LMFDB - Embedded newform 875.2.q.b.676.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(51,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 10]))

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

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

chi := DirichletCharacter("875.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.q (of order $15$, degree $8$, 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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$36$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			676.27
Character	$\chi$	$=$	875.676
Dual form			875.2.q.b.576.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38556 + 0.616889i) q^{2} +(-1.93883 - 2.15328i) q^{3} +(0.200952 + 0.223180i) q^{4} +(-1.35801 - 4.17954i) q^{6} +(-0.864026 - 2.50069i) q^{7} +(-0.796607 - 2.45170i) q^{8} +(-0.564002 + 5.36612i) q^{9} +O(q^{10})$	\(q+(1.38556 + 0.616889i) q^{2} +(-1.93883 - 2.15328i) q^{3} +(0.200952 + 0.223180i) q^{4} +(-1.35801 - 4.17954i) q^{6} +(-0.864026 - 2.50069i) q^{7} +(-0.796607 - 2.45170i) q^{8} +(-0.564002 + 5.36612i) q^{9} +(0.0311666 + 0.296530i) q^{11} +(0.0909585 - 0.865413i) q^{12} +(0.971725 + 0.705999i) q^{13} +(0.345493 - 3.99786i) q^{14} +(0.471470 - 4.48574i) q^{16} +(-6.46391 - 1.37395i) q^{17} +(-4.09176 + 7.08713i) q^{18} +(-2.07257 + 2.30182i) q^{19} +(-3.70950 + 6.70890i) q^{21} +(-0.139743 + 0.430086i) q^{22} +(6.05382 + 2.69533i) q^{23} +(-3.73473 + 6.46875i) q^{24} +(0.910856 + 1.57765i) q^{26} +(5.61583 - 4.08014i) q^{27} +(0.384476 - 0.695352i) q^{28} +(-1.97373 + 6.07451i) q^{29} +(1.12021 + 0.238107i) q^{31} +(0.842577 - 1.45939i) q^{32} +(0.578088 - 0.642032i) q^{33} +(-8.10853 - 5.89119i) q^{34} +(-1.31095 + 0.952458i) q^{36} +(0.288759 - 2.74736i) q^{37} +(-4.29163 + 1.91076i) q^{38} +(-0.363788 - 3.46121i) q^{39} +(-7.69071 - 5.58763i) q^{41} +(-9.27837 + 7.00720i) q^{42} -2.00893 q^{43} +(-0.0599166 + 0.0665441i) q^{44} +(6.72518 + 7.46907i) q^{46} +(-7.34097 + 1.56037i) q^{47} +(-10.5732 + 7.68185i) q^{48} +(-5.50692 + 4.32133i) q^{49} +(9.57389 + 16.5825i) q^{51} +(0.0377052 + 0.358741i) q^{52} +(-4.91135 - 5.45461i) q^{53} +(10.2980 - 2.18892i) q^{54} +(-5.44267 + 4.11040i) q^{56} +8.97484 q^{57} +(-6.48201 + 7.19900i) q^{58} +(11.2461 - 5.00707i) q^{59} +(-8.55099 - 3.80715i) q^{61} +(1.40522 + 1.02096i) q^{62} +(13.9063 - 3.22607i) q^{63} +(-5.23034 + 3.80006i) q^{64} +(1.19704 - 0.532954i) q^{66} +(8.06160 + 1.71355i) q^{67} +(-0.992297 - 1.71871i) q^{68} +(-5.93348 - 18.2614i) q^{69} +(-1.15037 + 3.54049i) q^{71} +(13.6054 - 2.89192i) q^{72} +(-0.872884 - 8.30494i) q^{73} +(2.09491 - 3.62849i) q^{74} -0.930207 q^{76} +(0.714602 - 0.334148i) q^{77} +(1.63113 - 5.02012i) q^{78} +(-7.57630 + 1.61039i) q^{79} +(-3.84052 - 0.816327i) q^{81} +(-7.20896 - 12.4863i) q^{82} +(-0.605097 - 1.86230i) q^{83} +(-2.24272 + 0.520280i) q^{84} +(-2.78349 - 1.23929i) q^{86} +(16.9069 - 7.52742i) q^{87} +(0.702177 - 0.312629i) q^{88} +(3.79878 + 1.69132i) q^{89} +(0.925891 - 3.03999i) q^{91} +(0.614983 + 1.89272i) q^{92} +(-1.65917 - 2.87377i) q^{93} +(-11.1339 - 2.36658i) q^{94} +(-4.77608 + 1.01519i) q^{96} +(1.23497 - 3.80086i) q^{97} +(-10.2959 + 2.59028i) q^{98} -1.60880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9}+O(q^{10}) $ 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9	$ 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9} + 36 q^{14} + 10 q^{16} + 22 q^{19} - 18 q^{21} - 100 q^{24} - 120 q^{26} + 48 q^{29} + 30 q^{31} + 40 q^{34} + 32 q^{36} - 26 q^{39} - 124 q^{41} + 30 q^{44} - 54 q^{46} + 76 q^{49} - 16 q^{51} + 58 q^{54} + 64 q^{56} + 78 q^{59} + 14 q^{61} - 68 q^{64} + 22 q^{66} - 148 q^{69} - 92 q^{71} - 12 q^{74} + 360 q^{76} - 18 q^{79} - 118 q^{81} + 102 q^{84} + 22 q^{86} + 84 q^{89} + 44 q^{91} - 10 q^{94} + 106 q^{96} + 88 q^{99}+O(q^{100}) $ 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9 + 36 * q^14 + 10 * q^16 + 22 * q^19 - 18 * q^21 - 100 * q^24 - 120 * q^26 + 48 * q^29 + 30 * q^31 + 40 * q^34 + 32 * q^36 - 26 * q^39 - 124 * q^41 + 30 * q^44 - 54 * q^46 + 76 * q^49 - 16 * q^51 + 58 * q^54 + 64 * q^56 + 78 * q^59 + 14 * q^61 - 68 * q^64 + 22 * q^66 - 148 * q^69 - 92 * q^71 - 12 * q^74 + 360 * q^76 - 18 * q^79 - 118 * q^81 + 102 * q^84 + 22 * q^86 + 84 * q^89 + 44 * q^91 - 10 * q^94 + 106 * q^96 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.38556	+	0.616889i	0.979736	+	0.436207i	0.833184	−	0.552996i	$-0.186516\pi$
$2$	1.38556	+	0.616889i	0.979736	+	0.436207i	0.146552	+	0.989203i	$0.453182\pi$
$3$	−1.93883	−	2.15328i	−1.11938	−	1.24320i	−0.966972	−	0.254882i	$-0.917963\pi$
$3$	−1.93883	−	2.15328i	−1.11938	−	1.24320i	−0.152409	−	0.988317i	$-0.548703\pi$
$4$	0.200952	+	0.223180i	0.100476	+	0.111590i
$5$		0			0
$5$		0			0
$6$	−1.35801	−	4.17954i	−0.554407	−	1.70629i
$7$	−0.864026	−	2.50069i	−0.326571	−	0.945173i
$7$	−0.864026	−	2.50069i	−0.326571	−	0.945173i
$8$	−0.796607	−	2.45170i	−0.281643	−	0.866808i
$9$	−0.564002	+	5.36612i	−0.188001	+	1.78871i
$10$		0			0
$11$	0.0311666	+	0.296530i	0.00939709	+	0.0894073i	0.998215	−	0.0597192i	$-0.0190205\pi$
$11$	0.0311666	+	0.296530i	0.00939709	+	0.0894073i	−0.988818	+	0.149126i	$0.952354\pi$
$12$	0.0909585	−	0.865413i	0.0262575	−	0.249823i
$13$	0.971725	+	0.705999i	0.269508	+	0.195809i	0.714328	−	0.699811i	$-0.246732\pi$
$13$	0.971725	+	0.705999i	0.269508	+	0.195809i	−0.444820	+	0.895620i	$0.646732\pi$
$14$	0.345493	−	3.99786i	0.0923369	−	1.06847i
$15$		0			0
$16$	0.471470	−	4.48574i	0.117867	−	1.12143i
$17$	−6.46391	−	1.37395i	−1.56773	−	0.333231i	−0.659499	−	0.751705i	$-0.729232\pi$
$17$	−6.46391	−	1.37395i	−1.56773	−	0.333231i	−0.908228	+	0.418475i	$0.862565\pi$
$18$	−4.09176	+	7.08713i	−0.964437	+	1.67045i
$19$	−2.07257	+	2.30182i	−0.475481	+	0.528075i	−0.932397	−	0.361435i	$-0.882287\pi$
$19$	−2.07257	+	2.30182i	−0.475481	+	0.528075i	0.456917	+	0.889509i	$0.348954\pi$
$20$		0			0
$21$	−3.70950	+	6.70890i	−0.809480	+	1.46400i
$22$	−0.139743	+	0.430086i	−0.0297934	+	0.0916946i
$23$	6.05382	+	2.69533i	1.26231	+	0.562016i	0.925211	−	0.379453i	$-0.123888\pi$
$23$	6.05382	+	2.69533i	1.26231	+	0.562016i	0.337098	+	0.941470i	$0.390555\pi$
$24$	−3.73473	+	6.46875i	−0.762349	+	1.32043i
$25$		0			0
$26$	0.910856	+	1.57765i	0.178634	+	0.309402i
$27$	5.61583	−	4.08014i	1.08077	−	0.785224i
$28$	0.384476	−	0.695352i	0.0726591	−	0.131409i
$29$	−1.97373	+	6.07451i	−0.366512	+	1.12801i	0.582517	+	0.812818i	$0.302068\pi$
$29$	−1.97373	+	6.07451i	−0.366512	+	1.12801i	−0.949029	+	0.315189i	$0.897932\pi$
$30$		0			0
$31$	1.12021	+	0.238107i	0.201195	+	0.0427654i	0.307407	−	0.951578i	$-0.400539\pi$
$31$	1.12021	+	0.238107i	0.201195	+	0.0427654i	−0.106212	+	0.994344i	$0.533872\pi$
$32$	0.842577	−	1.45939i	0.148948	−	0.257985i
$33$	0.578088	−	0.642032i	0.100632	−	0.111763i
$34$	−8.10853	−	5.89119i	−1.39060	−	1.01033i
$35$		0			0
$36$	−1.31095	+	0.952458i	−0.218491	+	0.158743i
$37$	0.288759	−	2.74736i	0.0474717	−	0.451663i	−0.944806	−	0.327629i	$-0.893750\pi$
$37$	0.288759	−	2.74736i	0.0474717	−	0.451663i	0.992278	−	0.124034i	$-0.0395831\pi$
$38$	−4.29163	+	1.91076i	−0.696195	+	0.309966i
$39$	−0.363788	−	3.46121i	−0.0582527	−	0.554237i
$40$		0			0
$41$	−7.69071	−	5.58763i	−1.20109	−	0.872641i	−0.206695	−	0.978405i	$-0.566271\pi$
$41$	−7.69071	−	5.58763i	−1.20109	−	0.872641i	−0.994391	+	0.105765i	$0.966271\pi$
$42$	−9.27837	+	7.00720i	−1.43168	+	1.08123i
$43$	−2.00893			−0.306359			−0.153180	−	0.988198i	$-0.548951\pi$
$43$	−2.00893			−0.306359			−0.153180	+	0.988198i	$0.548951\pi$
$44$	−0.0599166	+	0.0665441i	−0.00903276	+	0.0100319i
$45$		0			0
$46$	6.72518	+	7.46907i	0.991574	+	1.10125i
$47$	−7.34097	+	1.56037i	−1.07079	+	0.227604i	−0.709397	−	0.704810i	$-0.751032\pi$
$47$	−7.34097	+	1.56037i	−1.07079	+	0.227604i	−0.361394	+	0.932413i	$0.617699\pi$
$48$	−10.5732	+	7.68185i	−1.52610	+	1.10878i
$49$	−5.50692	+	4.32133i	−0.786702	+	0.617332i
$50$		0			0
$51$	9.57389	+	16.5825i	1.34061	+	2.32201i
$52$	0.0377052	+	0.358741i	0.00522877	+	0.0497484i
$53$	−4.91135	−	5.45461i	−0.674626	−	0.749248i	0.304498	−	0.952513i	$-0.401511\pi$
$53$	−4.91135	−	5.45461i	−0.674626	−	0.749248i	−0.979124	+	0.203265i	$0.934845\pi$
$54$	10.2980	−	2.18892i	1.40139	−	0.297874i
$55$		0			0
$56$	−5.44267	+	4.11040i	−0.727307	+	0.549276i
$57$	8.97484			1.18875
$58$	−6.48201	+	7.19900i	−0.851129	+	0.945275i
$59$	11.2461	−	5.00707i	1.46411	−	0.651865i	0.488740	−	0.872429i	$-0.337457\pi$
$59$	11.2461	−	5.00707i	1.46411	−	0.651865i	0.975372	+	0.220565i	$0.0707900\pi$
$60$		0			0
$61$	−8.55099	−	3.80715i	−1.09484	−	0.487455i	−0.221796	−	0.975093i	$-0.571192\pi$
$61$	−8.55099	−	3.80715i	−1.09484	−	0.487455i	−0.873046	+	0.487638i	$0.837859\pi$
$62$	1.40522	+	1.02096i	0.178464	+	0.129661i
$63$	13.9063	−	3.22607i	1.75203	−	0.406447i
$64$	−5.23034	+	3.80006i	−0.653792	+	0.475008i
$65$		0			0
$66$	1.19704	−	0.532954i	0.147345	−	0.0656022i
$67$	8.06160	+	1.71355i	0.984881	+	0.209343i	0.672082	−	0.740477i	$-0.265400\pi$
$67$	8.06160	+	1.71355i	0.984881	+	0.209343i	0.312799	+	0.949819i	$0.398734\pi$
$68$	−0.992297	−	1.71871i	−0.120334	−	0.208424i
$69$	−5.93348	−	18.2614i	−0.714307	−	2.19841i
$70$		0			0
$71$	−1.15037	+	3.54049i	−0.136524	+	0.420179i	−0.995824	−	0.0912938i	$-0.970900\pi$
$71$	−1.15037	+	3.54049i	−0.136524	+	0.420179i	0.859300	+	0.511472i	$0.170900\pi$
$72$	13.6054	−	2.89192i	1.60341	−	0.340816i
$73$	−0.872884	−	8.30494i	−0.102163	−	0.972019i	−0.918762	−	0.394813i	$-0.870809\pi$
$73$	−0.872884	−	8.30494i	−0.102163	−	0.972019i	0.816598	−	0.577206i	$-0.195857\pi$
$74$	2.09491	−	3.62849i	0.243528	−	0.421803i
$75$		0			0
$76$	−0.930207			−0.106702
$77$	0.714602	−	0.334148i	0.0814365	−	0.0380797i
$78$	1.63113	−	5.02012i	0.184690	−	0.568416i
$79$	−7.57630	+	1.61039i	−0.852400	+	0.181183i	−0.613338	−	0.789821i	$-0.710173\pi$
$79$	−7.57630	+	1.61039i	−0.852400	+	0.181183i	−0.239063	+	0.971004i	$0.576840\pi$
$80$		0			0
$81$	−3.84052	−	0.816327i	−0.426724	−	0.0907030i
$82$	−7.20896	−	12.4863i	−0.796096	−	1.37888i
$83$	−0.605097	−	1.86230i	−0.0664180	−	0.204414i	0.912340	−	0.409434i	$-0.134274\pi$
$83$	−0.605097	−	1.86230i	−0.0664180	−	0.204414i	−0.978758	+	0.205021i	$0.934274\pi$
$84$	−2.24272	+	0.520280i	−0.244701	+	0.0567672i
$85$		0			0
$86$	−2.78349	−	1.23929i	−0.300151	−	0.133636i
$87$	16.9069	−	7.52742i	1.81260	−	0.807024i
$88$	0.702177	−	0.312629i	0.0748524	−	0.0333264i
$89$	3.79878	+	1.69132i	0.402669	+	0.179280i	0.598071	−	0.801443i	$-0.295934\pi$
$89$	3.79878	+	1.69132i	0.402669	+	0.179280i	−0.195401	+	0.980723i	$0.562601\pi$
$90$		0			0
$91$	0.925891	−	3.03999i	0.0970598	−	0.318677i
$92$	0.614983	+	1.89272i	0.0641164	+	0.197330i
$93$	−1.65917	−	2.87377i	−0.172048	−	0.297997i
$94$	−11.1339	−	2.36658i	−1.14837	−	0.244095i
$95$		0			0
$96$	−4.77608	+	1.01519i	−0.487457	+	0.103612i
$97$	1.23497	−	3.80086i	0.125393	−	0.385919i	−0.868580	−	0.495549i	$-0.834967\pi$
$97$	1.23497	−	3.80086i	0.125393	−	0.385919i	0.993972	+	0.109630i	$0.0349668\pi$
$98$	−10.2959	+	2.59028i	−1.04005	+	0.261658i
$99$	−1.60880			−0.161690
$100$		0			0
$101$	1.53118	−	2.65208i	0.152358	−	0.263892i	−0.779736	−	0.626108i	$-0.784647\pi$
$101$	1.53118	−	2.65208i	0.152358	−	0.263892i	0.932094	+	0.362217i	$0.117980\pi$
$102$	3.03562	+	28.8820i	0.300571	+	2.85974i
$103$	8.40853	−	1.78729i	0.828517	−	0.176107i	0.225913	−	0.974147i	$-0.427463\pi$
$103$	8.40853	−	1.78729i	0.828517	−	0.176107i	0.602604	+	0.798041i	$0.294130\pi$
$104$	0.956819	−	2.94479i	0.0938238	−	0.288760i
$105$		0			0
$106$	−3.44006	−	10.5874i	−0.334128	−	1.02834i
$107$	−7.85178	−	13.5997i	−0.759060	−	1.31473i	−0.943330	−	0.331856i	$-0.892325\pi$
$107$	−7.85178	−	13.5997i	−0.759060	−	1.31473i	0.184270	−	0.982876i	$-0.441008\pi$
$108$	2.03912	+	0.433428i	0.196214	+	0.0417066i
$109$	12.8122	−	5.70436i	1.22719	−	0.546379i	0.312259	−	0.949997i	$-0.398914\pi$
$109$	12.8122	−	5.70436i	1.22719	−	0.546379i	0.914928	+	0.403618i	$0.132248\pi$
$110$		0			0
$111$	−6.47570	+	4.70487i	−0.614646	+	0.446567i
$112$	−11.6248	+	2.69679i	−1.09844	+	0.254823i
$113$	−4.31207	−	3.13291i	−0.405646	−	0.294719i	0.366191	−	0.930540i	$-0.380662\pi$
$113$	−4.31207	−	3.13291i	−0.405646	−	0.294719i	−0.771837	+	0.635821i	$0.780662\pi$
$114$	12.4351	+	5.53648i	1.16466	+	0.518539i
$115$		0			0
$116$	−1.75233	+	0.780188i	−0.162700	+	0.0724386i
$117$	−4.33653	+	4.81621i	−0.400913	+	0.445259i
$118$	18.6709			1.71879
$119$	2.14917	+	17.3514i	0.197014	+	1.59060i
$120$		0			0
$121$	10.6727	−	2.26854i	0.970242	−	0.206231i
$122$	−9.49929	−	10.5500i	−0.860025	−	0.955154i
$123$	2.87920	+	27.3937i	0.259608	+	2.47001i
$124$	0.171967	+	0.297856i	0.0154431	+	0.0267482i
$125$		0			0
$126$	21.2581	+	4.10876i	1.89382	+	0.366037i
$127$	7.59404	−	5.51739i	0.673862	−	0.489590i	−0.197454	−	0.980312i	$-0.563267\pi$
$127$	7.59404	−	5.51739i	0.673862	−	0.489590i	0.871316	+	0.490723i	$0.163267\pi$
$128$	−12.8878	+	2.73939i	−1.13913	+	0.242130i
$129$	3.89497	+	4.32580i	0.342933	+	0.380866i
$130$		0			0
$131$	4.77072	−	5.29843i	0.416820	−	0.462926i	−0.497769	−	0.867309i	$-0.665847\pi$
$131$	4.77072	−	5.29843i	0.416820	−	0.462926i	0.914589	+	0.404384i	$0.132514\pi$
$132$	0.259456			0.0225828
$133$	7.54691	+	3.19403i	0.654400	+	0.276957i
$134$	10.1127	+	7.34733i	0.873606	+	0.634712i
$135$		0			0
$136$	1.78068	+	16.9421i	0.152692	+	1.45277i
$137$	−14.2992	+	6.36641i	−1.22166	+	0.543919i	−0.913275	−	0.407343i	$-0.866455\pi$
$137$	−14.2992	+	6.36641i	−1.22166	+	0.543919i	−0.308386	+	0.951261i	$0.599789\pi$
$138$	3.04408	−	28.9625i	0.259129	−	2.46545i
$139$	−5.33788	+	3.87820i	−0.452753	+	0.328944i	−0.790682	−	0.612227i	$-0.790274\pi$
$139$	−5.33788	+	3.87820i	−0.452753	+	0.328944i	0.337929	+	0.941172i	$0.390274\pi$
$140$		0			0
$141$	17.5928	+	12.7819i	1.48158	+	1.07643i
$142$	−3.77800	+	4.19589i	−0.317042	+	0.352111i
$143$	−0.179065	+	0.310150i	−0.0149742	+	0.0259360i
$144$	23.8051	+	5.05993i	1.98376	+	0.421661i
$145$		0			0
$146$	3.91380	−	12.0454i	0.323908	−	0.996887i
$147$	19.9820	+	3.47966i	1.64809	+	0.286998i
$148$	0.671181	−	0.487642i	0.0551708	−	0.0400839i
$149$	−5.90514	−	10.2280i	−0.483768	−	0.837911i	0.516058	−	0.856554i	$-0.327399\pi$
$149$	−5.90514	−	10.2280i	−0.483768	−	0.837911i	−0.999826	+	0.0186424i	$0.994066\pi$
$150$		0			0
$151$	0.789055	−	1.36668i	0.0642124	−	0.111219i	−0.832132	−	0.554578i	$-0.812880\pi$
$151$	0.789055	−	1.36668i	0.0642124	−	0.111219i	0.896344	+	0.443359i	$0.146213\pi$
$152$	7.29442	+	3.24768i	0.591655	+	0.263422i
$153$	11.0184	−	33.9112i	0.890786	−	2.74156i
$154$	1.19625	−	0.0221504i	0.0963969	−	0.00178493i
$155$		0			0
$156$	0.699368	−	0.776726i	0.0559942	−	0.0621879i
$157$	−6.25969	+	10.8421i	−0.499578	+	0.865294i	−1.00000		0.000487578i	$-0.999845\pi$
$157$	−6.25969	+	10.8421i	−0.499578	+	0.865294i	0.500422	+	0.865782i	$0.333178\pi$
$158$	−11.4908	−	2.44245i	−0.914161	−	0.194311i
$159$	−2.22307	+	21.1511i	−0.176301	+	1.67739i
$160$		0			0
$161$	1.50954	−	17.4676i	0.118969	−	1.37664i
$162$	−4.81767	−	3.50024i	−0.378512	−	0.275005i
$163$	0.0586246	−	0.557776i	0.00459183	−	0.0436884i	−0.991986	−	0.126347i	$-0.959675\pi$
$163$	0.0586246	−	0.557776i	0.00459183	−	0.0436884i	0.996578	+	0.0826591i	$0.0263413\pi$
$164$	−0.298417	−	2.83925i	−0.0233025	−	0.221708i
$165$		0			0
$166$	0.310435	−	2.95360i	0.0240945	−	0.229243i
$167$	−5.45858	−	16.7998i	−0.422397	−	1.30001i	−0.905465	−	0.424422i	$-0.860477\pi$
$167$	−5.45858	−	16.7998i	−0.422397	−	1.30001i	0.483067	−	0.875583i	$-0.339523\pi$
$168$	19.4033	+	3.75025i	1.49699	+	0.289338i
$169$	−3.57141	−	10.9917i	−0.274724	−	0.845512i
$170$		0			0
$171$	−11.1829	−	12.4199i	−0.855180	−	0.949774i
$172$	−0.403699	−	0.448353i	−0.0307817	−	0.0341866i
$173$	−11.6504	−	5.18708i	−0.885761	−	0.394366i	−0.0871369	−	0.996196i	$-0.527772\pi$
$173$	−11.6504	−	5.18708i	−0.885761	−	0.394366i	−0.798624	+	0.601830i	$0.794438\pi$
$174$	28.0690			2.12790
$175$		0			0
$176$	1.34485			0.101372
$177$	−32.5858	−	14.5081i	−2.44930	−	1.09050i
$178$	4.22006	+	4.68685i	0.316307	+	0.351294i
$179$	−4.72778	−	5.25073i	−0.353371	−	0.392458i	0.540084	−	0.841611i	$-0.318392\pi$
$179$	−4.72778	−	5.25073i	−0.353371	−	0.392458i	−0.893455	+	0.449153i	$0.851726\pi$
$180$		0			0
$181$	−3.42377	−	10.5373i	−0.254487	−	0.783231i	−0.993930	−	0.110012i	$-0.964911\pi$
$181$	−3.42377	−	10.5373i	−0.254487	−	0.783231i	0.739443	−	0.673219i	$-0.235089\pi$
$182$	3.15821	−	3.64090i	0.234102	−	0.269881i
$183$	8.38101	+	25.7941i	0.619542	+	1.90675i
$184$	1.78565	−	16.9893i	0.131640	−	1.25247i
$185$		0			0
$186$	−0.526078	−	5.00530i	−0.0385739	−	0.367007i
$187$	0.205959	−	1.95957i	0.0150612	−	0.143298i
$188$	−1.82342	−	1.32480i	−0.132987	−	0.0966206i
$189$	−15.0554	−	10.5181i	−1.09512	−	0.765081i
$190$		0			0
$191$	−0.135216	+	1.28650i	−0.00978390	+	0.0930876i	−0.998324	−	0.0578701i	$-0.981569\pi$
$191$	−0.135216	+	1.28650i	−0.00978390	+	0.0930876i	0.988540	+	0.150958i	$0.0482357\pi$
$192$	18.3233	+	3.89474i	1.32237	+	0.281079i
$193$	−0.409705	+	0.709630i	−0.0294912	+	0.0510803i	−0.880394	−	0.474242i	$-0.842722\pi$
$193$	−0.409705	+	0.709630i	−0.0294912	+	0.0510803i	0.850903	+	0.525323i	$0.176055\pi$
$194$	4.05584	−	4.50446i	0.291192	−	0.323402i
$195$		0			0
$196$	−2.07106	−	0.360653i	−0.147933	−	0.0257609i
$197$	−6.95278	+	21.3985i	−0.495365	+	1.52458i	0.321021	+	0.947072i	$0.395974\pi$
$197$	−6.95278	+	21.3985i	−0.495365	+	1.52458i	−0.816387	+	0.577506i	$0.804026\pi$
$198$	−2.22908	−	0.992449i	−0.158414	−	0.0705303i
$199$	0.379861	−	0.657939i	0.0269276	−	0.0466400i	−0.852248	−	0.523139i	$-0.824761\pi$
$199$	0.379861	−	0.657939i	0.0269276	−	0.0466400i	0.879175	+	0.476499i	$0.158094\pi$
$200$		0			0
$201$	−11.9403	−	20.6812i	−0.842203	−	1.45874i
$202$	3.75757	−	2.73004i	0.264382	−	0.192085i
$203$	16.8958	−	0.312851i	1.18585	−	0.0219578i
$204$	−1.77698	+	5.46897i	−0.124413	+	0.382905i
$205$		0			0
$206$	12.7530	+	2.71074i	0.888547	+	0.188866i
$207$	−17.8779	+	30.9654i	−1.24260	+	2.15224i
$208$	3.62507	−	4.02604i	0.251353	−	0.279156i
$209$	−0.747156	−	0.542841i	−0.0516819	−	0.0375491i
$210$		0			0
$211$	8.51968	−	6.18991i	0.586519	−	0.426131i	−0.254550	−	0.967060i	$-0.581927\pi$
$211$	8.51968	−	6.18991i	0.586519	−	0.426131i	0.841068	+	0.540929i	$0.181927\pi$
$212$	0.230412	−	2.19223i	0.0158248	−	0.150563i
$213$	9.85405	−	4.38731i	0.675189	−	0.300613i
$214$	−2.48958	−	23.6868i	−0.170184	−	1.61920i
$215$		0			0
$216$	−14.4769	−	10.5181i	−0.985029	−	0.715665i
$217$	−0.372455	−	3.00702i	−0.0252839	−	0.204130i
$218$	21.2710			1.44065
$219$	−16.1905	+	17.9814i	−1.09405	+	1.21507i
$220$		0			0
$221$	−5.31113	−	5.89861i	−0.357266	−	0.396784i
$222$	−11.8748	+	2.52407i	−0.796987	+	0.169405i
$223$	−6.44579	+	4.68314i	−0.431642	+	0.313606i	−0.782305	−	0.622895i	$-0.785956\pi$
$223$	−6.44579	+	4.68314i	−0.431642	+	0.313606i	0.350663	+	0.936502i	$0.385956\pi$
$224$	−4.37748	−	0.846077i	−0.292483	−	0.0565309i
$225$		0			0
$226$	−4.04196	−	7.00089i	−0.268867	−	0.465692i
$227$	0.169571	+	1.61336i	0.0112548	+	0.107083i	0.998707	−	0.0508356i	$-0.0161884\pi$
$227$	0.169571	+	1.61336i	0.0112548	+	0.107083i	−0.987452	+	0.157918i	$0.949522\pi$
$228$	1.80351	+	2.00300i	0.119440	+	0.132652i
$229$	−8.32102	+	1.76869i	−0.549869	+	0.116878i	−0.474464	−	0.880275i	$-0.657358\pi$
$229$	−8.32102	+	1.76869i	−0.549869	+	0.116878i	−0.0754045	+	0.997153i	$0.524025\pi$
$230$		0			0
$231$	−2.10501	−	0.890887i	−0.138499	−	0.0586161i
$232$	16.4652			1.08099
$233$	−10.9855	+	12.2006i	−0.719684	+	0.799290i	−0.986379	−	0.164491i	$-0.947402\pi$
$233$	−10.9855	+	12.2006i	−0.719684	+	0.799290i	0.266695	+	0.963781i	$0.414068\pi$
$234$	−8.97958	+	3.99797i	−0.587013	+	0.261355i
$235$		0			0
$236$	3.37739	+	1.50371i	0.219849	+	0.0978833i
$237$	18.1568	+	13.1917i	1.17941	+	0.856890i
$238$	−7.72607	+	25.3671i	−0.500807	+	1.64430i
$239$	14.8595	−	10.7960i	0.961178	−	0.698337i	0.00775395	−	0.999970i	$-0.497532\pi$
$239$	14.8595	−	10.7960i	0.961178	−	0.698337i	0.953424	+	0.301633i	$0.0975318\pi$
$240$		0			0
$241$	7.73006	−	3.44164i	0.497937	−	0.221696i	−0.142372	−	0.989813i	$-0.545473\pi$
$241$	7.73006	−	3.44164i	0.497937	−	0.221696i	0.640309	+	0.768117i	$0.278806\pi$
$242$	16.1870	+	3.44066i	1.04054	+	0.221174i
$243$	−4.72402	−	8.18224i	−0.303046	−	0.524891i
$244$	−0.868659	−	2.67346i	−0.0556102	−	0.171151i
$245$		0			0
$246$	−12.9096	+	39.7317i	−0.823086	+	2.53320i
$247$	−3.63906	+	0.773505i	−0.231548	+	0.0492170i
$248$	−0.308596	−	2.93610i	−0.0195959	−	0.186442i
$249$	−2.83688	+	4.91362i	−0.179780	+	0.311388i
$250$		0			0
$251$	28.8626			1.82179			0.910895	−	0.412638i	$-0.135392\pi$
$251$	28.8626			1.82179			0.910895	+	0.412638i	$0.135392\pi$
$252$	3.51450	+	2.45532i	0.221392	+	0.154671i
$253$	−0.610572	+	1.87915i	−0.0383863	+	0.118141i
$254$	13.9256	−	2.95998i	0.873769	−	0.185725i
$255$		0			0
$256$	−6.89912	−	1.46645i	−0.431195	−	0.0916533i
$257$	13.9401	+	24.1450i	0.869560	+	1.50612i	0.862447	+	0.506148i	$0.168931\pi$
$257$	13.9401	+	24.1450i	0.869560	+	1.50612i	0.00711374	+	0.999975i	$0.497736\pi$
$258$	2.72816	+	8.39641i	0.169848	+	0.522738i
$259$	−7.11980	+	1.65169i	−0.442403	+	0.102631i
$260$		0			0
$261$	−31.4834	−	14.0173i	−1.94877	−	0.867649i
$262$	9.87865	−	4.39826i	0.610305	−	0.271725i
$263$	−6.30557	+	2.80742i	−0.388818	+	0.173113i	−0.591829	−	0.806063i	$-0.701594\pi$
$263$	−6.30557	+	2.80742i	−0.388818	+	0.173113i	0.203011	+	0.979176i	$0.434927\pi$
$264$	−2.03458	−	0.905853i	−0.125220	−	0.0557514i
$265$		0			0
$266$	8.48630	+	9.08111i	0.520329	+	0.556799i
$267$	−3.72326	−	11.4590i	−0.227860	−	0.701281i
$268$	1.23756	+	2.14352i	0.0755963	+	0.130937i
$269$	−17.1166	−	3.63825i	−1.04362	−	0.221828i	−0.345953	−	0.938252i	$-0.612444\pi$
$269$	−17.1166	−	3.63825i	−1.04362	−	0.221828i	−0.697665	+	0.716424i	$0.745778\pi$
$270$		0			0
$271$	−11.5918	+	2.46392i	−0.704153	+	0.149672i	−0.546053	−	0.837751i	$-0.683870\pi$
$271$	−11.5918	+	2.46392i	−0.704153	+	0.149672i	−0.158100	+	0.987423i	$0.550537\pi$
$272$	−9.21069	+	28.3476i	−0.558480	+	1.71883i
$273$	−8.34110	+	3.90030i	−0.504826	+	0.236057i
$274$	−23.7397			−1.43417
$275$		0			0
$276$	2.88322	−	4.99389i	0.173550	−	0.300597i
$277$	−1.44014	−	13.7020i	−0.0865296	−	0.823274i	−0.948598	−	0.316483i	$-0.897498\pi$
$277$	−1.44014	−	13.7020i	−0.0865296	−	0.823274i	0.862069	−	0.506791i	$-0.169169\pi$
$278$	−9.78835	+	2.08058i	−0.587066	+	0.124785i
$279$	−1.90951	+	5.87688i	−0.114320	+	0.351839i
$280$		0			0
$281$	−2.06261	−	6.34806i	−0.123045	−	0.378694i	0.870495	−	0.492178i	$-0.163799\pi$
$281$	−2.06261	−	6.34806i	−0.123045	−	0.378694i	−0.993540	+	0.113484i	$0.963799\pi$
$282$	16.4908	+	28.5629i	0.982011	+	1.70089i
$283$	3.57925	+	0.760794i	0.212765	+	0.0452245i	0.313061	−	0.949733i	$-0.398646\pi$
$283$	3.57925	+	0.760794i	0.212765	+	0.0452245i	−0.100296	+	0.994958i	$0.531979\pi$
$284$	−1.02133	+	0.454727i	−0.0606050	+	0.0269831i
$285$		0			0
$286$	−0.439433	+	0.319266i	−0.0259842	+	0.0188786i
$287$	−7.32796	+	24.0599i	−0.432556	+	1.42021i
$288$	7.35602	+	5.34446i	0.433458	+	0.314926i
$289$	24.3641	+	10.8476i	1.43318	+	0.638093i
$290$		0			0
$291$	−10.5787	+	4.70996i	−0.620136	+	0.276102i
$292$	1.67808	−	1.86370i	0.0982025	−	0.109065i
$293$	−29.0587			−1.69763			−0.848813	−	0.528693i	$-0.822682\pi$
$293$	−29.0587			−1.69763			−0.848813	+	0.528693i	$0.822682\pi$
$294$	25.5396	+	17.1479i	1.48950	+	1.00009i
$295$		0			0
$296$	−6.96574	+	1.48061i	−0.404875	+	0.0860589i
$297$	1.38491	+	1.53810i	0.0803608	+	0.0892497i
$298$	−1.87236	−	17.8143i	−0.108463	−	1.03195i
$299$	3.97974	+	6.89312i	0.230155	+	0.398639i
$300$		0			0
$301$	1.73577	+	5.02372i	0.100048	+	0.289562i
$302$	1.93637	−	1.40686i	0.111426	−	0.0809555i
$303$	−8.67936	+	1.84486i	−0.498616	+	0.105984i
$304$	9.34822	+	10.3823i	0.536157	+	0.595463i
$305$		0			0
$306$	36.1861	−	40.1887i	2.06862	−	2.29744i
$307$	−27.1407			−1.54900			−0.774502	−	0.632571i	$-0.782000\pi$
$307$	−27.1407			−1.54900			−0.774502	+	0.632571i	$0.782000\pi$
$308$	0.218176	+	0.0923370i	0.0124317	+	0.00526139i
$309$	−20.1512	−	14.6407i	−1.14636	−	0.832881i
$310$		0			0
$311$	2.28225	+	21.7142i	0.129415	+	1.23130i	0.845764	+	0.533557i	$0.179145\pi$
$311$	2.28225	+	21.7142i	0.129415	+	1.23130i	−0.716349	+	0.697742i	$0.754188\pi$
$312$	−8.19607	+	3.64912i	−0.464011	+	0.206591i
$313$	−1.17706	+	11.1989i	−0.0665311	+	0.633001i	0.909550	+	0.415594i	$0.136426\pi$
$313$	−1.17706	+	11.1989i	−0.0665311	+	0.633001i	−0.976081	+	0.217407i	$0.930240\pi$
$314$	−15.3615	+	11.1608i	−0.866901	+	0.629841i
$315$		0			0
$316$	−1.88188	−	1.36726i	−0.105864	−	0.0769146i
$317$	−1.70221	+	1.89050i	−0.0956057	+	0.106181i	−0.789049	−	0.614330i	$-0.789426\pi$
$317$	−1.70221	+	1.89050i	−0.0956057	+	0.106181i	0.693443	+	0.720511i	$0.256093\pi$
$318$	−16.1280	+	27.9346i	−0.904416	+	1.56649i
$319$	−1.86279	−	0.395948i	−0.104296	−	0.0221689i
$320$		0			0
$321$	−14.0608	+	43.2745i	−0.784795	+	2.41535i
$322$	12.8671	−	23.2711i	0.717056	−	1.29685i
$323$	16.5595	−	12.0312i	0.921395	−	0.669432i
$324$	−0.589571	−	1.02117i	−0.0327540	−	0.0567315i
$325$		0			0
$326$	0.425313	−	0.736665i	0.0235559	−	0.0408001i
$327$	−37.1238	−	16.5286i	−2.05295	−	0.914031i
$328$	−7.57273	+	23.3065i	−0.418134	+	1.28688i
$329$	10.2448	+	17.0093i	0.564814	+	0.937753i
$330$		0			0
$331$	2.36394	−	2.62543i	0.129934	−	0.144306i	−0.674667	−	0.738122i	$-0.735713\pi$
$331$	2.36394	−	2.62543i	0.129934	−	0.144306i	0.804601	+	0.593816i	$0.202379\pi$
$332$	0.294031	−	0.509277i	0.0161371	−	0.0279502i
$333$	14.5798	+	3.09903i	0.798968	+	0.169826i
$334$	2.80043	−	26.6444i	0.153233	−	1.45791i
$335$		0			0
$336$	28.3454	+	19.8029i	1.54637	+	1.08034i
$337$	−9.41531	−	6.84062i	−0.512885	−	0.372633i	0.301032	−	0.953614i	$-0.402669\pi$
$337$	−9.41531	−	6.84062i	−0.512885	−	0.372633i	−0.813917	+	0.580981i	$0.802669\pi$
$338$	1.83225	−	17.4327i	0.0996614	−	0.948215i
$339$	1.61433	+	15.3593i	0.0876781	+	0.834202i
$340$		0			0
$341$	−0.0356930	+	0.339597i	−0.00193289	+	0.0183902i
$342$	−7.83287	−	24.1071i	−0.423553	−	1.30356i
$343$	15.5644	+	10.0374i	0.840400	+	0.541967i
$344$	1.60033	+	4.92531i	0.0862840	+	0.265555i
$345$		0			0
$346$	−12.9424	−	14.3740i	−0.695787	−	0.772750i
$347$	−19.6409	−	21.8134i	−1.05438	−	1.17100i	−0.984847	−	0.173424i	$-0.944517\pi$
$347$	−19.6409	−	21.8134i	−1.05438	−	1.17100i	−0.0695298	−	0.997580i	$-0.522150\pi$
$348$	5.07743	+	2.26062i	0.272179	+	0.121182i
$349$	10.2072			0.546381			0.273190	−	0.961960i	$-0.411921\pi$
$349$	10.2072			0.546381			0.273190	+	0.961960i	$0.411921\pi$
$350$		0			0
$351$	8.33762			0.445029
$352$	0.459012	+	0.204366i	0.0244654	+	0.0108927i
$353$	16.1757	+	17.9649i	0.860945	+	0.956177i	0.999415	−	0.0341900i	$-0.0108852\pi$
$353$	16.1757	+	17.9649i	0.860945	+	0.956177i	−0.138470	+	0.990367i	$0.544218\pi$
$354$	−36.1995	−	40.2037i	−1.92398	−	2.13680i
$355$		0			0
$356$	0.385902	+	1.18768i	0.0204528	+	0.0629471i
$357$	33.1955	−	38.2690i	1.75689	−	2.02541i
$358$	−3.31148	−	10.1917i	−0.175017	−	0.538648i
$359$	−1.10371	+	10.5011i	−0.0582518	+	0.554228i	0.926008	+	0.377503i	$0.123217\pi$
$359$	−1.10371	+	10.5011i	−0.0582518	+	0.554228i	−0.984260	+	0.176726i	$0.943449\pi$
$360$		0			0
$361$	0.983200	+	9.35453i	0.0517474	+	0.492343i
$362$	1.75651	−	16.7121i	0.0923202	−	0.878368i
$363$	−25.5773	−	18.5830i	−1.34246	−	0.975353i
$364$	0.864522	−	0.404251i	0.0453133	−	0.0211885i
$365$		0			0
$366$	−4.29974	+	40.9093i	−0.224751	+	2.13836i
$367$	14.5704	+	3.09703i	0.760568	+	0.161664i	0.571839	−	0.820366i	$-0.306230\pi$
$367$	14.5704	+	3.09703i	0.760568	+	0.161664i	0.188728	+	0.982029i	$0.439563\pi$
$368$	14.9448	−	25.8851i	0.779049	−	1.34935i
$369$	34.3215	−	38.1178i	1.78670	−	1.98434i
$370$		0			0
$371$	−9.39675	+	16.9947i	−0.487855	+	0.882321i
$372$	0.307954	−	0.947784i	0.0159667	−	0.0491403i
$373$	8.29672	+	3.69394i	0.429588	+	0.191265i	0.610128	−	0.792303i	$-0.291118\pi$
$373$	8.29672	+	3.69394i	0.429588	+	0.191265i	−0.180540	+	0.983568i	$0.557785\pi$
$374$	1.49420	−	2.58804i	0.0772634	−	0.133824i
$375$		0			0
$376$	9.67344	+	16.7549i	0.498869	+	0.864067i
$377$	−6.20652	+	4.50930i	−0.319652	+	0.232241i
$378$	−14.3716	−	23.8610i	−0.739195	−	1.22728i
$379$	4.37202	−	13.4557i	0.224576	−	0.691173i	−0.773759	−	0.633480i	$-0.781626\pi$
$379$	4.37202	−	13.4557i	0.224576	−	0.691173i	0.998334	−	0.0576924i	$-0.0183743\pi$
$380$		0			0
$381$	−26.6040	−	5.65486i	−1.36297	−	0.289707i
$382$	−0.980975	+	1.69910i	−0.0501911	+	0.0869335i
$383$	4.29570	−	4.77086i	0.219500	−	0.243780i	−0.623331	−	0.781958i	$-0.714221\pi$
$383$	4.29570	−	4.77086i	0.219500	−	0.243780i	0.842831	+	0.538179i	$0.180888\pi$
$384$	30.8859	+	22.4399i	1.57614	+	1.14513i
$385$		0			0
$386$	−1.00543	+	0.730489i	−0.0511751	+	0.0371809i
$387$	1.13304	−	10.7802i	0.0575958	−	0.547987i
$388$	1.09644	−	0.488169i	0.0556636	−	0.0247830i
$389$	−1.61619	−	15.3770i	−0.0819440	−	0.779645i	−0.955910	−	0.293659i	$-0.905127\pi$
$389$	−1.61619	−	15.3770i	−0.0819440	−	0.779645i	0.873966	−	0.485987i	$-0.161540\pi$
$390$		0			0
$391$	−35.4281	−	25.7400i	−1.79168	−	1.30173i
$392$	14.9815	+	10.0589i	0.756678	+	0.508053i
$393$	−20.6586			−1.04209
$394$	−22.8340	+	25.3597i	−1.15036	+	1.27760i
$395$		0			0
$396$	−0.323291	−	0.359051i	−0.0162460	−	0.0180430i
$397$	22.6772	−	4.82019i	1.13814	−	0.241918i	0.399964	−	0.916531i	$-0.369023\pi$
$397$	22.6772	−	4.82019i	1.13814	−	0.241918i	0.738172	+	0.674613i	$0.235689\pi$
$398$	0.932194	−	0.677278i	0.0467267	−	0.0339489i
$399$	−7.75449	−	22.4433i	−0.388210	−	1.12357i
$400$		0			0
$401$	−0.524412	−	0.908308i	−0.0261879	−	0.0453588i	0.852634	−	0.522508i	$-0.175003\pi$
$401$	−0.524412	−	0.908308i	−0.0261879	−	0.0453588i	−0.878822	+	0.477149i	$0.841670\pi$
$402$	−3.78593	−	36.0208i	−0.188825	−	1.79655i
$403$	0.920430	+	1.02224i	0.0458499	+	0.0509214i
$404$	0.899583	−	0.191212i	0.0447559	−	0.00951316i
$405$		0			0
$406$	23.6031	+	9.98938i	1.17140	+	0.495764i
$407$	0.823676			0.0408281
$408$	33.0287	−	36.6821i	1.63516	−	1.81603i
$409$	5.20370	−	2.31684i	0.257307	−	0.114560i	−0.274030	−	0.961721i	$-0.588357\pi$
$409$	5.20370	−	2.31684i	0.257307	−	0.114560i	0.531336	+	0.847161i	$0.321690\pi$
$410$		0			0
$411$	41.4323	+	18.4468i	2.04370	+	0.909916i
$412$	2.08860	+	1.51745i	0.102898	+	0.0747596i
$413$	−22.2380	−	23.7967i	−1.09426	−	1.17096i
$414$	−43.8730	+	31.8756i	−2.15624	+	1.56660i
$415$		0			0
$416$	1.84908	−	0.823263i	0.0906585	−	0.0403638i
$417$	18.7001	+	3.97482i	0.915747	+	0.194648i
$418$	−0.700354	−	1.21305i	−0.0342554	−	0.0593321i
$419$	−6.28785	−	19.3520i	−0.307182	−	0.945407i	−0.978854	−	0.204559i	$-0.934424\pi$
$419$	−6.28785	−	19.3520i	−0.307182	−	0.945407i	0.671673	−	0.740848i	$-0.265576\pi$
$420$		0			0
$421$	9.00232	−	27.7063i	0.438746	−	1.35032i	−0.450452	−	0.892801i	$-0.648737\pi$
$421$	9.00232	−	27.7063i	0.438746	−	1.35032i	0.889198	−	0.457522i	$-0.151263\pi$
$422$	15.6230	−	3.32077i	0.760515	−	0.161652i
$423$	−4.23282	−	40.2726i	−0.205807	−	1.95812i
$424$	−9.46066	+	16.3864i	−0.459450	+	0.795792i
$425$		0			0
$426$	16.3598			0.792636
$427$	−2.13222	+	24.6729i	−0.103185	+	1.19400i
$428$	1.45734	−	4.48524i	0.0704433	−	0.216802i
$429$	1.01502	−	0.215748i	0.0490054	−	0.0104164i
$430$		0			0
$431$	−17.9763	−	3.82098i	−0.865888	−	0.184050i	−0.246507	−	0.969141i	$-0.579283\pi$
$431$	−17.9763	−	3.82098i	−0.865888	−	0.184050i	−0.619381	+	0.785091i	$0.712616\pi$
$432$	−15.6547	−	27.1148i	−0.753189	−	1.30456i
$433$	−4.04392	−	12.4459i	−0.194338	−	0.598112i	−0.999984	−	0.00571375i	$-0.998181\pi$
$433$	−4.04392	−	12.4459i	−0.194338	−	0.598112i	0.805645	−	0.592398i	$-0.201819\pi$
$434$	1.33894	−	4.39616i	0.0642714	−	0.211023i
$435$		0			0
$436$	3.84773	+	1.71312i	0.184273	+	0.0820436i
$437$	−18.7512	+	8.34856i	−0.896990	+	0.399366i
$438$	−33.5254	+	14.9265i	−1.60191	+	0.713214i
$439$	11.2173	+	4.99428i	0.535374	+	0.238364i	0.656570	−	0.754265i	$-0.272006\pi$
$439$	11.2173	+	4.99428i	0.535374	+	0.238364i	−0.121197	+	0.992629i	$0.538673\pi$
$440$		0			0
$441$	−20.0828	−	31.9880i	−0.956326	−	1.52324i
$442$	−3.72008	−	11.4492i	−0.176946	−	0.544585i
$443$	−0.410405	−	0.710842i	−0.0194989	−	0.0337731i	0.856111	−	0.516792i	$-0.172874\pi$
$443$	−0.410405	−	0.710842i	−0.0194989	−	0.0337731i	−0.875610	+	0.483018i	$0.839540\pi$
$444$	−2.35134	−	0.499792i	−0.111589	−	0.0237191i
$445$		0			0
$446$	−11.8200	+	2.51241i	−0.559692	+	0.118966i
$447$	−10.5748	+	32.5458i	−0.500169	+	1.53936i
$448$	14.0219	+	9.79611i	0.662474	+	0.462823i
$449$	31.7045			1.49623			0.748114	−	0.663570i	$-0.230960\pi$
$449$	31.7045			1.49623			0.748114	+	0.663570i	$0.230960\pi$
$450$		0			0
$451$	1.41721	−	2.45468i	0.0667337	−	0.115586i
$452$	−0.167319	−	1.59193i	−0.00787000	−	0.0748781i
$453$	−4.47270	+	0.950701i	−0.210146	+	0.0446678i
$454$	−0.760315	+	2.34001i	−0.0356834	+	0.109822i
$455$		0			0
$456$	−7.14942	−	22.0036i	−0.334802	−	1.03041i
$457$	−0.705719	−	1.22234i	−0.0330121	−	0.0571787i	0.849047	−	0.528317i	$-0.177177\pi$
$457$	−0.705719	−	1.22234i	−0.0330121	−	0.0571787i	−0.882059	+	0.471138i	$0.843843\pi$
$458$	−12.6203	−	2.68253i	−0.589709	−	0.125347i
$459$	−41.9061	+	18.6578i	−1.95601	+	0.870872i
$460$		0			0
$461$	−8.04550	+	5.84539i	−0.374716	+	0.272247i	−0.759164	−	0.650900i	$-0.774392\pi$
$461$	−8.04550	+	5.84539i	−0.374716	+	0.272247i	0.384448	+	0.923147i	$0.374392\pi$
$462$	−2.36702	−	2.53293i	−0.110124	−	0.117843i
$463$	9.91031	+	7.20026i	0.460571	+	0.334624i	0.793755	−	0.608237i	$-0.208123\pi$
$463$	9.91031	+	7.20026i	0.460571	+	0.334624i	−0.333184	+	0.942862i	$0.608123\pi$
$464$	26.3181	+	11.7176i	1.22179	+	0.543974i
$465$		0			0
$466$	−22.7475	+	10.1278i	−1.05376	+	0.469162i
$467$	23.6640	−	26.2816i	1.09504	−	1.21617i	0.120320	−	0.992735i	$-0.461608\pi$
$467$	23.6640	−	26.2816i	1.09504	−	1.21617i	0.974720	−	0.223430i	$-0.0717256\pi$
$468$	−1.94631			−0.0899684
$469$	−2.68038	−	21.6401i	−0.123769	−	0.999248i
$470$		0			0
$471$	35.4826	−	7.54205i	1.63495	−	0.347520i
$472$	−21.2345	−	23.5833i	−0.977399	−	1.08551i
$473$	−0.0626116	−	0.595710i	−0.00287889	−	0.0273908i
$474$	17.0194	+	29.4785i	0.781728	+	1.35399i
$475$		0			0
$476$	−3.44059	+	3.96644i	−0.157699	+	0.181801i
$477$	32.0401	−	23.2785i	1.46702	−	1.06585i
$478$	27.2486	−	5.79186i	1.24632	−	0.264913i
$479$	14.9312	+	16.5827i	0.682222	+	0.757685i	0.980441	−	0.196813i	$-0.0630592\pi$
$479$	14.9312	+	16.5827i	0.682222	+	0.757685i	−0.298219	+	0.954498i	$0.596392\pi$
$480$		0			0
$481$	2.22023	−	2.46581i	0.101234	−	0.112431i
$482$	12.8335			0.584552
$483$	−40.5394	+	30.6161i	−1.84461	+	1.39308i
$484$	2.65098	+	1.92605i	0.120499	+	0.0875479i
$485$		0			0
$486$	−1.49786	−	14.2511i	−0.0679441	−	0.646445i
$487$	10.2874	−	4.58024i	0.466166	−	0.207550i	−0.160192	−	0.987086i	$-0.551211\pi$
$487$	10.2874	−	4.58024i	0.466166	−	0.207550i	0.626358	+	0.779535i	$0.284545\pi$
$488$	−2.52222	+	23.9973i	−0.114175	+	1.08631i
$489$	−1.31471	+	0.955195i	−0.0594534	+	0.0431954i
$490$		0			0
$491$	28.1497	+	20.4520i	1.27038	+	0.922985i	0.999218	−	0.0395486i	$-0.0125920\pi$
$491$	28.1497	+	20.4520i	1.27038	+	0.922985i	0.271162	+	0.962534i	$0.412592\pi$
$492$	−5.53514	+	6.14739i	−0.249543	+	0.277146i
$493$	21.1040	−	36.5532i	0.950478	−	1.64628i
$494$	−5.51928	−	1.17316i	−0.248324	−	0.0527830i
$495$		0			0
$496$	1.59623	−	4.91270i	0.0716729	−	0.220587i
$497$	9.84762	−	0.182343i	0.441726	−	0.00817920i
$498$	−6.96181	+	5.05805i	−0.311966	+	0.226657i
$499$	−18.7370	−	32.4534i	−0.838784	−	1.45282i	−0.890912	−	0.454176i	$-0.849934\pi$
$499$	−18.7370	−	32.4534i	−0.838784	−	1.45282i	0.0521285	−	0.998640i	$-0.483399\pi$
$500$		0			0
$501$	−25.5915	+	44.3257i	−1.14334	+	1.98033i
$502$	39.9907	+	17.8050i	1.78487	+	0.794677i
$503$	−2.43561	+	7.49603i	−0.108598	+	0.334231i	−0.990558	−	0.137093i	$-0.956224\pi$
$503$	−2.43561	+	7.49603i	−0.108598	+	0.334231i	0.881960	+	0.471325i	$0.156224\pi$
$504$	−18.9873	−	31.5243i	−0.845759	−	1.40420i
$505$		0			0
$506$	−2.00521	+	2.22701i	−0.0891423	+	0.0990026i
$507$	−16.7438	+	29.0012i	−0.743620	+	1.28799i
$508$	2.75741	+	0.586105i	0.122340	+	0.0260042i
$509$	−2.82188	+	26.8484i	−0.125078	+	1.19003i	0.734348	+	0.678773i	$0.237488\pi$
$509$	−2.82188	+	26.8484i	−0.125078	+	1.19003i	−0.859425	+	0.511261i	$0.829179\pi$
$510$		0			0
$511$	−20.0139	+	9.35850i	−0.885362	+	0.413995i
$512$	12.6643	+	9.20115i	0.559688	+	0.406637i
$513$	−2.24745	+	21.3830i	−0.0992273	+	0.944085i
$514$	4.42003	+	42.0537i	0.194959	+	1.85491i
$515$		0			0
$516$	−0.182730	+	1.73856i	−0.00804422	+	0.0765357i
$517$	−0.691491	−	2.12819i	−0.0304117	−	0.0935977i
$518$	−10.8838	−	2.10361i	−0.478206	−	0.0924274i
$519$	11.4188	+	35.1434i	0.501229	+	1.54262i
$520$		0			0
$521$	16.9031	+	18.7727i	0.740536	+	0.822449i	0.989266	−	0.146124i	$-0.0466799\pi$
$521$	16.9031	+	18.7727i	0.740536	+	0.822449i	−0.248730	+	0.968573i	$0.580013\pi$
$522$	−34.9748	−	38.8435i	−1.53081	−	1.70013i
$523$	−9.56231	−	4.25741i	−0.418131	−	0.186164i	0.186877	−	0.982383i	$-0.440163\pi$
$523$	−9.56231	−	4.25741i	−0.418131	−	0.186164i	−0.605008	+	0.796220i	$0.706830\pi$
$524$	2.14119			0.0935381
$525$		0			0
$526$	−10.4686			−0.456452
$527$	−6.91377	−	3.07821i	−0.301169	−	0.134089i
$528$	−2.60743	−	2.89585i	−0.113474	−	0.126026i
$529$	13.9939	+	15.5418i	0.608431	+	0.675731i
$530$		0			0
$531$	20.5257	+	63.1717i	0.890741	+	2.74142i
$532$	0.803723	+	2.32616i	0.0348458	+	0.100852i
$533$	−3.52839	−	10.8593i	−0.152832	−	0.470367i
$534$	1.91016	−	18.1740i	0.0826607	−	0.786464i
$535$		0			0
$536$	−2.22082	−	21.1297i	−0.0959247	−	0.912663i
$537$	−2.13998	+	20.3605i	−0.0923468	+	0.878621i
$538$	−21.4716	−	15.6000i	−0.925707	−	0.672566i
$539$	−1.45304	−	1.49829i	−0.0625867	−	0.0645358i
$540$		0			0
$541$	2.44752	−	23.2866i	0.105227	−	1.00117i	−0.806740	−	0.590907i	$-0.798770\pi$
$541$	2.44752	−	23.2866i	0.105227	−	1.00117i	0.911967	−	0.410263i	$-0.134563\pi$
$542$	−17.5811	−	3.73697i	−0.755172	−	0.160517i
$543$	−16.0517	+	27.8023i	−0.688844	+	1.19311i
$544$	−7.45145	+	8.27568i	−0.319478	+	0.354817i
$545$		0			0
$546$	−13.9631	+	0.258547i	−0.597566	+	0.0110648i
$547$	10.7915	−	33.2127i	0.461409	−	1.42007i	−0.402034	−	0.915625i	$-0.631697\pi$
$547$	10.7915	−	33.2127i	0.461409	−	1.42007i	0.863443	−	0.504447i	$-0.168303\pi$
$548$	−4.29430	−	1.91194i	−0.183443	−	0.0816742i
$549$	25.2524	−	43.7384i	1.07775	−	1.86671i
$550$		0			0
$551$	−9.89175	−	17.1330i	−0.421403	−	0.729891i
$552$	−40.0448	+	29.0943i	−1.70442	+	1.23833i
$553$	10.5732	+	17.5546i	0.449619	+	0.746496i
$554$	6.45723	−	19.8733i	0.274341	−	0.844336i
$555$		0			0
$556$	−1.93819	−	0.411975i	−0.0821976	−	0.0174716i
$557$	11.7770	−	20.3983i	0.499006	−	0.864304i	−0.500993	−	0.865451i	$-0.667032\pi$
$557$	11.7770	−	20.3983i	0.499006	−	0.864304i	0.999999	+	0.00114721i	$0.000365170\pi$
$558$	−6.27112	+	6.96478i	−0.265478	+	0.294843i
$559$	−1.95213	−	1.41831i	−0.0825663	−	0.0599879i
$560$		0			0
$561$	−4.61882	+	3.35577i	−0.195007	+	0.141681i
$562$	1.05819	−	10.0680i	0.0446370	−	0.424693i
$563$	−1.59921	+	0.712014i	−0.0673986	+	0.0300078i	−0.440159	−	0.897920i	$-0.645078\pi$
$563$	−1.59921	+	0.712014i	−0.0673986	+	0.0300078i	0.372761	+	0.927928i	$0.378411\pi$
$564$	0.682641	+	6.49490i	0.0287444	+	0.273485i
$565$		0			0
$566$	4.48993	+	3.26213i	0.188726	+	0.137117i
$567$	1.27693	+	10.3093i	0.0536258	+	0.432949i
$568$	9.59662			0.402665
$569$	−5.88851	+	6.53985i	−0.246859	+	0.274165i	−0.853822	−	0.520566i	$-0.825721\pi$
$569$	−5.88851	+	6.53985i	−0.246859	+	0.274165i	0.606963	+	0.794730i	$0.292388\pi$
$570$		0			0
$571$	1.04634	+	1.16208i	0.0437882	+	0.0486317i	0.764641	−	0.644456i	$-0.222916\pi$
$571$	1.04634	+	1.16208i	0.0437882	+	0.0486317i	−0.720853	+	0.693088i	$0.756250\pi$
$572$	−0.105202	+	0.0223615i	−0.00439874	+	0.000934981i
$573$	3.03235	−	2.20313i	0.126678	−	0.0920372i
$574$	−24.9956	+	28.8159i	−1.04330	+	1.20275i
$575$		0			0
$576$	−17.4417	−	30.2099i	−0.726736	−	1.25874i
$577$	−1.53555	−	14.6098i	−0.0639259	−	0.608214i	−0.978849	−	0.204585i	$-0.934415\pi$
$577$	−1.53555	−	14.6098i	−0.0639259	−	0.608214i	0.914923	−	0.403629i	$-0.132251\pi$
$578$	27.0660	+	30.0599i	1.12580	+	1.25033i
$579$	2.32238	−	0.493637i	0.0965149	−	0.0205149i
$580$		0			0
$581$	−4.13421	+	3.12224i	−0.171516	+	0.129532i
$582$	−17.5629			−0.728008
$583$	1.46439	−	1.62637i	0.0606487	−	0.0673572i
$584$	−19.6659	+	8.75582i	−0.813781	+	0.362318i
$585$		0			0
$586$	−40.2624	−	17.9260i	−1.66323	−	0.740516i
$587$	6.29204	+	4.57144i	0.259700	+	0.188683i	0.710015	−	0.704187i	$-0.248688\pi$
$587$	6.29204	+	4.57144i	0.259700	+	0.188683i	−0.450315	+	0.892870i	$0.648688\pi$
$588$	3.23883	+	5.15882i	0.133567	+	0.212746i
$589$	−2.86979	+	2.08503i	−0.118248	+	0.0859120i
$590$		0			0
$591$	59.5572	−	26.5166i	2.44986	−	1.09075i
$592$	−12.1878	−	2.59059i	−0.500915	−	0.106473i
$593$	5.57226	+	9.65143i	0.228825	+	0.396337i	0.957460	−	0.288565i	$-0.0931783\pi$
$593$	5.57226	+	9.65143i	0.228825	+	0.396337i	−0.728635	+	0.684902i	$0.759845\pi$
$594$	0.970036	+	2.98546i	0.0398011	+	0.122495i
$595$		0			0
$596$	1.09603	−	3.37324i	0.0448953	−	0.138173i
$597$	−2.15321	+	0.457680i	−0.0881251	+	0.0187316i
$598$	1.26187	+	12.0059i	0.0516016	+	0.490956i
$599$	−8.65074	+	14.9835i	−0.353460	+	0.612210i	−0.986853	−	0.161620i	$-0.948328\pi$
$599$	−8.65074	+	14.9835i	−0.353460	+	0.612210i	0.633393	+	0.773830i	$0.281662\pi$
$600$		0			0
$601$	5.91240			0.241172			0.120586	−	0.992703i	$-0.461523\pi$
$601$	5.91240			0.241172			0.120586	+	0.992703i	$0.461523\pi$
$602$	−0.694073	+	8.03142i	−0.0282883	+	0.327336i
$603$	−13.7418	+	42.2931i	−0.559611	+	1.72231i
$604$	0.463578	−	0.0985365i	0.0188627	−	0.00400939i
$605$		0			0
$606$	−13.1638	−	2.79806i	−0.534744	−	0.113663i
$607$	−19.4043	−	33.6092i	−0.787595	−	1.36415i	−0.927437	−	0.373980i	$-0.877993\pi$
$607$	−19.4043	−	33.6092i	−0.787595	−	1.36415i	0.139842	−	0.990174i	$-0.455341\pi$
$608$	1.61295	+	4.96414i	0.0654137	+	0.201323i
$609$	−33.4317	−	35.7749i	−1.35472	−	1.44967i
$610$		0			0
$611$	−8.23503	−	3.66647i	−0.333154	−	0.148329i
$612$	9.78246	−	4.35543i	0.395432	−	0.176058i
$613$	−10.8976	+	4.85190i	−0.440148	+	0.195967i	−0.614832	−	0.788658i	$-0.710776\pi$
$613$	−10.8976	+	4.85190i	−0.440148	+	0.195967i	0.174684	+	0.984625i	$0.444110\pi$
$614$	−37.6050	−	16.7428i	−1.51762	−	0.675686i
$615$		0			0
$616$	−1.38849	−	1.48581i	−0.0559438	−	0.0598649i
$617$	8.08939	+	24.8966i	0.325667	+	1.00230i	0.971139	+	0.238515i	$0.0766607\pi$
$617$	8.08939	+	24.8966i	0.325667	+	1.00230i	−0.645472	+	0.763784i	$0.723339\pi$
$618$	−18.8889	−	32.7166i	−0.759824	−	1.31605i
$619$	23.8295	+	5.06511i	0.957787	+	0.203584i	0.660182	−	0.751105i	$-0.270479\pi$
$619$	23.8295	+	5.06511i	0.957787	+	0.203584i	0.297605	+	0.954689i	$0.403812\pi$
$620$		0			0
$621$	44.9946	−	9.56390i	1.80557	−	0.383786i
$622$	−10.2331	+	31.4941i	−0.410308	+	1.26280i
$623$	0.947238	−	10.9609i	0.0379503	−	0.439140i
$624$	−15.6976			−0.628407
$625$		0			0
$626$	−8.53938	+	14.7906i	−0.341302	+	0.591153i
$627$	0.279715	+	2.66131i	0.0111708	+	0.106283i
$628$	−3.67763	+	0.781705i	−0.146753	+	0.0311934i
$629$	−5.64124	+	17.3619i	−0.224931	+	0.692266i
$630$		0			0
$631$	4.79933	+	14.7708i	0.191058	+	0.588017i	1.00000		0.000127907i	$4.07141e-5\pi$
$631$	4.79933	+	14.7708i	0.191058	+	0.588017i	−0.808942	+	0.587889i	$0.799959\pi$
$632$	9.98354	+	17.2920i	0.397124	+	0.687839i
$633$	−29.8468	−	6.34413i	−1.18630	−	0.252157i
$634$	−3.52474	+	1.56931i	−0.139985	+	0.0623254i
$635$		0			0
$636$	−5.16722	+	3.75420i	−0.204893	+	0.148864i
$637$	−8.40206	+	0.311260i	−0.332902	+	0.0123326i
$638$	−2.33674	−	1.69774i	−0.0925126	−	0.0672143i
$639$	−18.3499	−	8.16989i	−0.725910	−	0.323196i
$640$		0			0
$641$	−26.9427	+	11.9957i	−1.06417	+	0.473800i	−0.862712	−	0.505696i	$-0.831236\pi$
$641$	−26.9427	+	11.9957i	−1.06417	+	0.473800i	−0.201461	+	0.979496i	$0.564569\pi$
$642$	−46.1776	+	51.2854i	−1.82248	+	2.02407i
$643$	36.3038			1.43168			0.715840	−	0.698264i	$-0.246044\pi$
$643$	36.3038			1.43168			0.715840	+	0.698264i	$0.246044\pi$
$644$	4.20175	−	3.17324i	0.165572	−	0.125043i
$645$		0			0
$646$	30.3660	−	6.45449i	1.19473	−	0.253949i
$647$	10.7279	+	11.9145i	0.421757	+	0.468408i	0.916153	−	0.400828i	$-0.131278\pi$
$647$	10.7279	+	11.9145i	0.421757	+	0.468408i	−0.494396	+	0.869237i	$0.664611\pi$
$648$	1.05799	+	10.0661i	0.0415618	+	0.395434i
$649$	1.83525	+	3.17875i	0.0720399	+	0.124777i
$650$		0			0
$651$	−5.75285	+	6.63210i	−0.225472	+	0.259932i
$652$	0.136265	−	0.0990022i	0.00533654	−	0.00387723i
$653$	17.8633	−	3.79695i	0.699044	−	0.148586i	0.155337	−	0.987862i	$-0.450354\pi$
$653$	17.8633	−	3.79695i	0.699044	−	0.148586i	0.543707	+	0.839275i	$0.317020\pi$
$654$	−41.2407	−	45.8025i	−1.61264	−	1.79102i
$655$		0			0
$656$	−28.6906	+	31.8641i	−1.12018	+	1.24408i
$657$	45.0576			1.75786
$658$	3.70189	+	29.8873i	0.144315	+	1.16513i
$659$	3.05262	+	2.21786i	0.118913	+	0.0863955i	0.645652	−	0.763632i	$-0.276586\pi$
$659$	3.05262	+	2.21786i	0.118913	+	0.0863955i	−0.526739	+	0.850027i	$0.676586\pi$
$660$		0			0
$661$	−0.186726	−	1.77658i	−0.00726282	−	0.0691011i	0.990290	−	0.139016i	$-0.0443939\pi$
$661$	−0.186726	−	1.77658i	−0.00726282	−	0.0691011i	−0.997553	+	0.0699148i	$0.977727\pi$
$662$	4.89497	−	2.17938i	0.190249	−	0.0847041i
$663$	−2.40402	+	22.8728i	−0.0933646	+	0.888304i
$664$	−4.08378	+	2.96704i	−0.158481	+	0.115143i
$665$		0			0
$666$	18.2894	+	13.2880i	0.708699	+	0.514900i
$667$	−28.3214	+	31.4541i	−1.09661	+	1.21791i
$668$	2.65245	−	4.59419i	0.102627	−	0.177754i
$669$	22.5814	+	4.79982i	0.873047	+	0.185572i
$670$		0			0
$671$	0.862429	−	2.65428i	0.0332937	−	0.102468i
$672$	6.66533	+	11.0664i	0.257121	+	0.426894i
$673$	22.2615	−	16.1740i	0.858119	−	0.623460i	−0.0692535	−	0.997599i	$-0.522062\pi$
$673$	22.2615	−	16.1740i	0.858119	−	0.623460i	0.927373	+	0.374139i	$0.122062\pi$
$674$	−8.82553	−	15.2863i	−0.339947	−	0.588805i
$675$		0			0
$676$	1.73543	−	3.00586i	0.0667474	−	0.115610i
$677$	26.8331	+	11.9469i	1.03128	+	0.459156i	0.851391	−	0.524531i	$-0.175759\pi$
$677$	26.8331	+	11.9469i	1.03128	+	0.459156i	0.179889	+	0.983687i	$0.442426\pi$
$678$	−7.23824	+	22.2770i	−0.277983	+	0.855543i
$679$	−10.5718	+	0.195753i	−0.405710	+	0.00751230i
$680$		0			0
$681$	3.14526	−	3.49316i	0.120527	−	0.133858i
$682$	−0.258948	+	0.448512i	−0.00991564	+	0.0171744i
$683$	19.3327	+	4.10929i	0.739746	+	0.157238i	0.562347	−	0.826901i	$-0.309899\pi$
$683$	19.3327	+	4.10929i	0.739746	+	0.157238i	0.177399	+	0.984139i	$0.443232\pi$
$684$	0.524639	−	4.99160i	0.0200601	−	0.190859i
$685$		0			0
$686$	15.3734	+	23.5089i	0.586961	+	0.897572i
$687$	19.9415	+	14.4883i	0.760816	+	0.552765i
$688$	−0.947151	+	9.01154i	−0.0361098	+	0.343562i
$689$	−0.921532	−	8.76779i	−0.0351076	−	0.334026i
$690$		0			0
$691$	−3.53308	+	33.6150i	−0.134405	+	1.27877i	0.694545	+	0.719450i	$0.255606\pi$
$691$	−3.53308	+	33.6150i	−0.134405	+	1.27877i	−0.828949	+	0.559324i	$0.811061\pi$
$692$	−1.18351	−	3.64248i	−0.0449904	−	0.138466i
$693$	1.39004	+	4.02310i	0.0528033	+	0.152825i
$694$	−13.7571	−	42.3399i	−0.522211	−	1.60720i
$695$		0			0
$696$	−31.9231	−	35.4542i	−1.21004	−	1.34389i
$697$	42.0349	+	46.6845i	1.59219	+	1.76830i
$698$	14.1427	+	6.29674i	0.535309	+	0.238335i
$699$	47.5704			1.79928
$700$		0			0
$701$	−39.9977			−1.51069			−0.755347	−	0.655325i	$-0.772532\pi$
$701$	−39.9977			−1.51069			−0.755347	+	0.655325i	$0.772532\pi$
$702$	11.5522	+	5.14339i	0.436011	+	0.194125i
$703$	5.72547	+	6.35877i	0.215940	+	0.239826i
$704$	−1.28985	−	1.43252i	−0.0486129	−	0.0539901i
$705$		0			0
$706$	11.3300	+	34.8700i	0.426409	+	1.31235i
$707$	−7.95501	−	1.53754i	−0.299179	−	0.0578251i
$708$	−3.31026	−	10.1879i	−0.124407	−	0.382885i
$709$	1.65323	−	15.7294i	0.0620884	−	0.590732i	−0.918605	−	0.395178i	$-0.870683\pi$
$709$	1.65323	−	15.7294i	0.0620884	−	0.590732i	0.980693	−	0.195554i	$-0.0626504\pi$
$710$		0			0
$711$	−4.36851	−	41.5636i	−0.163832	−	1.55876i
$712$	1.12049	−	10.6608i	0.0419923	−	0.399530i
$713$	6.13976	+	4.46079i	0.229936	+	0.167058i
$714$	69.6021	−	32.5459i	2.60479	−	1.21800i
$715$		0			0
$716$	0.221800	−	2.11029i	0.00828907	−	0.0788652i
$717$	−52.0568	−	11.0650i	−1.94410	−	0.413231i
$718$	−8.00729	+	13.8690i	−0.298829	+	0.517588i
$719$	−0.704671	+	0.782616i	−0.0262798	+	0.0291867i	−0.756141	−	0.654408i	$-0.772918\pi$
$719$	−0.704671	+	0.782616i	−0.0262798	+	0.0291867i	0.729862	+	0.683595i	$0.239584\pi$
$720$		0			0
$721$	−11.7346	−	19.4829i	−0.437021	−	0.725580i
$722$	−4.40843	+	13.5677i	−0.164065	+	0.504939i
$723$	−22.3981	−	9.97226i	−0.832993	−	0.370872i
$724$	1.66370	−	2.88160i	0.0618307	−	0.107094i
$725$		0			0
$726$	−23.9751	−	41.5261i	−0.889799	−	1.54118i
$727$	20.2978	−	14.7472i	0.752804	−	0.546944i	−0.143891	−	0.989594i	$-0.545961\pi$
$727$	20.2978	−	14.7472i	0.752804	−	0.546944i	0.896695	+	0.442650i	$0.145961\pi$
$728$	−8.19072	+	0.151663i	−0.303568	+	0.00562101i
$729$	−12.0995	+	37.2385i	−0.448131	+	1.37921i
$730$		0			0
$731$	12.9856	+	2.76016i	0.480288	+	0.102088i
$732$	−4.07254	+	7.05384i	−0.150525	+	0.260718i
$733$	8.67451	−	9.63402i	0.320400	−	0.355841i	−0.561332	−	0.827591i	$-0.689711\pi$
$733$	8.67451	−	9.63402i	0.320400	−	0.355841i	0.881732	+	0.471750i	$0.156378\pi$
$734$	18.2776	+	13.2794i	0.674637	+	0.490152i
$735$		0			0
$736$	9.03434	−	6.56383i	0.333010	−	0.241946i
$737$	−0.256866	+	2.44391i	−0.00946177	+	0.0900227i
$738$	71.0688	−	31.6419i	2.61608	−	1.16475i
$739$	−3.94087	−	37.4949i	−0.144967	−	1.37927i	−0.789056	−	0.614322i	$-0.789430\pi$
$739$	−3.94087	−	37.4949i	−0.144967	−	1.37927i	0.644088	−	0.764951i	$-0.277237\pi$
$740$		0			0
$741$	8.72107	+	6.33623i	0.320377	+	0.232767i
$742$	−23.5036	+	17.7503i	−0.862843	+	0.651636i
$743$	15.1585			0.556113			0.278057	−	0.960565i	$-0.410310\pi$
$743$	15.1585			0.556113			0.278057	+	0.960565i	$0.410310\pi$
$744$	−5.72393	+	6.35707i	−0.209850	+	0.233062i
$745$		0			0
$746$	9.21682	+	10.2363i	0.337452	+	0.374778i
$747$	10.3346	−	2.19668i	0.378123	−	0.0803725i
$748$	0.478723	−	0.347813i	0.0175038	−	0.0127173i
$749$	−27.2245	+	31.3854i	−0.994761	+	1.14680i
$750$		0			0
$751$	1.14689	+	1.98648i	0.0418508	+	0.0724877i	0.886192	−	0.463318i	$-0.153341\pi$
$751$	1.14689	+	1.98648i	0.0418508	+	0.0724877i	−0.844341	+	0.535806i	$0.820008\pi$
$752$	3.53837	+	33.6653i	0.129031	+	1.22765i
$753$	−55.9595	−	62.1494i	−2.03928	−	2.26485i
$754$	−11.3812	+	2.41915i	−0.414479	+	0.0881003i
$755$		0			0
$756$	−0.677981	−	5.47369i	−0.0246579	−	0.199076i
$757$	−46.5833			−1.69310			−0.846549	−	0.532311i	$-0.821324\pi$
$757$	−46.5833			−1.69310			−0.846549	+	0.532311i	$0.821324\pi$
$758$	14.3584	−	15.9466i	0.521519	−	0.579206i
$759$	5.23013	−	2.32860i	0.189842	−	0.0845230i
$760$		0			0
$761$	0.852466	+	0.379543i	0.0309019	+	0.0137584i	0.422129	−	0.906536i	$-0.361283\pi$
$761$	0.852466	+	0.379543i	0.0309019	+	0.0137584i	−0.391228	+	0.920294i	$0.627949\pi$
$762$	−33.3730	−	24.2469i	−1.20897	−	0.878372i
$763$	−25.3349	−	27.1107i	−0.917186	−	0.981472i
$764$	−0.314292	+	0.228346i	−0.0113707	+	0.00826128i
$765$		0			0
$766$	8.89503	−	3.96032i	0.321390	−	0.143092i
$767$	14.4631	+	3.07422i	0.522231	+	0.111004i
$768$	10.2185	+	17.6990i	0.368728	+	0.638656i
$769$	9.05322	+	27.8629i	0.326467	+	1.00476i	0.970774	+	0.239996i	$0.0771461\pi$
$769$	9.05322	+	27.8629i	0.326467	+	1.00476i	−0.644307	+	0.764767i	$0.722854\pi$
$770$		0			0
$771$	24.9636	−	76.8299i	0.899041	−	2.76696i
$772$	−0.240706	+	0.0511636i	−0.00866319	+	0.00184142i
$773$	4.82603	+	45.9166i	0.173580	+	1.65150i	0.641052	+	0.767497i	$0.278498\pi$
$773$	4.82603	+	45.9166i	0.173580	+	1.65150i	−0.467472	+	0.884008i	$0.654835\pi$
$774$	8.22007	−	14.2376i	0.295464	−	0.511759i
$775$		0			0
$776$	−10.3024			−0.369834
$777$	17.3606	+	12.1286i	0.622808	+	0.435111i
$778$	7.24659	−	22.3027i	0.259803	−	0.799591i
$779$	28.8013	−	6.12190i	1.03191	−	0.219340i
$780$		0			0
$781$	−1.08572	−	0.230776i	−0.0388500	−	0.00825782i
$782$	−33.2089	−	57.5194i	−1.18755	−	2.05689i
$783$	13.7007	+	42.1665i	0.489624	+	1.50691i
$784$	16.7880	+	26.7400i	0.599571	+	0.954998i
$785$		0			0
$786$	−28.6237	−	12.7441i	−1.02097	−	0.454566i
$787$	14.0236	−	6.24373i	0.499889	−	0.222565i	−0.141273	−	0.989971i	$-0.545119\pi$
$787$	14.0236	−	6.24373i	0.499889	−	0.222565i	0.641162	+	0.767406i	$0.278453\pi$
$788$	−6.17288	+	2.74834i	−0.219900	+	0.0979056i
$789$	18.2706	+	8.13459i	0.650450	+	0.289599i
$790$		0			0
$791$	−4.10869	+	13.4901i	−0.146088	+	0.479652i
$792$	1.28158	+	3.94429i	0.0455389	+	0.140154i
$793$	−5.62137	−	9.73649i	−0.199621	−	0.345753i
$794$	34.3940	+	7.31068i	1.22060	+	0.259446i
$795$		0			0
$796$	0.223172	−	0.0474367i	0.00791013	−	0.00168135i
$797$	1.38592	−	4.26542i	0.0490918	−	0.151089i	−0.923506	−	0.383585i	$-0.874689\pi$
$797$	1.38592	−	4.26542i	0.0490918	−	0.151089i	0.972597	+	0.232496i	$0.0746893\pi$
$798$	3.10075	−	35.8801i	0.109765	−	1.27014i
$799$	49.5952			1.75455
$800$		0			0
$801$	−11.2184	+	19.4308i	−0.396381	+	0.686553i
$802$	−0.166277	−	1.58202i	−0.00587143	−	0.0558629i
$803$	2.43546	−	0.517673i	0.0859456	−	0.0182683i
$804$	2.21619	−	6.82075i	0.0781592	−	0.240549i
$805$		0			0
$806$	0.644698	+	1.98418i	0.0227085	+	0.0698896i
$807$	25.3519	+	43.9108i	0.892430	+	1.54573i
$808$	−7.72186	−	1.64133i	−0.271654	−	0.0577418i
$809$	−28.5118	+	12.6943i	−1.00242	+	0.446307i	−0.841266	−	0.540622i	$-0.818189\pi$
$809$	−28.5118	+	12.6943i	−1.00242	+	0.446307i	−0.161156	+	0.986929i	$0.551522\pi$
$810$		0			0
$811$	21.7660	−	15.8139i	0.764308	−	0.555302i	−0.135921	−	0.990720i	$-0.543399\pi$
$811$	21.7660	−	15.8139i	0.764308	−	0.555302i	0.900229	+	0.435418i	$0.143399\pi$
$812$	3.46507	+	3.70793i	0.121600	+	0.130123i
$813$	27.7800	+	20.1834i	0.974289	+	0.707862i
$814$	1.14125	+	0.508117i	0.0400007	+	0.0178095i
$815$		0			0
$816$	78.8984	−	35.1278i	2.76200	−	1.22972i
$817$	4.16366	−	4.62421i	0.145668	−	0.161781i
$818$	8.63926			0.302065
$819$	15.7907	+	6.68300i	0.551773	+	0.233523i
$820$		0			0
$821$	13.8680	−	2.94774i	0.483998	−	0.102877i	0.0405509	−	0.999177i	$-0.487089\pi$
$821$	13.8680	−	2.94774i	0.483998	−	0.102877i	0.443447	+	0.896301i	$0.353755\pi$
$822$	46.0271	+	51.1183i	1.60538	+	1.78295i
$823$	−3.66019	−	34.8244i	−0.127586	−	1.21390i	−0.851628	−	0.524146i	$-0.824384\pi$
$823$	−3.66019	−	34.8244i	−0.127586	−	1.21390i	0.724042	−	0.689756i	$-0.242282\pi$
$824$	−11.0802	−	19.1915i	−0.385997	−	0.668566i
$825$		0			0
$826$	−16.1321	−	46.6900i	−0.561308	−	1.62455i
$827$	−12.1269	+	8.81071i	−0.421694	+	0.306378i	−0.778319	−	0.627869i	$-0.783927\pi$
$827$	−12.1269	+	8.81071i	−0.421694	+	0.306378i	0.356625	+	0.934248i	$0.383927\pi$
$828$	−10.5034	+	2.23257i	−0.365019	+	0.0775872i
$829$	−11.4129	−	12.6753i	−0.396387	−	0.440232i	0.511605	−	0.859221i	$-0.329051\pi$
$829$	−11.4129	−	12.6753i	−0.396387	−	0.440232i	−0.907991	+	0.418989i	$0.862385\pi$
$830$		0			0
$831$	−26.7121	+	29.6668i	−0.926634	+	1.02913i
$832$	−7.76529			−0.269213
$833$	41.5335	−	20.3664i	1.43905	−	0.705655i
$834$	23.4580	+	17.0432i	0.812283	+	0.590158i
$835$		0			0
$836$	−0.0289914	−	0.275835i	−0.00100269	−	0.00953994i
$837$	7.26241	−	3.23343i	0.251026	−	0.111764i
$838$	3.22588	−	30.6922i	0.111436	−	1.06024i
$839$	−5.30538	+	3.85458i	−0.183162	+	0.133075i	−0.675588	−	0.737279i	$-0.736110\pi$
$839$	−5.30538	+	3.85458i	−0.183162	+	0.133075i	0.492426	+	0.870354i	$0.336110\pi$
$840$		0			0
$841$	−9.54254	−	6.93306i	−0.329053	−	0.239071i
$842$	29.5649	−	32.8352i	1.01888	−	1.13158i
$843$	−9.67014	+	16.7492i	−0.333057	+	0.576872i
$844$	3.09351	+	0.657545i	0.106483	+	0.0226336i
$845$		0			0
$846$	18.9789	−	58.4111i	0.652509	−	2.00822i
$847$	−14.8944	−	24.7290i	−0.511777	−	0.849697i
$848$	−26.7835	+	19.4593i	−0.919748	+	0.668236i
$849$	−5.30135	−	9.18220i	−0.181942	−	0.315132i
$850$		0			0
$851$	9.15315	−	15.8537i	0.313766	−	0.543459i
$852$	2.95935	+	1.31759i	0.101386	+	0.0451398i
$853$	10.4090	−	32.0356i	0.356398	−	1.09688i	−0.598797	−	0.800901i	$-0.704354\pi$
$853$	10.4090	−	32.0356i	0.356398	−	1.09688i	0.955195	−	0.295979i	$-0.0956457\pi$
$854$	−18.1747	+	32.8703i	−0.621926	+	1.12480i
$855$		0			0
$856$	−27.0876	+	30.0838i	−0.925836	+	1.02824i
$857$	7.20257	−	12.4752i	0.246035	−	0.426145i	−0.716387	−	0.697703i	$-0.754205\pi$
$857$	7.20257	−	12.4752i	0.246035	−	0.426145i	0.962422	+	0.271558i	$0.0875388\pi$
$858$	1.53945	+	0.327221i	0.0525561	+	0.0111711i
$859$	1.32709	−	12.6264i	0.0452796	−	0.430807i	−0.948275	−	0.317451i	$-0.897173\pi$
$859$	1.32709	−	12.6264i	0.0452796	−	0.430807i	0.993554	−	0.113356i	$-0.0361601\pi$
$860$		0			0
$861$	66.0155	−	30.8689i	2.24980	−	1.05201i
$862$	−22.5501	−	16.3836i	−0.768058	−	0.558027i
$863$	−3.53361	+	33.6200i	−0.120285	+	1.14444i	0.753269	+	0.657713i	$0.228476\pi$
$863$	−3.53361	+	33.6200i	−0.120285	+	1.14444i	−0.873554	+	0.486727i	$0.838191\pi$
$864$	−1.22273	−	11.6335i	−0.0415981	−	0.395780i
$865$		0			0
$866$	2.07467	−	19.7391i	0.0705001	−	0.670763i
$867$	−23.8798	−	73.4944i	−0.811000	−	2.49600i
$868$	0.596261	−	0.687392i	0.0202384	−	0.0233316i
$869$	−0.713658	−	2.19641i	−0.0242092	−	0.0745082i
$870$		0			0
$871$	6.62389	+	7.35658i	0.224442	+	0.249268i
$872$	−24.1917	−	26.8676i	−0.819234	−	0.909852i
$873$	19.6993	+	8.77072i	0.666722	+	0.296844i
$874$	−31.1309			−1.05302
$875$		0			0
$876$	−7.26659			−0.245515
$877$	6.21711	+	2.76804i	0.209937	+	0.0934699i	0.509011	−	0.860760i	$-0.330011\pi$
$877$	6.21711	+	2.76804i	0.209937	+	0.0934699i	−0.299074	+	0.954230i	$0.596678\pi$
$878$	12.4613	+	13.8397i	0.420549	+	0.467067i
$879$	56.3397	+	62.5716i	1.90029	+	2.11049i
$880$		0			0
$881$	−9.86492	−	30.3611i	−0.332358	−	1.02289i	−0.968009	−	0.250915i	$-0.919268\pi$
$881$	−9.86492	−	30.3611i	−0.332358	−	1.02289i	0.635651	−	0.771976i	$-0.280732\pi$
$882$	−8.09284	−	56.7101i	−0.272500	−	1.90953i
$883$	−9.21002	−	28.3455i	−0.309942	−	0.953903i	−0.977787	−	0.209603i	$-0.932783\pi$
$883$	−9.21002	−	28.3455i	−0.309942	−	0.953903i	0.667845	−	0.744301i	$-0.267217\pi$
$884$	0.249168	−	2.37067i	0.00838042	−	0.0797344i
$885$		0			0
$886$	−0.130128	−	1.23809i	−0.00437174	−	0.0415943i
$887$	−1.39327	+	13.2561i	−0.0467814	+	0.445095i	0.945911	+	0.324425i	$0.105171\pi$
$887$	−1.39327	+	13.2561i	−0.0467814	+	0.445095i	−0.992693	+	0.120670i	$0.961496\pi$
$888$	16.6935	+	12.1286i	0.560199	+	0.407008i
$889$	−20.3588	−	14.2232i	−0.682811	−	0.477030i
$890$		0			0
$891$	0.122370	−	1.16427i	0.00409955	−	0.0390046i
$892$	−2.34047	−	0.497483i	−0.0783648	−	0.0166570i
$893$	11.6230	−	20.1316i	0.388948	−	0.673679i
$894$	−34.7291	+	38.5705i	−1.16151	+	1.28999i
$895$		0			0
$896$	17.9858	+	29.8615i	0.600862	+	0.997603i
$897$	7.12681	−	21.9341i	0.237957	−	0.732357i
$898$	43.9284	+	19.5582i	1.46591	+	0.652665i
$899$	−3.65737	+	6.33475i	−0.121980	+	0.211276i
$900$		0			0
$901$	24.2522	+	42.0060i	0.807957	+	1.39942i
$902$	3.47788	−	2.52683i	0.115801	−	0.0841343i
$903$	7.45214	−	13.4777i	0.247992	−	0.448511i
$904$	−4.24593	+	13.0676i	−0.141217	+	0.434623i
$905$		0			0
$906$	−6.78365	−	1.44191i	−0.225372	−	0.0479042i
$907$	−16.4021	+	28.4092i	−0.544622	+	0.943312i	0.454009	+	0.890997i	$0.349993\pi$
$907$	−16.4021	+	28.4092i	−0.544622	+	0.943312i	−0.998631	+	0.0523151i	$0.983340\pi$
$908$	−0.325994	+	0.362053i	−0.0108185	+	0.0120151i
$909$	13.3678	+	9.71226i	0.443381	+	0.322135i
$910$		0			0
$911$	−14.0742	+	10.2255i	−0.466300	+	0.338787i	−0.795997	−	0.605300i	$-0.793053\pi$
$911$	−14.0742	+	10.2255i	−0.466300	+	0.338787i	0.329698	+	0.944087i	$0.393053\pi$
$912$	4.23137	−	40.2588i	0.140115	−	1.33310i
$913$	0.533369	−	0.237471i	0.0176519	−	0.00785915i
$914$	−0.223764	−	2.12897i	−0.00740146	−	0.0704202i
$915$		0			0
$916$	−2.06686	−	1.50166i	−0.0682910	−	0.0496163i
$917$	−17.3718	−	7.35213i	−0.573666	−	0.242789i
$918$	−69.5731			−2.29625
$919$	−0.110059	+	0.122233i	−0.00363053	+	0.00403211i	−0.744957	−	0.667112i	$-0.767530\pi$
$919$	−0.110059	+	0.122233i	−0.00363053	+	0.00403211i	0.741327	+	0.671144i	$0.234197\pi$
$920$		0			0
$921$	52.6212	+	58.4417i	1.73393	+	1.92572i
$922$	−14.7534	+	3.13594i	−0.485879	+	0.103277i
$923$	−3.61743	+	2.62822i	−0.119069	+	0.0865088i
$924$	−0.224177	−	0.648820i	−0.00737488	−	0.0213446i
$925$		0			0
$926$	9.28952	+	16.0899i	0.305273	+	0.528748i
$927$	4.84838	+	46.1292i	0.159242	+	1.51508i
$928$	7.20203	+	7.99866i	0.236418	+	0.262569i
$929$	50.8083	−	10.7996i	1.66697	−	0.354325i	0.724668	−	0.689098i	$-0.241993\pi$
$929$	50.8083	−	10.7996i	1.66697	−	0.354325i	0.942299	+	0.334773i	$0.108660\pi$
$930$		0			0
$931$	1.46655	−	21.6322i	0.0480642	−	0.708967i
$932$	−4.93049			−0.161503
$933$	42.3319	−	47.0144i	1.38589	−	1.53918i
$934$	49.0006	−	21.8165i	1.60335	−	0.713857i
$935$		0			0
$936$	15.2624	+	6.79527i	0.498868	+	0.222110i
$937$	−47.7045	−	34.6594i	−1.55844	−	1.13227i	−0.937275	−	0.348592i	$-0.886660\pi$
$937$	−47.7045	−	34.6594i	−1.55844	−	1.13227i	−0.621164	−	0.783681i	$-0.713340\pi$
$938$	9.63573	−	31.6371i	0.314618	−	1.03299i
$939$	26.3966	−	19.1782i	0.861420	−	0.625858i
$940$		0			0
$941$	38.4799	−	17.1323i	1.25441	−	0.558499i	0.331477	−	0.943463i	$-0.392453\pi$
$941$	38.4799	−	17.1323i	1.25441	−	0.558499i	0.922931	+	0.384965i	$0.125786\pi$
$942$	53.8157	+	11.4389i	1.75341	+	0.372699i
$943$	−31.4976	−	54.5555i	−1.02570	−	1.77657i
$944$	−17.1582	−	52.8075i	−0.558452	−	1.71874i
$945$		0			0
$946$	0.280735	−	0.864014i	0.00912748	−	0.0280915i
$947$	−24.3411	+	5.17386i	−0.790980	+	0.168128i	−0.585649	−	0.810565i	$-0.699160\pi$
$947$	−24.3411	+	5.17386i	−0.790980	+	0.168128i	−0.205331	+	0.978693i	$0.565827\pi$
$948$	0.704525	+	6.70311i	0.0228819	+	0.217707i
$949$	5.01508	−	8.68637i	0.162796	−	0.281971i
$950$		0			0
$951$	7.37107			0.239023
$952$	40.8284	−	19.0913i	1.32325	−	0.618754i
$953$	−14.5003	+	44.6274i	−0.469712	+	1.44562i	0.383247	+	0.923646i	$0.374806\pi$
$953$	−14.5003	+	44.6274i	−0.469712	+	1.44562i	−0.852959	+	0.521978i	$0.825194\pi$
$954$	58.7536	−	12.4885i	1.90222	−	0.404329i
$955$		0			0
$956$	5.39549	+	1.14685i	0.174502	+	0.0370916i
$957$	2.75904	+	4.77879i	0.0891870	+	0.154476i
$958$	10.4583	+	32.1872i	0.337891	+	1.03992i
$959$	28.2753	+	30.2571i	0.913056	+	0.977053i
$960$		0			0
$961$	−27.1217	−	12.0754i	−0.874895	−	0.389528i
$962$	4.59739	−	2.04689i	0.148226	−	0.0659943i
$963$	77.4060	−	34.4634i	2.49437	−	1.11057i
$964$	2.32147	+	1.03359i	0.0747696	+	0.0332896i
$965$		0			0
$966$	−75.0564	+	17.4120i	−2.41490	+	0.560223i
$967$	18.7094	+	57.5816i	0.601654	+	1.85170i	0.518335	+	0.855178i	$0.326552\pi$
$967$	18.7094	+	57.5816i	0.601654	+	1.85170i	0.0833195	+	0.996523i	$0.473448\pi$
$968$	−14.0637	−	24.3591i	−0.452025	−	0.782930i
$969$	−58.0125	−	12.3309i	−1.86363	−	0.396127i
$970$		0			0
$971$	−25.6956	+	5.46178i	−0.824612	+	0.175277i	−0.600845	−	0.799366i	$-0.705169\pi$
$971$	−25.6956	+	5.46178i	−0.824612	+	0.175277i	−0.223768	+	0.974643i	$0.571836\pi$
$972$	0.876809	−	2.69854i	0.0281237	−	0.0865557i
$973$	14.3102	+	9.99753i	0.458765	+	0.320506i
$974$	17.0792			0.547254
$975$		0			0
$976$	−21.1094	+	36.5625i	−0.675695	+	1.17034i
$977$	0.443213	+	4.21689i	0.0141796	+	0.134910i	0.999321	−	0.0368326i	$-0.0117268\pi$
$977$	0.443213	+	4.21689i	0.0141796	+	0.134910i	−0.985142	+	0.171743i	$0.945060\pi$
$978$	−2.41086	+	0.512443i	−0.0770907	+	0.0163861i
$979$	−0.383134	+	1.17917i	−0.0122450	+	0.0376863i
$980$		0			0
$981$	23.3842	+	71.9691i	0.746600	+	2.29780i
$982$	26.3864	+	45.7026i	0.842025	+	1.45843i
$983$	−33.3872	−	7.09667i	−1.06489	−	0.226349i	−0.358034	−	0.933709i	$-0.616553\pi$
$983$	−33.3872	−	7.09667i	−1.06489	−	0.226349i	−0.706853	+	0.707360i	$0.749886\pi$
$984$	64.8677	−	28.8810i	2.06791	−	0.920691i
$985$		0			0
$986$	51.7901	−	37.6277i	1.64933	−	1.19831i
$987$	16.7630	−	55.0380i	0.533572	−	1.75188i
$988$	−0.903905	−	0.656726i	−0.0287571	−	0.0208932i
$989$	−12.1617	−	5.41475i	−0.386720	−	0.172179i
$990$		0			0
$991$	7.10897	−	3.16512i	0.225824	−	0.100543i	−0.290706	−	0.956812i	$-0.593890\pi$
$991$	7.10897	−	3.16512i	0.225824	−	0.100543i	0.516530	+	0.856269i	$0.327224\pi$
$992$	1.29135	−	1.43419i	0.0410004	−	0.0455356i
$993$	−10.2366			−0.324848
$994$	13.7569	+	5.82225i	0.436343	+	0.184670i
$995$		0			0
$996$	−1.66669	+	0.354267i	−0.0528112	+	0.0112254i
$997$	32.9447	+	36.5888i	1.04337	+	1.15878i	0.987058	+	0.160366i	$0.0512674\pi$
$997$	32.9447	+	36.5888i	1.04337	+	1.15878i	0.0563118	+	0.998413i	$0.482066\pi$
$998$	−5.94099	−	56.5247i	−0.188059	−	1.78926i
$999$	−9.58800	−	16.6069i	−0.303351	−	0.525419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.q.b.676.27		288
5.2	odd	4		875.2.u.a.74.5		144
5.3	odd	4		175.2.t.a.39.14	yes	144
5.4	even	2	inner	875.2.q.b.676.10		288
7.2	even	3	inner	875.2.q.b.51.10		288
25.9	even	10	inner	875.2.q.b.326.27		288
25.12	odd	20		175.2.t.a.109.5	yes	144
25.13	odd	20		875.2.u.a.424.14		144
25.16	even	5	inner	875.2.q.b.326.10		288
35.2	odd	12		875.2.u.a.324.14		144
35.9	even	6	inner	875.2.q.b.51.27		288
35.23	odd	12		175.2.t.a.114.5	yes	144
175.9	even	30	inner	875.2.q.b.576.10		288
175.16	even	15	inner	875.2.q.b.576.27		288
175.37	odd	60		175.2.t.a.9.14	✓	144
175.163	odd	60		875.2.u.a.674.5		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.t.a.9.14	✓	144	175.37	odd	60
175.2.t.a.39.14	yes	144	5.3	odd	4
175.2.t.a.109.5	yes	144	25.12	odd	20
175.2.t.a.114.5	yes	144	35.23	odd	12
875.2.q.b.51.10		288	7.2	even	3	inner
875.2.q.b.51.27		288	35.9	even	6	inner
875.2.q.b.326.10		288	25.16	even	5	inner
875.2.q.b.326.27		288	25.9	even	10	inner
875.2.q.b.576.10		288	175.9	even	30	inner
875.2.q.b.576.27		288	175.16	even	15	inner
875.2.q.b.676.10		288	5.4	even	2	inner
875.2.q.b.676.27		288	1.1	even	1	trivial
875.2.u.a.74.5		144	5.2	odd	4
875.2.u.a.324.14		144	35.2	odd	12
875.2.u.a.424.14		144	25.13	odd	20
875.2.u.a.674.5		144	175.163	odd	60

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.38556 + 0.616889i) q^{2} +(-1.93883 - 2.15328i) q^{3} +(0.200952 + 0.223180i) q^{4} +(-1.35801 - 4.17954i) q^{6} +(-0.864026 - 2.50069i) q^{7} +(-0.796607 - 2.45170i) q^{8} +(-0.564002 + 5.36612i) q^{9} +O(q^{10})\)	\(q+(1.38556 + 0.616889i) q^{2} +(-1.93883 - 2.15328i) q^{3} +(0.200952 + 0.223180i) q^{4} +(-1.35801 - 4.17954i) q^{6} +(-0.864026 - 2.50069i) q^{7} +(-0.796607 - 2.45170i) q^{8} +(-0.564002 + 5.36612i) q^{9} +(0.0311666 + 0.296530i) q^{11} +(0.0909585 - 0.865413i) q^{12} +(0.971725 + 0.705999i) q^{13} +(0.345493 - 3.99786i) q^{14} +(0.471470 - 4.48574i) q^{16} +(-6.46391 - 1.37395i) q^{17} +(-4.09176 + 7.08713i) q^{18} +(-2.07257 + 2.30182i) q^{19} +(-3.70950 + 6.70890i) q^{21} +(-0.139743 + 0.430086i) q^{22} +(6.05382 + 2.69533i) q^{23} +(-3.73473 + 6.46875i) q^{24} +(0.910856 + 1.57765i) q^{26} +(5.61583 - 4.08014i) q^{27} +(0.384476 - 0.695352i) q^{28} +(-1.97373 + 6.07451i) q^{29} +(1.12021 + 0.238107i) q^{31} +(0.842577 - 1.45939i) q^{32} +(0.578088 - 0.642032i) q^{33} +(-8.10853 - 5.89119i) q^{34} +(-1.31095 + 0.952458i) q^{36} +(0.288759 - 2.74736i) q^{37} +(-4.29163 + 1.91076i) q^{38} +(-0.363788 - 3.46121i) q^{39} +(-7.69071 - 5.58763i) q^{41} +(-9.27837 + 7.00720i) q^{42} -2.00893 q^{43} +(-0.0599166 + 0.0665441i) q^{44} +(6.72518 + 7.46907i) q^{46} +(-7.34097 + 1.56037i) q^{47} +(-10.5732 + 7.68185i) q^{48} +(-5.50692 + 4.32133i) q^{49} +(9.57389 + 16.5825i) q^{51} +(0.0377052 + 0.358741i) q^{52} +(-4.91135 - 5.45461i) q^{53} +(10.2980 - 2.18892i) q^{54} +(-5.44267 + 4.11040i) q^{56} +8.97484 q^{57} +(-6.48201 + 7.19900i) q^{58} +(11.2461 - 5.00707i) q^{59} +(-8.55099 - 3.80715i) q^{61} +(1.40522 + 1.02096i) q^{62} +(13.9063 - 3.22607i) q^{63} +(-5.23034 + 3.80006i) q^{64} +(1.19704 - 0.532954i) q^{66} +(8.06160 + 1.71355i) q^{67} +(-0.992297 - 1.71871i) q^{68} +(-5.93348 - 18.2614i) q^{69} +(-1.15037 + 3.54049i) q^{71} +(13.6054 - 2.89192i) q^{72} +(-0.872884 - 8.30494i) q^{73} +(2.09491 - 3.62849i) q^{74} -0.930207 q^{76} +(0.714602 - 0.334148i) q^{77} +(1.63113 - 5.02012i) q^{78} +(-7.57630 + 1.61039i) q^{79} +(-3.84052 - 0.816327i) q^{81} +(-7.20896 - 12.4863i) q^{82} +(-0.605097 - 1.86230i) q^{83} +(-2.24272 + 0.520280i) q^{84} +(-2.78349 - 1.23929i) q^{86} +(16.9069 - 7.52742i) q^{87} +(0.702177 - 0.312629i) q^{88} +(3.79878 + 1.69132i) q^{89} +(0.925891 - 3.03999i) q^{91} +(0.614983 + 1.89272i) q^{92} +(-1.65917 - 2.87377i) q^{93} +(-11.1339 - 2.36658i) q^{94} +(-4.77608 + 1.01519i) q^{96} +(1.23497 - 3.80086i) q^{97} +(-10.2959 + 2.59028i) q^{98} -1.60880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9}+O(q^{10}) \) 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9	\( 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9} + 36 q^{14} + 10 q^{16} + 22 q^{19} - 18 q^{21} - 100 q^{24} - 120 q^{26} + 48 q^{29} + 30 q^{31} + 40 q^{34} + 32 q^{36} - 26 q^{39} - 124 q^{41} + 30 q^{44} - 54 q^{46} + 76 q^{49} - 16 q^{51} + 58 q^{54} + 64 q^{56} + 78 q^{59} + 14 q^{61} - 68 q^{64} + 22 q^{66} - 148 q^{69} - 92 q^{71} - 12 q^{74} + 360 q^{76} - 18 q^{79} - 118 q^{81} + 102 q^{84} + 22 q^{86} + 84 q^{89} + 44 q^{91} - 10 q^{94} + 106 q^{96} + 88 q^{99}+O(q^{100}) \) 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9 + 36 * q^14 + 10 * q^16 + 22 * q^19 - 18 * q^21 - 100 * q^24 - 120 * q^26 + 48 * q^29 + 30 * q^31 + 40 * q^34 + 32 * q^36 - 26 * q^39 - 124 * q^41 + 30 * q^44 - 54 * q^46 + 76 * q^49 - 16 * q^51 + 58 * q^54 + 64 * q^56 + 78 * q^59 + 14 * q^61 - 68 * q^64 + 22 * q^66 - 148 * q^69 - 92 * q^71 - 12 * q^74 + 360 * q^76 - 18 * q^79 - 118 * q^81 + 102 * q^84 + 22 * q^86 + 84 * q^89 + 44 * q^91 - 10 * q^94 + 106 * q^96 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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