LMFDB - Embedded newform 99.9.k.a.28.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,9,Mod(19,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("99.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	99.k (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$40.3304823961$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			28.3
Character	$\chi$	$=$	99.28
Dual form			99.9.k.a.46.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.67744 + 2.16963i) q^{2} +(-167.227 + 121.498i) q^{4} +(217.294 - 668.763i) q^{5} +(-790.545 - 1088.09i) q^{7} +(1909.53 - 2628.24i) q^{8} +O(q^{10})$	\(q+(-6.67744 + 2.16963i) q^{2} +(-167.227 + 121.498i) q^{4} +(217.294 - 668.763i) q^{5} +(-790.545 - 1088.09i) q^{7} +(1909.53 - 2628.24i) q^{8} +4937.07i q^{10} +(14415.0 + 2562.63i) q^{11} +(18414.6 - 5983.26i) q^{13} +(7639.57 + 5550.47i) q^{14} +(9303.62 - 28633.6i) q^{16} +(-65096.6 - 21151.2i) q^{17} +(-117001. + 161038. i) q^{19} +(44915.7 + 138236. i) q^{20} +(-101815. + 14163.4i) q^{22} +350509. q^{23} +(-84005.1 - 61033.3i) q^{25} +(-109981. + 79905.7i) q^{26} +(264402. + 85909.3i) q^{28} +(-224769. - 309368. i) q^{29} +(-312538. - 961894. i) q^{31} +1.04305e6i q^{32} +480569. q^{34} +(-899456. + 292251. i) q^{35} +(-310990. + 225947. i) q^{37} +(431875. - 1.32917e6i) q^{38} +(-1.34274e6 - 1.84812e6i) q^{40} +(1.87467e6 - 2.58026e6i) q^{41} +823502. i q^{43} +(-2.72194e6 + 1.32285e6i) q^{44} +(-2.34050e6 + 760476. i) q^{46} +(-410370. - 298151. i) q^{47} +(1.22244e6 - 3.76228e6i) q^{49} +(693358. + 225286. i) q^{50} +(-2.35247e6 + 3.23790e6i) q^{52} +(-2.23998e6 - 6.89394e6i) q^{53} +(4.84609e6 - 9.08337e6i) q^{55} -4.36933e6 q^{56} +(2.17210e6 + 1.57812e6i) q^{58} +(-1.56962e7 + 1.14040e7i) q^{59} +(-2.18306e7 - 7.09320e6i) q^{61} +(4.17391e6 + 5.74489e6i) q^{62} +(118699. + 365318. i) q^{64} -1.36151e7i q^{65} -3.55334e7 q^{67} +(1.34558e7 - 4.37204e6i) q^{68} +(5.37199e6 - 3.90298e6i) q^{70} +(9.45943e6 - 2.91131e7i) q^{71} +(-2.84406e7 - 3.91452e7i) q^{73} +(1.58639e6 - 2.18348e6i) q^{74} -4.11455e7i q^{76} +(-8.60731e6 - 1.77107e7i) q^{77} +(4.20948e7 - 1.36774e7i) q^{79} +(-1.71275e7 - 1.24438e7i) q^{80} +(-6.91976e6 + 2.12968e7i) q^{82} +(-3.72684e7 - 1.21092e7i) q^{83} +(-2.82903e7 + 3.89382e7i) q^{85} +(-1.78670e6 - 5.49889e6i) q^{86} +(3.42610e7 - 3.29926e7i) q^{88} +2.40233e7 q^{89} +(-2.10679e7 - 1.53067e7i) q^{91} +(-5.86148e7 + 4.25862e7i) q^{92} +(3.38710e6 + 1.10054e6i) q^{94} +(8.22728e7 + 1.13239e8i) q^{95} +(3.79731e7 + 1.16869e8i) q^{97} +2.77746e7i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 5 q^{2} + 951 q^{4} + 708 q^{5} + 5470 q^{7} + 3845 q^{8}+O(q^{10}) $ 28 * q + 5 * q^2 + 951 * q^4 + 708 * q^5 + 5470 * q^7 + 3845 * q^8	\( 28 q + 5 q^{2} + 951 q^{4} + 708 q^{5} + 5470 q^{7} + 3845 q^{8} - 38567 q^{11} - 12500 q^{13} + 49262 q^{14} + 65335 q^{16} - 368200 q^{17} - 442685 q^{19} + 101488 q^{20} + 1686925 q^{22} - 704764 q^{23} - 960933 q^{25} - 659122 q^{26} - 2014380 q^{28} + 795320 q^{29} + 1317554 q^{31} + 897538 q^{34} - 8132260 q^{35} + 8163354 q^{37} - 1456780 q^{38} - 24701940 q^{40} + 13192700 q^{41} + 8229340 q^{44} + 38601510 q^{46} - 11954754 q^{47} - 11198359 q^{49} + 41838705 q^{50} - 81977530 q^{52} + 2537916 q^{53} + 40359452 q^{55} - 96646244 q^{56} - 13252700 q^{58} - 49581537 q^{59} - 29302910 q^{61} + 207755000 q^{62} + 22221799 q^{64} + 105502894 q^{67} - 335519000 q^{68} + 228302300 q^{70} - 30044916 q^{71} - 272936400 q^{73} + 400896650 q^{74} - 23326180 q^{77} + 319699810 q^{79} - 208513052 q^{80} - 197581295 q^{82} + 558510965 q^{83} - 360970180 q^{85} - 119645907 q^{86} + 85623835 q^{88} - 317966134 q^{89} + 285678712 q^{91} - 599604784 q^{92} - 650361480 q^{94} + 641153840 q^{95} + 85897149 q^{97}+O(q^{100}) \) 28 * q + 5 * q^2 + 951 * q^4 + 708 * q^5 + 5470 * q^7 + 3845 * q^8 - 38567 * q^11 - 12500 * q^13 + 49262 * q^14 + 65335 * q^16 - 368200 * q^17 - 442685 * q^19 + 101488 * q^20 + 1686925 * q^22 - 704764 * q^23 - 960933 * q^25 - 659122 * q^26 - 2014380 * q^28 + 795320 * q^29 + 1317554 * q^31 + 897538 * q^34 - 8132260 * q^35 + 8163354 * q^37 - 1456780 * q^38 - 24701940 * q^40 + 13192700 * q^41 + 8229340 * q^44 + 38601510 * q^46 - 11954754 * q^47 - 11198359 * q^49 + 41838705 * q^50 - 81977530 * q^52 + 2537916 * q^53 + 40359452 * q^55 - 96646244 * q^56 - 13252700 * q^58 - 49581537 * q^59 - 29302910 * q^61 + 207755000 * q^62 + 22221799 * q^64 + 105502894 * q^67 - 335519000 * q^68 + 228302300 * q^70 - 30044916 * q^71 - 272936400 * q^73 + 400896650 * q^74 - 23326180 * q^77 + 319699810 * q^79 - 208513052 * q^80 - 197581295 * q^82 + 558510965 * q^83 - 360970180 * q^85 - 119645907 * q^86 + 85623835 * q^88 - 317966134 * q^89 + 285678712 * q^91 - 599604784 * q^92 - 650361480 * q^94 + 641153840 * q^95 + 85897149 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	−6.67744	+	2.16963i	−0.417340	+	0.135602i	−0.510157	−	0.860081i	$-0.670413\pi$
$2$	−6.67744	+	2.16963i	−0.417340	+	0.135602i	0.0928173	+	0.995683i	$0.470413\pi$
$3$		0			0
$3$		0			0
$4$	−167.227	+	121.498i	−0.653232	+	0.474601i
$5$	217.294	−	668.763i	0.347671	−	1.07002i	−0.612467	−	0.790496i	$-0.709823\pi$
$5$	217.294	−	668.763i	0.347671	−	1.07002i	0.960138	−	0.279525i	$-0.0901771\pi$
$6$		0			0
$7$	−790.545	−	1088.09i	−0.329256	−	0.453183i	0.612009	−	0.790851i	$-0.290362\pi$
$7$	−790.545	−	1088.09i	−0.329256	−	0.453183i	−0.941265	+	0.337668i	$0.890362\pi$
$8$	1909.53	−	2628.24i	0.466193	−	0.641660i
$9$		0			0
$10$			4937.07i			0.493707i
$11$	14415.0	+	2562.63i	0.984563	+	0.175031i
$11$	14415.0	+	2562.63i	0.984563	+	0.175031i
$12$		0			0
$13$	18414.6	−	5983.26i	0.644746	−	0.209491i	0.0316498	−	0.999499i	$-0.489924\pi$
$13$	18414.6	−	5983.26i	0.644746	−	0.209491i	0.613096	+	0.790008i	$0.289924\pi$
$14$	7639.57	+	5550.47i	0.198864	+	0.144483i
$15$		0			0
$16$	9303.62	−	28633.6i	0.141962	−	0.436914i
$17$	−65096.6	−	21151.2i	−0.779404	−	0.253244i	−0.107819	−	0.994171i	$-0.534387\pi$
$17$	−65096.6	−	21151.2i	−0.779404	−	0.253244i	−0.671586	+	0.740927i	$0.734387\pi$
$18$		0			0
$19$	−117001.	+	161038.i	−0.897793	+	1.23571i	0.0733740	+	0.997304i	$0.476623\pi$
$19$	−117001.	+	161038.i	−0.897793	+	1.23571i	−0.971167	+	0.238401i	$0.923377\pi$
$20$	44915.7	+	138236.i	0.280723	+	0.863977i
$21$		0			0
$22$	−101815.	+	14163.4i	−0.434632	+	0.0604611i
$23$	350509.			1.25253			0.626265	−	0.779610i	$-0.284583\pi$
$23$	350509.			1.25253			0.626265	+	0.779610i	$0.284583\pi$
$24$		0			0
$25$	−84005.1	−	61033.3i	−0.215053	−	0.156245i
$26$	−109981.	+	79905.7i	−0.240671	+	0.174858i
$27$		0			0
$28$	264402.	+	85909.3i	0.430162	+	0.139768i
$29$	−224769.	−	309368.i	−0.317793	−	0.437405i	0.619998	−	0.784603i	$-0.287133\pi$
$29$	−224769.	−	309368.i	−0.317793	−	0.437405i	−0.937792	+	0.347198i	$0.887133\pi$
$30$		0			0
$31$	−312538.	−	961894.i	−0.338420	−	1.04155i	−0.965013	−	0.262203i	$-0.915551\pi$
$31$	−312538.	−	961894.i	−0.338420	−	1.04155i	0.626592	−	0.779347i	$-0.284449\pi$
$32$			1.04305e6i			0.994727i
$33$		0			0
$34$	480569.			0.359617
$35$	−899456.	+	292251.i	−0.599388	+	0.194753i
$36$		0			0
$37$	−310990.	+	225947.i	−0.165936	+	0.120559i	−0.667654	−	0.744472i	$-0.732701\pi$
$37$	−310990.	+	225947.i	−0.165936	+	0.120559i	0.501718	+	0.865031i	$0.332701\pi$
$38$	431875.	−	1.32917e6i	0.207121	−	0.637452i
$39$		0			0
$40$	−1.34274e6	−	1.84812e6i	−0.524508	−	0.721923i
$41$	1.87467e6	−	2.58026e6i	0.663420	−	0.913120i	−0.336168	−	0.941802i	$-0.609131\pi$
$41$	1.87467e6	−	2.58026e6i	0.663420	−	0.913120i	0.999589	+	0.0286824i	$0.00913114\pi$
$42$		0			0
$43$			823502.i			0.240875i	0.992721	+	0.120437i	$0.0384297\pi$
$43$			823502.i			0.240875i	−0.992721	+	0.120437i	$0.961570\pi$
$44$	−2.72194e6	+	1.32285e6i	−0.726218	+	0.352938i
$45$		0			0
$46$	−2.34050e6	+	760476.i	−0.522731	+	0.169846i
$47$	−410370.	−	298151.i	−0.0840978	−	0.0611006i	0.544942	−	0.838474i	$-0.316552\pi$
$47$	−410370.	−	298151.i	−0.0840978	−	0.0611006i	−0.629040	+	0.777373i	$0.716552\pi$
$48$		0			0
$49$	1.22244e6	−	3.76228e6i	0.212052	−	0.652630i
$50$	693358.	+	225286.i	0.110937	+	0.0360457i
$51$		0			0
$52$	−2.35247e6	+	3.23790e6i	−0.321744	+	0.442843i
$53$	−2.23998e6	−	6.89394e6i	−0.283883	−	0.873703i	−0.986731	−	0.162363i	$-0.948089\pi$
$53$	−2.23998e6	−	6.89394e6i	−0.283883	−	0.873703i	0.702848	−	0.711340i	$-0.251911\pi$
$54$		0			0
$55$	4.84609e6	−	9.08337e6i	0.529591	−	0.992650i
$56$	−4.36933e6			−0.444286
$57$		0			0
$58$	2.17210e6	+	1.57812e6i	0.191941	+	0.139453i
$59$	−1.56962e7	+	1.14040e7i	−1.29535	+	0.941126i	−0.999899	−	0.0142328i	$-0.995469\pi$
$59$	−1.56962e7	+	1.14040e7i	−1.29535	+	0.941126i	−0.295450	+	0.955358i	$0.595469\pi$
$60$		0			0
$61$	−2.18306e7	−	7.09320e6i	−1.57669	−	0.512298i	−0.615490	−	0.788145i	$-0.711042\pi$
$61$	−2.18306e7	−	7.09320e6i	−1.57669	−	0.512298i	−0.961202	+	0.275846i	$0.911042\pi$
$62$	4.17391e6	+	5.74489e6i	0.282472	+	0.388790i
$63$		0			0
$64$	118699.	+	365318.i	0.00707500	+	0.0217746i
$65$		−	1.36151e7i		−	0.762725i
$66$		0			0
$67$	−3.55334e7			−1.76335			−0.881673	−	0.471861i	$-0.843583\pi$
$67$	−3.55334e7			−1.76335			−0.881673	+	0.471861i	$0.843583\pi$
$68$	1.34558e7	−	4.37204e6i	0.629322	−	0.204479i
$69$		0			0
$70$	5.37199e6	−	3.90298e6i	0.223740	−	0.162556i
$71$	9.45943e6	−	2.91131e7i	0.372247	−	1.14566i	−0.573070	−	0.819506i	$-0.694248\pi$
$71$	9.45943e6	−	2.91131e7i	0.372247	−	1.14566i	0.945317	−	0.326153i	$-0.105752\pi$
$72$		0			0
$73$	−2.84406e7	−	3.91452e7i	−1.00149	−	1.37844i	−0.924405	−	0.381411i	$-0.875438\pi$
$73$	−2.84406e7	−	3.91452e7i	−1.00149	−	1.37844i	−0.0770868	−	0.997024i	$-0.524562\pi$
$74$	1.58639e6	−	2.18348e6i	0.0529034	−	0.0728153i
$75$		0			0
$76$		−	4.11455e7i		−	1.23330i
$77$	−8.60731e6	−	1.77107e7i	−0.244853	−	0.503817i
$78$		0			0
$79$	4.20948e7	−	1.36774e7i	1.08074	−	0.351152i	0.286076	−	0.958207i	$-0.407649\pi$
$79$	4.20948e7	−	1.36774e7i	1.08074	−	0.351152i	0.794660	+	0.607055i	$0.207649\pi$
$80$	−1.71275e7	−	1.24438e7i	−0.418151	−	0.303804i
$81$		0			0
$82$	−6.91976e6	+	2.12968e7i	−0.153051	+	0.471042i
$83$	−3.72684e7	−	1.21092e7i	−0.785286	−	0.255155i	−0.111191	−	0.993799i	$-0.535466\pi$
$83$	−3.72684e7	−	1.21092e7i	−0.785286	−	0.255155i	−0.674096	+	0.738644i	$0.735466\pi$
$84$		0			0
$85$	−2.82903e7	+	3.89382e7i	−0.541952	+	0.745934i
$86$	−1.78670e6	−	5.49889e6i	−0.0326631	−	0.100527i
$87$		0			0
$88$	3.42610e7	−	3.29926e7i	0.571307	−	0.550156i
$89$	2.40233e7			0.382888			0.191444	−	0.981503i	$-0.438683\pi$
$89$	2.40233e7			0.382888			0.191444	+	0.981503i	$0.438683\pi$
$90$		0			0
$91$	−2.10679e7	−	1.53067e7i	−0.307224	−	0.223211i
$92$	−5.86148e7	+	4.25862e7i	−0.818194	+	0.594453i
$93$		0			0
$94$	3.38710e6	+	1.10054e6i	0.0433827	+	0.0140959i
$95$	8.22728e7	+	1.13239e8i	1.01009	+	1.39028i
$96$		0			0
$97$	3.79731e7	+	1.16869e8i	0.428933	+	1.32012i	0.899177	+	0.437584i	$0.144166\pi$
$97$	3.79731e7	+	1.16869e8i	0.428933	+	1.32012i	−0.470244	+	0.882536i	$0.655834\pi$
$98$			2.77746e7i			0.301123i
$99$		0			0
$100$	2.14634e7			0.214634
$101$	−1.72564e6	+	560696.i	−0.0165831	+	0.00538817i	−0.317297	−	0.948326i	$-0.602775\pi$
$101$	−1.72564e6	+	560696.i	−0.0165831	+	0.00538817i	0.300714	+	0.953714i	$0.402775\pi$
$102$		0			0
$103$	−5.15046e7	+	3.74203e7i	−0.457612	+	0.332475i	−0.792594	−	0.609750i	$-0.791270\pi$
$103$	−5.15046e7	+	3.74203e7i	−0.457612	+	0.332475i	0.334982	+	0.942225i	$0.391270\pi$
$104$	1.94377e7	−	5.98231e7i	0.166154	−	0.511371i
$105$		0			0
$106$	2.99146e7	+	4.11739e7i	0.236952	+	0.326136i
$107$	−1.37406e7	+	1.89124e7i	−0.104827	+	0.144282i	−0.858208	−	0.513303i	$-0.828422\pi$
$107$	−1.37406e7	+	1.89124e7i	−0.104827	+	0.144282i	0.753381	+	0.657585i	$0.228422\pi$
$108$		0			0
$109$			1.51242e8i			1.07144i	0.844396	+	0.535719i	$0.179959\pi$
$109$			1.51242e8i			1.07144i	−0.844396	+	0.535719i	$0.820041\pi$
$110$	−1.26519e7	+	7.11678e7i	−0.0864142	+	0.486086i
$111$		0			0
$112$	−3.85109e7	+	1.25129e7i	−0.244744	+	0.0795220i
$113$	−1.05791e8	−	7.68614e7i	−0.648834	−	0.471405i	0.214040	−	0.976825i	$-0.431338\pi$
$113$	−1.05791e8	−	7.68614e7i	−0.648834	−	0.471405i	−0.862874	+	0.505420i	$0.831338\pi$
$114$		0			0
$115$	7.61637e7	−	2.34408e8i	0.435469	−	1.34023i
$116$	7.51752e7	+	2.44259e7i	0.415186	+	0.134902i
$117$		0			0
$118$	8.00680e7	−	1.10204e8i	0.412982	−	0.568421i
$119$	2.84474e7	+	8.75521e7i	0.141858	+	0.436595i
$120$		0			0
$121$	2.01225e8	+	7.38806e7i	0.938728	+	0.344659i
$122$	1.61162e8			0.727485
$123$		0			0
$124$	1.69133e8	+	1.22882e8i	0.715388	+	0.519760i
$125$	1.63150e8	−	1.18535e8i	0.668261	−	0.485520i
$126$		0			0
$127$	−3.18610e8	−	1.03523e8i	−1.22474	−	0.397942i	−0.375934	−	0.926646i	$-0.622678\pi$
$127$	−3.18610e8	−	1.03523e8i	−1.22474	−	0.397942i	−0.848806	+	0.528704i	$0.822678\pi$
$128$	−1.58536e8	−	2.18206e8i	−0.590591	−	0.812879i
$129$		0			0
$130$	2.95398e7	+	9.09141e7i	0.103427	+	0.318316i
$131$			3.32594e8i			1.12935i	0.825312	+	0.564677i	$0.190999\pi$
$131$			3.32594e8i			1.12935i	−0.825312	+	0.564677i	$0.809001\pi$
$132$		0			0
$133$	2.67719e8			0.855604
$134$	2.37272e8	−	7.70944e7i	0.735915	−	0.239113i
$135$		0			0
$136$	−1.79894e8	+	1.30701e8i	−0.525849	+	0.382052i
$137$	−2.38491e7	+	7.34000e7i	−0.0677002	+	0.208360i	−0.979183	−	0.202978i	$-0.934938\pi$
$137$	−2.38491e7	+	7.34000e7i	−0.0677002	+	0.208360i	0.911483	+	0.411337i	$0.134938\pi$
$138$		0			0
$139$	1.74632e8	+	2.40360e8i	0.467805	+	0.643878i	0.976104	−	0.217302i	$-0.0697256\pi$
$139$	1.74632e8	+	2.40360e8i	0.467805	+	0.643878i	−0.508299	+	0.861180i	$0.669726\pi$
$140$	1.14906e8	−	1.58154e8i	0.299110	−	0.411689i
$141$		0			0
$142$			2.14924e8i			0.528607i
$143$	2.80779e8	−	3.90588e7i	0.671460	−	0.0934060i
$144$		0			0
$145$	−2.55735e8	+	8.30934e7i	−0.578520	+	0.187973i
$146$	2.74841e8	+	1.99684e8i	0.604881	+	0.439472i
$147$		0			0
$148$	2.45539e7	−	7.55692e7i	0.0511769	−	0.157506i
$149$	−7.65026e8	−	2.48572e8i	−1.55214	−	0.504321i	−0.597447	−	0.801908i	$-0.703818\pi$
$149$	−7.65026e8	−	2.48572e8i	−1.55214	−	0.504321i	−0.954695	+	0.297587i	$0.903818\pi$
$150$		0			0
$151$	1.45478e8	−	2.00233e8i	0.279826	−	0.385148i	−0.645850	−	0.763464i	$-0.723497\pi$
$151$	1.45478e8	−	2.00233e8i	0.279826	−	0.385148i	0.925676	+	0.378317i	$0.123497\pi$
$152$	1.99830e8	+	6.15014e8i	0.374358	+	1.15216i
$153$		0			0
$154$	9.59005e7	+	9.95874e7i	0.170505	+	0.177060i
$155$	−7.11192e8			−1.23214
$156$		0			0
$157$	−2.83915e8	−	2.06276e8i	−0.467293	−	0.339508i	0.329092	−	0.944298i	$-0.393257\pi$
$157$	−2.83915e8	−	2.06276e8i	−0.467293	−	0.339508i	−0.796385	+	0.604789i	$0.793257\pi$
$158$	−2.51410e8	+	1.82660e8i	−0.403417	+	0.293100i
$159$		0			0
$160$	6.97551e8	+	2.26648e8i	1.06438	+	0.345838i
$161$	−2.77093e8	−	3.81386e8i	−0.412404	−	0.567625i
$162$		0			0
$163$	1.26055e8	+	3.87958e8i	0.178571	+	0.549585i	0.999779	−	0.0210449i	$-0.00669929\pi$
$163$	1.26055e8	+	3.87958e8i	0.178571	+	0.549585i	−0.821208	+	0.570629i	$0.806699\pi$
$164$			6.59258e8i			0.911339i
$165$		0			0
$166$	2.75130e8			0.362331
$167$	1.01780e9	−	3.30703e8i	1.30857	−	0.425179i	0.430014	−	0.902822i	$-0.358509\pi$
$167$	1.01780e9	−	3.30703e8i	1.30857	−	0.425179i	0.878554	+	0.477643i	$0.158509\pi$
$168$		0			0
$169$	−3.56642e8	+	2.59116e8i	−0.437206	+	0.317649i
$170$	1.04425e8	−	3.21387e8i	0.125028	−	0.384798i
$171$		0			0
$172$	−1.00054e8	−	1.37712e8i	−0.114319	−	0.157347i
$173$	−2.70031e7	+	3.71665e7i	−0.0301459	+	0.0414923i	−0.823824	−	0.566846i	$-0.808164\pi$
$173$	−2.70031e7	+	3.71665e7i	−0.0301459	+	0.0414923i	0.793678	+	0.608338i	$0.208164\pi$
$174$		0			0
$175$			1.39655e8i			0.148903i
$176$	2.07489e8	−	3.88911e8i	0.216244	−	0.405321i
$177$		0			0
$178$	−1.60414e8	+	5.21216e7i	−0.159795	+	0.0519204i
$179$	−8.32761e8	−	6.05036e8i	−0.811163	−	0.589345i	0.103004	−	0.994681i	$-0.467154\pi$
$179$	−8.32761e8	−	6.05036e8i	−0.811163	−	0.589345i	−0.914168	+	0.405336i	$0.867154\pi$
$180$		0			0
$181$	2.53006e8	−	7.78673e8i	0.235731	−	0.725506i	−0.761293	−	0.648409i	$-0.775435\pi$
$181$	2.53006e8	−	7.78673e8i	0.235731	−	0.725506i	0.997024	−	0.0770970i	$-0.0245651\pi$
$182$	1.73889e8	+	5.65001e7i	0.158485	+	0.0514948i
$183$		0			0
$184$	6.69307e8	−	9.21223e8i	0.583921	−	0.803699i
$185$	8.35289e7	+	2.57076e8i	0.0713099	+	0.219469i
$186$		0			0
$187$	−8.84164e8	−	4.71713e8i	−0.723047	−	0.385755i
$188$	1.04850e8			0.0839338
$189$		0			0
$190$	−7.95058e8	−	5.77644e8i	−0.610077	−	0.443247i
$191$	5.40048e8	−	3.92367e8i	0.405787	−	0.294822i	−0.366107	−	0.930573i	$-0.619310\pi$
$191$	5.40048e8	−	3.92367e8i	0.405787	−	0.294822i	0.771894	+	0.635751i	$0.219310\pi$
$192$		0			0
$193$	−2.09726e9	−	6.81442e8i	−1.51155	−	0.491134i	−0.568192	−	0.822896i	$-0.692357\pi$
$193$	−2.09726e9	−	6.81442e8i	−1.51155	−	0.491134i	−0.943363	+	0.331762i	$0.892357\pi$
$194$	−5.07126e8	−	6.98000e8i	−0.358022	−	0.492775i
$195$		0			0
$196$	2.52684e8	+	7.77681e8i	0.171219	+	0.526959i
$197$		−	2.23782e8i		−	0.148580i	−0.997237	−	0.0742899i	$-0.976331\pi$
$197$		−	2.23782e8i		−	0.148580i	0.997237	−	0.0742899i	$-0.0236690\pi$
$198$		0			0
$199$	1.49591e9			0.953880			0.476940	−	0.878936i	$-0.341746\pi$
$199$	1.49591e9			0.953880			0.476940	+	0.878936i	$0.341746\pi$
$200$	−3.20820e8	+	1.04241e8i	−0.200512	+	0.0651505i
$201$		0			0
$202$	1.03064e7	−	7.48802e6i	0.00619014	−	0.00449740i
$203$	−1.58931e8	+	4.89139e8i	−0.0935889	+	0.288037i
$204$		0			0
$205$	−1.31823e9	−	1.81438e9i	−0.746405	−	1.02734i
$206$	2.62731e8	−	3.61618e8i	0.145896	−	0.200808i
$207$		0			0
$208$		−	5.82942e8i		−	0.311438i
$209$	−2.09925e9	+	2.02153e9i	−1.10022	+	1.05949i
$210$		0			0
$211$	−1.47026e9	+	4.77716e8i	−0.741760	+	0.241013i	−0.655432	−	0.755254i	$-0.727513\pi$
$211$	−1.47026e9	+	4.77716e8i	−0.741760	+	0.241013i	−0.0863283	+	0.996267i	$0.527513\pi$
$212$	1.21218e9	+	8.80703e8i	0.600102	+	0.436000i
$213$		0			0
$214$	5.07194e7	−	1.56098e8i	0.0241835	−	0.0744292i
$215$	5.50728e8	+	1.78942e8i	0.257741	+	0.0837451i
$216$		0			0
$217$	−7.99553e8	+	1.10049e9i	−0.360585	+	0.496303i
$218$	−3.28140e8	−	1.00991e9i	−0.145289	−	0.447154i
$219$		0			0
$220$	2.93210e8	+	2.10778e9i	0.125167	+	0.899775i
$221$	−1.32528e9			−0.555570
$222$		0			0
$223$	−1.58942e9	−	1.15478e9i	−0.642716	−	0.466960i	0.218066	−	0.975934i	$-0.430025\pi$
$223$	−1.58942e9	−	1.15478e9i	−0.642716	−	0.466960i	−0.860782	+	0.508974i	$0.830025\pi$
$224$	1.13493e9	−	8.24575e8i	0.450793	−	0.327520i
$225$		0			0
$226$	8.73171e8	+	2.83710e8i	0.334708	+	0.108753i
$227$	3.86822e8	+	5.32415e8i	0.145683	+	0.200515i	0.875622	−	0.482997i	$-0.160452\pi$
$227$	3.86822e8	+	5.32415e8i	0.145683	+	0.200515i	−0.729939	+	0.683512i	$0.760452\pi$
$228$		0			0
$229$	3.66531e7	+	1.12807e8i	0.0133281	+	0.0410197i	0.957499	−	0.288435i	$-0.0931350\pi$
$229$	3.66531e7	+	1.12807e8i	0.0133281	+	0.0410197i	−0.944171	+	0.329455i	$0.893135\pi$
$230$			1.73049e9i			0.618383i
$231$		0			0
$232$	−1.24230e9			−0.428818
$233$	1.79732e7	−	5.83985e6i	0.00609820	−	0.00198143i	−0.305966	−	0.952042i	$-0.598979\pi$
$233$	1.79732e7	−	5.83985e6i	0.00609820	−	0.00198143i	0.312065	+	0.950061i	$0.398979\pi$
$234$		0			0
$235$	−2.88564e8	+	2.09654e8i	−0.0946173	+	0.0687435i
$236$	1.23928e9	−	3.81411e9i	0.399504	−	1.22955i
$237$		0			0
$238$	−3.79911e8	−	5.22903e8i	−0.118406	−	0.162972i
$239$	7.91860e8	−	1.08990e9i	0.242693	−	0.334038i	−0.670243	−	0.742142i	$-0.733810\pi$
$239$	7.91860e8	−	1.08990e9i	0.242693	−	0.334038i	0.912935	+	0.408104i	$0.133810\pi$
$240$		0			0
$241$		−	5.25935e9i		−	1.55906i	−0.626363	−	0.779531i	$-0.715457\pi$
$241$		−	5.25935e9i		−	1.55906i	0.626363	−	0.779531i	$-0.284543\pi$
$242$	−1.50396e9	−	5.67501e7i	−0.438505	−	0.0165465i
$243$		0			0
$244$	4.51249e9	−	1.46620e9i	1.27308	−	0.413650i
$245$	−2.25045e9	−	1.63504e9i	−0.624603	−	0.453801i
$246$		0			0
$247$	−1.19099e9	+	3.66550e9i	−0.319979	+	0.984795i
$248$	−3.12489e9	−	1.01534e9i	−0.826090	−	0.268413i
$249$		0			0
$250$	−8.32244e8	+	1.14549e9i	−0.213054	+	0.293244i
$251$	−1.84918e7	−	5.69120e7i	−0.00465892	−	0.0143387i	0.948700	−	0.316178i	$-0.102400\pi$
$251$	−1.84918e7	−	5.69120e7i	−0.00465892	−	0.0143387i	−0.953359	+	0.301839i	$0.902400\pi$
$252$		0			0
$253$	5.05259e9	+	8.98227e8i	1.23320	+	0.219232i
$254$	2.35210e9			0.565095
$255$		0			0
$256$	1.45248e9	+	1.05529e9i	0.338183	+	0.245704i
$257$	−9.77634e8	+	7.10292e8i	−0.224101	+	0.162819i	−0.694171	−	0.719810i	$-0.744229\pi$
$257$	−9.77634e8	+	7.10292e8i	−0.224101	+	0.162819i	0.470070	+	0.882629i	$0.344229\pi$
$258$		0			0
$259$	4.91703e8	+	1.59764e8i	0.109271	+	0.0355042i
$260$	1.65421e9	+	2.27682e9i	0.361990	+	0.498237i
$261$		0			0
$262$	−7.21607e8	−	2.22088e9i	−0.153142	−	0.471324i
$263$		−	4.22692e8i		−	0.0883490i	−0.999024	−	0.0441745i	$-0.985934\pi$
$263$		−	4.22692e8i		−	0.0883490i	0.999024	−	0.0441745i	$-0.0140658\pi$
$264$		0			0
$265$	−5.09714e9			−1.03358
$266$	−1.78768e9	+	5.80852e8i	−0.357078	+	0.116022i
$267$		0			0
$268$	5.94216e9	−	4.31723e9i	1.15187	−	0.836886i
$269$	1.37486e9	−	4.23137e9i	0.262572	−	0.808112i	−0.729671	−	0.683798i	$-0.760327\pi$
$269$	1.37486e9	−	4.23137e9i	0.262572	−	0.808112i	0.992243	−	0.124314i	$-0.0396731\pi$
$270$		0			0
$271$	8.33326e8	+	1.14697e9i	0.154503	+	0.212656i	0.879251	−	0.476359i	$-0.158044\pi$
$271$	8.33326e8	+	1.14697e9i	0.154503	+	0.212656i	−0.724748	+	0.689014i	$0.758044\pi$
$272$	−1.21127e9	+	1.66717e9i	−0.221291	+	0.304582i
$273$		0			0
$274$		−	5.41868e8i		−	0.0961371i
$275$	−1.05453e9	−	1.09507e9i	−0.184385	−	0.191474i
$276$		0			0
$277$	−3.22449e9	+	1.04770e9i	−0.547700	+	0.177958i	−0.569779	−	0.821798i	$-0.692971\pi$
$277$	−3.22449e9	+	1.04770e9i	−0.547700	+	0.177958i	0.0220796	+	0.999756i	$0.492971\pi$
$278$	−1.68759e9	−	1.22610e9i	−0.282545	−	0.205281i
$279$		0			0
$280$	−9.49431e8	+	2.92205e9i	−0.154465	+	0.475396i
$281$	8.68202e9	+	2.82096e9i	1.39250	+	0.452451i	0.906758	−	0.421651i	$-0.138549\pi$
$281$	8.68202e9	+	2.82096e9i	1.39250	+	0.452451i	0.485743	+	0.874102i	$0.338549\pi$
$282$		0			0
$283$	−3.81537e9	+	5.25141e9i	−0.594828	+	0.818711i	−0.995223	−	0.0976323i	$-0.968873\pi$
$283$	−3.81537e9	+	5.25141e9i	−0.594828	+	0.818711i	0.400394	+	0.916343i	$0.368873\pi$
$284$	1.95531e9	+	6.01781e9i	0.300567	+	0.925051i
$285$		0			0
$286$	−1.79014e9	+	8.69999e8i	−0.267561	+	0.130033i
$287$	−4.28956e9			−0.632245
$288$		0			0
$289$	−1.85331e9	−	1.34651e9i	−0.265678	−	0.193027i
$290$	1.52737e9	−	1.10970e9i	0.215950	−	0.156897i
$291$		0			0
$292$	9.51211e9	+	3.09067e9i	1.30841	+	0.425130i
$293$	5.45610e9	+	7.50968e9i	0.740307	+	1.01895i	0.998601	+	0.0528793i	$0.0168398\pi$
$293$	5.45610e9	+	7.50968e9i	0.740307	+	1.01895i	−0.258293	+	0.966066i	$0.583160\pi$
$294$		0			0
$295$	4.21585e9	+	1.29751e10i	0.556669	+	1.71325i
$296$			1.24881e9i			0.162678i
$297$		0			0
$298$	5.64773e9			0.716157
$299$	6.45449e9	−	2.09719e9i	0.807564	−	0.262393i
$300$		0			0
$301$	8.96046e8	−	6.51016e8i	0.109160	−	0.0793095i
$302$	−5.36986e8	+	1.65267e9i	−0.0645558	+	0.198682i
$303$		0			0
$304$	3.52257e9	+	4.84840e9i	0.412445	+	0.567681i
$305$	−9.48734e9	+	1.30582e10i	−1.09634	+	1.50898i
$306$		0			0
$307$		−	3.17364e9i		−	0.357276i	−0.983915	−	0.178638i	$-0.942831\pi$
$307$		−	3.17364e9i		−	0.357276i	0.983915	−	0.178638i	$-0.0571691\pi$
$308$	3.59119e9	+	1.91595e9i	0.399058	+	0.212902i
$309$		0			0
$310$	4.74894e9	−	1.54302e9i	0.514221	−	0.167080i
$311$	1.51260e9	+	1.09897e9i	0.161690	+	0.117474i	0.665688	−	0.746230i	$-0.268138\pi$
$311$	1.51260e9	+	1.09897e9i	0.161690	+	0.117474i	−0.503998	+	0.863705i	$0.668138\pi$
$312$		0			0
$313$	5.41074e8	−	1.66526e9i	0.0563741	−	0.173502i	−0.918905	−	0.394480i	$-0.870925\pi$
$313$	5.41074e8	−	1.66526e9i	0.0563741	−	0.173502i	0.975279	+	0.220978i	$0.0709249\pi$
$314$	2.34337e9	+	7.61406e8i	0.241058	+	0.0783245i
$315$		0			0
$316$	−5.37762e9	+	7.40166e9i	−0.539314	+	0.742303i
$317$	−5.21490e9	−	1.60498e10i	−0.516427	−	1.58940i	−0.780671	−	0.624943i	$-0.785122\pi$
$317$	−5.21490e9	−	1.60498e10i	−0.516427	−	1.58940i	0.264244	−	0.964456i	$-0.414878\pi$
$318$		0			0
$319$	−2.44725e9	−	5.03554e9i	−0.236328	−	0.486277i
$320$	2.70104e8			0.0257591
$321$		0			0
$322$	2.67774e9	+	1.94549e9i	0.249084	+	0.180970i
$323$	1.10225e10	−	8.00834e9i	1.01268	−	0.735754i
$324$		0			0
$325$	−1.91210e9	−	6.21278e8i	−0.171386	−	0.0556868i
$326$	−1.68345e9	−	2.31707e9i	−0.149049	−	0.205149i
$327$		0			0
$328$	−3.20181e9	−	9.85414e9i	−0.276630	−	0.851380i
$329$			6.82222e8i			0.0582294i
$330$		0			0
$331$	3.80681e9			0.317138			0.158569	−	0.987348i	$-0.449312\pi$
$331$	3.80681e9			0.317138			0.158569	+	0.987348i	$0.449312\pi$
$332$	7.70354e9	−	2.50303e9i	0.634071	−	0.206022i
$333$		0			0
$334$	−6.07879e9	+	4.41650e9i	−0.488462	+	0.354889i
$335$	−7.72121e9	+	2.37634e10i	−0.613064	+	1.88682i
$336$		0			0
$337$	9.51776e9	+	1.31001e10i	0.737930	+	1.01567i	0.998735	+	0.0502817i	$0.0160119\pi$
$337$	9.51776e9	+	1.31001e10i	0.737930	+	1.01567i	−0.260805	+	0.965391i	$0.583988\pi$
$338$	1.81927e9	−	2.50401e9i	0.139390	−	0.191853i
$339$		0			0
$340$		−	9.94874e9i		−	0.744479i
$341$	−2.04025e9	−	1.46666e10i	−0.150892	−	1.08471i
$342$		0			0
$343$	−1.24340e10	+	4.04006e9i	−0.898328	+	0.291885i
$344$	2.16436e9	+	1.57250e9i	0.154560	+	0.112294i
$345$		0			0
$346$	9.96736e7	−	3.06764e8i	0.00695466	−	0.0214042i
$347$	−5.39777e9	−	1.75384e9i	−0.372303	−	0.120968i	0.116888	−	0.993145i	$-0.462708\pi$
$347$	−5.39777e9	−	1.75384e9i	−0.372303	−	0.120968i	−0.489191	+	0.872177i	$0.662708\pi$
$348$		0			0
$349$	8.71903e9	−	1.20007e10i	0.587715	−	0.808920i	−0.406800	−	0.913517i	$-0.633355\pi$
$349$	8.71903e9	−	1.20007e10i	0.587715	−	0.808920i	0.994515	+	0.104597i	$0.0333554\pi$
$350$	−3.02999e8	−	9.32536e8i	−0.0201915	−	0.0621431i
$351$		0			0
$352$	−2.67295e9	+	1.50355e10i	−0.174108	+	0.979371i
$353$	9.89071e9			0.636984			0.318492	−	0.947926i	$-0.396824\pi$
$353$	9.89071e9			0.636984			0.318492	+	0.947926i	$0.396824\pi$
$354$		0			0
$355$	−1.74143e10	−	1.26522e10i	−1.09646	−	0.796625i
$356$	−4.01735e9	+	2.91878e9i	−0.250115	+	0.181719i
$357$		0			0
$358$	6.87341e9	+	2.23331e9i	0.418447	+	0.135962i
$359$	−7.63373e9	−	1.05069e10i	−0.459578	−	0.632555i	0.514843	−	0.857284i	$-0.327850\pi$
$359$	−7.63373e9	−	1.05069e10i	−0.459578	−	0.632555i	−0.974421	+	0.224730i	$0.927850\pi$
$360$		0			0
$361$	−6.99587e9	−	2.15311e10i	−0.411920	−	1.26776i
$362$			5.74847e9i			0.334748i
$363$		0			0
$364$	5.38286e9			0.306625
$365$	−3.23588e10	+	1.05140e10i	−1.82315	+	0.592376i
$366$		0			0
$367$	1.44759e10	−	1.05174e10i	0.797962	−	0.579754i	−0.112353	−	0.993668i	$-0.535839\pi$
$367$	1.44759e10	−	1.05174e10i	0.797962	−	0.579754i	0.910316	+	0.413915i	$0.135839\pi$
$368$	3.26101e9	−	1.00363e10i	0.177812	−	0.547248i
$369$		0			0
$370$	−1.11552e9	−	1.53538e9i	−0.0595210	−	0.0819236i
$371$	−5.73043e9	+	7.88726e9i	−0.302477	+	0.416323i
$372$		0			0
$373$			1.91399e10i			0.988789i	0.869238	+	0.494394i	$0.164610\pi$
$373$			1.91399e10i			0.988789i	−0.869238	+	0.494394i	$0.835390\pi$
$374$	6.92739e9	+	1.23152e9i	0.354065	+	0.0629442i
$375$		0			0
$376$	−1.56723e9	+	5.09223e8i	−0.0784116	+	0.0254775i
$377$	−5.99006e9	−	4.35204e9i	−0.296528	−	0.215440i
$378$		0			0
$379$	7.23013e9	−	2.22520e10i	0.350420	−	1.07848i	−0.608197	−	0.793786i	$-0.708107\pi$
$379$	7.23013e9	−	2.22520e10i	0.350420	−	1.07848i	0.958618	−	0.284697i	$-0.0918929\pi$
$380$	−2.75166e10	−	8.94067e9i	−1.31965	−	0.428781i
$381$		0			0
$382$	−2.75484e9	+	3.79171e9i	−0.129373	+	0.178066i
$383$	1.32385e9	+	4.07439e9i	0.0615239	+	0.189351i	0.977094	−	0.212806i	$-0.0682604\pi$
$383$	1.32385e9	+	4.07439e9i	0.0615239	+	0.189351i	−0.915570	+	0.402158i	$0.868260\pi$
$384$		0			0
$385$	−1.37146e10	+	1.90782e9i	−0.624223	+	0.0868348i
$386$	1.54828e10			0.697431
$387$		0			0
$388$	−2.05495e10	−	1.49301e10i	−0.906724	−	0.658773i
$389$	1.96672e10	−	1.42891e10i	0.858903	−	0.624029i	−0.0686834	−	0.997639i	$-0.521880\pi$
$389$	1.96672e10	−	1.42891e10i	0.858903	−	0.624029i	0.927586	+	0.373609i	$0.121880\pi$
$390$		0			0
$391$	−2.28170e10	−	7.41369e9i	−0.976228	−	0.317196i
$392$	−7.55389e9	−	1.03970e10i	−0.319909	−	0.440317i
$393$		0			0
$394$	4.85524e8	+	1.49429e9i	0.0201477	+	0.0620083i
$395$		−	3.11234e10i		−	1.27850i
$396$		0			0
$397$	9.11498e9			0.366939			0.183469	−	0.983025i	$-0.441267\pi$
$397$	9.11498e9			0.366939			0.183469	+	0.983025i	$0.441267\pi$
$398$	−9.98885e9	+	3.24558e9i	−0.398092	+	0.129348i
$399$		0			0
$400$	−2.52915e9	+	1.83754e9i	−0.0987950	+	0.0717788i
$401$	2.39904e9	−	7.38349e9i	0.0927813	−	0.285551i	−0.893888	−	0.448291i	$-0.852033\pi$
$401$	2.39904e9	−	7.38349e9i	0.0927813	−	0.285551i	0.986669	+	0.162739i	$0.0520329\pi$
$402$		0			0
$403$	−1.15105e10	−	1.58429e10i	−0.436390	−	0.600639i
$404$	2.20452e8	−	3.03426e8i	0.00827538	−	0.0113901i
$405$		0			0
$406$		−	3.61102e9i		−	0.132900i
$407$	−5.06194e9	+	2.46008e9i	−0.184476	+	0.0896542i
$408$		0			0
$409$	−3.69258e10	+	1.19979e10i	−1.31958	+	0.428758i	−0.882351	−	0.470591i	$-0.844041\pi$
$409$	−3.69258e10	+	1.19979e10i	−1.31958	+	0.428758i	−0.437230	+	0.899350i	$0.644041\pi$
$410$	1.27389e10	+	9.25536e9i	0.450814	+	0.327535i
$411$		0			0
$412$	4.06650e9	−	1.25154e10i	0.141134	−	0.434366i
$413$	2.48171e10	+	8.06357e9i	0.853004	+	0.277158i
$414$		0			0
$415$	−1.61964e10	+	2.22924e10i	−0.546042	+	0.751563i
$416$	6.24082e9	+	1.92073e10i	0.208386	+	0.641346i
$417$		0			0
$418$	9.63165e9	−	1.80533e10i	0.315497	−	0.591359i
$419$	2.41027e9			0.0782005			0.0391003	−	0.999235i	$-0.487551\pi$
$419$	2.41027e9			0.0782005			0.0391003	+	0.999235i	$0.487551\pi$
$420$		0			0
$421$	3.94463e10	+	2.86594e10i	1.25568	+	0.912303i	0.998537	−	0.0540713i	$-0.0172198\pi$
$421$	3.94463e10	+	2.86594e10i	1.25568	+	0.912303i	0.257140	+	0.966374i	$0.417220\pi$
$422$	8.78108e9	−	6.37983e9i	0.276884	−	0.201168i
$423$		0			0
$424$	−2.23962e10	−	7.27697e9i	−0.692965	−	0.225158i
$425$	4.17752e9	+	5.74987e9i	0.128045	+	0.176239i
$426$		0			0
$427$	9.54003e9	+	2.93612e10i	0.286971	+	0.883207i
$428$		−	4.83213e9i		−	0.144000i
$429$		0			0
$430$	−4.06569e9			−0.118922
$431$	6.49011e9	−	2.10877e9i	0.188080	−	0.0611110i	−0.213463	−	0.976951i	$-0.568474\pi$
$431$	6.49011e9	−	2.10877e9i	0.188080	−	0.0611110i	0.401543	+	0.915840i	$0.368474\pi$
$432$		0			0
$433$	2.53158e10	−	1.83930e10i	0.720177	−	0.523239i	−0.166264	−	0.986081i	$-0.553170\pi$
$433$	2.53158e10	−	1.83930e10i	0.720177	−	0.523239i	0.886441	+	0.462842i	$0.153170\pi$
$434$	2.95131e9	−	9.08319e9i	0.0831870	−	0.256023i
$435$		0			0
$436$	−1.83756e10	−	2.52919e10i	−0.508506	−	0.699898i
$437$	−4.10100e10	+	5.64455e10i	−1.12451	+	1.54776i
$438$		0			0
$439$			3.21529e9i			0.0865689i	0.999063	+	0.0432845i	$0.0137822\pi$
$439$			3.21529e9i			0.0865689i	−0.999063	+	0.0432845i	$0.986218\pi$
$440$	−1.46195e10	−	3.00816e10i	−0.390052	−	0.802584i
$441$		0			0
$442$	8.84948e9	−	2.87537e9i	0.231861	−	0.0753363i
$443$	−3.90304e10	−	2.83572e10i	−1.01342	−	0.736290i	−0.0484937	−	0.998823i	$-0.515442\pi$
$443$	−3.90304e10	−	2.83572e10i	−1.01342	−	0.736290i	−0.964923	+	0.262533i	$0.915442\pi$
$444$		0			0
$445$	5.22012e9	−	1.60659e10i	0.133119	−	0.409699i
$446$	1.31187e10	+	4.26252e9i	0.331552	+	0.107728i
$447$		0			0
$448$	3.03662e8	−	4.17955e8i	0.00753839	−	0.0103757i
$449$	9.74677e9	+	2.99975e10i	0.239814	+	0.738073i	0.996446	+	0.0842317i	$0.0268436\pi$
$449$	9.74677e9	+	2.99975e10i	0.239814	+	0.738073i	−0.756632	+	0.653841i	$0.773156\pi$
$450$		0			0
$451$	3.36355e10	−	3.23903e10i	0.813003	−	0.782904i
$452$	2.70296e10			0.647569
$453$		0			0
$454$	−3.73812e9	−	2.71591e9i	−0.0879894	−	0.0639280i
$455$	−1.48145e10	+	1.07634e10i	−0.345654	+	0.251132i
$456$		0			0
$457$	−4.79138e10	−	1.55681e10i	−1.09849	−	0.356921i	−0.296968	−	0.954887i	$-0.595976\pi$
$457$	−4.79138e10	−	1.55681e10i	−1.09849	−	0.356921i	−0.801521	+	0.597966i	$0.795976\pi$
$458$	−4.89497e8	−	6.73735e8i	−0.0111247	−	0.0153118i
$459$		0			0
$460$	1.57434e10	+	4.84532e10i	0.351615	+	1.08216i
$461$			5.01336e10i			1.11001i	0.831849	+	0.555003i	$0.187283\pi$
$461$			5.01336e10i			1.11001i	−0.831849	+	0.555003i	$0.812717\pi$
$462$		0			0
$463$	2.36331e10			0.514276			0.257138	−	0.966375i	$-0.417221\pi$
$463$	2.36331e10			0.514276			0.257138	+	0.966375i	$0.417221\pi$
$464$	−1.09495e10	+	3.55771e9i	−0.236223	+	0.0767535i
$465$		0			0
$466$	−1.07345e8	+	7.79904e7i	−0.00227634	+	0.00165386i
$467$	2.54200e10	−	7.82347e10i	0.534451	−	1.64487i	−0.210380	−	0.977620i	$-0.567470\pi$
$467$	2.54200e10	−	7.82347e10i	0.534451	−	1.64487i	0.744832	−	0.667253i	$-0.232530\pi$
$468$		0			0
$469$	2.80907e10	+	3.86636e10i	0.580593	+	0.799118i
$470$	1.47199e9	−	2.02603e9i	0.0301658	−	0.0415197i
$471$		0			0
$472$			6.30295e10i			1.26992i
$473$	−2.11034e9	+	1.18708e10i	−0.0421606	+	0.237156i
$474$		0			0
$475$	1.96574e10	−	6.38707e9i	0.386146	−	0.125466i
$476$	−1.53946e10	−	1.11848e10i	−0.299875	−	0.217872i
$477$		0			0
$478$	−2.92291e9	+	8.99579e9i	−0.0559892	+	0.172317i
$479$	6.05538e9	+	1.96751e9i	0.115027	+	0.0373745i	0.365965	−	0.930629i	$-0.380739\pi$
$479$	6.05538e9	+	1.96751e9i	0.115027	+	0.0373745i	−0.250938	+	0.968003i	$0.580739\pi$
$480$		0			0
$481$	−4.37485e9	+	6.02146e9i	−0.0817302	+	0.112492i
$482$	1.14108e10	+	3.51190e10i	0.211412	+	0.650659i
$483$		0			0
$484$	−4.26266e10	+	1.20935e10i	−0.776783	+	0.220379i
$485$	8.64092e10			1.56168
$486$		0			0
$487$	3.79044e10	+	2.75391e10i	0.673866	+	0.489592i	0.871317	−	0.490720i	$-0.163266\pi$
$487$	3.79044e10	+	2.75391e10i	0.673866	+	0.489592i	−0.197451	+	0.980313i	$0.563266\pi$
$488$	−6.03288e10	+	4.38314e10i	−1.06376	+	0.772870i
$489$		0			0
$490$	1.85747e10	+	6.03527e9i	0.322208	+	0.104692i
$491$	2.89700e10	+	3.98738e10i	0.498451	+	0.686059i	0.981919	−	0.189303i	$-0.0606229\pi$
$491$	2.89700e10	+	3.98738e10i	0.498451	+	0.686059i	−0.483468	+	0.875362i	$0.660623\pi$
$492$		0			0
$493$	8.08822e9	+	2.48930e10i	0.136919	+	0.421395i
$494$		−	2.70602e10i		−	0.454384i
$495$		0			0
$496$	−3.04502e10			−0.503110
$497$	−3.91558e10	+	1.27225e10i	−0.641758	+	0.208520i
$498$		0			0
$499$	7.57714e10	−	5.50511e10i	1.22209	−	0.887900i	0.225817	−	0.974170i	$-0.427495\pi$
$499$	7.57714e10	−	5.50511e10i	1.22209	−	0.887900i	0.996272	+	0.0862699i	$0.0274947\pi$
$500$	−1.28813e10	+	3.96447e10i	−0.206101	+	0.634315i
$501$		0			0
$502$	2.46956e8	+	3.39906e8i	0.00388870	+	0.00535234i
$503$	6.84195e10	−	9.41713e10i	1.06883	−	1.47112i	0.197571	−	0.980289i	$-0.436695\pi$
$503$	6.84195e10	−	9.41713e10i	1.06883	−	1.47112i	0.871257	−	0.490827i	$-0.163305\pi$
$504$		0			0
$505$			1.27588e9i			0.0196176i
$506$	−3.56872e10	+	4.96440e9i	−0.544390	+	0.0757294i
$507$		0			0
$508$	6.58581e10	−	2.13986e10i	0.988904	−	0.321314i
$509$	−4.75110e10	−	3.45187e10i	−0.707820	−	0.514261i	0.174650	−	0.984631i	$-0.444121\pi$
$509$	−4.75110e10	−	3.45187e10i	−0.707820	−	0.514261i	−0.882470	+	0.470369i	$0.844121\pi$
$510$		0			0
$511$	−2.01099e10	+	6.18920e10i	−0.294935	+	0.907718i
$512$	5.36797e10	+	1.74416e10i	0.781142	+	0.253808i
$513$		0			0
$514$	4.98701e9	−	6.86404e9i	0.0714477	−	0.0983393i
$515$	1.38337e10	+	4.25756e10i	0.196656	+	0.605246i
$516$		0			0
$517$	−5.15143e9	−	5.34948e9i	−0.0721050	−	0.0748771i
$518$	−3.62994e9			−0.0504174
$519$		0			0
$520$	−3.57838e10	−	2.59985e10i	−0.489410	−	0.355577i
$521$	3.03557e10	−	2.20547e10i	0.411993	−	0.299330i	−0.362415	−	0.932017i	$-0.618048\pi$
$521$	3.03557e10	−	2.20547e10i	0.411993	−	0.299330i	0.774408	+	0.632687i	$0.218048\pi$
$522$		0			0
$523$	6.75238e10	+	2.19398e10i	0.902506	+	0.293242i	0.723271	−	0.690564i	$-0.242638\pi$
$523$	6.75238e10	+	2.19398e10i	0.902506	+	0.293242i	0.179235	+	0.983806i	$0.442638\pi$
$524$	−4.04095e10	−	5.56189e10i	−0.535992	−	0.737730i
$525$		0			0
$526$	9.17086e8	+	2.82250e9i	0.0119803	+	0.0368715i
$527$			6.92266e10i			0.897492i
$528$		0			0
$529$	4.45459e10			0.568833
$530$	3.40359e10	−	1.10589e10i	0.431353	−	0.140155i
$531$		0			0
$532$	−4.47700e10	+	3.25273e10i	−0.558909	+	0.406071i
$533$	1.90829e10	−	5.87310e10i	0.236447	−	0.727710i
$534$		0			0
$535$	9.66214e9	+	1.32988e10i	0.117939	+	0.162329i
$536$	−6.78520e10	+	9.33903e10i	−0.822060	+	1.13147i
$537$		0			0
$538$			3.12376e10i			0.372863i
$539$	2.72628e10	−	5.11006e10i	0.323009	−	0.605439i
$540$		0			0
$541$	9.70889e9	−	3.15461e9i	0.113339	−	0.0368262i	−0.251798	−	0.967780i	$-0.581022\pi$
$541$	9.70889e9	−	3.15461e9i	0.113339	−	0.0368262i	0.365138	+	0.930954i	$0.381022\pi$
$542$	−8.05299e9	−	5.85084e9i	−0.0933169	−	0.0677987i
$543$		0			0
$544$	2.20617e10	−	6.78988e10i	0.251909	−	0.775295i
$545$	1.01145e11	+	3.28641e10i	1.14646	+	0.372508i
$546$		0			0
$547$	−6.31776e10	+	8.69564e10i	−0.705689	+	0.971298i	0.294190	+	0.955747i	$0.404950\pi$
$547$	−6.31776e10	+	8.69564e10i	−0.705689	+	0.971298i	−0.999879	+	0.0155510i	$0.995050\pi$
$548$	−4.92972e9	−	1.51721e10i	−0.0546638	−	0.168238i
$549$		0			0
$550$	9.41742e9	+	5.02431e9i	0.102916	+	0.0549068i
$551$	7.61185e10			0.825817
$552$		0			0
$553$	−4.81601e10	−	3.49903e10i	−0.514976	−	0.374152i
$554$	1.92582e10	−	1.39919e10i	0.204445	−	0.148538i
$555$		0			0
$556$	−5.84066e10	−	1.89774e10i	−0.611171	−	0.198581i
$557$	−7.15576e10	−	9.84906e10i	−0.743422	−	1.02323i	−0.998415	−	0.0562891i	$-0.982073\pi$
$557$	−7.15576e10	−	9.84906e10i	−0.743422	−	1.02323i	0.254993	−	0.966943i	$-0.417927\pi$
$558$		0			0
$559$	4.92723e9	+	1.51645e10i	0.0504610	+	0.155303i
$560$			2.84737e10i			0.289528i
$561$		0			0
$562$	−6.40941e10			−0.642499
$563$	−2.42499e9	+	7.87927e8i	−0.0241366	+	0.00784246i	−0.321060	−	0.947059i	$-0.604039\pi$
$563$	−2.42499e9	+	7.87927e8i	−0.0241366	+	0.00784246i	0.296924	+	0.954901i	$0.404039\pi$
$564$		0			0
$565$	−7.43898e10	+	5.40473e10i	−0.729994	+	0.530372i
$566$	1.40833e10	−	4.33439e10i	0.137227	−	0.422340i
$567$		0			0
$568$	−5.84532e10	−	8.04539e10i	−0.561584	−	0.772955i
$569$	−1.18370e11	+	1.62922e11i	−1.12926	+	1.55429i	−0.339779	+	0.940505i	$0.610352\pi$
$569$	−1.18370e11	+	1.62922e11i	−1.12926	+	1.55429i	−0.789476	+	0.613781i	$0.789648\pi$
$570$		0			0
$571$			1.60852e10i			0.151315i	0.997134	+	0.0756575i	$0.0241056\pi$
$571$			1.60852e10i			0.151315i	−0.997134	+	0.0756575i	$0.975894\pi$
$572$	−4.22084e10	+	4.06457e10i	−0.394289	+	0.379692i
$573$		0			0
$574$	2.86433e10	−	9.30677e9i	0.263861	−	0.0857337i
$575$	−2.94446e10	−	2.13927e10i	−0.269360	−	0.195702i
$576$		0			0
$577$	3.08362e10	−	9.49040e10i	0.278200	−	0.856212i	−0.710155	−	0.704046i	$-0.751375\pi$
$577$	3.08362e10	−	9.49040e10i	0.278200	−	0.856212i	0.988355	−	0.152166i	$-0.0486249\pi$
$578$	1.52968e10	+	4.97022e9i	0.137053	+	0.0445312i
$579$		0			0
$580$	3.26703e10	−	4.49668e10i	0.288696	−	0.397356i
$581$	1.62864e10	+	5.01243e10i	0.142929	+	0.439890i
$582$		0			0
$583$	−1.46226e10	−	1.05116e11i	−0.126576	−	0.909904i
$584$	−1.57191e11			−1.35138
$585$		0			0
$586$	−5.27260e10	−	3.83077e10i	−0.447131	−	0.324859i
$587$	1.26068e10	−	9.15934e9i	0.106182	−	0.0771457i	−0.533427	−	0.845846i	$-0.679096\pi$
$587$	1.26068e10	−	9.15934e9i	0.106182	−	0.0771457i	0.639609	+	0.768700i	$0.279096\pi$
$588$		0			0
$589$	1.91469e11	+	6.22121e10i	1.59088	+	0.516909i
$590$	−5.63022e10	−	7.74933e10i	−0.464640	−	0.639523i
$591$		0			0
$592$	3.57635e9	+	1.10069e10i	0.0291175	+	0.0896143i
$593$		−	5.77849e10i		−	0.467300i	−0.972321	−	0.233650i	$-0.924933\pi$
$593$		−	5.77849e10i		−	0.467300i	0.972321	−	0.233650i	$-0.0750670\pi$
$594$		0			0
$595$	6.47330e10			0.516486
$596$	1.58134e11	−	5.13810e10i	1.25326	−	0.407209i
$597$		0			0
$598$	−3.85493e10	+	2.80077e10i	−0.301448	+	0.219014i
$599$	−4.81704e10	+	1.48253e11i	−0.374173	+	1.15159i	0.569861	+	0.821741i	$0.306997\pi$
$599$	−4.81704e10	+	1.48253e11i	−0.374173	+	1.15159i	−0.944035	+	0.329846i	$0.893003\pi$
$600$		0			0
$601$	−1.24924e10	−	1.71943e10i	−0.0957518	−	0.131791i	0.758453	−	0.651728i	$-0.225956\pi$
$601$	−1.24924e10	−	1.71943e10i	−0.0957518	−	0.131791i	−0.854205	+	0.519937i	$0.825956\pi$
$602$	−4.57083e9	+	6.29120e9i	−0.0348024	+	0.0479014i
$603$		0			0
$604$			5.11596e10i			0.384397i
$605$	9.31336e10	−	1.18518e11i	0.695160	−	0.884631i
$606$		0			0
$607$	2.54030e10	−	8.25395e9i	0.187125	−	0.0608005i	−0.213956	−	0.976843i	$-0.568635\pi$
$607$	2.54030e10	−	8.25395e9i	0.187125	−	0.0608005i	0.401080	+	0.916043i	$0.368635\pi$
$608$	−1.67971e11	−	1.22038e11i	−1.22919	−	0.893059i
$609$		0			0
$610$	3.50196e10	−	1.07779e11i	0.252925	−	0.778424i
$611$	−9.34072e9	−	3.03498e9i	−0.0670217	−	0.0217767i
$612$		0			0
$613$	−8.46051e10	+	1.16449e11i	−0.599176	+	0.824696i	−0.995633	−	0.0933581i	$-0.970240\pi$
$613$	−8.46051e10	+	1.16449e11i	−0.599176	+	0.824696i	0.396456	+	0.918054i	$0.370240\pi$
$614$	6.88562e9	+	2.11918e10i	0.0484473	+	0.149106i
$615$		0			0
$616$	−6.29838e10	−	1.11970e10i	−0.437428	−	0.0777640i
$617$	1.08135e11			0.746152			0.373076	−	0.927801i	$-0.378303\pi$
$617$	1.08135e11			0.746152			0.373076	+	0.927801i	$0.378303\pi$
$618$		0			0
$619$	−1.38033e11	−	1.00287e11i	−0.940197	−	0.683093i	0.00827096	−	0.999966i	$-0.497367\pi$
$619$	−1.38033e11	−	1.00287e11i	−0.940197	−	0.683093i	−0.948468	+	0.316873i	$0.897367\pi$
$620$	1.18931e11	−	8.64083e10i	0.804873	−	0.584775i
$621$		0			0
$622$	−1.24846e10	−	4.05650e9i	−0.0834093	−	0.0271013i
$623$	−1.89915e10	−	2.61395e10i	−0.126068	−	0.173518i
$624$		0			0
$625$	−5.63545e10	−	1.73441e11i	−0.369325	−	1.13666i
$626$			1.22936e10i			0.0800536i
$627$		0			0
$628$	7.25405e10			0.466382
$629$	2.50234e10	−	8.13061e9i	0.159862	−	0.0519422i
$630$		0			0
$631$	1.61104e11	−	1.17049e11i	1.01622	−	0.738328i	0.0507169	−	0.998713i	$-0.483849\pi$
$631$	1.61104e11	−	1.17049e11i	1.01622	−	0.738328i	0.965505	+	0.260385i	$0.0838494\pi$
$632$	4.44336e10	−	1.36752e11i	0.278511	−	0.857170i
$633$		0			0
$634$	6.96443e10	+	9.58572e10i	0.431051	+	0.593291i
$635$	−1.38464e11	+	1.90580e11i	−0.851613	+	1.17214i
$636$		0			0
$637$		−	7.65950e10i		−	0.465203i
$638$	2.72666e10	+	2.83149e10i	0.164569	+	0.170896i
$639$		0			0
$640$	−1.80377e11	+	5.86080e10i	−1.07513	+	0.349331i
$641$	−2.29444e10	−	1.66701e10i	−0.135908	−	0.0987428i	0.517754	−	0.855529i	$-0.326768\pi$
$641$	−2.29444e10	−	1.66701e10i	−0.135908	−	0.0987428i	−0.653662	+	0.756787i	$0.726768\pi$
$642$		0			0
$643$	−6.16155e10	+	1.89633e11i	−0.360451	+	1.10935i	0.592330	+	0.805695i	$0.298208\pi$
$643$	−6.16155e10	+	1.89633e11i	−0.360451	+	1.10935i	−0.952781	+	0.303658i	$0.901792\pi$
$644$	9.26753e10	+	3.01120e10i	0.538791	+	0.175064i
$645$		0			0
$646$	−5.62272e10	+	7.73900e10i	−0.322861	+	0.444381i
$647$	8.63286e9	+	2.65692e10i	0.0492649	+	0.151622i	0.972663	−	0.232223i	$-0.0745998\pi$
$647$	8.63286e9	+	2.65692e10i	0.0492649	+	0.151622i	−0.923398	+	0.383845i	$0.874600\pi$
$648$		0			0
$649$	−2.55485e11	+	1.24164e11i	−1.44008	+	0.699871i
$650$	1.41158e10			0.0790776
$651$		0			0
$652$	−6.82160e10	−	4.95618e10i	−0.377482	−	0.274256i
$653$	−1.56085e11	+	1.13402e11i	−0.858435	+	0.623689i	−0.927459	−	0.373926i	$-0.878011\pi$
$653$	−1.56085e11	+	1.13402e11i	−0.858435	+	0.623689i	0.0690241	+	0.997615i	$0.478011\pi$
$654$		0			0
$655$	2.22427e11	+	7.22709e10i	1.20843	+	0.392643i
$656$	−5.64408e10	−	7.76842e10i	−0.304774	−	0.419486i
$657$		0			0
$658$	−1.48017e9	−	4.55550e9i	−0.00789602	−	0.0243014i
$659$			2.89730e11i			1.53621i	0.640322	+	0.768107i	$0.278801\pi$
$659$			2.89730e11i			1.53621i	−0.640322	+	0.768107i	$0.721199\pi$
$660$		0			0
$661$	−5.56337e10			−0.291428			−0.145714	−	0.989327i	$-0.546548\pi$
$661$	−5.56337e10			−0.291428			−0.145714	+	0.989327i	$0.546548\pi$
$662$	−2.54197e10	+	8.25936e9i	−0.132354	+	0.0430046i
$663$		0			0
$664$	−1.02991e11	+	7.48273e10i	−0.529818	+	0.384935i
$665$	5.81739e10	−	1.79041e11i	0.297469	−	0.915515i
$666$		0			0
$667$	−7.87837e10	−	1.08437e11i	−0.398046	−	0.547863i
$668$	−1.30024e11	+	1.78963e11i	−0.653008	+	0.898789i
$669$		0			0
$670$		−	1.75431e11i		−	0.870577i
$671$	−2.96511e11	−	1.58192e11i	−1.46268	−	0.780360i
$672$		0			0
$673$	1.64290e11	−	5.33811e10i	0.800851	−	0.260212i	0.120133	−	0.992758i	$-0.461668\pi$
$673$	1.64290e11	−	5.33811e10i	0.800851	−	0.260212i	0.680718	+	0.732546i	$0.261668\pi$
$674$	−9.19765e10	−	6.68249e10i	−0.445695	−	0.323816i
$675$		0			0
$676$	2.81584e10	−	8.66626e10i	0.134841	−	0.414997i
$677$	−6.96950e10	−	2.26453e10i	−0.331778	−	0.107801i	0.138391	−	0.990378i	$-0.455807\pi$
$677$	−6.96950e10	−	2.26453e10i	−0.331778	−	0.107801i	−0.470169	+	0.882577i	$0.655807\pi$
$678$		0			0
$679$	9.71450e10	−	1.33709e11i	0.457027	−	0.629043i
$680$	4.83179e10	+	1.48707e11i	0.225981	+	0.695498i
$681$		0			0
$682$	4.54448e10	+	9.35087e10i	0.210061	+	0.432230i
$683$	3.37571e11			1.55125			0.775625	−	0.631194i	$-0.217435\pi$
$683$	3.37571e11			1.55125			0.775625	+	0.631194i	$0.217435\pi$
$684$		0			0
$685$	4.39049e10	+	3.18988e10i	0.199412	+	0.144881i
$686$	7.42619e10	−	5.39545e10i	0.335328	−	0.243630i
$687$		0			0
$688$	2.35798e10	+	7.66155e9i	0.105241	+	0.0341950i
$689$	−8.24964e10	−	1.13547e11i	−0.366065	−	0.503845i
$690$		0			0
$691$	−7.88802e10	−	2.42768e11i	−0.345984	−	1.06483i	−0.961055	−	0.276357i	$-0.910873\pi$
$691$	−7.88802e10	−	2.42768e11i	−0.345984	−	1.06483i	0.615071	−	0.788471i	$-0.289127\pi$
$692$		−	9.49608e9i		−	0.0414114i
$693$		0			0
$694$	3.98484e10			0.171780
$695$	1.98691e11	−	6.45586e10i	0.851606	−	0.276703i
$696$		0			0
$697$	−1.76610e11	+	1.28315e11i	−0.748314	+	0.543682i
$698$	−3.21837e10	+	9.90511e10i	−0.135586	+	0.417290i
$699$		0			0
$700$	−1.69678e10	−	2.33541e10i	−0.0706695	−	0.0972683i
$701$	2.78124e10	−	3.82805e10i	0.115177	−	0.158528i	−0.747536	−	0.664221i	$-0.768763\pi$
$701$	2.78124e10	−	3.82805e10i	0.115177	−	0.158528i	0.862713	+	0.505693i	$0.168763\pi$
$702$		0			0
$703$		−	7.65174e10i		−	0.313285i
$704$	7.74867e8	+	5.57023e9i	0.00315455	+	0.0226768i
$705$		0			0
$706$	−6.60446e10	+	2.14592e10i	−0.265839	+	0.0863763i
$707$	1.97429e9	+	1.43440e9i	0.00790192	+	0.00574108i
$708$		0			0
$709$	−1.02491e11	+	3.15434e11i	−0.405601	+	1.24831i	0.514791	+	0.857315i	$0.327869\pi$
$709$	−1.02491e11	+	3.15434e11i	−0.405601	+	1.24831i	−0.920392	+	0.390996i	$0.872131\pi$
$710$	1.43734e11	+	4.67019e10i	0.565620	+	0.183781i
$711$		0			0
$712$	4.58731e10	−	6.31389e10i	0.178500	−	0.245684i
$713$	−1.09548e11	−	3.37153e11i	−0.423882	−	1.30457i
$714$		0			0
$715$	3.48906e10	−	1.96262e11i	0.133501	−	0.750951i
$716$	2.12771e11			0.809582
$717$		0			0
$718$	7.37699e10	+	5.35970e10i	0.277576	+	0.201671i
$719$	3.14538e11	−	2.28525e11i	1.17695	−	0.855103i	0.185124	−	0.982715i	$-0.440731\pi$
$719$	3.14538e11	−	2.28525e11i	1.17695	−	0.855103i	0.991824	+	0.127612i	$0.0407312\pi$
$720$		0			0
$721$	8.14334e10	+	2.64593e10i	0.301343	+	0.0979124i
$722$	9.34289e10	+	1.28594e11i	0.343821	+	0.473229i
$723$		0			0
$724$	5.22975e10	+	1.60955e11i	0.190339	+	0.585802i
$725$			3.97069e10i			0.143719i
$726$		0			0
$727$	3.54660e11			1.26962			0.634812	−	0.772667i	$-0.281078\pi$
$727$	3.54660e11			1.26962			0.634812	+	0.772667i	$0.281078\pi$
$728$	−8.04594e10	+	2.61429e10i	−0.286452	+	0.0930738i
$729$		0			0
$730$	1.93262e11	−	1.40413e11i	0.680544	−	0.494444i
$731$	1.74180e10	−	5.36072e10i	0.0610000	−	0.187739i
$732$		0			0
$733$	−3.31226e11	−	4.55894e11i	−1.14738	−	1.57924i	−0.749786	−	0.661680i	$-0.769844\pi$
$733$	−3.31226e11	−	4.55894e11i	−1.14738	−	1.57924i	−0.397599	−	0.917559i	$-0.630156\pi$
$734$	−7.38433e10	+	1.01637e11i	−0.254406	+	0.350159i
$735$		0			0
$736$			3.65598e11i			1.24593i
$737$	−5.12213e11	−	9.10591e10i	−1.73613	−	0.308641i
$738$		0			0
$739$	−1.78819e11	+	5.81018e10i	−0.599565	+	0.194810i	−0.593046	−	0.805168i	$-0.702075\pi$
$739$	−1.78819e11	+	5.81018e10i	−0.599565	+	0.194810i	−0.00651835	+	0.999979i	$0.502075\pi$
$740$	−4.52025e10	−	3.28415e10i	−0.150742	−	0.109521i
$741$		0			0
$742$	2.11521e10	−	6.50996e10i	0.0697813	−	0.214765i
$743$	3.87281e11	+	1.25835e11i	1.27078	+	0.412902i	0.865325	−	0.501211i	$-0.167112\pi$
$743$	3.87281e11	+	1.25835e11i	1.27078	+	0.412902i	0.405458	+	0.914114i	$0.367112\pi$
$744$		0			0
$745$	−3.32472e11	+	4.57608e11i	−1.07927	+	1.48549i
$746$	−4.15264e10	−	1.27805e11i	−0.134082	−	0.412661i
$747$		0			0
$748$	2.05169e11	−	2.85408e10i	0.655397	−	0.0911715i
$749$	3.14410e10			0.0999008
$750$		0			0
$751$	3.03886e11	+	2.20786e11i	0.955325	+	0.694085i	0.952060	−	0.305910i	$-0.0989607\pi$
$751$	3.03886e11	+	2.20786e11i	0.955325	+	0.694085i	0.00326502	+	0.999995i	$0.498961\pi$
$752$	−1.23551e10	+	8.97648e9i	−0.0386344	+	0.0280695i
$753$		0			0
$754$	4.94406e10	+	1.60642e10i	0.152967	+	0.0497020i
$755$	−1.02297e11	−	1.40800e11i	−0.314829	−	0.433325i
$756$		0			0
$757$	1.23949e11	+	3.81476e11i	0.377450	+	1.16167i	0.941811	+	0.336144i	$0.109123\pi$
$757$	1.23949e11	+	3.81476e11i	0.377450	+	1.16167i	−0.564360	+	0.825529i	$0.690877\pi$
$758$			1.64273e11i			0.497611i
$759$		0			0
$760$	4.54721e11			1.36298
$761$	−5.36336e11	+	1.74266e11i	−1.59918	+	0.519607i	−0.966906	−	0.255134i	$-0.917880\pi$
$761$	−5.36336e11	+	1.74266e11i	−1.59918	+	0.519607i	−0.632279	+	0.774741i	$0.717880\pi$
$762$		0			0
$763$	1.64565e11	−	1.19564e11i	0.485557	−	0.352778i
$764$	−4.26390e10	+	1.31229e11i	−0.125151	+	0.385174i
$765$		0			0
$766$	−1.76799e10	−	2.43342e10i	−0.0513527	−	0.0706810i
$767$	−2.20806e11	+	3.03914e11i	−0.638013	+	0.878150i
$768$		0			0
$769$			3.98817e11i			1.14043i	0.821495	+	0.570215i	$0.193140\pi$
$769$			3.98817e11i			1.14043i	−0.821495	+	0.570215i	$0.806860\pi$
$770$	8.74390e10	−	4.24949e10i	0.248738	−	0.120885i
$771$		0			0
$772$	4.33514e11	−	1.40857e11i	1.22049	−	0.396561i
$773$	1.15593e11	+	8.39832e10i	0.323753	+	0.235220i	0.737775	−	0.675047i	$-0.235877\pi$
$773$	1.15593e11	+	8.39832e10i	0.323753	+	0.235220i	−0.414022	+	0.910267i	$0.635877\pi$
$774$		0			0
$775$	−3.24527e10	+	9.98792e10i	−0.0899589	+	0.276865i
$776$	3.79671e11	+	1.23363e11i	1.04703	+	0.340202i
$777$		0			0
$778$	−1.00324e11	+	1.38085e11i	−0.273835	+	0.376901i
$779$	1.96182e11	+	6.03787e11i	0.532733	+	1.63958i
$780$		0			0
$781$	2.10964e11	−	3.95424e11i	0.567027	−	1.06282i
$782$	1.68444e11			0.450431
$783$		0			0
$784$	−9.63545e10	−	7.00056e10i	−0.255040	−	0.185297i
$785$	−1.99643e11	+	1.45049e11i	−0.525745	+	0.381976i
$786$		0			0
$787$	2.52231e11	+	8.19548e10i	0.657505	+	0.213636i	0.618721	−	0.785611i	$-0.287651\pi$
$787$	2.52231e11	+	8.19548e10i	0.657505	+	0.213636i	0.0387847	+	0.999248i	$0.487651\pi$
$788$	2.71890e10	+	3.74225e10i	0.0705161	+	0.0970571i
$789$		0			0
$790$	6.75264e10	+	2.07825e11i	0.173366	+	0.533567i
$791$			1.75872e11i			0.449253i
$792$		0			0
$793$	−4.44442e11			−1.12389
$794$	−6.08647e10	+	1.97761e10i	−0.153138	+	0.0497576i
$795$		0			0
$796$	−2.50157e11	+	1.81750e11i	−0.623105	+	0.452712i
$797$	1.33254e11	−	4.10115e11i	0.330254	−	1.01642i	−0.638759	−	0.769407i	$-0.720552\pi$
$797$	1.33254e11	−	4.10115e11i	0.330254	−	1.01642i	0.969013	−	0.247010i	$-0.0794482\pi$
$798$		0			0
$799$	2.04075e10	+	2.80885e10i	0.0500728	+	0.0689193i
$800$	6.36606e10	−	8.76212e10i	0.155421	−	0.213919i
$801$		0			0
$802$			5.45078e10i			0.131753i
$803$	−3.09656e11	−	6.37160e11i	−0.744763	−	1.53245i
$804$		0			0
$805$	−3.15268e11	+	1.02437e11i	−0.750752	+	0.243934i
$806$	1.11234e11	+	8.08162e10i	0.263571	+	0.191495i
$807$		0			0
$808$	−1.82152e9	+	5.60607e9i	−0.00427355	+	0.0131526i
$809$	6.52104e10	+	2.11881e10i	0.152238	+	0.0494651i	0.384145	−	0.923273i	$-0.374496\pi$
$809$	6.52104e10	+	2.11881e10i	0.152238	+	0.0494651i	−0.231907	+	0.972738i	$0.574496\pi$
$810$		0			0
$811$	−1.07499e11	+	1.47960e11i	−0.248498	+	0.342028i	−0.914984	−	0.403489i	$-0.867797\pi$
$811$	−1.07499e11	+	1.47960e11i	−0.248498	+	0.342028i	0.666487	+	0.745517i	$0.267797\pi$
$812$	−3.28517e10	−	1.01107e11i	−0.0755674	−	0.232572i
$813$		0			0
$814$	2.84633e10	−	2.74095e10i	0.0648317	−	0.0624315i
$815$	2.86843e11			0.650151
$816$		0			0
$817$	−1.32616e11	−	9.63508e10i	−0.297650	−	0.216256i
$818$	2.20538e11	−	1.60231e11i	0.492573	−	0.357876i
$819$		0			0
$820$	4.40887e11	+	1.43253e11i	0.975152	+	0.316846i
$821$	5.13013e11	+	7.06101e11i	1.12916	+	1.55416i	0.789655	+	0.613551i	$0.210260\pi$
$821$	5.13013e11	+	7.06101e11i	1.12916	+	1.55416i	0.339505	+	0.940604i	$0.389740\pi$
$822$		0			0
$823$	2.38003e10	+	7.32498e10i	0.0518780	+	0.159664i	0.973639	−	0.228094i	$-0.0732495\pi$
$823$	2.38003e10	+	7.32498e10i	0.0518780	+	0.159664i	−0.921761	+	0.387758i	$0.873249\pi$
$824$			2.06822e11i			0.448629i
$825$		0			0
$826$	−1.83210e11			−0.393575
$827$	2.40691e10	−	7.82051e9i	0.0514561	−	0.0167191i	−0.283176	−	0.959068i	$-0.591388\pi$
$827$	2.40691e10	−	7.82051e9i	0.0514561	−	0.0167191i	0.334632	+	0.942349i	$0.391388\pi$
$828$		0			0
$829$	−4.42821e10	+	3.21728e10i	−0.0937584	+	0.0681195i	−0.633677	−	0.773598i	$-0.718455\pi$
$829$	−4.42821e10	+	3.21728e10i	−0.0937584	+	0.0681195i	0.539918	+	0.841717i	$0.318455\pi$
$830$	5.97841e10	−	1.83997e11i	0.125972	−	0.387702i
$831$		0			0
$832$	4.37158e9	+	6.01696e9i	0.00912316	+	0.0125570i
$833$	−1.59153e11	+	2.19056e11i	−0.330549	+	0.454962i
$834$		0			0
$835$		−	7.52526e11i		−	1.54802i
$836$	1.05441e11	−	5.93111e11i	0.215865	−	1.21426i
$837$		0			0
$838$	−1.60944e10	+	5.22940e9i	−0.0326362	+	0.0106041i
$839$	−4.12964e11	−	3.00036e11i	−0.833421	−	0.605516i	0.0871039	−	0.996199i	$-0.472239\pi$
$839$	−4.12964e11	−	3.00036e11i	−0.833421	−	0.605516i	−0.920525	+	0.390683i	$0.872239\pi$
$840$		0			0
$841$	1.09397e11	−	3.36690e11i	0.218686	−	0.673048i
$842$	−3.25581e11	−	1.05788e11i	−0.647754	−	0.210468i
$843$		0			0
$844$	1.87826e11	−	2.58520e11i	0.370157	−	0.509477i
$845$	9.57908e10	+	2.94814e11i	0.187887	+	0.578257i
$846$		0			0
$847$	−7.86882e10	−	2.77357e11i	−0.152889	−	0.538896i
$848$	−2.18238e11			−0.422033
$849$		0			0
$850$	−4.03702e10	−	2.93307e10i	−0.0773367	−	0.0561884i
$851$	−1.09005e11	+	7.91967e10i	−0.207839	+	0.151004i
$852$		0			0
$853$	−7.49438e11	−	2.43507e11i	−1.41560	−	0.459955i	−0.501397	−	0.865217i	$-0.667180\pi$
$853$	−7.49438e11	−	2.43507e11i	−1.41560	−	0.459955i	−0.914201	+	0.405262i	$0.867180\pi$
$854$	−1.27406e11	−	1.75359e11i	−0.239529	−	0.329683i
$855$		0			0
$856$	2.34681e10	+	7.22274e10i	0.0437102	+	0.134526i
$857$			1.32237e11i			0.245150i	0.992459	+	0.122575i	$0.0391151\pi$
$857$			1.32237e11i			0.245150i	−0.992459	+	0.122575i	$0.960885\pi$
$858$		0			0
$859$	3.70268e11			0.680055			0.340027	−	0.940416i	$-0.389564\pi$
$859$	3.70268e11			0.680055			0.340027	+	0.940416i	$0.389564\pi$
$860$	−1.13838e11	+	3.69882e10i	−0.208110	+	0.0676191i
$861$		0			0
$862$	−3.87621e10	+	2.81623e10i	−0.0702066	+	0.0510081i
$863$	1.58241e11	−	4.87017e11i	0.285284	−	0.878013i	−0.701030	−	0.713132i	$-0.747276\pi$
$863$	1.58241e11	−	4.87017e11i	0.285284	−	0.878013i	0.986313	−	0.164881i	$-0.0527240\pi$
$864$		0			0
$865$	1.89880e10	+	2.61347e10i	0.0339168	+	0.0466824i
$866$	−1.29138e11	+	1.77744e11i	−0.229606	+	0.316026i
$867$		0			0
$868$		−	2.81176e11i		−	0.495336i
$869$	6.41846e11	−	8.92863e10i	1.12552	−	0.156569i
$870$		0			0
$871$	−6.54333e11	+	2.12606e11i	−1.13691	+	0.369404i
$872$	3.97501e11	+	2.88801e11i	0.687499	+	0.499497i
$873$		0			0
$874$	1.51376e11	−	4.65888e11i	0.259425	−	0.798428i
$875$	−2.57954e11	−	8.38144e10i	−0.440059	−	0.142984i
$876$		0			0
$877$	−7.70663e10	+	1.06073e11i	−0.130277	+	0.179310i	−0.869172	−	0.494510i	$-0.835348\pi$
$877$	−7.70663e10	+	1.06073e11i	−0.130277	+	0.179310i	0.738896	+	0.673820i	$0.235348\pi$
$878$	−6.97599e9	−	2.14699e10i	−0.0117389	−	0.0361287i
$879$		0			0
$880$	−2.15003e11	−	2.23269e11i	−0.358521	−	0.372304i
$881$	−1.82199e11			−0.302443			−0.151221	−	0.988500i	$-0.548321\pi$
$881$	−1.82199e11			−0.302443			−0.151221	+	0.988500i	$0.548321\pi$
$882$		0			0
$883$	−1.07332e11	−	7.79809e10i	−0.176557	−	0.128276i	0.495997	−	0.868324i	$-0.334803\pi$
$883$	−1.07332e11	−	7.79809e10i	−0.176557	−	0.128276i	−0.672554	+	0.740048i	$0.734803\pi$
$884$	2.21623e11	−	1.61019e11i	0.362916	−	0.263674i
$885$		0			0
$886$	3.22148e11	+	1.04672e11i	0.522781	+	0.169862i
$887$	−5.41297e11	−	7.45031e11i	−0.874462	−	1.20359i	−0.977924	−	0.208960i	$-0.932992\pi$
$887$	−5.41297e11	−	7.45031e11i	−0.874462	−	1.20359i	0.103462	−	0.994633i	$-0.467008\pi$
$888$		0			0
$889$	1.39233e11	+	4.28516e11i	0.222913	+	0.686056i
$890$			1.18605e11i			0.189035i
$891$		0			0
$892$	4.06098e11			0.641463
$893$	9.60277e10	−	3.12013e10i	0.151005	−	0.0490644i
$894$		0			0
$895$	−5.85580e11	+	4.25449e11i	−0.912629	+	0.663064i
$896$	−1.12098e11	+	3.45003e11i	−0.173927	+	0.535291i
$897$		0			0
$898$	−1.30167e11	−	1.79159e11i	−0.200168	−	0.275508i
$899$	−2.27330e11	+	3.12893e11i	−0.348032	+	0.479025i
$900$		0			0
$901$			4.96150e11i			0.752860i
$902$	−1.54324e11	+	2.89261e11i	−0.233135	+	0.436982i
$903$		0			0
$904$	−4.04020e11	+	1.31274e11i	−0.604964	+	0.196565i
$905$	−4.65771e11	−	3.38402e11i	−0.694349	−	0.504474i
$906$		0			0
$907$	1.00690e11	−	3.09892e11i	0.148784	−	0.457911i	−0.848694	−	0.528885i	$-0.822610\pi$
$907$	1.00690e11	−	3.09892e11i	0.148784	−	0.457911i	0.997478	+	0.0709731i	$0.0226105\pi$
$908$	−1.29375e11	−	4.20363e10i	−0.190329	−	0.0618417i
$909$		0			0
$910$	7.55704e10	−	1.04014e11i	0.110201	−	0.151679i
$911$	−1.01820e11	−	3.13368e11i	−0.147828	−	0.454969i	0.849536	−	0.527531i	$-0.176882\pi$
$911$	−1.01820e11	−	3.13368e11i	−0.147828	−	0.454969i	−0.997364	+	0.0725627i	$0.976882\pi$
$912$		0			0
$913$	−5.06191e11	−	2.70060e11i	−0.728504	−	0.388666i
$914$	3.53719e11			0.506843
$915$		0			0
$916$	−1.98352e10	−	1.44111e10i	−0.0281743	−	0.0204699i
$917$	3.61893e11	−	2.62931e11i	0.511803	−	0.371847i
$918$		0			0
$919$	−1.21241e12	−	3.93934e11i	−1.69975	−	0.552283i	−0.711177	−	0.703013i	$-0.751838\pi$
$919$	−1.21241e12	−	3.93934e11i	−1.69975	−	0.552283i	−0.988575	+	0.150730i	$0.951838\pi$
$920$	−4.70643e11	−	6.47785e11i	−0.656962	−	0.904231i
$921$		0			0
$922$	−1.08771e11	−	3.34764e11i	−0.150519	−	0.463249i
$923$		−	5.92704e11i		−	0.816641i
$924$		0			0
$925$	3.99150e10			0.0545217
$926$	−1.57808e11	+	5.12750e10i	−0.214628	+	0.0697368i
$927$		0			0
$928$	3.22686e11	−	2.34445e11i	0.435099	−	0.316118i
$929$	−1.67960e11	+	5.16929e11i	−0.225499	+	0.694014i	0.772742	+	0.634720i	$0.218885\pi$
$929$	−1.67960e11	+	5.16929e11i	−0.225499	+	0.694014i	−0.998241	+	0.0592934i	$0.981115\pi$
$930$		0			0
$931$	4.62845e11	+	6.37051e11i	0.616079	+	0.847961i
$932$	−2.29608e9	+	3.16029e9i	−0.00304316	+	0.00418855i
$933$		0			0
$934$			5.77560e11i			0.758943i
$935$	−5.07588e11	+	4.88796e11i	−0.664148	+	0.639560i
$936$		0			0
$937$	7.04197e11	−	2.28807e11i	0.913557	−	0.296833i	0.185736	−	0.982600i	$-0.440533\pi$
$937$	7.04197e11	−	2.28807e11i	0.913557	−	0.296833i	0.727821	+	0.685767i	$0.240533\pi$
$938$	−2.71460e11	−	1.97227e11i	−0.350667	−	0.254774i
$939$		0			0
$940$	2.27833e10	−	7.01198e10i	0.0291813	−	0.0898109i
$941$	1.85400e11	+	6.02401e10i	0.236456	+	0.0768293i	0.424848	−	0.905265i	$-0.360327\pi$
$941$	1.85400e11	+	6.02401e10i	0.236456	+	0.0768293i	−0.188392	+	0.982094i	$0.560327\pi$
$942$		0			0
$943$	6.57088e11	−	9.04405e11i	0.830954	−	1.14371i
$944$	1.80505e11	+	5.55537e11i	0.227301	+	0.699560i
$945$		0			0
$946$	−1.16636e10	−	8.38450e10i	−0.0145635	−	0.104692i
$947$	3.03034e11			0.376783			0.188392	−	0.982094i	$-0.439673\pi$
$947$	3.03034e11			0.376783			0.188392	+	0.982094i	$0.439673\pi$
$948$		0			0
$949$	−7.57938e11	−	5.50674e11i	−0.934477	−	0.678938i
$950$	−1.17403e11	+	8.52986e10i	−0.144141	+	0.104724i
$951$		0			0
$952$	2.84429e11	+	9.24165e10i	0.346279	+	0.112513i
$953$	−2.21859e11	−	3.05362e11i	−0.268970	−	0.370206i	0.653071	−	0.757296i	$-0.273480\pi$
$953$	−2.21859e11	−	3.05362e11i	−0.268970	−	0.370206i	−0.922042	+	0.387090i	$0.873480\pi$
$954$		0			0
$955$	−1.45052e11	−	4.46423e11i	−0.174385	−	0.536702i
$956$			2.78471e11i			0.333387i
$957$		0			0
$958$	−4.47032e10			−0.0530734
$959$	9.87197e10	−	3.20760e10i	0.116716	−	0.0379232i
$960$		0			0
$961$	−1.37556e11	+	9.99401e10i	−0.161282	+	0.117178i
$962$	1.61484e10	−	4.96997e10i	0.0188551	−	0.0580302i
$963$		0			0
$964$	6.39000e11	+	8.79507e11i	0.739933	+	1.01843i
$965$	−9.11447e11	+	1.25450e12i	−1.05105	+	1.44664i
$966$		0			0
$967$			9.05058e10i			0.103507i	0.998660	+	0.0517536i	$0.0164810\pi$
$967$			9.05058e10i			0.103507i	−0.998660	+	0.0517536i	$0.983519\pi$
$968$	5.78420e11	−	3.87789e11i	0.658782	−	0.441667i
$969$		0			0
$970$	−5.76992e11	+	1.87476e11i	−0.651753	+	0.211767i
$971$	−6.31302e11	−	4.58668e11i	−0.710167	−	0.515966i	0.173061	−	0.984911i	$-0.444634\pi$
$971$	−6.31302e11	−	4.58668e11i	−0.710167	−	0.515966i	−0.883228	+	0.468945i	$0.844634\pi$
$972$		0			0
$973$	1.23480e11	−	3.80031e11i	0.137767	−	0.424002i
$974$	−3.12854e11	−	1.01652e11i	−0.347621	−	0.112949i
$975$		0			0
$976$	−4.06207e11	+	5.59097e11i	−0.447660	+	0.616152i
$977$	−1.03690e11	−	3.19126e11i	−0.113805	−	0.350255i	0.877891	−	0.478860i	$-0.158950\pi$
$977$	−1.03690e11	−	3.19126e11i	−0.113805	−	0.350255i	−0.991696	+	0.128605i	$0.958950\pi$
$978$		0			0
$979$	3.46295e11	+	6.15629e10i	0.376978	+	0.0670175i
$980$	5.74991e11			0.623385
$981$		0			0
$982$	−2.79957e11	−	2.03400e11i	−0.301054	−	0.218729i
$983$	8.23027e11	−	5.97964e11i	0.881455	−	0.640415i	−0.0521809	−	0.998638i	$-0.516617\pi$
$983$	8.23027e11	−	5.97964e11i	0.881455	−	0.640415i	0.933636	+	0.358223i	$0.116617\pi$
$984$		0			0
$985$	−1.49657e11	−	4.86265e10i	−0.158983	−	0.0516569i
$986$	−1.08017e11	−	1.48673e11i	−0.114284	−	0.157298i
$987$		0			0
$988$	−2.46184e11	−	7.57676e11i	−0.258364	−	0.795163i
$989$			2.88645e11i			0.301703i
$990$		0			0
$991$	9.14619e11			0.948299			0.474150	−	0.880444i	$-0.342756\pi$
$991$	9.14619e11			0.948299			0.474150	+	0.880444i	$0.342756\pi$
$992$	1.00330e12	−	3.25992e11i	1.03606	−	0.336636i
$993$		0			0
$994$	2.33858e11	−	1.69907e11i	0.239555	−	0.174047i
$995$	3.25053e11	−	1.00041e12i	0.331636	−	1.02067i
$996$		0			0
$997$	−7.76915e11	−	1.06933e12i	−0.786308	−	1.08226i	−0.994558	−	0.104185i	$-0.966777\pi$
$997$	−7.76915e11	−	1.06933e12i	−0.786308	−	1.08226i	0.208250	−	0.978076i	$-0.433223\pi$
$998$	−3.86518e11	+	5.31996e11i	−0.389626	+	0.536274i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.9.k.a.28.3		28
3.2	odd	2		11.9.d.a.6.5	yes	28
11.2	odd	10	inner	99.9.k.a.46.3		28
33.2	even	10		11.9.d.a.2.5	✓	28
33.8	even	10		121.9.b.b.120.17		28
33.14	odd	10		121.9.b.b.120.12		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.9.d.a.2.5	✓	28	33.2	even	10
11.9.d.a.6.5	yes	28	3.2	odd	2
99.9.k.a.28.3		28	1.1	even	1	trivial
99.9.k.a.46.3		28	11.2	odd	10	inner
121.9.b.b.120.12		28	33.14	odd	10
121.9.b.b.120.17		28	33.8	even	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	99.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.67744 + 2.16963i) q^{2} +(-167.227 + 121.498i) q^{4} +(217.294 - 668.763i) q^{5} +(-790.545 - 1088.09i) q^{7} +(1909.53 - 2628.24i) q^{8} +O(q^{10})\)	\(q+(-6.67744 + 2.16963i) q^{2} +(-167.227 + 121.498i) q^{4} +(217.294 - 668.763i) q^{5} +(-790.545 - 1088.09i) q^{7} +(1909.53 - 2628.24i) q^{8} +4937.07i q^{10} +(14415.0 + 2562.63i) q^{11} +(18414.6 - 5983.26i) q^{13} +(7639.57 + 5550.47i) q^{14} +(9303.62 - 28633.6i) q^{16} +(-65096.6 - 21151.2i) q^{17} +(-117001. + 161038. i) q^{19} +(44915.7 + 138236. i) q^{20} +(-101815. + 14163.4i) q^{22} +350509. q^{23} +(-84005.1 - 61033.3i) q^{25} +(-109981. + 79905.7i) q^{26} +(264402. + 85909.3i) q^{28} +(-224769. - 309368. i) q^{29} +(-312538. - 961894. i) q^{31} +1.04305e6i q^{32} +480569. q^{34} +(-899456. + 292251. i) q^{35} +(-310990. + 225947. i) q^{37} +(431875. - 1.32917e6i) q^{38} +(-1.34274e6 - 1.84812e6i) q^{40} +(1.87467e6 - 2.58026e6i) q^{41} +823502. i q^{43} +(-2.72194e6 + 1.32285e6i) q^{44} +(-2.34050e6 + 760476. i) q^{46} +(-410370. - 298151. i) q^{47} +(1.22244e6 - 3.76228e6i) q^{49} +(693358. + 225286. i) q^{50} +(-2.35247e6 + 3.23790e6i) q^{52} +(-2.23998e6 - 6.89394e6i) q^{53} +(4.84609e6 - 9.08337e6i) q^{55} -4.36933e6 q^{56} +(2.17210e6 + 1.57812e6i) q^{58} +(-1.56962e7 + 1.14040e7i) q^{59} +(-2.18306e7 - 7.09320e6i) q^{61} +(4.17391e6 + 5.74489e6i) q^{62} +(118699. + 365318. i) q^{64} -1.36151e7i q^{65} -3.55334e7 q^{67} +(1.34558e7 - 4.37204e6i) q^{68} +(5.37199e6 - 3.90298e6i) q^{70} +(9.45943e6 - 2.91131e7i) q^{71} +(-2.84406e7 - 3.91452e7i) q^{73} +(1.58639e6 - 2.18348e6i) q^{74} -4.11455e7i q^{76} +(-8.60731e6 - 1.77107e7i) q^{77} +(4.20948e7 - 1.36774e7i) q^{79} +(-1.71275e7 - 1.24438e7i) q^{80} +(-6.91976e6 + 2.12968e7i) q^{82} +(-3.72684e7 - 1.21092e7i) q^{83} +(-2.82903e7 + 3.89382e7i) q^{85} +(-1.78670e6 - 5.49889e6i) q^{86} +(3.42610e7 - 3.29926e7i) q^{88} +2.40233e7 q^{89} +(-2.10679e7 - 1.53067e7i) q^{91} +(-5.86148e7 + 4.25862e7i) q^{92} +(3.38710e6 + 1.10054e6i) q^{94} +(8.22728e7 + 1.13239e8i) q^{95} +(3.79731e7 + 1.16869e8i) q^{97} +2.77746e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 5 q^{2} + 951 q^{4} + 708 q^{5} + 5470 q^{7} + 3845 q^{8}+O(q^{10}) \) 28 * q + 5 * q^2 + 951 * q^4 + 708 * q^5 + 5470 * q^7 + 3845 * q^8	\( 28 q + 5 q^{2} + 951 q^{4} + 708 q^{5} + 5470 q^{7} + 3845 q^{8} - 38567 q^{11} - 12500 q^{13} + 49262 q^{14} + 65335 q^{16} - 368200 q^{17} - 442685 q^{19} + 101488 q^{20} + 1686925 q^{22} - 704764 q^{23} - 960933 q^{25} - 659122 q^{26} - 2014380 q^{28} + 795320 q^{29} + 1317554 q^{31} + 897538 q^{34} - 8132260 q^{35} + 8163354 q^{37} - 1456780 q^{38} - 24701940 q^{40} + 13192700 q^{41} + 8229340 q^{44} + 38601510 q^{46} - 11954754 q^{47} - 11198359 q^{49} + 41838705 q^{50} - 81977530 q^{52} + 2537916 q^{53} + 40359452 q^{55} - 96646244 q^{56} - 13252700 q^{58} - 49581537 q^{59} - 29302910 q^{61} + 207755000 q^{62} + 22221799 q^{64} + 105502894 q^{67} - 335519000 q^{68} + 228302300 q^{70} - 30044916 q^{71} - 272936400 q^{73} + 400896650 q^{74} - 23326180 q^{77} + 319699810 q^{79} - 208513052 q^{80} - 197581295 q^{82} + 558510965 q^{83} - 360970180 q^{85} - 119645907 q^{86} + 85623835 q^{88} - 317966134 q^{89} + 285678712 q^{91} - 599604784 q^{92} - 650361480 q^{94} + 641153840 q^{95} + 85897149 q^{97}+O(q^{100}) \) 28 * q + 5 * q^2 + 951 * q^4 + 708 * q^5 + 5470 * q^7 + 3845 * q^8 - 38567 * q^11 - 12500 * q^13 + 49262 * q^14 + 65335 * q^16 - 368200 * q^17 - 442685 * q^19 + 101488 * q^20 + 1686925 * q^22 - 704764 * q^23 - 960933 * q^25 - 659122 * q^26 - 2014380 * q^28 + 795320 * q^29 + 1317554 * q^31 + 897538 * q^34 - 8132260 * q^35 + 8163354 * q^37 - 1456780 * q^38 - 24701940 * q^40 + 13192700 * q^41 + 8229340 * q^44 + 38601510 * q^46 - 11954754 * q^47 - 11198359 * q^49 + 41838705 * q^50 - 81977530 * q^52 + 2537916 * q^53 + 40359452 * q^55 - 96646244 * q^56 - 13252700 * q^58 - 49581537 * q^59 - 29302910 * q^61 + 207755000 * q^62 + 22221799 * q^64 + 105502894 * q^67 - 335519000 * q^68 + 228302300 * q^70 - 30044916 * q^71 - 272936400 * q^73 + 400896650 * q^74 - 23326180 * q^77 + 319699810 * q^79 - 208513052 * q^80 - 197581295 * q^82 + 558510965 * q^83 - 360970180 * q^85 - 119645907 * q^86 + 85623835 * q^88 - 317966134 * q^89 + 285678712 * q^91 - 599604784 * q^92 - 650361480 * q^94 + 641153840 * q^95 + 85897149 * q^97

Introduction

L-functions

Modular forms

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Database

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