LMFDB - Embedded newform 966.2.q.a.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			169.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	966.169
Dual form			966.2.q.a.463.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-2.42796 - 2.80202i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-2.42796 - 2.80202i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(3.11903 - 2.00448i) q^{10} +(0.504677 + 3.51011i) q^{11} +(-0.142315 - 0.989821i) q^{12} +(-1.29474 + 0.832078i) q^{13} +(0.654861 - 0.755750i) q^{14} +(1.54019 - 3.37255i) q^{15} +(0.841254 + 0.540641i) q^{16} +(4.65862 - 1.36789i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(-0.0720391 - 0.0211526i) q^{19} +(1.54019 + 3.37255i) q^{20} +(0.142315 - 0.989821i) q^{21} -3.54620 q^{22} +(4.70653 + 0.921186i) q^{23} +1.00000 q^{24} +(-1.24473 + 8.65726i) q^{25} +(-0.639348 - 1.39998i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(0.654861 + 0.755750i) q^{28} +(9.19256 - 2.69918i) q^{29} +(3.11903 + 2.00448i) q^{30} +(-3.19828 + 7.00326i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-2.98325 + 1.91722i) q^{33} +(0.690980 + 4.80587i) q^{34} +(0.527646 + 3.66986i) q^{35} +(0.841254 - 0.540641i) q^{36} +(6.22672 - 7.18602i) q^{37} +(0.0311895 - 0.0682955i) q^{38} +(-1.29474 - 0.832078i) q^{39} +(-3.55742 + 1.04455i) q^{40} +(4.33712 + 5.00531i) q^{41} +(0.959493 + 0.281733i) q^{42} +(4.25990 + 9.32787i) q^{43} +(0.504677 - 3.51011i) q^{44} +3.70760 q^{45} +(-1.58162 + 4.52753i) q^{46} -0.339548 q^{47} +(-0.142315 + 0.989821i) q^{48} +(0.415415 + 0.909632i) q^{49} +(-8.39200 - 2.46411i) q^{50} +(3.17954 + 3.66939i) q^{51} +(1.47672 - 0.433603i) q^{52} +(8.01770 + 5.15266i) q^{53} +(0.415415 - 0.909632i) q^{54} +(8.61004 - 9.93651i) q^{55} +(-0.841254 + 0.540641i) q^{56} +(-0.0106851 - 0.0743162i) q^{57} +(1.36347 + 9.48313i) q^{58} +(-6.97963 + 4.48554i) q^{59} +(-2.42796 + 2.80202i) q^{60} +(2.69167 - 5.89393i) q^{61} +(-6.47681 - 4.16240i) q^{62} +(0.959493 - 0.281733i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(5.47507 + 1.60763i) q^{65} +(-1.47314 - 3.22574i) q^{66} +(-0.191969 + 1.33517i) q^{67} -4.85529 q^{68} +(1.11722 + 4.66388i) q^{69} -3.70760 q^{70} +(0.745812 - 5.18723i) q^{71} +(0.415415 + 0.909632i) q^{72} +(-12.5295 - 3.67899i) q^{73} +(6.22672 + 7.18602i) q^{74} +(-8.39200 + 2.46411i) q^{75} +(0.0631616 + 0.0405915i) q^{76} +(1.47314 - 3.22574i) q^{77} +(1.00787 - 1.16314i) q^{78} +(-6.16678 + 3.96315i) q^{79} +(-0.527646 - 3.66986i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-5.57160 + 3.58065i) q^{82} +(3.10427 - 3.58252i) q^{83} +(-0.415415 + 0.909632i) q^{84} +(-15.1438 - 9.73233i) q^{85} +(-9.83918 + 2.88904i) q^{86} +(6.27399 + 7.24057i) q^{87} +(3.40255 + 0.999080i) q^{88} +(0.675148 + 1.47837i) q^{89} +(-0.527646 + 3.66986i) q^{90} +1.53906 q^{91} +(-4.25635 - 2.20985i) q^{92} -7.69900 q^{93} +(0.0483227 - 0.336092i) q^{94} +(0.115638 + 0.253212i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(-6.85536 - 7.91151i) q^{97} +(-0.959493 + 0.281733i) q^{98} +(-2.98325 - 1.91722i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{3} - q^{4} - 14 q^{5} - q^{6} + q^{7} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 - q^3 - q^4 - 14 * q^5 - q^6 + q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} - 14 q^{5} - q^{6} + q^{7} - q^{8} - q^{9} + 8 q^{10} - 4 q^{11} - q^{12} + 14 q^{13} + q^{14} - 3 q^{15} - q^{16} + 15 q^{17} - q^{18} - 11 q^{19} - 3 q^{20} + q^{21} - 26 q^{22} - q^{23} + 10 q^{24} + 7 q^{25} - 8 q^{26} - q^{27} + q^{28} + 19 q^{29} + 8 q^{30} - 5 q^{31} - q^{32} + 7 q^{33} - 18 q^{34} - 8 q^{35} - q^{36} - 2 q^{37} + 11 q^{38} + 14 q^{39} - 3 q^{40} + 2 q^{41} + q^{42} + 25 q^{43} - 4 q^{44} + 8 q^{45} - 23 q^{46} - 4 q^{47} - q^{48} - q^{49} - 15 q^{50} + 15 q^{51} - 8 q^{52} + 15 q^{53} - q^{54} + 54 q^{55} + q^{56} + 8 q^{58} - 17 q^{59} - 14 q^{60} + q^{61} - 16 q^{62} + q^{63} - q^{64} - 13 q^{65} - 4 q^{66} - 4 q^{67} + 26 q^{68} + 21 q^{69} - 8 q^{70} + 6 q^{71} - q^{72} - 25 q^{73} - 2 q^{74} - 15 q^{75} - 22 q^{76} + 4 q^{77} + 14 q^{78} + 3 q^{79} + 8 q^{80} - q^{81} + 2 q^{82} + 7 q^{83} + q^{84} + 12 q^{85} - 41 q^{86} + 8 q^{87} + 7 q^{88} - 41 q^{89} + 8 q^{90} + 30 q^{91} - q^{92} - 16 q^{93} - 15 q^{94} - 44 q^{95} - q^{96} - 4 q^{97} - q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 - 14 * q^5 - q^6 + q^7 - q^8 - q^9 + 8 * q^10 - 4 * q^11 - q^12 + 14 * q^13 + q^14 - 3 * q^15 - q^16 + 15 * q^17 - q^18 - 11 * q^19 - 3 * q^20 + q^21 - 26 * q^22 - q^23 + 10 * q^24 + 7 * q^25 - 8 * q^26 - q^27 + q^28 + 19 * q^29 + 8 * q^30 - 5 * q^31 - q^32 + 7 * q^33 - 18 * q^34 - 8 * q^35 - q^36 - 2 * q^37 + 11 * q^38 + 14 * q^39 - 3 * q^40 + 2 * q^41 + q^42 + 25 * q^43 - 4 * q^44 + 8 * q^45 - 23 * q^46 - 4 * q^47 - q^48 - q^49 - 15 * q^50 + 15 * q^51 - 8 * q^52 + 15 * q^53 - q^54 + 54 * q^55 + q^56 + 8 * q^58 - 17 * q^59 - 14 * q^60 + q^61 - 16 * q^62 + q^63 - q^64 - 13 * q^65 - 4 * q^66 - 4 * q^67 + 26 * q^68 + 21 * q^69 - 8 * q^70 + 6 * q^71 - q^72 - 25 * q^73 - 2 * q^74 - 15 * q^75 - 22 * q^76 + 4 * q^77 + 14 * q^78 + 3 * q^79 + 8 * q^80 - q^81 + 2 * q^82 + 7 * q^83 + q^84 + 12 * q^85 - 41 * q^86 + 8 * q^87 + 7 * q^88 - 41 * q^89 + 8 * q^90 + 30 * q^91 - q^92 - 16 * q^93 - 15 * q^94 - 44 * q^95 - q^96 - 4 * q^97 - q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	−2.42796	−	2.80202i	−1.08582	−	1.25310i	−0.965511	−	0.260363i	$-0.916158\pi$
$5$	−2.42796	−	2.80202i	−1.08582	−	1.25310i	−0.120306	−	0.992737i	$-0.538388\pi$
$6$	−0.959493	+	0.281733i	−0.391711	+	0.115017i
$7$	−0.841254	−	0.540641i	−0.317964	−	0.204343i
$7$	−0.841254	−	0.540641i	−0.317964	−	0.204343i
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	3.11903	−	2.00448i	0.986324	−	0.633872i
$11$	0.504677	+	3.51011i	0.152166	+	1.05834i	0.912580	+	0.408898i	$0.134087\pi$
$11$	0.504677	+	3.51011i	0.152166	+	1.05834i	−0.760414	+	0.649438i	$0.775004\pi$
$12$	−0.142315	−	0.989821i	−0.0410828	−	0.285737i
$13$	−1.29474	+	0.832078i	−0.359096	+	0.230777i	−0.707732	−	0.706481i	$-0.750281\pi$
$13$	−1.29474	+	0.832078i	−0.359096	+	0.230777i	0.348636	+	0.937258i	$0.386645\pi$
$14$	0.654861	−	0.755750i	0.175019	−	0.201983i
$15$	1.54019	−	3.37255i	0.397676	−	0.870789i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	4.65862	−	1.36789i	1.12988	−	0.331763i	0.337220	−	0.941426i	$-0.390513\pi$
$17$	4.65862	−	1.36789i	1.12988	−	0.331763i	0.792661	+	0.609663i	$0.208695\pi$
$18$	−0.654861	−	0.755750i	−0.154352	−	0.178132i
$19$	−0.0720391	−	0.0211526i	−0.0165269	−	0.00485274i	0.273459	−	0.961884i	$-0.411832\pi$
$19$	−0.0720391	−	0.0211526i	−0.0165269	−	0.00485274i	−0.289986	+	0.957031i	$0.593651\pi$
$20$	1.54019	+	3.37255i	0.344397	+	0.754125i
$21$	0.142315	−	0.989821i	0.0310556	−	0.215997i
$22$	−3.54620			−0.756052
$23$	4.70653	+	0.921186i	0.981379	+	0.192080i
$23$	4.70653	+	0.921186i	0.981379	+	0.192080i
$24$	1.00000			0.204124
$25$	−1.24473	+	8.65726i	−0.248945	+	1.73145i
$26$	−0.639348	−	1.39998i	−0.125386	−	0.274558i
$27$	−0.959493	−	0.281733i	−0.184655	−	0.0542195i
$28$	0.654861	+	0.755750i	0.123757	+	0.142823i
$29$	9.19256	−	2.69918i	1.70702	−	0.501225i	0.724797	−	0.688963i	$-0.241934\pi$
$29$	9.19256	−	2.69918i	1.70702	−	0.501225i	0.982219	+	0.187738i	$0.0601155\pi$
$30$	3.11903	+	2.00448i	0.569454	+	0.365966i
$31$	−3.19828	+	7.00326i	−0.574428	+	1.25782i	0.369978	+	0.929041i	$0.379365\pi$
$31$	−3.19828	+	7.00326i	−0.574428	+	1.25782i	−0.944406	+	0.328782i	$0.893362\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	−2.98325	+	1.91722i	−0.519318	+	0.333745i
$34$	0.690980	+	4.80587i	0.118502	+	0.824200i
$35$	0.527646	+	3.66986i	0.0891885	+	0.620320i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	6.22672	−	7.18602i	1.02367	−	1.18137i	0.0404030	−	0.999183i	$-0.487136\pi$
$37$	6.22672	−	7.18602i	1.02367	−	1.18137i	0.983263	−	0.182190i	$-0.0583187\pi$
$38$	0.0311895	−	0.0682955i	0.00505961	−	0.0110790i
$39$	−1.29474	−	0.832078i	−0.207324	−	0.133239i
$40$	−3.55742	+	1.04455i	−0.562477	+	0.165158i
$41$	4.33712	+	5.00531i	0.677345	+	0.781698i	0.985507	−	0.169636i	$-0.0542593\pi$
$41$	4.33712	+	5.00531i	0.677345	+	0.781698i	−0.308162	+	0.951334i	$0.599714\pi$
$42$	0.959493	+	0.281733i	0.148053	+	0.0434723i
$43$	4.25990	+	9.32787i	0.649628	+	1.42249i	0.891879	+	0.452274i	$0.149387\pi$
$43$	4.25990	+	9.32787i	0.649628	+	1.42249i	−0.242251	+	0.970214i	$0.577886\pi$
$44$	0.504677	−	3.51011i	0.0760829	−	0.529168i
$45$	3.70760			0.552696
$46$	−1.58162	+	4.52753i	−0.233197	+	0.667547i
$47$	−0.339548			−0.0495282			−0.0247641	−	0.999693i	$-0.507883\pi$
$47$	−0.339548			−0.0495282			−0.0247641	+	0.999693i	$0.507883\pi$
$48$	−0.142315	+	0.989821i	−0.0205414	+	0.142868i
$49$	0.415415	+	0.909632i	0.0593450	+	0.129947i
$50$	−8.39200	−	2.46411i	−1.18681	−	0.348478i
$51$	3.17954	+	3.66939i	0.445225	+	0.513817i
$52$	1.47672	−	0.433603i	0.204784	−	0.0601299i
$53$	8.01770	+	5.15266i	1.10132	+	0.707773i	0.959384	−	0.282104i	$-0.0910323\pi$
$53$	8.01770	+	5.15266i	1.10132	+	0.707773i	0.141932	+	0.989876i	$0.454669\pi$
$54$	0.415415	−	0.909632i	0.0565308	−	0.123785i
$55$	8.61004	−	9.93651i	1.16098	−	1.33984i
$56$	−0.841254	+	0.540641i	−0.112417	+	0.0722462i
$57$	−0.0106851	−	0.0743162i	−0.00141527	−	0.00984342i
$58$	1.36347	+	9.48313i	0.179032	+	1.24520i
$59$	−6.97963	+	4.48554i	−0.908670	+	0.583967i	−0.909350	−	0.416033i	$-0.863420\pi$
$59$	−6.97963	+	4.48554i	−0.908670	+	0.583967i	0.000679262		1.00000i	$0.499784\pi$
$60$	−2.42796	+	2.80202i	−0.313448	+	0.361739i
$61$	2.69167	−	5.89393i	0.344633	−	0.754641i	−0.655367	−	0.755311i	$-0.727486\pi$
$61$	2.69167	−	5.89393i	0.344633	−	0.754641i	1.00000		0.000669893i	$0.000213234\pi$
$62$	−6.47681	−	4.16240i	−0.822556	−	0.528625i
$63$	0.959493	−	0.281733i	0.120885	−	0.0354950i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	5.47507	+	1.60763i	0.679099	+	0.199401i
$66$	−1.47314	−	3.22574i	−0.181332	−	0.397061i
$67$	−0.191969	+	1.33517i	−0.0234527	+	0.163117i	−0.998182	−	0.0602723i	$-0.980803\pi$
$67$	−0.191969	+	1.33517i	−0.0234527	+	0.163117i	0.974729	+	0.223390i	$0.0717122\pi$
$68$	−4.85529			−0.588791
$69$	1.11722	+	4.66388i	0.134498	+	0.561466i
$70$	−3.70760			−0.443143
$71$	0.745812	−	5.18723i	0.0885115	−	0.615611i	−0.896490	−	0.443064i	$-0.853891\pi$
$71$	0.745812	−	5.18723i	0.0885115	−	0.615611i	0.985001	−	0.172547i	$-0.0551996\pi$
$72$	0.415415	+	0.909632i	0.0489571	+	0.107201i
$73$	−12.5295	−	3.67899i	−1.46647	−	0.430594i	−0.551518	−	0.834163i	$-0.685951\pi$
$73$	−12.5295	−	3.67899i	−1.46647	−	0.430594i	−0.914949	+	0.403570i	$0.867769\pi$
$74$	6.22672	+	7.18602i	0.723841	+	0.835357i
$75$	−8.39200	+	2.46411i	−0.969025	+	0.284531i
$76$	0.0631616	+	0.0405915i	0.00724514	+	0.00465617i
$77$	1.47314	−	3.22574i	0.167880	−	0.367607i
$78$	1.00787	−	1.16314i	0.114119	−	0.131700i
$79$	−6.16678	+	3.96315i	−0.693817	+	0.445889i	−0.839441	−	0.543451i	$-0.817117\pi$
$79$	−6.16678	+	3.96315i	−0.693817	+	0.445889i	0.145624	+	0.989340i	$0.453481\pi$
$80$	−0.527646	−	3.66986i	−0.0589927	−	0.410303i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	−5.57160	+	3.58065i	−0.615280	+	0.395416i
$83$	3.10427	−	3.58252i	0.340738	−	0.393233i	−0.559356	−	0.828927i	$-0.688952\pi$
$83$	3.10427	−	3.58252i	0.340738	−	0.393233i	0.900095	+	0.435694i	$0.143497\pi$
$84$	−0.415415	+	0.909632i	−0.0453255	+	0.0992490i
$85$	−15.1438	−	9.73233i	−1.64258	−	1.05562i
$86$	−9.83918	+	2.88904i	−1.06099	+	0.311533i
$87$	6.27399	+	7.24057i	0.672642	+	0.776270i
$88$	3.40255	+	0.999080i	0.362714	+	0.106502i
$89$	0.675148	+	1.47837i	0.0715655	+	0.156707i	0.942034	−	0.335518i	$-0.108911\pi$
$89$	0.675148	+	1.47837i	0.0715655	+	0.156707i	−0.870468	+	0.492224i	$0.836184\pi$
$90$	−0.527646	+	3.66986i	−0.0556188	+	0.386837i
$91$	1.53906			0.161337
$92$	−4.25635	−	2.20985i	−0.443756	−	0.230393i
$93$	−7.69900			−0.798349
$94$	0.0483227	−	0.336092i	0.00498411	−	0.0346652i
$95$	0.115638	+	0.253212i	0.0118642	+	0.0259790i
$96$	−0.959493	−	0.281733i	−0.0979278	−	0.0287542i
$97$	−6.85536	−	7.91151i	−0.696057	−	0.803292i	0.292158	−	0.956370i	$-0.405627\pi$
$97$	−6.85536	−	7.91151i	−0.696057	−	0.803292i	−0.988214	+	0.153078i	$0.951081\pi$
$98$	−0.959493	+	0.281733i	−0.0969234	+	0.0284593i
$99$	−2.98325	−	1.91722i	−0.299828	−	0.192688i
$100$	3.63334	−	7.95590i	0.363334	−	0.795590i
$101$	8.21804	−	9.48412i	0.817725	−	0.943705i	−0.181487	−	0.983393i	$-0.558091\pi$
$101$	8.21804	−	9.48412i	0.817725	−	0.943705i	0.999212	+	0.0396879i	$0.0126364\pi$
$102$	−4.08453	+	2.62497i	−0.404429	+	0.259911i
$103$	0.0388865	+	0.270462i	0.00383160	+	0.0266494i	0.991648	−	0.128977i	$-0.0411694\pi$
$103$	0.0388865	+	0.270462i	0.00383160	+	0.0266494i	−0.987816	+	0.155627i	$0.950260\pi$
$104$	0.219031	+	1.52339i	0.0214777	+	0.149381i
$105$	−3.11903	+	2.00448i	−0.304386	+	0.195617i
$106$	−6.24125	+	7.20279i	−0.606204	+	0.699597i
$107$	−3.73755	+	8.18410i	−0.361323	+	0.791187i	0.638445	+	0.769667i	$0.279578\pi$
$107$	−3.73755	+	8.18410i	−0.361323	+	0.791187i	−0.999768	+	0.0215200i	$0.993149\pi$
$108$	0.841254	+	0.540641i	0.0809497	+	0.0520232i
$109$	−5.31912	+	1.56183i	−0.509479	+	0.149597i	−0.526362	−	0.850261i	$-0.676444\pi$
$109$	−5.31912	+	1.56183i	−0.509479	+	0.149597i	0.0168823	+	0.999857i	$0.494626\pi$
$110$	8.61004	+	9.93651i	0.820935	+	0.947409i
$111$	9.12330	+	2.67884i	0.865946	+	0.254265i
$112$	−0.415415	−	0.909632i	−0.0392530	−	0.0859521i
$113$	2.86284	−	19.9115i	0.269313	−	1.87311i	−0.185667	−	0.982613i	$-0.559445\pi$
$113$	2.86284	−	19.9115i	0.269313	−	1.87311i	0.454980	−	0.890502i	$-0.349646\pi$
$114$	0.0750804			0.00703192
$115$	−8.84609	−	15.4244i	−0.824902	−	1.43833i
$116$	−9.58065			−0.889541
$117$	0.219031	−	1.52339i	0.0202494	−	0.140838i
$118$	−3.44657	−	7.54695i	−0.317283	−	0.694753i
$119$	−4.65862	−	1.36789i	−0.427055	−	0.125395i
$120$	−2.42796	−	2.80202i	−0.221641	−	0.255788i
$121$	−1.51172	+	0.443880i	−0.137429	+	0.0403527i
$122$	5.45088	+	3.50307i	0.493499	+	0.317153i
$123$	−2.75128	+	6.02447i	−0.248075	+	0.543208i
$124$	5.04177	−	5.81852i	0.452765	−	0.522518i
$125$	11.6848	−	7.50936i	1.04512	−	0.671658i
$126$	0.142315	+	0.989821i	0.0126784	+	0.0881803i
$127$	1.04446	+	7.26436i	0.0926806	+	0.644607i	0.982218	+	0.187745i	$0.0601178\pi$
$127$	1.04446	+	7.26436i	0.0926806	+	0.644607i	−0.889537	+	0.456863i	$0.848973\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	−6.71531	+	7.74988i	−0.591250	+	0.682339i
$130$	−2.37045	+	5.19055i	−0.207902	+	0.455242i
$131$	−0.913920	−	0.587341i	−0.0798495	−	0.0513162i	0.500107	−	0.865964i	$-0.333294\pi$
$131$	−0.913920	−	0.587341i	−0.0798495	−	0.0513162i	−0.579956	+	0.814648i	$0.696930\pi$
$132$	3.40255	−	0.999080i	0.296154	−	0.0869588i
$133$	0.0491672	+	0.0567420i	0.00426334	+	0.00492015i
$134$	−1.29426	−	0.380030i	−0.111807	−	0.0328296i
$135$	1.54019	+	3.37255i	0.132559	+	0.290263i
$136$	0.690980	−	4.80587i	0.0592511	−	0.412100i
$137$	17.3219			1.47991			0.739953	−	0.672659i	$-0.234848\pi$
$137$	17.3219			1.47991			0.739953	+	0.672659i	$0.234848\pi$
$138$	−4.77541	+	0.442111i	−0.406510	+	0.0376350i
$139$	16.2853			1.38130			0.690650	−	0.723189i	$-0.257324\pi$
$139$	16.2853			1.38130			0.690650	+	0.723189i	$0.257324\pi$
$140$	0.527646	−	3.66986i	0.0445943	−	0.310160i
$141$	−0.141053	−	0.308864i	−0.0118788	−	0.0260110i
$142$	5.02829	+	1.47644i	0.421965	+	0.123900i
$143$	−3.57411	−	4.12474i	−0.298882	−	0.344928i
$144$	−0.959493	+	0.281733i	−0.0799577	+	0.0234777i
$145$	−29.8823	−	19.2042i	−2.48159	−	1.59482i
$146$	5.42468	−	11.8784i	0.448950	−	0.983063i
$147$	−0.654861	+	0.755750i	−0.0540120	+	0.0623332i
$148$	−7.99903	+	5.14066i	−0.657516	+	0.422560i
$149$	3.03590	+	21.1152i	0.248711	+	1.72982i	0.605681	+	0.795707i	$0.292901\pi$
$149$	3.03590	+	21.1152i	0.248711	+	1.72982i	−0.356970	+	0.934116i	$0.616190\pi$
$150$	−1.24473	−	8.65726i	−0.101632	−	0.706863i
$151$	−4.95370	+	3.18355i	−0.403126	+	0.259074i	−0.726456	−	0.687213i	$-0.758834\pi$
$151$	−4.95370	+	3.18355i	−0.403126	+	0.259074i	0.323330	+	0.946286i	$0.395198\pi$
$152$	−0.0491672	+	0.0567420i	−0.00398799	+	0.00460238i
$153$	−2.01696	+	4.41653i	−0.163062	+	0.357055i
$154$	2.98325	+	1.91722i	0.240397	+	0.154494i
$155$	27.3885	−	8.04200i	2.19990	−	0.645949i
$156$	1.00787	+	1.16314i	0.0806941	+	0.0931260i
$157$	19.6496	+	5.76963i	1.56821	+	0.460467i	0.946478	−	0.322767i	$-0.104613\pi$
$157$	19.6496	+	5.76963i	1.56821	+	0.460467i	0.621727	+	0.783234i	$0.286431\pi$
$158$	−3.04518	−	6.66802i	−0.242262	−	0.530479i
$159$	−1.35635	+	9.43365i	−0.107566	+	0.748137i
$160$	3.70760			0.293111
$161$	−3.46135	−	3.31949i	−0.272793	−	0.261613i
$162$	1.00000			0.0785674
$163$	−1.57973	+	10.9872i	−0.123734	+	0.860587i	0.829533	+	0.558458i	$0.188607\pi$
$163$	−1.57973	+	10.9872i	−0.123734	+	0.860587i	−0.953267	+	0.302130i	$0.902302\pi$
$164$	−2.75128	−	6.02447i	−0.214839	−	0.470432i
$165$	12.6153	+	3.70419i	0.982100	+	0.288371i
$166$	3.10427	+	3.58252i	0.240938	+	0.278058i
$167$	−1.25571	+	0.368708i	−0.0971694	+	0.0285315i	−0.329956	−	0.943996i	$-0.607034\pi$
$167$	−1.25571	+	0.368708i	−0.0971694	+	0.0285315i	0.232786	+	0.972528i	$0.425216\pi$
$168$	−0.841254	−	0.540641i	−0.0649041	−	0.0417113i
$169$	−4.41640	+	9.67057i	−0.339723	+	0.743890i
$170$	11.7885	−	13.6046i	0.904134	−	1.04343i
$171$	0.0631616	−	0.0405915i	0.00483009	−	0.00310411i
$172$	−1.45938	−	10.1502i	−0.111276	−	0.773944i
$173$	3.70539	+	25.7716i	0.281716	+	1.95938i	0.282127	+	0.959377i	$0.408960\pi$
$173$	3.70539	+	25.7716i	0.281716	+	1.95938i	−0.000410655		1.00000i	$0.500131\pi$
$174$	−8.05975	+	5.17969i	−0.611008	+	0.392671i
$175$	5.72760	−	6.61000i	0.432966	−	0.499669i
$176$	−1.47314	+	3.22574i	−0.111042	+	0.243149i
$177$	−6.97963	−	4.48554i	−0.524621	−	0.337153i
$178$	−1.55940	+	0.457882i	−0.116882	+	0.0343197i
$179$	−7.27800	−	8.39926i	−0.543983	−	0.627790i	0.415487	−	0.909599i	$-0.363611\pi$
$179$	−7.27800	−	8.39926i	−0.543983	−	0.627790i	−0.959471	+	0.281809i	$0.909066\pi$
$180$	−3.55742	−	1.04455i	−0.265154	−	0.0778563i
$181$	1.33878	+	2.93153i	0.0995111	+	0.217899i	0.952839	−	0.303475i	$-0.0981469\pi$
$181$	1.33878	+	2.93153i	0.0995111	+	0.217899i	−0.853328	+	0.521374i	$0.825420\pi$
$182$	−0.219031	+	1.52339i	−0.0162356	+	0.112921i
$183$	6.47947			0.478976
$184$	2.79310	−	3.89854i	0.205910	−	0.287404i
$185$	−35.2536			−2.59189
$186$	1.09568	−	7.62064i	0.0803393	−	0.558772i
$187$	7.15255	+	15.6619i	0.523046	+	1.14531i
$188$	0.325794	+	0.0956618i	0.0237610	+	0.00697685i
$189$	0.654861	+	0.755750i	0.0476341	+	0.0549727i
$190$	−0.267092	+	0.0784253i	−0.0193769	+	0.00568957i
$191$	6.14957	+	3.95209i	0.444967	+	0.285963i	0.743875	−	0.668319i	$-0.232986\pi$
$191$	6.14957	+	3.95209i	0.444967	+	0.285963i	−0.298908	+	0.954282i	$0.596622\pi$
$192$	0.415415	−	0.909632i	0.0299800	−	0.0656470i
$193$	−3.92280	+	4.52715i	−0.282369	+	0.325872i	−0.879161	−	0.476524i	$-0.841896\pi$
$193$	−3.92280	+	4.52715i	−0.282369	+	0.325872i	0.596792	+	0.802396i	$0.296442\pi$
$194$	8.80660	−	5.65966i	0.632277	−	0.406340i
$195$	0.812079	+	5.64813i	0.0581542	+	0.404471i
$196$	−0.142315	−	0.989821i	−0.0101653	−	0.0707015i
$197$	6.40524	−	4.11640i	0.456354	−	0.293281i	−0.292197	−	0.956358i	$-0.594386\pi$
$197$	6.40524	−	4.11640i	0.456354	−	0.293281i	0.748551	+	0.663077i	$0.230750\pi$
$198$	2.32227	−	2.68004i	0.165036	−	0.190462i
$199$	9.98105	−	21.8554i	0.707538	−	1.54929i	−0.123048	−	0.992401i	$-0.539267\pi$
$199$	9.98105	−	21.8554i	0.707538	−	1.54929i	0.830586	−	0.556891i	$-0.188006\pi$
$200$	7.35785	+	4.72860i	0.520278	+	0.334363i
$201$	−1.29426	+	0.380030i	−0.0912902	+	0.0268052i
$202$	8.21804	+	9.48412i	0.578219	+	0.667301i
$203$	−9.19256	−	2.69918i	−0.645191	−	0.189445i
$204$	−2.01696	−	4.41653i	−0.141216	−	0.309219i
$205$	3.49459	−	24.3054i	0.244072	−	1.69756i
$206$	−0.273243			−0.0190377
$207$	−3.77831	+	2.95371i	−0.262610	+	0.205297i
$208$	−1.53906			−0.106715
$209$	0.0378913	−	0.263540i	0.00262100	−	0.0182294i
$210$	−1.54019	−	3.37255i	−0.106283	−	0.232728i
$211$	−0.447032	−	0.131260i	−0.0307750	−	0.00903634i	0.266309	−	0.963888i	$-0.414196\pi$
$211$	−0.447032	−	0.131260i	−0.0307750	−	0.00903634i	−0.297084	+	0.954851i	$0.596014\pi$
$212$	−6.24125	−	7.20279i	−0.428651	−	0.494690i
$213$	5.02829	−	1.47644i	0.344533	−	0.101164i
$214$	−7.56889	−	4.86423i	−0.517399	−	0.332512i
$215$	15.7940	−	34.5840i	1.07714	−	2.35861i
$216$	−0.654861	+	0.755750i	−0.0445576	+	0.0514222i
$217$	6.47681	−	4.16240i	0.439675	−	0.282562i
$218$	−0.788948	−	5.48725i	−0.0534343	−	0.371644i
$219$	−1.85841	−	12.9255i	−0.125580	−	0.873427i
$220$	−11.0607	+	7.10829i	−0.745713	+	0.479240i
$221$	−4.89350	+	5.64740i	−0.329172	+	0.379885i
$222$	−3.94996	+	8.64920i	−0.265104	+	0.580496i
$223$	−13.9892	−	8.99031i	−0.936786	−	0.602036i	−0.0193042	−	0.999814i	$-0.506145\pi$
$223$	−13.9892	−	8.99031i	−0.936786	−	0.602036i	−0.917482	+	0.397778i	$0.869781\pi$
$224$	0.959493	−	0.281733i	0.0641088	−	0.0188240i
$225$	−5.72760	−	6.61000i	−0.381840	−	0.440667i
$226$	19.3014	+	5.66740i	1.28391	+	0.376990i
$227$	6.85093	+	15.0015i	0.454713	+	0.995682i	0.988661	+	0.150165i	$0.0479803\pi$
$227$	6.85093	+	15.0015i	0.454713	+	0.995682i	−0.533949	+	0.845517i	$0.679292\pi$
$228$	−0.0106851	+	0.0743162i	−0.000707635	+	0.00492171i
$229$	−1.25964			−0.0832396			−0.0416198	−	0.999134i	$-0.513252\pi$
$229$	−1.25964			−0.0832396			−0.0416198	+	0.999134i	$0.513252\pi$
$230$	16.5263	−	6.56093i	1.08971	−	0.432615i
$231$	3.54620			0.233323
$232$	1.36347	−	9.48313i	0.0895161	−	0.622598i
$233$	−2.62075	−	5.73864i	−0.171691	−	0.375951i	0.804152	−	0.594424i	$-0.202620\pi$
$233$	−2.62075	−	5.73864i	−0.171691	−	0.375951i	−0.975843	+	0.218473i	$0.929893\pi$
$234$	1.47672	+	0.433603i	0.0965359	+	0.0283455i
$235$	0.824410	+	0.951419i	0.0537786	+	0.0620638i
$236$	7.96063	−	2.33745i	0.518193	−	0.152155i
$237$	−6.16678	−	3.96315i	−0.400575	−	0.257434i
$238$	2.01696	−	4.41653i	0.130740	−	0.286281i
$239$	15.7389	−	18.1636i	1.01806	−	1.17491i	0.0335796	−	0.999436i	$-0.489309\pi$
$239$	15.7389	−	18.1636i	1.01806	−	1.17491i	0.984484	−	0.175472i	$-0.0561453\pi$
$240$	3.11903	−	2.00448i	0.201333	−	0.129389i
$241$	1.92687	+	13.4016i	0.124120	+	0.863276i	0.952810	+	0.303567i	$0.0981777\pi$
$241$	1.92687	+	13.4016i	0.124120	+	0.863276i	−0.828690	+	0.559708i	$0.810913\pi$
$242$	−0.224222	−	1.55950i	−0.0144136	−	0.100248i
$243$	0.841254	−	0.540641i	0.0539664	−	0.0346821i
$244$	−4.24315	+	4.89686i	−0.271640	+	0.313489i
$245$	1.54019	−	3.37255i	0.0983993	−	0.215464i
$246$	−5.57160	−	3.58065i	−0.355232	−	0.228294i
$247$	0.110872	−	0.0325551i	0.00705464	−	0.00207143i
$248$	5.04177	+	5.81852i	0.320153	+	0.369476i
$249$	4.54834	+	1.33551i	0.288239	+	0.0846347i
$250$	5.77001	+	12.6345i	0.364927	+	0.799079i
$251$	0.336823	−	2.34266i	0.0212601	−	0.147867i	−0.976426	−	0.215851i	$-0.930748\pi$
$251$	0.336823	−	2.34266i	0.0212601	−	0.147867i	0.997686	+	0.0679837i	$0.0216566\pi$
$252$	−1.00000			−0.0629941
$253$	−0.858181	+	16.9853i	−0.0539534	+	1.06786i
$254$	−7.33906			−0.460493
$255$	2.56188	−	17.8182i	0.160431	−	1.11582i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	6.77778	+	1.99014i	0.422787	+	0.124141i	0.486203	−	0.873846i	$-0.338382\pi$
$257$	6.77778	+	1.99014i	0.422787	+	0.124141i	−0.0634166	+	0.997987i	$0.520200\pi$
$258$	−6.71531	−	7.74988i	−0.418077	−	0.482486i
$259$	−9.12330	+	2.67884i	−0.566894	+	0.166455i
$260$	−4.80037	−	3.08501i	−0.297706	−	0.191324i
$261$	−3.97994	+	8.71486i	−0.246352	+	0.539436i
$262$	0.711427	−	0.821030i	0.0439521	−	0.0507234i
$263$	−24.0083	+	15.4292i	−1.48041	+	0.951404i	−0.483301	+	0.875454i	$0.660562\pi$
$263$	−24.0083	+	15.4292i	−1.48041	+	0.951404i	−0.997112	+	0.0759494i	$0.975801\pi$
$264$	0.504677	+	3.51011i	0.0310607	+	0.216032i
$265$	−5.02882	−	34.9762i	−0.308918	−	2.14857i
$266$	−0.0631616	+	0.0405915i	−0.00387269	+	0.00248883i
$267$	−1.06430	+	1.22827i	−0.0651343	+	0.0751690i
$268$	0.560354	−	1.22700i	0.0342291	−	0.0749512i
$269$	−20.6803	−	13.2905i	−1.26090	−	0.810333i	−0.272496	−	0.962157i	$-0.587849\pi$
$269$	−20.6803	−	13.2905i	−1.26090	−	0.810333i	−0.988408	+	0.151824i	$0.951485\pi$
$270$	−3.55742	+	1.04455i	−0.216497	+	0.0635694i
$271$	10.4422	+	12.0509i	0.634317	+	0.732041i	0.978359	−	0.206913i	$-0.0663419\pi$
$271$	10.4422	+	12.0509i	0.634317	+	0.732041i	−0.344042	+	0.938954i	$0.611796\pi$
$272$	4.65862	+	1.36789i	0.282470	+	0.0829407i
$273$	0.639348	+	1.39998i	0.0386951	+	0.0847305i
$274$	−2.46516	+	17.1455i	−0.148926	+	1.03580i
$275$	−31.0161			−1.87034
$276$	0.242000	−	4.78972i	0.0145667	−	0.288307i
$277$	−7.27074			−0.436857			−0.218428	−	0.975853i	$-0.570093\pi$
$277$	−7.27074			−0.436857			−0.218428	+	0.975853i	$0.570093\pi$
$278$	−2.31764	+	16.1195i	−0.139003	+	0.966786i
$279$	−3.19828	−	7.00326i	−0.191476	−	0.419274i
$280$	3.55742	+	1.04455i	0.212596	+	0.0624239i
$281$	−8.74417	−	10.0913i	−0.521633	−	0.601997i	0.432406	−	0.901679i	$-0.357665\pi$
$281$	−8.74417	−	10.0913i	−0.521633	−	0.601997i	−0.954039	+	0.299682i	$0.903119\pi$
$282$	0.325794	−	0.0956618i	0.0194008	−	0.00569658i
$283$	9.94692	+	6.39250i	0.591283	+	0.379994i	0.801797	−	0.597596i	$-0.203877\pi$
$283$	9.94692	+	6.39250i	0.591283	+	0.379994i	−0.210514	+	0.977591i	$0.567514\pi$
$284$	−2.17701	+	4.76699i	−0.129182	+	0.282869i
$285$	−0.182292	+	0.210376i	−0.0107981	+	0.0124616i
$286$	4.59140	−	2.95071i	0.271495	−	0.174479i
$287$	−0.942547	−	6.55556i	−0.0556368	−	0.386962i
$288$	−0.142315	−	0.989821i	−0.00838598	−	0.0583258i
$289$	5.53029	−	3.55410i	0.325311	−	0.209065i
$290$	23.2614	−	26.8451i	1.36596	−	1.57640i
$291$	4.34874	−	9.52242i	0.254928	−	0.558214i
$292$	10.9855	+	7.05994i	0.642876	+	0.413151i
$293$	4.65567	−	1.36703i	0.271987	−	0.0798626i	−0.142895	−	0.989738i	$-0.545641\pi$
$293$	4.65567	−	1.36703i	0.271987	−	0.0798626i	0.414882	+	0.909875i	$0.363823\pi$
$294$	−0.654861	−	0.755750i	−0.0381923	−	0.0440762i
$295$	29.5148	+	8.66633i	1.71842	+	0.504573i
$296$	−3.94996	−	8.64920i	−0.229587	−	0.502725i
$297$	0.504677	−	3.51011i	0.0292843	−	0.203677i
$298$	−21.3323			−1.23575
$299$	−6.86022	+	2.72350i	−0.396737	+	0.157504i
$300$	8.74629			0.504967
$301$	1.45938	−	10.1502i	0.0841170	−	0.585047i
$302$	−2.44616	−	5.35634i	−0.140761	−	0.308223i
$303$	12.0410	+	3.53554i	0.691735	+	0.203112i
$304$	−0.0491672	−	0.0567420i	−0.00281993	−	0.00325437i
$305$	−23.0502	+	6.76814i	−1.31985	+	0.387543i
$306$	−4.08453	−	2.62497i	−0.233497	−	0.150059i
$307$	5.87013	−	12.8538i	0.335026	−	0.733604i	−0.664885	−	0.746946i	$-0.731520\pi$
$307$	5.87013	−	12.8538i	0.335026	−	0.733604i	0.999911	+	0.0133414i	$0.00424682\pi$
$308$	−2.32227	+	2.68004i	−0.132323	+	0.152709i
$309$	−0.229867	+	0.147726i	−0.0130767	+	0.00840386i
$310$	4.06235	+	28.2543i	0.230726	+	1.60473i
$311$	−2.67320	−	18.5925i	−0.151583	−	1.05428i	−0.913567	−	0.406688i	$-0.866684\pi$
$311$	−2.67320	−	18.5925i	−0.151583	−	1.05428i	0.761984	−	0.647596i	$-0.224225\pi$
$312$	−1.29474	+	0.832078i	−0.0733001	+	0.0471071i
$313$	−14.5712	+	16.8160i	−0.823611	+	0.950497i	−0.999424	−	0.0339262i	$-0.989199\pi$
$313$	−14.5712	+	16.8160i	−0.823611	+	0.950497i	0.175814	+	0.984423i	$0.443744\pi$
$314$	−8.50733	+	18.6285i	−0.480096	+	1.05126i
$315$	−3.11903	−	2.00448i	−0.175737	−	0.112940i
$316$	7.03353	−	2.06523i	0.395667	−	0.116178i
$317$	−9.37117	−	10.8149i	−0.526337	−	0.607426i	0.428869	−	0.903367i	$-0.358912\pi$
$317$	−9.37117	−	10.8149i	−0.526337	−	0.607426i	−0.955206	+	0.295941i	$0.904367\pi$
$318$	−9.14460	−	2.68510i	−0.512804	−	0.150573i
$319$	14.1137	+	30.9046i	0.790214	+	1.73033i
$320$	−0.527646	+	3.66986i	−0.0294963	+	0.205151i
$321$	−8.99716			−0.502172
$322$	3.77831	−	2.95371i	0.210557	−	0.164604i
$323$	−0.364537			−0.0202834
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	−5.59192	−	12.2446i	−0.310184	−	0.679208i
$326$	−10.6506	−	3.12730i	−0.589882	−	0.173205i
$327$	−3.63034	−	4.18963i	−0.200758	−	0.231687i
$328$	6.35469	−	1.86591i	0.350879	−	0.103027i
$329$	0.285646	+	0.183574i	0.0157482	+	0.0101207i
$330$	−5.46183	+	11.9597i	−0.300664	+	0.658362i
$331$	−10.4287	+	12.0354i	−0.573216	+	0.661526i	−0.966132	−	0.258048i	$-0.916921\pi$
$331$	−10.4287	+	12.0354i	−0.573216	+	0.661526i	0.392916	+	0.919574i	$0.371466\pi$
$332$	−3.98784	+	2.56283i	−0.218861	+	0.140654i
$333$	1.35320	+	9.41168i	0.0741546	+	0.515757i
$334$	−0.186250	−	1.29540i	−0.0101911	−	0.0708810i
$335$	4.20727	−	2.70385i	0.229868	−	0.147727i
$336$	0.654861	−	0.755750i	0.0357256	−	0.0412295i
$337$	−1.69148	+	3.70382i	−0.0921407	+	0.201760i	−0.950091	−	0.311972i	$-0.899010\pi$
$337$	−1.69148	+	3.70382i	−0.0921407	+	0.201760i	0.857950	+	0.513732i	$0.171738\pi$
$338$	−8.94362	−	5.74771i	−0.486469	−	0.312634i
$339$	19.3014	−	5.66740i	1.04831	−	0.307811i
$340$	11.7885	+	13.6046i	0.639319	+	0.737813i
$341$	−26.1963	−	7.69192i	−1.41861	−	0.416541i
$342$	0.0311895	+	0.0682955i	0.00168654	+	0.00369300i
$343$	0.142315	−	0.989821i	0.00768428	−	0.0534453i
$344$	10.2546			0.552889
$345$	10.3557	−	14.4542i	0.557532	−	0.778188i
$346$	−26.0366			−1.39974
$347$	0.705525	−	4.90704i	0.0378746	−	0.263424i	−0.962082	−	0.272761i	$-0.912063\pi$
$347$	0.705525	−	4.90704i	0.0378746	−	0.263424i	0.999956	+	0.00933748i	$0.00297226\pi$
$348$	−3.97994	−	8.71486i	−0.213347	−	0.467166i
$349$	−16.2005	−	4.75690i	−0.867193	−	0.254631i	−0.182272	−	0.983248i	$-0.558345\pi$
$349$	−16.2005	−	4.75690i	−0.867193	−	0.254631i	−0.684921	+	0.728617i	$0.740163\pi$
$350$	5.72760	+	6.61000i	0.306153	+	0.353320i
$351$	1.47672	−	0.433603i	0.0788213	−	0.0231440i
$352$	−2.98325	−	1.91722i	−0.159008	−	0.102188i
$353$	−6.56787	+	14.3816i	−0.349572	+	0.765457i	0.650410	+	0.759583i	$0.274597\pi$
$353$	−6.56787	+	14.3816i	−0.349572	+	0.765457i	−0.999983	+	0.00587383i	$0.998130\pi$
$354$	5.43318	−	6.27023i	0.288770	−	0.333259i
$355$	−16.3455	+	10.5046i	−0.867530	+	0.557528i
$356$	−0.231295	−	1.60869i	−0.0122586	−	0.0852606i
$357$	−0.690980	−	4.80587i	−0.0365705	−	0.254354i
$358$	9.34954	−	6.00858i	0.494138	−	0.317563i
$359$	13.4545	−	15.5273i	0.710100	−	0.819499i	−0.279980	−	0.960006i	$-0.590328\pi$
$359$	13.4545	−	15.5273i	0.710100	−	0.819499i	0.990080	+	0.140507i	$0.0448733\pi$
$360$	1.54019	−	3.37255i	0.0811753	−	0.177749i
$361$	−15.9791	−	10.2691i	−0.841004	−	0.540480i
$362$	−3.09222	+	0.907958i	−0.162523	+	0.0477212i
$363$	−1.03176	−	1.19071i	−0.0541532	−	0.0624961i
$364$	−1.47672	−	0.433603i	−0.0774009	−	0.0227270i
$365$	20.1125	+	44.0403i	1.05274	+	2.30518i
$366$	−0.922125	+	6.41352i	−0.0482002	+	0.335240i
$367$	−2.67721			−0.139749			−0.0698745	−	0.997556i	$-0.522260\pi$
$367$	−2.67721			−0.139749			−0.0698745	+	0.997556i	$0.522260\pi$
$368$	3.46135	+	3.31949i	0.180436	+	0.173041i
$369$	−6.62297			−0.344778
$370$	5.01711	−	34.8947i	0.260827	−	1.81409i
$371$	−3.95918	−	8.66939i	−0.205550	−	0.450092i
$372$	7.38714	+	2.16906i	0.383005	+	0.112461i
$373$	−3.01603	−	3.48068i	−0.156164	−	0.180223i	0.672276	−	0.740300i	$-0.265317\pi$
$373$	−3.01603	−	3.48068i	−0.156164	−	0.180223i	−0.828440	+	0.560078i	$0.810771\pi$
$374$	−16.5204	+	4.85083i	−0.854249	+	0.250830i
$375$	11.6848	+	7.50936i	0.603400	+	0.387782i
$376$	−0.141053	+	0.308864i	−0.00727427	+	0.0159284i
$377$	−9.65604	+	11.1437i	−0.497311	+	0.573928i
$378$	−0.841254	+	0.540641i	−0.0432694	+	0.0278076i
$379$	0.0553046	+	0.384652i	0.00284081	+	0.0197582i	0.991193	−	0.132429i	$-0.0422775\pi$
$379$	0.0553046	+	0.384652i	0.00284081	+	0.0197582i	−0.988352	+	0.152187i	$0.951368\pi$
$380$	−0.0396159	−	0.275535i	−0.00203225	−	0.0141346i
$381$	−6.17401	+	3.96779i	−0.316304	+	0.203276i
$382$	−4.78704	+	5.52453i	−0.244926	+	0.282660i
$383$	1.43863	−	3.15016i	0.0735105	−	0.160966i	−0.869309	−	0.494269i	$-0.835436\pi$
$383$	1.43863	−	3.15016i	0.0735105	−	0.160966i	0.942820	+	0.333303i	$0.108163\pi$
$384$	0.841254	+	0.540641i	0.0429300	+	0.0275895i
$385$	−12.6153	+	3.70419i	−0.642936	+	0.188783i
$386$	−3.92280	−	4.52715i	−0.199665	−	0.230426i
$387$	−9.83918	−	2.88904i	−0.500153	−	0.146858i
$388$	4.34874	+	9.52242i	0.220774	+	0.483427i
$389$	2.03788	−	14.1738i	0.103325	−	0.718640i	−0.870637	−	0.491926i	$-0.836293\pi$
$389$	2.03788	−	14.1738i	0.103325	−	0.718640i	0.973962	−	0.226713i	$-0.0727980\pi$
$390$	−5.70621			−0.288945
$391$	23.1860	−	2.14658i	1.17257	−	0.108557i
$392$	1.00000			0.0505076
$393$	0.154608	−	1.07532i	0.00779893	−	0.0542428i
$394$	3.16294	+	6.92587i	0.159347	+	0.348920i
$395$	26.0775	+	7.65704i	1.31210	+	0.385268i
$396$	2.32227	+	2.68004i	0.116698	+	0.134677i
$397$	33.3087	−	9.78032i	1.67172	−	0.490860i	0.697521	−	0.716565i	$-0.254286\pi$
$397$	33.3087	−	9.78032i	1.67172	−	0.490860i	0.974196	+	0.225704i	$0.0724683\pi$
$398$	20.2125	+	12.9898i	1.01316	+	0.651120i
$399$	−0.0311895	+	0.0682955i	−0.00156143	+	0.00341905i
$400$	−5.72760	+	6.61000i	−0.286380	+	0.330500i
$401$	12.7934	−	8.22179i	0.638870	−	0.410577i	−0.180714	−	0.983536i	$-0.557841\pi$
$401$	12.7934	−	8.22179i	0.638870	−	0.410577i	0.819584	+	0.572959i	$0.194205\pi$
$402$	−0.191969	−	1.33517i	−0.00957453	−	0.0665923i
$403$	−1.68632	−	11.7286i	−0.0840015	−	0.584244i
$404$	−10.5571	+	6.78466i	−0.525237	+	0.337549i
$405$	−2.42796	+	2.80202i	−0.120646	+	0.139233i
$406$	3.97994	−	8.71486i	0.197521	−	0.432511i
$407$	28.3662	+	18.2298i	1.40606	+	0.903619i
$408$	4.65862	−	1.36789i	0.230636	−	0.0677208i
$409$	−12.1606	−	14.0340i	−0.601301	−	0.693939i	0.370743	−	0.928735i	$-0.379103\pi$
$409$	−12.1606	−	14.0340i	−0.601301	−	0.693939i	−0.972045	+	0.234797i	$0.924558\pi$
$410$	23.5607	+	6.91803i	1.16358	+	0.341657i
$411$	7.19576	+	15.7565i	0.354941	+	0.777212i
$412$	0.0388865	−	0.270462i	0.00191580	−	0.0133247i
$413$	8.29670			0.408254
$414$	−2.38594	−	4.16021i	−0.117262	−	0.204463i
$415$	−17.5753			−0.862739
$416$	0.219031	−	1.52339i	0.0107389	−	0.0746905i
$417$	6.76516	+	14.8136i	0.331291	+	0.725426i
$418$	0.255465	+	0.0750113i	0.0124952	+	0.00366892i
$419$	4.21714	+	4.86684i	0.206021	+	0.237761i	0.849351	−	0.527828i	$-0.176993\pi$
$419$	4.21714	+	4.86684i	0.206021	+	0.237761i	−0.643331	+	0.765589i	$0.722448\pi$
$420$	3.55742	−	1.04455i	0.173584	−	0.0509689i
$421$	16.7068	+	10.7368i	0.814238	+	0.523279i	0.880233	−	0.474541i	$-0.157386\pi$
$421$	16.7068	+	10.7368i	0.814238	+	0.523279i	−0.0659955	+	0.997820i	$0.521022\pi$
$422$	0.193544	−	0.423802i	0.00942156	−	0.0206303i
$423$	0.222357	−	0.256613i	0.0108114	−	0.0124770i
$424$	8.01770	−	5.15266i	0.389374	−	0.250235i
$425$	6.04351	+	42.0335i	0.293153	+	2.03893i
$426$	0.745812	+	5.18723i	0.0361347	+	0.251322i
$427$	−5.45088	+	3.50307i	−0.263786	+	0.169525i
$428$	5.89189	−	6.79960i	0.284795	−	0.328671i
$429$	2.26726	−	4.96460i	0.109464	−	0.239693i
$430$	31.9843	+	20.5550i	1.54242	+	0.991252i
$431$	−37.7397	+	11.0814i	−1.81786	+	0.533772i	−0.999180	−	0.0404793i	$-0.987112\pi$
$431$	−37.7397	+	11.0814i	−1.81786	+	0.533772i	−0.818679	+	0.574251i	$0.805293\pi$
$432$	−0.654861	−	0.755750i	−0.0315070	−	0.0363610i
$433$	−32.4094	−	9.51625i	−1.55750	−	0.457322i	−0.614165	−	0.789178i	$-0.710507\pi$
$433$	−32.4094	−	9.51625i	−1.55750	−	0.457322i	−0.943330	+	0.331856i	$0.892325\pi$
$434$	3.19828	+	7.00326i	0.153522	+	0.336167i
$435$	5.05519	−	35.1596i	0.242378	−	1.68578i
$436$	5.54368			0.265494
$437$	−0.319569	−	0.165917i	−0.0152870	−	0.00793687i
$438$	13.0585			0.623957
$439$	3.50663	−	24.3891i	0.167362	−	1.16403i	−0.716947	−	0.697127i	$-0.754461\pi$
$439$	3.50663	−	24.3891i	0.167362	−	1.16403i	0.884309	−	0.466902i	$-0.154630\pi$
$440$	−5.46183	−	11.9597i	−0.260383	−	0.570158i
$441$	−0.959493	−	0.281733i	−0.0456901	−	0.0134158i
$442$	−4.89350	−	5.64740i	−0.232760	−	0.268619i
$443$	−2.20403	+	0.647162i	−0.104717	+	0.0307476i	−0.333671	−	0.942690i	$-0.608287\pi$
$443$	−2.20403	+	0.647162i	−0.104717	+	0.0307476i	0.228954	+	0.973437i	$0.426469\pi$
$444$	−7.99903	−	5.14066i	−0.379617	−	0.243965i
$445$	2.50318	−	5.48119i	0.118662	−	0.259834i
$446$	10.8897	−	12.5674i	0.515641	−	0.595081i
$447$	−17.9459	+	11.5331i	−0.848811	+	0.545498i
$448$	0.142315	+	0.989821i	0.00672374	+	0.0467647i
$449$	5.88403	+	40.9243i	0.277684	+	1.93134i	0.356167	+	0.934422i	$0.384083\pi$
$449$	5.88403	+	40.9243i	0.277684	+	1.93134i	−0.0784826	+	0.996915i	$0.525008\pi$
$450$	7.35785	−	4.72860i	0.346852	−	0.222908i
$451$	−15.3803	+	17.7498i	−0.724230	+	0.835806i
$452$	−8.35659	+	18.2984i	−0.393061	+	0.860683i
$453$	−4.95370	−	3.18355i	−0.232745	−	0.149576i
$454$	−15.8238	+	4.64627i	−0.742645	+	0.218060i
$455$	−3.73677	−	4.31247i	−0.175183	−	0.202172i
$456$	−0.0720391	−	0.0211526i	−0.00337354	−	0.000990561i
$457$	11.6630	+	25.5384i	0.545571	+	1.19463i	0.958820	+	0.284015i	$0.0916667\pi$
$457$	11.6630	+	25.5384i	0.545571	+	1.19463i	−0.413249	+	0.910618i	$0.635606\pi$
$458$	0.179266	−	1.24682i	0.00837655	−	0.0582602i
$459$	−4.85529			−0.226626
$460$	4.14221	+	17.2918i	0.193132	+	0.806235i
$461$	−24.1939			−1.12682			−0.563411	−	0.826177i	$-0.690511\pi$
$461$	−24.1939			−1.12682			−0.563411	+	0.826177i	$0.690511\pi$
$462$	−0.504677	+	3.51011i	−0.0234797	+	0.163305i
$463$	1.03069	+	2.25691i	0.0479004	+	0.104887i	0.932069	−	0.362280i	$-0.118002\pi$
$463$	1.03069	+	2.25691i	0.0479004	+	0.104887i	−0.884169	+	0.467168i	$0.845274\pi$
$464$	9.19256	+	2.69918i	0.426754	+	0.125306i
$465$	18.6929	+	21.5727i	0.866861	+	1.00041i
$466$	6.05320	−	1.77738i	0.280409	−	0.0823356i
$467$	33.2046	+	21.3393i	1.53652	+	0.987464i	0.988537	+	0.150977i	$0.0482418\pi$
$467$	33.2046	+	21.3393i	1.53652	+	0.987464i	0.547986	+	0.836487i	$0.315395\pi$
$468$	−0.639348	+	1.39998i	−0.0295539	+	0.0647140i
$469$	0.883343	−	1.01943i	0.0407890	−	0.0470730i
$470$	−1.05906	+	0.680617i	−0.0488508	+	0.0313945i
$471$	2.91448	+	20.2707i	0.134292	+	0.934023i
$472$	1.18074	+	8.21225i	0.0543481	+	0.378000i
$473$	−30.5919	+	19.6602i	−1.40662	+	0.903979i
$474$	4.80043	−	5.53999i	0.220491	−	0.254460i
$475$	0.272793	−	0.597332i	0.0125166	−	0.0274075i
$476$	4.08453	+	2.62497i	0.187214	+	0.120315i
$477$	−9.14460	+	2.68510i	−0.418702	+	0.122942i
$478$	15.7389	+	18.1636i	0.719880	+	0.830786i
$479$	−6.65494	−	1.95407i	−0.304072	−	0.0892836i	0.126137	−	0.992013i	$-0.459742\pi$
$479$	−6.65494	−	1.95407i	−0.304072	−	0.0892836i	−0.430209	+	0.902729i	$0.641560\pi$
$480$	1.54019	+	3.37255i	0.0702998	+	0.153935i
$481$	−2.08265	+	14.4851i	−0.0949605	+	0.660465i
$482$	−13.5395			−0.616705
$483$	1.58162	−	4.52753i	0.0719661	−	0.206010i
$484$	1.57554			0.0716153
$485$	−5.52363	+	38.4177i	−0.250815	+	1.74446i
$486$	0.415415	+	0.909632i	0.0188436	+	0.0412617i
$487$	29.4107	+	8.63575i	1.33272	+	0.391323i	0.869069	−	0.494692i	$-0.164719\pi$
$487$	29.4107	+	8.63575i	1.33272	+	0.391323i	0.463656	+	0.886015i	$0.346537\pi$
$488$	−4.24315	−	4.89686i	−0.192078	−	0.221670i
$489$	−10.6506	+	3.12730i	−0.481636	+	0.141421i
$490$	3.11903	+	2.00448i	0.140903	+	0.0905531i
$491$	9.12037	−	19.9708i	0.411596	−	0.901270i	−0.584365	−	0.811491i	$-0.698656\pi$
$491$	9.12037	−	19.9708i	0.411596	−	0.901270i	0.995962	−	0.0897796i	$-0.0286163\pi$
$492$	4.33712	−	5.00531i	0.195533	−	0.225657i
$493$	39.1325	−	25.1489i	1.76244	−	1.13265i
$494$	0.0164449	+	0.114377i	0.000739892	+	0.00514606i
$495$	1.87114	+	13.0141i	0.0841015	+	0.584939i
$496$	−6.47681	+	4.16240i	−0.290818	+	0.186897i
$497$	−3.43185	+	3.96056i	−0.153939	+	0.177655i
$498$	−1.96921	+	4.31198i	−0.0882426	+	0.193224i
$499$	−8.09556	−	5.20270i	−0.362407	−	0.232905i	0.346746	−	0.937959i	$-0.387286\pi$
$499$	−8.09556	−	5.20270i	−0.362407	−	0.232905i	−0.709154	+	0.705054i	$0.750923\pi$
$500$	−13.3271	+	3.91319i	−0.596006	+	0.175003i
$501$	−0.857028	−	0.989063i	−0.0382892	−	0.0441881i
$502$	2.27088	+	0.666789i	0.101354	+	0.0297603i
$503$	−5.33816	−	11.6889i	−0.238017	−	0.521184i	0.752497	−	0.658595i	$-0.228849\pi$
$503$	−5.33816	−	11.6889i	−0.238017	−	0.521184i	−0.990514	+	0.137411i	$0.956122\pi$
$504$	0.142315	−	0.989821i	0.00633921	−	0.0440902i
$505$	−46.5277			−2.07046
$506$	−16.6903	−	3.26671i	−0.741974	−	0.145223i
$507$	−10.6313			−0.472153
$508$	1.04446	−	7.26436i	0.0463403	−	0.322304i
$509$	−12.3623	−	27.0696i	−0.547948	−	1.19984i	−0.957733	−	0.287658i	$-0.907124\pi$
$509$	−12.3623	−	27.0696i	−0.547948	−	1.19984i	0.409785	−	0.912182i	$-0.365604\pi$
$510$	17.2723	+	5.07160i	0.764830	+	0.224574i
$511$	8.55147	+	9.86892i	0.378295	+	0.436575i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	0.0631616	+	0.0405915i	0.00278865	+	0.00179216i
$514$	−2.93446	+	6.42557i	−0.129433	+	0.283420i
$515$	0.663423	−	0.765631i	0.0292339	−	0.0337378i
$516$	8.62668	−	5.54403i	0.379769	−	0.244062i
$517$	−0.171362	−	1.19185i	−0.00753650	−	0.0524175i
$518$	−1.35320	−	9.41168i	−0.0594560	−	0.413525i
$519$	−21.9034	+	14.0764i	−0.961452	+	0.617887i
$520$	3.73677	−	4.31247i	0.163868	−	0.189114i
$521$	9.02201	−	19.7554i	0.395261	−	0.865501i	−0.602468	−	0.798143i	$-0.705816\pi$
$521$	9.02201	−	19.7554i	0.395261	−	0.865501i	0.997729	−	0.0673581i	$-0.0214570\pi$
$522$	−8.05975	−	5.17969i	−0.352766	−	0.226709i
$523$	36.5297	−	10.7261i	1.59733	−	0.469019i	0.642530	−	0.766261i	$-0.277885\pi$
$523$	36.5297	−	10.7261i	1.59733	−	0.469019i	0.954802	+	0.297242i	$0.0960667\pi$
$524$	0.711427	+	0.821030i	0.0310788	+	0.0358669i
$525$	8.39200	+	2.46411i	0.366257	+	0.107543i
$526$	−11.8554	−	25.9597i	−0.516920	−	1.13190i
$527$	−5.31986	+	37.0004i	−0.231737	+	1.61176i
$528$	−3.54620			−0.154329
$529$	21.3028	+	8.67117i	0.926210	+	0.377008i
$530$	35.3359			1.53489
$531$	1.18074	−	8.21225i	0.0512399	−	0.356381i
$532$	−0.0311895	−	0.0682955i	−0.00135224	−	0.00296099i
$533$	−9.78024	−	2.87174i	−0.423629	−	0.124389i
$534$	−1.06430	−	1.22827i	−0.0460569	−	0.0531525i
$535$	32.0066	−	9.39799i	1.38377	−	0.406311i
$536$	1.13477	+	0.729271i	0.0490145	+	0.0314997i
$537$	4.61685	−	10.1095i	0.199232	−	0.436256i
$538$	16.0983	−	18.5784i	0.694047	−	0.800973i
$539$	−2.98325	+	1.91722i	−0.128498	+	0.0825805i
$540$	−0.527646	−	3.66986i	−0.0227063	−	0.157926i
$541$	−4.17785	−	29.0576i	−0.179620	−	1.24928i	−0.857644	−	0.514243i	$-0.828073\pi$
$541$	−4.17785	−	29.0576i	−0.179620	−	1.24928i	0.678025	−	0.735039i	$-0.262836\pi$
$542$	−13.4143	+	8.62086i	−0.576195	+	0.370298i
$543$	−2.11046	+	2.43560i	−0.0905686	+	0.104522i
$544$	−2.01696	+	4.41653i	−0.0864765	+	0.189357i
$545$	17.2909	+	11.1122i	0.740661	+	0.475994i
$546$	−1.47672	+	0.433603i	−0.0631976	+	0.0185565i
$547$	−16.7743	−	19.3586i	−0.717219	−	0.827714i	0.273751	−	0.961801i	$-0.411736\pi$
$547$	−16.7743	−	19.3586i	−0.717219	−	0.827714i	−0.990970	+	0.134086i	$0.957190\pi$
$548$	−16.6202	−	4.88013i	−0.709980	−	0.208469i
$549$	2.69167	+	5.89393i	0.114878	+	0.251547i
$550$	4.41405	−	30.7004i	0.188216	−	1.30907i
$551$	−0.719318			−0.0306440
$552$	4.70653	+	0.921186i	0.200323	+	0.0392083i
$553$	7.33046			0.311723
$554$	1.03473	−	7.19674i	0.0439617	−	0.305760i
$555$	−14.6449	−	32.0678i	−0.621640	−	1.36120i
$556$	−15.6256	−	4.58810i	−0.662674	−	0.194579i
$557$	13.7142	+	15.8271i	0.581091	+	0.670615i	0.967839	−	0.251571i	$-0.0809471\pi$
$557$	13.7142	+	15.8271i	0.581091	+	0.670615i	−0.386748	+	0.922186i	$0.626402\pi$
$558$	7.38714	−	2.16906i	0.312723	−	0.0918236i
$559$	−13.2770	−	8.53259i	−0.561556	−	0.360890i
$560$	−1.54019	+	3.37255i	−0.0650850	+	0.142516i
$561$	−11.2753	+	13.0124i	−0.476043	+	0.549383i
$562$	11.2330	−	7.21902i	0.473836	−	0.304516i
$563$	0.0229477	+	0.159605i	0.000967129	+	0.00672653i	0.990299	−	0.138951i	$-0.0443730\pi$
$563$	0.0229477	+	0.159605i	0.000967129	+	0.00672653i	−0.989332	+	0.145677i	$0.953464\pi$
$564$	0.0483227	+	0.336092i	0.00203475	+	0.0141520i
$565$	−62.7431	+	40.3226i	−2.63962	+	1.69638i
$566$	−7.74302	+	8.93593i	−0.325464	+	0.375605i
$567$	−0.415415	+	0.909632i	−0.0174458	+	0.0382010i
$568$	−4.40865	−	2.83327i	−0.184983	−	0.118881i
$569$	8.02440	−	2.35618i	0.336400	−	0.0987760i	−0.109170	−	0.994023i	$-0.534819\pi$
$569$	8.02440	−	2.35618i	0.336400	−	0.0987760i	0.445570	+	0.895247i	$0.353001\pi$
$570$	−0.182292	−	0.210376i	−0.00763538	−	0.00881170i
$571$	−5.07728	−	1.49082i	−0.212478	−	0.0623891i	0.173761	−	0.984788i	$-0.444408\pi$
$571$	−5.07728	−	1.49082i	−0.212478	−	0.0623891i	−0.386239	+	0.922399i	$0.626226\pi$
$572$	2.26726	+	4.96460i	0.0947987	+	0.207580i
$573$	−1.04032	+	7.23560i	−0.0434601	+	0.302272i
$574$	6.62297			0.276437
$575$	−13.8333	+	39.5990i	−0.576888	+	1.65139i
$576$	1.00000			0.0416667
$577$	−2.27358	+	15.8131i	−0.0946504	+	0.658308i	0.886165	+	0.463370i	$0.153360\pi$
$577$	−2.27358	+	15.8131i	−0.0946504	+	0.658308i	−0.980816	+	0.194938i	$0.937549\pi$
$578$	2.73088	+	5.97980i	0.113590	+	0.248727i
$579$	−5.74764	−	1.68766i	−0.238864	−	0.0701367i
$580$	23.2614	+	26.8451i	0.965878	+	1.11468i
$581$	−4.54834	+	1.33551i	−0.188697	+	0.0554064i
$582$	8.80660	+	5.65966i	0.365045	+	0.234600i
$583$	−14.0400	+	30.7434i	−0.581479	+	1.27326i
$584$	−8.55147	+	9.86892i	−0.353862	+	0.408379i
$585$	−4.80037	+	3.08501i	−0.198471	+	0.127549i
$586$	0.690542	+	4.80283i	0.0285260	+	0.198403i
$587$	2.87564	+	20.0005i	0.118690	+	0.825509i	0.959001	+	0.283404i	$0.0914637\pi$
$587$	2.87564	+	20.0005i	0.118690	+	0.825509i	−0.840310	+	0.542106i	$0.817627\pi$
$588$	0.841254	−	0.540641i	0.0346927	−	0.0222957i
$589$	0.378538	−	0.436857i	0.0155974	−	0.0180004i
$590$	−12.7785	+	27.9810i	−0.526083	+	1.15196i
$591$	6.40524	+	4.11640i	0.263476	+	0.169326i
$592$	9.12330	−	2.67884i	0.374965	−	0.110100i
$593$	−14.7815	−	17.0587i	−0.607002	−	0.700518i	0.366182	−	0.930543i	$-0.380665\pi$
$593$	−14.7815	−	17.0587i	−0.607002	−	0.700518i	−0.973185	+	0.230025i	$0.926119\pi$
$594$	3.40255	+	0.999080i	0.139608	+	0.0409928i
$595$	7.47808	+	16.3747i	0.306572	+	0.671298i
$596$	3.03590	−	21.1152i	0.124355	−	0.864911i
$597$	24.0267			0.983347
$598$	−1.71947	−	7.17799i	−0.0703144	−	0.293530i
$599$	−42.3523			−1.73047			−0.865234	−	0.501368i	$-0.832830\pi$
$599$	−42.3523			−1.73047			−0.865234	+	0.501368i	$0.832830\pi$
$600$	−1.24473	+	8.65726i	−0.0508158	+	0.353431i
$601$	−7.65958	−	16.7721i	−0.312441	−	0.684150i	0.686641	−	0.726997i	$-0.259085\pi$
$601$	−7.65958	−	16.7721i	−0.312441	−	0.684150i	−0.999082	+	0.0428468i	$0.986357\pi$
$602$	9.83918	+	2.88904i	0.401015	+	0.117749i
$603$	−0.883343	−	1.01943i	−0.0359725	−	0.0415145i
$604$	5.64995	−	1.65897i	0.229893	−	0.0675027i
$605$	4.91415	+	3.15813i	0.199789	+	0.128396i
$606$	−5.21316	+	11.4152i	−0.211770	+	0.463712i
$607$	0.767346	−	0.885564i	0.0311456	−	0.0359439i	−0.739963	−	0.672648i	$-0.765157\pi$
$607$	0.767346	−	0.885564i	0.0311456	−	0.0359439i	0.771109	+	0.636704i	$0.219703\pi$
$608$	0.0631616	−	0.0405915i	0.00256154	−	0.00164620i
$609$	−1.36347	−	9.48313i	−0.0552505	−	0.384276i
$610$	−3.41887	−	23.7788i	−0.138426	−	0.962774i
$611$	0.439626	−	0.282530i	0.0177854	−	0.0114300i
$612$	3.17954	−	3.66939i	0.128525	−	0.148326i
$613$	−17.1299	+	37.5092i	−0.691870	+	1.51498i	0.157689	+	0.987489i	$0.449596\pi$
$613$	−17.1299	+	37.5092i	−0.691870	+	1.51498i	−0.849559	+	0.527494i	$0.823132\pi$
$614$	11.8875	+	7.63966i	0.479742	+	0.308312i
$615$	23.5607	−	6.91803i	0.950057	−	0.278962i
$616$	−2.32227	−	2.68004i	−0.0935668	−	0.107982i
$617$	−16.6969	−	4.90264i	−0.672191	−	0.197373i	−0.0722123	−	0.997389i	$-0.523006\pi$
$617$	−16.6969	−	4.90264i	−0.672191	−	0.197373i	−0.599978	+	0.800016i	$0.704824\pi$
$618$	−0.113509	−	0.248551i	−0.00456601	−	0.00999817i
$619$	1.08098	−	7.51837i	0.0434482	−	0.302189i	−0.956497	−	0.291741i	$-0.905765\pi$
$619$	1.08098	−	7.51837i	0.0434482	−	0.302189i	0.999945	−	0.0104474i	$-0.00332556\pi$
$620$	−28.5448			−1.14639
$621$	−4.25635	−	2.20985i	−0.170802	−	0.0886784i
$622$	18.7837			0.753157
$623$	0.231295	−	1.60869i	0.00926665	−	0.0644510i
$624$	−0.639348	−	1.39998i	−0.0255944	−	0.0560439i
$625$	−7.45155	−	2.18797i	−0.298062	−	0.0875189i
$626$	−14.5712	−	16.8160i	−0.582381	−	0.672103i
$627$	0.255465	−	0.0750113i	0.0102023	−	0.00299566i
$628$	−17.2281	−	11.0718i	−0.687477	−	0.441815i
$629$	19.1782	−	41.9944i	0.764685	−	1.67443i
$630$	2.42796	−	2.80202i	0.0967323	−	0.111635i
$631$	27.5502	−	17.7055i	1.09676	−	0.704844i	0.138390	−	0.990378i	$-0.455807\pi$
$631$	27.5502	−	17.7055i	1.09676	−	0.704844i	0.958368	+	0.285534i	$0.0921711\pi$
$632$	1.04323	+	7.25585i	0.0414976	+	0.288622i
$633$	−0.0663051	−	0.461162i	−0.00263539	−	0.0183295i
$634$	12.0385	−	7.73666i	0.478109	−	0.307262i
$635$	17.8189	−	20.5642i	0.707123	−	0.816064i
$636$	3.95918	−	8.66939i	0.156992	−	0.343764i
$637$	−1.29474	−	0.832078i	−0.0512994	−	0.0329681i
$638$	−32.5987	+	9.57183i	−1.29059	+	0.378952i
$639$	3.43185	+	3.96056i	0.135762	+	0.156677i
$640$	−3.55742	−	1.04455i	−0.140619	−	0.0412895i
$641$	−1.79115	−	3.92207i	−0.0707461	−	0.154912i	0.870955	−	0.491362i	$-0.163501\pi$
$641$	−1.79115	−	3.92207i	−0.0707461	−	0.154912i	−0.941701	+	0.336450i	$0.890774\pi$
$642$	1.28043	−	8.90558i	0.0505345	−	0.351475i
$643$	−15.4543			−0.609459			−0.304730	−	0.952439i	$-0.598566\pi$
$643$	−15.4543			−0.609459			−0.304730	+	0.952439i	$0.598566\pi$
$644$	2.38594	+	4.16021i	0.0940190	+	0.163935i
$645$	38.0198			1.49703
$646$	0.0518790	−	0.360827i	0.00204115	−	0.0141965i
$647$	13.8071	+	30.2334i	0.542815	+	1.18860i	0.960057	+	0.279803i	$0.0902692\pi$
$647$	13.8071	+	30.2334i	0.542815	+	1.18860i	−0.417243	+	0.908795i	$0.637003\pi$
$648$	−0.959493	−	0.281733i	−0.0376924	−	0.0110675i
$649$	−19.2672	−	22.2355i	−0.756302	−	0.872819i
$650$	12.9158	−	3.79242i	0.506599	−	0.148751i
$651$	6.47681	+	4.16240i	0.253846	+	0.163137i
$652$	4.61120	−	10.0971i	0.180589	−	0.395434i
$653$	−26.7998	+	30.9286i	−1.04876	+	1.21033i	−0.0716849	+	0.997427i	$0.522838\pi$
$653$	−26.7998	+	30.9286i	−1.04876	+	1.21033i	−0.977073	+	0.212904i	$0.931708\pi$
$654$	4.66364	−	2.99714i	0.182363	−	0.117197i
$655$	0.573224	+	3.98686i	0.0223977	+	0.155779i
$656$	0.942547	+	6.55556i	0.0368003	+	0.255952i
$657$	10.9855	−	7.05994i	0.428584	−	0.275434i
$658$	−0.222357	+	0.256613i	−0.00866837	+	0.0100038i
$659$	−6.47208	+	14.1719i	−0.252116	+	0.552058i	−0.992798	−	0.119798i	$-0.961775\pi$
$659$	−6.47208	+	14.1719i	−0.252116	+	0.552058i	0.740682	+	0.671856i	$0.234503\pi$
$660$	−11.0607	−	7.10829i	−0.430537	−	0.276690i
$661$	7.17764	−	2.10755i	0.279178	−	0.0819740i	−0.139146	−	0.990272i	$-0.544436\pi$
$661$	7.17764	−	2.10755i	0.279178	−	0.0819740i	0.418324	+	0.908298i	$0.362618\pi$
$662$	−10.4287	−	12.0354i	−0.405325	−	0.467770i
$663$	−7.16989	−	2.10527i	−0.278455	−	0.0817619i
$664$	−1.96921	−	4.31198i	−0.0764204	−	0.167337i
$665$	0.0396159	−	0.275535i	0.00153624	−	0.0106848i
$666$	−9.50846			−0.368445
$667$	45.7515	−	4.23571i	1.77151	−	0.164007i
$668$	1.30872			0.0506358
$669$	2.36655	−	16.4597i	0.0914962	−	0.636370i
$670$	2.07757	+	4.54924i	0.0802635	+	0.175752i
$671$	22.0467	+	6.47351i	0.851105	+	0.249907i
$672$	0.654861	+	0.755750i	0.0252618	+	0.0291537i
$673$	−6.79174	+	1.99424i	−0.261802	+	0.0768721i	−0.410000	−	0.912086i	$-0.634471\pi$
$673$	−6.79174	+	1.99424i	−0.261802	+	0.0768721i	0.148197	+	0.988958i	$0.452653\pi$
$674$	−3.42540	−	2.20137i	−0.131941	−	0.0847936i
$675$	3.63334	−	7.95590i	0.139847	−	0.306223i
$676$	6.96202	−	8.03460i	0.267770	−	0.309023i
$677$	13.7740	−	8.85202i	0.529378	−	0.340211i	−0.248494	−	0.968633i	$-0.579936\pi$
$677$	13.7740	−	8.85202i	0.529378	−	0.340211i	0.777872	+	0.628423i	$0.216299\pi$
$678$	2.86284	+	19.9115i	0.109947	+	0.764696i
$679$	1.48981	+	10.3619i	0.0571738	+	0.397652i
$680$	−15.1438	+	9.73233i	−0.580738	+	0.373218i
$681$	−10.7998	+	12.4637i	−0.413850	+	0.477608i
$682$	11.3417	−	24.8350i	0.434298	−	0.950980i
$683$	15.7823	+	10.1427i	0.603895	+	0.388099i	0.806563	−	0.591148i	$-0.201325\pi$
$683$	15.7823	+	10.1427i	0.603895	+	0.388099i	−0.202669	+	0.979247i	$0.564961\pi$
$684$	−0.0720391	+	0.0211526i	−0.00275448	+	0.000808789i
$685$	−42.0568	−	48.5361i	−1.60691	−	1.85447i
$686$	0.959493	+	0.281733i	0.0366336	+	0.0107566i
$687$	−0.523275	−	1.14581i	−0.0199642	−	0.0437155i
$688$	−1.45938	+	10.1502i	−0.0556382	+	0.386972i
$689$	−14.6682			−0.558815
$690$	12.8333	+	12.3073i	0.488556	+	0.468533i
$691$	−22.0217			−0.837743			−0.418872	−	0.908046i	$-0.637574\pi$
$691$	−22.0217			−0.837743			−0.418872	+	0.908046i	$0.637574\pi$
$692$	3.70539	−	25.7716i	0.140858	−	0.979689i
$693$	1.47314	+	3.22574i	0.0559601	+	0.122536i
$694$	4.75668	+	1.39669i	0.180561	+	0.0530176i
$695$	−39.5401	−	45.6317i	−1.49984	−	1.73091i
$696$	9.19256	−	2.69918i	0.348443	−	0.102312i
$697$	27.0517	+	17.3851i	1.02466	+	0.658507i
$698$	7.01405	−	15.3586i	0.265486	−	0.581333i
$699$	4.13135	−	4.76784i	0.156262	−	0.180336i
$700$	−7.35785	+	4.72860i	−0.278100	+	0.178724i
$701$	−2.32460	−	16.1680i	−0.0877990	−	0.610655i	−0.985452	−	0.169953i	$-0.945638\pi$
$701$	−2.32460	−	16.1680i	−0.0877990	−	0.610655i	0.897653	−	0.440703i	$-0.145271\pi$
$702$	0.219031	+	1.52339i	0.00826679	+	0.0574968i
$703$	−0.600570	+	0.385963i	−0.0226509	+	0.0145569i
$704$	2.32227	−	2.68004i	0.0875237	−	0.101008i
$705$	−0.522969	+	1.14514i	−0.0196962	+	0.0431286i
$706$	−13.3005	−	8.54774i	−0.500572	−	0.321698i
$707$	−12.0410	+	3.53554i	−0.452847	+	0.132968i
$708$	5.43318	+	6.27023i	0.204192	+	0.235650i
$709$	34.2638	+	10.0608i	1.28681	+	0.377840i	0.852406	−	0.522880i	$-0.175143\pi$
$709$	34.2638	+	10.0608i	1.28681	+	0.377840i	0.434399	+	0.900720i	$0.356961\pi$
$710$	−8.07149	−	17.6741i	−0.302918	−	0.663297i
$711$	1.04323	−	7.25585i	0.0391243	−	0.272116i
$712$	1.62524			0.0609083
$713$	−21.5041	+	30.0148i	−0.805335	+	1.12406i
$714$	4.85529			0.181705
$715$	−2.87979	+	20.0294i	−0.107698	+	0.749057i
$716$	4.61685	+	10.1095i	0.172540	+	0.377809i
$717$	23.0604	+	6.77114i	0.861206	+	0.252873i
$718$	13.4545	+	15.5273i	0.502116	+	0.579473i
$719$	3.87502	−	1.13781i	0.144514	−	0.0424331i	−0.208676	−	0.977985i	$-0.566915\pi$
$719$	3.87502	−	1.13781i	0.144514	−	0.0424331i	0.353189	+	0.935552i	$0.385097\pi$
$720$	3.11903	+	2.00448i	0.116239	+	0.0747025i
$721$	0.113509	−	0.248551i	0.00422731	−	0.00925651i
$722$	12.4387	−	14.3550i	0.462919	−	0.534237i
$723$	−11.3901	+	7.31998i	−0.423603	+	0.272233i
$724$	−0.458647	−	3.18996i	−0.0170455	−	0.118554i
$725$	11.9253	+	82.9422i	0.442894	+	3.08040i
$726$	1.32543	−	0.851800i	0.0491912	−	0.0316132i
$727$	−26.7900	+	30.9173i	−0.993586	+	1.14666i	−0.00439992	+	0.999990i	$0.501401\pi$
$727$	−26.7900	+	30.9173i	−0.993586	+	1.14666i	−0.989186	+	0.146669i	$0.953145\pi$
$728$	0.639348	−	1.39998i	0.0236958	−	0.0518866i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	−46.4544	+	13.6402i	−1.71935	+	0.504848i
$731$	32.6048	+	37.6279i	1.20593	+	1.39172i
$732$	−6.21701	−	1.82548i	−0.229787	−	0.0674716i
$733$	−2.32391	−	5.08864i	−0.0858354	−	0.187953i	0.861847	−	0.507169i	$-0.169308\pi$
$733$	−2.32391	−	5.08864i	−0.0858354	−	0.187953i	−0.947682	+	0.319215i	$0.896581\pi$
$734$	0.381006	−	2.64996i	0.0140632	−	0.0978117i
$735$	3.70760			0.136757
$736$	−3.77831	+	2.95371i	−0.139270	+	0.108875i
$737$	−4.78348			−0.176202
$738$	0.942547	−	6.55556i	0.0346956	−	0.241313i
$739$	−2.48090	−	5.43240i	−0.0912612	−	0.199834i	0.858497	−	0.512818i	$-0.171399\pi$
$739$	−2.48090	−	5.43240i	−0.0912612	−	0.199834i	−0.949758	+	0.312984i	$0.898671\pi$
$740$	33.8255	+	9.93208i	1.24345	+	0.365110i
$741$	0.0756712	+	0.0873292i	0.00277985	+	0.00320812i
$742$	9.14460	−	2.68510i	0.335709	−	0.0985730i
$743$	14.3527	+	9.22390i	0.526548	+	0.338392i	0.776757	−	0.629800i	$-0.216863\pi$
$743$	14.3527	+	9.22390i	0.526548	+	0.338392i	−0.250209	+	0.968192i	$0.580499\pi$
$744$	−3.19828	+	7.00326i	−0.117255	+	0.256752i
$745$	51.7940	−	59.7735i	1.89759	−	2.18993i
$746$	3.87448	−	2.48997i	0.141855	−	0.0911644i
$747$	0.674623	+	4.69211i	0.0246832	+	0.171675i
$748$	−2.45035	−	17.0426i	−0.0895938	−	0.623139i
$749$	7.56889	−	4.86423i	0.276561	−	0.177735i
$750$	−9.09584	+	10.4972i	−0.332133	+	0.383302i
$751$	20.7815	−	45.5052i	0.758329	−	1.66051i	0.00753603	−	0.999972i	$-0.497601\pi$
$751$	20.7815	−	45.5052i	0.758329	−	1.66051i	0.750793	−	0.660537i	$-0.229672\pi$
$752$	−0.285646	−	0.183574i	−0.0104164	−	0.00669424i
$753$	2.27088	−	0.666789i	0.0827553	−	0.0242992i
$754$	−9.65604	−	11.1437i	−0.351652	−	0.405828i
$755$	20.9477	+	6.15081i	0.762367	+	0.223851i
$756$	−0.415415	−	0.909632i	−0.0151085	−	0.0330830i
$757$	6.14382	−	42.7312i	0.223301	−	1.55309i	−0.502126	−	0.864794i	$-0.667449\pi$
$757$	6.14382	−	42.7312i	0.223301	−	1.55309i	0.725427	−	0.688299i	$-0.241642\pi$
$758$	−0.388608			−0.0141149
$759$	−15.8069	+	6.27532i	−0.573754	+	0.227780i
$760$	0.278368			0.0100975
$761$	−1.79602	+	12.4916i	−0.0651056	+	0.452820i	0.931027	+	0.364952i	$0.118914\pi$
$761$	−1.79602	+	12.4916i	−0.0651056	+	0.452820i	−0.996132	+	0.0878680i	$0.971995\pi$
$762$	−3.04875	−	6.67584i	−0.110445	−	0.241840i
$763$	5.31912	+	1.56183i	0.192565	+	0.0565422i
$764$	−4.78704	−	5.52453i	−0.173189	−	0.199871i
$765$	17.2723	−	5.07160i	0.624481	−	0.183364i
$766$	2.91336	+	1.87230i	0.105264	+	0.0676490i
$767$	5.30448	−	11.6152i	0.191534	−	0.419400i
$768$	−0.654861	+	0.755750i	−0.0236303	+	0.0272708i
$769$	−18.6723	+	12.0000i	−0.673341	+	0.432730i	−0.832128	−	0.554583i	$-0.812878\pi$
$769$	−18.6723	+	12.0000i	−0.673341	+	0.432730i	0.158788	+	0.987313i	$0.449241\pi$
$770$	−1.87114	−	13.0141i	−0.0674312	−	0.468994i
$771$	1.00530	+	6.99202i	0.0362050	+	0.251811i
$772$	5.03935	−	3.23859i	0.181370	−	0.116559i
$773$	13.7681	−	15.8893i	0.495205	−	0.571497i	−0.452044	−	0.891996i	$-0.649305\pi$
$773$	13.7681	−	15.8893i	0.495205	−	0.571497i	0.947249	+	0.320499i	$0.103850\pi$
$774$	4.25990	−	9.32787i	0.153119	−	0.335283i
$775$	−56.6481	−	36.4055i	−2.03486	−	1.30772i
$776$	−10.0444	+	2.94930i	−0.360572	+	0.105874i
$777$	−6.22672	−	7.18602i	−0.223382	−	0.257797i
$778$	13.7395	+	4.03428i	0.492585	+	0.144636i
$779$	−0.206567	−	0.452319i	−0.00740104	−	0.0162060i
$780$	0.812079	−	5.64813i	0.0290771	−	0.202236i
$781$	18.5841			0.664992
$782$	−1.17498	+	23.2555i	−0.0420173	+	0.831615i
$783$	−9.58065			−0.342384
$784$	−0.142315	+	0.989821i	−0.00508267	+	0.0353508i
$785$	−31.5418	−	69.0668i	−1.12577	−	2.46510i
$786$	1.04237	+	0.306068i	0.0371802	+	0.0109171i
$787$	−5.84679	−	6.74755i	−0.208415	−	0.240524i	0.641912	−	0.766778i	$-0.278141\pi$
$787$	−5.84679	−	6.74755i	−0.208415	−	0.240524i	−0.850327	+	0.526254i	$0.823596\pi$
$788$	−7.30551	+	2.14509i	−0.260248	+	0.0764157i
$789$	−24.0083	−	15.4292i	−0.854717	−	0.549293i
$790$	−11.2903	+	24.7224i	−0.401692	+	0.879582i
$791$	−13.1733	+	15.2028i	−0.468390	+	0.540551i
$792$	−2.98325	+	1.91722i	−0.106005	+	0.0681255i
$793$	1.41920	+	9.87078i	0.0503974	+	0.350522i
$794$	4.94045	+	34.3616i	0.175330	+	1.21945i
$795$	29.7264	−	19.1040i	1.05429	−	0.677549i
$796$	−15.7341	+	18.1582i	−0.557682	+	0.643599i
$797$	3.37051	−	7.38039i	0.119390	−	0.261427i	−0.840496	−	0.541817i	$-0.817737\pi$
$797$	3.37051	−	7.38039i	0.119390	−	0.261427i	0.959886	+	0.280390i	$0.0904638\pi$
$798$	−0.0631616	−	0.0405915i	−0.00223590	−	0.00143692i
$799$	−1.58183	+	0.464466i	−0.0559610	+	0.0164316i
$800$	−5.72760	−	6.61000i	−0.202501	−	0.233699i
$801$	−1.55940	−	0.457882i	−0.0550988	−	0.0161785i
$802$	6.31742	+	13.8332i	0.223076	+	0.488468i
$803$	6.59030	−	45.8366i	0.232567	−	1.61754i
$804$	1.34890			0.0475721
$805$	−0.897240	+	17.7584i	−0.0316236	+	0.625900i
$806$	11.8492			0.417371
$807$	3.49849	−	24.3326i	0.123153	−	0.856547i
$808$	−5.21316	−	11.4152i	−0.183398	−	0.401587i
$809$	−2.67207	−	0.784589i	−0.0939448	−	0.0275847i	0.234422	−	0.972135i	$-0.424680\pi$
$809$	−2.67207	−	0.784589i	−0.0939448	−	0.0275847i	−0.328367	+	0.944550i	$0.606498\pi$
$810$	−2.42796	−	2.80202i	−0.0853099	−	0.0984528i
$811$	14.3549	−	4.21498i	0.504069	−	0.148008i	−0.0198048	−	0.999804i	$-0.506304\pi$
$811$	14.3549	−	4.21498i	0.504069	−	0.148008i	0.523874	+	0.851796i	$0.324486\pi$
$812$	8.05975	+	5.17969i	0.282842	+	0.181771i
$813$	−6.62406	+	14.5047i	−0.232316	+	0.508701i
$814$	−22.0812	+	25.4831i	−0.773945	+	0.893181i
$815$	34.6220	−	22.2502i	1.21275	−	0.779390i
$816$	0.690980	+	4.80587i	0.0241891	+	0.168239i
$817$	−0.109570	−	0.762079i	−0.00383339	−	0.0266618i
$818$	15.6218	−	10.0395i	0.546204	−	0.351024i
$819$	−1.00787	+	1.16314i	−0.0352178	+	0.0406435i
$820$	−10.2006	+	22.3363i	−0.356222	+	0.780017i
$821$	−11.2823	−	7.25066i	−0.393753	−	0.253050i	0.328751	−	0.944417i	$-0.393372\pi$
$821$	−11.2823	−	7.25066i	−0.393753	−	0.253050i	−0.722504	+	0.691367i	$0.757009\pi$
$822$	−16.6202	+	4.88013i	−0.579696	+	0.170214i
$823$	−24.8232	−	28.6475i	−0.865283	−	0.998590i	−0.999970	−	0.00770175i	$-0.997548\pi$
$823$	−24.8232	−	28.6475i	−0.865283	−	0.998590i	0.134687	−	0.990888i	$-0.456997\pi$
$824$	0.262175	+	0.0769815i	0.00913329	+	0.00268178i
$825$	−12.8846	−	28.2132i	−0.448582	−	0.982259i
$826$	−1.18074	+	8.21225i	−0.0410833	+	0.285741i
$827$	44.1279			1.53448			0.767239	−	0.641361i	$-0.221630\pi$
$827$	44.1279			1.53448			0.767239	+	0.641361i	$0.221630\pi$
$828$	4.45741	−	1.76959i	0.154906	−	0.0614975i
$829$	−22.9461			−0.796951			−0.398476	−	0.917179i	$-0.630461\pi$
$829$	−22.9461			−0.796951			−0.398476	+	0.917179i	$0.630461\pi$
$830$	2.50123	−	17.3964i	0.0868190	−	0.603839i
$831$	−3.02038	−	6.61370i	−0.104776	−	0.229427i
$832$	1.47672	+	0.433603i	0.0511959	+	0.0150325i
$833$	3.17954	+	3.66939i	0.110165	+	0.127137i
$834$	−15.6256	+	4.58810i	−0.541071	+	0.158873i
$835$	4.08193	+	2.62330i	0.141261	+	0.0907830i
$836$	−0.110604	+	0.242190i	−0.00382533	+	0.00837630i
$837$	5.04177	−	5.81852i	0.174269	−	0.201117i
$838$	−5.41747	+	3.48159i	−0.187143	+	0.120270i
$839$	−6.25915	−	43.5334i	−0.216090	−	1.50294i	−0.752281	−	0.658842i	$-0.771047\pi$
$839$	−6.25915	−	43.5334i	−0.216090	−	1.50294i	0.536191	−	0.844097i	$-0.319863\pi$
$840$	0.527646	+	3.66986i	0.0182055	+	0.126622i
$841$	52.8213	−	33.9462i	1.82142	−	1.17056i
$842$	−13.0051	+	15.0087i	−0.448186	+	0.517234i
$843$	5.54692	−	12.1461i	0.191046	−	0.418332i
$844$	0.391944	+	0.251887i	0.0134913	+	0.00867031i
$845$	37.8199	−	11.1049i	1.30105	−	0.382021i
$846$	0.222357	+	0.256613i	0.00764478	+	0.00882255i
$847$	1.51172	+	0.443880i	0.0519432	+	0.0152519i
$848$	3.95918	+	8.66939i	0.135959	+	0.297708i
$849$	−1.68272	+	11.7036i	−0.0577508	+	0.401666i
$850$	−42.4658			−1.45656
$851$	35.9259	−	28.0852i	1.23152	−	0.962749i
$852$	−5.24057			−0.179539
$853$	−6.15267	+	42.7927i	−0.210663	+	1.46520i	0.560286	+	0.828299i	$0.310691\pi$
$853$	−6.15267	+	42.7927i	−0.210663	+	1.46520i	−0.770949	+	0.636896i	$0.780218\pi$
$854$	−2.69167	−	5.89393i	−0.0921070	−	0.201686i
$855$	−0.267092	−	0.0784253i	−0.00913436	−	0.00268209i
$856$	5.89189	+	6.79960i	0.201381	+	0.232405i
$857$	6.89400	−	2.02426i	0.235495	−	0.0691475i	−0.161856	−	0.986814i	$-0.551748\pi$
$857$	6.89400	−	2.02426i	0.235495	−	0.0691475i	0.397350	+	0.917667i	$0.369930\pi$
$858$	4.59140	+	2.95071i	0.156748	+	0.100736i
$859$	−9.74500	+	21.3386i	−0.332495	+	0.728063i	−0.999861	−	0.0166671i	$-0.994694\pi$
$859$	−9.74500	+	21.3386i	−0.332495	+	0.728063i	0.667366	+	0.744730i	$0.267422\pi$
$860$	−24.8977	+	28.7334i	−0.849003	+	0.979802i
$861$	5.57160	−	3.58065i	0.189880	−	0.122028i
$862$	−5.59767	−	38.9327i	−0.190657	−	1.32605i
$863$	−4.78878	−	33.3067i	−0.163012	−	1.13377i	−0.892916	−	0.450223i	$-0.851344\pi$
$863$	−4.78878	−	33.3067i	−0.163012	−	1.13377i	0.729904	−	0.683549i	$-0.239565\pi$
$864$	0.841254	−	0.540641i	0.0286200	−	0.0183930i
$865$	63.2158	−	72.9550i	2.14940	−	2.48054i
$866$	14.0317	−	30.7252i	0.476817	−	1.04408i
$867$	5.53029	+	3.55410i	0.187818	+	0.120704i
$868$	−7.38714	+	2.16906i	−0.250736	+	0.0736227i
$869$	−17.0233	−	19.6459i	−0.577476	−	0.666442i
$870$	34.0823	+	10.0075i	1.15550	+	0.339285i
$871$	−0.862418	−	1.88843i	−0.0292219	−	0.0639871i
$872$	−0.788948	+	5.48725i	−0.0267171	+	0.185822i
$873$	10.4684			0.354303
$874$	0.209707	−	0.292703i	0.00709345	−	0.00990084i
$875$	−13.8897			−0.469559
$876$	−1.85841	+	12.9255i	−0.0627899	+	0.436714i
$877$	4.45758	+	9.76074i	0.150522	+	0.329597i	0.969840	−	0.243742i	$-0.0783751\pi$
$877$	4.45758	+	9.76074i	0.150522	+	0.329597i	−0.819318	+	0.573339i	$0.805648\pi$
$878$	23.6418	+	6.94187i	0.797873	+	0.234277i
$879$	3.17753	+	3.66706i	0.107175	+	0.123687i
$880$	12.6153	−	3.70419i	0.425262	−	0.124868i
$881$	−39.1386	−	25.1529i	−1.31861	−	0.847422i	−0.323508	−	0.946226i	$-0.604862\pi$
$881$	−39.1386	−	25.1529i	−1.31861	−	0.847422i	−0.995107	+	0.0988035i	$0.968498\pi$
$882$	0.415415	−	0.909632i	0.0139878	−	0.0306289i
$883$	−30.3838	+	35.0648i	−1.02250	+	1.18003i	−0.0389750	+	0.999240i	$0.512409\pi$
$883$	−30.3838	+	35.0648i	−1.02250	+	1.18003i	−0.983523	+	0.180785i	$0.942136\pi$
$884$	6.28633	−	4.03998i	0.211432	−	0.135879i
$885$	4.37772	+	30.4477i	0.147156	+	1.02349i
$886$	−0.326908	−	2.27370i	−0.0109827	−	0.0763864i
$887$	−0.676949	+	0.435049i	−0.0227297	+	0.0146075i	−0.551956	−	0.833873i	$-0.686119\pi$
$887$	−0.676949	+	0.435049i	−0.0227297	+	0.0146075i	0.529227	+	0.848481i	$0.322482\pi$
$888$	6.22672	−	7.18602i	0.208955	−	0.241147i
$889$	3.04875	−	6.67584i	0.102252	−	0.223901i
$890$	5.06916	+	3.25775i	0.169919	+	0.109200i
$891$	3.40255	−	0.999080i	0.113990	−	0.0334704i
$892$	10.8897	+	12.5674i	0.364613	+	0.420786i
$893$	0.0244607	+	0.00718232i	0.000818547	+	0.000240347i
$894$	−8.86176	−	19.4046i	−0.296382	−	0.648985i
$895$	−5.86416	+	40.7862i	−0.196017	+	1.36333i
$896$	−1.00000			−0.0334077
$897$	−5.32723	−	5.10889i	−0.177871	−	0.170581i
$898$	−41.3451			−1.37971
$899$	−10.4973	+	73.0106i	−0.350106	+	2.43504i
$900$	3.63334	+	7.95590i	0.121111	+	0.265197i
$901$	44.3997	+	13.0369i	1.47917	+	0.434323i
$902$	−15.3803	−	17.7498i	−0.512108	−	0.591004i
$903$	9.83918	−	2.88904i	0.327427	−	0.0961413i
$904$	−16.9229	−	10.8757i	−0.562846	−	0.361719i
$905$	4.96368	−	10.8689i	0.164998	−	0.361296i
$906$	3.85613	−	4.45021i	0.128111	−	0.147848i
$907$	−3.57584	+	2.29805i	−0.118734	+	0.0763056i	−0.598660	−	0.801003i	$-0.704300\pi$
$907$	−3.57584	+	2.29805i	−0.118734	+	0.0763056i	0.479926	+	0.877309i	$0.340663\pi$
$908$	−2.34703	−	16.3239i	−0.0778888	−	0.541728i
$909$	1.78595	+	12.4216i	0.0592362	+	0.411997i
$910$	4.80037	−	3.08501i	0.159131	−	0.102267i
$911$	−23.1576	+	26.7253i	−0.767245	+	0.885447i	−0.996120	−	0.0880084i	$-0.971950\pi$
$911$	−23.1576	+	26.7253i	−0.767245	+	0.885447i	0.228875	+	0.973456i	$0.426495\pi$
$912$	0.0311895	−	0.0682955i	0.00103279	−	0.00226149i
$913$	14.1417	+	9.08831i	0.468021	+	0.300779i
$914$	−26.9382	+	7.90978i	−0.891037	+	0.261632i
$915$	−15.7319	−	18.1556i	−0.520081	−	0.600205i
$916$	1.20862	+	0.354883i	0.0399339	+	0.0117257i
$917$	0.451298	+	0.988205i	0.0149032	+	0.0326334i
$918$	0.690980	−	4.80587i	0.0228057	−	0.158617i
$919$	−30.3779			−1.00207			−0.501036	−	0.865426i	$-0.667048\pi$
$919$	−30.3779			−1.00207			−0.501036	+	0.865426i	$0.667048\pi$
$920$	−17.7053	+	1.63917i	−0.583727	+	0.0540419i
$921$	14.1308			0.465624
$922$	3.44315	−	23.9477i	0.113394	−	0.788674i
$923$	3.35055	+	7.33668i	0.110285	+	0.241490i
$924$	−3.40255	−	0.999080i	−0.111936	−	0.0328673i
$925$	54.4607	+	62.8510i	1.79066	+	2.06653i
$926$	−2.38062	+	0.699012i	−0.0782319	+	0.0229710i
$927$	−0.229867	−	0.147726i	−0.00754981	−	0.00485197i
$928$	−3.97994	+	8.71486i	−0.130648	+	0.286079i
$929$	3.04858	−	3.51824i	0.100021	−	0.115430i	−0.703532	−	0.710663i	$-0.748395\pi$
$929$	3.04858	−	3.51824i	0.100021	−	0.115430i	0.803553	+	0.595233i	$0.202940\pi$
$930$	−24.0134	+	15.4325i	−0.787431	+	0.506051i
$931$	−0.0106851	−	0.0743162i	−0.000350188	−	0.00243561i
$932$	0.897829	+	6.24454i	0.0294094	+	0.204547i
$933$	15.8018	−	10.1552i	0.517329	−	0.332467i
$934$	−25.8476	+	29.8297i	−0.845758	+	0.976057i
$935$	26.5188	−	58.0680i	0.867257	−	1.89903i
$936$	−1.29474	−	0.832078i	−0.0423198	−	0.0271973i
$937$	−34.8995	+	10.2474i	−1.14012	+	0.334769i	−0.796677	−	0.604405i	$-0.793411\pi$
$937$	−34.8995	+	10.2474i	−1.14012	+	0.334769i	−0.343441	+	0.939174i	$0.611593\pi$
$938$	0.883343	+	1.01943i	0.0288422	+	0.0332856i
$939$	−21.3495	−	6.26877i	−0.696713	−	0.204574i
$940$	−0.522969	−	1.14514i	−0.0170574	−	0.0373505i
$941$	−0.276980	+	1.92644i	−0.00902930	+	0.0628002i	−0.993838	−	0.110843i	$-0.964645\pi$
$941$	−0.276980	+	1.92644i	−0.00902930	+	0.0628002i	0.984809	+	0.173643i	$0.0555540\pi$
$942$	−20.4791			−0.667245
$943$	15.8020	+	27.5529i	0.514583	+	0.897246i
$944$	−8.29670			−0.270035
$945$	0.527646	−	3.66986i	0.0171643	−	0.119381i
$946$	−15.1064	−	33.0785i	−0.491153	−	1.07548i
$947$	−45.9150	−	13.4819i	−1.49204	−	0.438102i	−0.568846	−	0.822444i	$-0.692610\pi$
$947$	−45.9150	−	13.4819i	−1.49204	−	0.438102i	−0.923191	+	0.384342i	$0.874428\pi$
$948$	4.80043	+	5.53999i	0.155911	+	0.179931i
$949$	19.2836	−	5.66218i	0.625973	−	0.183802i
$950$	0.552430	+	0.355025i	0.0179232	+	0.0115185i
$951$	5.94466	−	13.0170i	0.192769	−	0.422105i
$952$	−3.17954	+	3.66939i	−0.103049	+	0.118925i
$953$	42.4727	−	27.2956i	1.37583	−	0.884190i	0.376715	−	0.926329i	$-0.377053\pi$
$953$	42.4727	−	27.2956i	1.37583	−	0.884190i	0.999112	+	0.0421386i	$0.0134171\pi$
$954$	−1.35635	−	9.43365i	−0.0439136	−	0.305426i
$955$	−3.85710	−	26.8267i	−0.124813	−	0.868092i
$956$	−20.2186	+	12.9937i	−0.653918	+	0.420247i
$957$	−22.2488	+	25.6765i	−0.719202	+	0.830004i
$958$	2.88127	−	6.30911i	0.0930897	−	0.203838i
$959$	−14.5721	−	9.36490i	−0.470557	−	0.302408i
$960$	−3.55742	+	1.04455i	−0.114815	+	0.0337127i
$961$	−18.5160	−	21.3686i	−0.597289	−	0.689308i
$962$	−14.0413	−	4.12290i	−0.452710	−	0.132928i
$963$	−3.73755	−	8.18410i	−0.120441	−	0.263729i
$964$	1.92687	−	13.4016i	0.0620602	−	0.431638i
$965$	22.2096			0.714951
$966$	4.25635	+	2.20985i	0.136946	+	0.0711009i
$967$	33.8855			1.08969			0.544843	−	0.838538i	$-0.316589\pi$
$967$	33.8855			1.08969			0.544843	+	0.838538i	$0.316589\pi$
$968$	−0.224222	+	1.55950i	−0.00720678	+	0.0501242i
$969$	−0.151434	−	0.331595i	−0.00486477	−	0.0106524i
$970$	−37.2405	−	10.9348i	−1.19572	−	0.351096i
$971$	−9.07366	−	10.4716i	−0.291188	−	0.336049i	0.591241	−	0.806495i	$-0.298638\pi$
$971$	−9.07366	−	10.4716i	−0.291188	−	0.336049i	−0.882428	+	0.470447i	$0.844093\pi$
$972$	−0.959493	+	0.281733i	−0.0307758	+	0.00903658i
$973$	−13.7001	−	8.80450i	−0.439204	−	0.282259i
$974$	−12.7334	+	27.8823i	−0.408005	+	0.893407i
$975$	8.81511	−	10.1732i	0.282310	−	0.325803i
$976$	5.45088	−	3.50307i	0.174478	−	0.112130i
$977$	−5.98979	−	41.6599i	−0.191630	−	1.33282i	−0.827693	−	0.561181i	$-0.810347\pi$
$977$	−5.98979	−	41.6599i	−0.191630	−	1.33282i	0.636063	−	0.771637i	$-0.280562\pi$
$978$	−1.57973	−	10.9872i	−0.0505141	−	0.351333i
$979$	−4.84849	+	3.11594i	−0.154959	+	0.0995858i
$980$	−2.42796	+	2.80202i	−0.0775584	+	0.0895071i
$981$	2.30293	−	5.04271i	0.0735268	−	0.161001i
$982$	18.4696	+	11.8697i	0.589388	+	0.378777i
$983$	−31.3263	+	9.19824i	−0.999155	+	0.293378i	−0.740109	−	0.672487i	$-0.765226\pi$
$983$	−31.3263	+	9.19824i	−0.999155	+	0.293378i	−0.259046	+	0.965865i	$0.583408\pi$
$984$	4.33712	+	5.00531i	0.138262	+	0.159563i
$985$	−27.0859	−	7.95313i	−0.863028	−	0.253408i
$986$	19.3238	+	42.3132i	0.615395	+	1.34753i
$987$	−0.0483227	+	0.336092i	−0.00153813	+	0.0106979i
$988$	−0.115553			−0.00367623
$989$	11.4566	+	47.8261i	0.364300	+	1.52078i
$990$	−13.1479			−0.417867
$991$	−0.858566	+	5.97145i	−0.0272732	+	0.189690i	−0.998904	−	0.0468152i	$-0.985093\pi$
$991$	−0.858566	+	5.97145i	−0.0272732	+	0.189690i	0.971630	+	0.236505i	$0.0760019\pi$
$992$	−3.19828	−	7.00326i	−0.101546	−	0.222354i
$993$	−15.2801	−	4.48663i	−0.484898	−	0.142379i
$994$	−3.43185	−	3.96056i	−0.108852	−	0.125621i
$995$	−85.4729	+	25.0971i	−2.70967	+	0.795632i
$996$	−3.98784	−	2.56283i	−0.126360	−	0.0812064i
$997$	19.2204	−	42.0867i	0.608715	−	1.33290i	−0.314734	−	0.949180i	$-0.601915\pi$
$997$	19.2204	−	42.0867i	0.608715	−	1.33290i	0.923449	−	0.383721i	$-0.125357\pi$
$998$	6.30187	−	7.27274i	0.199482	−	0.230215i
$999$	−7.99903	+	5.14066i	−0.253078	+	0.162643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.a.169.1	✓	10
23.3	even	11	inner	966.2.q.a.463.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.a.169.1	✓	10	1.1	even	1	trivial
966.2.q.a.463.1	yes	10	23.3	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-2.42796 - 2.80202i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-2.42796 - 2.80202i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(3.11903 - 2.00448i) q^{10} +(0.504677 + 3.51011i) q^{11} +(-0.142315 - 0.989821i) q^{12} +(-1.29474 + 0.832078i) q^{13} +(0.654861 - 0.755750i) q^{14} +(1.54019 - 3.37255i) q^{15} +(0.841254 + 0.540641i) q^{16} +(4.65862 - 1.36789i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(-0.0720391 - 0.0211526i) q^{19} +(1.54019 + 3.37255i) q^{20} +(0.142315 - 0.989821i) q^{21} -3.54620 q^{22} +(4.70653 + 0.921186i) q^{23} +1.00000 q^{24} +(-1.24473 + 8.65726i) q^{25} +(-0.639348 - 1.39998i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(0.654861 + 0.755750i) q^{28} +(9.19256 - 2.69918i) q^{29} +(3.11903 + 2.00448i) q^{30} +(-3.19828 + 7.00326i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-2.98325 + 1.91722i) q^{33} +(0.690980 + 4.80587i) q^{34} +(0.527646 + 3.66986i) q^{35} +(0.841254 - 0.540641i) q^{36} +(6.22672 - 7.18602i) q^{37} +(0.0311895 - 0.0682955i) q^{38} +(-1.29474 - 0.832078i) q^{39} +(-3.55742 + 1.04455i) q^{40} +(4.33712 + 5.00531i) q^{41} +(0.959493 + 0.281733i) q^{42} +(4.25990 + 9.32787i) q^{43} +(0.504677 - 3.51011i) q^{44} +3.70760 q^{45} +(-1.58162 + 4.52753i) q^{46} -0.339548 q^{47} +(-0.142315 + 0.989821i) q^{48} +(0.415415 + 0.909632i) q^{49} +(-8.39200 - 2.46411i) q^{50} +(3.17954 + 3.66939i) q^{51} +(1.47672 - 0.433603i) q^{52} +(8.01770 + 5.15266i) q^{53} +(0.415415 - 0.909632i) q^{54} +(8.61004 - 9.93651i) q^{55} +(-0.841254 + 0.540641i) q^{56} +(-0.0106851 - 0.0743162i) q^{57} +(1.36347 + 9.48313i) q^{58} +(-6.97963 + 4.48554i) q^{59} +(-2.42796 + 2.80202i) q^{60} +(2.69167 - 5.89393i) q^{61} +(-6.47681 - 4.16240i) q^{62} +(0.959493 - 0.281733i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(5.47507 + 1.60763i) q^{65} +(-1.47314 - 3.22574i) q^{66} +(-0.191969 + 1.33517i) q^{67} -4.85529 q^{68} +(1.11722 + 4.66388i) q^{69} -3.70760 q^{70} +(0.745812 - 5.18723i) q^{71} +(0.415415 + 0.909632i) q^{72} +(-12.5295 - 3.67899i) q^{73} +(6.22672 + 7.18602i) q^{74} +(-8.39200 + 2.46411i) q^{75} +(0.0631616 + 0.0405915i) q^{76} +(1.47314 - 3.22574i) q^{77} +(1.00787 - 1.16314i) q^{78} +(-6.16678 + 3.96315i) q^{79} +(-0.527646 - 3.66986i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-5.57160 + 3.58065i) q^{82} +(3.10427 - 3.58252i) q^{83} +(-0.415415 + 0.909632i) q^{84} +(-15.1438 - 9.73233i) q^{85} +(-9.83918 + 2.88904i) q^{86} +(6.27399 + 7.24057i) q^{87} +(3.40255 + 0.999080i) q^{88} +(0.675148 + 1.47837i) q^{89} +(-0.527646 + 3.66986i) q^{90} +1.53906 q^{91} +(-4.25635 - 2.20985i) q^{92} -7.69900 q^{93} +(0.0483227 - 0.336092i) q^{94} +(0.115638 + 0.253212i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(-6.85536 - 7.91151i) q^{97} +(-0.959493 + 0.281733i) q^{98} +(-2.98325 - 1.91722i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{3} - q^{4} - 14 q^{5} - q^{6} + q^{7} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 - q^3 - q^4 - 14 * q^5 - q^6 + q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} - 14 q^{5} - q^{6} + q^{7} - q^{8} - q^{9} + 8 q^{10} - 4 q^{11} - q^{12} + 14 q^{13} + q^{14} - 3 q^{15} - q^{16} + 15 q^{17} - q^{18} - 11 q^{19} - 3 q^{20} + q^{21} - 26 q^{22} - q^{23} + 10 q^{24} + 7 q^{25} - 8 q^{26} - q^{27} + q^{28} + 19 q^{29} + 8 q^{30} - 5 q^{31} - q^{32} + 7 q^{33} - 18 q^{34} - 8 q^{35} - q^{36} - 2 q^{37} + 11 q^{38} + 14 q^{39} - 3 q^{40} + 2 q^{41} + q^{42} + 25 q^{43} - 4 q^{44} + 8 q^{45} - 23 q^{46} - 4 q^{47} - q^{48} - q^{49} - 15 q^{50} + 15 q^{51} - 8 q^{52} + 15 q^{53} - q^{54} + 54 q^{55} + q^{56} + 8 q^{58} - 17 q^{59} - 14 q^{60} + q^{61} - 16 q^{62} + q^{63} - q^{64} - 13 q^{65} - 4 q^{66} - 4 q^{67} + 26 q^{68} + 21 q^{69} - 8 q^{70} + 6 q^{71} - q^{72} - 25 q^{73} - 2 q^{74} - 15 q^{75} - 22 q^{76} + 4 q^{77} + 14 q^{78} + 3 q^{79} + 8 q^{80} - q^{81} + 2 q^{82} + 7 q^{83} + q^{84} + 12 q^{85} - 41 q^{86} + 8 q^{87} + 7 q^{88} - 41 q^{89} + 8 q^{90} + 30 q^{91} - q^{92} - 16 q^{93} - 15 q^{94} - 44 q^{95} - q^{96} - 4 q^{97} - q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 - 14 * q^5 - q^6 + q^7 - q^8 - q^9 + 8 * q^10 - 4 * q^11 - q^12 + 14 * q^13 + q^14 - 3 * q^15 - q^16 + 15 * q^17 - q^18 - 11 * q^19 - 3 * q^20 + q^21 - 26 * q^22 - q^23 + 10 * q^24 + 7 * q^25 - 8 * q^26 - q^27 + q^28 + 19 * q^29 + 8 * q^30 - 5 * q^31 - q^32 + 7 * q^33 - 18 * q^34 - 8 * q^35 - q^36 - 2 * q^37 + 11 * q^38 + 14 * q^39 - 3 * q^40 + 2 * q^41 + q^42 + 25 * q^43 - 4 * q^44 + 8 * q^45 - 23 * q^46 - 4 * q^47 - q^48 - q^49 - 15 * q^50 + 15 * q^51 - 8 * q^52 + 15 * q^53 - q^54 + 54 * q^55 + q^56 + 8 * q^58 - 17 * q^59 - 14 * q^60 + q^61 - 16 * q^62 + q^63 - q^64 - 13 * q^65 - 4 * q^66 - 4 * q^67 + 26 * q^68 + 21 * q^69 - 8 * q^70 + 6 * q^71 - q^72 - 25 * q^73 - 2 * q^74 - 15 * q^75 - 22 * q^76 + 4 * q^77 + 14 * q^78 + 3 * q^79 + 8 * q^80 - q^81 + 2 * q^82 + 7 * q^83 + q^84 + 12 * q^85 - 41 * q^86 + 8 * q^87 + 7 * q^88 - 41 * q^89 + 8 * q^90 + 30 * q^91 - q^92 - 16 * q^93 - 15 * q^94 - 44 * q^95 - q^96 - 4 * q^97 - q^98 + 7 * q^99

Introduction

L-functions

Modular forms

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Database

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