LMFDB - Embedded newform 29.9.c.a.12.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,9,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, 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:	$11.8139796918$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.19
Character	$\chi$	$=$	29.12
Dual form			29.9.c.a.17.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(20.0740 + 20.0740i) q^{2} +(6.21683 + 6.21683i) q^{3} +549.928i q^{4} +611.920i q^{5} +249.593i q^{6} +794.354 q^{7} +(-5900.31 + 5900.31i) q^{8} -6483.70i q^{9} +O(q^{10})$	\(q+(20.0740 + 20.0740i) q^{2} +(6.21683 + 6.21683i) q^{3} +549.928i q^{4} +611.920i q^{5} +249.593i q^{6} +794.354 q^{7} +(-5900.31 + 5900.31i) q^{8} -6483.70i q^{9} +(-12283.7 + 12283.7i) q^{10} +(-5323.72 - 5323.72i) q^{11} +(-3418.81 + 3418.81i) q^{12} +44113.4i q^{13} +(15945.8 + 15945.8i) q^{14} +(-3804.20 + 3804.20i) q^{15} -96103.5 q^{16} +(15707.7 + 15707.7i) q^{17} +(130154. - 130154. i) q^{18} +(-100655. - 100655. i) q^{19} -336512. q^{20} +(4938.37 + 4938.37i) q^{21} -213736. i q^{22} +394140. q^{23} -73362.5 q^{24} +16179.4 q^{25} +(-885531. + 885531. i) q^{26} +(81096.8 - 81096.8i) q^{27} +436838. i q^{28} +(583961. + 399044. i) q^{29} -152731. q^{30} +(205131. + 205131. i) q^{31} +(-418699. - 418699. i) q^{32} -66193.4i q^{33} +630631. i q^{34} +486081. i q^{35} +3.56557e6 q^{36} +(80200.3 - 80200.3i) q^{37} -4.04110e6i q^{38} +(-274246. + 274246. i) q^{39} +(-3.61051e6 - 3.61051e6i) q^{40} +(1.98805e6 - 1.98805e6i) q^{41} +198265. i q^{42} +(846266. + 846266. i) q^{43} +(2.92766e6 - 2.92766e6i) q^{44} +3.96750e6 q^{45} +(7.91196e6 + 7.91196e6i) q^{46} +(1.49739e6 - 1.49739e6i) q^{47} +(-597459. - 597459. i) q^{48} -5.13380e6 q^{49} +(324785. + 324785. i) q^{50} +195304. i q^{51} -2.42592e7 q^{52} -1.06350e6 q^{53} +3.25587e6 q^{54} +(3.25769e6 - 3.25769e6i) q^{55} +(-4.68693e6 + 4.68693e6i) q^{56} -1.25151e6i q^{57} +(3.71203e6 + 1.97328e7i) q^{58} -1.90074e7 q^{59} +(-2.09204e6 - 2.09204e6i) q^{60} +(1.26730e7 + 1.26730e7i) q^{61} +8.23560e6i q^{62} -5.15035e6i q^{63} +7.79257e6i q^{64} -2.69939e7 q^{65} +(1.32876e6 - 1.32876e6i) q^{66} -2.92925e7i q^{67} +(-8.63810e6 + 8.63810e6i) q^{68} +(2.45031e6 + 2.45031e6i) q^{69} +(-9.75757e6 + 9.75757e6i) q^{70} -2.31349e7i q^{71} +(3.82558e7 + 3.82558e7i) q^{72} +(2.90091e7 - 2.90091e7i) q^{73} +3.21988e6 q^{74} +(100585. + 100585. i) q^{75} +(5.53531e7 - 5.53531e7i) q^{76} +(-4.22892e6 - 4.22892e6i) q^{77} -1.10104e7 q^{78} +(-3.05657e7 - 3.05657e7i) q^{79} -5.88076e7i q^{80} -4.15312e7 q^{81} +7.98161e7 q^{82} -6.94005e7 q^{83} +(-2.71575e6 + 2.71575e6i) q^{84} +(-9.61184e6 + 9.61184e6i) q^{85} +3.39758e7i q^{86} +(1.14960e6 + 6.11118e6i) q^{87} +6.28231e7 q^{88} +(7.31571e6 + 7.31571e6i) q^{89} +(7.96435e7 + 7.96435e7i) q^{90} +3.50417e7i q^{91} +2.16749e8i q^{92} +2.55054e6i q^{93} +6.01170e7 q^{94} +(6.15929e7 - 6.15929e7i) q^{95} -5.20597e6i q^{96} +(-5.69662e7 + 5.69662e7i) q^{97} +(-1.03056e8 - 1.03056e8i) q^{98} +(-3.45174e7 + 3.45174e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) $ 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8 + 15870 * q^10 - 8390 * q^11 + 5022 * q^12 + 12728 * q^14 - 35530 * q^15 - 245912 * q^16 + 76234 * q^17 - 465022 * q^18 - 164488 * q^19 + 4092 * q^20 - 514620 * q^21 + 733568 * q^23 - 482376 * q^24 - 1528354 * q^25 + 1405470 * q^26 - 1279754 * q^27 + 1420996 * q^29 + 3659852 * q^30 + 291062 * q^31 + 1592134 * q^32 - 10223688 * q^36 + 7994574 * q^37 - 309930 * q^39 + 9093994 * q^40 + 9561658 * q^41 - 5181022 * q^43 - 11400526 * q^44 + 9526060 * q^45 - 32561820 * q^46 + 5445034 * q^47 - 17683542 * q^48 + 45106458 * q^49 + 3122002 * q^50 + 56198616 * q^52 - 25331452 * q^53 - 42307016 * q^54 + 3037606 * q^55 - 25661184 * q^56 - 33846328 * q^58 + 27333008 * q^59 + 30592014 * q^60 - 49572406 * q^61 - 121974972 * q^65 + 133443354 * q^66 + 21192980 * q^68 - 28739184 * q^69 - 17976124 * q^70 - 186114192 * q^72 + 45787870 * q^73 + 91919252 * q^74 - 159074460 * q^75 + 243795016 * q^76 + 59851916 * q^77 + 163580208 * q^78 - 99827470 * q^79 - 75138586 * q^81 - 18178416 * q^82 - 177270160 * q^83 - 9436684 * q^84 + 156307616 * q^85 - 20584526 * q^87 + 563433236 * q^88 - 388451858 * q^89 + 306402752 * q^90 + 81569204 * q^94 - 44386260 * q^95 - 121157834 * q^97 - 129908712 * q^98 - 216447384 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	20.0740	+	20.0740i	1.25462	+	1.25462i	0.953625	+	0.300998i	$0.0973198\pi$
$2$	20.0740	+	20.0740i	1.25462	+	1.25462i	0.300998	+	0.953625i	$0.402680\pi$
$3$	6.21683	+	6.21683i	0.0767510	+	0.0767510i	0.744440	−	0.667689i	$-0.232716\pi$
$3$	6.21683	+	6.21683i	0.0767510	+	0.0767510i	−0.667689	+	0.744440i	$0.732716\pi$
$4$			549.928i			2.14816i
$5$			611.920i			0.979071i	0.871983	+	0.489536i	$0.162834\pi$
$5$			611.920i			0.979071i	−0.871983	+	0.489536i	$0.837166\pi$
$6$			249.593i			0.192587i
$7$	794.354			0.330843			0.165422	−	0.986223i	$-0.447102\pi$
$7$	794.354			0.330843			0.165422	+	0.986223i	$0.447102\pi$
$8$	−5900.31	+	5900.31i	−1.44050	+	1.44050i
$9$		−	6483.70i		−	0.988219i
$10$	−12283.7	+	12283.7i	−1.22837	+	1.22837i
$11$	−5323.72	−	5323.72i	−0.363617	−	0.363617i	0.501526	−	0.865143i	$-0.332772\pi$
$11$	−5323.72	−	5323.72i	−0.363617	−	0.363617i	−0.865143	+	0.501526i	$0.832772\pi$
$12$	−3418.81	+	3418.81i	−0.164873	+	0.164873i
$13$			44113.4i			1.54453i	0.635299	+	0.772266i	$0.280877\pi$
$13$			44113.4i			1.54453i	−0.635299	+	0.772266i	$0.719123\pi$
$14$	15945.8	+	15945.8i	0.415083	+	0.415083i
$15$	−3804.20	+	3804.20i	−0.0751448	+	0.0751448i
$16$	−96103.5			−1.46642
$17$	15707.7	+	15707.7i	0.188069	+	0.188069i	0.794861	−	0.606792i	$-0.207544\pi$
$17$	15707.7	+	15707.7i	0.188069	+	0.188069i	−0.606792	+	0.794861i	$0.707544\pi$
$18$	130154.	−	130154.i	1.23984	−	1.23984i
$19$	−100655.	−	100655.i	−0.772364	−	0.772364i	0.206156	−	0.978519i	$-0.433905\pi$
$19$	−100655.	−	100655.i	−0.772364	−	0.772364i	−0.978519	+	0.206156i	$0.933905\pi$
$20$	−336512.			−2.10320
$21$	4938.37	+	4938.37i	0.0253925	+	0.0253925i
$22$		−	213736.i		−	0.912405i
$23$	394140.			1.40844			0.704222	−	0.709980i	$-0.251296\pi$
$23$	394140.			1.40844			0.704222	+	0.709980i	$0.251296\pi$
$24$	−73362.5			−0.221120
$25$	16179.4			0.0414193
$26$	−885531.	+	885531.i	−1.93781	+	1.93781i
$27$	81096.8	−	81096.8i	0.152598	−	0.152598i
$28$			436838.i			0.710703i
$29$	583961.	+	399044.i	0.825642	+	0.564194i
$29$	583961.	+	399044.i	0.825642	+	0.564194i
$30$	−152731.			−0.188557
$31$	205131.	+	205131.i	0.222119	+	0.222119i	0.809390	−	0.587271i	$-0.199798\pi$
$31$	205131.	+	205131.i	0.222119	+	0.222119i	−0.587271	+	0.809390i	$0.699798\pi$
$32$	−418699.	−	418699.i	−0.399303	−	0.399303i
$33$		−	66193.4i		−	0.0558160i
$34$			630631.i			0.471911i
$35$			486081.i			0.323919i
$36$	3.56557e6			2.12285
$37$	80200.3	−	80200.3i	0.0427926	−	0.0427926i	−0.685387	−	0.728179i	$-0.740367\pi$
$37$	80200.3	−	80200.3i	0.0427926	−	0.0427926i	0.728179	+	0.685387i	$0.240367\pi$
$38$		−	4.04110e6i		−	1.93805i
$39$	−274246.	+	274246.i	−0.118545	+	0.118545i
$40$	−3.61051e6	−	3.61051e6i	−1.41036	−	1.41036i
$41$	1.98805e6	−	1.98805e6i	0.703545	−	0.703545i	−0.261625	−	0.965170i	$-0.584258\pi$
$41$	1.98805e6	−	1.98805e6i	0.703545	−	0.703545i	0.965170	+	0.261625i	$0.0842583\pi$
$42$			198265.i			0.0637161i
$43$	846266.	+	846266.i	0.247533	+	0.247533i	0.819957	−	0.572424i	$-0.193997\pi$
$43$	846266.	+	846266.i	0.247533	+	0.247533i	−0.572424	+	0.819957i	$0.693997\pi$
$44$	2.92766e6	−	2.92766e6i	0.781107	−	0.781107i
$45$	3.96750e6			0.967536
$46$	7.91196e6	+	7.91196e6i	1.76707	+	1.76707i
$47$	1.49739e6	−	1.49739e6i	0.306862	−	0.306862i	−0.536829	−	0.843691i	$-0.680378\pi$
$47$	1.49739e6	−	1.49739e6i	0.306862	−	0.306862i	0.843691	+	0.536829i	$0.180378\pi$
$48$	−597459.	−	597459.i	−0.112549	−	0.112549i
$49$	−5.13380e6			−0.890543
$50$	324785.	+	324785.i	0.0519656	+	0.0519656i
$51$			195304.i			0.0288689i
$52$	−2.42592e7			−3.31790
$53$	−1.06350e6			−0.134783			−0.0673916	−	0.997727i	$-0.521468\pi$
$53$	−1.06350e6			−0.134783			−0.0673916	+	0.997727i	$0.521468\pi$
$54$	3.25587e6			0.382906
$55$	3.25769e6	−	3.25769e6i	0.356007	−	0.356007i
$56$	−4.68693e6	+	4.68693e6i	−0.476581	+	0.476581i
$57$		−	1.25151e6i		−	0.118559i
$58$	3.71203e6	+	1.97328e7i	0.328019	+	1.74372i
$59$	−1.90074e7			−1.56860			−0.784302	−	0.620379i	$-0.786979\pi$
$59$	−1.90074e7			−1.56860			−0.784302	+	0.620379i	$0.786979\pi$
$60$	−2.09204e6	−	2.09204e6i	−0.161423	−	0.161423i
$61$	1.26730e7	+	1.26730e7i	0.915292	+	0.915292i	0.996682	−	0.0813900i	$-0.0259359\pi$
$61$	1.26730e7	+	1.26730e7i	0.915292	+	0.915292i	−0.0813900	+	0.996682i	$0.525936\pi$
$62$			8.23560e6i			0.557351i
$63$		−	5.15035e6i		−	0.326945i
$64$			7.79257e6i			0.464474i
$65$	−2.69939e7			−1.51221
$66$	1.32876e6	−	1.32876e6i	0.0700280	−	0.0700280i
$67$		−	2.92925e7i		−	1.45364i	−0.686827	−	0.726821i	$-0.740997\pi$
$67$		−	2.92925e7i		−	1.45364i	0.686827	−	0.726821i	$-0.259003\pi$
$68$	−8.63810e6	+	8.63810e6i	−0.404001	+	0.404001i
$69$	2.45031e6	+	2.45031e6i	0.108100	+	0.108100i
$70$	−9.75757e6	+	9.75757e6i	−0.406396	+	0.406396i
$71$		−	2.31349e7i		−	0.910405i	−0.890388	−	0.455202i	$-0.849567\pi$
$71$		−	2.31349e7i		−	0.910405i	0.890388	−	0.455202i	$-0.150433\pi$
$72$	3.82558e7	+	3.82558e7i	1.42353	+	1.42353i
$73$	2.90091e7	−	2.90091e7i	1.02151	−	1.02151i	0.0217481	−	0.999763i	$-0.493077\pi$
$73$	2.90091e7	−	2.90091e7i	1.02151	−	1.02151i	0.999763	−	0.0217481i	$-0.00692317\pi$
$74$	3.21988e6			0.107377
$75$	100585.	+	100585.i	0.00317897	+	0.00317897i
$76$	5.53531e7	−	5.53531e7i	1.65916	−	1.65916i
$77$	−4.22892e6	−	4.22892e6i	−0.120300	−	0.120300i
$78$	−1.10104e7			−0.297457
$79$	−3.05657e7	−	3.05657e7i	−0.784740	−	0.784740i	0.195886	−	0.980627i	$-0.437242\pi$
$79$	−3.05657e7	−	3.05657e7i	−0.784740	−	0.784740i	−0.980627	+	0.195886i	$0.937242\pi$
$80$		−	5.88076e7i		−	1.43573i
$81$	−4.15312e7			−0.964794
$82$	7.98161e7			1.76537
$83$	−6.94005e7			−1.46235			−0.731173	−	0.682192i	$-0.761027\pi$
$83$	−6.94005e7			−1.46235			−0.731173	+	0.682192i	$0.761027\pi$
$84$	−2.71575e6	+	2.71575e6i	−0.0545472	+	0.0545472i
$85$	−9.61184e6	+	9.61184e6i	−0.184133	+	0.184133i
$86$			3.39758e7i			0.621121i
$87$	1.14960e6	+	6.11118e6i	0.0200665	+	0.106671i
$88$	6.28231e7			1.04758
$89$	7.31571e6	+	7.31571e6i	0.116599	+	0.116599i	0.762999	−	0.646400i	$-0.223726\pi$
$89$	7.31571e6	+	7.31571e6i	0.116599	+	0.116599i	−0.646400	+	0.762999i	$0.723726\pi$
$90$	7.96435e7	+	7.96435e7i	1.21389	+	1.21389i
$91$			3.50417e7i			0.510998i
$92$			2.16749e8i			3.02556i
$93$			2.55054e6i			0.0340957i
$94$	6.01170e7			0.769991
$95$	6.15929e7	−	6.15929e7i	0.756199	−	0.756199i
$96$		−	5.20597e6i		−	0.0612938i
$97$	−5.69662e7	+	5.69662e7i	−0.643473	+	0.643473i	−0.951407	−	0.307935i	$-0.900362\pi$
$97$	−5.69662e7	+	5.69662e7i	−0.643473	+	0.643473i	0.307935	+	0.951407i	$0.400362\pi$
$98$	−1.03056e8	−	1.03056e8i	−1.11730	−	1.11730i
$99$	−3.45174e7	+	3.45174e7i	−0.359333	+	0.359333i
$100$			8.89752e6i			0.0889752i
$101$	−1.31590e8	−	1.31590e8i	−1.26456	−	1.26456i	−0.948860	−	0.315697i	$-0.897762\pi$
$101$	−1.31590e8	−	1.31590e8i	−1.26456	−	1.26456i	−0.315697	−	0.948860i	$-0.602238\pi$
$102$	−3.92053e6	+	3.92053e6i	−0.0362196	+	0.0362196i
$103$	2.10962e8			1.87437			0.937183	−	0.348837i	$-0.113423\pi$
$103$	2.10962e8			1.87437			0.937183	+	0.348837i	$0.113423\pi$
$104$	−2.60283e8	−	2.60283e8i	−2.22491	−	2.22491i
$105$	−3.02188e6	+	3.02188e6i	−0.0248611	+	0.0248611i
$106$	−2.13488e7	−	2.13488e7i	−0.169102	−	0.169102i
$107$	−6.78443e6			−0.0517581			−0.0258791	−	0.999665i	$-0.508238\pi$
$107$	−6.78443e6			−0.0517581			−0.0258791	+	0.999665i	$0.508238\pi$
$108$	4.45974e7	+	4.45974e7i	0.327804	+	0.327804i
$109$		−	9.22297e7i		−	0.653378i	−0.945132	−	0.326689i	$-0.894067\pi$
$109$		−	9.22297e7i		−	0.653378i	0.945132	−	0.326689i	$-0.105933\pi$
$110$	1.30789e8			0.893309
$111$	997184.			0.00656876
$112$	−7.63402e7			−0.485156
$113$	1.00147e8	−	1.00147e8i	0.614218	−	0.614218i	−0.329825	−	0.944042i	$-0.606990\pi$
$113$	1.00147e8	−	1.00147e8i	0.614218	−	0.614218i	0.944042	+	0.329825i	$0.106990\pi$
$114$	2.51228e7	−	2.51228e7i	0.148747	−	0.148747i
$115$			2.41182e8i			1.37897i
$116$	−2.19445e8	+	3.21137e8i	−1.21198	+	1.77361i
$117$	2.86018e8			1.52634
$118$	−3.81553e8	−	3.81553e8i	−1.96801	−	1.96801i
$119$	1.24775e7	+	1.24775e7i	0.0622212	+	0.0622212i
$120$		−	4.48919e7i		−	0.216493i
$121$		−	1.57675e8i		−	0.735565i
$122$			5.08794e8i			2.29669i
$123$	2.47188e7			0.107996
$124$	−1.12808e8	+	1.12808e8i	−0.477146	+	0.477146i
$125$			2.48932e8i			1.01962i
$126$	1.03388e8	−	1.03388e8i	0.410193	−	0.410193i
$127$	3.34834e8	+	3.34834e8i	1.28711	+	1.28711i	0.936536	+	0.350572i	$0.114013\pi$
$127$	3.34834e8	+	3.34834e8i	1.28711	+	1.28711i	0.350572	+	0.936536i	$0.385987\pi$
$128$	−2.63615e8	+	2.63615e8i	−0.982042	+	0.982042i
$129$			1.05222e7i			0.0379968i
$130$	−5.41874e8	−	5.41874e8i	−1.89725	−	1.89725i
$131$	−4.16423e7	+	4.16423e7i	−0.141400	+	0.141400i	−0.774263	−	0.632863i	$-0.781879\pi$
$131$	−4.16423e7	+	4.16423e7i	−0.141400	+	0.141400i	0.632863	+	0.774263i	$0.281879\pi$
$132$	3.64016e7			0.119902
$133$	−7.99559e7	−	7.99559e7i	−0.255531	−	0.255531i
$134$	5.88017e8	−	5.88017e8i	1.82377	−	1.82377i
$135$	4.96247e7	+	4.96247e7i	0.149404	+	0.149404i
$136$	−1.85360e8			−0.541828
$137$	1.44999e8	+	1.44999e8i	0.411608	+	0.411608i	0.882298	−	0.470691i	$-0.155995\pi$
$137$	1.44999e8	+	1.44999e8i	0.411608	+	0.411608i	−0.470691	+	0.882298i	$0.655995\pi$
$138$			9.83747e7i			0.271248i
$139$	−5.11596e8			−1.37047			−0.685233	−	0.728324i	$-0.740300\pi$
$139$	−5.11596e8			−1.37047			−0.685233	+	0.728324i	$0.740300\pi$
$140$	−2.67310e8			−0.695829
$141$	1.86180e7			0.0471039
$142$	4.64409e8	−	4.64409e8i	1.14221	−	1.14221i
$143$	2.34847e8	−	2.34847e8i	0.561619	−	0.561619i
$144$			6.23106e8i			1.44915i
$145$	−2.44183e8	+	3.57337e8i	−0.552386	+	0.808363i
$146$	1.16466e9			2.56322
$147$	−3.19160e7	−	3.19160e7i	−0.0683501	−	0.0683501i
$148$	4.41044e7	+	4.41044e7i	0.0919253	+	0.0919253i
$149$			2.79267e8i			0.566596i	0.959032	+	0.283298i	$0.0914286\pi$
$149$			2.79267e8i			0.566596i	−0.959032	+	0.283298i	$0.908571\pi$
$150$			4.03827e6i			0.00797683i
$151$		−	3.97145e8i		−	0.763909i	−0.924181	−	0.381954i	$-0.875251\pi$
$151$		−	3.97145e8i		−	0.763909i	0.924181	−	0.381954i	$-0.124749\pi$
$152$	1.18779e9			2.22519
$153$	1.01844e8	−	1.01844e8i	0.185853	−	0.185853i
$154$		−	1.69782e8i		−	0.301863i
$155$	−1.25524e8	+	1.25524e8i	−0.217470	+	0.217470i
$156$	−1.50815e8	−	1.50815e8i	−0.254652	−	0.254652i
$157$	−5.47929e8	+	5.47929e8i	−0.901832	+	0.901832i	−0.995595	−	0.0937621i	$-0.970111\pi$
$157$	−5.47929e8	+	5.47929e8i	−0.901832	+	0.901832i	0.0937621	+	0.995595i	$0.470111\pi$
$158$		−	1.22715e9i		−	1.96911i
$159$	−6.61163e6	−	6.61163e6i	−0.0103448	−	0.0103448i
$160$	2.56210e8	−	2.56210e8i	0.390946	−	0.390946i
$161$	3.13087e8			0.465974
$162$	−8.33697e8	−	8.33697e8i	−1.21045	−	1.21045i
$163$	9.10319e8	−	9.10319e8i	1.28957	−	1.28957i	0.354515	−	0.935050i	$-0.384646\pi$
$163$	9.10319e8	−	9.10319e8i	1.28957	−	1.28957i	0.935050	−	0.354515i	$-0.115354\pi$
$164$	1.09328e9	+	1.09328e9i	1.51133	+	1.51133i
$165$	4.05050e7			0.0546478
$166$	−1.39314e9	−	1.39314e9i	−1.83469	−	1.83469i
$167$		−	1.66222e7i		−	0.0213709i	−0.999943	−	0.0106854i	$-0.996599\pi$
$167$		−	1.66222e7i		−	0.0213709i	0.999943	−	0.0106854i	$-0.00340134\pi$
$168$	−5.82758e7			−0.0731562
$169$	−1.13026e9			−1.38558
$170$	−3.85896e8			−0.462034
$171$	−6.52618e8	+	6.52618e8i	−0.763264	+	0.763264i
$172$	−4.65386e8	+	4.65386e8i	−0.531740	+	0.531740i
$173$			2.24611e8i			0.250753i	0.992109	+	0.125376i	$0.0400139\pi$
$173$			2.24611e8i			0.250753i	−0.992109	+	0.125376i	$0.959986\pi$
$174$	−9.95985e7	+	1.45753e8i	−0.108657	+	0.159008i
$175$	1.28522e7			0.0137033
$176$	5.11628e8	+	5.11628e8i	0.533216	+	0.533216i
$177$	−1.18166e8	−	1.18166e8i	−0.120392	−	0.120392i
$178$			2.93711e8i			0.292577i
$179$			5.00147e8i			0.487176i	0.969879	+	0.243588i	$0.0783244\pi$
$179$			5.00147e8i			0.487176i	−0.969879	+	0.243588i	$0.921676\pi$
$180$			2.18184e9i			2.07842i
$181$	9.40900e8			0.876656			0.438328	−	0.898815i	$-0.355571\pi$
$181$	9.40900e8			0.876656			0.438328	+	0.898815i	$0.355571\pi$
$182$	−7.03425e8	+	7.03425e8i	−0.641110	+	0.641110i
$183$			1.57572e8i			0.140499i
$184$	−2.32555e9	+	2.32555e9i	−2.02887	+	2.02887i
$185$	4.90761e7	+	4.90761e7i	0.0418970	+	0.0418970i
$186$	−5.11994e7	+	5.11994e7i	−0.0427773	+	0.0427773i
$187$		−	1.67247e8i		−	0.136770i
$188$	8.23455e8	+	8.23455e8i	0.659187	+	0.659187i
$189$	6.44195e7	−	6.44195e7i	0.0504859	−	0.0504859i
$190$	2.47283e9			1.89749
$191$	4.83257e7	+	4.83257e7i	0.0363115	+	0.0363115i	0.725029	−	0.688718i	$-0.241826\pi$
$191$	4.83257e7	+	4.83257e7i	0.0363115	+	0.0363115i	−0.688718	+	0.725029i	$0.741826\pi$
$192$	−4.84452e7	+	4.84452e7i	−0.0356488	+	0.0356488i
$193$	−9.43429e8	−	9.43429e8i	−0.679955	−	0.679955i	0.280035	−	0.959990i	$-0.409654\pi$
$193$	−9.43429e8	−	9.43429e8i	−0.679955	−	0.679955i	−0.959990	+	0.280035i	$0.909654\pi$
$194$	−2.28707e9			−1.61463
$195$	−1.67816e8	−	1.67816e8i	−0.116064	−	0.116064i
$196$		−	2.82322e9i		−	1.91303i
$197$	−2.52304e9			−1.67517			−0.837585	−	0.546307i	$-0.816033\pi$
$197$	−2.52304e9			−1.67517			−0.837585	+	0.546307i	$0.816033\pi$
$198$	−1.38580e9			−0.901655
$199$	1.37871e9			0.879148			0.439574	−	0.898206i	$-0.355129\pi$
$199$	1.37871e9			0.879148			0.439574	+	0.898206i	$0.355129\pi$
$200$	−9.54635e7	+	9.54635e7i	−0.0596647	+	0.0596647i
$201$	1.82107e8	−	1.82107e8i	0.111569	−	0.111569i
$202$		−	5.28308e9i		−	3.17308i
$203$	4.63872e8	+	3.16982e8i	0.273158	+	0.186660i
$204$	−1.07403e8			−0.0620150
$205$	1.21653e9	+	1.21653e9i	0.688821	+	0.688821i
$206$	4.23484e9	+	4.23484e9i	2.35162	+	2.35162i
$207$		−	2.55549e9i		−	1.39185i
$208$		−	4.23945e9i		−	2.26494i
$209$			1.07172e9i			0.561689i
$210$	−1.21322e8			−0.0623827
$211$	1.37937e9	−	1.37937e9i	0.695908	−	0.695908i	−0.267617	−	0.963525i	$-0.586236\pi$
$211$	1.37937e9	−	1.37937e9i	0.695908	−	0.695908i	0.963525	+	0.267617i	$0.0862362\pi$
$212$		−	5.84851e8i		−	0.289536i
$213$	1.43826e8	−	1.43826e8i	0.0698745	−	0.0698745i
$214$	−1.36190e8	−	1.36190e8i	−0.0649369	−	0.0649369i
$215$	−5.17847e8	+	5.17847e8i	−0.242352	+	0.242352i
$216$			9.56991e8i			0.439636i
$217$	1.62947e8	+	1.62947e8i	0.0734865	+	0.0734865i
$218$	1.85142e9	−	1.85142e9i	0.819743	−	0.819743i
$219$	3.60690e8			0.156804
$220$	1.79149e9	+	1.79149e9i	0.764759	+	0.764759i
$221$	−6.92920e8	+	6.92920e8i	−0.290478	+	0.290478i
$222$	2.00174e7	+	2.00174e7i	0.00824132	+	0.00824132i
$223$	−4.01023e8			−0.162162			−0.0810811	−	0.996708i	$-0.525837\pi$
$223$	−4.01023e8			−0.162162			−0.0810811	+	0.996708i	$0.525837\pi$
$224$	−3.32595e8	−	3.32595e8i	−0.132107	−	0.132107i
$225$		−	1.04902e8i		−	0.0409313i
$226$	4.02068e9			1.54122
$227$	2.10240e9			0.791793			0.395896	−	0.918295i	$-0.370434\pi$
$227$	2.10240e9			0.791793			0.395896	+	0.918295i	$0.370434\pi$
$228$	6.88243e8			0.254684
$229$	−1.00039e9	+	1.00039e9i	−0.363772	+	0.363772i	−0.865199	−	0.501428i	$-0.832808\pi$
$229$	−1.00039e9	+	1.00039e9i	−0.363772	+	0.363772i	0.501428	+	0.865199i	$0.332808\pi$
$230$	−4.84148e9	+	4.84148e9i	−1.73008	+	1.73008i
$231$		−	5.25810e7i		−	0.0184663i
$232$	−5.80003e9	+	1.09107e9i	−2.00207	+	0.376618i
$233$	−8.44967e8			−0.286692			−0.143346	−	0.989673i	$-0.545786\pi$
$233$	−8.44967e8			−0.286692			−0.143346	+	0.989673i	$0.545786\pi$
$234$	5.74152e9	+	5.74152e9i	1.91498	+	1.91498i
$235$	9.16280e8	+	9.16280e8i	0.300439	+	0.300439i
$236$		−	1.04527e10i		−	3.36961i
$237$		−	3.80044e8i		−	0.120459i
$238$			5.00945e8i			0.156128i
$239$	7.32710e8			0.224564			0.112282	−	0.993676i	$-0.464184\pi$
$239$	7.32710e8			0.224564			0.112282	+	0.993676i	$0.464184\pi$
$240$	3.65597e8	−	3.65597e8i	0.110194	−	0.110194i
$241$			3.89329e9i			1.15411i	0.816704	+	0.577057i	$0.195799\pi$
$241$			3.89329e9i			1.15411i	−0.816704	+	0.577057i	$0.804201\pi$
$242$	3.16516e9	−	3.16516e9i	0.922857	−	0.922857i
$243$	−7.90269e8	−	7.90269e8i	−0.226647	−	0.226647i
$244$	−6.96924e9	+	6.96924e9i	−1.96619	+	1.96619i
$245$		−	3.14147e9i		−	0.871905i
$246$	4.96203e8	+	4.96203e8i	0.135494	+	0.135494i
$247$	4.44024e9	−	4.44024e9i	1.19294	−	1.19294i
$248$	−2.42068e9			−0.639926
$249$	−4.31452e8	−	4.31452e8i	−0.112237	−	0.112237i
$250$	−4.99704e9	+	4.99704e9i	−1.27924	+	1.27924i
$251$	−3.99268e9	−	3.99268e9i	−1.00593	−	1.00593i	−0.999982	−	0.00595117i	$-0.998106\pi$
$251$	−3.99268e9	−	3.99268e9i	−1.00593	−	1.00593i	−0.00595117	−	0.999982i	$-0.501894\pi$
$252$	2.83233e9			0.702330
$253$	−2.09829e9	−	2.09829e9i	−0.512134	−	0.512134i
$254$			1.34429e10i			3.22967i
$255$	−1.19510e8			−0.0282648
$256$	−8.58869e9			−1.99971
$257$	3.05072e9			0.699311			0.349655	−	0.936878i	$-0.386299\pi$
$257$	3.05072e9			0.699311			0.349655	+	0.936878i	$0.386299\pi$
$258$	−2.11222e8	+	2.11222e8i	−0.0476717	+	0.0476717i
$259$	6.37074e7	−	6.37074e7i	0.0141576	−	0.0141576i
$260$		−	1.48447e10i		−	3.24846i
$261$	2.58728e9	−	3.78623e9i	0.557547	−	0.815915i
$262$	−1.67185e9			−0.354808
$263$	6.32874e9	+	6.32874e9i	1.32280	+	1.32280i	0.911500	+	0.411300i	$0.134925\pi$
$263$	6.32874e9	+	6.32874e9i	1.32280	+	1.32280i	0.411300	+	0.911500i	$0.365075\pi$
$264$	3.90561e8	+	3.90561e8i	0.0804032	+	0.0804032i
$265$		−	6.50779e8i		−	0.131962i
$266$		−	3.21006e9i		−	0.641190i
$267$			9.09611e7i			0.0178983i
$268$	1.61088e10			3.12265
$269$	−3.97050e9	+	3.97050e9i	−0.758291	+	0.758291i	−0.976011	−	0.217720i	$-0.930138\pi$
$269$	−3.97050e9	+	3.97050e9i	−0.758291	+	0.758291i	0.217720	+	0.976011i	$0.430138\pi$
$270$			1.99233e9i			0.374892i
$271$	−1.00196e9	+	1.00196e9i	−0.185769	+	0.185769i	−0.793864	−	0.608095i	$-0.791934\pi$
$271$	−1.00196e9	+	1.00196e9i	−0.185769	+	0.185769i	0.608095	+	0.793864i	$0.291934\pi$
$272$	−1.50956e9	−	1.50956e9i	−0.275788	−	0.275788i
$273$	−2.17848e8	+	2.17848e8i	−0.0392196	+	0.0392196i
$274$			5.82142e9i			1.03283i
$275$	−8.61346e7	−	8.61346e7i	−0.0150608	−	0.0150608i
$276$	−1.34749e9	+	1.34749e9i	−0.232215	+	0.232215i
$277$	−9.30775e9			−1.58098			−0.790488	−	0.612477i	$-0.790173\pi$
$277$	−9.30775e9			−1.58098			−0.790488	+	0.612477i	$0.790173\pi$
$278$	−1.02698e10	−	1.02698e10i	−1.71942	−	1.71942i
$279$	1.33001e9	−	1.33001e9i	0.219502	−	0.219502i
$280$	−2.86803e9	−	2.86803e9i	−0.466607	−	0.466607i
$281$	−1.17971e10			−1.89212			−0.946061	−	0.323987i	$-0.894976\pi$
$281$	−1.17971e10			−1.89212			−0.946061	+	0.323987i	$0.894976\pi$
$282$	3.73737e8	+	3.73737e8i	0.0590976	+	0.0590976i
$283$		−	2.39229e9i		−	0.372964i	−0.982458	−	0.186482i	$-0.940291\pi$
$283$		−	2.39229e9i		−	0.372964i	0.982458	−	0.186482i	$-0.0597087\pi$
$284$	1.27225e10			1.95569
$285$	7.65826e8			0.116078
$286$	9.42863e9			1.40924
$287$	1.57922e9	−	1.57922e9i	0.232763	−	0.232763i
$288$	−2.71472e9	+	2.71472e9i	−0.394598	+	0.394598i
$289$		−	6.48229e9i		−	0.929260i
$290$	−1.20749e10	+	2.27146e9i	−1.70723	+	0.321154i
$291$	−7.08298e8			−0.0987744
$292$	1.59529e10	+	1.59529e10i	2.19437	+	2.19437i
$293$	−3.14928e9	−	3.14928e9i	−0.427308	−	0.427308i	0.460402	−	0.887710i	$-0.347705\pi$
$293$	−3.14928e9	−	3.14928e9i	−0.427308	−	0.427308i	−0.887710	+	0.460402i	$0.847705\pi$
$294$		−	1.28136e9i		−	0.171507i
$295$		−	1.16310e10i		−	1.53578i
$296$			9.46413e8i			0.123286i
$297$	−8.63473e8			−0.110974
$298$	−5.60599e9	+	5.60599e9i	−0.710865	+	0.710865i
$299$			1.73869e10i			2.17539i
$300$	−5.53144e7	+	5.53144e7i	−0.00682894	+	0.00682894i
$301$	6.72235e8	+	6.72235e8i	0.0818945	+	0.0818945i
$302$	7.97228e9	−	7.97228e9i	0.958417	−	0.958417i
$303$		−	1.63615e9i		−	0.194112i
$304$	9.67331e9	+	9.67331e9i	1.13261	+	1.13261i
$305$	−7.75485e9	+	7.75485e9i	−0.896136	+	0.896136i
$306$	4.08883e9			0.466351
$307$	3.87729e8	+	3.87729e8i	0.0436491	+	0.0436491i	0.728594	−	0.684945i	$-0.240174\pi$
$307$	3.87729e8	+	3.87729e8i	0.0436491	+	0.0436491i	−0.684945	+	0.728594i	$0.740174\pi$
$308$	2.32560e9	−	2.32560e9i	0.258424	−	0.258424i
$309$	1.31151e9	+	1.31151e9i	0.143860	+	0.143860i
$310$	−5.03953e9			−0.545686
$311$	5.05384e9	+	5.05384e9i	0.540232	+	0.540232i	0.923597	−	0.383365i	$-0.125235\pi$
$311$	5.05384e9	+	5.05384e9i	0.540232	+	0.540232i	−0.383365	+	0.923597i	$0.625235\pi$
$312$		−	3.23627e9i		−	0.341528i
$313$	1.03380e10			1.07710			0.538552	−	0.842592i	$-0.318971\pi$
$313$	1.03380e10			1.07710			0.538552	+	0.842592i	$0.318971\pi$
$314$	−2.19982e10			−2.26292
$315$	3.15160e9			0.320103
$316$	1.68089e10	−	1.68089e10i	1.68575	−	1.68575i
$317$	−1.20625e10	+	1.20625e10i	−1.19454	+	1.19454i	−0.218762	+	0.975778i	$0.570202\pi$
$317$	−1.20625e10	+	1.20625e10i	−1.19454	+	1.19454i	−0.975778	+	0.218762i	$0.929798\pi$
$318$		−	2.65443e8i		−	0.0259575i
$319$	−9.84449e8	−	5.23324e9i	−0.0950672	−	0.505368i
$320$	−4.76843e9			−0.454753
$321$	−4.21777e7	−	4.21777e7i	−0.00397249	−	0.00397249i
$322$	6.28490e9	+	6.28490e9i	0.584622	+	0.584622i
$323$		−	3.16212e9i		−	0.290515i
$324$		−	2.28392e10i		−	2.07253i
$325$			7.13729e8i			0.0639735i
$326$	3.65474e10			3.23584
$327$	5.73377e8	−	5.73377e8i	0.0501475	−	0.0501475i
$328$			2.34602e10i			2.02692i
$329$	1.18946e9	−	1.18946e9i	0.101523	−	0.101523i
$330$	8.13096e8	+	8.13096e8i	0.0685624	+	0.0685624i
$331$	4.11611e9	−	4.11611e9i	0.342906	−	0.342906i	−0.514553	−	0.857459i	$-0.672042\pi$
$331$	4.11611e9	−	4.11611e9i	0.342906	−	0.342906i	0.857459	+	0.514553i	$0.172042\pi$
$332$		−	3.81653e10i		−	3.14135i
$333$	−5.19995e8	−	5.19995e8i	−0.0422885	−	0.0422885i
$334$	3.33673e8	−	3.33673e8i	0.0268124	−	0.0268124i
$335$	1.79247e10			1.42322
$336$	−4.74594e8	−	4.74594e8i	−0.0372362	−	0.0372362i
$337$	−2.33990e9	+	2.33990e9i	−0.181417	+	0.181417i	−0.791973	−	0.610556i	$-0.790946\pi$
$337$	−2.33990e9	+	2.33990e9i	−0.181417	+	0.181417i	0.610556	+	0.791973i	$0.290946\pi$
$338$	−2.26888e10	−	2.26888e10i	−1.73838	−	1.73838i
$339$	1.24519e9			0.0942837
$340$	−5.28582e9	−	5.28582e9i	−0.395546	−	0.395546i
$341$		−	2.18412e9i		−	0.161532i
$342$	−2.62013e10			−1.91522
$343$	−8.65735e9			−0.625473
$344$	−9.98646e9			−0.713145
$345$	−1.49939e9	+	1.49939e9i	−0.105837	+	0.105837i
$346$	−4.50883e9	+	4.50883e9i	−0.314600	+	0.314600i
$347$		−	1.85893e9i		−	0.128217i	−0.997943	−	0.0641085i	$-0.979580\pi$
$347$		−	1.85893e9i		−	0.128217i	0.997943	−	0.0641085i	$-0.0204204\pi$
$348$	−3.36071e9	+	6.32199e8i	−0.229147	+	0.0431059i
$349$	1.60697e10			1.08319			0.541597	−	0.840639i	$-0.317820\pi$
$349$	1.60697e10			1.08319			0.541597	+	0.840639i	$0.317820\pi$
$350$	2.57994e8	+	2.57994e8i	0.0171925	+	0.0171925i
$351$	3.57745e9	+	3.57745e9i	0.235692	+	0.235692i
$352$			4.45807e9i			0.290387i
$353$			1.14940e10i			0.740237i	0.928984	+	0.370119i	$0.120683\pi$
$353$			1.14940e10i			0.740237i	−0.928984	+	0.370119i	$0.879317\pi$
$354$		−	4.74410e9i		−	0.302093i
$355$	1.41567e10			0.891351
$356$	−4.02312e9	+	4.02312e9i	−0.250474	+	0.250474i
$357$			1.55141e8i			0.00955109i
$358$	−1.00399e10	+	1.00399e10i	−0.611222	+	0.611222i
$359$	8.28711e8	+	8.28711e8i	0.0498914	+	0.0498914i	0.731612	−	0.681721i	$-0.238768\pi$
$359$	8.28711e8	+	8.28711e8i	0.0498914	+	0.0498914i	−0.681721	+	0.731612i	$0.738768\pi$
$360$	−2.34095e10	+	2.34095e10i	−1.39374	+	1.39374i
$361$			3.27938e9i			0.193091i
$362$	1.88876e10	+	1.88876e10i	1.09987	+	1.09987i
$363$	9.80239e8	−	9.80239e8i	0.0564554	−	0.0564554i
$364$	−1.92704e10			−1.09770
$365$	1.77513e10	+	1.77513e10i	1.00013	+	1.00013i
$366$	−3.16309e9	+	3.16309e9i	−0.176274	+	0.176274i
$367$	1.75412e10	+	1.75412e10i	0.966930	+	0.966930i	0.999470	−	0.0325400i	$-0.0103596\pi$
$367$	1.75412e10	+	1.75412e10i	0.966930	+	0.966930i	−0.0325400	+	0.999470i	$0.510360\pi$
$368$	−3.78783e10			−2.06537
$369$	−1.28899e10	−	1.28899e10i	−0.695256	−	0.695256i
$370$			1.97031e9i			0.105130i
$371$	−8.44799e8			−0.0445921
$372$	−1.40261e9			−0.0732430
$373$	−8.95807e9			−0.462785			−0.231392	−	0.972861i	$-0.574328\pi$
$373$	−8.95807e9			−0.462785			−0.231392	+	0.972861i	$0.574328\pi$
$374$	3.35730e9	−	3.35730e9i	0.171595	−	0.171595i
$375$	−1.54757e9	+	1.54757e9i	−0.0782572	+	0.0782572i
$376$			1.76701e10i			0.884071i
$377$	−1.76032e10	+	2.57605e10i	−0.871416	+	1.27523i
$378$	2.58631e9			0.126682
$379$	−6.23594e9	−	6.23594e9i	−0.302235	−	0.302235i	0.539653	−	0.841888i	$-0.318556\pi$
$379$	−6.23594e9	−	6.23594e9i	−0.302235	−	0.302235i	−0.841888	+	0.539653i	$0.818556\pi$
$380$	3.38717e10	+	3.38717e10i	1.62443	+	1.62443i
$381$			4.16322e9i			0.197574i
$382$			1.94018e9i			0.0911146i
$383$		−	1.24289e10i		−	0.577613i	−0.957388	−	0.288806i	$-0.906742\pi$
$383$		−	1.24289e10i		−	0.577613i	0.957388	−	0.288806i	$-0.0932584\pi$
$384$	−3.27770e9			−0.150746
$385$	2.58776e9	−	2.58776e9i	0.117782	−	0.117782i
$386$		−	3.78767e10i		−	1.70617i
$387$	5.48694e9	−	5.48694e9i	0.244617	−	0.244617i
$388$	−3.13273e10	−	3.13273e10i	−1.38228	−	1.38228i
$389$	−2.47082e10	+	2.47082e10i	−1.07905	+	1.07905i	−0.0824575	+	0.996595i	$0.526277\pi$
$389$	−2.47082e10	+	2.47082e10i	−1.07905	+	1.07905i	−0.996595	+	0.0824575i	$0.973723\pi$
$390$		−	6.73748e9i		−	0.291232i
$391$	6.19104e9	+	6.19104e9i	0.264884	+	0.264884i
$392$	3.02910e10	−	3.02910e10i	1.28283	−	1.28283i
$393$	−5.17767e8			−0.0217052
$394$	−5.06474e10	−	5.06474e10i	−2.10171	−	2.10171i
$395$	1.87038e10	−	1.87038e10i	0.768317	−	0.768317i
$396$	−1.89821e10	−	1.89821e10i	−0.771904	−	0.771904i
$397$	7.27841e9			0.293005			0.146502	−	0.989210i	$-0.453198\pi$
$397$	7.27841e9			0.293005			0.146502	+	0.989210i	$0.453198\pi$
$398$	2.76763e10	+	2.76763e10i	1.10300	+	1.10300i
$399$		−	9.94145e8i		−	0.0392246i
$400$	−1.55490e9			−0.0607382
$401$	3.47163e10			1.34263			0.671315	−	0.741173i	$-0.265730\pi$
$401$	3.47163e10			1.34263			0.671315	+	0.741173i	$0.265730\pi$
$402$	7.31121e9			0.279953
$403$	−9.04905e9	+	9.04905e9i	−0.343070	+	0.343070i
$404$	7.23652e10	−	7.23652e10i	2.71647	−	2.71647i
$405$		−	2.54138e10i		−	0.944603i
$406$	2.94867e9	+	1.56748e10i	0.108523	+	0.576898i
$407$	−8.53928e8			−0.0311203
$408$	−1.15235e9	−	1.15235e9i	−0.0415858	−	0.0415858i
$409$	−1.93736e9	−	1.93736e9i	−0.0692335	−	0.0692335i	0.671642	−	0.740876i	$-0.265589\pi$
$409$	−1.93736e9	−	1.93736e9i	−0.0692335	−	0.0692335i	−0.740876	+	0.671642i	$0.765589\pi$
$410$			4.88410e10i			1.72842i
$411$			1.80287e9i			0.0631827i
$412$			1.16014e11i			4.02643i
$413$	−1.50986e10			−0.518962
$414$	5.12988e10	−	5.12988e10i	1.74625	−	1.74625i
$415$		−	4.24675e10i		−	1.43174i
$416$	1.84703e10	−	1.84703e10i	0.616736	−	0.616736i
$417$	−3.18051e9	−	3.18051e9i	−0.105185	−	0.105185i
$418$	−2.15137e10	+	2.15137e10i	−0.704708	+	0.704708i
$419$			1.34874e10i			0.437595i	0.975770	+	0.218798i	$0.0702134\pi$
$419$			1.34874e10i			0.437595i	−0.975770	+	0.218798i	$0.929787\pi$
$420$	−1.66182e9	−	1.66182e9i	−0.0534056	−	0.0534056i
$421$	2.34442e10	−	2.34442e10i	0.746290	−	0.746290i	−0.227491	−	0.973780i	$-0.573052\pi$
$421$	2.34442e10	−	2.34442e10i	0.746290	−	0.746290i	0.973780	+	0.227491i	$0.0730521\pi$
$422$	5.53790e10			1.74621
$423$	−9.70861e9	−	9.70861e9i	−0.303246	−	0.303246i
$424$	6.27500e9	−	6.27500e9i	0.194156	−	0.194156i
$425$	2.54141e8	+	2.54141e8i	0.00778967	+	0.00778967i
$426$	5.77431e9			0.175332
$427$	1.00668e10	+	1.00668e10i	0.302818	+	0.302818i
$428$		−	3.73095e9i		−	0.111185i
$429$	2.92001e9			0.0862096
$430$	−2.07905e10			−0.608122
$431$	−6.18814e10			−1.79329			−0.896646	−	0.442749i	$-0.854003\pi$
$431$	−6.18814e10			−1.79329			−0.896646	+	0.442749i	$0.854003\pi$
$432$	−7.79368e9	+	7.79368e9i	−0.223773	+	0.223773i
$433$	−2.26965e10	+	2.26965e10i	−0.645665	+	0.645665i	−0.951942	−	0.306278i	$-0.900916\pi$
$433$	−2.26965e10	+	2.26965e10i	−0.645665	+	0.645665i	0.306278	+	0.951942i	$0.400916\pi$
$434$			6.54199e9i			0.184396i
$435$	−3.73955e9	+	7.03464e8i	−0.104439	+	0.0196465i
$436$	5.07197e10			1.40356
$437$	−3.96723e10	−	3.96723e10i	−1.08783	−	1.08783i
$438$	7.24048e9	+	7.24048e9i	0.196730	+	0.196730i
$439$		−	3.25674e10i		−	0.876850i	−0.898768	−	0.438425i	$-0.855537\pi$
$439$		−	3.25674e10i		−	0.876850i	0.898768	−	0.438425i	$-0.144463\pi$
$440$			3.84427e10i			1.02566i
$441$			3.32860e10i			0.880051i
$442$	−2.78193e10			−0.728882
$443$	2.07453e10	−	2.07453e10i	0.538647	−	0.538647i	−0.384485	−	0.923131i	$-0.625621\pi$
$443$	2.07453e10	−	2.07453e10i	0.538647	−	0.538647i	0.923131	+	0.384485i	$0.125621\pi$
$444$			5.48380e8i			0.0141107i
$445$	−4.47663e9	+	4.47663e9i	−0.114159	+	0.114159i
$446$	−8.05011e9	−	8.05011e9i	−0.203452	−	0.203452i
$447$	−1.73615e9	+	1.73615e9i	−0.0434869	+	0.0434869i
$448$			6.19006e9i			0.153668i
$449$	−1.97596e10	−	1.97596e10i	−0.486174	−	0.486174i	0.420922	−	0.907097i	$-0.361706\pi$
$449$	−1.97596e10	−	1.97596e10i	−0.486174	−	0.486174i	−0.907097	+	0.420922i	$0.861706\pi$
$450$	2.10581e9	−	2.10581e9i	0.0513534	−	0.0513534i
$451$	−2.11676e10			−0.511642
$452$	5.50734e10	+	5.50734e10i	1.31944	+	1.31944i
$453$	2.46899e9	−	2.46899e9i	0.0586308	−	0.0586308i
$454$	4.22035e10	+	4.22035e10i	0.993401	+	0.993401i
$455$	−2.14427e10			−0.500303
$456$	7.38431e9	+	7.38431e9i	0.170785	+	0.170785i
$457$		−	6.54866e10i		−	1.50137i	−0.660660	−	0.750685i	$-0.729724\pi$
$457$		−	6.54866e10i		−	1.50137i	0.660660	−	0.750685i	$-0.270276\pi$
$458$	−4.01637e10			−0.912792
$459$	2.54769e9			0.0573978
$460$	−1.32633e11			−2.96224
$461$	−5.52283e9	+	5.52283e9i	−0.122281	+	0.122281i	−0.765599	−	0.643318i	$-0.777557\pi$
$461$	−5.52283e9	+	5.52283e9i	−0.122281	+	0.122281i	0.643318	+	0.765599i	$0.277557\pi$
$462$	1.05551e9	−	1.05551e9i	0.0231683	−	0.0231683i
$463$			8.95161e10i			1.94795i	0.226660	+	0.973974i	$0.427219\pi$
$463$			8.95161e10i			1.94795i	−0.226660	+	0.973974i	$0.572781\pi$
$464$	−5.61207e10	−	3.83495e10i	−1.21074	−	0.827346i
$465$	−1.56072e9			−0.0333821
$466$	−1.69618e10	−	1.69618e10i	−0.359691	−	0.359691i
$467$	1.07668e10	+	1.07668e10i	0.226369	+	0.226369i	0.811174	−	0.584805i	$-0.198829\pi$
$467$	1.07668e10	+	1.07668e10i	0.226369	+	0.226369i	−0.584805	+	0.811174i	$0.698829\pi$
$468$			1.57289e11i			3.27881i
$469$		−	2.32686e10i		−	0.480927i
$470$			3.67868e10i			0.753876i
$471$	−6.81277e9			−0.138433
$472$	1.12149e11	−	1.12149e11i	2.25958	−	2.25958i
$473$		−	9.01056e9i		−	0.180014i
$474$	7.62899e9	−	7.62899e9i	0.151131	−	0.151131i
$475$	−1.62854e9	−	1.62854e9i	−0.0319908	−	0.0319908i
$476$	−6.86171e9	+	6.86171e9i	−0.133661	+	0.133661i
$477$			6.89545e9i			0.133195i
$478$	1.47084e10	+	1.47084e10i	0.281743	+	0.281743i
$479$	−2.15772e10	+	2.15772e10i	−0.409877	+	0.409877i	−0.881696	−	0.471818i	$-0.843598\pi$
$479$	−2.15772e10	+	2.15772e10i	−0.409877	+	0.409877i	0.471818	+	0.881696i	$0.343598\pi$
$480$	3.18563e9			0.0600110
$481$	3.53791e9	+	3.53791e9i	0.0660946	+	0.0660946i
$482$	−7.81538e10	+	7.81538e10i	−1.44798	+	1.44798i
$483$	1.94641e9	+	1.94641e9i	0.0357640	+	0.0357640i
$484$	8.67099e10			1.58011
$485$	−3.48587e10	−	3.48587e10i	−0.630006	−	0.630006i
$486$		−	3.17277e10i		−	0.568713i
$487$	3.34913e10			0.595411			0.297705	−	0.954658i	$-0.403779\pi$
$487$	3.34913e10			0.595411			0.297705	+	0.954658i	$0.403779\pi$
$488$	−1.49549e11			−2.63697
$489$	1.13186e10			0.197951
$490$	6.30619e10	−	6.30619e10i	1.09391	−	1.09391i
$491$	5.48553e10	−	5.48553e10i	0.943827	−	0.943827i	−0.0546769	−	0.998504i	$-0.517413\pi$
$491$	5.48553e10	−	5.48553e10i	0.943827	−	0.943827i	0.998504	+	0.0546769i	$0.0174129\pi$
$492$			1.35935e10i			0.231992i
$493$	2.90463e9	+	1.54407e10i	0.0491703	+	0.261385i
$494$	1.78267e11			2.99338
$495$	−2.11219e10	−	2.11219e10i	−0.351813	−	0.351813i
$496$	−1.97138e10	−	1.97138e10i	−0.325720	−	0.325720i
$497$		−	1.83773e10i		−	0.301201i
$498$		−	1.73219e10i		−	0.281629i
$499$		−	5.55823e10i		−	0.896466i	−0.893917	−	0.448233i	$-0.852053\pi$
$499$		−	5.55823e10i		−	0.896466i	0.893917	−	0.448233i	$-0.147947\pi$
$500$	−1.36895e11			−2.19031
$501$	1.03337e8	−	1.03337e8i	0.00164024	−	0.00164024i
$502$		−	1.60298e11i		−	2.52413i
$503$	−1.07769e10	+	1.07769e10i	−0.168354	+	0.168354i	−0.786255	−	0.617902i	$-0.787983\pi$
$503$	−1.07769e10	+	1.07769e10i	−0.168354	+	0.168354i	0.617902	+	0.786255i	$0.287983\pi$
$504$	3.03887e10	+	3.03887e10i	0.470966	+	0.470966i
$505$	8.05227e10	−	8.05227e10i	1.23809	−	1.23809i
$506$		−	8.42421e10i		−	1.28507i
$507$	−7.02665e9	−	7.02665e9i	−0.106345	−	0.106345i
$508$	−1.84135e11	+	1.84135e11i	−2.76491	+	2.76491i
$509$	−6.77380e10			−1.00916			−0.504582	−	0.863364i	$-0.668353\pi$
$509$	−6.77380e10			−1.00916			−0.504582	+	0.863364i	$0.668353\pi$
$510$	−2.39905e9	−	2.39905e9i	−0.0354616	−	0.0354616i
$511$	2.30435e10	−	2.30435e10i	0.337960	−	0.337960i
$512$	−1.04924e11	−	1.04924e11i	−1.52684	−	1.52684i
$513$	−1.63256e10			−0.235722
$514$	6.12401e10	+	6.12401e10i	0.877372	+	0.877372i
$515$			1.29092e11i			1.83514i
$516$	−5.78645e9			−0.0816232
$517$	−1.59433e10			−0.223160
$518$	2.55772e9			0.0355250
$519$	−1.39637e9	+	1.39637e9i	−0.0192455	+	0.0192455i
$520$	1.59272e11	−	1.59272e11i	2.17834	−	2.17834i
$521$			5.85247e10i			0.794306i	0.917752	+	0.397153i	$0.130002\pi$
$521$			5.85247e10i			0.794306i	−0.917752	+	0.397153i	$0.869998\pi$
$522$	1.27942e11	−	2.40677e10i	1.72318	−	0.324155i
$523$	1.29455e9			0.0173026			0.00865131	−	0.999963i	$-0.497246\pi$
$523$	1.29455e9			0.0173026			0.00865131	+	0.999963i	$0.497246\pi$
$524$	−2.29003e10	−	2.29003e10i	−0.303750	−	0.303750i
$525$	7.98999e7	+	7.98999e7i	0.00105174	+	0.00105174i
$526$			2.54086e11i			3.31923i
$527$			6.44428e9i			0.0835472i
$528$			6.36141e9i			0.0818498i
$529$	7.70357e10			0.983715
$530$	1.30637e10	−	1.30637e10i	0.165563	−	0.165563i
$531$			1.23238e11i			1.55012i
$532$	4.39700e10	−	4.39700e10i	0.548921	−	0.548921i
$533$	8.76996e10	+	8.76996e10i	1.08665	+	1.08665i
$534$	−1.82595e9	+	1.82595e9i	−0.0224556	+	0.0224556i
$535$		−	4.15153e9i		−	0.0506749i
$536$	1.72835e11	+	1.72835e11i	2.09398	+	2.09398i
$537$	−3.10933e9	+	3.10933e9i	−0.0373913	+	0.0373913i
$538$	−1.59407e11			−1.90274
$539$	2.73309e10	+	2.73309e10i	0.323817	+	0.323817i
$540$	−2.72900e10	+	2.72900e10i	−0.320944	+	0.320944i
$541$	1.07919e11	+	1.07919e11i	1.25982	+	1.25982i	0.951177	+	0.308645i	$0.0998756\pi$
$541$	1.07919e11	+	1.07919e11i	1.25982	+	1.25982i	0.308645	+	0.951177i	$0.400124\pi$
$542$	−4.02267e10			−0.466141
$543$	5.84942e9	+	5.84942e9i	0.0672843	+	0.0672843i
$544$		−	1.31536e10i		−	0.150193i
$545$	5.64372e10			0.639704
$546$	−8.74616e9			−0.0984117
$547$	−1.15887e11			−1.29445			−0.647223	−	0.762301i	$-0.724070\pi$
$547$	−1.15887e11			−1.29445			−0.647223	+	0.762301i	$0.724070\pi$
$548$	−7.97392e10	+	7.97392e10i	−0.884198	+	0.884198i
$549$	8.21679e10	−	8.21679e10i	0.904509	−	0.904509i
$550$		−	3.45813e9i		−	0.0377912i
$551$	−1.86129e10	−	9.89445e10i	−0.201933	−	1.07346i
$552$	−2.89151e10			−0.311436
$553$	−2.42800e10	−	2.42800e10i	−0.259626	−	0.259626i
$554$	−1.86843e11	−	1.86843e11i	−1.98353	−	1.98353i
$555$			6.10196e8i			0.00643128i
$556$		−	2.81341e11i		−	2.94398i
$557$		−	2.98756e10i		−	0.310382i	−0.987885	−	0.155191i	$-0.950401\pi$
$557$		−	2.98756e10i		−	0.310382i	0.987885	−	0.155191i	$-0.0495992\pi$
$558$	5.33972e10			0.550784
$559$	−3.73317e10	+	3.73317e10i	−0.382323	+	0.382323i
$560$		−	4.67140e10i		−	0.475002i
$561$	1.03974e9	−	1.03974e9i	0.0104972	−	0.0104972i
$562$	−2.36814e11	−	2.36814e11i	−2.37390	−	2.37390i
$563$	1.05870e11	−	1.05870e11i	1.05376	−	1.05376i	0.0552850	−	0.998471i	$-0.482393\pi$
$563$	1.05870e11	−	1.05870e11i	1.05376	−	1.05376i	0.998471	−	0.0552850i	$-0.0176067\pi$
$564$			1.02386e10i			0.101187i
$565$	6.12816e10	+	6.12816e10i	0.601363	+	0.601363i
$566$	4.80227e10	−	4.80227e10i	0.467930	−	0.467930i
$567$	−3.29905e10			−0.319196
$568$	1.36503e11	+	1.36503e11i	1.31144	+	1.31144i
$569$	−6.02839e10	+	6.02839e10i	−0.575112	+	0.575112i	−0.933552	−	0.358441i	$-0.883308\pi$
$569$	−6.02839e10	+	6.02839e10i	−0.575112	+	0.575112i	0.358441	+	0.933552i	$0.383308\pi$
$570$	1.53732e10	+	1.53732e10i	0.145634	+	0.145634i
$571$	3.32753e10			0.313024			0.156512	−	0.987676i	$-0.449975\pi$
$571$	3.32753e10			0.313024			0.156512	+	0.987676i	$0.449975\pi$
$572$	1.29149e11	+	1.29149e11i	1.20645	+	1.20645i
$573$			6.00866e8i			0.00557390i
$574$	6.34022e10			0.584059
$575$	6.37696e9			0.0583368
$576$	5.05247e10			0.459001
$577$	3.12857e10	−	3.12857e10i	0.282256	−	0.282256i	−0.551752	−	0.834008i	$-0.686041\pi$
$577$	3.12857e10	−	3.12857e10i	0.282256	−	0.282256i	0.834008	+	0.551752i	$0.186041\pi$
$578$	1.30125e11	−	1.30125e11i	1.16587	−	1.16587i
$579$		−	1.17303e10i		−	0.104374i
$580$	−1.96510e11	−	1.34283e11i	−1.73649	−	1.18661i
$581$	−5.51286e10			−0.483807
$582$	−1.42184e10	−	1.42184e10i	−0.123925	−	0.123925i
$583$	5.66180e9	+	5.66180e9i	0.0490095	+	0.0490095i
$584$			3.42326e11i			2.94298i
$585$			1.75020e11i			1.49439i
$586$		−	1.26437e11i		−	1.07222i
$587$	−1.57874e11			−1.32971			−0.664855	−	0.746972i	$-0.731507\pi$
$587$	−1.57874e11			−1.32971			−0.664855	+	0.746972i	$0.731507\pi$
$588$	1.75515e10	−	1.75515e10i	0.146827	−	0.146827i
$589$		−	4.12951e10i		−	0.343113i
$590$	2.33480e11	−	2.33480e11i	1.92682	−	1.92682i
$591$	−1.56853e10	−	1.56853e10i	−0.128571	−	0.128571i
$592$	−7.70753e9	+	7.70753e9i	−0.0627521	+	0.0627521i
$593$		−	6.54068e10i		−	0.528937i	−0.964394	−	0.264469i	$-0.914803\pi$
$593$		−	6.54068e10i		−	0.528937i	0.964394	−	0.264469i	$-0.0851966\pi$
$594$	−1.73333e10	−	1.73333e10i	−0.139231	−	0.139231i
$595$	−7.63521e9	+	7.63521e9i	−0.0609190	+	0.0609190i
$596$	−1.53577e11			−1.21714
$597$	8.57124e9	+	8.57124e9i	0.0674756	+	0.0674756i
$598$	−3.49024e11	+	3.49024e11i	−2.72929	+	2.72929i
$599$	−4.82866e10	−	4.82866e10i	−0.375076	−	0.375076i	0.494246	−	0.869322i	$-0.335444\pi$
$599$	−4.82866e10	−	4.82866e10i	−0.375076	−	0.375076i	−0.869322	+	0.494246i	$0.835444\pi$
$600$	−1.18696e9			−0.00915865
$601$	1.05132e11	+	1.05132e11i	0.805822	+	0.805822i	0.983999	−	0.178177i	$-0.0570199\pi$
$601$	1.05132e11	+	1.05132e11i	0.805822	+	0.805822i	−0.178177	+	0.983999i	$0.557020\pi$
$602$			2.69888e10i			0.205494i
$603$	−1.89924e11			−1.43652
$604$	2.18401e11			1.64100
$605$	9.64844e10			0.720171
$606$	3.28440e10	−	3.28440e10i	0.243538	−	0.243538i
$607$	−1.63798e11	+	1.63798e11i	−1.20657	+	1.20657i	−0.234441	+	0.972130i	$0.575326\pi$
$607$	−1.63798e11	+	1.63798e11i	−1.20657	+	1.20657i	−0.972130	+	0.234441i	$0.924674\pi$
$608$			8.42885e10i			0.616814i
$609$	9.13191e8	+	4.85444e9i	0.00663884	+	0.0352915i
$610$	−3.11341e11			−2.24863
$611$	6.60548e10	+	6.60548e10i	0.473958	+	0.473958i
$612$	5.60069e10	+	5.60069e10i	0.399242	+	0.399242i
$613$			5.11431e10i			0.362197i	0.983465	+	0.181099i	$0.0579653\pi$
$613$			5.11431e10i			0.362197i	−0.983465	+	0.181099i	$0.942035\pi$
$614$			1.55665e10i			0.109526i
$615$			1.51259e10i			0.105735i
$616$	4.99038e10			0.346586
$617$	1.36269e11	−	1.36269e11i	0.940282	−	0.940282i	−0.0580331	−	0.998315i	$-0.518483\pi$
$617$	1.36269e11	−	1.36269e11i	0.940282	−	0.940282i	0.998315	+	0.0580331i	$0.0184829\pi$
$618$			5.26546e10i			0.360979i
$619$	5.17225e10	−	5.17225e10i	0.352304	−	0.352304i	−0.508662	−	0.860966i	$-0.669860\pi$
$619$	5.17225e10	−	5.17225e10i	0.352304	−	0.352304i	0.860966	+	0.508662i	$0.169860\pi$
$620$	−6.90292e10	−	6.90292e10i	−0.467160	−	0.467160i
$621$	3.19635e10	−	3.19635e10i	0.214926	−	0.214926i
$622$			2.02901e11i			1.35557i
$623$	5.81127e9	+	5.81127e9i	0.0385761	+	0.0385761i
$624$	2.63560e10	−	2.63560e10i	0.173836	−	0.173836i
$625$	−1.46006e11			−0.956865
$626$	2.07524e11	+	2.07524e11i	1.35136	+	1.35136i
$627$	−6.66271e9	+	6.66271e9i	−0.0431102	+	0.0431102i
$628$	−3.01322e11	−	3.01322e11i	−1.93728	−	1.93728i
$629$	2.51952e9			0.0160959
$630$	6.32652e10	+	6.32652e10i	0.401608	+	0.401608i
$631$		−	4.63687e10i		−	0.292488i	−0.989249	−	0.146244i	$-0.953282\pi$
$631$		−	4.63687e10i		−	0.292488i	0.989249	−	0.146244i	$-0.0467184\pi$
$632$	3.60694e11			2.26084
$633$	1.71507e10			0.106823
$634$	−4.84285e11			−2.99739
$635$	−2.04892e11	+	2.04892e11i	−1.26017	+	1.26017i
$636$	3.63592e9	−	3.63592e9i	0.0222222	−	0.0222222i
$637$		−	2.26469e11i		−	1.37547i
$638$	8.52901e10	−	1.24814e11i	0.514773	−	0.753320i
$639$	−1.50000e11			−0.899679
$640$	−1.61311e11	−	1.61311e11i	−0.961489	−	0.961489i
$641$	−8.88685e10	−	8.88685e10i	−0.526400	−	0.526400i	0.393097	−	0.919497i	$-0.371404\pi$
$641$	−8.88685e10	−	8.88685e10i	−0.526400	−	0.526400i	−0.919497	+	0.393097i	$0.871404\pi$
$642$		−	1.69335e9i		−	0.00996795i
$643$		−	1.00662e11i		−	0.588871i	−0.955671	−	0.294436i	$-0.904868\pi$
$643$		−	1.00662e11i		−	0.588871i	0.955671	−	0.294436i	$-0.0951316\pi$
$644$			1.72175e11i			1.00099i
$645$	−6.43874e9			−0.0372016
$646$	6.34763e10	−	6.34763e10i	0.364487	−	0.364487i
$647$			1.24427e11i			0.710067i	0.934854	+	0.355033i	$0.115530\pi$
$647$			1.24427e11i			0.710067i	−0.934854	+	0.355033i	$0.884470\pi$
$648$	2.45047e11	−	2.45047e11i	1.38979	−	1.38979i
$649$	1.01190e11	+	1.01190e11i	0.570372	+	0.570372i
$650$	−1.43274e10	+	1.43274e10i	−0.0802626	+	0.0802626i
$651$			2.02603e9i			0.0112803i
$652$	5.00610e11	+	5.00610e11i	2.77019	+	2.77019i
$653$	2.97491e8	−	2.97491e8i	0.00163614	−	0.00163614i	−0.706288	−	0.707924i	$-0.749632\pi$
$653$	2.97491e8	−	2.97491e8i	0.00163614	−	0.00163614i	0.707924	+	0.706288i	$0.249632\pi$
$654$	2.30199e10			0.125832
$655$	−2.54818e10	−	2.54818e10i	−0.138441	−	0.138441i
$656$	−1.91058e11	+	1.91058e11i	−1.03169	+	1.03169i
$657$	−1.88087e11	−	1.88087e11i	−1.00948	−	1.00948i
$658$	4.77542e10			0.254746
$659$	1.61641e11	+	1.61641e11i	0.857055	+	0.857055i	0.990990	−	0.133935i	$-0.0427614\pi$
$659$	1.61641e11	+	1.61641e11i	0.857055	+	0.857055i	−0.133935	+	0.990990i	$0.542761\pi$
$660$			2.22749e10i			0.117392i
$661$	1.16819e11			0.611940			0.305970	−	0.952041i	$-0.401019\pi$
$661$	1.16819e11			0.611940			0.305970	+	0.952041i	$0.401019\pi$
$662$	1.65253e11			0.860435
$663$	−8.61553e9			−0.0445890
$664$	4.09484e11	−	4.09484e11i	2.10652	−	2.10652i
$665$	4.89266e10	−	4.89266e10i	0.250183	−	0.250183i
$666$		−	2.08767e10i		−	0.106112i
$667$	2.30163e11	+	1.57279e11i	1.16287	+	0.794635i
$668$	9.14101e9			0.0459080
$669$	−2.49309e9	−	2.49309e9i	−0.0124461	−	0.0124461i
$670$	3.59819e11	+	3.59819e11i	1.78560	+	1.78560i
$671$		−	1.34935e11i		−	0.665632i
$672$		−	4.13538e9i		−	0.0202786i
$673$		−	2.46972e11i		−	1.20389i	−0.798536	−	0.601947i	$-0.794392\pi$
$673$		−	2.46972e11i		−	1.20389i	0.798536	−	0.601947i	$-0.205608\pi$
$674$	−9.39420e10			−0.455219
$675$	1.31210e9	−	1.31210e9i	0.00632050	−	0.00632050i
$676$		−	6.21563e11i		−	2.97645i
$677$	3.20893e10	−	3.20893e10i	0.152759	−	0.152759i	−0.626590	−	0.779349i	$-0.715550\pi$
$677$	3.20893e10	−	3.20893e10i	0.152759	−	0.152759i	0.779349	+	0.626590i	$0.215550\pi$
$678$	2.49959e10	+	2.49959e10i	0.118290	+	0.118290i
$679$	−4.52513e10	+	4.52513e10i	−0.212888	+	0.212888i
$680$		−	1.13426e11i		−	0.530488i
$681$	1.30703e10	+	1.30703e10i	0.0607709	+	0.0607709i
$682$	4.38440e10	−	4.38440e10i	0.202662	−	0.202662i
$683$	3.02953e9			0.0139217			0.00696085	−	0.999976i	$-0.497784\pi$
$683$	3.02953e9			0.0139217			0.00696085	+	0.999976i	$0.497784\pi$
$684$	−3.58893e11	−	3.58893e11i	−1.63961	−	1.63961i
$685$	−8.87279e10	+	8.87279e10i	−0.402993	+	0.402993i
$686$	−1.73787e11	−	1.73787e11i	−0.784733	−	0.784733i
$687$	−1.24386e10			−0.0558397
$688$	−8.13291e10	−	8.13291e10i	−0.362988	−	0.362988i
$689$		−	4.69148e10i		−	0.208177i
$690$	−6.01974e10			−0.265572
$691$	1.26829e11			0.556298			0.278149	−	0.960538i	$-0.410279\pi$
$691$	1.26829e11			0.556298			0.278149	+	0.960538i	$0.410279\pi$
$692$	−1.23520e11			−0.538657
$693$	−2.74190e10	+	2.74190e10i	−0.118883	+	0.118883i
$694$	3.73161e10	−	3.73161e10i	0.160864	−	0.160864i
$695$		−	3.13056e11i		−	1.34178i
$696$	−4.28408e10	−	2.92748e10i	−0.182566	−	0.124755i
$697$	6.24553e10			0.264630
$698$	3.22583e11	+	3.22583e11i	1.35900	+	1.35900i
$699$	−5.25302e9	−	5.25302e9i	−0.0220039	−	0.0220039i
$700$			7.06778e9i			0.0294368i
$701$		−	5.63110e10i		−	0.233196i	−0.993179	−	0.116598i	$-0.962801\pi$
$701$		−	5.63110e10i		−	0.233196i	0.993179	−	0.116598i	$-0.0371989\pi$
$702$			1.43627e11i			0.591410i
$703$	−1.61452e10			−0.0661030
$704$	4.14855e10	−	4.14855e10i	0.168891	−	0.168891i
$705$			1.13927e10i			0.0461181i
$706$	−2.30729e11	+	2.30729e11i	−0.928719	+	0.928719i
$707$	−1.04529e11	−	1.04529e11i	−0.418370	−	0.418370i
$708$	6.49826e10	−	6.49826e10i	0.258621	−	0.258621i
$709$			1.07390e11i			0.424989i	0.977162	+	0.212494i	$0.0681588\pi$
$709$			1.07390e11i			0.424989i	−0.977162	+	0.212494i	$0.931841\pi$
$710$	2.84181e11	+	2.84181e11i	1.11831	+	1.11831i
$711$	−1.98179e11	+	1.98179e11i	−0.775495	+	0.775495i
$712$	−8.63299e10			−0.335924
$713$	8.08506e10	+	8.08506e10i	0.312842	+	0.312842i
$714$	−3.11429e9	+	3.11429e9i	−0.0119830	+	0.0119830i
$715$	1.43708e11	+	1.43708e11i	0.549865	+	0.549865i
$716$	−2.75045e11			−1.04653
$717$	4.55514e9	+	4.55514e9i	0.0172355	+	0.0172355i
$718$			3.32710e10i			0.125190i
$719$	−2.49655e11			−0.934166			−0.467083	−	0.884213i	$-0.654695\pi$
$719$	−2.49655e11			−0.934166			−0.467083	+	0.884213i	$0.654695\pi$
$720$	−3.81291e11			−1.41882
$721$	1.67578e11			0.620121
$722$	−6.58301e10	+	6.58301e10i	−0.242257	+	0.242257i
$723$	−2.42039e10	+	2.42039e10i	−0.0885794	+	0.0885794i
$724$			5.17428e11i			1.88319i
$725$	9.44815e9	+	6.45629e9i	0.0341975	+	0.0233685i
$726$	3.93546e10			0.141660
$727$	1.40969e11	+	1.40969e11i	0.504644	+	0.504644i	0.912877	−	0.408234i	$-0.133855\pi$
$727$	1.40969e11	+	1.40969e11i	0.504644	+	0.504644i	−0.408234	+	0.912877i	$0.633855\pi$
$728$	−2.06757e11	−	2.06757e11i	−0.736095	−	0.736095i
$729$			2.62661e11i			0.930004i
$730$			7.12676e11i			2.50958i
$731$			2.65858e10i			0.0931064i
$732$	−8.66532e10			−0.301815
$733$	2.71627e11	−	2.71627e11i	0.940931	−	0.940931i	−0.0574196	−	0.998350i	$-0.518287\pi$
$733$	2.71627e11	−	2.71627e11i	0.940931	−	0.940931i	0.998350	+	0.0574196i	$0.0182873\pi$
$734$			7.04243e11i			2.42627i
$735$	1.95300e10	−	1.95300e10i	0.0669196	−	0.0669196i
$736$	−1.65026e11	−	1.65026e11i	−0.562396	−	0.562396i
$737$	−1.55945e11	+	1.55945e11i	−0.528569	+	0.528569i
$738$		−	5.17504e11i		−	1.74457i
$739$	−3.28043e11	−	3.28043e11i	−1.09990	−	1.09990i	−0.994422	−	0.105476i	$-0.966363\pi$
$739$	−3.28043e11	−	3.28043e11i	−1.09990	−	1.09990i	−0.105476	−	0.994422i	$-0.533637\pi$
$740$	−2.69884e10	+	2.69884e10i	−0.0900014	+	0.0900014i
$741$	5.52085e10			0.183119
$742$	−1.69585e10	−	1.69585e10i	−0.0559462	−	0.0559462i
$743$	2.71803e11	−	2.71803e11i	0.891864	−	0.891864i	−0.102834	−	0.994699i	$-0.532791\pi$
$743$	2.71803e11	−	2.71803e11i	0.891864	−	0.891864i	0.994699	+	0.102834i	$0.0327911\pi$
$744$	−1.50489e10	−	1.50489e10i	−0.0491150	−	0.0491150i
$745$	−1.70889e11			−0.554738
$746$	−1.79824e11	−	1.79824e11i	−0.580620	−	0.580620i
$747$			4.49972e11i			1.44512i
$748$	9.19737e10			0.293804
$749$	−5.38924e9			−0.0171238
$750$	−6.21316e10			−0.196367
$751$	7.34609e10	−	7.34609e10i	0.230939	−	0.230939i	−0.582146	−	0.813084i	$-0.697787\pi$
$751$	7.34609e10	−	7.34609e10i	0.230939	−	0.230939i	0.813084	+	0.582146i	$0.197787\pi$
$752$	−1.43904e11	+	1.43904e11i	−0.449989	+	0.449989i
$753$		−	4.96436e10i		−	0.154413i
$754$	−8.70481e11	+	1.63750e11i	−2.69323	+	0.506637i
$755$	2.43021e11			0.747921
$756$	3.54261e10	+	3.54261e10i	0.108452	+	0.108452i
$757$	−2.17996e11	−	2.17996e11i	−0.663842	−	0.663842i	0.292441	−	0.956284i	$-0.405532\pi$
$757$	−2.17996e11	−	2.17996e11i	−0.663842	−	0.663842i	−0.956284	+	0.292441i	$0.905532\pi$
$758$		−	2.50360e11i		−	0.758383i
$759$		−	2.60895e10i		−	0.0786137i
$760$			7.26834e11i			2.17862i
$761$	4.32924e11			1.29084			0.645421	−	0.763827i	$-0.276682\pi$
$761$	4.32924e11			1.29084			0.645421	+	0.763827i	$0.276682\pi$
$762$	−8.35723e10	+	8.35723e10i	−0.247881	+	0.247881i
$763$		−	7.32630e10i		−	0.216166i
$764$	−2.65757e10	+	2.65757e10i	−0.0780029	+	0.0780029i
$765$	6.23203e10	+	6.23203e10i	0.181963	+	0.181963i
$766$	2.49497e11	−	2.49497e11i	0.724686	−	0.724686i
$767$		−	8.38479e11i		−	2.42276i
$768$	−5.33945e10	−	5.33945e10i	−0.153480	−	0.153480i
$769$	3.96199e11	−	3.96199e11i	1.13294	−	1.13294i	0.143258	−	0.989685i	$-0.454242\pi$
$769$	3.96199e11	−	3.96199e11i	1.13294	−	1.13294i	0.989685	−	0.143258i	$-0.0457580\pi$
$770$	1.03893e11			0.295545
$771$	1.89658e10	+	1.89658e10i	0.0536729	+	0.0536729i
$772$	5.18818e11	−	5.18818e11i	1.46065	−	1.46065i
$773$	2.74933e11	+	2.74933e11i	0.770031	+	0.770031i	0.978112	−	0.208081i	$-0.0667216\pi$
$773$	2.74933e11	+	2.74933e11i	0.770031	+	0.770031i	−0.208081	+	0.978112i	$0.566722\pi$
$774$	2.20289e11			0.613803
$775$	3.31891e9	+	3.31891e9i	0.00920001	+	0.00920001i
$776$		−	6.72236e11i		−	1.85385i
$777$	7.92117e8			0.00217323
$778$	−9.91982e11			−2.70761
$779$	−4.00215e11			−1.08678
$780$	9.22869e10	−	9.22869e10i	0.249323	−	0.249323i
$781$	−1.23164e11	+	1.23164e11i	−0.331039	+	0.331039i
$782$			2.48557e11i			0.664660i
$783$	7.97185e10	−	1.49962e10i	0.212086	−	0.0398965i
$784$	4.93376e11			1.30591
$785$	−3.35289e11	−	3.35289e11i	−0.882958	−	0.882958i
$786$	−1.03936e10	−	1.03936e10i	−0.0272319	−	0.0272319i
$787$			5.44016e11i			1.41812i	0.705149	+	0.709059i	$0.250880\pi$
$787$			5.44016e11i			1.41812i	−0.705149	+	0.709059i	$0.749120\pi$
$788$		−	1.38749e12i		−	3.59853i
$789$			7.86894e10i			0.203053i
$790$	7.50917e11			1.92790
$791$	7.95518e10	−	7.95518e10i	0.203210	−	0.203210i
$792$		−	4.07327e11i		−	1.03524i
$793$	−5.59049e11	+	5.59049e11i	−1.41370	+	1.41370i
$794$	1.46107e11	+	1.46107e11i	0.367610	+	0.367610i
$795$	4.04579e9	−	4.04579e9i	0.0101283	−	0.0101283i
$796$			7.58194e11i			1.88855i
$797$	−4.69297e11	−	4.69297e11i	−1.16309	−	1.16309i	−0.983795	−	0.179297i	$-0.942618\pi$
$797$	−4.69297e11	−	4.69297e11i	−1.16309	−	1.16309i	−0.179297	−	0.983795i	$-0.557382\pi$
$798$	1.99564e10	−	1.99564e10i	0.0492120	−	0.0492120i
$799$	4.70410e10			0.115422
$800$	−6.77431e9	−	6.77431e9i	−0.0165388	−	0.0165388i
$801$	4.74329e10	−	4.74329e10i	0.115226	−	0.115226i
$802$	6.96894e11	+	6.96894e11i	1.68449	+	1.68449i
$803$	−3.08873e11			−0.742878
$804$	1.00146e11	+	1.00146e11i	0.239667	+	0.239667i
$805$			1.91584e11i			0.456222i
$806$	−3.63300e11			−0.860847
$807$	−4.93679e10			−0.116399
$808$	1.55285e12			3.64320
$809$	7.82623e10	−	7.82623e10i	0.182709	−	0.182709i	−0.609826	−	0.792535i	$-0.708761\pi$
$809$	7.82623e10	−	7.82623e10i	0.182709	−	0.182709i	0.792535	+	0.609826i	$0.208761\pi$
$810$	5.10155e11	−	5.10155e11i	1.18512	−	1.18512i
$811$		−	2.62005e11i		−	0.605655i	−0.953045	−	0.302828i	$-0.902069\pi$
$811$		−	2.62005e11i		−	0.605655i	0.953045	−	0.302828i	$-0.0979307\pi$
$812$	−1.74317e11	+	2.55096e11i	−0.400974	+	0.586786i
$813$	−1.24581e10			−0.0285160
$814$	−1.71417e10	−	1.71417e10i	−0.0390442	−	0.0390442i
$815$	5.57042e11	+	5.57042e11i	1.26258	+	1.26258i
$816$		−	1.87694e10i		−	0.0423341i
$817$		−	1.70362e11i		−	0.382371i
$818$		−	7.77808e10i		−	0.173724i
$819$	2.27200e11			0.504978
$820$	−6.69002e11	+	6.69002e11i	−1.47970	+	1.47970i
$821$			5.72636e11i			1.26039i	0.776436	+	0.630196i	$0.217026\pi$
$821$			5.72636e11i			1.26039i	−0.776436	+	0.630196i	$0.782974\pi$
$822$	−3.61908e10	+	3.61908e10i	−0.0792704	+	0.0792704i
$823$	−1.06952e11	−	1.06952e11i	−0.233125	−	0.233125i	0.580871	−	0.813996i	$-0.302712\pi$
$823$	−1.06952e11	−	1.06952e11i	−0.233125	−	0.233125i	−0.813996	+	0.580871i	$0.802712\pi$
$824$	−1.24474e12	+	1.24474e12i	−2.70003	+	2.70003i
$825$		−	1.07097e9i		−	0.00231186i
$826$	−3.03088e11	−	3.03088e11i	−0.651102	−	0.651102i
$827$	−4.41988e11	+	4.41988e11i	−0.944905	+	0.944905i	−0.998560	−	0.0536545i	$-0.982913\pi$
$827$	−4.41988e11	+	4.41988e11i	−0.944905	+	0.944905i	0.0536545	+	0.998560i	$0.482913\pi$
$828$	1.40534e12			2.98991
$829$	−4.59189e11	−	4.59189e11i	−0.972239	−	0.972239i	0.0273859	−	0.999625i	$-0.491282\pi$
$829$	−4.59189e11	−	4.59189e11i	−0.972239	−	0.972239i	−0.999625	+	0.0273859i	$0.991282\pi$
$830$	8.52492e11	−	8.52492e11i	1.79630	−	1.79630i
$831$	−5.78647e10	−	5.78647e10i	−0.121342	−	0.121342i
$832$	−3.43757e11			−0.717395
$833$	−8.06402e10	−	8.06402e10i	−0.167483	−	0.167483i
$834$		−	1.27691e11i		−	0.263934i
$835$	1.01714e10			0.0209236
$836$	−5.89369e11			−1.20660
$837$	3.32710e10			0.0677897
$838$	−2.70746e11	+	2.70746e11i	−0.549017	+	0.549017i
$839$	1.09481e11	−	1.09481e11i	0.220949	−	0.220949i	−0.587949	−	0.808898i	$-0.700065\pi$
$839$	1.09481e11	−	1.09481e11i	0.220949	−	0.220949i	0.808898	+	0.587949i	$0.200065\pi$
$840$		−	3.56601e10i		−	0.0716251i
$841$	1.81775e11	+	4.66052e11i	0.363371	+	0.931645i
$842$	9.41237e11			1.87262
$843$	−7.33405e10	−	7.33405e10i	−0.145222	−	0.145222i
$844$	7.58557e11	+	7.58557e11i	1.49492	+	1.49492i
$845$		−	6.91629e11i		−	1.35658i
$846$		−	3.89781e11i		−	0.760920i
$847$		−	1.25250e11i		−	0.243357i
$848$	1.02206e11			0.197649
$849$	1.48725e10	−	1.48725e10i	0.0286254	−	0.0286254i
$850$			1.02032e10i			0.0195462i
$851$	3.16102e10	−	3.16102e10i	0.0602710	−	0.0602710i
$852$	7.90940e10	+	7.90940e10i	0.150101	+	0.150101i
$853$	−1.18637e11	+	1.18637e11i	−0.224090	+	0.224090i	−0.810218	−	0.586128i	$-0.800652\pi$
$853$	−1.18637e11	+	1.18637e11i	−0.224090	+	0.224090i	0.586128	+	0.810218i	$0.300652\pi$
$854$			4.04163e11i			0.759845i
$855$	−3.99350e11	−	3.99350e11i	−0.747290	−	0.747290i
$856$	4.00302e10	−	4.00302e10i	0.0745578	−	0.0745578i
$857$	−8.17055e11			−1.51471			−0.757353	−	0.653006i	$-0.773508\pi$
$857$	−8.17055e11			−1.51471			−0.757353	+	0.653006i	$0.773508\pi$
$858$	5.86163e10	+	5.86163e10i	0.108161	+	0.108161i
$859$	−2.73943e11	+	2.73943e11i	−0.503139	+	0.503139i	−0.912412	−	0.409273i	$-0.865782\pi$
$859$	−2.73943e11	+	2.73943e11i	−0.503139	+	0.503139i	0.409273	+	0.912412i	$0.365782\pi$
$860$	−2.84779e11	−	2.84779e11i	−0.520611	−	0.520611i
$861$	1.96354e10			0.0357296
$862$	−1.24220e12	−	1.24220e12i	−2.24990	−	2.24990i
$863$		−	7.79012e10i		−	0.140443i	−0.997531	−	0.0702217i	$-0.977629\pi$
$863$		−	7.79012e10i		−	0.140443i	0.997531	−	0.0702217i	$-0.0223707\pi$
$864$	−6.79103e10			−0.121865
$865$	−1.37444e11			−0.245505
$866$	−9.11217e11			−1.62013
$867$	4.02994e10	−	4.02994e10i	0.0713217	−	0.0713217i
$868$	−8.96092e10	+	8.96092e10i	−0.157861	+	0.157861i
$869$			3.25446e11i			0.570690i
$870$	−8.91889e10	−	6.09463e10i	−0.155680	−	0.106383i
$871$	1.29219e12			2.24520
$872$	5.44183e11	+	5.44183e11i	0.941194	+	0.941194i
$873$	3.69352e11	+	3.69352e11i	0.635892	+	0.635892i
$874$		−	1.59276e12i		−	2.72964i
$875$			1.97740e11i			0.337335i
$876$			1.98354e11i			0.336840i
$877$	5.68325e11			0.960723			0.480361	−	0.877071i	$-0.340505\pi$
$877$	5.68325e11			0.960723			0.480361	+	0.877071i	$0.340505\pi$
$878$	6.53757e11	−	6.53757e11i	1.10012	−	1.10012i
$879$		−	3.91571e10i		−	0.0655927i
$880$	−3.13075e11	+	3.13075e11i	−0.522057	+	0.522057i
$881$	3.87500e11	+	3.87500e11i	0.643232	+	0.643232i	0.951349	−	0.308116i	$-0.0996986\pi$
$881$	3.87500e11	+	3.87500e11i	0.643232	+	0.643232i	−0.308116	+	0.951349i	$0.599699\pi$
$882$	−6.68183e11	+	6.68183e11i	−1.10413	+	1.10413i
$883$			6.67133e10i			0.109741i	0.998493	+	0.0548706i	$0.0174746\pi$
$883$			6.67133e10i			0.109741i	−0.998493	+	0.0548706i	$0.982525\pi$
$884$	−3.81056e11	−	3.81056e11i	−0.623993	−	0.623993i
$885$	7.23078e10	−	7.23078e10i	0.117872	−	0.117872i
$886$	8.32879e11			1.35160
$887$	−5.47503e11	−	5.47503e11i	−0.884489	−	0.884489i	0.109498	−	0.993987i	$-0.465076\pi$
$887$	−5.47503e11	−	5.47503e11i	−0.884489	−	0.884489i	−0.993987	+	0.109498i	$0.965076\pi$
$888$	−5.88369e9	+	5.88369e9i	−0.00946233	+	0.00946233i
$889$	2.65977e11	+	2.65977e11i	0.425831	+	0.425831i
$890$	−1.79727e11			−0.286453
$891$	2.21101e11	+	2.21101e11i	0.350816	+	0.350816i
$892$		−	2.20534e11i		−	0.348350i
$893$	−3.01440e11			−0.474018
$894$	−6.97030e10			−0.109119
$895$	−3.06050e11			−0.476980
$896$	−2.09404e11	+	2.09404e11i	−0.324902	+	0.324902i
$897$	−1.08091e11	+	1.08091e11i	−0.166963	+	0.166963i
$898$		−	7.93306e11i		−	1.21993i
$899$	3.79324e10	+	2.01645e11i	0.0580727	+	0.308709i
$900$	5.76888e10			0.0879269
$901$	−1.67052e10	−	1.67052e10i	−0.0253485	−	0.0253485i
$902$	−4.24918e11	−	4.24918e11i	−0.641918	−	0.641918i
$903$			8.35835e9i			0.0125710i
$904$			1.18179e12i			1.76957i
$905$			5.75755e11i			0.858309i
$906$	9.91247e10			0.147119
$907$	−6.44186e10	+	6.44186e10i	−0.0951881	+	0.0951881i	−0.753097	−	0.657909i	$-0.771441\pi$
$907$	−6.44186e10	+	6.44186e10i	−0.0951881	+	0.0951881i	0.657909	+	0.753097i	$0.271441\pi$
$908$			1.15617e12i			1.70090i
$909$	−8.53192e11	+	8.53192e11i	−1.24966	+	1.24966i
$910$	−4.30440e11	−	4.30440e11i	−0.627692	−	0.627692i
$911$	4.14334e11	−	4.14334e11i	0.601557	−	0.601557i	−0.339168	−	0.940726i	$-0.610146\pi$
$911$	4.14334e11	−	4.14334e11i	0.601557	−	0.601557i	0.940726	+	0.339168i	$0.110146\pi$
$912$			1.20275e11i			0.173858i
$913$	3.69469e11	+	3.69469e11i	0.531734	+	0.531734i
$914$	1.31458e12	−	1.31458e12i	1.88365	−	1.88365i
$915$	−9.64213e10			−0.137559
$916$	−5.50144e11	−	5.50144e11i	−0.781439	−	0.781439i
$917$	−3.30787e10	+	3.30787e10i	−0.0467812	+	0.0467812i
$918$	5.11422e10	+	5.11422e10i	0.0720126	+	0.0720126i
$919$	6.05657e11			0.849111			0.424556	−	0.905402i	$-0.360430\pi$
$919$	6.05657e11			0.849111			0.424556	+	0.905402i	$0.360430\pi$
$920$	−1.42305e12	−	1.42305e12i	−1.98641	−	1.98641i
$921$			4.82090e9i			0.00670023i
$922$	−2.21730e11			−0.306832
$923$	1.02056e12			1.40615
$924$	2.89158e10			0.0396686
$925$	1.29759e9	−	1.29759e9i	0.00177244	−	0.00177244i
$926$	−1.79694e12	+	1.79694e12i	−2.44394	+	2.44394i
$927$		−	1.36781e12i		−	1.85228i
$928$	−7.74249e10	−	4.11583e11i	−0.104397	−	0.554965i
$929$	−1.06537e12			−1.43033			−0.715165	−	0.698955i	$-0.753649\pi$
$929$	−1.06537e12			−1.43033			−0.715165	+	0.698955i	$0.753649\pi$
$930$	−3.13299e10	−	3.13299e10i	−0.0418820	−	0.0418820i
$931$	5.16744e11	+	5.16744e11i	0.687823	+	0.687823i
$932$		−	4.64671e11i		−	0.615860i
$933$			6.28378e10i			0.0829267i
$934$			4.32263e11i			0.568016i
$935$	1.02341e11			0.133908
$936$	−1.68759e12	+	1.68759e12i	−2.19869	+	2.19869i
$937$		−	2.74262e11i		−	0.355802i	−0.984048	−	0.177901i	$-0.943069\pi$
$937$		−	2.74262e11i		−	0.355802i	0.984048	−	0.177901i	$-0.0569306\pi$
$938$	4.67094e11	−	4.67094e11i	0.603382	−	0.603382i
$939$	6.42695e10	+	6.42695e10i	0.0826689	+	0.0826689i
$940$	−5.03888e11	+	5.03888e11i	−0.645391	+	0.645391i
$941$			1.19059e10i			0.0151846i	0.999971	+	0.00759232i	$0.00241673\pi$
$941$			1.19059e10i			0.0151846i	−0.999971	+	0.00759232i	$0.997583\pi$
$942$	−1.36759e11	−	1.36759e11i	−0.173681	−	0.173681i
$943$	7.83571e11	−	7.83571e11i	0.990904	−	0.990904i
$944$	1.82667e12			2.30024
$945$	3.94196e10	+	3.94196e10i	0.0494293	+	0.0494293i
$946$	1.80878e11	−	1.80878e11i	0.225850	−	0.225850i
$947$	5.16974e11	+	5.16974e11i	0.642790	+	0.642790i	0.951240	−	0.308451i	$-0.0998105\pi$
$947$	5.16974e11	+	5.16974e11i	0.642790	+	0.642790i	−0.308451	+	0.951240i	$0.599811\pi$
$948$	2.08997e11			0.258766
$949$	1.27969e12	+	1.27969e12i	1.57776	+	1.57776i
$950$		−	6.53826e10i		−	0.0802727i
$951$	−1.49981e11			−0.183364
$952$	−1.47242e11			−0.179260
$953$	2.87469e10			0.0348514			0.0174257	−	0.999848i	$-0.494453\pi$
$953$	2.87469e10			0.0348514			0.0174257	+	0.999848i	$0.494453\pi$
$954$	−1.38419e11	+	1.38419e11i	−0.167110	+	0.167110i
$955$	−2.95714e10	+	2.95714e10i	−0.0355516	+	0.0355516i
$956$			4.02938e11i			0.482399i
$957$	2.64140e10	−	3.86544e10i	0.0314910	−	0.0460840i
$958$	−8.66282e11			−1.02848
$959$	1.15181e11	+	1.15181e11i	0.136178	+	0.136178i
$960$	−2.96445e10	−	2.96445e10i	−0.0349028	−	0.0349028i
$961$		−	7.68733e11i		−	0.901326i
$962$			1.42040e11i			0.165848i
$963$			4.39882e10i			0.0511483i
$964$	−2.14103e12			−2.47922
$965$	5.77303e11	−	5.77303e11i	0.665724	−	0.665724i
$966$			7.81444e10i			0.0897406i
$967$	−4.03310e11	+	4.03310e11i	−0.461246	+	0.461246i	−0.899064	−	0.437818i	$-0.855752\pi$
$967$	−4.03310e11	+	4.03310e11i	−0.461246	+	0.461246i	0.437818	+	0.899064i	$0.355752\pi$
$968$	9.30330e11	+	9.30330e11i	1.05958	+	1.05958i
$969$	1.96584e10	−	1.96584e10i	0.0222973	−	0.0222973i
$970$		−	1.39951e12i		−	1.58084i
$971$	1.09888e12	+	1.09888e12i	1.23616	+	1.23616i	0.961558	+	0.274602i	$0.0885461\pi$
$971$	1.09888e12	+	1.09888e12i	1.23616	+	1.23616i	0.274602	+	0.961558i	$0.411454\pi$
$972$	4.34591e11	−	4.34591e11i	0.486873	−	0.486873i
$973$	−4.06389e11			−0.453409
$974$	6.72304e11	+	6.72304e11i	0.747016	+	0.747016i
$975$	−4.43713e9	+	4.43713e9i	−0.00491003	+	0.00491003i
$976$	−1.21792e12	−	1.21792e12i	−1.34221	−	1.34221i
$977$	−7.05096e11			−0.773874			−0.386937	−	0.922106i	$-0.626467\pi$
$977$	−7.05096e11			−0.773874			−0.386937	+	0.922106i	$0.626467\pi$
$978$	2.27209e11	+	2.27209e11i	0.248354	+	0.248354i
$979$		−	7.78936e10i		−	0.0847951i
$980$	1.72759e12			1.87299
$981$	−5.97990e11			−0.645681
$982$	2.20233e12			2.36829
$983$	−7.63183e11	+	7.63183e11i	−0.817362	+	0.817362i	−0.985725	−	0.168363i	$-0.946152\pi$
$983$	−7.63183e11	+	7.63183e11i	−0.817362	+	0.817362i	0.168363	+	0.985725i	$0.446152\pi$
$984$	−1.45848e11	+	1.45848e11i	−0.155568	+	0.155568i
$985$		−	1.54390e12i		−	1.64011i
$986$	−2.51649e11	+	3.68264e11i	−0.266249	+	0.389629i
$987$	1.47893e10			0.0155840
$988$	2.44182e12	+	2.44182e12i	2.56262	+	2.56262i
$989$	3.33548e11	+	3.33548e11i	0.348636	+	0.348636i
$990$		−	8.48000e11i		−	0.882785i
$991$		−	3.96472e11i		−	0.411072i	−0.978650	−	0.205536i	$-0.934106\pi$
$991$		−	3.96472e11i		−	0.411072i	0.978650	−	0.205536i	$-0.0658937\pi$
$992$		−	1.71777e11i		−	0.177385i
$993$	5.11783e10			0.0526368
$994$	3.68906e11	−	3.68906e11i	0.377894	−	0.377894i
$995$			8.43663e11i			0.860749i
$996$	2.37267e11	−	2.37267e11i	0.241102	−	0.241102i
$997$	−4.87383e11	−	4.87383e11i	−0.493276	−	0.493276i	0.416061	−	0.909337i	$-0.363410\pi$
$997$	−4.87383e11	−	4.87383e11i	−0.493276	−	0.493276i	−0.909337	+	0.416061i	$0.863410\pi$
$998$	1.11576e12	−	1.11576e12i	1.12473	−	1.12473i
$999$		−	1.30080e10i		−	0.0130601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.c.a.12.19	✓	38
29.17	odd	4	inner	29.9.c.a.17.19	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.c.a.12.19	✓	38	1.1	even	1	trivial
29.9.c.a.17.19	yes	38	29.17	odd	4	inner

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(20.0740 + 20.0740i) q^{2} +(6.21683 + 6.21683i) q^{3} +549.928i q^{4} +611.920i q^{5} +249.593i q^{6} +794.354 q^{7} +(-5900.31 + 5900.31i) q^{8} -6483.70i q^{9} +O(q^{10})\)	\(q+(20.0740 + 20.0740i) q^{2} +(6.21683 + 6.21683i) q^{3} +549.928i q^{4} +611.920i q^{5} +249.593i q^{6} +794.354 q^{7} +(-5900.31 + 5900.31i) q^{8} -6483.70i q^{9} +(-12283.7 + 12283.7i) q^{10} +(-5323.72 - 5323.72i) q^{11} +(-3418.81 + 3418.81i) q^{12} +44113.4i q^{13} +(15945.8 + 15945.8i) q^{14} +(-3804.20 + 3804.20i) q^{15} -96103.5 q^{16} +(15707.7 + 15707.7i) q^{17} +(130154. - 130154. i) q^{18} +(-100655. - 100655. i) q^{19} -336512. q^{20} +(4938.37 + 4938.37i) q^{21} -213736. i q^{22} +394140. q^{23} -73362.5 q^{24} +16179.4 q^{25} +(-885531. + 885531. i) q^{26} +(81096.8 - 81096.8i) q^{27} +436838. i q^{28} +(583961. + 399044. i) q^{29} -152731. q^{30} +(205131. + 205131. i) q^{31} +(-418699. - 418699. i) q^{32} -66193.4i q^{33} +630631. i q^{34} +486081. i q^{35} +3.56557e6 q^{36} +(80200.3 - 80200.3i) q^{37} -4.04110e6i q^{38} +(-274246. + 274246. i) q^{39} +(-3.61051e6 - 3.61051e6i) q^{40} +(1.98805e6 - 1.98805e6i) q^{41} +198265. i q^{42} +(846266. + 846266. i) q^{43} +(2.92766e6 - 2.92766e6i) q^{44} +3.96750e6 q^{45} +(7.91196e6 + 7.91196e6i) q^{46} +(1.49739e6 - 1.49739e6i) q^{47} +(-597459. - 597459. i) q^{48} -5.13380e6 q^{49} +(324785. + 324785. i) q^{50} +195304. i q^{51} -2.42592e7 q^{52} -1.06350e6 q^{53} +3.25587e6 q^{54} +(3.25769e6 - 3.25769e6i) q^{55} +(-4.68693e6 + 4.68693e6i) q^{56} -1.25151e6i q^{57} +(3.71203e6 + 1.97328e7i) q^{58} -1.90074e7 q^{59} +(-2.09204e6 - 2.09204e6i) q^{60} +(1.26730e7 + 1.26730e7i) q^{61} +8.23560e6i q^{62} -5.15035e6i q^{63} +7.79257e6i q^{64} -2.69939e7 q^{65} +(1.32876e6 - 1.32876e6i) q^{66} -2.92925e7i q^{67} +(-8.63810e6 + 8.63810e6i) q^{68} +(2.45031e6 + 2.45031e6i) q^{69} +(-9.75757e6 + 9.75757e6i) q^{70} -2.31349e7i q^{71} +(3.82558e7 + 3.82558e7i) q^{72} +(2.90091e7 - 2.90091e7i) q^{73} +3.21988e6 q^{74} +(100585. + 100585. i) q^{75} +(5.53531e7 - 5.53531e7i) q^{76} +(-4.22892e6 - 4.22892e6i) q^{77} -1.10104e7 q^{78} +(-3.05657e7 - 3.05657e7i) q^{79} -5.88076e7i q^{80} -4.15312e7 q^{81} +7.98161e7 q^{82} -6.94005e7 q^{83} +(-2.71575e6 + 2.71575e6i) q^{84} +(-9.61184e6 + 9.61184e6i) q^{85} +3.39758e7i q^{86} +(1.14960e6 + 6.11118e6i) q^{87} +6.28231e7 q^{88} +(7.31571e6 + 7.31571e6i) q^{89} +(7.96435e7 + 7.96435e7i) q^{90} +3.50417e7i q^{91} +2.16749e8i q^{92} +2.55054e6i q^{93} +6.01170e7 q^{94} +(6.15929e7 - 6.15929e7i) q^{95} -5.20597e6i q^{96} +(-5.69662e7 + 5.69662e7i) q^{97} +(-1.03056e8 - 1.03056e8i) q^{98} +(-3.45174e7 + 3.45174e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8 + 15870 * q^10 - 8390 * q^11 + 5022 * q^12 + 12728 * q^14 - 35530 * q^15 - 245912 * q^16 + 76234 * q^17 - 465022 * q^18 - 164488 * q^19 + 4092 * q^20 - 514620 * q^21 + 733568 * q^23 - 482376 * q^24 - 1528354 * q^25 + 1405470 * q^26 - 1279754 * q^27 + 1420996 * q^29 + 3659852 * q^30 + 291062 * q^31 + 1592134 * q^32 - 10223688 * q^36 + 7994574 * q^37 - 309930 * q^39 + 9093994 * q^40 + 9561658 * q^41 - 5181022 * q^43 - 11400526 * q^44 + 9526060 * q^45 - 32561820 * q^46 + 5445034 * q^47 - 17683542 * q^48 + 45106458 * q^49 + 3122002 * q^50 + 56198616 * q^52 - 25331452 * q^53 - 42307016 * q^54 + 3037606 * q^55 - 25661184 * q^56 - 33846328 * q^58 + 27333008 * q^59 + 30592014 * q^60 - 49572406 * q^61 - 121974972 * q^65 + 133443354 * q^66 + 21192980 * q^68 - 28739184 * q^69 - 17976124 * q^70 - 186114192 * q^72 + 45787870 * q^73 + 91919252 * q^74 - 159074460 * q^75 + 243795016 * q^76 + 59851916 * q^77 + 163580208 * q^78 - 99827470 * q^79 - 75138586 * q^81 - 18178416 * q^82 - 177270160 * q^83 - 9436684 * q^84 + 156307616 * q^85 - 20584526 * q^87 + 563433236 * q^88 - 388451858 * q^89 + 306402752 * q^90 + 81569204 * q^94 - 44386260 * q^95 - 121157834 * q^97 - 129908712 * q^98 - 216447384 * q^99

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