LMFDB - Embedded newform 81.10.e.a.10.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,10,Mod(10,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, not 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:	$41.7179027293$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			10.15
Character	$\chi$	$=$	81.10
Dual form			81.10.e.a.73.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.907148 + 5.14469i) q^{2} +(455.478 - 165.780i) q^{4} +(1094.11 + 918.064i) q^{5} +(184.507 + 67.1550i) q^{7} +(2603.43 + 4509.28i) q^{8} +(-3730.64 + 6461.66i) q^{10} +(-59207.7 + 49681.1i) q^{11} +(-14755.5 + 83682.5i) q^{13} +(-178.117 + 1010.15i) q^{14} +(169273. - 142037. i) q^{16} +(-291379. + 504684. i) q^{17} +(-252779. - 437826. i) q^{19} +(650538. + 236776. i) q^{20} +(-309304. - 259537. i) q^{22} +(-670872. + 244178. i) q^{23} +(15070.2 + 85467.2i) q^{25} -443906. q^{26} +95171.7 q^{28} +(-201386. - 1.14212e6i) q^{29} +(8.13347e6 - 2.96034e6i) q^{31} +(2.92650e6 + 2.45563e6i) q^{32} +(-2.86077e6 - 1.04123e6i) q^{34} +(140217. + 242864. i) q^{35} +(-9.87736e6 + 1.71081e7i) q^{37} +(2.02317e6 - 1.69764e6i) q^{38} +(-1.29137e6 + 7.32375e6i) q^{40} +(103793. - 588640. i) q^{41} +(-1.41194e7 + 1.18476e7i) q^{43} +(-1.87316e7 + 3.24441e7i) q^{44} +(-1.86480e6 - 3.22993e6i) q^{46} +(3.64648e7 + 1.32721e7i) q^{47} +(-3.08831e7 - 2.59140e7i) q^{49} +(-426031. + 155063. i) q^{50} +(7.15212e6 + 4.05617e7i) q^{52} -5.57694e7 q^{53} -1.10390e8 q^{55} +(177531. + 1.00683e6i) q^{56} +(5.69316e6 - 2.07214e6i) q^{58} +(5.19028e7 + 4.35516e7i) q^{59} +(-3.83125e7 - 1.39446e7i) q^{61} +(2.26083e7 + 3.91588e7i) q^{62} +(4.65897e7 - 8.06957e7i) q^{64} +(-9.29700e7 + 7.80111e7i) q^{65} +(-2.13517e7 + 1.21092e8i) q^{67} +(-4.90502e7 + 2.78177e8i) q^{68} +(-1.12226e6 + 941689. i) q^{70} +(1.76388e7 - 3.05513e7i) q^{71} +(6.85145e7 + 1.18671e8i) q^{73} +(-9.69761e7 - 3.52964e7i) q^{74} +(-1.87718e8 - 1.57514e8i) q^{76} +(-1.42606e7 + 5.19042e6i) q^{77} +(4.61143e7 + 2.61527e8i) q^{79} +3.15602e8 q^{80} +3.12253e6 q^{82} +(6.64650e7 + 3.76941e8i) q^{83} +(-7.82133e8 + 2.84673e8i) q^{85} +(-7.37607e7 - 6.18926e7i) q^{86} +(-3.78169e8 - 1.37642e8i) q^{88} +(-1.46572e8 - 2.53870e8i) q^{89} +(-8.34219e6 + 1.44491e7i) q^{91} +(-2.65087e8 + 2.22435e8i) q^{92} +(-3.52019e7 + 1.99640e8i) q^{94} +(1.25385e8 - 7.11096e8i) q^{95} +(6.70759e8 - 5.62834e8i) q^{97} +(1.05304e8 - 1.82392e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) $ 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.907148	+	5.14469i	0.0400907	+	0.227365i	0.998270	−	0.0588046i	$-0.0187289\pi$
$2$	0.907148	+	5.14469i	0.0400907	+	0.227365i	−0.958179	+	0.286170i	$0.907618\pi$
$3$		0			0
$3$		0			0
$4$	455.478	−	165.780i	0.889605	−	0.323790i
$5$	1094.11	+	918.064i	0.782879	+	0.656913i	0.943972	−	0.330026i	$-0.107057\pi$
$5$	1094.11	+	918.064i	0.782879	+	0.656913i	−0.161093	+	0.986939i	$0.551502\pi$
$6$		0			0
$7$	184.507	+	67.1550i	0.0290450	+	0.0105715i	0.356502	−	0.934295i	$-0.383969\pi$
$7$	184.507	+	67.1550i	0.0290450	+	0.0105715i	−0.327457	+	0.944866i	$0.606192\pi$
$8$	2603.43	+	4509.28i	0.224720	+	0.389226i
$9$		0			0
$10$	−3730.64	+	6461.66i	−0.117973	+	0.204336i
$11$	−59207.7	+	49681.1i	−1.21930	+	1.02311i	−0.220440	+	0.975401i	$0.570749\pi$
$11$	−59207.7	+	49681.1i	−1.21930	+	1.02311i	−0.998861	+	0.0477142i	$0.984806\pi$
$12$		0			0
$13$	−14755.5	+	83682.5i	−0.143288	+	0.812624i	0.825439	+	0.564492i	$0.190928\pi$
$13$	−14755.5	+	83682.5i	−0.143288	+	0.812624i	−0.968726	+	0.248132i	$0.920183\pi$
$14$	−178.117	+	1010.15i	−0.00123916	+	0.00702764i
$15$		0			0
$16$	169273.	−	142037.i	0.645725	−	0.541828i
$17$	−291379.	+	504684.i	−0.846133	+	1.46555i	0.0385000	+	0.999259i	$0.487742\pi$
$17$	−291379.	+	504684.i	−0.846133	+	1.46555i	−0.884633	+	0.466287i	$0.845591\pi$
$18$		0			0
$19$	−252779.	−	437826.i	−0.444989	−	0.770744i	0.553062	−	0.833140i	$-0.313459\pi$
$19$	−252779.	−	437826.i	−0.444989	−	0.770744i	−0.998051	+	0.0623957i	$0.980126\pi$
$20$	650538.	+	236776.i	0.909154	+	0.330905i
$21$		0			0
$22$	−309304.	−	259537.i	−0.281504	−	0.236209i
$23$	−670872.	+	244178.i	−0.499879	+	0.181941i	−0.579639	−	0.814873i	$-0.696807\pi$
$23$	−670872.	+	244178.i	−0.499879	+	0.181941i	0.0797608	+	0.996814i	$0.474584\pi$
$24$		0			0
$25$	15070.2	+	85467.2i	0.00771593	+	0.0437592i
$26$	−443906.			−0.190507
$27$		0			0
$28$	95171.7			0.0292615
$29$	−201386.	−	1.14212e6i	−0.0528736	−	0.299861i	0.946891	−	0.321555i	$-0.104205\pi$
$29$	−201386.	−	1.14212e6i	−0.0528736	−	0.299861i	−0.999765	+	0.0216934i	$0.993094\pi$
$30$		0			0
$31$	8.13347e6	−	2.96034e6i	1.58179	−	0.575724i	0.606197	−	0.795315i	$-0.292694\pi$
$31$	8.13347e6	−	2.96034e6i	1.58179	−	0.575724i	0.975592	+	0.219591i	$0.0704722\pi$
$32$	2.92650e6	+	2.45563e6i	0.493371	+	0.413988i
$33$		0			0
$34$	−2.86077e6	−	1.04123e6i	−0.367137	−	0.133627i
$35$	140217.	+	242864.i	0.0157941	+	0.0273562i
$36$		0			0
$37$	−9.87736e6	+	1.71081e7i	−0.866429	+	1.50070i	−0.000808066		1.00000i	$0.500257\pi$
$37$	−9.87736e6	+	1.71081e7i	−0.866429	+	1.50070i	−0.865621	+	0.500700i	$0.833076\pi$
$38$	2.02317e6	−	1.69764e6i	0.157401	−	0.132075i
$39$		0			0
$40$	−1.29137e6	+	7.32375e6i	−0.0797595	+	0.452338i
$41$	103793.	−	588640.i	0.00573643	−	0.0325329i	−0.981805	−	0.189891i	$-0.939187\pi$
$41$	103793.	−	588640.i	0.00573643	−	0.0325329i	0.987542	+	0.157358i	$0.0502977\pi$
$42$		0			0
$43$	−1.41194e7	+	1.18476e7i	−0.629809	+	0.528473i	−0.900870	−	0.434090i	$-0.857070\pi$
$43$	−1.41194e7	+	1.18476e7i	−0.629809	+	0.528473i	0.271060	+	0.962562i	$0.412626\pi$
$44$	−1.87316e7	+	3.24441e7i	−0.753422	+	1.30496i
$45$		0			0
$46$	−1.86480e6	−	3.22993e6i	−0.0614075	−	0.106361i
$47$	3.64648e7	+	1.32721e7i	1.09002	+	0.396734i	0.823628	−	0.567131i	$-0.191947\pi$
$47$	3.64648e7	+	1.32721e7i	1.09002	+	0.396734i	0.266391	+	0.963865i	$0.414169\pi$
$48$		0			0
$49$	−3.08831e7	−	2.59140e7i	−0.765313	−	0.642174i
$50$	−426031.	+	155063.i	−0.00963999	+	0.00350867i
$51$		0			0
$52$	7.15212e6	+	4.05617e7i	0.135650	+	0.769310i
$53$	−5.57694e7			−0.970856			−0.485428	−	0.874277i	$-0.661336\pi$
$53$	−5.57694e7			−0.970856			−0.485428	+	0.874277i	$0.661336\pi$
$54$		0			0
$55$	−1.10390e8			−1.62666
$56$	177531.	+	1.00683e6i	0.00241228	+	0.0136807i
$57$		0			0
$58$	5.69316e6	−	2.07214e6i	0.0660583	−	0.0240433i
$59$	5.19028e7	+	4.35516e7i	0.557643	+	0.467918i	0.877519	−	0.479541i	$-0.159197\pi$
$59$	5.19028e7	+	4.35516e7i	0.557643	+	0.467918i	−0.319876	+	0.947459i	$0.603641\pi$
$60$		0			0
$61$	−3.83125e7	−	1.39446e7i	−0.354288	−	0.128950i	0.158744	−	0.987320i	$-0.449256\pi$
$61$	−3.83125e7	−	1.39446e7i	−0.354288	−	0.128950i	−0.513032	+	0.858369i	$0.671478\pi$
$62$	2.26083e7	+	3.91588e7i	0.194315	+	0.336563i
$63$		0			0
$64$	4.65897e7	−	8.06957e7i	0.347120	−	0.601230i
$65$	−9.29700e7	+	7.80111e7i	−0.646001	+	0.542059i
$66$		0			0
$67$	−2.13517e7	+	1.21092e8i	−0.129448	+	0.734138i	0.849118	+	0.528204i	$0.177134\pi$
$67$	−2.13517e7	+	1.21092e8i	−0.129448	+	0.734138i	−0.978566	+	0.205934i	$0.933977\pi$
$68$	−4.90502e7	+	2.78177e8i	−0.278196	+	1.57773i
$69$		0			0
$70$	−1.12226e6	+	941689.i	−0.00558667	+	0.00468777i
$71$	1.76388e7	−	3.05513e7i	0.0823772	−	0.142681i	−0.821893	−	0.569641i	$-0.807082\pi$
$71$	1.76388e7	−	3.05513e7i	0.0823772	−	0.142681i	0.904271	+	0.426960i	$0.140415\pi$
$72$		0			0
$73$	6.85145e7	+	1.18671e8i	0.282377	+	0.489092i	0.971970	−	0.235106i	$-0.0755437\pi$
$73$	6.85145e7	+	1.18671e8i	0.282377	+	0.489092i	−0.689592	+	0.724198i	$0.742210\pi$
$74$	−9.69761e7	−	3.52964e7i	−0.375943	−	0.136832i
$75$		0			0
$76$	−1.87718e8	−	1.57514e8i	−0.645424	−	0.541575i
$77$	−1.42606e7	+	5.19042e6i	−0.0462304	+	0.0168265i
$78$		0			0
$79$	4.61143e7	+	2.61527e8i	0.133203	+	0.755432i	0.976094	+	0.217348i	$0.0697406\pi$
$79$	4.61143e7	+	2.61527e8i	0.133203	+	0.755432i	−0.842891	+	0.538084i	$0.819148\pi$
$80$	3.15602e8			0.861458
$81$		0			0
$82$	3.12253e6			0.00762683
$83$	6.64650e7	+	3.76941e8i	0.153724	+	0.871811i	0.959943	+	0.280195i	$0.0903990\pi$
$83$	6.64650e7	+	3.76941e8i	0.153724	+	0.871811i	−0.806219	+	0.591617i	$0.798490\pi$
$84$		0			0
$85$	−7.82133e8	+	2.84673e8i	−1.62516	+	0.591509i
$86$	−7.37607e7	−	6.18926e7i	−0.145406	−	0.122010i
$87$		0			0
$88$	−3.78169e8	−	1.37642e8i	−0.672224	−	0.244670i
$89$	−1.46572e8	−	2.53870e8i	−0.247626	−	0.428901i	0.715241	−	0.698878i	$-0.246317\pi$
$89$	−1.46572e8	−	2.53870e8i	−0.247626	−	0.428901i	−0.962867	+	0.269977i	$0.912984\pi$
$90$		0			0
$91$	−8.34219e6	+	1.44491e7i	−0.0127525	+	0.0220879i
$92$	−2.65087e8	+	2.22435e8i	−0.385784	+	0.323711i
$93$		0			0
$94$	−3.52019e7	+	1.99640e8i	−0.0465041	+	0.263738i
$95$	1.25385e8	−	7.11096e8i	0.157939	−	0.895719i
$96$		0			0
$97$	6.70759e8	−	5.62834e8i	0.769297	−	0.645517i	−0.171232	−	0.985231i	$-0.554775\pi$
$97$	6.70759e8	−	5.62834e8i	0.769297	−	0.645517i	0.940529	+	0.339714i	$0.110330\pi$
$98$	1.05304e8	−	1.82392e8i	0.115326	−	0.199751i
$99$		0			0
$100$	2.10329e7	+	3.64301e7i	0.0210329	+	0.0364301i
$101$	1.40731e9	+	5.12217e8i	1.34568	+	0.489788i	0.911597	−	0.411085i	$-0.134850\pi$
$101$	1.40731e9	+	5.12217e8i	1.34568	+	0.489788i	0.434084	+	0.900872i	$0.357072\pi$
$102$		0			0
$103$	7.47118e8	+	6.26906e8i	0.654066	+	0.548826i	0.908302	−	0.418316i	$-0.137379\pi$
$103$	7.47118e8	+	6.26906e8i	0.654066	+	0.548826i	−0.254236	+	0.967142i	$0.581824\pi$
$104$	−4.15763e8	+	1.51325e8i	−0.348494	+	0.126842i
$105$		0			0
$106$	−5.05911e7	−	2.86917e8i	−0.0389223	−	0.220739i
$107$	−7.88612e8			−0.581616			−0.290808	−	0.956781i	$-0.593924\pi$
$107$	−7.88612e8			−0.581616			−0.290808	+	0.956781i	$0.593924\pi$
$108$		0			0
$109$	2.62080e9			1.77834			0.889168	−	0.457580i	$-0.151284\pi$
$109$	2.62080e9			1.77834			0.889168	+	0.457580i	$0.151284\pi$
$110$	−1.00140e8	−	5.67922e8i	−0.0652140	−	0.369847i
$111$		0			0
$112$	4.07705e7	−	1.48392e7i	0.0244830	−	0.00891109i
$113$	−8.06387e8	−	6.76639e8i	−0.465255	−	0.390395i	0.379805	−	0.925066i	$-0.375991\pi$
$113$	−8.06387e8	−	6.76639e8i	−0.465255	−	0.390395i	−0.845060	+	0.534671i	$0.820435\pi$
$114$		0			0
$115$	−9.58176e8	−	3.48748e8i	−0.510864	−	0.185939i
$116$	−2.81068e8	−	4.86824e8i	−0.144129	−	0.249638i
$117$		0			0
$118$	−1.76976e8	+	3.06531e8i	−0.0840321	+	0.145548i
$119$	−8.76535e7	+	7.35500e7i	−0.0400690	+	0.0336219i
$120$		0			0
$121$	6.27879e8	−	3.56088e9i	0.266282	−	1.51016i
$122$	3.69857e7	−	2.09756e8i	0.0151152	−	0.0857226i
$123$		0			0
$124$	3.21385e9	−	2.69674e9i	1.22075	−	1.02433i
$125$	1.33280e9	−	2.30848e9i	0.488282	−	0.845730i
$126$		0			0
$127$	1.21542e9	+	2.10516e9i	0.414580	+	0.718074i	0.995384	−	0.0959694i	$-0.0305951\pi$
$127$	1.21542e9	+	2.10516e9i	0.414580	+	0.718074i	−0.580804	+	0.814043i	$0.697262\pi$
$128$	2.29544e9	+	8.35472e8i	0.755825	+	0.275098i
$129$		0			0
$130$	−4.85681e8	−	4.07535e8i	−0.149144	−	0.125147i
$131$	−1.07316e9	+	3.90600e8i	−0.318379	+	0.115881i	−0.496266	−	0.868170i	$-0.665296\pi$
$131$	−1.07316e9	+	3.90600e8i	−0.318379	+	0.115881i	0.177887	+	0.984051i	$0.443074\pi$
$132$		0			0
$133$	−1.72372e7	−	9.77572e7i	−0.00477678	−	0.0270905i
$134$	−6.42348e8			−0.172107
$135$		0			0
$136$	−3.03435e9			−0.760572
$137$	−9.74321e8	−	5.52565e9i	−0.236298	−	1.34011i	−0.839863	−	0.542798i	$-0.817365\pi$
$137$	−9.74321e8	−	5.52565e9i	−0.236298	−	1.34011i	0.603566	−	0.797313i	$-0.293746\pi$
$138$		0			0
$139$	−5.57686e8	+	2.02981e8i	−0.126714	+	0.0461199i	−0.404599	−	0.914494i	$-0.632589\pi$
$139$	−5.57686e8	+	2.02981e8i	−0.126714	+	0.0461199i	0.277885	+	0.960614i	$0.410367\pi$
$140$	1.04128e8	+	8.73737e7i	0.0229082	+	0.0192223i
$141$		0			0
$142$	1.73178e8	+	6.30317e7i	0.0357434	+	0.0130095i
$143$	−3.28381e9	−	5.68772e9i	−0.656697	−	1.13743i
$144$		0			0
$145$	8.28200e8	−	1.43448e9i	0.155589	−	0.269488i
$146$	−5.48371e8	+	4.60138e8i	−0.0998819	+	0.0838109i
$147$		0			0
$148$	−1.66273e9	+	9.42982e9i	−0.284869	+	1.61557i
$149$	−7.28046e8	+	4.12896e9i	−0.121010	+	0.686281i	0.862588	+	0.505907i	$0.168842\pi$
$149$	−7.28046e8	+	4.12896e9i	−0.121010	+	0.686281i	−0.983598	+	0.180374i	$0.942269\pi$
$150$		0			0
$151$	3.26376e9	−	2.73862e9i	0.510883	−	0.428682i	−0.350557	−	0.936541i	$-0.614008\pi$
$151$	3.26376e9	−	2.73862e9i	0.510883	−	0.428682i	0.861440	+	0.507860i	$0.169563\pi$
$152$	1.31619e9	−	2.27970e9i	0.199996	−	0.346403i
$153$		0			0
$154$	−3.96395e7	−	6.86577e7i	−0.00567917	−	0.00983662i
$155$	1.16167e10	+	4.22812e9i	1.61655	+	0.588376i
$156$		0			0
$157$	−8.53048e9	−	7.15792e9i	−1.12053	−	0.940240i	−0.121903	−	0.992542i	$-0.538900\pi$
$157$	−8.53048e9	−	7.15792e9i	−1.12053	−	0.940240i	−0.998631	+	0.0523023i	$0.983344\pi$
$158$	−1.30365e9	+	4.74488e8i	−0.166419	+	0.0605715i
$159$		0			0
$160$	9.47481e8	+	5.37343e9i	0.114296	+	0.648204i
$161$	−1.40178e8			−0.0164424
$162$		0			0
$163$	1.05778e10			1.17368			0.586841	−	0.809702i	$-0.300371\pi$
$163$	1.05778e10			1.17368			0.586841	+	0.809702i	$0.300371\pi$
$164$	−5.03095e7	−	2.85319e8i	−0.00543066	−	0.0307988i
$165$		0			0
$166$	−1.87895e9	+	6.83883e8i	−0.192057	+	0.0699030i
$167$	−8.54492e8	−	7.17004e8i	−0.0850127	−	0.0713341i	0.599291	−	0.800531i	$-0.295449\pi$
$167$	−8.54492e8	−	7.17004e8i	−0.0850127	−	0.0713341i	−0.684304	+	0.729197i	$0.739894\pi$
$168$		0			0
$169$	3.17993e9	+	1.15740e9i	0.299866	+	0.109142i
$170$	−2.17406e9	−	3.76559e9i	−0.199642	−	0.345790i
$171$		0			0
$172$	−4.46698e9	+	7.73704e9i	−0.389167	+	0.674058i
$173$	−3.54444e9	+	2.97414e9i	−0.300843	+	0.252438i	−0.780695	−	0.624912i	$-0.785135\pi$
$173$	−3.54444e9	+	2.97414e9i	−0.300843	+	0.252438i	0.479852	+	0.877350i	$0.340690\pi$
$174$		0			0
$175$	−2.95900e6	+	1.67813e7i	−0.000238492	+	0.00135255i
$176$	−2.96570e9	+	1.68193e10i	−0.232981	+	1.32130i
$177$		0			0
$178$	1.17312e9	−	9.84366e8i	0.0875897	−	0.0734965i
$179$	2.67969e9	−	4.64136e9i	0.195095	−	0.337914i	−0.751837	−	0.659349i	$-0.770832\pi$
$179$	2.67969e9	−	4.64136e9i	0.195095	−	0.337914i	0.946932	+	0.321435i	$0.104165\pi$
$180$		0			0
$181$	7.67576e9	+	1.32948e10i	0.531579	+	0.920722i	0.999321	+	0.0368569i	$0.0117346\pi$
$181$	7.67576e9	+	1.32948e10i	0.531579	+	0.920722i	−0.467741	+	0.883865i	$0.654932\pi$
$182$	−8.19037e7	−	2.98105e7i	−0.00553328	−	0.00201395i
$183$		0			0
$184$	−2.84764e9	−	2.38945e9i	−0.183149	−	0.153680i
$185$	−2.65132e10	+	9.65002e9i	−1.66414	+	0.605697i
$186$		0			0
$187$	−7.82138e9	−	4.43572e10i	−0.467731	−	2.65263i
$188$	1.88092e10			1.09814
$189$		0			0
$190$	3.77211e9			0.209987
$191$	5.44011e9	+	3.08524e10i	0.295772	+	1.67741i	0.664048	+	0.747690i	$0.268837\pi$
$191$	5.44011e9	+	3.08524e10i	0.295772	+	1.67741i	−0.368276	+	0.929717i	$0.620052\pi$
$192$		0			0
$193$	−3.41260e10	+	1.24208e10i	−1.77042	+	0.644381i	−0.770447	+	0.637504i	$0.779967\pi$
$193$	−3.41260e10	+	1.24208e10i	−1.77042	+	0.644381i	−0.999976	+	0.00687698i	$0.997811\pi$
$194$	3.50408e9	+	2.94028e9i	0.177610	+	0.149032i
$195$		0			0
$196$	−1.83626e10	−	6.68344e9i	−0.888755	−	0.323480i
$197$	−1.35995e9	−	2.35550e9i	−0.0643316	−	0.111426i	0.832066	−	0.554677i	$-0.187158\pi$
$197$	−1.35995e9	−	2.35550e9i	−0.0643316	−	0.111426i	−0.896397	+	0.443252i	$0.853825\pi$
$198$		0			0
$199$	−9.70133e9	+	1.68032e10i	−0.438523	+	0.759544i	−0.997576	−	0.0695878i	$-0.977832\pi$
$199$	−9.70133e9	+	1.68032e10i	−0.438523	+	0.759544i	0.559053	+	0.829132i	$0.311165\pi$
$200$	−3.46161e8	+	2.90464e8i	−0.0152983	+	0.0128368i
$201$		0			0
$202$	−1.35857e9	+	7.70481e9i	−0.0574116	+	0.325597i
$203$	3.95418e7	−	2.24253e8i	0.00163427	−	0.00926842i
$204$		0			0
$205$	6.53970e8	−	5.48746e8i	0.0258622	−	0.0217010i
$206$	−2.54749e9	+	4.41239e9i	−0.0985622	+	0.170715i
$207$		0			0
$208$	9.38830e9	+	1.62610e10i	0.347778	+	0.602369i
$209$	3.67181e10	+	1.33643e10i	1.33114	+	0.484494i
$210$		0			0
$211$	1.69339e10	+	1.42092e10i	0.588146	+	0.493513i	0.887611	−	0.460595i	$-0.152364\pi$
$211$	1.69339e10	+	1.42092e10i	0.588146	+	0.493513i	−0.299465	+	0.954107i	$0.596808\pi$
$212$	−2.54017e10	+	9.24548e9i	−0.863678	+	0.314353i
$213$		0			0
$214$	−7.15388e8	−	4.05717e9i	−0.0233174	−	0.132239i
$215$	−2.63250e10			−0.840225
$216$		0			0
$217$	1.69948e9			0.0520293
$218$	2.37745e9	+	1.34832e10i	0.0712947	+	0.404332i
$219$		0			0
$220$	−5.02802e10	+	1.83005e10i	−1.44709	+	0.526696i
$221$	−3.79338e10	−	3.18302e10i	−1.06970	−	0.897583i
$222$		0			0
$223$	2.67249e10	+	9.72708e9i	0.723677	+	0.263397i	0.677486	−	0.735536i	$-0.263070\pi$
$223$	2.67249e10	+	9.72708e9i	0.723677	+	0.263397i	0.0461909	+	0.998933i	$0.485292\pi$
$224$	3.75052e8	+	6.49609e8i	0.00995349	+	0.0172399i
$225$		0			0
$226$	2.74959e9	−	4.76243e9i	0.0701099	−	0.121434i
$227$	2.46971e10	−	2.07233e10i	0.617348	−	0.518016i	−0.279621	−	0.960111i	$-0.590209\pi$
$227$	2.46971e10	−	2.07233e10i	0.617348	−	0.518016i	0.896969	+	0.442094i	$0.145764\pi$
$228$		0			0
$229$	2.77859e9	−	1.57582e10i	0.0667675	−	0.378657i	−0.933053	−	0.359738i	$-0.882866\pi$
$229$	2.77859e9	−	1.57582e10i	0.0667675	−	0.378657i	0.999821	−	0.0189197i	$-0.00602269\pi$
$230$	9.24991e8	−	5.24589e9i	0.0217953	−	0.123607i
$231$		0			0
$232$	4.62583e9	−	3.88154e9i	0.104832	−	0.0879646i
$233$	3.18571e10	−	5.51781e10i	0.708117	−	1.22649i	−0.257438	−	0.966295i	$-0.582878\pi$
$233$	3.18571e10	−	5.51781e10i	0.708117	−	1.22649i	0.965555	−	0.260199i	$-0.0837883\pi$
$234$		0			0
$235$	2.77118e10	+	4.79982e10i	0.592732	+	1.02664i
$236$	3.08605e10	+	1.12323e10i	0.647589	+	0.235703i
$237$		0			0
$238$	−4.57907e8	−	3.84230e8i	−0.00925084	−	0.00776238i
$239$	2.13641e10	−	7.77591e9i	0.423540	−	0.154156i	−0.121452	−	0.992597i	$-0.538755\pi$
$239$	2.13641e10	−	7.77591e9i	0.423540	−	0.154156i	0.544992	+	0.838441i	$0.316533\pi$
$240$		0			0
$241$	−1.27437e10	−	7.22729e10i	−0.243342	−	1.38006i	−0.824311	−	0.566137i	$-0.808437\pi$
$241$	−1.27437e10	−	7.22729e10i	−0.243342	−	1.38006i	0.580969	−	0.813926i	$-0.302674\pi$
$242$	1.88892e10			0.354034
$243$		0			0
$244$	−1.97622e10			−0.356929
$245$	−9.99869e9	−	5.67054e10i	−0.177295	−	1.00549i
$246$		0			0
$247$	4.03683e10	−	1.46928e10i	0.690087	−	0.251171i
$248$	3.45240e10	+	2.89690e10i	0.579546	+	0.486297i
$249$		0			0
$250$	1.30855e10	+	4.76273e9i	0.211865	+	0.0771127i
$251$	−5.54071e10	−	9.59678e10i	−0.881117	−	1.52614i	−0.850101	−	0.526620i	$-0.823459\pi$
$251$	−5.54071e10	−	9.59678e10i	−0.881117	−	1.52614i	−0.0310157	−	0.999519i	$-0.509874\pi$
$252$		0			0
$253$	2.75898e10	−	4.77869e10i	0.423356	−	0.733274i
$254$	−9.72786e9	+	8.16264e9i	−0.146644	+	0.123049i
$255$		0			0
$256$	6.06844e9	−	3.44158e10i	0.0883074	−	0.500816i
$257$	−1.07212e10	+	6.08031e10i	−0.153301	+	0.869414i	0.807021	+	0.590522i	$0.201078\pi$
$257$	−1.07212e10	+	6.08031e10i	−0.153301	+	0.869414i	−0.960322	+	0.278892i	$0.910033\pi$
$258$		0			0
$259$	−2.97133e9	+	2.49324e9i	−0.0410301	+	0.0344283i
$260$	−2.94131e10	+	5.09449e10i	−0.399172	+	0.691386i
$261$		0			0
$262$	−2.98303e9	−	5.16676e9i	−0.0391113	−	0.0677428i
$263$	−1.21927e11	−	4.43779e10i	−1.57145	−	0.571960i	−0.598126	−	0.801402i	$-0.704088\pi$
$263$	−1.21927e11	−	4.43779e10i	−1.57145	−	0.571960i	−0.973322	+	0.229442i	$0.926310\pi$
$264$		0			0
$265$	−6.10177e10	−	5.11999e10i	−0.760063	−	0.637768i
$266$	4.87294e8	−	1.77361e8i	0.00596793	−	0.00217215i
$267$		0			0
$268$	1.03494e10	+	5.86942e10i	0.122548	+	0.695007i
$269$	4.04716e10			0.471265			0.235632	−	0.971842i	$-0.424284\pi$
$269$	4.04716e10			0.471265			0.235632	+	0.971842i	$0.424284\pi$
$270$		0			0
$271$	1.12341e11			1.26525			0.632624	−	0.774459i	$-0.281978\pi$
$271$	1.12341e11			1.26525			0.632624	+	0.774459i	$0.281978\pi$
$272$	2.23611e10	+	1.26816e11i	0.247704	+	1.40480i
$273$		0			0
$274$	2.75439e10	−	1.00252e10i	0.295222	−	0.107452i
$275$	−5.13837e9	−	4.31161e9i	−0.0541787	−	0.0454613i
$276$		0			0
$277$	1.43770e11	+	5.23281e10i	1.46727	+	0.534042i	0.947357	−	0.320178i	$-0.103743\pi$
$277$	1.43770e11	+	5.23281e10i	1.46727	+	0.534042i	0.519912	+	0.854220i	$0.325965\pi$
$278$	−1.55018e9	−	2.68499e9i	−0.0155661	−	0.0269613i
$279$		0			0
$280$	−7.30094e8	+	1.26456e9i	−0.00709851	+	0.0122950i
$281$	1.22477e11	−	1.02770e11i	1.17186	−	0.983308i	0.171863	−	0.985121i	$-0.445021\pi$
$281$	1.22477e11	−	1.02770e11i	1.17186	−	0.983308i	0.999998	+	0.00181261i	$0.000576971\pi$
$282$		0			0
$283$	−2.63028e9	+	1.49170e10i	−0.0243760	+	0.138243i	−0.994567	−	0.104098i	$-0.966804\pi$
$283$	−2.63028e9	+	1.49170e10i	−0.0243760	+	0.138243i	0.970191	+	0.242341i	$0.0779154\pi$
$284$	2.96928e9	−	1.68396e10i	0.0270843	−	0.153603i
$285$		0			0
$286$	2.62827e10	−	2.20538e10i	0.232286	−	0.194911i
$287$	5.86807e7	−	1.01638e8i	0.000510536	−	0.000884274i
$288$		0			0
$289$	−1.10510e11	−	1.91409e11i	−0.931883	−	1.61407i
$290$	8.13128e9	+	2.95954e9i	0.0675100	+	0.0245716i
$291$		0			0
$292$	5.08801e10	+	4.26935e10i	0.409567	+	0.343668i
$293$	1.10660e10	−	4.02770e9i	0.0877176	−	0.0319266i	−0.297789	−	0.954632i	$-0.596249\pi$
$293$	1.10660e10	−	4.02770e9i	0.0877176	−	0.0319266i	0.385506	+	0.922705i	$0.374027\pi$
$294$		0			0
$295$	1.68040e10	+	9.53001e10i	0.129185	+	0.732646i
$296$	−1.02860e11			−0.778815
$297$		0			0
$298$	−2.19027e10			−0.160888
$299$	−1.05343e10	−	5.97433e10i	−0.0762232	−	0.432283i
$300$		0			0
$301$	−3.40076e9	+	1.23777e9i	−0.0238796	+	0.00869145i
$302$	1.70500e10	+	1.43067e10i	0.117949	+	0.0989710i
$303$		0			0
$304$	−1.04976e11	−	3.82082e10i	−0.704951	−	0.256581i
$305$	−2.91159e10	−	5.04303e10i	−0.192655	−	0.333689i
$306$		0			0
$307$	−4.49450e10	+	7.78470e10i	−0.288774	+	0.500172i	−0.973517	−	0.228613i	$-0.926581\pi$
$307$	−4.49450e10	+	7.78470e10i	−0.288774	+	0.500172i	0.684743	+	0.728784i	$0.259914\pi$
$308$	−5.63489e9	+	4.72824e9i	−0.0356786	+	0.0299379i
$309$		0			0
$310$	−1.12143e10	+	6.35997e10i	−0.0689678	+	0.391136i
$311$	4.08938e10	−	2.31921e11i	0.247877	−	1.40578i	−0.565838	−	0.824516i	$-0.691447\pi$
$311$	4.08938e10	−	2.31921e11i	0.247877	−	1.40578i	0.813715	−	0.581264i	$-0.197442\pi$
$312$		0			0
$313$	8.39524e10	−	7.04444e10i	0.494406	−	0.414856i	−0.361196	−	0.932490i	$-0.617632\pi$
$313$	8.39524e10	−	7.04444e10i	0.494406	−	0.414856i	0.855602	+	0.517634i	$0.173187\pi$
$314$	2.90869e10	−	5.03800e10i	0.168855	−	0.292466i
$315$		0			0
$316$	6.43601e10	+	1.11475e11i	0.363099	+	0.628906i
$317$	−1.22053e11	−	4.44236e10i	−0.678862	−	0.247086i	−0.0205033	−	0.999790i	$-0.506527\pi$
$317$	−1.22053e11	−	4.44236e10i	−0.678862	−	0.247086i	−0.658359	+	0.752704i	$0.728749\pi$
$318$		0			0
$319$	6.86653e10	+	5.76171e10i	0.371261	+	0.311525i
$320$	1.25058e11	−	4.55174e10i	0.666709	−	0.242662i
$321$		0			0
$322$	−1.27162e8	−	7.21174e8i	−0.000659185	−	0.00373842i
$323$	2.94618e11			1.50608
$324$		0			0
$325$	−7.37448e9			−0.0366654
$326$	9.59562e9	+	5.44194e10i	0.0470537	+	0.266855i
$327$		0			0
$328$	2.92456e9	−	1.06445e9i	0.0139517	−	0.00507802i
$329$	5.83672e9	+	4.89759e9i	0.0274655	+	0.0230463i
$330$		0			0
$331$	−3.81934e11	−	1.39012e11i	−1.74889	−	0.636543i	−0.749220	−	0.662322i	$-0.769571\pi$
$331$	−3.81934e11	−	1.39012e11i	−1.74889	−	0.636543i	−0.999668	+	0.0257789i	$0.991793\pi$
$332$	9.27628e10	+	1.60670e11i	0.419037	+	0.725793i
$333$		0			0
$334$	2.91361e9	−	5.04653e9i	0.0128107	−	0.0221888i
$335$	−1.34531e11	+	1.12885e11i	−0.583607	+	0.489705i
$336$		0			0
$337$	2.99839e10	−	1.70047e11i	0.126635	−	0.718182i	−0.853688	−	0.520784i	$-0.825640\pi$
$337$	2.99839e10	−	1.70047e11i	0.126635	−	0.718182i	0.980323	−	0.197398i	$-0.0632492\pi$
$338$	−3.06979e9	+	1.74097e10i	−0.0127933	+	0.0725547i
$339$		0			0
$340$	−3.09051e11	+	2.59324e11i	−1.25422	+	1.05242i
$341$	−3.34491e11	+	5.79355e11i	−1.33964	+	2.32033i
$342$		0			0
$343$	−7.91957e9	−	1.37171e10i	−0.0308943	−	0.0535104i
$344$	−9.01831e10	−	3.28240e10i	−0.347226	−	0.126380i
$345$		0			0
$346$	−1.85164e10	−	1.55371e10i	−0.0694566	−	0.0582810i
$347$	−1.03578e11	+	3.76992e10i	−0.383517	+	0.139589i	−0.526581	−	0.850125i	$-0.676526\pi$
$347$	−1.03578e11	+	3.76992e10i	−0.383517	+	0.139589i	0.143065	+	0.989713i	$0.454304\pi$
$348$		0			0
$349$	3.42227e10	+	1.94087e11i	0.123481	+	0.700295i	0.982198	+	0.187846i	$0.0601506\pi$
$349$	3.42227e10	+	1.94087e11i	0.123481	+	0.700295i	−0.858718	+	0.512449i	$0.828738\pi$
$350$	−8.90189e7			−0.000317085
$351$		0			0
$352$	−2.95270e11			−1.02512
$353$	5.02315e10	+	2.84877e11i	0.172183	+	0.976498i	0.941345	+	0.337445i	$0.109563\pi$
$353$	5.02315e10	+	2.84877e11i	0.172183	+	0.976498i	−0.769162	+	0.639054i	$0.779326\pi$
$354$		0			0
$355$	4.73468e10	−	1.72328e10i	0.158221	−	0.0575876i
$356$	−1.08847e11	−	9.13335e10i	−0.359163	−	0.301374i
$357$		0			0
$358$	2.63093e10	+	9.57578e9i	0.0846515	+	0.0308106i
$359$	5.82567e10	+	1.00903e11i	0.185106	+	0.320613i	0.943612	−	0.331053i	$-0.107404\pi$
$359$	5.82567e10	+	1.00903e11i	0.185106	+	0.320613i	−0.758506	+	0.651666i	$0.774070\pi$
$360$		0			0
$361$	3.35494e10	−	5.81093e10i	0.103969	−	0.180079i
$362$	−6.14347e10	+	5.15498e10i	−0.188029	+	0.157775i
$363$		0			0
$364$	−1.40431e9	+	7.96421e9i	−0.00419281	+	0.0237786i
$365$	−3.39851e10	+	1.92739e11i	−0.100224	+	0.568397i
$366$		0			0
$367$	9.61611e10	−	8.06888e10i	0.276696	−	0.232175i	−0.493870	−	0.869536i	$-0.664418\pi$
$367$	9.61611e10	−	8.06888e10i	0.276696	−	0.232175i	0.770566	+	0.637360i	$0.219974\pi$
$368$	−7.88783e10	+	1.36621e11i	−0.224204	+	0.388332i
$369$		0			0
$370$	−7.36978e10	−	1.27648e11i	−0.204431	−	0.354085i
$371$	−1.02898e10	−	3.74520e9i	−0.0281985	−	0.0102634i
$372$		0			0
$373$	4.11578e11	+	3.45355e11i	1.10094	+	0.923796i	0.997488	−	0.0708391i	$-0.0225677\pi$
$373$	4.11578e11	+	3.45355e11i	1.10094	+	0.923796i	0.103449	+	0.994635i	$0.467012\pi$
$374$	2.21109e11	−	8.04771e10i	0.584365	−	0.212692i
$375$		0			0
$376$	3.50861e10	+	1.98983e11i	0.0905294	+	0.513418i
$377$	9.85469e10			0.251251
$378$		0			0
$379$	−4.25777e11			−1.06000			−0.530000	−	0.847997i	$-0.677808\pi$
$379$	−4.25777e11			−1.06000			−0.530000	+	0.847997i	$0.677808\pi$
$380$	−6.07754e10	−	3.44675e11i	−0.149521	−	0.847975i
$381$		0			0
$382$	−1.53791e11	+	5.59753e10i	−0.369527	+	0.134497i
$383$	3.30812e11	+	2.77584e11i	0.785573	+	0.659174i	0.944646	−	0.328093i	$-0.106406\pi$
$383$	3.30812e11	+	2.77584e11i	0.785573	+	0.659174i	−0.159072	+	0.987267i	$0.550850\pi$
$384$		0			0
$385$	−2.03677e10	−	7.41323e9i	−0.0472464	−	0.0171963i
$386$	−9.48587e10	−	1.64300e11i	−0.217487	−	0.376699i
$387$		0			0
$388$	2.12209e11	−	3.67557e11i	0.475358	−	0.823345i
$389$	−2.79377e11	+	2.34425e11i	−0.618610	+	0.519075i	−0.897366	−	0.441287i	$-0.854522\pi$
$389$	−2.79377e11	+	2.34425e11i	−0.618610	+	0.519075i	0.278756	+	0.960362i	$0.410078\pi$
$390$		0			0
$391$	7.22459e10	−	4.09727e11i	0.156321	−	0.886541i
$392$	3.64514e10	−	2.06726e11i	0.0779698	−	0.442189i
$393$		0			0
$394$	1.08846e10	−	9.13330e9i	0.0227552	−	0.0190939i
$395$	−1.89645e11	+	3.28475e11i	−0.391971	+	0.678914i
$396$		0			0
$397$	−2.39849e11	−	4.15431e11i	−0.484597	−	0.839346i	0.515247	−	0.857042i	$-0.327700\pi$
$397$	−2.39849e11	−	4.15431e11i	−0.484597	−	0.839346i	−0.999843	+	0.0176957i	$0.994367\pi$
$398$	−9.52478e10	−	3.46674e10i	−0.190275	−	0.0692544i
$399$		0			0
$400$	1.46905e10	+	1.23268e10i	0.0286923	+	0.0240757i
$401$	6.45972e11	−	2.35115e11i	1.24757	−	0.454078i	0.367989	−	0.929830i	$-0.380046\pi$
$401$	6.45972e11	−	2.35115e11i	1.24757	−	0.454078i	0.879579	+	0.475753i	$0.157824\pi$
$402$		0			0
$403$	1.27716e11	+	7.24311e11i	0.241197	+	1.36789i
$404$	7.25912e11			1.35571
$405$		0			0
$406$	1.18958e9			0.00217284
$407$	−2.65134e11	−	1.50365e12i	−0.478950	−	2.71626i
$408$		0			0
$409$	2.60651e11	−	9.48691e10i	0.460579	−	0.167637i	−0.101301	−	0.994856i	$-0.532301\pi$
$409$	2.60651e11	−	9.48691e10i	0.460579	−	0.167637i	0.561880	+	0.827219i	$0.310078\pi$
$410$	3.41638e9	+	2.86668e9i	0.00597088	+	0.00501017i
$411$		0			0
$412$	4.44224e11	+	1.61684e11i	0.759565	+	0.276459i
$413$	6.65170e9	+	1.15211e10i	0.0112501	+	0.0194858i
$414$		0			0
$415$	−2.73337e11	+	4.73433e11i	−0.452357	+	0.783506i
$416$	−2.48675e11	+	2.08663e11i	−0.407110	+	0.341606i
$417$		0			0
$418$	−3.54465e10	+	2.01027e11i	−0.0567910	+	0.322078i
$419$	1.29260e10	−	7.33072e10i	0.0204881	−	0.116194i	−0.972849	−	0.231443i	$-0.925655\pi$
$419$	1.29260e10	−	7.33072e10i	0.0204881	−	0.116194i	0.993337	+	0.115249i	$0.0367665\pi$
$420$		0			0
$421$	−4.25319e11	+	3.56885e11i	−0.659850	+	0.553680i	−0.910042	−	0.414516i	$-0.863951\pi$
$421$	−4.25319e11	+	3.56885e11i	−0.659850	+	0.553680i	0.250192	+	0.968196i	$0.419506\pi$
$422$	−5.77404e10	+	1.00009e11i	−0.0886286	+	0.153509i
$423$		0			0
$424$	−1.45192e11	−	2.51480e11i	−0.218171	−	0.377883i
$425$	−4.75251e10	−	1.72977e10i	−0.0706598	−	0.0257181i
$426$		0			0
$427$	−6.13247e9	−	5.14576e9i	−0.00892710	−	0.00749072i
$428$	−3.59195e11	+	1.30736e11i	−0.517408	+	0.188321i
$429$		0			0
$430$	−2.38807e10	−	1.35434e11i	−0.0336852	−	0.191038i
$431$	−3.94250e10			−0.0550332			−0.0275166	−	0.999621i	$-0.508760\pi$
$431$	−3.94250e10			−0.0550332			−0.0275166	+	0.999621i	$0.508760\pi$
$432$		0			0
$433$	4.47404e11			0.611651			0.305826	−	0.952088i	$-0.401068\pi$
$433$	4.47404e11			0.611651			0.305826	+	0.952088i	$0.401068\pi$
$434$	1.54168e9	+	8.74332e9i	0.00208589	+	0.0118297i
$435$		0			0
$436$	1.19371e12	−	4.34476e11i	1.58202	−	0.575807i
$437$	2.76490e11	+	2.32002e11i	0.362671	+	0.304317i
$438$		0			0
$439$	1.45140e10	+	5.28268e9i	0.0186508	+	0.00678835i	0.351329	−	0.936252i	$-0.385730\pi$
$439$	1.45140e10	+	5.28268e9i	0.0186508	+	0.00678835i	−0.332678	+	0.943041i	$0.607952\pi$
$440$	−2.87393e11	−	4.97779e11i	−0.365543	−	0.633140i
$441$		0			0
$442$	1.29345e11	−	2.24032e11i	0.161194	−	0.279197i
$443$	5.26133e11	−	4.41478e11i	0.649050	−	0.544618i	−0.257732	−	0.966216i	$-0.582975\pi$
$443$	5.26133e11	−	4.41478e11i	0.649050	−	0.544618i	0.906783	+	0.421598i	$0.138531\pi$
$444$		0			0
$445$	7.27038e10	−	4.12324e11i	0.0878895	−	0.498446i
$446$	−2.57994e10	+	1.46315e11i	−0.0308746	+	0.175099i
$447$		0			0
$448$	1.40152e10	−	1.17602e10i	0.0164380	−	0.0137931i
$449$	−3.91200e11	+	6.77579e11i	−0.454246	+	0.786777i	−0.998644	−	0.0520499i	$-0.983425\pi$
$449$	−3.91200e11	+	6.77579e11i	−0.454246	+	0.786777i	0.544399	+	0.838827i	$0.316758\pi$
$450$		0			0
$451$	2.30990e10	+	4.00086e10i	0.0262904	+	0.0455364i
$452$	−4.79465e11	−	1.74511e11i	−0.540299	−	0.196653i
$453$		0			0
$454$	1.29019e11	+	1.08260e11i	0.142529	+	0.119596i
$455$	−2.23924e10	+	8.15018e9i	−0.0244935	+	0.00891489i
$456$		0			0
$457$	−1.29043e11	−	7.31841e11i	−0.138393	−	0.784863i	−0.972437	−	0.233166i	$-0.925091\pi$
$457$	−1.29043e11	−	7.31841e11i	−0.138393	−	0.784863i	0.834044	−	0.551697i	$-0.186020\pi$
$458$	8.35916e10			0.0887703
$459$		0			0
$460$	−4.94243e11			−0.514672
$461$	7.62424e10	+	4.32392e11i	0.0786217	+	0.445886i	0.998552	+	0.0538030i	$0.0171343\pi$
$461$	7.62424e10	+	4.32392e11i	0.0786217	+	0.445886i	−0.919930	+	0.392083i	$0.871755\pi$
$462$		0			0
$463$	4.88508e11	−	1.77802e11i	0.494034	−	0.179814i	−0.0829746	−	0.996552i	$-0.526442\pi$
$463$	4.88508e11	−	1.77802e11i	0.494034	−	0.179814i	0.577009	+	0.816738i	$0.304220\pi$
$464$	−1.96312e11	−	1.64726e11i	−0.196615	−	0.164979i
$465$		0			0
$466$	3.12774e11	+	1.13840e11i	0.307251	+	0.111830i
$467$	−6.70287e11	−	1.16097e12i	−0.652131	−	1.12952i	−0.982605	−	0.185709i	$-0.940542\pi$
$467$	−6.70287e11	−	1.16097e12i	−0.652131	−	1.12952i	0.330473	−	0.943815i	$-0.392792\pi$
$468$		0			0
$469$	−1.20714e10	+	2.09084e10i	−0.0115208	+	0.0199546i
$470$	−2.21797e11	+	1.86110e11i	−0.209660	+	0.175926i
$471$		0			0
$472$	−6.12609e10	+	3.47428e11i	−0.0568125	+	0.322200i
$473$	2.47376e11	−	1.40294e12i	0.227239	−	1.28873i
$474$		0			0
$475$	3.36103e10	−	2.82024e10i	0.0302936	−	0.0254194i
$476$	−2.77311e10	+	4.80316e10i	−0.0247591	+	0.0428841i
$477$		0			0
$478$	5.93851e10	+	1.02858e11i	0.0520298	+	0.0901182i
$479$	1.50548e12	+	5.47950e11i	1.30667	+	0.475588i	0.899163	−	0.437614i	$-0.144177\pi$
$479$	1.50548e12	+	5.47950e11i	1.30667	+	0.475588i	0.407505	+	0.913203i	$0.366399\pi$
$480$		0			0
$481$	−1.28590e12	−	1.07900e12i	−1.09536	−	0.919113i
$482$	3.60261e11	−	1.31124e11i	0.304023	−	0.110655i
$483$		0			0
$484$	−3.04339e11	−	1.72599e12i	−0.252089	−	1.42967i
$485$	1.25060e12			1.02631
$486$		0			0
$487$	1.04732e12			0.843721			0.421860	−	0.906661i	$-0.361377\pi$
$487$	1.04732e12			0.843721			0.421860	+	0.906661i	$0.361377\pi$
$488$	−3.68639e10	−	2.09066e11i	−0.0294247	−	0.166876i
$489$		0			0
$490$	2.82661e11	−	1.02880e11i	0.221505	−	0.0806214i
$491$	−1.52924e12	−	1.28319e12i	−1.18743	−	0.996375i	−0.999900	−	0.0141162i	$-0.995507\pi$
$491$	−1.52924e12	−	1.28319e12i	−1.18743	−	0.996375i	−0.187533	−	0.982258i	$-0.560049\pi$
$492$		0			0
$493$	6.35089e11	+	2.31153e11i	0.484198	+	0.176234i
$494$	1.12210e11	+	1.94354e11i	0.0847737	+	0.146832i
$495$		0			0
$496$	9.56299e11	−	1.65636e12i	0.709457	−	1.22882i
$497$	5.30615e9	−	4.45239e9i	0.00390100	−	0.00327333i
$498$		0			0
$499$	−3.11921e11	+	1.76899e12i	−0.225212	+	1.27724i	0.637067	+	0.770809i	$0.280148\pi$
$499$	−3.11921e11	+	1.76899e12i	−0.225212	+	1.27724i	−0.862279	+	0.506433i	$0.830964\pi$
$500$	2.24361e11	−	1.27242e12i	0.160540	−	0.910466i
$501$		0			0
$502$	4.43463e11	−	3.72109e11i	0.311667	−	0.261519i
$503$	−9.46141e11	+	1.63877e12i	−0.659022	+	1.14146i	0.321847	+	0.946792i	$0.395696\pi$
$503$	−9.46141e11	+	1.63877e12i	−0.659022	+	1.14146i	−0.980869	+	0.194668i	$0.937637\pi$
$504$		0			0
$505$	1.06949e12	+	1.85242e12i	0.731757	+	1.26744i
$506$	2.70877e11	+	9.85911e10i	0.183694	+	0.0668591i
$507$		0			0
$508$	9.02590e11	+	7.57363e11i	0.601317	+	0.504565i
$509$	−7.57896e11	+	2.75852e11i	−0.500472	+	0.182157i	−0.579906	−	0.814683i	$-0.696911\pi$
$509$	−7.57896e11	+	2.75852e11i	−0.500472	+	0.182157i	0.0794343	+	0.996840i	$0.474689\pi$
$510$		0			0
$511$	4.67207e9	+	2.64966e10i	0.00303121	+	0.0171908i
$512$	1.43325e12			0.921740
$513$		0			0
$514$	−3.22539e11			−0.203821
$515$	2.41886e11	+	1.37180e12i	0.151523	+	0.859329i
$516$		0			0
$517$	−2.81837e12	+	1.02580e12i	−1.73496	+	0.631476i
$518$	−1.55224e10	−	1.30249e10i	−0.00947273	−	0.00794857i
$519$		0			0
$520$	−5.93815e11	−	2.16131e11i	−0.356153	−	0.129629i
$521$	−1.54485e12	−	2.67577e12i	−0.918582	−	1.59103i	−0.801571	−	0.597900i	$-0.796002\pi$
$521$	−1.54485e12	−	2.67577e12i	−0.918582	−	1.59103i	−0.117011	−	0.993131i	$-0.537331\pi$
$522$		0			0
$523$	−1.66955e12	+	2.89174e12i	−0.975756	+	1.69006i	−0.298338	+	0.954460i	$0.596432\pi$
$523$	−1.66955e12	+	2.89174e12i	−0.975756	+	1.69006i	−0.677418	+	0.735599i	$0.736901\pi$
$524$	−4.24048e11	+	3.55819e11i	−0.245711	+	0.206176i
$525$		0			0
$526$	1.17705e11	−	6.67536e11i	0.0670436	−	0.380223i
$527$	−8.75890e11	+	4.96742e12i	−0.494654	+	2.80532i
$528$		0			0
$529$	−9.89316e11	+	8.30135e11i	−0.549268	+	0.460891i
$530$	2.08056e11	−	3.60363e11i	0.114535	−	0.198381i
$531$		0			0
$532$	−2.40574e10	−	4.16686e10i	−0.0130211	−	0.0225531i
$533$	4.77274e10	+	1.73713e10i	0.0256151	+	0.00932312i
$534$		0			0
$535$	−8.62825e11	−	7.23996e11i	−0.455335	−	0.382071i
$536$	−6.01624e11	+	2.18973e11i	−0.314835	+	0.114591i
$537$		0			0
$538$	3.67137e10	+	2.08214e11i	0.0188933	+	0.107149i
$539$	3.11596e12			1.59016
$540$		0			0
$541$	1.47396e12			0.739775			0.369887	−	0.929077i	$-0.379396\pi$
$541$	1.47396e12			0.739775			0.369887	+	0.929077i	$0.379396\pi$
$542$	1.01910e11	+	5.77958e11i	0.0507246	+	0.287673i
$543$		0			0
$544$	−2.09204e12	+	7.61440e11i	−1.02418	+	0.372769i
$545$	2.86743e12	+	2.40606e12i	1.39222	+	1.16821i
$546$		0			0
$547$	−3.60757e11	−	1.31305e11i	−0.172295	−	0.0627102i	0.254432	−	0.967091i	$-0.418111\pi$
$547$	−3.60757e11	−	1.31305e11i	−0.172295	−	0.0627102i	−0.426727	+	0.904380i	$0.640334\pi$
$548$	−1.35983e12	−	2.35529e12i	−0.644126	−	1.11566i
$549$		0			0
$550$	1.75206e10	−	3.03466e10i	0.00816428	−	0.0141409i
$551$	−4.49143e11	+	3.76876e11i	−0.207588	+	0.174187i
$552$		0			0
$553$	−9.05446e9	+	5.13504e10i	−0.00411718	+	0.0233497i
$554$	−1.38791e11	+	7.87122e11i	−0.0625990	+	0.355016i
$555$		0			0
$556$	−2.20363e11	+	1.84907e11i	−0.0977918	+	0.0820571i
$557$	−3.81518e11	+	6.60808e11i	−0.167945	+	0.290889i	−0.937697	−	0.347454i	$-0.887046\pi$
$557$	−3.81518e11	+	6.60808e11i	−0.167945	+	0.290889i	0.769752	+	0.638343i	$0.220380\pi$
$558$		0			0
$559$	−7.83099e11	−	1.35637e12i	−0.339206	−	0.587522i
$560$	5.82306e10	+	2.11942e10i	0.0250210	+	0.00910691i
$561$		0			0
$562$	6.39827e11	+	5.36879e11i	0.270551	+	0.227019i
$563$	−1.41052e12	+	5.13386e11i	−0.591685	+	0.215356i	−0.620470	−	0.784230i	$-0.713058\pi$
$563$	−1.41052e12	+	5.13386e11i	−0.591685	+	0.215356i	0.0287853	+	0.999586i	$0.490836\pi$
$564$		0			0
$565$	−2.61075e11	−	1.48063e12i	−0.107782	−	0.611264i
$566$	−7.91296e10			−0.0324090
$567$		0			0
$568$	1.83686e11			0.0740471
$569$	3.99286e11	+	2.26446e12i	0.159690	+	0.905649i	0.954371	+	0.298622i	$0.0965270\pi$
$569$	3.99286e11	+	2.26446e12i	0.159690	+	0.905649i	−0.794681	+	0.607027i	$0.792362\pi$
$570$		0			0
$571$	−2.41555e12	+	8.79189e11i	−0.950942	+	0.346114i	−0.770478	−	0.637467i	$-0.779982\pi$
$571$	−2.41555e12	+	8.79189e11i	−0.950942	+	0.346114i	−0.180464	+	0.983582i	$0.557760\pi$
$572$	−2.43861e12	−	2.04624e12i	−0.952490	−	0.799234i
$573$		0			0
$574$	5.76128e8	+	2.09693e8i	0.000221521	+	8.06271e-5i
$575$	−3.09793e10	−	5.36577e10i	−0.0118186	−	0.0204704i
$576$		0			0
$577$	−2.12565e11	+	3.68173e11i	−0.0798364	+	0.138281i	−0.903179	−	0.429264i	$-0.858773\pi$
$577$	−2.12565e11	+	3.68173e11i	−0.0798364	+	0.138281i	0.823343	+	0.567544i	$0.192106\pi$
$578$	8.84492e11	−	7.42177e11i	0.329624	−	0.276587i
$579$		0			0
$580$	1.39417e11	−	7.90675e11i	0.0511553	−	0.290116i
$581$	−1.30503e10	+	7.40117e10i	−0.00475146	+	0.0269468i
$582$		0			0
$583$	3.30198e12	−	2.77069e12i	1.18377	−	0.993297i
$584$	−3.56746e11	+	6.17902e11i	−0.126912	+	0.219817i
$585$		0			0
$586$	3.07598e10	+	5.32775e10i	0.0107757	+	0.0186640i
$587$	1.83556e12	+	6.68090e11i	0.638113	+	0.232254i	0.640759	−	0.767742i	$-0.278620\pi$
$587$	1.83556e12	+	6.68090e11i	0.638113	+	0.232254i	−0.00264550	+	0.999997i	$0.500842\pi$
$588$		0			0
$589$	−3.35209e12	−	2.81273e12i	−1.14762	−	0.962964i
$590$	−4.75046e11	+	1.72903e11i	−0.161399	+	0.0587446i
$591$		0			0
$592$	7.58010e11	+	4.29889e12i	0.253645	+	1.43849i
$593$	−3.96717e12			−1.31745			−0.658726	−	0.752383i	$-0.728905\pi$
$593$	−3.96717e12			−1.31745			−0.658726	+	0.752383i	$0.728905\pi$
$594$		0			0
$595$	−1.63426e11			−0.0534558
$596$	3.52891e11	+	2.00134e12i	0.114560	+	0.649701i
$597$		0			0
$598$	2.97804e11	−	1.08392e11i	0.0952304	−	0.0346610i
$599$	1.77280e12	+	1.48756e12i	0.562651	+	0.472121i	0.879198	−	0.476456i	$-0.158079\pi$
$599$	1.77280e12	+	1.48756e12i	0.562651	+	0.472121i	−0.316547	+	0.948577i	$0.602523\pi$
$600$		0			0
$601$	2.20183e12	+	8.01399e11i	0.688411	+	0.250561i	0.662455	−	0.749102i	$-0.269515\pi$
$601$	2.20183e12	+	8.01399e11i	0.688411	+	0.250561i	0.0259562	+	0.999663i	$0.491737\pi$
$602$	−9.45295e9	−	1.63730e10i	−0.00293348	−	0.00508094i
$603$		0			0
$604$	1.03256e12	−	1.78844e12i	0.315681	−	0.546776i
$605$	3.95608e12	−	3.31955e12i	1.20051	−	1.00735i
$606$		0			0
$607$	−4.62484e11	+	2.62288e12i	−0.138276	+	0.784203i	0.834246	+	0.551393i	$0.185903\pi$
$607$	−4.62484e11	+	2.62288e12i	−0.138276	+	0.784203i	−0.972522	+	0.232811i	$0.925208\pi$
$608$	3.35379e11	−	1.90203e12i	0.0995336	−	0.564483i
$609$		0			0
$610$	2.33036e11	−	1.95540e11i	0.0681457	−	0.0571810i
$611$	−1.64870e12	+	2.85563e12i	−0.478582	+	0.828928i
$612$		0			0
$613$	1.94423e12	+	3.36751e12i	0.556130	+	0.963246i	0.997815	+	0.0660752i	$0.0210477\pi$
$613$	1.94423e12	+	3.36751e12i	0.556130	+	0.963246i	−0.441684	+	0.897170i	$0.645619\pi$
$614$	−4.41271e11	−	1.60609e11i	−0.125299	−	0.0456051i
$615$		0			0
$616$	−6.05314e10	−	5.07919e10i	−0.0169382	−	0.0142129i
$617$	−2.68704e12	+	9.78002e11i	−0.746433	+	0.271679i	−0.687104	−	0.726559i	$-0.741118\pi$
$617$	−2.68704e12	+	9.78002e11i	−0.746433	+	0.271679i	−0.0593289	+	0.998238i	$0.518896\pi$
$618$		0			0
$619$	−7.72023e11	−	4.37836e12i	−0.211360	−	1.19868i	−0.887113	−	0.461553i	$-0.847293\pi$
$619$	−7.72023e11	−	4.37836e12i	−0.211360	−	1.19868i	0.675753	−	0.737128i	$-0.263819\pi$
$620$	5.99207e12			1.62860
$621$		0			0
$622$	1.23026e12			0.329563
$623$	−9.99489e9	−	5.66838e10i	−0.00265816	−	0.0150752i
$624$		0			0
$625$	3.73685e12	−	1.36010e12i	0.979592	−	0.356542i
$626$	4.38572e11	+	3.68006e11i	0.114145	+	0.0957790i
$627$		0			0
$628$	−5.07209e12	−	1.84609e12i	−1.30127	−	0.473624i
$629$	−5.75612e12	−	9.96989e12i	−1.46623	−	2.53958i
$630$		0			0
$631$	−1.86718e12	+	3.23406e12i	−0.468873	+	0.812111i	−0.999367	−	0.0355772i	$-0.988673\pi$
$631$	−1.86718e12	+	3.23406e12i	−0.468873	+	0.812111i	0.530494	+	0.847689i	$0.322006\pi$
$632$	−1.05924e12	+	8.88811e11i	−0.264101	+	0.221607i
$633$		0			0
$634$	1.17826e11	−	6.68224e11i	0.0289627	−	0.164256i
$635$	−6.02880e11	+	3.41910e12i	−0.147146	+	0.834508i
$636$		0			0
$637$	2.62425e12	−	2.20200e12i	0.631506	−	0.529896i
$638$	−2.34132e11	+	4.05529e11i	−0.0559459	+	0.0969012i
$639$		0			0
$640$	1.74444e12	+	3.02146e12i	0.411004	+	0.711879i
$641$	−2.03779e12	−	7.41693e11i	−0.476757	−	0.173525i	0.0924537	−	0.995717i	$-0.470529\pi$
$641$	−2.03779e12	−	7.41693e11i	−0.476757	−	0.173525i	−0.569211	+	0.822192i	$0.692751\pi$
$642$		0			0
$643$	−1.30814e11	−	1.09766e11i	−0.0301789	−	0.0253231i	0.627573	−	0.778557i	$-0.284048\pi$
$643$	−1.30814e11	−	1.09766e11i	−0.0301789	−	0.0253231i	−0.657752	+	0.753234i	$0.728493\pi$
$644$	−6.38480e10	+	2.32388e10i	−0.0146272	+	0.00532387i
$645$		0			0
$646$	2.67263e11	+	1.51572e12i	0.0603798	+	0.342431i
$647$	5.27913e12			1.18439			0.592193	−	0.805796i	$-0.298262\pi$
$647$	5.27913e12			1.18439			0.592193	+	0.805796i	$0.298262\pi$
$648$		0			0
$649$	−5.23673e12			−1.15867
$650$	−6.68974e9	−	3.79394e10i	−0.00146994	−	0.00833644i
$651$		0			0
$652$	4.81794e12	−	1.75359e12i	1.04411	−	0.380026i
$653$	−3.27196e12	−	2.74550e12i	−0.704204	−	0.590898i	0.218762	−	0.975778i	$-0.429798\pi$
$653$	−3.27196e12	−	2.74550e12i	−0.704204	−	0.590898i	−0.922966	+	0.384881i	$0.874243\pi$
$654$		0			0
$655$	−1.53275e12	−	5.57876e11i	−0.325376	−	0.118427i
$656$	−6.60392e10	−	1.14383e11i	−0.0139231	−	0.0241155i
$657$		0			0
$658$	−1.99018e10	+	3.44710e10i	−0.00413882	+	0.00716864i
$659$	5.65083e12	−	4.74161e12i	1.16715	−	0.979358i	0.167175	−	0.985927i	$-0.446536\pi$
$659$	5.65083e12	−	4.74161e12i	1.16715	−	0.979358i	0.999978	+	0.00656949i	$0.00209115\pi$
$660$		0			0
$661$	−5.24026e11	+	2.97190e12i	−0.106769	+	0.605518i	0.883730	+	0.467998i	$0.155024\pi$
$661$	−5.24026e11	+	2.97190e12i	−0.106769	+	0.605518i	−0.990499	+	0.137521i	$0.956087\pi$
$662$	3.68706e11	−	2.09104e12i	0.0746138	−	0.423156i
$663$		0			0
$664$	−1.52670e12	+	1.28105e12i	−0.304787	+	0.255747i
$665$	7.08880e10	−	1.22782e11i	0.0140564	−	0.0243465i
$666$		0			0
$667$	4.13984e11	+	7.17042e11i	0.0809874	+	0.140274i
$668$	−5.08067e11	−	1.84921e11i	−0.0987250	−	0.0359329i
$669$		0			0
$670$	−7.02797e11	−	5.89717e11i	−0.134739	−	0.113060i
$671$	2.96118e12	−	1.07778e12i	0.563915	−	0.205248i
$672$		0			0
$673$	−4.54704e11	−	2.57875e12i	−0.0854399	−	0.484554i	−0.997261	−	0.0739656i	$-0.976434\pi$
$673$	−4.54704e11	−	2.57875e12i	−0.0854399	−	0.484554i	0.911821	−	0.410588i	$-0.134677\pi$
$674$	9.02040e11			0.168367
$675$		0			0
$676$	1.64026e12			0.302101
$677$	−5.37665e11	−	3.04925e12i	−0.0983700	−	0.557884i	−0.993662	−	0.112405i	$-0.964145\pi$
$677$	−5.37665e11	−	3.04925e12i	−0.0983700	−	0.557884i	0.895292	−	0.445479i	$-0.146967\pi$
$678$		0			0
$679$	1.61557e11	−	5.88018e10i	0.0291683	−	0.0106164i
$680$	−3.31990e12	−	2.78573e12i	−0.595436	−	0.499630i
$681$		0			0
$682$	−3.28404e12	−	1.19529e12i	−0.581271	−	0.211565i
$683$	2.03687e11	+	3.52797e11i	0.0358155	+	0.0620342i	0.883378	−	0.468662i	$-0.155264\pi$
$683$	2.03687e11	+	3.52797e11i	0.0358155	+	0.0620342i	−0.847562	+	0.530696i	$0.821930\pi$
$684$		0			0
$685$	4.00689e12	−	6.94014e12i	0.695344	−	1.20437i
$686$	6.33860e10	−	5.31872e10i	0.0109279	−	0.00916956i
$687$		0			0
$688$	−7.07240e11	+	4.01096e12i	−0.120342	+	0.682496i
$689$	8.22906e11	−	4.66693e12i	0.139112	−	0.788941i
$690$		0			0
$691$	6.69121e12	−	5.61460e12i	1.11649	−	0.936844i	0.118066	−	0.993006i	$-0.462331\pi$
$691$	6.69121e12	−	5.61460e12i	1.11649	−	0.936844i	0.998422	+	0.0561618i	$0.0178863\pi$
$692$	−1.12136e12	+	1.94225e12i	−0.185895	+	0.321980i
$693$		0			0
$694$	−2.87911e11	−	4.98677e11i	−0.0471131	−	0.0816022i
$695$	−7.96517e11	−	2.89908e11i	−0.129498	−	0.0471335i
$696$		0			0
$697$	2.66834e11	+	2.23900e11i	0.0428247	+	0.0359342i
$698$	−9.67471e11	+	3.52131e11i	−0.154273	+	0.0561506i
$699$		0			0
$700$	1.43425e9	+	8.13406e9i	0.000225780	+	0.00128046i
$701$	6.21208e12			0.971642			0.485821	−	0.874058i	$-0.338521\pi$
$701$	6.21208e12			0.971642			0.485821	+	0.874058i	$0.338521\pi$
$702$		0			0
$703$	9.98715e12			1.54221
$704$	1.25059e12	+	7.09243e12i	0.191883	+	1.08822i
$705$		0			0
$706$	−1.42004e12	+	5.16852e11i	−0.215119	+	0.0782969i
$707$	2.25259e11	+	1.89015e11i	0.0339075	+	0.0284518i
$708$		0			0
$709$	9.71141e12	+	3.53466e12i	1.44336	+	0.525339i	0.940728	−	0.339162i	$-0.110143\pi$
$709$	9.71141e12	+	3.53466e12i	1.44336	+	0.525339i	0.502630	+	0.864501i	$0.332366\pi$
$710$	1.31608e11	+	2.27952e11i	0.0194366	+	0.0336652i
$711$		0			0
$712$	7.63181e11	−	1.32187e12i	0.111293	−	0.192765i
$713$	−4.73367e12	+	3.97202e12i	−0.685955	+	0.575584i
$714$		0			0
$715$	1.62886e12	−	9.23771e12i	0.233081	−	1.32187i
$716$	4.51093e11	−	2.55828e12i	0.0641442	−	0.363780i
$717$		0			0
$718$	−4.66270e11	+	3.91247e11i	−0.0654753	+	0.0549403i
$719$	−2.45754e12	+	4.25659e12i	−0.342943	+	0.593994i	−0.984978	−	0.172681i	$-0.944757\pi$
$719$	−2.45754e12	+	4.25659e12i	−0.342943	+	0.593994i	0.642035	+	0.766675i	$0.278090\pi$
$720$		0			0
$721$	9.57484e10	+	1.65841e11i	0.0131954	+	0.0228551i
$722$	3.29389e11	+	1.19888e11i	0.0451120	+	0.0164194i
$723$		0			0
$724$	5.70016e12	+	4.78300e12i	0.771016	+	0.646959i
$725$	9.45787e10	−	3.44238e10i	0.0127137	−	0.00462741i
$726$		0			0
$727$	8.30088e11	+	4.70766e12i	0.110210	+	0.625030i	0.989011	+	0.147842i	$0.0472327\pi$
$727$	8.30088e11	+	4.70766e12i	0.110210	+	0.625030i	−0.878801	+	0.477188i	$0.841656\pi$
$728$	−8.68733e10			−0.0114629
$729$		0			0
$730$	−1.02241e12			−0.133252
$731$	−1.86519e12	−	1.05780e13i	−0.241598	−	1.37017i
$732$		0			0
$733$	−6.56973e12	+	2.39119e12i	−0.840581	+	0.305947i	−0.726194	−	0.687490i	$-0.758713\pi$
$733$	−6.56973e12	+	2.39119e12i	−0.840581	+	0.305947i	−0.114387	+	0.993436i	$0.536490\pi$
$734$	5.02351e11	+	4.21523e11i	0.0638815	+	0.0536030i
$735$		0			0
$736$	−2.56292e12	−	9.32826e11i	−0.321947	−	0.117179i
$737$	−4.75178e12	−	8.23033e12i	−0.593271	−	1.02758i
$738$		0			0
$739$	−4.44786e12	+	7.70391e12i	−0.548594	+	0.950192i	0.449778	+	0.893141i	$0.351503\pi$
$739$	−4.44786e12	+	7.70391e12i	−0.548594	+	0.950192i	−0.998371	+	0.0570514i	$0.981830\pi$
$740$	−1.04764e13	+	8.79073e12i	−1.28431	+	1.07766i
$741$		0			0
$742$	9.93347e9	−	5.63355e10i	0.00120305	−	0.00682283i
$743$	−1.58790e12	+	9.00544e12i	−0.191150	+	1.08407i	0.726646	+	0.687012i	$0.241078\pi$
$743$	−1.58790e12	+	9.00544e12i	−0.191150	+	1.08407i	−0.917796	+	0.397053i	$0.870033\pi$
$744$		0			0
$745$	−4.58721e12	+	3.84912e12i	−0.545563	+	0.457782i
$746$	−1.40338e12	+	2.43073e12i	−0.165902	+	0.287351i
$747$		0			0
$748$	−1.09160e13	−	1.89071e13i	−1.27499	−	2.20835i
$749$	−1.45504e11	−	5.29592e10i	−0.0168930	−	0.00614856i
$750$		0			0
$751$	3.42252e12	+	2.87183e12i	0.392614	+	0.329442i	0.817630	−	0.575743i	$-0.195287\pi$
$751$	3.42252e12	+	2.87183e12i	0.392614	+	0.329442i	−0.425017	+	0.905186i	$0.639732\pi$
$752$	8.05764e12	−	2.93274e12i	0.918814	−	0.334421i
$753$		0			0
$754$	8.93967e10	+	5.06994e11i	0.0100728	+	0.0571257i
$755$	6.08512e12			0.681566
$756$		0			0
$757$	−1.65651e12			−0.183342			−0.0916711	−	0.995789i	$-0.529221\pi$
$757$	−1.65651e12			−0.183342			−0.0916711	+	0.995789i	$0.529221\pi$
$758$	−3.86243e11	−	2.19049e12i	−0.0424961	−	0.241008i
$759$		0			0
$760$	3.53296e12	−	1.28589e12i	0.384129	−	0.139812i
$761$	9.15880e12	+	7.68515e12i	0.989938	+	0.830656i	0.985559	−	0.169334i	$-0.0541617\pi$
$761$	9.15880e12	+	7.68515e12i	0.989938	+	0.830656i	0.00437896	+	0.999990i	$0.498606\pi$
$762$		0			0
$763$	4.83555e11	+	1.76000e11i	0.0516518	+	0.0187997i
$764$	7.59256e12	+	1.31507e13i	0.806247	+	1.39646i
$765$		0			0
$766$	−1.12799e12	+	1.95374e12i	−0.118379	+	0.205039i
$767$	−4.41036e12	+	3.70073e12i	−0.460145	+	0.386107i
$768$		0			0
$769$	1.84099e12	−	1.04408e13i	0.189838	−	1.07662i	−0.729743	−	0.683721i	$-0.760360\pi$
$769$	1.84099e12	−	1.04408e13i	0.189838	−	1.07662i	0.919581	−	0.392901i	$-0.128529\pi$
$770$	1.96623e10	−	1.11510e11i	0.00201570	−	0.0114316i
$771$		0			0
$772$	−1.34845e13	+	1.13148e13i	−1.36633	+	1.14649i
$773$	−4.34089e12	+	7.51864e12i	−0.437291	+	0.757411i	−0.997480	−	0.0709545i	$-0.977395\pi$
$773$	−4.34089e12	+	7.51864e12i	−0.437291	+	0.757411i	0.560188	+	0.828365i	$0.310729\pi$
$774$		0			0
$775$	3.75585e11	+	6.50532e11i	0.0373982	+	0.0647755i
$776$	4.28425e12	+	1.55934e12i	0.424128	+	0.154370i
$777$		0			0
$778$	−1.45948e12	−	1.22465e12i	−0.142820	−	0.119840i
$779$	−2.83959e11	+	1.03353e11i	−0.0276272	+	0.0100555i
$780$		0			0
$781$	4.73471e11	+	2.68519e12i	0.0455369	+	0.258253i
$782$	2.17346e12			0.207836
$783$		0			0
$784$	−8.90842e12			−0.842129
$785$	−2.76182e12	−	1.56631e13i	−0.259586	−	1.47219i
$786$		0			0
$787$	−3.55481e12	+	1.29384e12i	−0.330316	+	0.120225i	−0.501854	−	0.864952i	$-0.667349\pi$
$787$	−3.55481e12	+	1.29384e12i	−0.330316	+	0.120225i	0.171538	+	0.985177i	$0.445126\pi$
$788$	−1.00992e12	−	8.47425e11i	−0.0933081	−	0.0782948i
$789$		0			0
$790$	−1.86194e12	−	6.77690e11i	−0.170076	−	0.0619026i
$791$	−1.03344e11	−	1.78997e11i	−0.00938625	−	0.0162575i
$792$		0			0
$793$	1.73224e12	−	3.00033e12i	0.155553	−	0.269426i
$794$	1.91968e12	−	1.61081e12i	0.171411	−	0.143830i
$795$		0			0
$796$	−1.63310e12	+	9.26177e12i	−0.144180	+	0.817684i
$797$	2.06207e12	−	1.16946e13i	0.181026	−	1.02665i	−0.749930	−	0.661517i	$-0.769913\pi$
$797$	2.06207e12	−	1.16946e13i	0.181026	−	1.02665i	0.930956	−	0.365131i	$-0.118976\pi$
$798$		0			0
$799$	−1.73233e13	+	1.45360e13i	−1.50373	+	1.26178i
$800$	−1.65773e11	+	2.87126e11i	−0.0143089	+	0.0247838i
$801$		0			0
$802$	1.79559e12	+	3.11004e12i	0.153257	+	0.265450i
$803$	−9.95228e12	−	3.62233e12i	−0.844700	−	0.307446i
$804$		0			0
$805$	−1.53370e11	−	1.28693e11i	−0.0128724	−	0.0108012i
$806$	−3.61050e12	+	1.31411e12i	−0.301342	+	0.109680i
$807$		0			0
$808$	1.35410e12	+	7.67946e12i	0.111763	+	0.633839i
$809$	−2.18394e13			−1.79256			−0.896279	−	0.443491i	$-0.853740\pi$
$809$	−2.18394e13			−1.79256			−0.896279	+	0.443491i	$0.853740\pi$
$810$		0			0
$811$	−2.14963e13			−1.74490			−0.872450	−	0.488703i	$-0.837470\pi$
$811$	−2.14963e13			−1.74490			−0.872450	+	0.488703i	$0.837470\pi$
$812$	−1.91663e10	−	1.08697e11i	−0.00154716	−	0.00877439i
$813$		0			0
$814$	7.49529e12	−	2.72806e12i	0.598382	−	0.217793i
$815$	1.15732e13	+	9.71109e12i	0.918851	+	0.771007i
$816$		0			0
$817$	8.75628e12	+	3.18703e12i	0.687576	+	0.250257i
$818$	7.24521e11	+	1.25491e12i	0.0565797	+	0.0979990i
$819$		0			0
$820$	2.06898e11	−	3.58357e11i	0.0159806	−	0.0276792i
$821$	6.05960e12	−	5.08461e12i	0.465479	−	0.390583i	−0.379663	−	0.925125i	$-0.623960\pi$
$821$	6.05960e12	−	5.08461e12i	0.465479	−	0.390583i	0.845142	+	0.534542i	$0.179516\pi$
$822$		0			0
$823$	1.01349e12	−	5.74781e12i	0.0770056	−	0.436720i	−0.921792	−	0.387686i	$-0.873275\pi$
$823$	1.01349e12	−	5.74781e12i	0.0770056	−	0.436720i	0.998797	−	0.0490343i	$-0.0156144\pi$
$824$	−8.81824e11	+	5.00107e12i	−0.0666361	+	0.377912i
$825$		0			0
$826$	−5.32384e10	+	4.46723e10i	−0.00397937	+	0.00333909i
$827$	−1.17613e13	+	2.03711e13i	−0.874337	+	1.51440i	−0.0168693	+	0.999858i	$0.505370\pi$
$827$	−1.17613e13	+	2.03711e13i	−0.874337	+	1.51440i	−0.857468	+	0.514538i	$0.827963\pi$
$828$		0			0
$829$	−2.33620e12	−	4.04642e12i	−0.171797	−	0.297561i	0.767251	−	0.641346i	$-0.221624\pi$
$829$	−2.33620e12	−	4.04642e12i	−0.171797	−	0.297561i	−0.939048	+	0.343786i	$0.888291\pi$
$830$	−2.68362e12	−	9.76760e11i	−0.196277	−	0.0714391i
$831$		0			0
$832$	6.06537e12	+	5.08945e12i	0.438836	+	0.368227i
$833$	2.20771e13	−	8.03541e12i	1.58869	−	0.578236i
$834$		0			0
$835$	−2.76649e11	−	1.56896e12i	−0.0196943	−	0.111692i
$836$	1.89398e13			1.34106
$837$		0			0
$838$	3.88869e11			0.0272399
$839$	2.50514e12	+	1.42073e13i	0.174543	+	0.989883i	0.938670	+	0.344817i	$0.112059\pi$
$839$	2.50514e12	+	1.42073e13i	0.174543	+	0.989883i	−0.764127	+	0.645066i	$0.776830\pi$
$840$		0			0
$841$	1.23684e13	−	4.50172e12i	0.852572	−	0.310311i
$842$	−2.22189e12	−	1.86439e12i	−0.152342	−	0.127830i
$843$		0			0
$844$	1.00686e13	+	3.66467e12i	0.683012	+	0.248596i
$845$	2.41661e12	+	4.18569e12i	0.163062	+	0.282431i
$846$		0			0
$847$	3.54979e11	−	6.14842e11i	0.0236988	−	0.0410476i
$848$	−9.44026e12	+	7.92132e12i	−0.626906	+	0.526037i
$849$		0			0
$850$	4.58791e10	−	2.60193e11i	0.00301460	−	0.0170967i
$851$	2.44904e12	−	1.38892e13i	0.160071	−	0.907806i
$852$		0			0
$853$	1.97651e13	−	1.65849e13i	1.27829	−	1.07261i	0.284810	−	0.958584i	$-0.408069\pi$
$853$	1.97651e13	−	1.65849e13i	1.27829	−	1.07261i	0.993478	−	0.114027i	$-0.0363751\pi$
$854$	2.09103e10	−	3.62176e10i	0.00134524	−	0.00233002i
$855$		0			0
$856$	−2.05310e12	−	3.55607e12i	−0.130701	−	0.226380i
$857$	1.78402e13	+	6.49330e12i	1.12976	+	0.411199i	0.838205	−	0.545355i	$-0.183605\pi$
$857$	1.78402e13	+	6.49330e12i	1.12976	+	0.411199i	0.291555	+	0.956554i	$0.405827\pi$
$858$		0			0
$859$	3.00557e12	+	2.52197e12i	0.188346	+	0.158041i	0.732085	−	0.681213i	$-0.238547\pi$
$859$	3.00557e12	+	2.52197e12i	0.188346	+	0.158041i	−0.543739	+	0.839254i	$0.682992\pi$
$860$	−1.19905e13	+	4.36417e12i	−0.747468	+	0.272056i
$861$		0			0
$862$	−3.57644e10	−	2.02830e11i	−0.00220632	−	0.0125126i
$863$	−1.82170e13			−1.11796			−0.558982	−	0.829180i	$-0.688808\pi$
$863$	−1.82170e13			−1.11796			−0.558982	+	0.829180i	$0.688808\pi$
$864$		0			0
$865$	−6.60845e12			−0.401354
$866$	4.05861e11	+	2.30175e12i	0.0245215	+	0.139068i
$867$		0			0
$868$	7.74077e11	−	2.81741e11i	0.0462855	−	0.0168466i
$869$	−1.57233e13	−	1.31934e13i	−0.935308	−	0.784817i
$870$		0			0
$871$	−9.81820e12	−	3.57353e12i	−0.578030	−	0.210386i
$872$	6.82307e12	+	1.18179e13i	0.399628	+	0.692175i
$873$		0			0
$874$	−9.42764e11	+	1.63291e12i	−0.0546514	+	0.0946590i
$875$	4.00938e11	−	3.36427e11i	0.0231228	−	0.0194023i
$876$		0			0
$877$	1.13652e12	−	6.44550e12i	0.0648750	−	0.367924i	−0.935036	−	0.354554i	$-0.884633\pi$
$877$	1.13652e12	−	6.44550e12i	0.0648750	−	0.367924i	0.999911	−	0.0133704i	$-0.00425607\pi$
$878$	−1.40114e10	+	7.94625e10i	−0.000795711	+	0.00451270i
$879$		0			0
$880$	−1.86860e13	+	1.56794e13i	−1.05038	+	0.881371i
$881$	−2.23804e12	+	3.87640e12i	−0.125163	+	0.216789i	−0.921797	−	0.387674i	$-0.873279\pi$
$881$	−2.23804e12	+	3.87640e12i	−0.125163	+	0.216789i	0.796634	+	0.604463i	$0.206612\pi$
$882$		0			0
$883$	1.32627e12	+	2.29716e12i	0.0734188	+	0.127165i	0.900398	−	0.435068i	$-0.143276\pi$
$883$	1.32627e12	+	2.29716e12i	0.0734188	+	0.127165i	−0.826979	+	0.562233i	$0.809942\pi$
$884$	−2.25548e13	−	8.20929e12i	−1.24224	−	0.452137i
$885$		0			0
$886$	2.74855e12	+	2.30630e12i	0.149848	+	0.125738i
$887$	1.72144e13	−	6.26554e12i	0.933762	−	0.339862i	0.170063	−	0.985433i	$-0.445603\pi$
$887$	1.72144e13	−	6.26554e12i	0.933762	−	0.339862i	0.763700	+	0.645572i	$0.223381\pi$
$888$		0			0
$889$	8.28804e10	+	4.70038e11i	0.00445035	+	0.0252392i
$890$	2.18723e12			0.116853
$891$		0			0
$892$	1.37852e13			0.729071
$893$	−3.40667e12	−	1.93202e13i	−0.179266	−	1.01667i
$894$		0			0
$895$	7.19293e12	−	2.61801e12i	0.374716	−	0.136386i
$896$	3.67418e11	+	3.08300e11i	0.0190447	+	0.0159804i
$897$		0			0
$898$	−3.84081e12	−	1.39794e12i	−0.197097	−	0.0717374i
$899$	−5.01903e12	−	8.69322e12i	−0.256272	−	0.443876i
$900$		0			0
$901$	1.62501e13	−	2.81459e13i	0.821474	−	1.42283i
$902$	−1.84878e11	+	1.55131e11i	−0.00929940	+	0.00780312i
$903$		0			0
$904$	9.51779e11	−	5.39781e12i	0.0474000	−	0.268819i
$905$	−3.80739e12	+	2.15928e13i	−0.188673	+	1.07002i
$906$		0			0
$907$	−9.38776e11	+	7.87726e11i	−0.0460605	+	0.0386494i	−0.665527	−	0.746373i	$-0.731793\pi$
$907$	−9.38776e11	+	7.87726e11i	−0.0460605	+	0.0386494i	0.619467	+	0.785023i	$0.287349\pi$
$908$	7.81346e12	−	1.35333e13i	0.381467	−	0.660721i
$909$		0			0
$910$	−6.22434e10	−	1.07809e11i	−0.00300890	−	0.00521156i
$911$	1.00971e13	+	3.67505e12i	0.485696	+	0.176779i	0.573249	−	0.819381i	$-0.305683\pi$
$911$	1.00971e13	+	3.67505e12i	0.485696	+	0.176779i	−0.0875534	+	0.996160i	$0.527905\pi$
$912$		0			0
$913$	−2.26621e13	−	1.90158e13i	−1.07940	−	0.905723i
$914$	3.64804e12	−	1.32778e12i	0.172902	−	0.0629314i
$915$		0			0
$916$	−1.34681e12	−	7.63814e12i	−0.0632086	−	0.358474i
$917$	−2.24237e11			−0.0104724
$918$		0			0
$919$	2.42068e13			1.11948			0.559741	−	0.828668i	$-0.310901\pi$
$919$	2.42068e13			1.11948			0.559741	+	0.828668i	$0.310901\pi$
$920$	−9.21948e11	−	5.22862e12i	−0.0424288	−	0.240626i
$921$		0			0
$922$	−2.15536e12	+	7.84488e11i	−0.0982271	+	0.0357517i
$923$	2.29634e12	+	1.92686e12i	0.104143	+	0.0873862i
$924$		0			0
$925$	−1.61103e12	−	5.86368e11i	−0.0723547	−	0.0263350i
$926$	1.35789e12	+	2.35193e12i	0.0606896	+	0.105117i
$927$		0			0
$928$	2.21526e12	−	3.83694e12i	0.0980525	−	0.169832i
$929$	−7.54594e12	+	6.33179e12i	−0.332386	+	0.278905i	−0.793671	−	0.608347i	$-0.791833\pi$
$929$	−7.54594e12	+	6.33179e12i	−0.332386	+	0.278905i	0.461285	+	0.887252i	$0.347388\pi$
$930$		0			0
$931$	−3.53923e12	+	2.00720e13i	−0.154396	+	0.875621i
$932$	5.36276e12	−	3.04137e13i	0.232818	−	1.32038i
$933$		0			0
$934$	5.36479e12	−	4.50160e12i	0.230670	−	0.193556i
$935$	3.21654e13	−	5.57120e13i	1.37637	−	2.38395i
$936$		0			0
$937$	1.17519e13	+	2.03549e13i	0.498058	+	0.862662i	0.999997	−	0.00224054i	$-0.000713188\pi$
$937$	1.17519e13	+	2.03549e13i	0.498058	+	0.862662i	−0.501939	+	0.864903i	$0.667380\pi$
$938$	−1.18518e11	−	4.31369e10i	−0.00499885	−	0.00181943i
$939$		0			0
$940$	2.05792e13	+	1.72680e13i	0.859714	+	0.721385i
$941$	−3.08292e13	+	1.12209e13i	−1.28177	+	0.466525i	−0.891016	−	0.453972i	$-0.850007\pi$
$941$	−3.08292e13	+	1.12209e13i	−1.28177	+	0.466525i	−0.390750	+	0.920497i	$0.627784\pi$
$942$		0			0
$943$	7.41008e10	+	4.20246e11i	0.00305155	+	0.0173062i
$944$	1.49717e13			0.613615
$945$		0			0
$946$	7.44209e12			0.302124
$947$	2.80461e12	+	1.59058e13i	0.113318	+	0.642657i	0.987569	+	0.157184i	$0.0502416\pi$
$947$	2.80461e12	+	1.59058e13i	0.113318	+	0.642657i	−0.874252	+	0.485473i	$0.838647\pi$
$948$		0			0
$949$	−1.09416e13	+	3.98243e12i	−0.437909	+	0.159386i
$950$	1.75582e11	+	1.47331e11i	0.00699398	+	0.00586865i
$951$		0			0
$952$	−5.59858e11	−	2.03772e11i	−0.0220908	−	0.00804039i
$953$	8.93212e12	+	1.54709e13i	0.350781	+	0.607571i	0.986387	−	0.164443i	$-0.0525827\pi$
$953$	8.93212e12	+	1.54709e13i	0.350781	+	0.607571i	−0.635605	+	0.772014i	$0.719249\pi$
$954$		0			0
$955$	−2.23724e13	+	3.87501e13i	−0.870357	+	1.50750i
$956$	8.44180e12	−	7.08351e12i	0.326869	−	0.274276i
$957$		0			0
$958$	−1.45334e12	+	8.24231e12i	−0.0557472	+	0.316158i
$959$	1.91306e11	−	1.08495e12i	0.00730373	−	0.0414215i
$960$		0			0
$961$	3.71359e13	−	3.11607e13i	1.40455	−	1.17856i
$962$	4.38462e12	−	7.59439e12i	0.165061	−	0.285894i
$963$		0			0
$964$	−1.77859e13	−	3.08060e13i	−0.663328	−	1.14892i
$965$	−4.87406e13	−	1.77401e13i	−1.80933	−	0.658542i
$966$		0			0
$967$	−1.60735e12	−	1.34873e12i	−0.0591142	−	0.0496027i	0.612752	−	0.790275i	$-0.290063\pi$
$967$	−1.60735e12	−	1.34873e12i	−0.0591142	−	0.0496027i	−0.671866	+	0.740673i	$0.734507\pi$
$968$	1.76916e13	−	6.43923e12i	0.647633	−	0.235719i
$969$		0			0
$970$	1.13448e12	+	6.43395e12i	0.0411456	+	0.233348i
$971$	−2.47097e13			−0.892033			−0.446017	−	0.895025i	$-0.647158\pi$
$971$	−2.47097e13			−0.892033			−0.446017	+	0.895025i	$0.647158\pi$
$972$		0			0
$973$	−1.16528e11			−0.00416795
$974$	9.50073e11	+	5.38813e12i	0.0338253	+	0.191833i
$975$		0			0
$976$	−8.46593e12	+	3.08135e12i	−0.298642	+	0.108697i
$977$	5.99662e12	+	5.03176e12i	0.210562	+	0.176683i	0.741969	−	0.670434i	$-0.233892\pi$
$977$	5.99662e12	+	5.03176e12i	0.210562	+	0.176683i	−0.531407	+	0.847117i	$0.678336\pi$
$978$		0			0
$979$	2.12908e13	+	7.74920e12i	0.740745	+	0.269609i
$980$	−1.39548e13	−	2.41705e13i	−0.483289	−	0.837081i
$981$		0			0
$982$	5.21435e12	−	9.03151e12i	0.178936	−	0.309927i
$983$	3.61046e13	−	3.02953e13i	1.23331	−	1.03487i	0.235290	−	0.971925i	$-0.424396\pi$
$983$	3.61046e13	−	3.02953e13i	1.23331	−	1.03487i	0.998017	−	0.0629428i	$-0.0200486\pi$
$984$		0			0
$985$	6.74572e11	−	3.82569e12i	0.0228331	−	0.129493i
$986$	−6.13094e11	+	3.47703e12i	−0.0206576	+	0.117155i
$987$		0			0
$988$	1.59511e13	−	1.33845e13i	0.532578	−	0.446886i
$989$	6.57941e12	−	1.13959e13i	0.218677	−	0.378760i
$990$		0			0
$991$	1.16773e13	+	2.02256e13i	0.384601	+	0.666148i	0.991714	−	0.128468i	$-0.0410059\pi$
$991$	1.16773e13	+	2.02256e13i	0.384601	+	0.666148i	−0.607113	+	0.794615i	$0.707673\pi$
$992$	3.10721e13	+	1.13093e13i	1.01875	+	0.370795i
$993$		0			0
$994$	2.77197e10	+	2.32596e10i	0.000900636	+	0.000755723i
$995$	−2.60407e13	+	9.47804e12i	−0.842265	+	0.306559i
$996$		0			0
$997$	4.45742e11	+	2.52793e12i	0.0142875	+	0.0810282i	0.991118	−	0.132987i	$-0.0424569\pi$
$997$	4.45742e11	+	2.52793e12i	0.0142875	+	0.0810282i	−0.976830	+	0.214015i	$0.931346\pi$
$998$	−9.38387e12			−0.299430
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.10.15		156
3.2	odd	2		27.10.e.a.13.12	✓	156
27.2	odd	18		27.10.e.a.25.12	yes	156
27.25	even	9	inner	81.10.e.a.73.15		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.13.12	✓	156	3.2	odd	2
27.10.e.a.25.12	yes	156	27.2	odd	18
81.10.e.a.10.15		156	1.1	even	1	trivial
81.10.e.a.73.15		156	27.25	even	9	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.907148 + 5.14469i) q^{2} +(455.478 - 165.780i) q^{4} +(1094.11 + 918.064i) q^{5} +(184.507 + 67.1550i) q^{7} +(2603.43 + 4509.28i) q^{8} +(-3730.64 + 6461.66i) q^{10} +(-59207.7 + 49681.1i) q^{11} +(-14755.5 + 83682.5i) q^{13} +(-178.117 + 1010.15i) q^{14} +(169273. - 142037. i) q^{16} +(-291379. + 504684. i) q^{17} +(-252779. - 437826. i) q^{19} +(650538. + 236776. i) q^{20} +(-309304. - 259537. i) q^{22} +(-670872. + 244178. i) q^{23} +(15070.2 + 85467.2i) q^{25} -443906. q^{26} +95171.7 q^{28} +(-201386. - 1.14212e6i) q^{29} +(8.13347e6 - 2.96034e6i) q^{31} +(2.92650e6 + 2.45563e6i) q^{32} +(-2.86077e6 - 1.04123e6i) q^{34} +(140217. + 242864. i) q^{35} +(-9.87736e6 + 1.71081e7i) q^{37} +(2.02317e6 - 1.69764e6i) q^{38} +(-1.29137e6 + 7.32375e6i) q^{40} +(103793. - 588640. i) q^{41} +(-1.41194e7 + 1.18476e7i) q^{43} +(-1.87316e7 + 3.24441e7i) q^{44} +(-1.86480e6 - 3.22993e6i) q^{46} +(3.64648e7 + 1.32721e7i) q^{47} +(-3.08831e7 - 2.59140e7i) q^{49} +(-426031. + 155063. i) q^{50} +(7.15212e6 + 4.05617e7i) q^{52} -5.57694e7 q^{53} -1.10390e8 q^{55} +(177531. + 1.00683e6i) q^{56} +(5.69316e6 - 2.07214e6i) q^{58} +(5.19028e7 + 4.35516e7i) q^{59} +(-3.83125e7 - 1.39446e7i) q^{61} +(2.26083e7 + 3.91588e7i) q^{62} +(4.65897e7 - 8.06957e7i) q^{64} +(-9.29700e7 + 7.80111e7i) q^{65} +(-2.13517e7 + 1.21092e8i) q^{67} +(-4.90502e7 + 2.78177e8i) q^{68} +(-1.12226e6 + 941689. i) q^{70} +(1.76388e7 - 3.05513e7i) q^{71} +(6.85145e7 + 1.18671e8i) q^{73} +(-9.69761e7 - 3.52964e7i) q^{74} +(-1.87718e8 - 1.57514e8i) q^{76} +(-1.42606e7 + 5.19042e6i) q^{77} +(4.61143e7 + 2.61527e8i) q^{79} +3.15602e8 q^{80} +3.12253e6 q^{82} +(6.64650e7 + 3.76941e8i) q^{83} +(-7.82133e8 + 2.84673e8i) q^{85} +(-7.37607e7 - 6.18926e7i) q^{86} +(-3.78169e8 - 1.37642e8i) q^{88} +(-1.46572e8 - 2.53870e8i) q^{89} +(-8.34219e6 + 1.44491e7i) q^{91} +(-2.65087e8 + 2.22435e8i) q^{92} +(-3.52019e7 + 1.99640e8i) q^{94} +(1.25385e8 - 7.11096e8i) q^{95} +(6.70759e8 - 5.62834e8i) q^{97} +(1.05304e8 - 1.82392e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) \) 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Introduction

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