LMFDB - Embedded newform 322.2.k.a.97.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(83,322)]

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([11, 21]))

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

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

chi := DirichletCharacter("322.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.k (of order $22$, 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:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			97.2
Character	$\chi$	$=$	322.97
Dual form			322.2.k.a.83.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(-1.70070 - 1.47367i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.0506866 - 0.352533i) q^{5} +(1.21663 + 1.89312i) q^{6} +(-2.46109 + 0.971103i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.293752 + 2.04309i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(-1.70070 - 1.47367i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.0506866 - 0.352533i) q^{5} +(1.21663 + 1.89312i) q^{6} +(-2.46109 + 0.971103i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.293752 + 2.04309i) q^{9} +(-0.147953 + 0.323973i) q^{10} +(1.11200 + 3.78713i) q^{11} +(-0.633998 - 2.15920i) q^{12} +(-4.94840 - 2.25986i) q^{13} +(2.63499 - 0.238397i) q^{14} +(-0.605719 + 0.524859i) q^{15} +(0.415415 + 0.909632i) q^{16} +(0.299955 - 0.192770i) q^{17} +(0.293752 - 2.04309i) q^{18} +(6.58234 + 4.23021i) q^{19} +(0.233234 - 0.269166i) q^{20} +(5.61667 + 1.97527i) q^{21} -3.94701i q^{22} +(-1.27171 + 4.62415i) q^{23} +2.25035i q^{24} +(4.67575 + 1.37293i) q^{25} +(4.11128 + 3.56244i) q^{26} +(-1.13865 + 1.77178i) q^{27} +(-2.59542 - 0.513622i) q^{28} +(-4.56067 + 2.93096i) q^{29} +(0.729053 - 0.332947i) q^{30} +(-2.36517 + 2.04943i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(3.68979 - 8.07950i) q^{33} +(-0.342115 + 0.100454i) q^{34} +(0.217601 + 0.916836i) q^{35} +(-0.857457 + 1.87757i) q^{36} +(7.71567 - 1.10935i) q^{37} +(-5.12392 - 5.91332i) q^{38} +(5.08548 + 11.1356i) q^{39} +(-0.299619 + 0.192553i) q^{40} +(-4.14319 - 0.595701i) q^{41} +(-4.83266 - 3.47766i) q^{42} +(-2.04884 - 1.77533i) q^{43} +(-1.11200 + 3.78713i) q^{44} +0.735144 q^{45} +(2.52297 - 4.07856i) q^{46} +12.5685i q^{47} +(0.633998 - 2.15920i) q^{48} +(5.11392 - 4.77994i) q^{49} +(-4.09956 - 2.63462i) q^{50} +(-0.794214 - 0.114191i) q^{51} +(-2.94108 - 4.57642i) q^{52} +(-7.68644 + 3.51028i) q^{53} +(1.59169 - 1.37921i) q^{54} +(1.39145 - 0.200060i) q^{55} +(2.34558 + 1.22403i) q^{56} +(-4.96068 - 16.8945i) q^{57} +(5.20168 - 1.52735i) q^{58} +(-5.12076 - 2.33857i) q^{59} +(-0.793324 + 0.114063i) q^{60} +(-7.15317 - 8.25520i) q^{61} +(2.84676 - 1.30007i) q^{62} +(-2.70700 - 4.74296i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-1.04749 + 1.62993i) q^{65} +(-5.81658 + 6.71269i) q^{66} +(2.18847 - 7.45323i) q^{67} +0.356558 q^{68} +(8.97727 - 5.99023i) q^{69} +(0.0495157 - 0.941003i) q^{70} +(-10.0458 - 2.94971i) q^{71} +(1.35170 - 1.55994i) q^{72} +(-5.30445 + 8.25389i) q^{73} +(-7.71567 - 1.10935i) q^{74} +(-5.92884 - 9.22546i) q^{75} +(3.25039 + 7.11736i) q^{76} +(-6.41442 - 8.24059i) q^{77} +(-1.74221 - 12.1173i) q^{78} +(-2.42918 - 1.10937i) q^{79} +(0.341731 - 0.100341i) q^{80} +(10.4890 - 3.07984i) q^{81} +(3.80753 + 1.73884i) q^{82} +(-0.216785 - 1.50778i) q^{83} +(3.65713 + 4.69831i) q^{84} +(-0.0527539 - 0.115515i) q^{85} +(1.46568 + 2.28064i) q^{86} +(12.0756 + 1.73621i) q^{87} +(2.13391 - 3.32043i) q^{88} +(-9.48954 + 10.9515i) q^{89} +(-0.705366 - 0.207114i) q^{90} +(14.3730 + 0.756309i) q^{91} +(-3.56984 + 3.20254i) q^{92} +7.04265 q^{93} +(3.54094 - 12.0593i) q^{94} +(1.82492 - 2.10607i) q^{95} +(-1.21663 + 1.89312i) q^{96} +(-1.69112 + 11.7620i) q^{97} +(-6.25343 + 3.14556i) q^{98} +(-7.41078 + 3.38439i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{2} - 8 q^{4} - 11 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) $ 80 * q - 8 * q^2 - 8 * q^4 - 11 * q^7 - 8 * q^8 - 6 * q^9	$ 80 q - 8 q^{2} - 8 q^{4} - 11 q^{7} - 8 q^{8} - 6 q^{9} + 11 q^{14} - 8 q^{16} - 6 q^{18} - 33 q^{21} + 18 q^{23} - 58 q^{25} - 11 q^{28} + 16 q^{29} + 22 q^{30} - 8 q^{32} + 47 q^{35} + 16 q^{36} - 22 q^{37} - 30 q^{39} - 22 q^{42} + 44 q^{43} - 4 q^{46} + 17 q^{49} + 8 q^{50} - 88 q^{51} + 44 q^{53} + 11 q^{56} - 22 q^{57} - 28 q^{58} + 121 q^{63} - 8 q^{64} - 154 q^{65} + 58 q^{70} + 42 q^{71} - 28 q^{72} + 22 q^{74} + 38 q^{77} + 58 q^{78} - 88 q^{79} - 26 q^{81} - 11 q^{84} + 26 q^{85} - 132 q^{86} + 22 q^{88} - 4 q^{92} + 152 q^{93} - 68 q^{95} - 27 q^{98} - 44 q^{99}+O(q^{100}) $ 80 * q - 8 * q^2 - 8 * q^4 - 11 * q^7 - 8 * q^8 - 6 * q^9 + 11 * q^14 - 8 * q^16 - 6 * q^18 - 33 * q^21 + 18 * q^23 - 58 * q^25 - 11 * q^28 + 16 * q^29 + 22 * q^30 - 8 * q^32 + 47 * q^35 + 16 * q^36 - 22 * q^37 - 30 * q^39 - 22 * q^42 + 44 * q^43 - 4 * q^46 + 17 * q^49 + 8 * q^50 - 88 * q^51 + 44 * q^53 + 11 * q^56 - 22 * q^57 - 28 * q^58 + 121 * q^63 - 8 * q^64 - 154 * q^65 + 58 * q^70 + 42 * q^71 - 28 * q^72 + 22 * q^74 + 38 * q^77 + 58 * q^78 - 88 * q^79 - 26 * q^81 - 11 * q^84 + 26 * q^85 - 132 * q^86 + 22 * q^88 - 4 * q^92 + 152 * q^93 - 68 * q^95 - 27 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$185$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{22}\right)$

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
$3$	−1.70070	−	1.47367i	−0.981902	−	0.850823i	0.00691181	−	0.999976i	$-0.497800\pi$
$3$	−1.70070	−	1.47367i	−0.981902	−	0.850823i	−0.988814	+	0.149153i	$0.952345\pi$
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.0506866	−	0.352533i	0.0226677	−	0.157657i	−0.975344	−	0.220692i	$-0.929169\pi$
$5$	0.0506866	−	0.352533i	0.0226677	−	0.157657i	0.998011	+	0.0630341i	$0.0200777\pi$
$6$	1.21663	+	1.89312i	0.496689	+	0.772863i
$7$	−2.46109	+	0.971103i	−0.930204	+	0.367042i
$7$	−2.46109	+	0.971103i	−0.930204	+	0.367042i
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	0.293752	+	2.04309i	0.0979172	+	0.681029i
$10$	−0.147953	+	0.323973i	−0.0467870	+	0.102449i
$11$	1.11200	+	3.78713i	0.335281	+	1.14186i	0.938786	+	0.344502i	$0.111952\pi$
$11$	1.11200	+	3.78713i	0.335281	+	1.14186i	−0.603505	+	0.797359i	$0.706230\pi$
$12$	−0.633998	−	2.15920i	−0.183020	−	0.623307i
$13$	−4.94840	−	2.25986i	−1.37244	−	0.626772i	−0.413531	−	0.910490i	$-0.635705\pi$
$13$	−4.94840	−	2.25986i	−1.37244	−	0.626772i	−0.958908	+	0.283719i	$0.908432\pi$
$14$	2.63499	−	0.238397i	0.704230	−	0.0637143i
$15$	−0.605719	+	0.524859i	−0.156396	+	0.135518i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	0.299955	−	0.192770i	0.0727499	−	0.0467535i	−0.503760	−	0.863844i	$-0.668050\pi$
$17$	0.299955	−	0.192770i	0.0727499	−	0.0467535i	0.576510	+	0.817090i	$0.304414\pi$
$18$	0.293752	−	2.04309i	0.0692379	−	0.481560i
$19$	6.58234	+	4.23021i	1.51009	+	0.970477i	0.993449	+	0.114275i	$0.0364546\pi$
$19$	6.58234	+	4.23021i	1.51009	+	0.970477i	0.516642	+	0.856201i	$0.327182\pi$
$20$	0.233234	−	0.269166i	0.0521527	−	0.0601874i
$21$	5.61667	+	1.97527i	1.22566	+	0.431040i
$22$		−	3.94701i		−	0.841505i
$23$	−1.27171	+	4.62415i	−0.265170	+	0.964202i
$23$	−1.27171	+	4.62415i	−0.265170	+	0.964202i
$24$			2.25035i			0.459352i
$25$	4.67575	+	1.37293i	0.935151	+	0.274585i
$26$	4.11128	+	3.56244i	0.806288	+	0.698652i
$27$	−1.13865	+	1.77178i	−0.219134	+	0.340978i
$28$	−2.59542	−	0.513622i	−0.490488	−	0.0970654i
$29$	−4.56067	+	2.93096i	−0.846895	+	0.544266i	−0.890605	−	0.454778i	$-0.849719\pi$
$29$	−4.56067	+	2.93096i	−0.846895	+	0.544266i	0.0437102	+	0.999044i	$0.486082\pi$
$30$	0.729053	−	0.332947i	0.133106	−	0.0607876i
$31$	−2.36517	+	2.04943i	−0.424797	+	0.368089i	−0.840865	−	0.541245i	$-0.817953\pi$
$31$	−2.36517	+	2.04943i	−0.424797	+	0.368089i	0.416068	+	0.909334i	$0.363408\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$	3.68979	−	8.07950i	0.642309	−	1.40646i
$34$	−0.342115	+	0.100454i	−0.0586722	+	0.0172277i
$35$	0.217601	+	0.916836i	0.0367813	+	0.154974i
$36$	−0.857457	+	1.87757i	−0.142909	+	0.312928i
$37$	7.71567	−	1.10935i	1.26845	−	0.182375i	0.524962	−	0.851126i	$-0.324080\pi$
$37$	7.71567	−	1.10935i	1.26845	−	0.182375i	0.743487	+	0.668750i	$0.233170\pi$
$38$	−5.12392	−	5.91332i	−0.831209	−	0.959266i
$39$	5.08548	+	11.1356i	0.814328	+	1.78313i
$40$	−0.299619	+	0.192553i	−0.0473739	+	0.0304454i
$41$	−4.14319	−	0.595701i	−0.647058	−	0.0930328i	−0.189031	−	0.981971i	$-0.560535\pi$
$41$	−4.14319	−	0.595701i	−0.647058	−	0.0930328i	−0.458027	+	0.888938i	$0.651444\pi$
$42$	−4.83266	−	3.47766i	−0.745695	−	0.536614i
$43$	−2.04884	−	1.77533i	−0.312445	−	0.270735i	0.484495	−	0.874794i	$-0.339004\pi$
$43$	−2.04884	−	1.77533i	−0.312445	−	0.270735i	−0.796939	+	0.604059i	$0.793549\pi$
$44$	−1.11200	+	3.78713i	−0.167640	+	0.570931i
$45$	0.735144			0.109589
$46$	2.52297	−	4.07856i	0.371992	−	0.601350i
$47$			12.5685i			1.83330i	0.399693	+	0.916649i	$0.369117\pi$
$47$			12.5685i			1.83330i	−0.399693	+	0.916649i	$0.630883\pi$
$48$	0.633998	−	2.15920i	0.0915098	−	0.311654i
$49$	5.11392	−	4.77994i	0.730560	−	0.682849i
$50$	−4.09956	−	2.63462i	−0.579765	−	0.372592i
$51$	−0.794214	−	0.114191i	−0.111212	−	0.0159899i
$52$	−2.94108	−	4.57642i	−0.407855	−	0.634635i
$53$	−7.68644	+	3.51028i	−1.05581	+	0.482174i	−0.866206	−	0.499686i	$-0.833449\pi$
$53$	−7.68644	+	3.51028i	−1.05581	+	0.482174i	−0.189607	+	0.981860i	$0.560721\pi$
$54$	1.59169	−	1.37921i	0.216602	−	0.187687i
$55$	1.39145	−	0.200060i	0.187623	−	0.0269761i
$56$	2.34558	+	1.22403i	0.313441	+	0.163568i
$57$	−4.96068	−	16.8945i	−0.657058	−	2.23773i
$58$	5.20168	−	1.52735i	0.683013	−	0.200551i
$59$	−5.12076	−	2.33857i	−0.666666	−	0.304456i	0.0531853	−	0.998585i	$-0.483063\pi$
$59$	−5.12076	−	2.33857i	−0.666666	−	0.304456i	−0.719851	+	0.694129i	$0.755790\pi$
$60$	−0.793324	+	0.114063i	−0.102418	+	0.0147254i
$61$	−7.15317	−	8.25520i	−0.915870	−	1.05697i	−0.998176	−	0.0603634i	$-0.980774\pi$
$61$	−7.15317	−	8.25520i	−0.915870	−	1.05697i	0.0823063	−	0.996607i	$-0.473771\pi$
$62$	2.84676	−	1.30007i	0.361539	−	0.165109i
$63$	−2.70700	−	4.74296i	−0.341050	−	0.597556i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−1.04749	+	1.62993i	−0.129925	+	0.202168i
$66$	−5.81658	+	6.71269i	−0.715972	+	0.826276i
$67$	2.18847	−	7.45323i	0.267364	−	0.910557i	−0.710918	−	0.703275i	$-0.751720\pi$
$67$	2.18847	−	7.45323i	0.267364	−	0.910557i	0.978281	−	0.207282i	$-0.0664616\pi$
$68$	0.356558			0.0432390
$69$	8.97727	−	5.99023i	1.08074	−	0.721139i
$70$	0.0495157	−	0.941003i	0.00591826	−	0.112471i
$71$	−10.0458	−	2.94971i	−1.19222	−	0.350067i	−0.375345	−	0.926885i	$-0.622476\pi$
$71$	−10.0458	−	2.94971i	−1.19222	−	0.350067i	−0.816872	+	0.576819i	$0.804294\pi$
$72$	1.35170	−	1.55994i	0.159299	−	0.183841i
$73$	−5.30445	+	8.25389i	−0.620839	+	0.966045i	0.378345	+	0.925665i	$0.376493\pi$
$73$	−5.30445	+	8.25389i	−0.620839	+	0.966045i	−0.999184	+	0.0403804i	$0.987143\pi$
$74$	−7.71567	−	1.10935i	−0.896929	−	0.128959i
$75$	−5.92884	−	9.22546i	−0.684604	−	1.06526i
$76$	3.25039	+	7.11736i	0.372845	+	0.816417i
$77$	−6.41442	−	8.24059i	−0.730991	−	0.939102i
$78$	−1.74221	−	12.1173i	−0.197266	−	1.37202i
$79$	−2.42918	−	1.10937i	−0.273305	−	0.124814i	0.274048	−	0.961716i	$-0.411637\pi$
$79$	−2.42918	−	1.10937i	−0.273305	−	0.124814i	−0.547353	+	0.836902i	$0.684364\pi$
$80$	0.341731	−	0.100341i	0.0382067	−	0.0112185i
$81$	10.4890	−	3.07984i	1.16544	−	0.342205i
$82$	3.80753	+	1.73884i	0.420472	+	0.192023i
$83$	−0.216785	−	1.50778i	−0.0237953	−	0.165500i	0.974459	−	0.224567i	$-0.0720966\pi$
$83$	−0.216785	−	1.50778i	−0.0237953	−	0.165500i	−0.998254	+	0.0590667i	$0.981188\pi$
$84$	3.65713	+	4.69831i	0.399026	+	0.512627i
$85$	−0.0527539	−	0.115515i	−0.00572196	−	0.0125294i
$86$	1.46568	+	2.28064i	0.158048	+	0.245928i
$87$	12.0756	+	1.73621i	1.29464	+	0.186141i
$88$	2.13391	−	3.32043i	0.227476	−	0.353959i
$89$	−9.48954	+	10.9515i	−1.00589	+	1.16086i	−0.0189407	+	0.999821i	$0.506029\pi$
$89$	−9.48954	+	10.9515i	−1.00589	+	1.16086i	−0.986948	+	0.161037i	$0.948516\pi$
$90$	−0.705366	−	0.207114i	−0.0743521	−	0.0218317i
$91$	14.3730	+	0.756309i	1.50670	+	0.0792827i
$92$	−3.56984	+	3.20254i	−0.372181	+	0.333888i
$93$	7.04265			0.730288
$94$	3.54094	−	12.0593i	0.365220	−	1.24383i
$95$	1.82492	−	2.10607i	0.187233	−	0.216079i
$96$	−1.21663	+	1.89312i	−0.124172	+	0.193216i
$97$	−1.69112	+	11.7620i	−0.171707	+	1.19425i	0.703571	+	0.710625i	$0.251588\pi$
$97$	−1.69112	+	11.7620i	−0.171707	+	1.19425i	−0.875277	+	0.483621i	$0.839321\pi$
$98$	−6.25343	+	3.14556i	−0.631692	+	0.317750i
$99$	−7.41078	+	3.38439i	−0.744811	+	0.340144i
$100$	3.19124	+	3.68288i	0.319124	+	0.368288i
$101$	13.4997	−	1.94096i	1.34327	−	0.193133i	0.567095	−	0.823652i	$-0.308067\pi$
$101$	13.4997	−	1.94096i	1.34327	−	0.193133i	0.776173	+	0.630520i	$0.217158\pi$
$102$	0.729872	+	0.333321i	0.0722681	+	0.0330037i
$103$	−6.64398	+	1.95085i	−0.654650	+	0.192223i	−0.592157	−	0.805823i	$-0.701723\pi$
$103$	−6.64398	+	1.95085i	−0.654650	+	0.192223i	−0.0624935	+	0.998045i	$0.519905\pi$
$104$	1.53262	+	5.21964i	0.150286	+	0.511828i
$105$	0.981038	−	1.87994i	0.0957395	−	0.183463i
$106$	8.36404	−	1.20257i	0.812388	−	0.116804i
$107$	2.98868	−	2.58971i	0.288927	−	0.250356i	−0.498322	−	0.866992i	$-0.666050\pi$
$107$	2.98868	−	2.58971i	0.288927	−	0.250356i	0.787249	+	0.616636i	$0.211505\pi$
$108$	−1.91579	+	0.874911i	−0.184347	+	0.0841884i
$109$	−2.56422	−	3.99001i	−0.245608	−	0.382174i	0.696460	−	0.717596i	$-0.254757\pi$
$109$	−2.56422	−	3.99001i	−0.245608	−	0.382174i	−0.942068	+	0.335422i	$0.891121\pi$
$110$	−1.39145	−	0.200060i	−0.132669	−	0.0190750i
$111$	−14.7569	−	9.48368i	−1.40066	−	0.900151i
$112$	−1.90572	−	1.83527i	−0.180074	−	0.173417i
$113$	0.984782	−	3.35386i	0.0926405	−	0.315505i	−0.900116	−	0.435651i	$-0.856518\pi$
$113$	0.984782	−	3.35386i	0.0926405	−	0.315505i	0.992756	+	0.120146i	$0.0383364\pi$
$114$			17.6078i			1.64912i
$115$	1.56570	+	0.682702i	0.146003	+	0.0636623i
$116$	−5.42127			−0.503353
$117$	3.16349	−	10.7738i	0.292464	−	0.996042i
$118$	4.25448	+	3.68653i	0.391656	+	0.339372i
$119$	−0.551018	+	0.765711i	−0.0505117	+	0.0701926i
$120$	0.793324	+	0.114063i	0.0724202	+	0.0104125i
$121$	−3.85199	+	2.47552i	−0.350181	+	0.225047i
$122$	4.53766	+	9.93609i	0.410821	+	0.899572i
$123$	6.16848	+	7.11880i	0.556193	+	0.641881i
$124$	−3.09772	+	0.445384i	−0.278183	+	0.0399967i
$125$	1.46077	−	3.19863i	0.130655	−	0.286094i
$126$	1.26110	+	5.31348i	0.112348	+	0.473363i
$127$	−2.85940	+	0.839596i	−0.253731	+	0.0745021i	−0.406124	−	0.913818i	$-0.633120\pi$
$127$	−2.85940	+	0.839596i	−0.253731	+	0.0745021i	0.152394	+	0.988320i	$0.451302\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$	0.868222	+	6.03862i	0.0764427	+	0.531671i
$130$	1.46426	−	1.26879i	0.128424	−	0.111280i
$131$	2.03886	−	0.931118i	0.178136	−	0.0813522i	−0.324351	−	0.945937i	$-0.605146\pi$
$131$	2.03886	−	0.931118i	0.178136	−	0.0813522i	0.502487	+	0.864585i	$0.332418\pi$
$132$	7.47215	−	4.80206i	0.650368	−	0.417966i
$133$	−20.3077	−	4.01880i	−1.76090	−	0.348474i
$134$	−4.19963	+	6.53476i	−0.362793	+	0.564517i
$135$	0.566895	+	0.491217i	0.0487905	+	0.0422772i
$136$	−0.342115	−	0.100454i	−0.0293361	−	0.00861385i
$137$			15.4518i			1.32013i	0.751207	+	0.660067i	$0.229472\pi$
$137$			15.4518i			1.32013i	−0.751207	+	0.660067i	$0.770528\pi$
$138$	−10.3013	+	3.21839i	−0.876902	+	0.273968i
$139$		−	1.00553i		−	0.0852879i	−0.999090	−	0.0426439i	$-0.986422\pi$
$139$		−	1.00553i		−	0.0852879i	0.999090	−	0.0426439i	$-0.0135781\pi$
$140$	−0.312621	+	0.888936i	−0.0264213	+	0.0751288i
$141$	18.5217	−	21.3752i	1.55981	−	1.80012i
$142$	8.80785	+	5.66046i	0.739138	+	0.475015i
$143$	3.05574	−	21.2532i	0.255534	−	1.77728i
$144$	−1.73643	+	1.11594i	−0.144702	+	0.0929946i
$145$	0.802096	+	1.75634i	0.0666104	+	0.145856i
$146$	7.41498	−	6.42511i	0.613668	−	0.531746i
$147$	−15.7413	+	0.593042i	−1.29832	+	0.0489133i
$148$	7.09060	+	3.23817i	0.582843	+	0.266176i
$149$	1.35517	+	4.61530i	0.111020	+	0.378100i	0.996194	−	0.0871598i	$-0.0277791\pi$
$149$	1.35517	+	4.61530i	0.111020	+	0.378100i	−0.885174	+	0.465260i	$0.845961\pi$
$150$	3.08957	+	10.5221i	0.252262	+	0.859126i
$151$	−5.43731	+	11.9060i	−0.442482	+	0.968900i	0.548654	+	0.836049i	$0.315140\pi$
$151$	−5.43731	+	11.9060i	−0.442482	+	0.968900i	−0.991136	+	0.132851i	$0.957587\pi$
$152$	−1.11353	−	7.74480i	−0.0903195	−	0.628186i
$153$	0.481958	+	0.556209i	0.0389640	+	0.0449668i
$154$	3.83295	+	9.71394i	0.308868	+	0.782771i
$155$	0.602610	+	0.937679i	0.0484028	+	0.0753162i
$156$	−1.74221	+	12.1173i	−0.139488	+	0.970162i
$157$	7.86241	+	5.05287i	0.627489	+	0.403263i	0.815379	−	0.578927i	$-0.196529\pi$
$157$	7.86241	+	5.05287i	0.627489	+	0.403263i	−0.187890	+	0.982190i	$0.560165\pi$
$158$	2.01824	+	1.74881i	0.160562	+	0.139128i
$159$	18.2454	+	5.35732i	1.44695	+	0.424863i
$160$	−0.356158			−0.0281568
$161$	−1.36073	−	12.6154i	−0.107240	−	0.994233i
$162$	−10.9318			−0.858883
$163$	9.34852	+	2.74497i	0.732233	+	0.215003i	0.626533	−	0.779395i	$-0.284473\pi$
$163$	9.34852	+	2.74497i	0.732233	+	0.215003i	0.105700	+	0.994398i	$0.466292\pi$
$164$	−3.16341	−	2.74111i	−0.247021	−	0.214045i
$165$	−2.66127	−	1.71029i	−0.207179	−	0.133146i
$166$	−0.216785	+	1.50778i	−0.0168258	+	0.117026i
$167$	−0.0385634	−	0.0600059i	−0.00298413	−	0.00464340i	0.839758	−	0.542960i	$-0.182697\pi$
$167$	−0.0385634	−	0.0600059i	−0.00298413	−	0.00464340i	−0.842742	+	0.538317i	$0.819060\pi$
$168$	−2.18533	−	5.53832i	−0.168602	−	0.427291i
$169$	10.8665	+	12.5406i	0.835883	+	0.964661i
$170$	0.0180727	+	0.125698i	0.00138611	+	0.00964062i
$171$	−6.70912	+	14.6909i	−0.513059	+	1.12344i
$172$	−0.763777	−	2.60119i	−0.0582375	−	0.198339i
$173$	−0.459715	−	1.56565i	−0.0349515	−	0.119034i	0.940170	−	0.340707i	$-0.110666\pi$
$173$	−0.459715	−	1.56565i	−0.0349515	−	0.119034i	−0.975121	+	0.221673i	$0.928848\pi$
$174$	−11.0973	−	5.06798i	−0.841286	−	0.384202i
$175$	−12.8407	+	1.16175i	−0.970666	+	0.0878197i
$176$	−2.98295	+	2.58474i	−0.224848	+	0.194832i
$177$	5.26261	+	11.5235i	0.395562	+	0.866161i
$178$	12.1905	−	7.83439i	0.913720	−	0.587212i
$179$	−2.45312	+	17.0618i	−0.183354	+	1.27526i	0.665406	+	0.746481i	$0.268258\pi$
$179$	−2.45312	+	17.0618i	−0.183354	+	1.27526i	−0.848761	+	0.528777i	$0.822651\pi$
$180$	0.618443	+	0.397449i	0.0460960	+	0.0296241i
$181$	3.52695	−	4.07032i	0.262156	−	0.302544i	−0.609377	−	0.792880i	$-0.708581\pi$
$181$	3.52695	−	4.07032i	0.262156	−	0.302544i	0.871533	+	0.490336i	$0.163126\pi$
$182$	−13.5777	−	4.77501i	−1.00645	−	0.353948i
$183$			24.5811i			1.81709i
$184$	4.32749	−	2.06708i	0.319027	−	0.152387i
$185$		−	2.77626i		−	0.204114i
$186$	−6.75737	−	1.98414i	−0.495474	−	0.145484i
$187$	1.06359	+	0.921609i	0.0777777	+	0.0673947i
$188$	−6.79502	+	10.5733i	−0.495578	+	0.771134i
$189$	1.08175	−	5.46625i	0.0786854	−	0.397611i
$190$	−2.34435	+	1.50662i	−0.170077	+	0.109302i
$191$	−8.02100	+	3.66307i	−0.580379	+	0.265050i	−0.683898	−	0.729577i	$-0.739717\pi$
$191$	−8.02100	+	3.66307i	−0.580379	+	0.265050i	0.103520	+	0.994627i	$0.466990\pi$
$192$	1.70070	−	1.47367i	0.122738	−	0.106353i
$193$	−2.27293	−	15.8085i	−0.163609	−	1.13792i	−0.891760	−	0.452508i	$-0.850529\pi$
$193$	−2.27293	−	15.8085i	−0.163609	−	1.13792i	0.728152	−	0.685416i	$-0.240380\pi$
$194$	4.93634	−	10.8091i	0.354409	−	0.776047i
$195$	4.18345	−	1.22837i	0.299583	−	0.0879654i
$196$	6.88633	−	1.25635i	0.491881	−	0.0897391i
$197$	4.51482	−	9.88608i	0.321668	−	0.704354i	−0.677857	−	0.735194i	$-0.737091\pi$
$197$	4.51482	−	9.88608i	0.321668	−	0.704354i	0.999524	+	0.0308401i	$0.00981828\pi$
$198$	8.06408	−	1.15944i	0.573089	−	0.0823978i
$199$	−12.9438	−	14.9379i	−0.917561	−	1.05892i	−0.998066	−	0.0621675i	$-0.980199\pi$
$199$	−12.9438	−	14.9379i	−0.917561	−	1.05892i	0.0805048	−	0.996754i	$-0.474347\pi$
$200$	−2.02438	−	4.43277i	−0.143145	−	0.313444i
$201$	−14.7055	+	9.45067i	−1.03725	+	0.666599i
$202$	−13.4997	−	1.94096i	−0.949834	−	0.136566i
$203$	8.37794	−	11.6422i	0.588016	−	0.817125i
$204$	−0.606399	−	0.525448i	−0.0424565	−	0.0367887i
$205$	−0.420008	+	1.43042i	−0.0293346	+	0.0999046i
$206$	6.92447			0.482450
$207$	−9.82111	−	1.23987i	−0.682614	−	0.0861767i
$208$		−	5.44000i		−	0.377196i
$209$	−8.70078	+	29.6321i	−0.601845	+	2.04970i
$210$	−1.47094	+	1.52740i	−0.101504	+	0.105401i
$211$	−10.8072	−	6.94538i	−0.744000	−	0.478140i	0.112910	−	0.993605i	$-0.463983\pi$
$211$	−10.8072	−	6.94538i	−0.744000	−	0.478140i	−0.856910	+	0.515465i	$0.827619\pi$
$212$	−8.36404	−	1.20257i	−0.574445	−	0.0825927i
$213$	12.7380	+	19.8208i	0.872796	+	1.35810i
$214$	−3.59722	+	1.64280i	−0.245901	+	0.112299i
$215$	−0.729710	+	0.632297i	−0.0497658	+	0.0431223i
$216$	2.08468	−	0.299731i	0.141844	−	0.0203941i
$217$	3.83069	−	7.34066i	0.260044	−	0.498317i
$218$	1.33624	+	4.55081i	0.0905015	+	0.308220i
$219$	21.1848	−	6.22042i	1.43154	−	0.420337i
$220$	1.27872	+	0.583973i	0.0862114	+	0.0393714i
$221$	−1.91993	+	0.276044i	−0.129148	+	0.0185688i
$222$	11.4873	+	13.2570i	0.770975	+	0.889753i
$223$	24.1994	−	11.0515i	1.62051	−	0.740062i	0.621451	−	0.783453i	$-0.286543\pi$
$223$	24.1994	−	11.0515i	1.62051	−	0.740062i	0.999058	+	0.0433912i	$0.0138162\pi$
$224$	1.31147	+	2.29784i	0.0876261	+	0.153531i
$225$	−1.43150	+	9.95627i	−0.0954331	+	0.663752i
$226$	−1.88978	+	2.94056i	−0.125707	+	0.195603i
$227$	4.36859	−	5.04162i	0.289953	−	0.334624i	−0.592020	−	0.805923i	$-0.701669\pi$
$227$	4.36859	−	5.04162i	0.289953	−	0.334624i	0.881973	+	0.471299i	$0.156215\pi$
$228$	4.96068	−	16.8945i	0.328529	−	1.11887i
$229$	13.8151			0.912928			0.456464	−	0.889742i	$-0.349116\pi$
$229$	13.8151			0.912928			0.456464	+	0.889742i	$0.349116\pi$
$230$	−1.30994	−	1.09616i	−0.0863751	−	0.0722785i
$231$	−1.23486	+	23.4675i	−0.0812481	+	1.54405i
$232$	5.20168	+	1.52735i	0.341507	+	0.100275i
$233$	10.9033	−	12.5830i	0.714297	−	0.824342i	−0.276312	−	0.961068i	$-0.589112\pi$
$233$	10.9033	−	12.5830i	0.714297	−	0.824342i	0.990609	+	0.136725i	$0.0436578\pi$
$234$	−6.07068	+	9.44617i	−0.396853	+	0.617515i
$235$	4.43079	+	0.637052i	0.289033	+	0.0415567i
$236$	−3.04353	−	4.73582i	−0.198117	−	0.308276i
$237$	2.49648	+	5.46653i	0.162164	+	0.355089i
$238$	0.744424	−	0.579455i	0.0482538	−	0.0375605i
$239$	1.71493	+	11.9276i	0.110930	+	0.771532i	0.967019	+	0.254704i	$0.0819781\pi$
$239$	1.71493	+	11.9276i	0.110930	+	0.771532i	−0.856089	+	0.516828i	$0.827113\pi$
$240$	−0.729053	−	0.332947i	−0.0470602	−	0.0214917i
$241$	22.7214	−	6.67161i	1.46361	−	0.429756i	0.549597	−	0.835430i	$-0.314781\pi$
$241$	22.7214	−	6.67161i	1.46361	−	0.429756i	0.914018	+	0.405674i	$0.132963\pi$
$242$	4.39339	−	1.29002i	0.282418	−	0.0829254i
$243$	−16.6300	−	7.59465i	−1.06681	−	0.487197i
$244$	−1.55453	−	10.8120i	−0.0995188	−	0.692168i
$245$	−1.42588	−	2.04510i	−0.0910960	−	0.130657i
$246$	−3.91301	−	8.56830i	−0.249485	−	0.546295i
$247$	−23.0123	−	35.8079i	−1.46424	−	2.27840i
$248$	3.09772	+	0.445384i	0.196705	+	0.0282819i
$249$	−1.85327	+	2.88375i	−0.117446	+	0.182750i
$250$	−2.30275	+	2.65752i	−0.145639	+	0.168076i
$251$	6.02371	+	1.76872i	0.380213	+	0.111641i	0.466254	−	0.884651i	$-0.345603\pi$
$251$	6.02371	+	1.76872i	0.380213	+	0.111641i	−0.0860408	+	0.996292i	$0.527422\pi$
$252$	0.286966	−	5.45354i	0.0180772	−	0.343541i
$253$	−18.9264	+	0.325923i	−1.18989	+	0.0204906i
$254$	2.98012			0.186989
$255$	−0.0805120	+	0.274199i	−0.00504186	+	0.0171710i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	6.28816	−	9.78458i	0.392245	−	0.610345i	−0.587827	−	0.808986i	$-0.700017\pi$
$257$	6.28816	−	9.78458i	0.392245	−	0.610345i	0.980072	+	0.198641i	$0.0636529\pi$
$258$	0.868222	−	6.03862i	0.0540532	−	0.375948i
$259$	−17.9117	+	10.2229i	−1.11298	+	0.635221i
$260$	−1.76241	+	0.804866i	−0.109300	+	0.0499157i
$261$	−7.32792	−	8.45687i	−0.453587	−	0.523467i
$262$	−2.21860	+	0.318987i	−0.137066	+	0.0197071i
$263$	5.61192	+	2.56288i	0.346046	+	0.158034i	0.580854	−	0.814008i	$-0.302719\pi$
$263$	5.61192	+	2.56288i	0.346046	+	0.158034i	−0.234808	+	0.972042i	$0.575446\pi$
$264$	−8.52238	+	2.50240i	−0.524516	+	0.154012i
$265$	0.847889	+	2.88764i	0.0520854	+	0.177387i
$266$	18.3529	+	9.57735i	1.12529	+	0.587225i
$267$	32.2778	−	4.64085i	1.97537	−	0.284015i
$268$	5.87057	−	5.08688i	0.358602	−	0.310731i
$269$	−22.7886	+	10.4072i	−1.38944	+	0.634537i	−0.962882	−	0.269921i	$-0.913002\pi$
$269$	−22.7886	+	10.4072i	−1.38944	+	0.634537i	−0.426561	+	0.904459i	$0.640275\pi$
$270$	−0.405540	−	0.631032i	−0.0246804	−	0.0384034i
$271$	−9.26399	−	1.33196i	−0.562747	−	0.0809109i	−0.144930	−	0.989442i	$-0.546296\pi$
$271$	−9.26399	−	1.33196i	−0.562747	−	0.0809109i	−0.417817	+	0.908531i	$0.637205\pi$
$272$	0.299955	+	0.192770i	0.0181875	+	0.0116884i
$273$	−23.3297	−	22.4673i	−1.41198	−	1.35978i
$274$	4.35326	−	14.8259i	0.262990	−	0.895663i
$275$			19.2344i			1.15988i
$276$	10.7907	−	0.185823i	0.649525	−	0.0111852i
$277$	18.3173			1.10058			0.550290	−	0.834974i	$-0.314517\pi$
$277$	18.3173			1.10058			0.550290	+	0.834974i	$0.314517\pi$
$278$	−0.283290	+	0.964798i	−0.0169906	+	0.0578648i
$279$	−4.88194	−	4.23023i	−0.292274	−	0.253257i
$280$	0.550400	−	0.764852i	0.0328927	−	0.0457087i
$281$	3.63436	+	0.522542i	0.216808	+	0.0311723i	0.249863	−	0.968281i	$-0.419615\pi$
$281$	3.63436	+	0.522542i	0.216808	+	0.0311723i	−0.0330549	+	0.999454i	$0.510524\pi$
$282$	−23.7936	+	15.2912i	−1.41689	+	0.910578i
$283$	−4.65000	−	10.1821i	−0.276414	−	0.605261i	0.719607	−	0.694381i	$-0.244322\pi$
$283$	−4.65000	−	10.1821i	−0.276414	−	0.605261i	−0.996021	+	0.0891200i	$0.971595\pi$
$284$	−6.85633	−	7.91263i	−0.406848	−	0.469528i
$285$	−6.20731	+	0.892477i	−0.367689	+	0.0528658i
$286$	−8.91967	+	19.5314i	−0.527431	+	1.15491i
$287$	10.7752	−	2.55739i	0.636043	−	0.150958i
$288$	1.98049	−	0.581523i	0.116701	−	0.0342666i
$289$	−7.00924	+	15.3481i	−0.412308	+	0.902829i
$290$	−0.274786	−	1.91118i	−0.0161360	−	0.112228i
$291$	20.2093	−	17.5115i	1.18469	−	1.02654i
$292$	−8.92478	+	4.07581i	−0.522283	+	0.238519i
$293$	2.57149	−	1.65260i	0.150228	−	0.0965457i	−0.463367	−	0.886166i	$-0.653359\pi$
$293$	2.57149	−	1.65260i	0.150228	−	0.0965457i	0.613595	+	0.789621i	$0.289723\pi$
$294$	15.2708	+	3.86582i	0.890609	+	0.225459i
$295$	−1.08398	+	1.68670i	−0.0631115	+	0.0982035i
$296$	−5.89108	−	5.10465i	−0.342412	−	0.296702i
$297$	−7.97612	−	2.34200i	−0.462821	−	0.135897i
$298$		−	4.81014i		−	0.278644i
$299$	16.7428	−	20.0082i	0.968264	−	1.15711i
$300$		−	10.9663i		−	0.633141i
$301$	6.76640	+	2.37961i	0.390009	+	0.137158i
$302$	8.57138	−	9.89190i	0.493228	−	0.569215i
$303$	−25.8193	−	16.5931i	−1.48328	−	0.953246i
$304$	−1.11353	+	7.74480i	−0.0638655	+	0.444194i
$305$	−3.27280	+	2.10330i	−0.187400	+	0.120435i
$306$	−0.305733	−	0.669462i	−0.0174776	−	0.0382706i
$307$	−17.8547	+	15.4712i	−1.01902	+	0.882986i	−0.993170	−	0.116680i	$-0.962775\pi$
$307$	−17.8547	+	15.4712i	−1.01902	+	0.882986i	−0.0258503	+	0.999666i	$0.508229\pi$
$308$	−0.940955	−	10.4003i	−0.0536159	−	0.592613i
$309$	14.1743	+	6.47321i	0.806350	+	0.368248i
$310$	−0.314025	−	1.06947i	−0.0178354	−	0.0607419i
$311$	−2.75901	−	9.39632i	−0.156449	−	0.532817i	0.843542	−	0.537063i	$-0.180466\pi$
$311$	−2.75901	−	9.39632i	−0.156449	−	0.532817i	−0.999991	+	0.00424676i	$0.998648\pi$
$312$	5.08548	−	11.1356i	0.287909	−	0.630432i
$313$	2.66868	+	18.5611i	0.150843	+	1.04913i	0.914811	+	0.403881i	$0.132339\pi$
$313$	2.66868	+	18.5611i	0.150843	+	1.04913i	−0.763969	+	0.645253i	$0.776752\pi$
$314$	−6.12037	−	7.06329i	−0.345393	−	0.398604i
$315$	−1.80926	+	0.713901i	−0.101940	+	0.0402237i
$316$	−1.44379	−	2.24658i	−0.0812194	−	0.126380i
$317$	0.0226976	−	0.157865i	0.00127482	−	0.00886659i	−0.989174	−	0.146747i	$-0.953120\pi$
$317$	0.0226976	−	0.157865i	0.00127482	−	0.00886659i	0.990449	+	0.137880i	$0.0440289\pi$
$318$	−15.9970	−	10.2806i	−0.897065	−	0.576508i
$319$	−16.1714	−	14.0126i	−0.905424	−	0.784554i
$320$	0.341731	+	0.100341i	0.0191033	+	0.00560925i
$321$	−8.89923			−0.496707
$322$	−2.24856	+	12.4878i	−0.125307	+	0.695915i
$323$	2.78986			0.155232
$324$	10.4890	+	3.07984i	0.582721	+	0.171102i
$325$	−20.0349	−	17.3603i	−1.11133	−	0.962977i
$326$	−8.19649	−	5.26757i	−0.453962	−	0.291743i
$327$	−1.51897	+	10.5646i	−0.0839990	+	0.584226i
$328$	2.26301	+	3.52132i	0.124954	+	0.194432i
$329$	−12.2053	−	30.9321i	−0.672898	−	1.70534i
$330$	2.07162	+	2.39078i	0.114039	+	0.131608i
$331$	−1.16379	−	8.09436i	−0.0639679	−	0.444906i	−0.996484	−	0.0837790i	$-0.973301\pi$
$331$	−1.16379	−	8.09436i	−0.0639679	−	0.444906i	0.932516	−	0.361127i	$-0.117608\pi$
$332$	0.632793	−	1.38562i	0.0347291	−	0.0760460i
$333$	4.53298	+	15.4379i	0.248406	+	0.845993i
$334$	0.0200957	+	0.0684398i	0.00109959	+	0.00374486i
$335$	−2.51658	−	1.14928i	−0.137496	−	0.0627921i
$336$	0.536478	+	5.92966i	0.0292673	+	0.323489i
$337$	−19.9144	+	17.2560i	−1.08481	+	0.939992i	−0.998416	−	0.0562693i	$-0.982079\pi$
$337$	−19.9144	+	17.2560i	−1.08481	+	0.939992i	−0.0863928	+	0.996261i	$0.527534\pi$
$338$	−6.89322	−	15.0940i	−0.374942	−	0.821008i
$339$	−6.61730	+	4.25268i	−0.359403	+	0.230974i
$340$	0.0180727	−	0.125698i	0.000980129	−	0.00681695i
$341$	−10.3915	−	6.67823i	−0.562733	−	0.361647i
$342$	10.5763	−	12.2057i	0.571899	−	0.660006i
$343$	−7.94400	+	16.7300i	−0.428936	+	0.903335i
$344$			2.71100i			0.146167i
$345$	−1.65672	−	3.46841i	−0.0891951	−	0.186733i
$346$			1.63174i			0.0877230i
$347$	−27.2634	−	8.00525i	−1.46358	−	0.429745i	−0.549571	−	0.835447i	$-0.685209\pi$
$347$	−27.2634	−	8.00525i	−1.46358	−	0.429745i	−0.914005	+	0.405703i	$0.867027\pi$
$348$	9.21999	+	7.98916i	0.494243	+	0.428264i
$349$	15.2178	−	23.6793i	0.814588	−	1.26752i	−0.145927	−	0.989295i	$-0.546617\pi$
$349$	15.2178	−	23.6793i	0.814588	−	1.26752i	0.960515	−	0.278228i	$-0.0897470\pi$
$350$	12.6479	+	2.50296i	0.676057	+	0.133789i
$351$	9.63846	−	6.19426i	0.514463	−	0.330625i
$352$	3.59032	−	1.63965i	0.191365	−	0.0873934i
$353$	−8.24575	+	7.14498i	−0.438877	+	0.380289i	−0.846086	−	0.533046i	$-0.821047\pi$
$353$	−8.24575	+	7.14498i	−0.438877	+	0.380289i	0.407210	+	0.913335i	$0.366502\pi$
$354$	−1.80289	−	12.5394i	−0.0958226	−	0.666461i
$355$	−1.54906	+	3.39196i	−0.0822154	+	0.180027i
$356$	−13.9039	+	4.08257i	−0.736907	+	0.216376i
$357$	2.06552	−	0.490230i	0.109319	−	0.0259457i
$358$	7.16061	−	15.6795i	0.378450	−	0.828690i
$359$	26.2762	−	3.77795i	1.38680	−	0.199392i	0.591844	−	0.806053i	$-0.298400\pi$
$359$	26.2762	−	3.77795i	1.38680	−	0.199392i	0.794961	+	0.606660i	$0.207491\pi$
$360$	−0.481417	−	0.555585i	−0.0253729	−	0.0292819i
$361$	17.5396	+	38.4063i	0.923136	+	2.02139i
$362$	−4.53082	+	2.91178i	−0.238135	+	0.153040i
$363$	10.1992	+	1.46642i	0.535319	+	0.0769672i
$364$	11.6824	+	8.40688i	0.612326	+	0.440640i
$365$	2.64090	+	2.28836i	0.138231	+	0.119778i
$366$	6.92529	−	23.5854i	0.361991	−	1.23283i
$367$	−25.0829			−1.30932			−0.654659	−	0.755925i	$-0.727188\pi$
$367$	−25.0829			−1.30932			−0.654659	+	0.755925i	$0.727188\pi$
$368$	−4.73456	+	0.764151i	−0.246806	+	0.0398341i
$369$		−	8.63989i		−	0.449775i
$370$	−0.782162	+	2.66380i	−0.0406627	+	0.138484i
$371$	15.5082	−	16.1034i	0.805144	−	0.836048i
$372$	5.92465	+	3.80754i	0.307179	+	0.197412i
$373$	−5.45671	−	0.784557i	−0.282538	−	0.0406228i	−0.000410959	−	1.00000i	$-0.500131\pi$
$373$	−5.45671	−	0.784557i	−0.282538	−	0.0406228i	−0.282127	+	0.959377i	$0.591040\pi$
$374$	−0.760863	−	1.18393i	−0.0393433	−	0.0612194i
$375$	−7.19805	+	3.28724i	−0.371706	+	0.169752i
$376$	9.49861	−	8.23059i	0.489853	−	0.424460i
$377$	29.1915	−	4.19711i	1.50344	−	0.216162i
$378$	−2.57795	+	4.94006i	−0.132595	+	0.254089i
$379$	3.58972	+	12.2255i	0.184391	+	0.627980i	0.998858	+	0.0477697i	$0.0152113\pi$
$379$	3.58972	+	12.2255i	0.184391	+	0.627980i	−0.814467	+	0.580210i	$0.802970\pi$
$380$	2.67385	−	0.785114i	0.137166	−	0.0402755i
$381$	6.10028	+	2.78591i	0.312527	+	0.142726i
$382$	8.72809	−	1.25491i	0.446568	−	0.0642068i
$383$	25.5388	+	29.4733i	1.30497	+	1.50602i	0.716794	+	0.697285i	$0.245609\pi$
$383$	25.5388	+	29.4733i	1.30497	+	1.50602i	0.588177	+	0.808732i	$0.299846\pi$
$384$	−2.04699	+	0.934831i	−0.104460	+	0.0477054i
$385$	−3.23020	+	1.84361i	−0.164626	+	0.0939589i
$386$	−2.27293	+	15.8085i	−0.115689	+	0.804634i
$387$	3.02530	−	4.70746i	0.153785	−	0.239294i
$388$	−7.78166	+	8.98051i	−0.395054	+	0.455916i
$389$	−4.95966	+	16.8911i	−0.251465	+	0.856411i	0.732910	+	0.680326i	$0.238162\pi$
$389$	−4.95966	+	16.8911i	−0.251465	+	0.856411i	−0.984375	+	0.176085i	$0.943657\pi$
$390$	−4.36006			−0.220780
$391$	0.509939	+	1.63219i	0.0257887	+	0.0825432i
$392$	−6.96134	−	0.734647i	−0.351601	−	0.0371053i
$393$	−4.83967	−	1.42105i	−0.244129	−	0.0716827i
$394$	−7.11717	+	8.21365i	−0.358558	+	0.413798i
$395$	−0.514217	+	0.800137i	−0.0258730	+	0.0402592i
$396$	−8.06408	−	1.15944i	−0.405235	−	0.0582640i
$397$	9.87841	+	15.3711i	0.495783	+	0.771453i	0.995503	−	0.0947337i	$-0.0302000\pi$
$397$	9.87841	+	15.3711i	0.495783	+	0.771453i	−0.499720	+	0.866187i	$0.666564\pi$
$398$	8.21097	+	17.9795i	0.411579	+	0.901232i
$399$	28.6150	+	36.7616i	1.43254	+	1.84038i
$400$	0.693522	+	4.82355i	0.0346761	+	0.241177i
$401$	−35.4568	−	16.1926i	−1.77063	−	0.808618i	−0.980727	−	0.195383i	$-0.937405\pi$
$401$	−35.4568	−	16.1926i	−1.77063	−	0.808618i	−0.789900	−	0.613236i	$-0.789868\pi$
$402$	16.7724	−	4.92482i	0.836532	−	0.245628i
$403$	16.3352	−	4.79646i	0.813716	−	0.238929i
$404$	12.4060	+	5.66564i	0.617222	+	0.281876i
$405$	−0.554095	−	3.85382i	−0.0275332	−	0.191498i
$406$	−11.3186	+	8.81030i	−0.561731	+	0.437248i
$407$	12.7811	+	27.9866i	0.633534	+	1.38725i
$408$	0.433800	+	0.675006i	0.0214763	+	0.0334178i
$409$	25.8688	+	3.71937i	1.27913	+	0.183911i	0.748182	−	0.663494i	$-0.230927\pi$
$409$	25.8688	+	3.71937i	1.27913	+	0.183911i	0.530948	+	0.847405i	$0.321836\pi$
$410$	0.805990	−	1.25414i	0.0398050	−	0.0619378i
$411$	22.7708	−	26.2789i	1.12320	−	1.29624i
$412$	−6.64398	−	1.95085i	−0.327325	−	0.0961114i
$413$	14.8736	+	0.782652i	0.731883	+	0.0385118i
$414$	9.07397	+	3.95657i	0.445961	+	0.194455i
$415$	−0.542528			−0.0266317
$416$	−1.53262	+	5.21964i	−0.0751431	+	0.255914i
$417$	−1.48182	+	1.71011i	−0.0725649	+	0.0837444i
$418$	16.6967	−	25.9805i	0.816661	−	1.27075i
$419$	−3.64250	+	25.3341i	−0.177948	+	1.23765i	0.683554	+	0.729900i	$0.260433\pi$
$419$	−3.64250	+	25.3341i	−0.177948	+	1.23765i	−0.861502	+	0.507754i	$0.830476\pi$
$420$	1.84167	−	1.05112i	0.0898645	−	0.0512893i
$421$	9.45139	−	4.31630i	0.460632	−	0.210364i	−0.171562	−	0.985173i	$-0.554882\pi$
$421$	9.45139	−	4.31630i	0.460632	−	0.210364i	0.632195	+	0.774809i	$0.282154\pi$
$422$	8.41272	+	9.70879i	0.409525	+	0.472617i
$423$	−25.6785	+	3.69201i	−1.24853	+	0.179511i
$424$	7.68644	+	3.51028i	0.373286	+	0.170474i
$425$	1.66718	−	0.489527i	0.0808699	−	0.0237456i
$426$	−6.63790	−	22.6066i	−0.321607	−	1.09529i
$427$	25.6212	+	13.3703i	1.23990	+	0.647035i
$428$	3.91434	−	0.562797i	0.189207	−	0.0272038i
$429$	−36.5170	+	31.6422i	−1.76306	+	1.52770i
$430$	0.878290	−	0.401102i	0.0423549	−	0.0193428i
$431$	−12.9551	−	20.1585i	−0.624024	−	0.971000i	−0.999032	−	0.0439789i	$-0.985997\pi$
$431$	−12.9551	−	20.1585i	−0.624024	−	0.971000i	0.375008	−	0.927021i	$-0.377640\pi$
$432$	−2.08468	−	0.299731i	−0.100299	−	0.0144208i
$433$	−0.0893022	−	0.0573910i	−0.00429159	−	0.00275804i	0.538493	−	0.842630i	$-0.318994\pi$
$433$	−0.0893022	−	0.0573910i	−0.00429159	−	0.00275804i	−0.542785	+	0.839872i	$0.682630\pi$
$434$	−5.74362	+	5.96408i	−0.275703	+	0.286285i
$435$	1.22414	−	4.16905i	0.0586931	−	0.199890i
$436$		−	4.74293i		−	0.227145i
$437$	−27.9320	+	25.0581i	−1.33617	+	1.19869i
$438$	−22.0792			−1.05498
$439$	−8.99743	+	30.6424i	−0.429424	+	1.46248i	0.406507	+	0.913648i	$0.366747\pi$
$439$	−8.99743	+	30.6424i	−0.429424	+	1.46248i	−0.835931	+	0.548835i	$0.815072\pi$
$440$	−1.06240	−	0.920576i	−0.0506480	−	0.0438867i
$441$	11.2681	+	9.04407i	0.536574	+	0.430670i
$442$	1.91993	+	0.276044i	0.0913218	+	0.0131301i
$443$	28.2670	−	18.1661i	1.34301	−	0.863098i	0.345838	−	0.938294i	$-0.387595\pi$
$443$	28.2670	−	18.1661i	1.34301	−	0.863098i	0.997169	+	0.0751959i	$0.0239582\pi$
$444$	−7.28702	−	15.9564i	−0.345827	−	0.757255i
$445$	3.37977	+	3.90047i	0.160217	+	0.184900i
$446$	−26.3327	+	3.78607i	−1.24689	+	0.179276i
$447$	4.49667	−	9.84634i	0.212685	−	0.465716i
$448$	−0.610969	−	2.57424i	−0.0288656	−	0.121621i
$449$	−0.699891	+	0.205506i	−0.0330299	+	0.00969845i	−0.298206	−	0.954502i	$-0.596388\pi$
$449$	−0.699891	+	0.205506i	−0.0330299	+	0.00969845i	0.265176	+	0.964200i	$0.414570\pi$
$450$	4.17852	−	9.14968i	0.196977	−	0.431320i
$451$	−2.35124	−	16.3532i	−0.110715	−	0.770042i
$452$	2.64169	−	2.28903i	0.124254	−	0.107667i
$453$	26.7928	−	12.2359i	1.25884	−	0.574892i
$454$	−5.61202	+	3.60662i	−0.263385	+	0.169267i
$455$	0.995141	−	5.02862i	0.0466529	−	0.235745i
$456$	−9.51947	+	14.8126i	−0.445790	+	0.693663i
$457$	−15.9600	−	13.8295i	−0.746580	−	0.646915i	0.196112	−	0.980582i	$-0.437169\pi$
$457$	−15.9600	−	13.8295i	−0.746580	−	0.646915i	−0.942691	+	0.333667i	$0.891714\pi$
$458$	−13.2555	−	3.89217i	−0.619389	−	0.181869i
$459$			0.750951i			0.0350514i
$460$	0.948058	+	1.42081i	0.0442034	+	0.0662456i
$461$		−	23.1457i		−	1.07800i	−0.842304	−	0.539002i	$-0.818801\pi$
$461$		−	23.1457i		−	1.07800i	0.842304	−	0.539002i	$-0.181199\pi$
$462$	7.79641	−	22.1690i	0.362722	−	1.03140i
$463$	−7.51361	+	8.67117i	−0.349187	+	0.402983i	−0.902988	−	0.429666i	$-0.858631\pi$
$463$	−7.51361	+	8.67117i	−0.349187	+	0.402983i	0.553801	+	0.832649i	$0.313177\pi$
$464$	−4.56067	−	2.93096i	−0.211724	−	0.136067i
$465$	0.356967	−	2.48276i	0.0165540	−	0.115135i
$466$	−14.0067	+	9.00153i	−0.648846	+	0.416988i
$467$	2.57244	+	5.63287i	0.119039	+	0.260658i	0.959766	−	0.280800i	$-0.0905998\pi$
$467$	2.57244	+	5.63287i	0.119039	+	0.260658i	−0.840728	+	0.541458i	$0.817872\pi$
$468$	8.48607	−	7.35322i	0.392269	−	0.339903i
$469$	1.85184	+	20.4683i	0.0855101	+	0.945138i
$470$	−4.07184	−	1.85955i	−0.187820	−	0.0857744i
$471$	−5.92539	−	20.1800i	−0.273028	−	0.929847i
$472$	1.58601	+	5.40145i	0.0730019	+	0.248622i
$473$	4.44508	−	9.73337i	0.204385	−	0.447541i
$474$	−0.855255	−	5.94843i	−0.0392832	−	0.273221i
$475$	24.9696	+	28.8165i	1.14568	+	1.32219i
$476$	−0.877520	+	0.346254i	−0.0402211	+	0.0158705i
$477$	−9.42971	−	14.6729i	−0.431757	−	0.671827i
$478$	1.71493	−	11.9276i	0.0784390	−	0.545555i
$479$	20.7553	+	13.3386i	0.948332	+	0.609456i	0.920746	−	0.390163i	$-0.127581\pi$
$479$	20.7553	+	13.3386i	0.948332	+	0.609456i	0.0275864	+	0.999619i	$0.491218\pi$
$480$	0.605719	+	0.524859i	0.0276472	+	0.0239564i
$481$	−40.6872	−	11.9468i	−1.85518	−	0.544729i
$482$	−23.6806			−1.07862
$483$	−16.2767	+	23.4603i	−0.740617	+	1.06748i
$484$	−4.57887			−0.208130
$485$	4.06076	+	1.19235i	0.184390	+	0.0541417i
$486$	13.8167	+	11.9722i	0.626737	+	0.543071i
$487$	−2.30547	−	1.48163i	−0.104471	−	0.0671393i	0.487362	−	0.873200i	$-0.337959\pi$
$487$	−2.30547	−	1.48163i	−0.104471	−	0.0671393i	−0.591833	+	0.806061i	$0.701596\pi$
$488$	−1.55453	+	10.8120i	−0.0703704	+	0.489437i
$489$	−11.8539	−	18.4450i	−0.536052	−	0.834112i
$490$	0.791948	+	2.36398i	0.0357766	+	0.106794i
$491$	−1.09295	−	1.26133i	−0.0493239	−	0.0569229i	0.730551	−	0.682858i	$-0.239263\pi$
$491$	−1.09295	−	1.26133i	−0.0493239	−	0.0569229i	−0.779875	+	0.625935i	$0.784718\pi$
$492$	1.34054	+	9.32365i	0.0604361	+	0.420343i
$493$	−0.802996	+	1.75832i	−0.0361651	+	0.0791906i
$494$	11.9919	+	40.8407i	0.539542	+	1.83751i
$495$	0.817481	+	2.78408i	0.0367430	+	0.125135i
$496$	−2.84676	−	1.30007i	−0.127823	−	0.0583749i
$497$	27.5881	−	2.49600i	1.23749	−	0.111961i
$498$	2.59065	−	2.24481i	0.116090	−	0.100592i
$499$	−0.421913	−	0.923861i	−0.0188874	−	0.0413577i	0.899953	−	0.435986i	$-0.143600\pi$
$499$	−0.421913	−	0.923861i	−0.0188874	−	0.0413577i	−0.918841	+	0.394629i	$0.870873\pi$
$500$	2.95818	−	1.90111i	0.132294	−	0.0850202i
$501$	−0.0228438	+	0.158882i	−0.00102059	+	0.00709833i
$502$	−5.28140	−	3.39415i	−0.235720	−	0.151488i
$503$	−16.8414	+	19.4361i	−0.750923	+	0.866611i	−0.994657	−	0.103231i	$-0.967082\pi$
$503$	−16.8414	+	19.4361i	−0.750923	+	0.866611i	0.243734	+	0.969842i	$0.421628\pi$
$504$	−1.81178	+	5.15179i	−0.0807032	+	0.229479i
$505$		−	4.85746i		−	0.216154i
$506$	18.2515	+	5.01945i	0.811380	+	0.223142i
$507$		−	37.3414i		−	1.65839i
$508$	−2.85940	−	0.839596i	−0.126865	−	0.0372510i
$509$	−9.53513	−	8.26224i	−0.422637	−	0.366217i	0.417421	−	0.908713i	$-0.362934\pi$
$509$	−9.53513	−	8.26224i	−0.422637	−	0.366217i	−0.840058	+	0.542496i	$0.817479\pi$
$510$	0.154501	−	0.240409i	0.00684143	−	0.0106455i
$511$	5.03936	−	25.4647i	0.222928	−	1.12649i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	−14.9900	+	6.84569i	−0.661823	+	0.302245i
$514$	−8.79008	+	7.61665i	−0.387714	+	0.335956i
$515$	0.350977	+	2.44110i	0.0154659	+	0.107568i
$516$	−2.53433	+	5.54941i	−0.111568	+	0.244299i
$517$	−47.5983	+	13.9761i	−2.09337	+	0.614670i
$518$	20.0663	−	4.76251i	0.881661	−	0.209253i
$519$	−1.52540	+	3.34017i	−0.0669578	+	0.146617i
$520$	1.91778	−	0.275735i	0.0841001	−	0.0120918i
$521$	−7.18402	−	8.29081i	−0.314738	−	0.363227i	0.576235	−	0.817284i	$-0.304521\pi$
$521$	−7.18402	−	8.29081i	−0.314738	−	0.363227i	−0.890972	+	0.454058i	$0.849976\pi$
$522$	4.64851	+	10.1788i	0.203460	+	0.445515i
$523$	9.12480	−	5.86415i	0.399000	−	0.256422i	−0.325719	−	0.945467i	$-0.605606\pi$
$523$	9.12480	−	5.86415i	0.399000	−	0.256422i	0.724718	+	0.689045i	$0.241970\pi$
$524$	2.21860	+	0.318987i	0.0969201	+	0.0139350i
$525$	23.5503	+	16.9472i	1.02782	+	0.739635i
$526$	−4.66255	−	4.04012i	−0.203297	−	0.176158i
$527$	−0.314378	+	1.07067i	−0.0136945	+	0.0466392i
$528$	8.88217			0.386547
$529$	−19.7655	−	11.7612i	−0.859370	−	0.511355i
$530$		−	3.00955i		−	0.130727i
$531$	3.27367	−	11.1491i	0.142065	−	0.483830i
$532$	−14.9112	−	14.3600i	−0.646482	−	0.622585i
$533$	19.1560	+	12.3108i	0.829736	+	0.533239i
$534$	−32.2778	−	4.64085i	−1.39680	−	0.200829i
$535$	−0.761470	−	1.18487i	−0.0329212	−	0.0512264i
$536$	−7.06591	+	3.22690i	−0.305201	+	0.139381i
$537$	29.3155	−	25.4020i	1.26506	−	1.09618i
$538$	24.7975	−	3.56534i	1.06910	−	0.153713i
$539$	23.7889	+	14.0518i	1.02466	+	0.605252i
$540$	0.211330	+	0.719724i	0.00909420	+	0.0309720i
$541$	9.44827	−	2.77426i	0.406213	−	0.119275i	−0.0722416	−	0.997387i	$-0.523015\pi$
$541$	9.44827	−	2.77426i	0.406213	−	0.119275i	0.478455	+	0.878112i	$0.341197\pi$
$542$	8.51348	+	3.88798i	0.365685	+	0.167003i
$543$	−11.9966	+	1.72485i	−0.514823	+	0.0740204i
$544$	−0.233496	−	0.269468i	−0.0100110	−	0.0115534i
$545$	−1.53658	+	0.701733i	−0.0658199	+	0.0300589i
$546$	16.0549	+	28.1299i	0.687086	+	1.20385i
$547$	−0.649552	+	4.51773i	−0.0277728	+	0.193164i	−0.998985	−	0.0450536i	$-0.985654\pi$
$547$	−0.649552	+	4.51773i	−0.0277728	+	0.193164i	0.971212	+	0.238218i	$0.0765632\pi$
$548$	−8.35385	+	12.9988i	−0.356859	+	0.555283i
$549$	14.7648	−	17.0395i	0.630148	−	0.727230i
$550$	5.41895	−	18.4552i	0.231065	−	0.786934i
$551$	−42.4184			−1.80709
$552$	−10.4060	−	2.86180i	−0.442908	−	0.121806i
$553$	7.05575	+	0.371274i	0.300041	+	0.0157882i
$554$	−17.5753	−	5.16058i	−0.746704	−	0.219252i
$555$	−4.09128	+	4.72159i	−0.173665	+	0.200420i
$556$	0.543630	−	0.845905i	0.0230551	−	0.0358744i
$557$	0.233117	+	0.0335171i	0.00987747	+	0.00142017i	0.147252	−	0.989099i	$-0.452957\pi$
$557$	0.233117	+	0.0335171i	0.00987747	+	0.00142017i	−0.137374	+	0.990519i	$0.543866\pi$
$558$	3.49240	+	5.43428i	0.147845	+	0.230051i
$559$	6.12647	+	13.4151i	0.259122	+	0.567399i
$560$	−0.743589	+	0.578805i	−0.0314224	+	0.0244590i
$561$	−0.450712	−	3.13477i	−0.0190291	−	0.132350i
$562$	−3.33993	−	1.52529i	−0.140886	−	0.0643406i
$563$	8.78805	−	2.58040i	0.370372	−	0.108751i	−0.0912494	−	0.995828i	$-0.529086\pi$
$563$	8.78805	−	2.58040i	0.370372	−	0.108751i	0.461621	+	0.887077i	$0.347268\pi$
$564$	27.1378	−	7.96838i	1.14271	−	0.335529i
$565$	−1.13243	−	0.517164i	−0.0476417	−	0.0217572i
$566$	1.59302	+	11.0797i	0.0669595	+	0.465714i
$567$	−22.8235	+	17.7656i	−0.958496	+	0.746087i
$568$	4.34936	+	9.52376i	0.182495	+	0.399608i
$569$	−0.438292	−	0.681996i	−0.0183742	−	0.0285908i	0.831945	−	0.554858i	$-0.187227\pi$
$569$	−0.438292	−	0.681996i	−0.0183742	−	0.0285908i	−0.850319	+	0.526267i	$0.823591\pi$
$570$	6.20731	+	0.892477i	0.259996	+	0.0373817i
$571$	6.27740	−	9.76782i	0.262701	−	0.408771i	−0.684697	−	0.728827i	$-0.740066\pi$
$571$	6.27740	−	9.76782i	0.262701	−	0.408771i	0.947398	+	0.320057i	$0.103702\pi$
$572$	14.0610	−	16.2272i	0.587919	−	0.678495i
$573$	19.0395	+	5.59050i	0.795386	+	0.233546i
$574$	−11.0593	−	0.581940i	−0.461605	−	0.0242897i
$575$	−12.2948	+	19.8754i	−0.512730	+	0.828862i
$576$	−2.06410			−0.0860040
$577$	0.321950	−	1.09646i	0.0134029	−	0.0456462i	−0.952520	−	0.304476i	$-0.901519\pi$
$577$	0.321950	−	1.09646i	0.0134029	−	0.0456462i	0.965923	+	0.258830i	$0.0833369\pi$
$578$	11.0494	−	12.7517i	0.459594	−	0.530399i
$579$	−19.4310	+	30.2352i	−0.807524	+	1.25653i
$580$	−0.274786	+	1.91118i	−0.0114099	+	0.0793573i
$581$	1.99773	+	3.50025i	0.0828799	+	0.145215i
$582$	−24.3243	+	11.1085i	−1.00827	+	0.460463i
$583$	−21.8412	−	25.2061i	−0.904570	−	1.04393i
$584$	9.71155	−	1.39631i	0.401867	−	0.0577798i
$585$	−3.63779	−	1.66132i	−0.150404	−	0.0686872i
$586$	−2.93292	+	0.861182i	−0.121158	+	0.0355751i
$587$	−10.1013	−	34.4020i	−0.416927	−	1.41992i	−0.853895	−	0.520446i	$-0.825766\pi$
$587$	−10.1013	−	34.4020i	−0.416927	−	1.41992i	0.436967	−	0.899477i	$-0.356052\pi$
$588$	−13.5631	−	8.01150i	−0.559331	−	0.330389i
$589$	−24.2379	+	3.48488i	−0.998705	+	0.143592i
$590$	1.51527	−	1.31299i	0.0623825	−	0.0540547i
$591$	−22.2472	+	10.1599i	−0.915127	+	0.417924i
$592$	4.21430	+	6.55759i	0.173207	+	0.269515i
$593$	8.74135	+	1.25682i	0.358964	+	0.0516112i	0.319438	−	0.947607i	$-0.396506\pi$
$593$	8.74135	+	1.25682i	0.358964	+	0.0516112i	0.0395264	+	0.999219i	$0.487415\pi$
$594$	6.99321	+	4.49426i	0.286935	+	0.184402i
$595$	0.242009	+	0.233063i	0.00992140	+	0.00955466i
$596$	−1.35517	+	4.61530i	−0.0555101	+	0.189050i
$597$			44.4799i			1.82044i
$598$	−21.7016	+	14.4808i	−0.887445	+	0.592162i
$599$	−10.0997			−0.412662			−0.206331	−	0.978482i	$-0.566152\pi$
$599$	−10.0997			−0.412662			−0.206331	+	0.978482i	$0.566152\pi$
$600$	−3.08957	+	10.5221i	−0.126131	+	0.429563i
$601$	20.8309	+	18.0501i	0.849711	+	0.736279i	0.966442	−	0.256885i	$-0.0826961\pi$
$601$	20.8309	+	18.0501i	0.849711	+	0.736279i	−0.116731	+	0.993164i	$0.537242\pi$
$602$	−5.82190	−	4.18953i	−0.237283	−	0.170753i
$603$	15.8705	+	2.28183i	0.646295	+	0.0929232i
$604$	−11.0110	+	7.07637i	−0.448033	+	0.287933i
$605$	0.677459	+	1.48343i	0.0275426	+	0.0603099i
$606$	20.0986	+	23.1951i	0.816451	+	0.942235i
$607$	33.9371	−	4.87942i	1.37746	−	0.198049i	0.586519	−	0.809936i	$-0.300498\pi$
$607$	33.9371	−	4.87942i	1.37746	−	0.198049i	0.790946	+	0.611886i	$0.209589\pi$
$608$	3.25039	−	7.11736i	0.131821	−	0.288647i
$609$	−31.4052	+	7.45369i	−1.27260	+	0.302039i
$610$	3.73280	−	1.09605i	0.151136	−	0.0443777i
$611$	28.4029	−	62.1937i	1.14906	−	2.51609i
$612$	0.104739	+	0.728479i	0.00423384	+	0.0294470i
$613$	11.1666	−	9.67589i	0.451013	−	0.390805i	−0.399522	−	0.916724i	$-0.630824\pi$
$613$	11.1666	−	9.67589i	0.451013	−	0.390805i	0.850535	+	0.525918i	$0.176278\pi$
$614$	21.4902	−	9.81423i	0.867272	−	0.396070i
$615$	2.82227	−	1.81376i	0.113805	−	0.0731380i
$616$	−2.02727	+	10.2441i	−0.0816810	+	0.412748i
$617$	15.6465	−	24.3464i	0.629904	−	0.980150i	−0.368813	−	0.929504i	$-0.620236\pi$
$617$	15.6465	−	24.3464i	0.629904	−	0.980150i	0.998717	−	0.0506459i	$-0.0161280\pi$
$618$	−11.7765	−	10.2044i	−0.473719	−	0.410480i
$619$	22.2210	+	6.52468i	0.893139	+	0.262249i	0.695928	−	0.718112i	$-0.254993\pi$
$619$	22.2210	+	6.52468i	0.893139	+	0.262249i	0.197211	+	0.980361i	$0.436812\pi$
$620$			1.11462i			0.0447643i
$621$	−6.74492	−	7.51848i	−0.270664	−	0.301706i
$622$			9.79301i			0.392664i
$623$	12.7196	−	36.1680i	0.509598	−	1.44904i
$624$	−8.01676	+	9.25183i	−0.320927	+	0.370370i
$625$	19.4442	+	12.4960i	0.777768	+	0.499841i
$626$	2.66868	−	18.5611i	0.106662	−	0.741850i
$627$	58.4654	−	37.5734i	2.33488	−	1.50054i
$628$	3.88250	+	8.50148i	0.154928	+	0.339246i
$629$	2.10051	−	1.82010i	0.0837528	−	0.0725722i
$630$	1.93710	−	0.175256i	0.0771758	−	0.00698238i
$631$	−13.8845	−	6.34086i	−0.552735	−	0.252426i	0.119410	−	0.992845i	$-0.461900\pi$
$631$	−13.8845	−	6.34086i	−0.552735	−	0.252426i	−0.672145	+	0.740419i	$0.734627\pi$
$632$	0.752370	+	2.56234i	0.0299277	+	0.101924i
$633$	8.14471	+	27.7383i	0.323723	+	1.10250i
$634$	−0.0662539	+	0.145076i	−0.00263128	+	0.00576170i
$635$	0.151052	+	1.05059i	0.00599431	+	0.0416913i
$636$	12.4526	+	14.3710i	0.493777	+	0.569849i
$637$	−36.1077	+	12.0963i	−1.43064	+	0.479273i
$638$	11.5685	+	18.0010i	0.458002	+	0.712666i
$639$	3.07555	−	21.3909i	0.121667	−	0.846212i
$640$	−0.299619	−	0.192553i	−0.0118435	−	0.00761134i
$641$	22.2066	+	19.2422i	0.877110	+	0.760020i	0.971879	−	0.235479i	$-0.0756660\pi$
$641$	22.2066	+	19.2422i	0.877110	+	0.760020i	−0.0947697	+	0.995499i	$0.530211\pi$
$642$	8.53875	+	2.50720i	0.336998	+	0.0989514i
$643$	−39.5726			−1.56059			−0.780295	−	0.625411i	$-0.784931\pi$
$643$	−39.5726			−1.56059			−0.780295	+	0.625411i	$0.784931\pi$
$644$	5.67569	−	11.3484i	0.223653	−	0.447190i
$645$	2.17282			0.0855546
$646$	−2.67685	−	0.785995i	−0.105319	−	0.0309246i
$647$	10.9682	+	9.50400i	0.431205	+	0.373641i	0.843249	−	0.537523i	$-0.180640\pi$
$647$	10.9682	+	9.50400i	0.431205	+	0.373641i	−0.412045	+	0.911164i	$0.635185\pi$
$648$	−9.19641	−	5.91017i	−0.361269	−	0.232174i
$649$	3.16218	−	21.9934i	0.124126	−	0.863318i
$650$	14.3324	+	22.3016i	0.562161	+	0.874740i
$651$	−17.3326	+	6.83913i	−0.679317	+	0.268047i
$652$	6.38043	+	7.36341i	0.249877	+	0.288373i
$653$	1.40557	+	9.77598i	0.0550044	+	0.382564i	0.998665	+	0.0516497i	$0.0164479\pi$
$653$	1.40557	+	9.77598i	0.0550044	+	0.382564i	−0.943661	+	0.330914i	$0.892643\pi$
$654$	4.43384	−	9.70876i	0.173377	−	0.379642i
$655$	−0.224907	−	0.765962i	−0.00878783	−	0.0299286i
$656$	−1.17928	−	4.01624i	−0.0460430	−	0.156808i
$657$	−18.4216	−	8.41287i	−0.718696	−	0.328217i
$658$	2.99629	+	33.1178i	0.116807	+	1.29106i
$659$	30.1938	−	26.1631i	1.17618	−	1.01917i	0.176793	−	0.984248i	$-0.443428\pi$
$659$	30.1938	−	26.1631i	1.17618	−	1.01917i	0.999390	−	0.0349201i	$-0.0111177\pi$
$660$	−1.31415	−	2.87758i	−0.0511531	−	0.112010i
$661$	4.80122	−	3.08556i	0.186746	−	0.120014i	−0.443927	−	0.896063i	$-0.646415\pi$
$661$	4.80122	−	3.08556i	0.186746	−	0.120014i	0.630673	+	0.776048i	$0.282779\pi$
$662$	−1.16379	+	8.09436i	−0.0452321	+	0.314596i
$663$	3.67203	+	2.35987i	0.142610	+	0.0916498i
$664$	−0.997536	+	1.15122i	−0.0387119	+	0.0446759i
$665$	−2.44609	+	6.95542i	−0.0948551	+	0.269720i
$666$		−	16.0897i		−	0.623462i
$667$	−7.75335	−	24.8165i	−0.300211	−	0.960900i
$668$		−	0.0713291i		−	0.00275981i
$669$	−57.4422	−	16.8665i	−2.22084	−	0.652098i
$670$	2.09085	+	1.81173i	0.0807766	+	0.0699933i
$671$	23.3092	−	36.2698i	0.899840	−	1.40018i
$672$	1.15583	−	5.84061i	0.0445872	−	0.225306i
$673$	−17.9880	+	11.5602i	−0.693388	+	0.445613i	−0.839289	−	0.543686i	$-0.817028\pi$
$673$	−17.9880	+	11.5602i	−0.693388	+	0.445613i	0.145901	+	0.989299i	$0.453392\pi$
$674$	23.9693	−	10.9464i	0.923264	−	0.421641i
$675$	−7.75657	+	6.72111i	−0.298550	+	0.258695i
$676$	2.36151	+	16.4247i	0.0908274	+	0.631718i
$677$	−21.3203	+	46.6850i	−0.819406	+	1.79425i	−0.259379	+	0.965776i	$0.583518\pi$
$677$	−21.3203	+	46.6850i	−0.819406	+	1.79425i	−0.560027	+	0.828474i	$0.689209\pi$
$678$	7.54738	−	2.21611i	0.289855	−	0.0851092i
$679$	−7.26009	−	30.5895i	−0.278617	−	1.17392i
$680$	−0.0527539	+	0.115515i	−0.00202302	+	0.00442980i
$681$	−14.8594	+	2.13645i	−0.569412	+	0.0818690i
$682$	8.08913	+	9.33535i	0.309749	+	0.357469i
$683$	−1.43306	−	3.13796i	−0.0548345	−	0.120071i	0.880231	−	0.474545i	$-0.157387\pi$
$683$	−1.43306	−	3.13796i	−0.0548345	−	0.120071i	−0.935066	+	0.354474i	$0.884660\pi$
$684$	−13.5866	+	8.73156i	−0.519496	+	0.333860i
$685$	5.44725	+	0.783196i	0.208129	+	0.0299244i
$686$	12.3356	−	13.8142i	0.470975	−	0.527430i
$687$	−23.4954	−	20.3589i	−0.896406	−	0.776740i
$688$	0.763777	−	2.60119i	0.0291187	−	0.0991693i
$689$	45.9683			1.75125
$690$	0.612453	+	3.79466i	0.0233157	+	0.144460i
$691$		−	21.5311i		−	0.819083i	−0.912292	−	0.409541i	$-0.865689\pi$
$691$		−	21.5311i		−	0.819083i	0.912292	−	0.409541i	$-0.134311\pi$
$692$	0.459715	−	1.56565i	0.0174757	−	0.0595169i
$693$	14.9520	−	15.5259i	0.567979	−	0.589780i
$694$	23.9037	+	15.3620i	0.907372	+	0.583132i
$695$	−0.354482	−	0.0509668i	−0.0134463	−	0.00193328i
$696$	−6.59571	−	10.2631i	−0.250010	−	0.389022i
$697$	−1.35761	+	0.619998i	−0.0514230	+	0.0234841i
$698$	−21.2726	+	18.4328i	−0.805178	+	0.697691i
$699$	−37.0865	+	5.33223i	−1.40274	+	0.201683i
$700$	−11.4304	−	5.96488i	−0.432027	−	0.225451i
$701$	−14.4426	−	49.1869i	−0.545488	−	1.85776i	−0.513173	−	0.858285i	$-0.671530\pi$
$701$	−14.4426	−	49.1869i	−0.545488	−	1.85776i	−0.0323156	−	0.999478i	$-0.510288\pi$
$702$	−10.9932	+	3.22788i	−0.414910	+	0.121829i
$703$	55.4799	+	25.3368i	2.09247	+	0.955597i
$704$	−3.90683	+	0.561718i	−0.147244	+	0.0211705i
$705$	−6.59667	−	7.61296i	−0.248445	−	0.286721i
$706$	9.92471	−	4.53246i	0.373521	−	0.170581i
$707$	−31.3390	+	17.8865i	−1.17863	+	0.672689i
$708$	−1.80289	+	12.5394i	−0.0677568	+	0.471259i
$709$	−1.44625	+	2.25041i	−0.0543151	+	0.0845160i	−0.867349	−	0.497700i	$-0.834178\pi$
$709$	−1.44625	+	2.25041i	−0.0543151	+	0.0845160i	0.813034	+	0.582216i	$0.197814\pi$
$710$	2.44194	−	2.81814i	0.0916442	−	0.105763i
$711$	1.55297	−	5.28891i	0.0582408	−	0.198350i
$712$	14.4909			0.543070
$713$	−6.46907	−	13.5432i	−0.242268	−	0.507197i
$714$	−2.11997	−	0.111553i	−0.0793378	−	0.00417477i
$715$	−7.33755	−	2.15450i	−0.274409	−	0.0805737i
$716$	−11.2880	+	13.0270i	−0.421852	+	0.486843i
$717$	14.6607	−	22.8126i	0.547515	−	0.851950i
$718$	−26.2762	−	3.77795i	−0.980619	−	0.140992i
$719$	−6.69276	−	10.4141i	−0.249598	−	0.388382i	0.693735	−	0.720231i	$-0.255964\pi$
$719$	−6.69276	−	10.4141i	−0.249598	−	0.388382i	−0.943333	+	0.331849i	$0.892328\pi$
$720$	0.305390	+	0.668711i	0.0113812	+	0.0249214i
$721$	14.4569	−	11.2532i	0.538405	−	0.419091i
$722$	−6.00879	−	41.7921i	−0.223624	−	1.55534i
$723$	−48.4742	−	22.1374i	−1.80277	−	0.823299i
$724$	5.16764	−	1.51736i	0.192054	−	0.0563921i
$725$	−25.3486	+	7.44301i	−0.941422	+	0.276426i
$726$	−9.37292	−	4.28047i	−0.347862	−	0.158863i
$727$	−6.07988	−	42.2865i	−0.225490	−	1.56832i	−0.716764	−	0.697315i	$-0.754378\pi$
$727$	−6.07988	−	42.2865i	−0.225490	−	1.56832i	0.491274	−	0.871005i	$-0.336531\pi$
$728$	−8.84073	−	11.3577i	−0.327659	−	0.420943i
$729$	3.46696	+	7.59158i	0.128406	+	0.281170i
$730$	−1.88922	−	2.93969i	−0.0699233	−	0.108803i
$731$	−0.956790	−	0.137566i	−0.0353881	−	0.00508805i
$732$	−13.2895	+	20.6789i	−0.491195	+	0.764315i
$733$	−15.0108	+	17.3234i	−0.554436	+	0.639854i	−0.961911	−	0.273363i	$-0.911864\pi$
$733$	−15.0108	+	17.3234i	−0.554436	+	0.639854i	0.407475	+	0.913217i	$0.366410\pi$
$734$	24.0669	+	7.06667i	0.888325	+	0.260836i
$735$	−0.588806	+	5.57939i	−0.0217185	+	0.205799i
$736$	4.75806	+	0.600682i	0.175385	+	0.0221414i
$737$	30.6599			1.12937
$738$	−2.43414	+	8.28991i	−0.0896019	+	0.305156i
$739$	3.11050	−	3.58971i	0.114422	−	0.132050i	−0.695649	−	0.718382i	$-0.744883\pi$
$739$	3.11050	−	3.58971i	0.114422	−	0.132050i	0.810071	+	0.586332i	$0.199429\pi$
$740$	1.50096	−	2.33554i	0.0551763	−	0.0858560i
$741$	−13.6318	+	94.8112i	−0.500776	+	3.48298i
$742$	−19.4168	+	11.0820i	−0.712815	+	0.406832i
$743$	26.6877	−	12.1879i	0.979076	−	0.447129i	0.139412	−	0.990235i	$-0.455479\pi$
$743$	26.6877	−	12.1879i	0.979076	−	0.447129i	0.839665	+	0.543105i	$0.182752\pi$
$744$	−4.61195	−	5.32248i	−0.169082	−	0.195131i
$745$	1.69573	−	0.243810i	0.0621269	−	0.00893249i
$746$	5.01464	+	2.29011i	0.183599	+	0.0838469i
$747$	3.01684	−	0.885823i	0.110380	−	0.0324106i
$748$	0.396492	+	1.35033i	0.0144972	+	0.0493729i
$749$	−4.84054	+	9.27581i	−0.176869	+	0.338931i
$750$	7.83260	−	1.12616i	0.286006	−	0.0411215i
$751$	−3.29145	+	2.85206i	−0.120107	+	0.104073i	−0.712843	−	0.701323i	$-0.752593\pi$
$751$	−3.29145	+	2.85206i	−0.120107	+	0.104073i	0.592737	+	0.805396i	$0.298047\pi$
$752$	−11.4327	+	5.22113i	−0.416907	+	0.190395i
$753$	−7.63804	−	11.8850i	−0.278346	−	0.433114i
$754$	−29.1915	−	4.19711i	−1.06309	−	0.152850i
$755$	3.92167	+	2.52031i	0.142724	+	0.0917233i
$756$	3.86530	−	4.01366i	0.140580	−	0.145975i
$757$	6.25908	−	21.3165i	0.227490	−	0.774761i	−0.764072	−	0.645131i	$-0.776803\pi$
$757$	6.25908	−	21.3165i	0.227490	−	0.774761i	0.991562	−	0.129630i	$-0.0413790\pi$
$758$		−	12.7416i		−	0.462795i
$759$	32.6685	+	27.3369i	1.18579	+	0.992267i
$760$	−2.78673			−0.101086
$761$	−4.11368	+	14.0099i	−0.149121	+	0.507859i	−0.999842	−	0.0177578i	$-0.994347\pi$
$761$	−4.11368	+	14.0099i	−0.149121	+	0.507859i	0.850721	+	0.525617i	$0.176165\pi$
$762$	−5.06830	−	4.39170i	−0.183605	−	0.159095i
$763$	10.1855	+	7.32964i	0.368739	+	0.265351i
$764$	−8.72809	−	1.25491i	−0.315771	−	0.0454011i
$765$	0.220511	−	0.141714i	0.00797258	−	0.00512366i
$766$	−16.2007	−	35.4746i	−0.585355	−	1.28175i
$767$	20.0547	+	23.1444i	0.724133	+	0.835694i
$768$	2.22745	−	0.320259i	0.0803762	−	0.0115563i
$769$	11.6376	−	25.4828i	0.419663	−	0.918934i	−0.575229	−	0.817992i	$-0.695087\pi$
$769$	11.6376	−	25.4828i	0.419663	−	0.918934i	0.994892	−	0.100942i	$-0.0321856\pi$
$770$	3.61876	−	0.858874i	0.130411	−	0.0309517i
$771$	−25.1135	+	7.37400i	−0.904442	+	0.265568i
$772$	6.63464	−	14.5278i	0.238786	−	0.522868i
$773$	0.509589	+	3.54427i	0.0183286	+	0.127478i	0.996931	−	0.0782802i	$-0.0249429\pi$
$773$	0.509589	+	3.54427i	0.0183286	+	0.127478i	−0.978603	+	0.205759i	$0.934034\pi$
$774$	−4.22900	+	3.66445i	−0.152008	+	0.131716i
$775$	−13.8727	+	6.33544i	−0.498322	+	0.227576i
$776$	9.99655	−	6.42439i	0.358855	−	0.230622i
$777$	45.5277	+	9.00972i	1.63330	+	0.323222i
$778$	9.51753	−	14.8096i	0.341220	−	0.530948i
$779$	−24.7519	−	21.4477i	−0.886830	−	0.768443i
$780$	4.18345	+	1.22837i	0.149791	+	0.0439827i
$781$		−	41.3248i		−	1.47872i
$782$	−0.0294427	−	1.70974i	−0.00105287	−	0.0611401i
$783$		−	11.4178i		−	0.408040i
$784$	6.47239	+	2.66613i	0.231157	+	0.0952188i
$785$	2.17982	−	2.51565i	0.0778011	−	0.0897872i
$786$	4.24327	+	2.72698i	0.151352	+	0.0972683i
$787$	1.53072	−	10.6464i	0.0545644	−	0.379504i	−0.944181	−	0.329427i	$-0.893144\pi$
$787$	1.53072	−	10.6464i	0.0545644	−	0.379504i	0.998745	−	0.0500767i	$-0.0159466\pi$
$788$	9.14293	−	5.87580i	0.325703	−	0.209317i
$789$	−5.76738	−	12.6288i	−0.205324	−	0.449597i
$790$	0.718812	−	0.622854i	0.0255742	−	0.0221601i
$791$	0.833305	+	9.21047i	0.0296289	+	0.327487i
$792$	7.41078	+	3.38439i	0.263331	+	0.120259i
$793$	16.7412	+	57.0152i	0.594496	+	2.02467i
$794$	−5.14772	−	17.5315i	−0.182686	−	0.622171i
$795$	2.81342	−	6.16054i	0.0997819	−	0.218492i
$796$	−2.81295	−	19.5645i	−0.0997025	−	0.693446i
$797$	−5.75061	−	6.63656i	−0.203697	−	0.235079i	0.644705	−	0.764432i	$-0.276980\pi$
$797$	−5.75061	−	6.63656i	−0.203697	−	0.235079i	−0.848402	+	0.529353i	$0.822435\pi$
$798$	−17.0989	−	43.3343i	−0.605296	−	1.53402i
$799$	2.42282	+	3.76998i	0.0857131	+	0.133372i
$800$	0.693522	−	4.82355i	0.0245197	−	0.170538i
$801$	−25.1625	−	16.1709i	−0.889072	−	0.571372i
$802$	29.4586	+	25.5260i	1.04022	+	0.901354i
$803$	−37.1571	−	10.9103i	−1.31125	−	0.385016i
$804$	−17.4805			−0.616489
$805$	−4.51631	−	0.159731i	−0.159179	−	0.00562976i
$806$	−17.0249			−0.599675
$807$	54.0934	+	15.8832i	1.90418	+	0.559117i
$808$	−10.3073	−	8.93132i	−0.362609	−	0.314203i
$809$	−26.0372	−	16.7331i	−0.915420	−	0.588305i	−0.00409495	−	0.999992i	$-0.501303\pi$
$809$	−26.0372	−	16.7331i	−0.915420	−	0.588305i	−0.911325	+	0.411687i	$0.864940\pi$
$810$	−0.554095	+	3.85382i	−0.0194689	+	0.135409i
$811$	1.54721	+	2.40751i	0.0543301	+	0.0845392i	0.867356	−	0.497688i	$-0.165818\pi$
$811$	1.54721	+	2.40751i	0.0543301	+	0.0845392i	−0.813026	+	0.582228i	$0.802181\pi$
$812$	13.3422	−	5.26461i	0.468221	−	0.184752i
$813$	13.7924	+	15.9173i	0.483722	+	0.558245i
$814$	−4.37860	−	30.4538i	−0.153470	−	1.06741i
$815$	1.44154	−	3.15653i	0.0504948	−	0.110568i
$816$	−0.226057	−	0.769879i	−0.00791358	−	0.0269512i
$817$	−5.97613	−	20.3528i	−0.209078	−	0.712055i
$818$	−23.7731	−	10.8568i	−0.831205	−	0.379599i
$819$	2.67689	+	29.5875i	0.0935380	+	1.03387i
$820$	−1.12667	+	0.976269i	−0.0393452	+	0.0340928i
$821$	−1.03049	−	2.25645i	−0.0359642	−	0.0787506i	0.890797	−	0.454401i	$-0.150147\pi$
$821$	−1.03049	−	2.25645i	−0.0359642	−	0.0787506i	−0.926761	+	0.375650i	$0.877419\pi$
$822$	−29.2520	+	18.7991i	−1.02028	+	0.655695i
$823$	5.86587	−	40.7980i	0.204471	−	1.42213i	−0.586338	−	0.810066i	$-0.699431\pi$
$823$	5.86587	−	40.7980i	0.204471	−	1.42213i	0.790809	−	0.612062i	$-0.209660\pi$
$824$	5.82523	+	3.74365i	0.202932	+	0.130416i
$825$	28.3451	−	32.7120i	0.986849	−	1.13888i
$826$	−14.0506	−	4.94133i	−0.488884	−	0.171931i
$827$			23.8402i			0.829006i	0.910048	+	0.414503i	$0.136045\pi$
$827$			23.8402i			0.829006i	−0.910048	+	0.414503i	$0.863955\pi$
$828$	−7.59172	−	6.35273i	−0.263830	−	0.220773i
$829$			41.1528i			1.42930i	0.699484	+	0.714648i	$0.253413\pi$
$829$			41.1528i			1.42930i	−0.699484	+	0.714648i	$0.746587\pi$
$830$	0.520552	+	0.152848i	0.0180686	+	0.00530543i
$831$	−31.1523	−	26.9936i	−1.08066	−	0.936399i
$832$	2.94108	−	4.57642i	0.101964	−	0.158659i
$833$	0.612521	−	2.41958i	0.0212226	−	0.0838334i
$834$	1.90359	−	1.22336i	0.0659158	−	0.0423615i
$835$	−0.0231087	+	0.0105534i	−0.000799709	+	0.000365215i
$836$	−23.3399	+	20.2241i	−0.807227	+	0.699466i
$837$	−0.938030	−	6.52414i	−0.0324231	−	0.225507i
$838$	10.6324	−	23.2817i	0.367290	−	0.804254i
$839$	−6.67239	+	1.95919i	−0.230357	+	0.0676388i	−0.394874	−	0.918735i	$-0.629212\pi$
$839$	−6.67239	+	1.95919i	−0.230357	+	0.0676388i	0.164517	+	0.986374i	$0.447393\pi$
$840$	−2.06321	+	0.489680i	−0.0711874	+	0.0168956i
$841$	0.162104	−	0.354957i	0.00558978	−	0.0122399i
$842$	−10.2846	+	1.47870i	−0.354430	+	0.0509594i
$843$	−5.41092	−	6.24454i	−0.186362	−	0.215073i
$844$	−5.33666	−	11.6857i	−0.183695	−	0.402237i
$845$	4.97175	−	3.19515i	0.171033	−	0.109917i
$846$	25.6785	+	3.69201i	0.882844	+	0.126934i
$847$	7.07610	−	9.83316i	0.243138	−	0.337871i
$848$	−6.38612	−	5.53361i	−0.219300	−	0.190025i
$849$	−7.09673	+	24.1692i	−0.243559	+	0.829486i
$850$	−1.73756			−0.0595978
$851$	−4.68233	+	37.0892i	−0.160508	+	1.27140i
$852$			23.5610i			0.807187i
$853$	−4.43085	+	15.0901i	−0.151709	+	0.516675i	−0.999916	−	0.0129913i	$-0.995865\pi$
$853$	−4.43085	+	15.0901i	−0.151709	+	0.516675i	0.848206	+	0.529666i	$0.177683\pi$
$854$	−20.8166	−	20.0471i	−0.712328	−	0.685997i
$855$	4.83897	+	3.10982i	0.165489	+	0.106353i
$856$	−3.91434	−	0.562797i	−0.133789	−	0.0192360i
$857$	−7.95913	−	12.3847i	−0.271879	−	0.423052i	0.678287	−	0.734797i	$-0.262723\pi$
$857$	−7.95913	−	12.3847i	−0.271879	−	0.423052i	−0.950166	+	0.311746i	$0.899086\pi$
$858$	43.9525	−	20.0724i	1.50051	−	0.685261i
$859$	−13.4305	+	11.6376i	−0.458242	+	0.397069i	−0.853162	−	0.521647i	$-0.825318\pi$
$859$	−13.4305	+	11.6376i	−0.458242	+	0.397069i	0.394920	+	0.918716i	$0.370772\pi$
$860$	−0.955717	+	0.137411i	−0.0325897	+	0.00468569i
$861$	−22.0943	−	11.5298i	−0.752970	−	0.392934i
$862$	6.75100	+	22.9918i	0.229940	+	0.783104i
$863$	−0.190133	+	0.0558282i	−0.00647222	+	0.00190042i	−0.284967	−	0.958537i	$-0.591983\pi$
$863$	−0.190133	+	0.0558282i	−0.00647222	+	0.00190042i	0.278495	+	0.960438i	$0.410164\pi$
$864$	1.91579	+	0.874911i	0.0651764	+	0.0297651i
$865$	−0.575243	+	0.0827074i	−0.0195588	+	0.00281214i
$866$	0.0695159	+	0.0802256i	0.00236225	+	0.00272618i
$867$	34.5387	−	15.7733i	1.17299	−	0.535689i
$868$	7.19124	−	4.10433i	0.244087	−	0.139310i
$869$	1.50007	−	10.4332i	0.0508865	−	0.353924i
$870$	−2.34911	+	3.65529i	−0.0796424	+	0.123926i
$871$	−27.6726	+	31.9359i	−0.937651	+	1.08211i
$872$	−1.33624	+	4.55081i	−0.0452507	+	0.154110i
$873$	−24.5275			−0.830130
$874$	33.8602	−	16.1737i	1.14534	−	0.547084i
$875$	−0.488876	+	9.29067i	−0.0165270	+	0.314082i
$876$	21.1848	+	6.22042i	0.715769	+	0.210169i
$877$	−5.69451	+	6.57181i	−0.192290	+	0.221914i	−0.843705	−	0.536807i	$-0.819630\pi$
$877$	−5.69451	+	6.57181i	−0.192290	+	0.221914i	0.651415	+	0.758722i	$0.274176\pi$
$878$	17.2659	−	26.8663i	0.582697	−	0.906694i
$879$	−6.80872	−	0.978947i	−0.229653	−	0.0330191i
$880$	0.760010	+	1.18260i	0.0256199	+	0.0398654i
$881$	12.4054	+	27.1640i	0.417948	+	0.915179i	0.995131	+	0.0985638i	$0.0314248\pi$
$881$	12.4054	+	27.1640i	0.417948	+	0.915179i	−0.577183	+	0.816615i	$0.695848\pi$
$882$	−8.26361	−	11.8523i	−0.278250	−	0.399088i
$883$	7.73700	+	53.8120i	0.260371	+	1.81092i	0.530047	+	0.847968i	$0.322174\pi$
$883$	7.73700	+	53.8120i	0.260371	+	1.81092i	−0.269677	+	0.962951i	$0.586917\pi$
$884$	−1.76439	−	0.805769i	−0.0593428	−	0.0271010i
$885$	4.32916	−	1.27116i	0.145523	−	0.0427295i
$886$	−32.2400	+	9.46652i	−1.08312	+	0.318034i
$887$	25.7135	+	11.7430i	0.863376	+	0.394290i	0.797343	−	0.603527i	$-0.206238\pi$
$887$	25.7135	+	11.7430i	0.863376	+	0.394290i	0.0660331	+	0.997817i	$0.478966\pi$
$888$	2.49642	+	17.3630i	0.0837745	+	0.582664i
$889$	6.22191	−	4.84309i	0.208676	−	0.162432i
$890$	−2.14398	−	4.69466i	−0.0718664	−	0.157365i
$891$	23.3275	+	36.2983i	0.781501	+	1.21604i
$892$	26.3327	+	3.78607i	0.881683	+	0.126767i
$893$	−53.1672	+	82.7298i	−1.77917	+	2.76845i
$894$	−7.08856	+	8.18064i	−0.237077	+	0.273601i
$895$	5.89050	+	1.72961i	0.196898	+	0.0578144i
$896$	−0.139027	+	2.64210i	−0.00464458	+	0.0882662i
$897$	−57.9602	+	9.35468i	−1.93523	+	0.312344i
$898$	0.729438			0.0243417
$899$	4.77995	−	16.2790i	0.159420	−	0.542935i
$900$	−6.58702	+	7.60183i	−0.219567	+	0.253394i
$901$	−1.62891	+	2.53464i	−0.0542670	+	0.0844411i
$902$	−2.35124	+	16.3532i	−0.0782876	+	0.544502i
$903$	−8.00089	−	14.0184i	−0.266253	−	0.466505i
$904$	−3.17957	+	1.45206i	−0.105751	+	0.0482949i
$905$	−1.25615	−	1.44967i	−0.0417559	−	0.0481888i
$906$	−29.1548	+	4.19182i	−0.968602	+	0.139264i
$907$	4.83862	+	2.20972i	0.160664	+	0.0733727i	0.494124	−	0.869392i	$-0.335489\pi$
$907$	4.83862	+	2.20972i	0.160664	+	0.0733727i	−0.333460	+	0.942764i	$0.608216\pi$
$908$	6.40079	−	1.87944i	0.212418	−	0.0623715i
$909$	7.93111	+	27.0109i	0.263058	+	0.895894i
$910$	−2.37156	+	4.54456i	−0.0786163	+	0.150651i
$911$	−40.8454	+	5.87268i	−1.35327	+	0.194570i	−0.780504	−	0.625151i	$-0.785038\pi$
$911$	−40.8454	+	5.87268i	−1.35327	+	0.194570i	−0.572763	+	0.819721i	$0.694128\pi$
$912$	13.3071	−	11.5306i	0.440641	−	0.381817i
$913$	5.46907	−	2.49764i	0.181000	−	0.0826598i
$914$	11.4173	+	17.7657i	0.377652	+	0.587638i
$915$	8.66563	+	1.24593i	0.286477	+	0.0411892i
$916$	11.6220	+	7.46901i	0.384002	+	0.246783i
$917$	−4.11362	+	4.27151i	−0.135844	+	0.141058i
$918$	0.211567	−	0.720532i	0.00698277	−	0.0237811i
$919$			20.2384i			0.667602i	0.942644	+	0.333801i	$0.108331\pi$
$919$			20.2384i			0.667602i	−0.942644	+	0.333801i	$0.891669\pi$
$920$	−0.509367	−	1.63036i	−0.0167933	−	0.0537512i
$921$	53.1649			1.75184
$922$	−6.52091	+	22.2082i	−0.214755	+	0.731387i
$923$	43.0447	+	37.2984i	1.41683	+	1.22769i
$924$	−13.7263	+	19.0745i	−0.451564	+	0.627506i
$925$	37.5997	+	5.40601i	1.23627	+	0.177749i
$926$	9.65221	−	6.20310i	0.317191	−	0.203846i
$927$	−5.93743	−	13.0012i	−0.195011	−	0.427014i
$928$	3.55018	+	4.09713i	0.116540	+	0.134495i
$929$	49.7757	−	7.15666i	1.63309	−	0.234802i	0.736104	−	0.676868i	$-0.236663\pi$
$929$	49.7757	−	7.15666i	1.63309	−	0.234802i	0.896982	+	0.442066i	$0.145754\pi$
$930$	−1.04198	+	2.28162i	−0.0341680	+	0.0748174i
$931$	53.8817	−	9.83021i	1.76590	−	0.322172i
$932$	15.9753	−	4.69078i	0.523289	−	0.153651i
$933$	−9.15481	+	20.0462i	−0.299715	+	0.656284i
$934$	−0.881280	−	6.12944i	−0.0288364	−	0.200561i
$935$	0.378807	−	0.328238i	0.0123883	−	0.0107345i
$936$	−10.2140	+	4.66456i	−0.333854	+	0.152466i
$937$	−13.3327	+	8.56839i	−0.435559	+	0.279917i	−0.739990	−	0.672617i	$-0.765170\pi$
$937$	−13.3327	+	8.56839i	−0.435559	+	0.279917i	0.304431	+	0.952534i	$0.401534\pi$
$938$	3.98975	−	20.1609i	0.130270	−	0.658277i
$939$	22.8143	−	35.4997i	0.744515	−	1.15849i
$940$	3.38300	+	2.93139i	0.110341	+	0.0956114i
$941$	−16.6311	−	4.88333i	−0.542158	−	0.159192i	−0.000824304	−	1.00000i	$-0.500262\pi$
$941$	−16.6311	−	4.88333i	−0.542158	−	0.159192i	−0.541334	+	0.840808i	$0.682081\pi$
$942$			21.0320i			0.685259i
$943$	8.02355	−	18.4012i	0.261283	−	0.599225i
$944$		−	5.62948i		−	0.183224i
$945$	−1.87220	−	0.658416i	−0.0609027	−	0.0214183i
$946$	−7.00723	+	8.08678i	−0.227825	+	0.262924i
$947$	40.6693	+	26.1366i	1.32158	+	0.849325i	0.995383	−	0.0959785i	$-0.0305980\pi$
$947$	40.6693	+	26.1366i	1.32158	+	0.849325i	0.326192	+	0.945303i	$0.394234\pi$
$948$	−0.855255	+	5.94843i	−0.0277774	+	0.193196i
$949$	44.9012	−	28.8562i	1.45755	−	0.936713i
$950$	−15.8396	−	34.6840i	−0.513906	−	1.12530i
$951$	−0.271243	+	0.235033i	−0.00879566	+	0.00762148i
$952$	0.939526	−	0.0850024i	0.0304502	−	0.00275494i
$953$	17.1637	+	7.83841i	0.555987	+	0.253911i	0.673534	−	0.739156i	$-0.264776\pi$
$953$	17.1637	+	7.83841i	0.555987	+	0.253911i	−0.117546	+	0.993067i	$0.537503\pi$
$954$	4.91390	+	16.7352i	0.159093	+	0.541823i
$955$	0.884794	+	3.01333i	0.0286313	+	0.0975091i
$956$	−5.00585	+	10.9613i	−0.161901	+	0.354514i
$957$	6.85284	+	47.6625i	0.221521	+	1.54071i
$958$	−16.1566	−	18.6457i	−0.521996	−	0.602416i
$959$	−15.0052	−	38.0282i	−0.484545	−	1.22799i
$960$	−0.433314	−	0.674249i	−0.0139851	−	0.0217613i
$961$	−3.01790	+	20.9899i	−0.0973515	+	0.677095i
$962$	35.6733	+	22.9258i	1.15015	+	0.739158i
$963$	6.16893	+	5.34540i	0.198791	+	0.172253i
$964$	22.7214	+	6.67161i	0.731807	+	0.214878i
$965$	−5.68824			−0.183111
$966$	22.2270	−	17.9243i	0.715141	−	0.576706i
$967$	−46.1642			−1.48454			−0.742270	−	0.670101i	$-0.766251\pi$
$967$	−46.1642			−1.48454			−0.742270	+	0.670101i	$0.766251\pi$
$968$	4.39339	+	1.29002i	0.141209	+	0.0414627i
$969$	−4.74473	−	4.11134i	−0.152423	−	0.132075i
$970$	−3.56035	−	2.28810i	−0.114316	−	0.0734664i
$971$	4.05689	−	28.2163i	0.130192	−	0.905503i	−0.815110	−	0.579306i	$-0.803324\pi$
$971$	4.05689	−	28.2163i	0.130192	−	0.905503i	0.945302	−	0.326197i	$-0.105767\pi$
$972$	−9.88404	−	15.3799i	−0.317031	−	0.493309i
$973$	0.976472	+	2.47470i	0.0313043	+	0.0793352i
$974$	1.79466	+	2.07114i	0.0575045	+	0.0663637i
$975$	8.49004	+	59.0495i	0.271899	+	1.89110i
$976$	4.53766	−	9.93609i	0.145247	−	0.318047i
$977$	−1.46546	−	4.99091i	−0.0468843	−	0.159673i	0.932724	−	0.360592i	$-0.117425\pi$
$977$	−1.46546	−	4.99091i	−0.0468843	−	0.159673i	−0.979608	+	0.200919i	$0.935607\pi$
$978$	6.17716	+	21.0375i	0.197524	+	0.672705i
$979$	−52.0271	−	23.7600i	−1.66279	−	0.759373i
$980$	−0.0938592	−	2.49134i	−0.00299822	−	0.0795829i
$981$	7.39869	−	6.41100i	0.236222	−	0.204688i
$982$	0.693317	+	1.51815i	0.0221246	+	0.0484462i
$983$	31.5908	−	20.3022i	1.00759	−	0.647539i	0.0708219	−	0.997489i	$-0.477438\pi$
$983$	31.5908	−	20.3022i	1.00759	−	0.647539i	0.936768	+	0.349950i	$0.113801\pi$
$984$	1.34054	−	9.32365i	0.0427348	−	0.297227i
$985$	−3.25633	−	2.09271i	−0.103755	−	0.0666794i
$986$	1.26584	−	1.46086i	0.0403127	−	0.0465233i
$987$	−24.8261	+	70.5929i	−0.790224	+	2.24700i
$988$		−	42.5649i		−	1.35417i
$989$	10.8149	−	7.21643i	0.343894	−	0.229469i
$990$		−	2.90162i		−	0.0922195i
$991$	49.4786	+	14.5282i	1.57174	+	0.461505i	0.947507	−	0.319734i	$-0.103594\pi$
$991$	49.4786	+	14.5282i	1.57174	+	0.461505i	0.624233	+	0.781238i	$0.285412\pi$
$992$	2.36517	+	2.04943i	0.0750943	+	0.0650696i
$993$	−9.94914	+	15.4812i	−0.315727	+	0.491280i
$994$	−27.1738	−	5.37757i	−0.861900	−	0.170566i
$995$	−5.92218	+	3.80596i	−0.187746	+	0.120657i
$996$	−3.11815	+	1.42401i	−0.0988023	+	0.0451215i
$997$	12.8067	−	11.0971i	0.405594	−	0.351449i	−0.428047	−	0.903757i	$-0.640798\pi$
$997$	12.8067	−	11.0971i	0.405594	−	0.351449i	0.833640	+	0.552308i	$0.186253\pi$
$998$	0.144541	+	1.00530i	0.00457536	+	0.0318224i
$999$	−6.81995	+	14.9336i	−0.215774	+	0.472478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.k.a.97.2	yes	80
7.6	odd	2	inner	322.2.k.a.97.7	yes	80
23.14	odd	22	inner	322.2.k.a.83.7	yes	80
161.83	even	22	inner	322.2.k.a.83.2	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.k.a.83.2	✓	80	161.83	even	22	inner
322.2.k.a.83.7	yes	80	23.14	odd	22	inner
322.2.k.a.97.2	yes	80	1.1	even	1	trivial
322.2.k.a.97.7	yes	80	7.6	odd	2	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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-1.70070 - 1.47367i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.0506866 - 0.352533i) q^{5} +(1.21663 + 1.89312i) q^{6} +(-2.46109 + 0.971103i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.293752 + 2.04309i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-1.70070 - 1.47367i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.0506866 - 0.352533i) q^{5} +(1.21663 + 1.89312i) q^{6} +(-2.46109 + 0.971103i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.293752 + 2.04309i) q^{9} +(-0.147953 + 0.323973i) q^{10} +(1.11200 + 3.78713i) q^{11} +(-0.633998 - 2.15920i) q^{12} +(-4.94840 - 2.25986i) q^{13} +(2.63499 - 0.238397i) q^{14} +(-0.605719 + 0.524859i) q^{15} +(0.415415 + 0.909632i) q^{16} +(0.299955 - 0.192770i) q^{17} +(0.293752 - 2.04309i) q^{18} +(6.58234 + 4.23021i) q^{19} +(0.233234 - 0.269166i) q^{20} +(5.61667 + 1.97527i) q^{21} -3.94701i q^{22} +(-1.27171 + 4.62415i) q^{23} +2.25035i q^{24} +(4.67575 + 1.37293i) q^{25} +(4.11128 + 3.56244i) q^{26} +(-1.13865 + 1.77178i) q^{27} +(-2.59542 - 0.513622i) q^{28} +(-4.56067 + 2.93096i) q^{29} +(0.729053 - 0.332947i) q^{30} +(-2.36517 + 2.04943i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(3.68979 - 8.07950i) q^{33} +(-0.342115 + 0.100454i) q^{34} +(0.217601 + 0.916836i) q^{35} +(-0.857457 + 1.87757i) q^{36} +(7.71567 - 1.10935i) q^{37} +(-5.12392 - 5.91332i) q^{38} +(5.08548 + 11.1356i) q^{39} +(-0.299619 + 0.192553i) q^{40} +(-4.14319 - 0.595701i) q^{41} +(-4.83266 - 3.47766i) q^{42} +(-2.04884 - 1.77533i) q^{43} +(-1.11200 + 3.78713i) q^{44} +0.735144 q^{45} +(2.52297 - 4.07856i) q^{46} +12.5685i q^{47} +(0.633998 - 2.15920i) q^{48} +(5.11392 - 4.77994i) q^{49} +(-4.09956 - 2.63462i) q^{50} +(-0.794214 - 0.114191i) q^{51} +(-2.94108 - 4.57642i) q^{52} +(-7.68644 + 3.51028i) q^{53} +(1.59169 - 1.37921i) q^{54} +(1.39145 - 0.200060i) q^{55} +(2.34558 + 1.22403i) q^{56} +(-4.96068 - 16.8945i) q^{57} +(5.20168 - 1.52735i) q^{58} +(-5.12076 - 2.33857i) q^{59} +(-0.793324 + 0.114063i) q^{60} +(-7.15317 - 8.25520i) q^{61} +(2.84676 - 1.30007i) q^{62} +(-2.70700 - 4.74296i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-1.04749 + 1.62993i) q^{65} +(-5.81658 + 6.71269i) q^{66} +(2.18847 - 7.45323i) q^{67} +0.356558 q^{68} +(8.97727 - 5.99023i) q^{69} +(0.0495157 - 0.941003i) q^{70} +(-10.0458 - 2.94971i) q^{71} +(1.35170 - 1.55994i) q^{72} +(-5.30445 + 8.25389i) q^{73} +(-7.71567 - 1.10935i) q^{74} +(-5.92884 - 9.22546i) q^{75} +(3.25039 + 7.11736i) q^{76} +(-6.41442 - 8.24059i) q^{77} +(-1.74221 - 12.1173i) q^{78} +(-2.42918 - 1.10937i) q^{79} +(0.341731 - 0.100341i) q^{80} +(10.4890 - 3.07984i) q^{81} +(3.80753 + 1.73884i) q^{82} +(-0.216785 - 1.50778i) q^{83} +(3.65713 + 4.69831i) q^{84} +(-0.0527539 - 0.115515i) q^{85} +(1.46568 + 2.28064i) q^{86} +(12.0756 + 1.73621i) q^{87} +(2.13391 - 3.32043i) q^{88} +(-9.48954 + 10.9515i) q^{89} +(-0.705366 - 0.207114i) q^{90} +(14.3730 + 0.756309i) q^{91} +(-3.56984 + 3.20254i) q^{92} +7.04265 q^{93} +(3.54094 - 12.0593i) q^{94} +(1.82492 - 2.10607i) q^{95} +(-1.21663 + 1.89312i) q^{96} +(-1.69112 + 11.7620i) q^{97} +(-6.25343 + 3.14556i) q^{98} +(-7.41078 + 3.38439i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{2} - 8 q^{4} - 11 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) 80 * q - 8 * q^2 - 8 * q^4 - 11 * q^7 - 8 * q^8 - 6 * q^9	\( 80 q - 8 q^{2} - 8 q^{4} - 11 q^{7} - 8 q^{8} - 6 q^{9} + 11 q^{14} - 8 q^{16} - 6 q^{18} - 33 q^{21} + 18 q^{23} - 58 q^{25} - 11 q^{28} + 16 q^{29} + 22 q^{30} - 8 q^{32} + 47 q^{35} + 16 q^{36} - 22 q^{37} - 30 q^{39} - 22 q^{42} + 44 q^{43} - 4 q^{46} + 17 q^{49} + 8 q^{50} - 88 q^{51} + 44 q^{53} + 11 q^{56} - 22 q^{57} - 28 q^{58} + 121 q^{63} - 8 q^{64} - 154 q^{65} + 58 q^{70} + 42 q^{71} - 28 q^{72} + 22 q^{74} + 38 q^{77} + 58 q^{78} - 88 q^{79} - 26 q^{81} - 11 q^{84} + 26 q^{85} - 132 q^{86} + 22 q^{88} - 4 q^{92} + 152 q^{93} - 68 q^{95} - 27 q^{98} - 44 q^{99}+O(q^{100}) \) 80 * q - 8 * q^2 - 8 * q^4 - 11 * q^7 - 8 * q^8 - 6 * q^9 + 11 * q^14 - 8 * q^16 - 6 * q^18 - 33 * q^21 + 18 * q^23 - 58 * q^25 - 11 * q^28 + 16 * q^29 + 22 * q^30 - 8 * q^32 + 47 * q^35 + 16 * q^36 - 22 * q^37 - 30 * q^39 - 22 * q^42 + 44 * q^43 - 4 * q^46 + 17 * q^49 + 8 * q^50 - 88 * q^51 + 44 * q^53 + 11 * q^56 - 22 * q^57 - 28 * q^58 + 121 * q^63 - 8 * q^64 - 154 * q^65 + 58 * q^70 + 42 * q^71 - 28 * q^72 + 22 * q^74 + 38 * q^77 + 58 * q^78 - 88 * q^79 - 26 * q^81 - 11 * q^84 + 26 * q^85 - 132 * q^86 + 22 * q^88 - 4 * q^92 + 152 * q^93 - 68 * q^95 - 27 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more