LMFDB - Embedded newform 315.2.bv.a.23.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(23,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 4]))

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

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

chi := DirichletCharacter("315.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bv (of order $12$, degree $4$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.15
Character	$\chi$	$=$	315.23
Dual form			315.2.bv.a.137.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.710963 - 0.710963i) q^{2} +(-0.818385 + 1.52651i) q^{3} -0.989064i q^{4} +(2.18368 - 0.481173i) q^{5} +(1.66714 - 0.503454i) q^{6} +(1.29429 + 2.30756i) q^{7} +(-2.12511 + 2.12511i) q^{8} +(-1.66049 - 2.49855i) q^{9} +O(q^{10})$	\(q+(-0.710963 - 0.710963i) q^{2} +(-0.818385 + 1.52651i) q^{3} -0.989064i q^{4} +(2.18368 - 0.481173i) q^{5} +(1.66714 - 0.503454i) q^{6} +(1.29429 + 2.30756i) q^{7} +(-2.12511 + 2.12511i) q^{8} +(-1.66049 - 2.49855i) q^{9} +(-1.89461 - 1.21042i) q^{10} +(0.104894 + 0.0605605i) q^{11} +(1.50982 + 0.809434i) q^{12} +(3.34642 - 0.896671i) q^{13} +(0.720394 - 2.56078i) q^{14} +(-1.05258 + 3.72721i) q^{15} +1.04363 q^{16} +(-0.241535 + 0.901422i) q^{17} +(-0.595829 + 2.95693i) q^{18} +(3.49949 + 2.02043i) q^{19} +(-0.475910 - 2.15980i) q^{20} +(-4.58174 + 0.0872857i) q^{21} +(-0.0315194 - 0.117632i) q^{22} +(2.75260 + 0.737558i) q^{23} +(-1.50486 - 4.98318i) q^{24} +(4.53695 - 2.10146i) q^{25} +(-3.01668 - 1.74168i) q^{26} +(5.17300 - 0.489990i) q^{27} +(2.28232 - 1.28014i) q^{28} +(-0.427950 - 0.741231i) q^{29} +(3.39825 - 1.90156i) q^{30} +9.87039 q^{31} +(3.50825 + 3.50825i) q^{32} +(-0.178290 + 0.110560i) q^{33} +(0.812600 - 0.469155i) q^{34} +(3.93665 + 4.41619i) q^{35} +(-2.47123 + 1.64233i) q^{36} +(0.951119 + 3.54962i) q^{37} +(-1.05156 - 3.92446i) q^{38} +(-1.36988 + 5.84218i) q^{39} +(-3.61803 + 5.66312i) q^{40} +(-10.5145 - 6.07057i) q^{41} +(3.31951 + 3.19539i) q^{42} +(0.882506 - 3.29356i) q^{43} +(0.0598982 - 0.103747i) q^{44} +(-4.82823 - 4.65706i) q^{45} +(-1.43262 - 2.48138i) q^{46} +(-1.60987 - 1.60987i) q^{47} +(-0.854088 + 1.59311i) q^{48} +(-3.64962 + 5.97329i) q^{49} +(-4.71966 - 1.73154i) q^{50} +(-1.17837 - 1.10642i) q^{51} +(-0.886865 - 3.30982i) q^{52} +(-1.81389 - 0.486031i) q^{53} +(-4.02617 - 3.32945i) q^{54} +(0.258195 + 0.0817729i) q^{55} +(-7.65433 - 2.15330i) q^{56} +(-5.94815 + 3.68853i) q^{57} +(-0.222731 + 0.831244i) q^{58} -8.22069 q^{59} +(3.68645 + 1.04106i) q^{60} -4.70394 q^{61} +(-7.01748 - 7.01748i) q^{62} +(3.61639 - 7.06553i) q^{63} -7.07572i q^{64} +(6.87607 - 3.56825i) q^{65} +(0.205362 + 0.0481534i) q^{66} +(-8.57179 + 8.57179i) q^{67} +(0.891564 + 0.238894i) q^{68} +(-3.37858 + 3.59828i) q^{69} +(0.340935 - 5.93856i) q^{70} +13.1640i q^{71} +(8.83844 + 1.78097i) q^{72} +(1.43188 - 5.34386i) q^{73} +(1.84744 - 3.19986i) q^{74} +(-0.505062 + 8.64551i) q^{75} +(1.99834 - 3.46122i) q^{76} +(-0.00398355 + 0.320431i) q^{77} +(5.12751 - 3.17964i) q^{78} -14.3237i q^{79} +(2.27895 - 0.502164i) q^{80} +(-3.48553 + 8.29766i) q^{81} +(3.15950 + 11.7914i) q^{82} +(-9.55321 - 2.55978i) q^{83} +(0.0863311 + 4.53164i) q^{84} +(-0.0936971 + 2.08464i) q^{85} +(-2.96903 + 1.71417i) q^{86} +(1.48173 - 0.0466597i) q^{87} +(-0.351609 + 0.0942134i) q^{88} +(4.89683 - 8.48156i) q^{89} +(0.121690 + 6.74369i) q^{90} +(6.40036 + 6.56150i) q^{91} +(0.729492 - 2.72250i) q^{92} +(-8.07778 + 15.0673i) q^{93} +2.28912i q^{94} +(8.61395 + 2.72812i) q^{95} +(-8.22649 + 2.48429i) q^{96} +(-15.0920 - 4.04390i) q^{97} +(6.84154 - 1.65204i) q^{98} +(-0.0228620 - 0.362643i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7	$ 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 4 q^{10} - 24 q^{11} + 26 q^{12} - 4 q^{13} - 14 q^{15} - 136 q^{16} + 18 q^{17} - 10 q^{18} - 12 q^{20} - 16 q^{21} + 4 q^{22} - 30 q^{23} + 2 q^{25} - 32 q^{27} - 4 q^{28} + 10 q^{30} - 8 q^{31} - 34 q^{33} + 8 q^{36} - 4 q^{37} - 30 q^{38} + 18 q^{40} - 36 q^{41} + 8 q^{42} - 4 q^{43} + 22 q^{45} + 4 q^{46} + 38 q^{48} + 36 q^{50} - 40 q^{51} + 26 q^{52} + 4 q^{55} + 24 q^{56} + 32 q^{57} + 6 q^{58} + 22 q^{60} + 16 q^{61} + 14 q^{63} + 4 q^{66} - 4 q^{67} + 114 q^{68} + 18 q^{70} - 46 q^{72} - 4 q^{73} + 6 q^{75} - 24 q^{76} - 54 q^{77} + 54 q^{78} - 36 q^{80} - 64 q^{81} - 8 q^{82} - 12 q^{83} - 4 q^{85} - 120 q^{86} - 28 q^{87} - 6 q^{88} - 24 q^{90} - 16 q^{91} + 72 q^{92} - 38 q^{93} + 192 q^{96} - 4 q^{97} - 12 q^{98}+O(q^{100}) $ 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 4 * q^10 - 24 * q^11 + 26 * q^12 - 4 * q^13 - 14 * q^15 - 136 * q^16 + 18 * q^17 - 10 * q^18 - 12 * q^20 - 16 * q^21 + 4 * q^22 - 30 * q^23 + 2 * q^25 - 32 * q^27 - 4 * q^28 + 10 * q^30 - 8 * q^31 - 34 * q^33 + 8 * q^36 - 4 * q^37 - 30 * q^38 + 18 * q^40 - 36 * q^41 + 8 * q^42 - 4 * q^43 + 22 * q^45 + 4 * q^46 + 38 * q^48 + 36 * q^50 - 40 * q^51 + 26 * q^52 + 4 * q^55 + 24 * q^56 + 32 * q^57 + 6 * q^58 + 22 * q^60 + 16 * q^61 + 14 * q^63 + 4 * q^66 - 4 * q^67 + 114 * q^68 + 18 * q^70 - 46 * q^72 - 4 * q^73 + 6 * q^75 - 24 * q^76 - 54 * q^77 + 54 * q^78 - 36 * q^80 - 64 * q^81 - 8 * q^82 - 12 * q^83 - 4 * q^85 - 120 * q^86 - 28 * q^87 - 6 * q^88 - 24 * q^90 - 16 * q^91 + 72 * q^92 - 38 * q^93 + 192 * q^96 - 4 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.710963	−	0.710963i	−0.502727	−	0.502727i	0.409558	−	0.912284i	$-0.365683\pi$
$2$	−0.710963	−	0.710963i	−0.502727	−	0.502727i	−0.912284	+	0.409558i	$0.865683\pi$
$3$	−0.818385	+	1.52651i	−0.472495	+	0.881334i
$3$	−0.818385	+	1.52651i	−0.472495	+	0.881334i
$4$		−	0.989064i		−	0.494532i
$5$	2.18368	−	0.481173i	0.976573	−	0.215187i
$5$	2.18368	−	0.481173i	0.976573	−	0.215187i
$6$	1.66714	−	0.503454i	0.680606	−	0.205534i
$7$	1.29429	+	2.30756i	0.489196	+	0.872174i
$7$	1.29429	+	2.30756i	0.489196	+	0.872174i
$8$	−2.12511	+	2.12511i	−0.751341	+	0.751341i
$9$	−1.66049	−	2.49855i	−0.553498	−	0.832851i
$10$	−1.89461	−	1.21042i	−0.599129	−	0.382769i
$11$	0.104894	+	0.0605605i	0.0316267	+	0.0182597i	0.515730	−	0.856751i	$-0.327521\pi$
$11$	0.104894	+	0.0605605i	0.0316267	+	0.0182597i	−0.484103	+	0.875011i	$0.660854\pi$
$12$	1.50982	+	0.809434i	0.435847	+	0.233664i
$13$	3.34642	−	0.896671i	0.928131	−	0.248692i	0.237073	−	0.971492i	$-0.423812\pi$
$13$	3.34642	−	0.896671i	0.928131	−	0.248692i	0.691057	+	0.722800i	$0.257145\pi$
$14$	0.720394	−	2.56078i	0.192533	−	0.684397i
$15$	−1.05258	+	3.72721i	−0.271774	+	0.962361i
$16$	1.04363			0.260907
$17$	−0.241535	+	0.901422i	−0.0585809	+	0.218627i	−0.989011	−	0.147843i	$-0.952767\pi$
$17$	−0.241535	+	0.901422i	−0.0585809	+	0.218627i	0.930430	+	0.366470i	$0.119434\pi$
$18$	−0.595829	+	2.95693i	−0.140438	+	0.696954i
$19$	3.49949	+	2.02043i	0.802838	+	0.463519i	0.844463	−	0.535615i	$-0.179920\pi$
$19$	3.49949	+	2.02043i	0.802838	+	0.463519i	−0.0416245	+	0.999133i	$0.513253\pi$
$20$	−0.475910	−	2.15980i	−0.106417	−	0.482946i
$21$	−4.58174	+	0.0872857i	−0.999819	+	0.0190473i
$22$	−0.0315194	−	0.117632i	−0.00671995	−	0.0250792i
$23$	2.75260	+	0.737558i	0.573958	+	0.153791i	0.534111	−	0.845414i	$-0.320646\pi$
$23$	2.75260	+	0.737558i	0.573958	+	0.153791i	0.0398466	+	0.999206i	$0.487313\pi$
$24$	−1.50486	−	4.98318i	−0.307177	−	1.01719i
$25$	4.53695	−	2.10146i	0.907389	−	0.420291i
$26$	−3.01668	−	1.74168i	−0.591620	−	0.341572i
$27$	5.17300	−	0.489990i	0.995544	−	0.0942986i
$28$	2.28232	−	1.28014i	0.431318	−	0.241923i
$29$	−0.427950	−	0.741231i	−0.0794683	−	0.137643i	0.823552	−	0.567240i	$-0.191989\pi$
$29$	−0.427950	−	0.741231i	−0.0794683	−	0.137643i	−0.903021	+	0.429597i	$0.858656\pi$
$30$	3.39825	−	1.90156i	0.620433	−	0.347177i
$31$	9.87039			1.77277			0.886387	−	0.462944i	$-0.153207\pi$
$31$	9.87039			1.77277			0.886387	+	0.462944i	$0.153207\pi$
$32$	3.50825	+	3.50825i	0.620176	+	0.620176i
$33$	−0.178290	+	0.110560i	−0.0310363	+	0.0192461i
$34$	0.812600	−	0.469155i	0.139360	−	0.0804594i
$35$	3.93665	+	4.41619i	0.665416	+	0.746473i
$36$	−2.47123	+	1.64233i	−0.411871	+	0.273722i
$37$	0.951119	+	3.54962i	0.156363	+	0.583554i	0.998985	+	0.0450487i	$0.0143443\pi$
$37$	0.951119	+	3.54962i	0.156363	+	0.583554i	−0.842622	+	0.538506i	$0.818989\pi$
$38$	−1.05156	−	3.92446i	−0.170585	−	0.636631i
$39$	−1.36988	+	5.84218i	−0.219356	+	0.935498i
$40$	−3.61803	+	5.66312i	−0.572060	+	0.895418i
$41$	−10.5145	−	6.07057i	−1.64210	−	0.948064i	−0.980087	−	0.198568i	$-0.936371\pi$
$41$	−10.5145	−	6.07057i	−1.64210	−	0.948064i	−0.662009	−	0.749496i	$-0.730296\pi$
$42$	3.31951	+	3.19539i	0.512211	+	0.493060i
$43$	0.882506	−	3.29356i	0.134581	−	0.502263i	−0.865418	−	0.501050i	$-0.832947\pi$
$43$	0.882506	−	3.29356i	0.134581	−	0.502263i	0.999999	−	0.00121294i	$-0.000386091\pi$
$44$	0.0598982	−	0.103747i	0.00902999	−	0.0156404i
$45$	−4.82823	−	4.65706i	−0.719749	−	0.694234i
$46$	−1.43262	−	2.48138i	−0.211229	−	0.365859i
$47$	−1.60987	−	1.60987i	−0.234824	−	0.234824i	0.579879	−	0.814703i	$-0.303100\pi$
$47$	−1.60987	−	1.60987i	−0.234824	−	0.234824i	−0.814703	+	0.579879i	$0.803100\pi$
$48$	−0.854088	+	1.59311i	−0.123277	+	0.229946i
$49$	−3.64962	+	5.97329i	−0.521375	+	0.853328i
$50$	−4.71966	−	1.73154i	−0.667460	−	0.244877i
$51$	−1.17837	−	1.10642i	−0.165004	−	0.154929i
$52$	−0.886865	−	3.30982i	−0.122986	−	0.458990i
$53$	−1.81389	−	0.486031i	−0.249157	−	0.0667615i	0.132079	−	0.991239i	$-0.457835\pi$
$53$	−1.81389	−	0.486031i	−0.249157	−	0.0667615i	−0.381236	+	0.924478i	$0.624501\pi$
$54$	−4.02617	−	3.32945i	−0.547893	−	0.453080i
$55$	0.258195	+	0.0817729i	0.0348150	+	0.0110263i
$56$	−7.65433	−	2.15330i	−1.02285	−	0.287747i
$57$	−5.94815	+	3.68853i	−0.787851	+	0.488558i
$58$	−0.222731	+	0.831244i	−0.0292460	+	0.109148i
$59$	−8.22069			−1.07024			−0.535121	−	0.844775i	$-0.679734\pi$
$59$	−8.22069			−1.07024			−0.535121	+	0.844775i	$0.679734\pi$
$60$	3.68645	+	1.04106i	0.475918	+	0.134401i
$61$	−4.70394			−0.602278			−0.301139	−	0.953580i	$-0.597367\pi$
$61$	−4.70394			−0.602278			−0.301139	+	0.953580i	$0.597367\pi$
$62$	−7.01748	−	7.01748i	−0.891221	−	0.891221i
$63$	3.61639	−	7.06553i	0.455622	−	0.890173i
$64$		−	7.07572i		−	0.884465i
$65$	6.87607	−	3.56825i	0.852872	−	0.442587i
$66$	0.205362	+	0.0481534i	0.0252783	+	0.00592727i
$67$	−8.57179	+	8.57179i	−1.04721	+	1.04721i	−0.0483818	+	0.998829i	$0.515406\pi$
$67$	−8.57179	+	8.57179i	−1.04721	+	1.04721i	−0.998829	+	0.0483818i	$0.984594\pi$
$68$	0.891564	+	0.238894i	0.108118	+	0.0289701i
$69$	−3.37858	+	3.59828i	−0.406733	+	0.433182i
$70$	0.340935	−	5.93856i	0.0407495	−	0.709794i
$71$			13.1640i			1.56227i	0.624359	+	0.781137i	$0.285360\pi$
$71$			13.1640i			1.56227i	−0.624359	+	0.781137i	$0.714640\pi$
$72$	8.83844	+	1.78097i	1.04162	+	0.209889i
$73$	1.43188	−	5.34386i	0.167589	−	0.625451i	−0.830107	−	0.557605i	$-0.811721\pi$
$73$	1.43188	−	5.34386i	0.167589	−	0.625451i	0.997696	−	0.0678464i	$-0.0216128\pi$
$74$	1.84744	−	3.19986i	0.214761	−	0.371976i
$75$	−0.505062	+	8.64551i	−0.0583196	+	0.998298i
$76$	1.99834	−	3.46122i	0.229225	−	0.397029i
$77$	−0.00398355	+	0.320431i	−0.000453967	+	0.0365165i
$78$	5.12751	−	3.17964i	0.580576	−	0.360024i
$79$		−	14.3237i		−	1.61155i	−0.592224	−	0.805773i	$-0.701750\pi$
$79$		−	14.3237i		−	1.61155i	0.592224	−	0.805773i	$-0.298250\pi$
$80$	2.27895	−	0.502164i	0.254794	−	0.0561437i
$81$	−3.48553	+	8.29766i	−0.387281	+	0.921962i
$82$	3.15950	+	11.7914i	0.348908	+	1.30214i
$83$	−9.55321	−	2.55978i	−1.04860	−	0.280972i	−0.306928	−	0.951733i	$-0.599301\pi$
$83$	−9.55321	−	2.55978i	−1.04860	−	0.280972i	−0.741674	+	0.670761i	$0.765968\pi$
$84$	0.0863311	+	4.53164i	0.00941949	+	0.494442i
$85$	−0.0936971	+	2.08464i	−0.0101629	+	0.226111i
$86$	−2.96903	+	1.71417i	−0.320158	+	0.184844i
$87$	1.48173	−	0.0466597i	0.158858	−	0.00500244i
$88$	−0.351609	+	0.0942134i	−0.0374817	+	0.0100432i
$89$	4.89683	−	8.48156i	0.519063	−	0.899044i	−0.480691	−	0.876890i	$-0.659614\pi$
$89$	4.89683	−	8.48156i	0.519063	−	0.899044i	0.999755	−	0.0221541i	$-0.00705246\pi$
$90$	0.121690	+	6.74369i	0.0128273	+	0.710847i
$91$	6.40036	+	6.56150i	0.670940	+	0.687832i
$92$	0.729492	−	2.72250i	0.0760548	−	0.283840i
$93$	−8.07778	+	15.0673i	−0.837627	+	1.56241i
$94$			2.28912i			0.236104i
$95$	8.61395	+	2.72812i	0.883773	+	0.279900i
$96$	−8.22649	+	2.48429i	−0.839612	+	0.253552i
$97$	−15.0920	−	4.04390i	−1.53236	−	0.410596i	−0.608574	−	0.793497i	$-0.708258\pi$
$97$	−15.0920	−	4.04390i	−1.53236	−	0.410596i	−0.923789	+	0.382901i	$0.874925\pi$
$98$	6.84154	−	1.65204i	0.691100	−	0.166882i
$99$	−0.0228620	−	0.362643i	−0.00229771	−	0.0364470i
$100$	−2.07847	−	4.48733i	−0.207847	−	0.448733i
$101$	10.7103	+	6.18362i	1.06572	+	0.615293i	0.927009	−	0.375040i	$-0.122371\pi$
$101$	10.7103	+	6.18362i	1.06572	+	0.615293i	0.138710	+	0.990333i	$0.455704\pi$
$102$	0.0511523	+	1.62440i	0.00506483	+	0.160839i
$103$	−1.66793	+	6.22481i	−0.164346	+	0.613348i	0.833777	+	0.552102i	$0.186174\pi$
$103$	−1.66793	+	6.22481i	−0.164346	+	0.613348i	−0.998123	+	0.0612462i	$0.980493\pi$
$104$	−5.20600	+	9.01706i	−0.510490	+	0.884195i
$105$	−9.96308	+	2.39521i	−0.972297	+	0.233749i
$106$	0.944060	+	1.63516i	0.0916952	+	0.158821i
$107$	3.75703	−	1.00669i	0.363206	−	0.0973207i	−0.0726007	−	0.997361i	$-0.523130\pi$
$107$	3.75703	−	1.00669i	0.363206	−	0.0973207i	0.435806	+	0.900040i	$0.356463\pi$
$108$	−0.484631	−	5.11642i	−0.0466336	−	0.492328i
$109$	0.811903	−	0.468752i	0.0777662	−	0.0448983i	−0.460613	−	0.887601i	$-0.652370\pi$
$109$	0.811903	−	0.468752i	0.0777662	−	0.0448983i	0.538379	+	0.842703i	$0.319037\pi$
$110$	−0.125430	−	0.241705i	−0.0119592	−	0.0230456i
$111$	−6.19693	−	1.45306i	−0.588187	−	0.137918i
$112$	1.35076	+	2.40823i	0.127634	+	0.227556i
$113$	1.91258	+	7.13786i	0.179921	+	0.671473i	0.995661	+	0.0930547i	$0.0296632\pi$
$113$	1.91258	+	7.13786i	0.179921	+	0.671473i	−0.815740	+	0.578418i	$0.803670\pi$
$114$	6.85132	+	1.60650i	0.641685	+	0.150463i
$115$	6.36571	+	0.286116i	0.593605	+	0.0266804i
$116$	−0.733125	+	0.423270i	−0.0680689	+	0.0392996i
$117$	−7.79709	−	6.87230i	−0.720841	−	0.635344i
$118$	5.84461	+	5.84461i	0.538040	+	0.538040i
$119$	−2.39270	+	0.609346i	−0.219338	+	0.0558587i
$120$	−5.68390	−	10.1576i	−0.518866	−	0.927256i
$121$	−5.49266	−	9.51357i	−0.499333	−	0.864870i
$122$	3.34433	+	3.34433i	0.302781	+	0.302781i
$123$	17.8718	−	11.0825i	1.61144	−	0.999279i
$124$		−	9.76244i		−	0.876693i
$125$	8.89609	−	6.77197i	0.795690	−	0.605703i
$126$	−7.59445	+	2.45221i	−0.676567	+	0.218461i
$127$	−8.43292	+	8.43292i	−0.748301	+	0.748301i	−0.974160	−	0.225859i	$-0.927481\pi$
$127$	−8.43292	+	8.43292i	−0.748301	+	0.748301i	0.225859	+	0.974160i	$0.427481\pi$
$128$	1.98592	−	1.98592i	0.175532	−	0.175532i
$129$	4.30544	+	4.04256i	0.379072	+	0.355927i
$130$	−7.42553	−	2.35174i	−0.651262	−	0.206261i
$131$	17.5423	−	10.1280i	1.53268	−	0.884891i	0.533438	−	0.845839i	$-0.320900\pi$
$131$	17.5423	−	10.1280i	1.53268	−	0.884891i	0.999237	−	0.0390517i	$-0.0124337\pi$
$132$	0.109351	+	0.176340i	0.00951779	+	0.0153484i
$133$	−0.132900	+	10.6903i	−0.0115239	+	0.926966i
$134$	12.1884			1.05292
$135$	11.0604	−	3.55909i	0.951929	−	0.306317i
$136$	−1.40233	−	2.42891i	−0.120249	−	0.208278i
$137$	1.86899	−	0.500795i	0.159679	−	0.0427858i	−0.178094	−	0.984013i	$-0.556993\pi$
$137$	1.86899	−	0.500795i	0.159679	−	0.0427858i	0.337773	+	0.941228i	$0.390326\pi$
$138$	4.96029	−	0.156200i	0.422248	−	0.0132966i
$139$	−16.3914	−	9.46356i	−1.39030	−	0.802689i	−0.396950	−	0.917840i	$-0.629931\pi$
$139$	−16.3914	−	9.46356i	−1.39030	−	0.802689i	−0.993348	+	0.115152i	$0.963265\pi$
$140$	4.36790	−	3.89360i	0.369155	−	0.329069i
$141$	3.77498	−	1.14000i	0.317911	−	0.0960051i
$142$	9.35909	−	9.35909i	0.785397	−	0.785397i
$143$	0.405322	+	0.108606i	0.0338947	+	0.00908206i
$144$	−1.73293	−	2.60755i	−0.144411	−	0.217296i
$145$	−1.29117	−	1.41270i	−0.107226	−	0.117318i
$146$	−4.81730	+	2.78127i	−0.398682	+	0.230179i
$147$	−6.13153	−	10.4597i	−0.505720	−	0.862698i
$148$	3.51080	−	0.940717i	0.288586	−	0.0773264i
$149$	−8.21240	−	14.2243i	−0.672786	−	1.16530i	−0.977111	−	0.212732i	$-0.931764\pi$
$149$	−8.21240	−	14.2243i	−0.672786	−	1.16530i	0.304324	−	0.952568i	$-0.401569\pi$
$150$	6.50572	−	5.78756i	0.531190	−	0.472552i
$151$	−5.82977	+	10.0975i	−0.474420	+	0.821719i	−0.999571	−	0.0292899i	$-0.990675\pi$
$151$	−5.82977	+	10.0975i	−0.474420	+	0.821719i	0.525151	+	0.851009i	$0.324009\pi$
$152$	−11.7305	+	3.14317i	−0.951466	+	0.254944i
$153$	2.65332	−	0.893317i	0.214508	−	0.0722204i
$154$	0.230647	−	0.224983i	0.0185861	−	0.0181296i
$155$	21.5538	−	4.74936i	1.73124	−	0.381478i
$156$	5.77829	+	1.35490i	0.462634	+	0.108479i
$157$	−8.22380	+	8.22380i	−0.656331	+	0.656331i	−0.954510	−	0.298179i	$-0.903621\pi$
$157$	−8.22380	+	8.22380i	−0.656331	+	0.656331i	0.298179	+	0.954510i	$0.403621\pi$
$158$	−10.1836	+	10.1836i	−0.810168	+	0.810168i
$159$	2.22639	−	2.37117i	0.176565	−	0.188046i
$160$	9.34897	+	5.97283i	0.739101	+	0.472194i
$161$	1.86071	+	7.30640i	0.146645	+	0.575825i
$162$	8.37741	−	3.42125i	0.658191	−	0.268799i
$163$	5.79560	−	1.55293i	0.453946	−	0.121635i	−0.0245990	−	0.999697i	$-0.507831\pi$
$163$	5.79560	−	1.55293i	0.453946	−	0.121635i	0.478545	+	0.878063i	$0.341164\pi$
$164$	−6.00418	+	10.3996i	−0.468848	+	0.812069i
$165$	−0.336130	+	0.327217i	−0.0261677	+	0.0254738i
$166$	4.97207	+	8.61189i	0.385908	+	0.668412i
$167$	−1.84540	+	0.494474i	−0.142801	+	0.0382635i	−0.329512	−	0.944152i	$-0.606884\pi$
$167$	−1.84540	+	0.494474i	−0.142801	+	0.0382635i	0.186710	+	0.982415i	$0.440217\pi$
$168$	9.55123	−	9.92222i	0.736894	−	0.765516i
$169$	−0.863805	+	0.498718i	−0.0664465	+	0.0383629i
$170$	1.54872	−	1.41549i	0.118781	−	0.108563i
$171$	−0.762725	−	12.0986i	−0.0583271	−	0.925201i
$172$	−3.25754	−	0.872855i	−0.248385	−	0.0665546i
$173$	−5.85048	+	5.85048i	−0.444804	+	0.444804i	−0.893623	−	0.448819i	$-0.851845\pi$
$173$	−5.85048	+	5.85048i	−0.444804	+	0.444804i	0.448819	+	0.893623i	$0.351845\pi$
$174$	−1.08663	−	1.02028i	−0.0823770	−	0.0773472i
$175$	10.7214	+	7.74936i	0.810458	+	0.585796i
$176$	0.109470	+	0.0632025i	0.00825161	+	0.00476407i
$177$	6.72769	−	12.5490i	0.505684	−	0.943241i
$178$	−9.51155	+	2.54861i	−0.712920	+	0.191026i
$179$	−3.09413	−	5.35918i	−0.231266	−	0.400564i	0.726915	−	0.686727i	$-0.240953\pi$
$179$	−3.09413	−	5.35918i	−0.231266	−	0.400564i	−0.958181	+	0.286163i	$0.907620\pi$
$180$	−4.60613	+	4.77542i	−0.343321	+	0.355939i
$181$	24.4464			1.81709			0.908544	−	0.417790i	$-0.137195\pi$
$181$	24.4464			1.81709			0.908544	+	0.417790i	$0.137195\pi$
$182$	0.114564	−	9.21540i	0.00849208	−	0.683091i
$183$	3.84963	−	7.18063i	0.284573	−	0.530808i
$184$	−7.41699	+	4.28220i	−0.546788	+	0.315688i
$185$	3.78492	+	7.29360i	0.278273	+	0.536236i
$186$	16.4553	−	4.96929i	1.20656	−	0.364366i
$187$	−0.0799261	+	0.0799261i	−0.00584478	+	0.00584478i
$188$	−1.59226	+	1.59226i	−0.116128	+	0.116128i
$189$	7.82604	+	11.3028i	0.569261	+	0.822157i
$190$	−4.18461	−	8.06380i	−0.303583	−	0.585009i
$191$			10.0891i			0.730021i	0.931003	+	0.365011i	$0.118935\pi$
$191$			10.0891i			0.730021i	−0.931003	+	0.365011i	$0.881065\pi$
$192$	10.8012	+	5.79066i	0.779509	+	0.417905i
$193$	−10.5817	−	10.5817i	−0.761685	−	0.761685i	0.214942	−	0.976627i	$-0.431044\pi$
$193$	−10.5817	−	10.5817i	−0.761685	−	0.761685i	−0.976627	+	0.214942i	$0.931044\pi$
$194$	7.85481	+	13.6049i	0.563943	+	0.976777i
$195$	−0.180284	+	13.4166i	−0.0129104	+	0.960785i
$196$	5.90797	+	3.60971i	0.421998	+	0.257836i
$197$	−14.2460	−	14.2460i	−1.01499	−	1.01499i	−0.999886	−	0.0151024i	$-0.995193\pi$
$197$	−14.2460	−	14.2460i	−1.01499	−	1.01499i	−0.0151024	−	0.999886i	$-0.504807\pi$
$198$	−0.241572	+	0.274080i	−0.0171678	+	0.0194780i
$199$	10.4498	−	6.03320i	0.740768	−	0.427682i	−0.0815808	−	0.996667i	$-0.525997\pi$
$199$	10.4498	−	6.03320i	0.740768	−	0.427682i	0.822348	+	0.568984i	$0.192664\pi$
$200$	−5.17569	+	14.1074i	−0.365977	+	0.997541i
$201$	−6.06994	−	20.1000i	−0.428141	−	1.41774i
$202$	−3.21833	−	12.0110i	−0.226441	−	0.845089i
$203$	1.15654	−	1.94689i	0.0811732	−	0.136645i
$204$	−1.09432	+	1.16548i	−0.0766175	+	0.0815998i
$205$	−25.8814	−	8.19690i	−1.80764	−	0.572497i
$206$	5.61144	−	3.23977i	0.390968	−	0.225725i
$207$	−2.72785	−	8.10223i	−0.189599	−	0.563144i
$208$	3.49241	−	0.935790i	0.242155	−	0.0648853i
$209$	0.244717	+	0.423862i	0.0169274	+	0.0293191i
$210$	8.78629	+	5.38047i	0.606311	+	0.371288i
$211$	−0.746483	+	1.29295i	−0.0513900	+	0.0890101i	−0.890576	−	0.454834i	$-0.849698\pi$
$211$	−0.746483	+	1.29295i	−0.0513900	+	0.0890101i	0.839186	+	0.543844i	$0.183032\pi$
$212$	−0.480715	+	1.79405i	−0.0330157	+	0.123216i
$213$	−20.0950	−	10.7732i	−1.37689	−	0.738166i
$214$	−3.38683	−	1.95539i	−0.231519	−	0.133668i
$215$	0.342344	−	7.61673i	0.0233477	−	0.519456i
$216$	−9.95192	+	12.0345i	−0.677143	+	0.818843i
$217$	12.7752	+	22.7765i	0.867234	+	1.54617i
$218$	−0.910498	−	0.243967i	−0.0616667	−	0.0165236i
$219$	6.98564	+	6.55912i	0.472046	+	0.443224i
$220$	0.0808786	−	0.255371i	0.00545283	−	0.0172171i
$221$			3.23312i			0.217483i
$222$	3.37272	+	5.43886i	0.226362	+	0.365032i
$223$	−1.69730	+	6.33440i	−0.113659	+	0.424183i	−0.999183	−	0.0404114i	$-0.987133\pi$
$223$	−1.69730	+	6.33440i	−0.113659	+	0.424183i	0.885524	+	0.464594i	$0.153800\pi$
$224$	−3.55478	+	12.6362i	−0.237514	+	0.844289i
$225$	−12.7842	−	7.84634i	−0.852278	−	0.523089i
$226$	3.71498	−	6.43453i	0.247116	−	0.428018i
$227$	0.652752	−	0.174904i	0.0433247	−	0.0116088i	−0.237092	−	0.971487i	$-0.576194\pi$
$227$	0.652752	−	0.174904i	0.0433247	−	0.0116088i	0.280416	+	0.959878i	$0.409527\pi$
$228$	3.64819	+	5.88309i	0.241607	+	0.389617i
$229$	6.98020	−	4.03002i	0.461265	−	0.266311i	−0.251311	−	0.967906i	$-0.580862\pi$
$229$	6.98020	−	4.03002i	0.461265	−	0.266311i	0.712576	+	0.701595i	$0.247528\pi$
$230$	−4.32236	−	4.72920i	−0.285008	−	0.311834i
$231$	−0.485883	−	0.268317i	−0.0319687	−	0.0176540i
$232$	2.48464	+	0.665758i	0.163125	+	0.0437091i
$233$	3.27979	+	12.2404i	0.214866	+	0.801892i	0.986214	+	0.165478i	$0.0529166\pi$
$233$	3.27979	+	12.2404i	0.214866	+	0.801892i	−0.771347	+	0.636415i	$0.780417\pi$
$234$	0.657496	+	10.4294i	0.0429818	+	0.681791i
$235$	−4.29007	−	2.74082i	−0.279854	−	0.178792i
$236$			8.13078i			0.529269i
$237$	21.8654	+	11.7223i	1.42031	+	0.761447i
$238$	2.13434	+	1.26790i	0.138349	+	0.0821856i
$239$	−0.782315	+	1.35501i	−0.0506038	+	0.0876483i	−0.890218	−	0.455535i	$-0.849448\pi$
$239$	−0.782315	+	1.35501i	−0.0506038	+	0.0876483i	0.839614	+	0.543184i	$0.182781\pi$
$240$	−1.09850	+	3.88981i	−0.0709076	+	0.251086i
$241$	2.23507	−	3.87125i	0.143973	−	0.249369i	−0.785016	−	0.619475i	$-0.787345\pi$
$241$	2.23507	−	3.87125i	0.143973	−	0.249369i	0.928989	+	0.370106i	$0.120679\pi$
$242$	−2.85872	+	10.6689i	−0.183765	+	0.685822i
$243$	−9.81399	−	12.1114i	−0.629568	−	0.776945i
$244$			4.65250i			0.297846i
$245$	−5.09544	+	14.7999i	−0.325535	+	0.945530i
$246$	−20.5854	−	4.82689i	−1.31248	−	0.307751i
$247$	13.5224	+	3.62333i	0.860412	+	0.230547i
$248$	−20.9757	+	20.9757i	−1.33196	+	1.33196i
$249$	11.7257	−	12.4882i	0.743088	−	0.791410i
$250$	−11.1394	−	1.51017i	−0.704518	−	0.0955115i
$251$			1.01516i			0.0640765i	0.999487	+	0.0320382i	$0.0101998\pi$
$251$			1.01516i			0.0640765i	−0.999487	+	0.0320382i	$0.989800\pi$
$252$	−6.98826	−	3.57684i	−0.440219	−	0.225319i
$253$	0.244064	+	0.244064i	0.0153442	+	0.0153442i
$254$	11.9910			0.752381
$255$	−3.10555	−	1.84907i	−0.194477	−	0.115793i
$256$	−16.9753			−1.06095
$257$	1.83742	−	6.85733i	0.114615	−	0.427749i	−0.884643	−	0.466269i	$-0.845598\pi$
$257$	1.83742	−	6.85733i	0.114615	−	0.427749i	0.999258	+	0.0385205i	$0.0122645\pi$
$258$	−0.186897	−	5.93511i	−0.0116357	−	0.369504i
$259$	−6.95993	+	6.78900i	−0.432469	+	0.421848i
$260$	−3.52923	−	6.80087i	−0.218873	−	0.421772i
$261$	−1.14140	+	2.30006i	−0.0706507	+	0.142370i
$262$	−19.6726	−	5.27125i	−1.21538	−	0.325659i
$263$	4.96840	+	18.5423i	0.306365	+	1.14337i	0.931764	+	0.363064i	$0.118269\pi$
$263$	4.96840	+	18.5423i	0.306365	+	1.14337i	−0.625399	+	0.780305i	$0.715064\pi$
$264$	0.143933	−	0.613839i	0.00885849	−	0.0377792i
$265$	−4.19483	−	0.188542i	−0.257686	−	0.0115821i
$266$	7.69489	−	7.50591i	0.471804	−	0.460217i
$267$	8.93974	+	14.4163i	0.547103	+	0.882261i
$268$	8.47804	+	8.47804i	0.517879	+	0.517879i
$269$	8.25562	+	14.2992i	0.503354	+	0.871835i	0.999992	+	0.00387729i	$0.00123418\pi$
$269$	8.25562	+	14.2992i	0.503354	+	0.871835i	−0.496638	+	0.867958i	$0.665432\pi$
$270$	−10.3939	−	5.33317i	−0.632554	−	0.324566i
$271$	3.22518	−	5.58617i	0.195916	−	0.339336i	−0.751285	−	0.659978i	$-0.770565\pi$
$271$	3.22518	−	5.58617i	0.195916	−	0.339336i	0.947200	+	0.320643i	$0.103899\pi$
$272$	−0.252073	+	0.940748i	−0.0152842	+	0.0570412i
$273$	−15.2542	+	4.40041i	−0.923225	+	0.266325i
$274$	−1.68483	−	0.972737i	−0.101784	−	0.0587652i
$275$	0.603163	+	0.0543297i	0.0363721	+	0.00327621i
$276$	3.55893	+	3.34163i	0.214222	+	0.201143i
$277$	0.00951838	+	0.0355231i	0.000571904	+	0.00213438i	0.966211	−	0.257752i	$-0.0829817\pi$
$277$	0.00951838	+	0.0355231i	0.000571904	+	0.00213438i	−0.965639	+	0.259886i	$0.916315\pi$
$278$	4.92541	+	18.3819i	0.295407	+	1.10247i
$279$	−16.3897	−	24.6617i	−0.981227	−	1.47646i
$280$	−17.7507	−	1.01908i	−1.06081	−	0.0609014i
$281$	3.73498	−	2.15639i	0.222810	−	0.128640i	−0.384441	−	0.923150i	$-0.625606\pi$
$281$	3.73498	−	2.15639i	0.222810	−	0.128640i	0.607251	+	0.794510i	$0.292272\pi$
$282$	−3.49437	−	1.87338i	−0.208087	−	0.111558i
$283$	−16.2585	−	16.2585i	−0.966467	−	0.966467i	0.0329891	−	0.999456i	$-0.489497\pi$
$283$	−16.2585	−	16.2585i	−0.966467	−	0.966467i	−0.999456	+	0.0329891i	$0.989497\pi$
$284$	13.0200			0.772594
$285$	−11.2140	+	10.9167i	−0.664263	+	0.646648i
$286$	−0.210954	−	0.365383i	−0.0124740	−	0.0216056i
$287$	0.399310	−	32.1200i	0.0235705	−	1.89598i
$288$	2.94012	−	14.5910i	0.173248	−	0.859780i
$289$	13.9682	+	8.06455i	0.821659	+	0.474385i
$290$	−0.0864025	+	1.92235i	−0.00507373	+	0.112884i
$291$	18.5242	−	19.7287i	1.08591	−	1.15652i
$292$	−5.28541	−	1.41622i	−0.309305	−	0.0828781i
$293$	−7.46194	−	27.8483i	−0.435931	−	1.62692i	−0.738828	−	0.673894i	$-0.764621\pi$
$293$	−7.46194	−	27.8483i	−0.435931	−	1.62692i	0.302897	−	0.953023i	$-0.402046\pi$
$294$	−3.07714	+	11.7957i	−0.179462	+	0.687940i
$295$	−17.9514	+	3.95557i	−1.04517	+	0.230302i
$296$	−9.56459	−	5.52212i	−0.555930	−	0.320966i
$297$	0.572290	+	0.261882i	0.0332076	+	0.0151960i
$298$	−4.27424	+	15.9517i	−0.247600	+	0.924055i
$299$	9.87272			0.570954
$300$	8.55096	+	0.499539i	0.493690	+	0.0288409i
$301$	8.74229	−	2.22639i	0.503897	−	0.128327i
$302$	11.3237	−	3.03417i	0.651603	−	0.174597i
$303$	−18.2046	+	11.2889i	−1.04582	+	0.648531i
$304$	3.65216	+	2.10858i	0.209466	+	0.120935i
$305$	−10.2719	+	2.26341i	−0.588168	+	0.129602i
$306$	−2.52153	−	1.25130i	−0.144146	−	0.0715318i
$307$	0.586998	−	0.586998i	0.0335017	−	0.0335017i	−0.690157	−	0.723659i	$-0.742459\pi$
$307$	0.586998	−	0.586998i	0.0335017	−	0.0335017i	0.723659	+	0.690157i	$0.242459\pi$
$308$	0.316927	+	0.00393998i	0.0180586	+	0.000224501i
$309$	−8.13725	−	7.64041i	−0.462912	−	0.434648i
$310$	−18.7006	−	11.9473i	−1.06212	−	0.678563i
$311$		−	8.72873i		−	0.494961i	−0.968893	−	0.247480i	$-0.920397\pi$
$311$		−	8.72873i		−	0.494961i	0.968893	−	0.247480i	$-0.0796026\pi$
$312$	−9.50416	−	15.3265i	−0.538067	−	0.867690i
$313$	−9.07433	−	9.07433i	−0.512912	−	0.512912i	0.402506	−	0.915417i	$-0.368139\pi$
$313$	−9.07433	−	9.07433i	−0.512912	−	0.512912i	−0.915417	+	0.402506i	$0.868139\pi$
$314$	11.6936			0.659910
$315$	4.49730	−	17.1690i	0.253394	−	0.967363i
$316$	−14.1671			−0.796961
$317$	6.75880	+	6.75880i	0.379612	+	0.379612i	0.870962	−	0.491350i	$-0.163496\pi$
$317$	6.75880	+	6.75880i	0.379612	+	0.379612i	−0.491350	+	0.870962i	$0.663496\pi$
$318$	−3.26870	+	0.102931i	−0.183300	+	0.00577211i
$319$		−	0.103667i		−	0.00580426i
$320$	−3.40464	−	15.4511i	−0.190325	−	0.863744i
$321$	−1.53796	+	6.55902i	−0.0858408	+	0.366089i
$322$	3.87168	−	6.51748i	0.215760	−	0.363205i
$323$	−2.66651	+	2.66651i	−0.148369	+	0.148369i
$324$	8.20691	+	3.44741i	0.455939	+	0.191523i
$325$	13.2982	−	11.1005i	0.737653	−	0.615746i
$326$	−5.22453	−	3.01638i	−0.289360	−	0.167062i
$327$	0.0511084	+	1.62300i	0.00282630	+	0.0897522i
$328$	35.2453	−	9.44394i	1.94609	−	0.521454i
$329$	1.63123	−	5.79851i	0.0899323	−	0.319682i
$330$	0.471615	+	0.00633725i	0.0259616	+	0.000348854i
$331$	3.15803			0.173581			0.0867904	−	0.996227i	$-0.472339\pi$
$331$	3.15803			0.173581			0.0867904	+	0.996227i	$0.472339\pi$
$332$	−2.53178	+	9.44873i	−0.138950	+	0.518567i
$333$	7.28959	−	8.27054i	0.399467	−	0.453223i
$334$	1.66356	+	0.960459i	0.0910261	+	0.0525540i
$335$	−14.5936	+	22.8426i	−0.797332	+	1.24802i
$336$	−4.78163	+	0.0910936i	−0.260859	+	0.00496956i
$337$	5.82249	+	21.7298i	0.317171	+	1.18370i	0.921951	+	0.387307i	$0.126595\pi$
$337$	5.82249	+	21.7298i	0.317171	+	1.18370i	−0.604780	+	0.796393i	$0.706739\pi$
$338$	0.968703	+	0.259563i	0.0526905	+	0.0141184i
$339$	−12.4613	−	2.92193i	−0.676803	−	0.158697i
$340$	2.06184	+	0.0926724i	0.111819	+	0.00502586i
$341$	1.03534	+	0.597756i	0.0560670	+	0.0323703i
$342$	−8.05937	+	9.14390i	−0.435801	+	0.494446i
$343$	−18.5074	−	0.690527i	−0.999305	−	0.0372849i
$344$	5.12376	+	8.87461i	0.276255	+	0.478487i
$345$	−5.64636	+	9.48319i	−0.303990	+	0.510558i
$346$	8.31895			0.447230
$347$	1.34085	+	1.34085i	0.0719806	+	0.0719806i	0.742181	−	0.670200i	$-0.233792\pi$
$347$	1.34085	+	1.34085i	0.0719806	+	0.0719806i	−0.670200	+	0.742181i	$0.733792\pi$
$348$	−0.0461494	−	1.46552i	−0.00247387	−	0.0785603i
$349$	16.8429	−	9.72424i	0.901579	−	0.520527i	0.0238666	−	0.999715i	$-0.492402\pi$
$349$	16.8429	−	9.72424i	0.901579	−	0.520527i	0.877712	+	0.479189i	$0.159069\pi$
$350$	−2.11298	−	13.1320i	−0.112944	−	0.701934i
$351$	16.8717	−	6.27819i	0.900544	−	0.335105i
$352$	0.155532	+	0.580455i	0.00828990	+	0.0309383i
$353$	−8.16894	−	30.4869i	−0.434789	−	1.62265i	−0.741571	−	0.670874i	$-0.765919\pi$
$353$	−8.16894	−	30.4869i	−0.434789	−	1.62265i	0.306782	−	0.951780i	$-0.400748\pi$
$354$	−13.7050	+	4.13874i	−0.728413	+	0.219972i
$355$	6.33414	+	28.7459i	0.336181	+	1.52568i
$356$	−8.38881	−	4.84328i	−0.444606	−	0.256693i
$357$	1.02797	−	4.15117i	0.0544061	−	0.219703i
$358$	−1.61037	+	6.00999i	−0.0851108	+	0.317638i
$359$	−14.5148	+	25.1404i	−0.766063	+	1.32686i	0.173620	+	0.984813i	$0.444454\pi$
$359$	−14.5148	+	25.1404i	−0.766063	+	1.32686i	−0.939683	+	0.342047i	$0.888880\pi$
$360$	20.1573	−	0.363740i	1.06238	−	0.0191708i
$361$	−1.33571	−	2.31352i	−0.0703007	−	0.121764i
$362$	−17.3805	−	17.3805i	−0.913498	−	0.913498i
$363$	19.0177	−	0.598869i	0.998172	−	0.0314325i
$364$	6.48974	−	6.33036i	0.340155	−	0.331801i
$365$	0.555460	−	12.3583i	0.0290741	−	0.646861i
$366$	−7.84211	+	2.36822i	−0.409914	+	0.123789i
$367$	0.230691	+	0.860950i	0.0120420	+	0.0449412i	0.971685	−	0.236278i	$-0.0759277\pi$
$367$	0.230691	+	0.860950i	0.0120420	+	0.0449412i	−0.959643	+	0.281220i	$0.909261\pi$
$368$	2.87269	+	0.769735i	0.149749	+	0.0401252i
$369$	2.29168	+	36.3513i	0.119300	+	1.89237i
$370$	2.49454	−	7.87642i	0.129685	−	0.409476i
$371$	−1.22616	−	4.81472i	−0.0636591	−	0.249968i
$372$	14.9025	+	7.98944i	0.772659	+	0.414233i
$373$	−1.90778	+	7.11994i	−0.0987812	+	0.368657i	−0.997566	−	0.0697345i	$-0.977785\pi$
$373$	−1.90778	+	7.11994i	−0.0987812	+	0.368657i	0.898784	+	0.438391i	$0.144451\pi$
$374$	0.113649			0.00587665
$375$	3.05709	+	19.1221i	0.157867	+	0.987460i
$376$	6.84232			0.352865
$377$	−2.09674	−	2.09674i	−0.107988	−	0.107988i
$378$	2.47184	−	13.5999i	0.127138	−	0.699503i
$379$		−	2.97705i		−	0.152921i	−0.997073	−	0.0764604i	$-0.975638\pi$
$379$		−	2.97705i		−	0.152921i	0.997073	−	0.0764604i	$-0.0243619\pi$
$380$	2.69829	−	8.51975i	0.138419	−	0.437054i
$381$	−5.97160	−	19.7743i	−0.305934	−	1.01307i
$382$	7.17297	−	7.17297i	0.367001	−	0.367001i
$383$	13.5733	+	3.63695i	0.693561	+	0.185839i	0.588345	−	0.808610i	$-0.299780\pi$
$383$	13.5733	+	3.63695i	0.693561	+	0.185839i	0.105217	+	0.994449i	$0.466446\pi$
$384$	1.40629	+	4.65678i	0.0717644	+	0.237640i
$385$	0.145484	+	0.701637i	0.00741455	+	0.0357587i
$386$			15.0463i			0.765838i
$387$	−9.69452	+	3.26394i	−0.492800	+	0.165916i
$388$	−3.99967	+	14.9270i	−0.203053	+	0.757802i
$389$	8.43797	−	14.6150i	0.427822	−	0.741009i	−0.568857	−	0.822436i	$-0.692614\pi$
$389$	8.43797	−	14.6150i	0.427822	−	0.741009i	0.996679	+	0.0814268i	$0.0259477\pi$
$390$	9.66690	−	9.41055i	0.489503	−	0.476522i
$391$	−1.32970	+	2.30311i	−0.0672459	+	0.116473i
$392$	−4.93807	−	20.4498i	−0.249410	−	1.03287i
$393$	1.10427	+	35.0672i	0.0557029	+	1.76890i
$394$			20.2568i			1.02052i
$395$	−6.89219	−	31.2785i	−0.346784	−	1.57379i
$396$	−0.358677	+	0.0226119i	−0.0180242	+	0.00113629i
$397$	−4.51043	−	16.8331i	−0.226372	−	0.844831i	−0.981850	−	0.189658i	$-0.939262\pi$
$397$	−4.51043	−	16.8331i	−0.226372	−	0.844831i	0.755478	−	0.655173i	$-0.227404\pi$
$398$	−11.7188	−	3.14005i	−0.587411	−	0.157396i
$399$	−16.2101	−	8.95165i	−0.811521	−	0.448143i
$400$	4.73488	−	2.19314i	0.236744	−	0.109657i
$401$	−24.3570	+	14.0625i	−1.21633	+	0.702250i	−0.964131	−	0.265425i	$-0.914488\pi$
$401$	−24.3570	+	14.0625i	−1.21633	+	0.702250i	−0.252201	+	0.967675i	$0.581154\pi$
$402$	−9.97484	+	18.6058i	−0.497500	+	0.927975i
$403$	33.0305	−	8.85050i	1.64537	−	0.440875i
$404$	6.11599	−	10.5932i	0.304282	−	0.527032i
$405$	−3.61868	+	19.7966i	−0.179814	+	0.983701i
$406$	−2.20642	+	0.561907i	−0.109503	+	0.0278870i
$407$	−0.115200	+	0.429934i	−0.00571027	+	0.0213110i
$408$	4.85542	−	0.152897i	0.240379	−	0.00756955i
$409$			36.9845i			1.82877i	0.404851	+	0.914383i	$0.367323\pi$
$409$			36.9845i			1.82877i	−0.404851	+	0.914383i	$0.632677\pi$
$410$	12.5730	+	24.2284i	0.620938	+	1.19656i
$411$	−0.765083	+	3.26288i	−0.0377388	+	0.160946i
$412$	6.15673	+	1.64969i	0.303320	+	0.0812744i
$413$	−10.6400	−	18.9697i	−0.523558	−	0.933438i
$414$	−3.82099	+	7.69979i	−0.187791	+	0.378424i
$415$	−22.0929	−	0.992995i	−1.08450	−	0.0487442i
$416$	14.8858	+	8.59433i	0.729837	+	0.421372i
$417$	27.8607	−	17.2768i	1.36434	−	0.846050i
$418$	0.127365	−	0.475334i	0.00622965	−	0.0232494i
$419$	−13.3236	+	23.0772i	−0.650901	+	1.12739i	0.332004	+	0.943278i	$0.392275\pi$
$419$	−13.3236	+	23.0772i	−0.650901	+	1.12739i	−0.982905	+	0.184115i	$0.941058\pi$
$420$	2.36902	+	9.85412i	0.115596	+	0.480832i
$421$	−2.16698	−	3.75332i	−0.105612	−	0.182926i	0.808376	−	0.588667i	$-0.200347\pi$
$421$	−2.16698	−	3.75332i	−0.105612	−	0.182926i	−0.913988	+	0.405741i	$0.867014\pi$
$422$	1.44996	−	0.388515i	0.0705829	−	0.0189126i
$423$	−1.34917	+	6.69553i	−0.0655987	+	0.325548i
$424$	4.88760	−	2.82186i	0.237363	−	0.137041i
$425$	0.798467	+	4.59728i	0.0387314	+	0.223001i
$426$	6.62745	+	21.9461i	0.321101	+	1.06329i
$427$	−6.08827	−	10.8546i	−0.294632	−	0.525291i
$428$	−0.995683	−	3.71594i	−0.0481282	−	0.179617i
$429$	−0.497497	+	0.529849i	−0.0240194	+	0.0255813i
$430$	−5.65860	+	5.17182i	−0.272882	+	0.249407i
$431$	−23.8600	+	13.7756i	−1.14930	+	0.663547i	−0.948716	−	0.316129i	$-0.897617\pi$
$431$	−23.8600	+	13.7756i	−1.14930	+	0.663547i	−0.200582	+	0.979677i	$0.564283\pi$
$432$	5.39868	−	0.511366i	0.259744	−	0.0246031i
$433$	15.4624	+	15.4624i	0.743077	+	0.743077i	0.973169	−	0.230092i	$-0.0739026\pi$
$433$	15.4624	+	15.4624i	0.743077	+	0.743077i	−0.230092	+	0.973169i	$0.573903\pi$
$434$	7.11057	−	25.2759i	0.341318	−	1.21328i
$435$	3.21317	−	0.814857i	0.154060	−	0.0390694i
$436$	−0.463626	−	0.803024i	−0.0222037	−	0.0384579i
$437$	8.14252	+	8.14252i	0.389510	+	0.389510i
$438$	−0.303243	−	9.62982i	−0.0144895	−	0.460131i
$439$		−	4.34027i		−	0.207150i	−0.994622	−	0.103575i	$-0.966972\pi$
$439$		−	4.34027i		−	0.207150i	0.994622	−	0.103575i	$-0.0330281\pi$
$440$	−0.722470	+	0.374917i	−0.0344424	+	0.0178735i
$441$	20.9848	−	0.799841i	0.999274	−	0.0380877i
$442$	2.29863	−	2.29863i	0.109335	−	0.109335i
$443$	7.33399	−	7.33399i	0.348448	−	0.348448i	−0.511083	−	0.859531i	$-0.670756\pi$
$443$	7.33399	−	7.33399i	0.348448	−	0.348448i	0.859531	+	0.511083i	$0.170756\pi$
$444$	−1.43717	+	6.12916i	−0.0682050	+	0.290877i
$445$	6.61204	−	20.8773i	0.313441	−	0.989678i
$446$	5.71024	−	3.29681i	0.270388	−	0.156108i
$447$	28.4345	−	0.895404i	1.34491	−	0.0423511i
$448$	16.3276	−	9.15804i	0.771407	−	0.432677i
$449$	11.6894			0.551659			0.275830	−	0.961207i	$-0.411047\pi$
$449$	11.6894			0.551659			0.275830	+	0.961207i	$0.411047\pi$
$450$	3.51061	+	14.6675i	0.165492	+	0.691434i
$451$	−0.735274	−	1.27353i	−0.0346227	−	0.0599683i
$452$	7.05979	−	1.89167i	0.332065	−	0.0889765i
$453$	−10.6429	−	17.1628i	−0.500048	−	0.806380i
$454$	−0.588433	−	0.339732i	−0.0276165	−	0.0159444i
$455$	17.1336	+	11.2486i	0.803235	+	0.527341i
$456$	4.80194	−	20.4790i	0.224871	−	0.959019i
$457$	−7.59714	+	7.59714i	−0.355379	+	0.355379i	−0.862106	−	0.506727i	$-0.830855\pi$
$457$	−7.59714	+	7.59714i	−0.355379	+	0.355379i	0.506727	+	0.862106i	$0.330855\pi$
$458$	−7.82786	−	2.09747i	−0.365772	−	0.0980083i
$459$	−0.807774	+	4.78141i	−0.0377037	+	0.223177i
$460$	0.282986	−	6.29609i	0.0131943	−	0.293557i
$461$	9.90299	−	5.71749i	0.461228	−	0.266290i	−0.251332	−	0.967901i	$-0.580869\pi$
$461$	9.90299	−	5.71749i	0.461228	−	0.266290i	0.712561	+	0.701611i	$0.247535\pi$
$462$	0.154681	+	0.536208i	0.00719642	+	0.0249467i
$463$	−4.53813	+	1.21599i	−0.210905	+	0.0565118i	−0.362724	−	0.931896i	$-0.618153\pi$
$463$	−4.53813	+	1.21599i	−0.210905	+	0.0565118i	0.151820	+	0.988408i	$0.451487\pi$
$464$	−0.446620	−	0.773568i	−0.0207338	−	0.0359120i
$465$	−10.3893	+	36.7890i	−0.481794	+	1.70605i
$466$	6.37063	−	11.0342i	0.295114	−	0.511152i
$467$	34.4175	−	9.22213i	1.59265	−	0.426750i	0.649838	−	0.760073i	$-0.274837\pi$
$467$	34.4175	−	9.22213i	1.59265	−	0.426750i	0.942813	+	0.333323i	$0.108170\pi$
$468$	−6.79714	+	7.71182i	−0.314198	+	0.356479i
$469$	−30.8743	−	8.68549i	−1.42564	−	0.401059i
$470$	1.10146	+	4.99871i	0.0508066	+	0.230573i
$471$	−5.82352	−	19.2840i	−0.268334	−	0.888559i
$472$	17.4699	−	17.4699i	0.804117	−	0.804117i
$473$	0.292029	−	0.292029i	0.0134275	−	0.0134275i
$474$	−7.21135	−	23.8796i	−0.331228	−	1.09683i
$475$	20.1228	+	1.81256i	0.923300	+	0.0831660i
$476$	0.602682	+	2.36653i	0.0276239	+	0.108470i
$477$	1.79758	+	5.33915i	0.0823056	+	0.244463i
$478$	1.51956	−	0.407165i	0.0695030	−	0.0186233i
$479$	6.68234	−	11.5741i	0.305324	−	0.528836i	−0.672010	−	0.740542i	$-0.734569\pi$
$479$	6.68234	−	11.5741i	0.305324	−	0.528836i	0.977333	+	0.211706i	$0.0679020\pi$
$480$	−16.7687	+	9.38327i	−0.765381	+	0.428286i
$481$	6.36569	+	11.0257i	0.290250	+	0.502729i
$482$	−4.34137	+	1.16327i	−0.197744	+	0.0529853i
$483$	−12.6761	−	3.13904i	−0.576783	−	0.142831i
$484$	−9.40953	+	5.43259i	−0.427706	+	0.246936i
$485$	−34.9020	−	1.56872i	−1.58482	−	0.0712319i
$486$	−1.63336	+	15.5881i	−0.0740906	+	0.707092i
$487$	−20.5056	−	5.49446i	−0.929198	−	0.248978i	−0.237686	−	0.971342i	$-0.576389\pi$
$487$	−20.5056	−	5.49446i	−0.929198	−	0.248978i	−0.691513	+	0.722364i	$0.743055\pi$
$488$	9.99641	−	9.99641i	0.452516	−	0.452516i
$489$	−2.37247	+	10.1180i	−0.107287	+	0.457550i
$490$	14.1448	−	6.89950i	0.638998	−	0.311688i
$491$	31.4667	+	18.1673i	1.42007	+	0.819880i	0.996305	−	0.0858910i	$-0.0273737\pi$
$491$	31.4667	+	18.1673i	1.42007	+	0.819880i	0.423769	+	0.905771i	$0.360707\pi$
$492$	−10.9613	−	17.6763i	−0.494175	−	0.796909i
$493$	0.771527	−	0.206730i	0.0347478	−	0.00931066i
$494$	−7.03790	−	12.1900i	−0.316650	−	0.548454i
$495$	−0.224417	−	0.780897i	−0.0100868	−	0.0350987i
$496$	10.3010			0.462529
$497$	−30.3766	+	17.0380i	−1.36258	+	0.764258i
$498$	−17.2152	+	0.542109i	−0.771433	+	0.0242925i
$499$	−8.22223	+	4.74711i	−0.368078	+	0.212510i	−0.672618	−	0.739990i	$-0.734830\pi$
$499$	−8.22223	+	4.74711i	−0.368078	+	0.212510i	0.304541	+	0.952499i	$0.401497\pi$
$500$	−6.69791	−	8.79880i	−0.299540	−	0.393494i
$501$	0.755426	−	3.22170i	0.0337500	−	0.143935i
$502$	0.721743	−	0.721743i	0.0322130	−	0.0322130i
$503$	21.4715	−	21.4715i	0.957366	−	0.957366i	−0.0417614	−	0.999128i	$-0.513297\pi$
$503$	21.4715	−	21.4715i	0.957366	−	0.957366i	0.999128	+	0.0417614i	$0.0132969\pi$
$504$	7.32983	+	22.7003i	0.326496	+	1.01115i
$505$	26.3634	+	8.34954i	1.17315	+	0.371550i
$506$		−	0.347041i		−	0.0154279i
$507$	−0.0543756	−	1.72675i	−0.00241490	−	0.0766878i
$508$	8.34069	+	8.34069i	0.370058	+	0.370058i
$509$	0.454304	+	0.786877i	0.0201367	+	0.0348777i	0.875918	−	0.482460i	$-0.160257\pi$
$509$	0.454304	+	0.786877i	0.0201367	+	0.0348777i	−0.855781	+	0.517337i	$0.826923\pi$
$510$	0.893315	+	3.52255i	0.0395567	+	0.155981i
$511$	14.1845	−	3.61236i	0.627486	−	0.159801i
$512$	8.09695	+	8.09695i	0.357838	+	0.357838i
$513$	19.0928	+	8.73697i	0.842970	+	0.385747i
$514$	−6.18164	+	3.56897i	−0.272661	+	0.157421i
$515$	−0.647029	+	14.3956i	−0.0285115	+	0.634344i
$516$	3.99835	−	4.25835i	0.176017	−	0.187463i
$517$	−0.0713710	−	0.266360i	−0.00313889	−	0.0117145i
$518$	9.77498	+	0.121521i	0.429488	+	0.00533932i
$519$	−4.14290	−	13.7188i	−0.181853	−	0.602188i
$520$	−7.02949	+	22.1954i	−0.308264	+	0.973332i
$521$	−9.65270	+	5.57299i	−0.422893	+	0.244157i	−0.696314	−	0.717737i	$-0.745178\pi$
$521$	−9.65270	+	5.57299i	−0.422893	+	0.244157i	0.273422	+	0.961894i	$0.411845\pi$
$522$	2.44675	−	0.823770i	0.107091	−	0.0360554i
$523$	−10.9374	+	2.93066i	−0.478258	+	0.128149i	−0.489891	−	0.871783i	$-0.662964\pi$
$523$	−10.9374	+	2.93066i	−0.478258	+	0.128149i	0.0116332	+	0.999932i	$0.496297\pi$
$524$	−10.0173	−	17.3504i	−0.437607	−	0.757957i
$525$	−20.6037	+	10.0243i	−0.899219	+	0.437498i
$526$	9.65056	−	16.7153i	0.420784	−	0.728820i
$527$	−2.38405	+	8.89739i	−0.103851	+	0.387576i
$528$	−0.186068	+	0.115384i	−0.00809757	+	0.00502142i
$529$	−12.8857	−	7.43959i	−0.560250	−	0.323460i
$530$	2.84832	+	3.11642i	0.123723	+	0.135368i
$531$	13.6504	+	20.5398i	0.592377	+	0.891352i
$532$	10.5734	+	0.131446i	0.458414	+	0.00569893i
$533$	−40.6294	−	10.8866i	−1.75986	−	0.471552i
$534$	3.89361	−	16.6053i	0.168493	−	0.718580i
$535$	7.71977	−	4.00608i	0.333755	−	0.173198i
$536$		−	36.4320i		−	1.57362i
$537$	10.7131	−	0.337355i	0.462302	−	0.0145579i
$538$	4.29673	−	16.0356i	0.185245	−	0.691344i
$539$	−0.744569	+	0.405539i	−0.0320708	+	0.0174678i
$540$	−3.52016	−	10.9395i	−0.151484	−	0.470759i
$541$	19.3231	−	33.4685i	0.830764	−	1.43892i	−0.0666700	−	0.997775i	$-0.521237\pi$
$541$	19.3231	−	33.4685i	0.830764	−	1.43892i	0.897434	−	0.441150i	$-0.145429\pi$
$542$	−6.26454	+	1.67858i	−0.269085	+	0.0721011i
$543$	−20.0066	+	37.3178i	−0.858564	+	1.60146i
$544$	−4.00978	+	2.31505i	−0.171918	+	0.0992568i
$545$	1.54739	−	1.41427i	0.0662828	−	0.0605808i
$546$	13.9737	+	7.71663i	0.598019	+	0.330241i
$547$	10.9936	+	2.94572i	0.470052	+	0.125950i	0.486067	−	0.873922i	$-0.338431\pi$
$547$	10.9936	+	2.94572i	0.470052	+	0.125950i	−0.0160147	+	0.999872i	$0.505098\pi$
$548$	−0.495318	−	1.84855i	−0.0211589	−	0.0789662i
$549$	7.81086	+	11.7530i	0.333359	+	0.501608i
$550$	−0.390200	−	0.467453i	−0.0166382	−	0.0199323i
$551$		−	3.45857i		−	0.147340i
$552$	−0.466891	−	14.8266i	−0.0198722	−	0.631063i
$553$	33.0528	−	18.5391i	1.40555	−	0.788362i
$554$	0.0184884	−	0.0320228i	0.000785496	−	0.00136052i
$555$	−14.2313	−	0.191231i	−0.604085	−	0.00811730i
$556$	−9.36006	+	16.2121i	−0.396955	+	0.687546i
$557$	6.64956	−	24.8165i	0.281751	−	1.05151i	−0.669430	−	0.742875i	$-0.733462\pi$
$557$	6.64956	−	24.8165i	0.281751	−	1.05151i	0.951181	−	0.308634i	$-0.0998718\pi$
$558$	−5.88107	+	29.1860i	−0.248965	+	1.23554i
$559$		−	11.8130i		−	0.499635i
$560$	4.10840	+	4.60886i	0.173611	+	0.194760i
$561$	−0.0565981	−	0.187419i	−0.00238957	−	0.00791282i
$562$	−4.18855	−	1.12232i	−0.176683	−	0.0473421i
$563$	29.9243	−	29.9243i	1.26116	−	1.26116i	0.310625	−	0.950533i	$-0.399462\pi$
$563$	29.9243	−	29.9243i	1.26116	−	1.26116i	0.950533	−	0.310625i	$-0.100538\pi$
$564$	−1.12753	−	3.73370i	−0.0474776	−	0.157217i
$565$	7.61102	+	14.6665i	0.320198	+	0.617026i
$566$			23.1184i			0.971737i
$567$	−23.6586	+	2.69654i	−0.993567	+	0.113244i
$568$	−27.9749	−	27.9749i	−1.17380	−	1.17380i
$569$	−28.3702			−1.18934			−0.594670	−	0.803970i	$-0.702717\pi$
$569$	−28.3702			−1.18934			−0.594670	+	0.803970i	$0.702717\pi$
$570$	15.7341	+	0.211425i	0.659030	+	0.00885560i
$571$	−39.0499			−1.63419			−0.817094	−	0.576505i	$-0.804416\pi$
$571$	−39.0499			−1.63419			−0.817094	+	0.576505i	$0.804416\pi$
$572$	0.107418	−	0.400889i	0.00449137	−	0.0167620i
$573$	−15.4011	−	8.25676i	−0.643392	−	0.344931i
$574$	−23.1200	+	22.5522i	−0.965011	+	0.941311i
$575$	14.0384	−	2.43822i	0.585440	−	0.101681i
$576$	−17.6791	+	11.7492i	−0.736627	+	0.489549i
$577$	−0.273278	−	0.0732247i	−0.0113767	−	0.00304838i	0.253126	−	0.967433i	$-0.418541\pi$
$577$	−0.273278	−	0.0732247i	−0.0113767	−	0.00304838i	−0.264503	+	0.964385i	$0.585208\pi$
$578$	−4.19728	−	15.6645i	−0.174584	−	0.651556i
$579$	24.8129	−	7.49319i	1.03119	−	0.311406i
$580$	−1.39725	+	1.27705i	−0.0580175	+	0.0530265i
$581$	−6.45781	−	25.3577i	−0.267915	−	1.05201i
$582$	−27.1964	+	0.856415i	−1.12733	+	0.0354996i
$583$	−0.160832	−	0.160832i	−0.00666097	−	0.00666097i
$584$	8.31339	+	14.3992i	0.344010	+	0.595843i
$585$	−20.3331	−	11.2552i	−0.840672	−	0.465344i
$586$	−14.4940	+	25.1043i	−0.598740	+	1.03705i
$587$	2.93399	−	10.9498i	0.121099	−	0.451947i	−0.878572	−	0.477610i	$-0.841503\pi$
$587$	2.93399	−	10.9498i	0.121099	−	0.451947i	0.999671	+	0.0256634i	$0.00816980\pi$
$588$	−10.3453	+	6.06447i	−0.426631	+	0.250094i
$589$	34.5413	+	19.9425i	1.42325	+	0.821714i
$590$	15.5750	+	9.95050i	0.641214	+	0.409656i
$591$	33.4055	−	10.0880i	1.37412	−	0.414967i
$592$	0.992612	+	3.70448i	0.0407961	+	0.152253i
$593$	4.43810	+	16.5632i	0.182251	+	0.680170i	0.995202	+	0.0978381i	$0.0311927\pi$
$593$	4.43810	+	16.5632i	0.182251	+	0.680170i	−0.812951	+	0.582331i	$0.802141\pi$
$594$	−0.220688	−	0.593065i	−0.00905494	−	0.0243338i
$595$	−4.93170	+	2.48192i	−0.202180	+	0.101749i
$596$	−14.0687	+	8.12259i	−0.576278	+	0.332714i
$597$	0.657804	+	20.8893i	0.0269221	+	0.854941i
$598$	−7.01914	−	7.01914i	−0.287034	−	0.287034i
$599$	−15.6952			−0.641289			−0.320645	−	0.947200i	$-0.603900\pi$
$599$	−15.6952			−0.641289			−0.320645	+	0.947200i	$0.603900\pi$
$600$	−17.2994	−	19.4460i	−0.706244	−	0.793880i
$601$	−19.8713	−	34.4181i	−0.810567	−	1.40394i	−0.912468	−	0.409148i	$-0.865826\pi$
$601$	−19.8713	−	34.4181i	−0.810567	−	1.40394i	0.101901	−	0.994795i	$-0.467507\pi$
$602$	−7.79832	−	4.63256i	−0.317836	−	0.188809i
$603$	35.6505	+	7.18367i	1.45180	+	0.292541i
$604$	9.98702	+	5.76601i	0.406366	+	0.234616i
$605$	−16.5719	−	18.1317i	−0.673744	−	0.737159i
$606$	20.9688	+	4.91677i	0.851798	+	0.199730i
$607$	12.0342	+	3.22455i	0.488453	+	0.130881i	0.494636	−	0.869100i	$-0.335301\pi$
$607$	12.0342	+	3.22455i	0.488453	+	0.130881i	−0.00618297	+	0.999981i	$0.501968\pi$
$608$	5.18890	+	19.3652i	0.210438	+	0.785364i
$609$	2.02546	+	3.35878i	0.0820756	+	0.136105i
$610$	8.91215	+	5.69375i	0.360842	+	0.230533i
$611$	−6.83083	−	3.94378i	−0.276346	−	0.159548i
$612$	−0.883547	−	2.62430i	−0.0357153	−	0.106081i
$613$	−3.81177	+	14.2257i	−0.153956	+	0.574571i	0.845237	+	0.534392i	$0.179459\pi$
$613$	−3.81177	+	14.2257i	−0.153956	+	0.574571i	−0.999193	+	0.0401789i	$0.987207\pi$
$614$	−0.834668			−0.0336844
$615$	33.6937	−	32.8002i	1.35866	−	1.32263i
$616$	−0.672487	−	0.689418i	−0.0270953	−	0.0277774i
$617$	−20.4208	+	5.47173i	−0.822109	+	0.220283i	−0.645268	−	0.763956i	$-0.723254\pi$
$617$	−20.4208	+	5.47173i	−0.822109	+	0.220283i	−0.176841	+	0.984239i	$0.556588\pi$
$618$	0.353234	+	11.2173i	0.0142092	+	0.451227i
$619$	38.7747	+	22.3866i	1.55849	+	0.899793i	0.997402	+	0.0720360i	$0.0229496\pi$
$619$	38.7747	+	22.3866i	1.55849	+	0.899793i	0.561086	+	0.827758i	$0.310384\pi$
$620$	−4.69742	−	21.3181i	−0.188653	−	0.856155i
$621$	14.6006	+	2.46664i	0.585902	+	0.0989828i
$622$	−6.20580	+	6.20580i	−0.248830	+	0.248830i
$623$	25.9096	+	0.322104i	1.03805	+	0.0129048i
$624$	−1.42964	+	6.09706i	−0.0572315	+	0.244078i
$625$	16.1678	−	19.0684i	0.646710	−	0.762736i
$626$			12.9030i			0.515709i
$627$	−0.847303	+	0.0266816i	−0.0338380	+	0.00106556i
$628$	8.13386	+	8.13386i	0.324576	+	0.324576i
$629$	−3.42944			−0.136741
$630$	−15.4039	+	9.00910i	−0.613707	+	0.358931i
$631$	−30.6236			−1.21911			−0.609553	−	0.792745i	$-0.708651\pi$
$631$	−30.6236			−1.21911			−0.609553	+	0.792745i	$0.708651\pi$
$632$	30.4396	+	30.4396i	1.21082	+	1.21082i
$633$	−1.36279	−	2.19764i	−0.0541661	−	0.0873485i
$634$		−	9.61051i		−	0.381682i
$635$	−14.3571	+	22.4725i	−0.569746	+	0.891795i
$636$	−2.34524	−	2.20205i	−0.0929948	−	0.0873168i
$637$	−6.85710	+	23.2617i	−0.271688	+	0.921661i
$638$	−0.0737037	+	0.0737037i	−0.00291796	+	0.00291796i
$639$	32.8908	−	21.8587i	1.30114	−	0.864715i
$640$	3.38105	−	5.29219i	0.133648	−	0.209192i
$641$	37.2954	+	21.5325i	1.47308	+	0.850482i	0.999541	−	0.0302911i	$-0.00964344\pi$
$641$	37.2954	+	21.5325i	1.47308	+	0.850482i	0.473538	+	0.880774i	$0.342977\pi$
$642$	5.75666	−	3.56979i	0.227197	−	0.140888i
$643$	−22.1703	+	5.94051i	−0.874311	+	0.234271i	−0.667951	−	0.744205i	$-0.732828\pi$
$643$	−22.1703	+	5.94051i	−0.874311	+	0.234271i	−0.206360	+	0.978476i	$0.566162\pi$
$644$	7.22649	−	1.84036i	0.284764	−	0.0725205i
$645$	11.3469	+	6.75601i	0.446783	+	0.266018i
$646$	3.79158			0.149178
$647$	−12.6574	+	47.2381i	−0.497615	+	1.85712i	0.0172498	+	0.999851i	$0.494509\pi$
$647$	−12.6574	+	47.2381i	−0.497615	+	1.85712i	−0.514864	+	0.857272i	$0.672158\pi$
$648$	−10.2263	−	25.0406i	−0.401728	−	0.983688i
$649$	−0.862300	−	0.497849i	−0.0338482	−	0.0195423i
$650$	−17.3466	−	1.56249i	−0.680389	−	0.0612859i
$651$	−45.2236	+	0.861544i	−1.77245	+	0.0337666i
$652$	−1.53594	−	5.73222i	−0.0601522	−	0.224491i
$653$	−36.3914	−	9.75106i	−1.42411	−	0.381588i	−0.537168	−	0.843475i	$-0.680506\pi$
$653$	−36.3914	−	9.75106i	−1.42411	−	0.381588i	−0.886939	+	0.461887i	$0.847173\pi$
$654$	1.11756	−	1.19023i	0.0437000	−	0.0465417i
$655$	33.4334	−	30.5573i	1.30635	−	1.19397i
$656$	−10.9733	−	6.33541i	−0.428434	−	0.247356i
$657$	−15.7295	+	5.29580i	−0.613667	+	0.206609i
$658$	−5.28226	+	2.96278i	−0.205924	+	0.115501i
$659$	−11.4519	−	19.8352i	−0.446102	−	0.772671i	0.552026	−	0.833827i	$-0.313855\pi$
$659$	−11.4519	−	19.8352i	−0.446102	−	0.772671i	−0.998128	+	0.0611555i	$0.980521\pi$
$660$	0.323638	+	0.332454i	0.0125976	+	0.0129408i
$661$	12.9761			0.504712			0.252356	−	0.967634i	$-0.418795\pi$
$661$	12.9761			0.504712			0.252356	+	0.967634i	$0.418795\pi$
$662$	−2.24524	−	2.24524i	−0.0872637	−	0.0872637i
$663$	−4.93540	−	2.64593i	−0.191675	−	0.102760i
$664$	25.7415	−	14.8618i	0.998963	−	0.576752i
$665$	4.85366	+	23.4082i	0.188217	+	0.907730i
$666$	−11.0627	+	0.697420i	−0.428670	+	0.0270245i
$667$	−0.631276	−	2.35595i	−0.0244431	−	0.0912229i
$668$	0.489066	+	1.82522i	0.0189225	+	0.0706198i
$669$	−8.28051	−	7.77493i	−0.320143	−	0.300596i
$670$	26.6157	−	5.86475i	1.02825	−	0.226575i
$671$	−0.493414	−	0.284873i	−0.0190481	−	0.0109974i
$672$	−16.3801	−	15.7677i	−0.631876	−	0.608251i
$673$	−12.0013	+	44.7896i	−0.462618	+	1.72651i	0.202050	+	0.979375i	$0.435240\pi$
$673$	−12.0013	+	44.7896i	−0.462618	+	1.72651i	−0.664668	+	0.747139i	$0.731427\pi$
$674$	11.3095	−	19.5887i	0.435627	−	0.754528i
$675$	22.4399	−	13.0939i	0.863713	−	0.503984i
$676$	0.493264	+	0.854358i	0.0189717	+	0.0328599i
$677$	−25.5532	−	25.5532i	−0.982088	−	0.982088i	0.0177549	−	0.999842i	$-0.494348\pi$
$677$	−25.5532	−	25.5532i	−0.982088	−	0.982088i	−0.999842	+	0.0177549i	$0.994348\pi$
$678$	6.78212	+	10.9369i	0.260466	+	0.420028i
$679$	−10.2020	−	40.0597i	−0.391515	−	1.53735i
$680$	−4.23098	−	4.62922i	−0.162251	−	0.177522i
$681$	−0.267208	+	1.13957i	−0.0102394	+	0.0436686i
$682$	−0.311108	−	1.16107i	−0.0119130	−	0.0444598i
$683$	24.1225	+	6.46361i	0.923022	+	0.247323i	0.688877	−	0.724879i	$-0.258104\pi$
$683$	24.1225	+	6.46361i	0.923022	+	0.247323i	0.234145	+	0.972202i	$0.424771\pi$
$684$	−11.9663	+	0.754384i	−0.457541	+	0.0288446i
$685$	3.84032	−	1.99288i	0.146731	−	0.0761442i
$686$	12.6671	+	13.6490i	0.483633	+	0.521121i
$687$	0.439396	+	13.9535i	0.0167640	+	0.532359i
$688$	0.921007	−	3.43724i	0.0351131	−	0.131044i
$689$	−6.50586			−0.247853
$690$	10.7565	−	2.72785i	0.409495	−	0.103847i
$691$	−24.7751			−0.942489			−0.471244	−	0.882003i	$-0.656195\pi$
$691$	−24.7751			−0.942489			−0.471244	+	0.882003i	$0.656195\pi$
$692$	5.78650	+	5.78650i	0.219970	+	0.219970i
$693$	0.807229	−	0.522121i	0.0306641	−	0.0198337i
$694$		−	1.90659i		−	0.0723732i
$695$	−40.3472	−	12.7783i	−1.53045	−	0.484710i
$696$	−3.04968	+	3.24800i	−0.115598	+	0.123115i
$697$	8.01179	−	8.01179i	0.303468	−	0.303468i
$698$	−18.8882	−	5.06109i	−0.714930	−	0.191565i
$699$	−21.3692	−	5.01067i	−0.808258	−	0.189521i
$700$	7.66461	−	10.6041i	0.289695	−	0.400797i
$701$		−	1.93177i		−	0.0729618i	−0.999334	−	0.0364809i	$-0.988385\pi$
$701$		−	1.93177i		−	0.0729618i	0.999334	−	0.0364809i	$-0.0116148\pi$
$702$	−16.4587	−	7.53158i	−0.621194	−	0.284261i
$703$	−3.84334	+	14.3435i	−0.144954	+	0.540977i
$704$	0.428509	−	0.742199i	0.0161500	−	0.0279727i
$705$	7.69484	−	4.30581i	0.289804	−	0.162166i
$706$	−15.8672	+	27.4829i	−0.597172	+	1.03433i
$707$	−0.406746	+	32.7181i	−0.0152973	+	1.23049i
$708$	−12.4118	−	6.65411i	−0.466463	−	0.250077i
$709$		−	5.72418i		−	0.214976i	−0.994206	−	0.107488i	$-0.965719\pi$
$709$		−	5.72418i		−	0.214976i	0.994206	−	0.107488i	$-0.0342808\pi$
$710$	15.9339	−	24.9406i	0.597990	−	0.936005i
$711$	−35.7886	+	23.7845i	−1.34218	+	0.891987i
$712$	7.61796	+	28.4306i	0.285495	+	1.06548i
$713$	27.1693	+	7.27999i	1.01750	+	0.272638i
$714$	−3.68218	+	2.22048i	−0.137802	+	0.0830993i
$715$	0.937353	+	0.0421306i	0.0350550	+	0.00157560i
$716$	−5.30057	+	3.06029i	−0.198092	+	0.114368i
$717$	−1.42821	−	2.30313i	−0.0533374	−	0.0860121i
$718$	28.1934	−	7.55440i	1.05217	−	0.281928i
$719$	−8.63075	+	14.9489i	−0.321872	+	0.557499i	−0.980874	−	0.194642i	$-0.937646\pi$
$719$	−8.63075	+	14.9489i	−0.321872	+	0.557499i	0.659002	+	0.752141i	$0.270979\pi$
$720$	−5.03886	−	4.86023i	−0.187787	−	0.181130i
$721$	−16.5229	+	4.20786i	−0.615344	+	0.156709i
$722$	−0.695187	+	2.59447i	−0.0258722	+	0.0965563i
$723$	4.08038	+	6.58004i	0.151751	+	0.244714i
$724$		−	24.1791i		−	0.898607i
$725$	−3.49925	−	2.46361i	−0.129959	−	0.0914961i
$726$	−13.9467	−	13.0951i	−0.517609	−	0.486006i
$727$	−44.3502	−	11.8836i	−1.64486	−	0.440739i	−0.686692	−	0.726949i	$-0.740938\pi$
$727$	−44.3502	−	11.8836i	−1.64486	−	0.440739i	−0.958167	+	0.286210i	$0.907605\pi$
$728$	−27.5454	−	0.342440i	−1.02090	−	0.0126917i
$729$	26.5198	−	5.06943i	0.982216	−	0.187757i
$730$	−9.18118	+	8.39136i	−0.339811	+	0.310578i
$731$	2.75573	+	1.59102i	0.101924	+	0.0588461i
$732$	−7.10210	−	3.80753i	−0.262501	−	0.140730i
$733$	−4.52961	+	16.9047i	−0.167305	+	0.624390i	0.830430	+	0.557123i	$0.188095\pi$
$733$	−4.52961	+	16.9047i	−0.167305	+	0.624390i	−0.997735	+	0.0672675i	$0.978572\pi$
$734$	0.448091	−	0.776116i	0.0165393	−	0.0286470i
$735$	−18.4222	−	19.8903i	−0.679513	−	0.733663i
$736$	7.06928	+	12.2444i	0.260577	+	0.451333i
$737$	−1.41824	+	0.380016i	−0.0522415	+	0.0139981i
$738$	24.2151	−	27.4737i	0.891371	−	1.01132i
$739$	−44.4824	+	25.6819i	−1.63631	+	0.944724i	−0.654222	+	0.756302i	$0.727004\pi$
$739$	−44.4824	+	25.6819i	−1.63631	+	0.944724i	−0.982088	+	0.188422i	$0.939663\pi$
$740$	7.21383	−	3.74353i	0.265186	−	0.137615i
$741$	−16.5976	+	17.6769i	−0.609729	+	0.649378i
$742$	−2.55133	+	4.29484i	−0.0936624	+	0.157669i
$743$	10.0224	+	37.4042i	0.367687	+	1.37223i	0.863742	+	0.503935i	$0.168115\pi$
$743$	10.0224	+	37.4042i	0.367687	+	1.37223i	−0.496055	+	0.868291i	$0.665219\pi$
$744$	−14.8535	−	49.1859i	−0.544556	−	1.80324i
$745$	−24.7776	−	27.1098i	−0.907782	−	0.993226i
$746$	6.41838	−	3.70565i	0.234993	−	0.135674i
$747$	9.46731	+	28.1197i	0.346391	+	1.02885i
$748$	0.0790520	+	0.0790520i	0.00289043	+	0.00289043i
$749$	7.18569	+	7.36660i	0.262559	+	0.269170i
$750$	11.4216	−	15.7686i	0.417059	−	0.575787i
$751$	8.37596	+	14.5076i	0.305643	+	0.529390i	0.977404	−	0.211378i	$-0.0677952\pi$
$751$	8.37596	+	14.5076i	0.305643	+	0.529390i	−0.671761	+	0.740768i	$0.734462\pi$
$752$	−1.68010	−	1.68010i	−0.0612671	−	0.0612671i
$753$	−1.54966	−	0.830793i	−0.0564727	−	0.0302758i
$754$			2.98141i			0.108577i
$755$	−7.87175	+	24.8548i	−0.286482	+	0.904557i
$756$	11.1792	−	7.74045i	0.406583	−	0.281518i
$757$	34.0239	−	34.0239i	1.23662	−	1.23662i	0.275248	−	0.961373i	$-0.411240\pi$
$757$	34.0239	−	34.0239i	1.23662	−	1.23662i	0.961373	−	0.275248i	$-0.0887600\pi$
$758$	−2.11657	+	2.11657i	−0.0768773	+	0.0768773i
$759$	−0.572306	+	0.172829i	−0.0207734	+	0.00627330i
$760$	−24.1032	+	12.5081i	−0.874315	+	0.453715i
$761$	−18.1267	+	10.4654i	−0.657091	+	0.379372i	−0.791168	−	0.611599i	$-0.790527\pi$
$761$	−18.1267	+	10.4654i	−0.657091	+	0.379372i	0.134076	+	0.990971i	$0.457193\pi$
$762$	−9.81324	+	18.3044i	−0.355496	+	0.663099i
$763$	2.13251	+	1.26681i	0.0772021	+	0.0458616i
$764$	9.97875			0.361019
$765$	5.36417	−	3.22742i	0.193942	−	0.116688i
$766$	−7.06436	−	12.2358i	−0.255246	−	0.442098i
$767$	−27.5099	+	7.37126i	−0.993325	+	0.266161i
$768$	13.8923	−	25.9130i	0.501295	−	0.935055i
$769$	29.8771	+	17.2496i	1.07740	+	0.622035i	0.930193	−	0.367071i	$-0.119640\pi$
$769$	29.8771	+	17.2496i	1.07740	+	0.622035i	0.147203	+	0.989106i	$0.452973\pi$
$770$	0.395404	−	0.602272i	0.0142494	−	0.0217044i
$771$	8.96410	+	8.41678i	0.322834	+	0.303123i
$772$	−10.4659	+	10.4659i	−0.376677	+	0.376677i
$773$	24.9772	+	6.69262i	0.898367	+	0.240717i	0.678315	−	0.734771i	$-0.262711\pi$
$773$	24.9772	+	6.69262i	0.898367	+	0.240717i	0.220052	+	0.975488i	$0.429377\pi$
$774$	9.21299	+	4.57190i	0.331154	+	0.164334i
$775$	44.7814	−	20.7422i	1.60860	−	0.745082i
$776$	40.6660	−	23.4785i	1.45982	−	0.842830i
$777$	−4.66761	−	16.1804i	−0.167450	−	0.580470i
$778$	−16.3898	+	4.39163i	−0.587603	+	0.157448i
$779$	−24.5304	−	42.4878i	−0.878891	−	1.52228i
$780$	13.2699	+	0.178312i	0.475139	+	0.00638459i
$781$	−0.797216	+	1.38082i	−0.0285266	+	0.0494096i
$782$	2.58280	−	0.692058i	0.0923606	−	0.0247480i
$783$	−2.57698	−	3.62470i	−0.0920938	−	0.129536i
$784$	−3.80884	+	6.23389i	−0.136030	+	0.222639i
$785$	−14.0011	+	21.9152i	−0.499721	+	0.782189i
$786$	24.1464	−	25.7165i	0.861272	−	0.917279i
$787$	−29.1842	+	29.1842i	−1.04030	+	1.04030i	−0.0411515	+	0.999153i	$0.513103\pi$
$787$	−29.1842	+	29.1842i	−1.04030	+	1.04030i	−0.999153	+	0.0411515i	$0.986897\pi$
$788$	−14.0902	+	14.0902i	−0.501944	+	0.501944i
$789$	−32.3712	−	7.59042i	−1.15245	−	0.270226i
$790$	−17.3378	+	27.1380i	−0.616850	+	0.965525i
$791$	−13.9956	+	13.6519i	−0.497625	+	0.485404i
$792$	0.819242	+	0.722073i	0.0291105	+	0.0256578i
$793$	−15.7414	+	4.21789i	−0.558993	+	0.149782i
$794$	−8.76099	+	15.1745i	−0.310916	+	0.538522i
$795$	3.72080	−	6.24917i	0.131963	−	0.221635i
$796$	−5.96722	−	10.3355i	−0.211503	−	0.366333i
$797$	24.2719	−	6.50363i	0.859754	−	0.230370i	0.198102	−	0.980181i	$-0.436522\pi$
$797$	24.2719	−	6.50363i	0.859754	−	0.230370i	0.661652	+	0.749811i	$0.269856\pi$
$798$	5.16051	+	17.8891i	0.182680	+	0.633267i
$799$	1.84001	−	1.06233i	0.0650950	−	0.0375826i
$800$	23.2892	+	8.54430i	0.823396	+	0.302086i
$801$	−29.3228	+	1.84858i	−1.03607	+	0.0653165i
$802$	27.3149	+	7.31900i	0.964522	+	0.258443i
$803$	0.473822	−	0.473822i	0.0167208	−	0.0167208i
$804$	−19.8802	+	6.00356i	−0.701119	+	0.211729i
$805$	7.57885	+	15.0595i	0.267119	+	0.530779i
$806$	−29.7758	−	17.1911i	−1.04881	−	0.605530i
$807$	−28.5841	+	0.900116i	−1.00621	+	0.0316856i
$808$	−35.9016	+	9.61979i	−1.26301	+	0.338423i
$809$	5.69093	+	9.85698i	0.200083	+	0.346553i	0.948555	−	0.316613i	$-0.102546\pi$
$809$	5.69093	+	9.85698i	0.200083	+	0.346553i	−0.748472	+	0.663166i	$0.769212\pi$
$810$	16.6474	−	11.5019i	0.584930	−	0.404135i
$811$	−6.86800			−0.241168			−0.120584	−	0.992703i	$-0.538477\pi$
$811$	−6.86800			−0.241168			−0.120584	+	0.992703i	$0.538477\pi$
$812$	−1.92559	−	1.14389i	−0.0675751	−	0.0401427i
$813$	5.88793	+	9.49491i	0.206499	+	0.333001i
$814$	0.387570	−	0.223764i	0.0135843	−	0.00784291i
$815$	11.9085	−	6.17978i	0.417138	−	0.216468i
$816$	−1.22977	−	1.15469i	−0.0430507	−	0.0404221i
$817$	9.74273	−	9.74273i	0.340855	−	0.340855i
$818$	26.2946	−	26.2946i	0.919369	−	0.919369i
$819$	5.76650	−	26.8870i	0.201498	−	0.939507i
$820$	−8.10726	+	25.5984i	−0.283118	+	0.893934i
$821$		−	6.97789i		−	0.243530i	−0.992559	−	0.121765i	$-0.961145\pi$
$821$		−	6.97789i		−	0.243530i	0.992559	−	0.121765i	$-0.0388554\pi$
$822$	2.86374	−	1.77584i	0.0998843	−	0.0619397i
$823$	−29.7706	−	29.7706i	−1.03774	−	1.03774i	−0.999259	−	0.0384779i	$-0.987749\pi$
$823$	−29.7706	−	29.7706i	−1.03774	−	1.03774i	−0.0384779	−	0.999259i	$-0.512251\pi$
$824$	−9.68387	−	16.7730i	−0.337354	−	0.584314i
$825$	−0.576554	+	0.876274i	−0.0200730	+	0.0305080i
$826$	−5.92213	+	21.0514i	−0.206057	+	0.732471i
$827$	−20.7012	−	20.7012i	−0.719851	−	0.719851i	0.248724	−	0.968574i	$-0.419989\pi$
$827$	−20.7012	−	20.7012i	−0.719851	−	0.719851i	−0.968574	+	0.248724i	$0.919989\pi$
$828$	−8.01362	+	2.69802i	−0.278493	+	0.0937627i
$829$	1.79485	−	1.03626i	0.0623376	−	0.0359906i	−0.468507	−	0.883460i	$-0.655208\pi$
$829$	1.79485	−	1.03626i	0.0623376	−	0.0359906i	0.530845	+	0.847469i	$0.321875\pi$
$830$	15.0012	+	16.4132i	0.520701	+	0.569711i
$831$	−0.0620162	−	0.0145416i	−0.00215132	−	0.000504443i
$832$	−6.34459	−	23.6783i	−0.219959	−	0.820899i
$833$	−4.50295	−	4.73261i	−0.156018	−	0.163975i
$834$	−32.0911	−	7.52474i	−1.11122	−	0.260561i
$835$	−3.79184	+	1.96773i	−0.131222	+	0.0680961i
$836$	0.419226	−	0.242040i	0.0144992	−	0.00837114i
$837$	51.0595	−	4.83639i	1.76488	−	0.167170i
$838$	25.8796	−	6.93442i	0.893996	−	0.239545i
$839$	13.8236	+	23.9431i	0.477243	+	0.826609i	0.999660	−	0.0260815i	$-0.00830295\pi$
$839$	13.8236	+	23.9431i	0.477243	+	0.826609i	−0.522417	+	0.852690i	$0.674970\pi$
$840$	16.0826	−	26.2628i	0.554901	−	0.906152i
$841$	14.1337	−	24.4803i	0.487370	−	0.844149i
$842$	−1.12783	+	4.20911i	−0.0388676	+	0.145056i
$843$	0.235113	+	7.46626i	0.00809771	+	0.257152i
$844$	1.27881	+	0.738319i	0.0440183	+	0.0254140i
$845$	−1.64631	+	1.50468i	−0.0566347	+	0.0517626i
$846$	5.71948	−	3.80106i	0.196640	−	0.130683i
$847$	14.8440	−	24.9880i	0.510046	−	0.858596i
$848$	−1.89303	−	0.507235i	−0.0650068	−	0.0174185i
$849$	38.1245	−	11.5131i	1.30843	−	0.395129i
$850$	2.70082	−	3.83618i	0.0926372	−	0.131580i
$851$			10.4722i			0.358983i
$852$	−10.6554	+	19.8752i	−0.365047	+	0.680913i
$853$	−4.86109	+	18.1418i	−0.166440	+	0.621164i	0.831412	+	0.555657i	$0.187533\pi$
$853$	−4.86109	+	18.1418i	−0.166440	+	0.621164i	−0.997852	+	0.0655073i	$0.979133\pi$
$854$	−3.38869	+	12.0458i	−0.115959	+	0.412197i
$855$	−7.48705	−	26.0524i	−0.256052	−	0.890975i
$856$	−5.84478	+	10.1235i	−0.199770	+	0.346012i
$857$	23.7589	−	6.36618i	0.811589	−	0.217465i	0.170923	−	0.985284i	$-0.445325\pi$
$857$	23.7589	−	6.36618i	0.811589	−	0.217465i	0.640666	+	0.767820i	$0.278658\pi$
$858$	0.730405	−	0.0230005i	0.0249356	−	0.000785223i
$859$	7.64162	−	4.41189i	0.260729	−	0.150532i	−0.363938	−	0.931423i	$-0.618568\pi$
$859$	7.64162	−	4.41189i	0.260729	−	0.150532i	0.624667	+	0.780891i	$0.285235\pi$
$860$	−7.53343	−	0.338600i	−0.256888	−	0.0115462i
$861$	48.7048	+	26.8961i	1.65986	+	0.916615i
$862$	26.7575	+	7.16966i	0.911366	+	0.244200i
$863$	8.78841	+	32.7988i	0.299161	+	1.11648i	0.937856	+	0.347024i	$0.112808\pi$
$863$	8.78841	+	32.7988i	0.299161	+	1.11648i	−0.638695	+	0.769460i	$0.720525\pi$
$864$	19.8672	+	16.4291i	0.675895	+	0.558931i
$865$	−9.96051	+	15.5907i	−0.338667	+	0.530099i
$866$		−	21.9864i		−	0.747130i
$867$	−23.7420	+	14.7228i	−0.806321	+	0.500011i
$868$	22.5274	−	12.6354i	0.764629	−	0.428875i
$869$	0.867453	−	1.50247i	0.0294263	−	0.0509679i
$870$	−2.86378	−	1.70511i	−0.0970912	−	0.0578088i
$871$	−20.9988	+	36.3709i	−0.711516	+	1.23238i
$872$	−0.729234	+	2.72154i	−0.0246950	+	0.0921629i
$873$	14.9563	+	44.4231i	0.506195	+	1.50349i
$874$		−	11.5781i		−	0.391634i
$875$	27.1408	+	11.7633i	0.917527	+	0.397673i
$876$	6.48738	−	6.90924i	0.219188	−	0.233442i
$877$	10.0414	+	2.69059i	0.339075	+	0.0908548i	0.424339	−	0.905504i	$-0.360507\pi$
$877$	10.0414	+	2.69059i	0.339075	+	0.0908548i	−0.0852639	+	0.996358i	$0.527173\pi$
$878$	−3.08577	+	3.08577i	−0.104140	+	0.104140i
$879$	48.6176	+	11.3999i	1.63983	+	0.384509i
$880$	0.269459	+	0.0853403i	0.00908346	+	0.00287682i
$881$		−	1.98877i		−	0.0670032i	−0.999439	−	0.0335016i	$-0.989334\pi$
$881$		−	1.98877i		−	0.0670032i	0.999439	−	0.0335016i	$-0.0106659\pi$
$882$	−15.4880	−	14.3507i	−0.521510	−	0.483214i
$883$	−11.3186	−	11.3186i	−0.380903	−	0.380903i	0.490525	−	0.871427i	$-0.336805\pi$
$883$	−11.3186	−	11.3186i	−0.380903	−	0.380903i	−0.871427	+	0.490525i	$0.836805\pi$
$884$	3.19776			0.107552
$885$	8.65290	−	30.6402i	0.290864	−	1.02996i
$886$	−10.4284			−0.350349
$887$	−8.63747	+	32.2355i	−0.290018	+	1.08236i	0.655076	+	0.755563i	$0.272636\pi$
$887$	−8.63747	+	32.2355i	−0.290018	+	1.08236i	−0.945094	+	0.326798i	$0.894030\pi$
$888$	16.2571	−	10.0813i	0.545553	−	0.338305i
$889$	−30.3741	−	8.54478i	−1.01871	−	0.286583i
$890$	−19.5439	+	10.1421i	−0.655112	+	0.339962i
$891$	−0.868120	+	0.659288i	−0.0290831	+	0.0220870i
$892$	6.26513	+	1.67874i	0.209772	+	0.0562082i
$893$	−2.38109	−	8.88636i	−0.0796802	−	0.297371i
$894$	−20.8525	−	19.5793i	−0.697411	−	0.654829i
$895$	−9.33528	−	10.2139i	−0.312044	−	0.341415i
$896$	7.15298	+	2.01226i	0.238964	+	0.0672250i
$897$	−8.07969	+	15.0709i	−0.269773	+	0.503201i
$898$	−8.31076	−	8.31076i	−0.277334	−	0.277334i
$899$	−4.22403	−	7.31624i	−0.140879	−	0.244010i
$900$	−7.76053	+	12.6444i	−0.258684	+	0.421478i
$901$	0.876238	−	1.51769i	0.0291917	−	0.0505615i
$902$	−0.382681	+	1.42819i	−0.0127419	+	0.0475534i
$903$	−3.75594	+	15.1673i	−0.124990	+	0.504735i
$904$	−19.2332	−	11.1043i	−0.639687	−	0.369323i
$905$	53.3832	−	11.7629i	1.77452	−	0.391013i
$906$	−4.63541	+	19.7688i	−0.154001	+	0.656776i
$907$	7.52530	+	28.0848i	0.249873	+	0.932540i	0.970871	+	0.239603i	$0.0770172\pi$
$907$	7.52530	+	28.0848i	0.249873	+	0.932540i	−0.720998	+	0.692938i	$0.756316\pi$
$908$	−0.172991	−	0.645613i	−0.00574092	−	0.0214254i
$909$	−2.33435	−	37.0282i	−0.0774256	−	1.22815i
$910$	−4.18403	−	20.1787i	−0.138699	−	0.668916i
$911$	37.6433	−	21.7334i	1.24718	−	0.720059i	0.276633	−	0.960976i	$-0.410781\pi$
$911$	37.6433	−	21.7334i	1.24718	−	0.720059i	0.970546	+	0.240916i	$0.0774480\pi$
$912$	−6.20764	+	3.84945i	−0.205556	+	0.127468i
$913$	−0.847052	−	0.847052i	−0.0280333	−	0.0280333i
$914$	10.8026			0.357317
$915$	4.95126	−	17.5326i	0.163683	−	0.579609i
$916$	−3.98595	−	6.90386i	−0.131699	−	0.228110i
$917$	46.0758	+	27.3711i	1.52156	+	0.903875i
$918$	3.97370	−	2.82510i	0.131152	−	0.0932423i
$919$	8.43928	+	4.87242i	0.278386	+	0.160726i	0.632693	−	0.774403i	$-0.281950\pi$
$919$	8.43928	+	4.87242i	0.278386	+	0.160726i	−0.354306	+	0.935129i	$0.615283\pi$
$920$	−14.1359	+	12.9198i	−0.466046	+	0.425954i
$921$	0.415671	+	1.37645i	0.0136968	+	0.0453556i
$922$	−11.1056	−	2.97573i	−0.365743	−	0.0980005i
$923$	11.8037	+	44.0522i	0.388525	+	1.45000i
$924$	−0.265382	+	0.480569i	−0.00873044	+	0.0158096i
$925$	11.7746	+	14.1057i	0.387145	+	0.463793i
$926$	4.09096	+	2.36192i	0.134437	+	0.0776175i
$927$	18.3226	−	6.16883i	0.601793	−	0.202611i
$928$	1.09907	−	4.10178i	0.0360787	−	0.134647i
$929$	5.51052			0.180794			0.0903972	−	0.995906i	$-0.471186\pi$
$929$	5.51052			0.180794			0.0903972	+	0.995906i	$0.471186\pi$
$930$	33.5421	−	18.7692i	1.09989	−	0.615466i
$931$	−24.8405	+	13.5297i	−0.814113	+	0.443417i
$932$	12.1065	−	3.24392i	0.396561	−	0.106258i
$933$	13.3245	+	7.14346i	0.436225	+	0.233866i
$934$	−31.0261	−	17.9130i	−1.01521	−	0.586130i
$935$	−0.136075	+	0.212992i	−0.00445013	+	0.00696557i
$936$	31.1741	−	1.96530i	1.01896	−	0.0642377i
$937$	11.3797	−	11.3797i	0.371757	−	0.371757i	−0.496360	−	0.868117i	$-0.665330\pi$
$937$	11.3797	−	11.3797i	0.371757	−	0.371757i	0.868117	+	0.496360i	$0.165330\pi$
$938$	15.7754	+	28.1255i	0.515085	+	0.918331i
$939$	21.2784	−	6.42580i	0.694394	−	0.209698i
$940$	−2.71085	+	4.24316i	−0.0884181	+	0.138396i
$941$		−	26.4492i		−	0.862219i	−0.902300	−	0.431109i	$-0.858122\pi$
$941$		−	26.4492i		−	0.862219i	0.902300	−	0.431109i	$-0.141878\pi$
$942$	−9.56989	+	17.8505i	−0.311804	+	0.581601i
$943$	−24.4650	−	24.4650i	−0.796689	−	0.796689i
$944$	−8.57933			−0.279233
$945$	22.5282	+	20.9160i	0.732842	+	0.680399i
$946$	−0.415244			−0.0135007
$947$	27.3758	+	27.3758i	0.889594	+	0.889594i	0.994484	−	0.104890i	$-0.0334490\pi$
$947$	27.3758	+	27.3758i	0.889594	+	0.889594i	−0.104890	+	0.994484i	$0.533449\pi$
$948$	11.5941	−	21.6263i	0.376560	−	0.702389i
$949$		−	19.1667i		−	0.622178i
$950$	−13.0179	−	15.5953i	−0.422358	−	0.505977i
$951$	−15.8487	+	4.78611i	−0.513929	+	0.155200i
$952$	3.78983	−	6.37969i	0.122829	−	0.206767i
$953$	18.0771	−	18.0771i	0.585574	−	0.585574i	−0.350856	−	0.936430i	$-0.614109\pi$
$953$	18.0771	−	18.0771i	0.585574	−	0.585574i	0.936430	+	0.350856i	$0.114109\pi$
$954$	2.51793	−	5.07395i	0.0815209	−	0.164275i
$955$	4.85460	+	22.0314i	0.157091	+	0.712919i
$956$	1.34019	+	0.773759i	0.0433449	+	0.0250252i
$957$	0.158250	+	0.0848398i	0.00511549	+	0.00274248i
$958$	−12.9797	+	3.47789i	−0.419354	+	0.112366i
$959$	3.57463	+	3.66463i	0.115431	+	0.118337i
$960$	26.3727	+	7.44773i	0.851175	+	0.240375i
$961$	66.4246			2.14273
$962$	3.31309	−	12.3646i	0.106818	−	0.398652i
$963$	−8.75380	−	7.71553i	−0.282087	−	0.248629i
$964$	−3.82891	−	2.21062i	−0.123321	−	0.0711994i
$965$	−28.1986	−	18.0154i	−0.907745	−	0.579936i
$966$	6.78050	+	11.2440i	0.218159	+	0.361769i
$967$	−5.27518	−	19.6872i	−0.169638	−	0.633099i	−0.997403	−	0.0720236i	$-0.977054\pi$
$967$	−5.27518	−	19.6872i	−0.169638	−	0.633099i	0.827764	−	0.561076i	$-0.189612\pi$
$968$	31.8900	+	8.54489i	1.02498	+	0.274643i
$969$	−1.88824	−	6.25270i	−0.0606589	−	0.200866i
$970$	23.6987	+	25.9293i	0.760921	+	0.832541i
$971$	−17.4846	−	10.0947i	−0.561108	−	0.323956i	0.192482	−	0.981300i	$-0.438346\pi$
$971$	−17.4846	−	10.0947i	−0.561108	−	0.323956i	−0.753590	+	0.657345i	$0.771680\pi$
$972$	−11.9789	+	9.70666i	−0.384224	+	0.311341i
$973$	0.622494	−	50.0726i	0.0199562	−	1.60525i
$974$	10.6724	+	18.4851i	0.341965	+	0.592301i
$975$	6.06203	+	29.3844i	0.194140	+	0.941055i
$976$	−4.90916			−0.157138
$977$	−10.2785	−	10.2785i	−0.328838	−	0.328838i	0.523306	−	0.852145i	$-0.324698\pi$
$977$	−10.2785	−	10.2785i	−0.328838	−	0.328838i	−0.852145	+	0.523306i	$0.824698\pi$
$978$	8.88023	−	5.50676i	0.283958	−	0.176087i
$979$	1.02730	−	0.593109i	0.0328325	−	0.0189559i
$980$	14.6380	+	5.03971i	0.467595	+	0.160988i
$981$	−2.51936	−	1.25022i	−0.0804370	−	0.0399165i
$982$	−9.45538	−	35.2880i	−0.301733	−	1.12608i
$983$	2.00960	+	7.49995i	0.0640964	+	0.239211i	0.990540	−	0.137222i	$-0.0438173\pi$
$983$	2.00960	+	7.49995i	0.0640964	+	0.239211i	−0.926444	+	0.376433i	$0.877151\pi$
$984$	−14.4279	+	61.5312i	−0.459944	+	1.96154i
$985$	−37.9636	−	24.2540i	−1.20962	−	0.772798i
$986$	−0.695505	−	0.401550i	−0.0221494	−	0.0127880i
$987$	7.51653	+	7.23550i	0.239254	+	0.230308i
$988$	3.58370	−	13.3745i	0.114013	−	0.425501i
$989$	4.85838	−	8.41496i	0.154488	−	0.267580i
$990$	−0.395636	+	0.714741i	−0.0125742	+	0.0227160i
$991$	26.1823	+	45.3492i	0.831710	+	1.44056i	0.896682	+	0.442676i	$0.145971\pi$
$991$	26.1823	+	45.3492i	0.831710	+	1.44056i	−0.0649720	+	0.997887i	$0.520696\pi$
$992$	34.6278	+	34.6278i	1.09943	+	1.09943i
$993$	−2.58448	+	4.82077i	−0.0820160	+	0.152983i
$994$	33.7100	+	9.48323i	1.06922	+	0.300790i
$995$	19.9161	−	18.2028i	0.631382	−	0.577066i
$996$	−12.3517	−	11.5975i	−0.391377	−	0.367481i
$997$	−7.87549	−	29.3917i	−0.249419	−	0.930846i	−0.971110	−	0.238630i	$-0.923302\pi$
$997$	−7.87549	−	29.3917i	−0.249419	−	0.930846i	0.721691	−	0.692215i	$-0.243365\pi$
$998$	9.22072	+	2.47068i	0.291877	+	0.0782081i
$999$	6.65941	+	17.8962i	0.210695	+	0.566209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bv.a.23.15	✓	176
3.2	odd	2		945.2.by.a.233.30		176
5.2	odd	4	inner	315.2.bv.a.212.30	yes	176
7.4	even	3		315.2.bx.a.158.30	yes	176
9.2	odd	6		315.2.bx.a.128.30	yes	176
9.7	even	3		945.2.ca.a.548.15		176
15.2	even	4		945.2.by.a.422.15		176
21.11	odd	6		945.2.ca.a.368.15		176
35.32	odd	12		315.2.bx.a.32.30	yes	176
45.2	even	12		315.2.bx.a.2.30	yes	176
45.7	odd	12		945.2.ca.a.737.15		176
63.11	odd	6	inner	315.2.bv.a.263.30	yes	176
63.25	even	3		945.2.by.a.683.15		176
105.32	even	12		945.2.ca.a.557.15		176
315.137	even	12	inner	315.2.bv.a.137.15	yes	176
315.277	odd	12		945.2.by.a.872.30		176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bv.a.23.15	✓	176	1.1	even	1	trivial
315.2.bv.a.137.15	yes	176	315.137	even	12	inner
315.2.bv.a.212.30	yes	176	5.2	odd	4	inner
315.2.bv.a.263.30	yes	176	63.11	odd	6	inner
315.2.bx.a.2.30	yes	176	45.2	even	12
315.2.bx.a.32.30	yes	176	35.32	odd	12
315.2.bx.a.128.30	yes	176	9.2	odd	6
315.2.bx.a.158.30	yes	176	7.4	even	3
945.2.by.a.233.30		176	3.2	odd	2
945.2.by.a.422.15		176	15.2	even	4
945.2.by.a.683.15		176	63.25	even	3
945.2.by.a.872.30		176	315.277	odd	12
945.2.ca.a.368.15		176	21.11	odd	6
945.2.ca.a.548.15		176	9.7	even	3
945.2.ca.a.557.15		176	105.32	even	12
945.2.ca.a.737.15		176	45.7	odd	12

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.710963 - 0.710963i) q^{2} +(-0.818385 + 1.52651i) q^{3} -0.989064i q^{4} +(2.18368 - 0.481173i) q^{5} +(1.66714 - 0.503454i) q^{6} +(1.29429 + 2.30756i) q^{7} +(-2.12511 + 2.12511i) q^{8} +(-1.66049 - 2.49855i) q^{9} +O(q^{10})\)	\(q+(-0.710963 - 0.710963i) q^{2} +(-0.818385 + 1.52651i) q^{3} -0.989064i q^{4} +(2.18368 - 0.481173i) q^{5} +(1.66714 - 0.503454i) q^{6} +(1.29429 + 2.30756i) q^{7} +(-2.12511 + 2.12511i) q^{8} +(-1.66049 - 2.49855i) q^{9} +(-1.89461 - 1.21042i) q^{10} +(0.104894 + 0.0605605i) q^{11} +(1.50982 + 0.809434i) q^{12} +(3.34642 - 0.896671i) q^{13} +(0.720394 - 2.56078i) q^{14} +(-1.05258 + 3.72721i) q^{15} +1.04363 q^{16} +(-0.241535 + 0.901422i) q^{17} +(-0.595829 + 2.95693i) q^{18} +(3.49949 + 2.02043i) q^{19} +(-0.475910 - 2.15980i) q^{20} +(-4.58174 + 0.0872857i) q^{21} +(-0.0315194 - 0.117632i) q^{22} +(2.75260 + 0.737558i) q^{23} +(-1.50486 - 4.98318i) q^{24} +(4.53695 - 2.10146i) q^{25} +(-3.01668 - 1.74168i) q^{26} +(5.17300 - 0.489990i) q^{27} +(2.28232 - 1.28014i) q^{28} +(-0.427950 - 0.741231i) q^{29} +(3.39825 - 1.90156i) q^{30} +9.87039 q^{31} +(3.50825 + 3.50825i) q^{32} +(-0.178290 + 0.110560i) q^{33} +(0.812600 - 0.469155i) q^{34} +(3.93665 + 4.41619i) q^{35} +(-2.47123 + 1.64233i) q^{36} +(0.951119 + 3.54962i) q^{37} +(-1.05156 - 3.92446i) q^{38} +(-1.36988 + 5.84218i) q^{39} +(-3.61803 + 5.66312i) q^{40} +(-10.5145 - 6.07057i) q^{41} +(3.31951 + 3.19539i) q^{42} +(0.882506 - 3.29356i) q^{43} +(0.0598982 - 0.103747i) q^{44} +(-4.82823 - 4.65706i) q^{45} +(-1.43262 - 2.48138i) q^{46} +(-1.60987 - 1.60987i) q^{47} +(-0.854088 + 1.59311i) q^{48} +(-3.64962 + 5.97329i) q^{49} +(-4.71966 - 1.73154i) q^{50} +(-1.17837 - 1.10642i) q^{51} +(-0.886865 - 3.30982i) q^{52} +(-1.81389 - 0.486031i) q^{53} +(-4.02617 - 3.32945i) q^{54} +(0.258195 + 0.0817729i) q^{55} +(-7.65433 - 2.15330i) q^{56} +(-5.94815 + 3.68853i) q^{57} +(-0.222731 + 0.831244i) q^{58} -8.22069 q^{59} +(3.68645 + 1.04106i) q^{60} -4.70394 q^{61} +(-7.01748 - 7.01748i) q^{62} +(3.61639 - 7.06553i) q^{63} -7.07572i q^{64} +(6.87607 - 3.56825i) q^{65} +(0.205362 + 0.0481534i) q^{66} +(-8.57179 + 8.57179i) q^{67} +(0.891564 + 0.238894i) q^{68} +(-3.37858 + 3.59828i) q^{69} +(0.340935 - 5.93856i) q^{70} +13.1640i q^{71} +(8.83844 + 1.78097i) q^{72} +(1.43188 - 5.34386i) q^{73} +(1.84744 - 3.19986i) q^{74} +(-0.505062 + 8.64551i) q^{75} +(1.99834 - 3.46122i) q^{76} +(-0.00398355 + 0.320431i) q^{77} +(5.12751 - 3.17964i) q^{78} -14.3237i q^{79} +(2.27895 - 0.502164i) q^{80} +(-3.48553 + 8.29766i) q^{81} +(3.15950 + 11.7914i) q^{82} +(-9.55321 - 2.55978i) q^{83} +(0.0863311 + 4.53164i) q^{84} +(-0.0936971 + 2.08464i) q^{85} +(-2.96903 + 1.71417i) q^{86} +(1.48173 - 0.0466597i) q^{87} +(-0.351609 + 0.0942134i) q^{88} +(4.89683 - 8.48156i) q^{89} +(0.121690 + 6.74369i) q^{90} +(6.40036 + 6.56150i) q^{91} +(0.729492 - 2.72250i) q^{92} +(-8.07778 + 15.0673i) q^{93} +2.28912i q^{94} +(8.61395 + 2.72812i) q^{95} +(-8.22649 + 2.48429i) q^{96} +(-15.0920 - 4.04390i) q^{97} +(6.84154 - 1.65204i) q^{98} +(-0.0228620 - 0.362643i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7	\( 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 4 q^{10} - 24 q^{11} + 26 q^{12} - 4 q^{13} - 14 q^{15} - 136 q^{16} + 18 q^{17} - 10 q^{18} - 12 q^{20} - 16 q^{21} + 4 q^{22} - 30 q^{23} + 2 q^{25} - 32 q^{27} - 4 q^{28} + 10 q^{30} - 8 q^{31} - 34 q^{33} + 8 q^{36} - 4 q^{37} - 30 q^{38} + 18 q^{40} - 36 q^{41} + 8 q^{42} - 4 q^{43} + 22 q^{45} + 4 q^{46} + 38 q^{48} + 36 q^{50} - 40 q^{51} + 26 q^{52} + 4 q^{55} + 24 q^{56} + 32 q^{57} + 6 q^{58} + 22 q^{60} + 16 q^{61} + 14 q^{63} + 4 q^{66} - 4 q^{67} + 114 q^{68} + 18 q^{70} - 46 q^{72} - 4 q^{73} + 6 q^{75} - 24 q^{76} - 54 q^{77} + 54 q^{78} - 36 q^{80} - 64 q^{81} - 8 q^{82} - 12 q^{83} - 4 q^{85} - 120 q^{86} - 28 q^{87} - 6 q^{88} - 24 q^{90} - 16 q^{91} + 72 q^{92} - 38 q^{93} + 192 q^{96} - 4 q^{97} - 12 q^{98}+O(q^{100}) \) 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 4 * q^10 - 24 * q^11 + 26 * q^12 - 4 * q^13 - 14 * q^15 - 136 * q^16 + 18 * q^17 - 10 * q^18 - 12 * q^20 - 16 * q^21 + 4 * q^22 - 30 * q^23 + 2 * q^25 - 32 * q^27 - 4 * q^28 + 10 * q^30 - 8 * q^31 - 34 * q^33 + 8 * q^36 - 4 * q^37 - 30 * q^38 + 18 * q^40 - 36 * q^41 + 8 * q^42 - 4 * q^43 + 22 * q^45 + 4 * q^46 + 38 * q^48 + 36 * q^50 - 40 * q^51 + 26 * q^52 + 4 * q^55 + 24 * q^56 + 32 * q^57 + 6 * q^58 + 22 * q^60 + 16 * q^61 + 14 * q^63 + 4 * q^66 - 4 * q^67 + 114 * q^68 + 18 * q^70 - 46 * q^72 - 4 * q^73 + 6 * q^75 - 24 * q^76 - 54 * q^77 + 54 * q^78 - 36 * q^80 - 64 * q^81 - 8 * q^82 - 12 * q^83 - 4 * q^85 - 120 * q^86 - 28 * q^87 - 6 * q^88 - 24 * q^90 - 16 * q^91 + 72 * q^92 - 38 * q^93 + 192 * q^96 - 4 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more