$649$	8.24329	+	57.3333i	0.323577	+	2.25053i
$650$	−15.0761	−	9.68882i	−0.591333	−	0.380027i
$651$	−0.118873	+	0.260295i	−0.00465900	+	0.0102018i
$652$	12.6472	−	14.5957i	0.495304	−	0.571611i
$653$	1.07732	−	7.49295i	0.0421589	−	0.293222i	−0.957824	−	0.287356i	$-0.907224\pi$
$653$	1.07732	−	7.49295i	0.0421589	−	0.293222i	0.999983	−	0.00586590i	$-0.00186719\pi$
$654$	5.98451	+	13.1042i	0.234013	+	0.512417i
$655$	−16.3536	−	4.80186i	−0.638990	−	0.187624i
$656$	4.51038	+	1.32437i	0.176101	+	0.0517078i
$657$	−3.71842	−	8.14220i	−0.145069	−	0.317657i
$658$	−0.967433	+	6.72864i	−0.0377144	+	0.262310i
$659$	−25.7575	+	29.7257i	−1.00337	+	1.15795i	−0.0159408	+	0.999873i	$0.505074\pi$
$659$	−25.7575	+	29.7257i	−1.00337	+	1.15795i	−0.987427	+	0.158075i	$0.949471\pi$
$660$	9.02317	−	19.7580i	0.351226	−	0.769079i
$661$	8.92252	+	5.73415i	0.347046	+	0.223033i	0.702538	−	0.711647i	$-0.252050\pi$
$661$	8.92252	+	5.73415i	0.347046	+	0.223033i	−0.355492	+	0.934679i	$0.615687\pi$
$662$	−0.383230	−	2.66542i	−0.0148947	−	0.103595i
$663$	−1.41956	+	0.912298i	−0.0551312	+	0.0354307i
$664$	4.19807	+	4.84483i	0.162917	+	0.188016i
$665$	10.5248	−	3.09037i	0.408135	−	0.119839i
$666$	1.43642			0.0556600
$667$	−17.7979	+	14.3545i	−0.689138	+	0.555809i
$668$	24.0899			0.932068
$669$	15.9814	−	4.69255i	0.617875	−	0.181424i
$670$	−19.8433	−	22.9003i	−0.766612	−	0.884717i
$671$	−25.9963	+	16.7068i	−1.00357	+	0.644958i
$672$	−0.188677	−	1.31228i	−0.00727837	−	0.0506222i
$673$	−31.6207	−	20.3214i	−1.21889	−	0.783333i	−0.236765	−	0.971567i	$-0.576087\pi$
$673$	−31.6207	−	20.3214i	−1.21889	−	0.783333i	−0.982124	+	0.188234i	$0.939724\pi$
$674$	−4.08173	+	8.93774i	−0.157222	+	0.344269i
$675$	−10.3015	+	11.8886i	−0.396506	+	0.457592i
$676$	−3.99262	+	27.7693i	−0.153562	+	1.06805i
$677$	19.0621	+	41.7402i	0.732617	+	1.60421i	0.795331	+	0.606176i	$0.207297\pi$
$677$	19.0621	+	41.7402i	0.732617	+	1.60421i	−0.0627139	+	0.998032i	$0.519976\pi$
$678$	−8.76127	−	2.57254i	−0.336474	−	0.0987978i
$679$	6.91278	+	2.02977i	0.265288	+	0.0778956i
$680$	−0.230420	−	0.504550i	−0.00883621	−	0.0193486i
$681$	−1.65111	+	11.4837i	−0.0632706	+	0.440057i
$682$	−0.829330	+	0.957098i	−0.0317567	+	0.0366492i
$683$	−15.6143	+	34.1905i	−0.597464	+	1.30826i	0.333361	+	0.942799i	$0.391817\pi$
$683$	−15.6143	+	34.1905i	−0.597464	+	1.30826i	−0.930825	+	0.365465i	$0.880910\pi$
$684$	−4.10558	−	2.63850i	−0.156981	−	0.100886i
$685$	3.36589	+	23.4103i	0.128604	+	0.894460i
$686$	−0.841254	+	0.540641i	−0.0321192	+	0.0206418i
$687$	−4.04292	−	4.66578i	−0.154247	−	0.178010i
$688$	−1.47677	+	0.433618i	−0.0563013	+	0.0165315i
$689$	−43.0288			−1.63927
$690$	−12.9990	−	12.0925i	−0.494862	−	0.460354i
$691$	−1.77610			−0.0675659			−0.0337829	−	0.999429i	$-0.510755\pi$
$691$	−1.77610			−0.0675659			−0.0337829	+	0.999429i	$0.510755\pi$
$692$	20.3914	−	5.98746i	0.775165	−	0.227609i
$693$	4.77345	+	5.50885i	0.181328	+	0.209264i
$694$	18.0674	−	11.6112i	0.685827	−	0.440754i
$695$	−1.07846	−	7.50087i	−0.0409084	−	0.284524i
$696$	−5.31749	−	3.41735i	−0.201559	−	0.129534i
$697$	0.387909	−	0.849402i	0.0146931	−	0.0321734i
$698$	−1.99254	+	2.29952i	−0.0754188	+	0.0870380i
$699$	−4.20122	+	29.2201i	−0.158905	+	1.10521i
$700$	−1.16188	−	2.54417i	−0.0439150	−	0.0961604i
$701$	12.6224	+	3.70627i	0.476741	+	0.139984i	0.511271	−	0.859420i	$-0.329175\pi$
$701$	12.6224	+	3.70627i	0.476741	+	0.139984i	−0.0345293	+	0.999404i	$0.510993\pi$
$702$	34.5778	+	10.1530i	1.30505	+	0.383199i
$703$	−1.88685	−	4.13163i	−0.0711639	−	0.155827i
$704$	0.835020	−	5.80769i	0.0314710	−	0.218886i
$705$	−16.4797	+	19.0186i	−0.620662	+	0.716282i
$706$	6.43924	−	14.1000i	0.242344	−	0.530659i
$707$	−13.2819	−	8.53577i	−0.499518	−	0.321020i
$708$	1.86261	+	12.9548i	0.0700013	+	0.486870i
$709$	14.3350	−	9.21255i	0.538363	−	0.345985i	−0.243036	−	0.970017i	$-0.578143\pi$
$709$	14.3350	−	9.21255i	0.538363	−	0.345985i	0.781398	+	0.624033i	$0.214507\pi$
$710$	−27.9856	−	32.2971i	−1.05028	−	1.21209i
$711$	8.00812	−	2.35140i	0.300328	−	0.0881842i
$712$	0.625189			0.0234299
$713$	0.528562	+	0.890012i	0.0197948	+	0.0333312i
$714$	−0.263357			−0.00985590
$715$	−100.724	+	29.5752i	−3.76686	+	1.10605i
$716$	−3.34273	−	3.85772i	−0.124924	−	0.144170i
$717$	17.5877	−	11.3029i	0.656826	−	0.422116i
$718$	4.35804	+	30.3108i	0.162641	+	1.13119i
$719$	17.5332	+	11.2679i	0.653878	+	0.420222i	0.825082	−	0.565014i	$-0.191129\pi$
$719$	17.5332	+	11.2679i	0.653878	+	0.420222i	−0.171203	+	0.985236i	$0.554765\pi$
$720$	−1.44105	+	3.15547i	−0.0537049	+	0.117597i
$721$	8.30976	−	9.58997i	0.309471	−	0.357149i
$722$	0.507775	−	3.53166i	0.0188974	−	0.131435i
$723$	−13.5774	−	29.7304i	−0.504949	−	1.10568i
$724$	3.59915	+	1.05681i	0.133761	+	0.0392759i
$725$	−12.7948	−	3.75689i	−0.475186	−	0.139527i
$726$	−12.9021	−	28.2516i	−0.478840	−	1.04851i
$727$	−4.90108	+	34.0878i	−0.181771	+	1.26424i	0.670802	+	0.741637i	$0.265950\pi$
$727$	−4.90108	+	34.0878i	−0.181771	+	1.26424i	−0.852573	+	0.522608i	$0.824959\pi$
$728$	−4.19596	+	4.84239i	−0.155513	+	0.179471i
$729$	11.2176	−	24.5631i	0.415466	−	0.909743i
$730$	16.9250	+	10.8770i	0.626421	+	0.402576i
$731$	0.0435108	+	0.302625i	0.00160931	+	0.0111930i
$732$	−5.87399	+	3.77498i	−0.217109	+	0.139527i
$733$	−20.6597	−	23.8426i	−0.763083	−	0.880645i	0.232684	−	0.972552i	$-0.425249\pi$
$733$	−20.6597	−	23.8426i	−0.763083	−	0.880645i	−0.995768	+	0.0919071i	$0.970704\pi$
$734$	−25.2827	+	7.42366i	−0.933201	+	0.274012i
$735$	−3.70195			−0.136548
$736$	−4.28943	−	2.14494i	−0.158111	−	0.0790635i
$737$	−63.6721			−2.34539
$738$	−5.60337	+	1.64530i	−0.206263	+	0.0605643i
$739$	10.4130	+	12.0172i	0.383048	+	0.442061i	0.914229	−	0.405197i	$-0.132797\pi$
$739$	10.4130	+	12.0172i	0.383048	+	0.442061i	−0.531181	+	0.847258i	$0.678252\pi$
$740$	−2.71602	+	1.74548i	−0.0998427	+	0.0641650i
$741$	−4.74912	−	33.0308i	−0.174463	−	1.21342i
$742$	−5.64942	−	3.63066i	−0.207397	−	0.133286i
$743$	9.56636	−	20.9474i	0.350956	−	0.768486i	−0.649015	−	0.760776i	$-0.724819\pi$
$743$	9.56636	−	20.9474i	0.350956	−	0.768486i	0.999970	−	0.00770975i	$-0.00245411\pi$
$744$	−0.187391	+	0.216261i	−0.00687010	+	0.00792852i
$745$	6.75553	−	46.9858i	0.247504	−	1.72143i
$746$	−12.6994	−	27.8078i	−0.464957	−	1.01811i
$747$	−7.64152	−	2.24375i	−0.279588	−	0.0820946i
$748$	−1.11832	−	0.328368i	−0.0408897	−	0.0120063i
$749$	−6.43849	−	14.0983i	−0.235257	−	0.515141i
$750$	−1.16068	+	8.07268i	−0.0423819	+	0.294773i
$751$	−9.63876	+	11.1237i	−0.351723	+	0.405910i	−0.903850	−	0.427850i	$-0.859271\pi$
$751$	−9.63876	+	11.1237i	−0.351723	+	0.405910i	0.552126	+	0.833760i	$0.313817\pi$
$752$	−2.82392	+	6.18353i	−0.102978	+	0.225490i
$753$	2.52234	+	1.62101i	0.0919193	+	0.0590729i
$754$	4.34754	+	30.2378i	0.158328	+	1.10120i
$755$	35.5773	−	22.8641i	1.29479	−	0.832110i
$756$	3.68317	+	4.25061i	0.133956	+	0.154593i
$757$	23.3289	−	6.84999i	0.847905	−	0.248967i	0.171213	−	0.985234i	$-0.445231\pi$
$757$	23.3289	−	6.84999i	0.847905	−	0.248967i	0.676691	+	0.736267i	$0.263413\pi$
$758$	−2.94307			−0.106897
$759$	−37.0907	+	4.00305i	−1.34631	+	0.145301i
$760$	10.9691			0.397893
$761$	21.7862	−	6.39700i	0.789749	−	0.231891i	0.138106	−	0.990417i	$-0.455898\pi$
$761$	21.7862	−	6.39700i	0.789749	−	0.231891i	0.651642	+	0.758526i	$0.274080\pi$
$762$	−7.48703	−	8.64049i	−0.271226	−	0.313012i
$763$	9.14123	−	5.87471i	0.330935	−	0.212679i
$764$	0.926655	+	6.44502i	0.0335252	+	0.233173i
$765$	0.579698	+	0.372549i	0.0209590	+	0.0134695i
$766$	1.23509	−	2.70447i	0.0446257	−	0.0977166i
$767$	41.4224	−	47.8040i	1.49567	−	1.72610i
$768$	0.188677	−	1.31228i	0.00680830	−	0.0473527i
$769$	−8.78609	−	19.2389i	−0.316835	−	0.693771i	0.682476	−	0.730908i	$-0.260903\pi$
$769$	−8.78609	−	19.2389i	−0.316835	−	0.693771i	−0.999310	+	0.0371374i	$0.988176\pi$
$770$	−15.7199	−	4.61578i	−0.566506	−	0.166341i
$771$	−13.5692	−	3.98428i	−0.488684	−	0.143490i
$772$	6.52473	+	14.2872i	0.234830	+	0.514206i
$773$	−6.65702	+	46.3006i	−0.239436	+	1.66532i	0.415471	+	0.909606i	$0.363617\pi$
$773$	−6.65702	+	46.3006i	−0.239436	+	1.66532i	−0.654908	+	0.755709i	$0.727292\pi$
$774$	1.25215	−	1.44506i	0.0450076	−	0.0519415i
$775$	−0.250780	+	0.549133i	−0.00900830	+	0.0197254i
$776$	6.06091	+	3.89511i	0.217574	+	0.139826i
$777$	0.218154	+	1.51729i	0.00782622	+	0.0544326i
$778$	4.95301	−	3.18311i	0.177574	−	0.114120i
$779$	12.0929	+	13.9560i	0.433274	+	0.500025i
$780$	−22.7591	+	6.68266i	−0.814905	+	0.239278i
$781$	−89.7989			−3.21326
$782$	−0.543006	+	0.782762i	−0.0194178	+	0.0279915i
$783$	26.8154			0.958305
$784$	−0.959493	+	0.281733i	−0.0342676	+	0.0100619i
$785$	31.0967	+	35.8875i	1.10989	+	1.28088i
$786$	−6.80780	+	4.37511i	−0.242826	+	0.156055i
$787$	0.0780650	+	0.542954i	0.00278272	+	0.0193542i	0.991165	−	0.132631i	$-0.0423425\pi$
$787$	0.0780650	+	0.542954i	0.00278272	+	0.0193542i	−0.988383	+	0.151985i	$0.951433\pi$
$788$	17.0383	+	10.9499i	0.606965	+	0.390073i
$789$	−11.7442	+	25.7163i	−0.418106	+	0.915525i
$790$	−12.2846	+	14.1772i	−0.437068	+	0.504403i
$791$	−0.980181	+	6.81731i	−0.0348512	+	0.242396i
$792$	3.02807	+	6.63054i	0.107598	+	0.235606i
$793$	32.3788	+	9.50729i	1.14981	+	0.337614i
$794$	−17.3464	−	5.09337i	−0.615602	−	0.180757i
$795$	−10.3274	−	22.6138i	−0.366274	−	0.802028i
$796$	1.79219	−	12.4649i	0.0635224	−	0.441808i
$797$	17.5574	−	20.2624i	0.621916	−	0.717730i	−0.354154	−	0.935187i	$-0.615231\pi$
$797$	17.5574	−	20.2624i	0.621916	−	0.717730i	0.976070	+	0.217458i	$0.0697764\pi$
$798$	2.16353	−	4.73747i	0.0765881	−	0.167704i
$799$	1.13599	+	0.730056i	0.0401884	+	0.0258275i
$800$	−0.398043	−	2.76845i	−0.0140729	−	0.0978795i
$801$	−0.653393	+	0.419910i	−0.0230865	+	0.0148368i
$802$	1.14253	+	1.31855i	0.0403440	+	0.0465595i
$803$	40.5628	−	11.9103i	1.43143	−	0.420306i
$804$	−14.3870			−0.507392
$805$	−7.63290	+	11.0031i	−0.269024	+	0.387808i
$806$	1.38297			0.0487132
$807$	5.89386	−	1.73059i	0.207474	−	0.0609198i
$808$	−10.3391	−	11.9320i	−0.363728	−	0.419765i
$809$	−0.555429	+	0.356952i	−0.0195278	+	0.0125498i	−0.550368	−	0.834922i	$-0.685513\pi$
$809$	−0.555429	+	0.356952i	−0.0195278	+	0.0125498i	0.530840	+	0.847472i	$0.321876\pi$
$810$	1.48210	+	10.3082i	0.0520757	+	0.362194i
$811$	−0.330893	−	0.212652i	−0.0116192	−	0.00746722i	0.534818	−	0.844967i	$-0.320380\pi$
$811$	−0.330893	−	0.212652i	−0.0116192	−	0.00746722i	−0.546438	+	0.837500i	$0.684016\pi$
$812$	−1.98059	+	4.33688i	−0.0695049	+	0.152195i
$813$	11.2469	−	12.9797i	0.394447	−	0.455216i
$814$	−0.965474	+	6.71502i	−0.0338399	+	0.235361i
$815$	−22.4022	−	49.0539i	−0.784714	−	1.71828i
$816$	−0.252690	−	0.0741963i	−0.00884590	−	0.00259739i
$817$	−5.80128	−	1.70341i	−0.202961	−	0.0595948i
$818$	11.6199	+	25.4441i	0.406282	+	0.889633i
$819$	1.13284	−	7.87908i	0.0395847	−	0.275317i
$820$	8.59570	−	9.91997i	0.300175	−	0.346420i
$821$	−4.38726	+	9.60676i	−0.153116	+	0.335278i	−0.970609	−	0.240660i	$-0.922636\pi$
$821$	−4.38726	+	9.60676i	−0.153116	+	0.335278i	0.817493	+	0.575939i	$0.195363\pi$
$822$	9.44677	+	6.07107i	0.329494	+	0.211753i
$823$	3.45629	+	24.0391i	0.120479	+	0.837949i	0.957015	+	0.290037i	$0.0936678\pi$
$823$	3.45629	+	24.0391i	0.120479	+	0.837949i	−0.836536	+	0.547911i	$0.815423\pi$
$824$	10.6750	−	6.86038i	0.371880	−	0.238993i
$825$	−14.2477	−	16.4427i	−0.496040	−	0.572461i
$826$	9.47208	−	2.78125i	0.329576	−	0.0967722i
$827$	9.48091			0.329684			0.164842	−	0.986320i	$-0.447289\pi$
$827$	9.48091			0.329684			0.164842	+	0.986320i	$0.447289\pi$
$828$	5.92360	−	0.639311i	0.205859	−	0.0222176i
$829$	30.4926			1.05905			0.529526	−	0.848294i	$-0.322370\pi$
$829$	30.4926			1.05905			0.529526	+	0.848294i	$0.322370\pi$
$830$	17.1753	−	5.04312i	0.596163	−	0.175049i
$831$	−10.6972	−	12.3453i	−0.371083	−	0.428253i
$832$	−5.39025	+	3.46411i	−0.186873	+	0.120096i
$833$	0.0282701	+	0.196623i	0.000979500	+	0.00681257i
$834$	−3.02684	−	1.94523i	−0.104811	−	0.0673578i
$835$	27.9434	−	61.1875i	0.967022	−	2.11748i
$836$	15.0941	−	17.4195i	0.522040	−	0.602467i
$837$	0.172765	−	1.20161i	0.00597162	−	0.0415336i
$838$	−9.64142	−	21.1118i	−0.333057	−	0.729294i
$839$	−18.2325	−	5.35355i	−0.629457	−	0.184825i	−0.0485834	−	0.998819i	$-0.515471\pi$
$839$	−18.2325	−	5.35355i	−0.629457	−	0.184825i	−0.580873	+	0.813994i	$0.697289\pi$
$840$	−3.55199	−	1.04296i	−0.122555	−	0.0359855i
$841$	−2.60415	−	5.70228i	−0.0897981	−	0.196630i
$842$	−1.14200	+	7.94278i	−0.0393559	+	0.273726i
$843$	18.5553	−	21.4140i	0.639080	−	0.737538i
$844$	−2.64498	+	5.79171i	−0.0910441	+	0.199359i
$845$	65.9017	+	42.3524i	2.26709	+	1.45697i
$846$	−1.20187	−	8.35919i	−0.0413211	−	0.287395i
$847$	−19.7077	+	12.6653i	−0.677163	+	0.435186i
$848$	−4.39771	−	5.07522i	−0.151018	−	0.174284i
$849$	−26.8850	+	7.89415i	−0.922691	+	0.270927i
$850$	−0.555592			−0.0190567
$851$	4.95957	+	2.48004i	0.170012	+	0.0850146i
$852$	−20.2905			−0.695142
$853$	−20.9963	+	6.16507i	−0.718900	+	0.211088i	−0.620666	−	0.784075i	$-0.713138\pi$
$853$	−20.9963	+	6.16507i	−0.718900	+	0.211088i	−0.0982342	+	0.995163i	$0.531319\pi$
$854$	3.44894	+	3.98029i	0.118020	+	0.136203i
$855$	−11.4640	+	7.36747i	−0.392061	+	0.251962i
$856$	−2.20573	−	15.3412i	−0.0753902	−	0.524350i
$857$	5.17169	+	3.32364i	0.176662	+	0.113533i	0.625983	−	0.779837i	$-0.284698\pi$
$857$	5.17169	+	3.32364i	0.176662	+	0.113533i	−0.449322	+	0.893370i	$0.648334\pi$
$858$	−20.7052	+	45.3381i	−0.706865	+	1.54782i
$859$	−22.1390	+	25.5497i	−0.755372	+	0.871746i	−0.995077	−	0.0991000i	$-0.968404\pi$
$859$	−22.1390	+	25.5497i	−0.755372	+	0.871746i	0.239706	+	0.970846i	$0.422949\pi$
$860$	−0.611621	+	4.25392i	−0.0208561	+	0.145057i
$861$	−2.58894	−	5.66899i	−0.0882308	−	0.193199i
$862$	32.8588	+	9.64821i	1.11917	+	0.328619i
$863$	−30.5789	−	8.97878i	−1.04092	−	0.305641i	−0.283776	−	0.958891i	$-0.591587\pi$
$863$	−30.5789	−	8.97878i	−1.04092	−	0.305641i	−0.757143	+	0.653249i	$0.773405\pi$
$864$	2.33644	+	5.11610i	0.0794874	+	0.174053i
$865$	8.44534	−	58.7386i	0.287150	−	1.99717i
$866$	3.71626	−	4.28880i	0.126284	−	0.145739i
$867$	9.34094	−	20.4538i	0.317235	−	0.694648i
$868$	0.181576	+	0.116692i	0.00616310	+	0.00396078i
$869$	5.60982	+	39.0172i	0.190300	+	1.32357i
$870$	−14.8480	+	9.54224i	−0.503395	+	0.323512i
$871$	45.5338	+	52.5488i	1.54285	+	1.78055i
$872$	10.4260	−	3.06136i	0.353070	−	0.103671i
$873$	−8.95050			−0.302929
$874$	−9.62001	−	16.1985i	−0.325402	−	0.547923i
$875$	6.15166			0.207964
$876$	9.16537	−	2.69120i	0.309669	−	0.0909271i
$877$	21.4235	+	24.7240i	0.723419	+	0.834870i	0.991714	−	0.128467i	$-0.0410057\pi$
$877$	21.4235	+	24.7240i	0.723419	+	0.834870i	−0.268295	+	0.963337i	$0.586460\pi$
$878$	11.8904	−	7.64151i	0.401282	−	0.257888i
$879$	−3.98686	−	27.7292i	−0.134473	−	0.935283i
$880$	−13.7827	−	8.85762i	−0.464616	−	0.298590i
$881$	−4.81957	+	10.5534i	−0.162376	+	0.355553i	−0.973279	−	0.229628i	$-0.926249\pi$
$881$	−4.81957	+	10.5534i	−0.162376	+	0.355553i	0.810903	+	0.585181i	$0.198976\pi$
$882$	0.813552	−	0.938890i	0.0273937	−	0.0316141i
$883$	−3.69461	+	25.6966i	−0.124334	+	0.864759i	0.828223	+	0.560398i	$0.189352\pi$
$883$	−3.69461	+	25.6966i	−0.124334	+	0.864759i	−0.952557	+	0.304361i	$0.901557\pi$
$884$	0.528739	+	1.15778i	0.0177834	+	0.0389402i
$885$	35.0651	+	10.2961i	1.17870	+	0.346098i
$886$	13.5188	+	3.96948i	0.454173	+	0.133357i
$887$	−16.9521	−	37.1199i	−0.569195	−	1.24636i	−0.947225	−	0.320570i	$-0.896125\pi$
$887$	−16.9521	−	37.1199i	−0.569195	−	1.24636i	0.378029	−	0.925794i	$-0.376602\pi$
$888$	−0.218154	+	1.51729i	−0.00732076	+	0.0509170i
$889$	−5.64730	+	6.51733i	−0.189404	+	0.218584i
$890$	0.725195	−	1.58796i	0.0243086	−	0.0532284i
$891$	18.4094	+	11.8310i	0.616738	+	0.396353i
$892$	−1.78794	−	12.4354i	−0.0598647	−	0.416368i
$893$	−22.4651	+	14.4375i	−0.751767	+	0.483131i
$894$	−14.7593	−	17.0331i	−0.493625	−	0.569673i
$895$	−13.6759	+	4.01561i	−0.457135	+	0.134227i
$896$	−1.00000			−0.0334077
$897$	29.8284	+	27.7483i	0.995940	+	0.926490i
$898$	−24.3470			−0.812468
$899$	0.987382	−	0.289921i	0.0329310	−	0.00966942i
$900$	2.27544	+	2.62600i	0.0758480	+	0.0875332i
$901$	−1.12223	+	0.721212i	−0.0373868	+	0.0240270i
$902$	−3.92525	−	27.3007i	−0.130697	−	0.909015i
$903$	1.71659	+	1.10318i	0.0571245	+	0.0367117i
$904$	−2.86114	+	6.26501i	−0.0951600	+	0.208371i
$905$	6.85913	−	7.91586i	0.228005	−	0.263132i
$906$	2.85761	−	19.8751i	0.0949378	−	0.660307i
$907$	−9.68741	−	21.2125i	−0.321665	−	0.704349i	0.677859	−	0.735192i	$-0.262908\pi$
$907$	−9.68741	−	21.2125i	−0.321665	−	0.704349i	−0.999524	+	0.0308433i	$0.990181\pi$
$908$	8.39650	+	2.46543i	0.278648	+	0.0818183i
$909$	18.8197	+	5.52595i	0.624209	+	0.183284i
$910$	7.43235	+	16.2746i	0.246380	+	0.539497i
$911$	3.32186	−	23.1040i	0.110058	−	0.765471i	−0.857802	−	0.513981i	$-0.828170\pi$
$911$	3.32186	−	23.1040i	0.110058	−	0.765471i	0.967860	−	0.251490i	$-0.0809206\pi$
$912$	3.41059	−	3.93603i	0.112936	−	0.130335i
$913$	15.6254	−	34.2148i	0.517124	−	1.13234i
$914$	−18.3667	−	11.8036i	−0.607518	−	0.390428i
$915$	2.77471	+	19.2985i	0.0917291	+	0.637990i
$916$	−3.91746	+	2.51760i	−0.129436	+	0.0831837i
$917$	3.99724	+	4.61306i	0.132001	+	0.152337i
$918$	1.07199	−	0.314765i	0.0353810	−	0.0103888i
$919$	50.5291			1.66680			0.833401	−	0.552669i	$-0.186390\pi$
$919$	50.5291			1.66680			0.833401	+	0.552669i	$0.186390\pi$
$920$	−10.4236	+	8.40695i	−0.343657	+	0.277169i
$921$	−26.4472			−0.871463
$922$	−17.6975	+	5.19646i	−0.582837	+	0.171136i
$923$	64.2179	+	74.1114i	2.11376	+	2.43941i
$924$	−6.54399	+	4.20556i	−0.215281	+	0.138353i
$925$	0.460229	+	3.20096i	0.0151322	+	0.105247i
$926$	3.07358	+	1.97527i	0.101004	+	0.0649113i
$927$	−6.54875	+	14.3398i	−0.215089	+	0.470979i
$928$	−3.12220	+	3.60321i	−0.102491	+	0.118281i
$929$	4.30905	−	29.9701i	0.141375	−	0.983287i	−0.788401	−	0.615162i	$-0.789091\pi$
$929$	4.30905	−	29.9701i	0.141375	−	0.983287i	0.929776	−	0.368125i	$-0.120000\pi$
$930$	0.331928	+	0.726822i	0.0108844	+	0.0238334i
$931$	−3.76924	−	1.10675i	−0.123532	−	0.0362722i
$932$	21.3648	+	6.27326i	0.699826	+	0.205488i
$933$	−2.43560	−	5.33323i	−0.0797380	−	0.174602i
$934$	1.16396	−	8.09550i	0.0380858	−	0.264893i
$935$	−2.13125	+	2.45959i	−0.0696992	+	0.0804372i
$936$	3.30675	−	7.24077i	0.108084	−	0.236672i
$937$	−12.6818	−	8.15013i	−0.414298	−	0.266253i	0.316845	−	0.948477i	$-0.397376\pi$
$937$	−12.6818	−	8.15013i	−0.414298	−	0.266253i	−0.731143	+	0.682224i	$0.761013\pi$
$938$	1.54437	+	10.7414i	0.0504256	+	0.350718i
$939$	27.7626	−	17.8419i	0.905997	−	0.582249i
$940$	12.4303	+	14.3453i	0.405431	+	0.467892i
$941$	−30.1883	+	8.86408i	−0.984110	+	0.288961i	−0.733920	−	0.679236i	$-0.762311\pi$
$941$	−30.1883	+	8.86408i	−0.984110	+	0.288961i	−0.250190	+	0.968197i	$0.580493\pi$
$942$	22.5462			0.734594
$943$	−22.1876	−	3.99370i	−0.722529	−	0.130053i
$944$	9.87197			0.321305
$945$	15.0687	−	4.42458i	0.490186	−	0.143931i
$946$	5.91379	+	6.82488i	0.192274	+	0.221896i
$947$	13.7463	−	8.83418i	0.446693	−	0.287072i	−0.297892	−	0.954600i	$-0.596284\pi$
$947$	13.7463	−	8.83418i	0.446693	−	0.287072i	0.744585	+	0.667527i	$0.232647\pi$
$948$	1.26757	+	8.81613i	0.0411687	+	0.286334i
$949$	−38.8373	−	24.9592i	−1.26071	−	0.810210i
$950$	4.56429	−	9.99440i	0.148085	−	0.324261i
$951$	29.1156	−	33.6012i	0.944137	−	1.08959i
$952$	−0.0282701	+	0.196623i	−0.000916238	+	0.00637258i
$953$	22.7376	+	49.7883i	0.736542	+	1.61280i	0.789161	+	0.614187i	$0.210516\pi$
$953$	22.7376	+	49.7883i	0.736542	+	1.61280i	−0.0526189	+	0.998615i	$0.516757\pi$
$954$	8.00490	+	2.35045i	0.259168	+	0.0760986i
$955$	17.4450	+	5.12231i	0.564507	+	0.165754i
$956$	−6.55083	−	14.3443i	−0.211869	−	0.463928i
$957$	−5.27809	+	36.7099i	−0.170617	+	1.18666i
$958$	−6.03928	+	6.96970i	−0.195120	+	0.225181i
$959$	3.51860	−	7.70466i	0.113622	−	0.248797i
$960$	−3.11428	−	2.00142i	−0.100513	−	0.0645957i
$961$	4.40513	+	30.6384i	0.142101	+	0.988334i
$962$	6.23237	−	4.00530i	0.200940	−	0.129136i
$963$	12.6092	+	14.5518i	0.406325	+	0.468925i
$964$	−23.6542	+	6.94549i	−0.761849	+	0.223699i
$965$	43.8573			1.41182
$966$	1.57495	+	6.16003i	0.0506730	+	0.198196i
$967$	19.2111			0.617787			0.308893	−	0.951097i	$-0.400041\pi$
$967$	19.2111			0.617787			0.308893	+	0.951097i	$0.400041\pi$
$968$	−22.4776	+	6.60002i	−0.722457	+	0.212133i
$969$	−0.677495	−	0.781871i	−0.0217643	−	0.0251173i
$970$	16.9238	−	10.8763i	0.543392	−	0.349217i
$971$	0.155140	+	1.07902i	0.00497868	+	0.0346275i	0.992159	−	0.124979i	$-0.0398865\pi$
$971$	0.155140	+	1.07902i	0.00497868	+	0.0346275i	−0.987181	+	0.159607i	$0.948977\pi$
$972$	−10.0348	−	6.44900i	−0.321868	−	0.206852i
$973$	−1.12739	+	2.46865i	−0.0361426	+	0.0791412i
$974$	−25.1673	+	29.0446i	−0.806411	+	0.930648i
$975$	−3.38128	+	23.5173i	−0.108288	+	0.753157i
$976$	2.18786	+	4.79074i	0.0700317	+	0.153348i
$977$	17.4729	+	5.13050i	0.559007	+	0.164139i	0.549017	−	0.835811i	$-0.315002\pi$
$977$	17.4729	+	5.13050i	0.559007	+	0.164139i	0.00998924	+	0.999950i	$0.496820\pi$
$978$	−24.5673	−	7.21361i	−0.785575	−	0.230666i
$979$	−1.52384	−	3.33675i	−0.0487022	−	0.106643i
$980$	−0.397385	+	2.76387i	−0.0126940	+	0.0882887i
$981$	−8.84022	+	10.2022i	−0.282247	+	0.325730i
$982$	1.66173	−	3.63868i	0.0530279	−	0.116115i
$983$	−26.4617	−	17.0059i	−0.843998	−	0.542404i	0.0456995	−	0.998955i	$-0.485448\pi$
$983$	−26.4617	−	17.0059i	−0.843998	−	0.542404i	−0.889697	+	0.456551i	$0.849085\pi$
$984$	−0.886931	−	6.16874i	−0.0282743	−	0.196652i
$985$	47.5760	−	30.5753i	1.51590	−	0.974209i
$986$	0.620207	+	0.715758i	0.0197514	+	0.0227944i
$987$	8.64731	−	2.53908i	0.275247	−	0.0808198i
$988$	−25.1706			−0.800784
$989$	6.81830	−	2.82751i	0.216809	−	0.0899095i
$990$	20.3538			0.646885
$991$	−4.57615	+	1.34368i	−0.145366	+	0.0426834i	−0.353606	−	0.935394i	$-0.615045\pi$
$991$	−4.57615	+	1.34368i	−0.145366	+	0.0426834i	0.208240	+	0.978078i	$0.433227\pi$
$992$	0.141345	+	0.163121i	0.00448771	+	0.00517910i
$993$	−3.00334	+	1.93013i	−0.0953083	+	0.0612509i
$994$	2.17808	+	15.1489i	0.0690847	+	0.480494i
$995$	−29.5816	−	19.0109i	−0.937800	−	0.602688i
$996$	3.53063	−	7.73100i	0.111872	−	0.244966i
$997$	−0.416551	+	0.480726i	−0.0131923	+	0.0152247i	−0.762307	−	0.647215i	$-0.775934\pi$
$997$	−0.416551	+	0.480726i	−0.0131923	+	0.0152247i	0.749115	+	0.662440i	$0.230479\pi$
$998$	−2.89338	+	20.1239i	−0.0915884	+	0.637011i
$999$	−2.70146	−	5.91538i	−0.0854705	−	0.187154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.d.239.3	yes	40
23.8	even	11		7406.2.a.bu.1.5		20
23.15	odd	22		7406.2.a.bv.1.5		20
23.18	even	11	inner	322.2.i.d.225.3	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.d.225.3	✓	40	23.18	even	11	inner
322.2.i.d.239.3	yes	40	1.1	even	1	trivial
7406.2.a.bu.1.5		20	23.8	even	11
7406.2.a.bv.1.5		20	23.15	odd	22

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{2} +(0.868196 + 1.00195i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.397385 - 2.76387i) q^{5} +(-1.11531 - 0.716766i) q^{6} +(-0.415415 + 0.909632i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.176802 - 1.22968i) q^{9} +O(q^{10})\)	\(q+(-0.959493 + 0.281733i) q^{2} +(0.868196 + 1.00195i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.397385 - 2.76387i) q^{5} +(-1.11531 - 0.716766i) q^{6} +(-0.415415 + 0.909632i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.176802 - 1.22968i) q^{9} +(1.15996 + 2.53996i) q^{10} +(5.62974 + 1.65304i) q^{11} +(1.27207 + 0.373513i) q^{12} +(-2.66173 - 5.82838i) q^{13} +(0.142315 - 0.989821i) q^{14} +(2.42426 - 2.79775i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-0.167110 - 0.107395i) q^{17} +(0.176802 + 1.22968i) q^{18} +(3.30475 - 2.12383i) q^{19} +(-1.82857 - 2.11028i) q^{20} +(-1.27207 + 0.373513i) q^{21} -5.86741 q^{22} +(-1.51266 + 4.55103i) q^{23} -1.32577 q^{24} +(-2.68362 + 0.787983i) q^{25} +(4.19596 + 4.84239i) q^{26} +(4.73151 - 3.04076i) q^{27} +(0.142315 + 0.989821i) q^{28} +(4.01087 + 2.57763i) q^{29} +(-1.53784 + 3.36741i) q^{30} +(0.141345 - 0.163121i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(3.23145 + 7.07589i) q^{33} +(0.190598 + 0.0559646i) q^{34} +(2.67919 + 0.786681i) q^{35} +(-0.516082 - 1.13006i) q^{36} +(0.164549 - 1.14446i) q^{37} +(-2.57253 + 2.96886i) q^{38} +(3.52885 - 7.72710i) q^{39} +(2.34903 + 1.50963i) q^{40} +(0.668992 + 4.65294i) q^{41} +(1.11531 - 0.716766i) q^{42} +(-1.00790 - 1.16318i) q^{43} +(5.62974 - 1.65304i) q^{44} -3.46895 q^{45} +(0.169209 - 4.79285i) q^{46} -6.79783 q^{47} +(1.27207 - 0.373513i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(2.35292 - 1.51213i) q^{50} +(-0.0374797 - 0.260677i) q^{51} +(-5.39025 - 3.46411i) q^{52} +(2.78971 - 6.10862i) q^{53} +(-3.68317 + 4.25061i) q^{54} +(2.33162 - 16.2168i) q^{55} +(-0.415415 - 0.909632i) q^{56} +(4.99715 + 1.46729i) q^{57} +(-4.57460 - 1.34322i) q^{58} +(4.10096 + 8.97986i) q^{59} +(0.526842 - 3.66427i) q^{60} +(-3.44894 + 3.98029i) q^{61} +(-0.0896632 + 0.196335i) q^{62} +(1.04511 + 0.671654i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-15.0512 + 9.67281i) q^{65} +(-5.09406 - 5.87886i) q^{66} +(-10.4122 + 3.05731i) q^{67} -0.198645 q^{68} +(-5.87319 + 2.43558i) q^{69} -2.79230 q^{70} +(-14.6847 + 4.31183i) q^{71} +(0.813552 + 0.938890i) q^{72} +(6.06131 - 3.89537i) q^{73} +(0.164549 + 1.14446i) q^{74} +(-3.11943 - 2.00474i) q^{75} +(1.63190 - 3.57336i) q^{76} +(-3.84234 + 4.43429i) q^{77} +(-1.20893 + 8.40829i) q^{78} +(2.79084 + 6.11108i) q^{79} +(-2.67919 - 0.786681i) q^{80} +(3.57856 + 1.05076i) q^{81} +(-1.95278 - 4.27599i) q^{82} +(0.912329 - 6.34538i) q^{83} +(-0.868196 + 1.00195i) q^{84} +(-0.230420 + 0.504550i) q^{85} +(1.29478 + 0.832107i) q^{86} +(0.899560 + 6.25658i) q^{87} +(-4.93598 + 3.17216i) q^{88} +(-0.409412 - 0.472486i) q^{89} +(3.32843 - 0.977316i) q^{90} +6.40741 q^{91} +(1.18795 + 4.64637i) q^{92} +0.286155 q^{93} +(6.52247 - 1.91517i) q^{94} +(-7.18327 - 8.28993i) q^{95} +(-1.11531 + 0.716766i) q^{96} +(-1.02532 - 7.13128i) q^{97} +(0.841254 + 0.540641i) q^{98} +(3.02807 - 6.63054i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Introduction

L-functions

Modular forms

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Database

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