LMFDB - Embedded newform 51.4.h.a.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [51,4,Mod(19,51)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(51, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("51.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	51.h (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.00909741029$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	51.19
Dual form			51.4.h.a.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.320127 + 0.320127i) q^{2} +(-2.77164 + 1.14805i) q^{3} -7.79504i q^{4} +(-2.81499 - 6.79598i) q^{5} +(-1.25480 - 0.519754i) q^{6} +(6.62120 - 15.9850i) q^{7} +(5.05641 - 5.05641i) q^{8} +(6.36396 - 6.36396i) q^{9} +(1.27442 - 3.07673i) q^{10} +(-0.780283 - 0.323204i) q^{11} +(8.94910 + 21.6050i) q^{12} -29.3566i q^{13} +(7.23685 - 2.99760i) q^{14} +(15.6043 + 15.6043i) q^{15} -59.1229 q^{16} +(-14.8387 + 68.5041i) q^{17} +4.07455 q^{18} +(-13.1225 - 13.1225i) q^{19} +(-52.9749 + 21.9429i) q^{20} +51.9061i q^{21} +(-0.146323 - 0.353256i) q^{22} +(111.142 + 46.0364i) q^{23} +(-8.20953 + 19.8196i) q^{24} +(50.1271 - 50.1271i) q^{25} +(9.39783 - 9.39783i) q^{26} +(-10.3325 + 24.9447i) q^{27} +(-124.604 - 51.6125i) q^{28} +(76.9723 + 185.828i) q^{29} +9.99068i q^{30} +(98.5318 - 40.8132i) q^{31} +(-59.3781 - 59.3781i) q^{32} +2.53372 q^{33} +(-26.6803 + 17.1797i) q^{34} -127.272 q^{35} +(-49.6073 - 49.6073i) q^{36} +(-64.8054 + 26.8433i) q^{37} -8.40173i q^{38} +(33.7028 + 81.3658i) q^{39} +(-48.5970 - 20.1296i) q^{40} +(73.4502 - 177.324i) q^{41} +(-16.6165 + 16.6165i) q^{42} +(359.226 - 359.226i) q^{43} +(-2.51939 + 6.08234i) q^{44} +(-61.1638 - 25.3349i) q^{45} +(20.8419 + 50.3169i) q^{46} -235.021i q^{47} +(163.867 - 67.8761i) q^{48} +(30.8578 + 30.8578i) q^{49} +32.0941 q^{50} +(-37.5187 - 206.904i) q^{51} -228.836 q^{52} +(-36.0951 - 36.0951i) q^{53} +(-11.2932 + 4.67779i) q^{54} +6.21260i q^{55} +(-47.3472 - 114.306i) q^{56} +(51.4362 + 21.3056i) q^{57} +(-34.8475 + 84.1292i) q^{58} +(106.903 - 106.903i) q^{59} +(121.636 - 121.636i) q^{60} +(-355.057 + 857.183i) q^{61} +(44.6081 + 18.4773i) q^{62} +(-59.5908 - 143.865i) q^{63} +434.966i q^{64} +(-199.507 + 82.6384i) q^{65} +(0.811111 + 0.811111i) q^{66} +158.409 q^{67} +(533.992 + 115.668i) q^{68} -360.896 q^{69} +(-40.7433 - 40.7433i) q^{70} +(-536.934 + 222.405i) q^{71} -64.3576i q^{72} +(186.196 + 449.517i) q^{73} +(-29.3392 - 12.1527i) q^{74} +(-81.3858 + 196.483i) q^{75} +(-102.290 + 102.290i) q^{76} +(-10.3328 + 10.3328i) q^{77} +(-15.2582 + 36.8366i) q^{78} +(1026.47 + 425.176i) q^{79} +(166.430 + 401.798i) q^{80} -81.0000i q^{81} +(80.2797 - 33.2529i) q^{82} +(-1038.74 - 1038.74i) q^{83} +404.610 q^{84} +(507.323 - 91.9949i) q^{85} +229.996 q^{86} +(-426.679 - 426.679i) q^{87} +(-5.57969 + 2.31118i) q^{88} +1043.96i q^{89} +(-11.4698 - 27.6906i) q^{90} +(-469.265 - 194.376i) q^{91} +(358.855 - 866.353i) q^{92} +(-226.239 + 226.239i) q^{93} +(75.2364 - 75.2364i) q^{94} +(-52.2406 + 126.120i) q^{95} +(232.744 + 96.4057i) q^{96} +(-195.970 - 473.115i) q^{97} +19.7568i q^{98} +(-7.02255 + 2.90883i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 32 q^{5} - 24 q^{6} + 128 q^{10} + 112 q^{11} + 256 q^{14} - 1024 q^{16} - 112 q^{17} - 32 q^{19} - 640 q^{20} + 728 q^{22} + 208 q^{23} + 456 q^{24} + 296 q^{25} + 1472 q^{26} - 328 q^{28} - 1272 q^{29}+ \cdots + 1008 q^{99}+O(q^{100}) $ 40 * q + 32 * q^5 - 24 * q^6 + 128 * q^10 + 112 * q^11 + 256 * q^14 - 1024 * q^16 - 112 * q^17 - 32 * q^19 - 640 * q^20 + 728 * q^22 + 208 * q^23 + 456 * q^24 + 296 * q^25 + 1472 * q^26 - 328 * q^28 - 1272 * q^29 - 192 * q^31 - 960 * q^32 - 912 * q^33 + 24 * q^34 - 992 * q^35 - 216 * q^36 - 1120 * q^37 - 48 * q^39 + 2984 * q^40 - 1320 * q^41 + 1032 * q^42 + 672 * q^43 + 3744 * q^44 + 504 * q^45 - 384 * q^46 - 2096 * q^49 - 448 * q^50 + 960 * q^52 + 2120 * q^53 - 216 * q^54 + 5680 * q^56 + 768 * q^57 + 1000 * q^58 - 832 * q^59 - 1320 * q^60 - 208 * q^61 - 4432 * q^62 - 2376 * q^65 - 1248 * q^66 - 2272 * q^67 - 4560 * q^68 + 3456 * q^69 - 4792 * q^70 + 256 * q^71 - 1416 * q^73 - 2704 * q^74 + 96 * q^75 - 264 * q^76 + 6048 * q^77 - 4872 * q^78 + 1920 * q^79 + 1312 * q^80 + 8328 * q^82 + 4960 * q^83 - 3888 * q^84 + 3192 * q^85 - 15616 * q^86 - 1872 * q^87 - 248 * q^88 - 1152 * q^90 + 1232 * q^91 + 944 * q^92 + 2544 * q^93 - 10000 * q^94 + 4528 * q^95 + 4416 * q^96 + 1008 * q^97 + 1008 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

Coefficient data

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

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

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

$2$	0.320127	+	0.320127i	0.113182	+	0.113182i	0.761430	−	0.648248i	$-0.224498\pi$
$2$	0.320127	+	0.320127i	0.113182	+	0.113182i	−0.648248	+	0.761430i	$0.724498\pi$
$3$	−2.77164	+	1.14805i	−0.533402	+	0.220942i
$3$	−2.77164	+	1.14805i	−0.533402	+	0.220942i
$4$		−	7.79504i		−	0.974380i
$5$	−2.81499	−	6.79598i	−0.251780	−	0.607851i	0.746568	−	0.665309i	$-0.231700\pi$
$5$	−2.81499	−	6.79598i	−0.251780	−	0.607851i	−0.998348	+	0.0574583i	$0.981700\pi$
$6$	−1.25480	−	0.519754i	−0.0853781	−	0.0353648i
$7$	6.62120	−	15.9850i	0.357511	−	0.863109i	−0.638137	−	0.769923i	$-0.720295\pi$
$7$	6.62120	−	15.9850i	0.357511	−	0.863109i	0.995649	−	0.0931862i	$-0.0297052\pi$
$8$	5.05641	−	5.05641i	0.223464	−	0.223464i
$9$	6.36396	−	6.36396i	0.235702	−	0.235702i
$10$	1.27442	−	3.07673i	0.0403008	−	0.0972947i
$11$	−0.780283	−	0.323204i	−0.0213877	−	0.00885906i	0.371964	−	0.928247i	$-0.378684\pi$
$11$	−0.780283	−	0.323204i	−0.0213877	−	0.00885906i	−0.393352	+	0.919388i	$0.628684\pi$
$12$	8.94910	+	21.6050i	0.215282	+	0.519736i
$13$		−	29.3566i		−	0.626311i	−0.949702	−	0.313156i	$-0.898614\pi$
$13$		−	29.3566i		−	0.626311i	0.949702	−	0.313156i	$-0.101386\pi$
$14$	7.23685	−	2.99760i	0.138152	−	0.0572245i
$15$	15.6043	+	15.6043i	0.268600	+	0.268600i
$16$	−59.1229			−0.923796
$17$	−14.8387	+	68.5041i	−0.211700	+	0.977335i
$17$	−14.8387	+	68.5041i	−0.211700	+	0.977335i
$18$	4.07455			0.0533545
$19$	−13.1225	−	13.1225i	−0.158448	−	0.158448i	0.623431	−	0.781879i	$-0.285738\pi$
$19$	−13.1225	−	13.1225i	−0.158448	−	0.158448i	−0.781879	+	0.623431i	$0.785738\pi$
$20$	−52.9749	+	21.9429i	−0.592278	+	0.245329i
$21$			51.9061i			0.539373i
$22$	−0.146323	−	0.353256i	−0.00141801	−	0.00342338i
$23$	111.142	+	46.0364i	1.00759	+	0.417358i	0.824576	−	0.565751i	$-0.191414\pi$
$23$	111.142	+	46.0364i	1.00759	+	0.417358i	0.183016	+	0.983110i	$0.441414\pi$
$24$	−8.20953	+	19.8196i	−0.0698235	+	0.168569i
$25$	50.1271	−	50.1271i	0.401017	−	0.401017i
$26$	9.39783	−	9.39783i	0.0708871	−	0.0708871i
$27$	−10.3325	+	24.9447i	−0.0736475	+	0.177801i
$28$	−124.604	−	51.6125i	−0.840996	−	0.348352i
$29$	76.9723	+	185.828i	0.492876	+	1.18991i	0.953250	+	0.302182i	$0.0977151\pi$
$29$	76.9723	+	185.828i	0.492876	+	1.18991i	−0.460375	+	0.887725i	$0.652285\pi$
$30$			9.99068i			0.0608013i
$31$	98.5318	−	40.8132i	0.570866	−	0.236460i	−0.0785291	−	0.996912i	$-0.525022\pi$
$31$	98.5318	−	40.8132i	0.570866	−	0.236460i	0.649395	+	0.760452i	$0.275022\pi$
$32$	−59.3781	−	59.3781i	−0.328021	−	0.328021i
$33$	2.53372			0.0133656
$34$	−26.6803	+	17.1797i	−0.134577	+	0.0866559i
$35$	−127.272			−0.614656
$36$	−49.6073	−	49.6073i	−0.229664	−	0.229664i
$37$	−64.8054	+	26.8433i	−0.287944	+	0.119270i	−0.521980	−	0.852957i	$-0.674807\pi$
$37$	−64.8054	+	26.8433i	−0.287944	+	0.119270i	0.234036	+	0.972228i	$0.424807\pi$
$38$		−	8.40173i		−	0.0358669i
$39$	33.7028	+	81.3658i	0.138379	+	0.334076i
$40$	−48.5970	−	20.1296i	−0.192097	−	0.0795690i
$41$	73.4502	−	177.324i	0.279780	−	0.675449i	−0.720049	−	0.693923i	$-0.755881\pi$
$41$	73.4502	−	177.324i	0.279780	−	0.675449i	0.999829	+	0.0184739i	$0.00588075\pi$
$42$	−16.6165	+	16.6165i	−0.0610473	+	0.0610473i
$43$	359.226	−	359.226i	1.27399	−	1.27399i	0.330010	−	0.943977i	$-0.392948\pi$
$43$	359.226	−	359.226i	1.27399	−	1.27399i	0.943977	−	0.330010i	$-0.107052\pi$
$44$	−2.51939	+	6.08234i	−0.00863208	+	0.0208397i
$45$	−61.1638	−	25.3349i	−0.202617	−	0.0839267i
$46$	20.8419	+	50.3169i	0.0668038	+	0.161279i
$47$		−	235.021i		−	0.729389i	−0.931127	−	0.364694i	$-0.881173\pi$
$47$		−	235.021i		−	0.729389i	0.931127	−	0.364694i	$-0.118827\pi$
$48$	163.867	−	67.8761i	0.492754	−	0.204106i
$49$	30.8578	+	30.8578i	0.0899644	+	0.0899644i
$50$	32.0941			0.0907758
$51$	−37.5187	−	206.904i	−0.103013	−	0.568086i
$52$	−228.836			−0.610265
$53$	−36.0951	−	36.0951i	−0.0935480	−	0.0935480i	0.658784	−	0.752332i	$-0.271071\pi$
$53$	−36.0951	−	36.0951i	−0.0935480	−	0.0935480i	−0.752332	+	0.658784i	$0.771071\pi$
$54$	−11.2932	+	4.67779i	−0.0284594	+	0.0117883i
$55$			6.21260i			0.0152310i
$56$	−47.3472	−	114.306i	−0.112983	−	0.272765i
$57$	51.4362	+	21.3056i	0.119524	+	0.0495086i
$58$	−34.8475	+	84.1292i	−0.0788913	+	0.190461i
$59$	106.903	−	106.903i	0.235891	−	0.235891i	−0.579255	−	0.815146i	$-0.696657\pi$
$59$	106.903	−	106.903i	0.235891	−	0.235891i	0.815146	+	0.579255i	$0.196657\pi$
$60$	121.636	−	121.636i	0.261719	−	0.261719i
$61$	−355.057	+	857.183i	−0.745252	+	1.79920i	−0.162206	+	0.986757i	$0.551861\pi$
$61$	−355.057	+	857.183i	−0.745252	+	1.79920i	−0.583046	+	0.812439i	$0.698139\pi$
$62$	44.6081	+	18.4773i	0.0913747	+	0.0378486i
$63$	−59.5908	−	143.865i	−0.119170	−	0.287703i
$64$			434.966i			0.849543i
$65$	−199.507	+	82.6384i	−0.380704	+	0.157693i
$66$	0.811111	+	0.811111i	0.00151274	+	0.00151274i
$67$	158.409			0.288847			0.144424	−	0.989516i	$-0.453867\pi$
$67$	158.409			0.288847			0.144424	+	0.989516i	$0.453867\pi$
$68$	533.992	+	115.668i	0.952295	+	0.206277i
$69$	−360.896			−0.629664
$70$	−40.7433	−	40.7433i	−0.0695679	−	0.0695679i
$71$	−536.934	+	222.405i	−0.897497	+	0.371756i	−0.783257	−	0.621698i	$-0.786443\pi$
$71$	−536.934	+	222.405i	−0.897497	+	0.371756i	−0.114240	+	0.993453i	$0.536443\pi$
$72$		−	64.3576i		−	0.105342i
$73$	186.196	+	449.517i	0.298528	+	0.720711i	0.999968	+	0.00798265i	$0.00254098\pi$
$73$	186.196	+	449.517i	0.298528	+	0.720711i	−0.701440	+	0.712729i	$0.747459\pi$
$74$	−29.3392	−	12.1527i	−0.0460893	−	0.0190908i
$75$	−81.3858	+	196.483i	−0.125302	+	0.302505i
$76$	−102.290	+	102.290i	−0.154388	+	0.154388i
$77$	−10.3328	+	10.3328i	−0.0152927	+	0.0152927i
$78$	−15.2582	+	36.8366i	−0.0221494	+	0.0534733i
$79$	1026.47	+	425.176i	1.46185	+	0.605519i	0.964985	−	0.262307i	$-0.0844833\pi$
$79$	1026.47	+	425.176i	1.46185	+	0.605519i	0.496868	+	0.867826i	$0.334483\pi$
$80$	166.430	+	401.798i	0.232593	+	0.561530i
$81$		−	81.0000i		−	0.111111i
$82$	80.2797	−	33.2529i	0.108115	−	0.0447826i
$83$	−1038.74	−	1038.74i	−1.37369	−	1.37369i	−0.854897	−	0.518798i	$-0.826380\pi$
$83$	−1038.74	−	1038.74i	−1.37369	−	1.37369i	−0.518798	−	0.854897i	$-0.673620\pi$
$84$	404.610			0.525555
$85$	507.323	−	91.9949i	0.647376	−	0.117391i
$86$	229.996			0.288385
$87$	−426.679	−	426.679i	−0.525802	−	0.525802i
$88$	−5.57969	+	2.31118i	−0.00675905	+	0.00279969i
$89$			1043.96i			1.24337i	0.783267	+	0.621685i	$0.213552\pi$
$89$			1043.96i			1.24337i	−0.783267	+	0.621685i	$0.786448\pi$
$90$	−11.4698	−	27.6906i	−0.0134336	−	0.0324316i
$91$	−469.265	−	194.376i	−0.540575	−	0.223913i
$92$	358.855	−	866.353i	0.406666	−	0.981777i
$93$	−226.239	+	226.239i	−0.252257	+	0.252257i
$94$	75.2364	−	75.2364i	0.0825536	−	0.0825536i
$95$	−52.2406	+	126.120i	−0.0564187	+	0.136207i
$96$	232.744	+	96.4057i	0.247441	+	0.102493i
$97$	−195.970	−	473.115i	−0.205132	−	0.495232i	0.787513	−	0.616299i	$-0.211369\pi$
$97$	−195.970	−	473.115i	−0.205132	−	0.495232i	−0.992644	+	0.121067i	$0.961369\pi$
$98$			19.7568i			0.0203647i
$99$	−7.02255	+	2.90883i	−0.00712922	+	0.00295302i
$100$	−390.743	−	390.743i	−0.390743	−	0.390743i
$101$	−182.348			−0.179647			−0.0898234	−	0.995958i	$-0.528630\pi$
$101$	−182.348			−0.179647			−0.0898234	+	0.995958i	$0.528630\pi$
$102$	54.2248	−	78.2463i	0.0526378	−	0.0759563i
$103$	−856.328			−0.819190			−0.409595	−	0.912268i	$-0.634330\pi$
$103$	−856.328			−0.819190			−0.409595	+	0.912268i	$0.634330\pi$
$104$	−148.439	−	148.439i	−0.139958	−	0.139958i
$105$	352.753	−	146.115i	0.327859	−	0.135804i
$106$		−	23.1100i		−	0.0211759i
$107$	−522.112	−	1260.49i	−0.471724	−	1.13884i	−0.963401	−	0.268064i	$-0.913616\pi$
$107$	−522.112	−	1260.49i	−0.471724	−	1.13884i	0.491677	−	0.870778i	$-0.336384\pi$
$108$	194.445	+	80.5419i	0.173245	+	0.0717606i
$109$	325.783	−	786.510i	0.286279	−	0.691138i	−0.713678	−	0.700474i	$-0.752972\pi$
$109$	325.783	−	786.510i	0.286279	−	0.691138i	0.999956	+	0.00933646i	$0.00297193\pi$
$110$	−1.98882	+	1.98882i	−0.00172388	+	0.00172388i
$111$	148.800	−	148.800i	0.127238	−	0.127238i
$112$	−391.465	+	945.080i	−0.330267	+	0.797336i
$113$	2078.13	+	860.790i	1.73004	+	0.716605i	0.999428	+	0.0338073i	$0.0107632\pi$
$113$	2078.13	+	860.790i	1.73004	+	0.716605i	0.730608	+	0.682797i	$0.239237\pi$
$114$	9.64561	+	23.2866i	0.00792451	+	0.0191315i
$115$		−	884.908i		−	0.717549i
$116$	1448.53	−	600.002i	1.15942	−	0.480248i
$117$	−186.824	−	186.824i	−0.147623	−	0.147623i
$118$	68.4450			0.0533972
$119$	996.788	+	690.776i	0.767861	+	0.532129i
$120$	157.803			0.120045
$121$	−940.655	−	940.655i	−0.706728	−	0.706728i
$122$	−388.070	+	160.744i	−0.287985	+	0.119287i
$123$			575.804i			0.422101i
$124$	−318.141	−	768.059i	−0.230402	−	0.556240i
$125$	−1331.27	−	551.429i	−0.952578	−	0.394571i
$126$	26.9784	−	65.1316i	0.0190748	−	0.0460507i
$127$	838.437	−	838.437i	0.585821	−	0.585821i	−0.350676	−	0.936497i	$-0.614048\pi$
$127$	838.437	−	838.437i	0.585821	−	0.585821i	0.936497	+	0.350676i	$0.114048\pi$
$128$	−614.269	+	614.269i	−0.424174	+	0.424174i
$129$	−583.235	+	1408.05i	−0.398070	+	0.961025i
$130$	−90.3222	−	37.4127i	−0.0609368	−	0.0252408i
$131$	425.101	+	1026.29i	0.283521	+	0.684481i	0.999913	−	0.0132179i	$-0.00420751\pi$
$131$	425.101	+	1026.29i	0.283521	+	0.684481i	−0.716391	+	0.697699i	$0.754208\pi$
$132$		−	19.7504i		−	0.0130231i
$133$	−296.650	+	122.877i	−0.193405	+	0.0801109i
$134$	50.7111	+	50.7111i	0.0326923	+	0.0326923i
$135$	198.610			0.126619
$136$	271.355	+	421.416i	0.171092	+	0.265707i
$137$	−2073.16			−1.29286			−0.646431	−	0.762973i	$-0.723739\pi$
$137$	−2073.16			−1.29286			−0.646431	+	0.762973i	$0.723739\pi$
$138$	−115.533	−	115.533i	−0.0712666	−	0.0712666i
$139$	649.385	−	268.984i	0.396260	−	0.164136i	−0.175650	−	0.984453i	$-0.556203\pi$
$139$	649.385	−	268.984i	0.396260	−	0.164136i	0.571910	+	0.820316i	$0.306203\pi$
$140$			992.093i			0.598908i
$141$	269.815	+	651.392i	0.161153	+	0.389058i
$142$	−243.085	−	100.689i	−0.143656	−	0.0595044i
$143$	−9.48816	+	22.9064i	−0.00554853	+	0.0133953i
$144$	−376.256	+	376.256i	−0.217741	+	0.217741i
$145$	1046.20	−	1046.20i	0.599190	−	0.599190i
$146$	−84.2960	+	203.509i	−0.0477835	+	0.115360i
$147$	−120.953	−	50.1003i	−0.0678641	−	0.0281102i
$148$	209.244	+	505.160i	0.116215	+	0.280567i
$149$			3157.78i			1.73621i	0.496381	+	0.868105i	$0.334662\pi$
$149$			3157.78i			1.73621i	−0.496381	+	0.868105i	$0.665338\pi$
$150$	−88.9532	+	36.8456i	−0.0484200	+	0.0200562i
$151$	47.4059	+	47.4059i	0.0255486	+	0.0255486i	0.719766	−	0.694217i	$-0.244249\pi$
$151$	47.4059	+	47.4059i	0.0255486	+	0.0255486i	−0.694217	+	0.719766i	$0.744249\pi$
$152$	−132.706			−0.0708148
$153$	341.525	+	530.390i	0.180462	+	0.280258i
$154$	−6.61563			−0.00346170
$155$	−554.732	−	554.732i	−0.287465	−	0.287465i
$156$	634.250	−	262.715i	0.325517	−	0.134833i
$157$			1016.92i			0.516934i	0.966020	+	0.258467i	$0.0832174\pi$
$157$			1016.92i			0.516934i	−0.966020	+	0.258467i	$0.916783\pi$
$158$	192.489	+	464.709i	0.0969214	+	0.233989i
$159$	141.482	+	58.6036i	0.0705674	+	0.0292300i
$160$	−236.384	+	570.681i	−0.116799	+	0.281977i
$161$	1471.78	−	1471.78i	0.720451	−	0.720451i
$162$	25.9303	−	25.9303i	0.0125758	−	0.0125758i
$163$	−1111.76	+	2684.03i	−0.534232	+	1.28975i	0.394466	+	0.918911i	$0.370930\pi$
$163$	−1111.76	+	2684.03i	−0.534232	+	1.28975i	−0.928697	+	0.370839i	$0.879070\pi$
$164$	−1382.25	−	572.547i	−0.658144	−	0.272612i
$165$	−7.13238	−	17.2191i	−0.00336518	−	0.00812427i
$166$		−	665.058i		−	0.310955i
$167$	1818.85	−	753.394i	0.842797	−	0.349098i	0.0808413	−	0.996727i	$-0.474239\pi$
$167$	1818.85	−	753.394i	0.842797	−	0.349098i	0.761956	+	0.647629i	$0.224239\pi$
$168$	262.459	+	262.459i	0.120531	+	0.120531i
$169$	1335.19			0.607734
$170$	191.858	+	132.958i	0.0865578	+	0.0599847i
$171$	−167.022			−0.0746931
$172$	−2800.18	−	2800.18i	−1.24135	−	1.24135i
$173$	−2131.81	+	883.025i	−0.936870	+	0.388064i	−0.798281	−	0.602286i	$-0.794257\pi$
$173$	−2131.81	+	883.025i	−0.936870	+	0.388064i	−0.138589	+	0.990350i	$0.544257\pi$
$174$		−	273.183i		−	0.119022i
$175$	−469.380	−	1133.18i	−0.202753	−	0.489490i
$176$	46.1326	+	19.1088i	0.0197578	+	0.00818396i
$177$	−173.566	+	419.026i	−0.0737064	+	0.177943i
$178$	−334.201	+	334.201i	−0.140727	+	0.140727i
$179$	2566.64	−	2566.64i	1.07173	−	1.07173i	0.0745092	−	0.997220i	$-0.476261\pi$
$179$	2566.64	−	2566.64i	1.07173	−	1.07173i	0.997220	−	0.0745092i	$-0.0237390\pi$
$180$	−197.486	+	476.774i	−0.0817765	+	0.197426i
$181$	552.051	+	228.667i	0.226705	+	0.0939043i	0.493145	−	0.869947i	$-0.335847\pi$
$181$	552.051	+	228.667i	0.226705	+	0.0939043i	−0.266440	+	0.963852i	$0.585847\pi$
$182$	−87.9993	−	212.449i	−0.0358403	−	0.0865263i
$183$		−	2783.42i		−	1.12435i
$184$	794.757	−	329.199i	0.318425	−	0.131896i
$185$	364.853	+	364.853i	0.144997	+	0.144997i
$186$	−144.850			−0.0571018
$187$	33.7192	−	48.6567i	0.0131860	−	0.0190274i
$188$	−1831.99			−0.710702
$189$	330.328	+	330.328i	0.127132	+	0.127132i
$190$	−57.0980	+	23.6508i	−0.0218017	+	0.00903057i
$191$		−	1047.20i		−	0.396718i	−0.980129	−	0.198359i	$-0.936439\pi$
$191$		−	1047.20i		−	0.396718i	0.980129	−	0.198359i	$-0.0635611\pi$
$192$	−499.363	−	1205.57i	−0.187700	−	0.453148i
$193$	1393.77	+	577.318i	0.519822	+	0.215317i	0.627139	−	0.778907i	$-0.284226\pi$
$193$	1393.77	+	577.318i	0.519822	+	0.215317i	−0.107317	+	0.994225i	$0.534226\pi$
$194$	88.7212	−	214.192i	0.0328341	−	0.0792685i
$195$	458.088	−	458.088i	0.168227	−	0.168227i
$196$	240.538	−	240.538i	0.0876595	−	0.0876595i
$197$	596.973	−	1441.22i	0.215901	−	0.521232i	−0.778409	−	0.627758i	$-0.783973\pi$
$197$	596.973	−	1441.22i	0.215901	−	0.521232i	0.994310	+	0.106526i	$0.0339727\pi$
$198$	−3.17930	−	1.31691i	−0.00114113	−	0.000472670i
$199$	902.921	+	2179.84i	0.321640	+	0.776508i	0.999159	+	0.0410026i	$0.0130552\pi$
$199$	902.921	+	2179.84i	0.321640	+	0.776508i	−0.677519	+	0.735505i	$0.736945\pi$
$200$		−	506.927i		−	0.179226i
$201$	−439.053	+	181.862i	−0.154072	+	0.0638186i
$202$	−58.3745	−	58.3745i	−0.0203328	−	0.0203328i
$203$	3480.10			1.20323
$204$	−1612.83	+	292.460i	−0.553531	+	0.100374i
$205$	−1411.85			−0.481016
$206$	−274.134	−	274.134i	−0.0927174	−	0.0927174i
$207$	1000.27	−	414.327i	0.335864	−	0.139119i
$208$			1735.65i			0.578584i
$209$	5.99803	+	14.4805i	0.00198513	+	0.00479253i
$210$	159.701	+	66.1503i	0.0524782	+	0.0217372i
$211$	−251.245	+	606.560i	−0.0819737	+	0.197902i	−0.959552	−	0.281531i	$-0.909158\pi$
$211$	−251.245	+	606.560i	−0.0819737	+	0.197902i	0.877578	+	0.479433i	$0.159158\pi$
$212$	−281.363	+	281.363i	−0.0911513	+	0.0911513i
$213$	1232.85	−	1232.85i	0.396590	−	0.396590i
$214$	236.374	−	570.658i	0.0755057	−	0.182287i
$215$	−3452.51	−	1430.08i	−1.09516	−	0.453630i
$216$	73.8858	+	178.376i	0.0232745	+	0.0561896i
$217$		−	1845.26i		−	0.577256i
$218$	356.075	−	147.491i	0.110626	−	0.0458227i
$219$	−1032.14	−	1032.14i	−0.318471	−	0.318471i
$220$	48.4275			0.0148408
$221$	2011.05	+	435.612i	0.612116	+	0.132590i
$222$	95.2695			0.0288021
$223$	3084.19	+	3084.19i	0.926154	+	0.926154i	0.997455	−	0.0713006i	$-0.0227149\pi$
$223$	3084.19	+	3084.19i	0.926154	+	0.926154i	−0.0713006	+	0.997455i	$0.522715\pi$
$224$	−1342.31	+	556.005i	−0.400389	+	0.165847i
$225$		−	638.014i		−	0.189041i
$226$	389.703	+	940.827i	0.114702	+	0.276915i
$227$	−5839.10	−	2418.63i	−1.70729	−	0.707182i	−1.00000		0.000256354i	$-0.999918\pi$
$227$	−5839.10	−	2418.63i	−1.70729	−	0.707182i	−0.707288	−	0.706925i	$-0.750082\pi$
$228$	166.078	−	400.947i	0.0482402	−	0.116462i
$229$	−1286.81	+	1286.81i	−0.371332	+	0.371332i	−0.867962	−	0.496631i	$-0.834570\pi$
$229$	−1286.81	+	1286.81i	−0.371332	+	0.371332i	0.496631	+	0.867962i	$0.334570\pi$
$230$	283.283	−	283.283i	0.0812135	−	0.0812135i
$231$	16.7763	−	40.5015i	0.00477834	−	0.0115359i
$232$	1328.82	+	550.417i	0.376041	+	0.155761i
$233$	573.863	+	1385.43i	0.161352	+	0.389538i	0.983792	−	0.179314i	$-0.0573878\pi$
$233$	573.863	+	1385.43i	0.161352	+	0.389538i	−0.822440	+	0.568852i	$0.807388\pi$
$234$		−	119.615i		−	0.0334165i
$235$	−1597.20	+	661.580i	−0.443360	+	0.183646i
$236$	−833.312	−	833.312i	−0.229847	−	0.229847i
$237$	−3333.11			−0.913540
$238$	97.9628	+	540.234i	0.0266806	+	0.147135i
$239$	1601.04			0.433315			0.216658	−	0.976248i	$-0.430484\pi$
$239$	1601.04			0.433315			0.216658	+	0.976248i	$0.430484\pi$
$240$	−922.569	−	922.569i	−0.248132	−	0.248132i
$241$	−3382.81	+	1401.21i	−0.904175	+	0.374522i	−0.785824	−	0.618450i	$-0.787761\pi$
$241$	−3382.81	+	1401.21i	−0.904175	+	0.374522i	−0.118351	+	0.992972i	$0.537761\pi$
$242$		−	602.257i		−	0.159978i
$243$	92.9921	+	224.503i	0.0245492	+	0.0592669i
$244$	6681.77	+	2767.68i	1.75310	+	0.726158i
$245$	122.845	−	296.573i	0.0320337	−	0.0773362i
$246$	−184.330	+	184.330i	−0.0477742	+	0.0477742i
$247$	−385.232	+	385.232i	−0.0992378	+	0.0992378i
$248$	291.849	−	704.586i	0.0747276	−	0.180408i
$249$	4071.54	+	1686.49i	1.03624	+	0.429224i
$250$	−249.647	−	602.702i	−0.0631563	−	0.152473i
$251$			6432.51i			1.61759i	0.588088	+	0.808797i	$0.299881\pi$
$251$			6432.51i			1.61759i	−0.588088	+	0.808797i	$0.700119\pi$
$252$	−1121.43	+	464.513i	−0.280332	+	0.116117i
$253$	−71.8428	−	71.8428i	−0.0178526	−	0.0178526i
$254$	536.812			0.132609
$255$	−1300.50	+	837.409i	−0.319375	+	0.205649i
$256$	3086.44			0.753526
$257$	3641.57	+	3641.57i	0.883870	+	0.883870i	0.993925	−	0.110055i	$-0.0351028\pi$
$257$	3641.57	+	3641.57i	0.883870	+	0.883870i	−0.110055	+	0.993925i	$0.535103\pi$
$258$	−637.465	+	264.047i	−0.153825	+	0.0637164i
$259$			1213.65i			0.291168i
$260$	644.169	+	1555.16i	0.153653	+	0.370950i
$261$	1672.45	+	692.751i	0.396636	+	0.164292i
$262$	−192.455	+	464.628i	−0.0453814	+	0.109560i
$263$	1016.05	−	1016.05i	0.238221	−	0.238221i	−0.577892	−	0.816113i	$-0.696125\pi$
$263$	1016.05	−	1016.05i	0.238221	−	0.238221i	0.816113	+	0.577892i	$0.196125\pi$
$264$	12.8115	−	12.8115i	0.00298672	−	0.00298672i
$265$	−143.694	+	346.909i	−0.0333097	+	0.0804168i
$266$	−134.302	−	55.6296i	−0.0309570	−	0.0128228i
$267$	−1198.52	−	2893.49i	−0.274713	−	0.663216i
$268$		−	1234.81i		−	0.281447i
$269$	−4668.12	+	1933.60i	−1.05807	+	0.438266i	−0.842765	−	0.538281i	$-0.819074\pi$
$269$	−4668.12	+	1933.60i	−1.05807	+	0.438266i	−0.215302	+	0.976547i	$0.569074\pi$
$270$	63.5803	+	63.5803i	0.0143310	+	0.0143310i
$271$	−7587.91			−1.70086			−0.850429	−	0.526090i	$-0.823658\pi$
$271$	−7587.91			−1.70086			−0.850429	+	0.526090i	$0.823658\pi$
$272$	877.305	−	4050.16i	0.195568	−	0.902857i
$273$	1523.79			0.337816
$274$	−663.674	−	663.674i	−0.146329	−	0.146329i
$275$	−55.3146	+	22.9121i	−0.0121294	+	0.00502418i
$276$			2813.20i			0.613532i
$277$	−1226.17	−	2960.24i	−0.265970	−	0.642108i	0.733316	−	0.679888i	$-0.237971\pi$
$277$	−1226.17	−	2960.24i	−0.265970	−	0.642108i	−0.999286	+	0.0377799i	$0.987971\pi$
$278$	293.994	+	121.776i	0.0634267	+	0.0262722i
$279$	367.319	−	886.786i	0.0788201	−	0.190289i
$280$	−643.542	+	643.542i	−0.137353	+	0.137353i
$281$	−928.811	+	928.811i	−0.197182	+	0.197182i	−0.798791	−	0.601609i	$-0.794527\pi$
$281$	−928.811	+	928.811i	−0.197182	+	0.197182i	0.601609	+	0.798791i	$0.294527\pi$
$282$	−122.153	+	294.903i	−0.0257947	+	0.0622739i
$283$	1004.92	+	416.251i	0.211082	+	0.0874331i	0.485719	−	0.874115i	$-0.338558\pi$
$283$	1004.92	+	416.251i	0.211082	+	0.0874331i	−0.274637	+	0.961548i	$0.588558\pi$
$284$	1733.66	+	4185.42i	0.362231	+	0.874503i
$285$		−	409.534i		−	0.0851183i
$286$	−10.3704	+	4.29555i	−0.00214410	+	0.000888116i
$287$	−2348.20	−	2348.20i	−0.482962	−	0.482962i
$288$	−755.760			−0.154631
$289$	−4472.63	−	2033.02i	−0.910366	−	0.413804i
$290$	669.836			0.135635
$291$	1086.32	+	1086.32i	0.218836	+	0.218836i
$292$	3504.00	−	1451.40i	0.702247	−	0.290880i
$293$		−	8873.35i		−	1.76924i	−0.466315	−	0.884619i	$-0.654419\pi$
$293$		−	8873.35i		−	1.76924i	0.466315	−	0.884619i	$-0.345581\pi$
$294$	−22.6818	−	54.7587i	−0.00449942	−	0.0108626i
$295$	−1027.44	−	425.580i	−0.202779	−	0.0839939i
$296$	−191.952	+	463.413i	−0.0376925	+	0.0909978i
$297$	16.1245	−	16.1245i	0.00315029	−	0.00315029i
$298$	−1010.89	+	1010.89i	−0.196507	+	0.196507i
$299$	1351.47	−	3262.74i	0.261396	−	0.631067i
$300$	1531.59	+	634.406i	0.294755	+	0.122091i
$301$	−3363.72	−	8120.74i	−0.644125	−	1.55505i
$302$			30.3518i			0.00578328i
$303$	505.403	−	209.345i	0.0958239	−	0.0396916i
$304$	775.841	+	775.841i	0.146373	+	0.146373i
$305$	6824.88			1.28128
$306$	−60.4609	+	279.123i	−0.0112952	+	0.0521452i
$307$	4654.23			0.865248			0.432624	−	0.901574i	$-0.357588\pi$
$307$	4654.23			0.865248			0.432624	+	0.901574i	$0.357588\pi$
$308$	80.5448	+	80.5448i	0.0149009	+	0.0149009i
$309$	2373.43	−	983.108i	0.436957	−	0.180994i
$310$		−	355.169i		−	0.0650717i
$311$	2454.04	+	5924.58i	0.447447	+	1.08023i	0.973275	+	0.229641i	$0.0737553\pi$
$311$	2454.04	+	5924.58i	0.447447	+	1.08023i	−0.525829	+	0.850591i	$0.676245\pi$
$312$	581.835	+	241.004i	0.105577	+	0.0437313i
$313$	2271.45	−	5483.76i	0.410191	−	0.990290i	−0.574895	−	0.818227i	$-0.694957\pi$
$313$	2271.45	−	5483.76i	0.410191	−	0.990290i	0.985086	−	0.172062i	$-0.0550430\pi$
$314$	−325.542	+	325.542i	−0.0585076	+	0.0585076i
$315$	−809.956	+	809.956i	−0.144876	+	0.144876i
$316$	3314.26	−	8001.34i	0.590006	−	1.42440i
$317$	−6868.17	−	2844.89i	−1.21689	−	0.504053i	−0.320472	−	0.947258i	$-0.603842\pi$
$317$	−6868.17	−	2844.89i	−1.21689	−	0.504053i	−0.896420	+	0.443205i	$0.853842\pi$
$318$	26.5315	+	64.0526i	0.00467865	+	0.0112953i
$319$		−	169.876i		−	0.0298157i
$320$	2956.02	−	1224.42i	0.516396	−	0.213898i
$321$	2894.21	+	2894.21i	0.503237	+	0.503237i
$322$	942.314			0.163084
$323$	1093.67	−	704.225i	0.188400	−	0.121313i
$324$	−631.398			−0.108264
$325$	−1471.56	−	1471.56i	−0.251162	−	0.251162i
$326$	−1215.13	+	503.324i	−0.206442	+	0.0855109i
$327$			2553.94i			0.431905i
$328$	−525.231	−	1268.02i	−0.0884178	−	0.213459i
$329$	−3756.80	−	1556.12i	−0.629542	−	0.260765i
$330$	3.22903	−	7.79556i	0.000538643	−	0.00130040i
$331$	−4454.94	+	4454.94i	−0.739776	+	0.739776i	−0.972535	−	0.232759i	$-0.925225\pi$
$331$	−4454.94	+	4454.94i	−0.739776	+	0.739776i	0.232759	+	0.972535i	$0.425225\pi$
$332$	−8097.03	+	8097.03i	−1.33850	+	1.33850i
$333$	−241.589	+	583.248i	−0.0397568	+	0.0959814i
$334$	823.445	+	341.082i	0.134901	+	0.0558778i
$335$	−445.920	−	1076.55i	−0.0727261	−	0.175576i
$336$		−	3068.84i		−	0.498271i
$337$	110.753	−	45.8752i	0.0179023	−	0.00741537i	−0.373714	−	0.927544i	$-0.621916\pi$
$337$	110.753	−	45.8752i	0.0179023	−	0.00741537i	0.391617	+	0.920128i	$0.371916\pi$
$338$	427.430	+	427.430i	0.0687845	+	0.0687845i
$339$	−6748.06			−1.08113
$340$	−717.104	−	3954.60i	−0.114384	−	0.630790i
$341$	−90.0737			−0.0143043
$342$	−53.4683	−	53.4683i	−0.00845390	−	0.00845390i
$343$	6180.43	−	2560.02i	0.972921	−	0.402997i
$344$		−	3632.79i		−	0.569381i
$345$	1015.92	+	2452.64i	0.158537	+	0.382742i
$346$	−965.129	−	399.770i	−0.149959	−	0.0621149i
$347$	−1454.50	+	3511.48i	−0.225019	+	0.543245i	−0.995558	−	0.0941481i	$-0.969987\pi$
$347$	−1454.50	+	3511.48i	−0.225019	+	0.543245i	0.770539	+	0.637393i	$0.219987\pi$
$348$	−3325.98	+	3325.98i	−0.512331	+	0.512331i
$349$	−1357.28	+	1357.28i	−0.208177	+	0.208177i	−0.803492	−	0.595315i	$-0.797027\pi$
$349$	−1357.28	+	1357.28i	−0.208177	+	0.208177i	0.595315	+	0.803492i	$0.297027\pi$
$350$	212.501	−	513.024i	0.0324534	−	0.0783494i
$351$	732.292	+	303.325i	0.111359	+	0.0461263i
$352$	27.1405	+	65.5230i	0.00410964	+	0.00992156i
$353$			10588.6i			1.59652i	0.602310	+	0.798262i	$0.294247\pi$
$353$			10588.6i			1.59652i	−0.602310	+	0.798262i	$0.705753\pi$
$354$	−189.705	+	78.5783i	−0.0284822	+	0.0117977i
$355$	3022.92	+	3022.92i	0.451944	+	0.451944i
$356$	8137.74			1.21151
$357$	−3555.78	−	770.218i	−0.527148	−	0.114186i
$358$	1643.30			0.242601
$359$	5887.75	+	5887.75i	0.865582	+	0.865582i	0.991980	−	0.126398i	$-0.0403416\pi$
$359$	5887.75	+	5887.75i	0.865582	+	0.865582i	−0.126398	+	0.991980i	$0.540342\pi$
$360$	−437.373	+	181.166i	−0.0640322	+	0.0265230i
$361$		−	6514.60i		−	0.949789i
$362$	103.524	+	249.929i	0.0150306	+	0.0362872i
$363$	3687.07	+	1527.24i	0.533116	+	0.220824i
$364$	−1515.17	+	3657.94i	−0.218177	+	0.526725i
$365$	2530.77	−	2530.77i	0.362922	−	0.362922i
$366$	891.048	−	891.048i	0.127256	−	0.127256i
$367$	−1909.17	+	4609.14i	−0.271547	+	0.655572i	−0.999550	−	0.0300018i	$-0.990449\pi$
$367$	−1909.17	+	4609.14i	−0.271547	+	0.655572i	0.728003	+	0.685574i	$0.240449\pi$
$368$	−6571.01	−	2721.80i	−0.930809	−	0.385554i
$369$	−661.052	−	1595.92i	−0.0932601	−	0.225150i
$370$			233.598i			0.0328221i
$371$	−815.973	+	337.987i	−0.114187	+	0.0472976i
$372$	1763.54	+	1763.54i	0.245794	+	0.245794i
$373$	−7799.78			−1.08273			−0.541364	−	0.840789i	$-0.682092\pi$
$373$	−7799.78			−1.08273			−0.541364	+	0.840789i	$0.682092\pi$
$374$	26.3707	−	4.78190i	0.00364598	−	0.000661140i
$375$	4322.86			0.595284
$376$	−1188.36	−	1188.36i	−0.162992	−	0.162992i
$377$	5455.26	−	2259.64i	0.745252	−	0.308694i
$378$			211.494i			0.0287780i
$379$	3664.91	+	8847.87i	0.496711	+	1.19917i	0.951245	+	0.308438i	$0.0998061\pi$
$379$	3664.91	+	8847.87i	0.496711	+	1.19917i	−0.454533	+	0.890730i	$0.650194\pi$
$380$	983.111	+	407.218i	0.132717	+	0.0549732i
$381$	−1361.28	+	3286.41i	−0.183045	+	0.441911i
$382$	335.238	−	335.238i	0.0449012	−	0.0449012i
$383$	−4955.65	+	4955.65i	−0.661154	+	0.661154i	−0.955652	−	0.294498i	$-0.904847\pi$
$383$	−4955.65	+	4955.65i	−0.661154	+	0.661154i	0.294498	+	0.955652i	$0.404847\pi$
$384$	997.321	−	2407.75i	0.132537	−	0.319973i
$385$	99.3085	+	41.1349i	0.0131460	+	0.00544527i
$386$	261.368	+	630.998i	0.0344644	+	0.0832045i
$387$		−	4572.20i		−	0.600563i
$388$	−3687.95	+	1527.60i	−0.482544	+	0.199876i
$389$	5699.40	+	5699.40i	0.742856	+	0.742856i	0.973127	−	0.230271i	$-0.0739611\pi$
$389$	5699.40	+	5699.40i	0.742856	+	0.742856i	−0.230271	+	0.973127i	$0.573961\pi$
$390$	293.292			0.0380806
$391$	−4802.87	+	6930.54i	−0.621206	+	0.896400i
$392$	312.059			0.0402076
$393$	−2356.45	−	2356.45i	−0.302462	−	0.302462i
$394$	652.480	−	270.266i	0.0834302	−	0.0345579i
$395$		−	8172.70i		−	1.04105i
$396$	22.6745	+	54.7410i	0.00287736	+	0.00694657i
$397$	−512.686	−	212.361i	−0.0648135	−	0.0268466i	0.350041	−	0.936734i	$-0.386168\pi$
$397$	−512.686	−	212.361i	−0.0648135	−	0.0268466i	−0.414855	+	0.909888i	$0.636168\pi$
$398$	−408.777	+	986.876i	−0.0514828	+	0.124290i
$399$	681.139	−	681.139i	0.0854626	−	0.0854626i
$400$	−2963.66	+	2963.66i	−0.370458	+	0.370458i
$401$	4773.23	−	11523.6i	0.594423	−	1.43506i	−0.284768	−	0.958596i	$-0.591917\pi$
$401$	4773.23	−	11523.6i	0.594423	−	1.43506i	0.879192	−	0.476468i	$-0.158083\pi$
$402$	−198.772	−	82.3339i	−0.0246613	−	0.0102150i
$403$	−1198.14	−	2892.56i	−0.148098	−	0.357540i
$404$			1421.41i			0.175044i
$405$	−550.474	+	228.014i	−0.0675390	+	0.0279756i
$406$	1114.07	+	1114.07i	0.136184	+	0.136184i
$407$	59.2424			0.00721507
$408$	−1235.90	−	856.483i	−0.149967	−	0.103927i
$409$	3703.58			0.447751			0.223875	−	0.974618i	$-0.428129\pi$
$409$	3703.58			0.447751			0.223875	+	0.974618i	$0.428129\pi$
$410$	−451.972	−	451.972i	−0.0544423	−	0.0544423i
$411$	5746.05	−	2380.09i	0.689615	−	0.285648i
$412$			6675.11i			0.798202i
$413$	−1001.02	−	2416.67i	−0.119266	−	0.287933i
$414$	452.852	+	187.577i	0.0537595	+	0.0222679i
$415$	−4135.22	+	9983.31i	−0.489133	+	1.18087i
$416$	−1743.14	+	1743.14i	−0.205443	+	0.205443i
$417$	−1491.05	+	1491.05i	−0.175101	+	0.175101i
$418$	−2.71547	+	6.55573i	−0.000317747	+	0.000767108i
$419$	−11310.5	−	4684.95i	−1.31874	−	0.546241i	−0.391319	−	0.920255i	$-0.627981\pi$
$419$	−11310.5	−	4684.95i	−1.31874	−	0.546241i	−0.927423	+	0.374015i	$0.877981\pi$
$420$	−1138.97	−	2749.72i	−0.132324	−	0.319459i
$421$		−	13087.7i		−	1.51510i	−0.652780	−	0.757548i	$-0.726397\pi$
$421$		−	13087.7i		−	1.51510i	0.652780	−	0.757548i	$-0.273603\pi$
$422$	−274.606	+	113.746i	−0.0316769	+	0.0131210i
$423$	−1495.66	−	1495.66i	−0.171919	−	0.171919i
$424$	−365.024			−0.0418092
$425$	2690.10	+	4177.74i	0.307032	+	0.476823i
$426$	789.339			0.0897737
$427$	11351.2	+	11351.2i	1.28647	+	1.28647i
$428$	−9825.56	+	4069.88i	−1.10966	+	0.459638i
$429$		−	74.3813i		−	0.00837100i
$430$	−647.435	−	1563.05i	−0.0726095	−	0.175295i
$431$	−5560.46	−	2303.22i	−0.621434	−	0.257406i	0.0496745	−	0.998765i	$-0.484182\pi$
$431$	−5560.46	−	2303.22i	−0.621434	−	0.257406i	−0.671109	+	0.741359i	$0.734182\pi$
$432$	610.885	−	1474.81i	0.0680352	−	0.164251i
$433$	11424.0	−	11424.0i	1.26790	−	1.26790i	0.320736	−	0.947168i	$-0.396070\pi$
$433$	11424.0	−	11424.0i	1.26790	−	1.26790i	0.947168	−	0.320736i	$-0.103930\pi$
$434$	590.718	−	590.718i	0.0653350	−	0.0653350i
$435$	−1698.61	+	4100.80i	−0.187223	+	0.451996i
$436$	−6130.88	−	2539.49i	−0.673430	−	0.278944i
$437$	−854.344	−	2062.57i	−0.0935213	−	0.225780i
$438$		−	660.828i		−	0.0720904i
$439$	−1194.57	+	494.807i	−0.129872	+	0.0537946i	−0.446673	−	0.894697i	$-0.647391\pi$
$439$	−1194.57	+	494.807i	−0.129872	+	0.0537946i	0.316801	+	0.948492i	$0.397391\pi$
$440$	31.4135	+	31.4135i	0.00340359	+	0.00340359i
$441$	392.755			0.0424096
$442$	504.339	+	783.241i	0.0542736	+	0.0842873i
$443$	1279.76			0.137253			0.0686267	−	0.997642i	$-0.478138\pi$
$443$	1279.76			0.137253			0.0686267	+	0.997642i	$0.478138\pi$
$444$	−1159.90	−	1159.90i	−0.123978	−	0.123978i
$445$	7094.76	−	2938.74i	0.755784	−	0.313056i
$446$			1974.66i			0.209648i
$447$	−3625.29	−	8752.22i	−0.383602	−	0.926098i
$448$	6952.93	+	2880.00i	0.733248	+	0.303721i
$449$	4447.36	−	10736.9i	0.467448	−	1.12852i	−0.497826	−	0.867277i	$-0.665868\pi$
$449$	4447.36	−	10736.9i	0.467448	−	1.12852i	0.965274	−	0.261241i	$-0.0841318\pi$
$450$	204.245	−	204.245i	0.0213961	−	0.0213961i
$451$	−114.624	+	114.624i	−0.0119677	+	0.0119677i
$452$	6709.89	−	16199.1i	0.698245	−	1.68571i
$453$	−185.817	−	76.9677i	−0.0192725	−	0.00798291i
$454$	−1094.98	−	2643.52i	−0.113194	−	0.273274i
$455$			3736.28i			0.384966i
$456$	367.812	−	152.353i	0.0377728	−	0.0156460i
$457$	13259.6	+	13259.6i	1.35724	+	1.35724i	0.877300	+	0.479942i	$0.159342\pi$
$457$	13259.6	+	13259.6i	1.35724	+	1.35724i	0.479942	+	0.877300i	$0.340658\pi$
$458$	−823.886			−0.0840560
$459$	−1555.50	−	1077.96i	−0.158180	−	0.109619i
$460$	−6897.89			−0.699165
$461$	5405.53	+	5405.53i	0.546119	+	0.546119i	0.925316	−	0.379197i	$-0.123800\pi$
$461$	5405.53	+	5405.53i	0.546119	+	0.546119i	−0.379197	+	0.925316i	$0.623800\pi$
$462$	18.3361	−	7.59507i	0.00184648	−	0.000764837i
$463$		−	4635.96i		−	0.465337i	−0.972556	−	0.232669i	$-0.925254\pi$
$463$		−	4635.96i		−	0.465337i	0.972556	−	0.232669i	$-0.0747458\pi$
$464$	−4550.83	−	10986.7i	−0.455316	−	1.09923i
$465$	2174.38	+	900.656i	0.216848	+	0.0898213i
$466$	−259.803	+	627.221i	−0.0258265	+	0.0623508i
$467$	5158.09	−	5158.09i	0.511109	−	0.511109i	−0.403757	−	0.914866i	$-0.632296\pi$
$467$	5158.09	−	5158.09i	0.511109	−	0.511109i	0.914866	+	0.403757i	$0.132296\pi$
$468$	−1456.30	+	1456.30i	−0.143841	+	0.143841i
$469$	1048.86	−	2532.17i	0.103266	−	0.249307i
$470$	−723.094	−	299.516i	−0.0709657	−	0.0293949i
$471$	−1167.47	−	2818.52i	−0.114213	−	0.275734i
$472$		−	1081.09i		−	0.105426i
$473$	−396.401	+	164.195i	−0.0385339	+	0.0159613i
$474$	−1067.02	−	1067.02i	−0.103396	−	0.103396i
$475$	−1315.59			−0.127081
$476$	5384.62	−	7770.00i	0.518495	−	0.748188i
$477$	−459.416			−0.0440989
$478$	512.534	+	512.534i	0.0490435	+	0.0490435i
$479$	−9023.05	+	3737.47i	−0.860696	+	0.356512i	−0.768980	−	0.639273i	$-0.779235\pi$
$479$	−9023.05	+	3737.47i	−0.860696	+	0.356512i	−0.0917164	+	0.995785i	$0.529235\pi$
$480$		−	1853.10i		−	0.176213i
$481$	788.026	+	1902.46i	0.0747004	+	0.180343i
$482$	−1531.49	−	634.365i	−0.144725	−	0.0599472i
$483$	−2389.57	+	5768.93i	−0.225112	+	0.543469i
$484$	−7332.44	+	7332.44i	−0.688621	+	0.688621i
$485$	−2663.62	+	2663.62i	−0.249379	+	0.249379i
$486$	−42.1001	+	101.639i	−0.00392942	+	0.00948646i
$487$	7412.70	+	3070.44i	0.689736	+	0.285698i	0.699890	−	0.714250i	$-0.253232\pi$
$487$	7412.70	+	3070.44i	0.689736	+	0.285698i	−0.0101543	+	0.999948i	$0.503232\pi$
$488$	2538.96	+	6129.58i	0.235519	+	0.568593i
$489$		−	8715.51i		−	0.805989i
$490$	134.267	−	55.6152i	0.0123787	−	0.00512742i
$491$	1498.20	+	1498.20i	0.137705	+	0.137705i	0.772599	−	0.634894i	$-0.218956\pi$
$491$	1498.20	+	1498.20i	0.137705	+	0.137705i	−0.634894	+	0.772599i	$0.718956\pi$
$492$	4488.41			0.411287
$493$	−13872.1	+	2515.49i	−1.26728	+	0.229801i
$494$	−246.646			−0.0224638
$495$	39.5368	+	39.5368i	0.00358999	+	0.00358999i
$496$	−5825.49	+	2413.00i	−0.527363	+	0.218441i
$497$			10055.5i			0.907545i
$498$	763.520	+	1843.30i	0.0687031	+	0.165864i
$499$	−503.819	−	208.689i	−0.0451985	−	0.0187218i	0.359970	−	0.932964i	$-0.382787\pi$
$499$	−503.819	−	208.689i	−0.0451985	−	0.0187218i	−0.405168	+	0.914242i	$0.632787\pi$
$500$	−4298.41	+	10377.3i	−0.384462	+	0.928173i
$501$	−4176.27	+	4176.27i	−0.372419	+	0.372419i
$502$	−2059.22	+	2059.22i	−0.183082	+	0.183082i
$503$	4410.24	−	10647.3i	0.390940	−	0.943813i	−0.598795	−	0.800902i	$-0.704354\pi$
$503$	4410.24	−	10647.3i	0.390940	−	0.943813i	0.989736	−	0.142911i	$-0.0456462\pi$
$504$	−1028.76	−	426.125i	−0.0909216	−	0.0376609i
$505$	513.308	+	1239.23i	0.0452315	+	0.109198i
$506$		−	45.9976i		−	0.00404119i
$507$	−3700.67	+	1532.87i	−0.324167	+	0.134274i
$508$	−6535.65	−	6535.65i	−0.570812	−	0.570812i
$509$	−13687.9			−1.19196			−0.595979	−	0.803000i	$-0.703236\pi$
$509$	−13687.9			−1.19196			−0.595979	+	0.803000i	$0.703236\pi$
$510$	−684.403	−	148.248i	−0.0594233	−	0.0128717i
$511$	8418.36			0.728780
$512$	5902.21	+	5902.21i	0.509459	+	0.509459i
$513$	462.925	−	191.750i	0.0398414	−	0.0165029i
$514$			2331.53i			0.200076i
$515$	2410.55	+	5819.59i	0.206256	+	0.497945i
$516$	10975.8	+	4546.34i	0.936404	+	0.387871i
$517$	−75.9595	+	183.383i	−0.00646170	+	0.0155999i
$518$	−388.521	+	388.521i	−0.0329549	+	0.0329549i
$519$	4894.85	−	4894.85i	0.413989	−	0.413989i
$520$	−590.935	+	1426.64i	−0.0498350	+	0.120312i
$521$	4882.56	+	2022.42i	0.410573	+	0.170065i	0.578403	−	0.815751i	$-0.303676\pi$
$521$	4882.56	+	2022.42i	0.410573	+	0.170065i	−0.167830	+	0.985816i	$0.553676\pi$
$522$	313.627	+	757.163i	0.0262971	+	0.0634868i
$523$			551.260i			0.0460897i	0.999734	+	0.0230448i	$0.00733605\pi$
$523$			551.260i			0.0460897i	−0.999734	+	0.0230448i	$0.992664\pi$
$524$	7999.93	−	3313.68i	0.666944	−	0.276257i
$525$	2601.91	+	2601.91i	0.216298	+	0.216298i
$526$	650.527			0.0539246
$527$	1333.79	+	7355.45i	0.110248	+	0.607985i
$528$	−149.801			−0.0123470
$529$	1629.74	+	1629.74i	0.133947	+	0.133947i
$530$	−157.055	+	65.0544i	−0.0128718	+	0.00533167i
$531$		−	1360.65i		−	0.111200i
$532$	957.827	+	2312.40i	0.0780584	+	0.188450i
$533$	−5205.64	−	2156.25i	−0.423042	−	0.175230i
$534$	542.604	−	1309.96i	0.0439715	−	0.106157i
$535$	−7096.52	+	7096.52i	−0.573476	+	0.573476i
$536$	800.983	−	800.983i	0.0645470	−	0.0645470i
$537$	−4167.16	+	10060.4i	−0.334872	+	0.808453i
$538$	−2113.39	−	875.393i	−0.169358	−	0.0701503i
$539$	−14.1045	−	34.0512i	−0.00112713	−	0.00272113i
$540$		−	1548.17i		−	0.123375i
$541$	−16512.4	+	6839.64i	−1.31224	+	0.543548i	−0.925537	−	0.378657i	$-0.876386\pi$
$541$	−16512.4	+	6839.64i	−1.31224	+	0.543548i	−0.386703	+	0.922204i	$0.626386\pi$
$542$	−2429.09	−	2429.09i	−0.192506	−	0.192506i
$543$	−1792.61			−0.141672
$544$	4948.74	−	3186.55i	0.390028	−	0.251144i
$545$	−6262.18			−0.492188
$546$	487.805	+	487.805i	0.0382346	+	0.0382346i
$547$	13493.5	−	5589.20i	1.05474	−	0.436887i	0.213157	−	0.977018i	$-0.431625\pi$
$547$	13493.5	−	5589.20i	1.05474	−	0.436887i	0.841581	+	0.540131i	$0.181625\pi$
$548$			16160.4i			1.25974i
$549$	3195.51	+	7714.64i	0.248417	+	0.599732i
$550$	−25.0425	−	10.3729i	−0.00194148	−	0.000804188i
$551$	1428.45	−	3448.59i	0.110443	−	0.266633i
$552$	−1824.84	+	1824.84i	−0.140707	+	0.140707i
$553$	13592.9	−	13592.9i	1.04526	−	1.04526i
$554$	555.122	−	1340.18i	0.0425720	−	0.102778i
$555$	−1430.11	−	592.370i	−0.109378	−	0.0453058i
$556$	−2096.74	−	5061.98i	−0.159931	−	0.386107i
$557$			17809.6i			1.35479i	0.735619	+	0.677395i	$0.236891\pi$
$557$			17809.6i			1.35479i	−0.735619	+	0.677395i	$0.763109\pi$
$558$	401.473	−	166.295i	0.0304582	−	0.0126162i
$559$	−10545.6	−	10545.6i	−0.797913	−	0.797913i
$560$	7524.71			0.567816
$561$	−37.5970	+	173.570i	−0.00282949	+	0.0130626i
$562$	−594.675			−0.0446349
$563$	−3846.68	−	3846.68i	−0.287955	−	0.287955i	0.548316	−	0.836271i	$-0.315269\pi$
$563$	−3846.68	−	3846.68i	−0.287955	−	0.287955i	−0.836271	+	0.548316i	$0.815269\pi$
$564$	5077.63	−	2103.22i	0.379090	−	0.157024i
$565$		−	16546.1i		−	1.23203i
$566$	188.448	+	454.955i	0.0139948	+	0.0337865i
$567$	−1294.78	−	536.317i	−0.0959010	−	0.0397235i
$568$	−1590.39	+	3839.53i	−0.117484	+	0.283632i
$569$	5419.10	−	5419.10i	0.399263	−	0.399263i	−0.478710	−	0.877973i	$-0.658896\pi$
$569$	5419.10	−	5419.10i	0.399263	−	0.399263i	0.877973	+	0.478710i	$0.158896\pi$
$570$	131.103	−	131.103i	0.00963385	−	0.00963385i
$571$	−2665.53	+	6435.16i	−0.195357	+	0.471634i	−0.990956	−	0.134190i	$-0.957157\pi$
$571$	−2665.53	+	6435.16i	−0.195357	+	0.471634i	0.795598	+	0.605825i	$0.207157\pi$
$572$	178.557	+	73.9605i	0.0130521	+	0.00540637i
$573$	1202.24	+	2902.47i	0.0876517	+	0.211610i
$574$		−	1503.44i		−	0.109325i
$575$	7878.88	−	3263.54i	0.571430	−	0.236694i
$576$	2768.11	+	2768.11i	0.200239	+	0.200239i
$577$	9597.05			0.692427			0.346214	−	0.938156i	$-0.387467\pi$
$577$	9597.05			0.692427			0.346214	+	0.938156i	$0.387467\pi$
$578$	−780.984	−	2082.63i	−0.0562018	−	0.149872i
$579$	−4525.81			−0.324847
$580$	−8155.20	−	8155.20i	−0.583839	−	0.583839i
$581$	−23482.0	+	9726.56i	−1.67676	+	0.694536i
$582$			695.519i			0.0495364i
$583$	16.4983	+	39.8305i	0.00117203	+	0.00282952i
$584$	3214.43	+	1331.46i	0.227763	+	0.0943427i
$585$	−743.746	+	1795.56i	−0.0525643	+	0.126901i
$586$	2840.60	−	2840.60i	0.200246	−	0.200246i
$587$	191.586	−	191.586i	0.0134712	−	0.0134712i	−0.700339	−	0.713810i	$-0.746968\pi$
$587$	191.586	−	191.586i	0.0134712	−	0.0134712i	0.713810	+	0.700339i	$0.246968\pi$
$588$	−390.534	+	942.832i	−0.0273901	+	0.0661254i
$589$	−1828.56	−	757.413i	−0.127919	−	0.0529858i
$590$	−192.672	−	465.151i	−0.0134444	−	0.0324575i
$591$			4679.90i			0.325728i
$592$	3831.48	−	1587.05i	0.266002	−	0.110181i
$593$	−2738.28	−	2738.28i	−0.189625	−	0.189625i	0.605909	−	0.795534i	$-0.292810\pi$
$593$	−2738.28	−	2738.28i	−0.189625	−	0.189625i	−0.795534	+	0.605909i	$0.792810\pi$
$594$	10.3238			0.000713112
$595$	1888.55	−	8718.68i	0.130123	−	0.600724i
$596$	24615.0			1.69173
$597$	−5005.14	−	5005.14i	−0.343127	−	0.343127i
$598$	1477.13	−	611.848i	0.101011	−	0.0418400i
$599$		−	24689.8i		−	1.68414i	−0.539369	−	0.842069i	$-0.681337\pi$
$599$		−	24689.8i		−	1.68414i	0.539369	−	0.842069i	$-0.318663\pi$
$600$	581.978	+	1405.02i	0.0395986	+	0.0955994i
$601$	−15867.1	−	6572.35i	−1.07692	−	0.446076i	−0.227495	−	0.973779i	$-0.573053\pi$
$601$	−15867.1	−	6572.35i	−1.07692	−	0.446076i	−0.849429	+	0.527703i	$0.823053\pi$
$602$	1522.85	−	3676.48i	0.103101	−	0.248907i
$603$	1008.11	−	1008.11i	0.0680820	−	0.0680820i
$604$	369.531	−	369.531i	0.0248941	−	0.0248941i
$605$	−3744.74	+	9040.60i	−0.251645	+	0.607525i
$606$	228.810	+	94.7762i	0.0153379	+	0.00635317i
$607$	−43.1573	−	104.191i	−0.00288583	−	0.00696701i	0.922430	−	0.386164i	$-0.126200\pi$
$607$	−43.1573	−	104.191i	−0.00288583	−	0.00696701i	−0.925316	+	0.379197i	$0.876200\pi$
$608$			1558.38i			0.103948i
$609$	−9645.58	+	3995.33i	−0.641804	+	0.265844i
$610$	2184.83	+	2184.83i	0.145018	+	0.145018i
$611$	−6899.40			−0.456825
$612$	4134.41	−	2662.20i	0.273078	−	0.175838i
$613$	−4185.29			−0.275762			−0.137881	−	0.990449i	$-0.544029\pi$
$613$	−4185.29			−0.275762			−0.137881	+	0.990449i	$0.544029\pi$
$614$	1489.94	+	1489.94i	0.0979304	+	0.0979304i
$615$	3913.15	−	1620.88i	0.256575	−	0.106277i
$616$			104.494i			0.00683472i
$617$	419.698	+	1013.24i	0.0273847	+	0.0661126i	0.936980	−	0.349382i	$-0.113608\pi$
$617$	419.698	+	1013.24i	0.0273847	+	0.0661126i	−0.909596	+	0.415495i	$0.863608\pi$
$618$	1074.52	+	445.080i	0.0699409	+	0.0289705i
$619$	8007.15	−	19331.0i	0.519926	−	1.25521i	−0.418022	−	0.908437i	$-0.637276\pi$
$619$	8007.15	−	19331.0i	0.519926	−	1.25521i	0.937948	−	0.346776i	$-0.112724\pi$
$620$	−4324.15	+	4324.15i	−0.280100	+	0.280100i
$621$	−2296.73	+	2296.73i	−0.148413	+	0.148413i
$622$	−1111.01	+	2682.22i	−0.0716198	+	0.172906i
$623$	16687.8	+	6912.29i	1.07316	+	0.444519i
$624$	−1992.61	−	4810.58i	−0.127834	−	0.308618i
$625$			1738.23i			0.111247i
$626$	2482.65	−	1028.35i	0.158509	−	0.0656566i
$627$	−33.2487	−	33.2487i	−0.00211775	−	0.00211775i
$628$	7926.90			0.503690
$629$	−877.248	−	4837.75i	−0.0556092	−	0.306667i
$630$	−518.577			−0.0327946
$631$	−18464.3	−	18464.3i	−1.16490	−	1.16490i	−0.983389	−	0.181510i	$-0.941902\pi$
$631$	−18464.3	−	18464.3i	−1.16490	−	1.16490i	−0.181510	−	0.983389i	$-0.558098\pi$
$632$	7340.10	−	3040.37i	0.461983	−	0.191360i
$633$		−	1969.61i		−	0.123673i
$634$	−1287.96	−	3109.41i	−0.0806805	−	0.194780i
$635$	−8058.19	−	3337.81i	−0.503590	−	0.208594i
$636$	456.817	−	1102.85i	0.0284811	−	0.0687594i
$637$	905.879	−	905.879i	0.0563457	−	0.0563457i
$638$	54.3818	−	54.3818i	0.00337460	−	0.00337460i
$639$	−2001.65	+	4832.40i	−0.123919	+	0.299166i
$640$	5903.72	+	2445.40i	0.364633	+	0.151036i
$641$	6892.92	+	16641.0i	0.424733	+	1.02540i	0.980933	+	0.194348i	$0.0622590\pi$
$641$	6892.92	+	16641.0i	0.424733	+	1.02540i	−0.556199	+	0.831049i	$0.687741\pi$
$642$			1853.03i			0.113915i
$643$	16581.1	−	6868.13i	1.01695	−	0.421233i	0.188962	−	0.981984i	$-0.439488\pi$
$643$	16581.1	−	6868.13i	1.01695	−	0.421233i	0.827984	+	0.560752i	$0.189488\pi$
$644$	−11472.6	−	11472.6i	−0.701993	−	0.701993i
$645$	11210.9			0.684386
$646$	575.553	+	124.671i	0.0350539	+	0.00759303i
$647$	−15336.8			−0.931917			−0.465959	−	0.884807i	$-0.654290\pi$
$647$	−15336.8			−0.931917			−0.465959	+	0.884807i	$0.654290\pi$
$648$	−409.570	−	409.570i	−0.0248293	−	0.0248293i
$649$	−117.966	+	48.8631i	−0.00713493	+	0.00295538i
$650$		−	942.172i		−	0.0568539i
$651$	2118.46	+	5114.40i	0.127540	+	0.307910i
$652$	20922.1	+	8666.21i	1.25671	+	0.520545i
$653$	8172.70	−	19730.6i	0.489774	−	1.18242i	−0.465060	−	0.885279i	$-0.653967\pi$
$653$	8172.70	−	19730.6i	0.489774	−	1.18242i	0.954834	−	0.297139i	$-0.0960326\pi$
$654$	−817.584	+	817.584i	−0.0488839	+	0.0488839i
$655$	5777.96	−	5777.96i	0.344677	−	0.344677i
$656$	−4342.59	+	10483.9i	−0.258460	+	0.623977i
$657$	4045.65	+	1675.76i	0.240237	+	0.0995095i
$658$	−704.498	−	1700.81i	−0.0417389	−	0.100767i
$659$			9454.54i			0.558872i	0.960164	+	0.279436i	$0.0901474\pi$
$659$			9454.54i			0.558872i	−0.960164	+	0.279436i	$0.909853\pi$
$660$	−134.223	+	55.5972i	−0.00791612	+	0.00327897i
$661$	−11521.9	−	11521.9i	−0.677985	−	0.677985i	0.281559	−	0.959544i	$-0.409149\pi$
$661$	−11521.9	−	11521.9i	−0.677985	−	0.677985i	−0.959544	+	0.281559i	$0.909149\pi$
$662$	−2852.29			−0.167458
$663$	−6074.00	+	1101.42i	−0.355799	+	0.0645184i
$664$	−10504.6			−0.613943
$665$	1670.13	+	1670.13i	0.0973909	+	0.0973909i
$666$	−264.053	+	109.374i	−0.0153631	+	0.00636361i
$667$			24196.7i			1.40465i
$668$	−5872.73	−	14178.0i	−0.340154	−	0.821205i
$669$	−12089.1	−	5007.45i	−0.698639	−	0.289386i
$670$	201.880	−	487.382i	0.0116408	−	0.0281033i
$671$	554.089	−	554.089i	0.0318784	−	0.0318784i
$672$	3082.09	−	3082.09i	0.176926	−	0.176926i
$673$	−10045.5	+	24251.9i	−0.575370	+	1.38907i	0.321559	+	0.946890i	$0.395793\pi$
$673$	−10045.5	+	24251.9i	−0.575370	+	1.38907i	−0.896928	+	0.442176i	$0.854207\pi$
$674$	50.1407	+	20.7690i	0.00286550	+	0.00118693i
$675$	732.473	+	1768.35i	0.0417672	+	0.100835i
$676$		−	10407.9i		−	0.592164i
$677$	−10189.6	+	4220.66i	−0.578460	+	0.239606i	−0.652677	−	0.757636i	$-0.726354\pi$
$677$	−10189.6	+	4220.66i	−0.578460	+	0.239606i	0.0742173	+	0.997242i	$0.476354\pi$
$678$	−2160.23	−	2160.23i	−0.122365	−	0.122365i
$679$	−8860.30			−0.500776
$680$	2100.07	−	3030.40i	0.118433	−	0.170898i
$681$	18960.6			1.06692
$682$	−28.8350	−	28.8350i	−0.00161899	−	0.00161899i
$683$	4393.52	−	1819.86i	0.246140	−	0.101954i	−0.256203	−	0.966623i	$-0.582472\pi$
$683$	4393.52	−	1819.86i	0.246140	−	0.101954i	0.502343	+	0.864669i	$0.332472\pi$
$684$			1301.95i			0.0727794i
$685$	5835.92	+	14089.2i	0.325517	+	0.785867i
$686$	2798.05	+	1158.99i	0.155729	+	0.0645051i
$687$	2089.25	−	5043.90i	0.116026	−	0.280112i
$688$	−21238.5	+	21238.5i	−1.17690	+	1.17690i
$689$	−1059.63	+	1059.63i	−0.0585902	+	0.0585902i
$690$	−459.934	+	1110.38i	−0.0253759	+	0.0612630i
$691$	−1261.70	−	522.611i	−0.0694604	−	0.0287715i	0.347683	−	0.937612i	$-0.386969\pi$
$691$	−1261.70	−	522.611i	−0.0694604	−	0.0287715i	−0.417143	+	0.908841i	$0.636969\pi$
$692$	6883.21	+	16617.5i	0.378122	+	0.912867i
$693$			131.515i			0.00720903i
$694$	−1589.74	+	658.493i	−0.0869536	+	0.0360174i
$695$	−3656.02	−	3656.02i	−0.199541	−	0.199541i
$696$	−4314.93			−0.234996
$697$	11057.5	+	7662.90i	0.600910	+	0.416432i
$698$	−869.005			−0.0471237
$699$	−3181.08	−	3181.08i	−0.172131	−	0.172131i
$700$	−8833.21	+	3658.84i	−0.476949	+	0.197559i
$701$			8823.67i			0.475414i	0.971337	+	0.237707i	$0.0763958\pi$
$701$			8823.67i			0.475414i	−0.971337	+	0.237707i	$0.923604\pi$
$702$	137.324	+	331.529i	0.00738312	+	0.0178244i
$703$	1202.66	+	498.158i	0.0645223	+	0.0267260i
$704$	140.583	−	339.397i	0.00752615	−	0.0181697i
$705$	3667.32	−	3667.32i	0.195914	−	0.195914i
$706$	−3389.69	+	3389.69i	−0.180698	+	0.180698i
$707$	−1207.36	+	2914.83i	−0.0642257	+	0.155055i
$708$	3266.32	+	1352.96i	0.173384	+	0.0718181i
$709$	11842.1	+	28589.4i	0.627278	+	1.51438i	0.842992	+	0.537926i	$0.180792\pi$
$709$	11842.1	+	28589.4i	0.627278	+	1.51438i	−0.215714	+	0.976456i	$0.569208\pi$
$710$			1935.44i			0.102304i
$711$	9238.19	−	3826.58i	0.487284	−	0.201840i
$712$	5278.71	+	5278.71i	0.277848	+	0.277848i
$713$	12829.9			0.673888
$714$	−891.734	−	1384.87i	−0.0467399	−	0.0725874i
$715$	182.381			0.00953938
$716$	−20007.0	−	20007.0i	−1.04427	−	1.04427i
$717$	−4437.49	+	1838.07i	−0.231131	+	0.0957377i
$718$			3769.66i			0.195936i
$719$	−1998.86	−	4825.68i	−0.103679	−	0.250303i	0.863524	−	0.504307i	$-0.168252\pi$
$719$	−1998.86	−	4825.68i	−0.103679	−	0.250303i	−0.967203	+	0.254005i	$0.918252\pi$
$720$	3616.18	+	1497.87i	0.187177	+	0.0775311i
$721$	−5669.92	+	13688.4i	−0.292870	+	0.707050i
$722$	2085.50	−	2085.50i	0.107499	−	0.107499i
$723$	7767.28	−	7767.28i	0.399541	−	0.399541i
$724$	1782.47	−	4303.26i	0.0914984	−	0.220897i
$725$	13173.4	+	5456.60i	0.674825	+	0.279522i
$726$	691.422	+	1669.24i	0.0353458	+	0.0853324i
$727$			25678.0i			1.30997i	0.755644	+	0.654983i	$0.227324\pi$
$727$			25678.0i			1.30997i	−0.755644	+	0.654983i	$0.772676\pi$
$728$	−3355.64	+	1389.95i	−0.170836	+	0.0707625i
$729$	−515.481	−	515.481i	−0.0261891	−	0.0261891i
$730$	1620.33			0.0821523
$731$	19278.0	+	29938.9i	0.975408	+	1.51482i
$732$	−21696.9			−1.09555
$733$	5734.46	+	5734.46i	0.288959	+	0.288959i	0.836669	−	0.547709i	$-0.184500\pi$
$733$	5734.46	+	5734.46i	0.288959	+	0.288959i	−0.547709	+	0.836669i	$0.684500\pi$
$734$	−2086.68	+	864.333i	−0.104933	+	0.0434647i
$735$			963.026i			0.0483289i
$736$	−3865.83	−	9332.93i	−0.193609	−	0.467414i
$737$	−123.604	−	51.1985i	−0.00617777	−	0.00255892i
$738$	299.276	−	722.517i	0.0149275	−	0.0360382i
$739$	17620.9	−	17620.9i	0.877123	−	0.877123i	−0.116113	−	0.993236i	$-0.537043\pi$
$739$	17620.9	−	17620.9i	0.877123	−	0.877123i	0.993236	+	0.116113i	$0.0370434\pi$
$740$	2844.04	−	2844.04i	0.141282	−	0.141282i
$741$	625.458	−	1509.99i	0.0310078	−	0.0748595i
$742$	−369.414	−	153.016i	−0.0182771	−	0.00757062i
$743$	−8310.78	−	20064.0i	−0.410354	−	0.990682i	−0.985043	−	0.172310i	$-0.944877\pi$
$743$	−8310.78	−	20064.0i	−0.410354	−	0.990682i	0.574689	−	0.818372i	$-0.305123\pi$
$744$			2287.92i			0.112741i
$745$	21460.2	−	8889.10i	1.05536	−	0.437143i
$746$	−2496.92	−	2496.92i	−0.122545	−	0.122545i
$747$	−13221.0			−0.647566
$748$	−379.281	−	262.842i	−0.0185399	−	0.0128482i
$749$	−23605.9			−1.15159
$750$	1383.86	+	1383.86i	0.0673754	+	0.0673754i
$751$	−7931.34	+	3285.27i	−0.385378	+	0.159629i	−0.566957	−	0.823748i	$-0.691879\pi$
$751$	−7931.34	+	3285.27i	−0.385378	+	0.159629i	0.181579	+	0.983376i	$0.441879\pi$
$752$			13895.1i			0.673806i
$753$	−7384.84	−	17828.6i	−0.357395	−	0.862828i
$754$	2469.75	+	1023.00i	0.119288	+	0.0494106i
$755$	188.723	−	455.617i	0.00909712	−	0.0219624i
$756$	2574.92	−	2574.92i	0.123874	−	0.123874i
$757$	−2669.64	+	2669.64i	−0.128177	+	0.128177i	−0.768285	−	0.640108i	$-0.778890\pi$
$757$	−2669.64	+	2669.64i	−0.128177	+	0.128177i	0.640108	+	0.768285i	$0.278890\pi$
$758$	−1659.20	+	4005.67i	−0.0795053	+	0.191943i
$759$	281.601	+	116.643i	0.0134670	+	0.00557823i
$760$	373.565	+	901.865i	0.0178298	+	0.0430449i
$761$		−	27931.4i		−	1.33050i	−0.746620	−	0.665251i	$-0.768324\pi$
$761$		−	27931.4i		−	1.33050i	0.746620	−	0.665251i	$-0.231676\pi$
$762$	−1487.85	+	616.287i	−0.0707337	+	0.0292989i
$763$	−10415.3	−	10415.3i	−0.494179	−	0.494179i
$764$	−8163.00			−0.386554
$765$	2643.13	−	3814.04i	0.124919	−	0.180257i
$766$	−3172.87			−0.149661
$767$	−3138.30	−	3138.30i	−0.147741	−	0.147741i
$768$	−8554.50	+	3543.39i	−0.401932	+	0.166486i
$769$			19283.6i			0.904272i	0.891949	+	0.452136i	$0.149338\pi$
$769$			19283.6i			0.904272i	−0.891949	+	0.452136i	$0.850662\pi$
$770$	18.6229	+	44.9597i	0.000871588	+	0.00210420i
$771$	−14273.8	−	5912.40i	−0.666743	−	0.276174i
$772$	4500.22	−	10864.5i	0.209801	−	0.506504i
$773$	19044.5	−	19044.5i	0.886137	−	0.886137i	−0.108012	−	0.994150i	$-0.534449\pi$
$773$	19044.5	−	19044.5i	0.886137	−	0.886137i	0.994150	+	0.108012i	$0.0344486\pi$
$774$	1463.68	−	1463.68i	0.0679729	−	0.0679729i
$775$	2893.27	−	6984.97i	0.134102	−	0.323752i
$776$	−3383.17	−	1401.36i	−0.156506	−	0.0648270i
$777$	−1393.33	−	3363.79i	−0.0643313	−	0.155309i
$778$			3649.06i			0.168156i
$779$	−3290.79	+	1363.09i	−0.151354	+	0.0626929i
$780$	−3570.81	−	3570.81i	−0.163917	−	0.163917i
$781$	490.842			0.0224888
$782$	−3756.18	+	681.123i	−0.171766	+	0.0311469i
$783$	−5430.73			−0.247865
$784$	−1824.40	−	1824.40i	−0.0831087	−	0.0831087i
$785$	6910.94	−	2862.60i	0.314219	−	0.130154i
$786$		−	1508.73i		−	0.0684663i
$787$	−8148.10	−	19671.3i	−0.369058	−	0.890984i	−0.993905	−	0.110237i	$-0.964839\pi$
$787$	−8148.10	−	19671.3i	−0.369058	−	0.890984i	0.624848	−	0.780747i	$-0.285161\pi$
$788$	−11234.4	−	4653.43i	−0.507878	−	0.210370i
$789$	−1649.64	+	3982.58i	−0.0744344	+	0.179701i
$790$	2616.30	−	2616.30i	0.117828	−	0.117828i
$791$	27519.5	−	27519.5i	1.23702	−	1.23702i
$792$	−20.8006	+	50.2172i	−0.000933230	+	0.00225302i
$793$	25163.9	+	10423.2i	1.12686	+	0.466760i
$794$	−96.1419	−	232.107i	−0.00429716	−	0.0103743i
$795$		−	1126.47i		−	0.0502540i
$796$	16992.0	−	7038.30i	0.756614	−	0.313400i
$797$	−342.645	−	342.645i	−0.0152285	−	0.0152285i	0.699452	−	0.714680i	$-0.253428\pi$
$797$	−342.645	−	342.645i	−0.0152285	−	0.0152285i	−0.714680	+	0.699452i	$0.753428\pi$
$798$	436.101			0.0193456
$799$	16099.9	+	3487.39i	0.712857	+	0.154412i
$800$	−5952.91			−0.263084
$801$	6643.74	+	6643.74i	0.293065	+	0.293065i
$802$	5217.05	−	2160.97i	0.229701	−	0.0951454i
$803$		−	410.929i		−	0.0180590i
$804$	1417.62	+	3422.44i	0.0621836	+	0.150124i
$805$	−14145.3	−	5859.15i	−0.619322	−	0.256532i
$806$	542.429	−	1309.54i	0.0237050	−	0.0572290i
$807$	10718.5	−	10718.5i	0.467544	−	0.467544i
$808$	−922.028	+	922.028i	−0.0401446	+	0.0401446i
$809$	−10783.6	+	26033.8i	−0.468640	+	1.13140i	0.496118	+	0.868255i	$0.334758\pi$
$809$	−10783.6	+	26033.8i	−0.468640	+	1.13140i	−0.964757	+	0.263141i	$0.915242\pi$
$810$	−249.215	−	103.228i	−0.0108105	−	0.00447786i
$811$	−3498.47	−	8446.05i	−0.151477	−	0.365698i	0.829866	−	0.557963i	$-0.188417\pi$
$811$	−3498.47	−	8446.05i	−0.151477	−	0.365698i	−0.981343	+	0.192265i	$0.938417\pi$
$812$		−	27127.5i		−	1.17240i
$813$	21030.9	−	8711.30i	0.907241	−	0.375792i
$814$	18.9651	+	18.9651i	0.000816616	+	0.000816616i
$815$	21370.2			0.918484
$816$	2218.22	+	12232.8i	0.0951632	+	0.524795i
$817$	−9427.90			−0.403721
$818$	1185.61	+	1185.61i	0.0506773	+	0.0506773i
$819$	−4223.38	+	1749.38i	−0.180192	+	0.0746378i
$820$			11005.5i			0.468692i
$821$	5959.55	+	14387.6i	0.253337	+	0.611610i	0.998469	−	0.0553066i	$-0.0176136\pi$
$821$	5959.55	+	14387.6i	0.253337	+	0.611610i	−0.745132	+	0.666917i	$0.767614\pi$
$822$	2601.40	+	1077.53i	0.110382	+	0.0457218i
$823$	−7245.49	+	17492.2i	−0.306880	+	0.740873i	0.692923	+	0.721012i	$0.256323\pi$
$823$	−7245.49	+	17492.2i	−0.306880	+	0.740873i	−0.999803	+	0.0198616i	$0.993677\pi$
$824$	−4329.95	+	4329.95i	−0.183059	+	0.183059i
$825$	127.008	−	127.008i	0.00535982	−	0.00535982i
$826$	453.188	−	1094.09i	0.0190901	−	0.0460876i
$827$	−14193.7	−	5879.24i	−0.596813	−	0.247208i	0.0637656	−	0.997965i	$-0.479689\pi$
$827$	−14193.7	−	5879.24i	−0.596813	−	0.247208i	−0.660579	+	0.750757i	$0.729689\pi$
$828$	−3229.70	−	7797.18i	−0.135555	−	0.327259i
$829$		−	20953.6i		−	0.877865i	−0.898520	−	0.438932i	$-0.855357\pi$
$829$		−	20953.6i		−	0.877865i	0.898520	−	0.438932i	$-0.144643\pi$
$830$	−4519.72	+	1872.13i	−0.189014	+	0.0782922i
$831$	6797.02	+	6797.02i	0.283738	+	0.283738i
$832$	12769.1			0.532079
$833$	−2571.77	+	1656.00i	−0.106971	+	0.0688798i
$834$	−954.652			−0.0396366
$835$	−10240.1	−	10240.1i	−0.424399	−	0.424399i
$836$	112.876	−	46.7549i	0.00466974	−	0.00193427i
$837$			2879.55i			0.118915i
$838$	−2121.01	−	5120.56i	−0.0874331	−	0.211082i
$839$	19210.5	+	7957.27i	0.790491	+	0.327432i	0.741141	−	0.671350i	$-0.234285\pi$
$839$	19210.5	+	7957.27i	0.790491	+	0.327432i	0.0493498	+	0.998782i	$0.484285\pi$
$840$	1044.85	−	2522.48i	0.0429174	−	0.103612i
$841$	−11361.5	+	11361.5i	−0.465846	+	0.465846i
$842$	4189.72	−	4189.72i	0.171481	−	0.171481i
$843$	1508.01	−	3640.65i	0.0616115	−	0.148743i
$844$	4728.16	+	1958.47i	0.192832	+	0.0798735i
$845$	−3758.55	−	9073.94i	−0.153015	−	0.369412i
$846$		−	957.603i		−	0.0389161i
$847$	−21264.6	+	8808.10i	−0.862646	+	0.357320i
$848$	2134.05	+	2134.05i	0.0864192	+	0.0864192i
$849$	−3263.15			−0.131909
$850$	−476.233	+	2198.58i	−0.0192173	+	0.0887183i
$851$	−8438.34			−0.339909
$852$	−9610.14	−	9610.14i	−0.386430	−	0.386430i
$853$	−40362.0	+	16718.5i	−1.62013	+	0.671079i	−0.994075	−	0.108700i	$-0.965331\pi$
$853$	−40362.0	+	16718.5i	−1.62013	+	0.671079i	−0.626054	+	0.779780i	$0.715331\pi$
$854$			7267.62i			0.291209i
$855$	470.166	+	1135.08i	0.0188062	+	0.0454023i
$856$	−9013.57	−	3733.54i	−0.359904	−	0.149077i
$857$	3331.44	−	8042.81i	0.132789	−	0.320580i	−0.843474	−	0.537170i	$-0.819493\pi$
$857$	3331.44	−	8042.81i	0.132789	−	0.320580i	0.976263	+	0.216590i	$0.0694934\pi$
$858$	23.8114	−	23.8114i	0.000947446	−	0.000947446i
$859$	18945.0	−	18945.0i	0.752496	−	0.752496i	−0.222449	−	0.974944i	$-0.571405\pi$
$859$	18945.0	−	18945.0i	0.752496	−	0.752496i	0.974944	+	0.222449i	$0.0714050\pi$
$860$	−11147.5	+	26912.4i	−0.442008	+	1.06710i
$861$	9204.22	+	3812.51i	0.364319	+	0.150906i
$862$	−1042.73	−	2517.38i	−0.0412013	−	0.0994688i
$863$		−	11524.3i		−	0.454566i	−0.973829	−	0.227283i	$-0.927016\pi$
$863$		−	11524.3i		−	0.454566i	0.973829	−	0.227283i	$-0.0729843\pi$
$864$	2094.69	−	867.651i	0.0824803	−	0.0341644i
$865$	12002.0	+	12002.0i	0.471771	+	0.471771i
$866$	7314.26			0.287008
$867$	14730.5	+	499.994i	0.577018	+	0.0195856i
$868$	−14383.9			−0.562467
$869$	−663.515	−	663.515i	−0.0259013	−	0.0259013i
$870$	−1856.54	+	769.005i	−0.0723479	+	0.0299675i
$871$		−	4650.36i		−	0.180908i
$872$	−2329.63	−	5624.22i	−0.0904714	−	0.218417i
$873$	−4258.03	−	1763.73i	−0.165077	−	0.0683773i
$874$	386.785	−	933.782i	0.0149693	−	0.0361392i
$875$	−17629.2	+	17629.2i	−0.681115	+	0.681115i
$876$	−8045.53	+	8045.53i	−0.310312	+	0.310312i
$877$	−2368.68	+	5718.51i	−0.0912027	+	0.220183i	−0.962898	−	0.269865i	$-0.913021\pi$
$877$	−2368.68	+	5718.51i	−0.0912027	+	0.220183i	0.871695	+	0.490048i	$0.163021\pi$
$878$	−540.814	−	224.013i	−0.0207877	−	0.00861055i
$879$	10187.1	+	24593.7i	0.390900	+	0.943715i
$880$		−	367.307i		−	0.0140704i
$881$	−1207.71	+	500.251i	−0.0461848	+	0.0191304i	−0.405656	−	0.914026i	$-0.632957\pi$
$881$	−1207.71	+	500.251i	−0.0461848	+	0.0191304i	0.359471	+	0.933156i	$0.382957\pi$
$882$	125.732	+	125.732i	0.00480000	+	0.00480000i
$883$	1681.42			0.0640821			0.0320410	−	0.999487i	$-0.489799\pi$
$883$	1681.42			0.0640821			0.0320410	+	0.999487i	$0.489799\pi$
$884$	3395.62	−	15676.2i	0.129193	−	0.596433i
$885$	3336.28			0.126721
$886$	409.686	+	409.686i	0.0155346	+	0.0155346i
$887$	17295.2	−	7163.90i	0.654696	−	0.271184i	−0.0305088	−	0.999534i	$-0.509713\pi$
$887$	17295.2	−	7163.90i	0.654696	−	0.271184i	0.685205	+	0.728351i	$0.259713\pi$
$888$		−	1504.79i		−	0.0568663i
$889$	−7850.95	−	18953.9i	−0.296189	−	0.715064i
$890$	3211.99	+	1330.45i	0.120973	+	0.0501088i
$891$	−26.1795	+	63.2029i	−0.000984340	+	0.00237641i
$892$	24041.4	−	24041.4i	0.902426	−	0.902426i
$893$	−3084.06	+	3084.06i	−0.115570	+	0.115570i
$894$	1641.27	−	3962.37i	0.0614007	−	0.148234i
$895$	−24667.9	−	10217.8i	−0.921292	−	0.381612i
$896$	5751.89	+	13886.3i	0.214461	+	0.517755i
$897$			10594.7i			0.394366i
$898$	4860.88	−	2013.44i	0.180634	−	0.0748212i
$899$	15168.4	+	15168.4i	0.562732	+	0.562732i
$900$	−4973.35			−0.184198
$901$	3008.27	−	1937.06i	0.111232	−	0.0716235i
$902$	−73.3883			−0.00270905
$903$	18646.0	+	18646.0i	0.687155	+	0.687155i
$904$	14860.4	−	6155.38i	0.546736	−	0.226466i
$905$		−	4395.42i		−	0.161446i
$906$	−34.8454	−	84.1243i	−0.00127777	−	0.00308481i
$907$	7420.13	+	3073.52i	0.271644	+	0.112519i	0.514348	−	0.857582i	$-0.328034\pi$
$907$	7420.13	+	3073.52i	0.271644	+	0.112519i	−0.242703	+	0.970101i	$0.578034\pi$
$908$	−18853.3	+	45516.0i	−0.689064	+	1.66355i
$909$	−1160.46	+	1160.46i	−0.0423431	+	0.0423431i
$910$	−1196.08	+	1196.08i	−0.0435712	+	0.0435712i
$911$	−13540.2	+	32688.9i	−0.492433	+	1.18884i	0.461045	+	0.887377i	$0.347475\pi$
$911$	−13540.2	+	32688.9i	−0.492433	+	1.18884i	−0.953478	+	0.301462i	$0.902525\pi$
$912$	−3041.06	−	1259.65i	−0.110416	−	0.0457358i
$913$	474.787	+	1146.24i	0.0172105	+	0.0415497i
$914$			8489.53i			0.307231i
$915$	−18916.1	+	7835.30i	−0.683439	+	0.283090i
$916$	10030.7	+	10030.7i	0.361818	+	0.361818i
$917$	19219.9			0.692143
$918$	−152.872	−	843.041i	−0.00549622	−	0.0303099i
$919$	−18134.4			−0.650924			−0.325462	−	0.945555i	$-0.605520\pi$
$919$	−18134.4			−0.650924			−0.325462	+	0.945555i	$0.605520\pi$
$920$	−4474.46	−	4474.46i	−0.160346	−	0.160346i
$921$	−12899.9	+	5343.30i	−0.461525	+	0.191170i
$922$			3460.91i			0.123622i
$923$	6529.06	+	15762.5i	0.232835	+	0.562113i
$924$	−315.710	−	130.772i	−0.0112404	−	0.00465592i
$925$	−1902.93	+	4594.08i	−0.0676411	+	0.163300i
$926$	1484.09	−	1484.09i	0.0526678	−	0.0526678i
$927$	−5449.64	+	5449.64i	−0.193085	+	0.193085i
$928$	6463.62	−	15604.6i	0.228641	−	0.551988i
$929$	14173.8	+	5870.97i	0.500567	+	0.207342i	0.618657	−	0.785661i	$-0.287677\pi$
$929$	14173.8	+	5870.97i	0.500567	+	0.207342i	−0.118090	+	0.993003i	$0.537677\pi$
$930$	407.752	+	984.400i	0.0143771	+	0.0347094i
$931$		−	809.863i		−	0.0285093i
$932$	10799.5	−	4473.28i	0.379558	−	0.157218i
$933$	−13603.4	−	13603.4i	−0.477338	−	0.477338i
$934$	3302.49			0.115697
$935$	−425.589	−	92.1868i	−0.0148858	−	0.00322442i
$936$	−1889.32			−0.0659769
$937$	−4570.78	−	4570.78i	−0.159361	−	0.159361i	0.622923	−	0.782283i	$-0.285945\pi$
$937$	−4570.78	−	4570.78i	−0.159361	−	0.159361i	−0.782283	+	0.622923i	$0.785945\pi$
$938$	1146.38	−	474.848i	0.0399049	−	0.0165291i
$939$			17806.7i			0.618851i
$940$	5157.04	+	12450.2i	0.178941	+	0.432001i
$941$	6274.82	+	2599.12i	0.217379	+	0.0900412i	0.488715	−	0.872443i	$-0.337466\pi$
$941$	6274.82	+	2599.12i	0.217379	+	0.0900412i	−0.271337	+	0.962485i	$0.587466\pi$
$942$	528.546	−	1276.02i	0.0182813	−	0.0441349i
$943$	16326.7	−	16326.7i	0.563809	−	0.563809i
$944$	−6320.41	+	6320.41i	−0.217915	+	0.217915i
$945$	1315.04	−	3174.78i	0.0452678	−	0.109286i
$946$	−179.462	−	74.3355i	−0.00616787	−	0.00255482i
$947$	−14083.5	−	34000.5i	−0.483265	−	1.16670i	−0.958050	−	0.286603i	$-0.907474\pi$
$947$	−14083.5	−	34000.5i	−0.483265	−	1.16670i	0.474785	−	0.880102i	$-0.342526\pi$
$948$			25981.7i			0.890135i
$949$	13196.3	−	5466.07i	0.451390	−	0.186972i
$950$	−421.155	−	421.155i	−0.0143832	−	0.0143832i
$951$	22302.2			0.760460
$952$	8533.02	−	1547.33i	0.290501	−	0.0526777i
$953$	−20402.5			−0.693497			−0.346748	−	0.937958i	$-0.612714\pi$
$953$	−20402.5			−0.693497			−0.346748	+	0.937958i	$0.612714\pi$
$954$	−147.071	−	147.071i	−0.00499120	−	0.00499120i
$955$	−7116.78	+	2947.87i	−0.241145	+	0.0998856i
$956$		−	12480.1i		−	0.422214i
$957$	195.026	+	470.834i	0.00658756	+	0.0159038i
$958$	−4084.98	−	1692.05i	−0.137766	−	0.0570645i
$959$	−13726.8	+	33139.5i	−0.462213	+	1.11588i
$960$	−6787.33	+	6787.33i	−0.228187	+	0.228187i
$961$	−13022.6	+	13022.6i	−0.437133	+	0.437133i
$962$	−356.761	+	861.298i	−0.0119568	+	0.0288663i
$963$	−11344.4	−	4699.01i	−0.379614	−	0.157241i
$964$	10922.5	+	26369.2i	0.364926	+	0.881010i
$965$		−	11097.2i		−	0.370187i
$966$	−2611.75	+	1081.82i	−0.0869894	+	0.0360322i
$967$	−39299.3	−	39299.3i	−1.30691	−	1.30691i	−0.923635	−	0.383273i	$-0.874797\pi$
$967$	−39299.3	−	39299.3i	−1.30691	−	1.30691i	−0.383273	−	0.923635i	$-0.625203\pi$
$968$	−9512.68			−0.315857
$969$	−2222.76	+	3207.44i	−0.0736898	+	0.106334i
$970$	−1705.39			−0.0564504
$971$	−23219.7	−	23219.7i	−0.767410	−	0.767410i	0.210240	−	0.977650i	$-0.432575\pi$
$971$	−23219.7	−	23219.7i	−0.767410	−	0.767410i	−0.977650	+	0.210240i	$0.932575\pi$
$972$	1750.01	−	724.877i	0.0577485	−	0.0239202i
$973$		−	12161.4i		−	0.400696i
$974$	1390.07	+	3355.93i	0.0457298	+	0.110401i
$975$	5768.06	+	2389.21i	0.189462	+	0.0784779i
$976$	20992.0	−	50679.1i	0.688460	−	1.66209i
$977$	−35164.1	+	35164.1i	−1.15148	+	1.15148i	−0.165229	+	0.986255i	$0.552836\pi$
$977$	−35164.1	+	35164.1i	−1.15148	+	1.15148i	−0.986255	+	0.165229i	$0.947164\pi$
$978$	2790.07	−	2790.07i	0.0912234	−	0.0912234i
$979$	337.413	−	814.587i	0.0110151	−	0.0265928i
$980$	−2311.80	−	957.579i	−0.0753548	−	0.0312130i
$981$	−2932.05	−	7078.59i	−0.0954262	−	0.230379i
$982$			959.230i			0.0311714i
$983$	10706.6	−	4434.82i	0.347393	−	0.143895i	−0.202163	−	0.979352i	$-0.564797\pi$
$983$	10706.6	−	4434.82i	0.347393	−	0.143895i	0.549556	+	0.835457i	$0.314797\pi$
$984$	2911.50	+	2911.50i	0.0943245	+	0.0943245i
$985$	−11475.0			−0.371191
$986$	−5246.11	−	3635.56i	−0.169442	−	0.117424i
$987$	12199.0			0.393413
$988$	3002.90	+	3002.90i	0.0966953	+	0.0966953i
$989$	56462.4	−	23387.5i	1.81537	−	0.751950i
$990$			25.3136i			0.000812644i
$991$	8281.33	+	19992.9i	0.265454	+	0.640863i	0.999259	−	0.0384976i	$-0.0122572\pi$
$991$	8281.33	+	19992.9i	0.265454	+	0.640863i	−0.733805	+	0.679361i	$0.762257\pi$
$992$	−8274.05	−	3427.22i	−0.264820	−	0.109692i
$993$	7232.99	−	17462.0i	0.231150	−	0.558046i
$994$	−3219.03	+	3219.03i	−0.102718	+	0.102718i
$995$	12272.5	−	12272.5i	0.391019	−	0.391019i
$996$	13146.2	−	31737.8i	0.418227	−	1.00969i
$997$	−9023.53	−	3737.67i	−0.286638	−	0.118729i	0.234732	−	0.972060i	$-0.424579\pi$
$997$	−9023.53	−	3737.67i	−0.286638	−	0.118729i	−0.521370	+	0.853331i	$0.674579\pi$
$998$	−94.4792	−	228.093i	−0.00299668	−	0.00723462i
$999$		−	1893.91i		−	0.0599806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.4.h.a.19.5	✓	40
3.2	odd	2		153.4.l.c.19.6		40
17.3	odd	16		867.4.a.v.1.11		20
17.9	even	8	inner	51.4.h.a.43.5	yes	40
17.14	odd	16		867.4.a.w.1.11		20
51.26	odd	8		153.4.l.c.145.6		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.4.h.a.19.5	✓	40	1.1	even	1	trivial
51.4.h.a.43.5	yes	40	17.9	even	8	inner
153.4.l.c.19.6		40	3.2	odd	2
153.4.l.c.145.6		40	51.26	odd	8
867.4.a.v.1.11		20	17.3	odd	16
867.4.a.w.1.11		20	17.14	odd	16

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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	51.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.320127 + 0.320127i) q^{2} +(-2.77164 + 1.14805i) q^{3} -7.79504i q^{4} +(-2.81499 - 6.79598i) q^{5} +(-1.25480 - 0.519754i) q^{6} +(6.62120 - 15.9850i) q^{7} +(5.05641 - 5.05641i) q^{8} +(6.36396 - 6.36396i) q^{9} +(1.27442 - 3.07673i) q^{10} +(-0.780283 - 0.323204i) q^{11} +(8.94910 + 21.6050i) q^{12} -29.3566i q^{13} +(7.23685 - 2.99760i) q^{14} +(15.6043 + 15.6043i) q^{15} -59.1229 q^{16} +(-14.8387 + 68.5041i) q^{17} +4.07455 q^{18} +(-13.1225 - 13.1225i) q^{19} +(-52.9749 + 21.9429i) q^{20} +51.9061i q^{21} +(-0.146323 - 0.353256i) q^{22} +(111.142 + 46.0364i) q^{23} +(-8.20953 + 19.8196i) q^{24} +(50.1271 - 50.1271i) q^{25} +(9.39783 - 9.39783i) q^{26} +(-10.3325 + 24.9447i) q^{27} +(-124.604 - 51.6125i) q^{28} +(76.9723 + 185.828i) q^{29} +9.99068i q^{30} +(98.5318 - 40.8132i) q^{31} +(-59.3781 - 59.3781i) q^{32} +2.53372 q^{33} +(-26.6803 + 17.1797i) q^{34} -127.272 q^{35} +(-49.6073 - 49.6073i) q^{36} +(-64.8054 + 26.8433i) q^{37} -8.40173i q^{38} +(33.7028 + 81.3658i) q^{39} +(-48.5970 - 20.1296i) q^{40} +(73.4502 - 177.324i) q^{41} +(-16.6165 + 16.6165i) q^{42} +(359.226 - 359.226i) q^{43} +(-2.51939 + 6.08234i) q^{44} +(-61.1638 - 25.3349i) q^{45} +(20.8419 + 50.3169i) q^{46} -235.021i q^{47} +(163.867 - 67.8761i) q^{48} +(30.8578 + 30.8578i) q^{49} +32.0941 q^{50} +(-37.5187 - 206.904i) q^{51} -228.836 q^{52} +(-36.0951 - 36.0951i) q^{53} +(-11.2932 + 4.67779i) q^{54} +6.21260i q^{55} +(-47.3472 - 114.306i) q^{56} +(51.4362 + 21.3056i) q^{57} +(-34.8475 + 84.1292i) q^{58} +(106.903 - 106.903i) q^{59} +(121.636 - 121.636i) q^{60} +(-355.057 + 857.183i) q^{61} +(44.6081 + 18.4773i) q^{62} +(-59.5908 - 143.865i) q^{63} +434.966i q^{64} +(-199.507 + 82.6384i) q^{65} +(0.811111 + 0.811111i) q^{66} +158.409 q^{67} +(533.992 + 115.668i) q^{68} -360.896 q^{69} +(-40.7433 - 40.7433i) q^{70} +(-536.934 + 222.405i) q^{71} -64.3576i q^{72} +(186.196 + 449.517i) q^{73} +(-29.3392 - 12.1527i) q^{74} +(-81.3858 + 196.483i) q^{75} +(-102.290 + 102.290i) q^{76} +(-10.3328 + 10.3328i) q^{77} +(-15.2582 + 36.8366i) q^{78} +(1026.47 + 425.176i) q^{79} +(166.430 + 401.798i) q^{80} -81.0000i q^{81} +(80.2797 - 33.2529i) q^{82} +(-1038.74 - 1038.74i) q^{83} +404.610 q^{84} +(507.323 - 91.9949i) q^{85} +229.996 q^{86} +(-426.679 - 426.679i) q^{87} +(-5.57969 + 2.31118i) q^{88} +1043.96i q^{89} +(-11.4698 - 27.6906i) q^{90} +(-469.265 - 194.376i) q^{91} +(358.855 - 866.353i) q^{92} +(-226.239 + 226.239i) q^{93} +(75.2364 - 75.2364i) q^{94} +(-52.2406 + 126.120i) q^{95} +(232.744 + 96.4057i) q^{96} +(-195.970 - 473.115i) q^{97} +19.7568i q^{98} +(-7.02255 + 2.90883i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 32 q^{5} - 24 q^{6} + 128 q^{10} + 112 q^{11} + 256 q^{14} - 1024 q^{16} - 112 q^{17} - 32 q^{19} - 640 q^{20} + 728 q^{22} + 208 q^{23} + 456 q^{24} + 296 q^{25} + 1472 q^{26} - 328 q^{28} - 1272 q^{29}+ \cdots + 1008 q^{99}+O(q^{100}) \) 40 * q + 32 * q^5 - 24 * q^6 + 128 * q^10 + 112 * q^11 + 256 * q^14 - 1024 * q^16 - 112 * q^17 - 32 * q^19 - 640 * q^20 + 728 * q^22 + 208 * q^23 + 456 * q^24 + 296 * q^25 + 1472 * q^26 - 328 * q^28 - 1272 * q^29 - 192 * q^31 - 960 * q^32 - 912 * q^33 + 24 * q^34 - 992 * q^35 - 216 * q^36 - 1120 * q^37 - 48 * q^39 + 2984 * q^40 - 1320 * q^41 + 1032 * q^42 + 672 * q^43 + 3744 * q^44 + 504 * q^45 - 384 * q^46 - 2096 * q^49 - 448 * q^50 + 960 * q^52 + 2120 * q^53 - 216 * q^54 + 5680 * q^56 + 768 * q^57 + 1000 * q^58 - 832 * q^59 - 1320 * q^60 - 208 * q^61 - 4432 * q^62 - 2376 * q^65 - 1248 * q^66 - 2272 * q^67 - 4560 * q^68 + 3456 * q^69 - 4792 * q^70 + 256 * q^71 - 1416 * q^73 - 2704 * q^74 + 96 * q^75 - 264 * q^76 + 6048 * q^77 - 4872 * q^78 + 1920 * q^79 + 1312 * q^80 + 8328 * q^82 + 4960 * q^83 - 3888 * q^84 + 3192 * q^85 - 15616 * q^86 - 1872 * q^87 - 248 * q^88 - 1152 * q^90 + 1232 * q^91 + 944 * q^92 + 2544 * q^93 - 10000 * q^94 + 4528 * q^95 + 4416 * q^96 + 1008 * q^97 + 1008 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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