LMFDB - Embedded newform 55.4.g.b.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,4,Mod(16,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("55.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	55.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.24510505032$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.3
Character	$\chi$	$=$	55.31
Dual form			55.4.g.b.16.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.513572 + 1.58061i) q^{2} +(-1.60233 + 1.16416i) q^{3} +(4.23755 + 3.07876i) q^{4} +(1.54508 + 4.75528i) q^{5} +(-1.01717 - 3.13054i) q^{6} +(-7.13418 - 5.18329i) q^{7} +(-17.7990 + 12.9317i) q^{8} +(-7.13127 + 21.9478i) q^{9} -8.30978 q^{10} +(5.41658 + 36.0785i) q^{11} -10.3741 q^{12} +(3.19453 - 9.83177i) q^{13} +(11.8567 - 8.61439i) q^{14} +(-8.01163 - 5.82079i) q^{15} +(1.64980 + 5.07758i) q^{16} +(-15.0140 - 46.2082i) q^{17} +(-31.0286 - 22.5436i) q^{18} +(78.6063 - 57.1108i) q^{19} +(-8.09301 + 24.9077i) q^{20} +17.4655 q^{21} +(-59.8080 - 9.96743i) q^{22} +196.403 q^{23} +(13.4652 - 41.4418i) q^{24} +(-20.2254 + 14.6946i) q^{25} +(13.8996 + 10.0986i) q^{26} +(-30.6490 - 94.3280i) q^{27} +(-14.2734 - 43.9289i) q^{28} +(136.759 + 99.3611i) q^{29} +(13.3150 - 9.67390i) q^{30} +(12.6165 - 38.8296i) q^{31} -184.879 q^{32} +(-50.6802 - 51.5038i) q^{33} +80.7481 q^{34} +(13.6251 - 41.9337i) q^{35} +(-97.7912 + 71.0495i) q^{36} +(-118.029 - 85.7530i) q^{37} +(49.9001 + 153.577i) q^{38} +(6.32704 + 19.4726i) q^{39} +(-88.9951 - 64.6587i) q^{40} +(127.285 - 92.4781i) q^{41} +(-8.96978 + 27.6061i) q^{42} +266.051 q^{43} +(-88.1242 + 169.561i) q^{44} -115.386 q^{45} +(-100.867 + 310.438i) q^{46} +(-390.791 + 283.926i) q^{47} +(-8.55463 - 6.21530i) q^{48} +(-81.9627 - 252.255i) q^{49} +(-12.8393 - 39.5153i) q^{50} +(77.8509 + 56.5620i) q^{51} +(43.8067 - 31.8274i) q^{52} +(-106.579 + 328.016i) q^{53} +164.837 q^{54} +(-163.195 + 81.5018i) q^{55} +194.010 q^{56} +(-59.4669 + 183.020i) q^{57} +(-227.287 + 165.134i) q^{58} +(624.802 + 453.945i) q^{59} +(-16.0289 - 49.3318i) q^{60} +(-247.365 - 761.311i) q^{61} +(54.8951 + 39.8836i) q^{62} +(164.638 - 119.616i) q^{63} +(81.7505 - 251.602i) q^{64} +51.6887 q^{65} +(107.436 - 53.6549i) q^{66} +128.194 q^{67} +(78.6417 - 242.034i) q^{68} +(-314.702 + 228.645i) q^{69} +(59.2835 + 43.0720i) q^{70} +(-89.3032 - 274.847i) q^{71} +(-156.894 - 482.869i) q^{72} +(-20.6190 - 14.9806i) q^{73} +(196.159 - 142.518i) q^{74} +(15.3009 - 47.0912i) q^{75} +508.929 q^{76} +(148.363 - 285.467i) q^{77} -34.0281 q^{78} +(-66.1652 + 203.635i) q^{79} +(-21.5962 + 15.6906i) q^{80} +(-345.165 - 250.777i) q^{81} +(80.8020 + 248.683i) q^{82} +(-160.112 - 492.774i) q^{83} +(74.0108 + 53.7720i) q^{84} +(196.535 - 142.791i) q^{85} +(-136.637 + 420.525i) q^{86} -334.804 q^{87} +(-562.968 - 572.117i) q^{88} +6.39690 q^{89} +(59.2593 - 182.381i) q^{90} +(-73.7513 + 53.5834i) q^{91} +(832.270 + 604.680i) q^{92} +(24.9881 + 76.9053i) q^{93} +(-248.078 - 763.505i) q^{94} +(393.032 + 285.554i) q^{95} +(296.237 - 215.229i) q^{96} +(-100.607 + 309.636i) q^{97} +440.812 q^{98} +(-830.472 - 138.404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 4 q^{3} - 36 q^{4} - 30 q^{5} + 30 q^{6} + 81 q^{7} - 10 q^{8} - 48 q^{9} - 70 q^{10} - 72 q^{11} + 10 q^{12} + 65 q^{13} - 47 q^{14} + 20 q^{15} - 60 q^{16} - 142 q^{17} + 283 q^{18} - 17 q^{19}+ \cdots + 5980 q^{99}+O(q^{100}) $ 24 * q + 6 * q^2 + 4 * q^3 - 36 * q^4 - 30 * q^5 + 30 * q^6 + 81 * q^7 - 10 * q^8 - 48 * q^9 - 70 * q^10 - 72 * q^11 + 10 * q^12 + 65 * q^13 - 47 * q^14 + 20 * q^15 - 60 * q^16 - 142 * q^17 + 283 * q^18 - 17 * q^19 - 55 * q^20 - 200 * q^21 + 87 * q^22 - 182 * q^23 + 70 * q^24 - 150 * q^25 + 736 * q^26 + 643 * q^27 - 52 * q^28 + 80 * q^29 - 210 * q^31 - 504 * q^32 + 993 * q^33 + 1046 * q^34 + 80 * q^35 - 2242 * q^36 + 560 * q^37 + 187 * q^38 - 1294 * q^39 - 50 * q^40 + 293 * q^41 - 2231 * q^42 - 3658 * q^43 + 1293 * q^44 + 1310 * q^45 - 57 * q^46 - 1824 * q^47 + 1977 * q^48 + 73 * q^49 + 150 * q^50 - 1769 * q^51 + 3342 * q^52 + 838 * q^53 + 2784 * q^54 + 290 * q^55 + 8652 * q^56 + 273 * q^57 - 3896 * q^58 + 1653 * q^59 - 875 * q^60 - 888 * q^61 - 2200 * q^62 + 3149 * q^63 - 4644 * q^64 - 2050 * q^65 - 4497 * q^66 + 3966 * q^67 - 3783 * q^68 - 3384 * q^69 - 235 * q^70 + 1664 * q^71 - 4264 * q^72 - 2210 * q^73 + 1552 * q^74 - 25 * q^75 + 3048 * q^76 - 1304 * q^77 + 10064 * q^78 + 12 * q^79 - 275 * q^80 + 5005 * q^81 + 4099 * q^82 + 1945 * q^83 - 7584 * q^84 + 1865 * q^85 - 5156 * q^86 - 3844 * q^87 + 619 * q^88 + 4568 * q^89 - 210 * q^90 - 4885 * q^91 + 3390 * q^92 + 2844 * q^93 - 8932 * q^94 - 85 * q^95 - 1249 * q^96 - 3255 * q^97 - 7778 * q^98 + 5980 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.513572	+	1.58061i	−0.181575	+	0.558831i	−0.999873	−	0.0159640i	$-0.994918\pi$
$2$	−0.513572	+	1.58061i	−0.181575	+	0.558831i	0.818297	+	0.574795i	$0.194918\pi$
$3$	−1.60233	+	1.16416i	−0.308368	+	0.224042i	−0.731196	−	0.682168i	$-0.761037\pi$
$3$	−1.60233	+	1.16416i	−0.308368	+	0.224042i	0.422828	+	0.906210i	$0.361037\pi$
$4$	4.23755	+	3.07876i	0.529694	+	0.384845i
$5$	1.54508	+	4.75528i	0.138197	+	0.425325i
$5$	1.54508	+	4.75528i	0.138197	+	0.425325i
$6$	−1.01717	−	3.13054i	−0.0692099	−	0.213006i
$7$	−7.13418	−	5.18329i	−0.385210	−	0.279871i	0.378280	−	0.925691i	$-0.376516\pi$
$7$	−7.13418	−	5.18329i	−0.385210	−	0.279871i	−0.763490	+	0.645820i	$0.776516\pi$
$8$	−17.7990	+	12.9317i	−0.786613	+	0.571508i
$9$	−7.13127	+	21.9478i	−0.264121	+	0.812882i
$10$	−8.30978			−0.262778
$11$	5.41658	+	36.0785i	0.148469	+	0.988917i
$11$	5.41658	+	36.0785i	0.148469	+	0.988917i
$12$	−10.3741			−0.249562
$13$	3.19453	−	9.83177i	0.0681542	−	0.209757i	−0.911179	−	0.412011i	$-0.864827\pi$
$13$	3.19453	−	9.83177i	0.0681542	−	0.209757i	0.979333	+	0.202254i	$0.0648266\pi$
$14$	11.8567	−	8.61439i	0.226345	−	0.164450i
$15$	−8.01163	−	5.82079i	−0.137906	−	0.100195i
$16$	1.64980	+	5.07758i	0.0257782	+	0.0793371i
$17$	−15.0140	−	46.2082i	−0.214201	−	0.659243i	−0.999209	−	0.0397580i	$-0.987341\pi$
$17$	−15.0140	−	46.2082i	−0.214201	−	0.659243i	0.785008	−	0.619485i	$-0.212659\pi$
$18$	−31.0286	−	22.5436i	−0.406306	−	0.295198i
$19$	78.6063	−	57.1108i	0.949133	−	0.689585i	−0.00146880	−	0.999999i	$-0.500468\pi$
$19$	78.6063	−	57.1108i	0.949133	−	0.689585i	0.950602	+	0.310414i	$0.100468\pi$
$20$	−8.09301	+	24.9077i	−0.0904826	+	0.278477i
$21$	17.4655			0.181489
$22$	−59.8080	−	9.96743i	−0.579596	−	0.0965938i
$23$	196.403			1.78056			0.890281	−	0.455411i	$-0.150508\pi$
$23$	196.403			1.78056			0.890281	+	0.455411i	$0.150508\pi$
$24$	13.4652	−	41.4418i	0.114524	−	0.352469i
$25$	−20.2254	+	14.6946i	−0.161803	+	0.117557i
$26$	13.8996	+	10.0986i	0.104844	+	0.0761734i
$27$	−30.6490	−	94.3280i	−0.218459	−	0.672349i
$28$	−14.2734	−	43.9289i	−0.0963362	−	0.296492i
$29$	136.759	+	99.3611i	0.875706	+	0.636238i	0.932112	−	0.362170i	$-0.117964\pi$
$29$	136.759	+	99.3611i	0.875706	+	0.636238i	−0.0564061	+	0.998408i	$0.517964\pi$
$30$	13.3150	−	9.67390i	0.0810324	−	0.0588735i
$31$	12.6165	−	38.8296i	0.0730965	−	0.224968i	−0.907833	−	0.419332i	$-0.862264\pi$
$31$	12.6165	−	38.8296i	0.0730965	−	0.224968i	0.980929	+	0.194364i	$0.0622643\pi$
$32$	−184.879			−1.02132
$33$	−50.6802	−	51.5038i	−0.267342	−	0.271687i
$34$	80.7481			0.407299
$35$	13.6251	−	41.9337i	0.0658017	−	0.202517i
$36$	−97.7912	+	71.0495i	−0.452737	+	0.328933i
$37$	−118.029	−	85.7530i	−0.524428	−	0.381019i	0.293841	−	0.955854i	$-0.405066\pi$
$37$	−118.029	−	85.7530i	−0.524428	−	0.381019i	−0.818269	+	0.574835i	$0.805066\pi$
$38$	49.9001	+	153.577i	0.213023	+	0.655617i
$39$	6.32704	+	19.4726i	0.0259779	+	0.0799517i
$40$	−88.9951	−	64.6587i	−0.351784	−	0.255586i
$41$	127.285	−	92.4781i	0.484844	−	0.352260i	−0.318354	−	0.947972i	$-0.603130\pi$
$41$	127.285	−	92.4781i	0.484844	−	0.352260i	0.803198	+	0.595712i	$0.203130\pi$
$42$	−8.96978	+	27.6061i	−0.0329540	+	0.101422i
$43$	266.051			0.943546			0.471773	−	0.881720i	$-0.343614\pi$
$43$	266.051			0.943546			0.471773	+	0.881720i	$0.343614\pi$
$44$	−88.1242	+	169.561i	−0.301937	+	0.580961i
$45$	−115.386			−0.382240
$46$	−100.867	+	310.438i	−0.323306	+	0.995034i
$47$	−390.791	+	283.926i	−1.21282	+	0.881167i	−0.995484	−	0.0949290i	$-0.969738\pi$
$47$	−390.791	+	283.926i	−1.21282	+	0.881167i	−0.217339	+	0.976096i	$0.569738\pi$
$48$	−8.55463	−	6.21530i	−0.0257241	−	0.0186896i
$49$	−81.9627	−	252.255i	−0.238958	−	0.735438i
$50$	−12.8393	−	39.5153i	−0.0363151	−	0.111766i
$51$	77.8509	+	56.5620i	0.213751	+	0.155299i
$52$	43.8067	−	31.8274i	0.116825	−	0.0848783i
$53$	−106.579	+	328.016i	−0.276221	+	0.850122i	0.712672	+	0.701497i	$0.247485\pi$
$53$	−106.579	+	328.016i	−0.276221	+	0.850122i	−0.988894	+	0.148625i	$0.952515\pi$
$54$	164.837			0.415397
$55$	−163.195	+	81.5018i	−0.400094	+	0.199813i
$56$	194.010			0.462960
$57$	−59.4669	+	183.020i	−0.138186	+	0.425292i
$58$	−227.287	+	165.134i	−0.514556	+	0.373847i
$59$	624.802	+	453.945i	1.37868	+	1.00167i	0.997002	+	0.0773772i	$0.0246546\pi$
$59$	624.802	+	453.945i	1.37868	+	1.00167i	0.381681	+	0.924294i	$0.375345\pi$
$60$	−16.0289	−	49.3318i	−0.0344887	−	0.106145i
$61$	−247.365	−	761.311i	−0.519211	−	1.59797i	−0.775488	−	0.631363i	$-0.782496\pi$
$61$	−247.365	−	761.311i	−0.519211	−	1.59797i	0.256277	−	0.966603i	$-0.417504\pi$
$62$	54.8951	+	39.8836i	0.112447	+	0.0816972i
$63$	164.638	−	119.616i	0.329244	−	0.239210i
$64$	81.7505	−	251.602i	0.159669	−	0.491411i
$65$	51.6887			0.0986337
$66$	107.436	−	53.6549i	0.200370	−	0.100068i
$67$	128.194			0.233751			0.116876	−	0.993147i	$-0.462712\pi$
$67$	128.194			0.233751			0.116876	+	0.993147i	$0.462712\pi$
$68$	78.6417	−	242.034i	0.140246	−	0.431632i
$69$	−314.702	+	228.645i	−0.549068	+	0.398921i
$70$	59.2835	+	43.0720i	0.101225	+	0.0735441i
$71$	−89.3032	−	274.847i	−0.149272	−	0.459413i	0.848263	−	0.529575i	$-0.177648\pi$
$71$	−89.3032	−	274.847i	−0.149272	−	0.459413i	−0.997536	+	0.0701617i	$0.977648\pi$
$72$	−156.894	−	482.869i	−0.256807	−	0.790371i
$73$	−20.6190	−	14.9806i	−0.0330585	−	0.0240184i	0.571133	−	0.820857i	$-0.306504\pi$
$73$	−20.6190	−	14.9806i	−0.0330585	−	0.0240184i	−0.604192	+	0.796839i	$0.706504\pi$
$74$	196.159	−	142.518i	0.308149	−	0.223883i
$75$	15.3009	−	47.0912i	0.0235572	−	0.0725016i
$76$	508.929			0.768134
$77$	148.363	−	285.467i	0.219578	−	0.422493i
$78$	−34.0281			−0.0493965
$79$	−66.1652	+	203.635i	−0.0942299	+	0.290010i	−0.987052	−	0.160399i	$-0.948722\pi$
$79$	−66.1652	+	203.635i	−0.0942299	+	0.290010i	0.892822	+	0.450409i	$0.148722\pi$
$80$	−21.5962	+	15.6906i	−0.0301816	+	0.0219282i
$81$	−345.165	−	250.777i	−0.473478	−	0.344002i
$82$	80.8020	+	248.683i	0.108818	+	0.334908i
$83$	−160.112	−	492.774i	−0.211742	−	0.651675i	−0.999369	−	0.0355224i	$-0.988690\pi$
$83$	−160.112	−	492.774i	−0.211742	−	0.651675i	0.787627	−	0.616153i	$-0.211310\pi$
$84$	74.0108	+	53.7720i	0.0961338	+	0.0698453i
$85$	196.535	−	142.791i	0.250791	−	0.182210i
$86$	−136.637	+	420.525i	−0.171325	+	0.527283i
$87$	−334.804			−0.412584
$88$	−562.968	−	572.117i	−0.681962	−	0.693044i
$89$	6.39690			0.00761876			0.00380938	−	0.999993i	$-0.498787\pi$
$89$	6.39690			0.00761876			0.00380938	+	0.999993i	$0.498787\pi$
$90$	59.2593	−	182.381i	0.0694053	−	0.213608i
$91$	−73.7513	+	53.5834i	−0.0849586	+	0.0617260i
$92$	832.270	+	604.680i	0.943154	+	0.685241i
$93$	24.9881	+	76.9053i	0.0278617	+	0.0857496i
$94$	−248.078	−	763.505i	−0.272205	−	0.837761i
$95$	393.032	+	285.554i	0.424465	+	0.308392i
$96$	296.237	−	215.229i	0.314944	−	0.228820i
$97$	−100.607	+	309.636i	−0.105310	+	0.324111i	−0.989803	−	0.142442i	$-0.954504\pi$
$97$	−100.607	+	309.636i	−0.105310	+	0.324111i	0.884493	+	0.466553i	$0.154504\pi$
$98$	440.812			0.454375
$99$	−830.472	−	138.404i	−0.843086	−	0.140506i
$100$	−130.948			−0.130948
$101$	−388.019	+	1194.20i	−0.382271	+	1.17651i	0.556170	+	0.831069i	$0.312270\pi$
$101$	−388.019	+	1194.20i	−0.382271	+	1.17651i	−0.938441	+	0.345441i	$0.887730\pi$
$102$	−129.385	+	94.0035i	−0.125598	+	0.0912523i
$103$	1183.44	+	859.822i	1.13212	+	0.822532i	0.986002	−	0.166735i	$-0.0533226\pi$
$103$	1183.44	+	859.822i	1.13212	+	0.822532i	0.146117	+	0.989267i	$0.453323\pi$
$104$	70.2823	+	216.307i	0.0662668	+	0.203948i
$105$	26.9856	+	83.0532i	0.0250812	+	0.0771920i
$106$	−463.730	−	336.920i	−0.424920	−	0.308722i
$107$	1271.09	−	923.500i	1.14842	−	0.834375i	0.160149	−	0.987093i	$-0.448803\pi$
$107$	1271.09	−	923.500i	1.14842	−	0.834375i	0.988270	+	0.152718i	$0.0488025\pi$
$108$	160.537	−	494.081i	0.143034	−	0.440213i
$109$	−1292.93			−1.13615			−0.568074	−	0.822977i	$-0.692311\pi$
$109$	−1292.93			−1.13615			−0.568074	+	0.822977i	$0.692311\pi$
$110$	−45.0105	−	299.805i	−0.0390144	−	0.259866i
$111$	288.951			0.247081
$112$	14.5485	−	44.7758i	0.0122742	−	0.0377760i
$113$	−808.914	+	587.710i	−0.673418	+	0.489267i	−0.871168	−	0.490986i	$-0.836637\pi$
$113$	−808.914	+	587.710i	−0.673418	+	0.489267i	0.197750	+	0.980253i	$0.436637\pi$
$114$	−258.744	−	187.988i	−0.212575	−	0.154445i
$115$	303.460	+	933.954i	0.246068	+	0.757319i
$116$	273.613	+	842.096i	0.219003	+	0.674023i
$117$	193.005	+	140.226i	0.152507	+	0.110803i
$118$	−1038.39	+	754.436i	−0.810100	+	0.588572i
$119$	−132.398	+	407.479i	−0.101991	+	0.313896i
$120$	217.872			0.165741
$121$	−1272.32	+	390.844i	−0.955914	+	0.293647i
$122$	1330.38			0.987269
$123$	−96.2933	+	296.360i	−0.0705892	+	0.217251i
$124$	173.010	−	125.699i	0.125297	−	0.0910334i
$125$	−101.127	−	73.4732i	−0.0723607	−	0.0525731i
$126$	104.514	+	321.660i	0.0738954	+	0.227427i
$127$	199.689	+	614.578i	0.139524	+	0.429409i	0.996266	−	0.0863348i	$-0.0275155\pi$
$127$	199.689	+	614.578i	0.139524	+	0.429409i	−0.856743	+	0.515744i	$0.827515\pi$
$128$	−840.864	−	610.923i	−0.580645	−	0.421863i
$129$	−426.301	+	309.726i	−0.290959	+	0.211394i
$130$	−26.5459	+	81.6998i	−0.0179094	+	0.0551196i
$131$	−367.577			−0.245155			−0.122578	−	0.992459i	$-0.539116\pi$
$131$	−367.577			−0.245155			−0.122578	+	0.992459i	$0.539116\pi$
$132$	−56.1922	−	374.283i	−0.0370523	−	0.246796i
$133$	−856.814			−0.558610
$134$	−65.8367	+	202.624i	−0.0424434	+	0.130627i
$135$	401.201	−	291.489i	0.255777	−	0.185833i
$136$	864.787	+	628.304i	0.545256	+	0.396152i
$137$	−244.552	−	752.652i	−0.152507	−	0.469368i	0.845393	−	0.534145i	$-0.179366\pi$
$137$	−244.552	−	752.652i	−0.152507	−	0.469368i	−0.997900	+	0.0647770i	$0.979366\pi$
$138$	−199.776	−	614.848i	−0.123233	−	0.379271i
$139$	−1544.90	−	1122.44i	−0.942713	−	0.684921i	0.00635929	−	0.999980i	$-0.497976\pi$
$139$	−1544.90	−	1122.44i	−0.942713	−	0.684921i	−0.949072	+	0.315059i	$0.897976\pi$
$140$	186.841	−	135.748i	0.112792	−	0.0819485i
$141$	295.639	−	909.884i	0.176577	−	0.543447i
$142$	480.290			0.283838
$143$	372.019	+	61.9996i	0.217551	+	0.0362564i
$144$	−123.207			−0.0713003
$145$	−261.186	+	803.848i	−0.149588	+	0.460386i
$146$	34.2679	−	24.8971i	0.0194249	−	0.0141130i
$147$	424.996	+	308.778i	0.238456	+	0.173249i
$148$	−236.141	−	726.766i	−0.131153	−	0.403647i
$149$	−608.528	−	1872.86i	−0.334581	−	1.02973i	−0.966928	−	0.255049i	$-0.917908\pi$
$149$	−608.528	−	1872.86i	−0.334581	−	1.02973i	0.632347	−	0.774685i	$-0.282092\pi$
$150$	66.5749	+	48.3695i	0.0362388	+	0.0263290i
$151$	2146.79	−	1559.73i	1.15697	−	0.840591i	0.167582	−	0.985858i	$-0.446404\pi$
$151$	2146.79	−	1559.73i	1.15697	−	0.840591i	0.989392	+	0.145267i	$0.0464042\pi$
$152$	−660.573	+	2033.03i	−0.352497	+	1.08487i
$153$	1121.24			0.592462
$154$	375.017	+	381.112i	0.196232	+	0.199421i
$155$	204.139			0.105786
$156$	−33.1405	+	101.996i	−0.0170087	+	0.0523475i
$157$	1666.70	−	1210.93i	0.847243	−	0.615558i	−0.0771416	−	0.997020i	$-0.524579\pi$
$157$	1666.70	−	1210.93i	0.847243	−	0.615558i	0.924384	+	0.381462i	$0.124579\pi$
$158$	−287.888	−	209.163i	−0.144957	−	0.105317i
$159$	−211.088	−	649.663i	−0.105286	−	0.324035i
$160$	−285.654	−	879.154i	−0.141144	−	0.434395i
$161$	−1401.18	−	1018.02i	−0.685890	−	0.498328i
$162$	573.649	−	416.781i	0.278211	−	0.202132i
$163$	−67.9729	+	209.199i	−0.0326629	+	0.100526i	−0.966059	−	0.258322i	$-0.916830\pi$
$163$	−67.9729	+	209.199i	−0.0326629	+	0.100526i	0.933396	+	0.358848i	$0.116830\pi$
$164$	824.096			0.392385
$165$	166.610	−	320.577i	0.0786095	−	0.151254i
$166$	861.115			0.402623
$167$	306.205	−	942.403i	0.141886	−	0.436679i	−0.854712	−	0.519103i	$-0.826266\pi$
$167$	306.205	−	942.403i	0.141886	−	0.436679i	0.996597	+	0.0824240i	$0.0262662\pi$
$168$	−310.868	+	225.859i	−0.142762	+	0.103723i
$169$	1690.95	+	1228.55i	0.769664	+	0.559194i
$170$	124.763	+	383.980i	0.0562874	+	0.173235i
$171$	692.894	+	2132.51i	0.309865	+	0.953667i
$172$	1127.41	+	819.109i	0.499791	+	0.363119i
$173$	1259.56	−	915.122i	0.553540	−	0.402170i	−0.275549	−	0.961287i	$-0.588860\pi$
$173$	1259.56	−	915.122i	0.553540	−	0.402170i	0.829089	+	0.559117i	$0.188860\pi$
$174$	171.946	−	529.196i	0.0749150	−	0.230565i
$175$	220.458			0.0952291
$176$	−174.255	+	87.0256i	−0.0746306	+	0.0372716i
$177$	−1529.60			−0.649558
$178$	−3.28527	+	10.1110i	−0.00138338	+	0.00425760i
$179$	1087.73	−	790.285i	0.454196	−	0.329992i	−0.337054	−	0.941485i	$-0.609431\pi$
$179$	1087.73	−	790.285i	0.454196	−	0.329992i	0.791250	+	0.611493i	$0.209431\pi$
$180$	−488.956	−	355.247i	−0.202470	−	0.147103i
$181$	−460.346	−	1416.80i	−0.189046	−	0.581823i	0.810949	−	0.585117i	$-0.198951\pi$
$181$	−460.346	−	1416.80i	−0.189046	−	0.581823i	−0.999995	+	0.00329412i	$0.998951\pi$
$182$	−46.8181	−	144.091i	−0.0190681	−	0.0586854i
$183$	1282.65	+	931.897i	0.518120	+	0.376436i
$184$	−3495.79	+	2539.84i	−1.40061	+	1.01761i
$185$	225.415	−	693.757i	0.0895830	−	0.275708i
$186$	−134.391			−0.0529786
$187$	1585.80	−	791.972i	0.620135	−	0.309704i
$188$	−2530.14			−0.981538
$189$	−270.273	+	831.816i	−0.104018	+	0.320136i
$190$	−653.201	+	474.578i	−0.249411	+	0.181208i
$191$	−3393.75	−	2465.71i	−1.28567	−	0.934095i	−0.285963	−	0.958241i	$-0.592314\pi$
$191$	−3393.75	−	2465.71i	−1.28567	−	0.934095i	−0.999708	+	0.0241454i	$0.992314\pi$
$192$	161.914	+	498.320i	0.0608600	+	0.187308i
$193$	1042.07	+	3207.17i	0.388653	+	1.19615i	0.933795	+	0.357808i	$0.116476\pi$
$193$	1042.07	+	3207.17i	0.388653	+	1.19615i	−0.545142	+	0.838344i	$0.683524\pi$
$194$	−437.746	−	318.041i	−0.162002	−	0.117701i
$195$	−82.8221	+	60.1738i	−0.0304155	+	0.0220981i
$196$	429.313	−	1321.29i	0.156455	−	0.481519i
$197$	−5256.04			−1.90090			−0.950450	−	0.310878i	$-0.899377\pi$
$197$	−5256.04			−1.90090			−0.950450	+	0.310878i	$0.899377\pi$
$198$	645.271	−	1241.57i	0.231603	−	0.445630i
$199$	3413.08			1.21581			0.607907	−	0.794008i	$-0.292009\pi$
$199$	3413.08			1.21581			0.607907	+	0.794008i	$0.292009\pi$
$200$	169.966	−	523.100i	0.0600919	−	0.184944i
$201$	−205.408	+	149.238i	−0.0720814	+	0.0523702i
$202$	−1688.29	−	1226.62i	−0.588059	−	0.427250i
$203$	−460.645	−	1417.72i	−0.159266	−	0.490170i
$204$	155.756	+	479.369i	0.0534565	+	0.164522i
$205$	636.426	+	462.391i	0.216829	+	0.157535i
$206$	−1966.83	+	1428.99i	−0.665221	+	0.483312i
$207$	−1400.61	+	4310.62i	−0.470284	+	1.44739i
$208$	55.1919			0.0183984
$209$	2486.25	+	2526.66i	0.822860	+	0.836232i
$210$	−145.134			−0.0476914
$211$	−336.362	+	1035.22i	−0.109745	+	0.337760i	−0.990815	−	0.135226i	$-0.956824\pi$
$211$	−336.362	+	1035.22i	−0.109745	+	0.337760i	0.881070	+	0.472986i	$0.156824\pi$
$212$	−1461.52	+	1061.85i	−0.473478	+	0.344002i
$213$	463.058	+	336.431i	0.148959	+	0.108225i
$214$	806.901	+	2483.38i	0.257750	+	0.793274i
$215$	411.072	+	1265.15i	0.130395	+	0.401314i
$216$	1765.35	+	1282.60i	0.556096	+	0.404027i
$217$	−291.274	+	211.623i	−0.0911195	+	0.0662022i
$218$	664.013	−	2043.62i	0.206297	−	0.634915i
$219$	50.4782			0.0155753
$220$	−942.470	−	157.069i	−0.288824	−	0.0481346i
$221$	−502.271			−0.152880
$222$	−148.397	+	456.720i	−0.0448638	+	0.138077i
$223$	158.125	−	114.885i	0.0474835	−	0.0344988i	−0.563790	−	0.825918i	$-0.690657\pi$
$223$	158.125	−	114.885i	0.0474835	−	0.0344988i	0.611274	+	0.791419i	$0.290657\pi$
$224$	1318.96	+	958.283i	0.393424	+	0.285839i
$225$	−178.282	−	548.695i	−0.0528242	−	0.162576i
$226$	−513.507	−	1580.41i	−0.151141	−	0.465166i
$227$	1565.97	+	1137.74i	0.457873	+	0.332664i	0.792696	−	0.609617i	$-0.208677\pi$
$227$	1565.97	+	1137.74i	0.457873	+	0.332664i	−0.334823	+	0.942281i	$0.608677\pi$
$228$	−815.471	+	592.474i	−0.236868	+	0.172095i
$229$	1076.38	−	3312.76i	0.310608	−	0.955954i	−0.666916	−	0.745132i	$-0.732386\pi$
$229$	1076.38	−	3312.76i	0.310608	−	0.955954i	0.977525	−	0.210821i	$-0.0676138\pi$
$230$	−1632.07			−0.467893
$231$	94.6030	+	630.128i	0.0269455	+	0.179478i
$232$	−3719.09			−1.05246
$233$	291.450	−	896.990i	0.0819463	−	0.252205i	−0.901686	−	0.432391i	$-0.857670\pi$
$233$	291.450	−	896.990i	0.0819463	−	0.252205i	0.983633	+	0.180186i	$0.0576700\pi$
$234$	−320.765	+	233.049i	−0.0896114	+	0.0651065i
$235$	−1953.95	−	1419.63i	−0.542391	−	0.394070i
$236$	1250.04	+	3847.23i	0.344792	+	1.06116i
$237$	−131.046	−	403.317i	−0.0359170	−	0.110541i
$238$	−576.072	−	418.540i	−0.156896	−	0.113991i
$239$	−325.810	+	236.715i	−0.0881795	+	0.0640661i	−0.631001	−	0.775782i	$-0.717356\pi$
$239$	−325.810	+	236.715i	−0.0881795	+	0.0640661i	0.542822	+	0.839848i	$0.317356\pi$
$240$	16.3379	−	50.2829i	0.00439419	−	0.0135239i
$241$	4356.62			1.16446			0.582229	−	0.813025i	$-0.302181\pi$
$241$	4356.62			1.16446			0.582229	+	0.813025i	$0.302181\pi$
$242$	35.6556	−	2211.78i	0.00947118	−	0.587514i
$243$	3522.93			0.930026
$244$	1295.67	−	3987.68i	0.339947	−	1.04625i
$245$	1072.91	−	779.512i	0.279777	−	0.203270i
$246$	−418.978	−	304.405i	−0.108590	−	0.0788949i
$247$	−310.390	−	955.281i	−0.0799580	−	0.246085i
$248$	277.573	+	854.283i	0.0710723	+	0.218738i
$249$	830.219	+	603.190i	0.211297	+	0.153516i
$250$	168.069	−	122.109i	0.0425184	−	0.0308914i
$251$	1616.68	−	4975.62i	0.406549	−	1.25123i	−0.513046	−	0.858361i	$-0.671483\pi$
$251$	1616.68	−	4975.62i	0.406549	−	1.25123i	0.919595	−	0.392868i	$-0.128517\pi$
$252$	1065.93			0.266458
$253$	1063.83	+	7085.95i	0.264358	+	1.76083i
$254$	−1073.96			−0.265301
$255$	−148.682	+	457.596i	−0.0365131	+	0.112376i
$256$	3109.68	−	2259.32i	0.759200	−	0.551591i
$257$	−5996.74	−	4356.89i	−1.45551	−	1.05749i	−0.984504	−	0.175361i	$-0.943891\pi$
$257$	−5996.74	−	4356.89i	−1.45551	−	1.05749i	−0.471006	−	0.882130i	$-0.656109\pi$
$258$	−270.621	−	832.884i	−0.0653027	−	0.200981i
$259$	397.557	+	1223.56i	0.0953784	+	0.293545i
$260$	219.033	+	159.137i	0.0522457	+	0.0379587i
$261$	−3156.02	+	2292.98i	−0.748478	+	0.543801i
$262$	188.777	−	580.996i	0.0445141	−	0.137000i
$263$	774.208			0.181520			0.0907599	−	0.995873i	$-0.471070\pi$
$263$	774.208			0.181520			0.0907599	+	0.995873i	$0.471070\pi$
$264$	1568.09	+	261.334i	0.365566	+	0.0609242i
$265$	−1724.48			−0.399751
$266$	440.036	−	1354.29i	0.101430	−	0.312169i
$267$	−10.2499	+	7.44700i	−0.00234938	+	0.00170693i
$268$	543.227	+	394.677i	0.123817	+	0.0899581i
$269$	−1050.73	−	3233.82i	−0.238157	−	0.732972i	−0.996687	−	0.0813336i	$-0.974082\pi$
$269$	−1050.73	−	3233.82i	−0.238157	−	0.732972i	0.758530	−	0.651638i	$-0.225918\pi$
$270$	254.686	+	783.844i	0.0574064	+	0.176679i
$271$	896.097	+	651.053i	0.200864	+	0.145936i	0.683670	−	0.729791i	$-0.260383\pi$
$271$	896.097	+	651.053i	0.200864	+	0.145936i	−0.482807	+	0.875727i	$0.660383\pi$
$272$	209.856	−	152.469i	0.0467808	−	0.0339882i
$273$	55.7940	−	171.716i	0.0123693	−	0.0380687i
$274$	1315.25			0.289989
$275$	−639.713	−	650.109i	−0.140277	−	0.142557i
$276$	−2037.51			−0.444361
$277$	2363.53	−	7274.18i	0.512673	−	1.57785i	−0.274803	−	0.961501i	$-0.588613\pi$
$277$	2363.53	−	7274.18i	0.512673	−	1.57785i	0.787476	−	0.616345i	$-0.211387\pi$
$278$	2567.56	−	1865.44i	0.553929	−	0.402453i
$279$	762.253	+	553.809i	0.163566	+	0.118838i
$280$	299.763	+	922.575i	0.0639795	+	0.196909i
$281$	1524.53	+	4692.02i	0.323651	+	0.996094i	0.972046	+	0.234790i	$0.0754403\pi$
$281$	1524.53	+	4692.02i	0.323651	+	0.996094i	−0.648396	+	0.761304i	$0.724560\pi$
$282$	1286.34	+	934.583i	0.271633	+	0.197353i
$283$	−4667.08	+	3390.83i	−0.980314	+	0.712240i	−0.957779	−	0.287506i	$-0.907174\pi$
$283$	−4667.08	+	3390.83i	−0.980314	+	0.712240i	−0.0225352	+	0.999746i	$0.507174\pi$
$284$	467.761	−	1439.62i	0.0977343	−	0.300795i
$285$	−962.195			−0.199984
$286$	−289.056	+	556.177i	−0.0597631	+	0.114991i
$287$	−1387.42			−0.285354
$288$	1318.43	−	4057.70i	0.269753	−	0.830216i
$289$	2064.92	−	1500.25i	0.420297	−	0.305364i
$290$	−1136.43	−	825.668i	−0.230116	−	0.167189i
$291$	−199.260	−	613.261i	−0.0401404	−	0.123539i
$292$	−41.2525	−	126.962i	−0.00826753	−	0.0254449i
$293$	−4884.99	−	3549.15i	−0.974007	−	0.707658i	−0.0176458	−	0.999844i	$-0.505617\pi$
$293$	−4884.99	−	3549.15i	−0.974007	−	0.707658i	−0.956361	+	0.292187i	$0.905617\pi$
$294$	−706.325	+	513.175i	−0.140115	+	0.101799i
$295$	−1193.27	+	3672.49i	−0.235507	+	0.724816i
$296$	3209.74			0.630278
$297$	3237.20	−	1616.71i	0.632463	−	0.315861i
$298$	3272.78			0.636199
$299$	627.417	−	1930.99i	0.121353	−	0.373486i
$300$	209.821	−	152.444i	0.0403800	−	0.0293378i
$301$	−1898.06	−	1379.02i	−0.363463	−	0.264071i
$302$	1362.80	+	4194.28i	0.259671	+	0.799184i
$303$	−768.505	−	2365.22i	−0.145708	−	0.448443i
$304$	419.670	+	304.908i	0.0791767	+	0.0575252i
$305$	3238.05	−	2352.58i	0.607902	−	0.441667i
$306$	−575.837	+	1772.24i	−0.107576	+	0.331086i
$307$	−9098.53			−1.69147			−0.845734	−	0.533605i	$-0.820837\pi$
$307$	−9098.53			−1.69147			−0.845734	+	0.533605i	$0.820837\pi$
$308$	1507.58	−	752.907i	0.278903	−	0.139288i
$309$	−2897.23			−0.533391
$310$	−104.840	+	322.666i	−0.0192082	+	0.0591167i
$311$	−3086.37	+	2242.38i	−0.562739	+	0.408854i	−0.832460	−	0.554085i	$-0.813068\pi$
$311$	−3086.37	+	2242.38i	−0.562739	+	0.408854i	0.269721	+	0.962938i	$0.413068\pi$
$312$	−364.431	−	264.774i	−0.0661276	−	0.0480445i
$313$	800.302	+	2463.08i	0.144523	+	0.444797i	0.996949	−	0.0780510i	$-0.0248697\pi$
$313$	800.302	+	2463.08i	0.144523	+	0.444797i	−0.852426	+	0.522848i	$0.824870\pi$
$314$	1058.04	+	3256.31i	0.190155	+	0.585236i
$315$	823.188	+	598.081i	0.147242	+	0.106978i
$316$	−907.324	+	659.209i	−0.161522	+	0.117353i
$317$	−2153.51	+	6627.82i	−0.381556	+	1.17431i	0.557392	+	0.830249i	$0.311802\pi$
$317$	−2153.51	+	6627.82i	−0.381556	+	1.17431i	−0.938948	+	0.344059i	$0.888198\pi$
$318$	1135.28			0.200198
$319$	−2844.04	+	5472.25i	−0.499171	+	0.960462i
$320$	1322.75			0.231075
$321$	−961.599	+	2959.50i	−0.167200	+	0.514589i
$322$	2328.69	−	1691.90i	0.403022	−	0.292813i
$323$	−3819.18	−	2774.80i	−0.657910	−	0.478000i
$324$	−690.573	−	2125.36i	−0.118411	−	0.364432i
$325$	79.8634	+	245.794i	0.0136308	+	0.0419514i
$326$	−295.754	−	214.878i	−0.0502463	−	0.0365061i
$327$	2071.70	−	1505.17i	0.350352	−	0.254545i
$328$	−1069.65	+	3292.04i	−0.180066	+	0.554185i
$329$	4259.64			0.713804
$330$	421.142	+	427.985i	0.0702518	+	0.0713934i
$331$	−2383.56			−0.395808			−0.197904	−	0.980221i	$-0.563413\pi$
$331$	−2383.56			−0.395808			−0.197904	+	0.980221i	$0.563413\pi$
$332$	838.652	−	2581.11i	0.138636	−	0.426676i
$333$	2723.79	−	1978.95i	0.448236	−	0.325663i
$334$	1332.32	+	967.985i	0.218267	+	0.158580i
$335$	198.070	+	609.596i	0.0323036	+	0.0994203i
$336$	28.8146	+	88.6822i	0.00467847	+	0.0143988i
$337$	7957.89	+	5781.75i	1.28633	+	0.934575i	0.999724	−	0.0234731i	$-0.00747239\pi$
$337$	7957.89	+	5781.75i	1.28633	+	0.934575i	0.286608	+	0.958048i	$0.407472\pi$
$338$	−2810.29	+	2041.79i	−0.452247	+	0.328577i
$339$	611.956	−	1883.41i	0.0980440	−	0.301748i
$340$	1272.45			0.202965
$341$	1469.25	+	244.862i	0.233327	+	0.0388856i
$342$	−3726.52			−0.589203
$343$	−1657.46	+	5101.12i	−0.260916	+	0.803017i
$344$	−4735.46	+	3440.51i	−0.742206	+	0.539244i
$345$	−1573.51	−	1143.22i	−0.245551	−	0.178403i
$346$	799.581	+	2460.86i	0.124236	+	0.382360i
$347$	2947.10	+	9070.25i	0.455933	+	1.40322i	0.870036	+	0.492988i	$0.164095\pi$
$347$	2947.10	+	9070.25i	0.455933	+	1.40322i	−0.414103	+	0.910230i	$0.635905\pi$
$348$	−1418.75	−	1030.78i	−0.218543	−	0.158781i
$349$	−8466.06	+	6150.95i	−1.29850	+	0.943418i	−0.999940	−	0.0109714i	$-0.996508\pi$
$349$	−8466.06	+	6150.95i	−1.29850	+	0.943418i	−0.298564	+	0.954390i	$0.596508\pi$
$350$	−113.221	+	348.459i	−0.0172912	+	0.0532170i
$351$	−1025.32			−0.155919
$352$	−1001.41	−	6670.18i	−0.151635	−	1.01000i
$353$	8203.85			1.23696			0.618480	−	0.785800i	$-0.287749\pi$
$353$	8203.85			1.23696			0.618480	+	0.785800i	$0.287749\pi$
$354$	785.561	−	2417.71i	0.117944	−	0.362993i
$355$	1168.99	−	849.323i	0.174771	−	0.126979i
$356$	27.1072	+	19.6945i	0.00403561	+	0.00293205i
$357$	−262.226	−	807.048i	−0.0388752	−	0.119646i
$358$	690.505	+	2125.15i	0.101939	+	0.313737i
$359$	−10481.8	−	7615.50i	−1.54097	−	1.11958i	−0.949721	−	0.313098i	$-0.898633\pi$
$359$	−10481.8	−	7615.50i	−1.54097	−	1.11958i	−0.591254	−	0.806486i	$-0.701367\pi$
$360$	2053.77	−	1492.15i	0.300675	−	0.218453i
$361$	797.758	−	2455.25i	0.116308	−	0.357960i
$362$	2475.84			0.359467
$363$	1583.67	−	2107.44i	0.228984	−	0.304717i
$364$	−477.496			−0.0687571
$365$	39.3788	−	121.196i	0.00564707	−	0.0173799i
$366$	−2131.70	+	1548.77i	−0.304442	+	0.221190i
$367$	1018.81	+	740.206i	0.144908	+	0.105282i	0.657877	−	0.753125i	$-0.271455\pi$
$367$	1018.81	+	740.206i	0.144908	+	0.105282i	−0.512969	+	0.858407i	$0.671455\pi$
$368$	324.027	+	997.253i	0.0458997	+	0.141265i
$369$	1121.99	+	3453.12i	0.158288	+	0.487160i
$370$	980.794	+	712.589i	0.137808	+	0.100124i
$371$	2460.55	−	1787.70i	0.344328	−	0.250169i
$372$	−130.885	+	402.823i	−0.0182421	+	0.0561435i
$373$	−14100.6			−1.95738			−0.978691	−	0.205339i	$-0.934170\pi$
$373$	−14100.6			−1.95738			−0.978691	+	0.205339i	$0.934170\pi$
$374$	437.378	+	2913.27i	0.0604713	+	0.402785i
$375$	247.573			0.0340923
$376$	3284.03	−	10107.2i	0.450428	−	1.38628i
$377$	1413.78	−	1027.17i	0.193138	−	0.140323i
$378$	−1175.97	−	854.395i	−0.160015	−	0.116258i
$379$	−3680.74	−	11328.2i	−0.498857	−	1.53532i	−0.810858	−	0.585243i	$-0.800999\pi$
$379$	−3680.74	−	11328.2i	−0.498857	−	1.53532i	0.312001	−	0.950082i	$-0.399001\pi$
$380$	786.339	+	2420.10i	0.106153	+	0.326707i
$381$	−1035.43	−	752.286i	−0.139230	−	0.101157i
$382$	5640.26	−	4097.89i	0.755448	−	0.548865i
$383$	2650.80	−	8158.32i	0.353654	−	1.08843i	−0.603132	−	0.797641i	$-0.706081\pi$
$383$	2650.80	−	8158.32i	0.353654	−	1.08843i	0.956786	−	0.290793i	$-0.0939192\pi$
$384$	2058.55			0.273567
$385$	1586.71	+	264.436i	0.210042	+	0.0350049i
$386$	−5604.48			−0.739017
$387$	−1897.29	+	5839.25i	−0.249210	+	0.766991i
$388$	−1379.62	+	1002.36i	−0.180515	+	0.131152i
$389$	8059.98	+	5855.92i	1.05053	+	0.763256i	0.972314	−	0.233680i	$-0.0750768\pi$
$389$	8059.98	+	5855.92i	1.05053	+	0.763256i	0.0782185	+	0.996936i	$0.475077\pi$
$390$	−52.5763	−	161.813i	−0.00682643	−	0.0210096i
$391$	−2948.79	−	9075.45i	−0.381399	−	1.17382i
$392$	4720.96	+	3429.98i	0.608277	+	0.441939i
$393$	588.978	−	427.917i	0.0755979	−	0.0549251i
$394$	2699.36	−	8307.77i	0.345156	−	1.06228i
$395$	−1070.57			−0.136371
$396$	−3093.06	−	3143.32i	−0.392505	−	0.398883i
$397$	9843.58			1.24442			0.622211	−	0.782850i	$-0.286235\pi$
$397$	9843.58			1.24442			0.622211	+	0.782850i	$0.286235\pi$
$398$	−1752.87	+	5394.77i	−0.220762	+	0.679435i
$399$	1372.90	−	997.467i	0.172257	−	0.125152i
$400$	−107.981	−	78.4529i	−0.0134976	−	0.00980661i
$401$	1540.77	+	4742.01i	0.191877	+	0.590536i	0.999999	+	0.00152094i	$0.000484131\pi$
$401$	1540.77	+	4742.01i	0.191877	+	0.590536i	−0.808122	+	0.589015i	$0.799516\pi$
$402$	−130.395	−	401.315i	−0.0161779	−	0.0497904i
$403$	−341.460	−	248.085i	−0.0422068	−	0.0306650i
$404$	−5320.92	+	3865.87i	−0.655261	+	0.476075i
$405$	659.207	−	2028.83i	0.0808797	−	0.248922i
$406$	2477.44			0.302841
$407$	2454.53	−	4722.80i	0.298935	−	0.575185i
$408$	−2117.12			−0.256894
$409$	−3724.04	+	11461.4i	−0.450224	+	1.38565i	0.426427	+	0.904522i	$0.359772\pi$
$409$	−3724.04	+	11461.4i	−0.450224	+	1.38565i	−0.876651	+	0.481126i	$0.840228\pi$
$410$	−1057.71	+	768.473i	−0.127407	+	0.0925663i
$411$	1268.06	+	921.298i	0.152187	+	0.110570i
$412$	2367.72	+	7287.09i	0.283129	+	0.871381i
$413$	−2104.52	−	6477.05i	−0.250743	−	0.771707i
$414$	−6094.12	−	4427.63i	−0.723453	−	0.525619i
$415$	2095.89	−	1522.76i	0.247912	−	0.180119i
$416$	−590.604	+	1817.69i	−0.0696075	+	0.214230i
$417$	3782.14			0.444154
$418$	−5270.54	+	2632.18i	−0.616723	+	0.308001i
$419$	811.934			0.0946673			0.0473336	−	0.998879i	$-0.484928\pi$
$419$	811.934			0.0946673			0.0473336	+	0.998879i	$0.484928\pi$
$420$	−141.348	+	435.025i	−0.0164216	+	0.0505405i
$421$	10794.6	−	7842.71i	1.24963	−	0.907911i	0.251431	−	0.967875i	$-0.419099\pi$
$421$	10794.6	−	7842.71i	1.24963	−	0.907911i	0.998201	+	0.0599644i	$0.0190987\pi$
$422$	−1463.53	−	1063.32i	−0.168824	−	0.122658i
$423$	−3444.72	−	10601.7i	−0.395952	−	1.21862i
$424$	−2344.82	−	7216.61i	−0.268572	−	0.826580i
$425$	982.676	+	713.956i	0.112157	+	0.0814870i
$426$	−769.582	+	559.134i	−0.0875267	+	0.0635918i
$427$	−2181.35	+	6713.50i	−0.247220	+	0.760864i
$428$	8229.55			0.929416
$429$	−668.273	+	333.746i	−0.0752087	+	0.0375603i
$430$	−2210.83			−0.247943
$431$	−2610.68	+	8034.84i	−0.291768	+	0.897969i	0.692520	+	0.721399i	$0.256500\pi$
$431$	−2610.68	+	8034.84i	−0.291768	+	0.897969i	−0.984288	+	0.176571i	$0.943500\pi$
$432$	428.393	−	311.245i	0.0477108	−	0.0346639i
$433$	6173.45	+	4485.28i	0.685167	+	0.497803i	0.875068	−	0.484000i	$-0.160817\pi$
$433$	6173.45	+	4485.28i	0.685167	+	0.497803i	−0.189901	+	0.981803i	$0.560817\pi$
$434$	−184.904	−	569.075i	−0.0204508	−	0.0629411i
$435$	−517.301	−	1592.09i	−0.0570177	−	0.175482i
$436$	−5478.86	−	3980.62i	−0.601811	−	0.437242i
$437$	15438.5	−	11216.8i	1.68999	−	1.22785i
$438$	−25.9242	+	79.7865i	−0.00282810	+	0.00870399i
$439$	1738.52			0.189009			0.0945043	−	0.995524i	$-0.469873\pi$
$439$	1738.52			0.189009			0.0945043	+	0.995524i	$0.469873\pi$
$440$	1850.74	−	3561.04i	0.200524	−	0.385832i
$441$	6120.95			0.660938
$442$	257.952	−	793.896i	0.0277592	−	0.0854339i
$443$	−1319.84	+	958.922i	−0.141552	+	0.102844i	−0.656308	−	0.754493i	$-0.727883\pi$
$443$	−1319.84	+	958.922i	−0.141552	+	0.102844i	0.514755	+	0.857337i	$0.327883\pi$
$444$	1224.45	+	889.612i	0.130877	+	0.0950881i
$445$	9.88375	+	30.4191i	0.00105289	+	0.00324045i
$446$	100.379	+	308.936i	0.0106572	+	0.0327994i
$447$	3155.36	+	2292.50i	0.333878	+	0.242576i
$448$	−1887.35	+	1371.24i	−0.199038	+	0.144609i
$449$	698.894	−	2150.97i	0.0734585	−	0.226082i	−0.907585	−	0.419867i	$-0.862077\pi$
$449$	698.894	−	2150.97i	0.0734585	−	0.226082i	0.981044	+	0.193785i	$0.0620766\pi$
$450$	958.835			0.100444
$451$	4025.93	+	4091.35i	0.420340	+	0.427171i
$452$	−5237.24			−0.544998
$453$	−1624.08	+	4998.40i	−0.168446	+	0.518423i
$454$	−2602.57	+	1890.88i	−0.269042	+	0.195470i
$455$	−368.756	−	267.917i	−0.0379946	−	0.0276047i
$456$	−1308.32	−	4026.60i	−0.134359	−	0.413515i
$457$	−1966.81	−	6053.21i	−0.201320	−	0.619600i	−0.999844	−	0.0176375i	$-0.994386\pi$
$457$	−1966.81	−	6053.21i	−0.201320	−	0.619600i	0.798524	−	0.601963i	$-0.205614\pi$
$458$	4683.39	+	3402.69i	0.477818	+	0.347155i
$459$	−3898.56	+	2832.47i	−0.396447	+	0.288036i
$460$	−1589.49	+	4891.96i	−0.161110	+	0.495845i
$461$	−2491.39			−0.251704			−0.125852	−	0.992049i	$-0.540166\pi$
$461$	−2491.39			−0.251704			−0.125852	+	0.992049i	$0.540166\pi$
$462$	−1044.57	−	174.086i	−0.105190	−	0.0175307i
$463$	−12869.2			−1.29175			−0.645877	−	0.763442i	$-0.723508\pi$
$463$	−12869.2			−1.29175			−0.645877	+	0.763442i	$0.723508\pi$
$464$	−278.888	+	858.330i	−0.0279031	+	0.0858771i
$465$	−327.098	+	237.651i	−0.0326211	+	0.0237006i
$466$	1268.11	+	921.338i	0.126061	+	0.0915884i
$467$	3973.06	+	12227.8i	0.393686	+	1.21164i	0.929980	+	0.367610i	$0.119824\pi$
$467$	3973.06	+	12227.8i	0.393686	+	1.21164i	−0.536294	+	0.844031i	$0.680176\pi$
$468$	386.145	+	1188.43i	0.0381400	+	0.117383i
$469$	−914.556	−	664.464i	−0.0900432	−	0.0654202i
$470$	3247.38	−	2359.36i	0.318703	−	0.231552i
$471$	−1260.88	+	3880.60i	−0.123351	+	0.379637i
$472$	−16991.2			−1.65695
$473$	1441.09	+	9598.75i	0.140087	+	0.933089i
$474$	704.790			0.0682955
$475$	−750.623	+	2310.18i	−0.0725073	+	0.223155i
$476$	−1815.58	+	1319.09i	−0.174825	+	0.127018i
$477$	−6439.19	−	4678.34i	−0.618092	−	0.449070i
$478$	−206.828	−	636.550i	−0.0197909	−	0.0609103i
$479$	−1580.83	−	4865.29i	−0.150793	−	0.464094i	0.846917	−	0.531725i	$-0.178456\pi$
$479$	−1580.83	−	4865.29i	−0.150793	−	0.464094i	−0.997710	+	0.0676310i	$0.978456\pi$
$480$	1481.19	+	1076.14i	0.140847	+	0.102331i
$481$	−1220.15	+	886.492i	−0.115663	+	0.0840344i
$482$	−2237.44	+	6886.12i	−0.211437	+	0.650735i
$483$	3430.28			0.323153
$484$	−6594.85	−	2260.95i	−0.619351	−	0.212336i
$485$	−1627.85			−0.152406
$486$	−1809.28	+	5568.40i	−0.168870	+	0.519728i
$487$	−3210.72	+	2332.73i	−0.298751	+	0.217055i	−0.727055	−	0.686580i	$-0.759111\pi$
$487$	−3210.72	+	2332.73i	−0.298751	+	0.217055i	0.428304	+	0.903635i	$0.359111\pi$
$488$	14247.9	+	10351.7i	1.32167	+	0.960248i
$489$	−134.626	−	414.336i	−0.0124499	−	0.0383168i
$490$	681.092	+	2096.19i	0.0627931	+	0.193257i
$491$	−34.1538	−	24.8142i	−0.00313918	−	0.00228075i	0.586215	−	0.810156i	$-0.300618\pi$
$491$	−34.1538	−	24.8142i	−0.00313918	−	0.00228075i	−0.589354	+	0.807875i	$0.700618\pi$
$492$	−1320.47	+	959.379i	−0.120999	+	0.0879108i
$493$	2538.01	−	7811.18i	0.231858	−	0.713586i
$494$	1669.34			0.152039
$495$	−624.999	−	4162.97i	−0.0567508	−	0.378004i
$496$	217.975			0.0197326
$497$	−787.505	+	2423.69i	−0.0710753	+	0.218747i
$498$	−1379.79	+	1002.47i	−0.124156	+	0.0902047i
$499$	128.316	+	93.2271i	0.0115115	+	0.00836356i	0.593526	−	0.804815i	$-0.297735\pi$
$499$	128.316	+	93.2271i	0.0115115	+	0.00836356i	−0.582015	+	0.813178i	$0.697735\pi$
$500$	−202.325	−	622.693i	−0.0180965	−	0.0556953i
$501$	606.466	+	1866.51i	0.0540816	+	0.166446i
$502$	7034.26	+	5110.69i	0.625407	+	0.454385i
$503$	7153.70	−	5197.47i	0.634131	−	0.460723i	−0.223698	−	0.974658i	$-0.571813\pi$
$503$	7153.70	−	5197.47i	0.634131	−	0.460723i	0.857829	+	0.513936i	$0.171813\pi$
$504$	−1383.54	+	4258.10i	−0.122277	+	0.376331i
$505$	−6278.29			−0.553228
$506$	−11746.5	−	1957.64i	−1.03201	−	0.171991i
$507$	−4139.68			−0.362623
$508$	−1045.95	+	3219.10i	−0.0913514	+	0.281151i
$509$	−8914.50	+	6476.76i	−0.776284	+	0.564003i	−0.903861	−	0.427826i	$-0.859280\pi$
$509$	−8914.50	+	6476.76i	−0.776284	+	0.564003i	0.127578	+	0.991829i	$0.459280\pi$
$510$	−646.924	−	470.018i	−0.0561692	−	0.0408093i
$511$	69.4511	+	213.749i	0.00601240	+	0.0185043i
$512$	−595.391	−	1832.43i	−0.0513922	−	0.158169i
$513$	−7796.35	−	5664.38i	−0.670989	−	0.487502i
$514$	9966.31	−	7240.95i	0.855243	−	0.621371i
$515$	−2260.18	+	6956.11i	−0.193389	+	0.595190i
$516$	−2760.05			−0.235473
$517$	−12360.4	−	12561.2i	−1.05147	−	1.06855i
$518$	−2138.14			−0.181360
$519$	−952.876	+	2932.65i	−0.0805907	+	0.248033i
$520$	−920.008	+	668.425i	−0.0775865	+	0.0563699i
$521$	17523.5	+	12731.6i	1.47355	+	1.07060i	0.979565	+	0.201126i	$0.0644600\pi$
$521$	17523.5	+	12731.6i	1.47355	+	1.07060i	0.493984	+	0.869471i	$0.335540\pi$
$522$	−2003.48	−	6166.06i	−0.167988	−	0.517014i
$523$	−4100.48	−	12620.0i	−0.342833	−	1.05513i	−0.962734	−	0.270451i	$-0.912827\pi$
$523$	−4100.48	−	12620.0i	−0.342833	−	1.05513i	0.619901	−	0.784680i	$-0.287173\pi$
$524$	−1557.63	−	1131.68i	−0.129857	−	0.0943468i
$525$	−353.246	+	256.648i	−0.0293656	+	0.0213353i
$526$	−397.612	+	1223.72i	−0.0329595	+	0.101439i
$527$	−1983.67			−0.163966
$528$	177.902	−	342.304i	0.0146633	−	0.0282138i
$529$	26407.3			2.17040
$530$	885.646	−	2725.74i	0.0725849	−	0.223393i
$531$	−14418.7	+	10475.8i	−1.17838	+	0.856143i
$532$	−3630.79	−	2637.93i	−0.295893	−	0.214979i
$533$	−502.606	−	1546.86i	−0.0408448	−	0.125707i
$534$	−6.50675	−	20.0257i	−0.000527294	−	0.00162284i
$535$	6355.45	+	4617.50i	0.513589	+	0.373144i
$536$	−2281.72	+	1657.77i	−0.183872	+	0.133591i
$537$	−822.888	+	2532.59i	−0.0661270	+	0.203518i
$538$	5651.04			0.452851
$539$	8657.05	−	4323.46i	0.691810	−	0.345500i
$540$	2597.54			0.207000
$541$	2101.81	−	6468.71i	0.167031	−	0.514069i	−0.832149	−	0.554552i	$-0.812890\pi$
$541$	2101.81	−	6468.71i	0.167031	−	0.514069i	0.999180	+	0.0404828i	$0.0128896\pi$
$542$	−1489.27	+	1082.02i	−0.118025	+	0.0857505i
$543$	2387.01	+	1734.26i	0.188649	+	0.137061i
$544$	2775.77	+	8542.95i	0.218769	+	0.673301i
$545$	−1997.69	−	6148.25i	−0.157012	−	0.483233i
$546$	242.763	+	176.378i	0.0190280	+	0.0138247i
$547$	20010.7	−	14538.6i	1.56416	−	1.13643i	0.631666	−	0.775240i	$-0.282371\pi$
$547$	20010.7	−	14538.6i	1.56416	−	1.13643i	0.932493	−	0.361188i	$-0.117629\pi$
$548$	1280.94	−	3942.32i	0.0998521	−	0.307313i
$549$	18473.1			1.43609
$550$	1356.11	−	677.261i	0.105136	−	0.0525064i
$551$	16424.7			1.26990
$552$	2644.62	−	8139.30i	0.203918	−	0.627594i
$553$	1527.54	−	1109.82i	0.117464	−	0.0853424i
$554$	10283.8	+	7471.64i	0.788661	+	0.572996i
$555$	446.454	+	1374.04i	0.0341458	+	0.105090i
$556$	−3090.89	−	9512.79i	−0.235761	−	0.725597i
$557$	−15719.3	−	11420.8i	−1.19578	−	0.868785i	−0.201917	−	0.979403i	$-0.564717\pi$
$557$	−15719.3	−	11420.8i	−1.19578	−	0.868785i	−0.993863	+	0.110618i	$0.964717\pi$
$558$	−1266.83	+	920.406i	−0.0961097	+	0.0698278i
$559$	849.911	−	2615.76i	0.0643066	−	0.197915i
$560$	235.400			0.0177633
$561$	−1618.99	+	3115.12i	−0.121843	+	0.234439i
$562$	−8199.22			−0.615415
$563$	3808.06	−	11720.0i	0.285063	−	0.877334i	−0.701317	−	0.712850i	$-0.747404\pi$
$563$	3808.06	−	11720.0i	0.285063	−	0.877334i	0.986380	−	0.164484i	$-0.0525958\pi$
$564$	4054.11	−	2945.48i	0.302675	−	0.219906i
$565$	−4044.57	−	2938.55i	−0.301162	−	0.218807i
$566$	−2962.71	−	9118.28i	−0.220021	−	0.677155i
$567$	1162.62	+	3578.18i	0.0861120	+	0.265026i
$568$	5143.76	+	3737.16i	0.379978	+	0.276070i
$569$	−15429.2	+	11209.9i	−1.13677	+	0.825914i	−0.986666	−	0.162756i	$-0.947962\pi$
$569$	−15429.2	+	11209.9i	−1.13677	+	0.825914i	−0.150107	+	0.988670i	$0.547962\pi$
$570$	494.157	−	1520.86i	0.0363122	−	0.111757i
$571$	−4453.84			−0.326423			−0.163211	−	0.986591i	$-0.552185\pi$
$571$	−4453.84			−0.326423			−0.163211	+	0.986591i	$0.552185\pi$
$572$	1385.57	+	1408.09i	0.101282	+	0.102928i
$573$	8308.37			0.605737
$574$	712.539	−	2192.97i	0.0518133	−	0.159465i
$575$	−3972.34	+	2886.08i	−0.288101	+	0.209318i
$576$	4939.13	+	3588.49i	0.357287	+	0.259584i
$577$	983.969	+	3028.35i	0.0709934	+	0.218495i	0.980258	−	0.197724i	$-0.0633550\pi$
$577$	983.969	+	3028.35i	0.0709934	+	0.218495i	−0.909264	+	0.416219i	$0.863355\pi$
$578$	1310.83	+	4034.33i	0.0943313	+	0.290322i
$579$	−5403.40	−	3925.80i	−0.387837	−	0.281780i
$580$	−3581.65	+	2602.22i	−0.256413	+	0.186295i
$581$	−1411.92	+	4345.45i	−0.100820	+	0.310292i
$582$	1071.66			0.0763262
$583$	−12411.6	−	2068.48i	−0.881710	−	0.146943i
$584$	560.724			0.0397310
$585$	−368.606	+	1134.45i	−0.0260512	+	0.0801775i
$586$	8118.63	−	5898.53i	0.572317	−	0.415812i
$587$	−19347.8	−	14057.0i	−1.36042	−	0.988405i	−0.998418	−	0.0562293i	$-0.982092\pi$
$587$	−19347.8	−	14057.0i	−1.36042	−	0.988405i	−0.362005	−	0.932176i	$-0.617908\pi$
$588$	850.291	+	2616.93i	0.0596350	+	0.183538i
$589$	−1225.85	−	3772.79i	−0.0857563	−	0.263931i
$590$	−5191.96	−	3772.18i	−0.362288	−	0.263217i
$591$	8421.89	−	6118.86i	0.586176	−	0.425882i
$592$	240.693	−	740.777i	0.0167102	−	0.0514286i
$593$	6201.48			0.429451			0.214725	−	0.976674i	$-0.431114\pi$
$593$	6201.48			0.429451			0.214725	+	0.976674i	$0.431114\pi$
$594$	892.850	+	5947.06i	0.0616735	+	0.410793i
$595$	−2142.25			−0.147603
$596$	3187.41	−	9809.84i	0.219063	−	0.674206i
$597$	−5468.87	+	3973.37i	−0.374918	+	0.272394i
$598$	2729.93	+	1983.41i	0.186681	+	0.135631i
$599$	−2639.25	−	8122.78i	−0.180028	−	0.554070i	0.819799	−	0.572651i	$-0.194085\pi$
$599$	−2639.25	−	8122.78i	−0.180028	−	0.554070i	−0.999827	+	0.0185813i	$0.994085\pi$
$600$	336.631	+	1036.04i	0.0229048	+	0.0704939i
$601$	6649.77	+	4831.34i	0.451331	+	0.327911i	0.790121	−	0.612951i	$-0.210018\pi$
$601$	6649.77	+	4831.34i	0.451331	+	0.327911i	−0.338790	+	0.940862i	$0.610018\pi$
$602$	3154.49	−	2291.87i	0.213567	−	0.155166i
$603$	−914.183	+	2813.57i	−0.0617387	+	0.190012i
$604$	13899.2			0.936340
$605$	−3824.42	−	5446.36i	−0.257000	−	0.365993i
$606$	4133.18			0.277061
$607$	−7570.64	+	23300.0i	−0.506232	+	1.55802i	0.292459	+	0.956278i	$0.405527\pi$
$607$	−7570.64	+	23300.0i	−0.506232	+	1.55802i	−0.798690	+	0.601743i	$0.794473\pi$
$608$	−14532.7	+	10558.6i	−0.969372	+	0.704290i
$609$	2388.55	+	1735.39i	0.158931	+	0.115470i
$610$	2055.55	+	6326.33i	0.136437	+	0.419911i
$611$	1543.10	+	4749.17i	0.102172	+	0.314453i
$612$	4751.30	+	3452.02i	0.313824	+	0.228006i
$613$	−7941.79	+	5770.05i	−0.523272	+	0.380180i	−0.817835	−	0.575452i	$-0.804826\pi$
$613$	−7941.79	+	5770.05i	−0.523272	+	0.380180i	0.294563	+	0.955632i	$0.404826\pi$
$614$	4672.75	−	14381.3i	0.307129	−	0.945245i
$615$	−1558.06			−0.102158
$616$	1050.87	+	6999.61i	0.0687352	+	0.457829i
$617$	−4396.62			−0.286874			−0.143437	−	0.989659i	$-0.545815\pi$
$617$	−4396.62			−0.286874			−0.143437	+	0.989659i	$0.545815\pi$
$618$	1487.94	−	4579.40i	0.0968506	−	0.298075i
$619$	6049.48	−	4395.21i	0.392810	−	0.285393i	−0.373796	−	0.927511i	$-0.621944\pi$
$619$	6049.48	−	4395.21i	0.392810	−	0.285393i	0.766606	+	0.642118i	$0.221944\pi$
$620$	865.052	+	628.497i	0.0560344	+	0.0407114i
$621$	−6019.57	−	18526.3i	−0.388981	−	1.19716i
$622$	−1959.26	−	6029.98i	−0.126301	−	0.388714i
$623$	−45.6366	−	33.1570i	−0.00293482	−	0.00213227i
$624$	−88.4355	+	64.2521i	−0.00567348	+	0.00412202i
$625$	193.136	−	594.410i	0.0123607	−	0.0380423i
$626$	−4304.19			−0.274808
$627$	−6925.21	−	1154.14i	−0.441095	−	0.0735116i
$628$	10790.9			0.685674
$629$	−2190.41	+	6741.40i	−0.138851	+	0.427340i
$630$	−1368.10	+	993.984i	−0.0865182	+	0.0628592i
$631$	−1754.36	−	1274.62i	−0.110682	−	0.0804149i	0.531068	−	0.847329i	$-0.321791\pi$
$631$	−1754.36	−	1274.62i	−0.110682	−	0.0804149i	−0.641749	+	0.766915i	$0.721791\pi$
$632$	−1455.69	−	4480.14i	−0.0916204	−	0.281979i
$633$	−666.194	−	2050.33i	−0.0418307	−	0.128742i
$634$	−9370.04	−	6807.73i	−0.586959	−	0.426451i
$635$	−2613.96	+	1899.15i	−0.163357	+	0.118686i
$636$	1105.66	−	3402.87i	0.0689344	−	0.212158i
$637$	−2741.95			−0.170549
$638$	−7188.90	−	7305.72i	−0.446099	−	0.453348i
$639$	6669.13			0.412874
$640$	1605.91	−	4942.47i	0.0991860	−	0.305263i
$641$	−17786.2	+	12922.5i	−1.09597	+	0.796266i	−0.980397	−	0.197033i	$-0.936869\pi$
$641$	−17786.2	+	12922.5i	−1.09597	+	0.796266i	−0.115569	+	0.993299i	$0.536869\pi$
$642$	−4183.97	−	3039.83i	−0.257209	−	0.186873i
$643$	8817.08	+	27136.2i	0.540765	+	1.66430i	0.730852	+	0.682536i	$0.239123\pi$
$643$	8817.08	+	27136.2i	0.540765	+	1.66430i	−0.190087	+	0.981767i	$0.560877\pi$
$644$	−2803.34	−	8627.79i	−0.171533	−	0.527923i
$645$	−2131.51	−	1548.63i	−0.130121	−	0.0945384i
$646$	6347.31	−	4611.59i	0.386581	−	0.280868i
$647$	−8800.62	+	27085.5i	−0.534757	+	1.64581i	0.209416	+	0.977827i	$0.432844\pi$
$647$	−8800.62	+	27085.5i	−0.534757	+	1.64581i	−0.744173	+	0.667987i	$0.767156\pi$
$648$	9386.60			0.569044
$649$	−12993.4	+	25000.8i	−0.785878	+	1.51212i
$650$	−429.521			−0.0259188
$651$	220.353	−	678.177i	0.0132662	−	0.0408293i
$652$	−932.113	+	677.220i	−0.0559883	+	0.0406779i
$653$	−2246.11	−	1631.90i	−0.134605	−	0.0977963i	0.518445	−	0.855111i	$-0.326511\pi$
$653$	−2246.11	−	1631.90i	−0.134605	−	0.0977963i	−0.653050	+	0.757315i	$0.726511\pi$
$654$	1315.13	+	4047.57i	0.0786327	+	0.242007i
$655$	−567.937	−	1747.93i	−0.0338796	−	0.104271i
$656$	679.561	+	493.730i	0.0404457	+	0.0293855i
$657$	475.831	−	345.711i	0.0282556	−	0.0205289i
$658$	−2187.63	+	6732.85i	−0.129609	+	0.398896i
$659$	6085.26			0.359709			0.179854	−	0.983693i	$-0.442437\pi$
$659$	6085.26			0.359709			0.179854	+	0.983693i	$0.442437\pi$
$660$	1693.00	−	845.508i	0.0998483	−	0.0498657i
$661$	−18103.8			−1.06529			−0.532645	−	0.846339i	$-0.678802\pi$
$661$	−18103.8			−1.06529			−0.532645	+	0.846339i	$0.678802\pi$
$662$	1224.13	−	3767.49i	0.0718689	−	0.221190i
$663$	804.802	−	584.723i	0.0471432	−	0.0342515i
$664$	9222.28	+	6700.38i	0.538997	+	0.391604i
$665$	−1323.85	−	4074.39i	−0.0771980	−	0.237591i
$666$	1729.09	+	5321.59i	0.100602	+	0.309621i
$667$	26859.9	+	19514.9i	1.55925	+	1.13286i
$668$	4199.00	−	3050.75i	0.243210	−	0.176702i
$669$	−119.624	+	368.165i	−0.00691320	+	0.0212767i
$670$	−1065.26			−0.0614247
$671$	26127.1	−	13048.3i	1.50317	−	0.750705i
$672$	−3229.00			−0.185359
$673$	1616.11	−	4973.89i	0.0925656	−	0.284887i	−0.894046	−	0.447975i	$-0.852145\pi$
$673$	1616.11	−	4973.89i	0.0925656	−	0.284887i	0.986612	+	0.163088i	$0.0521453\pi$
$674$	−13225.7	+	9609.00i	−0.755836	+	0.549147i
$675$	2006.00	+	1457.45i	0.114387	+	0.0831069i
$676$	3383.09	+	10412.1i	0.192483	+	0.592403i
$677$	−2249.73	−	6923.97i	−0.127717	−	0.393072i	0.866669	−	0.498883i	$-0.166256\pi$
$677$	−2249.73	−	6923.97i	−0.127717	−	0.393072i	−0.994386	+	0.105811i	$0.966256\pi$
$678$	2662.66	+	1934.53i	0.150824	+	0.109580i
$679$	2322.68	−	1687.53i	0.131276	−	0.0953775i
$680$	−1651.60	+	5083.09i	−0.0931409	+	0.286658i
$681$	−3833.71			−0.215724
$682$	−1141.60	+	2196.57i	−0.0640970	+	0.123330i
$683$	−4696.64			−0.263122			−0.131561	−	0.991308i	$-0.541999\pi$
$683$	−4696.64			−0.263122			−0.131561	+	0.991308i	$0.541999\pi$
$684$	−3629.31	+	11169.9i	−0.202880	+	0.624402i
$685$	3201.22	−	2325.82i	0.178558	−	0.129730i
$686$	−7211.68	−	5239.59i	−0.401375	−	0.291616i
$687$	2131.86	+	6561.20i	0.118393	+	0.364375i
$688$	438.933	+	1350.90i	0.0243229	+	0.0748582i
$689$	2884.51	+	2095.72i	0.159493	+	0.115879i
$690$	2615.11	−	1899.99i	0.144283	−	0.104828i
$691$	−3763.53	+	11582.9i	−0.207194	+	0.637679i	0.792422	+	0.609974i	$0.208820\pi$
$691$	−3763.53	+	11582.9i	−0.207194	+	0.637679i	−0.999616	+	0.0277052i	$0.991180\pi$
$692$	8154.89			0.447980
$693$	5207.35	+	5291.97i	0.285441	+	0.290080i
$694$	−15850.1			−0.866948
$695$	2950.51	−	9080.72i	0.161035	−	0.495613i
$696$	5959.19	−	4329.60i	0.324544	−	0.235795i
$697$	−6184.31	−	4493.16i	−0.336079	−	0.244176i
$698$	−5374.34	−	16540.5i	−0.291435	−	0.896946i
$699$	577.241	+	1776.56i	0.0312350	+	0.0961313i
$700$	934.204	+	678.739i	0.0504423	+	0.0366485i
$701$	−10201.7	+	7412.00i	−0.549664	+	0.399354i	−0.827662	−	0.561227i	$-0.810329\pi$
$701$	−10201.7	+	7412.00i	−0.549664	+	0.399354i	0.277998	+	0.960582i	$0.410329\pi$
$702$	526.576	−	1620.63i	0.0283110	−	0.0871323i
$703$	−14175.2			−0.760497
$704$	9520.25	+	1586.62i	0.509670	+	0.0849402i
$705$	4783.54			0.255544
$706$	−4213.27	+	12967.1i	−0.224601	+	0.691252i
$707$	8958.09	−	6508.43i	0.476526	−	0.346216i
$708$	−6481.76	−	4709.28i	−0.344067	−	0.249979i
$709$	1027.56	+	3162.51i	0.0544301	+	0.167519i	0.974576	−	0.224057i	$-0.0719302\pi$
$709$	1027.56	+	3162.51i	0.0544301	+	0.167519i	−0.920146	+	0.391576i	$0.871930\pi$
$710$	742.089	+	2283.92i	0.0392255	+	0.120724i
$711$	−3997.51	−	2904.36i	−0.210856	−	0.153196i
$712$	−113.859	+	82.7231i	−0.00599302	+	0.00435418i
$713$	2477.93	−	7626.27i	0.130153	−	0.400570i
$714$	1410.30			0.0739205
$715$	279.975	+	1864.85i	0.0146440	+	0.0975405i
$716$	7042.43			0.367581
$717$	246.480	−	758.589i	0.0128382	−	0.0395119i
$718$	17420.3	−	12656.6i	0.905461	−	0.657856i
$719$	−15422.5	−	11205.1i	−0.799945	−	0.581194i	0.110953	−	0.993826i	$-0.464610\pi$
$719$	−15422.5	−	11205.1i	−0.799945	−	0.581194i	−0.910898	+	0.412631i	$0.864610\pi$
$720$	−190.365	−	585.883i	−0.00985346	−	0.0303258i
$721$	−3986.20	−	12268.3i	−0.205900	−	0.633695i
$722$	3471.09	+	2521.89i	0.178920	+	0.129993i
$723$	−6980.72	+	5071.79i	−0.359081	+	0.260888i
$724$	2411.25	−	7421.07i	0.123775	−	0.380942i
$725$	−4226.08			−0.216486
$726$	2517.72	+	3585.49i	0.128707	+	0.183292i
$727$	8017.43			0.409009			0.204505	−	0.978866i	$-0.434442\pi$
$727$	8017.43			0.409009			0.204505	+	0.978866i	$0.434442\pi$
$728$	619.773	−	1907.47i	0.0315526	−	0.0971090i
$729$	3674.57	−	2669.73i	0.186688	−	0.135637i
$730$	171.339	+	124.485i	0.00868706	+	0.00631152i
$731$	−3994.49	−	12293.8i	−0.202109	−	0.622026i
$732$	2566.19	+	7897.93i	0.129575	+	0.398792i
$733$	−7048.24	−	5120.85i	−0.355161	−	0.258039i	0.395870	−	0.918306i	$-0.370443\pi$
$733$	−7048.24	−	5120.85i	−0.355161	−	0.258039i	−0.751031	+	0.660267i	$0.770443\pi$
$734$	−1693.21	+	1230.19i	−0.0851465	+	0.0618626i
$735$	−811.671	+	2498.06i	−0.0407332	+	0.125364i
$736$	−36310.9			−1.81853
$737$	694.370	+	4625.03i	0.0347048	+	0.231161i
$738$	−6034.27			−0.300982
$739$	7036.29	−	21655.5i	0.350249	−	1.07796i	−0.608464	−	0.793581i	$-0.708214\pi$
$739$	7036.29	−	21655.5i	0.350249	−	1.07796i	0.958713	−	0.284375i	$-0.0917859\pi$
$740$	3091.12	−	2245.83i	0.153557	−	0.111565i
$741$	1609.44	+	1169.33i	0.0797900	+	0.0579708i
$742$	1561.99	+	4807.30i	0.0772807	+	0.237846i
$743$	2610.92	+	8035.57i	0.128917	+	0.396765i	0.994594	−	0.103837i	$-0.0331120\pi$
$743$	2610.92	+	8035.57i	0.128917	+	0.396765i	−0.865678	+	0.500602i	$0.833112\pi$
$744$	−1439.28	−	1045.70i	−0.0709230	−	0.0515286i
$745$	7965.73	−	5787.44i	0.391734	−	0.284611i
$746$	7241.70	−	22287.7i	0.355412	−	1.09385i
$747$	11957.1			0.585660
$748$	9158.21	+	1526.28i	0.447670	+	0.0746074i
$749$	−13855.0			−0.675900
$750$	−127.147	+	391.317i	−0.00619032	+	0.0190518i
$751$	7661.19	−	5566.18i	0.372251	−	0.270456i	−0.385893	−	0.922544i	$-0.626106\pi$
$751$	7661.19	−	5566.18i	0.372251	−	0.270456i	0.758144	+	0.652087i	$0.226106\pi$
$752$	−2086.38	−	1515.85i	−0.101174	−	0.0735070i
$753$	3201.97	+	9854.64i	0.154962	+	0.476923i
$754$	897.479	+	2762.16i	0.0433478	+	0.133411i
$755$	10733.9	+	7798.66i	0.517415	+	0.375924i
$756$	−3706.26	+	2692.76i	−0.178301	+	0.129543i
$757$	11862.4	−	36508.7i	0.569546	−	1.75288i	−0.0844943	−	0.996424i	$-0.526927\pi$
$757$	11862.4	−	36508.7i	0.569546	−	1.75288i	0.654041	−	0.756459i	$-0.273073\pi$
$758$	19795.8			0.948567
$759$	−9953.77	−	10115.5i	−0.476020	−	0.483756i
$760$	−10688.3			−0.510138
$761$	576.611	−	1774.63i	0.0274667	−	0.0845338i	−0.936383	−	0.350979i	$-0.885849\pi$
$761$	576.611	−	1774.63i	0.0274667	−	0.0845338i	0.963850	+	0.266445i	$0.0858490\pi$
$762$	1720.84	−	1250.27i	0.0818104	−	0.0594388i
$763$	9224.00	+	6701.63i	0.437655	+	0.317975i
$764$	−6789.89	−	20897.1i	−0.321531	−	0.989570i
$765$	1732.41	+	5331.80i	0.0818762	+	0.251989i
$766$	11533.8	+	8379.77i	0.544037	+	0.395266i
$767$	6459.03	−	4692.76i	0.304071	−	0.220920i
$768$	−2352.52	+	7240.33i	−0.110533	+	0.340186i
$769$	−29983.8			−1.40604			−0.703019	−	0.711171i	$-0.748165\pi$
$769$	−29983.8			−1.40604			−0.703019	+	0.711171i	$0.748165\pi$
$770$	−1232.86	+	2372.16i	−0.0577002	+	0.111022i
$771$	14680.8			0.685755
$772$	−5458.28	+	16798.9i	−0.254466	+	0.783166i
$773$	−5652.66	+	4106.90i	−0.263017	+	0.191093i	−0.711476	−	0.702710i	$-0.751973\pi$
$773$	−5652.66	+	4106.90i	−0.263017	+	0.191093i	0.448459	+	0.893803i	$0.351973\pi$
$774$	−8255.20	−	5997.75i	−0.383368	−	0.278533i
$775$	315.413	+	970.741i	0.0146193	+	0.0449936i
$776$	−2213.43	−	6812.25i	−0.102394	−	0.315136i
$777$	−2061.43	−	1497.72i	−0.0951781	−	0.0691509i
$778$	−13395.3	+	9732.27i	−0.617282	+	0.448482i
$779$	4723.92	−	14538.7i	0.217268	−	0.668683i
$780$	−536.224			−0.0246152
$781$	9432.35	−	4710.66i	0.432159	−	0.215827i
$782$	15859.2			0.725222
$783$	5181.01	−	15945.5i	0.236467	−	0.727772i
$784$	1145.62	−	832.344i	0.0521877	−	0.0379166i
$785$	8333.50	+	6054.64i	0.378899	+	0.275286i
$786$	373.889	+	1150.71i	0.0169672	+	0.0522195i
$787$	5528.50	+	17015.0i	0.250406	+	0.770671i	0.994700	+	0.102819i	$0.0327863\pi$
$787$	5528.50	+	17015.0i	0.250406	+	0.770671i	−0.744294	+	0.667852i	$0.767214\pi$
$788$	−22272.7	−	16182.1i	−1.00690	−	0.731553i
$789$	−1240.53	+	901.301i	−0.0559749	+	0.0406681i
$790$	549.818	−	1692.17i	0.0247616	−	0.0762083i
$791$	8817.21			0.396339
$792$	16571.4	−	8276.00i	0.743483	−	0.371306i
$793$	−8275.25			−0.370571
$794$	−5055.39	+	15558.9i	−0.225956	+	0.695422i
$795$	2763.18	−	2007.57i	0.123270	−	0.0895612i
$796$	14463.1	+	10508.1i	0.644010	+	0.467901i
$797$	−668.935	−	2058.77i	−0.0297301	−	0.0914999i	0.935090	−	0.354409i	$-0.115318\pi$
$797$	−668.935	−	2058.77i	−0.0297301	−	0.0914999i	−0.964821	+	0.262909i	$0.915318\pi$
$798$	871.528	+	2682.29i	0.0386614	+	0.118987i
$799$	18987.0	+	13794.9i	0.840692	+	0.610798i
$800$	3739.26	−	2716.74i	0.165254	−	0.120064i
$801$	−45.6180	+	140.398i	−0.00201228	+	0.00619315i
$802$	−8286.59			−0.364850
$803$	428.793	−	825.047i	0.0188441	−	0.0362581i
$804$	−1329.89			−0.0583355
$805$	2676.01	−	8235.92i	0.117164	−	0.360594i
$806$	567.491	−	412.306i	0.0248003	−	0.0180185i
$807$	5448.29	+	3958.42i	0.237657	+	0.172668i
$808$	−8536.74	−	26273.4i	−0.371685	−	1.14393i
$809$	7640.70	+	23515.7i	0.332055	+	1.02196i	0.968154	+	0.250354i	$0.0805470\pi$
$809$	7640.70	+	23515.7i	0.332055	+	1.02196i	−0.636099	+	0.771608i	$0.719453\pi$
$810$	2868.25	+	2083.90i	0.124420	+	0.0903962i
$811$	−21074.2	+	15311.3i	−0.912471	+	0.662949i	−0.941639	−	0.336625i	$-0.890714\pi$
$811$	−21074.2	+	15311.3i	−0.912471	+	0.662949i	0.0291675	+	0.999575i	$0.490714\pi$
$812$	2412.82	−	7425.88i	0.104277	−	0.320933i
$813$	−2193.77			−0.0946357
$814$	6204.34	+	6305.16i	0.267152	+	0.271494i
$815$	−1099.82			−0.0472702
$816$	−158.759	+	488.610i	−0.00681088	+	0.0209617i
$817$	20913.3	−	15194.4i	0.895550	−	0.650655i
$818$	−16203.5	−	11772.5i	−0.692594	−	0.503199i
$819$	−650.098	−	2000.80i	−0.0277366	−	0.0853644i
$820$	1273.30	+	3918.81i	0.0542263	+	0.166891i
$821$	−10384.4	−	7544.72i	−0.441436	−	0.320722i	0.344769	−	0.938687i	$-0.387957\pi$
$821$	−10384.4	−	7544.72i	−0.441436	−	0.320722i	−0.786205	+	0.617966i	$0.787957\pi$
$822$	−2107.46	+	1531.16i	−0.0894233	+	0.0649698i
$823$	2321.77	−	7145.67i	0.0983375	−	0.302652i	−0.889772	−	0.456406i	$-0.849136\pi$
$823$	2321.77	−	7145.67i	0.0983375	−	0.302652i	0.988109	+	0.153754i	$0.0491365\pi$
$824$	−32183.2			−1.36062
$825$	1781.86	+	296.959i	0.0751956	+	0.0125319i
$826$	11318.5			0.476783
$827$	3100.60	−	9542.67i	0.130373	−	0.401247i	−0.864469	−	0.502687i	$-0.832345\pi$
$827$	3100.60	−	9542.67i	0.130373	−	0.401247i	0.994842	+	0.101440i	$0.0323450\pi$
$828$	−19206.5	+	13954.4i	−0.806127	+	0.585686i
$829$	−1167.06	−	847.922i	−0.0488949	−	0.0355242i	0.563069	−	0.826410i	$-0.309620\pi$
$829$	−1167.06	−	847.922i	−0.0488949	−	0.0355242i	−0.611964	+	0.790885i	$0.709620\pi$
$830$	1330.50	+	4094.85i	0.0556412	+	0.171246i
$831$	4681.16	+	14407.1i	0.195412	+	0.601418i
$832$	−2212.54	−	1607.50i	−0.0921947	−	0.0669834i
$833$	−10425.7	+	7574.70i	−0.433648	+	0.315063i
$834$	−1942.40	+	5978.10i	−0.0806473	+	0.248207i
$835$	4954.51			0.205339
$836$	2756.65	+	18361.4i	0.114044	+	0.759621i
$837$	−4049.40			−0.167226
$838$	−416.987	+	1283.35i	−0.0171892	+	0.0529030i
$839$	26763.2	−	19444.6i	1.10127	−	0.800122i	0.120006	−	0.992773i	$-0.461709\pi$
$839$	26763.2	−	19444.6i	1.10127	−	0.800122i	0.981267	+	0.192652i	$0.0617087\pi$
$840$	−1554.34	−	1129.29i	−0.0638451	−	0.0463861i
$841$	1293.73	+	3981.68i	0.0530455	+	0.163257i
$842$	6852.50	+	21089.8i	0.280467	+	0.863187i
$843$	−7905.05	−	5743.35i	−0.322971	−	0.234652i
$844$	−4612.54	+	3351.21i	−0.188116	+	0.136675i
$845$	−3229.43	+	9939.17i	−0.131474	+	0.404636i
$846$	18526.4			0.752896
$847$	11102.8	+	3806.45i	0.450411	+	0.154417i
$848$	−1841.36			−0.0745667
$849$	3530.72	−	10866.4i	0.142725	−	0.439264i
$850$	−1633.16	+	1186.56i	−0.0659024	+	0.0478809i
$851$	−23181.3	−	16842.2i	−0.933777	−	0.678429i
$852$	926.441	+	2851.29i	0.0372528	+	0.114652i
$853$	1026.02	+	3157.77i	0.0411844	+	0.126753i	0.969535	−	0.244954i	$-0.0787728\pi$
$853$	1026.02	+	3157.77i	0.0411844	+	0.126753i	−0.928350	+	0.371706i	$0.878773\pi$
$854$	−9491.17	−	6895.74i	−0.380306	−	0.276308i
$855$	−9070.10	+	6589.81i	−0.362796	+	0.263587i
$856$	−10681.7	+	32874.8i	−0.426509	+	1.31266i
$857$	14357.0			0.572259			0.286130	−	0.958191i	$-0.407631\pi$
$857$	14357.0			0.572259			0.286130	+	0.958191i	$0.407631\pi$
$858$	−184.316	−	1227.68i	−0.00733385	−	0.0488490i
$859$	−36024.5			−1.43090			−0.715448	−	0.698666i	$-0.753778\pi$
$859$	−36024.5			−1.43090			−0.715448	+	0.698666i	$0.753778\pi$
$860$	−2153.16	+	6626.73i	−0.0853745	+	0.262756i
$861$	2223.10	−	1615.17i	0.0879941	−	0.0639314i
$862$	−11359.2	−	8252.95i	−0.448835	−	0.326098i
$863$	7711.52	+	23733.6i	0.304175	+	0.936155i	0.979984	+	0.199078i	$0.0637947\pi$
$863$	7711.52	+	23733.6i	0.304175	+	0.936155i	−0.675808	+	0.737077i	$0.736205\pi$
$864$	5666.37	+	17439.3i	0.223118	+	0.686686i
$865$	6297.79	+	4575.61i	0.247551	+	0.179856i
$866$	−10260.0	+	7454.33i	−0.402597	+	0.292504i
$867$	−1562.15	+	4807.79i	−0.0611917	+	0.188329i
$868$	−1885.82			−0.0737431
$869$	−7705.26	−	1284.14i	−0.300786	−	0.0501281i
$870$	2782.15			0.108418
$871$	409.519	−	1260.37i	0.0159311	−	0.0490310i
$872$	23012.9	−	16719.8i	0.893710	−	0.649318i
$873$	−6078.38	−	4416.20i	−0.235649	−	0.171209i
$874$	9800.55	+	30163.0i	0.379300	+	1.16737i
$875$	340.627	+	1048.34i	0.0131603	+	0.0405033i
$876$	213.904	+	155.410i	0.00825017	+	0.00599410i
$877$	−19479.0	+	14152.3i	−0.750009	+	0.544914i	−0.895830	−	0.444398i	$-0.853418\pi$
$877$	−19479.0	+	14152.3i	−0.750009	+	0.544914i	0.145821	+	0.989311i	$0.453418\pi$
$878$	−892.854	+	2747.92i	−0.0343193	+	0.105624i
$879$	11959.1			0.458898
$880$	−683.071	−	694.171i	−0.0261663	−	0.0265915i
$881$	−37851.9			−1.44752			−0.723759	−	0.690052i	$-0.757587\pi$
$881$	−37851.9			−1.44752			−0.723759	+	0.690052i	$0.757587\pi$
$882$	−3143.55	+	9674.85i	−0.120010	+	0.369353i
$883$	27507.3	−	19985.2i	1.04835	−	0.761672i	0.0764528	−	0.997073i	$-0.475641\pi$
$883$	27507.3	−	19985.2i	1.04835	−	0.761672i	0.971898	+	0.235402i	$0.0756405\pi$
$884$	−2128.40	−	1546.37i	−0.0809795	−	0.0588350i
$885$	−2363.36	−	7273.68i	−0.0897667	−	0.276274i
$886$	−837.850	−	2578.64i	−0.0317699	−	0.0977777i
$887$	−11980.7	−	8704.49i	−0.453521	−	0.329502i	0.337464	−	0.941339i	$-0.390431\pi$
$887$	−11980.7	−	8704.49i	−0.453521	−	0.329502i	−0.790984	+	0.611837i	$0.790431\pi$
$888$	−5143.05	+	3736.64i	−0.194357	+	0.141209i
$889$	1760.92	−	5419.56i	0.0664335	−	0.204461i
$890$	−53.1568			−0.00200204
$891$	7178.06	−	13811.4i	0.269892	−	0.519304i
$892$	1023.77			0.0384285
$893$	−14503.4	+	44636.7i	−0.543490	+	1.67269i
$894$	−5244.07	+	3810.04i	−0.196183	+	0.142536i
$895$	5438.67	+	3951.42i	0.203122	+	0.147577i
$896$	2832.28	+	8716.88i	0.105603	+	0.325012i
$897$	1242.65	+	3824.49i	0.0462553	+	0.142359i
$898$	3040.93	+	2209.36i	0.113003	+	0.0821018i
$899$	5583.57	−	4056.70i	0.207144	−	0.150499i
$900$	933.823	−	2874.01i	0.0345860	−	0.106445i
$901$	16757.2			0.619604
$902$	−8534.45	+	4262.23i	−0.315040	+	0.157336i
$903$	4646.71			0.171243
$904$	6797.76	−	20921.3i	0.250100	−	0.769727i
$905$	6026.01	−	4378.15i	0.221339	−	0.160812i
$906$	−7066.46	−	5134.08i	−0.259125	−	0.188265i
$907$	5074.65	+	15618.2i	0.185778	+	0.571767i	0.999961	−	0.00884224i	$-0.00281461\pi$
$907$	5074.65	+	15618.2i	0.185778	+	0.571767i	−0.814183	+	0.580609i	$0.802815\pi$
$908$	3133.04	+	9642.51i	0.114508	+	0.352421i
$909$	−23443.0	−	17032.3i	−0.855397	−	0.621482i
$910$	612.857	−	445.266i	0.0223253	−	0.0162203i
$911$	−7310.67	+	22499.9i	−0.265876	+	0.818283i	0.725614	+	0.688102i	$0.241556\pi$
$911$	−7310.67	+	22499.9i	−0.265876	+	0.818283i	−0.991490	+	0.130181i	$0.958444\pi$
$912$	−1027.41			−0.0373036
$913$	16911.3	−	8445.76i	0.613015	−	0.306149i
$914$	10577.9			0.382807
$915$	−2449.64	+	7539.21i	−0.0885055	+	0.272392i
$916$	14760.4	−	10724.1i	0.532422	−	0.386827i
$917$	2622.36	+	1905.26i	0.0944361	+	0.0686119i
$918$	−2474.85	−	7616.80i	−0.0889784	−	0.273847i
$919$	−3440.64	−	10589.2i	−0.123500	−	0.380094i	0.870125	−	0.492831i	$-0.164038\pi$
$919$	−3440.64	−	10589.2i	−0.123500	−	0.380094i	−0.993625	+	0.112738i	$0.964038\pi$
$920$	−17478.9	−	12699.2i	−0.626374	−	0.455087i
$921$	14578.8	−	10592.1i	0.521594	−	0.378960i
$922$	1279.51	−	3937.93i	0.0457033	−	0.140660i
$923$	−2987.51			−0.106539
$924$	−1539.13	+	2961.46i	−0.0547983	+	0.105438i
$925$	3647.29			0.129646
$926$	6609.26	−	20341.2i	0.234550	−	0.721872i
$927$	−27310.7	+	19842.4i	−0.967638	+	0.703030i
$928$	−25283.9	−	18369.8i	−0.894380	−	0.649805i
$929$	119.554	+	367.951i	0.00422223	+	0.0129947i	0.953145	−	0.302512i	$-0.0978254\pi$
$929$	119.554	+	367.951i	0.00422223	+	0.0129947i	−0.948923	+	0.315507i	$0.897825\pi$
$930$	−207.645	−	639.066i	−0.00732146	−	0.0225331i
$931$	−20849.3	−	15147.9i	−0.733951	−	0.533246i
$932$	3996.65	−	2903.74i	0.140466	−	0.102055i
$933$	2334.89	−	7186.04i	0.0819301	−	0.252155i
$934$	−21367.9			−0.748587
$935$	6216.25	+	6317.26i	0.217426	+	0.220959i
$936$	−5248.66			−0.183288
$937$	12580.0	−	38717.4i	0.438604	−	1.34988i	−0.450744	−	0.892653i	$-0.648841\pi$
$937$	12580.0	−	38717.4i	0.438604	−	1.34988i	0.889348	−	0.457231i	$-0.151159\pi$
$938$	1519.95	−	1104.31i	0.0529085	−	0.0384403i
$939$	−4149.76	−	3014.97i	−0.144220	−	0.104782i
$940$	−3909.28	−	12031.5i	−0.135645	−	0.417473i
$941$	10208.0	+	31417.0i	0.353636	+	1.08838i	0.956796	+	0.290760i	$0.0939081\pi$
$941$	10208.0	+	31417.0i	0.353636	+	1.08838i	−0.603160	+	0.797620i	$0.706092\pi$
$942$	−5486.18	−	3985.94i	−0.189755	−	0.137865i
$943$	24999.3	−	18163.0i	0.863296	−	0.627221i
$944$	−1274.14	+	3921.40i	−0.0439298	+	0.135202i
$945$	−4373.11			−0.150537
$946$	−15912.0	−	2651.85i	−0.546875	−	0.0911406i
$947$	−11956.8			−0.410288			−0.205144	−	0.978732i	$-0.565766\pi$
$947$	−11956.8			−0.410288			−0.205144	+	0.978732i	$0.565766\pi$
$948$	686.405	−	2112.54i	0.0235162	−	0.0723755i
$949$	−213.154	+	154.865i	−0.00729111	+	0.00529730i
$950$	−3266.00	−	2372.89i	−0.111540	−	0.0810387i
$951$	−4265.21	−	13127.0i	−0.145435	−	0.447604i
$952$	−2912.87	−	8964.88i	−0.0991665	−	0.305203i
$953$	37268.2	+	27076.9i	1.26677	+	0.920365i	0.999069	−	0.0431366i	$-0.0137351\pi$
$953$	37268.2	+	27076.9i	1.26677	+	0.920365i	0.267704	+	0.963501i	$0.413735\pi$
$954$	10701.6	−	7775.20i	0.363185	−	0.263869i
$955$	6481.49	−	19948.0i	0.219619	−	0.675918i
$956$	−2109.43			−0.0713637
$957$	−1813.49	−	12079.2i	−0.0612559	−	0.408011i
$958$	8502.02			0.286730
$959$	−2156.54	+	6637.14i	−0.0726155	+	0.223487i
$960$	−2119.48	+	1539.89i	−0.0712562	+	0.0517706i
$961$	22752.9	+	16530.9i	0.763750	+	0.554897i
$962$	−774.565	−	2383.87i	−0.0259594	−	0.0798949i
$963$	11204.3	+	34483.3i	0.374926	+	1.15390i
$964$	18461.4	+	13413.0i	0.616806	+	0.448136i
$965$	−13640.9	+	9910.71i	−0.455043	+	0.330608i
$966$	−1761.69	+	5421.94i	−0.0586766	+	0.180588i
$967$	−14540.7			−0.483555			−0.241778	−	0.970332i	$-0.577730\pi$
$967$	−14540.7			−0.483555			−0.241778	+	0.970332i	$0.577730\pi$
$968$	17591.8	−	23410.0i	0.584113	−	0.777299i
$969$	9349.88			0.309970
$970$	836.021	−	2573.01i	0.0276732	−	0.0851694i
$971$	25035.5	−	18189.4i	0.827423	−	0.601158i	−0.0914062	−	0.995814i	$-0.529136\pi$
$971$	25035.5	−	18189.4i	0.827423	−	0.601158i	0.918829	+	0.394656i	$0.129136\pi$
$972$	14928.6	+	10846.3i	0.492629	+	0.357916i
$973$	5203.71	+	16015.4i	0.171452	+	0.527676i
$974$	−2038.20	−	6272.93i	−0.0670515	−	0.206363i
$975$	−414.110	−	300.869i	−0.0136022	−	0.00988258i
$976$	3457.51	−	2512.03i	0.113394	−	0.0823854i
$977$	1417.95	−	4364.01i	0.0464323	−	0.142904i	−0.925153	−	0.379596i	$-0.876063\pi$
$977$	1417.95	−	4364.01i	0.0464323	−	0.142904i	0.971585	+	0.236692i	$0.0760631\pi$
$978$	724.046			0.0236732
$979$	34.6493	+	230.791i	0.00113115	+	0.00753432i
$980$	6946.43			0.226424
$981$	9220.24	−	28377.0i	0.300081	−	0.923554i
$982$	56.7620	−	41.2400i	0.00184455	−	0.00134014i
$983$	1417.66	+	1029.99i	0.0459983	+	0.0334198i	0.610547	−	0.791980i	$-0.290950\pi$
$983$	1417.66	+	1029.99i	0.0459983	+	0.0334198i	−0.564549	+	0.825400i	$0.690950\pi$
$984$	−2118.53	−	6520.17i	−0.0686344	−	0.211235i
$985$	−8121.03	−	24994.0i	−0.262698	−	0.808501i
$986$	11043.0	+	8023.21i	0.356674	+	0.259139i
$987$	−6825.34	+	4958.90i	−0.220114	+	0.159922i
$988$	1625.79	−	5003.67i	0.0523515	−	0.161121i
$989$	52253.4			1.68004
$990$	6901.03	+	1150.11i	0.221545	+	0.0369220i
$991$	−23938.4			−0.767335			−0.383668	−	0.923471i	$-0.625339\pi$
$991$	−23938.4			−0.767335			−0.383668	+	0.923471i	$0.625339\pi$
$992$	−2332.53	+	7178.80i	−0.0746552	+	0.229765i
$993$	3819.24	−	2774.84i	0.122054	−	0.0886777i
$994$	−3426.48	−	2489.48i	−0.109337	−	0.0794382i
$995$	5273.50	+	16230.2i	0.168021	+	0.517117i
$996$	1661.02	+	5112.10i	0.0528428	+	0.162634i
$997$	−25846.8	−	18778.8i	−0.821039	−	0.596520i	0.0959709	−	0.995384i	$-0.469404\pi$
$997$	−25846.8	−	18778.8i	−0.821039	−	0.596520i	−0.917010	+	0.398864i	$0.869404\pi$
$998$	−213.256	+	154.939i	−0.00676402	+	0.00491435i
$999$	−4471.44	+	13761.7i	−0.141612	+	0.435836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.4.g.b.31.3	yes	24
11.4	even	5		605.4.a.p.1.6		12
11.5	even	5	inner	55.4.g.b.16.3	✓	24
11.7	odd	10		605.4.a.t.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.4.g.b.16.3	✓	24	11.5	even	5	inner
55.4.g.b.31.3	yes	24	1.1	even	1	trivial
605.4.a.p.1.6		12	11.4	even	5
605.4.a.t.1.7		12	11.7	odd	10

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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	55.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.513572 + 1.58061i) q^{2} +(-1.60233 + 1.16416i) q^{3} +(4.23755 + 3.07876i) q^{4} +(1.54508 + 4.75528i) q^{5} +(-1.01717 - 3.13054i) q^{6} +(-7.13418 - 5.18329i) q^{7} +(-17.7990 + 12.9317i) q^{8} +(-7.13127 + 21.9478i) q^{9} -8.30978 q^{10} +(5.41658 + 36.0785i) q^{11} -10.3741 q^{12} +(3.19453 - 9.83177i) q^{13} +(11.8567 - 8.61439i) q^{14} +(-8.01163 - 5.82079i) q^{15} +(1.64980 + 5.07758i) q^{16} +(-15.0140 - 46.2082i) q^{17} +(-31.0286 - 22.5436i) q^{18} +(78.6063 - 57.1108i) q^{19} +(-8.09301 + 24.9077i) q^{20} +17.4655 q^{21} +(-59.8080 - 9.96743i) q^{22} +196.403 q^{23} +(13.4652 - 41.4418i) q^{24} +(-20.2254 + 14.6946i) q^{25} +(13.8996 + 10.0986i) q^{26} +(-30.6490 - 94.3280i) q^{27} +(-14.2734 - 43.9289i) q^{28} +(136.759 + 99.3611i) q^{29} +(13.3150 - 9.67390i) q^{30} +(12.6165 - 38.8296i) q^{31} -184.879 q^{32} +(-50.6802 - 51.5038i) q^{33} +80.7481 q^{34} +(13.6251 - 41.9337i) q^{35} +(-97.7912 + 71.0495i) q^{36} +(-118.029 - 85.7530i) q^{37} +(49.9001 + 153.577i) q^{38} +(6.32704 + 19.4726i) q^{39} +(-88.9951 - 64.6587i) q^{40} +(127.285 - 92.4781i) q^{41} +(-8.96978 + 27.6061i) q^{42} +266.051 q^{43} +(-88.1242 + 169.561i) q^{44} -115.386 q^{45} +(-100.867 + 310.438i) q^{46} +(-390.791 + 283.926i) q^{47} +(-8.55463 - 6.21530i) q^{48} +(-81.9627 - 252.255i) q^{49} +(-12.8393 - 39.5153i) q^{50} +(77.8509 + 56.5620i) q^{51} +(43.8067 - 31.8274i) q^{52} +(-106.579 + 328.016i) q^{53} +164.837 q^{54} +(-163.195 + 81.5018i) q^{55} +194.010 q^{56} +(-59.4669 + 183.020i) q^{57} +(-227.287 + 165.134i) q^{58} +(624.802 + 453.945i) q^{59} +(-16.0289 - 49.3318i) q^{60} +(-247.365 - 761.311i) q^{61} +(54.8951 + 39.8836i) q^{62} +(164.638 - 119.616i) q^{63} +(81.7505 - 251.602i) q^{64} +51.6887 q^{65} +(107.436 - 53.6549i) q^{66} +128.194 q^{67} +(78.6417 - 242.034i) q^{68} +(-314.702 + 228.645i) q^{69} +(59.2835 + 43.0720i) q^{70} +(-89.3032 - 274.847i) q^{71} +(-156.894 - 482.869i) q^{72} +(-20.6190 - 14.9806i) q^{73} +(196.159 - 142.518i) q^{74} +(15.3009 - 47.0912i) q^{75} +508.929 q^{76} +(148.363 - 285.467i) q^{77} -34.0281 q^{78} +(-66.1652 + 203.635i) q^{79} +(-21.5962 + 15.6906i) q^{80} +(-345.165 - 250.777i) q^{81} +(80.8020 + 248.683i) q^{82} +(-160.112 - 492.774i) q^{83} +(74.0108 + 53.7720i) q^{84} +(196.535 - 142.791i) q^{85} +(-136.637 + 420.525i) q^{86} -334.804 q^{87} +(-562.968 - 572.117i) q^{88} +6.39690 q^{89} +(59.2593 - 182.381i) q^{90} +(-73.7513 + 53.5834i) q^{91} +(832.270 + 604.680i) q^{92} +(24.9881 + 76.9053i) q^{93} +(-248.078 - 763.505i) q^{94} +(393.032 + 285.554i) q^{95} +(296.237 - 215.229i) q^{96} +(-100.607 + 309.636i) q^{97} +440.812 q^{98} +(-830.472 - 138.404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 4 q^{3} - 36 q^{4} - 30 q^{5} + 30 q^{6} + 81 q^{7} - 10 q^{8} - 48 q^{9} - 70 q^{10} - 72 q^{11} + 10 q^{12} + 65 q^{13} - 47 q^{14} + 20 q^{15} - 60 q^{16} - 142 q^{17} + 283 q^{18} - 17 q^{19}+ \cdots + 5980 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 4 * q^3 - 36 * q^4 - 30 * q^5 + 30 * q^6 + 81 * q^7 - 10 * q^8 - 48 * q^9 - 70 * q^10 - 72 * q^11 + 10 * q^12 + 65 * q^13 - 47 * q^14 + 20 * q^15 - 60 * q^16 - 142 * q^17 + 283 * q^18 - 17 * q^19 - 55 * q^20 - 200 * q^21 + 87 * q^22 - 182 * q^23 + 70 * q^24 - 150 * q^25 + 736 * q^26 + 643 * q^27 - 52 * q^28 + 80 * q^29 - 210 * q^31 - 504 * q^32 + 993 * q^33 + 1046 * q^34 + 80 * q^35 - 2242 * q^36 + 560 * q^37 + 187 * q^38 - 1294 * q^39 - 50 * q^40 + 293 * q^41 - 2231 * q^42 - 3658 * q^43 + 1293 * q^44 + 1310 * q^45 - 57 * q^46 - 1824 * q^47 + 1977 * q^48 + 73 * q^49 + 150 * q^50 - 1769 * q^51 + 3342 * q^52 + 838 * q^53 + 2784 * q^54 + 290 * q^55 + 8652 * q^56 + 273 * q^57 - 3896 * q^58 + 1653 * q^59 - 875 * q^60 - 888 * q^61 - 2200 * q^62 + 3149 * q^63 - 4644 * q^64 - 2050 * q^65 - 4497 * q^66 + 3966 * q^67 - 3783 * q^68 - 3384 * q^69 - 235 * q^70 + 1664 * q^71 - 4264 * q^72 - 2210 * q^73 + 1552 * q^74 - 25 * q^75 + 3048 * q^76 - 1304 * q^77 + 10064 * q^78 + 12 * q^79 - 275 * q^80 + 5005 * q^81 + 4099 * q^82 + 1945 * q^83 - 7584 * q^84 + 1865 * q^85 - 5156 * q^86 - 3844 * q^87 + 619 * q^88 + 4568 * q^89 - 210 * q^90 - 4885 * q^91 + 3390 * q^92 + 2844 * q^93 - 8932 * q^94 - 85 * q^95 - 1249 * q^96 - 3255 * q^97 - 7778 * q^98 + 5980 * q^99

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