LMFDB - Embedded newform 350.2.x.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(3,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("350.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.x (of order $60$, degree $16$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$20$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.8
Character	$\chi$	$=$	350.3
Dual form			350.2.x.a.117.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.544639 + 0.838671i) q^{2} +(0.637721 - 1.66132i) q^{3} +(-0.406737 - 0.913545i) q^{4} +(-1.80729 + 1.31671i) q^{5} +(1.04597 + 1.43966i) q^{6} +(-0.155100 + 2.64120i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-0.123863 - 0.111527i) q^{9} +O(q^{10})$	\(q+(-0.544639 + 0.838671i) q^{2} +(0.637721 - 1.66132i) q^{3} +(-0.406737 - 0.913545i) q^{4} +(-1.80729 + 1.31671i) q^{5} +(1.04597 + 1.43966i) q^{6} +(-0.155100 + 2.64120i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-0.123863 - 0.111527i) q^{9} +(-0.119964 - 2.23285i) q^{10} +(0.796380 + 0.884470i) q^{11} +(-1.77708 + 0.0931326i) q^{12} +(4.00727 + 2.04181i) q^{13} +(-2.13062 - 1.56858i) q^{14} +(1.03493 + 3.84217i) q^{15} +(-0.669131 + 0.743145i) q^{16} +(-0.749255 + 0.925253i) q^{17} +(0.160995 - 0.0431385i) q^{18} +(-1.37068 - 0.610266i) q^{19} +(1.93796 + 1.11549i) q^{20} +(4.28897 + 1.94202i) q^{21} +(-1.17552 + 0.186184i) q^{22} +(5.47642 + 3.55643i) q^{23} +(0.889758 - 1.54111i) q^{24} +(1.53257 - 4.75933i) q^{25} +(-3.89492 + 2.24873i) q^{26} +(4.49241 - 2.28900i) q^{27} +(2.47594 - 0.932582i) q^{28} +(-2.18517 + 3.00763i) q^{29} +(-3.78598 - 1.22464i) q^{30} +(5.39181 - 0.566702i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(1.97726 - 0.758998i) q^{33} +(-0.367909 - 1.13231i) q^{34} +(-3.19738 - 4.97763i) q^{35} +(-0.0515053 + 0.158517i) q^{36} +(0.258761 + 4.93746i) q^{37} +(1.25834 - 0.817174i) q^{38} +(5.94761 - 5.35526i) q^{39} +(-1.99101 + 1.01777i) q^{40} +(-8.58901 + 2.79074i) q^{41} +(-3.96466 + 2.53933i) q^{42} +(-0.920409 - 0.920409i) q^{43} +(0.484086 - 1.08728i) q^{44} +(0.370705 + 0.0384698i) q^{45} +(-5.96534 + 2.65594i) q^{46} +(-3.80921 + 3.08463i) q^{47} +(0.807883 + 1.58556i) q^{48} +(-6.95189 - 0.819301i) q^{49} +(3.15681 + 3.87744i) q^{50} +(1.05933 + 1.83481i) q^{51} +(0.235379 - 4.49130i) q^{52} +(-2.94324 - 1.12980i) q^{53} +(-0.527027 + 5.01433i) q^{54} +(-2.60387 - 0.549892i) q^{55} +(-0.566365 + 2.58442i) q^{56} +(-1.88796 + 1.88796i) q^{57} +(-1.33228 - 3.47072i) q^{58} +(-10.9257 - 2.32233i) q^{59} +(3.08906 - 2.50820i) q^{60} +(-3.11585 - 14.6589i) q^{61} +(-2.46131 + 4.83060i) q^{62} +(0.313777 - 0.309850i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-9.93074 + 1.58627i) q^{65} +(-0.440342 + 2.07165i) q^{66} +(7.48284 + 6.05948i) q^{67} +(1.15001 + 0.308144i) q^{68} +(9.40079 - 6.83008i) q^{69} +(5.91601 + 0.0294668i) q^{70} +(1.52517 + 1.10810i) q^{71} +(-0.104892 - 0.129530i) q^{72} +(8.51385 + 0.446192i) q^{73} +(-4.28183 - 2.47212i) q^{74} +(-6.92942 - 5.58122i) q^{75} +1.50039i q^{76} +(-2.45958 + 1.96622i) q^{77} +(1.25199 + 7.90477i) q^{78} +(11.9441 + 1.25538i) q^{79} +(0.230808 - 2.22412i) q^{80} +(-0.990119 - 9.42035i) q^{81} +(2.33740 - 8.72330i) q^{82} +(1.36603 - 8.62478i) q^{83} +(0.0296426 - 4.70806i) q^{84} +(0.135833 - 2.65875i) q^{85} +(1.27321 - 0.270629i) q^{86} +(3.60311 + 5.54831i) q^{87} +(0.648214 + 0.998162i) q^{88} +(6.65017 - 1.41354i) q^{89} +(-0.234164 + 0.289947i) q^{90} +(-6.01435 + 10.2673i) q^{91} +(1.02150 - 6.44949i) q^{92} +(2.49700 - 9.31892i) q^{93} +(-0.512350 - 4.87468i) q^{94} +(3.28075 - 0.701856i) q^{95} +(-1.76977 - 0.186010i) q^{96} +(-0.495018 - 3.12542i) q^{97} +(4.47339 - 5.38412i) q^{98} -0.198371i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 12 q^{5} - 8 q^{7}+O(q^{10}) $ 320 * q + 12 * q^5 - 8 * q^7	$ 320 q + 12 q^{5} - 8 q^{7} + 12 q^{10} - 16 q^{15} - 40 q^{16} + 36 q^{17} + 8 q^{18} - 72 q^{22} + 44 q^{23} - 12 q^{25} - 24 q^{28} - 80 q^{29} + 20 q^{30} - 48 q^{33} - 28 q^{35} + 80 q^{36} - 4 q^{37} - 24 q^{38} - 40 q^{39} - 36 q^{42} + 88 q^{43} - 228 q^{45} - 12 q^{47} + 32 q^{50} - 52 q^{53} + 152 q^{57} + 32 q^{58} - 120 q^{59} - 8 q^{60} + 136 q^{63} + 8 q^{65} - 32 q^{67} - 144 q^{68} + 92 q^{70} + 8 q^{72} + 12 q^{73} - 432 q^{75} + 144 q^{77} - 16 q^{78} + 12 q^{80} - 40 q^{81} - 192 q^{82} + 60 q^{84} - 24 q^{85} + 24 q^{87} + 4 q^{88} - 300 q^{89} - 8 q^{92} - 68 q^{93} + 20 q^{95} - 40 q^{98}+O(q^{100}) $ 320 * q + 12 * q^5 - 8 * q^7 + 12 * q^10 - 16 * q^15 - 40 * q^16 + 36 * q^17 + 8 * q^18 - 72 * q^22 + 44 * q^23 - 12 * q^25 - 24 * q^28 - 80 * q^29 + 20 * q^30 - 48 * q^33 - 28 * q^35 + 80 * q^36 - 4 * q^37 - 24 * q^38 - 40 * q^39 - 36 * q^42 + 88 * q^43 - 228 * q^45 - 12 * q^47 + 32 * q^50 - 52 * q^53 + 152 * q^57 + 32 * q^58 - 120 * q^59 - 8 * q^60 + 136 * q^63 + 8 * q^65 - 32 * q^67 - 144 * q^68 + 92 * q^70 + 8 * q^72 + 12 * q^73 - 432 * q^75 + 144 * q^77 - 16 * q^78 + 12 * q^80 - 40 * q^81 - 192 * q^82 + 60 * q^84 - 24 * q^85 + 24 * q^87 + 4 * q^88 - 300 * q^89 - 8 * q^92 - 68 * q^93 + 20 * q^95 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−0.544639	+	0.838671i	−0.385118	+	0.593030i
$2$	−0.544639	+	0.838671i	−0.385118	+	0.593030i
$3$	0.637721	−	1.66132i	0.368189	−	0.959164i	−0.616889	−	0.787050i	$-0.711607\pi$
$3$	0.637721	−	1.66132i	0.368189	−	0.959164i	0.985077	−	0.172113i	$-0.0550596\pi$
$4$	−0.406737	−	0.913545i	−0.203368	−	0.456773i
$5$	−1.80729	+	1.31671i	−0.808243	+	0.588849i
$5$	−1.80729	+	1.31671i	−0.808243	+	0.588849i
$6$	1.04597	+	1.43966i	0.427017	+	0.587738i
$7$	−0.155100	+	2.64120i	−0.0586223	+	0.998280i
$7$	−0.155100	+	2.64120i	−0.0586223	+	0.998280i
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$	−0.123863	−	0.111527i	−0.0412878	−	0.0371757i
$10$	−0.119964	−	2.23285i	−0.0379358	−	0.706088i
$11$	0.796380	+	0.884470i	0.240118	+	0.266678i	0.851144	−	0.524933i	$-0.175910\pi$
$11$	0.796380	+	0.884470i	0.240118	+	0.266678i	−0.611026	+	0.791611i	$0.709243\pi$
$12$	−1.77708	+	0.0931326i	−0.512998	+	0.0268851i
$13$	4.00727	+	2.04181i	1.11142	+	0.566295i	0.910581	−	0.413330i	$-0.135634\pi$
$13$	4.00727	+	2.04181i	1.11142	+	0.566295i	0.200835	+	0.979625i	$0.435634\pi$
$14$	−2.13062	−	1.56858i	−0.569433	−	0.419220i
$15$	1.03493	+	3.84217i	0.267217	+	0.992045i
$16$	−0.669131	+	0.743145i	−0.167283	+	0.185786i
$17$	−0.749255	+	0.925253i	−0.181721	+	0.224407i	−0.859864	−	0.510523i	$-0.829452\pi$
$17$	−0.749255	+	0.925253i	−0.181721	+	0.224407i	0.678143	+	0.734930i	$0.262785\pi$
$18$	0.160995	−	0.0431385i	0.0379469	−	0.0101679i
$19$	−1.37068	−	0.610266i	−0.314455	−	0.140005i	0.243440	−	0.969916i	$-0.421724\pi$
$19$	−1.37068	−	0.610266i	−0.314455	−	0.140005i	−0.557895	+	0.829911i	$0.688391\pi$
$20$	1.93796	+	1.11549i	0.433341	+	0.249430i
$21$	4.28897	+	1.94202i	0.935930	+	0.423784i
$22$	−1.17552	+	0.186184i	−0.250621	+	0.0396945i
$23$	5.47642	+	3.55643i	1.14191	+	0.741566i	0.969894	−	0.243527i	$-0.0783046\pi$
$23$	5.47642	+	3.55643i	1.14191	+	0.741566i	0.172018	+	0.985094i	$0.444971\pi$
$24$	0.889758	−	1.54111i	0.181621	−	0.314577i
$25$	1.53257	−	4.75933i	0.306514	−	0.951866i
$26$	−3.89492	+	2.24873i	−0.763856	+	0.441013i
$27$	4.49241	−	2.28900i	0.864564	−	0.440517i
$28$	2.47594	−	0.932582i	0.467909	−	0.176242i
$29$	−2.18517	+	3.00763i	−0.405777	+	0.558504i	−0.962182	−	0.272407i	$-0.912180\pi$
$29$	−2.18517	+	3.00763i	−0.405777	+	0.558504i	0.556405	+	0.830911i	$0.312180\pi$
$30$	−3.78598	−	1.22464i	−0.691222	−	0.223587i
$31$	5.39181	−	0.566702i	0.968397	−	0.101783i	0.392896	−	0.919583i	$-0.371473\pi$
$31$	5.39181	−	0.566702i	0.968397	−	0.101783i	0.575502	+	0.817800i	$0.304807\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	1.97726	−	0.758998i	0.344196	−	0.132125i
$34$	−0.367909	−	1.13231i	−0.0630959	−	0.194189i
$35$	−3.19738	−	4.97763i	−0.540455	−	0.841373i
$36$	−0.0515053	+	0.158517i	−0.00858421	+	0.0264195i
$37$	0.258761	+	4.93746i	0.0425401	+	0.811713i	0.933707	+	0.358038i	$0.116554\pi$
$37$	0.258761	+	4.93746i	0.0425401	+	0.811713i	−0.891167	+	0.453675i	$0.850113\pi$
$38$	1.25834	−	0.817174i	0.204129	−	0.132563i
$39$	5.94761	−	5.35526i	0.952380	−	0.857527i
$40$	−1.99101	+	1.01777i	−0.314807	+	0.160924i
$41$	−8.58901	+	2.79074i	−1.34138	+	0.435840i	−0.889784	−	0.456383i	$-0.849145\pi$
$41$	−8.58901	+	2.79074i	−1.34138	+	0.435840i	−0.451595	+	0.892223i	$0.649145\pi$
$42$	−3.96466	+	2.53933i	−0.611760	+	0.391828i
$43$	−0.920409	−	0.920409i	−0.140361	−	0.140361i	0.633435	−	0.773796i	$-0.281644\pi$
$43$	−0.920409	−	0.920409i	−0.140361	−	0.140361i	−0.773796	+	0.633435i	$0.781644\pi$
$44$	0.484086	−	1.08728i	0.0729788	−	0.163913i
$45$	0.370705	+	0.0384698i	0.0552614	+	0.00573474i
$46$	−5.96534	+	2.65594i	−0.879542	+	0.391597i
$47$	−3.80921	+	3.08463i	−0.555630	+	0.449940i	−0.865550	−	0.500822i	$-0.833031\pi$
$47$	−3.80921	+	3.08463i	−0.555630	+	0.449940i	0.309920	+	0.950763i	$0.399698\pi$
$48$	0.807883	+	1.58556i	0.116608	+	0.228856i
$49$	−6.95189	−	0.819301i	−0.993127	−	0.117043i
$50$	3.15681	+	3.87744i	0.446441	+	0.548353i
$51$	1.05933	+	1.83481i	0.148335	+	0.256924i
$52$	0.235379	−	4.49130i	0.0326412	−	0.622831i
$53$	−2.94324	−	1.12980i	−0.404285	−	0.155190i	0.147724	−	0.989029i	$-0.452805\pi$
$53$	−2.94324	−	1.12980i	−0.404285	−	0.155190i	−0.552009	+	0.833838i	$0.686139\pi$
$54$	−0.527027	+	5.01433i	−0.0717193	+	0.682363i
$55$	−2.60387	−	0.549892i	−0.351106	−	0.0741474i
$56$	−0.566365	+	2.58442i	−0.0756838	+	0.345358i
$57$	−1.88796	+	1.88796i	−0.250066	+	0.250066i
$58$	−1.33228	−	3.47072i	−0.174937	−	0.455727i
$59$	−10.9257	−	2.32233i	−1.42241	−	0.302342i	−0.568463	−	0.822709i	$-0.692462\pi$
$59$	−10.9257	−	2.32233i	−1.42241	−	0.302342i	−0.853943	+	0.520367i	$0.825795\pi$
$60$	3.08906	−	2.50820i	0.398796	−	0.323808i
$61$	−3.11585	−	14.6589i	−0.398943	−	1.87688i	−0.475338	−	0.879803i	$-0.657674\pi$
$61$	−3.11585	−	14.6589i	−0.398943	−	1.87688i	0.0763942	−	0.997078i	$-0.475659\pi$
$62$	−2.46131	+	4.83060i	−0.312587	+	0.613487i
$63$	0.313777	−	0.309850i	0.0395321	−	0.0390374i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	−9.93074	+	1.58627i	−1.23176	+	0.196752i
$66$	−0.440342	+	2.07165i	−0.0542024	+	0.255002i
$67$	7.48284	+	6.05948i	0.914174	+	0.740284i	0.966046	−	0.258370i	$-0.0831853\pi$
$67$	7.48284	+	6.05948i	0.914174	+	0.740284i	−0.0518717	+	0.998654i	$0.516519\pi$
$68$	1.15001	+	0.308144i	0.139459	+	0.0373680i
$69$	9.40079	−	6.83008i	1.13172	−	0.822245i
$70$	5.91601	+	0.0294668i	0.707098	+	0.00352196i
$71$	1.52517	+	1.10810i	0.181004	+	0.131507i	0.674598	−	0.738185i	$-0.264317\pi$
$71$	1.52517	+	1.10810i	0.181004	+	0.131507i	−0.493594	+	0.869693i	$0.664317\pi$
$72$	−0.104892	−	0.129530i	−0.0123616	−	0.0152653i
$73$	8.51385	+	0.446192i	0.996470	+	0.0522228i	0.543592	−	0.839350i	$-0.317064\pi$
$73$	8.51385	+	0.446192i	0.996470	+	0.0522228i	0.452878	+	0.891572i	$0.350397\pi$
$74$	−4.28183	−	2.47212i	−0.497753	−	0.287378i
$75$	−6.92942	−	5.58122i	−0.800141	−	0.644464i
$76$			1.50039i			0.172107i
$77$	−2.45958	+	1.96622i	−0.280295	+	0.224071i
$78$	1.25199	+	7.90477i	0.141760	+	0.895039i
$79$	11.9441	+	1.25538i	1.34382	+	0.141241i	0.748974	−	0.662600i	$-0.230547\pi$
$79$	11.9441	+	1.25538i	1.34382	+	0.141241i	0.594845	+	0.803841i	$0.297214\pi$
$80$	0.230808	−	2.22412i	0.0258051	−	0.248665i
$81$	−0.990119	−	9.42035i	−0.110013	−	1.04671i
$82$	2.33740	−	8.72330i	0.258123	−	0.963327i
$83$	1.36603	−	8.62478i	0.149941	−	0.946692i	−0.791904	−	0.610646i	$-0.790910\pi$
$83$	1.36603	−	8.62478i	0.149941	−	0.946692i	0.941845	−	0.336047i	$-0.109090\pi$
$84$	0.0296426	−	4.70806i	0.00323427	−	0.513692i
$85$	0.135833	−	2.65875i	0.0147331	−	0.288382i
$86$	1.27321	−	0.270629i	0.137294	−	0.0291827i
$87$	3.60311	+	5.54831i	0.386294	+	0.594841i
$88$	0.648214	+	0.998162i	0.0690998	+	0.106404i
$89$	6.65017	−	1.41354i	0.704917	−	0.149835i	0.158513	−	0.987357i	$-0.449330\pi$
$89$	6.65017	−	1.41354i	0.704917	−	0.149835i	0.546403	+	0.837522i	$0.315997\pi$
$90$	−0.234164	+	0.289947i	−0.0246830	+	0.0305631i
$91$	−6.01435	+	10.2673i	−0.630475	+	1.07631i
$92$	1.02150	−	6.44949i	0.106499	−	0.672405i
$93$	2.49700	−	9.31892i	0.258927	−	0.966327i
$94$	−0.512350	−	4.87468i	−0.0528448	−	0.502785i
$95$	3.28075	−	0.701856i	0.336598	−	0.0720089i
$96$	−1.76977	−	0.186010i	−0.180626	−	0.0189846i
$97$	−0.495018	−	3.12542i	−0.0502615	−	0.317339i	−0.999991	−	0.00426657i	$-0.998642\pi$
$97$	−0.495018	−	3.12542i	−0.0502615	−	0.317339i	0.949729	−	0.313072i	$-0.101358\pi$
$98$	4.47339	−	5.38412i	0.451881	−	0.543878i
$99$		−	0.198371i		−	0.0199371i
$100$	−4.97122	+	0.535721i	−0.497122	+	0.0535721i
$101$	−17.1689	−	9.91250i	−1.70837	−	0.986330i	−0.936577	−	0.350461i	$-0.886025\pi$
$101$	−17.1689	−	9.91250i	−1.70837	−	0.986330i	−0.771797	−	0.635869i	$-0.780642\pi$
$102$	−2.11575	−	0.110882i	−0.209490	−	0.0109789i
$103$	−4.22188	−	5.21359i	−0.415994	−	0.513710i	0.525475	−	0.850809i	$-0.323888\pi$
$103$	−4.22188	−	5.21359i	−0.415994	−	0.513710i	−0.941469	+	0.337099i	$0.890554\pi$
$104$	3.63852	+	2.64354i	0.356787	+	0.259221i
$105$	−10.3085	+	2.13753i	−1.00600	+	0.208601i
$106$	2.55053	−	1.85307i	0.247730	−	0.179986i
$107$	15.0614	+	4.03569i	1.45604	+	0.390145i	0.898120	−	0.439750i	$-0.144933\pi$
$107$	15.0614	+	4.03569i	1.45604	+	0.390145i	0.557920	+	0.829895i	$0.311600\pi$
$108$	−3.91833	−	3.17300i	−0.377041	−	0.305322i
$109$	1.94749	−	9.16223i	0.186536	−	0.877583i	−0.780937	−	0.624609i	$-0.785258\pi$
$109$	1.94749	−	9.16223i	0.186536	−	0.877583i	0.967473	−	0.252973i	$-0.0814085\pi$
$110$	1.87935	−	1.88430i	0.179189	−	0.179661i
$111$	8.36772	+	2.71884i	0.794229	+	0.258061i
$112$	−1.85901	−	1.88257i	−0.175660	−	0.177886i
$113$	−5.21707	+	10.2391i	−0.490781	+	0.963211i	0.504242	+	0.863562i	$0.331772\pi$
$113$	−5.21707	+	10.2391i	−0.490781	+	0.963211i	−0.995023	+	0.0996489i	$0.968228\pi$
$114$	−0.555119	−	2.61163i	−0.0519917	−	0.244602i
$115$	−14.5802	+	0.783348i	−1.35961	+	0.0730475i
$116$	3.63640	+	0.772941i	0.337631	+	0.0717658i
$117$	−0.268637	−	0.699824i	−0.0248355	−	0.0646987i
$118$	7.89824	−	7.89824i	0.727092	−	0.727092i
$119$	−2.32757	−	2.12244i	−0.213368	−	0.194564i
$120$	0.421135	+	3.95677i	0.0384442	+	0.361202i
$121$	1.00175	−	9.53099i	0.0910680	−	0.866454i
$122$	13.9910	+	5.37065i	1.26669	+	0.486235i
$123$	−0.841083	+	16.0488i	−0.0758379	+	1.44707i
$124$	−2.71075	−	4.69516i	−0.243433	−	0.421638i
$125$	3.49684	+	10.6194i	0.312767	+	0.949830i
$126$	0.0889672	+	0.431912i	0.00792583	+	0.0384777i
$127$	−0.517773	−	1.01619i	−0.0459449	−	0.0901720i	0.866893	−	0.498495i	$-0.166114\pi$
$127$	−0.517773	−	1.01619i	−0.0459449	−	0.0901720i	−0.912838	+	0.408323i	$0.866114\pi$
$128$	−0.777146	+	0.629320i	−0.0686906	+	0.0556246i
$129$	−2.11606	+	0.942130i	−0.186309	+	0.0829500i
$130$	4.07831	−	9.19256i	0.357692	−	0.806241i
$131$	1.29633	−	2.91162i	0.113261	−	0.254389i	−0.848017	−	0.529969i	$-0.822203\pi$
$131$	1.29633	−	2.91162i	0.113261	−	0.254389i	0.961278	+	0.275580i	$0.0888700\pi$
$132$	−1.49760	−	1.49760i	−0.130349	−	0.130349i
$133$	1.82443	−	3.52559i	0.158198	−	0.305707i
$134$	−9.15736	+	2.97541i	−0.791075	+	0.257036i
$135$	−5.10513	+	10.0520i	−0.439380	+	0.865143i
$136$	−0.884772	+	0.796652i	−0.0758686	+	0.0683124i
$137$	−3.91866	+	2.54481i	−0.334794	+	0.217418i	−0.701077	−	0.713086i	$-0.747297\pi$
$137$	−3.91866	+	2.54481i	−0.334794	+	0.217418i	0.366283	+	0.930504i	$0.380630\pi$
$138$	0.608145	+	11.6041i	0.0517687	+	0.987806i
$139$	0.781698	−	2.40582i	0.0663027	−	0.204059i	−0.912416	−	0.409263i	$-0.865786\pi$
$139$	0.781698	−	2.40582i	0.0663027	−	0.204059i	0.978719	+	0.205204i	$0.0657858\pi$
$140$	−3.24680	+	4.94553i	−0.274405	+	0.417974i
$141$	2.69535	+	8.29545i	0.226990	+	0.698603i
$142$	−1.76000	+	0.675600i	−0.147696	+	0.0566951i
$143$	1.38539	+	5.17036i	0.115852	+	0.432367i
$144$	0.165761	−	0.0174222i	0.0138135	−	0.00145185i
$145$	−0.0109334	−	8.31289i	−0.000907966	−	0.690348i
$146$	−5.01118	+	6.89730i	−0.414728	+	0.570825i
$147$	−5.79449	+	11.0268i	−0.477921	+	0.909478i
$148$	4.40534	−	2.24464i	0.362117	−	0.184508i
$149$	18.2297	−	10.5249i	1.49343	−	0.862235i	0.493463	−	0.869767i	$-0.335731\pi$
$149$	18.2297	−	10.5249i	1.49343	−	0.862235i	0.999972	+	0.00753181i	$0.00239747\pi$
$150$	8.45484	−	2.77175i	0.690334	−	0.226313i
$151$	−6.38792	+	11.0642i	−0.519841	+	0.900392i	0.479893	+	0.877327i	$0.340676\pi$
$151$	−6.38792	+	11.0642i	−0.519841	+	0.900392i	−0.999734	+	0.0230645i	$0.992658\pi$
$152$	−1.25834	−	0.817174i	−0.102065	−	0.0662815i
$153$	0.195996	−	0.0310427i	0.0158453	−	0.00250965i
$154$	−0.309426	−	3.13366i	−0.0249343	−	0.252517i
$155$	−8.99837	+	8.12362i	−0.722766	+	0.652505i
$156$	−7.31138	−	3.25524i	−0.585379	−	0.260628i
$157$	13.1571	−	3.52543i	1.05005	−	0.281360i	0.307777	−	0.951459i	$-0.400415\pi$
$157$	13.1571	−	3.52543i	1.05005	−	0.281360i	0.742272	+	0.670099i	$0.233748\pi$
$158$	−7.55808	+	9.33345i	−0.601289	+	0.742530i
$159$	−3.75393	+	4.16916i	−0.297706	+	0.330636i
$160$	1.73960	+	1.40492i	0.137527	+	0.111068i
$161$	−10.2426	+	13.9127i	−0.807233	+	1.09648i
$162$	8.43983	+	4.30031i	0.663096	+	0.337864i
$163$	−6.20855	+	0.325376i	−0.486291	+	0.0254854i	−0.293906	−	0.955834i	$-0.594955\pi$
$163$	−6.20855	+	0.325376i	−0.486291	+	0.0254854i	−0.192385	+	0.981320i	$0.561622\pi$
$164$	6.04293	+	6.71136i	0.471874	+	0.524069i
$165$	−2.57409	+	3.97519i	−0.200393	+	0.309468i
$166$	6.48935	+	5.84304i	0.503671	+	0.453508i
$167$	11.0243	+	1.74608i	0.853086	+	0.135116i	0.567638	−	0.823278i	$-0.307857\pi$
$167$	11.0243	+	1.74608i	0.853086	+	0.135116i	0.285449	+	0.958394i	$0.407857\pi$
$168$	3.93237	+	2.58905i	0.303389	+	0.199750i
$169$	4.24803	+	5.84691i	0.326771	+	0.449762i
$170$	2.15583	+	1.56198i	0.165345	+	0.119798i
$171$	0.101716	+	0.228457i	0.00777840	+	0.0174706i
$172$	−0.466472	+	1.21520i	−0.0355681	+	0.0926581i
$173$	12.1754	−	18.7484i	0.925675	−	1.42541i	0.0207774	−	0.999784i	$-0.493386\pi$
$173$	12.1754	−	18.7484i	0.925675	−	1.42541i	0.904897	−	0.425630i	$-0.139947\pi$
$174$	−6.61560			−0.501527
$175$	12.3326	+	4.78600i	0.932261	+	0.361788i
$176$	−1.19017			−0.0897126
$177$	−10.8257	+	16.6701i	−0.813709	+	1.25300i
$178$	−2.43645	+	6.34717i	−0.182620	+	0.475740i
$179$	0.710571	+	1.59597i	0.0531105	+	0.119288i	0.938152	−	0.346225i	$-0.112537\pi$
$179$	0.710571	+	1.59597i	0.0531105	+	0.119288i	−0.885041	+	0.465513i	$0.845870\pi$
$180$	−0.115635	−	0.354303i	−0.00861895	−	0.0264082i
$181$	0.588748	+	0.810342i	0.0437613	+	0.0602322i	0.830337	−	0.557262i	$-0.188148\pi$
$181$	0.588748	+	0.810342i	0.0437613	+	0.0602322i	−0.786576	+	0.617494i	$0.788148\pi$
$182$	−5.33525	−	10.6360i	−0.395475	−	0.788396i
$183$	−26.3402	−	4.17188i	−1.94712	−	0.308394i
$184$	4.85265	+	4.36934i	0.357742	+	0.322112i
$185$	−6.96884	−	8.58269i	−0.512359	−	0.631012i
$186$	6.45554	+	7.16961i	0.473343	+	0.525701i
$187$	−1.41505	+	0.0741597i	−0.103479	+	0.00542309i
$188$	4.36730	+	2.22525i	0.318518	+	0.162293i
$189$	5.34893	+	12.2204i	0.389077	+	0.888901i
$190$	−1.19820	+	3.13373i	−0.0869265	+	0.227344i
$191$	−5.43228	+	6.03316i	−0.393066	+	0.436544i	−0.906900	−	0.421345i	$-0.861558\pi$
$191$	−5.43228	+	6.03316i	−0.393066	+	0.436544i	0.513834	+	0.857890i	$0.328225\pi$
$192$	1.11989	−	1.38294i	0.0808208	−	0.0998053i
$193$	−19.1910	+	5.14220i	−1.38140	+	0.370144i	−0.871628	−	0.490168i	$-0.836935\pi$
$193$	−19.1910	+	5.14220i	−1.38140	+	0.370144i	−0.509768	+	0.860312i	$0.670269\pi$
$194$	2.89081	+	1.28707i	0.207548	+	0.0924062i
$195$	−3.69775	+	17.5097i	−0.264801	+	1.25390i
$196$	2.07912	+	6.68411i	0.148509	+	0.477436i
$197$	−3.44399	+	0.545474i	−0.245374	+	0.0388634i	−0.277910	−	0.960607i	$-0.589642\pi$
$197$	−3.44399	+	0.545474i	−0.245374	+	0.0388634i	0.0325358	+	0.999471i	$0.489642\pi$
$198$	0.166368	+	0.108041i	0.0118233	+	0.00767812i
$199$	−8.86693	+	15.3580i	−0.628560	+	1.08870i	0.359281	+	0.933229i	$0.383022\pi$
$199$	−8.86693	+	15.3580i	−0.628560	+	1.08870i	−0.987841	+	0.155468i	$0.950311\pi$
$200$	2.25823	−	4.46099i	0.159681	−	0.315440i
$201$	14.8387	−	8.56713i	1.04664	−	0.604279i
$202$	17.6642	−	9.00036i	1.24285	−	0.633263i
$203$	−7.60485	−	6.23797i	−0.533756	−	0.437820i
$204$	1.24531	−	1.71403i	0.0871893	−	0.120006i
$205$	11.8482	−	16.3529i	0.827516	−	1.14213i
$206$	6.67189	−	0.701243i	0.464852	−	0.0488579i
$207$	−0.281690	−	1.05128i	−0.0195788	−	0.0730690i
$208$	−4.19874	+	1.61175i	−0.291130	+	0.111755i
$209$	−0.551820	−	1.69833i	−0.0381702	−	0.117476i
$210$	3.82172	−	9.80959i	0.263724	−	0.676926i
$211$	5.06946	−	15.6022i	0.348996	−	1.07410i	−0.610413	−	0.792083i	$-0.708997\pi$
$211$	5.06946	−	15.6022i	0.348996	−	1.07410i	0.959409	−	0.282017i	$-0.0910034\pi$
$212$	0.164996	+	3.14831i	0.0113320	+	0.216227i
$213$	2.81354	−	1.82714i	0.192781	−	0.125193i
$214$	−11.5876	+	10.4336i	−0.792114	+	0.713223i
$215$	2.87535	+	0.451535i	0.196097	+	0.0307944i
$216$	4.79518	−	1.55805i	0.326270	−	0.106012i
$217$	0.660504	+	14.3287i	0.0448379	+	0.972699i
$218$	6.62341	+	6.62341i	0.448594	+	0.448594i
$219$	6.17073	−	13.8597i	0.416979	−	0.936551i
$220$	0.556740	+	2.60242i	0.0375354	+	0.175455i
$221$	−4.89165	+	2.17790i	−0.329048	+	0.146502i
$222$	−6.83759	+	5.53697i	−0.458909	+	0.371617i
$223$	1.17648	+	2.30897i	0.0787830	+	0.154620i	0.927038	−	0.374968i	$-0.122346\pi$
$223$	1.17648	+	2.30897i	0.0787830	+	0.154620i	−0.848255	+	0.529589i	$0.822346\pi$
$224$	2.59135	−	0.533778i	0.173142	−	0.0356645i
$225$	−0.720623	+	0.418583i	−0.0480416	+	0.0279056i
$226$	−5.74579	−	9.95200i	−0.382204	−	0.661997i
$227$	0.483778	−	9.23103i	0.0321095	−	0.612685i	−0.934427	−	0.356155i	$-0.884087\pi$
$227$	0.483778	−	9.23103i	0.0321095	−	0.612685i	0.966536	−	0.256530i	$-0.0825792\pi$
$228$	2.49264	+	0.956834i	0.165079	+	0.0633679i
$229$	−0.467757	+	4.45041i	−0.0309103	+	0.294092i	0.968136	+	0.250425i	$0.0805705\pi$
$229$	−0.467757	+	4.45041i	−0.0309103	+	0.294092i	−0.999046	+	0.0436662i	$0.986096\pi$
$230$	7.28399	−	12.6546i	0.480292	−	0.834423i
$231$	1.69799	+	5.34005i	0.111720	+	0.351350i
$232$	−2.62877	+	2.62877i	−0.172587	+	0.172587i
$233$	−9.60244	−	25.0152i	−0.629077	−	1.63880i	−0.761925	−	0.647665i	$-0.775746\pi$
$233$	−9.60244	−	25.0152i	−0.629077	−	1.63880i	0.132849	−	0.991136i	$-0.457588\pi$
$234$	0.733232	+	0.155853i	0.0479329	+	0.0101884i
$235$	2.82277	−	10.5904i	0.184137	−	0.690843i
$236$	2.32233	+	10.9257i	0.151171	+	0.711203i
$237$	9.70260	−	19.0424i	0.630252	−	1.23694i
$238$	3.04771	−	0.796101i	0.197554	−	0.0516035i
$239$	28.6642	+	9.31356i	1.85413	+	0.602444i	0.996036	+	0.0889546i	$0.0283526\pi$
$239$	28.6642	+	9.31356i	1.85413	+	0.602444i	0.858096	+	0.513489i	$0.171647\pi$
$240$	−3.54779	−	1.80182i	−0.229009	−	0.116307i
$241$	2.57539	−	12.1163i	0.165895	−	0.780477i	−0.813984	−	0.580887i	$-0.802706\pi$
$241$	2.57539	−	12.1163i	0.165895	−	0.780477i	0.979880	−	0.199590i	$-0.0639609\pi$
$242$	7.44777	+	6.03109i	0.478761	+	0.387693i
$243$	−1.67121	−	0.447799i	−0.107208	−	0.0287263i
$244$	−12.1243	+	8.80878i	−0.776176	+	0.563925i
$245$	13.6428	−	7.67288i	0.871609	−	0.490202i
$246$	−13.0016	−	9.44621i	−0.828951	−	0.602268i
$247$	−4.24664	−	5.24416i	−0.270207	−	0.333678i
$248$	5.41408	+	0.283740i	0.343794	+	0.0180175i
$249$	−13.4574	−	7.76962i	−0.852826	−	0.492379i
$250$	−10.8107	−	2.85105i	−0.683729	−	0.180316i
$251$			18.9280i			1.19472i	0.801972	+	0.597362i	$0.203784\pi$
$251$			18.9280i			1.19472i	−0.801972	+	0.597362i	$0.796216\pi$
$252$	−0.410687	−	0.160622i	−0.0258708	−	0.0101182i
$253$	1.21576	+	7.67599i	0.0764341	+	0.482586i
$254$	1.13425	+	0.119214i	0.0711689	+	0.00748015i
$255$	−4.33041	−	1.92120i	−0.271181	−	0.120310i
$256$	−0.104528	−	0.994522i	−0.00653303	−	0.0621576i
$257$	−2.23142	+	8.32779i	−0.139192	+	0.519473i	0.860753	+	0.509023i	$0.169993\pi$
$257$	−2.23142	+	8.32779i	−0.139192	+	0.519473i	−0.999945	+	0.0104503i	$0.996673\pi$
$258$	0.362352	−	2.28780i	0.0225590	−	0.142432i
$259$	−13.0810	−	0.0823594i	−0.812811	−	0.00511756i
$260$	5.48832	+	8.42699i	0.340371	+	0.522620i
$261$	0.606096	−	0.128830i	0.0375164	−	0.00797435i
$262$	1.73585	+	2.67298i	0.107241	+	0.165137i
$263$	−11.8419	−	18.2350i	−0.730204	−	1.12442i	−0.987429	−	0.158064i	$-0.949475\pi$
$263$	−11.8419	−	18.2350i	−0.730204	−	1.12442i	0.257225	−	0.966352i	$-0.417192\pi$
$264$	2.07165	−	0.440342i	0.127501	−	0.0271012i
$265$	6.80689	−	1.83350i	0.418144	−	0.112631i
$266$	1.96315	+	3.45027i	0.120369	+	0.211549i
$267$	1.89262	−	11.9495i	0.115826	−	0.731298i
$268$	2.49207	−	9.30053i	0.152227	−	0.568120i
$269$	−0.280339	−	2.66725i	−0.0170926	−	0.162625i	0.982646	−	0.185491i	$-0.0593876\pi$
$269$	−0.280339	−	2.66725i	−0.0170926	−	0.162625i	−0.999739	+	0.0228659i	$0.992721\pi$
$270$	−5.64990	−	9.75626i	−0.343842	−	0.593747i
$271$	22.0148	+	2.31384i	1.33730	+	0.140556i	0.746028	−	0.665915i	$-0.231959\pi$
$271$	22.0148	+	2.31384i	1.33730	+	0.140556i	0.591274	+	0.806471i	$0.298625\pi$
$272$	−0.186247	−	1.17592i	−0.0112929	−	0.0713006i
$273$	13.2218	+	16.5394i	0.800222	+	1.00101i
$274$		−	4.67247i		−	0.282274i
$275$	5.42999	−	2.43472i	0.327441	−	0.146819i
$276$	−10.0632	−	5.81001i	−0.605735	−	0.349722i
$277$	−12.2572	−	0.642374i	−0.736465	−	0.0385965i	−0.319585	−	0.947558i	$-0.603543\pi$
$277$	−12.2572	−	0.642374i	−0.736465	−	0.0385965i	−0.416881	+	0.908961i	$0.636877\pi$
$278$	1.59195	+	1.96589i	0.0954786	+	0.117906i
$279$	−0.731050	−	0.531139i	−0.0437668	−	0.0317985i
$280$	−2.37934	−	5.41653i	−0.142193	−	0.323699i
$281$	−10.2519	+	7.44843i	−0.611576	+	0.444336i	−0.849969	−	0.526833i	$-0.823379\pi$
$281$	−10.2519	+	7.44843i	−0.611576	+	0.444336i	0.238393	+	0.971169i	$0.423379\pi$
$282$	−8.42514	−	2.25751i	−0.501710	−	0.134433i
$283$	4.38451	+	3.55051i	0.260632	+	0.211056i	0.750726	−	0.660614i	$-0.229704\pi$
$283$	4.38451	+	3.55051i	0.260632	+	0.211056i	−0.490093	+	0.871670i	$0.663037\pi$
$284$	0.391958	−	1.84402i	0.0232584	−	0.109422i
$285$	0.926196	−	5.89797i	0.0548631	−	0.349365i
$286$	−5.09077	−	1.65409i	−0.301024	−	0.0978085i
$287$	−6.03875	−	23.1182i	−0.356456	−	1.36462i
$288$	−0.0756687	+	0.148508i	−0.00445882	+	0.00875092i
$289$	3.23979	+	15.2420i	0.190576	+	0.896589i
$290$	6.97773	+	4.51836i	0.409747	+	0.265327i
$291$	−5.50801	−	1.17076i	−0.322885	−	0.0686314i
$292$	−3.05528	−	7.95927i	−0.178797	−	0.465781i
$293$	5.35633	−	5.35633i	0.312920	−	0.312920i	−0.533120	−	0.846040i	$-0.678980\pi$
$293$	5.35633	−	5.35633i	0.312920	−	0.312920i	0.846040	+	0.533120i	$0.178980\pi$
$294$	−6.09197	−	10.8653i	−0.355291	−	0.633678i
$295$	22.8037	−	10.1888i	1.32768	−	0.593216i
$296$	−0.516813	+	4.91715i	−0.0300392	+	0.285803i
$297$	5.60221	+	2.15049i	0.325073	+	0.124784i
$298$	−1.10166	+	21.0210i	−0.0638176	+	1.21771i
$299$	14.6839	+	25.4333i	0.849195	+	1.47085i
$300$	−2.28025	+	8.60043i	−0.131650	+	0.496546i
$301$	2.57374	−	2.28823i	0.148348	−	0.131891i
$302$	−5.80011	−	11.3834i	−0.333759	−	0.655038i
$303$	−27.4168	+	22.2017i	−1.57506	+	1.27546i
$304$	1.37068	−	0.610266i	0.0786138	−	0.0350011i
$305$	24.9327	+	22.3902i	1.42764	+	1.28206i
$306$	−0.0807125	+	0.181283i	−0.00461402	+	0.0103633i
$307$	−22.2591	−	22.2591i	−1.27039	−	1.27039i	−0.945881	−	0.324514i	$-0.894799\pi$
$307$	−22.2591	−	22.2591i	−1.27039	−	1.27039i	−0.324514	−	0.945881i	$-0.605201\pi$
$308$	2.79663	+	1.44721i	0.159353	+	0.0824622i
$309$	−11.3538	+	3.68908i	−0.645897	+	0.209865i
$310$	−1.91218	−	11.9711i	−0.108605	−	0.679913i
$311$	13.6607	−	12.3001i	0.774624	−	0.697475i	−0.183755	−	0.982972i	$-0.558825\pi$
$311$	13.6607	−	12.3001i	0.774624	−	0.697475i	0.958380	+	0.285497i	$0.0921587\pi$
$312$	6.71214	−	4.35891i	0.380000	−	0.246775i
$313$	−0.851297	−	16.2437i	−0.0481182	−	0.918150i	−0.910914	−	0.412597i	$-0.864622\pi$
$313$	−0.851297	−	16.2437i	−0.0481182	−	0.918150i	0.862796	−	0.505553i	$-0.168711\pi$
$314$	−4.20918	+	12.9545i	−0.237538	+	0.731067i
$315$	−0.159103	+	0.973140i	−0.00896442	+	0.0548302i
$316$	−3.71127	−	11.4221i	−0.208775	−	0.642543i
$317$	−21.0433	+	8.07775i	−1.18191	+	0.453692i	−0.868386	−	0.495889i	$-0.834842\pi$
$317$	−21.0433	+	8.07775i	−1.18191	+	0.453692i	−0.313522	+	0.949581i	$0.601509\pi$
$318$	−1.45202	−	5.41900i	−0.0814250	−	0.303882i
$319$	−4.40039	+	0.462500i	−0.246375	+	0.0258950i
$320$	−2.12572	+	0.693779i	−0.118831	+	0.0387834i
$321$	16.3095	−	22.4482i	0.910310	−	1.25293i
$322$	−6.08965	−	16.1676i	−0.339363	−	0.900985i
$323$	1.59164	−	0.810980i	0.0885611	−	0.0451242i
$324$	−8.20320	+	4.73612i	−0.455734	+	0.263118i
$325$	15.8591	−	15.9427i	0.879702	−	0.884342i
$326$	3.10853	−	5.38414i	0.172166	−	0.298200i
$327$	−13.9794	−	9.07836i	−0.773065	−	0.502034i
$328$	−8.91984	+	1.41276i	−0.492516	+	0.0780068i
$329$	−7.55633	−	10.5393i	−0.416594	−	0.581051i
$330$	−1.93192	−	4.32386i	−0.106349	−	0.238021i
$331$	12.4562	+	5.54584i	0.684652	+	0.304827i	0.719427	−	0.694568i	$-0.244405\pi$
$331$	12.4562	+	5.54584i	0.684652	+	0.304827i	−0.0347746	+	0.999395i	$0.511071\pi$
$332$	−8.43474	+	2.26008i	−0.462916	+	0.124038i
$333$	0.518609	−	0.640429i	0.0284196	−	0.0350953i
$334$	−7.46865	+	8.29478i	−0.408666	+	0.453870i
$335$	−21.5022	−	1.09853i	−1.17479	−	0.0600189i
$336$	−4.31308	+	1.88786i	−0.235298	+	0.102991i
$337$	15.9182	+	8.11072i	0.867119	+	0.441819i	0.830178	−	0.557498i	$-0.188239\pi$
$337$	15.9182	+	8.11072i	0.867119	+	0.441819i	0.0369408	+	0.999317i	$0.488239\pi$
$338$	−7.21727	+	0.378241i	−0.392568	+	0.0205736i
$339$	13.6834	+	15.1969i	0.743178	+	0.825383i
$340$	−2.48413	+	0.957320i	−0.134721	+	0.0519180i
$341$	4.79516	+	4.31758i	0.259672	+	0.233810i
$342$	−0.246999	−	0.0391208i	−0.0133562	−	0.00211541i
$343$	3.24218	−	18.2343i	0.175061	−	0.984558i
$344$	−0.765094	−	1.05306i	−0.0412511	−	0.0567773i
$345$	−7.99673	+	24.7220i	−0.430529	+	1.33099i
$346$	9.09256	+	20.4222i	0.488819	+	1.09791i
$347$	9.46059	−	24.6457i	0.507871	−	1.32305i	−0.404819	−	0.914397i	$-0.632666\pi$
$347$	9.46059	−	24.6457i	0.507871	−	1.32305i	0.912690	−	0.408652i	$-0.134001\pi$
$348$	3.60311	−	5.54831i	0.193147	−	0.297421i
$349$	−30.8264			−1.65010			−0.825049	−	0.565061i	$-0.808853\pi$
$349$	−30.8264			−1.65010			−0.825049	+	0.565061i	$0.808853\pi$
$350$	−10.7307	+	7.73639i	−0.573581	+	0.413527i
$351$	22.6760			1.21035
$352$	0.648214	−	0.998162i	0.0345499	−	0.0532022i
$353$	−11.2714	+	29.3630i	−0.599916	+	1.56283i	0.210884	+	0.977511i	$0.432366\pi$
$353$	−11.2714	+	29.3630i	−0.599916	+	1.56283i	−0.810800	+	0.585323i	$0.800968\pi$
$354$	−8.08463	−	18.1584i	−0.429693	−	0.965107i
$355$	−4.21546	+	0.00554429i	−0.223733	+	0.000294261i
$356$	−3.99620	−	5.50029i	−0.211798	−	0.291515i
$357$	−5.01040	+	2.51331i	−0.265178	+	0.133019i
$358$	−1.72550	−	0.273292i	−0.0911953	−	0.0144439i
$359$	9.28204	+	8.35759i	0.489888	+	0.441097i	0.876683	−	0.481069i	$-0.159751\pi$
$359$	9.28204	+	8.35759i	0.489888	+	0.441097i	−0.386795	+	0.922166i	$0.626418\pi$
$360$	0.360123	+	0.0959872i	0.0189801	+	0.00505897i
$361$	−11.2071	−	12.4468i	−0.589850	−	0.655094i
$362$	−1.00026	+	0.0524217i	−0.0525727	+	0.00275522i
$363$	−15.1952	−	7.74234i	−0.797541	−	0.406367i
$364$	11.8259	+	1.31828i	0.619847	+	0.0690969i
$365$	−15.9745	+	10.4038i	−0.836142	+	0.544562i
$366$	17.8447	−	19.8186i	0.932759	−	1.03593i
$367$	−13.2959	+	16.4191i	−0.694040	+	0.857068i	−0.995337	−	0.0964623i	$-0.969247\pi$
$367$	−13.2959	+	16.4191i	−0.694040	+	0.857068i	0.301296	+	0.953531i	$0.402581\pi$
$368$	−6.30738	+	1.69006i	−0.328795	+	0.0881003i
$369$	1.37511	+	0.612237i	0.0715852	+	0.0318718i
$370$	10.9935	−	1.17009i	0.571527	−	0.0608301i
$371$	3.44053	−	7.59845i	0.178624	−	0.394492i
$372$	−9.52888	+	1.50923i	−0.494049	+	0.0782497i
$373$	24.9618	+	16.2104i	1.29248	+	0.839343i	0.993379	−	0.114880i	$-0.0366484\pi$
$373$	24.9618	+	16.2104i	1.29248	+	0.839343i	0.299096	+	0.954223i	$0.403315\pi$
$374$	0.708496	−	1.22715i	0.0366355	−	0.0634545i
$375$	19.8723	+	0.962852i	1.02620	+	0.0497215i
$376$	−4.24485	+	2.45077i	−0.218912	+	0.126389i
$377$	−14.8976	+	7.59070i	−0.767265	+	0.390941i
$378$	−13.1621	−	2.16971i	−0.676985	−	0.111598i
$379$	3.55065	−	4.88706i	0.182385	−	0.251031i	−0.708029	−	0.706184i	$-0.750415\pi$
$379$	3.55065	−	4.88706i	0.182385	−	0.251031i	0.890413	+	0.455153i	$0.150415\pi$
$380$	−1.97558	−	2.71164i	−0.101345	−	0.139104i
$381$	−2.01841	+	0.212143i	−0.103406	+	0.0108684i
$382$	−2.10120	−	7.84179i	−0.107507	−	0.401221i
$383$	22.7068	−	8.71632i	1.16026	−	0.445383i	0.299353	−	0.954142i	$-0.403229\pi$
$383$	22.7068	−	8.71632i	1.16026	−	0.445383i	0.860909	+	0.508759i	$0.169896\pi$
$384$	0.549900	+	1.69242i	0.0280620	+	0.0863659i
$385$	1.85624	−	6.79207i	0.0946026	−	0.346156i
$386$	6.13953	−	18.8955i	0.312494	−	0.961758i
$387$	0.0113544	+	0.216655i	0.000577178	+	0.0110132i
$388$	−2.65387	+	1.72345i	−0.134730	+	0.0874947i
$389$	−0.813032	+	0.732057i	−0.0412223	+	0.0371168i	−0.689484	−	0.724301i	$-0.742163\pi$
$389$	−0.813032	+	0.732057i	−0.0412223	+	0.0371168i	0.648262	+	0.761417i	$0.275496\pi$
$390$	−12.6710	−	12.6377i	−0.641619	−	0.639934i
$391$	−7.39383	+	2.40240i	−0.373922	+	0.121495i
$392$	−6.73813	−	1.89673i	−0.340327	−	0.0957993i
$393$	−4.01043	−	4.01043i	−0.202299	−	0.202299i
$394$	1.41826	−	3.18546i	0.0714508	−	0.160481i
$395$	−23.2394	+	13.4581i	−1.16930	+	0.677149i
$396$	−0.181221	+	0.0806849i	−0.00910671	+	0.00405457i
$397$	−18.8085	+	15.2308i	−0.943971	+	0.764413i	−0.971948	−	0.235196i	$-0.924427\pi$
$397$	−18.8085	+	15.2308i	−0.943971	+	0.764413i	0.0279768	+	0.999609i	$0.491094\pi$
$398$	−8.05100	−	15.8010i	−0.403560	−	0.792032i
$399$	−4.69365	−	5.27930i	−0.234977	−	0.264296i
$400$	2.51138	+	4.32354i	0.125569	+	0.216177i
$401$	−7.70862	−	13.3517i	−0.384950	−	0.666753i	0.606812	−	0.794845i	$-0.292448\pi$
$401$	−7.70862	−	13.3517i	−0.384950	−	0.666753i	−0.991762	+	0.128092i	$0.959115\pi$
$402$	−0.896738	+	17.1108i	−0.0447252	+	0.853408i
$403$	22.7635	+	8.73810i	1.13393	+	0.435276i
$404$	−2.07228	+	19.7164i	−0.103100	+	0.980927i
$405$	14.1933	+	15.7216i	0.705269	+	0.781212i
$406$	9.37350	−	2.98052i	0.465199	−	0.147921i
$407$	−4.16096	+	4.16096i	−0.206251	+	0.206251i
$408$	0.759257	+	1.97793i	0.0375888	+	0.0979222i
$409$	−4.95656	−	1.05355i	−0.245086	−	0.0520946i	0.0837307	−	0.996488i	$-0.473316\pi$
$409$	−4.95656	−	1.05355i	−0.245086	−	0.0520946i	−0.328817	+	0.944394i	$0.606650\pi$
$410$	7.26167	+	18.8432i	0.358628	+	0.930598i
$411$	1.72873	+	8.13303i	0.0852719	+	0.401173i
$412$	−3.04566	+	5.97744i	−0.150049	+	0.294487i
$413$	7.82832	−	28.4968i	0.385206	−	1.40224i
$414$	1.03510	+	0.336323i	0.0508722	+	0.0165294i
$415$	8.88748	+	17.3861i	0.436269	+	0.853450i
$416$	0.935075	−	4.39918i	0.0458458	−	0.215688i
$417$	−3.49833	−	2.83289i	−0.171314	−	0.138727i
$418$	1.72488	+	0.462180i	0.0843666	+	0.0226060i
$419$	17.9948	−	13.0740i	0.879104	−	0.638707i	−0.0539099	−	0.998546i	$-0.517168\pi$
$419$	17.9948	−	13.0740i	0.879104	−	0.638707i	0.933014	+	0.359839i	$0.117168\pi$
$420$	6.14556	+	8.54785i	0.299873	+	0.417092i
$421$	0.193191	+	0.140361i	0.00941555	+	0.00684080i	0.592483	−	0.805583i	$-0.298148\pi$
$421$	0.193191	+	0.140361i	0.00941555	+	0.00684080i	−0.583068	+	0.812424i	$0.698148\pi$
$422$	10.3241	+	12.7492i	0.502568	+	0.620620i
$423$	0.815841	+	0.0427564i	0.0396676	+	0.00207889i
$424$	−2.73026	−	1.57632i	−0.132593	−	0.0765527i
$425$	3.25530	+	4.98397i	0.157905	+	0.241758i
$426$			3.35476i			0.162539i
$427$	39.2004	−	5.95598i	1.89704	−	0.288230i
$428$	−2.43924	−	15.4007i	−0.117905	−	0.744422i
$429$	9.47312	+	0.995665i	0.457367	+	0.0480712i
$430$	−1.94472	+	2.16555i	−0.0937826	+	0.104432i
$431$	1.26337	+	12.0202i	0.0608544	+	0.578991i	0.981882	+	0.189494i	$0.0606847\pi$
$431$	1.26337	+	12.0202i	0.0608544	+	0.578991i	−0.921028	+	0.389498i	$0.872649\pi$
$432$	−1.30495	+	4.87015i	−0.0627845	+	0.234315i
$433$	−0.00205175	+	0.0129542i	−9.86007e−5	+	0.000622540i	−0.987738	−	0.156123i	$-0.950100\pi$
$433$	−0.00205175	+	0.0129542i	−9.86007e−5	+	0.000622540i	0.987639	+	0.156746i	$0.0501003\pi$
$434$	−12.3768	−	7.25005i	−0.594107	−	0.348014i
$435$	−13.8174	−	5.28314i	−0.662491	−	0.253307i
$436$	−9.16223	+	1.94749i	−0.438791	+	0.0932680i
$437$	−5.33605	−	8.21679i	−0.255258	−	0.393062i
$438$	8.26289	+	12.7237i	0.394816	+	0.607963i
$439$	−38.5207	+	8.18783i	−1.83849	+	0.390784i	−0.990305	−	0.138909i	$-0.955640\pi$
$439$	−38.5207	+	8.18783i	−1.83849	+	0.390784i	−0.848189	+	0.529693i	$0.822307\pi$
$440$	−2.48579	−	0.950458i	−0.118506	−	0.0453113i
$441$	0.769710	+	0.876805i	0.0366528	+	0.0417526i
$442$	0.837641	−	5.28866i	0.0398425	−	0.251556i
$443$	−0.935559	+	3.49155i	−0.0444497	+	0.165889i	−0.984583	−	0.174919i	$-0.944034\pi$
$443$	−0.935559	+	3.49155i	−0.0444497	+	0.165889i	0.940133	+	0.340807i	$0.110700\pi$
$444$	−0.919677	−	8.75014i	−0.0436459	−	0.415263i
$445$	−10.1576	+	11.3110i	−0.481514	+	0.536192i
$446$	−2.57723	−	0.270877i	−0.122035	−	0.0128264i
$447$	−5.85980	−	36.9973i	−0.277159	−	1.74991i
$448$	−0.963685	+	2.46400i	−0.0455298	+	0.116413i
$449$		−	6.78785i		−	0.320338i	−0.987090	−	0.160169i	$-0.948796\pi$
$449$		−	6.78785i		−	0.320338i	0.987090	−	0.160169i	$-0.0512040\pi$
$450$	0.0414261	−	0.832342i	0.00195284	−	0.0392370i
$451$	−9.30845	−	5.37423i	−0.438318	−	0.253063i
$452$	11.4758	+	0.601423i	0.539778	+	0.0282886i
$453$	14.3075	+	17.6683i	0.672224	+	0.830127i
$454$	7.47831	+	5.43331i	0.350974	+	0.254998i
$455$	−2.64939	−	26.4751i	−0.124205	−	1.24117i
$456$	−2.16006	+	1.56937i	−0.101154	+	0.0734926i
$457$	20.6124	+	5.52308i	0.964209	+	0.258359i	0.706381	−	0.707832i	$-0.250327\pi$
$457$	20.6124	+	5.52308i	0.964209	+	0.258359i	0.257828	+	0.966191i	$0.416993\pi$
$458$	−3.47767	−	2.81616i	−0.162501	−	0.131591i
$459$	−1.24806	+	5.87166i	−0.0582544	+	0.274065i
$460$	6.64594	+	13.0011i	0.309868	+	0.606179i
$461$	7.11038	+	2.31030i	0.331164	+	0.107602i	0.469879	−	0.882731i	$-0.344297\pi$
$461$	7.11038	+	2.31030i	0.331164	+	0.107602i	−0.138716	+	0.990332i	$0.544297\pi$
$462$	−5.40334	−	1.48434i	−0.251386	−	0.0690580i
$463$	−6.20767	+	12.1832i	−0.288495	+	0.566203i	−0.989082	−	0.147364i	$-0.952921\pi$
$463$	−6.20767	+	12.1832i	−0.288495	+	0.566203i	0.700588	+	0.713566i	$0.252921\pi$
$464$	−0.772941	−	3.63640i	−0.0358829	−	0.168816i
$465$	7.75749	+	20.1298i	0.359745	+	0.933496i
$466$	26.2094	+	5.57098i	1.21413	+	0.258071i
$467$	−2.40429	−	6.26340i	−0.111257	−	0.289835i	0.866636	−	0.498942i	$-0.166278\pi$
$467$	−2.40429	−	6.26340i	−0.111257	−	0.289835i	−0.977893	+	0.209106i	$0.932945\pi$
$468$	−0.530056	+	0.530056i	−0.0245019	+	0.0245019i
$469$	−17.1649	+	18.8239i	−0.792602	+	0.869205i
$470$	7.34448	+	8.13533i	0.338776	+	0.375255i
$471$	2.53368	−	24.1064i	0.116746	−	1.11076i
$472$	−10.4279	−	4.00290i	−0.479983	−	0.184248i
$473$	0.0810785	−	1.54707i	0.00372799	−	0.0711343i
$474$	10.6859	+	18.5085i	0.490820	+	0.850125i
$475$	−5.00512	+	5.58824i	−0.229651	+	0.256406i
$476$	−0.992238	+	2.98962i	−0.0454791	+	0.137029i
$477$	0.238556	+	0.468192i	0.0109227	+	0.0214370i
$478$	−23.4226	+	18.9673i	−1.07133	+	0.867543i
$479$	33.2011	−	14.7821i	1.51700	−	0.675411i	0.531807	−	0.846866i	$-0.321513\pi$
$479$	33.2011	−	14.7821i	1.51700	−	0.675411i	0.985192	+	0.171454i	$0.0548466\pi$
$480$	3.44340	−	1.99409i	0.157169	−	0.0910173i
$481$	−9.04440	+	20.3141i	−0.412389	+	0.926242i
$482$	8.75889	+	8.75889i	0.398956	+	0.398956i
$483$	16.5815	+	25.8887i	0.754486	+	1.17798i
$484$	−9.11444	+	2.96146i	−0.414293	+	0.134612i
$485$	5.00990	+	4.99674i	0.227488	+	0.226890i
$486$	1.28576	−	1.15771i	0.0583234	−	0.0525146i
$487$	24.8552	−	16.1411i	1.12629	−	0.731424i	0.159556	−	0.987189i	$-0.448994\pi$
$487$	24.8552	−	16.1411i	1.12629	−	0.731424i	0.966739	+	0.255764i	$0.0823271\pi$
$488$	−0.784328	−	14.9659i	−0.0355048	−	0.677473i
$489$	−3.41877	+	10.5219i	−0.154602	+	0.475816i
$490$	−0.995400	+	15.6208i	−0.0449676	+	0.705676i
$491$	−11.5247	−	35.4694i	−0.520103	−	1.60071i	−0.773800	−	0.633430i	$-0.781647\pi$
$491$	−11.5247	−	35.4694i	−0.520103	−	1.60071i	0.253697	−	0.967284i	$-0.418353\pi$
$492$	15.0034	−	5.75928i	0.676407	−	0.259648i
$493$	−1.14557	−	4.27533i	−0.0515939	−	0.192551i
$494$	6.71101	−	0.705355i	0.301942	−	0.0317354i
$495$	0.261197	+	0.358514i	0.0117399	+	0.0161140i
$496$	−3.18668	+	4.38609i	−0.143086	+	0.196941i
$497$	−3.16327	+	3.85641i	−0.141892	+	0.172984i
$498$	13.8456	−	7.05466i	0.620434	−	0.316127i
$499$	14.3310	−	8.27403i	0.641545	−	0.370396i	−0.143664	−	0.989626i	$-0.545889\pi$
$499$	14.3310	−	8.27403i	0.641545	−	0.370396i	0.785210	+	0.619230i	$0.212555\pi$
$500$	8.27903	−	7.51383i	0.370249	−	0.336029i
$501$	9.93123	−	17.2014i	0.443695	−	0.768502i
$502$	−15.8743	−	10.3089i	−0.708507	−	0.460110i
$503$	−26.8746	+	4.25652i	−1.19828	+	0.189789i	−0.723506	−	0.690318i	$-0.757470\pi$
$503$	−26.8746	+	4.25652i	−1.19828	+	0.189789i	−0.474775	+	0.880107i	$0.657470\pi$
$504$	0.358385	−	0.256950i	0.0159637	−	0.0114455i
$505$	44.0811	−	4.69173i	1.96158	−	0.208779i
$506$	−7.09978	−	3.16103i	−0.315624	−	0.140525i
$507$	12.4226	−	3.32864i	0.551709	−	0.147830i
$508$	−0.717736	+	0.886330i	−0.0318444	+	0.0393245i
$509$	5.74290	−	6.37813i	0.254549	−	0.282706i	−0.602303	−	0.798268i	$-0.705750\pi$
$509$	5.74290	−	6.37813i	0.254549	−	0.282706i	0.856852	+	0.515562i	$0.172417\pi$
$510$	3.96976	−	2.58542i	0.175784	−	0.114484i
$511$	−2.49898	+	22.4176i	−0.110548	+	0.991695i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$	−7.55454	+	0.395917i	−0.333541	+	0.0174802i
$514$	−5.76895	−	6.40707i	−0.254458	−	0.282604i
$515$	14.4949	+	3.86347i	0.638722	+	0.170245i
$516$	1.72136	+	1.54992i	0.0757786	+	0.0682313i
$517$	−5.76184	−	0.912586i	−0.253406	−	0.0401355i
$518$	7.19347	−	10.9258i	0.316063	−	0.480050i
$519$	−23.3826	−	32.1834i	−1.02638	−	1.41269i
$520$	−10.0566	+	0.0132268i	−0.441012	+	0.000580032i
$521$	−9.66748	−	21.7135i	−0.423540	−	0.951286i	−0.991724	−	0.128385i	$-0.959021\pi$
$521$	−9.66748	−	21.7135i	−0.423540	−	0.951286i	0.568185	−	0.822901i	$-0.307646\pi$
$522$	−0.222058	+	0.578480i	−0.00971920	+	0.0253194i
$523$	7.96110	−	12.2590i	0.348115	−	0.536050i	−0.620632	−	0.784102i	$-0.713124\pi$
$523$	7.96110	−	12.2590i	0.348115	−	0.536050i	0.968747	+	0.248052i	$0.0797905\pi$
$524$	−3.18716			−0.139232
$525$	15.8159	−	17.4363i	0.690261	−	0.760985i
$526$	21.7427			0.948026
$527$	−3.51550	+	5.41339i	−0.153138	+	0.235811i
$528$	−0.758998	+	1.97726i	−0.0330311	+	0.0860490i
$529$	7.98803	+	17.9414i	0.347306	+	0.780062i
$530$	−2.16960	+	6.70733i	−0.0942412	+	0.291348i
$531$	1.09429	+	1.50616i	0.0474882	+	0.0653619i
$532$	−3.96285	−	0.232711i	−0.171811	−	0.0100893i
$533$	−40.1166	−	6.35385i	−1.73764	−	0.275216i
$534$	8.99091	+	8.09545i	0.389075	+	0.350324i
$535$	−32.5341	+	12.5378i	−1.40657	+	0.542055i
$536$	6.44280	+	7.15546i	0.278287	+	0.309069i
$537$	3.10456	−	0.162703i	0.133972	−	0.00702116i
$538$	2.38963	+	1.21758i	0.103024	+	0.0524935i
$539$	−4.81170	−	6.80121i	−0.207255	−	0.292949i
$540$	11.2594	+	0.575234i	0.484530	+	0.0247541i
$541$	25.2629	−	28.0573i	1.08614	−	1.20628i	0.108916	−	0.994051i	$-0.465262\pi$
$541$	25.2629	−	28.0573i	1.08614	−	1.20628i	0.977221	−	0.212226i	$-0.0680713\pi$
$542$	−13.9306	+	17.2029i	−0.598373	+	0.738929i
$543$	1.72169	−	0.461327i	0.0738850	−	0.0197974i
$544$	1.08765	+	0.484252i	0.0466325	+	0.0207621i
$545$	8.54429	+	19.1231i	0.365997	+	0.819142i
$546$	−21.0723	+	2.08073i	−0.901810	+	0.0890472i
$547$	17.6435	−	2.79446i	0.754383	−	0.119483i	0.232614	−	0.972569i	$-0.425272\pi$
$547$	17.6435	−	2.79446i	0.754383	−	0.119483i	0.521769	+	0.853087i	$0.325272\pi$
$548$	3.91866	+	2.54481i	0.167397	+	0.108709i
$549$	−1.24893	+	2.16320i	−0.0533028	+	0.0923232i
$550$	−0.915455	+	5.88002i	−0.0390351	+	0.250725i
$551$	4.83063	−	2.78897i	0.205792	−	0.118814i
$552$	10.3535	−	5.27538i	0.440675	−	0.224535i
$553$	−5.16824	+	31.3521i	−0.219776	+	1.33323i
$554$	7.21450	−	9.92991i	0.306515	−	0.421881i
$555$	−18.7028	+	6.10411i	−0.793889	+	0.259105i
$556$	−2.51577	+	0.264418i	−0.106692	+	0.0112138i
$557$	2.49253	+	9.30227i	0.105612	+	0.394150i	0.998414	−	0.0563000i	$-0.0179303\pi$
$557$	2.49253	+	9.30227i	0.105612	+	0.394150i	−0.892802	+	0.450450i	$0.851264\pi$
$558$	0.843609	−	0.323831i	0.0357128	−	0.0137089i
$559$	−1.80903	−	5.56762i	−0.0765138	−	0.235485i
$560$	5.83856	+	0.954571i	0.246724	+	0.0403380i
$561$	−0.779205	+	2.39815i	−0.0328981	+	0.101250i
$562$	−0.663203	−	12.6547i	−0.0279755	−	0.533805i
$563$	−1.70474	+	1.10707i	−0.0718463	+	0.0466575i	−0.580062	−	0.814572i	$-0.696972\pi$
$563$	−1.70474	+	1.10707i	−0.0718463	+	0.0466575i	0.508216	+	0.861230i	$0.330305\pi$
$564$	6.48197	−	5.83639i	0.272940	−	0.245756i
$565$	−4.05311	−	25.3743i	−0.170516	−	1.06750i
$566$	−5.36569	+	1.74342i	−0.225537	+	0.0732813i
$567$	25.0346	−	1.15401i	1.05136	−	0.0484637i
$568$	1.33305	+	1.33305i	0.0559334	+	0.0559334i
$569$	−5.17236	+	11.6173i	−0.216837	+	0.487023i	−0.988911	−	0.148509i	$-0.952553\pi$
$569$	−5.17236	+	11.6173i	−0.216837	+	0.487023i	0.772074	+	0.635532i	$0.219219\pi$
$570$	4.44201	+	3.98904i	0.186055	+	0.167082i
$571$	−40.2631	+	17.9263i	−1.68496	+	0.750193i	−0.685199	+	0.728356i	$0.740285\pi$
$571$	−40.2631	+	17.9263i	−1.68496	+	0.750193i	−0.999762	+	0.0218366i	$0.993049\pi$
$572$	4.15987	−	3.36860i	0.173933	−	0.140848i
$573$	6.55874	+	12.8722i	0.273995	+	0.537746i
$574$	22.6775	+	7.52653i	0.946539	+	0.314151i
$575$	25.3192	−	20.6136i	1.05588	−	0.859647i
$576$	−0.0833373	−	0.144344i	−0.00347239	−	0.00601435i
$577$	−1.09815	+	20.9540i	−0.0457166	+	0.872325i	0.875486	+	0.483243i	$0.160541\pi$
$577$	−1.09815	+	20.9540i	−0.0457166	+	0.872325i	−0.921203	+	0.389082i	$0.872792\pi$
$578$	−14.5475	−	5.58428i	−0.605098	−	0.232275i
$579$	−3.69564	+	35.1616i	−0.153585	+	1.46127i
$580$	−7.58976	+	3.39115i	−0.315148	+	0.140810i
$581$	22.5679	+	4.94566i	0.936274	+	0.205181i
$582$	3.98176	−	3.98176i	0.165049	−	0.165049i
$583$	−1.34466	−	3.50296i	−0.0556901	−	0.145078i
$584$	8.33923	+	1.77256i	0.345080	+	0.0733490i
$585$	1.40697	+	0.911066i	0.0581709	+	0.0376679i
$586$	1.57493	+	7.40947i	0.0650598	+	0.306082i
$587$	−18.6464	+	36.5956i	−0.769619	+	1.51046i	0.0879689	+	0.996123i	$0.471962\pi$
$587$	−18.6464	+	36.5956i	−0.769619	+	1.51046i	−0.857587	+	0.514338i	$0.828038\pi$
$588$	12.4303	+	0.808512i	0.512619	+	0.0333425i
$589$	−7.73628	−	2.51367i	−0.318768	−	0.103574i
$590$	−3.87472	+	24.6740i	−0.159520	+	1.01581i
$591$	−1.29010	+	6.06943i	−0.0530675	+	0.249663i
$592$	−3.84239	−	3.11151i	−0.157921	−	0.127882i
$593$	1.36327	+	0.365286i	0.0559827	+	0.0150005i	0.286702	−	0.958020i	$-0.407441\pi$
$593$	1.36327	+	0.365286i	0.0559827	+	0.0150005i	−0.230719	+	0.973020i	$0.574108\pi$
$594$	−4.85473	+	3.52717i	−0.199192	+	0.144722i
$595$	7.00122	+	0.771133i	0.287022	+	0.0316134i
$596$	−17.0297	−	12.3728i	−0.697563	−	0.506809i
$597$	19.8599	+	24.5249i	0.812811	+	1.00374i
$598$	−29.3276	−	1.53700i	−1.19930	−	0.0628525i
$599$	−7.54025	−	4.35336i	−0.308086	−	0.177874i	0.337984	−	0.941152i	$-0.390255\pi$
$599$	−7.54025	−	4.35336i	−0.308086	−	0.177874i	−0.646070	+	0.763278i	$0.723589\pi$
$600$	−5.97101	−	6.59650i	−0.243766	−	0.269301i
$601$			27.0501i			1.10340i	0.834043	+	0.551699i	$0.186020\pi$
$601$			27.0501i			1.10340i	−0.834043	+	0.551699i	$0.813980\pi$
$602$	0.517312	+	3.40478i	0.0210840	+	0.138769i
$603$	−0.251053	−	1.58509i	−0.0102237	−	0.0645497i
$604$	12.7058	+	1.33544i	0.516994	+	0.0543382i
$605$	10.7391	+	18.5442i	0.436605	+	0.753931i
$606$	−3.68765	−	35.0856i	−0.149800	−	1.42526i
$607$	−10.6024	+	39.5687i	−0.430338	+	1.60604i	0.321645	+	0.946860i	$0.395764\pi$
$607$	−10.6024	+	39.5687i	−0.430338	+	1.60604i	−0.751983	+	0.659183i	$0.770902\pi$
$608$	−0.234713	+	1.48192i	−0.00951889	+	0.0600999i
$609$	−15.2130	+	8.65601i	−0.616464	+	0.350759i
$610$	−32.3573	+	8.71575i	−1.31011	+	0.352890i
$611$	−21.5627	+	4.58330i	−0.872335	+	0.185421i
$612$	−0.108078	−	0.166425i	−0.00436878	−	0.00672733i
$613$	14.3056	+	22.0287i	0.577799	+	0.889733i	0.999858	−	0.0168355i	$-0.00535917\pi$
$613$	14.3056	+	22.0287i	0.577799	+	0.889733i	−0.422059	+	0.906568i	$0.638693\pi$
$614$	30.7912	−	6.54488i	1.24263	−	0.264130i
$615$	−19.6115	−	30.1123i	−0.790812	−	1.21424i
$616$	−2.73688	+	1.55725i	−0.110272	+	0.0627433i
$617$	4.28106	−	27.0295i	0.172349	−	1.08817i	−0.738144	−	0.674643i	$-0.764297\pi$
$617$	4.28106	−	27.0295i	0.172349	−	1.08817i	0.910493	−	0.413525i	$-0.135703\pi$
$618$	3.08981	−	11.5313i	0.124290	−	0.463858i
$619$	−1.25158	−	11.9079i	−0.0503051	−	0.478621i	−0.990453	−	0.137853i	$-0.955980\pi$
$619$	−1.25158	−	11.9079i	−0.0503051	−	0.478621i	0.940148	−	0.340768i	$-0.110687\pi$
$620$	11.0813	+	4.91624i	0.445034	+	0.197441i
$621$	32.7429	+	3.44142i	1.31393	+	0.138100i
$622$	2.87561	+	18.1559i	0.115302	+	0.727985i
$623$	2.70199	+	17.7837i	0.108253	+	0.712488i
$624$			8.00330i			0.320389i
$625$	−20.3025	−	14.5880i	−0.812098	−	0.583521i
$626$	14.0868	+	8.13301i	0.563021	+	0.325060i
$627$	−3.17337	−	0.166309i	−0.126732	−	0.00664176i
$628$	−8.57210	−	10.5857i	−0.342064	−	0.422414i
$629$	−4.76228	−	3.46000i	−0.189884	−	0.137959i
$630$	−0.729490	−	0.663445i	−0.0290636	−	0.0264323i
$631$	−26.1646	+	19.0097i	−1.04160	+	0.756763i	−0.970596	−	0.240713i	$-0.922619\pi$
$631$	−26.1646	+	19.0097i	−1.04160	+	0.756763i	−0.0709990	+	0.997476i	$0.522619\pi$
$632$	11.6007	+	3.10839i	0.461450	+	0.123645i
$633$	−22.6874	−	18.3719i	−0.901742	−	0.730216i
$634$	4.68641	−	22.0478i	0.186121	−	0.875631i
$635$	2.27378	+	1.15479i	0.0902324	+	0.0458263i
$636$	5.33558	+	1.73363i	0.211569	+	0.0687431i
$637$	−26.1852	−	17.4776i	−1.03750	−	0.692486i
$638$	2.00874	−	3.94237i	0.0795268	−	0.156080i
$639$	−0.0653294	−	0.307350i	−0.00258439	−	0.0121586i
$640$	0.575896	−	2.16064i	0.0227643	−	0.0854066i
$641$	−24.0543	−	5.11290i	−0.950087	−	0.201947i	−0.293298	−	0.956021i	$-0.594753\pi$
$641$	−24.0543	−	5.11290i	−0.950087	−	0.201947i	−0.656790	+	0.754074i	$0.728086\pi$
$642$	9.94380	+	25.9045i	0.392450	+	1.02237i
$643$	−16.3346	+	16.3346i	−0.644173	+	0.644173i	−0.951579	−	0.307406i	$-0.900539\pi$
$643$	−16.3346	+	16.3346i	−0.644173	+	0.644173i	0.307406	+	0.951579i	$0.400539\pi$
$644$	16.8760	+	3.69830i	0.665006	+	0.145733i
$645$	2.58382	−	4.48893i	0.101738	−	0.176751i
$646$	−0.186723	+	1.77655i	−0.00734652	+	0.0698975i
$647$	−36.4158	−	13.9787i	−1.43165	−	0.549560i	−0.485776	−	0.874083i	$-0.661463\pi$
$647$	−36.4158	−	13.9787i	−1.43165	−	0.549560i	−0.945878	+	0.324523i	$0.894796\pi$
$648$	0.495739	−	9.45926i	0.0194745	−	0.371595i
$649$	−6.64698	−	11.5129i	−0.260917	−	0.451921i
$650$	4.73322	+	21.9835i	0.185652	+	0.862265i
$651$	24.2259	+	8.04044i	0.949486	+	0.315130i
$652$	2.82249	+	5.53945i	0.110537	+	0.216942i
$653$	1.67500	−	1.35639i	0.0655477	−	0.0530795i	−0.595987	−	0.802994i	$-0.703239\pi$
$653$	1.67500	−	1.35639i	0.0655477	−	0.0530795i	0.661534	+	0.749915i	$0.269906\pi$
$654$	15.2275	−	6.77972i	0.595443	−	0.265108i
$655$	1.49089	+	6.96902i	0.0582540	+	0.272302i
$656$	3.67325	−	8.25025i	0.143416	−	0.322118i
$657$	−1.00479	−	1.00479i	−0.0392006	−	0.0392006i
$658$	12.9545	−	0.597155i	0.505018	−	0.0232795i
$659$	18.0102	−	5.85188i	0.701579	−	0.227957i	0.0635605	−	0.997978i	$-0.479754\pi$
$659$	18.0102	−	5.85188i	0.701579	−	0.227957i	0.638018	+	0.770021i	$0.279754\pi$
$660$	4.67850	+	0.734695i	0.182110	+	0.0285980i
$661$	−7.44379	+	6.70242i	−0.289530	+	0.260694i	−0.801077	−	0.598561i	$-0.795739\pi$
$661$	−7.44379	+	6.70242i	−0.289530	+	0.260694i	0.511547	+	0.859255i	$0.329073\pi$
$662$	−11.4352	+	7.42613i	−0.444443	+	0.288625i
$663$	0.498686	+	9.51550i	0.0193674	+	0.369551i
$664$	2.69842	−	8.30490i	0.104719	−	0.322292i
$665$	1.34490	+	8.77398i	0.0521529	+	0.340240i
$666$	0.254654	+	0.783745i	0.00986765	+	0.0303695i
$667$	−22.6634	+	8.69965i	−0.877529	+	0.336852i
$668$	−2.88887	−	10.7814i	−0.111774	−	0.417145i
$669$	4.58621	−	0.482031i	0.177313	−	0.0186364i
$670$	12.6322	−	17.4350i	0.488026	−	0.673571i
$671$	10.4840	−	14.4299i	0.404729	−	0.557062i
$672$	0.765781	−	4.64546i	0.0295406	−	0.179203i
$673$	−37.3395	+	19.0254i	−1.43933	+	0.733377i	−0.987336	−	0.158643i	$-0.949288\pi$
$673$	−37.3395	+	19.0254i	−1.43933	+	0.733377i	−0.451996	+	0.892020i	$0.649288\pi$
$674$	−15.4719	+	8.93270i	−0.595955	+	0.344075i
$675$	−4.00915	−	24.8889i	−0.154312	−	0.957974i
$676$	3.61359	−	6.25892i	0.138984	−	0.240728i
$677$	−14.3893	−	9.34450i	−0.553024	−	0.359138i	0.237673	−	0.971345i	$-0.423615\pi$
$677$	−14.3893	−	9.34450i	−0.553024	−	0.359138i	−0.790698	+	0.612207i	$0.790282\pi$
$678$	−20.1977	+	3.19900i	−0.775687	+	0.122857i
$679$	8.33165	−	0.822690i	0.319739	−	0.0315719i
$680$	0.550080	−	2.60476i	0.0210946	−	0.0998881i
$681$	−15.0272	−	6.69053i	−0.575843	−	0.256382i
$682$	−6.23266	+	1.67004i	−0.238661	+	0.0639490i
$683$	28.2183	−	34.8467i	1.07974	−	1.33337i	0.140515	−	0.990079i	$-0.455124\pi$
$683$	28.2183	−	34.8467i	1.07974	−	1.33337i	0.939228	−	0.343293i	$-0.111543\pi$
$684$	0.167335	−	0.185844i	0.00639820	−	0.00710592i
$685$	3.73138	−	9.75893i	0.142569	−	0.372869i
$686$	13.5267	+	12.6502i	0.516453	+	0.482987i
$687$	7.09526	+	3.61522i	0.270701	+	0.137929i
$688$	1.29987	−	0.0681234i	0.0495571	−	0.00259718i
$689$	−9.48750	−	10.5369i	−0.361445	−	0.401425i
$690$	−16.3783	−	20.1712i	−0.623510	−	0.767904i
$691$	14.4535	+	13.0140i	0.549838	+	0.495076i	0.896578	−	0.442885i	$-0.146045\pi$
$691$	14.4535	+	13.0140i	0.549838	+	0.495076i	−0.346741	+	0.937961i	$0.612712\pi$
$692$	−22.0797	−	3.49708i	−0.839343	−	0.132939i
$693$	0.523939	+	0.0307674i	0.0199028	+	0.00116876i
$694$	15.5170	+	21.3573i	0.589017	+	0.810712i
$695$	1.75500	+	5.37727i	0.0665711	+	0.203971i
$696$	2.69081	+	6.04365i	0.101995	+	0.229084i
$697$	3.85322	−	10.0380i	0.145951	−	0.380216i
$698$	16.7893	−	25.8532i	0.635483	−	0.978557i
$699$	−47.6820			−1.80350
$700$	−0.643910	−	13.2131i	−0.0243375	−	0.499407i
$701$	−9.44330			−0.356668			−0.178334	−	0.983970i	$-0.557071\pi$
$701$	−9.44330			−0.356668			−0.178334	+	0.983970i	$0.557071\pi$
$702$	−12.3502	+	19.0177i	−0.466129	+	0.717776i
$703$	2.65848	−	6.92558i	0.100267	−	0.261203i
$704$	0.484086	+	1.08728i	0.0182447	+	0.0409782i
$705$	−15.7939	−	11.4433i	−0.594834	−	0.430978i
$706$	−18.4870	−	25.4452i	−0.695769	−	0.957643i
$707$	28.8438	−	43.8092i	1.08478	−	1.64762i
$708$	19.6321	+	3.10942i	0.737820	+	0.116859i
$709$	−24.1144	−	21.7127i	−0.905637	−	0.815439i	0.0777479	−	0.996973i	$-0.475227\pi$
$709$	−24.1144	−	21.7127i	−0.905637	−	0.815439i	−0.983385	+	0.181534i	$0.941894\pi$
$710$	2.29125	−	3.53840i	0.0859892	−	0.132794i
$711$	−1.33943	−	1.48759i	−0.0502325	−	0.0557889i
$712$	6.78942	−	0.355818i	0.254444	−	0.0133349i
$713$	31.5432	+	16.0721i	1.18130	+	0.601904i
$714$	0.621014	−	5.57092i	0.0232408	−	0.208486i
$715$	−9.31165	−	7.52017i	−0.348236	−	0.281238i
$716$	1.16897	−	1.29828i	0.0436866	−	0.0485189i
$717$	33.7526	−	41.6809i	1.26051	−	1.55660i
$718$	−12.0646	+	3.23271i	−0.450248	+	0.120644i
$719$	12.9172	+	5.75111i	0.481731	+	0.214480i	0.633210	−	0.773980i	$-0.281737\pi$
$719$	12.9172	+	5.75111i	0.481731	+	0.214480i	−0.151479	+	0.988460i	$0.548404\pi$
$720$	−0.276639	+	0.249746i	−0.0103097	+	0.00930749i
$721$	14.4250	−	10.3422i	0.537213	−	0.385164i
$722$	16.5426	−	2.62009i	0.615652	−	0.0975097i
$723$	−18.4866	−	12.0053i	−0.687524	−	0.446483i
$724$	0.500819	−	0.867443i	0.0186128	−	0.0322383i
$725$	10.9654	+	15.0094i	0.407244	+	0.557434i
$726$	14.7692	−	8.52698i	0.548135	−	0.316466i
$727$	25.1670	−	12.8232i	0.933393	−	0.475588i	0.0799650	−	0.996798i	$-0.474519\pi$
$727$	25.1670	−	12.8232i	0.933393	−	0.475588i	0.853428	+	0.521210i	$0.174519\pi$
$728$	−7.54646	+	9.20006i	−0.279691	+	0.340977i
$729$	14.8932	−	20.4988i	0.551601	−	0.759214i
$730$	−0.0250731	−	19.0637i	−0.000927996	−	0.705577i
$731$	1.54123	−	0.161990i	0.0570046	−	0.00599142i
$732$	6.90232	+	25.7598i	0.255117	+	0.952110i
$733$	3.61243	−	1.38668i	0.133428	−	0.0512182i	−0.290738	−	0.956803i	$-0.593901\pi$
$733$	3.61243	−	1.38668i	0.133428	−	0.0512182i	0.424166	+	0.905585i	$0.360567\pi$
$734$	−6.52872	−	20.0933i	−0.240980	−	0.741659i
$735$	−4.04679	−	27.5583i	−0.149268	−	1.01650i
$736$	2.01784	−	6.21028i	0.0743787	−	0.228914i
$737$	0.599755	+	11.4440i	0.0220922	+	0.421545i
$738$	−1.26240	+	0.819813i	−0.0464697	+	0.0301777i
$739$	5.20284	−	4.68465i	0.191389	−	0.172328i	−0.567865	−	0.823122i	$-0.692230\pi$
$739$	5.20284	−	4.68465i	0.191389	−	0.172328i	0.759254	+	0.650794i	$0.225564\pi$
$740$	−5.00620	+	9.85724i	−0.184031	+	0.362359i
$741$	−11.4204	+	3.71071i	−0.419539	+	0.136316i
$742$	4.49875	+	7.02389i	0.165154	+	0.257855i
$743$	−25.4586	−	25.4586i	−0.933985	−	0.933985i	0.0639667	−	0.997952i	$-0.479625\pi$
$743$	−25.4586	−	25.4586i	−0.933985	−	0.933985i	−0.997952	+	0.0639667i	$0.979625\pi$
$744$	3.92406	−	8.81357i	0.143863	−	0.323121i
$745$	−19.0881	+	43.0247i	−0.699332	+	1.57630i
$746$	−27.1904	+	12.1059i	−0.995511	+	0.443230i
$747$	−1.13110	+	0.915944i	−0.0413847	+	0.0335126i
$748$	0.643301	+	1.26255i	0.0235214	+	0.0461634i
$749$	−12.9951	+	39.1542i	−0.474830	+	1.43066i
$750$	−11.6307	+	16.1419i	−0.424694	+	0.589418i
$751$	−4.61288	−	7.98974i	−0.168326	−	0.291550i	0.769505	−	0.638640i	$-0.220503\pi$
$751$	−4.61288	−	7.98974i	−0.168326	−	0.291550i	−0.937832	+	0.347091i	$0.887170\pi$
$752$	0.256526	−	4.89481i	0.00935455	−	0.178496i
$753$	31.4454	+	12.0708i	1.14594	+	0.439884i
$754$	1.74771	−	16.6284i	0.0636479	−	0.605569i
$755$	−3.02350	−	28.4072i	−0.110036	−	1.03384i
$756$	8.98826	−	9.85696i	0.326900	−	0.358494i
$757$	−23.4358	+	23.4358i	−0.851789	+	0.851789i	−0.990353	−	0.138564i	$-0.955751\pi$
$757$	−23.4358	+	23.4358i	−0.851789	+	0.851789i	0.138564	+	0.990353i	$0.455751\pi$
$758$	2.16481	+	5.63951i	0.0786293	+	0.204836i
$759$	13.5276	+	2.87538i	0.491021	+	0.104370i
$760$	3.35015	−	0.179993i	0.121523	−	0.00652902i
$761$	1.83858	+	8.64984i	0.0666485	+	0.313556i	0.998826	−	0.0484455i	$-0.0154267\pi$
$761$	1.83858	+	8.64984i	0.0666485	+	0.313556i	−0.932177	+	0.362002i	$0.882093\pi$
$762$	0.921385	−	1.80832i	0.0333783	−	0.0655085i
$763$	23.8972	+	6.56478i	0.865138	+	0.237661i
$764$	7.72108	+	2.50873i	0.279339	+	0.0907627i
$765$	−0.313347	+	0.314172i	−0.0113291	+	0.0113589i
$766$	−5.05688	+	23.7908i	−0.182713	+	0.859595i
$767$	−39.0405	−	31.6144i	−1.40967	−	1.14153i
$768$	−1.71888	−	0.460572i	−0.0620247	−	0.0166195i
$769$	−20.4004	+	14.8217i	−0.735657	+	0.534486i	−0.891348	−	0.453320i	$-0.850240\pi$
$769$	−20.4004	+	14.8217i	−0.735657	+	0.534486i	0.155691	+	0.987806i	$0.450240\pi$
$770$	4.68533	+	5.25600i	0.168847	+	0.189413i
$771$	12.4121	+	9.01792i	0.447011	+	0.324772i
$772$	12.5033	+	15.4403i	0.450004	+	0.555708i
$773$	39.6465	+	2.07779i	1.42599	+	0.0747327i	0.749637	−	0.661849i	$-0.230228\pi$
$773$	39.6465	+	2.07779i	1.42599	+	0.0747327i	0.676348	+	0.736582i	$0.263561\pi$
$774$	−0.187887	−	0.108476i	−0.00675345	−	0.00389910i
$775$	5.56621	−	26.5299i	0.199944	−	0.952983i
$776$		−	3.16438i		−	0.113595i
$777$	−8.47883	+	21.6791i	−0.304176	+	0.777735i
$778$	−0.171146	−	1.08057i	−0.00613588	−	0.0387404i
$779$	13.4759	+	1.41637i	0.482823	+	0.0507468i
$780$	17.5000	−	3.74379i	0.626599	−	0.134049i
$781$	0.234533	+	2.23143i	0.00839226	+	0.0798470i
$782$	2.01215	−	7.50943i	0.0719542	−	0.268537i
$783$	−2.93223	+	18.5134i	−0.104789	+	0.661614i
$784$	5.26058	−	4.61804i	0.187878	−	0.164930i
$785$	−19.1367	+	23.6955i	−0.683017	+	0.845727i
$786$	5.54766	−	1.17919i	0.197879	−	0.0420604i
$787$	3.58896	+	5.52651i	0.127932	+	0.196999i	0.896832	−	0.442370i	$-0.145862\pi$
$787$	3.58896	+	5.52651i	0.127932	+	0.196999i	−0.768900	+	0.639369i	$0.779196\pi$
$788$	1.89911	+	2.92438i	0.0676531	+	0.104177i
$789$	−37.8459	+	8.04440i	−1.34735	+	0.286388i
$790$	1.37021	−	26.8200i	0.0487498	−	0.954213i
$791$	−26.2343	−	15.3674i	−0.932784	−	0.546402i
$792$	0.0310321	−	0.195929i	0.00110268	−	0.00696203i
$793$	17.4446	−	65.1042i	0.619476	−	2.31192i
$794$	−2.52980	−	24.0694i	−0.0897792	−	0.854192i
$795$	1.29487	−	12.4777i	0.0459242	−	0.442538i
$796$	17.6367	+	1.85369i	0.625117	+	0.0657024i
$797$	2.81826	+	17.7938i	0.0998278	+	0.630288i	0.985976	+	0.166886i	$0.0533712\pi$
$797$	2.81826	+	17.7938i	0.0998278	+	0.630288i	−0.886148	+	0.463402i	$0.846629\pi$
$798$	6.98394	−	1.06112i	0.247229	−	0.0375632i
$799$		−	5.83566i		−	0.206451i
$800$	−4.99382	−	0.248545i	−0.176558	−	0.00878738i
$801$	−0.981360	−	0.566588i	−0.0346746	−	0.0200194i
$802$	15.3961	+	0.806875i	0.543655	+	0.0284918i
$803$	6.38562	+	7.88558i	0.225343	+	0.278276i
$804$	−13.8619	−	10.0713i	−0.488872	−	0.355186i
$805$	0.192415	−	38.6308i	0.00678173	−	1.36156i
$806$	−19.7263	+	14.3320i	−0.694829	+	0.504823i
$807$	−4.60994	−	1.23523i	−0.162277	−	0.0434821i
$808$	−15.4069	−	12.4763i	−0.542013	−	0.438914i
$809$	8.13941	−	38.2929i	0.286166	−	1.34631i	−0.566591	−	0.823999i	$-0.691738\pi$
$809$	8.13941	−	38.2929i	0.286166	−	1.34631i	0.852757	−	0.522308i	$-0.174929\pi$
$810$	−20.9154	+	3.34088i	−0.734894	+	0.117387i
$811$	−45.4626	−	14.7717i	−1.59641	−	0.518704i	−0.630192	−	0.776439i	$-0.717024\pi$
$811$	−45.4626	−	14.7717i	−1.59641	−	0.518704i	−0.966216	+	0.257735i	$0.917024\pi$
$812$	−2.60550	+	9.48459i	−0.0914351	+	0.332844i
$813$	17.8833	−	35.0980i	0.627195	−	1.23094i
$814$	−1.22345	−	5.75590i	−0.0428820	−	0.201744i
$815$	10.7922	−	8.76288i	0.378034	−	0.306950i
$816$	−2.07235	−	0.440493i	−0.0725469	−	0.0154203i
$817$	0.699892	+	1.82328i	0.0244861	+	0.0637885i
$818$	3.58311	−	3.58311i	0.125281	−	0.125281i
$819$	1.89004	−	0.600982i	0.0660434	−	0.0210000i
$820$	−19.7582	−	4.17258i	−0.689986	−	0.145713i
$821$	−4.19047	+	39.8697i	−0.146249	+	1.39146i	0.637532	+	0.770424i	$0.279955\pi$
$821$	−4.19047	+	39.8697i	−0.146249	+	1.39146i	−0.783781	+	0.621038i	$0.786711\pi$
$822$	−7.76247	−	2.97973i	−0.270747	−	0.103930i
$823$	−2.04787	+	39.0757i	−0.0713842	+	1.36209i	0.694676	+	0.719323i	$0.255548\pi$
$823$	−2.04787	+	39.0757i	−0.0713842	+	1.36209i	−0.766060	+	0.642769i	$0.777785\pi$
$824$	−3.35432	−	5.80985i	−0.116853	−	0.202396i
$825$	−0.582035	−	10.5736i	−0.0202638	−	0.368127i
$826$	19.6358	+	22.0858i	0.683217	+	0.768465i
$827$	−8.49208	−	16.6666i	−0.295298	−	0.579556i	0.694919	−	0.719088i	$-0.255440\pi$
$827$	−8.49208	−	16.6666i	−0.295298	−	0.579556i	−0.990218	+	0.139532i	$0.955440\pi$
$828$	−0.845818	+	0.684930i	−0.0293942	+	0.0238030i
$829$	−17.5603	+	7.81833i	−0.609893	+	0.271542i	−0.688353	−	0.725375i	$-0.741666\pi$
$829$	−17.5603	+	7.81833i	−0.609893	+	0.271542i	0.0784606	+	0.996917i	$0.475000\pi$
$830$	−19.4217	−	2.01548i	−0.674136	−	0.0699583i
$831$	−8.88388	+	19.9535i	−0.308178	+	0.692180i
$832$	3.18019	+	3.18019i	0.110253	+	0.110253i
$833$	5.96680	−	5.81839i	0.206737	−	0.201595i
$834$	4.28119	−	1.39104i	0.148246	−	0.0481679i
$835$	−22.2231	+	11.3601i	−0.769064	+	0.393133i
$836$	−1.32705	+	1.19488i	−0.0458971	+	0.0413260i
$837$	22.9250	−	14.8877i	0.792405	−	0.514594i
$838$	1.16410	+	22.2123i	0.0402131	+	0.767312i
$839$	5.59267	−	17.2125i	0.193080	−	0.594240i	−0.806913	−	0.590670i	$-0.798864\pi$
$839$	5.59267	−	17.2125i	0.193080	−	0.594240i	0.999994	−	0.00357029i	$-0.00113646\pi$
$840$	−10.5159	+	0.498608i	−0.362834	+	0.0172036i
$841$	4.69061	+	14.4362i	0.161745	+	0.497801i
$842$	−0.222936	+	0.0855772i	−0.00768289	+	0.00294919i
$843$	5.83639	+	21.7817i	0.201016	+	0.750202i
$844$	−16.3153	+	1.71480i	−0.561594	+	0.0590259i
$845$	−15.3761	−	4.97364i	−0.528953	−	0.171098i
$846$	−0.480197	+	0.660935i	−0.0165095	+	0.0227234i
$847$	25.0179	+	4.12407i	0.859625	+	0.141705i
$848$	2.80902	−	1.43127i	0.0964620	−	0.0491499i
$849$	8.69463	−	5.01985i	0.298399	−	0.172281i
$850$	−5.95287	+	0.0156588i	−0.204182	+	0.000537093i
$851$	−16.1426	+	27.9598i	−0.553362	+	0.958451i
$852$	−2.81354	−	1.82714i	−0.0963903	−	0.0625966i
$853$	36.2784	−	5.74594i	1.24215	−	0.196737i	0.499439	−	0.866349i	$-0.333540\pi$
$853$	36.2784	−	5.74594i	1.24215	−	0.196737i	0.742711	+	0.669612i	$0.233540\pi$
$854$	−16.3550	+	36.1201i	−0.559655	+	1.23600i
$855$	−0.484641	−	0.278958i	−0.0165744	−	0.00954017i
$856$	14.2446	+	6.34212i	0.486872	+	0.216769i
$857$	9.20489	−	2.46644i	0.314433	−	0.0842520i	−0.0981513	−	0.995172i	$-0.531293\pi$
$857$	9.20489	−	2.46644i	0.314433	−	0.0842520i	0.412584	+	0.910919i	$0.364626\pi$
$858$	−5.99447	+	7.40255i	−0.204648	+	0.252719i
$859$	8.18814	−	9.09385i	0.279376	−	0.310278i	−0.587083	−	0.809527i	$-0.699724\pi$
$859$	8.18814	−	9.09385i	0.279376	−	0.310278i	0.866459	+	0.499248i	$0.166391\pi$
$860$	−0.757013	−	2.81042i	−0.0258139	−	0.0958345i
$861$	−42.2577	−	4.71064i	−1.44014	−	0.160538i
$862$	−10.7690	−	5.48710i	−0.366795	−	0.186891i
$863$	−46.4225	+	2.43290i	−1.58024	+	0.0828168i	−0.822126	−	0.569306i	$-0.807212\pi$
$863$	−46.4225	+	2.43290i	−1.58024	+	0.0828168i	−0.758113	+	0.652123i	$0.773879\pi$
$864$	−3.37372	−	3.74690i	−0.114776	−	0.127472i
$865$	2.68177	+	49.9151i	0.0911830	+	1.69716i
$866$	−0.00974686	−	0.00877612i	−0.000331212	−	0.000298225i
$867$	27.3879	+	4.33782i	0.930143	+	0.147320i
$868$	12.8213	−	6.43143i	0.435184	−	0.218297i
$869$	8.40172	+	11.5640i	0.285009	+	0.392281i
$870$	11.9563	−	8.71080i	0.405356	−	0.295324i
$871$	17.6135	+	39.5605i	0.596809	+	1.34046i
$872$	3.35681	−	8.74478i	0.113676	−	0.296135i
$873$	−0.287254	+	0.442333i	−0.00972209	+	0.0149707i
$874$	9.79740			0.331402
$875$	−28.5904	+	7.58879i	−0.966531	+	0.256548i
$876$	−15.1713			−0.512591
$877$	10.7933	−	16.6203i	0.364465	−	0.561227i	−0.608099	−	0.793861i	$-0.708068\pi$
$877$	10.7933	−	16.6203i	0.364465	−	0.561227i	0.972564	+	0.232634i	$0.0747344\pi$
$878$	14.1130	−	36.7656i	0.476291	−	1.24078i
$879$	−5.48274	−	12.3144i	−0.184928	−	0.415356i
$880$	2.15098	−	1.56711i	0.0725096	−	0.0528271i
$881$	28.8581	+	39.7198i	0.972254	+	1.33819i	0.940900	+	0.338685i	$0.109982\pi$
$881$	28.8581	+	39.7198i	0.972254	+	1.33819i	0.0313545	+	0.999508i	$0.490018\pi$
$882$	−1.15456	+	0.167991i	−0.0388762	+	0.00565655i
$883$	50.2355	+	7.95652i	1.69056	+	0.267758i	0.926200	−	0.377033i	$-0.123056\pi$
$883$	50.2355	+	7.95652i	1.69056	+	0.267758i	0.764359	+	0.644791i	$0.223056\pi$
$884$	3.97923	+	3.58291i	0.133836	+	0.120506i
$885$	−2.38449	−	44.3819i	−0.0801539	−	1.49188i
$886$	−2.41872	−	2.68626i	−0.0812585	−	0.0902467i
$887$	−17.2678	+	0.904968i	−0.579797	+	0.0303859i	−0.339981	−	0.940432i	$-0.610420\pi$
$887$	−17.2678	+	0.904968i	−0.579797	+	0.0303859i	−0.239816	+	0.970818i	$0.577087\pi$
$888$	7.83938	+	3.99436i	0.263072	+	0.134042i
$889$	2.76426	−	1.20993i	0.0927103	−	0.0405798i
$890$	−3.95399	−	14.6792i	−0.132538	−	0.492049i
$891$	7.54351	−	8.37791i	0.252717	−	0.280671i
$892$	1.63084	−	2.01391i	0.0546044	−	0.0674308i
$893$	7.10365	−	1.90342i	0.237714	−	0.0636954i
$894$	34.2200	+	15.2357i	1.14449	+	0.509560i
$895$	−3.38562	−	1.94876i	−0.113169	−	0.0651398i
$896$	−1.54163	−	2.15021i	−0.0515021	−	0.0718334i
$897$	51.6172	−	8.17536i	1.72345	−	0.272967i
$898$	5.69277	+	3.69693i	0.189970	+	0.123368i
$899$	−10.0776	+	17.4549i	−0.336107	+	0.582155i
$900$	0.675499	+	0.488069i	0.0225166	+	0.0162690i
$901$	3.25059	−	1.87673i	0.108293	−	0.0625229i
$902$	9.57695	−	4.87970i	0.318878	−	0.162476i
$903$	−2.16015	−	5.73506i	−0.0718855	−	0.190851i
$904$	−6.75458	+	9.29689i	−0.224654	+	0.309210i
$905$	−2.13102	−	0.689312i	−0.0708374	−	0.0229135i
$906$	−22.6103	+	2.37643i	−0.751175	+	0.0789517i
$907$	−12.4166	−	46.3393i	−0.412285	−	1.53867i	−0.790212	−	0.612834i	$-0.790029\pi$
$907$	−12.4166	−	46.3393i	−0.412285	−	1.53867i	0.377926	−	0.925836i	$-0.376637\pi$
$908$	−8.62974	+	3.31265i	−0.286388	+	0.109934i
$909$	1.02109	+	3.14260i	0.0338675	+	0.104233i
$910$	23.6469	+	12.1974i	0.783886	+	0.404340i
$911$	−5.04615	+	15.5305i	−0.167186	+	0.514547i	−0.999191	−	0.0402221i	$-0.987193\pi$
$911$	−5.04615	+	15.5305i	−0.167186	+	0.514547i	0.832004	+	0.554769i	$0.187193\pi$
$912$	−0.139736	−	2.66632i	−0.00462711	−	0.0882906i
$913$	8.71623	−	5.66039i	0.288465	−	0.187331i
$914$	−15.8584	+	14.2789i	−0.524549	+	0.472306i
$915$	53.0974	−	27.1425i	1.75535	−	0.897304i
$916$	4.25591	−	1.38283i	0.140619	−	0.0456899i
$917$	7.48910	+	3.87547i	0.247312	+	0.127979i
$918$	−4.24464	−	4.24464i	−0.140094	−	0.140094i
$919$	11.5924	−	26.0369i	0.382397	−	0.858878i	−0.615119	−	0.788434i	$-0.710892\pi$
$919$	11.5924	−	26.0369i	0.382397	−	0.858878i	0.997516	−	0.0704433i	$-0.0224414\pi$
$920$	−14.5233	−	1.50715i	−0.478818	−	0.0496892i
$921$	−51.1746	+	22.7844i	−1.68626	+	0.750772i
$922$	−5.81018	+	4.70499i	−0.191348	+	0.154951i
$923$	3.84924	+	7.55455i	0.126699	+	0.248661i
$924$	4.18774	−	3.72319i	0.137767	−	0.122484i
$925$	23.8956	+	6.33548i	0.785681	+	0.208309i
$926$	−6.83678	−	11.8417i	−0.224671	−	0.389141i
$927$	−0.0585199	+	1.11663i	−0.00192205	+	0.0366748i
$928$	3.47072	+	1.33228i	0.113932	+	0.0437343i
$929$	1.06778	−	10.1593i	0.0350329	−	0.333315i	−0.962942	−	0.269708i	$-0.913073\pi$
$929$	1.06778	−	10.1593i	0.0350329	−	0.333315i	0.997975	−	0.0636074i	$-0.0202605\pi$
$930$	−21.1073	−	4.45748i	−0.692135	−	0.146167i
$931$	9.02882	+	5.36550i	0.295907	+	0.175847i
$932$	−18.9469	+	18.9469i	−0.620625	+	0.620625i
$933$	−11.7227	−	30.5388i	−0.383785	−	0.999794i
$934$	6.56240	+	1.39488i	0.214728	+	0.0456419i
$935$	2.45976	−	1.99723i	0.0804426	−	0.0653165i
$936$	−0.155853	−	0.733232i	−0.00509422	−	0.0239664i
$937$	−26.1014	+	51.2270i	−0.852697	+	1.67351i	−0.120191	+	0.992751i	$0.538351\pi$
$937$	−26.1014	+	51.2270i	−0.852697	+	1.67351i	−0.732506	+	0.680761i	$0.761649\pi$
$938$	−6.43834	−	24.6479i	−0.210219	−	0.804783i
$939$	−27.5289	−	8.94469i	−0.898372	−	0.291899i
$940$	−10.8230	+	1.72878i	−0.353006	+	0.0563867i
$941$	−5.34549	+	25.1486i	−0.174258	+	0.819820i	0.800985	+	0.598685i	$0.204310\pi$
$941$	−5.34549	+	25.1486i	−0.174258	+	0.819820i	−0.975243	+	0.221136i	$0.929024\pi$
$942$	18.8374	+	15.2542i	0.613754	+	0.497008i
$943$	−56.9621	−	15.2629i	−1.85494	−	0.497030i
$944$	9.03655	−	6.56544i	0.294115	−	0.213687i
$945$	−25.7577	−	15.0428i	−0.837897	−	0.489341i
$946$	1.25332	+	0.910593i	0.0407491	+	0.0296059i
$947$	−12.0656	−	14.8997i	−0.392078	−	0.484176i	0.542439	−	0.840095i	$-0.317501\pi$
$947$	−12.0656	−	14.8997i	−0.392078	−	0.484176i	−0.934517	+	0.355919i	$0.884168\pi$
$948$	−21.3425	−	1.11851i	−0.693173	−	0.0363277i
$949$	33.2062	+	19.1716i	1.07792	+	0.622337i
$950$	−1.96071	−	7.24122i	−0.0636138	−	0.234936i
$951$			40.1110i			1.30069i
$952$	−1.96689	−	2.46042i	−0.0637473	−	0.0797427i
$953$	1.07216	+	6.76932i	0.0347305	+	0.219280i	0.998949	−	0.0458277i	$-0.0145925\pi$
$953$	1.07216	+	6.76932i	0.0347305	+	0.219280i	−0.964219	+	0.265108i	$0.914593\pi$
$954$	−0.522585	−	0.0549259i	−0.0169193	−	0.00177829i
$955$	1.87379	−	18.0564i	0.0606346	−	0.584291i
$956$	−3.15041	−	29.9742i	−0.101892	−	0.969435i
$957$	−2.03786	+	7.60541i	−0.0658748	+	0.245848i
$958$	−5.68532	+	35.8957i	−0.183685	+	1.15974i
$959$	−6.11357	−	10.7447i	−0.197417	−	0.346964i
$960$	−0.203024	+	3.97393i	−0.00655259	+	0.128258i
$961$	−1.57212	+	0.334165i	−0.0507137	+	0.0107795i
$962$	−12.1109	−	18.6491i	−0.390470	−	0.601271i
$963$	−1.41547	−	2.17963i	−0.0456128	−	0.0702375i
$964$	−12.1163	+	2.57539i	−0.390238	+	0.0829477i
$965$	27.9128	−	34.5623i	0.898545	−	1.11260i
$966$	−30.7431	−	0.193562i	−0.989142	−	0.00622777i
$967$	−4.24001	+	26.7704i	−0.136350	+	0.860877i	0.820786	+	0.571236i	$0.193536\pi$
$967$	−4.24001	+	26.7704i	−0.136350	+	0.860877i	−0.957135	+	0.289641i	$0.906464\pi$
$968$	2.48039	−	9.25694i	0.0797228	−	0.297529i
$969$	−0.332277	−	3.16140i	−0.0106743	−	0.101559i
$970$	−6.91921	+	1.48024i	−0.222162	+	0.0475275i
$971$	21.8726	+	2.29891i	0.701926	+	0.0737754i	0.448766	−	0.893649i	$-0.351864\pi$
$971$	21.8726	+	2.29891i	0.701926	+	0.0737754i	0.253160	+	0.967424i	$0.418530\pi$
$972$	0.270657	+	1.70886i	0.00868134	+	0.0548118i
$973$	6.23301	+	2.43776i	0.199821	+	0.0781511i
$974$			29.6364i			0.949611i
$975$	−16.3723	−	36.5140i	−0.524333	−	1.16938i
$976$	12.9786	+	7.49320i	0.415435	+	0.239851i
$977$	−10.2935	−	0.539458i	−0.329317	−	0.0172588i	−0.113039	−	0.993591i	$-0.536059\pi$
$977$	−10.2935	−	0.539458i	−0.329317	−	0.0172588i	−0.216278	+	0.976332i	$0.569392\pi$
$978$	−6.96240	−	8.59785i	−0.222633	−	0.274929i
$979$	6.54629	+	4.75616i	0.209220	+	0.152008i
$980$	−12.5586	−	9.34251i	−0.401169	−	0.298435i
$981$	−1.26306	+	0.917667i	−0.0403264	+	0.0292988i
$982$	36.0240	+	9.65260i	1.14957	+	0.308027i
$983$	16.1939	+	13.1135i	0.516505	+	0.418257i	0.851809	−	0.523853i	$-0.175506\pi$
$983$	16.1939	+	13.1135i	0.516505	+	0.418257i	−0.335304	+	0.942110i	$0.608839\pi$
$984$	−3.34132	+	15.7197i	−0.106517	+	0.501124i
$985$	5.50605	−	5.52055i	0.175437	−	0.175899i
$986$	4.20951	+	1.36775i	0.134058	+	0.0435581i
$987$	−22.3280	+	5.83235i	−0.710708	+	0.185646i
$988$	−3.06351	+	6.01249i	−0.0974634	+	0.191283i
$989$	−1.76718	−	8.31391i	−0.0561930	−	0.264367i
$990$	−0.442933	+	0.0237973i	−0.0140773	+	0.000756329i
$991$	−1.90869	−	0.405704i	−0.0606315	−	0.0128876i	0.177496	−	0.984122i	$-0.443200\pi$
$991$	−1.90869	−	0.405704i	−0.0606315	−	0.0128876i	−0.238128	+	0.971234i	$0.576534\pi$
$992$	−1.94289	−	5.06141i	−0.0616870	−	0.160700i
$993$	17.1570	−	17.1570i	0.544460	−	0.544460i
$994$	−1.51142	−	4.75329i	−0.0479393	−	0.150765i
$995$	−4.19685	−	39.4314i	−0.133049	−	1.25006i
$996$	−1.62429	+	15.4541i	−0.0514677	+	0.489682i
$997$	30.1360	+	11.5681i	0.954418	+	0.366367i	0.785221	−	0.619216i	$-0.212549\pi$
$997$	30.1360	+	11.5681i	0.954418	+	0.366367i	0.169197	+	0.985582i	$0.445883\pi$
$998$	−0.866058	+	16.5254i	−0.0274146	+	0.523102i
$999$	12.4643	+	21.5888i	0.394352	+	0.683038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.x.a.3.8	✓	320
7.5	odd	6	inner	350.2.x.a.103.13	yes	320
25.17	odd	20	inner	350.2.x.a.17.13	yes	320
175.117	even	60	inner	350.2.x.a.117.8	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.x.a.3.8	✓	320	1.1	even	1	trivial
350.2.x.a.17.13	yes	320	25.17	odd	20	inner
350.2.x.a.103.13	yes	320	7.5	odd	6	inner
350.2.x.a.117.8	yes	320	175.117	even	60	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.544639 + 0.838671i) q^{2} +(0.637721 - 1.66132i) q^{3} +(-0.406737 - 0.913545i) q^{4} +(-1.80729 + 1.31671i) q^{5} +(1.04597 + 1.43966i) q^{6} +(-0.155100 + 2.64120i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-0.123863 - 0.111527i) q^{9} +O(q^{10})\)	\(q+(-0.544639 + 0.838671i) q^{2} +(0.637721 - 1.66132i) q^{3} +(-0.406737 - 0.913545i) q^{4} +(-1.80729 + 1.31671i) q^{5} +(1.04597 + 1.43966i) q^{6} +(-0.155100 + 2.64120i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-0.123863 - 0.111527i) q^{9} +(-0.119964 - 2.23285i) q^{10} +(0.796380 + 0.884470i) q^{11} +(-1.77708 + 0.0931326i) q^{12} +(4.00727 + 2.04181i) q^{13} +(-2.13062 - 1.56858i) q^{14} +(1.03493 + 3.84217i) q^{15} +(-0.669131 + 0.743145i) q^{16} +(-0.749255 + 0.925253i) q^{17} +(0.160995 - 0.0431385i) q^{18} +(-1.37068 - 0.610266i) q^{19} +(1.93796 + 1.11549i) q^{20} +(4.28897 + 1.94202i) q^{21} +(-1.17552 + 0.186184i) q^{22} +(5.47642 + 3.55643i) q^{23} +(0.889758 - 1.54111i) q^{24} +(1.53257 - 4.75933i) q^{25} +(-3.89492 + 2.24873i) q^{26} +(4.49241 - 2.28900i) q^{27} +(2.47594 - 0.932582i) q^{28} +(-2.18517 + 3.00763i) q^{29} +(-3.78598 - 1.22464i) q^{30} +(5.39181 - 0.566702i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(1.97726 - 0.758998i) q^{33} +(-0.367909 - 1.13231i) q^{34} +(-3.19738 - 4.97763i) q^{35} +(-0.0515053 + 0.158517i) q^{36} +(0.258761 + 4.93746i) q^{37} +(1.25834 - 0.817174i) q^{38} +(5.94761 - 5.35526i) q^{39} +(-1.99101 + 1.01777i) q^{40} +(-8.58901 + 2.79074i) q^{41} +(-3.96466 + 2.53933i) q^{42} +(-0.920409 - 0.920409i) q^{43} +(0.484086 - 1.08728i) q^{44} +(0.370705 + 0.0384698i) q^{45} +(-5.96534 + 2.65594i) q^{46} +(-3.80921 + 3.08463i) q^{47} +(0.807883 + 1.58556i) q^{48} +(-6.95189 - 0.819301i) q^{49} +(3.15681 + 3.87744i) q^{50} +(1.05933 + 1.83481i) q^{51} +(0.235379 - 4.49130i) q^{52} +(-2.94324 - 1.12980i) q^{53} +(-0.527027 + 5.01433i) q^{54} +(-2.60387 - 0.549892i) q^{55} +(-0.566365 + 2.58442i) q^{56} +(-1.88796 + 1.88796i) q^{57} +(-1.33228 - 3.47072i) q^{58} +(-10.9257 - 2.32233i) q^{59} +(3.08906 - 2.50820i) q^{60} +(-3.11585 - 14.6589i) q^{61} +(-2.46131 + 4.83060i) q^{62} +(0.313777 - 0.309850i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-9.93074 + 1.58627i) q^{65} +(-0.440342 + 2.07165i) q^{66} +(7.48284 + 6.05948i) q^{67} +(1.15001 + 0.308144i) q^{68} +(9.40079 - 6.83008i) q^{69} +(5.91601 + 0.0294668i) q^{70} +(1.52517 + 1.10810i) q^{71} +(-0.104892 - 0.129530i) q^{72} +(8.51385 + 0.446192i) q^{73} +(-4.28183 - 2.47212i) q^{74} +(-6.92942 - 5.58122i) q^{75} +1.50039i q^{76} +(-2.45958 + 1.96622i) q^{77} +(1.25199 + 7.90477i) q^{78} +(11.9441 + 1.25538i) q^{79} +(0.230808 - 2.22412i) q^{80} +(-0.990119 - 9.42035i) q^{81} +(2.33740 - 8.72330i) q^{82} +(1.36603 - 8.62478i) q^{83} +(0.0296426 - 4.70806i) q^{84} +(0.135833 - 2.65875i) q^{85} +(1.27321 - 0.270629i) q^{86} +(3.60311 + 5.54831i) q^{87} +(0.648214 + 0.998162i) q^{88} +(6.65017 - 1.41354i) q^{89} +(-0.234164 + 0.289947i) q^{90} +(-6.01435 + 10.2673i) q^{91} +(1.02150 - 6.44949i) q^{92} +(2.49700 - 9.31892i) q^{93} +(-0.512350 - 4.87468i) q^{94} +(3.28075 - 0.701856i) q^{95} +(-1.76977 - 0.186010i) q^{96} +(-0.495018 - 3.12542i) q^{97} +(4.47339 - 5.38412i) q^{98} -0.198371i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 12 q^{5} - 8 q^{7}+O(q^{10}) \) 320 * q + 12 * q^5 - 8 * q^7	\( 320 q + 12 q^{5} - 8 q^{7} + 12 q^{10} - 16 q^{15} - 40 q^{16} + 36 q^{17} + 8 q^{18} - 72 q^{22} + 44 q^{23} - 12 q^{25} - 24 q^{28} - 80 q^{29} + 20 q^{30} - 48 q^{33} - 28 q^{35} + 80 q^{36} - 4 q^{37} - 24 q^{38} - 40 q^{39} - 36 q^{42} + 88 q^{43} - 228 q^{45} - 12 q^{47} + 32 q^{50} - 52 q^{53} + 152 q^{57} + 32 q^{58} - 120 q^{59} - 8 q^{60} + 136 q^{63} + 8 q^{65} - 32 q^{67} - 144 q^{68} + 92 q^{70} + 8 q^{72} + 12 q^{73} - 432 q^{75} + 144 q^{77} - 16 q^{78} + 12 q^{80} - 40 q^{81} - 192 q^{82} + 60 q^{84} - 24 q^{85} + 24 q^{87} + 4 q^{88} - 300 q^{89} - 8 q^{92} - 68 q^{93} + 20 q^{95} - 40 q^{98}+O(q^{100}) \) 320 * q + 12 * q^5 - 8 * q^7 + 12 * q^10 - 16 * q^15 - 40 * q^16 + 36 * q^17 + 8 * q^18 - 72 * q^22 + 44 * q^23 - 12 * q^25 - 24 * q^28 - 80 * q^29 + 20 * q^30 - 48 * q^33 - 28 * q^35 + 80 * q^36 - 4 * q^37 - 24 * q^38 - 40 * q^39 - 36 * q^42 + 88 * q^43 - 228 * q^45 - 12 * q^47 + 32 * q^50 - 52 * q^53 + 152 * q^57 + 32 * q^58 - 120 * q^59 - 8 * q^60 + 136 * q^63 + 8 * q^65 - 32 * q^67 - 144 * q^68 + 92 * q^70 + 8 * q^72 + 12 * q^73 - 432 * q^75 + 144 * q^77 - 16 * q^78 + 12 * q^80 - 40 * q^81 - 192 * q^82 + 60 * q^84 - 24 * q^85 + 24 * q^87 + 4 * q^88 - 300 * q^89 - 8 * q^92 - 68 * q^93 + 20 * q^95 - 40 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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