LMFDB - Embedded newform 115.4.l.a.102.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(7,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("115.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, 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:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$680$
Relative dimension:	$34$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			102.24
Character	$\chi$	$=$	115.102
Dual form			115.4.l.a.53.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.147738 - 2.06565i) q^{2} +(5.23771 - 1.13939i) q^{3} +(3.67351 + 0.528171i) q^{4} +(4.29113 + 10.3241i) q^{5} +(-1.57978 - 10.9876i) q^{6} +(3.96906 - 2.16727i) q^{7} +(5.15538 - 23.6989i) q^{8} +(1.57536 - 0.719443i) q^{9} +(21.9598 - 7.33871i) q^{10} +(42.7289 + 37.0248i) q^{11} +(19.8426 - 1.41917i) q^{12} +(-21.9447 + 40.1887i) q^{13} +(-3.89044 - 8.51886i) q^{14} +(34.2389 + 49.1852i) q^{15} +(-19.7043 - 5.78569i) q^{16} +(-90.8184 - 67.9858i) q^{17} +(-1.25337 - 3.36042i) q^{18} +(16.5939 - 115.413i) q^{19} +(10.3107 + 40.1920i) q^{20} +(18.3194 - 15.8739i) q^{21} +(82.7927 - 82.7927i) q^{22} +(20.3555 - 108.410i) q^{23} -130.002i q^{24} +(-88.1723 + 88.6038i) q^{25} +(79.7736 + 51.2674i) q^{26} +(-108.427 + 81.1677i) q^{27} +(15.7251 - 5.86515i) q^{28} +(-67.4393 + 9.69631i) q^{29} +(106.657 - 63.4589i) q^{30} +(88.1264 - 56.6354i) q^{31} +(52.9426 - 141.945i) q^{32} +(265.987 + 145.240i) q^{33} +(-153.852 + 177.555i) q^{34} +(39.4068 + 31.6768i) q^{35} +(6.16708 - 1.81082i) q^{36} +(-231.464 - 86.3316i) q^{37} +(-235.952 - 51.3281i) q^{38} +(-69.1493 + 235.501i) q^{39} +(266.791 - 48.4707i) q^{40} +(15.1490 - 33.1717i) q^{41} +(-30.0833 - 40.1866i) q^{42} +(31.9600 + 146.918i) q^{43} +(137.409 + 158.579i) q^{44} +(14.1876 + 13.1769i) q^{45} +(-220.929 - 58.0635i) q^{46} +(-68.7986 - 68.7986i) q^{47} +(-109.797 - 7.85287i) q^{48} +(-174.383 + 271.346i) q^{49} +(169.998 + 195.223i) q^{50} +(-553.143 - 252.612i) q^{51} +(-101.841 + 136.043i) q^{52} +(-139.225 - 254.972i) q^{53} +(151.645 + 235.964i) q^{54} +(-198.891 + 600.013i) q^{55} +(-30.8999 - 105.236i) q^{56} +(-44.5871 - 623.409i) q^{57} +(10.0658 + 140.738i) q^{58} +(226.305 + 770.724i) q^{59} +(99.7988 + 198.766i) q^{60} +(262.454 + 408.387i) q^{61} +(-103.969 - 190.405i) q^{62} +(4.69347 - 6.26975i) q^{63} +(-434.828 - 198.579i) q^{64} +(-509.078 - 54.1032i) q^{65} +(339.311 - 527.978i) q^{66} +(583.034 + 41.6994i) q^{67} +(-297.714 - 297.714i) q^{68} +(-16.9051 - 591.012i) q^{69} +(71.2549 - 76.7207i) q^{70} +(-45.9008 - 52.9724i) q^{71} +(-8.92842 - 41.0433i) q^{72} +(523.201 + 698.914i) q^{73} +(-212.527 + 465.368i) q^{74} +(-360.867 + 564.545i) q^{75} +(121.916 - 415.207i) q^{76} +(249.836 + 54.3486i) q^{77} +(476.245 + 177.630i) q^{78} +(-363.747 + 106.806i) q^{79} +(-24.8218 - 228.255i) q^{80} +(-506.051 + 584.014i) q^{81} +(-66.2829 - 36.1932i) q^{82} +(299.616 - 803.302i) q^{83} +(75.6807 - 48.6370i) q^{84} +(312.175 - 1229.35i) q^{85} +(308.202 - 44.3127i) q^{86} +(-342.180 + 127.627i) q^{87} +(1097.73 - 821.750i) q^{88} +(-1217.74 - 782.593i) q^{89} +(29.3148 - 27.3599i) q^{90} +207.072i q^{91} +(132.035 - 387.493i) q^{92} +(397.051 - 397.051i) q^{93} +(-152.278 + 131.949i) q^{94} +(1262.74 - 323.938i) q^{95} +(115.567 - 803.788i) q^{96} +(201.836 + 541.144i) q^{97} +(534.741 + 400.302i) q^{98} +(93.9505 + 27.5864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 680 q - 18 q^{2} - 26 q^{3} - 22 q^{5} - 76 q^{6} - 22 q^{7} - 50 q^{8} - 22 q^{10} - 44 q^{11} - 222 q^{12} + 78 q^{13} - 22 q^{15} + 788 q^{16} - 22 q^{17} - 86 q^{18} - 22 q^{20} - 44 q^{21} - 944 q^{23}+ \cdots - 10314 q^{98}+O(q^{100}) $ 680 * q - 18 * q^2 - 26 * q^3 - 22 * q^5 - 76 * q^6 - 22 * q^7 - 50 * q^8 - 22 * q^10 - 44 * q^11 - 222 * q^12 + 78 * q^13 - 22 * q^15 + 788 * q^16 - 22 * q^17 - 86 * q^18 - 22 * q^20 - 44 * q^21 - 944 * q^23 + 350 * q^25 + 268 * q^26 + 682 * q^27 + 682 * q^28 - 22 * q^30 + 1012 * q^31 - 582 * q^32 + 1914 * q^33 + 326 * q^35 - 2468 * q^36 + 2354 * q^37 - 22 * q^38 - 22 * q^40 - 2292 * q^41 - 7282 * q^42 - 22 * q^43 + 52 * q^46 - 2416 * q^47 - 1378 * q^48 + 598 * q^50 - 44 * q^51 - 794 * q^52 - 22 * q^53 - 2710 * q^55 + 11572 * q^56 + 7634 * q^57 - 2066 * q^58 - 22 * q^60 - 1100 * q^61 - 3970 * q^62 - 22 * q^63 - 22 * q^65 - 10956 * q^66 - 22 * q^67 + 1792 * q^70 - 11412 * q^71 - 556 * q^72 - 1122 * q^73 + 13078 * q^75 - 2156 * q^76 - 4238 * q^77 + 9158 * q^78 + 8096 * q^80 + 11280 * q^81 + 6494 * q^82 - 22 * q^83 - 8118 * q^85 + 10428 * q^86 + 6282 * q^87 - 1430 * q^88 - 37224 * q^90 + 666 * q^92 + 1564 * q^93 - 11162 * q^95 - 16748 * q^96 - 12694 * q^97 - 10314 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

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

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

$2$	0.147738	−	2.06565i	0.0522332	−	0.730316i	−0.902092	−	0.431545i	$-0.857969\pi$
$2$	0.147738	−	2.06565i	0.0522332	−	0.730316i	0.954325	−	0.298771i	$-0.0965767\pi$
$3$	5.23771	−	1.13939i	1.00800	−	0.219277i	0.321891	−	0.946777i	$-0.395682\pi$
$3$	5.23771	−	1.13939i	1.00800	−	0.219277i	0.686108	+	0.727500i	$0.259318\pi$
$4$	3.67351	+	0.528171i	0.459188	+	0.0660213i
$5$	4.29113	+	10.3241i	0.383811	+	0.923412i
$5$	4.29113	+	10.3241i	0.383811	+	0.923412i
$6$	−1.57978	−	10.9876i	−0.107490	−	0.747611i
$7$	3.96906	−	2.16727i	0.214309	−	0.117022i	−0.368509	−	0.929624i	$-0.620132\pi$
$7$	3.96906	−	2.16727i	0.214309	−	0.117022i	0.582818	+	0.812602i	$0.301950\pi$
$8$	5.15538	−	23.6989i	0.227838	−	1.04735i
$9$	1.57536	−	0.719443i	0.0583467	−	0.0266460i
$10$	21.9598	−	7.33871i	0.694430	−	0.232070i
$11$	42.7289	+	37.0248i	1.17120	+	1.01485i	0.999559	+	0.0296944i	$0.00945340\pi$
$11$	42.7289	+	37.0248i	1.17120	+	1.01485i	0.171644	+	0.985159i	$0.445092\pi$
$12$	19.8426	−	1.41917i	0.477338	−	0.0341399i
$13$	−21.9447	+	40.1887i	−0.468182	+	0.857411i	0.531763	+	0.846893i	$0.321530\pi$
$13$	−21.9447	+	40.1887i	−0.468182	+	0.857411i	−0.999945	+	0.0105180i	$0.996652\pi$
$14$	−3.89044	−	8.51886i	−0.0742688	−	0.162626i
$15$	34.2389	+	49.1852i	0.589363	+	0.846637i
$16$	−19.7043	−	5.78569i	−0.307879	−	0.0904014i
$17$	−90.8184	−	67.9858i	−1.29569	−	0.969940i	−0.999892	−	0.0146888i	$-0.995324\pi$
$17$	−90.8184	−	67.9858i	−1.29569	−	0.969940i	−0.295796	−	0.955251i	$-0.595585\pi$
$18$	−1.25337	−	3.36042i	−0.0164124	−	0.0440033i
$19$	16.5939	−	115.413i	0.200364	−	1.39356i	−0.602843	−	0.797860i	$-0.705966\pi$
$19$	16.5939	−	115.413i	0.200364	−	1.39356i	0.803207	−	0.595700i	$-0.203125\pi$
$20$	10.3107	+	40.1920i	0.115277	+	0.449360i
$21$	18.3194	−	15.8739i	0.190363	−	0.164951i
$22$	82.7927	−	82.7927i	0.802339	−	0.802339i
$23$	20.3555	−	108.410i	0.184540	−	0.982825i
$23$	20.3555	−	108.410i	0.184540	−	0.982825i
$24$		−	130.002i		−	1.10569i
$25$	−88.1723	+	88.6038i	−0.705379	+	0.708831i
$26$	79.7736	+	51.2674i	0.601726	+	0.386706i
$27$	−108.427	+	81.1677i	−0.772846	+	0.578546i
$28$	15.7251	−	5.86515i	0.106134	−	0.0395860i
$29$	−67.4393	+	9.69631i	−0.431834	+	0.0620883i	−0.354804	−	0.934941i	$-0.615453\pi$
$29$	−67.4393	+	9.69631i	−0.431834	+	0.0620883i	−0.0770291	+	0.997029i	$0.524543\pi$
$30$	106.657	−	63.4589i	0.649097	−	0.386199i
$31$	88.1264	−	56.6354i	0.510580	−	0.328130i	−0.259856	−	0.965647i	$-0.583675\pi$
$31$	88.1264	−	56.6354i	0.510580	−	0.328130i	0.770436	+	0.637518i	$0.220039\pi$
$32$	52.9426	−	141.945i	0.292469	−	0.784141i
$33$	265.987	+	145.240i	1.40310	+	0.766153i
$34$	−153.852	+	177.555i	−0.776040	+	0.895598i
$35$	39.4068	+	31.6768i	0.190313	+	0.152982i
$36$	6.16708	−	1.81082i	0.0285513	−	0.00838342i
$37$	−231.464	−	86.3316i	−1.02844	−	0.383590i	−0.222093	−	0.975026i	$-0.571289\pi$
$37$	−231.464	−	86.3316i	−1.02844	−	0.383590i	−0.806352	+	0.591435i	$0.798561\pi$
$38$	−235.952	−	51.3281i	−1.00727	−	0.219119i
$39$	−69.1493	+	235.501i	−0.283916	+	0.966931i
$40$	266.791	−	48.4707i	1.05458	−	0.191597i
$41$	15.1490	−	33.1717i	0.0577044	−	0.126355i	−0.878583	−	0.477589i	$-0.841511\pi$
$41$	15.1490	−	33.1717i	0.0577044	−	0.126355i	0.936288	+	0.351234i	$0.114238\pi$
$42$	−30.0833	−	40.1866i	−0.110523	−	0.147641i
$43$	31.9600	+	146.918i	0.113346	+	0.521041i	0.998450	+	0.0556494i	$0.0177229\pi$
$43$	31.9600	+	146.918i	0.113346	+	0.521041i	−0.885105	+	0.465392i	$0.845913\pi$
$44$	137.409	+	158.579i	0.470801	+	0.543333i
$45$	14.1876	+	13.1769i	0.0469993	+	0.0436510i
$46$	−220.929	−	58.0635i	−0.708134	−	0.186109i
$47$	−68.7986	−	68.7986i	−0.213517	−	0.213517i	0.592243	−	0.805760i	$-0.298243\pi$
$47$	−68.7986	−	68.7986i	−0.213517	−	0.213517i	−0.805760	+	0.592243i	$0.798243\pi$
$48$	−109.797	−	7.85287i	−0.330164	−	0.0236138i
$49$	−174.383	+	271.346i	−0.508406	+	0.791096i
$50$	169.998	+	195.223i	0.480826	+	0.552174i
$51$	−553.143	−	252.612i	−1.51874	−	0.693584i
$52$	−101.841	+	136.043i	−0.271591	+	0.362803i
$53$	−139.225	−	254.972i	−0.360831	−	0.660812i	0.632697	−	0.774399i	$-0.281948\pi$
$53$	−139.225	−	254.972i	−0.360831	−	0.660812i	−0.993528	+	0.113587i	$0.963766\pi$
$54$	151.645	+	235.964i	0.382153	+	0.594641i
$55$	−198.891	+	600.013i	−0.487607	+	1.47101i
$56$	−30.8999	−	105.236i	−0.0737353	−	0.251119i
$57$	−44.5871	−	623.409i	−0.103609	−	1.44864i
$58$	10.0658	+	140.738i	0.0227880	+	0.318618i
$59$	226.305	+	770.724i	0.499363	+	1.70067i	0.694152	+	0.719829i	$0.255780\pi$
$59$	226.305	+	770.724i	0.499363	+	1.70067i	−0.194789	+	0.980845i	$0.562402\pi$
$60$	99.7988	+	198.766i	0.214733	+	0.427676i
$61$	262.454	+	408.387i	0.550882	+	0.857189i	0.999329	−	0.0366202i	$-0.0116592\pi$
$61$	262.454	+	408.387i	0.550882	+	0.857189i	−0.448447	+	0.893809i	$0.648023\pi$
$62$	−103.969	−	190.405i	−0.212969	−	0.390024i
$63$	4.69347	−	6.26975i	0.00938607	−	0.0125383i
$64$	−434.828	−	198.579i	−0.849274	−	0.387850i
$65$	−509.078	−	54.1032i	−0.971437	−	0.103241i
$66$	339.311	−	527.978i	0.632822	−	0.984691i
$67$	583.034	+	41.6994i	1.06312	+	0.0760357i	0.591924	−	0.805994i	$-0.298369\pi$
$67$	583.034	+	41.6994i	1.06312	+	0.0760357i	0.471194	+	0.882030i	$0.343823\pi$
$68$	−297.714	−	297.714i	−0.530928	−	0.530928i
$69$	−16.9051	−	591.012i	−0.0294946	−	1.03115i
$70$	71.2549	−	76.7207i	0.121666	−	0.130998i
$71$	−45.9008	−	52.9724i	−0.0767243	−	0.0885446i	0.716090	−	0.698008i	$-0.245930\pi$
$71$	−45.9008	−	52.9724i	−0.0767243	−	0.0885446i	−0.792814	+	0.609464i	$0.791385\pi$
$72$	−8.92842	−	41.0433i	−0.0146142	−	0.0671805i
$73$	523.201	+	698.914i	0.838849	+	1.12057i	0.991217	+	0.132247i	$0.0422193\pi$
$73$	523.201	+	698.914i	0.838849	+	1.12057i	−0.152368	+	0.988324i	$0.548690\pi$
$74$	−212.527	+	465.368i	−0.333861	+	0.731053i
$75$	−360.867	+	564.545i	−0.555591	+	0.869173i
$76$	121.916	−	415.207i	0.184009	−	0.626678i
$77$	249.836	+	54.3486i	0.369760	+	0.0804363i
$78$	476.245	+	177.630i	0.691335	+	0.257855i
$79$	−363.747	+	106.806i	−0.518034	+	0.152109i	−0.530290	−	0.847816i	$-0.677917\pi$
$79$	−363.747	+	106.806i	−0.518034	+	0.152109i	0.0122558	+	0.999925i	$0.496099\pi$
$80$	−24.8218	−	228.255i	−0.0346895	−	0.318996i
$81$	−506.051	+	584.014i	−0.694171	+	0.801116i
$82$	−66.2829	−	36.1932i	−0.0892649	−	0.0487423i
$83$	299.616	−	803.302i	0.396231	−	1.06234i	−0.573724	−	0.819049i	$-0.694502\pi$
$83$	299.616	−	803.302i	0.396231	−	1.06234i	0.969954	−	0.243287i	$-0.0782256\pi$
$84$	75.6807	−	48.6370i	0.0983029	−	0.0631754i
$85$	312.175	−	1229.35i	0.398355	−	1.56873i
$86$	308.202	−	44.3127i	0.386445	−	0.0555624i
$87$	−342.180	+	127.627i	−0.421673	+	0.157276i
$88$	1097.73	−	821.750i	1.32975	−	0.995441i
$89$	−1217.74	−	782.593i	−1.45034	−	0.932075i	−0.999215	−	0.0396121i	$-0.987388\pi$
$89$	−1217.74	−	782.593i	−1.45034	−	0.932075i	−0.451121	−	0.892463i	$-0.648976\pi$
$90$	29.3148	−	27.3599i	0.0343339	−	0.0320443i
$91$			207.072i			0.238539i
$92$	132.035	−	387.493i	0.149626	−	0.439118i
$93$	397.051	−	397.051i	0.442713	−	0.442713i
$94$	−152.278	+	131.949i	−0.167088	+	0.144782i
$95$	1262.74	−	323.938i	1.36373	−	0.349845i
$96$	115.567	−	803.788i	0.122865	−	0.854544i
$97$	201.836	+	541.144i	0.211272	+	0.566442i	0.998754	−	0.0498951i	$-0.0158887\pi$
$97$	201.836	+	541.144i	0.211272	+	0.566442i	−0.787483	+	0.616337i	$0.788616\pi$
$98$	534.741	+	400.302i	0.551194	+	0.412619i
$99$	93.9505	+	27.5864i	0.0953776	+	0.0280054i
$100$	−370.700	+	278.917i	−0.370700	+	0.278917i
$101$	−628.068	−	1375.28i	−0.618763	−	1.35490i	−0.916416	−	0.400228i	$-0.868931\pi$
$101$	−628.068	−	1375.28i	−0.618763	−	1.35490i	0.297653	−	0.954674i	$-0.403796\pi$
$102$	−603.527	+	1105.28i	−0.585864	+	1.07293i
$103$	−126.331	+	9.03539i	−0.120852	+	0.00864353i	−0.131634	−	0.991298i	$-0.542022\pi$
$103$	−126.331	+	9.03539i	−0.120852	+	0.00864353i	0.0107820	+	0.999942i	$0.496568\pi$
$104$	839.295	+	727.253i	0.791343	+	0.685702i
$105$	242.494	+	121.014i	0.225381	+	0.112474i
$106$	−547.250	+	249.921i	−0.501449	+	0.229004i
$107$	366.469	−	1684.63i	0.331102	−	1.52205i	−0.447357	−	0.894356i	$-0.647634\pi$
$107$	366.469	−	1684.63i	0.331102	−	1.52205i	0.778459	−	0.627696i	$-0.216002\pi$
$108$	−441.179	+	240.902i	−0.393078	+	0.214637i
$109$	192.838	+	1341.22i	0.169454	+	1.17858i	0.880015	+	0.474946i	$0.157532\pi$
$109$	192.838	+	1341.22i	0.169454	+	1.17858i	−0.710561	+	0.703636i	$0.751559\pi$
$110$	1210.03	+	499.482i	1.04884	+	0.432943i
$111$	−1310.71	−	188.451i	−1.12078	−	0.161144i
$112$	−90.7466	+	19.7407i	−0.0765602	+	0.0166547i
$113$	−98.8699	+	1382.38i	−0.0823088	+	1.15083i	0.773591	+	0.633686i	$0.218459\pi$
$113$	−98.8699	+	1382.38i	−0.0823088	+	1.15083i	−0.855899	+	0.517142i	$0.826996\pi$
$114$	−1294.33			−1.06338
$115$	1206.58	−	255.049i	0.978381	−	0.206812i
$116$	−252.860			−0.202392
$117$	−5.65732	+	79.0997i	−0.00447025	+	0.0625023i
$118$	1625.48	−	353.601i	1.26811	−	0.275861i
$119$	−507.808	−	73.0117i	−0.391182	−	0.0562435i
$120$	1342.15	−	557.856i	1.02101	−	0.424376i
$121$	265.501	+	1846.60i	0.199475	+	1.38738i
$122$	882.356	−	481.803i	0.654793	−	0.357544i
$123$	41.5505	−	191.005i	0.0304592	−	0.140019i
$124$	353.646	−	161.505i	0.256116	−	0.116964i
$125$	−1293.11	−	530.085i	−0.925275	−	0.379298i
$126$	−12.2577	−	10.6213i	−0.00866667	−	0.00750971i
$127$	167.403	−	11.9729i	0.116966	−	0.00836554i	−0.0127337	−	0.999919i	$-0.504053\pi$
$127$	167.403	−	11.9729i	0.116966	−	0.00836554i	0.129699	+	0.991553i	$0.458599\pi$
$128$	106.402	−	194.860i	0.0734739	−	0.134557i
$129$	334.795	+	733.099i	0.228504	+	0.500355i
$130$	−186.968	+	1043.58i	−0.126140	+	0.704063i
$131$	389.884	+	114.480i	0.260033	+	0.0763527i	0.409151	−	0.912467i	$-0.365825\pi$
$131$	389.884	+	114.480i	0.260033	+	0.0763527i	−0.149117	+	0.988820i	$0.547643\pi$
$132$	900.395	+	674.027i	0.593707	+	0.444444i
$133$	−184.270	−	494.047i	−0.120137	−	0.322100i
$134$	172.272	−	1198.18i	0.111060	−	0.772440i
$135$	−1303.26	−	771.109i	−0.830862	−	0.491603i
$136$	−2079.39	+	1801.80i	−1.31108	+	1.13605i
$137$	1921.23	−	1921.23i	1.19812	−	1.19812i	0.223387	−	0.974730i	$-0.428289\pi$
$137$	1921.23	−	1921.23i	1.19812	−	1.19812i	0.974730	−	0.223387i	$-0.0717112\pi$
$138$	−1223.32	−	52.3949i	−0.754607	−	0.0323200i
$139$		−	71.8753i		−	0.0438589i	−0.999760	−	0.0219294i	$-0.993019\pi$
$139$		−	71.8753i		−	0.0438589i	0.999760	−	0.0219294i	$-0.00698091\pi$
$140$	128.031	+	137.178i	0.0772897	+	0.0828121i
$141$	−438.736	−	281.959i	−0.262044	−	0.168406i
$142$	−116.203	+	86.9888i	−0.0686731	+	0.0514080i
$143$	−2425.65	+	904.721i	−1.41848	+	0.529067i
$144$	−35.2038	+	5.06154i	−0.0203725	+	0.00292913i
$145$	−389.497	−	654.639i	−0.223075	−	0.374930i
$146$	1521.01	−	977.491i	0.862187	−	0.554094i
$147$	−604.200	+	1619.92i	−0.339004	+	0.908905i
$148$	−804.687	−	439.392i	−0.446925	−	0.244039i
$149$	471.198	−	543.791i	0.259074	−	0.298987i	−0.611279	−	0.791415i	$-0.709345\pi$
$149$	471.198	−	543.791i	0.259074	−	0.298987i	0.870354	+	0.492427i	$0.163890\pi$
$150$	1112.84	+	828.827i	0.605751	+	0.451156i
$151$	2666.93	−	783.082i	1.43730	−	0.422029i	0.531977	−	0.846759i	$-0.321449\pi$
$151$	2666.93	−	783.082i	1.43730	−	0.422029i	0.905320	+	0.424730i	$0.139631\pi$
$152$	−2649.62	−	988.257i	−1.41390	−	0.527357i
$153$	−191.984	−	41.7635i	−0.101444	−	0.0220678i
$154$	149.175	−	508.044i	0.0780576	−	0.265840i
$155$	962.870	+	666.792i	0.498965	+	0.345536i
$156$	−378.405	+	828.591i	−0.194209	+	0.425259i
$157$	−578.736	−	773.100i	−0.294192	−	0.392994i	0.628955	−	0.777442i	$-0.283483\pi$
$157$	−578.736	−	773.100i	−0.294192	−	0.392994i	−0.923147	+	0.384447i	$0.874392\pi$
$158$	166.883	+	767.151i	0.0840287	+	0.386274i
$159$	−1019.73	−	1176.84i	−0.508618	−	0.586976i
$160$	1692.63	−	62.5209i	0.836338	−	0.0308920i
$161$	−154.161	−	474.401i	−0.0754633	−	0.232224i
$162$	1131.60	+	1131.60i	0.548809	+	0.548809i
$163$	−3049.14	−	218.079i	−1.46520	−	0.104793i	−0.684184	−	0.729310i	$-0.739841\pi$
$163$	−3049.14	−	218.079i	−1.46520	−	0.104793i	−0.781011	+	0.624517i	$0.785296\pi$
$164$	73.1703	−	113.855i	0.0348393	−	0.0542110i
$165$	−358.079	+	3369.31i	−0.168948	+	1.58970i
$166$	−1615.07	−	737.579i	−0.755144	−	0.344863i
$167$	−869.403	+	1161.39i	−0.402853	+	0.538148i	−0.955393	−	0.295338i	$-0.904568\pi$
$167$	−869.403	+	1161.39i	−0.402853	+	0.538148i	0.552540	+	0.833486i	$0.313659\pi$
$168$	−281.750	−	515.986i	−0.129390	−	0.236960i
$169$	54.2240	+	84.3742i	0.0246809	+	0.0384043i
$170$	−2493.28	−	826.465i	−1.12486	−	0.372865i
$171$	−56.8919	−	193.756i	−0.0254423	−	0.0866485i
$172$	39.8077	+	556.584i	0.0176471	+	0.246739i
$173$	33.2517	+	464.920i	0.0146132	+	0.204319i	0.999513	+	0.0311955i	$0.00993144\pi$
$173$	33.2517	+	464.920i	0.0146132	+	0.204319i	−0.984900	+	0.173124i	$0.944614\pi$
$174$	213.078	+	725.678i	0.0928357	+	0.316170i
$175$	−157.933	+	542.768i	−0.0682206	+	0.234454i
$176$	−627.726	−	976.761i	−0.268845	−	0.418330i
$177$	2063.48	+	3778.98i	0.876275	+	1.60478i
$178$	−1796.46	+	2399.80i	−0.756465	+	1.01052i
$179$	2913.55	+	1330.57i	1.21659	+	0.555596i	0.917158	−	0.398523i	$-0.130477\pi$
$179$	2913.55	+	1330.57i	1.21659	+	0.555596i	0.299427	+	0.954119i	$0.403204\pi$
$180$	45.1588	+	55.8989i	0.0186997	+	0.0231470i
$181$	−210.631	+	327.749i	−0.0864978	+	0.134593i	−0.881806	−	0.471612i	$-0.843672\pi$
$181$	−210.631	+	327.749i	−0.0864978	+	0.134593i	0.795309	+	0.606205i	$0.207309\pi$
$182$	427.737	+	30.5923i	0.174209	+	0.0124596i
$183$	1839.97	+	1839.97i	0.743250	+	0.743250i
$184$	−2464.25	−	1041.30i	−0.987319	−	0.417203i
$185$	−101.951	−	2760.11i	−0.0405166	−	1.09690i
$186$	−761.507	−	878.826i	−0.300196	−	0.346444i
$187$	−1363.41	−	6267.49i	−0.533167	−	2.45093i
$188$	−216.395	−	289.070i	−0.0839480	−	0.112141i
$189$	−254.442	+	557.151i	−0.0979257	+	0.214427i
$190$	−482.585	−	2656.23i	−0.184265	−	1.01423i
$191$	−433.018	+	1474.72i	−0.164042	+	0.558676i	0.835910	+	0.548867i	$0.184941\pi$
$191$	−433.018	+	1474.72i	−0.164042	+	0.558676i	−0.999952	+	0.00980942i	$0.996878\pi$
$192$	−2503.76	−	544.661i	−0.941113	−	0.204727i
$193$	490.720	+	183.029i	0.183020	+	0.0682629i	0.439303	−	0.898339i	$-0.355225\pi$
$193$	490.720	+	183.029i	0.183020	+	0.0682629i	−0.256283	+	0.966602i	$0.582498\pi$
$194$	1147.63	−	336.975i	0.424717	−	0.124708i
$195$	−2728.05	+	296.664i	−1.00185	+	0.108947i
$196$	−783.916	+	904.687i	−0.285684	+	0.329696i
$197$	1742.87	+	951.677i	0.630325	+	0.344184i	0.762448	−	0.647050i	$-0.223997\pi$
$197$	1742.87	+	951.677i	0.630325	+	0.344184i	−0.132123	+	0.991233i	$0.542179\pi$
$198$	70.8637	−	189.993i	0.0254347	−	0.0681930i
$199$	−1974.10	+	1268.68i	−0.703219	+	0.451931i	−0.842763	−	0.538285i	$-0.819073\pi$
$199$	−1974.10	+	1268.68i	−0.703219	+	0.451931i	0.139544	+	0.990216i	$0.455436\pi$
$200$	1645.25	+	2546.37i	0.581684	+	0.900279i
$201$	3101.28	−	445.896i	1.08829	−	0.156473i
$202$	−2933.62	+	1094.18i	−1.02183	+	0.381122i
$203$	−246.656	+	184.645i	−0.0852802	+	0.0638400i
$204$	−1898.55	−	1220.13i	−0.651595	−	0.418755i
$205$	407.473	+	14.0550i	0.138825	+	0.00478851i
$206$			262.290i			0.0887118i
$207$	−45.9273	−	185.429i	−0.0154211	−	0.0622618i
$208$	664.924	−	664.924i	0.221655	−	0.221655i
$209$	4982.19	−	4317.09i	1.64893	−	1.42880i
$210$	285.797	−	483.028i	0.0939138	−	0.158724i
$211$	268.060	−	1864.40i	0.0874598	−	0.608296i	−0.898205	−	0.439578i	$-0.855128\pi$
$211$	268.060	−	1864.40i	0.0874598	−	0.608296i	0.985664	−	0.168718i	$-0.0539628\pi$
$212$	−376.776	−	1010.18i	−0.122062	−	0.327260i
$213$	−300.772	−	225.155i	−0.0967537	−	0.0724289i
$214$	−3425.71	−	1005.88i	−1.09428	−	0.321311i
$215$	−1379.64	+	960.402i	−0.437632	+	0.304646i
$216$	1364.60	+	2988.06i	0.429858	+	0.941257i
$217$	227.035	−	415.784i	0.0710237	−	0.130070i
$218$	2798.97	−	200.186i	0.869588	−	0.0621942i
$219$	3536.71	+	3064.58i	1.09127	+	0.945594i
$220$	−1047.54	+	2099.11i	−0.321022	+	0.643280i
$221$	4725.25	−	2157.95i	1.43826	−	0.656829i
$222$	−582.915	+	2679.62i	−0.176228	+	0.810109i
$223$	−1969.50	+	1075.43i	−0.591425	+	0.322942i	−0.746940	−	0.664891i	$-0.768478\pi$
$223$	−1969.50	+	1075.43i	−0.591425	+	0.322942i	0.155515	+	0.987833i	$0.450296\pi$
$224$	−97.5001	−	678.128i	−0.0290826	−	0.202274i
$225$	−75.1578	+	203.018i	−0.0222690	+	0.0601534i
$226$	2840.90	+	408.460i	0.836169	+	0.120223i
$227$	2959.87	−	643.881i	0.865435	−	0.188264i	0.242131	−	0.970244i	$-0.422154\pi$
$227$	2959.87	−	643.881i	0.865435	−	0.188264i	0.623304	+	0.781980i	$0.285790\pi$
$228$	165.475	−	2313.65i	0.0480652	−	0.672040i
$229$	4485.65			1.29441			0.647205	−	0.762316i	$-0.275938\pi$
$229$	4485.65			1.29441			0.647205	+	0.762316i	$0.275938\pi$
$230$	−348.584	−	2530.04i	−0.0999345	−	0.725329i
$231$	1370.50			0.390355
$232$	−117.883	+	1648.23i	−0.0333596	+	0.466428i
$233$	3281.71	−	713.893i	0.922713	−	0.200724i	0.273976	−	0.961737i	$-0.411661\pi$
$233$	3281.71	−	713.893i	0.922713	−	0.200724i	0.648737	+	0.761013i	$0.275298\pi$
$234$	162.556	+	23.3720i	0.0454129	+	0.00652939i
$235$	415.057	−	1005.51i	0.115214	−	0.279115i
$236$	424.259	+	2950.79i	0.117021	+	0.813898i
$237$	−1783.51	+	973.869i	−0.488824	+	0.266918i
$238$	−225.839	+	1038.16i	−0.0615082	+	0.282749i
$239$	−397.220	+	181.404i	−0.107506	+	0.0490965i	−0.468442	−	0.883494i	$-0.655185\pi$
$239$	−397.220	+	181.404i	−0.107506	+	0.0490965i	0.360936	+	0.932591i	$0.382457\pi$
$240$	−390.082	−	1167.25i	−0.104915	−	0.313941i
$241$	2726.43	+	2362.46i	0.728733	+	0.631450i	0.938091	−	0.346388i	$-0.112592\pi$
$241$	2726.43	+	2362.46i	0.728733	+	0.631450i	−0.209358	+	0.977839i	$0.567138\pi$
$242$	3853.64	−	275.618i	1.02364	−	0.0732124i
$243$	−232.538	+	425.862i	−0.0613882	+	0.112424i
$244$	748.429	+	1638.83i	0.196366	+	0.429981i
$245$	−3549.69	−	635.963i	−0.925639	−	0.165837i
$246$	−388.409	−	114.047i	−0.100667	−	0.0295585i
$247$	4274.17	+	3199.60i	1.10105	+	0.824234i
$248$	−887.872	−	2380.48i	−0.227338	−	0.609518i
$249$	654.026	−	4548.85i	0.166455	−	1.15772i
$250$	−1286.01	+	2592.79i	−0.325337	+	0.655931i
$251$	1079.93	−	935.762i	0.271571	−	0.235318i	−0.508419	−	0.861110i	$-0.669770\pi$
$251$	1079.93	−	935.762i	0.271571	−	0.235318i	0.779990	+	0.625792i	$0.215224\pi$
$252$	20.5530	−	20.5530i	0.00513777	−	0.00513777i
$253$	4883.61	−	3878.56i	1.21356	−	0.963807i
$254$		−	347.564i		−	0.0858587i
$255$	234.369	−	6794.68i	0.0575560	−	1.66862i
$256$	−3603.92	−	2316.10i	−0.879864	−	0.565454i
$257$	−3605.30	+	2698.89i	−0.875067	+	0.655067i	−0.939386	−	0.342863i	$-0.888603\pi$
$257$	−3605.30	+	2698.89i	−0.875067	+	0.655067i	0.0643187	+	0.997929i	$0.479513\pi$
$258$	1563.78	−	583.261i	0.377352	−	0.140745i
$259$	−1105.80	+	158.990i	−0.265294	+	0.0381435i
$260$	−1841.53	−	467.629i	−0.439257	−	0.111543i
$261$	−99.2653	+	63.7939i	−0.0235416	+	0.0151293i
$262$	294.077	−	788.450i	0.0693439	−	0.185918i
$263$	−4230.00	−	2309.75i	−0.991760	−	0.541542i	−0.100453	−	0.994942i	$-0.532029\pi$
$263$	−4230.00	−	2309.75i	−0.991760	−	0.541542i	−0.891307	+	0.453400i	$0.850211\pi$
$264$	4813.29	−	5554.84i	1.12211	−	1.29499i
$265$	2034.91	−	2531.49i	0.471711	−	0.586822i
$266$	−1047.75	+	307.647i	−0.241510	+	0.0709136i
$267$	−7269.84	−	2711.51i	−1.66632	−	0.621505i
$268$	2119.75	+	461.124i	0.483151	+	0.105103i
$269$	200.775	−	683.776i	0.0455073	−	0.154984i	−0.933605	−	0.358304i	$-0.883355\pi$
$269$	200.775	−	683.776i	0.0455073	−	0.154984i	0.979112	+	0.203320i	$0.0651733\pi$
$270$	−1785.38	+	2578.14i	−0.402424	+	0.581114i
$271$	−1061.37	+	2324.07i	−0.237909	+	0.520948i	−0.990495	−	0.137545i	$-0.956079\pi$
$271$	−1061.37	+	2324.07i	−0.237909	+	0.520948i	0.752586	+	0.658494i	$0.228806\pi$
$272$	1396.16	+	1865.06i	0.311231	+	0.415756i
$273$	235.937	+	1084.58i	0.0523060	+	0.240447i
$274$	−3684.75	−	4252.42i	−0.812422	−	0.937585i
$275$	−7048.04	+	521.381i	−1.54550	+	0.114329i
$276$	250.054	−	2180.01i	0.0545344	−	0.475440i
$277$	−258.265	−	258.265i	−0.0560205	−	0.0560205i	0.678542	−	0.734562i	$-0.262612\pi$
$277$	−258.265	−	258.265i	−0.0560205	−	0.0560205i	−0.734562	+	0.678542i	$0.762612\pi$
$278$	−148.469	−	10.6187i	−0.0320308	−	0.00229089i
$279$	98.0849	−	152.623i	0.0210473	−	0.0327502i
$280$	953.862	−	770.592i	0.203586	−	0.164470i
$281$	−2253.62	−	1029.19i	−0.478434	−	0.218493i	0.161576	−	0.986860i	$-0.448342\pi$
$281$	−2253.62	−	1029.19i	−0.478434	−	0.218493i	−0.640010	+	0.768367i	$0.721070\pi$
$282$	−647.245	+	864.618i	−0.136677	+	0.182579i
$283$	482.929	+	884.418i	0.101439	+	0.185771i	0.923469	−	0.383672i	$-0.125341\pi$
$283$	482.929	+	884.418i	0.101439	+	0.185771i	−0.822031	+	0.569443i	$0.807159\pi$
$284$	−140.639	−	218.838i	−0.0293851	−	0.0457241i
$285$	6244.78	−	3135.45i	1.29793	−	0.651678i
$286$	1510.47	+	5144.20i	0.312294	+	1.06358i
$287$	−11.7647	−	164.493i	−0.00241969	−	0.0338317i
$288$	−18.7174	−	261.703i	−0.00382962	−	0.0535451i
$289$	2241.76	+	7634.73i	0.456292	+	1.55399i
$290$	−1409.80	+	707.847i	−0.285469	+	0.143332i
$291$	1673.74	+	2604.39i	0.337169	+	0.524645i
$292$	1552.84	+	2843.81i	0.311208	+	0.569935i
$293$	2618.46	−	3497.86i	0.522090	−	0.697430i	−0.459555	−	0.888149i	$-0.651991\pi$
$293$	2618.46	−	3497.86i	0.522090	−	0.697430i	0.981645	+	0.190719i	$0.0610820\pi$
$294$	3256.92	+	1487.39i	0.646081	+	0.295055i
$295$	−6985.90	+	5643.67i	−1.37876	+	1.11385i
$296$	−3239.25	+	5040.37i	−0.636073	+	0.989748i
$297$	−7638.19	−	546.294i	−1.49230	−	0.106731i
$298$	−1053.67	−	1053.67i	−0.204823	−	0.204823i
$299$	3910.15	+	3197.08i	0.756287	+	0.618368i
$300$	−1623.82	+	1883.26i	−0.312505	+	0.362434i
$301$	445.262	+	513.860i	0.0852641	+	0.0984000i
$302$	−1223.56	−	5624.63i	−0.233140	−	1.07173i
$303$	−4856.62	−	6487.69i	−0.920811	−	1.23006i
$304$	−994.717	+	2178.13i	−0.187668	+	0.410935i
$305$	−3089.98	+	4462.03i	−0.580104	+	0.837689i
$306$	−114.632	+	390.400i	−0.0214152	+	0.0729336i
$307$	−1788.47	−	389.058i	−0.332487	−	0.0723281i	0.0432230	−	0.999065i	$-0.486237\pi$
$307$	−1788.47	−	389.058i	−0.332487	−	0.0723281i	−0.375710	+	0.926737i	$0.622601\pi$
$308$	889.070	+	331.606i	0.164479	+	0.0613474i
$309$	−651.392	+	191.266i	−0.119924	+	0.0352128i
$310$	1519.61	−	1890.44i	0.278413	−	0.346354i
$311$	1585.35	−	1829.59i	0.289058	−	0.333590i	−0.592585	−	0.805508i	$-0.701893\pi$
$311$	1585.35	−	1829.59i	0.289058	−	0.333590i	0.881643	+	0.471918i	$0.156438\pi$
$312$	5224.62	+	2852.86i	0.948031	+	0.517664i
$313$	1128.80	−	3026.44i	0.203846	−	0.546532i	−0.794292	−	0.607537i	$-0.792158\pi$
$313$	1128.80	−	3026.44i	0.203846	−	0.546532i	0.998137	+	0.0610048i	$0.0194305\pi$
$314$	−1682.45	+	1081.25i	−0.302377	+	0.194326i
$315$	84.8696	+	21.5514i	0.0151805	+	0.00385486i
$316$	−1392.64	+	200.231i	−0.247918	+	0.0356452i
$317$	5316.65	−	1983.01i	0.941996	−	0.351346i	0.168898	−	0.985633i	$-0.445979\pi$
$317$	5316.65	−	1983.01i	0.941996	−	0.351346i	0.773098	+	0.634287i	$0.218706\pi$
$318$	−2581.58	+	1932.55i	−0.455245	+	0.340792i
$319$	−3240.61	−	2082.61i	−0.568775	−	0.365530i
$320$	184.239	−	5341.32i	0.0321852	−	0.933090i
$321$		−	9241.17i		−	1.60683i
$322$	−1002.72	+	248.355i	−0.173538	+	0.0429822i
$323$	−9353.50	+	9353.50i	−1.61128	+	1.61128i
$324$	−2167.44	+	1878.10i	−0.371646	+	0.322033i
$325$	−1625.96	−	5487.92i	−0.277514	−	0.936662i
$326$	−900.946	+	6266.22i	−0.153064	+	1.06458i
$327$	2538.21	+	6805.20i	0.429245	+	1.15085i
$328$	−708.034	−	530.028i	−0.119191	−	0.0892252i
$329$	−422.171	−	123.961i	−0.0707449	−	0.0207726i
$330$	6906.90	+	1237.44i	1.15216	+	0.206421i
$331$	177.122	+	387.844i	0.0294125	+	0.0644043i	0.923768	−	0.382952i	$-0.125093\pi$
$331$	177.122	+	387.844i	0.0294125	+	0.0644043i	−0.894356	+	0.447357i	$0.852365\pi$
$332$	1524.92	−	2792.69i	0.252081	−	0.461653i
$333$	−426.750	+	30.5218i	−0.0702275	+	0.00502277i
$334$	2270.57	+	1967.46i	0.371976	+	0.322319i
$335$	2071.37	+	6198.21i	0.337824	+	1.01088i
$336$	−452.812	+	206.792i	−0.0735206	+	0.0335757i
$337$	0.229437	−	1.05471i	3.70868e−5	−	0.000170485i	−0.977128	−	0.212651i	$-0.931790\pi$
$337$	0.229437	−	1.05471i	3.70868e−5	−	0.000170485i	0.977165	+	0.212480i	$0.0681541\pi$
$338$	182.298	−	99.5423i	0.0293364	−	0.0160189i
$339$	1057.23	+	7353.17i	0.169383	+	1.17808i
$340$	1796.09	−	4351.15i	0.286489	−	0.694041i
$341$	5862.46	+	842.894i	0.930996	+	0.133857i
$342$	−408.636	+	88.8934i	−0.0646097	+	0.0140550i
$343$	−214.714	+	3002.10i	−0.0338002	+	0.472589i
$344$	3646.56			0.571538
$345$	6029.10	−	2710.64i	0.940857	−	0.423003i
$346$	965.272			0.149981
$347$	−811.048	+	11339.9i	−0.125474	+	1.75435i	0.412105	+	0.911136i	$0.364794\pi$
$347$	−811.048	+	11339.9i	−0.125474	+	1.75435i	−0.537579	+	0.843213i	$0.680661\pi$
$348$	−1324.41	+	288.108i	−0.204011	+	0.0443799i
$349$	−9432.89	−	1356.25i	−1.44679	−	0.208018i	−0.626260	−	0.779615i	$-0.715415\pi$
$349$	−9432.89	−	1356.25i	−1.44679	−	0.208018i	−0.820535	+	0.571597i	$0.806324\pi$
$350$	1097.83	+	406.421i	0.167662	+	0.0620689i
$351$	−882.620	−	6138.76i	−0.134219	−	0.933512i
$352$	7517.64	−	4104.94i	1.13833	−	0.621575i
$353$	−1546.68	+	7109.97i	−0.233205	+	1.07203i	0.700407	+	0.713743i	$0.253002\pi$
$353$	−1546.68	+	7109.97i	−0.233205	+	1.07203i	−0.933613	+	0.358284i	$0.883362\pi$
$354$	8110.89	−	3704.12i	1.21777	−	0.556135i
$355$	349.923	−	701.194i	0.0523155	−	0.104832i
$356$	−4060.03	−	3518.03i	−0.604441	−	0.523751i
$357$	−2742.94	+	196.179i	−0.406644	+	0.0290837i
$358$	3178.93	−	5821.78i	0.469307	−	0.859471i
$359$	−5480.86	−	12001.4i	−0.805762	−	1.76437i	−0.624639	−	0.780913i	$-0.714754\pi$
$359$	−5480.86	−	12001.4i	−0.805762	−	1.76437i	−0.181123	−	0.983460i	$-0.557973\pi$
$360$	385.420	−	268.300i	0.0564262	−	0.0392795i
$361$	−6463.72	−	1897.92i	−0.942371	−	0.276705i
$362$	645.895	+	483.511i	0.0937775	+	0.0702010i
$363$	3494.62	+	9369.45i	0.505290	+	1.35473i
$364$	−109.369	+	760.680i	−0.0157486	+	0.109534i
$365$	−4970.51	+	8400.69i	−0.712789	+	1.20469i
$366$	4072.56	−	3528.90i	0.581629	−	0.503985i
$367$	−2965.57	+	2965.57i	−0.421802	+	0.421802i	−0.885824	−	0.464022i	$-0.846406\pi$
$367$	−2965.57	+	2965.57i	−0.421802	+	0.421802i	0.464022	+	0.885824i	$0.346406\pi$
$368$	−1028.31	+	2018.36i	−0.145665	+	0.285908i
$369$		−	63.1562i		−	0.00890998i
$370$	−5716.47	−	197.179i	−0.803203	−	0.0277049i
$371$	−1105.19	−	710.260i	−0.154659	−	0.0993932i
$372$	1668.28	−	1248.86i	0.232517	−	0.174060i
$373$	5673.91	−	2116.26i	0.787625	−	0.293769i	0.0767161	−	0.997053i	$-0.475556\pi$
$373$	5673.91	−	2116.26i	0.787625	−	0.293769i	0.710909	+	0.703284i	$0.248284\pi$
$374$	−13147.8	+	1890.37i	−1.81780	+	0.261361i
$375$	−7376.92	−	1303.07i	−1.01585	−	0.179441i
$376$	−1985.13	+	1275.77i	−0.272275	+	0.174981i
$377$	1090.25	−	2923.08i	0.148941	−	0.399328i
$378$	1113.29	+	607.900i	0.151485	+	0.0827170i
$379$	6658.97	−	7684.86i	0.902502	−	1.04154i	−0.0964301	−	0.995340i	$-0.530742\pi$
$379$	6658.97	−	7684.86i	0.902502	−	1.04154i	0.998932	−	0.0462030i	$-0.0147121\pi$
$380$	4809.78	−	523.044i	0.649307	−	0.0706095i
$381$	863.168	−	253.449i	0.116067	−	0.0340803i
$382$	2982.28	+	1112.33i	0.399442	+	0.148984i
$383$	−12372.5	−	2691.48i	−1.65067	−	0.359081i	−0.711540	−	0.702645i	$-0.752002\pi$
$383$	−12372.5	−	2691.48i	−1.65067	−	0.359081i	−0.939129	+	0.343564i	$0.888366\pi$
$384$	335.278	−	1141.85i	0.0445563	−	0.151745i
$385$	510.983	+	2812.54i	0.0676419	+	0.372313i
$386$	450.572	−	986.614i	0.0594132	−	0.130097i
$387$	156.048	+	208.455i	0.0204970	+	0.0273808i
$388$	455.631	+	2094.50i	0.0596164	+	0.274052i
$389$	6260.01	+	7224.44i	0.815926	+	0.941629i	0.999141	−	0.0414440i	$-0.0131958\pi$
$389$	6260.01	+	7224.44i	0.815926	+	0.941629i	−0.183215	+	0.983073i	$0.558650\pi$
$390$	209.767	+	5679.02i	0.0272358	+	0.737354i
$391$	−9218.97	+	8461.71i	−1.19239	+	1.09444i
$392$	5531.58	+	5531.58i	0.712722	+	0.712722i
$393$	2172.54	+	155.383i	0.278855	+	0.0199441i
$394$	2223.31	−	3459.54i	0.284287	−	0.442359i
$395$	−2663.55	−	3297.02i	−0.339286	−	0.419978i
$396$	330.558	+	150.961i	0.0419473	+	0.0191567i
$397$	−1099.10	+	1468.22i	−0.138947	+	0.185612i	−0.864617	−	0.502431i	$-0.832439\pi$
$397$	−1099.10	+	1468.22i	−0.138947	+	0.185612i	0.725670	+	0.688043i	$0.241530\pi$
$398$	2328.99	+	4265.23i	0.293321	+	0.537178i
$399$	−1528.07	−	2377.72i	−0.191727	−	0.298333i
$400$	2250.00	−	1235.73i	0.281251	−	0.154467i
$401$	2829.57	+	9636.64i	0.352375	+	1.20008i	0.924906	+	0.380195i	$0.124143\pi$
$401$	2829.57	+	9636.64i	0.352375	+	1.20008i	−0.572532	+	0.819882i	$0.694039\pi$
$402$	−462.887	−	6472.01i	−0.0574297	−	0.802971i
$403$	342.197	+	4784.54i	0.0422979	+	0.591402i
$404$	−1580.83	−	5383.82i	−0.194676	−	0.663007i
$405$	−8200.92	−	2718.42i	−1.00619	−	0.333529i
$406$	344.970	+	536.784i	0.0421689	+	0.0656161i
$407$	−6693.79	−	12258.8i	−0.815230	−	1.49298i
$408$	−8838.29	+	11806.6i	−1.07245	+	1.43263i
$409$	2519.30	+	1150.52i	0.304575	+	0.139095i	0.561839	−	0.827246i	$-0.310094\pi$
$409$	2519.30	+	1150.52i	0.304575	+	0.139095i	−0.257264	+	0.966341i	$0.582821\pi$
$410$	89.2319	−	839.618i	0.0107484	−	0.101136i
$411$	7873.82	−	12251.9i	0.944981	−	1.47042i
$412$	−468.851	−	33.5329i	−0.0560646	−	0.00400982i
$413$	2568.59	+	2568.59i	0.306034	+	0.306034i
$414$	−389.815	+	67.4746i	−0.0462763	+	0.00801014i
$415$	9579.03	−	353.823i	1.13305	−	0.0418517i
$416$	4542.76	+	5242.63i	0.535402	+	0.617887i
$417$	−81.8943	−	376.462i	−0.00961722	−	0.0442097i
$418$	−8181.53	−	10929.2i	−0.957348	−	1.27887i
$419$	2583.14	−	5656.28i	0.301180	−	0.659492i	−0.697170	−	0.716905i	$-0.745558\pi$
$419$	2583.14	−	5656.28i	0.301180	−	0.659492i	0.998351	+	0.0574130i	$0.0182852\pi$
$420$	826.888	+	572.624i	0.0960666	+	0.0665266i
$421$	1812.72	−	6173.56i	0.209849	−	0.714681i	−0.785544	−	0.618806i	$-0.787617\pi$
$421$	1812.72	−	6173.56i	0.209849	−	0.714681i	0.995393	−	0.0958754i	$-0.0305650\pi$
$422$	−3811.58	−	829.159i	−0.439680	−	0.0956465i
$423$	−157.879	−	58.8859i	−0.0181474	−	0.00676863i
$424$	−6760.30	+	1985.00i	−0.774315	+	0.227359i
$425$	14031.5	−	2052.39i	1.60147	−	0.234249i
$426$	−509.526	+	588.024i	−0.0579498	+	0.0668776i
$427$	1926.78	+	1052.10i	0.218369	+	0.119238i
$428$	2236.00	−	5994.95i	0.252526	−	0.677049i
$429$	−11674.0	+	7502.44i	−1.31382	+	0.844339i
$430$	1780.02	+	2991.74i	0.199629	+	0.335522i
$431$	8288.72	−	1191.74i	0.926342	−	0.133188i	0.337399	−	0.941362i	$-0.390453\pi$
$431$	8288.72	−	1191.74i	0.926342	−	0.133188i	0.588944	+	0.808174i	$0.299544\pi$
$432$	2606.09	−	972.022i	0.290244	−	0.108256i
$433$	−210.083	+	157.266i	−0.0233163	+	0.0174544i	−0.610872	−	0.791729i	$-0.709181\pi$
$433$	−210.083	+	157.266i	−0.0233163	+	0.0174544i	0.587556	+	0.809184i	$0.300090\pi$
$434$	−825.320	−	530.401i	−0.0912825	−	0.0586637i
$435$	−2785.96	−	2985.02i	−0.307073	−	0.329014i
$436$			5028.83i			0.552379i
$437$	−12174.1	−	4148.24i	−1.33265	−	0.454090i
$438$	6852.84	−	6852.84i	0.747583	−	0.747583i
$439$	6694.96	−	5801.22i	0.727866	−	0.630700i	−0.209998	−	0.977702i	$-0.567346\pi$
$439$	6694.96	−	5801.22i	0.727866	−	0.630700i	0.937864	+	0.347002i	$0.112800\pi$
$440$	13194.3	+	7806.78i	1.42958	+	0.845849i
$441$	−79.4988	+	552.926i	−0.00858426	+	0.0597048i
$442$	−3759.46	−	10079.5i	−0.404568	−	1.08469i
$443$	1073.24	+	803.420i	0.115105	+	0.0861662i	0.655279	−	0.755387i	$-0.272551\pi$
$443$	1073.24	+	803.420i	0.115105	+	0.0861662i	−0.540175	+	0.841553i	$0.681642\pi$
$444$	−4715.36	−	1384.56i	−0.504012	−	0.147991i
$445$	2854.05	−	15930.2i	0.304034	−	1.69700i
$446$	1930.49	+	4227.18i	0.204958	+	0.448795i
$447$	1848.41	−	3385.10i	0.195585	−	0.358188i
$448$	−2156.24	+	154.217i	−0.227394	+	0.0162635i
$449$	3396.52	+	2943.10i	0.356997	+	0.309339i	0.814831	−	0.579698i	$-0.196829\pi$
$449$	3396.52	+	2943.10i	0.356997	+	0.309339i	−0.457835	+	0.889037i	$0.651375\pi$
$450$	408.259	+	185.243i	0.0427678	+	0.0194054i
$451$	1875.47	−	856.501i	0.195815	−	0.0894258i
$452$	−1093.33	+	5025.97i	−0.113774	+	0.523013i
$453$	13076.4	−	7140.25i	1.35625	−	0.740570i
$454$	−892.744	−	6209.17i	−0.0922876	−	0.641874i
$455$	−2137.82	+	888.573i	−0.220269	+	0.0915537i
$456$	−15004.0	−	2157.25i	−1.54084	−	0.221540i
$457$	11164.8	−	2428.75i	1.14282	−	0.248604i	0.398975	−	0.916962i	$-0.369366\pi$
$457$	11164.8	−	2428.75i	1.14282	−	0.248604i	0.743840	+	0.668357i	$0.233002\pi$
$458$	662.700	−	9265.76i	0.0676112	−	0.945328i
$459$	15365.4			1.56252
$460$	4567.07	−	299.646i	0.462915	−	0.0303719i
$461$	−18562.8			−1.87539			−0.937695	−	0.347459i	$-0.887045\pi$
$461$	−18562.8			−1.87539			−0.937695	+	0.347459i	$0.887045\pi$
$462$	202.474	−	2830.96i	0.0203895	−	0.285082i
$463$	4477.77	−	974.080i	0.449459	−	0.0977739i	0.0178624	−	0.999840i	$-0.494314\pi$
$463$	4477.77	−	974.080i	0.449459	−	0.0977739i	0.431597	+	0.902067i	$0.357950\pi$
$464$	1384.94	+	199.125i	0.138565	+	0.0199227i
$465$	5802.98	+	2395.38i	0.578724	+	0.238888i
$466$	−989.816	−	6884.32i	−0.0983956	−	0.684356i
$467$	−10916.5	+	5960.87i	−1.08170	+	0.590655i	−0.918293	−	0.395903i	$-0.870432\pi$
$467$	−10916.5	+	5960.87i	−1.08170	+	0.590655i	−0.163412	+	0.986558i	$0.552250\pi$
$468$	−62.5603	+	287.585i	−0.00617917	+	0.0284052i
$469$	2404.47	−	1098.09i	0.236734	−	0.108113i
$470$	−2015.70	−	1005.91i	−0.197824	−	0.0987218i
$471$	−3912.12	−	3389.87i	−0.382720	−	0.331628i
$472$	19432.0	−	1389.80i	1.89498	−	0.135532i
$473$	−4073.98	+	7460.95i	−0.396030	+	0.725274i
$474$	1748.18	+	3827.97i	0.169402	+	0.370938i
$475$	8762.94	+	11646.6i	0.846466	+	1.12501i
$476$	−1826.87	−	536.418i	−0.175913	−	0.0516527i
$477$	−402.767	−	301.508i	−0.0386613	−	0.0289415i
$478$	316.032	+	847.316i	0.0302406	+	0.0810781i
$479$	−2134.07	+	14842.8i	−0.203566	+	1.41583i	0.590026	+	0.807384i	$0.299118\pi$
$479$	−2134.07	+	14842.8i	−0.203566	+	1.41583i	−0.793592	+	0.608450i	$0.791792\pi$
$480$	8794.27	−	2256.04i	0.836253	−	0.214528i
$481$	8548.97	−	7407.72i	0.810394	−	0.702210i
$482$	5282.81	−	5282.81i	0.499222	−	0.499222i
$483$	−1347.98	−	2309.12i	−0.126988	−	0.217534i
$484$			6923.73i			0.650237i
$485$	−4720.70	+	4405.89i	−0.441971	+	0.412497i
$486$	845.325	+	543.257i	0.0788986	+	0.0507050i
$487$	−9451.21	+	7075.09i	−0.879415	+	0.658322i	−0.940494	−	0.339811i	$-0.889637\pi$
$487$	−9451.21	+	7075.09i	−0.879415	+	0.658322i	0.0610786	+	0.998133i	$0.480546\pi$
$488$	11031.4	−	4114.48i	1.02329	−	0.381668i
$489$	−16219.0	+	2331.94i	−1.49989	+	0.215652i
$490$	−1838.10	+	7238.45i	−0.169463	+	0.667347i
$491$	4300.87	−	2764.00i	0.395306	−	0.254048i	−0.327854	−	0.944729i	$-0.606325\pi$
$491$	4300.87	−	2764.00i	0.395306	−	0.254048i	0.723160	+	0.690681i	$0.242689\pi$
$492$	253.519	−	679.711i	0.0232307	−	0.0622840i
$493$	6783.94	+	3704.31i	0.619743	+	0.338406i
$494$	7240.70	−	8356.21i	0.659462	−	0.761060i
$495$	118.351	+	1088.33i	0.0107464	+	0.0988216i
$496$	−2064.14	+	606.086i	−0.186860	+	0.0548671i
$497$	−296.989	−	110.771i	−0.0268044	−	0.00999751i
$498$	−9299.68	−	2023.02i	−0.836805	−	0.182036i
$499$	−455.648	+	1551.79i	−0.0408770	+	0.139214i	−0.977403	−	0.211383i	$-0.932203\pi$
$499$	−455.648	+	1551.79i	−0.0408770	+	0.139214i	0.936526	+	0.350597i	$0.114021\pi$
$500$	−4470.28	−	2630.26i	−0.399834	−	0.235257i
$501$	−3230.40	+	7073.60i	−0.288072	+	0.630789i
$502$	−1773.41	−	2368.99i	−0.157671	−	0.210624i
$503$	821.080	+	3774.44i	0.0727836	+	0.334581i	0.999112	−	0.0421366i	$-0.0134165\pi$
$503$	821.080	+	3774.44i	0.0727836	+	0.334581i	−0.926328	+	0.376717i	$0.877053\pi$
$504$	−124.389	−	143.553i	−0.0109935	−	0.0126872i
$505$	11503.3	−	12385.7i	1.01364	−	1.09140i
$506$	−7290.24	−	10660.8i	−0.640495	−	0.936623i
$507$	380.145	+	380.145i	0.0332995	+	0.0332995i
$508$	621.280	+	44.4348i	0.0542615	+	0.00388086i
$509$	−11556.4	+	17982.1i	−1.00634	+	1.56590i	−0.195443	+	0.980715i	$0.562614\pi$
$509$	−11556.4	+	17982.1i	−1.00634	+	1.56590i	−0.810900	+	0.585185i	$0.801022\pi$
$510$	−14000.8	−	1487.96i	−1.21562	−	0.129192i
$511$	3591.35	+	1640.12i	0.310904	+	0.141985i
$512$	−4252.28	+	5680.38i	−0.367043	+	0.490312i
$513$	7568.60	+	13860.9i	0.651388	+	1.19293i
$514$	5042.31	+	7845.99i	0.432698	+	0.673291i
$515$	−635.386	−	1265.48i	−0.0543659	−	0.108279i
$516$	842.671	+	2869.87i	0.0718925	+	0.244843i
$517$	−392.434	−	5486.94i	−0.0333834	−	0.466761i
$518$	165.048	+	2307.68i	0.0139996	+	0.195741i
$519$	703.890	+	2397.23i	0.0595325	+	0.202749i
$520$	−3906.68	+	11785.7i	−0.329460	+	0.993915i
$521$	2321.07	+	3611.65i	0.195178	+	0.303703i	0.925024	−	0.379909i	$-0.124045\pi$
$521$	2321.07	+	3611.65i	0.195178	+	0.303703i	−0.729846	+	0.683612i	$0.760408\pi$
$522$	117.110	+	214.472i	0.00981951	+	0.0179831i
$523$	608.417	−	812.750i	0.0508685	−	0.0679523i	−0.774386	−	0.632714i	$-0.781941\pi$
$523$	608.417	−	812.750i	0.0508685	−	0.0679523i	0.825254	+	0.564762i	$0.191032\pi$
$524$	1371.78	+	626.470i	0.114363	+	0.0522280i
$525$	−208.781	+	3022.81i	−0.0173561	+	0.251288i
$526$	−5396.06	+	8396.44i	−0.447300	+	0.696012i
$527$	−11853.9	−	847.808i	−0.979818	−	0.0700780i
$528$	−4400.77	−	4400.77i	−0.362725	−	0.362725i
$529$	−11338.3	−	4413.47i	−0.931890	−	0.362741i
$530$	−4928.52	−	4577.40i	−0.403927	−	0.375150i
$531$	911.004	+	1051.35i	0.0744524	+	0.0859226i
$532$	−415.976	−	1912.21i	−0.0339001	−	0.155836i
$533$	1000.69	+	1336.76i	0.0813220	+	0.108633i
$534$	−6675.05	+	14616.3i	−0.540932	+	1.18448i
$535$	18964.8	−	3445.53i	1.53256	−	0.278436i
$536$	3993.99	−	13602.3i	0.321854	−	1.09614i
$537$	16776.4	+	3649.48i	1.34815	+	0.293271i
$538$	−1382.78	−	515.749i	−0.110810	−	0.0413300i
$539$	−17497.7	+	5137.79i	−1.39829	+	0.410576i
$540$	−4380.24	−	3521.02i	−0.349066	−	0.280593i
$541$	−9627.75	+	11111.0i	−0.765119	+	0.882994i	−0.995942	−	0.0900018i	$-0.971313\pi$
$541$	−9627.75	+	11111.0i	−0.765119	+	0.882994i	0.230823	+	0.972996i	$0.425858\pi$
$542$	4643.89	+	2535.76i	0.368030	+	0.200960i
$543$	−729.791	+	1956.65i	−0.0576765	+	0.154637i
$544$	−14458.4	+	9291.84i	−1.13952	+	0.732324i
$545$	−13019.3	+	7746.22i	−1.02328	+	0.608828i
$546$	2275.22	−	327.127i	0.178334	−	0.0256406i
$547$	19367.2	−	7223.60i	1.51386	−	0.564641i	0.550969	−	0.834526i	$-0.314258\pi$
$547$	19367.2	−	7223.60i	1.51386	−	0.564641i	0.962893	+	0.269885i	$0.0869857\pi$
$548$	8072.40	−	6042.92i	0.629263	−	0.471060i
$549$	707.270	+	454.535i	0.0549828	+	0.0353353i
$550$	35.7258	+	14635.8i	0.00276973	+	1.13468i
$551$			7944.30i			0.614226i
$552$	−14093.5	−	2646.26i	−1.08670	−	0.204044i
$553$	−1212.26	+	1212.26i	−0.0932195	+	0.0932195i
$554$	−571.640	+	495.329i	−0.0438388	+	0.0379865i
$555$	−3678.84	−	14340.5i	−0.281366	−	1.09679i
$556$	37.9624	−	264.034i	0.00289562	−	0.0201395i
$557$	−3032.28	−	8129.86i	−0.230668	−	0.618444i	0.769119	−	0.639106i	$-0.220695\pi$
$557$	−3032.28	−	8129.86i	−0.230668	−	0.618444i	−0.999787	+	0.0206617i	$0.993423\pi$
$558$	−300.774	−	225.157i	−0.0228186	−	0.0170818i
$559$	−6605.80	−	1939.64i	−0.499813	−	0.146758i
$560$	−593.210	−	852.163i	−0.0447638	−	0.0643044i
$561$	−14282.3	−	31273.8i	−1.07486	−	2.35362i
$562$	−2458.90	+	4503.13i	−0.184559	+	0.337995i
$563$	1731.19	−	123.817i	0.129593	−	0.00926869i	−0.00639188	−	0.999980i	$-0.502035\pi$
$563$	1731.19	−	123.817i	0.129593	−	0.00926869i	0.135985	+	0.990711i	$0.456580\pi$
$564$	−1462.78	−	1267.51i	−0.109209	−	0.0946305i
$565$	−14696.1	+	4911.25i	−1.09428	+	0.365695i
$566$	1898.24	−	866.898i	0.140970	−	0.0643788i
$567$	−742.831	+	3414.74i	−0.0550193	+	0.252920i
$568$	−1492.02	+	814.706i	−0.110218	+	0.0601836i
$569$	−71.3585	−	496.310i	−0.00525748	−	0.0365666i	0.987024	−	0.160574i	$-0.0513345\pi$
$569$	−71.3585	−	496.310i	−0.00525748	−	0.0365666i	−0.992281	+	0.124007i	$0.960425\pi$
$570$	−5554.14	−	13362.7i	−0.408136	−	0.981935i
$571$	−2927.61	−	420.927i	−0.214565	−	0.0308498i	0.0341940	−	0.999415i	$-0.489114\pi$
$571$	−2927.61	−	420.927i	−0.214565	−	0.0308498i	−0.248759	+	0.968565i	$0.580023\pi$
$572$	−9388.49	+	2042.34i	−0.686281	+	0.149291i
$573$	−587.731	+	8217.55i	−0.0428496	+	0.599116i
$574$	−341.522			−0.0248342
$575$	7810.72	+	11362.3i	0.566486	+	0.824071i
$576$	−827.877			−0.0598869
$577$	556.799	−	7785.07i	0.0401731	−	0.561693i	−0.937011	−	0.349299i	$-0.886420\pi$
$577$	556.799	−	7785.07i	0.0401731	−	0.561693i	0.977184	−	0.212393i	$-0.0681258\pi$
$578$	16101.8	−	3502.74i	1.15873	−	0.252067i
$579$	2778.80	+	399.531i	0.199452	+	0.0286769i
$580$	−1085.06	−	2610.54i	−0.0776803	−	0.186891i
$581$	−551.779	−	3837.71i	−0.0394004	−	0.274036i
$582$	5627.01	−	3072.58i	0.400768	−	0.218836i
$583$	3491.34	−	16049.4i	0.248021	−	1.14014i
$584$	19260.8	−	8796.11i	1.36476	−	0.623263i
$585$	−840.906	+	281.021i	−0.0594311	+	0.0198612i
$586$	−6838.49	−	5925.58i	−0.482074	−	0.417719i
$587$	7273.62	−	520.219i	0.511438	−	0.0365788i	0.186764	−	0.982405i	$-0.440200\pi$
$587$	7273.62	−	520.219i	0.511438	−	0.0365788i	0.324674	+	0.945826i	$0.394745\pi$
$588$	−3075.13	+	5631.68i	−0.215674	+	0.394977i
$589$	−5074.12	−	11110.8i	−0.354967	−	0.777269i
$590$	10625.7	+	15264.2i	0.741448	+	1.06511i
$591$	10213.0	+	2998.80i	0.710838	+	0.208721i
$592$	4061.34	+	3040.28i	0.281959	+	0.211072i
$593$	−3424.26	−	9180.80i	−0.237129	−	0.635768i	0.762812	−	0.646620i	$-0.223818\pi$
$593$	−3424.26	−	9180.80i	−0.237129	−	0.635768i	−0.999941	+	0.0108525i	$0.996545\pi$
$594$	−2256.90	+	15697.1i	−0.155895	+	1.08427i
$595$	−1425.29	−	5555.94i	−0.0982040	−	0.382809i
$596$	2018.16	−	1748.75i	0.138703	−	0.120187i
$597$	−8894.27	+	8894.27i	−0.609745	+	0.609745i
$598$	7181.71	−	7604.65i	0.491107	−	0.520029i
$599$		−	1121.14i		−	0.0764752i	−0.999269	−	0.0382376i	$-0.987826\pi$
$599$		−	1121.14i		−	0.0764752i	0.999269	−	0.0382376i	$-0.0121744\pi$
$600$	11518.7	+	11462.6i	0.783747	+	0.779930i
$601$	6145.38	+	3949.40i	0.417097	+	0.268052i	0.732313	−	0.680968i	$-0.238441\pi$
$601$	6145.38	+	3949.40i	0.417097	+	0.268052i	−0.315216	+	0.949020i	$0.602077\pi$
$602$	1127.24	−	843.838i	0.0763167	−	0.0571300i
$603$	948.488	−	353.768i	0.0640554	−	0.0238914i
$604$	10210.6	−	1468.06i	0.687853	−	0.0988984i
$605$	−17925.1	+	10665.1i	−1.20456	+	0.716688i
$606$	−14118.8	+	9073.58i	−0.946428	+	0.608233i
$607$	−6513.26	+	17462.7i	−0.435528	+	1.16769i	0.515037	+	0.857168i	$0.327778\pi$
$607$	−6513.26	+	17462.7i	−0.435528	+	1.16769i	−0.950565	+	0.310527i	$0.899495\pi$
$608$	−15503.8	−	8465.71i	−1.03415	−	0.564687i
$609$	−1081.53	+	1248.16i	−0.0719637	+	0.0830506i
$610$	8760.47	+	7042.01i	0.581477	+	0.467414i
$611$	4274.70	−	1255.16i	0.283037	−	0.0831072i
$612$	−683.195	−	254.818i	−0.0451250	−	0.0168308i
$613$	−9728.80	−	2116.37i	−0.641015	−	0.139444i	−0.119702	−	0.992810i	$-0.538194\pi$
$613$	−9728.80	−	2116.37i	−0.641015	−	0.139444i	−0.521313	+	0.853365i	$0.674558\pi$
$614$	−1067.88	+	3636.87i	−0.0701892	+	0.239042i
$615$	2150.24	−	390.657i	0.140986	−	0.0256143i
$616$	2576.00	−	5640.66i	0.168490	−	0.368942i
$617$	2193.93	+	2930.74i	0.143151	+	0.191227i	0.866386	−	0.499374i	$-0.166437\pi$
$617$	2193.93	+	2930.74i	0.143151	+	0.191227i	−0.723235	+	0.690602i	$0.757346\pi$
$618$	298.852	+	1373.80i	0.0194524	+	0.0894214i
$619$	−10575.4	−	12204.6i	−0.686688	−	0.792481i	0.300201	−	0.953876i	$-0.402946\pi$
$619$	−10575.4	−	12204.6i	−0.686688	−	0.792481i	−0.986890	+	0.161395i	$0.948401\pi$
$620$	3184.93	+	2958.03i	0.206306	+	0.191608i
$621$	6592.27	+	13406.8i	0.425988	+	0.866337i
$622$	−3545.07	−	3545.07i	−0.228528	−	0.228528i
$623$	−6529.37	−	466.990i	−0.419894	−	0.0300314i
$624$	2725.07	−	4240.29i	0.174824	−	0.272031i
$625$	−76.2804	−	15624.8i	−0.00488195	−	0.999988i
$626$	−6084.78	−	2778.83i	−0.388493	−	0.177419i
$627$	21176.4	−	28288.4i	1.34881	−	1.80180i
$628$	−1717.66	−	3145.66i	−0.109144	−	0.199881i
$629$	15151.9	+	23576.8i	0.960484	+	1.49454i
$630$	57.0559	−	172.126i	0.00360819	−	0.0108852i
$631$	1913.19	+	6515.73i	0.120702	+	0.411073i	0.997571	−	0.0696562i	$-0.0221902\pi$
$631$	1913.19	+	6515.73i	0.120702	+	0.411073i	−0.876869	+	0.480729i	$0.840372\pi$
$632$	655.924	+	9171.02i	0.0412836	+	0.577221i
$633$	−720.264	−	10070.6i	−0.0452258	−	0.632339i
$634$	−3310.72	−	11275.3i	−0.207390	−	0.706307i
$635$	841.958	+	1676.90i	0.0526175	+	0.104797i
$636$	−3124.43	−	4861.71i	−0.194798	−	0.303112i
$637$	−7078.25	−	12962.9i	−0.440268	−	0.806290i
$638$	−4780.70	+	6386.27i	−0.296661	+	0.396293i
$639$	−110.421	−	50.4275i	−0.00683597	−	0.00312188i
$640$	2468.33	+	262.326i	0.152452	+	0.0162021i
$641$	16451.6	−	25599.3i	1.01373	−	1.57739i	0.214180	−	0.976794i	$-0.431292\pi$
$641$	16451.6	−	25599.3i	1.01373	−	1.57739i	0.799550	−	0.600600i	$-0.205072\pi$
$642$	−19089.0	−	1365.27i	−1.17349	−	0.0839298i
$643$	−4860.31	−	4860.31i	−0.298090	−	0.298090i	0.542175	−	0.840265i	$-0.317601\pi$
$643$	−4860.31	−	4860.31i	−0.298090	−	0.298090i	−0.840265	+	0.542175i	$0.817601\pi$
$644$	−315.747	−	1824.14i	−0.0193201	−	0.111617i
$645$	−6131.90	+	6602.27i	−0.374331	+	0.403045i
$646$	17939.2	+	20702.9i	1.09258	+	1.26090i
$647$	−5686.52	−	26140.5i	−0.345534	−	1.58839i	−0.742037	−	0.670359i	$-0.766140\pi$
$647$	−5686.52	−	26140.5i	−0.345534	−	1.58839i	0.396503	−	0.918034i	$-0.370224\pi$
$648$	11231.6	+	15003.7i	0.680893	+	0.909567i
$649$	−18866.1	+	41311.1i	−1.14108	+	2.49861i
$650$	−11576.3	+	2547.88i	−0.698554	+	0.153748i
$651$	715.403	−	2436.44i	0.0430704	−	0.146684i
$652$	−11085.8	−	2411.58i	−0.665882	−	0.144854i
$653$	14307.7	+	5336.49i	0.857432	+	0.319805i	0.739451	−	0.673210i	$-0.235085\pi$
$653$	14307.7	+	5336.49i	0.857432	+	0.319805i	0.117981	+	0.993016i	$0.462358\pi$
$654$	14432.1	−	4237.65i	0.862906	−	0.253372i
$655$	491.144	+	4516.44i	0.0292986	+	0.269423i
$656$	−490.421	+	565.976i	−0.0291886	+	0.0336855i
$657$	1327.06	+	724.628i	0.0788028	+	0.0430296i
$658$	−318.430	+	853.743i	−0.0188658	+	0.0505811i
$659$	21689.1	−	13938.7i	1.28207	−	0.823938i	0.290931	−	0.956744i	$-0.406035\pi$
$659$	21689.1	−	13938.7i	1.28207	−	0.823938i	0.991142	+	0.132806i	$0.0423986\pi$
$660$	−3094.98	+	12188.1i	−0.182533	+	0.718818i
$661$	−23603.4	+	3393.66i	−1.38890	+	0.199694i	−0.795863	−	0.605477i	$-0.792982\pi$
$661$	−23603.4	+	3393.66i	−1.38890	+	0.199694i	−0.593042	+	0.805171i	$0.702073\pi$
$662$	827.316	−	308.573i	0.0485718	−	0.0181163i
$663$	22290.7	−	16686.6i	1.30573	−	0.977459i
$664$	−17492.7	−	11241.9i	−1.02236	−	0.657034i
$665$	4309.84	−	4022.43i	0.251321	−	0.234561i
$666$			886.023i			0.0515506i
$667$	−321.588	+	7508.45i	−0.0186686	+	0.435875i
$668$	−3807.17	+	3807.17i	−0.220515	+	0.220515i
$669$	−9090.36	+	7876.84i	−0.525342	+	0.455211i
$670$	13109.3	−	3363.00i	0.755906	−	0.193917i
$671$	−3906.05	+	27167.2i	−0.224727	+	1.56301i
$672$	−1283.33	−	3440.75i	−0.0736692	−	0.197515i
$673$	−3756.71	−	2812.24i	−0.215172	−	0.161076i	0.486255	−	0.873817i	$-0.338362\pi$
$673$	−3756.71	−	2812.24i	−0.215172	−	0.161076i	−0.701427	+	0.712741i	$0.747453\pi$
$674$	−2.14475	−	0.629756i	−0.000122571	−	3.59901e-5i
$675$	2368.52	−	16763.8i	0.135058	−	0.955911i
$676$	154.628	+	338.589i	0.00879770	+	0.0192643i
$677$	−3802.15	+	6963.12i	−0.215847	+	0.395295i	−0.963059	−	0.269292i	$-0.913210\pi$
$677$	−3802.15	+	6963.12i	−0.215847	+	0.395295i	0.747211	+	0.664586i	$0.231392\pi$
$678$	15345.2	−	1097.51i	0.869219	−	0.0621678i
$679$	1973.91	+	1710.40i	0.111563	+	0.0966703i
$680$	−27524.9	−	13736.0i	−1.55225	−	0.774633i
$681$	14769.3	−	6744.93i	0.831075	−	0.379539i
$682$	2607.23	−	11985.2i	0.146387	−	0.672930i
$683$	−2284.89	+	1247.65i	−0.128007	+	0.0698973i	−0.541977	−	0.840394i	$-0.682324\pi$
$683$	−2284.89	+	1247.65i	−0.128007	+	0.0698973i	0.413969	+	0.910291i	$0.364142\pi$
$684$	−106.657	−	741.813i	−0.00596216	−	0.0414677i
$685$	28079.2	+	11590.6i	1.56620	+	0.646505i
$686$	6169.55	+	887.047i	0.343374	+	0.0493697i
$687$	23494.5	−	5110.92i	1.30476	−	0.283834i
$688$	220.273	−	3079.82i	0.0122061	−	0.170664i
$689$	13302.2			0.735523
$690$	−4708.49	−	12854.4i	−0.259782	−	0.709218i
$691$	18954.3			1.04349			0.521747	−	0.853100i	$-0.325280\pi$
$691$	18954.3			1.04349			0.521747	+	0.853100i	$0.325280\pi$
$692$	−123.407	+	1725.45i	−0.00677921	+	0.0947857i
$693$	432.683	−	94.1244i	0.0237175	−	0.00515944i
$694$	23304.4	+	3350.67i	1.27468	+	0.183271i
$695$	742.044	−	308.426i	0.0404998	−	0.0168335i
$696$	1260.54	+	8767.25i	0.0686504	+	0.477474i
$697$	−3631.01	+	1982.68i	−0.197324	+	0.107747i
$698$	−4195.12	+	19284.6i	−0.227489	+	1.04575i
$699$	16375.3	−	7478.33i	0.886079	−	0.404659i
$700$	−866.842	+	1910.45i	−0.0468051	+	0.103154i
$701$	−16377.3	−	14191.0i	−0.882401	−	0.764605i	0.0904830	−	0.995898i	$-0.471159\pi$
$701$	−16377.3	−	14191.0i	−0.882401	−	0.764605i	−0.972884	+	0.231293i	$0.925704\pi$
$702$	−12810.9	+	916.253i	−0.688769	+	0.0492617i
$703$	−13804.7	+	25281.5i	−0.740619	+	1.35634i
$704$	−11227.4	−	24584.5i	−0.601061	−	1.31614i
$705$	1028.28	−	5739.46i	0.0549324	−	0.306611i
$706$	14458.2	+	4245.30i	0.770737	+	0.226309i
$707$	−5473.44	−	4097.37i	−0.291160	−	0.217959i
$708$	5584.26	+	14972.0i	0.296426	+	0.794748i
$709$	5169.14	−	35952.2i	0.273810	−	1.90439i	−0.133412	−	0.991061i	$-0.542593\pi$
$709$	5169.14	−	35952.2i	0.273810	−	1.90439i	0.407222	−	0.913329i	$-0.366497\pi$
$710$	−1396.72	−	826.410i	−0.0738282	−	0.0436826i
$711$	−496.191	+	429.952i	−0.0261725	+	0.0226786i
$712$	−24824.5	+	24824.5i	−1.30665	+	1.30665i
$713$	−4345.97	−	10706.6i	−0.228272	−	0.562364i
$714$			5694.93i			0.298498i
$715$	−19749.2	−	21160.3i	−1.03298	−	1.10678i
$716$	10000.2	+	6426.72i	0.521961	+	0.335444i
$717$	−1873.83	+	1402.73i	−0.0976005	+	0.0730628i
$718$	−25600.4	+	9548.45i	−1.33064	+	0.496302i
$719$	9913.76	−	1425.38i	0.514215	−	0.0739330i	0.119678	−	0.992813i	$-0.461814\pi$
$719$	9913.76	−	1425.38i	0.514215	−	0.0739330i	0.394538	+	0.918880i	$0.370905\pi$
$720$	−203.320	−	341.726i	−0.0105240	−	0.0176880i
$721$	−481.835	+	309.656i	−0.0248883	+	0.0159947i
$722$	−4875.37	+	13071.4i	−0.251305	+	0.673775i
$723$	16972.0	+	9267.42i	0.873024	+	0.476707i
$724$	−946.863	+	1092.74i	−0.0486048	+	0.0560930i
$725$	5087.15	−	6830.33i	0.260596	−	0.349893i
$726$	19870.2	−	5834.43i	1.01578	−	0.298259i
$727$	20270.8	+	7560.62i	1.03412	+	0.385705i	0.808491	−	0.588509i	$-0.200285\pi$
$727$	20270.8	+	7560.62i	1.03412	+	0.385705i	0.225625	+	0.974214i	$0.427558\pi$
$728$	4907.37	+	1067.53i	0.249834	+	0.0543481i
$729$	5145.48	−	17523.9i	0.261417	−	0.890306i
$730$	16618.5	+	11508.4i	0.842573	+	0.583486i
$731$	7085.77	−	15515.7i	0.358518	−	0.785045i
$732$	5787.34	+	7730.97i	0.292221	+	0.390362i
$733$	990.979	+	4555.45i	0.0499354	+	0.229549i	0.995350	−	0.0963193i	$-0.0307070\pi$
$733$	990.979	+	4555.45i	0.0499354	+	0.229549i	−0.945415	+	0.325868i	$0.894343\pi$
$734$	5687.68	+	6563.94i	0.286017	+	0.330081i
$735$	−19316.9	+	713.512i	−0.969407	+	0.0358072i
$736$	−14310.5	−	8628.85i	−0.716701	−	0.432151i
$737$	23368.5	+	23368.5i	1.16796	+	1.16796i
$738$	−130.458	−	9.33057i	−0.00650710	−	0.000465397i
$739$	−745.199	+	1159.55i	−0.0370942	+	0.0577196i	−0.859305	−	0.511463i	$-0.829104\pi$
$739$	−745.199	+	1159.55i	−0.0370942	+	0.0577196i	0.822211	+	0.569182i	$0.192740\pi$
$740$	1083.29	−	10193.1i	0.0538143	−	0.506361i
$741$	26032.5	+	11888.6i	1.29059	+	0.589393i
$742$	−1630.42	+	2177.99i	−0.0806667	+	0.107758i
$743$	−9344.20	−	17112.6i	−0.461380	−	0.844955i	−0.999997	−	0.00240408i	$-0.999235\pi$
$743$	−9344.20	−	17112.6i	−0.461380	−	0.844955i	0.538617	−	0.842551i	$-0.318947\pi$
$744$	−7362.72	−	11456.6i	−0.362810	−	0.564543i
$745$	7636.11	+	2531.19i	0.375524	+	0.124477i
$746$	−3533.19	−	12032.9i	−0.173404	−	0.590560i
$747$	−105.927	−	1481.05i	−0.00518829	−	0.0725417i
$748$	−1698.19	−	23743.8i	−0.0830106	−	1.16064i
$749$	−2196.52	−	7480.65i	−0.107155	−	0.364936i
$750$	−3781.53	+	15045.6i	−0.184109	+	0.732516i
$751$	−5101.96	−	7938.80i	−0.247900	−	0.385740i	0.694896	−	0.719110i	$-0.255450\pi$
$751$	−5101.96	−	7938.80i	−0.247900	−	0.385740i	−0.942796	+	0.333370i	$0.891814\pi$
$752$	957.578	+	1753.67i	0.0464352	+	0.0850397i
$753$	4590.14	−	6131.71i	0.222144	−	0.296749i
$754$	−5876.98	−	2683.93i	−0.283856	−	0.129633i
$755$	19528.8	+	24173.3i	0.941356	+	1.16524i
$756$	−1228.97	+	1912.31i	−0.0591232	+	0.0919974i
$757$	121.646	+	8.70031i	0.00584057	+	0.000417726i	0.0742592	−	0.997239i	$-0.476341\pi$
$757$	121.646	+	8.70031i	0.00584057	+	0.000417726i	−0.0684186	+	0.997657i	$0.521795\pi$
$758$	−14890.4	−	14890.4i	−0.713515	−	0.713515i
$759$	21159.7	−	25879.2i	1.01192	−	1.23762i
$760$	−1167.05	−	31595.6i	−0.0557019	−	1.50802i
$761$	−10896.7	−	12575.5i	−0.519060	−	0.599027i	0.434335	−	0.900751i	$-0.356983\pi$
$761$	−10896.7	−	12575.5i	−0.519060	−	0.599027i	−0.953395	+	0.301724i	$0.902438\pi$
$762$	−396.013	−	1820.44i	−0.0188268	−	0.0865455i
$763$	3672.17	+	4905.45i	0.174235	+	0.232751i
$764$	−2369.60	+	5188.70i	−0.112211	+	0.245708i
$765$	−392.659	−	2161.26i	−0.0185577	−	0.102145i
$766$	−7387.53	+	25159.6i	−0.348462	+	1.18675i
$767$	−35940.6	−	7818.41i	−1.69197	−	0.368066i
$768$	−21515.3	−	8024.78i	−1.01089	−	0.377043i
$769$	8734.49	−	2564.68i	0.409589	−	0.120266i	−0.0704460	−	0.997516i	$-0.522442\pi$
$769$	8734.49	−	2564.68i	0.409589	−	0.120266i	0.480035	+	0.877250i	$0.340624\pi$
$770$	5885.20	−	639.992i	0.275439	−	0.0299529i
$771$	−15808.4	+	18243.9i	−0.738425	+	0.852188i
$772$	1705.99	+	931.544i	0.0795338	+	0.0434287i
$773$	−7719.50	+	20696.8i	−0.359186	+	0.963016i	0.624164	+	0.781294i	$0.285440\pi$
$773$	−7719.50	+	20696.8i	−0.359186	+	0.963016i	−0.983350	+	0.181722i	$0.941833\pi$
$774$	453.648	−	291.542i	0.0210673	−	0.0135391i
$775$	−2752.20	+	12802.0i	−0.127564	+	0.593370i
$776$	13865.1	−	1993.49i	0.641400	−	0.0922194i
$777$	−5610.71	+	2092.69i	−0.259052	+	0.0966213i
$778$	15848.0	−	11863.6i	0.730305	−	0.546699i
$779$	−3577.08	−	2298.85i	−0.164521	−	0.105731i
$780$	−10178.2	−	351.078i	−0.467229	−	0.0161162i
$781$		−	3962.92i		−	0.181568i
$782$	16116.9	+	20293.2i	0.737006	+	0.927986i
$783$	6525.24	−	6525.24i	0.297820	−	0.297820i
$784$	5006.02	−	4337.74i	0.228044	−	0.197601i
$785$	5498.10	−	9292.38i	0.249982	−	0.422496i
$786$	641.933	−	4464.74i	0.0291310	−	0.202611i
$787$	−2827.55	−	7580.96i	−0.128070	−	0.343370i	0.857051	−	0.515232i	$-0.172294\pi$
$787$	−2827.55	−	7580.96i	−0.128070	−	0.343370i	−0.985121	+	0.171862i	$0.945022\pi$
$788$	5899.78	+	4416.52i	0.266715	+	0.199660i
$789$	−24787.3	−	7278.19i	−1.11844	−	0.328404i
$790$	−7203.99	+	5014.86i	−0.324439	+	0.225849i
$791$	2603.58	+	5701.04i	0.117032	+	0.256265i
$792$	1138.12	−	2084.30i	0.0510621	−	0.0935133i
$793$	−22172.0	+	1585.77i	−0.992877	+	0.0710120i
$794$	2870.44	+	2487.25i	0.128298	+	0.111170i
$795$	7773.91	−	15577.8i	0.346808	−	0.694951i
$796$	−7921.97	+	3617.84i	−0.352747	+	0.161094i
$797$	−4244.94	+	19513.7i	−0.188662	+	0.867264i	0.781329	+	0.624120i	$0.214542\pi$
$797$	−4244.94	+	19513.7i	−0.188662	+	0.867264i	−0.969990	+	0.243144i	$0.921821\pi$
$798$	−5137.28	+	2805.16i	−0.227892	+	0.124438i
$799$	1570.85	+	10925.5i	0.0695528	+	0.483751i
$800$	7908.77	+	17206.5i	0.349521	+	0.760427i
$801$	−2481.41	−	356.772i	−0.109458	−	0.0157377i
$802$	20323.9	−	4421.20i	0.894841	−	0.194661i
$803$	−3521.37	+	49235.2i	−0.154753	+	2.16373i
$804$	11628.1			0.510063
$805$	4236.21	−	3627.28i	0.185474	−	0.158814i
$806$	9933.71			0.434119
$807$	272.510	−	3810.19i	0.0118870	−	0.166202i
$808$	−35830.5	+	7794.44i	−1.56004	+	0.339366i
$809$	24326.9	+	3497.68i	1.05722	+	0.152005i	0.648929	−	0.760849i	$-0.275217\pi$
$809$	24326.9	+	3497.68i	1.05722	+	0.152005i	0.408287	+	0.912854i	$0.366126\pi$
$810$	−6826.87	+	16538.6i	−0.296138	+	0.717416i
$811$	4958.06	+	34484.1i	0.214674	+	1.49309i	0.757271	+	0.653100i	$0.226532\pi$
$811$	4958.06	+	34484.1i	0.214674	+	1.49309i	−0.542597	+	0.839993i	$0.682559\pi$
$812$	−1003.62	+	548.017i	−0.0433745	+	0.0236843i
$813$	−2911.10	+	13382.1i	−0.125580	+	0.577283i
$814$	−26311.2	+	12015.9i	−1.13293	+	0.517392i
$815$	−10832.8	−	32415.3i	−0.465591	−	1.39320i
$816$	9437.74	+	8177.85i	0.404886	+	0.350836i
$817$	17486.6	−	1250.67i	0.748812	−	0.0535561i
$818$	2748.77	−	5034.00i	0.117492	−	0.215171i
$819$	148.976	+	326.213i	0.00635611	+	0.0139179i
$820$	1489.43	+	266.847i	0.0634308	+	0.0113643i
$821$	−22893.4	−	6722.11i	−0.973185	−	0.285753i	−0.243777	−	0.969831i	$-0.578386\pi$
$821$	−22893.4	−	6722.11i	−0.973185	−	0.285753i	−0.729408	+	0.684078i	$0.760205\pi$
$822$	−24144.8	−	18074.6i	−1.02451	−	0.766939i
$823$	−9973.36	−	26739.6i	−0.422417	−	1.13254i	−0.957674	−	0.287855i	$-0.907058\pi$
$823$	−9973.36	−	26739.6i	−0.422417	−	1.13254i	0.535257	−	0.844689i	$-0.320215\pi$
$824$	−437.157	+	3040.49i	−0.0184819	+	0.128544i
$825$	−36321.6	+	10761.3i	−1.53279	+	0.454136i
$826$	5685.27	−	4926.31i	0.239487	−	0.207516i
$827$	−13273.6	+	13273.6i	−0.558125	+	0.558125i	−0.928773	−	0.370648i	$-0.879136\pi$
$827$	−13273.6	+	13273.6i	−0.558125	+	0.558125i	0.370648	+	0.928773i	$0.379136\pi$
$828$	−70.7762	−	705.432i	−0.00297058	−	0.0296080i
$829$		−	40313.5i		−	1.68896i	−0.535590	−	0.844478i	$-0.679911\pi$
$829$		−	40313.5i		−	1.68896i	0.535590	−	0.844478i	$-0.320089\pi$
$830$	684.314	−	19839.2i	0.0286179	−	0.829671i
$831$	−1646.99	−	1058.45i	−0.0687525	−	0.0441846i
$832$	17522.8	−	13117.4i	0.730162	−	0.546592i
$833$	34284.9	−	12787.6i	1.42605	−	0.531890i
$834$	−789.736	+	113.547i	−0.0327894	+	0.00471440i
$835$	−15720.9	−	3992.10i	−0.651552	−	0.165452i
$836$	20582.3	−	13227.4i	0.851499	−	0.547225i
$837$	−4958.35	+	13293.8i	−0.204762	+	0.548988i
$838$	−11302.2	−	6171.49i	−0.465906	−	0.254404i
$839$	−16788.6	+	19375.1i	−0.690830	+	0.797260i	−0.987483	−	0.157725i	$-0.949584\pi$
$839$	−16788.6	+	19375.1i	−0.690830	+	0.797260i	0.296653	+	0.954985i	$0.404129\pi$
$840$	4118.05	−	5122.97i	0.169150	−	0.210428i
$841$	−18947.0	+	5563.35i	−0.776868	+	0.228109i
$842$	−12484.6	−	4656.50i	−0.510982	−	0.190586i
$843$	−12976.5	−	2822.86i	−0.530171	−	0.115332i
$844$	1969.44	−	6707.30i	0.0803210	−	0.273548i
$845$	−638.402	+	921.873i	−0.0259902	+	0.0375306i
$846$	−144.962	+	317.423i	−0.00589114	+	0.0128998i
$847$	5055.87	+	6753.86i	0.205103	+	0.273985i
$848$	1268.14	+	5829.54i	0.0513539	+	0.236070i
$849$	3537.14	+	4082.08i	0.142985	+	0.165014i
$850$	−2166.53	−	29287.3i	−0.0874253	−	1.18182i
$851$	−14070.8	+	23335.6i	−0.566791	+	0.939994i
$852$	−985.967	−	985.967i	−0.0396463	−	0.0396463i
$853$	−39599.6	−	2832.22i	−1.58953	−	0.113685i	−0.751656	−	0.659556i	$-0.770744\pi$
$853$	−39599.6	−	2832.22i	−1.58953	−	0.113685i	−0.837870	+	0.545871i	$0.816199\pi$
$854$	2457.93	−	3824.61i	0.0984878	−	0.153250i
$855$	1756.22	−	1418.79i	0.0702472	−	0.0567503i
$856$	−38034.6	−	17369.8i	−1.51869	−	0.693561i
$857$	26984.4	−	36046.9i	1.07558	−	1.43680i	0.184566	−	0.982820i	$-0.440912\pi$
$857$	26984.4	−	36046.9i	1.07558	−	1.43680i	0.891011	−	0.453982i	$-0.149997\pi$
$858$	13772.7	+	25222.8i	0.548009	+	1.00360i
$859$	1712.21	+	2664.24i	0.0680089	+	0.105824i	0.873592	−	0.486658i	$-0.161784\pi$
$859$	1712.21	+	2664.24i	0.0680089	+	0.105824i	−0.805583	+	0.592482i	$0.798148\pi$
$860$	−5575.39	+	2799.36i	−0.221069	+	0.110997i
$861$	−249.042	−	848.161i	−0.00985754	−	0.0335717i
$862$	−1237.15	−	17297.6i	−0.0488834	−	0.683479i
$863$	2148.78	+	30043.9i	0.0847572	+	1.18506i	0.844762	+	0.535143i	$0.179742\pi$
$863$	2148.78	+	30043.9i	0.0847572	+	1.18506i	−0.760004	+	0.649918i	$0.774803\pi$
$864$	5780.89	+	19687.9i	0.227627	+	0.775227i
$865$	−4657.17	+	2338.33i	−0.183062	+	0.0919138i
$866$	293.819	+	457.192i	0.0115293	+	0.0179400i
$867$	20440.7	+	37434.3i	0.800694	+	1.46636i
$868$	1053.62	−	1407.47i	0.0412007	−	0.0550377i
$869$	−19496.9	−	8903.95i	−0.761091	−	0.347579i
$870$	−6577.59	+	5313.81i	−0.256323	+	0.207075i
$871$	−14470.3	+	22516.3i	−0.562927	+	0.875931i
$872$	32779.5	+	2344.44i	1.27300	+	0.0910467i
$873$	707.287	+	707.287i	0.0274204	+	0.0274204i
$874$	−10367.4	+	24534.6i	−0.401238	+	0.949537i
$875$	−6281.28	+	698.581i	−0.242681	+	0.0269901i
$876$	11373.5	+	13125.7i	0.438671	+	0.506253i
$877$	6862.18	+	31544.9i	0.264218	+	1.21459i	0.897620	+	0.440769i	$0.145294\pi$
$877$	6862.18	+	31544.9i	0.264218	+	1.21459i	−0.633402	+	0.773823i	$0.718342\pi$
$878$	−10994.2	−	14686.5i	−0.422591	−	0.564516i
$879$	9729.32	−	21304.2i	0.373335	−	0.817491i
$880$	7390.48	−	10672.1i	0.283106	−	0.408814i
$881$	6237.17	−	21241.9i	0.238519	−	0.812323i	−0.750027	−	0.661407i	$-0.769960\pi$
$881$	6237.17	−	21241.9i	0.238519	−	0.812323i	0.988547	−	0.150916i	$-0.0482222\pi$
$882$	1130.40	+	245.904i	0.0431550	+	0.00938779i
$883$	−25399.5	−	9473.51i	−0.968018	−	0.361052i	−0.184784	−	0.982779i	$-0.559159\pi$
$883$	−25399.5	−	9473.51i	−0.968018	−	0.361052i	−0.783234	+	0.621727i	$0.786431\pi$
$884$	18498.0	−	5431.50i	0.703795	−	0.206653i
$885$	−30159.8	+	37519.6i	−1.14555	+	1.42509i
$886$	1818.14	−	2098.24i	0.0689408	−	0.0795620i
$887$	33844.2	+	18480.3i	1.28115	+	0.699559i	0.968192	−	0.250209i	$-0.0804992\pi$
$887$	33844.2	+	18480.3i	1.28115	+	0.699559i	0.312955	+	0.949768i	$0.398681\pi$
$888$	−11223.3	+	30090.8i	−0.424132	+	1.13714i
$889$	638.485	−	410.329i	0.0240878	−	0.0154803i
$890$	−32484.5	−	8248.96i	−1.22346	−	0.310681i
$891$	−43245.9	+	6217.83i	−1.62603	+	0.233788i
$892$	−7803.00	+	2910.37i	−0.292897	+	0.109245i
$893$	−9081.92	+	6798.64i	−0.340330	+	0.254768i
$894$	−6719.34	−	4318.26i	−0.251374	−	0.161548i
$895$	−1234.48	+	35789.3i	−0.0461053	+	1.33665i
$896$		−	1004.01i		−	0.0374349i
$897$	24123.0	+	12290.2i	0.897930	+	0.457478i
$898$	6581.19	−	6581.19i	0.244563	−	0.244563i
$899$	−5394.03	+	4673.96i	−0.200112	+	0.173398i
$900$	−383.321	+	706.092i	−0.0141971	+	0.0261515i
$901$	−4690.26	+	32621.5i	−0.173424	+	1.20619i
$902$	−1492.15	−	4000.60i	−0.0550810	−	0.147678i
$903$	2917.65	+	2184.12i	0.107523	+	0.0804907i
$904$	32251.2	+	9469.81i	1.18657	+	0.348408i
$905$	−4287.55	−	768.156i	−0.157484	−	0.0282148i
$906$	−12817.3	−	28066.1i	−0.470009	−	1.02918i
$907$	−16166.7	+	29607.1i	−0.591848	+	1.08389i	0.394451	+	0.918917i	$0.370935\pi$
$907$	−16166.7	+	29607.1i	−0.591848	+	1.08389i	−0.986298	+	0.164971i	$0.947247\pi$
$908$	11213.2	−	801.983i	0.409827	−	0.0293114i
$909$	−1978.87	−	1714.70i	−0.0722055	−	0.0625664i
$910$	1519.64	+	4547.26i	0.0553577	+	0.165648i
$911$	37048.4	−	16919.5i	1.34739	−	0.615331i	0.394567	−	0.918867i	$-0.370895\pi$
$911$	37048.4	−	16919.5i	1.34739	−	0.615331i	0.952820	+	0.303536i	$0.0981674\pi$
$912$	−2728.30	+	12541.8i	−0.0990602	+	0.455373i
$913$	42544.3	−	23231.0i	1.54218	−	0.842095i
$914$	−3367.48	−	23421.3i	−0.121867	−	0.847602i
$915$	−11100.4	+	26891.6i	−0.401058	+	0.971593i
$916$	16478.1	+	2369.19i	0.594378	+	0.0854587i
$917$	1795.59	−	390.606i	0.0646625	−	0.0140665i
$918$	2270.06	−	31739.6i	0.0816156	−	1.14113i
$919$	51164.5			1.83652			0.918260	−	0.395978i	$-0.129594\pi$
$919$	51164.5			1.83652			0.918260	+	0.395978i	$0.129594\pi$
$920$	175.977	−	29909.4i	0.00630631	−	1.07183i
$921$	−9810.79			−0.351006
$922$	−2742.43	+	38344.1i	−0.0979577	+	1.36963i
$923$	3136.17	−	682.233i	0.111840	−	0.0243293i
$924$	5034.53	+	723.856i	0.179246	+	0.0257718i
$925$	28058.0	−	12896.5i	0.997343	−	0.458417i
$926$	−1350.57	−	9393.40i	−0.0479291	−	0.333354i
$927$	−192.517	+	105.122i	−0.00682101	+	0.00372455i
$928$	−2194.08	+	10086.0i	−0.0776121	+	0.356777i
$929$	−11966.6	+	5464.97i	−0.422617	+	0.193003i	−0.615360	−	0.788247i	$-0.710989\pi$
$929$	−11966.6	+	5464.97i	−0.422617	+	0.193003i	0.192742	+	0.981249i	$0.438262\pi$
$930$	5805.32	−	11633.0i	0.204692	−	0.410173i
$931$	28423.2	+	24628.9i	1.00057	+	0.867002i
$932$	12432.5	−	889.187i	0.436951	−	0.0312514i
$933$	6218.98	−	11389.2i	0.218221	−	0.399642i
$934$	10700.3	+	23430.3i	0.374864	+	0.820838i
$935$	58855.3	−	40970.5i	2.05858	−	1.43303i
$936$	1845.41	+	541.861i	0.0644434	+	0.0189223i
$937$	4332.01	+	3242.90i	0.151036	+	0.113064i	0.672123	−	0.740439i	$-0.265383\pi$
$937$	4332.01	+	3242.90i	0.151036	+	0.113064i	−0.521087	+	0.853503i	$0.674473\pi$
$938$	−1913.02	−	5129.01i	−0.0665911	−	0.178538i
$939$	2464.04	−	17137.8i	0.0856346	−	0.595602i
$940$	2055.79	−	3474.51i	0.0713325	−	0.120560i
$941$	14392.8	−	12471.4i	0.498609	−	0.432047i	−0.368900	−	0.929469i	$-0.620265\pi$
$941$	14392.8	−	12471.4i	0.498609	−	0.432047i	0.867509	+	0.497422i	$0.165720\pi$
$942$	−7580.24	+	7580.24i	−0.262184	+	0.262184i
$943$	−3287.77	−	2317.53i	−0.113536	−	0.0800308i
$944$		−	16495.9i		−	0.568745i
$945$	−6843.91	−	236.068i	−0.235590	−	0.00812622i
$946$	14809.8	+	9517.67i	0.508993	+	0.327110i
$947$	−130.702	+	97.8423i	−0.00448495	+	0.00335739i	−0.601518	−	0.798859i	$-0.705437\pi$
$947$	−130.702	+	97.8423i	−0.00448495	+	0.00335739i	0.597033	+	0.802217i	$0.296346\pi$
$948$	−7066.10	+	2635.52i	−0.242085	+	0.0902929i
$949$	−39570.0	+	5689.30i	−1.35352	+	0.194607i
$950$	25352.3	−	16380.5i	0.865827	−	0.559425i
$951$	25587.7	−	16444.2i	0.872488	−	0.560714i
$952$	−4348.24	+	11658.1i	−0.148033	+	0.396891i
$953$	−48090.0	−	26259.1i	−1.63462	−	0.892568i	−0.991980	−	0.126396i	$-0.959659\pi$
$953$	−48090.0	−	26259.1i	−1.63462	−	0.892568i	−0.642636	−	0.766172i	$-0.722159\pi$
$954$	−682.312	+	787.430i	−0.0231558	+	0.0267233i
$955$	−17083.3	+	1857.73i	−0.578850	+	0.0629475i
$956$	−1555.00	+	456.590i	−0.0526071	+	0.0154468i
$957$	−19346.3	−	7215.80i	−0.653477	−	0.243734i
$958$	30344.7	+	6601.08i	1.02337	+	0.222621i
$959$	3461.66	−	11789.3i	0.116562	−	0.396973i
$960$	−5120.88	−	28186.2i	−0.172162	−	0.947611i
$961$	−7816.93	+	17116.7i	−0.262392	+	0.574559i
$962$	−14038.7	−	18753.5i	−0.470506	−	0.628522i
$963$	−634.675	−	2917.56i	−0.0212379	−	0.0976292i
$964$	8767.77	+	10118.5i	0.292936	+	0.338067i
$965$	216.143	+	5851.63i	0.00721024	+	0.195203i
$966$	−4968.98	+	2443.30i	−0.165501	+	0.0813789i
$967$	−31706.1	−	31706.1i	−1.05440	−	1.05440i	−0.998433	−	0.0559626i	$-0.982177\pi$
$967$	−31706.1	−	31706.1i	−1.05440	−	1.05440i	−0.0559626	−	0.998433i	$-0.517823\pi$
$968$	45131.1	+	3227.84i	1.49852	+	0.107176i
$969$	−38333.6	+	59648.3i	−1.27085	+	1.97748i
$970$	8403.58	+	10402.2i	0.278168	+	0.344324i
$971$	−34352.5	−	15688.2i	−1.13535	−	0.518496i	−0.243082	−	0.970006i	$-0.578158\pi$
$971$	−34352.5	−	15688.2i	−1.13535	−	0.518496i	−0.892266	+	0.451510i	$0.850886\pi$
$972$	−1079.16	+	1441.59i	−0.0356111	+	0.0475709i
$973$	−155.773	−	285.278i	−0.00513244	−	0.00939936i
$974$	13218.3	+	20568.1i	0.434848	+	0.676637i
$975$	−14769.2	−	26891.5i	−0.485122	−	0.883301i
$976$	−2808.66	−	9565.43i	−0.0921139	−	0.313711i
$977$	515.430	+	7206.66i	0.0168783	+	0.235989i	0.998888	+	0.0471563i	$0.0150159\pi$
$977$	515.430	+	7206.66i	0.0168783	+	0.235989i	−0.982009	+	0.188833i	$0.939530\pi$
$978$	2420.80	+	33847.2i	0.0791499	+	1.10666i
$979$	−23057.2	−	78525.7i	−0.752720	−	2.56353i
$980$	−12703.9	−	4211.06i	−0.414094	−	0.137263i
$981$	1268.72	+	1974.16i	0.0412916	+	0.0642510i
$982$	−5074.04	−	9292.42i	−0.164887	−	0.301968i
$983$	27940.6	−	37324.3i	0.906580	−	1.21105i	−0.0703571	−	0.997522i	$-0.522414\pi$
$983$	27940.6	−	37324.3i	0.906580	−	1.21105i	0.976937	−	0.213527i	$-0.0684952\pi$
$984$	−4312.39	−	1969.40i	−0.139709	−	0.0638031i
$985$	−2346.29	+	22077.2i	−0.0758976	+	0.714151i
$986$	8654.04	−	13466.0i	0.279514	−	0.434932i
$987$	−2352.45	−	168.251i	−0.0758657	−	0.00542602i
$988$	14011.3	+	14011.3i	0.451171	+	0.451171i
$989$	16577.9	−	474.187i	0.533009	−	0.0152460i
$990$	2265.58	−	83.6843i	0.0727323	−	0.00268653i
$991$	19552.3	+	22564.5i	0.626739	+	0.723295i	0.976972	−	0.213367i	$-0.0684431\pi$
$991$	19552.3	+	22564.5i	0.626739	+	0.723295i	−0.350233	+	0.936663i	$0.613898\pi$
$992$	−3373.45	−	15507.5i	−0.107971	−	0.496334i
$993$	1369.62	+	1829.60i	0.0437701	+	0.0584700i
$994$	−272.690	+	597.108i	−0.00870142	+	0.0190535i
$995$	−21569.1	−	14936.7i	−0.687222	−	0.475904i
$996$	4805.14	−	16364.8i	0.152868	−	0.520621i
$997$	−22810.6	−	4962.13i	−0.724591	−	0.157625i	−0.164881	−	0.986313i	$-0.552724\pi$
$997$	−22810.6	−	4962.13i	−0.724591	−	0.157625i	−0.559710	+	0.828688i	$0.689088\pi$
$998$	3138.14	+	1170.47i	0.0995352	+	0.0371247i
$999$	32104.4	−	9426.69i	1.01675	−	0.298546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.l.a.102.24	yes	680
5.3	odd	4	inner	115.4.l.a.33.11	yes	680
23.7	odd	22	inner	115.4.l.a.7.11	✓	680
115.53	even	44	inner	115.4.l.a.53.24	yes	680

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.l.a.7.11	✓	680	23.7	odd	22	inner
115.4.l.a.33.11	yes	680	5.3	odd	4	inner
115.4.l.a.53.24	yes	680	115.53	even	44	inner
115.4.l.a.102.24	yes	680	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.147738 - 2.06565i) q^{2} +(5.23771 - 1.13939i) q^{3} +(3.67351 + 0.528171i) q^{4} +(4.29113 + 10.3241i) q^{5} +(-1.57978 - 10.9876i) q^{6} +(3.96906 - 2.16727i) q^{7} +(5.15538 - 23.6989i) q^{8} +(1.57536 - 0.719443i) q^{9} +(21.9598 - 7.33871i) q^{10} +(42.7289 + 37.0248i) q^{11} +(19.8426 - 1.41917i) q^{12} +(-21.9447 + 40.1887i) q^{13} +(-3.89044 - 8.51886i) q^{14} +(34.2389 + 49.1852i) q^{15} +(-19.7043 - 5.78569i) q^{16} +(-90.8184 - 67.9858i) q^{17} +(-1.25337 - 3.36042i) q^{18} +(16.5939 - 115.413i) q^{19} +(10.3107 + 40.1920i) q^{20} +(18.3194 - 15.8739i) q^{21} +(82.7927 - 82.7927i) q^{22} +(20.3555 - 108.410i) q^{23} -130.002i q^{24} +(-88.1723 + 88.6038i) q^{25} +(79.7736 + 51.2674i) q^{26} +(-108.427 + 81.1677i) q^{27} +(15.7251 - 5.86515i) q^{28} +(-67.4393 + 9.69631i) q^{29} +(106.657 - 63.4589i) q^{30} +(88.1264 - 56.6354i) q^{31} +(52.9426 - 141.945i) q^{32} +(265.987 + 145.240i) q^{33} +(-153.852 + 177.555i) q^{34} +(39.4068 + 31.6768i) q^{35} +(6.16708 - 1.81082i) q^{36} +(-231.464 - 86.3316i) q^{37} +(-235.952 - 51.3281i) q^{38} +(-69.1493 + 235.501i) q^{39} +(266.791 - 48.4707i) q^{40} +(15.1490 - 33.1717i) q^{41} +(-30.0833 - 40.1866i) q^{42} +(31.9600 + 146.918i) q^{43} +(137.409 + 158.579i) q^{44} +(14.1876 + 13.1769i) q^{45} +(-220.929 - 58.0635i) q^{46} +(-68.7986 - 68.7986i) q^{47} +(-109.797 - 7.85287i) q^{48} +(-174.383 + 271.346i) q^{49} +(169.998 + 195.223i) q^{50} +(-553.143 - 252.612i) q^{51} +(-101.841 + 136.043i) q^{52} +(-139.225 - 254.972i) q^{53} +(151.645 + 235.964i) q^{54} +(-198.891 + 600.013i) q^{55} +(-30.8999 - 105.236i) q^{56} +(-44.5871 - 623.409i) q^{57} +(10.0658 + 140.738i) q^{58} +(226.305 + 770.724i) q^{59} +(99.7988 + 198.766i) q^{60} +(262.454 + 408.387i) q^{61} +(-103.969 - 190.405i) q^{62} +(4.69347 - 6.26975i) q^{63} +(-434.828 - 198.579i) q^{64} +(-509.078 - 54.1032i) q^{65} +(339.311 - 527.978i) q^{66} +(583.034 + 41.6994i) q^{67} +(-297.714 - 297.714i) q^{68} +(-16.9051 - 591.012i) q^{69} +(71.2549 - 76.7207i) q^{70} +(-45.9008 - 52.9724i) q^{71} +(-8.92842 - 41.0433i) q^{72} +(523.201 + 698.914i) q^{73} +(-212.527 + 465.368i) q^{74} +(-360.867 + 564.545i) q^{75} +(121.916 - 415.207i) q^{76} +(249.836 + 54.3486i) q^{77} +(476.245 + 177.630i) q^{78} +(-363.747 + 106.806i) q^{79} +(-24.8218 - 228.255i) q^{80} +(-506.051 + 584.014i) q^{81} +(-66.2829 - 36.1932i) q^{82} +(299.616 - 803.302i) q^{83} +(75.6807 - 48.6370i) q^{84} +(312.175 - 1229.35i) q^{85} +(308.202 - 44.3127i) q^{86} +(-342.180 + 127.627i) q^{87} +(1097.73 - 821.750i) q^{88} +(-1217.74 - 782.593i) q^{89} +(29.3148 - 27.3599i) q^{90} +207.072i q^{91} +(132.035 - 387.493i) q^{92} +(397.051 - 397.051i) q^{93} +(-152.278 + 131.949i) q^{94} +(1262.74 - 323.938i) q^{95} +(115.567 - 803.788i) q^{96} +(201.836 + 541.144i) q^{97} +(534.741 + 400.302i) q^{98} +(93.9505 + 27.5864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 680 q - 18 q^{2} - 26 q^{3} - 22 q^{5} - 76 q^{6} - 22 q^{7} - 50 q^{8} - 22 q^{10} - 44 q^{11} - 222 q^{12} + 78 q^{13} - 22 q^{15} + 788 q^{16} - 22 q^{17} - 86 q^{18} - 22 q^{20} - 44 q^{21} - 944 q^{23}+ \cdots - 10314 q^{98}+O(q^{100}) \) 680 * q - 18 * q^2 - 26 * q^3 - 22 * q^5 - 76 * q^6 - 22 * q^7 - 50 * q^8 - 22 * q^10 - 44 * q^11 - 222 * q^12 + 78 * q^13 - 22 * q^15 + 788 * q^16 - 22 * q^17 - 86 * q^18 - 22 * q^20 - 44 * q^21 - 944 * q^23 + 350 * q^25 + 268 * q^26 + 682 * q^27 + 682 * q^28 - 22 * q^30 + 1012 * q^31 - 582 * q^32 + 1914 * q^33 + 326 * q^35 - 2468 * q^36 + 2354 * q^37 - 22 * q^38 - 22 * q^40 - 2292 * q^41 - 7282 * q^42 - 22 * q^43 + 52 * q^46 - 2416 * q^47 - 1378 * q^48 + 598 * q^50 - 44 * q^51 - 794 * q^52 - 22 * q^53 - 2710 * q^55 + 11572 * q^56 + 7634 * q^57 - 2066 * q^58 - 22 * q^60 - 1100 * q^61 - 3970 * q^62 - 22 * q^63 - 22 * q^65 - 10956 * q^66 - 22 * q^67 + 1792 * q^70 - 11412 * q^71 - 556 * q^72 - 1122 * q^73 + 13078 * q^75 - 2156 * q^76 - 4238 * q^77 + 9158 * q^78 + 8096 * q^80 + 11280 * q^81 + 6494 * q^82 - 22 * q^83 - 8118 * q^85 + 10428 * q^86 + 6282 * q^87 - 1430 * q^88 - 37224 * q^90 + 666 * q^92 + 1564 * q^93 - 11162 * q^95 - 16748 * q^96 - 12694 * q^97 - 10314 * q^98

Introduction

L-functions

Modular forms

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Representations

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Database

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