LMFDB - Embedded newform 43.7.b.b.42.11

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			42.11
Root			$0.567672i$ of defining polynomial
Character	$\chi$	$=$	43.42
Dual form			43.7.b.b.42.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.567672i q^{2} +31.6476i q^{3} +63.6777 q^{4} -195.481i q^{5} -17.9654 q^{6} -418.179i q^{7} +72.4791i q^{8} -272.568 q^{9} +O(q^{10})$	\(q+0.567672i q^{2} +31.6476i q^{3} +63.6777 q^{4} -195.481i q^{5} -17.9654 q^{6} -418.179i q^{7} +72.4791i q^{8} -272.568 q^{9} +110.969 q^{10} +1184.88 q^{11} +2015.25i q^{12} -15.3814 q^{13} +237.389 q^{14} +6186.48 q^{15} +4034.23 q^{16} -2662.44 q^{17} -154.730i q^{18} -2354.99i q^{19} -12447.8i q^{20} +13234.3 q^{21} +672.625i q^{22} +2891.76 q^{23} -2293.79 q^{24} -22587.6 q^{25} -8.73158i q^{26} +14444.9i q^{27} -26628.7i q^{28} +27723.8i q^{29} +3511.89i q^{30} +50974.7 q^{31} +6928.78i q^{32} +37498.6i q^{33} -1511.40i q^{34} -81745.9 q^{35} -17356.5 q^{36} -64225.2i q^{37} +1336.86 q^{38} -486.783i q^{39} +14168.3 q^{40} -87526.9 q^{41} +7512.77i q^{42} +(-77107.2 - 19386.6i) q^{43} +75450.6 q^{44} +53281.8i q^{45} +1641.57i q^{46} -111128. q^{47} +127674. i q^{48} -57224.7 q^{49} -12822.4i q^{50} -84259.9i q^{51} -979.452 q^{52} +221242. q^{53} -8200.00 q^{54} -231621. i q^{55} +30309.2 q^{56} +74529.6 q^{57} -15738.0 q^{58} -196251. q^{59} +393941. q^{60} +191470. i q^{61} +28936.9i q^{62} +113982. i q^{63} +254258. q^{64} +3006.76i q^{65} -21286.9 q^{66} +180423. q^{67} -169538. q^{68} +91517.0i q^{69} -46404.9i q^{70} -167558. i q^{71} -19755.5i q^{72} +652509. i q^{73} +36458.9 q^{74} -714844. i q^{75} -149960. i q^{76} -495493. i q^{77} +276.333 q^{78} +321108. q^{79} -788614. i q^{80} -655850. q^{81} -49686.6i q^{82} +49368.9 q^{83} +842734. q^{84} +520456. i q^{85} +(11005.3 - 43771.6i) q^{86} -877390. q^{87} +85879.2i q^{88} +1.33745e6i q^{89} -30246.6 q^{90} +6432.17i q^{91} +184140. q^{92} +1.61323e6i q^{93} -63084.1i q^{94} -460354. q^{95} -219279. q^{96} +830874. q^{97} -32484.9i q^{98} -322961. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			0.567672i			0.0709590i	0.999370	+	0.0354795i	$0.0112959\pi$
$2$			0.567672i			0.0709590i	−0.999370	+	0.0354795i	$0.988704\pi$
$3$			31.6476i			1.17213i	0.810263	+	0.586066i	$0.199324\pi$
$3$			31.6476i			1.17213i	−0.810263	+	0.586066i	$0.800676\pi$
$4$	63.6777			0.994965
$5$		−	195.481i		−	1.56384i	−0.623376	−	0.781922i	$-0.714239\pi$
$5$		−	195.481i		−	1.56384i	0.623376	−	0.781922i	$-0.285761\pi$
$6$	−17.9654			−0.0831734
$7$		−	418.179i		−	1.21918i	−0.792716	−	0.609591i	$-0.791334\pi$
$7$		−	418.179i		−	1.21918i	0.792716	−	0.609591i	$-0.208666\pi$
$8$			72.4791i			0.141561i
$9$	−272.568			−0.373894
$10$	110.969			0.110969
$11$	1184.88			0.890220			0.445110	−	0.895476i	$-0.353165\pi$
$11$	1184.88			0.890220			0.445110	+	0.895476i	$0.353165\pi$
$12$			2015.25i			1.16623i
$13$	−15.3814			−0.00700109			−0.00350054	−	0.999994i	$-0.501114\pi$
$13$	−15.3814			−0.00700109			−0.00350054	+	0.999994i	$0.501114\pi$
$14$	237.389			0.0865119
$15$	6186.48			1.83303
$16$	4034.23			0.984920
$17$	−2662.44			−0.541918			−0.270959	−	0.962591i	$-0.587341\pi$
$17$	−2662.44			−0.541918			−0.270959	+	0.962591i	$0.587341\pi$
$18$		−	154.730i		−	0.0265311i
$19$		−	2354.99i		−	0.343343i	−0.985154	−	0.171671i	$-0.945083\pi$
$19$		−	2354.99i		−	0.343343i	0.985154	−	0.171671i	$-0.0549167\pi$
$20$		−	12447.8i		−	1.55597i
$21$	13234.3			1.42904
$22$			672.625i			0.0631691i
$23$	2891.76			0.237672			0.118836	−	0.992914i	$-0.462084\pi$
$23$	2891.76			0.237672			0.118836	+	0.992914i	$0.462084\pi$
$24$	−2293.79			−0.165928
$25$	−22587.6			−1.44561
$26$		−	8.73158i		−	0.000496790i
$27$			14444.9i			0.733879i
$28$		−	26628.7i		−	1.21304i
$29$			27723.8i			1.13673i	0.822775	+	0.568367i	$0.192424\pi$
$29$			27723.8i			1.13673i	−0.822775	+	0.568367i	$0.807576\pi$
$30$			3511.89i			0.130070i
$31$	50974.7			1.71108			0.855539	−	0.517738i	$-0.173226\pi$
$31$	50974.7			1.71108			0.855539	+	0.517738i	$0.173226\pi$
$32$			6928.78i			0.211450i
$33$			37498.6i			1.04345i
$34$		−	1511.40i		−	0.0384540i
$35$	−81745.9			−1.90661
$36$	−17356.5			−0.372011
$37$		−	64225.2i		−	1.26795i	−0.773355	−	0.633973i	$-0.781423\pi$
$37$		−	64225.2i		−	1.26795i	0.773355	−	0.633973i	$-0.218577\pi$
$38$	1336.86			0.0243633
$39$		−	486.783i		−	0.00820620i
$40$	14168.3			0.221379
$41$	−87526.9			−1.26996			−0.634980	−	0.772529i	$-0.718992\pi$
$41$	−87526.9			−1.26996			−0.634980	+	0.772529i	$0.718992\pi$
$42$			7512.77i			0.101403i
$43$	−77107.2	−	19386.6i	−0.969817	−	0.243836i
$43$	−77107.2	−	19386.6i	−0.969817	−	0.243836i
$44$	75450.6			0.885737
$45$			53281.8i			0.584711i
$46$			1641.57i			0.0168650i
$47$	−111128.			−1.07036			−0.535179	−	0.844739i	$-0.679756\pi$
$47$	−111128.			−1.07036			−0.535179	+	0.844739i	$0.679756\pi$
$48$			127674.i			1.15446i
$49$	−57224.7			−0.486402
$50$		−	12822.4i		−	0.102579i
$51$		−	84259.9i		−	0.635200i
$52$	−979.452			−0.00696583
$53$	221242.			1.48607			0.743036	−	0.669251i	$-0.233385\pi$
$53$	221242.			1.48607			0.743036	+	0.669251i	$0.233385\pi$
$54$	−8200.00			−0.0520754
$55$		−	231621.i		−	1.39216i
$56$	30309.2			0.172588
$57$	74529.6			0.402443
$58$	−15738.0			−0.0806615
$59$	−196251.			−0.955554			−0.477777	−	0.878481i	$-0.658557\pi$
$59$	−196251.			−0.955554			−0.477777	+	0.878481i	$0.658557\pi$
$60$	393941.			1.82380
$61$			191470.i			0.843553i	0.906700	+	0.421776i	$0.138593\pi$
$61$			191470.i			0.843553i	−0.906700	+	0.421776i	$0.861407\pi$
$62$			28936.9i			0.121416i
$63$			113982.i			0.455844i
$64$	254258.			0.969916
$65$			3006.76i			0.0109486i
$66$	−21286.9			−0.0740425
$67$	180423.			0.599883			0.299941	−	0.953958i	$-0.403033\pi$
$67$	180423.			0.599883			0.299941	+	0.953958i	$0.403033\pi$
$68$	−169538.			−0.539190
$69$			91517.0i			0.278583i
$70$		−	46404.9i		−	0.135291i
$71$		−	167558.i		−	0.468156i	−0.972218	−	0.234078i	$-0.924793\pi$
$71$		−	167558.i		−	0.468156i	0.972218	−	0.234078i	$-0.0752071\pi$
$72$		−	19755.5i		−	0.0529287i
$73$			652509.i			1.67733i	0.544650	+	0.838664i	$0.316663\pi$
$73$			652509.i			1.67733i	−0.544650	+	0.838664i	$0.683337\pi$
$74$	36458.9			0.0899722
$75$		−	714844.i		−	1.69444i
$76$		−	149960.i		−	0.341614i
$77$		−	495493.i		−	1.08534i
$78$	276.333			0.000582304
$79$	321108.			0.651283			0.325641	−	0.945493i	$-0.394420\pi$
$79$	321108.			0.651283			0.325641	+	0.945493i	$0.394420\pi$
$80$		−	788614.i		−	1.54026i
$81$	−655850.			−1.23410
$82$		−	49686.6i		−	0.0901151i
$83$	49368.9			0.0863414			0.0431707	−	0.999068i	$-0.486254\pi$
$83$	49368.9			0.0863414			0.0431707	+	0.999068i	$0.486254\pi$
$84$	842734.			1.42185
$85$			520456.i			0.847476i
$86$	11005.3	−	43771.6i	0.0173023	−	0.0688172i
$87$	−877390.			−1.33240
$88$			85879.2i			0.126020i
$89$			1.33745e6i			1.89718i	0.316511	+	0.948589i	$0.397489\pi$
$89$			1.33745e6i			1.89718i	−0.316511	+	0.948589i	$0.602511\pi$
$90$	−30246.6			−0.0414905
$91$			6432.17i			0.00853559i
$92$	184140.			0.236475
$93$			1.61323e6i			2.00561i
$94$		−	63084.1i		−	0.0759515i
$95$	−460354.			−0.536935
$96$	−219279.			−0.247847
$97$	830874.			0.910374			0.455187	−	0.890396i	$-0.349572\pi$
$97$	830874.			0.910374			0.455187	+	0.890396i	$0.349572\pi$
$98$		−	32484.9i		−	0.0345146i
$99$	−322961.			−0.332847
$100$	−1.43833e6			−1.43833
$101$	−392754.			−0.381203			−0.190601	−	0.981668i	$-0.561044\pi$
$101$	−392754.			−0.381203			−0.190601	+	0.981668i	$0.561044\pi$
$102$	47832.0			0.0450732
$103$	−1.70809e6			−1.56315			−0.781574	−	0.623812i	$-0.785583\pi$
$103$	−1.70809e6			−1.56315			−0.781574	+	0.623812i	$0.785583\pi$
$104$		−	1114.83i		−	0.000991079i
$105$		−	2.58706e6i		−	2.23480i
$106$			125593.i			0.105450i
$107$	−1.45488e6			−1.18762			−0.593808	−	0.804607i	$-0.702376\pi$
$107$	−1.45488e6			−1.18762			−0.593808	+	0.804607i	$0.702376\pi$
$108$			919822.i			0.730184i
$109$	746414.			0.576369			0.288184	−	0.957575i	$-0.406948\pi$
$109$	746414.			0.576369			0.288184	+	0.957575i	$0.406948\pi$
$110$	131485.			0.0987867
$111$	2.03257e6			1.48620
$112$		−	1.68703e6i		−	1.20080i
$113$		−	938948.i		−	0.650738i	−0.945587	−	0.325369i	$-0.894511\pi$
$113$		−	938948.i		−	0.650738i	0.945587	−	0.325369i	$-0.105489\pi$
$114$			42308.4i			0.0285570i
$115$		−	565282.i		−	0.371682i
$116$			1.76539e6i			1.13101i
$117$	4192.48			0.00261766
$118$		−	111406.i		−	0.0678052i
$119$			1.11338e6i			0.660696i
$120$			448391.i			0.259485i
$121$	−367615.			−0.207509
$122$	−108692.			−0.0598577
$123$		−	2.77001e6i		−	1.48856i
$124$	3.24596e6			1.70246
$125$			1.36106e6i			0.696864i
$126$	−64704.6			−0.0323462
$127$	1.01692e6			0.496451			0.248225	−	0.968702i	$-0.420153\pi$
$127$	1.01692e6			0.496451			0.248225	+	0.968702i	$0.420153\pi$
$128$			587777.i			0.280274i
$129$	613540.	−	2.44026e6i	0.285807	−	1.13675i
$130$	−1706.85			−0.000776903
$131$			3.69800e6i			1.64495i	0.568801	+	0.822475i	$0.307407\pi$
$131$			3.69800e6i			1.64495i	−0.568801	+	0.822475i	$0.692593\pi$
$132$			2.38783e6i			1.03820i
$133$	−984806.			−0.418597
$134$			102421.i			0.0425671i
$135$	2.82371e6			1.14767
$136$		−	192972.i		−	0.0767144i
$137$		−	3225.02i		−	0.00125421i	−1.00000		0.000627105i	$-0.999800\pi$
$137$		−	3225.02i		−	0.00125421i	1.00000		0.000627105i	$-0.000199614\pi$
$138$	−51951.7			−0.0197680
$139$	2.48038e6			0.923579			0.461790	−	0.886989i	$-0.347207\pi$
$139$	2.48038e6			0.923579			0.461790	+	0.886989i	$0.347207\pi$
$140$	−5.20539e6			−1.89701
$141$		−	3.51692e6i		−	1.25460i
$142$	95118.1			0.0332199
$143$	−18225.1			−0.00623250
$144$	−1.09960e6			−0.368255
$145$	5.41946e6			1.77767
$146$	−370411.			−0.119022
$147$		−	1.81102e6i		−	0.570128i
$148$		−	4.08972e6i		−	1.26156i
$149$			4.35151e6i			1.31547i	0.753249	+	0.657736i	$0.228486\pi$
$149$			4.35151e6i			1.31547i	−0.753249	+	0.657736i	$0.771514\pi$
$150$	405797.			0.120236
$151$			5.04923e6i			1.46654i	0.679937	+	0.733271i	$0.262007\pi$
$151$			5.04923e6i			1.46654i	−0.679937	+	0.733271i	$0.737993\pi$
$152$	170687.			0.0486039
$153$	725698.			0.202620
$154$	281278.			0.0770146
$155$		−	9.96457e6i		−	2.67586i
$156$		−	30997.3i		−	0.00816488i
$157$		−	4.88104e6i		−	1.26129i	−0.776073	−	0.630643i	$-0.782791\pi$
$157$		−	4.88104e6i		−	1.26129i	0.776073	−	0.630643i	$-0.217209\pi$
$158$			182284.i			0.0462144i
$159$			7.00177e6i			1.74187i
$160$	1.35444e6			0.330674
$161$		−	1.20927e6i		−	0.289765i
$162$		−	372308.i		−	0.0875703i
$163$			3.64275e6i			0.841137i	0.907261	+	0.420569i	$0.138169\pi$
$163$			3.64275e6i			0.841137i	−0.907261	+	0.420569i	$0.861831\pi$
$164$	−5.57352e6			−1.26357
$165$	7.33025e6			1.63180
$166$			28025.3i			0.00612670i
$167$	−8.62839e6			−1.85259			−0.926297	−	0.376793i	$-0.877027\pi$
$167$	−8.62839e6			−1.85259			−0.926297	+	0.376793i	$0.877027\pi$
$168$			959214.i			0.202296i
$169$	−4.82657e6			−0.999951
$170$	−295448.			−0.0601361
$171$			641895.i			0.128374i
$172$	−4.91001e6	−	1.23450e6i	−0.964933	−	0.242608i
$173$	−2.87792e6			−0.555827			−0.277914	−	0.960606i	$-0.589643\pi$
$173$	−2.87792e6			−0.555827			−0.277914	+	0.960606i	$0.589643\pi$
$174$		−	498070.i		−	0.0945459i
$175$			9.44568e6i			1.76246i
$176$	4.78009e6			0.876795
$177$		−	6.21086e6i		−	1.12004i
$178$	−759234.			−0.134622
$179$			2.16118e6i			0.376819i	0.982091	+	0.188409i	$0.0603331\pi$
$179$			2.16118e6i			0.376819i	−0.982091	+	0.188409i	$0.939667\pi$
$180$			3.39287e6i			0.581767i
$181$	7.68800e6			1.29652			0.648258	−	0.761421i	$-0.275498\pi$
$181$	7.68800e6			1.29652			0.648258	+	0.761421i	$0.275498\pi$
$182$	−3651.37			−0.000605677
$183$	−6.05957e6			−0.988755
$184$			209592.i			0.0336450i
$185$	−1.25548e7			−1.98287
$186$	−915784.			−0.142316
$187$	−3.15468e6			−0.482426
$188$	−7.07636e6			−1.06497
$189$	6.04058e6			0.894732
$190$		−	261330.i		−	0.0381004i
$191$		−	9.03078e6i		−	1.29606i	−0.761614	−	0.648030i	$-0.775593\pi$
$191$		−	9.03078e6i		−	1.29606i	0.761614	−	0.648030i	$-0.224407\pi$
$192$			8.04663e6i			1.13687i
$193$	1.15620e7			1.60827			0.804137	−	0.594443i	$-0.202628\pi$
$193$	1.15620e7			1.60827			0.804137	+	0.594443i	$0.202628\pi$
$194$			471664.i			0.0645992i
$195$	−95156.7			−0.0128332
$196$	−3.64394e6			−0.483953
$197$	934269.			0.122201			0.0611003	−	0.998132i	$-0.480539\pi$
$197$	934269.			0.122201			0.0611003	+	0.998132i	$0.480539\pi$
$198$		−	183336.i		−	0.0236185i
$199$		−	3.67317e6i		−	0.466103i	−0.972464	−	0.233051i	$-0.925129\pi$
$199$		−	3.67317e6i		−	0.466103i	0.972464	−	0.233051i	$-0.0748711\pi$
$200$		−	1.63713e6i		−	0.204642i
$201$			5.70994e6i			0.703142i
$202$		−	222955.i		−	0.0270498i
$203$	1.15935e7			1.38588
$204$		−	5.36548e6i		−	0.632001i
$205$			1.71098e7i			1.98602i
$206$		−	969638.i		−	0.110920i
$207$	−788201.			−0.0888640
$208$	−62052.1			−0.00689551
$209$		−	2.79038e6i		−	0.305650i
$210$	1.46860e6			0.158579
$211$		−	1.58871e7i		−	1.69121i	−0.533806	−	0.845607i	$-0.679239\pi$
$211$		−	1.58871e7i		−	1.69121i	0.533806	−	0.845607i	$-0.320761\pi$
$212$	1.40882e7			1.47859
$213$	5.30281e6			0.548741
$214$		−	825896.i		−	0.0842721i
$215$	−3.78971e6	+	1.50730e7i	−0.381321	+	1.51664i
$216$	−1.04696e6			−0.103889
$217$		−	2.13166e7i		−	2.08611i
$218$			423719.i			0.0408986i
$219$	−2.06503e7			−1.96605
$220$		−	1.47491e7i		−	1.38516i
$221$	40952.1			0.00379402
$222$			1.15383e6i			0.105459i
$223$		−	14369.2i		−	0.00129574i	−1.00000		0.000647870i	$-0.999794\pi$
$223$		−	14369.2i		−	0.00129574i	1.00000		0.000647870i	$-0.000206224\pi$
$224$	2.89747e6			0.257795
$225$	6.15668e6			0.540504
$226$	533015.			0.0461757
$227$		−	1.05446e7i		−	0.901475i	−0.892657	−	0.450737i	$-0.851161\pi$
$227$		−	1.05446e7i		−	0.901475i	0.892657	−	0.450737i	$-0.148839\pi$
$228$	4.74588e6			0.400417
$229$	−2.56800e6			−0.213840			−0.106920	−	0.994268i	$-0.534099\pi$
$229$	−2.56800e6			−0.213840			−0.106920	+	0.994268i	$0.534099\pi$
$230$	320895.			0.0263742
$231$	1.56811e7			1.27216
$232$	−2.00940e6			−0.160917
$233$			1.82065e7i			1.43933i	0.694323	+	0.719663i	$0.255704\pi$
$233$			1.82065e7i			1.43933i	−0.694323	+	0.719663i	$0.744296\pi$
$234$			2379.95i			0.000185747i
$235$			2.17233e7i			1.67387i
$236$	−1.24968e7			−0.950743
$237$			1.01623e7i			0.763390i
$238$	−632034.			−0.0468824
$239$	1.45860e7			1.06842			0.534212	−	0.845351i	$-0.320608\pi$
$239$	1.45860e7			1.06842			0.534212	+	0.845351i	$0.320608\pi$
$240$	2.49577e7			1.80539
$241$		−	1.31046e7i		−	0.936210i	−0.883673	−	0.468105i	$-0.844937\pi$
$241$		−	1.31046e7i		−	0.936210i	0.883673	−	0.468105i	$-0.155063\pi$
$242$		−	208685.i		−	0.0147246i
$243$		−	1.02257e7i		−	0.712645i
$244$			1.21924e7i			0.839305i
$245$			1.11863e7i			0.760658i
$246$	1.57246e6			0.105627
$247$			36223.0i			0.00240377i
$248$			3.69460e6i			0.242222i
$249$			1.56240e6i			0.101203i
$250$	−772637.			−0.0494488
$251$	1.75490e6			0.110977			0.0554883	−	0.998459i	$-0.482328\pi$
$251$	1.75490e6			0.110977			0.0554883	+	0.998459i	$0.482328\pi$
$252$			7.25814e6i			0.453549i
$253$	3.42639e6			0.211580
$254$			577278.i			0.0352277i
$255$	−1.64712e7			−0.993354
$256$	1.59388e7			0.950028
$257$		−	1.47353e7i		−	0.868082i	−0.900893	−	0.434041i	$-0.857087\pi$
$257$		−	1.47353e7i		−	0.868082i	0.900893	−	0.434041i	$-0.142913\pi$
$258$	1.38527e6	+	348289.i	0.0806629	+	0.0202806i
$259$	−2.68577e7			−1.54585
$260$			191464.i			0.0108935i
$261$		−	7.55663e6i		−	0.425017i
$262$	−2.09925e6			−0.116724
$263$		−	1.12596e7i		−	0.618951i	−0.950907	−	0.309475i	$-0.899847\pi$
$263$		−	1.12596e7i		−	0.618951i	0.950907	−	0.309475i	$-0.100153\pi$
$264$	−2.71787e6			−0.147712
$265$		−	4.32485e7i		−	2.32399i
$266$		−	559047.i		−	0.0297032i
$267$	−4.23271e7			−2.22374
$268$	1.14889e7			0.596862
$269$	−1.96066e6			−0.100727			−0.0503634	−	0.998731i	$-0.516038\pi$
$269$	−1.96066e6			−0.100727			−0.0503634	+	0.998731i	$0.516038\pi$
$270$			1.60294e6i			0.0814378i
$271$	6.70792e6			0.337039			0.168519	−	0.985698i	$-0.446101\pi$
$271$	6.70792e6			0.337039			0.168519	+	0.985698i	$0.446101\pi$
$272$	−1.07409e7			−0.533746
$273$	−203563.			−0.0100048
$274$	1830.75			8.89975e−5
$275$	−2.67637e7			−1.28691
$276$			5.82760e6i			0.277180i
$277$			2.17631e7i			1.02396i	0.858998	+	0.511979i	$0.171087\pi$
$277$			2.17631e7i			1.02396i	−0.858998	+	0.511979i	$0.828913\pi$
$278$			1.40804e6i			0.0655363i
$279$	−1.38941e7			−0.639761
$280$		−	5.92487e6i		−	0.269901i
$281$	2.86481e7			1.29115			0.645575	−	0.763697i	$-0.276618\pi$
$281$	2.86481e7			1.29115			0.645575	+	0.763697i	$0.276618\pi$
$282$	1.99646e6			0.0890252
$283$	−3.20199e7			−1.41274			−0.706369	−	0.707844i	$-0.749668\pi$
$283$	−3.20199e7			−1.41274			−0.706369	+	0.707844i	$0.749668\pi$
$284$		−	1.06697e7i		−	0.465799i
$285$		−	1.45691e7i		−	0.629358i
$286$		−	10345.9i		−	0.000442252i
$287$			3.66019e7i			1.54831i
$288$		−	1.88857e6i		−	0.0790597i
$289$	−1.70490e7			−0.706325
$290$			3.07648e6i			0.126142i
$291$			2.62951e7i			1.06708i
$292$			4.15503e7i			1.66888i
$293$	7.53752e6			0.299658			0.149829	−	0.988712i	$-0.452128\pi$
$293$	7.53752e6			0.299658			0.149829	+	0.988712i	$0.452128\pi$
$294$	1.02807e6			0.0404557
$295$			3.83632e7i			1.49434i
$296$	4.65499e6			0.179491
$297$			1.71156e7i			0.653314i
$298$	−2.47023e6			−0.0933446
$299$	−44479.2			−0.00166396
$300$		−	4.55197e7i		−	1.68591i
$301$	−8.10708e6	+	3.22446e7i	−0.297280	+	1.18238i
$302$	−2.86631e6			−0.104064
$303$		−	1.24297e7i		−	0.446820i
$304$		−	9.50056e6i		−	0.338165i
$305$	3.74287e7			1.31919
$306$			411959.i			0.0143777i
$307$	4.65611e7			1.60919			0.804596	−	0.593823i	$-0.202382\pi$
$307$	4.65611e7			1.60919			0.804596	+	0.593823i	$0.202382\pi$
$308$		−	3.15519e7i		−	1.07987i
$309$		−	5.40570e7i		−	1.83222i
$310$	5.65661e6			0.189876
$311$	−8.46971e6			−0.281571			−0.140785	−	0.990040i	$-0.544963\pi$
$311$	−8.46971e6			−0.281571			−0.140785	+	0.990040i	$0.544963\pi$
$312$	35281.6			0.00116168
$313$			4.97624e6i			0.162281i	0.996703	+	0.0811406i	$0.0258563\pi$
$313$			4.97624e6i			0.162281i	−0.996703	+	0.0811406i	$0.974144\pi$
$314$	2.77083e6			0.0894996
$315$	2.22813e7			0.712869
$316$	2.04474e7			0.648004
$317$	−4.15142e7			−1.30322			−0.651611	−	0.758553i	$-0.725907\pi$
$317$	−4.15142e7			−1.30322			−0.651611	+	0.758553i	$0.725907\pi$
$318$	−3.97471e6			−0.123602
$319$			3.28494e7i			1.01194i
$320$		−	4.97024e7i		−	1.51680i
$321$		−	4.60434e7i		−	1.39204i
$322$	686470.			0.0205615
$323$			6.27002e6i			0.186064i
$324$	−4.17630e7			−1.22788
$325$	347429.			0.0101208
$326$	−2.06789e6			−0.0596863
$327$			2.36222e7i			0.675580i
$328$		−	6.34387e6i		−	0.179777i
$329$			4.64713e7i			1.30496i
$330$			4.16118e6i			0.115791i
$331$		−	2.14901e7i		−	0.592589i	−0.955097	−	0.296295i	$-0.904249\pi$
$331$		−	2.14901e7i		−	0.592589i	0.955097	−	0.296295i	$-0.0957510\pi$
$332$	3.14370e6			0.0859066
$333$			1.75058e7i			0.474077i
$334$		−	4.89810e6i		−	0.131458i
$335$		−	3.52691e7i		−	0.938124i
$336$	5.33904e7			1.40749
$337$	−5.08482e6			−0.132858			−0.0664288	−	0.997791i	$-0.521161\pi$
$337$	−5.08482e6			−0.132858			−0.0664288	+	0.997791i	$0.521161\pi$
$338$		−	2.73991e6i		−	0.0709556i
$339$	2.97154e7			0.762751
$340$			3.31415e7i			0.843209i
$341$	6.03991e7			1.52324
$342$	−364386.			−0.00910927
$343$		−	2.52682e7i		−	0.626169i
$344$	1.40513e6	−	5.58866e6i	0.0345175	−	0.137288i
$345$	1.78898e7			0.435660
$346$		−	1.63371e6i		−	0.0394410i
$347$		−	3.64450e6i		−	0.0872267i	−0.999048	−	0.0436134i	$-0.986113\pi$
$347$		−	3.64450e6i		−	0.0872267i	0.999048	−	0.0436134i	$-0.0138870\pi$
$348$	−5.58702e7			−1.32569
$349$		−	4.18869e7i		−	0.985375i	−0.870206	−	0.492687i	$-0.836015\pi$
$349$		−	4.18869e7i		−	0.985375i	0.870206	−	0.492687i	$-0.163985\pi$
$350$	−5.36205e6			−0.125062
$351$		−	222183.i		−	0.00513795i
$352$			8.20979e6i			0.188237i
$353$	3.31754e7			0.754209			0.377104	−	0.926171i	$-0.376920\pi$
$353$	3.31754e7			0.754209			0.377104	+	0.926171i	$0.376920\pi$
$354$	3.52573e6			0.0794766
$355$	−3.27544e7			−0.732123
$356$			8.51659e7i			1.88762i
$357$	−3.52357e7			−0.774424
$358$	−1.22684e6			−0.0267387
$359$	6.09915e6			0.131821			0.0659107	−	0.997826i	$-0.479005\pi$
$359$	6.09915e6			0.131821			0.0659107	+	0.997826i	$0.479005\pi$
$360$	−3.86182e6			−0.0827722
$361$	4.14999e7			0.882116
$362$			4.36426e6i			0.0919994i
$363$		−	1.16341e7i		−	0.243228i
$364$			409586.i			0.00849261i
$365$	1.27553e8			2.62308
$366$		−	3.43985e6i		−	0.0701611i
$367$	−4.06076e7			−0.821502			−0.410751	−	0.911748i	$-0.634733\pi$
$367$	−4.06076e7			−0.821502			−0.410751	+	0.911748i	$0.634733\pi$
$368$	1.16660e7			0.234088
$369$	2.38571e7			0.474830
$370$		−	7.12700e6i		−	0.140702i
$371$		−	9.25188e7i		−	1.81179i
$372$			1.02727e8i			1.99551i
$373$		−	2.63198e7i		−	0.507172i	−0.967313	−	0.253586i	$-0.918390\pi$
$373$		−	2.63198e7i		−	0.507172i	0.967313	−	0.253586i	$-0.0816101\pi$
$374$		−	1.79083e6i		−	0.0342325i
$375$	−4.30743e7			−0.816816
$376$		−	8.05444e6i		−	0.151521i
$377$		−	426430.i		−	0.00795837i
$378$			3.42907e6i			0.0634893i
$379$	−3.23575e7			−0.594370			−0.297185	−	0.954820i	$-0.596048\pi$
$379$	−3.23575e7			−0.594370			−0.297185	+	0.954820i	$0.596048\pi$
$380$	−2.93143e7			−0.534231
$381$			3.21831e7i			0.581906i
$382$	5.12653e6			0.0919672
$383$			4.85406e7i			0.863991i	0.901876	+	0.431995i	$0.142190\pi$
$383$			4.85406e7i			0.863991i	−0.901876	+	0.431995i	$0.857810\pi$
$384$	−1.86017e7			−0.328518
$385$	−9.68592e7			−1.69730
$386$			6.56341e6i			0.114122i
$387$	2.10170e7	+	5.28418e6i	0.362608	+	0.0911685i
$388$	5.29082e7			0.905790
$389$			1.25283e7i			0.212834i	0.994322	+	0.106417i	$0.0339379\pi$
$389$			1.25283e7i			0.212834i	−0.994322	+	0.106417i	$0.966062\pi$
$390$		−	54017.8i		−	0.000910632i
$391$	−7.69914e6			−0.128799
$392$		−	4.14760e6i		−	0.0688555i
$393$	−1.17033e8			−1.92810
$394$			530359.i			0.00867124i
$395$		−	6.27703e7i		−	1.01851i
$396$	−2.05655e7			−0.331171
$397$	−5.82784e7			−0.931399			−0.465700	−	0.884943i	$-0.654197\pi$
$397$	−5.82784e7			−0.931399			−0.465700	+	0.884943i	$0.654197\pi$
$398$	2.08516e6			0.0330742
$399$		−	3.11667e7i		−	0.490651i
$400$	−9.11238e7			−1.42381
$401$	1.27270e8			1.97375			0.986877	−	0.161474i	$-0.0516249\pi$
$401$	1.27270e8			1.97375			0.986877	+	0.161474i	$0.0516249\pi$
$402$	−3.24137e6			−0.0498943
$403$	−784062.			−0.0119794
$404$	−2.50097e7			−0.379283
$405$			1.28206e8i			1.92994i
$406$			6.58131e6i			0.0983409i
$407$		−	7.60993e7i		−	1.12875i
$408$	6.10708e6			0.0899194
$409$		−	1.89469e7i		−	0.276928i	−0.990367	−	0.138464i	$-0.955783\pi$
$409$		−	1.89469e7i		−	0.276928i	0.990367	−	0.138464i	$-0.0442166\pi$
$410$	−9.71276e6			−0.140926
$411$	102064.			0.00147010
$412$	−1.08768e8			−1.55528
$413$			8.20680e7i			1.16499i
$414$		−	447440.i		−	0.00630571i
$415$		−	9.65065e6i		−	0.135024i
$416$		−	106574.i		−	0.00148038i
$417$			7.84981e7i			1.08256i
$418$	1.58402e6			0.0216887
$419$		−	7.41669e7i		−	1.00825i	−0.863631	−	0.504124i	$-0.831815\pi$
$419$		−	7.41669e7i		−	1.00825i	0.863631	−	0.504124i	$-0.168185\pi$
$420$		−	1.64738e8i		−	2.22355i
$421$		−	7.12823e7i		−	0.955291i	−0.878553	−	0.477645i	$-0.841490\pi$
$421$		−	7.12823e7i		−	0.955291i	0.878553	−	0.477645i	$-0.158510\pi$
$422$	9.01869e6			0.120007
$423$	3.02899e7			0.400200
$424$			1.60354e7i			0.210370i
$425$	6.01384e7			0.783402
$426$			3.01026e6i			0.0389381i
$427$	8.00689e7			1.02844
$428$	−9.26436e7			−1.18164
$429$		−	576781.i		−	0.00730532i
$430$	−8.55650e6	−	2.15131e6i	−0.107619	−	0.0270582i
$431$	−6.60708e7			−0.825235			−0.412617	−	0.910904i	$-0.635385\pi$
$431$	−6.60708e7			−0.825235			−0.412617	+	0.910904i	$0.635385\pi$
$432$			5.82743e7i			0.722812i
$433$		−	2.98848e7i		−	0.368118i	−0.982915	−	0.184059i	$-0.941076\pi$
$433$		−	2.98848e7i		−	0.368118i	0.982915	−	0.184059i	$-0.0589237\pi$
$434$	1.21008e7			0.148029
$435$			1.71513e8i			2.08367i
$436$	4.75300e7			0.573467
$437$		−	6.81005e6i		−	0.0816029i
$438$		−	1.17226e7i		−	0.139509i
$439$	−4.16010e7			−0.491711			−0.245855	−	0.969306i	$-0.579069\pi$
$439$	−4.16010e7			−0.491711			−0.245855	+	0.969306i	$0.579069\pi$
$440$	1.67877e7			0.197076
$441$	1.55977e7			0.181863
$442$			23247.4i			0.000269220i
$443$	1.05065e8			1.20851			0.604253	−	0.796793i	$-0.293472\pi$
$443$	1.05065e8			1.20851			0.604253	+	0.796793i	$0.293472\pi$
$444$	1.29430e8			1.47872
$445$	2.61446e8			2.96689
$446$	8157.00			9.19445e−5
$447$	−1.37715e8			−1.54191
$448$		−	1.06325e8i		−	1.18250i
$449$			1.11616e8i			1.23307i	0.787326	+	0.616537i	$0.211465\pi$
$449$			1.11616e8i			1.23307i	−0.787326	+	0.616537i	$0.788535\pi$
$450$			3.49498e6i			0.0383536i
$451$	−1.03709e8			−1.13054
$452$		−	5.97901e7i		−	0.647462i
$453$	−1.59796e8			−1.71898
$454$	5.98589e6			0.0639678
$455$	1.25736e6			0.0133483
$456$			5.40184e6i			0.0569701i
$457$			9.44586e7i			0.989676i	0.868985	+	0.494838i	$0.164773\pi$
$457$			9.44586e7i			0.989676i	−0.868985	+	0.494838i	$0.835227\pi$
$458$		−	1.45778e6i		−	0.0151739i
$459$		−	3.84589e7i		−	0.397703i
$460$		−	3.59959e7i		−	0.369811i
$461$	−7.58053e7			−0.773743			−0.386871	−	0.922134i	$-0.626444\pi$
$461$	−7.58053e7			−0.773743			−0.386871	+	0.922134i	$0.626444\pi$
$462$			8.90175e6i			0.0902713i
$463$			1.66599e8i			1.67853i	0.543723	+	0.839265i	$0.317014\pi$
$463$			1.66599e8i			1.67853i	−0.543723	+	0.839265i	$0.682986\pi$
$464$			1.11844e8i			1.11959i
$465$	3.15354e8			3.13646
$466$	−1.03353e7			−0.102133
$467$		−	1.95492e8i		−	1.91945i	−0.280937	−	0.959726i	$-0.590645\pi$
$467$		−	1.95492e8i		−	1.91945i	0.280937	−	0.959726i	$-0.409355\pi$
$468$	266968.			0.00260448
$469$		−	7.54490e7i		−	0.731366i
$470$	−1.23317e7			−0.118776
$471$	1.54473e8			1.47839
$472$		−	1.42241e7i		−	0.135269i
$473$	−9.13630e7	−	2.29709e7i	−0.863350	−	0.217067i
$474$	−5.76885e6			−0.0541694
$475$			5.31936e7i			0.496339i
$476$			7.08974e7i			0.657370i
$477$	−6.03036e7			−0.555633
$478$			8.28009e6i			0.0758143i
$479$	1.51297e8			1.37665			0.688326	−	0.725402i	$-0.258346\pi$
$479$	1.51297e8			1.37665			0.688326	+	0.725402i	$0.258346\pi$
$480$			4.28648e7i			0.387594i
$481$			987873.i			0.00887699i
$482$	7.43913e6			0.0664326
$483$	3.82705e7			0.339643
$484$	−2.34089e7			−0.206464
$485$		−	1.62420e8i		−	1.42368i
$486$	5.80484e6			0.0505686
$487$	−4.60012e7			−0.398275			−0.199137	−	0.979972i	$-0.563814\pi$
$487$	−4.60012e7			−0.398275			−0.199137	+	0.979972i	$0.563814\pi$
$488$	−1.38776e7			−0.119414
$489$	−1.15284e8			−0.985924
$490$	−6.35017e6			−0.0539755
$491$		−	1.19775e8i		−	1.01187i	−0.862573	−	0.505933i	$-0.831148\pi$
$491$		−	1.19775e8i		−	1.01187i	0.862573	−	0.505933i	$-0.168852\pi$
$492$		−	1.76388e8i		−	1.48107i
$493$		−	7.38130e7i		−	0.616016i
$494$	−20562.8			−0.000170569
$495$			6.31327e7i			0.520521i
$496$	2.05644e8			1.68527
$497$	−7.00693e7			−0.570767
$498$	−886934.			−0.00718130
$499$			4.05522e7i			0.326372i	0.986595	+	0.163186i	$0.0521771\pi$
$499$			4.05522e7i			0.326372i	−0.986595	+	0.163186i	$0.947823\pi$
$500$			8.66693e7i			0.693355i
$501$		−	2.73068e8i		−	2.17149i
$502$			996209.i			0.00787479i
$503$		−	6.33952e7i		−	0.498141i	−0.968485	−	0.249071i	$-0.919875\pi$
$503$		−	6.33952e7i		−	0.498141i	0.968485	−	0.249071i	$-0.0801251\pi$
$504$	−8.26134e6			−0.0645296
$505$			7.67757e7i			0.596142i
$506$			1.94507e6i			0.0150135i
$507$		−	1.52749e8i		−	1.17207i
$508$	6.47553e7			0.493951
$509$	−1.40835e8			−1.06797			−0.533984	−	0.845494i	$-0.679306\pi$
$509$	−1.40835e8			−1.06797			−0.533984	+	0.845494i	$0.679306\pi$
$510$		−	9.35023e6i		−	0.0704874i
$511$	2.72866e8			2.04497
$512$			4.66658e7i			0.347687i
$513$	3.40177e7			0.251972
$514$	8.36484e6			0.0615982
$515$			3.33899e8i			2.44452i
$516$	3.90688e7	−	1.55390e8i	0.284368	−	1.13103i
$517$	−1.31673e8			−0.952853
$518$		−	1.52463e7i		−	0.109692i
$519$		−	9.10791e7i		−	0.651503i
$520$	−217927.			−0.00154989
$521$			1.55851e8i			1.10203i	0.834494	+	0.551017i	$0.185760\pi$
$521$			1.55851e8i			1.10203i	−0.834494	+	0.551017i	$0.814240\pi$
$522$	4.28969e6			0.0301588
$523$			1.98296e8i			1.38614i	0.720869	+	0.693071i	$0.243743\pi$
$523$			1.98296e8i			1.38614i	−0.720869	+	0.693071i	$0.756257\pi$
$524$			2.35480e8i			1.63667i
$525$	−2.98933e8			−2.06584
$526$	6.39177e6			0.0439201
$527$	−1.35717e8			−0.927264
$528$			1.51278e8i			1.02772i
$529$	−1.39674e8			−0.943512
$530$	2.45510e7			0.164908
$531$	5.34918e7			0.357276
$532$	−6.27103e7			−0.416489
$533$	1.34629e6			0.00889110
$534$		−	2.40279e7i		−	0.157795i
$535$			2.84401e8i			1.85725i
$536$			1.30769e7i			0.0849199i
$537$	−6.83961e7			−0.441681
$538$		−	1.11301e6i		−	0.00714747i
$539$	−6.78046e7			−0.433005
$540$	1.79807e8			1.14189
$541$	−4.07648e7			−0.257450			−0.128725	−	0.991680i	$-0.541089\pi$
$541$	−4.07648e7			−0.257450			−0.128725	+	0.991680i	$0.541089\pi$
$542$			3.80790e6i			0.0239159i
$543$			2.43306e8i			1.51969i
$544$		−	1.84475e7i		−	0.114588i
$545$		−	1.45909e8i		−	0.901351i
$546$		−	115557.i		−	0.000709934i
$547$	−1.28177e8			−0.783157			−0.391578	−	0.920145i	$-0.628071\pi$
$547$	−1.28177e8			−0.783157			−0.391578	+	0.920145i	$0.628071\pi$
$548$		−	205362.i		−	0.00124789i
$549$		−	5.21888e7i		−	0.315399i
$550$		−	1.51930e7i		−	0.0913179i
$551$	6.52892e7			0.390289
$552$	−6.63307e6			−0.0394364
$553$		−	1.34281e8i		−	0.794032i
$554$	−1.23543e7			−0.0726590
$555$		−	3.97328e8i		−	2.32418i
$556$	1.57945e8			0.918929
$557$	−6.31632e6			−0.0365509			−0.0182755	−	0.999833i	$-0.505818\pi$
$557$	−6.31632e6			−0.0365509			−0.0182755	+	0.999833i	$0.505818\pi$
$558$		−	7.88729e6i		−	0.0453968i
$559$	1.18602e6	+	298193.i	0.00678977	+	0.00170711i
$560$	−3.29782e8			−1.87786
$561$		−	9.98380e7i		−	0.565467i
$562$			1.62627e7i			0.0916187i
$563$	−2.95599e8			−1.65645			−0.828224	−	0.560398i	$-0.810648\pi$
$563$	−2.95599e8			−1.65645			−0.828224	+	0.560398i	$0.810648\pi$
$564$		−	2.23950e8i		−	1.24828i
$565$	−1.83546e8			−1.01765
$566$		−	1.81768e7i		−	0.100246i
$567$			2.74263e8i			1.50459i
$568$	1.21445e7			0.0662725
$569$	−9.63612e7			−0.523077			−0.261538	−	0.965193i	$-0.584230\pi$
$569$	−9.63612e7			−0.523077			−0.261538	+	0.965193i	$0.584230\pi$
$570$	8.27047e6			0.0446586
$571$		−	1.90132e8i		−	1.02128i	−0.859794	−	0.510641i	$-0.829408\pi$
$571$		−	1.90132e8i		−	1.02128i	0.859794	−	0.510641i	$-0.170592\pi$
$572$	−1.16054e6			−0.00620112
$573$	2.85802e8			1.51915
$574$	−2.07779e7			−0.109867
$575$	−6.53179e7			−0.343581
$576$	−6.93026e7			−0.362645
$577$		−	2.43390e8i		−	1.26699i	−0.773745	−	0.633497i	$-0.781619\pi$
$577$		−	2.43390e8i		−	1.26699i	0.773745	−	0.633497i	$-0.218381\pi$
$578$		−	9.67822e6i		−	0.0501201i
$579$			3.65909e8i			1.88511i
$580$	3.45099e8			1.76872
$581$		−	2.06450e7i		−	0.105266i
$582$	−1.49270e7			−0.0757188
$583$	2.62146e8			1.32293
$584$	−4.72933e7			−0.237444
$585$		−	819548.i		−	0.00409361i
$586$			4.27884e6i			0.0212634i
$587$		−	4.66573e6i		−	0.0230678i	−0.999933	−	0.0115339i	$-0.996329\pi$
$587$		−	4.66573e6i		−	0.0230678i	0.999933	−	0.0115339i	$-0.00367143\pi$
$588$		−	1.15322e8i		−	0.567257i
$589$		−	1.20045e8i		−	0.587486i
$590$	−2.17777e7			−0.106037
$591$			2.95673e7i			0.143235i
$592$		−	2.59099e8i		−	1.24882i
$593$		−	4.86626e7i		−	0.233363i	−0.993169	−	0.116681i	$-0.962774\pi$
$593$		−	4.86626e7i		−	0.233363i	0.993169	−	0.116681i	$-0.0372256\pi$
$594$	−9.71603e6			−0.0463585
$595$	2.17644e8			1.03323
$596$			2.77094e8i			1.30885i
$597$	1.16247e8			0.546334
$598$		−	25249.6i		−	0.000118073i
$599$	2.58627e8			1.20335			0.601677	−	0.798739i	$-0.294499\pi$
$599$	2.58627e8			1.20335			0.601677	+	0.798739i	$0.294499\pi$
$600$	5.18113e7			0.239867
$601$			3.22569e8i			1.48594i	0.669327	+	0.742968i	$0.266582\pi$
$601$			3.22569e8i			1.48594i	−0.669327	+	0.742968i	$0.733418\pi$
$602$	−1.83044e7	−	4.60217e6i	−0.0839007	−	0.0210947i
$603$	−4.91775e7			−0.224292
$604$			3.21524e8i			1.45916i
$605$			7.18616e7i			0.324512i
$606$	7.05599e6			0.0317059
$607$			8.42013e6i			0.0376489i	0.999823	+	0.0188245i	$0.00599237\pi$
$607$			8.42013e6i			0.0376489i	−0.999823	+	0.0188245i	$0.994008\pi$
$608$	1.63172e7			0.0725997
$609$			3.66906e8i			1.62444i
$610$			2.12473e7i			0.0936081i
$611$	1.70930e6			0.00749366
$612$	4.62108e7			0.201600
$613$	−2.68866e8			−1.16722			−0.583611	−	0.812033i	$-0.698361\pi$
$613$	−2.68866e8			−1.16722			−0.583611	+	0.812033i	$0.698361\pi$
$614$			2.64314e7i			0.114187i
$615$	−5.41484e8			−2.32788
$616$	3.59129e7			0.153641
$617$	1.31437e8			0.559581			0.279790	−	0.960061i	$-0.409735\pi$
$617$	1.31437e8			0.559581			0.279790	+	0.960061i	$0.409735\pi$
$618$	3.06867e7			0.130012
$619$	−1.09866e8			−0.463224			−0.231612	−	0.972808i	$-0.574400\pi$
$619$	−1.09866e8			−0.463224			−0.231612	+	0.972808i	$0.574400\pi$
$620$		−	6.34521e8i		−	2.66239i
$621$			4.17713e7i			0.174423i
$622$		−	4.80802e6i		−	0.0199800i
$623$	5.59294e8			2.31300
$624$		−	1.96380e6i		−	0.00808245i
$625$	−8.68709e7			−0.355823
$626$	−2.82487e6			−0.0115153
$627$	8.83088e7			0.358263
$628$		−	3.10814e8i		−	1.25493i
$629$			1.70996e8i			0.687123i
$630$			1.26485e7i			0.0505845i
$631$		−	4.55728e8i		−	1.81392i	−0.421220	−	0.906958i	$-0.638398\pi$
$631$		−	4.55728e8i		−	1.81392i	0.421220	−	0.906958i	$-0.361602\pi$
$632$			2.32736e7i			0.0921961i
$633$	5.02790e8			1.98233
$634$		−	2.35664e7i		−	0.0924754i
$635$		−	1.98788e8i		−	0.776372i
$636$			4.45857e8i			1.73310i
$637$	880196.			0.00340534
$638$	−1.86477e7			−0.0718064
$639$			4.56711e7i			0.175041i
$640$	1.14899e8			0.438305
$641$		−	6.65150e7i		−	0.252549i	−0.991995	−	0.126274i	$-0.959698\pi$
$641$		−	6.65150e7i		−	0.252549i	0.991995	−	0.126274i	$-0.0403020\pi$
$642$	2.61376e7			0.0987780
$643$	−7.14740e7			−0.268853			−0.134427	−	0.990924i	$-0.542919\pi$
$643$	−7.14740e7			−0.268853			−0.134427	+	0.990924i	$0.542919\pi$
$644$		−	7.70037e7i		−	0.288306i
$645$	−4.77022e8	−	1.19935e8i	−1.77770	−	0.446958i
$646$	−3.55932e6			−0.0132029
$647$		−	2.68031e8i		−	0.989627i	−0.868999	−	0.494813i	$-0.835236\pi$
$647$		−	2.68031e8i		−	0.989627i	0.868999	−	0.494813i	$-0.164764\pi$
$648$		−	4.75354e7i		−	0.174700i
$649$	−2.32534e8			−0.850653
$650$			197226.i			0.000718165i
$651$	6.74617e8			2.44520
$652$			2.31962e8i			0.836902i
$653$			4.14641e8i			1.48913i	0.667549	+	0.744566i	$0.267343\pi$
$653$			4.14641e8i			1.48913i	−0.667549	+	0.744566i	$0.732657\pi$
$654$	−1.34097e7			−0.0479385
$655$	7.22887e8			2.57245
$656$	−3.53104e8			−1.25081
$657$		−	1.77853e8i		−	0.627142i
$658$	−2.63805e7			−0.0925987
$659$	−2.34687e7			−0.0820036			−0.0410018	−	0.999159i	$-0.513055\pi$
$659$	−2.34687e7			−0.0820036			−0.0410018	+	0.999159i	$0.513055\pi$
$660$	4.66774e8			1.62358
$661$	−1.37046e8			−0.474527			−0.237264	−	0.971445i	$-0.576251\pi$
$661$	−1.37046e8			−0.474527			−0.237264	+	0.971445i	$0.576251\pi$
$662$	1.21993e7			0.0420496
$663$			1.29603e6i			0.00444709i
$664$			3.57821e6i			0.0122225i
$665$			1.92511e8i			0.654620i
$666$	−9.93754e6			−0.0336400
$667$			8.01704e7i			0.270170i
$668$	−5.49437e8			−1.84327
$669$	454750.			0.00151878
$670$	2.00213e7			0.0665683
$671$			2.26870e8i			0.750947i
$672$			9.16980e7i			0.302170i
$673$		−	2.12788e8i		−	0.698075i	−0.937109	−	0.349037i	$-0.886509\pi$
$673$		−	2.12788e8i		−	0.698075i	0.937109	−	0.349037i	$-0.113491\pi$
$674$		−	2.88651e6i		−	0.00942744i
$675$		−	3.26277e8i		−	1.06090i
$676$	−3.07345e8			−0.994916
$677$			2.63101e8i			0.847923i	0.905680	+	0.423962i	$0.139361\pi$
$677$			2.63101e8i			0.847923i	−0.905680	+	0.423962i	$0.860639\pi$
$678$			1.68686e7i			0.0541241i
$679$		−	3.47454e8i		−	1.10991i
$680$	−3.77222e7			−0.119969
$681$	3.33712e8			1.05665
$682$			3.42869e7i			0.108087i
$683$	−1.47190e8			−0.461972			−0.230986	−	0.972957i	$-0.574195\pi$
$683$	−1.47190e8			−0.461972			−0.230986	+	0.972957i	$0.574195\pi$
$684$			4.08744e7i			0.127727i
$685$	−630428.			−0.00196139
$686$	1.43440e7			0.0444323
$687$		−	8.12710e7i		−	0.250649i
$688$	−3.11068e8	−	7.82102e7i	−0.955192	−	0.240158i
$689$	−3.40301e6			−0.0104041
$690$			1.01555e7i			0.0309140i
$691$		−	6.71399e7i		−	0.203492i	−0.994810	−	0.101746i	$-0.967557\pi$
$691$		−	6.71399e7i		−	0.203492i	0.994810	−	0.101746i	$-0.0324428\pi$
$692$	−1.83259e8			−0.553029
$693$			1.35056e8i			0.405801i
$694$	2.06888e6			0.00618952
$695$		−	4.84866e8i		−	1.44433i
$696$		−	6.35925e7i		−	0.188616i
$697$	2.33036e8			0.688215
$698$	2.37780e7			0.0699213
$699$	−5.76192e8			−1.68708
$700$			6.01480e8i			1.75359i
$701$	−3.36019e8			−0.975461			−0.487730	−	0.872994i	$-0.662175\pi$
$701$	−3.36019e8			−0.975461			−0.487730	+	0.872994i	$0.662175\pi$
$702$	126127.			0.000364584
$703$	−1.51250e8			−0.435340
$704$	3.01265e8			0.863438
$705$	−6.87490e8			−1.96200
$706$			1.88327e7i			0.0535179i
$707$			1.64241e8i			0.464755i
$708$		−	3.95494e8i		−	1.11440i
$709$	−2.25368e8			−0.632344			−0.316172	−	0.948702i	$-0.602398\pi$
$709$	−2.25368e8			−0.632344			−0.316172	+	0.948702i	$0.602398\pi$
$710$		−	1.85937e7i		−	0.0519508i
$711$	−8.75239e7			−0.243510
$712$	−9.69373e7			−0.268566
$713$	1.47406e8			0.406675
$714$		−	2.00023e7i		−	0.0549523i
$715$			3.56266e6i			0.00974667i
$716$			1.37619e8i			0.374921i
$717$			4.61613e8i			1.25233i
$718$			3.46232e6i			0.00935392i
$719$	−9.20364e7			−0.247613			−0.123806	−	0.992306i	$-0.539510\pi$
$719$	−9.20364e7			−0.247613			−0.123806	+	0.992306i	$0.539510\pi$
$720$			2.14951e8i			0.575894i
$721$			7.14289e8i			1.90576i
$722$			2.35583e7i			0.0625941i
$723$	4.14729e8			1.09736
$724$	4.89554e8			1.28999
$725$		−	6.26215e8i		−	1.64327i
$726$	6.60437e6			0.0172592
$727$			3.95452e8i			1.02918i	0.857437	+	0.514589i	$0.172056\pi$
$727$			3.95452e8i			1.02918i	−0.857437	+	0.514589i	$0.827944\pi$
$728$	−466198.			−0.00120830
$729$	−1.54497e8			−0.398783
$730$			7.24082e7i			0.186131i
$731$	2.05294e8	+	5.16158e7i	0.525561	+	0.132139i
$732$	−3.85860e8			−0.983777
$733$			1.77578e8i			0.450897i	0.974255	+	0.225448i	$0.0723847\pi$
$733$			1.77578e8i			0.450897i	−0.974255	+	0.225448i	$0.927615\pi$
$734$		−	2.30518e7i		−	0.0582930i
$735$	−3.54020e8			−0.891591
$736$			2.00364e7i			0.0502557i
$737$	2.13780e8			0.534028
$738$			1.35430e7i			0.0336935i
$739$		−	5.97778e8i		−	1.48118i	−0.671959	−	0.740588i	$-0.734547\pi$
$739$		−	5.97778e8i		−	1.48118i	0.671959	−	0.740588i	$-0.265453\pi$
$740$	−7.99460e8			−1.97289
$741$	−1.14637e6			−0.00281754
$742$	5.25203e7			0.128563
$743$		−	1.67085e8i		−	0.407353i	−0.979038	−	0.203676i	$-0.934711\pi$
$743$		−	1.67085e8i		−	0.407353i	0.979038	−	0.203676i	$-0.0652890\pi$
$744$	−1.16925e8			−0.283916
$745$	8.50636e8			2.05719
$746$	1.49410e7			0.0359884
$747$	−1.34564e7			−0.0322825
$748$	−2.00883e8			−0.479997
$749$			6.08401e8i			1.44792i
$750$		−	2.44521e7i		−	0.0579605i
$751$		−	6.80726e8i		−	1.60714i	−0.595213	−	0.803568i	$-0.702932\pi$
$751$		−	6.80726e8i		−	1.60714i	0.595213	−	0.803568i	$-0.297068\pi$
$752$	−4.48315e8			−1.05422
$753$			5.55383e7i			0.130079i
$754$	242073.			0.000564718
$755$	9.87027e8			2.29344
$756$	3.84650e8			0.890227
$757$			3.37278e8i			0.777499i	0.921343	+	0.388750i	$0.127093\pi$
$757$			3.37278e8i			0.777499i	−0.921343	+	0.388750i	$0.872907\pi$
$758$		−	1.83684e7i		−	0.0421759i
$759$			1.08437e8i			0.248000i
$760$		−	3.33661e7i		−	0.0760089i
$761$			7.23483e7i			0.164163i	0.996626	+	0.0820813i	$0.0261567\pi$
$761$			7.23483e7i			0.164163i	−0.996626	+	0.0820813i	$0.973843\pi$
$762$	−1.82694e7			−0.0412915
$763$		−	3.12135e8i		−	0.702698i
$764$		−	5.75060e8i		−	1.28953i
$765$		−	1.41860e8i		−	0.316866i
$766$	−2.75552e7			−0.0613079
$767$	3.01861e6			0.00668992
$768$			5.04425e8i			1.11356i
$769$	5.73294e8			1.26066			0.630330	−	0.776327i	$-0.282919\pi$
$769$	5.73294e8			1.26066			0.630330	+	0.776327i	$0.282919\pi$
$770$		−	5.49843e7i		−	0.120439i
$771$	4.66337e8			1.01751
$772$	7.36241e8			1.60018
$773$		−	2.85371e8i		−	0.617833i	−0.951089	−	0.308916i	$-0.900034\pi$
$773$		−	2.85371e8i		−	0.617833i	0.951089	−	0.308916i	$-0.0999663\pi$
$774$	−2.99968e6	+	1.19308e7i	−0.00646923	+	0.0257303i
$775$	−1.15140e9			−2.47355
$776$			6.02210e7i			0.128873i
$777$		−	8.49979e8i		−	1.81195i
$778$	−7.11194e6			−0.0151025
$779$			2.06125e8i			0.436031i
$780$	−6.05936e6			−0.0127686
$781$		−	1.98537e8i		−	0.416762i
$782$		−	4.37059e6i		−	0.00913944i
$783$	−4.00469e8			−0.834225
$784$	−2.30858e8			−0.479067
$785$	−9.54148e8			−1.97245
$786$		−	6.64362e7i		−	0.136816i
$787$	−7.65928e8			−1.57132			−0.785658	−	0.618661i	$-0.787675\pi$
$787$	−7.65928e8			−1.57132			−0.785658	+	0.618661i	$0.787675\pi$
$788$	5.94922e7			0.121585
$789$	3.56339e8			0.725492
$790$	3.56330e7			0.0722721
$791$	−3.92648e8			−0.793368
$792$		−	2.34080e7i		−	0.0471181i
$793$		−	2.94508e6i		−	0.00590578i
$794$		−	3.30830e7i		−	0.0660912i
$795$	1.36871e9			2.72402
$796$		−	2.33899e8i		−	0.463756i
$797$	5.22530e8			1.03214			0.516068	−	0.856548i	$-0.327395\pi$
$797$	5.22530e8			1.03214			0.516068	+	0.856548i	$0.327395\pi$
$798$	1.76925e7			0.0348161
$799$	2.95871e8			0.580046
$800$		−	1.56505e8i		−	0.305674i
$801$		−	3.64547e8i		−	0.709342i
$802$			7.22477e7i			0.140056i
$803$			7.73146e8i			1.49319i
$804$			3.63596e8i			0.699602i
$805$	−2.36389e8			−0.453148
$806$		−	445090.i		−	0.000850047i
$807$		−	6.20500e7i		−	0.118065i
$808$		−	2.84664e7i		−	0.0539634i
$809$	8.16709e8			1.54249			0.771244	−	0.636539i	$-0.219635\pi$
$809$	8.16709e8			1.54249			0.771244	+	0.636539i	$0.219635\pi$
$810$	−7.27789e7			−0.136946
$811$		−	9.77049e6i		−	0.0183170i	−0.999958	−	0.00915849i	$-0.997085\pi$
$811$		−	9.77049e6i		−	0.0183170i	0.999958	−	0.00915849i	$-0.00291528\pi$
$812$	7.38248e8			1.37891
$813$			2.12289e8i			0.395054i
$814$	4.31995e7			0.0800950
$815$	7.12087e8			1.31541
$816$		−	3.39924e8i		−	0.625621i
$817$	−4.56553e7	+	1.81587e8i	−0.0837192	+	0.332979i
$818$	1.07556e7			0.0196506
$819$		−	1.75321e6i		−	0.00319140i
$820$			1.08951e9i			1.97602i
$821$	−5.36071e8			−0.968708			−0.484354	−	0.874872i	$-0.660945\pi$
$821$	−5.36071e8			−0.968708			−0.484354	+	0.874872i	$0.660945\pi$
$822$			57938.8i			0.000104317i
$823$	3.77961e8			0.678028			0.339014	−	0.940781i	$-0.389907\pi$
$823$	3.77961e8			0.678028			0.339014	+	0.940781i	$0.389907\pi$
$824$		−	1.23801e8i		−	0.221281i
$825$		−	8.47006e8i		−	1.50843i
$826$	−4.65877e7			−0.0826668
$827$	1.74527e8			0.308564			0.154282	−	0.988027i	$-0.450694\pi$
$827$	1.74527e8			0.308564			0.154282	+	0.988027i	$0.450694\pi$
$828$	−5.01909e7			−0.0884166
$829$		−	2.37876e8i		−	0.417530i	−0.977966	−	0.208765i	$-0.933056\pi$
$829$		−	2.37876e8i		−	0.417530i	0.977966	−	0.208765i	$-0.0669444\pi$
$830$	5.47841e6			0.00958120
$831$	−6.88750e8			−1.20021
$832$	−3.91083e6			−0.00679046
$833$	1.52358e8			0.263590
$834$	−4.45612e7			−0.0768172
$835$			1.68668e9i			2.89717i
$836$		−	1.77685e8i		−	0.304111i
$837$			7.36327e8i			1.25572i
$838$	4.21025e7			0.0715444
$839$		−	9.56731e8i		−	1.61996i	−0.586458	−	0.809980i	$-0.699478\pi$
$839$		−	9.56731e8i		−	1.61996i	0.586458	−	0.809980i	$-0.300522\pi$
$840$	1.87508e8			0.316360
$841$	−1.73785e8			−0.292162
$842$	4.04650e7			0.0677865
$843$			9.06642e8i			1.51340i
$844$		−	1.01166e9i		−	1.68270i
$845$			9.43501e8i			1.56377i
$846$			1.71947e7i			0.0283978i
$847$			1.53729e8i			0.252991i
$848$	8.92541e8			1.46366
$849$		−	1.01335e9i		−	1.65591i
$850$			3.41389e7i			0.0555895i
$851$		−	1.85724e8i		−	0.301355i
$852$	3.37671e8			0.545978
$853$	−7.13424e8			−1.14948			−0.574739	−	0.818337i	$-0.694896\pi$
$853$	−7.13424e8			−1.14948			−0.574739	+	0.818337i	$0.694896\pi$
$854$			4.54529e7i			0.0729773i
$855$	1.25478e8			0.200756
$856$		−	1.05448e8i		−	0.168120i
$857$	7.21224e8			1.14585			0.572925	−	0.819608i	$-0.305809\pi$
$857$	7.21224e8			1.14585			0.572925	+	0.819608i	$0.305809\pi$
$858$	327423.			0.000518378
$859$		−	4.86567e8i		−	0.767649i	−0.923406	−	0.383825i	$-0.874607\pi$
$859$		−	4.86567e8i		−	0.767649i	0.923406	−	0.383825i	$-0.125393\pi$
$860$	−2.41320e8	+	9.59812e8i	−0.379401	+	1.50901i
$861$	−1.15836e9			−1.81483
$862$		−	3.75065e7i		−	0.0585579i
$863$		−	9.85425e7i		−	0.153317i	−0.997057	−	0.0766586i	$-0.975575\pi$
$863$		−	9.85425e7i		−	0.153317i	0.997057	−	0.0766586i	$-0.0244252\pi$
$864$	−1.00086e8			−0.155179
$865$			5.62577e8i			0.869227i
$866$	1.69648e7			0.0261213
$867$		−	5.39558e8i		−	0.827906i
$868$		−	1.35739e9i		−	2.07561i
$869$	3.80475e8			0.579785
$870$	−9.73630e7			−0.147855
$871$	−2.77515e6			−0.00419983
$872$			5.40994e7i			0.0815912i
$873$	−2.26470e8			−0.340383
$874$	3.86588e6			0.00579047
$875$	5.69167e8			0.849603
$876$	−1.31497e9			−1.95615
$877$	7.95537e7			0.117940			0.0589700	−	0.998260i	$-0.481218\pi$
$877$	7.95537e7			0.117940			0.0589700	+	0.998260i	$0.481218\pi$
$878$		−	2.36157e7i		−	0.0348913i
$879$			2.38544e8i			0.351238i
$880$		−	9.34415e8i		−	1.37117i
$881$	−8.34212e8			−1.21997			−0.609984	−	0.792414i	$-0.708824\pi$
$881$	−8.34212e8			−1.21997			−0.609984	+	0.792414i	$0.708824\pi$
$882$			8.85436e6i			0.0129048i
$883$	−8.05325e8			−1.16974			−0.584869	−	0.811127i	$-0.698854\pi$
$883$	−8.05325e8			−1.16974			−0.584869	+	0.811127i	$0.698854\pi$
$884$	2.60774e6			0.00377491
$885$	−1.21410e9			−1.75156
$886$			5.96427e7i			0.0857544i
$887$		−	5.93266e8i		−	0.850117i	−0.905166	−	0.425058i	$-0.860254\pi$
$887$		−	5.93266e8i		−	0.850117i	0.905166	−	0.425058i	$-0.139746\pi$
$888$			1.47319e8i			0.210388i
$889$		−	4.25255e8i		−	0.605263i
$890$			1.48415e8i			0.210528i
$891$	−7.77105e8			−1.09862
$892$		−	914998.i		−	0.00128922i
$893$			2.61704e8i			0.367499i
$894$		−	7.81768e7i		−	0.109412i
$895$	4.22469e8			0.589286
$896$	2.45796e8			0.341705
$897$		−	1.40766e6i		−	0.00195038i
$898$	−6.33615e7			−0.0874977
$899$			1.41321e9i			1.94504i
$900$	3.92043e8			0.537782
$901$	−5.89044e8			−0.805330
$902$		−	5.88728e7i		−	0.0802223i
$903$	−1.02046e9	−	2.56570e8i	−1.38591	−	0.348451i
$904$	6.80541e7			0.0921190
$905$		−	1.50285e9i		−	2.02755i
$906$		−	9.07117e7i		−	0.121977i
$907$	−6.81217e8			−0.912985			−0.456492	−	0.889727i	$-0.650894\pi$
$907$	−6.81217e8			−0.912985			−0.456492	+	0.889727i	$0.650894\pi$
$908$		−	6.71458e8i		−	0.896936i
$909$	1.07052e8			0.142529
$910$			713771.i			0.000947185i
$911$			8.80151e8i			1.16413i	0.813142	+	0.582066i	$0.197755\pi$
$911$			8.80151e8i			1.16413i	−0.813142	+	0.582066i	$0.802245\pi$
$912$	3.00670e8			0.396374
$913$	5.84963e7			0.0768628
$914$	−5.36215e7			−0.0702264
$915$			1.18453e9i			1.54626i
$916$	−1.63525e8			−0.212763
$917$	1.54643e9			2.00549
$918$	2.18320e7			0.0282206
$919$	−3.46603e8			−0.446566			−0.223283	−	0.974754i	$-0.571677\pi$
$919$	−3.46603e8			−0.446566			−0.223283	+	0.974754i	$0.571677\pi$
$920$	4.09711e7			0.0526156
$921$			1.47354e9i			1.88618i
$922$		−	4.30325e7i		−	0.0549040i
$923$			2.57728e6i			0.00327760i
$924$	9.98540e8			1.26575
$925$			1.45070e9i			1.83295i
$926$	−9.45735e7			−0.119107
$927$	4.65573e8			0.584451
$928$	−1.92092e8			−0.240362
$929$		−	4.84799e8i		−	0.604665i	−0.953203	−	0.302332i	$-0.902235\pi$
$929$		−	4.84799e8i		−	0.604665i	0.953203	−	0.302332i	$-0.0977652\pi$
$930$			1.79018e8i			0.222560i
$931$			1.34764e8i			0.167003i
$932$			1.15935e9i			1.43208i
$933$		−	2.68046e8i		−	0.330038i
$934$	1.10975e8			0.136202
$935$			6.16679e8i			0.754440i
$936$			303867.i			0.000370558i
$937$		−	7.54972e7i		−	0.0917724i	−0.998947	−	0.0458862i	$-0.985389\pi$
$937$		−	7.54972e7i		−	0.0917724i	0.998947	−	0.0458862i	$-0.0146112\pi$
$938$	4.28303e7			0.0518970
$939$	−1.57486e8			−0.190215
$940$			1.38329e9i			1.66544i
$941$	4.78328e8			0.574060			0.287030	−	0.957922i	$-0.407332\pi$
$941$	4.78328e8			0.574060			0.287030	+	0.957922i	$0.407332\pi$
$942$			8.76900e7i			0.104905i
$943$	−2.53106e8			−0.301834
$944$	−7.91721e8			−0.941144
$945$		−	1.18082e9i		−	1.39922i
$946$	1.30399e7	−	5.18642e7i	0.0154029	−	0.0612625i
$947$	6.33377e8			0.745783			0.372891	−	0.927875i	$-0.378366\pi$
$947$	6.33377e8			0.745783			0.372891	+	0.927875i	$0.378366\pi$
$948$			6.47111e8i			0.759546i
$949$		−	1.00365e7i		−	0.0117431i
$950$	−3.01965e7			−0.0352198
$951$		−	1.31382e9i		−	1.52755i
$952$	−8.06967e7			−0.0935287
$953$		−	1.12237e9i		−	1.29675i	−0.761319	−	0.648377i	$-0.775448\pi$
$953$		−	1.12237e9i		−	1.29675i	0.761319	−	0.648377i	$-0.224552\pi$
$954$		−	3.42327e7i		−	0.0394272i
$955$	−1.76534e9			−2.02684
$956$	9.28806e8			1.06304
$957$	−1.03960e9			−1.18613
$958$			8.58871e7i			0.0976859i
$959$	−1.34863e6			−0.00152911
$960$	1.57296e9			1.77789
$961$	1.71092e9			1.92779
$962$	−560788.			−0.000629903
$963$	3.96555e8			0.444042
$964$		−	8.34473e8i		−	0.931496i
$965$		−	2.26014e9i		−	2.51509i
$966$			2.17251e7i			0.0241007i
$967$	8.29537e8			0.917395			0.458698	−	0.888592i	$-0.348316\pi$
$967$	8.29537e8			0.917395			0.458698	+	0.888592i	$0.348316\pi$
$968$		−	2.66444e7i		−	0.0293751i
$969$	−1.98431e8			−0.218091
$970$	9.22011e7			0.101023
$971$	−9.65276e8			−1.05437			−0.527186	−	0.849750i	$-0.676753\pi$
$971$	−9.65276e8			−1.05437			−0.527186	+	0.849750i	$0.676753\pi$
$972$		−	6.51148e8i		−	0.709057i
$973$		−	1.03724e9i		−	1.12601i
$974$		−	2.61136e7i		−	0.0282612i
$975$			1.09953e7i			0.0118630i
$976$			7.72436e8i			0.830832i
$977$	−9.55447e7			−0.102453			−0.0512263	−	0.998687i	$-0.516313\pi$
$977$	−9.55447e7			−0.102453			−0.0512263	+	0.998687i	$0.516313\pi$
$978$		−	6.54437e7i		−	0.0699602i
$979$			1.58472e9i			1.68890i
$980$			7.12320e8i			0.756827i
$981$	−2.03449e8			−0.215501
$982$	6.79931e7			0.0718010
$983$		−	1.33824e9i		−	1.40888i	−0.709766	−	0.704438i	$-0.751199\pi$
$983$		−	1.33824e9i		−	1.40888i	0.709766	−	0.704438i	$-0.248801\pi$
$984$	2.00768e8			0.210722
$985$		−	1.82631e8i		−	0.191103i
$986$	4.19016e7			0.0437119
$987$	−1.47070e9			−1.52958
$988$			2.30660e6i			0.00239167i
$989$	−2.22975e8	−	5.60614e7i	−0.230498	−	0.0579529i
$990$	−3.58387e7			−0.0369357
$991$			2.01139e8i			0.206669i	0.994647	+	0.103335i	$0.0329512\pi$
$991$			2.01139e8i			0.206669i	−0.994647	+	0.103335i	$0.967049\pi$
$992$			3.53193e8i			0.361807i
$993$	6.80108e8			0.694593
$994$		−	3.97764e7i		−	0.0405011i
$995$	−7.18033e8			−0.728913
$996$			9.94904e7i			0.100694i
$997$		−	4.40460e8i		−	0.444448i	−0.974996	−	0.222224i	$-0.928668\pi$
$997$		−	4.40460e8i		−	0.444448i	0.974996	−	0.222224i	$-0.0713317\pi$
$998$	−2.30204e7			−0.0231590
$999$	9.27730e8			0.930519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.b.b.42.11	yes	20
43.42	odd	2	inner	43.7.b.b.42.10	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.b.b.42.10	✓	20	43.42	odd	2	inner
43.7.b.b.42.11	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)

\(f(q)\)	\(=\)	\(q+0.567672i q^{2} +31.6476i q^{3} +63.6777 q^{4} -195.481i q^{5} -17.9654 q^{6} -418.179i q^{7} +72.4791i q^{8} -272.568 q^{9} +O(q^{10})\)	\(q+0.567672i q^{2} +31.6476i q^{3} +63.6777 q^{4} -195.481i q^{5} -17.9654 q^{6} -418.179i q^{7} +72.4791i q^{8} -272.568 q^{9} +110.969 q^{10} +1184.88 q^{11} +2015.25i q^{12} -15.3814 q^{13} +237.389 q^{14} +6186.48 q^{15} +4034.23 q^{16} -2662.44 q^{17} -154.730i q^{18} -2354.99i q^{19} -12447.8i q^{20} +13234.3 q^{21} +672.625i q^{22} +2891.76 q^{23} -2293.79 q^{24} -22587.6 q^{25} -8.73158i q^{26} +14444.9i q^{27} -26628.7i q^{28} +27723.8i q^{29} +3511.89i q^{30} +50974.7 q^{31} +6928.78i q^{32} +37498.6i q^{33} -1511.40i q^{34} -81745.9 q^{35} -17356.5 q^{36} -64225.2i q^{37} +1336.86 q^{38} -486.783i q^{39} +14168.3 q^{40} -87526.9 q^{41} +7512.77i q^{42} +(-77107.2 - 19386.6i) q^{43} +75450.6 q^{44} +53281.8i q^{45} +1641.57i q^{46} -111128. q^{47} +127674. i q^{48} -57224.7 q^{49} -12822.4i q^{50} -84259.9i q^{51} -979.452 q^{52} +221242. q^{53} -8200.00 q^{54} -231621. i q^{55} +30309.2 q^{56} +74529.6 q^{57} -15738.0 q^{58} -196251. q^{59} +393941. q^{60} +191470. i q^{61} +28936.9i q^{62} +113982. i q^{63} +254258. q^{64} +3006.76i q^{65} -21286.9 q^{66} +180423. q^{67} -169538. q^{68} +91517.0i q^{69} -46404.9i q^{70} -167558. i q^{71} -19755.5i q^{72} +652509. i q^{73} +36458.9 q^{74} -714844. i q^{75} -149960. i q^{76} -495493. i q^{77} +276.333 q^{78} +321108. q^{79} -788614. i q^{80} -655850. q^{81} -49686.6i q^{82} +49368.9 q^{83} +842734. q^{84} +520456. i q^{85} +(11005.3 - 43771.6i) q^{86} -877390. q^{87} +85879.2i q^{88} +1.33745e6i q^{89} -30246.6 q^{90} +6432.17i q^{91} +184140. q^{92} +1.61323e6i q^{93} -63084.1i q^{94} -460354. q^{95} -219279. q^{96} +830874. q^{97} -32484.9i q^{98} -322961. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 796 q^{4} - 258 q^{6} - 2736 q^{9}+O(q^{10}) \) 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

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Database

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