LMFDB - Embedded newform 43.7.b.b.42.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(42,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.b (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:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 1038 x^{18} + 455829 x^{16} + 110435384 x^{14} + 16133606976 x^{12} + 1458210485616 x^{10} + \cdots + 64\!\cdots\!40 $ x^20 + 1038x^18 + 455829x^16 + 110435384x^14 + 16133606976x^12 + 1458210485616x^10 + 80362197690736x^8 + 2545997652841536x^6 + 40210452531479040x^4 + 212033222410436608*x^2 + 64236717122519040
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.16
Root			$11.0119i$ of defining polynomial
Character	$\chi$	$=$	43.42
Dual form			43.7.b.b.42.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.0119i q^{2} +50.0401i q^{3} -57.2623 q^{4} -30.3065i q^{5} -551.037 q^{6} +75.1486i q^{7} +74.1946i q^{8} -1775.01 q^{9} +O(q^{10})$	\(q+11.0119i q^{2} +50.0401i q^{3} -57.2623 q^{4} -30.3065i q^{5} -551.037 q^{6} +75.1486i q^{7} +74.1946i q^{8} -1775.01 q^{9} +333.733 q^{10} +604.862 q^{11} -2865.41i q^{12} +2635.68 q^{13} -827.530 q^{14} +1516.54 q^{15} -4481.81 q^{16} +4989.55 q^{17} -19546.3i q^{18} +3038.63i q^{19} +1735.42i q^{20} -3760.44 q^{21} +6660.70i q^{22} -12445.5 q^{23} -3712.70 q^{24} +14706.5 q^{25} +29023.9i q^{26} -52342.4i q^{27} -4303.18i q^{28} -4449.10i q^{29} +16700.0i q^{30} -29312.5 q^{31} -44604.9i q^{32} +30267.4i q^{33} +54944.5i q^{34} +2277.49 q^{35} +101641. q^{36} +83027.3i q^{37} -33461.2 q^{38} +131890. i q^{39} +2248.58 q^{40} -33442.2 q^{41} -41409.7i q^{42} +(30046.7 - 73610.9i) q^{43} -34635.8 q^{44} +53794.4i q^{45} -137048. i q^{46} -157085. q^{47} -224270. i q^{48} +112002. q^{49} +161947. i q^{50} +249678. i q^{51} -150925. q^{52} +212620. q^{53} +576391. q^{54} -18331.3i q^{55} -5575.61 q^{56} -152053. q^{57} +48993.1 q^{58} -263304. q^{59} -86840.7 q^{60} -133532. i q^{61} -322787. i q^{62} -133389. i q^{63} +204350. q^{64} -79878.2i q^{65} -333302. q^{66} -157955. q^{67} -285713. q^{68} -622771. i q^{69} +25079.5i q^{70} +485322. i q^{71} -131696. i q^{72} -48573.5i q^{73} -914290. q^{74} +735915. i q^{75} -173999. i q^{76} +45454.5i q^{77} -1.45236e6 q^{78} +762200. q^{79} +135828. i q^{80} +1.32524e6 q^{81} -368262. i q^{82} +268573. q^{83} +215332. q^{84} -151216. i q^{85} +(810597. + 330872. i) q^{86} +222633. q^{87} +44877.5i q^{88} +1.32878e6i q^{89} -592379. q^{90} +198067. i q^{91} +712656. q^{92} -1.46680e6i q^{93} -1.72980e6i q^{94} +92090.4 q^{95} +2.23203e6 q^{96} +1.43066e6 q^{97} +1.23335e6i q^{98} -1.07364e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 796 q^{4} - 258 q^{6} - 2736 q^{9}+O(q^{10}) $ 20 * q - 796 * q^4 - 258 * q^6 - 2736 * q^9	$ 20 q - 796 q^{4} - 258 q^{6} - 2736 q^{9} - 1962 q^{10} + 2616 q^{11} - 5612 q^{13} - 3876 q^{14} + 4048 q^{15} + 14900 q^{16} + 3328 q^{17} + 10544 q^{21} - 836 q^{23} + 26966 q^{24} - 57904 q^{25} + 17116 q^{31} - 150472 q^{35} - 132110 q^{36} + 2266 q^{38} + 401286 q^{40} - 141936 q^{41} + 58160 q^{43} + 88544 q^{44} + 48452 q^{47} - 20644 q^{49} + 12292 q^{52} + 425212 q^{53} + 173740 q^{54} + 447864 q^{56} - 92904 q^{57} + 86502 q^{58} - 918856 q^{59} + 429848 q^{60} - 156892 q^{64} - 1246176 q^{66} + 1098496 q^{67} - 2589854 q^{68} - 1224106 q^{74} + 855716 q^{78} - 401492 q^{79} + 470644 q^{81} + 1354360 q^{83} - 637268 q^{84} + 3046356 q^{86} + 2116740 q^{87} - 683716 q^{90} - 485998 q^{92} - 2711660 q^{95} - 2480062 q^{96} + 7814560 q^{97} + 3744560 q^{99}+O(q^{100}) $ 20 * q - 796 * q^4 - 258 * q^6 - 2736 * q^9 - 1962 * q^10 + 2616 * q^11 - 5612 * q^13 - 3876 * q^14 + 4048 * q^15 + 14900 * q^16 + 3328 * q^17 + 10544 * q^21 - 836 * q^23 + 26966 * q^24 - 57904 * q^25 + 17116 * q^31 - 150472 * q^35 - 132110 * q^36 + 2266 * q^38 + 401286 * q^40 - 141936 * q^41 + 58160 * q^43 + 88544 * q^44 + 48452 * q^47 - 20644 * q^49 + 12292 * q^52 + 425212 * q^53 + 173740 * q^54 + 447864 * q^56 - 92904 * q^57 + 86502 * q^58 - 918856 * q^59 + 429848 * q^60 - 156892 * q^64 - 1246176 * q^66 + 1098496 * q^67 - 2589854 * q^68 - 1224106 * q^74 + 855716 * q^78 - 401492 * q^79 + 470644 * q^81 + 1354360 * q^83 - 637268 * q^84 + 3046356 * q^86 + 2116740 * q^87 - 683716 * q^90 - 485998 * q^92 - 2711660 * q^95 - 2480062 * q^96 + 7814560 * q^97 + 3744560 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$			11.0119i			1.37649i	0.725478	+	0.688245i	$0.241619\pi$
$2$			11.0119i			1.37649i	−0.725478	+	0.688245i	$0.758381\pi$
$3$			50.0401i			1.85334i	0.375880	+	0.926668i	$0.377340\pi$
$3$			50.0401i			1.85334i	−0.375880	+	0.926668i	$0.622660\pi$
$4$	−57.2623			−0.894724
$5$		−	30.3065i		−	0.242452i	−0.992625	−	0.121226i	$-0.961317\pi$
$5$		−	30.3065i		−	0.242452i	0.992625	−	0.121226i	$-0.0386826\pi$
$6$	−551.037			−2.55110
$7$			75.1486i			0.219092i	0.993982	+	0.109546i	$0.0349397\pi$
$7$			75.1486i			0.219092i	−0.993982	+	0.109546i	$0.965060\pi$
$8$			74.1946i			0.144911i
$9$	−1775.01			−2.43486
$10$	333.733			0.333733
$11$	604.862			0.454442			0.227221	−	0.973843i	$-0.427036\pi$
$11$	604.862			0.454442			0.227221	+	0.973843i	$0.427036\pi$
$12$		−	2865.41i		−	1.65822i
$13$	2635.68			1.19967			0.599836	−	0.800123i	$-0.295233\pi$
$13$	2635.68			1.19967			0.599836	+	0.800123i	$0.295233\pi$
$14$	−827.530			−0.301578
$15$	1516.54			0.449345
$16$	−4481.81			−1.09419
$17$	4989.55			1.01558			0.507791	−	0.861481i	$-0.330462\pi$
$17$	4989.55			1.01558			0.507791	+	0.861481i	$0.330462\pi$
$18$		−	19546.3i		−	3.35155i
$19$			3038.63i			0.443014i	0.975159	+	0.221507i	$0.0710975\pi$
$19$			3038.63i			0.443014i	−0.975159	+	0.221507i	$0.928902\pi$
$20$			1735.42i			0.216928i
$21$	−3760.44			−0.406051
$22$			6660.70i			0.625535i
$23$	−12445.5			−1.02289			−0.511443	−	0.859317i	$-0.670889\pi$
$23$	−12445.5			−1.02289			−0.511443	+	0.859317i	$0.670889\pi$
$24$	−3712.70			−0.268569
$25$	14706.5			0.941217
$26$			29023.9i			1.65134i
$27$		−	52342.4i		−	2.65927i
$28$		−	4303.18i		−	0.196027i
$29$		−	4449.10i		−	0.182422i	−0.995832	−	0.0912111i	$-0.970926\pi$
$29$		−	4449.10i		−	0.182422i	0.995832	−	0.0912111i	$-0.0290738\pi$
$30$			16700.0i			0.618519i
$31$	−29312.5			−0.983939			−0.491969	−	0.870612i	$-0.663723\pi$
$31$	−29312.5			−0.983939			−0.491969	+	0.870612i	$0.663723\pi$
$32$		−	44604.9i		−	1.36123i
$33$			30267.4i			0.842234i
$34$			54944.5i			1.39794i
$35$	2277.49			0.0531193
$36$	101641.			2.17852
$37$			83027.3i			1.63914i	0.572980	+	0.819570i	$0.305787\pi$
$37$			83027.3i			1.63914i	−0.572980	+	0.819570i	$0.694213\pi$
$38$	−33461.2			−0.609804
$39$			131890.i			2.22339i
$40$	2248.58			0.0351340
$41$	−33442.2			−0.485225			−0.242612	−	0.970123i	$-0.578004\pi$
$41$	−33442.2			−0.485225			−0.242612	+	0.970123i	$0.578004\pi$
$42$		−	41409.7i		−	0.558925i
$43$	30046.7	−	73610.9i	0.377912	−	0.925841i
$43$	30046.7	−	73610.9i	0.377912	−	0.925841i
$44$	−34635.8			−0.406600
$45$			53794.4i			0.590336i
$46$		−	137048.i		−	1.40799i
$47$	−157085.			−1.51301			−0.756503	−	0.653991i	$-0.773093\pi$
$47$	−157085.			−1.51301			−0.756503	+	0.653991i	$0.773093\pi$
$48$		−	224270.i		−	2.02791i
$49$	112002.			0.951999
$50$			161947.i			1.29558i
$51$			249678.i			1.88221i
$52$	−150925.			−1.07337
$53$	212620.			1.42816			0.714078	−	0.700066i	$-0.246846\pi$
$53$	212620.			1.42816			0.714078	+	0.700066i	$0.246846\pi$
$54$	576391.			3.66046
$55$		−	18331.3i		−	0.110180i
$56$	−5575.61			−0.0317489
$57$	−152053.			−0.821054
$58$	48993.1			0.251102
$59$	−263304.			−1.28204			−0.641019	−	0.767525i	$-0.721488\pi$
$59$	−263304.			−1.28204			−0.641019	+	0.767525i	$0.721488\pi$
$60$	−86840.7			−0.402040
$61$		−	133532.i		−	0.588296i	−0.955760	−	0.294148i	$-0.904964\pi$
$61$		−	133532.i		−	0.588296i	0.955760	−	0.294148i	$-0.0950359\pi$
$62$		−	322787.i		−	1.35438i
$63$		−	133389.i		−	0.533457i
$64$	204350.			0.779532
$65$		−	79878.2i		−	0.290863i
$66$	−333302.			−1.15933
$67$	−157955.			−0.525182			−0.262591	−	0.964907i	$-0.584577\pi$
$67$	−157955.			−0.525182			−0.262591	+	0.964907i	$0.584577\pi$
$68$	−285713.			−0.908665
$69$		−	622771.i		−	1.89575i
$70$			25079.5i			0.0731182i
$71$			485322.i			1.35599i	0.735068	+	0.677993i	$0.237150\pi$
$71$			485322.i			1.35599i	−0.735068	+	0.677993i	$0.762850\pi$
$72$		−	131696.i		−	0.352838i
$73$		−	48573.5i		−	0.124862i	−0.998049	−	0.0624310i	$-0.980115\pi$
$73$		−	48573.5i		−	0.124862i	0.998049	−	0.0624310i	$-0.0198853\pi$
$74$	−914290.			−2.25626
$75$			735915.i			1.74439i
$76$		−	173999.i		−	0.396375i
$77$			45454.5i			0.0995646i
$78$	−1.45236e6			−3.06048
$79$	762200.			1.54592			0.772961	−	0.634454i	$-0.218775\pi$
$79$	762200.			1.54592			0.772961	+	0.634454i	$0.218775\pi$
$80$			135828.i			0.265289i
$81$	1.32524e6			2.49367
$82$		−	368262.i		−	0.667907i
$83$	268573.			0.469708			0.234854	−	0.972031i	$-0.424539\pi$
$83$	268573.			0.469708			0.234854	+	0.972031i	$0.424539\pi$
$84$	215332.			0.363304
$85$		−	151216.i		−	0.246230i
$86$	810597.	+	330872.i	1.27441	+	0.520192i
$87$	222633.			0.338090
$88$			44877.5i			0.0658538i
$89$			1.32878e6i			1.88488i	0.334381	+	0.942438i	$0.391473\pi$
$89$			1.32878e6i			1.88488i	−0.334381	+	0.942438i	$0.608527\pi$
$90$	−592379.			−0.812592
$91$			198067.i			0.262838i
$92$	712656.			0.915201
$93$		−	1.46680e6i		−	1.82357i
$94$		−	1.72980e6i		−	2.08264i
$95$	92090.4			0.107410
$96$	2.23203e6			2.52282
$97$	1.43066e6			1.56755			0.783774	−	0.621046i	$-0.213292\pi$
$97$	1.43066e6			1.56755			0.783774	+	0.621046i	$0.213292\pi$
$98$			1.23335e6i			1.31042i
$99$	−1.07364e6			−1.10650
$100$	−842129.			−0.842129
$101$	909346.			0.882602			0.441301	−	0.897359i	$-0.354517\pi$
$101$	909346.			0.882602			0.441301	+	0.897359i	$0.354517\pi$
$102$	−2.74943e6			−2.59085
$103$	634146.			0.580333			0.290167	−	0.956976i	$-0.406289\pi$
$103$	634146.			0.580333			0.290167	+	0.956976i	$0.406289\pi$
$104$			195553.i			0.173846i
$105$			113966.i			0.0984480i
$106$			2.34135e6i			1.96584i
$107$	−481718.			−0.393225			−0.196613	−	0.980481i	$-0.562994\pi$
$107$	−481718.			−0.393225			−0.196613	+	0.980481i	$0.562994\pi$
$108$			2.99725e6i			2.37931i
$109$	1.74683e6			1.34888			0.674438	−	0.738332i	$-0.264386\pi$
$109$	1.74683e6			1.34888			0.674438	+	0.738332i	$0.264386\pi$
$110$	201863.			0.151662
$111$	−4.15469e6			−3.03788
$112$		−	336802.i		−	0.239729i
$113$			1.35156e6i			0.936701i	0.883543	+	0.468350i	$0.155151\pi$
$113$			1.35156e6i			0.936701i	−0.883543	+	0.468350i	$0.844849\pi$
$114$		−	1.67440e6i		−	1.13017i
$115$			377178.i			0.248001i
$116$			254766.i			0.163218i
$117$	−4.67835e6			−2.92103
$118$		−	2.89948e6i		−	1.76471i
$119$			374958.i			0.222506i
$120$			112519.i			0.0651152i
$121$	−1.40570e6			−0.793482
$122$	1.47044e6			0.809783
$123$		−	1.67345e6i		−	0.899284i
$124$	1.67850e6			0.880354
$125$		−	919243.i		−	0.470652i
$126$	1.46887e6			0.734299
$127$	−376971.			−0.184034			−0.0920168	−	0.995757i	$-0.529331\pi$
$127$	−376971.			−0.184034			−0.0920168	+	0.995757i	$0.529331\pi$
$128$		−	604434.i		−	0.288216i
$129$	3.68349e6	+	1.50354e6i	1.71590	+	0.700399i
$130$	879613.			0.400370
$131$		−	1.97348e6i		−	0.877847i	−0.898524	−	0.438923i	$-0.855360\pi$
$131$		−	1.97348e6i		−	0.877847i	0.898524	−	0.438923i	$-0.144640\pi$
$132$		−	1.73318e6i		−	0.753567i
$133$	−228349.			−0.0970608
$134$		−	1.73939e6i		−	0.722907i
$135$	−1.58632e6			−0.644746
$136$			370197.i			0.147169i
$137$			3.58675e6i			1.39489i	0.716638	+	0.697445i	$0.245680\pi$
$137$			3.58675e6i			1.39489i	−0.716638	+	0.697445i	$0.754320\pi$
$138$	6.85791e6			2.60948
$139$	−952415.			−0.354635			−0.177318	−	0.984154i	$-0.556742\pi$
$139$	−952415.			−0.354635			−0.177318	+	0.984154i	$0.556742\pi$
$140$	−130414.			−0.0475271
$141$		−	7.86053e6i		−	2.80411i
$142$	−5.34433e6			−1.86650
$143$	1.59422e6			0.545181
$144$	7.95527e6			2.66420
$145$	−134837.			−0.0442287
$146$	534887.			0.171871
$147$			5.60457e6i			1.76437i
$148$		−	4.75434e6i		−	1.46658i
$149$		−	3.30681e6i		−	0.999656i	−0.866125	−	0.499828i	$-0.833396\pi$
$149$		−	3.30681e6i		−	0.999656i	0.866125	−	0.499828i	$-0.166604\pi$
$150$	−8.10384e6			−2.40114
$151$		−	5.46323e6i		−	1.58679i	−0.608709	−	0.793393i	$-0.708312\pi$
$151$		−	5.46323e6i		−	1.58679i	0.608709	−	0.793393i	$-0.291688\pi$
$152$	−225450.			−0.0641977
$153$	−8.85650e6			−2.47279
$154$	−500542.			−0.137050
$155$			888361.i			0.238558i
$156$		−	7.55230e6i		−	1.98932i
$157$			833342.i			0.215340i	0.994187	+	0.107670i	$0.0343390\pi$
$157$			833342.i			0.215340i	−0.994187	+	0.107670i	$0.965661\pi$
$158$			8.39328e6i			2.12795i
$159$			1.06395e7i			2.64685i
$160$	−1.35182e6			−0.330034
$161$		−	935258.i		−	0.224106i
$162$			1.45934e7i			3.43251i
$163$			1.39941e6i			0.323134i	0.986862	+	0.161567i	$0.0516547\pi$
$163$			1.39941e6i			0.323134i	−0.986862	+	0.161567i	$0.948345\pi$
$164$	1.91498e6			0.434142
$165$	917299.			0.204202
$166$			2.95750e6i			0.646548i
$167$	6.41130e6			1.37657			0.688283	−	0.725442i	$-0.258365\pi$
$167$	6.41130e6			1.37657			0.688283	+	0.725442i	$0.258365\pi$
$168$		−	279004.i		−	0.0588414i
$169$	2.11999e6			0.439211
$170$	1.66518e6			0.338933
$171$		−	5.39360e6i		−	1.07867i
$172$	−1.72054e6	+	4.21513e6i	−0.338127	+	0.828373i
$173$	−5.06186e6			−0.977624			−0.488812	−	0.872389i	$-0.662570\pi$
$173$	−5.06186e6			−0.977624			−0.488812	+	0.872389i	$0.662570\pi$
$174$			2.45162e6i			0.465377i
$175$			1.10517e6i			0.206213i
$176$	−2.71088e6			−0.497247
$177$		−	1.31757e7i		−	2.37605i
$178$	−1.46324e7			−2.59451
$179$		−	428340.i		−	0.0746843i	−0.999303	−	0.0373422i	$-0.988111\pi$
$179$		−	428340.i		−	0.0746843i	0.999303	−	0.0373422i	$-0.0118891\pi$
$180$		−	3.08039e6i		−	0.528188i
$181$	2.17931e6			0.367522			0.183761	−	0.982971i	$-0.441173\pi$
$181$	2.17931e6			0.367522			0.183761	+	0.982971i	$0.441173\pi$
$182$	−2.18110e6			−0.361794
$183$	6.68195e6			1.09031
$184$		−	923385.i		−	0.148228i
$185$	2.51627e6			0.397413
$186$	1.61523e7			2.51013
$187$	3.01799e6			0.461523
$188$	8.99504e6			1.35372
$189$	3.93346e6			0.582625
$190$			1.01409e6i			0.147848i
$191$		−	4.92816e6i		−	0.707269i	−0.935384	−	0.353635i	$-0.884946\pi$
$191$		−	4.92816e6i		−	0.707269i	0.935384	−	0.353635i	$-0.115054\pi$
$192$			1.02257e7i			1.44473i
$193$	−3.40731e6			−0.473958			−0.236979	−	0.971515i	$-0.576157\pi$
$193$	−3.40731e6			−0.473958			−0.236979	+	0.971515i	$0.576157\pi$
$194$			1.57543e7i			2.15772i
$195$	3.99711e6			0.539067
$196$	−6.41348e6			−0.851776
$197$	−646332.			−0.0845390			−0.0422695	−	0.999106i	$-0.513459\pi$
$197$	−646332.			−0.0845390			−0.0422695	+	0.999106i	$0.513459\pi$
$198$		−	1.18228e7i		−	1.52309i
$199$			6.52813e6i			0.828379i	0.910191	+	0.414190i	$0.135935\pi$
$199$			6.52813e6i			0.828379i	−0.910191	+	0.414190i	$0.864065\pi$
$200$			1.09114e6i			0.136393i
$201$		−	7.90409e6i		−	0.973338i
$202$			1.00136e7i			1.21489i
$203$	334343.			0.0399673
$204$		−	1.42971e7i		−	1.68406i
$205$			1.01352e6i			0.117644i
$206$			6.98316e6i			0.798823i
$207$	2.20908e7			2.49058
$208$	−1.18126e7			−1.31267
$209$			1.83795e6i			0.201324i
$210$	−1.25498e6			−0.135513
$211$		−	2.63536e6i		−	0.280539i	−0.990113	−	0.140269i	$-0.955203\pi$
$211$		−	2.63536e6i		−	0.280539i	0.990113	−	0.140269i	$-0.0447968\pi$
$212$	−1.21751e7			−1.27781
$213$	−2.42856e7			−2.51310
$214$		−	5.30464e6i		−	0.541271i
$215$	−2.23089e6	−	910610.i	−0.224472	−	0.0916257i
$216$	3.88352e6			0.385358
$217$		−	2.20279e6i		−	0.215573i
$218$			1.92360e7i			1.85671i
$219$	2.43062e6			0.231411
$220$			1.04969e6i			0.0985811i
$221$	1.31508e7			1.21836
$222$		−	4.57512e7i		−	4.18161i
$223$		−	1.69760e7i		−	1.53081i	−0.643551	−	0.765403i	$-0.722540\pi$
$223$		−	1.69760e7i		−	1.53081i	0.643551	−	0.765403i	$-0.277460\pi$
$224$	3.35200e6			0.298235
$225$	−2.61042e7			−2.29173
$226$	−1.48833e7			−1.28936
$227$			1.01092e7i			0.864247i	0.901814	+	0.432124i	$0.142236\pi$
$227$			1.01092e7i			0.864247i	−0.901814	+	0.432124i	$0.857764\pi$
$228$	8.70693e6			0.734616
$229$	7.19101e6			0.598802			0.299401	−	0.954127i	$-0.403213\pi$
$229$	7.19101e6			0.598802			0.299401	+	0.954127i	$0.403213\pi$
$230$	−4.15346e6			−0.341371
$231$	−2.27455e6			−0.184527
$232$	330099.			0.0264350
$233$			1.30168e7i			1.02905i	0.857475	+	0.514526i	$0.172032\pi$
$233$			1.30168e7i			1.02905i	−0.857475	+	0.514526i	$0.827968\pi$
$234$		−	5.15177e7i		−	4.02076i
$235$			4.76069e6i			0.366831i
$236$	1.50774e7			1.14707
$237$			3.81405e7i			2.86511i
$238$	−4.12900e6			−0.306277
$239$	−5.98455e6			−0.438367			−0.219183	−	0.975684i	$-0.570339\pi$
$239$	−5.98455e6			−0.438367			−0.219183	+	0.975684i	$0.570339\pi$
$240$	−6.79686e6			−0.491671
$241$		−	1.94706e7i		−	1.39101i	−0.718523	−	0.695503i	$-0.755182\pi$
$241$		−	1.94706e7i		−	1.39101i	0.718523	−	0.695503i	$-0.244818\pi$
$242$		−	1.54795e7i		−	1.09222i
$243$			2.81574e7i			1.96233i
$244$			7.64636e6i			0.526363i
$245$		−	3.39438e6i		−	0.230814i
$246$	1.84279e7			1.23786
$247$			8.00885e6i			0.531471i
$248$		−	2.17483e6i		−	0.142584i
$249$			1.34394e7i			0.870527i
$250$	1.01226e7			0.647848
$251$	−6.05694e6			−0.383029			−0.191515	−	0.981490i	$-0.561340\pi$
$251$	−6.05694e6			−0.383029			−0.191515	+	0.981490i	$0.561340\pi$
$252$			7.63819e6i			0.477297i
$253$	−7.52779e6			−0.464842
$254$		−	4.15118e6i		−	0.253320i
$255$	7.56686e6			0.456347
$256$	1.97343e7			1.17626
$257$		−	1.73952e7i		−	1.02478i	−0.858754	−	0.512388i	$-0.828761\pi$
$257$		−	1.73952e7i		−	1.02478i	0.858754	−	0.512388i	$-0.171239\pi$
$258$	−1.65568e7	+	4.05623e7i	−0.964092	+	2.36191i
$259$	−6.23938e6			−0.359122
$260$			4.57402e6i			0.260242i
$261$			7.89719e6i			0.444172i
$262$	2.17318e7			1.20835
$263$		−	2.18225e7i		−	1.19960i	−0.800149	−	0.599801i	$-0.795246\pi$
$263$		−	2.18225e7i		−	1.19960i	0.800149	−	0.599801i	$-0.204754\pi$
$264$	−2.24567e6			−0.122049
$265$		−	6.44376e6i		−	0.346259i
$266$		−	2.51456e6i		−	0.133603i
$267$	−6.64922e7			−3.49331
$268$	9.04488e6			0.469893
$269$	759715.			0.0390296			0.0195148	−	0.999810i	$-0.493788\pi$
$269$	759715.			0.0390296			0.0195148	+	0.999810i	$0.493788\pi$
$270$		−	1.74684e7i		−	0.887486i
$271$	3.82518e7			1.92196			0.960978	−	0.276624i	$-0.0892155\pi$
$271$	3.82518e7			1.92196			0.960978	+	0.276624i	$0.0892155\pi$
$272$	−2.23622e7			−1.11124
$273$	−9.91131e6			−0.487128
$274$	−3.94970e7			−1.92005
$275$	8.89542e6			0.427729
$276$			3.56614e7i			1.69617i
$277$		−	2.70372e7i		−	1.27210i	−0.771647	−	0.636052i	$-0.780567\pi$
$277$		−	2.70372e7i		−	1.27210i	0.771647	−	0.636052i	$-0.219433\pi$
$278$		−	1.04879e7i		−	0.488152i
$279$	5.20300e7			2.39575
$280$			168977.i			0.00769759i
$281$	−1.84904e7			−0.833352			−0.416676	−	0.909055i	$-0.636805\pi$
$281$	−1.84904e7			−0.833352			−0.416676	+	0.909055i	$0.636805\pi$
$282$	8.65595e7			3.85983
$283$	3.01118e7			1.32855			0.664274	−	0.747489i	$-0.268741\pi$
$283$	3.01118e7			1.32855			0.664274	+	0.747489i	$0.268741\pi$
$284$		−	2.77907e7i		−	1.21323i
$285$			4.60821e6i			0.199066i
$286$			1.75555e7i			0.750436i
$287$		−	2.51313e6i		−	0.106309i
$288$			7.91742e7i			3.31441i
$289$	758046.			0.0314052
$290$		−	1.48481e6i		−	0.0608803i
$291$			7.15903e7i			2.90520i
$292$			2.78143e6i			0.111717i
$293$	1.61065e6			0.0640324			0.0320162	−	0.999487i	$-0.489807\pi$
$293$	1.61065e6			0.0640324			0.0320162	+	0.999487i	$0.489807\pi$
$294$	−6.17171e7			−2.42864
$295$			7.97982e6i			0.310833i
$296$	−6.16018e6			−0.237530
$297$		−	3.16600e7i		−	1.20848i
$298$	3.64143e7			1.37602
$299$	−3.28022e7			−1.22713
$300$		−	4.21402e7i		−	1.56075i
$301$	5.53175e6	+	2.25796e6i	0.202844	+	0.0827976i
$302$	6.01606e7			2.18420
$303$			4.55037e7i			1.63576i
$304$		−	1.36186e7i		−	0.484743i
$305$	−4.04689e6			−0.142634
$306$		−	9.75271e7i		−	3.40378i
$307$	3.91736e7			1.35388			0.676938	−	0.736040i	$-0.263307\pi$
$307$	3.91736e7			1.35388			0.676938	+	0.736040i	$0.263307\pi$
$308$		−	2.60283e6i		−	0.0890829i
$309$			3.17327e7i			1.07555i
$310$	−9.78256e6			−0.328373
$311$	−2.65437e7			−0.882429			−0.441215	−	0.897402i	$-0.645452\pi$
$311$	−2.65437e7			−0.882429			−0.441215	+	0.897402i	$0.645452\pi$
$312$	−9.78549e6			−0.322195
$313$		−	3.65208e7i		−	1.19099i	−0.803359	−	0.595495i	$-0.796956\pi$
$313$		−	3.65208e7i		−	1.19099i	0.803359	−	0.595495i	$-0.203044\pi$
$314$	−9.17669e6			−0.296413
$315$	−4.04257e6			−0.129338
$316$	−4.36453e7			−1.38317
$317$	3.58851e7			1.12651			0.563257	−	0.826282i	$-0.309548\pi$
$317$	3.58851e7			1.12651			0.563257	+	0.826282i	$0.309548\pi$
$318$	−1.17161e8			−3.64337
$319$		−	2.69109e6i		−	0.0829004i
$320$		−	6.19313e6i		−	0.188999i
$321$		−	2.41052e7i		−	0.728779i
$322$	1.02990e7			0.308480
$323$			1.51614e7i			0.449916i
$324$	−7.58862e7			−2.23114
$325$	3.87616e7			1.12915
$326$	−1.54102e7			−0.444790
$327$			8.74117e7i			2.49992i
$328$		−	2.48123e6i		−	0.0703145i
$329$		−	1.18047e7i		−	0.331487i
$330$			1.01012e7i			0.281081i
$331$			4.13224e7i			1.13947i	0.821829	+	0.569734i	$0.192954\pi$
$331$			4.13224e7i			1.13947i	−0.821829	+	0.569734i	$0.807046\pi$
$332$	−1.53791e7			−0.420259
$333$		−	1.47374e8i		−	3.99107i
$334$			7.06008e7i			1.89483i
$335$			4.78707e6i			0.127331i
$336$	1.68536e7			0.444298
$337$	5.37649e7			1.40478			0.702392	−	0.711790i	$-0.252115\pi$
$337$	5.37649e7			1.40478			0.702392	+	0.711790i	$0.252115\pi$
$338$			2.33452e7i			0.604570i
$339$	−6.76323e7			−1.73602
$340$			8.65898e6i			0.220308i
$341$	−1.77300e7			−0.447143
$342$	5.93939e7			1.48478
$343$			1.72579e7i			0.427667i
$344$	5.46153e6	+	2.22930e6i	0.134165	+	0.0547637i
$345$	−1.88740e7			−0.459629
$346$		−	5.57408e7i		−	1.34569i
$347$		−	7.03541e7i		−	1.68384i	−0.539603	−	0.841920i	$-0.681426\pi$
$347$		−	7.03541e7i		−	1.68384i	0.539603	−	0.841920i	$-0.318574\pi$
$348$	−1.27485e7			−0.302497
$349$			5.74051e7i			1.35044i	0.737618	+	0.675218i	$0.235951\pi$
$349$			5.74051e7i			1.35044i	−0.737618	+	0.675218i	$0.764049\pi$
$350$	−1.21701e7			−0.283850
$351$		−	1.37958e8i		−	3.19025i
$352$		−	2.69798e7i		−	0.618602i
$353$	−6.11985e7			−1.39129			−0.695644	−	0.718387i	$-0.744881\pi$
$353$	−6.11985e7			−1.39129			−0.695644	+	0.718387i	$0.744881\pi$
$354$	1.45090e8			3.27061
$355$	1.47084e7			0.328762
$356$		−	7.60890e7i		−	1.68644i
$357$	−1.87629e7			−0.412378
$358$	4.71684e6			0.102802
$359$	1.65832e7			0.358414			0.179207	−	0.983811i	$-0.442647\pi$
$359$	1.65832e7			0.358414			0.179207	+	0.983811i	$0.442647\pi$
$360$	−3.99125e6			−0.0855464
$361$	3.78126e7			0.803739
$362$			2.39984e7i			0.505891i
$363$		−	7.03415e7i		−	1.47059i
$364$		−	1.13418e7i		−	0.235168i
$365$	−1.47209e6			−0.0302731
$366$			7.35811e7i			1.50080i
$367$	−7.49850e6			−0.151697			−0.0758484	−	0.997119i	$-0.524166\pi$
$367$	−7.49850e6			−0.151697			−0.0758484	+	0.997119i	$0.524166\pi$
$368$	5.57782e7			1.11923
$369$	5.93602e7			1.18145
$370$			2.77090e7i			0.547035i
$371$			1.59780e7i			0.312897i
$372$			8.39925e7i			1.63159i
$373$			2.28773e7i			0.440837i	0.975405	+	0.220419i	$0.0707423\pi$
$373$			2.28773e7i			0.440837i	−0.975405	+	0.220419i	$0.929258\pi$
$374$			3.32339e7i			0.635282i
$375$	4.59990e7			0.872277
$376$		−	1.16548e7i		−	0.219251i
$377$		−	1.17264e7i		−	0.218847i
$378$			4.33149e7i			0.801977i
$379$	−3.49753e7			−0.642457			−0.321228	−	0.947002i	$-0.604096\pi$
$379$	−3.49753e7			−0.642457			−0.321228	+	0.947002i	$0.604096\pi$
$380$	−5.27331e6			−0.0961020
$381$		−	1.88637e7i		−	0.341076i
$382$	5.42685e7			0.973549
$383$		−	3.06385e7i		−	0.545345i	−0.962107	−	0.272672i	$-0.912093\pi$
$383$		−	3.06385e7i		−	0.545345i	0.962107	−	0.272672i	$-0.0879075\pi$
$384$	3.02459e7			0.534162
$385$	1.37757e6			0.0241397
$386$		−	3.75210e7i		−	0.652398i
$387$	−5.33332e7	+	1.30660e8i	−0.920162	+	2.25429i
$388$	−8.19229e7			−1.40252
$389$			8.00209e6i			0.135942i	0.997687	+	0.0679711i	$0.0216526\pi$
$389$			8.00209e6i			0.135942i	−0.997687	+	0.0679711i	$0.978347\pi$
$390$			4.40159e7i			0.742020i
$391$	−6.20972e7			−1.03882
$392$			8.30992e6i			0.137955i
$393$	9.87531e7			1.62695
$394$		−	7.11736e6i		−	0.116367i
$395$		−	2.30996e7i		−	0.374812i
$396$	6.14790e7			0.990013
$397$	−7.52627e7			−1.20284			−0.601421	−	0.798932i	$-0.705399\pi$
$397$	−7.52627e7			−1.20284			−0.601421	+	0.798932i	$0.705399\pi$
$398$	−7.18872e7			−1.14026
$399$		−	1.14266e7i		−	0.179886i
$400$	−6.59119e7			−1.02987
$401$	−3.64743e7			−0.565658			−0.282829	−	0.959170i	$-0.591273\pi$
$401$	−3.64743e7			−0.565658			−0.282829	+	0.959170i	$0.591273\pi$
$402$	8.70392e7			1.33979
$403$	−7.72584e7			−1.18040
$404$	−5.20713e7			−0.789685
$405$		−	4.01633e7i		−	0.604595i
$406$			3.68176e6i			0.0550145i
$407$			5.02201e7i			0.744894i
$408$	−1.85247e7			−0.272754
$409$			1.19043e8i			1.73993i	0.493111	+	0.869966i	$0.335860\pi$
$409$			1.19043e8i			1.73993i	−0.493111	+	0.869966i	$0.664140\pi$
$410$	−1.11608e7			−0.161935
$411$	−1.79481e8			−2.58520
$412$	−3.63127e7			−0.519238
$413$		−	1.97869e7i		−	0.280884i
$414$			2.43262e8i			3.42826i
$415$		−	8.13951e6i		−	0.113882i
$416$		−	1.17564e8i		−	1.63303i
$417$		−	4.76589e7i		−	0.657258i
$418$	−2.02394e7			−0.277121
$419$			1.30796e8i			1.77809i	0.457824	+	0.889043i	$0.348629\pi$
$419$			1.30796e8i			1.77809i	−0.457824	+	0.889043i	$0.651371\pi$
$420$		−	6.52595e6i		−	0.0880838i
$421$		−	1.08991e8i		−	1.46064i	−0.683105	−	0.730320i	$-0.739371\pi$
$421$		−	1.08991e8i		−	1.46064i	0.683105	−	0.730320i	$-0.260629\pi$
$422$	2.90204e7			0.386159
$423$	2.78827e8			3.68395
$424$			1.57752e7i			0.206956i
$425$	7.33789e7			0.955882
$426$		−	2.67431e8i		−	3.45925i
$427$	1.00347e7			0.128891
$428$	2.75843e7			0.351828
$429$			7.97750e7i			1.01040i
$430$	1.00276e7	−	2.45664e7i	0.126122	−	0.308984i
$431$	−2.84336e7			−0.355141			−0.177570	−	0.984108i	$-0.556824\pi$
$431$	−2.84336e7			−0.355141			−0.177570	+	0.984108i	$0.556824\pi$
$432$			2.34589e8i			2.90976i
$433$		−	1.31732e7i		−	0.162266i	−0.996703	−	0.0811330i	$-0.974146\pi$
$433$		−	1.31732e7i		−	0.162266i	0.996703	−	0.0811330i	$-0.0258539\pi$
$434$	2.42570e7			0.296734
$435$		−	6.74724e6i		−	0.0819706i
$436$	−1.00028e8			−1.20687
$437$		−	3.78171e7i		−	0.453153i
$438$			2.67658e7i			0.318535i
$439$	9.21820e7			1.08956			0.544782	−	0.838578i	$-0.316612\pi$
$439$	9.21820e7			1.08956			0.544782	+	0.838578i	$0.316612\pi$
$440$	1.36008e6			0.0159664
$441$	−1.98804e8			−2.31798
$442$			1.44816e8i			1.67707i
$443$	−1.32293e8			−1.52169			−0.760843	−	0.648935i	$-0.775214\pi$
$443$	−1.32293e8			−1.52169			−0.760843	+	0.648935i	$0.775214\pi$
$444$	2.37908e8			2.71806
$445$	4.02707e7			0.456992
$446$	1.86938e8			2.10714
$447$	1.65473e8			1.85270
$448$			1.53566e7i			0.170789i
$449$		−	8.50172e7i		−	0.939221i	−0.882874	−	0.469610i	$-0.844394\pi$
$449$		−	8.50172e7i		−	0.939221i	0.882874	−	0.469610i	$-0.155606\pi$
$450$		−	2.87457e8i		−	3.15454i
$451$	−2.02279e7			−0.220506
$452$		−	7.73936e7i		−	0.838089i
$453$	2.73380e8			2.94085
$454$	−1.11321e8			−1.18963
$455$	6.00273e6			0.0637257
$456$		−	1.12815e7i		−	0.118980i
$457$			923905.i			0.00968008i	0.999988	+	0.00484004i	$0.00154064\pi$
$457$			923905.i			0.00968008i	−0.999988	+	0.00484004i	$0.998459\pi$
$458$			7.91868e7i			0.824245i
$459$		−	2.61165e8i		−	2.70071i
$460$		−	2.15981e7i		−	0.221892i
$461$	−6.17034e7			−0.629806			−0.314903	−	0.949124i	$-0.601972\pi$
$461$	−6.17034e7			−0.629806			−0.314903	+	0.949124i	$0.601972\pi$
$462$		−	2.50471e7i		−	0.253999i
$463$		−	1.17785e8i		−	1.18672i	−0.804938	−	0.593358i	$-0.797802\pi$
$463$		−	1.17785e8i		−	1.18672i	0.804938	−	0.593358i	$-0.202198\pi$
$464$			1.99400e7i			0.199605i
$465$	−4.44536e7			−0.442129
$466$	−1.43340e8			−1.41648
$467$			2.00013e6i			0.0196385i	0.999952	+	0.00981923i	$0.00312561\pi$
$467$			2.00013e6i			0.0196385i	−0.999952	+	0.00981923i	$0.996874\pi$
$468$	2.67894e8			2.61351
$469$		−	1.18701e7i		−	0.115063i
$470$	−5.24243e7			−0.504940
$471$	−4.17005e7			−0.399097
$472$		−	1.95357e7i		−	0.185782i
$473$	1.81741e7	−	4.45245e7i	0.171739	−	0.420741i
$474$	−4.20001e8			−3.94380
$475$			4.46877e7i			0.416972i
$476$		−	2.14709e7i		−	0.199081i
$477$	−3.77402e8			−3.47735
$478$		−	6.59014e7i		−	0.603408i
$479$	5.60261e7			0.509781			0.254890	−	0.966970i	$-0.417961\pi$
$479$	5.60261e7			0.509781			0.254890	+	0.966970i	$0.417961\pi$
$480$		−	6.76452e7i		−	0.611664i
$481$			2.18833e8i			1.96643i
$482$	2.14409e8			1.91471
$483$	4.68004e7			0.415344
$484$	8.04938e7			0.709948
$485$		−	4.33583e7i		−	0.380056i
$486$	−3.10066e8			−2.70113
$487$	−8.02252e7			−0.694582			−0.347291	−	0.937757i	$-0.612898\pi$
$487$	−8.02252e7			−0.694582			−0.347291	+	0.937757i	$0.612898\pi$
$488$	9.90735e6			0.0852507
$489$	−7.00266e7			−0.598875
$490$	3.73787e7			0.317713
$491$		−	4.73660e7i		−	0.400149i	−0.979781	−	0.200075i	$-0.935882\pi$
$491$		−	4.73660e7i		−	0.400149i	0.979781	−	0.200075i	$-0.0641185\pi$
$492$			9.58256e7i			0.804611i
$493$		−	2.21990e7i		−	0.185265i
$494$	−8.81928e7			−0.731564
$495$			3.25382e7i			0.268274i
$496$	1.31373e8			1.07662
$497$	−3.64713e7			−0.297086
$498$	−1.47994e8			−1.19827
$499$			1.29386e8i			1.04132i	0.853763	+	0.520662i	$0.174315\pi$
$499$			1.29386e8i			1.04132i	−0.853763	+	0.520662i	$0.825685\pi$
$500$			5.26380e7i			0.421104i
$501$			3.20822e8i			2.55124i
$502$		−	6.66985e7i		−	0.527236i
$503$			4.95506e7i			0.389355i	0.980867	+	0.194677i	$0.0623660\pi$
$503$			4.95506e7i			0.389355i	−0.980867	+	0.194677i	$0.937634\pi$
$504$	9.89677e6			0.0773040
$505$		−	2.75591e7i		−	0.213989i
$506$		−	8.28954e7i		−	0.639851i
$507$			1.06084e8i			0.814007i
$508$	2.15863e7			0.164659
$509$	1.13027e8			0.857098			0.428549	−	0.903519i	$-0.359025\pi$
$509$	1.13027e8			0.857098			0.428549	+	0.903519i	$0.359025\pi$
$510$			8.33256e7i			0.628157i
$511$	3.65022e6			0.0273563
$512$			1.78629e8i			1.33089i
$513$	1.59049e8			1.17809
$514$	1.91554e8			1.41059
$515$		−	1.92188e7i		−	0.140703i
$516$	−2.10925e8	−	8.60961e7i	−1.53525	−	0.626664i
$517$	−9.50147e7			−0.687573
$518$		−	6.87076e7i		−	0.494328i
$519$		−	2.53296e8i		−	1.81187i
$520$	5.92653e6			0.0421493
$521$			3.09027e7i			0.218516i	0.994013	+	0.109258i	$0.0348475\pi$
$521$			3.09027e7i			0.218516i	−0.994013	+	0.109258i	$0.965152\pi$
$522$	−8.69632e7			−0.611398
$523$			1.39183e8i			0.972932i	0.873699	+	0.486466i	$0.161714\pi$
$523$			1.39183e8i			0.972932i	−0.873699	+	0.486466i	$0.838286\pi$
$524$			1.13006e8i			0.785431i
$525$	−5.53030e7			−0.382182
$526$	2.40308e8			1.65124
$527$	−1.46256e8			−0.999270
$528$		−	1.35653e8i		−	0.921567i
$529$	6.85340e6			0.0462955
$530$	7.09581e7			0.476623
$531$	4.67367e8			3.12158
$532$	1.30758e7			0.0868426
$533$	−8.81428e7			−0.582110
$534$		−	7.32207e8i		−	4.80850i
$535$			1.45992e7i			0.0953383i
$536$		−	1.17194e7i		−	0.0761047i
$537$	2.14342e7			0.138415
$538$			8.36591e6i			0.0537238i
$539$	6.77456e7			0.432628
$540$	9.08362e7			0.576870
$541$	6.32657e7			0.399555			0.199777	−	0.979841i	$-0.435978\pi$
$541$	6.32657e7			0.399555			0.199777	+	0.979841i	$0.435978\pi$
$542$			4.21225e8i			2.64555i
$543$			1.09053e8i			0.681143i
$544$		−	2.22558e8i		−	1.38244i
$545$		−	5.29405e7i		−	0.327038i
$546$		−	1.09143e8i		−	0.670527i
$547$	−1.95485e8			−1.19441			−0.597203	−	0.802090i	$-0.703721\pi$
$547$	−1.95485e8			−1.19441			−0.597203	+	0.802090i	$0.703721\pi$
$548$		−	2.05386e8i		−	1.24804i
$549$			2.37021e8i			1.43242i
$550$			9.79556e7i			0.588764i
$551$	1.35192e7			0.0808156
$552$	4.62063e7			0.274716
$553$			5.72782e7i			0.338699i
$554$	2.97731e8			1.75104
$555$			1.25914e8i			0.736540i
$556$	5.45375e7			0.317301
$557$	3.96240e7			0.229294			0.114647	−	0.993406i	$-0.463426\pi$
$557$	3.96240e7			0.229294			0.114647	+	0.993406i	$0.463426\pi$
$558$			5.72950e8i			3.29772i
$559$	7.91934e7	−	1.94015e8i	0.453371	−	1.11071i
$560$	−1.02073e7			−0.0581228
$561$			1.51021e8i			0.855357i
$562$		−	2.03615e8i		−	1.14710i
$563$	2.83973e8			1.59130			0.795649	−	0.605758i	$-0.207130\pi$
$563$	2.83973e8			1.59130			0.795649	+	0.605758i	$0.207130\pi$
$564$			4.50112e8i			2.50890i
$565$	4.09612e7			0.227105
$566$			3.31589e8i			1.82873i
$567$			9.95897e7i			0.546343i
$568$	−3.60083e7			−0.196498
$569$	−1.60879e8			−0.873296			−0.436648	−	0.899632i	$-0.643834\pi$
$569$	−1.60879e8			−0.873296			−0.436648	+	0.899632i	$0.643834\pi$
$570$	−5.07452e7			−0.274013
$571$		−	2.43494e8i		−	1.30792i	−0.756530	−	0.653959i	$-0.773107\pi$
$571$		−	2.43494e8i		−	1.30792i	0.756530	−	0.653959i	$-0.226893\pi$
$572$	−9.12889e7			−0.487787
$573$	2.46606e8			1.31081
$574$	2.76744e7			0.146333
$575$	−1.83029e8			−0.962758
$576$	−3.62723e8			−1.89805
$577$			2.31171e8i			1.20339i	0.798727	+	0.601693i	$0.205507\pi$
$577$			2.31171e8i			1.20339i	−0.798727	+	0.601693i	$0.794493\pi$
$578$			8.34754e6i			0.0432290i
$579$		−	1.70502e8i		−	0.878403i
$580$	7.72106e6			0.0395725
$581$			2.01829e7i			0.102909i
$582$	−7.88347e8			−3.99897
$583$	1.28606e8			0.649014
$584$	3.60389e6			0.0180939
$585$			1.41785e8i			0.708209i
$586$			1.77364e7i			0.0881399i
$587$		−	2.10877e8i		−	1.04259i	−0.853375	−	0.521297i	$-0.825448\pi$
$587$		−	2.10877e8i		−	1.04259i	0.853375	−	0.521297i	$-0.174552\pi$
$588$		−	3.20931e8i		−	1.57863i
$589$		−	8.90700e7i		−	0.435898i
$590$	−8.78732e7			−0.427859
$591$		−	3.23425e7i		−	0.156679i
$592$		−	3.72113e8i		−	1.79353i
$593$		−	2.60310e8i		−	1.24832i	−0.781295	−	0.624162i	$-0.785440\pi$
$593$		−	2.60310e8i		−	1.24832i	0.781295	−	0.624162i	$-0.214560\pi$
$594$	3.48637e8			1.66347
$595$	1.13637e7			0.0539470
$596$			1.89356e8i			0.894417i
$597$	−3.26668e8			−1.53527
$598$		−	3.61215e8i		−	1.68913i
$599$	1.98069e8			0.921587			0.460794	−	0.887507i	$-0.347565\pi$
$599$	1.98069e8			0.921587			0.460794	+	0.887507i	$0.347565\pi$
$600$	−5.46009e7			−0.252782
$601$		−	2.10475e8i		−	0.969565i	−0.874635	−	0.484783i	$-0.838899\pi$
$601$		−	2.10475e8i		−	0.969565i	0.874635	−	0.484783i	$-0.161101\pi$
$602$	−2.48645e7	+	6.09152e7i	−0.113970	+	0.279213i
$603$	2.80372e8			1.27874
$604$			3.12837e8i			1.41974i
$605$			4.26020e7i			0.192382i
$606$	−5.01083e8			−2.25160
$607$		−	6.23544e7i		−	0.278805i	−0.990236	−	0.139403i	$-0.955482\pi$
$607$		−	6.23544e7i		−	0.278805i	0.990236	−	0.139403i	$-0.0445182\pi$
$608$	1.35538e8			0.603045
$609$			1.67306e7i			0.0740728i
$610$		−	4.45640e7i		−	0.196334i
$611$	−4.14025e8			−1.81511
$612$	5.07144e8			2.21247
$613$	−3.02341e7			−0.131255			−0.0656276	−	0.997844i	$-0.520905\pi$
$613$	−3.02341e7			−0.131255			−0.0656276	+	0.997844i	$0.520905\pi$
$614$			4.31377e8i			1.86360i
$615$	−5.07164e7			−0.218033
$616$	−3.37248e6			−0.0144280
$617$	5.23405e7			0.222834			0.111417	−	0.993774i	$-0.464461\pi$
$617$	5.23405e7			0.222834			0.111417	+	0.993774i	$0.464461\pi$
$618$	−3.49438e8			−1.48049
$619$	−6.04729e7			−0.254970			−0.127485	−	0.991841i	$-0.540690\pi$
$619$	−6.04729e7			−0.254970			−0.127485	+	0.991841i	$0.540690\pi$
$620$		−	5.08696e7i		−	0.213444i
$621$			6.51425e8i			2.72013i
$622$		−	2.92297e8i		−	1.21465i
$623$	−9.98558e7			−0.412961
$624$		−	5.91104e8i		−	2.43282i
$625$	2.01930e8			0.827106
$626$	4.02165e8			1.63938
$627$	−9.19714e7			−0.373121
$628$		−	4.77191e7i		−	0.192670i
$629$			4.14269e8i			1.66468i
$630$		−	4.45165e7i		−	0.178032i
$631$		−	5.68881e7i		−	0.226430i	−0.993571	−	0.113215i	$-0.963885\pi$
$631$		−	5.68881e7i		−	0.226430i	0.993571	−	0.113215i	$-0.0361149\pi$
$632$			5.65511e7i			0.224021i
$633$	1.31874e8			0.519933
$634$			3.95164e8i			1.55064i
$635$			1.14247e7i			0.0446194i
$636$		−	6.09243e8i		−	2.36820i
$637$	2.95200e8			1.14209
$638$	2.96341e7			0.114111
$639$		−	8.61452e8i		−	3.30163i
$640$	−1.83183e7			−0.0698787
$641$		−	5.01358e8i		−	1.90359i	−0.306734	−	0.951795i	$-0.599236\pi$
$641$		−	5.01358e8i		−	1.90359i	0.306734	−	0.951795i	$-0.400764\pi$
$642$	2.65445e8			1.00316
$643$	−2.03232e8			−0.764468			−0.382234	−	0.924065i	$-0.624845\pi$
$643$	−2.03232e8			−0.764468			−0.382234	+	0.924065i	$0.624845\pi$
$644$			5.35550e7i			0.200513i
$645$	4.55670e7	−	1.11634e8i	0.169813	−	0.416023i
$646$	−1.66956e8			−0.619305
$647$		−	1.76979e8i		−	0.653443i	−0.945121	−	0.326722i	$-0.894056\pi$
$647$		−	1.76979e8i		−	0.653443i	0.945121	−	0.326722i	$-0.105944\pi$
$648$			9.83254e7i			0.361361i
$649$	−1.59263e8			−0.582612
$650$			4.26840e8i			1.55426i
$651$	1.10228e8			0.399530
$652$		−	8.01335e7i		−	0.289115i
$653$		−	7.16442e7i		−	0.257301i	−0.991690	−	0.128651i	$-0.958935\pi$
$653$		−	7.16442e7i		−	0.257301i	0.991690	−	0.128651i	$-0.0410646\pi$
$654$	−9.62570e8			−3.44112
$655$	−5.98093e7			−0.212836
$656$	1.49882e8			0.530929
$657$			8.62184e7i			0.304021i
$658$	1.29992e8			0.456289
$659$	−4.47258e8			−1.56279			−0.781397	−	0.624035i	$-0.785492\pi$
$659$	−4.47258e8			−1.56279			−0.781397	+	0.624035i	$0.785492\pi$
$660$	−5.25267e7			−0.182704
$661$	−1.23912e8			−0.429049			−0.214525	−	0.976719i	$-0.568820\pi$
$661$	−1.23912e8			−0.429049			−0.214525	+	0.976719i	$0.568820\pi$
$662$	−4.55039e8			−1.56847
$663$			6.58070e8i			2.25804i
$664$			1.99266e7i			0.0680659i
$665$			6.92046e6i			0.0235326i
$666$	1.62287e9			5.49366
$667$			5.53710e7i			0.186597i
$668$	−3.67126e8			−1.23165
$669$	8.49480e8			2.83710
$670$	−5.27148e7			−0.175270
$671$		−	8.07685e7i		−	0.267346i
$672$			1.67734e8i			0.552731i
$673$			1.92398e7i			0.0631185i	0.999502	+	0.0315592i	$0.0100473\pi$
$673$			1.92398e7i			0.0631185i	−0.999502	+	0.0315592i	$0.989953\pi$
$674$			5.92055e8i			1.93367i
$675$		−	7.69775e8i		−	2.50295i
$676$	−1.21396e8			−0.392973
$677$			4.42129e8i			1.42490i	0.701725	+	0.712448i	$0.252414\pi$
$677$			4.42129e8i			1.42490i	−0.701725	+	0.712448i	$0.747586\pi$
$678$		−	7.44761e8i		−	2.38962i
$679$			1.07512e8i			0.343437i
$680$	1.12194e7			0.0356815
$681$	−5.05864e8			−1.60174
$682$		−	1.95242e8i		−	0.615488i
$683$	9.46019e6			0.0296919			0.0148459	−	0.999890i	$-0.495274\pi$
$683$	9.46019e6			0.0296919			0.0148459	+	0.999890i	$0.495274\pi$
$684$			3.08850e8i			0.965116i
$685$	1.08702e8			0.338194
$686$	−1.90043e8			−0.588680
$687$			3.59839e8i			1.10978i
$688$	−1.34664e8	+	3.29910e8i	−0.413509	+	1.01305i
$689$	5.60397e8			1.71332
$690$		−	2.07839e8i		−	0.632675i
$691$			4.38108e8i			1.32784i	0.747802	+	0.663922i	$0.231109\pi$
$691$			4.38108e8i			1.32784i	−0.747802	+	0.663922i	$0.768891\pi$
$692$	2.89854e8			0.874703
$693$		−	8.06823e7i		−	0.242426i
$694$	7.74733e8			2.31779
$695$			2.88644e7i			0.0859821i
$696$			1.65182e7i			0.0489930i
$697$	−1.66861e8			−0.492785
$698$	−6.32140e8			−1.85886
$699$	−6.51363e8			−1.90718
$700$		−	6.32848e7i		−	0.184504i
$701$	1.11880e8			0.324786			0.162393	−	0.986726i	$-0.448079\pi$
$701$	1.11880e8			0.324786			0.162393	+	0.986726i	$0.448079\pi$
$702$	1.51918e9			4.39135
$703$	−2.52289e8			−0.726161
$704$	1.23603e8			0.354252
$705$	−2.38225e8			−0.679862
$706$		−	6.73913e8i		−	1.91509i
$707$			6.83360e7i			0.193371i
$708$			7.54474e8i			2.12591i
$709$	−1.44384e8			−0.405117			−0.202559	−	0.979270i	$-0.564926\pi$
$709$	−1.44384e8			−0.405117			−0.202559	+	0.979270i	$0.564926\pi$
$710$			1.61968e8i			0.452537i
$711$	−1.35291e9			−3.76410
$712$	−9.85882e7			−0.273140
$713$	3.64808e8			1.00646
$714$		−	2.06616e8i		−	0.567634i
$715$		−	4.83154e7i		−	0.132180i
$716$			2.45277e7i			0.0668219i
$717$		−	2.99467e8i		−	0.812441i
$718$			1.82613e8i			0.493353i
$719$	1.65815e8			0.446105			0.223052	−	0.974806i	$-0.428398\pi$
$719$	1.65815e8			0.446105			0.223052	+	0.974806i	$0.428398\pi$
$720$		−	2.41096e8i		−	0.645942i
$721$			4.76551e7i			0.127146i
$722$			4.16389e8i			1.10634i
$723$	9.74312e8			2.57800
$724$	−1.24793e8			−0.328831
$725$		−	6.54307e7i		−	0.171699i
$726$	7.74594e8			2.02425
$727$			6.29238e8i			1.63761i	0.574069	+	0.818807i	$0.305364\pi$
$727$			6.29238e8i			1.63761i	−0.574069	+	0.818807i	$0.694636\pi$
$728$	−1.46955e7			−0.0380882
$729$	−4.42898e8			−1.14320
$730$		−	1.62106e7i		−	0.0416706i
$731$	1.49919e8	−	3.67285e8i	0.383801	−	0.940267i
$732$	−3.82624e8			−0.975527
$733$		−	5.55695e8i		−	1.41099i	−0.708714	−	0.705495i	$-0.750725\pi$
$733$		−	5.55695e8i		−	1.41099i	0.708714	−	0.705495i	$-0.249275\pi$
$734$		−	8.25729e7i		−	0.208809i
$735$	1.69855e8			0.427776
$736$			5.55128e8i			1.39239i
$737$	−9.55412e7			−0.238665
$738$			6.53669e8i			1.62626i
$739$		−	1.18378e8i		−	0.293318i	−0.989187	−	0.146659i	$-0.953148\pi$
$739$		−	1.18378e8i		−	0.293318i	0.989187	−	0.146659i	$-0.0468519\pi$
$740$	−1.44087e8			−0.355575
$741$	−4.00764e8			−0.984994
$742$	−1.75949e8			−0.430700
$743$		−	2.35083e8i		−	0.573132i	−0.958060	−	0.286566i	$-0.907486\pi$
$743$		−	2.35083e8i		−	0.573132i	0.958060	−	0.286566i	$-0.0925138\pi$
$744$	1.08829e8			0.264256
$745$	−1.00218e8			−0.242369
$746$	−2.51923e8			−0.606808
$747$	−4.76719e8			−1.14367
$748$	−1.72817e8			−0.412936
$749$		−	3.62004e7i		−	0.0861525i
$750$			5.06537e8i			1.20068i
$751$			2.67999e8i			0.632722i	0.948639	+	0.316361i	$0.102461\pi$
$751$			2.67999e8i			0.632722i	−0.948639	+	0.316361i	$0.897539\pi$
$752$	7.04025e8			1.65552
$753$		−	3.03090e8i		−	0.709882i
$754$	1.29130e8			0.301240
$755$	−1.65571e8			−0.384720
$756$	−2.25239e8			−0.521289
$757$			3.48844e8i			0.804162i	0.915604	+	0.402081i	$0.131713\pi$
$757$			3.48844e8i			0.804162i	−0.915604	+	0.402081i	$0.868287\pi$
$758$		−	3.85145e8i		−	0.884335i
$759$		−	3.76691e8i		−	0.861509i
$760$			6.83260e6i			0.0155649i
$761$		−	3.74723e8i		−	0.850269i	−0.905130	−	0.425135i	$-0.860227\pi$
$761$		−	3.74723e8i		−	0.850269i	0.905130	−	0.425135i	$-0.139773\pi$
$762$	2.07725e8			0.469488
$763$			1.31272e8i			0.295528i
$764$			2.82198e8i			0.632811i
$765$			2.68410e8i			0.599534i
$766$	3.37389e8			0.750661
$767$	−6.93984e8			−1.53803
$768$			9.87508e8i			2.18000i
$769$	1.68131e8			0.369716			0.184858	−	0.982765i	$-0.440817\pi$
$769$	1.68131e8			0.369716			0.184858	+	0.982765i	$0.440817\pi$
$770$			1.51697e7i			0.0332280i
$771$	8.70456e8			1.89926
$772$	1.95111e8			0.424061
$773$		−	1.56150e8i		−	0.338068i	−0.985610	−	0.169034i	$-0.945935\pi$
$773$		−	1.56150e8i		−	0.338068i	0.985610	−	0.169034i	$-0.0540647\pi$
$774$	−1.43882e9	−	5.87300e8i	−3.10301	−	1.26659i
$775$	−4.31085e8			−0.926100
$776$			1.06147e8i			0.227155i
$777$		−	3.12219e8i		−	0.665574i
$778$	−8.81183e7			−0.187123
$779$		−	1.01618e8i		−	0.214961i
$780$	−2.28884e8			−0.482316
$781$			2.93553e8i			0.616217i
$782$		−	6.83809e8i		−	1.42993i
$783$	−2.32877e8			−0.485110
$784$	−5.01971e8			−1.04167
$785$	2.52557e7			0.0522096
$786$			1.08746e9i			2.23947i
$787$	3.87835e8			0.795650			0.397825	−	0.917461i	$-0.369765\pi$
$787$	3.87835e8			0.795650			0.397825	+	0.917461i	$0.369765\pi$
$788$	3.70105e7			0.0756391
$789$	1.09200e9			2.22327
$790$	2.54371e8			0.515925
$791$	−1.01568e8			−0.205224
$792$		−	7.96580e7i		−	0.160344i
$793$		−	3.51947e8i		−	0.705762i
$794$		−	8.28787e8i		−	1.65570i
$795$	3.22446e8			0.641735
$796$		−	3.73816e8i		−	0.741171i
$797$	8.28482e8			1.63647			0.818235	−	0.574883i	$-0.194953\pi$
$797$	8.28482e8			1.63647			0.818235	+	0.574883i	$0.194953\pi$
$798$	1.25829e8			0.247612
$799$	−7.83782e8			−1.53658
$800$		−	6.55983e8i		−	1.28122i
$801$		−	2.35860e9i		−	4.58940i
$802$		−	4.01652e8i		−	0.778623i
$803$		−	2.93803e7i		−	0.0567426i
$804$			4.52607e8i			0.870869i
$805$	−2.83444e7			−0.0543350
$806$		−	8.50763e8i		−	1.62481i
$807$			3.80162e7i			0.0723349i
$808$			6.74685e7i			0.127899i
$809$	5.00126e8			0.944569			0.472284	−	0.881446i	$-0.343430\pi$
$809$	5.00126e8			0.944569			0.472284	+	0.881446i	$0.343430\pi$
$810$	4.42275e8			0.832219
$811$			6.53394e8i			1.22493i	0.790496	+	0.612467i	$0.209823\pi$
$811$			6.53394e8i			1.22493i	−0.790496	+	0.612467i	$0.790177\pi$
$812$	−1.91453e7			−0.0357597
$813$			1.91412e9i			3.56203i
$814$	−5.53020e8			−1.02534
$815$	4.24113e7			0.0783445
$816$		−	1.11901e9i		−	2.05950i
$817$	2.23676e8	+	9.13008e7i	0.410160	+	0.167420i
$818$	−1.31089e9			−2.39500
$819$		−	3.51572e8i		−	0.639974i
$820$		−	5.80363e7i		−	0.105259i
$821$	6.62105e7			0.119646			0.0598229	−	0.998209i	$-0.480946\pi$
$821$	6.62105e7			0.119646			0.0598229	+	0.998209i	$0.480946\pi$
$822$		−	1.97644e9i		−	3.55850i
$823$	1.68404e7			0.0302102			0.0151051	−	0.999886i	$-0.495192\pi$
$823$	1.68404e7			0.0302102			0.0151051	+	0.999886i	$0.495192\pi$
$824$			4.70502e7i			0.0840968i
$825$			4.45128e8i			0.792725i
$826$	2.17892e8			0.386634
$827$	5.77846e8			1.02163			0.510817	−	0.859689i	$-0.329343\pi$
$827$	5.77846e8			1.02163			0.510817	+	0.859689i	$0.329343\pi$
$828$	−1.26497e9			−2.22838
$829$		−	1.53214e8i		−	0.268927i	−0.990919	−	0.134464i	$-0.957069\pi$
$829$		−	1.53214e8i		−	0.268927i	0.990919	−	0.134464i	$-0.0429311\pi$
$830$	8.96316e7			0.156757
$831$	1.35294e9			2.35764
$832$	5.38600e8			0.935182
$833$	5.58838e8			0.966832
$834$	5.24816e8			0.904709
$835$		−	1.94304e8i		−	0.333751i
$836$		−	1.05246e8i		−	0.180130i
$837$			1.53429e9i			2.61656i
$838$	−1.44032e9			−2.44752
$839$			4.17573e8i			0.707044i	0.935426	+	0.353522i	$0.115016\pi$
$839$			4.17573e8i			0.707044i	−0.935426	+	0.353522i	$0.884984\pi$
$840$	−8.45565e6			−0.0142662
$841$	5.75029e8			0.966722
$842$	1.20020e9			2.01056
$843$		−	9.25263e8i		−	1.54448i
$844$			1.50907e8i			0.251005i
$845$		−	6.42495e7i		−	0.106488i
$846$			3.07042e9i			5.07092i
$847$		−	1.05637e8i		−	0.173846i
$848$	−9.52921e8			−1.56268
$849$			1.50680e9i			2.46225i
$850$			8.08042e8i			1.31576i
$851$		−	1.03331e9i		−	1.67665i
$852$	1.39065e9			2.24853
$853$	−1.66126e8			−0.267665			−0.133832	−	0.991004i	$-0.542728\pi$
$853$	−1.66126e8			−0.267665			−0.133832	+	0.991004i	$0.542728\pi$
$854$			1.10502e8i			0.177417i
$855$	−1.63461e8			−0.261527
$856$		−	3.57408e7i		−	0.0569828i
$857$	−3.66098e8			−0.581640			−0.290820	−	0.956778i	$-0.593928\pi$
$857$	−3.66098e8			−0.581640			−0.290820	+	0.956778i	$0.593928\pi$
$858$	−8.78476e8			−1.39081
$859$			1.53078e8i			0.241509i	0.992682	+	0.120754i	$0.0385314\pi$
$859$			1.53078e8i			0.241509i	−0.992682	+	0.120754i	$0.961469\pi$
$860$	1.27746e8	+	5.21437e7i	0.200841	+	0.0819797i
$861$	1.25757e8			0.197026
$862$		−	3.13109e8i		−	0.488848i
$863$		−	3.72244e8i		−	0.579155i	−0.957155	−	0.289578i	$-0.906485\pi$
$863$		−	3.72244e8i		−	0.579155i	0.957155	−	0.289578i	$-0.0935149\pi$
$864$	−2.33473e9			−3.61989
$865$			1.53407e8i			0.237027i
$866$	1.45062e8			0.223357
$867$			3.79327e7i			0.0582044i
$868$			1.26137e8i			0.192878i
$869$	4.61026e8			0.702532
$870$	7.43000e7			0.112832
$871$	−4.16319e8			−0.630045
$872$			1.29606e8i			0.195467i
$873$	−2.53944e9			−3.81676
$874$	4.16439e8			0.623760
$875$	6.90798e7			0.103116
$876$	−1.39183e8			−0.207049
$877$	−8.02743e8			−1.19008			−0.595042	−	0.803695i	$-0.702865\pi$
$877$	−8.02743e8			−1.19008			−0.595042	+	0.803695i	$0.702865\pi$
$878$			1.01510e9i			1.49977i
$879$			8.05973e7i			0.118674i
$880$			8.21574e7i			0.120559i
$881$	−5.95543e8			−0.870934			−0.435467	−	0.900205i	$-0.643417\pi$
$881$	−5.95543e8			−0.870934			−0.435467	+	0.900205i	$0.643417\pi$
$882$		−	2.18921e9i		−	3.19068i
$883$	−1.95039e7			−0.0283295			−0.0141647	−	0.999900i	$-0.504509\pi$
$883$	−1.95039e7			−0.0283295			−0.0141647	+	0.999900i	$0.504509\pi$
$884$	−7.53048e8			−1.09010
$885$	−3.99311e8			−0.576078
$886$		−	1.45680e9i		−	2.09459i
$887$		−	5.45638e8i		−	0.781868i	−0.920419	−	0.390934i	$-0.872152\pi$
$887$		−	5.45638e8i		−	0.781868i	0.920419	−	0.390934i	$-0.127848\pi$
$888$		−	3.08256e8i		−	0.440222i
$889$		−	2.83289e7i		−	0.0403203i
$890$			4.43457e8i			0.629045i
$891$	8.01586e8			1.13323
$892$			9.72084e8i			1.36965i
$893$		−	4.77323e8i		−	0.670282i
$894$			1.82218e9i			2.55022i
$895$	−1.29815e7			−0.0181074
$896$	4.54223e7			0.0631459
$897$		−	1.64143e9i		−	2.27428i
$898$	9.36202e8			1.29283
$899$			1.30414e8i			0.179492i
$900$	1.49479e9			2.05046
$901$	1.06088e9			1.45041
$902$		−	2.22748e8i		−	0.303525i
$903$	−1.12989e8	+	2.76809e8i	−0.153452	+	0.375939i
$904$	−1.00279e8			−0.135738
$905$		−	6.60474e7i		−	0.0891066i
$906$			3.01044e9i			4.04805i
$907$	9.36250e8			1.25479			0.627393	−	0.778703i	$-0.284122\pi$
$907$	9.36250e8			1.25479			0.627393	+	0.778703i	$0.284122\pi$
$908$		−	5.78875e8i		−	0.773263i
$909$	−1.61410e9			−2.14901
$910$			6.61016e7i			0.0877178i
$911$			9.19474e8i			1.21614i	0.793883	+	0.608071i	$0.208056\pi$
$911$			9.19474e8i			1.21614i	−0.793883	+	0.608071i	$0.791944\pi$
$912$	6.81475e8			0.898391
$913$	1.62450e8			0.213455
$914$	−1.01740e7			−0.0133245
$915$		−	2.02507e8i		−	0.264348i
$916$	−4.11774e8			−0.535763
$917$	1.48304e8			0.192329
$918$	2.87593e9			3.71749
$919$	6.53282e8			0.841693			0.420847	−	0.907132i	$-0.361733\pi$
$919$	6.53282e8			0.841693			0.420847	+	0.907132i	$0.361733\pi$
$920$	−2.79846e7			−0.0359381
$921$			1.96025e9i			2.50919i
$922$		−	6.79473e8i		−	0.866921i
$923$			1.27915e9i			1.62674i
$924$	1.30246e8			0.165101
$925$			1.22104e9i			1.54279i
$926$	1.29704e9			1.63350
$927$	−1.12562e9			−1.41303
$928$	−1.98452e8			−0.248319
$929$			3.68817e8i			0.460007i	0.973190	+	0.230003i	$0.0738737\pi$
$929$			3.68817e8i			0.460007i	−0.973190	+	0.230003i	$0.926126\pi$
$930$		−	4.89520e8i		−	0.608585i
$931$			3.40332e8i			0.421749i
$932$		−	7.45373e8i		−	0.920717i
$933$		−	1.32825e9i		−	1.63544i
$934$	−2.20253e7			−0.0270321
$935$		−	9.14648e7i		−	0.111897i
$936$		−	3.47108e8i		−	0.423290i
$937$		−	3.54151e8i		−	0.430497i	−0.976559	−	0.215248i	$-0.930944\pi$
$937$		−	3.54151e8i		−	0.430497i	0.976559	−	0.215248i	$-0.0690561\pi$
$938$	1.30713e8			0.158383
$939$	1.82751e9			2.20730
$940$		−	2.72608e8i		−	0.328213i
$941$	9.86119e8			1.18348			0.591739	−	0.806129i	$-0.298441\pi$
$941$	9.86119e8			1.18348			0.591739	+	0.806129i	$0.298441\pi$
$942$		−	4.59202e8i		−	0.549353i
$943$	4.16203e8			0.496329
$944$	1.18008e9			1.40280
$945$		−	1.19209e8i		−	0.141259i
$946$	4.90300e8	+	2.00132e8i	0.579146	+	0.236397i
$947$	−1.60092e9			−1.88503			−0.942515	−	0.334163i	$-0.891547\pi$
$947$	−1.60092e9			−1.88503			−0.942515	+	0.334163i	$0.891547\pi$
$948$		−	2.18402e9i		−	2.56349i
$949$		−	1.28024e8i		−	0.149793i
$950$	−4.92097e8			−0.573958
$951$			1.79569e9i			2.08781i
$952$	−2.78198e7			−0.0322436
$953$		−	9.21284e8i		−	1.06442i	−0.846611	−	0.532212i	$-0.821361\pi$
$953$		−	9.21284e8i		−	1.06442i	0.846611	−	0.532212i	$-0.178639\pi$
$954$		−	4.15592e9i		−	4.78654i
$955$	−1.49355e8			−0.171479
$956$	3.42689e8			0.392217
$957$	1.34662e8			0.153642
$958$			6.16954e8i			0.701708i
$959$	−2.69539e8			−0.305609
$960$	3.09905e8			0.350279
$961$	−2.82796e7			−0.0318642
$962$	−2.40977e9			−2.70677
$963$	8.55054e8			0.957447
$964$			1.11493e9i			1.24457i
$965$			1.03264e8i			0.114912i
$966$			5.15362e8i			0.571717i
$967$	−6.21408e8			−0.687223			−0.343611	−	0.939112i	$-0.611650\pi$
$967$	−6.21408e8			−0.687223			−0.343611	+	0.939112i	$0.611650\pi$
$968$		−	1.04295e8i		−	0.114985i
$969$	−7.58678e8			−0.833847
$970$	4.77458e8			0.523143
$971$	−4.82750e8			−0.527308			−0.263654	−	0.964617i	$-0.584928\pi$
$971$	−4.82750e8			−0.527308			−0.263654	+	0.964617i	$0.584928\pi$
$972$		−	1.61236e9i		−	1.75575i
$973$		−	7.15726e7i		−	0.0776977i
$974$		−	8.83433e8i		−	0.956085i
$975$			1.93964e9i			2.09270i
$976$			5.98466e8i			0.643709i
$977$	−1.01822e9			−1.09184			−0.545921	−	0.837837i	$-0.683820\pi$
$977$	−1.01822e9			−1.09184			−0.545921	+	0.837837i	$0.683820\pi$
$978$		−	7.71127e8i		−	0.824346i
$979$			8.03729e8i			0.856567i
$980$			1.94370e8i			0.206515i
$981$	−3.10065e9			−3.28432
$982$	5.21590e8			0.550802
$983$		−	3.17690e8i		−	0.334459i	−0.985918	−	0.167229i	$-0.946518\pi$
$983$		−	3.17690e8i		−	0.334459i	0.985918	−	0.167229i	$-0.0534821\pi$
$984$	1.24161e8			0.130316
$985$			1.95881e7i			0.0204967i
$986$	2.44453e8			0.255015
$987$	5.90708e8			0.614357
$988$		−	4.58606e8i		−	0.475520i
$989$	−3.73944e8	+	9.16121e8i	−0.386561	+	0.947030i
$990$	−3.58308e8			−0.369276
$991$		−	4.19024e8i		−	0.430544i	−0.976554	−	0.215272i	$-0.930936\pi$
$991$		−	4.19024e8i		−	0.430544i	0.976554	−	0.215272i	$-0.0690638\pi$
$992$			1.30748e9i			1.33937i
$993$	−2.06778e9			−2.11182
$994$		−	4.01619e8i		−	0.408935i
$995$	1.97845e8			0.200842
$996$		−	7.69572e8i		−	0.778881i
$997$		−	1.66962e9i		−	1.68474i	−0.538900	−	0.842370i	$-0.681160\pi$
$997$		−	1.66962e9i		−	1.68474i	0.538900	−	0.842370i	$-0.318840\pi$
$998$	−1.42479e9			−1.43337
$999$	4.34585e9			4.35892

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.b.b.42.16	yes	20
43.42	odd	2	inner	43.7.b.b.42.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.b.b.42.5	✓	20	43.42	odd	2	inner
43.7.b.b.42.16	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+11.0119i q^{2} +50.0401i q^{3} -57.2623 q^{4} -30.3065i q^{5} -551.037 q^{6} +75.1486i q^{7} +74.1946i q^{8} -1775.01 q^{9} +O(q^{10})\)	\(q+11.0119i q^{2} +50.0401i q^{3} -57.2623 q^{4} -30.3065i q^{5} -551.037 q^{6} +75.1486i q^{7} +74.1946i q^{8} -1775.01 q^{9} +333.733 q^{10} +604.862 q^{11} -2865.41i q^{12} +2635.68 q^{13} -827.530 q^{14} +1516.54 q^{15} -4481.81 q^{16} +4989.55 q^{17} -19546.3i q^{18} +3038.63i q^{19} +1735.42i q^{20} -3760.44 q^{21} +6660.70i q^{22} -12445.5 q^{23} -3712.70 q^{24} +14706.5 q^{25} +29023.9i q^{26} -52342.4i q^{27} -4303.18i q^{28} -4449.10i q^{29} +16700.0i q^{30} -29312.5 q^{31} -44604.9i q^{32} +30267.4i q^{33} +54944.5i q^{34} +2277.49 q^{35} +101641. q^{36} +83027.3i q^{37} -33461.2 q^{38} +131890. i q^{39} +2248.58 q^{40} -33442.2 q^{41} -41409.7i q^{42} +(30046.7 - 73610.9i) q^{43} -34635.8 q^{44} +53794.4i q^{45} -137048. i q^{46} -157085. q^{47} -224270. i q^{48} +112002. q^{49} +161947. i q^{50} +249678. i q^{51} -150925. q^{52} +212620. q^{53} +576391. q^{54} -18331.3i q^{55} -5575.61 q^{56} -152053. q^{57} +48993.1 q^{58} -263304. q^{59} -86840.7 q^{60} -133532. i q^{61} -322787. i q^{62} -133389. i q^{63} +204350. q^{64} -79878.2i q^{65} -333302. q^{66} -157955. q^{67} -285713. q^{68} -622771. i q^{69} +25079.5i q^{70} +485322. i q^{71} -131696. i q^{72} -48573.5i q^{73} -914290. q^{74} +735915. i q^{75} -173999. i q^{76} +45454.5i q^{77} -1.45236e6 q^{78} +762200. q^{79} +135828. i q^{80} +1.32524e6 q^{81} -368262. i q^{82} +268573. q^{83} +215332. q^{84} -151216. i q^{85} +(810597. + 330872. i) q^{86} +222633. q^{87} +44877.5i q^{88} +1.32878e6i q^{89} -592379. q^{90} +198067. i q^{91} +712656. q^{92} -1.46680e6i q^{93} -1.72980e6i q^{94} +92090.4 q^{95} +2.23203e6 q^{96} +1.43066e6 q^{97} +1.23335e6i q^{98} -1.07364e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 796 q^{4} - 258 q^{6} - 2736 q^{9}+O(q^{10}) \) 20 * q - 796 * q^4 - 258 * q^6 - 2736 * q^9	\( 20 q - 796 q^{4} - 258 q^{6} - 2736 q^{9} - 1962 q^{10} + 2616 q^{11} - 5612 q^{13} - 3876 q^{14} + 4048 q^{15} + 14900 q^{16} + 3328 q^{17} + 10544 q^{21} - 836 q^{23} + 26966 q^{24} - 57904 q^{25} + 17116 q^{31} - 150472 q^{35} - 132110 q^{36} + 2266 q^{38} + 401286 q^{40} - 141936 q^{41} + 58160 q^{43} + 88544 q^{44} + 48452 q^{47} - 20644 q^{49} + 12292 q^{52} + 425212 q^{53} + 173740 q^{54} + 447864 q^{56} - 92904 q^{57} + 86502 q^{58} - 918856 q^{59} + 429848 q^{60} - 156892 q^{64} - 1246176 q^{66} + 1098496 q^{67} - 2589854 q^{68} - 1224106 q^{74} + 855716 q^{78} - 401492 q^{79} + 470644 q^{81} + 1354360 q^{83} - 637268 q^{84} + 3046356 q^{86} + 2116740 q^{87} - 683716 q^{90} - 485998 q^{92} - 2711660 q^{95} - 2480062 q^{96} + 7814560 q^{97} + 3744560 q^{99}+O(q^{100}) \) 20 * q - 796 * q^4 - 258 * q^6 - 2736 * q^9 - 1962 * q^10 + 2616 * q^11 - 5612 * q^13 - 3876 * q^14 + 4048 * q^15 + 14900 * q^16 + 3328 * q^17 + 10544 * q^21 - 836 * q^23 + 26966 * q^24 - 57904 * q^25 + 17116 * q^31 - 150472 * q^35 - 132110 * q^36 + 2266 * q^38 + 401286 * q^40 - 141936 * q^41 + 58160 * q^43 + 88544 * q^44 + 48452 * q^47 - 20644 * q^49 + 12292 * q^52 + 425212 * q^53 + 173740 * q^54 + 447864 * q^56 - 92904 * q^57 + 86502 * q^58 - 918856 * q^59 + 429848 * q^60 - 156892 * q^64 - 1246176 * q^66 + 1098496 * q^67 - 2589854 * q^68 - 1224106 * q^74 + 855716 * q^78 - 401492 * q^79 + 470644 * q^81 + 1354360 * q^83 - 637268 * q^84 + 3046356 * q^86 + 2116740 * q^87 - 683716 * q^90 - 485998 * q^92 - 2711660 * q^95 - 2480062 * q^96 + 7814560 * q^97 + 3744560 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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