LMFDB - Embedded newform 201.4.e.a.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(37,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("201.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.e (of order $3$, degree $2$, 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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.5
Character	$\chi$	$=$	201.37
Dual form			201.4.e.a.163.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18372 - 2.05026i) q^{2} +3.00000 q^{3} +(1.19762 - 2.07434i) q^{4} -11.7568 q^{5} +(-3.55115 - 6.15078i) q^{6} +(-6.15324 + 10.6577i) q^{7} -24.6101 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(-1.18372 - 2.05026i) q^{2} +3.00000 q^{3} +(1.19762 - 2.07434i) q^{4} -11.7568 q^{5} +(-3.55115 - 6.15078i) q^{6} +(-6.15324 + 10.6577i) q^{7} -24.6101 q^{8} +9.00000 q^{9} +(13.9167 + 24.1045i) q^{10} +(-9.68619 + 16.7770i) q^{11} +(3.59287 - 6.22303i) q^{12} +(31.4840 + 54.5319i) q^{13} +29.1348 q^{14} -35.2704 q^{15} +(19.5504 + 33.8623i) q^{16} +(14.4078 + 24.9550i) q^{17} +(-10.6535 - 18.4523i) q^{18} +(15.2816 + 26.4685i) q^{19} +(-14.0802 + 24.3877i) q^{20} +(-18.4597 + 31.9732i) q^{21} +45.8629 q^{22} +(-29.9767 - 51.9211i) q^{23} -73.8302 q^{24} +13.2226 q^{25} +(74.5364 - 129.101i) q^{26} +27.0000 q^{27} +(14.7385 + 25.5279i) q^{28} +(-51.4108 + 89.0461i) q^{29} +(41.7502 + 72.3136i) q^{30} +(-33.2582 + 57.6049i) q^{31} +(-52.1560 + 90.3368i) q^{32} +(-29.0586 + 50.3309i) q^{33} +(34.1095 - 59.0794i) q^{34} +(72.3425 - 125.301i) q^{35} +(10.7786 - 18.6691i) q^{36} +(11.4720 + 19.8701i) q^{37} +(36.1782 - 62.6626i) q^{38} +(94.4520 + 163.596i) q^{39} +289.336 q^{40} +(-57.9800 + 100.424i) q^{41} +87.4045 q^{42} +160.358 q^{43} +(23.2008 + 40.1850i) q^{44} -105.811 q^{45} +(-70.9678 + 122.920i) q^{46} +(-45.1387 + 78.1825i) q^{47} +(58.6513 + 101.587i) q^{48} +(95.7752 + 165.887i) q^{49} +(-15.6518 - 27.1097i) q^{50} +(43.2234 + 74.8651i) q^{51} +150.824 q^{52} -151.543 q^{53} +(-31.9604 - 55.3570i) q^{54} +(113.879 - 197.244i) q^{55} +(151.432 - 262.288i) q^{56} +(45.8448 + 79.4056i) q^{57} +243.423 q^{58} -235.204 q^{59} +(-42.2407 + 73.1630i) q^{60} +(241.559 + 418.392i) q^{61} +157.473 q^{62} +(-55.3792 + 95.9196i) q^{63} +559.758 q^{64} +(-370.152 - 641.121i) q^{65} +137.589 q^{66} +(-502.202 + 220.353i) q^{67} +69.0204 q^{68} +(-89.9300 - 155.763i) q^{69} -342.533 q^{70} +(-257.726 + 446.394i) q^{71} -221.491 q^{72} +(-439.110 - 760.561i) q^{73} +(27.1593 - 47.0412i) q^{74} +39.6677 q^{75} +73.2064 q^{76} +(-119.203 - 206.466i) q^{77} +(223.609 - 387.302i) q^{78} +(-185.610 + 321.486i) q^{79} +(-229.851 - 398.113i) q^{80} +81.0000 q^{81} +274.528 q^{82} +(-414.603 - 718.113i) q^{83} +(44.2156 + 76.5836i) q^{84} +(-169.390 - 293.392i) q^{85} +(-189.819 - 328.776i) q^{86} +(-154.232 + 267.138i) q^{87} +(238.378 - 412.883i) q^{88} -1473.31 q^{89} +(125.251 + 216.941i) q^{90} -774.915 q^{91} -143.603 q^{92} +(-99.7746 + 172.815i) q^{93} +213.726 q^{94} +(-179.663 - 311.185i) q^{95} +(-156.468 + 271.010i) q^{96} +(-515.494 - 892.862i) q^{97} +(226.742 - 392.728i) q^{98} +(-87.1757 + 150.993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9}+O(q^{10}) $ 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9} - 2 q^{10} + 16 q^{11} - 198 q^{12} + 88 q^{13} + 214 q^{14} + 12 q^{15} - 298 q^{16} + 52 q^{17} + 18 q^{18} - 2 q^{19} + 164 q^{20} - 42 q^{21} - 506 q^{22} + 160 q^{23} + 324 q^{24} + 572 q^{25} + 353 q^{26} + 864 q^{27} - 433 q^{28} + 48 q^{29} - 6 q^{30} + 292 q^{31} - 525 q^{32} + 48 q^{33} + 138 q^{34} - 328 q^{35} - 594 q^{36} - 616 q^{37} - 194 q^{38} + 264 q^{39} - 1794 q^{40} + 124 q^{41} + 642 q^{42} - 292 q^{43} - 179 q^{44} + 36 q^{45} + 1324 q^{46} + 402 q^{47} - 894 q^{48} + 172 q^{49} + 171 q^{50} + 156 q^{51} - 3344 q^{52} + 852 q^{53} + 54 q^{54} + 1238 q^{55} - 47 q^{56} - 6 q^{57} - 3320 q^{58} + 1200 q^{59} + 492 q^{60} - 454 q^{61} - 5810 q^{62} - 126 q^{63} + 2340 q^{64} - 24 q^{65} - 1518 q^{66} + 110 q^{67} + 906 q^{68} + 480 q^{69} - 10 q^{70} + 406 q^{71} + 972 q^{72} + 1274 q^{73} - 1945 q^{74} + 1716 q^{75} - 2698 q^{76} + 1436 q^{77} + 1059 q^{78} + 1236 q^{79} + 6697 q^{80} + 2592 q^{81} + 2950 q^{82} + 2190 q^{83} - 1299 q^{84} + 2032 q^{85} + 273 q^{86} + 144 q^{87} + 1938 q^{88} - 2160 q^{89} - 18 q^{90} - 3020 q^{91} - 3020 q^{92} + 876 q^{93} - 2886 q^{94} - 102 q^{95} - 1575 q^{96} + 1860 q^{97} + 2612 q^{98} + 144 q^{99}+O(q^{100}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9 - 2 * q^10 + 16 * q^11 - 198 * q^12 + 88 * q^13 + 214 * q^14 + 12 * q^15 - 298 * q^16 + 52 * q^17 + 18 * q^18 - 2 * q^19 + 164 * q^20 - 42 * q^21 - 506 * q^22 + 160 * q^23 + 324 * q^24 + 572 * q^25 + 353 * q^26 + 864 * q^27 - 433 * q^28 + 48 * q^29 - 6 * q^30 + 292 * q^31 - 525 * q^32 + 48 * q^33 + 138 * q^34 - 328 * q^35 - 594 * q^36 - 616 * q^37 - 194 * q^38 + 264 * q^39 - 1794 * q^40 + 124 * q^41 + 642 * q^42 - 292 * q^43 - 179 * q^44 + 36 * q^45 + 1324 * q^46 + 402 * q^47 - 894 * q^48 + 172 * q^49 + 171 * q^50 + 156 * q^51 - 3344 * q^52 + 852 * q^53 + 54 * q^54 + 1238 * q^55 - 47 * q^56 - 6 * q^57 - 3320 * q^58 + 1200 * q^59 + 492 * q^60 - 454 * q^61 - 5810 * q^62 - 126 * q^63 + 2340 * q^64 - 24 * q^65 - 1518 * q^66 + 110 * q^67 + 906 * q^68 + 480 * q^69 - 10 * q^70 + 406 * q^71 + 972 * q^72 + 1274 * q^73 - 1945 * q^74 + 1716 * q^75 - 2698 * q^76 + 1436 * q^77 + 1059 * q^78 + 1236 * q^79 + 6697 * q^80 + 2592 * q^81 + 2950 * q^82 + 2190 * q^83 - 1299 * q^84 + 2032 * q^85 + 273 * q^86 + 144 * q^87 + 1938 * q^88 - 2160 * q^89 - 18 * q^90 - 3020 * q^91 - 3020 * q^92 + 876 * q^93 - 2886 * q^94 - 102 * q^95 - 1575 * q^96 + 1860 * q^97 + 2612 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.18372	−	2.05026i	−0.418508	−	0.724876i	0.577282	−	0.816545i	$-0.304113\pi$
$2$	−1.18372	−	2.05026i	−0.418508	−	0.724876i	−0.995790	+	0.0916685i	$0.970780\pi$
$3$	3.00000			0.577350
$3$	3.00000			0.577350
$4$	1.19762	−	2.07434i	0.149703	−	0.259293i
$5$	−11.7568			−1.05156			−0.525781	−	0.850620i	$-0.676227\pi$
$5$	−11.7568			−1.05156			−0.525781	+	0.850620i	$0.676227\pi$
$6$	−3.55115	−	6.15078i	−0.241625	−	0.418508i
$7$	−6.15324	+	10.6577i	−0.332244	+	0.575463i	−0.982951	−	0.183865i	$-0.941139\pi$
$7$	−6.15324	+	10.6577i	−0.332244	+	0.575463i	0.650708	+	0.759328i	$0.274472\pi$
$8$	−24.6101			−1.08762
$9$	9.00000			0.333333
$10$	13.9167	+	24.1045i	0.440086	+	0.762252i
$11$	−9.68619	+	16.7770i	−0.265500	+	0.459859i	−0.967694	−	0.252126i	$-0.918870\pi$
$11$	−9.68619	+	16.7770i	−0.265500	+	0.459859i	0.702195	+	0.711985i	$0.252204\pi$
$12$	3.59287	−	6.22303i	0.0864310	−	0.149703i
$13$	31.4840	+	54.5319i	0.671700	+	1.16342i	0.977422	+	0.211297i	$0.0677688\pi$
$13$	31.4840	+	54.5319i	0.671700	+	1.16342i	−0.305722	+	0.952121i	$0.598898\pi$
$14$	29.1348			0.556186
$15$	−35.2704			−0.607119
$16$	19.5504	+	33.8623i	0.305475	+	0.529099i
$17$	14.4078	+	24.9550i	0.205553	+	0.356028i	0.950309	−	0.311309i	$-0.100767\pi$
$17$	14.4078	+	24.9550i	0.205553	+	0.356028i	−0.744756	+	0.667337i	$0.767434\pi$
$18$	−10.6535	−	18.4523i	−0.139503	−	0.241625i
$19$	15.2816	+	26.4685i	0.184518	+	0.319595i	0.943414	−	0.331617i	$-0.107594\pi$
$19$	15.2816	+	26.4685i	0.184518	+	0.319595i	−0.758896	+	0.651212i	$0.774261\pi$
$20$	−14.0802	+	24.3877i	−0.157422	+	0.272662i
$21$	−18.4597	+	31.9732i	−0.191821	+	0.332244i
$22$	45.8629			0.444455
$23$	−29.9767	−	51.9211i	−0.271764	−	0.470708i	0.697550	−	0.716536i	$-0.254274\pi$
$23$	−29.9767	−	51.9211i	−0.271764	−	0.470708i	−0.969314	+	0.245828i	$0.920940\pi$
$24$	−73.8302			−0.627939
$25$	13.2226			0.105781
$26$	74.5364	−	129.101i	0.562223	−	0.973798i
$27$	27.0000			0.192450
$28$	14.7385	+	25.5279i	0.0994757	+	0.172297i
$29$	−51.4108	+	89.0461i	−0.329198	+	0.570187i	−0.982353	−	0.187037i	$-0.940112\pi$
$29$	−51.4108	+	89.0461i	−0.329198	+	0.570187i	0.653155	+	0.757224i	$0.273445\pi$
$30$	41.7502	+	72.3136i	0.254084	+	0.440086i
$31$	−33.2582	+	57.6049i	−0.192689	+	0.333747i	−0.946140	−	0.323757i	$-0.895054\pi$
$31$	−33.2582	+	57.6049i	−0.192689	+	0.333747i	0.753452	+	0.657503i	$0.228387\pi$
$32$	−52.1560	+	90.3368i	−0.288124	+	0.499045i
$33$	−29.0586	+	50.3309i	−0.153286	+	0.265500i
$34$	34.1095	−	59.0794i	0.172051	−	0.298001i
$35$	72.3425	−	125.301i	0.349375	−	0.605135i
$36$	10.7786	−	18.6691i	0.0499009	−	0.0864310i
$37$	11.4720	+	19.8701i	0.0509726	+	0.0882872i	0.890386	−	0.455206i	$-0.150435\pi$
$37$	11.4720	+	19.8701i	0.0509726	+	0.0882872i	−0.839413	+	0.543494i	$0.817101\pi$
$38$	36.1782	−	62.6626i	0.154444	−	0.267506i
$39$	94.4520	+	163.596i	0.387806	+	0.671700i
$40$	289.336			1.14370
$41$	−57.9800	+	100.424i	−0.220853	+	0.382528i	−0.955067	−	0.296390i	$-0.904217\pi$
$41$	−57.9800	+	100.424i	−0.220853	+	0.382528i	0.734215	+	0.678918i	$0.237551\pi$
$42$	87.4045			0.321114
$43$	160.358			0.568707			0.284354	−	0.958719i	$-0.408221\pi$
$43$	160.358			0.568707			0.284354	+	0.958719i	$0.408221\pi$
$44$	23.2008	+	40.1850i	0.0794921	+	0.137684i
$45$	−105.811			−0.350520
$46$	−70.9678	+	122.920i	−0.227470	+	0.393990i
$47$	−45.1387	+	78.1825i	−0.140088	+	0.242640i	−0.927530	−	0.373749i	$-0.878072\pi$
$47$	−45.1387	+	78.1825i	−0.140088	+	0.242640i	0.787441	+	0.616390i	$0.211405\pi$
$48$	58.6513	+	101.587i	0.176366	+	0.305475i
$49$	95.7752	+	165.887i	0.279228	+	0.483637i
$50$	−15.6518	−	27.1097i	−0.0442700	−	0.0766779i
$51$	43.2234	+	74.8651i	0.118676	+	0.205553i
$52$	150.824			0.402221
$53$	−151.543			−0.392754			−0.196377	−	0.980528i	$-0.562918\pi$
$53$	−151.543			−0.392754			−0.196377	+	0.980528i	$0.562918\pi$
$54$	−31.9604	−	55.3570i	−0.0805418	−	0.139503i
$55$	113.879	−	197.244i	0.279189	−	0.483570i
$56$	151.432	−	262.288i	0.361356	−	0.625887i
$57$	45.8448	+	79.4056i	0.106532	+	0.184518i
$58$	243.423			0.551087
$59$	−235.204			−0.518998			−0.259499	−	0.965743i	$-0.583557\pi$
$59$	−235.204			−0.518998			−0.259499	+	0.965743i	$0.583557\pi$
$60$	−42.2407	+	73.1630i	−0.0908874	+	0.157422i
$61$	241.559	+	418.392i	0.507024	+	0.878191i	0.999967	+	0.00812954i	$0.00258774\pi$
$61$	241.559	+	418.392i	0.507024	+	0.878191i	−0.492943	+	0.870062i	$0.664079\pi$
$62$	157.473			0.322567
$63$	−55.3792	+	95.9196i	−0.110748	+	0.191821i
$64$	559.758			1.09328
$65$	−370.152	−	641.121i	−0.706333	−	1.22340i
$66$	137.589			0.256606
$67$	−502.202	+	220.353i	−0.915728	+	0.401798i
$67$	−502.202	+	220.353i	−0.915728	+	0.401798i
$68$	69.0204			0.123088
$69$	−89.9300	−	155.763i	−0.156903	−	0.271764i
$70$	−342.533			−0.584864
$71$	−257.726	+	446.394i	−0.430795	+	0.746159i	−0.996942	−	0.0781456i	$-0.975100\pi$
$71$	−257.726	+	446.394i	−0.430795	+	0.746159i	0.566147	+	0.824304i	$0.308433\pi$
$72$	−221.491			−0.362541
$73$	−439.110	−	760.561i	−0.704027	−	1.21941i	−0.967042	−	0.254618i	$-0.918050\pi$
$73$	−439.110	−	760.561i	−0.704027	−	1.21941i	0.263015	−	0.964792i	$-0.415283\pi$
$74$	27.1593	−	47.0412i	0.0426649	−	0.0738977i
$75$	39.6677			0.0610725
$76$	73.2064			0.110491
$77$	−119.203	−	206.466i	−0.176421	−	0.305571i
$78$	223.609	−	387.302i	0.324599	−	0.562223i
$79$	−185.610	+	321.486i	−0.264339	+	0.457849i	−0.967390	−	0.253291i	$-0.918487\pi$
$79$	−185.610	+	321.486i	−0.264339	+	0.457849i	0.703051	+	0.711139i	$0.251820\pi$
$80$	−229.851	−	398.113i	−0.321226	−	0.556380i
$81$	81.0000			0.111111
$82$	274.528			0.369714
$83$	−414.603	−	718.113i	−0.548296	−	0.949676i	−0.998391	−	0.0566959i	$-0.981943\pi$
$83$	−414.603	−	718.113i	−0.548296	−	0.949676i	0.450096	−	0.892980i	$-0.351390\pi$
$84$	44.2156	+	76.5836i	0.0574323	+	0.0994757i
$85$	−169.390	−	293.392i	−0.216152	−	0.374386i
$86$	−189.819	−	328.776i	−0.238008	−	0.412242i
$87$	−154.232	+	267.138i	−0.190062	+	0.329198i
$88$	238.378	−	412.883i	0.288763	−	0.500153i
$89$	−1473.31			−1.75472			−0.877361	−	0.479830i	$-0.840698\pi$
$89$	−1473.31			−1.75472			−0.877361	+	0.479830i	$0.840698\pi$
$90$	125.251	+	216.941i	0.146695	+	0.254084i
$91$	−774.915			−0.892672
$92$	−143.603			−0.162735
$93$	−99.7746	+	172.815i	−0.111249	+	0.192689i
$94$	213.726			0.234512
$95$	−179.663	−	311.185i	−0.194032	−	0.336073i
$96$	−156.468	+	271.010i	−0.166348	+	0.288124i
$97$	−515.494	−	892.862i	−0.539593	−	0.934602i	−0.998926	−	0.0463380i	$-0.985245\pi$
$97$	−515.494	−	892.862i	−0.539593	−	0.934602i	0.459333	−	0.888264i	$-0.348088\pi$
$98$	226.742	−	392.728i	0.233718	−	0.404811i
$99$	−87.1757	+	150.993i	−0.0884999	+	0.153286i
$100$	15.8357	−	27.4282i	0.0158357	−	0.0274282i
$101$	397.077	−	687.757i	0.391194	−	0.677568i	−0.601413	−	0.798938i	$-0.705395\pi$
$101$	397.077	−	687.757i	0.391194	−	0.677568i	0.992607	+	0.121370i	$0.0387288\pi$
$102$	102.329	−	177.238i	0.0993337	−	0.172051i
$103$	−225.435	+	390.465i	−0.215658	+	0.373531i	−0.953476	−	0.301469i	$-0.902523\pi$
$103$	−225.435	+	390.465i	−0.215658	+	0.373531i	0.737818	+	0.675000i	$0.235856\pi$
$104$	−774.824	−	1342.03i	−0.730555	−	1.26536i
$105$	217.028	−	375.903i	0.201712	−	0.349375i
$106$	179.384	+	310.702i	0.164371	+	0.284698i
$107$	516.477			0.466633			0.233317	−	0.972401i	$-0.425042\pi$
$107$	516.477			0.466633			0.233317	+	0.972401i	$0.425042\pi$
$108$	32.3358	−	56.0073i	0.0288103	−	0.0499009i
$109$	−353.354			−0.310506			−0.155253	−	0.987875i	$-0.549619\pi$
$109$	−353.354			−0.310506			−0.155253	+	0.987875i	$0.549619\pi$
$110$	−539.201			−0.467371
$111$	34.4160	+	59.6103i	0.0294291	+	0.0509726i
$112$	−481.194			−0.405969
$113$	−2.64612	+	4.58322i	−0.00220289	+	0.00381551i	−0.867125	−	0.498091i	$-0.834035\pi$
$113$	−2.64612	+	4.58322i	−0.00220289	+	0.00381551i	0.864922	+	0.501907i	$0.167368\pi$
$114$	108.535	−	187.988i	0.0891685	−	0.154444i
$115$	352.430	+	610.426i	0.285776	+	0.494979i
$116$	123.141	+	213.287i	0.0985637	+	0.170717i
$117$	283.356	+	490.787i	0.223900	+	0.387806i
$118$	278.415	+	482.229i	0.217205	+	0.376210i
$119$	−354.619			−0.273175
$120$	868.008			0.660316
$121$	477.855	+	827.670i	0.359020	+	0.621841i
$122$	571.875	−	990.517i	0.424387	−	0.735059i
$123$	−173.940	+	301.273i	−0.127509	+	0.220853i
$124$	79.6616	+	137.978i	0.0576921	+	0.0999256i
$125$	1314.15			0.940326
$126$	262.213			0.185395
$127$	−619.092	+	1072.30i	−0.432563	+	0.749222i	−0.997093	−	0.0761910i	$-0.975724\pi$
$127$	−619.092	+	1072.30i	−0.432563	+	0.749222i	0.564530	+	0.825413i	$0.309057\pi$
$128$	−245.349	−	424.956i	−0.169422	−	0.293447i
$129$	481.075			0.328343
$130$	−876.310	+	1517.81i	−0.591212	+	1.02401i
$131$	746.368			0.497790			0.248895	−	0.968530i	$-0.419933\pi$
$131$	746.368			0.497790			0.248895	+	0.968530i	$0.419933\pi$
$132$	69.6024	+	120.555i	0.0458948	+	0.0794921i
$133$	−376.126			−0.245220
$134$	1046.25	+	768.809i	0.674493	+	0.495634i
$135$	−317.434			−0.202373
$136$	−354.577	−	614.145i	−0.223564	−	0.387224i
$137$	1217.34			0.759155			0.379577	−	0.925160i	$-0.376069\pi$
$137$	1217.34			0.759155			0.379577	+	0.925160i	$0.376069\pi$
$138$	−212.903	+	368.760i	−0.131330	+	0.227470i
$139$	1035.20			0.631685			0.315843	−	0.948812i	$-0.397713\pi$
$139$	1035.20			0.631685			0.315843	+	0.948812i	$0.397713\pi$
$140$	−173.278	−	300.126i	−0.104605	−	0.181181i
$141$	−135.416	+	234.547i	−0.0808801	+	0.140088i
$142$	1220.30			0.721164
$143$	−1219.84			−0.713344
$144$	175.954	+	304.761i	0.101825	+	0.176366i
$145$	604.427	−	1046.90i	0.346172	−	0.599587i
$146$	−1039.57	+	1800.58i	−0.589281	+	1.02066i
$147$	287.326	+	497.662i	0.161212	+	0.279228i
$148$	54.9566			0.0305230
$149$	679.458			0.373579			0.186790	−	0.982400i	$-0.440192\pi$
$149$	679.458			0.373579			0.186790	+	0.982400i	$0.440192\pi$
$150$	−46.9554	−	81.3292i	−0.0255593	−	0.0442700i
$151$	227.827	+	394.608i	0.122783	+	0.212667i	0.920864	−	0.389883i	$-0.127485\pi$
$151$	227.827	+	394.608i	0.122783	+	0.212667i	−0.798081	+	0.602550i	$0.794151\pi$
$152$	−376.082	−	651.393i	−0.200686	−	0.347598i
$153$	129.670	+	224.595i	0.0685177	+	0.118676i
$154$	−282.206	+	488.794i	−0.147667	+	0.255767i
$155$	391.010	−	677.250i	0.202624	−	0.350955i
$156$	452.472			0.232223
$157$	−1445.42	−	2503.53i	−0.734756	−	1.27263i	−0.954830	−	0.297152i	$-0.903963\pi$
$157$	−1445.42	−	2503.53i	−0.734756	−	1.27263i	0.220074	−	0.975483i	$-0.429370\pi$
$158$	878.841			0.442512
$159$	−454.628			−0.226757
$160$	613.188	−	1062.07i	0.302980	−	0.524776i
$161$	737.815			0.361167
$162$	−95.8812	−	166.071i	−0.0465008	−	0.0805418i
$163$	310.689	−	538.130i	0.149295	−	0.258586i	−0.781672	−	0.623690i	$-0.785633\pi$
$163$	310.689	−	538.130i	0.149295	−	0.258586i	0.930967	+	0.365103i	$0.118966\pi$
$164$	138.876	+	240.541i	0.0661245	+	0.114531i
$165$	341.636	−	591.731i	0.161190	−	0.279189i
$166$	−981.545	+	1700.09i	−0.458932	+	0.794893i
$167$	862.622	−	1494.11i	0.399711	−	0.692319i	−0.593979	−	0.804480i	$-0.702444\pi$
$167$	862.622	−	1494.11i	0.399711	−	0.692319i	0.993690	+	0.112161i	$0.0357772\pi$
$168$	454.296	−	786.863i	0.208629	−	0.361356i
$169$	−883.986	+	1531.11i	−0.402361	+	0.696909i
$170$	−401.019	+	694.586i	−0.180922	+	0.313366i
$171$	137.535	+	238.217i	0.0615060	+	0.106532i
$172$	192.049	−	332.638i	0.0851371	−	0.147462i
$173$	1754.64	+	3039.13i	0.771115	+	1.33561i	0.936952	+	0.349458i	$0.113634\pi$
$173$	1754.64	+	3039.13i	0.771115	+	1.33561i	−0.165837	+	0.986153i	$0.553033\pi$
$174$	730.270			0.318170
$175$	−81.3618	+	140.923i	−0.0351450	+	0.0608729i
$176$	−757.476			−0.324414
$177$	−705.611			−0.299644
$178$	1743.98	+	3020.66i	0.734365	+	1.27196i
$179$	−36.5734			−0.0152717			−0.00763583	−	0.999971i	$-0.502431\pi$
$179$	−36.5734			−0.0152717			−0.00763583	+	0.999971i	$0.502431\pi$
$180$	−126.722	+	219.489i	−0.0524739	+	0.0908874i
$181$	1700.20	−	2944.84i	0.698205	−	1.20933i	−0.270883	−	0.962612i	$-0.587316\pi$
$181$	1700.20	−	2944.84i	0.698205	−	1.20933i	0.969088	−	0.246715i	$-0.0793510\pi$
$182$	917.281	+	1588.78i	0.373590	+	0.647077i
$183$	724.677	+	1255.18i	0.292730	+	0.507024i
$184$	737.728	+	1277.78i	0.295576	+	0.511953i
$185$	−134.874	−	233.609i	−0.0536008	−	0.0928394i
$186$	472.420			0.186234
$187$	−558.227			−0.218297
$188$	108.118	+	187.266i	0.0419433	+	0.0726479i
$189$	−166.138	+	287.759i	−0.0639404	+	0.110748i
$190$	−425.341	+	736.712i	−0.162408	+	0.281298i
$191$	1665.19	+	2884.20i	0.630834	+	1.09264i	0.987382	+	0.158359i	$0.0506204\pi$
$191$	1665.19	+	2884.20i	0.630834	+	1.09264i	−0.356548	+	0.934277i	$0.616046\pi$
$192$	1679.28			0.631205
$193$	−1312.15			−0.489382			−0.244691	−	0.969601i	$-0.578686\pi$
$193$	−1312.15			−0.489382			−0.244691	+	0.969601i	$0.578686\pi$
$194$	−1220.40	+	2113.79i	−0.451647	+	0.782276i
$195$	−1110.45	−	1923.36i	−0.407802	−	0.706333i
$196$	458.810			0.167205
$197$	−1773.53	+	3071.84i	−0.641414	+	1.11096i	0.343703	+	0.939078i	$0.388319\pi$
$197$	−1773.53	+	3071.84i	−0.641414	+	1.11096i	−0.985117	+	0.171884i	$0.945015\pi$
$198$	412.766			0.148152
$199$	−415.228	−	719.197i	−0.147913	−	0.256194i	0.782543	−	0.622597i	$-0.213922\pi$
$199$	−415.228	−	719.197i	−0.147913	−	0.256194i	−0.930456	+	0.366403i	$0.880589\pi$
$200$	−325.409			−0.115049
$201$	−1506.61	+	661.060i	−0.528696	+	0.231978i
$202$	−1880.11			−0.654871
$203$	−632.686	−	1095.84i	−0.218748	−	0.378883i
$204$	207.061			0.0710646
$205$	681.660	−	1180.67i	0.232240	−	0.402251i
$206$	1067.41			0.361018
$207$	−269.790	−	467.290i	−0.0905879	−	0.156903i
$208$	−1231.05	+	2132.24i	−0.410375	+	0.710791i
$209$	−592.083			−0.195958
$210$	−1027.60			−0.337671
$211$	−2282.84	−	3953.99i	−0.744819	−	1.29007i	−0.950279	−	0.311399i	$-0.899202\pi$
$211$	−2282.84	−	3953.99i	−0.744819	−	1.29007i	0.205460	−	0.978666i	$-0.434131\pi$
$212$	−181.491	+	314.351i	−0.0587964	+	0.101838i
$213$	−773.178	+	1339.18i	−0.248720	+	0.430795i
$214$	−611.364	−	1058.91i	−0.195290	−	0.338251i
$215$	−1885.30			−0.598030
$216$	−664.472			−0.209313
$217$	−409.292	−	708.914i	−0.128039	−	0.221771i
$218$	418.271	+	724.467i	0.129949	+	0.225078i
$219$	−1317.33	−	2281.68i	−0.406470	−	0.704027i
$220$	−272.767	−	472.447i	−0.0835908	−	0.144784i
$221$	−907.230	+	1571.37i	−0.276140	+	0.478288i
$222$	81.4778	−	141.124i	0.0246326	−	0.0426649i
$223$	−2358.69			−0.708295			−0.354148	−	0.935190i	$-0.615229\pi$
$223$	−2358.69			−0.708295			−0.354148	+	0.935190i	$0.615229\pi$
$224$	−641.857	−	1111.73i	−0.191455	−	0.331609i
$225$	119.003			0.0352602
$226$	12.5291			0.00368770
$227$	216.495	−	374.981i	0.0633009	−	0.109640i	−0.832638	−	0.553817i	$-0.813171\pi$
$227$	216.495	−	374.981i	0.0633009	−	0.109640i	0.895939	+	0.444177i	$0.146504\pi$
$228$	219.619			0.0637923
$229$	2449.01	+	4241.82i	0.706705	+	1.22405i	0.966073	+	0.258270i	$0.0831525\pi$
$229$	2449.01	+	4241.82i	0.706705	+	1.22405i	−0.259368	+	0.965779i	$0.583514\pi$
$230$	834.355	−	1445.15i	0.239199	−	0.414305i
$231$	−357.609	−	619.397i	−0.101857	−	0.176421i
$232$	1265.22	−	2191.43i	0.358043	−	0.620149i
$233$	−1192.29	+	2065.10i	−0.335234	+	0.580642i	−0.983530	−	0.180747i	$-0.942149\pi$
$233$	−1192.29	+	2065.10i	−0.335234	+	0.580642i	0.648296	+	0.761388i	$0.275482\pi$
$234$	670.828	−	1161.91i	0.187408	−	0.324599i
$235$	530.687	−	919.177i	0.147311	−	0.255151i
$236$	−281.685	+	487.893i	−0.0776955	+	0.134573i
$237$	−556.831	+	964.459i	−0.152616	+	0.264339i
$238$	419.769	+	727.061i	0.114326	+	0.198018i
$239$	2181.15	−	3777.86i	0.590322	−	1.02247i	−0.403867	−	0.914818i	$-0.632334\pi$
$239$	2181.15	−	3777.86i	0.590322	−	1.02247i	0.994189	−	0.107650i	$-0.0343324\pi$
$240$	−689.552	−	1194.34i	−0.185460	−	0.321226i
$241$	4923.91			1.31609			0.658043	−	0.752980i	$-0.271384\pi$
$241$	4923.91			1.31609			0.658043	+	0.752980i	$0.271384\pi$
$242$	1131.29	−	1959.46i	0.300505	−	0.520490i
$243$	243.000			0.0641500
$244$	1157.19			0.303612
$245$	−1126.01	−	1950.31i	−0.293625	−	0.508574i
$246$	823.584			0.213454
$247$	−962.253	+	1666.67i	−0.247881	+	0.429343i
$248$	818.487	−	1417.66i	0.209573	−	0.362990i
$249$	−1243.81	−	2154.34i	−0.316559	−	0.548296i
$250$	−1555.58	−	2694.34i	−0.393534	−	0.681620i
$251$	1720.50	+	2979.99i	0.432657	+	0.749384i	0.997101	−	0.0760873i	$-0.0242428\pi$
$251$	1720.50	+	2979.99i	0.432657	+	0.749384i	−0.564444	+	0.825471i	$0.690909\pi$
$252$	132.647	+	229.751i	0.0331586	+	0.0574323i
$253$	1161.44			0.288613
$254$	2931.32			0.724124
$255$	−508.169	−	880.175i	−0.124795	−	0.216152i
$256$	1658.19	−	2872.06i	0.404831	−	0.701187i
$257$	−2125.70	+	3681.82i	−0.515943	+	0.893640i	0.483886	+	0.875131i	$0.339225\pi$
$257$	−2125.70	+	3681.82i	−0.515943	+	0.893640i	−0.999829	+	0.0185084i	$0.994108\pi$
$258$	−569.457	−	986.328i	−0.137414	−	0.238008i
$259$	−282.360			−0.0677414
$260$	−1773.21			−0.422960
$261$	−462.697	+	801.414i	−0.109733	+	0.190062i
$262$	−883.489	−	1530.25i	−0.208329	−	0.360836i
$263$	4850.89			1.13733			0.568666	−	0.822568i	$-0.307460\pi$
$263$	4850.89			1.13733			0.568666	+	0.822568i	$0.307460\pi$
$264$	715.134	−	1238.65i	0.166718	−	0.288763i
$265$	1781.66			0.413005
$266$	445.227	+	771.156i	0.102626	+	0.177754i
$267$	−4419.92			−1.01309
$268$	−144.360	+	1305.64i	−0.0329038	+	0.297592i
$269$	−7429.06			−1.68386			−0.841929	−	0.539589i	$-0.818580\pi$
$269$	−7429.06			−1.68386			−0.841929	+	0.539589i	$0.818580\pi$
$270$	375.752	+	650.822i	0.0846946	+	0.146695i
$271$	5201.22			1.16587			0.582937	−	0.812517i	$-0.301903\pi$
$271$	5201.22			1.16587			0.582937	+	0.812517i	$0.301903\pi$
$272$	−563.357	+	975.763i	−0.125583	+	0.217516i
$273$	−2324.75			−0.515385
$274$	−1440.99	−	2495.86i	−0.317712	−	0.550293i
$275$	−128.076	+	221.835i	−0.0280847	+	0.0486442i
$276$	−430.809			−0.0939552
$277$	−4974.82			−1.07909			−0.539545	−	0.841956i	$-0.681404\pi$
$277$	−4974.82			−1.07909			−0.539545	+	0.841956i	$0.681404\pi$
$278$	−1225.38	−	2122.42i	−0.264365	−	0.457894i
$279$	−299.324	+	518.444i	−0.0642296	+	0.111249i
$280$	−1780.36	+	3083.67i	−0.379988	+	0.658158i
$281$	1699.63	+	2943.85i	0.360825	+	0.624966i	0.988097	−	0.153834i	$-0.0491620\pi$
$281$	1699.63	+	2943.85i	0.360825	+	0.624966i	−0.627272	+	0.778800i	$0.715829\pi$
$282$	641.178			0.135396
$283$	5096.29			1.07047			0.535235	−	0.844703i	$-0.320223\pi$
$283$	5096.29			1.07047			0.535235	+	0.844703i	$0.320223\pi$
$284$	617.317	+	1069.22i	0.128982	+	0.223404i
$285$	−538.989	−	933.556i	−0.112024	−	0.194032i
$286$	1443.95	+	2500.99i	0.298540	+	0.517086i
$287$	−713.530	−	1235.87i	−0.146754	−	0.254185i
$288$	−469.404	+	813.031i	−0.0960412	+	0.166348i
$289$	2041.33	−	3535.69i	0.415496	−	0.719660i
$290$	−2861.88			−0.579502
$291$	−1546.48	−	2678.59i	−0.311534	−	0.539593i
$292$	−2103.55			−0.421579
$293$	5043.81			1.00567			0.502837	−	0.864381i	$-0.332289\pi$
$293$	5043.81			1.00567			0.502837	+	0.864381i	$0.332289\pi$
$294$	680.225	−	1178.18i	0.134937	−	0.233718i
$295$	2765.24			0.545758
$296$	−282.327	−	489.005i	−0.0554390	−	0.0960231i
$297$	−261.527	+	452.978i	−0.0510954	+	0.0884999i
$298$	−804.286	−	1393.06i	−0.156346	−	0.270799i
$299$	1887.57	−	3269.37i	0.365087	−	0.632349i
$300$	47.5070	−	82.2845i	0.00914272	−	0.0158357i
$301$	−986.723	+	1709.06i	−0.188949	+	0.327270i
$302$	539.366	−	934.210i	0.102772	−	0.178006i
$303$	1191.23	−	2063.27i	0.225856	−	0.391194i
$304$	−597.524	+	1034.94i	−0.112731	+	0.195257i
$305$	−2839.96	−	4918.96i	−0.533167	−	0.923472i
$306$	306.986	−	531.715i	0.0573504	−	0.0993337i
$307$	−2609.42	−	4519.65i	−0.485106	−	0.840228i	0.514748	−	0.857342i	$-0.327886\pi$
$307$	−2609.42	−	4519.65i	−0.485106	−	0.840228i	−0.999854	+	0.0171140i	$0.994552\pi$
$308$	−571.041			−0.105643
$309$	−676.306	+	1171.40i	−0.124510	+	0.215658i
$310$	−1851.38			−0.339199
$311$	10455.3			1.90633			0.953163	−	0.302458i	$-0.0978071\pi$
$311$	10455.3			1.90633			0.953163	+	0.302458i	$0.0978071\pi$
$312$	−2324.47	−	4026.10i	−0.421786	−	0.730555i
$313$	4491.93			0.811179			0.405589	−	0.914055i	$-0.367066\pi$
$313$	4491.93			0.811179			0.405589	+	0.914055i	$0.367066\pi$
$314$	−3421.93	+	5926.96i	−0.615002	+	1.06521i
$315$	651.083	−	1127.71i	0.116458	−	0.201712i
$316$	444.582	+	770.039i	0.0791446	+	0.137083i
$317$	3774.67	+	6537.92i	0.668791	+	1.15838i	0.978243	+	0.207464i	$0.0665211\pi$
$317$	3774.67	+	6537.92i	0.668791	+	1.15838i	−0.309452	+	0.950915i	$0.600146\pi$
$318$	538.151	+	932.105i	0.0948994	+	0.164371i
$319$	−995.949	−	1725.03i	−0.174804	−	0.302769i
$320$	−6580.97			−1.14965
$321$	1549.43			0.269411
$322$	−873.365	−	1512.71i	−0.151151	−	0.261802i
$323$	−440.349	+	762.706i	−0.0758565	+	0.131387i
$324$	97.0074	−	168.022i	0.0166336	−	0.0288103i
$325$	416.300	+	721.053i	0.0710528	+	0.123067i
$326$	−1471.07			−0.249924
$327$	−1060.06			−0.179271
$328$	1426.89	−	2471.45i	0.240204	−	0.416046i
$329$	−555.499	−	962.152i	−0.0930870	−	0.161231i
$330$	−1617.60			−0.269837
$331$	−655.469	+	1135.31i	−0.108845	+	0.188526i	−0.915303	−	0.402766i	$-0.868049\pi$
$331$	−655.469	+	1135.31i	−0.108845	+	0.188526i	0.806457	+	0.591292i	$0.201382\pi$
$332$	−1986.15			−0.328326
$333$	103.248	+	178.831i	0.0169909	+	0.0294291i
$334$	−4084.41			−0.669128
$335$	5904.30	−	2590.65i	0.962944	−	0.422515i
$336$	−1443.58			−0.234386
$337$	−1650.44	−	2858.65i	−0.266781	−	0.462079i	0.701248	−	0.712918i	$-0.252627\pi$
$337$	−1650.44	−	2858.65i	−0.266781	−	0.462079i	−0.968029	+	0.250839i	$0.919293\pi$
$338$	4185.56			0.673564
$339$	−7.93837	+	13.7497i	−0.00127184	+	0.00220289i
$340$	−811.460			−0.129434
$341$	−644.291	−	1115.94i	−0.102318	−	0.177219i
$342$	325.604	−	563.963i	0.0514815	−	0.0891685i
$343$	−6578.44			−1.03558
$344$	−3946.43			−0.618538
$345$	1057.29	+	1831.28i	0.164993	+	0.285776i
$346$	4154.00	−	7194.94i	0.645435	−	1.11793i
$347$	3235.85	−	5604.65i	0.500603	−	0.867071i	−0.499396	−	0.866374i	$-0.666445\pi$
$347$	3235.85	−	5604.65i	0.500603	−	0.867071i	1.00000		0.000696878i	$-0.000221823\pi$
$348$	369.424	+	639.861i	0.0569058	+	0.0985637i
$349$	−9597.96			−1.47211			−0.736056	−	0.676921i	$-0.763314\pi$
$349$	−9597.96			−1.47211			−0.736056	+	0.676921i	$0.763314\pi$
$350$	385.238			0.0588338
$351$	850.068	+	1472.36i	0.129269	+	0.223900i
$352$	−1010.39	−	1750.04i	−0.152993	−	0.264993i
$353$	2172.47	+	3762.83i	0.327561	+	0.567352i	0.982027	−	0.188739i	$-0.0604400\pi$
$353$	2172.47	+	3762.83i	0.327561	+	0.567352i	−0.654466	+	0.756091i	$0.727107\pi$
$354$	835.244	+	1446.69i	0.125403	+	0.217205i
$355$	3030.03	−	5248.17i	0.453007	−	0.784631i
$356$	−1764.47	+	3056.15i	−0.262687	+	0.454987i
$357$	−1063.86			−0.157718
$358$	43.2926	+	74.9850i	0.00639130	+	0.0110701i
$359$	205.452			0.0302043			0.0151021	−	0.999886i	$-0.495193\pi$
$359$	205.452			0.0302043			0.0151021	+	0.999886i	$0.495193\pi$
$360$	2604.02			0.381234
$361$	2962.44	−	5131.10i	0.431906	−	0.748083i
$362$	−8050.25			−1.16882
$363$	1433.57	+	2483.01i	0.207280	+	0.359020i
$364$	−928.056	+	1607.44i	−0.133636	+	0.231464i
$365$	5162.54	+	8941.77i	0.740327	+	1.28228i
$366$	1715.63	−	2971.55i	0.245020	−	0.424387i
$367$	−3292.71	+	5703.14i	−0.468332	+	0.811176i	−0.999345	−	0.0361883i	$-0.988478\pi$
$367$	−3292.71	+	5703.14i	−0.468332	+	0.811176i	0.531013	+	0.847364i	$0.321812\pi$
$368$	1172.11	−	2030.16i	0.166034	−	0.287580i
$369$	−521.820	+	903.819i	−0.0736175	+	0.127509i
$370$	−319.306	+	553.055i	−0.0448647	+	0.0777080i
$371$	932.478	−	1615.10i	0.130490	−	0.226016i
$372$	238.985	+	413.934i	0.0333085	+	0.0576921i
$373$	−3283.53	+	5687.24i	−0.455803	+	0.789474i	−0.998734	−	0.0503032i	$-0.983981\pi$
$373$	−3283.53	+	5687.24i	−0.455803	+	0.789474i	0.542931	+	0.839777i	$0.317315\pi$
$374$	660.783	+	1144.51i	0.0913590	+	0.158238i
$375$	3942.44			0.542898
$376$	1110.87	−	1924.08i	0.152363	−	0.263901i
$377$	−6474.47			−0.884488
$378$	786.640			0.107038
$379$	−1289.26	−	2233.06i	−0.174735	−	0.302651i	0.765334	−	0.643633i	$-0.222574\pi$
$379$	−1289.26	−	2233.06i	−0.174735	−	0.302651i	−0.940070	+	0.340982i	$0.889240\pi$
$380$	−860.674			−0.116189
$381$	−1857.28	+	3216.90i	−0.249741	+	0.432563i
$382$	3942.24	−	6828.17i	0.528018	−	0.914553i
$383$	5377.09	+	9313.40i	0.717380	+	1.24254i	0.962034	+	0.272929i	$0.0879924\pi$
$383$	5377.09	+	9313.40i	0.717380	+	1.24254i	−0.244654	+	0.969611i	$0.578674\pi$
$384$	−736.046	−	1274.87i	−0.0978156	−	0.169422i
$385$	1401.45	+	2427.38i	0.185518	+	0.321326i
$386$	1553.22	+	2690.25i	0.204810	+	0.354741i
$387$	1443.22			0.189569
$388$	−2469.47			−0.323114
$389$	677.172	+	1172.90i	0.0882621	+	0.152875i	0.906777	−	0.421611i	$-0.138535\pi$
$389$	677.172	+	1172.90i	0.0882621	+	0.152875i	−0.818514	+	0.574486i	$0.805202\pi$
$390$	−2628.93	+	4553.44i	−0.341336	+	0.591212i
$391$	863.795	−	1496.14i	0.111724	−	0.193511i
$392$	−2357.03	−	4082.50i	−0.303694	−	0.526014i
$393$	2239.10			0.287399
$394$	8397.43			1.07375
$395$	2182.18	−	3779.66i	0.277969	−	0.481456i
$396$	208.807	+	361.665i	0.0264974	+	0.0458948i
$397$	−13234.2			−1.67307			−0.836533	−	0.547917i	$-0.815421\pi$
$397$	−13234.2			−1.67307			−0.836533	+	0.547917i	$0.815421\pi$
$398$	−983.027	+	1702.65i	−0.123806	+	0.214438i
$399$	−1128.38			−0.141578
$400$	258.507	+	447.747i	0.0323134	+	0.0559684i
$401$	69.7364			0.00868447			0.00434223	−	0.999991i	$-0.498618\pi$
$401$	69.7364			0.00868447			0.00434223	+	0.999991i	$0.498618\pi$
$402$	3138.74	+	2306.43i	0.389419	+	0.286155i
$403$	−4188.41			−0.517716
$404$	−951.096	−	1647.35i	−0.117126	−	0.202868i
$405$	−952.302			−0.116840
$406$	−1497.84	+	2594.34i	−0.183095	+	0.317131i
$407$	−444.481			−0.0541329
$408$	−1063.73	−	1842.44i	−0.129075	−	0.223564i
$409$	−5076.59	+	8792.90i	−0.613743	+	1.06303i	0.376860	+	0.926270i	$0.377004\pi$
$409$	−5076.59	+	8792.90i	−0.613743	+	1.06303i	−0.990604	+	0.136764i	$0.956330\pi$
$410$	−3227.57			−0.388777
$411$	3652.01			0.438298
$412$	539.973	+	935.260i	0.0645693	+	0.111837i
$413$	1447.27	−	2506.74i	0.172434	−	0.298665i
$414$	−638.710	+	1106.28i	−0.0758234	+	0.131330i
$415$	4874.40	+	8442.72i	0.576567	+	0.998643i
$416$	−6568.32			−0.774130
$417$	3105.59			0.364704
$418$	700.859	+	1213.92i	0.0820099	+	0.142045i
$419$	6750.04	+	11691.4i	0.787019	+	1.36316i	0.927785	+	0.373115i	$0.121710\pi$
$419$	6750.04	+	11691.4i	0.787019	+	1.36316i	−0.140766	+	0.990043i	$0.544956\pi$
$420$	−519.834	−	900.379i	−0.0603936	−	0.104605i
$421$	6325.45	+	10956.0i	0.732265	+	1.26832i	0.955913	+	0.293651i	$0.0948702\pi$
$421$	6325.45	+	10956.0i	0.732265	+	1.26832i	−0.223648	+	0.974670i	$0.571796\pi$
$422$	−5404.47	+	9360.81i	−0.623425	+	1.07980i
$423$	−406.248	+	703.642i	−0.0466961	+	0.0808801i
$424$	3729.47			0.427168
$425$	190.508	+	329.970i	0.0217435	+	0.0376609i
$426$	3660.90			0.416364
$427$	−5945.48			−0.673822
$428$	618.545	−	1071.35i	0.0698563	−	0.120995i
$429$	−3659.52			−0.411849
$430$	2231.67	+	3865.36i	0.250280	+	0.433498i
$431$	5709.29	−	9888.78i	0.638067	−	1.10516i	−0.347789	−	0.937573i	$-0.613068\pi$
$431$	5709.29	−	9888.78i	0.638067	−	1.10516i	0.985856	−	0.167592i	$-0.0535991\pi$
$432$	527.861	+	914.283i	0.0587887	+	0.101825i
$433$	−4957.28	+	8586.25i	−0.550188	+	0.952954i	0.448072	+	0.893997i	$0.352111\pi$
$433$	−4957.28	+	8586.25i	−0.550188	+	0.952954i	−0.998261	+	0.0589565i	$0.981223\pi$
$434$	−968.972	+	1678.31i	−0.107171	+	0.185625i
$435$	1813.28	−	3140.69i	0.199862	−	0.346172i
$436$	−423.184	+	732.977i	−0.0464836	+	0.0805120i
$437$	916.183	−	1586.88i	0.100291	−	0.173708i
$438$	−3118.70	+	5401.74i	−0.340222	+	0.589281i
$439$	3301.68	+	5718.68i	0.358954	+	0.621726i	0.987786	−	0.155815i	$-0.0498002\pi$
$439$	3301.68	+	5718.68i	0.358954	+	0.621726i	−0.628833	+	0.777541i	$0.716467\pi$
$440$	−2802.56	+	4854.18i	−0.303652	+	0.525941i
$441$	861.977	+	1492.99i	0.0930760	+	0.161212i
$442$	4295.62			0.462267
$443$	7568.12	−	13108.4i	0.811676	−	1.40586i	−0.100015	−	0.994986i	$-0.531889\pi$
$443$	7568.12	−	13108.4i	0.811676	−	1.40586i	0.911691	−	0.410877i	$-0.134778\pi$
$444$	164.870			0.0176225
$445$	17321.4			1.84520
$446$	2792.03	+	4835.94i	0.296427	+	0.513426i
$447$	2038.37			0.215686
$448$	−3444.33	+	5965.76i	−0.363235	+	0.629142i
$449$	1259.33	−	2181.22i	0.132364	−	0.229261i	−0.792223	−	0.610231i	$-0.791077\pi$
$449$	1259.33	−	2181.22i	0.132364	−	0.229261i	0.924587	+	0.380970i	$0.124410\pi$
$450$	−140.866	−	243.988i	−0.0147567	−	0.0255593i
$451$	−1123.21	−	1945.46i	−0.117273	−	0.203122i
$452$	6.33811	+	10.9779i	0.000659557	+	0.00114239i
$453$	683.481	+	1183.82i	0.0708891	+	0.122783i
$454$	−1025.08			−0.105968
$455$	9110.53			0.938700
$456$	−1128.25	−	1954.18i	−0.115866	−	0.200686i
$457$	−3705.67	+	6418.41i	−0.379308	+	0.656981i	−0.990962	−	0.134145i	$-0.957171\pi$
$457$	−3705.67	+	6418.41i	−0.379308	+	0.656981i	0.611653	+	0.791126i	$0.290505\pi$
$458$	5797.89	−	10042.2i	0.591523	−	1.02455i
$459$	389.010	+	673.786i	0.0395587	+	0.0685177i
$460$	1688.31			0.171126
$461$	7155.59			0.722926			0.361463	−	0.932386i	$-0.382277\pi$
$461$	7155.59			0.722926			0.361463	+	0.932386i	$0.382277\pi$
$462$	−846.617	+	1466.38i	−0.0852558	+	0.147667i
$463$	2186.98	+	3787.96i	0.219520	+	0.380219i	0.954661	−	0.297695i	$-0.0962177\pi$
$463$	2186.98	+	3787.96i	0.219520	+	0.380219i	−0.735142	+	0.677914i	$0.762884\pi$
$464$	−4020.41			−0.402247
$465$	1173.03	−	2031.75i	0.116985	−	0.202624i
$466$	5645.33			0.561191
$467$	−7980.14	−	13822.0i	−0.790743	−	1.36961i	−0.925507	−	0.378730i	$-0.876361\pi$
$467$	−7980.14	−	13822.0i	−0.790743	−	1.36961i	0.134764	−	0.990878i	$-0.456972\pi$
$468$	1357.41			0.134074
$469$	741.706	−	6708.23i	0.0730252	−	0.660463i
$470$	−2512.74			−0.246604
$471$	−4336.25	−	7510.60i	−0.424212	−	0.734756i
$472$	5788.38			0.564474
$473$	−1553.26	+	2690.33i	−0.150992	+	0.261525i
$474$	2636.52			0.255484
$475$	202.062	+	349.982i	0.0195184	+	0.0338069i
$476$	−424.699	+	735.601i	−0.0408951	+	0.0708324i
$477$	−1363.88			−0.130918
$478$	−10327.5			−0.988216
$479$	535.890	+	928.189i	0.0511178	+	0.0885387i	0.890452	−	0.455077i	$-0.150388\pi$
$479$	535.890	+	928.189i	0.0511178	+	0.0885387i	−0.839334	+	0.543616i	$0.817055\pi$
$480$	1839.56	−	3186.22i	0.174925	−	0.302980i
$481$	−722.370	+	1251.18i	−0.0684766	+	0.118605i
$482$	−5828.52	−	10095.3i	−0.550792	−	0.954000i
$483$	2213.44			0.208520
$484$	2289.16			0.214985
$485$	6060.57	+	10497.2i	0.567415	+	0.982791i
$486$	−287.644	−	498.213i	−0.0268473	−	0.0465008i
$487$	−5117.83	−	8864.34i	−0.476203	−	0.824808i	0.523425	−	0.852072i	$-0.324654\pi$
$487$	−5117.83	−	8864.34i	−0.476203	−	0.824808i	−0.999628	+	0.0272636i	$0.991321\pi$
$488$	−5944.79	−	10296.7i	−0.551450	−	0.955140i
$489$	932.068	−	1614.39i	0.0861955	−	0.149295i
$490$	−2665.76	+	4617.23i	−0.245769	+	0.425684i
$491$	−1910.97			−0.175643			−0.0878215	−	0.996136i	$-0.527990\pi$
$491$	−1910.97			−0.175643			−0.0878215	+	0.996136i	$0.527990\pi$
$492$	416.629	+	721.623i	0.0381770	+	0.0661245i
$493$	−2962.86			−0.270671
$494$	4556.15			0.414961
$495$	1024.91	−	1775.19i	0.0930630	−	0.161190i
$496$	−2600.85			−0.235447
$497$	−3171.70	−	5493.55i	−0.286258	−	0.495813i
$498$	−2944.64	+	5100.26i	−0.264964	+	0.458932i
$499$	−698.926	−	1210.58i	−0.0627018	−	0.108603i	0.832970	−	0.553318i	$-0.186638\pi$
$499$	−698.926	−	1210.58i	−0.0627018	−	0.108603i	−0.895672	+	0.444715i	$0.853305\pi$
$500$	1573.85	−	2725.99i	0.140770	−	0.243820i
$501$	2587.87	−	4482.32i	0.230773	−	0.399711i
$502$	4073.17	−	7054.94i	0.362140	−	0.627246i
$503$	−1168.28	+	2023.53i	−0.103561	+	0.179373i	−0.913149	−	0.407625i	$-0.866357\pi$
$503$	−1168.28	+	2023.53i	−0.103561	+	0.179373i	0.809588	+	0.586998i	$0.199690\pi$
$504$	1362.89	−	2360.59i	0.120452	−	0.208629i
$505$	−4668.36	+	8085.83i	−0.411365	+	0.712504i
$506$	−1374.82	−	2381.25i	−0.120787	−	0.209209i
$507$	−2651.96	+	4593.33i	−0.232303	+	0.402361i
$508$	1482.88	+	2568.42i	0.129512	+	0.224321i
$509$	7090.87			0.617480			0.308740	−	0.951146i	$-0.400093\pi$
$509$	7090.87			0.617480			0.308740	+	0.951146i	$0.400093\pi$
$510$	−1203.06	+	2083.76i	−0.104455	+	0.180922i
$511$	10807.8			0.935635
$512$	−11776.9			−1.01654
$513$	412.604	+	714.650i	0.0355105	+	0.0615060i
$514$	10064.9			0.863704
$515$	2650.40	−	4590.63i	0.226778	−	0.392791i
$516$	576.146	−	997.914i	0.0491539	−	0.0851371i
$517$	−874.444	−	1514.58i	−0.0743868	−	0.128842i
$518$	334.235	+	578.912i	0.0283503	+	0.0491041i
$519$	5263.93	+	9117.39i	0.445204	+	0.771115i
$520$	9109.46	+	15778.0i	0.768224	+	1.33060i
$521$	−18181.8			−1.52891			−0.764454	−	0.644679i	$-0.776991\pi$
$521$	−18181.8			−1.52891			−0.764454	+	0.644679i	$0.776991\pi$
$522$	2190.81			0.183696
$523$	−10578.6	−	18322.7i	−0.884457	−	1.53192i	−0.846334	−	0.532652i	$-0.821196\pi$
$523$	−10578.6	−	18322.7i	−0.884457	−	1.53192i	−0.0381228	−	0.999273i	$-0.512138\pi$
$524$	893.867	−	1548.22i	0.0745206	−	0.129073i
$525$	−244.085	+	422.768i	−0.0202910	+	0.0351450i
$526$	−5742.08	−	9945.58i	−0.475982	−	0.824425i
$527$	−1916.71			−0.158431
$528$	−2272.43			−0.187301
$529$	4286.30	−	7424.09i	0.352289	−	0.610182i
$530$	−2108.98	−	3652.86i	−0.172846	−	0.299377i
$531$	−2116.83			−0.172999
$532$	−450.457	+	780.214i	−0.0367101	+	0.0635838i
$533$	−7301.77			−0.593386
$534$	5231.94	+	9061.99i	0.423986	+	0.734365i
$535$	−6072.13			−0.490693
$536$	12359.2	−	5422.92i	0.995966	−	0.437004i
$537$	−109.720			−0.00881710
$538$	8793.91	+	15231.5i	0.704707	+	1.22059i
$539$	−3710.79			−0.296540
$540$	−380.166	+	658.467i	−0.0302958	+	0.0524739i
$541$	−13686.2			−1.08764			−0.543820	−	0.839202i	$-0.683023\pi$
$541$	−13686.2			−1.08764			−0.543820	+	0.839202i	$0.683023\pi$
$542$	−6156.78	−	10663.9i	−0.487927	−	0.845114i
$543$	5100.61	−	8834.52i	0.403109	−	0.698205i
$544$	−3005.81			−0.236899
$545$	4154.31			0.326516
$546$	2751.84	+	4766.33i	0.215692	+	0.373590i
$547$	8449.56	−	14635.1i	0.660470	−	1.14397i	−0.320022	−	0.947410i	$-0.603690\pi$
$547$	8449.56	−	14635.1i	0.660470	−	1.14397i	0.980492	−	0.196558i	$-0.0629763\pi$
$548$	1457.91	−	2525.18i	0.113648	−	0.196843i
$549$	2174.03	+	3765.53i	0.169008	+	0.292730i
$550$	606.426			0.0470147
$551$	−3142.56			−0.242972
$552$	2213.18	+	3833.35i	0.170651	+	0.295576i
$553$	−2284.21	−	3956.37i	−0.175650	−	0.304235i
$554$	5888.79	+	10199.7i	0.451608	+	0.782208i
$555$	−404.623	−	700.827i	−0.0309465	−	0.0536008i
$556$	1239.78	−	2147.35i	0.0945651	−	0.163792i
$557$	−5018.67	+	8692.59i	−0.381774	+	0.661251i	−0.991316	−	0.131502i	$-0.958020\pi$
$557$	−5018.67	+	8692.59i	−0.381774	+	0.661251i	0.609542	+	0.792754i	$0.291353\pi$
$558$	1417.26			0.107522
$559$	5048.72	+	8744.64i	0.382000	+	0.661644i
$560$	5657.31			0.426901
$561$	−1674.68			−0.126034
$562$	4023.78	−	6969.38i	0.302016	−	0.523106i
$563$	−23534.4			−1.76173			−0.880867	−	0.473363i	$-0.843040\pi$
$563$	−23534.4			−1.76173			−0.880867	+	0.473363i	$0.843040\pi$
$564$	324.355	+	561.799i	0.0242160	+	0.0419433i
$565$	31.1100	−	53.8840i	0.00231647	−	0.00401224i
$566$	−6032.57	−	10448.7i	−0.448000	−	0.775958i
$567$	−498.413	+	863.276i	−0.0369160	+	0.0639404i
$568$	6342.66	−	10985.8i	0.468542	−	0.811539i
$569$	−1609.68	+	2788.04i	−0.118596	+	0.205414i	−0.919211	−	0.393764i	$-0.871173\pi$
$569$	−1609.68	+	2788.04i	−0.118596	+	0.205414i	0.800616	+	0.599178i	$0.204506\pi$
$570$	−1276.02	+	2210.14i	−0.0937661	+	0.162408i
$571$	−8159.46	+	14132.6i	−0.598009	+	1.03578i	0.395106	+	0.918636i	$0.370708\pi$
$571$	−8159.46	+	14132.6i	−0.598009	+	1.03578i	−0.993115	+	0.117146i	$0.962625\pi$
$572$	−1460.91	+	2530.37i	−0.106790	+	0.184965i
$573$	4995.58	+	8652.61i	0.364212	+	0.630834i
$574$	−1689.24	+	2925.84i	−0.122835	+	0.212757i
$575$	−396.369	−	686.531i	−0.0287473	−	0.0497918i
$576$	5037.83			0.364426
$577$	9906.16	−	17158.0i	0.714729	−	1.23795i	−0.248334	−	0.968674i	$-0.579883\pi$
$577$	9906.16	−	17158.0i	0.714729	−	1.23795i	0.963064	−	0.269273i	$-0.0867835\pi$
$578$	−9665.44			−0.695553
$579$	−3936.45			−0.282545
$580$	−1447.75	−	2507.58i	−0.103646	−	0.179520i
$581$	10204.6			0.728672
$582$	−3661.20	+	6341.38i	−0.260759	+	0.451647i
$583$	1467.87	−	2542.43i	0.104276	−	0.180611i
$584$	10806.5	+	18717.5i	0.765715	+	1.32626i
$585$	−3331.36	−	5770.09i	−0.235444	−	0.407802i
$586$	−5970.45	−	10341.1i	−0.420883	−	0.728990i
$587$	−8502.23	−	14726.3i	−0.597827	−	1.03547i	−0.993141	−	0.116921i	$-0.962697\pi$
$587$	−8502.23	−	14726.3i	−0.597827	−	1.03547i	0.395314	−	0.918546i	$-0.370636\pi$
$588$	1376.43			0.0965358
$589$	−2032.96			−0.142218
$590$	−3273.27	−	5669.47i	−0.228404	−	0.395607i
$591$	−5320.58	+	9215.52i	−0.370321	+	0.641414i
$592$	−448.565	+	776.938i	−0.0311418	+	0.0539391i
$593$	617.017	+	1068.70i	0.0427282	+	0.0740074i	0.886599	−	0.462540i	$-0.153062\pi$
$593$	617.017	+	1068.70i	0.0427282	+	0.0740074i	−0.843870	+	0.536547i	$0.819728\pi$
$594$	1238.30			0.0855353
$595$	4169.18			0.287260
$596$	813.734	−	1409.43i	0.0559259	−	0.0968665i
$597$	−1245.69	−	2157.59i	−0.0853978	−	0.147913i
$598$	−8937.41			−0.611167
$599$	9667.44	−	16744.5i	0.659434	−	1.14217i	−0.321329	−	0.946968i	$-0.604129\pi$
$599$	9667.44	−	16744.5i	0.659434	−	1.14217i	0.980762	−	0.195205i	$-0.0625373\pi$
$600$	−976.226			−0.0664238
$601$	7563.79	+	13100.9i	0.513367	+	0.889177i	0.999880	+	0.0155040i	$0.00493528\pi$
$601$	7563.79	+	13100.9i	0.513367	+	0.889177i	−0.486513	+	0.873673i	$0.661731\pi$
$602$	4672.01			0.316307
$603$	−4519.82	+	1983.18i	−0.305243	+	0.133933i
$604$	1091.40			0.0735242
$605$	−5618.05	−	9730.76i	−0.377531	−	0.653903i
$606$	−5640.32			−0.378090
$607$	−660.911	+	1144.73i	−0.0441937	+	0.0765456i	−0.887276	−	0.461239i	$-0.847405\pi$
$607$	−660.911	+	1144.73i	−0.0441937	+	0.0765456i	0.843082	+	0.537784i	$0.180739\pi$
$608$	−3188.11			−0.212656
$609$	−1898.06	−	3287.53i	−0.126294	−	0.218748i
$610$	−6723.43	+	11645.3i	−0.446268	+	0.772960i
$611$	−5684.59			−0.376389
$612$	621.184			0.0410292
$613$	−6114.32	−	10590.3i	−0.402863	−	0.697779i	0.591207	−	0.806520i	$-0.298652\pi$
$613$	−6114.32	−	10590.3i	−0.402863	−	0.697779i	−0.994070	+	0.108740i	$0.965318\pi$
$614$	−6177.63	+	10700.0i	−0.406041	+	0.703283i
$615$	2044.98	−	3542.01i	0.134084	−	0.232240i
$616$	2933.60	+	5081.14i	0.191880	+	0.332345i
$617$	−19090.7			−1.24565			−0.622823	−	0.782363i	$-0.714014\pi$
$617$	−19090.7			−1.24565			−0.622823	+	0.782363i	$0.714014\pi$
$618$	3202.22			0.208434
$619$	3707.34	+	6421.30i	0.240728	+	0.416953i	0.960922	−	0.276820i	$-0.0892805\pi$
$619$	3707.34	+	6421.30i	0.240728	+	0.416953i	−0.720194	+	0.693773i	$0.755947\pi$
$620$	−936.566	−	1622.18i	−0.0606668	−	0.105078i
$621$	−809.370	−	1401.87i	−0.0523009	−	0.0905879i
$622$	−12376.2	−	21436.1i	−0.797812	−	1.38185i
$623$	9065.62	−	15702.1i	0.582996	−	1.00978i
$624$	−3693.15	+	6396.73i	−0.236930	+	0.410375i
$625$	−17103.0			−1.09459
$626$	−5317.18	−	9209.62i	−0.339484	−	0.588004i
$627$	−1776.25			−0.113136
$628$	−6924.25			−0.439980
$629$	−330.573	+	572.569i	−0.0209552	+	0.0362954i
$630$	−3082.79			−0.194955
$631$	7003.83	+	12131.0i	0.441867	+	0.765336i	0.997828	−	0.0658725i	$-0.0209830\pi$
$631$	7003.83	+	12131.0i	0.441867	+	0.765336i	−0.555961	+	0.831208i	$0.687650\pi$
$632$	4567.88	−	7911.81i	0.287501	−	0.497966i
$633$	−6848.51	−	11862.0i	−0.430022	−	0.744819i
$634$	8936.29	−	15478.1i	0.559788	−	0.969581i
$635$	7278.55	−	12606.8i	0.454867	−	0.787852i
$636$	−544.472	+	943.054i	−0.0339461	+	0.0587964i
$637$	−6030.77	+	10445.6i	−0.375115	+	0.649717i
$638$	−2357.85	+	4083.91i	−0.146313	+	0.253422i
$639$	−2319.53	+	4017.55i	−0.143598	+	0.248720i
$640$	2884.52	+	4996.13i	0.178157	+	0.308577i
$641$	−572.627	+	991.820i	−0.0352846	+	0.0611147i	−0.883128	−	0.469131i	$-0.844567\pi$
$641$	−572.627	+	991.820i	−0.0352846	+	0.0611147i	0.847844	+	0.530246i	$0.177900\pi$
$642$	−1834.09	−	3176.74i	−0.112750	−	0.195290i
$643$	−7160.06			−0.439137			−0.219569	−	0.975597i	$-0.570465\pi$
$643$	−7160.06			−0.439137			−0.219569	+	0.975597i	$0.570465\pi$
$644$	883.624	−	1530.48i	0.0540678	−	0.0936481i
$645$	−5655.90			−0.345273
$646$	2084.99			0.126986
$647$	−10692.7	−	18520.2i	−0.649724	−	1.12536i	−0.983189	−	0.182593i	$-0.941551\pi$
$647$	−10692.7	−	18520.2i	−0.649724	−	1.12536i	0.333464	−	0.942763i	$-0.391782\pi$
$648$	−1993.42			−0.120847
$649$	2278.23	−	3946.01i	0.137794	−	0.238666i
$650$	985.563	−	1707.05i	0.0594723	−	0.103009i
$651$	−1227.88	−	2126.74i	−0.0739235	−	0.128039i
$652$	−744.177	−	1288.95i	−0.0446998	−	0.0774222i
$653$	9621.86	+	16665.5i	0.576619	+	0.998734i	0.995864	+	0.0908604i	$0.0289617\pi$
$653$	9621.86	+	16665.5i	0.576619	+	0.998734i	−0.419244	+	0.907873i	$0.637705\pi$
$654$	1254.81	+	2173.40i	0.0750261	+	0.129949i
$655$	−8774.91			−0.523457
$656$	−4534.13			−0.269860
$657$	−3951.99	−	6845.05i	−0.234676	−	0.406470i
$658$	−1315.11	+	2277.83i	−0.0779153	+	0.134953i
$659$	−2051.33	+	3553.01i	−0.121257	+	0.210024i	−0.920264	−	0.391299i	$-0.872026\pi$
$659$	−2051.33	+	3553.01i	−0.121257	+	0.210024i	0.799006	+	0.601323i	$0.205359\pi$
$660$	−818.302	−	1417.34i	−0.0482612	−	0.0835908i
$661$	17364.6			1.02179			0.510897	−	0.859642i	$-0.329313\pi$
$661$	17364.6			1.02179			0.510897	+	0.859642i	$0.329313\pi$
$662$	3103.56			0.182211
$663$	−2721.69	+	4714.11i	−0.159429	+	0.276140i
$664$	10203.4	+	17672.8i	0.596339	+	1.03289i
$665$	4422.04			0.257864
$666$	244.433	−	423.371i	0.0142216	−	0.0246326i
$667$	6164.49			0.357856
$668$	−2066.19	−	3578.75i	−0.119676	−	0.207284i
$669$	−7076.08			−0.408934
$670$	−12300.5	−	9038.74i	−0.709271	−	0.521190i
$671$	−9359.15			−0.538459
$672$	−1925.57	−	3335.18i	−0.110536	−	0.191455i
$673$	24833.6			1.42239			0.711193	−	0.702997i	$-0.248155\pi$
$673$	24833.6			1.42239			0.711193	+	0.702997i	$0.248155\pi$
$674$	−3907.31	+	6767.67i	−0.223300	+	0.386767i
$675$	357.010			0.0203575
$676$	2117.36	+	3667.38i	0.120469	+	0.208659i
$677$	12833.7	−	22228.7i	0.728568	−	1.26192i	−0.228920	−	0.973445i	$-0.573519\pi$
$677$	12833.7	−	22228.7i	0.728568	−	1.26192i	0.957488	−	0.288472i	$-0.0931473\pi$
$678$	37.5872			0.00212909
$679$	12687.8			0.717106
$680$	4168.69	+	7220.39i	0.235091	+	0.407190i
$681$	649.486	−	1124.94i	0.0365468	−	0.0633009i
$682$	−1525.32	+	2641.93i	−0.0856414	+	0.148335i
$683$	−214.725	−	371.914i	−0.0120296	−	0.0208359i	0.859948	−	0.510382i	$-0.170496\pi$
$683$	−214.725	−	371.914i	−0.0120296	−	0.0208359i	−0.871978	+	0.489546i	$0.837163\pi$
$684$	658.858			0.0368305
$685$	−14312.0			−0.798298
$686$	7787.02	+	13487.5i	0.433396	+	0.750664i
$687$	7347.04	+	12725.5i	0.408016	+	0.706705i
$688$	3135.07	+	5430.10i	0.173726	+	0.300902i
$689$	−4771.17	−	8263.90i	−0.263813	−	0.456937i
$690$	2503.07	−	4335.44i	0.138102	−	0.239199i
$691$	666.549	−	1154.50i	0.0366957	−	0.0635588i	−0.847094	−	0.531443i	$-0.821650\pi$
$691$	666.549	−	1154.50i	0.0366957	−	0.0635588i	0.883790	+	0.467884i	$0.154983\pi$
$692$	8405.59			0.461753
$693$	−1072.83	−	1858.19i	−0.0588071	−	0.101857i
$694$	−15321.3			−0.838025
$695$	−12170.6			−0.664256
$696$	3795.67	−	6574.29i	0.206716	−	0.358043i
$697$	−3341.46			−0.181588
$698$	11361.3	+	19678.3i	0.616090	+	1.06710i
$699$	−3576.87	+	6195.31i	−0.193547	+	0.335234i
$700$	194.881	+	337.544i	0.0105226	+	0.0182257i
$701$	−10302.5	+	17844.5i	−0.555094	+	0.961452i	0.442802	+	0.896620i	$0.353985\pi$
$701$	−10302.5	+	17844.5i	−0.555094	+	0.961452i	−0.997896	+	0.0648323i	$0.979349\pi$
$702$	2012.48	−	3485.72i	0.108200	−	0.187408i
$703$	−350.622	+	607.295i	−0.0188107	+	0.0325812i
$704$	−5421.93	+	9391.05i	−0.290265	+	0.502754i
$705$	1592.06	−	2757.53i	0.0850503	−	0.147311i
$706$	5143.19	−	8908.26i	0.274173	−	0.474882i
$707$	4886.62	+	8463.87i	0.259944	+	0.450236i
$708$	−845.056	+	1463.68i	−0.0448575	+	0.0776955i
$709$	11825.6	+	20482.5i	0.626402	+	1.08496i	0.988268	+	0.152729i	$0.0488063\pi$
$709$	11825.6	+	20482.5i	0.626402	+	1.08496i	−0.361866	+	0.932230i	$0.617860\pi$
$710$	−14346.8			−0.758348
$711$	−1670.49	+	2893.38i	−0.0881130	+	0.152616i
$712$	36258.2			1.90848
$713$	3987.88			0.209463
$714$	1259.31	+	2181.18i	0.0660061	+	0.114326i
$715$	14341.4			0.750125
$716$	−43.8012	+	75.8659i	−0.00228621	+	0.00395983i
$717$	6543.45	−	11333.6i	0.340822	−	0.590322i
$718$	−243.197	−	421.229i	−0.0126407	−	0.0218944i
$719$	4879.14	+	8450.91i	0.253075	+	0.438339i	0.964371	−	0.264554i	$-0.0852247\pi$
$719$	4879.14	+	8450.91i	0.253075	+	0.438339i	−0.711296	+	0.702893i	$0.751891\pi$
$720$	−2068.65	−	3583.02i	−0.107075	−	0.185460i
$721$	−2774.32	−	4805.26i	−0.143302	−	0.248207i
$722$	−14026.8			−0.723024
$723$	14771.7			0.759843
$724$	−4072.41	−	7053.61i	−0.209047	−	0.362079i
$725$	−679.783	+	1177.42i	−0.0348228	+	0.0603148i
$726$	3393.88	−	5878.37i	0.173497	−	0.300505i
$727$	12526.4	+	21696.3i	0.639034	+	1.10684i	0.985645	+	0.168830i	$0.0539989\pi$
$727$	12526.4	+	21696.3i	0.639034	+	1.10684i	−0.346612	+	0.938009i	$0.612668\pi$
$728$	19070.7			0.970890
$729$	729.000			0.0370370
$730$	12222.0	−	21169.1i	0.619665	−	1.07329i
$731$	2310.41	+	4001.74i	0.116900	+	0.202476i
$732$	3471.56			0.175290
$733$	−3994.26	+	6918.26i	−0.201271	+	0.348611i	−0.948938	−	0.315462i	$-0.897840\pi$
$733$	−3994.26	+	6918.26i	−0.201271	+	0.348611i	0.747667	+	0.664073i	$0.231174\pi$
$734$	15590.6			0.784003
$735$	−3378.03	−	5850.92i	−0.169525	−	0.293625i
$736$	6253.84			0.313206
$737$	1167.56	−	10559.8i	0.0583552	−	0.527783i
$738$	2470.75			0.123238
$739$	7517.58	+	13020.8i	0.374206	+	0.648145i	0.990208	−	0.139600i	$-0.0445818\pi$
$739$	7517.58	+	13020.8i	0.374206	+	0.648145i	−0.616001	+	0.787745i	$0.711248\pi$
$740$	−646.114			−0.0320968
$741$	−2886.76	+	5000.01i	−0.143114	+	0.247881i
$742$	−4415.16			−0.218444
$743$	4775.76	+	8271.86i	0.235808	+	0.408432i	0.959507	−	0.281684i	$-0.0908929\pi$
$743$	4775.76	+	8271.86i	0.235808	+	0.408432i	−0.723699	+	0.690116i	$0.757560\pi$
$744$	2455.46	−	4252.98i	0.120997	−	0.209573i
$745$	−7988.25			−0.392842
$746$	15547.1			0.763028
$747$	−3731.42	−	6463.02i	−0.182765	−	0.316559i
$748$	−668.545	+	1157.95i	−0.0326797	+	0.0566029i
$749$	−3178.01	+	5504.48i	−0.155036	+	0.268530i
$750$	−4666.74	−	8083.02i	−0.227207	−	0.393534i
$751$	−2067.40			−0.100453			−0.0502267	−	0.998738i	$-0.515994\pi$
$751$	−2067.40			−0.100453			−0.0502267	+	0.998738i	$0.515994\pi$
$752$	−3529.92			−0.171174
$753$	5161.50	+	8939.97i	0.249795	+	0.432657i
$754$	7663.95	+	13274.3i	0.370165	+	0.641145i
$755$	−2678.52	−	4639.33i	−0.129114	−	0.223633i
$756$	397.940	+	689.253i	0.0191441	+	0.0331586i
$757$	12056.1	−	20881.7i	0.578844	−	1.00259i	−0.416768	−	0.909013i	$-0.636837\pi$
$757$	12056.1	−	20881.7i	0.578844	−	1.00259i	0.995612	−	0.0935745i	$-0.0298293\pi$
$758$	−3052.24	+	5286.63i	−0.146256	+	0.253323i
$759$	3484.32			0.166631
$760$	4421.52	+	7658.30i	0.211033	+	0.365521i
$761$	−8861.84			−0.422131			−0.211065	−	0.977472i	$-0.567693\pi$
$761$	−8861.84			−0.422131			−0.211065	+	0.977472i	$0.567693\pi$
$762$	8793.97			0.418073
$763$	2174.27	−	3765.95i	0.103164	−	0.178685i
$764$	7977.10			0.377751
$765$	−1524.51	−	2640.52i	−0.0720506	−	0.124795i
$766$	12729.9	−	22048.9i	0.600458	−	1.04002i
$767$	−7405.15	−	12826.1i	−0.348611	−	0.603812i
$768$	4974.56	−	8616.19i	0.233729	−	0.404831i
$769$	−10931.4	+	18933.8i	−0.512611	+	0.887868i	0.487282	+	0.873245i	$0.337988\pi$
$769$	−10931.4	+	18933.8i	−0.512611	+	0.887868i	−0.999893	+	0.0146236i	$0.995345\pi$
$770$	3317.84	−	5746.66i	0.155281	−	0.268955i
$771$	−6377.09	+	11045.4i	−0.297880	+	0.515943i
$772$	−1571.46	+	2721.85i	−0.0732618	+	0.126893i
$773$	−19988.2	+	34620.6i	−0.930048	+	1.61089i	−0.146813	+	0.989164i	$0.546902\pi$
$773$	−19988.2	+	34620.6i	−0.930048	+	1.61089i	−0.783235	+	0.621726i	$0.786432\pi$
$774$	−1708.37	−	2958.98i	−0.0793361	−	0.137414i
$775$	−439.759	+	761.685i	−0.0203827	+	0.0353039i
$776$	12686.4	+	21973.4i	0.586873	+	1.01649i
$777$	−847.081			−0.0391105
$778$	1603.16	−	2776.76i	0.0738768	−	0.127958i
$779$	−3544.11			−0.163005
$780$	−5319.62			−0.244196
$781$	−4992.77	−	8647.72i	−0.228752	−	0.396210i
$782$	−4089.96			−0.187029
$783$	−1388.09	+	2404.24i	−0.0633542	+	0.109733i
$784$	−3744.89	+	6486.34i	−0.170594	+	0.295478i
$785$	16993.5	+	29433.6i	0.772641	+	1.33825i
$786$	−2650.47	−	4590.75i	−0.120279	−	0.208329i
$787$	−8588.89	−	14876.4i	−0.389023	−	0.673807i	0.603296	−	0.797518i	$-0.293854\pi$
$787$	−8588.89	−	14876.4i	−0.389023	−	0.673807i	−0.992318	+	0.123711i	$0.960521\pi$
$788$	4248.03	+	7357.81i	0.192043	+	0.332628i
$789$	14552.7			0.656639
$790$	−10332.4			−0.465328
$791$	−32.5645	−	56.4033i	−0.00146379	−	0.00253536i
$792$	2145.40	−	3715.94i	0.0962545	−	0.166718i
$793$	−15210.5	+	26345.3i	−0.681135	+	1.17976i
$794$	15665.6	+	27133.6i	0.700191	+	1.21277i
$795$	5344.97			0.238448
$796$	−1989.15			−0.0885722
$797$	−2577.13	+	4463.71i	−0.114538	+	0.198385i	−0.917595	−	0.397517i	$-0.869872\pi$
$797$	−2577.13	+	4463.71i	−0.114538	+	0.198385i	0.803057	+	0.595902i	$0.203205\pi$
$798$	1335.68	+	2313.47i	0.0592514	+	0.102626i
$799$	−2601.40			−0.115182
$800$	−689.636	+	1194.49i	−0.0304779	+	0.0527893i
$801$	−13259.8			−0.584908
$802$	−82.5483	−	142.978i	−0.00363451	−	0.00629516i
$803$	17013.2			0.747676
$804$	−433.081	+	3916.92i	−0.0189970	+	0.171815i
$805$	−8674.35			−0.379789
$806$	4957.89	+	8587.32i	0.216668	+	0.375280i
$807$	−22287.2			−0.972175
$808$	−9772.09	+	16925.8i	−0.425471	+	0.736938i
$809$	−5473.56			−0.237874			−0.118937	−	0.992902i	$-0.537949\pi$
$809$	−5473.56			−0.237874			−0.118937	+	0.992902i	$0.537949\pi$
$810$	1127.26	+	1952.47i	0.0488985	+	0.0846946i
$811$	15878.7	−	27502.7i	0.687518	−	1.19082i	−0.285120	−	0.958492i	$-0.592034\pi$
$811$	15878.7	−	27502.7i	0.687518	−	1.19082i	0.972638	−	0.232324i	$-0.0746331\pi$
$812$	−3030.88			−0.130989
$813$	15603.7			0.673117
$814$	526.140	+	911.301i	0.0226550	+	0.0392396i
$815$	−3652.72	+	6326.69i	−0.156993	+	0.271919i
$816$	−1690.07	+	2927.29i	−0.0725053	+	0.125583i
$817$	2450.53	+	4244.45i	0.104937	+	0.181756i
$818$	24037.0			1.02742
$819$	−6974.24			−0.297557
$820$	−1632.74	−	2827.99i	−0.0695340	−	0.120436i
$821$	14186.3	+	24571.3i	0.603050	+	1.04451i	0.992356	+	0.123405i	$0.0393815\pi$
$821$	14186.3	+	24571.3i	0.603050	+	1.04451i	−0.389306	+	0.921108i	$0.627285\pi$
$822$	−4322.96	−	7487.58i	−0.183431	−	0.317712i
$823$	−13736.7	−	23792.7i	−0.581813	−	1.00773i	−0.995265	−	0.0972035i	$-0.969010\pi$
$823$	−13736.7	−	23792.7i	−0.581813	−	1.00773i	0.413452	−	0.910526i	$-0.364323\pi$
$824$	5547.98	−	9609.38i	0.234555	−	0.406261i
$825$	−384.229	+	665.505i	−0.0162147	+	0.0280847i
$826$	−6852.62			−0.288660
$827$	10573.8	+	18314.4i	0.444604	+	0.770076i	0.998025	−	0.0628256i	$-0.0200112\pi$
$827$	10573.8	+	18314.4i	0.444604	+	0.770076i	−0.553421	+	0.832902i	$0.686678\pi$
$828$	−1292.43			−0.0542451
$829$	−45305.2			−1.89809			−0.949044	−	0.315143i	$-0.897947\pi$
$829$	−45305.2			−1.89809			−0.949044	+	0.315143i	$0.897947\pi$
$830$	11539.8	−	19987.6i	0.482595	−	0.835879i
$831$	−14924.5			−0.623013
$832$	17623.4	+	30524.7i	0.734355	+	1.27194i
$833$	−2759.82	+	4780.15i	−0.114792	+	0.198826i
$834$	−3676.14	−	6367.27i	−0.152631	−	0.264365i
$835$	−10141.7	+	17565.9i	−0.420320	+	0.728016i
$836$	−709.091	+	1228.18i	−0.0293355	+	0.0508105i
$837$	−897.972	+	1555.33i	−0.0370830	+	0.0642296i
$838$	15980.3	−	27678.7i	0.658747	−	1.14098i
$839$	−14276.5	+	24727.6i	−0.587461	+	1.01751i	0.407103	+	0.913382i	$0.366539\pi$
$839$	−14276.5	+	24727.6i	−0.587461	+	1.01751i	−0.994564	+	0.104130i	$0.966794\pi$
$840$	−5341.07	+	9251.00i	−0.219386	+	0.379988i
$841$	6908.37	+	11965.6i	0.283258	+	0.490616i
$842$	14975.1	−	25937.6i	0.612917	−	1.06160i
$843$	5098.90	+	8831.56i	0.208322	+	0.360825i
$844$	−10935.9			−0.446006
$845$	10392.9	−	18001.0i	0.423107	−	0.732842i
$846$	1923.53			0.0781707
$847$	−11761.4			−0.477129
$848$	−2962.72	−	5131.58i	−0.119977	−	0.207806i
$849$	15288.9			0.618036
$850$	451.016	−	781.183i	0.0181997	−	0.0315228i
$851$	687.785	−	1191.28i	0.0277050	−	0.0479865i
$852$	1851.95	+	3207.67i	0.0744680	+	0.128982i
$853$	−7261.75	−	12577.7i	−0.291486	−	0.504868i	0.682675	−	0.730722i	$-0.260816\pi$
$853$	−7261.75	−	12577.7i	−0.291486	−	0.504868i	−0.974161	+	0.225853i	$0.927483\pi$
$854$	7037.78	+	12189.8i	0.282000	+	0.488438i
$855$	−1616.97	−	2800.67i	−0.0646773	−	0.112024i
$856$	−12710.6			−0.507521
$857$	11028.4			0.439584			0.219792	−	0.975547i	$-0.429462\pi$
$857$	11028.4			0.439584			0.219792	+	0.975547i	$0.429462\pi$
$858$	4331.84	+	7502.97i	0.172362	+	0.298540i
$859$	16953.7	−	29364.7i	0.673403	−	1.16637i	−0.303530	−	0.952822i	$-0.598165\pi$
$859$	16953.7	−	29364.7i	0.673403	−	1.16637i	0.976933	−	0.213547i	$-0.0685016\pi$
$860$	−2257.88	+	3910.76i	−0.0895268	+	0.155065i
$861$	−2140.59	−	3707.61i	−0.0847284	−	0.146754i
$862$	−27032.8			−1.06814
$863$	30310.7			1.19558			0.597792	−	0.801651i	$-0.296045\pi$
$863$	30310.7			1.19558			0.597792	+	0.801651i	$0.296045\pi$
$864$	−1408.21	+	2439.09i	−0.0554494	+	0.0960412i
$865$	−20629.0	−	35730.5i	−0.810875	−	1.40448i
$866$	23472.1			0.921032
$867$	6123.99	−	10607.1i	0.239887	−	0.415496i
$868$	−1960.71			−0.0766714
$869$	−3595.71	−	6227.96i	−0.140364	−	0.243117i
$870$	−8585.65			−0.334576
$871$	−27827.6	−	20448.5i	−1.08255	−	0.795487i
$872$	8696.06			0.337713
$873$	−4639.45	−	8035.76i	−0.179864	−	0.311534i
$874$	−4338.01			−0.167889
$875$	−8086.26	+	14005.8i	−0.312418	+	0.541123i
$876$	−6310.66			−0.243399
$877$	19534.3	+	33834.3i	0.752138	+	1.30274i	0.946785	+	0.321868i	$0.104311\pi$
$877$	19534.3	+	33834.3i	0.752138	+	1.30274i	−0.194647	+	0.980873i	$0.562356\pi$
$878$	7816.52	−	13538.6i	0.300450	−	0.520394i
$879$	15131.4			0.580627
$880$	8905.51			0.341142
$881$	13620.0	+	23590.6i	0.520851	+	0.902141i	0.999706	+	0.0242467i	$0.00771872\pi$
$881$	13620.0	+	23590.6i	0.520851	+	0.902141i	−0.478855	+	0.877894i	$0.658948\pi$
$882$	2040.67	−	3534.55i	0.0779060	−	0.134937i
$883$	−7365.00	+	12756.6i	−0.280693	+	0.486175i	−0.971556	−	0.236811i	$-0.923898\pi$
$883$	−7365.00	+	12756.6i	−0.280693	+	0.486175i	0.690863	+	0.722986i	$0.257231\pi$
$884$	2173.04	+	3763.81i	0.0826779	+	0.143202i
$885$	8295.73			0.315094
$886$	−35834.1			−1.35877
$887$	−20850.5	−	36114.1i	−0.789278	−	1.36707i	−0.926410	−	0.376517i	$-0.877122\pi$
$887$	−20850.5	−	36114.1i	−0.789278	−	1.36707i	0.137131	−	0.990553i	$-0.456212\pi$
$888$	−846.982	−	1467.02i	−0.0320077	−	0.0554390i
$889$	−7618.85	−	13196.2i	−0.287433	−	0.497849i
$890$	−20503.7	−	35513.4i	−0.772229	−	1.33754i
$891$	−784.582	+	1358.94i	−0.0295000	+	0.0510954i
$892$	−2824.83	+	4892.74i	−0.106034	+	0.183656i
$893$	−2759.17			−0.103395
$894$	−2412.86	−	4179.19i	−0.0902663	−	0.156346i
$895$	429.987			0.0160591
$896$	6038.76			0.225157
$897$	5662.71	−	9808.11i	0.210783	−	0.365087i
$898$	−5962.76			−0.221581
$899$	−3419.66	−	5923.02i	−0.126865	−	0.219737i
$900$	142.521	−	246.854i	0.00527855	−	0.00914272i
$901$	−2183.39	−	3781.75i	−0.0807318	−	0.139832i
$902$	−2659.13	+	4605.75i	−0.0981589	+	0.170016i
$903$	−2960.17	+	5127.17i	−0.109090	+	0.188949i
$904$	65.1213	−	112.793i	0.00239591	−	0.00414984i
$905$	−19989.0	+	34621.9i	−0.734205	+	1.27168i
$906$	1618.10	−	2802.63i	0.0593352	−	0.102772i
$907$	−9109.23	+	15777.6i	−0.333481	+	0.577605i	−0.983192	−	0.182576i	$-0.941557\pi$
$907$	−9109.23	+	15777.6i	−0.333481	+	0.577605i	0.649711	+	0.760181i	$0.274890\pi$
$908$	−518.559	−	898.171i	−0.0189526	−	0.0328269i
$909$	3573.69	−	6189.81i	0.130398	−	0.225856i
$910$	−10784.3	−	18679.0i	−0.392853	−	0.680441i
$911$	4567.22			0.166102			0.0830509	−	0.996545i	$-0.473534\pi$
$911$	4567.22			0.166102			0.0830509	+	0.996545i	$0.473534\pi$
$912$	−1792.57	+	3104.83i	−0.0650855	+	0.112731i
$913$	16063.7			0.582290
$914$	17545.9			0.634974
$915$	−8519.89	−	14756.9i	−0.307824	−	0.533167i
$916$	11732.0			0.423183
$917$	−4592.58	+	7954.59i	−0.165388	+	0.286460i
$918$	920.957	−	1595.15i	0.0331112	−	0.0573504i
$919$	14062.6	+	24357.2i	0.504769	+	0.874286i	0.999985	+	0.00551569i	$0.00175571\pi$
$919$	14062.6	+	24357.2i	0.504769	+	0.874286i	−0.495216	+	0.868770i	$0.664911\pi$
$920$	−8673.33	−	15022.6i	−0.310816	−	0.538350i
$921$	−7828.26	−	13558.9i	−0.280076	−	0.485106i
$922$	−8470.20	−	14670.8i	−0.302550	−	0.524032i
$923$	−32457.0			−1.15746
$924$	−1713.12			−0.0609931
$925$	151.690	+	262.734i	0.00539192	+	0.00933908i
$926$	5177.53	−	8967.75i	0.183741	−	0.318249i
$927$	−2028.92	+	3514.19i	−0.0718861	+	0.124510i
$928$	−5362.75	−	9288.56i	−0.189699	−	0.328569i
$929$	−23447.4			−0.828079			−0.414040	−	0.910259i	$-0.635883\pi$
$929$	−23447.4			−0.828079			−0.414040	+	0.910259i	$0.635883\pi$
$930$	−5554.15			−0.195836
$931$	−2927.20	+	5070.06i	−0.103045	+	0.178479i
$932$	2855.82	+	4946.43i	0.100371	+	0.173847i
$933$	31366.0			1.10062
$934$	−18892.5	+	32722.7i	−0.661864	+	1.14638i
$935$	6562.96			0.229553
$936$	−6973.42	−	12078.3i	−0.243518	−	0.421786i
$937$	−27515.3			−0.959322			−0.479661	−	0.877454i	$-0.659240\pi$
$937$	−27515.3			−0.959322			−0.479661	+	0.877454i	$0.659240\pi$
$938$	−14631.6	+	6419.96i	−0.509316	+	0.223475i
$939$	13475.8			0.468334
$940$	−1271.13	−	2201.65i	−0.0441059	−	0.0763936i
$941$	−47403.2			−1.64219			−0.821095	−	0.570792i	$-0.806636\pi$
$941$	−47403.2			−1.64219			−0.821095	+	0.570792i	$0.806636\pi$
$942$	−10265.8	+	17780.9i	−0.355072	+	0.615002i
$943$	6952.19			0.240079
$944$	−4598.33	−	7964.54i	−0.158541	−	0.274601i
$945$	1953.25	−	3383.12i	0.0672372	−	0.116458i
$946$	7354.49			0.252764
$947$	9680.45			0.332178			0.166089	−	0.986111i	$-0.446886\pi$
$947$	9680.45			0.332178			0.166089	+	0.986111i	$0.446886\pi$
$948$	1333.75	+	2310.12i	0.0456942	+	0.0791446i
$949$	27649.9	−	47891.0i	0.945789	−	1.63815i
$950$	478.370	−	828.561i	0.0163372	−	0.0282969i
$951$	11324.0	+	19613.8i	0.386126	+	0.668791i
$952$	8727.19			0.297111
$953$	7704.89			0.261895			0.130948	−	0.991389i	$-0.458198\pi$
$953$	7704.89			0.261895			0.130948	+	0.991389i	$0.458198\pi$
$954$	1614.45	+	2796.31i	0.0547902	+	0.0948994i
$955$	−19577.4	−	33909.0i	−0.663360	−	1.14897i
$956$	−5224.39	−	9048.91i	−0.176746	−	0.306132i
$957$	−2987.85	−	5175.10i	−0.100923	−	0.174804i
$958$	1268.69	−	2197.43i	0.0427864	−	0.0741082i
$959$	−7490.58	+	12974.1i	−0.252225	+	0.436866i
$960$	−19742.9			−0.663750
$961$	12683.3	+	21968.1i	0.425742	+	0.737407i
$962$	3420.33			0.114632
$963$	4648.30			0.155544
$964$	5896.98	−	10213.9i	0.197022	−	0.341252i
$965$	15426.7			0.514615
$966$	−2620.09	−	4538.14i	−0.0872672	−	0.151151i
$967$	12725.4	−	22041.0i	0.423185	−	0.732978i	−0.573064	−	0.819511i	$-0.694245\pi$
$967$	12725.4	−	22041.0i	0.423185	−	0.732978i	0.996249	+	0.0865324i	$0.0275786\pi$
$968$	−11760.1	−	20369.0i	−0.390478	−	0.676328i
$969$	−1321.05	+	2288.12i	−0.0437958	+	0.0758565i
$970$	14348.0	−	24851.5i	0.474935	−	0.822611i
$971$	−2161.15	+	3743.21i	−0.0714258	+	0.123713i	−0.899526	−	0.436866i	$-0.856088\pi$
$971$	−2161.15	+	3743.21i	−0.0714258	+	0.123713i	0.828101	+	0.560580i	$0.189422\pi$
$972$	291.022	−	504.065i	0.00960344	−	0.0166336i
$973$	−6369.82	+	11032.8i	−0.209874	+	0.363512i
$974$	−12116.1	+	20985.8i	−0.398589	+	0.690377i
$975$	1248.90	+	2163.16i	0.0410224	+	0.0710528i
$976$	−9445.16	+	16359.5i	−0.309767	+	0.536531i
$977$	−6573.39	−	11385.5i	−0.215252	−	0.372828i	0.738098	−	0.674693i	$-0.235724\pi$
$977$	−6573.39	−	11385.5i	−0.215252	−	0.372828i	−0.953351	+	0.301865i	$0.902391\pi$
$978$	−4413.22			−0.144294
$979$	14270.7	−	24717.7i	0.465878	−	0.806925i
$980$	−5394.14			−0.175826
$981$	−3180.18			−0.103502
$982$	2262.04	+	3917.98i	0.0735079	+	0.127319i
$983$	30772.5			0.998465			0.499233	−	0.866468i	$-0.333615\pi$
$983$	30772.5			0.998465			0.499233	+	0.866468i	$0.333615\pi$
$984$	4280.68	−	7414.35i	0.138682	−	0.240204i
$985$	20851.0	−	36115.0i	0.674486	−	1.16824i
$986$	3507.19	+	6074.64i	0.113278	+	0.196203i
$987$	−1666.50	−	2886.46i	−0.0537438	−	0.0930870i
$988$	2304.83	+	3992.09i	0.0742171	+	0.128548i
$989$	−4807.00	−	8325.97i	−0.154554	−	0.267695i
$990$	−4852.81			−0.155790
$991$	−1473.68			−0.0472380			−0.0236190	−	0.999721i	$-0.507519\pi$
$991$	−1473.68			−0.0472380			−0.0236190	+	0.999721i	$0.507519\pi$
$992$	−3469.23	−	6008.88i	−0.111036	−	0.192321i
$993$	−1966.41	+	3405.92i	−0.0628419	+	0.108845i
$994$	−7508.80	+	13005.6i	−0.239602	+	0.415003i
$995$	4881.76	+	8455.46i	0.155540	+	0.269403i
$996$	−5958.45			−0.189559
$997$	4648.79			0.147672			0.0738358	−	0.997270i	$-0.476476\pi$
$997$	4648.79			0.147672			0.0738358	+	0.997270i	$0.476476\pi$
$998$	−1654.66	+	2865.96i	−0.0524824	+	0.0909022i
$999$	309.744	+	536.493i	0.00980969	+	0.0169909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.e.a.37.5	✓	32
67.29	even	3	inner	201.4.e.a.163.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.e.a.37.5	✓	32	1.1	even	1	trivial
201.4.e.a.163.5	yes	32	67.29	even	3	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18372 - 2.05026i) q^{2} +3.00000 q^{3} +(1.19762 - 2.07434i) q^{4} -11.7568 q^{5} +(-3.55115 - 6.15078i) q^{6} +(-6.15324 + 10.6577i) q^{7} -24.6101 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(-1.18372 - 2.05026i) q^{2} +3.00000 q^{3} +(1.19762 - 2.07434i) q^{4} -11.7568 q^{5} +(-3.55115 - 6.15078i) q^{6} +(-6.15324 + 10.6577i) q^{7} -24.6101 q^{8} +9.00000 q^{9} +(13.9167 + 24.1045i) q^{10} +(-9.68619 + 16.7770i) q^{11} +(3.59287 - 6.22303i) q^{12} +(31.4840 + 54.5319i) q^{13} +29.1348 q^{14} -35.2704 q^{15} +(19.5504 + 33.8623i) q^{16} +(14.4078 + 24.9550i) q^{17} +(-10.6535 - 18.4523i) q^{18} +(15.2816 + 26.4685i) q^{19} +(-14.0802 + 24.3877i) q^{20} +(-18.4597 + 31.9732i) q^{21} +45.8629 q^{22} +(-29.9767 - 51.9211i) q^{23} -73.8302 q^{24} +13.2226 q^{25} +(74.5364 - 129.101i) q^{26} +27.0000 q^{27} +(14.7385 + 25.5279i) q^{28} +(-51.4108 + 89.0461i) q^{29} +(41.7502 + 72.3136i) q^{30} +(-33.2582 + 57.6049i) q^{31} +(-52.1560 + 90.3368i) q^{32} +(-29.0586 + 50.3309i) q^{33} +(34.1095 - 59.0794i) q^{34} +(72.3425 - 125.301i) q^{35} +(10.7786 - 18.6691i) q^{36} +(11.4720 + 19.8701i) q^{37} +(36.1782 - 62.6626i) q^{38} +(94.4520 + 163.596i) q^{39} +289.336 q^{40} +(-57.9800 + 100.424i) q^{41} +87.4045 q^{42} +160.358 q^{43} +(23.2008 + 40.1850i) q^{44} -105.811 q^{45} +(-70.9678 + 122.920i) q^{46} +(-45.1387 + 78.1825i) q^{47} +(58.6513 + 101.587i) q^{48} +(95.7752 + 165.887i) q^{49} +(-15.6518 - 27.1097i) q^{50} +(43.2234 + 74.8651i) q^{51} +150.824 q^{52} -151.543 q^{53} +(-31.9604 - 55.3570i) q^{54} +(113.879 - 197.244i) q^{55} +(151.432 - 262.288i) q^{56} +(45.8448 + 79.4056i) q^{57} +243.423 q^{58} -235.204 q^{59} +(-42.2407 + 73.1630i) q^{60} +(241.559 + 418.392i) q^{61} +157.473 q^{62} +(-55.3792 + 95.9196i) q^{63} +559.758 q^{64} +(-370.152 - 641.121i) q^{65} +137.589 q^{66} +(-502.202 + 220.353i) q^{67} +69.0204 q^{68} +(-89.9300 - 155.763i) q^{69} -342.533 q^{70} +(-257.726 + 446.394i) q^{71} -221.491 q^{72} +(-439.110 - 760.561i) q^{73} +(27.1593 - 47.0412i) q^{74} +39.6677 q^{75} +73.2064 q^{76} +(-119.203 - 206.466i) q^{77} +(223.609 - 387.302i) q^{78} +(-185.610 + 321.486i) q^{79} +(-229.851 - 398.113i) q^{80} +81.0000 q^{81} +274.528 q^{82} +(-414.603 - 718.113i) q^{83} +(44.2156 + 76.5836i) q^{84} +(-169.390 - 293.392i) q^{85} +(-189.819 - 328.776i) q^{86} +(-154.232 + 267.138i) q^{87} +(238.378 - 412.883i) q^{88} -1473.31 q^{89} +(125.251 + 216.941i) q^{90} -774.915 q^{91} -143.603 q^{92} +(-99.7746 + 172.815i) q^{93} +213.726 q^{94} +(-179.663 - 311.185i) q^{95} +(-156.468 + 271.010i) q^{96} +(-515.494 - 892.862i) q^{97} +(226.742 - 392.728i) q^{98} +(-87.1757 + 150.993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9}+O(q^{10}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9} - 2 q^{10} + 16 q^{11} - 198 q^{12} + 88 q^{13} + 214 q^{14} + 12 q^{15} - 298 q^{16} + 52 q^{17} + 18 q^{18} - 2 q^{19} + 164 q^{20} - 42 q^{21} - 506 q^{22} + 160 q^{23} + 324 q^{24} + 572 q^{25} + 353 q^{26} + 864 q^{27} - 433 q^{28} + 48 q^{29} - 6 q^{30} + 292 q^{31} - 525 q^{32} + 48 q^{33} + 138 q^{34} - 328 q^{35} - 594 q^{36} - 616 q^{37} - 194 q^{38} + 264 q^{39} - 1794 q^{40} + 124 q^{41} + 642 q^{42} - 292 q^{43} - 179 q^{44} + 36 q^{45} + 1324 q^{46} + 402 q^{47} - 894 q^{48} + 172 q^{49} + 171 q^{50} + 156 q^{51} - 3344 q^{52} + 852 q^{53} + 54 q^{54} + 1238 q^{55} - 47 q^{56} - 6 q^{57} - 3320 q^{58} + 1200 q^{59} + 492 q^{60} - 454 q^{61} - 5810 q^{62} - 126 q^{63} + 2340 q^{64} - 24 q^{65} - 1518 q^{66} + 110 q^{67} + 906 q^{68} + 480 q^{69} - 10 q^{70} + 406 q^{71} + 972 q^{72} + 1274 q^{73} - 1945 q^{74} + 1716 q^{75} - 2698 q^{76} + 1436 q^{77} + 1059 q^{78} + 1236 q^{79} + 6697 q^{80} + 2592 q^{81} + 2950 q^{82} + 2190 q^{83} - 1299 q^{84} + 2032 q^{85} + 273 q^{86} + 144 q^{87} + 1938 q^{88} - 2160 q^{89} - 18 q^{90} - 3020 q^{91} - 3020 q^{92} + 876 q^{93} - 2886 q^{94} - 102 q^{95} - 1575 q^{96} + 1860 q^{97} + 2612 q^{98} + 144 q^{99}+O(q^{100}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9 - 2 * q^10 + 16 * q^11 - 198 * q^12 + 88 * q^13 + 214 * q^14 + 12 * q^15 - 298 * q^16 + 52 * q^17 + 18 * q^18 - 2 * q^19 + 164 * q^20 - 42 * q^21 - 506 * q^22 + 160 * q^23 + 324 * q^24 + 572 * q^25 + 353 * q^26 + 864 * q^27 - 433 * q^28 + 48 * q^29 - 6 * q^30 + 292 * q^31 - 525 * q^32 + 48 * q^33 + 138 * q^34 - 328 * q^35 - 594 * q^36 - 616 * q^37 - 194 * q^38 + 264 * q^39 - 1794 * q^40 + 124 * q^41 + 642 * q^42 - 292 * q^43 - 179 * q^44 + 36 * q^45 + 1324 * q^46 + 402 * q^47 - 894 * q^48 + 172 * q^49 + 171 * q^50 + 156 * q^51 - 3344 * q^52 + 852 * q^53 + 54 * q^54 + 1238 * q^55 - 47 * q^56 - 6 * q^57 - 3320 * q^58 + 1200 * q^59 + 492 * q^60 - 454 * q^61 - 5810 * q^62 - 126 * q^63 + 2340 * q^64 - 24 * q^65 - 1518 * q^66 + 110 * q^67 + 906 * q^68 + 480 * q^69 - 10 * q^70 + 406 * q^71 + 972 * q^72 + 1274 * q^73 - 1945 * q^74 + 1716 * q^75 - 2698 * q^76 + 1436 * q^77 + 1059 * q^78 + 1236 * q^79 + 6697 * q^80 + 2592 * q^81 + 2950 * q^82 + 2190 * q^83 - 1299 * q^84 + 2032 * q^85 + 273 * q^86 + 144 * q^87 + 1938 * q^88 - 2160 * q^89 - 18 * q^90 - 3020 * q^91 - 3020 * q^92 + 876 * q^93 - 2886 * q^94 - 102 * q^95 - 1575 * q^96 + 1860 * q^97 + 2612 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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