LMFDB - Embedded newform 670.2.k.b.131.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("670.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.k (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			131.1
Character	$\chi$	$=$	670.131
Dual form			670.2.k.b.491.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(-0.325974 + 2.26720i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.951514 - 2.08352i) q^{6} +(3.43296 + 1.00801i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-2.15545 - 0.632899i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.325974 + 2.26720i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.951514 - 2.08352i) q^{6} +(3.43296 + 1.00801i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-2.15545 - 0.632899i) q^{9} +(0.142315 + 0.989821i) q^{10} +(-0.744365 - 1.62993i) q^{11} +(-1.49997 + 1.73105i) q^{12} +(4.18624 - 4.83118i) q^{13} +(-3.00991 - 1.93435i) q^{14} +(2.19773 - 0.645312i) q^{15} +(0.415415 + 0.909632i) q^{16} +(1.85294 - 1.19081i) q^{17} +(1.88984 + 1.21452i) q^{18} +(4.61455 - 1.35495i) q^{19} +(0.142315 - 0.989821i) q^{20} +(-3.40441 + 7.45463i) q^{21} +(0.255008 + 1.77362i) q^{22} +(0.588567 - 4.09358i) q^{23} +(1.92690 - 1.23835i) q^{24} +(-0.654861 + 0.755750i) q^{25} +(-5.37776 + 3.45608i) q^{26} +(-0.717011 + 1.57004i) q^{27} +(2.34302 + 2.70399i) q^{28} -1.95555 q^{29} -2.29051 q^{30} +(0.179027 + 0.206608i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(3.93803 - 1.15631i) q^{33} +(-2.11337 + 0.620541i) q^{34} +(-0.509187 - 3.54147i) q^{35} +(-1.47111 - 1.69776i) q^{36} -3.50693 q^{37} -4.80936 q^{38} +(9.58863 + 11.0659i) q^{39} +(-0.415415 + 0.909632i) q^{40} +(-6.73507 + 4.32836i) q^{41} +(5.36672 - 6.19353i) q^{42} +(8.62684 - 5.54413i) q^{43} +(0.255008 - 1.77362i) q^{44} +(0.319703 + 2.22359i) q^{45} +(-1.71802 + 3.76194i) q^{46} +(-0.409428 + 2.84763i) q^{47} +(-2.19773 + 0.645312i) q^{48} +(4.88038 + 3.13643i) q^{49} +(0.841254 - 0.540641i) q^{50} +(2.09579 + 4.58915i) q^{51} +(6.13362 - 1.80099i) q^{52} +(2.78499 + 1.78981i) q^{53} +(1.13030 - 1.30443i) q^{54} +(-1.17342 + 1.35420i) q^{55} +(-1.48631 - 3.25457i) q^{56} +(1.56773 + 10.9038i) q^{57} +(1.87633 + 0.550941i) q^{58} +(7.23604 + 8.35084i) q^{59} +(2.19773 + 0.645312i) q^{60} +(-3.26701 + 7.15376i) q^{61} +(-0.113567 - 0.248676i) q^{62} +(-6.76163 - 4.34543i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-6.13362 - 1.80099i) q^{65} -4.10428 q^{66} +(6.37098 - 5.13912i) q^{67} +2.20259 q^{68} +(9.08909 + 2.66880i) q^{69} +(-0.509187 + 3.54147i) q^{70} +(9.21563 + 5.92253i) q^{71} +(0.933210 + 2.04344i) q^{72} +(-3.40684 + 7.45993i) q^{73} +(3.36487 + 0.988015i) q^{74} +(-1.49997 - 1.73105i) q^{75} +(4.61455 + 1.35495i) q^{76} +(-0.912392 - 6.34583i) q^{77} +(-6.08261 - 13.3191i) q^{78} +(-10.6653 + 12.3084i) q^{79} +(0.654861 - 0.755750i) q^{80} +(-8.99536 - 5.78097i) q^{81} +(7.68169 - 2.25555i) q^{82} +(-4.64025 - 10.1607i) q^{83} +(-6.89425 + 4.43067i) q^{84} +(-1.85294 - 1.19081i) q^{85} +(-9.83936 + 2.88910i) q^{86} +(0.637457 - 4.43361i) q^{87} +(-0.744365 + 1.62993i) q^{88} +(-0.454759 - 3.16292i) q^{89} +(0.319703 - 2.22359i) q^{90} +(19.2411 - 12.3655i) q^{91} +(2.70829 - 3.12553i) q^{92} +(-0.526779 + 0.338540i) q^{93} +(1.19511 - 2.61693i) q^{94} +(-3.14946 - 3.63467i) q^{95} +2.29051 q^{96} +5.62635 q^{97} +(-3.79905 - 4.38434i) q^{98} +(0.572864 + 3.98436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{2} + 2 q^{3} - 5 q^{4} + 5 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9}+O(q^{10}) $ 50 * q - 5 * q^2 + 2 * q^3 - 5 * q^4 + 5 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9	\( 50 q - 5 q^{2} + 2 q^{3} - 5 q^{4} + 5 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9} + 5 q^{10} + 30 q^{11} - 9 q^{12} + 20 q^{13} - 21 q^{14} - 2 q^{15} - 5 q^{16} + 2 q^{17} - q^{18} + 4 q^{19} + 5 q^{20} + 23 q^{21} - 3 q^{22} - 5 q^{23} + 2 q^{24} - 5 q^{25} - 2 q^{26} + 2 q^{27} - 10 q^{28} + 26 q^{29} - 2 q^{30} + 3 q^{31} - 5 q^{32} + 38 q^{33} + 2 q^{34} - 12 q^{35} - q^{36} + 22 q^{37} - 40 q^{38} - 35 q^{39} + 5 q^{40} - 18 q^{41} - 10 q^{42} + 87 q^{43} - 3 q^{44} + 12 q^{45} + 17 q^{46} + 35 q^{47} + 2 q^{48} + 60 q^{49} - 5 q^{50} + 19 q^{51} - 24 q^{52} - 9 q^{53} + 2 q^{54} + 25 q^{55} + 12 q^{56} + 64 q^{57} + 4 q^{58} - 49 q^{59} - 2 q^{60} - 47 q^{61} - 19 q^{62} - 24 q^{63} - 5 q^{64} + 24 q^{65} - 6 q^{66} - 21 q^{67} + 2 q^{68} - 25 q^{69} - 12 q^{70} + 92 q^{71} - q^{72} + 18 q^{73} - 22 q^{74} - 9 q^{75} + 4 q^{76} - 65 q^{77} + 31 q^{78} - 58 q^{79} + 5 q^{80} - 77 q^{81} - 18 q^{82} - 49 q^{83} - 54 q^{84} - 2 q^{85} - q^{86} - 147 q^{87} + 30 q^{88} - 21 q^{89} + 12 q^{90} + 62 q^{91} + 6 q^{92} - 34 q^{93} - 9 q^{94} + 7 q^{95} + 2 q^{96} + 98 q^{97} - 39 q^{98} - 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 + 2 * q^3 - 5 * q^4 + 5 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9 + 5 * q^10 + 30 * q^11 - 9 * q^12 + 20 * q^13 - 21 * q^14 - 2 * q^15 - 5 * q^16 + 2 * q^17 - q^18 + 4 * q^19 + 5 * q^20 + 23 * q^21 - 3 * q^22 - 5 * q^23 + 2 * q^24 - 5 * q^25 - 2 * q^26 + 2 * q^27 - 10 * q^28 + 26 * q^29 - 2 * q^30 + 3 * q^31 - 5 * q^32 + 38 * q^33 + 2 * q^34 - 12 * q^35 - q^36 + 22 * q^37 - 40 * q^38 - 35 * q^39 + 5 * q^40 - 18 * q^41 - 10 * q^42 + 87 * q^43 - 3 * q^44 + 12 * q^45 + 17 * q^46 + 35 * q^47 + 2 * q^48 + 60 * q^49 - 5 * q^50 + 19 * q^51 - 24 * q^52 - 9 * q^53 + 2 * q^54 + 25 * q^55 + 12 * q^56 + 64 * q^57 + 4 * q^58 - 49 * q^59 - 2 * q^60 - 47 * q^61 - 19 * q^62 - 24 * q^63 - 5 * q^64 + 24 * q^65 - 6 * q^66 - 21 * q^67 + 2 * q^68 - 25 * q^69 - 12 * q^70 + 92 * q^71 - q^72 + 18 * q^73 - 22 * q^74 - 9 * q^75 + 4 * q^76 - 65 * q^77 + 31 * q^78 - 58 * q^79 + 5 * q^80 - 77 * q^81 - 18 * q^82 - 49 * q^83 - 54 * q^84 - 2 * q^85 - q^86 - 147 * q^87 + 30 * q^88 - 21 * q^89 + 12 * q^90 + 62 * q^91 + 6 * q^92 - 34 * q^93 - 9 * q^94 + 7 * q^95 + 2 * q^96 + 98 * q^97 - 39 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$3$	−0.325974	+	2.26720i	−0.188201	+	1.30897i	0.648461	+	0.761248i	$0.275413\pi$
$3$	−0.325974	+	2.26720i	−0.188201	+	1.30897i	−0.836662	+	0.547720i	$0.815496\pi$
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$6$	0.951514	−	2.08352i	0.388454	−	0.850595i
$7$	3.43296	+	1.00801i	1.29754	+	0.380991i	0.856337	−	0.516417i	$-0.172735\pi$
$7$	3.43296	+	1.00801i	1.29754	+	0.380991i	0.441201	+	0.897408i	$0.354553\pi$
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	−2.15545	−	0.632899i	−0.718485	−	0.210966i
$10$	0.142315	+	0.989821i	0.0450039	+	0.313009i
$11$	−0.744365	−	1.62993i	−0.224435	−	0.491443i	0.763597	−	0.645693i	$-0.223431\pi$
$11$	−0.744365	−	1.62993i	−0.224435	−	0.491443i	−0.988032	+	0.154249i	$0.950704\pi$
$12$	−1.49997	+	1.73105i	−0.433003	+	0.499712i
$13$	4.18624	−	4.83118i	1.16105	−	1.33993i	0.230803	−	0.973000i	$-0.425865\pi$
$13$	4.18624	−	4.83118i	1.16105	−	1.33993i	0.930250	−	0.366927i	$-0.119590\pi$
$14$	−3.00991	−	1.93435i	−0.804434	−	0.516978i
$15$	2.19773	−	0.645312i	0.567452	−	0.166619i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	1.85294	−	1.19081i	0.449403	−	0.288814i	−0.296297	−	0.955096i	$-0.595752\pi$
$17$	1.85294	−	1.19081i	0.449403	−	0.288814i	0.745700	+	0.666282i	$0.232115\pi$
$18$	1.88984	+	1.21452i	0.445439	+	0.286266i
$19$	4.61455	−	1.35495i	1.05865	−	0.310848i	0.294343	−	0.955700i	$-0.404899\pi$
$19$	4.61455	−	1.35495i	1.05865	−	0.310848i	0.764307	+	0.644852i	$0.223081\pi$
$20$	0.142315	−	0.989821i	0.0318226	−	0.221331i
$21$	−3.40441	+	7.45463i	−0.742904	+	1.62673i
$22$	0.255008	+	1.77362i	0.0543679	+	0.378137i
$23$	0.588567	−	4.09358i	0.122725	−	0.853569i	−0.831723	−	0.555191i	$-0.812645\pi$
$23$	0.588567	−	4.09358i	0.122725	−	0.853569i	0.954448	−	0.298378i	$-0.0964457\pi$
$24$	1.92690	−	1.23835i	0.393327	−	0.252776i
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	−5.37776	+	3.45608i	−1.05467	+	0.677793i
$27$	−0.717011	+	1.57004i	−0.137989	+	0.302154i
$28$	2.34302	+	2.70399i	0.442789	+	0.511006i
$29$	−1.95555			−0.363136			−0.181568	−	0.983378i	$-0.558117\pi$
$29$	−1.95555			−0.363136			−0.181568	+	0.983378i	$0.558117\pi$
$30$	−2.29051			−0.418189
$31$	0.179027	+	0.206608i	0.0321541	+	0.0371079i	0.771599	−	0.636109i	$-0.219457\pi$
$31$	0.179027	+	0.206608i	0.0321541	+	0.0371079i	−0.739445	+	0.673217i	$0.764912\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$	3.93803	−	1.15631i	0.685523	−	0.201288i
$34$	−2.11337	+	0.620541i	−0.362440	+	0.106422i
$35$	−0.509187	−	3.54147i	−0.0860683	−	0.598618i
$36$	−1.47111	−	1.69776i	−0.245186	−	0.282959i
$37$	−3.50693			−0.576535			−0.288268	−	0.957550i	$-0.593079\pi$
$37$	−3.50693			−0.576535			−0.288268	+	0.957550i	$0.593079\pi$
$38$	−4.80936			−0.780182
$39$	9.58863	+	11.0659i	1.53541	+	1.77196i
$40$	−0.415415	+	0.909632i	−0.0656829	+	0.143825i
$41$	−6.73507	+	4.32836i	−1.05184	+	0.675977i	−0.947888	−	0.318605i	$-0.896786\pi$
$41$	−6.73507	+	4.32836i	−1.05184	+	0.675977i	−0.103953	+	0.994582i	$0.533149\pi$
$42$	5.36672	−	6.19353i	0.828103	−	0.955682i
$43$	8.62684	−	5.54413i	1.31558	−	0.845473i	0.320765	−	0.947159i	$-0.396060\pi$
$43$	8.62684	−	5.54413i	1.31558	−	0.845473i	0.994817	+	0.101686i	$0.0324238\pi$
$44$	0.255008	−	1.77362i	0.0384439	−	0.267383i
$45$	0.319703	+	2.22359i	0.0476586	+	0.331473i
$46$	−1.71802	+	3.76194i	−0.253308	+	0.554668i
$47$	−0.409428	+	2.84763i	−0.0597212	+	0.415370i	0.937927	+	0.346832i	$0.112743\pi$
$47$	−0.409428	+	2.84763i	−0.0597212	+	0.415370i	−0.997649	+	0.0685380i	$0.978167\pi$
$48$	−2.19773	+	0.645312i	−0.317215	+	0.0931428i
$49$	4.88038	+	3.13643i	0.697196	+	0.448061i
$50$	0.841254	−	0.540641i	0.118971	−	0.0764582i
$51$	2.09579	+	4.58915i	0.293470	+	0.642610i
$52$	6.13362	−	1.80099i	0.850580	−	0.249753i
$53$	2.78499	+	1.78981i	0.382548	+	0.245849i	0.717755	−	0.696296i	$-0.245170\pi$
$53$	2.78499	+	1.78981i	0.382548	+	0.245849i	−0.335207	+	0.942145i	$0.608806\pi$
$54$	1.13030	−	1.30443i	0.153814	−	0.177511i
$55$	−1.17342	+	1.35420i	−0.158224	+	0.182600i
$56$	−1.48631	−	3.25457i	−0.198617	−	0.434910i
$57$	1.56773	+	10.9038i	0.207651	+	1.44424i
$58$	1.87633	+	0.550941i	0.246375	+	0.0723421i
$59$	7.23604	+	8.35084i	0.942052	+	1.08719i	0.996063	+	0.0886462i	$0.0282540\pi$
$59$	7.23604	+	8.35084i	0.942052	+	1.08719i	−0.0540107	+	0.998540i	$0.517201\pi$
$60$	2.19773	+	0.645312i	0.283726	+	0.0833094i
$61$	−3.26701	+	7.15376i	−0.418298	+	0.915945i	0.576784	+	0.816896i	$0.304307\pi$
$61$	−3.26701	+	7.15376i	−0.418298	+	0.915945i	−0.995083	+	0.0990488i	$0.968420\pi$
$62$	−0.113567	−	0.248676i	−0.0144230	−	0.0315819i
$63$	−6.76163	−	4.34543i	−0.851885	−	0.547473i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−6.13362	−	1.80099i	−0.760782	−	0.223386i
$66$	−4.10428			−0.505202
$67$	6.37098	−	5.13912i	0.778340	−	0.627843i
$67$	6.37098	−	5.13912i	0.778340	−	0.627843i
$68$	2.20259			0.267103
$69$	9.08909	+	2.66880i	1.09420	+	0.321286i
$70$	−0.509187	+	3.54147i	−0.0608595	+	0.423287i
$71$	9.21563	+	5.92253i	1.09369	+	0.702874i	0.957681	−	0.287833i	$-0.0929347\pi$
$71$	9.21563	+	5.92253i	1.09369	+	0.702874i	0.136013	+	0.990707i	$0.456571\pi$
$72$	0.933210	+	2.04344i	0.109980	+	0.240822i
$73$	−3.40684	+	7.45993i	−0.398740	+	0.873119i	0.598656	+	0.801006i	$0.295702\pi$
$73$	−3.40684	+	7.45993i	−0.398740	+	0.873119i	−0.997396	+	0.0721132i	$0.977026\pi$
$74$	3.36487	+	0.988015i	0.391158	+	0.114854i
$75$	−1.49997	−	1.73105i	−0.173201	−	0.199885i
$76$	4.61455	+	1.35495i	0.529325	+	0.155424i
$77$	−0.912392	−	6.34583i	−0.103977	−	0.723174i
$78$	−6.08261	−	13.3191i	−0.688720	−	1.50809i
$79$	−10.6653	+	12.3084i	−1.19994	+	1.38481i	−0.297091	+	0.954849i	$0.596017\pi$
$79$	−10.6653	+	12.3084i	−1.19994	+	1.38481i	−0.902850	+	0.429957i	$0.858529\pi$
$80$	0.654861	−	0.755750i	0.0732157	−	0.0844954i
$81$	−8.99536	−	5.78097i	−0.999485	−	0.642330i
$82$	7.68169	−	2.25555i	0.848301	−	0.249084i
$83$	−4.64025	−	10.1607i	−0.509333	−	1.11528i	−0.973322	−	0.229443i	$-0.926309\pi$
$83$	−4.64025	−	10.1607i	−0.509333	−	1.11528i	0.463989	−	0.885841i	$-0.346418\pi$
$84$	−6.89425	+	4.43067i	−0.752224	+	0.483425i
$85$	−1.85294	−	1.19081i	−0.200979	−	0.129161i
$86$	−9.83936	+	2.88910i	−1.06101	+	0.311539i
$87$	0.637457	−	4.43361i	0.0683426	−	0.475333i
$88$	−0.744365	+	1.62993i	−0.0793496	+	0.173751i
$89$	−0.454759	−	3.16292i	−0.0482044	−	0.335269i	−0.999625	−	0.0273753i	$-0.991285\pi$
$89$	−0.454759	−	3.16292i	−0.0482044	−	0.335269i	0.951421	−	0.307893i	$-0.0996240\pi$
$90$	0.319703	−	2.22359i	0.0336997	−	0.234387i
$91$	19.2411	−	12.3655i	2.01701	−	1.29625i
$92$	2.70829	−	3.12553i	0.282359	−	0.325859i
$93$	−0.526779	+	0.338540i	−0.0546245	+	0.0351050i
$94$	1.19511	−	2.61693i	0.123267	−	0.269916i
$95$	−3.14946	−	3.63467i	−0.323128	−	0.372910i
$96$	2.29051			0.233775
$97$	5.62635			0.571269			0.285635	−	0.958339i	$-0.407796\pi$
$97$	5.62635			0.571269			0.285635	+	0.958339i	$0.407796\pi$
$98$	−3.79905	−	4.38434i	−0.383762	−	0.442885i
$99$	0.572864	+	3.98436i	0.0575750	+	0.400443i
$100$	−0.959493	+	0.281733i	−0.0959493	+	0.0281733i
$101$	−7.10201	+	2.08534i	−0.706677	+	0.207499i	−0.615272	−	0.788315i	$-0.710954\pi$
$101$	−7.10201	+	2.08534i	−0.706677	+	0.207499i	−0.0914046	+	0.995814i	$0.529136\pi$
$102$	−0.717987	−	4.99371i	−0.0710913	−	0.494451i
$103$	−5.68408	−	6.55978i	−0.560069	−	0.646354i	0.403130	−	0.915143i	$-0.367922\pi$
$103$	−5.68408	−	6.55978i	−0.560069	−	0.646354i	−0.963199	+	0.268788i	$0.913377\pi$
$104$	−6.39256			−0.626842
$105$	8.19521			0.799771
$106$	−2.16793	−	2.50193i	−0.210568	−	0.243009i
$107$	−2.83148	+	6.20007i	−0.273729	+	0.599383i	−0.995710	−	0.0925298i	$-0.970505\pi$
$107$	−2.83148	+	6.20007i	−0.273729	+	0.599383i	0.721981	+	0.691913i	$0.243232\pi$
$108$	−1.45201	+	0.933152i	−0.139720	+	0.0897926i
$109$	4.62113	−	5.33307i	0.442624	−	0.510815i	−0.489972	−	0.871738i	$-0.662993\pi$
$109$	4.62113	−	5.33307i	0.442624	−	0.510815i	0.932596	+	0.360923i	$0.117538\pi$
$110$	1.50741	−	0.968753i	0.143726	−	0.0923669i
$111$	1.14317	−	7.95090i	0.108505	−	0.754666i
$112$	0.509187	+	3.54147i	0.0481137	+	0.334638i
$113$	3.94801	−	8.64494i	0.371398	−	0.813248i	−0.627989	−	0.778223i	$-0.716122\pi$
$113$	3.94801	−	8.64494i	0.371398	−	0.813248i	0.999386	−	0.0350254i	$-0.0111512\pi$
$114$	1.56773	−	10.9038i	0.146831	−	1.02123i
$115$	−3.96815	+	1.16515i	−0.370032	+	0.108651i
$116$	−1.64511	−	1.05725i	−0.152745	−	0.0981630i
$117$	−12.0809	+	7.76392i	−1.11688	+	0.717774i
$118$	−4.59023	−	10.0512i	−0.422565	−	0.925288i
$119$	7.56141	−	2.22023i	0.693153	−	0.203528i
$120$	−1.92690	−	1.23835i	−0.175901	−	0.113045i
$121$	5.10087	−	5.88671i	0.463715	−	0.535156i
$122$	5.15012	−	5.94356i	0.466270	−	0.538105i
$123$	−7.61781	−	16.6807i	−0.686875	−	1.50405i
$124$	0.0389062	+	0.270599i	0.00349388	+	0.0243005i
$125$	0.959493	+	0.281733i	0.0858197	+	0.0251989i
$126$	5.26348	+	6.07439i	0.468908	+	0.541149i
$127$	−18.9552	−	5.56575i	−1.68200	−	0.493881i	−0.705378	−	0.708831i	$-0.749223\pi$
$127$	−18.9552	−	5.56575i	−1.68200	−	0.493881i	−0.976625	+	0.214951i	$0.931041\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$	9.75753	+	21.3660i	0.859103	+	1.88117i
$130$	5.37776	+	3.45608i	0.471661	+	0.303118i
$131$	−0.101414	+	0.705352i	−0.00886060	+	0.0616269i	−0.993772	−	0.111432i	$-0.964456\pi$
$131$	−0.101414	+	0.705352i	−0.00886060	+	0.0616269i	0.984911	+	0.173059i	$0.0553652\pi$
$132$	3.93803	+	1.15631i	0.342761	+	0.100644i
$133$	17.2074			1.49207
$134$	−7.56077	+	3.13604i	−0.653151	+	0.270912i
$135$	1.72601			0.148551
$136$	−2.11337	−	0.620541i	−0.181220	−	0.0532110i
$137$	−2.08346	+	14.4908i	−0.178002	+	1.23803i	0.683377	+	0.730066i	$0.260510\pi$
$137$	−2.08346	+	14.4908i	−0.178002	+	1.23803i	−0.861379	+	0.507963i	$0.830399\pi$
$138$	−7.96903	−	5.12139i	−0.678369	−	0.435961i
$139$	−5.05797	−	11.0754i	−0.429011	−	0.939404i	−0.993486	−	0.113953i	$-0.963649\pi$
$139$	−5.05797	−	11.0754i	−0.429011	−	0.939404i	0.564475	−	0.825450i	$-0.309079\pi$
$140$	1.48631	−	3.25457i	0.125616	−	0.275061i
$141$	−6.32269	−	1.85651i	−0.532466	−	0.156346i
$142$	−7.17376	−	8.27896i	−0.602009	−	0.694755i
$143$	−10.9906	−	3.22713i	−0.919079	−	0.269866i
$144$	−0.319703	−	2.22359i	−0.0266420	−	0.185299i
$145$	0.812363	+	1.77883i	0.0674631	+	0.147724i
$146$	5.37054	−	6.19794i	0.444469	−	0.512945i
$147$	−8.70178	+	10.0424i	−0.717711	+	0.828282i
$148$	−2.95021	−	1.89599i	−0.242506	−	0.155849i
$149$	−15.1716	+	4.45478i	−1.24291	+	0.364950i	−0.836106	−	0.548568i	$-0.815173\pi$
$149$	−15.1716	+	4.45478i	−1.24291	+	0.364950i	−0.406799	+	0.913518i	$0.633355\pi$
$150$	0.951514	+	2.08352i	0.0776908	+	0.170119i
$151$	−9.40510	+	6.04429i	−0.765376	+	0.491877i	−0.864151	−	0.503232i	$-0.832144\pi$
$151$	−9.40510	+	6.04429i	−0.765376	+	0.491877i	0.0987749	+	0.995110i	$0.468508\pi$
$152$	−4.04589	−	2.60014i	−0.328165	−	0.210899i
$153$	−4.74758	+	1.39402i	−0.383819	+	0.112700i
$154$	−0.912392	+	6.34583i	−0.0735226	+	0.511361i
$155$	0.113567	−	0.248676i	0.00912190	−	0.0199742i
$156$	2.08381	+	14.4932i	0.166838	+	1.16039i
$157$	−2.63784	+	18.3466i	−0.210522	+	1.46422i	0.560895	+	0.827887i	$0.310457\pi$
$157$	−2.63784	+	18.3466i	−0.210522	+	1.46422i	−0.771418	+	0.636329i	$0.780452\pi$
$158$	13.7010	−	8.80508i	1.08999	−	0.700495i
$159$	−4.96568	+	5.73070i	−0.393804	+	0.454474i
$160$	−0.841254	+	0.540641i	−0.0665069	+	0.0427414i
$161$	6.14689	−	13.4598i	0.484443	−	1.06078i
$162$	7.00230	+	8.08109i	0.550153	+	0.634910i
$163$	9.11579			0.714004			0.357002	−	0.934104i	$-0.383799\pi$
$163$	9.11579			0.714004			0.357002	+	0.934104i	$0.383799\pi$
$164$	−8.00599			−0.625163
$165$	−2.68773	−	3.10181i	−0.209240	−	0.241475i
$166$	1.58968	+	11.0565i	0.123383	+	0.858147i
$167$	20.3666	−	5.98016i	1.57601	−	0.462759i	0.627267	−	0.778804i	$-0.284173\pi$
$167$	20.3666	−	5.98016i	1.57601	−	0.462759i	0.948744	+	0.316045i	$0.102355\pi$
$168$	7.86325	−	2.30886i	0.606663	−	0.178132i
$169$	−3.96558	−	27.5812i	−0.305045	−	2.12163i
$170$	1.44239	+	1.66461i	0.110626	+	0.127669i
$171$	−10.8040			−0.826203
$172$	10.2547			0.781917
$173$	−0.159763	−	0.184377i	−0.0121466	−	0.0140179i	0.749644	−	0.661842i	$-0.230225\pi$
$173$	−0.159763	−	0.184377i	−0.0121466	−	0.0140179i	−0.761790	+	0.647824i	$0.775679\pi$
$174$	−1.86073	+	4.07443i	−0.141062	+	0.308882i
$175$	−3.00991	+	1.93435i	−0.227528	+	0.146223i
$176$	1.17342	−	1.35420i	0.0884498	−	0.102076i
$177$	−21.2918	+	13.6834i	−1.60039	+	1.02851i
$178$	−0.454759	+	3.16292i	−0.0340856	+	0.237071i
$179$	−1.44074	−	10.0205i	−0.107686	−	0.748970i	−0.970089	−	0.242749i	$-0.921951\pi$
$179$	−1.44074	−	10.0205i	−0.107686	−	0.748970i	0.862404	−	0.506221i	$-0.168958\pi$
$180$	−0.933210	+	2.04344i	−0.0695574	+	0.152309i
$181$	−0.991794	+	6.89808i	−0.0737194	+	0.512730i	0.919186	+	0.393824i	$0.128848\pi$
$181$	−0.991794	+	6.89808i	−0.0737194	+	0.512730i	−0.992905	+	0.118906i	$0.962061\pi$
$182$	−21.9454	+	6.44376i	−1.62670	+	0.477643i
$183$	−15.1540	−	9.73891i	−1.12022	−	0.719921i
$184$	−3.47915	+	2.23591i	−0.256486	+	0.164834i
$185$	1.45683	+	3.19001i	0.107108	+	0.234534i
$186$	0.600819	−	0.176416i	0.0440542	−	0.0129355i
$187$	−3.32020	−	2.13376i	−0.242797	−	0.156036i
$188$	−1.88398	+	2.17423i	−0.137403	+	0.158572i
$189$	−4.04408	+	4.66712i	−0.294164	+	0.339483i
$190$	1.99788	+	4.37475i	0.144942	+	0.317378i
$191$	−2.21356	−	15.3956i	−0.160167	−	1.11399i	−0.898316	−	0.439350i	$-0.855209\pi$
$191$	−2.21356	−	15.3956i	−0.160167	−	1.11399i	0.738149	−	0.674638i	$-0.235700\pi$
$192$	−2.19773	−	0.645312i	−0.158608	−	0.0465714i
$193$	0.287069	+	0.331295i	0.0206637	+	0.0238471i	0.765987	−	0.642856i	$-0.222250\pi$
$193$	0.287069	+	0.331295i	0.0206637	+	0.0238471i	−0.745324	+	0.666703i	$0.767705\pi$
$194$	−5.39844	−	1.58513i	−0.387586	−	0.113805i
$195$	6.08261	−	13.3191i	0.435585	−	0.953797i
$196$	2.40995	+	5.27706i	0.172139	+	0.376933i
$197$	−8.59229	−	5.52193i	−0.612176	−	0.393421i	0.197497	−	0.980304i	$-0.436719\pi$
$197$	−8.59229	−	5.52193i	−0.612176	−	0.393421i	−0.809672	+	0.586882i	$0.800355\pi$
$198$	0.572864	−	3.98436i	0.0407117	−	0.283156i
$199$	−13.1742	−	3.86829i	−0.933894	−	0.274216i	−0.220828	−	0.975313i	$-0.570876\pi$
$199$	−13.1742	−	3.86829i	−0.933894	−	0.274216i	−0.713066	+	0.701097i	$0.752694\pi$
$200$	1.00000			0.0707107
$201$	9.57463	+	16.1195i	0.675343	+	1.13698i
$202$	7.40184			0.520792
$203$	−6.71332	−	1.97121i	−0.471183	−	0.138352i
$204$	−0.717987	+	4.99371i	−0.0502692	+	0.349630i
$205$	6.73507	+	4.32836i	0.470397	+	0.302306i
$206$	3.60573	+	7.89545i	0.251223	+	0.550102i
$207$	−3.85945	+	8.45101i	−0.268250	+	0.587386i
$208$	6.13362	+	1.80099i	0.425290	+	0.124876i
$209$	−5.64340	−	6.51283i	−0.390362	−	0.450502i
$210$	−7.86325	−	2.30886i	−0.542616	−	0.159326i
$211$	1.74210	+	12.1166i	0.119931	+	0.834141i	0.957629	+	0.288006i	$0.0929923\pi$
$211$	1.74210	+	12.1166i	0.119931	+	0.834141i	−0.837697	+	0.546135i	$0.816099\pi$
$212$	1.37524	+	3.01136i	0.0944521	+	0.206821i
$213$	−16.4316	+	18.9631i	−1.12587	+	1.29933i
$214$	4.46354	−	5.15121i	0.305122	−	0.352129i
$215$	−8.62684	−	5.54413i	−0.588346	−	0.378107i
$216$	1.65610	−	0.486274i	0.112683	−	0.0330867i
$217$	0.406330	+	0.889738i	0.0275834	+	0.0603993i
$218$	−5.93644	+	3.81512i	−0.402067	+	0.258392i
$219$	−15.8026	−	10.1557i	−1.06784	−	0.686260i
$220$	−1.71928	+	0.504825i	−0.115914	+	0.0340353i
$221$	2.00382	−	13.9369i	0.134792	−	0.937496i
$222$	−3.33689	+	7.30677i	−0.223957	+	0.490398i
$223$	1.18437	+	8.23746i	0.0793112	+	0.551621i	0.990274	+	0.139132i	$0.0444314\pi$
$223$	1.18437	+	8.23746i	0.0793112	+	0.551621i	−0.910963	+	0.412489i	$0.864660\pi$
$224$	0.509187	−	3.54147i	0.0340215	−	0.236625i
$225$	1.88984	−	1.21452i	0.125989	−	0.0809682i
$226$	−6.22365	+	7.18248i	−0.413991	+	0.477771i
$227$	8.69352	−	5.58699i	0.577009	−	0.370821i	−0.219349	−	0.975646i	$-0.570393\pi$
$227$	8.69352	−	5.58699i	0.577009	−	0.370821i	0.796358	+	0.604825i	$0.206757\pi$
$228$	−4.57617	+	10.0204i	−0.303065	+	0.663619i
$229$	3.68498	+	4.25269i	0.243510	+	0.281026i	0.864327	−	0.502930i	$-0.167745\pi$
$229$	3.68498	+	4.25269i	0.243510	+	0.281026i	−0.620817	+	0.783955i	$0.713199\pi$
$230$	4.13567			0.272698
$231$	14.6847			0.966180
$232$	1.28061	+	1.47790i	0.0840762	+	0.0970291i
$233$	0.351860	+	2.44724i	0.0230511	+	0.160324i	0.998096	−	0.0616854i	$-0.0196475\pi$
$233$	0.351860	+	2.44724i	0.0230511	+	0.160324i	−0.975045	+	0.222009i	$0.928738\pi$
$234$	13.7789	−	4.04584i	0.900753	−	0.264485i
$235$	2.76038	−	0.810521i	0.180067	−	0.0528725i
$236$	1.57254	+	10.9373i	0.102364	+	0.711956i
$237$	−24.4290	−	28.1926i	−1.58684	−	1.83131i
$238$	−7.88063			−0.510825
$239$	−12.4270			−0.803838			−0.401919	−	0.915675i	$-0.631657\pi$
$239$	−12.4270			−0.803838			−0.401919	+	0.915675i	$0.631657\pi$
$240$	1.49997	+	1.73105i	0.0968225	+	0.111739i
$241$	−6.57362	+	14.3942i	−0.423444	+	0.927213i	0.570901	+	0.821019i	$0.306594\pi$
$241$	−6.57362	+	14.3942i	−0.423444	+	0.927213i	−0.994345	+	0.106195i	$0.966133\pi$
$242$	−6.55272	+	4.21118i	−0.421225	+	0.270705i
$243$	12.6480	−	14.5965i	0.811368	−	0.936368i
$244$	−6.61600	+	4.25185i	−0.423546	+	0.272197i
$245$	0.825613	−	5.74226i	0.0527465	−	0.366860i
$246$	2.60974	+	18.1512i	0.166391	+	1.15728i
$247$	12.7716	−	27.9659i	0.812636	−	1.77943i
$248$	0.0389062	−	0.270599i	0.00247055	−	0.0171830i
$249$	24.5490	−	7.20823i	1.55573	−	0.456803i
$250$	−0.841254	−	0.540641i	−0.0532055	−	0.0341931i
$251$	25.2980	−	16.2580i	1.59680	−	1.02620i	0.628041	−	0.778180i	$-0.283857\pi$
$251$	25.2980	−	16.2580i	1.59680	−	1.02620i	0.968755	−	0.248019i	$-0.0797794\pi$
$252$	−3.33892	−	7.31122i	−0.210332	−	0.460564i
$253$	−7.11036	+	2.08779i	−0.447025	+	0.131258i
$254$	16.6193	+	10.6806i	1.04279	+	0.670160i
$255$	3.30381	−	3.81280i	0.206893	−	0.238767i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	8.32313	+	18.2251i	0.519183	+	1.13685i	0.969748	+	0.244108i	$0.0784951\pi$
$257$	8.32313	+	18.2251i	0.519183	+	1.13685i	−0.450565	+	0.892743i	$0.648778\pi$
$258$	−3.34278	−	23.2496i	−0.208112	−	1.44745i
$259$	−12.0391	−	3.53501i	−0.748076	−	0.219655i
$260$	−4.18624	−	4.83118i	−0.259619	−	0.299617i
$261$	4.21509	+	1.23766i	0.260908	+	0.0766094i
$262$	0.296027	−	0.648208i	0.0182886	−	0.0400464i
$263$	6.20312	+	13.5829i	0.382501	+	0.837559i	0.998749	+	0.0500074i	$0.0159245\pi$
$263$	6.20312	+	13.5829i	0.382501	+	0.837559i	−0.616248	+	0.787552i	$0.711348\pi$
$264$	−3.45274	−	2.21894i	−0.212501	−	0.136566i
$265$	0.471137	−	3.27683i	0.0289417	−	0.201294i
$266$	−16.5104	−	4.84788i	−1.01232	−	0.297243i
$267$	7.31921			0.447928
$268$	8.13803	−	0.878889i	0.497109	−	0.0536867i
$269$	21.4280			1.30649			0.653244	−	0.757147i	$-0.273408\pi$
$269$	21.4280			1.30649			0.653244	+	0.757147i	$0.273408\pi$
$270$	−1.65610	−	0.486274i	−0.100787	−	0.0295937i
$271$	−2.45929	+	17.1047i	−0.149391	+	1.03904i	0.767828	+	0.640656i	$0.221337\pi$
$271$	−2.45929	+	17.1047i	−0.149391	+	1.03904i	−0.917219	+	0.398382i	$0.869572\pi$
$272$	1.85294	+	1.19081i	0.112351	+	0.0722035i
$273$	21.7629	+	47.6542i	1.31715	+	2.88416i
$274$	6.08158	−	13.3168i	0.367402	−	0.804497i
$275$	1.71928	+	0.504825i	0.103676	+	0.0304421i
$276$	6.20337	+	7.15907i	0.373399	+	0.430925i
$277$	16.1207	+	4.73345i	0.968596	+	0.284406i	0.727509	−	0.686098i	$-0.240678\pi$
$277$	16.1207	+	4.73345i	0.968596	+	0.284406i	0.241087	+	0.970503i	$0.422496\pi$
$278$	1.73278	+	12.0518i	0.103925	+	0.722817i
$279$	−0.255122	−	0.558640i	−0.0152738	−	0.0334449i
$280$	−2.34302	+	2.70399i	−0.140022	+	0.161594i
$281$	−4.72275	+	5.45034i	−0.281736	+	0.325140i	−0.878925	−	0.476960i	$-0.841739\pi$
$281$	−4.72275	+	5.45034i	−0.281736	+	0.325140i	0.597189	+	0.802100i	$0.296284\pi$
$282$	5.54353	+	3.56261i	0.330113	+	0.212151i
$283$	8.53944	−	2.50741i	0.507617	−	0.149050i	−0.0178884	−	0.999840i	$-0.505694\pi$
$283$	8.53944	−	2.50741i	0.507617	−	0.149050i	0.525506	+	0.850790i	$0.323876\pi$
$284$	4.55072	+	9.96469i	0.270036	+	0.591296i
$285$	9.26717	−	5.95565i	0.548940	−	0.352782i
$286$	9.63620	+	6.19281i	0.569800	+	0.366189i
$287$	−27.4843	+	8.07011i	−1.62234	+	0.476363i
$288$	−0.319703	+	2.22359i	−0.0188387	+	0.131026i
$289$	−5.04671	+	11.0508i	−0.296865	+	0.650044i
$290$	−0.278303	−	1.93564i	−0.0163425	−	0.113665i
$291$	−1.83404	+	12.7561i	−0.107514	+	0.747773i
$292$	−6.89916	+	4.43382i	−0.403743	+	0.259470i
$293$	21.7561	−	25.1079i	1.27101	−	1.46682i	0.453111	−	0.891454i	$-0.350314\pi$
$293$	21.7561	−	25.1079i	1.27101	−	1.46682i	0.817896	−	0.575366i	$-0.195140\pi$
$294$	11.1786	−	7.18403i	0.651947	−	0.418981i
$295$	4.59023	−	10.0512i	0.267253	−	0.585203i
$296$	2.29655	+	2.65036i	0.133484	+	0.154049i
$297$	3.09277			0.179461
$298$	15.8121			0.915970
$299$	−17.3129	−	19.9801i	−1.00123	−	1.15548i
$300$	−0.325974	−	2.26720i	−0.0188201	−	0.130897i
$301$	35.2042	−	10.3369i	2.02913	−	0.595808i
$302$	10.7270	−	3.14973i	0.617270	−	0.181247i
$303$	−2.41281	−	16.7814i	−0.138612	−	0.964069i
$304$	3.14946	+	3.63467i	0.180634	+	0.208463i
$305$	7.86446			0.450317
$306$	4.94801			0.282859
$307$	13.7269	+	15.8417i	0.783438	+	0.904136i	0.997353	−	0.0727166i	$-0.0231669\pi$
$307$	13.7269	+	15.8417i	0.783438	+	0.904136i	−0.213915	+	0.976852i	$0.568621\pi$
$308$	2.66326	−	5.83173i	0.151753	−	0.332293i
$309$	16.7252	−	10.7486i	0.951463	−	0.611468i
$310$	−0.179027	+	0.206608i	−0.0101680	+	0.0117345i
$311$	14.8797	−	9.56262i	0.843752	−	0.542247i	−0.0458681	−	0.998948i	$-0.514605\pi$
$311$	14.8797	−	9.56262i	0.843752	−	0.542247i	0.889620	+	0.456701i	$0.150969\pi$
$312$	2.08381	−	14.4932i	0.117972	−	0.820516i
$313$	−1.25201	−	8.70793i	−0.0707678	−	0.492201i	−0.994123	−	0.108255i	$-0.965474\pi$
$313$	−1.25201	−	8.70793i	−0.0707678	−	0.492201i	0.923355	−	0.383946i	$-0.125435\pi$
$314$	7.69981	−	16.8602i	0.434526	−	0.951478i
$315$	−1.14386	+	7.95575i	−0.0644495	+	0.448256i
$316$	−15.6267	+	4.58840i	−0.879069	+	0.258118i
$317$	−7.59768	−	4.88273i	−0.426728	−	0.274242i	0.309599	−	0.950867i	$-0.399805\pi$
$317$	−7.59768	−	4.88273i	−0.426728	−	0.274242i	−0.736327	+	0.676626i	$0.763442\pi$
$318$	6.37906	−	4.09958i	0.357720	−	0.229893i
$319$	1.45564	+	3.18741i	0.0815003	+	0.178461i
$320$	0.959493	−	0.281733i	0.0536373	−	0.0157493i
$321$	−13.1338	−	8.44059i	−0.733058	−	0.471108i
$322$	−9.68996	+	11.1828i	−0.540001	+	0.623194i
$323$	6.93698	−	8.00570i	0.385984	−	0.445449i
$324$	−4.44195	−	9.72652i	−0.246775	−	0.540362i
$325$	0.909756	+	6.32749i	0.0504642	+	0.350986i
$326$	−8.74653	−	2.56821i	−0.484426	−	0.142240i
$327$	10.5848	+	12.2155i	0.585339	+	0.675517i
$328$	7.68169	+	2.25555i	0.424150	+	0.124542i
$329$	−4.27599	+	9.36311i	−0.235743	+	0.516205i
$330$	1.70498	+	3.73338i	0.0938560	+	0.205516i
$331$	−13.4532	−	8.64585i	−0.739455	−	0.475219i	0.115900	−	0.993261i	$-0.463025\pi$
$331$	−13.4532	−	8.64585i	−0.739455	−	0.475219i	−0.855355	+	0.518042i	$0.826661\pi$
$332$	1.58968	−	11.0565i	0.0872449	−	0.606802i
$333$	7.55902	+	2.21953i	0.414232	+	0.121629i
$334$	−21.2264			−1.16146
$335$	−7.32131	−	3.66038i	−0.400006	−	0.199988i
$336$	−8.19521			−0.447085
$337$	15.8787	+	4.66239i	0.864965	+	0.253977i	0.683973	−	0.729508i	$-0.260251\pi$
$337$	15.8787	+	4.66239i	0.864965	+	0.253977i	0.180993	+	0.983484i	$0.442069\pi$
$338$	−3.96558	+	27.5812i	−0.215699	+	1.50022i
$339$	18.3129	+	11.7690i	0.994618	+	0.639202i
$340$	−0.914989	−	2.00355i	−0.0496222	−	0.108658i
$341$	0.203496	−	0.445593i	0.0110199	−	0.0241302i
$342$	10.3664	+	3.04384i	0.560549	+	0.164592i
$343$	−2.80855	−	3.24124i	−0.151647	−	0.175010i
$344$	−9.83936	−	2.88910i	−0.530503	−	0.155770i
$345$	−1.34812	−	9.37639i	−0.0725804	−	0.504808i
$346$	0.101347	+	0.221919i	0.00544844	+	0.0119304i
$347$	−9.78243	+	11.2895i	−0.525148	+	0.606054i	−0.954912	−	0.296888i	$-0.904051\pi$
$347$	−9.78243	+	11.2895i	−0.525148	+	0.606054i	0.429764	+	0.902941i	$0.358597\pi$
$348$	2.93326	−	3.38516i	0.157239	−	0.181464i
$349$	−20.8980	−	13.4303i	−1.11865	−	0.718910i	−0.155486	−	0.987838i	$-0.549694\pi$
$349$	−20.8980	−	13.4303i	−1.11865	−	0.718910i	−0.963160	+	0.268928i	$0.913331\pi$
$350$	3.43296	−	1.00801i	0.183500	−	0.0538803i
$351$	4.58354	+	10.0365i	0.244651	+	0.535711i
$352$	−1.50741	+	0.968753i	−0.0803451	+	0.0516347i
$353$	−29.9373	−	19.2395i	−1.59340	−	1.02402i	−0.970309	−	0.241869i	$-0.922239\pi$
$353$	−29.9373	−	19.2395i	−1.59340	−	1.02402i	−0.623093	−	0.782148i	$-0.714124\pi$
$354$	24.2844	−	7.13053i	1.29070	−	0.378984i
$355$	1.55901	−	10.8431i	0.0827435	−	0.575494i
$356$	1.32744	−	2.90668i	0.0703539	−	0.154054i
$357$	2.56888	+	17.8670i	0.135960	+	0.945620i
$358$	−1.44074	+	10.0205i	−0.0761452	+	0.529602i
$359$	−30.3228	+	19.4873i	−1.60038	+	1.02850i	−0.633335	+	0.773878i	$0.718314\pi$
$359$	−30.3228	+	19.4873i	−1.60038	+	1.02850i	−0.967041	+	0.254621i	$0.918049\pi$
$360$	1.47111	−	1.69776i	0.0775345	−	0.0894796i
$361$	3.47435	−	2.23283i	0.182861	−	0.117517i
$362$	2.89503	−	6.33923i	0.152159	−	0.333183i
$363$	11.6836	+	13.4836i	0.613230	+	0.707705i
$364$	22.8719			1.19881
$365$	8.20105			0.429262
$366$	11.7964	+	13.6138i	0.616609	+	0.711605i
$367$	−0.214364	−	1.49094i	−0.0111897	−	0.0778262i	0.983461	−	0.181118i	$-0.0579716\pi$
$367$	−0.214364	−	1.49094i	−0.0111897	−	0.0778262i	−0.994651	+	0.103292i	$0.967062\pi$
$368$	3.96815	−	1.16515i	0.206854	−	0.0607378i
$369$	17.2565	−	5.06698i	0.898340	−	0.263776i
$370$	−0.499088	−	3.47123i	−0.0259463	−	0.180461i
$371$	7.75664	+	8.95164i	0.402704	+	0.464746i
$372$	−0.626184			−0.0324661
$373$	−0.784527			−0.0406213			−0.0203106	−	0.999794i	$-0.506466\pi$
$373$	−0.784527			−0.0406213			−0.0203106	+	0.999794i	$0.506466\pi$
$374$	2.58456	+	2.98274i	0.133644	+	0.154234i
$375$	−0.951514	+	2.08352i	−0.0491360	+	0.107593i
$376$	2.42021	−	1.55538i	0.124813	−	0.0802125i
$377$	−8.18638	+	9.44759i	−0.421620	+	0.486576i
$378$	5.19515	−	3.33872i	0.267210	−	0.171725i
$379$	−2.02501	+	14.0842i	−0.104018	+	0.723458i	0.869348	+	0.494200i	$0.164539\pi$
$379$	−2.02501	+	14.0842i	−0.104018	+	0.723458i	−0.973366	+	0.229258i	$0.926370\pi$
$380$	−0.684444	−	4.76041i	−0.0351112	−	0.244204i
$381$	18.7976	−	41.1609i	0.963029	−	2.10874i
$382$	−2.21356	+	15.3956i	−0.113255	+	0.787708i
$383$	−35.2029	+	10.3365i	−1.79879	+	0.528171i	−0.997536	−	0.0701577i	$-0.977650\pi$
$383$	−35.2029	+	10.3365i	−1.79879	+	0.528171i	−0.801250	+	0.598329i	$0.795832\pi$
$384$	1.92690	+	1.23835i	0.0983318	+	0.0631940i
$385$	−5.39335	+	3.46609i	−0.274870	+	0.176648i
$386$	−0.182104	−	0.398752i	−0.00926884	−	0.0202959i
$387$	−22.1036	+	6.49022i	−1.12359	+	0.329916i
$388$	4.73319	+	3.04184i	0.240291	+	0.154426i
$389$	−0.259122	+	0.299043i	−0.0131380	+	0.0151621i	−0.762281	−	0.647247i	$-0.775920\pi$
$389$	−0.259122	+	0.299043i	−0.0131380	+	0.0151621i	0.749143	+	0.662409i	$0.230466\pi$
$390$	−9.58863	+	11.0659i	−0.485539	+	0.560342i
$391$	−3.78409	−	8.28601i	−0.191370	−	0.419041i
$392$	−0.825613	−	5.74226i	−0.0416998	−	0.290028i
$393$	−1.56611	−	0.459853i	−0.0790000	−	0.0231965i
$394$	6.68854	+	7.71898i	0.336964	+	0.388877i
$395$	15.6267	+	4.58840i	0.786263	+	0.230868i
$396$	−1.67218	+	3.66157i	−0.0840303	+	0.184001i
$397$	−14.9719	−	32.7840i	−0.751420	−	1.64538i	−0.763797	−	0.645456i	$-0.776667\pi$
$397$	−14.9719	−	32.7840i	−0.751420	−	1.64538i	0.0123776	−	0.999923i	$-0.496060\pi$
$398$	11.5507	+	7.42320i	0.578986	+	0.372091i
$399$	−5.60916	+	39.0126i	−0.280809	+	1.95307i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	−5.96669			−0.297962			−0.148981	−	0.988840i	$-0.547599\pi$
$401$	−5.96669			−0.297962			−0.148981	+	0.988840i	$0.547599\pi$
$402$	−4.64540	−	18.1640i	−0.231692	−	0.905940i
$403$	1.74761			0.0870545
$404$	−7.10201	−	2.08534i	−0.353338	−	0.103749i
$405$	−1.52175	+	10.5840i	−0.0756161	+	0.525922i
$406$	5.88603	+	3.78272i	0.292119	+	0.187733i
$407$	2.61044	+	5.71606i	0.129394	+	0.283334i
$408$	2.09579	−	4.58915i	0.103757	−	0.227197i
$409$	−33.8647	−	9.94356i	−1.67450	−	0.491677i	−0.699639	−	0.714496i	$-0.746656\pi$
$409$	−33.8647	−	9.94356i	−1.67450	−	0.491677i	−0.974860	+	0.222819i	$0.928474\pi$
$410$	−5.24281	−	6.05052i	−0.258924	−	0.298814i
$411$	−32.1743	−	9.44722i	−1.58704	−	0.465997i
$412$	−1.23527	−	8.59148i	−0.0608573	−	0.423272i
$413$	16.4233	+	35.9621i	0.808140	+	1.76958i
$414$	6.08404	−	7.02136i	0.299014	−	0.345081i
$415$	−7.31489	+	8.44183i	−0.359074	+	0.414393i
$416$	−5.37776	−	3.45608i	−0.263667	−	0.169448i
$417$	26.7589	−	7.85713i	1.31039	−	0.384765i
$418$	3.57992	+	7.83894i	0.175100	+	0.383415i
$419$	−29.5062	+	18.9625i	−1.44147	+	0.926379i	−0.441904	+	0.897062i	$0.645697\pi$
$419$	−29.5062	+	18.9625i	−1.44147	+	0.926379i	−0.999570	+	0.0293170i	$0.990667\pi$
$420$	6.89425	+	4.43067i	0.336405	+	0.216194i
$421$	12.3568	−	3.62829i	0.602235	−	0.176832i	0.0336183	−	0.999435i	$-0.489297\pi$
$421$	12.3568	−	3.62829i	0.602235	−	0.176832i	0.568617	+	0.822603i	$0.307479\pi$
$422$	1.74210	−	12.1166i	0.0848043	−	0.589827i
$423$	2.68477	−	5.87882i	0.130538	−	0.285838i
$424$	−0.471137	−	3.27683i	−0.0228804	−	0.159137i
$425$	−0.313461	+	2.18017i	−0.0152051	+	0.105754i
$426$	21.1085	−	13.5656i	1.02271	−	0.657257i
$427$	−18.4266	+	21.2654i	−0.891725	+	1.02911i
$428$	−5.73400	+	3.68502i	−0.277163	+	0.178122i
$429$	10.8992	−	23.8659i	0.526218	−	1.15226i
$430$	6.71543	+	7.75002i	0.323847	+	0.373739i
$431$	21.6764			1.04411			0.522057	−	0.852911i	$-0.325165\pi$
$431$	21.6764			1.04411			0.522057	+	0.852911i	$0.325165\pi$
$432$	−1.72601			−0.0830428
$433$	1.65737	+	1.91270i	0.0796479	+	0.0919186i	0.794175	−	0.607689i	$-0.207903\pi$
$433$	1.65737	+	1.91270i	0.0796479	+	0.0919186i	−0.714527	+	0.699608i	$0.753358\pi$
$434$	−0.139202	−	0.968173i	−0.00668192	−	0.0464738i
$435$	−4.29777	+	1.26194i	−0.206062	+	0.0605053i
$436$	6.77082	−	1.98809i	0.324263	−	0.0952123i
$437$	−2.83063	−	19.6875i	−0.135408	−	0.941780i
$438$	12.3013	+	14.1965i	0.587779	+	0.678333i
$439$	35.8765			1.71229			0.856146	−	0.516734i	$-0.172852\pi$
$439$	35.8765			1.71229			0.856146	+	0.516734i	$0.172852\pi$
$440$	1.79186			0.0854236
$441$	−8.53439	−	9.84921i	−0.406399	−	0.469010i
$442$	−5.84912	+	12.8078i	−0.278214	+	0.609205i
$443$	1.20560	−	0.774792i	0.0572798	−	0.0368115i	−0.511688	−	0.859172i	$-0.670979\pi$
$443$	1.20560	−	0.774792i	0.0572798	−	0.0368115i	0.568967	+	0.822360i	$0.307343\pi$
$444$	5.26028	−	6.07068i	0.249642	−	0.288102i
$445$	−2.68818	+	1.72759i	−0.127432	+	0.0818955i
$446$	1.18437	−	8.23746i	0.0560815	−	0.390055i
$447$	−5.15433	−	35.8492i	−0.243792	−	1.69561i
$448$	−1.48631	+	3.25457i	−0.0702216	+	0.153764i
$449$	−2.57440	+	17.9053i	−0.121493	+	0.845006i	0.834372	+	0.551201i	$0.185830\pi$
$449$	−2.57440	+	17.9053i	−0.121493	+	0.845006i	−0.955866	+	0.293804i	$0.905079\pi$
$450$	−2.15545	+	0.632899i	−0.101609	+	0.0298351i
$451$	12.0683	+	7.75582i	0.568274	+	0.365207i
$452$	7.99509	−	5.13813i	0.376057	−	0.241677i
$453$	−10.6378	−	23.2935i	−0.499807	−	1.09443i
$454$	−9.91541	+	2.91143i	−0.465353	+	0.136640i
$455$	−19.2411	−	12.3655i	−0.902035	−	0.579703i
$456$	7.21389	−	8.32527i	0.337821	−	0.389866i
$457$	−12.4392	+	14.3556i	−0.581881	+	0.671526i	−0.968008	−	0.250919i	$-0.919267\pi$
$457$	−12.4392	+	14.3556i	−0.581881	+	0.671526i	0.386127	+	0.922446i	$0.373813\pi$
$458$	−2.33759	−	5.11861i	−0.109228	−	0.239177i
$459$	0.541038	+	3.76300i	0.0252535	+	0.175642i
$460$	−3.96815	−	1.16515i	−0.185016	−	0.0543255i
$461$	−4.52739	−	5.22488i	−0.210861	−	0.243347i	0.640460	−	0.767992i	$-0.278744\pi$
$461$	−4.52739	−	5.22488i	−0.210861	−	0.243347i	−0.851321	+	0.524644i	$0.824198\pi$
$462$	−14.0898	−	4.13715i	−0.655519	−	0.192478i
$463$	−0.679199	+	1.48724i	−0.0315650	+	0.0691178i	−0.924758	−	0.380556i	$-0.875733\pi$
$463$	−0.679199	+	1.48724i	−0.0315650	+	0.0691178i	0.893193	+	0.449674i	$0.148460\pi$
$464$	−0.812363	−	1.77883i	−0.0377130	−	0.0825800i
$465$	0.526779	+	0.338540i	0.0244288	+	0.0156994i
$466$	0.351860	−	2.44724i	0.0162996	−	0.113366i
$467$	36.9417	+	10.8471i	1.70946	+	0.501942i	0.982740	−	0.184993i	$-0.0592261\pi$
$467$	36.9417	+	10.8471i	1.70946	+	0.501942i	0.726719	+	0.686935i	$0.241044\pi$
$468$	−14.3606			−0.663818
$469$	27.0516	−	11.2204i	1.24913	−	0.518110i
$470$	−2.87691			−0.132702
$471$	−40.7355	−	11.9610i	−1.87699	−	0.551134i
$472$	1.57254	−	10.9373i	0.0723821	−	0.503429i
$473$	−15.4581	−	9.93431i	−0.710764	−	0.456780i
$474$	15.4967	+	33.9331i	0.711787	+	1.55860i
$475$	−1.99788	+	4.37475i	−0.0916691	+	0.200727i
$476$	7.56141	+	2.22023i	0.346577	+	0.101764i
$477$	−4.87016	−	5.62047i	−0.222989	−	0.257343i
$478$	11.9236	+	3.50110i	0.545375	+	0.160137i
$479$	−3.15725	−	21.9592i	−0.144258	−	1.00334i	−0.925402	−	0.378988i	$-0.876272\pi$
$479$	−3.15725	−	21.9592i	−0.144258	−	1.00334i	0.781143	−	0.624352i	$-0.214637\pi$
$480$	−0.951514	−	2.08352i	−0.0434305	−	0.0950994i
$481$	−14.6808	+	16.9426i	−0.669388	+	0.772515i
$482$	10.3627	−	11.9592i	0.472006	−	0.544724i
$483$	28.5123	+	18.3238i	1.29736	+	0.833760i
$484$	7.47372	−	2.19448i	0.339715	−	0.0997492i
$485$	−2.33727	−	5.11791i	−0.106130	−	0.232392i
$486$	−16.2480	+	10.4419i	−0.737022	+	0.473656i
$487$	−5.50950	−	3.54074i	−0.249659	−	0.160446i	0.409826	−	0.912164i	$-0.365589\pi$
$487$	−5.50950	−	3.54074i	−0.249659	−	0.160446i	−0.659485	+	0.751717i	$0.729226\pi$
$488$	7.54589	−	2.21567i	0.341586	−	0.100299i
$489$	−2.97151	+	20.6673i	−0.134376	+	0.934608i
$490$	−2.40995	+	5.27706i	−0.108871	+	0.238393i
$491$	−1.16793	−	8.12315i	−0.0527081	−	0.366593i	−0.999056	−	0.0434430i	$-0.986167\pi$
$491$	−1.16793	−	8.12315i	−0.0527081	−	0.366593i	0.946348	−	0.323150i	$-0.104742\pi$
$492$	2.60974	−	18.1512i	0.117656	−	0.818318i
$493$	−3.62350	+	2.32868i	−0.163194	+	0.104879i
$494$	−20.1331	+	23.2349i	−0.905833	+	1.04539i
$495$	3.38632	−	2.17626i	0.152204	−	0.0978154i
$496$	−0.113567	+	0.248676i	−0.00509930	+	0.0111659i
$497$	25.6670	+	29.6212i	1.15132	+	1.32869i
$498$	−25.5854			−1.14651
$499$	9.32780			0.417569			0.208785	−	0.977962i	$-0.433049\pi$
$499$	9.32780			0.417569			0.208785	+	0.977962i	$0.433049\pi$
$500$	0.654861	+	0.755750i	0.0292863	+	0.0337981i
$501$	6.91925	+	48.1244i	0.309129	+	2.15004i
$502$	−28.8537	+	8.47221i	−1.28780	+	0.378133i
$503$	−5.16037	+	1.51522i	−0.230089	+	0.0675604i	−0.394745	−	0.918791i	$-0.629167\pi$
$503$	−5.16037	+	1.51522i	−0.230089	+	0.0675604i	0.164655	+	0.986351i	$0.447349\pi$
$504$	1.14386	+	7.95575i	0.0509518	+	0.354377i
$505$	4.84717	+	5.59394i	0.215696	+	0.248927i
$506$	7.41054			0.329439
$507$	63.8248			2.83456
$508$	−12.9371	−	14.9302i	−0.573989	−	0.662419i
$509$	−15.6367	+	34.2397i	−0.693087	+	1.51765i	0.155071	+	0.987903i	$0.450439\pi$
$509$	−15.6367	+	34.2397i	−0.693087	+	1.51765i	−0.848157	+	0.529744i	$0.822288\pi$
$510$	−4.24418	+	2.72757i	−0.187935	+	0.120779i
$511$	−19.2152	+	22.1756i	−0.850031	+	0.980989i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	−1.18136	+	8.21653i	−0.0521582	+	0.362768i
$514$	−2.85138	−	19.8318i	−0.125769	−	0.874742i
$515$	−3.60573	+	7.89545i	−0.158888	+	0.347915i
$516$	−3.34278	+	23.2496i	−0.147158	+	1.02350i
$517$	4.94621	−	1.45234i	0.217534	−	0.0638738i
$518$	10.5556	+	6.78364i	0.463784	+	0.298056i
$519$	0.470098	−	0.302113i	0.0206350	−	0.0132613i
$520$	2.65557	+	5.81488i	0.116454	+	0.254999i
$521$	−24.5098	+	7.19673i	−1.07379	+	0.315294i	−0.770393	−	0.637569i	$-0.779940\pi$
$521$	−24.5098	+	7.19673i	−1.07379	+	0.315294i	−0.303400	+	0.952863i	$0.598122\pi$
$522$	−3.69566	−	2.37506i	−0.161755	−	0.103953i
$523$	9.62764	−	11.1109i	0.420987	−	0.485845i	−0.505150	−	0.863032i	$-0.668563\pi$
$523$	9.62764	−	11.1109i	0.420987	−	0.485845i	0.926137	+	0.377186i	$0.123108\pi$
$524$	−0.466657	+	0.538551i	−0.0203860	+	0.0235267i
$525$	−3.40441	−	7.45463i	−0.148581	−	0.325347i
$526$	−2.12509	−	14.7803i	−0.0926584	−	0.644454i
$527$	0.577756	+	0.169644i	0.0251674	+	0.00738983i
$528$	2.68773	+	3.10181i	0.116968	+	0.134989i
$529$	5.65739	+	1.66116i	0.245974	+	0.0722244i
$530$	−1.37524	+	3.01136i	−0.0597367	+	0.130805i
$531$	−10.3117	−	22.5795i	−0.447491	−	0.979868i
$532$	14.4758	+	9.30301i	0.627604	+	0.403337i
$533$	−7.28350	+	50.6579i	−0.315483	+	2.19424i
$534$	−7.02273	−	2.06206i	−0.303903	−	0.0892340i
$535$	6.81602			0.294682
$536$	−8.05600	−	1.44946i	−0.347966	−	0.0626072i
$537$	23.1882			1.00064
$538$	−20.5600	−	6.03697i	−0.886405	−	0.260272i
$539$	1.47938	−	10.2893i	0.0637215	−	0.443193i
$540$	1.45201	+	0.933152i	0.0624847	+	0.0401565i
$541$	−10.7532	−	23.5463i	−0.462317	−	1.01233i	−0.986953	−	0.161007i	$-0.948526\pi$
$541$	−10.7532	−	23.5463i	−0.462317	−	1.01233i	0.524636	−	0.851327i	$-0.324201\pi$
$542$	7.17863	−	15.7190i	0.308348	−	0.675189i
$543$	−15.3160	−	4.49719i	−0.657273	−	0.192993i
$544$	−1.44239	−	1.66461i	−0.0618420	−	0.0713694i
$545$	−6.77082	−	1.98809i	−0.290030	−	0.0851605i
$546$	−7.45564	−	51.8551i	−0.319072	−	2.21920i
$547$	8.06879	+	17.6682i	0.344997	+	0.755437i	1.00000		0.000188598i	$-6.00325e-5\pi$
$547$	8.06879	+	17.6682i	0.344997	+	0.755437i	−0.655003	+	0.755626i	$0.727333\pi$
$548$	−9.58701	+	11.0640i	−0.409537	+	0.472631i
$549$	11.5695	−	13.3519i	0.493774	−	0.569846i
$550$	−1.50741	−	0.968753i	−0.0642761	−	0.0413077i
$551$	−9.02397	+	2.64968i	−0.384434	+	0.112880i
$552$	−3.93515	−	8.61677i	−0.167491	−	0.366754i
$553$	−49.0206	+	31.5036i	−2.08457	+	1.33967i
$554$	−14.1341	−	9.08343i	−0.600500	−	0.385918i
$555$	−7.70728	+	2.26306i	−0.327156	+	0.0960617i
$556$	1.73278	−	12.0518i	0.0734863	−	0.511109i
$557$	−6.68602	+	14.6403i	−0.283296	+	0.620331i	−0.996766	−	0.0803541i	$-0.974395\pi$
$557$	−6.68602	+	14.6403i	−0.283296	+	0.620331i	0.713471	+	0.700685i	$0.247122\pi$
$558$	0.0874010	+	0.607887i	0.00369998	+	0.0257339i
$559$	9.32932	−	64.8868i	0.394588	−	2.74442i
$560$	3.00991	−	1.93435i	0.127192	−	0.0817414i
$561$	5.91997	−	6.83201i	0.249941	−	0.288448i
$562$	6.06698	−	3.89901i	0.255920	−	0.164470i
$563$	−0.956541	+	2.09453i	−0.0403134	+	0.0882741i	−0.928717	−	0.370789i	$-0.879087\pi$
$563$	−0.956541	+	2.09453i	−0.0403134	+	0.0882741i	0.888404	+	0.459063i	$0.151815\pi$
$564$	−4.31528	−	4.98010i	−0.181706	−	0.209700i
$565$	−9.50378			−0.399827
$566$	−8.89995			−0.374093
$567$	−25.0535	−	28.9133i	−1.05215	−	1.21424i
$568$	−1.55901	−	10.8431i	−0.0654145	−	0.454968i
$569$	10.5508	−	3.09800i	0.442314	−	0.129875i	−0.0529897	−	0.998595i	$-0.516875\pi$
$569$	10.5508	−	3.09800i	0.442314	−	0.129875i	0.495303	+	0.868720i	$0.335057\pi$
$570$	−10.5697	+	3.10354i	−0.442716	+	0.129993i
$571$	2.66286	+	18.5206i	0.111437	+	0.775063i	0.966524	+	0.256577i	$0.0825949\pi$
$571$	2.66286	+	18.5206i	0.111437	+	0.775063i	−0.855086	+	0.518485i	$0.826496\pi$
$572$	−7.50115	−	8.65679i	−0.313639	−	0.361959i
$573$	35.6265			1.48832
$574$	28.6446			1.19560
$575$	2.70829	+	3.12553i	0.112943	+	0.130344i
$576$	0.933210	−	2.04344i	0.0388837	−	0.0851435i
$577$	−27.5874	+	17.7294i	−1.14848	+	0.738083i	−0.969336	−	0.245740i	$-0.920969\pi$
$577$	−27.5874	+	17.7294i	−1.14848	+	0.738083i	−0.179143	+	0.983823i	$0.557333\pi$
$578$	7.95564	−	9.18130i	0.330911	−	0.381892i
$579$	−0.844689	+	0.542848i	−0.0351041	+	0.0225600i
$580$	−0.278303	+	1.93564i	−0.0115559	+	0.0803732i
$581$	−5.68770	−	39.5588i	−0.235965	−	1.64118i
$582$	5.35355	−	11.7226i	0.221912	−	0.485919i
$583$	0.844212	−	5.87162i	0.0349637	−	0.243178i
$584$	7.86885	−	2.31050i	0.325615	−	0.0956092i
$585$	12.0809	+	7.76392i	0.499483	+	0.320998i
$586$	−27.9486	+	17.9615i	−1.15454	+	0.741981i
$587$	2.50047	+	5.47526i	0.103205	+	0.225988i	0.954189	−	0.299204i	$-0.0967210\pi$
$587$	2.50047	+	5.47526i	0.103205	+	0.225988i	−0.850984	+	0.525192i	$0.823994\pi$
$588$	−12.7497	+	3.74366i	−0.525790	+	0.154386i
$589$	1.10607	+	0.710829i	0.0455749	+	0.0292892i
$590$	−7.23604	+	8.35084i	−0.297903	+	0.343799i
$591$	15.3202	−	17.6804i	0.630188	−	0.727276i
$592$	−1.45683	−	3.19001i	−0.0598753	−	0.131109i
$593$	1.07513	+	7.47771i	0.0441504	+	0.307073i	0.999916	+	0.0129440i	$0.00412031\pi$
$593$	1.07513	+	7.47771i	0.0441504	+	0.307073i	−0.955766	+	0.294129i	$0.904971\pi$
$594$	−2.96749	−	0.871334i	−0.121758	−	0.0357513i
$595$	−5.16072	−	5.95578i	−0.211569	−	0.244163i
$596$	−15.1716	−	4.45478i	−0.621453	−	0.182475i
$597$	13.0646	−	28.6076i	0.534700	−	1.17083i
$598$	10.9825	+	24.0484i	0.449110	+	0.983413i
$599$	−10.0535	−	6.46102i	−0.410776	−	0.263990i	0.318892	−	0.947791i	$-0.396689\pi$
$599$	−10.0535	−	6.46102i	−0.410776	−	0.263990i	−0.729668	+	0.683801i	$0.760326\pi$
$600$	−0.325974	+	2.26720i	−0.0133078	+	0.0925580i
$601$	−27.1978	−	7.98599i	−1.10942	−	0.325755i	−0.324832	−	0.945772i	$-0.605308\pi$
$601$	−27.1978	−	7.98599i	−1.10942	−	0.325755i	−0.784589	+	0.620016i	$0.787126\pi$
$602$	−36.6904			−1.49539
$603$	−16.9849	+	7.04495i	−0.691679	+	0.286893i
$604$	−11.1799			−0.454902
$605$	−7.47372	−	2.19448i	−0.303850	−	0.0892184i
$606$	−2.41281	+	16.7814i	−0.0980136	+	0.681700i
$607$	−16.8994	−	10.8606i	−0.685927	−	0.440819i	0.150709	−	0.988578i	$-0.451844\pi$
$607$	−16.8994	−	10.8606i	−0.685927	−	0.440819i	−0.836636	+	0.547760i	$0.815481\pi$
$608$	−1.99788	−	4.37475i	−0.0810248	−	0.177420i
$609$	6.65749	−	14.5779i	0.269775	−	0.590725i
$610$	−7.54589	−	2.21567i	−0.305524	−	0.0897100i
$611$	12.0434	+	13.8989i	0.487226	+	0.562288i
$612$	−4.74758	−	1.39402i	−0.191910	−	0.0563498i
$613$	−3.03962	−	21.1411i	−0.122769	−	0.853879i	−0.954396	−	0.298544i	$-0.903499\pi$
$613$	−3.03962	−	21.1411i	−0.122769	−	0.853879i	0.831627	−	0.555335i	$-0.187410\pi$
$614$	−8.70777	−	19.0674i	−0.351417	−	0.769496i
$615$	−12.0087	+	13.8588i	−0.484238	+	0.558841i
$616$	−4.19837	+	4.84517i	−0.169157	+	0.195218i
$617$	10.5904	+	6.80605i	0.426354	+	0.274001i	0.736172	−	0.676795i	$-0.236632\pi$
$617$	10.5904	+	6.80605i	0.426354	+	0.274001i	−0.309818	+	0.950796i	$0.600268\pi$
$618$	−19.0759	+	5.60120i	−0.767347	+	0.225313i
$619$	17.1070	+	37.4590i	0.687587	+	1.50560i	0.854400	+	0.519616i	$0.173925\pi$
$619$	17.1070	+	37.4590i	0.687587	+	1.50560i	−0.166813	+	0.985989i	$0.553348\pi$
$620$	0.229983	−	0.147801i	0.00923634	−	0.00593584i
$621$	6.00505	+	3.85921i	0.240974	+	0.154865i
$622$	−16.9711	+	4.98316i	−0.680479	+	0.199807i
$623$	1.62708	−	11.3166i	0.0651875	−	0.453389i
$624$	−6.08261	+	13.3191i	−0.243499	+	0.533189i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	−1.25201	+	8.70793i	−0.0500404	+	0.348039i
$627$	16.6055	−	10.6717i	0.663159	−	0.426186i
$628$	−12.1380	+	14.0080i	−0.484359	+	0.558980i
$629$	−6.49811	+	4.17608i	−0.259097	+	0.166511i
$630$	3.33892	−	7.31122i	0.133026	−	0.291286i
$631$	−5.27103	−	6.08309i	−0.209836	−	0.242164i	0.641069	−	0.767483i	$-0.278491\pi$
$631$	−5.27103	−	6.08309i	−0.209836	−	0.242164i	−0.850905	+	0.525319i	$0.823946\pi$
$632$	16.2864			0.647837
$633$	−28.0386			−1.11444
$634$	5.91429	+	6.82546i	0.234887	+	0.271074i
$635$	2.81149	+	19.5544i	0.111571	+	0.775991i
$636$	−7.27565	+	2.13632i	−0.288498	+	0.0847108i
$637$	35.5830	−	10.4481i	1.40985	−	0.413970i
$638$	−0.498680	−	3.46840i	−0.0197430	−	0.137315i
$639$	−16.1155	−	18.5983i	−0.637520	−	0.735737i
$640$	−1.00000			−0.0395285
$641$	−25.1677			−0.994065			−0.497032	−	0.867732i	$-0.665577\pi$
$641$	−25.1677			−0.994065			−0.497032	+	0.867732i	$0.665577\pi$
$642$	10.2238	+	11.7989i	0.403502	+	0.465666i
$643$	−4.52238	+	9.90264i	−0.178345	+	0.390522i	−0.977600	−	0.210470i	$-0.932500\pi$
$643$	−4.52238	+	9.90264i	−0.178345	+	0.390522i	0.799255	+	0.600992i	$0.205228\pi$
$644$	12.4480	−	7.99985i	0.490520	−	0.315238i
$645$	15.3818	−	17.7515i	0.605657	−	0.698966i
$646$	−8.91145	+	5.72704i	−0.350616	+	0.225327i
$647$	3.85363	−	26.8026i	0.151502	−	1.05372i	−0.762203	−	0.647338i	$-0.775882\pi$
$647$	3.85363	−	26.8026i	0.151502	−	1.05372i	0.913705	−	0.406379i	$-0.133209\pi$
$648$	1.52175	+	10.5840i	0.0597798	+	0.415778i
$649$	8.22505	−	18.0103i	0.322861	−	0.706968i
$650$	0.909756	−	6.32749i	0.0356836	−	0.248185i
$651$	−2.14967	+	0.631199i	−0.0842520	+	0.0247386i
$652$	7.66869	+	4.92837i	0.300329	+	0.193010i
$653$	22.6714	−	14.5700i	0.887202	−	0.570170i	−0.0157672	−	0.999876i	$-0.505019\pi$
$653$	22.6714	−	14.5700i	0.887202	−	0.570170i	0.902969	+	0.429706i	$0.141383\pi$
$654$	−6.71451	−	14.7027i	−0.262558	−	0.574922i
$655$	0.683739	−	0.200764i	0.0267159	−	0.00784450i
$656$	−6.73507	−	4.32836i	−0.262960	−	0.168994i
$657$	12.0647	−	13.9234i	0.470687	−	0.543202i
$658$	6.74067	−	7.77915i	0.262779	−	0.303263i
$659$	−11.0749	−	24.2506i	−0.431415	−	0.944668i	−0.993095	−	0.117313i	$-0.962572\pi$
$659$	−11.0749	−	24.2506i	−0.431415	−	0.944668i	0.561680	−	0.827355i	$-0.310155\pi$
$660$	−0.584100	−	4.06250i	−0.0227361	−	0.158133i
$661$	−21.7680	−	6.39167i	−0.846678	−	0.248607i	−0.170511	−	0.985356i	$-0.554542\pi$
$661$	−21.7680	−	6.39167i	−0.846678	−	0.248607i	−0.676167	+	0.736749i	$0.736360\pi$
$662$	10.4724	+	12.0858i	0.407023	+	0.469730i
$663$	30.9445	+	9.08612i	1.20178	+	0.352876i
$664$	−4.64025	+	10.1607i	−0.180077	+	0.394313i
$665$	−7.14821	−	15.6524i	−0.277196	−	0.606974i
$666$	−6.62752	−	4.25925i	−0.256811	−	0.165042i
$667$	−1.15097	+	8.00518i	−0.0445658	+	0.309962i
$668$	20.3666	+	5.98016i	0.788006	+	0.231379i
$669$	−19.0620			−0.736981
$670$	5.99350	+	5.57476i	0.231549	+	0.215372i
$671$	14.0920			0.544016
$672$	7.86325	+	2.30886i	0.303331	+	0.0890661i
$673$	−3.02479	+	21.0379i	−0.116597	+	0.810951i	0.844661	+	0.535302i	$0.179802\pi$
$673$	−3.02479	+	21.0379i	−0.116597	+	0.810951i	−0.961258	+	0.275650i	$0.911107\pi$
$674$	−13.9219	−	8.94707i	−0.536252	−	0.344628i
$675$	−0.717011	−	1.57004i	−0.0275978	−	0.0604307i
$676$	11.5755	−	25.3467i	0.445210	−	0.974875i
$677$	3.20212	+	0.940227i	0.123067	+	0.0361359i	0.342686	−	0.939450i	$-0.388663\pi$
$677$	3.20212	+	0.940227i	0.123067	+	0.0361359i	−0.219619	+	0.975586i	$0.570481\pi$
$678$	−14.2554	−	16.4516i	−0.547474	−	0.631819i
$679$	19.3151	+	5.67141i	0.741244	+	0.217649i
$680$	0.313461	+	2.18017i	0.0120207	+	0.0836057i
$681$	9.83295	+	21.5312i	0.376800	+	0.825076i
$682$	−0.320791	+	0.370212i	−0.0122837	+	0.0141762i
$683$	28.0405	−	32.3604i	1.07294	−	1.23824i	0.103053	−	0.994676i	$-0.467139\pi$
$683$	28.0405	−	32.3604i	1.07294	−	1.23824i	0.969885	−	0.243561i	$-0.0783157\pi$
$684$	−9.08891	−	5.84109i	−0.347523	−	0.223339i
$685$	14.0468	−	4.12450i	0.536699	−	0.157589i
$686$	1.78162	+	3.90120i	0.0680226	+	0.148949i
$687$	−10.8429	+	6.96831i	−0.413683	+	0.265858i
$688$	8.62684	+	5.54413i	0.328895	+	0.211368i
$689$	20.3055	−	5.96224i	0.773578	−	0.227143i
$690$	−1.34812	+	9.37639i	−0.0513221	+	0.356953i
$691$	16.8956	−	36.9962i	0.642739	−	1.40740i	−0.255029	−	0.966933i	$-0.582085\pi$
$691$	16.8956	−	36.9962i	0.642739	−	1.40740i	0.897768	−	0.440469i	$-0.145188\pi$
$692$	−0.0347199	−	0.241482i	−0.00131985	−	0.00917978i
$693$	−2.04964	+	14.2556i	−0.0778596	+	0.541525i
$694$	12.5668	−	8.07619i	0.477029	−	0.306568i
$695$	−7.97339	+	9.20178i	−0.302448	+	0.349043i
$696$	−3.76815	+	2.42164i	−0.142831	+	0.0917921i
$697$	−7.32539	+	16.0404i	−0.277469	+	0.607572i
$698$	16.2677	+	18.7740i	0.615743	+	0.710606i
$699$	−5.66308			−0.214197
$700$	−3.57789			−0.135232
$701$	−12.7522	−	14.7168i	−0.481643	−	0.555846i	0.461970	−	0.886895i	$-0.347143\pi$
$701$	−12.7522	−	14.7168i	−0.481643	−	0.555846i	−0.943613	+	0.331050i	$0.892597\pi$
$702$	−1.57025	−	10.9213i	−0.0592653	−	0.412199i
$703$	−16.1829	+	4.75173i	−0.610349	+	0.179215i
$704$	1.71928	−	0.504825i	0.0647977	−	0.0190263i
$705$	0.937800	+	6.52254i	0.0353196	+	0.245653i
$706$	23.3042	+	26.8945i	0.877066	+	1.01219i
$707$	−26.4830			−0.995995
$708$	−25.3096			−0.951192
$709$	−13.6875	−	15.7962i	−0.514045	−	0.593239i	0.438085	−	0.898934i	$-0.355657\pi$
$709$	−13.6875	−	15.7962i	−0.514045	−	0.593239i	−0.952130	+	0.305694i	$0.901111\pi$
$710$	−4.55072	+	9.96469i	−0.170786	+	0.373968i
$711$	30.7786	−	19.7802i	1.15429	−	0.741815i
$712$	−2.09257	+	2.41495i	−0.0784224	+	0.0905043i
$713$	0.951134	−	0.611257i	0.0356203	−	0.0228917i
$714$	2.56888	−	17.8670i	0.0961380	−	0.668654i
$715$	1.63016	+	11.3380i	0.0609644	+	0.424017i
$716$	4.20549	−	9.20873i	0.157166	−	0.344146i
$717$	4.05089	−	28.1745i	0.151283	−	1.05220i
$718$	34.5847	−	10.1550i	1.29069	−	0.378981i
$719$	24.0902	+	15.4818i	0.898412	+	0.577374i	0.906319	−	0.422594i	$-0.138880\pi$
$719$	24.0902	+	15.4818i	0.898412	+	0.577374i	−0.00790686	+	0.999969i	$0.502517\pi$
$720$	−1.88984	+	1.21452i	−0.0704300	+	0.0452626i
$721$	−12.9009	−	28.2491i	−0.480455	−	1.05205i
$722$	−3.96268	+	1.16355i	−0.147476	+	0.0433028i
$723$	−30.4917	−	19.5959i	−1.13400	−	0.728778i
$724$	−4.56373	+	5.26683i	−0.169610	+	0.195740i
$725$	1.28061	−	1.47790i	0.0475607	−	0.0548880i
$726$	−7.41157	−	16.2291i	−0.275069	−	0.602317i
$727$	−1.61388	−	11.2248i	−0.0598555	−	0.416304i	−0.997615	−	0.0690195i	$-0.978013\pi$
$727$	−1.61388	−	11.2248i	−0.0598555	−	0.416304i	0.937760	−	0.347284i	$-0.112896\pi$
$728$	−21.9454	−	6.44376i	−0.813351	−	0.238822i
$729$	7.96345	+	9.19031i	0.294943	+	0.340382i
$730$	−7.86885	−	2.31050i	−0.291239	−	0.0855155i
$731$	9.38298	−	20.5459i	0.347042	−	0.759916i
$732$	−7.48314	−	16.3858i	−0.276585	−	0.605636i
$733$	−13.5114	−	8.68324i	−0.499055	−	0.320723i	0.266783	−	0.963757i	$-0.414039\pi$
$733$	−13.5114	−	8.68324i	−0.499055	−	0.320723i	−0.765838	+	0.643034i	$0.777676\pi$
$734$	−0.214364	+	1.49094i	−0.00791233	+	0.0550315i
$735$	12.7497	+	3.74366i	0.470281	+	0.138087i
$736$	−4.13567			−0.152443
$737$	−13.1188	−	6.55889i	−0.483236	−	0.241600i
$738$	−17.9851			−0.662040
$739$	−35.9983	−	10.5701i	−1.32422	−	0.388826i	−0.458206	−	0.888846i	$-0.651508\pi$
$739$	−35.9983	−	10.5701i	−1.32422	−	0.388826i	−0.866014	+	0.500020i	$0.833326\pi$
$740$	−0.499088	+	3.47123i	−0.0183468	+	0.127605i
$741$	59.2410	+	38.0719i	2.17627	+	1.39860i
$742$	−4.92047	−	10.7743i	−0.180636	−	0.395538i
$743$	−2.10598	+	4.61145i	−0.0772609	+	0.169178i	−0.944321	−	0.329026i	$-0.893280\pi$
$743$	−2.10598	+	4.61145i	−0.0772609	+	0.169178i	0.867060	+	0.498204i	$0.166007\pi$
$744$	0.600819	+	0.176416i	0.0220271	+	0.00646774i
$745$	10.3547	+	11.9500i	0.379368	+	0.437814i
$746$	0.752748	+	0.221027i	0.0275601	+	0.00809237i
$747$	3.57113	+	24.8378i	0.130661	+	0.908767i
$748$	−1.63953	−	3.59007i	−0.0599472	−	0.131266i
$749$	−15.9701	+	18.4305i	−0.583534	+	0.673434i
$750$	1.49997	−	1.73105i	0.0547711	−	0.0632092i
$751$	24.9598	+	16.0407i	0.910796	+	0.585333i	0.909973	−	0.414667i	$-0.136102\pi$
$751$	24.9598	+	16.0407i	0.910796	+	0.585333i	0.000822351		1.00000i	$0.499738\pi$
$752$	−2.76038	+	0.810521i	−0.100661	+	0.0295566i
$753$	28.6137	+	62.6553i	1.04274	+	2.28329i
$754$	10.5165	−	6.75852i	0.382987	−	0.246131i
$755$	9.40510	+	6.04429i	0.342287	+	0.219974i
$756$	−5.92533	+	1.73984i	−0.215502	+	0.0632772i
$757$	−5.71657	+	39.7596i	−0.207772	+	1.44509i	0.572633	+	0.819812i	$0.305922\pi$
$757$	−5.71657	+	39.7596i	−0.207772	+	1.44509i	−0.780405	+	0.625275i	$0.784987\pi$
$758$	5.91096	−	12.9432i	0.214696	−	0.470118i
$759$	−2.41564	−	16.8012i	−0.0876823	−	0.609844i
$760$	−0.684444	+	4.76041i	−0.0248274	+	0.172678i
$761$	38.1229	−	24.5001i	1.38195	−	0.888128i	0.382595	−	0.923916i	$-0.375030\pi$
$761$	38.1229	−	24.5001i	1.38195	−	0.888128i	0.999359	+	0.0357877i	$0.0113940\pi$
$762$	−29.6325	+	34.1977i	−1.07347	+	1.23885i
$763$	21.2399	−	13.6501i	0.768938	−	0.494166i
$764$	6.46134	−	14.1484i	0.233763	−	0.511869i
$765$	3.24026	+	3.73946i	0.117152	+	0.135200i
$766$	36.6891			1.32563
$767$	70.6362			2.55052
$768$	−1.49997	−	1.73105i	−0.0541254	−	0.0624641i
$769$	−7.31355	−	50.8669i	−0.263733	−	1.83431i	−0.504125	−	0.863631i	$-0.668185\pi$
$769$	−7.31355	−	50.8669i	−0.263733	−	1.83431i	0.240391	−	0.970676i	$-0.422724\pi$
$770$	6.15139	−	1.80621i	0.221681	−	0.0650913i
$771$	−44.0331	+	12.9293i	−1.58581	+	0.465637i
$772$	0.0623860	+	0.433904i	0.00224532	+	0.0156166i
$773$	14.4766	+	16.7069i	0.520686	+	0.600904i	0.953803	−	0.300434i	$-0.0971316\pi$
$773$	14.4766	+	16.7069i	0.520686	+	0.600904i	−0.433116	+	0.901338i	$0.642586\pi$
$774$	23.0368			0.828041
$775$	−0.273381			−0.00982015
$776$	−3.68448	−	4.25211i	−0.132265	−	0.152642i
$777$	11.9390	−	26.1428i	0.428310	−	0.937869i
$778$	0.332876	−	0.213927i	0.0119342	−	0.00766964i
$779$	−25.2146	+	29.0992i	−0.903406	+	1.04259i
$780$	12.3178	−	7.91620i	0.441050	−	0.283445i
$781$	2.79352	−	19.4294i	0.0999601	−	0.695238i
$782$	1.29637	+	9.01647i	0.0463582	+	0.322428i
$783$	1.40215	−	3.07028i	0.0501087	−	0.109723i
$784$	−0.825613	+	5.74226i	−0.0294862	+	0.205081i
$785$	17.7844	−	5.22198i	0.634753	−	0.186380i
$786$	1.37312	+	0.882451i	0.0489776	+	0.0314760i
$787$	−33.9169	+	21.7971i	−1.20901	+	0.776982i	−0.980492	−	0.196558i	$-0.937023\pi$
$787$	−33.9169	+	21.7971i	−1.20901	+	0.776982i	−0.228515	+	0.973540i	$0.573387\pi$
$788$	−4.24292	−	9.29069i	−0.151148	−	0.330967i
$789$	−32.8173	+	9.63602i	−1.16833	+	0.343051i
$790$	−13.7010	−	8.80508i	−0.487459	−	0.313271i
$791$	22.2676	−	25.6981i	0.791743	−	0.913721i
$792$	2.63603	−	3.04214i	0.0936672	−	0.108098i
$793$	20.8846	+	45.7309i	0.741633	+	1.62395i
$794$	5.12915	+	35.6741i	0.182027	+	1.26602i
$795$	7.27565	+	2.13632i	0.258041	+	0.0757676i
$796$	−8.99148	−	10.3767i	−0.318695	−	0.367793i
$797$	−28.4306	−	8.34799i	−1.00706	−	0.295701i	−0.263713	−	0.964601i	$-0.584947\pi$
$797$	−28.4306	−	8.34799i	−1.00706	−	0.295701i	−0.743352	+	0.668900i	$0.766765\pi$
$798$	16.3731	−	35.8520i	0.579600	−	1.26915i
$799$	2.63235	+	5.76403i	0.0931257	+	0.203917i
$800$	0.841254	+	0.540641i	0.0297428	+	0.0191145i
$801$	−1.02159	+	7.10534i	−0.0360963	+	0.251055i
$802$	5.72500	+	1.68101i	0.202157	+	0.0593586i
$803$	14.6951			0.518580
$804$	−0.660171	+	18.7370i	−0.0232824	+	0.660804i
$805$	−14.7970			−0.521525
$806$	−1.67682	−	0.492358i	−0.0590634	−	0.0173426i
$807$	−6.98497	+	48.5815i	−0.245883	+	1.71015i
$808$	6.22682	+	4.00174i	0.219059	+	0.140781i
$809$	11.7884	+	25.8130i	0.414459	+	0.907538i	0.995597	+	0.0937333i	$0.0298801\pi$
$809$	11.7884	+	25.8130i	0.414459	+	0.907538i	−0.581139	+	0.813805i	$0.697393\pi$
$810$	4.44195	−	9.72652i	0.156074	−	0.341755i
$811$	−10.0867	−	2.96174i	−0.354194	−	0.104001i	0.0997953	−	0.995008i	$-0.468181\pi$
$811$	−10.0867	−	2.96174i	−0.354194	−	0.104001i	−0.453989	+	0.891007i	$0.649999\pi$
$812$	−4.58189	−	5.28778i	−0.160793	−	0.185565i
$813$	−37.9781	−	11.1514i	−1.33195	−	0.391096i
$814$	−0.894295	−	6.21996i	−0.0313450	−	0.218009i
$815$	−3.78683	−	8.29201i	−0.132647	−	0.290456i
$816$	−3.30381	+	3.81280i	−0.115657	+	0.133475i
$817$	32.2969	−	37.2727i	1.12993	−	1.30401i
$818$	29.6915	+	19.0816i	1.03814	+	0.667171i
$819$	−49.2993	+	14.4756i	−1.72266	+	0.505818i
$820$	3.32581	+	7.28250i	0.116142	+	0.254316i
$821$	−16.8621	+	10.8366i	−0.588490	+	0.378200i	−0.800737	−	0.599017i	$-0.795558\pi$
$821$	−16.8621	+	10.8366i	−0.588490	+	0.378200i	0.212247	+	0.977216i	$0.431922\pi$
$822$	28.2094	+	18.1291i	0.983916	+	0.632324i
$823$	−42.3373	+	12.4313i	−1.47579	+	0.433330i	−0.917975	−	0.396639i	$-0.870177\pi$
$823$	−42.3373	+	12.4313i	−1.47579	+	0.433330i	−0.557810	+	0.829968i	$0.688358\pi$
$824$	−1.23527	+	8.59148i	−0.0430326	+	0.299298i
$825$	−1.70498	+	3.73338i	−0.0593598	+	0.129980i
$826$	−5.62639	−	39.1324i	−0.195767	−	1.36159i
$827$	−3.00433	+	20.8956i	−0.104471	+	0.726610i	0.868501	+	0.495687i	$0.165084\pi$
$827$	−3.00433	+	20.8956i	−0.104471	+	0.726610i	−0.972972	+	0.230923i	$0.925825\pi$
$828$	−7.81574	+	5.02287i	−0.271616	+	0.174557i
$829$	−9.05188	+	10.4464i	−0.314385	+	0.362820i	−0.890846	−	0.454305i	$-0.849888\pi$
$829$	−9.05188	+	10.4464i	−0.314385	+	0.362820i	0.576461	+	0.817124i	$0.304433\pi$
$830$	9.39693	−	6.03904i	0.326172	−	0.209618i
$831$	−15.9866	+	35.0058i	−0.554569	+	1.21434i
$832$	4.18624	+	4.83118i	0.145132	+	0.167491i
$833$	12.7779			0.442729
$834$	−27.8886			−0.965703
$835$	−13.9003	−	16.0418i	−0.481040	−	0.555150i
$836$	−1.22643	−	8.52999i	−0.0424169	−	0.295016i
$837$	−0.452746	+	0.132938i	−0.0156492	+	0.00459502i
$838$	33.6534	−	9.88153i	1.16254	−	0.341352i
$839$	5.84678	+	40.6652i	0.201853	+	1.40392i	0.798780	+	0.601623i	$0.205479\pi$
$839$	5.84678	+	40.6652i	0.201853	+	1.40392i	−0.596927	+	0.802296i	$0.703612\pi$
$840$	−5.36672	−	6.19353i	−0.185169	−	0.213697i
$841$	−25.1758			−0.868132
$842$	−12.8785			−0.443822
$843$	−10.8175	−	12.4841i	−0.372575	−	0.429975i
$844$	−5.08518	+	11.1350i	−0.175039	+	0.383282i
$845$	−23.4414	+	15.0649i	−0.806408	+	0.518247i
$846$	−4.23227	+	4.88430i	−0.145508	+	0.167926i
$847$	23.4449	−	15.0671i	0.805578	−	0.517713i
$848$	−0.471137	+	3.27683i	−0.0161789	+	0.112527i
$849$	2.90115	+	20.1780i	0.0995673	+	0.692506i
$850$	0.914989	−	2.00355i	0.0313839	−	0.0687211i
$851$	−2.06406	+	14.3559i	−0.0707551	+	0.492113i
$852$	−24.0754	+	7.06916i	−0.824808	+	0.242186i
$853$	−16.0139	−	10.2915i	−0.548305	−	0.352374i	0.236974	−	0.971516i	$-0.423844\pi$
$853$	−16.0139	−	10.2915i	−0.548305	−	0.352374i	−0.785279	+	0.619142i	$0.787481\pi$
$854$	23.6713	−	15.2126i	0.810017	−	0.520566i
$855$	4.48815	+	9.82767i	0.153491	+	0.336099i
$856$	6.53992	−	1.92030i	0.223530	−	0.0656343i
$857$	−9.12587	−	5.86484i	−0.311734	−	0.200339i	0.375413	−	0.926858i	$-0.377501\pi$
$857$	−9.12587	−	5.86484i	−0.311734	−	0.200339i	−0.687147	+	0.726518i	$0.741137\pi$
$858$	−17.1815	+	19.8285i	−0.586566	+	0.676934i
$859$	33.8549	−	39.0706i	1.15511	−	1.33307i	0.221345	−	0.975195i	$-0.428955\pi$
$859$	33.8549	−	39.0706i	1.15511	−	1.33307i	0.933769	−	0.357877i	$-0.116499\pi$
$860$	−4.25998	−	9.32805i	−0.145264	−	0.318084i
$861$	−9.33739	−	64.9429i	−0.318217	−	2.21325i
$862$	−20.7983	−	6.10694i	−0.708394	−	0.208003i
$863$	31.9713	+	36.8969i	1.08832	+	1.25598i	0.964614	+	0.263665i	$0.0849312\pi$
$863$	31.9713	+	36.8969i	1.08832	+	1.25598i	0.123702	+	0.992319i	$0.460523\pi$
$864$	1.65610	+	0.486274i	0.0563415	+	0.0165434i
$865$	−0.101347	+	0.221919i	−0.00344590	+	0.00754546i
$866$	−1.05136	−	2.30216i	−0.0357267	−	0.0782305i
$867$	−23.4092	−	15.0442i	−0.795017	−	0.510926i
$868$	−0.139202	+	0.968173i	−0.00472483	+	0.0328619i
$869$	28.0008	+	8.22177i	0.949862	+	0.278905i
$870$	4.47921			0.151859
$871$	1.84246	−	52.2929i	0.0624294	−	1.77188i
$872$	−7.05666			−0.238969
$873$	−12.1273	−	3.56091i	−0.410448	−	0.120519i
$874$	−2.83063	+	19.6875i	−0.0957476	+	0.665939i
$875$	3.00991	+	1.93435i	0.101754	+	0.0653931i
$876$	−7.80341	−	17.0871i	−0.263653	−	0.577319i
$877$	2.45815	−	5.38260i	0.0830059	−	0.181757i	−0.863578	−	0.504215i	$-0.831782\pi$
$877$	2.45815	−	5.38260i	0.0830059	−	0.181757i	0.946584	+	0.322458i	$0.104509\pi$
$878$	−34.4233	−	10.1076i	−1.16173	−	0.341114i
$879$	49.8327	+	57.5100i	1.68082	+	1.93976i
$880$	−1.71928	−	0.504825i	−0.0579568	−	0.0170177i
$881$	5.70034	+	39.6467i	0.192049	+	1.33573i	0.826573	+	0.562829i	$0.190287\pi$
$881$	5.70034	+	39.6467i	0.192049	+	1.33573i	−0.634524	+	0.772903i	$0.718804\pi$
$882$	5.41384	+	11.8547i	0.182294	+	0.399167i
$883$	10.2304	−	11.8065i	0.344281	−	0.397321i	−0.557031	−	0.830492i	$-0.688060\pi$
$883$	10.2304	−	11.8065i	0.344281	−	0.397321i	0.901312	+	0.433170i	$0.142605\pi$
$884$	9.22056	−	10.6411i	0.310121	−	0.357899i
$885$	21.2918	+	13.6834i	0.715715	+	0.459962i
$886$	−1.37505	+	0.403751i	−0.0461957	+	0.0135643i
$887$	−15.9681	−	34.9653i	−0.536156	−	1.17402i	−0.962953	−	0.269671i	$-0.913085\pi$
$887$	−15.9681	−	34.9653i	−0.536156	−	1.17402i	0.426796	−	0.904348i	$-0.359642\pi$
$888$	−6.75751	+	4.34279i	−0.226767	+	0.145734i
$889$	−59.4622	−	38.2140i	−1.99430	−	1.28166i
$890$	3.06601	−	0.900260i	0.102773	−	0.0301768i
$891$	−2.72675	+	18.9650i	−0.0913497	+	0.635351i
$892$	−3.45715	+	7.57011i	−0.115754	+	0.253466i
$893$	1.96909	+	13.6953i	0.0658930	+	0.458296i
$894$	−5.15433	+	35.8492i	−0.172387	+	1.19898i
$895$	−8.51650	+	5.47322i	−0.284675	+	0.182950i
$896$	2.34302	−	2.70399i	0.0782748	−	0.0903340i
$897$	50.9425	−	32.7388i	1.70092	−	1.09312i
$898$	7.51464	−	16.4548i	0.250767	−	0.549103i
$899$	−0.350095	−	0.404031i	−0.0116763	−	0.0134752i
$900$	2.24645			0.0748817
$901$	7.29174			0.242923
$902$	−9.39438	−	10.8417i	−0.312799	−	0.360989i
$903$	11.9601	+	83.1844i	0.398008	+	2.76820i
$904$	−9.11881	+	2.67752i	−0.303287	+	0.0890532i
$905$	6.68672	−	1.96340i	0.222274	−	0.0652655i
$906$	3.64435	+	25.3470i	0.121075	+	0.842097i
$907$	−21.8678	−	25.2368i	−0.726109	−	0.837975i	0.265919	−	0.963996i	$-0.414325\pi$
$907$	−21.8678	−	25.2368i	−0.726109	−	0.837975i	−0.992028	+	0.126021i	$0.959779\pi$
$908$	10.3340			0.342946
$909$	16.6279			0.551512
$910$	14.9779	+	17.2854i	0.496513	+	0.573006i
$911$	−17.4382	+	38.1843i	−0.577753	+	1.26510i	0.364812	+	0.931081i	$0.381133\pi$
$911$	−17.4382	+	38.1843i	−0.577753	+	1.26510i	−0.942565	+	0.334022i	$0.891594\pi$
$912$	−9.26717	+	5.95565i	−0.306867	+	0.197211i
$913$	−13.1073	+	15.1266i	−0.433787	+	0.500617i
$914$	15.9798	−	10.2696i	0.528563	−	0.339687i
$915$	−2.56361	+	17.8303i	−0.0847503	+	0.589451i
$916$	0.800822	+	5.56984i	0.0264599	+	0.184033i
$917$	−1.05915	+	2.31922i	−0.0349763	+	0.0765874i
$918$	0.541038	−	3.76300i	0.0178569	−	0.124198i
$919$	36.7429	−	10.7887i	1.21204	−	0.355886i	0.387594	−	0.921830i	$-0.373306\pi$
$919$	36.7429	−	10.7887i	1.21204	−	0.355886i	0.824444	+	0.565944i	$0.191488\pi$
$920$	3.47915	+	2.23591i	0.114704	+	0.0737158i
$921$	−40.3910	+	25.9577i	−1.33093	+	0.855336i
$922$	2.87198	+	6.28875i	0.0945835	+	0.207109i
$923$	67.1916	−	19.7292i	2.21164	−	0.649395i
$924$	12.3535	+	7.93913i	0.406401	+	0.261178i
$925$	2.29655	−	2.65036i	0.0755101	−	0.0871433i
$926$	1.07069	−	1.23564i	0.0351850	−	0.0406057i
$927$	8.10010	+	17.7368i	0.266042	+	0.582551i
$928$	0.278303	+	1.93564i	0.00913575	+	0.0635406i
$929$	19.0233	+	5.58573i	0.624133	+	0.183262i	0.578482	−	0.815695i	$-0.303645\pi$
$929$	19.0233	+	5.58573i	0.624133	+	0.183262i	0.0456515	+	0.998957i	$0.485464\pi$
$930$	−0.410063	−	0.473238i	−0.0134465	−	0.0155181i
$931$	26.7705	+	7.86051i	0.877366	+	0.257618i
$932$	−1.02707	+	2.24898i	−0.0336429	+	0.0736677i
$933$	16.8300	+	36.8525i	0.550988	+	1.20650i
$934$	−32.3893	−	20.8154i	−1.05981	−	0.681100i
$935$	−0.561679	+	3.90656i	−0.0183689	+	0.127758i
$936$	13.7789	+	4.04584i	0.450377	+	0.132243i
$937$	−27.3680			−0.894073			−0.447036	−	0.894516i	$-0.647521\pi$
$937$	−27.3680			−0.894073			−0.447036	+	0.894516i	$0.647521\pi$
$938$	−29.1170	+	3.14457i	−0.950704	+	0.102674i
$939$	20.1507			0.657594
$940$	2.76038	+	0.810521i	0.0900336	+	0.0264363i
$941$	−0.786800	+	5.47232i	−0.0256490	+	0.178392i	−0.998619	−	0.0525396i	$-0.983268\pi$
$941$	−0.786800	+	5.47232i	−0.0256490	+	0.178392i	0.972970	+	0.230932i	$0.0741775\pi$
$942$	35.7156	+	22.9530i	1.16368	+	0.747850i
$943$	13.7544	+	30.1180i	0.447906	+	0.980778i
$944$	−4.59023	+	10.0512i	−0.149399	+	0.327139i
$945$	5.92533	+	1.73984i	0.192751	+	0.0565968i
$946$	12.0331	+	13.8870i	0.391230	+	0.451504i
$947$	−5.85557	−	1.71935i	−0.190281	−	0.0558714i	0.185204	−	0.982700i	$-0.440705\pi$
$947$	−5.85557	−	1.71935i	−0.190281	−	0.0558714i	−0.375484	+	0.926829i	$0.622524\pi$
$948$	−5.30894	−	36.9245i	−0.172426	−	1.19925i
$949$	21.7784	+	47.6881i	0.706957	+	1.54802i
$950$	3.14946	−	3.63467i	0.102182	−	0.117924i
$951$	13.5468	−	15.6338i	0.439284	−	0.506961i
$952$	−6.62961	−	4.26059i	−0.214867	−	0.138087i
$953$	−0.368464	+	0.108191i	−0.0119357	+	0.00350464i	−0.287695	−	0.957722i	$-0.592889\pi$
$953$	−0.368464	+	0.108191i	−0.0119357	+	0.00350464i	0.275759	+	0.961227i	$0.411071\pi$
$954$	3.08942	+	6.76488i	0.100024	+	0.219021i
$955$	−13.0848	+	8.40909i	−0.423414	+	0.272112i
$956$	−10.4543	−	6.71856i	−0.338116	−	0.217294i
$957$	−7.70100	+	2.26122i	−0.248938	+	0.0730947i
$958$	−3.15725	+	21.9592i	−0.102006	+	0.709468i
$959$	−21.7592	+	47.6461i	−0.702642	+	1.53857i
$960$	0.325974	+	2.26720i	0.0105208	+	0.0731735i
$961$	4.40112	−	30.6105i	0.141972	−	0.987435i
$962$	18.8594	−	12.1202i	0.608052	−	0.390772i
$963$	10.0271	−	11.5719i	0.323120	−	0.372900i
$964$	−13.3122	+	8.55522i	−0.428757	+	0.275545i
$965$	0.182104	−	0.398752i	0.00586213	−	0.0128363i
$966$	−22.1950	−	25.6144i	−0.714112	−	0.824129i
$967$	−10.5575			−0.339506			−0.169753	−	0.985487i	$-0.554297\pi$
$967$	−10.5575			−0.339506			−0.169753	+	0.985487i	$0.554297\pi$
$968$	−7.78924			−0.250356
$969$	15.8892	+	18.3372i	0.510436	+	0.589074i
$970$	0.800713	+	5.56908i	0.0257094	+	0.178812i
$971$	42.9851	−	12.6216i	1.37946	−	0.405045i	0.493877	−	0.869532i	$-0.335579\pi$
$971$	42.9851	−	12.6216i	1.37946	−	0.405045i	0.885580	+	0.464486i	$0.153761\pi$
$972$	18.5316	−	5.44138i	0.594403	−	0.174532i
$973$	−6.19971	−	43.1199i	−0.198754	−	1.38236i
$974$	4.28878	+	4.94952i	0.137422	+	0.158593i
$975$	−14.6422			−0.468927
$976$	−7.86446			−0.251735
$977$	−7.26620	−	8.38564i	−0.232466	−	0.268280i	0.627517	−	0.778603i	$-0.284071\pi$
$977$	−7.26620	−	8.38564i	−0.232466	−	0.268280i	−0.859983	+	0.510323i	$0.829526\pi$
$978$	8.67380	−	18.9930i	0.277357	−	0.607328i
$979$	−4.81684	+	3.09559i	−0.153947	+	0.0989356i
$980$	3.79905	−	4.38434i	0.121356	−	0.140053i
$981$	−13.3359	+	8.57048i	−0.425783	+	0.273634i
$982$	−1.16793	+	8.12315i	−0.0372703	+	0.259220i
$983$	−8.72407	−	60.6772i	−0.278255	−	1.93530i	−0.347447	−	0.937700i	$-0.612951\pi$
$983$	−8.72407	−	60.6772i	−0.278255	−	1.93530i	0.0691921	−	0.997603i	$-0.477958\pi$
$984$	−7.61781	+	16.6807i	−0.242847	+	0.531760i
$985$	−1.45356	+	10.1097i	−0.0463142	+	0.322122i
$986$	4.13279	−	1.21350i	0.131615	−	0.0386456i
$987$	−19.8342	−	12.7466i	−0.631329	−	0.405730i
$988$	25.8636	−	16.6215i	0.822831	−	0.528802i
$989$	−17.6179	−	38.5777i	−0.560215	−	1.22670i
$990$	−3.86227	+	1.13407i	−0.122751	+	0.0360430i
$991$	25.8570	+	16.6173i	0.821374	+	0.527865i	0.882526	−	0.470263i	$-0.155841\pi$
$991$	25.8570	+	16.6173i	0.821374	+	0.527865i	−0.0611521	+	0.998128i	$0.519477\pi$
$992$	0.179027	−	0.206608i	0.00568410	−	0.00655981i
$993$	23.9873	−	27.6828i	0.761213	−	0.878487i
$994$	−16.2820	−	35.6526i	−0.516433	−	1.13083i
$995$	1.95404	+	13.5906i	0.0619471	+	0.430852i
$996$	24.5490	+	7.20823i	0.777864	+	0.228402i
$997$	−33.1869	−	38.2998i	−1.05104	−	1.21297i	−0.976448	−	0.215751i	$-0.930780\pi$
$997$	−33.1869	−	38.2998i	−1.05104	−	1.21297i	−0.0745921	−	0.997214i	$-0.523765\pi$
$998$	−8.94995	−	2.62794i	−0.283306	−	0.0831861i
$999$	2.51451	−	5.50600i	0.0795555	−	0.174202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.k.b.131.1	✓	50
67.22	even	11	inner	670.2.k.b.491.1	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.k.b.131.1	✓	50	1.1	even	1	trivial
670.2.k.b.491.1	yes	50	67.22	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.325974 + 2.26720i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.951514 - 2.08352i) q^{6} +(3.43296 + 1.00801i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-2.15545 - 0.632899i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.325974 + 2.26720i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.951514 - 2.08352i) q^{6} +(3.43296 + 1.00801i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-2.15545 - 0.632899i) q^{9} +(0.142315 + 0.989821i) q^{10} +(-0.744365 - 1.62993i) q^{11} +(-1.49997 + 1.73105i) q^{12} +(4.18624 - 4.83118i) q^{13} +(-3.00991 - 1.93435i) q^{14} +(2.19773 - 0.645312i) q^{15} +(0.415415 + 0.909632i) q^{16} +(1.85294 - 1.19081i) q^{17} +(1.88984 + 1.21452i) q^{18} +(4.61455 - 1.35495i) q^{19} +(0.142315 - 0.989821i) q^{20} +(-3.40441 + 7.45463i) q^{21} +(0.255008 + 1.77362i) q^{22} +(0.588567 - 4.09358i) q^{23} +(1.92690 - 1.23835i) q^{24} +(-0.654861 + 0.755750i) q^{25} +(-5.37776 + 3.45608i) q^{26} +(-0.717011 + 1.57004i) q^{27} +(2.34302 + 2.70399i) q^{28} -1.95555 q^{29} -2.29051 q^{30} +(0.179027 + 0.206608i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(3.93803 - 1.15631i) q^{33} +(-2.11337 + 0.620541i) q^{34} +(-0.509187 - 3.54147i) q^{35} +(-1.47111 - 1.69776i) q^{36} -3.50693 q^{37} -4.80936 q^{38} +(9.58863 + 11.0659i) q^{39} +(-0.415415 + 0.909632i) q^{40} +(-6.73507 + 4.32836i) q^{41} +(5.36672 - 6.19353i) q^{42} +(8.62684 - 5.54413i) q^{43} +(0.255008 - 1.77362i) q^{44} +(0.319703 + 2.22359i) q^{45} +(-1.71802 + 3.76194i) q^{46} +(-0.409428 + 2.84763i) q^{47} +(-2.19773 + 0.645312i) q^{48} +(4.88038 + 3.13643i) q^{49} +(0.841254 - 0.540641i) q^{50} +(2.09579 + 4.58915i) q^{51} +(6.13362 - 1.80099i) q^{52} +(2.78499 + 1.78981i) q^{53} +(1.13030 - 1.30443i) q^{54} +(-1.17342 + 1.35420i) q^{55} +(-1.48631 - 3.25457i) q^{56} +(1.56773 + 10.9038i) q^{57} +(1.87633 + 0.550941i) q^{58} +(7.23604 + 8.35084i) q^{59} +(2.19773 + 0.645312i) q^{60} +(-3.26701 + 7.15376i) q^{61} +(-0.113567 - 0.248676i) q^{62} +(-6.76163 - 4.34543i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-6.13362 - 1.80099i) q^{65} -4.10428 q^{66} +(6.37098 - 5.13912i) q^{67} +2.20259 q^{68} +(9.08909 + 2.66880i) q^{69} +(-0.509187 + 3.54147i) q^{70} +(9.21563 + 5.92253i) q^{71} +(0.933210 + 2.04344i) q^{72} +(-3.40684 + 7.45993i) q^{73} +(3.36487 + 0.988015i) q^{74} +(-1.49997 - 1.73105i) q^{75} +(4.61455 + 1.35495i) q^{76} +(-0.912392 - 6.34583i) q^{77} +(-6.08261 - 13.3191i) q^{78} +(-10.6653 + 12.3084i) q^{79} +(0.654861 - 0.755750i) q^{80} +(-8.99536 - 5.78097i) q^{81} +(7.68169 - 2.25555i) q^{82} +(-4.64025 - 10.1607i) q^{83} +(-6.89425 + 4.43067i) q^{84} +(-1.85294 - 1.19081i) q^{85} +(-9.83936 + 2.88910i) q^{86} +(0.637457 - 4.43361i) q^{87} +(-0.744365 + 1.62993i) q^{88} +(-0.454759 - 3.16292i) q^{89} +(0.319703 - 2.22359i) q^{90} +(19.2411 - 12.3655i) q^{91} +(2.70829 - 3.12553i) q^{92} +(-0.526779 + 0.338540i) q^{93} +(1.19511 - 2.61693i) q^{94} +(-3.14946 - 3.63467i) q^{95} +2.29051 q^{96} +5.62635 q^{97} +(-3.79905 - 4.38434i) q^{98} +(0.572864 + 3.98436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{2} + 2 q^{3} - 5 q^{4} + 5 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9}+O(q^{10}) \) 50 * q - 5 * q^2 + 2 * q^3 - 5 * q^4 + 5 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9	\( 50 q - 5 q^{2} + 2 q^{3} - 5 q^{4} + 5 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9} + 5 q^{10} + 30 q^{11} - 9 q^{12} + 20 q^{13} - 21 q^{14} - 2 q^{15} - 5 q^{16} + 2 q^{17} - q^{18} + 4 q^{19} + 5 q^{20} + 23 q^{21} - 3 q^{22} - 5 q^{23} + 2 q^{24} - 5 q^{25} - 2 q^{26} + 2 q^{27} - 10 q^{28} + 26 q^{29} - 2 q^{30} + 3 q^{31} - 5 q^{32} + 38 q^{33} + 2 q^{34} - 12 q^{35} - q^{36} + 22 q^{37} - 40 q^{38} - 35 q^{39} + 5 q^{40} - 18 q^{41} - 10 q^{42} + 87 q^{43} - 3 q^{44} + 12 q^{45} + 17 q^{46} + 35 q^{47} + 2 q^{48} + 60 q^{49} - 5 q^{50} + 19 q^{51} - 24 q^{52} - 9 q^{53} + 2 q^{54} + 25 q^{55} + 12 q^{56} + 64 q^{57} + 4 q^{58} - 49 q^{59} - 2 q^{60} - 47 q^{61} - 19 q^{62} - 24 q^{63} - 5 q^{64} + 24 q^{65} - 6 q^{66} - 21 q^{67} + 2 q^{68} - 25 q^{69} - 12 q^{70} + 92 q^{71} - q^{72} + 18 q^{73} - 22 q^{74} - 9 q^{75} + 4 q^{76} - 65 q^{77} + 31 q^{78} - 58 q^{79} + 5 q^{80} - 77 q^{81} - 18 q^{82} - 49 q^{83} - 54 q^{84} - 2 q^{85} - q^{86} - 147 q^{87} + 30 q^{88} - 21 q^{89} + 12 q^{90} + 62 q^{91} + 6 q^{92} - 34 q^{93} - 9 q^{94} + 7 q^{95} + 2 q^{96} + 98 q^{97} - 39 q^{98} - 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 + 2 * q^3 - 5 * q^4 + 5 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9 + 5 * q^10 + 30 * q^11 - 9 * q^12 + 20 * q^13 - 21 * q^14 - 2 * q^15 - 5 * q^16 + 2 * q^17 - q^18 + 4 * q^19 + 5 * q^20 + 23 * q^21 - 3 * q^22 - 5 * q^23 + 2 * q^24 - 5 * q^25 - 2 * q^26 + 2 * q^27 - 10 * q^28 + 26 * q^29 - 2 * q^30 + 3 * q^31 - 5 * q^32 + 38 * q^33 + 2 * q^34 - 12 * q^35 - q^36 + 22 * q^37 - 40 * q^38 - 35 * q^39 + 5 * q^40 - 18 * q^41 - 10 * q^42 + 87 * q^43 - 3 * q^44 + 12 * q^45 + 17 * q^46 + 35 * q^47 + 2 * q^48 + 60 * q^49 - 5 * q^50 + 19 * q^51 - 24 * q^52 - 9 * q^53 + 2 * q^54 + 25 * q^55 + 12 * q^56 + 64 * q^57 + 4 * q^58 - 49 * q^59 - 2 * q^60 - 47 * q^61 - 19 * q^62 - 24 * q^63 - 5 * q^64 + 24 * q^65 - 6 * q^66 - 21 * q^67 + 2 * q^68 - 25 * q^69 - 12 * q^70 + 92 * q^71 - q^72 + 18 * q^73 - 22 * q^74 - 9 * q^75 + 4 * q^76 - 65 * q^77 + 31 * q^78 - 58 * q^79 + 5 * q^80 - 77 * q^81 - 18 * q^82 - 49 * q^83 - 54 * q^84 - 2 * q^85 - q^86 - 147 * q^87 + 30 * q^88 - 21 * q^89 + 12 * q^90 + 62 * q^91 + 6 * q^92 - 34 * q^93 - 9 * q^94 + 7 * q^95 + 2 * q^96 + 98 * q^97 - 39 * q^98 - 4 * q^99

Introduction

L-functions

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