LMFDB - Embedded newform 51.4.h.a.49.9

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			49.9
Character	$\chi$	$=$	51.49
Dual form			51.4.h.a.25.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.10148 + 3.10148i) q^{2} +(1.14805 + 2.77164i) q^{3} +11.2384i q^{4} +(14.1902 - 5.87778i) q^{5} +(-5.03553 + 12.1568i) q^{6} +(-30.3663 - 12.5781i) q^{7} +(-10.0437 + 10.0437i) q^{8} +(-6.36396 + 6.36396i) q^{9} +(62.2405 + 25.7809i) q^{10} +(-9.27937 + 22.4024i) q^{11} +(-31.1487 + 12.9022i) q^{12} -35.4963i q^{13} +(-55.1697 - 133.191i) q^{14} +(32.5822 + 32.5822i) q^{15} +27.6061 q^{16} +(-27.6397 - 64.4131i) q^{17} -39.4754 q^{18} +(85.2385 + 85.2385i) q^{19} +(66.0566 + 159.475i) q^{20} -98.6047i q^{21} +(-98.2604 + 40.7008i) q^{22} +(-6.73036 + 16.2485i) q^{23} +(-39.3683 - 16.3069i) q^{24} +(78.4256 - 78.4256i) q^{25} +(110.091 - 110.091i) q^{26} +(-24.9447 - 10.3325i) q^{27} +(141.358 - 341.268i) q^{28} +(-148.649 + 61.5726i) q^{29} +202.106i q^{30} +(-3.83777 - 9.26519i) q^{31} +(165.969 + 165.969i) q^{32} -72.7445 q^{33} +(114.052 - 285.500i) q^{34} -504.836 q^{35} +(-71.5205 - 71.5205i) q^{36} +(-58.4926 - 141.214i) q^{37} +528.731i q^{38} +(98.3830 - 40.7516i) q^{39} +(-83.4879 + 201.558i) q^{40} +(118.200 + 48.9599i) q^{41} +(305.821 - 305.821i) q^{42} +(-388.481 + 388.481i) q^{43} +(-251.766 - 104.285i) q^{44} +(-52.9000 + 127.712i) q^{45} +(-71.2686 + 29.5204i) q^{46} -313.972i q^{47} +(31.6931 + 76.5140i) q^{48} +(521.365 + 521.365i) q^{49} +486.471 q^{50} +(146.798 - 150.557i) q^{51} +398.921 q^{52} +(47.5976 + 47.5976i) q^{53} +(-45.3198 - 109.412i) q^{54} +372.437i q^{55} +(431.322 - 178.660i) q^{56} +(-138.392 + 334.108i) q^{57} +(-651.999 - 270.067i) q^{58} +(-190.559 + 190.559i) q^{59} +(-366.170 + 366.170i) q^{60} +(-343.420 - 142.249i) q^{61} +(16.8330 - 40.6386i) q^{62} +(273.297 - 113.203i) q^{63} +808.654i q^{64} +(-208.640 - 503.700i) q^{65} +(-225.616 - 225.616i) q^{66} +546.810 q^{67} +(723.898 - 310.625i) q^{68} -52.7618 q^{69} +(-1565.74 - 1565.74i) q^{70} +(-262.350 - 633.368i) q^{71} -127.836i q^{72} +(529.771 - 219.438i) q^{73} +(256.558 - 619.385i) q^{74} +(307.404 + 127.331i) q^{75} +(-957.941 + 957.941i) q^{76} +(563.561 - 563.561i) q^{77} +(431.523 + 178.743i) q^{78} +(34.7038 - 83.7824i) q^{79} +(391.736 - 162.262i) q^{80} -81.0000i q^{81} +(214.746 + 518.442i) q^{82} +(106.789 + 106.789i) q^{83} +1108.16 q^{84} +(-770.819 - 751.576i) q^{85} -2409.73 q^{86} +(-341.314 - 341.314i) q^{87} +(-131.804 - 318.203i) q^{88} +611.215i q^{89} +(-560.165 + 232.028i) q^{90} +(-446.477 + 1077.89i) q^{91} +(-182.607 - 75.6382i) q^{92} +(21.2738 - 21.2738i) q^{93} +(973.777 - 973.777i) q^{94} +(1710.56 + 708.539i) q^{95} +(-269.466 + 650.549i) q^{96} +(437.503 - 181.220i) q^{97} +3234.01i q^{98} +(-83.5144 - 201.622i) 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 $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	3.10148	+	3.10148i	1.09654	+	1.09654i	0.994812	+	0.101727i	$0.0324367\pi$
$2$	3.10148	+	3.10148i	1.09654	+	1.09654i	0.101727	+	0.994812i	$0.467563\pi$
$3$	1.14805	+	2.77164i	0.220942	+	0.533402i
$3$	1.14805	+	2.77164i	0.220942	+	0.533402i
$4$			11.2384i			1.40480i
$5$	14.1902	−	5.87778i	1.26921	−	0.525725i	0.356487	−	0.934300i	$-0.383974\pi$
$5$	14.1902	−	5.87778i	1.26921	−	0.525725i	0.912724	+	0.408576i	$0.133974\pi$
$6$	−5.03553	+	12.1568i	−0.342624	+	0.827168i
$7$	−30.3663	−	12.5781i	−1.63963	−	0.679155i	−0.643366	−	0.765559i	$-0.722463\pi$
$7$	−30.3663	−	12.5781i	−1.63963	−	0.679155i	−0.996260	+	0.0864033i	$0.972463\pi$
$8$	−10.0437	+	10.0437i	−0.443874	+	0.443874i
$9$	−6.36396	+	6.36396i	−0.235702	+	0.235702i
$10$	62.2405	+	25.7809i	1.96822	+	0.815262i
$11$	−9.27937	+	22.4024i	−0.254349	+	0.614052i	−0.998546	−	0.0539077i	$-0.982832\pi$
$11$	−9.27937	+	22.4024i	−0.254349	+	0.614052i	0.744197	+	0.667960i	$0.232832\pi$
$12$	−31.1487	+	12.9022i	−0.749321	+	0.310379i
$13$		−	35.4963i		−	0.757301i	−0.925540	−	0.378650i	$-0.876388\pi$
$13$		−	35.4963i		−	0.757301i	0.925540	−	0.378650i	$-0.123612\pi$
$14$	−55.1697	−	133.191i	−1.05319	−	2.54263i
$15$	32.5822	+	32.5822i	0.560845	+	0.560845i
$16$	27.6061			0.431345
$17$	−27.6397	−	64.4131i	−0.394330	−	0.918969i
$17$	−27.6397	−	64.4131i	−0.394330	−	0.918969i
$18$	−39.4754			−0.516913
$19$	85.2385	+	85.2385i	1.02921	+	1.02921i	0.999560	+	0.0296525i	$0.00944006\pi$
$19$	85.2385	+	85.2385i	1.02921	+	1.02921i	0.0296525	+	0.999560i	$0.490560\pi$
$20$	66.0566	+	159.475i	0.738536	+	1.78298i
$21$		−	98.6047i		−	1.02463i
$22$	−98.2604	+	40.7008i	−0.952236	+	0.394429i
$23$	−6.73036	+	16.2485i	−0.0610164	+	0.147307i	−0.951447	−	0.307812i	$-0.900403\pi$
$23$	−6.73036	+	16.2485i	−0.0610164	+	0.147307i	0.890431	+	0.455119i	$0.150403\pi$
$24$	−39.3683	−	16.3069i	−0.334834	−	0.138693i
$25$	78.4256	−	78.4256i	0.627405	−	0.627405i
$26$	110.091	−	110.091i	0.830410	−	0.830410i
$27$	−24.9447	−	10.3325i	−0.177801	−	0.0736475i
$28$	141.358	−	341.268i	0.954075	−	2.30334i
$29$	−148.649	+	61.5726i	−0.951845	+	0.394267i	−0.803924	−	0.594732i	$-0.797258\pi$
$29$	−148.649	+	61.5726i	−0.951845	+	0.394267i	−0.147921	+	0.988999i	$0.547258\pi$
$30$			202.106i			1.22998i
$31$	−3.83777	−	9.26519i	−0.0222349	−	0.0536799i	0.912372	−	0.409362i	$-0.134249\pi$
$31$	−3.83777	−	9.26519i	−0.0222349	−	0.0536799i	−0.934607	+	0.355682i	$0.884249\pi$
$32$	165.969	+	165.969i	0.916861	+	0.916861i
$33$	−72.7445			−0.383733
$34$	114.052	−	285.500i	0.575287	−	1.44008i
$35$	−504.836			−2.43808
$36$	−71.5205	−	71.5205i	−0.331114	−	0.331114i
$37$	−58.4926	−	141.214i	−0.259895	−	0.627443i	0.739036	−	0.673666i	$-0.235281\pi$
$37$	−58.4926	−	141.214i	−0.259895	−	0.627443i	−0.998931	+	0.0462235i	$0.985281\pi$
$38$			528.731i			2.25714i
$39$	98.3830	−	40.7516i	0.403946	−	0.167320i
$40$	−83.4879	+	201.558i	−0.330015	+	0.796726i
$41$	118.200	+	48.9599i	0.450236	+	0.186494i	0.596267	−	0.802786i	$-0.296650\pi$
$41$	118.200	+	48.9599i	0.450236	+	0.186494i	−0.146031	+	0.989280i	$0.546650\pi$
$42$	305.821	−	305.821i	1.12355	−	1.12355i
$43$	−388.481	+	388.481i	−1.37774	+	1.37774i	−0.529309	+	0.848429i	$0.677549\pi$
$43$	−388.481	+	388.481i	−1.37774	+	1.37774i	−0.848429	+	0.529309i	$0.822451\pi$
$44$	−251.766	−	104.285i	−0.862618	−	0.357308i
$45$	−52.9000	+	127.712i	−0.175242	+	0.423071i
$46$	−71.2686	+	29.5204i	−0.228434	+	0.0946206i
$47$		−	313.972i		−	0.974415i	−0.873286	−	0.487207i	$-0.838016\pi$
$47$		−	313.972i		−	0.974415i	0.873286	−	0.487207i	$-0.161984\pi$
$48$	31.6931	+	76.5140i	0.0953023	+	0.230080i
$49$	521.365	+	521.365i	1.52002	+	1.52002i
$50$	486.471			1.37595
$51$	146.798	−	150.557i	0.403056	−	0.413376i
$52$	398.921			1.06385
$53$	47.5976	+	47.5976i	0.123359	+	0.123359i	0.766091	−	0.642732i	$-0.222199\pi$
$53$	47.5976	+	47.5976i	0.123359	+	0.123359i	−0.642732	+	0.766091i	$0.722199\pi$
$54$	−45.3198	−	109.412i	−0.114208	−	0.275723i
$55$			372.437i			0.913080i
$56$	431.322	−	178.660i	1.02925	−	0.426328i
$57$	−138.392	+	334.108i	−0.321588	+	0.776381i
$58$	−651.999	−	270.067i	−1.47606	−	0.611406i
$59$	−190.559	+	190.559i	−0.420487	+	0.420487i	−0.885371	−	0.464885i	$-0.846096\pi$
$59$	−190.559	+	190.559i	−0.420487	+	0.420487i	0.464885	+	0.885371i	$0.346096\pi$
$60$	−366.170	+	366.170i	−0.787873	+	0.787873i
$61$	−343.420	−	142.249i	−0.720827	−	0.298576i	−0.00805052	−	0.999968i	$-0.502563\pi$
$61$	−343.420	−	142.249i	−0.720827	−	0.298576i	−0.712776	+	0.701391i	$0.752563\pi$
$62$	16.8330	−	40.6386i	0.0344806	−	0.0832436i
$63$	273.297	−	113.203i	0.546542	−	0.226385i
$64$			808.654i			1.57940i
$65$	−208.640	−	503.700i	−0.398132	−	0.961175i
$66$	−225.616	−	225.616i	−0.420778	−	0.420778i
$67$	546.810			0.997067			0.498533	−	0.866870i	$-0.333872\pi$
$67$	546.810			0.997067			0.498533	+	0.866870i	$0.333872\pi$
$68$	723.898	−	310.625i	1.29096	−	0.553953i
$69$	−52.7618			−0.0920547
$70$	−1565.74	−	1565.74i	−2.67345	−	2.67345i
$71$	−262.350	−	633.368i	−0.438524	−	1.05869i	−0.976459	−	0.215704i	$-0.930795\pi$
$71$	−262.350	−	633.368i	−0.438524	−	1.05869i	0.537935	−	0.842986i	$-0.319205\pi$
$72$		−	127.836i		−	0.209244i
$73$	529.771	−	219.438i	0.849384	−	0.351826i	0.0848374	−	0.996395i	$-0.472963\pi$
$73$	529.771	−	219.438i	0.849384	−	0.351826i	0.764547	+	0.644568i	$0.222963\pi$
$74$	256.558	−	619.385i	0.403030	−	0.973001i
$75$	307.404	+	127.331i	0.473279	+	0.196039i
$76$	−957.941	+	957.941i	−1.44583	+	1.44583i
$77$	563.561	−	563.561i	0.834074	−	0.834074i
$78$	431.523	+	178.743i	0.626415	+	0.259470i
$79$	34.7038	−	83.7824i	0.0494239	−	0.119320i	−0.897239	−	0.441545i	$-0.854431\pi$
$79$	34.7038	−	83.7824i	0.0494239	−	0.119320i	0.946663	+	0.322225i	$0.104431\pi$
$80$	391.736	−	162.262i	0.547468	−	0.226768i
$81$		−	81.0000i		−	0.111111i
$82$	214.746	+	518.442i	0.289203	+	0.698199i
$83$	106.789	+	106.789i	0.141224	+	0.141224i	0.774184	−	0.632960i	$-0.218160\pi$
$83$	106.789	+	106.789i	0.141224	+	0.141224i	−0.632960	+	0.774184i	$0.718160\pi$
$84$	1108.16			1.43940
$85$	−770.819	−	751.576i	−0.983612	−	0.959057i
$86$	−2409.73			−3.02149
$87$	−341.314	−	341.314i	−0.420606	−	0.420606i
$88$	−131.804	−	318.203i	−0.159663	−	0.385461i
$89$			611.215i			0.727962i	0.931406	+	0.363981i	$0.118583\pi$
$89$			611.215i			0.727962i	−0.931406	+	0.363981i	$0.881417\pi$
$90$	−560.165	+	232.028i	−0.656073	+	0.271754i
$91$	−446.477	+	1077.89i	−0.514325	+	1.24169i
$92$	−182.607	−	75.6382i	−0.206936	−	0.0857156i
$93$	21.2738	−	21.2738i	0.0237203	−	0.0237203i
$94$	973.777	−	973.777i	1.06848	−	1.06848i
$95$	1710.56	+	708.539i	1.84737	+	0.765206i
$96$	−269.466	+	650.549i	−0.286482	+	0.691629i
$97$	437.503	−	181.220i	0.457955	−	0.189691i	−0.141766	−	0.989900i	$-0.545278\pi$
$97$	437.503	−	181.220i	0.457955	−	0.189691i	0.599721	+	0.800209i	$0.295278\pi$
$98$			3234.01i			3.33351i
$99$	−83.5144	−	201.622i	−0.0847829	−	0.204684i
$100$	881.376	+	881.376i	0.881376	+	0.881376i
$101$	−612.477			−0.603404			−0.301702	−	0.953402i	$-0.597555\pi$
$101$	−612.477			−0.603404			−0.301702	+	0.953402i	$0.597555\pi$
$102$	922.240	−	11.6571i	0.895249	−	0.0113159i
$103$	1748.00			1.67219			0.836096	−	0.548583i	$-0.184832\pi$
$103$	1748.00			1.67219			0.836096	+	0.548583i	$0.184832\pi$
$104$	356.515	+	356.515i	0.336146	+	0.336146i
$105$	−579.577	−	1399.22i	−0.538675	−	1.30048i
$106$			295.246i			0.270536i
$107$	480.322	−	198.956i	0.433967	−	0.179755i	−0.154996	−	0.987915i	$-0.549536\pi$
$107$	480.322	−	198.956i	0.433967	−	0.179755i	0.588963	+	0.808160i	$0.299536\pi$
$108$	116.120	−	280.338i	0.103460	−	0.249774i
$109$	822.066	+	340.511i	0.722382	+	0.299221i	0.713418	−	0.700739i	$-0.247146\pi$
$109$	822.066	+	340.511i	0.722382	+	0.299221i	0.00896493	+	0.999960i	$0.497146\pi$
$110$	−1155.11	+	1155.11i	−1.00123	+	1.00123i
$111$	324.241	−	324.241i	0.277257	−	0.277257i
$112$	−838.294	−	347.233i	−0.707244	−	0.292950i
$113$	729.892	−	1762.11i	0.607632	−	1.46695i	−0.257936	−	0.966162i	$-0.583042\pi$
$113$	729.892	−	1762.11i	0.607632	−	1.46695i	0.865568	−	0.500791i	$-0.166958\pi$
$114$	−1465.45	+	607.010i	−1.20397	+	0.498699i
$115$			270.130i			0.219041i
$116$	−691.975	−	1670.58i	−0.553865	−	1.33715i
$117$	225.897	+	225.897i	0.178497	+	0.178497i
$118$	−1182.03			−0.922160
$119$	29.1180	+	2303.64i	0.0224306	+	1.77458i
$120$	−654.493			−0.497890
$121$	525.399	+	525.399i	0.394740	+	0.394740i
$122$	−623.928	−	1506.29i	−0.463014	−	1.11782i
$123$			383.815i			0.281361i
$124$	104.126	−	43.1302i	0.0754093	−	0.0312356i
$125$	−82.8148	+	199.933i	−0.0592574	+	0.143060i
$126$	1198.72	+	496.527i	0.847545	+	0.351065i
$127$	−488.380	+	488.380i	−0.341234	+	0.341234i	−0.856831	−	0.515597i	$-0.827570\pi$
$127$	−488.380	+	488.380i	−0.341234	+	0.341234i	0.515597	+	0.856831i	$0.327570\pi$
$128$	−1180.27	+	1180.27i	−0.815016	+	0.815016i
$129$	−1522.72	−	630.733i	−1.03929	−	0.430488i
$130$	915.126	−	2209.31i	0.617399	−	1.49053i
$131$	−2697.13	+	1117.19i	−1.79885	+	0.745109i	−0.811964	+	0.583707i	$0.801602\pi$
$131$	−2697.13	+	1117.19i	−1.79885	+	0.745109i	−0.986889	+	0.161402i	$0.948398\pi$
$132$		−	817.530i		−	0.539067i
$133$	−1516.24	−	3660.52i	−0.988529	−	2.38652i
$134$	1695.92	+	1695.92i	1.09332	+	1.09332i
$135$	−414.703			−0.264385
$136$	924.553	+	369.342i	0.582940	+	0.232874i
$137$	288.798			0.180100			0.0900498	−	0.995937i	$-0.471297\pi$
$137$	288.798			0.180100			0.0900498	+	0.995937i	$0.471297\pi$
$138$	−163.640	−	163.640i	−0.100942	−	0.100942i
$139$	725.418	+	1751.31i	0.442656	+	1.06867i	0.975013	+	0.222146i	$0.0713061\pi$
$139$	725.418	+	1751.31i	0.442656	+	1.06867i	−0.532358	+	0.846519i	$0.678694\pi$
$140$		−	5673.53i		−	3.42501i
$141$	870.216	−	360.455i	0.519755	−	0.215289i
$142$	1150.71	−	2778.05i	0.680036	−	1.64175i
$143$	795.202	+	329.384i	0.465022	+	0.192618i
$144$	−175.684	+	175.684i	−0.101669	+	0.101669i
$145$	−1747.46	+	1747.46i	−1.00082	+	1.00082i
$146$	2323.66	+	962.491i	1.31717	+	0.545591i
$147$	−846.483	+	2043.59i	−0.474944	+	1.14662i
$148$	1587.01	−	657.361i	0.881429	−	0.365100i
$149$		−	1741.86i		−	0.957708i	−0.877895	−	0.478854i	$-0.841052\pi$
$149$		−	1741.86i		−	0.957708i	0.877895	−	0.478854i	$-0.158948\pi$
$150$	558.493	+	1348.32i	0.304005	+	0.733933i
$151$	−1445.53	−	1445.53i	−0.779042	−	0.779042i	0.200626	−	0.979668i	$-0.435702\pi$
$151$	−1445.53	−	1445.53i	−0.779042	−	0.779042i	−0.979668	+	0.200626i	$0.935702\pi$
$152$	−1712.22			−0.913682
$153$	585.820	+	234.025i	0.309547	+	0.123659i
$154$	3495.74			1.82919
$155$	−108.918	−	108.918i	−0.0564417	−	0.0564417i
$156$	457.981	+	1105.66i	0.235050	+	0.567461i
$157$			2739.20i			1.39243i	0.717832	+	0.696216i	$0.245135\pi$
$157$			2739.20i			1.39243i	−0.717832	+	0.696216i	$0.754865\pi$
$158$	367.483	−	152.216i	0.185034	−	0.0766436i
$159$	−77.2789	+	186.568i	−0.0385448	+	0.0930553i
$160$	3330.68	+	1379.61i	1.64571	+	0.681674i
$161$	408.752	−	408.752i	0.200088	−	0.200088i
$162$	251.220	−	251.220i	0.121838	−	0.121838i
$163$	−647.547	−	268.223i	−0.311165	−	0.128889i	0.221636	−	0.975130i	$-0.428860\pi$
$163$	−647.547	−	268.223i	−0.311165	−	0.128889i	−0.532800	+	0.846241i	$0.678860\pi$
$164$	−550.229	+	1328.37i	−0.261986	+	0.632489i
$165$	−1032.26	+	427.576i	−0.487039	+	0.201738i
$166$			662.406i			0.309715i
$167$	228.576	+	551.832i	0.105915	+	0.255701i	0.967948	−	0.251151i	$-0.0808091\pi$
$167$	228.576	+	551.832i	0.105915	+	0.255701i	−0.862033	+	0.506852i	$0.830809\pi$
$168$	990.360	+	990.360i	0.454809	+	0.454809i
$169$	937.011			0.426496
$170$	−59.6819	−	4721.68i	−0.0269258	−	2.13021i
$171$	−1084.91			−0.485176
$172$	−4365.89	−	4365.89i	−1.93544	−	1.93544i
$173$	952.894	+	2300.49i	0.418770	+	1.01100i	0.982705	+	0.185181i	$0.0592870\pi$
$173$	952.894	+	2300.49i	0.418770	+	1.01100i	−0.563935	+	0.825819i	$0.690713\pi$
$174$		−	2117.16i		−	0.922421i
$175$	−3367.94	+	1395.05i	−1.45481	+	0.602604i
$176$	−256.167	+	618.442i	−0.109712	+	0.264868i
$177$	−746.933	−	309.390i	−0.317192	−	0.131385i
$178$	−1895.67	+	1895.67i	−0.798239	+	0.798239i
$179$	1796.06	−	1796.06i	0.749963	−	0.749963i	−0.224509	−	0.974472i	$-0.572078\pi$
$179$	1796.06	−	1796.06i	0.749963	−	0.749963i	0.974472	+	0.224509i	$0.0720777\pi$
$180$	−1435.27	−	594.510i	−0.594328	−	0.246179i
$181$	391.473	−	945.100i	0.160762	−	0.388115i	−0.822888	−	0.568204i	$-0.807639\pi$
$181$	391.473	−	945.100i	0.160762	−	0.388115i	0.983650	+	0.180089i	$0.0576386\pi$
$182$	−4727.80	+	1958.32i	−1.92554	+	0.797584i
$183$		−	1115.15i		−	0.450459i
$184$	−95.5979	−	230.794i	−0.0383020	−	0.0924692i
$185$	−1660.05	−	1660.05i	−0.659724	−	0.659724i
$186$	131.961			0.0520206
$187$	1699.49	−	21.4815i	0.664592	−	0.00840042i
$188$	3528.53			1.36885
$189$	627.517	+	627.517i	0.241509	+	0.241509i
$190$	3107.76	+	7502.81i	1.18664	+	2.86479i
$191$		−	4381.51i		−	1.65987i	−0.557861	−	0.829935i	$-0.688378\pi$
$191$		−	4381.51i		−	1.65987i	0.557861	−	0.829935i	$-0.311622\pi$
$192$	−2241.30	+	928.375i	−0.842456	+	0.348957i
$193$	1087.86	−	2626.33i	0.405730	−	0.979519i	−0.580518	−	0.814247i	$-0.697150\pi$
$193$	1087.86	−	2626.33i	0.405730	−	0.979519i	0.986248	−	0.165272i	$-0.0528501\pi$
$194$	1918.96	+	794.857i	0.710170	+	0.294162i
$195$	1156.55	−	1156.55i	0.424728	−	0.424728i
$196$	−5859.29	+	5859.29i	−2.13531	+	2.13531i
$197$	−1971.22	−	816.507i	−0.712913	−	0.295298i	−0.00340354	−	0.999994i	$-0.501083\pi$
$197$	−1971.22	−	816.507i	−0.712913	−	0.295298i	−0.709509	+	0.704696i	$0.751083\pi$
$198$	366.307	−	884.344i	0.131476	−	0.317412i
$199$	−1966.44	+	814.528i	−0.700490	+	0.290152i	−0.704363	−	0.709840i	$-0.748767\pi$
$199$	−1966.44	+	814.528i	−0.700490	+	0.290152i	0.00387288	+	0.999993i	$0.498767\pi$
$200$			1575.37i			0.556978i
$201$	627.765	+	1515.56i	0.220294	+	0.531838i
$202$	−1899.59	−	1899.59i	−0.661656	−	0.661656i
$203$	5288.40			1.82844
$204$	1692.01	+	1649.77i	0.580708	+	0.566211i
$205$	1965.05			0.669489
$206$	5421.40	+	5421.40i	1.83362	+	1.83362i
$207$	−60.5732	−	146.237i	−0.0203388	−	0.0491022i
$208$		−	979.913i		−	0.326658i
$209$	−2700.50	+	1118.59i	−0.893770	+	0.370211i
$210$	2542.12	−	6137.21i	0.835346	−	2.01670i
$211$	−700.253	−	290.054i	−0.228471	−	0.0946358i	0.265511	−	0.964108i	$-0.414459\pi$
$211$	−700.253	−	290.054i	−0.228471	−	0.0946358i	−0.493982	+	0.869472i	$0.664459\pi$
$212$	−534.919	+	534.919i	−0.173294	+	0.173294i
$213$	1454.28	−	1454.28i	0.467819	−	0.467819i
$214$	2106.77	+	872.651i	0.672970	+	0.278753i
$215$	−3229.22	+	7796.03i	−1.02433	+	2.47295i
$216$	354.315	−	146.762i	0.111611	−	0.0462310i
$217$			329.622i			0.103116i
$218$	1493.53	+	3605.71i	0.464013	+	1.12023i
$219$	1216.41	+	1216.41i	0.375330	+	0.375330i
$220$	−4185.58			−1.28269
$221$	−2286.43	+	981.107i	−0.695936	+	0.298626i
$222$	2011.25			0.608047
$223$	−2128.53	−	2128.53i	−0.639180	−	0.639180i	0.311173	−	0.950353i	$-0.399278\pi$
$223$	−2128.53	−	2128.53i	−0.639180	−	0.639180i	−0.950353	+	0.311173i	$0.899278\pi$
$224$	−2952.29	−	7127.47i	−0.880618	−	2.12600i
$225$			998.195i			0.295761i
$226$	7728.91	−	3201.42i	2.27486	−	0.942280i
$227$	1100.16	−	2656.01i	0.321674	−	0.776589i	−0.677484	−	0.735538i	$-0.736929\pi$
$227$	1100.16	−	2656.01i	0.321674	−	0.776589i	0.999157	−	0.0410507i	$-0.0130705\pi$
$228$	−3754.83	−	1555.30i	−1.09066	−	0.451765i
$229$	2808.48	−	2808.48i	0.810436	−	0.810436i	−0.174263	−	0.984699i	$-0.555754\pi$
$229$	2808.48	−	2808.48i	0.810436	−	0.810436i	0.984699	+	0.174263i	$0.0557543\pi$
$230$	−837.802	+	837.802i	−0.240187	+	0.240187i
$231$	2208.98	+	914.990i	0.629179	+	0.260615i
$232$	874.576	−	2111.41i	0.247494	−	0.597504i
$233$	−4912.30	+	2034.74i	−1.38118	+	0.572105i	−0.944797	−	0.327655i	$-0.893741\pi$
$233$	−4912.30	+	2034.74i	−1.38118	+	0.572105i	−0.436385	+	0.899760i	$0.643741\pi$
$234$			1401.23i			0.391459i
$235$	−1845.46	−	4455.33i	−0.512274	−	1.23674i
$236$	−2141.58	−	2141.58i	−0.590698	−	0.590698i
$237$	272.056			0.0745652
$238$	−7054.40	+	7235.01i	−1.92130	+	1.97049i
$239$	653.157			0.176775			0.0883874	−	0.996086i	$-0.471829\pi$
$239$	653.157			0.176775			0.0883874	+	0.996086i	$0.471829\pi$
$240$	899.465	+	899.465i	0.241918	+	0.241918i
$241$	−197.944	−	477.879i	−0.0529074	−	0.127730i	0.895216	−	0.445633i	$-0.147021\pi$
$241$	−197.944	−	477.879i	−0.0529074	−	0.127730i	−0.948123	+	0.317903i	$0.897021\pi$
$242$			3259.03i			0.865695i
$243$	224.503	−	92.9921i	0.0592669	−	0.0245492i
$244$	1598.65	−	3859.48i	0.419439	−	1.01261i
$245$	10462.8	+	4333.82i	2.72833	+	1.13011i
$246$	−1190.39	+	1190.39i	−0.308523	+	0.308523i
$247$	3025.65	−	3025.65i	0.779423	−	0.779423i
$248$	131.603	+	54.5116i	0.0336967	+	0.0139576i
$249$	−173.381	+	418.578i	−0.0441267	+	0.106531i
$250$	−876.935	+	363.238i	−0.221849	+	0.0918929i
$251$		−	4658.77i		−	1.17155i	−0.810474	−	0.585774i	$-0.800790\pi$
$251$		−	4658.77i		−	1.17155i	0.810474	−	0.585774i	$-0.199210\pi$
$252$	1272.22	+	3071.41i	0.318025	+	0.767780i
$253$	−301.552	−	301.552i	−0.0749345	−	0.0749345i
$254$	−3029.40			−0.748352
$255$	1198.16	−	2999.28i	0.294241	−	0.736557i
$256$	−851.930			−0.207991
$257$	−3720.91	−	3720.91i	−0.903129	−	0.903129i	0.0925769	−	0.995706i	$-0.470490\pi$
$257$	−3720.91	−	3720.91i	−0.903129	−	0.903129i	−0.995706	+	0.0925769i	$0.970490\pi$
$258$	−2766.49	−	6678.90i	−0.667575	−	1.61167i
$259$			5023.86i			1.20528i
$260$	5660.77	−	2344.77i	1.35025	−	0.559294i
$261$	554.153	−	1337.84i	0.131422	−	0.317282i
$262$	−11830.1	−	4900.17i	−2.78955	−	1.15547i
$263$	−1119.45	+	1119.45i	−0.262466	+	0.262466i	−0.826055	−	0.563589i	$-0.809420\pi$
$263$	−1119.45	+	1119.45i	−0.262466	+	0.262466i	0.563589	+	0.826055i	$0.309420\pi$
$264$	730.626	−	730.626i	0.170329	−	0.170329i
$265$	955.188	+	395.652i	0.221422	+	0.0917159i
$266$	6650.45	−	16055.6i	1.53295	−	3.70087i
$267$	−1694.07	+	701.705i	−0.388296	+	0.160838i
$268$			6145.25i			1.40068i
$269$	120.806	+	291.651i	0.0273816	+	0.0661050i	0.936979	−	0.349386i	$-0.113610\pi$
$269$	120.806	+	291.651i	0.0273816	+	0.0661050i	−0.909597	+	0.415491i	$0.863610\pi$
$270$	−1286.19	−	1286.19i	−0.289908	−	0.289908i
$271$	−413.058			−0.0925885			−0.0462943	−	0.998928i	$-0.514741\pi$
$271$	−413.058			−0.0925885			−0.0462943	+	0.998928i	$0.514741\pi$
$272$	−763.022	−	1778.19i	−0.170092	−	0.396392i
$273$	−3500.11			−0.775956
$274$	895.700	+	895.700i	0.197486	+	0.197486i
$275$	1029.18	+	2484.66i	0.225680	+	0.544839i
$276$		−	592.957i		−	0.129318i
$277$	432.799	−	179.271i	0.0938785	−	0.0388858i	−0.335250	−	0.942129i	$-0.608821\pi$
$277$	432.799	−	179.271i	0.0938785	−	0.0388858i	0.429128	+	0.903243i	$0.358821\pi$
$278$	−3181.80	+	7681.54i	−0.686444	+	1.65722i
$279$	83.3867	+	34.5399i	0.0178933	+	0.00741165i
$280$	5070.44	−	5070.44i	1.08220	−	1.08220i
$281$	−965.659	+	965.659i	−0.205005	+	0.205005i	−0.802140	−	0.597135i	$-0.796305\pi$
$281$	−965.659	+	965.659i	−0.205005	+	0.205005i	0.597135	+	0.802140i	$0.296305\pi$
$282$	3816.90	+	1581.01i	0.806005	+	0.333858i
$283$	−2739.67	+	6614.15i	−0.575465	+	1.38929i	0.321381	+	0.946950i	$0.395853\pi$
$283$	−2739.67	+	6614.15i	−0.575465	+	1.38929i	−0.896845	+	0.442344i	$0.854147\pi$
$284$	7118.02	−	2948.38i	1.48724	−	0.616036i
$285$			5554.51i			1.15446i
$286$	1444.73	+	3487.88i	0.298701	+	0.721129i
$287$	−2973.46	−	2973.46i	−0.611560	−	0.611560i
$288$	−2112.45			−0.432212
$289$	−3385.10	+	3560.71i	−0.689008	+	0.724754i
$290$	−10839.4			−2.19487
$291$	1004.55	+	1004.55i	0.202364	+	0.202364i
$292$	2466.13	+	5953.76i	0.494244	+	1.19321i
$293$			769.318i			0.153393i	0.997055	+	0.0766963i	$0.0244372\pi$
$293$			769.318i			0.153393i	−0.997055	+	0.0766963i	$0.975563\pi$
$294$	−8963.50	+	3712.80i	−1.77810	+	0.736514i
$295$	−1584.01	+	3824.14i	−0.312626	+	0.754747i
$296$	2005.80	+	830.828i	0.393866	+	0.163145i
$297$	462.943	−	462.943i	0.0904468	−	0.0904468i
$298$	5402.33	−	5402.33i	1.05016	−	1.05016i
$299$	576.763	+	238.903i	0.111555	+	0.0462077i
$300$	−1430.99	+	3454.72i	−0.275394	+	0.664861i
$301$	16683.1	−	6910.36i	3.19467	−	1.32328i
$302$		−	8966.55i		−	1.70850i
$303$	−703.155	−	1697.57i	−0.133317	−	0.321857i
$304$	2353.10	+	2353.10i	0.443945	+	0.443945i
$305$	−5709.32			−1.07185
$306$	1091.09	+	2542.73i	0.203834	+	0.475027i
$307$	−420.567			−0.0781857			−0.0390929	−	0.999236i	$-0.512447\pi$
$307$	−420.567			−0.0781857			−0.0390929	+	0.999236i	$0.512447\pi$
$308$	6333.50	+	6333.50i	1.17170	+	1.17170i
$309$	2006.80	+	4844.83i	0.369458	+	0.891951i
$310$		−	675.611i		−	0.123781i
$311$	3282.14	−	1359.51i	0.598434	−	0.247880i	−0.0628401	−	0.998024i	$-0.520016\pi$
$311$	3282.14	−	1359.51i	0.598434	−	0.247880i	0.661275	+	0.750144i	$0.270016\pi$
$312$	−578.834	+	1397.43i	−0.105032	+	0.253570i
$313$	6018.22	+	2492.83i	1.08680	+	0.450169i	0.852891	−	0.522088i	$-0.174847\pi$
$313$	6018.22	+	2492.83i	1.08680	+	0.450169i	0.233913	+	0.972258i	$0.424847\pi$
$314$	−8495.57	+	8495.57i	−1.52686	+	1.52686i
$315$	3212.76	−	3212.76i	0.574661	−	0.574661i
$316$	941.578	+	390.014i	0.167620	+	0.0694304i
$317$	−2260.27	+	5456.77i	−0.400471	+	0.966823i	0.587080	+	0.809529i	$0.300277\pi$
$317$	−2260.27	+	5456.77i	−0.400471	+	0.966823i	−0.987552	+	0.157295i	$0.949723\pi$
$318$	−818.315	+	338.957i	−0.144305	+	0.0597729i
$319$		−	3901.46i		−	0.684764i
$320$	4753.09	+	11475.0i	0.830331	+	2.00460i
$321$	1102.87	+	1102.87i	0.191763	+	0.191763i
$322$	2535.47			0.438809
$323$	3134.51	−	7846.44i	0.539965	−	1.35166i
$324$	910.308			0.156088
$325$	−2783.82	−	2783.82i	−0.475134	−	0.475134i
$326$	−1176.47	−	2840.24i	−0.199873	−	0.482536i
$327$			2669.40i			0.451431i
$328$	−1678.90	+	695.425i	−0.282628	+	0.117068i
$329$	−3949.18	+	9534.16i	−0.661779	+	1.59768i
$330$	−4527.66	−	1875.42i	−0.755270	−	0.312843i
$331$	−6263.20	+	6263.20i	−1.04005	+	1.04005i	−0.0408867	+	0.999164i	$0.513018\pi$
$331$	−6263.20	+	6263.20i	−1.04005	+	1.04005i	−0.999164	+	0.0408867i	$0.986982\pi$
$332$	−1200.13	+	1200.13i	−0.198391	+	0.198391i
$333$	1270.92	+	526.433i	0.209148	+	0.0866317i
$334$	−1002.57	+	2420.42i	−0.164246	+	0.396525i
$335$	7759.35	−	3214.03i	1.26549	−	0.524183i
$336$		−	2722.09i		−	0.441970i
$337$	−3140.02	−	7580.69i	−0.507561	−	1.22536i	−0.945283	−	0.326250i	$-0.894215\pi$
$337$	−3140.02	−	7580.69i	−0.507561	−	1.22536i	0.437722	−	0.899110i	$-0.355785\pi$
$338$	2906.12	+	2906.12i	0.467669	+	0.467669i
$339$	5721.90			0.916728
$340$	8446.49	−	8662.75i	1.34728	−	1.38177i
$341$	243.175			0.0386177
$342$	−3364.82	−	3364.82i	−0.532014	−	0.532014i
$343$	−4959.83	−	11974.1i	−0.780775	−	1.88496i
$344$		−	7803.59i		−	1.22309i
$345$	−748.702	+	310.122i	−0.116837	+	0.0483954i
$346$	−4179.54	+	10090.3i	−0.649403	+	1.56780i
$347$	−4736.58	−	1961.96i	−0.732775	−	0.303525i	−0.0150834	−	0.999886i	$-0.504801\pi$
$347$	−4736.58	−	1961.96i	−0.732775	−	0.303525i	−0.717692	+	0.696361i	$0.754801\pi$
$348$	3835.81	−	3835.81i	0.590865	−	0.590865i
$349$	−372.255	+	372.255i	−0.0570956	+	0.0570956i	−0.735078	−	0.677982i	$-0.762855\pi$
$349$	−372.255	+	372.255i	−0.0570956	+	0.0570956i	0.677982	+	0.735078i	$0.262855\pi$
$350$	−14772.3	−	6118.90i	−2.25604	−	0.934482i
$351$	−366.764	+	885.447i	−0.0557733	+	0.134649i
$352$	−5258.21	+	2178.02i	−0.796203	+	0.329798i
$353$		−	2498.19i		−	0.376672i	−0.982105	−	0.188336i	$-0.939691\pi$
$353$		−	2498.19i		−	0.376672i	0.982105	−	0.188336i	$-0.0603093\pi$
$354$	−1357.03	−	3276.17i	−0.203744	−	0.491882i
$355$	−7445.60	−	7445.60i	−1.11316	−	1.11316i
$356$	−6869.05			−1.02264
$357$	−6351.44	+	2725.40i	−0.941607	+	0.404044i
$358$	11140.9			1.64473
$359$	3683.94	+	3683.94i	0.541590	+	0.541590i	0.923995	−	0.382405i	$-0.124904\pi$
$359$	3683.94	+	3683.94i	0.541590	+	0.541590i	−0.382405	+	0.923995i	$0.624904\pi$
$360$	−751.391	−	1814.02i	−0.110005	−	0.265575i
$361$			7672.19i			1.11856i
$362$	4145.36	−	1717.06i	0.601865	−	0.249301i
$363$	−853.031	+	2059.40i	−0.123340	+	0.297770i
$364$	−12113.7	−	5017.68i	−1.74432	−	0.722521i
$365$	6227.76	−	6227.76i	0.893084	−	0.893084i
$366$	3458.60	−	3458.60i	0.493946	−	0.493946i
$367$	4953.51	+	2051.81i	0.704553	+	0.291835i	0.706048	−	0.708164i	$-0.250476\pi$
$367$	4953.51	+	2051.81i	0.704553	+	0.291835i	−0.00149555	+	0.999999i	$0.500476\pi$
$368$	−185.799	+	448.558i	−0.0263191	+	0.0635399i
$369$	−1063.80	+	440.639i	−0.150079	+	0.0621646i
$370$		−	10297.2i		−	1.44683i
$371$	−846.674	−	2044.05i	−0.118483	−	0.286043i
$372$	239.083	+	239.083i	0.0333222	+	0.0333222i
$373$	6085.54			0.844764			0.422382	−	0.906418i	$-0.361194\pi$
$373$	6085.54			0.844764			0.422382	+	0.906418i	$0.361194\pi$
$374$	5337.55	+	5204.30i	0.737963	+	0.719540i
$375$	−649.216			−0.0894010
$376$	3153.45	+	3153.45i	0.432518	+	0.432518i
$377$	2185.60	+	5276.51i	0.298579	+	0.720832i
$378$			3892.46i			0.529647i
$379$	−5629.32	+	2331.74i	−0.762952	+	0.316025i	−0.730014	−	0.683432i	$-0.760486\pi$
$379$	−5629.32	+	2331.74i	−0.762952	+	0.316025i	−0.0329382	+	0.999457i	$0.510486\pi$
$380$	−7962.82	+	19224.0i	−1.07496	+	2.59518i
$381$	−1914.30	−	792.927i	−0.257408	−	0.106622i
$382$	13589.2	−	13589.2i	1.82011	−	1.82011i
$383$	−4813.71	+	4813.71i	−0.642217	+	0.642217i	−0.951100	−	0.308883i	$-0.900045\pi$
$383$	−4813.71	+	4813.71i	−0.642217	+	0.642217i	0.308883	+	0.951100i	$0.400045\pi$
$384$	−4626.29	−	1916.27i	−0.614803	−	0.254660i
$385$	4684.56	−	11309.5i	0.620123	−	1.49711i
$386$	11519.5	−	4771.53i	1.51898	−	0.629182i
$387$		−	4944.55i		−	0.649472i
$388$	2036.61	+	4916.82i	0.266478	+	0.643334i
$389$	3245.79	+	3245.79i	0.423055	+	0.423055i	0.886254	−	0.463199i	$-0.153299\pi$
$389$	3245.79	+	3245.79i	0.423055	+	0.423055i	−0.463199	+	0.886254i	$0.653299\pi$
$390$	7174.02			0.931463
$391$	1232.64	−	15.5806i	0.159431	−	0.00201520i
$392$	−10472.9			−1.34939
$393$	−6192.89	−	6192.89i	−0.794886	−	0.794886i
$394$	−3581.33	−	8646.09i	−0.457931	−	1.10554i
$395$		−	1392.87i		−	0.177425i
$396$	2265.90	−	938.565i	0.287539	−	0.119103i
$397$	−1756.69	+	4241.04i	−0.222081	+	0.536150i	−0.995172	−	0.0981444i	$-0.968709\pi$
$397$	−1756.69	+	4241.04i	−0.222081	+	0.536150i	0.773092	+	0.634294i	$0.218709\pi$
$398$	−8625.13	−	3572.65i	−1.08628	−	0.449951i
$399$	8404.92	−	8404.92i	1.05457	−	1.05457i
$400$	2165.02	−	2165.02i	0.270628	−	0.270628i
$401$	−1659.84	−	687.528i	−0.206704	−	0.0856197i	0.276929	−	0.960890i	$-0.410683\pi$
$401$	−1659.84	−	687.528i	−0.206704	−	0.0856197i	−0.483634	+	0.875271i	$0.660683\pi$
$402$	−2753.48	+	6647.48i	−0.341619	+	0.824742i
$403$	−328.880	+	136.227i	−0.0406518	+	0.0168385i
$404$		−	6883.24i		−	0.847659i
$405$	−476.100	−	1149.41i	−0.0584138	−	0.141024i
$406$	16401.9	+	16401.9i	2.00495	+	2.00495i
$407$	3706.30			0.451387
$408$	37.7499	+	2986.55i	0.00458063	+	0.362393i
$409$	−11163.3			−1.34961			−0.674803	−	0.737998i	$-0.735772\pi$
$409$	−11163.3			−1.34961			−0.674803	+	0.737998i	$0.735772\pi$
$410$	6094.57	+	6094.57i	0.734121	+	0.734121i
$411$	331.554	+	800.443i	0.0397916	+	0.0960655i
$412$			19644.7i			2.34909i
$413$	8183.46	−	3389.70i	0.975017	−	0.403865i
$414$	265.684	−	641.417i	0.0315402	−	0.0761448i
$415$	2143.03	+	887.673i	0.253488	+	0.104998i
$416$	5891.31	−	5891.31i	0.694339	−	0.694339i
$417$	−4021.19	+	4021.19i	−0.472227	+	0.472227i
$418$	−11844.8	−	4906.29i	−1.38600	−	0.574102i
$419$	1692.23	−	4085.40i	0.197305	−	0.476337i	−0.794000	−	0.607917i	$-0.792005\pi$
$419$	1692.23	−	4085.40i	0.197305	−	0.476337i	0.991305	+	0.131581i	$0.0420052\pi$
$420$	15725.0	−	6513.50i	1.82691	−	0.756729i
$421$			11888.9i			1.37632i	0.725559	+	0.688160i	$0.241581\pi$
$421$			11888.9i			1.37632i	−0.725559	+	0.688160i	$0.758419\pi$
$422$	−1272.22	−	3071.42i	−0.146756	−	0.354299i
$423$	1998.10	+	1998.10i	0.229672	+	0.229672i
$424$	−956.115			−0.109512
$425$	−7219.29	−	2883.98i	−0.823970	−	0.329161i
$426$	9020.83			1.02596
$427$	8639.17	+	8639.17i	0.979107	+	0.979107i
$428$	2235.94	+	5398.03i	0.252519	+	0.609635i
$429$			2582.16i			0.290601i
$430$	−34194.6	+	14163.9i	−3.83491	+	1.58847i
$431$	952.700	−	2300.02i	0.106473	−	0.257049i	−0.861660	−	0.507487i	$-0.830575\pi$
$431$	952.700	−	2300.02i	0.106473	−	0.257049i	0.968133	+	0.250438i	$0.0805746\pi$
$432$	−688.626	−	285.238i	−0.0766934	−	0.0317674i
$433$	−1298.56	+	1298.56i	−0.144122	+	0.144122i	−0.775486	−	0.631364i	$-0.782495\pi$
$433$	−1298.56	+	1298.56i	−0.144122	+	0.144122i	0.631364	+	0.775486i	$0.282495\pi$
$434$	−1022.31	+	1022.31i	−0.113071	+	0.113071i
$435$	−6849.49	−	2837.15i	−0.754960	−	0.312715i
$436$	−3826.79	+	9238.68i	−0.420344	+	1.01480i
$437$	−1958.68	+	811.314i	−0.214409	+	0.0888110i
$438$			7545.33i			0.823128i
$439$	−1409.49	−	3402.81i	−0.153238	−	0.369948i	0.828554	−	0.559909i	$-0.189164\pi$
$439$	−1409.49	−	3402.81i	−0.153238	−	0.369948i	−0.981792	+	0.189961i	$0.939164\pi$
$440$	−3740.66	−	3740.66i	−0.405293	−	0.405293i
$441$	−6635.90			−0.716542
$442$	−10134.2	−	4048.43i	−1.09058	−	0.435666i
$443$	−16524.1			−1.77220			−0.886099	−	0.463497i	$-0.846595\pi$
$443$	−16524.1			−1.77220			−0.886099	+	0.463497i	$0.846595\pi$
$444$	3643.94	+	3643.94i	0.389490	+	0.389490i
$445$	3592.59	+	8673.27i	0.382708	+	0.923938i
$446$		−	13203.2i		−	1.40177i
$447$	4827.80	−	1999.74i	0.510843	−	0.211598i
$448$	10171.4	−	24555.8i	1.07266	−	2.58963i
$449$	7226.66	+	2993.38i	0.759570	+	0.314624i	0.728640	−	0.684897i	$-0.240153\pi$
$449$	7226.66	+	2993.38i	0.759570	+	0.314624i	0.0309307	+	0.999522i	$0.490153\pi$
$450$	−3095.88	+	3095.88i	−0.324314	+	0.324314i
$451$	−2193.64	+	2193.64i	−0.229034	+	0.229034i
$452$	19803.3	+	8202.79i	2.06077	+	0.853599i
$453$	2346.94	−	5666.02i	0.243419	−	0.587666i
$454$	11649.7	−	4825.45i	1.20429	−	0.498832i
$455$			17919.8i			1.84636i
$456$	−1965.72	−	4745.67i	−0.201871	−	0.487360i
$457$	−2384.11	−	2384.11i	−0.244035	−	0.244035i	0.574482	−	0.818517i	$-0.305204\pi$
$457$	−2384.11	−	2384.11i	−0.244035	−	0.244035i	−0.818517	+	0.574482i	$0.805204\pi$
$458$	17420.9			1.77735
$459$	23.9193	+	1892.35i	0.00243237	+	0.192435i
$460$	−3035.82			−0.307708
$461$	4367.31	+	4367.31i	0.441228	+	0.441228i	0.892425	−	0.451197i	$-0.149003\pi$
$461$	4367.31	+	4367.31i	0.441228	+	0.441228i	−0.451197	+	0.892425i	$0.649003\pi$
$462$	4013.29	+	9688.94i	0.404145	+	0.975693i
$463$		−	13819.6i		−	1.38715i	−0.720383	−	0.693577i	$-0.756034\pi$
$463$		−	13819.6i		−	1.38715i	0.720383	−	0.693577i	$-0.243966\pi$
$464$	−4103.62	+	1699.78i	−0.410573	+	0.170065i
$465$	176.837	−	426.923i	0.0176358	−	0.0425765i
$466$	−21546.1	−	8924.69i	−2.14186	−	0.887186i
$467$	4160.60	−	4160.60i	0.412269	−	0.412269i	−0.470259	−	0.882528i	$-0.655840\pi$
$467$	4160.60	−	4160.60i	0.412269	−	0.412269i	0.882528	+	0.470259i	$0.155840\pi$
$468$	−2538.72	+	2538.72i	−0.250752	+	0.250752i
$469$	−16604.6	−	6877.85i	−1.63482	−	0.677163i
$470$	8094.46	−	19541.8i	0.794404	−	1.91786i
$471$	−7592.07	+	3144.74i	−0.742726	+	0.307647i
$472$		−	3827.85i		−	0.373287i
$473$	−5098.04	−	12307.8i	−0.495577	−	1.19643i
$474$	843.778	+	843.778i	0.0817637	+	0.0817637i
$475$	13369.8			1.29147
$476$	−25889.2	+	327.238i	−2.49292	+	0.0315104i
$477$	−605.819			−0.0581520
$478$	2025.75	+	2025.75i	0.193841	+	0.193841i
$479$	−1773.81	−	4282.36i	−0.169202	−	0.408489i	0.816420	−	0.577459i	$-0.195956\pi$
$479$	−1773.81	−	4282.36i	−0.169202	−	0.408489i	−0.985621	+	0.168971i	$0.945956\pi$
$480$			10815.3i			1.02843i
$481$	−5012.56	+	2076.27i	−0.475163	+	0.196819i
$482$	868.213	−	2096.05i	0.0820457	−	0.198076i
$483$	1602.18	+	663.645i	0.150935	+	0.0625195i
$484$	−5904.62	+	5904.62i	−0.554529	+	0.554529i
$485$	5143.09	−	5143.09i	0.481517	−	0.481517i
$486$	984.704	+	407.878i	0.0919076	+	0.0380694i
$487$	−6637.65	+	16024.7i	−0.617619	+	1.49106i	0.236841	+	0.971548i	$0.423888\pi$
$487$	−6637.65	+	16024.7i	−0.617619	+	1.49106i	−0.854461	+	0.519516i	$0.826112\pi$
$488$	4877.93	−	2020.51i	0.452487	−	0.187426i
$489$		−	2102.70i		−	0.194453i
$490$	19008.8	+	45891.3i	1.75251	+	4.23093i
$491$	−12195.7	−	12195.7i	−1.12094	−	1.12094i	−0.991600	−	0.129343i	$-0.958713\pi$
$491$	−12195.7	−	12195.7i	−1.12094	−	1.12094i	−0.129343	−	0.991600i	$-0.541287\pi$
$492$	−4313.45			−0.395255
$493$	8074.70	+	7873.12i	0.737660	+	0.719245i
$494$	18768.0			1.70934
$495$	−2370.17	−	2370.17i	−0.215215	−	0.215215i
$496$	−105.946	−	255.775i	−0.00959093	−	0.0231545i
$497$			22532.9i			2.03368i
$498$	−1835.95	+	760.475i	−0.165202	+	0.0684291i
$499$	−95.7457	+	231.151i	−0.00858951	+	0.0207369i	−0.928116	−	0.372291i	$-0.878572\pi$
$499$	−95.7457	+	231.151i	−0.00858951	+	0.0207369i	0.919527	+	0.393028i	$0.128572\pi$
$500$	−2246.91	−	930.703i	−0.200970	−	0.0832446i
$501$	−1267.06	+	1267.06i	−0.112990	+	0.112990i
$502$	14449.1	−	14449.1i	1.28465	−	1.28465i
$503$	12113.1	+	5017.40i	1.07375	+	0.444761i	0.848312	−	0.529497i	$-0.177619\pi$
$503$	12113.1	+	5017.40i	1.07375	+	0.444761i	0.225436	+	0.974258i	$0.427619\pi$
$504$	−1607.94	+	3881.90i	−0.142109	+	0.343083i
$505$	−8691.19	+	3600.01i	−0.765847	+	0.317224i
$506$		−	1870.52i		−	0.164337i
$507$	1075.74	+	2597.06i	0.0942310	+	0.227494i
$508$	−5488.59	−	5488.59i	−0.479364	−	0.479364i
$509$	−4410.32			−0.384055			−0.192028	−	0.981390i	$-0.561506\pi$
$509$	−4410.32			−0.384055			−0.192028	+	0.981390i	$0.561506\pi$
$510$	13018.3	−	5586.14i	1.13031	−	0.485017i
$511$	−18847.3			−1.63162
$512$	6799.91	+	6799.91i	0.586946	+	0.586946i
$513$	−1245.53	−	3006.97i	−0.107196	−	0.258794i
$514$		−	23080.7i		−	1.98063i
$515$	24804.5	−	10274.4i	2.12237	−	0.879113i
$516$	7088.40	−	17112.9i	0.604747	−	1.45999i
$517$	7033.72	+	2913.46i	0.598342	+	0.247841i
$518$	−15581.4	+	15581.4i	−1.32164	+	1.32164i
$519$	−5282.16	+	5282.16i	−0.446745	+	0.446745i
$520$	7154.55	+	2963.51i	0.603361	+	0.249920i
$521$	−4507.02	+	10880.9i	−0.378995	+	0.914975i	0.613160	+	0.789959i	$0.289898\pi$
$521$	−4507.02	+	10880.9i	−0.378995	+	0.914975i	−0.992155	+	0.125016i	$0.960102\pi$
$522$	5867.99	−	2430.60i	0.492021	−	0.203802i
$523$		−	16556.5i		−	1.38425i	−0.721777	−	0.692126i	$-0.756674\pi$
$523$		−	16556.5i		−	1.38425i	0.721777	−	0.692126i	$-0.243326\pi$
$524$	−12555.4	−	30311.4i	−1.04673	−	2.52702i
$525$	−7733.14	−	7733.14i	−0.642860	−	0.642860i
$526$	−6943.93			−0.575608
$527$	−490.725	+	503.289i	−0.0405623	+	0.0416008i
$528$	−2008.19			−0.165521
$529$	8384.65	+	8384.65i	0.689131	+	0.689131i
$530$	1735.39	+	4189.61i	0.142228	+	0.343368i
$531$		−	2425.42i		−	0.198219i
$532$	41138.2	−	17040.0i	3.35257	−	1.38868i
$533$	1737.89	−	4195.65i	0.141232	−	0.340964i
$534$	−7430.44	−	3077.79i	−0.602147	−	0.249417i
$535$	5646.45	−	5646.45i	0.456294	−	0.456294i
$536$	−5492.01	+	5492.01i	−0.442572	+	0.442572i
$537$	7039.98	+	2916.05i	0.565731	+	0.234333i
$538$	−529.872	+	1279.23i	−0.0424618	+	0.102512i
$539$	−16517.8	+	6841.89i	−1.31998	+	0.546755i
$540$		−	4660.59i		−	0.371407i
$541$	6020.15	+	14533.9i	0.478423	+	1.15501i	0.960348	+	0.278802i	$0.0899375\pi$
$541$	6020.15	+	14533.9i	0.478423	+	1.15501i	−0.481926	+	0.876212i	$0.660063\pi$
$542$	−1281.09	−	1281.09i	−0.101527	−	0.101527i
$543$	3068.91			0.242540
$544$	6103.27	−	15278.0i	0.481021	−	1.20411i
$545$	13666.8			1.07416
$546$	−10855.5	−	10855.5i	−0.850866	−	0.850866i
$547$	−4768.76	−	11512.8i	−0.372756	−	0.899913i	−0.993281	−	0.115726i	$-0.963081\pi$
$547$	−4768.76	−	11512.8i	−0.372756	−	0.899913i	0.620525	−	0.784187i	$-0.286919\pi$
$548$			3245.61i			0.253003i
$549$	3090.78	−	1280.24i	0.240276	−	0.0995254i
$550$	−4514.15	+	10898.1i	−0.349971	+	0.844904i
$551$	−17919.0	−	7422.29i	−1.38544	−	0.573866i
$552$	529.926	−	529.926i	0.0408607	−	0.0408607i
$553$	−2107.65	+	2107.65i	−0.162073	+	0.162073i
$554$	1898.32	+	786.311i	0.145581	+	0.0603017i
$555$	2695.23	−	6506.86i	0.206137	−	0.497659i
$556$	−19681.9	+	8152.51i	−1.50126	+	0.621841i
$557$		−	8819.07i		−	0.670873i	−0.942063	−	0.335436i	$-0.891116\pi$
$557$		−	8819.07i		−	0.670873i	0.942063	−	0.335436i	$-0.108884\pi$
$558$	151.497	+	365.747i	0.0114935	+	0.0277479i
$559$	13789.6	+	13789.6i	1.04336	+	1.04336i
$560$	−13936.5			−1.05165
$561$	2010.63	+	4685.70i	0.151317	+	0.352639i
$562$	−5989.95			−0.449592
$563$	8057.59	+	8057.59i	0.603174	+	0.603174i	0.941153	−	0.337980i	$-0.109744\pi$
$563$	8057.59	+	8057.59i	0.603174	+	0.603174i	−0.337980	+	0.941153i	$0.609744\pi$
$564$	4050.93	+	9779.81i	0.302438	+	0.730149i
$565$		−	29294.9i		−	2.18132i
$566$	−29010.7	+	12016.6i	−2.15443	+	0.892396i
$567$	−1018.83	+	2459.67i	−0.0754617	+	0.182181i
$568$	8996.35	+	3726.41i	0.664575	+	0.275276i
$569$	−7327.39	+	7327.39i	−0.539860	+	0.539860i	−0.923488	−	0.383628i	$-0.874675\pi$
$569$	−7327.39	+	7327.39i	−0.539860	+	0.539860i	0.383628	+	0.923488i	$0.374675\pi$
$570$	−17227.2	+	17227.2i	−1.26591	+	1.26591i
$571$	−7063.11	−	2925.63i	−0.517656	−	0.214420i	0.108531	−	0.994093i	$-0.465385\pi$
$571$	−7063.11	−	2925.63i	−0.517656	−	0.214420i	−0.626187	+	0.779673i	$0.715385\pi$
$572$	−3701.73	+	8936.78i	−0.270590	+	0.653261i
$573$	12144.0	−	5030.20i	0.885378	−	0.366735i
$574$		−	18444.3i		−	1.34120i
$575$	746.468	+	1802.13i	0.0541389	+	0.130703i
$576$	−5146.24	−	5146.24i	−0.372269	−	0.372269i
$577$	8346.67			0.602212			0.301106	−	0.953591i	$-0.402644\pi$
$577$	8346.67			0.602212			0.301106	+	0.953591i	$0.402644\pi$
$578$	−21542.3	+	544.675i	−1.55024	+	0.0391963i
$579$	8528.15			0.612121
$580$	−19638.6	−	19638.6i	−1.40594	−	1.40594i
$581$	−1899.57	−	4585.98i	−0.135641	−	0.327467i
$582$			6231.19i			0.443799i
$583$	−1507.98	+	624.624i	−0.107125	+	0.0443727i
$584$	−3116.90	+	7524.86i	−0.220853	+	0.533187i
$585$	4533.30	+	1877.76i	0.320392	+	0.132711i
$586$	−2386.02	+	2386.02i	−0.168201	+	0.168201i
$587$	2900.82	−	2900.82i	0.203968	−	0.203968i	−0.597729	−	0.801698i	$-0.703930\pi$
$587$	2900.82	−	2900.82i	0.203968	−	0.203968i	0.801698	+	0.597729i	$0.203930\pi$
$588$	−22966.6	−	9513.08i	−1.61076	−	0.667199i
$589$	462.625	−	1116.88i	0.0323636	−	0.0781325i
$590$	−16773.3	+	6947.73i	−1.17042	+	0.484802i
$591$		−	6400.91i		−	0.445513i
$592$	−1614.75	−	3898.35i	−0.112104	−	0.270644i
$593$	−14179.7	−	14179.7i	−0.981940	−	0.981940i	0.0178999	−	0.999840i	$-0.494302\pi$
$593$	−14179.7	−	14179.7i	−0.981940	−	0.981940i	−0.999840	+	0.0178999i	$0.994302\pi$
$594$	2871.62			0.198357
$595$	13953.5	+	32518.1i	0.961408	+	2.24052i
$596$	19575.6			1.34538
$597$	−4515.15	−	4515.15i	−0.309536	−	0.309536i
$598$	1047.87	+	2529.77i	0.0716562	+	0.172993i
$599$			96.8780i			0.00660822i	0.999995	+	0.00330411i	$0.00105173\pi$
$599$			96.8780i			0.00660822i	−0.999995	+	0.00330411i	$0.998948\pi$
$600$	−4366.36	+	1808.61i	−0.297093	+	0.123060i
$601$	7082.35	−	17098.3i	0.480690	−	1.16049i	−0.478591	−	0.878038i	$-0.658852\pi$
$601$	7082.35	−	17098.3i	0.480690	−	1.16049i	0.959282	−	0.282452i	$-0.0911476\pi$
$602$	73174.6	+	30309.9i	4.95411	+	2.05206i
$603$	−3479.88	+	3479.88i	−0.235011	+	0.235011i
$604$	16245.4	−	16245.4i	1.09440	−	1.09440i
$605$	10543.7	+	4367.34i	0.708533	+	0.293484i
$606$	3084.15	−	7445.79i	0.206741	−	0.499116i
$607$	−1862.54	+	771.490i	−0.124544	+	0.0515878i	−0.444085	−	0.895985i	$-0.646471\pi$
$607$	−1862.54	+	771.490i	−0.124544	+	0.0515878i	0.319541	+	0.947572i	$0.396471\pi$
$608$			28294.0i			1.88729i
$609$	6071.35	+	14657.5i	0.403979	+	0.975293i
$610$	−17707.3	−	17707.3i	−1.17533	−	1.17533i
$611$	−11144.8			−0.737925
$612$	−2630.06	+	6583.66i	−0.173715	+	0.434851i
$613$	26672.3			1.75740			0.878698	−	0.477378i	$-0.158413\pi$
$613$	26672.3			1.75740			0.878698	+	0.477378i	$0.158413\pi$
$614$	−1304.38	−	1304.38i	−0.0857337	−	0.0857337i
$615$	2255.98	+	5446.42i	0.147918	+	0.357107i
$616$			11320.5i			0.740448i
$617$	10628.3	−	4402.38i	0.693482	−	0.287250i	−0.00796782	−	0.999968i	$-0.502536\pi$
$617$	10628.3	−	4402.38i	0.693482	−	0.287250i	0.701450	+	0.712718i	$0.252536\pi$
$618$	−8802.12	+	21250.2i	−0.572934	+	1.38318i
$619$	28126.9	+	11650.6i	1.82636	+	0.756503i	0.971252	+	0.238052i	$0.0765089\pi$
$619$	28126.9	+	11650.6i	1.82636	+	0.756503i	0.855107	+	0.518451i	$0.173491\pi$
$620$	1224.05	−	1224.05i	0.0792891	−	0.0792891i
$621$	335.774	−	335.774i	0.0216975	−	0.0216975i
$622$	14396.0	+	5963.01i	0.928016	+	0.384397i
$623$	7687.94	−	18560.3i	0.494399	−	1.19359i
$624$	2715.97	−	1124.99i	0.174240	−	0.0721725i
$625$			17187.7i			1.10001i
$626$	10933.9	+	26396.8i	0.698095	+	1.68535i
$627$	−6200.63	−	6200.63i	−0.394943	−	0.394943i
$628$	−30784.1			−1.95608
$629$	−7479.29	+	7670.79i	−0.474116	+	0.486255i
$630$	19928.6			1.26028
$631$	−2083.53	−	2083.53i	−0.131449	−	0.131449i	0.638321	−	0.769770i	$-0.279629\pi$
$631$	−2083.53	−	2083.53i	−0.131449	−	0.131449i	−0.769770	+	0.638321i	$0.779629\pi$
$632$	492.932	+	1190.04i	0.0310250	+	0.0749010i
$633$		−	2273.84i		−	0.142776i
$634$	−23934.3	+	9913.90i	−1.49929	+	0.621027i
$635$	−4059.62	+	9800.80i	−0.253703	+	0.612493i
$636$	−2096.72	−	868.489i	−0.130724	−	0.0541475i
$637$	18506.5	−	18506.5i	1.15111	−	1.15111i
$638$	12100.3	−	12100.3i	0.750870	−	0.750870i
$639$	5700.31	+	2361.15i	0.352897	+	0.146175i
$640$	−9810.91	+	23685.6i	−0.605953	+	1.46290i
$641$	22435.1	−	9292.91i	1.38242	−	0.572618i	0.437293	−	0.899319i	$-0.355937\pi$
$641$	22435.1	−	9292.91i	1.38242	−	0.572618i	0.945128	+	0.326701i	$0.105937\pi$
$642$			6841.04i			0.420552i
$643$	392.931	+	948.619i	0.0240990	+	0.0581802i	0.935471	−	0.353404i	$-0.114976\pi$
$643$	392.931	+	948.619i	0.0240990	+	0.0581802i	−0.911372	+	0.411584i	$0.864976\pi$
$644$	4593.71	+	4593.71i	0.281083	+	0.281083i
$645$	−25315.1			−1.54540
$646$	34057.2	−	14613.9i	2.07425	−	0.890059i
$647$	−10184.4			−0.618839			−0.309419	−	0.950926i	$-0.600135\pi$
$647$	−10184.4			−0.618839			−0.309419	+	0.950926i	$0.600135\pi$
$648$	813.542	+	813.542i	0.0493194	+	0.0493194i
$649$	−2500.71	−	6037.26i	−0.151251	−	0.365151i
$650$		−	17267.9i		−	1.04201i
$651$	−913.592	+	378.422i	−0.0550023	+	0.0227827i
$652$	3014.39	−	7277.38i	0.181062	−	0.437123i
$653$	−19392.6	−	8032.67i	−1.16216	−	0.481383i	−0.283567	−	0.958953i	$-0.591518\pi$
$653$	−19392.6	−	8032.67i	−1.16216	−	0.481383i	−0.878594	+	0.477570i	$0.841518\pi$
$654$	−8279.08	+	8279.08i	−0.495012	+	0.495012i
$655$	−31706.3	+	31706.3i	−1.89140	+	1.89140i
$656$	3263.02	+	1351.59i	0.194207	+	0.0804431i
$657$	−1974.95	+	4767.94i	−0.117275	+	0.283128i
$658$	−41818.3	+	17321.7i	−2.47758	+	1.02625i
$659$			2158.18i			0.127573i	0.997964	+	0.0637866i	$0.0203177\pi$
$659$			2158.18i			0.127573i	−0.997964	+	0.0637866i	$0.979682\pi$
$660$	−4805.26	−	11600.9i	−0.283401	−	0.684190i
$661$	7849.97	+	7849.97i	0.461919	+	0.461919i	0.899284	−	0.437365i	$-0.144088\pi$
$661$	7849.97	+	7849.97i	0.461919	+	0.461919i	−0.437365	+	0.899284i	$0.644088\pi$
$662$	−38850.4			−2.28091
$663$	−5344.21	−	5210.79i	−0.313050	−	0.305234i
$664$	−2145.11			−0.125371
$665$	−43031.4	−	43031.4i	−2.50930	−	2.50930i
$666$	2309.02	+	5574.46i	0.134343	+	0.324334i
$667$		−	2829.74i		−	0.164270i
$668$	−6201.69	+	2568.82i	−0.359207	+	0.148789i
$669$	3455.86	−	8343.18i	0.199718	−	0.482162i
$670$	34033.7	+	14097.2i	1.96244	+	0.812871i
$671$	6373.45	−	6373.45i	0.366683	−	0.366683i
$672$	16365.4	−	16365.4i	0.939447	−	0.939447i
$673$	7115.94	+	2947.52i	0.407577	+	0.168824i	0.577046	−	0.816712i	$-0.304205\pi$
$673$	7115.94	+	2947.52i	0.407577	+	0.168824i	−0.169469	+	0.985536i	$0.554205\pi$
$674$	13772.6	−	33250.1i	0.787095	−	1.90022i
$675$	−2766.64	+	1145.98i	−0.157760	+	0.0653462i
$676$			10530.5i			0.599140i
$677$	−7334.40	−	17706.8i	−0.416372	−	1.00521i	−0.983390	−	0.181506i	$-0.941903\pi$
$677$	−7334.40	−	17706.8i	−0.416372	−	1.00521i	0.567017	−	0.823706i	$-0.308097\pi$
$678$	17746.3	+	17746.3i	1.00523	+	1.00523i
$679$	−15564.7			−0.879706
$680$	15290.5	−	193.272i	0.862301	−	0.0108995i
$681$	8624.54			0.485305
$682$	754.201	+	754.201i	0.0423458	+	0.0423458i
$683$	4270.16	+	10309.1i	0.239229	+	0.577549i	0.997203	−	0.0747346i	$-0.0238109\pi$
$683$	4270.16	+	10309.1i	0.239229	+	0.577549i	−0.757975	+	0.652284i	$0.773811\pi$
$684$		−	12192.6i		−	0.681573i
$685$	4098.10	−	1697.49i	0.228584	−	0.0946828i
$686$	21754.6	−	52520.3i	1.21078	−	2.92308i
$687$	11008.4	+	4559.82i	0.611348	+	0.253229i
$688$	−10724.4	+	10724.4i	−0.594280	+	0.594280i
$689$	1689.54	−	1689.54i	0.0934199	−	0.0934199i
$690$	−3283.92	−	1360.25i	−0.181184	−	0.0750488i
$691$	−8903.52	+	21495.0i	−0.490168	+	1.18337i	0.464467	+	0.885590i	$0.346246\pi$
$691$	−8903.52	+	21495.0i	−0.490168	+	1.18337i	−0.954635	+	0.297779i	$0.903754\pi$
$692$	−25853.7	+	10709.0i	−1.42025	+	0.588286i
$693$			7172.96i			0.393186i
$694$	−8605.45	−	20775.4i	−0.470689	−	1.13634i
$695$	20587.7	+	20587.7i	1.12365	+	1.12365i
$696$	6856.13			0.373392
$697$	−113.340	−	8966.84i	−0.00615936	−	0.487293i
$698$	−2309.09			−0.125215
$699$	−11279.1	−	11279.1i	−0.610324	−	0.610324i
$700$	−15678.1	−	37850.2i	−0.846535	−	2.04372i
$701$		−	12642.2i		−	0.681153i	−0.940217	−	0.340576i	$-0.889378\pi$
$701$		−	12642.2i		−	0.681153i	0.940217	−	0.340576i	$-0.110622\pi$
$702$	−3883.71	+	1608.68i	−0.208805	+	0.0864899i
$703$	7051.01	−	17022.6i	0.378284	−	0.913259i
$704$	−18115.8	−	7503.80i	−0.969836	−	0.401719i
$705$	10229.9	−	10229.9i	0.546496	−	0.546496i
$706$	7748.08	−	7748.08i	0.413035	−	0.413035i
$707$	18598.7	+	7703.82i	0.989357	+	0.409805i
$708$	3477.04	−	8394.31i	0.184569	−	0.445590i
$709$	6237.95	−	2583.84i	0.330425	−	0.136866i	−0.211303	−	0.977421i	$-0.567771\pi$
$709$	6237.95	−	2583.84i	0.330425	−	0.136866i	0.541727	+	0.840554i	$0.317771\pi$
$710$		−	46184.8i		−	2.44124i
$711$	312.334	+	754.042i	0.0164746	+	0.0397733i
$712$	−6138.88	−	6138.88i	−0.323124	−	0.323124i
$713$	176.375			0.00926410
$714$	−28151.6	−	11246.1i	−1.47556	−	0.589459i
$715$	13220.1			0.691476
$716$	20184.7	+	20184.7i	1.05355	+	1.05355i
$717$	749.857	+	1810.31i	0.0390571	+	0.0942921i
$718$			22851.3i			1.18775i
$719$	−5925.14	+	2454.27i	−0.307330	+	0.127300i	−0.531018	−	0.847360i	$-0.678190\pi$
$719$	−5925.14	+	2454.27i	−0.307330	+	0.127300i	0.223688	+	0.974661i	$0.428190\pi$
$720$	−1460.36	+	3525.62i	−0.0755895	+	0.182489i
$721$	−53080.4	−	21986.6i	−2.74177	−	1.13568i
$722$	−23795.1	+	23795.1i	−1.22654	+	1.22654i
$723$	1097.26	−	1097.26i	0.0564419	−	0.0564419i
$724$	10621.4	+	4399.52i	0.545222	+	0.225838i
$725$	−6829.05	+	16486.8i	−0.349827	+	0.844557i
$726$	−9032.85	+	3741.53i	−0.461764	+	0.191269i
$727$		−	5828.20i		−	0.297326i	−0.988888	−	0.148663i	$-0.952503\pi$
$727$		−	5828.20i		−	0.297326i	0.988888	−	0.148663i	$-0.0474970\pi$
$728$	−6341.76	−	15310.4i	−0.322859	−	0.779450i
$729$	515.481	+	515.481i	0.0261891	+	0.0261891i
$730$	38630.5			1.95860
$731$	35760.7	+	14285.8i	1.80938	+	0.722816i
$732$	12532.4			0.632803
$733$	8245.31	+	8245.31i	0.415481	+	0.415481i	0.883643	−	0.468162i	$-0.155084\pi$
$733$	8245.31	+	8245.31i	0.415481	+	0.415481i	−0.468162	+	0.883643i	$0.655084\pi$
$734$	8999.56	+	21726.9i	0.452561	+	1.09258i
$735$			33974.4i			1.70499i
$736$	−3813.79	+	1579.72i	−0.191003	+	0.0791161i
$737$	−5074.06	+	12249.9i	−0.253603	+	0.612251i
$738$	−4665.98	−	1932.71i	−0.232733	−	0.0964012i
$739$	−9261.33	+	9261.33i	−0.461006	+	0.461006i	−0.898985	−	0.437979i	$-0.855694\pi$
$739$	−9261.33	+	9261.33i	−0.461006	+	0.461006i	0.437979	+	0.898985i	$0.355694\pi$
$740$	18656.2	−	18656.2i	0.926778	−	0.926778i
$741$	11859.6	+	4912.41i	0.587954	+	0.243538i
$742$	3713.65	−	8965.53i	0.183736	−	0.443578i
$743$	14071.2	−	5828.48i	0.694781	−	0.287788i	−0.00720941	−	0.999974i	$-0.502295\pi$
$743$	14071.2	−	5828.48i	0.694781	−	0.287788i	0.701991	+	0.712186i	$0.252295\pi$
$744$			427.337i			0.0210577i
$745$	−10238.2	−	24717.3i	−0.503490	−	1.21553i
$746$	18874.2	+	18874.2i	0.926317	+	0.926317i
$747$	−1359.20			−0.0665735
$748$	241.416	+	19099.5i	0.0118009	+	0.933617i
$749$	−17088.1			−0.833625
$750$	−2013.53	−	2013.53i	−0.0980317	−	0.0980317i
$751$	−861.528	−	2079.91i	−0.0418610	−	0.101061i	0.901566	−	0.432641i	$-0.142418\pi$
$751$	−861.528	−	2079.91i	−0.0418610	−	0.101061i	−0.943427	+	0.331580i	$0.892418\pi$
$752$		−	8667.52i		−	0.420308i
$753$	12912.4	−	5348.50i	0.624907	−	0.258845i
$754$	−9586.38	+	23143.6i	−0.463018	+	1.11782i
$755$	−29008.8	−	12015.9i	−1.39833	−	0.579208i
$756$	−7052.26	+	7052.26i	−0.339270	+	0.339270i
$757$	−18222.9	+	18222.9i	−0.874929	+	0.874929i	−0.993005	−	0.118075i	$-0.962328\pi$
$757$	−18222.9	+	18222.9i	−0.874929	+	0.874929i	0.118075	+	0.993005i	$0.462328\pi$
$758$	−24691.1	−	10227.4i	−1.18314	−	0.490073i
$759$	489.597	−	1181.99i	0.0234140	−	0.0565264i
$760$	−24296.8	+	10064.1i	−1.15966	+	0.480345i
$761$			31638.6i			1.50709i	0.657395	+	0.753547i	$0.271659\pi$
$761$			31638.6i			1.50709i	−0.657395	+	0.753547i	$0.728341\pi$
$762$	−3477.90	−	8396.40i	−0.165343	−	0.399173i
$763$	−20680.1	−	20680.1i	−0.981220	−	0.981220i
$764$	49241.0			2.33178
$765$	9688.46	−	122.462i	0.457892	−	0.00578773i
$766$	−29859.3			−1.40843
$767$	6764.16	+	6764.16i	0.318435	+	0.318435i
$768$	−978.058	−	2361.24i	−0.0459540	−	0.110943i
$769$		−	31684.4i		−	1.48578i	−0.669412	−	0.742891i	$-0.733454\pi$
$769$		−	31684.4i		−	1.48578i	0.669412	−	0.742891i	$-0.266546\pi$
$770$	49605.4	−	20547.2i	2.32163	−	0.961650i
$771$	6041.23	−	14584.8i	0.282191	−	0.681270i
$772$	29515.6	+	12225.8i	1.37602	+	0.569968i
$773$	−16853.6	+	16853.6i	−0.784192	+	0.784192i	−0.980535	−	0.196343i	$-0.937093\pi$
$773$	−16853.6	+	16853.6i	−0.784192	+	0.784192i	0.196343	+	0.980535i	$0.437093\pi$
$774$	15335.4	−	15335.4i	0.712171	−	0.712171i
$775$	−1027.61	−	425.649i	−0.0476293	−	0.0197287i
$776$	−2574.04	+	6214.28i	−0.119076	+	0.287474i
$777$	−13924.3	+	5767.65i	−0.642899	+	0.266298i
$778$			20133.5i			0.927792i
$779$	5901.89	+	14248.4i	0.271447	+	0.655330i
$780$	12997.7	+	12997.7i	0.596657	+	0.596657i
$781$	16623.4			0.761629
$782$	3871.34	+	3774.70i	0.177032	+	0.172612i
$783$	4344.22			0.198275
$784$	14392.8	+	14392.8i	0.655650	+	0.655650i
$785$	16100.4	+	38869.8i	0.732036	+	1.76729i
$786$		−	38414.3i		−	1.74325i
$787$	−8050.64	+	3334.69i	−0.364644	+	0.151040i	−0.557479	−	0.830191i	$-0.688231\pi$
$787$	−8050.64	+	3334.69i	−0.364644	+	0.151040i	0.192836	+	0.981231i	$0.438231\pi$
$788$	9176.21	−	22153.3i	0.414834	−	1.00150i
$789$	−4387.91	−	1817.53i	−0.197990	−	0.0820100i
$790$	4319.97	−	4319.97i	0.194554	−	0.194554i
$791$	−44328.2	+	44328.2i	−1.99258	+	1.99258i
$792$	2863.83	+	1186.24i	0.128487	+	0.0532211i
$793$	−5049.33	+	12190.2i	−0.226112	+	0.545883i
$794$	−18601.8	+	7705.14i	−0.831429	+	0.344389i
$795$			3101.67i			0.138371i
$796$	−9153.96	−	22099.6i	−0.407605	−	0.984045i
$797$	−5085.49	−	5085.49i	−0.226019	−	0.226019i	0.585008	−	0.811027i	$-0.301091\pi$
$797$	−5085.49	−	5085.49i	−0.226019	−	0.226019i	−0.811027	+	0.585008i	$0.801091\pi$
$798$	52135.4			2.31275
$799$	−20223.9	+	8678.08i	−0.895457	+	0.384241i
$800$	26032.5			1.15049
$801$	−3889.75	−	3889.75i	−0.171582	−	0.171582i
$802$	−3015.60	−	7280.31i	−0.132774	−	0.320545i
$803$			13904.4i			0.611053i
$804$	−17032.4	+	7055.06i	−0.747123	+	0.309469i
$805$	3397.73	−	8202.84i	0.148763	−	0.359145i
$806$	−1442.52	−	597.511i	−0.0630404	−	0.0261122i
$807$	−669.659	+	669.659i	−0.0292108	+	0.0292108i
$808$	6151.56	−	6151.56i	0.267835	−	0.267835i
$809$	−17501.4	−	7249.30i	−0.760587	−	0.315046i	−0.0315342	−	0.999503i	$-0.510039\pi$
$809$	−17501.4	−	7249.30i	−0.760587	−	0.315046i	−0.729053	+	0.684457i	$0.760039\pi$
$810$	2088.25	−	5041.48i	0.0905847	−	0.218691i
$811$	15374.2	−	6368.21i	0.665675	−	0.275731i	−0.0241496	−	0.999708i	$-0.507688\pi$
$811$	15374.2	−	6368.21i	0.665675	−	0.275731i	0.689824	+	0.723977i	$0.257688\pi$
$812$			59433.0i			2.56858i
$813$	−474.211	−	1144.85i	−0.0204567	−	0.0493869i
$814$	11495.0	+	11495.0i	0.494963	+	0.494963i
$815$	−10765.4			−0.462694
$816$	4052.52	−	4156.28i	0.173856	−	0.178307i
$817$	−66227.0			−2.83597
$818$	−34622.7	−	34622.7i	−1.47990	−	1.47990i
$819$	−4018.30	−	9701.03i	−0.171442	−	0.413897i
$820$			22084.0i			0.940495i
$821$	−3307.09	+	1369.84i	−0.140583	+	0.0582312i	−0.451865	−	0.892086i	$-0.649241\pi$
$821$	−3307.09	+	1369.84i	−0.140583	+	0.0582312i	0.311283	+	0.950317i	$0.399241\pi$
$822$	−1454.25	+	3510.87i	−0.0617065	+	0.148973i
$823$	18390.8	+	7617.71i	0.778934	+	0.322645i	0.736485	−	0.676454i	$-0.236484\pi$
$823$	18390.8	+	7617.71i	0.778934	+	0.322645i	0.0424485	+	0.999099i	$0.486484\pi$
$824$	−17556.5	+	17556.5i	−0.742243	+	0.742243i
$825$	−5705.03	+	5705.03i	−0.240756	+	0.240756i
$826$	35894.0	+	14867.8i	1.51200	+	0.626290i
$827$	10540.9	−	25447.9i	0.443219	−	1.07002i	−0.531594	−	0.846999i	$-0.678407\pi$
$827$	10540.9	−	25447.9i	0.443219	−	1.07002i	0.974813	−	0.223025i	$-0.0715932\pi$
$828$	1643.46	−	680.744i	0.0689786	−	0.0285719i
$829$			3808.15i			0.159545i	0.996813	+	0.0797723i	$0.0254193\pi$
$829$			3808.15i			0.159545i	−0.996813	+	0.0797723i	$0.974581\pi$
$830$	3893.47	+	9399.68i	0.162825	+	0.393093i
$831$	993.749	+	993.749i	0.0414835	+	0.0414835i
$832$	28704.2			1.19608
$833$	19172.4	−	47993.1i	0.797460	−	1.99623i
$834$	−24943.3			−1.03563
$835$	6487.09	+	6487.09i	0.268856	+	0.268856i
$836$	−12571.1	−	30349.3i	−0.520071	−	1.25556i
$837$			270.771i			0.0111819i
$838$	17919.2	−	7422.38i	0.738674	−	0.305969i
$839$	11502.8	−	27770.3i	0.473327	−	1.14271i	−0.489356	−	0.872084i	$-0.662768\pi$
$839$	11502.8	−	27770.3i	0.473327	−	1.14271i	0.962684	−	0.270629i	$-0.0872318\pi$
$840$	19874.5	+	8232.30i	0.816353	+	0.338144i
$841$	1059.82	−	1059.82i	0.0434550	−	0.0434550i
$842$	−36873.3	+	36873.3i	−1.50919	+	1.50919i
$843$	−3785.08	−	1567.83i	−0.154644	−	0.0640558i
$844$	3259.74	−	7869.70i	0.132944	−	0.320955i
$845$	13296.4	−	5507.55i	0.541313	−	0.224219i
$846$			12394.2i			0.503688i
$847$	−9345.88	−	22563.0i	−0.379136	−	0.915316i
$848$	1313.98	+	1313.98i	0.0532103	+	0.0532103i
$849$	−21477.3			−0.868197
$850$	−13445.9	−	31335.1i	−0.542577	−	1.26445i
$851$	2688.19			0.108284
$852$	16343.7	+	16343.7i	0.657190	+	0.657190i
$853$	16507.4	+	39852.4i	0.662606	+	1.59967i	0.793705	+	0.608302i	$0.208149\pi$
$853$	16507.4	+	39852.4i	0.662606	+	1.59967i	−0.131100	+	0.991369i	$0.541851\pi$
$854$			53588.4i			2.14726i
$855$	−15395.1	+	6376.85i	−0.615790	+	0.255069i
$856$	−2825.96	+	6822.48i	−0.112838	+	0.272415i
$857$	21055.7	+	8721.57i	0.839265	+	0.347635i	0.760564	−	0.649263i	$-0.224923\pi$
$857$	21055.7	+	8721.57i	0.839265	+	0.347635i	0.0787016	+	0.996898i	$0.474923\pi$
$858$	−8008.53	+	8008.53i	−0.318656	+	0.318656i
$859$	34423.0	−	34423.0i	1.36729	−	1.36729i	0.502997	−	0.864288i	$-0.332231\pi$
$859$	34423.0	−	34423.0i	1.36729	−	1.36729i	0.864288	−	0.502997i	$-0.167769\pi$
$860$	−87614.6	−	36291.2i	−3.47399	−	1.43897i
$861$	4827.68	−	11655.0i	0.191088	−	0.461327i
$862$	10088.2	−	4178.69i	0.398616	−	0.165112i
$863$		−	29580.9i		−	1.16680i	−0.812187	−	0.583398i	$-0.801723\pi$
$863$		−	29580.9i		−	1.16680i	0.812187	−	0.583398i	$-0.198277\pi$
$864$	−2425.20	−	5854.94i	−0.0954940	−	0.230543i
$865$	27043.5	+	27043.5i	1.06302	+	1.06302i
$866$	−8054.93			−0.316071
$867$	−13755.3	−	5294.39i	−0.538816	−	0.207390i
$868$	−3704.41			−0.144857
$869$	1554.90	+	1554.90i	0.0606977	+	0.0606977i
$870$	−12444.2	−	30042.9i	−0.484939	−	1.17075i
$871$		−	19409.7i		−	0.755079i
$872$	−11676.6	+	4836.61i	−0.453463	+	0.187831i
$873$	−1630.98	+	3937.53i	−0.0632305	+	0.152652i
$874$	−8591.10	−	3558.55i	−0.332492	−	0.137723i
$875$	5029.56	−	5029.56i	0.194320	−	0.194320i
$876$	−13670.4	+	13670.4i	−0.527262	+	0.527262i
$877$	−37189.1	−	15404.2i	−1.43191	−	0.593117i	−0.474089	−	0.880477i	$-0.657222\pi$
$877$	−37189.1	−	15404.2i	−1.43191	−	0.593117i	−0.957823	+	0.287360i	$0.907222\pi$
$878$	6182.24	−	14925.3i	0.237632	−	0.573693i
$879$	−2132.27	+	883.215i	−0.0818199	+	0.0338909i
$880$			10281.5i			0.393852i
$881$	15006.5	+	36229.0i	0.573874	+	1.38546i	0.898232	+	0.439521i	$0.144852\pi$
$881$	15006.5	+	36229.0i	0.573874	+	1.38546i	−0.324358	+	0.945934i	$0.605148\pi$
$882$	−20581.1	−	20581.1i	−0.785716	−	0.785716i
$883$	−2775.62			−0.105784			−0.0528918	−	0.998600i	$-0.516844\pi$
$883$	−2775.62			−0.105784			−0.0528918	+	0.998600i	$0.516844\pi$
$884$	−11026.0	−	25695.7i	−0.419509	−	0.977648i
$885$	−12417.7			−0.471656
$886$	−51249.2	−	51249.2i	−1.94328	−	1.94328i
$887$	−8537.38	−	20611.1i	−0.323176	−	0.780216i	−0.999066	−	0.0432133i	$-0.986240\pi$
$887$	−8537.38	−	20611.1i	−0.323176	−	0.780216i	0.675890	−	0.737003i	$-0.263760\pi$
$888$			6513.17i			0.246135i
$889$	20973.2	−	8687.38i	0.791246	−	0.327745i
$890$	−15757.6	+	38042.3i	−0.593480	+	1.43279i
$891$	1814.59	+	751.629i	0.0682280	+	0.0282610i
$892$	23921.2	−	23921.2i	0.897917	−	0.897917i
$893$	26762.5	−	26762.5i	1.00288	−	1.00288i
$894$	21175.5	+	8771.17i	0.792185	+	0.328134i
$895$	14929.6	−	36043.2i	0.557588	−	1.34614i
$896$	50686.0	−	20994.8i	1.88984	−	0.782799i
$897$			1872.85i			0.0697131i
$898$	13129.4	+	31697.3i	0.487901	+	1.17790i
$899$	1140.96	+	1140.96i	0.0423284	+	0.0423284i
$900$	−11218.1			−0.415484
$901$	1750.33	−	4381.49i	0.0647190	−	0.162007i
$902$	−13607.0			−0.502289
$903$	38306.0	+	38306.0i	1.41168	+	1.41168i
$904$	10367.4	+	25029.0i	0.381431	+	0.920855i
$905$		−	15712.2i		−	0.577116i
$906$	24852.0	−	10294.1i	0.911318	−	0.377480i
$907$	−12777.8	+	30848.3i	−0.467783	+	1.12933i	0.497346	+	0.867552i	$0.334308\pi$
$907$	−12777.8	+	30848.3i	−0.467783	+	1.12933i	−0.965129	+	0.261775i	$0.915692\pi$
$908$	29849.2	+	12364.0i	1.09095	+	0.451886i
$909$	3897.78	−	3897.78i	0.142224	−	0.142224i
$910$	−55578.0	+	55578.0i	−2.02461	+	2.02461i
$911$	23350.5	+	9672.11i	0.849218	+	0.351758i	0.764482	−	0.644646i	$-0.222995\pi$
$911$	23350.5	+	9672.11i	0.849218	+	0.351758i	0.0847368	+	0.996403i	$0.472995\pi$
$912$	−3820.46	+	9223.41i	−0.138715	+	0.334888i
$913$	−3383.25	+	1401.39i	−0.122639	+	0.0507987i
$914$		−	14788.6i		−	0.535188i
$915$	−6554.58	−	15824.2i	−0.236817	−	0.571727i
$916$	31562.8	+	31562.8i	1.13850	+	1.13850i
$917$	95954.2			3.45549
$918$	−5794.92	+	5943.29i	−0.208345	+	0.213679i
$919$	33518.4			1.20312			0.601562	−	0.798826i	$-0.294545\pi$
$919$	33518.4			1.20312			0.601562	+	0.798826i	$0.294545\pi$
$920$	−2713.11	−	2713.11i	−0.0972267	−	0.0972267i
$921$	−482.832	−	1165.66i	−0.0172745	−	0.0417044i
$922$			27090.3i			0.967648i
$923$	−22482.2	+	9312.45i	−0.801746	+	0.332094i
$924$	−10283.0	+	24825.4i	−0.366110	+	0.883868i
$925$	−15662.1	−	6487.45i	−0.556720	−	0.230601i
$926$	42861.3	−	42861.3i	1.52107	−	1.52107i
$927$	−11124.2	+	11124.2i	−0.394140	+	0.394140i
$928$	−34890.4	−	14452.1i	−1.23420	−	0.511221i
$929$	−1130.85	+	2730.12i	−0.0399377	+	0.0964181i	−0.942590	−	0.333953i	$-0.891617\pi$
$929$	−1130.85	+	2730.12i	−0.0399377	+	0.0964181i	0.902652	+	0.430371i	$0.141617\pi$
$930$	1872.55	−	775.636i	0.0660251	−	0.0273485i
$931$			88880.7i			3.12884i
$932$	−22867.2	−	55206.2i	−0.803690	−	1.94028i
$933$	7536.12	+	7536.12i	0.264439	+	0.264439i
$934$	25808.0			0.904137
$935$	23989.8	−	10294.0i	0.839092	−	0.360054i
$936$	−4537.70			−0.158461
$937$	−10680.8	−	10680.8i	−0.372388	−	0.372388i	0.495958	−	0.868346i	$-0.334817\pi$
$937$	−10680.8	−	10680.8i	−0.372388	−	0.372388i	−0.868346	+	0.495958i	$0.834817\pi$
$938$	−30167.3	−	72830.4i	−1.05010	−	2.53518i
$939$			19542.2i			0.679165i
$940$	50070.6	−	20739.9i	1.73736	−	0.719640i
$941$	−17931.1	+	43289.5i	−0.621187	+	1.49968i	0.229124	+	0.973397i	$0.426414\pi$
$941$	−17931.1	+	43289.5i	−0.621187	+	1.49968i	−0.850311	+	0.526280i	$0.823586\pi$
$942$	−33300.0	−	13793.3i	−1.15178	−	0.477081i
$943$	−1591.05	+	1591.05i	−0.0549435	+	0.0549435i
$944$	−5260.59	+	5260.59i	−0.181375	+	0.181375i
$945$	12593.0	+	5216.19i	0.433493	+	0.179558i
$946$	22360.8	−	53983.7i	0.768512	−	1.85535i
$947$	−30143.3	+	12485.7i	−1.03434	+	0.428440i	−0.834279	−	0.551343i	$-0.814116\pi$
$947$	−30143.3	+	12485.7i	−1.03434	+	0.428440i	−0.200066	+	0.979782i	$0.564116\pi$
$948$			3057.47i			0.104749i
$949$	−7789.26	−	18804.9i	−0.266438	−	0.643239i
$950$	41466.0	+	41466.0i	1.41614	+	1.41614i
$951$	−17719.1			−0.604187
$952$	−23429.6	−	22844.7i	−0.797646	−	0.777733i
$953$	−20967.3			−0.712693			−0.356347	−	0.934354i	$-0.615978\pi$
$953$	−20967.3			−0.712693			−0.356347	+	0.934354i	$0.615978\pi$
$954$	−1878.93	−	1878.93i	−0.0637660	−	0.0637660i
$955$	−25753.6	−	62174.6i	−0.872634	−	2.10673i
$956$			7340.41i			0.248333i
$957$	10813.4	−	4479.07i	0.365254	−	0.151293i
$958$	7780.22	−	18783.1i	0.262388	−	0.633460i
$959$	−8769.71	−	3632.53i	−0.295296	−	0.122316i
$960$	−26347.7	+	26347.7i	−0.885800	+	0.885800i
$961$	20994.3	−	20994.3i	0.704720	−	0.704720i
$962$	−21985.9	−	9106.85i	−0.736854	−	0.305215i
$963$	−1790.60	+	4322.89i	−0.0599183	+	0.144656i
$964$	5370.58	−	2224.57i	0.179434	−	0.0743241i
$965$		−	43662.4i		−	1.45652i
$966$	2910.85	+	7027.42i	0.0969515	+	0.234062i
$967$	8726.06	+	8726.06i	0.290187	+	0.290187i	0.837154	−	0.546967i	$-0.184218\pi$
$967$	8726.06	+	8726.06i	0.290187	+	0.290187i	−0.546967	+	0.837154i	$0.684218\pi$
$968$	−10553.9			−0.350430
$969$	25346.1	−	320.373i	0.840282	−	0.0106211i
$970$	31902.4			1.05600
$971$	−5672.65	−	5672.65i	−0.187481	−	0.187481i	0.607125	−	0.794606i	$-0.292323\pi$
$971$	−5672.65	−	5672.65i	−0.187481	−	0.187481i	−0.794606	+	0.607125i	$0.792323\pi$
$972$	1045.08	+	2523.04i	0.0344865	+	0.0832579i
$973$		−	62305.3i		−	2.05284i
$974$	−70286.8	+	29113.8i	−2.31225	+	0.957767i
$975$	4519.78	−	10911.7i	0.148460	−	0.358415i
$976$	−9480.48	−	3926.94i	−0.310925	−	0.128789i
$977$	17438.5	−	17438.5i	0.571042	−	0.571042i	−0.361377	−	0.932420i	$-0.617693\pi$
$977$	17438.5	−	17438.5i	0.571042	−	0.571042i	0.932420	+	0.361377i	$0.117693\pi$
$978$	6521.49	−	6521.49i	0.213225	−	0.213225i
$979$	−13692.7	−	5671.69i	−0.447007	−	0.185156i
$980$	−48705.0	+	117584.i	−1.58758	+	3.83275i
$981$	−7398.60	+	3064.60i	−0.240794	+	0.0997402i
$982$		−	75649.3i		−	2.45832i
$983$	9747.59	+	23532.8i	0.316276	+	0.763559i	0.999445	+	0.0332985i	$0.0106012\pi$
$983$	9747.59	+	23532.8i	0.316276	+	0.763559i	−0.683169	+	0.730260i	$0.739399\pi$
$984$	−3854.93	−	3854.93i	−0.124889	−	0.124889i
$985$	−32771.3			−1.06008
$986$	625.196	+	49461.9i	0.0201930	+	1.59755i
$987$	−30959.1			−0.998419
$988$	34003.4	+	34003.4i	1.09493	+	1.09493i
$989$	−3697.62	−	8926.85i	−0.118885	−	0.287015i
$990$		−	14702.1i		−	0.471983i
$991$	24184.4	−	10017.5i	0.775218	−	0.321106i	0.0402342	−	0.999190i	$-0.487190\pi$
$991$	24184.4	−	10017.5i	0.775218	−	0.321106i	0.734984	+	0.678084i	$0.237190\pi$
$992$	900.787	−	2174.69i	0.0288307	−	0.0696033i
$993$	−24549.8	−	10168.9i	−0.784556	−	0.324974i
$994$	−69885.4	+	69885.4i	−2.23001	+	2.23001i
$995$	−23116.7	+	23116.7i	−0.736530	+	0.736530i
$996$	−4704.13	−	1948.52i	−0.149655	−	0.0619890i
$997$	−5625.82	+	13581.9i	−0.178708	+	0.431438i	−0.987696	−	0.156386i	$-0.950016\pi$
$997$	−5625.82	+	13581.9i	−0.178708	+	0.431438i	0.808988	+	0.587825i	$0.200016\pi$
$998$	−1013.86	+	419.955i	−0.0321576	+	0.0133201i
$999$			4126.91i			0.130700i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.4.h.a.49.9	yes	40
3.2	odd	2		153.4.l.c.100.2		40
17.5	odd	16		867.4.a.v.1.3		20
17.8	even	8	inner	51.4.h.a.25.9	✓	40
17.12	odd	16		867.4.a.w.1.3		20
51.8	odd	8		153.4.l.c.127.2		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.4.h.a.25.9	✓	40	17.8	even	8	inner
51.4.h.a.49.9	yes	40	1.1	even	1	trivial
153.4.l.c.100.2		40	3.2	odd	2
153.4.l.c.127.2		40	51.8	odd	8
867.4.a.v.1.3		20	17.5	odd	16
867.4.a.w.1.3		20	17.12	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+(3.10148 + 3.10148i) q^{2} +(1.14805 + 2.77164i) q^{3} +11.2384i q^{4} +(14.1902 - 5.87778i) q^{5} +(-5.03553 + 12.1568i) q^{6} +(-30.3663 - 12.5781i) q^{7} +(-10.0437 + 10.0437i) q^{8} +(-6.36396 + 6.36396i) q^{9} +(62.2405 + 25.7809i) q^{10} +(-9.27937 + 22.4024i) q^{11} +(-31.1487 + 12.9022i) q^{12} -35.4963i q^{13} +(-55.1697 - 133.191i) q^{14} +(32.5822 + 32.5822i) q^{15} +27.6061 q^{16} +(-27.6397 - 64.4131i) q^{17} -39.4754 q^{18} +(85.2385 + 85.2385i) q^{19} +(66.0566 + 159.475i) q^{20} -98.6047i q^{21} +(-98.2604 + 40.7008i) q^{22} +(-6.73036 + 16.2485i) q^{23} +(-39.3683 - 16.3069i) q^{24} +(78.4256 - 78.4256i) q^{25} +(110.091 - 110.091i) q^{26} +(-24.9447 - 10.3325i) q^{27} +(141.358 - 341.268i) q^{28} +(-148.649 + 61.5726i) q^{29} +202.106i q^{30} +(-3.83777 - 9.26519i) q^{31} +(165.969 + 165.969i) q^{32} -72.7445 q^{33} +(114.052 - 285.500i) q^{34} -504.836 q^{35} +(-71.5205 - 71.5205i) q^{36} +(-58.4926 - 141.214i) q^{37} +528.731i q^{38} +(98.3830 - 40.7516i) q^{39} +(-83.4879 + 201.558i) q^{40} +(118.200 + 48.9599i) q^{41} +(305.821 - 305.821i) q^{42} +(-388.481 + 388.481i) q^{43} +(-251.766 - 104.285i) q^{44} +(-52.9000 + 127.712i) q^{45} +(-71.2686 + 29.5204i) q^{46} -313.972i q^{47} +(31.6931 + 76.5140i) q^{48} +(521.365 + 521.365i) q^{49} +486.471 q^{50} +(146.798 - 150.557i) q^{51} +398.921 q^{52} +(47.5976 + 47.5976i) q^{53} +(-45.3198 - 109.412i) q^{54} +372.437i q^{55} +(431.322 - 178.660i) q^{56} +(-138.392 + 334.108i) q^{57} +(-651.999 - 270.067i) q^{58} +(-190.559 + 190.559i) q^{59} +(-366.170 + 366.170i) q^{60} +(-343.420 - 142.249i) q^{61} +(16.8330 - 40.6386i) q^{62} +(273.297 - 113.203i) q^{63} +808.654i q^{64} +(-208.640 - 503.700i) q^{65} +(-225.616 - 225.616i) q^{66} +546.810 q^{67} +(723.898 - 310.625i) q^{68} -52.7618 q^{69} +(-1565.74 - 1565.74i) q^{70} +(-262.350 - 633.368i) q^{71} -127.836i q^{72} +(529.771 - 219.438i) q^{73} +(256.558 - 619.385i) q^{74} +(307.404 + 127.331i) q^{75} +(-957.941 + 957.941i) q^{76} +(563.561 - 563.561i) q^{77} +(431.523 + 178.743i) q^{78} +(34.7038 - 83.7824i) q^{79} +(391.736 - 162.262i) q^{80} -81.0000i q^{81} +(214.746 + 518.442i) q^{82} +(106.789 + 106.789i) q^{83} +1108.16 q^{84} +(-770.819 - 751.576i) q^{85} -2409.73 q^{86} +(-341.314 - 341.314i) q^{87} +(-131.804 - 318.203i) q^{88} +611.215i q^{89} +(-560.165 + 232.028i) q^{90} +(-446.477 + 1077.89i) q^{91} +(-182.607 - 75.6382i) q^{92} +(21.2738 - 21.2738i) q^{93} +(973.777 - 973.777i) q^{94} +(1710.56 + 708.539i) q^{95} +(-269.466 + 650.549i) q^{96} +(437.503 - 181.220i) q^{97} +3234.01i q^{98} +(-83.5144 - 201.622i) 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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