LMFDB - Embedded newform 637.2.w.b.92.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(92,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("637.92");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.w (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$174$
Relative dimension:	$29$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			92.14
Character	$\chi$	$=$	637.92
Dual form			637.2.w.b.547.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.118827 + 0.149004i) q^{2} +(1.11947 + 0.539107i) q^{3} +(0.436959 + 1.91444i) q^{4} +(0.156007 + 0.0751292i) q^{5} +(-0.213352 + 0.102745i) q^{6} +(0.0412747 + 2.64543i) q^{7} +(-0.680602 - 0.327760i) q^{8} +(-0.907899 - 1.13847i) q^{9} +O(q^{10})$	\(q+(-0.118827 + 0.149004i) q^{2} +(1.11947 + 0.539107i) q^{3} +(0.436959 + 1.91444i) q^{4} +(0.156007 + 0.0751292i) q^{5} +(-0.213352 + 0.102745i) q^{6} +(0.0412747 + 2.64543i) q^{7} +(-0.680602 - 0.327760i) q^{8} +(-0.907899 - 1.13847i) q^{9} +(-0.0297324 + 0.0143184i) q^{10} +(-2.91767 + 3.65864i) q^{11} +(-0.542929 + 2.37873i) q^{12} +(0.623490 - 0.781831i) q^{13} +(-0.399084 - 0.308198i) q^{14} +(0.134142 + 0.168209i) q^{15} +(-3.40871 + 1.64155i) q^{16} +(-0.0503226 + 0.220478i) q^{17} +0.277519 q^{18} +2.92632 q^{19} +(-0.0756617 + 0.331496i) q^{20} +(-1.37996 + 2.98372i) q^{21} +(-0.198455 - 0.869489i) q^{22} +(0.891659 + 3.90661i) q^{23} +(-0.585213 - 0.733834i) q^{24} +(-3.09876 - 3.88572i) q^{25} +(0.0424088 + 0.185805i) q^{26} +(-1.23206 - 5.39802i) q^{27} +(-5.04649 + 1.23496i) q^{28} +(-0.643531 + 2.81949i) q^{29} -0.0410036 q^{30} +7.49183 q^{31} +(0.496638 - 2.17591i) q^{32} +(-5.23864 + 2.52279i) q^{33} +(-0.0268724 - 0.0336969i) q^{34} +(-0.192310 + 0.415807i) q^{35} +(1.78282 - 2.23559i) q^{36} +(0.461841 - 2.02346i) q^{37} +(-0.347725 + 0.436033i) q^{38} +(1.11947 - 0.539107i) q^{39} +(-0.0815545 - 0.102266i) q^{40} +(0.210667 + 0.101452i) q^{41} +(-0.280610 - 0.560166i) q^{42} +(9.99641 - 4.81402i) q^{43} +(-8.27917 - 3.98704i) q^{44} +(-0.0561066 - 0.245819i) q^{45} +(-0.688054 - 0.331349i) q^{46} +(-6.33496 + 7.94379i) q^{47} -4.70092 q^{48} +(-6.99659 + 0.218379i) q^{49} +0.947202 q^{50} +(-0.175196 + 0.219688i) q^{51} +(1.76921 + 0.852008i) q^{52} +(2.63869 + 11.5609i) q^{53} +(0.950729 + 0.457847i) q^{54} +(-0.730049 + 0.351573i) q^{55} +(0.838976 - 1.81401i) q^{56} +(3.27592 + 1.57760i) q^{57} +(-0.343647 - 0.430920i) q^{58} +(3.22231 - 1.55178i) q^{59} +(-0.263413 + 0.330309i) q^{60} +(0.269832 - 1.18221i) q^{61} +(-0.890230 + 1.11631i) q^{62} +(2.97427 - 2.44877i) q^{63} +(-4.45260 - 5.58338i) q^{64} +(0.156007 - 0.0751292i) q^{65} +(0.246584 - 1.08035i) q^{66} +6.12150 q^{67} -0.444082 q^{68} +(-1.10790 + 4.85402i) q^{69} +(-0.0391054 - 0.0780640i) q^{70} +(-0.892093 - 3.90852i) q^{71} +(0.244772 + 1.07242i) q^{72} +(2.34057 + 2.93498i) q^{73} +(0.246624 + 0.309257i) q^{74} +(-1.37414 - 6.02049i) q^{75} +(1.27868 + 5.60227i) q^{76} +(-9.79911 - 7.56748i) q^{77} +(-0.0526935 + 0.230865i) q^{78} +8.60507 q^{79} -0.655113 q^{80} +(0.558781 - 2.44818i) q^{81} +(-0.0401495 + 0.0193350i) q^{82} +(8.78311 + 11.0137i) q^{83} +(-6.31516 - 1.33810i) q^{84} +(-0.0244150 + 0.0306155i) q^{85} +(-0.470533 + 2.06154i) q^{86} +(-2.24042 + 2.80940i) q^{87} +(3.18493 - 1.53378i) q^{88} +(3.67484 + 4.60810i) q^{89} +(0.0432950 + 0.0208498i) q^{90} +(2.09401 + 1.61713i) q^{91} +(-7.08937 + 3.41406i) q^{92} +(8.38686 + 4.03890i) q^{93} +(-0.430894 - 1.88787i) q^{94} +(0.456527 + 0.219852i) q^{95} +(1.72902 - 2.16812i) q^{96} +7.72816 q^{97} +(0.798843 - 1.06847i) q^{98} +6.81420 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9}+O(q^{10}) $ 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9	\( 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9} - 10 q^{10} - 5 q^{11} + 25 q^{12} - 29 q^{13} + 15 q^{14} - 10 q^{15} - 51 q^{16} - 9 q^{17} + 44 q^{18} + 24 q^{19} + 63 q^{20} - 28 q^{21} - 8 q^{22} - 13 q^{23} - 48 q^{24} - 49 q^{25} - 3 q^{26} - 9 q^{27} - 44 q^{28} + 2 q^{29} - 22 q^{30} + 10 q^{31} + 24 q^{32} - 26 q^{33} + 118 q^{34} + 5 q^{35} - 55 q^{36} - 32 q^{37} + 16 q^{38} + 42 q^{40} - 14 q^{41} + 4 q^{42} - 50 q^{43} + 35 q^{44} - q^{45} + 4 q^{46} - 24 q^{47} - 116 q^{48} - 25 q^{49} + 156 q^{50} + 12 q^{51} - 31 q^{52} - 30 q^{53} - 78 q^{54} + 25 q^{55} + 3 q^{56} - 63 q^{57} - 12 q^{58} - 4 q^{59} + 128 q^{60} - 42 q^{61} - 38 q^{62} - 85 q^{63} - 105 q^{64} - 4 q^{65} + 15 q^{66} + 94 q^{67} + 214 q^{68} + 32 q^{69} - 57 q^{70} - 29 q^{71} - 64 q^{72} - 66 q^{73} - 90 q^{74} + 131 q^{75} - 21 q^{76} - 82 q^{77} + 19 q^{78} + 6 q^{79} + 22 q^{80} + 49 q^{81} - 50 q^{82} + 25 q^{83} + 89 q^{84} - 86 q^{85} - 28 q^{86} + 24 q^{87} + 48 q^{88} - 50 q^{89} - 155 q^{90} - 5 q^{91} - 98 q^{92} + 89 q^{93} - 28 q^{94} - 130 q^{95} - 105 q^{96} - 42 q^{97} + 195 q^{98} + 438 q^{99}+O(q^{100}) \) 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9 - 10 * q^10 - 5 * q^11 + 25 * q^12 - 29 * q^13 + 15 * q^14 - 10 * q^15 - 51 * q^16 - 9 * q^17 + 44 * q^18 + 24 * q^19 + 63 * q^20 - 28 * q^21 - 8 * q^22 - 13 * q^23 - 48 * q^24 - 49 * q^25 - 3 * q^26 - 9 * q^27 - 44 * q^28 + 2 * q^29 - 22 * q^30 + 10 * q^31 + 24 * q^32 - 26 * q^33 + 118 * q^34 + 5 * q^35 - 55 * q^36 - 32 * q^37 + 16 * q^38 + 42 * q^40 - 14 * q^41 + 4 * q^42 - 50 * q^43 + 35 * q^44 - q^45 + 4 * q^46 - 24 * q^47 - 116 * q^48 - 25 * q^49 + 156 * q^50 + 12 * q^51 - 31 * q^52 - 30 * q^53 - 78 * q^54 + 25 * q^55 + 3 * q^56 - 63 * q^57 - 12 * q^58 - 4 * q^59 + 128 * q^60 - 42 * q^61 - 38 * q^62 - 85 * q^63 - 105 * q^64 - 4 * q^65 + 15 * q^66 + 94 * q^67 + 214 * q^68 + 32 * q^69 - 57 * q^70 - 29 * q^71 - 64 * q^72 - 66 * q^73 - 90 * q^74 + 131 * q^75 - 21 * q^76 - 82 * q^77 + 19 * q^78 + 6 * q^79 + 22 * q^80 + 49 * q^81 - 50 * q^82 + 25 * q^83 + 89 * q^84 - 86 * q^85 - 28 * q^86 + 24 * q^87 + 48 * q^88 - 50 * q^89 - 155 * q^90 - 5 * q^91 - 98 * q^92 + 89 * q^93 - 28 * q^94 - 130 * q^95 - 105 * q^96 - 42 * q^97 + 195 * q^98 + 438 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{1}{7}\right)$

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 $

$2$	−0.118827	+	0.149004i	−0.0840232	+	0.105362i	−0.822066	−	0.569392i	$-0.807179\pi$
$2$	−0.118827	+	0.149004i	−0.0840232	+	0.105362i	0.738043	+	0.674754i	$0.235750\pi$
$3$	1.11947	+	0.539107i	0.646325	+	0.311254i	0.728175	−	0.685391i	$-0.240369\pi$
$3$	1.11947	+	0.539107i	0.646325	+	0.311254i	−0.0818505	+	0.996645i	$0.526083\pi$
$4$	0.436959	+	1.91444i	0.218480	+	0.957222i
$5$	0.156007	+	0.0751292i	0.0697686	+	0.0335988i	0.468443	−	0.883494i	$-0.344815\pi$
$5$	0.156007	+	0.0751292i	0.0697686	+	0.0335988i	−0.398674	+	0.917093i	$0.630530\pi$
$6$	−0.213352	+	0.102745i	−0.0871005	+	0.0419454i
$7$	0.0412747	+	2.64543i	0.0156004	+	0.999878i
$7$	0.0412747	+	2.64543i	0.0156004	+	0.999878i
$8$	−0.680602	−	0.327760i	−0.240629	−	0.115881i
$9$	−0.907899	−	1.13847i	−0.302633	−	0.379490i
$10$	−0.0297324	+	0.0143184i	−0.00940221	+	0.00452786i
$11$	−2.91767	+	3.65864i	−0.879711	+	1.10312i	0.114257	+	0.993451i	$0.463551\pi$
$11$	−2.91767	+	3.65864i	−0.879711	+	1.10312i	−0.993968	+	0.109671i	$0.965020\pi$
$12$	−0.542929	+	2.37873i	−0.156730	+	0.686679i
$13$	0.623490	−	0.781831i	0.172925	−	0.216841i
$13$	0.623490	−	0.781831i	0.172925	−	0.216841i
$14$	−0.399084	−	0.308198i	−0.106660	−	0.0823693i
$15$	0.134142	+	0.168209i	0.0346354	+	0.0434315i
$16$	−3.40871	+	1.64155i	−0.852179	+	0.410388i
$17$	−0.0503226	+	0.220478i	−0.0122050	+	0.0534737i	−0.980664	−	0.195700i	$-0.937302\pi$
$17$	−0.0503226	+	0.220478i	−0.0122050	+	0.0534737i	0.968459	+	0.249174i	$0.0801591\pi$
$18$	0.277519			0.0654119
$19$	2.92632			0.671343			0.335672	−	0.941979i	$-0.391037\pi$
$19$	2.92632			0.671343			0.335672	+	0.941979i	$0.391037\pi$
$20$	−0.0756617	+	0.331496i	−0.0169185	+	0.0741247i
$21$	−1.37996	+	2.98372i	−0.301133	+	0.651102i
$22$	−0.198455	−	0.869489i	−0.0423108	−	0.185376i
$23$	0.891659	+	3.90661i	0.185924	+	0.814585i	0.978737	+	0.205120i	$0.0657585\pi$
$23$	0.891659	+	3.90661i	0.185924	+	0.814585i	−0.792813	+	0.609465i	$0.791384\pi$
$24$	−0.585213	−	0.733834i	−0.119456	−	0.149793i
$25$	−3.09876	−	3.88572i	−0.619751	−	0.777143i
$26$	0.0424088	+	0.185805i	0.00831704	+	0.0364394i
$27$	−1.23206	−	5.39802i	−0.237111	−	1.03885i
$28$	−5.04649	+	1.23496i	−0.953697	+	0.233386i
$29$	−0.643531	+	2.81949i	−0.119501	+	0.523567i	0.879374	+	0.476132i	$0.157962\pi$
$29$	−0.643531	+	2.81949i	−0.119501	+	0.523567i	−0.998874	+	0.0474346i	$0.984895\pi$
$30$	−0.0410036			−0.00748619
$31$	7.49183			1.34557			0.672786	−	0.739837i	$-0.265097\pi$
$31$	7.49183			1.34557			0.672786	+	0.739837i	$0.265097\pi$
$32$	0.496638	−	2.17591i	0.0877941	−	0.384651i
$33$	−5.23864	+	2.52279i	−0.911930	+	0.439162i
$34$	−0.0268724	−	0.0336969i	−0.00460858	−	0.00577898i
$35$	−0.192310	+	0.415807i	−0.0325063	+	0.0702843i
$36$	1.78282	−	2.23559i	0.297137	−	0.372598i
$37$	0.461841	−	2.02346i	0.0759261	−	0.332654i	−0.922672	−	0.385586i	$-0.873999\pi$
$37$	0.461841	−	2.02346i	0.0759261	−	0.332654i	0.998598	+	0.0529317i	$0.0168566\pi$
$38$	−0.347725	+	0.436033i	−0.0564084	+	0.0707339i
$39$	1.11947	−	0.539107i	0.179258	−	0.0863262i
$40$	−0.0815545	−	0.102266i	−0.0128949	−	0.0161697i
$41$	0.210667	+	0.101452i	0.0329006	+	0.0158441i	0.450262	−	0.892897i	$-0.351331\pi$
$41$	0.210667	+	0.101452i	0.0329006	+	0.0158441i	−0.417361	+	0.908741i	$0.637045\pi$
$42$	−0.280610	−	0.560166i	−0.0432991	−	0.0864355i
$43$	9.99641	−	4.81402i	1.52444	−	0.734131i	0.530880	−	0.847447i	$-0.321862\pi$
$43$	9.99641	−	4.81402i	1.52444	−	0.734131i	0.993559	+	0.113316i	$0.0361472\pi$
$44$	−8.27917	−	3.98704i	−1.24813	−	0.601069i
$45$	−0.0561066	−	0.245819i	−0.00836388	−	0.0366446i
$46$	−0.688054	−	0.331349i	−0.101448	−	0.0488548i
$47$	−6.33496	+	7.94379i	−0.924049	+	1.15872i	0.0629540	+	0.998016i	$0.479948\pi$
$47$	−6.33496	+	7.94379i	−0.924049	+	1.15872i	−0.987003	+	0.160704i	$0.948624\pi$
$48$	−4.70092			−0.678519
$49$	−6.99659	+	0.218379i	−0.999513	+	0.0311970i
$50$	0.947202			0.133955
$51$	−0.175196	+	0.219688i	−0.0245323	+	0.0307625i
$52$	1.76921	+	0.852008i	0.245346	+	0.118152i
$53$	2.63869	+	11.5609i	0.362452	+	1.58801i	0.746950	+	0.664881i	$0.231518\pi$
$53$	2.63869	+	11.5609i	0.362452	+	1.58801i	−0.384497	+	0.923126i	$0.625625\pi$
$54$	0.950729	+	0.457847i	0.129378	+	0.0623051i
$55$	−0.730049	+	0.351573i	−0.0984398	+	0.0474061i
$56$	0.838976	−	1.81401i	0.112113	−	0.242408i
$57$	3.27592	+	1.57760i	0.433906	+	0.208958i
$58$	−0.343647	−	0.430920i	−0.0451231	−	0.0565826i
$59$	3.22231	−	1.55178i	0.419509	−	0.202025i	−0.212207	−	0.977225i	$-0.568065\pi$
$59$	3.22231	−	1.55178i	0.419509	−	0.202025i	0.631716	+	0.775200i	$0.282351\pi$
$60$	−0.263413	+	0.330309i	−0.0340064	+	0.0426427i
$61$	0.269832	−	1.18221i	0.0345484	−	0.151367i	−0.954712	−	0.297533i	$-0.903836\pi$
$61$	0.269832	−	1.18221i	0.0345484	−	0.151367i	0.989260	+	0.146166i	$0.0466934\pi$
$62$	−0.890230	+	1.11631i	−0.113059	+	0.141772i
$63$	2.97427	−	2.44877i	0.374722	−	0.308516i
$64$	−4.45260	−	5.58338i	−0.556575	−	0.697923i
$65$	0.156007	−	0.0751292i	0.0193503	−	0.00931863i
$66$	0.246584	−	1.08035i	0.0303523	−	0.132982i
$67$	6.12150			0.747860			0.373930	−	0.927457i	$-0.378010\pi$
$67$	6.12150			0.747860			0.373930	+	0.927457i	$0.378010\pi$
$68$	−0.444082			−0.0538528
$69$	−1.10790	+	4.85402i	−0.133375	+	0.584356i
$70$	−0.0391054	−	0.0780640i	−0.00467399	−	0.00933043i
$71$	−0.892093	−	3.90852i	−0.105872	−	0.463856i	−0.999875	−	0.0157950i	$-0.994972\pi$
$71$	−0.892093	−	3.90852i	−0.105872	−	0.463856i	0.894003	−	0.448060i	$-0.147885\pi$
$72$	0.244772	+	1.07242i	0.0288467	+	0.126386i
$73$	2.34057	+	2.93498i	0.273943	+	0.343513i	0.899703	−	0.436502i	$-0.143783\pi$
$73$	2.34057	+	2.93498i	0.273943	+	0.343513i	−0.625761	+	0.780015i	$0.715211\pi$
$74$	0.246624	+	0.309257i	0.0286695	+	0.0359504i
$75$	−1.37414	−	6.02049i	−0.158672	−	0.695187i
$76$	1.27868	+	5.60227i	0.146675	+	0.642625i
$77$	−9.79911	−	7.56748i	−1.11671	−	0.862395i
$78$	−0.0526935	+	0.230865i	−0.00596637	+	0.0261404i
$79$	8.60507			0.968146			0.484073	−	0.875028i	$-0.339157\pi$
$79$	8.60507			0.968146			0.484073	+	0.875028i	$0.339157\pi$
$80$	−0.655113			−0.0732438
$81$	0.558781	−	2.44818i	0.0620868	−	0.272020i
$82$	−0.0401495	+	0.0193350i	−0.00443378	+	0.00213519i
$83$	8.78311	+	11.0137i	0.964072	+	1.20891i	0.977915	+	0.209004i	$0.0670221\pi$
$83$	8.78311	+	11.0137i	0.964072	+	1.20891i	−0.0138428	+	0.999904i	$0.504406\pi$
$84$	−6.31516	−	1.33810i	−0.689041	−	0.145998i
$85$	−0.0244150	+	0.0306155i	−0.00264818	+	0.00332071i
$86$	−0.470533	+	2.06154i	−0.0507389	+	0.222302i
$87$	−2.24042	+	2.80940i	−0.240198	+	0.301199i
$88$	3.18493	−	1.53378i	0.339515	−	0.163502i
$89$	3.67484	+	4.60810i	0.389532	+	0.488457i	0.937472	−	0.348060i	$-0.113159\pi$
$89$	3.67484	+	4.60810i	0.389532	+	0.488457i	−0.547940	+	0.836517i	$0.684588\pi$
$90$	0.0432950	+	0.0208498i	0.00456370	+	0.00219776i
$91$	2.09401	+	1.61713i	0.219512	+	0.169521i
$92$	−7.08937	+	3.41406i	−0.739118	+	0.355941i
$93$	8.38686	+	4.03890i	0.869677	+	0.418814i
$94$	−0.430894	−	1.88787i	−0.0444433	−	0.194719i
$95$	0.456527	+	0.219852i	0.0468387	+	0.0225563i
$96$	1.72902	−	2.16812i	0.176467	−	0.221283i
$97$	7.72816			0.784676			0.392338	−	0.919821i	$-0.371666\pi$
$97$	7.72816			0.784676			0.392338	+	0.919821i	$0.371666\pi$
$98$	0.798843	−	1.06847i	0.0806953	−	0.107932i
$99$	6.81420			0.684853
$100$	6.08496	−	7.63030i	0.608496	−	0.763030i
$101$	−1.14367	−	0.550764i	−0.113800	−	0.0548030i	0.376118	−	0.926572i	$-0.377259\pi$
$101$	−1.14367	−	0.550764i	−0.113800	−	0.0548030i	−0.489917	+	0.871769i	$0.662973\pi$
$102$	−0.0119165	−	0.0522097i	−0.00117991	−	0.00516953i
$103$	−9.32711	−	4.49170i	−0.919028	−	0.442580i	−0.0863038	−	0.996269i	$-0.527506\pi$
$103$	−9.32711	−	4.49170i	−0.919028	−	0.442580i	−0.832724	+	0.553688i	$0.813220\pi$
$104$	−0.680602	+	0.327760i	−0.0667385	+	0.0321396i
$105$	−0.439449	+	0.361807i	−0.0428858	+	0.0353088i
$106$	−2.03616	−	0.980564i	−0.197770	−	0.0952408i
$107$	−2.93290	−	3.67774i	−0.283534	−	0.355541i	0.619586	−	0.784929i	$-0.287301\pi$
$107$	−2.93290	−	3.67774i	−0.283534	−	0.355541i	−0.903120	+	0.429388i	$0.858729\pi$
$108$	9.79585	−	4.71743i	0.942606	−	0.453935i
$109$	−10.2711	+	12.8795i	−0.983789	+	1.23363i	−0.0114798	+	0.999934i	$0.503654\pi$
$109$	−10.2711	+	12.8795i	−0.983789	+	1.23363i	−0.972309	+	0.233698i	$0.924917\pi$
$110$	0.0343635	−	0.150556i	0.00327643	−	0.0143550i
$111$	1.60787	−	2.01621i	0.152613	−	0.191370i
$112$	−4.48330	−	8.94976i	−0.423632	−	0.845673i
$113$	−4.84769	−	6.07881i	−0.456032	−	0.571846i	0.499657	−	0.866223i	$-0.333459\pi$
$113$	−4.84769	−	6.07881i	−0.456032	−	0.571846i	−0.955689	+	0.294377i	$0.904888\pi$
$114$	−0.624335	+	0.300664i	−0.0584743	+	0.0281597i
$115$	−0.154395	+	0.676450i	−0.0143974	+	0.0630793i
$116$	−5.67896			−0.527278
$117$	−1.45616			−0.134622
$118$	−0.151675	+	0.664531i	−0.0139628	+	0.0611750i
$119$	−0.585336	−	0.124025i	−0.0536576	−	0.0113693i
$120$	−0.0361652	−	0.158450i	−0.00330142	−	0.0144645i
$121$	−2.42514	−	10.6252i	−0.220467	−	0.965929i
$122$	0.144091	+	0.180684i	0.0130454	+	0.0163584i
$123$	0.181141	+	0.227144i	0.0163329	+	0.0204809i
$124$	3.27363	+	14.3427i	0.293980	+	1.28801i
$125$	−0.384151	−	1.68308i	−0.0343595	−	0.150539i
$126$	0.0114545	+	0.734157i	0.00102045	+	0.0654039i
$127$	4.19478	−	18.3785i	0.372227	−	1.63083i	−0.348284	−	0.937389i	$-0.613236\pi$
$127$	4.19478	−	18.3785i	0.372227	−	1.63083i	0.720511	−	0.693443i	$-0.243907\pi$
$128$	5.82478			0.514843
$129$	13.7859			1.21378
$130$	−0.00734329	+	0.0321731i	−0.000644050	+	0.00282177i
$131$	3.90891	−	1.88243i	0.341523	−	0.164469i	−0.255258	−	0.966873i	$-0.582160\pi$
$131$	3.90891	−	1.88243i	0.341523	−	0.164469i	0.596781	+	0.802404i	$0.296446\pi$
$132$	−7.11882	−	8.92672i	−0.619614	−	0.776971i
$133$	0.120783	+	7.74136i	0.0104732	+	0.671261i
$134$	−0.727397	+	0.912127i	−0.0628376	+	0.0787958i
$135$	0.213338	−	0.934695i	0.0183612	−	0.0804457i
$136$	0.106514	−	0.133564i	0.00913347	−	0.0114530i
$137$	16.8017	−	8.09129i	1.43547	−	0.691286i	0.455464	−	0.890254i	$-0.349473\pi$
$137$	16.8017	−	8.09129i	1.43547	−	0.691286i	0.980006	+	0.198969i	$0.0637592\pi$
$138$	−0.591621	−	0.741869i	−0.0503621	−	0.0631521i
$139$	−10.1368	−	4.88161i	−0.859789	−	0.414053i	−0.0485873	−	0.998819i	$-0.515472\pi$
$139$	−10.1368	−	4.88161i	−0.859789	−	0.414053i	−0.811202	+	0.584766i	$0.801186\pi$
$140$	−0.880072	−	0.186475i	−0.0743796	−	0.0157600i
$141$	−11.3743	+	5.47759i	−0.957891	+	0.461296i
$142$	0.688389	+	0.331511i	0.0577683	+	0.0278198i
$143$	1.04130	+	4.56225i	0.0870783	+	0.381515i
$144$	4.96362	+	2.39035i	0.413635	+	0.199196i
$145$	−0.312222	+	0.391514i	−0.0259286	+	0.0325135i
$146$	−0.715446			−0.0592107
$147$	−7.95019	−	3.52744i	−0.655720	−	0.290939i
$148$	4.07560			0.335012
$149$	12.5658	−	15.7570i	1.02943	−	1.29087i	0.0734949	−	0.997296i	$-0.476585\pi$
$149$	12.5658	−	15.7570i	1.02943	−	1.29087i	0.955937	−	0.293571i	$-0.0948438\pi$
$150$	1.06036	+	0.510643i	0.0865782	+	0.0416939i
$151$	2.28343	+	10.0044i	0.185823	+	0.814145i	0.978788	+	0.204877i	$0.0656794\pi$
$151$	2.28343	+	10.0044i	0.185823	+	0.814145i	−0.792965	+	0.609268i	$0.791463\pi$
$152$	−1.99166	−	0.959131i	−0.161545	−	0.0777958i
$153$	0.296695	−	0.142881i	0.0239864	−	0.0115512i
$154$	2.29198	−	0.560887i	0.184693	−	0.0451976i
$155$	1.16878	+	0.562855i	0.0938787	+	0.0452096i
$156$	1.52125	+	1.90759i	0.121798	+	0.152729i
$157$	9.37422	−	4.51439i	0.748144	−	0.360287i	−0.0206472	−	0.999787i	$-0.506573\pi$
$157$	9.37422	−	4.51439i	0.748144	−	0.360287i	0.768792	+	0.639500i	$0.220858\pi$
$158$	−1.02251	+	1.28219i	−0.0813467	+	0.102006i
$159$	−3.27861	+	14.3645i	−0.260011	+	1.13918i
$160$	0.240954	−	0.302147i	0.0190491	−	0.0238868i
$161$	−10.2979	+	2.52006i	−0.811585	+	0.198609i
$162$	0.298390	+	0.374170i	0.0234438	+	0.0293976i
$163$	4.52106	−	2.17723i	0.354117	−	0.170534i	−0.248365	−	0.968667i	$-0.579893\pi$
$163$	4.52106	−	2.17723i	0.354117	−	0.170534i	0.602481	+	0.798133i	$0.294179\pi$
$164$	−0.102171	+	0.447640i	−0.00797820	+	0.0349548i
$165$	−1.00680			−0.0783794
$166$	−2.68475			−0.208377
$167$	−1.13853	+	4.98822i	−0.0881020	+	0.386000i	−0.999685	−	0.0251171i	$-0.992004\pi$
$167$	−1.13853	+	4.98822i	−0.0881020	+	0.386000i	0.911583	+	0.411117i	$0.134861\pi$
$168$	1.91715	−	1.57843i	0.147912	−	0.121778i
$169$	−0.222521	−	0.974928i	−0.0171170	−	0.0749945i
$170$	−0.00166067	−	0.00727587i	−0.000127368	−	0.000558034i
$171$	−2.65680	−	3.33152i	−0.203171	−	0.254768i
$172$	13.5842	+	17.0340i	1.03579	+	1.29883i
$173$	−4.60025	−	20.1550i	−0.349751	−	1.53236i	−0.777747	−	0.628577i	$-0.783638\pi$
$173$	−4.60025	−	20.1550i	−0.349751	−	1.53236i	0.427997	−	0.903780i	$-0.359219\pi$
$174$	−0.152390	−	0.667664i	−0.0115526	−	0.0506154i
$175$	10.1515	−	8.35792i	0.767380	−	0.631799i
$176$	3.93966	−	17.2608i	0.296963	−	1.30108i
$177$	4.44385			0.334020
$178$	−1.12329			−0.0841944
$179$	1.92133	−	8.41790i	0.143607	−	0.629184i	−0.850973	−	0.525209i	$-0.823987\pi$
$179$	1.92133	−	8.41790i	0.143607	−	0.629184i	0.994580	−	0.103974i	$-0.0331559\pi$
$180$	0.446091	−	0.214826i	0.0332497	−	0.0160122i
$181$	−6.85572	−	8.59680i	−0.509581	−	0.638995i	0.458779	−	0.888550i	$-0.348287\pi$
$181$	−6.85572	−	8.59680i	−0.509581	−	0.638995i	−0.968361	+	0.249555i	$0.919716\pi$
$182$	−0.489784	+	0.119858i	−0.0363052	+	0.00888450i
$183$	0.939406	−	1.17798i	0.0694429	−	0.0870786i
$184$	0.673569	−	2.95110i	0.0496561	−	0.217558i
$185$	0.224071	−	0.280976i	0.0164740	−	0.0206578i
$186$	−1.59840	+	0.769747i	−0.117200	+	0.0564406i
$187$	−0.659825	−	0.827394i	−0.0482512	−	0.0605051i
$188$	−17.9761	−	8.65681i	−1.31104	−	0.631363i
$189$	14.2292	−	3.48214i	1.03502	−	0.253288i
$190$	−0.0870064	+	0.0419001i	−0.00631211	+	0.00303975i
$191$	−5.31901	−	2.56150i	−0.384870	−	0.185344i	0.231436	−	0.972850i	$-0.425657\pi$
$191$	−5.31901	−	2.56150i	−0.384870	−	0.185344i	−0.616307	+	0.787506i	$0.711372\pi$
$192$	−1.97450	−	8.65085i	−0.142497	−	0.624321i
$193$	−3.75576	−	1.80868i	−0.270346	−	0.130192i	0.293800	−	0.955867i	$-0.405080\pi$
$193$	−3.75576	−	1.80868i	−0.270346	−	0.130192i	−0.564146	+	0.825675i	$0.690794\pi$
$194$	−0.918312	+	1.15153i	−0.0659310	+	0.0826749i
$195$	0.215148			0.0154071
$196$	−3.47530	−	13.2992i	−0.248236	−	0.949940i
$197$	2.12116			0.151126			0.0755632	−	0.997141i	$-0.475925\pi$
$197$	2.12116			0.151126			0.0755632	+	0.997141i	$0.475925\pi$
$198$	−0.809709	+	1.01534i	−0.0575435	+	0.0721573i
$199$	20.7381	+	9.98694i	1.47008	+	0.707955i	0.985950	−	0.167038i	$-0.0534204\pi$
$199$	20.7381	+	9.98694i	1.47008	+	0.707955i	0.484134	+	0.874994i	$0.339135\pi$
$200$	0.835434	+	3.66027i	0.0590741	+	0.258820i
$201$	6.85281	+	3.30014i	0.483360	+	0.232774i
$202$	0.217965	−	0.104966i	0.0153360	−	0.00738541i
$203$	−7.48533	−	1.58604i	−0.525368	−	0.111318i
$204$	−0.497135	−	0.239408i	−0.0348064	−	0.0167619i
$205$	0.0252436	+	0.0316544i	0.00176309	+	0.00221084i
$206$	1.77759	−	0.856043i	0.123851	−	0.0596433i
$207$	3.63802	−	4.56193i	0.252860	−	0.317076i
$208$	−0.841883	+	3.68853i	−0.0583741	+	0.255754i
$209$	−8.53803	+	10.7063i	−0.590588	+	0.740574i
$210$	−0.00169241	−	0.108472i	−0.000116787	−	0.00748528i
$211$	−8.79320	−	11.0263i	−0.605349	−	0.759083i	0.380852	−	0.924636i	$-0.375631\pi$
$211$	−8.79320	−	11.0263i	−0.605349	−	0.759083i	−0.986201	+	0.165553i	$0.947059\pi$
$212$	−20.9796	+	10.1033i	−1.44089	+	0.693895i
$213$	1.10844	−	4.85639i	0.0759490	−	0.332754i
$214$	0.896506			0.0612839
$215$	1.92119			0.131024
$216$	−0.930714	+	4.07772i	−0.0633271	+	0.277454i
$217$	0.309223	+	19.8191i	0.0209914	+	1.34541i
$218$	−0.698621	−	3.06086i	−0.0473166	−	0.207307i
$219$	1.03792	+	4.54743i	0.0701362	+	0.307287i
$220$	−0.992069	−	1.24401i	−0.0668853	−	0.0838715i
$221$	0.141001	+	0.176810i	0.00948475	+	0.0118935i
$222$	0.109365	+	0.479160i	0.00734010	+	0.0321591i
$223$	2.08020	+	9.11397i	0.139301	+	0.610317i	0.995589	+	0.0938188i	$0.0299074\pi$
$223$	2.08020	+	9.11397i	0.139301	+	0.610317i	−0.856288	+	0.516498i	$0.827235\pi$
$224$	5.77673	+	1.22401i	0.385974	+	0.0817827i
$225$	−1.61041	+	7.05567i	−0.107361	+	0.470378i
$226$	1.48180			0.0985680
$227$	−24.9599			−1.65665			−0.828323	−	0.560251i	$-0.810705\pi$
$227$	−24.9599			−1.65665			−0.828323	+	0.560251i	$0.810705\pi$
$228$	−1.58878	+	6.96091i	−0.105220	+	0.460997i
$229$	23.8441	−	11.4827i	1.57566	−	0.758800i	0.577331	−	0.816510i	$-0.304094\pi$
$229$	23.8441	−	11.4827i	1.57566	−	0.758800i	0.998333	+	0.0577102i	$0.0183800\pi$
$230$	−0.0824474	−	0.103386i	−0.00543642	−	0.00681706i
$231$	−6.89010	−	13.7543i	−0.453335	−	0.904968i
$232$	1.36211	−	1.70803i	0.0894267	−	0.112138i
$233$	4.10562	−	17.9879i	0.268968	−	1.17843i	−0.642248	−	0.766497i	$-0.721998\pi$
$233$	4.10562	−	17.9879i	0.268968	−	1.17843i	0.911216	−	0.411929i	$-0.135145\pi$
$234$	0.173030	−	0.216973i	0.0113113	−	0.0141840i
$235$	−1.58511	+	0.763349i	−0.103401	+	0.0497954i
$236$	4.37882	+	5.49087i	0.285037	+	0.357425i
$237$	9.63310	+	4.63906i	0.625737	+	0.301339i
$238$	0.0880337	−	0.0724799i	0.00570638	−	0.00469817i
$239$	5.19813	−	2.50329i	0.336239	−	0.161924i	−0.258143	−	0.966107i	$-0.583111\pi$
$239$	5.19813	−	2.50329i	0.336239	−	0.161924i	0.594383	+	0.804182i	$0.297396\pi$
$240$	−0.733377	−	0.353176i	−0.0473393	−	0.0227974i
$241$	0.739444	+	3.23972i	0.0476318	+	0.208689i	0.993144	−	0.116899i	$-0.0372952\pi$
$241$	0.739444	+	3.23972i	0.0476318	+	0.208689i	−0.945512	+	0.325587i	$0.894438\pi$
$242$	1.87137	+	0.901205i	0.120296	+	0.0579317i
$243$	−8.41112	+	10.5472i	−0.539574	+	0.676604i
$244$	2.38118			0.152440
$245$	−1.10793	−	0.491580i	−0.0707828	−	0.0314059i
$246$	−0.0553697			−0.00353025
$247$	1.82453	−	2.28789i	0.116092	−	0.145575i
$248$	−5.09895	−	2.45553i	−0.323784	−	0.155926i
$249$	3.89486	+	17.0645i	0.246827	+	1.08142i
$250$	0.296432	+	0.142754i	0.0187480	+	0.00902858i
$251$	−20.9816	+	10.1042i	−1.32435	+	0.637772i	−0.956396	−	0.292073i	$-0.905655\pi$
$251$	−20.9816	+	10.1042i	−1.32435	+	0.637772i	−0.367951	+	0.929845i	$0.619941\pi$
$252$	5.98767	+	4.62405i	0.377188	+	0.291288i
$253$	−16.8945	−	8.13594i	−1.06215	−	0.511502i
$254$	2.24002	+	2.80890i	0.140552	+	0.176246i
$255$	−0.0438368	+	0.0211107i	−0.00274517	+	0.00132200i
$256$	8.21306	−	10.2989i	0.513316	−	0.643678i
$257$	−3.05755	+	13.3960i	−0.190725	+	0.835619i	0.785501	+	0.618861i	$0.212406\pi$
$257$	−3.05755	+	13.3960i	−0.190725	+	0.835619i	−0.976225	+	0.216758i	$0.930452\pi$
$258$	−1.63814	+	2.05416i	−0.101986	+	0.127886i
$259$	5.37197	+	1.13825i	0.333798	+	0.0707273i
$260$	0.212000	+	0.265839i	0.0131477	+	0.0164866i
$261$	3.79417	−	1.82718i	0.234853	−	0.113099i
$262$	−0.183993	+	0.806127i	−0.0113671	+	0.0498027i
$263$	−13.7531			−0.848053			−0.424027	−	0.905650i	$-0.639384\pi$
$263$	−13.7531			−0.848053			−0.424027	+	0.905650i	$0.639384\pi$
$264$	4.39230			0.270327
$265$	−0.456903	+	2.00182i	−0.0280673	+	0.122971i
$266$	−1.16785	−	0.901884i	−0.0716053	−	0.0552980i
$267$	1.62960	+	7.13975i	0.0997299	+	0.436945i
$268$	2.67485	+	11.7193i	0.163392	+	0.715868i
$269$	11.1951	+	14.0383i	0.682579	+	0.855927i	0.995589	−	0.0938226i	$-0.0299087\pi$
$269$	11.1951	+	14.0383i	0.682579	+	0.855927i	−0.313010	+	0.949750i	$0.601337\pi$
$270$	0.113923	+	0.142855i	0.00693313	+	0.00869388i
$271$	1.55468	+	6.81150i	0.0944401	+	0.413769i	0.999944	−	0.0105685i	$-0.00336413\pi$
$271$	1.55468	+	6.81150i	0.0944401	+	0.413769i	−0.905504	+	0.424338i	$0.860507\pi$
$272$	−0.190390	−	0.834153i	−0.0115441	−	0.0505780i
$273$	1.47238	+	2.93922i	0.0891122	+	0.177890i
$274$	−0.790861	+	3.46499i	−0.0477777	+	0.209328i
$275$	23.2576			1.40249
$276$	−9.77687			−0.588498
$277$	−3.83061	+	16.7830i	−0.230159	+	1.00839i	0.719348	+	0.694650i	$0.244441\pi$
$277$	−3.83061	+	16.7830i	−0.230159	+	1.00839i	−0.949508	+	0.313744i	$0.898417\pi$
$278$	1.93190	−	0.930353i	0.115868	−	0.0557989i
$279$	−6.80182	−	8.52922i	−0.407214	−	0.510631i
$280$	0.267172	−	0.219968i	0.0159666	−	0.0131456i
$281$	−3.09498	+	3.88098i	−0.184631	+	0.231520i	−0.865530	−	0.500858i	$-0.833018\pi$
$281$	−3.09498	+	3.88098i	−0.184631	+	0.231520i	0.680899	+	0.732378i	$0.261589\pi$
$282$	0.535392	−	2.34570i	0.0318821	−	0.139685i
$283$	1.16934	−	1.46630i	0.0695100	−	0.0871628i	−0.745861	−	0.666102i	$-0.767962\pi$
$283$	1.16934	−	1.46630i	0.0695100	−	0.0871628i	0.815371	+	0.578939i	$0.196533\pi$
$284$	7.09283	−	3.41573i	0.420882	−	0.202686i
$285$	0.392543	+	0.492234i	0.0232523	+	0.0291574i
$286$	−0.803529	−	0.386959i	−0.0475137	−	0.0228814i
$287$	−0.259688	+	0.561491i	−0.0153289	+	0.0331438i
$288$	−2.92811	+	1.41010i	−0.172540	+	0.0830911i
$289$	15.2704	+	7.35383i	0.898258	+	0.432578i
$290$	−0.0212368	−	0.0930446i	−0.00124707	−	0.00546377i
$291$	8.65143	+	4.16631i	0.507156	+	0.244233i
$292$	−4.59612	+	5.76335i	−0.268968	+	0.337275i
$293$	−19.3922			−1.13290			−0.566452	−	0.824095i	$-0.691684\pi$
$293$	−19.3922			−1.13290			−0.566452	+	0.824095i	$0.691684\pi$
$294$	1.47030	−	0.765455i	0.0857495	−	0.0446422i
$295$	0.619289			0.0360564
$296$	−0.977538	+	1.22579i	−0.0568183	+	0.0712478i
$297$	23.3442	+	11.2420i	1.35457	+	0.652325i
$298$	0.854707	+	3.74472i	0.0495118	+	0.216926i
$299$	3.61025	+	1.73861i	0.208786	+	0.100546i
$300$	10.9255	−	5.26142i	0.630782	−	0.303768i
$301$	13.1477	+	26.2461i	0.757824	+	1.51280i
$302$	−1.76203	−	0.848547i	−0.101393	−	0.0488284i
$303$	−0.983383	−	1.23312i	−0.0564939	−	0.0708411i
$304$	−9.97498	+	4.80370i	−0.572104	+	0.275511i
$305$	0.130914	−	0.164161i	0.00749613	−	0.00939985i
$306$	−0.0139655	+	0.0611868i	−0.000798354	+	0.00349782i
$307$	−18.0142	+	22.5891i	−1.02813	+	1.28923i	−0.0716475	+	0.997430i	$0.522826\pi$
$307$	−18.0142	+	22.5891i	−1.02813	+	1.28923i	−0.956479	+	0.291800i	$0.905746\pi$
$308$	10.2057	−	22.0665i	0.581524	−	1.25736i
$309$	−8.01989	−	10.0566i	−0.456236	−	0.572101i
$310$	−0.222750	+	0.107271i	−0.0126514	+	0.00609257i
$311$	3.89443	−	17.0626i	0.220833	−	0.967532i	−0.736020	−	0.676960i	$-0.763297\pi$
$311$	3.89443	−	17.0626i	0.220833	−	0.967532i	0.956853	−	0.290572i	$-0.0938457\pi$
$312$	−0.938609			−0.0531383
$313$	−18.2105			−1.02932			−0.514660	−	0.857395i	$-0.672082\pi$
$313$	−18.2105			−1.02932			−0.514660	+	0.857395i	$0.672082\pi$
$314$	−0.441246	+	1.93323i	−0.0249010	+	0.109098i
$315$	0.647982	−	0.158572i	0.0365096	−	0.00893453i
$316$	3.76007	+	16.4739i	0.211520	+	0.926731i
$317$	−0.273978	−	1.20038i	−0.0153881	−	0.0674198i	0.966651	−	0.256098i	$-0.0824369\pi$
$317$	−0.273978	−	1.20038i	−0.0153881	−	0.0674198i	−0.982039	+	0.188678i	$0.939580\pi$
$318$	−1.75079	−	2.19542i	−0.0981793	−	0.123113i
$319$	−8.43791	−	10.5808i	−0.472432	−	0.592411i
$320$	−0.275163	−	1.20557i	−0.0153821	−	0.0673934i
$321$	−1.30059	−	5.69826i	−0.0725919	−	0.318046i
$322$	0.848162	−	1.83387i	0.0472662	−	0.102198i
$323$	−0.147260	+	0.645188i	−0.00819376	+	0.0358992i
$324$	4.93107			0.273948
$325$	−4.97002			−0.275687
$326$	−0.212807	+	0.932369i	−0.0117863	+	0.0516391i
$327$	−18.4415	+	8.88098i	−1.01982	+	0.491119i
$328$	−0.110128	−	0.138096i	−0.00608081	−	0.00762510i
$329$	−21.2762	−	16.4308i	−1.17299	−	0.905860i
$330$	0.119635	−	0.150017i	0.00658568	−	0.00825819i
$331$	2.67593	−	11.7240i	0.147083	−	0.644411i	−0.846604	−	0.532223i	$-0.821357\pi$
$331$	2.67593	−	11.7240i	0.147083	−	0.644411i	0.993687	−	0.112188i	$-0.0357860\pi$
$332$	−17.2472	+	21.6273i	−0.946564	+	1.18695i
$333$	−2.72295	+	1.31130i	−0.149217	+	0.0718589i
$334$	−0.607977	−	0.762379i	−0.0332670	−	0.0417155i
$335$	0.954998	+	0.459903i	0.0521771	+	0.0251272i
$336$	−0.194029	−	12.4359i	−0.0105851	−	0.678436i
$337$	−28.8249	+	13.8813i	−1.57019	+	0.756164i	−0.997955	−	0.0639252i	$-0.979638\pi$
$337$	−28.8249	+	13.8813i	−1.57019	+	0.756164i	−0.572236	+	0.820089i	$0.693924\pi$
$338$	0.171710	+	0.0826910i	0.00933977	+	0.00449780i
$339$	−2.14970	−	9.41845i	−0.116756	−	0.511540i
$340$	−0.0692800	−	0.0333635i	−0.00375723	−	0.00180939i
$341$	−21.8587	+	27.4099i	−1.18371	+	1.48433i
$342$	0.812109			0.0439138
$343$	−0.866488	−	18.5000i	−0.0467860	−	0.998905i
$344$	−8.38142			−0.451896
$345$	−0.537519	+	0.674028i	−0.0289391	+	0.0362884i
$346$	3.54981	+	1.70950i	0.190839	+	0.0919032i
$347$	−1.97299	−	8.64421i	−0.105915	−	0.464046i	−0.999874	−	0.0158955i	$-0.994940\pi$
$347$	−1.97299	−	8.64421i	−0.105915	−	0.464046i	0.893958	−	0.448150i	$-0.147917\pi$
$348$	−6.35741	−	3.06157i	−0.340793	−	0.164117i
$349$	−2.19199	+	1.05561i	−0.117335	+	0.0565053i	−0.491630	−	0.870804i	$-0.663599\pi$
$349$	−2.19199	+	1.05561i	−0.117335	+	0.0565053i	0.374296	+	0.927309i	$0.377885\pi$
$350$	0.0390955	+	2.50576i	0.00208974	+	0.133938i
$351$	−4.98852	−	2.40235i	−0.266268	−	0.128228i
$352$	6.51187	+	8.16562i	0.347084	+	0.435229i
$353$	−28.7349	+	13.8380i	−1.52940	+	0.736521i	−0.994133	−	0.108160i	$-0.965504\pi$
$353$	−28.7349	+	13.8380i	−1.52940	+	0.736521i	−0.535269	+	0.844682i	$0.679790\pi$
$354$	−0.528048	+	0.662152i	−0.0280655	+	0.0351930i
$355$	0.154470	−	0.676779i	0.00819844	−	0.0359197i
$356$	−7.21619	+	9.04882i	−0.382458	+	0.479587i
$357$	−0.588402	−	0.454400i	−0.0311415	−	0.0240494i
$358$	1.02600	+	1.28656i	0.0542256	+	0.0679967i
$359$	15.4436	−	7.43725i	0.815083	−	0.392523i	0.0205834	−	0.999788i	$-0.493448\pi$
$359$	15.4436	−	7.43725i	0.815083	−	0.392523i	0.794499	+	0.607265i	$0.207733\pi$
$360$	−0.0423836	+	0.185694i	−0.00223381	+	0.00978696i
$361$	−10.4367			−0.549298
$362$	2.09560			0.110142
$363$	3.01327	−	13.2020i	0.158156	−	0.692925i
$364$	−2.18090	+	4.71549i	−0.114310	+	0.247159i
$365$	0.144643	+	0.633723i	0.00757097	+	0.0331706i
$366$	0.0638969	+	0.279951i	0.00333994	+	0.0146332i
$367$	6.91740	+	8.67414i	0.361085	+	0.452786i	0.928878	−	0.370385i	$-0.120774\pi$
$367$	6.91740	+	8.67414i	0.361085	+	0.452786i	−0.567793	+	0.823171i	$0.692203\pi$
$368$	−9.45231	−	11.8528i	−0.492736	−	0.617871i
$369$	−0.0757644	−	0.331945i	−0.00394413	−	0.0172804i
$370$	0.0152410	+	0.0667750i	0.000792339	+	0.00347147i
$371$	−30.4745	+	7.45764i	−1.58216	+	0.387182i
$372$	−4.06753	+	17.8210i	−0.210892	+	0.923976i
$373$	0.190197			0.00984802			0.00492401	−	0.999988i	$-0.498433\pi$
$373$	0.190197			0.00984802			0.00492401	+	0.999988i	$0.498433\pi$
$374$	0.201690			0.0104291
$375$	0.477313	−	2.09125i	0.0246484	−	0.107992i
$376$	6.91524	−	3.33021i	0.356626	−	0.171742i
$377$	1.80313	+	2.26106i	0.0928661	+	0.116450i
$378$	−1.17196	+	2.53398i	−0.0602791	+	0.130334i
$379$	−3.93804	+	4.93814i	−0.202283	+	0.253655i	−0.872618	−	0.488404i	$-0.837579\pi$
$379$	−3.93804	+	4.93814i	−0.202283	+	0.253655i	0.670334	+	0.742059i	$0.266151\pi$
$380$	−0.221410	+	0.970062i	−0.0113581	+	0.0497631i
$381$	14.6039	−	18.3127i	0.748182	−	0.938190i
$382$	1.01371	−	0.488179i	0.0518661	−	0.0249774i
$383$	−14.3334	−	17.9735i	−0.732400	−	0.918401i	0.266568	−	0.963816i	$-0.414110\pi$
$383$	−14.3334	−	17.9735i	−0.732400	−	0.918401i	−0.998968	+	0.0454151i	$0.985539\pi$
$384$	6.52065	+	3.14018i	0.332756	+	0.160247i
$385$	−0.960194	−	1.91678i	−0.0489360	−	0.0976882i
$386$	0.715785	−	0.344704i	0.0364325	−	0.0175450i
$387$	−14.5563	−	7.00997i	−0.739941	−	0.356337i
$388$	3.37689	+	14.7951i	0.171436	+	0.751109i
$389$	20.6982	+	9.96772i	1.04944	+	0.505383i	0.877426	−	0.479712i	$-0.159259\pi$
$389$	20.6982	+	9.96772i	1.04944	+	0.505383i	0.172013	+	0.985095i	$0.444973\pi$
$390$	−0.0255653	+	0.0320579i	−0.00129455	+	0.00162331i
$391$	−0.906192			−0.0458281
$392$	4.83347	+	2.14458i	0.244127	+	0.108318i
$393$	5.39073			0.271926
$394$	−0.252051	+	0.316061i	−0.0126981	+	0.0159229i
$395$	1.34245	+	0.646492i	0.0675462	+	0.0325285i
$396$	2.97753	+	13.0454i	0.149626	+	0.655556i
$397$	8.70256	+	4.19093i	0.436769	+	0.210337i	0.639329	−	0.768933i	$-0.279212\pi$
$397$	8.70256	+	4.19093i	0.436769	+	0.210337i	−0.202561	+	0.979270i	$0.564926\pi$
$398$	−3.95233	+	1.90334i	−0.198113	+	0.0954060i
$399$	−4.03821	+	8.73132i	−0.202163	+	0.437113i
$400$	16.9414	+	8.15853i	0.847068	+	0.407927i
$401$	0.217735	+	0.273031i	0.0108732	+	0.0136345i	0.787238	−	0.616649i	$-0.211510\pi$
$401$	0.217735	+	0.273031i	0.0108732	+	0.0136345i	−0.776365	+	0.630283i	$0.782939\pi$
$402$	−1.30603	+	0.628952i	−0.0651390	+	0.0313693i
$403$	4.67108	−	5.85735i	0.232683	−	0.291775i
$404$	0.554668	−	2.43016i	0.0275958	−	0.120905i
$405$	0.271104	−	0.339953i	0.0134712	−	0.0168924i
$406$	1.12578	−	0.926881i	0.0558718	−	0.0460003i
$407$	6.05560	+	7.59349i	0.300165	+	0.376395i
$408$	0.191244	−	0.0920981i	0.00946797	−	0.00455954i
$409$	5.23813	−	22.9497i	0.259009	−	1.13479i	−0.663305	−	0.748350i	$-0.730847\pi$
$409$	5.23813	−	22.9497i	0.259009	−	1.13479i	0.922313	−	0.386443i	$-0.126296\pi$
$410$	−0.00771625			−0.000381078
$411$	23.1711			1.14294
$412$	4.52354	−	19.8189i	0.222859	−	0.976409i
$413$	4.23814	+	8.46035i	0.208545	+	0.416307i
$414$	0.247452	+	1.08416i	0.0121616	+	0.0532835i
$415$	0.542782	+	2.37808i	0.0266441	+	0.116735i
$416$	−1.39155	−	1.74495i	−0.0682263	−	0.0855531i
$417$	−8.71607	−	10.9296i	−0.426828	−	0.535225i
$418$	−0.580743	−	2.54440i	−0.0284051	−	0.124451i
$419$	5.78969	+	25.3663i	0.282845	+	1.23923i	0.894127	+	0.447813i	$0.147797\pi$
$419$	5.78969	+	25.3663i	0.282845	+	1.23923i	−0.611282	+	0.791413i	$0.709346\pi$
$420$	−0.884681	−	0.683206i	−0.0431680	−	0.0333370i
$421$	7.15799	−	31.3612i	0.348859	−	1.52845i	−0.430916	−	0.902392i	$-0.641809\pi$
$421$	7.15799	−	31.3612i	0.348859	−	1.52845i	0.779775	−	0.626060i	$-0.215333\pi$
$422$	2.68783			0.130842
$423$	14.7953			0.719370
$424$	1.99330	−	8.73320i	0.0968030	−	0.424122i
$425$	1.01265	−	0.487667i	0.0491208	−	0.0236553i
$426$	0.591909	+	0.742231i	0.0286781	+	0.0359612i
$427$	3.13859	+	0.665026i	0.151887	+	0.0321828i
$428$	5.75928	−	7.22190i	0.278385	−	0.349084i
$429$	−1.29384	+	5.66867i	−0.0624670	+	0.273686i
$430$	−0.228288	+	0.286265i	−0.0110090	+	0.0138049i
$431$	20.0748	−	9.66752i	0.966969	−	0.465668i	0.117365	−	0.993089i	$-0.462555\pi$
$431$	20.0748	−	9.66752i	0.966969	−	0.465668i	0.849604	+	0.527421i	$0.176841\pi$
$432$	13.0609	+	16.3778i	0.628392	+	0.787978i
$433$	12.6637	+	6.09854i	0.608581	+	0.293077i	0.712679	−	0.701490i	$-0.247482\pi$
$433$	12.6637	+	6.09854i	0.608581	+	0.293077i	−0.104099	+	0.994567i	$0.533196\pi$
$434$	−2.98987	−	2.30896i	−0.143518	−	0.110834i
$435$	−0.560590	+	0.269966i	−0.0268782	+	0.0129439i
$436$	−29.1451	−	14.0356i	−1.39580	−	0.672181i
$437$	2.60928	+	11.4320i	0.124819	+	0.546866i
$438$	−0.800918	−	0.385702i	−0.0382694	−	0.0184295i
$439$	−9.16681	+	11.4948i	−0.437508	+	0.548618i	−0.950885	−	0.309546i	$-0.899823\pi$
$439$	−9.16681	+	11.4948i	−0.437508	+	0.548618i	0.513377	+	0.858163i	$0.328394\pi$
$440$	0.612104			0.0291809
$441$	6.60082	+	7.76714i	0.314325	+	0.369864i
$442$	−0.0431000			−0.00205006
$443$	6.40302	−	8.02913i	0.304217	−	0.381475i	−0.606100	−	0.795389i	$-0.707267\pi$
$443$	6.40302	−	8.02913i	0.304217	−	0.381475i	0.910316	+	0.413913i	$0.135838\pi$
$444$	4.56250	+	2.19718i	0.216527	+	0.104274i
$445$	0.227099	+	0.994984i	0.0107655	+	0.0471668i
$446$	−1.60520	−	0.773025i	−0.0760085	−	0.0366038i
$447$	22.5618	−	10.8652i	1.06713	−	0.513905i
$448$	14.5867	−	12.0095i	0.689155	−	0.567395i
$449$	−12.0629	−	5.80917i	−0.569282	−	0.274152i	0.127021	−	0.991900i	$-0.459459\pi$
$449$	−12.0629	−	5.80917i	−0.569282	−	0.274152i	−0.696303	+	0.717748i	$0.745173\pi$
$450$	−0.859964	−	1.07836i	−0.0405391	−	0.0508344i
$451$	−0.985831	+	0.474751i	−0.0464210	+	0.0223552i
$452$	9.51929	−	11.9368i	0.447750	−	0.561461i
$453$	−2.83720	+	12.4306i	−0.133303	+	0.584040i
$454$	2.96590	−	3.71912i	0.139197	−	0.174547i
$455$	0.205188	+	0.409605i	0.00961937	+	0.0192026i
$456$	−1.71252	−	2.14743i	−0.0801961	−	0.100563i
$457$	−8.99121	+	4.32994i	−0.420591	+	0.202546i	−0.632195	−	0.774810i	$-0.717846\pi$
$457$	−8.99121	+	4.32994i	−0.420591	+	0.202546i	0.211604	+	0.977356i	$0.432131\pi$
$458$	−1.12235	+	4.91733i	−0.0524439	+	0.229772i
$459$	1.25214			0.0584451
$460$	−1.36249			−0.0635264
$461$	−7.60681	+	33.3276i	−0.354285	+	1.55222i	0.412888	+	0.910782i	$0.364520\pi$
$461$	−7.60681	+	33.3276i	−0.354285	+	1.55222i	−0.767173	+	0.641440i	$0.778337\pi$
$462$	2.86818	+	0.607728i	0.133440	+	0.0282741i
$463$	5.41444	+	23.7222i	0.251630	+	1.10246i	0.929947	+	0.367695i	$0.119853\pi$
$463$	5.41444	+	23.7222i	0.251630	+	1.10246i	−0.678316	+	0.734770i	$0.737290\pi$
$464$	−2.43473	−	10.6672i	−0.113029	−	0.495214i
$465$	1.00497	+	1.26020i	0.0466045	+	0.0584402i
$466$	2.19241	+	2.74920i	0.101562	+	0.127354i
$467$	−7.66967	−	33.6030i	−0.354910	−	1.55496i	−0.765679	−	0.643223i	$-0.777597\pi$
$467$	−7.66967	−	33.6030i	−0.354910	−	1.55496i	0.410769	−	0.911739i	$-0.365260\pi$
$468$	−0.636281	−	2.78773i	−0.0294121	−	0.128863i
$469$	0.252663	+	16.1940i	0.0116669	+	0.747769i
$470$	0.0746114	−	0.326894i	0.00344157	−	0.0150785i
$471$	12.9279			0.595685
$472$	−2.70172			−0.124357
$473$	−11.5535	+	50.6190i	−0.531229	+	2.32747i
$474$	−1.83591	+	0.884126i	−0.0843260	+	0.0406093i
$475$	−9.06794	−	11.3708i	−0.416066	−	0.521730i
$476$	−0.0183293	−	1.17479i	−0.000840124	−	0.0538463i
$477$	10.7660	−	13.5002i	0.492942	−	0.618130i
$478$	−0.244677	+	1.07200i	−0.0111913	+	0.0490322i
$479$	−11.5151	+	14.4394i	−0.526136	+	0.659754i	−0.971899	−	0.235397i	$-0.924361\pi$
$479$	−11.5151	+	14.4394i	−0.526136	+	0.659754i	0.445763	+	0.895151i	$0.352932\pi$
$480$	0.432629	−	0.208343i	0.0197467	−	0.00950953i
$481$	−1.29405	−	1.62269i	−0.0590035	−	0.0739881i
$482$	−0.570597	−	0.274785i	−0.0259900	−	0.0125161i
$483$	−12.8867	−	2.73052i	−0.586365	−	0.124243i
$484$	19.2817	−	9.28558i	0.876441	−	0.422072i
$485$	1.20565	+	0.580611i	0.0547458	+	0.0263642i
$486$	−0.572111	−	2.50658i	−0.0259515	−	0.113701i
$487$	−29.5060	−	14.2093i	−1.33704	−	0.643886i	−0.377648	−	0.925949i	$-0.623267\pi$
$487$	−29.5060	−	14.2093i	−1.33704	−	0.643886i	−0.959396	+	0.282063i	$0.908981\pi$
$488$	−0.571130	+	0.716174i	−0.0258538	+	0.0324197i
$489$	6.23494			0.281954
$490$	0.204899	−	0.106673i	0.00925638	−	0.00481898i
$491$	−7.20637			−0.325219			−0.162609	−	0.986691i	$-0.551991\pi$
$491$	−7.20637			−0.325219			−0.162609	+	0.986691i	$0.551991\pi$
$492$	−0.355703	+	0.446037i	−0.0160363	+	0.0201089i
$493$	−0.589252	−	0.283769i	−0.0265386	−	0.0127803i
$494$	0.124101	+	0.543724i	0.00558359	+	0.0244633i
$495$	1.06307	+	0.511945i	0.0477812	+	0.0230102i
$496$	−25.5375	+	12.2982i	−1.14667	+	0.552206i
$497$	10.3029	−	2.52129i	0.462147	−	0.113095i
$498$	−3.00549	−	1.44737i	−0.134679	−	0.0648581i
$499$	−8.99668	−	11.2815i	−0.402747	−	0.505029i	0.538557	−	0.842589i	$-0.318970\pi$
$499$	−8.99668	−	11.2815i	−0.402747	−	0.505029i	−0.941304	+	0.337560i	$0.890398\pi$
$500$	3.05430	−	1.47087i	0.136592	−	0.0657794i
$501$	−3.96373	+	4.97036i	−0.177086	+	0.222059i
$502$	0.987608	−	4.32699i	0.0440791	−	0.193123i
$503$	22.0099	−	27.5995i	0.981373	−	1.23060i	0.00833318	−	0.999965i	$-0.497347\pi$
$503$	22.0099	−	27.5995i	0.981373	−	1.23060i	0.973040	−	0.230637i	$-0.0740811\pi$
$504$	−2.82690	+	0.691791i	−0.125920	+	0.0308148i
$505$	−0.137043	−	0.171846i	−0.00609833	−	0.00764706i
$506$	3.21980	−	1.55058i	0.143138	−	0.0689315i
$507$	0.276486	−	1.21136i	0.0122792	−	0.0537985i
$508$	37.0177			1.64239
$509$	26.2923			1.16539			0.582694	−	0.812692i	$-0.301999\pi$
$509$	26.2923			1.16539			0.582694	+	0.812692i	$0.301999\pi$
$510$	0.00206341	−	0.00904038i	9.13692e−5	−	0.000400315i
$511$	−7.66767	+	6.31295i	−0.339198	+	0.279268i
$512$	3.15091	+	13.8050i	0.139252	+	0.610102i
$513$	−3.60541	−	15.7963i	−0.159183	−	0.697424i
$514$	−1.63274	−	2.04739i	−0.0720170	−	0.0903065i
$515$	−1.11764	−	1.40148i	−0.0492491	−	0.0617564i
$516$	6.02389	+	26.3924i	0.265187	+	1.16186i
$517$	−10.5802	−	46.3547i	−0.465315	−	2.03868i
$518$	−0.807937	+	0.665191i	−0.0354987	+	0.0292268i
$519$	5.71588	−	25.0429i	0.250899	−	1.09926i
$520$	−0.130803			−0.00573610
$521$	−22.4173			−0.982121			−0.491060	−	0.871125i	$-0.663391\pi$
$521$	−22.4173			−0.982121			−0.491060	+	0.871125i	$0.663391\pi$
$522$	−0.178592	+	0.782464i	−0.00781677	+	0.0342475i
$523$	24.0193	−	11.5671i	1.05029	−	0.505793i	0.172585	−	0.984995i	$-0.444788\pi$
$523$	24.0193	−	11.5671i	1.05029	−	0.505793i	0.877705	+	0.479202i	$0.159074\pi$
$524$	5.31185	+	6.66085i	0.232049	+	0.290980i
$525$	15.8701	−	3.88368i	0.692627	−	0.169498i
$526$	1.63424	−	2.04927i	0.0712562	−	0.0893524i
$527$	−0.377009	+	1.65178i	−0.0164228	+	0.0719528i
$528$	13.7157	−	17.1990i	0.596900	−	0.748489i
$529$	6.25573	−	3.01260i	0.271988	−	0.130983i
$530$	−0.243987	−	0.305950i	−0.0105981	−	0.0132896i
$531$	−4.69219	−	2.25964i	−0.203624	−	0.0980600i
$532$	−14.7676	+	3.61389i	−0.640258	+	0.156682i
$533$	0.210667	−	0.101452i	0.00912498	−	0.00439436i
$534$	−1.25749	−	0.605576i	−0.0544170	−	0.0262058i
$535$	−0.181248	−	0.794102i	−0.00783606	−	0.0343320i
$536$	−4.16630	−	2.00638i	−0.179957	−	0.0866626i
$537$	6.68902	−	8.38776i	0.288652	−	0.361959i
$538$	−3.42204			−0.147534
$539$	19.6148	−	26.2352i	0.844868	−	1.13003i
$540$	1.88264			0.0810160
$541$	−7.26612	+	9.11143i	−0.312395	+	0.391731i	−0.913097	−	0.407742i	$-0.866316\pi$
$541$	−7.26612	+	9.11143i	−0.312395	+	0.391731i	0.600702	+	0.799473i	$0.294888\pi$
$542$	−1.19968	−	0.577735i	−0.0515306	−	0.0248158i
$543$	−3.04016	−	13.3198i	−0.130466	−	0.571607i
$544$	0.454749	+	0.218996i	0.0194972	+	0.00938935i
$545$	−2.56999	+	1.23764i	−0.110086	+	0.0530147i
$546$	−0.612913	−	0.129868i	−0.0262303	−	0.00555784i
$547$	−29.8394	−	14.3699i	−1.27584	−	0.614413i	−0.331523	−	0.943447i	$-0.607563\pi$
$547$	−29.8394	−	14.3699i	−1.27584	−	0.614413i	−0.944318	+	0.329034i	$0.893277\pi$
$548$	22.8320	+	28.6304i	0.975335	+	1.22303i
$549$	−1.59089	+	0.766132i	−0.0678975	+	0.0326977i
$550$	−2.76362	+	3.46547i	−0.117841	+	0.147768i
$551$	−1.88318	+	8.25073i	−0.0802260	+	0.351493i
$552$	2.34499	−	2.94053i	0.0998096	−	0.125157i
$553$	0.355172	+	22.7641i	0.0151035	+	0.968029i
$554$	−2.04556	−	2.56505i	−0.0869074	−	0.108978i
$555$	0.402316	−	0.193745i	0.0170774	−	0.00822403i
$556$	4.91621	−	21.5393i	0.208494	−	0.913471i
$557$	−40.0675			−1.69771			−0.848857	−	0.528623i	$-0.822709\pi$
$557$	−40.0675			−1.69771			−0.848857	+	0.528623i	$0.822709\pi$
$558$	2.07913			0.0880164
$559$	2.46891	−	10.8170i	0.104424	−	0.457511i
$560$	−0.0270396	−	1.73305i	−0.00114263	−	0.0732349i
$561$	−0.292598	−	1.28196i	−0.0123535	−	0.0541243i
$562$	−0.210515	−	0.922328i	−0.00888005	−	0.0389060i
$563$	24.3468	+	30.5300i	1.02610	+	1.28668i	0.957313	+	0.289053i	$0.0933405\pi$
$563$	24.3468	+	30.5300i	1.02610	+	1.28668i	0.0687839	+	0.997632i	$0.478088\pi$
$564$	−15.4567	−	19.3820i	−0.650843	−	0.816131i
$565$	−0.299579	−	1.31254i	−0.0126034	−	0.0552190i
$566$	0.0795366	+	0.348472i	0.00334317	+	0.0146474i
$567$	6.49955	+	1.37717i	0.272955	+	0.0578356i
$568$	−0.673897	+	2.95254i	−0.0282761	+	0.123886i
$569$	12.2284			0.512642			0.256321	−	0.966592i	$-0.417490\pi$
$569$	12.2284			0.512642			0.256321	+	0.966592i	$0.417490\pi$
$570$	−0.119989			−0.00502580
$571$	8.76437	−	38.3992i	0.366778	−	1.60696i	−0.368795	−	0.929511i	$-0.620229\pi$
$571$	8.76437	−	38.3992i	0.366778	−	1.60696i	0.735572	−	0.677446i	$-0.236913\pi$
$572$	−8.27917	+	3.98704i	−0.346170	+	0.166706i
$573$	−4.57354	−	5.73503i	−0.191062	−	0.239584i
$574$	−0.0528065	−	0.105415i	−0.00220410	−	0.00439993i
$575$	12.4170	−	15.5704i	0.517823	−	0.649329i
$576$	−2.31400	+	10.1383i	−0.0964167	+	0.422429i
$577$	−2.41734	+	3.03124i	−0.100635	+	0.126192i	−0.829599	−	0.558360i	$-0.811431\pi$
$577$	−2.41734	+	3.03124i	−0.100635	+	0.126192i	0.728964	+	0.684552i	$0.240002\pi$
$578$	−2.91028	+	1.40152i	−0.121052	+	0.0582955i
$579$	−3.22938	−	4.04951i	−0.134208	−	0.168292i
$580$	−0.885960	−	0.426656i	−0.0367875	−	0.0177159i
$581$	−28.7734	+	23.6897i	−1.19372	+	0.982814i
$582$	−1.64882	+	0.794029i	−0.0683457	+	0.0329135i
$583$	−49.9959	−	24.0768i	−2.07062	−	0.997158i
$584$	−0.631024	−	2.76470i	−0.0261120	−	0.114404i
$585$	−0.227171	−	0.109400i	−0.00939237	−	0.00452313i
$586$	2.30431	−	2.88951i	0.0951902	−	0.119365i
$587$	24.7214			1.02036			0.510180	−	0.860067i	$-0.329579\pi$
$587$	24.7214			1.02036			0.510180	+	0.860067i	$0.329579\pi$
$588$	3.27919	−	16.7615i	0.135231	−	0.691234i
$589$	21.9235			0.903341
$590$	−0.0735881	+	0.0922765i	−0.00302957	+	0.00379896i
$591$	2.37457	+	1.14353i	0.0976767	+	0.0470386i
$592$	1.74732	+	7.65552i	0.0718145	+	0.314640i
$593$	−17.2762	−	8.31977i	−0.709447	−	0.341652i	0.0441166	−	0.999026i	$-0.485953\pi$
$593$	−17.2762	−	8.31977i	−0.709447	−	0.341652i	−0.753564	+	0.657375i	$0.771667\pi$
$594$	−4.44901	+	2.14253i	−0.182545	+	0.0879091i
$595$	−0.0819988	−	0.0633246i	−0.00336162	−	0.00259605i
$596$	35.6567	+	17.1714i	1.46056	+	0.703367i
$597$	17.8316	+	22.3601i	0.729798	+	0.915138i
$598$	−0.688054	+	0.331349i	−0.0281366	+	0.0135499i
$599$	15.1305	−	18.9731i	0.618216	−	0.775219i	−0.369876	−	0.929081i	$-0.620600\pi$
$599$	15.1305	−	18.9731i	0.618216	−	0.775219i	0.988092	+	0.153862i	$0.0491712\pi$
$600$	−1.03804	+	4.54795i	−0.0423778	+	0.185669i
$601$	5.50643	−	6.90485i	0.224612	−	0.281655i	−0.656738	−	0.754119i	$-0.728064\pi$
$601$	5.50643	−	6.90485i	0.224612	−	0.281655i	0.881350	+	0.472464i	$0.156635\pi$
$602$	−5.47308	−	1.15967i	−0.223066	−	0.0472647i
$603$	−5.55770	−	6.96913i	−0.226327	−	0.283805i
$604$	−18.1551	+	8.74302i	−0.738719	+	0.355748i
$605$	0.419925	−	1.83981i	0.0170724	−	0.0747989i
$606$	0.300593			0.0122107
$607$	38.1123			1.54693			0.773465	−	0.633839i	$-0.218522\pi$
$607$	38.1123			1.54693			0.773465	+	0.633839i	$0.218522\pi$
$608$	1.45332	−	6.36741i	0.0589399	−	0.258233i
$609$	−7.52454	−	5.81092i	−0.304910	−	0.235470i
$610$	0.00890458	+	0.0390135i	0.000360536	+	0.00157961i
$611$	2.26092	+	9.90574i	0.0914671	+	0.400743i
$612$	0.403181	+	0.505573i	0.0162976	+	0.0204366i
$613$	0.312313	+	0.391629i	0.0126142	+	0.0158177i	0.788099	−	0.615549i	$-0.211066\pi$
$613$	0.312313	+	0.391629i	0.0126142	+	0.0158177i	−0.775484	+	0.631367i	$0.782494\pi$
$614$	−1.22530	−	5.36839i	−0.0494491	−	0.216650i
$615$	0.0111942	+	0.0490451i	0.000451394	+	0.00197769i
$616$	4.18897	+	8.36220i	0.168778	+	0.336923i
$617$	6.50611	−	28.5051i	0.261926	−	1.14757i	−0.657233	−	0.753687i	$-0.728273\pi$
$617$	6.50611	−	28.5051i	0.261926	−	1.14757i	0.919159	−	0.393886i	$-0.128870\pi$
$618$	2.45145			0.0986120
$619$	26.0191			1.04580			0.522899	−	0.852395i	$-0.324851\pi$
$619$	26.0191			1.04580			0.522899	+	0.852395i	$0.324851\pi$
$620$	−0.566845	+	2.48351i	−0.0227650	+	0.0997402i
$621$	19.9894	−	9.62638i	0.802147	−	0.386293i
$622$	2.07964	+	2.60778i	0.0833858	+	0.104562i
$623$	−12.0387	+	9.91172i	−0.482321	+	0.397105i
$624$	−2.93097	+	3.67532i	−0.117333	+	0.147131i
$625$	−5.46315	+	23.9356i	−0.218526	+	0.957424i
$626$	2.16390	−	2.71344i	0.0864867	−	0.108451i
$627$	−15.3299	+	7.38250i	−0.612218	+	0.294828i
$628$	12.7387	+	15.9738i	0.508329	+	0.637425i
$629$	0.422886	+	0.203651i	0.0168616	+	0.00812011i
$630$	−0.0533696	+	0.115394i	−0.00212630	+	0.00459743i
$631$	25.6464	−	12.3506i	1.02097	−	0.491672i	0.152964	−	0.988232i	$-0.451118\pi$
$631$	25.6464	−	12.3506i	1.02097	−	0.491672i	0.868002	+	0.496560i	$0.165404\pi$
$632$	−5.85663	−	2.82040i	−0.232964	−	0.112190i
$633$	−3.89933	−	17.0841i	−0.154984	−	0.679031i
$634$	0.211417	+	0.101813i	0.00839643	+	0.00404351i
$635$	2.03518	−	2.55204i	0.0807637	−	0.101275i
$636$	−28.9328			−1.14726
$637$	−4.19157	+	5.60631i	−0.166076	+	0.222130i
$638$	2.57923			0.102113
$639$	−3.63979	+	4.56416i	−0.143988	+	0.180555i
$640$	0.908708	+	0.437611i	0.0359198	+	0.0172981i
$641$	−8.40370	−	36.8190i	−0.331926	−	1.45426i	−0.815397	−	0.578902i	$-0.803481\pi$
$641$	−8.40370	−	36.8190i	−0.331926	−	1.45426i	0.483471	−	0.875360i	$-0.339376\pi$
$642$	1.00361	+	0.483313i	0.0396093	+	0.0190748i
$643$	8.72841	−	4.20338i	0.344215	−	0.165765i	−0.253787	−	0.967260i	$-0.581676\pi$
$643$	8.72841	−	4.20338i	0.344215	−	0.165765i	0.598001	+	0.801495i	$0.295962\pi$
$644$	−9.32427	−	18.6135i	−0.367428	−	0.733475i
$645$	2.15071	+	1.03573i	0.0846840	+	0.0407817i
$646$	−0.0786372	−	0.0986079i	−0.00309394	−	0.00387968i
$647$	−14.7493	+	7.10287i	−0.579853	+	0.279242i	−0.700732	−	0.713425i	$-0.747143\pi$
$647$	−14.7493	+	7.10287i	−0.579853	+	0.279242i	0.120879	+	0.992667i	$0.461429\pi$
$648$	−1.18272	+	1.48309i	−0.0464618	+	0.0582612i
$649$	−3.72422	+	16.3169i	−0.146189	+	0.640494i
$650$	0.590571	−	0.740553i	0.0231641	−	0.0290469i
$651$	−10.3385	+	22.3535i	−0.405196	+	0.876105i
$652$	6.14370	+	7.70396i	0.240606	+	0.301710i
$653$	0.274694	−	0.132286i	0.0107496	−	0.00517674i	−0.428501	−	0.903541i	$-0.640958\pi$
$653$	0.274694	−	0.132286i	0.0107496	−	0.00517674i	0.439251	+	0.898364i	$0.355244\pi$
$654$	0.868047	−	3.80316i	0.0339433	−	0.148715i
$655$	0.751244			0.0293535
$656$	−0.884640			−0.0345394
$657$	1.21638	−	5.32933i	0.0474557	−	0.207917i
$658$	4.97644	−	1.21782i	0.194002	−	0.0474756i
$659$	4.00007	+	17.5254i	0.155821	+	0.682694i	0.991128	+	0.132911i	$0.0424325\pi$
$659$	4.00007	+	17.5254i	0.155821	+	0.682694i	−0.835307	+	0.549783i	$0.814710\pi$
$660$	−0.439931	−	1.92746i	−0.0171243	−	0.0750265i
$661$	−18.1190	−	22.7206i	−0.704749	−	0.883728i	0.292619	−	0.956229i	$-0.405473\pi$
$661$	−18.1190	−	22.7206i	−0.704749	−	0.883728i	−0.997368	+	0.0725015i	$0.976902\pi$
$662$	1.42896	+	1.79185i	0.0555379	+	0.0696423i
$663$	0.0625266	+	0.273947i	0.00242833	+	0.0106392i
$664$	−2.36795	−	10.3747i	−0.0918944	−	0.402616i
$665$	−0.562759	+	1.21678i	−0.0218229	+	0.0471849i
$666$	0.128170	−	0.561548i	0.00496647	−	0.0217595i
$667$	−11.5885			−0.448708
$668$	−10.0472			−0.388736
$669$	−2.58469	+	11.3242i	−0.0999297	+	0.437821i
$670$	−0.182007	+	0.0876498i	−0.00703153	+	0.00338621i
$671$	3.53801	+	4.43652i	0.136583	+	0.171270i
$672$	5.80698	+	4.48451i	0.224009	+	0.172994i
$673$	−11.3555	+	14.2394i	−0.437723	+	0.548888i	−0.950942	−	0.309371i	$-0.899882\pi$
$673$	−11.3555	+	14.2394i	−0.437723	+	0.548888i	0.513218	+	0.858258i	$0.328453\pi$
$674$	1.35679	−	5.94449i	0.0522617	−	0.228973i
$675$	−17.1573	+	21.5146i	−0.660385	+	0.828097i
$676$	1.76921	−	0.852008i	0.0680466	−	0.0327695i
$677$	−30.5113	−	38.2600i	−1.17265	−	1.47045i	−0.852224	−	0.523177i	$-0.824747\pi$
$677$	−30.5113	−	38.2600i	−1.17265	−	1.47045i	−0.320422	−	0.947275i	$-0.603825\pi$
$678$	1.65883	+	0.798849i	0.0637069	+	0.0306796i
$679$	0.318978	+	20.4443i	0.0122412	+	0.784581i
$680$	0.0266514	−	0.0128347i	0.00102204	−	0.000492187i
$681$	−27.9418	−	13.4561i	−1.07073	−	0.515637i
$682$	−1.48679	−	6.51407i	−0.0569322	−	0.249436i
$683$	−33.7299	−	16.2435i	−1.29064	−	0.621539i	−0.342536	−	0.939505i	$-0.611286\pi$
$683$	−33.7299	−	16.2435i	−1.29064	−	0.621539i	−0.948102	+	0.317966i	$0.897000\pi$
$684$	5.21710	−	6.54203i	0.199481	−	0.250141i
$685$	3.22909			0.123377
$686$	2.85953	+	2.06918i	0.109177	+	0.0790017i
$687$	32.8831			1.25457
$688$	−26.1725	+	32.8192i	−0.997816	+	1.25122i
$689$	10.6838	+	5.14507i	0.407022	+	0.196012i
$690$	−0.0365612	−	0.160185i	−0.00139186	−	0.00609814i
$691$	−28.8021	−	13.8704i	−1.09568	−	0.527653i	−0.203385	−	0.979099i	$-0.565194\pi$
$691$	−28.8021	−	13.8704i	−1.09568	−	0.527653i	−0.892299	+	0.451445i	$0.850909\pi$
$692$	36.5755	−	17.6138i	1.39039	−	0.669578i
$693$	0.281254	+	18.0265i	0.0106840	+	0.684770i
$694$	1.52247	+	0.733181i	0.0577920	+	0.0278312i
$695$	−1.21466	−	1.52313i	−0.0460746	−	0.0577757i
$696$	2.44564	−	1.17776i	0.0927019	−	0.0446429i
$697$	−0.0329692	+	0.0413420i	−0.00124880	+	0.00156594i
$698$	0.103177	−	0.452050i	0.00390532	−	0.0171103i
$699$	14.2935	−	17.9235i	0.540630	−	0.677929i
$700$	20.4366	+	15.7824i	0.772429	+	0.596518i
$701$	26.2281	+	32.8890i	0.990622	+	1.24220i	0.970174	+	0.242409i	$0.0779377\pi$
$701$	26.2281	+	32.8890i	0.990622	+	1.24220i	0.0204476	+	0.999791i	$0.493491\pi$
$702$	0.950729	−	0.457847i	0.0358829	−	0.0172803i
$703$	1.35149	−	5.92127i	0.0509725	−	0.223325i
$704$	33.4188			1.25952
$705$	−2.18601			−0.0823297
$706$	1.35256	−	5.92593i	0.0509041	−	0.223025i
$707$	1.40980	−	3.04824i	0.0530210	−	0.114641i
$708$	1.94178	+	8.50751i	0.0729767	+	0.319732i
$709$	−4.67503	−	20.4826i	−0.175574	−	0.769241i	−0.983639	−	0.180148i	$-0.942342\pi$
$709$	−4.67503	−	20.4826i	−0.175574	−	0.769241i	0.808065	−	0.589093i	$-0.200515\pi$
$710$	0.0824876	+	0.103436i	0.00309571	+	0.00388189i
$711$	−7.81253	−	9.79661i	−0.292993	−	0.367402i
$712$	−0.990747	−	4.34075i	−0.0371298	−	0.162676i
$713$	6.68015	+	29.2677i	0.250174	+	1.09608i
$714$	0.137625	−	0.0336793i	0.00515050	−	0.00126042i
$715$	−0.180307	+	0.789977i	−0.00674311	+	0.0295435i
$716$	16.9552			0.633644
$717$	7.16868			0.267719
$718$	−0.726934	+	3.18490i	−0.0271289	+	0.118860i
$719$	24.2612	−	11.6836i	0.904788	−	0.435723i	0.0771724	−	0.997018i	$-0.475411\pi$
$719$	24.2612	−	11.6836i	0.904788	−	0.435723i	0.827616	+	0.561295i	$0.189697\pi$
$720$	0.594776	+	0.745826i	0.0221660	+	0.0277953i
$721$	11.4975	−	24.8596i	0.428189	−	0.925820i
$722$	1.24016	−	1.55511i	0.0461538	−	0.0578751i
$723$	−0.918771	+	4.02540i	−0.0341694	+	0.149706i
$724$	13.4624	−	16.8813i	0.500327	−	0.627390i
$725$	12.9499	−	6.23634i	0.480947	−	0.231612i
$726$	1.60909	+	2.01774i	0.0597191	+	0.0748853i
$727$	16.9645	+	8.16969i	0.629180	+	0.302997i	0.721165	−	0.692763i	$-0.243607\pi$
$727$	16.9645	+	8.16969i	0.629180	+	0.302997i	−0.0919850	+	0.995760i	$0.529321\pi$
$728$	−0.895159	−	1.78696i	−0.0331768	−	0.0662290i
$729$	−21.8894	+	10.5414i	−0.810720	+	0.390422i
$730$	−0.111615	−	0.0537509i	−0.00413105	−	0.00198941i
$731$	0.558339	+	2.44624i	0.0206509	+	0.0904775i
$732$	2.66566	+	1.28371i	0.0985255	+	0.0474474i
$733$	−18.1984	+	22.8201i	−0.672175	+	0.842880i	−0.994607	−	0.103712i	$-0.966928\pi$
$733$	−18.1984	+	22.8201i	−0.672175	+	0.842880i	0.322433	+	0.946592i	$0.395499\pi$
$734$	−2.11445			−0.0780459
$735$	−0.975273	−	1.14760i	−0.0359735	−	0.0423298i
$736$	8.94328			0.329654
$737$	−17.8605	+	22.3964i	−0.657900	+	0.824981i
$738$	0.0584640	+	0.0281548i	0.00215209	+	0.00103639i
$739$	11.9930	+	52.5448i	0.441170	+	1.93289i	0.348904	+	0.937158i	$0.386554\pi$
$739$	11.9930	+	52.5448i	0.441170	+	1.93289i	0.0922660	+	0.995734i	$0.470589\pi$
$740$	0.635823	+	0.306196i	0.0233733	+	0.0112560i
$741$	3.27592	−	1.57760i	0.120344	−	0.0579545i
$742$	2.50997	−	5.42700i	0.0921439	−	0.199231i
$743$	−21.0071	−	10.1165i	−0.770676	−	0.371138i	0.00685992	−	0.999976i	$-0.497816\pi$
$743$	−21.0071	−	10.1165i	−0.770676	−	0.371138i	−0.777536	+	0.628838i	$0.783531\pi$
$744$	−4.38432	−	5.49776i	−0.160737	−	0.201558i
$745$	3.14417	−	1.51415i	0.115194	−	0.0554743i
$746$	−0.0226005	+	0.0283401i	−0.000827462	+	0.00103760i
$747$	4.56455	−	19.9986i	0.167008	−	0.731711i
$748$	1.29568	−	1.62474i	0.0473749	−	0.0594062i
$749$	9.60816	−	7.91059i	0.351074	−	0.289046i
$750$	0.254887	+	0.319618i	0.00930714	+	0.0116708i
$751$	−12.2308	+	5.89005i	−0.446309	+	0.214931i	−0.643519	−	0.765430i	$-0.722526\pi$
$751$	−12.2308	+	5.89005i	−0.446309	+	0.214931i	0.197210	+	0.980361i	$0.436812\pi$
$752$	8.55394	−	37.4773i	0.311930	−	1.36665i
$753$	−28.9355			−1.05447
$754$	−0.551167			−0.0200723
$755$	−0.395388	+	1.73231i	−0.0143896	+	0.0630452i
$756$	12.8840	+	25.7195i	0.468585	+	0.935410i
$757$	7.22461	+	31.6531i	0.262583	+	1.15045i	0.918438	+	0.395565i	$0.129451\pi$
$757$	7.22461	+	31.6531i	0.262583	+	1.15045i	−0.655855	+	0.754887i	$0.727692\pi$
$758$	−0.267859	−	1.17357i	−0.00972907	−	0.0426258i
$759$	−14.5267	−	18.2158i	−0.527284	−	0.661193i
$760$	−0.238654	−	0.299263i	−0.00865690	−	0.0108554i
$761$	−0.434967	−	1.90571i	−0.0157675	−	0.0690820i	0.966432	−	0.256922i	$-0.0827084\pi$
$761$	−0.434967	−	1.90571i	−0.0157675	−	0.0690820i	−0.982200	+	0.187840i	$0.939851\pi$
$762$	0.993336	+	4.35209i	0.0359848	+	0.157659i
$763$	−34.4957	−	26.6398i	−1.24883	−	0.964424i
$764$	2.57966	−	11.3022i	0.0933288	−	0.408900i
$765$	0.0570211			0.00206160
$766$	4.38130			0.158303
$767$	0.795846	−	3.48683i	0.0287363	−	0.125902i
$768$	14.7464	−	7.10151i	0.532116	−	0.256254i
$769$	−3.94374	−	4.94529i	−0.142215	−	0.178332i	0.705623	−	0.708588i	$-0.250667\pi$
$769$	−3.94374	−	4.94529i	−0.142215	−	0.178332i	−0.847838	+	0.530256i	$0.822096\pi$
$770$	0.399705	+	0.0846921i	0.0144044	+	0.00305209i
$771$	−10.6447	+	13.3480i	−0.383360	+	0.480718i
$772$	1.82150	−	7.98051i	0.0655572	−	0.287225i
$773$	−9.52337	+	11.9419i	−0.342532	+	0.429521i	−0.923023	−	0.384745i	$-0.874289\pi$
$773$	−9.52337	+	11.9419i	−0.342532	+	0.429521i	0.580491	+	0.814267i	$0.302861\pi$
$774$	2.77420	−	1.33598i	0.0997164	−	0.0480209i
$775$	−23.2153	−	29.1111i	−0.833920	−	1.04570i
$776$	−5.25980	−	2.53299i	−0.188816	−	0.0909289i
$777$	5.40011	+	4.17030i	0.193728	+	0.149609i
$778$	−3.94473	+	1.89968i	−0.141425	+	0.0681068i
$779$	0.616477	+	0.296880i	0.0220876	+	0.0106368i
$780$	0.0940109	+	0.411888i	0.00336613	+	0.0147480i
$781$	16.9027	+	8.13991i	0.604826	+	0.291269i
$782$	0.107680	−	0.135026i	0.00385062	−	0.00482853i
$783$	16.0126			0.572242
$784$	23.4909	−	12.2296i	0.838961	−	0.436773i
$785$	1.80161			0.0643022
$786$	−0.640563	+	0.803241i	−0.0228481	+	0.0286506i
$787$	1.09571	+	0.527668i	0.0390580	+	0.0188093i	0.453311	−	0.891353i	$-0.350243\pi$
$787$	1.09571	+	0.527668i	0.0390580	+	0.0188093i	−0.414253	+	0.910162i	$0.635957\pi$
$788$	0.926861	+	4.06084i	0.0330181	+	0.144662i
$789$	−15.3962	−	7.41440i	−0.548118	−	0.263960i
$790$	−0.255849	+	0.123211i	−0.00910271	+	0.00438364i
$791$	15.8810	−	13.0751i	0.564662	−	0.464897i
$792$	−4.63776	−	2.23343i	−0.164795	−	0.0793613i
$793$	−0.756052	−	0.948059i	−0.0268482	−	0.0336666i
$794$	−1.65856	+	0.798722i	−0.0588602	+	0.0283456i
$795$	−1.59068	+	1.99466i	−0.0564158	+	0.0707431i
$796$	−10.0577	+	44.0658i	−0.356487	+	1.56187i
$797$	−2.20262	+	2.76200i	−0.0780210	+	0.0978352i	−0.819310	−	0.573351i	$-0.805643\pi$
$797$	−2.20262	+	2.76200i	−0.0780210	+	0.0978352i	0.741289	+	0.671186i	$0.234215\pi$
$798$	−0.821154	−	1.63922i	−0.0290685	−	0.0580279i
$799$	−1.43264	−	1.79647i	−0.0506831	−	0.0635546i
$800$	−9.99395	+	4.81283i	−0.353339	+	0.170159i
$801$	1.90980	−	8.36737i	0.0674794	−	0.295647i
$802$	−0.0665555			−0.00235016
$803$	−17.5670			−0.619928
$804$	−3.32354	+	14.5614i	−0.117212	+	0.513540i
$805$	−1.79587	−	0.380521i	−0.0632962	−	0.0134116i
$806$	0.317719	+	1.39202i	0.0111912	+	0.0490318i
$807$	4.96446	+	21.7507i	0.174757	+	0.765662i
$808$	0.597867	+	0.749701i	0.0210329	+	0.0263744i
$809$	10.0743	+	12.6328i	0.354193	+	0.444144i	0.926726	−	0.375738i	$-0.122611\pi$
$809$	10.0743	+	12.6328i	0.354193	+	0.444144i	−0.572533	+	0.819882i	$0.694039\pi$
$810$	0.0184400	+	0.0807910i	0.000647917	+	0.00283871i
$811$	1.61709	+	7.08494i	0.0567837	+	0.248786i	0.995351	−	0.0963093i	$-0.0307038\pi$
$811$	1.61709	+	7.08494i	0.0567837	+	0.248786i	−0.938568	+	0.345095i	$0.887847\pi$
$812$	−0.234398	−	15.0233i	−0.00822574	−	0.527214i
$813$	−1.93171	+	8.46339i	−0.0677481	+	0.296824i
$814$	−1.85103			−0.0648785
$815$	0.868892			0.0304360
$816$	0.236562	−	1.03645i	0.00828134	−	0.0362829i
$817$	29.2527	−	14.0873i	1.02342	−	0.492854i
$818$	2.79717	+	3.50755i	0.0978009	+	0.122638i
$819$	−0.0601025	−	3.85216i	−0.00210015	−	0.134605i
$820$	−0.0495702	+	0.0621591i	−0.00173107	+	0.00217069i
$821$	−2.13308	+	9.34565i	−0.0744451	+	0.326165i	−0.998414	−	0.0563030i	$-0.982069\pi$
$821$	−2.13308	+	9.34565i	−0.0744451	+	0.326165i	0.923969	+	0.382468i	$0.124926\pi$
$822$	−2.75334	+	3.45258i	−0.0960339	+	0.120423i
$823$	−19.1905	+	9.24166i	−0.668939	+	0.322144i	−0.737348	−	0.675513i	$-0.763922\pi$
$823$	−19.1905	+	9.24166i	−0.668939	+	0.322144i	0.0684087	+	0.997657i	$0.478208\pi$
$824$	4.87585	+	6.11412i	0.169858	+	0.212995i
$825$	26.0361	+	12.5383i	0.906461	+	0.436529i
$826$	−1.76423	−	0.373817i	−0.0613854	−	0.0130068i
$827$	−38.2670	+	18.4284i	−1.33067	+	0.640818i	−0.957899	−	0.287104i	$-0.907307\pi$
$827$	−38.2670	+	18.4284i	−1.33067	+	0.640818i	−0.372773	+	0.927923i	$0.621593\pi$
$828$	10.3232	+	4.97141i	0.358757	+	0.172768i
$829$	2.77899	+	12.1755i	0.0965183	+	0.422874i	0.999983	−	0.00578765i	$-0.00184228\pi$
$829$	2.77899	+	12.1755i	0.0965183	+	0.422874i	−0.903465	+	0.428662i	$0.858985\pi$
$830$	−0.418841	−	0.201703i	−0.0145382	−	0.00700122i
$831$	−13.3361	+	16.7229i	−0.462624	+	0.580112i
$832$	−7.14142			−0.247584
$833$	0.303939	−	1.55358i	0.0105309	−	0.0538285i
$834$	2.66426			0.0922557
$835$	−0.552380	+	0.692662i	−0.0191159	+	0.0239706i
$836$	−24.2275	−	11.6673i	−0.837925	−	0.403523i
$837$	−9.23041	−	40.4411i	−0.319050	−	1.39785i
$838$	−4.46765	−	2.15151i	−0.154332	−	0.0743226i
$839$	44.2648	−	21.3168i	1.52819	−	0.735938i	0.534196	−	0.845361i	$-0.320614\pi$
$839$	44.2648	−	21.3168i	1.52819	−	0.735938i	0.993995	+	0.109422i	$0.0349001\pi$
$840$	0.417676	−	0.102212i	0.0144112	−	0.00352667i
$841$	18.5927	+	8.95376i	0.641127	+	0.308750i
$842$	3.82239	+	4.79312i	0.131728	+	0.165182i
$843$	−5.55699	+	2.67610i	−0.191393	+	0.0921699i
$844$	17.2670	−	21.6521i	0.594355	−	0.745298i
$845$	0.0385306	−	0.168814i	0.00132549	−	0.00580737i
$846$	−1.75807	+	2.20455i	−0.0604438	+	0.0757941i
$847$	28.0082	−	6.85408i	0.962372	−	0.235509i
$848$	−27.9723	−	35.0761i	−0.960572	−	1.20452i
$849$	2.09953	−	1.01108i	0.0720558	−	0.0347002i
$850$	−0.0476657	+	0.208837i	−0.00163492	+	0.00716306i
$851$	8.31666			0.285091
$852$	9.78163			0.335113
$853$	4.86266	−	21.3047i	0.166494	−	0.729459i	−0.820886	−	0.571092i	$-0.806520\pi$
$853$	4.86266	−	21.3047i	0.166494	−	0.729459i	0.987380	−	0.158367i	$-0.0506230\pi$
$854$	−0.472040	+	0.388640i	−0.0161529	+	0.0132990i
$855$	−0.164186	−	0.719345i	−0.00561503	−	0.0246011i
$856$	0.790719	+	3.46437i	0.0270262	+	0.118410i
$857$	−9.51173	−	11.9273i	−0.324915	−	0.407430i	0.592368	−	0.805668i	$-0.298193\pi$
$857$	−9.51173	−	11.9273i	−0.324915	−	0.407430i	−0.917282	+	0.398238i	$0.869622\pi$
$858$	−0.690912	−	0.866376i	−0.0235873	−	0.0295776i
$859$	−7.46558	−	32.7088i	−0.254722	−	1.11601i	−0.926807	−	0.375537i	$-0.877458\pi$
$859$	−7.46558	−	32.7088i	−0.254722	−	1.11601i	0.672085	−	0.740474i	$-0.265399\pi$
$860$	0.839481	+	3.67801i	0.0286261	+	0.125419i
$861$	−0.593416	+	0.488571i	−0.0202236	+	0.0166505i
$862$	−0.944925	+	4.13999i	−0.0321843	+	0.141008i
$863$	0.971460			0.0330689			0.0165344	−	0.999863i	$-0.494737\pi$
$863$	0.971460			0.0330689			0.0165344	+	0.999863i	$0.494737\pi$
$864$	−12.3575			−0.420411
$865$	0.796557	−	3.48994i	0.0270837	−	0.118662i
$866$	−2.41350	+	1.16228i	−0.0820140	+	0.0394959i
$867$	13.1302	+	16.4648i	0.445925	+	0.559172i
$868$	−37.8075	+	9.25214i	−1.28327	+	0.314038i
$869$	−25.1068	+	31.4829i	−0.851689	+	1.06798i
$870$	0.0263871	−	0.115609i	0.000894606	−	0.00391952i
$871$	3.81669	−	4.78598i	0.129324	−	0.162167i
$872$	11.2119	−	5.39936i	0.379683	−	0.182845i
$873$	−7.01639	−	8.79827i	−0.237469	−	0.297776i
$874$	−2.01346	−	0.969633i	−0.0681064	−	0.0327983i
$875$	4.43660	−	1.08571i	0.149985	−	0.0367038i
$876$	−8.25227	+	3.97409i	−0.278818	+	0.134272i
$877$	−5.82661	−	2.80595i	−0.196751	−	0.0947501i	0.332914	−	0.942957i	$-0.391968\pi$
$877$	−5.82661	−	2.80595i	−0.196751	−	0.0947501i	−0.529665	+	0.848207i	$0.677682\pi$
$878$	−0.623512	−	2.73178i	−0.0210425	−	0.0921932i
$879$	−21.7089	−	10.4545i	−0.732224	−	0.352620i
$880$	1.91140	−	2.39682i	0.0644334	−	0.0807969i
$881$	39.4169			1.32799			0.663994	−	0.747738i	$-0.268860\pi$
$881$	39.4169			1.32799			0.663994	+	0.747738i	$0.268860\pi$
$882$	−1.94169	+	0.0606043i	−0.0653800	+	0.00204065i
$883$	0.779647			0.0262372			0.0131186	−	0.999914i	$-0.495824\pi$
$883$	0.779647			0.0262372			0.0131186	+	0.999914i	$0.495824\pi$
$884$	−0.276880	+	0.347197i	−0.00931249	+	0.0116775i
$885$	0.693273	+	0.333863i	0.0233041	+	0.0112227i
$886$	0.435523	+	1.90815i	0.0146317	+	0.0641056i
$887$	−1.45842	−	0.702336i	−0.0489688	−	0.0235821i	0.409239	−	0.912427i	$-0.365794\pi$
$887$	−1.45842	−	0.702336i	−0.0489688	−	0.0235821i	−0.458208	+	0.888845i	$0.651508\pi$
$888$	−1.75516	+	0.845239i	−0.0588992	+	0.0283644i
$889$	48.7923	+	10.3384i	1.63644	+	0.346740i
$890$	−0.175242	−	0.0843921i	−0.00587413	−	0.00282883i
$891$	7.32667	+	9.18736i	0.245453	+	0.307788i
$892$	−16.5392	+	7.96487i	−0.553774	+	0.266684i
$893$	−18.5381	+	23.2460i	−0.620354	+	0.777899i
$894$	−1.06199	+	4.65286i	−0.0355181	+	0.155615i
$895$	0.932172	−	1.16891i	0.0311591	−	0.0390722i
$896$	0.240416	+	15.4090i	0.00803174	+	0.514780i
$897$	3.10426	+	3.89262i	0.103648	+	0.129971i
$898$	2.29898	−	1.10713i	0.0767180	−	0.0369455i
$899$	−4.82123	+	21.1232i	−0.160797	+	0.704497i
$900$	−14.2114			−0.473713
$901$	−2.68170			−0.0893404
$902$	0.0464033	−	0.203306i	0.00154506	−	0.00676935i
$903$	0.569011	+	36.4697i	0.0189355	+	1.21364i
$904$	1.30695	+	5.72612i	0.0434685	+	0.190448i
$905$	−0.423672	−	1.85623i	−0.0140833	−	0.0617031i
$906$	−1.51507	−	1.89984i	−0.0503349	−	0.0631180i
$907$	−0.335402	−	0.420581i	−0.0111369	−	0.0139652i	0.776232	−	0.630448i	$-0.217129\pi$
$907$	−0.335402	−	0.420581i	−0.0111369	−	0.0139652i	−0.787369	+	0.616482i	$0.788557\pi$
$908$	−10.9065	−	47.7843i	−0.361944	−	1.58578i
$909$	0.411311	+	1.80207i	0.0136423	+	0.0597710i
$910$	−0.0854147	−	0.0180982i	−0.00283147	−	0.000599951i
$911$	−8.76495	+	38.4017i	−0.290396	+	1.27231i	0.593580	+	0.804775i	$0.297714\pi$
$911$	−8.76495	+	38.4017i	−0.290396	+	1.27231i	−0.883976	+	0.467532i	$0.845143\pi$
$912$	−13.7564			−0.455519
$913$	−65.9213			−2.18168
$914$	0.423218	−	1.85424i	0.0139988	−	0.0613328i
$915$	0.235055	−	0.113196i	0.00777067	−	0.00374216i
$916$	32.4020	+	40.6308i	1.07059	+	1.34248i
$917$	5.14118	+	10.2631i	0.169777	+	0.338916i
$918$	−0.148788	+	0.186575i	−0.00491075	+	0.00615788i
$919$	−4.48316	+	19.6420i	−0.147886	+	0.647931i	0.845585	+	0.533841i	$0.179252\pi$
$919$	−4.48316	+	19.6420i	−0.147886	+	0.647931i	−0.993471	+	0.114089i	$0.963605\pi$
$920$	0.326795	−	0.409788i	0.0107741	−	0.0135103i
$921$	−32.3443	+	15.5762i	−1.06578	+	0.513253i
$922$	−4.06206	−	5.09366i	−0.133777	−	0.167751i
$923$	−3.61201	−	1.73945i	−0.118891	−	0.0572548i
$924$	23.3212	−	19.2008i	0.767211	−	0.631660i
$925$	−9.29370	+	4.47561i	−0.305575	+	0.147157i
$926$	−4.17809	−	2.01206i	−0.137300	−	0.0661204i
$927$	3.35441	+	14.6966i	0.110173	+	0.482701i
$928$	5.81538	+	2.80054i	0.190899	+	0.0919322i
$929$	17.2956	−	21.6880i	0.567449	−	0.711559i	−0.412466	−	0.910973i	$-0.635332\pi$
$929$	17.2956	−	21.6880i	0.567449	−	0.711559i	0.979915	+	0.199414i	$0.0639039\pi$
$930$	−0.307192			−0.0100732
$931$	−20.4742	+	0.639045i	−0.671016	+	0.0209439i
$932$	36.2308			1.18678
$933$	13.5583	−	17.0015i	0.443878	−	0.556605i
$934$	5.91835	+	2.85013i	0.193654	+	0.0932590i
$935$	−0.0407761	−	0.178652i	−0.00133352	−	0.00584253i
$936$	0.991063	+	0.477271i	0.0323939	+	0.0156001i
$937$	−48.2425	+	23.2324i	−1.57601	+	0.758968i	−0.998356	−	0.0573115i	$-0.981747\pi$
$937$	−48.2425	+	23.2324i	−1.57601	+	0.758968i	−0.577657	+	0.816280i	$0.696033\pi$
$938$	−2.44299	−	1.88663i	−0.0797665	−	0.0616007i
$939$	−20.3861	−	9.81742i	−0.665275	−	0.320379i
$940$	−2.15402	−	2.70105i	−0.0702563	−	0.0880986i
$941$	−49.0827	+	23.6370i	−1.60005	+	0.770544i	−0.999577	−	0.0290990i	$-0.990736\pi$
$941$	−49.0827	+	23.6370i	−1.60005	+	0.770544i	−0.600475	+	0.799643i	$0.705022\pi$
$942$	−1.53618	+	1.92630i	−0.0500513	+	0.0627624i
$943$	−0.208490	+	0.913453i	−0.00678936	+	0.0297461i
$944$	−8.43661	+	10.5792i	−0.274588	+	0.344323i
$945$	2.48147	+	0.525791i	0.0807224	+	0.0171040i
$946$	−6.16958	−	7.73641i	−0.200590	−	0.251532i
$947$	−11.8523	+	5.70778i	−0.385149	+	0.185478i	−0.616431	−	0.787409i	$-0.711422\pi$
$947$	−11.8523	+	5.70778i	−0.385149	+	0.185478i	0.231282	+	0.972887i	$0.425708\pi$
$948$	−4.67194	+	20.4691i	−0.151738	+	0.664806i
$949$	3.75398			0.121859
$950$	2.77181			0.0899295
$951$	0.340422	−	1.49149i	0.0110389	−	0.0483647i
$952$	0.357730	+	0.276261i	0.0115941	+	0.00895368i
$953$	6.80152	+	29.7994i	0.220323	+	0.965297i	0.957236	+	0.289310i	$0.0934257\pi$
$953$	6.80152	+	29.7994i	0.220323	+	0.965297i	−0.736913	+	0.675988i	$0.763717\pi$
$954$	0.732287	+	3.20836i	0.0237087	+	0.103875i
$955$	−0.637361	−	0.799226i	−0.0206245	−	0.0258623i
$956$	7.06378	+	8.85770i	0.228459	+	0.286479i
$957$	−3.74178	−	16.3938i	−0.120955	−	0.529936i
$958$	−0.783235	−	3.43158i	−0.0253052	−	0.110869i
$959$	22.0984	+	44.1138i	0.713595	+	1.42451i
$960$	0.341895	−	1.49794i	0.0110346	−	0.0483457i
$961$	25.1275			0.810565
$962$	0.395554			0.0127532
$963$	−1.52422	+	6.67804i	−0.0491173	+	0.215197i
$964$	−5.87915	+	2.83125i	−0.189355	+	0.0911884i
$965$	−0.450042	−	0.564334i	−0.0144874	−	0.0181666i
$966$	1.93814	−	1.59571i	0.0623587	−	0.0513412i
$967$	7.09232	−	8.89349i	0.228074	−	0.285995i	−0.654606	−	0.755970i	$-0.727166\pi$
$967$	7.09232	−	8.89349i	0.228074	−	0.285995i	0.882680	+	0.469975i	$0.155737\pi$
$968$	−1.83197	+	8.02641i	−0.0588819	+	0.257978i
$969$	−0.512678	+	0.642878i	−0.0164696	+	0.0206522i
$970$	−0.229777	+	0.110655i	−0.00737769	+	0.00355291i
$971$	−37.0304	−	46.4347i	−1.18836	−	1.49016i	−0.831070	−	0.556168i	$-0.812271\pi$
$971$	−37.0304	−	46.4347i	−1.18836	−	1.49016i	−0.357293	−	0.933992i	$-0.616300\pi$
$972$	−23.8674	−	11.4939i	−0.765547	−	0.368668i
$973$	12.4956	−	27.0176i	0.400589	−	0.866144i
$974$	5.62335	−	2.70806i	0.180184	−	0.0867719i
$975$	−5.56377	−	2.67937i	−0.178183	−	0.0858086i
$976$	1.02088	+	4.47276i	0.0326775	+	0.143170i
$977$	22.5674	+	10.8679i	0.721995	+	0.347695i	0.758530	−	0.651638i	$-0.225918\pi$
$977$	22.5674	+	10.8679i	0.721995	+	0.347695i	−0.0365351	+	0.999332i	$0.511632\pi$
$978$	−0.740877	+	0.929031i	−0.0236906	+	0.0297071i
$979$	−27.5813			−0.881504
$980$	0.456983	−	2.33586i	0.0145978	−	0.0746164i
$981$	23.9880			0.765878
$982$	0.856309	−	1.07378i	0.0273259	−	0.0342656i
$983$	37.3990	+	18.0104i	1.19284	+	0.574443i	0.921628	−	0.388075i	$-0.126860\pi$
$983$	37.3990	+	18.0104i	1.19284	+	0.574443i	0.271216	+	0.962519i	$0.412574\pi$
$984$	−0.0488362	−	0.213965i	−0.00155684	−	0.00682096i
$985$	0.330916	+	0.159361i	0.0105439	+	0.00507766i
$986$	0.112302	−	0.0540816i	0.00357641	−	0.00172231i
$987$	−14.9600	−	29.8639i	−0.476184	−	0.950578i
$988$	5.17728	+	2.49324i	0.164711	+	0.0793207i
$989$	27.7199	+	34.7596i	0.881441	+	1.10529i
$990$	−0.202602	+	0.0975682i	−0.00643913	+	0.00310092i
$991$	8.74717	−	10.9686i	0.277863	−	0.348429i	−0.623243	−	0.782028i	$-0.714185\pi$
$991$	8.74717	−	10.9686i	0.277863	−	0.348429i	0.901106	+	0.433599i	$0.142757\pi$
$992$	3.72073	−	16.3016i	0.118133	−	0.517576i
$993$	9.31613	−	11.6821i	0.295638	−	0.370719i
$994$	−0.848575	+	1.83477i	−0.0269152	+	0.0581953i
$995$	2.48498	+	3.11607i	0.0787793	+	0.0987861i
$996$	−30.9671	+	14.9130i	−0.981231	+	0.472536i
$997$	−0.538245	+	2.35821i	−0.0170464	+	0.0746852i	−0.982736	−	0.185015i	$-0.940767\pi$
$997$	−0.538245	+	2.35821i	−0.0170464	+	0.0746852i	0.965689	+	0.259700i	$0.0836238\pi$
$998$	2.75003			0.0870508
$999$	−11.4917			−0.363580

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.w.b.92.14	✓	174
49.8	even	7	inner	637.2.w.b.547.14	yes	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.w.b.92.14	✓	174	1.1	even	1	trivial
637.2.w.b.547.14	yes	174	49.8	even	7	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.w (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.118827 + 0.149004i) q^{2} +(1.11947 + 0.539107i) q^{3} +(0.436959 + 1.91444i) q^{4} +(0.156007 + 0.0751292i) q^{5} +(-0.213352 + 0.102745i) q^{6} +(0.0412747 + 2.64543i) q^{7} +(-0.680602 - 0.327760i) q^{8} +(-0.907899 - 1.13847i) q^{9} +O(q^{10})\)	\(q+(-0.118827 + 0.149004i) q^{2} +(1.11947 + 0.539107i) q^{3} +(0.436959 + 1.91444i) q^{4} +(0.156007 + 0.0751292i) q^{5} +(-0.213352 + 0.102745i) q^{6} +(0.0412747 + 2.64543i) q^{7} +(-0.680602 - 0.327760i) q^{8} +(-0.907899 - 1.13847i) q^{9} +(-0.0297324 + 0.0143184i) q^{10} +(-2.91767 + 3.65864i) q^{11} +(-0.542929 + 2.37873i) q^{12} +(0.623490 - 0.781831i) q^{13} +(-0.399084 - 0.308198i) q^{14} +(0.134142 + 0.168209i) q^{15} +(-3.40871 + 1.64155i) q^{16} +(-0.0503226 + 0.220478i) q^{17} +0.277519 q^{18} +2.92632 q^{19} +(-0.0756617 + 0.331496i) q^{20} +(-1.37996 + 2.98372i) q^{21} +(-0.198455 - 0.869489i) q^{22} +(0.891659 + 3.90661i) q^{23} +(-0.585213 - 0.733834i) q^{24} +(-3.09876 - 3.88572i) q^{25} +(0.0424088 + 0.185805i) q^{26} +(-1.23206 - 5.39802i) q^{27} +(-5.04649 + 1.23496i) q^{28} +(-0.643531 + 2.81949i) q^{29} -0.0410036 q^{30} +7.49183 q^{31} +(0.496638 - 2.17591i) q^{32} +(-5.23864 + 2.52279i) q^{33} +(-0.0268724 - 0.0336969i) q^{34} +(-0.192310 + 0.415807i) q^{35} +(1.78282 - 2.23559i) q^{36} +(0.461841 - 2.02346i) q^{37} +(-0.347725 + 0.436033i) q^{38} +(1.11947 - 0.539107i) q^{39} +(-0.0815545 - 0.102266i) q^{40} +(0.210667 + 0.101452i) q^{41} +(-0.280610 - 0.560166i) q^{42} +(9.99641 - 4.81402i) q^{43} +(-8.27917 - 3.98704i) q^{44} +(-0.0561066 - 0.245819i) q^{45} +(-0.688054 - 0.331349i) q^{46} +(-6.33496 + 7.94379i) q^{47} -4.70092 q^{48} +(-6.99659 + 0.218379i) q^{49} +0.947202 q^{50} +(-0.175196 + 0.219688i) q^{51} +(1.76921 + 0.852008i) q^{52} +(2.63869 + 11.5609i) q^{53} +(0.950729 + 0.457847i) q^{54} +(-0.730049 + 0.351573i) q^{55} +(0.838976 - 1.81401i) q^{56} +(3.27592 + 1.57760i) q^{57} +(-0.343647 - 0.430920i) q^{58} +(3.22231 - 1.55178i) q^{59} +(-0.263413 + 0.330309i) q^{60} +(0.269832 - 1.18221i) q^{61} +(-0.890230 + 1.11631i) q^{62} +(2.97427 - 2.44877i) q^{63} +(-4.45260 - 5.58338i) q^{64} +(0.156007 - 0.0751292i) q^{65} +(0.246584 - 1.08035i) q^{66} +6.12150 q^{67} -0.444082 q^{68} +(-1.10790 + 4.85402i) q^{69} +(-0.0391054 - 0.0780640i) q^{70} +(-0.892093 - 3.90852i) q^{71} +(0.244772 + 1.07242i) q^{72} +(2.34057 + 2.93498i) q^{73} +(0.246624 + 0.309257i) q^{74} +(-1.37414 - 6.02049i) q^{75} +(1.27868 + 5.60227i) q^{76} +(-9.79911 - 7.56748i) q^{77} +(-0.0526935 + 0.230865i) q^{78} +8.60507 q^{79} -0.655113 q^{80} +(0.558781 - 2.44818i) q^{81} +(-0.0401495 + 0.0193350i) q^{82} +(8.78311 + 11.0137i) q^{83} +(-6.31516 - 1.33810i) q^{84} +(-0.0244150 + 0.0306155i) q^{85} +(-0.470533 + 2.06154i) q^{86} +(-2.24042 + 2.80940i) q^{87} +(3.18493 - 1.53378i) q^{88} +(3.67484 + 4.60810i) q^{89} +(0.0432950 + 0.0208498i) q^{90} +(2.09401 + 1.61713i) q^{91} +(-7.08937 + 3.41406i) q^{92} +(8.38686 + 4.03890i) q^{93} +(-0.430894 - 1.88787i) q^{94} +(0.456527 + 0.219852i) q^{95} +(1.72902 - 2.16812i) q^{96} +7.72816 q^{97} +(0.798843 - 1.06847i) q^{98} +6.81420 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9}+O(q^{10}) \) 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9	\( 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9} - 10 q^{10} - 5 q^{11} + 25 q^{12} - 29 q^{13} + 15 q^{14} - 10 q^{15} - 51 q^{16} - 9 q^{17} + 44 q^{18} + 24 q^{19} + 63 q^{20} - 28 q^{21} - 8 q^{22} - 13 q^{23} - 48 q^{24} - 49 q^{25} - 3 q^{26} - 9 q^{27} - 44 q^{28} + 2 q^{29} - 22 q^{30} + 10 q^{31} + 24 q^{32} - 26 q^{33} + 118 q^{34} + 5 q^{35} - 55 q^{36} - 32 q^{37} + 16 q^{38} + 42 q^{40} - 14 q^{41} + 4 q^{42} - 50 q^{43} + 35 q^{44} - q^{45} + 4 q^{46} - 24 q^{47} - 116 q^{48} - 25 q^{49} + 156 q^{50} + 12 q^{51} - 31 q^{52} - 30 q^{53} - 78 q^{54} + 25 q^{55} + 3 q^{56} - 63 q^{57} - 12 q^{58} - 4 q^{59} + 128 q^{60} - 42 q^{61} - 38 q^{62} - 85 q^{63} - 105 q^{64} - 4 q^{65} + 15 q^{66} + 94 q^{67} + 214 q^{68} + 32 q^{69} - 57 q^{70} - 29 q^{71} - 64 q^{72} - 66 q^{73} - 90 q^{74} + 131 q^{75} - 21 q^{76} - 82 q^{77} + 19 q^{78} + 6 q^{79} + 22 q^{80} + 49 q^{81} - 50 q^{82} + 25 q^{83} + 89 q^{84} - 86 q^{85} - 28 q^{86} + 24 q^{87} + 48 q^{88} - 50 q^{89} - 155 q^{90} - 5 q^{91} - 98 q^{92} + 89 q^{93} - 28 q^{94} - 130 q^{95} - 105 q^{96} - 42 q^{97} + 195 q^{98} + 438 q^{99}+O(q^{100}) \) 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9 - 10 * q^10 - 5 * q^11 + 25 * q^12 - 29 * q^13 + 15 * q^14 - 10 * q^15 - 51 * q^16 - 9 * q^17 + 44 * q^18 + 24 * q^19 + 63 * q^20 - 28 * q^21 - 8 * q^22 - 13 * q^23 - 48 * q^24 - 49 * q^25 - 3 * q^26 - 9 * q^27 - 44 * q^28 + 2 * q^29 - 22 * q^30 + 10 * q^31 + 24 * q^32 - 26 * q^33 + 118 * q^34 + 5 * q^35 - 55 * q^36 - 32 * q^37 + 16 * q^38 + 42 * q^40 - 14 * q^41 + 4 * q^42 - 50 * q^43 + 35 * q^44 - q^45 + 4 * q^46 - 24 * q^47 - 116 * q^48 - 25 * q^49 + 156 * q^50 + 12 * q^51 - 31 * q^52 - 30 * q^53 - 78 * q^54 + 25 * q^55 + 3 * q^56 - 63 * q^57 - 12 * q^58 - 4 * q^59 + 128 * q^60 - 42 * q^61 - 38 * q^62 - 85 * q^63 - 105 * q^64 - 4 * q^65 + 15 * q^66 + 94 * q^67 + 214 * q^68 + 32 * q^69 - 57 * q^70 - 29 * q^71 - 64 * q^72 - 66 * q^73 - 90 * q^74 + 131 * q^75 - 21 * q^76 - 82 * q^77 + 19 * q^78 + 6 * q^79 + 22 * q^80 + 49 * q^81 - 50 * q^82 + 25 * q^83 + 89 * q^84 - 86 * q^85 - 28 * q^86 + 24 * q^87 + 48 * q^88 - 50 * q^89 - 155 * q^90 - 5 * q^91 - 98 * q^92 + 89 * q^93 - 28 * q^94 - 130 * q^95 - 105 * q^96 - 42 * q^97 + 195 * q^98 + 438 * q^99

Introduction

L-functions

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