LMFDB - Embedded newform 49.7.d.e.19.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,7,Mod(19,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("49.19"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	49.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$11.2726500974$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	49.19
Dual form			49.7.d.e.31.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.22006 + 12.5055i) q^{2} +(5.48749 - 3.16820i) q^{3} +(-72.2584 - 125.155i) q^{4} +(169.953 + 98.1223i) q^{5} +91.4984i q^{6} +1162.67 q^{8} +(-344.425 + 596.562i) q^{9} +(-2454.14 + 1416.90i) q^{10} +(388.746 + 673.327i) q^{11} +(-793.034 - 457.858i) q^{12} +1858.37i q^{13} +1243.49 q^{15} +(-3770.02 + 6529.86i) q^{16} +(1942.83 - 1121.69i) q^{17} +(-4973.54 - 8614.42i) q^{18} +(-5366.70 - 3098.47i) q^{19} -28360.6i q^{20} -11227.1 q^{22} +(662.628 - 1147.71i) q^{23} +(6380.15 - 3683.58i) q^{24} +(11443.5 + 19820.7i) q^{25} +(-23239.9 - 13417.6i) q^{26} +8984.07i q^{27} -19588.9 q^{29} +(-8978.03 + 15550.4i) q^{30} +(-43676.8 + 25216.8i) q^{31} +(-17234.0 - 29850.1i) q^{32} +(4266.47 + 2463.25i) q^{33} +32394.8i q^{34} +99550.4 q^{36} +(7033.78 - 12182.9i) q^{37} +(77495.8 - 44742.2i) q^{38} +(5887.70 + 10197.8i) q^{39} +(197599. + 114084. i) q^{40} +60374.1i q^{41} +59618.8 q^{43} +(56180.3 - 97307.1i) q^{44} +(-117072. + 67591.5i) q^{45} +(9568.43 + 16573.0i) q^{46} +(-155091. - 89541.8i) q^{47} +47776.7i q^{48} -330490. q^{50} +(7107.50 - 12310.6i) q^{51} +(232585. - 134283. i) q^{52} +(94548.6 + 163763. i) q^{53} +(-112350. - 64865.5i) q^{54} +152579. i q^{55} -39266.3 q^{57} +(141433. - 244969. i) q^{58} +(94989.9 - 54842.5i) q^{59} +(-89852.3 - 155629. i) q^{60} +(261423. + 150933. i) q^{61} -728267. i q^{62} +15158.7 q^{64} +(-182348. + 315836. i) q^{65} +(-61608.4 + 35569.6i) q^{66} +(-111524. - 193166. i) q^{67} +(-280772. - 162104. i) q^{68} -8397.36i q^{69} +667143. q^{71} +(-400453. + 693605. i) q^{72} +(-226606. + 130831. i) q^{73} +(101569. + 175922. i) q^{74} +(125592. + 72510.5i) q^{75} +895561. i q^{76} -170038. q^{78} +(252972. - 438160. i) q^{79} +(-1.28145e6 + 739846. i) q^{80} +(-222622. - 385593. i) q^{81} +(-755009. - 435905. i) q^{82} +230815. i q^{83} +440253. q^{85} +(-430451. + 745564. i) q^{86} +(-107494. + 62061.6i) q^{87} +(451984. + 782859. i) q^{88} +(697220. + 402540. i) q^{89} -1.95206e6i q^{90} -191522. q^{92} +(-159784. + 276754. i) q^{93} +(2.23953e6 - 1.29299e6i) q^{94} +(-608057. - 1.05319e6i) q^{95} +(-189142. - 109201. i) q^{96} -474359. i q^{97} -535575. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{2} - 564 q^{4} + 1880 q^{8} + 1252 q^{9} + 3872 q^{11} + 44864 q^{15} - 37908 q^{16} + 19436 q^{18} + 159744 q^{22} - 40032 q^{23} + 28860 q^{25} + 68032 q^{29} - 21192 q^{30} + 82060 q^{32}+ \cdots - 8949984 q^{99}+O(q^{100}) $ 24 * q - 20 * q^2 - 564 * q^4 + 1880 * q^8 + 1252 * q^9 + 3872 * q^11 + 44864 * q^15 - 37908 * q^16 + 19436 * q^18 + 159744 * q^22 - 40032 * q^23 + 28860 * q^25 + 68032 * q^29 - 21192 * q^30 + 82060 * q^32 - 563240 * q^36 + 169632 * q^37 - 492128 * q^39 - 241536 * q^43 + 404312 * q^44 + 118872 * q^46 - 2091048 * q^50 + 539424 * q^51 + 15856 * q^53 + 1853888 * q^57 - 971304 * q^58 + 429912 * q^60 - 11496 * q^64 + 267904 * q^65 - 1508352 * q^67 + 5037248 * q^71 - 2550364 * q^72 + 3876024 * q^74 - 135184 * q^78 - 232224 * q^79 - 528204 * q^81 + 1508256 * q^85 + 1560848 * q^86 - 1812720 * q^88 + 7305776 * q^92 - 164384 * q^93 - 2305600 * q^95 - 8949984 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−7.22006	+	12.5055i	−0.902507	+	1.56319i	−0.0782778	+	0.996932i	$0.524942\pi$
$2$	−7.22006	+	12.5055i	−0.902507	+	1.56319i	−0.824229	+	0.566256i	$0.808391\pi$
$3$	5.48749	−	3.16820i	0.203240	−	0.117341i	−0.394926	−	0.918713i	$-0.629230\pi$
$3$	5.48749	−	3.16820i	0.203240	−	0.117341i	0.598166	+	0.801372i	$0.295896\pi$
$4$	−72.2584	−	125.155i	−1.12904	−	1.95555i
$5$	169.953	+	98.1223i	1.35962	+	0.784978i	0.989573	−	0.144034i	$-0.0460073\pi$
$5$	169.953	+	98.1223i	1.35962	+	0.784978i	0.370050	+	0.929012i	$0.379341\pi$
$6$			91.4984i			0.423604i
$7$		0			0
$7$		0			0
$8$	1162.67			2.27084
$9$	−344.425	+	596.562i	−0.472462	+	0.818329i
$10$	−2454.14	+	1416.90i	−2.45414	+	1.41690i
$11$	388.746	+	673.327i	0.292070	+	0.505881i	0.974299	−	0.225258i	$-0.0723225\pi$
$11$	388.746	+	673.327i	0.292070	+	0.505881i	−0.682229	+	0.731139i	$0.738989\pi$
$12$	−793.034	−	457.858i	−0.458932	−	0.264964i
$13$			1858.37i			0.845868i	0.906160	+	0.422934i	$0.139000\pi$
$13$			1858.37i			0.845868i	−0.906160	+	0.422934i	$0.861000\pi$
$14$		0			0
$15$	1243.49			0.368440
$16$	−3770.02	+	6529.86i	−0.920414	+	1.59420i
$17$	1942.83	−	1121.69i	0.395447	−	0.228311i	−0.289071	−	0.957308i	$-0.593346\pi$
$17$	1942.83	−	1121.69i	0.395447	−	0.228311i	0.684517	+	0.728996i	$0.260013\pi$
$18$	−4973.54	−	8614.42i	−0.852801	−	1.47709i
$19$	−5366.70	−	3098.47i	−0.782432	−	0.451737i	0.0548594	−	0.998494i	$-0.482529\pi$
$19$	−5366.70	−	3098.47i	−0.782432	−	0.451737i	−0.837292	+	0.546757i	$0.815862\pi$
$20$		−	28360.6i		−	3.54508i
$21$		0			0
$22$	−11227.1			−1.05438
$23$	662.628	−	1147.71i	0.0544611	−	0.0943294i	−0.837510	−	0.546423i	$-0.815989\pi$
$23$	662.628	−	1147.71i	0.0544611	−	0.0943294i	0.891971	+	0.452093i	$0.149323\pi$
$24$	6380.15	−	3683.58i	0.461527	−	0.266463i
$25$	11443.5	+	19820.7i	0.732382	+	1.26852i
$26$	−23239.9	−	13417.6i	−1.32225	−	0.763402i
$27$			8984.07i			0.456438i
$28$		0			0
$29$	−19588.9			−0.803186			−0.401593	−	0.915818i	$-0.631543\pi$
$29$	−19588.9			−0.803186			−0.401593	+	0.915818i	$0.631543\pi$
$30$	−8978.03	+	15550.4i	−0.332520	+	0.575941i
$31$	−43676.8	+	25216.8i	−1.46611	+	0.846457i	−0.999282	−	0.0378935i	$-0.987935\pi$
$31$	−43676.8	+	25216.8i	−1.46611	+	0.846457i	−0.466824	+	0.884350i	$0.654602\pi$
$32$	−17234.0	−	29850.1i	−0.525939	−	0.910953i
$33$	4266.47	+	2463.25i	0.118721	+	0.0685436i
$34$			32394.8i			0.824210i
$35$		0			0
$36$	99550.4			2.13371
$37$	7033.78	−	12182.9i	0.138862	−	0.240516i	−0.788204	−	0.615414i	$-0.788989\pi$
$37$	7033.78	−	12182.9i	0.138862	−	0.240516i	0.927066	+	0.374898i	$0.122322\pi$
$38$	77495.8	−	44742.2i	1.41230	−	0.815392i
$39$	5887.70	+	10197.8i	0.0992548	+	0.171914i
$40$	197599.	+	114084.i	3.08749	+	1.78256i
$41$			60374.1i			0.875990i	0.898977	+	0.437995i	$0.144311\pi$
$41$			60374.1i			0.875990i	−0.898977	+	0.437995i	$0.855689\pi$
$42$		0			0
$43$	59618.8			0.749856			0.374928	−	0.927054i	$-0.377667\pi$
$43$	59618.8			0.749856			0.374928	+	0.927054i	$0.377667\pi$
$44$	56180.3	−	97307.1i	0.659517	−	1.14232i
$45$	−117072.	+	67591.5i	−1.28474	+	0.741745i
$46$	9568.43	+	16573.0i	0.0983031	+	0.170266i
$47$	−155091.	−	89541.8i	−1.49380	−	0.862447i	−0.493827	−	0.869560i	$-0.664402\pi$
$47$	−155091.	−	89541.8i	−1.49380	−	0.862447i	−0.999975	+	0.00711370i	$0.997736\pi$
$48$			47776.7i			0.432009i
$49$		0			0
$50$	−330490.			−2.64392
$51$	7107.50	−	12310.6i	0.0535805	−	0.0928041i
$52$	232585.	−	134283.i	1.65414	−	0.955017i
$53$	94548.6	+	163763.i	0.635079	+	1.09999i	0.986498	+	0.163771i	$0.0523657\pi$
$53$	94548.6	+	163763.i	0.635079	+	1.09999i	−0.351420	+	0.936218i	$0.614301\pi$
$54$	−112350.	−	64865.5i	−0.713498	−	0.411939i
$55$			152579.i			0.917076i
$56$		0			0
$57$	−39266.3			−0.212029
$58$	141433.	−	244969.i	0.724881	−	1.25553i
$59$	94989.9	−	54842.5i	0.462510	−	0.267031i	−0.250589	−	0.968094i	$-0.580624\pi$
$59$	94989.9	−	54842.5i	0.462510	−	0.267031i	0.713099	+	0.701063i	$0.247291\pi$
$60$	−89852.3	−	155629.i	−0.415983	−	0.720503i
$61$	261423.	+	150933.i	1.15174	+	0.664958i	0.949311	−	0.314339i	$-0.101783\pi$
$61$	261423.	+	150933.i	1.15174	+	0.664958i	0.202430	+	0.979297i	$0.435116\pi$
$62$		−	728267.i		−	3.05573i
$63$		0			0
$64$	15158.7			0.0578258
$65$	−182348.	+	315836.i	−0.663988	+	1.15006i
$66$	−61608.4	+	35569.6i	−0.214293	+	0.123722i
$67$	−111524.	−	193166.i	−0.370805	−	0.642253i	0.618885	−	0.785482i	$-0.287585\pi$
$67$	−111524.	−	193166.i	−0.370805	−	0.642253i	−0.989690	+	0.143229i	$0.954251\pi$
$68$	−280772.	−	162104.i	−0.892949	−	0.515544i
$69$		−	8397.36i		−	0.0255620i
$70$		0			0
$71$	667143.			1.86399			0.931996	−	0.362469i	$-0.118066\pi$
$71$	667143.			1.86399			0.931996	+	0.362469i	$0.118066\pi$
$72$	−400453.	+	693605.i	−1.07289	+	1.85830i
$73$	−226606.	+	130831.i	−0.582510	+	0.336312i	−0.762130	−	0.647424i	$-0.775846\pi$
$73$	−226606.	+	130831.i	−0.582510	+	0.336312i	0.179620	+	0.983736i	$0.442513\pi$
$74$	101569.	+	175922.i	0.250648	+	0.434135i
$75$	125592.	+	72510.5i	0.297699	+	0.171877i
$76$			895561.i			2.04011i
$77$		0			0
$78$	−170038.			−0.358313
$79$	252972.	−	438160.i	0.513087	−	0.888693i	−0.486798	−	0.873515i	$-0.661835\pi$
$79$	252972.	−	438160.i	0.513087	−	0.888693i	0.999885	−	0.0151783i	$-0.00483160\pi$
$80$	−1.28145e6	+	739846.i	−2.50283	+	1.44501i
$81$	−222622.	−	385593.i	−0.418903	−	0.725562i
$82$	−755009.	−	435905.i	−1.36934	−	0.790587i
$83$			230815.i			0.403673i	0.979419	+	0.201836i	$0.0646909\pi$
$83$			230815.i			0.403673i	−0.979419	+	0.201836i	$0.935309\pi$
$84$		0			0
$85$	440253.			0.716878
$86$	−430451.	+	745564.i	−0.676751	+	1.17217i
$87$	−107494.	+	62061.6i	−0.163240	+	0.0942465i
$88$	451984.	+	782859.i	0.663246	+	1.14878i
$89$	697220.	+	402540.i	0.989008	+	0.571004i	0.904978	−	0.425459i	$-0.139887\pi$
$89$	697220.	+	402540.i	0.989008	+	0.571004i	0.0840304	+	0.996463i	$0.473221\pi$
$90$		−	1.95206e6i		−	2.67772i
$91$		0			0
$92$	−191522.			−0.245955
$93$	−159784.	+	276754.i	−0.198648	+	0.344068i
$94$	2.23953e6	−	1.29299e6i	2.69633	−	1.55673i
$95$	−608057.	−	1.05319e6i	−0.709208	−	1.22838i
$96$	−189142.	−	109201.i	−0.213784	−	0.123428i
$97$		−	474359.i		−	0.519747i	−0.965643	−	0.259873i	$-0.916319\pi$
$97$		−	474359.i		−	0.519747i	0.965643	−	0.259873i	$-0.0836808\pi$
$98$		0			0
$99$	−535575.			−0.551969
$100$	1.65377e6	−	2.86442e6i	1.65377	−	2.86442i
$101$	29015.8	−	16752.3i	0.0281624	−	0.0162596i	−0.485853	−	0.874041i	$-0.661491\pi$
$101$	29015.8	−	16752.3i	0.0281624	−	0.0162596i	0.514015	+	0.857781i	$0.328158\pi$
$102$	102633.	+	177766.i	0.0967135	+	0.167513i
$103$	1.17270e6	+	677057.i	1.07318	+	0.619603i	0.929050	−	0.369955i	$-0.120627\pi$
$103$	1.17270e6	+	677057.i	1.07318	+	0.619603i	0.144134	+	0.989558i	$0.453960\pi$
$104$			2.16068e6i			1.92083i
$105$		0			0
$106$	−2.73058e6			−2.29265
$107$	−655790.	+	1.13586e6i	−0.535320	+	0.927201i	0.463828	+	0.885925i	$0.346476\pi$
$107$	−655790.	+	1.13586e6i	−0.535320	+	0.927201i	−0.999148	+	0.0412758i	$0.986858\pi$
$108$	1.12440e6	−	649175.i	0.892588	−	0.515336i
$109$	255297.	+	442188.i	0.197136	+	0.341450i	0.947599	−	0.319463i	$-0.103502\pi$
$109$	255297.	+	442188.i	0.197136	+	0.341450i	−0.750462	+	0.660913i	$0.770169\pi$
$110$	−1.90807e6	−	1.10163e6i	−1.43356	−	0.827667i
$111$		−	89137.8i		−	0.0651768i
$112$		0			0
$113$	765635.			0.530624			0.265312	−	0.964163i	$-0.414525\pi$
$113$	765635.			0.530624			0.265312	+	0.964163i	$0.414525\pi$
$114$	283505.	−	491045.i	0.191358	−	0.331441i
$115$	225231.	−	130037.i	0.148093	−	0.0855016i
$116$	1.41546e6	+	2.45165e6i	0.906827	+	1.57067i
$117$	−1.10863e6	−	640070.i	−0.692198	−	0.399641i
$118$			1.58386e6i			0.963988i
$119$		0			0
$120$	1.44577e6			0.836670
$121$	583534.	−	1.01071e6i	0.329390	−	0.570520i
$122$	−3.77498e6	+	2.17949e6i	−2.07891	+	1.20026i
$123$	191277.	+	331302.i	0.102789	+	0.178037i
$124$	6.31203e6	+	3.64425e6i	3.31058	+	1.91136i
$125$			1.42512e6i			0.729660i
$126$		0			0
$127$	2.07098e6			1.01103			0.505516	−	0.862817i	$-0.331302\pi$
$127$	2.07098e6			1.01103			0.505516	+	0.862817i	$0.331302\pi$
$128$	993528.	−	1.72084e6i	0.473751	−	0.820561i
$129$	327158.	−	188885.i	0.152401	−	0.0879888i
$130$	−2.63312e6	−	4.56070e6i	−1.19851	−	2.07588i
$131$	−488490.	−	282030.i	−0.217291	−	0.125453i	0.387404	−	0.921910i	$-0.373372\pi$
$131$	−488490.	−	282030.i	−0.217291	−	0.125453i	−0.604695	+	0.796457i	$0.706705\pi$
$132$		−	711962.i		−	0.309553i
$133$		0			0
$134$	3.22085e6			1.33862
$135$	−881538.	+	1.52687e6i	−0.358294	+	0.620583i
$136$	2.25887e6	−	1.30416e6i	0.897998	−	0.518459i
$137$	692383.	+	1.19924e6i	0.269268	+	0.466386i	0.968673	−	0.248340i	$-0.0798850\pi$
$137$	692383.	+	1.19924e6i	0.269268	+	0.466386i	−0.699405	+	0.714725i	$0.746552\pi$
$138$	105013.	+	60629.4i	0.0399583	+	0.0230699i
$139$		−	83634.4i		−	0.0311416i	−0.999879	−	0.0155708i	$-0.995043\pi$
$139$		−	83634.4i		−	0.0311416i	0.999879	−	0.0155708i	$-0.00495654\pi$
$140$		0			0
$141$	−1.13475e6			−0.404801
$142$	−4.81681e6	+	8.34296e6i	−1.68227	+	2.91377i
$143$	−1.25129e6	+	722434.i	−0.427908	+	0.247053i
$144$	−2.59698e6	−	4.49809e6i	−0.869722	−	1.50640i
$145$	−3.32919e6	−	1.92211e6i	−1.09203	−	0.630483i
$146$		−	3.77843e6i		−	1.21410i
$147$		0			0
$148$	−2.03300e6			−0.627122
$149$	2.30903e6	−	3.99935e6i	0.698024	−	1.20901i	−0.271127	−	0.962544i	$-0.587396\pi$
$149$	2.30903e6	−	3.99935e6i	0.698024	−	1.20901i	0.969151	−	0.246469i	$-0.0792704\pi$
$150$	−1.81356e6	+	1.04706e6i	−0.537351	+	0.310240i
$151$	2.36877e6	+	4.10283e6i	0.688005	+	1.19166i	0.972482	+	0.232977i	$0.0748467\pi$
$151$	2.36877e6	+	4.10283e6i	0.688005	+	1.19166i	−0.284477	+	0.958683i	$0.591820\pi$
$152$	−6.23971e6	−	3.60250e6i	−1.77678	−	1.02582i
$153$			1.54536e6i			0.431474i
$154$		0			0
$155$	−9.89732e6			−2.65780
$156$	850871.	−	1.47375e6i	0.224125	−	0.388196i
$157$	−2.92557e6	+	1.68908e6i	−0.755983	+	0.436467i	−0.827852	−	0.560947i	$-0.810437\pi$
$157$	−2.92557e6	+	1.68908e6i	−0.755983	+	0.436467i	0.0718686	+	0.997414i	$0.477104\pi$
$158$	3.65294e6	+	6.32708e6i	0.926130	+	1.60410i
$159$	1.03767e6	+	599098.i	0.258147	+	0.149041i
$160$		−	6.76415e6i		−	1.65140i
$161$		0			0
$162$	6.42939e6			1.51225
$163$	84140.3	−	145735.i	0.0194286	−	0.0336513i	−0.856148	−	0.516731i	$-0.827149\pi$
$163$	84140.3	−	145735.i	0.0194286	−	0.0336513i	0.875576	+	0.483080i	$0.160482\pi$
$164$	7.55614e6	−	4.36254e6i	1.71304	−	0.989026i
$165$	483400.	+	837273.i	0.107610	+	0.186387i
$166$	−2.88645e6	−	1.66650e6i	−0.631016	−	0.364317i
$167$		−	4.88624e6i		−	1.04912i	−0.851373	−	0.524561i	$-0.824230\pi$
$167$		−	4.88624e6i		−	1.04912i	0.851373	−	0.524561i	$-0.175770\pi$
$168$		0			0
$169$	1.37326e6			0.284507
$170$	−3.17865e6	+	5.50558e6i	−0.646987	+	1.12061i
$171$	3.69685e6	−	2.13438e6i	0.739339	−	0.426858i
$172$	−4.30796e6	−	7.46161e6i	−0.846616	−	1.46638i
$173$	−6.04154e6	−	3.48808e6i	−1.16683	−	0.673672i	−0.213902	−	0.976855i	$-0.568617\pi$
$173$	−6.04154e6	−	3.48808e6i	−1.16683	−	0.673672i	−0.952932	+	0.303183i	$0.901951\pi$
$174$		−	1.79235e6i		−	0.340232i
$175$		0			0
$176$	−5.86231e6			−1.07530
$177$	347504.	−	601895.i	0.0626672	−	0.108543i
$178$	−1.00679e7	+	5.81273e6i	−1.78517	+	1.03067i
$179$	−4.02728e6	−	6.97544e6i	−0.702186	−	1.21622i	−0.967697	−	0.252114i	$-0.918874\pi$
$179$	−4.02728e6	−	6.97544e6i	−0.702186	−	1.21622i	0.265511	−	0.964108i	$-0.414459\pi$
$180$	1.69189e7	+	9.76812e6i	2.90104	+	1.67492i
$181$		−	259107.i		−	0.0436962i	−0.999761	−	0.0218481i	$-0.993045\pi$
$181$		−	259107.i		−	0.0436962i	0.999761	−	0.0218481i	$-0.00695501\pi$
$182$		0			0
$183$	1.91274e6			0.312107
$184$	770419.	−	1.33441e6i	0.123673	−	0.214207i
$185$	2.39082e6	−	1.38034e6i	0.377600	−	0.218008i
$186$	−2.30730e6	−	3.99635e6i	−0.358562	−	0.621048i
$187$	1.51053e6	+	872107.i	0.230997	+	0.133366i
$188$			2.58806e7i			3.89494i
$189$		0			0
$190$	1.75608e7			2.56026
$191$	2.11803e6	−	3.66854e6i	0.303971	−	0.526494i	−0.673060	−	0.739588i	$-0.735021\pi$
$191$	2.11803e6	−	3.66854e6i	0.303971	−	0.526494i	0.977032	+	0.213094i	$0.0683540\pi$
$192$	83183.0	−	48025.8i	0.0117525	−	0.00678532i
$193$	2.94466e6	+	5.10031e6i	0.409604	+	0.709454i	0.994845	−	0.101405i	$-0.0323337\pi$
$193$	2.94466e6	+	5.10031e6i	0.409604	+	0.709454i	−0.585242	+	0.810859i	$0.699000\pi$
$194$	5.93209e6	+	3.42490e6i	0.812461	+	0.469075i
$195$			2.31086e6i			0.311652i
$196$		0			0
$197$	−5.55238e6			−0.726241			−0.363120	−	0.931742i	$-0.618289\pi$
$197$	−5.55238e6			−0.726241			−0.363120	+	0.931742i	$0.618289\pi$
$198$	3.86688e6	−	6.69764e6i	0.498156	−	0.862831i
$199$	3.11259e6	−	1.79705e6i	0.394968	−	0.228035i	−0.289342	−	0.957226i	$-0.593437\pi$
$199$	3.11259e6	−	1.79705e6i	0.394968	−	0.228035i	0.684311	+	0.729191i	$0.260103\pi$
$200$	1.33050e7	+	2.30449e7i	1.66313	+	2.88062i
$201$	−1.22398e6	−	706664.i	−0.150725	−	0.0870211i
$202$			483809.i			0.0586976i
$203$		0			0
$204$	−2.05431e6			−0.241977
$205$	−5.92405e6	+	1.02608e7i	−0.687634	+	1.19102i
$206$	−1.69339e7	+	9.77678e6i	−1.93711	+	1.11839i
$207$	456452.	+	790597.i	0.0514616	+	0.0891342i
$208$	−1.21349e7	−	7.00609e6i	−1.34849	−	0.778549i
$209$		−	4.81806e6i		−	0.527757i
$210$		0			0
$211$	6.78263e6			0.722023			0.361012	−	0.932561i	$-0.382432\pi$
$211$	6.78263e6			0.722023			0.361012	+	0.932561i	$0.382432\pi$
$212$	1.36639e7	−	2.36665e7i	1.43406	−	2.48386i
$213$	3.66094e6	−	2.11364e6i	0.378838	−	0.218722i
$214$	−9.46968e6	−	1.64020e7i	−0.966260	−	1.67361i
$215$	1.01324e7	+	5.84994e6i	1.01952	+	0.588621i
$216$			1.04455e7i			1.03650i
$217$		0			0
$218$	−7.37305e6			−0.711668
$219$	−828999.	+	1.43587e6i	−0.0789263	+	0.136704i
$220$	1.90960e7	−	1.10251e7i	1.79339	−	1.03541i
$221$	2.08452e6	+	3.61050e6i	0.193121	+	0.334496i
$222$	1.11471e6	+	643580.i	0.101884	+	0.0588225i
$223$		−	1.77881e7i		−	1.60404i	−0.597298	−	0.802019i	$-0.703759\pi$
$223$		−	1.77881e7i		−	1.60404i	0.597298	−	0.802019i	$-0.296241\pi$
$224$		0			0
$225$	−1.57657e7			−1.38409
$226$	−5.52793e6	+	9.57465e6i	−0.478891	+	0.829464i
$227$	1.94394e7	−	1.12233e7i	1.66190	−	0.959498i	0.690092	−	0.723721i	$-0.257570\pi$
$227$	1.94394e7	−	1.12233e7i	1.66190	−	0.959498i	0.971807	−	0.235777i	$-0.0757634\pi$
$228$	2.83732e6	+	4.91438e6i	0.239389	+	0.414633i
$229$	8.02807e6	+	4.63501e6i	0.668505	+	0.385961i	0.795510	−	0.605941i	$-0.207203\pi$
$229$	8.02807e6	+	4.63501e6i	0.668505	+	0.385961i	−0.127005	+	0.991902i	$0.540536\pi$
$230$			3.75551e6i			0.308663i
$231$		0			0
$232$	−2.27755e7			−1.82391
$233$	441893.	−	765381.i	0.0349341	−	0.0605076i	−0.848030	−	0.529949i	$-0.822211\pi$
$233$	441893.	−	765381.i	0.0349341	−	0.0605076i	0.882964	+	0.469441i	$0.155545\pi$
$234$	1.60088e7	−	9.24268e6i	1.24943	−	0.721357i
$235$	−1.75721e7	−	3.04358e7i	−1.35400	−	2.34520i
$236$	−1.37276e7	−	7.92566e6i	−1.04438	−	0.602975i
$237$		−	3.20587e6i		−	0.240824i
$238$		0			0
$239$	1.79896e7			1.31773			0.658867	−	0.752260i	$-0.271036\pi$
$239$	1.79896e7			1.31773			0.658867	+	0.752260i	$0.271036\pi$
$240$	−4.68796e6	+	8.11979e6i	−0.339117	+	0.587369i
$241$	−1.51156e7	+	8.72701e6i	−1.07988	+	0.623468i	−0.930864	−	0.365367i	$-0.880944\pi$
$241$	−1.51156e7	+	8.72701e6i	−1.07988	+	0.623468i	−0.149015	+	0.988835i	$0.547610\pi$
$242$	8.42630e6	+	1.45948e7i	0.594553	+	1.02980i
$243$	−8.11521e6	−	4.68532e6i	−0.565563	−	0.326528i
$244$		−	4.36246e7i		−	3.00305i
$245$		0			0
$246$	−5.52414e6			−0.371073
$247$	5.75810e6	−	9.97333e6i	0.382110	−	0.661834i
$248$	−5.07817e7	+	2.93189e7i	−3.32930	+	1.92217i
$249$	731268.	+	1.26659e6i	0.0473673	+	0.0820425i
$250$	−1.78218e7	−	1.02894e7i	−1.14060	−	0.658523i
$251$			1.06645e7i			0.674402i	0.941433	+	0.337201i	$0.109480\pi$
$251$			1.06645e7i			0.674402i	−0.941433	+	0.337201i	$0.890520\pi$
$252$		0			0
$253$	1.03038e6			0.0636259
$254$	−1.49526e7	+	2.58987e7i	−0.912464	+	1.58043i
$255$	2.41588e6	−	1.39481e6i	0.145698	−	0.0841190i
$256$	1.48317e7	+	2.56893e7i	0.884040	+	1.53120i
$257$	−489121.	−	282394.i	−0.0288149	−	0.0166363i	0.485523	−	0.874224i	$-0.338629\pi$
$257$	−489121.	−	282394.i	−0.0288149	−	0.0166363i	−0.514338	+	0.857587i	$0.671962\pi$
$258$			5.45503e6i			0.317642i
$259$		0			0
$260$	5.27046e7			2.99867
$261$	6.74691e6	−	1.16860e7i	0.379475	−	0.657270i
$262$	7.05385e6	−	4.07254e6i	0.392213	−	0.226445i
$263$	532134.	+	921683.i	0.0292519	+	0.0506657i	0.880281	−	0.474453i	$-0.157354\pi$
$263$	532134.	+	921683.i	0.0292519	+	0.0506657i	−0.851029	+	0.525119i	$0.824021\pi$
$264$	4.96051e6	+	2.86395e6i	0.269597	+	0.155652i
$265$			3.71093e7i			1.99409i
$266$		0			0
$267$	5.10131e6			0.268008
$268$	−1.61171e7	+	2.79157e7i	−0.837305	+	1.45026i
$269$	−1.67504e7	+	9.67084e6i	−0.860534	+	0.496829i	−0.864191	−	0.503164i	$-0.832169\pi$
$269$	−1.67504e7	+	9.67084e6i	−0.860534	+	0.496829i	0.00365736	+	0.999993i	$0.498836\pi$
$270$	−1.27295e7	−	2.20481e7i	−0.646726	−	1.12016i
$271$	1.42909e7	+	8.25084e6i	0.718044	+	0.414563i	0.814032	−	0.580820i	$-0.197268\pi$
$271$	1.42909e7	+	8.25084e6i	0.718044	+	0.414563i	−0.0959886	+	0.995382i	$0.530601\pi$
$272$			1.69152e7i			0.840564i
$273$		0			0
$274$	−1.99962e7			−0.972065
$275$	−8.89720e6	+	1.54104e7i	−0.427814	+	0.740996i
$276$	−1.05097e6	+	606780.i	−0.0499879	+	0.0288605i
$277$	9.10881e6	+	1.57769e7i	0.428570	+	0.742306i	0.996746	−	0.0806013i	$-0.0256841\pi$
$277$	9.10881e6	+	1.57769e7i	0.428570	+	0.742306i	−0.568176	+	0.822907i	$0.692351\pi$
$278$	1.04589e6	+	603845.i	0.0486801	+	0.0281055i
$279$		−	3.47412e7i		−	1.59968i
$280$		0			0
$281$	−4.82451e6			−0.217437			−0.108719	−	0.994073i	$-0.534675\pi$
$281$	−4.82451e6			−0.217437			−0.108719	+	0.994073i	$0.534675\pi$
$282$	8.19293e6	−	1.41906e7i	0.365336	−	0.632780i
$283$	−2.26374e7	+	1.30697e7i	−0.998772	+	0.576641i	−0.907885	−	0.419220i	$-0.862304\pi$
$283$	−2.26374e7	+	1.30697e7i	−0.998772	+	0.576641i	−0.0908872	+	0.995861i	$0.528970\pi$
$284$	−4.82067e7	−	8.34965e7i	−2.10452	−	3.64513i
$285$	−6.67341e6	−	3.85290e6i	−0.288279	−	0.166438i
$286$		−	2.08641e7i		−	0.891868i
$287$		0			0
$288$	2.37432e7			0.993945
$289$	−9.55239e6	+	1.65452e7i	−0.395748	+	0.685455i
$290$	4.80738e7	−	2.77554e7i	1.97113	−	1.13803i
$291$	−1.50286e6	−	2.60304e6i	−0.0609875	−	0.105633i
$292$	3.27484e7	+	1.89073e7i	1.31535	+	0.759419i
$293$			1.60696e7i			0.638853i	0.947611	+	0.319427i	$0.103490\pi$
$293$			1.60696e7i			0.638853i	−0.947611	+	0.319427i	$0.896510\pi$
$294$		0			0
$295$	2.15251e7			0.838453
$296$	8.17798e6	−	1.41647e7i	0.315334	−	0.546175i
$297$	−6.04922e6	+	3.49252e6i	−0.230903	+	0.133312i
$298$	3.33426e7	+	5.77511e7i	1.25994	+	2.18228i
$299$	2.13287e6	+	1.23141e6i	0.0797903	+	0.0460669i
$300$		−	2.09580e7i		−	0.776221i
$301$		0			0
$302$	−6.84105e7			−2.48372
$303$	106149.	−	183856.i	0.00381583	−	0.00660920i
$304$	4.04651e7	−	2.33625e7i	1.44032	−	0.831571i
$305$	2.96197e7	+	5.13029e7i	1.04395	+	1.80818i
$306$	−1.93255e7	−	1.11576e7i	−0.674475	−	0.389408i
$307$			5.12280e7i			1.77048i	0.465131	+	0.885242i	$0.346007\pi$
$307$			5.12280e7i			1.77048i	−0.465131	+	0.885242i	$0.653993\pi$
$308$		0			0
$309$	8.58021e6			0.290819
$310$	7.14592e7	−	1.23771e8i	2.39868	−	4.15464i
$311$	2.17415e7	−	1.25524e7i	0.722783	−	0.417299i	−0.0929934	−	0.995667i	$-0.529644\pi$
$311$	2.17415e7	−	1.25524e7i	0.722783	−	0.417299i	0.815776	+	0.578368i	$0.196310\pi$
$312$	6.84546e6	+	1.18567e7i	0.225392	+	0.390391i
$313$	−3.67750e7	−	2.12320e7i	−1.19928	−	0.692403i	−0.238883	−	0.971048i	$-0.576781\pi$
$313$	−3.67750e7	−	2.12320e7i	−1.19928	−	0.692403i	−0.960394	+	0.278645i	$0.910115\pi$
$314$		−	4.87810e7i		−	1.57566i
$315$		0			0
$316$	−7.31174e7			−2.31718
$317$	9.88523e6	−	1.71217e7i	0.310320	−	0.537489i	−0.668112	−	0.744061i	$-0.732897\pi$
$317$	9.88523e6	−	1.71217e7i	0.310320	−	0.537489i	0.978431	+	0.206572i	$0.0662306\pi$
$318$	−1.49840e7	+	8.65104e6i	−0.465959	+	0.269022i
$319$	−7.61510e6	−	1.31897e7i	−0.234587	−	0.406316i
$320$	2.57626e6	+	1.48740e6i	0.0786212	+	0.0453920i
$321$			8.31070e6i			0.251259i
$322$		0			0
$323$	−1.39021e7			−0.412547
$324$	−3.21727e7	+	5.57247e7i	−0.945916	+	1.63837i
$325$	−3.68342e7	+	2.12662e7i	−1.07300	+	0.619499i
$326$	1.21499e6	+	2.10443e6i	0.0350689	+	0.0607411i
$327$	2.80188e6	+	1.61767e6i	0.0801321	+	0.0462643i
$328$			7.01953e7i			1.98924i
$329$		0			0
$330$	−1.39607e7			−0.388477
$331$	−1.06909e7	+	1.85172e7i	−0.294802	+	0.510611i	−0.974939	−	0.222474i	$-0.928587\pi$
$331$	−1.06909e7	+	1.85172e7i	−0.294802	+	0.510611i	0.680137	+	0.733085i	$0.261920\pi$
$332$	2.88877e7	−	1.66783e7i	0.789402	−	0.455762i
$333$	4.84522e6	+	8.39217e6i	0.131214	+	0.227270i
$334$	6.11049e7	+	3.52789e7i	1.63997	+	0.946839i
$335$		−	4.37721e7i		−	1.16430i
$336$		0			0
$337$	5.18725e7			1.35534			0.677669	−	0.735367i	$-0.262990\pi$
$337$	5.18725e7			1.35534			0.677669	+	0.735367i	$0.262990\pi$
$338$	−9.91503e6	+	1.71733e7i	−0.256770	+	0.444738i
$339$	4.20141e6	−	2.42569e6i	0.107844	−	0.0622638i
$340$	−3.18120e7	−	5.50999e7i	−0.809382	−	1.40189i
$341$	−3.39583e7	−	1.96058e7i	−0.856412	−	0.494450i
$342$			6.16413e7i			1.54097i
$343$		0			0
$344$	6.93171e7			1.70281
$345$	823969.	−	1.42716e6i	0.0200657	−	0.0347547i
$346$	8.72405e7	−	5.03683e7i	2.10615	−	1.21599i
$347$	−1.19958e7	−	2.07774e7i	−0.287106	−	0.497282i	0.686012	−	0.727591i	$-0.259360\pi$
$347$	−1.19958e7	−	2.07774e7i	−0.287106	−	0.497282i	−0.973118	+	0.230308i	$0.926027\pi$
$348$	1.55347e7	+	8.96894e6i	0.368607	+	0.212816i
$349$			5.60641e7i			1.31889i	0.751753	+	0.659445i	$0.229209\pi$
$349$			5.60641e7i			1.31889i	−0.751753	+	0.659445i	$0.770791\pi$
$350$		0			0
$351$	−1.66957e7			−0.386086
$352$	1.33993e7	−	2.32082e7i	0.307222	−	0.532125i
$353$	−3.03329e7	+	1.75127e7i	−0.689588	+	0.398134i	−0.803458	−	0.595362i	$-0.797009\pi$
$353$	−3.03329e7	+	1.75127e7i	−0.689588	+	0.398134i	0.113869	+	0.993496i	$0.463675\pi$
$354$	5.01800e6	+	8.69142e6i	0.113115	+	0.195921i
$355$	1.13383e8	+	6.54616e7i	2.53433	+	1.46319i
$356$		−	1.16348e8i		−	2.57874i
$357$		0			0
$358$	1.16309e8			2.53491
$359$	5.84289e6	−	1.01202e7i	0.126283	−	0.218728i	−0.795951	−	0.605361i	$-0.793029\pi$
$359$	5.84289e6	−	1.01202e7i	0.126283	−	0.218728i	0.922234	+	0.386633i	$0.126362\pi$
$360$	−1.36116e8	+	7.85868e7i	−2.91744	+	1.68439i
$361$	−4.32194e6	−	7.48583e6i	−0.0918666	−	0.159118i
$362$	3.24026e6	+	1.87077e6i	0.0683053	+	0.0394361i
$363$		−	7.39501e6i		−	0.154603i
$364$		0			0
$365$	−5.13498e7			−1.05599
$366$	−1.38101e7	+	2.39198e7i	−0.281678	+	0.487881i
$367$	−2.65848e7	+	1.53487e7i	−0.537817	+	0.310509i	−0.744194	−	0.667964i	$-0.767166\pi$
$367$	−2.65848e7	+	1.53487e7i	−0.537817	+	0.310509i	0.206377	+	0.978473i	$0.433833\pi$
$368$	4.99624e6	+	8.65374e6i	0.100254	+	0.173644i
$369$	−3.60169e7	−	2.07944e7i	−0.716848	−	0.413872i
$370$			3.98646e7i			0.787013i
$371$		0			0
$372$	4.61829e7			0.897124
$373$	−521217.	+	902775.i	−0.0100437	+	0.0173961i	−0.871004	−	0.491277i	$-0.836530\pi$
$373$	−521217.	+	902775.i	−0.0100437	+	0.0173961i	0.860960	+	0.508673i	$0.169864\pi$
$374$	−2.18123e7	+	1.25933e7i	−0.416952	+	0.240727i
$375$	4.51506e6	+	7.82031e6i	0.0856189	+	0.148296i
$376$	−1.80320e8	−	1.04108e8i	−3.39219	−	1.95848i
$377$		−	3.64035e7i		−	0.679389i
$378$		0			0
$379$	1.99959e6			0.0367303			0.0183651	−	0.999831i	$-0.494154\pi$
$379$	1.99959e6			0.0367303			0.0183651	+	0.999831i	$0.494154\pi$
$380$	−8.78745e7	+	1.52203e8i	−1.60145	+	2.77379i
$381$	1.13645e7	−	6.56129e6i	0.205483	−	0.118635i
$382$	3.05846e7	+	5.29741e7i	0.548673	+	0.950329i
$383$	3.31246e7	+	1.91245e7i	0.589595	+	0.340403i	0.764937	−	0.644105i	$-0.222770\pi$
$383$	3.31246e7	+	1.91245e7i	0.589595	+	0.340403i	−0.175342	+	0.984508i	$0.556103\pi$
$384$		−	1.25908e7i		−	0.222361i
$385$		0			0
$386$	−8.50425e7			−1.47868
$387$	−2.05342e7	+	3.55663e7i	−0.354279	+	0.613629i
$388$	−5.93685e7	+	3.42764e7i	−1.01639	+	0.586813i
$389$	−1.81978e7	−	3.15194e7i	−0.309150	−	0.535463i	0.669027	−	0.743238i	$-0.266711\pi$
$389$	−1.81978e7	−	3.15194e7i	−0.309150	−	0.535463i	−0.978177	+	0.207775i	$0.933378\pi$
$390$	−2.88984e7	−	1.66845e7i	−0.487170	−	0.281268i
$391$		−	2.97306e6i		−	0.0497364i
$392$		0			0
$393$	−3.57411e6			−0.0588831
$394$	4.00885e7	−	6.94353e7i	0.655437	−	1.13525i
$395$	8.59866e7	−	4.96444e7i	1.39521	−	0.805525i
$396$	3.86998e7	+	6.70300e7i	0.623194	+	1.07940i
$397$	−3.80990e7	−	2.19965e7i	−0.608895	−	0.351546i	0.163638	−	0.986520i	$-0.447677\pi$
$397$	−3.80990e7	−	2.19965e7i	−0.608895	−	0.351546i	−0.772533	+	0.634975i	$0.781011\pi$
$398$			5.18993e7i			0.823213i
$399$		0			0
$400$	−1.72568e8			−2.69638
$401$	5.16194e7	−	8.94075e7i	0.800534	−	1.38657i	−0.118730	−	0.992927i	$-0.537882\pi$
$401$	5.16194e7	−	8.94075e7i	0.800534	−	1.38657i	0.919265	−	0.393640i	$-0.128784\pi$
$402$	1.76744e7	−	1.02043e7i	0.272061	−	0.157074i
$403$	−4.68622e7	−	8.11677e7i	−0.715991	−	1.24013i
$404$	−4.19327e6	−	2.42098e6i	−0.0635929	−	0.0367154i
$405$		−	8.73769e7i		−	1.31532i
$406$		0			0
$407$	1.09374e7			0.162230
$408$	8.26369e6	−	1.43131e7i	0.121673	−	0.210744i
$409$	7.13325e7	−	4.11838e7i	1.04260	−	0.601945i	0.122031	−	0.992526i	$-0.461059\pi$
$409$	7.13325e7	−	4.11838e7i	1.04260	−	0.601945i	0.920568	+	0.390581i	$0.127726\pi$
$410$	−8.55439e7	−	1.48166e8i	−1.24119	−	2.14980i
$411$	7.59888e6	+	4.38722e6i	0.109452	+	0.0631922i
$412$		−	1.95692e8i		−	2.79822i
$413$		0			0
$414$	−1.31824e7			−0.185778
$415$	−2.26481e7	+	3.92276e7i	−0.316874	+	0.548842i
$416$	5.54726e7	−	3.20271e7i	0.770546	−	0.444875i
$417$	−264971.	−	458943.i	−0.00365418	−	0.00632922i
$418$	6.02523e7	+	3.47867e7i	0.824983	+	0.476304i
$419$		−	5.01770e7i		−	0.682123i	−0.940041	−	0.341061i	$-0.889214\pi$
$419$		−	5.01770e7i		−	0.682123i	0.940041	−	0.341061i	$-0.110786\pi$
$420$		0			0
$421$	6.31813e7			0.846725			0.423362	−	0.905960i	$-0.360850\pi$
$421$	6.31813e7			0.846725			0.423362	+	0.905960i	$0.360850\pi$
$422$	−4.89710e7	+	8.48203e7i	−0.651631	+	1.12866i
$423$	1.06834e8	−	6.16809e7i	1.41153	−	0.814947i
$424$	1.09929e8	+	1.90403e8i	1.44216	+	2.49790i
$425$	4.44654e7	+	2.56721e7i	0.579236	+	0.334422i
$426$			6.10425e7i			0.789594i
$427$		0			0
$428$	1.89545e8			2.41758
$429$	−4.57764e6	+	7.92870e6i	−0.0579788	+	0.100422i
$430$	−1.46313e8	+	8.44737e7i	−1.84025	+	1.06247i
$431$	−2.21729e7	−	3.84046e7i	−0.276944	−	0.479680i	0.693680	−	0.720283i	$-0.255988\pi$
$431$	−2.21729e7	−	3.84046e7i	−0.276944	−	0.479680i	−0.970624	+	0.240603i	$0.922655\pi$
$432$	−5.86647e7	−	3.38701e7i	−0.727656	−	0.420112i
$433$			1.68992e7i			0.208162i	0.994569	+	0.104081i	$0.0331901\pi$
$433$			1.68992e7i			0.208162i	−0.994569	+	0.104081i	$0.966810\pi$
$434$		0			0
$435$	−2.43585e7			−0.295926
$436$	3.68948e7	−	6.39036e7i	0.445149	−	0.771021i
$437$	−7.11226e6	+	4.10626e6i	−0.0852243	+	0.0492043i
$438$	−1.19708e7	−	2.07341e7i	−0.142463	−	0.246753i
$439$	−5.08374e7	−	2.93510e7i	−0.600882	−	0.346920i	0.168506	−	0.985701i	$-0.446106\pi$
$439$	−5.08374e7	−	2.93510e7i	−0.600882	−	0.346920i	−0.769389	+	0.638781i	$0.779439\pi$
$440$			1.77399e8i			2.08254i
$441$		0			0
$442$	−6.02015e7			−0.697173
$443$	2.86788e7	−	4.96732e7i	0.329876	−	0.571361i	−0.652611	−	0.757693i	$-0.726327\pi$
$443$	2.86788e7	−	4.96732e7i	0.329876	−	0.571361i	0.982487	+	0.186331i	$0.0596598\pi$
$444$	−1.11561e7	+	6.44095e6i	−0.127456	+	0.0735870i
$445$	7.89963e7	+	1.36826e8i	0.896452	+	1.55270i
$446$	2.22449e8	+	1.28431e8i	2.50741	+	1.44766i
$447$		−	2.92619e7i		−	0.327627i
$448$		0			0
$449$	−1.03104e8			−1.13903			−0.569515	−	0.821981i	$-0.692869\pi$
$449$	−1.03104e8			−1.13903			−0.569515	+	0.821981i	$0.692869\pi$
$450$	1.13829e8	−	1.97158e8i	1.24915	−	2.16360i
$451$	−4.06516e7	+	2.34702e7i	−0.443147	+	0.255851i
$452$	−5.53236e7	−	9.58232e7i	−0.599094	−	1.03766i
$453$	2.59972e7	+	1.50095e7i	0.279661	+	0.161462i
$454$			3.24132e8i			3.46381i
$455$		0			0
$456$	−4.56538e7			−0.481485
$457$	−8.01272e7	+	1.38784e8i	−0.839520	+	1.45409i	0.0507761	+	0.998710i	$0.483831\pi$
$457$	−8.01272e7	+	1.38784e8i	−0.839520	+	1.45409i	−0.890296	+	0.455382i	$0.849503\pi$
$458$	−1.15926e8	+	6.69300e7i	−1.20666	+	0.696666i
$459$	1.00774e7	+	1.74545e7i	0.104210	+	0.180497i
$460$	−3.25497e7	−	1.87926e7i	−0.334405	−	0.193069i
$461$			1.11301e8i			1.13604i	0.823013	+	0.568022i	$0.192291\pi$
$461$			1.11301e8i			1.13604i	−0.823013	+	0.568022i	$0.807709\pi$
$462$		0			0
$463$	−22327.8			−0.000224959			−0.000112479	−	1.00000i	$-0.500036\pi$
$463$	−22327.8			−0.000224959			−0.000112479		1.00000i	$0.500036\pi$
$464$	7.38505e7	−	1.27913e8i	0.739264	−	1.28044i
$465$	−5.43114e7	+	3.13567e7i	−0.540172	+	0.311869i
$466$	6.38098e6	+	1.10522e7i	0.0630565	+	0.109217i
$467$	−8.10138e7	−	4.67733e7i	−0.795442	−	0.459249i	0.0464330	−	0.998921i	$-0.485215\pi$
$467$	−8.10138e7	−	4.67733e7i	−0.795442	−	0.459249i	−0.841875	+	0.539673i	$0.818548\pi$
$468$			1.85002e8i			1.80484i
$469$		0			0
$470$	5.07486e8			4.88799
$471$	−1.07027e7	+	1.85376e7i	−0.102431	+	0.177415i
$472$	1.10442e8	−	6.37638e7i	1.05029	−	0.606384i
$473$	2.31766e7	+	4.01430e7i	0.219011	+	0.379338i
$474$	4.00910e7	+	2.31465e7i	0.376454	+	0.217346i
$475$		−	1.41829e8i		−	1.32338i
$476$		0			0
$477$	−1.30260e8			−1.20020
$478$	−1.29886e8	+	2.24969e8i	−1.18926	+	2.05986i
$479$	5.56820e6	−	3.21480e6i	0.0506650	−	0.0292515i	−0.474454	−	0.880281i	$-0.657354\pi$
$479$	5.56820e6	−	3.21480e6i	0.0506650	−	0.0292515i	0.525119	+	0.851029i	$0.324021\pi$
$480$	−2.14302e7	−	3.71182e7i	−0.193777	−	0.335632i
$481$	2.26403e7	+	1.30714e7i	0.203445	+	0.117459i
$482$		−	2.52038e8i		−	2.25074i
$483$		0			0
$484$	−1.68661e8			−1.48757
$485$	4.65452e7	−	8.06186e7i	0.407990	−	0.706659i
$486$	1.17185e8	−	6.76565e7i	1.02085	−	0.589388i
$487$	−8.69857e7	−	1.50664e8i	−0.753114	−	1.30443i	−0.946306	−	0.323271i	$-0.895217\pi$
$487$	−8.69857e7	−	1.50664e8i	−0.753114	−	1.30443i	0.193192	−	0.981161i	$-0.438116\pi$
$488$	3.03949e8	+	1.75485e8i	2.61542	+	1.51001i
$489$		−	1.06629e6i		−	0.00911906i
$490$		0			0
$491$	7.52300e6			0.0635545			0.0317773	−	0.999495i	$-0.489883\pi$
$491$	7.52300e6			0.0635545			0.0317773	+	0.999495i	$0.489883\pi$
$492$	2.76428e7	−	4.78788e7i	0.232106	−	0.402020i
$493$	−3.80579e7	+	2.19727e7i	−0.317617	+	0.183376i
$494$	8.31477e7	+	1.44016e8i	0.689714	+	1.19462i
$495$	−9.10225e7	−	5.25519e7i	−0.750470	−	0.433284i
$496$		−	3.80271e8i		−	3.11636i
$497$		0			0
$498$	−2.11192e7			−0.170997
$499$	1.22263e8	−	2.11765e8i	0.983992	−	1.70432i	0.337660	−	0.941268i	$-0.390365\pi$
$499$	1.22263e8	−	2.11765e8i	0.983992	−	1.70432i	0.646332	−	0.763056i	$-0.276302\pi$
$500$	1.78361e8	−	1.02977e8i	1.42689	−	0.823814i
$501$	−1.54806e7	−	2.68132e7i	−0.123105	−	0.213224i
$502$	−1.33365e8	−	7.69982e7i	−1.05422	−	0.608653i
$503$			1.51896e8i			1.19355i	0.802407	+	0.596777i	$0.203552\pi$
$503$			1.51896e8i			1.19355i	−0.802407	+	0.596777i	$0.796448\pi$
$504$		0			0
$505$	6.57508e6			0.0510537
$506$	−7.43937e6	+	1.28854e7i	−0.0574229	+	0.0994593i
$507$	7.53576e6	−	4.35077e6i	0.0578233	−	0.0333843i
$508$	−1.49646e8	−	2.59194e8i	−1.14149	−	1.97713i
$509$	−4.96640e7	−	2.86735e7i	−0.376607	−	0.217434i	0.299734	−	0.954023i	$-0.403102\pi$
$509$	−4.96640e7	−	2.86735e7i	−0.376607	−	0.217434i	−0.676341	+	0.736589i	$0.736435\pi$
$510$			4.02824e7i			0.303672i
$511$		0			0
$512$	−3.01172e8			−2.24391
$513$	2.78368e7	−	4.82148e7i	0.206190	−	0.357132i
$514$	7.06296e6	−	4.07780e6i	0.0520112	−	0.0300287i
$515$	1.32869e8	+	2.30135e8i	0.972750	+	1.68485i
$516$	−4.72798e7	−	2.72970e7i	−0.344133	−	0.198685i
$517$		−	1.39236e8i		−	1.00758i
$518$		0			0
$519$	−4.42038e7			−0.316197
$520$	−2.12011e8	+	3.67213e8i	−1.50781	+	2.61161i
$521$	8.24826e7	−	4.76213e7i	0.583242	−	0.336735i	−0.179178	−	0.983817i	$-0.557344\pi$
$521$	8.24826e7	−	4.76213e7i	0.583242	−	0.336735i	0.762421	+	0.647081i	$0.224011\pi$
$522$	9.74261e7	+	1.68747e8i	0.684958	+	1.18638i
$523$	−7.32785e7	−	4.23073e7i	−0.512237	−	0.295740i	0.221515	−	0.975157i	$-0.428900\pi$
$523$	−7.32785e7	−	4.23073e7i	−0.512237	−	0.295740i	−0.733753	+	0.679416i	$0.762233\pi$
$524$			8.15161e7i			0.566565i
$525$		0			0
$526$	−1.53681e7			−0.105600
$527$	−5.65710e7	+	9.79839e7i	−0.386511	+	0.669457i
$528$	−3.21694e7	+	1.85730e7i	−0.218545	+	0.126177i
$529$	7.31398e7	+	1.26682e8i	0.494068	+	0.855751i
$530$	−4.64071e8	−	2.67931e8i	−3.11714	−	1.79968i
$531$			7.55565e7i			0.504647i
$532$		0			0
$533$	−1.12198e8			−0.740972
$534$	−3.68318e7	+	6.37945e7i	−0.241879	+	0.418947i
$535$	−2.22907e8	+	1.28695e8i	−1.45567	+	0.840429i
$536$	−1.29666e8	−	2.24589e8i	−0.842040	−	1.45846i
$537$	−4.41992e7	−	2.55184e7i	−0.285425	−	0.164790i
$538$		−	2.79296e8i		−	1.79357i
$539$		0			0
$540$	2.54794e8			1.61811
$541$	−5.51966e7	+	9.56033e7i	−0.348594	+	0.603783i	−0.986000	−	0.166745i	$-0.946674\pi$
$541$	−5.51966e7	+	9.56033e7i	−0.348594	+	0.603783i	0.637406	+	0.770528i	$0.280008\pi$
$542$	−2.06362e8	+	1.19143e8i	−1.29608	+	0.748291i
$543$	−820903.	−	1.42185e6i	−0.00512734	−	0.00888082i
$544$	−6.69653e7	−	3.86625e7i	−0.415962	−	0.240156i
$545$			1.00202e8i			0.618992i
$546$		0			0
$547$	1.45987e8			0.891972			0.445986	−	0.895040i	$-0.352853\pi$
$547$	1.45987e8			0.891972			0.445986	+	0.895040i	$0.352853\pi$
$548$	1.00061e8	−	1.73311e8i	0.608027	−	1.05313i
$549$	−1.80081e8	+	1.03970e8i	−1.08831	+	0.628335i
$550$	−1.28477e8	−	2.22528e8i	−0.772211	−	1.33751i
$551$	1.05128e8	+	6.06955e7i	0.628438	+	0.362829i
$552$		−	9.76338e6i		−	0.0580474i
$553$		0			0
$554$	−2.63064e8			−1.54715
$555$	8.74640e6	−	1.51492e7i	0.0511624	−	0.0886158i
$556$	−1.04673e7	+	6.04329e6i	−0.0608989	+	0.0351600i
$557$	−2.19297e7	−	3.79833e7i	−0.126901	−	0.219800i	0.795573	−	0.605857i	$-0.207170\pi$
$557$	−2.19297e7	−	3.79833e7i	−0.126901	−	0.219800i	−0.922475	+	0.386058i	$0.873836\pi$
$558$	4.34456e8	+	2.50833e8i	2.50059	+	1.44372i
$559$			1.10794e8i			0.634280i
$560$		0			0
$561$	1.10520e7			0.0625971
$562$	3.48332e7	−	6.03329e7i	0.196239	−	0.339895i
$563$	2.00596e8	−	1.15814e8i	1.12408	−	0.648989i	0.181641	−	0.983365i	$-0.441859\pi$
$563$	2.00596e8	−	1.15814e8i	1.12408	−	0.648989i	0.942440	+	0.334376i	$0.108526\pi$
$564$	8.19949e7	+	1.42019e8i	0.457035	+	0.791608i
$565$	1.30122e8	+	7.51259e7i	0.721448	+	0.416528i
$566$		−	3.77455e8i		−	2.08169i
$567$		0			0
$568$	7.75669e8			4.23283
$569$	−7.46882e7	+	1.29364e8i	−0.405429	+	0.702224i	−0.994371	−	0.105951i	$-0.966211\pi$
$569$	−7.46882e7	+	1.29364e8i	−0.405429	+	0.702224i	0.588942	+	0.808175i	$0.299545\pi$
$570$	9.63648e7	−	5.56363e7i	0.520348	−	0.300423i
$571$	1.00448e8	+	1.73981e8i	0.539551	+	0.934531i	0.998928	+	0.0462890i	$0.0147395\pi$
$571$	1.00448e8	+	1.73981e8i	0.539551	+	0.934531i	−0.459377	+	0.888242i	$0.651927\pi$
$572$	1.80833e8	+	1.04404e8i	0.966250	+	0.557864i
$573$		−	2.68414e7i		−	0.142673i
$574$		0			0
$575$	3.03311e7			0.159545
$576$	−5.22103e6	+	9.04309e6i	−0.0273205	+	0.0473205i
$577$	1.78272e7	−	1.02926e7i	0.0928018	−	0.0535791i	−0.452881	−	0.891571i	$-0.649604\pi$
$577$	1.78272e7	−	1.02926e7i	0.0928018	−	0.0535791i	0.545683	+	0.837992i	$0.316270\pi$
$578$	−1.37938e8	−	2.38915e8i	−0.714330	−	1.23726i
$579$	3.23176e7	+	1.86586e7i	0.166496	+	0.0961264i
$580$			5.55554e8i			2.84736i
$581$		0			0
$582$	4.34030e7			0.220167
$583$	−7.35107e7	+	1.27324e8i	−0.370975	+	0.642548i
$584$	−2.63469e8	+	1.52114e8i	−1.32279	+	0.763713i
$585$	−1.25610e8	−	2.17563e8i	−0.627419	−	1.08672i
$586$	−2.00958e8	−	1.16023e8i	−0.998648	−	0.576569i
$587$			6.90917e7i			0.341595i	0.985306	+	0.170798i	$0.0546344\pi$
$587$			6.90917e7i			0.341595i	−0.985306	+	0.170798i	$0.945366\pi$
$588$		0			0
$589$	3.12534e8			1.52950
$590$	−1.55412e8	+	2.69182e8i	−0.756709	+	1.31066i
$591$	−3.04686e7	+	1.75911e7i	−0.147601	+	0.0852177i
$592$	5.30350e7	+	9.18593e7i	0.255621	+	0.442749i
$593$	5.93495e7	+	3.42654e7i	0.284612	+	0.164321i	0.635509	−	0.772093i	$-0.280790\pi$
$593$	5.93495e7	+	3.42654e7i	0.284612	+	0.164321i	−0.350898	+	0.936414i	$0.614123\pi$
$594$		−	1.00865e8i		−	0.481260i
$595$		0			0
$596$	−6.67387e8			−3.15238
$597$	1.13869e7	−	1.97226e7i	0.0535156	−	0.0926918i
$598$	−3.07988e7	+	1.77817e7i	−0.144023	+	0.0831514i
$599$	−9.49861e6	−	1.64521e7i	−0.0441957	−	0.0765492i	0.843081	−	0.537786i	$-0.180739\pi$
$599$	−9.49861e6	−	1.64521e7i	−0.0441957	−	0.0765492i	−0.887277	+	0.461237i	$0.847406\pi$
$600$	1.46022e8	+	8.43059e7i	0.676028	+	0.390305i
$601$		−	1.67730e7i		−	0.0772659i	−0.999253	−	0.0386329i	$-0.987700\pi$
$601$		−	1.67730e7i		−	0.0772659i	0.999253	−	0.0386329i	$-0.0123003\pi$
$602$		0			0
$603$	1.53647e8			0.700765
$604$	3.42327e8	−	5.92927e8i	1.55357	−	2.69086i
$605$	1.98346e8	−	1.14515e8i	0.895691	−	0.517128i
$606$	1.53281e6	+	2.65490e6i	0.00688762	+	0.0119297i
$607$	−1.25939e8	−	7.27108e7i	−0.563110	−	0.325112i	0.191283	−	0.981535i	$-0.438735\pi$
$607$	−1.25939e8	−	7.27108e7i	−0.563110	−	0.325112i	−0.754393	+	0.656423i	$0.772069\pi$
$608$			2.13596e8i			0.950345i
$609$		0			0
$610$	−8.55425e8			−3.76871
$611$	1.66402e8	−	2.88217e8i	0.729516	−	1.26356i
$612$	1.93410e8	−	1.11665e8i	0.843769	−	0.487150i
$613$	−1.72220e8	−	2.98294e8i	−0.747657	−	1.29498i	−0.948943	−	0.315447i	$-0.897846\pi$
$613$	−1.72220e8	−	2.98294e8i	−0.747657	−	1.29498i	0.201287	−	0.979532i	$-0.435488\pi$
$614$	−6.40631e8	−	3.69869e8i	−2.76760	−	1.59787i
$615$			7.50743e7i			0.322750i
$616$		0			0
$617$	2.54785e8			1.08472			0.542361	−	0.840146i	$-0.317531\pi$
$617$	2.54785e8			1.08472			0.542361	+	0.840146i	$0.317531\pi$
$618$	−6.19496e7	+	1.07300e8i	−0.262466	+	0.454605i
$619$	−1.89969e8	+	1.09679e8i	−0.800962	+	0.462435i	−0.843807	−	0.536646i	$-0.819691\pi$
$619$	−1.89969e8	+	1.09679e8i	−0.800962	+	0.462435i	0.0428456	+	0.999082i	$0.486358\pi$
$620$	7.15164e8	+	1.23870e9i	3.00076	+	5.19746i
$621$	1.03111e7	+	5.95310e6i	0.0430555	+	0.0248581i
$622$			3.62517e8i			1.50646i
$623$		0			0
$624$	−8.87869e7			−0.365422
$625$	3.89684e7	−	6.74953e7i	0.159615	−	0.276461i
$626$	5.31035e8	−	3.06593e8i	2.16471	−	1.24980i
$627$	−1.52646e7	−	2.64391e7i	−0.0619274	−	0.107261i
$628$	4.22795e8	+	2.44101e8i	1.70707	+	0.985575i
$629$		−	3.15590e7i		−	0.126815i
$630$		0			0
$631$	−3.29543e8			−1.31167			−0.655835	−	0.754905i	$-0.727683\pi$
$631$	−3.29543e8			−1.31167			−0.655835	+	0.754905i	$0.727683\pi$
$632$	2.94123e8	−	5.09437e8i	1.16514	−	2.01808i
$633$	3.72196e7	−	2.14888e7i	0.146744	−	0.0847228i
$634$	1.42744e8	+	2.47240e8i	0.560131	+	0.970175i
$635$	3.51969e8	+	2.03210e8i	1.37462	+	0.793639i
$636$		−	1.73160e8i		−	0.673093i
$637$		0			0
$638$	2.19926e8			0.846865
$639$	−2.29781e8	+	3.97992e8i	−0.880666	+	1.52536i
$640$	3.37706e8	−	1.94974e8i	1.28824	−	0.743768i
$641$	−1.82843e8	−	3.16694e8i	−0.694233	−	1.20245i	−0.970439	−	0.241348i	$-0.922410\pi$
$641$	−1.82843e8	−	3.16694e8i	−0.694233	−	1.20245i	0.276206	−	0.961099i	$-0.410923\pi$
$642$	−1.03929e8	−	6.00037e7i	−0.392766	−	0.226763i
$643$		−	3.47395e8i		−	1.30674i	−0.757037	−	0.653372i	$-0.773354\pi$
$643$		−	3.47395e8i		−	1.30674i	0.757037	−	0.653372i	$-0.226646\pi$
$644$		0			0
$645$	7.41351e7			0.276277
$646$	1.00374e8	−	1.73853e8i	0.372327	−	0.644889i
$647$	−2.46067e8	+	1.42067e8i	−0.908533	+	0.524542i	−0.879959	−	0.475050i	$-0.842430\pi$
$647$	−2.46067e8	+	1.42067e8i	−0.908533	+	0.524542i	−0.0285742	+	0.999592i	$0.509097\pi$
$648$	−2.58837e8	−	4.48319e8i	−0.951264	−	1.64764i
$649$	7.38539e7	+	4.26396e7i	0.270171	+	0.155983i
$650$		−	6.14173e8i		−	2.23641i
$651$		0			0
$652$	−2.43194e7			−0.0877424
$653$	3.30338e7	−	5.72161e7i	0.118637	−	0.205484i	−0.800591	−	0.599211i	$-0.795481\pi$
$653$	3.30338e7	−	5.72161e7i	0.118637	−	0.205484i	0.919228	+	0.393727i	$0.128814\pi$
$654$	−4.04595e7	+	2.33593e7i	−0.144640	+	0.0835077i
$655$	−5.53468e7	−	9.58636e7i	−0.196956	−	0.341138i
$656$	−3.94235e8	−	2.27612e8i	−1.39651	−	0.806274i
$657$		−	1.80246e8i		−	0.635580i
$658$		0			0
$659$	−4.59493e7			−0.160555			−0.0802773	−	0.996773i	$-0.525581\pi$
$659$	−4.59493e7			−0.160555			−0.0802773	+	0.996773i	$0.525581\pi$
$660$	6.98594e7	−	1.21000e8i	0.242992	−	0.420875i
$661$	4.11179e8	−	2.37394e8i	1.42373	−	0.821988i	0.427111	−	0.904199i	$-0.359531\pi$
$661$	4.11179e8	−	2.37394e8i	1.42373	−	0.821988i	0.996615	+	0.0822109i	$0.0261981\pi$
$662$	−1.54378e8	−	2.67390e8i	−0.532121	−	0.921661i
$663$	2.28776e7	+	1.32084e7i	0.0785000	+	0.0453220i
$664$			2.68362e8i			0.916677i
$665$		0			0
$666$	−1.39931e8			−0.473687
$667$	−1.29802e7	+	2.24823e7i	−0.0437424	+	0.0757640i
$668$	−6.11539e8	+	3.53072e8i	−2.05161	+	1.18450i
$669$	−5.63563e7	−	9.76119e7i	−0.188219	−	0.326005i
$670$	5.47392e8	+	3.16037e8i	1.82001	+	1.05078i
$671$			2.34698e8i			0.776858i
$672$		0			0
$673$	3.68856e7			0.121007			0.0605037	−	0.998168i	$-0.480729\pi$
$673$	3.68856e7			0.121007			0.0605037	+	0.998168i	$0.480729\pi$
$674$	−3.74523e8	+	6.48692e8i	−1.22320	+	2.11865i
$675$	−1.78070e8	+	1.02809e8i	−0.579002	+	0.334287i
$676$	−9.92297e7	−	1.71871e8i	−0.321219	−	0.556368i
$677$	3.62339e8	+	2.09196e8i	1.16775	+	0.674199i	0.953148	−	0.302503i	$-0.0978223\pi$
$677$	3.62339e8	+	2.09196e8i	1.16775	+	0.674199i	0.214599	+	0.976702i	$0.431156\pi$
$678$			7.00544e7i			0.224774i
$679$		0			0
$680$	5.11869e8			1.62792
$681$	7.11155e7	−	1.23176e8i	0.225177	−	0.390017i
$682$	4.90362e8	−	2.83111e8i	1.54584	−	0.892489i
$683$	1.94524e8	+	3.36926e8i	0.610536	+	1.05748i	0.991150	+	0.132745i	$0.0423792\pi$
$683$	1.94524e8	+	3.36926e8i	0.610536	+	1.05748i	−0.380614	+	0.924734i	$0.624287\pi$
$684$	−5.34257e8	−	3.08454e8i	−1.66948	−	0.963877i
$685$			2.71753e8i			0.845478i
$686$		0			0
$687$	5.87385e7			0.181156
$688$	−2.24764e8	+	3.89303e8i	−0.690179	+	1.19542i
$689$	−3.04333e8	+	1.75707e8i	−0.930445	+	0.537193i
$690$	1.18982e7	+	2.06083e7i	0.0362188	+	0.0627328i
$691$	9.31641e7	+	5.37883e7i	0.282367	+	0.163025i	0.634495	−	0.772927i	$-0.281208\pi$
$691$	9.31641e7	+	5.37883e7i	0.282367	+	0.163025i	−0.352127	+	0.935952i	$0.614542\pi$
$692$			1.00817e9i			3.04240i
$693$		0			0
$694$	3.46443e8			1.03646
$695$	8.20640e6	−	1.42139e7i	0.0244455	−	0.0423408i
$696$	−1.24980e8	+	7.21572e7i	−0.370692	+	0.214019i
$697$	6.77213e7	+	1.17297e8i	0.199999	+	0.346408i
$698$	−7.01110e8	−	4.04786e8i	−2.06167	−	1.19031i
$699$		−	5.60002e6i		−	0.0163968i
$700$		0			0
$701$	3.62675e8			1.05284			0.526421	−	0.850224i	$-0.323533\pi$
$701$	3.62675e8			1.05284			0.526421	+	0.850224i	$0.323533\pi$
$702$	1.20544e8	−	2.08789e8i	0.348446	−	0.603526i
$703$	−7.54964e7	+	4.35879e7i	−0.217300	+	0.125458i
$704$	5.89287e6	+	1.02068e7i	0.0168892	+	0.0292530i
$705$	−1.92853e8	−	1.11344e8i	−0.550376	−	0.317760i
$706$		−	5.05771e8i		−	1.43727i
$707$		0			0
$708$	−1.00440e8			−0.283014
$709$	−5.20169e7	+	9.00959e7i	−0.145951	+	0.252794i	−0.929727	−	0.368249i	$-0.879957\pi$
$709$	−5.20169e7	+	9.00959e7i	−0.145951	+	0.252794i	0.783777	+	0.621043i	$0.213291\pi$
$710$	−1.63726e9	+	9.45273e8i	−4.57449	+	2.64108i
$711$	1.74260e8	+	3.01827e8i	0.484829	+	0.839748i
$712$	8.10638e8	+	4.68022e8i	2.24588	+	1.29666i
$713$			6.68375e7i			0.184396i
$714$		0			0
$715$	−2.83548e8			−0.775725
$716$	−5.82009e8	+	1.00807e9i	−1.58559	+	2.74632i
$717$	9.87176e7	−	5.69947e7i	0.267816	−	0.154624i
$718$	8.43720e7	+	1.46137e8i	0.227942	+	0.394808i
$719$	−5.70581e8	−	3.29425e8i	−1.53508	−	0.886278i	−0.999116	−	0.0420368i	$-0.986615\pi$
$719$	−5.70581e8	−	3.29425e8i	−1.53508	−	0.886278i	−0.535963	−	0.844241i	$-0.680051\pi$
$720$		−	1.01929e9i		−	2.73085i
$721$		0			0
$722$	1.24819e8			0.331641
$723$	−5.52979e7	+	9.57787e7i	−0.146317	+	0.253428i
$724$	−3.24286e7	+	1.87227e7i	−0.0854501	+	0.0493346i
$725$	−2.24165e8	−	3.88265e8i	−0.588239	−	1.01886i
$726$	9.24784e7	+	5.33924e7i	0.241674	+	0.139531i
$727$		−	2.03821e8i		−	0.530452i	−0.964186	−	0.265226i	$-0.914553\pi$
$727$		−	2.03821e8i		−	0.530452i	0.964186	−	0.265226i	$-0.0854466\pi$
$728$		0			0
$729$	2.65207e8			0.684547
$730$	3.70749e8	−	6.42156e8i	0.953040	−	1.65071i
$731$	1.15829e8	−	6.68741e7i	0.296528	−	0.171201i
$732$	−1.38212e8	−	2.39390e8i	−0.352380	−	0.610340i
$733$	−1.88057e8	−	1.08575e8i	−0.477504	−	0.275687i	0.241872	−	0.970308i	$-0.422239\pi$
$733$	−1.88057e8	−	1.08575e8i	−0.477504	−	0.275687i	−0.719376	+	0.694621i	$0.755572\pi$
$734$		−	4.43274e8i		−	1.12095i
$735$		0			0
$736$	−4.56789e7			−0.114573
$737$	8.67093e7	−	1.50185e8i	0.216602	−	0.375166i
$738$	5.20088e8	−	3.00273e8i	1.29392	−	0.747045i
$739$	1.98472e8	+	3.43763e8i	0.491774	+	0.851777i	0.999955	−	0.00947280i	$-0.00301533\pi$
$739$	1.98472e8	+	3.43763e8i	0.491774	+	0.851777i	−0.508181	+	0.861250i	$0.669682\pi$
$740$	−3.45514e8	−	1.99483e8i	−0.852650	−	0.492277i
$741$		−	7.29714e7i		−	0.179349i
$742$		0			0
$743$	−3.43381e7			−0.0837163			−0.0418581	−	0.999124i	$-0.513328\pi$
$743$	−3.43381e7			−0.0837163			−0.0418581	+	0.999124i	$0.513328\pi$
$744$	−1.85776e8	+	3.21774e8i	−0.451098	+	0.781325i
$745$	7.84851e8	−	4.53134e8i	1.89810	−	1.09587i
$746$	−7.52644e6	−	1.30362e7i	−0.0181290	−	0.0314003i
$747$	−1.37695e8	−	7.94984e7i	−0.330337	−	0.190720i
$748$		−	2.52068e8i		−	0.602301i
$749$		0			0
$750$	−1.30396e8			−0.309087
$751$	1.09113e8	−	1.88989e8i	0.257606	−	0.446186i	−0.707994	−	0.706218i	$-0.750400\pi$
$751$	1.09113e8	−	1.88989e8i	0.257606	−	0.446186i	0.965600	+	0.260032i	$0.0837332\pi$
$752$	1.16939e9	−	6.75148e8i	2.74983	−	1.58762i
$753$	3.37873e7	+	5.85213e7i	0.0791349	+	0.137066i
$754$	4.55244e8	+	2.62835e8i	1.06201	+	0.613153i
$755$			9.29716e8i			2.16028i
$756$		0			0
$757$	−8.34617e8			−1.92397			−0.961987	−	0.273094i	$-0.911953\pi$
$757$	−8.34617e8			−1.92397			−0.961987	+	0.273094i	$0.911953\pi$
$758$	−1.44372e7	+	2.50059e7i	−0.0331493	+	0.0574163i
$759$	5.65418e6	−	3.26444e6i	0.0129314	−	0.00746592i
$760$	−7.06971e8	−	1.22451e9i	−1.61050	−	2.78947i
$761$	6.79608e8	+	3.92372e8i	1.54207	+	0.890316i	0.998708	+	0.0508188i	$0.0161831\pi$
$761$	6.79608e8	+	3.92372e8i	1.54207	+	0.890316i	0.543364	+	0.839497i	$0.317150\pi$
$762$			1.89491e8i			0.428277i
$763$		0			0
$764$	−6.12183e8			−1.37278
$765$	−1.51634e8	+	2.62638e8i	−0.338698	+	0.586642i
$766$	−4.78322e8	+	2.76159e8i	−1.06423	+	0.614432i
$767$	1.01918e8	+	1.76527e8i	0.225873	+	0.391223i
$768$	1.62778e8	+	9.39798e7i	0.359345	+	0.207468i
$769$		−	6.31305e8i		−	1.38823i	−0.719866	−	0.694113i	$-0.755797\pi$
$769$		−	6.31305e8i		−	1.38823i	0.719866	−	0.694113i	$-0.244203\pi$
$770$		0			0
$771$	−3.57872e6			−0.00780846
$772$	4.25553e8	−	7.37080e8i	0.924916	−	1.60200i
$773$	−4.50465e8	+	2.60076e8i	−0.975265	+	0.563069i	−0.900837	−	0.434157i	$-0.857046\pi$
$773$	−4.50465e8	+	2.60076e8i	−0.975265	+	0.563069i	−0.0744276	+	0.997226i	$0.523713\pi$
$774$	−2.96516e8	−	5.13581e8i	−0.639478	−	1.10761i
$775$	−9.99628e8	−	5.77135e8i	−2.14750	−	1.23986i
$776$		−	5.51523e8i		−	1.18026i
$777$		0			0
$778$	5.25555e8			1.11604
$779$	1.87067e8	−	3.24010e8i	0.395718	−	0.685403i
$780$	2.89216e8	−	1.66979e8i	0.609451	−	0.351866i
$781$	2.59349e8	+	4.49206e8i	0.544417	+	0.942958i
$782$	3.71797e7	+	2.14657e7i	0.0777473	+	0.0448874i
$783$		−	1.75988e8i		−	0.366605i
$784$		0			0
$785$	−6.62946e8			−1.37047
$786$	2.58053e7	−	4.46961e7i	0.0531424	−	0.0920453i
$787$	−3.47971e8	+	2.00901e8i	−0.713870	+	0.412153i	−0.812492	−	0.582972i	$-0.801890\pi$
$787$	−3.47971e8	+	2.00901e8i	−0.713870	+	0.412153i	0.0986226	+	0.995125i	$0.468556\pi$
$788$	4.01206e8	+	6.94910e8i	0.819953	+	1.42020i
$789$	5.84015e6	+	3.37181e6i	0.0118903	+	0.00686488i
$790$			1.43374e9i			2.90797i
$791$		0			0
$792$	−6.22698e8			−1.25344
$793$	−2.80489e8	+	4.85822e8i	−0.562466	+	0.974221i
$794$	5.50154e8	−	3.17632e8i	1.09906	−	0.634545i
$795$	1.17570e8	+	2.03637e8i	0.233988	+	0.405280i
$796$	−4.49821e8	−	2.59704e8i	−0.891868	−	0.514920i
$797$		−	7.28759e8i		−	1.43949i	−0.694238	−	0.719746i	$-0.744258\pi$
$797$		−	7.28759e8i		−	1.43949i	0.694238	−	0.719746i	$-0.255742\pi$
$798$		0			0
$799$	−4.01754e8			−0.787625
$800$	3.94433e8	−	6.83178e8i	0.770377	−	1.33433i
$801$	−4.80280e8	+	2.77290e8i	−0.934538	+	0.539556i
$802$	7.45390e8	+	1.29105e9i	1.44498	+	2.50277i
$803$	−1.76184e8	−	1.01720e8i	−0.340268	−	0.196454i
$804$			2.04250e8i			0.393000i
$805$		0			0
$806$	1.35339e9			2.58475
$807$	−6.12783e7	+	1.06137e8i	−0.116597	+	0.201951i
$808$	3.37358e7	−	1.94774e7i	0.0639525	−	0.0369230i
$809$	1.45313e8	+	2.51690e8i	0.274448	+	0.475358i	0.969996	−	0.243122i	$-0.0781716\pi$
$809$	1.45313e8	+	2.51690e8i	0.274448	+	0.475358i	−0.695548	+	0.718480i	$0.744838\pi$
$810$	1.09269e9	+	6.30866e8i	2.05609	+	1.18709i
$811$			9.60970e8i			1.80155i	0.434281	+	0.900777i	$0.357002\pi$
$811$			9.60970e8i			1.80155i	−0.434281	+	0.900777i	$0.642998\pi$
$812$		0			0
$813$	1.04561e8			0.194580
$814$	−7.89687e7	+	1.36778e8i	−0.146414	+	0.253596i
$815$	2.85998e7	−	1.65121e7i	0.0528311	−	0.0305020i
$816$	5.35908e7	+	9.28220e7i	0.0986325	+	0.170836i
$817$	−3.19957e8	−	1.84727e8i	−0.586712	−	0.338738i
$818$			1.18940e9i			2.17304i
$819$		0			0
$820$	1.71225e9			3.10546
$821$	4.51271e8	−	7.81624e8i	0.815470	−	1.41243i	−0.0935208	−	0.995617i	$-0.529812\pi$
$821$	4.51271e8	−	7.81624e8i	0.815470	−	1.41243i	0.908990	−	0.416817i	$-0.136855\pi$
$822$	−1.09729e8	+	6.33519e7i	−0.197563	+	0.114063i
$823$	−1.56775e8	−	2.71542e8i	−0.281240	−	0.487122i	0.690451	−	0.723380i	$-0.257412\pi$
$823$	−1.56775e8	−	2.71542e8i	−0.281240	−	0.487122i	−0.971690	+	0.236258i	$0.924079\pi$
$824$	1.36346e9	+	7.87195e8i	2.43703	+	1.40702i
$825$			1.12753e8i			0.200800i
$826$		0			0
$827$	1.74812e8			0.309069			0.154535	−	0.987987i	$-0.450612\pi$
$827$	1.74812e8			0.309069			0.154535	+	0.987987i	$0.450612\pi$
$828$	6.59649e7	−	1.14255e8i	0.116204	−	0.201272i
$829$	3.05696e8	−	1.76493e8i	0.536569	−	0.309788i	−0.207118	−	0.978316i	$-0.566409\pi$
$829$	3.05696e8	−	1.76493e8i	0.536569	−	0.309788i	0.743687	+	0.668528i	$0.233075\pi$
$830$	−3.27041e8	−	5.66451e8i	−0.571963	−	0.990668i
$831$	9.99689e7	+	5.77171e7i	0.174206	+	0.100578i
$832$			2.81705e7i			0.0489130i
$833$		0			0
$834$	7.65241e6			0.0131917
$835$	4.79449e8	−	8.30431e8i	0.823537	−	1.42641i
$836$	−6.03006e8	+	3.48146e8i	−1.03205	+	0.595857i
$837$	−2.26549e8	−	3.92395e8i	−0.386355	−	0.669187i
$838$	6.27489e8	+	3.62281e8i	1.06629	+	0.615621i
$839$		−	7.39162e8i		−	1.25157i	−0.779997	−	0.625783i	$-0.784779\pi$
$839$		−	7.39162e8i		−	1.25157i	0.779997	−	0.625783i	$-0.215221\pi$
$840$		0			0
$841$	−2.11098e8			−0.354893
$842$	−4.56173e8	+	7.90114e8i	−0.764175	+	1.32359i
$843$	−2.64744e7	+	1.52850e7i	−0.0441920	+	0.0255143i
$844$	−4.90102e8	−	8.48882e8i	−0.815191	−	1.41195i
$845$	2.33390e8	+	1.34748e8i	0.386822	+	0.223332i
$846$			1.78136e9i			2.94198i
$847$		0			0
$848$	−1.42580e9			−2.33814
$849$	−8.28148e7	+	1.43439e8i	−0.135327	+	0.234393i
$850$	−6.42086e8	+	3.70708e8i	−1.04553	+	0.603637i
$851$	−9.32157e6	−	1.61454e7i	−0.0151252	−	0.0261976i
$852$	−5.29067e8	−	3.05457e8i	−0.855445	−	0.493891i
$853$		−	4.44098e8i		−	0.715537i	−0.933810	−	0.357768i	$-0.883538\pi$
$853$		−	4.44098e8i		−	0.715537i	0.933810	−	0.357768i	$-0.116462\pi$
$854$		0			0
$855$	8.37721e8			1.34030
$856$	−7.62468e8	+	1.32063e9i	−1.21563	+	2.10553i
$857$	6.60329e8	−	3.81241e8i	1.04910	−	0.605699i	0.126704	−	0.991941i	$-0.459560\pi$
$857$	6.60329e8	−	3.81241e8i	1.04910	−	0.605699i	0.922398	+	0.386241i	$0.126227\pi$
$858$	−6.61016e7	−	1.14491e8i	−0.104653	−	0.181264i
$859$	−1.21243e8	−	6.99996e7i	−0.191283	−	0.110437i	0.401300	−	0.915947i	$-0.368559\pi$
$859$	−1.21243e8	−	6.99996e7i	−0.191283	−	0.110437i	−0.592583	+	0.805509i	$0.701892\pi$
$860$		−	1.69083e9i		−	2.65830i
$861$		0			0
$862$	6.40359e8			0.999774
$863$	2.78151e6	−	4.81772e6i	0.00432761	−	0.00749564i	−0.863853	−	0.503743i	$-0.831956\pi$
$863$	2.78151e6	−	4.81772e6i	0.00432761	−	0.00749564i	0.868181	+	0.496247i	$0.165289\pi$
$864$	2.68175e8	−	1.54831e8i	0.415794	−	0.240059i
$865$	−6.84518e8	−	1.18562e9i	−1.05764	−	1.83188i
$866$	−2.11333e8	−	1.22013e8i	−0.325396	−	0.187868i
$867$			1.21056e8i			0.185750i
$868$		0			0
$869$	3.93367e8			0.599430
$870$	1.75870e8	−	3.04615e8i	0.267075	−	0.462588i
$871$	3.58974e8	−	2.07254e8i	0.543261	−	0.313652i
$872$	2.96827e8	+	5.14120e8i	0.447666	+	0.775380i
$873$	2.82984e8	+	1.63381e8i	0.425323	+	0.245561i
$874$		−	1.18590e8i		−	0.177629i
$875$		0			0
$876$	2.39609e8			0.356443
$877$	−6.54586e8	+	1.13378e9i	−0.970438	+	1.68085i	−0.276204	+	0.961099i	$0.589077\pi$
$877$	−6.54586e8	+	1.13378e9i	−0.970438	+	1.68085i	−0.694234	+	0.719749i	$0.744257\pi$
$878$	7.34097e8	−	4.23831e8i	1.08460	−	0.626195i
$879$	5.09116e7	+	8.81815e7i	0.0749636	+	0.129841i
$880$	−9.96317e8	−	5.75224e8i	−1.46201	−	0.844090i
$881$			6.23452e8i			0.911748i	0.890044	+	0.455874i	$0.150673\pi$
$881$			6.23452e8i			0.911748i	−0.890044	+	0.455874i	$0.849327\pi$
$882$		0			0
$883$	−1.02846e9			−1.49384			−0.746921	−	0.664913i	$-0.768469\pi$
$883$	−1.02846e9			−1.49384			−0.746921	+	0.664913i	$0.768469\pi$
$884$	3.01249e8	−	5.21778e8i	0.436082	−	0.755317i
$885$	1.18119e8	−	6.81958e7i	0.170407	−	0.0983847i
$886$	4.14126e8	+	7.17286e8i	0.595430	+	1.03132i
$887$	−2.16811e8	−	1.25176e8i	−0.310679	−	0.179370i	0.336552	−	0.941665i	$-0.390739\pi$
$887$	−2.16811e8	−	1.25176e8i	−0.310679	−	0.179370i	−0.647230	+	0.762295i	$0.724073\pi$
$888$		−	1.03638e8i		−	0.148006i
$889$		0			0
$890$	−2.28143e9			−3.23622
$891$	1.73087e8	−	2.99796e8i	0.244699	−	0.423830i
$892$	−2.22627e9	+	1.28534e9i	−3.13678	+	1.81102i
$893$	5.54885e8	+	9.61088e8i	0.779199	+	1.34961i
$894$	3.65934e8	+	2.11272e8i	0.512142	+	0.295685i
$895$		−	1.58066e9i		−	2.20480i
$896$		0			0
$897$	1.56054e7			0.0216221
$898$	7.44414e8	−	1.28936e9i	1.02798	−	1.78052i
$899$	8.55580e8	−	4.93969e8i	1.17756	−	0.679862i
$900$	1.13920e9	+	1.97316e9i	1.56269	+	2.70666i
$901$	3.67384e8	+	2.12109e8i	0.502280	+	0.289991i
$902$		−	6.77824e8i		−	0.923629i
$903$		0			0
$904$	8.90182e8			1.20496
$905$	2.54242e7	−	4.40359e7i	0.0343005	−	0.0594103i
$906$	−3.75402e8	+	2.16738e8i	−0.504791	+	0.291441i
$907$	−3.85357e8	−	6.67458e8i	−0.516466	−	0.894545i	−0.999817	−	0.0191188i	$-0.993914\pi$
$907$	−3.85357e8	−	6.67458e8i	−0.516466	−	0.894545i	0.483351	−	0.875427i	$-0.339419\pi$
$908$	−2.80932e9	−	1.62196e9i	−3.75269	−	2.16662i
$909$			2.30796e7i			0.0307282i
$910$		0			0
$911$	−3.02151e8			−0.399640			−0.199820	−	0.979833i	$-0.564036\pi$
$911$	−3.02151e8			−0.399640			−0.199820	+	0.979833i	$0.564036\pi$
$912$	1.48035e8	−	2.56403e8i	0.195154	−	0.338017i
$913$	−1.55414e8	+	8.97283e7i	−0.204210	+	0.117901i
$914$	−1.15705e9	−	2.00406e9i	−1.51535	−	2.62466i
$915$	3.25076e8	+	1.87683e8i	0.424347	+	0.244997i
$916$		−	1.33967e9i		−	1.74306i
$917$		0			0
$918$	−2.91037e8			−0.376201
$919$	−4.45150e8	+	7.71022e8i	−0.573535	+	0.993392i	0.422664	+	0.906286i	$0.361095\pi$
$919$	−4.45150e8	+	7.71022e8i	−0.573535	+	0.993392i	−0.996199	+	0.0871052i	$0.972238\pi$
$920$	2.61870e8	−	1.51191e8i	0.336296	−	0.194161i
$921$	1.62301e8	+	2.81113e8i	0.207750	+	0.359834i
$922$	−1.39187e9	−	8.03597e8i	−1.77585	−	1.02529i
$923$			1.23980e9i			1.57669i
$924$		0			0
$925$	3.21964e8			0.406801
$926$	161208.	−	279220.i	0.000203027	−	0.000351652i
$927$	−8.07812e8	+	4.66391e8i	−1.01408	+	0.585478i
$928$	3.37594e8	+	5.84731e8i	0.422427	+	0.731664i
$929$	9.40647e8	+	5.43083e8i	1.17322	+	0.677359i	0.954436	−	0.298415i	$-0.0964579\pi$
$929$	9.40647e8	+	5.43083e8i	1.17322	+	0.677359i	0.218783	+	0.975773i	$0.429791\pi$
$930$		−	9.05589e8i		−	1.12585i
$931$		0			0
$932$	−1.27722e8			−0.157768
$933$	7.95373e7	−	1.37763e8i	0.0979323	−	0.169624i
$934$	1.16985e9	−	6.75412e8i	1.43578	−	0.828950i
$935$	1.71146e8	+	2.96434e8i	0.209379	+	0.362655i
$936$	−1.28898e9	−	7.44191e8i	−1.57187	−	0.907522i
$937$		−	1.06570e9i		−	1.29543i	−0.761882	−	0.647716i	$-0.775724\pi$
$937$		−	1.06570e9i		−	1.29543i	0.761882	−	0.647716i	$-0.224276\pi$
$938$		0			0
$939$	−2.69070e8			−0.324989
$940$	−2.53946e9	+	4.39848e9i	−3.05744	+	5.29565i
$941$	9.54393e8	−	5.51019e8i	1.14540	−	0.661299i	0.197640	−	0.980275i	$-0.436672\pi$
$941$	9.54393e8	−	5.51019e8i	1.14540	−	0.661299i	0.947763	+	0.318976i	$0.103339\pi$
$942$	−1.54548e8	−	2.67685e8i	−0.184889	−	0.320237i
$943$	6.92918e7	+	4.00056e7i	0.0826317	+	0.0477074i
$944$			8.27028e8i			0.983115i
$945$		0			0
$946$	−6.69345e8			−0.790635
$947$	−5.02919e8	+	8.71081e8i	−0.592172	+	1.02567i	0.401767	+	0.915742i	$0.368396\pi$
$947$	−5.02919e8	+	8.71081e8i	−0.592172	+	1.02567i	−0.993939	+	0.109930i	$0.964937\pi$
$948$	−4.01231e8	+	2.31651e8i	−0.470944	+	0.271900i
$949$	−2.43133e8	−	4.21119e8i	−0.284476	−	0.492727i
$950$	1.77364e9	+	1.02401e9i	2.06869	+	1.19436i
$951$		−	1.25274e8i		−	0.145653i
$952$		0			0
$953$	9.08482e8			1.04963			0.524817	−	0.851215i	$-0.324134\pi$
$953$	9.08482e8			1.04963			0.524817	+	0.851215i	$0.324134\pi$
$954$	9.40482e8	−	1.62896e9i	1.08319	−	1.87614i
$955$	7.19931e8	−	4.15653e8i	0.826573	−	0.477222i
$956$	−1.29990e9	−	2.25149e9i	−1.48777	−	2.57689i
$957$	−8.35755e7	−	4.82524e7i	−0.0953550	−	0.0550532i
$958$			9.28441e7i			0.105599i
$959$		0			0
$960$	1.88496e7			0.0213053
$961$	8.28021e8	−	1.43417e9i	0.932978	−	1.61596i
$962$	−3.26929e8	+	1.88752e8i	−0.367221	+	0.212015i
$963$	−4.51741e8	−	7.82438e8i	−0.505837	−	0.876135i
$964$	2.18446e9	+	1.26120e9i	2.43845	+	1.40784i
$965$			1.15575e9i			1.28612i
$966$		0			0
$967$	1.34738e9			1.49009			0.745043	−	0.667016i	$-0.232429\pi$
$967$	1.34738e9			1.49009			0.745043	+	0.667016i	$0.232429\pi$
$968$	6.78458e8	−	1.17512e9i	0.747992	−	1.29556i
$969$	−7.62877e7	+	4.40447e7i	−0.0838462	+	0.0484086i
$970$	6.72117e8	+	1.16414e9i	0.736427	+	1.27553i
$971$	8.17032e8	+	4.71714e8i	0.892445	+	0.515253i	0.874741	−	0.484590i	$-0.161031\pi$
$971$	8.17032e8	+	4.71714e8i	0.892445	+	0.515253i	0.0177033	+	0.999843i	$0.494365\pi$
$972$			1.35421e9i			1.47465i
$973$		0			0
$974$	2.51217e9			2.71876
$975$	−1.34751e8	+	2.33396e8i	−0.145385	+	0.251814i
$976$	−1.97114e9	+	1.13804e9i	−2.12016	+	1.22407i
$977$	−6.24017e8	−	1.08083e9i	−0.669133	−	1.15897i	−0.978147	−	0.207915i	$-0.933332\pi$
$977$	−6.24017e8	−	1.08083e9i	−0.669133	−	1.15897i	0.309014	−	0.951057i	$-0.400001\pi$
$978$	1.33345e7	+	7.69870e6i	0.0142548	+	0.00823002i
$979$			6.25943e8i			0.667094i
$980$		0			0
$981$	−3.51723e8			−0.372558
$982$	−5.43165e7	+	9.40789e7i	−0.0573584	+	0.0993477i
$983$	−1.47112e9	+	8.49350e8i	−1.54877	+	0.894182i	−0.550533	+	0.834814i	$0.685575\pi$
$983$	−1.47112e9	+	8.49350e8i	−1.54877	+	0.894182i	−0.998236	+	0.0593687i	$0.981091\pi$
$984$	2.22393e8	+	3.85196e8i	0.233419	+	0.404293i
$985$	−9.43643e8	−	5.44813e8i	−0.987413	−	0.570083i
$986$		−	6.34578e8i		−	0.661994i
$987$		0			0
$988$	−1.66429e9			−1.72567
$989$	3.95051e7	−	6.84249e7i	0.0408380	−	0.0707335i
$990$	1.31437e9	−	7.58855e8i	1.35461	−	0.782083i
$991$	5.11721e8	+	8.86327e8i	0.525790	+	0.910695i	0.999549	+	0.0300400i	$0.00956348\pi$
$991$	5.11721e8	+	8.86327e8i	0.525790	+	0.910695i	−0.473759	+	0.880655i	$0.657103\pi$
$992$	1.50545e9	+	8.69171e8i	1.54216	+	0.890369i
$993$			1.35484e8i			0.138369i
$994$		0			0
$995$	7.05324e8			0.716010
$996$	1.05680e8	−	1.83044e8i	0.106959	−	0.185258i
$997$	−1.41864e9	+	8.19050e8i	−1.43148	+	0.826465i	−0.997234	−	0.0743287i	$-0.976319\pi$
$997$	−1.41864e9	+	8.19050e8i	−1.43148	+	0.826465i	−0.434246	+	0.900794i	$0.642985\pi$
$998$	1.76548e9	+	3.05791e9i	1.77612	+	3.07633i
$999$	1.09452e8	+	6.31920e7i	0.109781	+	0.0633820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.7.d.e.19.2		24
7.2	even	3		49.7.b.c.48.12	yes	12
7.3	odd	6	inner	49.7.d.e.31.2		24
7.4	even	3	inner	49.7.d.e.31.1		24
7.5	odd	6		49.7.b.c.48.11	✓	12
7.6	odd	2	inner	49.7.d.e.19.1		24
21.2	odd	6		441.7.d.e.244.2		12
21.5	even	6		441.7.d.e.244.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.7.b.c.48.11	✓	12	7.5	odd	6
49.7.b.c.48.12	yes	12	7.2	even	3
49.7.d.e.19.1		24	7.6	odd	2	inner
49.7.d.e.19.2		24	1.1	even	1	trivial
49.7.d.e.31.1		24	7.4	even	3	inner
49.7.d.e.31.2		24	7.3	odd	6	inner
441.7.d.e.244.1		12	21.5	even	6
441.7.d.e.244.2		12	21.2	odd	6

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	49.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-7.22006 + 12.5055i) q^{2} +(5.48749 - 3.16820i) q^{3} +(-72.2584 - 125.155i) q^{4} +(169.953 + 98.1223i) q^{5} +91.4984i q^{6} +1162.67 q^{8} +(-344.425 + 596.562i) q^{9} +(-2454.14 + 1416.90i) q^{10} +(388.746 + 673.327i) q^{11} +(-793.034 - 457.858i) q^{12} +1858.37i q^{13} +1243.49 q^{15} +(-3770.02 + 6529.86i) q^{16} +(1942.83 - 1121.69i) q^{17} +(-4973.54 - 8614.42i) q^{18} +(-5366.70 - 3098.47i) q^{19} -28360.6i q^{20} -11227.1 q^{22} +(662.628 - 1147.71i) q^{23} +(6380.15 - 3683.58i) q^{24} +(11443.5 + 19820.7i) q^{25} +(-23239.9 - 13417.6i) q^{26} +8984.07i q^{27} -19588.9 q^{29} +(-8978.03 + 15550.4i) q^{30} +(-43676.8 + 25216.8i) q^{31} +(-17234.0 - 29850.1i) q^{32} +(4266.47 + 2463.25i) q^{33} +32394.8i q^{34} +99550.4 q^{36} +(7033.78 - 12182.9i) q^{37} +(77495.8 - 44742.2i) q^{38} +(5887.70 + 10197.8i) q^{39} +(197599. + 114084. i) q^{40} +60374.1i q^{41} +59618.8 q^{43} +(56180.3 - 97307.1i) q^{44} +(-117072. + 67591.5i) q^{45} +(9568.43 + 16573.0i) q^{46} +(-155091. - 89541.8i) q^{47} +47776.7i q^{48} -330490. q^{50} +(7107.50 - 12310.6i) q^{51} +(232585. - 134283. i) q^{52} +(94548.6 + 163763. i) q^{53} +(-112350. - 64865.5i) q^{54} +152579. i q^{55} -39266.3 q^{57} +(141433. - 244969. i) q^{58} +(94989.9 - 54842.5i) q^{59} +(-89852.3 - 155629. i) q^{60} +(261423. + 150933. i) q^{61} -728267. i q^{62} +15158.7 q^{64} +(-182348. + 315836. i) q^{65} +(-61608.4 + 35569.6i) q^{66} +(-111524. - 193166. i) q^{67} +(-280772. - 162104. i) q^{68} -8397.36i q^{69} +667143. q^{71} +(-400453. + 693605. i) q^{72} +(-226606. + 130831. i) q^{73} +(101569. + 175922. i) q^{74} +(125592. + 72510.5i) q^{75} +895561. i q^{76} -170038. q^{78} +(252972. - 438160. i) q^{79} +(-1.28145e6 + 739846. i) q^{80} +(-222622. - 385593. i) q^{81} +(-755009. - 435905. i) q^{82} +230815. i q^{83} +440253. q^{85} +(-430451. + 745564. i) q^{86} +(-107494. + 62061.6i) q^{87} +(451984. + 782859. i) q^{88} +(697220. + 402540. i) q^{89} -1.95206e6i q^{90} -191522. q^{92} +(-159784. + 276754. i) q^{93} +(2.23953e6 - 1.29299e6i) q^{94} +(-608057. - 1.05319e6i) q^{95} +(-189142. - 109201. i) q^{96} -474359. i q^{97} -535575. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{2} - 564 q^{4} + 1880 q^{8} + 1252 q^{9} + 3872 q^{11} + 44864 q^{15} - 37908 q^{16} + 19436 q^{18} + 159744 q^{22} - 40032 q^{23} + 28860 q^{25} + 68032 q^{29} - 21192 q^{30} + 82060 q^{32}+ \cdots - 8949984 q^{99}+O(q^{100}) \) 24 * q - 20 * q^2 - 564 * q^4 + 1880 * q^8 + 1252 * q^9 + 3872 * q^11 + 44864 * q^15 - 37908 * q^16 + 19436 * q^18 + 159744 * q^22 - 40032 * q^23 + 28860 * q^25 + 68032 * q^29 - 21192 * q^30 + 82060 * q^32 - 563240 * q^36 + 169632 * q^37 - 492128 * q^39 - 241536 * q^43 + 404312 * q^44 + 118872 * q^46 - 2091048 * q^50 + 539424 * q^51 + 15856 * q^53 + 1853888 * q^57 - 971304 * q^58 + 429912 * q^60 - 11496 * q^64 + 267904 * q^65 - 1508352 * q^67 + 5037248 * q^71 - 2550364 * q^72 + 3876024 * q^74 - 135184 * q^78 - 232224 * q^79 - 528204 * q^81 + 1508256 * q^85 + 1560848 * q^86 - 1812720 * q^88 + 7305776 * q^92 - 164384 * q^93 - 2305600 * q^95 - 8949984 * q^99

Introduction

L-functions

Modular forms

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Database

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