LMFDB - Embedded newform 105.4.d.a.64.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(64,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("105.64");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.d (of order $2$, degree $1$, 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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.84052224.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 6x^{3} + 36x^{2} - 36x + 18 $ x^6 - 2x^5 + 2x^4 + 6x^3 + 36x^2 - 36*x + 18
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.2
Root			$2.09148 - 2.09148i$ of defining polynomial
Character	$\chi$	$=$	105.64
Dual form			105.4.d.a.64.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.18296i q^{2} +3.00000i q^{3} -2.13122 q^{4} +(-11.0627 - 1.61735i) q^{5} +9.54887 q^{6} -7.00000i q^{7} -18.6801i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-3.18296i q^{2} +3.00000i q^{3} -2.13122 q^{4} +(-11.0627 - 1.61735i) q^{5} +9.54887 q^{6} -7.00000i q^{7} -18.6801i q^{8} -9.00000 q^{9} +(-5.14795 + 35.2122i) q^{10} -68.7204 q^{11} -6.39365i q^{12} -56.2290i q^{13} -22.2807 q^{14} +(4.85205 - 33.1882i) q^{15} -76.5076 q^{16} +37.9780i q^{17} +28.6466i q^{18} +26.0335 q^{19} +(23.5771 + 3.44692i) q^{20} +21.0000 q^{21} +218.734i q^{22} -25.5222i q^{23} +56.0403 q^{24} +(119.768 + 35.7846i) q^{25} -178.974 q^{26} -27.0000i q^{27} +14.9185i q^{28} -148.336 q^{29} +(-105.637 - 15.4439i) q^{30} +75.7982 q^{31} +94.0799i q^{32} -206.161i q^{33} +120.882 q^{34} +(-11.3214 + 77.4392i) q^{35} +19.1809 q^{36} +120.199i q^{37} -82.8634i q^{38} +168.687 q^{39} +(-30.2122 + 206.653i) q^{40} +345.670 q^{41} -66.8421i q^{42} -287.989i q^{43} +146.458 q^{44} +(99.5646 + 14.5561i) q^{45} -81.2360 q^{46} -528.711i q^{47} -229.523i q^{48} -49.0000 q^{49} +(113.901 - 381.218i) q^{50} -113.934 q^{51} +119.836i q^{52} -361.728i q^{53} -85.9398 q^{54} +(760.235 + 111.145i) q^{55} -130.761 q^{56} +78.1004i q^{57} +472.146i q^{58} +705.748 q^{59} +(-10.3408 + 70.7313i) q^{60} -393.171 q^{61} -241.262i q^{62} +63.0000i q^{63} -312.609 q^{64} +(-90.9419 + 622.046i) q^{65} -656.202 q^{66} +591.202i q^{67} -80.9393i q^{68} +76.5666 q^{69} +(246.486 + 36.0357i) q^{70} -668.829 q^{71} +168.121i q^{72} +251.755i q^{73} +382.588 q^{74} +(-107.354 + 359.305i) q^{75} -55.4830 q^{76} +481.042i q^{77} -536.923i q^{78} -295.651 q^{79} +(846.384 + 123.740i) q^{80} +81.0000 q^{81} -1100.25i q^{82} +916.511i q^{83} -44.7555 q^{84} +(61.4237 - 420.141i) q^{85} -916.658 q^{86} -445.007i q^{87} +1283.70i q^{88} +736.838 q^{89} +(46.3316 - 316.910i) q^{90} -393.603 q^{91} +54.3933i q^{92} +227.395i q^{93} -1682.86 q^{94} +(-288.002 - 42.1052i) q^{95} -282.240 q^{96} -142.964i q^{97} +155.965i q^{98} +618.483 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 14 q^{5} - 6 q^{6} - 54 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 14 * q^5 - 6 * q^6 - 54 * q^9	$ 6 q - 6 q^{4} - 14 q^{5} - 6 q^{6} - 54 q^{9} - 84 q^{10} - 132 q^{11} + 14 q^{14} - 24 q^{15} - 138 q^{16} + 276 q^{19} + 334 q^{20} + 126 q^{21} + 126 q^{24} + 366 q^{25} - 196 q^{26} - 340 q^{29} - 54 q^{30} - 732 q^{31} + 72 q^{34} + 56 q^{35} + 54 q^{36} + 612 q^{39} + 12 q^{40} - 412 q^{41} + 612 q^{44} + 126 q^{45} - 1344 q^{46} - 294 q^{49} + 1216 q^{50} - 912 q^{51} + 54 q^{54} + 1860 q^{55} - 294 q^{56} + 1760 q^{59} + 624 q^{60} - 1740 q^{61} + 1626 q^{64} - 16 q^{65} - 1116 q^{66} - 1080 q^{69} + 126 q^{70} - 2036 q^{71} - 1960 q^{74} + 936 q^{75} - 900 q^{76} + 3240 q^{79} + 3794 q^{80} + 486 q^{81} - 126 q^{84} + 432 q^{85} - 5864 q^{86} + 3876 q^{89} + 756 q^{90} - 1428 q^{91} - 4224 q^{94} - 828 q^{95} + 906 q^{96} + 1188 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 14 * q^5 - 6 * q^6 - 54 * q^9 - 84 * q^10 - 132 * q^11 + 14 * q^14 - 24 * q^15 - 138 * q^16 + 276 * q^19 + 334 * q^20 + 126 * q^21 + 126 * q^24 + 366 * q^25 - 196 * q^26 - 340 * q^29 - 54 * q^30 - 732 * q^31 + 72 * q^34 + 56 * q^35 + 54 * q^36 + 612 * q^39 + 12 * q^40 - 412 * q^41 + 612 * q^44 + 126 * q^45 - 1344 * q^46 - 294 * q^49 + 1216 * q^50 - 912 * q^51 + 54 * q^54 + 1860 * q^55 - 294 * q^56 + 1760 * q^59 + 624 * q^60 - 1740 * q^61 + 1626 * q^64 - 16 * q^65 - 1116 * q^66 - 1080 * q^69 + 126 * q^70 - 2036 * q^71 - 1960 * q^74 + 936 * q^75 - 900 * q^76 + 3240 * q^79 + 3794 * q^80 + 486 * q^81 - 126 * q^84 + 432 * q^85 - 5864 * q^86 + 3876 * q^89 + 756 * q^90 - 1428 * q^91 - 4224 * q^94 - 828 * q^95 + 906 * q^96 + 1188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	3.18296i		−	1.12535i	−0.826680	−	0.562673i	$-0.809773\pi$
$2$		−	3.18296i		−	1.12535i	0.826680	−	0.562673i	$-0.190227\pi$
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−2.13122			−0.266402
$5$	−11.0627	−	1.61735i	−0.989481	−	0.144660i
$5$	−11.0627	−	1.61735i	−0.989481	−	0.144660i
$6$	9.54887			0.649718
$7$		−	7.00000i		−	0.377964i
$7$		−	7.00000i		−	0.377964i
$8$		−	18.6801i		−	0.825551i
$9$	−9.00000			−0.333333
$10$	−5.14795	+	35.2122i	−0.162793	+	1.11351i
$11$	−68.7204			−1.88363			−0.941817	−	0.336127i	$-0.890883\pi$
$11$	−68.7204			−1.88363			−0.941817	+	0.336127i	$0.890883\pi$
$12$		−	6.39365i		−	0.153807i
$13$		−	56.2290i		−	1.19962i	−0.800141	−	0.599812i	$-0.795242\pi$
$13$		−	56.2290i		−	1.19962i	0.800141	−	0.599812i	$-0.204758\pi$
$14$	−22.2807			−0.425341
$15$	4.85205	−	33.1882i	0.0835195	−	0.571277i
$16$	−76.5076			−1.19543
$17$			37.9780i			0.541825i	0.962604	+	0.270912i	$0.0873253\pi$
$17$			37.9780i			0.541825i	−0.962604	+	0.270912i	$0.912675\pi$
$18$			28.6466i			0.375115i
$19$	26.0335			0.314341			0.157171	−	0.987571i	$-0.449763\pi$
$19$	26.0335			0.314341			0.157171	+	0.987571i	$0.449763\pi$
$20$	23.5771	+	3.44692i	0.263600	+	0.0385377i
$21$	21.0000			0.218218
$22$			218.734i			2.11974i
$23$		−	25.5222i		−	0.231380i	−0.993285	−	0.115690i	$-0.963092\pi$
$23$		−	25.5222i		−	0.231380i	0.993285	−	0.115690i	$-0.0369079\pi$
$24$	56.0403			0.476632
$25$	119.768	+	35.7846i	0.958147	+	0.286277i
$26$	−178.974			−1.34999
$27$		−	27.0000i		−	0.192450i
$28$			14.9185i			0.100690i
$29$	−148.336			−0.949835			−0.474917	−	0.880030i	$-0.657522\pi$
$29$	−148.336			−0.949835			−0.474917	+	0.880030i	$0.657522\pi$
$30$	−105.637	−	15.4439i	−0.642884	−	0.0939883i
$31$	75.7982			0.439153			0.219577	−	0.975595i	$-0.429532\pi$
$31$	75.7982			0.439153			0.219577	+	0.975595i	$0.429532\pi$
$32$			94.0799i			0.519723i
$33$		−	206.161i		−	1.08752i
$34$	120.882			0.609740
$35$	−11.3214	+	77.4392i	−0.0546764	+	0.373989i
$36$	19.1809			0.0888007
$37$			120.199i			0.534070i	0.963687	+	0.267035i	$0.0860439\pi$
$37$			120.199i			0.534070i	−0.963687	+	0.267035i	$0.913956\pi$
$38$		−	82.8634i		−	0.353743i
$39$	168.687			0.692603
$40$	−30.2122	+	206.653i	−0.119424	+	0.816867i
$41$	345.670			1.31670			0.658348	−	0.752713i	$-0.271255\pi$
$41$	345.670			1.31670			0.658348	+	0.752713i	$0.271255\pi$
$42$		−	66.8421i		−	0.245570i
$43$		−	287.989i		−	1.02135i	−0.859774	−	0.510674i	$-0.829396\pi$
$43$		−	287.989i		−	1.02135i	0.859774	−	0.510674i	$-0.170604\pi$
$44$	146.458			0.501804
$45$	99.5646	+	14.5561i	0.329827	+	0.0482200i
$46$	−81.2360			−0.260383
$47$		−	528.711i		−	1.64086i	−0.571747	−	0.820430i	$-0.693734\pi$
$47$		−	528.711i		−	1.64086i	0.571747	−	0.820430i	$-0.306266\pi$
$48$		−	229.523i		−	0.690183i
$49$	−49.0000			−0.142857
$50$	113.901	−	381.218i	0.322160	−	1.07825i
$51$	−113.934			−0.312823
$52$			119.836i			0.319582i
$53$		−	361.728i		−	0.937493i	−0.883333	−	0.468747i	$-0.844706\pi$
$53$		−	361.728i		−	0.937493i	0.883333	−	0.468747i	$-0.155294\pi$
$54$	−85.9398			−0.216573
$55$	760.235	+	111.145i	1.86382	+	0.272487i
$56$	−130.761			−0.312029
$57$			78.1004i			0.181485i
$58$			472.146i			1.06889i
$59$	705.748			1.55730			0.778649	−	0.627460i	$-0.215905\pi$
$59$	705.748			1.55730			0.778649	+	0.627460i	$0.215905\pi$
$60$	−10.3408	+	70.7313i	−0.0222498	+	0.152189i
$61$	−393.171			−0.825253			−0.412627	−	0.910900i	$-0.635389\pi$
$61$	−393.171			−0.825253			−0.412627	+	0.910900i	$0.635389\pi$
$62$		−	241.262i		−	0.494199i
$63$			63.0000i			0.125988i
$64$	−312.609			−0.610564
$65$	−90.9419	+	622.046i	−0.173538	+	1.18701i
$66$	−656.202			−1.22383
$67$			591.202i			1.07801i	0.842302	+	0.539006i	$0.181200\pi$
$67$			591.202i			1.07801i	−0.842302	+	0.539006i	$0.818800\pi$
$68$		−	80.9393i		−	0.144343i
$69$	76.5666			0.133587
$70$	246.486	+	36.0357i	0.420867	+	0.0615298i
$71$	−668.829			−1.11796			−0.558981	−	0.829180i	$-0.688808\pi$
$71$	−668.829			−1.11796			−0.558981	+	0.829180i	$0.688808\pi$
$72$			168.121i			0.275184i
$73$			251.755i			0.403639i	0.979423	+	0.201819i	$0.0646854\pi$
$73$			251.755i			0.403639i	−0.979423	+	0.201819i	$0.935315\pi$
$74$	382.588			0.601013
$75$	−107.354	+	359.305i	−0.165282	+	0.553186i
$76$	−55.4830			−0.0837412
$77$			481.042i			0.711946i
$78$		−	536.923i		−	0.779418i
$79$	−295.651			−0.421054			−0.210527	−	0.977588i	$-0.567518\pi$
$79$	−295.651			−0.421054			−0.210527	+	0.977588i	$0.567518\pi$
$80$	846.384	+	123.740i	1.18286	+	0.172931i
$81$	81.0000			0.111111
$82$		−	1100.25i		−	1.48174i
$83$			916.511i			1.21205i	0.795445	+	0.606025i	$0.207237\pi$
$83$			916.511i			1.21205i	−0.795445	+	0.606025i	$0.792763\pi$
$84$	−44.7555			−0.0581337
$85$	61.4237	−	420.141i	0.0783804	−	0.536125i
$86$	−916.658			−1.14937
$87$		−	445.007i		−	0.548387i
$88$			1283.70i			1.55504i
$89$	736.838			0.877580			0.438790	−	0.898590i	$-0.355407\pi$
$89$	736.838			0.877580			0.438790	+	0.898590i	$0.355407\pi$
$90$	46.3316	−	316.910i	0.0542642	−	0.371169i
$91$	−393.603			−0.453415
$92$			54.3933i			0.0616401i
$93$			227.395i			0.253545i
$94$	−1682.86			−1.84653
$95$	−288.002	−	42.1052i	−0.311035	−	0.0454727i
$96$	−282.240			−0.300062
$97$		−	142.964i		−	0.149647i	−0.997197	−	0.0748236i	$-0.976161\pi$
$97$		−	142.964i		−	0.149647i	0.997197	−	0.0748236i	$-0.0238394\pi$
$98$			155.965i			0.160764i
$99$	618.483			0.627878
$100$	−255.252	−	76.2648i	−0.255252	−	0.0762648i
$101$	−566.067			−0.557681			−0.278840	−	0.960337i	$-0.589950\pi$
$101$	−566.067			−0.557681			−0.278840	+	0.960337i	$0.589950\pi$
$102$			362.647i			0.352033i
$103$		−	1340.79i		−	1.28264i	−0.767275	−	0.641318i	$-0.778388\pi$
$103$		−	1340.79i		−	1.28264i	0.767275	−	0.641318i	$-0.221612\pi$
$104$	−1050.36			−0.990351
$105$	−232.318	−	33.9643i	−0.215923	−	0.0315674i
$106$	−1151.36			−1.05500
$107$		−	1637.85i		−	1.47978i	−0.672727	−	0.739891i	$-0.734877\pi$
$107$		−	1637.85i		−	1.47978i	0.672727	−	0.739891i	$-0.265123\pi$
$108$			57.5428i			0.0512691i
$109$	586.693			0.515550			0.257775	−	0.966205i	$-0.417011\pi$
$109$	586.693			0.515550			0.257775	+	0.966205i	$0.417011\pi$
$110$	353.769	−	2419.80i	0.306641	−	2.09744i
$111$	−360.597			−0.308345
$112$			535.554i			0.451831i
$113$			1617.17i			1.34629i	0.739509	+	0.673146i	$0.235058\pi$
$113$			1617.17i			1.34629i	−0.739509	+	0.673146i	$0.764942\pi$
$114$	248.590			0.204233
$115$	−41.2783	+	282.345i	−0.0334715	+	0.228946i
$116$	316.135			0.253038
$117$			506.061i			0.399875i
$118$		−	2246.37i		−	1.75250i
$119$	265.846			0.204790
$120$	−619.959	−	90.6367i	−0.471619	−	0.0689496i
$121$	3391.49			2.54807
$122$			1251.45i			0.928695i
$123$			1037.01i			0.760195i
$124$	−161.542			−0.116991
$125$	−1267.09	−	589.583i	−0.906656	−	0.421871i
$126$	200.526			0.141780
$127$		−	2042.94i		−	1.42741i	−0.700446	−	0.713706i	$-0.747015\pi$
$127$		−	2042.94i		−	1.42741i	0.700446	−	0.713706i	$-0.252985\pi$
$128$			1747.66i			1.20682i
$129$	863.968			0.589675
$130$	1979.95	+	289.464i	1.33579	+	0.195290i
$131$	−2631.04			−1.75477			−0.877384	−	0.479788i	$-0.840714\pi$
$131$	−2631.04			−1.75477			−0.877384	+	0.479788i	$0.840714\pi$
$132$			439.374i			0.289716i
$133$		−	182.234i		−	0.118810i
$134$	1881.77			1.21314
$135$	−43.6684	+	298.694i	−0.0278398	+	0.190426i
$136$	709.432			0.447304
$137$		−	1588.54i		−	0.990641i	−0.868710	−	0.495320i	$-0.835051\pi$
$137$		−	1588.54i		−	0.990641i	0.868710	−	0.495320i	$-0.164949\pi$
$138$		−	243.708i		−	0.150332i
$139$	−1733.49			−1.05779			−0.528894	−	0.848688i	$-0.677393\pi$
$139$	−1733.49			−1.05779			−0.528894	+	0.848688i	$0.677393\pi$
$140$	24.1284	−	165.040i	0.0145659	−	0.0996314i
$141$	1586.13			0.947351
$142$			2128.85i			1.25809i
$143$			3864.07i			2.25965i
$144$	688.569			0.398477
$145$	1641.00	+	239.910i	0.939844	+	0.137403i
$146$	801.324			0.454233
$147$		−	147.000i		−	0.0824786i
$148$		−	256.170i		−	0.142277i
$149$	1370.68			0.753629			0.376815	−	0.926289i	$-0.377019\pi$
$149$	1370.68			0.753629			0.376815	+	0.926289i	$0.377019\pi$
$150$	1143.65	+	341.703i	0.622526	+	0.185999i
$151$	−3694.08			−1.99086			−0.995429	−	0.0955015i	$-0.969555\pi$
$151$	−3694.08			−1.99086			−0.995429	+	0.0955015i	$0.969555\pi$
$152$		−	486.308i		−	0.259505i
$153$		−	341.802i		−	0.180608i
$154$	1531.14			0.801186
$155$	−838.536	−	122.592i	−0.434534	−	0.0635280i
$156$	−359.508			−0.184511
$157$		−	1054.56i		−	0.536071i	−0.963409	−	0.268036i	$-0.913626\pi$
$157$		−	1054.56i		−	0.536071i	0.963409	−	0.268036i	$-0.0863745\pi$
$158$			941.044i			0.473832i
$159$	1085.18			0.541262
$160$	152.160	−	1040.78i	0.0751831	−	0.514256i
$161$	−178.655			−0.0874535
$162$		−	257.820i		−	0.125038i
$163$		−	1380.12i		−	0.663185i	−0.943423	−	0.331593i	$-0.892414\pi$
$163$		−	1380.12i		−	0.663185i	0.943423	−	0.331593i	$-0.107586\pi$
$164$	−736.697			−0.350771
$165$	−333.434	+	2280.71i	−0.157320	+	1.07608i
$166$	2917.22			1.36398
$167$			3143.10i			1.45641i	0.685359	+	0.728205i	$0.259645\pi$
$167$			3143.10i			1.45641i	−0.685359	+	0.728205i	$0.740355\pi$
$168$		−	392.282i		−	0.180150i
$169$	−964.696			−0.439097
$170$	−1337.29	−	195.509i	−0.603326	−	0.0882050i
$171$	−234.301			−0.104780
$172$			613.767i			0.272089i
$173$		−	3306.12i		−	1.45295i	−0.687195	−	0.726473i	$-0.741158\pi$
$173$		−	3306.12i		−	1.45295i	0.687195	−	0.726473i	$-0.258842\pi$
$174$	−1416.44			−0.617125
$175$	250.492	−	838.379i	0.108203	−	0.362145i
$176$	5257.63			2.25176
$177$			2117.24i			0.899106i
$178$		−	2345.32i		−	0.987581i
$179$	−2839.60			−1.18571			−0.592854	−	0.805310i	$-0.701999\pi$
$179$	−2839.60			−1.18571			−0.592854	+	0.805310i	$0.701999\pi$
$180$	−212.194	−	31.0223i	−0.0878666	−	0.0128459i
$181$	741.522			0.304513			0.152257	−	0.988341i	$-0.451346\pi$
$181$	741.522			0.304513			0.152257	+	0.988341i	$0.451346\pi$
$182$			1252.82i			0.510249i
$183$		−	1179.51i		−	0.476460i
$184$	−476.757			−0.191016
$185$	194.404	−	1329.73i	0.0772586	−	0.528452i
$186$	723.787			0.285326
$187$		−	2609.86i		−	1.02060i
$188$			1126.80i			0.437129i
$189$	−189.000			−0.0727393
$190$	−134.019	+	916.696i	−0.0511725	+	0.350022i
$191$	4428.76			1.67777			0.838885	−	0.544309i	$-0.183208\pi$
$191$	4428.76			1.67777			0.838885	+	0.544309i	$0.183208\pi$
$192$		−	937.827i		−	0.352510i
$193$		−	815.034i		−	0.303976i	−0.988382	−	0.151988i	$-0.951432\pi$
$193$		−	815.034i		−	0.303976i	0.988382	−	0.151988i	$-0.0485675\pi$
$194$	−455.048			−0.168405
$195$	−1866.14	−	272.826i	−0.685318	−	0.100192i
$196$	104.430			0.0380574
$197$		−	1609.61i		−	0.582133i	−0.956703	−	0.291067i	$-0.905990\pi$
$197$		−	1609.61i		−	0.582133i	0.956703	−	0.291067i	$-0.0940102\pi$
$198$		−	1968.61i		−	0.706579i
$199$	273.622			0.0974700			0.0487350	−	0.998812i	$-0.484481\pi$
$199$	273.622			0.0974700			0.0487350	+	0.998812i	$0.484481\pi$
$200$	668.460	−	2237.28i	0.236336	−	0.790999i
$201$	−1773.60			−0.622390
$202$			1801.77i			0.627584i
$203$			1038.35i			0.359004i
$204$	242.818			0.0833366
$205$	−3824.05	−	559.069i	−1.30285	−	0.190473i
$206$	−4267.66			−1.44341
$207$			229.700i			0.0771267i
$208$			4301.95i			1.43407i
$209$	−1789.03			−0.592104
$210$	−108.107	+	739.457i	−0.0355242	+	0.242987i
$211$	−5157.70			−1.68280			−0.841399	−	0.540414i	$-0.818267\pi$
$211$	−5157.70			−1.68280			−0.841399	+	0.540414i	$0.818267\pi$
$212$			770.920i			0.249750i
$213$		−	2006.49i		−	0.645456i
$214$	−5213.20			−1.66527
$215$	−465.779	+	3185.95i	−0.147748	+	1.01060i
$216$	−504.362			−0.158877
$217$		−	530.587i		−	0.165984i
$218$		−	1867.42i		−	0.580172i
$219$	−755.264			−0.233041
$220$	−1620.23	−	236.874i	−0.496525	−	0.0725910i
$221$	2135.46			0.649986
$222$			1147.76i			0.346995i
$223$		−	1444.38i		−	0.433733i	−0.976201	−	0.216867i	$-0.930416\pi$
$223$		−	1444.38i		−	0.433733i	0.976201	−	0.216867i	$-0.0695837\pi$
$224$	658.559			0.196437
$225$	−1077.92	−	322.062i	−0.319382	−	0.0954257i
$226$	5147.40			1.51504
$227$			1635.20i			0.478114i	0.971006	+	0.239057i	$0.0768383\pi$
$227$			1635.20i			0.478114i	−0.971006	+	0.239057i	$0.923162\pi$
$228$		−	166.449i		−	0.0483480i
$229$	2807.34			0.810105			0.405052	−	0.914293i	$-0.367253\pi$
$229$	2807.34			0.810105			0.405052	+	0.914293i	$0.367253\pi$
$230$	898.693	+	131.387i	0.257644	+	0.0376670i
$231$	−1443.13			−0.411042
$232$			2770.92i			0.784137i
$233$		−	579.805i		−	0.163023i	−0.996672	−	0.0815113i	$-0.974025\pi$
$233$		−	579.805i		−	0.163023i	0.996672	−	0.0815113i	$-0.0259747\pi$
$234$	1610.77			0.449997
$235$	−855.110	+	5848.99i	−0.237367	+	1.62360i
$236$	−1504.10			−0.414867
$237$		−	886.952i		−	0.243096i
$238$		−	846.177i		−	0.230460i
$239$	1695.51			0.458886			0.229443	−	0.973322i	$-0.426310\pi$
$239$	1695.51			0.458886			0.229443	+	0.973322i	$0.426310\pi$
$240$	−371.219	+	2539.15i	−0.0998419	+	0.682923i
$241$	−1182.39			−0.316035			−0.158018	−	0.987436i	$-0.550510\pi$
$241$	−1182.39			−0.316035			−0.158018	+	0.987436i	$0.550510\pi$
$242$		−	10795.0i		−	2.86746i
$243$			243.000i			0.0641500i
$244$	837.933			0.219849
$245$	542.074	+	79.2501i	0.141354	+	0.0206657i
$246$	3300.76			0.855482
$247$		−	1463.84i		−	0.377091i
$248$		−	1415.92i		−	0.362544i
$249$	−2749.53			−0.699778
$250$	−1876.62	+	4033.09i	−0.474751	+	1.02030i
$251$	2411.68			0.606469			0.303234	−	0.952916i	$-0.401934\pi$
$251$	2411.68			0.606469			0.303234	+	0.952916i	$0.401934\pi$
$252$		−	134.267i		−	0.0335635i
$253$			1753.89i			0.435835i
$254$	−6502.58			−1.60633
$255$	1260.42	+	184.271i	0.309532	+	0.0452530i
$256$	3061.85			0.747523
$257$			1054.74i			0.256003i	0.991774	+	0.128002i	$0.0408562\pi$
$257$			1054.74i			0.256003i	−0.991774	+	0.128002i	$0.959144\pi$
$258$		−	2749.97i		−	0.663588i
$259$	841.392			0.201859
$260$	193.817	−	1325.72i	0.0462308	−	0.316221i
$261$	1335.02			0.316612
$262$			8374.48i			1.97472i
$263$			3390.76i			0.794993i	0.917604	+	0.397496i	$0.130121\pi$
$263$			3390.76i			0.794993i	−0.917604	+	0.397496i	$0.869879\pi$
$264$	−3851.11			−0.897800
$265$	−585.040	+	4001.70i	−0.135618	+	0.927632i
$266$	−580.044			−0.133702
$267$			2210.51i			0.506671i
$268$		−	1259.98i		−	0.287184i
$269$	8792.06			1.99279			0.996397	−	0.0848151i	$-0.0270300\pi$
$269$	8792.06			1.99279			0.996397	+	0.0848151i	$0.0270300\pi$
$270$	950.730	+	138.995i	0.214295	+	0.0313294i
$271$	1593.15			0.357111			0.178556	−	0.983930i	$-0.442858\pi$
$271$	1593.15			0.357111			0.178556	+	0.983930i	$0.442858\pi$
$272$		−	2905.61i		−	0.647715i
$273$		−	1180.81i		−	0.261779i
$274$	−5056.24			−1.11481
$275$	−8230.52	−	2459.13i	−1.80480	−	0.539241i
$276$	−163.180			−0.0355880
$277$		−	208.765i		−	0.0452833i	−0.999744	−	0.0226417i	$-0.992792\pi$
$277$		−	208.765i		−	0.0452833i	0.999744	−	0.0226417i	$-0.00720768\pi$
$278$			5517.62i			1.19038i
$279$	−682.184			−0.146384
$280$	1446.57	+	211.486i	0.308747	+	0.0451381i
$281$	2445.06			0.519075			0.259538	−	0.965733i	$-0.416430\pi$
$281$	2445.06			0.519075			0.259538	+	0.965733i	$0.416430\pi$
$282$		−	5048.59i		−	1.06610i
$283$		−	3894.53i		−	0.818042i	−0.912525	−	0.409021i	$-0.865870\pi$
$283$		−	3894.53i		−	0.818042i	0.912525	−	0.409021i	$-0.134130\pi$
$284$	1425.42			0.297828
$285$	126.316	−	864.005i	0.0262537	−	0.179576i
$286$	12299.2			2.54289
$287$		−	2419.69i		−	0.497665i
$288$		−	846.719i		−	0.173241i
$289$	3470.67			0.706426
$290$	763.624	−	5223.22i	0.154626	−	1.05765i
$291$	428.892			0.0863988
$292$		−	536.543i		−	0.107530i
$293$			5746.21i			1.14572i	0.819652	+	0.572862i	$0.194167\pi$
$293$			5746.21i			1.14572i	−0.819652	+	0.572862i	$0.805833\pi$
$294$	−467.895			−0.0928169
$295$	−7807.50	−	1141.44i	−1.54092	−	0.225279i
$296$	2245.33			0.440902
$297$			1855.45i			0.362505i
$298$		−	4362.83i		−	0.848093i
$299$	−1435.09			−0.277569
$300$	228.794	−	765.757i	0.0440315	−	0.147370i
$301$	−2015.93			−0.386033
$302$			11758.1i			2.24040i
$303$		−	1698.20i		−	0.321977i
$304$	−1991.76			−0.375774
$305$	4349.55	+	635.895i	0.816573	+	0.119381i
$306$	−1087.94			−0.203247
$307$			1979.55i			0.368008i	0.982925	+	0.184004i	$0.0589060\pi$
$307$			1979.55i			0.368008i	−0.982925	+	0.184004i	$0.941094\pi$
$308$		−	1025.21i		−	0.189664i
$309$	4022.36			0.740531
$310$	−390.206	+	2669.02i	−0.0714909	+	0.489001i
$311$	3495.57			0.637348			0.318674	−	0.947864i	$-0.396762\pi$
$311$	3495.57			0.637348			0.318674	+	0.947864i	$0.396762\pi$
$312$		−	3151.09i		−	0.571779i
$313$			1448.68i			0.261611i	0.991408	+	0.130805i	$0.0417563\pi$
$313$			1448.68i			0.261611i	−0.991408	+	0.130805i	$0.958244\pi$
$314$	−3356.62			−0.603265
$315$	101.893	−	696.953i	0.0182255	−	0.124663i
$316$	630.096			0.112170
$317$		−	9453.34i		−	1.67493i	−0.546492	−	0.837465i	$-0.684037\pi$
$317$		−	9453.34i		−	1.67493i	0.546492	−	0.837465i	$-0.315963\pi$
$318$		−	3454.09i		−	0.609107i
$319$	10193.7			1.78914
$320$	3458.31	+	505.598i	0.604142	+	0.0883243i
$321$	4913.54			0.854353
$322$			568.652i			0.0984154i
$323$			988.699i			0.170318i
$324$	−172.629			−0.0296002
$325$	2012.13	−	6734.45i	0.343425	−	1.14942i
$326$	−4392.86			−0.746313
$327$			1760.08i			0.297653i
$328$		−	6457.14i		−	1.08700i
$329$	−3700.98			−0.620187
$330$	7259.39	+	1061.31i	1.21096	+	0.177040i
$331$	−791.305			−0.131402			−0.0657010	−	0.997839i	$-0.520928\pi$
$331$	−791.305			−0.131402			−0.0657010	+	0.997839i	$0.520928\pi$
$332$		−	1953.28i		−	0.322893i
$333$		−	1081.79i		−	0.178023i
$334$	10004.4			1.63896
$335$	956.179	−	6540.31i	0.155945	−	1.06667i
$336$	−1606.66			−0.260865
$337$			5959.06i			0.963237i	0.876381	+	0.481618i	$0.159951\pi$
$337$			5959.06i			0.963237i	−0.876381	+	0.481618i	$0.840049\pi$
$338$			3070.59i			0.494136i
$339$	−4851.52			−0.777282
$340$	−130.907	+	895.411i	−0.0208807	+	0.142825i
$341$	−5208.88			−0.827204
$342$			745.771i			0.117914i
$343$			343.000i			0.0539949i
$344$	−5379.67			−0.843175
$345$	−847.036	−	123.835i	−0.132182	−	0.0193248i
$346$	−10523.2			−1.63507
$347$		−	4560.34i		−	0.705509i	−0.935716	−	0.352755i	$-0.885245\pi$
$347$		−	4560.34i		−	0.705509i	0.935716	−	0.352755i	$-0.114755\pi$
$348$			948.405i			0.146092i
$349$	9404.92			1.44250			0.721252	−	0.692673i	$-0.243567\pi$
$349$	9404.92			1.44250			0.721252	+	0.692673i	$0.243567\pi$
$350$	−2668.52	−	797.306i	−0.407539	−	0.121765i
$351$	−1518.18			−0.230868
$352$		−	6465.20i		−	0.978967i
$353$		−	1391.37i		−	0.209788i	−0.994483	−	0.104894i	$-0.966550\pi$
$353$		−	1391.37i		−	0.209788i	0.994483	−	0.104894i	$-0.0334503\pi$
$354$	6739.10			1.01180
$355$	7399.08	+	1081.73i	1.10620	+	0.161725i
$356$	−1570.36			−0.233789
$357$			797.538i			0.118236i
$358$			9038.32i			1.33433i
$359$	−4306.80			−0.633159			−0.316579	−	0.948566i	$-0.602534\pi$
$359$	−4306.80			−0.633159			−0.316579	+	0.948566i	$0.602534\pi$
$360$	271.910	−	1859.88i	0.0398081	−	0.272289i
$361$	−6181.26			−0.901189
$362$		−	2360.23i		−	0.342682i
$363$			10174.5i			1.47113i
$364$	838.852			0.120791
$365$	407.175	−	2785.09i	0.0583904	−	0.399393i
$366$	−3754.34			−0.536182
$367$			6405.46i			0.911069i	0.890218	+	0.455534i	$0.150552\pi$
$367$			6405.46i			0.911069i	−0.890218	+	0.455534i	$0.849448\pi$
$368$			1952.64i			0.276599i
$369$	−3111.03			−0.438899
$370$	−4232.47	−	618.778i	−0.594691	−	0.0869426i
$371$	−2532.09			−0.354339
$372$		−	484.627i		−	0.0675450i
$373$			10293.2i			1.42885i	0.699712	+	0.714425i	$0.253312\pi$
$373$			10293.2i			1.42885i	−0.699712	+	0.714425i	$0.746688\pi$
$374$	−8307.08			−1.14853
$375$	1768.75	−	3801.27i	0.243568	−	0.523458i
$376$	−9876.37			−1.35461
$377$			8340.75i			1.13944i
$378$			601.579i			0.0818568i
$379$	−3832.35			−0.519405			−0.259702	−	0.965689i	$-0.583625\pi$
$379$	−3832.35			−0.519405			−0.259702	+	0.965689i	$0.583625\pi$
$380$	613.793	+	89.7353i	0.0828604	+	0.0121140i
$381$	6128.81			0.824116
$382$		−	14096.6i		−	1.88807i
$383$			13514.8i			1.80307i	0.432705	+	0.901536i	$0.357559\pi$
$383$			13514.8i			1.80307i	−0.432705	+	0.901536i	$0.642441\pi$
$384$	−5242.98			−0.696757
$385$	778.014	−	5321.65i	0.102990	−	0.704458i
$386$	−2594.22			−0.342078
$387$			2591.90i			0.340449i
$388$			304.687i			0.0398663i
$389$	6444.44			0.839965			0.419982	−	0.907532i	$-0.362036\pi$
$389$	6444.44			0.839965			0.419982	+	0.907532i	$0.362036\pi$
$390$	−868.392	+	5939.84i	−0.112751	+	0.771219i
$391$	969.282			0.125367
$392$			915.324i			0.117936i
$393$		−	7893.11i		−	1.01312i
$394$	−5123.33			−0.655101
$395$	3270.71	+	478.170i	0.416626	+	0.0609098i
$396$	−1318.12			−0.167268
$397$			2811.16i			0.355386i	0.984086	+	0.177693i	$0.0568634\pi$
$397$			2811.16i			0.355386i	−0.984086	+	0.177693i	$0.943137\pi$
$398$		−	870.926i		−	0.109687i
$399$	546.703			0.0685949
$400$	−9163.20	−	2737.80i	−1.14540	−	0.342225i
$401$	9918.99			1.23524			0.617619	−	0.786477i	$-0.288097\pi$
$401$	9918.99			1.23524			0.617619	+	0.786477i	$0.288097\pi$
$402$			5645.31i			0.700404i
$403$		−	4262.05i		−	0.526819i
$404$	1206.41			0.148567
$405$	−896.082	−	131.005i	−0.109942	−	0.0160733i
$406$	3305.02			0.404003
$407$		−	8260.11i		−	1.00599i
$408$			2128.30i			0.258251i
$409$	562.052			0.0679504			0.0339752	−	0.999423i	$-0.489183\pi$
$409$	562.052			0.0679504			0.0339752	+	0.999423i	$0.489183\pi$
$410$	−1779.49	+	12171.8i	−0.214348	+	1.46615i
$411$	4765.61			0.571947
$412$			2857.50i			0.341697i
$413$		−	4940.24i		−	0.588603i
$414$	731.124			0.0867942
$415$	1482.32	−	10139.1i	0.175335	−	1.19930i
$416$	5290.01			0.623472
$417$		−	5200.46i		−	0.610714i
$418$			5694.40i			0.666322i
$419$	−354.260			−0.0413049			−0.0206525	−	0.999787i	$-0.506574\pi$
$419$	−354.260			−0.0413049			−0.0206525	+	0.999787i	$0.506574\pi$
$420$	495.119	+	72.3853i	0.0575222	+	0.00840962i
$421$	−2969.20			−0.343729			−0.171864	−	0.985121i	$-0.554979\pi$
$421$	−2969.20			−0.343729			−0.171864	+	0.985121i	$0.554979\pi$
$422$			16416.7i			1.89373i
$423$			4758.40i			0.546954i
$424$	−6757.11			−0.773948
$425$	−1359.03	+	4548.56i	−0.155112	+	0.519148i
$426$	−6386.56			−0.726361
$427$			2752.20i			0.311916i
$428$			3490.61i			0.394217i
$429$	−11592.2			−1.30461
$430$	10140.7	+	1482.56i	1.13728	+	0.166268i
$431$	−4583.08			−0.512202			−0.256101	−	0.966650i	$-0.582438\pi$
$431$	−4583.08			−0.512202			−0.256101	+	0.966650i	$0.582438\pi$
$432$			2065.71i			0.230061i
$433$			247.808i			0.0275033i	0.999905	+	0.0137516i	$0.00437742\pi$
$433$			247.808i			0.0275033i	−0.999905	+	0.0137516i	$0.995623\pi$
$434$	−1688.84			−0.186790
$435$	−719.731	+	4922.99i	−0.0793298	+	0.542619i
$436$	−1250.37			−0.137344
$437$		−	664.431i		−	0.0727324i
$438$			2403.97i			0.262252i
$439$	3793.19			0.412390			0.206195	−	0.978511i	$-0.433892\pi$
$439$	3793.19			0.412390			0.206195	+	0.978511i	$0.433892\pi$
$440$	2076.19	−	14201.3i	0.224952	−	1.53868i
$441$	441.000			0.0476190
$442$		−	6797.09i		−	0.731458i
$443$		−	13157.7i		−	1.41115i	−0.708635	−	0.705575i	$-0.750689\pi$
$443$		−	13157.7i		−	1.41115i	0.708635	−	0.705575i	$-0.249311\pi$
$444$	768.510			0.0821438
$445$	−8151.44	−	1191.72i	−0.868349	−	0.126951i
$446$	−4597.38			−0.488100
$447$			4112.05i			0.435108i
$448$			2188.26i			0.230772i
$449$	8705.75			0.915033			0.457517	−	0.889201i	$-0.348739\pi$
$449$	8705.75			0.915033			0.457517	+	0.889201i	$0.348739\pi$
$450$	−1025.11	+	3430.96i	−0.107387	+	0.359415i
$451$	−23754.6			−2.48017
$452$		−	3446.55i		−	0.358655i
$453$		−	11082.2i		−	1.14942i
$454$	5204.76			0.538043
$455$	4354.32	+	636.593i	0.448646	+	0.0655911i
$456$	1458.92			0.149825
$457$		−	11239.4i		−	1.15045i	−0.817994	−	0.575227i	$-0.804914\pi$
$457$		−	11239.4i		−	1.15045i	0.817994	−	0.575227i	$-0.195086\pi$
$458$		−	8935.63i		−	0.911648i
$459$	1025.41			0.104274
$460$	87.9729	−	601.739i	0.00891687	−	0.0609918i
$461$	−12534.3			−1.26633			−0.633167	−	0.774015i	$-0.718246\pi$
$461$	−12534.3			−1.26633			−0.633167	+	0.774015i	$0.718246\pi$
$462$			4593.41i			0.462565i
$463$		−	12563.8i		−	1.26110i	−0.776150	−	0.630549i	$-0.782830\pi$
$463$		−	12563.8i		−	1.26110i	0.776150	−	0.630549i	$-0.217170\pi$
$464$	11348.8			1.13546
$465$	367.776	−	2515.61i	0.0366779	−	0.250878i
$466$	−1845.49			−0.183457
$467$		−	4817.97i		−	0.477407i	−0.971093	−	0.238703i	$-0.923278\pi$
$467$		−	4817.97i		−	0.477407i	0.971093	−	0.238703i	$-0.0767223\pi$
$468$		−	1078.52i		−	0.106527i
$469$	4138.41			0.407450
$470$	18617.1	+	2721.78i	1.82711	+	0.267120i
$471$	3163.68			0.309501
$472$		−	13183.4i		−	1.28563i
$473$			19790.7i			1.92384i
$474$	−2823.13			−0.273567
$475$	3117.99	+	931.598i	0.301185	+	0.0899887i
$476$	−566.575			−0.0545566
$477$			3255.55i			0.312498i
$478$		−	5396.75i		−	0.516405i
$479$	7088.81			0.676192			0.338096	−	0.941112i	$-0.390217\pi$
$479$	7088.81			0.676192			0.338096	+	0.941112i	$0.390217\pi$
$480$	3122.34	+	456.480i	0.296906	+	0.0434070i
$481$	6758.66			0.640683
$482$			3763.50i			0.355649i
$483$		−	535.966i		−	0.0504913i
$484$	−7227.99			−0.678812
$485$	−231.222	+	1581.57i	−0.0216480	+	0.148073i
$486$	773.459			0.0721909
$487$		−	16131.5i		−	1.50101i	−0.660867	−	0.750503i	$-0.729811\pi$
$487$		−	16131.5i		−	1.50101i	0.660867	−	0.750503i	$-0.270189\pi$
$488$			7344.48i			0.681289i
$489$	4140.36			0.382890
$490$	252.250	−	1725.40i	0.0232561	−	0.159073i
$491$	−3961.20			−0.364087			−0.182043	−	0.983290i	$-0.558271\pi$
$491$	−3961.20			−0.364087			−0.182043	+	0.983290i	$0.558271\pi$
$492$		−	2210.09i		−	0.202518i
$493$		−	5633.49i		−	0.514644i
$494$	−4659.32			−0.424358
$495$	−6842.12	−	1000.30i	−0.621273	−	0.0908289i
$496$	−5799.14			−0.524978
$497$			4681.80i			0.422550i
$498$			8751.65i			0.787492i
$499$	12981.0			1.16455			0.582274	−	0.812992i	$-0.302163\pi$
$499$	12981.0			1.16455			0.582274	+	0.812992i	$0.302163\pi$
$500$	2700.44	+	1256.53i	0.241535	+	0.112387i
$501$	−9429.30			−0.840859
$502$		−	7676.26i		−	0.682486i
$503$		−	9611.24i		−	0.851976i	−0.904729	−	0.425988i	$-0.859927\pi$
$503$		−	9611.24i		−	0.851976i	0.904729	−	0.425988i	$-0.140073\pi$
$504$	1176.85			0.104010
$505$	6262.25	+	915.528i	0.551815	+	0.0806742i
$506$	5582.57			0.490465
$507$		−	2894.09i		−	0.253513i
$508$			4353.94i			0.380265i
$509$	2605.16			0.226860			0.113430	−	0.993546i	$-0.463816\pi$
$509$	2605.16			0.226860			0.113430	+	0.993546i	$0.463816\pi$
$510$	586.527	−	4011.87i	0.0509252	−	0.348331i
$511$	1762.28			0.152561
$512$			4235.53i			0.365597i
$513$		−	702.904i		−	0.0604950i
$514$	3357.19			0.288092
$515$	−2168.52	+	14832.8i	−0.185546	+	1.26915i
$516$	−1841.30			−0.157091
$517$			36333.2i			3.09078i
$518$		−	2678.12i		−	0.227162i
$519$	9918.36			0.838858
$520$	11619.9	+	1698.80i	0.979933	+	0.143264i
$521$	−342.674			−0.0288154			−0.0144077	−	0.999896i	$-0.504586\pi$
$521$	−342.674			−0.0288154			−0.0144077	+	0.999896i	$0.504586\pi$
$522$		−	4249.31i		−	0.356297i
$523$		−	10494.7i		−	0.877441i	−0.898624	−	0.438720i	$-0.855432\pi$
$523$		−	10494.7i		−	0.877441i	0.898624	−	0.438720i	$-0.144568\pi$
$524$	5607.31			0.467474
$525$	2515.14	+	751.477i	0.209085	+	0.0624708i
$526$	10792.6			0.894642
$527$			2878.66i			0.237944i
$528$			15772.9i			1.30005i
$529$	11515.6			0.946463
$530$	12737.2	+	1862.16i	1.04391	+	0.152617i
$531$	−6351.73			−0.519099
$532$			388.381i			0.0316512i
$533$		−	19436.7i		−	1.57954i
$534$	7035.97			0.570180
$535$	−2648.97	+	18119.1i	−0.214065	+	1.46422i
$536$	11043.7			0.889953
$537$		−	8518.80i		−	0.684568i
$538$		−	27984.8i		−	2.24258i
$539$	3367.30			0.269090
$540$	93.0669	−	636.581i	0.00741659	−	0.0507298i
$541$	−4026.52			−0.319988			−0.159994	−	0.987118i	$-0.551148\pi$
$541$	−4026.52			−0.319988			−0.159994	+	0.987118i	$0.551148\pi$
$542$		−	5070.93i		−	0.401873i
$543$			2224.57i			0.175811i
$544$	−3572.97			−0.281599
$545$	−6490.43	−	948.887i	−0.510127	−	0.0745795i
$546$	−3758.46			−0.294592
$547$			16182.8i			1.26495i	0.774581	+	0.632475i	$0.217961\pi$
$547$			16182.8i			1.26495i	−0.774581	+	0.632475i	$0.782039\pi$
$548$			3385.51i			0.263909i
$549$	3538.54			0.275084
$550$	−7827.31	+	26197.4i	−0.606832	+	2.03102i
$551$	−3861.69			−0.298573
$552$		−	1430.27i		−	0.110283i
$553$			2069.55i			0.159144i
$554$	−664.491			−0.0509594
$555$	3989.19	+	583.211i	0.305102	+	0.0446053i
$556$	3694.44			0.281797
$557$			10934.3i			0.831779i	0.909415	+	0.415890i	$0.136530\pi$
$557$			10934.3i			0.831779i	−0.909415	+	0.415890i	$0.863470\pi$
$558$			2171.36i			0.164733i
$559$	−16193.3			−1.22523
$560$	866.177	−	5924.69i	0.0653619	−	0.447078i
$561$	7829.59			0.589243
$562$		−	7782.52i		−	0.584139i
$563$			164.542i			0.0123173i	0.999981	+	0.00615863i	$0.00196037\pi$
$563$			164.542i			0.0123173i	−0.999981	+	0.00615863i	$0.998040\pi$
$564$	−3380.39			−0.252376
$565$	2615.54	−	17890.4i	0.194755	−	1.33213i
$566$	−12396.1			−0.920579
$567$		−	567.000i		−	0.0419961i
$568$			12493.8i			0.922935i
$569$	−21924.4			−1.61532			−0.807660	−	0.589648i	$-0.799266\pi$
$569$	−21924.4			−1.61532			−0.807660	+	0.589648i	$0.799266\pi$
$570$	−2750.09	−	402.057i	−0.202085	−	0.0295444i
$571$	−6765.55			−0.495848			−0.247924	−	0.968779i	$-0.579748\pi$
$571$	−6765.55			−0.495848			−0.247924	+	0.968779i	$0.579748\pi$
$572$		−	8235.18i		−	0.601976i
$573$			13286.3i			0.968661i
$574$	−7701.77			−0.560044
$575$	913.302	−	3056.75i	0.0662388	−	0.221696i
$576$	2813.48			0.203521
$577$			26134.4i			1.88560i	0.333365	+	0.942798i	$0.391816\pi$
$577$			26134.4i			1.88560i	−0.333365	+	0.942798i	$0.608184\pi$
$578$		−	11047.0i		−	0.794973i
$579$	2445.10			0.175501
$580$	−3497.32	−	511.301i	−0.250376	−	0.0366045i
$581$	6415.58			0.458112
$582$		−	1365.14i		−	0.0972285i
$583$			24858.1i			1.76589i
$584$	4702.80			0.333225
$585$	818.477	−	5598.42i	0.0578459	−	0.395668i
$586$	18289.9			1.28933
$587$		−	6342.06i		−	0.445937i	−0.974826	−	0.222968i	$-0.928425\pi$
$587$		−	6342.06i		−	0.445937i	0.974826	−	0.222968i	$-0.0715747\pi$
$588$			313.289i			0.0219725i
$589$	1973.29			0.138044
$590$	−3633.16	+	24851.0i	−0.253516	+	1.73406i
$591$	4828.84			0.336095
$592$		−	9196.14i		−	0.638444i
$593$		−	24801.2i		−	1.71748i	−0.512413	−	0.858739i	$-0.671248\pi$
$593$		−	24801.2i		−	1.71748i	0.512413	−	0.858739i	$-0.328752\pi$
$594$	5905.82			0.407944
$595$	−2940.99	−	429.966i	−0.202636	−	0.0296250i
$596$	−2921.22			−0.200768
$597$			820.865i			0.0562743i
$598$			4567.82i			0.312361i
$599$	−12339.2			−0.841681			−0.420841	−	0.907135i	$-0.638265\pi$
$599$	−12339.2			−0.841681			−0.420841	+	0.907135i	$0.638265\pi$
$600$	6711.85	+	2005.38i	0.456684	+	0.136449i
$601$	3221.02			0.218616			0.109308	−	0.994008i	$-0.465137\pi$
$601$	3221.02			0.218616			0.109308	+	0.994008i	$0.465137\pi$
$602$			6416.60i			0.434421i
$603$		−	5320.81i		−	0.359337i
$604$	7872.87			0.530369
$605$	−37519.1	−	5485.22i	−2.52127	−	0.368605i
$606$	−5405.30			−0.362336
$607$		−	20076.6i		−	1.34248i	−0.741241	−	0.671239i	$-0.765762\pi$
$607$		−	20076.6i		−	1.34248i	0.741241	−	0.671239i	$-0.234238\pi$
$608$			2449.23i			0.163370i
$609$	−3115.05			−0.207271
$610$	2024.03	−	13844.4i	0.134345	−	0.918926i
$611$	−29728.9			−1.96842
$612$			728.454i			0.0481144i
$613$			7428.07i			0.489424i	0.969596	+	0.244712i	$0.0786934\pi$
$613$			7428.07i			0.489424i	−0.969596	+	0.244712i	$0.921307\pi$
$614$	6300.81			0.414137
$615$	1677.21	−	11472.2i	0.109970	−	0.752199i
$616$	8985.92			0.587748
$617$		−	2200.68i		−	0.143592i	−0.997419	−	0.0717959i	$-0.977127\pi$
$617$		−	2200.68i		−	0.143592i	0.997419	−	0.0717959i	$-0.0228730\pi$
$618$		−	12803.0i		−	0.833353i
$619$	5674.34			0.368451			0.184225	−	0.982884i	$-0.441022\pi$
$619$	5674.34			0.368451			0.184225	+	0.982884i	$0.441022\pi$
$620$	1787.10	+	261.270i	0.115761	+	0.0169240i
$621$	−689.099			−0.0445291
$622$		−	11126.2i		−	0.717237i
$623$		−	5157.86i		−	0.331694i
$624$	−12905.8			−0.827960
$625$	13063.9	+	8571.73i	0.836091	+	0.548591i
$626$	4611.08			0.294403
$627$		−	5367.09i		−	0.341851i
$628$			2247.50i			0.142810i
$629$	−4564.92			−0.289372
$630$	−2218.37	−	324.321i	−0.140289	−	0.0205099i
$631$	−4650.60			−0.293403			−0.146701	−	0.989181i	$-0.546866\pi$
$631$	−4650.60			−0.293403			−0.146701	+	0.989181i	$0.546866\pi$
$632$			5522.78i			0.347602i
$633$		−	15473.1i		−	0.971564i
$634$	−30089.6			−1.88487
$635$	−3304.14	+	22600.5i	−0.206489	+	1.41240i
$636$	−2312.76			−0.144193
$637$			2755.22i			0.171375i
$638$		−	32446.0i		−	2.01340i
$639$	6019.46			0.372654
$640$	2826.58	−	19333.9i	0.174578	−	1.19412i
$641$	15808.8			0.974119			0.487060	−	0.873369i	$-0.338069\pi$
$641$	15808.8			0.974119			0.487060	+	0.873369i	$0.338069\pi$
$642$		−	15639.6i		−	0.961442i
$643$		−	18829.6i		−	1.15485i	−0.816444	−	0.577424i	$-0.804058\pi$
$643$		−	18829.6i		−	1.15485i	0.816444	−	0.577424i	$-0.195942\pi$
$644$	380.753			0.0232978
$645$	−9557.85	−	1397.34i	−0.583473	−	0.0853025i
$646$	3146.99			0.191667
$647$			21519.7i			1.30761i	0.756661	+	0.653807i	$0.226829\pi$
$647$			21519.7i			1.30761i	−0.756661	+	0.653807i	$0.773171\pi$
$648$		−	1513.09i		−	0.0917279i
$649$	−48499.2			−2.93338
$650$	−21435.5	−	6404.53i	−1.29349	−	0.386471i
$651$	1591.76			0.0958311
$652$			2941.33i			0.176674i
$653$		−	4298.98i		−	0.257629i	−0.991669	−	0.128815i	$-0.958883\pi$
$653$		−	4298.98i		−	0.257629i	0.991669	−	0.128815i	$-0.0411172\pi$
$654$	5602.25			0.334962
$655$	29106.5	+	4255.30i	1.73631	+	0.253845i
$656$	−26446.4			−1.57402
$657$		−	2265.79i		−	0.134546i
$658$			11780.1i			0.697925i
$659$	1199.37			0.0708964			0.0354482	−	0.999372i	$-0.488714\pi$
$659$	1199.37			0.0708964			0.0354482	+	0.999372i	$0.488714\pi$
$660$	710.621	−	4860.68i	0.0419104	−	0.286669i
$661$	14967.5			0.880739			0.440369	−	0.897817i	$-0.354847\pi$
$661$	14967.5			0.880739			0.440369	+	0.897817i	$0.354847\pi$
$662$			2518.69i			0.147873i
$663$			6406.39i			0.375269i
$664$	17120.5			1.00061
$665$	−294.736	+	2016.01i	−0.0171871	+	0.117560i
$666$	−3443.29			−0.200338
$667$			3785.85i			0.219773i
$668$		−	6698.63i		−	0.387991i
$669$	4333.13			0.250416
$670$	−20817.5	−	3043.48i	−1.20037	−	0.175492i
$671$	27018.9			1.55447
$672$			1975.68i			0.113413i
$673$			23664.3i			1.35541i	0.735333	+	0.677706i	$0.237026\pi$
$673$			23664.3i			1.35541i	−0.735333	+	0.677706i	$0.762974\pi$
$674$	18967.4			1.08397
$675$	966.185	−	3233.75i	0.0550940	−	0.184395i
$676$	2055.98			0.116976
$677$		−	4413.97i		−	0.250580i	−0.992120	−	0.125290i	$-0.960014\pi$
$677$		−	4413.97i		−	0.250580i	0.992120	−	0.125290i	$-0.0399861\pi$
$678$			15442.2i			0.874711i
$679$	−1000.75			−0.0565613
$680$	−7848.27	−	1147.40i	−0.442599	−	0.0647070i
$681$	−4905.59			−0.276039
$682$			16579.6i			0.930890i
$683$			26357.7i			1.47664i	0.674449	+	0.738322i	$0.264381\pi$
$683$			26357.7i			1.47664i	−0.674449	+	0.738322i	$0.735619\pi$
$684$	499.347			0.0279137
$685$	−2569.22	+	17573.6i	−0.143306	+	0.980221i
$686$	1091.75			0.0607629
$687$			8422.01i			0.467714i
$688$			22033.4i			1.22095i
$689$	−20339.6			−1.12464
$690$	−394.161	+	2696.08i	−0.0217470	+	0.148751i
$691$	19098.2			1.05142			0.525708	−	0.850665i	$-0.323800\pi$
$691$	19098.2			1.05142			0.525708	+	0.850665i	$0.323800\pi$
$692$			7046.05i			0.387068i
$693$		−	4329.38i		−	0.237315i
$694$	−14515.4			−0.793942
$695$	19177.1	+	2803.66i	1.04666	+	0.153020i
$696$	−8312.76			−0.452722
$697$			13127.9i			0.713419i
$698$		−	29935.4i		−	1.62331i
$699$	1739.41			0.0941211
$700$	−533.853	+	1786.77i	−0.0288254	+	0.0964763i
$701$	−7008.54			−0.377616			−0.188808	−	0.982014i	$-0.560462\pi$
$701$	−7008.54			−0.377616			−0.188808	+	0.982014i	$0.560462\pi$
$702$			4832.31i			0.259806i
$703$			3129.20i			0.167880i
$704$	21482.6			1.15008
$705$	−17547.0	−	2565.33i	−0.937386	−	0.137044i
$706$	−4428.67			−0.236084
$707$			3962.47i			0.210784i
$708$		−	4512.30i		−	0.239524i
$709$	−31728.6			−1.68066			−0.840332	−	0.542071i	$-0.817640\pi$
$709$	−31728.6			−1.68066			−0.840332	+	0.542071i	$0.817640\pi$
$710$	3443.10	−	23550.9i	0.181996	−	1.24486i
$711$	2660.86			0.140351
$712$		−	13764.2i		−	0.724487i
$713$		−	1934.54i		−	0.101611i
$714$	2538.53			0.133056
$715$	6249.56	−	42747.2i	0.326881	−	2.23588i
$716$	6051.80			0.315875
$717$			5086.54i			0.264938i
$718$			13708.4i			0.712522i
$719$	8033.78			0.416703			0.208352	−	0.978054i	$-0.433190\pi$
$719$	8033.78			0.416703			0.208352	+	0.978054i	$0.433190\pi$
$720$	−7617.46	−	1113.66i	−0.394286	−	0.0576438i
$721$	−9385.50			−0.484791
$722$			19674.7i			1.01415i
$723$		−	3547.17i		−	0.182463i
$724$	−1580.34			−0.0811229
$725$	−17765.9	−	5308.13i	−0.910081	−	0.271916i
$726$	32384.9			1.65553
$727$			20514.4i			1.04654i	0.852166	+	0.523272i	$0.175289\pi$
$727$			20514.4i			1.04654i	−0.852166	+	0.523272i	$0.824711\pi$
$728$			7352.53i			0.374317i
$729$	−729.000			−0.0370370
$730$	−8864.84	−	1296.02i	−0.449455	−	0.0657094i
$731$	10937.3			0.553391
$732$			2513.80i			0.126930i
$733$			39200.4i			1.97531i	0.156653	+	0.987654i	$0.449930\pi$
$733$			39200.4i			1.97531i	−0.156653	+	0.987654i	$0.550070\pi$
$734$	20388.3			1.02527
$735$	−237.750	+	1626.22i	−0.0119314	+	0.0816111i
$736$	2401.12			0.120254
$737$		−	40627.6i		−	2.03058i
$738$			9902.27i			0.493913i
$739$	18386.2			0.915221			0.457611	−	0.889153i	$-0.348705\pi$
$739$	18386.2			0.915221			0.457611	+	0.889153i	$0.348705\pi$
$740$	−414.316	+	2833.94i	−0.0205818	+	0.140781i
$741$	4391.51			0.217714
$742$			8059.55i			0.398754i
$743$		−	10118.8i		−	0.499628i	−0.968294	−	0.249814i	$-0.919631\pi$
$743$		−	10118.8i		−	0.499628i	0.968294	−	0.249814i	$-0.0803695\pi$
$744$	4247.75			0.209315
$745$	−15163.5	−	2216.87i	−0.745702	−	0.109020i
$746$	32762.8			1.60795
$747$		−	8248.60i		−	0.404017i
$748$			5562.18i			0.271890i
$749$	−11464.9			−0.559305
$750$	−12099.3	−	5629.85i	−0.589071	−	0.274098i
$751$	−16116.3			−0.783077			−0.391538	−	0.920162i	$-0.628057\pi$
$751$	−16116.3			−0.783077			−0.391538	+	0.920162i	$0.628057\pi$
$752$			40450.4i			1.96154i
$753$			7235.03i			0.350145i
$754$	26548.3			1.28227
$755$	40866.6	+	5974.61i	1.96992	+	0.287998i
$756$	402.800			0.0193779
$757$		−	16856.5i		−	0.809324i	−0.914466	−	0.404662i	$-0.867389\pi$
$757$		−	16856.5i		−	0.809324i	0.914466	−	0.404662i	$-0.132611\pi$
$758$			12198.2i			0.584510i
$759$	−5261.68			−0.251630
$760$	−786.529	+	5379.89i	−0.0375400	+	0.256775i
$761$	19917.5			0.948765			0.474383	−	0.880319i	$-0.342671\pi$
$761$	19917.5			0.948765			0.474383	+	0.880319i	$0.342671\pi$
$762$		−	19507.7i		−	0.927415i
$763$		−	4106.85i		−	0.194860i
$764$	−9438.65			−0.446961
$765$	−552.813	+	3781.27i	−0.0261268	+	0.178708i
$766$	43017.2			2.02908
$767$		−	39683.5i		−	1.86817i
$768$			9185.56i			0.431583i
$769$	−2378.22			−0.111523			−0.0557613	−	0.998444i	$-0.517759\pi$
$769$	−2378.22			−0.111523			−0.0557613	+	0.998444i	$0.517759\pi$
$770$	−16938.6	−	2476.38i	−0.792758	−	0.115900i
$771$	−3164.22			−0.147803
$772$			1737.01i			0.0809799i
$773$			7153.02i			0.332828i	0.986056	+	0.166414i	$0.0532188\pi$
$773$			7153.02i			0.332828i	−0.986056	+	0.166414i	$0.946781\pi$
$774$	8249.92			0.383123
$775$	9078.23	+	2712.41i	0.420774	+	0.125720i
$776$	−2670.58			−0.123541
$777$			2524.18i			0.116544i
$778$		−	20512.4i		−	0.945250i
$779$	8998.99			0.413892
$780$	3977.15	+	581.450i	0.182570	+	0.0266914i
$781$	45962.1			2.10583
$782$		−	3085.18i		−	0.141082i
$783$			4005.06i			0.182796i
$784$	3748.87			0.170776
$785$	−1705.59	+	11666.3i	−0.0775481	+	0.530432i
$786$	−25123.4			−1.14011
$787$		−	28137.0i		−	1.27443i	−0.770687	−	0.637214i	$-0.780087\pi$
$787$		−	28137.0i		−	1.27443i	0.770687	−	0.637214i	$-0.219913\pi$
$788$			3430.44i			0.155082i
$789$	−10172.3			−0.458989
$790$	1522.00	−	10410.5i	0.0685445	−	0.468848i
$791$	11320.2			0.508851
$792$		−	11553.3i		−	0.518345i
$793$			22107.6i			0.989993i
$794$	8947.81			0.399932
$795$	−12005.1	−	1755.12i	−0.535569	−	0.0782990i
$796$	−583.147			−0.0259662
$797$		−	40807.1i		−	1.81363i	−0.421530	−	0.906815i	$-0.638507\pi$
$797$		−	40807.1i		−	1.81363i	0.421530	−	0.906815i	$-0.361493\pi$
$798$		−	1740.13i		−	0.0771930i
$799$	20079.4			0.889059
$800$	−3366.61	+	11267.8i	−0.148785	+	0.497971i
$801$	−6631.54			−0.292527
$802$		−	31571.7i		−	1.39007i
$803$		−	17300.7i		−	0.760308i
$804$	3779.93			0.165806
$805$	1976.42	+	288.948i	0.0865336	+	0.0126510i
$806$	−13565.9			−0.592853
$807$			26376.2i			1.15054i
$808$			10574.2i			0.460394i
$809$	−15233.3			−0.662020			−0.331010	−	0.943627i	$-0.607389\pi$
$809$	−15233.3			−0.662020			−0.331010	+	0.943627i	$0.607389\pi$
$810$	−416.984	+	2852.19i	−0.0180881	+	0.123723i
$811$	−26847.5			−1.16245			−0.581223	−	0.813744i	$-0.697426\pi$
$811$	−26847.5			−1.16245			−0.581223	+	0.813744i	$0.697426\pi$
$812$		−	2212.95i		−	0.0956393i
$813$			4779.46i			0.206178i
$814$	−26291.6			−1.13209
$815$	−2232.13	+	15267.9i	−0.0959365	+	0.656210i
$816$	8716.82			0.373958
$817$		−	7497.36i		−	0.321052i
$818$		−	1788.99i		−	0.0764676i
$819$	3542.42			0.151138
$820$	8149.89	+	1191.50i	0.347081	+	0.0507425i
$821$	23640.8			1.00496			0.502479	−	0.864590i	$-0.332422\pi$
$821$	23640.8			1.00496			0.502479	+	0.864590i	$0.332422\pi$
$822$		−	15168.7i		−	0.643638i
$823$		−	21191.6i		−	0.897562i	−0.893642	−	0.448781i	$-0.851858\pi$
$823$		−	21191.6i		−	0.897562i	0.893642	−	0.448781i	$-0.148142\pi$
$824$	−25046.0			−1.05888
$825$	7377.39	−	24691.6i	0.311331	−	1.04200i
$826$	−15724.6			−0.662382
$827$			8177.77i			0.343856i	0.985110	+	0.171928i	$0.0549996\pi$
$827$			8177.77i			0.343856i	−0.985110	+	0.171928i	$0.945000\pi$
$828$		−	489.540i		−	0.0205467i
$829$	−28931.0			−1.21208			−0.606040	−	0.795434i	$-0.707243\pi$
$829$	−28931.0			−1.21208			−0.606040	+	0.795434i	$0.707243\pi$
$830$	−32272.4	−	4718.16i	−1.34963	−	0.197313i
$831$	626.296			0.0261443
$832$			17577.7i			0.732448i
$833$		−	1860.92i		−	0.0774035i
$834$	−16552.9			−0.687264
$835$	5083.49	−	34771.3i	0.210684	−	1.44109i
$836$	3812.81			0.157738
$837$		−	2046.55i		−	0.0845151i
$838$			1127.60i			0.0464823i
$839$	41631.2			1.71307			0.856537	−	0.516085i	$-0.172611\pi$
$839$	41631.2			1.71307			0.856537	+	0.516085i	$0.172611\pi$
$840$	−634.457	+	4339.71i	−0.0260605	+	0.178255i
$841$	−2385.58			−0.0978137
$842$			9450.83i			0.386814i
$843$			7335.18i			0.299688i
$844$	10992.2			0.448301
$845$	10672.2	+	1560.25i	0.434478	+	0.0635198i
$846$	15145.8			0.615512
$847$		−	23740.4i		−	0.963081i
$848$			27674.9i			1.12071i
$849$	11683.6			0.472297
$850$	14477.9	+	4325.73i	0.584220	+	0.174554i
$851$	3067.74			0.123573
$852$			4276.26i			0.171951i
$853$		−	38242.1i		−	1.53503i	−0.641029	−	0.767517i	$-0.721492\pi$
$853$		−	38242.1i		−	1.53503i	0.641029	−	0.767517i	$-0.278508\pi$
$854$	8760.13			0.351014
$855$	2592.01	+	378.947i	0.103678	+	0.0151576i
$856$	−30595.1			−1.22164
$857$		−	1118.45i		−	0.0445805i	−0.999752	−	0.0222903i	$-0.992904\pi$
$857$		−	1118.45i		−	0.0445805i	0.999752	−	0.0222903i	$-0.00709579\pi$
$858$			36897.5i			1.46814i
$859$	−34103.0			−1.35458			−0.677288	−	0.735718i	$-0.736845\pi$
$859$	−34103.0			−1.35458			−0.677288	+	0.735718i	$0.736845\pi$
$860$	992.676	−	6789.95i	0.0393604	−	0.269227i
$861$	7259.07			0.287327
$862$			14587.7i			0.576405i
$863$		−	12332.6i		−	0.486450i	−0.969970	−	0.243225i	$-0.921795\pi$
$863$		−	12332.6i		−	0.486450i	0.969970	−	0.243225i	$-0.0782054\pi$
$864$	2540.16			0.100021
$865$	−5347.15	+	36574.7i	−0.210183	+	1.43766i
$866$	788.764			0.0309507
$867$			10412.0i			0.407855i
$868$			1130.80i			0.0442186i
$869$	20317.2			0.793112
$870$	15669.7	+	2290.87i	0.610634	+	0.0892734i
$871$	33242.6			1.29321
$872$		−	10959.5i		−	0.425613i
$873$			1286.67i			0.0498824i
$874$	−2114.86			−0.0818491
$875$	−4127.08	+	8869.63i	−0.159452	+	0.342684i
$876$	1609.63			0.0620826
$877$		−	17287.9i		−	0.665644i	−0.942990	−	0.332822i	$-0.891999\pi$
$877$		−	17287.9i		−	0.665644i	0.942990	−	0.332822i	$-0.108001\pi$
$878$		−	12073.6i		−	0.464081i
$879$	−17238.6			−0.661484
$880$	−58163.8	−	8503.43i	−2.22807	−	0.325739i
$881$	−15797.0			−0.604103			−0.302052	−	0.953292i	$-0.597671\pi$
$881$	−15797.0			−0.604103			−0.302052	+	0.953292i	$0.597671\pi$
$882$		−	1403.68i		−	0.0535879i
$883$			40601.9i			1.54741i	0.633545	+	0.773706i	$0.281599\pi$
$883$			40601.9i			1.54741i	−0.633545	+	0.773706i	$0.718401\pi$
$884$	−4551.13			−0.173157
$885$	3424.32	−	23422.5i	0.130065	−	0.889649i
$886$	−41880.3			−1.58803
$887$			3654.03i			0.138320i	0.997606	+	0.0691602i	$0.0220320\pi$
$887$			3654.03i			0.138320i	−0.997606	+	0.0691602i	$0.977968\pi$
$888$			6735.98i			0.254555i
$889$	−14300.6			−0.539511
$890$	−3793.21	+	25945.7i	−0.142864	+	0.977193i
$891$	−5566.35			−0.209293
$892$			3078.28i			0.115547i
$893$		−	13764.2i		−	0.515791i
$894$	13088.5			0.489647
$895$	31413.7	+	4592.62i	1.17324	+	0.171524i
$896$	12233.6			0.456135
$897$		−	4305.26i		−	0.160255i
$898$		−	27710.0i		−	1.02973i
$899$	−11243.6			−0.417123
$900$	2297.27	+	686.383i	0.0850841	+	0.0254216i
$901$	13737.7			0.507957
$902$			75609.7i			2.79105i
$903$		−	6047.78i		−	0.222876i
$904$	30209.0			1.11143
$905$	−8203.26	−	1199.30i	−0.301310	−	0.0440509i
$906$	−35274.3			−1.29350
$907$			8732.15i			0.319676i	0.987143	+	0.159838i	$0.0510972\pi$
$907$			8732.15i			0.319676i	−0.987143	+	0.159838i	$0.948903\pi$
$908$		−	3484.96i		−	0.127370i
$909$	5094.60			0.185894
$910$	2026.25	−	13859.6i	0.0738126	−	0.504881i
$911$	−29118.5			−1.05899			−0.529495	−	0.848313i	$-0.677619\pi$
$911$	−29118.5			−1.05899			−0.529495	+	0.848313i	$0.677619\pi$
$912$		−	5975.28i		−	0.216953i
$913$		−	62983.0i		−	2.28306i
$914$	−35774.6			−1.29466
$915$	−1907.69	+	13048.7i	−0.0689248	+	0.471448i
$916$	−5983.04			−0.215814
$917$			18417.3i			0.663240i
$918$		−	3263.82i		−	0.117344i
$919$	36147.4			1.29749			0.648745	−	0.761006i	$-0.275294\pi$
$919$	36147.4			1.29749			0.648745	+	0.761006i	$0.275294\pi$
$920$	5274.23	+	771.082i	0.189007	+	0.0276324i
$921$	−5938.64			−0.212470
$922$			39896.1i			1.42506i
$923$			37607.5i			1.34113i
$924$	3075.62			0.109503
$925$	−4301.27	+	14396.0i	−0.152892	+	0.511717i
$926$	−39990.0			−1.41917
$927$			12067.1i			0.427546i
$928$		−	13955.4i		−	0.493651i
$929$	380.568			0.0134403			0.00672015	−	0.999977i	$-0.497861\pi$
$929$	380.568			0.0134403			0.00672015	+	0.999977i	$0.497861\pi$
$930$	−8007.07	−	1170.62i	−0.282325	−	0.0412753i
$931$	−1275.64			−0.0449059
$932$			1235.69i			0.0434295i
$933$			10486.7i			0.367973i
$934$	−15335.4			−0.537247
$935$	−4221.06	+	28872.2i	−0.147640	+	1.00986i
$936$	9453.26			0.330117
$937$		−	11577.5i		−	0.403650i	−0.979422	−	0.201825i	$-0.935313\pi$
$937$		−	11577.5i		−	0.403650i	0.979422	−	0.201825i	$-0.0646872\pi$
$938$		−	13172.4i		−	0.458522i
$939$	−4346.04			−0.151041
$940$	1822.43	−	12465.5i	0.0632351	−	0.432531i
$941$	37835.3			1.31073			0.655364	−	0.755313i	$-0.272515\pi$
$941$	37835.3			1.31073			0.655364	+	0.755313i	$0.272515\pi$
$942$		−	10069.9i		−	0.348295i
$943$		−	8822.25i		−	0.304657i
$944$	−53995.1			−1.86164
$945$	2090.86	+	305.679i	0.0719742	+	0.0105225i
$946$	62993.0			2.16499
$947$			32719.8i			1.12276i	0.827559	+	0.561379i	$0.189729\pi$
$947$			32719.8i			1.12276i	−0.827559	+	0.561379i	$0.810271\pi$
$948$			1890.29i			0.0647612i
$949$	14155.9			0.484215
$950$	2965.24	−	9924.42i	0.101268	−	0.338937i
$951$	28360.0			0.967021
$952$		−	4966.03i		−	0.169065i
$953$			42719.5i			1.45207i	0.687659	+	0.726033i	$0.258638\pi$
$953$			42719.5i			1.45207i	−0.687659	+	0.726033i	$0.741362\pi$
$954$	10362.3			0.351668
$955$	−48994.3	−	7162.86i	−1.66012	−	0.242706i
$956$	−3613.51			−0.122248
$957$			30581.0i			1.03296i
$958$		−	22563.4i		−	0.760949i
$959$	−11119.8			−0.374427
$960$	−1516.79	+	10374.9i	−0.0509941	+	0.348802i
$961$	−24045.6			−0.807144
$962$		−	21512.5i		−	0.720989i
$963$			14740.6i			0.493261i
$964$	2519.93			0.0841924
$965$	−1318.19	+	9016.50i	−0.0439732	+	0.300779i
$966$	−1705.96			−0.0568201
$967$		−	56616.7i		−	1.88280i	−0.337286	−	0.941402i	$-0.609509\pi$
$967$		−	56616.7i		−	1.88280i	0.337286	−	0.941402i	$-0.390491\pi$
$968$		−	63353.3i		−	2.10357i
$969$	−2966.10			−0.0983331
$970$	5034.07	+	735.971i	0.166633	+	0.0243615i
$971$	−26230.8			−0.866927			−0.433463	−	0.901171i	$-0.642709\pi$
$971$	−26230.8			−0.866927			−0.433463	+	0.901171i	$0.642709\pi$
$972$		−	517.886i		−	0.0170897i
$973$			12134.4i			0.399806i
$974$	−51346.0			−1.68915
$975$	20203.4	+	6036.40i	0.663615	+	0.198276i
$976$	30080.6			0.986534
$977$		−	35339.9i		−	1.15724i	−0.815597	−	0.578620i	$-0.803591\pi$
$977$		−	35339.9i		−	1.15724i	0.815597	−	0.578620i	$-0.196409\pi$
$978$		−	13178.6i		−	0.430884i
$979$	−50635.8			−1.65304
$980$	−1155.28	−	168.899i	−0.0376571	−	0.00550539i
$981$	−5280.23			−0.171850
$982$			12608.3i			0.409723i
$983$			25377.6i			0.823419i	0.911315	+	0.411710i	$0.135068\pi$
$983$			25377.6i			0.823419i	−0.911315	+	0.411710i	$0.864932\pi$
$984$	19371.4			0.627580
$985$	−2603.31	+	17806.7i	−0.0842115	+	0.576010i
$986$	−17931.1			−0.579152
$987$		−	11102.9i		−	0.358065i
$988$			3119.75i			0.100458i
$989$	−7350.12			−0.236320
$990$	−3183.92	+	21778.2i	−0.102214	+	0.699147i
$991$	−15086.3			−0.483585			−0.241792	−	0.970328i	$-0.577735\pi$
$991$	−15086.3			−0.483585			−0.241792	+	0.970328i	$0.577735\pi$
$992$			7131.08i			0.228238i
$993$		−	2373.91i		−	0.0758649i
$994$	14902.0			0.475515
$995$	−3027.00	−	442.542i	−0.0964447	−	0.0141000i
$996$	5859.85			0.186422
$997$		−	1393.06i		−	0.0442513i	−0.999755	−	0.0221256i	$-0.992957\pi$
$997$		−	1393.06i		−	0.0442513i	0.999755	−	0.0221256i	$-0.00704338\pi$
$998$		−	41318.0i		−	1.31052i
$999$	3245.37			0.102782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.d.a.64.2	✓	6
3.2	odd	2		315.4.d.a.64.5		6
5.2	odd	4		525.4.a.q.1.3		3
5.3	odd	4		525.4.a.r.1.1		3
5.4	even	2	inner	105.4.d.a.64.5	yes	6
15.2	even	4		1575.4.a.bd.1.1		3
15.8	even	4		1575.4.a.bc.1.3		3
15.14	odd	2		315.4.d.a.64.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.d.a.64.2	✓	6	1.1	even	1	trivial
105.4.d.a.64.5	yes	6	5.4	even	2	inner
315.4.d.a.64.2		6	15.14	odd	2
315.4.d.a.64.5		6	3.2	odd	2
525.4.a.q.1.3		3	5.2	odd	4
525.4.a.r.1.1		3	5.3	odd	4
1575.4.a.bc.1.3		3	15.8	even	4
1575.4.a.bd.1.1		3	15.2	even	4

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.18296i q^{2} +3.00000i q^{3} -2.13122 q^{4} +(-11.0627 - 1.61735i) q^{5} +9.54887 q^{6} -7.00000i q^{7} -18.6801i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-3.18296i q^{2} +3.00000i q^{3} -2.13122 q^{4} +(-11.0627 - 1.61735i) q^{5} +9.54887 q^{6} -7.00000i q^{7} -18.6801i q^{8} -9.00000 q^{9} +(-5.14795 + 35.2122i) q^{10} -68.7204 q^{11} -6.39365i q^{12} -56.2290i q^{13} -22.2807 q^{14} +(4.85205 - 33.1882i) q^{15} -76.5076 q^{16} +37.9780i q^{17} +28.6466i q^{18} +26.0335 q^{19} +(23.5771 + 3.44692i) q^{20} +21.0000 q^{21} +218.734i q^{22} -25.5222i q^{23} +56.0403 q^{24} +(119.768 + 35.7846i) q^{25} -178.974 q^{26} -27.0000i q^{27} +14.9185i q^{28} -148.336 q^{29} +(-105.637 - 15.4439i) q^{30} +75.7982 q^{31} +94.0799i q^{32} -206.161i q^{33} +120.882 q^{34} +(-11.3214 + 77.4392i) q^{35} +19.1809 q^{36} +120.199i q^{37} -82.8634i q^{38} +168.687 q^{39} +(-30.2122 + 206.653i) q^{40} +345.670 q^{41} -66.8421i q^{42} -287.989i q^{43} +146.458 q^{44} +(99.5646 + 14.5561i) q^{45} -81.2360 q^{46} -528.711i q^{47} -229.523i q^{48} -49.0000 q^{49} +(113.901 - 381.218i) q^{50} -113.934 q^{51} +119.836i q^{52} -361.728i q^{53} -85.9398 q^{54} +(760.235 + 111.145i) q^{55} -130.761 q^{56} +78.1004i q^{57} +472.146i q^{58} +705.748 q^{59} +(-10.3408 + 70.7313i) q^{60} -393.171 q^{61} -241.262i q^{62} +63.0000i q^{63} -312.609 q^{64} +(-90.9419 + 622.046i) q^{65} -656.202 q^{66} +591.202i q^{67} -80.9393i q^{68} +76.5666 q^{69} +(246.486 + 36.0357i) q^{70} -668.829 q^{71} +168.121i q^{72} +251.755i q^{73} +382.588 q^{74} +(-107.354 + 359.305i) q^{75} -55.4830 q^{76} +481.042i q^{77} -536.923i q^{78} -295.651 q^{79} +(846.384 + 123.740i) q^{80} +81.0000 q^{81} -1100.25i q^{82} +916.511i q^{83} -44.7555 q^{84} +(61.4237 - 420.141i) q^{85} -916.658 q^{86} -445.007i q^{87} +1283.70i q^{88} +736.838 q^{89} +(46.3316 - 316.910i) q^{90} -393.603 q^{91} +54.3933i q^{92} +227.395i q^{93} -1682.86 q^{94} +(-288.002 - 42.1052i) q^{95} -282.240 q^{96} -142.964i q^{97} +155.965i q^{98} +618.483 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 14 q^{5} - 6 q^{6} - 54 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 14 * q^5 - 6 * q^6 - 54 * q^9	\( 6 q - 6 q^{4} - 14 q^{5} - 6 q^{6} - 54 q^{9} - 84 q^{10} - 132 q^{11} + 14 q^{14} - 24 q^{15} - 138 q^{16} + 276 q^{19} + 334 q^{20} + 126 q^{21} + 126 q^{24} + 366 q^{25} - 196 q^{26} - 340 q^{29} - 54 q^{30} - 732 q^{31} + 72 q^{34} + 56 q^{35} + 54 q^{36} + 612 q^{39} + 12 q^{40} - 412 q^{41} + 612 q^{44} + 126 q^{45} - 1344 q^{46} - 294 q^{49} + 1216 q^{50} - 912 q^{51} + 54 q^{54} + 1860 q^{55} - 294 q^{56} + 1760 q^{59} + 624 q^{60} - 1740 q^{61} + 1626 q^{64} - 16 q^{65} - 1116 q^{66} - 1080 q^{69} + 126 q^{70} - 2036 q^{71} - 1960 q^{74} + 936 q^{75} - 900 q^{76} + 3240 q^{79} + 3794 q^{80} + 486 q^{81} - 126 q^{84} + 432 q^{85} - 5864 q^{86} + 3876 q^{89} + 756 q^{90} - 1428 q^{91} - 4224 q^{94} - 828 q^{95} + 906 q^{96} + 1188 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 14 * q^5 - 6 * q^6 - 54 * q^9 - 84 * q^10 - 132 * q^11 + 14 * q^14 - 24 * q^15 - 138 * q^16 + 276 * q^19 + 334 * q^20 + 126 * q^21 + 126 * q^24 + 366 * q^25 - 196 * q^26 - 340 * q^29 - 54 * q^30 - 732 * q^31 + 72 * q^34 + 56 * q^35 + 54 * q^36 + 612 * q^39 + 12 * q^40 - 412 * q^41 + 612 * q^44 + 126 * q^45 - 1344 * q^46 - 294 * q^49 + 1216 * q^50 - 912 * q^51 + 54 * q^54 + 1860 * q^55 - 294 * q^56 + 1760 * q^59 + 624 * q^60 - 1740 * q^61 + 1626 * q^64 - 16 * q^65 - 1116 * q^66 - 1080 * q^69 + 126 * q^70 - 2036 * q^71 - 1960 * q^74 + 936 * q^75 - 900 * q^76 + 3240 * q^79 + 3794 * q^80 + 486 * q^81 - 126 * q^84 + 432 * q^85 - 5864 * q^86 + 3876 * q^89 + 756 * q^90 - 1428 * q^91 - 4224 * q^94 - 828 * q^95 + 906 * q^96 + 1188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more