LMFDB - Embedded newform 115.4.l.a.102.32

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			102.32
Character	$\chi$	$=$	115.102
Dual form			115.4.l.a.53.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.371284 - 5.19124i) q^{2} +(-8.92216 + 1.94090i) q^{3} +(-18.8925 - 2.71633i) q^{4} +(-8.89093 - 6.77874i) q^{5} +(6.76299 + 47.0376i) q^{6} +(8.66048 - 4.72898i) q^{7} +(-12.2652 + 56.3824i) q^{8} +(51.2777 - 23.4178i) q^{9} +(-38.4911 + 43.6381i) q^{10} +(-37.0225 - 32.0802i) q^{11} +(173.834 - 12.4329i) q^{12} +(-1.59878 + 2.92795i) q^{13} +(-21.3338 - 46.7144i) q^{14} +(92.4831 + 43.2246i) q^{15} +(141.632 + 41.5868i) q^{16} +(53.9561 + 40.3910i) q^{17} +(-102.528 - 274.890i) q^{18} +(9.07100 - 63.0902i) q^{19} +(149.559 + 152.218i) q^{20} +(-68.0917 + 59.0018i) q^{21} +(-180.282 + 180.282i) q^{22} +(2.23227 + 110.282i) q^{23} -526.858i q^{24} +(33.0974 + 120.539i) q^{25} +(14.6061 + 9.38676i) q^{26} +(-214.697 + 160.720i) q^{27} +(-176.464 + 65.8175i) q^{28} +(-284.031 + 40.8374i) q^{29} +(258.727 - 464.053i) q^{30} +(58.5463 - 37.6254i) q^{31} +(107.157 - 287.298i) q^{32} +(392.585 + 214.367i) q^{33} +(229.713 - 265.102i) q^{34} +(-109.056 - 16.6621i) q^{35} +(-1032.38 + 303.133i) q^{36} +(347.295 + 129.534i) q^{37} +(-324.148 - 70.5141i) q^{38} +(8.58174 - 29.2267i) q^{39} +(491.251 - 418.150i) q^{40} +(20.3768 - 44.6189i) q^{41} +(281.011 + 375.387i) q^{42} +(11.1703 + 51.3489i) q^{43} +(612.307 + 706.640i) q^{44} +(-614.650 - 139.393i) q^{45} +(573.326 + 29.3576i) q^{46} +(-446.522 - 446.522i) q^{47} +(-1344.37 - 96.1516i) q^{48} +(-132.799 + 206.639i) q^{49} +(638.033 - 127.062i) q^{50} +(-559.800 - 255.652i) q^{51} +(38.1583 - 50.9735i) q^{52} +(74.9943 + 137.342i) q^{53} +(754.624 + 1174.22i) q^{54} +(111.701 + 536.188i) q^{55} +(160.408 + 546.301i) q^{56} +(41.5187 + 580.507i) q^{57} +(106.541 + 1489.63i) q^{58} +(-30.6951 - 104.538i) q^{59} +(-1629.83 - 1067.84i) q^{60} +(-44.3946 - 69.0793i) q^{61} +(-173.585 - 317.897i) q^{62} +(333.348 - 445.301i) q^{63} +(-377.474 - 172.387i) q^{64} +(34.0625 - 15.1945i) q^{65} +(1258.59 - 1958.41i) q^{66} +(-686.850 - 49.1245i) q^{67} +(-909.651 - 909.651i) q^{68} +(-233.962 - 979.617i) q^{69} +(-126.988 + 559.951i) q^{70} +(71.9064 + 82.9844i) q^{71} +(691.416 + 3178.39i) q^{72} +(279.988 + 374.020i) q^{73} +(801.388 - 1754.80i) q^{74} +(-529.253 - 1011.23i) q^{75} +(-342.748 + 1167.29i) q^{76} +(-472.339 - 102.751i) q^{77} +(-148.536 - 55.4012i) q^{78} +(820.499 - 240.920i) q^{79} +(-977.331 - 1329.83i) q^{80} +(606.896 - 700.395i) q^{81} +(-224.062 - 122.347i) q^{82} +(-179.405 + 481.004i) q^{83} +(1446.69 - 929.732i) q^{84} +(-205.920 - 724.869i) q^{85} +(270.711 - 38.9224i) q^{86} +(2454.90 - 915.632i) q^{87} +(2262.85 - 1693.95i) q^{88} +(-253.124 - 162.673i) q^{89} +(-951.830 + 3139.04i) q^{90} +32.9181i q^{91} +(257.388 - 2089.56i) q^{92} +(-449.332 + 449.332i) q^{93} +(-2483.79 + 2152.21i) q^{94} +(-508.322 + 499.441i) q^{95} +(-398.453 + 2771.30i) q^{96} +(4.94555 + 13.2595i) q^{97} +(1023.41 + 766.113i) q^{98} +(-2649.67 - 778.015i) 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 $

$2$	0.371284	−	5.19124i	0.131269	−	1.83538i	−0.325207	−	0.945643i	$-0.605434\pi$
$2$	0.371284	−	5.19124i	0.131269	−	1.83538i	0.456476	−	0.889736i	$-0.349112\pi$
$3$	−8.92216	+	1.94090i	−1.71707	+	0.373526i	−0.960042	−	0.279857i	$-0.909713\pi$
$3$	−8.92216	+	1.94090i	−1.71707	+	0.373526i	−0.757028	+	0.653382i	$0.773349\pi$
$4$	−18.8925	−	2.71633i	−2.36156	−	0.339541i
$5$	−8.89093	−	6.77874i	−0.795229	−	0.606309i
$5$	−8.89093	−	6.77874i	−0.795229	−	0.606309i
$6$	6.76299	+	47.0376i	0.460163	+	3.20051i
$7$	8.66048	−	4.72898i	0.467622	−	0.255341i	−0.228119	−	0.973633i	$-0.573258\pi$
$7$	8.66048	−	4.72898i	0.467622	−	0.255341i	0.695742	+	0.718292i	$0.255076\pi$
$8$	−12.2652	+	56.3824i	−0.542052	+	2.49177i
$9$	51.2777	−	23.4178i	1.89918	−	0.867325i
$10$	−38.4911	+	43.6381i	−1.21720	+	1.37996i
$11$	−37.0225	−	32.0802i	−1.01479	−	0.879321i	−0.0220694	−	0.999756i	$-0.507025\pi$
$11$	−37.0225	−	32.0802i	−1.01479	−	0.879321i	−0.992721	+	0.120435i	$0.961571\pi$
$12$	173.834	−	12.4329i	4.18180	−	0.299088i
$13$	−1.59878	+	2.92795i	−0.0341094	+	0.0624667i	−0.894178	−	0.447712i	$-0.852239\pi$
$13$	−1.59878	+	2.92795i	−0.0341094	+	0.0624667i	0.860068	+	0.510179i	$0.170421\pi$
$14$	−21.3338	−	46.7144i	−0.407263	−	0.891782i
$15$	92.4831	+	43.2246i	1.59194	+	0.744036i
$16$	141.632	+	41.5868i	2.21299	+	0.649793i
$17$	53.9561	+	40.3910i	0.769781	+	0.576251i	0.910359	−	0.413819i	$-0.135805\pi$
$17$	53.9561	+	40.3910i	0.769781	+	0.576251i	−0.140578	+	0.990070i	$0.544896\pi$
$18$	−102.528	−	274.890i	−1.34257	−	3.59956i
$19$	9.07100	−	63.0902i	0.109528	−	0.761784i	−0.858838	−	0.512248i	$-0.828813\pi$
$19$	9.07100	−	63.0902i	0.109528	−	0.761784i	0.968366	−	0.249536i	$-0.0802780\pi$
$20$	149.559	+	152.218i	1.67212	+	1.70185i
$21$	−68.0917	+	59.0018i	−0.707563	+	0.613107i
$22$	−180.282	+	180.282i	−1.74710	+	1.74710i
$23$	2.23227	+	110.282i	0.0202374	+	0.999795i
$23$	2.23227	+	110.282i	0.0202374	+	0.999795i
$24$		−	526.858i		−	4.48102i
$25$	33.0974	+	120.539i	0.264779	+	0.964309i
$26$	14.6061	+	9.38676i	0.110173	+	0.0708036i
$27$	−214.697	+	160.720i	−1.53032	+	1.14558i
$28$	−176.464	+	65.8175i	−1.19102	+	0.444227i
$29$	−284.031	+	40.8374i	−1.81873	+	0.261494i	−0.965568	−	0.260152i	$-0.916227\pi$
$29$	−284.031	+	40.8374i	−1.81873	+	0.261494i	−0.853162	+	0.521646i	$0.825318\pi$
$30$	258.727	−	464.053i	1.57456	−	2.82414i
$31$	58.5463	−	37.6254i	0.339201	−	0.217991i	−0.359939	−	0.932976i	$-0.617203\pi$
$31$	58.5463	−	37.6254i	0.339201	−	0.217991i	0.699140	+	0.714985i	$0.253566\pi$
$32$	107.157	−	287.298i	0.591962	−	1.58711i
$33$	392.585	+	214.367i	2.07092	+	1.13081i
$34$	229.713	−	265.102i	1.15869	−	1.33720i
$35$	−109.056	−	16.6621i	−0.526682	−	0.0804688i
$36$	−1032.38	+	303.133i	−4.77952	+	1.40339i
$37$	347.295	+	129.534i	1.54311	+	0.575549i	0.969823	−	0.243809i	$-0.0783969\pi$
$37$	347.295	+	129.534i	1.54311	+	0.575549i	0.573283	+	0.819358i	$0.305670\pi$
$38$	−324.148	−	70.5141i	−1.38378	−	0.301024i
$39$	8.58174	−	29.2267i	0.0352353	−	0.120001i
$40$	491.251	−	418.150i	1.94184	−	1.65288i
$41$	20.3768	−	44.6189i	0.0776175	−	0.169959i	−0.866845	−	0.498578i	$-0.833856\pi$
$41$	20.3768	−	44.6189i	0.0776175	−	0.169959i	0.944463	+	0.328619i	$0.106583\pi$
$42$	281.011	+	375.387i	1.03240	+	1.37913i
$43$	11.1703	+	51.3489i	0.0396151	+	0.182108i	0.992703	−	0.120587i	$-0.0384775\pi$
$43$	11.1703	+	51.3489i	0.0396151	+	0.182108i	−0.953088	+	0.302694i	$0.902114\pi$
$44$	612.307	+	706.640i	2.09793	+	2.42113i
$45$	−614.650	−	139.393i	−2.03615	−	0.461765i
$46$	573.326	+	29.3576i	1.83766	+	0.0940987i
$47$	−446.522	−	446.522i	−1.38579	−	1.38579i	−0.833958	−	0.551827i	$-0.813931\pi$
$47$	−446.522	−	446.522i	−1.38579	−	1.38579i	−0.551827	−	0.833958i	$-0.686069\pi$
$48$	−1344.37	−	96.1516i	−4.04258	−	0.289131i
$49$	−132.799	+	206.639i	−0.387169	+	0.602447i
$50$	638.033	−	127.062i	1.80463	−	0.359386i
$51$	−559.800	−	255.652i	−1.53701	−	0.701930i
$52$	38.1583	−	50.9735i	0.101762	−	0.135938i
$53$	74.9943	+	137.342i	0.194363	+	0.355950i	0.956626	−	0.291317i	$-0.0940936\pi$
$53$	74.9943	+	137.342i	0.194363	+	0.355950i	−0.762263	+	0.647267i	$0.775912\pi$
$54$	754.624	+	1174.22i	1.90169	+	2.95909i
$55$	111.701	+	536.188i	0.273851	+	1.31454i
$56$	160.408	+	546.301i	0.382777	+	1.30362i
$57$	41.5187	+	580.507i	0.0964786	+	1.34895i
$58$	106.541	+	1489.63i	0.241198	+	3.37238i
$59$	−30.6951	−	104.538i	−0.0677315	−	0.230672i	0.918670	−	0.395026i	$-0.129264\pi$
$59$	−30.6951	−	104.538i	−0.0677315	−	0.230672i	−0.986401	+	0.164354i	$0.947446\pi$
$60$	−1629.83	−	1067.84i	−3.50683	−	2.29762i
$61$	−44.3946	−	69.0793i	−0.0931826	−	0.144995i	0.791533	−	0.611127i	$-0.209284\pi$
$61$	−44.3946	−	69.0793i	−0.0931826	−	0.144995i	−0.884715	+	0.466132i	$0.845647\pi$
$62$	−173.585	−	317.897i	−0.355570	−	0.651178i
$63$	333.348	−	445.301i	0.666633	−	0.890518i
$64$	−377.474	−	172.387i	−0.737254	−	0.336693i
$65$	34.0625	−	15.1945i	0.0649989	−	0.0289945i
$66$	1258.59	−	1958.41i	2.34730	−	3.65247i
$67$	−686.850	−	49.1245i	−1.25242	−	0.0895748i	−0.570682	−	0.821171i	$-0.693321\pi$
$67$	−686.850	−	49.1245i	−1.25242	−	0.0895748i	−0.681738	+	0.731597i	$0.738775\pi$
$68$	−909.651	−	909.651i	−1.62223	−	1.62223i
$69$	−233.962	−	979.617i	−0.408198	−	1.70916i
$70$	−126.988	+	559.951i	−0.216828	+	0.956099i
$71$	71.9064	+	82.9844i	0.120193	+	0.138710i	0.812657	−	0.582742i	$-0.198020\pi$
$71$	71.9064	+	82.9844i	0.120193	+	0.138710i	−0.692464	+	0.721453i	$0.743475\pi$
$72$	691.416	+	3178.39i	1.13172	+	5.20245i
$73$	279.988	+	374.020i	0.448906	+	0.599668i	0.966724	−	0.255823i	$-0.0823465\pi$
$73$	279.988	+	374.020i	0.448906	+	0.599668i	−0.517818	+	0.855491i	$0.673256\pi$
$74$	801.388	−	1754.80i	1.25891	−	2.75663i
$75$	−529.253	−	1011.23i	−0.814839	−	1.55688i
$76$	−342.748	+	1167.29i	−0.517314	+	1.76181i
$77$	−472.339	−	102.751i	−0.699065	−	0.152072i
$78$	−148.536	−	55.4012i	−0.215621	−	0.0804225i
$79$	820.499	−	240.920i	1.16852	−	0.343110i	0.360784	−	0.932649i	$-0.382509\pi$
$79$	820.499	−	240.920i	1.16852	−	0.343110i	0.807739	+	0.589540i	$0.200691\pi$
$80$	−977.331	−	1329.83i	−1.36586	−	1.85849i
$81$	606.896	−	700.395i	0.832505	−	0.960762i
$82$	−224.062	−	122.347i	−0.301750	−	0.164768i
$83$	−179.405	+	481.004i	−0.237256	+	0.636109i	−0.999943	−	0.0106588i	$-0.996607\pi$
$83$	−179.405	+	481.004i	−0.237256	+	0.636109i	0.762687	+	0.646768i	$0.223880\pi$
$84$	1446.69	−	929.732i	1.87913	−	1.20764i
$85$	−205.920	−	724.869i	−0.262767	−	0.924977i
$86$	270.711	−	38.9224i	0.339437	−	0.0488036i
$87$	2454.90	−	915.632i	3.02521	−	1.12835i
$88$	2262.85	−	1693.95i	2.74114	−	2.05199i
$89$	−253.124	−	162.673i	−0.301473	−	0.193745i	0.381155	−	0.924511i	$-0.375527\pi$
$89$	−253.124	−	162.673i	−0.301473	−	0.193745i	−0.682628	+	0.730766i	$0.739163\pi$
$90$	−951.830	+	3139.04i	−1.11480	+	3.67649i
$91$			32.9181i			0.0379204i
$92$	257.388	−	2089.56i	0.291680	−	2.36795i
$93$	−449.332	+	449.332i	−0.501006	+	0.501006i
$94$	−2483.79	+	2152.21i	−2.72535	+	2.36153i
$95$	−508.322	+	499.441i	−0.548976	+	0.539385i
$96$	−398.453	+	2771.30i	−0.423613	+	2.94630i
$97$	4.94555	+	13.2595i	0.00517675	+	0.0138794i	0.939512	−	0.342515i	$-0.111279\pi$
$97$	4.94555	+	13.2595i	0.00517675	+	0.0138794i	−0.934336	+	0.356394i	$0.884006\pi$
$98$	1023.41	+	766.113i	1.05490	+	0.789685i
$99$	−2649.67	−	778.015i	−2.68992	−	0.789832i
$100$	−297.870	−	2367.18i	−0.297870	−	2.36718i
$101$	145.267	+	318.090i	0.143115	+	0.313378i	0.967593	−	0.252517i	$-0.0812582\pi$
$101$	145.267	+	318.090i	0.143115	+	0.313378i	−0.824478	+	0.565894i	$0.808531\pi$
$102$	−1534.99	+	2811.13i	−1.49007	+	2.72886i
$103$	−416.377	+	29.7799i	−0.398319	+	0.0284883i	−0.269062	−	0.963123i	$-0.586714\pi$
$103$	−416.377	+	29.7799i	−0.398319	+	0.0284883i	−0.129257	+	0.991611i	$0.541259\pi$
$104$	−145.476	−	126.055i	−0.137164	−	0.118853i
$105$	1005.36	−	63.0052i	0.934408	−	0.0585589i
$106$	740.818	−	338.320i	0.678817	−	0.310005i
$107$	−248.763	+	1143.54i	−0.224755	+	1.03318i	0.717049	+	0.697023i	$0.245492\pi$
$107$	−248.763	+	1143.54i	−0.224755	+	1.03318i	−0.941805	+	0.336161i	$0.890871\pi$
$108$	4492.74	−	2453.22i	4.00291	−	2.18575i
$109$	129.769	+	902.562i	0.114033	+	0.793117i	0.963928	+	0.266164i	$0.0857564\pi$
$109$	129.769	+	902.562i	0.114033	+	0.793117i	−0.849895	+	0.526953i	$0.823335\pi$
$110$	2824.95	−	380.790i	2.44862	−	0.330062i
$111$	−3350.03	−	481.662i	−2.86460	−	0.411868i
$112$	1423.26	−	309.611i	1.20076	−	0.261210i
$113$	−8.96354	+	125.327i	−0.00746212	+	0.104334i	−0.999818	−	0.0190745i	$-0.993928\pi$
$113$	−8.96354	+	125.327i	−0.00746212	+	0.104334i	0.992356	+	0.123409i	$0.0393826\pi$
$114$	3028.96			2.48849
$115$	727.723	−	995.638i	0.590091	−	0.807337i
$116$	5476.98			4.38383
$117$	−13.4159	+	187.579i	−0.0106009	+	0.148219i
$118$	−554.077	+	120.532i	−0.432262	+	0.0940328i
$119$	658.295	+	94.6485i	0.507107	+	0.0729110i
$120$	−3571.44	+	4684.26i	−2.71688	+	3.56344i
$121$	152.106	+	1057.92i	0.114280	+	0.794832i
$122$	−375.090	+	204.815i	−0.278353	+	0.151992i
$123$	−95.2041	+	437.646i	−0.0697908	+	0.320823i
$124$	−1208.29	+	551.807i	−0.875061	+	0.399627i
$125$	522.833	−	1296.06i	0.374109	−	0.927385i
$126$	−2187.89	−	1895.82i	−1.54693	−	1.34042i
$127$	−745.138	+	53.2933i	−0.520632	+	0.0372364i	−0.329183	−	0.944266i	$-0.606773\pi$
$127$	−745.138	+	53.2933i	−0.520632	+	0.0372364i	−0.191449	+	0.981503i	$0.561319\pi$
$128$	140.572	−	257.439i	0.0970698	−	0.177770i
$129$	−199.326	−	436.462i	−0.136044	−	0.297894i
$130$	−66.2313	−	182.468i	−0.0446836	−	0.123104i
$131$	−911.996	−	267.786i	−0.608255	−	0.178600i	−0.0369222	−	0.999318i	$-0.511755\pi$
$131$	−911.996	−	267.786i	−0.608255	−	0.178600i	−0.571333	+	0.820718i	$0.693574\pi$
$132$	−6834.61	−	5116.33i	−4.50664	−	3.37363i
$133$	−219.793	−	589.288i	−0.143297	−	0.384194i
$134$	−510.034	+	3547.36i	−0.328807	+	2.28691i
$135$	2998.34	+	26.4226i	1.91153	+	0.0168452i
$136$	−2939.13	+	2546.77i	−1.85315	+	1.60576i
$137$	−429.936	+	429.936i	−0.268116	+	0.268116i	−0.828341	−	0.560225i	$-0.810715\pi$
$137$	−429.936	+	429.936i	−0.268116	+	0.268116i	0.560225	+	0.828341i	$0.310715\pi$
$138$	−5172.29	+	850.834i	−3.19054	+	0.524839i
$139$			658.992i			0.402122i	0.979579	+	0.201061i	$0.0644390\pi$
$139$			658.992i			0.402122i	−0.979579	+	0.201061i	$0.935561\pi$
$140$	2015.09	+	611.022i	1.21647	+	0.368863i
$141$	4850.59	+	3117.29i	2.89712	+	1.86186i
$142$	457.489	−	342.472i	0.270364	−	0.202392i
$143$	153.120	−	57.1108i	0.0895422	−	0.0333975i
$144$	8236.42	−	1184.22i	4.76644	−	0.685311i
$145$	2802.12	+	1562.29i	1.60485	+	0.894764i
$146$	2045.58	−	1314.62i	1.15954	−	0.745194i
$147$	783.789	−	2101.42i	0.439767	−	1.17906i
$148$	−6209.41	−	3390.59i	−3.44872	−	1.88314i
$149$	637.079	−	735.228i	0.350279	−	0.404243i	−0.553080	−	0.833128i	$-0.686548\pi$
$149$	637.079	−	735.228i	0.350279	−	0.404243i	0.903359	+	0.428884i	$0.141093\pi$
$150$	−5446.02	+	2372.03i	−2.96444	+	1.29117i
$151$	−3441.12	+	1010.40i	−1.85453	+	0.544540i	−0.854864	+	0.518853i	$0.826359\pi$
$151$	−3441.12	+	1010.40i	−1.85453	+	0.544540i	−0.999670	+	0.0256872i	$0.991823\pi$
$152$	3445.92	+	1285.26i	1.83882	+	0.685846i
$153$	3712.62	+	807.630i	1.96175	+	0.426752i
$154$	−708.777	+	2413.87i	−0.370876	+	1.26309i
$155$	−775.584	−	62.3449i	−0.401912	−	0.0323075i
$156$	−241.520	+	528.855i	−0.123956	+	0.271425i
$157$	−262.876	−	351.162i	−0.133629	−	0.178508i	0.728735	−	0.684795i	$-0.240108\pi$
$157$	−262.876	−	351.162i	−0.133629	−	0.178508i	−0.862365	+	0.506287i	$0.831018\pi$
$158$	−946.035	−	4348.85i	−0.476345	−	2.18972i
$159$	−935.677	−	1079.83i	−0.466692	−	0.538591i
$160$	−2900.24	+	1827.96i	−1.43303	+	0.903206i
$161$	540.852	+	944.535i	0.264752	+	0.462359i
$162$	−3410.59	−	3410.59i	−1.65408	−	1.65408i
$163$	1306.61	+	93.4503i	0.627861	+	0.0449055i	0.381644	−	0.924309i	$-0.375358\pi$
$163$	1306.61	+	93.4503i	0.627861	+	0.0449055i	0.246217	+	0.969215i	$0.420813\pi$
$164$	−506.168	+	787.613i	−0.241007	+	0.375013i
$165$	−2037.30	−	4567.15i	−0.961235	−	2.15486i
$166$	2430.40	+	1109.92i	1.13636	+	0.518957i
$167$	354.824	−	473.989i	0.164414	−	0.219631i	−0.710767	−	0.703428i	$-0.751652\pi$
$167$	354.824	−	473.989i	0.164414	−	0.219631i	0.875180	+	0.483797i	$0.160743\pi$
$168$	−2491.50	−	4562.85i	−1.14419	−	2.09543i
$169$	1181.77	+	1838.87i	0.537902	+	0.836992i
$170$	−3839.42	+	799.847i	−1.73218	+	0.360855i
$171$	−1012.29	−	3447.55i	−0.452701	−	1.54176i
$172$	−71.5536	−	1000.45i	−0.0317204	−	0.443510i
$173$	43.9809	+	614.933i	0.0193283	+	0.270246i	0.997922	+	0.0644412i	$0.0205265\pi$
$173$	43.9809	+	614.933i	0.0193283	+	0.270246i	−0.978593	+	0.205804i	$0.934019\pi$
$174$	−3841.79	−	13083.9i	−1.67383	−	5.70053i
$175$	856.664	+	887.406i	0.370044	+	0.383323i
$176$	−3909.44	−	6083.21i	−1.67435	−	2.60534i
$177$	476.763	+	873.127i	0.202462	+	0.370781i
$178$	−938.455	+	1253.63i	−0.395170	+	0.527885i
$179$	−3031.44	−	1384.41i	−1.26581	−	0.578076i	−0.334532	−	0.942384i	$-0.608578\pi$
$179$	−3031.44	−	1384.41i	−1.26581	−	0.578076i	−0.931279	+	0.364308i	$0.881306\pi$
$180$	11233.6	+	4303.07i	4.65170	+	1.78184i
$181$	197.966	−	308.042i	0.0812969	−	0.126500i	−0.798224	−	0.602361i	$-0.794227\pi$
$181$	197.966	−	308.042i	0.0812969	−	0.126500i	0.879521	+	0.475860i	$0.157863\pi$
$182$	170.886	+	12.2220i	0.0695982	+	0.00497776i
$183$	530.171	+	530.171i	0.214160	+	0.214160i
$184$	−6245.32	−	1226.77i	−2.50223	−	0.491514i
$185$	−2209.70	−	3505.90i	−0.878163	−	1.39329i
$186$	2165.76	+	2499.42i	0.853770	+	0.985303i
$187$	−701.838	−	3226.30i	−0.274457	−	1.26166i
$188$	7223.02	+	9648.82i	2.80209	+	3.74315i
$189$	−1099.34	+	2407.22i	−0.423096	+	0.926451i
$190$	2403.98	+	2824.25i	0.917912	+	1.07838i
$191$	−1051.47	+	3580.98i	−0.398334	+	1.35660i	0.479460	+	0.877564i	$0.340833\pi$
$191$	−1051.47	+	3580.98i	−0.398334	+	1.35660i	−0.877794	+	0.479038i	$0.840986\pi$
$192$	3702.47	+	805.422i	1.39168	+	0.302741i
$193$	3408.26	+	1271.22i	1.27115	+	0.474115i	0.892342	−	0.451360i	$-0.149061\pi$
$193$	3408.26	+	1271.22i	1.27115	+	0.474115i	0.378809	+	0.925475i	$0.376334\pi$
$194$	70.6696	−	20.7505i	0.0261535	−	0.00767936i
$195$	−274.420	+	201.679i	−0.100778	+	0.0740644i
$196$	3070.21	−	3543.21i	1.11888	−	1.29126i
$197$	2341.90	+	1278.77i	0.846970	+	0.462481i	0.843256	−	0.537512i	$-0.180636\pi$
$197$	2341.90	+	1278.77i	0.846970	+	0.462481i	0.00371446	+	0.999993i	$0.498818\pi$
$198$	−5022.64	+	13466.2i	−1.80274	+	4.83335i
$199$	−3206.69	+	2060.81i	−1.14229	+	0.734107i	−0.968090	−	0.250603i	$-0.919371\pi$
$199$	−3206.69	+	2060.81i	−1.14229	+	0.734107i	−0.174203	+	0.984710i	$0.555735\pi$
$200$	−7202.21	+	387.676i	−2.54637	+	0.137064i
$201$	6223.53	−	894.809i	2.18395	−	0.314005i
$202$	1705.22	−	636.013i	0.593953	−	0.221533i
$203$	−2266.72	+	1696.85i	−0.783708	+	0.586677i
$204$	9881.58	+	6350.51i	3.39142	+	2.17953i
$205$	−483.628	+	258.575i	−0.164771	+	0.0880959i
$206$			2172.57i			0.734806i
$207$	2697.01	+	5602.71i	0.905581	+	1.88123i
$208$	−348.202	+	348.202i	−0.116074	+	0.116074i
$209$	−2359.77	+	2044.76i	−0.781000	+	0.676740i
$210$	46.1985	−	5242.44i	0.0151810	−	1.72268i
$211$	−198.343	+	1379.51i	−0.0647133	+	0.450091i	0.931542	+	0.363633i	$0.118464\pi$
$211$	−198.343	+	1379.51i	−0.0647133	+	0.450091i	−0.996256	+	0.0864576i	$0.972445\pi$
$212$	−1043.76	−	2798.44i	−0.338142	−	0.906593i
$213$	−802.624	−	600.837i	−0.258192	−	0.193280i
$214$	5844.05	+	1715.97i	1.86678	+	0.548136i
$215$	248.767	−	532.260i	0.0789104	−	0.168836i
$216$	−6428.49	−	14076.4i	−2.02502	−	4.43417i
$217$	329.109	−	602.719i	0.102956	−	0.188549i
$218$	4733.59	−	338.553i	1.47064	−	0.105182i
$219$	−3224.03	−	2793.64i	−0.994793	−	0.861993i
$220$	−653.853	−	10433.4i	−0.200376	−	3.19735i
$221$	−204.527	+	93.4044i	−0.0622533	+	0.0284301i
$222$	−3744.24	+	17212.0i	−1.13197	+	5.20357i
$223$	−3879.26	+	2118.23i	−1.16491	+	0.636087i	−0.940961	−	0.338514i	$-0.890076\pi$
$223$	−3879.26	+	2118.23i	−1.16491	+	0.636087i	−0.223946	+	0.974602i	$0.571894\pi$
$224$	−430.599	−	2994.88i	−0.128440	−	0.893321i
$225$	4519.91	+	5405.88i	1.33923	+	1.60174i
$226$	647.273	+	93.0637i	0.190513	+	0.0273916i
$227$	1224.79	−	266.437i	0.358115	−	0.0779032i	−0.0299083	−	0.999553i	$-0.509522\pi$
$227$	1224.79	−	266.437i	0.358115	−	0.0779032i	0.388024	+	0.921649i	$0.373158\pi$
$228$	792.457	−	11080.0i	0.230183	−	3.21838i
$229$	−2492.34			−0.719208			−0.359604	−	0.933105i	$-0.617088\pi$
$229$	−2492.34			−0.719208			−0.359604	+	0.933105i	$0.617088\pi$
$230$	−4898.40	−	4147.44i	−1.40431	−	1.18902i
$231$	4413.71			1.25715
$232$	1181.19	−	16515.2i	0.334263	−	4.67361i
$233$	−2807.16	+	610.660i	−0.789283	+	0.171698i	−0.589100	−	0.808060i	$-0.700517\pi$
$233$	−2807.16	+	610.660i	−0.789283	+	0.171698i	−0.200183	+	0.979758i	$0.564154\pi$
$234$	968.784	+	139.290i	0.270647	+	0.0389132i
$235$	943.142	+	6996.85i	0.261803	+	1.94223i
$236$	295.947	+	2058.36i	0.0816293	+	0.567744i
$237$	−6853.02	+	3742.03i	−1.87828	+	1.02562i
$238$	735.757	−	3382.22i	0.200387	−	0.921163i
$239$	2962.62	−	1352.98i	0.801823	−	0.366180i	0.0280205	−	0.999607i	$-0.491080\pi$
$239$	2962.62	−	1352.98i	0.801823	−	0.366180i	0.773802	+	0.633427i	$0.218352\pi$
$240$	11301.0	+	9968.04i	3.03947	+	2.68098i
$241$	−4377.64	−	3793.24i	−1.17008	−	1.01388i	−0.999593	−	0.0285166i	$-0.990922\pi$
$241$	−4377.64	−	3793.24i	−1.17008	−	1.01388i	−0.170483	−	0.985361i	$-0.554533\pi$
$242$	5548.39	−	396.829i	1.47382	−	0.105410i
$243$	−585.119	+	1071.56i	−0.154467	+	0.282884i
$244$	651.082	+	1425.67i	0.170825	+	0.374054i
$245$	2581.46	−	937.007i	0.673158	−	0.244340i
$246$	2236.58	+	656.718i	0.579670	+	0.170207i
$247$	170.223	+	127.427i	0.0438502	+	0.0328258i
$248$	1403.33	+	3762.47i	0.359320	+	0.963375i
$249$	667.103	−	4639.80i	0.169783	−	1.18087i
$250$	−6534.03	−	3195.36i	−1.65299	−	0.808368i
$251$	4949.42	−	4288.69i	1.24464	−	1.07849i	0.250756	−	0.968050i	$-0.419321\pi$
$251$	4949.42	−	4288.69i	1.24464	−	1.07849i	0.993883	−	0.110436i	$-0.0352246\pi$
$252$	−7507.36	+	7507.36i	−1.87666	+	1.87666i
$253$	3455.20	−	4154.51i	0.858604	−	1.03238i
$254$			3887.97i			0.960445i
$255$	3244.15	+	6067.72i	0.796691	+	1.49010i
$256$	−4077.02	−	2620.14i	−0.995366	−	0.639683i
$257$	−1514.00	+	1133.36i	−0.367473	+	0.275087i	−0.767016	−	0.641627i	$-0.778260\pi$
$257$	−1514.00	+	1133.36i	−0.367473	+	0.275087i	0.399543	+	0.916714i	$0.369169\pi$
$258$	−2339.79	+	872.695i	−0.564607	+	0.210588i
$259$	3620.31	−	520.522i	0.868552	−	0.124879i
$260$	−684.799	+	194.537i	−0.163344	+	0.0464026i
$261$	−13608.1	+	8745.41i	−3.22729	+	2.07405i
$262$	−1728.75	+	4634.96i	−0.407643	+	1.09293i
$263$	−942.116	−	514.434i	−0.220887	−	0.120614i	0.364996	−	0.931009i	$-0.381070\pi$
$263$	−942.116	−	514.434i	−0.220887	−	0.120614i	−0.585883	+	0.810396i	$0.699252\pi$
$264$	−16901.7	+	19505.6i	−3.94026	+	4.54730i
$265$	264.235	−	1729.46i	0.0612522	−	0.400906i
$266$	−3140.74	+	922.204i	−0.723952	+	0.212571i
$267$	2574.15	+	960.107i	0.590019	+	0.220066i
$268$	12842.9	+	2793.80i	2.92725	+	0.636785i
$269$	949.984	−	3235.35i	0.215322	−	0.733319i	−0.779011	−	0.627010i	$-0.784279\pi$
$269$	949.984	−	3235.35i	0.215322	−	0.733319i	0.994333	−	0.106309i	$-0.0339032\pi$
$270$	1250.40	−	15555.3i	0.281841	−	3.50617i
$271$	2575.99	−	5640.64i	0.577419	−	1.26437i	−0.365334	−	0.930877i	$-0.619045\pi$
$271$	2575.99	−	5640.64i	0.577419	−	1.26437i	0.942752	−	0.333494i	$-0.108228\pi$
$272$	5962.16	+	7964.51i	1.32908	+	1.77544i
$273$	−63.8906	−	293.700i	−0.0141642	−	0.0651119i
$274$	2072.27	+	2391.52i	0.456899	+	0.527289i
$275$	2641.55	−	5524.41i	0.579242	−	1.21140i
$276$	1759.16	+	19142.9i	0.383655	+	4.17489i
$277$	−2624.87	−	2624.87i	−0.569361	−	0.569361i	0.362589	−	0.931949i	$-0.381893\pi$
$277$	−2624.87	−	2624.87i	−0.569361	−	0.569361i	−0.931949	+	0.362589i	$0.881893\pi$
$278$	3420.98	+	244.674i	0.738046	+	0.0527861i
$279$	2121.02	−	3300.37i	0.455133	−	0.708201i
$280$	2277.05	−	5944.49i	0.486000	−	1.26876i
$281$	−6522.57	−	2978.76i	−1.38471	−	0.632377i	−0.422922	−	0.906166i	$-0.638996\pi$
$281$	−6522.57	−	2978.76i	−1.38471	−	0.632377i	−0.961790	+	0.273790i	$0.911723\pi$
$282$	17983.5	−	24023.2i	3.79753	−	5.07290i
$283$	−1571.33	−	2877.68i	−0.330056	−	0.604453i	0.658974	−	0.752166i	$-0.270991\pi$
$283$	−1571.33	−	2877.68i	−0.330056	−	0.604453i	−0.989030	+	0.147713i	$0.952809\pi$
$284$	−1133.08	−	1763.10i	−0.236746	−	0.368384i
$285$	3565.96	−	5442.69i	0.741156	−	1.13122i
$286$	−239.625	−	816.086i	−0.0495430	−	0.168728i
$287$	−34.5293	−	482.783i	−0.00710174	−	0.0992953i
$288$	−1233.13	−	17241.4i	−0.252301	−	3.52763i
$289$	−104.325	−	355.300i	−0.0212346	−	0.0723183i
$290$	9150.58	−	13966.4i	1.85290	−	2.82806i
$291$	−69.8604	−	108.705i	−0.0140732	−	0.0218983i
$292$	−4273.71	−	7826.71i	−0.856506	−	1.56857i
$293$	−875.687	+	1169.78i	−0.174601	+	0.233240i	−0.879302	−	0.476265i	$-0.841990\pi$
$293$	−875.687	+	1169.78i	−0.174601	+	0.233240i	0.704701	+	0.709505i	$0.251081\pi$
$294$	−10618.0	−	4849.06i	−2.10630	−	0.961914i
$295$	−435.727	+	1137.51i	−0.0859965	+	0.224503i
$296$	−11563.1	+	17992.6i	−2.27058	+	3.53310i
$297$	13104.6	+	937.257i	2.56028	+	0.183115i
$298$	−3580.21	−	3580.21i	−0.695959	−	0.695959i
$299$	−326.468	−	169.780i	−0.0631442	−	0.0328383i
$300$	7252.09	+	20542.2i	1.39567	+	3.95335i
$301$	339.568	+	391.882i	0.0650244	+	0.0750422i
$302$	3967.61	+	18238.8i	0.755995	+	3.47525i
$303$	−1913.47	−	2556.10i	−0.362793	−	0.484635i
$304$	3908.46	−	8558.33i	0.737386	−	1.61465i
$305$	−73.5613	+	915.118i	−0.0138102	+	0.171802i
$306$	5571.04	−	18973.2i	1.04077	−	3.54453i
$307$	−3601.39	−	783.435i	−0.669519	−	0.145645i	−0.135057	−	0.990838i	$-0.543122\pi$
$307$	−3601.39	−	783.435i	−0.669519	−	0.145645i	−0.534461	+	0.845193i	$0.679486\pi$
$308$	8644.56	+	3224.25i	1.59925	+	0.596490i
$309$	3657.18	−	1073.85i	0.673300	−	0.197699i
$310$	−611.610	+	4003.09i	−0.112055	+	0.733421i
$311$	−3538.41	+	4083.55i	−0.645161	+	0.744556i	−0.980279	−	0.197621i	$-0.936679\pi$
$311$	−3538.41	+	4083.55i	−0.645161	+	0.744556i	0.335117	+	0.942176i	$0.391224\pi$
$312$	1542.62	+	842.332i	0.279915	+	0.152845i
$313$	141.386	−	379.070i	0.0255323	−	0.0684547i	−0.923558	−	0.383458i	$-0.874733\pi$
$313$	141.386	−	379.070i	0.0255323	−	0.0684547i	0.949090	+	0.315004i	$0.102006\pi$
$314$	−1920.56	+	1234.27i	−0.345171	+	0.221828i
$315$	−5982.35	+	1699.46i	−1.07005	+	0.303980i
$316$	−16155.7	+	2322.84i	−2.87604	+	0.413512i
$317$	−6159.38	+	2297.33i	−1.09131	+	0.407037i	−0.829742	−	0.558148i	$-0.811512\pi$
$317$	−6159.38	+	2297.33i	−1.09131	+	0.407037i	−0.261568	+	0.965185i	$0.584239\pi$
$318$	−5953.05	+	4456.40i	−1.04978	+	0.785856i
$319$	11825.6	+	7599.84i	2.07557	+	1.33389i
$320$	2187.53	+	4091.47i	0.382146	+	0.714751i
$321$		−	10685.7i		−	1.85800i
$322$	5104.11	−	2457.00i	0.883357	−	0.425227i
$323$	3037.72	−	3037.72i	0.523291	−	0.523291i
$324$	−13368.3	+	11583.7i	−2.29223	+	1.98623i
$325$	−405.847	−	95.8075i	−0.0692687	−	0.0163521i
$326$	970.245	−	6748.20i	0.164837	−	1.14647i
$327$	−2909.60	−	7800.93i	−0.492052	−	1.31924i
$328$	2265.80	+	1696.15i	0.381426	+	0.285532i
$329$	−5978.69	−	1755.50i	−1.00187	−	0.294176i
$330$	−24465.6	+	8880.41i	−4.08117	+	1.48136i
$331$	353.103	+	773.187i	0.0586353	+	0.128393i	0.936681	−	0.350183i	$-0.113880\pi$
$331$	353.103	+	773.187i	0.0586353	+	0.128393i	−0.878046	+	0.478576i	$0.841153\pi$
$332$	4695.98	−	8600.05i	0.776282	−	1.42165i
$333$	20841.9	−	1490.64i	3.42982	−	0.245305i
$334$	−2328.85	−	2017.96i	−0.381524	−	0.330592i
$335$	5773.74	+	5092.74i	0.941651	+	0.830585i
$336$	−12097.6	+	5524.80i	−1.96423	+	0.897032i
$337$	−360.741	+	1658.30i	−0.0583110	+	0.268051i	−0.997067	−	0.0765307i	$-0.975616\pi$
$337$	−360.741	+	1658.30i	−0.0583110	+	0.268051i	0.938756	+	0.344582i	$0.111979\pi$
$338$	9984.79	−	5452.11i	1.60681	−	0.877383i
$339$	−163.272	−	1135.58i	−0.0261585	−	0.181936i
$340$	1921.36	+	14253.9i	0.306472	+	2.27361i
$341$	−3374.56	−	485.188i	−0.535902	−	0.0770511i
$342$	−18272.9	+	3975.02i	−2.88913	+	0.628493i
$343$	−414.361	+	5793.53i	−0.0652286	+	0.912014i
$344$	−3032.18			−0.475245
$345$	−4560.43	+	10295.7i	−0.711667	+	1.60667i
$346$	3208.59			0.498540
$347$	−609.345	+	8519.76i	−0.0942691	+	1.31805i	0.701594	+	0.712577i	$0.252472\pi$
$347$	−609.345	+	8519.76i	−0.0942691	+	1.31805i	−0.795863	+	0.605477i	$0.792982\pi$
$348$	−48866.5	+	10630.2i	−7.52735	+	1.63747i
$349$	6301.09	+	905.960i	0.966445	+	0.138954i	0.607426	−	0.794376i	$-0.292202\pi$
$349$	6301.09	+	905.960i	0.966445	+	0.138954i	0.359019	+	0.933330i	$0.383111\pi$
$350$	4924.80	−	4117.67i	0.752119	−	0.628853i
$351$	−127.327	−	885.581i	−0.0193625	−	0.134669i
$352$	−13183.8	+	7198.88i	−1.99630	+	1.09006i
$353$	1488.14	−	6840.86i	0.224378	−	1.03145i	−0.717777	−	0.696273i	$-0.754840\pi$
$353$	1488.14	−	6840.86i	0.224378	−	1.03145i	0.942155	−	0.335177i	$-0.108796\pi$
$354$	4709.62	−	2150.81i	0.707100	−	0.322922i
$355$	−76.7854	−	1225.24i	−0.0114798	−	0.183181i
$356$	4340.28	+	3760.87i	0.646163	+	0.559904i
$357$	−6057.11	+	433.213i	−0.897973	+	0.0642243i
$358$	−8312.32	+	15222.9i	−1.22715	+	2.24736i
$359$	−4031.45	−	8827.65i	−0.592680	−	1.29779i	−0.933809	−	0.357771i	$-0.883537\pi$
$359$	−4031.45	−	8827.65i	−0.592680	−	1.29779i	0.341130	−	0.940016i	$-0.389190\pi$
$360$	15398.1	−	32945.8i	2.25431	−	4.82332i
$361$	2683.07	+	787.821i	0.391175	+	0.114859i
$362$	−1525.62	−	1142.06i	−0.221504	−	0.165816i
$363$	−3410.43	−	9143.72i	−0.493116	−	1.32210i
$364$	89.4164	−	621.905i	0.0128755	−	0.0895513i
$365$	46.0303	−	5223.35i	0.00660093	−	0.749049i
$366$	2949.09	−	2555.40i	0.421178	−	0.364953i
$367$	4334.43	−	4334.43i	0.616500	−	0.616500i	−0.328132	−	0.944632i	$-0.606419\pi$
$367$	4334.43	−	4334.43i	0.616500	−	0.616500i	0.944632	+	0.328132i	$0.106419\pi$
$368$	−4270.09	+	15712.2i	−0.604875	+	2.22569i
$369$		−	2765.14i		−	0.390101i
$370$	−19020.4	+	10169.4i	−2.67249	+	1.42887i
$371$	1298.97	+	834.800i	0.181777	+	0.116821i
$372$	9709.55	−	7268.47i	1.35327	−	1.01305i
$373$	−7413.74	+	2765.18i	−1.02914	+	0.383849i	−0.806615	−	0.591078i	$-0.798703\pi$
$373$	−7413.74	+	2765.18i	−1.02914	+	0.383849i	−0.222525	+	0.974927i	$0.571430\pi$
$374$	−17009.1	+	2445.53i	−2.35165	+	0.338116i
$375$	−2149.28	+	12578.4i	−0.295969	+	1.73212i
$376$	30652.7	−	19699.3i	4.20423	−	2.70190i
$377$	334.533	−	896.918i	0.0457012	−	0.122530i
$378$	12088.3	+	6600.69i	1.64485	+	0.898156i
$379$	−5607.14	+	6470.99i	−0.759946	+	0.877025i	−0.995493	−	0.0948384i	$-0.969767\pi$
$379$	−5607.14	+	6470.99i	−0.759946	+	0.877025i	0.235546	+	0.971863i	$0.424312\pi$
$380$	10960.1	−	8054.92i	1.47958	−	1.08739i
$381$	6544.80	−	1921.73i	0.880053	−	0.258407i
$382$	18199.3	+	6788.00i	2.43759	+	0.909174i
$383$	−1319.87	−	287.120i	−0.176089	−	0.0383059i	0.123656	−	0.992325i	$-0.460538\pi$
$383$	−1319.87	−	287.120i	−0.176089	−	0.0383059i	−0.299745	+	0.954019i	$0.596902\pi$
$384$	−754.545	+	2569.74i	−0.100274	+	0.341502i
$385$	3503.01	+	4115.42i	0.463714	+	0.544782i
$386$	7864.62	−	17221.1i	1.03704	−	2.27081i
$387$	1775.26	+	2371.47i	0.233182	+	0.311495i
$388$	−57.4165	−	263.940i	−0.00751259	−	0.0345348i
$389$	6319.38	+	7292.95i	0.823663	+	0.950558i	0.999426	−	0.0338744i	$-0.0107846\pi$
$389$	6319.38	+	7292.95i	0.823663	+	0.950558i	−0.175763	+	0.984433i	$0.556239\pi$
$390$	945.077	+	1499.46i	0.122707	+	0.194687i
$391$	−4333.94	+	6040.53i	−0.560555	+	0.781286i
$392$	−10022.0	−	10022.0i	−1.29130	−	1.29130i
$393$	8656.71	+	619.140i	1.11113	+	0.0794695i
$394$	7507.92	−	11682.5i	0.960008	−	1.49380i
$395$	−8928.14	−	3419.94i	−1.13727	−	0.435635i
$396$	47945.6	+	21896.0i	6.08424	+	2.77858i
$397$	−9008.56	+	12034.0i	−1.13886	+	1.52134i	−0.319930	+	0.947441i	$0.603659\pi$
$397$	−9008.56	+	12034.0i	−1.13886	+	1.52134i	−0.818929	+	0.573896i	$0.805432\pi$
$398$	9507.58	+	17411.8i	1.19742	+	2.19291i
$399$	3104.78	+	4831.13i	0.389557	+	0.606163i
$400$	−325.177	+	18448.5i	−0.0406471	+	2.30606i
$401$	−2527.48	−	8607.79i	−0.314753	−	1.07195i	−0.953214	−	0.302297i	$-0.902247\pi$
$401$	−2527.48	−	8607.79i	−0.314753	−	1.07195i	0.638460	−	0.769655i	$-0.279572\pi$
$402$	−2334.46	−	32640.0i	−0.289633	−	4.04959i
$403$	16.5626	+	231.576i	0.00204725	+	0.0286243i
$404$	−1880.42	−	6404.11i	−0.231570	−	0.788655i
$405$	−10143.7	+	2113.18i	−1.24455	+	0.259271i
$406$	7967.14	+	12397.1i	0.973897	+	1.51541i
$407$	−8702.24	−	15937.0i	−1.05984	−	1.94095i
$408$	21280.4	−	28427.2i	2.58219	−	3.44941i
$409$	2417.74	+	1104.15i	0.292298	+	0.133488i	0.556167	−	0.831071i	$-0.312272\pi$
$409$	2417.74	+	1104.15i	0.292298	+	0.133488i	−0.263869	+	0.964558i	$0.584999\pi$
$410$	1162.76	+	2606.63i	0.140060	+	0.313982i
$411$	3001.49	−	4670.41i	0.360225	−	0.560522i
$412$	7947.30	+	568.402i	0.950328	+	0.0679688i
$413$	−760.191	−	760.191i	−0.0905728	−	0.0905728i
$414$	30086.4	−	11920.6i	3.57165	−	1.41514i
$415$	4855.68	−	3060.43i	0.574352	−	0.362002i
$416$	669.875	+	773.076i	0.0789502	+	0.0911134i
$417$	−1279.04	−	5879.63i	−0.150203	−	0.690472i
$418$	9738.66	+	13009.3i	1.13955	+	1.52227i
$419$	3169.70	−	6940.68i	0.369571	−	0.809247i	−0.629899	−	0.776677i	$-0.716904\pi$
$419$	3169.70	−	6940.68i	0.369571	−	0.809247i	0.999469	−	0.0325696i	$-0.0103691\pi$
$420$	−19164.8	−	1540.56i	−2.22654	−	0.178980i
$421$	−1723.98	+	5871.35i	−0.199577	+	0.679696i	0.797502	+	0.603316i	$0.206154\pi$
$421$	−1723.98	+	5871.35i	−0.199577	+	0.679696i	−0.997079	+	0.0763800i	$0.975664\pi$
$422$	7087.70	+	1541.84i	0.817592	+	0.177856i
$423$	−33353.2	−	12440.1i	−3.83378	−	1.42992i
$424$	−8663.49	+	2543.83i	−0.992302	+	0.291366i
$425$	−3082.87	+	7840.64i	−0.351862	+	0.894886i
$426$	−3417.09	+	3943.53i	−0.388635	+	0.448508i
$427$	−711.153	−	388.319i	−0.0805974	−	0.0440095i
$428$	7806.00	−	20928.7i	0.881582	−	2.36361i
$429$	−1255.31	+	806.742i	−0.141275	+	0.0907922i
$430$	−2670.72	−	1489.03i	−0.299520	−	0.166993i
$431$	256.708	−	36.9090i	0.0286895	−	0.00412493i	−0.127955	−	0.991780i	$-0.540841\pi$
$431$	256.708	−	36.9090i	0.0286895	−	0.00412493i	0.156645	+	0.987655i	$0.449932\pi$
$432$	−37091.8	+	13834.5i	−4.13097	+	1.54077i
$433$	−2343.96	+	1754.66i	−0.260146	+	0.194743i	−0.721387	−	0.692532i	$-0.756495\pi$
$433$	−2343.96	+	1754.66i	−0.260146	+	0.194743i	0.461241	+	0.887275i	$0.347404\pi$
$434$	−3006.66	−	1932.26i	−0.332545	−	0.213713i
$435$	−28033.2	−	8500.33i	−3.08986	−	0.936919i
$436$		−	17404.1i		−	1.91171i
$437$	6977.93	+	859.530i	0.763844	+	0.0940890i
$438$	−15699.5	+	15699.5i	−1.71267	+	1.71267i
$439$	11706.3	−	10143.6i	1.27269	−	1.10280i	0.283072	−	0.959099i	$-0.408646\pi$
$439$	11706.3	−	10143.6i	1.27269	−	1.10280i	0.989622	−	0.143697i	$-0.0458990\pi$
$440$	−31601.6	−	278.487i	−3.42397	−	0.0301735i
$441$	−1970.61	+	13705.9i	−0.212785	+	1.47995i
$442$	408.947	+	1096.43i	0.0440081	+	0.117990i
$443$	−7992.09	−	5982.81i	−0.857146	−	0.641652i	0.0775933	−	0.996985i	$-0.475276\pi$
$443$	−7992.09	−	5982.81i	−0.857146	−	0.641652i	−0.934740	+	0.355333i	$0.884367\pi$
$444$	61982.1	+	18199.6i	6.62509	+	1.94530i
$445$	1147.79	+	3162.18i	0.122271	+	0.336858i
$446$	9555.95	+	20924.6i	1.01455	+	2.22154i
$447$	−4257.12	+	7796.33i	−0.450458	+	0.824952i
$448$	−4084.32	+	292.116i	−0.430728	+	0.0308062i
$449$	702.476	+	608.699i	0.0738349	+	0.0639783i	0.690996	−	0.722858i	$-0.257172\pi$
$449$	702.476	+	608.699i	0.0738349	+	0.0639783i	−0.617161	+	0.786837i	$0.711717\pi$
$450$	29741.4	−	21456.8i	3.11560	−	2.24774i
$451$	−2185.78	+	998.212i	−0.228214	+	0.104222i
$452$	509.773	−	2343.39i	0.0530480	−	0.243858i
$453$	28741.1	−	15693.9i	2.98096	−	1.62773i
$454$	−928.391	−	6457.10i	−0.0959725	−	0.667504i
$455$	223.143	−	292.672i	0.0229914	−	0.0301554i
$456$	−33239.6	−	4779.13i	−3.41357	−	0.490797i
$457$	−3906.06	+	849.712i	−0.399820	+	0.0869756i	−0.407979	−	0.912991i	$-0.633766\pi$
$457$	−3906.06	+	849.712i	−0.399820	+	0.0869756i	0.00815912	+	0.999967i	$0.497403\pi$
$458$	−925.367	+	12938.3i	−0.0944096	+	1.32002i
$459$	−18075.9			−1.83815
$460$	−16453.0	+	16833.4i	−1.66766	+	1.70622i
$461$	−879.284			−0.0888337			−0.0444169	−	0.999013i	$-0.514143\pi$
$461$	−879.284			−0.0888337			−0.0444169	+	0.999013i	$0.514143\pi$
$462$	1638.74	−	22912.6i	0.165024	−	2.30734i
$463$	13299.9	−	2893.23i	1.33499	−	0.290410i	0.512255	−	0.858833i	$-0.328810\pi$
$463$	13299.9	−	2893.23i	1.33499	−	0.290410i	0.822736	+	0.568424i	$0.192447\pi$
$464$	−41926.0	−	6028.05i	−4.19475	−	0.603114i
$465$	7040.89	−	949.077i	0.702179	−	0.0946503i
$466$	2127.82	+	14799.3i	0.211523	+	1.47117i
$467$	−8458.90	+	4618.91i	−0.838183	+	0.457682i	−0.840175	−	0.542316i	$-0.817548\pi$
$467$	−8458.90	+	4618.91i	−0.838183	+	0.457682i	0.00199203	+	0.999998i	$0.499366\pi$
$468$	762.986	−	3507.39i	0.0753611	−	0.346430i
$469$	−6180.76	+	2822.66i	−0.608531	+	0.277907i
$470$	36672.5	−	2298.25i	3.59910	−	0.225554i
$471$	3026.99	+	2622.90i	0.296128	+	0.256597i
$472$	6270.58	−	448.480i	0.611497	−	0.0437351i
$473$	1233.73	−	2259.41i	0.119930	−	0.219636i
$474$	16881.4	+	36965.0i	1.63584	+	3.58198i
$475$	7905.03	−	994.716i	0.763595	−	0.0960857i
$476$	−12179.7	−	3576.29i	−1.17281	−	0.344368i
$477$	7061.78	+	5286.38i	0.677854	+	0.507435i
$478$	−5923.67	−	15882.0i	−0.566825	−	1.51972i
$479$	−1422.45	+	9893.34i	−0.135685	+	0.943712i	0.802271	+	0.596960i	$0.203625\pi$
$479$	−1422.45	+	9893.34i	−0.135685	+	0.943712i	−0.937957	+	0.346753i	$0.887284\pi$
$480$	22328.5	−	21938.4i	2.12324	−	2.08614i
$481$	−934.519	+	809.765i	−0.0885871	+	0.0767612i
$482$	−21317.0	+	21317.0i	−2.01444	+	2.01444i
$483$	−6658.81	−	7377.55i	−0.627301	−	0.695011i
$484$		−	20399.9i		−	1.91585i
$485$	45.9124	−	151.414i	0.00429850	−	0.0141760i
$486$	5345.50	+	3435.34i	0.498923	+	0.320639i
$487$	11838.5	−	8862.16i	1.10154	−	0.824605i	0.115869	−	0.993264i	$-0.463035\pi$
$487$	11838.5	−	8862.16i	1.10154	−	0.824605i	0.985674	+	0.168659i	$0.0539437\pi$
$488$	4439.37	−	1655.80i	0.411805	−	0.153595i
$489$	−11839.1	+	1702.21i	−1.09485	+	0.157416i
$490$	−3905.77	−	13748.9i	−0.360091	−	1.26757i
$491$	−1574.89	+	1012.12i	−0.144753	+	0.0930271i	−0.611013	−	0.791621i	$-0.709238\pi$
$491$	−1574.89	+	1012.12i	−0.144753	+	0.0930271i	0.466260	+	0.884648i	$0.345601\pi$
$492$	2987.43	−	8009.62i	0.273748	−	0.733947i
$493$	−16974.7	−	9268.87i	−1.55071	−	0.846752i
$494$	724.704	−	836.353i	0.0660040	−	0.0761727i
$495$	18284.1	+	24878.7i	1.66022	+	2.25902i
$496$	9856.72	−	2894.20i	0.892298	−	0.262002i
$497$	1015.18	+	378.641i	0.0916234	+	0.0341738i
$498$	−23838.6	−	5185.77i	−2.14505	−	0.466627i
$499$	2520.98	−	8585.67i	0.226161	−	0.770235i	−0.765732	−	0.643160i	$-0.777623\pi$
$499$	2520.98	−	8585.67i	0.226161	−	0.770235i	0.991893	−	0.127075i	$-0.0405589\pi$
$500$	−13398.2	+	23065.6i	−1.19837	+	2.06305i
$501$	−2245.83	+	4917.68i	−0.200272	+	0.438535i
$502$	−20426.0	−	27285.9i	−1.81605	−	2.42596i
$503$	4406.81	+	20257.8i	0.390636	+	1.79573i	0.580881	+	0.813989i	$0.302708\pi$
$503$	4406.81	+	20257.8i	0.390636	+	1.79573i	−0.190244	+	0.981737i	$0.560928\pi$
$504$	21018.5	+	24256.7i	1.85762	+	2.14381i
$505$	864.692	−	3812.85i	0.0761946	−	0.335979i
$506$	−20284.2	−	19479.3i	−1.78210	−	1.71138i
$507$	−14113.0	−	14113.0i	−1.23625	−	1.23625i
$508$	14222.3	+	1017.20i	1.24215	+	0.0888402i
$509$	564.169	−	877.864i	0.0491284	−	0.0764453i	−0.815821	−	0.578305i	$-0.803714\pi$
$509$	564.169	−	877.864i	0.0491284	−	0.0764453i	0.864949	+	0.501860i	$0.167351\pi$
$510$	32703.5	−	14588.3i	2.83948	−	1.26663i
$511$	4193.56	+	1915.14i	0.363038	+	0.165794i
$512$	−13709.3	+	18313.5i	−1.18334	+	1.58076i
$513$	8192.37	+	15003.2i	0.705072	+	1.29124i
$514$	5321.44	+	8280.32i	0.456651	+	0.710562i
$515$	3903.85	+	2557.74i	0.334028	+	0.218850i
$516$	2580.18	+	8787.30i	0.220128	+	0.749689i
$517$	2206.85	+	30855.8i	0.187732	+	2.62483i
$518$	−1357.99	−	18987.1i	−0.115186	−	1.61051i
$519$	−1585.93	−	5401.16i	−0.134132	−	0.456811i
$520$	438.918	+	2106.89i	0.0370150	+	0.177679i
$521$	−6639.59	−	10331.4i	−0.558322	−	0.868766i	0.441269	−	0.897375i	$-0.354529\pi$
$521$	−6639.59	−	10331.4i	−0.558322	−	0.868766i	−0.999591	+	0.0286092i	$0.990892\pi$
$522$	40347.0	+	73890.0i	3.38303	+	6.19555i
$523$	−8740.03	+	11675.3i	−0.730736	+	0.976148i	0.269179	+	0.963090i	$0.413248\pi$
$523$	−8740.03	+	11675.3i	−0.730736	+	0.976148i	−0.999915	+	0.0130583i	$0.995843\pi$
$524$	16502.5	+	7536.43i	1.37579	+	0.628303i
$525$	−9365.66	−	6254.88i	−0.778573	−	0.519972i
$526$	−3020.34	+	4699.74i	−0.250367	+	0.389579i
$527$	4678.66	+	334.625i	0.386728	+	0.0276593i
$528$	46687.5	+	46687.5i	3.84813	+	3.84813i
$529$	−12157.0	+	492.357i	−0.999181	+	0.0404666i
$530$	−8879.95	−	2013.83i	−0.727774	−	0.165047i
$531$	−4022.01	−	4641.65i	−0.328702	−	0.379342i
$532$	2551.74	+	11730.2i	0.207955	+	0.955953i
$533$	98.0640	+	130.998i	0.00796927	+	0.0106457i
$534$	5939.88	−	13006.5i	0.481355	−	1.05402i
$535$	9963.53	−	8480.88i	0.805160	−	0.685347i
$536$	11194.1	−	38123.8i	0.902077	−	3.07219i
$537$	29733.9	+	6468.22i	2.38941	+	0.519785i
$538$	−16442.7	−	6132.83i	−1.31765	−	0.491459i
$539$	11545.6	−	3390.09i	0.922640	−	0.270912i
$540$	−56574.4	−	8643.68i	−4.50847	−	0.688824i
$541$	−12049.0	+	13905.2i	−0.957533	+	1.10505i	0.0368616	+	0.999320i	$0.488264\pi$
$541$	−12049.0	+	13905.2i	−0.957533	+	1.10505i	−0.994395	+	0.105732i	$0.966282\pi$
$542$	−28325.5	−	15466.9i	−2.24480	−	1.22575i
$543$	−1168.41	+	3132.63i	−0.0923412	+	0.247576i
$544$	17386.0	−	11173.3i	1.37026	−	0.880611i
$545$	4964.47	−	8904.29i	0.390191	−	0.699849i
$546$	−1548.39	+	222.625i	−0.121364	+	0.0174496i
$547$	13216.3	−	4929.42i	1.03307	−	0.385314i	0.224971	−	0.974365i	$-0.427771\pi$
$547$	13216.3	−	4929.42i	1.03307	−	0.385314i	0.808096	+	0.589051i	$0.200498\pi$
$548$	9290.40	−	6954.71i	0.724209	−	0.542136i
$549$	−3894.14	−	2502.61i	−0.302728	−	0.194551i
$550$	−27697.7	−	15764.0i	−2.14734	−	1.22215i
$551$			18290.0i			1.41412i
$552$	58102.8	−	1176.09i	4.48010	−	0.0906844i
$553$	5966.61	−	5966.61i	0.458818	−	0.458818i
$554$	−14600.9	+	12651.7i	−1.11973	+	0.970253i
$555$	26519.9	+	26991.4i	2.02830	+	2.06436i
$556$	1790.04	−	12450.0i	0.136537	−	0.949637i
$557$	−4138.47	−	11095.7i	−0.314816	−	0.844055i	−0.993929	−	0.110021i	$-0.964908\pi$
$557$	−4138.47	−	11095.7i	−0.314816	−	0.844055i	0.679113	−	0.734034i	$-0.262365\pi$
$558$	−16345.5	−	12236.1i	−1.24007	−	0.928306i
$559$	−168.206	−	49.3897i	−0.0127269	−	0.00373696i
$560$	−14752.9	−	6895.18i	−1.11326	−	0.520311i
$561$	12523.8	+	27423.3i	0.942524	+	2.06384i
$562$	−17885.2	+	32754.2i	−1.34242	+	2.45846i
$563$	−3839.01	+	274.571i	−0.287380	+	0.0205538i	−0.214285	−	0.976771i	$-0.568742\pi$
$563$	−3839.01	+	274.571i	−0.287380	+	0.0205538i	−0.0730948	+	0.997325i	$0.523288\pi$
$564$	−83172.2	−	72069.2i	−6.20954	−	5.38060i
$565$	929.251	−	1053.51i	0.0691927	−	0.0784451i
$566$	−15522.1	+	7088.71i	−1.15273	+	0.526432i
$567$	1943.86	−	8935.76i	0.143976	−	0.661846i
$568$	−5560.81	+	3036.43i	−0.410786	+	0.224306i
$569$	2099.98	+	14605.7i	0.154720	+	1.07610i	0.908171	+	0.418598i	$0.137479\pi$
$569$	2099.98	+	14605.7i	0.154720	+	1.07610i	−0.753451	+	0.657504i	$0.771612\pi$
$570$	−26930.3	−	20532.5i	−1.97892	−	1.50880i
$571$	8734.13	+	1255.78i	0.640126	+	0.0920362i	0.454732	−	0.890628i	$-0.349735\pi$
$571$	8734.13	+	1255.78i	0.640126	+	0.0920362i	0.185394	+	0.982664i	$0.440644\pi$
$572$	−3047.95	+	663.041i	−0.222799	+	0.0484670i
$573$	2431.08	−	33990.9i	0.177242	−	2.47817i
$574$	−2519.06			−0.183177
$575$	−13219.3	+	3919.11i	−0.958753	+	0.284240i
$576$	−23392.9			−1.69220
$577$	665.905	−	9310.57i	0.0480450	−	0.671757i	−0.915177	−	0.403052i	$-0.867950\pi$
$577$	665.905	−	9310.57i	0.0480450	−	0.671757i	0.963222	−	0.268706i	$-0.0865959\pi$
$578$	−1883.18	+	409.661i	−0.135519	+	0.0294803i
$579$	−32876.4	−	4726.91i	−2.35975	−	0.339281i
$580$	−48695.4	−	37127.0i	−3.48615	−	2.65796i
$581$	720.923	+	5014.13i	0.0514784	+	0.358040i
$582$	−590.251	+	322.301i	−0.0420390	+	0.0229550i
$583$	1629.47	−	7490.56i	0.115756	−	0.532122i
$584$	−24522.3	+	11198.9i	−1.73757	+	0.793520i
$585$	1390.83	−	1576.81i	0.0982967	−	0.111441i
$586$	5747.48	+	4980.22i	0.405164	+	0.351077i
$587$	12957.1	−	926.713i	0.911070	−	0.0651610i	0.392070	−	0.919935i	$-0.371759\pi$
$587$	12957.1	−	926.713i	0.911070	−	0.0651610i	0.519000	+	0.854774i	$0.326304\pi$
$588$	−20515.9	+	37572.0i	−1.43888	+	2.63511i
$589$	−1842.72	−	4035.00i	−0.128910	−	0.282274i
$590$	5743.32	+	2684.30i	0.400760	+	0.187307i
$591$	−23376.7	−	6864.03i	−1.62706	−	0.477747i
$592$	43801.0	+	32789.0i	3.04090	+	2.27639i
$593$	516.957	+	1386.02i	0.0357991	+	0.0959812i	0.953619	−	0.301015i	$-0.0973254\pi$
$593$	516.957	+	1386.02i	0.0357991	+	0.0959812i	−0.917820	+	0.396996i	$0.870053\pi$
$594$	9731.05	−	67680.9i	0.672171	−	4.67505i
$595$	−5211.26	−	5303.92i	−0.359060	−	0.365445i
$596$	−14033.1	+	12159.8i	−0.964463	+	0.835712i
$597$	24610.8	−	24610.8i	1.68719	−	1.68719i
$598$	−1002.58	+	1631.73i	−0.0685595	+	0.111583i
$599$			10501.8i			0.716348i	0.933655	+	0.358174i	$0.116601\pi$
$599$			10501.8i			0.716348i	−0.933655	+	0.358174i	$0.883399\pi$
$600$	63506.8	−	17437.6i	4.32109	−	1.18648i
$601$	16007.3	+	10287.3i	1.08644	+	0.698213i	0.956037	−	0.293247i	$-0.0947360\pi$
$601$	16007.3	+	10287.3i	1.08644	+	0.698213i	0.130405	+	0.991461i	$0.458372\pi$
$602$	2160.43	−	1617.28i	0.146267	−	0.109494i
$603$	−36370.5	+	13565.5i	−2.45625	+	0.916136i
$604$	67756.0	−	9741.84i	4.56449	−	0.656275i
$605$	5819.01	−	10437.0i	0.391035	−	0.701362i
$606$	−13979.8	+	8984.26i	−0.937111	+	0.602245i
$607$	−1341.61	+	3597.00i	−0.0897106	+	0.240523i	−0.974055	−	0.226312i	$-0.927333\pi$
$607$	−1341.61	+	3597.00i	−0.0897106	+	0.240523i	0.884344	+	0.466835i	$0.154606\pi$
$608$	−17153.7	−	9366.62i	−1.14420	−	0.624780i
$609$	16930.7	−	19539.0i	1.12654	−	1.30010i
$610$	4723.28	+	721.643i	0.313508	+	0.0478992i
$611$	2021.29	−	593.503i	0.133834	−	0.0392972i
$612$	−67946.8	−	25342.9i	−4.48789	−	1.67390i
$613$	1722.83	+	374.778i	0.113514	+	0.0246936i	0.268964	−	0.963150i	$-0.413319\pi$
$613$	1722.83	+	374.778i	0.113514	+	0.0246936i	−0.155449	+	0.987844i	$0.549682\pi$
$614$	−5404.14	+	18404.8i	−0.355201	+	1.20970i
$615$	3813.14	−	3245.72i	0.250017	−	0.212813i
$616$	11586.7	−	25371.4i	0.757860	−	1.65948i
$617$	1859.89	+	2484.52i	0.121355	+	0.162112i	0.857105	−	0.515142i	$-0.172261\pi$
$617$	1859.89	+	2484.52i	0.121355	+	0.162112i	−0.735749	+	0.677254i	$0.763170\pi$
$618$	−4216.73	−	19384.0i	−0.274469	−	1.26171i
$619$	18467.1	+	21312.1i	1.19912	+	1.38386i	0.903521	+	0.428543i	$0.140973\pi$
$619$	18467.1	+	21312.1i	1.19912	+	1.38386i	0.295597	+	0.955313i	$0.404481\pi$
$620$	14483.4	+	3284.60i	0.938172	+	0.212762i
$621$	−18203.8	−	23318.4i	−1.17632	−	1.50682i
$622$	19884.9	+	19884.9i	1.28185	+	1.28185i
$623$	−2961.46	−	211.808i	−0.190447	−	0.0136210i
$624$	2430.89	−	3782.54i	0.155951	−	0.242665i
$625$	−13434.1	+	7979.03i	−0.859784	+	0.510658i
$626$	−1915.35	−	874.710i	−0.122289	−	0.0558474i
$627$	17085.6	−	22823.7i	1.08825	−	1.45373i
$628$	4012.52	+	7348.38i	0.254963	+	0.466930i
$629$	13506.7	+	21016.8i	0.856194	+	1.33226i
$630$	6601.14	+	31686.8i	0.417454	+	2.00386i
$631$	2261.44	+	7701.75i	0.142673	+	0.485898i	0.999562	−	0.0296025i	$-0.00942414\pi$
$631$	2261.44	+	7701.75i	0.142673	+	0.485898i	−0.856889	+	0.515501i	$0.827606\pi$
$632$	3520.05	+	49216.7i	0.221551	+	3.09768i
$633$	−907.831	−	12693.1i	−0.0570032	−	0.797009i
$634$	9639.09	+	32827.7i	0.603813	+	2.05640i
$635$	6986.23	+	4577.27i	0.436599	+	0.286052i
$636$	14744.1	+	22942.3i	0.919248	+	1.43038i
$637$	−392.713	−	719.201i	−0.0244268	−	0.0447343i
$638$	43843.2	−	58567.7i	2.72064	−	3.63435i
$639$	5630.50	+	2571.37i	0.348575	+	0.159189i
$640$	−2994.93	+	1335.97i	−0.184976	+	0.0825137i
$641$	−6330.74	+	9850.83i	−0.390093	+	0.606996i	−0.979646	−	0.200734i	$-0.935667\pi$
$641$	−6330.74	+	9850.83i	−0.390093	+	0.606996i	0.589553	+	0.807729i	$0.299304\pi$
$642$	−55472.0	−	3967.44i	−3.41013	−	0.243898i
$643$	6776.34	+	6776.34i	0.415603	+	0.415603i	0.883685	−	0.468082i	$-0.155055\pi$
$643$	6776.34	+	6776.34i	0.415603	+	0.415603i	−0.468082	+	0.883685i	$0.655055\pi$
$644$	−7652.37	−	19313.8i	−0.468239	−	1.18178i
$645$	−1186.47	+	5231.73i	−0.0724300	+	0.319379i
$646$	−14641.6	−	16897.4i	−0.891746	−	1.02913i
$647$	−3791.18	−	17427.8i	−0.230366	−	1.05898i	−0.936437	−	0.350835i	$-0.885898\pi$
$647$	−3791.18	−	17427.8i	−0.230366	−	1.05898i	0.706071	−	0.708141i	$-0.250466\pi$
$648$	32046.3	+	42808.8i	1.94274	+	2.59520i
$649$	−2217.18	+	4854.95i	−0.134102	+	0.293642i
$650$	−648.044	+	2071.27i	−0.0391052	+	0.124988i
$651$	−1766.55	+	6016.32i	−0.106354	+	0.362209i
$652$	−24431.2	−	5314.68i	−1.46748	−	0.319232i
$653$	−1067.68	−	398.222i	−0.0639837	−	0.0238647i	0.317269	−	0.948336i	$-0.397234\pi$
$653$	−1067.68	−	398.222i	−0.0639837	−	0.0238647i	−0.381252	+	0.924471i	$0.624507\pi$
$654$	−41576.8	+	12208.0i	−2.48590	+	0.729927i
$655$	6293.24	+	8563.05i	0.375416	+	0.510818i
$656$	4741.55	−	5472.04i	0.282205	−	0.325682i
$657$	23115.9	+	12622.2i	1.37266	+	0.749527i
$658$	−11333.0	+	30385.0i	−0.671439	+	1.80020i
$659$	6234.35	−	4006.57i	0.368522	−	0.236834i	−0.343252	−	0.939243i	$-0.611529\pi$
$659$	6234.35	−	4006.57i	0.368522	−	0.236834i	0.711774	+	0.702409i	$0.247892\pi$
$660$	26083.8	+	91819.0i	1.53835	+	5.41522i
$661$	19507.3	−	2804.73i	1.14788	−	0.165040i	0.457990	−	0.888957i	$-0.348570\pi$
$661$	19507.3	−	2804.73i	1.14788	−	0.165040i	0.689886	+	0.723918i	$0.257660\pi$
$662$	4144.90	−	1545.97i	0.243347	−	0.0907639i
$663$	1643.53	−	1230.33i	0.0962739	−	0.0720698i
$664$	−24919.7	−	16014.9i	−1.45644	−	0.935994i
$665$	−2040.46	+	6729.24i	−0.118986	+	0.392404i
$666$		−	108749.i		−	6.32722i
$667$	−5137.65	−	31232.2i	−0.298247	−	1.81307i
$668$	−7991.02	+	7991.02i	−0.462847	+	0.462847i
$669$	30500.1	−	26428.5i	1.76263	−	1.52733i
$670$	28581.3	−	28082.0i	1.64805	−	1.61926i
$671$	−572.478	+	3981.67i	−0.0329363	+	0.229077i
$672$	9654.63	+	25885.1i	0.554219	+	1.48592i
$673$	527.096	+	394.579i	0.0301903	+	0.0226002i	0.614266	−	0.789099i	$-0.289452\pi$
$673$	527.096	+	394.579i	0.0301903	+	0.0226002i	−0.584076	+	0.811699i	$0.698543\pi$
$674$	8474.68	+	2488.39i	0.484321	+	0.142209i
$675$	−26479.0	−	20559.9i	−1.50989	−	1.17237i
$676$	−17331.6	−	37951.0i	−0.986096	−	2.15925i
$677$	−9700.40	+	17765.0i	−0.550689	+	1.00851i	0.443019	+	0.896512i	$0.353907\pi$
$677$	−9700.40	+	17765.0i	−0.550689	+	1.00851i	−0.993708	+	0.112000i	$0.964274\pi$
$678$	−5955.69	+	425.960i	−0.337356	+	0.0241281i
$679$	105.535	+	91.4466i	0.00596474	+	0.00516848i
$680$	43395.5	−	2719.58i	2.44727	−	0.153369i
$681$	−10410.6	+	4754.38i	−0.585810	+	0.267531i
$682$	−3771.65	+	17338.0i	−0.211765	+	0.973469i
$683$	−13414.7	+	7324.98i	−0.751537	+	0.410370i	−0.808872	−	0.587985i	$-0.799921\pi$
$683$	−13414.7	+	7324.98i	−0.751537	+	0.410370i	0.0573353	+	0.998355i	$0.481740\pi$
$684$	9760.03	+	67882.5i	0.545591	+	3.79467i
$685$	6736.95	−	908.108i	0.375775	−	0.0506526i
$686$	29921.7	+	4302.09i	1.66533	+	0.239438i
$687$	22237.1	−	4837.38i	1.23493	−	0.268642i
$688$	−553.372	+	7737.15i	−0.0306644	+	0.428745i
$689$	−522.030			−0.0288647
$690$	51754.0	+	27496.9i	2.85542	+	1.51708i
$691$	8122.94			0.447194			0.223597	−	0.974682i	$-0.428220\pi$
$691$	8122.94			0.447194			0.223597	+	0.974682i	$0.428220\pi$
$692$	839.453	−	11737.1i	0.0461145	−	0.644764i
$693$	−26626.7	+	5792.28i	−1.45954	+	0.317504i
$694$	44001.9	+	6326.51i	2.40675	+	0.346039i
$695$	4467.14	−	5859.05i	0.243810	−	0.319779i
$696$	21515.6	+	149644.i	1.17176	+	8.14977i
$697$	2901.66	−	1584.42i	0.157687	−	0.0861038i
$698$	7042.54	−	32374.1i	0.381897	−	1.75555i
$699$	23860.7	−	10896.8i	1.29112	−	0.589635i
$700$	−13774.0	−	19092.3i	−0.743729	−	1.03089i
$701$	−16655.7	−	14432.2i	−0.897399	−	0.777600i	0.0782514	−	0.996934i	$-0.475066\pi$
$701$	−16655.7	−	14432.2i	−0.897399	−	0.777600i	−0.975650	+	0.219333i	$0.929612\pi$
$702$	−4644.53	+	332.184i	−0.249710	+	0.0178596i
$703$	11322.7	−	20735.9i	0.607457	−	1.11247i
$704$	8444.83	+	18491.6i	0.452097	+	0.989955i
$705$	−21995.0	−	60596.5i	−1.17501	−	3.23716i
$706$	−34960.0	−	10265.2i	−1.86365	−	0.547217i
$707$	2762.32	+	2067.85i	0.146942	+	0.109999i
$708$	−6635.55	−	17790.6i	−0.352230	−	0.944366i
$709$	607.917	−	4228.16i	0.0322014	−	0.223966i	−0.967366	−	0.253384i	$-0.918456\pi$
$709$	607.917	−	4228.16i	0.0322014	−	0.223966i	0.999567	+	0.0294182i	$0.00936546\pi$
$710$	−6389.03	−	56.3028i	−0.337713	−	0.00297607i
$711$	36431.5	−	31568.1i	1.92164	−	1.66511i
$712$	12276.5	−	12276.5i	0.646183	−	0.646183i
$713$	4280.08	+	6372.59i	0.224811	+	0.334720i
$714$			31604.7i			1.65655i
$715$	−1748.52	−	530.192i	−0.0914558	−	0.0277316i
$716$	53510.9	+	34389.4i	2.79301	+	1.79496i
$717$	−23806.9	+	17821.6i	−1.24001	+	0.928259i
$718$	−47323.2	+	17650.7i	−2.45973	+	0.917433i
$719$	−26135.1	+	3757.66i	−1.35560	+	0.194906i	−0.781513	−	0.623889i	$-0.785552\pi$
$719$	−26135.1	+	3757.66i	−1.35560	+	0.194906i	−0.574086	+	0.818795i	$0.694642\pi$
$720$	−81256.9	−	45303.7i	−4.20593	−	2.34496i
$721$	−3465.20	+	2226.95i	−0.178989	+	0.115029i
$722$	5085.94	−	13635.9i	0.262160	−	0.702877i
$723$	46420.3	+	25347.4i	2.38781	+	1.30384i
$724$	−4576.82	+	5281.94i	−0.234940	+	0.271135i
$725$	−14323.2	−	32885.1i	−0.733723	−	1.68458i
$726$	−48733.4	+	14309.4i	−2.49128	+	0.731505i
$727$	−26835.0	−	10008.9i	−1.36899	−	0.510606i	−0.445860	−	0.895103i	$-0.647102\pi$
$727$	−26835.0	−	10008.9i	−1.36899	−	0.510606i	−0.923126	+	0.384497i	$0.874375\pi$
$728$	−1856.00	−	403.748i	−0.0944890	−	0.0205548i
$729$	−3908.90	+	13312.5i	−0.198593	+	0.676345i
$730$	−27098.6	−	2178.30i	−1.37392	−	0.110442i
$731$	−1471.33	+	3221.76i	−0.0744448	+	0.163011i
$732$	−8576.14	−	11456.4i	−0.433037	−	0.578470i
$733$	−4521.21	−	20783.7i	−0.227824	−	1.04729i	−0.938904	−	0.344178i	$-0.888157\pi$
$733$	−4521.21	−	20783.7i	−0.227824	−	1.04729i	0.711080	−	0.703111i	$-0.248206\pi$
$734$	−20891.7	−	24110.4i	−1.05058	−	1.21244i
$735$	−21213.6	+	13370.5i	−1.06459	+	0.670990i
$736$	31922.9	+	11176.1i	1.59877	+	0.559722i
$737$	23853.0	+	23853.0i	1.19218	+	1.19218i
$738$	−14354.5	−	1026.65i	−0.715983	−	0.0512081i
$739$	6635.58	−	10325.2i	0.330303	−	0.513961i	−0.635891	−	0.771779i	$-0.719367\pi$
$739$	6635.58	−	10325.2i	0.330303	−	0.513961i	0.966194	+	0.257818i	$0.0830034\pi$
$740$	32223.5	+	72237.5i	1.60076	+	3.58852i
$741$	−1766.07	−	806.539i	−0.0875552	−	0.0399851i
$742$	4815.93	−	6433.33i	0.238273	−	0.318295i
$743$	10354.4	+	18962.7i	0.511261	+	0.936304i	0.998028	+	0.0627724i	$0.0199942\pi$
$743$	10354.4	+	18962.7i	0.511261	+	0.936304i	−0.486767	+	0.873532i	$0.661824\pi$
$744$	−19823.3	−	30845.6i	−0.976823	−	1.51997i
$745$	−10648.1	+	2218.27i	−0.523648	+	0.109089i
$746$	11602.1	+	39513.2i	0.569415	+	1.93925i
$747$	2064.54	+	28866.1i	0.101121	+	1.41386i
$748$	4495.78	+	62859.3i	0.219762	+	3.07268i
$749$	3253.40	+	11080.0i	0.158714	+	0.540529i
$750$	64499.5	+	15827.6i	3.14025	+	0.770589i
$751$	−10386.2	−	16161.2i	−0.504657	−	0.785262i	0.491680	−	0.870776i	$-0.336383\pi$
$751$	−10386.2	−	16161.2i	−0.504657	−	0.785262i	−0.996337	+	0.0855143i	$0.972747\pi$
$752$	−44672.2	−	81811.0i	−2.16626	−	3.96721i
$753$	−35835.6	+	47870.7i	−1.73429	+	2.31674i
$754$	−4531.91	−	2069.65i	−0.218889	−	0.0999632i
$755$	37444.1	+	14343.0i	1.80494	+	0.691386i
$756$	27308.1	−	42492.2i	1.31374	−	2.04421i
$757$	−14506.3	−	1037.51i	−0.696487	−	0.0498137i	−0.281394	−	0.959592i	$-0.590797\pi$
$757$	−14506.3	−	1037.51i	−0.696487	−	0.0498137i	−0.415094	+	0.909779i	$0.636251\pi$
$758$	31510.6	+	31510.6i	1.50992	+	1.50992i
$759$	−22764.4	+	43773.4i	−1.08866	+	2.09338i
$760$	−21925.0	−	34786.2i	−1.04645	−	1.66030i
$761$	−18814.9	−	21713.6i	−0.896241	−	1.03432i	−0.999214	−	0.0396334i	$-0.987381\pi$
$761$	−18814.9	−	21713.6i	−0.896241	−	1.03432i	0.102973	−	0.994684i	$-0.467164\pi$
$762$	−7546.15	−	34689.1i	−0.358751	−	1.64915i
$763$	5392.06	+	7202.95i	0.255840	+	0.341762i
$764$	29592.1	−	64797.6i	1.40131	−	3.06845i
$765$	−27533.9	−	32347.4i	−1.30130	−	1.52879i
$766$	−1980.56	+	6745.15i	−0.0934208	+	0.318162i
$767$	355.156	+	77.2595i	0.0167196	+	0.00363713i
$768$	41461.2	+	15464.2i	1.94805	+	0.726586i
$769$	−9229.77	+	2710.11i	−0.432814	+	0.127086i	−0.490880	−	0.871227i	$-0.663325\pi$
$769$	−9229.77	+	2710.11i	−0.432814	+	0.127086i	0.0580661	+	0.998313i	$0.481507\pi$
$770$	22664.7	−	16657.0i	1.06075	−	0.779579i
$771$	11308.4	−	13050.6i	0.528225	−	0.609604i
$772$	−60937.6	−	33274.4i	−2.84092	−	1.55126i
$773$	−10528.3	+	28227.4i	−0.489878	+	1.31342i	0.423350	+	0.905966i	$0.360854\pi$
$773$	−10528.3	+	28227.4i	−0.489878	+	1.31342i	−0.913228	+	0.407449i	$0.866419\pi$
$774$	12970.0	−	8335.31i	0.602322	−	0.387089i
$775$	6473.05	+	5811.79i	0.300024	+	0.269375i
$776$	−808.263	+	116.211i	−0.0373904	+	0.00537593i
$777$	−31290.7	+	11670.8i	−1.44472	+	0.538852i
$778$	40205.7	−	30097.6i	1.85276	−	1.38696i
$779$	−2630.18	−	1690.31i	−0.120970	−	0.0777429i
$780$	5732.31	−	3064.81i	0.263140	−	0.140690i
$781$		−	5379.05i		−	0.246450i
$782$	29748.7	+	24741.3i	1.36037	+	1.13139i
$783$	54417.2	−	54417.2i	2.48367	−	2.48367i
$784$	−27402.0	+	23744.0i	−1.24827	+	1.08163i
$785$	−43.2172	+	4904.13i	−0.00196495	+	0.222975i
$786$	6428.21	−	44709.2i	0.291713	−	2.02891i
$787$	7064.79	+	18941.4i	0.319990	+	0.857928i	0.992981	+	0.118276i	$0.0377368\pi$
$787$	7064.79	+	18941.4i	0.319990	+	0.857928i	−0.672990	+	0.739651i	$0.734990\pi$
$788$	−40770.7	−	30520.6i	−1.84314	−	1.37976i
$789$	9404.17	+	2761.31i	0.424331	+	0.124595i
$790$	−21068.6	+	45078.3i	−0.948845	+	2.03014i
$791$	515.039	+	1127.78i	0.0231513	+	0.0506943i
$792$	76365.3	−	139853.i	3.42616	−	6.27455i
$793$	273.238	−	19.5424i	0.0122358	−	0.000875120i
$794$	59126.7	+	51233.6i	2.64273	+	2.28994i
$795$	999.165	+	15943.4i	0.0445745	+	0.711263i
$796$	66180.2	−	30223.5i	2.94686	−	1.34578i
$797$	5053.00	−	23228.3i	0.224575	−	1.03236i	−0.717397	−	0.696665i	$-0.754666\pi$
$797$	5053.00	−	23228.3i	0.224575	−	1.03236i	0.941972	−	0.335692i	$-0.108970\pi$
$798$	26232.3	−	14323.9i	1.16367	−	0.635414i
$799$	−6057.11	−	42128.1i	−0.268191	−	1.86531i
$800$	38177.1	+	3407.69i	1.68721	+	0.150600i
$801$	−16789.1	−	2413.91i	−0.740591	−	0.106481i
$802$	−45623.5	+	9924.78i	−2.00875	+	0.436978i
$803$	1632.78	−	22829.2i	0.0717552	−	1.00327i
$804$	−120009.			−5.26415
$805$	1594.08	−	12064.1i	0.0697936	−	0.528203i
$806$	1208.31			0.0528052
$807$	−2196.43	+	30710.1i	−0.0958092	+	1.33959i
$808$	−19716.4	+	4289.05i	−0.858443	+	0.186743i
$809$	7827.12	+	1125.37i	0.340157	+	0.0489071i	0.310277	−	0.950646i	$-0.399578\pi$
$809$	7827.12	+	1125.37i	0.340157	+	0.0489071i	0.0298801	+	0.999553i	$0.490487\pi$
$810$	7203.82	+	53442.8i	0.312490	+	2.31826i
$811$	−2649.38	−	18426.8i	−0.114713	−	0.797847i	−0.963230	−	0.268678i	$-0.913413\pi$
$811$	−2649.38	−	18426.8i	−0.114713	−	0.797847i	0.848517	−	0.529168i	$-0.177496\pi$
$812$	47433.3	−	25900.5i	2.04998	−	1.11937i
$813$	−12035.5	+	55326.4i	−0.519193	+	2.38669i
$814$	−85963.5	+	39258.2i	−3.70150	+	1.69042i
$815$	−10983.5	−	9688.00i	−0.472067	−	0.416388i
$816$	−68653.6	−	59488.7i	−2.94529	−	2.55211i
$817$	3340.94	−	238.948i	0.143066	−	0.0102323i
$818$	6629.55	−	12141.1i	0.283370	−	0.518954i
$819$	770.868	+	1687.97i	0.0328893	+	0.0720174i
$820$	9839.33	−	3571.43i	0.419029	−	0.152097i
$821$	2262.57	+	664.351i	0.0961807	+	0.0282412i	0.329469	−	0.944166i	$-0.393130\pi$
$821$	2262.57	+	664.351i	0.0961807	+	0.0282412i	−0.233288	+	0.972408i	$0.574949\pi$
$822$	−23130.8	−	17315.5i	−0.981483	−	0.734729i
$823$	−10885.4	−	29184.9i	−0.461046	−	1.23611i	−0.934711	−	0.355408i	$-0.884342\pi$
$823$	−10885.4	−	29184.9i	−0.461046	−	1.23611i	0.473665	−	0.880705i	$-0.342931\pi$
$824$	3427.91	−	23841.6i	0.144923	−	1.00796i
$825$	−12846.0	+	54416.6i	−0.542110	+	2.29642i
$826$	−4228.58	+	3664.08i	−0.178125	+	0.154346i
$827$	−25635.6	+	25635.6i	−1.07792	+	1.07792i	−0.0812196	+	0.996696i	$0.525882\pi$
$827$	−25635.6	+	25635.6i	−1.07792	+	1.07792i	−0.996696	+	0.0812196i	$0.974118\pi$
$828$	−35734.5	−	113175.i	−1.49983	−	4.75014i
$829$		−	29541.9i		−	1.23768i	−0.785518	−	0.618839i	$-0.787604\pi$
$829$		−	29541.9i		−	1.23768i	0.785518	−	0.618839i	$-0.212396\pi$
$830$	−14084.6	−	26343.3i	−0.589016	−	1.10167i
$831$	28514.1	+	18324.9i	1.19030	+	0.764961i
$832$	1108.24	−	829.617i	0.0461794	−	0.0345695i
$833$	−15511.7	+	5785.57i	−0.645197	+	0.240646i
$834$	−30997.4	+	4456.76i	−1.28699	+	0.185042i
$835$	−6367.77	+	1808.95i	−0.263911	+	0.0749716i
$836$	50136.3	−	32220.6i	2.07416	−	1.33298i
$837$	−6522.56	+	17487.7i	−0.269358	+	0.722177i
$838$	−34853.8	−	19031.6i	−1.43676	−	0.784531i
$839$	25144.4	−	29018.2i	1.03466	−	1.19406i	0.0539607	−	0.998543i	$-0.482815\pi$
$839$	25144.4	−	29018.2i	1.03466	−	1.19406i	0.980700	−	0.195519i	$-0.0626391\pi$
$840$	−8778.56	+	57457.2i	−0.360582	+	2.36008i
$841$	55604.6	−	16327.0i	2.27991	−	0.669441i
$842$	29839.5	+	11129.6i	1.22130	+	0.455522i
$843$	63976.9	+	13917.3i	2.61386	+	0.568609i
$844$	7494.39	−	25523.6i	0.305649	−	1.04094i
$845$	1958.18	−	24360.2i	0.0797202	−	0.991735i
$846$	−76963.0	+	168525.i	−3.12771	+	6.84873i
$847$	6320.20	+	8442.80i	0.256393	+	0.342501i
$848$	4909.96	+	22570.7i	0.198831	+	0.914011i
$849$	19604.9	+	22625.3i	0.792509	+	0.914604i
$850$	39558.0	+	18915.0i	1.59627	+	0.763271i
$851$	−13510.0	+	38589.4i	−0.544202	+	1.55444i
$852$	13531.5	+	13531.5i	0.544110	+	0.544110i
$853$	−37854.9	−	2707.44i	−1.51949	−	0.108676i	−0.713523	−	0.700632i	$-0.752902\pi$
$853$	−37854.9	−	2707.44i	−1.51949	−	0.108676i	−0.805971	+	0.591956i	$0.798356\pi$
$854$	−2279.89	+	3547.59i	−0.0913541	+	0.142150i
$855$	−14369.8	+	37514.0i	−0.574780	+	1.50053i
$856$	−61424.7	−	28051.7i	−2.45263	−	1.12008i
$857$	2906.93	−	3883.20i	0.115868	−	0.154781i	−0.738858	−	0.673861i	$-0.764634\pi$
$857$	2906.93	−	3883.20i	0.115868	−	0.154781i	0.854726	+	0.519080i	$0.173725\pi$
$858$	3721.91	+	6816.16i	0.148093	+	0.271212i
$859$	5954.22	+	9264.95i	0.236502	+	0.368005i	0.939135	−	0.343548i	$-0.111629\pi$
$859$	5954.22	+	9264.95i	0.236502	+	0.368005i	−0.702633	+	0.711552i	$0.747992\pi$
$860$	−6145.62	+	9379.98i	−0.243679	+	0.371924i
$861$	1245.11	+	4240.44i	0.0492835	+	0.167844i
$862$	−96.2918	−	1346.34i	−0.00380477	−	0.0531977i
$863$	1010.09	+	14123.0i	0.0398424	+	0.557070i	0.977694	+	0.210034i	$0.0673574\pi$
$863$	1010.09	+	14123.0i	0.0398424	+	0.557070i	−0.937852	+	0.347036i	$0.887188\pi$
$864$	23168.4	+	78904.4i	0.912275	+	3.10692i
$865$	3777.44	−	5765.46i	0.148482	−	0.226626i
$866$	8238.60	+	12819.5i	0.323278	+	0.503031i
$867$	1620.41	+	2967.56i	0.0634740	+	0.116244i
$868$	−7854.88	+	10492.9i	−0.307157	+	0.410313i
$869$	−38105.7	−	17402.3i	−1.48751	−	0.679323i
$870$	−54535.5	+	142371.i	−2.12520	+	5.54808i
$871$	1241.96	−	1932.52i	0.0483147	−	0.0751792i
$872$	−52480.3	−	3753.46i	−2.03808	−	0.145766i
$873$	564.106	+	564.106i	0.0218695	+	0.0218695i
$874$	7052.82	−	35905.0i	0.272958	−	1.38959i
$875$	−1601.05	−	13697.0i	−0.0618578	−	0.529191i
$876$	53321.5	+	61536.3i	2.05658	+	2.37343i
$877$	−8955.98	−	41170.0i	−0.344837	−	1.58519i	−0.743916	−	0.668273i	$-0.767034\pi$
$877$	−8955.98	−	41170.0i	−0.344837	−	1.58519i	0.399079	−	0.916916i	$-0.369330\pi$
$878$	−48311.4	−	64536.5i	−1.85698	−	2.48064i
$879$	5542.59	−	12136.6i	0.212682	−	0.465708i
$880$	−6477.90	+	80586.5i	−0.248148	+	3.08701i
$881$	9908.49	−	33745.2i	0.378917	−	1.29047i	−0.520681	−	0.853751i	$-0.674322\pi$
$881$	9908.49	−	33745.2i	0.378917	−	1.29047i	0.899598	−	0.436720i	$-0.143860\pi$
$882$	70418.7	+	15318.7i	2.68835	+	0.584814i
$883$	29977.4	+	11181.0i	1.14249	+	0.426127i	0.848246	−	0.529603i	$-0.177659\pi$
$883$	29977.4	+	11181.0i	1.14249	+	0.426127i	0.294246	+	0.955730i	$0.404932\pi$
$884$	4117.75	−	1209.08i	0.156668	−	0.0460020i
$885$	1679.83	−	10994.8i	0.0638043	−	0.417610i
$886$	−34025.5	+	39267.5i	−1.29019	+	1.48896i
$887$	−3310.67	−	1807.76i	−0.125323	−	0.0684316i	0.415364	−	0.909655i	$-0.363654\pi$
$887$	−3310.67	−	1807.76i	−0.125323	−	0.0684316i	−0.540688	+	0.841223i	$0.681836\pi$
$888$	68246.2	−	182975.i	2.57905	−	6.91469i
$889$	−6201.23	+	3985.29i	−0.233951	+	0.150351i
$890$	16841.8	−	4784.39i	0.634312	−	0.180195i
$891$	−44937.6	+	6461.05i	−1.68964	+	0.242933i
$892$	79042.7	−	29481.4i	2.96698	−	1.10663i
$893$	−32221.6	+	24120.8i	−1.20745	+	0.903886i
$894$	38892.0	+	24994.4i	1.45497	+	0.935052i
$895$	17567.7	+	32858.0i	0.656117	+	1.22718i
$896$		−	2894.31i		−	0.107915i
$897$	3242.32	+	881.165i	0.120689	+	0.0327996i
$898$	3420.72	−	3420.72i	0.127117	−	0.127117i
$899$	−15092.4	+	13077.7i	−0.559911	+	0.485166i
$900$	−70708.1	−	114408.i	−2.61882	−	4.23734i
$901$	−1500.98	+	10439.5i	−0.0554993	+	0.386006i
$902$	4370.41	+	11717.5i	0.161329	+	0.432540i
$903$	−3790.28	−	2837.37i	−0.139682	−	0.104564i
$904$	−6956.29	−	2042.55i	−0.255932	−	0.0751484i
$905$	−3848.24	+	1396.82i	−0.141348	+	0.0513058i
$906$	−70799.3	−	155029.i	−2.59619	−	5.68487i
$907$	1500.82	−	2748.55i	0.0549437	−	0.100622i	−0.848764	−	0.528772i	$-0.822653\pi$
$907$	1500.82	−	2748.55i	0.0549437	−	0.100622i	0.903708	+	0.428150i	$0.140835\pi$
$908$	−23863.1	+	1706.72i	−0.872163	+	0.0623784i
$909$	14897.9	+	12909.1i	0.543601	+	0.471033i
$910$	−1436.48	−	1267.05i	−0.0523285	−	0.0461565i
$911$	−33772.7	+	15423.5i	−1.22825	+	0.560924i	−0.920575	−	0.390566i	$-0.872279\pi$
$911$	−33772.7	+	15423.5i	−1.22825	+	0.560924i	−0.307678	+	0.951491i	$0.599552\pi$
$912$	−18261.0	+	83944.7i	−0.663030	+	3.04790i
$913$	22072.7	−	12052.6i	0.800110	−	0.436893i
$914$	2960.79	+	20592.8i	0.107149	+	0.745239i
$915$	−1119.82	−	8307.61i	−0.0404593	−	0.300154i
$916$	47086.5	+	6770.02i	1.69845	+	0.244201i
$917$	−9164.68	+	1993.65i	−0.330037	+	0.0717953i
$918$	−6711.31	+	93836.3i	−0.241292	+	3.37370i
$919$	−6515.19			−0.233859			−0.116929	−	0.993140i	$-0.537305\pi$
$919$	−6515.19			−0.233859			−0.116929	+	0.993140i	$0.537305\pi$
$920$	47210.8	+	53242.5i	1.69184	+	1.90799i
$921$	33652.7			1.20401
$922$	−326.465	+	4564.57i	−0.0116611	+	0.163044i
$923$	−357.937	+	77.8644i	−0.0127645	+	0.00277675i
$924$	−83386.0	−	11989.1i	−2.96883	−	0.426853i
$925$	−4119.33	+	46149.7i	−0.146425	+	1.64042i
$926$	−10081.4	−	70117.4i	−0.357769	−	2.48834i
$927$	−20653.5	+	11277.7i	−0.731769	+	0.399576i
$928$	−18703.2	+	85977.4i	−0.661599	+	3.04132i
$929$	38044.0	−	17374.1i	1.34358	−	0.613591i	0.391706	−	0.920090i	$-0.371885\pi$
$929$	38044.0	−	17374.1i	1.34358	−	0.613591i	0.951871	+	0.306499i	$0.0991576\pi$
$930$	−2312.71	−	36903.3i	−0.0815449	−	1.30119i
$931$	11832.3	+	10252.8i	0.416529	+	0.360924i
$932$	54693.0	−	3911.72i	1.92224	−	0.137481i
$933$	23644.5	−	43301.8i	0.829676	−	1.51944i
$934$	20837.2	+	45627.1i	0.729993	+	1.59846i
$935$	−15630.2	+	33442.4i	−0.546699	+	1.16971i
$936$	−10411.6	−	3057.12i	−0.363583	−	0.106758i
$937$	−38186.8	−	28586.3i	−1.33139	−	0.996664i	−0.998558	−	0.0536762i	$-0.982906\pi$
$937$	−38186.8	−	28586.3i	−1.33139	−	0.996664i	−0.332828	−	0.942987i	$-0.608003\pi$
$938$	12358.3	+	33133.8i	0.430183	+	1.15337i
$939$	−525.731	+	3656.54i	−0.0182711	+	0.127078i
$940$	1187.47	−	134750.i	0.0412033	−	4.67559i
$941$	−5921.72	+	5131.20i	−0.205146	+	0.177760i	−0.751374	−	0.659876i	$-0.770609\pi$
$941$	−5921.72	+	5131.20i	−0.205146	+	0.177760i	0.546228	+	0.837636i	$0.316063\pi$
$942$	14740.0	−	14740.0i	0.509825	−	0.509825i
$943$	4966.13	+	2147.58i	0.171495	+	0.0741621i
$944$		−	16082.4i		−	0.554487i
$945$	26092.0	−	13950.3i	0.898174	−	0.480214i
$946$	−11271.0	−	7243.46i	−0.387371	−	0.248948i
$947$	37289.9	−	27914.9i	1.27958	−	0.957879i	0.279579	−	0.960123i	$-0.409805\pi$
$947$	37289.9	−	27914.9i	1.27958	−	0.957879i	0.999997	+	0.00224396i	$0.000714274\pi$
$948$	139635.	−	52081.3i	4.78391	−	1.78431i
$949$	−1542.75	+	221.814i	−0.0527712	+	0.00758735i
$950$	−2228.79	−	41406.2i	−0.0761173	−	1.41410i
$951$	50496.0	−	32451.8i	1.72182	−	1.10654i
$952$	−13410.7	+	35955.4i	−0.456557	+	1.22408i
$953$	46246.8	+	25252.7i	1.57196	+	0.858357i	0.999255	+	0.0385972i	$0.0122889\pi$
$953$	46246.8	+	25252.7i	1.57196	+	0.858357i	0.572708	+	0.819759i	$0.305893\pi$
$954$	30064.8	−	34696.6i	1.02032	−	1.17751i
$955$	33623.1	−	24710.6i	1.13929	−	0.837296i
$956$	−59646.4	+	17513.8i	−2.01789	+	0.592505i
$957$	−120260.	−	44854.8i	−4.06213	−	1.51510i
$958$	50830.5	+	11057.5i	1.71426	+	0.372914i
$959$	−1690.29	+	5756.61i	−0.0569159	+	0.193838i
$960$	−27458.6	−	32259.0i	−0.923150	−	1.08454i
$961$	−10363.6	+	22693.2i	−0.347878	+	0.761746i
$962$	3856.71	+	5151.96i	0.129257	+	0.172667i
$963$	14023.3	+	64463.9i	0.469256	+	2.15713i
$964$	72400.8	+	83555.0i	2.41896	+	2.79162i
$965$	−21685.4	−	34406.0i	−0.723396	−	1.14774i
$966$	−40770.9	+	31828.3i	−1.35795	+	1.06010i
$967$	3222.80	+	3222.80i	0.107175	+	0.107175i	0.758661	−	0.651486i	$-0.225854\pi$
$967$	3222.80	+	3222.80i	0.107175	+	0.107175i	−0.651486	+	0.758661i	$0.725854\pi$
$968$	−61513.8	−	4399.55i	−2.04249	−	0.146082i
$969$	−21207.1	+	32998.9i	−0.703065	+	1.09399i
$970$	−768.981	−	294.560i	−0.0254541	−	0.00975025i
$971$	−4638.71	−	2118.43i	−0.153309	−	0.0700140i	0.337283	−	0.941403i	$-0.390492\pi$
$971$	−4638.71	−	2118.43i	−0.153309	−	0.0700140i	−0.490592	+	0.871389i	$0.663219\pi$
$972$	13965.1	−	18655.2i	0.460833	−	0.615601i
$973$	3116.36	+	5707.19i	0.102678	+	0.188041i
$974$	−41610.1	−	64746.6i	−1.36886	−	2.13000i
$975$	3806.98	+	67.1026i	0.125047	+	0.00220411i
$976$	−3414.89	−	11630.0i	−0.111996	−	0.381422i
$977$	400.570	+	5600.70i	0.0131171	+	0.183401i	0.999786	+	0.0206632i	$0.00657778\pi$
$977$	400.570	+	5600.70i	0.0131171	+	0.183401i	−0.986669	+	0.162737i	$0.947968\pi$
$978$	4440.88	+	62091.7i	0.145198	+	2.03014i
$979$	4152.71	+	14142.8i	0.135568	+	0.461702i
$980$	−51315.5	+	10690.3i	−1.67267	+	0.348458i
$981$	27790.2	+	43242.5i	0.904459	+	1.40737i
$982$	4669.42	+	8551.40i	0.151738	+	0.277888i
$983$	−24427.0	+	32630.7i	−0.792574	+	1.05876i	0.204234	+	0.978922i	$0.434530\pi$
$983$	−24427.0	+	32630.7i	−0.792574	+	1.05876i	−0.996808	+	0.0798332i	$0.974561\pi$
$984$	−23507.8	−	10735.7i	−0.761588	−	0.347806i
$985$	−12153.2	−	27244.6i	−0.393129	−	0.881304i
$986$	−54419.3	+	84678.1i	−1.75767	+	2.73499i
$987$	56750.1	+	4058.84i	1.83017	+	0.130896i
$988$	−2869.79	−	2869.79i	−0.0924092	−	0.0924092i
$989$	−5637.90	+	1346.50i	−0.181269	+	0.0432924i
$990$	135940.	−	85680.1i	4.36410	−	2.75060i
$991$	8610.53	+	9937.08i	0.276007	+	0.318529i	0.876781	−	0.480890i	$-0.159686\pi$
$991$	8610.53	+	9937.08i	0.276007	+	0.318529i	−0.600774	+	0.799419i	$0.705141\pi$
$992$	−4536.09	−	20852.1i	−0.145182	−	0.667392i
$993$	−4651.11	−	6213.16i	−0.148639	−	0.198559i
$994$	2342.53	−	5129.43i	0.0747491	−	0.163678i
$995$	42480.2	+	3414.75i	1.35348	+	0.108799i
$996$	−25206.5	+	85845.4i	−0.801906	+	2.73104i
$997$	−36536.0	−	7947.93i	−1.16059	−	0.252471i	−0.409273	−	0.912412i	$-0.634218\pi$
$997$	−36536.0	−	7947.93i	−1.16059	−	0.252471i	−0.751317	+	0.659941i	$0.770581\pi$
$998$	−43634.2	−	16274.7i	−1.38399	−	0.516200i
$999$	−95382.1	+	28006.7i	−3.02078	+	0.886980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.l.a.102.32	yes	680
5.3	odd	4	inner	115.4.l.a.33.3	yes	680
23.7	odd	22	inner	115.4.l.a.7.3	✓	680
115.53	even	44	inner	115.4.l.a.53.32	yes	680

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.l.a.7.3	✓	680	23.7	odd	22	inner
115.4.l.a.33.3	yes	680	5.3	odd	4	inner
115.4.l.a.53.32	yes	680	115.53	even	44	inner
115.4.l.a.102.32	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+(0.371284 - 5.19124i) q^{2} +(-8.92216 + 1.94090i) q^{3} +(-18.8925 - 2.71633i) q^{4} +(-8.89093 - 6.77874i) q^{5} +(6.76299 + 47.0376i) q^{6} +(8.66048 - 4.72898i) q^{7} +(-12.2652 + 56.3824i) q^{8} +(51.2777 - 23.4178i) q^{9} +(-38.4911 + 43.6381i) q^{10} +(-37.0225 - 32.0802i) q^{11} +(173.834 - 12.4329i) q^{12} +(-1.59878 + 2.92795i) q^{13} +(-21.3338 - 46.7144i) q^{14} +(92.4831 + 43.2246i) q^{15} +(141.632 + 41.5868i) q^{16} +(53.9561 + 40.3910i) q^{17} +(-102.528 - 274.890i) q^{18} +(9.07100 - 63.0902i) q^{19} +(149.559 + 152.218i) q^{20} +(-68.0917 + 59.0018i) q^{21} +(-180.282 + 180.282i) q^{22} +(2.23227 + 110.282i) q^{23} -526.858i q^{24} +(33.0974 + 120.539i) q^{25} +(14.6061 + 9.38676i) q^{26} +(-214.697 + 160.720i) q^{27} +(-176.464 + 65.8175i) q^{28} +(-284.031 + 40.8374i) q^{29} +(258.727 - 464.053i) q^{30} +(58.5463 - 37.6254i) q^{31} +(107.157 - 287.298i) q^{32} +(392.585 + 214.367i) q^{33} +(229.713 - 265.102i) q^{34} +(-109.056 - 16.6621i) q^{35} +(-1032.38 + 303.133i) q^{36} +(347.295 + 129.534i) q^{37} +(-324.148 - 70.5141i) q^{38} +(8.58174 - 29.2267i) q^{39} +(491.251 - 418.150i) q^{40} +(20.3768 - 44.6189i) q^{41} +(281.011 + 375.387i) q^{42} +(11.1703 + 51.3489i) q^{43} +(612.307 + 706.640i) q^{44} +(-614.650 - 139.393i) q^{45} +(573.326 + 29.3576i) q^{46} +(-446.522 - 446.522i) q^{47} +(-1344.37 - 96.1516i) q^{48} +(-132.799 + 206.639i) q^{49} +(638.033 - 127.062i) q^{50} +(-559.800 - 255.652i) q^{51} +(38.1583 - 50.9735i) q^{52} +(74.9943 + 137.342i) q^{53} +(754.624 + 1174.22i) q^{54} +(111.701 + 536.188i) q^{55} +(160.408 + 546.301i) q^{56} +(41.5187 + 580.507i) q^{57} +(106.541 + 1489.63i) q^{58} +(-30.6951 - 104.538i) q^{59} +(-1629.83 - 1067.84i) q^{60} +(-44.3946 - 69.0793i) q^{61} +(-173.585 - 317.897i) q^{62} +(333.348 - 445.301i) q^{63} +(-377.474 - 172.387i) q^{64} +(34.0625 - 15.1945i) q^{65} +(1258.59 - 1958.41i) q^{66} +(-686.850 - 49.1245i) q^{67} +(-909.651 - 909.651i) q^{68} +(-233.962 - 979.617i) q^{69} +(-126.988 + 559.951i) q^{70} +(71.9064 + 82.9844i) q^{71} +(691.416 + 3178.39i) q^{72} +(279.988 + 374.020i) q^{73} +(801.388 - 1754.80i) q^{74} +(-529.253 - 1011.23i) q^{75} +(-342.748 + 1167.29i) q^{76} +(-472.339 - 102.751i) q^{77} +(-148.536 - 55.4012i) q^{78} +(820.499 - 240.920i) q^{79} +(-977.331 - 1329.83i) q^{80} +(606.896 - 700.395i) q^{81} +(-224.062 - 122.347i) q^{82} +(-179.405 + 481.004i) q^{83} +(1446.69 - 929.732i) q^{84} +(-205.920 - 724.869i) q^{85} +(270.711 - 38.9224i) q^{86} +(2454.90 - 915.632i) q^{87} +(2262.85 - 1693.95i) q^{88} +(-253.124 - 162.673i) q^{89} +(-951.830 + 3139.04i) q^{90} +32.9181i q^{91} +(257.388 - 2089.56i) q^{92} +(-449.332 + 449.332i) q^{93} +(-2483.79 + 2152.21i) q^{94} +(-508.322 + 499.441i) q^{95} +(-398.453 + 2771.30i) q^{96} +(4.94555 + 13.2595i) q^{97} +(1023.41 + 766.113i) q^{98} +(-2649.67 - 778.015i) 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

Varieties

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Database

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