LMFDB - Embedded newform 925.2.ba.a.299.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(99,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("925.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.ba (of order $18$, degree $6$, not 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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 37)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			299.6
Character	$\chi$	$=$	925.299
Dual form			925.2.ba.a.99.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93010 + 1.61954i) q^{2} +(-0.812851 - 0.968719i) q^{3} +(0.755055 + 4.28213i) q^{4} -3.18617i q^{6} +(1.09182 - 2.99976i) q^{7} +(-2.95820 + 5.12375i) q^{8} +(0.243256 - 1.37957i) q^{9} +O(q^{10})$	\(q+(1.93010 + 1.61954i) q^{2} +(-0.812851 - 0.968719i) q^{3} +(0.755055 + 4.28213i) q^{4} -3.18617i q^{6} +(1.09182 - 2.99976i) q^{7} +(-2.95820 + 5.12375i) q^{8} +(0.243256 - 1.37957i) q^{9} +(2.73288 - 4.73349i) q^{11} +(3.53443 - 4.21217i) q^{12} +(-0.265964 - 1.50836i) q^{13} +(6.96557 - 4.02158i) q^{14} +(-5.83582 + 2.12407i) q^{16} +(-0.140027 + 0.794131i) q^{17} +(2.70379 - 2.26875i) q^{18} +(1.35888 + 1.61945i) q^{19} +(-3.79342 + 1.38069i) q^{21} +(12.9408 - 4.71007i) q^{22} +(1.74842 + 3.02834i) q^{23} +(7.36805 - 1.29919i) q^{24} +(1.92951 - 3.34201i) q^{26} +(-4.81961 + 2.78260i) q^{27} +(13.6698 + 2.41035i) q^{28} +(0.122232 + 0.0705708i) q^{29} +3.37454i q^{31} +(-3.58452 - 1.30466i) q^{32} +(-6.80685 + 1.20023i) q^{33} +(-1.55639 + 1.30597i) q^{34} +6.09119 q^{36} +(-6.05878 - 0.539604i) q^{37} +5.32646i q^{38} +(-1.24498 + 1.48371i) q^{39} +(0.0732041 + 0.415161i) q^{41} +(-9.55775 - 3.47874i) q^{42} -2.00540 q^{43} +(22.3329 + 8.12851i) q^{44} +(-1.52992 + 8.67663i) q^{46} +(-1.46007 + 0.842972i) q^{47} +(6.80128 + 3.92672i) q^{48} +(-2.44419 - 2.05092i) q^{49} +(0.883111 - 0.509864i) q^{51} +(6.25815 - 2.27778i) q^{52} +(-2.49727 - 6.86119i) q^{53} +(-13.8088 - 2.43487i) q^{54} +(12.1402 + 14.4681i) q^{56} +(0.464224 - 2.63275i) q^{57} +(0.121628 + 0.334169i) q^{58} +(3.65272 + 10.0358i) q^{59} +(11.3492 - 2.00116i) q^{61} +(-5.46521 + 6.51318i) q^{62} +(-3.87281 - 2.23597i) q^{63} +(1.40484 + 2.43325i) q^{64} +(-15.0817 - 8.70742i) q^{66} +(-2.64152 + 7.25752i) q^{67} -3.50630 q^{68} +(1.51241 - 4.15532i) q^{69} +(6.78889 - 5.69655i) q^{71} +(6.34900 + 5.32744i) q^{72} -8.77446i q^{73} +(-10.8201 - 10.8539i) q^{74} +(-5.90867 + 7.04167i) q^{76} +(-11.2155 - 13.3662i) q^{77} +(-4.80587 + 0.847405i) q^{78} +(-1.54413 + 4.24247i) q^{79} +(2.66406 + 0.969637i) q^{81} +(-0.531080 + 0.919858i) q^{82} +(-10.3202 - 1.81973i) q^{83} +(-8.77654 - 15.2014i) q^{84} +(-3.87061 - 3.24783i) q^{86} +(-0.0309934 - 0.175772i) q^{87} +(16.1688 + 28.0052i) q^{88} +(-0.914163 - 2.51164i) q^{89} +(-4.81510 - 0.849032i) q^{91} +(-11.6476 + 9.77350i) q^{92} +(3.26898 - 2.74300i) q^{93} +(-4.18331 - 0.737630i) q^{94} +(1.64984 + 4.53289i) q^{96} +(7.71809 + 13.3681i) q^{97} +(-1.39597 - 7.91695i) q^{98} +(-5.86542 - 4.92167i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{4} + 6 q^{9}+O(q^{10}) $ 36 * q + 6 * q^4 + 6 * q^9	$ 36 q + 6 q^{4} + 6 q^{9} + 18 q^{11} - 18 q^{14} - 6 q^{16} - 12 q^{19} - 24 q^{21} - 90 q^{24} - 30 q^{26} + 36 q^{29} + 66 q^{34} - 144 q^{36} + 12 q^{39} - 48 q^{41} + 36 q^{46} - 42 q^{49} + 162 q^{51} - 90 q^{54} + 162 q^{56} + 12 q^{59} + 84 q^{61} - 12 q^{64} - 162 q^{66} + 72 q^{69} - 18 q^{71} - 30 q^{74} - 138 q^{76} + 12 q^{79} - 90 q^{81} + 48 q^{84} - 84 q^{86} - 36 q^{89} - 6 q^{91} - 36 q^{94} + 30 q^{96} - 120 q^{99}+O(q^{100}) $ 36 * q + 6 * q^4 + 6 * q^9 + 18 * q^11 - 18 * q^14 - 6 * q^16 - 12 * q^19 - 24 * q^21 - 90 * q^24 - 30 * q^26 + 36 * q^29 + 66 * q^34 - 144 * q^36 + 12 * q^39 - 48 * q^41 + 36 * q^46 - 42 * q^49 + 162 * q^51 - 90 * q^54 + 162 * q^56 + 12 * q^59 + 84 * q^61 - 12 * q^64 - 162 * q^66 + 72 * q^69 - 18 * q^71 - 30 * q^74 - 138 * q^76 + 12 * q^79 - 90 * q^81 + 48 * q^84 - 84 * q^86 - 36 * q^89 - 6 * q^91 - 36 * q^94 + 30 * q^96 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.93010	+	1.61954i	1.36478	+	1.14519i	0.974473	+	0.224506i	$0.0720770\pi$
$2$	1.93010	+	1.61954i	1.36478	+	1.14519i	0.390311	+	0.920683i	$0.372367\pi$
$3$	−0.812851	−	0.968719i	−0.469300	−	0.559290i	0.478528	−	0.878072i	$-0.341171\pi$
$3$	−0.812851	−	0.968719i	−0.469300	−	0.559290i	−0.947828	+	0.318782i	$0.896726\pi$
$4$	0.755055	+	4.28213i	0.377527	+	2.14106i
$5$		0			0
$5$		0			0
$6$		−	3.18617i		−	1.30075i
$7$	1.09182	−	2.99976i	0.412671	−	1.13380i	−0.543094	−	0.839672i	$-0.682747\pi$
$7$	1.09182	−	2.99976i	0.412671	−	1.13380i	0.955765	−	0.294132i	$-0.0950306\pi$
$8$	−2.95820	+	5.12375i	−1.04588	+	1.81152i
$9$	0.243256	−	1.37957i	0.0810854	−	0.459858i
$10$		0			0
$11$	2.73288	−	4.73349i	0.823995	−	1.42720i	−0.0786894	−	0.996899i	$-0.525074\pi$
$11$	2.73288	−	4.73349i	0.823995	−	1.42720i	0.902685	−	0.430303i	$-0.141593\pi$
$12$	3.53443	−	4.21217i	1.02030	−	1.21595i
$13$	−0.265964	−	1.50836i	−0.0737651	−	0.418343i	−0.999220	−	0.0394852i	$-0.987428\pi$
$13$	−0.265964	−	1.50836i	−0.0737651	−	0.418343i	0.925455	−	0.378857i	$-0.123683\pi$
$14$	6.96557	−	4.02158i	1.86163	−	1.07481i
$15$		0			0
$16$	−5.83582	+	2.12407i	−1.45896	+	0.531017i
$17$	−0.140027	+	0.794131i	−0.0339615	+	0.192605i	−0.997069	−	0.0765134i	$-0.975621\pi$
$17$	−0.140027	+	0.794131i	−0.0339615	+	0.192605i	0.963107	+	0.269118i	$0.0867323\pi$
$18$	2.70379	−	2.26875i	0.637289	−	0.534749i
$19$	1.35888	+	1.61945i	0.311749	+	0.371527i	0.899054	−	0.437838i	$-0.144256\pi$
$19$	1.35888	+	1.61945i	0.311749	+	0.371527i	−0.587305	+	0.809365i	$0.699811\pi$
$20$		0			0
$21$	−3.79342	+	1.38069i	−0.827792	+	0.301292i
$22$	12.9408	−	4.71007i	2.75899	−	1.00419i
$23$	1.74842	+	3.02834i	0.364570	+	0.631453i	0.988707	−	0.149861i	$-0.0478827\pi$
$23$	1.74842	+	3.02834i	0.364570	+	0.631453i	−0.624137	+	0.781315i	$0.714549\pi$
$24$	7.36805	−	1.29919i	1.50400	−	0.265195i
$25$		0			0
$26$	1.92951	−	3.34201i	0.378408	−	0.655422i
$27$	−4.81961	+	2.78260i	−0.927534	+	0.535512i
$28$	13.6698	+	2.41035i	2.58334	+	0.455513i
$29$	0.122232	+	0.0705708i	0.0226980	+	0.0131047i	0.511306	−	0.859399i	$-0.329162\pi$
$29$	0.122232	+	0.0705708i	0.0226980	+	0.0131047i	−0.488608	+	0.872503i	$0.662495\pi$
$30$		0			0
$31$			3.37454i			0.606085i	0.952977	+	0.303042i	$0.0980024\pi$
$31$			3.37454i			0.606085i	−0.952977	+	0.303042i	$0.901998\pi$
$32$	−3.58452	−	1.30466i	−0.633660	−	0.230633i
$33$	−6.80685	+	1.20023i	−1.18492	+	0.208933i
$34$	−1.55639	+	1.30597i	−0.266919	+	0.223972i
$35$		0			0
$36$	6.09119			1.01520
$37$	−6.05878	−	0.539604i	−0.996057	−	0.0887103i
$37$	−6.05878	−	0.539604i	−0.996057	−	0.0887103i
$38$			5.32646i			0.864066i
$39$	−1.24498	+	1.48371i	−0.199357	+	0.237584i
$40$		0			0
$41$	0.0732041	+	0.415161i	0.0114326	+	0.0648373i	0.989990	−	0.141135i	$-0.0450753\pi$
$41$	0.0732041	+	0.415161i	0.0114326	+	0.0648373i	−0.978558	+	0.205973i	$0.933964\pi$
$42$	−9.55775	−	3.47874i	−1.47479	−	0.536781i
$43$	−2.00540			−0.305820			−0.152910	−	0.988240i	$-0.548865\pi$
$43$	−2.00540			−0.305820			−0.152910	+	0.988240i	$0.548865\pi$
$44$	22.3329	+	8.12851i	3.36681	+	1.22542i
$45$		0			0
$46$	−1.52992	+	8.67663i	−0.225575	+	1.27930i
$47$	−1.46007	+	0.842972i	−0.212973	+	0.122960i	−0.602692	−	0.797974i	$-0.705905\pi$
$47$	−1.46007	+	0.842972i	−0.212973	+	0.122960i	0.389719	+	0.920934i	$0.372572\pi$
$48$	6.80128	+	3.92672i	0.981680	+	0.566773i
$49$	−2.44419	−	2.05092i	−0.349171	−	0.292989i
$50$		0			0
$51$	0.883111	−	0.509864i	0.123660	−	0.0713953i
$52$	6.25815	−	2.27778i	0.867850	−	0.315872i
$53$	−2.49727	−	6.86119i	−0.343026	−	0.942457i	−0.984511	−	0.175321i	$-0.943904\pi$
$53$	−2.49727	−	6.86119i	−0.343026	−	0.942457i	0.641485	−	0.767136i	$-0.278319\pi$
$54$	−13.8088	−	2.43487i	−1.87915	−	0.331344i
$55$		0			0
$56$	12.1402	+	14.4681i	1.62230	+	1.93339i
$57$	0.464224	−	2.63275i	0.0614880	−	0.348716i
$58$	0.121628	+	0.334169i	0.0159705	+	0.0438785i
$59$	3.65272	+	10.0358i	0.475544	+	1.30655i	0.913240	+	0.407422i	$0.133572\pi$
$59$	3.65272	+	10.0358i	0.475544	+	1.30655i	−0.437696	+	0.899123i	$0.644205\pi$
$60$		0			0
$61$	11.3492	−	2.00116i	1.45311	−	0.256222i	0.609332	−	0.792915i	$-0.291438\pi$
$61$	11.3492	−	2.00116i	1.45311	−	0.256222i	0.843778	+	0.536693i	$0.180327\pi$
$62$	−5.46521	+	6.51318i	−0.694082	+	0.827175i
$63$	−3.87281	−	2.23597i	−0.487928	−	0.281705i
$64$	1.40484	+	2.43325i	0.175605	+	0.304156i
$65$		0			0
$66$	−15.0817	−	8.70742i	−1.85643	−	1.07181i
$67$	−2.64152	+	7.25752i	−0.322713	+	0.886648i	0.667188	+	0.744889i	$0.267498\pi$
$67$	−2.64152	+	7.25752i	−0.322713	+	0.886648i	−0.989901	+	0.141758i	$0.954724\pi$
$68$	−3.50630			−0.425201
$69$	1.51241	−	4.15532i	0.182073	−	0.500241i
$70$		0			0
$71$	6.78889	−	5.69655i	0.805693	−	0.676056i	−0.143883	−	0.989595i	$-0.545959\pi$
$71$	6.78889	−	5.69655i	0.805693	−	0.676056i	0.949576	+	0.313538i	$0.101514\pi$
$72$	6.34900	+	5.32744i	0.748237	+	0.627845i
$73$		−	8.77446i		−	1.02697i	−0.858098	−	0.513486i	$-0.828354\pi$
$73$		−	8.77446i		−	1.02697i	0.858098	−	0.513486i	$-0.171646\pi$
$74$	−10.8201	−	10.8539i	−1.25781	−	1.26174i
$75$		0			0
$76$	−5.90867	+	7.04167i	−0.677770	+	0.807735i
$77$	−11.2155	−	13.3662i	−1.27813	−	1.52321i
$78$	−4.80587	+	0.847405i	−0.544158	+	0.0959497i
$79$	−1.54413	+	4.24247i	−0.173729	+	0.477316i	−0.995745	−	0.0921478i	$-0.970627\pi$
$79$	−1.54413	+	4.24247i	−0.173729	+	0.477316i	0.822017	+	0.569463i	$0.192849\pi$
$80$		0			0
$81$	2.66406	+	0.969637i	0.296006	+	0.107737i
$82$	−0.531080	+	0.919858i	−0.0586480	+	0.101581i
$83$	−10.3202	−	1.81973i	−1.13279	−	0.199741i	−0.424338	−	0.905504i	$-0.639493\pi$
$83$	−10.3202	−	1.81973i	−1.13279	−	0.199741i	−0.708448	+	0.705763i	$0.750604\pi$
$84$	−8.77654	−	15.2014i	−0.957599	−	1.65861i
$85$		0			0
$86$	−3.87061	−	3.24783i	−0.417379	−	0.350222i
$87$	−0.0309934	−	0.175772i	−0.00332284	−	0.0188448i
$88$	16.1688	+	28.0052i	1.72360	+	2.98537i
$89$	−0.914163	−	2.51164i	−0.0969011	−	0.266234i	0.881766	−	0.471688i	$-0.156355\pi$
$89$	−0.914163	−	2.51164i	−0.0969011	−	0.266234i	−0.978667	+	0.205454i	$0.934133\pi$
$90$		0			0
$91$	−4.81510	−	0.849032i	−0.504759	−	0.0890027i
$92$	−11.6476	+	9.77350i	−1.21435	+	1.01896i
$93$	3.26898	−	2.74300i	0.338977	−	0.284436i
$94$	−4.18331	−	0.737630i	−0.431475	−	0.0760807i
$95$		0			0
$96$	1.64984	+	4.53289i	0.168386	+	0.462636i
$97$	7.71809	+	13.3681i	0.783654	+	1.35733i	0.929800	+	0.368065i	$0.119980\pi$
$97$	7.71809	+	13.3681i	0.783654	+	1.35733i	−0.146146	+	0.989263i	$0.546687\pi$
$98$	−1.39597	−	7.91695i	−0.141015	−	0.799733i
$99$	−5.86542	−	4.92167i	−0.589497	−	0.494646i
$100$		0			0
$101$	8.33907	+	14.4437i	0.829769	+	1.43720i	0.898219	+	0.439547i	$0.144861\pi$
$101$	8.33907	+	14.4437i	0.829769	+	1.43720i	−0.0684504	+	0.997655i	$0.521805\pi$
$102$	2.53023	+	0.446149i	0.250531	+	0.0441753i
$103$	−2.20034	+	3.81111i	−0.216806	+	0.375520i	−0.953830	−	0.300348i	$-0.902897\pi$
$103$	−2.20034	+	3.81111i	−0.216806	+	0.375520i	0.737024	+	0.675867i	$0.236231\pi$
$104$	8.51521	+	3.09928i	0.834985	+	0.303910i
$105$		0			0
$106$	6.29202	−	17.2872i	0.611135	−	1.67908i
$107$	8.34584	−	1.47160i	0.806823	−	0.142265i	0.245001	−	0.969523i	$-0.421212\pi$
$107$	8.34584	−	1.47160i	0.806823	−	0.142265i	0.561822	+	0.827258i	$0.310101\pi$
$108$	−15.5545	−	18.5372i	−1.49673	−	1.78374i
$109$	6.61006	−	7.87757i	0.633129	−	0.754534i	−0.350139	−	0.936698i	$-0.613866\pi$
$109$	6.61006	−	7.87757i	0.633129	−	0.754534i	0.983268	+	0.182164i	$0.0583101\pi$
$110$		0			0
$111$	4.40216	+	6.30787i	0.417835	+	0.598717i
$112$			19.8252i			1.87331i
$113$	8.79256	+	7.37783i	0.827134	+	0.694048i	0.954631	−	0.297791i	$-0.0962498\pi$
$113$	8.79256	+	7.37783i	0.827134	+	0.694048i	−0.127497	+	0.991839i	$0.540694\pi$
$114$	5.15984	−	4.32962i	0.483263	−	0.405506i
$115$		0			0
$116$	−0.209901	+	0.576699i	−0.0194888	+	0.0535452i
$117$	−2.14559			−0.198360
$118$	−9.20325	+	25.2857i	−0.847228	+	2.32774i
$119$	2.22932	+	1.28710i	0.204362	+	0.117988i
$120$		0			0
$121$	−9.43730	−	16.3459i	−0.857937	−	1.48599i
$122$	25.1459	+	14.5180i	2.27660	+	1.31440i
$123$	0.342670	−	0.408378i	0.0308975	−	0.0368222i
$124$	−14.4502	+	2.54796i	−1.29767	+	0.228814i
$125$		0			0
$126$	−3.85364	−	10.5878i	−0.343310	−	0.943236i
$127$	−0.699449	−	1.92172i	−0.0620660	−	0.170525i	0.904783	−	0.425872i	$-0.140033\pi$
$127$	−0.699449	−	1.92172i	−0.0620660	−	0.170525i	−0.966850	+	0.255347i	$0.917810\pi$
$128$	−2.55407	+	14.4848i	−0.225750	+	1.28029i
$129$	1.63009	+	1.94267i	0.143521	+	0.171042i
$130$		0			0
$131$	−19.0577	−	3.36038i	−1.66508	−	0.293598i	−0.739782	−	0.672846i	$-0.765072\pi$
$131$	−19.0577	−	3.36038i	−1.66508	−	0.293598i	−0.925295	+	0.379248i	$0.876183\pi$
$132$	−10.2791	−	28.2416i	−0.894680	−	2.45811i
$133$	6.34163	−	2.30816i	0.549889	−	0.200143i
$134$	−16.8523	+	9.72965i	−1.45581	+	0.840514i
$135$		0			0
$136$	−3.65471	−	3.06666i	−0.313388	−	0.262964i
$137$	−14.7681	−	8.52635i	−1.26172	−	0.728456i	−0.288314	−	0.957536i	$-0.593095\pi$
$137$	−14.7681	−	8.52635i	−1.26172	−	0.728456i	−0.973408	+	0.229080i	$0.926428\pi$
$138$	9.64881	−	5.57074i	0.821361	−	0.474213i
$139$	1.47009	−	8.33729i	0.124691	−	0.707160i	−0.856799	−	0.515650i	$-0.827551\pi$
$139$	1.47009	−	8.33729i	0.124691	−	0.707160i	0.981491	−	0.191510i	$-0.0613384\pi$
$140$		0			0
$141$	2.00342	+	0.729186i	0.168719	+	0.0614086i
$142$	22.3290			1.87381
$143$	−7.86664	−	2.86322i	−0.657841	−	0.239435i
$144$	1.51071	+	8.56765i	0.125892	+	0.713971i
$145$		0			0
$146$	14.2106	−	16.9355i	1.17608	−	1.40160i
$147$			4.03483i			0.332787i
$148$	−2.26406	−	26.3519i	−0.186105	−	2.16611i
$149$	−8.48511			−0.695128			−0.347564	−	0.937656i	$-0.612991\pi$
$149$	−8.48511			−0.695128			−0.347564	+	0.937656i	$0.612991\pi$
$150$		0			0
$151$	−9.09996	+	7.63577i	−0.740544	+	0.621391i	−0.932984	−	0.359918i	$-0.882805\pi$
$151$	−9.09996	+	7.63577i	−0.740544	+	0.621391i	0.192439	+	0.981309i	$0.438360\pi$
$152$	−12.3175	+	2.17191i	−0.999081	+	0.176165i
$153$	1.06150	+	0.386355i	0.0858173	+	0.0312349i
$154$		−	43.9620i		−	3.54256i
$155$		0			0
$156$	−7.29348	−	4.21089i	−0.583946	−	0.337141i
$157$	−22.1873	−	3.91222i	−1.77074	−	0.312230i	−0.809332	−	0.587351i	$-0.800171\pi$
$157$	−22.1873	−	3.91222i	−1.77074	−	0.312230i	−0.961409	+	0.275122i	$0.911282\pi$
$158$	−9.85119	+	5.68759i	−0.783719	+	0.452480i
$159$	−4.61665	+	7.99628i	−0.366125	+	0.634146i
$160$		0			0
$161$	10.9933	−	1.93841i	0.866392	−	0.152768i
$162$	3.57151	+	6.18604i	0.280605	+	0.486021i
$163$	18.3564	−	6.68120i	1.43779	−	0.523312i	0.498635	−	0.866812i	$-0.333835\pi$
$163$	18.3564	−	6.68120i	1.43779	−	0.523312i	0.939152	+	0.343501i	$0.111613\pi$
$164$	−1.72250	+	0.626939i	−0.134505	+	0.0489557i
$165$		0			0
$166$	−16.9718	−	20.2262i	−1.31727	−	1.56986i
$167$	−11.6123	+	9.74390i	−0.898589	+	0.754006i	−0.969914	−	0.243447i	$-0.921722\pi$
$167$	−11.6123	+	9.74390i	−0.898589	+	0.754006i	0.0713251	+	0.997453i	$0.477277\pi$
$168$	4.14737	−	23.5209i	0.319977	−	1.81468i
$169$	10.0116	−	3.64393i	0.770123	−	0.280302i
$170$		0			0
$171$	2.56471	−	1.48074i	0.196128	−	0.113235i
$172$	−1.51419	−	8.58737i	−0.115456	−	0.654781i
$173$	−5.04521	+	6.01265i	−0.383580	+	0.457133i	−0.922941	−	0.384942i	$-0.874222\pi$
$173$	−5.04521	+	6.01265i	−0.383580	+	0.457133i	0.539361	+	0.842075i	$0.318666\pi$
$174$	0.224850	−	0.389452i	0.0170459	−	0.0295243i
$175$		0			0
$176$	−5.89437	+	33.4287i	−0.444305	+	2.51978i
$177$	6.75271	−	11.6960i	0.507565	−	0.879128i
$178$	2.30329	−	6.32824i	0.172639	−	0.474321i
$179$		−	3.28655i		−	0.245648i	−0.992428	−	0.122824i	$-0.960805\pi$
$179$		−	3.28655i		−	0.245648i	0.992428	−	0.122824i	$-0.0391951\pi$
$180$		0			0
$181$	3.52659	+	20.0003i	0.262129	+	1.48661i	0.777088	+	0.629392i	$0.216696\pi$
$181$	3.52659	+	20.0003i	0.262129	+	1.48661i	−0.514959	+	0.857215i	$0.672193\pi$
$182$	−7.91856	−	9.43697i	−0.586962	−	0.699515i
$183$	−11.1637	−	9.36749i	−0.825247	−	0.692465i
$184$	−20.6886			−1.52519
$185$		0			0
$186$	10.7518			0.788363
$187$	3.37634	+	2.83308i	0.246902	+	0.207176i
$188$	−4.71215	−	5.61572i	−0.343669	−	0.409568i
$189$	3.08498	+	17.4958i	0.224399	+	1.27263i
$190$		0			0
$191$			8.10362i			0.586357i	0.956058	+	0.293179i	$0.0947131\pi$
$191$			8.10362i			0.586357i	−0.956058	+	0.293179i	$0.905287\pi$
$192$	1.21521	−	3.33876i	0.0877002	−	0.240954i
$193$	−3.13586	+	5.43147i	−0.225724	+	0.390966i	−0.956536	−	0.291613i	$-0.905808\pi$
$193$	−3.13586	+	5.43147i	−0.225724	+	0.390966i	0.730812	+	0.682579i	$0.239141\pi$
$194$	−6.75360	+	38.3015i	−0.484880	+	2.74989i
$195$		0			0
$196$	6.93681	−	12.0149i	0.495487	−	0.858208i
$197$	3.00637	−	3.58285i	0.214195	−	0.255268i	−0.648239	−	0.761437i	$-0.724494\pi$
$197$	3.00637	−	3.58285i	0.214195	−	0.255268i	0.862434	+	0.506169i	$0.168939\pi$
$198$	−3.34996	−	18.9986i	−0.238071	−	1.35017i
$199$	−16.7401	+	9.66490i	−1.18667	+	0.685126i	−0.957549	−	0.288271i	$-0.906920\pi$
$199$	−16.7401	+	9.66490i	−1.18667	+	0.685126i	−0.229125	+	0.973397i	$0.573586\pi$
$200$		0			0
$201$	9.17766	−	3.34040i	0.647342	−	0.235613i
$202$	−7.29698	+	41.3832i	−0.513413	+	2.91171i
$203$	0.345152	−	0.289617i	0.0242249	−	0.0203271i
$204$	2.85010	+	3.39662i	0.199547	+	0.237811i
$205$		0			0
$206$	−10.4191	+	3.79225i	−0.725935	+	0.264219i
$207$	4.60314	−	1.67541i	0.319940	−	0.116449i
$208$	4.75597	+	8.23757i	0.329767	+	0.571173i
$209$	11.3793	−	2.00648i	0.787124	−	0.138791i
$210$		0			0
$211$	−5.13734	+	8.89813i	−0.353669	+	0.612573i	−0.986889	−	0.161399i	$-0.948399\pi$
$211$	−5.13734	+	8.89813i	−0.353669	+	0.612573i	0.633220	+	0.773972i	$0.281733\pi$
$212$	27.4949	−	15.8742i	1.88836	−	1.09024i
$213$	−11.0367	−	1.94607i	−0.756223	−	0.133343i
$214$	18.4916	+	10.6761i	1.26406	+	0.729804i
$215$		0			0
$216$		−	32.9260i		−	2.24033i
$217$	10.1228	+	3.68440i	0.687182	+	0.250114i
$218$	25.5161	−	4.49918i	1.72817	−	0.304723i
$219$	−8.49998	+	7.13233i	−0.574375	+	0.481958i
$220$		0			0
$221$	1.23507			0.0830801
$222$	−1.71927	+	19.3043i	−0.115390	+	1.29562i
$223$			14.0167i			0.938628i	0.883031	+	0.469314i	$0.155499\pi$
$223$			14.0167i			0.938628i	−0.883031	+	0.469314i	$0.844501\pi$
$224$	−7.82734	+	9.32826i	−0.522986	+	0.623271i
$225$		0			0
$226$	5.02176	+	28.4798i	0.334043	+	1.89445i
$227$	−3.18969	−	1.16095i	−0.211707	−	0.0770552i	0.233990	−	0.972239i	$-0.424822\pi$
$227$	−3.18969	−	1.16095i	−0.211707	−	0.0770552i	−0.445697	+	0.895184i	$0.647044\pi$
$228$	11.6243			0.769836
$229$	−2.11117	−	0.768402i	−0.139510	−	0.0507774i	0.271322	−	0.962489i	$-0.412539\pi$
$229$	−2.11117	−	0.768402i	−0.139510	−	0.0507774i	−0.410831	+	0.911711i	$0.634762\pi$
$230$		0			0
$231$	−3.83148	+	21.7294i	−0.252093	+	1.42969i
$232$	−0.723175	+	0.417525i	−0.0474788	+	0.0274119i
$233$	−8.69062	−	5.01753i	−0.569341	−	0.328709i	0.187545	−	0.982256i	$-0.439947\pi$
$233$	−8.69062	−	5.01753i	−0.569341	−	0.328709i	−0.756886	+	0.653547i	$0.773280\pi$
$234$	−4.14119	−	3.47487i	−0.270718	−	0.227159i
$235$		0			0
$236$	−40.2164	+	23.2190i	−2.61787	+	1.51143i
$237$	5.36491	−	1.95267i	0.348489	−	0.126839i
$238$	2.21829	+	6.09471i	0.143791	+	0.395061i
$239$	−0.0459930	−	0.00810981i	−0.00297504	−	0.000524580i	0.172160	−	0.985069i	$-0.444925\pi$
$239$	−0.0459930	−	0.00810981i	−0.00297504	−	0.000524580i	−0.175136	+	0.984544i	$0.556036\pi$
$240$		0			0
$241$	0.670857	+	0.799496i	0.0432137	+	0.0515000i	0.787218	−	0.616674i	$-0.211520\pi$
$241$	0.670857	+	0.799496i	0.0432137	+	0.0515000i	−0.744005	+	0.668174i	$0.767076\pi$
$242$	8.25796	−	46.8332i	0.530842	−	3.01055i
$243$	4.48406	+	12.3198i	0.287652	+	0.790318i
$244$	17.1385	+	47.0875i	1.09718	+	3.01447i
$245$		0			0
$246$	1.32277	−	0.233240i	0.0843369	−	0.0148709i
$247$	2.08129	−	2.48039i	0.132430	−	0.157823i
$248$	−17.2903	−	9.98256i	−1.09793	−	0.633893i
$249$	6.62597	+	11.4765i	0.419904	+	0.727295i
$250$		0			0
$251$	−3.41584	−	1.97214i	−0.215606	−	0.124480i	0.388308	−	0.921530i	$-0.373060\pi$
$251$	−3.41584	−	1.97214i	−0.215606	−	0.124480i	−0.603914	+	0.797050i	$0.706393\pi$
$252$	6.65051	−	18.2721i	0.418943	−	1.15104i
$253$	19.1129			1.20162
$254$	1.76230	−	4.84189i	0.110577	−	0.303807i
$255$		0			0
$256$	−24.0837	+	20.2086i	−1.50523	+	1.26304i
$257$	12.7799	+	10.7236i	0.797186	+	0.668918i	0.947513	−	0.319718i	$-0.103588\pi$
$257$	12.7799	+	10.7236i	0.797186	+	0.668918i	−0.150327	+	0.988636i	$0.548033\pi$
$258$			6.38953i			0.397795i
$259$	−8.23381	+	17.5858i	−0.511624	+	1.09273i
$260$		0			0
$261$	0.127092	−	0.151462i	0.00786677	−	0.00937525i
$262$	−31.3409	−	37.3506i	−1.93625	−	2.30753i
$263$	13.6921	−	2.41429i	0.844292	−	0.148872i	0.265261	−	0.964177i	$-0.414542\pi$
$263$	13.6921	−	2.41429i	0.844292	−	0.148872i	0.579032	+	0.815305i	$0.303431\pi$
$264$	13.9863	−	38.4271i	0.860799	−	2.36503i
$265$		0			0
$266$	15.9781	+	5.81556i	0.979682	+	0.356575i
$267$	−1.69000	+	2.92716i	−0.103426	+	0.179139i
$268$	−33.0721	−	5.83151i	−2.02020	−	0.356216i
$269$	−3.35403	−	5.80935i	−0.204499	−	0.354202i	0.745474	−	0.666535i	$-0.232223\pi$
$269$	−3.35403	−	5.80935i	−0.204499	−	0.354202i	−0.949973	+	0.312332i	$0.898890\pi$
$270$		0			0
$271$	3.46200	+	2.90496i	0.210302	+	0.176464i	0.741854	−	0.670561i	$-0.233947\pi$
$271$	3.46200	+	2.90496i	0.210302	+	0.176464i	−0.531552	+	0.847025i	$0.678391\pi$
$272$	−0.869616	−	4.93184i	−0.0527282	−	0.299037i
$273$	3.09149	+	5.35461i	0.187105	+	0.324076i
$274$	−14.6950	−	40.3742i	−0.887758	−	2.43909i
$275$		0			0
$276$	18.9355	+	3.33885i	1.13979	+	0.200975i
$277$	6.69345	−	5.61647i	0.402170	−	0.337461i	−0.419161	−	0.907912i	$-0.637676\pi$
$277$	6.69345	−	5.61647i	0.402170	−	0.337461i	0.821332	+	0.570451i	$0.193231\pi$
$278$	16.3400	−	13.7109i	0.980008	−	0.822325i
$279$	4.65543	+	0.820877i	0.278713	+	0.0491446i
$280$		0			0
$281$	0.335767	+	0.922512i	0.0200302	+	0.0550324i	0.949305	−	0.314357i	$-0.101789\pi$
$281$	0.335767	+	0.922512i	0.0200302	+	0.0550324i	−0.929275	+	0.369390i	$0.879567\pi$
$282$	2.68585	+	4.65203i	0.159940	+	0.277024i
$283$	−1.09689	−	6.22077i	−0.0652033	−	0.369786i	−0.999897	−	0.0143328i	$-0.995438\pi$
$283$	−1.09689	−	6.22077i	−0.0652033	−	0.369786i	0.934694	−	0.355453i	$-0.115674\pi$
$284$	29.5194	+	24.7697i	1.75165	+	1.46981i
$285$		0			0
$286$	−10.5463	−	18.2666i	−0.623613	−	1.08013i
$287$	1.32531	+	0.233688i	0.0782307	+	0.0137942i
$288$	−2.67183	+	4.62775i	−0.157439	+	0.272693i
$289$	15.3637	+	5.59194i	0.903749	+	0.328938i
$290$		0			0
$291$	6.67629	−	18.3430i	0.391371	−	1.07528i
$292$	37.5733	−	6.62519i	2.19881	−	0.387710i
$293$	−2.79580	−	3.33190i	−0.163332	−	0.194652i	0.678171	−	0.734904i	$-0.262773\pi$
$293$	−2.79580	−	3.33190i	−0.163332	−	0.194652i	−0.841503	+	0.540253i	$0.818329\pi$
$294$	−6.53458	+	7.78761i	−0.381105	+	0.454183i
$295$		0			0
$296$	20.6879	−	29.4474i	1.20246	−	1.71160i
$297$			30.4181i			1.76504i
$298$	−16.3771	−	13.7420i	−0.948699	−	0.796053i
$299$	4.10280	−	3.44266i	0.237271	−	0.199094i
$300$		0			0
$301$	−2.18954	+	6.01572i	−0.126203	+	0.346740i
$302$	−29.9303			−1.72229
$303$	7.21345	−	19.8188i	0.414402	−	1.13856i
$304$	−11.3700	−	6.56448i	−0.652115	−	0.376499i
$305$		0			0
$306$	1.42308	+	2.46485i	0.0813521	+	0.140906i
$307$	−14.2892	−	8.24984i	−0.815525	−	0.470844i	0.0333459	−	0.999444i	$-0.489384\pi$
$307$	−14.2892	−	8.24984i	−0.815525	−	0.470844i	−0.848871	+	0.528600i	$0.822717\pi$
$308$	48.7672	−	58.1185i	2.77877	−	3.31161i
$309$	5.48044	−	0.966350i	0.311771	−	0.0549737i
$310$		0			0
$311$	−7.85426	−	21.5794i	−0.445374	−	1.22366i	−0.935912	−	0.352235i	$-0.885422\pi$
$311$	−7.85426	−	21.5794i	−0.445374	−	1.22366i	0.490537	−	0.871420i	$-0.336801\pi$
$312$	−3.91927	−	10.7681i	−0.221885	−	0.609624i
$313$	−5.53206	+	31.3739i	−0.312691	+	1.77336i	0.272196	+	0.962242i	$0.412250\pi$
$313$	−5.53206	+	31.3739i	−0.312691	+	1.77336i	−0.584887	+	0.811115i	$0.698861\pi$
$314$	−36.4877	−	43.4843i	−2.05912	−	2.45396i
$315$		0			0
$316$	−19.3327	−	3.40888i	−1.08755	−	0.191765i
$317$	3.03720	+	8.34465i	0.170586	+	0.468682i	0.995297	−	0.0968731i	$-0.0308841\pi$
$317$	3.03720	+	8.34465i	0.170586	+	0.468682i	−0.824710	+	0.565555i	$0.808662\pi$
$318$	−21.8609	+	7.95672i	−1.22590	+	0.446191i
$319$	0.668093	−	0.385724i	0.0374060	−	0.0215964i
$320$		0			0
$321$	−8.20949	−	6.88858i	−0.458209	−	0.384483i
$322$	24.3574	+	14.0628i	1.35739	+	0.783687i
$323$	−1.47634	+	0.852363i	−0.0821455	+	0.0474267i
$324$	−2.14060	+	12.1400i	−0.118922	+	0.674442i
$325$		0			0
$326$	46.2502	+	16.8337i	2.56156	+	0.932331i
$327$	−13.0041			−0.719131
$328$	−2.34374	−	0.853050i	−0.129411	−	0.0471018i
$329$	0.934576	+	5.30025i	0.0515249	+	0.292212i
$330$		0			0
$331$	9.58689	−	11.4252i	0.526943	−	0.627986i	−0.435265	−	0.900302i	$-0.643345\pi$
$331$	9.58689	−	11.4252i	0.526943	−	0.627986i	0.962208	+	0.272316i	$0.0877897\pi$
$332$		−	45.5663i		−	2.50078i
$333$	−2.21826	+	8.22728i	−0.121560	+	0.450852i
$334$	−38.1936			−2.08986
$335$		0			0
$336$	19.2050	−	16.1149i	1.04772	−	0.879143i
$337$	29.4061	−	5.18509i	1.60185	−	0.282450i	0.699885	−	0.714256i	$-0.253235\pi$
$337$	29.4061	−	5.18509i	1.60185	−	0.282450i	0.901966	+	0.431806i	$0.142124\pi$
$338$	25.2248	+	9.18109i	1.37205	+	0.499386i
$339$		−	14.5146i		−	0.788325i
$340$		0			0
$341$	15.9733	+	9.22222i	0.865005	+	0.499411i
$342$	7.34825	+	1.29569i	0.397348	+	0.0700631i
$343$	10.5313	−	6.08023i	0.568635	−	0.328302i
$344$	5.93237	−	10.2752i	0.319852	−	0.554000i
$345$		0			0
$346$	−19.4755	+	3.43405i	−1.04701	+	0.184616i
$347$	3.27450	+	5.67160i	0.175784	+	0.304467i	0.940432	−	0.339981i	$-0.110421\pi$
$347$	3.27450	+	5.67160i	0.175784	+	0.304467i	−0.764648	+	0.644448i	$0.777087\pi$
$348$	0.729278	−	0.265435i	0.0390934	−	0.0142288i
$349$	29.2299	−	10.6388i	1.56464	−	0.569483i	0.592848	−	0.805314i	$-0.298003\pi$
$349$	29.2299	−	10.6388i	1.56464	−	0.569483i	0.971794	+	0.235831i	$0.0757812\pi$
$350$		0			0
$351$	5.47899	+	6.52961i	0.292447	+	0.348525i
$352$	−15.9717	+	13.4018i	−0.851293	+	0.714320i
$353$	3.34538	−	18.9726i	0.178056	−	1.00981i	−0.756500	−	0.653994i	$-0.773092\pi$
$353$	3.34538	−	18.9726i	0.178056	−	1.00981i	0.934556	−	0.355815i	$-0.115797\pi$
$354$	31.9756	−	11.6382i	1.69949	−	0.618562i
$355$		0			0
$356$	10.0649	−	5.81099i	0.533440	−	0.307982i
$357$	−0.565270	−	3.20581i	−0.0299173	−	0.169669i
$358$	5.32271	−	6.34335i	0.281314	−	0.335257i
$359$	6.15563	−	10.6619i	0.324882	−	0.562712i	−0.656607	−	0.754233i	$-0.728009\pi$
$359$	6.15563	−	10.6619i	0.324882	−	0.562712i	0.981488	+	0.191521i	$0.0613422\pi$
$360$		0			0
$361$	2.52325	−	14.3101i	0.132803	−	0.753161i
$362$	−25.5846	+	44.3139i	−1.34470	+	2.32909i
$363$	−8.16344	+	22.4289i	−0.428469	+	1.17721i
$364$		−	21.2599i		−	1.11432i
$365$		0			0
$366$	−6.37603	−	36.1603i	−0.333281	−	1.89013i
$367$	17.4658	+	20.8149i	0.911707	+	1.08653i	0.995934	+	0.0900839i	$0.0287135\pi$
$367$	17.4658	+	20.8149i	0.911707	+	1.08653i	−0.0842269	+	0.996447i	$0.526842\pi$
$368$	−16.6358	−	13.9591i	−0.867204	−	0.727670i
$369$	0.590553			0.0307430
$370$		0			0
$371$	−23.3085			−1.21012
$372$	14.2141	+	11.9271i	0.736968	+	0.618390i
$373$	5.48405	+	6.53564i	0.283954	+	0.338403i	0.889101	−	0.457711i	$-0.151330\pi$
$373$	5.48405	+	6.53564i	0.283954	+	0.338403i	−0.605148	+	0.796113i	$0.706886\pi$
$374$	1.92836	+	10.9362i	0.0997129	+	0.565500i
$375$		0			0
$376$		−	9.97472i		−	0.514407i
$377$	0.0739366	−	0.203139i	0.00380793	−	0.0104622i
$378$	−22.3809	+	38.7648i	−1.15115	+	1.99385i
$379$	−0.430632	+	2.44224i	−0.0221201	+	0.125449i	−0.993868	−	0.110571i	$-0.964732\pi$
$379$	−0.430632	+	2.44224i	−0.0221201	+	0.125449i	0.971748	+	0.236020i	$0.0758432\pi$
$380$		0			0
$381$	−1.29306	+	2.23964i	−0.0662453	+	0.114740i
$382$	−13.1242	+	15.6408i	−0.671490	+	0.800251i
$383$	−1.50726	−	8.54812i	−0.0770176	−	0.436789i	−0.998795	−	0.0490699i	$-0.984374\pi$
$383$	−1.50726	−	8.54812i	−0.0770176	−	0.436789i	0.921778	−	0.387719i	$-0.126737\pi$
$384$	16.1078	−	9.29984i	0.821998	−	0.474581i
$385$		0			0
$386$	−14.8490	+	5.40460i	−0.755795	+	0.275087i
$387$	−0.487826	+	2.76660i	−0.0247976	+	0.140634i
$388$	−51.4165	+	43.1435i	−2.61028	+	2.19028i
$389$	−19.5961	−	23.3537i	−0.993561	−	1.18408i	−0.982901	−	0.184137i	$-0.941051\pi$
$389$	−19.5961	−	23.3537i	−0.993561	−	1.18408i	−0.0106603	−	0.999943i	$-0.503393\pi$
$390$		0			0
$391$	−2.64973	+	0.964422i	−0.134002	+	0.0487729i
$392$	17.7388	−	6.45641i	0.895946	−	0.326098i
$393$	12.2358	+	21.1930i	0.617214	+	1.06905i
$394$	11.6052	−	2.04630i	0.584660	−	0.103091i
$395$		0			0
$396$	16.6465	−	28.8326i	0.836518	−	1.44889i
$397$	2.57749	−	1.48812i	0.129361	−	0.0746865i	−0.433923	−	0.900950i	$-0.642871\pi$
$397$	2.57749	−	1.48812i	0.129361	−	0.0746865i	0.563284	+	0.826263i	$0.309538\pi$
$398$	−47.9627	−	8.45712i	−2.40415	−	0.423917i
$399$	−7.39076	−	4.26706i	−0.370001	−	0.213620i
$400$		0			0
$401$			14.5237i			0.725279i	0.931930	+	0.362639i	$0.118124\pi$
$401$			14.5237i			0.725279i	−0.931930	+	0.362639i	$0.881876\pi$
$402$	23.1237	+	8.41633i	1.15330	+	0.419768i
$403$	5.09000	−	0.897505i	0.253551	−	0.0447079i
$404$	−55.5533	+	46.6148i	−2.76388	+	2.31917i
$405$		0			0
$406$	1.13522			0.0563402
$407$	−19.1122	+	27.2045i	−0.947354	+	1.34848i
$408$			6.03312i			0.298684i
$409$	−18.9147	+	22.5417i	−0.935272	+	1.11461i	0.0579428	+	0.998320i	$0.481546\pi$
$409$	−18.9147	+	22.5417i	−0.935272	+	1.11461i	−0.993215	+	0.116294i	$0.962899\pi$
$410$		0			0
$411$	3.74462	+	21.2368i	0.184708	+	1.04753i
$412$	−17.9810	−	6.54456i	−0.885862	−	0.322427i
$413$	34.0931			1.67761
$414$	11.5979	+	4.22129i	0.570005	+	0.207465i
$415$		0			0
$416$	−1.01454	+	5.75373i	−0.0497418	+	0.282100i
$417$	−9.27145	+	5.35287i	−0.454025	+	0.262131i
$418$	25.2128	+	14.5566i	1.23320	+	0.711986i
$419$	−26.4711	−	22.2119i	−1.29320	−	1.08512i	−0.991278	−	0.131789i	$-0.957928\pi$
$419$	−26.4711	−	22.2119i	−1.29320	−	1.08512i	−0.301921	−	0.953333i	$-0.597628\pi$
$420$		0			0
$421$	−1.37981	+	0.796635i	−0.0672480	+	0.0388256i	−0.533247	−	0.845960i	$-0.679028\pi$
$421$	−1.37981	+	0.796635i	−0.0672480	+	0.0388256i	0.465999	+	0.884785i	$0.345695\pi$
$422$	−24.3265	+	8.85411i	−1.18419	+	0.431011i
$423$	0.807772	+	2.21933i	0.0392752	+	0.107908i
$424$	42.5425	+	7.50139i	2.06604	+	0.364299i
$425$		0			0
$426$	−18.1502	−	21.6305i	−0.879379	−	1.04800i
$427$	6.38827	−	36.2297i	0.309150	−	1.75328i
$428$	12.6031	+	34.6268i	0.609195	+	1.67375i
$429$	3.62075	+	9.94793i	0.174812	+	0.480291i
$430$		0			0
$431$	−15.9475	+	2.81198i	−0.768165	+	0.135448i	−0.543980	−	0.839098i	$-0.683083\pi$
$431$	−15.9475	+	2.81198i	−0.768165	+	0.135448i	−0.224185	+	0.974547i	$0.571972\pi$
$432$	22.2159	−	26.4759i	1.06887	−	1.27382i
$433$	18.6058	+	10.7421i	0.894139	+	0.516231i	0.875294	−	0.483591i	$-0.160668\pi$
$433$	18.6058	+	10.7421i	0.894139	+	0.516231i	0.0188448	+	0.999822i	$0.494001\pi$
$434$	13.5710	+	23.5056i	0.651427	+	1.12830i
$435$		0			0
$436$	38.7237	+	22.3571i	1.85453	+	1.07071i
$437$	−2.52837	+	6.94663i	−0.120948	+	0.332302i
$438$	−27.9569			−1.33583
$439$	0.818338	−	2.24837i	0.0390572	−	0.107309i	−0.918631	−	0.395116i	$-0.870704\pi$
$439$	0.818338	−	2.24837i	0.0390572	−	0.107309i	0.957688	+	0.287808i	$0.0929264\pi$
$440$		0			0
$441$	−3.42397	+	2.87305i	−0.163046	+	0.136812i
$442$	2.38381	+	2.00026i	0.113386	+	0.0951425i
$443$			6.54020i			0.310734i	0.987857	+	0.155367i	$0.0496561\pi$
$443$			6.54020i			0.310734i	−0.987857	+	0.155367i	$0.950344\pi$
$444$	−23.6872	+	23.6134i	−1.12415	+	1.12064i
$445$		0			0
$446$	−22.7006	+	27.0536i	−1.07491	+	1.28102i
$447$	6.89714	+	8.21969i	0.326223	+	0.388778i
$448$	8.83301	−	1.55750i	0.417320	−	0.0735848i
$449$	13.2795	−	36.4852i	0.626699	−	1.72184i	−0.0632647	−	0.997997i	$-0.520151\pi$
$449$	13.2795	−	36.4852i	0.626699	−	1.72184i	0.689964	−	0.723844i	$-0.257627\pi$
$450$		0			0
$451$	2.16522	+	0.788076i	0.101956	+	0.0371090i
$452$	−24.9540	+	43.2215i	−1.17374	+	2.03297i
$453$	14.7938	+	2.60855i	0.695075	+	0.122560i
$454$	−4.27620	−	7.40659i	−0.200692	−	0.347609i
$455$		0			0
$456$	12.1163	+	10.1668i	0.567396	+	0.476102i
$457$	−2.66111	−	15.0919i	−0.124481	−	0.705969i	−0.981615	−	0.190874i	$-0.938868\pi$
$457$	−2.66111	−	15.0919i	−0.124481	−	0.705969i	0.857133	−	0.515095i	$-0.172243\pi$
$458$	−2.83029	−	4.90221i	−0.132251	−	0.229065i
$459$	−1.53488	−	4.21704i	−0.0716419	−	0.196835i
$460$		0			0
$461$	−15.9863	−	2.81882i	−0.744557	−	0.131285i	−0.211516	−	0.977375i	$-0.567840\pi$
$461$	−15.9863	−	2.81882i	−0.744557	−	0.131285i	−0.533041	+	0.846089i	$0.678951\pi$
$462$	−42.5868	+	35.7346i	−1.98132	+	1.66252i
$463$	6.39158	−	5.36317i	0.297042	−	0.249248i	−0.482070	−	0.876133i	$-0.660115\pi$
$463$	6.39158	−	5.36317i	0.297042	−	0.249248i	0.779112	+	0.626885i	$0.215670\pi$
$464$	−0.863223	−	0.152210i	−0.0400741	−	0.00706615i
$465$		0			0
$466$	−8.64762	−	23.7591i	−0.400593	−	1.10062i
$467$	3.33737	+	5.78049i	0.154435	+	0.267489i	0.932853	−	0.360257i	$-0.117311\pi$
$467$	3.33737	+	5.78049i	0.154435	+	0.267489i	−0.778418	+	0.627746i	$0.783978\pi$
$468$	−1.62004	−	9.18768i	−0.0748862	−	0.424701i
$469$	18.8868	+	15.8479i	0.872110	+	0.731788i
$470$		0			0
$471$	14.2452	+	24.6733i	0.656382	+	1.13689i
$472$	−62.2262	−	10.9722i	−2.86420	−	0.505035i
$473$	−5.48052	+	9.49254i	−0.251995	+	0.436467i
$474$	13.5172	+	4.91987i	0.620867	+	0.225977i
$475$		0			0
$476$	−3.82827	+	10.5181i	−0.175468	+	0.482095i
$477$	−10.0730	+	1.77614i	−0.461211	+	0.0813240i
$478$	−0.0756368	−	0.0901404i	−0.00345954	−	0.00412292i
$479$	−22.6567	+	27.0012i	−1.03521	+	1.23372i	−0.0633927	+	0.997989i	$0.520192\pi$
$479$	−22.6567	+	27.0012i	−1.03521	+	1.23372i	−0.971819	+	0.235729i	$0.924252\pi$
$480$		0			0
$481$	0.797502	+	9.28231i	0.0363630	+	0.423237i
$482$			2.62958i			0.119774i
$483$	−10.8137	−	9.07375i	−0.492039	−	0.412870i
$484$	62.8695	−	52.7538i	2.85770	−	2.39790i
$485$		0			0
$486$	−11.2979	+	31.0406i	−0.512481	+	1.40803i
$487$	−7.27548			−0.329683			−0.164842	−	0.986320i	$-0.552711\pi$
$487$	−7.27548			−0.329683			−0.164842	+	0.986320i	$0.552711\pi$
$488$	−23.3196	+	64.0701i	−1.05563	+	2.90032i
$489$	−21.3933	−	12.3514i	−0.967436	−	0.558550i
$490$		0			0
$491$	11.2013	+	19.4012i	0.505506	+	0.875562i	0.999980	+	0.00636940i	$0.00202746\pi$
$491$	11.2013	+	19.4012i	0.505506	+	0.875562i	−0.494474	+	0.869193i	$0.664639\pi$
$492$	2.00746	+	1.15901i	0.0905035	+	0.0522522i
$493$	−0.0731583	+	0.0871867i	−0.00329488	+	0.00392669i
$494$	8.03419	−	1.41665i	0.361475	−	0.0637379i
$495$		0			0
$496$	−7.16774	−	19.6932i	−0.321841	−	0.884251i
$497$	−9.67604	−	26.5847i	−0.434030	−	1.19249i
$498$	−5.79795	+	32.8818i	−0.259812	+	1.47347i
$499$	14.4636	+	17.2370i	0.647478	+	0.771634i	0.985531	−	0.169493i	$-0.0542130\pi$
$499$	14.4636	+	17.2370i	0.647478	+	0.771634i	−0.338054	+	0.941127i	$0.609769\pi$
$500$		0			0
$501$	18.8782	+	3.32874i	0.843416	+	0.148717i
$502$	−3.39894	−	9.33850i	−0.151702	−	0.416798i
$503$	−26.6639	+	9.70488i	−1.18889	+	0.432719i	−0.859332	−	0.511417i	$-0.829121\pi$
$503$	−26.6639	+	9.70488i	−1.18889	+	0.432719i	−0.329554	+	0.944137i	$0.606898\pi$
$504$	22.9131	−	13.2289i	1.02063	−	0.589261i
$505$		0			0
$506$	36.8896	+	30.9541i	1.63994	+	1.37608i
$507$	−11.6679	−	6.73646i	−0.518189	−	0.299177i
$508$	7.70093	−	4.44613i	0.341673	−	0.197265i
$509$	−0.834169	+	4.73081i	−0.0369739	+	0.209689i	−0.997698	−	0.0678167i	$-0.978397\pi$
$509$	−0.834169	+	4.73081i	−0.0369739	+	0.209689i	0.960724	+	0.277506i	$0.0895078\pi$
$510$		0			0
$511$	−26.3213	−	9.58017i	−1.16439	−	0.423802i
$512$	−49.7961			−2.20070
$513$	−11.0556	−	4.02389i	−0.488115	−	0.177659i
$514$	7.29906	+	41.3950i	0.321948	+	1.82586i
$515$		0			0
$516$	−7.08794	+	8.44708i	−0.312029	+	0.371862i
$517$			9.21498i			0.405274i
$518$	−44.3729	+	20.6072i	−1.94963	+	0.905428i
$519$	9.92557			0.435684
$520$		0			0
$521$	−7.02658	+	5.89600i	−0.307840	+	0.258309i	−0.783599	−	0.621267i	$-0.786618\pi$
$521$	−7.02658	+	5.89600i	−0.307840	+	0.258309i	0.475758	+	0.879576i	$0.342174\pi$
$522$	0.490598	−	0.0865056i	0.0214729	−	0.00378625i
$523$	−10.1854	−	3.70717i	−0.445375	−	0.162103i	0.109590	−	0.993977i	$-0.465046\pi$
$523$	−10.1854	−	3.70717i	−0.445375	−	0.162103i	−0.554965	+	0.831874i	$0.687268\pi$
$524$		−	84.1447i		−	3.67588i
$525$		0			0
$526$	30.3371	+	17.5152i	1.32276	+	0.763697i
$527$	−2.67983	−	0.472526i	−0.116735	−	0.0205835i
$528$	37.1742	−	21.4625i	1.61780	−	0.934037i
$529$	5.38609	−	9.32898i	0.234178	−	0.405608i
$530$		0			0
$531$	14.7336	−	2.59794i	0.639385	−	0.112741i
$532$	14.6721	+	25.4129i	0.636118	+	1.10179i
$533$	0.606741	−	0.220836i	0.0262809	−	0.00956545i
$534$	−8.00251	+	2.91268i	−0.346303	+	0.126044i
$535$		0			0
$536$	−29.3716	−	35.0037i	−1.26866	−	1.51193i
$537$	−3.18374	+	2.67148i	−0.137389	+	0.115283i
$538$	2.93489	−	16.6446i	0.126532	−	0.717599i
$539$	−16.3877	+	5.96464i	−0.705869	+	0.256915i
$540$		0			0
$541$	5.20115	−	3.00288i	0.223615	−	0.129104i	−0.384008	−	0.923330i	$-0.625457\pi$
$541$	5.20115	−	3.00288i	0.223615	−	0.129104i	0.607623	+	0.794226i	$0.292123\pi$
$542$	1.97728	+	11.2137i	0.0849315	+	0.481671i
$543$	16.5080	−	19.6735i	0.708427	−	0.844271i
$544$	1.53800	−	2.66389i	0.0659412	−	0.114214i
$545$		0			0
$546$	−2.70516	+	15.3417i	−0.115770	+	0.656564i
$547$	20.8920	−	36.1860i	0.893276	−	1.54720i	0.0573527	−	0.998354i	$-0.481734\pi$
$547$	20.8920	−	36.1860i	0.893276	−	1.54720i	0.835924	−	0.548846i	$-0.184933\pi$
$548$	25.3602	−	69.6767i	1.08334	−	2.97644i
$549$		−	16.1438i		−	0.689000i
$550$		0			0
$551$	0.0518131	+	0.293846i	0.00220731	+	0.0125183i
$552$	16.8168	+	20.0415i	0.715770	+	0.853022i
$553$	11.0405	+	9.26408i	0.469490	+	0.393949i
$554$	22.0151			0.935332
$555$		0			0
$556$	36.8113			1.56115
$557$	−6.02971	−	5.05953i	−0.255487	−	0.214379i	0.506044	−	0.862508i	$-0.331107\pi$
$557$	−6.02971	−	5.05953i	−0.255487	−	0.214379i	−0.761531	+	0.648129i	$0.775552\pi$
$558$	7.65597	+	9.12403i	0.324103	+	0.386251i
$559$	0.533363	+	3.02485i	0.0225589	+	0.127938i
$560$		0			0
$561$		−	5.57360i		−	0.235317i
$562$	−0.845985	+	2.32432i	−0.0356857	+	0.0980457i
$563$	11.6103	−	20.1096i	0.489314	−	0.847517i	−0.510610	−	0.859812i	$-0.670580\pi$
$563$	11.6103	−	20.1096i	0.489314	−	0.847517i	0.999924	+	0.0122951i	$0.00391375\pi$
$564$	−1.60978	+	9.12949i	−0.0677838	+	0.384421i
$565$		0			0
$566$	7.95770	−	13.7831i	0.334487	−	0.579348i
$567$	5.81737	−	6.93287i	0.244306	−	0.291153i
$568$	9.10484	+	51.6361i	0.382031	+	2.16660i
$569$	−35.3242	+	20.3944i	−1.48087	+	0.854978i	−0.999765	−	0.0216869i	$-0.993096\pi$
$569$	−35.3242	+	20.3944i	−1.48087	+	0.854978i	−0.481101	+	0.876665i	$0.659763\pi$
$570$		0			0
$571$	−33.6112	+	12.2335i	−1.40658	+	0.511954i	−0.930125	−	0.367243i	$-0.880302\pi$
$571$	−33.6112	+	12.2335i	−1.40658	+	0.511954i	−0.476458	+	0.879197i	$0.658080\pi$
$572$	6.32094	−	35.8478i	0.264292	−	1.49887i
$573$	7.85013	−	6.58704i	0.327944	−	0.275177i
$574$	2.17951	+	2.59744i	0.0909710	+	0.108415i
$575$		0			0
$576$	3.69858	−	1.34617i	0.154108	−	0.0560906i
$577$	9.98213	−	3.63320i	0.415561	−	0.151252i	−0.125774	−	0.992059i	$-0.540141\pi$
$577$	9.98213	−	3.63320i	0.415561	−	0.151252i	0.541335	+	0.840807i	$0.317919\pi$
$578$	20.5971	+	35.6752i	0.856726	+	1.48389i
$579$	7.81055	−	1.37721i	0.324596	−	0.0572350i
$580$		0			0
$581$	−16.7266	+	28.9713i	−0.693935	+	1.20193i
$582$	42.5931	−	24.5911i	1.76554	−	1.01934i
$583$	−39.3021	−	6.93003i	−1.62773	−	0.287012i
$584$	44.9581	+	25.9566i	1.86038	+	1.07409i
$585$		0			0
$586$		−	10.9588i		−	0.452704i
$587$	−9.59573	−	3.49256i	−0.396058	−	0.144153i	0.136310	−	0.990666i	$-0.456476\pi$
$587$	−9.59573	−	3.49256i	−0.396058	−	0.144153i	−0.532368	+	0.846513i	$0.678698\pi$
$588$	−17.2777	+	3.04652i	−0.712519	+	0.125636i
$589$	−5.46490	+	4.58559i	−0.225177	+	0.188946i
$590$		0			0
$591$	−5.91451			−0.243290
$592$	36.5041	−	9.72022i	1.50031	−	0.399499i
$593$		−	9.92034i		−	0.407380i	−0.979035	−	0.203690i	$-0.934707\pi$
$593$		−	9.92034i		−	0.407380i	0.979035	−	0.203690i	$-0.0652934\pi$
$594$	−49.2634	+	58.7098i	−2.02130	+	2.40889i
$595$		0			0
$596$	−6.40673	−	36.3343i	−0.262430	−	1.48831i
$597$	22.9698	+	8.36031i	0.940090	+	0.342165i
$598$	13.4943			0.551825
$599$	16.4377	+	5.98284i	0.671627	+	0.244452i	0.655248	−	0.755414i	$-0.272564\pi$
$599$	16.4377	+	5.98284i	0.671627	+	0.244452i	0.0163788	+	0.999866i	$0.494786\pi$
$600$		0			0
$601$	8.06439	−	45.7354i	0.328953	−	1.86559i	−0.151344	−	0.988481i	$-0.548360\pi$
$601$	8.06439	−	45.7354i	0.328953	−	1.86559i	0.480297	−	0.877106i	$-0.340529\pi$
$602$	−13.9687	+	8.06486i	−0.569324	+	0.328699i
$603$	9.36973	+	5.40962i	0.381565	+	0.220297i
$604$	−39.5683	−	33.2018i	−1.61001	−	1.35096i
$605$		0			0
$606$	46.0200	−	26.5697i	1.86944	−	1.07932i
$607$	38.9499	−	14.1766i	1.58093	−	0.575411i	0.605523	−	0.795828i	$-0.292964\pi$
$607$	38.9499	−	14.1766i	1.58093	−	0.575411i	0.975406	+	0.220417i	$0.0707418\pi$
$608$	−2.75811	−	7.57783i	−0.111856	−	0.307322i
$609$	−0.561115	−	0.0989397i	−0.0227375	−	0.00400924i
$610$		0			0
$611$	1.65983	+	1.97811i	0.0671494	+	0.0800256i
$612$	−0.852929	+	4.83720i	−0.0344776	+	0.195532i
$613$	−8.88414	−	24.4090i	−0.358827	−	0.985869i	−0.979437	−	0.201750i	$-0.935337\pi$
$613$	−8.88414	−	24.4090i	−0.358827	−	0.985869i	0.620610	−	0.784119i	$-0.286885\pi$
$614$	−14.2185	−	39.0649i	−0.573810	−	1.57653i
$615$		0			0
$616$	101.663	−	17.9259i	4.09610	−	0.722254i
$617$	−10.9472	+	13.0464i	−0.440720	+	0.525229i	−0.939983	−	0.341221i	$-0.889160\pi$
$617$	−10.9472	+	13.0464i	−0.440720	+	0.525229i	0.499264	+	0.866450i	$0.333604\pi$
$618$	12.1428	+	7.01066i	0.488456	+	0.282010i
$619$	−2.04260	−	3.53788i	−0.0820989	−	0.142199i	0.822052	−	0.569412i	$-0.192829\pi$
$619$	−2.04260	−	3.53788i	−0.0820989	−	0.142199i	−0.904151	+	0.427212i	$0.859496\pi$
$620$		0			0
$621$	−16.8533	−	9.73028i	−0.676301	−	0.390463i
$622$	19.7893	−	54.3706i	0.793478	−	2.18006i
$623$	−8.53244			−0.341845
$624$	4.11400	−	11.3031i	0.164692	−	0.452487i
$625$		0			0
$626$	−61.4887	+	51.5952i	−2.45758	+	2.06216i
$627$	−11.1934	−	9.39239i	−0.447022	−	0.375096i
$628$		−	97.9629i		−	3.90915i
$629$	1.27691	−	4.73591i	0.0509136	−	0.188833i
$630$		0			0
$631$	−23.5841	+	28.1064i	−0.938867	+	1.11890i	0.0538642	+	0.998548i	$0.482846\pi$
$631$	−23.5841	+	28.1064i	−0.938867	+	1.11890i	−0.992731	+	0.120350i	$0.961598\pi$
$632$	−17.1695	−	20.4618i	−0.682967	−	0.813929i
$633$	12.7957	−	2.25622i	0.508583	−	0.0896768i
$634$	−7.65242	+	21.0249i	−0.303916	+	0.835004i
$635$		0			0
$636$	−37.7269	−	13.7315i	−1.49597	−	0.544489i
$637$	−2.44345	+	4.23219i	−0.0968131	+	0.167685i
$638$	1.91418	+	0.337521i	0.0757831	+	0.0133626i
$639$	−6.20738	−	10.7515i	−0.245560	−	0.425323i
$640$		0			0
$641$	−24.6811	−	20.7099i	−0.974847	−	0.817993i	0.00845730	−	0.999964i	$-0.497308\pi$
$641$	−24.6811	−	20.7099i	−0.974847	−	0.817993i	−0.983304	+	0.181971i	$0.941752\pi$
$642$	−4.68875	−	26.5912i	−0.185050	−	1.04947i
$643$	11.2782	+	19.5344i	0.444769	+	0.770363i	0.998036	−	0.0626409i	$-0.0199523\pi$
$643$	11.2782	+	19.5344i	0.444769	+	0.770363i	−0.553267	+	0.833004i	$0.686619\pi$
$644$	16.6011	+	45.6110i	0.654173	+	1.79733i
$645$		0			0
$646$	−4.22991	−	0.745847i	−0.166423	−	0.0293450i
$647$	−5.99443	+	5.02992i	−0.235665	+	0.197747i	−0.752970	−	0.658054i	$-0.771380\pi$
$647$	−5.99443	+	5.02992i	−0.235665	+	0.197747i	0.517305	+	0.855801i	$0.326935\pi$
$648$	−12.8490	+	10.7816i	−0.504756	+	0.423541i
$649$	57.4867	+	10.1365i	2.25655	+	0.397891i
$650$		0			0
$651$	−4.65920	−	12.8010i	−0.182608	−	0.501712i
$652$	42.4699	+	73.5599i	1.66325	+	2.88083i
$653$	5.84235	+	33.1336i	0.228629	+	1.29662i	0.855625	+	0.517596i	$0.173173\pi$
$653$	5.84235	+	33.1336i	0.228629	+	1.29662i	−0.626996	+	0.779022i	$0.715716\pi$
$654$	−25.0992	−	21.0608i	−0.981458	−	0.823541i
$655$		0			0
$656$	−1.30904	−	2.26732i	−0.0511093	−	0.0885239i
$657$	−12.1050	−	2.13444i	−0.472262	−	0.0832725i
$658$	−6.78015	+	11.7436i	−0.264318	+	0.457812i
$659$	−25.7385	−	9.36806i	−1.00263	−	0.364928i	−0.212032	−	0.977263i	$-0.568008\pi$
$659$	−25.7385	−	9.36806i	−1.00263	−	0.364928i	−0.790598	+	0.612335i	$0.790230\pi$
$660$		0			0
$661$	12.3983	−	34.0640i	0.482237	−	1.32493i	−0.425334	−	0.905036i	$-0.639844\pi$
$661$	12.3983	−	34.0640i	0.482237	−	1.32493i	0.907571	−	0.419898i	$-0.137934\pi$
$662$	37.0072	−	6.52537i	1.43833	−	0.253616i
$663$	−1.00393	−	1.19644i	−0.0389895	−	0.0464659i
$664$	39.8530	−	47.4949i	1.54660	−	1.84316i
$665$		0			0
$666$	−17.6059	+	12.2869i	−0.682214	+	0.476107i
$667$			0.493548i			0.0191103i
$668$	−50.4926	−	42.3683i	−1.95362	−	1.63928i
$669$	13.5782	−	11.3935i	0.524965	−	0.440498i
$670$		0			0
$671$	21.5434	−	59.1901i	0.831675	−	2.28501i
$672$	15.3989			0.594026
$673$	−4.18387	+	11.4951i	−0.161276	+	0.443103i	−0.993840	−	0.110827i	$-0.964650\pi$
$673$	−4.18387	+	11.4951i	−0.161276	+	0.443103i	0.832564	+	0.553930i	$0.186872\pi$
$674$	65.1540	+	37.6167i	2.50964	+	1.44894i
$675$		0			0
$676$	23.1631	+	40.1196i	0.890887	+	1.54306i
$677$	−1.60205	−	0.924945i	−0.0615719	−	0.0355485i	0.468898	−	0.883252i	$-0.344651\pi$
$677$	−1.60205	−	0.924945i	−0.0615719	−	0.0355485i	−0.530470	+	0.847704i	$0.677985\pi$
$678$	23.5070	−	28.0146i	0.902781	−	1.07589i
$679$	48.5280	−	8.55680i	1.86234	−	0.328380i
$680$		0			0
$681$	1.46811	+	4.03360i	0.0562581	+	0.154568i
$682$	15.8943	+	43.6693i	0.608625	+	1.67218i
$683$	−1.74385	+	9.88984i	−0.0667264	+	0.378424i	0.933097	+	0.359625i	$0.117095\pi$
$683$	−1.74385	+	9.88984i	−0.0667264	+	0.378424i	−0.999823	+	0.0187992i	$0.994016\pi$
$684$	8.27720	+	9.86438i	0.316486	+	0.377174i
$685$		0			0
$686$	30.1735	+	5.32041i	1.15203	+	0.203134i
$687$	0.971699	+	2.66972i	0.0370726	+	0.101856i
$688$	11.7032	−	4.25960i	0.446179	−	0.162396i
$689$	−9.68493	+	5.59160i	−0.368967	+	0.213023i
$690$		0			0
$691$	5.08725	+	4.26871i	0.193528	+	0.162389i	0.734403	−	0.678714i	$-0.237462\pi$
$691$	5.08725	+	4.26871i	0.193528	+	0.162389i	−0.540875	+	0.841103i	$0.681907\pi$
$692$	−29.5563	−	17.0644i	−1.12356	−	0.648690i
$693$	−21.1679	+	12.2213i	−0.804100	+	0.464248i
$694$	−2.86530	+	16.2499i	−0.108765	+	0.616839i
$695$		0			0
$696$	0.992298	+	0.361167i	0.0376130	+	0.0136900i
$697$	−0.339943			−0.0128763
$698$	73.6466	+	26.8052i	2.78756	+	1.01459i
$699$	2.20361	+	12.4973i	0.0833481	+	0.472690i
$700$		0			0
$701$	10.4394	−	12.4412i	0.394290	−	0.469897i	−0.531980	−	0.846757i	$-0.678552\pi$
$701$	10.4394	−	12.4412i	0.394290	−	0.469897i	0.926270	+	0.376860i	$0.122996\pi$
$702$			21.4762i			0.810568i
$703$	−7.35930	−	10.5452i	−0.277561	−	0.397718i
$704$	15.3570			0.578789
$705$		0			0
$706$	37.1838	−	31.2009i	1.39943	−	1.17426i
$707$	52.4325	−	9.24527i	1.97193	−	0.347704i
$708$	55.1826	+	20.0848i	2.07389	+	0.754834i
$709$		−	18.3839i		−	0.690421i	−0.938525	−	0.345210i	$-0.887808\pi$
$709$		−	18.3839i		−	0.690421i	0.938525	−	0.345210i	$-0.112192\pi$
$710$		0			0
$711$	5.47719	+	3.16226i	0.205411	+	0.118594i
$712$	15.5733	+	2.74599i	0.583635	+	0.102911i
$713$	−10.2193	+	5.90009i	−0.382714	+	0.220960i
$714$	4.10091	−	7.10299i	0.153473	−	0.265823i
$715$		0			0
$716$	14.0734	−	2.48152i	0.525948	−	0.0927389i
$717$	0.0295294	+	0.0511464i	0.00110279	+	0.00191010i
$718$	29.1483	−	10.6091i	1.08780	−	0.395929i
$719$	−27.7891	+	10.1144i	−1.03636	+	0.377203i	−0.803498	−	0.595307i	$-0.797030\pi$
$719$	−27.7891	+	10.1144i	−1.03636	+	0.377203i	−0.232859	+	0.972511i	$0.574808\pi$
$720$		0			0
$721$	9.03003	+	10.7616i	0.336296	+	0.400782i
$722$	28.0459	−	23.5333i	1.04376	−	0.875818i
$723$	0.229180	−	1.29974i	0.00852328	−	0.0483379i
$724$	−82.9809	+	30.2026i	−3.08396	+	1.12247i
$725$		0			0
$726$	−52.0807	+	30.0688i	−1.93290	+	1.11596i
$727$	−1.65853	−	9.40598i	−0.0615114	−	0.348848i	−0.999994	−	0.00352135i	$-0.998879\pi$
$727$	−1.65853	−	9.40598i	−0.0615114	−	0.348848i	0.938482	−	0.345327i	$-0.112232\pi$
$728$	18.5942	−	22.1598i	0.689149	−	0.821295i
$729$	12.5421	−	21.7236i	0.464524	−	0.804578i
$730$		0			0
$731$	0.280809	−	1.59255i	0.0103861	−	0.0589026i
$732$	31.6835	−	54.8775i	1.17106	−	2.02833i
$733$	−4.26436	+	11.7162i	−0.157508	+	0.432749i	−0.993196	−	0.116455i	$-0.962847\pi$
$733$	−4.26436	+	11.7162i	−0.157508	+	0.432749i	0.835688	+	0.549204i	$0.185069\pi$
$734$			68.4614i			2.52696i
$735$		0			0
$736$	−2.31628	−	13.1363i	−0.0853790	−	0.484209i
$737$	27.1345	+	32.3376i	0.999511	+	1.19117i
$738$	1.13982	+	0.956426i	0.0419575	+	0.0352065i
$739$	−42.1916			−1.55204			−0.776022	−	0.630706i	$-0.782765\pi$
$739$	−42.1916			−1.55204			−0.776022	+	0.630706i	$0.782765\pi$
$740$		0			0
$741$	−4.09458			−0.150418
$742$	−44.9877	−	37.7492i	−1.65155	−	1.38582i
$743$	−11.8604	−	14.1347i	−0.435116	−	0.518551i	0.503275	−	0.864126i	$-0.332128\pi$
$743$	−11.8604	−	14.1347i	−0.435116	−	0.518551i	−0.938391	+	0.345575i	$0.887684\pi$
$744$	4.38415	+	24.8638i	0.160731	+	0.911550i
$745$		0			0
$746$			21.4961i			0.787027i
$747$	−5.02090	+	13.7948i	−0.183705	+	0.504725i
$748$	−9.58231	+	16.5970i	−0.350364	+	0.606848i
$749$	4.69775	−	26.6423i	0.171652	−	0.973488i
$750$		0			0
$751$	−17.8761	+	30.9623i	−0.652307	+	1.12983i	0.330254	+	0.943892i	$0.392865\pi$
$751$	−17.8761	+	30.9623i	−0.652307	+	1.12983i	−0.982562	+	0.185937i	$0.940468\pi$
$752$	6.73019	−	8.02073i	0.245425	−	0.292486i
$753$	0.866125	+	4.91204i	0.0315633	+	0.179005i
$754$	0.471697	−	0.272334i	0.0171782	−	0.00991783i
$755$		0			0
$756$	−72.5899	+	26.4206i	−2.64007	+	0.960907i
$757$	6.39109	−	36.2457i	0.232288	−	1.31737i	−0.615962	−	0.787776i	$-0.711233\pi$
$757$	6.39109	−	36.2457i	0.232288	−	1.31737i	0.848250	−	0.529595i	$-0.177656\pi$
$758$	−4.78647	+	4.01632i	−0.173852	+	0.145879i
$759$	−15.5359	−	18.5150i	−0.563918	−	0.672051i
$760$		0			0
$761$	11.1361	−	4.05322i	0.403684	−	0.146929i	−0.132195	−	0.991224i	$-0.542202\pi$
$761$	11.1361	−	4.05322i	0.403684	−	0.146929i	0.535879	+	0.844295i	$0.319980\pi$
$762$	−6.12292	+	2.22856i	−0.221810	+	0.0807322i
$763$	−16.4138	−	28.4296i	−0.594220	−	1.02922i
$764$	−34.7007	+	6.11867i	−1.25543	+	0.221366i
$765$		0			0
$766$	10.9349	−	18.9398i	0.395093	−	0.684322i
$767$	14.1660	−	8.17875i	0.511505	−	0.295318i
$768$	39.1530	+	6.90372i	1.41281	+	0.249117i
$769$	35.2131	+	20.3303i	1.26982	+	0.733129i	0.974953	−	0.222410i	$-0.0713925\pi$
$769$	35.2131	+	20.3303i	1.26982	+	0.733129i	0.294863	+	0.955539i	$0.404726\pi$
$770$		0			0
$771$		−	21.0968i		−	0.759781i
$772$	−25.6260	−	9.32710i	−0.922300	−	0.335690i
$773$	20.2643	−	3.57314i	0.728856	−	0.128517i	0.203107	−	0.979157i	$-0.434896\pi$
$773$	20.2643	−	3.57314i	0.728856	−	0.128517i	0.525749	+	0.850640i	$0.323785\pi$
$774$	−5.42217	+	4.54974i	−0.194896	+	0.163537i
$775$		0			0
$776$	−91.3266			−3.27844
$777$	23.7285	−	6.31837i	0.851256	−	0.226670i
$778$		−	76.8116i		−	2.75383i
$779$	−0.572857	+	0.682705i	−0.0205247	+	0.0244604i
$780$		0			0
$781$	−8.41135	−	47.7032i	−0.300982	−	1.70695i
$782$	−6.67615	−	2.42992i	−0.238739	−	0.0868938i
$783$	−0.785482			−0.0280708
$784$	18.6202	+	6.77719i	0.665007	+	0.242043i
$785$		0			0
$786$	−10.7067	+	60.7210i	−0.381897	+	2.16584i
$787$	−17.5786	+	10.1490i	−0.626609	+	0.361773i	−0.779438	−	0.626480i	$-0.784495\pi$
$787$	−17.5786	+	10.1490i	−0.626609	+	0.361773i	0.152828	+	0.988253i	$0.451162\pi$
$788$	17.6122	+	10.1684i	0.627409	+	0.362235i
$789$	−13.4684	−	11.3014i	−0.479489	−	0.402339i
$790$		0			0
$791$	31.7317	−	18.3203i	1.12825	−	0.651395i
$792$	42.5685	−	15.4937i	1.51261	−	0.550543i
$793$	−6.03693	−	16.5863i	−0.214378	−	0.588997i
$794$	7.38488	+	1.30215i	0.262080	+	0.0462117i
$795$		0			0
$796$	−54.0260	−	64.3857i	−1.91490	−	2.28209i
$797$	0.0312890	−	0.177449i	0.00110831	−	0.00628557i	−0.984249	−	0.176790i	$-0.943429\pi$
$797$	0.0312890	−	0.177449i	0.00110831	−	0.00628557i	0.985357	+	0.170505i	$0.0545397\pi$
$798$	−7.35420	−	20.2055i	−0.260336	−	0.715267i
$799$	−0.464982	−	1.27753i	−0.0164499	−	0.0451956i
$800$		0			0
$801$	−3.68737	+	0.650184i	−0.130287	+	0.0229731i
$802$	−23.5217	+	28.0321i	−0.830582	+	0.989849i
$803$	−41.5338	−	23.9796i	−1.46570	−	0.846220i
$804$	21.2336	+	36.7777i	0.748853	+	1.29705i
$805$		0			0
$806$	11.2777	+	6.51121i	0.397241	+	0.229347i
$807$	−2.90130	+	7.97125i	−0.102130	+	0.280601i
$808$	−98.6746			−3.47136
$809$	8.22721	−	22.6041i	0.289253	−	0.794717i	−0.706918	−	0.707296i	$-0.749915\pi$
$809$	8.22721	−	22.6041i	0.289253	−	0.794717i	0.996171	−	0.0874217i	$-0.0278628\pi$
$810$		0			0
$811$	31.4326	−	26.3751i	1.10375	−	0.926154i	0.106076	−	0.994358i	$-0.466171\pi$
$811$	31.4326	−	26.3751i	1.10375	−	0.926154i	0.997671	+	0.0682040i	$0.0217269\pi$
$812$	1.50079	+	1.25931i	0.0526673	+	0.0441931i
$813$		−	5.71501i		−	0.200434i
$814$	−80.9472	+	21.5544i	−2.83720	+	0.755481i
$815$		0			0
$816$	−4.07069	+	4.85126i	−0.142503	+	0.169828i
$817$	−2.72510	−	3.24764i	−0.0953390	−	0.113621i
$818$	−73.0144	+	12.8744i	−2.55289	+	0.450143i
$819$	−2.34261	+	6.43625i	−0.0818572	+	0.224901i
$820$		0			0
$821$	9.77043	+	3.55615i	0.340991	+	0.124110i	0.506839	−	0.862041i	$-0.330814\pi$
$821$	9.77043	+	3.55615i	0.340991	+	0.124110i	−0.165848	+	0.986151i	$0.553036\pi$
$822$	−27.1664	+	47.0536i	−0.947536	+	1.64118i
$823$	−8.42523	−	1.48559i	−0.293685	−	0.0517846i	0.0248645	−	0.999691i	$-0.492085\pi$
$823$	−8.42523	−	1.48559i	−0.293685	−	0.0517846i	−0.318549	+	0.947906i	$0.603196\pi$
$824$	−13.0181	−	22.5480i	−0.453507	−	0.785498i
$825$		0			0
$826$	65.8029	+	55.2152i	2.28957	+	1.92118i
$827$	5.02812	+	28.5159i	0.174845	+	0.991595i	0.938323	+	0.345761i	$0.112379\pi$
$827$	5.02812	+	28.5159i	0.174845	+	0.991595i	−0.763478	+	0.645834i	$0.776510\pi$
$828$	10.6499	+	18.4462i	0.370110	+	0.641050i
$829$	−2.47167	−	6.79085i	−0.0858446	−	0.235856i	0.889341	−	0.457244i	$-0.151163\pi$
$829$	−2.47167	−	6.79085i	−0.0858446	−	0.235856i	−0.975186	+	0.221388i	$0.928941\pi$
$830$		0			0
$831$	−10.8816	−	1.91871i	−0.377477	−	0.0665594i
$832$	3.29657	−	2.76615i	0.114288	−	0.0958990i
$833$	1.97095	−	1.65383i	0.0682895	−	0.0573017i
$834$	−26.5640	−	4.68395i	−0.919836	−	0.162192i
$835$		0			0
$836$	17.1840	+	47.2127i	0.594322	+	1.63289i
$837$	−9.38999	−	16.2639i	−0.324566	−	0.562164i
$838$	−15.1187	−	85.7422i	−0.522266	−	2.96191i
$839$	−2.80572	−	2.35428i	−0.0968643	−	0.0812788i	0.593069	−	0.805151i	$-0.297916\pi$
$839$	−2.80572	−	2.35428i	−0.0968643	−	0.0812788i	−0.689934	+	0.723872i	$0.742360\pi$
$840$		0			0
$841$	−14.4900	−	25.0975i	−0.499657	−	0.865431i
$842$	−3.95336	−	0.697083i	−0.136242	−	0.0240231i
$843$	0.620726	−	1.07513i	0.0213789	−	0.0370294i
$844$	−41.9819	−	15.2802i	−1.44508	−	0.525965i
$845$		0			0
$846$	−2.03523	+	5.59175i	−0.0699727	+	0.192248i
$847$	−59.3377	+	10.4628i	−2.03887	+	0.359507i
$848$	29.1473	+	34.7363i	1.00092	+	1.19285i
$849$	−5.13456	+	6.11914i	−0.176218	+	0.210008i
$850$		0			0
$851$	−8.95916	−	19.2915i	−0.307116	−	0.661305i
$852$		−	48.7300i		−	1.66946i
$853$	−24.3983	−	20.4726i	−0.835381	−	0.700968i	0.121138	−	0.992636i	$-0.461345\pi$
$853$	−24.3983	−	20.4726i	−0.835381	−	0.700968i	−0.956520	+	0.291667i	$0.905790\pi$
$854$	71.0055	−	59.5807i	2.42976	−	2.03881i
$855$		0			0
$856$	−17.1486	+	47.1153i	−0.586126	+	1.61037i
$857$	−2.91354			−0.0995246			−0.0497623	−	0.998761i	$-0.515846\pi$
$857$	−2.91354			−0.0995246			−0.0497623	+	0.998761i	$0.515846\pi$
$858$	−9.12270	+	25.0644i	−0.311444	+	0.855685i
$859$	27.9477	+	16.1356i	0.953564	+	0.550541i	0.894186	−	0.447695i	$-0.147755\pi$
$859$	27.9477	+	16.1356i	0.953564	+	0.550541i	0.0593778	+	0.998236i	$0.481088\pi$
$860$		0			0
$861$	−0.850903	−	1.47381i	−0.0289987	−	0.0502272i
$862$	−35.3344	−	20.4003i	−1.20349	−	0.694837i
$863$	11.4053	−	13.5923i	0.388240	−	0.462686i	−0.536157	−	0.844118i	$-0.680125\pi$
$863$	11.4053	−	13.5923i	0.388240	−	0.462686i	0.924397	+	0.381432i	$0.124569\pi$
$864$	20.9063	−	3.68635i	0.711248	−	0.125412i
$865$		0			0
$866$	18.5138	+	50.8662i	0.629123	+	1.72850i
$867$	−7.07142	−	19.4286i	−0.240158	−	0.659828i
$868$	−8.13381	+	46.1291i	−0.276080	+	1.56572i
$869$	15.8618	+	18.9033i	0.538074	+	0.641252i
$870$		0			0
$871$	11.6495	+	2.05412i	0.394727	+	0.0696011i
$872$	20.8088	+	57.1718i	0.704675	+	1.93608i
$873$	20.3198	−	7.39581i	0.687721	−	0.250310i
$874$	−16.1303	+	9.31286i	−0.545617	+	0.315012i
$875$		0			0
$876$	−36.9595	−	31.0127i	−1.24875	−	1.04782i
$877$	−2.75913	−	1.59299i	−0.0931693	−	0.0537913i	0.452691	−	0.891667i	$-0.350464\pi$
$877$	−2.75913	−	1.59299i	−0.0931693	−	0.0537913i	−0.545861	+	0.837876i	$0.683797\pi$
$878$	5.22079	−	3.01423i	0.176193	−	0.101725i
$879$	−0.955106	+	5.41668i	−0.0322149	+	0.182700i
$880$		0			0
$881$	5.23136	+	1.90406i	0.176249	+	0.0641493i	0.428637	−	0.903477i	$-0.358994\pi$
$881$	5.23136	+	1.90406i	0.176249	+	0.0641493i	−0.252388	+	0.967626i	$0.581216\pi$
$882$	−11.2616			−0.379198
$883$	12.2671	+	4.46487i	0.412822	+	0.150255i	0.540078	−	0.841615i	$-0.318395\pi$
$883$	12.2671	+	4.46487i	0.412822	+	0.150255i	−0.127256	+	0.991870i	$0.540617\pi$
$884$	0.932549	+	5.28875i	0.0313650	+	0.177880i
$885$		0			0
$886$	−10.5921	+	12.6232i	−0.355850	+	0.424085i
$887$		−	4.57250i		−	0.153529i	−0.997049	−	0.0767647i	$-0.975541\pi$
$887$		−	4.57250i		−	0.153529i	0.997049	−	0.0767647i	$-0.0244590\pi$
$888$	−45.3425	+	3.89566i	−1.52159	+	0.130730i
$889$	−6.52838			−0.218955
$890$		0			0
$891$	11.8703	−	9.96038i	0.397671	−	0.333685i
$892$	−60.0213	+	10.5834i	−2.00966	+	0.354358i
$893$	−3.34921	−	1.21901i	−0.112077	−	0.0407927i
$894$			27.0350i			0.904185i
$895$		0			0
$896$	40.6625	+	23.4765i	1.35844	+	0.784295i
$897$	−6.66994	−	1.17609i	−0.222703	−	0.0392685i
$898$	84.7200	−	48.9131i	2.82714	−	1.63225i
$899$	−0.238144	+	0.412477i	−0.00794255	+	0.0137569i
$900$		0			0
$901$	5.79837	−	1.02241i	0.193172	−	0.0340614i
$902$	2.90276	+	5.02773i	0.0966513	+	0.167405i
$903$	7.60732	−	2.76884i	0.253156	−	0.0921411i
$904$	−63.8123	+	23.2258i	−2.12237	+	0.772478i
$905$		0			0
$906$	24.3289	+	28.9940i	0.808272	+	0.963261i
$907$	9.92846	−	8.33097i	0.329669	−	0.276625i	−0.462896	−	0.886413i	$-0.653190\pi$
$907$	9.92846	−	8.33097i	0.329669	−	0.276625i	0.792565	+	0.609787i	$0.208745\pi$
$908$	2.56296	−	14.5353i	0.0850548	−	0.482369i
$909$	21.9547	−	7.99086i	0.728191	−	0.265040i
$910$		0			0
$911$	−5.79091	+	3.34338i	−0.191861	+	0.110771i	−0.592854	−	0.805310i	$-0.701999\pi$
$911$	−5.79091	+	3.34338i	−0.191861	+	0.110771i	0.400992	+	0.916081i	$0.368665\pi$
$912$	2.88300	+	16.3503i	0.0954655	+	0.541412i
$913$	−36.8175	+	43.8774i	−1.21848	+	1.45213i
$914$	19.3058	−	33.4386i	0.638578	−	1.10605i
$915$		0			0
$916$	1.69635	−	9.62047i	0.0560489	−	0.317869i
$917$	−30.8880	+	53.4996i	−1.02001	+	1.76671i
$918$	3.86721	−	10.6251i	0.127637	−	0.350680i
$919$			1.26433i			0.0417065i	0.999783	+	0.0208533i	$0.00663828\pi$
$919$			1.26433i			0.0417065i	−0.999783	+	0.0208533i	$0.993362\pi$
$920$		0			0
$921$	3.62318	+	20.5481i	0.119388	+	0.677082i
$922$	−26.2899	−	31.3311i	−0.865812	−	1.03184i
$923$	−10.3980	−	8.72498i	−0.342255	−	0.287186i
$924$	−95.9410			−3.15623
$925$		0			0
$926$	21.0222			0.690833
$927$	4.72246	+	3.96261i	0.155106	+	0.130149i
$928$	−0.346073	−	0.412434i	−0.0113604	−	0.0135388i
$929$	3.85014	+	21.8352i	0.126319	+	0.716391i	0.980516	+	0.196441i	$0.0629383\pi$
$929$	3.85014	+	21.8352i	0.126319	+	0.716391i	−0.854197	+	0.519950i	$0.825951\pi$
$930$		0			0
$931$		−	6.74521i		−	0.221065i
$932$	14.9238	−	41.0029i	0.488846	−	1.34309i
$933$	−14.5200	+	25.1494i	−0.475364	+	0.823355i
$934$	−2.92031	+	16.5619i	−0.0955556	+	0.541923i
$935$		0			0
$936$	6.34707	−	10.9935i	0.207461	−	0.359332i
$937$	12.1065	−	14.4280i	0.395503	−	0.471342i	−0.531140	−	0.847284i	$-0.678236\pi$
$937$	12.1065	−	14.4280i	0.395503	−	0.471342i	0.926643	+	0.375942i	$0.122681\pi$
$938$	10.7870	+	61.1759i	0.352207	+	1.99746i
$939$	34.8892	−	20.1433i	1.13857	−	0.657352i
$940$		0			0
$941$	−16.9915	+	6.18442i	−0.553908	+	0.201606i	−0.603782	−	0.797149i	$-0.706340\pi$
$941$	−16.9915	+	6.18442i	−0.553908	+	0.201606i	0.0498737	+	0.998756i	$0.484118\pi$
$942$	−12.4650	+	70.6925i	−0.406132	+	2.30329i
$943$	−1.12926	+	0.947561i	−0.0367737	+	0.0308568i
$944$	−42.6333	−	50.8083i	−1.38759	−	1.65367i
$945$		0			0
$946$	−25.9515	+	9.44557i	−0.843756	+	0.307102i
$947$	2.46229	−	0.896201i	0.0800138	−	0.0291226i	−0.301703	−	0.953402i	$-0.597555\pi$
$947$	2.46229	−	0.896201i	0.0800138	−	0.0291226i	0.381717	+	0.924279i	$0.375333\pi$
$948$	12.4124	+	21.4989i	0.403135	+	0.698251i
$949$	−13.2350	+	2.33369i	−0.429626	+	0.0757547i
$950$		0			0
$951$	5.61482	−	9.72516i	0.182073	−	0.315360i
$952$	−13.1896	+	7.61500i	−0.427476	+	0.246803i
$953$	43.8886	+	7.73875i	1.42169	+	0.250683i	0.831026	−	0.556234i	$-0.187754\pi$
$953$	43.8886	+	7.73875i	1.42169	+	0.250683i	0.590666	+	0.806916i	$0.298865\pi$
$954$	−22.3184	−	12.8855i	−0.722585	−	0.417185i
$955$		0			0
$956$		−	0.203071i		−	0.00656780i
$957$	−0.916718	−	0.333658i	−0.0296333	−	0.0107856i
$958$	−87.4592	+	15.4214i	−2.82568	+	0.498244i
$959$	−41.7012	+	34.9915i	−1.34660	+	1.12993i
$960$		0			0
$961$	19.6125			0.632661
$962$	−13.4938	+	19.2073i	−0.435059	+	0.619269i
$963$		−	11.8717i		−	0.382560i
$964$	−2.91701	+	3.47636i	−0.0939506	+	0.111966i
$965$		0			0
$966$	−6.17610	−	35.0264i	−0.198713	−	1.12696i
$967$	−19.1549	−	6.97181i	−0.615980	−	0.224198i	0.0151377	−	0.999885i	$-0.495181\pi$
$967$	−19.1549	−	6.97181i	−0.615980	−	0.224198i	−0.631118	+	0.775687i	$0.717404\pi$
$968$	111.670			3.58920
$969$	2.02574	+	0.737310i	0.0650762	+	0.0236858i
$970$		0			0
$971$	7.13666	−	40.4740i	0.229026	−	1.29887i	−0.625810	−	0.779975i	$-0.715232\pi$
$971$	7.13666	−	40.4740i	0.229026	−	1.29887i	0.854837	−	0.518897i	$-0.173657\pi$
$972$	−49.3694	+	28.5035i	−1.58353	+	0.914249i
$973$	−23.4048	−	13.5128i	−0.750324	−	0.433200i
$974$	−14.0424	−	11.7829i	−0.449947	−	0.377550i
$975$		0			0
$976$	−61.9811	+	35.7848i	−1.98397	+	1.14544i
$977$	−24.7518	+	9.00892i	−0.791881	+	0.288221i	−0.706118	−	0.708095i	$-0.749555\pi$
$977$	−24.7518	+	9.00892i	−0.791881	+	0.288221i	−0.0857630	+	0.996316i	$0.527333\pi$
$978$	−21.2874	−	58.4867i	−0.680696	−	1.87020i
$979$	−14.3871	−	2.53684i	−0.459815	−	0.0810778i
$980$		0			0
$981$	−9.25975	−	11.0353i	−0.295641	−	0.352331i
$982$	−9.80149	+	55.5870i	−0.312778	+	1.77385i
$983$	12.8142	+	35.2068i	0.408710	+	1.12292i	0.957869	+	0.287204i	$0.0927258\pi$
$983$	12.8142	+	35.2068i	0.408710	+	1.12292i	−0.549159	+	0.835718i	$0.685052\pi$
$984$	1.07874	+	2.96382i	0.0343891	+	0.0944832i
$985$		0			0
$986$	−0.282405	+	0.0497956i	−0.00899361	+	0.00158582i
$987$	4.37478	−	5.21365i	0.139251	−	0.165952i
$988$	12.1928	+	7.03954i	0.387906	+	0.223958i
$989$	−3.50627	−	6.07303i	−0.111493	−	0.193111i
$990$		0			0
$991$	49.3800	+	28.5095i	1.56861	+	0.905635i	0.996332	+	0.0855733i	$0.0272722\pi$
$991$	49.3800	+	28.5095i	1.56861	+	0.905635i	0.572275	+	0.820062i	$0.306061\pi$
$992$	4.40262	−	12.0961i	0.139783	−	0.384052i
$993$	−18.8605			−0.598521
$994$	24.3794	−	66.9818i	0.773267	−	2.12453i
$995$		0			0
$996$	−44.1409	+	37.0386i	−1.39866	+	1.17361i
$997$	9.11139	+	7.64536i	0.288560	+	0.242131i	0.775564	−	0.631269i	$-0.217466\pi$
$997$	9.11139	+	7.64536i	0.288560	+	0.242131i	−0.487003	+	0.873400i	$0.661910\pi$
$998$			56.6934i			1.79460i
$999$	30.7024	−	14.2585i	0.971382	−	0.451119i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.ba.a.299.6		36
5.2	odd	4		37.2.h.a.3.1	✓	18
5.3	odd	4		925.2.bb.a.151.3		18
5.4	even	2	inner	925.2.ba.a.299.1		36
15.2	even	4		333.2.bl.d.262.3		18
20.7	even	4		592.2.bq.d.225.2		18
37.25	even	18	inner	925.2.ba.a.99.1		36
185.7	odd	36		1369.2.b.g.1368.17		18
185.32	even	36		1369.2.a.m.1.2		18
185.42	even	36		1369.2.a.m.1.17		18
185.62	odd	36		37.2.h.a.25.1	yes	18
185.67	odd	36		1369.2.b.g.1368.2		18
185.99	even	18	inner	925.2.ba.a.99.6		36
185.173	odd	36		925.2.bb.a.876.3		18
555.62	even	36		333.2.bl.d.136.3		18
740.247	even	36		592.2.bq.d.321.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.h.a.3.1	✓	18	5.2	odd	4
37.2.h.a.25.1	yes	18	185.62	odd	36
333.2.bl.d.136.3		18	555.62	even	36
333.2.bl.d.262.3		18	15.2	even	4
592.2.bq.d.225.2		18	20.7	even	4
592.2.bq.d.321.2		18	740.247	even	36
925.2.ba.a.99.1		36	37.25	even	18	inner
925.2.ba.a.99.6		36	185.99	even	18	inner
925.2.ba.a.299.1		36	5.4	even	2	inner
925.2.ba.a.299.6		36	1.1	even	1	trivial
925.2.bb.a.151.3		18	5.3	odd	4
925.2.bb.a.876.3		18	185.173	odd	36
1369.2.a.m.1.2		18	185.32	even	36
1369.2.a.m.1.17		18	185.42	even	36
1369.2.b.g.1368.2		18	185.67	odd	36
1369.2.b.g.1368.17		18	185.7	odd	36

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.93010 + 1.61954i) q^{2} +(-0.812851 - 0.968719i) q^{3} +(0.755055 + 4.28213i) q^{4} -3.18617i q^{6} +(1.09182 - 2.99976i) q^{7} +(-2.95820 + 5.12375i) q^{8} +(0.243256 - 1.37957i) q^{9} +O(q^{10})\)	\(q+(1.93010 + 1.61954i) q^{2} +(-0.812851 - 0.968719i) q^{3} +(0.755055 + 4.28213i) q^{4} -3.18617i q^{6} +(1.09182 - 2.99976i) q^{7} +(-2.95820 + 5.12375i) q^{8} +(0.243256 - 1.37957i) q^{9} +(2.73288 - 4.73349i) q^{11} +(3.53443 - 4.21217i) q^{12} +(-0.265964 - 1.50836i) q^{13} +(6.96557 - 4.02158i) q^{14} +(-5.83582 + 2.12407i) q^{16} +(-0.140027 + 0.794131i) q^{17} +(2.70379 - 2.26875i) q^{18} +(1.35888 + 1.61945i) q^{19} +(-3.79342 + 1.38069i) q^{21} +(12.9408 - 4.71007i) q^{22} +(1.74842 + 3.02834i) q^{23} +(7.36805 - 1.29919i) q^{24} +(1.92951 - 3.34201i) q^{26} +(-4.81961 + 2.78260i) q^{27} +(13.6698 + 2.41035i) q^{28} +(0.122232 + 0.0705708i) q^{29} +3.37454i q^{31} +(-3.58452 - 1.30466i) q^{32} +(-6.80685 + 1.20023i) q^{33} +(-1.55639 + 1.30597i) q^{34} +6.09119 q^{36} +(-6.05878 - 0.539604i) q^{37} +5.32646i q^{38} +(-1.24498 + 1.48371i) q^{39} +(0.0732041 + 0.415161i) q^{41} +(-9.55775 - 3.47874i) q^{42} -2.00540 q^{43} +(22.3329 + 8.12851i) q^{44} +(-1.52992 + 8.67663i) q^{46} +(-1.46007 + 0.842972i) q^{47} +(6.80128 + 3.92672i) q^{48} +(-2.44419 - 2.05092i) q^{49} +(0.883111 - 0.509864i) q^{51} +(6.25815 - 2.27778i) q^{52} +(-2.49727 - 6.86119i) q^{53} +(-13.8088 - 2.43487i) q^{54} +(12.1402 + 14.4681i) q^{56} +(0.464224 - 2.63275i) q^{57} +(0.121628 + 0.334169i) q^{58} +(3.65272 + 10.0358i) q^{59} +(11.3492 - 2.00116i) q^{61} +(-5.46521 + 6.51318i) q^{62} +(-3.87281 - 2.23597i) q^{63} +(1.40484 + 2.43325i) q^{64} +(-15.0817 - 8.70742i) q^{66} +(-2.64152 + 7.25752i) q^{67} -3.50630 q^{68} +(1.51241 - 4.15532i) q^{69} +(6.78889 - 5.69655i) q^{71} +(6.34900 + 5.32744i) q^{72} -8.77446i q^{73} +(-10.8201 - 10.8539i) q^{74} +(-5.90867 + 7.04167i) q^{76} +(-11.2155 - 13.3662i) q^{77} +(-4.80587 + 0.847405i) q^{78} +(-1.54413 + 4.24247i) q^{79} +(2.66406 + 0.969637i) q^{81} +(-0.531080 + 0.919858i) q^{82} +(-10.3202 - 1.81973i) q^{83} +(-8.77654 - 15.2014i) q^{84} +(-3.87061 - 3.24783i) q^{86} +(-0.0309934 - 0.175772i) q^{87} +(16.1688 + 28.0052i) q^{88} +(-0.914163 - 2.51164i) q^{89} +(-4.81510 - 0.849032i) q^{91} +(-11.6476 + 9.77350i) q^{92} +(3.26898 - 2.74300i) q^{93} +(-4.18331 - 0.737630i) q^{94} +(1.64984 + 4.53289i) q^{96} +(7.71809 + 13.3681i) q^{97} +(-1.39597 - 7.91695i) q^{98} +(-5.86542 - 4.92167i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{4} + 6 q^{9}+O(q^{10}) \) 36 * q + 6 * q^4 + 6 * q^9	\( 36 q + 6 q^{4} + 6 q^{9} + 18 q^{11} - 18 q^{14} - 6 q^{16} - 12 q^{19} - 24 q^{21} - 90 q^{24} - 30 q^{26} + 36 q^{29} + 66 q^{34} - 144 q^{36} + 12 q^{39} - 48 q^{41} + 36 q^{46} - 42 q^{49} + 162 q^{51} - 90 q^{54} + 162 q^{56} + 12 q^{59} + 84 q^{61} - 12 q^{64} - 162 q^{66} + 72 q^{69} - 18 q^{71} - 30 q^{74} - 138 q^{76} + 12 q^{79} - 90 q^{81} + 48 q^{84} - 84 q^{86} - 36 q^{89} - 6 q^{91} - 36 q^{94} + 30 q^{96} - 120 q^{99}+O(q^{100}) \) 36 * q + 6 * q^4 + 6 * q^9 + 18 * q^11 - 18 * q^14 - 6 * q^16 - 12 * q^19 - 24 * q^21 - 90 * q^24 - 30 * q^26 + 36 * q^29 + 66 * q^34 - 144 * q^36 + 12 * q^39 - 48 * q^41 + 36 * q^46 - 42 * q^49 + 162 * q^51 - 90 * q^54 + 162 * q^56 + 12 * q^59 + 84 * q^61 - 12 * q^64 - 162 * q^66 + 72 * q^69 - 18 * q^71 - 30 * q^74 - 138 * q^76 + 12 * q^79 - 90 * q^81 + 48 * q^84 - 84 * q^86 - 36 * q^89 - 6 * q^91 - 36 * q^94 + 30 * q^96 - 120 * q^99

Introduction

L-functions

Modular forms

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