LMFDB - Embedded newform 138.5.h.a.7.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,5,Mod(7,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("138.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	138.h (of order $22$, degree $10$, 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:	$14.2650549056$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			7.5
Character	$\chi$	$=$	138.7
Dual form			138.5.h.a.79.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85223 + 2.13758i) q^{2} +(4.37128 - 2.80925i) q^{3} +(-1.13852 - 7.91857i) q^{4} +(-19.2776 + 8.80377i) q^{5} +(-2.09159 + 14.5473i) q^{6} +(14.6430 + 49.8696i) q^{7} +(19.0354 + 12.2333i) q^{8} +(11.2162 - 24.5601i) q^{9} +O(q^{10})$	\(q+(-1.85223 + 2.13758i) q^{2} +(4.37128 - 2.80925i) q^{3} +(-1.13852 - 7.91857i) q^{4} +(-19.2776 + 8.80377i) q^{5} +(-2.09159 + 14.5473i) q^{6} +(14.6430 + 49.8696i) q^{7} +(19.0354 + 12.2333i) q^{8} +(11.2162 - 24.5601i) q^{9} +(16.8876 - 57.5140i) q^{10} +(78.2998 - 67.8472i) q^{11} +(-27.2220 - 31.4159i) q^{12} +(-156.158 - 45.8521i) q^{13} +(-133.723 - 61.0690i) q^{14} +(-59.5357 + 92.6393i) q^{15} +(-61.4076 + 18.0309i) q^{16} +(105.428 + 15.1583i) q^{17} +(31.7242 + 69.4664i) q^{18} +(-664.579 + 95.5520i) q^{19} +(91.6612 + 142.628i) q^{20} +(204.105 + 176.858i) q^{21} +293.041i q^{22} +(-371.823 + 376.283i) q^{23} +117.576 q^{24} +(-115.170 + 132.913i) q^{25} +(387.253 - 248.872i) q^{26} +(-19.9662 - 138.868i) q^{27} +(378.224 - 172.729i) q^{28} +(-126.244 + 878.048i) q^{29} +(-87.7507 - 298.851i) q^{30} +(-1120.67 - 720.209i) q^{31} +(75.1981 - 164.661i) q^{32} +(151.671 - 516.543i) q^{33} +(-227.679 + 197.285i) q^{34} +(-721.322 - 832.450i) q^{35} +(-207.250 - 60.8542i) q^{36} +(-1732.66 - 791.278i) q^{37} +(1026.70 - 1597.58i) q^{38} +(-811.421 + 238.255i) q^{39} +(-474.655 - 68.2451i) q^{40} +(940.575 + 2059.57i) q^{41} +(-756.097 + 108.710i) q^{42} +(-103.156 - 160.514i) q^{43} +(-626.398 - 542.777i) q^{44} +572.203i q^{45} +(-115.636 - 1491.76i) q^{46} -1985.50 q^{47} +(-217.776 + 251.327i) q^{48} +(-252.707 + 162.405i) q^{49} +(-70.7920 - 492.369i) q^{50} +(503.439 - 229.913i) q^{51} +(-185.295 + 1288.75i) q^{52} +(-994.260 - 3386.14i) q^{53} +(333.824 + 214.536i) q^{54} +(-912.119 + 1997.26i) q^{55} +(-331.334 + 1128.42i) q^{56} +(-2636.63 + 2284.65i) q^{57} +(-1643.07 - 1896.20i) q^{58} +(3430.68 + 1007.34i) q^{59} +(801.354 + 365.966i) q^{60} +(529.316 - 823.632i) q^{61} +(3615.24 - 1061.53i) q^{62} +(1389.04 + 199.714i) q^{63} +(212.692 + 465.732i) q^{64} +(3414.02 - 490.862i) q^{65} +(823.225 + 1280.96i) q^{66} +(2715.42 + 2352.93i) q^{67} -852.098i q^{68} +(-568.269 + 2689.38i) q^{69} +3115.48 q^{70} +(4420.32 - 5101.33i) q^{71} +(513.956 - 330.299i) q^{72} +(438.813 + 3052.01i) q^{73} +(4900.69 - 2238.07i) q^{74} +(-130.053 + 904.540i) q^{75} +(1513.27 + 5153.73i) q^{76} +(4530.06 + 2911.29i) q^{77} +(993.646 - 2175.78i) q^{78} +(-1779.17 + 6059.30i) q^{79} +(1025.05 - 888.210i) q^{80} +(-477.393 - 550.941i) q^{81} +(-6144.66 - 1804.24i) q^{82} +(-3971.87 - 1813.89i) q^{83} +(1168.09 - 1817.58i) q^{84} +(-2165.85 + 635.950i) q^{85} +(534.180 + 76.8035i) q^{86} +(1914.81 + 4192.85i) q^{87} +(2320.46 - 333.632i) q^{88} +(5751.74 + 8949.88i) q^{89} +(-1223.13 - 1059.85i) q^{90} -8458.95i q^{91} +(3402.95 + 2515.90i) q^{92} -6922.00 q^{93} +(3677.59 - 4244.17i) q^{94} +(11970.2 - 7692.81i) q^{95} +(-133.862 - 931.030i) q^{96} +(11247.7 - 5136.67i) q^{97} +(120.916 - 840.991i) q^{98} +(-788.104 - 2684.04i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 128 q^{4} - 432 q^{9}+O(q^{10}) $ 160 * q - 128 * q^4 - 432 * q^9	$ 160 q - 128 q^{4} - 432 q^{9} + 208 q^{13} - 1024 q^{16} - 1980 q^{17} - 3828 q^{19} - 3168 q^{20} + 3120 q^{23} + 9768 q^{25} + 4416 q^{26} + 5280 q^{28} - 828 q^{29} - 7748 q^{31} + 16464 q^{35} - 3456 q^{36} - 3520 q^{37} - 9072 q^{39} - 5472 q^{41} - 7216 q^{43} - 1280 q^{46} + 6960 q^{47} + 13888 q^{49} - 7296 q^{50} + 17424 q^{51} + 1664 q^{52} + 14784 q^{53} + 37316 q^{55} - 15840 q^{57} - 9984 q^{58} - 29808 q^{59} - 44968 q^{61} - 8192 q^{64} - 5852 q^{67} - 10584 q^{69} + 4352 q^{70} + 30048 q^{71} + 17084 q^{73} + 4176 q^{75} - 14160 q^{77} - 6912 q^{78} + 28424 q^{79} - 11664 q^{81} - 128 q^{82} - 35904 q^{83} - 91892 q^{85} + 8064 q^{87} - 15312 q^{89} - 6720 q^{92} + 11952 q^{93} + 21248 q^{94} + 224268 q^{95} + 41712 q^{97} + 62976 q^{98} + 17820 q^{99}+O(q^{100}) $ 160 * q - 128 * q^4 - 432 * q^9 + 208 * q^13 - 1024 * q^16 - 1980 * q^17 - 3828 * q^19 - 3168 * q^20 + 3120 * q^23 + 9768 * q^25 + 4416 * q^26 + 5280 * q^28 - 828 * q^29 - 7748 * q^31 + 16464 * q^35 - 3456 * q^36 - 3520 * q^37 - 9072 * q^39 - 5472 * q^41 - 7216 * q^43 - 1280 * q^46 + 6960 * q^47 + 13888 * q^49 - 7296 * q^50 + 17424 * q^51 + 1664 * q^52 + 14784 * q^53 + 37316 * q^55 - 15840 * q^57 - 9984 * q^58 - 29808 * q^59 - 44968 * q^61 - 8192 * q^64 - 5852 * q^67 - 10584 * q^69 + 4352 * q^70 + 30048 * q^71 + 17084 * q^73 + 4176 * q^75 - 14160 * q^77 - 6912 * q^78 + 28424 * q^79 - 11664 * q^81 - 128 * q^82 - 35904 * q^83 - 91892 * q^85 + 8064 * q^87 - 15312 * q^89 - 6720 * q^92 + 11952 * q^93 + 21248 * q^94 + 224268 * q^95 + 41712 * q^97 + 62976 * q^98 + 17820 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{19}{22}\right)$

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 $

$2$	−1.85223	+	2.13758i	−0.463056	+	0.534396i
$2$	−1.85223	+	2.13758i	−0.463056	+	0.534396i
$3$	4.37128	−	2.80925i	0.485698	−	0.312139i
$3$	4.37128	−	2.80925i	0.485698	−	0.312139i
$4$	−1.13852	−	7.91857i	−0.0711574	−	0.494911i
$5$	−19.2776	+	8.80377i	−0.771103	+	0.352151i	−0.761805	−	0.647806i	$-0.775687\pi$
$5$	−19.2776	+	8.80377i	−0.771103	+	0.352151i	−0.00929742	+	0.999957i	$0.502960\pi$
$6$	−2.09159	+	14.5473i	−0.0580998	+	0.404093i
$7$	14.6430	+	49.8696i	0.298837	+	1.01775i	0.962853	+	0.270027i	$0.0870328\pi$
$7$	14.6430	+	49.8696i	0.298837	+	1.01775i	−0.664015	+	0.747719i	$0.731149\pi$
$8$	19.0354	+	12.2333i	0.297428	+	0.191145i
$9$	11.2162	−	24.5601i	0.138472	−	0.303211i
$10$	16.8876	−	57.5140i	0.168876	−	0.575140i
$11$	78.2998	−	67.8472i	0.647106	−	0.560720i	−0.268258	−	0.963347i	$-0.586448\pi$
$11$	78.2998	−	67.8472i	0.647106	−	0.560720i	0.915364	+	0.402627i	$0.131903\pi$
$12$	−27.2220	−	31.4159i	−0.189042	−	0.218166i
$13$	−156.158	−	45.8521i	−0.924012	−	0.271314i	−0.215084	−	0.976595i	$-0.569003\pi$
$13$	−156.158	−	45.8521i	−0.924012	−	0.271314i	−0.708928	+	0.705281i	$0.750821\pi$
$14$	−133.723	−	61.0690i	−0.682258	−	0.311577i
$15$	−59.5357	+	92.6393i	−0.264603	+	0.411730i
$16$	−61.4076	+	18.0309i	−0.239873	+	0.0704331i
$17$	105.428	+	15.1583i	0.364803	+	0.0524507i	0.322279	−	0.946645i	$-0.395551\pi$
$17$	105.428	+	15.1583i	0.364803	+	0.0524507i	0.0425239	+	0.999095i	$0.486460\pi$
$18$	31.7242	+	69.4664i	0.0979143	+	0.214402i
$19$	−664.579	+	95.5520i	−1.84094	+	0.264687i	−0.972802	−	0.231639i	$-0.925591\pi$
$19$	−664.579	+	95.5520i	−1.84094	+	0.264687i	−0.868136	+	0.496326i	$0.834682\pi$
$20$	91.6612	+	142.628i	0.229153	+	0.356569i
$21$	204.105	+	176.858i	0.462823	+	0.401039i
$22$			293.041i			0.605456i
$23$	−371.823	+	376.283i	−0.702879	+	0.711310i
$23$	−371.823	+	376.283i	−0.702879	+	0.711310i
$24$	117.576			0.204124
$25$	−115.170	+	132.913i	−0.184271	+	0.212660i
$26$	387.253	−	248.872i	0.572859	−	0.368154i
$27$	−19.9662	−	138.868i	−0.0273885	−	0.190491i
$28$	378.224	−	172.729i	0.482429	−	0.220318i
$29$	−126.244	+	878.048i	−0.150112	+	1.04405i	0.765917	+	0.642940i	$0.222286\pi$
$29$	−126.244	+	878.048i	−0.150112	+	1.04405i	−0.916029	+	0.401113i	$0.868624\pi$
$30$	−87.7507	−	298.851i	−0.0975008	−	0.332057i
$31$	−1120.67	−	720.209i	−1.16615	−	0.749437i	−0.193358	−	0.981128i	$-0.561938\pi$
$31$	−1120.67	−	720.209i	−1.16615	−	0.749437i	−0.972789	+	0.231691i	$0.925574\pi$
$32$	75.1981	−	164.661i	0.0734357	−	0.160802i
$33$	151.671	−	516.543i	0.139275	−	0.474328i
$34$	−227.679	+	197.285i	−0.196954	+	0.170661i
$35$	−721.322	−	832.450i	−0.588835	−	0.679551i
$36$	−207.250	−	60.8542i	−0.159915	−	0.0469554i
$37$	−1732.66	−	791.278i	−1.26564	−	0.577997i	−0.334406	−	0.942429i	$-0.608536\pi$
$37$	−1732.66	−	791.278i	−1.26564	−	0.577997i	−0.931230	+	0.364432i	$0.881263\pi$
$38$	1026.70	−	1597.58i	0.711011	−	1.10635i
$39$	−811.421	+	238.255i	−0.533479	+	0.156643i
$40$	−474.655	−	68.2451i	−0.296660	−	0.0426532i
$41$	940.575	+	2059.57i	0.559533	+	1.22521i	0.952186	+	0.305520i	$0.0988303\pi$
$41$	940.575	+	2059.57i	0.559533	+	1.22521i	−0.392652	+	0.919687i	$0.628442\pi$
$42$	−756.097	+	108.710i	−0.428627	+	0.0616272i
$43$	−103.156	−	160.514i	−0.0557902	−	0.0868112i	0.812238	−	0.583326i	$-0.198249\pi$
$43$	−103.156	−	160.514i	−0.0557902	−	0.0868112i	−0.868028	+	0.496515i	$0.834613\pi$
$44$	−626.398	−	542.777i	−0.323553	−	0.280360i
$45$			572.203i			0.282570i
$46$	−115.636	−	1491.76i	−0.0546483	−	0.704992i
$47$	−1985.50			−0.898823			−0.449412	−	0.893325i	$-0.648366\pi$
$47$	−1985.50			−0.898823			−0.449412	+	0.893325i	$0.648366\pi$
$48$	−217.776	+	251.327i	−0.0945210	+	0.109083i
$49$	−252.707	+	162.405i	−0.105251	+	0.0676404i
$50$	−70.7920	−	492.369i	−0.0283168	−	0.196948i
$51$	503.439	−	229.913i	0.193556	−	0.0883941i
$52$	−185.295	+	1288.75i	−0.0685261	+	0.476610i
$53$	−994.260	−	3386.14i	−0.353955	−	1.20546i	−0.923532	−	0.383523i	$-0.874711\pi$
$53$	−994.260	−	3386.14i	−0.353955	−	1.20546i	0.569576	−	0.821939i	$-0.307107\pi$
$54$	333.824	+	214.536i	0.114480	+	0.0735719i
$55$	−912.119	+	1997.26i	−0.301527	+	0.660252i
$56$	−331.334	+	1128.42i	−0.105655	+	0.359828i
$57$	−2636.63	+	2284.65i	−0.811521	+	0.703187i
$58$	−1643.07	−	1896.20i	−0.488427	−	0.563675i
$59$	3430.68	+	1007.34i	0.985544	+	0.289382i	0.734511	−	0.678596i	$-0.237411\pi$
$59$	3430.68	+	1007.34i	0.985544	+	0.289382i	0.251033	+	0.967978i	$0.419230\pi$
$60$	801.354	+	365.966i	0.222598	+	0.101657i
$61$	529.316	−	823.632i	0.142251	−	0.221347i	−0.762816	−	0.646615i	$-0.776184\pi$
$61$	529.316	−	823.632i	0.142251	−	0.221347i	0.905067	+	0.425268i	$0.139820\pi$
$62$	3615.24	−	1061.53i	0.940488	−	0.276152i
$63$	1389.04	+	199.714i	0.349972	+	0.0503184i
$64$	212.692	+	465.732i	0.0519269	+	0.113704i
$65$	3414.02	−	490.862i	0.808052	−	0.116180i
$66$	823.225	+	1280.96i	0.188986	+	0.294069i
$67$	2715.42	+	2352.93i	0.604906	+	0.524154i	0.902585	−	0.430512i	$-0.141667\pi$
$67$	2715.42	+	2352.93i	0.604906	+	0.524154i	−0.297679	+	0.954666i	$0.596213\pi$
$68$		−	852.098i		−	0.184277i
$69$	−568.269	+	2689.38i	−0.119359	+	0.564878i
$70$	3115.48			0.635813
$71$	4420.32	−	5101.33i	0.876874	−	1.01197i	−0.122935	−	0.992415i	$-0.539231\pi$
$71$	4420.32	−	5101.33i	0.876874	−	1.01197i	0.999809	−	0.0195521i	$-0.00622402\pi$
$72$	513.956	−	330.299i	0.0991427	−	0.0637151i
$73$	438.813	+	3052.01i	0.0823443	+	0.572717i	0.988666	+	0.150130i	$0.0479691\pi$
$73$	438.813	+	3052.01i	0.0823443	+	0.572717i	−0.906322	+	0.422588i	$0.861122\pi$
$74$	4900.69	−	2238.07i	0.894940	−	0.408705i
$75$	−130.053	+	904.540i	−0.0231206	+	0.160807i
$76$	1513.27	+	5153.73i	0.261993	+	0.892266i
$77$	4530.06	+	2911.29i	0.764051	+	0.491025i
$78$	993.646	−	2175.78i	0.163321	−	0.357623i
$79$	−1779.17	+	6059.30i	−0.285078	+	0.970886i	0.685092	+	0.728457i	$0.259762\pi$
$79$	−1779.17	+	6059.30i	−0.285078	+	0.970886i	−0.970169	+	0.242429i	$0.922056\pi$
$80$	1025.05	−	888.210i	0.160164	−	0.138783i
$81$	−477.393	−	550.941i	−0.0727623	−	0.0839722i
$82$	−6144.66	−	1804.24i	−0.913841	−	0.268328i
$83$	−3971.87	−	1813.89i	−0.576553	−	0.263303i	0.105725	−	0.994395i	$-0.466284\pi$
$83$	−3971.87	−	1813.89i	−0.576553	−	0.263303i	−0.682278	+	0.731092i	$0.739011\pi$
$84$	1168.09	−	1817.58i	0.165545	−	0.257593i
$85$	−2165.85	+	635.950i	−0.299771	+	0.0880208i
$86$	534.180	+	76.8035i	0.0722256	+	0.0103845i
$87$	1914.81	+	4192.85i	0.252981	+	0.553950i
$88$	2320.46	−	333.632i	0.299647	−	0.0430827i
$89$	5751.74	+	8949.88i	0.726138	+	1.12989i	0.986401	+	0.164355i	$0.0525544\pi$
$89$	5751.74	+	8949.88i	0.726138	+	1.12989i	−0.260263	+	0.965538i	$0.583809\pi$
$90$	−1223.13	−	1059.85i	−0.151004	−	0.130846i
$91$		−	8458.95i		−	1.02149i
$92$	3402.95	+	2515.90i	0.402050	+	0.297247i
$93$	−6922.00			−0.800324
$94$	3677.59	−	4244.17i	0.416206	−	0.480327i
$95$	11970.2	−	7692.81i	1.32634	−	0.852389i
$96$	−133.862	−	931.030i	−0.0145249	−	0.101023i
$97$	11247.7	−	5136.67i	1.19542	−	0.545932i	0.284568	−	0.958656i	$-0.408150\pi$
$97$	11247.7	−	5136.67i	1.19542	−	0.545932i	0.910856	+	0.412724i	$0.135423\pi$
$98$	120.916	−	840.991i	0.0125902	−	0.0875668i
$99$	−788.104	−	2684.04i	−0.0804106	−	0.273853i
$100$	1183.60	+	760.655i	0.118360	+	0.0760655i
$101$	−4006.00	+	8771.93i	−0.392707	+	0.859909i	0.605251	+	0.796035i	$0.293073\pi$
$101$	−4006.00	+	8771.93i	−0.392707	+	0.859909i	−0.997958	+	0.0638738i	$0.979654\pi$
$102$	−441.025	+	1501.99i	−0.0423899	+	0.144367i
$103$	−12408.5	+	10752.0i	−1.16962	+	1.01348i	−0.170012	+	0.985442i	$0.554381\pi$
$103$	−12408.5	+	10752.0i	−1.16962	+	1.01348i	−0.999607	+	0.0280382i	$0.991074\pi$
$104$	−2411.61	−	2783.14i	−0.222967	−	0.257317i
$105$	−5491.67	−	1612.50i	−0.498110	−	0.146258i
$106$	9079.75	+	4146.58i	0.808094	+	0.369044i
$107$	6026.95	−	9378.11i	0.526417	−	0.819121i	−0.471617	−	0.881804i	$-0.656329\pi$
$107$	6026.95	−	9378.11i	0.526417	−	0.819121i	0.998033	+	0.0626831i	$0.0199657\pi$
$108$	−1076.91	+	316.208i	−0.0923273	+	0.0271097i
$109$	−14381.4	−	2067.73i	−1.21045	−	0.174037i	−0.492616	−	0.870247i	$-0.663959\pi$
$109$	−14381.4	−	2067.73i	−1.21045	−	0.174037i	−0.717838	+	0.696210i	$0.754868\pi$
$110$	−2579.86	−	5649.11i	−0.213212	−	0.466869i
$111$	−9796.83	+	1408.57i	−0.795132	+	0.114323i
$112$	−1798.39	−	2798.34i	−0.143366	−	0.223082i
$113$	1034.29	+	896.220i	0.0810003	+	0.0701871i	0.694420	−	0.719570i	$-0.255661\pi$
$113$	1034.29	+	896.220i	0.0810003	+	0.0701871i	−0.613420	+	0.789757i	$0.710207\pi$
$114$		−	9867.71i		−	0.759288i
$115$	3855.13	−	10527.3i	0.291503	−	0.796012i
$116$	7096.62			0.527394
$117$	−2877.63	+	3320.97i	−0.210215	+	0.242601i
$118$	−8507.66	+	5467.54i	−0.611007	+	0.392670i
$119$	787.850	+	5479.62i	0.0556352	+	0.386951i
$120$	−2266.57	+	1035.11i	−0.157401	+	0.0718825i
$121$	−556.010	+	3867.14i	−0.0379762	+	0.264131i
$122$	780.168	+	2657.01i	0.0524166	+	0.178514i
$123$	9897.38	+	6360.66i	0.654199	+	0.420428i
$124$	−4427.13	+	9694.06i	−0.287924	+	0.630467i
$125$	4781.73	−	16285.1i	0.306031	−	1.04224i
$126$	−2999.72	+	2599.27i	−0.188947	+	0.163723i
$127$	1864.44	+	2151.68i	0.115595	+	0.133404i	0.810598	−	0.585603i	$-0.199142\pi$
$127$	1864.44	+	2151.68i	0.115595	+	0.133404i	−0.695003	+	0.719007i	$0.744597\pi$
$128$	−1389.49	−	407.992i	−0.0848080	−	0.0249019i
$129$	−901.849	−	411.860i	−0.0541944	−	0.0247497i
$130$	−5274.28	+	8206.94i	−0.312087	+	0.485618i
$131$	−19344.0	+	5679.92i	−1.12721	+	0.330979i	−0.791610	−	0.611026i	$-0.790757\pi$
$131$	−19344.0	+	5679.92i	−1.12721	+	0.330979i	−0.335599	+	0.942005i	$0.608939\pi$
$132$	−4262.96	−	612.921i	−0.244660	−	0.0351769i
$133$	−14496.6	−	31743.1i	−0.819525	−	1.79451i
$134$	−10059.1	+	1446.29i	−0.560211	+	0.0805462i
$135$	1607.46	+	2501.26i	0.0882010	+	0.137243i
$136$	1821.43	+	1578.28i	0.0984769	+	0.0853307i
$137$		−	21721.5i		−	1.15731i	−0.815574	−	0.578653i	$-0.803578\pi$
$137$		−	21721.5i		−	1.15731i	0.815574	−	0.578653i	$-0.196422\pi$
$138$	−4696.21	−	6196.07i	−0.246598	−	0.325355i
$139$	35213.5			1.82255			0.911276	−	0.411796i	$-0.135098\pi$
$139$	35213.5			1.82255			0.911276	+	0.411796i	$0.135098\pi$
$140$	−5770.58	+	6659.60i	−0.294417	+	0.339776i
$141$	−8679.18	+	5577.77i	−0.436557	+	0.280558i
$142$	2717.07	+	18897.6i	0.134748	+	0.937196i
$143$	−15338.1	+	7004.67i	−0.750065	+	0.342543i
$144$	−245.920	+	1710.41i	−0.0118596	+	0.0824851i
$145$	−5296.45	−	18038.1i	−0.251912	−	0.857934i
$146$	−7336.71	−	4715.01i	−0.344188	−	0.221196i
$147$	−648.416	+	1419.83i	−0.0300068	+	0.0657056i
$148$	−4293.13	+	14621.0i	−0.195997	+	0.667506i
$149$	−5739.11	+	4972.97i	−0.258507	+	0.223998i	−0.774466	−	0.632616i	$-0.781981\pi$
$149$	−5739.11	+	4972.97i	−0.258507	+	0.223998i	0.515959	+	0.856613i	$0.327436\pi$
$150$	−1692.64	−	1953.41i	−0.0752285	−	0.0868183i
$151$	33871.2	+	9945.50i	1.48552	+	0.436187i	0.921107	−	0.389309i	$-0.127286\pi$
$151$	33871.2	+	9945.50i	1.48552	+	0.436187i	0.564409	+	0.825496i	$0.309104\pi$
$152$	−13819.4	−	6311.12i	−0.598140	−	0.273162i
$153$	1554.79	−	2419.30i	0.0664185	−	0.103349i
$154$	−14613.8	+	4291.00i	−0.616200	+	0.180933i
$155$	27944.3	+	4017.78i	1.16313	+	0.167233i
$156$	2810.46	+	6154.04i	0.115486	+	0.252878i
$157$	−7688.12	+	1105.38i	−0.311904	+	0.0448450i	−0.296489	−	0.955036i	$-0.595816\pi$
$157$	−7688.12	+	1105.38i	−0.311904	+	0.0448450i	−0.0154146	+	0.999881i	$0.504907\pi$
$158$	−9656.82	−	15026.3i	−0.386830	−	0.601919i
$159$	−13858.7	−	12008.6i	−0.548187	−	0.475007i
$160$			3836.29i			0.149855i
$161$	−24209.7	−	13032.7i	−0.933979	−	0.502786i
$162$	2061.92			0.0785674
$163$	−4079.53	+	4708.02i	−0.153545	+	0.177200i	−0.827310	−	0.561745i	$-0.810130\pi$
$163$	−4079.53	+	4708.02i	−0.153545	+	0.177200i	0.673766	+	0.738945i	$0.264676\pi$
$164$	15238.0	−	9792.88i	0.566553	−	0.364102i
$165$	1623.68	+	11293.0i	0.0596394	+	0.414801i
$166$	11234.2	−	5130.47i	0.407685	−	0.186183i
$167$	−3476.68	+	24180.8i	−0.124661	+	0.867039i	0.827505	+	0.561458i	$0.189760\pi$
$167$	−3476.68	+	24180.8i	−0.124661	+	0.867039i	−0.952166	+	0.305580i	$0.901150\pi$
$168$	1721.66	+	5863.44i	0.0609999	+	0.207747i
$169$	−1744.12	−	1120.88i	−0.0610664	−	0.0392450i
$170$	2652.24	−	5807.60i	0.0917731	−	0.200955i
$171$	−5107.29	+	17393.8i	−0.174662	+	0.594844i
$172$	−1153.60	+	999.597i	−0.0389939	+	0.0337884i
$173$	−12970.1	−	14968.3i	−0.433362	−	0.500126i	0.496499	−	0.868037i	$-0.334619\pi$
$173$	−12970.1	−	14968.3i	−0.433362	−	0.500126i	−0.929861	+	0.367911i	$0.880073\pi$
$174$	−12509.2	−	3673.04i	−0.413173	−	0.121318i
$175$	−8314.74	−	3797.21i	−0.271502	−	0.123991i
$176$	−3584.85	+	5578.14i	−0.115730	+	0.180080i
$177$	17826.3	−	5234.29i	0.569004	−	0.167075i
$178$	−29784.6	−	4282.39i	−0.940053	−	0.135159i
$179$	22376.3	+	48997.3i	0.698365	+	1.52921i	0.841942	+	0.539568i	$0.181412\pi$
$179$	22376.3	+	48997.3i	0.698365	+	1.52921i	−0.143577	+	0.989639i	$0.545860\pi$
$180$	4531.03	−	651.464i	0.139847	−	0.0201069i
$181$	4368.38	+	6797.34i	0.133341	+	0.207483i	0.901503	−	0.432773i	$-0.142465\pi$
$181$	4368.38	+	6797.34i	0.133341	+	0.207483i	−0.768162	+	0.640256i	$0.778828\pi$
$182$	18081.7	+	15667.9i	0.545879	+	0.473007i
$183$		−	5087.31i		−	0.151910i
$184$	−11681.0	+	2614.07i	−0.345019	+	0.0772114i
$185$	40367.6			1.17948
$186$	12821.1	−	14796.3i	0.370595	−	0.427690i
$187$	9283.44	−	5966.11i	0.265476	−	0.170611i
$188$	2260.53	+	15722.3i	0.0639579	+	0.444837i
$189$	6632.93	−	3029.16i	0.185687	−	0.0848004i
$190$	−5727.58	+	39836.2i	−0.158659	+	1.10350i
$191$	−12485.6	−	42522.0i	−0.342249	−	1.16559i	−0.933342	−	0.358989i	$-0.883121\pi$
$191$	−12485.6	−	42522.0i	−0.342249	−	1.16559i	0.591093	−	0.806604i	$-0.298697\pi$
$192$	2238.10	+	1438.34i	0.0607122	+	0.0390174i
$193$	9118.49	−	19966.7i	0.244798	−	0.536033i	−0.746852	−	0.664990i	$-0.768436\pi$
$193$	9118.49	−	19966.7i	0.244798	−	0.536033i	0.991650	+	0.128957i	$0.0411629\pi$
$194$	−9853.30	+	33557.3i	−0.261805	+	0.891626i
$195$	13544.7	−	11736.5i	0.356205	−	0.308653i
$196$	1573.72	+	1816.17i	0.0409653	+	0.0472765i
$197$	14462.7	+	4246.64i	0.372664	+	0.109424i	0.462701	−	0.886514i	$-0.346880\pi$
$197$	14462.7	+	4246.64i	0.372664	+	0.109424i	−0.0900371	+	0.995938i	$0.528699\pi$
$198$	7197.10	+	3286.80i	0.183581	+	0.0838385i
$199$	−17788.3	+	27679.2i	−0.449189	+	0.698951i	−0.989823	−	0.142307i	$-0.954548\pi$
$199$	−17788.3	+	27679.2i	−0.449189	+	0.698951i	0.540634	+	0.841258i	$0.318184\pi$
$200$	−3818.26	+	1121.14i	−0.0954565	+	0.0280286i
$201$	18479.8	+	2657.00i	0.457410	+	0.0657657i
$202$	−11330.7	−	24810.8i	−0.277686	−	0.608047i
$203$	−45636.5	+	6561.54i	−1.10744	+	0.159226i
$204$	−2393.76	−	3724.76i	−0.0575201	−	0.0895030i
$205$	−36264.0	−	31422.9i	−0.862915	−	0.747720i
$206$		−	46439.3i		−	1.09434i
$207$	5071.09	+	13352.5i	0.118348	+	0.311617i
$208$	10416.0			0.240755
$209$	−45553.4	+	52571.5i	−1.04287	+	1.20353i
$210$	13618.7	−	8752.18i	0.308813	−	0.198462i
$211$	−7483.81	−	52051.0i	−0.168096	−	1.16913i	−0.882814	−	0.469722i	$-0.844354\pi$
$211$	−7483.81	−	52051.0i	−0.168096	−	1.16913i	0.714718	−	0.699413i	$-0.246555\pi$
$212$	−25681.4	+	11728.3i	−0.571409	+	0.260954i
$213$	4991.57	−	34717.1i	0.110022	−	0.765217i
$214$	8883.22	+	30253.5i	0.193974	+	0.660614i
$215$	3401.73	+	2186.16i	0.0735906	+	0.0472938i
$216$	1318.75	−	2887.66i	0.0282654	−	0.0618926i
$217$	19506.6	−	66433.2i	0.414249	−	1.41080i
$218$	31057.6	−	26911.5i	0.653513	−	0.566273i
$219$	10492.0	+	12108.5i	0.218762	+	0.252465i
$220$	16853.9	+	4948.76i	0.348222	+	0.102247i
$221$	−15768.4	−	7201.19i	−0.322852	−	0.147441i
$222$	15135.0	−	23550.5i	0.307098	−	0.477853i
$223$	44373.3	−	13029.2i	0.892303	−	0.262004i	0.196729	−	0.980458i	$-0.436968\pi$
$223$	44373.3	−	13029.2i	0.892303	−	0.262004i	0.695574	+	0.718454i	$0.255150\pi$
$224$	9312.70	+	1338.96i	0.185601	+	0.0266854i
$225$	1972.58	+	4319.35i	0.0389646	+	0.0853205i
$226$	−3831.49	+	550.885i	−0.0750154	+	0.0107856i
$227$	27799.6	+	43257.1i	0.539495	+	0.839470i	0.998808	−	0.0488041i	$-0.0155410\pi$
$227$	27799.6	+	43257.1i	0.539495	+	0.839470i	−0.459314	+	0.888274i	$0.651905\pi$
$228$	21093.0	+	18277.2i	0.405760	+	0.351593i
$229$		−	60706.1i		−	1.15761i	−0.815467	−	0.578804i	$-0.803520\pi$
$229$		−	60706.1i		−	1.15761i	0.815467	−	0.578804i	$-0.196480\pi$
$230$	15362.3	+	27739.5i	0.290403	+	0.524377i
$231$	27980.7			0.524366
$232$	−13144.5	+	15169.6i	−0.244213	+	0.281837i
$233$	−16184.2	+	10400.9i	−0.298111	+	0.191584i	−0.681142	−	0.732151i	$-0.738517\pi$
$233$	−16184.2	+	10400.9i	−0.298111	+	0.191584i	0.383031	+	0.923735i	$0.374880\pi$
$234$	−1768.81	−	12302.4i	−0.0323035	−	0.224676i
$235$	38275.6	−	17479.9i	0.693085	−	0.316521i
$236$	4070.79	−	28313.0i	0.0730894	−	0.508348i
$237$	9244.84	+	31485.0i	0.164590	+	0.560541i
$238$	−13172.4	−	8465.39i	−0.232547	−	0.149449i
$239$	13457.2	−	29467.1i	0.235591	−	0.515872i	−0.754500	−	0.656300i	$-0.772121\pi$
$239$	13457.2	−	29467.1i	0.235591	−	0.515872i	0.990091	+	0.140428i	$0.0448478\pi$
$240$	1985.57	−	6762.23i	0.0344717	−	0.117400i
$241$	−68320.1	+	59199.7i	−1.17629	+	1.01926i	−0.176904	+	0.984228i	$0.556608\pi$
$241$	−68320.1	+	59199.7i	−1.17629	+	1.01926i	−0.999386	+	0.0350335i	$0.988846\pi$
$242$	−7236.47	−	8351.33i	−0.123565	−	0.142602i
$243$	−3634.55	−	1067.20i	−0.0615515	−	0.0180732i
$244$	−7124.62	−	3253.71i	−0.119669	−	0.0546511i
$245$	3441.80	−	5355.54i	0.0573394	−	0.0892218i
$246$	−31928.6	+	9375.09i	−0.527606	+	0.154919i
$247$	108161.	+	15551.1i	1.77286	+	0.254899i
$248$	−12521.8	−	27418.9i	−0.203593	−	0.445807i
$249$	−22457.9	+	3228.95i	−0.362218	+	0.0520791i
$250$	25953.9	+	40385.0i	0.415262	+	0.646160i
$251$	27403.4	+	23745.1i	0.434967	+	0.376901i	0.844643	−	0.535330i	$-0.179813\pi$
$251$	27403.4	+	23745.1i	0.434967	+	0.376901i	−0.409676	+	0.912231i	$0.634358\pi$
$252$		−	11226.6i		−	0.176785i
$253$	−3583.93	+	54690.0i	−0.0559911	+	0.854411i
$254$	−8052.75			−0.124818
$255$	−7680.98	+	8864.33i	−0.118124	+	0.136322i
$256$	3445.77	−	2214.46i	0.0525783	−	0.0337901i
$257$	2002.59	+	13928.3i	0.0303197	+	0.210878i	0.999349	−	0.0360659i	$-0.0114826\pi$
$257$	2002.59	+	13928.3i	0.0303197	+	0.210878i	−0.969030	+	0.246944i	$0.920574\pi$
$258$	2550.81	−	1164.92i	0.0383212	−	0.0175007i
$259$	14089.3	−	97993.5i	0.210035	−	1.46082i
$260$	−7773.85	−	26475.3i	−0.114998	−	0.391647i
$261$	20148.9	+	12948.9i	0.295782	+	0.190087i
$262$	23688.2	−	51870.0i	0.345088	−	0.755638i
$263$	−11591.7	+	39477.6i	−0.167585	+	0.570741i	0.832281	+	0.554354i	$0.187035\pi$
$263$	−11591.7	+	39477.6i	−0.167585	+	0.570741i	−0.999866	+	0.0163873i	$0.994784\pi$
$264$	9206.14	−	7977.17i	0.132090	−	0.114457i
$265$	48977.7	+	56523.3i	0.697440	+	0.804889i
$266$	94704.4	+	27807.7i	1.33846	+	0.393009i
$267$	50285.0	+	22964.4i	0.705368	+	0.322131i
$268$	15540.3	−	24181.1i	0.216366	−	0.336672i
$269$	−53704.3	+	15769.0i	−0.742172	+	0.217921i	−0.630895	−	0.775868i	$-0.717312\pi$
$269$	−53704.3	+	15769.0i	−0.742172	+	0.217921i	−0.111277	+	0.993789i	$0.535494\pi$
$270$	−8324.04	−	1196.82i	−0.114184	−	0.0164172i
$271$	16122.3	+	35302.9i	0.219527	+	0.480698i	0.987068	−	0.160302i	$-0.0512470\pi$
$271$	16122.3	+	35302.9i	0.219527	+	0.480698i	−0.767541	+	0.641000i	$0.778520\pi$
$272$	−6747.40	+	970.129i	−0.0912007	+	0.0131127i
$273$	−23763.3	−	36976.5i	−0.318847	−	0.496135i
$274$	46431.5	+	40233.1i	0.618459	+	0.535898i
$275$			18221.0i			0.240939i
$276$	21943.1	+	1437.97i	0.288057	+	0.0188769i
$277$	−1704.98			−0.0222208			−0.0111104	−	0.999938i	$-0.503537\pi$
$277$	−1704.98			−0.0222208			−0.0111104	+	0.999938i	$0.503537\pi$
$278$	−65223.4	+	75271.8i	−0.843944	+	0.973964i
$279$	−30258.0	+	19445.6i	−0.388716	+	0.249812i
$280$	−3547.04	−	24670.2i	−0.0452428	−	0.314671i
$281$	−7742.59	+	3535.92i	−0.0980559	+	0.0447806i	−0.463839	−	0.885919i	$-0.653528\pi$
$281$	−7742.59	+	3535.92i	−0.0980559	+	0.0447806i	0.365783	+	0.930700i	$0.380801\pi$
$282$	4152.86	−	28883.8i	0.0522214	−	0.363208i
$283$	29674.2	+	101061.i	0.370516	+	1.26186i	0.908137	+	0.418674i	$0.137505\pi$
$283$	29674.2	+	101061.i	0.370516	+	1.26186i	−0.537621	+	0.843187i	$0.680677\pi$
$284$	−45427.8	−	29194.7i	−0.563229	−	0.361966i
$285$	30714.3	−	67254.9i	0.378138	−	0.828007i
$286$	13436.5	−	45760.7i	0.164269	−	0.559449i
$287$	−88937.1	+	77064.5i	−1.07974	+	0.935601i
$288$	−3200.65	−	3693.74i	−0.0385880	−	0.0445330i
$289$	−69252.5	−	20334.4i	−0.829163	−	0.243464i
$290$	48368.1	+	22089.0i	0.575126	+	0.262651i
$291$	34736.8	−	54051.6i	0.410208	−	0.638296i
$292$	23668.0	−	6949.54i	0.277585	−	0.0815062i
$293$	−43214.5	−	6213.30i	−0.503378	−	0.0723748i	−0.114052	−	0.993475i	$-0.536383\pi$
$293$	−43214.5	−	6213.30i	−0.503378	−	0.0723748i	−0.389326	+	0.921100i	$0.627292\pi$
$294$	−1834.00	−	4015.89i	−0.0212180	−	0.0464609i
$295$	−75003.6	+	10783.9i	−0.861862	+	0.123917i
$296$	−23301.9	−	36258.4i	−0.265954	−	0.413833i
$297$	−10985.2	−	9518.69i	−0.124536	−	0.107911i
$298$		−	21478.9i		−	0.241869i
$299$	75316.5	−	41710.7i	0.842457	−	0.466558i
$300$	7310.73			0.0812303
$301$	6494.25	−	7494.76i	0.0716796	−	0.0827227i
$302$	−83996.5	+	53981.3i	−0.920974	+	0.591874i
$303$	7131.18	+	49598.4i	0.0776741	+	0.540235i
$304$	39087.3	−	17850.6i	0.422949	−	0.193154i
$305$	−2952.86	+	20537.6i	−0.0317427	+	0.220775i
$306$	2291.63	+	7804.59i	0.0244738	+	0.0833503i
$307$	−125107.	−	80401.2i	−1.32741	−	0.853072i	−0.331499	−	0.943455i	$-0.607554\pi$
$307$	−125107.	−	80401.2i	−1.32741	−	0.853072i	−0.995907	+	0.0903831i	$0.971191\pi$
$308$	17895.7	−	39186.1i	0.188646	−	0.413077i
$309$	−24035.9	+	81858.6i	−0.251735	+	0.857329i
$310$	−60347.5	+	52291.4i	−0.627966	+	0.544135i
$311$	40371.2	+	46590.8i	0.417398	+	0.481703i	0.925043	−	0.379863i	$-0.124029\pi$
$311$	40371.2	+	46590.8i	0.417398	+	0.481703i	−0.507644	+	0.861567i	$0.669484\pi$
$312$	−18360.4	−	5391.09i	−0.188613	−	0.0553818i
$313$	−126725.	−	57873.3i	−1.29352	−	0.590731i	−0.354649	−	0.934999i	$-0.615400\pi$
$313$	−126725.	−	57873.3i	−1.29352	−	0.590731i	−0.938871	+	0.344268i	$0.888127\pi$
$314$	11877.3	−	18481.4i	0.120464	−	0.187446i
$315$	−28535.5	+	8378.79i	−0.287584	+	0.0844423i
$316$	50006.6	+	7189.86i	0.500787	+	0.0720023i
$317$	−14228.2	−	31155.4i	−0.141589	−	0.310038i	0.825531	−	0.564357i	$-0.190876\pi$
$317$	−14228.2	−	31155.4i	−0.141589	−	0.310038i	−0.967120	+	0.254319i	$0.918149\pi$
$318$	51338.9	−	7381.42i	0.507683	−	0.0729938i
$319$	49688.2	+	77316.3i	0.488283	+	0.759784i
$320$	−8200.39	−	7105.68i	−0.0800819	−	0.0693914i
$321$		−	57925.6i		−	0.562160i
$322$	72700.3	−	27610.6i	0.701172	−	0.266296i
$323$	−71513.6			−0.685463
$324$	−3819.15	+	4407.53i	−0.0363812	+	0.0419861i
$325$	24079.0	−	15474.6i	0.227967	−	0.146505i
$326$	−2507.59	−	17440.6i	−0.0235950	−	0.164107i
$327$	−68674.0	+	31362.4i	−0.642239	+	0.293301i
$328$	−7291.16	+	50711.1i	−0.0677718	+	0.471363i
$329$	−29073.7	−	99016.0i	−0.268602	−	0.914774i
$330$	−27147.1	−	17446.4i	−0.249284	−	0.160205i
$331$	43849.0	−	96015.9i	0.400224	−	0.876369i	−0.597023	−	0.802224i	$-0.703650\pi$
$331$	43849.0	−	96015.9i	0.400224	−	0.876369i	0.997247	−	0.0741452i	$-0.0236228\pi$
$332$	−9841.40	+	33516.7i	−0.0892854	+	0.304078i
$333$	−38867.7	+	33679.0i	−0.350510	+	0.303718i
$334$	−45248.9	−	52220.1i	−0.405616	−	0.468106i
$335$	−73061.4	−	21452.8i	−0.651026	−	0.191158i
$336$	−15722.5	−	7180.22i	−0.139265	−	0.0636003i
$337$	−65134.5	+	101351.i	−0.573523	+	0.892420i	−0.999927	−	0.0121133i	$-0.996144\pi$
$337$	−65134.5	+	101351.i	−0.573523	+	0.892420i	0.426403	+	0.904533i	$0.359780\pi$
$338$	5626.46	−	1652.08i	0.0492495	−	0.0144610i
$339$	7038.89	+	1012.04i	0.0612498	+	0.00880640i
$340$	7501.67	+	16426.4i	0.0648934	+	0.142097i
$341$	−136612.	+	19641.9i	−1.17485	+	0.168917i
$342$	−27720.9	−	43134.5i	−0.237004	−	0.368785i
$343$	82511.9	+	71497.0i	0.701340	+	0.607714i
$344$		−	4317.39i		−	0.0364841i
$345$	−12721.9	−	56847.7i	−0.106884	−	0.477611i
$346$	56019.5			0.467936
$347$	−63340.7	+	73099.0i	−0.526046	+	0.607090i	−0.955134	−	0.296173i	$-0.904289\pi$
$347$	−63340.7	+	73099.0i	−0.526046	+	0.607090i	0.429088	+	0.903263i	$0.358835\pi$
$348$	31021.3	−	19936.2i	0.256154	−	0.164620i
$349$	−4192.93	−	29162.5i	−0.0344244	−	0.239427i	0.965343	−	0.260984i	$-0.0840469\pi$
$349$	−4192.93	−	29162.5i	−0.0344244	−	0.239427i	−0.999768	+	0.0215566i	$0.993138\pi$
$350$	23517.6	−	10740.1i	0.191981	−	0.0876746i
$351$	−3249.51	+	22600.9i	−0.0263757	+	0.183447i
$352$	−5283.78	−	17994.9i	−0.0426441	−	0.145233i
$353$	−16063.4	−	10323.3i	−0.128910	−	0.0828456i	0.474596	−	0.880203i	$-0.342594\pi$
$353$	−16063.4	−	10323.3i	−0.128910	−	0.0828456i	−0.603507	+	0.797358i	$0.706230\pi$
$354$	−21829.7	+	47800.3i	−0.174197	+	0.381439i
$355$	−40302.2	+	137257.i	−0.319795	+	1.08912i
$356$	64321.8	−	55735.2i	0.507526	−	0.439774i
$357$	18837.5	+	21739.7i	0.147804	+	0.170575i
$358$	−146182.	−	42922.9i	−1.14058	−	0.334906i
$359$	67656.5	+	30897.7i	0.524953	+	0.239738i	0.660222	−	0.751071i	$-0.270462\pi$
$359$	67656.5	+	30897.7i	0.524953	+	0.239738i	−0.135268	+	0.990809i	$0.543190\pi$
$360$	−6999.94	+	10892.1i	−0.0540119	+	0.0840441i
$361$	307493.	−	90288.0i	2.35950	−	0.692812i
$362$	−22621.1	−	3252.42i	−0.172622	−	0.0248193i
$363$	8433.28	+	18466.3i	0.0640005	+	0.140142i
$364$	−66982.8	+	9630.67i	−0.505546	+	0.0726865i
$365$	−35328.5	−	54972.1i	−0.265179	−	0.412626i
$366$	10874.5	+	9422.84i	0.0811799	+	0.0703428i
$367$		−	127719.i		−	0.948253i	−0.880457	−	0.474126i	$-0.842764\pi$
$367$		−	127719.i		−	0.948253i	0.880457	−	0.474126i	$-0.157236\pi$
$368$	16048.0	−	29810.9i	0.118502	−	0.220130i
$369$	61132.9			0.448975
$370$	−74770.0	+	86289.1i	−0.546165	+	0.630308i
$371$	154306.	−	99166.7i	1.12108	−	0.720474i
$372$	7880.83	+	54812.4i	0.0569490	+	0.396089i
$373$	−175340.	+	80075.3i	−1.26027	+	0.575547i	−0.929729	−	0.368243i	$-0.879959\pi$
$373$	−175340.	+	80075.3i	−1.26027	+	0.575547i	−0.330543	+	0.943791i	$0.607232\pi$
$374$	−4441.99	+	30894.7i	−0.0317566	+	0.220872i
$375$	−24846.6	−	84619.7i	−0.176687	−	0.601740i
$376$	−37794.8	−	24289.2i	−0.267335	−	0.171806i
$377$	59974.5	−	131326.i	0.421972	−	0.923990i
$378$	−5810.61	+	19789.1i	−0.0406666	+	0.138498i
$379$	−62225.6	+	53918.8i	−0.433202	+	0.375372i	−0.843990	−	0.536359i	$-0.819799\pi$
$379$	−62225.6	+	53918.8i	−0.433202	+	0.375372i	0.410787	+	0.911731i	$0.365254\pi$
$380$	−74544.4	−	86028.8i	−0.516236	−	0.595768i
$381$	14194.6	+	4167.91i	0.0977852	+	0.0287123i
$382$	114020.	+	52071.4i	0.781368	+	0.356839i
$383$	−16862.5	+	26238.6i	−0.114954	+	0.178872i	−0.893963	−	0.448141i	$-0.852086\pi$
$383$	−16862.5	+	26238.6i	−0.114954	+	0.178872i	0.779009	+	0.627013i	$0.215723\pi$
$384$	−7220.02	+	2119.99i	−0.0489639	+	0.0143771i
$385$	−112959.	−	16241.0i	−0.762077	−	0.109570i
$386$	25791.0	+	56474.4i	0.173098	+	0.379033i
$387$	−5099.25	+	733.162i	−0.0340475	+	0.00489529i
$388$	−53480.9	−	83217.9i	−0.355251	−	0.552781i
$389$	131144.	+	113637.i	0.866663	+	0.750968i	0.969852	−	0.243694i	$-0.0783592\pi$
$389$	131144.	+	113637.i	0.866663	+	0.750968i	−0.103189	+	0.994662i	$0.532905\pi$
$390$			50691.6i			0.333278i
$391$	−44904.4	+	34034.6i	−0.293721	+	0.222621i
$392$	−6797.12			−0.0442336
$393$	−68601.9	+	79170.8i	−0.444172	+	0.512602i
$394$	−35865.7	+	23049.5i	−0.231040	+	0.148480i
$395$	−19046.6	−	132472.i	−0.122074	−	0.849043i
$396$	−20356.5	+	9296.48i	−0.129811	+	0.0592827i
$397$	−38873.0	+	270368.i	−0.246642	+	1.71543i	0.370711	+	0.928748i	$0.379114\pi$
$397$	−38873.0	+	270368.i	−0.246642	+	1.71543i	−0.617354	+	0.786686i	$0.711795\pi$
$398$	−26218.5	−	89292.1i	−0.165517	−	0.563699i
$399$	−152543.	−	98033.4i	−0.958178	−	0.615784i
$400$	4675.75	−	10238.5i	0.0292234	−	0.0639904i
$401$	57568.8	−	196061.i	0.358013	−	1.21928i	−0.561917	−	0.827194i	$-0.689936\pi$
$401$	57568.8	−	196061.i	0.358013	−	1.21928i	0.919929	−	0.392085i	$-0.128246\pi$
$402$	−39908.4	+	34580.8i	−0.246952	+	0.213985i
$403$	141978.	+	163851.i	0.874201	+	1.00888i
$404$	74022.0	+	21734.8i	0.453522	+	0.133166i
$405$	14053.3	+	6417.95i	0.0856781	+	0.0391279i
$406$	70503.3	−	109705.i	0.427718	−	0.665542i
$407$	−189353.	+	55598.9i	−1.14310	+	0.335643i
$408$	12395.8	+	1782.24i	0.0744651	+	0.0107065i
$409$	−48976.7	−	107244.i	−0.292781	−	0.641101i	0.704890	−	0.709317i	$-0.250997\pi$
$409$	−48976.7	−	107244.i	−0.292781	−	0.641101i	−0.997671	+	0.0682161i	$0.978269\pi$
$410$	134338.	−	19314.9i	0.799157	−	0.114901i
$411$	−61021.1	−	94950.7i	−0.361241	−	0.562101i
$412$	99267.9	+	86016.1i	0.584809	+	0.506740i
$413$			185837.i			1.08951i
$414$	−37934.8	−	13891.9i	−0.221328	−	0.0810515i
$415$	92537.2			0.537304
$416$	−19292.9	+	22265.1i	−0.111483	+	0.128659i
$417$	153928.	−	98923.7i	0.885210	−	0.568890i
$418$	−28000.6	−	194749.i	−0.160256	−	1.11461i
$419$	−22610.8	+	10326.0i	−0.128792	+	0.0588172i	−0.478769	−	0.877941i	$-0.658917\pi$
$419$	−22610.8	+	10326.0i	−0.128792	+	0.0588172i	0.349977	+	0.936758i	$0.386189\pi$
$420$	−6516.32	+	45322.0i	−0.0369406	+	0.256928i
$421$	−19284.0	−	65675.4i	−0.108801	−	0.370543i	0.887035	−	0.461702i	$-0.152761\pi$
$421$	−19284.0	−	65675.4i	−0.108801	−	0.370543i	−0.995836	+	0.0911590i	$0.970943\pi$
$422$	125125.	+	80413.0i	0.702618	+	0.451545i
$423$	−22269.8	+	48764.0i	−0.124462	+	0.272533i
$424$	22497.5	−	76619.6i	0.125142	−	0.426195i
$425$	−14156.8	+	12267.0i	−0.0783769	+	0.0679140i
$426$	64965.2	+	74973.9i	0.357982	+	0.413134i
$427$	48825.0	+	14336.3i	0.267785	+	0.0786287i
$428$	−81123.0	−	37047.6i	−0.442850	−	0.202243i
$429$	−47369.2	+	73707.9i	−0.257384	+	0.400497i
$430$	−10973.9	+	3222.22i	−0.0593502	+	0.0174268i
$431$	167812.	+	24127.7i	0.903375	+	0.129886i	0.578321	−	0.815810i	$-0.303708\pi$
$431$	167812.	+	24127.7i	0.903375	+	0.129886i	0.325054	+	0.945695i	$0.394617\pi$
$432$	3729.99	+	8167.54i	0.0199867	+	0.0437647i
$433$	−53934.9	+	7754.67i	−0.287670	+	0.0413606i	−0.284639	−	0.958635i	$-0.591874\pi$
$433$	−53934.9	+	7754.67i	−0.287670	+	0.0413606i	−0.00303055	+	0.999995i	$0.500965\pi$
$434$	105876.	+	164746.i	0.562106	+	0.874654i
$435$	−73825.8	−	63970.4i	−0.390148	−	0.338065i
$436$			116234.i			0.611451i
$437$	211151.	−	285598.i	1.10568	−	1.49552i
$438$	−45316.5			−0.236215
$439$	62632.3	−	72281.6i	0.324990	−	0.375058i	−0.569619	−	0.821909i	$-0.692909\pi$
$439$	62632.3	−	72281.6i	0.324990	−	0.375058i	0.894608	+	0.446851i	$0.147455\pi$
$440$	−41795.7	+	26860.4i	−0.215887	+	0.138742i
$441$	1154.26	+	8028.06i	0.00593508	+	0.0412794i
$442$	44599.8	−	20368.0i	0.228291	−	0.104257i
$443$	45158.1	−	314081.i	0.230106	−	1.60042i	−0.467534	−	0.883975i	$-0.654858\pi$
$443$	45158.1	−	314081.i	0.230106	−	1.60042i	0.697640	−	0.716448i	$-0.254233\pi$
$444$	22307.7	+	75973.2i	0.113159	+	0.385385i
$445$	−189672.	−	121895.i	−0.957820	−	0.615554i
$446$	−54338.5	+	118985.i	−0.273173	+	0.598165i
$447$	−11117.0	+	37860.9i	−0.0556379	+	0.189485i
$448$	−20111.4	+	17426.6i	−0.100204	+	0.0868274i
$449$	85703.7	+	98907.3i	0.425115	+	0.490609i	0.927388	−	0.374100i	$-0.122048\pi$
$449$	85703.7	+	98907.3i	0.425115	+	0.490609i	−0.502273	+	0.864709i	$0.667503\pi$
$450$	−12886.6	−	3783.86i	−0.0636377	−	0.0186857i
$451$	213383.	+	97448.8i	1.04908	+	0.479097i
$452$	5919.22	−	9210.48i	0.0289726	−	0.0450822i
$453$	176000.	−	51678.3i	0.857663	−	0.251833i
$454$	−143957.	−	20697.8i	−0.698426	−	0.100418i
$455$	74470.7	+	163068.i	0.359718	+	0.787673i
$456$	−78138.2	+	11234.6i	−0.375780	+	0.0540290i
$457$	42844.7	+	66667.6i	0.205147	+	0.319214i	0.928547	−	0.371214i	$-0.121058\pi$
$457$	42844.7	+	66667.6i	0.205147	+	0.319214i	−0.723401	+	0.690428i	$0.757422\pi$
$458$	129764.	+	112441.i	0.618620	+	0.536038i
$459$		−	14943.2i		−	0.0709283i
$460$	−87750.0	−	18541.7i	−0.414698	−	0.0876260i
$461$	374932.			1.76421			0.882106	−	0.471051i	$-0.156125\pi$
$461$	374932.			1.76421			0.882106	+	0.471051i	$0.156125\pi$
$462$	−51826.6	+	59811.1i	−0.242811	+	0.280219i
$463$	255229.	−	164026.i	1.19061	−	0.765156i	0.213299	−	0.976987i	$-0.431579\pi$
$463$	255229.	−	164026.i	1.19061	−	0.765156i	0.977306	+	0.211831i	$0.0679427\pi$
$464$	−8079.63	−	56195.1i	−0.0375280	−	0.261013i
$465$	133439.	−	60939.7i	0.617132	−	0.281835i
$466$	7743.88	−	53859.8i	0.0356604	−	0.248024i
$467$	−41726.8	−	142109.i	−0.191329	−	0.651608i	−0.998149	−	0.0608106i	$-0.980631\pi$
$467$	−41726.8	−	142109.i	−0.191329	−	0.651608i	0.806820	−	0.590797i	$-0.201187\pi$
$468$	29573.5	+	19005.8i	0.135024	+	0.0867748i
$469$	−77577.4	+	169871.i	−0.352687	+	0.772277i
$470$	−33530.4	+	114194.i	−0.151790	+	0.516949i
$471$	−30501.6	+	26429.8i	−0.137493	+	0.119139i
$472$	52981.3	+	61143.6i	0.237815	+	0.274453i
$473$	−18967.5	−	5569.37i	−0.0847790	−	0.0248934i
$474$	−84425.4	−	38555.8i	−0.375765	−	0.171606i
$475$	63839.2	−	99335.7i	0.282944	−	0.440269i
$476$	42493.7	−	12477.3i	0.187547	−	0.0550689i
$477$	−94315.7	−	13560.5i	−0.414521	−	0.0595992i
$478$	38062.7	+	83345.7i	0.166588	+	0.364777i
$479$	327305.	−	47059.4i	1.42653	−	0.205104i	0.614593	−	0.788845i	$-0.289320\pi$
$479$	327305.	−	47059.4i	1.42653	−	0.205104i	0.811940	+	0.583740i	$0.198411\pi$
$480$	10777.1	+	16769.5i	0.0467756	+	0.0727843i
$481$	234286.	+	203010.i	1.01264	+	0.877462i
$482$		−	255691.i		−	1.10058i
$483$	−142440.	+	11041.4i	−0.610571	+	0.0473291i
$484$	31255.2			0.133423
$485$	−171607.	+	198045.i	−0.729544	+	0.841939i
$486$	9013.25	−	5792.46i	0.0381600	−	0.0245240i
$487$	−9131.62	−	63511.8i	−0.0385026	−	0.267791i	0.961472	−	0.274902i	$-0.0886456\pi$
$487$	−9131.62	−	63511.8i	−0.0385026	−	0.267791i	−0.999975	+	0.00711104i	$0.997736\pi$
$488$	20151.5	−	9202.87i	0.0846189	−	0.0386441i
$489$	−4606.73	+	32040.5i	−0.0192653	+	0.133993i
$490$	5072.92	+	17276.8i	0.0211284	+	0.0719567i
$491$	241669.	+	155311.i	1.00244	+	0.644228i	0.935425	−	0.353524i	$-0.115017\pi$
$491$	241669.	+	155311.i	1.00244	+	0.644228i	0.0670130	+	0.997752i	$0.478653\pi$
$492$	39099.0	−	85614.8i	0.161523	−	0.353687i
$493$	−26619.4	+	90657.3i	−0.109523	+	0.373000i
$494$	−233580.	+	202398.i	−0.957153	+	0.829377i
$495$	38822.4	+	44803.4i	0.158442	+	0.182852i
$496$	81803.4	+	24019.7i	0.332513	+	0.0976345i
$497$	319128.	+	145741.i	1.29197	+	0.590022i
$498$	34694.9	−	53986.3i	0.139896	−	0.217683i
$499$	−316199.	+	92844.5i	−1.26987	+	0.372868i	−0.846160	−	0.532929i	$-0.821091\pi$
$499$	−316199.	+	92844.5i	−1.26987	+	0.372868i	−0.423712	+	0.905797i	$0.639273\pi$
$500$	−134399.	−	19323.6i	−0.537595	−	0.0772944i
$501$	52732.5	+	115468.i	0.210089	+	0.460031i
$502$	−101514.	+	14595.6i	−0.402829	+	0.0579180i
$503$	−29001.2	−	45126.8i	−0.114625	−	0.178360i	0.779201	−	0.626775i	$-0.215625\pi$
$503$	−29001.2	−	45126.8i	−0.114625	−	0.178360i	−0.893826	+	0.448414i	$0.851989\pi$
$504$	23997.8	+	20794.2i	0.0944734	+	0.0818617i
$505$		−	204369.i		−	0.801370i
$506$	−110266.	−	108959.i	−0.430667	−	0.425562i
$507$	−10772.9			−0.0419097
$508$	14915.5	−	17213.4i	0.0577977	−	0.0667022i
$509$	284797.	−	183028.i	1.09926	−	0.706450i	0.140332	−	0.990105i	$-0.455183\pi$
$509$	284797.	−	183028.i	1.09926	−	0.706450i	0.958927	+	0.283654i	$0.0915468\pi$
$510$	−4721.31	−	32837.5i	−0.0181519	−	0.126249i
$511$	−145777.	+	66574.1i	−0.558273	+	0.254955i
$512$	−1648.75	+	11467.3i	−0.00628949	+	0.0437443i
$513$	26538.2	+	90381.0i	0.100841	+	0.343433i
$514$	−33482.2	−	21517.7i	−0.126732	−	0.0814459i
$515$	144547.	−	316514.i	0.544998	−	1.19338i
$516$	−2234.57	+	7610.26i	−0.00839258	+	0.0285825i
$517$	−155464.	+	134711.i	−0.581634	+	0.503988i
$518$	183373.	+	211623.i	0.683400	+	0.788686i
$519$	−98745.6	−	28994.3i	−0.366592	−	0.107641i
$520$	70992.1	+	32421.0i	0.262545	+	0.119900i
$521$	−212169.	+	330142.i	−0.781640	+	1.21626i	0.190462	+	0.981695i	$0.439002\pi$
$521$	−212169.	+	330142.i	−0.781640	+	1.21626i	−0.972101	+	0.234561i	$0.924635\pi$
$522$	−64999.8	+	19085.7i	−0.238545	+	0.0700433i
$523$	−228579.	−	32864.7i	−0.835667	−	0.120151i	−0.288820	−	0.957383i	$-0.593263\pi$
$523$	−228579.	−	32864.7i	−0.835667	−	0.120151i	−0.546847	+	0.837233i	$0.684172\pi$
$524$	67000.4	+	146710.i	0.244014	+	0.534317i
$525$	−47013.4	+	6759.50i	−0.170570	+	0.0245243i
$526$	−62916.3	−	97899.6i	−0.227401	−	0.353842i
$527$	−107233.	−	92917.6i	−0.386105	−	0.334562i
$528$			34454.4i			0.123588i
$529$	−3336.54	−	279821.i	−0.0119230	−	0.999929i
$530$	−211541.			−0.753083
$531$	63219.5	−	72959.2i	0.224214	−	0.258756i
$532$	−234855.	+	150932.i	−0.829807	+	0.533285i
$533$	−52442.6	−	364746.i	−0.184599	−	1.28392i
$534$	−142227.	+	64953.1i	−0.498770	+	0.227781i
$535$	−33622.1	+	233847.i	−0.117467	+	0.817004i
$536$	22905.1	+	78007.5i	0.0797263	+	0.271523i
$537$	235459.	+	151320.i	0.816520	+	0.524745i
$538$	65764.9	−	144005.i	0.227211	−	0.497523i
$539$	−8768.18	+	29861.7i	−0.0301809	+	0.102787i
$540$	17976.3	−	15576.5i	0.0616471	−	0.0534175i
$541$	−191101.	−	220543.i	−0.652933	−	0.753525i	0.328672	−	0.944444i	$-0.393399\pi$
$541$	−191101.	−	220543.i	−0.652933	−	0.753525i	−0.981606	+	0.190919i	$0.938853\pi$
$542$	−105325.	−	30926.2i	−0.358536	−	0.105276i
$543$	38190.9	+	17441.2i	0.129527	+	0.0591529i
$544$	10424.0	−	16220.0i	0.0352237	−	0.0548092i
$545$	295443.	−	86749.7i	0.994672	−	0.292062i
$546$	123055.	+	17692.7i	0.412777	+	0.0593483i
$547$	24130.9	+	52839.3i	0.0806490	+	0.176597i	0.945661	−	0.325155i	$-0.105416\pi$
$547$	24130.9	+	52839.3i	0.0806490	+	0.176597i	−0.865012	+	0.501752i	$0.832689\pi$
$548$	−172003.	+	24730.3i	−0.572763	+	0.0823509i
$549$	−14291.5	−	22238.1i	−0.0474170	−	0.0737823i
$550$	−38948.8	−	33749.4i	−0.128757	−	0.111568i
$551$		−	595595.i		−	1.96177i
$552$	−43717.3	+	44241.6i	−0.143475	+	0.145195i
$553$	−328227.			−1.07331
$554$	3158.01	−	3644.54i	0.0102895	−	0.0118747i
$555$	176458.	−	113403.i	0.572870	−	0.368161i
$556$	−40091.3	−	278841.i	−0.129688	−	0.902000i
$557$	134950.	−	61629.4i	0.434972	−	0.198645i	−0.185881	−	0.982572i	$-0.559514\pi$
$557$	134950.	−	61629.4i	0.434972	−	0.198645i	0.620853	+	0.783927i	$0.286787\pi$
$558$	14478.0	−	100697.i	0.0464987	−	0.323405i
$559$	8748.74	+	29795.5i	0.0279977	+	0.0953513i
$560$	59304.5	+	38112.7i	0.189109	+	0.121533i
$561$	23820.2	−	52159.1i	0.0756869	−	0.165731i
$562$	6782.70	−	23099.8i	0.0214749	−	0.0731366i
$563$	−379787.	+	329087.i	−1.19818	+	1.03823i	−0.199890	+	0.979818i	$0.564058\pi$
$563$	−379787.	+	329087.i	−1.19818	+	1.03823i	−0.998293	+	0.0584123i	$0.981396\pi$
$564$	54049.4	+	62376.3i	0.169915	+	0.196093i
$565$	−27828.8	−	8171.26i	−0.0871760	−	0.0255972i
$566$	−270990.	−	123757.i	−0.845903	−	0.386311i
$567$	20484.7	−	31874.9i	0.0637183	−	0.0991476i
$568$	146549.	−	43030.6i	0.454240	−	0.133377i
$569$	−495759.	−	71279.5i	−1.53125	−	0.220161i	−0.675427	−	0.737427i	$-0.736041\pi$
$569$	−495759.	−	71279.5i	−1.53125	−	0.220161i	−0.855825	+	0.517266i	$0.826950\pi$
$570$	86873.1	+	190225.i	0.267384	+	0.585489i
$571$	−201248.	+	28935.1i	−0.617248	+	0.0887468i	−0.443844	−	0.896104i	$-0.646386\pi$
$571$	−201248.	+	28935.1i	−0.617248	+	0.0887468i	−0.173404	+	0.984851i	$0.555477\pi$
$572$	72929.7	+	113481.i	0.222901	+	0.346841i
$573$	−174033.	−	150800.i	−0.530057	−	0.459297i
$574$		−	332851.i		−	1.01024i
$575$	−7190.12	−	92756.4i	−0.0217470	−	0.280549i
$576$	13824.0			0.0416667
$577$	−342910.	+	395739.i	−1.02998	+	1.18866i	−0.0481610	+	0.998840i	$0.515336\pi$
$577$	−342910.	+	395739.i	−1.02998	+	1.18866i	−0.981819	+	0.189820i	$0.939209\pi$
$578$	171738.	−	110369.i	0.514055	−	0.330363i
$579$	−16232.0	−	112896.i	−0.0484190	−	0.336761i
$580$	−136806.	+	62477.0i	−0.406675	+	0.185722i
$581$	32297.9	−	224637.i	0.0956801	−	0.665470i
$582$	51199.2	+	174369.i	0.151153	+	0.514781i
$583$	−307590.	−	197676.i	−0.904973	−	0.581591i
$584$	−28983.2	+	63464.4i	−0.0849808	+	0.186082i
$585$	26236.8	−	89354.2i	0.0766652	−	0.261098i
$586$	93324.4	−	80866.1i	0.271769	−	0.235489i
$587$	−212026.	−	244691.i	−0.615337	−	0.710137i	0.359477	−	0.933154i	$-0.382955\pi$
$587$	−212026.	−	244691.i	−0.615337	−	0.710137i	−0.974815	+	0.223017i	$0.928410\pi$
$588$	11981.3	+	3518.02i	0.0346536	+	0.0101752i
$589$	813589.	+	371554.i	2.34517	+	1.07100i
$590$	115872.	−	180301.i	0.332870	−	0.517956i
$591$	75150.5	−	22066.2i	0.215158	−	0.0631760i
$592$	120666.	+	17349.1i	0.344302	+	0.0495032i
$593$	83703.2	+	183284.i	0.238030	+	0.521214i	0.990516	−	0.137394i	$-0.0438727\pi$
$593$	83703.2	+	183284.i	0.238030	+	0.521214i	−0.752486	+	0.658608i	$0.771145\pi$
$594$	40694.0	−	5850.91i	0.115334	−	0.0165825i
$595$	−63429.1	−	98697.6i	−0.179166	−	0.278787i
$596$	45912.9	+	39783.8i	0.129253	+	0.111999i
$597$			170965.i			0.479689i
$598$	−50343.1	+	238253.i	−0.140779	+	0.666248i
$599$	−620488.			−1.72934			−0.864669	−	0.502342i	$-0.832472\pi$
$599$	−620488.			−1.72934			−0.864669	+	0.502342i	$0.832472\pi$
$600$	−13541.1	+	15627.3i	−0.0376142	+	0.0434091i
$601$	878.256	−	564.421i	0.00243149	−	0.00156262i	−0.539425	−	0.842034i	$-0.681358\pi$
$601$	878.256	−	564.421i	0.00243149	−	0.00156262i	0.541856	+	0.840471i	$0.317722\pi$
$602$	3991.86	+	27764.0i	0.0110149	+	0.0766106i
$603$	88244.8	−	40300.0i	0.242691	−	0.110833i
$604$	40191.1	−	279535.i	0.110168	−	0.766236i
$605$	−23326.9	−	79444.0i	−0.0637302	−	0.217045i
$606$	−119229.	−	76624.0i	−0.324667	−	0.208651i
$607$	−259575.	+	568389.i	−0.704506	+	1.54265i	0.129915	+	0.991525i	$0.458530\pi$
$607$	−259575.	+	568389.i	−0.704506	+	1.54265i	−0.834421	+	0.551128i	$0.814198\pi$
$608$	−34241.4	+	116616.i	−0.0926284	+	0.315464i
$609$	−181057.	+	156887.i	−0.488181	+	0.423011i
$610$	−38431.4	−	44352.2i	−0.103283	−	0.119194i
$611$	310052.	+	91039.4i	0.830524	+	0.243864i
$612$	−20927.6	−	9557.30i	−0.0558748	−	0.0255172i
$613$	64356.2	−	100140.i	0.171265	−	0.266494i	−0.745001	−	0.667063i	$-0.767551\pi$
$613$	64356.2	−	100140.i	0.171265	−	0.266494i	0.916267	+	0.400569i	$0.131188\pi$
$614$	403590.	−	118505.i	1.07054	−	0.314340i
$615$	−246795.	−	35483.8i	−0.652509	−	0.0938166i
$616$	50616.7	+	110835.i	0.133393	+	0.292089i
$617$	−684418.	+	98404.5i	−1.79784	+	0.258490i	−0.958495	−	0.285109i	$-0.907970\pi$
$617$	−684418.	+	98404.5i	−1.79784	+	0.258490i	−0.839345	+	0.543599i	$0.817061\pi$
$618$	−130460.	−	202999.i	−0.341586	−	0.531518i
$619$	95502.1	+	82753.1i	0.249248	+	0.215975i	0.770520	−	0.637416i	$-0.219997\pi$
$619$	95502.1	+	82753.1i	0.249248	+	0.215975i	−0.521272	+	0.853391i	$0.674542\pi$
$620$		−	225853.i		−	0.587548i
$621$	59677.6	+	44121.4i	0.154749	+	0.114411i
$622$	−174368.			−0.450699
$623$	−362104.	+	417890.i	−0.932948	+	1.07668i
$624$	45531.4	−	29261.3i	0.116934	−	0.0751492i
$625$	35547.0	+	247235.i	0.0910003	+	0.632921i
$626$	358432.	−	163691.i	0.914657	−	0.417710i
$627$	−51440.4	+	357776.i	−0.130849	+	0.910072i
$628$	17506.1	+	59620.4i	0.0443886	+	0.151174i
$629$	−170676.	−	109687.i	−0.431392	−	0.277238i
$630$	34943.9	−	76516.5i	0.0880421	−	0.192785i
$631$	13993.4	−	47657.0i	0.0351450	−	0.119693i	−0.940052	−	0.341030i	$-0.889224\pi$
$631$	13993.4	−	47657.0i	0.0351450	−	0.119693i	0.975197	+	0.221338i	$0.0710423\pi$
$632$	−107992.	+	93576.0i	−0.270370	+	0.234277i
$633$	−178938.	−	206506.i	−0.446577	−	0.515377i
$634$	92951.0	+	27292.9i	0.231247	+	0.0679001i
$635$	−54884.8	−	25065.0i	−0.136114	−	0.0621614i
$636$	−79312.9	+	123413.i	−0.196078	+	0.305104i
$637$	46908.8	−	13773.7i	0.115605	−	0.0339446i
$638$	−257304.	−	36994.7i	−0.632128	−	0.0908862i
$639$	−75709.6	−	165781.i	−0.185417	−	0.406006i
$640$	30377.9	−	4367.69i	0.0741649	−	0.0106633i
$641$	154453.	+	240334.i	0.375907	+	0.584923i	0.976733	−	0.214457i	$-0.0687981\pi$
$641$	154453.	+	240334.i	0.375907	+	0.584923i	−0.600826	+	0.799379i	$0.705162\pi$
$642$	123821.	+	107291.i	0.300416	+	0.260312i
$643$		−	234850.i		−	0.568026i	−0.958820	−	0.284013i	$-0.908334\pi$
$643$		−	234850.i		−	0.568026i	0.958820	−	0.284013i	$-0.0916658\pi$
$644$	−75637.4	+	206544.i	−0.182375	+	0.498013i
$645$	21011.4			0.0505051
$646$	132459.	−	152866.i	0.317408	−	0.366308i
$647$	−532937.	+	342498.i	−1.27311	+	0.818180i	−0.990022	−	0.140913i	$-0.954996\pi$
$647$	−532937.	+	342498.i	−1.27311	+	0.818180i	−0.283091	+	0.959093i	$0.591360\pi$
$648$	−2347.54	−	16327.5i	−0.00559065	−	0.0388839i
$649$	336967.	−	153888.i	0.800014	−	0.365354i
$650$	−11521.4	+	80133.4i	−0.0272697	+	0.189665i
$651$	−101359.	−	345197.i	−0.239167	−	0.814527i
$652$	41925.4	+	26943.8i	0.0986240	+	0.0633818i
$653$	−246640.	+	540067.i	−0.578413	+	1.26655i	0.363783	+	0.931484i	$0.381485\pi$
$653$	−246640.	+	540067.i	−0.578413	+	1.26655i	−0.942196	+	0.335063i	$0.891242\pi$
$654$	60160.1	−	204886.i	0.140654	−	0.479025i
$655$	322901.	−	279796.i	0.752640	−	0.652166i
$656$	−94894.3	−	109514.i	−0.220512	−	0.254485i
$657$	79879.4	+	23454.7i	0.185056	+	0.0543374i
$658$	265506.	+	121253.i	0.613229	+	0.280052i
$659$	−262549.	+	408534.i	−0.604560	+	0.940714i	0.395195	+	0.918597i	$0.370677\pi$
$659$	−262549.	+	408534.i	−0.604560	+	0.940714i	−0.999755	+	0.0221170i	$0.992959\pi$
$660$	87575.6	−	25714.5i	0.201046	−	0.0590324i
$661$	87302.1	+	12552.1i	0.199812	+	0.0287286i	0.241494	−	0.970402i	$-0.422363\pi$
$661$	87302.1	+	12552.1i	0.199812	+	0.0287286i	−0.0416821	+	0.999131i	$0.513272\pi$
$662$	124024.	+	271574.i	0.283001	+	0.619687i
$663$	−89158.1	+	12819.0i	−0.202831	+	0.0291626i
$664$	−53416.3	−	83117.3i	−0.121154	−	0.188519i
$665$	558918.	+	484305.i	1.26388	+	1.09516i
$666$		−	145464.i		−	0.327949i
$667$	−283454.	−	373982.i	−0.637134	−	0.840619i
$668$	195436.			0.437977
$669$	157366.	−	181610.i	0.351608	−	0.405777i
$670$	181183.	−	116439.i	0.403616	−	0.259388i
$671$	−14435.7	−	100403.i	−0.0320623	−	0.222998i
$672$	44469.9	−	20308.7i	0.0984754	−	0.0449722i
$673$	75988.7	−	528513.i	0.167772	−	1.16688i	−0.715705	−	0.698403i	$-0.753894\pi$
$673$	75988.7	−	528513.i	0.167772	−	1.16688i	0.883476	−	0.468476i	$-0.155197\pi$
$674$	−96002.9	−	326956.i	−0.211332	−	0.719729i
$675$	20756.9	+	13339.6i	0.0455569	+	0.0292776i
$676$	−6890.03	+	15087.1i	−0.0150774	+	0.0330150i
$677$	−46704.2	+	159060.i	−0.101901	+	0.347043i	−0.994623	−	0.103566i	$-0.966975\pi$
$677$	−46704.2	+	159060.i	−0.101901	+	0.347043i	0.892722	+	0.450609i	$0.148793\pi$
$678$	−15200.9	+	13171.7i	−0.0330682	+	0.0286538i
$679$	420865.	+	485704.i	0.912857	+	1.05349i
$680$	−49007.5	−	14389.9i	−0.105985	−	0.0311200i
$681$	243040.	+	110993.i	0.524063	+	0.239331i
$682$	211051.	−	328401.i	0.453751	−	0.706050i
$683$	265246.	−	77883.3i	0.568601	−	0.166956i	0.0152197	−	0.999884i	$-0.495155\pi$
$683$	265246.	−	77883.3i	0.568601	−	0.166956i	0.553382	+	0.832928i	$0.313337\pi$
$684$	143549.	+	20639.2i	0.306823	+	0.0441145i
$685$	191231.	+	418737.i	0.407546	+	0.892402i
$686$	−305661.	+	43947.5i	−0.649520	+	0.0933868i
$687$	−170539.	−	265363.i	−0.361335	−	0.562248i
$688$	9228.77	+	7996.78i	0.0194970	+	0.0168942i
$689$			574362.i			1.20989i
$690$	145080.	+	78100.7i	0.304727	+	0.164043i
$691$	876348.			1.83536			0.917678	−	0.397325i	$-0.130061\pi$
$691$	876348.			1.83536			0.917678	+	0.397325i	$0.130061\pi$
$692$	−103761.	+	119746.i	−0.216681	+	0.250063i
$693$	122312.	−	78604.8i	0.254684	−	0.163675i
$694$	−38934.0	−	270792.i	−0.0808370	−	0.562233i
$695$	−678831.	+	310012.i	−1.40537	+	0.641813i
$696$	−14843.2	+	103237.i	−0.0306415	+	0.213116i
$697$	67943.5	+	231394.i	0.139856	+	0.476307i
$698$	70103.4	+	45052.7i	0.143889	+	0.0924720i
$699$	−41526.7	+	90930.8i	−0.0849910	+	0.186104i
$700$	−20602.0	+	70164.0i	−0.0420449	+	0.143192i
$701$	424507.	−	367838.i	0.863872	−	0.748549i	−0.105429	−	0.994427i	$-0.533622\pi$
$701$	424507.	−	367838.i	0.863872	−	0.748549i	0.969301	+	0.245878i	$0.0790762\pi$
$702$	−42292.4	−	48808.0i	−0.0858199	−	0.0990414i
$703$	1.22709e6	+	360307.i	2.48295	+	0.729059i
$704$	48252.3	+	22036.1i	0.0973583	+	0.0444621i
$705$	118208.	−	183935.i	0.237831	−	0.370073i
$706$	51819.9	−	15215.7i	0.103965	−	0.0305269i
$707$	−496112.	−	71330.2i	−0.992524	−	0.142703i
$708$	−61743.7	−	135200.i	−0.123176	−	0.269718i
$709$	−739388.	+	106308.i	−1.47089	+	0.211482i	−0.830694	−	0.556730i	$-0.812056\pi$
$709$	−739388.	+	106308.i	−1.47089	+	0.211482i	−0.640196	+	0.768212i	$0.721147\pi$
$710$	−218749.	−	340380.i	−0.433939	−	0.675222i
$711$	128861.	+	111659.i	0.254908	+	0.220879i
$712$			240727.i			0.474860i
$713$	687692.	−	153898.i	1.35274	−	0.302728i
$714$	−81361.7			−0.159597
$715$	234014.	−	270066.i	0.457751	−	0.528272i
$716$	362513.	−	232973.i	0.707127	−	0.454443i
$717$	−23955.5	−	166614.i	−0.0465979	−	0.324095i
$718$	−191362.	+	87391.9i	−0.371198	+	0.169520i
$719$	51863.3	−	360717.i	0.100323	−	0.697764i	−0.876136	−	0.482064i	$-0.839887\pi$
$719$	51863.3	−	360717.i	0.100323	−	0.697764i	0.976460	−	0.215701i	$-0.0692035\pi$
$720$	−10317.3	−	35137.6i	−0.0199023	−	0.0677809i
$721$	−717896.	−	461364.i	−1.38099	−	0.887509i
$722$	−376548.	+	824524.i	−0.722346	+	1.58172i
$723$	−132340.	+	450707.i	−0.253171	+	0.862220i
$724$	48851.7	−	42330.3i	0.0931972	−	0.0807558i
$725$	−102164.	−	117904.i	−0.194367	−	0.224312i
$726$	−55093.6	−	16176.9i	−0.104527	−	0.0306919i
$727$	161941.	+	73956.0i	0.306400	+	0.139928i	0.562681	−	0.826674i	$-0.309770\pi$
$727$	161941.	+	73956.0i	0.306400	+	0.139928i	−0.256281	+	0.966602i	$0.582497\pi$
$728$	103481.	−	161019.i	0.195253	−	0.303820i
$729$	−18885.7	+	5545.34i	−0.0355368	+	0.0104345i
$730$	182944.	+	26303.3i	0.343299	+	0.0493589i
$731$	−8442.43	−	18486.3i	−0.0157991	−	0.0345952i
$732$	−40284.2	+	5792.00i	−0.0751818	+	0.0108095i
$733$	−64848.7	−	100907.i	−0.120696	−	0.187807i	0.775648	−	0.631166i	$-0.217423\pi$
$733$	−64848.7	−	100907.i	−0.120696	−	0.187807i	−0.896344	+	0.443359i	$0.853787\pi$
$734$	273010.	+	236565.i	0.506742	+	0.439094i
$735$		−	33079.4i		−	0.0612327i
$736$	33998.7	+	89520.5i	0.0627635	+	0.165260i
$737$	372256.			0.685342
$738$	−113232.	+	130677.i	−0.207901	+	0.239930i
$739$	653882.	−	420225.i	1.19732	−	0.769472i	0.218831	−	0.975763i	$-0.429776\pi$
$739$	653882.	−	420225.i	1.19732	−	0.769472i	0.978491	+	0.206291i	$0.0661394\pi$
$740$	−45959.3	−	319654.i	−0.0839286	−	0.583736i
$741$	516487.	−	235872.i	0.940640	−	0.429576i
$742$	−73833.3	+	513522.i	−0.134105	+	0.932720i
$743$	182552.	+	621715.i	0.330681	+	1.12620i	0.942224	+	0.334984i	$0.108731\pi$
$743$	182552.	+	621715.i	0.330681	+	1.12620i	−0.611543	+	0.791211i	$0.709451\pi$
$744$	−131763.	−	84679.0i	−0.238039	−	0.152978i
$745$	66855.3	−	146393.i	0.120455	−	0.263759i
$746$	153603.	−	523122.i	0.276008	−	0.939995i
$747$	−89098.7	+	77204.5i	−0.159673	+	0.138357i
$748$	−57812.4	−	66719.1i	−0.103328	−	0.119247i
$749$	555935.	+	163237.i	0.990970	+	0.290975i
$750$	226903.	+	103623.i	0.403383	+	0.184219i
$751$	−556243.	+	865531.i	−0.986245	+	1.53463i	−0.148250	+	0.988950i	$0.547364\pi$
$751$	−556243.	+	865531.i	−0.986245	+	1.53463i	−0.837995	+	0.545677i	$0.816272\pi$
$752$	121925.	−	35800.3i	0.215604	−	0.0633069i
$753$	186494.	+	26813.8i	0.328908	+	0.0472899i
$754$	169633.	+	371445.i	0.298379	+	0.653360i
$755$	−740513.	+	106470.i	−1.29909	+	0.186781i
$756$	−31538.3	−	49074.6i	−0.0551817	−	0.0858643i
$757$	−672374.	−	582616.i	−1.17333	−	1.01669i	−0.999490	−	0.0319203i	$-0.989838\pi$
$757$	−672374.	−	582616.i	−1.17333	−	1.01669i	−0.173838	−	0.984774i	$-0.555617\pi$
$758$		−	232882.i		−	0.405320i
$759$	137972.	+	249134.i	0.239500	+	0.432463i
$760$	321967.			0.557422
$761$	184771.	−	213237.i	0.319054	−	0.368208i	−0.573456	−	0.819237i	$-0.694397\pi$
$761$	184771.	−	213237.i	0.319054	−	0.368208i	0.892509	+	0.451029i	$0.148943\pi$
$762$	−35200.9	+	22622.2i	−0.0606238	+	0.0389606i
$763$	−107470.	−	747473.i	−0.184603	−	1.28394i
$764$	−322498.	+	147280.i	−0.552511	+	0.252323i
$765$	−8673.61	+	60326.3i	−0.0148210	+	0.103082i
$766$	−24854.0	−	84644.9i	−0.0423583	−	0.144259i
$767$	−489540.	−	314608.i	−0.832142	−	0.534785i
$768$	8841.46	−	19360.1i	0.0149900	−	0.0328235i
$769$	−223097.	+	759799.i	−0.377260	+	1.28483i	0.524061	+	0.851681i	$0.324416\pi$
$769$	−223097.	+	759799.i	−0.377260	+	1.28483i	−0.901322	+	0.433151i	$0.857402\pi$
$770$	243942.	−	211377.i	0.411438	−	0.356513i
$771$	47882.0	+	55258.8i	0.0805497	+	0.0929593i
$772$	−168489.	−	49472.9i	−0.282708	−	0.0830105i
$773$	−135458.	−	61861.4i	−0.226696	−	0.103529i	0.298829	−	0.954307i	$-0.403404\pi$
$773$	−135458.	−	61861.4i	−0.226696	−	0.103529i	−0.525525	+	0.850778i	$0.676131\pi$
$774$	7877.78	−	12258.1i	0.0131499	−	0.0204616i
$775$	224792.	−	66004.8i	0.374263	−	0.109894i
$776$	276944.	+	39818.5i	0.459905	+	0.0661243i
$777$	−213700.	−	467938.i	−0.353967	−	0.775079i
$778$	−485818.	+	69850.1i	−0.802628	+	0.115400i
$779$	−821883.	−	1.27887e6i	−1.35436	−	2.10743i
$780$	−108358.	−	93892.3i	−0.178102	−	0.154327i
$781$		−	699339.i		−	1.14653i
$782$	10421.3	−	159026.i	0.0170415	−	0.260049i
$783$	124454.			0.202994
$784$	12589.8	−	14529.4i	0.0204827	−	0.0236383i
$785$	138477.	−	88993.6i	0.224718	−	0.144417i
$786$	−42168.0	−	293285.i	−0.0682555	−	0.474727i
$787$	324800.	−	148331.i	0.524404	−	0.239487i	−0.135581	−	0.990766i	$-0.543290\pi$
$787$	324800.	−	148331.i	0.524404	−	0.239487i	0.659985	+	0.751279i	$0.270563\pi$
$788$	17161.2	−	119359.i	0.0276373	−	0.192222i
$789$	60232.1	+	205132.i	0.0967551	+	0.329518i
$790$	318448.	+	204654.i	0.510252	+	0.327919i
$791$	−29548.9	+	64703.1i	−0.0472268	+	0.103412i
$792$	17832.8	−	60732.8i	0.0284294	−	0.0968218i
$793$	−120422.	+	104346.i	−0.191496	+	0.165932i
$794$	−505932.	−	583877.i	−0.802511	−	0.926147i
$795$	372884.	+	109489.i	0.589983	+	0.173235i
$796$	239432.	+	109345.i	0.377882	+	0.172573i
$797$	−227337.	+	353743.i	−0.357893	+	0.556892i	−0.972782	−	0.231721i	$-0.925564\pi$
$797$	−227337.	+	353743.i	−0.357893	+	0.556892i	0.614889	+	0.788613i	$0.289201\pi$
$798$	492099.	−	144493.i	0.772763	−	0.226904i
$799$	−209327.	−	30096.7i	−0.327893	−	0.0471439i
$800$	13225.0	+	28958.7i	0.0206641	+	0.0452480i
$801$	284322.	−	40879.4i	0.443145	−	0.0637147i
$802$	312467.	+	486208.i	0.485797	+	0.755915i
$803$	241429.	+	209200.i	0.374420	+	0.324437i
$804$		−	149359.i		−	0.231057i
$805$	581441.	+	38102.9i	0.897251	+	0.0587984i
$806$	−613222.			−0.943946
$807$	−190457.	+	219800.i	−0.292449	+	0.337505i
$808$	−183566.	+	117970.i	−0.281170	+	0.180697i
$809$	64070.2	+	445618.i	0.0978947	+	0.680872i	0.978382	+	0.206804i	$0.0663061\pi$
$809$	64070.2	+	445618.i	0.0978947	+	0.680872i	−0.880488	+	0.474069i	$0.842785\pi$
$810$	−39748.9	+	18152.7i	−0.0605836	+	0.0276676i
$811$	141115.	−	981474.i	0.214551	−	1.49223i	−0.543152	−	0.839634i	$-0.682769\pi$
$811$	141115.	−	981474.i	0.214551	−	1.49223i	0.757703	−	0.652600i	$-0.226322\pi$
$812$	103916.	+	353905.i	0.157605	+	0.536754i
$813$	169650.	+	109027.i	0.256669	+	0.164951i
$814$	231876.	−	507739.i	0.349951	−	0.766287i
$815$	37195.0	−	126674.i	0.0559976	−	0.190710i
$816$	−26769.4	+	23195.8i	−0.0402030	+	0.0348361i
$817$	83892.8	+	96817.4i	0.125684	+	0.145047i
$818$	319959.	+	93948.4i	0.478176	+	0.140405i
$819$	−207752.	−	94877.3i	−0.309726	−	0.141447i
$820$	−207538.	+	322935.i	−0.308652	+	0.480272i
$821$	144251.	−	42355.9i	0.214009	−	0.0628387i	−0.172971	−	0.984927i	$-0.555337\pi$
$821$	144251.	−	42355.9i	0.214009	−	0.0628387i	0.386980	+	0.922088i	$0.373518\pi$
$822$	315990.	+	45432.5i	0.467659	+	0.0672393i
$823$	314203.	+	688009.i	0.463886	+	1.01577i	0.986585	+	0.163251i	$0.0521980\pi$
$823$	314203.	+	688009.i	0.463886	+	1.01577i	−0.522699	+	0.852517i	$0.675075\pi$
$824$	−367733.	+	52872.0i	−0.541599	+	0.0778702i
$825$	51187.3	+	79649.0i	0.0752063	+	0.117023i
$826$	−397242.	−	344212.i	−0.582231	−	0.504506i
$827$		−	356841.i		−	0.521752i	−0.965372	−	0.260876i	$-0.915989\pi$
$827$		−	356841.i		−	0.521752i	0.965372	−	0.260876i	$-0.0840113\pi$
$828$	99958.9	−	55357.8i	0.145801	−	0.0807455i
$829$	−688184.			−1.00137			−0.500686	−	0.865629i	$-0.666919\pi$
$829$	−688184.			−1.00137			−0.500686	+	0.865629i	$0.666919\pi$
$830$	−171400.	+	197806.i	−0.248802	+	0.287133i
$831$	−7452.96	+	4789.73i	−0.0107926	+	0.00693599i
$832$	−11858.9	−	82480.2i	−0.0171315	−	0.119152i
$833$	−29104.1	+	13291.4i	−0.0419435	+	0.0191550i
$834$	−73652.3	+	512263.i	−0.105890	+	0.736480i
$835$	−145861.	−	496756.i	−0.209202	−	0.712476i
$836$	468154.	+	300865.i	0.669849	+	0.430486i
$837$	−77638.6	+	170005.i	−0.110822	+	0.242667i
$838$	19807.6	−	67458.5i	0.0282062	−	0.0960613i
$839$	−1.00064e6	+	867059.i	−1.42152	+	1.23176i	−0.488192	+	0.872736i	$0.662343\pi$
$839$	−1.00064e6	+	867059.i	−1.42152	+	1.23176i	−0.933330	+	0.359020i	$0.883111\pi$
$840$	−84809.8	−	97875.8i	−0.120195	−	0.138713i
$841$	−76400.1	−	22433.1i	−0.108019	−	0.0317174i
$842$	176105.	+	80424.4i	0.248398	+	0.113439i
$843$	−23911.8	+	37207.4i	−0.0336478	+	0.0523570i
$844$	−403649.	+	118522.i	−0.566656	+	0.166385i
$845$	43490.3	+	6252.96i	0.0609086	+	0.00875734i
$846$	−62988.4	−	137925.i	−0.0880076	−	0.192710i
$847$	−200994.	+	28898.6i	−0.280167	+	0.0402819i
$848$	122110.	+	190007.i	0.169809	+	0.264228i
$849$	413621.	+	358404.i	0.573835	+	0.497231i
$850$		−	52982.6i		−	0.0733323i
$851$	941985.	−	357754.i	1.30072	−	0.493998i
$852$	−280593.			−0.386543
$853$	−381049.	+	439754.i	−0.523700	+	0.604382i	−0.954553	−	0.298040i	$-0.903667\pi$
$853$	−381049.	+	439754.i	−0.523700	+	0.604382i	0.430853	+	0.902422i	$0.358213\pi$
$854$	−121080.	+	77813.3i	−0.166018	+	0.106694i
$855$	−54675.2	−	380274.i	−0.0747925	−	0.520193i
$856$	229451.	−	104787.i	0.313142	−	0.143007i
$857$	−142678.	+	992347.i	−0.194265	+	1.35115i	0.626295	+	0.779586i	$0.284570\pi$
$857$	−142678.	+	992347.i	−0.194265	+	1.35115i	−0.820561	+	0.571559i	$0.806339\pi$
$858$	−69818.3	−	237779.i	−0.0948407	−	0.322998i
$859$	465563.	+	299199.i	0.630946	+	0.405485i	0.816660	−	0.577119i	$-0.195823\pi$
$859$	465563.	+	299199.i	0.630946	+	0.405485i	−0.185713	+	0.982604i	$0.559460\pi$
$860$	13438.3	−	29425.8i	0.0181697	−	0.0397861i
$861$	−172276.	+	586717.i	−0.232390	+	0.791449i
$862$	−362400.	+	314022.i	−0.487724	+	0.422615i
$863$	817614.	+	943577.i	1.09781	+	1.26694i	0.961062	+	0.276332i	$0.0891191\pi$
$863$	817614.	+	943577.i	1.09781	+	1.26694i	0.136746	+	0.990606i	$0.456335\pi$
$864$	−24367.6	−	7154.97i	−0.0326426	−	0.00958474i
$865$	381809.	+	174366.i	0.510287	+	0.233040i
$866$	83323.4	−	129654.i	0.111104	−	0.172882i
$867$	−359847.	+	105660.i	−0.478717	+	0.140564i
$868$	−548265.	−	78828.6i	−0.727698	−	0.104627i
$869$	271797.	+	595153.i	0.359920	+	0.788115i
$870$	273484.	−	39321.1i	0.361321	−	0.0519501i
$871$	−316148.	−	491936.i	−0.416730	−	0.648444i
$872$	−248461.	−	215292.i	−0.326757	−	0.283136i
$873$		−	333859.i		−	0.438061i
$874$	219390.	+	980345.i	0.287206	+	1.28338i
$875$	882149.			1.15219
$876$	83936.3	−	96867.7i	0.109381	−	0.126232i
$877$	26404.8	−	16969.3i	0.0343307	−	0.0220630i	−0.523363	−	0.852110i	$-0.675323\pi$
$877$	26404.8	−	16969.3i	0.0343307	−	0.0220630i	0.557694	+	0.830047i	$0.311686\pi$
$878$	38498.6	+	267764.i	0.0499408	+	0.347346i
$879$	−206357.	+	94240.2i	−0.267080	+	0.121972i
$880$	19998.6	−	139093.i	0.0258246	−	0.179614i
$881$	−252077.	−	858497.i	−0.324775	−	1.10608i	−0.946462	−	0.322815i	$-0.895371\pi$
$881$	−252077.	−	858497.i	−0.324775	−	1.10608i	0.621687	−	0.783266i	$-0.286447\pi$
$882$	−19298.6	−	12402.4i	−0.0248078	−	0.0159430i
$883$	−250653.	+	548854.i	−0.321478	+	0.703940i	−0.999517	−	0.0310870i	$-0.990103\pi$
$883$	−250653.	+	548854.i	−0.321478	+	0.703940i	0.678038	+	0.735027i	$0.262830\pi$
$884$	−39070.5	+	133062.i	−0.0499971	+	0.170274i
$885$	−297567.	+	257843.i	−0.379925	+	0.329207i
$886$	587732.	+	678279.i	0.748707	+	0.864054i
$887$	272844.	+	80114.4i	0.346791	+	0.101827i	0.450489	−	0.892782i	$-0.351249\pi$
$887$	272844.	+	80114.4i	0.346791	+	0.101827i	−0.103698	+	0.994609i	$0.533068\pi$
$888$	−203718.	−	93034.9i	−0.258347	−	0.117983i
$889$	−80002.2	+	124486.i	−0.101228	+	0.157513i
$890$	611877.	−	179663.i	0.772474	−	0.226819i
$891$	−74759.6	−	10748.8i	−0.0941698	−	0.0135396i
$892$	−153692.	−	336539.i	−0.193162	−	0.422967i
$893$	1.31952e6	−	189718.i	1.65468	−	0.237907i
$894$	−60339.6	−	93890.3i	−0.0754966	−	0.117475i
$895$	−862722.	−	747553.i	−1.07702	−	0.933246i
$896$		−	75267.7i		−	0.0937546i
$897$	212054.	−	393912.i	0.263549	−	0.489570i
$898$	−370165.			−0.459032
$899$	773856.	−	893078.i	0.957505	−	1.10502i
$900$	31957.3	−	20537.7i	0.0394534	−	0.0253552i
$901$	−53494.9	−	372065.i	−0.0658966	−	0.458321i
$902$	−603538.	+	275627.i	−0.741809	+	0.338773i
$903$	7333.51	−	51005.7i	0.00899366	−	0.0625523i
$904$	8724.44	+	29712.7i	0.0106758	+	0.0363585i
$905$	−144054.	−	92577.9i	−0.175885	−	0.113034i
$906$	−215525.	+	471935.i	−0.262568	+	0.574944i
$907$	428870.	−	1.46060e6i	0.521328	−	1.77548i	−0.103404	−	0.994639i	$-0.532974\pi$
$907$	428870.	−	1.46060e6i	0.521328	−	1.77548i	0.624732	−	0.780839i	$-0.285208\pi$
$908$	310884.	−	269382.i	0.377074	−	0.326736i
$909$	170507.	+	196775.i	0.206355	+	0.238146i
$910$	−486508.	−	142852.i	−0.587499	−	0.172505i
$911$	−982981.	−	448912.i	−1.18443	−	0.540910i	−0.276898	−	0.960899i	$-0.589307\pi$
$911$	−982981.	−	448912.i	−1.18443	−	0.540910i	−0.907529	+	0.419989i	$0.862034\pi$
$912$	120715.	−	187836.i	0.145134	−	0.225834i
$913$	−434065.	+	127453.i	−0.520730	+	0.152900i
$914$	−221866.	−	31899.5i	−0.265581	−	0.0381848i
$915$	44787.5	+	98070.9i	0.0534952	+	0.117138i
$916$	−480706.	+	69115.0i	−0.572912	+	0.0823724i
$917$	−566511.	−	881508.i	−0.673705	−	1.04830i
$918$	31942.4	+	27678.3i	0.0379038	+	0.0328438i
$919$		−	1.03973e6i		−	1.23108i	−0.788104	−	0.615542i	$-0.788937\pi$
$919$		−	1.03973e6i		−	1.23108i	0.788104	−	0.615542i	$-0.211063\pi$
$920$	202167.	−	153230.i	0.238855	−	0.181037i
$921$	−772744.			−0.910996
$922$	−694459.	+	801448.i	−0.816930	+	0.942787i
$923$	−924176.	+	593932.i	−1.08480	+	0.697161i
$924$	−31856.5	−	221567.i	−0.0373125	−	0.259514i
$925$	304720.	−	139161.i	0.356138	−	0.162643i
$926$	−122123.	+	849385.i	−0.142422	+	0.990565i
$927$	124894.	+	425350.i	0.145339	+	0.494979i
$928$	135087.	+	86815.1i	0.156862	+	0.100809i
$929$	−132976.	+	291177.i	−0.154079	+	0.337385i	−0.970892	−	0.239517i	$-0.923011\pi$
$929$	−132976.	+	291177.i	−0.154079	+	0.337385i	0.816814	+	0.576901i	$0.195738\pi$
$930$	−116896.	+	398112.i	−0.135156	+	0.460298i
$931$	152425.	−	132077.i	0.175856	−	0.152380i
$932$	100786.	+	116314.i	0.116030	+	0.133906i
$933$	307359.	+	90248.8i	0.353088	+	0.103676i
$934$	381056.	+	174023.i	0.436813	+	0.199486i
$935$	−126438.	+	196741.i	−0.144629	+	0.225047i
$936$	−95403.3	+	28012.9i	−0.108896	+	0.0319747i
$937$	−829767.	−	119302.i	−0.945098	−	0.135885i	−0.347500	−	0.937680i	$-0.612969\pi$
$937$	−829767.	−	119302.i	−0.945098	−	0.135885i	−0.597598	+	0.801796i	$0.703878\pi$
$938$	−219422.	−	480467.i	−0.249388	−	0.546083i
$939$	−716531.	+	103022.i	−0.812651	+	0.116842i
$940$	−181993.	−	283187.i	−0.205968	−	0.320492i
$941$	−643785.	−	557843.i	−0.727046	−	0.629989i	0.210604	−	0.977572i	$-0.432457\pi$
$941$	−643785.	−	557843.i	−0.727046	−	0.629989i	−0.937649	+	0.347583i	$0.887003\pi$
$942$		−	114154.i		−	0.128644i
$943$	−1.12471e6	−	411874.i	−1.26479	−	0.463170i
$944$	−228833.			−0.256788
$945$	−101199.	+	116790.i	−0.113321	+	0.130780i
$946$	47037.1	−	30228.9i	0.0525604	−	0.0337785i
$947$	−98939.7	−	688141.i	−0.110324	−	0.767322i	−0.967604	−	0.252471i	$-0.918757\pi$
$947$	−98939.7	−	688141.i	−0.110324	−	0.767322i	0.857280	−	0.514850i	$-0.172152\pi$
$948$	238791.	−	109052.i	0.265706	−	0.121344i
$949$	71417.1	−	496717.i	0.0792993	−	0.551539i
$950$	94093.7	+	320454.i	0.104259	+	0.355073i
$951$	−149719.	−	96218.3i	−0.165545	−	0.106389i
$952$	−52036.8	+	113945.i	−0.0574165	+	0.125725i
$953$	312793.	−	1.06528e6i	0.344407	−	1.17294i	−0.587190	−	0.809449i	$-0.699766\pi$
$953$	312793.	−	1.06528e6i	0.344407	−	1.17294i	0.931597	−	0.363493i	$-0.118416\pi$
$954$	203681.	−	176490.i	0.223796	−	0.193921i
$955$	615046.	+	709801.i	0.674374	+	0.778269i
$956$	−248659.	−	73012.9i	−0.272075	−	0.0798884i
$957$	434402.	+	198385.i	0.474316	+	0.216613i
$958$	−505650.	+	786806.i	−0.550958	+	0.857308i
$959$	1.08324e6	−	318068.i	1.17784	−	0.345846i
$960$	−55807.8	−	8023.96i	−0.0605554	−	0.00870655i
$961$	353550.	+	774165.i	0.382828	+	0.838276i
$962$	−867903.	+	124786.i	−0.937823	+	0.134839i
$963$	−162728.	−	253209.i	−0.175472	−	0.273040i
$964$	546561.	+	473598.i	0.588145	+	0.509631i
$965$			465187.i			0.499543i
$966$	240228.	−	324927.i	0.257436	−	0.348203i
$967$	−99253.1			−0.106143			−0.0530715	−	0.998591i	$-0.516901\pi$
$967$	−99253.1			−0.106143			−0.0530715	+	0.998591i	$0.516901\pi$
$968$	−57891.7	+	66810.6i	−0.0617825	+	0.0713009i
$969$	−312606.	+	200900.i	−0.332928	+	0.213960i
$970$	−105483.	−	733649.i	−0.112108	−	0.779731i
$971$	1.18570e6	−	541490.i	1.25758	−	0.574318i	0.328608	−	0.944467i	$-0.393421\pi$
$971$	1.18570e6	−	541490.i	1.25758	−	0.574318i	0.928972	+	0.370149i	$0.120693\pi$
$972$	−4312.70	+	29995.5i	−0.00456475	+	0.0317485i
$973$	515633.	+	1.75608e6i	0.544647	+	1.85490i
$974$	152676.	+	98118.6i	0.160935	+	0.103427i
$975$	61783.9	−	135288.i	0.0649930	−	0.142315i
$976$	−17653.2	+	60121.2i	−0.0185321	+	0.0631144i
$977$	−491205.	+	425632.i	−0.514605	+	0.445907i	−0.873041	−	0.487647i	$-0.837855\pi$
$977$	−491205.	+	425632.i	−0.514605	+	0.445907i	0.358436	+	0.933554i	$0.383310\pi$
$978$	−59956.5	−	69193.5i	−0.0626843	−	0.0723416i
$979$	1.05758e6	+	310535.i	1.10344	+	0.324000i
$980$	−46326.8	−	21156.7i	−0.0482370	−	0.0220291i
$981$	−212089.	+	330016.i	−0.220384	+	0.342924i
$982$	−779616.	+	228916.i	−0.808458	+	0.237385i
$983$	−1.39208e6	−	200150.i	−1.44064	−	0.207133i	−0.622712	−	0.782451i	$-0.713969\pi$
$983$	−1.39208e6	−	200150.i	−1.44064	−	0.207133i	−0.817930	+	0.575318i	$0.804878\pi$
$984$	110589.	+	242155.i	0.114214	+	0.250094i
$985$	−316192.	+	45461.6i	−0.325896	+	0.0468568i
$986$	−144482.	−	224819.i	−0.148614	−	0.231249i
$987$	−405251.	−	351152.i	−0.415996	−	0.360463i
$988$		−	874183.i		−	0.895547i
$989$	98754.5	+	20866.9i	0.100963	+	0.0213337i
$990$	−167679.			−0.171083
$991$	−687248.	+	793126.i	−0.699787	+	0.807597i	−0.988724	−	0.149751i	$-0.952153\pi$
$991$	−687248.	+	793126.i	−0.699787	+	0.807597i	0.288937	+	0.957348i	$0.406698\pi$
$992$	−202862.	+	130372.i	−0.206148	+	0.132483i
$993$	−78056.6	−	542895.i	−0.0791609	−	0.550576i
$994$	−902630.	+	412217.i	−0.913560	+	0.417209i
$995$	99234.6	−	690192.i	0.100234	−	0.697146i
$996$	51137.4	+	174158.i	0.0515490	+	0.175560i
$997$	−1.06147e6	−	682164.i	−1.06787	−	0.686276i	−0.116143	−	0.993233i	$-0.537053\pi$
$997$	−1.06147e6	−	682164.i	−1.06787	−	0.686276i	−0.951723	+	0.306957i	$0.900689\pi$
$998$	387210.	−	847871.i	0.388763	−	0.851273i
$999$	−75288.6	+	256409.i	−0.0754394	+	0.256923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.5.h.a.7.5	✓	160
23.10	odd	22	inner	138.5.h.a.79.5	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.5.h.a.7.5	✓	160	1.1	even	1	trivial
138.5.h.a.79.5	yes	160	23.10	odd	22	inner

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	138.h (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85223 + 2.13758i) q^{2} +(4.37128 - 2.80925i) q^{3} +(-1.13852 - 7.91857i) q^{4} +(-19.2776 + 8.80377i) q^{5} +(-2.09159 + 14.5473i) q^{6} +(14.6430 + 49.8696i) q^{7} +(19.0354 + 12.2333i) q^{8} +(11.2162 - 24.5601i) q^{9} +O(q^{10})\)	\(q+(-1.85223 + 2.13758i) q^{2} +(4.37128 - 2.80925i) q^{3} +(-1.13852 - 7.91857i) q^{4} +(-19.2776 + 8.80377i) q^{5} +(-2.09159 + 14.5473i) q^{6} +(14.6430 + 49.8696i) q^{7} +(19.0354 + 12.2333i) q^{8} +(11.2162 - 24.5601i) q^{9} +(16.8876 - 57.5140i) q^{10} +(78.2998 - 67.8472i) q^{11} +(-27.2220 - 31.4159i) q^{12} +(-156.158 - 45.8521i) q^{13} +(-133.723 - 61.0690i) q^{14} +(-59.5357 + 92.6393i) q^{15} +(-61.4076 + 18.0309i) q^{16} +(105.428 + 15.1583i) q^{17} +(31.7242 + 69.4664i) q^{18} +(-664.579 + 95.5520i) q^{19} +(91.6612 + 142.628i) q^{20} +(204.105 + 176.858i) q^{21} +293.041i q^{22} +(-371.823 + 376.283i) q^{23} +117.576 q^{24} +(-115.170 + 132.913i) q^{25} +(387.253 - 248.872i) q^{26} +(-19.9662 - 138.868i) q^{27} +(378.224 - 172.729i) q^{28} +(-126.244 + 878.048i) q^{29} +(-87.7507 - 298.851i) q^{30} +(-1120.67 - 720.209i) q^{31} +(75.1981 - 164.661i) q^{32} +(151.671 - 516.543i) q^{33} +(-227.679 + 197.285i) q^{34} +(-721.322 - 832.450i) q^{35} +(-207.250 - 60.8542i) q^{36} +(-1732.66 - 791.278i) q^{37} +(1026.70 - 1597.58i) q^{38} +(-811.421 + 238.255i) q^{39} +(-474.655 - 68.2451i) q^{40} +(940.575 + 2059.57i) q^{41} +(-756.097 + 108.710i) q^{42} +(-103.156 - 160.514i) q^{43} +(-626.398 - 542.777i) q^{44} +572.203i q^{45} +(-115.636 - 1491.76i) q^{46} -1985.50 q^{47} +(-217.776 + 251.327i) q^{48} +(-252.707 + 162.405i) q^{49} +(-70.7920 - 492.369i) q^{50} +(503.439 - 229.913i) q^{51} +(-185.295 + 1288.75i) q^{52} +(-994.260 - 3386.14i) q^{53} +(333.824 + 214.536i) q^{54} +(-912.119 + 1997.26i) q^{55} +(-331.334 + 1128.42i) q^{56} +(-2636.63 + 2284.65i) q^{57} +(-1643.07 - 1896.20i) q^{58} +(3430.68 + 1007.34i) q^{59} +(801.354 + 365.966i) q^{60} +(529.316 - 823.632i) q^{61} +(3615.24 - 1061.53i) q^{62} +(1389.04 + 199.714i) q^{63} +(212.692 + 465.732i) q^{64} +(3414.02 - 490.862i) q^{65} +(823.225 + 1280.96i) q^{66} +(2715.42 + 2352.93i) q^{67} -852.098i q^{68} +(-568.269 + 2689.38i) q^{69} +3115.48 q^{70} +(4420.32 - 5101.33i) q^{71} +(513.956 - 330.299i) q^{72} +(438.813 + 3052.01i) q^{73} +(4900.69 - 2238.07i) q^{74} +(-130.053 + 904.540i) q^{75} +(1513.27 + 5153.73i) q^{76} +(4530.06 + 2911.29i) q^{77} +(993.646 - 2175.78i) q^{78} +(-1779.17 + 6059.30i) q^{79} +(1025.05 - 888.210i) q^{80} +(-477.393 - 550.941i) q^{81} +(-6144.66 - 1804.24i) q^{82} +(-3971.87 - 1813.89i) q^{83} +(1168.09 - 1817.58i) q^{84} +(-2165.85 + 635.950i) q^{85} +(534.180 + 76.8035i) q^{86} +(1914.81 + 4192.85i) q^{87} +(2320.46 - 333.632i) q^{88} +(5751.74 + 8949.88i) q^{89} +(-1223.13 - 1059.85i) q^{90} -8458.95i q^{91} +(3402.95 + 2515.90i) q^{92} -6922.00 q^{93} +(3677.59 - 4244.17i) q^{94} +(11970.2 - 7692.81i) q^{95} +(-133.862 - 931.030i) q^{96} +(11247.7 - 5136.67i) q^{97} +(120.916 - 840.991i) q^{98} +(-788.104 - 2684.04i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 128 q^{4} - 432 q^{9}+O(q^{10}) \) 160 * q - 128 * q^4 - 432 * q^9	\( 160 q - 128 q^{4} - 432 q^{9} + 208 q^{13} - 1024 q^{16} - 1980 q^{17} - 3828 q^{19} - 3168 q^{20} + 3120 q^{23} + 9768 q^{25} + 4416 q^{26} + 5280 q^{28} - 828 q^{29} - 7748 q^{31} + 16464 q^{35} - 3456 q^{36} - 3520 q^{37} - 9072 q^{39} - 5472 q^{41} - 7216 q^{43} - 1280 q^{46} + 6960 q^{47} + 13888 q^{49} - 7296 q^{50} + 17424 q^{51} + 1664 q^{52} + 14784 q^{53} + 37316 q^{55} - 15840 q^{57} - 9984 q^{58} - 29808 q^{59} - 44968 q^{61} - 8192 q^{64} - 5852 q^{67} - 10584 q^{69} + 4352 q^{70} + 30048 q^{71} + 17084 q^{73} + 4176 q^{75} - 14160 q^{77} - 6912 q^{78} + 28424 q^{79} - 11664 q^{81} - 128 q^{82} - 35904 q^{83} - 91892 q^{85} + 8064 q^{87} - 15312 q^{89} - 6720 q^{92} + 11952 q^{93} + 21248 q^{94} + 224268 q^{95} + 41712 q^{97} + 62976 q^{98} + 17820 q^{99}+O(q^{100}) \) 160 * q - 128 * q^4 - 432 * q^9 + 208 * q^13 - 1024 * q^16 - 1980 * q^17 - 3828 * q^19 - 3168 * q^20 + 3120 * q^23 + 9768 * q^25 + 4416 * q^26 + 5280 * q^28 - 828 * q^29 - 7748 * q^31 + 16464 * q^35 - 3456 * q^36 - 3520 * q^37 - 9072 * q^39 - 5472 * q^41 - 7216 * q^43 - 1280 * q^46 + 6960 * q^47 + 13888 * q^49 - 7296 * q^50 + 17424 * q^51 + 1664 * q^52 + 14784 * q^53 + 37316 * q^55 - 15840 * q^57 - 9984 * q^58 - 29808 * q^59 - 44968 * q^61 - 8192 * q^64 - 5852 * q^67 - 10584 * q^69 + 4352 * q^70 + 30048 * q^71 + 17084 * q^73 + 4176 * q^75 - 14160 * q^77 - 6912 * q^78 + 28424 * q^79 - 11664 * q^81 - 128 * q^82 - 35904 * q^83 - 91892 * q^85 + 8064 * q^87 - 15312 * q^89 - 6720 * q^92 + 11952 * q^93 + 21248 * q^94 + 224268 * q^95 + 41712 * q^97 + 62976 * q^98 + 17820 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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