LMFDB - Embedded newform 175.2.n.a.29.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(29,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("175.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.n (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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.9
Character	$\chi$	$=$	175.29
Dual form			175.2.n.a.169.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03051 + 0.334833i) q^{2} +(-1.58321 + 2.17910i) q^{3} +(-0.668196 - 0.485473i) q^{4} +(-2.00240 + 0.995194i) q^{5} +(-2.36115 + 1.71547i) q^{6} +1.00000i q^{7} +(-1.79981 - 2.47723i) q^{8} +(-1.31487 - 4.04676i) q^{9} +O(q^{10})$	\(q+(1.03051 + 0.334833i) q^{2} +(-1.58321 + 2.17910i) q^{3} +(-0.668196 - 0.485473i) q^{4} +(-2.00240 + 0.995194i) q^{5} +(-2.36115 + 1.71547i) q^{6} +1.00000i q^{7} +(-1.79981 - 2.47723i) q^{8} +(-1.31487 - 4.04676i) q^{9} +(-2.39671 + 0.355089i) q^{10} +(-1.20073 + 3.69547i) q^{11} +(2.11579 - 0.687461i) q^{12} +(2.12541 - 0.690588i) q^{13} +(-0.334833 + 1.03051i) q^{14} +(1.00158 - 5.93902i) q^{15} +(-0.514809 - 1.58442i) q^{16} +(4.12875 + 5.68273i) q^{17} -4.61049i q^{18} +(-5.15646 + 3.74639i) q^{19} +(1.82113 + 0.307124i) q^{20} +(-2.17910 - 1.58321i) q^{21} +(-2.47473 + 3.40618i) q^{22} +(4.94286 + 1.60603i) q^{23} +8.24760 q^{24} +(3.01918 - 3.98554i) q^{25} +2.42149 q^{26} +(3.21497 + 1.04461i) q^{27} +(0.485473 - 0.668196i) q^{28} +(-4.72713 - 3.43446i) q^{29} +(3.02072 - 5.78485i) q^{30} +(0.520209 - 0.377954i) q^{31} +4.31891i q^{32} +(-6.15179 - 8.46722i) q^{33} +(2.35195 + 7.23856i) q^{34} +(-0.995194 - 2.00240i) q^{35} +(-1.08600 + 3.34237i) q^{36} +(6.79092 - 2.20650i) q^{37} +(-6.56820 + 2.13414i) q^{38} +(-1.86011 + 5.72482i) q^{39} +(6.06926 + 3.16923i) q^{40} +(-0.201628 - 0.620549i) q^{41} +(-1.71547 - 2.36115i) q^{42} +0.957977i q^{43} +(2.59638 - 1.88638i) q^{44} +(6.66021 + 6.79467i) q^{45} +(4.55591 + 3.31006i) q^{46} +(1.01412 - 1.39581i) q^{47} +(4.26766 + 1.38665i) q^{48} -1.00000 q^{49} +(4.44578 - 3.09622i) q^{50} -18.9199 q^{51} +(-1.75545 - 0.570381i) q^{52} +(-5.94778 + 8.18641i) q^{53} +(2.96329 + 2.15295i) q^{54} +(-1.27337 - 8.59476i) q^{55} +(2.47723 - 1.79981i) q^{56} -17.1678i q^{57} +(-3.72139 - 5.12205i) q^{58} +(-0.235963 - 0.726220i) q^{59} +(-3.55249 + 3.48219i) q^{60} +(3.07593 - 9.46675i) q^{61} +(0.662631 - 0.215302i) q^{62} +(4.04676 - 1.31487i) q^{63} +(-2.47573 + 7.61952i) q^{64} +(-3.56864 + 3.49803i) q^{65} +(-3.50438 - 10.7854i) q^{66} +(-1.61593 - 2.22413i) q^{67} -5.80158i q^{68} +(-11.3253 + 8.22830i) q^{69} +(-0.355089 - 2.39671i) q^{70} +(10.3133 + 7.49305i) q^{71} +(-7.65823 + 10.5407i) q^{72} +(-9.69099 - 3.14879i) q^{73} +7.73692 q^{74} +(3.90491 + 12.8890i) q^{75} +5.26430 q^{76} +(-3.69547 - 1.20073i) q^{77} +(-3.83372 + 5.27666i) q^{78} +(3.52524 + 2.56124i) q^{79} +(2.60766 + 2.66030i) q^{80} +(2.96089 - 2.15121i) q^{81} -0.706994i q^{82} +(6.22474 + 8.56762i) q^{83} +(0.687461 + 2.11579i) q^{84} +(-13.9228 - 7.27018i) q^{85} +(-0.320762 + 0.987205i) q^{86} +(14.9681 - 4.86342i) q^{87} +(11.3156 - 3.67667i) q^{88} +(-0.431368 + 1.32762i) q^{89} +(4.58834 + 9.23203i) q^{90} +(0.690588 + 2.12541i) q^{91} +(-2.52311 - 3.47277i) q^{92} +1.73197i q^{93} +(1.51242 - 1.09884i) q^{94} +(6.59690 - 12.6334i) q^{95} +(-9.41133 - 6.83773i) q^{96} +(-6.50724 + 8.95645i) q^{97} +(-1.03051 - 0.334833i) q^{98} +16.5335 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9}+O(q^{10}) $ 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9	$ 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9} - 4 q^{10} + 8 q^{11} - 40 q^{12} - 4 q^{14} - 18 q^{15} - 32 q^{16} + 12 q^{19} + 12 q^{20} + 4 q^{21} - 30 q^{22} + 10 q^{23} - 28 q^{24} + 4 q^{25} + 12 q^{26} + 30 q^{27} - 2 q^{29} + 28 q^{30} + 12 q^{31} + 20 q^{33} + 2 q^{35} - 14 q^{36} - 70 q^{37} - 70 q^{38} - 4 q^{39} - 30 q^{40} + 4 q^{41} + 50 q^{42} + 22 q^{44} - 52 q^{45} - 4 q^{46} - 10 q^{47} + 30 q^{48} - 56 q^{49} - 54 q^{50} - 44 q^{51} - 20 q^{53} + 54 q^{54} - 2 q^{55} + 12 q^{56} + 10 q^{58} - 6 q^{59} + 16 q^{60} - 4 q^{61} + 50 q^{62} + 20 q^{63} + 24 q^{64} - 18 q^{65} - 74 q^{66} + 10 q^{67} - 78 q^{69} + 8 q^{70} - 8 q^{71} + 140 q^{72} + 40 q^{73} + 60 q^{74} - 8 q^{75} + 52 q^{76} - 20 q^{77} - 90 q^{78} + 124 q^{80} - 72 q^{81} - 30 q^{83} - 12 q^{84} + 96 q^{85} - 20 q^{86} + 30 q^{87} + 140 q^{88} + 38 q^{89} - 8 q^{90} + 8 q^{91} + 80 q^{92} + 88 q^{94} - 70 q^{95} - 28 q^{96} - 30 q^{97} + 60 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9 - 4 * q^10 + 8 * q^11 - 40 * q^12 - 4 * q^14 - 18 * q^15 - 32 * q^16 + 12 * q^19 + 12 * q^20 + 4 * q^21 - 30 * q^22 + 10 * q^23 - 28 * q^24 + 4 * q^25 + 12 * q^26 + 30 * q^27 - 2 * q^29 + 28 * q^30 + 12 * q^31 + 20 * q^33 + 2 * q^35 - 14 * q^36 - 70 * q^37 - 70 * q^38 - 4 * q^39 - 30 * q^40 + 4 * q^41 + 50 * q^42 + 22 * q^44 - 52 * q^45 - 4 * q^46 - 10 * q^47 + 30 * q^48 - 56 * q^49 - 54 * q^50 - 44 * q^51 - 20 * q^53 + 54 * q^54 - 2 * q^55 + 12 * q^56 + 10 * q^58 - 6 * q^59 + 16 * q^60 - 4 * q^61 + 50 * q^62 + 20 * q^63 + 24 * q^64 - 18 * q^65 - 74 * q^66 + 10 * q^67 - 78 * q^69 + 8 * q^70 - 8 * q^71 + 140 * q^72 + 40 * q^73 + 60 * q^74 - 8 * q^75 + 52 * q^76 - 20 * q^77 - 90 * q^78 + 124 * q^80 - 72 * q^81 - 30 * q^83 - 12 * q^84 + 96 * q^85 - 20 * q^86 + 30 * q^87 + 140 * q^88 + 38 * q^89 - 8 * q^90 + 8 * q^91 + 80 * q^92 + 88 * q^94 - 70 * q^95 - 28 * q^96 - 30 * q^97 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	1.03051	+	0.334833i	0.728681	+	0.236763i	0.649783	−	0.760120i	$-0.274860\pi$
$2$	1.03051	+	0.334833i	0.728681	+	0.236763i	0.0788979	+	0.996883i	$0.474860\pi$
$3$	−1.58321	+	2.17910i	−0.914066	+	1.25810i	0.0516935	+	0.998663i	$0.483538\pi$
$3$	−1.58321	+	2.17910i	−0.914066	+	1.25810i	−0.965759	+	0.259440i	$0.916462\pi$
$4$	−0.668196	−	0.485473i	−0.334098	−	0.242737i
$5$	−2.00240	+	0.995194i	−0.895499	+	0.445064i
$5$	−2.00240	+	0.995194i	−0.895499	+	0.445064i
$6$	−2.36115	+	1.71547i	−0.963934	+	0.700339i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−1.79981	−	2.47723i	−0.636329	−	0.875832i
$9$	−1.31487	−	4.04676i	−0.438291	−	1.34892i
$10$	−2.39671	+	0.355089i	−0.757907	+	0.112289i
$11$	−1.20073	+	3.69547i	−0.362034	+	1.11423i	0.589783	+	0.807562i	$0.299213\pi$
$11$	−1.20073	+	3.69547i	−0.362034	+	1.11423i	−0.951817	+	0.306665i	$0.900787\pi$
$12$	2.11579	−	0.687461i	0.610775	−	0.198453i
$13$	2.12541	−	0.690588i	0.589483	−	0.191535i	0.000938449	−	1.00000i	$-0.499701\pi$
$13$	2.12541	−	0.690588i	0.589483	−	0.191535i	0.588544	+	0.808465i	$0.299701\pi$
$14$	−0.334833	+	1.03051i	−0.0894879	+	0.275415i
$15$	1.00158	−	5.93902i	0.258608	−	1.53345i
$16$	−0.514809	−	1.58442i	−0.128702	−	0.396105i
$17$	4.12875	+	5.68273i	1.00137	+	1.37827i	0.924482	+	0.381226i	$0.124498\pi$
$17$	4.12875	+	5.68273i	1.00137	+	1.37827i	0.0768864	+	0.997040i	$0.475502\pi$
$18$		−	4.61049i		−	1.08670i
$19$	−5.15646	+	3.74639i	−1.18297	+	0.859481i	−0.992504	−	0.122212i	$-0.961001\pi$
$19$	−5.15646	+	3.74639i	−1.18297	+	0.859481i	−0.190470	+	0.981693i	$0.561001\pi$
$20$	1.82113	+	0.307124i	0.407218	+	0.0686750i
$21$	−2.17910	−	1.58321i	−0.475518	−	0.345484i
$22$	−2.47473	+	3.40618i	−0.527615	+	0.726199i
$23$	4.94286	+	1.60603i	1.03066	+	0.334881i	0.775050	−	0.631900i	$-0.217725\pi$
$23$	4.94286	+	1.60603i	1.03066	+	0.334881i	0.255607	+	0.966781i	$0.417725\pi$
$24$	8.24760			1.68353
$25$	3.01918	−	3.98554i	0.603835	−	0.797109i
$26$	2.42149			0.474893
$27$	3.21497	+	1.04461i	0.618720	+	0.201034i
$28$	0.485473	−	0.668196i	0.0917458	−	0.126277i
$29$	−4.72713	−	3.43446i	−0.877807	−	0.637764i	0.0548634	−	0.998494i	$-0.482528\pi$
$29$	−4.72713	−	3.43446i	−0.877807	−	0.637764i	−0.932670	+	0.360730i	$0.882528\pi$
$30$	3.02072	−	5.78485i	0.551505	−	1.05617i
$31$	0.520209	−	0.377954i	0.0934322	−	0.0678825i	−0.540088	−	0.841608i	$-0.681609\pi$
$31$	0.520209	−	0.377954i	0.0934322	−	0.0678825i	0.633521	+	0.773726i	$0.281609\pi$
$32$			4.31891i			0.763482i
$33$	−6.15179	−	8.46722i	−1.07089	−	1.47395i
$34$	2.35195	+	7.23856i	0.403356	+	1.24140i
$35$	−0.995194	−	2.00240i	−0.168219	−	0.338467i
$36$	−1.08600	+	3.34237i	−0.181000	+	0.557061i
$37$	6.79092	−	2.20650i	1.11642	−	0.362747i	0.308020	−	0.951380i	$-0.400334\pi$
$37$	6.79092	−	2.20650i	1.11642	−	0.362747i	0.808401	+	0.588633i	$0.200334\pi$
$38$	−6.56820	+	2.13414i	−1.06550	+	0.346203i
$39$	−1.86011	+	5.72482i	−0.297856	+	0.916705i
$40$	6.06926	+	3.16923i	0.959634	+	0.501099i
$41$	−0.201628	−	0.620549i	−0.0314891	−	0.0969134i	0.934077	−	0.357072i	$-0.116225\pi$
$41$	−0.201628	−	0.620549i	−0.0314891	−	0.0969134i	−0.965566	+	0.260159i	$0.916225\pi$
$42$	−1.71547	−	2.36115i	−0.264703	−	0.364333i
$43$			0.957977i			0.146090i	0.997329	+	0.0730450i	$0.0232717\pi$
$43$			0.957977i			0.146090i	−0.997329	+	0.0730450i	$0.976728\pi$
$44$	2.59638	−	1.88638i	0.391419	−	0.284382i
$45$	6.66021	+	6.79467i	0.992846	+	1.01289i
$46$	4.55591	+	3.31006i	0.671733	+	0.488042i
$47$	1.01412	−	1.39581i	0.147924	−	0.203600i	−0.728624	−	0.684914i	$-0.759840\pi$
$47$	1.01412	−	1.39581i	0.147924	−	0.203600i	0.876549	+	0.481313i	$0.159840\pi$
$48$	4.26766	+	1.38665i	0.615983	+	0.200145i
$49$	−1.00000			−0.142857
$50$	4.44578	−	3.09622i	0.628729	−	0.437872i
$51$	−18.9199			−2.64932
$52$	−1.75545	−	0.570381i	−0.243437	−	0.0790976i
$53$	−5.94778	+	8.18641i	−0.816990	+	1.12449i	0.173217	+	0.984884i	$0.444584\pi$
$53$	−5.94778	+	8.18641i	−0.816990	+	1.12449i	−0.990207	+	0.139606i	$0.955416\pi$
$54$	2.96329	+	2.15295i	0.403252	+	0.292980i
$55$	−1.27337	−	8.59476i	−0.171701	−	1.15892i
$56$	2.47723	−	1.79981i	0.331033	−	0.240510i
$57$		−	17.1678i		−	2.27393i
$58$	−3.72139	−	5.12205i	−0.488642	−	0.672558i
$59$	−0.235963	−	0.726220i	−0.0307198	−	0.0945458i	0.934521	−	0.355908i	$-0.115828\pi$
$59$	−0.235963	−	0.726220i	−0.0307198	−	0.0945458i	−0.965241	+	0.261362i	$0.915828\pi$
$60$	−3.55249	+	3.48219i	−0.458624	+	0.449549i
$61$	3.07593	−	9.46675i	0.393833	−	1.21209i	−0.536034	−	0.844197i	$-0.680078\pi$
$61$	3.07593	−	9.46675i	0.393833	−	1.21209i	0.929867	−	0.367897i	$-0.119922\pi$
$62$	0.662631	−	0.215302i	0.0841543	−	0.0273434i
$63$	4.04676	−	1.31487i	0.509844	−	0.165658i
$64$	−2.47573	+	7.61952i	−0.309466	+	0.952440i
$65$	−3.56864	+	3.49803i	−0.442636	+	0.433877i
$66$	−3.50438	−	10.7854i	−0.431359	−	1.32759i
$67$	−1.61593	−	2.22413i	−0.197417	−	0.271721i	0.698819	−	0.715298i	$-0.253709\pi$
$67$	−1.61593	−	2.22413i	−0.197417	−	0.271721i	−0.896236	+	0.443577i	$0.853709\pi$
$68$		−	5.80158i		−	0.703545i
$69$	−11.3253	+	8.22830i	−1.36340	+	0.990570i
$70$	−0.355089	−	2.39671i	−0.0424413	−	0.286462i
$71$	10.3133	+	7.49305i	1.22396	+	0.889261i	0.996423	−	0.0845072i	$-0.0269316\pi$
$71$	10.3133	+	7.49305i	1.22396	+	0.889261i	0.227541	+	0.973769i	$0.426932\pi$
$72$	−7.65823	+	10.5407i	−0.902531	+	1.24223i
$73$	−9.69099	−	3.14879i	−1.13424	−	0.368538i	−0.319057	−	0.947736i	$-0.603366\pi$
$73$	−9.69099	−	3.14879i	−1.13424	−	0.368538i	−0.815187	+	0.579197i	$0.803366\pi$
$74$	7.73692			0.899399
$75$	3.90491	+	12.8890i	0.450900	+	1.48830i
$76$	5.26430			0.603857
$77$	−3.69547	−	1.20073i	−0.421138	−	0.136836i
$78$	−3.83372	+	5.27666i	−0.434083	+	0.597464i
$79$	3.52524	+	2.56124i	0.396620	+	0.288162i	0.768163	−	0.640254i	$-0.221171\pi$
$79$	3.52524	+	2.56124i	0.396620	+	0.288162i	−0.371543	+	0.928416i	$0.621171\pi$
$80$	2.60766	+	2.66030i	0.291545	+	0.297431i
$81$	2.96089	−	2.15121i	0.328988	−	0.239024i
$82$		−	0.706994i		−	0.0780744i
$83$	6.22474	+	8.56762i	0.683254	+	0.940419i	0.999967	−	0.00810282i	$-0.00257924\pi$
$83$	6.22474	+	8.56762i	0.683254	+	0.940419i	−0.316713	+	0.948521i	$0.602579\pi$
$84$	0.687461	+	2.11579i	0.0750082	+	0.230851i
$85$	−13.9228	−	7.27018i	−1.51014	−	0.788561i
$86$	−0.320762	+	0.987205i	−0.0345887	+	0.106453i
$87$	14.9681	−	4.86342i	1.60475	−	0.521414i
$88$	11.3156	−	3.67667i	1.20625	−	0.391934i
$89$	−0.431368	+	1.32762i	−0.0457249	+	0.140727i	−0.971313	−	0.237807i	$-0.923572\pi$
$89$	−0.431368	+	1.32762i	−0.0457249	+	0.140727i	0.925588	+	0.378534i	$0.123572\pi$
$90$	4.58834	+	9.23203i	0.483653	+	0.973142i
$91$	0.690588	+	2.12541i	0.0723932	+	0.222804i
$92$	−2.52311	−	3.47277i	−0.263053	−	0.362061i
$93$			1.73197i			0.179596i
$94$	1.51242	−	1.09884i	0.155995	−	0.113337i
$95$	6.59690	−	12.6334i	0.676827	−	1.29616i
$96$	−9.41133	−	6.83773i	−0.960539	−	0.697873i
$97$	−6.50724	+	8.95645i	−0.660710	+	0.909389i	−0.999505	−	0.0314709i	$-0.989981\pi$
$97$	−6.50724	+	8.95645i	−0.660710	+	0.909389i	0.338795	+	0.940860i	$0.389981\pi$
$98$	−1.03051	−	0.334833i	−0.104097	−	0.0338232i
$99$	16.5335			1.66168
$100$	−3.95228	+	1.19740i	−0.395228	+	0.119740i
$101$	−8.27731			−0.823623			−0.411811	−	0.911269i	$-0.635104\pi$
$101$	−8.27731			−0.823623			−0.411811	+	0.911269i	$0.635104\pi$
$102$	−19.4972	−	6.33501i	−1.93051	−	0.627259i
$103$	−4.05337	+	5.57898i	−0.399390	+	0.549713i	−0.960591	−	0.277966i	$-0.910340\pi$
$103$	−4.05337	+	5.57898i	−0.399390	+	0.549713i	0.561201	+	0.827680i	$0.310340\pi$
$104$	−5.53608	−	4.02220i	−0.542857	−	0.394409i
$105$	5.93902	+	1.00158i	0.579589	+	0.0977445i
$106$	−8.87032	+	6.44467i	−0.861562	+	0.625961i
$107$			12.0065i			1.16071i	0.814362	+	0.580357i	$0.197087\pi$
$107$			12.0065i			1.16071i	−0.814362	+	0.580357i	$0.802913\pi$
$108$	−1.64110	−	2.25878i	−0.157915	−	0.217351i
$109$	0.360059	+	1.10815i	0.0344874	+	0.106141i	0.966818	−	0.255465i	$-0.0822285\pi$
$109$	0.360059	+	1.10815i	0.0344874	+	0.106141i	−0.932331	+	0.361606i	$0.882229\pi$
$110$	1.56559	−	9.28335i	0.149273	−	0.885133i
$111$	−5.94325	+	18.2914i	−0.564108	+	1.73615i
$112$	1.58442	−	0.514809i	0.149714	−	0.0486449i
$113$	18.4253	−	5.98673i	1.73330	−	0.563184i	0.739382	−	0.673286i	$-0.235118\pi$
$113$	18.4253	−	5.98673i	1.73330	−	0.563184i	0.993920	+	0.110102i	$0.0351179\pi$
$114$	5.74833	−	17.6915i	0.538381	−	1.65697i
$115$	−11.4959	+	1.70319i	−1.07200	+	0.158823i
$116$	1.49131	+	4.58979i	0.138465	+	0.426152i
$117$	−5.58929	−	7.69300i	−0.516730	−	0.711218i
$118$		−	0.827386i		−	0.0761670i
$119$	−5.68273	+	4.12875i	−0.520935	+	0.378482i
$120$	−16.5150	+	8.20796i	−1.50760	+	0.749281i
$121$	−3.31558	−	2.40891i	−0.301416	−	0.218992i
$122$	6.33956	−	8.72566i	0.573957	−	0.789984i
$123$	1.67146	+	0.543089i	0.150710	+	0.0489687i
$124$	−0.531088			−0.0476931
$125$	−2.07920	+	10.9853i	−0.185969	+	0.982556i
$126$	4.61049			0.410735
$127$	−0.752993	−	0.244662i	−0.0668173	−	0.0217103i	0.275418	−	0.961325i	$-0.411184\pi$
$127$	−0.752993	−	0.244662i	−0.0668173	−	0.0217103i	−0.342235	+	0.939614i	$0.611184\pi$
$128$	−0.0253510	+	0.0348927i	−0.00224073	+	0.00308410i
$129$	−2.08753	−	1.51668i	−0.183796	−	0.133536i
$130$	−4.84878	+	2.40985i	−0.425266	+	0.211358i
$131$	1.66351	−	1.20861i	0.145342	−	0.105597i	−0.512738	−	0.858545i	$-0.671369\pi$
$131$	1.66351	−	1.20861i	0.145342	−	0.105597i	0.658080	+	0.752948i	$0.271369\pi$
$132$			8.64429i			0.752389i
$133$	−3.74639	−	5.15646i	−0.324853	−	0.447122i
$134$	−0.920516	−	2.83306i	−0.0795204	−	0.244739i
$135$	−7.47722	+	1.10780i	−0.643536	+	0.0953443i
$136$	6.64646	−	20.4557i	0.569929	−	1.75406i
$137$	7.56640	−	2.45847i	0.646441	−	0.210041i	0.0325968	−	0.999469i	$-0.489622\pi$
$137$	7.56640	−	2.45847i	0.646441	−	0.210041i	0.613844	+	0.789427i	$0.289622\pi$
$138$	−14.4259	+	4.68726i	−1.22802	+	0.399006i
$139$	4.66431	−	14.3553i	0.395622	−	1.21760i	−0.532854	−	0.846207i	$-0.678881\pi$
$139$	4.66431	−	14.3553i	0.395622	−	1.21760i	0.928476	−	0.371392i	$-0.121119\pi$
$140$	−0.307124	+	1.82113i	−0.0259567	+	0.153914i
$141$	1.43606	+	4.41973i	0.120938	+	0.372208i
$142$	8.11904	+	11.1749i	0.681334	+	0.937776i
$143$			8.68361i			0.726160i
$144$	−5.73486	+	4.16662i	−0.477905	+	0.347219i
$145$	12.8836	+	2.17274i	1.06992	+	0.180436i
$146$	−8.93234	−	6.48972i	−0.739246	−	0.537093i
$147$	1.58321	−	2.17910i	0.130581	−	0.179729i
$148$	−5.60887	−	1.82243i	−0.461046	−	0.149803i
$149$	−3.74915			−0.307143			−0.153571	−	0.988138i	$-0.549077\pi$
$149$	−3.74915			−0.307143			−0.153571	+	0.988138i	$0.549077\pi$
$150$	−0.291624	+	14.5898i	−0.0238110	+	1.19125i
$151$	0.172096			0.0140050			0.00700248	−	0.999975i	$-0.497771\pi$
$151$	0.172096			0.0140050			0.00700248	+	0.999975i	$0.497771\pi$
$152$	18.5613	+	6.03094i	1.50552	+	0.489174i
$153$	17.5679	−	24.1801i	1.42028	−	1.95485i
$154$	−3.40618	−	2.47473i	−0.274478	−	0.199420i
$155$	−0.665526	+	1.27452i	−0.0534563	+	0.102372i
$156$	4.02216	−	2.92227i	0.322031	−	0.233969i
$157$		−	6.90269i		−	0.550895i	−0.961316	−	0.275447i	$-0.911174\pi$
$157$		−	6.90269i		−	0.550895i	0.961316	−	0.275447i	$-0.0888259\pi$
$158$	2.77521	+	3.81975i	0.220784	+	0.303883i
$159$	−8.42243	−	25.9216i	−0.667942	−	2.05572i
$160$	−4.29815	−	8.64816i	−0.339799	−	0.683697i
$161$	−1.60603	+	4.94286i	−0.126573	+	0.389552i
$162$	3.77153	−	1.22544i	0.296319	−	0.0962799i
$163$	9.52841	−	3.09597i	0.746323	−	0.242495i	0.0889246	−	0.996038i	$-0.471657\pi$
$163$	9.52841	−	3.09597i	0.746323	−	0.242495i	0.657398	+	0.753543i	$0.271657\pi$
$164$	−0.166532	+	0.512534i	−0.0130040	+	0.0400221i
$165$	20.7448	+	10.8325i	1.61498	+	0.843308i
$166$	3.54594	+	10.9133i	0.275218	+	0.847034i
$167$	4.61709	+	6.35488i	0.357281	+	0.491755i	0.949389	−	0.314104i	$-0.101704\pi$
$167$	4.61709	+	6.35488i	0.357281	+	0.491755i	−0.592108	+	0.805859i	$0.701704\pi$
$168$			8.24760i			0.636316i
$169$	−6.47676	+	4.70564i	−0.498213	+	0.361973i
$170$	−11.9133	−	12.1538i	−0.913708	−	0.932154i
$171$	21.9409	+	15.9410i	1.67786	+	1.21904i
$172$	0.465072	−	0.640116i	0.0354614	−	0.0488084i
$173$	19.5169	+	6.34143i	1.48384	+	0.482130i	0.935259	−	0.353965i	$-0.115167\pi$
$173$	19.5169	+	6.34143i	1.48384	+	0.482130i	0.548585	+	0.836095i	$0.315167\pi$
$174$	17.0532			1.29280
$175$	3.98554	+	3.01918i	0.301279	+	0.228228i
$176$	6.47333			0.487945
$177$	1.95608	+	0.635571i	0.147028	+	0.0477724i
$178$	−0.889059	+	1.22368i	−0.0666378	+	0.0917190i
$179$	0.138259	+	0.100451i	0.0103340	+	0.00750805i	0.592940	−	0.805246i	$-0.297967\pi$
$179$	0.138259	+	0.100451i	0.0103340	+	0.00750805i	−0.582606	+	0.812755i	$0.697967\pi$
$180$	−1.15170	−	7.77353i	−0.0858427	−	0.579405i
$181$	16.5075	−	11.9934i	1.22700	−	0.891465i	0.230335	−	0.973111i	$-0.426018\pi$
$181$	16.5075	−	11.9934i	1.22700	−	0.891465i	0.996661	+	0.0816467i	$0.0260179\pi$
$182$			2.42149i			0.179493i
$183$	15.7591	+	21.6906i	1.16495	+	1.60342i
$184$	−4.91771	−	15.1351i	−0.362538	−	1.11578i
$185$	−11.4022	+	11.1766i	−0.838307	+	0.821719i
$186$	−0.579919	+	1.78481i	−0.0425217	+	0.130868i
$187$	−25.9579	+	8.43424i	−1.89823	+	0.616772i
$188$	−1.35526	+	0.440351i	−0.0988426	+	0.0321159i
$189$	−1.04461	+	3.21497i	−0.0759839	+	0.233854i
$190$	11.0283	−	10.8100i	0.800074	−	0.784242i
$191$	−0.182058	−	0.560317i	−0.0131733	−	0.0405431i	0.944254	−	0.329218i	$-0.106785\pi$
$191$	−0.182058	−	0.560317i	−0.0131733	−	0.0405431i	−0.957427	+	0.288675i	$0.906785\pi$
$192$	−12.6841	−	17.4581i	−0.915395	−	1.25993i
$193$		−	9.74725i		−	0.701623i	−0.936446	−	0.350811i	$-0.885906\pi$
$193$		−	9.74725i		−	0.701623i	0.936446	−	0.350811i	$-0.114094\pi$
$194$	−9.70469	+	7.05087i	−0.696756	+	0.506223i
$195$	−1.97264	−	13.3145i	−0.141264	−	0.953473i
$196$	0.668196	+	0.485473i	0.0477283	+	0.0346766i
$197$	−2.12986	+	2.93151i	−0.151746	+	0.208861i	−0.878122	−	0.478437i	$-0.841203\pi$
$197$	−2.12986	+	2.93151i	−0.151746	+	0.208861i	0.726375	+	0.687298i	$0.241203\pi$
$198$	17.0380	+	5.53597i	1.21083	+	0.393424i
$199$	3.85851			0.273522			0.136761	−	0.990604i	$-0.456331\pi$
$199$	3.85851			0.273522			0.136761	+	0.990604i	$0.456331\pi$
$200$	−15.3070	−	0.305961i	−1.08237	−	0.0216347i
$201$	7.40495			0.522305
$202$	−8.52985	−	2.77152i	−0.600158	−	0.195003i
$203$	3.43446	−	4.72713i	0.241052	−	0.331780i
$204$	12.6422	+	9.18510i	0.885132	+	0.643086i
$205$	1.02131	+	1.04192i	0.0713311	+	0.0727712i
$206$	−6.04506	+	4.39200i	−0.421180	+	0.306005i
$207$		−	22.1143i		−	1.53705i
$208$	−2.18836	−	3.01202i	−0.151736	−	0.208846i
$209$	−7.65315	−	23.5540i	−0.529380	−	1.62926i
$210$	5.78485	+	3.02072i	0.399193	+	0.208449i
$211$	3.22549	−	9.92705i	0.222052	−	0.683406i	−0.776525	−	0.630086i	$-0.783020\pi$
$211$	3.22549	−	9.92705i	0.222052	−	0.683406i	0.998577	−	0.0533203i	$-0.0169804\pi$
$212$	7.94856	−	2.58265i	0.545910	−	0.177377i
$213$	−32.6562	+	10.6106i	−2.23757	+	0.727029i
$214$	−4.02018	+	12.3728i	−0.274814	+	0.845789i
$215$	−0.953373	−	1.91825i	−0.0650195	−	0.130823i
$216$	−3.19860	−	9.84429i	−0.217637	−	0.669819i
$217$	0.377954	+	0.520209i	0.0256572	+	0.0353141i
$218$			1.26252i			0.0855084i
$219$	22.2044	−	16.1324i	1.50043	−	1.09013i
$220$	−3.32166	+	6.36118i	−0.223946	+	0.428870i
$221$	12.6997	+	9.22688i	0.854275	+	0.620667i
$222$	−12.2492	+	16.8595i	−0.822110	+	1.13154i
$223$	−9.58256	−	3.11356i	−0.641696	−	0.208500i	−0.0299467	−	0.999551i	$-0.509534\pi$
$223$	−9.58256	−	3.11356i	−0.641696	−	0.208500i	−0.611749	+	0.791052i	$0.709534\pi$
$224$	−4.31891			−0.288569
$225$	−20.0984	−	6.97741i	−1.33989	−	0.465161i
$226$	20.9920			1.39636
$227$	−17.9785	−	5.84157i	−1.19328	−	0.387719i	−0.355993	−	0.934489i	$-0.615857\pi$
$227$	−17.9785	−	5.84157i	−1.19328	−	0.387719i	−0.837283	+	0.546770i	$0.815857\pi$
$228$	−8.33449	+	11.4714i	−0.551965	+	0.759714i
$229$	12.7540	+	9.26633i	0.842809	+	0.612337i	0.923154	−	0.384431i	$-0.125602\pi$
$229$	12.7540	+	9.26633i	0.842809	+	0.612337i	−0.0803449	+	0.996767i	$0.525602\pi$
$230$	−12.4169	−	2.09404i	−0.818746	−	0.138077i
$231$	8.46722	−	6.15179i	0.557102	−	0.404758i
$232$			17.8916i			1.17464i
$233$	−0.136891	−	0.188414i	−0.00896801	−	0.0123434i	0.804509	−	0.593940i	$-0.202428\pi$
$233$	−0.136891	−	0.188414i	−0.00896801	−	0.0123434i	−0.813477	+	0.581596i	$0.802428\pi$
$234$	−3.18395	−	9.79919i	−0.208141	−	0.640593i
$235$	−0.641560	+	3.80422i	−0.0418508	+	0.248160i
$236$	−0.194891	+	0.599812i	−0.0126863	+	0.0390444i
$237$	−11.1624	+	3.62688i	−0.725074	+	0.235591i
$238$	−7.23856	+	2.35195i	−0.469206	+	0.152454i
$239$	7.28392	−	22.4176i	0.471158	−	1.45007i	−0.379912	−	0.925023i	$-0.624046\pi$
$239$	7.28392	−	22.4176i	0.471158	−	1.45007i	0.851070	−	0.525052i	$-0.175954\pi$
$240$	−9.92552	+	1.47053i	−0.640690	+	0.0949225i
$241$	0.907156	+	2.79194i	0.0584351	+	0.179845i	0.976013	−	0.217710i	$-0.0698588\pi$
$241$	0.907156	+	2.79194i	0.0584351	+	0.179845i	−0.917578	+	0.397555i	$0.869859\pi$
$242$	−2.61015	−	3.59257i	−0.167787	−	0.230939i
$243$			19.9991i			1.28295i
$244$	−6.65118	+	4.83237i	−0.425798	+	0.309361i
$245$	2.00240	−	0.995194i	0.127928	−	0.0635806i
$246$	1.54061	+	1.11932i	0.0982256	+	0.0713651i
$247$	−8.37239	+	11.5236i	−0.532722	+	0.733229i
$248$	−1.87255	−	0.608430i	−0.118907	−	0.0386353i
$249$	−28.5248			−1.80768
$250$	−5.82088	+	10.6243i	−0.368145	+	0.671939i
$251$	−11.1248			−0.702191			−0.351096	−	0.936340i	$-0.614191\pi$
$251$	−11.1248			−0.702191			−0.351096	+	0.936340i	$0.614191\pi$
$252$	−3.34237	−	1.08600i	−0.210549	−	0.0684117i
$253$	−11.8701	+	16.3378i	−0.746267	+	1.02715i
$254$	−0.694046	−	0.504254i	−0.0435483	−	0.0316397i
$255$	37.8851	−	18.8290i	2.37246	−	1.17912i
$256$	12.9253	−	9.39077i	0.807830	−	0.586923i
$257$		−	23.1468i		−	1.44386i	−0.691966	−	0.721930i	$-0.743255\pi$
$257$		−	23.1468i		−	1.44386i	0.691966	−	0.721930i	$-0.256745\pi$
$258$	−1.64338	−	2.26192i	−0.102313	−	0.140821i
$259$	2.20650	+	6.79092i	0.137106	+	0.421967i
$260$	4.08275	−	0.604887i	0.253201	−	0.0375135i
$261$	−7.68289	+	23.6455i	−0.475559	+	1.46362i
$262$	2.11895	−	0.688488i	0.130909	−	0.0425349i
$263$	−27.5402	+	8.94835i	−1.69820	+	0.551779i	−0.988300	−	0.152522i	$-0.951260\pi$
$263$	−27.5402	+	8.94835i	−1.69820	+	0.551779i	−0.709901	+	0.704301i	$0.751260\pi$
$264$	−9.90316	+	30.4788i	−0.609497	+	1.87584i
$265$	3.76273	−	22.3116i	0.231143	−	1.37059i
$266$	−2.13414	−	6.56820i	−0.130852	−	0.402722i
$267$	−2.21006	−	3.04189i	−0.135253	−	0.186160i
$268$			2.27065i			0.138702i
$269$	−7.60170	+	5.52296i	−0.463484	+	0.336741i	−0.794896	−	0.606745i	$-0.792475\pi$
$269$	−7.60170	+	5.52296i	−0.463484	+	0.336741i	0.331412	+	0.943486i	$0.392475\pi$
$270$	−8.07628	−	1.36202i	−0.491507	−	0.0828899i
$271$	−11.6500	−	8.46422i	−0.707687	−	0.514165i	0.174740	−	0.984615i	$-0.444092\pi$
$271$	−11.6500	−	8.46422i	−0.707687	−	0.514165i	−0.882427	+	0.470450i	$0.844092\pi$
$272$	6.87832	−	9.46719i	0.417059	−	0.574033i
$273$	−5.72482	−	1.86011i	−0.346482	−	0.112579i
$274$	8.62043			0.520779
$275$	11.1033	+	15.9429i	0.669551	+	0.961391i
$276$	11.5621			0.695958
$277$	2.72923	+	0.886780i	0.163984	+	0.0532815i	0.389858	−	0.920875i	$-0.372524\pi$
$277$	2.72923	+	0.886780i	0.163984	+	0.0532815i	−0.225875	+	0.974156i	$0.572524\pi$
$278$	9.61324	−	13.2315i	0.576564	−	0.793572i
$279$	−2.21350	−	1.60820i	−0.132519	−	0.0962804i
$280$	−3.16923	+	6.06926i	−0.189398	+	0.362707i
$281$	−21.2310	+	15.4252i	−1.26653	+	0.920191i	−0.999059	−	0.0433733i	$-0.986190\pi$
$281$	−21.2310	+	15.4252i	−1.26653	+	0.920191i	−0.267476	+	0.963565i	$0.586190\pi$
$282$			5.03542i			0.299855i
$283$	12.6986	+	17.4781i	0.754854	+	1.03897i	0.997625	+	0.0688841i	$0.0219439\pi$
$283$	12.6986	+	17.4781i	0.754854	+	1.03897i	−0.242770	+	0.970084i	$0.578056\pi$
$284$	−3.25363	−	10.0137i	−0.193068	−	0.594201i
$285$	17.0853	+	34.3767i	1.01204	+	2.03630i
$286$	−2.90756	+	8.94854i	−0.171927	+	0.529138i
$287$	0.620549	−	0.201628i	0.0366298	−	0.0119018i
$288$	17.4776	−	5.67882i	1.02988	−	0.334627i
$289$	−9.99362	+	30.7572i	−0.587860	+	1.80925i
$290$	12.5491	+	6.55287i	0.736910	+	0.384798i
$291$	−9.21467	−	28.3598i	−0.540174	−	1.66248i
$292$	4.94683	+	6.80872i	0.289491	+	0.398450i
$293$			25.5957i			1.49532i	0.664084	+	0.747658i	$0.268822\pi$
$293$			25.5957i			1.49532i	−0.664084	+	0.747658i	$0.731178\pi$
$294$	2.36115	−	1.71547i	0.137705	−	0.100048i
$295$	1.19522	+	1.21935i	0.0695885	+	0.0709934i
$296$	−17.6884	−	12.8514i	−1.02812	−	0.746971i
$297$	−7.72062	+	10.6265i	−0.447996	+	0.616614i
$298$	−3.86354	−	1.25534i	−0.223809	−	0.0727199i
$299$	11.6147			0.671696
$300$	3.64803	−	10.5081i	0.210619	−	0.606687i
$301$	−0.957977			−0.0552169
$302$	0.177346	+	0.0576233i	0.0102051	+	0.00331585i
$303$	13.1047	−	18.0371i	0.752845	−	1.03620i
$304$	8.59045	+	6.24133i	0.492696	+	0.357965i
$305$	3.26202	+	22.0173i	0.186783	+	1.26071i
$306$	26.2002	−	19.0356i	1.49777	−	1.08819i
$307$		−	13.8294i		−	0.789286i	−0.918834	−	0.394643i	$-0.870868\pi$
$307$		−	13.8294i		−	0.789286i	0.918834	−	0.394643i	$-0.129132\pi$
$308$	1.88638	+	2.59638i	0.107486	+	0.147942i
$309$	−5.73983	−	17.6654i	−0.326528	−	1.00495i
$310$	−1.11258	+	1.09057i	−0.0631905	+	0.0619400i
$311$	3.66490	−	11.2794i	0.207818	−	0.639597i	−0.791768	−	0.610821i	$-0.790839\pi$
$311$	3.66490	−	11.2794i	0.207818	−	0.639597i	0.999586	−	0.0287752i	$-0.00916069\pi$
$312$	17.5295	−	5.69569i	0.992414	−	0.322455i
$313$	2.49543	−	0.810816i	0.141050	−	0.0458300i	−0.237641	−	0.971353i	$-0.576374\pi$
$313$	2.49543	−	0.810816i	0.141050	−	0.0458300i	0.378691	+	0.925523i	$0.376374\pi$
$314$	2.31125	−	7.11329i	0.130431	−	0.401426i
$315$	−6.79467	+	6.66021i	−0.382836	+	0.375261i
$316$	−1.11214	−	3.42282i	−0.0625628	−	0.192549i
$317$	12.6997	+	17.4796i	0.713285	+	0.981753i	0.999720	+	0.0236532i	$0.00752976\pi$
$317$	12.6997	+	17.4796i	0.713285	+	0.981753i	−0.286435	+	0.958100i	$0.592470\pi$
$318$		−	29.5326i		−	1.65610i
$319$	18.3680	−	13.3451i	1.02841	−	0.747184i
$320$	−2.62550	−	17.7211i	−0.146770	−	0.990641i
$321$	−26.1634	−	19.0088i	−1.46030	−	1.06097i
$322$	−3.31006	+	4.55591i	−0.184463	+	0.253891i
$323$	−42.5795	−	13.8349i	−2.36919	−	0.769795i
$324$	−3.02281			−0.167934
$325$	3.66462	−	10.5559i	0.203277	−	0.585537i
$326$	10.8558			0.601245
$327$	−2.98481	−	0.969824i	−0.165060	−	0.0536314i
$328$	−1.17435	+	1.61635i	−0.0648425	+	0.0892480i
$329$	1.39581	+	1.01412i	0.0769538	+	0.0559102i
$330$	17.7507	+	18.1090i	0.977144	+	0.996870i
$331$	−23.0393	+	16.7390i	−1.26636	+	0.920061i	−0.999051	−	0.0435513i	$-0.986133\pi$
$331$	−23.0393	+	16.7390i	−1.26636	+	0.920061i	−0.267304	+	0.963612i	$0.586133\pi$
$332$		−	8.74680i		−	0.480043i
$333$	−17.8584	−	24.5800i	−0.978635	−	1.34698i
$334$	2.63013	+	8.09472i	0.143915	+	0.442923i
$335$	5.44917	+	2.84543i	0.297720	+	0.155463i
$336$	−1.38665	+	4.26766i	−0.0756477	+	0.232820i
$337$	−6.24267	+	2.02836i	−0.340060	+	0.110492i	−0.474068	−	0.880488i	$-0.657215\pi$
$337$	−6.24267	+	2.02836i	−0.340060	+	0.110492i	0.134009	+	0.990980i	$0.457215\pi$
$338$	−8.24998	+	2.68058i	−0.448740	+	0.145804i
$339$	−16.1253	+	49.6287i	−0.875808	+	2.69546i
$340$	5.77370	+	11.6171i	0.313123	+	0.630023i
$341$	0.772086	+	2.37624i	0.0418108	+	0.128680i
$342$	17.2727	+	23.7738i	0.934001	+	1.28554i
$343$		−	1.00000i		−	0.0539949i
$344$	2.37313	−	1.72418i	0.127950	−	0.0929614i
$345$	14.4889	−	27.7472i	0.780058	−	1.49386i
$346$	17.9891	+	13.0698i	0.967098	+	0.702637i
$347$	8.09221	−	11.1380i	0.434413	−	0.597918i	−0.534546	−	0.845139i	$-0.679517\pi$
$347$	8.09221	−	11.1380i	0.434413	−	0.597918i	0.968959	+	0.247221i	$0.0795175\pi$
$348$	−12.3627	−	4.01688i	−0.662709	−	0.215327i
$349$	14.7554			0.789836			0.394918	−	0.918716i	$-0.370773\pi$
$349$	14.7554			0.789836			0.394918	+	0.918716i	$0.370773\pi$
$350$	3.09622	+	4.44578i	0.165500	+	0.237637i
$351$	7.55451			0.403230
$352$	−15.9604	−	5.18585i	−0.850692	−	0.276407i
$353$	18.8654	−	25.9660i	1.00411	−	1.38203i	0.0813325	−	0.996687i	$-0.474082\pi$
$353$	18.8654	−	25.9660i	1.00411	−	1.38203i	0.922773	−	0.385345i	$-0.125918\pi$
$354$	1.80296	+	1.30992i	0.0958260	+	0.0696217i
$355$	−28.1083	−	4.74032i	−1.49184	−	0.251590i
$356$	0.932760	−	0.677690i	0.0494362	−	0.0359175i
$357$		−	18.9199i		−	1.00135i
$358$	0.108843	+	0.149809i	0.00575252	+	0.00791767i
$359$	−0.329224	−	1.01325i	−0.0173758	−	0.0534772i	0.941993	−	0.335633i	$-0.108950\pi$
$359$	−0.329224	−	1.01325i	−0.0173758	−	0.0534772i	−0.959368	+	0.282156i	$0.908950\pi$
$360$	4.84482	−	28.7280i	0.255344	−	1.51410i
$361$	6.68236	−	20.5662i	0.351703	−	1.08243i
$362$	21.0270	−	6.83208i	1.10515	−	0.359086i
$363$	10.4985	−	3.41117i	0.551028	−	0.179040i
$364$	0.570381	−	1.75545i	0.0298961	−	0.0920107i
$365$	22.5389	−	3.33928i	1.17974	−	0.174786i
$366$	8.97723	+	27.6291i	0.469247	+	1.44419i
$367$	3.56817	+	4.91117i	0.186257	+	0.256361i	0.891927	−	0.452180i	$-0.149354\pi$
$367$	3.56817	+	4.91117i	0.186257	+	0.256361i	−0.705669	+	0.708541i	$0.749354\pi$
$368$		−	8.65836i		−	0.451348i
$369$	−2.24610	+	1.63189i	−0.116927	+	0.0849526i
$370$	−15.4924	+	7.69974i	−0.805411	+	0.400290i
$371$	−8.18641	−	5.94778i	−0.425017	−	0.308793i
$372$	0.840822	−	1.15729i	0.0435946	−	0.0600028i
$373$	36.0268	+	11.7058i	1.86540	+	0.606104i	0.993122	+	0.117087i	$0.0373557\pi$
$373$	36.0268	+	11.7058i	1.86540	+	0.606104i	0.872274	+	0.489017i	$0.162644\pi$
$374$	−29.5739			−1.52923
$375$	−20.6463	−	21.9228i	−1.06617	−	1.13209i
$376$	−5.28297			−0.272448
$377$	−12.4189	−	4.03514i	−0.639606	−	0.207821i
$378$	−2.15295	+	2.96329i	−0.110736	+	0.152415i
$379$	−0.378625	−	0.275087i	−0.0194486	−	0.0141303i	0.578018	−	0.816024i	$-0.303826\pi$
$379$	−0.378625	−	0.275087i	−0.0194486	−	0.0141303i	−0.597467	+	0.801893i	$0.703826\pi$
$380$	−10.5412	+	5.23900i	−0.540753	+	0.268755i
$381$	1.72529	−	1.25350i	0.0883892	−	0.0642185i
$382$		−	0.638371i		−	0.0326619i
$383$	1.01849	+	1.40183i	0.0520425	+	0.0716303i	0.834245	−	0.551394i	$-0.185904\pi$
$383$	1.01849	+	1.40183i	0.0520425	+	0.0716303i	−0.782203	+	0.623024i	$0.785904\pi$
$384$	−0.0358986	−	0.110485i	−0.00183194	−	0.00563815i
$385$	8.59476	−	1.27337i	0.438030	−	0.0648971i
$386$	3.26370	−	10.0446i	0.166118	−	0.511259i
$387$	3.87671	−	1.25962i	0.197064	−	0.0640300i
$388$	8.69623	−	2.82558i	0.441484	−	0.143447i
$389$	1.42480	−	4.38509i	0.0722403	−	0.222333i	−0.908417	−	0.418065i	$-0.862708\pi$
$389$	1.42480	−	4.38509i	0.0722403	−	0.222333i	0.980657	+	0.195732i	$0.0627084\pi$
$390$	2.42532	−	14.3813i	0.122811	−	0.728223i
$391$	11.2812	+	34.7199i	0.570513	+	1.75586i
$392$	1.79981	+	2.47723i	0.0909042	+	0.125119i
$393$			5.53844i			0.279377i
$394$	−3.17641	+	2.30780i	−0.160025	+	0.116265i
$395$	−9.60785	−	1.62031i	−0.483423	−	0.0815267i
$396$	−11.0476	−	8.02658i	−0.555165	−	0.403351i
$397$	18.8369	−	25.9268i	0.945398	−	1.30123i	−0.00814343	−	0.999967i	$-0.502592\pi$
$397$	18.8369	−	25.9268i	0.945398	−	1.30123i	0.953541	−	0.301262i	$-0.0974078\pi$
$398$	3.97623	+	1.29196i	0.199310	+	0.0647599i
$399$	17.1678			0.859463
$400$	−7.86908	−	2.73185i	−0.393454	−	0.136592i
$401$	−36.7072			−1.83307			−0.916535	−	0.399956i	$-0.869026\pi$
$401$	−36.7072			−1.83307			−0.916535	+	0.399956i	$0.869026\pi$
$402$	7.63088	+	2.47942i	0.380593	+	0.123662i
$403$	0.844646	−	1.16256i	0.0420748	−	0.0579110i
$404$	5.53087	+	4.01841i	0.275171	+	0.199923i
$405$	−3.78800	+	7.25425i	−0.188227	+	0.360466i
$406$	5.12205	−	3.72139i	0.254203	−	0.184689i
$407$			27.7451i			1.37527i
$408$	34.0523	+	46.8689i	1.68584	+	2.32036i
$409$	5.85545	+	18.0212i	0.289533	+	0.891091i	0.985003	+	0.172536i	$0.0551962\pi$
$409$	5.85545	+	18.0212i	0.289533	+	0.891091i	−0.695470	+	0.718555i	$0.744804\pi$
$410$	0.703596	+	1.41568i	0.0347481	+	0.0699155i
$411$	−6.62193	+	20.3802i	−0.326636	+	1.00528i
$412$	5.41689	−	1.76005i	0.266871	−	0.0867117i
$413$	0.726220	−	0.235963i	0.0357350	−	0.0116110i
$414$	7.40460	−	22.7890i	0.363916	−	1.12002i
$415$	−20.9908	−	10.9609i	−1.03040	−	0.538051i
$416$	2.98258	+	9.17945i	0.146233	+	0.450059i
$417$	23.8970	+	32.8914i	1.17024	+	1.61070i
$418$		−	26.8351i		−	1.31255i
$419$	22.8721	−	16.6176i	1.11738	−	0.811821i	0.133566	−	0.991040i	$-0.457357\pi$
$419$	22.8721	−	16.6176i	1.11738	−	0.811821i	0.983809	+	0.179219i	$0.0573571\pi$
$420$	−3.48219	−	3.55249i	−0.169913	−	0.173344i
$421$	19.1053	+	13.8808i	0.931134	+	0.676509i	0.946270	−	0.323377i	$-0.104818\pi$
$421$	19.1053	+	13.8808i	0.931134	+	0.676509i	−0.0151360	+	0.999885i	$0.504818\pi$
$422$	6.64781	−	9.14992i	0.323610	−	0.445411i
$423$	−6.98197	−	2.26858i	−0.339475	−	0.110302i
$424$	30.9845			1.50474
$425$	35.1142	+	0.701872i	1.70329	+	0.0340458i
$426$	−37.2053			−1.80260
$427$	9.46675	+	3.07593i	0.458128	+	0.148855i
$428$	5.82884	−	8.02271i	0.281747	−	0.387792i
$429$	−18.9224	−	13.7480i	−0.913584	−	0.663758i
$430$	−0.340167	−	2.29599i	−0.0164043	−	0.110723i
$431$	−26.7969	+	19.4691i	−1.29076	+	0.937792i	−0.999820	−	0.0189497i	$-0.993968\pi$
$431$	−26.7969	+	19.4691i	−1.29076	+	0.937792i	−0.290939	+	0.956742i	$0.593968\pi$
$432$		−	5.63163i		−	0.270952i
$433$	−14.3451	−	19.7443i	−0.689381	−	0.948851i	0.310618	−	0.950535i	$-0.399464\pi$
$433$	−14.3451	−	19.7443i	−0.689381	−	0.948851i	−0.999999	+	0.00168384i	$0.999464\pi$
$434$	0.215302	+	0.662631i	0.0103348	+	0.0318073i
$435$	−25.1320	+	24.6346i	−1.20499	+	1.18114i
$436$	0.297386	−	0.915259i	0.0142422	−	0.0438329i
$437$	−31.5045	+	10.2364i	−1.50706	+	0.489675i
$438$	28.2835	−	9.18987i	1.35144	−	0.439109i
$439$	−3.83788	+	11.8118i	−0.183172	+	0.563745i	−0.999912	−	0.0132604i	$-0.995779\pi$
$439$	−3.83788	+	11.8118i	−0.183172	+	0.563745i	0.816740	+	0.577006i	$0.195779\pi$
$440$	−18.9993	+	18.6234i	−0.905758	+	0.887835i
$441$	1.31487	+	4.04676i	0.0626130	+	0.192703i
$442$	9.99771	+	13.7607i	0.475543	+	0.654528i
$443$		−	7.55360i		−	0.358882i	−0.983769	−	0.179441i	$-0.942571\pi$
$443$		−	7.55360i		−	0.358882i	0.983769	−	0.179441i	$-0.0574289\pi$
$444$	12.8513	−	9.33699i	0.609894	−	0.443114i
$445$	−0.457465	−	3.08771i	−0.0216859	−	0.146371i
$446$	−8.83240	−	6.41711i	−0.418226	−	0.303859i
$447$	5.93569	−	8.16978i	0.280749	−	0.386417i
$448$	−7.61952	−	2.47573i	−0.359988	−	0.116967i
$449$	−5.46297			−0.257813			−0.128907	−	0.991657i	$-0.541147\pi$
$449$	−5.46297			−0.257813			−0.128907	+	0.991657i	$0.541147\pi$
$450$	−18.3753	−	13.9199i	−0.866221	−	0.656190i
$451$	2.53532			0.119384
$452$	−15.2181	−	4.94465i	−0.715798	−	0.232577i
$453$	−0.272463	+	0.375014i	−0.0128014	+	0.0176197i
$454$	−16.5711	−	12.0396i	−0.777720	−	0.565046i
$455$	−3.49803	−	3.56864i	−0.163990	−	0.167301i
$456$	−42.5284	+	30.8987i	−1.99158	+	1.44697i
$457$		−	0.354917i		−	0.0166023i	−0.999966	−	0.00830116i	$-0.997358\pi$
$457$		−	0.354917i		−	0.0166023i	0.999966	−	0.00830116i	$-0.00264237\pi$
$458$	10.0405	+	13.8195i	0.469160	+	0.645743i
$459$	7.33757	+	22.5827i	0.342488	+	1.05407i
$460$	8.50835	+	4.44287i	0.396704	+	0.207150i
$461$	6.46313	−	19.8915i	0.301018	−	0.926438i	−0.680115	−	0.733105i	$-0.738070\pi$
$461$	6.46313	−	19.8915i	0.301018	−	0.926438i	0.981133	−	0.193333i	$-0.0619296\pi$
$462$	10.7854	−	3.50438i	0.501781	−	0.163039i
$463$	8.89199	−	2.88918i	0.413246	−	0.134272i	−0.0950132	−	0.995476i	$-0.530289\pi$
$463$	8.89199	−	2.88918i	0.413246	−	0.134272i	0.508259	+	0.861204i	$0.330289\pi$
$464$	−3.00806	+	9.25786i	−0.139646	+	0.429785i
$465$	−1.72364	−	3.46808i	−0.0799320	−	0.160828i
$466$	−0.0779800	−	0.239998i	−0.00361236	−	0.0111177i
$467$	−12.0224	−	16.5474i	−0.556329	−	0.765721i	0.434525	−	0.900660i	$-0.356916\pi$
$467$	−12.0224	−	16.5474i	−0.556329	−	0.765721i	−0.990854	+	0.134939i	$0.956916\pi$
$468$			7.85388i			0.363046i
$469$	2.22413	−	1.61593i	0.102701	−	0.0746165i
$470$	−1.93491	+	3.70547i	−0.0892508	+	0.170921i
$471$	15.0416	+	10.9284i	0.693082	+	0.503554i
$472$	−1.37432	+	1.89159i	−0.0632584	+	0.0870677i
$473$	−3.54018	−	1.15027i	−0.162778	−	0.0528896i
$474$	−12.7173			−0.584127
$475$	−0.636873	+	31.8623i	−0.0292217	+	1.46194i
$476$	5.80158			0.265915
$477$	40.9491	+	13.3052i	1.87493	+	0.609201i
$478$	15.0123	−	20.6627i	0.686647	−	0.945089i
$479$	7.76930	+	5.64473i	0.354988	+	0.257914i	0.750959	−	0.660349i	$-0.229592\pi$
$479$	7.76930	+	5.64473i	0.354988	+	0.257914i	−0.395970	+	0.918263i	$0.629592\pi$
$480$	25.6501	+	4.32574i	1.17076	+	0.197442i
$481$	12.9097	−	9.37945i	0.588632	−	0.427666i
$482$			3.18087i			0.144885i
$483$	−8.22830	−	11.3253i	−0.374400	−	0.515318i
$484$	1.04600	+	3.21925i	0.0475453	+	0.146329i
$485$	4.11667	−	24.4103i	0.186928	−	1.10842i
$486$	−6.69637	+	20.6093i	−0.303754	+	0.934858i
$487$	−9.00420	+	2.92564i	−0.408019	+	0.132574i	−0.505833	−	0.862631i	$-0.668815\pi$
$487$	−9.00420	+	2.92564i	−0.408019	+	0.132574i	0.0978141	+	0.995205i	$0.468815\pi$
$488$	−28.9874	+	9.41858i	−1.31220	+	0.426359i
$489$	−8.33904	+	25.6649i	−0.377104	+	1.16061i
$490$	2.39671	−	0.355089i	0.108272	−	0.0160413i
$491$	−12.8195	−	39.4544i	−0.578536	−	1.78055i	−0.623809	−	0.781577i	$-0.714416\pi$
$491$	−12.8195	−	39.4544i	−0.578536	−	1.78055i	0.0452724	−	0.998975i	$-0.485584\pi$
$492$	−0.853206	−	1.17434i	−0.0384655	−	0.0529432i
$493$		−	41.0431i		−	1.84849i
$494$	−12.4863	+	9.07184i	−0.561786	+	0.408161i
$495$	−33.1066	+	16.4541i	−1.48803	+	0.739555i
$496$	−0.866645	−	0.629655i	−0.0389135	−	0.0282723i
$497$	−7.49305	+	10.3133i	−0.336109	+	0.462615i
$498$	−29.3950	−	9.55103i	−1.31722	−	0.427992i
$499$	23.6709			1.05965			0.529827	−	0.848106i	$-0.322257\pi$
$499$	23.6709			1.05965			0.529827	+	0.848106i	$0.322257\pi$
$500$	6.72238	−	6.33095i	0.300634	−	0.283129i
$501$	−21.1577			−0.945257
$502$	−11.4642	−	3.72495i	−0.511673	−	0.166253i
$503$	10.3206	−	14.2051i	0.460175	−	0.633376i	−0.514370	−	0.857568i	$-0.671974\pi$
$503$	10.3206	−	14.2051i	0.460175	−	0.633376i	0.974545	+	0.224192i	$0.0719743\pi$
$504$	−10.5407	−	7.65823i	−0.469518	−	0.341125i
$505$	16.5744	−	8.23753i	0.737553	−	0.366565i
$506$	−17.7027	+	12.8618i	−0.786980	+	0.571775i
$507$		−	21.5635i		−	0.957670i
$508$	0.384370	+	0.529040i	0.0170537	+	0.0234724i
$509$	−4.63196	−	14.2557i	−0.205308	−	0.631873i	−0.999701	−	0.0244686i	$-0.992211\pi$
$509$	−4.63196	−	14.2557i	−0.205308	−	0.631873i	0.794392	−	0.607405i	$-0.207789\pi$
$510$	45.3456	−	6.71826i	2.00794	−	0.297489i
$511$	3.14879	−	9.69099i	0.139294	−	0.428704i
$512$	16.5460	−	5.37613i	0.731237	−	0.237593i
$513$	−20.4914	+	6.65804i	−0.904715	+	0.293960i
$514$	7.75032	−	23.8530i	0.341852	−	1.05211i
$515$	2.56428	−	15.2052i	0.112996	−	0.670022i
$516$	0.658572	+	2.02688i	0.0289920	+	0.0892282i
$517$	3.94051	+	5.42365i	0.173303	+	0.238532i
$518$			7.73692i			0.339941i
$519$	−44.7179	+	32.4895i	−1.96290	+	1.42613i
$520$	15.0883	+	2.54456i	0.661665	+	0.111586i
$521$	11.2778	+	8.19378i	0.494088	+	0.358976i	0.806754	−	0.590887i	$-0.201222\pi$
$521$	11.2778	+	8.19378i	0.494088	+	0.358976i	−0.312666	+	0.949863i	$0.601222\pi$
$522$	−15.8346	+	21.7944i	−0.693061	+	0.953916i
$523$	−3.89819	−	1.26660i	−0.170456	−	0.0553845i	0.222546	−	0.974922i	$-0.428563\pi$
$523$	−3.89819	−	1.26660i	−0.170456	−	0.0553845i	−0.393002	+	0.919538i	$0.628563\pi$
$524$	−1.69830			−0.0741906
$525$	−12.8890	+	3.90491i	−0.562524	+	0.170424i
$526$	−31.3767			−1.36809
$527$	4.29562	+	1.39573i	0.187120	+	0.0607990i
$528$	−10.2486	+	14.1060i	−0.446014	+	0.613886i
$529$	3.24513	+	2.35772i	0.141092	+	0.102510i
$530$	11.3482	−	21.7325i	0.492934	−	0.943998i
$531$	−2.62858	+	1.90978i	−0.114071	+	0.0828772i
$532$			5.26430i			0.228236i
$533$	−0.857086	−	1.17968i	−0.0371245	−	0.0510975i
$534$	−1.25896	−	3.87469i	−0.0544807	−	0.167674i
$535$	−11.9488	−	24.0418i	−0.516592	−	1.03942i
$536$	−2.60132	+	8.00603i	−0.112360	+	0.345808i
$537$	−0.437785	+	0.142245i	−0.0188918	+	0.00613832i
$538$	−9.68290	+	3.14616i	−0.417459	+	0.135641i
$539$	1.20073	−	3.69547i	0.0517192	−	0.159175i
$540$	5.53406	+	2.88976i	0.238148	+	0.124355i
$541$	0.708335	+	2.18003i	0.0304537	+	0.0937269i	0.965128	−	0.261778i	$-0.0843089\pi$
$541$	0.708335	+	2.18003i	0.0304537	+	0.0937269i	−0.934674	+	0.355505i	$0.884309\pi$
$542$	−9.17134	−	12.6233i	−0.393943	−	0.542216i
$543$			54.9597i			2.35855i
$544$	−24.5432	+	17.8317i	−1.05228	+	0.764527i
$545$	−1.82380	−	1.86062i	−0.0781231	−	0.0797002i
$546$	−5.27666	−	3.83372i	−0.225820	−	0.164068i
$547$	6.30500	−	8.67808i	0.269582	−	0.371048i	−0.652666	−	0.757645i	$-0.726350\pi$
$547$	6.30500	−	8.67808i	0.269582	−	0.371048i	0.922249	+	0.386597i	$0.126350\pi$
$548$	−6.24936	−	2.03054i	−0.266960	−	0.0867404i
$549$	−42.3542			−1.80763
$550$	6.10382	+	20.1470i	0.260268	+	0.859071i
$551$	37.2421			1.58657
$552$	40.7667	+	13.2459i	1.73515	+	0.563783i
$553$	−2.56124	+	3.52524i	−0.108915	+	0.149908i
$554$	2.51557	+	1.82767i	0.106877	+	0.0776503i
$555$	−6.30280	−	42.5414i	−0.267539	−	1.80578i
$556$	−10.0858	+	7.32775i	−0.427732	+	0.310766i
$557$			16.7497i			0.709709i	0.934922	+	0.354854i	$0.115470\pi$
$557$			16.7497i			0.709709i	−0.934922	+	0.354854i	$0.884530\pi$
$558$	−1.74255	−	2.39842i	−0.0737682	−	0.101533i
$559$	0.661567	+	2.03609i	0.0279813	+	0.0861176i
$560$	−2.66030	+	2.60766i	−0.112418	+	0.110194i
$561$	22.7177	−	69.9180i	0.959144	−	2.95194i
$562$	−27.0436	+	8.78700i	−1.14077	+	0.370657i
$563$	17.8470	−	5.79885i	0.752162	−	0.244392i	0.0922510	−	0.995736i	$-0.470594\pi$
$563$	17.8470	−	5.79885i	0.752162	−	0.244392i	0.659911	+	0.751343i	$0.270594\pi$
$564$	1.18609	−	3.65041i	0.0499435	−	0.153710i
$565$	−30.9367	+	30.3245i	−1.30152	+	1.27576i
$566$	7.23379	+	22.2633i	0.304059	+	0.935797i
$567$	2.15121	+	2.96089i	0.0903425	+	0.124346i
$568$		−	39.0345i		−	1.63785i
$569$	19.2376	−	13.9770i	0.806483	−	0.585944i	−0.106326	−	0.994331i	$-0.533909\pi$
$569$	19.2376	−	13.9770i	0.806483	−	0.585944i	0.912809	+	0.408387i	$0.133909\pi$
$570$	6.09609	+	41.1462i	0.255337	+	1.72342i
$571$	−22.4615	−	16.3193i	−0.939986	−	0.682940i	0.00843096	−	0.999964i	$-0.497316\pi$
$571$	−22.4615	−	16.3193i	−0.939986	−	0.682940i	−0.948417	+	0.317024i	$0.897316\pi$
$572$	4.21566	−	5.80235i	0.176265	−	0.242609i
$573$	1.50922	+	0.490376i	0.0630486	+	0.0204857i
$574$	0.706994			0.0295093
$575$	21.3243	−	14.8511i	0.889284	−	0.619333i
$576$	34.0897			1.42040
$577$	−20.4243	−	6.63627i	−0.850277	−	0.276272i	−0.148715	−	0.988880i	$-0.547514\pi$
$577$	−20.4243	−	6.63627i	−0.850277	−	0.276272i	−0.701562	+	0.712609i	$0.747514\pi$
$578$	−20.5970	+	28.3494i	−0.856724	+	1.17918i
$579$	21.2402	+	15.4319i	0.882714	+	0.641329i
$580$	−7.55394	−	7.70644i	−0.313660	−	0.319992i
$581$	−8.56762	+	6.22474i	−0.355445	+	0.258246i
$582$		−	32.3105i		−	1.33931i
$583$	−23.1110	−	31.8095i	−0.957159	−	1.31742i
$584$	9.64167	+	29.6740i	0.398975	+	1.22792i
$585$	18.8480	+	9.84200i	0.779269	+	0.406917i
$586$	−8.57028	+	26.3766i	−0.354035	+	1.08961i
$587$	0.826003	−	0.268385i	0.0340928	−	0.0110774i	−0.291921	−	0.956442i	$-0.594294\pi$
$587$	0.826003	−	0.268385i	0.0340928	−	0.0110774i	0.326014	+	0.945365i	$0.394294\pi$
$588$	−2.11579	+	0.687461i	−0.0872536	+	0.0283504i
$589$	−1.26647	+	3.89781i	−0.0521842	+	0.160606i
$590$	0.823409	+	1.65675i	0.0338992	+	0.0682075i
$591$	−3.01602	−	9.28237i	−0.124063	−	0.381826i
$592$	−6.99206	−	9.62374i	−0.287372	−	0.395533i
$593$			1.48792i			0.0611015i	0.999533	+	0.0305507i	$0.00972611\pi$
$593$			1.48792i			0.0611015i	−0.999533	+	0.0305507i	$0.990274\pi$
$594$	−11.5143	+	8.36562i	−0.472437	+	0.343246i
$595$	7.27018	−	13.9228i	0.298048	−	0.570780i
$596$	2.50517	+	1.82011i	0.102616	+	0.0745548i
$597$	−6.10882	+	8.40807i	−0.250017	+	0.344119i
$598$	11.9691	+	3.88899i	0.489452	+	0.159033i
$599$	−18.2242			−0.744622			−0.372311	−	0.928108i	$-0.621435\pi$
$599$	−18.2242			−0.744622			−0.372311	+	0.928108i	$0.621435\pi$
$600$	24.9010	−	32.8712i	1.01658	−	1.34196i
$601$	39.6429			1.61707			0.808534	−	0.588450i	$-0.200262\pi$
$601$	39.6429			1.61707			0.808534	+	0.588450i	$0.200262\pi$
$602$	−0.987205	−	0.320762i	−0.0402355	−	0.0130733i
$603$	−6.87580	+	9.46373i	−0.280004	+	0.385393i
$604$	−0.114994	−	0.0835479i	−0.00467903	−	0.00339951i
$605$	9.03643	+	1.52394i	0.367383	+	0.0619571i
$606$	19.5439	−	14.1995i	0.793918	−	0.576815i
$607$			37.1742i			1.50885i	0.656385	+	0.754426i	$0.272085\pi$
$607$			37.1742i			1.50885i	−0.656385	+	0.754426i	$0.727915\pi$
$608$	−16.1803	−	22.2703i	−0.656198	−	0.903180i
$609$	4.86342	+	14.9681i	0.197076	+	0.606537i
$610$	−4.01059	+	23.7813i	−0.162384	+	0.962877i
$611$	1.19149	−	3.66702i	0.0482024	−	0.148352i
$612$	−23.4776	+	7.62834i	−0.949026	+	0.308357i
$613$	25.4549	−	8.27079i	1.02811	−	0.334054i	0.254069	−	0.967186i	$-0.418231\pi$
$613$	25.4549	−	8.27079i	1.02811	−	0.334054i	0.774044	+	0.633132i	$0.218231\pi$
$614$	4.63054	−	14.2514i	0.186874	−	0.575138i
$615$	−3.88740	+	0.575944i	−0.156755	+	0.0232243i
$616$	3.67667	+	11.3156i	0.148137	+	0.455919i
$617$	3.54694	+	4.88195i	0.142794	+	0.196540i	0.874424	−	0.485163i	$-0.161240\pi$
$617$	3.54694	+	4.88195i	0.142794	+	0.196540i	−0.731629	+	0.681703i	$0.761240\pi$
$618$		−	20.1262i		−	0.809596i
$619$	−16.4516	+	11.9528i	−0.661246	+	0.480424i	−0.867084	−	0.498163i	$-0.834008\pi$
$619$	−16.4516	+	11.9528i	−0.661246	+	0.480424i	0.205837	+	0.978586i	$0.434008\pi$
$620$	1.06345	−	0.528535i	0.0427091	−	0.0212265i
$621$	14.2135	+	10.3267i	0.570366	+	0.414395i
$622$	7.55344	−	10.3964i	0.302865	−	0.416858i
$623$	−1.32762	−	0.431368i	−0.0531898	−	0.0172824i
$624$	10.0281			0.401446
$625$	−6.76914	−	24.0661i	−0.270765	−	0.962645i
$626$	2.84306			0.113631
$627$	63.4430	+	20.6139i	2.53367	+	0.823239i
$628$	−3.35107	+	4.61235i	−0.133722	+	0.184053i
$629$	40.5770	+	29.4809i	1.61791	+	1.17548i
$630$	−9.23203	+	4.58834i	−0.367813	+	0.182804i
$631$	14.5049	−	10.5384i	0.577432	−	0.419529i	−0.260366	−	0.965510i	$-0.583843\pi$
$631$	14.5049	−	10.5384i	0.577432	−	0.419529i	0.837797	+	0.545981i	$0.183843\pi$
$632$		−	13.3426i		−	0.530739i
$633$	16.5254	+	22.7453i	0.656826	+	0.904043i
$634$	7.23440	+	22.2652i	0.287315	+	0.884264i
$635$	1.75128	−	0.259464i	0.0694973	−	0.0102965i
$636$	−6.95639	+	21.4096i	−0.275839	+	0.848945i
$637$	−2.12541	+	0.690588i	−0.0842118	+	0.0273621i
$638$	23.3968	−	7.60208i	0.926288	−	0.300969i
$639$	16.7619	−	51.5879i	0.663092	−	2.04079i
$640$	0.0160378	−	0.0950981i	0.000633948	−	0.00375908i
$641$	0.606586	+	1.86688i	0.0239587	+	0.0737373i	0.962321	−	0.271916i	$-0.0876573\pi$
$641$	0.606586	+	1.86688i	0.0239587	+	0.0737373i	−0.938362	+	0.345653i	$0.887657\pi$
$642$	−20.5968	−	28.3491i	−0.812893	−	1.11885i
$643$			44.6024i			1.75895i	0.475948	+	0.879474i	$0.342105\pi$
$643$			44.6024i			1.75895i	−0.475948	+	0.879474i	$0.657895\pi$
$644$	3.47277	−	2.52311i	0.136846	−	0.0994247i
$645$	5.68944	+	0.959493i	0.224022	+	0.0377800i
$646$	−39.2462	−	28.5140i	−1.54412	−	1.12187i
$647$	12.3281	−	16.9682i	0.484668	−	0.667088i	−0.494726	−	0.869049i	$-0.664731\pi$
$647$	12.3281	−	16.9682i	0.484668	−	0.667088i	0.979394	+	0.201961i	$0.0647314\pi$
$648$	−10.6581	−	3.46302i	−0.418689	−	0.136040i
$649$	2.96706			0.116467
$650$	7.31090	−	9.65095i	0.286757	−	0.378541i
$651$	−1.73197			−0.0678811
$652$	−7.86986	−	2.55707i	−0.308207	−	0.100143i
$653$	−14.5892	+	20.0803i	−0.570920	+	0.785805i	−0.992663	−	0.120911i	$-0.961418\pi$
$653$	−14.5892	+	20.0803i	−0.570920	+	0.785805i	0.421743	+	0.906715i	$0.361418\pi$
$654$	−2.75115	−	1.99883i	−0.107578	−	0.0781603i
$655$	−2.12820	+	4.07563i	−0.0831558	+	0.159248i
$656$	−0.879409	+	0.638928i	−0.0343352	+	0.0249460i
$657$			43.3574i			1.69153i
$658$	1.09884	+	1.51242i	0.0428373	+	0.0589604i
$659$	4.63827	+	14.2751i	0.180681	+	0.556080i	0.999847	−	0.0174764i	$-0.00556321\pi$
$659$	4.63827	+	14.2751i	0.180681	+	0.556080i	−0.819166	+	0.573557i	$0.805563\pi$
$660$	−8.60275	−	17.3093i	−0.334862	−	0.673763i
$661$	6.93189	−	21.3342i	0.269619	−	0.829803i	−0.720974	−	0.692963i	$-0.756305\pi$
$661$	6.93189	−	21.3342i	0.269619	−	0.829803i	0.990593	−	0.136841i	$-0.0436949\pi$
$662$	−29.3470	+	9.53543i	−1.14060	+	0.370605i
$663$	−40.2126	+	13.0659i	−1.56173	+	0.507436i
$664$	10.0206	−	30.8402i	0.388874	−	1.19683i
$665$	12.6334	+	6.59690i	0.489904	+	0.255817i
$666$	−10.1731	−	31.3095i	−0.394199	−	1.21322i
$667$	−17.8497	−	24.5680i	−0.691143	−	0.951277i
$668$		−	6.48778i		−	0.251020i
$669$	21.9559	−	15.9519i	0.848866	−	0.616737i
$670$	4.66268	+	4.75681i	0.180135	+	0.183771i
$671$	31.2908	+	22.7341i	1.20797	+	0.877639i
$672$	6.83773	−	9.41133i	0.263771	−	0.363050i
$673$	35.4813	+	11.5286i	1.36770	+	0.444394i	0.898607	−	0.438754i	$-0.144580\pi$
$673$	35.4813	+	11.5286i	1.36770	+	0.444394i	0.469096	+	0.883147i	$0.344580\pi$
$674$	−7.11229			−0.273955
$675$	13.8699	−	9.65954i	0.533852	−	0.371796i
$676$	6.61221			0.254316
$677$	−27.9149	−	9.07011i	−1.07286	−	0.348592i	−0.281257	−	0.959632i	$-0.590751\pi$
$677$	−27.9149	−	9.07011i	−1.07286	−	0.348592i	−0.791600	+	0.611040i	$0.790751\pi$
$678$	−33.2346	+	45.7436i	−1.27637	+	1.75677i
$679$	−8.95645	−	6.50724i	−0.343717	−	0.249725i
$680$	7.04855	+	47.5749i	0.270299	+	1.82441i
$681$	41.1931	−	29.9285i	1.57852	−	1.14686i
$682$			2.70726i			0.103666i
$683$	−4.07402	−	5.60741i	−0.155888	−	0.214562i	0.723928	−	0.689875i	$-0.242335\pi$
$683$	−4.07402	−	5.60741i	−0.155888	−	0.214562i	−0.879816	+	0.475314i	$0.842335\pi$
$684$	−6.92189	−	21.3034i	−0.264665	−	0.814555i
$685$	−12.7043	+	12.4529i	−0.485405	+	0.475800i
$686$	0.334833	−	1.03051i	0.0127840	−	0.0393451i
$687$	−40.3845	+	13.1217i	−1.54077	+	0.500625i
$688$	1.51784	−	0.493175i	0.0578670	−	0.0188021i
$689$	−6.98803	+	21.5069i	−0.266223	+	0.819349i
$690$	24.2217	−	23.7423i	0.922103	−	0.903856i
$691$	4.66411	+	14.3546i	0.177431	+	0.546077i	0.999736	−	0.0229703i	$-0.00731231\pi$
$691$	4.66411	+	14.3546i	0.177431	+	0.546077i	−0.822305	+	0.569047i	$0.807312\pi$
$692$	−9.96254	−	13.7123i	−0.378719	−	0.521262i
$693$			16.5335i			0.628056i
$694$	12.0685	−	8.76825i	0.458113	−	0.332838i
$695$	4.94649	+	33.3868i	0.187631	+	1.26644i
$696$	−38.9875	−	28.3261i	−1.47782	−	1.07370i
$697$	2.69394	−	3.70789i	0.102040	−	0.140446i
$698$	15.2055	+	4.94058i	0.575538	+	0.187004i
$699$	0.627299			0.0237266
$700$	−1.19740	−	3.95228i	−0.0452574	−	0.149382i
$701$	−22.7749			−0.860195			−0.430098	−	0.902782i	$-0.641521\pi$
$701$	−22.7749			−0.860195			−0.430098	+	0.902782i	$0.641521\pi$
$702$	7.78500	+	2.52950i	0.293826	+	0.0954698i
$703$	−26.7507	+	36.8192i	−1.00892	+	1.38866i
$704$	−25.1850	−	18.2980i	−0.949196	−	0.689632i
$705$	−7.27404	−	7.42089i	−0.273956	−	0.279487i
$706$	28.1353	−	20.4415i	1.05889	−	0.769325i
$707$		−	8.27731i		−	0.311300i
$708$	−0.998496	−	1.37431i	−0.0375258	−	0.0516498i
$709$	8.80251	+	27.0913i	0.330585	+	1.01744i	0.968856	+	0.247625i	$0.0796499\pi$
$709$	8.80251	+	27.0913i	0.330585	+	1.01744i	−0.638271	+	0.769812i	$0.720350\pi$
$710$	−27.3787	−	14.2965i	−1.02750	−	0.536540i
$711$	5.72948	−	17.6335i	0.214872	−	0.661309i
$712$	4.06519	−	1.32086i	0.152349	−	0.0495013i
$713$	3.17832	−	1.03270i	0.119029	−	0.0386749i
$714$	6.33501	−	19.4972i	0.237082	−	0.729663i
$715$	−8.64187	−	17.3880i	−0.323188	−	0.650275i
$716$	−0.0436178	−	0.134242i	−0.00163007	−	0.00501685i
$717$	37.3182	+	51.3641i	1.39367	+	1.91823i
$718$		−	1.15440i		−	0.0430817i
$719$	−8.44303	+	6.13422i	−0.314872	+	0.228768i	−0.733984	−	0.679167i	$-0.762341\pi$
$719$	−8.44303	+	6.13422i	−0.314872	+	0.228768i	0.419112	+	0.907934i	$0.362341\pi$
$720$	7.33687	−	14.0505i	0.273429	−	0.523632i
$721$	−5.57898	−	4.05337i	−0.207772	−	0.150955i
$722$	13.7725	−	18.9562i	0.512558	−	0.705476i
$723$	−7.52013	−	2.44344i	−0.279677	−	0.0908725i
$724$	−16.8528			−0.626328
$725$	−27.9603	+	8.47095i	−1.03842	+	0.314603i
$726$	11.9610			0.443913
$727$	−24.0315	−	7.80830i	−0.891279	−	0.289594i	−0.172646	−	0.984984i	$-0.555232\pi$
$727$	−24.0315	−	7.80830i	−0.891279	−	0.289594i	−0.718633	+	0.695390i	$0.755232\pi$
$728$	4.02220	−	5.53608i	0.149073	−	0.205181i
$729$	−34.6974	−	25.2092i	−1.28509	−	0.933673i
$730$	24.3446	+	4.10559i	0.901035	+	0.151955i
$731$	−5.44393	+	3.95524i	−0.201351	+	0.146290i
$732$		−	22.1442i		−	0.818474i
$733$	−15.9868	−	22.0040i	−0.590488	−	0.812736i	0.404308	−	0.914623i	$-0.367512\pi$
$733$	−15.9868	−	22.0040i	−0.590488	−	0.812736i	−0.994796	+	0.101886i	$0.967512\pi$
$734$	2.03262	+	6.25575i	0.0750253	+	0.230904i
$735$	−1.00158	+	5.93902i	−0.0369439	+	0.219064i
$736$	−6.93630	+	21.3477i	−0.255676	+	0.786888i
$737$	10.1595	−	3.30103i	0.374230	−	0.121595i
$738$	−2.86104	+	0.929607i	−0.105316	+	0.0342193i
$739$	15.5929	−	47.9900i	0.573594	−	1.76534i	−0.0673231	−	0.997731i	$-0.521446\pi$
$739$	15.5929	−	47.9900i	0.573594	−	1.76534i	0.640917	−	0.767610i	$-0.278554\pi$
$740$	13.0448	−	1.93268i	0.479538	−	0.0710468i
$741$	−11.8558	−	36.4885i	−0.435535	−	1.34044i
$742$	−6.44467	−	8.87032i	−0.236591	−	0.325640i
$743$			12.4526i			0.456841i	0.973563	+	0.228421i	$0.0733562\pi$
$743$			12.4526i			0.456841i	−0.973563	+	0.228421i	$0.926644\pi$
$744$	4.29047	−	3.11721i	0.157296	−	0.114282i
$745$	7.50729	−	3.73114i	0.275046	−	0.136698i
$746$	33.2065	+	24.1259i	1.21578	+	0.883312i
$747$	26.4864	−	36.4554i	0.969087	−	1.33383i
$748$	21.4396	+	6.96614i	0.783908	+	0.254707i
$749$	−12.0065			−0.438708
$750$	−13.9357	−	29.5047i	−0.508860	−	1.07736i
$751$	25.4002			0.926868			0.463434	−	0.886131i	$-0.346617\pi$
$751$	25.4002			0.926868			0.463434	+	0.886131i	$0.346617\pi$
$752$	−2.73363	−	0.888212i	−0.0996854	−	0.0323897i
$753$	17.6129	−	24.2420i	0.641849	−	0.883429i
$754$	−11.4467	−	8.31651i	−0.416864	−	0.302870i
$755$	−0.344604	+	0.171269i	−0.0125414	+	0.00623311i
$756$	2.25878	−	1.64110i	0.0821511	−	0.0596862i
$757$			49.1681i			1.78705i	0.449018	+	0.893523i	$0.351774\pi$
$757$			49.1681i			1.78705i	−0.449018	+	0.893523i	$0.648226\pi$
$758$	−0.298068	−	0.410256i	−0.0108263	−	0.0149012i
$759$	−16.8088	−	51.7322i	−0.610122	−	1.87776i
$760$	−43.1691	+	6.39579i	−1.56591	+	0.232000i
$761$	1.49278	−	4.59430i	0.0541131	−	0.166543i	−0.920347	−	0.391102i	$-0.872094\pi$
$761$	1.49278	−	4.59430i	0.0541131	−	0.166543i	0.974461	+	0.224559i	$0.0720940\pi$
$762$	2.19764	−	0.714056i	0.0796120	−	0.0258675i
$763$	−1.10815	+	0.360059i	−0.0401176	+	0.0130350i
$764$	−0.150368	+	0.462786i	−0.00544013	+	0.0167430i
$765$	−11.1140	+	65.9017i	−0.401826	+	2.38268i
$766$	0.580186	+	1.78563i	0.0209630	+	0.0645173i
$767$	−1.00304	−	1.38056i	−0.0362176	−	0.0498492i
$768$			43.0330i			1.55282i
$769$	15.6362	−	11.3604i	0.563856	−	0.409665i	−0.269012	−	0.963137i	$-0.586697\pi$
$769$	15.6362	−	11.3604i	0.563856	−	0.409665i	0.832868	+	0.553471i	$0.186697\pi$
$770$	9.28335	+	1.56559i	0.334549	+	0.0564198i
$771$	50.4392	+	36.6463i	1.81652	+	1.31978i
$772$	−4.73203	+	6.51308i	−0.170309	+	0.234411i
$773$	42.0704	+	13.6695i	1.51317	+	0.491658i	0.943826	−	0.330443i	$-0.107198\pi$
$773$	42.0704	+	13.6695i	1.51317	+	0.491658i	0.569341	+	0.822101i	$0.307198\pi$
$774$	4.41675			0.158757
$775$	0.0642507	−	3.21442i	0.00230795	−	0.115466i
$776$	33.8990			1.21690
$777$	−18.2914	−	5.94325i	−0.656202	−	0.213213i
$778$	2.93654	−	4.04181i	0.105280	−	0.144906i
$779$	3.36451	+	2.44446i	0.120546	+	0.0875818i
$780$	−5.14573	+	9.85438i	−0.184247	+	0.352843i
$781$	−40.0739	+	29.1154i	−1.43396	+	1.04183i
$782$			39.5565i			1.41454i
$783$	−11.6099	−	15.9797i	−0.414904	−	0.571067i
$784$	0.514809	+	1.58442i	0.0183860	+	0.0565864i
$785$	6.86952	+	13.8219i	0.245184	+	0.493325i
$786$	−1.85445	+	5.70741i	−0.0661461	+	0.203577i
$787$	49.0264	−	15.9296i	1.74760	−	0.567830i	0.751802	−	0.659388i	$-0.229185\pi$
$787$	49.0264	−	15.9296i	1.74760	−	0.567830i	0.995800	+	0.0915580i	$0.0291847\pi$
$788$	2.84633	−	0.924830i	0.101396	−	0.0329457i
$789$	24.1025	−	74.1799i	0.858072	−	2.64088i
$790$	−9.35845	−	4.88677i	−0.332959	−	0.173864i
$791$	5.98673	+	18.4253i	0.212864	+	0.655127i
$792$	−29.7572	−	40.9573i	−1.05738	−	1.45535i
$793$		−	22.2449i		−	0.789941i
$794$	28.0928	−	20.4106i	0.996976	−	0.724345i
$795$	42.6621	+	43.5233i	1.51307	+	1.54361i
$796$	−2.57824	−	1.87320i	−0.0913833	−	0.0663939i
$797$	−1.21019	+	1.66569i	−0.0428672	+	0.0590017i	−0.829913	−	0.557893i	$-0.811610\pi$
$797$	−1.21019	+	1.66569i	−0.0428672	+	0.0590017i	0.787045	+	0.616895i	$0.211610\pi$
$798$	17.6915	+	5.74833i	0.626274	+	0.203489i
$799$	12.1191			0.428742
$800$	17.2132	+	13.0395i	0.608578	+	0.461018i
$801$	5.93974			0.209870
$802$	−37.8271	−	12.2908i	−1.33572	−	0.434002i
$803$	23.2726	−	32.0319i	0.821271	−	1.13038i
$804$	−4.94796	−	3.59490i	−0.174501	−	0.126782i
$805$	−1.70319	−	11.4959i	−0.0600296	−	0.405176i
$806$	1.25968	−	0.915210i	0.0443703	−	0.0322369i
$807$		−	25.3089i		−	0.890914i
$808$	14.8976	+	20.5048i	0.524095	+	0.721355i
$809$	14.1045	+	43.4092i	0.495888	+	1.52619i	0.815569	+	0.578660i	$0.196424\pi$
$809$	14.1045	+	43.4092i	0.495888	+	1.52619i	−0.319681	+	0.947525i	$0.603576\pi$
$810$	−6.33254	+	6.20722i	−0.222503	+	0.218100i
$811$	−14.5558	+	44.7982i	−0.511123	+	1.57308i	0.279103	+	0.960261i	$0.409963\pi$
$811$	−14.5558	+	44.7982i	−0.511123	+	1.57308i	−0.790227	+	0.612815i	$0.790037\pi$
$812$	−4.58979	+	1.49131i	−0.161070	+	0.0523349i
$813$	36.8887	−	11.9859i	1.29374	−	0.420363i
$814$	−9.28997	+	28.5916i	−0.325613	+	1.00213i
$815$	−15.9986	+	15.6820i	−0.560405	+	0.549316i
$816$	9.74014	+	29.9771i	0.340973	+	1.04941i
$817$	−3.58895	−	4.93977i	−0.125562	−	0.172821i
$818$			20.5316i			0.717872i
$819$	7.69300	−	5.58929i	0.268815	−	0.195306i
$820$	−0.176607	−	1.19203i	−0.00616738	−	0.0416274i
$821$	−15.0760	−	10.9534i	−0.526157	−	0.382276i	0.292761	−	0.956186i	$-0.405426\pi$
$821$	−15.0760	−	10.9534i	−0.526157	−	0.382276i	−0.818918	+	0.573910i	$0.805426\pi$
$822$	−13.6479	+	18.7848i	−0.476026	+	0.655194i
$823$	−20.6075	−	6.69579i	−0.718334	−	0.233401i	−0.0730330	−	0.997330i	$-0.523268\pi$
$823$	−20.6075	−	6.69579i	−0.718334	−	0.233401i	−0.645301	+	0.763929i	$0.723268\pi$
$824$	21.1157			0.735600
$825$	−52.3198	−	1.04578i	−1.82154	−	0.0364095i
$826$	0.827386			0.0287884
$827$	−10.5250	−	3.41978i	−0.365990	−	0.118917i	0.120248	−	0.992744i	$-0.461631\pi$
$827$	−10.5250	−	3.41978i	−0.365990	−	0.118917i	−0.486238	+	0.873827i	$0.661631\pi$
$828$	−10.7359	+	14.7767i	−0.373098	+	0.513526i
$829$	23.5312	+	17.0964i	0.817272	+	0.593783i	0.915930	−	0.401338i	$-0.131455\pi$
$829$	23.5312	+	17.0964i	0.817272	+	0.593783i	−0.0986576	+	0.995121i	$0.531455\pi$
$830$	−17.9612	−	18.3238i	−0.623442	−	0.636028i
$831$	−6.25332	+	4.54330i	−0.216925	+	0.157605i
$832$			17.9043i			0.620720i
$833$	−4.12875	−	5.68273i	−0.143053	−	0.196895i
$834$	13.6130	+	41.8964i	0.471379	+	1.45075i
$835$	−15.5696	−	8.13008i	−0.538807	−	0.281353i
$836$	−6.32102	+	19.4541i	−0.218617	+	0.672834i
$837$	2.06726	−	0.671695i	0.0714551	−	0.0232172i
$838$	29.1340	−	9.46622i	1.00642	−	0.327005i
$839$	−5.14999	+	15.8500i	−0.177797	+	0.547204i	−0.999750	−	0.0223515i	$-0.992885\pi$
$839$	−5.14999	+	15.8500i	−0.177797	+	0.547204i	0.821953	+	0.569556i	$0.192885\pi$
$840$	−8.20796	−	16.5150i	−0.283202	−	0.569820i
$841$	1.58877	+	4.88972i	0.0547850	+	0.168611i
$842$	15.0404	+	20.7014i	0.518327	+	0.713417i
$843$		−	70.6858i		−	2.43455i
$844$	−6.97458	+	5.06733i	−0.240075	+	0.174425i
$845$	8.28602	−	15.8682i	0.285048	−	0.545883i
$846$	−6.43540	−	4.67559i	−0.221253	−	0.160750i
$847$	2.40891	−	3.31558i	0.0827710	−	0.113925i
$848$	16.0327	+	5.20933i	0.550565	+	0.178889i
$849$	−58.1912			−1.99712
$850$	35.9505	+	12.4807i	1.23309	+	0.428084i
$851$	37.1103			1.27212
$852$	26.9719	+	8.76371i	0.924043	+	0.300240i
$853$	−15.2772	+	21.0273i	−0.523083	+	0.719962i	−0.986057	−	0.166410i	$-0.946782\pi$
$853$	−15.2772	+	21.0273i	−0.523083	+	0.719962i	0.462974	+	0.886372i	$0.346782\pi$
$854$	8.72566	+	6.33956i	0.298586	+	0.216935i
$855$	−59.7986	−	10.0847i	−2.04507	−	0.344890i
$856$	29.7429	−	21.6094i	1.01659	−	0.738596i
$857$			6.76094i			0.230949i	0.993310	+	0.115475i	$0.0368389\pi$
$857$			6.76094i			0.230949i	−0.993310	+	0.115475i	$0.963161\pi$
$858$	−14.8965	−	20.5033i	−0.508558	−	0.699970i
$859$	2.69769	+	8.30264i	0.0920440	+	0.283282i	0.986472	−	0.163930i	$-0.0524170\pi$
$859$	2.69769	+	8.30264i	0.0920440	+	0.283282i	−0.894428	+	0.447212i	$0.852417\pi$
$860$	−0.294218	+	1.74460i	−0.0100327	+	0.0594905i
$861$	−0.543089	+	1.67146i	−0.0185084	+	0.0569631i
$862$	−34.1333	+	11.0906i	−1.16259	+	0.377747i
$863$	−37.8185	+	12.2880i	−1.28736	+	0.418288i	−0.871166	−	0.490989i	$-0.836635\pi$
$863$	−37.8185	+	12.2880i	−1.28736	+	0.418288i	−0.416191	+	0.909277i	$0.636635\pi$
$864$	−4.51155	+	13.8851i	−0.153486	+	0.472382i
$865$	−45.3915	+	6.72507i	−1.54336	+	0.228659i
$866$	−8.17170	−	25.1499i	−0.277686	−	0.854629i
$867$	−51.2010	−	70.4721i	−1.73888	−	2.39336i
$868$		−	0.531088i		−	0.0180263i
$869$	−13.6978	+	9.95207i	−0.464668	+	0.337601i
$870$	−34.1472	+	16.9712i	−1.15770	+	0.575379i
$871$	−4.97046	−	3.61125i	−0.168418	−	0.122363i
$872$	2.09709	−	2.88640i	0.0710166	−	0.0977459i
$873$	44.8008	+	14.5567i	1.51628	+	0.492669i
$874$	−35.8932			−1.21411
$875$	−10.9853	−	2.07920i	−0.371371	−	0.0702897i
$876$	−22.6687			−0.765906
$877$	37.8198	+	12.2884i	1.27708	+	0.414950i	0.867552	−	0.497346i	$-0.165692\pi$
$877$	37.8198	+	12.2884i	1.27708	+	0.414950i	0.409532	+	0.912296i	$0.365692\pi$
$878$	−7.90995	+	10.8871i	−0.266948	+	0.367422i
$879$	−55.7756	−	40.5233i	−1.88126	−	1.36682i
$880$	−12.9622	+	6.44222i	−0.436954	+	0.217167i
$881$	−26.7746	+	19.4529i	−0.902058	+	0.655384i	−0.938994	−	0.343934i	$-0.888240\pi$
$881$	−26.7746	+	19.4529i	−0.902058	+	0.655384i	0.0369355	+	0.999318i	$0.488240\pi$
$882$			4.61049i			0.155243i
$883$	−26.3380	−	36.2512i	−0.886345	−	1.21995i	−0.974623	−	0.223853i	$-0.928136\pi$
$883$	−26.3380	−	36.2512i	−0.886345	−	1.21995i	0.0882779	−	0.996096i	$-0.471864\pi$
$884$	−4.00650	−	12.3307i	−0.134753	−	0.414727i
$885$	−4.54937	+	0.674020i	−0.152925	+	0.0226570i
$886$	2.52919	−	7.78406i	0.0849699	−	0.261511i
$887$	−27.1205	+	8.81200i	−0.910618	+	0.295878i	−0.726613	−	0.687047i	$-0.758906\pi$
$887$	−27.1205	+	8.81200i	−0.910618	+	0.295878i	−0.184006	+	0.982925i	$0.558906\pi$
$888$	56.0088	−	18.1984i	1.87953	−	0.610697i
$889$	0.244662	−	0.752993i	0.00820571	−	0.0252546i
$890$	0.562444	−	3.33509i	0.0188532	−	0.111792i
$891$	4.39452	+	13.5249i	0.147222	+	0.453102i
$892$	4.89148	+	6.73255i	0.163779	+	0.225422i
$893$			10.9968i			0.367992i
$894$	8.85230	−	6.43157i	0.296065	−	0.215104i
$895$	−0.376817	−	0.0635481i	−0.0125956	−	0.00212418i
$896$	−0.0348927	−	0.0253510i	−0.00116568	−	0.000846917i
$897$	−18.3885	+	25.3096i	−0.613974	+	0.845063i
$898$	−5.62964	−	1.82918i	−0.187864	−	0.0610406i
$899$	−3.75716			−0.125308
$900$	10.0423	+	14.4195i	0.334744	+	0.480650i
$901$	−71.0781			−2.36795
$902$	2.61268	+	0.848910i	0.0869926	+	0.0282656i
$903$	1.51668	−	2.08753i	0.0504718	−	0.0694685i
$904$	−47.9925	−	34.8686i	−1.59621	−	1.15971i
$905$	−21.1188	+	40.4438i	−0.702014	+	1.34440i
$906$	−0.406343	+	0.295226i	−0.0134999	+	0.00980822i
$907$		−	36.1881i		−	1.20161i	−0.799396	−	0.600804i	$-0.794847\pi$
$907$		−	36.1881i		−	1.20161i	0.799396	−	0.600804i	$-0.205153\pi$
$908$	9.17725	+	12.6314i	0.304558	+	0.419188i
$909$	10.8836	+	33.4963i	0.360987	+	1.11100i
$910$	−2.40985	−	4.84878i	−0.0798858	−	0.160735i
$911$	10.1760	−	31.3186i	0.337147	−	1.03763i	−0.628508	−	0.777803i	$-0.716334\pi$
$911$	10.1760	−	31.3186i	0.337147	−	1.03763i	0.965655	−	0.259828i	$-0.0836658\pi$
$912$	−27.2009	+	8.83812i	−0.900713	+	0.292659i
$913$	−39.1357	+	12.7159i	−1.29520	+	0.420836i
$914$	0.118838	−	0.365745i	0.00393081	−	0.0120978i
$915$	−53.1424	−	27.7498i	−1.75683	−	0.917379i
$916$	−4.02363	−	12.3835i	−0.132944	−	0.409161i
$917$	1.20861	+	1.66351i	0.0399119	+	0.0549340i
$918$			25.7286i			0.849169i
$919$	5.51905	−	4.00983i	0.182057	−	0.132272i	−0.493024	−	0.870016i	$-0.664109\pi$
$919$	5.51905	−	4.00983i	0.182057	−	0.132272i	0.675081	+	0.737744i	$0.264109\pi$
$920$	24.9096	+	25.4125i	0.821245	+	0.837824i
$921$	30.1357	+	21.8948i	0.993004	+	0.721460i
$922$	13.3206	−	18.3343i	0.438692	−	0.603807i
$923$	27.0946	+	8.80357i	0.891829	+	0.289773i
$924$	−8.64429			−0.284376
$925$	11.7089	−	33.7274i	0.384986	−	1.10895i
$926$	10.1307			0.332915
$927$	27.9065	+	9.06737i	0.916570	+	0.297811i
$928$	14.8331	−	20.4161i	0.486921	−	0.670190i
$929$	7.76195	+	5.63939i	0.254661	+	0.185022i	0.707790	−	0.706423i	$-0.249692\pi$
$929$	7.76195	+	5.63939i	0.254661	+	0.185022i	−0.453129	+	0.891445i	$0.649692\pi$
$930$	−0.615002	−	4.15102i	−0.0201667	−	0.136117i
$931$	5.15646	−	3.74639i	0.168996	−	0.122783i
$932$			0.192354i			0.00630077i
$933$	18.7766	+	25.8438i	0.614720	+	0.846089i
$934$	−6.84856	−	21.0777i	−0.224092	−	0.689684i
$935$	43.5843	−	42.7218i	1.42536	−	1.39715i
$936$	−8.99764	+	27.6919i	−0.294097	+	0.905138i
$937$	−4.64554	+	1.50943i	−0.151763	+	0.0493108i	−0.383913	−	0.923369i	$-0.625424\pi$
$937$	−4.64554	+	1.50943i	−0.151763	+	0.0493108i	0.232150	+	0.972680i	$0.425424\pi$
$938$	2.83306	−	0.920516i	0.0925025	−	0.0300559i
$939$	−2.18394	+	6.72149i	−0.0712703	+	0.219347i
$940$	2.27553	−	2.23050i	0.0742197	−	0.0727510i
$941$	−11.4243	−	35.1605i	−0.372423	−	1.14620i	−0.945201	−	0.326490i	$-0.894134\pi$
$941$	−11.4243	−	35.1605i	−0.372423	−	1.14620i	0.572778	−	0.819711i	$-0.305866\pi$
$942$	11.8414	+	16.2983i	0.385813	+	0.531026i
$943$		−	3.39111i		−	0.110430i
$944$	−1.02916	+	0.747730i	−0.0334964	+	0.0243365i
$945$	−1.10780	−	7.47722i	−0.0360368	−	0.243234i
$946$	−3.26304	−	2.37074i	−0.106091	−	0.0770793i
$947$	−20.4890	+	28.2007i	−0.665804	+	0.916400i	−0.999656	−	0.0262251i	$-0.991651\pi$
$947$	−20.4890	+	28.2007i	−0.665804	+	0.916400i	0.333852	+	0.942625i	$0.391651\pi$
$948$	9.21941	+	2.99557i	0.299432	+	0.0972915i
$949$	−22.7718			−0.739205
$950$	−11.3249	+	32.6212i	−0.367427	+	1.05837i
$951$	−58.1960			−1.88714
$952$	20.4557	+	6.64646i	0.662973	+	0.215413i
$953$	−10.1623	+	13.9872i	−0.329189	+	0.453090i	−0.941245	−	0.337725i	$-0.890343\pi$
$953$	−10.1623	+	13.9872i	−0.329189	+	0.453090i	0.612056	+	0.790814i	$0.290343\pi$
$954$	37.7434	+	27.4222i	1.22199	+	0.887826i
$955$	0.922176	+	0.940793i	0.0298409	+	0.0304433i
$956$	−15.7502	+	11.4432i	−0.509399	+	0.370100i
$957$			61.1538i			1.97682i
$958$	6.11630	+	8.41837i	0.197609	+	0.271985i
$959$	2.45847	+	7.56640i	0.0793882	+	0.244332i
$960$	42.7728	+	22.3350i	1.38049	+	0.720859i
$961$	−9.45176	+	29.0895i	−0.304895	+	0.938372i
$962$	16.4441	−	5.34302i	0.530180	−	0.172266i
$963$	48.5875	−	15.7870i	1.56571	−	0.508730i
$964$	0.749253	−	2.30596i	0.0241318	−	0.0742701i
$965$	9.70041	+	19.5179i	0.312267	+	0.628302i
$966$	−4.68726	−	14.4259i	−0.150810	−	0.464146i
$967$	22.9780	+	31.6265i	0.738922	+	1.01704i	0.998680	+	0.0513647i	$0.0163571\pi$
$967$	22.9780	+	31.6265i	0.738922	+	1.01704i	−0.259758	+	0.965674i	$0.583643\pi$
$968$			12.5490i			0.403341i
$969$	97.5598	−	70.8814i	3.13407	−	2.27704i
$970$	12.4156	−	23.7767i	0.398642	−	0.763423i
$971$	−24.0642	−	17.4837i	−0.772258	−	0.561078i	0.130387	−	0.991463i	$-0.458378\pi$
$971$	−24.0642	−	17.4837i	−0.772258	−	0.561078i	−0.902646	+	0.430385i	$0.858378\pi$
$972$	9.70904	−	13.3634i	0.311418	−	0.428630i
$973$	14.3553	+	4.66431i	0.460209	+	0.149531i
$974$	−10.2585			−0.328704
$975$	17.2005	+	24.6978i	0.550858	+	0.790963i
$976$	−16.5828			−0.530803
$977$	−23.4027	−	7.60399i	−0.748717	−	0.243273i	−0.0902882	−	0.995916i	$-0.528779\pi$
$977$	−23.4027	−	7.60399i	−0.748717	−	0.243273i	−0.658429	+	0.752643i	$0.728779\pi$
$978$	−17.1869	+	23.6558i	−0.549577	+	0.756428i
$979$	−4.38821	−	3.18822i	−0.140248	−	0.101896i
$980$	−1.82113	−	0.307124i	−0.0581740	−	0.00981072i
$981$	4.01098	−	2.91415i	0.128061	−	0.0930416i
$982$		−	44.9505i		−	1.43443i
$983$	−2.58100	−	3.55244i	−0.0823212	−	0.113305i	0.765870	−	0.642995i	$-0.222308\pi$
$983$	−2.58100	−	3.55244i	−0.0823212	−	0.113305i	−0.848192	+	0.529690i	$0.822308\pi$
$984$	−1.66295	−	5.11804i	−0.0530129	−	0.163157i
$985$	1.34741	−	7.98966i	0.0429321	−	0.254572i
$986$	13.7426	−	42.2953i	0.437653	−	1.34696i
$987$	−4.41973	+	1.43606i	−0.140682	+	0.0457102i
$988$	11.1888	−	3.63546i	0.355963	−	0.115659i
$989$	−1.53854	+	4.73514i	−0.0489228	+	0.150569i
$990$	−39.6261	+	5.87088i	−1.25940	+	0.186589i
$991$	7.11743	+	21.9052i	0.226093	+	0.695842i	0.998179	+	0.0603238i	$0.0192133\pi$
$991$	7.11743	+	21.9052i	0.226093	+	0.695842i	−0.772086	+	0.635518i	$0.780787\pi$
$992$	1.63235	+	2.24673i	0.0518271	+	0.0713338i
$993$		−	76.7063i		−	2.43420i
$994$	−11.1749	+	8.11904i	−0.354446	+	0.257520i
$995$	−7.72626	+	3.83996i	−0.244939	+	0.121735i
$996$	19.0601	+	13.8480i	0.603943	+	0.438791i
$997$	−20.3652	+	28.0303i	−0.644972	+	0.887728i	−0.998869	−	0.0475568i	$-0.984856\pi$
$997$	−20.3652	+	28.0303i	−0.644972	+	0.887728i	0.353897	+	0.935285i	$0.384856\pi$
$998$	24.3931	+	7.92579i	0.772149	+	0.250886i
$999$	24.1375			0.763677

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.n.a.29.9	✓	56
5.2	odd	4		875.2.h.d.351.5		56
5.3	odd	4		875.2.h.e.351.10		56
5.4	even	2		875.2.n.c.274.6		56
25.6	even	5		875.2.n.c.99.6		56
25.8	odd	20		875.2.h.e.526.10		56
25.12	odd	20		4375.2.a.p.1.8		28
25.13	odd	20		4375.2.a.o.1.21		28
25.17	odd	20		875.2.h.d.526.5		56
25.19	even	10	inner	175.2.n.a.169.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.29.9	✓	56	1.1	even	1	trivial
175.2.n.a.169.9	yes	56	25.19	even	10	inner
875.2.h.d.351.5		56	5.2	odd	4
875.2.h.d.526.5		56	25.17	odd	20
875.2.h.e.351.10		56	5.3	odd	4
875.2.h.e.526.10		56	25.8	odd	20
875.2.n.c.99.6		56	25.6	even	5
875.2.n.c.274.6		56	5.4	even	2
4375.2.a.o.1.21		28	25.13	odd	20
4375.2.a.p.1.8		28	25.12	odd	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03051 + 0.334833i) q^{2} +(-1.58321 + 2.17910i) q^{3} +(-0.668196 - 0.485473i) q^{4} +(-2.00240 + 0.995194i) q^{5} +(-2.36115 + 1.71547i) q^{6} +1.00000i q^{7} +(-1.79981 - 2.47723i) q^{8} +(-1.31487 - 4.04676i) q^{9} +O(q^{10})\)	\(q+(1.03051 + 0.334833i) q^{2} +(-1.58321 + 2.17910i) q^{3} +(-0.668196 - 0.485473i) q^{4} +(-2.00240 + 0.995194i) q^{5} +(-2.36115 + 1.71547i) q^{6} +1.00000i q^{7} +(-1.79981 - 2.47723i) q^{8} +(-1.31487 - 4.04676i) q^{9} +(-2.39671 + 0.355089i) q^{10} +(-1.20073 + 3.69547i) q^{11} +(2.11579 - 0.687461i) q^{12} +(2.12541 - 0.690588i) q^{13} +(-0.334833 + 1.03051i) q^{14} +(1.00158 - 5.93902i) q^{15} +(-0.514809 - 1.58442i) q^{16} +(4.12875 + 5.68273i) q^{17} -4.61049i q^{18} +(-5.15646 + 3.74639i) q^{19} +(1.82113 + 0.307124i) q^{20} +(-2.17910 - 1.58321i) q^{21} +(-2.47473 + 3.40618i) q^{22} +(4.94286 + 1.60603i) q^{23} +8.24760 q^{24} +(3.01918 - 3.98554i) q^{25} +2.42149 q^{26} +(3.21497 + 1.04461i) q^{27} +(0.485473 - 0.668196i) q^{28} +(-4.72713 - 3.43446i) q^{29} +(3.02072 - 5.78485i) q^{30} +(0.520209 - 0.377954i) q^{31} +4.31891i q^{32} +(-6.15179 - 8.46722i) q^{33} +(2.35195 + 7.23856i) q^{34} +(-0.995194 - 2.00240i) q^{35} +(-1.08600 + 3.34237i) q^{36} +(6.79092 - 2.20650i) q^{37} +(-6.56820 + 2.13414i) q^{38} +(-1.86011 + 5.72482i) q^{39} +(6.06926 + 3.16923i) q^{40} +(-0.201628 - 0.620549i) q^{41} +(-1.71547 - 2.36115i) q^{42} +0.957977i q^{43} +(2.59638 - 1.88638i) q^{44} +(6.66021 + 6.79467i) q^{45} +(4.55591 + 3.31006i) q^{46} +(1.01412 - 1.39581i) q^{47} +(4.26766 + 1.38665i) q^{48} -1.00000 q^{49} +(4.44578 - 3.09622i) q^{50} -18.9199 q^{51} +(-1.75545 - 0.570381i) q^{52} +(-5.94778 + 8.18641i) q^{53} +(2.96329 + 2.15295i) q^{54} +(-1.27337 - 8.59476i) q^{55} +(2.47723 - 1.79981i) q^{56} -17.1678i q^{57} +(-3.72139 - 5.12205i) q^{58} +(-0.235963 - 0.726220i) q^{59} +(-3.55249 + 3.48219i) q^{60} +(3.07593 - 9.46675i) q^{61} +(0.662631 - 0.215302i) q^{62} +(4.04676 - 1.31487i) q^{63} +(-2.47573 + 7.61952i) q^{64} +(-3.56864 + 3.49803i) q^{65} +(-3.50438 - 10.7854i) q^{66} +(-1.61593 - 2.22413i) q^{67} -5.80158i q^{68} +(-11.3253 + 8.22830i) q^{69} +(-0.355089 - 2.39671i) q^{70} +(10.3133 + 7.49305i) q^{71} +(-7.65823 + 10.5407i) q^{72} +(-9.69099 - 3.14879i) q^{73} +7.73692 q^{74} +(3.90491 + 12.8890i) q^{75} +5.26430 q^{76} +(-3.69547 - 1.20073i) q^{77} +(-3.83372 + 5.27666i) q^{78} +(3.52524 + 2.56124i) q^{79} +(2.60766 + 2.66030i) q^{80} +(2.96089 - 2.15121i) q^{81} -0.706994i q^{82} +(6.22474 + 8.56762i) q^{83} +(0.687461 + 2.11579i) q^{84} +(-13.9228 - 7.27018i) q^{85} +(-0.320762 + 0.987205i) q^{86} +(14.9681 - 4.86342i) q^{87} +(11.3156 - 3.67667i) q^{88} +(-0.431368 + 1.32762i) q^{89} +(4.58834 + 9.23203i) q^{90} +(0.690588 + 2.12541i) q^{91} +(-2.52311 - 3.47277i) q^{92} +1.73197i q^{93} +(1.51242 - 1.09884i) q^{94} +(6.59690 - 12.6334i) q^{95} +(-9.41133 - 6.83773i) q^{96} +(-6.50724 + 8.95645i) q^{97} +(-1.03051 - 0.334833i) q^{98} +16.5335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9}+O(q^{10}) \) 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9	\( 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9} - 4 q^{10} + 8 q^{11} - 40 q^{12} - 4 q^{14} - 18 q^{15} - 32 q^{16} + 12 q^{19} + 12 q^{20} + 4 q^{21} - 30 q^{22} + 10 q^{23} - 28 q^{24} + 4 q^{25} + 12 q^{26} + 30 q^{27} - 2 q^{29} + 28 q^{30} + 12 q^{31} + 20 q^{33} + 2 q^{35} - 14 q^{36} - 70 q^{37} - 70 q^{38} - 4 q^{39} - 30 q^{40} + 4 q^{41} + 50 q^{42} + 22 q^{44} - 52 q^{45} - 4 q^{46} - 10 q^{47} + 30 q^{48} - 56 q^{49} - 54 q^{50} - 44 q^{51} - 20 q^{53} + 54 q^{54} - 2 q^{55} + 12 q^{56} + 10 q^{58} - 6 q^{59} + 16 q^{60} - 4 q^{61} + 50 q^{62} + 20 q^{63} + 24 q^{64} - 18 q^{65} - 74 q^{66} + 10 q^{67} - 78 q^{69} + 8 q^{70} - 8 q^{71} + 140 q^{72} + 40 q^{73} + 60 q^{74} - 8 q^{75} + 52 q^{76} - 20 q^{77} - 90 q^{78} + 124 q^{80} - 72 q^{81} - 30 q^{83} - 12 q^{84} + 96 q^{85} - 20 q^{86} + 30 q^{87} + 140 q^{88} + 38 q^{89} - 8 q^{90} + 8 q^{91} + 80 q^{92} + 88 q^{94} - 70 q^{95} - 28 q^{96} - 30 q^{97} + 60 q^{99}+O(q^{100}) \) 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9 - 4 * q^10 + 8 * q^11 - 40 * q^12 - 4 * q^14 - 18 * q^15 - 32 * q^16 + 12 * q^19 + 12 * q^20 + 4 * q^21 - 30 * q^22 + 10 * q^23 - 28 * q^24 + 4 * q^25 + 12 * q^26 + 30 * q^27 - 2 * q^29 + 28 * q^30 + 12 * q^31 + 20 * q^33 + 2 * q^35 - 14 * q^36 - 70 * q^37 - 70 * q^38 - 4 * q^39 - 30 * q^40 + 4 * q^41 + 50 * q^42 + 22 * q^44 - 52 * q^45 - 4 * q^46 - 10 * q^47 + 30 * q^48 - 56 * q^49 - 54 * q^50 - 44 * q^51 - 20 * q^53 + 54 * q^54 - 2 * q^55 + 12 * q^56 + 10 * q^58 - 6 * q^59 + 16 * q^60 - 4 * q^61 + 50 * q^62 + 20 * q^63 + 24 * q^64 - 18 * q^65 - 74 * q^66 + 10 * q^67 - 78 * q^69 + 8 * q^70 - 8 * q^71 + 140 * q^72 + 40 * q^73 + 60 * q^74 - 8 * q^75 + 52 * q^76 - 20 * q^77 - 90 * q^78 + 124 * q^80 - 72 * q^81 - 30 * q^83 - 12 * q^84 + 96 * q^85 - 20 * q^86 + 30 * q^87 + 140 * q^88 + 38 * q^89 - 8 * q^90 + 8 * q^91 + 80 * q^92 + 88 * q^94 - 70 * q^95 - 28 * q^96 - 30 * q^97 + 60 * q^99

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