LMFDB - Embedded newform 75.2.i.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,2,Mod(4,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("75.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.i (of order $10$, 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:	$0.598878015160$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.2
Root			$-0.536547i$ of defining polynomial
Character	$\chi$	$=$	75.19
Dual form			75.2.i.a.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.510286 + 0.165802i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.38513 + 1.00636i) q^{4} +(2.22820 - 0.187439i) q^{5} +(-0.434076 - 0.315374i) q^{6} +2.57318i q^{7} +(1.17071 - 1.61134i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.510286 + 0.165802i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.38513 + 1.00636i) q^{4} +(2.22820 - 0.187439i) q^{5} +(-0.434076 - 0.315374i) q^{6} +2.57318i q^{7} +(1.17071 - 1.61134i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-1.10594 + 0.465087i) q^{10} +(-1.58949 - 4.89194i) q^{11} +(-1.62832 - 0.529073i) q^{12} +(1.40274 + 0.455776i) q^{13} +(-0.426639 - 1.31306i) q^{14} +(1.46134 + 1.69248i) q^{15} +(0.727915 - 2.24029i) q^{16} +(0.404314 - 0.556490i) q^{17} -0.536547i q^{18} +(-6.54709 - 4.75674i) q^{19} +(-2.89772 + 2.50199i) q^{20} +(-2.08175 + 1.51248i) q^{21} +(1.62219 + 2.23275i) q^{22} +(0.354506 - 0.115186i) q^{23} +1.99173 q^{24} +(4.92973 - 0.835300i) q^{25} -0.791365 q^{26} +(-0.951057 + 0.309017i) q^{27} +(-2.58954 - 3.56419i) q^{28} +(0.0288595 - 0.0209676i) q^{29} +(-1.02632 - 0.621354i) q^{30} +(3.63169 + 2.63858i) q^{31} +5.24733i q^{32} +(3.02338 - 4.16133i) q^{33} +(-0.114049 + 0.351005i) q^{34} +(0.482313 + 5.73355i) q^{35} +(-0.529073 - 1.62832i) q^{36} +(1.81590 + 0.590022i) q^{37} +(4.12957 + 1.34178i) q^{38} +(0.455776 + 1.40274i) q^{39} +(2.30654 - 3.80982i) q^{40} +(-1.59739 + 4.91625i) q^{41} +(0.811515 - 1.11695i) q^{42} +11.4506i q^{43} +(7.12469 + 5.17639i) q^{44} +(-0.510286 + 2.17706i) q^{45} +(-0.161802 + 0.117556i) q^{46} +(-5.00860 - 6.89374i) q^{47} +(2.24029 - 0.727915i) q^{48} +0.378747 q^{49} +(-2.37708 + 1.24360i) q^{50} +0.687859 q^{51} +(-2.40165 + 0.780343i) q^{52} +(-5.36247 - 7.38080i) q^{53} +(0.434076 - 0.315374i) q^{54} +(-4.45863 - 10.6023i) q^{55} +(4.14627 + 3.01244i) q^{56} -8.09265i q^{57} +(-0.0112501 + 0.0154845i) q^{58} +(0.0544457 - 0.167567i) q^{59} +(-3.72739 - 0.873670i) q^{60} +(-1.98127 - 6.09772i) q^{61} +(-2.29069 - 0.744289i) q^{62} +(-2.44724 - 0.795156i) q^{63} +(0.585811 + 1.80294i) q^{64} +(3.21100 + 0.752633i) q^{65} +(-0.852834 + 2.62475i) q^{66} +(0.0490435 - 0.0675025i) q^{67} +1.17770i q^{68} +(0.301561 + 0.219097i) q^{69} +(-1.19675 - 2.84579i) q^{70} +(-9.83589 + 7.14619i) q^{71} +(1.17071 + 1.61134i) q^{72} +(-11.4619 + 3.72421i) q^{73} -1.02446 q^{74} +(3.57340 + 3.49726i) q^{75} +13.8556 q^{76} +(12.5878 - 4.09004i) q^{77} +(-0.465153 - 0.640228i) q^{78} +(4.01019 - 2.91357i) q^{79} +(1.20202 - 5.12825i) q^{80} +(-0.809017 - 0.587785i) q^{81} -2.77354i q^{82} +(-5.50356 + 7.57501i) q^{83} +(1.36140 - 4.18996i) q^{84} +(0.796583 - 1.31575i) q^{85} +(-1.89853 - 5.84308i) q^{86} +(0.0339264 + 0.0110233i) q^{87} +(-9.74340 - 3.16582i) q^{88} +(0.00380677 + 0.0117160i) q^{89} +(-0.100570 - 1.19553i) q^{90} +(-1.17279 + 3.60949i) q^{91} +(-0.375120 + 0.516308i) q^{92} +4.48902i q^{93} +(3.69882 + 2.68735i) q^{94} +(-15.4798 - 9.37179i) q^{95} +(-4.24518 + 3.08430i) q^{96} +(4.47917 + 6.16504i) q^{97} +(-0.193269 + 0.0627970i) q^{98} +5.14369 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9	$ 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} + 10 q^{17} - 2 q^{19} + 20 q^{20} + 4 q^{21} - 30 q^{22} - 20 q^{23} + 24 q^{24} - 10 q^{25} + 12 q^{26} + 30 q^{28} + 16 q^{29} - 20 q^{30} + 6 q^{31} + 10 q^{33} - 36 q^{34} + 10 q^{35} - 2 q^{36} - 10 q^{37} + 30 q^{38} - 8 q^{39} + 10 q^{40} - 14 q^{41} - 10 q^{42} + 26 q^{44} + 16 q^{46} + 40 q^{47} + 20 q^{50} - 32 q^{51} + 40 q^{52} + 10 q^{53} - 2 q^{54} + 10 q^{55} + 10 q^{58} + 12 q^{59} - 30 q^{60} - 10 q^{62} - 10 q^{63} + 8 q^{64} - 70 q^{65} + 16 q^{66} - 40 q^{67} - 12 q^{69} + 30 q^{70} - 8 q^{71} - 30 q^{72} - 20 q^{73} - 52 q^{74} - 32 q^{76} - 40 q^{77} - 20 q^{79} - 4 q^{81} + 10 q^{83} + 12 q^{84} - 20 q^{85} - 36 q^{86} + 40 q^{87} - 40 q^{88} + 18 q^{89} + 30 q^{90} + 26 q^{91} + 10 q^{92} - 38 q^{94} - 40 q^{95} - 26 q^{96} + 40 q^{97} + 60 q^{98} - 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 + 10 * q^17 - 2 * q^19 + 20 * q^20 + 4 * q^21 - 30 * q^22 - 20 * q^23 + 24 * q^24 - 10 * q^25 + 12 * q^26 + 30 * q^28 + 16 * q^29 - 20 * q^30 + 6 * q^31 + 10 * q^33 - 36 * q^34 + 10 * q^35 - 2 * q^36 - 10 * q^37 + 30 * q^38 - 8 * q^39 + 10 * q^40 - 14 * q^41 - 10 * q^42 + 26 * q^44 + 16 * q^46 + 40 * q^47 + 20 * q^50 - 32 * q^51 + 40 * q^52 + 10 * q^53 - 2 * q^54 + 10 * q^55 + 10 * q^58 + 12 * q^59 - 30 * q^60 - 10 * q^62 - 10 * q^63 + 8 * q^64 - 70 * q^65 + 16 * q^66 - 40 * q^67 - 12 * q^69 + 30 * q^70 - 8 * q^71 - 30 * q^72 - 20 * q^73 - 52 * q^74 - 32 * q^76 - 40 * q^77 - 20 * q^79 - 4 * q^81 + 10 * q^83 + 12 * q^84 - 20 * q^85 - 36 * q^86 + 40 * q^87 - 40 * q^88 + 18 * q^89 + 30 * q^90 + 26 * q^91 + 10 * q^92 - 38 * q^94 - 40 * q^95 - 26 * q^96 + 40 * q^97 + 60 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.510286	+	0.165802i	−0.360827	+	0.117240i	−0.483820	−	0.875168i	$-0.660751\pi$
$2$	−0.510286	+	0.165802i	−0.360827	+	0.117240i	0.122993	+	0.992408i	$0.460751\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	−1.38513	+	1.00636i	−0.692566	+	0.503179i
$5$	2.22820	−	0.187439i	0.996480	−	0.0838251i
$5$	2.22820	−	0.187439i	0.996480	−	0.0838251i
$6$	−0.434076	−	0.315374i	−0.177211	−	0.128751i
$7$			2.57318i			0.972570i	0.873800	+	0.486285i	$0.161648\pi$
$7$			2.57318i			0.972570i	−0.873800	+	0.486285i	$0.838352\pi$
$8$	1.17071	−	1.61134i	0.413907	−	0.569695i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	−1.10594	+	0.465087i	−0.349729	+	0.147074i
$11$	−1.58949	−	4.89194i	−0.479248	−	1.47497i	−0.840141	−	0.542368i	$-0.817528\pi$
$11$	−1.58949	−	4.89194i	−0.479248	−	1.47497i	0.360893	−	0.932607i	$-0.382472\pi$
$12$	−1.62832	−	0.529073i	−0.470056	−	0.152730i
$13$	1.40274	+	0.455776i	0.389049	+	0.126410i	0.497009	−	0.867746i	$-0.334432\pi$
$13$	1.40274	+	0.455776i	0.389049	+	0.126410i	−0.107960	+	0.994155i	$0.534432\pi$
$14$	−0.426639	−	1.31306i	−0.114024	−	0.350930i
$15$	1.46134	+	1.69248i	0.377317	+	0.436996i
$16$	0.727915	−	2.24029i	0.181979	−	0.560073i
$17$	0.404314	−	0.556490i	0.0980605	−	0.134969i	−0.757167	−	0.653221i	$-0.773417\pi$
$17$	0.404314	−	0.556490i	0.0980605	−	0.134969i	0.855228	+	0.518252i	$0.173417\pi$
$18$		−	0.536547i		−	0.126465i
$19$	−6.54709	−	4.75674i	−1.50201	−	1.09127i	−0.969574	−	0.244799i	$-0.921278\pi$
$19$	−6.54709	−	4.75674i	−1.50201	−	1.09127i	−0.532432	−	0.846473i	$-0.678722\pi$
$20$	−2.89772	+	2.50199i	−0.647950	+	0.559462i
$21$	−2.08175	+	1.51248i	−0.454274	+	0.330050i
$22$	1.62219	+	2.23275i	0.345852	+	0.476024i
$23$	0.354506	−	0.115186i	0.0739197	−	0.0240180i	−0.271824	−	0.962347i	$-0.587627\pi$
$23$	0.354506	−	0.115186i	0.0739197	−	0.0240180i	0.345743	+	0.938329i	$0.387627\pi$
$24$	1.99173			0.406559
$25$	4.92973	−	0.835300i	0.985947	−	0.167060i
$26$	−0.791365			−0.155200
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	−2.58954	−	3.56419i	−0.489377	−	0.673569i
$29$	0.0288595	−	0.0209676i	0.00535907	−	0.00389359i	−0.585102	−	0.810959i	$-0.698946\pi$
$29$	0.0288595	−	0.0209676i	0.00535907	−	0.00389359i	0.590462	+	0.807066i	$0.298946\pi$
$30$	−1.02632	−	0.621354i	−0.187379	−	0.113443i
$31$	3.63169	+	2.63858i	0.652272	+	0.473903i	0.864044	−	0.503416i	$-0.167924\pi$
$31$	3.63169	+	2.63858i	0.652272	+	0.473903i	−0.211773	+	0.977319i	$0.567924\pi$
$32$			5.24733i			0.927606i
$33$	3.02338	−	4.16133i	0.526304	−	0.724395i
$34$	−0.114049	+	0.351005i	−0.0195592	+	0.0601969i
$35$	0.482313	+	5.73355i	0.0815258	+	0.969148i
$36$	−0.529073	−	1.62832i	−0.0881789	−	0.271387i
$37$	1.81590	+	0.590022i	0.298532	+	0.0969991i	0.454454	−	0.890770i	$-0.349835\pi$
$37$	1.81590	+	0.590022i	0.298532	+	0.0969991i	−0.155921	+	0.987770i	$0.549835\pi$
$38$	4.12957	+	1.34178i	0.669905	+	0.217665i
$39$	0.455776	+	1.40274i	0.0729826	+	0.224617i
$40$	2.30654	−	3.80982i	0.364696	−	0.602385i
$41$	−1.59739	+	4.91625i	−0.249470	+	0.767789i	0.745399	+	0.666618i	$0.232259\pi$
$41$	−1.59739	+	4.91625i	−0.249470	+	0.767789i	−0.994869	+	0.101171i	$0.967741\pi$
$42$	0.811515	−	1.11695i	0.125219	−	0.172350i
$43$			11.4506i			1.74620i	0.487543	+	0.873099i	$0.337893\pi$
$43$			11.4506i			1.74620i	−0.487543	+	0.873099i	$0.662107\pi$
$44$	7.12469	+	5.17639i	1.07409	+	0.780370i
$45$	−0.510286	+	2.17706i	−0.0760690	+	0.324538i
$46$	−0.161802	+	0.117556i	−0.0238564	+	0.0173327i
$47$	−5.00860	−	6.89374i	−0.730579	−	1.00556i	−0.999106	−	0.0422836i	$-0.986537\pi$
$47$	−5.00860	−	6.89374i	−0.730579	−	1.00556i	0.268527	−	0.963272i	$-0.413463\pi$
$48$	2.24029	−	0.727915i	0.323358	−	0.105065i
$49$	0.378747			0.0541067
$50$	−2.37708	+	1.24360i	−0.336170	+	0.175872i
$51$	0.687859			0.0963196
$52$	−2.40165	+	0.780343i	−0.333049	+	0.108214i
$53$	−5.36247	−	7.38080i	−0.736592	−	1.01383i	−0.998807	−	0.0488220i	$-0.984453\pi$
$53$	−5.36247	−	7.38080i	−0.736592	−	1.01383i	0.262216	−	0.965009i	$-0.415547\pi$
$54$	0.434076	−	0.315374i	0.0590702	−	0.0429170i
$55$	−4.45863	−	10.6023i	−0.601202	−	1.42961i
$56$	4.14627	+	3.01244i	0.554068	+	0.402554i
$57$		−	8.09265i		−	1.07190i
$58$	−0.0112501	+	0.0154845i	−0.00147721	+	0.00203321i
$59$	0.0544457	−	0.167567i	0.00708822	−	0.0218153i	−0.947450	−	0.319904i	$-0.896349\pi$
$59$	0.0544457	−	0.167567i	0.00708822	−	0.0218153i	0.954538	+	0.298089i	$0.0963492\pi$
$60$	−3.72739	−	0.873670i	−0.481204	−	0.112790i
$61$	−1.98127	−	6.09772i	−0.253676	−	0.780733i	−0.994088	−	0.108580i	$-0.965370\pi$
$61$	−1.98127	−	6.09772i	−0.253676	−	0.780733i	0.740412	−	0.672153i	$-0.234630\pi$
$62$	−2.29069	−	0.744289i	−0.290918	−	0.0945248i
$63$	−2.44724	−	0.795156i	−0.308323	−	0.100180i
$64$	0.585811	+	1.80294i	0.0732263	+	0.225367i
$65$	3.21100	+	0.752633i	0.398276	+	0.0933527i
$66$	−0.852834	+	2.62475i	−0.104977	+	0.323085i
$67$	0.0490435	−	0.0675025i	0.00599161	−	0.00824675i	−0.806011	−	0.591901i	$-0.798378\pi$
$67$	0.0490435	−	0.0675025i	0.00599161	−	0.00824675i	0.812002	+	0.583654i	$0.198378\pi$
$68$			1.17770i			0.142817i
$69$	0.301561	+	0.219097i	0.0363037	+	0.0263762i
$70$	−1.19675	−	2.84579i	−0.143039	−	0.340137i
$71$	−9.83589	+	7.14619i	−1.16731	+	0.848097i	−0.990684	−	0.136182i	$-0.956517\pi$
$71$	−9.83589	+	7.14619i	−1.16731	+	0.848097i	−0.176622	+	0.984279i	$0.556517\pi$
$72$	1.17071	+	1.61134i	0.137969	+	0.189898i
$73$	−11.4619	+	3.72421i	−1.34152	+	0.435886i	−0.889831	−	0.456290i	$-0.849178\pi$
$73$	−11.4619	+	3.72421i	−1.34152	+	0.435886i	−0.451688	+	0.892176i	$0.649178\pi$
$74$	−1.02446			−0.119091
$75$	3.57340	+	3.49726i	0.412620	+	0.403829i
$76$	13.8556			1.58934
$77$	12.5878	−	4.09004i	1.43452	−	0.466103i
$78$	−0.465153	−	0.640228i	−0.0526682	−	0.0724916i
$79$	4.01019	−	2.91357i	0.451182	−	0.327803i	−0.338881	−	0.940829i	$-0.610048\pi$
$79$	4.01019	−	2.91357i	0.451182	−	0.327803i	0.790062	+	0.613027i	$0.210048\pi$
$80$	1.20202	−	5.12825i	0.134390	−	0.573356i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		−	2.77354i		−	0.306287i
$83$	−5.50356	+	7.57501i	−0.604095	+	0.831465i	−0.996075	−	0.0885084i	$-0.971790\pi$
$83$	−5.50356	+	7.57501i	−0.604095	+	0.831465i	0.391981	+	0.919973i	$0.371790\pi$
$84$	1.36140	−	4.18996i	0.148541	−	0.457162i
$85$	0.796583	−	1.31575i	0.0864016	−	0.142714i
$86$	−1.89853	−	5.84308i	−0.204724	−	0.630075i
$87$	0.0339264	+	0.0110233i	0.00363729	+	0.00118183i
$88$	−9.74340	−	3.16582i	−1.03865	−	0.337478i
$89$	0.00380677	+	0.0117160i	0.000403517	+	0.00124190i	0.951258	−	0.308396i	$-0.0997922\pi$
$89$	0.00380677	+	0.0117160i	0.000403517	+	0.00124190i	−0.950855	+	0.309638i	$0.899792\pi$
$90$	−0.100570	−	1.19553i	−0.0106010	−	0.126020i
$91$	−1.17279	+	3.60949i	−0.122942	+	0.378377i
$92$	−0.375120	+	0.516308i	−0.0391089	+	0.0538288i
$93$			4.48902i			0.465490i
$94$	3.69882	+	2.68735i	0.381504	+	0.277179i
$95$	−15.4798	−	9.37179i	−1.58820	−	0.961525i
$96$	−4.24518	+	3.08430i	−0.433272	+	0.314790i
$97$	4.47917	+	6.16504i	0.454790	+	0.625965i	0.973418	−	0.229035i	$-0.0735570\pi$
$97$	4.47917	+	6.16504i	0.454790	+	0.625965i	−0.518628	+	0.855000i	$0.673557\pi$
$98$	−0.193269	+	0.0627970i	−0.0195231	+	0.00634345i
$99$	5.14369			0.516960
$100$	−5.98772	+	6.11808i	−0.598772	+	0.611808i
$101$	8.27518			0.823411			0.411706	−	0.911317i	$-0.364933\pi$
$101$	8.27518			0.823411			0.411706	+	0.911317i	$0.364933\pi$
$102$	−0.351005	+	0.114049i	−0.0347547	+	0.0112925i
$103$	6.10475	+	8.40247i	0.601519	+	0.827920i	0.995846	−	0.0910504i	$-0.0290224\pi$
$103$	6.10475	+	8.40247i	0.601519	+	0.827920i	−0.394328	+	0.918970i	$0.629022\pi$
$104$	2.37660	−	1.72670i	0.233045	−	0.169317i
$105$	−4.35505	+	3.76030i	−0.425009	+	0.366967i
$106$	3.96015	+	2.87722i	0.384643	+	0.279460i
$107$		−	12.2737i		−	1.18655i	−0.805001	−	0.593274i	$-0.797835\pi$
$107$		−	12.2737i		−	1.18655i	0.805001	−	0.593274i	$-0.202165\pi$
$108$	1.00636	−	1.38513i	0.0968368	−	0.133284i
$109$	1.30684	−	4.02203i	0.125172	−	0.385241i	−0.868760	−	0.495233i	$-0.835083\pi$
$109$	1.30684	−	4.02203i	0.125172	−	0.385241i	0.993932	+	0.109992i	$0.0350826\pi$
$110$	4.03306	+	4.67095i	0.384537	+	0.445357i
$111$	0.590022	+	1.81590i	0.0560024	+	0.172358i
$112$	5.76467	+	1.87305i	0.544710	+	0.176987i
$113$	17.4696	+	5.67623i	1.64340	+	0.533974i	0.977296	−	0.211880i	$-0.0679586\pi$
$113$	17.4696	+	5.67623i	1.64340	+	0.533974i	0.666109	+	0.745855i	$0.267959\pi$
$114$	1.34178	+	4.12957i	0.125669	+	0.386770i
$115$	0.768320	−	0.323106i	0.0716462	−	0.0301297i
$116$	−0.0188733	+	0.0580859i	−0.00175234	+	0.00539314i
$117$	−0.866938	+	1.19324i	−0.0801485	+	0.110315i
$118$			0.0945341i			0.00870257i
$119$	1.43195	+	1.04037i	0.131267	+	0.0953707i
$120$	4.43796	−	0.373326i	0.405128	−	0.0340799i
$121$	−12.5054	+	9.08571i	−1.13685	+	0.825974i
$122$	2.02203	+	2.78309i	0.183066	+	0.251969i
$123$	−4.91625	+	1.59739i	−0.443283	+	0.144031i
$124$	−7.68573			−0.690199
$125$	10.8279	−	2.78524i	0.968473	−	0.249119i
$126$	1.38063			0.122996
$127$	−0.328591	+	0.106766i	−0.0291577	+	0.00947391i	−0.323560	−	0.946208i	$-0.604880\pi$
$127$	−0.328591	+	0.106766i	−0.0291577	+	0.00947391i	0.294402	+	0.955682i	$0.404880\pi$
$128$	−6.76647	−	9.31325i	−0.598077	−	0.823182i
$129$	−9.26372	+	6.73048i	−0.815625	+	0.592586i
$130$	−1.76332	+	0.148332i	−0.154653	+	0.0130096i
$131$	3.69438	+	2.68413i	0.322780	+	0.234513i	0.737361	−	0.675499i	$-0.236072\pi$
$131$	3.69438	+	2.68413i	0.322780	+	0.234513i	−0.414581	+	0.910012i	$0.636072\pi$
$132$			8.80660i			0.766516i
$133$	12.2400	−	16.8468i	1.06134	−	1.46081i
$134$	−0.0138342	+	0.0425771i	−0.00119509	+	0.00367810i
$135$	−2.06122	+	0.866816i	−0.177402	+	0.0746036i
$136$	−0.423362	−	1.30297i	−0.0363030	−	0.111729i
$137$	−4.58174	−	1.48870i	−0.391445	−	0.127188i	0.106680	−	0.994293i	$-0.465978\pi$
$137$	−4.58174	−	1.48870i	−0.391445	−	0.127188i	−0.498125	+	0.867105i	$0.665978\pi$
$138$	−0.190209	−	0.0618027i	−0.0161917	−	0.00526100i
$139$	1.15595	+	3.55766i	0.0980468	+	0.301757i	0.988036	−	0.154225i	$-0.0492881\pi$
$139$	1.15595	+	3.55766i	0.0980468	+	0.301757i	−0.889989	+	0.455982i	$0.849288\pi$
$140$	−6.43807	−	7.45635i	−0.544116	−	0.630177i
$141$	2.63318	−	8.10408i	0.221753	−	0.682487i
$142$	3.83427	−	5.27742i	0.321765	−	0.442871i
$143$		−	7.58655i		−	0.634419i
$144$	1.90570	+	1.38458i	0.158809	+	0.115381i
$145$	0.0603745	−	0.0521294i	0.00501383	−	0.00432911i
$146$	5.23139	−	3.80083i	0.432953	−	0.314559i
$147$	0.222622	+	0.306412i	0.0183615	+	0.0252725i
$148$	−3.10904	+	1.01019i	−0.255561	+	0.0830369i
$149$	−8.64621			−0.708325			−0.354163	−	0.935184i	$-0.615234\pi$
$149$	−8.64621			−0.708325			−0.354163	+	0.935184i	$0.615234\pi$
$150$	−2.40331	−	1.19213i	−0.196229	−	0.0973369i
$151$	−1.24898			−0.101641			−0.0508205	−	0.998708i	$-0.516184\pi$
$151$	−1.24898			−0.101641			−0.0508205	+	0.998708i	$0.516184\pi$
$152$	−15.3295	+	4.98084i	−1.24338	+	0.404000i
$153$	0.404314	+	0.556490i	0.0326868	+	0.0449895i
$154$	−5.74527	+	4.17418i	−0.462967	+	0.336365i
$155$	8.58671	+	5.19856i	0.689701	+	0.417558i
$156$	−2.04296	−	1.48430i	−0.163568	−	0.118839i
$157$			3.86574i			0.308520i	0.988030	+	0.154260i	$0.0492993\pi$
$157$			3.86574i			0.308520i	−0.988030	+	0.154260i	$0.950701\pi$
$158$	−1.56327	+	2.15166i	−0.124367	+	0.171176i
$159$	2.81922	−	8.67665i	0.223578	−	0.688103i
$160$	0.983552	+	11.6921i	0.0777566	+	0.924341i
$161$	0.296394	+	0.912208i	0.0233592	+	0.0718921i
$162$	0.510286	+	0.165802i	0.0400919	+	0.0130266i
$163$	6.63277	+	2.15512i	0.519519	+	0.168802i	0.557027	−	0.830494i	$-0.311942\pi$
$163$	6.63277	+	2.15512i	0.519519	+	0.168802i	−0.0375081	+	0.999296i	$0.511942\pi$
$164$	−2.73491	−	8.41719i	−0.213561	−	0.657272i
$165$	5.95671	−	9.83897i	0.463729	−	0.765963i
$166$	1.55244	−	4.77793i	0.120493	−	0.370839i
$167$	−9.38069	+	12.9114i	−0.725900	+	0.999115i	0.273408	+	0.961898i	$0.411849\pi$
$167$	−9.38069	+	12.9114i	−0.725900	+	0.999115i	−0.999307	+	0.0372169i	$0.988151\pi$
$168$			5.12507i			0.395407i
$169$	−8.75729	−	6.36254i	−0.673637	−	0.489426i
$170$	−0.188331	+	0.803486i	−0.0144443	+	0.0616246i
$171$	6.54709	−	4.75674i	0.500669	−	0.363757i
$172$	−11.5234	−	15.8606i	−0.878649	−	1.20936i
$173$	−7.29774	+	2.37118i	−0.554837	+	0.180277i	−0.572997	−	0.819558i	$-0.694219\pi$
$173$	−7.29774	+	2.37118i	−0.554837	+	0.180277i	0.0181597	+	0.999835i	$0.494219\pi$
$174$	−0.0191399			−0.00145099
$175$	2.14938	+	12.6851i	0.162478	+	0.958903i
$176$	−12.1164			−0.913306
$177$	0.167567	−	0.0544457i	0.0125951	−	0.00409239i
$178$	−0.00388509	−	0.00534737i	−0.000291200	−	0.000400802i
$179$	8.58312	−	6.23600i	0.641532	−	0.466100i	−0.218844	−	0.975760i	$-0.570229\pi$
$179$	8.58312	−	6.23600i	0.641532	−	0.466100i	0.860376	+	0.509659i	$0.170229\pi$
$180$	−1.48409	−	3.52905i	−0.110618	−	0.263040i
$181$	−12.2223	−	8.88005i	−0.908480	−	0.660049i	0.0321503	−	0.999483i	$-0.489764\pi$
$181$	−12.2223	−	8.88005i	−0.908480	−	0.660049i	−0.940630	+	0.339434i	$0.889764\pi$
$182$		−	2.03633i		−	0.150942i
$183$	3.76860	−	5.18703i	0.278583	−	0.383436i
$184$	0.229419	−	0.706079i	0.0169130	−	0.0520528i
$185$	4.15678	+	0.974317i	0.305613	+	0.0716332i
$186$	−0.744289	−	2.29069i	−0.0545739	−	0.167961i
$187$	−3.36497	−	1.09334i	−0.246071	−	0.0799532i
$188$	13.8751	+	4.50831i	1.01195	+	0.328802i
$189$	−0.795156	−	2.44724i	−0.0578391	−	0.178010i
$190$	9.45300	+	2.21571i	0.685793	+	0.160744i
$191$	3.78359	−	11.6447i	0.273771	−	0.842580i	−0.715771	−	0.698335i	$-0.753925\pi$
$191$	3.78359	−	11.6447i	0.273771	−	0.842580i	0.989542	−	0.144245i	$-0.0460754\pi$
$192$	−1.11428	+	1.53367i	−0.0804161	+	0.110683i
$193$		−	14.2421i		−	1.02517i	−0.858637	−	0.512585i	$-0.828688\pi$
$193$		−	14.2421i		−	1.02517i	0.858637	−	0.512585i	$-0.171312\pi$
$194$	−3.30783	−	2.40328i	−0.237489	−	0.172546i
$195$	1.27849	+	3.04014i	0.0915543	+	0.217709i
$196$	−0.524614	+	0.381154i	−0.0374724	+	0.0272253i
$197$	10.4325	+	14.3591i	0.743286	+	1.02304i	0.998423	+	0.0561399i	$0.0178793\pi$
$197$	10.4325	+	14.3591i	0.743286	+	1.02304i	−0.255137	+	0.966905i	$0.582121\pi$
$198$	−2.62475	+	0.852834i	−0.186533	+	0.0606083i
$199$	18.9550			1.34369			0.671843	−	0.740693i	$-0.265503\pi$
$199$	18.9550			1.34369			0.671843	+	0.740693i	$0.265503\pi$
$200$	4.42532	−	8.92137i	0.312917	−	0.630836i
$201$	0.0834377			0.00588524
$202$	−4.22271	+	1.37204i	−0.297109	+	0.0965366i
$203$	0.0539535	+	0.0742606i	0.00378679	+	0.00521207i
$204$	−0.952776	+	0.692232i	−0.0667077	+	0.0484660i
$205$	−2.63780	+	11.2538i	−0.184232	+	0.785998i
$206$	−4.50832	−	3.27548i	−0.314109	−	0.228214i
$207$			0.372750i			0.0259079i
$208$	2.04214	−	2.81077i	0.141597	−	0.194892i
$209$	−12.8632	+	39.5888i	−0.889764	+	2.73841i
$210$	1.59886	−	2.64090i	0.110332	−	0.182240i
$211$	−3.33022	−	10.2494i	−0.229262	−	0.705596i	−0.997831	−	0.0658288i	$-0.979031\pi$
$211$	−3.33022	−	10.2494i	−0.229262	−	0.705596i	0.768569	−	0.639767i	$-0.220969\pi$
$212$	14.8555	+	4.82683i	1.02028	+	0.331508i
$213$	−11.5628	−	3.75698i	−0.792269	−	0.257424i
$214$	2.03501	+	6.26312i	0.139111	+	0.428138i
$215$	2.14628	+	25.5142i	0.146375	+	1.74005i
$216$	−0.615477	+	1.89424i	−0.0418779	+	0.128887i
$217$	−6.78954	+	9.34500i	−0.460904	+	0.634380i
$218$			2.26907i			0.153681i
$219$	−9.75012	−	7.08387i	−0.658852	−	0.478684i
$220$	16.8455	+	10.1986i	1.13572	+	0.687588i
$221$	0.820780	−	0.596332i	0.0552116	−	0.0401136i
$222$	−0.602161	−	0.828803i	−0.0404144	−	0.0556256i
$223$	26.2213	−	8.51983i	1.75591	−	0.570530i	0.759147	−	0.650920i	$-0.225617\pi$
$223$	26.2213	−	8.51983i	1.75591	−	0.570530i	0.996763	+	0.0803900i	$0.0256166\pi$
$224$	−13.5023			−0.902162
$225$	−0.728954	+	4.94658i	−0.0485969	+	0.329772i
$226$	−9.85565			−0.655588
$227$	3.78731	−	1.23057i	0.251372	−	0.0816758i	−0.180620	−	0.983553i	$-0.557811\pi$
$227$	3.78731	−	1.23057i	0.251372	−	0.0816758i	0.431993	+	0.901877i	$0.357811\pi$
$228$	8.14410	+	11.2094i	0.539356	+	0.742360i
$229$	9.68373	−	7.03564i	0.639919	−	0.464928i	−0.219903	−	0.975522i	$-0.570574\pi$
$229$	9.68373	−	7.03564i	0.639919	−	0.464928i	0.859822	+	0.510593i	$0.170574\pi$
$230$	−0.338492	+	0.292265i	−0.0223195	+	0.0192714i
$231$	10.7079	+	7.77971i	0.704525	+	0.511867i
$232$		−	0.0710494i		−	0.00466462i
$233$	−12.4129	+	17.0849i	−0.813197	+	1.11927i	0.177625	+	0.984098i	$0.443159\pi$
$233$	−12.4129	+	17.0849i	−0.813197	+	1.11927i	−0.990822	+	0.135172i	$0.956841\pi$
$234$	0.244545	−	0.752633i	0.0159864	−	0.0492012i
$235$	−12.4523	−	14.4218i	−0.812299	−	0.940776i
$236$	0.0932174	+	0.286894i	0.00606793	+	0.0186752i
$237$	4.71426	+	1.53176i	0.306224	+	0.0994983i
$238$	−0.903200	−	0.293467i	−0.0585457	−	0.0190227i
$239$	−8.09778	−	24.9224i	−0.523802	−	1.61210i	−0.766673	−	0.642038i	$-0.778089\pi$
$239$	−8.09778	−	24.9224i	−0.523802	−	1.61210i	0.242871	−	0.970059i	$-0.421911\pi$
$240$	4.85537	−	2.04185i	0.313413	−	0.131801i
$241$	−2.52607	+	7.77443i	−0.162718	+	0.500795i	−0.998861	−	0.0477169i	$-0.984805\pi$
$241$	−2.52607	+	7.77443i	−0.162718	+	0.500795i	0.836143	+	0.548512i	$0.184805\pi$
$242$	4.87491	−	6.70974i	0.313371	−	0.431318i
$243$		−	1.00000i		−	0.0641500i
$244$	8.88081	+	6.45228i	0.568535	+	0.413065i
$245$	0.843923	−	0.0709917i	0.0539162	−	0.00453549i
$246$	2.24384	−	1.63025i	0.143062	−	0.103941i
$247$	−7.01583	−	9.65646i	−0.446406	−	0.614426i
$248$	8.50330	−	2.76289i	0.539960	−	0.175444i
$249$	−9.36322			−0.593370
$250$	−5.06351	+	3.21655i	−0.320244	+	0.203432i
$251$	24.8145			1.56628			0.783139	−	0.621847i	$-0.213618\pi$
$251$	24.8145			1.56628			0.783139	+	0.621847i	$0.213618\pi$
$252$	4.18996	−	1.36140i	0.263943	−	0.0857602i
$253$	−1.12697	−	1.55114i	−0.0708518	−	0.0975191i
$254$	0.149973	−	0.108962i	0.00941017	−	0.00683689i
$255$	1.53269	−	0.128931i	0.0959806	−	0.00807400i
$256$	1.92965	+	1.40197i	0.120603	+	0.0876232i
$257$			24.2995i			1.51576i	0.652392	+	0.757882i	$0.273766\pi$
$257$			24.2995i			1.51576i	−0.652392	+	0.757882i	$0.726234\pi$
$258$	3.61122	−	4.97042i	0.224825	−	0.309445i
$259$	−1.51823	+	4.67264i	−0.0943384	+	0.290344i
$260$	−5.20508	+	2.18892i	−0.322805	+	0.135751i
$261$	0.0110233	+	0.0339264i	0.000682328	+	0.00209999i
$262$	−2.33023	−	0.757137i	−0.143962	−	0.0467761i
$263$	−8.10556	−	2.63366i	−0.499810	−	0.162398i	0.0482528	−	0.998835i	$-0.484635\pi$
$263$	−8.10556	−	2.63366i	−0.499810	−	0.162398i	−0.548063	+	0.836437i	$0.684635\pi$
$264$	−3.16582	−	9.74340i	−0.194843	−	0.599665i
$265$	−13.3321	−	15.4408i	−0.818984	−	0.948518i
$266$	−3.45264	+	10.6261i	−0.211695	+	0.651530i
$267$	−0.00724092	+	0.00996627i	−0.000443137	+	0.000609926i
$268$			0.142855i			0.00872627i
$269$	2.08979	+	1.51832i	0.127417	+	0.0925737i	0.649668	−	0.760218i	$-0.274908\pi$
$269$	2.08979	+	1.51832i	0.127417	+	0.0925737i	−0.522252	+	0.852791i	$0.674908\pi$
$270$	0.908093	−	0.784079i	0.0552648	−	0.0477175i
$271$	10.9940	−	7.98759i	0.667837	−	0.485212i	−0.201464	−	0.979496i	$-0.564570\pi$
$271$	10.9940	−	7.98759i	0.667837	−	0.485212i	0.869300	+	0.494284i	$0.164570\pi$
$272$	−0.952393	−	1.31086i	−0.0577473	−	0.0794824i
$273$	−3.60949	+	1.17279i	−0.218456	+	0.0709807i
$274$	2.58483			0.156155
$275$	−11.9220	−	22.7883i	−0.718923	−	1.37418i
$276$	−0.638192			−0.0384146
$277$	−8.69242	+	2.82434i	−0.522277	+	0.169698i	−0.558278	−	0.829654i	$-0.688538\pi$
$277$	−8.69242	+	2.82434i	−0.522277	+	0.169698i	0.0360015	+	0.999352i	$0.488538\pi$
$278$	−1.17974	−	1.62377i	−0.0707558	−	0.0973870i
$279$	−3.63169	+	2.63858i	−0.217424	+	0.157968i
$280$	9.80335	+	5.93514i	0.585862	+	0.354692i
$281$	−8.42195	−	6.11890i	−0.502411	−	0.365023i	0.307526	−	0.951540i	$-0.400499\pi$
$281$	−8.42195	−	6.11890i	−0.502411	−	0.365023i	−0.809937	+	0.586517i	$0.800499\pi$
$282$			4.57199i			0.272258i
$283$	−2.83069	+	3.89611i	−0.168267	+	0.231600i	−0.884820	−	0.465933i	$-0.845719\pi$
$283$	−2.83069	+	3.89611i	−0.168267	+	0.231600i	0.716553	+	0.697533i	$0.245719\pi$
$284$	6.43238	−	19.7968i	0.381692	−	1.17473i
$285$	−1.51687	−	18.0320i	−0.0898519	−	1.06813i
$286$	1.25787	+	3.87131i	0.0743791	+	0.228915i
$287$	−12.6504	−	4.11036i	−0.746729	−	0.242627i
$288$	−4.99051	−	1.62151i	−0.294068	−	0.0955486i
$289$	5.10708	+	15.7180i	0.300416	+	0.924586i
$290$	−0.0221651	+	0.0366112i	−0.00130158	+	0.00214988i
$291$	−2.35484	+	7.24744i	−0.138043	+	0.424853i
$292$	12.1284	−	16.6933i	0.709762	−	0.976904i
$293$		−	24.4506i		−	1.42842i	−0.699932	−	0.714210i	$-0.746786\pi$
$293$		−	24.4506i		−	1.42842i	0.699932	−	0.714210i	$-0.253214\pi$
$294$	−0.164405	−	0.119447i	−0.00958827	−	0.00696629i
$295$	0.0899073	−	0.383577i	0.00523460	−	0.0223327i
$296$	3.07661	−	2.23529i	0.178825	−	0.129924i
$297$	3.02338	+	4.16133i	0.175435	+	0.241465i
$298$	4.41205	−	1.43356i	0.255583	−	0.0830439i
$299$	0.549778			0.0317945
$300$	−8.46912	−	1.24805i	−0.488965	−	0.0720564i
$301$	−29.4644			−1.69830
$302$	0.637340	−	0.207084i	0.0366748	−	0.0119164i
$303$	4.86403	+	6.69476i	0.279431	+	0.384604i
$304$	−15.4222	+	11.2049i	−0.884524	+	0.642645i
$305$	−5.55761	−	13.2156i	−0.318228	−	0.756721i
$306$	−0.298583	−	0.216933i	−0.0170689	−	0.0124012i
$307$		−	9.51655i		−	0.543138i	−0.962419	−	0.271569i	$-0.912457\pi$
$307$		−	9.51655i		−	0.543138i	0.962419	−	0.271569i	$-0.0875426\pi$
$308$	−13.3198	+	18.3331i	−0.758965	+	1.04463i
$309$	−3.20946	+	9.87769i	−0.182580	+	0.561922i
$310$	−5.24361	−	1.22906i	−0.297817	−	0.0698060i
$311$	7.71967	+	23.7587i	0.437742	+	1.34723i	0.890250	+	0.455471i	$0.150529\pi$
$311$	7.71967	+	23.7587i	0.437742	+	1.34723i	−0.452508	+	0.891760i	$0.649471\pi$
$312$	2.79386	+	0.907781i	0.158171	+	0.0513930i
$313$	−9.39797	−	3.05359i	−0.531205	−	0.172599i	0.0311197	−	0.999516i	$-0.490093\pi$
$313$	−9.39797	−	3.05359i	−0.531205	−	0.172599i	−0.562324	+	0.826917i	$0.690093\pi$
$314$	−0.640948	−	1.97264i	−0.0361708	−	0.111322i
$315$	−5.60198	−	1.31306i	−0.315636	−	0.0739825i
$316$	−2.62255	+	8.07137i	−0.147530	+	0.454050i
$317$	14.5365	−	20.0078i	0.816453	−	1.12375i	−0.173842	−	0.984773i	$-0.555618\pi$
$317$	14.5365	−	20.0078i	0.816453	−	1.12375i	0.990296	−	0.138978i	$-0.0443816\pi$
$318$			4.89501i			0.274499i
$319$	−0.148444	−	0.107851i	−0.00831128	−	0.00603850i
$320$	1.64324	+	3.90750i	0.0918601	+	0.218436i
$321$	9.92967	−	7.21433i	0.554220	−	0.402664i
$322$	−0.302492	−	0.416345i	−0.0168572	−	0.0232020i
$323$	−5.29416	+	1.72018i	−0.294575	+	0.0957132i
$324$	1.71212			0.0951176
$325$	7.29582	+	1.07515i	0.404699	+	0.0596386i
$326$	−3.74194			−0.207247
$327$	4.02203	−	1.30684i	0.222419	−	0.0722683i
$328$	6.05167	+	8.32941i	0.334148	+	0.459915i
$329$	17.7388	−	12.8880i	0.977974	−	0.710540i
$330$	−1.40830	+	6.00833i	−0.0775246	+	0.330748i
$331$	−0.872336	−	0.633789i	−0.0479479	−	0.0348362i	0.563553	−	0.826080i	$-0.309434\pi$
$331$	−0.872336	−	0.633789i	−0.0479479	−	0.0348362i	−0.611501	+	0.791244i	$0.709434\pi$
$332$		−	16.0309i		−	0.879812i
$333$	−1.12229	+	1.54470i	−0.0615011	+	0.0846490i
$334$	2.64610	−	8.14386i	0.144788	−	0.445612i
$335$	0.0966260	−	0.159602i	0.00527924	−	0.00871997i
$336$	1.87305	+	5.76467i	0.102184	+	0.314489i
$337$	−13.3727	−	4.34507i	−0.728460	−	0.236691i	−0.0787727	−	0.996893i	$-0.525100\pi$
$337$	−13.3727	−	4.34507i	−0.728460	−	0.236691i	−0.649687	+	0.760202i	$0.725100\pi$
$338$	5.52365	+	1.79474i	0.300447	+	0.0976211i
$339$	5.67623	+	17.4696i	0.308290	+	0.948820i
$340$	0.220746	+	2.62414i	0.0119716	+	0.142314i
$341$	7.13524	−	21.9600i	0.386395	−	1.18920i
$342$	−2.55222	+	3.51282i	−0.138008	+	0.189952i
$343$			18.9868i			1.02519i
$344$	18.4508	+	13.4053i	0.994799	+	0.722764i
$345$	0.713005	+	0.431667i	0.0383869	+	0.0232402i
$346$	3.33079	−	2.41996i	0.179064	−	0.130098i
$347$	3.34793	+	4.60804i	0.179726	+	0.247372i	0.889369	−	0.457189i	$-0.151144\pi$
$347$	3.34793	+	4.60804i	0.179726	+	0.247372i	−0.709643	+	0.704561i	$0.751144\pi$
$348$	−0.0580859	+	0.0188733i	−0.00311373	+	0.00101171i
$349$	28.4950			1.52530			0.762651	−	0.646810i	$-0.223897\pi$
$349$	28.4950			1.52530			0.762651	+	0.646810i	$0.223897\pi$
$350$	−3.20001	−	6.11666i	−0.171048	−	0.326949i
$351$	−1.47492			−0.0787256
$352$	25.6696	−	8.34056i	1.36820	−	0.444554i
$353$	−7.50341	−	10.3276i	−0.399366	−	0.549681i	0.561218	−	0.827668i	$-0.310333\pi$
$353$	−7.50341	−	10.3276i	−0.399366	−	0.549681i	−0.960585	+	0.277987i	$0.910333\pi$
$354$	−0.0764797	+	0.0555658i	−0.00406485	+	0.00295329i
$355$	−20.5768	+	17.7668i	−1.09211	+	0.942962i
$356$	−0.0170634	−	0.0123973i	−0.000904359	−	0.000657056i
$357$			1.76999i			0.0936776i
$358$	−3.34591	+	4.60524i	−0.176837	+	0.243395i
$359$	1.39620	−	4.29707i	0.0736888	−	0.226791i	−0.907428	−	0.420208i	$-0.861957\pi$
$359$	1.39620	−	4.29707i	0.0736888	−	0.226791i	0.981117	+	0.193417i	$0.0619571\pi$
$360$	2.91059	+	3.37095i	0.153402	+	0.177665i
$361$	14.3665	+	44.2156i	0.756132	+	2.32714i
$362$	7.70923	+	2.50488i	0.405188	+	0.131654i
$363$	−14.7010	−	4.77664i	−0.771602	−	0.250709i
$364$	−2.00796	−	6.17987i	−0.105246	−	0.323913i
$365$	−24.8414	+	10.4467i	−1.30026	+	0.546805i
$366$	−1.06304	+	3.27171i	−0.0555662	+	0.171015i
$367$	−1.78361	+	2.45493i	−0.0931039	+	0.128146i	−0.853028	−	0.521866i	$-0.825236\pi$
$367$	−1.78361	+	2.45493i	−0.0931039	+	0.128146i	0.759924	+	0.650012i	$0.225236\pi$
$368$		−	0.878043i		−	0.0457711i
$369$	−4.18201	−	3.03841i	−0.217707	−	0.158173i
$370$	−2.28269	+	0.192023i	−0.118672	+	0.00998279i
$371$	18.9921	−	13.7986i	0.986022	−	0.716387i
$372$	−4.51756	−	6.21789i	−0.234225	−	0.322382i
$373$	−14.6138	+	4.74831i	−0.756674	+	0.245858i	−0.661850	−	0.749636i	$-0.730229\pi$
$373$	−14.6138	+	4.74831i	−0.756674	+	0.245858i	−0.0948232	+	0.995494i	$0.530229\pi$
$374$	1.89838			0.0981626
$375$	8.61776	+	7.12280i	0.445019	+	0.367820i
$376$	−16.9718			−0.875252
$377$	0.0500388	−	0.0162586i	0.00257713	−	0.000837359i
$378$	0.811515	+	1.11695i	0.0417398	+	0.0574499i
$379$	8.38117	−	6.08927i	0.430512	−	0.312785i	−0.351342	−	0.936247i	$-0.614275\pi$
$379$	8.38117	−	6.08927i	0.430512	−	0.312785i	0.781853	+	0.623462i	$0.214275\pi$
$380$	30.8730	−	2.59707i	1.58375	−	0.133227i
$381$	−0.279516	−	0.203080i	−0.0143200	−	0.0104041i
$382$			6.56946i			0.336123i
$383$	−9.10278	+	12.5289i	−0.465130	+	0.640197i	−0.975563	−	0.219721i	$-0.929485\pi$
$383$	−9.10278	+	12.5289i	−0.465130	+	0.640197i	0.510432	+	0.859918i	$0.329485\pi$
$384$	3.55734	−	10.9484i	0.181535	−	0.558707i
$385$	27.2816	−	11.4729i	1.39040	−	0.584711i
$386$	2.36137	+	7.26756i	0.120191	+	0.369909i
$387$	−10.8902	−	3.53843i	−0.553578	−	0.179868i
$388$	−12.4085	−	4.03176i	−0.629945	−	0.204681i
$389$	6.61139	+	20.3478i	0.335211	+	1.03167i	0.966618	+	0.256221i	$0.0824776\pi$
$389$	6.61139	+	20.3478i	0.335211	+	1.03167i	−0.631407	+	0.775451i	$0.717522\pi$
$390$	−1.15646	−	1.33937i	−0.0585594	−	0.0678215i
$391$	0.0792318	−	0.243850i	0.00400693	−	0.0123320i
$392$	0.443401	−	0.610289i	0.0223951	−	0.0308243i
$393$			4.56651i			0.230350i
$394$	−7.70434	−	5.59753i	−0.388139	−	0.282000i
$395$	8.38938	−	7.24368i	0.422116	−	0.364469i
$396$	−7.12469	+	5.17639i	−0.358029	+	0.260123i
$397$	7.34827	+	10.1140i	0.368799	+	0.507608i	0.952574	−	0.304307i	$-0.0984249\pi$
$397$	7.34827	+	10.1140i	0.368799	+	0.507608i	−0.583775	+	0.811916i	$0.698425\pi$
$398$	−9.67249	+	3.14278i	−0.484838	+	0.157534i
$399$	20.8238			1.04250
$400$	1.71711	−	11.6521i	0.0858555	−	0.582603i
$401$	−33.0478			−1.65033			−0.825164	−	0.564893i	$-0.808917\pi$
$401$	−33.0478			−1.65033			−0.825164	+	0.564893i	$0.808917\pi$
$402$	−0.0425771	+	0.0138342i	−0.00212355	+	0.000689985i
$403$	3.89170	+	5.35647i	0.193860	+	0.266825i
$404$	−11.4622	+	8.32779i	−0.570267	+	0.414323i
$405$	−1.91282	−	1.15806i	−0.0950490	−	0.0575445i
$406$	−0.0398443	−	0.0289486i	−0.00197744	−	0.00143669i
$407$		−	9.82111i		−	0.486815i
$408$	0.805282	−	1.10837i	0.0398674	−	0.0548727i
$409$	−0.932426	+	2.86971i	−0.0461055	+	0.141898i	−0.971459	−	0.237207i	$-0.923768\pi$
$409$	−0.932426	+	2.86971i	−0.0461055	+	0.141898i	0.925354	+	0.379105i	$0.123768\pi$
$410$	−0.519869	−	6.18000i	−0.0256745	−	0.305209i
$411$	−1.48870	−	4.58174i	−0.0734321	−	0.226001i
$412$	−16.9118	−	5.49497i	−0.833183	−	0.270718i
$413$	0.431179	+	0.140098i	0.0212169	+	0.00689379i
$414$	−0.0618027	−	0.190209i	−0.00303744	−	0.00934827i
$415$	−10.8432	+	17.9102i	−0.532271	+	0.879177i
$416$	−2.39161	+	7.36062i	−0.117258	+	0.360884i
$417$	−2.19876	+	3.02633i	−0.107674	+	0.148200i
$418$		−	22.3343i		−	1.09241i
$419$	5.75511	+	4.18133i	0.281156	+	0.204272i	0.719421	−	0.694574i	$-0.244407\pi$
$419$	5.75511	+	4.18133i	0.281156	+	0.204272i	−0.438266	+	0.898845i	$0.644407\pi$
$420$	2.24811	−	9.59124i	0.109697	−	0.468005i
$421$	17.6826	−	12.8472i	0.861798	−	0.626133i	−0.0665758	−	0.997781i	$-0.521207\pi$
$421$	17.6826	−	12.8472i	0.861798	−	0.626133i	0.928373	+	0.371649i	$0.121207\pi$
$422$	3.39873	+	4.67796i	0.165448	+	0.227719i
$423$	8.10408	−	2.63318i	0.394034	−	0.128029i
$424$	−18.1709			−0.882455
$425$	1.52832	−	3.08107i	0.0741345	−	0.149454i
$426$	6.52325			0.316052
$427$	15.6905	−	5.09816i	0.759318	−	0.246717i
$428$	12.3518	+	17.0008i	0.597045	+	0.821763i
$429$	6.13764	−	4.45926i	0.296328	−	0.215295i
$430$	−5.32552	−	12.6637i	−0.256819	−	0.610697i
$431$	−3.23115	−	2.34757i	−0.155639	−	0.113078i	0.507240	−	0.861805i	$-0.330666\pi$
$431$	−3.23115	−	2.34757i	−0.155639	−	0.113078i	−0.662879	+	0.748726i	$0.730666\pi$
$432$			2.35558i			0.113333i
$433$	14.8071	−	20.3802i	0.711583	−	0.979410i	−0.288178	−	0.957577i	$-0.593050\pi$
$433$	14.8071	−	20.3802i	0.711583	−	0.979410i	0.999762	−	0.0218335i	$-0.00695037\pi$
$434$	1.91519	−	5.89435i	0.0919321	−	0.282938i
$435$	0.0776608	+	0.0182031i	0.00372355	+	0.000872771i
$436$	2.23746	+	6.88620i	0.107155	+	0.329789i
$437$	−2.86890	−	0.932161i	−0.137238	−	0.0445913i
$438$	6.14987	+	1.99822i	0.293852	+	0.0954784i
$439$	0.529997	+	1.63116i	0.0252954	+	0.0778511i	0.962907	−	0.269833i	$-0.0869683\pi$
$439$	0.529997	+	1.63116i	0.0252954	+	0.0778511i	−0.937612	+	0.347684i	$0.886968\pi$
$440$	−22.3036	−	5.22779i	−1.06328	−	0.249225i
$441$	−0.117039	+	0.360209i	−0.00557329	+	0.0171528i
$442$	−0.319960	+	0.440387i	−0.0152189	+	0.0209471i
$443$		−	11.7475i		−	0.558140i	−0.960271	−	0.279070i	$-0.909974\pi$
$443$		−	11.7475i		−	0.558140i	0.960271	−	0.279070i	$-0.0900261\pi$
$444$	−2.64471	−	1.92149i	−0.125512	−	0.0911899i
$445$	0.0106783	+	0.0253921i	0.000506199	+	0.00120370i
$446$	−11.9678	+	8.69510i	−0.566691	+	0.411725i
$447$	−5.08212	−	6.99493i	−0.240376	−	0.330849i
$448$	−4.63929	+	1.50740i	−0.219186	+	0.0712178i
$449$	−12.8415			−0.606030			−0.303015	−	0.952986i	$-0.597993\pi$
$449$	−12.8415			−0.606030			−0.303015	+	0.952986i	$0.597993\pi$
$450$	−0.448178	−	2.64503i	−0.0211273	−	0.124688i
$451$	26.5890			1.25203
$452$	−29.9101	+	9.71837i	−1.40685	+	0.457114i
$453$	−0.734135	−	1.01045i	−0.0344927	−	0.0474751i
$454$	−1.72858	+	1.25589i	−0.0811263	+	0.0589417i
$455$	−1.93666	+	8.26249i	−0.0907921	+	0.387351i
$456$	−13.0400	−	9.47412i	−0.610654	−	0.443666i
$457$		−	13.6882i		−	0.640309i	−0.947365	−	0.320155i	$-0.896265\pi$
$457$		−	13.6882i		−	0.640309i	0.947365	−	0.320155i	$-0.103735\pi$
$458$	−3.77495	+	5.19577i	−0.176392	+	0.242783i
$459$	−0.212560	+	0.654193i	−0.00992146	+	0.0305351i
$460$	−0.739065	+	1.22075i	−0.0344591	+	0.0569177i
$461$	3.00160	+	9.23799i	0.139799	+	0.430256i	0.996306	−	0.0858796i	$-0.0273700\pi$
$461$	3.00160	+	9.23799i	0.139799	+	0.430256i	−0.856507	+	0.516136i	$0.827370\pi$
$462$	−6.75396	−	2.19450i	−0.314223	−	0.102097i
$463$	−20.2328	−	6.57403i	−0.940297	−	0.305521i	−0.201531	−	0.979482i	$-0.564592\pi$
$463$	−20.2328	−	6.57403i	−0.940297	−	0.305521i	−0.738767	+	0.673961i	$0.764592\pi$
$464$	−0.0259664	−	0.0799163i	−0.00120546	−	0.00371002i
$465$	0.841416	+	10.0024i	0.0390197	+	0.463852i
$466$	3.50143	−	10.7763i	0.162201	−	0.499202i
$467$	−8.17106	+	11.2465i	−0.378112	+	0.520426i	−0.955083	−	0.296338i	$-0.904234\pi$
$467$	−8.17106	+	11.2465i	−0.378112	+	0.520426i	0.576971	+	0.816764i	$0.304234\pi$
$468$		−	2.52524i		−	0.116729i
$469$	0.173696	+	0.126198i	0.00802054	+	0.00582727i
$470$	8.74541	+	5.29464i	0.403396	+	0.244224i
$471$	−3.12745	+	2.27223i	−0.144105	+	0.104699i
$472$	−0.206267	−	0.283902i	−0.00949419	−	0.0130676i
$473$	56.0156	−	18.2006i	2.57560	−	0.836862i
$474$	−2.65959			−0.122159
$475$	−36.2487	−	17.9807i	−1.66321	−	0.825010i
$476$	−3.03042			−0.138899
$477$	8.67665	−	2.81922i	0.397277	−	0.129083i
$478$	8.26438	+	11.3749i	0.378004	+	0.520278i
$479$	−10.0057	+	7.26958i	−0.457173	+	0.332155i	−0.792421	−	0.609974i	$-0.791180\pi$
$479$	−10.0057	+	7.26958i	−0.457173	+	0.332155i	0.335249	+	0.942130i	$0.391180\pi$
$480$	−8.88098	+	7.66815i	−0.405360	+	0.350001i
$481$	2.27831	+	1.65529i	0.103882	+	0.0754747i
$482$		−	4.38601i		−	0.199777i
$483$	−0.563776	+	0.775971i	−0.0256527	+	0.0353079i
$484$	8.17817	−	25.1698i	0.371735	−	1.14408i
$485$	11.1360	+	12.8974i	0.505661	+	0.585639i
$486$	0.165802	+	0.510286i	0.00752094	+	0.0231471i
$487$	33.5990	+	10.9170i	1.52251	+	0.494695i	0.946489	−	0.322737i	$-0.104603\pi$
$487$	33.5990	+	10.9170i	1.52251	+	0.494695i	0.576026	+	0.817432i	$0.304603\pi$
$488$	−12.1450	−	3.94614i	−0.549778	−	0.178634i
$489$	2.15512	+	6.63277i	0.0974578	+	0.299944i
$490$	−0.418872	+	0.176150i	−0.0189227	+	0.00795766i
$491$	−6.70374	+	20.6320i	−0.302536	+	0.931109i	0.678050	+	0.735016i	$0.262825\pi$
$491$	−6.70374	+	20.6320i	−0.302536	+	0.931109i	−0.980585	+	0.196093i	$0.937175\pi$
$492$	5.20211	−	7.16009i	0.234529	−	0.322802i
$493$		−	0.0245375i		−	0.00110511i
$494$	5.18114	+	3.76432i	0.233111	+	0.169365i
$495$	11.4612	−	0.964125i	0.515141	−	0.0433342i
$496$	8.55475	−	6.21539i	0.384120	−	0.279079i
$497$	−18.3884	−	25.3095i	−0.824834	−	1.13529i
$498$	4.77793	−	1.55244i	0.214104	−	0.0695666i
$499$	−38.7869			−1.73634			−0.868171	−	0.496265i	$-0.834704\pi$
$499$	−38.7869			−1.73634			−0.868171	+	0.496265i	$0.834704\pi$
$500$	−12.1951	+	14.7546i	−0.545380	+	0.659846i
$501$	−15.9594			−0.713013
$502$	−12.6625	+	4.11430i	−0.565155	+	0.183630i
$503$	−3.77337	−	5.19360i	−0.168246	−	0.231571i	0.716565	−	0.697520i	$-0.245713\pi$
$503$	−3.77337	−	5.19360i	−0.168246	−	0.231571i	−0.884812	+	0.465949i	$0.845713\pi$
$504$	−4.14627	+	3.01244i	−0.184689	+	0.134185i
$505$	18.4387	−	1.55109i	0.820513	−	0.0690225i
$506$	0.832257	+	0.604670i	0.0369983	+	0.0268809i
$507$		−	10.8246i		−	0.480737i
$508$	0.347697	−	0.478564i	0.0154266	−	0.0212328i
$509$	2.22343	−	6.84300i	0.0985516	−	0.303311i	−0.889611	−	0.456718i	$-0.849025\pi$
$509$	2.22343	−	6.84300i	0.0985516	−	0.303311i	0.988163	+	0.153408i	$0.0490247\pi$
$510$	−0.760732	+	0.319915i	−0.0336858	+	0.0141661i
$511$	−9.58307	−	29.4937i	−0.423930	−	1.30472i
$512$	20.6796	+	6.71922i	0.913919	+	0.296950i
$513$	7.69657	+	2.50077i	0.339812	+	0.110412i
$514$	−4.02891	−	12.3997i	−0.177708	−	0.546928i
$515$	15.1775	+	17.5781i	0.668802	+	0.774583i
$516$	6.05820	−	18.6452i	0.266697	−	0.820810i
$517$	−25.7627	+	35.4593i	−1.13304	+	1.55950i
$518$		−	2.63611i		−	0.115824i
$519$	−6.20783	−	4.51025i	−0.272493	−	0.197978i
$520$	4.97189	−	4.29290i	0.218032	−	0.188256i
$521$	8.51120	−	6.18375i	0.372882	−	0.270915i	−0.385523	−	0.922698i	$-0.625979\pi$
$521$	8.51120	−	6.18375i	0.372882	−	0.270915i	0.758405	+	0.651783i	$0.225979\pi$
$522$	−0.0112501	−	0.0154845i	−0.000492404	−	0.000677737i
$523$	10.7700	−	3.49938i	0.470938	−	0.153017i	−0.0639269	−	0.997955i	$-0.520362\pi$
$523$	10.7700	−	3.49938i	0.470938	−	0.153017i	0.534865	+	0.844938i	$0.320362\pi$
$524$	−7.81840			−0.341548
$525$	−8.99908	+	9.19499i	−0.392752	+	0.401302i
$526$	4.57282			0.199385
$527$	2.93669	−	0.954188i	0.127924	−	0.0415651i
$528$	−7.12183	−	9.80235i	−0.309938	−	0.426593i
$529$	−18.4950	+	13.4374i	−0.804130	+	0.584234i
$530$	9.36329	+	5.66872i	0.406715	+	0.246234i
$531$	0.142541	+	0.103562i	0.00618573	+	0.00449420i
$532$			35.6529i			1.54575i
$533$	−4.48142	+	6.16814i	−0.194112	+	0.267172i
$534$	0.00204251	−	0.00628621i	8.83882e−5	−	0.000272031i
$535$	−2.30057	−	27.3483i	−0.0994624	−	1.18237i
$536$	−0.0513540	−	0.158051i	−0.00221815	−	0.00682678i
$537$	10.0901	+	3.27846i	0.435418	+	0.141476i
$538$	−1.31813	−	0.428287i	−0.0568287	−	0.0184648i
$539$	−0.602013	−	1.85281i	−0.0259305	−	0.0798060i
$540$	1.98274	−	3.27498i	0.0853234	−	0.140933i
$541$	5.22898	−	16.0931i	0.224811	−	0.691898i	−0.773499	−	0.633797i	$-0.781495\pi$
$541$	5.22898	−	16.0931i	0.224811	−	0.691898i	0.998311	−	0.0581012i	$-0.0185046\pi$
$542$	−4.28572	+	5.89879i	−0.184087	+	0.253375i
$543$		−	15.1076i		−	0.648331i
$544$	2.92009	+	2.12157i	0.125198	+	0.0909614i
$545$	2.15801	−	9.20684i	0.0924390	−	0.394378i
$546$	1.64742	−	1.19692i	0.0705032	−	0.0512235i
$547$	25.9429	+	35.7073i	1.10924	+	1.52674i	0.822533	+	0.568717i	$0.192560\pi$
$547$	25.9429	+	35.7073i	1.10924	+	1.52674i	0.286705	+	0.958019i	$0.407440\pi$
$548$	7.84448	−	2.54883i	0.335100	−	0.108881i
$549$	6.41152			0.273637
$550$	9.86197	+	9.65185i	0.420516	+	0.411556i
$551$	−0.288683			−0.0122983
$552$	0.706079	−	0.229419i	0.0300527	−	0.00976472i
$553$	7.49715	+	10.3189i	0.318811	+	0.438806i
$554$	3.96734	−	2.88244i	0.168556	−	0.122463i
$555$	1.65506	+	3.93560i	0.0702532	+	0.167057i
$556$	−5.18143	−	3.76453i	−0.219741	−	0.159652i
$557$			17.8472i			0.756210i	0.925763	+	0.378105i	$0.123424\pi$
$557$			17.8472i			0.756210i	−0.925763	+	0.378105i	$0.876576\pi$
$558$	1.41572	−	1.94857i	0.0599323	−	0.0824897i
$559$	−5.21891	+	16.0621i	−0.220736	+	0.679356i
$560$	13.1959	+	3.09302i	0.557629	+	0.130704i
$561$	−1.09334	−	3.36497i	−0.0461610	−	0.142069i
$562$	5.31213	+	1.72602i	0.224079	+	0.0728076i
$563$	20.3586	+	6.61490i	0.858012	+	0.278785i	0.704798	−	0.709408i	$-0.251038\pi$
$563$	20.3586	+	6.61490i	0.858012	+	0.278785i	0.153214	+	0.988193i	$0.451038\pi$
$564$	4.50831	+	13.8751i	0.189834	+	0.584249i
$565$	39.9897	+	9.37328i	1.68238	+	0.394337i
$566$	0.798480	−	2.45747i	0.0335626	−	0.103295i
$567$	1.51248	−	2.08175i	0.0635181	−	0.0874251i
$568$			24.2151i			1.01604i
$569$	−21.0929	−	15.3249i	−0.884262	−	0.642454i	0.0501135	−	0.998744i	$-0.484042\pi$
$569$	−21.0929	−	15.3249i	−0.884262	−	0.642454i	−0.934376	+	0.356289i	$0.884042\pi$
$570$	3.76379	+	8.95000i	0.157648	+	0.374874i
$571$	7.71705	−	5.60676i	0.322948	−	0.234636i	−0.414484	−	0.910057i	$-0.636038\pi$
$571$	7.71705	−	5.60676i	0.322948	−	0.234636i	0.737433	+	0.675421i	$0.236038\pi$
$572$	7.63478	+	10.5084i	0.319226	+	0.439377i
$573$	11.6447	−	3.78359i	0.486464	−	0.158062i
$574$	7.13683			0.297885
$575$	1.65141	−	0.863956i	0.0688684	−	0.0360295i
$576$	−1.89572			−0.0789885
$577$	−8.65941	+	2.81361i	−0.360496	+	0.117132i	−0.483664	−	0.875254i	$-0.660694\pi$
$577$	−8.65941	+	2.81361i	−0.360496	+	0.117132i	0.123169	+	0.992386i	$0.460694\pi$
$578$	−5.21214	−	7.17390i	−0.216797	−	0.298395i
$579$	11.5221	−	8.37130i	0.478843	−	0.347900i
$580$	−0.0311658	+	0.132964i	−0.00129409	+	0.00552105i
$581$	−19.4919	−	14.1617i	−0.808658	−	0.587525i
$582$		−	4.08871i		−	0.169482i
$583$	−27.5829	+	37.9646i	−1.14237	+	1.57233i
$584$	−7.41761	+	22.8291i	−0.306943	+	0.944673i
$585$	−1.70805	+	2.82127i	−0.0706192	+	0.116645i
$586$	4.05396	+	12.4768i	0.167468	+	0.515412i
$587$	−28.0072	−	9.10008i	−1.15598	−	0.375600i	−0.332587	−	0.943073i	$-0.607921\pi$
$587$	−28.0072	−	9.10008i	−1.15598	−	0.375600i	−0.823393	+	0.567472i	$0.807921\pi$
$588$	−0.616721	−	0.200385i	−0.0254331	−	0.00826373i
$589$	−11.2260	−	34.5501i	−0.462559	−	1.42361i
$590$	0.0177193	+	0.210641i	0.000729494	+	0.00867194i
$591$	−5.48469	+	16.8802i	−0.225610	+	0.694357i
$592$	2.64364	−	3.63866i	0.108653	−	0.149548i
$593$			33.7757i			1.38700i	0.720456	+	0.693501i	$0.243933\pi$
$593$			33.7757i			1.38700i	−0.720456	+	0.693501i	$0.756067\pi$
$594$	−2.23275	−	1.62219i	−0.0916108	−	0.0665592i
$595$	3.38567	+	2.04975i	0.138799	+	0.0840316i
$596$	11.9761	−	8.70118i	0.490562	−	0.356414i
$597$	11.1415	+	15.3349i	0.455991	+	0.627617i
$598$	−0.280544	+	0.0911543i	−0.0114723	+	0.00372758i
$599$	12.0575			0.492656			0.246328	−	0.969187i	$-0.420776\pi$
$599$	12.0575			0.492656			0.246328	+	0.969187i	$0.420776\pi$
$600$	9.81867	−	1.66369i	0.400846	−	0.0679198i
$601$	0.0653240			0.00266462			0.00133231	−	0.999999i	$-0.499576\pi$
$601$	0.0653240			0.00266462			0.00133231	+	0.999999i	$0.499576\pi$
$602$	15.0353	−	4.88526i	0.612793	−	0.199108i
$603$	0.0490435	+	0.0675025i	0.00199720	+	0.00274892i
$604$	1.73001	−	1.25692i	0.0703930	−	0.0511435i
$605$	−26.1615	+	22.5888i	−1.06362	+	0.918363i
$606$	−3.59205	−	2.60978i	−0.145917	−	0.106015i
$607$		−	25.9556i		−	1.05350i	−0.850019	−	0.526752i	$-0.823410\pi$
$607$		−	25.9556i		−	1.05350i	0.850019	−	0.526752i	$-0.176590\pi$
$608$	24.9602	−	34.3548i	1.01227	−	1.39327i
$609$	−0.0283650	+	0.0872986i	−0.00114941	+	0.00353752i
$610$	5.02714	+	5.82226i	0.203543	+	0.235736i
$611$	−3.88373	−	11.9529i	−0.157119	−	0.483563i
$612$	−1.12006	−	0.363928i	−0.0452756	−	0.0147109i
$613$	−11.9559	−	3.88472i	−0.482896	−	0.156902i	0.0574448	−	0.998349i	$-0.481705\pi$
$613$	−11.9559	−	3.88472i	−0.482896	−	0.156902i	−0.540341	+	0.841446i	$0.681705\pi$
$614$	1.57786	+	4.85617i	0.0636774	+	0.195979i
$615$	−10.6550	+	4.48078i	−0.429649	+	0.180683i
$616$	8.14623	−	25.0715i	0.328221	−	1.01016i
$617$	−1.09165	+	1.50253i	−0.0439483	+	0.0604896i	−0.830426	−	0.557130i	$-0.811903\pi$
$617$	−1.09165	+	1.50253i	−0.0439483	+	0.0604896i	0.786477	+	0.617619i	$0.211903\pi$
$618$		−	5.57259i		−	0.224162i
$619$	−14.5814	−	10.5940i	−0.586077	−	0.425810i	0.254833	−	0.966985i	$-0.417980\pi$
$619$	−14.5814	−	10.5940i	−0.586077	−	0.425810i	−0.840910	+	0.541175i	$0.817980\pi$
$620$	−17.1253	+	1.44060i	−0.687770	+	0.0578560i
$621$	−0.301561	+	0.219097i	−0.0121012	+	0.00879206i
$622$	−7.87848	−	10.8438i	−0.315898	−	0.434797i
$623$	−0.0301475	+	0.00979552i	−0.00120783	+	0.000392449i
$624$	3.47430			0.139083
$625$	23.6045	−	8.23562i	0.944182	−	0.329425i
$626$	5.30195			0.211908
$627$	−39.5888	+	12.8632i	−1.58102	+	0.513705i
$628$	−3.89032	−	5.35456i	−0.155241	−	0.213670i
$629$	1.06254	−	0.771977i	0.0423661	−	0.0307807i
$630$	3.07632	−	0.258784i	0.122564	−	0.0103102i
$631$	−17.3636	−	12.6154i	−0.691233	−	0.502210i	0.185832	−	0.982582i	$-0.440502\pi$
$631$	−17.3636	−	12.6154i	−0.691233	−	0.502210i	−0.877065	+	0.480371i	$0.840502\pi$
$632$		−	9.87272i		−	0.392716i
$633$	6.33446	−	8.71864i	0.251772	−	0.346535i
$634$	−4.10046	+	12.6199i	−0.162850	+	0.501201i
$635$	−0.712153	+	0.299485i	−0.0282609	+	0.0118847i
$636$	4.82683	+	14.8555i	0.191396	+	0.589057i
$637$	0.531281	+	0.172624i	0.0210501	+	0.00683960i
$638$	0.0936310	+	0.0304225i	0.00370689	+	0.00120444i
$639$	−3.75698	−	11.5628i	−0.148624	−	0.457417i
$640$	−16.8227	−	19.4835i	−0.664975	−	0.770151i
$641$	12.2648	−	37.7471i	0.484430	−	1.49092i	−0.348374	−	0.937355i	$-0.613266\pi$
$641$	12.2648	−	37.7471i	0.484430	−	1.49092i	0.832805	−	0.553567i	$-0.186734\pi$
$642$	−3.87082	+	5.32773i	−0.152769	+	0.210269i
$643$			1.26211i			0.0497729i	0.999690	+	0.0248864i	$0.00792242\pi$
$643$			1.26211i			0.0497729i	−0.999690	+	0.0248864i	$0.992078\pi$
$644$	−1.32855	−	0.965250i	−0.0523523	−	0.0380362i
$645$	−19.3798	+	16.7332i	−0.763081	+	0.658870i
$646$	2.41633	−	1.75557i	0.0950692	−	0.0690718i
$647$	−17.0032	−	23.4029i	−0.668466	−	0.920064i	0.331259	−	0.943540i	$-0.392527\pi$
$647$	−17.0032	−	23.4029i	−0.668466	−	0.920064i	−0.999724	+	0.0234758i	$0.992527\pi$
$648$	−1.89424	+	0.615477i	−0.0744129	+	0.0241782i
$649$	−0.906266			−0.0355740
$650$	−3.90122	+	0.661028i	−0.153018	+	0.0259276i
$651$	−11.5511			−0.452722
$652$	−11.3561	+	3.68982i	−0.444739	+	0.144504i
$653$	−10.2743	−	14.1413i	−0.402063	−	0.553393i	0.559197	−	0.829035i	$-0.311110\pi$
$653$	−10.2743	−	14.1413i	−0.402063	−	0.553393i	−0.961260	+	0.275642i	$0.911110\pi$
$654$	−1.83571	+	1.33372i	−0.0717821	+	0.0521527i
$655$	8.73493	+	5.28830i	0.341302	+	0.206631i
$656$	9.85106	+	7.15721i	0.384619	+	0.279442i
$657$		−	12.0518i		−	0.470186i
$658$	−6.91503	+	9.51772i	−0.269576	+	0.371039i
$659$	−3.50406	+	10.7844i	−0.136499	+	0.420100i	−0.995820	−	0.0913359i	$-0.970886\pi$
$659$	−3.50406	+	10.7844i	−0.136499	+	0.420100i	0.859321	+	0.511436i	$0.170886\pi$
$660$	1.65070	+	19.6228i	0.0642533	+	0.763818i
$661$	1.43350	+	4.41185i	0.0557565	+	0.171601i	0.975057	−	0.221956i	$-0.0712443\pi$
$661$	1.43350	+	4.41185i	0.0557565	+	0.171601i	−0.919300	+	0.393557i	$0.871244\pi$
$662$	0.550225	+	0.178779i	0.0213851	+	0.00694844i
$663$	0.964885	+	0.313510i	0.0374730	+	0.0121757i
$664$	5.76285	+	17.7362i	0.223642	+	0.688299i
$665$	24.1153	−	39.8324i	0.935151	−	1.54463i
$666$	0.316575	−	0.974317i	0.0122670	−	0.0377540i
$667$	0.00781569	−	0.0107574i	0.000302625	−	0.000416527i
$668$		−	27.3243i		−	1.05721i
$669$	22.3052	+	16.2057i	0.862369	+	0.626547i
$670$	−0.0228446	+	0.0974634i	−0.000882565	+	0.00376534i
$671$	−26.6805	+	19.3845i	−1.02999	+	0.748330i
$672$	−7.93647	−	10.9236i	−0.306156	−	0.421387i
$673$	−7.16302	+	2.32741i	−0.276114	+	0.0897149i	−0.443801	−	0.896125i	$-0.646370\pi$
$673$	−7.16302	+	2.32741i	−0.276114	+	0.0897149i	0.167687	+	0.985840i	$0.446370\pi$
$674$	7.54435			0.290598
$675$	−4.43033	+	2.31779i	−0.170524	+	0.0892118i
$676$	18.5330			0.712807
$677$	30.0707	−	9.77055i	1.15571	−	0.375513i	0.332418	−	0.943132i	$-0.392136\pi$
$677$	30.0707	−	9.77055i	1.15571	−	0.375513i	0.823291	+	0.567619i	$0.192136\pi$
$678$	−5.79300	−	7.97338i	−0.222479	−	0.306216i
$679$	−15.8638	+	11.5257i	−0.608795	+	0.442316i
$680$	−1.18756	−	2.82393i	−0.0455409	−	0.108293i
$681$	3.22167	+	2.34068i	0.123455	+	0.0896952i
$682$			12.3889i			0.474397i
$683$	18.0215	−	24.8045i	0.689575	−	0.949118i	−0.310424	−	0.950598i	$-0.600471\pi$
$683$	18.0215	−	24.8045i	0.689575	−	0.949118i	0.999999	+	0.00148011i	$0.000471134\pi$
$684$	−4.28161	+	13.1774i	−0.163711	+	0.503852i
$685$	−10.4881	−	2.45832i	−0.400729	−	0.0939276i
$686$	−3.14806	−	9.68873i	−0.120193	−	0.369917i
$687$	11.3839	+	3.69886i	0.434323	+	0.141120i
$688$	25.6526	+	8.33505i	0.977998	+	0.317771i
$689$	−4.15813	−	12.7974i	−0.158412	−	0.487542i
$690$	−0.435408	−	0.102056i	−0.0165757	−	0.00388521i
$691$	−10.7334	+	33.0341i	−0.408318	+	1.25667i	0.509774	+	0.860308i	$0.329729\pi$
$691$	−10.7334	+	33.0341i	−0.408318	+	1.25667i	−0.918092	+	0.396366i	$0.870271\pi$
$692$	7.72208	−	10.6285i	0.293550	−	0.404036i
$693$			13.2356i			0.502780i
$694$	−2.47243	−	1.79632i	−0.0938520	−	0.0681875i
$695$	3.24254	+	7.71050i	0.122996	+	0.292476i
$696$	0.0574802	−	0.0417618i	0.00217878	−	0.00158298i
$697$	2.09000	+	2.87663i	0.0791643	+	0.108960i
$698$	−14.5406	+	4.72453i	−0.550370	+	0.178826i
$699$	−21.1181			−0.798761
$700$	−15.7429	−	15.4075i	−0.595026	−	0.582348i
$701$	−19.5437			−0.738154			−0.369077	−	0.929399i	$-0.620326\pi$
$701$	−19.5437			−0.738154			−0.369077	+	0.929399i	$0.620326\pi$
$702$	0.752633	−	0.244545i	0.0284063	−	0.00922977i
$703$	−9.08230	−	12.5007i	−0.342545	−	0.471473i
$704$	7.88873	−	5.73150i	0.297318	−	0.216014i
$705$	4.34822	−	18.5511i	0.163763	−	0.698673i
$706$	5.54122	+	4.02593i	0.208547	+	0.151518i
$707$			21.2935i			0.800825i
$708$	−0.177310	+	0.244046i	−0.00666372	+	0.00917182i
$709$	7.82140	−	24.0718i	0.293739	−	0.904035i	−0.689904	−	0.723901i	$-0.742347\pi$
$709$	7.82140	−	24.0718i	0.293739	−	0.904035i	0.983642	−	0.180133i	$-0.0576529\pi$
$710$	7.55432	−	12.4778i	0.283508	−	0.468284i
$711$	1.53176	+	4.71426i	0.0574453	+	0.176799i
$712$	0.0233351	+	0.00758205i	0.000874522	+	0.000284149i
$713$	1.59139	+	0.517073i	0.0595979	+	0.0193645i
$714$	−0.293467	−	0.903200i	−0.0109827	−	0.0338014i
$715$	−1.42201	−	16.9043i	−0.0531802	−	0.632186i
$716$	−5.61311	+	17.2754i	−0.209772	+	0.645611i
$717$	15.4029	−	21.2003i	0.575232	−	0.791738i
$718$			2.42423i			0.0904715i
$719$	−7.43539	−	5.40213i	−0.277293	−	0.201465i	0.440443	−	0.897781i	$-0.354822\pi$
$719$	−7.43539	−	5.40213i	−0.277293	−	0.201465i	−0.717736	+	0.696315i	$0.754822\pi$
$720$	4.50581	+	2.72791i	0.167922	+	0.101663i
$721$	−21.6211	+	15.7086i	−0.805210	+	0.585019i
$722$	−14.6621	−	20.1806i	−0.545666	−	0.751045i
$723$	−7.77443	+	2.52607i	−0.289134	+	0.0939454i
$724$	25.8661			0.961305
$725$	0.124755	−	0.127471i	0.00463329	−	0.00473416i
$726$	8.29369			0.307808
$727$	−12.4254	+	4.03726i	−0.460833	+	0.149734i	−0.530227	−	0.847856i	$-0.677893\pi$
$727$	−12.4254	+	4.03726i	−0.460833	+	0.149734i	0.0693942	+	0.997589i	$0.477893\pi$
$728$	4.44312	+	6.11542i	0.164673	+	0.226653i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	10.9442	−	9.44957i	0.405062	−	0.349744i
$731$	6.37213	+	4.62963i	0.235682	+	0.171233i
$732$			10.9773i			0.405732i
$733$	−5.69030	+	7.83202i	−0.210176	+	0.289282i	−0.901070	−	0.433674i	$-0.857217\pi$
$733$	−5.69030	+	7.83202i	−0.210176	+	0.289282i	0.690894	+	0.722956i	$0.257217\pi$
$734$	0.503121	−	1.54845i	0.0185705	−	0.0571542i
$735$	0.553479	+	0.641020i	0.0204154	+	0.0236444i
$736$	0.604419	+	1.86021i	0.0222792	+	0.0685683i
$737$	−0.408172	−	0.132623i	−0.0150352	−	0.00488524i
$738$	2.63780	+	0.857072i	0.0970986	+	0.0315493i
$739$	−2.82260	−	8.68707i	−0.103831	−	0.319559i	0.885623	−	0.464404i	$-0.153732\pi$
$739$	−2.82260	−	8.68707i	−0.103831	−	0.319559i	−0.989454	+	0.144845i	$0.953732\pi$
$740$	−6.73820	+	2.83365i	−0.247701	+	0.104167i
$741$	3.68844	−	11.3518i	0.135498	−	0.417021i
$742$	−7.40359	+	10.1902i	−0.271794	+	0.374093i
$743$		−	6.35760i		−	0.233238i	−0.993177	−	0.116619i	$-0.962794\pi$
$743$		−	6.35760i		−	0.233238i	0.993177	−	0.116619i	$-0.0372056\pi$
$744$	7.23334	+	5.25533i	0.265187	+	0.192670i
$745$	−19.2655	+	1.62063i	−0.705832	+	0.0593754i
$746$	6.66994	−	4.84600i	0.244204	−	0.177425i
$747$	−5.50356	−	7.57501i	−0.201365	−	0.277155i
$748$	5.76122	−	1.87193i	0.210651	−	0.0684446i
$749$	31.5825			1.15400
$750$	−5.57850	−	2.20582i	−0.203698	−	0.0805453i
$751$	35.0142			1.27768			0.638842	−	0.769338i	$-0.279414\pi$
$751$	35.0142			1.27768			0.638842	+	0.769338i	$0.279414\pi$
$752$	−19.0898	+	6.20266i	−0.696134	+	0.226188i
$753$	14.5856	+	20.0754i	0.531529	+	0.731586i
$754$	−0.0228384	+	0.0165931i	−0.000831725	+	0.000604284i
$755$	−2.78298	+	0.234108i	−0.101283	+	0.00852006i
$756$	3.56419	+	2.58954i	0.129628	+	0.0941806i
$757$		−	11.5175i		−	0.418609i	−0.977850	−	0.209305i	$-0.932880\pi$
$757$		−	11.5175i		−	0.418609i	0.977850	−	0.209305i	$-0.0671200\pi$
$758$	−3.26718	+	4.49689i	−0.118669	+	0.163334i
$759$	0.592481	−	1.82347i	0.0215057	−	0.0661878i
$760$	−33.2235	+	13.9716i	−1.20514	+	0.506804i
$761$	12.6925	+	39.0635i	0.460102	+	1.41605i	0.865039	+	0.501705i	$0.167294\pi$
$761$	12.6925	+	39.0635i	0.460102	+	1.41605i	−0.404936	+	0.914345i	$0.632706\pi$
$762$	0.176304	+	0.0572847i	0.00638683	+	0.00207521i
$763$	10.3494	+	3.36273i	0.374674	+	0.121739i
$764$	6.47795	+	19.9371i	0.234364	+	0.721298i
$765$	1.00520	+	1.16419i	0.0363430	+	0.0420912i
$766$	2.56771	−	7.90259i	0.0927750	−	0.285532i
$767$	0.152746	−	0.210236i	0.00551533	−	0.00759120i
$768$			2.38518i			0.0860677i
$769$	14.5193	+	10.5489i	0.523578	+	0.380402i	0.817950	−	0.575289i	$-0.195111\pi$
$769$	14.5193	+	10.5489i	0.523578	+	0.380402i	−0.294372	+	0.955691i	$0.595111\pi$
$770$	−12.0192	+	10.3778i	−0.433141	+	0.373989i
$771$	−19.6587	+	14.2829i	−0.707992	+	0.514386i
$772$	14.3327	+	19.7272i	0.515844	+	0.709998i
$773$	−49.4776	+	16.0762i	−1.77958	+	0.578222i	−0.998908	−	0.0467133i	$-0.985125\pi$
$773$	−49.4776	+	16.0762i	−1.77958	+	0.578222i	−0.780676	+	0.624935i	$0.785125\pi$
$774$	6.14378			0.220833
$775$	20.1073	+	9.97394i	0.722275	+	0.358275i
$776$	15.1778			0.544850
$777$	−4.67264	+	1.51823i	−0.167630	+	0.0544663i
$778$	−6.74741	−	9.28701i	−0.241906	−	0.332955i
$779$	33.8435	−	24.5888i	1.21257	−	0.880984i
$780$	−4.83034	−	2.92438i	−0.172954	−	0.104710i
$781$	50.5928	+	36.7578i	1.81035	+	1.31530i
$782$			0.137570i			0.00491951i
$783$	−0.0209676	+	0.0288595i	−0.000749322	+	0.00103135i
$784$	0.275695	−	0.848502i	0.00984626	−	0.0303037i
$785$	0.724589	+	8.61364i	0.0258617	+	0.307434i
$786$	−0.757137	−	2.33023i	−0.0270062	−	0.0831165i
$787$	11.9113	+	3.87021i	0.424592	+	0.137958i	0.513516	−	0.858080i	$-0.328343\pi$
$787$	11.9113	+	3.87021i	0.424592	+	0.137958i	−0.0889240	+	0.996038i	$0.528343\pi$
$788$	−28.9008	−	9.39044i	−1.02955	−	0.334521i
$789$	−2.63366	−	8.10556i	−0.0937607	−	0.288566i
$790$	−3.07997	+	5.08733i	−0.109580	+	0.180999i
$791$	−14.6060	+	44.9525i	−0.519328	+	1.59833i
$792$	6.02175	−	8.28823i	0.213974	−	0.294509i
$793$		−	9.45650i		−	0.335810i
$794$	−5.42665	−	3.94269i	−0.192585	−	0.139921i
$795$	4.65543	−	19.8617i	0.165111	−	0.704423i
$796$	−26.2552	+	19.0755i	−0.930591	+	0.676114i
$797$	14.7779	+	20.3400i	0.523460	+	0.720481i	0.986116	−	0.166057i	$-0.0531035\pi$
$797$	14.7779	+	20.3400i	0.523460	+	0.720481i	−0.462656	+	0.886538i	$0.653104\pi$
$798$	−10.6261	+	3.45264i	−0.376161	+	0.122222i
$799$	−5.86134			−0.207359
$800$	4.38310	+	25.8679i	0.154966	+	0.914570i
$801$	−0.0123190			−0.000435270
$802$	16.8638	−	5.47939i	0.595483	−	0.193484i
$803$	36.4372	+	50.1516i	1.28584	+	1.76981i
$804$	−0.115572	+	0.0839682i	−0.00407592	+	0.00296133i
$805$	0.831409	+	1.97703i	0.0293033	+	0.0696810i
$806$	−2.87400	−	2.08808i	−0.101232	−	0.0735495i
$807$			2.58312i			0.0909302i
$808$	9.68781	−	13.3341i	0.340816	−	0.469093i
$809$	1.49157	−	4.59059i	0.0524409	−	0.161396i	−0.921406	−	0.388601i	$-0.872959\pi$
$809$	1.49157	−	4.59059i	0.0524409	−	0.161396i	0.973847	+	0.227204i	$0.0729585\pi$
$810$	1.16810	+	0.273793i	0.0410427	+	0.00962009i
$811$	−11.3898	−	35.0543i	−0.399952	−	1.23092i	−0.925038	−	0.379875i	$-0.875967\pi$
$811$	−11.3898	−	35.0543i	−0.399952	−	1.23092i	0.525086	−	0.851049i	$-0.324033\pi$
$812$	−0.149465	−	0.0485643i	−0.00524521	−	0.00170427i
$813$	12.9242	+	4.19933i	0.453271	+	0.147277i
$814$	1.62836	+	5.01158i	0.0570740	+	0.175656i
$815$	15.1831	+	3.55879i	0.531840	+	0.124659i
$816$	0.500703	−	1.54100i	0.0175281	−	0.0539460i
$817$	54.4675	−	74.9680i	1.90558	−	2.62280i
$818$		−	1.61897i		−	0.0566061i
$819$	−3.07042	−	2.23079i	−0.107289	−	0.0779500i
$820$	−7.67163	−	18.2425i	−0.267905	−	0.637057i
$821$	−11.4772	+	8.33868i	−0.400557	+	0.291022i	−0.769768	−	0.638324i	$-0.779628\pi$
$821$	−11.4772	+	8.33868i	−0.400557	+	0.291022i	0.369211	+	0.929346i	$0.379628\pi$
$822$	1.51933	+	2.09117i	0.0529926	+	0.0729380i
$823$	−24.7212	+	8.03241i	−0.861728	+	0.279992i	−0.706350	−	0.707863i	$-0.749660\pi$
$823$	−24.7212	+	8.03241i	−0.861728	+	0.279992i	−0.155378	+	0.987855i	$0.549660\pi$
$824$	20.6861			0.720634
$825$	11.4285	−	23.0397i	0.397890	−	0.802139i
$826$	−0.243253			−0.00846386
$827$	40.8326	−	13.2673i	1.41989	−	0.461350i	0.504322	−	0.863516i	$-0.331743\pi$
$827$	40.8326	−	13.2673i	1.41989	−	0.461350i	0.915567	+	0.402166i	$0.131743\pi$
$828$	−0.375120	−	0.516308i	−0.0130363	−	0.0179429i
$829$	−4.56100	+	3.31376i	−0.158410	+	0.115092i	−0.664167	−	0.747585i	$-0.731213\pi$
$829$	−4.56100	+	3.31376i	−0.158410	+	0.115092i	0.505756	+	0.862676i	$0.331213\pi$
$830$	2.56358	−	10.9372i	0.0889832	−	0.379634i
$831$	−7.39421	−	5.37221i	−0.256502	−	0.186360i
$832$			2.79605i			0.0969355i
$833$	0.153132	−	0.210769i	0.00530572	−	0.00730270i
$834$	0.620224	−	1.90885i	0.0214766	−	0.0660981i
$835$	−18.4819	+	30.5275i	−0.639594	+	1.05645i
$836$	−22.0233	−	67.7806i	−0.761690	−	2.34424i
$837$	−4.26931	−	1.38718i	−0.147569	−	0.0479481i
$838$	−3.63003	−	1.17947i	−0.125397	−	0.0407441i
$839$	7.12687	+	21.9343i	0.246047	+	0.757255i	0.995463	+	0.0951546i	$0.0303346\pi$
$839$	7.12687	+	21.9343i	0.246047	+	0.757255i	−0.749416	+	0.662100i	$0.769665\pi$
$840$	0.960635	+	11.4197i	0.0331451	+	0.394016i
$841$	−8.96110	+	27.5794i	−0.309003	+	0.951015i
$842$	−6.89311	+	9.48755i	−0.237552	+	0.326963i
$843$		−	10.4101i		−	0.358543i
$844$	14.9273	+	10.8453i	0.513820	+	0.373312i
$845$	−20.7056	−	12.5355i	−0.712293	−	0.431236i
$846$	−3.69882	+	2.68735i	−0.127168	+	0.0923929i
$847$	−23.3792	−	32.1787i	−0.803317	−	1.10567i
$848$	−20.4386	+	6.64089i	−0.701863	+	0.228049i
$849$	−4.81586			−0.165280
$850$	−0.269034	+	1.82563i	−0.00922779	+	0.0626185i
$851$	0.711711			0.0243971
$852$	19.7968	−	6.43238i	0.678229	−	0.220370i
$853$	−22.9504	−	31.5886i	−0.785808	−	1.08157i	−0.994617	−	0.103616i	$-0.966959\pi$
$853$	−22.9504	−	31.5886i	−0.785808	−	1.08157i	0.208809	−	0.977956i	$-0.433041\pi$
$854$	−7.16138	+	5.20305i	−0.245057	+	0.178045i
$855$	13.6966	−	11.8261i	0.468415	−	0.404445i
$856$	−19.7772	−	14.3690i	−0.675970	−	0.491121i
$857$		−	12.7315i		−	0.434899i	−0.976072	−	0.217450i	$-0.930226\pi$
$857$		−	12.7315i		−	0.434899i	0.976072	−	0.217450i	$-0.0697738\pi$
$858$	−2.39260	+	3.29313i	−0.0816821	+	0.112426i
$859$	−4.50752	+	13.8727i	−0.153795	+	0.473331i	−0.998037	−	0.0626308i	$-0.980051\pi$
$859$	−4.50752	+	13.8727i	−0.153795	+	0.473331i	0.844242	+	0.535962i	$0.180051\pi$
$860$	−28.6493	−	33.1806i	−0.976931	−	1.13145i
$861$	−4.11036	−	12.6504i	−0.140081	−	0.431124i
$862$	2.03805	+	0.662201i	0.0694161	+	0.0225547i
$863$	−16.6573	−	5.41229i	−0.567021	−	0.184236i	0.0114567	−	0.999934i	$-0.496353\pi$
$863$	−16.6573	−	5.41229i	−0.567021	−	0.184236i	−0.578478	+	0.815698i	$0.696353\pi$
$864$	−1.62151	−	4.99051i	−0.0551650	−	0.169781i
$865$	−15.8164	+	6.65134i	−0.537773	+	0.226152i
$866$	−4.17677	+	12.8548i	−0.141933	+	0.436824i
$867$	−9.71424	+	13.3705i	−0.329913	+	0.454086i
$868$		−	19.7768i		−	0.671267i
$869$	−20.6272	−	14.9865i	−0.699729	−	0.508383i
$870$	−0.0426474	+	0.00358755i	−0.00144588	+	0.000121629i
$871$	0.0995611	−	0.0723353i	0.00337350	−	0.00245099i
$872$	−4.95094	−	6.81438i	−0.167660	−	0.230764i
$873$	−7.24744	+	2.35484i	−0.245289	+	0.0796992i
$874$	1.61851			0.0547470
$875$	7.16691	+	27.8620i	0.242286	+	0.941908i
$876$	20.6341			0.697162
$877$	8.66169	−	2.81435i	0.292485	−	0.0950340i	−0.159100	−	0.987263i	$-0.550859\pi$
$877$	8.66169	−	2.81435i	0.292485	−	0.0950340i	0.451584	+	0.892229i	$0.350859\pi$
$878$	−0.540900	−	0.744485i	−0.0182545	−	0.0251252i
$879$	19.7809	−	14.3717i	0.667195	−	0.484745i
$880$	−26.9977	+	2.27108i	−0.910092	+	0.0765579i
$881$	36.5744	+	26.5728i	1.23222	+	0.895261i	0.997055	−	0.0766939i	$-0.0244364\pi$
$881$	36.5744	+	26.5728i	1.23222	+	0.895261i	0.235167	+	0.971955i	$0.424436\pi$
$882$		−	0.203215i		−	0.00684262i
$883$	−2.49354	+	3.43206i	−0.0839142	+	0.115498i	−0.848910	−	0.528537i	$-0.822741\pi$
$883$	−2.49354	+	3.43206i	−0.0839142	+	0.115498i	0.764996	+	0.644035i	$0.222741\pi$
$884$	−0.536766	+	1.65200i	−0.0180534	+	0.0555626i
$885$	0.363166	−	0.152724i	0.0122077	−	0.00513377i
$886$	1.94776	+	5.99458i	0.0654362	+	0.201392i
$887$	12.1607	+	3.95124i	0.408316	+	0.132670i	0.505971	−	0.862551i	$-0.331134\pi$
$887$	12.1607	+	3.95124i	0.408316	+	0.132670i	−0.0976554	+	0.995220i	$0.531134\pi$
$888$	3.61678	+	1.17516i	0.121371	+	0.0394359i
$889$	−0.274727	−	0.845523i	−0.00921405	−	0.0283579i
$890$	−0.00965906	−	0.0111868i	−0.000323772	−	0.000374982i
$891$	−1.58949	+	4.89194i	−0.0532498	+	0.163886i
$892$	−27.7460	+	38.1891i	−0.929005	+	1.27867i
$893$			68.9586i			2.30761i
$894$	3.75311	+	2.72679i	0.125523	+	0.0911976i
$895$	17.9560	−	15.5038i	0.600203	−	0.518236i
$896$	23.9647	−	17.4113i	0.800603	−	0.581672i
$897$	0.323151	+	0.444779i	0.0107897	+	0.0148508i
$898$	6.55287	−	2.12916i	0.218672	−	0.0710508i
$899$	0.160134			0.00534076
$900$	−3.96833	−	7.58525i	−0.132278	−	0.252842i
$901$	−6.27546			−0.209066
$902$	−13.5680	+	4.40851i	−0.451765	+	0.146787i
$903$	−17.3187	−	23.8372i	−0.576332	−	0.793253i
$904$	29.5981	−	21.5043i	0.984419	−	0.715223i
$905$	−28.8983	−	17.4956i	−0.960611	−	0.581573i
$906$	0.542154	+	0.393898i	0.0180118	+	0.0130864i
$907$		−	9.51928i		−	0.316082i	−0.987433	−	0.158041i	$-0.949482\pi$
$907$		−	9.51928i		−	0.316082i	0.987433	−	0.158041i	$-0.0505179\pi$
$908$	−4.00753	+	5.51589i	−0.132994	+	0.183051i
$909$	−2.55717	+	7.87016i	−0.0848160	+	0.261037i
$910$	−0.381686	−	4.53734i	−0.0126528	−	0.150411i
$911$	−12.8107	−	39.4274i	−0.424438	−	1.30629i	−0.903531	−	0.428522i	$-0.859034\pi$
$911$	−12.8107	−	39.4274i	−0.424438	−	1.30629i	0.479093	−	0.877764i	$-0.340966\pi$
$912$	−18.1299	−	5.89076i	−0.600341	−	0.195063i
$913$	45.8043	+	14.8827i	1.51590	+	0.492546i
$914$	2.26954	+	6.98492i	0.0750697	+	0.231041i
$915$	7.42493	−	12.2641i	0.245461	−	0.405439i
$916$	−6.33287	+	19.4906i	−0.209244	+	0.643987i
$917$	−6.90674	+	9.50631i	−0.228081	+	0.313926i
$918$		−	0.369069i		−	0.0121811i
$919$	12.8372	+	9.32675i	0.423459	+	0.307661i	0.779028	−	0.626989i	$-0.215713\pi$
$919$	12.8372	+	9.32675i	0.423459	+	0.307661i	−0.355569	+	0.934650i	$0.615713\pi$
$920$	0.378845	−	1.61629i	0.0124901	−	0.0532874i
$921$	7.69905	−	5.59369i	0.253692	−	0.184318i
$922$	−3.06336	−	4.21635i	−0.100886	−	0.138858i
$923$	−17.0542	+	5.54125i	−0.561346	+	0.182393i
$924$	−22.6610			−0.745491
$925$	9.44476	+	1.39183i	0.310542	+	0.0457631i
$926$	11.4145			0.375104
$927$	−9.87769	+	3.20946i	−0.324426	+	0.105412i
$928$	0.110024	+	0.151435i	0.00361172	+	0.00497110i
$929$	−23.7938	+	17.2872i	−0.780650	+	0.567175i	−0.905174	−	0.425041i	$-0.860260\pi$
$929$	−23.7938	+	17.2872i	−0.780650	+	0.567175i	0.124524	+	0.992217i	$0.460260\pi$
$930$	−2.08779	−	4.96460i	−0.0684612	−	0.162796i
$931$	−2.47969	−	1.80160i	−0.0812685	−	0.0590451i
$932$		−	36.1567i		−	1.18435i
$933$	−14.6837	+	20.2103i	−0.480722	+	0.661657i
$934$	2.30489	−	7.09372i	0.0754182	−	0.232114i
$935$	−7.70275	−	1.80546i	−0.251907	−	0.0590449i
$936$	0.907781	+	2.79386i	0.0296718	+	0.0913203i
$937$	−55.2688	−	17.9579i	−1.80555	−	0.586660i	−0.805571	−	0.592499i	$-0.798141\pi$
$937$	−55.2688	−	17.9579i	−1.80555	−	0.586660i	−0.999983	+	0.00583887i	$0.998141\pi$
$938$	−0.109559	−	0.0355978i	−0.00357722	−	0.00116231i
$939$	−3.05359	−	9.39797i	−0.0996500	−	0.306691i
$940$	31.7616	+	7.44466i	1.03595	+	0.242818i
$941$	10.5779	−	32.5553i	0.344828	−	1.06127i	−0.616848	−	0.787083i	$-0.711591\pi$
$941$	10.5779	−	32.5553i	0.344828	−	1.06127i	0.961676	−	0.274189i	$-0.0884095\pi$
$942$	1.21916	−	1.67802i	0.0397222	−	0.0546730i
$943$			1.92684i			0.0627464i
$944$	−0.335766	−	0.243948i	−0.0109282	−	0.00793984i
$945$	−2.23047	−	5.30389i	−0.0725573	−	0.172536i
$946$	−25.5663	+	18.5750i	−0.831232	+	0.603925i
$947$	22.3420	+	30.7511i	0.726016	+	0.999275i	0.999303	+	0.0373427i	$0.0118893\pi$
$947$	22.3420	+	30.7511i	0.726016	+	0.999275i	−0.273286	+	0.961933i	$0.588111\pi$
$948$	−8.07137	+	2.62255i	−0.262146	+	0.0851764i
$949$	−17.7755			−0.577017
$950$	21.4785	+	3.16518i	0.696854	+	0.102692i
$951$	24.7310			0.801958
$952$	3.35278	−	1.08939i	0.108664	−	0.0353072i
$953$	−9.94235	−	13.6845i	−0.322064	−	0.443284i	0.617032	−	0.786938i	$-0.288335\pi$
$953$	−9.94235	−	13.6845i	−0.322064	−	0.443284i	−0.939096	+	0.343655i	$0.888335\pi$
$954$	−3.96015	+	2.87722i	−0.128214	+	0.0931533i
$955$	6.24792	−	26.6559i	0.202178	−	0.862564i
$956$	36.2973	+	26.3716i	1.17394	+	0.852917i
$957$		−	0.183487i		−	0.00593130i
$958$	3.90047	−	5.36853i	0.126018	−	0.173449i
$959$	3.83069	−	11.7897i	0.123699	−	0.380708i
$960$	−2.19536	+	3.62618i	−0.0708550	+	0.117035i
$961$	−3.35243	−	10.3177i	−0.108143	−	0.332829i
$962$	−1.43704	−	0.466923i	−0.0463321	−	0.0150542i
$963$	11.6730	+	3.79280i	0.376158	+	0.122221i
$964$	−4.32492	−	13.3107i	−0.139296	−	0.428710i
$965$	−2.66952	−	31.7343i	−0.0859349	−	1.02156i
$966$	0.159030	−	0.489443i	0.00511669	−	0.0157476i
$967$	13.3924	−	18.4330i	0.430670	−	0.592767i	−0.537437	−	0.843304i	$-0.680607\pi$
$967$	13.3924	−	18.4330i	0.430670	−	0.592767i	0.968107	+	0.250537i	$0.0806073\pi$
$968$			30.7872i			0.989537i
$969$	−4.50348	−	3.27197i	−0.144673	−	0.105111i
$970$	−7.82098	−	4.73497i	−0.251116	−	0.152031i
$971$	−35.5849	+	25.8539i	−1.14197	+	0.829692i	−0.987393	−	0.158288i	$-0.949402\pi$
$971$	−35.5849	+	25.8539i	−1.14197	+	0.829692i	−0.154580	+	0.987980i	$0.549402\pi$
$972$	1.00636	+	1.38513i	0.0322789	+	0.0444281i
$973$	−9.15450	+	2.97448i	−0.293480	+	0.0953574i
$974$	−18.9552			−0.607362
$975$	3.41856	+	6.53440i	0.109482	+	0.209268i
$976$	−15.1029			−0.483431
$977$	−17.7211	+	5.75794i	−0.566948	+	0.184213i	−0.578445	−	0.815721i	$-0.696340\pi$
$977$	−17.7211	+	5.75794i	−0.566948	+	0.184213i	0.0114968	+	0.999934i	$0.496340\pi$
$978$	−2.19946	−	3.02729i	−0.0703308	−	0.0968021i
$979$	0.0512634	−	0.0372450i	0.00163838	−	0.00119036i
$980$	−1.09750	+	0.947621i	−0.0350584	+	0.0302706i
$981$	3.42135	+	2.48575i	0.109235	+	0.0793640i
$982$		−	11.6397i		−	0.371438i
$983$	32.0387	−	44.0975i	1.02188	−	1.40649i	0.110998	−	0.993821i	$-0.464595\pi$
$983$	32.0387	−	44.0975i	1.02188	−	1.40649i	0.910880	−	0.412672i	$-0.135405\pi$
$984$	−3.18155	+	9.79181i	−0.101424	+	0.312152i
$985$	25.9371	+	30.0395i	0.826426	+	0.957138i
$986$	0.00406837	+	0.0125212i	0.000129563	+	0.000398755i
$987$	20.8533	+	6.77563i	0.663767	+	0.215671i
$988$	19.4357	+	6.31504i	0.618332	+	0.200908i
$989$	1.31895	+	4.05930i	0.0419401	+	0.129078i
$990$	−5.68862	+	2.39226i	−0.180796	+	0.0760311i
$991$	11.1881	−	34.4335i	0.355403	−	1.09382i	−0.600373	−	0.799720i	$-0.704981\pi$
$991$	11.1881	−	34.4335i	0.355403	−	1.09382i	0.955776	−	0.294097i	$-0.0950188\pi$
$992$	−13.8455	+	19.0567i	−0.439595	+	0.605051i
$993$		−	1.07827i		−	0.0342178i
$994$	13.5797	+	9.86626i	0.430723	+	0.312939i
$995$	42.2356	−	3.55290i	1.33896	−	0.112635i
$996$	12.9693	−	9.42275i	0.410948	−	0.298571i
$997$	−4.22750	−	5.81865i	−0.133886	−	0.184279i	0.736810	−	0.676100i	$-0.236331\pi$
$997$	−4.22750	−	5.81865i	−0.133886	−	0.184279i	−0.870696	+	0.491821i	$0.836331\pi$
$998$	19.7924	−	6.43096i	0.626519	−	0.203568i
$999$	−1.90935			−0.0604092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.i.a.19.2	yes	16
3.2	odd	2		225.2.m.b.19.3		16
5.2	odd	4		375.2.g.d.151.2		16
5.3	odd	4		375.2.g.e.151.3		16
5.4	even	2		375.2.i.c.349.3		16
25.2	odd	20		1875.2.a.p.1.3		8
25.3	odd	20		375.2.g.e.226.3		16
25.4	even	10	inner	75.2.i.a.4.2	✓	16
25.11	even	5		1875.2.b.h.1249.10		16
25.14	even	10		1875.2.b.h.1249.7		16
25.21	even	5		375.2.i.c.274.3		16
25.22	odd	20		375.2.g.d.226.2		16
25.23	odd	20		1875.2.a.m.1.6		8
75.2	even	20		5625.2.a.t.1.6		8
75.23	even	20		5625.2.a.bd.1.3		8
75.29	odd	10		225.2.m.b.154.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.4.2	✓	16	25.4	even	10	inner
75.2.i.a.19.2	yes	16	1.1	even	1	trivial
225.2.m.b.19.3		16	3.2	odd	2
225.2.m.b.154.3		16	75.29	odd	10
375.2.g.d.151.2		16	5.2	odd	4
375.2.g.d.226.2		16	25.22	odd	20
375.2.g.e.151.3		16	5.3	odd	4
375.2.g.e.226.3		16	25.3	odd	20
375.2.i.c.274.3		16	25.21	even	5
375.2.i.c.349.3		16	5.4	even	2
1875.2.a.m.1.6		8	25.23	odd	20
1875.2.a.p.1.3		8	25.2	odd	20
1875.2.b.h.1249.7		16	25.14	even	10
1875.2.b.h.1249.10		16	25.11	even	5
5625.2.a.t.1.6		8	75.2	even	20
5625.2.a.bd.1.3		8	75.23	even	20

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.510286 + 0.165802i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.38513 + 1.00636i) q^{4} +(2.22820 - 0.187439i) q^{5} +(-0.434076 - 0.315374i) q^{6} +2.57318i q^{7} +(1.17071 - 1.61134i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.510286 + 0.165802i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.38513 + 1.00636i) q^{4} +(2.22820 - 0.187439i) q^{5} +(-0.434076 - 0.315374i) q^{6} +2.57318i q^{7} +(1.17071 - 1.61134i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-1.10594 + 0.465087i) q^{10} +(-1.58949 - 4.89194i) q^{11} +(-1.62832 - 0.529073i) q^{12} +(1.40274 + 0.455776i) q^{13} +(-0.426639 - 1.31306i) q^{14} +(1.46134 + 1.69248i) q^{15} +(0.727915 - 2.24029i) q^{16} +(0.404314 - 0.556490i) q^{17} -0.536547i q^{18} +(-6.54709 - 4.75674i) q^{19} +(-2.89772 + 2.50199i) q^{20} +(-2.08175 + 1.51248i) q^{21} +(1.62219 + 2.23275i) q^{22} +(0.354506 - 0.115186i) q^{23} +1.99173 q^{24} +(4.92973 - 0.835300i) q^{25} -0.791365 q^{26} +(-0.951057 + 0.309017i) q^{27} +(-2.58954 - 3.56419i) q^{28} +(0.0288595 - 0.0209676i) q^{29} +(-1.02632 - 0.621354i) q^{30} +(3.63169 + 2.63858i) q^{31} +5.24733i q^{32} +(3.02338 - 4.16133i) q^{33} +(-0.114049 + 0.351005i) q^{34} +(0.482313 + 5.73355i) q^{35} +(-0.529073 - 1.62832i) q^{36} +(1.81590 + 0.590022i) q^{37} +(4.12957 + 1.34178i) q^{38} +(0.455776 + 1.40274i) q^{39} +(2.30654 - 3.80982i) q^{40} +(-1.59739 + 4.91625i) q^{41} +(0.811515 - 1.11695i) q^{42} +11.4506i q^{43} +(7.12469 + 5.17639i) q^{44} +(-0.510286 + 2.17706i) q^{45} +(-0.161802 + 0.117556i) q^{46} +(-5.00860 - 6.89374i) q^{47} +(2.24029 - 0.727915i) q^{48} +0.378747 q^{49} +(-2.37708 + 1.24360i) q^{50} +0.687859 q^{51} +(-2.40165 + 0.780343i) q^{52} +(-5.36247 - 7.38080i) q^{53} +(0.434076 - 0.315374i) q^{54} +(-4.45863 - 10.6023i) q^{55} +(4.14627 + 3.01244i) q^{56} -8.09265i q^{57} +(-0.0112501 + 0.0154845i) q^{58} +(0.0544457 - 0.167567i) q^{59} +(-3.72739 - 0.873670i) q^{60} +(-1.98127 - 6.09772i) q^{61} +(-2.29069 - 0.744289i) q^{62} +(-2.44724 - 0.795156i) q^{63} +(0.585811 + 1.80294i) q^{64} +(3.21100 + 0.752633i) q^{65} +(-0.852834 + 2.62475i) q^{66} +(0.0490435 - 0.0675025i) q^{67} +1.17770i q^{68} +(0.301561 + 0.219097i) q^{69} +(-1.19675 - 2.84579i) q^{70} +(-9.83589 + 7.14619i) q^{71} +(1.17071 + 1.61134i) q^{72} +(-11.4619 + 3.72421i) q^{73} -1.02446 q^{74} +(3.57340 + 3.49726i) q^{75} +13.8556 q^{76} +(12.5878 - 4.09004i) q^{77} +(-0.465153 - 0.640228i) q^{78} +(4.01019 - 2.91357i) q^{79} +(1.20202 - 5.12825i) q^{80} +(-0.809017 - 0.587785i) q^{81} -2.77354i q^{82} +(-5.50356 + 7.57501i) q^{83} +(1.36140 - 4.18996i) q^{84} +(0.796583 - 1.31575i) q^{85} +(-1.89853 - 5.84308i) q^{86} +(0.0339264 + 0.0110233i) q^{87} +(-9.74340 - 3.16582i) q^{88} +(0.00380677 + 0.0117160i) q^{89} +(-0.100570 - 1.19553i) q^{90} +(-1.17279 + 3.60949i) q^{91} +(-0.375120 + 0.516308i) q^{92} +4.48902i q^{93} +(3.69882 + 2.68735i) q^{94} +(-15.4798 - 9.37179i) q^{95} +(-4.24518 + 3.08430i) q^{96} +(4.47917 + 6.16504i) q^{97} +(-0.193269 + 0.0627970i) q^{98} +5.14369 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9	\( 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} + 10 q^{17} - 2 q^{19} + 20 q^{20} + 4 q^{21} - 30 q^{22} - 20 q^{23} + 24 q^{24} - 10 q^{25} + 12 q^{26} + 30 q^{28} + 16 q^{29} - 20 q^{30} + 6 q^{31} + 10 q^{33} - 36 q^{34} + 10 q^{35} - 2 q^{36} - 10 q^{37} + 30 q^{38} - 8 q^{39} + 10 q^{40} - 14 q^{41} - 10 q^{42} + 26 q^{44} + 16 q^{46} + 40 q^{47} + 20 q^{50} - 32 q^{51} + 40 q^{52} + 10 q^{53} - 2 q^{54} + 10 q^{55} + 10 q^{58} + 12 q^{59} - 30 q^{60} - 10 q^{62} - 10 q^{63} + 8 q^{64} - 70 q^{65} + 16 q^{66} - 40 q^{67} - 12 q^{69} + 30 q^{70} - 8 q^{71} - 30 q^{72} - 20 q^{73} - 52 q^{74} - 32 q^{76} - 40 q^{77} - 20 q^{79} - 4 q^{81} + 10 q^{83} + 12 q^{84} - 20 q^{85} - 36 q^{86} + 40 q^{87} - 40 q^{88} + 18 q^{89} + 30 q^{90} + 26 q^{91} + 10 q^{92} - 38 q^{94} - 40 q^{95} - 26 q^{96} + 40 q^{97} + 60 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 + 10 * q^17 - 2 * q^19 + 20 * q^20 + 4 * q^21 - 30 * q^22 - 20 * q^23 + 24 * q^24 - 10 * q^25 + 12 * q^26 + 30 * q^28 + 16 * q^29 - 20 * q^30 + 6 * q^31 + 10 * q^33 - 36 * q^34 + 10 * q^35 - 2 * q^36 - 10 * q^37 + 30 * q^38 - 8 * q^39 + 10 * q^40 - 14 * q^41 - 10 * q^42 + 26 * q^44 + 16 * q^46 + 40 * q^47 + 20 * q^50 - 32 * q^51 + 40 * q^52 + 10 * q^53 - 2 * q^54 + 10 * q^55 + 10 * q^58 + 12 * q^59 - 30 * q^60 - 10 * q^62 - 10 * q^63 + 8 * q^64 - 70 * q^65 + 16 * q^66 - 40 * q^67 - 12 * q^69 + 30 * q^70 - 8 * q^71 - 30 * q^72 - 20 * q^73 - 52 * q^74 - 32 * q^76 - 40 * q^77 - 20 * q^79 - 4 * q^81 + 10 * q^83 + 12 * q^84 - 20 * q^85 - 36 * q^86 + 40 * q^87 - 40 * q^88 + 18 * q^89 + 30 * q^90 + 26 * q^91 + 10 * q^92 - 38 * q^94 - 40 * q^95 - 26 * q^96 + 40 * q^97 + 60 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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