LMFDB - Embedded newform 345.2.m.c.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,2,Mod(16,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("345.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.m (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.75483886973$
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			151.3
Character	$\chi$	$=$	345.151
Dual form			345.2.m.c.16.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.615779 - 0.710647i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.158794 - 1.10444i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(-0.133822 - 0.930750i) q^{6} +(0.864280 + 0.253775i) q^{7} +(-2.46475 + 1.58400i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.615779 - 0.710647i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.158794 - 1.10444i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(-0.133822 - 0.930750i) q^{6} +(0.864280 + 0.253775i) q^{7} +(-2.46475 + 1.58400i) q^{8} +(0.415415 + 0.909632i) q^{9} +(0.902231 - 0.264919i) q^{10} +(2.95534 - 3.41064i) q^{11} +(0.730692 - 0.843263i) q^{12} +(5.85238 - 1.71841i) q^{13} +(-0.351861 - 0.770467i) q^{14} +(-0.841254 + 0.540641i) q^{15} +(0.502202 + 0.147460i) q^{16} +(-0.180812 - 1.25758i) q^{17} +(0.390623 - 0.855346i) q^{18} +(0.225633 - 1.56932i) q^{19} +(0.938668 + 0.603245i) q^{20} +(0.589877 + 0.680754i) q^{21} -4.24360 q^{22} +(-1.58757 + 4.52544i) q^{23} -2.92985 q^{24} +(-0.654861 - 0.755750i) q^{25} +(-4.82496 - 3.10081i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(0.417522 - 0.914247i) q^{28} +(-0.532814 - 3.70580i) q^{29} +(0.902231 + 0.264919i) q^{30} +(3.33288 - 2.14191i) q^{31} +(2.22975 + 4.88248i) q^{32} +(4.33012 - 1.27144i) q^{33} +(-0.782353 + 0.902883i) q^{34} +(-0.589877 + 0.680754i) q^{35} +(1.07060 - 0.314356i) q^{36} +(-2.70297 - 5.91868i) q^{37} +(-1.25417 + 0.806006i) q^{38} +(5.85238 + 1.71841i) q^{39} +(-0.416961 - 2.90003i) q^{40} +(-2.82646 + 6.18909i) q^{41} +(0.120542 - 0.838389i) q^{42} +(6.83542 + 4.39286i) q^{43} +(-3.29756 - 3.80558i) q^{44} -1.00000 q^{45} +(4.19359 - 1.65847i) q^{46} -4.16466 q^{47} +(0.342756 + 0.395562i) q^{48} +(-5.20620 - 3.34582i) q^{49} +(-0.133822 + 0.930750i) q^{50} +(0.527788 - 1.15570i) q^{51} +(-0.968559 - 6.73647i) q^{52} +(10.5343 + 3.09316i) q^{53} +(0.791048 - 0.508376i) q^{54} +(1.87474 + 4.10510i) q^{55} +(-2.53221 + 0.743524i) q^{56} +(1.03825 - 1.19821i) q^{57} +(-2.30542 + 2.66060i) q^{58} +(-11.9901 + 3.52062i) q^{59} +(0.463519 + 1.01496i) q^{60} +(-7.38677 + 4.74719i) q^{61} +(-3.57446 - 1.04956i) q^{62} +(0.128193 + 0.891599i) q^{63} +(2.53154 - 5.54330i) q^{64} +(-0.868042 + 6.03736i) q^{65} +(-3.56994 - 2.29426i) q^{66} +(1.50531 + 1.73722i) q^{67} -1.41763 q^{68} +(-3.78219 + 2.94873i) q^{69} +0.847010 q^{70} +(-1.72414 - 1.98977i) q^{71} +(-2.46475 - 1.58400i) q^{72} +(-2.41877 + 16.8229i) q^{73} +(-2.54166 + 5.56546i) q^{74} +(-0.142315 - 0.989821i) q^{75} +(-1.69738 - 0.498397i) q^{76} +(3.41977 - 2.19776i) q^{77} +(-2.38259 - 5.21714i) q^{78} +(1.81937 - 0.534217i) q^{79} +(-0.342756 + 0.395562i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(6.13874 - 1.80250i) q^{82} +(-0.771263 - 1.68883i) q^{83} +(0.845521 - 0.543384i) q^{84} +(1.21904 + 0.357944i) q^{85} +(-1.08734 - 7.56260i) q^{86} +(1.55528 - 3.40558i) q^{87} +(-1.88171 + 13.0876i) q^{88} +(6.62590 + 4.25821i) q^{89} +(0.615779 + 0.710647i) q^{90} +5.49418 q^{91} +(4.74598 + 2.47200i) q^{92} +3.96180 q^{93} +(2.56451 + 2.95960i) q^{94} +(1.33377 + 0.857161i) q^{95} +(-0.763879 + 5.31290i) q^{96} +(-3.28889 + 7.20166i) q^{97} +(0.828171 + 5.76005i) q^{98} +(4.33012 + 1.27144i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9}+O(q^{10}) $ 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9} + 15 q^{11} - 4 q^{12} - 19 q^{13} + 55 q^{14} + 5 q^{15} + 12 q^{16} + 5 q^{17} - 11 q^{19} + 4 q^{20} + 8 q^{21} - 18 q^{22} + 14 q^{23} + 66 q^{24} - 5 q^{25} - 18 q^{26} - 5 q^{27} + 10 q^{28} - 22 q^{29} + 6 q^{31} + 33 q^{32} + 4 q^{33} + 18 q^{34} - 8 q^{35} - 15 q^{36} + 25 q^{37} - 97 q^{38} - 19 q^{39} + 22 q^{40} - 42 q^{41} - 11 q^{42} - 25 q^{43} + 25 q^{44} - 50 q^{45} - 44 q^{46} + 86 q^{47} - 10 q^{48} - 8 q^{49} - 11 q^{50} - 17 q^{51} - 67 q^{52} - 26 q^{53} - 4 q^{55} - 132 q^{56} + 22 q^{57} + 8 q^{58} - 76 q^{59} + 4 q^{60} + 13 q^{61} - 8 q^{62} + 8 q^{63} + 76 q^{64} + 8 q^{65} + 4 q^{66} + 84 q^{67} + 66 q^{68} + 25 q^{69} + 22 q^{70} + 55 q^{71} - 59 q^{73} + 17 q^{74} - 5 q^{75} + 82 q^{76} - 56 q^{77} - 7 q^{78} + 7 q^{79} + 10 q^{80} - 5 q^{81} - 150 q^{82} + 19 q^{83} + 10 q^{84} + 6 q^{85} + 44 q^{86} - 11 q^{87} - 62 q^{88} - 74 q^{89} - 56 q^{91} + 41 q^{92} + 28 q^{93} - 161 q^{94} + 11 q^{95} - 44 q^{96} - 68 q^{97} - 198 q^{98} + 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9 + 15 * q^11 - 4 * q^12 - 19 * q^13 + 55 * q^14 + 5 * q^15 + 12 * q^16 + 5 * q^17 - 11 * q^19 + 4 * q^20 + 8 * q^21 - 18 * q^22 + 14 * q^23 + 66 * q^24 - 5 * q^25 - 18 * q^26 - 5 * q^27 + 10 * q^28 - 22 * q^29 + 6 * q^31 + 33 * q^32 + 4 * q^33 + 18 * q^34 - 8 * q^35 - 15 * q^36 + 25 * q^37 - 97 * q^38 - 19 * q^39 + 22 * q^40 - 42 * q^41 - 11 * q^42 - 25 * q^43 + 25 * q^44 - 50 * q^45 - 44 * q^46 + 86 * q^47 - 10 * q^48 - 8 * q^49 - 11 * q^50 - 17 * q^51 - 67 * q^52 - 26 * q^53 - 4 * q^55 - 132 * q^56 + 22 * q^57 + 8 * q^58 - 76 * q^59 + 4 * q^60 + 13 * q^61 - 8 * q^62 + 8 * q^63 + 76 * q^64 + 8 * q^65 + 4 * q^66 + 84 * q^67 + 66 * q^68 + 25 * q^69 + 22 * q^70 + 55 * q^71 - 59 * q^73 + 17 * q^74 - 5 * q^75 + 82 * q^76 - 56 * q^77 - 7 * q^78 + 7 * q^79 + 10 * q^80 - 5 * q^81 - 150 * q^82 + 19 * q^83 + 10 * q^84 + 6 * q^85 + 44 * q^86 - 11 * q^87 - 62 * q^88 - 74 * q^89 - 56 * q^91 + 41 * q^92 + 28 * q^93 - 161 * q^94 + 11 * q^95 - 44 * q^96 - 68 * q^97 - 198 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$	$1$

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 $

$2$	−0.615779	−	0.710647i	−0.435422	−	0.502503i	0.495051	−	0.868864i	$-0.335149\pi$
$2$	−0.615779	−	0.710647i	−0.435422	−	0.502503i	−0.930473	+	0.366360i	$0.880604\pi$
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$4$	0.158794	−	1.10444i	0.0793972	−	0.552220i
$5$	−0.415415	+	0.909632i	−0.185779	+	0.406800i
$5$	−0.415415	+	0.909632i	−0.185779	+	0.406800i
$6$	−0.133822	−	0.930750i	−0.0546324	−	0.379977i
$7$	0.864280	+	0.253775i	0.326667	+	0.0959181i	0.440954	−	0.897530i	$-0.354640\pi$
$7$	0.864280	+	0.253775i	0.326667	+	0.0959181i	−0.114287	+	0.993448i	$0.536458\pi$
$8$	−2.46475	+	1.58400i	−0.871419	+	0.560027i
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$	0.902231	−	0.264919i	0.285311	−	0.0837747i
$11$	2.95534	−	3.41064i	0.891067	−	1.02835i	−0.108346	−	0.994113i	$-0.534556\pi$
$11$	2.95534	−	3.41064i	0.891067	−	1.02835i	0.999414	−	0.0342334i	$-0.0108990\pi$
$12$	0.730692	−	0.843263i	0.210932	−	0.243429i
$13$	5.85238	−	1.71841i	1.62316	−	0.476602i	0.661293	−	0.750128i	$-0.270008\pi$
$13$	5.85238	−	1.71841i	1.62316	−	0.476602i	0.961865	+	0.273526i	$0.0881899\pi$
$14$	−0.351861	−	0.770467i	−0.0940387	−	0.205916i
$15$	−0.841254	+	0.540641i	−0.217211	+	0.139593i
$16$	0.502202	+	0.147460i	0.125551	+	0.0368650i
$17$	−0.180812	−	1.25758i	−0.0438534	−	0.305007i	−0.999929	−	0.0118880i	$-0.996216\pi$
$17$	−0.180812	−	1.25758i	−0.0438534	−	0.305007i	0.956076	−	0.293119i	$-0.0946933\pi$
$18$	0.390623	−	0.855346i	0.0920708	−	0.201607i
$19$	0.225633	−	1.56932i	0.0517639	−	0.360026i	−0.947433	−	0.319954i	$-0.896332\pi$
$19$	0.225633	−	1.56932i	0.0517639	−	0.360026i	0.999197	−	0.0400713i	$-0.0127585\pi$
$20$	0.938668	+	0.603245i	0.209893	+	0.134890i
$21$	0.589877	+	0.680754i	0.128722	+	0.148553i
$22$	−4.24360			−0.904738
$23$	−1.58757	+	4.52544i	−0.331032	+	0.943619i
$23$	−1.58757	+	4.52544i	−0.331032	+	0.943619i
$24$	−2.92985			−0.598053
$25$	−0.654861	−	0.755750i	−0.130972	−	0.151150i
$26$	−4.82496	−	3.10081i	−0.946252	−	0.608119i
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$	0.417522	−	0.914247i	0.0789043	−	0.172776i
$29$	−0.532814	−	3.70580i	−0.0989410	−	0.688150i	−0.977565	−	0.210635i	$-0.932447\pi$
$29$	−0.532814	−	3.70580i	−0.0989410	−	0.688150i	0.878624	−	0.477515i	$-0.158462\pi$
$30$	0.902231	+	0.264919i	0.164724	+	0.0483674i
$31$	3.33288	−	2.14191i	0.598602	−	0.384698i	−0.205965	−	0.978559i	$-0.566033\pi$
$31$	3.33288	−	2.14191i	0.598602	−	0.384698i	0.804568	+	0.593861i	$0.202397\pi$
$32$	2.22975	+	4.88248i	0.394168	+	0.863108i
$33$	4.33012	−	1.27144i	0.753777	−	0.221329i
$34$	−0.782353	+	0.902883i	−0.134172	+	0.154843i
$35$	−0.589877	+	0.680754i	−0.0997074	+	0.115068i
$36$	1.07060	−	0.314356i	0.178433	−	0.0523927i
$37$	−2.70297	−	5.91868i	−0.444365	−	0.973025i	−0.990776	−	0.135507i	$-0.956734\pi$
$37$	−2.70297	−	5.91868i	−0.444365	−	0.973025i	0.546411	−	0.837517i	$-0.315994\pi$
$38$	−1.25417	+	0.806006i	−0.203453	+	0.130751i
$39$	5.85238	+	1.71841i	0.937130	+	0.275166i
$40$	−0.416961	−	2.90003i	−0.0659273	−	0.458535i
$41$	−2.82646	+	6.18909i	−0.441420	+	0.966574i	0.549916	+	0.835220i	$0.314660\pi$
$41$	−2.82646	+	6.18909i	−0.441420	+	0.966574i	−0.991336	+	0.131354i	$0.958068\pi$
$42$	0.120542	−	0.838389i	0.0186000	−	0.129366i
$43$	6.83542	+	4.39286i	1.04239	+	0.669905i	0.945577	−	0.325398i	$-0.105498\pi$
$43$	6.83542	+	4.39286i	1.04239	+	0.669905i	0.0968147	+	0.995302i	$0.469135\pi$
$44$	−3.29756	−	3.80558i	−0.497125	−	0.573713i
$45$	−1.00000			−0.149071
$46$	4.19359	−	1.65847i	0.618310	−	0.244527i
$47$	−4.16466			−0.607478			−0.303739	−	0.952755i	$-0.598235\pi$
$47$	−4.16466			−0.607478			−0.303739	+	0.952755i	$0.598235\pi$
$48$	0.342756	+	0.395562i	0.0494726	+	0.0570945i
$49$	−5.20620	−	3.34582i	−0.743742	−	0.477974i
$50$	−0.133822	+	0.930750i	−0.0189252	+	0.131628i
$51$	0.527788	−	1.15570i	0.0739051	−	0.161830i
$52$	−0.968559	−	6.73647i	−0.134315	−	0.934181i
$53$	10.5343	+	3.09316i	1.44700	+	0.424878i	0.908550	−	0.417777i	$-0.137191\pi$
$53$	10.5343	+	3.09316i	1.44700	+	0.424878i	0.538453	+	0.842656i	$0.319009\pi$
$54$	0.791048	−	0.508376i	0.107648	−	0.0691812i
$55$	1.87474	+	4.10510i	0.252789	+	0.553532i
$56$	−2.53221	+	0.743524i	−0.338381	+	0.0993575i
$57$	1.03825	−	1.19821i	0.137520	−	0.158706i
$58$	−2.30542	+	2.66060i	−0.302716	+	0.349353i
$59$	−11.9901	+	3.52062i	−1.56098	+	0.458345i	−0.944359	−	0.328915i	$-0.893317\pi$
$59$	−11.9901	+	3.52062i	−1.56098	+	0.458345i	−0.616621	+	0.787260i	$0.711499\pi$
$60$	0.463519	+	1.01496i	0.0598400	+	0.131031i
$61$	−7.38677	+	4.74719i	−0.945779	+	0.607815i	−0.920028	−	0.391853i	$-0.871834\pi$
$61$	−7.38677	+	4.74719i	−0.945779	+	0.607815i	−0.0257509	+	0.999668i	$0.508198\pi$
$62$	−3.57446	−	1.04956i	−0.453957	−	0.133294i
$63$	0.128193	+	0.891599i	0.0161507	+	0.112331i
$64$	2.53154	−	5.54330i	0.316443	−	0.692913i
$65$	−0.868042	+	6.03736i	−0.107667	+	0.748843i
$66$	−3.56994	−	2.29426i	−0.439429	−	0.282404i
$67$	1.50531	+	1.73722i	0.183903	+	0.212236i	0.840214	−	0.542255i	$-0.182429\pi$
$67$	1.50531	+	1.73722i	0.183903	+	0.212236i	−0.656311	+	0.754491i	$0.727884\pi$
$68$	−1.41763			−0.171913
$69$	−3.78219	+	2.94873i	−0.455322	+	0.354986i
$70$	0.847010			0.101237
$71$	−1.72414	−	1.98977i	−0.204618	−	0.236142i	0.644160	−	0.764890i	$-0.277207\pi$
$71$	−1.72414	−	1.98977i	−0.204618	−	0.236142i	−0.848779	+	0.528748i	$0.822661\pi$
$72$	−2.46475	−	1.58400i	−0.290473	−	0.186676i
$73$	−2.41877	+	16.8229i	−0.283096	+	1.96898i	−0.0389331	+	0.999242i	$0.512396\pi$
$73$	−2.41877	+	16.8229i	−0.283096	+	1.96898i	−0.244163	+	0.969734i	$0.578513\pi$
$74$	−2.54166	+	5.56546i	−0.295462	+	0.646971i
$75$	−0.142315	−	0.989821i	−0.0164331	−	0.114295i
$76$	−1.69738	−	0.498397i	−0.194703	−	0.0571701i
$77$	3.41977	−	2.19776i	0.389719	−	0.250457i
$78$	−2.38259	−	5.21714i	−0.269775	−	0.590725i
$79$	1.81937	−	0.534217i	0.204696	−	0.0601041i	−0.177777	−	0.984071i	$-0.556891\pi$
$79$	1.81937	−	0.534217i	0.204696	−	0.0601041i	0.382473	+	0.923967i	$0.375072\pi$
$80$	−0.342756	+	0.395562i	−0.0383213	+	0.0442252i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	6.13874	−	1.80250i	0.677910	−	0.199052i
$83$	−0.771263	−	1.68883i	−0.0846572	−	0.185373i	0.862569	−	0.505940i	$-0.168854\pi$
$83$	−0.771263	−	1.68883i	−0.0846572	−	0.185373i	−0.947226	+	0.320566i	$0.896127\pi$
$84$	0.845521	−	0.543384i	0.0922539	−	0.0592880i
$85$	1.21904	+	0.357944i	0.132224	+	0.0388244i
$86$	−1.08734	−	7.56260i	−0.117251	−	0.815496i
$87$	1.55528	−	3.40558i	0.166743	−	0.365116i
$88$	−1.88171	+	13.0876i	−0.200591	+	1.39514i
$89$	6.62590	+	4.25821i	0.702344	+	0.451369i	0.842455	−	0.538767i	$-0.181110\pi$
$89$	6.62590	+	4.25821i	0.702344	+	0.451369i	−0.140111	+	0.990136i	$0.544746\pi$
$90$	0.615779	+	0.710647i	0.0649088	+	0.0749088i
$91$	5.49418			0.575947
$92$	4.74598	+	2.47200i	0.494802	+	0.257723i
$93$	3.96180			0.410819
$94$	2.56451	+	2.95960i	0.264509	+	0.305260i
$95$	1.33377	+	0.857161i	0.136842	+	0.0879428i
$96$	−0.763879	+	5.31290i	−0.0779631	+	0.542245i
$97$	−3.28889	+	7.20166i	−0.333936	+	0.731218i	−0.999891	−	0.0147743i	$-0.995297\pi$
$97$	−3.28889	+	7.20166i	−0.333936	+	0.731218i	0.665955	+	0.745992i	$0.268024\pi$
$98$	0.828171	+	5.76005i	0.0836579	+	0.581853i
$99$	4.33012	+	1.27144i	0.435193	+	0.127784i
$100$	−0.938668	+	0.603245i	−0.0938668	+	0.0603245i
$101$	−2.63829	−	5.77706i	−0.262520	−	0.574839i	0.731770	−	0.681552i	$-0.238695\pi$
$101$	−2.63829	−	5.77706i	−0.262520	−	0.574839i	−0.994290	+	0.106713i	$0.965967\pi$
$102$	−1.14629	+	0.336582i	−0.113500	+	0.0333266i
$103$	−9.08561	+	10.4854i	−0.895232	+	1.03315i	0.104024	+	0.994575i	$0.466828\pi$
$103$	−9.08561	+	10.4854i	−0.895232	+	1.03315i	−0.999256	+	0.0385780i	$0.987717\pi$
$104$	−11.7027	+	13.5056i	−1.14754	+	1.32433i
$105$	−0.864280	+	0.253775i	−0.0843451	+	0.0247659i
$106$	−4.28868	−	9.39090i	−0.416553	−	0.912125i
$107$	−7.59129	+	4.87862i	−0.733877	+	0.471634i	−0.853439	−	0.521192i	$-0.825487\pi$
$107$	−7.59129	+	4.87862i	−0.733877	+	0.471634i	0.119562	+	0.992827i	$0.461851\pi$
$108$	1.07060	+	0.314356i	0.103018	+	0.0302489i
$109$	−0.402223	−	2.79752i	−0.0385260	−	0.267954i	0.961449	−	0.274982i	$-0.0886720\pi$
$109$	−0.402223	−	2.79752i	−0.0385260	−	0.267954i	−0.999975	+	0.00702803i	$0.997763\pi$
$110$	1.76285	−	3.86011i	0.168081	−	0.368047i
$111$	0.925996	−	6.44044i	0.0878917	−	0.611300i
$112$	0.396621	+	0.254893i	0.0374772	+	0.0240851i
$113$	−7.90467	−	9.12248i	−0.743609	−	0.858171i	0.250323	−	0.968162i	$-0.419463\pi$
$113$	−7.90467	−	9.12248i	−0.743609	−	0.858171i	−0.993933	+	0.109992i	$0.964918\pi$
$114$	−1.49083			−0.139629
$115$	−3.45698	−	3.32404i	−0.322365	−	0.309969i
$116$	−4.17744			−0.387866
$117$	3.99429	+	4.60966i	0.369272	+	0.426163i
$118$	9.88518	+	6.35282i	0.910004	+	0.584824i
$119$	0.162870	−	1.13278i	0.0149302	−	0.103842i
$120$	1.21710	−	2.66508i	0.111106	−	0.243288i
$121$	−1.33299	−	9.27114i	−0.121181	−	0.842831i
$122$	7.92219	+	2.32617i	0.717241	+	0.210601i
$123$	−5.72385	+	3.67849i	−0.516102	+	0.331679i
$124$	−1.83637	−	4.02108i	−0.164911	−	0.361104i
$125$	0.959493	−	0.281733i	0.0858197	−	0.0251989i
$126$	0.554674	−	0.640127i	0.0494143	−	0.0570271i
$127$	−11.2472	+	12.9799i	−0.998024	+	1.15178i	−0.00961731	+	0.999954i	$0.503061\pi$
$127$	−11.2472	+	12.9799i	−0.998024	+	1.15178i	−0.988407	+	0.151828i	$0.951484\pi$
$128$	4.80201	−	1.41000i	0.424442	−	0.124627i
$129$	3.37536	+	7.39102i	0.297184	+	0.650743i
$130$	4.82496	−	3.10081i	0.423177	−	0.271959i
$131$	−10.5199	−	3.08892i	−0.919129	−	0.269881i	−0.212250	−	0.977215i	$-0.568079\pi$
$131$	−10.5199	−	3.08892i	−0.919129	−	0.269881i	−0.706879	+	0.707335i	$0.749897\pi$
$132$	−0.716627	−	4.98425i	−0.0623744	−	0.433823i
$133$	0.593264	−	1.29907i	0.0514425	−	0.112643i
$134$	0.307613	−	2.13949i	0.0265737	−	0.184824i
$135$	−0.841254	−	0.540641i	−0.0724036	−	0.0465310i
$136$	2.43765	+	2.81320i	0.209027	+	0.241230i
$137$	20.8050			1.77749			0.888744	−	0.458405i	$-0.151579\pi$
$137$	20.8050			1.77749			0.888744	+	0.458405i	$0.151579\pi$
$138$	4.42450	+	0.872033i	0.376639	+	0.0742324i
$139$	5.01420			0.425299			0.212649	−	0.977129i	$-0.431791\pi$
$139$	5.01420			0.425299			0.212649	+	0.977129i	$0.431791\pi$
$140$	0.658183	+	0.759584i	0.0556266	+	0.0641965i
$141$	−3.50354	−	2.25159i	−0.295051	−	0.189618i
$142$	−0.352331	+	2.45052i	−0.0295670	+	0.205643i
$143$	11.4349	−	25.0388i	0.956231	−	2.09385i
$144$	0.0744881	+	0.518076i	0.00620734	+	0.0431730i
$145$	3.59225	+	1.05478i	0.298320	+	0.0875948i
$146$	13.4446	−	8.64032i	1.11268	−	0.715078i
$147$	−2.57085	−	5.62937i	−0.212040	−	0.464302i
$148$	−6.96604	+	2.04541i	−0.572605	+	0.168132i
$149$	11.5790	−	13.3629i	0.948589	−	1.09473i	−0.0468089	−	0.998904i	$-0.514905\pi$
$149$	11.5790	−	13.3629i	0.948589	−	1.09473i	0.995398	−	0.0958264i	$-0.0305494\pi$
$150$	−0.615779	+	0.710647i	−0.0502782	+	0.0580241i
$151$	−15.6692	+	4.60090i	−1.27514	+	0.374416i	−0.848110	−	0.529821i	$-0.822259\pi$
$151$	−15.6692	+	4.60090i	−1.27514	+	0.374416i	−0.427033	+	0.904236i	$0.640441\pi$
$152$	1.92966	+	4.22537i	0.156516	+	0.342722i
$153$	1.06882	−	0.686889i	0.0864090	−	0.0555317i
$154$	−3.66765	−	1.07692i	−0.295548	−	0.0867807i
$155$	0.563823	+	3.92147i	0.0452873	+	0.314980i
$156$	2.82721	−	6.19072i	0.226358	−	0.495655i
$157$	2.08040	−	14.4695i	0.166034	−	1.15479i	−0.720949	−	0.692988i	$-0.756294\pi$
$157$	2.08040	−	14.4695i	0.166034	−	1.15479i	0.886983	−	0.461803i	$-0.152797\pi$
$158$	−1.49997	−	0.963974i	−0.119331	−	0.0766896i
$159$	7.18976	+	8.29743i	0.570185	+	0.658029i
$160$	−5.36753			−0.424340
$161$	−2.52055	+	3.50836i	−0.198647	+	0.276497i
$162$	0.940321			0.0738786
$163$	−0.542188	−	0.625718i	−0.0424674	−	0.0490100i	0.734118	−	0.679021i	$-0.237596\pi$
$163$	−0.542188	−	0.625718i	−0.0424674	−	0.0490100i	−0.776586	+	0.630011i	$0.783050\pi$
$164$	6.38665	+	4.10445i	0.498714	+	0.320504i
$165$	−0.642256	+	4.46699i	−0.0499996	+	0.347755i
$166$	−0.725235	+	1.58804i	−0.0562892	+	0.123256i
$167$	−1.93010	−	13.4242i	−0.149356	−	1.03879i	−0.917278	−	0.398248i	$-0.869618\pi$
$167$	−1.93010	−	13.4242i	−0.149356	−	1.03879i	0.767922	−	0.640544i	$-0.221291\pi$
$168$	−2.53221	−	0.743524i	−0.195364	−	0.0573641i
$169$	20.3611	−	13.0853i	1.56624	−	1.00656i
$170$	−0.496290	−	1.08672i	−0.0380637	−	0.0833479i
$171$	1.52123	−	0.446674i	0.116331	−	0.0341580i
$172$	5.93707	−	6.85175i	0.452698	−	0.522441i
$173$	1.82429	−	2.10534i	0.138698	−	0.160066i	−0.682151	−	0.731212i	$-0.738955\pi$
$173$	1.82429	−	2.10534i	0.138698	−	0.160066i	0.820849	+	0.571145i	$0.193501\pi$
$174$	−3.37787	+	0.991832i	−0.256076	+	0.0751906i
$175$	−0.374192	−	0.819367i	−0.0282863	−	0.0619383i
$176$	1.98711	−	1.27704i	0.149784	−	0.0962603i
$177$	−11.9901	−	3.52062i	−0.901232	−	0.264626i
$178$	−1.05401	−	7.33079i	−0.0790013	−	0.549466i
$179$	1.54952	−	3.39298i	0.115817	−	0.253603i	−0.842842	−	0.538161i	$-0.819119\pi$
$179$	1.54952	−	3.39298i	0.115817	−	0.253603i	0.958659	+	0.284557i	$0.0918466\pi$
$180$	−0.158794	+	1.10444i	−0.0118358	+	0.0823201i
$181$	11.6314	+	7.47506i	0.864557	+	0.555617i	0.896083	−	0.443886i	$-0.146401\pi$
$181$	11.6314	+	7.47506i	0.864557	+	0.555617i	−0.0315265	+	0.999503i	$0.510037\pi$
$182$	−3.38320	−	3.90442i	−0.250780	−	0.289415i
$183$	−8.78067			−0.649086
$184$	−3.25531	−	13.6688i	−0.239985	−	1.00767i
$185$	6.50667			0.478380
$186$	−2.43959	−	2.81544i	−0.178880	−	0.206438i
$187$	−4.82350	−	3.09988i	−0.352729	−	0.226685i
$188$	−0.661325	+	4.59962i	−0.0482321	+	0.335462i
$189$	−0.374192	+	0.819367i	−0.0272185	+	0.0596001i
$190$	−0.212168	−	1.47566i	−0.0153923	−	0.107056i
$191$	0.0538563	+	0.0158136i	0.00389690	+	0.00114423i	0.283680	−	0.958919i	$-0.408445\pi$
$191$	0.0538563	+	0.0158136i	0.00389690	+	0.00114423i	−0.279784	+	0.960063i	$0.590263\pi$
$192$	5.12660	−	3.29467i	0.369981	−	0.237772i
$193$	−6.38292	−	13.9766i	−0.459453	−	1.00606i	−0.987612	−	0.156916i	$-0.949845\pi$
$193$	−6.38292	−	13.9766i	−0.459453	−	1.00606i	0.528159	−	0.849145i	$-0.322882\pi$
$194$	7.14307	−	2.09739i	0.512842	−	0.150584i
$195$	−3.99429	+	4.60966i	−0.286037	+	0.330104i
$196$	−4.52197	+	5.21863i	−0.322998	+	0.372760i
$197$	−10.9960	+	3.22873i	−0.783436	+	0.230038i	−0.648903	−	0.760871i	$-0.724772\pi$
$197$	−10.9960	+	3.22873i	−0.783436	+	0.230038i	−0.134533	+	0.990909i	$0.542954\pi$
$198$	−1.76285	−	3.86011i	−0.125281	−	0.274326i
$199$	8.36830	−	5.37798i	0.593213	−	0.381235i	−0.209316	−	0.977848i	$-0.567124\pi$
$199$	8.36830	−	5.37798i	0.593213	−	0.381235i	0.802529	+	0.596613i	$0.203487\pi$
$200$	2.81117	+	0.825434i	0.198780	+	0.0583670i
$201$	0.327136	+	2.27528i	0.0230744	+	0.160486i
$202$	−2.48084	+	5.43229i	−0.174551	+	0.382214i
$203$	0.479941	−	3.33806i	0.0336853	−	0.234286i
$204$	−1.19259	−	0.766428i	−0.0834977	−	0.0536607i
$205$	−4.45564	−	5.14208i	−0.311195	−	0.359139i
$206$	13.0461			0.908966
$207$	−4.77599	+	0.435827i	−0.331954	+	0.0302921i
$208$	3.19247			0.221358
$209$	−4.68555	−	5.40741i	−0.324106	−	0.374038i
$210$	0.712550	+	0.457928i	0.0491706	+	0.0316000i
$211$	−2.52921	+	17.5911i	−0.174118	+	1.21102i	0.695951	+	0.718089i	$0.254983\pi$
$211$	−2.52921	+	17.5911i	−0.174118	+	1.21102i	−0.870069	+	0.492930i	$0.835926\pi$
$212$	5.08900	−	11.1434i	0.349514	−	0.765329i
$213$	−0.374692	−	2.60604i	−0.0256735	−	0.178563i
$214$	8.14153	+	2.39057i	0.556544	+	0.163416i
$215$	−6.83542	+	4.39286i	−0.466172	+	0.299590i
$216$	−1.21710	−	2.66508i	−0.0828134	−	0.181336i
$217$	3.42410	−	1.00541i	0.232443	−	0.0682515i
$218$	−1.74037	+	2.00850i	−0.117873	+	0.136033i
$219$	−11.1300	+	12.8447i	−0.752094	+	0.867962i
$220$	4.83153	−	1.41867i	0.325742	−	0.0956464i
$221$	−3.21922	−	7.04910i	−0.216548	−	0.474174i
$222$	−5.14709	+	3.30783i	−0.345450	+	0.222007i
$223$	−4.24243	−	1.24569i	−0.284094	−	0.0834175i	0.136581	−	0.990629i	$-0.456389\pi$
$223$	−4.24243	−	1.24569i	−0.284094	−	0.0834175i	−0.420675	+	0.907211i	$0.638207\pi$
$224$	0.688077	+	4.78568i	0.0459741	+	0.319757i
$225$	0.415415	−	0.909632i	0.0276943	−	0.0606421i
$226$	−1.61533	+	11.2349i	−0.107450	+	0.747332i
$227$	3.85969	+	2.48047i	0.256177	+	0.164635i	0.662426	−	0.749128i	$-0.269527\pi$
$227$	3.85969	+	2.48047i	0.256177	+	0.164635i	−0.406249	+	0.913762i	$0.633163\pi$
$228$	−1.15848	−	1.33695i	−0.0767220	−	0.0885419i
$229$	−21.0759			−1.39273			−0.696366	−	0.717687i	$-0.745201\pi$
$229$	−21.0759			−1.39273			−0.696366	+	0.717687i	$0.745201\pi$
$230$	−0.233485	+	4.50357i	−0.0153955	+	0.296957i
$231$	4.06509			0.267463
$232$	7.18322	+	8.28988i	0.471602	+	0.544257i
$233$	7.63511	+	4.90679i	0.500193	+	0.321454i	0.766293	−	0.642491i	$-0.222099\pi$
$233$	7.63511	+	4.90679i	0.500193	+	0.321454i	−0.266101	+	0.963945i	$0.585735\pi$
$234$	0.816238	−	5.67706i	0.0533591	−	0.371121i
$235$	1.73006	−	3.78831i	0.112857	−	0.247122i
$236$	1.98434	+	13.8014i	0.129170	+	0.898395i
$237$	1.81937	+	0.534217i	0.118181	+	0.0347011i
$238$	−0.905301	+	0.581802i	−0.0586820	+	0.0377126i
$239$	−1.58410	−	3.46870i	−0.102467	−	0.224372i	0.851454	−	0.524429i	$-0.175721\pi$
$239$	−1.58410	−	3.46870i	−0.102467	−	0.224372i	−0.953921	+	0.300058i	$0.902994\pi$
$240$	−0.502202	+	0.147460i	−0.0324170	+	0.00951849i
$241$	14.4378	−	16.6621i	0.930017	−	1.07330i	−0.0671244	−	0.997745i	$-0.521382\pi$
$241$	14.4378	−	16.6621i	0.930017	−	1.07330i	0.997142	−	0.0755527i	$-0.0240721\pi$
$242$	−5.76768	+	6.65626i	−0.370761	+	0.427881i
$243$	−0.959493	+	0.281733i	−0.0615515	+	0.0180732i
$244$	4.07000	+	8.91207i	0.260555	+	0.570537i
$245$	5.20620	−	3.34582i	0.332612	−	0.213757i
$246$	6.13874	+	1.80250i	0.391392	+	0.114923i
$247$	−1.37624	−	9.57196i	−0.0875680	−	0.609049i
$248$	−4.82192	+	10.5585i	−0.306192	+	0.670467i
$249$	0.264223	−	1.83771i	0.0167445	−	0.116460i
$250$	−0.791048	−	0.508376i	−0.0500303	−	0.0321525i
$251$	11.9112	+	13.7463i	0.751830	+	0.867658i	0.994744	−	0.102390i	$-0.0326490\pi$
$251$	11.9112	+	13.7463i	0.751830	+	0.867658i	−0.242915	+	0.970048i	$0.578104\pi$
$252$	1.00507			0.0633137
$253$	10.7428	+	18.7888i	0.675396	+	1.18124i
$254$	16.1499			1.01334
$255$	0.832006	+	0.960186i	0.0521022	+	0.0601292i
$256$	−14.2122	−	9.13363i	−0.888262	−	0.570852i
$257$	−1.20331	+	8.36918i	−0.0750602	+	0.522055i	0.917253	+	0.398305i	$0.130401\pi$
$257$	−1.20331	+	8.36918i	−0.0750602	+	0.522055i	−0.992313	+	0.123750i	$0.960508\pi$
$258$	3.17392	−	6.94993i	0.197600	−	0.432683i
$259$	−0.834107	−	5.80134i	−0.0518289	−	0.360478i
$260$	6.53006	+	1.91740i	0.404977	+	0.118912i
$261$	3.14958	−	2.02411i	0.194954	−	0.125289i
$262$	4.28281	+	9.37804i	0.264593	+	0.579377i
$263$	−13.1208	+	3.85261i	−0.809062	+	0.237562i	−0.660000	−	0.751266i	$-0.729444\pi$
$263$	−13.1208	+	3.85261i	−0.809062	+	0.237562i	−0.149062	+	0.988828i	$0.547626\pi$
$264$	−8.65869	+	9.99266i	−0.532905	+	0.615006i
$265$	−7.18976	+	8.29743i	−0.441663	+	0.509707i
$266$	−1.28850	+	0.378337i	−0.0790029	+	0.0231973i
$267$	3.27190	+	7.16446i	0.200237	+	0.438458i
$268$	2.15769	−	1.38667i	0.131802	−	0.0847041i
$269$	27.8210	+	8.16897i	1.69627	+	0.498071i	0.979874	−	0.199619i	$-0.0639704\pi$
$269$	27.8210	+	8.16897i	1.69627	+	0.498071i	0.716400	+	0.697690i	$0.245789\pi$
$270$	0.133822	+	0.930750i	0.00814412	+	0.0566436i
$271$	−3.69698	+	8.09527i	−0.224576	+	0.491752i	−0.988059	−	0.154075i	$-0.950760\pi$
$271$	−3.69698	+	8.09527i	−0.224576	+	0.491752i	0.763483	+	0.645828i	$0.223488\pi$
$272$	0.0946378	−	0.658220i	0.00573826	−	0.0399105i
$273$	4.62200	+	2.97038i	0.279736	+	0.179776i
$274$	−12.8113	−	14.7850i	−0.773956	−	0.893193i
$275$	−4.51292			−0.272140
$276$	2.65611	+	4.64544i	0.159879	+	0.279623i
$277$	−19.9351			−1.19778			−0.598892	−	0.800830i	$-0.704392\pi$
$277$	−19.9351			−1.19778			−0.598892	+	0.800830i	$0.704392\pi$
$278$	−3.08764	−	3.56332i	−0.185184	−	0.213714i
$279$	3.33288	+	2.14191i	0.199534	+	0.128233i
$280$	0.375585	−	2.61225i	0.0224455	−	0.156112i
$281$	6.59863	−	14.4490i	0.393641	−	0.861954i	−0.604235	−	0.796807i	$-0.706521\pi$
$281$	6.59863	−	14.4490i	0.393641	−	0.861954i	0.997876	−	0.0651473i	$-0.0207517\pi$
$282$	0.557322	+	3.87626i	0.0331880	+	0.230828i
$283$	2.27967	+	0.669371i	0.135512	+	0.0397900i	0.348785	−	0.937203i	$-0.386594\pi$
$283$	2.27967	+	0.669371i	0.135512	+	0.0397900i	−0.213273	+	0.976993i	$0.568412\pi$
$284$	−2.47136	+	1.58825i	−0.146648	+	0.0942452i
$285$	0.658621	+	1.44218i	0.0390133	+	0.0854273i
$286$	−24.8351	+	7.29225i	−1.46853	+	0.431200i
$287$	−4.01350	+	4.63182i	−0.236909	+	0.273408i
$288$	−3.51498	+	4.05651i	−0.207122	+	0.239032i
$289$	14.7626	−	4.33468i	0.868387	−	0.254981i
$290$	−1.46246	−	3.20234i	−0.0858785	−	0.188048i
$291$	−6.66030	+	4.28031i	−0.390434	+	0.250916i
$292$	18.1958	+	5.34278i	1.06483	+	0.312662i
$293$	−3.92314	−	27.2861i	−0.229193	−	1.59407i	−0.701522	−	0.712647i	$-0.747496\pi$
$293$	−3.92314	−	27.2861i	−0.229193	−	1.59407i	0.472330	−	0.881422i	$-0.343413\pi$
$294$	−2.41742	+	5.29341i	−0.140987	+	0.308718i
$295$	1.77841	−	12.3691i	0.103543	−	0.720157i
$296$	16.0373	+	10.3065i	0.932149	+	0.599056i
$297$	2.95534	+	3.41064i	0.171486	+	0.197905i
$298$	−16.6264			−0.963142
$299$	−1.51451	+	29.2127i	−0.0875865	+	1.68941i
$300$	−1.11580			−0.0644206
$301$	4.79292	+	5.53132i	0.276259	+	0.318820i
$302$	12.9184	+	8.30214i	0.743370	+	0.477735i
$303$	0.903839	−	6.28634i	0.0519242	−	0.361141i
$304$	0.344725	−	0.754841i	0.0197713	−	0.0432931i
$305$	−1.24962	−	8.69129i	−0.0715530	−	0.497662i
$306$	−1.14629	−	0.336582i	−0.0655292	−	0.0192411i
$307$	−19.8316	+	12.7450i	−1.13185	+	0.727397i	−0.965946	−	0.258745i	$-0.916691\pi$
$307$	−19.8316	+	12.7450i	−1.13185	+	0.727397i	−0.165906	+	0.986142i	$0.553055\pi$
$308$	−1.88425	−	4.12593i	−0.107365	−	0.235096i
$309$	−13.3121	+	3.90879i	−0.757300	+	0.222363i
$310$	2.43959	−	2.81544i	0.138560	−	0.159906i
$311$	−5.40269	+	6.23503i	−0.306358	+	0.353556i	−0.887963	−	0.459915i	$-0.847880\pi$
$311$	−5.40269	+	6.23503i	−0.306358	+	0.353556i	0.581604	+	0.813472i	$0.302425\pi$
$312$	−17.1466	+	5.03469i	−0.970734	+	0.285033i
$313$	2.09669	+	4.59111i	0.118512	+	0.259505i	0.959586	−	0.281415i	$-0.0908036\pi$
$313$	2.09669	+	4.59111i	0.118512	+	0.259505i	−0.841074	+	0.540920i	$0.818076\pi$
$314$	−11.5638	+	7.43158i	−0.652581	+	0.419388i
$315$	−0.864280	−	0.253775i	−0.0486966	−	0.0142986i
$316$	−0.301103	−	2.09422i	−0.0169384	−	0.117809i
$317$	−5.58060	+	12.2198i	−0.313438	+	0.686333i	−0.999136	−	0.0415525i	$-0.986770\pi$
$317$	−5.58060	+	12.2198i	−0.313438	+	0.686333i	0.685698	+	0.727886i	$0.259497\pi$
$318$	1.46924	−	10.2188i	0.0823907	−	0.573040i
$319$	−14.2138	−	9.13465i	−0.795820	−	0.511442i
$320$	3.99073	+	4.60554i	0.223088	+	0.257458i
$321$	−9.02378			−0.503658
$322$	4.04531	−	0.369150i	0.225436	−	0.0205719i
$323$	−2.01433			−0.112080
$324$	0.730692	+	0.843263i	0.0405940	+	0.0468479i
$325$	−5.13118	−	3.29761i	−0.284627	−	0.182919i
$326$	−0.110797	+	0.770608i	−0.00613647	+	0.0426801i
$327$	1.17408	−	2.57089i	0.0649270	−	0.142170i
$328$	−2.83698	−	19.7316i	−0.156646	−	1.08950i
$329$	−3.59943	−	1.05689i	−0.198443	−	0.0582682i
$330$	3.56994	−	2.29426i	0.196519	−	0.126295i
$331$	13.0818	+	28.6451i	0.719040	+	1.57448i	0.815245	+	0.579117i	$0.196603\pi$
$331$	13.0818	+	28.6451i	0.719040	+	1.57448i	−0.0962043	+	0.995362i	$0.530670\pi$
$332$	−1.98768	+	0.583637i	−0.109088	+	0.0320312i
$333$	4.26096	−	4.91741i	0.233499	−	0.269473i
$334$	−8.35132	+	9.63793i	−0.456964	+	0.527364i
$335$	−2.20556	+	0.647612i	−0.120503	+	0.0353828i
$336$	0.195854	+	0.428859i	0.0106847	+	0.0233962i
$337$	0.587465	−	0.377541i	0.0320013	−	0.0205660i	−0.524542	−	0.851384i	$-0.675764\pi$
$337$	0.587465	−	0.377541i	0.0320013	−	0.0205660i	0.556544	+	0.830818i	$0.312127\pi$
$338$	−21.8369	−	6.41190i	−1.18777	−	0.348762i
$339$	−1.71785	−	11.9479i	−0.0933008	−	0.648921i
$340$	0.588905	−	1.28952i	0.0319378	−	0.0699341i
$341$	2.54449	−	17.6973i	0.137792	−	0.958363i
$342$	−1.25417	−	0.806006i	−0.0678177	−	0.0435838i
$343$	−7.77966	−	8.97821i	−0.420062	−	0.484778i
$344$	−23.8058			−1.28352
$345$	−1.11108	−	4.66535i	−0.0598188	−	0.251174i
$346$	−2.61952			−0.140826
$347$	−0.0315978	−	0.0364658i	−0.00169626	−	0.00195758i	0.754901	−	0.655839i	$-0.227685\pi$
$347$	−0.0315978	−	0.0364658i	−0.00169626	−	0.00195758i	−0.756597	+	0.653881i	$0.773140\pi$
$348$	−3.51429	−	2.25849i	−0.188386	−	0.121068i
$349$	−2.86522	+	19.9280i	−0.153372	+	1.06672i	0.757144	+	0.653248i	$0.226594\pi$
$349$	−2.86522	+	19.9280i	−0.153372	+	1.06672i	−0.910516	+	0.413475i	$0.864315\pi$
$350$	−0.351861	+	0.770467i	−0.0188077	+	0.0411832i
$351$	0.868042	+	6.03736i	0.0463327	+	0.322251i
$352$	23.2420	+	6.82448i	1.23880	+	0.363746i
$353$	15.2042	−	9.77112i	0.809236	−	0.520064i	−0.0693817	−	0.997590i	$-0.522103\pi$
$353$	15.2042	−	9.77112i	0.809236	−	0.520064i	0.878618	+	0.477526i	$0.158466\pi$
$354$	4.88135	+	10.6887i	0.259441	+	0.568096i
$355$	2.52619	−	0.741757i	0.134076	−	0.0393684i
$356$	5.75509	−	6.64172i	0.305019	−	0.352011i
$357$	0.749444	−	0.864904i	0.0396648	−	0.0457756i
$358$	−3.36538	+	0.988163i	−0.177866	+	0.0522261i
$359$	−10.6691	−	23.3620i	−0.563092	−	1.23300i	−0.950395	−	0.311046i	$-0.899321\pi$
$359$	−10.6691	−	23.3620i	−0.563092	−	1.23300i	0.387303	−	0.921952i	$-0.373407\pi$
$360$	2.46475	−	1.58400i	0.129903	−	0.0834839i
$361$	15.8185	+	4.64474i	0.832554	+	0.244460i
$362$	−1.85026	−	12.8688i	−0.0972474	−	0.676370i
$363$	3.89098	−	8.52005i	0.204223	−	0.447187i
$364$	0.872446	−	6.06799i	0.0457286	−	0.318049i
$365$	−14.2979	−	9.18870i	−0.748386	−	0.480958i
$366$	5.40695	+	6.23995i	0.282626	+	0.326168i
$367$	−11.0459			−0.576593			−0.288296	−	0.957541i	$-0.593089\pi$
$367$	−11.0459			−0.576593			−0.288296	+	0.957541i	$0.593089\pi$
$368$	−1.46460	+	2.03858i	−0.0763478	+	0.106268i
$369$	−6.80395			−0.354200
$370$	−4.00667	−	4.62395i	−0.208297	−	0.240388i
$371$	8.31965	+	5.34671i	0.431935	+	0.277587i
$372$	0.629111	−	4.37557i	0.0326179	−	0.226863i
$373$	−9.34401	+	20.4605i	−0.483815	+	1.05941i	0.497582	+	0.867417i	$0.334221\pi$
$373$	−9.34401	+	20.4605i	−0.483815	+	1.05941i	−0.981397	+	0.191989i	$0.938506\pi$
$374$	0.767294	+	5.33665i	0.0396758	+	0.275951i
$375$	0.959493	+	0.281733i	0.0495480	+	0.0145486i
$376$	10.2648	−	6.59681i	0.529368	−	0.340204i
$377$	−9.48632	−	20.7721i	−0.488570	−	1.06982i
$378$	0.812700	−	0.238630i	0.0418008	−	0.0122738i
$379$	20.5953	−	23.7682i	1.05791	−	1.22089i	0.0834072	−	0.996516i	$-0.473420\pi$
$379$	20.5953	−	23.7682i	1.05791	−	1.22089i	0.974502	−	0.224377i	$-0.0720348\pi$
$380$	1.15848	−	1.33695i	0.0594286	−	0.0685843i
$381$	−16.4792	+	4.83873i	−0.844254	+	0.247895i
$382$	−0.0219257	−	0.0480105i	−0.00112181	−	0.00245643i
$383$	5.82350	−	3.74254i	0.297567	−	0.191235i	−0.383335	−	0.923609i	$-0.625224\pi$
$383$	5.82350	−	3.74254i	0.297567	−	0.191235i	0.680902	+	0.732375i	$0.261588\pi$
$384$	4.80201	+	1.41000i	0.245052	+	0.0719536i
$385$	0.578523	+	4.02372i	0.0294843	+	0.205068i
$386$	−6.00199	+	13.1425i	−0.305493	+	0.668937i
$387$	−1.15635	+	8.04258i	−0.0587805	+	0.408827i
$388$	7.43154	+	4.77596i	0.377279	+	0.242463i
$389$	0.835840	+	0.964610i	0.0423788	+	0.0489077i	0.776543	−	0.630064i	$-0.216971\pi$
$389$	0.835840	+	0.964610i	0.0423788	+	0.0489077i	−0.734164	+	0.678972i	$0.762426\pi$
$390$	5.73544			0.290425
$391$	5.97814	+	1.17824i	0.302328	+	0.0595863i
$392$	18.1317			0.915790
$393$	−7.17991	−	8.28606i	−0.362179	−	0.417976i
$394$	9.06563	+	5.82612i	0.456720	+	0.293516i
$395$	−0.269855	+	1.87688i	−0.0135779	+	0.0944362i
$396$	2.09182	−	4.58046i	0.105118	−	0.230177i
$397$	−3.44533	−	23.9628i	−0.172916	−	1.20266i	−0.872683	−	0.488287i	$-0.837622\pi$
$397$	−3.44533	−	23.9628i	−0.172916	−	1.20266i	0.699767	−	0.714371i	$-0.253287\pi$
$398$	−8.97487	−	2.63526i	−0.449870	−	0.132094i
$399$	1.20141	−	0.772102i	0.0601459	−	0.0386534i
$400$	−0.217430	−	0.476105i	−0.0108715	−	0.0238052i
$401$	−27.9586	+	8.20940i	−1.39619	+	0.409958i	−0.891373	−	0.453270i	$-0.850257\pi$
$401$	−27.9586	+	8.20940i	−1.39619	+	0.409958i	−0.504815	+	0.863228i	$0.668439\pi$
$402$	1.41548	−	1.63355i	0.0705976	−	0.0814739i
$403$	15.8246	−	18.2625i	0.788278	−	0.909721i
$404$	−6.79936	+	1.99647i	−0.338281	+	0.0993282i
$405$	−0.415415	−	0.909632i	−0.0206421	−	0.0452000i
$406$	−2.66772	+	1.71444i	−0.132397	+	0.0850863i
$407$	−28.1747	−	8.27283i	−1.39657	−	0.410069i
$408$	0.529752	+	3.68451i	0.0262267	+	0.182410i
$409$	8.35990	−	18.3056i	0.413370	−	0.905154i	−0.582368	−	0.812926i	$-0.697874\pi$
$409$	8.35990	−	18.3056i	0.413370	−	0.905154i	0.995738	−	0.0922289i	$-0.0293992\pi$
$410$	−0.910516	+	6.33278i	−0.0449672	+	0.312754i
$411$	17.5022	+	11.2480i	0.863322	+	0.554823i
$412$	10.1377	+	11.6995i	0.499449	+	0.576394i
$413$	−11.2563			−0.553884
$414$	3.25067	+	3.12567i	0.159762	+	0.153618i
$415$	1.85661			0.0911374
$416$	21.4395	+	24.7425i	1.05116	+	1.21310i
$417$	4.21821	+	2.71088i	0.206567	+	0.132752i
$418$	−0.957497	+	6.65954i	−0.0468327	+	0.325729i
$419$	−14.7899	+	32.3854i	−0.722536	+	1.58213i	0.0877810	+	0.996140i	$0.472022\pi$
$419$	−14.7899	+	32.3854i	−0.722536	+	1.58213i	−0.810317	+	0.585992i	$0.800705\pi$
$420$	0.143037	+	0.994843i	0.00697948	+	0.0485434i
$421$	8.86182	+	2.60207i	0.431899	+	0.126817i	0.490454	−	0.871467i	$-0.336831\pi$
$421$	8.86182	+	2.60207i	0.431899	+	0.126817i	−0.0585548	+	0.998284i	$0.518649\pi$
$422$	14.0585	−	9.03484i	0.684356	−	0.439809i
$423$	−1.73006	−	3.78831i	−0.0841185	−	0.184194i
$424$	−30.8640	+	9.06249i	−1.49889	+	0.440114i
$425$	−0.832006	+	0.960186i	−0.0403582	+	0.0465759i
$426$	−1.62125	+	1.87102i	−0.0785497	+	0.0906512i
$427$	−7.58895	+	2.22832i	−0.367255	+	0.107836i
$428$	4.18269	+	9.15882i	0.202178	+	0.442708i
$429$	23.1566	−	14.8819i	1.11801	−	0.718503i
$430$	7.33088	+	2.15254i	0.353526	+	0.103805i
$431$	−1.85785	−	12.9217i	−0.0894897	−	0.622414i	−0.984371	−	0.176109i	$-0.943649\pi$
$431$	−1.85785	−	12.9217i	−0.0894897	−	0.622414i	0.894881	−	0.446305i	$-0.147260\pi$
$432$	−0.217430	+	0.476105i	−0.0104611	+	0.0229066i
$433$	−3.68802	+	25.6508i	−0.177235	+	1.23270i	0.685889	+	0.727706i	$0.259413\pi$
$433$	−3.68802	+	25.6508i	−0.177235	+	1.23270i	−0.863124	+	0.504991i	$0.831496\pi$
$434$	−2.82298	−	1.81422i	−0.135507	−	0.0870853i
$435$	2.45174	+	2.82946i	0.117552	+	0.135662i
$436$	−3.15357			−0.151028
$437$	6.74363	+	3.51250i	0.322592	+	0.168025i
$438$	15.9816			0.763632
$439$	2.94967	+	3.40410i	0.140780	+	0.162469i	0.821761	−	0.569832i	$-0.192992\pi$
$439$	2.94967	+	3.40410i	0.140780	+	0.162469i	−0.680981	+	0.732301i	$0.738446\pi$
$440$	−11.1232	−	7.14845i	−0.530278	−	0.340789i
$441$	0.880732	−	6.12563i	0.0419396	−	0.291697i
$442$	−3.02710	+	6.62842i	−0.143984	+	0.315282i
$443$	−2.07980	−	14.4653i	−0.0988141	−	0.687267i	−0.977665	−	0.210170i	$-0.932598\pi$
$443$	−2.07980	−	14.4653i	−0.0988141	−	0.687267i	0.878851	−	0.477097i	$-0.158311\pi$
$444$	−6.96604	−	2.04541i	−0.330594	−	0.0970710i
$445$	−6.62590	+	4.25821i	−0.314098	+	0.201858i
$446$	1.72715	+	3.78194i	0.0817831	+	0.179080i
$447$	16.9654	−	4.98149i	0.802436	−	0.235616i
$448$	3.59471	−	4.14852i	0.169834	−	0.195999i
$449$	7.39752	−	8.53720i	0.349111	−	0.402895i	−0.553851	−	0.832616i	$-0.686842\pi$
$449$	7.39752	−	8.53720i	0.349111	−	0.402895i	0.902962	+	0.429720i	$0.141388\pi$
$450$	−0.902231	+	0.264919i	−0.0425316	+	0.0124884i
$451$	12.7556	+	27.9309i	0.600638	+	1.31521i
$452$	−11.3304	+	7.28164i	−0.532939	+	0.342499i
$453$	−15.6692	−	4.60090i	−0.736204	−	0.216169i
$454$	−0.613977	−	4.27030i	−0.0288154	−	0.200415i
$455$	−2.28237	+	4.99768i	−0.106999	+	0.234295i
$456$	−0.661072	+	4.59786i	−0.0309575	+	0.215314i
$457$	29.4790	+	18.9450i	1.37897	+	0.886210i	0.999244	−	0.0388895i	$-0.0123820\pi$
$457$	29.4790	+	18.9450i	1.37897	+	0.886210i	0.379726	+	0.925099i	$0.376018\pi$
$458$	12.9781	+	14.9775i	0.606426	+	0.699853i
$459$	1.27051			0.0593023
$460$	−4.22016	+	3.29019i	−0.196766	+	0.153406i
$461$	24.5923			1.14538			0.572688	−	0.819773i	$-0.305901\pi$
$461$	24.5923			1.14538			0.572688	+	0.819773i	$0.305901\pi$
$462$	−2.50320	−	2.88885i	−0.116459	−	0.134401i
$463$	−33.9466	−	21.8162i	−1.57763	−	1.01388i	−0.976706	−	0.214580i	$-0.931162\pi$
$463$	−33.9466	−	21.8162i	−1.57763	−	1.01388i	−0.600927	−	0.799304i	$-0.705202\pi$
$464$	0.278877	−	1.93963i	0.0129465	−	0.0900450i
$465$	−1.64579	+	3.60378i	−0.0763217	+	0.167121i
$466$	−1.21455	−	8.44736i	−0.0562628	−	0.391317i
$467$	28.9213	+	8.49207i	1.33832	+	0.392966i	0.871070	−	0.491159i	$-0.163426\pi$
$467$	28.9213	+	8.49207i	1.33832	+	0.392966i	0.467250	+	0.884125i	$0.345245\pi$
$468$	5.72536	−	3.67946i	0.264655	−	0.170083i
$469$	0.860147	+	1.88346i	0.0397179	+	0.0869700i
$470$	−3.75749	+	1.10330i	−0.173320	+	0.0508913i
$471$	9.57294	−	11.0478i	0.441098	−	0.509054i
$472$	23.9759	−	27.6697i	1.10358	−	1.27360i
$473$	35.1834	−	10.3308i	1.61774	−	0.475010i
$474$	−0.740694	−	1.62189i	−0.0340212	−	0.0744960i
$475$	−1.33377	+	0.857161i	−0.0611975	+	0.0393292i
$476$	−1.22523	−	0.359760i	−0.0561583	−	0.0164896i
$477$	1.56248	+	10.8673i	0.0715412	+	0.497580i
$478$	−1.48956	+	3.26169i	−0.0681311	+	0.149186i
$479$	1.62941	−	11.3328i	0.0744497	−	0.517809i	−0.918136	−	0.396265i	$-0.870306\pi$
$479$	1.62941	−	11.3328i	0.0744497	−	0.517809i	0.992586	−	0.121544i	$-0.0387847\pi$
$480$	−4.51545	−	2.90191i	−0.206101	−	0.132453i
$481$	−25.9895	−	29.9935i	−1.18502	−	1.36759i
$482$	−20.7313			−0.944285
$483$	−4.01719	+	1.58870i	−0.182788	+	0.0722886i
$484$	−10.4511			−0.475049
$485$	−5.18461	−	5.98335i	−0.235421	−	0.271690i
$486$	0.791048	+	0.508376i	0.0358827	+	0.0230604i
$487$	1.00015	−	6.95617i	0.0453210	−	0.315214i	−0.954533	−	0.298106i	$-0.903645\pi$
$487$	1.00015	−	6.95617i	0.0453210	−	0.315214i	0.999854	−	0.0171080i	$-0.00544590\pi$
$488$	10.6870	−	23.4012i	0.483777	−	1.05932i
$489$	−0.117829	−	0.819517i	−0.00532840	−	0.0370598i
$490$	−5.58356	−	1.63948i	−0.252240	−	0.0740643i
$491$	−35.5128	+	22.8227i	−1.60267	+	1.02997i	−0.636773	+	0.771051i	$0.719731\pi$
$491$	−35.5128	+	22.8227i	−1.60267	+	1.02997i	−0.965898	+	0.258923i	$0.916632\pi$
$492$	3.15376	+	6.90577i	0.142182	+	0.311336i
$493$	−4.56399	+	1.34011i	−0.205552	+	0.0603554i
$494$	−5.95482	+	6.87223i	−0.267920	+	0.309196i
$495$	−2.95534	+	3.41064i	−0.132832	+	0.153297i
$496$	1.98962	−	0.584206i	0.0893367	−	0.0262316i
$497$	−0.985188	−	2.15726i	−0.0441917	−	0.0967664i
$498$	−1.46867	+	0.943855i	−0.0658126	+	0.0422952i
$499$	−10.3915	−	3.05123i	−0.465189	−	0.136592i	0.0407345	−	0.999170i	$-0.487030\pi$
$499$	−10.3915	−	3.05123i	−0.465189	−	0.136592i	−0.505924	+	0.862578i	$0.668848\pi$
$500$	−0.158794	−	1.10444i	−0.00710150	−	0.0493920i
$501$	5.63394	−	12.3366i	0.251706	−	0.551159i
$502$	2.43407	−	16.9293i	0.108638	−	0.755594i
$503$	−13.0508	−	8.38722i	−0.581905	−	0.373968i	0.216324	−	0.976322i	$-0.430593\pi$
$503$	−13.0508	−	8.38722i	−0.581905	−	0.373968i	−0.798229	+	0.602354i	$0.794230\pi$
$504$	−1.72825	−	1.99451i	−0.0769824	−	0.0888424i
$505$	6.35098			0.282615
$506$	6.73703	−	19.2041i	0.299497	−	0.853728i
$507$	24.2033			1.07490
$508$	12.5495	+	14.4830i	0.556796	+	0.642577i
$509$	21.8178	+	14.0214i	0.967055	+	0.621489i	0.925942	−	0.377666i	$-0.123273\pi$
$509$	21.8178	+	14.0214i	0.967055	+	0.621489i	0.0411134	+	0.999154i	$0.486910\pi$
$510$	0.170021	−	1.18253i	0.00752868	−	0.0523631i
$511$	−6.35975	+	13.9259i	−0.281339	+	0.616046i
$512$	0.836295	+	5.81656i	0.0369594	+	0.257058i
$513$	1.52123	+	0.446674i	0.0671640	+	0.0197211i
$514$	6.68850	−	4.29844i	0.295017	−	0.189596i
$515$	−5.76352	−	12.6203i	−0.253971	−	0.556119i
$516$	8.69892	−	2.55423i	0.382949	−	0.112444i
$517$	−12.3080	+	14.2042i	−0.541304	+	0.624698i
$518$	−3.60908	+	4.16510i	−0.158574	+	0.183004i
$519$	2.67293	−	0.784842i	0.117328	−	0.0344507i
$520$	−7.42366	−	16.2555i	−0.325549	−	0.712853i
$521$	12.5551	−	8.06866i	0.550048	−	0.353494i	−0.235909	−	0.971775i	$-0.575807\pi$
$521$	12.5551	−	8.06866i	0.550048	−	0.353494i	0.785957	+	0.618281i	$0.212170\pi$
$522$	−3.37787	−	0.991832i	−0.147845	−	0.0434113i
$523$	3.03062	+	21.0784i	0.132520	+	0.921695i	0.942254	+	0.334899i	$0.108702\pi$
$523$	3.03062	+	21.0784i	0.132520	+	0.921695i	−0.809734	+	0.586797i	$0.800389\pi$
$524$	−5.08203	+	11.1281i	−0.222010	+	0.486133i
$525$	0.128193	−	0.891599i	0.00559478	−	0.0389126i
$526$	10.8174	+	6.95189i	0.471659	+	0.303117i
$527$	−3.29624	−	3.80406i	−0.143586	−	0.165708i
$528$	2.36208			0.102796
$529$	−17.9592	−	14.3689i	−0.780835	−	0.624737i
$530$	10.3238			0.448439
$531$	−8.18334	−	9.44408i	−0.355127	−	0.409838i
$532$	−1.34053	−	0.861509i	−0.0581195	−	0.0373512i
$533$	−5.90612	+	41.0779i	−0.255822	+	1.77928i
$534$	3.07664	−	6.73689i	0.133139	−	0.291534i
$535$	−1.28422	−	8.93193i	−0.0555216	−	0.386161i
$536$	−6.46197	−	1.89740i	−0.279114	−	0.0819554i
$537$	3.13793	−	2.01662i	0.135411	−	0.0870237i
$538$	−11.3263	−	24.8012i	−0.488312	−	1.06925i
$539$	−26.7975	+	7.86844i	−1.15425	+	0.338918i
$540$	−0.730692	+	0.843263i	−0.0314440	+	0.0362883i
$541$	26.6365	−	30.7402i	1.14519	−	1.32162i	0.205873	−	0.978579i	$-0.433997\pi$
$541$	26.6365	−	30.7402i	1.14519	−	1.32162i	0.939319	−	0.343044i	$-0.111458\pi$
$542$	8.02940	−	2.35765i	0.344892	−	0.101270i
$543$	5.74365	+	12.5768i	0.246484	+	0.539724i
$544$	5.73692	−	3.68690i	0.245968	−	0.158074i
$545$	2.71181	+	0.796258i	0.116161	+	0.0341080i
$546$	−0.735240	−	5.11371i	−0.0314654	−	0.218847i
$547$	−2.96184	+	6.48552i	−0.126639	+	0.277301i	−0.962323	−	0.271910i	$-0.912345\pi$
$547$	−2.96184	+	6.48552i	−0.126639	+	0.277301i	0.835683	+	0.549211i	$0.185072\pi$
$548$	3.30371	−	22.9778i	0.141128	−	0.981564i
$549$	−7.38677	−	4.74719i	−0.315260	−	0.202605i
$550$	2.77896	+	3.20710i	0.118495	+	0.136751i
$551$	−5.93579			−0.252873
$552$	4.65135	−	13.2589i	0.197975	−	0.564334i
$553$	1.70802			0.0726324
$554$	12.2756	+	14.1668i	0.521541	+	0.601890i
$555$	5.47376	+	3.51777i	0.232348	+	0.149321i
$556$	0.796226	−	5.53788i	0.0337675	−	0.234858i
$557$	2.77611	−	6.07882i	0.117627	−	0.257568i	−0.841656	−	0.540015i	$-0.818419\pi$
$557$	2.77611	−	6.07882i	0.117627	−	0.257568i	0.959283	+	0.282447i	$0.0911460\pi$
$558$	−0.530174	−	3.68744i	−0.0224441	−	0.156102i
$559$	47.5522	+	13.9626i	2.01124	+	0.590555i
$560$	−0.396621	+	0.254893i	−0.0167603	+	0.0107712i
$561$	−2.38187	−	5.21556i	−0.100563	−	0.220201i
$562$	−14.3314	+	4.20809i	−0.604535	+	0.177507i
$563$	10.9399	−	12.6253i	0.461062	−	0.532093i	−0.476842	−	0.878989i	$-0.658219\pi$
$563$	10.9399	−	12.6253i	0.461062	−	0.532093i	0.937904	+	0.346896i	$0.112764\pi$
$564$	−3.04308	+	3.51191i	−0.128137	+	0.147878i
$565$	11.5818	−	3.40073i	0.487251	−	0.143070i
$566$	−0.928085	−	2.03222i	−0.0390103	−	0.0854207i
$567$	−0.757774	+	0.486991i	−0.0318235	+	0.0204517i
$568$	7.40136	+	2.17324i	0.310554	+	0.0911869i
$569$	−0.402557	−	2.79985i	−0.0168761	−	0.117376i	0.979642	−	0.200752i	$-0.0643386\pi$
$569$	−0.402557	−	2.79985i	−0.0168761	−	0.117376i	−0.996518	+	0.0833766i	$0.973430\pi$
$570$	0.619315	−	1.35611i	0.0259402	−	0.0568012i
$571$	−3.65963	+	25.4533i	−0.153151	+	1.06519i	0.757745	+	0.652551i	$0.226301\pi$
$571$	−3.65963	+	25.4533i	−0.153151	+	1.06519i	−0.910896	+	0.412636i	$0.864608\pi$
$572$	−25.8381	−	16.6051i	−1.08035	−	0.694296i
$573$	0.0367573	+	0.0424202i	0.00153556	+	0.00177213i
$574$	5.76302			0.240544
$575$	4.45974	−	1.76372i	0.185984	−	0.0735524i
$576$	6.09401			0.253917
$577$	18.6947	+	21.5748i	0.778270	+	0.898171i	0.996983	−	0.0776180i	$-0.0247315\pi$
$577$	18.6947	+	21.5748i	0.778270	+	0.898171i	−0.218713	+	0.975789i	$0.570186\pi$
$578$	−12.1709	−	7.82177i	−0.506243	−	0.325343i
$579$	2.18669	−	15.2088i	0.0908758	−	0.632055i
$580$	1.73537	−	3.79993i	0.0720574	−	0.157784i
$581$	−0.238003	−	1.65535i	−0.00987405	−	0.0686755i
$582$	7.14307	+	2.09739i	0.296090	+	0.0869397i
$583$	41.6822	−	26.7875i	1.72630	−	1.10943i
$584$	−20.6858	−	45.2956i	−0.855985	−	1.87434i
$585$	−5.85238	+	1.71841i	−0.241966	+	0.0710476i
$586$	−16.9750	+	19.5902i	−0.701230	+	0.809262i
$587$	−24.8334	+	28.6593i	−1.02498	+	1.18289i	−0.0420155	+	0.999117i	$0.513378\pi$
$587$	−24.8334	+	28.6593i	−1.02498	+	1.18289i	−0.982968	+	0.183777i	$0.941168\pi$
$588$	−6.62553	+	1.94543i	−0.273232	+	0.0802282i
$589$	−2.60932	−	5.71362i	−0.107515	−	0.235426i
$590$	−9.88518	+	6.35282i	−0.406966	+	0.261541i
$591$	−10.9960	−	3.22873i	−0.452317	−	0.132812i
$592$	−0.484670	−	3.37095i	−0.0199198	−	0.138545i
$593$	−10.3610	+	22.6873i	−0.425473	+	0.931657i	0.568566	+	0.822637i	$0.307498\pi$
$593$	−10.3610	+	22.6873i	−0.425473	+	0.931657i	−0.994040	+	0.109019i	$0.965229\pi$
$594$	0.603927	−	4.20040i	0.0247794	−	0.172345i
$595$	0.962758	+	0.618727i	0.0394692	+	0.0253653i
$596$	−12.9198	−	14.9103i	−0.529216	−	0.610748i
$597$	9.94742			0.407121
$598$	21.6925	−	16.9123i	0.887073	−	0.691595i
$599$	10.9837			0.448783			0.224391	−	0.974499i	$-0.427961\pi$
$599$	10.9837			0.448783			0.224391	+	0.974499i	$0.427961\pi$
$600$	1.91864	+	2.21423i	0.0783283	+	0.0903956i
$601$	2.00770	+	1.29027i	0.0818957	+	0.0526312i	0.580948	−	0.813941i	$-0.302682\pi$
$601$	2.00770	+	1.29027i	0.0818957	+	0.0526312i	−0.499052	+	0.866572i	$0.666318\pi$
$602$	0.979438	−	6.81214i	0.0399189	−	0.277642i
$603$	−0.954905	+	2.09095i	−0.0388867	+	0.0851500i
$604$	2.59323	+	18.0363i	0.105517	+	0.733886i
$605$	8.98707	+	2.63884i	0.365376	+	0.107284i
$606$	−5.02393	+	3.22869i	−0.204083	+	0.131156i
$607$	16.4438	+	36.0070i	0.667434	+	1.46148i	0.875429	+	0.483347i	$0.160579\pi$
$607$	16.4438	+	36.0070i	0.667434	+	1.46148i	−0.207994	+	0.978130i	$0.566693\pi$
$608$	8.16525	−	2.39753i	0.331145	−	0.0972329i
$609$	2.20845	−	2.54868i	0.0894907	−	0.103278i
$610$	−5.40695	+	6.23995i	−0.218921	+	0.252648i
$611$	−24.3732	+	7.15661i	−0.986033	+	0.289525i
$612$	−0.588905	−	1.28952i	−0.0238051	−	0.0521258i
$613$	18.6595	−	11.9918i	0.753652	−	0.484343i	−0.106543	−	0.994308i	$-0.533978\pi$
$613$	18.6595	−	11.9918i	0.753652	−	0.484343i	0.860195	+	0.509966i	$0.170342\pi$
$614$	21.2691	+	6.24518i	0.858352	+	0.252035i
$615$	−0.968303	−	6.73470i	−0.0390458	−	0.271569i
$616$	−4.94764	+	10.8338i	−0.199346	+	0.436507i
$617$	−2.90172	+	20.1819i	−0.116819	+	0.812494i	0.844203	+	0.536023i	$0.180074\pi$
$617$	−2.90172	+	20.1819i	−0.116819	+	0.812494i	−0.961022	+	0.276471i	$0.910835\pi$
$618$	10.9751	+	7.05326i	0.441483	+	0.283724i
$619$	−25.9638	−	29.9638i	−1.04357	−	1.20435i	−0.978453	−	0.206468i	$-0.933803\pi$
$619$	−25.9638	−	29.9638i	−1.04357	−	1.20435i	−0.0651181	−	0.997878i	$-0.520742\pi$
$620$	4.42056			0.177534
$621$	−4.25344	−	2.21545i	−0.170685	−	0.0889031i
$622$	7.75777			0.311058
$623$	4.64600	+	5.36177i	0.186138	+	0.214815i
$624$	2.68568	+	1.72598i	0.107513	+	0.0690945i
$625$	−0.142315	+	0.989821i	−0.00569259	+	0.0395929i
$626$	1.97156	−	4.31712i	0.0787995	−	0.172547i
$627$	−1.01827	−	7.08220i	−0.0406657	−	0.282836i
$628$	−15.6503	−	4.59535i	−0.624516	−	0.183374i
$629$	−6.95446	+	4.46936i	−0.277292	+	0.178205i
$630$	0.351861	+	0.770467i	0.0140185	+	0.0306962i
$631$	22.5292	−	6.61517i	0.896874	−	0.263346i	0.199368	−	0.979925i	$-0.436111\pi$
$631$	22.5292	−	6.61517i	0.896874	−	0.263346i	0.697506	+	0.716579i	$0.254293\pi$
$632$	−3.63810	+	4.19859i	−0.144716	+	0.167011i
$633$	−11.6382	+	13.4312i	−0.462575	+	0.533840i
$634$	12.1204	−	3.55887i	0.481362	−	0.141341i
$635$	−7.13471	−	15.6228i	−0.283132	−	0.619973i
$636$	10.3057	−	6.62307i	0.408648	−	0.262622i
$637$	−36.2181	−	10.6346i	−1.43501	−	0.421358i
$638$	2.26105	+	15.7259i	0.0895156	+	0.622595i
$639$	1.09372	−	2.39492i	0.0432670	−	0.0947414i
$640$	−0.712249	+	4.95380i	−0.0281541	+	0.195816i
$641$	−8.66045	−	5.56573i	−0.342067	−	0.219833i	0.358316	−	0.933600i	$-0.383351\pi$
$641$	−8.66045	−	5.56573i	−0.342067	−	0.219833i	−0.700383	+	0.713767i	$0.746987\pi$
$642$	5.55665	+	6.41272i	0.219304	+	0.253090i
$643$	0.936695			0.0369397			0.0184698	−	0.999829i	$-0.494121\pi$
$643$	0.936695			0.0369397			0.0184698	+	0.999829i	$0.494121\pi$
$644$	3.47452	+	3.34091i	0.136915	+	0.131650i
$645$	−8.12528			−0.319933
$646$	1.24038	+	1.43148i	0.0488022	+	0.0563208i
$647$	−13.5759	−	8.72469i	−0.533723	−	0.343003i	0.245856	−	0.969306i	$-0.420931\pi$
$647$	−13.5759	−	8.72469i	−0.533723	−	0.343003i	−0.779580	+	0.626303i	$0.784567\pi$
$648$	0.416961	−	2.90003i	0.0163798	−	0.113924i
$649$	−23.4273	+	51.2986i	−0.919601	+	2.01364i
$650$	0.816238	+	5.67706i	0.0320155	+	0.222673i
$651$	3.42410	+	1.00541i	0.134201	+	0.0394050i
$652$	−0.777164	+	0.499453i	−0.0304361	+	0.0195601i
$653$	6.38623	+	13.9839i	0.249912	+	0.547232i	0.992461	−	0.122560i	$-0.0391105\pi$
$653$	6.38623	+	13.9839i	0.249912	+	0.547232i	−0.742549	+	0.669792i	$0.766383\pi$
$654$	−2.54997	+	0.748738i	−0.0997117	+	0.0292780i
$655$	7.17991	−	8.28606i	0.280542	−	0.323763i
$656$	−2.33210	+	2.69139i	−0.0910532	+	0.105081i
$657$	−16.3075	+	4.78831i	−0.636215	+	0.186810i
$658$	1.46538	+	3.20874i	0.0571265	+	0.125090i
$659$	6.20684	−	3.98889i	0.241784	−	0.155385i	−0.414137	−	0.910214i	$-0.635917\pi$
$659$	6.20684	−	3.98889i	0.241784	−	0.155385i	0.655921	+	0.754829i	$0.272280\pi$
$660$	4.83153	+	1.41867i	0.188067	+	0.0552215i
$661$	−5.72123	−	39.7920i	−0.222530	−	1.54773i	−0.728419	−	0.685132i	$-0.759745\pi$
$661$	−5.72123	−	39.7920i	−0.222530	−	1.54773i	0.505889	−	0.862598i	$-0.331164\pi$
$662$	12.3011	−	26.9356i	0.478095	−	1.04688i
$663$	1.10285	−	7.67052i	0.0428313	−	0.297898i
$664$	4.57607	+	2.94086i	0.177586	+	0.114128i
$665$	0.935222	+	1.07930i	0.0362664	+	0.0418536i
$666$	−6.11836			−0.237082
$667$	17.6163	+	3.47202i	0.682104	+	0.134437i
$668$	−15.1327			−0.585500
$669$	−2.89549	−	3.34157i	−0.111946	−	0.129193i
$670$	1.81836	+	1.16859i	0.0702495	+	0.0451466i
$671$	−5.63944	+	39.2231i	−0.217708	+	1.51419i
$672$	−2.00849	+	4.39797i	−0.0774791	+	0.169656i
$673$	−5.73027	−	39.8549i	−0.220885	−	1.53629i	−0.734701	−	0.678391i	$-0.762677\pi$
$673$	−5.73027	−	39.8549i	−0.220885	−	1.53629i	0.513815	−	0.857901i	$-0.328232\pi$
$674$	−0.630047	−	0.184998i	−0.0242685	−	0.00712587i
$675$	0.841254	−	0.540641i	0.0323799	−	0.0208093i
$676$	−11.2187	−	24.5655i	−0.431487	−	0.944825i
$677$	8.53445	−	2.50594i	0.328006	−	0.0963111i	−0.113584	−	0.993528i	$-0.536233\pi$
$677$	8.53445	−	2.50594i	0.328006	−	0.0963111i	0.441589	+	0.897217i	$0.354415\pi$
$678$	−7.43293	+	8.57806i	−0.285460	+	0.329438i
$679$	−4.67012	+	5.38961i	−0.179223	+	0.206834i
$680$	−3.57161	+	1.04872i	−0.136965	+	0.0402166i
$681$	1.90593	+	4.17341i	0.0730356	+	0.159926i
$682$	−14.1434	+	9.08940i	−0.541578	+	0.348051i
$683$	−18.0467	−	5.29900i	−0.690539	−	0.202761i	−0.0824097	−	0.996599i	$-0.526262\pi$
$683$	−18.0467	−	5.29900i	−0.690539	−	0.202761i	−0.608129	+	0.793838i	$0.708080\pi$
$684$	−0.251761	−	1.75104i	−0.00962633	−	0.0669526i
$685$	−8.64269	+	18.9249i	−0.330220	+	0.723081i
$686$	−1.58978	+	11.0572i	−0.0606982	+	0.422165i
$687$	−17.7301	−	11.3945i	−0.676447	−	0.434726i
$688$	2.78499	+	3.21405i	0.106177	+	0.122535i
$689$	66.9662			2.55121
$690$	−2.63123	+	3.66241i	−0.100169	+	0.139426i
$691$	28.9522			1.10139			0.550697	−	0.834705i	$-0.314362\pi$
$691$	28.9522			1.10139			0.550697	+	0.834705i	$0.314362\pi$
$692$	−2.03554	−	2.34914i	−0.0773796	−	0.0893008i
$693$	3.41977	+	2.19776i	0.129906	+	0.0834858i
$694$	−0.00645704	+	0.0449097i	−0.000245106	+	0.00170475i
$695$	−2.08297	+	4.56107i	−0.0790116	+	0.173011i
$696$	1.56106	+	10.8574i	0.0591719	+	0.411550i
$697$	8.29432	+	2.43543i	0.314170	+	0.0922485i
$698$	15.9261	−	10.2351i	0.602813	−	0.387404i
$699$	3.77025	+	8.25570i	0.142604	+	0.312259i
$700$	−0.964361	+	0.283162i	−0.0364494	+	0.0107025i
$701$	−16.9755	+	19.5908i	−0.641157	+	0.739935i	−0.979579	−	0.201060i	$-0.935561\pi$
$701$	−16.9755	+	19.5908i	−0.641157	+	0.739935i	0.338422	+	0.940994i	$0.390107\pi$
$702$	3.75591	−	4.33455i	0.141758	−	0.163597i
$703$	−9.89815	+	2.90636i	−0.373316	+	0.109615i
$704$	−11.4247	−	25.0165i	−0.430583	−	0.942845i
$705$	3.50354	−	2.25159i	0.131951	−	0.0847996i
$706$	−16.3062	−	4.78794i	−0.613693	−	0.180197i
$707$	−0.814149	−	5.66253i	−0.0306192	−	0.212961i
$708$	−5.79227	+	12.6833i	−0.217687	+	0.476668i
$709$	2.46420	−	17.1389i	0.0925450	−	0.643664i	−0.889767	−	0.456414i	$-0.849133\pi$
$709$	2.46420	−	17.1389i	0.0925450	−	0.643664i	0.982312	−	0.187250i	$-0.0599574\pi$
$710$	−2.08270	−	1.33847i	−0.0781625	−	0.0502320i
$711$	1.24174	+	1.43304i	0.0465687	+	0.0537432i
$712$	−23.0761			−0.864814
$713$	4.40189	+	18.4832i	0.164852	+	0.692200i
$714$	−1.07613			−0.0402733
$715$	18.0259	+	20.8030i	0.674131	+	0.777989i
$716$	−3.50129	−	2.25014i	−0.130849	−	0.0840917i
$717$	0.542689	−	3.77449i	0.0202671	−	0.140961i
$718$	−10.0323	+	21.9678i	−0.374404	+	0.819830i
$719$	4.67080	+	32.4861i	0.174191	+	1.21153i	0.869909	+	0.493213i	$0.164178\pi$
$719$	4.67080	+	32.4861i	0.174191	+	1.21153i	−0.695717	+	0.718316i	$0.744913\pi$
$720$	−0.502202	−	0.147460i	−0.0187160	−	0.00549550i
$721$	−10.5134	+	6.75658i	−0.391541	+	0.251628i
$722$	−6.43995	−	14.1015i	−0.239670	−	0.524804i
$723$	21.1540	−	6.21137i	0.786726	−	0.231003i
$724$	10.1028	−	11.6592i	0.375466	−	0.433311i
$725$	−2.45174	+	2.82946i	−0.0910553	+	0.105083i
$726$	−8.45073	+	2.48136i	−0.313636	+	0.0920918i
$727$	−10.8336	−	23.7222i	−0.401794	−	0.879807i	−0.997085	−	0.0762965i	$-0.975690\pi$
$727$	−10.8336	−	23.7222i	−0.401794	−	0.879807i	0.595291	−	0.803510i	$-0.297037\pi$
$728$	−13.5418	+	8.70276i	−0.501891	+	0.322546i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	2.27442	+	15.8190i	0.0841802	+	0.585486i
$731$	4.28843	−	9.39035i	0.158613	−	0.347315i
$732$	−1.39432	+	9.69772i	−0.0515356	+	0.358438i
$733$	−15.1570	−	9.74078i	−0.559835	−	0.359784i	0.229917	−	0.973210i	$-0.426154\pi$
$733$	−15.1570	−	9.74078i	−0.559835	−	0.359784i	−0.789752	+	0.613426i	$0.789791\pi$
$734$	6.80185	+	7.84976i	0.251061	+	0.289740i
$735$	6.18862			0.228271
$736$	−25.6353	+	2.33931i	−0.944928	+	0.0862282i
$737$	10.3737			0.382122
$738$	4.18973	+	4.83521i	0.154226	+	0.177986i
$739$	−8.03551	−	5.16411i	−0.295591	−	0.189965i	0.384436	−	0.923151i	$-0.374396\pi$
$739$	−8.03551	−	5.16411i	−0.295591	−	0.189965i	−0.680027	+	0.733187i	$0.738032\pi$
$740$	1.03322	−	7.18623i	0.0379820	−	0.264171i
$741$	4.01722	−	8.79649i	0.147576	−	0.323147i
$742$	−1.32344	−	9.20473i	−0.0485850	−	0.337916i
$743$	−36.5922	−	10.7445i	−1.34244	−	0.394176i	−0.469900	−	0.882720i	$-0.655710\pi$
$743$	−36.5922	−	10.7445i	−1.34244	−	0.394176i	−0.872539	+	0.488544i	$0.837528\pi$
$744$	−9.76482	+	6.27547i	−0.357996	+	0.230070i
$745$	7.34522	+	16.0838i	0.269108	+	0.589264i
$746$	20.2941	−	5.95887i	0.743018	−	0.218170i
$747$	1.21582	−	1.40313i	0.0444846	−	0.0513379i
$748$	−4.18957	+	4.83502i	−0.153186	+	0.176786i
$749$	−7.79907	+	2.29001i	−0.284972	+	0.0836753i
$750$	−0.390623	−	0.855346i	−0.0142635	−	0.0312328i
$751$	44.5671	−	28.6415i	1.62628	−	1.04514i	0.674536	−	0.738242i	$-0.264344\pi$
$751$	44.5671	−	28.6415i	1.62628	−	1.04514i	0.951741	−	0.306903i	$-0.0992927\pi$
$752$	−2.09150	−	0.614120i	−0.0762692	−	0.0223947i
$753$	2.58856	+	18.0038i	0.0943322	+	0.656095i
$754$	−8.92019	+	19.5325i	−0.324854	+	0.711331i
$755$	2.32410	−	16.1645i	0.0845828	−	0.588286i
$756$	0.845521	+	0.543384i	0.0307513	+	0.0197627i
$757$	−9.90467	−	11.4306i	−0.359991	−	0.415452i	0.546645	−	0.837364i	$-0.315905\pi$
$757$	−9.90467	−	11.4306i	−0.359991	−	0.415452i	−0.906637	+	0.421912i	$0.861359\pi$
$758$	−29.5730			−1.07414
$759$	−1.12057	+	21.6142i	−0.0406742	+	0.784545i
$760$	−4.64514			−0.168497
$761$	−16.1810	−	18.6739i	−0.586562	−	0.676928i	0.382441	−	0.923980i	$-0.375084\pi$
$761$	−16.1810	−	18.6739i	−0.586562	−	0.676928i	−0.969002	+	0.247052i	$0.920538\pi$
$762$	13.5862	+	8.73130i	0.492175	+	0.316302i
$763$	0.362309	−	2.51992i	0.0131165	−	0.0912272i
$764$	0.0260173	−	0.0569699i	0.000941272	−	0.00206110i
$765$	0.180812	+	1.25758i	0.00653728	+	0.0454678i
$766$	−6.24561	−	1.83388i	−0.225663	−	0.0662607i
$767$	−64.1208	+	41.2079i	−2.31527	+	1.48793i
$768$	−7.01805	−	15.3674i	−0.253242	−	0.554523i
$769$	−31.8496	+	9.35190i	−1.14853	+	0.337238i	−0.799964	−	0.600047i	$-0.795148\pi$
$769$	−31.8496	+	9.35190i	−1.14853	+	0.337238i	−0.348563	+	0.937285i	$0.613330\pi$
$770$	2.50320	−	2.88885i	0.0902090	−	0.104107i
$771$	−5.53700	+	6.39004i	−0.199410	+	0.230132i
$772$	−16.4499	+	4.83014i	−0.592046	+	0.173840i
$773$	22.1410	+	48.4819i	0.796355	+	1.74377i	0.657491	+	0.753463i	$0.271618\pi$
$773$	22.1410	+	48.4819i	0.796355	+	1.74377i	0.138864	+	0.990311i	$0.455655\pi$
$774$	6.42749	−	4.13070i	0.231031	−	0.148475i
$775$	−3.80132	−	1.11617i	−0.136547	−	0.0400939i
$776$	−3.30113	−	22.9598i	−0.118504	−	0.824210i
$777$	2.43475	−	5.33135i	0.0873460	−	0.191261i
$778$	0.170805	−	1.18797i	0.00612365	−	0.0425909i
$779$	9.07489	+	5.83208i	0.325142	+	0.208956i
$780$	4.45682	+	5.14344i	0.159580	+	0.184165i
$781$	−11.8818			−0.425164
$782$	−2.84390	−	4.97388i	−0.101698	−	0.177866i
$783$	3.74391			0.133796
$784$	−2.12119	−	2.44798i	−0.0757567	−	0.0874279i
$785$	12.2977	+	7.90324i	0.438923	+	0.282079i
$786$	−1.46722	+	10.2048i	−0.0523341	+	0.363992i
$787$	−4.27477	+	9.36044i	−0.152379	+	0.333663i	−0.970392	−	0.241537i	$-0.922349\pi$
$787$	−4.27477	+	9.36044i	−0.152379	+	0.333663i	0.818013	+	0.575200i	$0.195076\pi$
$788$	1.81983	+	12.6572i	0.0648287	+	0.450893i
$789$	−13.1208	−	3.85261i	−0.467112	−	0.137157i
$790$	1.49997	−	0.963974i	0.0533666	−	0.0342967i
$791$	−4.51679	−	9.89039i	−0.160598	−	0.351662i
$792$	−12.6866	+	3.72512i	−0.450798	+	0.132366i
$793$	−35.0725	+	40.4758i	−1.24546	+	1.43734i
$794$	−14.9075	+	17.2042i	−0.529048	+	0.610554i
$795$	−10.5343	+	3.09316i	−0.373614	+	0.109703i
$796$	−4.61082	−	10.0963i	−0.163426	−	0.357853i
$797$	2.17298	−	1.39649i	0.0769710	−	0.0494663i	−0.501589	−	0.865106i	$-0.667251\pi$
$797$	2.17298	−	1.39649i	0.0769710	−	0.0494663i	0.578560	+	0.815640i	$0.303615\pi$
$798$	−1.28850	−	0.378337i	−0.0456123	−	0.0133930i
$799$	0.753022	+	5.23738i	0.0266400	+	0.185285i
$800$	2.22975	−	4.88248i	0.0788337	−	0.172622i
$801$	−1.12090	+	7.79605i	−0.0396052	+	0.275460i
$802$	23.0503	+	14.8136i	0.813936	+	0.523085i
$803$	50.2287	+	57.9670i	1.77253	+	2.04561i
$804$	2.56486			0.0904555
$805$	−2.14424	−	3.75020i	−0.0755745	−	0.132177i
$806$	−22.7226			−0.800371
$807$	18.9880	+	21.9133i	0.668409	+	0.771385i
$808$	15.6536	+	10.0599i	0.550690	+	0.353907i
$809$	3.22855	−	22.4551i	0.113510	−	0.789478i	−0.850950	−	0.525247i	$-0.823973\pi$
$809$	3.22855	−	22.4551i	0.113510	−	0.789478i	0.964460	−	0.264231i	$-0.0851180\pi$
$810$	−0.390623	+	0.855346i	−0.0137251	+	0.0300538i
$811$	−4.63604	−	32.2443i	−0.162793	−	1.13225i	−0.893337	−	0.449387i	$-0.851643\pi$
$811$	−4.63604	−	32.2443i	−0.162793	−	1.13225i	0.730544	−	0.682865i	$-0.239266\pi$
$812$	−3.61048	−	1.06013i	−0.126703	−	0.0372033i
$813$	−7.48673	+	4.81143i	−0.262571	+	0.168744i
$814$	11.4703	+	25.1165i	0.402034	+	0.880332i
$815$	0.794406	−	0.233259i	0.0278268	−	0.00817070i
$816$	0.435475	−	0.502565i	0.0152447	−	0.0175933i
$817$	8.43608	−	9.73576i	0.295141	−	0.340611i
$818$	−18.1567	+	5.33128i	−0.634833	+	0.186404i
$819$	2.28237	+	4.99768i	0.0797523	+	0.174633i
$820$	−6.38665	+	4.10445i	−0.223032	+	0.143334i
$821$	−14.5384	−	4.26886i	−0.507393	−	0.148984i	0.0180093	−	0.999838i	$-0.494267\pi$
$821$	−14.5384	−	4.26886i	−0.507393	−	0.148984i	−0.525403	+	0.850854i	$0.676085\pi$
$822$	−2.78415	−	19.3642i	−0.0971085	−	0.675404i
$823$	−13.7277	+	30.0595i	−0.478518	+	1.04781i	0.504350	+	0.863499i	$0.331732\pi$
$823$	−13.7277	+	30.0595i	−0.478518	+	1.04781i	−0.982868	+	0.184309i	$0.940995\pi$
$824$	5.78496	−	40.2353i	0.201529	−	1.40166i
$825$	−3.79651	−	2.43987i	−0.132178	−	0.0849454i
$826$	6.93137	+	7.99923i	0.241173	+	0.278329i
$827$	37.7559			1.31290			0.656451	−	0.754369i	$-0.272057\pi$
$827$	37.7559			1.31290			0.656451	+	0.754369i	$0.272057\pi$
$828$	−0.277056	+	5.34400i	−0.00962836	+	0.185717i
$829$	22.1388			0.768913			0.384456	−	0.923143i	$-0.374389\pi$
$829$	22.1388			0.768913			0.384456	+	0.923143i	$0.374389\pi$
$830$	−1.14326	−	1.31939i	−0.0396832	−	0.0457968i
$831$	−16.7705	−	10.7777i	−0.581761	−	0.373875i
$832$	5.28985	−	36.7917i	0.183393	−	1.27552i
$833$	−3.26628	+	7.15216i	−0.113170	+	0.247808i
$834$	−0.671008	−	4.66696i	−0.0232351	−	0.161604i
$835$	13.0128	+	3.82091i	0.450328	+	0.132228i
$836$	−6.71620	+	4.31624i	−0.232284	+	0.149280i
$837$	1.64579	+	3.60378i	0.0568868	+	0.124565i
$838$	32.1219	−	9.43185i	1.10963	−	0.325818i
$839$	8.67390	−	10.0102i	0.299456	−	0.345591i	−0.586002	−	0.810309i	$-0.699299\pi$
$839$	8.67390	−	10.0102i	0.299456	−	0.345591i	0.885458	+	0.464718i	$0.153844\pi$
$840$	1.72825	−	1.99451i	0.0596303	−	0.0688170i
$841$	14.3762	−	4.22124i	0.495732	−	0.145560i
$842$	−3.60778	−	7.89993i	−0.124332	−	0.272249i
$843$	13.3628	−	8.58777i	0.460240	−	0.295778i
$844$	19.0267	+	5.58673i	0.654924	+	0.192303i
$845$	3.44448	+	23.9569i	0.118494	+	0.824143i
$846$	−1.62681	+	3.56223i	−0.0559310	+	0.122472i
$847$	1.20071	−	8.35114i	0.0412570	−	0.286949i
$848$	4.83425	+	3.10678i	0.166009	+	0.106687i
$849$	1.55589	+	1.79559i	0.0533980	+	0.0616245i
$850$	1.19469			0.0409774
$851$	31.0758	−	2.83578i	1.06526	−	0.0972094i
$852$	−2.93772			−0.100644
$853$	1.07819	+	1.24430i	0.0369165	+	0.0426039i	0.773908	−	0.633299i	$-0.218299\pi$
$853$	1.07819	+	1.24430i	0.0369165	+	0.0426039i	−0.736991	+	0.675902i	$0.763754\pi$
$854$	6.25667	+	4.02091i	0.214099	+	0.137593i
$855$	−0.225633	+	1.56932i	−0.00771650	+	0.0536695i
$856$	10.9829	−	24.0491i	0.375387	−	0.821982i
$857$	−0.945059	−	6.57303i	−0.0322826	−	0.224530i	0.967293	−	0.253662i	$-0.0816350\pi$
$857$	−0.945059	−	6.57303i	−0.0322826	−	0.224530i	−0.999576	+	0.0291313i	$0.990726\pi$
$858$	−24.8351	−	7.29225i	−0.847857	−	0.248953i
$859$	−13.8894	+	8.92618i	−0.473900	+	0.304557i	−0.755702	−	0.654915i	$-0.772704\pi$
$859$	−13.8894	+	8.92618i	−0.473900	+	0.304557i	0.281802	+	0.959473i	$0.409068\pi$
$860$	3.76622	+	8.24687i	0.128427	+	0.281216i
$861$	−5.88052	+	1.72668i	−0.200408	+	0.0588450i
$862$	−8.03871	+	9.27717i	−0.273800	+	0.315982i
$863$	30.1138	−	34.7532i	1.02509	−	1.18301i	0.0421428	−	0.999112i	$-0.486582\pi$
$863$	30.1138	−	34.7532i	1.02509	−	1.18301i	0.982945	−	0.183902i	$-0.0588730\pi$
$864$	−5.15011	+	1.51221i	−0.175210	+	0.0514464i
$865$	1.15725	+	2.53403i	0.0393477	+	0.0861594i
$866$	20.4997	−	13.1743i	0.696607	−	0.447682i
$867$	14.7626	+	4.33468i	0.501363	+	0.147214i
$868$	−0.566683	−	3.94137i	−0.0192345	−	0.133779i
$869$	3.55484	−	7.78402i	0.120590	−	0.264055i
$870$	0.501016	−	3.48464i	0.0169860	−	0.118140i
$871$	11.7949	+	7.58014i	0.399656	+	0.256843i
$872$	5.42264	+	6.25807i	0.183634	+	0.211925i
$873$	−7.91711			−0.267954
$874$	−1.65644	−	6.95526i	−0.0560300	−	0.235265i
$875$	0.900767			0.0304515
$876$	12.4188	+	14.3320i	0.419592	+	0.484235i
$877$	−44.3982	−	28.5330i	−1.49922	−	0.963490i	−0.994996	−	0.0999179i	$-0.968142\pi$
$877$	−44.3982	−	28.5330i	−1.49922	−	0.963490i	−0.504225	−	0.863572i	$-0.668222\pi$
$878$	0.602769	−	4.19235i	0.0203425	−	0.141485i
$879$	11.4516	−	25.0755i	0.386253	−	0.845776i
$880$	0.336159	+	2.33804i	0.0113319	+	0.0788152i
$881$	5.08266	+	1.49240i	0.171239	+	0.0502804i	0.366228	−	0.930525i	$-0.380649\pi$
$881$	5.08266	+	1.49240i	0.171239	+	0.0502804i	−0.194989	+	0.980805i	$0.562467\pi$
$882$	−4.89550	+	3.14614i	−0.164840	+	0.105936i
$883$	−0.670678	−	1.46858i	−0.0225701	−	0.0494217i	0.898011	−	0.439973i	$-0.145012\pi$
$883$	−0.670678	−	1.46858i	−0.0225701	−	0.0494217i	−0.920581	+	0.390551i	$0.872285\pi$
$884$	−8.29650	+	2.43607i	−0.279042	+	0.0819340i
$885$	8.18334	−	9.44408i	0.275080	−	0.317459i
$886$	−8.99903	+	10.3854i	−0.302328	+	0.348905i
$887$	30.5848	−	8.98051i	1.02694	−	0.301536i	0.275472	−	0.961309i	$-0.411166\pi$
$887$	30.5848	−	8.98051i	1.02694	−	0.301536i	0.751465	+	0.659773i	$0.229348\pi$
$888$	7.91929	+	17.3408i	0.265754	+	0.581920i
$889$	−13.0147	+	8.36403i	−0.436498	+	0.280520i
$890$	7.10617	+	2.08656i	0.238199	+	0.0699416i
$891$	0.642256	+	4.46699i	0.0215164	+	0.149650i
$892$	−2.04946	+	4.48770i	−0.0686211	+	0.150259i
$893$	−0.939687	+	6.53567i	−0.0314454	+	0.218708i
$894$	−13.9870	−	8.98891i	−0.467796	−	0.300634i
$895$	2.44267	+	2.81899i	0.0816494	+	0.0942285i
$896$	4.50810			0.150605
$897$	−17.0677	+	23.7565i	−0.569873	+	0.793206i
$898$	−10.6222			−0.354467
$899$	−9.71329	−	11.2097i	−0.323956	−	0.373866i
$900$	−0.938668	−	0.603245i	−0.0312889	−	0.0201082i
$901$	1.98515	−	13.8070i	0.0661349	−	0.459978i
$902$	11.9944	−	26.2640i	0.399369	−	0.874496i
$903$	1.04160	+	7.24449i	0.0346623	+	0.241082i
$904$	33.9330	+	9.96362i	1.12859	+	0.331385i
$905$	−11.6314	+	7.47506i	−0.386642	+	0.248479i
$906$	6.37916	+	13.9684i	0.211933	+	0.464069i
$907$	37.0207	−	10.8703i	1.22925	−	0.360941i	0.398285	−	0.917262i	$-0.369606\pi$
$907$	37.0207	−	10.8703i	1.22925	−	0.360941i	0.830968	+	0.556321i	$0.187787\pi$
$908$	3.35243	−	3.86891i	0.111254	−	0.128394i
$909$	4.15901	−	4.79975i	0.137946	−	0.159198i
$910$	4.95702	−	1.45551i	0.164324	−	0.0482498i
$911$	15.5421	+	34.0325i	0.514934	+	1.12755i	0.971322	+	0.237767i	$0.0764156\pi$
$911$	15.5421	+	34.0325i	0.514934	+	1.12755i	−0.456388	+	0.889781i	$0.650857\pi$
$912$	0.698099	−	0.448641i	0.0231164	−	0.0148560i
$913$	−8.03934	−	2.36056i	−0.266063	−	0.0781232i
$914$	−4.68934	−	32.6151i	−0.155110	−	1.07881i
$915$	3.64762	−	7.98718i	0.120587	−	0.264048i
$916$	−3.34673	+	23.2770i	−0.110579	+	0.769094i
$917$	−8.30825	−	5.33939i	−0.274363	−	0.176322i
$918$	−0.782353	−	0.902883i	−0.0258215	−	0.0297996i
$919$	−11.9517			−0.394250			−0.197125	−	0.980378i	$-0.563161\pi$
$919$	−11.9517			−0.394250			−0.197125	+	0.980378i	$0.563161\pi$
$920$	13.7859	+	2.71708i	0.454506	+	0.0895794i
$921$	−23.5739			−0.776787
$922$	−15.1434	−	17.4764i	−0.498722	−	0.575555i
$923$	−13.5096	−	8.68208i	−0.444673	−	0.285774i
$924$	0.645514	−	4.48965i	0.0212359	−	0.147699i
$925$	−2.70297	+	5.91868i	−0.0888731	+	0.194605i
$926$	5.40003	+	37.5580i	0.177456	+	1.23423i
$927$	−13.3121	−	3.90879i	−0.437227	−	0.128382i
$928$	16.9054	−	10.8645i	0.554948	−	0.356644i
$929$	4.98378	+	10.9130i	0.163513	+	0.358043i	0.973598	−	0.228269i	$-0.0733066\pi$
$929$	4.98378	+	10.9130i	0.163513	+	0.358043i	−0.810085	+	0.586312i	$0.800579\pi$
$930$	3.57446	−	1.04956i	0.117211	−	0.0344163i
$931$	−6.42534	+	7.41524i	−0.210582	+	0.243025i
$932$	6.63166	−	7.65335i	0.217227	−	0.250694i
$933$	−7.91594	+	2.32433i	−0.259156	+	0.0760952i
$934$	−11.7743	−	25.7821i	−0.385267	−	0.843616i
$935$	4.82350	−	3.09988i	0.157745	−	0.101377i
$936$	−17.1466	−	5.03469i	−0.560453	−	0.164564i
$937$	−1.43461	−	9.97790i	−0.0468665	−	0.325964i	−0.999744	−	0.0226095i	$-0.992803\pi$
$937$	−1.43461	−	9.97790i	−0.0468665	−	0.325964i	0.952878	−	0.303354i	$-0.0981065\pi$
$938$	0.808814	−	1.77106i	0.0264087	−	0.0578270i
$939$	−0.718294	+	4.99585i	−0.0234407	+	0.163033i
$940$	−3.90923	−	2.51231i	−0.127505	−	0.0819426i
$941$	−0.993249	−	1.14627i	−0.0323790	−	0.0373673i	0.739329	−	0.673344i	$-0.235143\pi$
$941$	−0.993249	−	1.14627i	−0.0323790	−	0.0373673i	−0.771708	+	0.635977i	$0.780597\pi$
$942$	−13.7459			−0.447865
$943$	−23.5211	−	22.6166i	−0.765954	−	0.736499i
$944$	−6.54061			−0.212879
$945$	−0.589877	−	0.680754i	−0.0191887	−	0.0221449i
$946$	−29.0068	−	18.6415i	−0.943091	−	0.606088i
$947$	5.62282	−	39.1076i	0.182717	−	1.27083i	−0.667586	−	0.744533i	$-0.732672\pi$
$947$	5.62282	−	39.1076i	0.182717	−	1.27083i	0.850303	−	0.526293i	$-0.176419\pi$
$948$	0.878917	−	1.92456i	0.0285459	−	0.0625068i
$949$	14.7532	+	102.611i	0.478909	+	3.33088i
$950$	1.43045	+	0.420017i	0.0464098	+	0.0136271i
$951$	−11.3012	+	7.26286i	−0.366468	+	0.235514i
$952$	1.39289	+	3.05001i	0.0451439	+	0.0988513i
$953$	5.79456	−	1.70143i	0.187704	−	0.0551149i	−0.186530	−	0.982449i	$-0.559724\pi$
$953$	5.79456	−	1.70143i	0.187704	−	0.0551149i	0.374234	+	0.927334i	$0.377906\pi$
$954$	6.76068	−	7.80224i	0.218885	−	0.252607i
$955$	−0.0367573	+	0.0424202i	−0.00118944	+	0.00137268i
$956$	−4.08252	+	1.19874i	−0.132038	+	0.0387699i
$957$	−7.01884	−	15.3691i	−0.226887	−	0.496813i
$958$	−9.05698	+	5.82057i	−0.292618	+	0.188054i
$959$	17.9813	+	5.27979i	0.580646	+	0.170493i
$960$	0.867268	+	6.03198i	0.0279909	+	0.194681i
$961$	−6.35758	+	13.9212i	−0.205083	+	0.449069i
$962$	−5.31099	+	36.9388i	−0.171233	+	1.19095i
$963$	−7.59129	−	4.87862i	−0.244626	−	0.157211i
$964$	−16.1096	−	18.5915i	−0.518855	−	0.598791i
$965$	15.3652			0.494622
$966$	3.60271	+	1.87651i	0.115915	+	0.0603757i
$967$	−34.1074			−1.09682			−0.548410	−	0.836210i	$-0.684767\pi$
$967$	−34.1074			−1.09682			−0.548410	+	0.836210i	$0.684767\pi$
$968$	17.9709	+	20.7396i	0.577607	+	0.666594i
$969$	−1.69456	−	1.08903i	−0.0544372	−	0.0349847i
$970$	−1.05948	+	7.36885i	−0.0340179	+	0.236599i
$971$	8.42973	−	18.4585i	0.270523	−	0.592363i	−0.724801	−	0.688959i	$-0.758068\pi$
$971$	8.42973	−	18.4585i	0.270523	−	0.592363i	0.995324	+	0.0965959i	$0.0307955\pi$
$972$	0.158794	+	1.10444i	0.00509333	+	0.0354249i
$973$	4.33367	+	1.27248i	0.138931	+	0.0407938i
$974$	−5.55925	+	3.57271i	−0.178130	+	0.114477i
$975$	−2.53380	−	5.54825i	−0.0811466	−	0.177686i
$976$	−4.40967	+	1.29480i	−0.141150	+	0.0414454i
$977$	19.1863	−	22.1421i	0.613823	−	0.708390i	−0.360699	−	0.932682i	$-0.617462\pi$
$977$	19.1863	−	22.1421i	0.613823	−	0.708390i	0.974522	+	0.224293i	$0.0720071\pi$
$978$	−0.509831	+	0.588376i	−0.0163026	+	0.0188142i
$979$	34.1050	−	10.0141i	1.09000	−	0.320053i
$980$	−2.86854	−	6.28123i	−0.0916322	−	0.200646i
$981$	2.37763	−	1.52801i	0.0759118	−	0.0487856i
$982$	38.0869	+	11.1833i	1.21540	+	0.356875i
$983$	−4.38960	−	30.5303i	−0.140006	−	0.973766i	−0.931799	−	0.362976i	$-0.881761\pi$
$983$	−4.38960	−	30.5303i	−0.140006	−	0.973766i	0.791792	−	0.610791i	$-0.209148\pi$
$984$	8.28111	−	18.1331i	0.263992	−	0.578062i
$985$	1.63097	−	11.3436i	0.0519669	−	0.361438i
$986$	3.76275	+	2.41817i	0.119830	+	0.0770103i
$987$	−2.45664	−	2.83511i	−0.0781957	−	0.0902426i
$988$	−10.7902			−0.343282
$989$	−30.7314	+	23.9593i	−0.977200	+	0.761861i
$990$	4.24360			0.134870
$991$	−26.3531	−	30.4131i	−0.837135	−	0.966105i	0.162654	−	0.986683i	$-0.447995\pi$
$991$	−26.3531	−	30.4131i	−0.837135	−	0.966105i	−0.999788	+	0.0205783i	$0.993449\pi$
$992$	17.8893	+	11.4968i	0.567986	+	0.365023i
$993$	−4.48162	+	31.1704i	−0.142220	+	0.989162i
$994$	−0.926393	+	2.02852i	−0.0293834	+	0.0643407i
$995$	1.41567	+	9.84617i	0.0448796	+	0.312145i
$996$	−1.98768	−	0.583637i	−0.0629822	−	0.0184932i
$997$	−2.04480	+	1.31411i	−0.0647594	+	0.0416184i	−0.572620	−	0.819821i	$-0.694073\pi$
$997$	−2.04480	+	1.31411i	−0.0647594	+	0.0416184i	0.507860	+	0.861439i	$0.330437\pi$
$998$	4.23055	+	9.26361i	0.133916	+	0.293234i
$999$	6.24311	−	1.83314i	0.197523	−	0.0579980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.m.c.151.3	yes	50
23.4	even	11		7935.2.a.bv.1.14		25
23.16	even	11	inner	345.2.m.c.16.3	✓	50
23.19	odd	22		7935.2.a.bw.1.14		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.c.16.3	✓	50	23.16	even	11	inner
345.2.m.c.151.3	yes	50	1.1	even	1	trivial
7935.2.a.bv.1.14		25	23.4	even	11
7935.2.a.bw.1.14		25	23.19	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.615779 - 0.710647i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.158794 - 1.10444i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(-0.133822 - 0.930750i) q^{6} +(0.864280 + 0.253775i) q^{7} +(-2.46475 + 1.58400i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.615779 - 0.710647i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.158794 - 1.10444i) q^{4} +(-0.415415 + 0.909632i) q^{5} +(-0.133822 - 0.930750i) q^{6} +(0.864280 + 0.253775i) q^{7} +(-2.46475 + 1.58400i) q^{8} +(0.415415 + 0.909632i) q^{9} +(0.902231 - 0.264919i) q^{10} +(2.95534 - 3.41064i) q^{11} +(0.730692 - 0.843263i) q^{12} +(5.85238 - 1.71841i) q^{13} +(-0.351861 - 0.770467i) q^{14} +(-0.841254 + 0.540641i) q^{15} +(0.502202 + 0.147460i) q^{16} +(-0.180812 - 1.25758i) q^{17} +(0.390623 - 0.855346i) q^{18} +(0.225633 - 1.56932i) q^{19} +(0.938668 + 0.603245i) q^{20} +(0.589877 + 0.680754i) q^{21} -4.24360 q^{22} +(-1.58757 + 4.52544i) q^{23} -2.92985 q^{24} +(-0.654861 - 0.755750i) q^{25} +(-4.82496 - 3.10081i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(0.417522 - 0.914247i) q^{28} +(-0.532814 - 3.70580i) q^{29} +(0.902231 + 0.264919i) q^{30} +(3.33288 - 2.14191i) q^{31} +(2.22975 + 4.88248i) q^{32} +(4.33012 - 1.27144i) q^{33} +(-0.782353 + 0.902883i) q^{34} +(-0.589877 + 0.680754i) q^{35} +(1.07060 - 0.314356i) q^{36} +(-2.70297 - 5.91868i) q^{37} +(-1.25417 + 0.806006i) q^{38} +(5.85238 + 1.71841i) q^{39} +(-0.416961 - 2.90003i) q^{40} +(-2.82646 + 6.18909i) q^{41} +(0.120542 - 0.838389i) q^{42} +(6.83542 + 4.39286i) q^{43} +(-3.29756 - 3.80558i) q^{44} -1.00000 q^{45} +(4.19359 - 1.65847i) q^{46} -4.16466 q^{47} +(0.342756 + 0.395562i) q^{48} +(-5.20620 - 3.34582i) q^{49} +(-0.133822 + 0.930750i) q^{50} +(0.527788 - 1.15570i) q^{51} +(-0.968559 - 6.73647i) q^{52} +(10.5343 + 3.09316i) q^{53} +(0.791048 - 0.508376i) q^{54} +(1.87474 + 4.10510i) q^{55} +(-2.53221 + 0.743524i) q^{56} +(1.03825 - 1.19821i) q^{57} +(-2.30542 + 2.66060i) q^{58} +(-11.9901 + 3.52062i) q^{59} +(0.463519 + 1.01496i) q^{60} +(-7.38677 + 4.74719i) q^{61} +(-3.57446 - 1.04956i) q^{62} +(0.128193 + 0.891599i) q^{63} +(2.53154 - 5.54330i) q^{64} +(-0.868042 + 6.03736i) q^{65} +(-3.56994 - 2.29426i) q^{66} +(1.50531 + 1.73722i) q^{67} -1.41763 q^{68} +(-3.78219 + 2.94873i) q^{69} +0.847010 q^{70} +(-1.72414 - 1.98977i) q^{71} +(-2.46475 - 1.58400i) q^{72} +(-2.41877 + 16.8229i) q^{73} +(-2.54166 + 5.56546i) q^{74} +(-0.142315 - 0.989821i) q^{75} +(-1.69738 - 0.498397i) q^{76} +(3.41977 - 2.19776i) q^{77} +(-2.38259 - 5.21714i) q^{78} +(1.81937 - 0.534217i) q^{79} +(-0.342756 + 0.395562i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(6.13874 - 1.80250i) q^{82} +(-0.771263 - 1.68883i) q^{83} +(0.845521 - 0.543384i) q^{84} +(1.21904 + 0.357944i) q^{85} +(-1.08734 - 7.56260i) q^{86} +(1.55528 - 3.40558i) q^{87} +(-1.88171 + 13.0876i) q^{88} +(6.62590 + 4.25821i) q^{89} +(0.615779 + 0.710647i) q^{90} +5.49418 q^{91} +(4.74598 + 2.47200i) q^{92} +3.96180 q^{93} +(2.56451 + 2.95960i) q^{94} +(1.33377 + 0.857161i) q^{95} +(-0.763879 + 5.31290i) q^{96} +(-3.28889 + 7.20166i) q^{97} +(0.828171 + 5.76005i) q^{98} +(4.33012 + 1.27144i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9}+O(q^{10}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9} + 15 q^{11} - 4 q^{12} - 19 q^{13} + 55 q^{14} + 5 q^{15} + 12 q^{16} + 5 q^{17} - 11 q^{19} + 4 q^{20} + 8 q^{21} - 18 q^{22} + 14 q^{23} + 66 q^{24} - 5 q^{25} - 18 q^{26} - 5 q^{27} + 10 q^{28} - 22 q^{29} + 6 q^{31} + 33 q^{32} + 4 q^{33} + 18 q^{34} - 8 q^{35} - 15 q^{36} + 25 q^{37} - 97 q^{38} - 19 q^{39} + 22 q^{40} - 42 q^{41} - 11 q^{42} - 25 q^{43} + 25 q^{44} - 50 q^{45} - 44 q^{46} + 86 q^{47} - 10 q^{48} - 8 q^{49} - 11 q^{50} - 17 q^{51} - 67 q^{52} - 26 q^{53} - 4 q^{55} - 132 q^{56} + 22 q^{57} + 8 q^{58} - 76 q^{59} + 4 q^{60} + 13 q^{61} - 8 q^{62} + 8 q^{63} + 76 q^{64} + 8 q^{65} + 4 q^{66} + 84 q^{67} + 66 q^{68} + 25 q^{69} + 22 q^{70} + 55 q^{71} - 59 q^{73} + 17 q^{74} - 5 q^{75} + 82 q^{76} - 56 q^{77} - 7 q^{78} + 7 q^{79} + 10 q^{80} - 5 q^{81} - 150 q^{82} + 19 q^{83} + 10 q^{84} + 6 q^{85} + 44 q^{86} - 11 q^{87} - 62 q^{88} - 74 q^{89} - 56 q^{91} + 41 q^{92} + 28 q^{93} - 161 q^{94} + 11 q^{95} - 44 q^{96} - 68 q^{97} - 198 q^{98} + 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9 + 15 * q^11 - 4 * q^12 - 19 * q^13 + 55 * q^14 + 5 * q^15 + 12 * q^16 + 5 * q^17 - 11 * q^19 + 4 * q^20 + 8 * q^21 - 18 * q^22 + 14 * q^23 + 66 * q^24 - 5 * q^25 - 18 * q^26 - 5 * q^27 + 10 * q^28 - 22 * q^29 + 6 * q^31 + 33 * q^32 + 4 * q^33 + 18 * q^34 - 8 * q^35 - 15 * q^36 + 25 * q^37 - 97 * q^38 - 19 * q^39 + 22 * q^40 - 42 * q^41 - 11 * q^42 - 25 * q^43 + 25 * q^44 - 50 * q^45 - 44 * q^46 + 86 * q^47 - 10 * q^48 - 8 * q^49 - 11 * q^50 - 17 * q^51 - 67 * q^52 - 26 * q^53 - 4 * q^55 - 132 * q^56 + 22 * q^57 + 8 * q^58 - 76 * q^59 + 4 * q^60 + 13 * q^61 - 8 * q^62 + 8 * q^63 + 76 * q^64 + 8 * q^65 + 4 * q^66 + 84 * q^67 + 66 * q^68 + 25 * q^69 + 22 * q^70 + 55 * q^71 - 59 * q^73 + 17 * q^74 - 5 * q^75 + 82 * q^76 - 56 * q^77 - 7 * q^78 + 7 * q^79 + 10 * q^80 - 5 * q^81 - 150 * q^82 + 19 * q^83 + 10 * q^84 + 6 * q^85 + 44 * q^86 - 11 * q^87 - 62 * q^88 - 74 * q^89 - 56 * q^91 + 41 * q^92 + 28 * q^93 - 161 * q^94 + 11 * q^95 - 44 * q^96 - 68 * q^97 - 198 * q^98 + 4 * q^99

Introduction

L-functions

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