LMFDB - Embedded newform 76.7.g.a.7.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(7,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("76.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.8
Character	$\chi$	$=$	76.7
Dual form			76.7.g.a.11.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.07398 + 3.73615i) q^{2} +(-0.173689 + 0.100280i) q^{3} +(36.0824 - 52.8588i) q^{4} +(-61.9026 - 107.218i) q^{5} +(0.854016 - 1.35830i) q^{6} +472.399i q^{7} +(-57.7582 + 508.732i) q^{8} +(-364.480 + 631.298i) q^{9} +O(q^{10})$	\(q+(-7.07398 + 3.73615i) q^{2} +(-0.173689 + 0.100280i) q^{3} +(36.0824 - 52.8588i) q^{4} +(-61.9026 - 107.218i) q^{5} +(0.854016 - 1.35830i) q^{6} +472.399i q^{7} +(-57.7582 + 508.732i) q^{8} +(-364.480 + 631.298i) q^{9} +(838.481 + 527.184i) q^{10} -2179.49i q^{11} +(-0.966471 + 12.7993i) q^{12} +(-154.219 + 267.115i) q^{13} +(-1764.95 - 3341.74i) q^{14} +(21.5036 + 12.4151i) q^{15} +(-1492.12 - 3814.55i) q^{16} +(-1509.76 - 2614.99i) q^{17} +(219.704 - 5827.54i) q^{18} +(4667.94 + 5025.55i) q^{19} +(-7901.03 - 596.602i) q^{20} +(-47.3719 - 82.0506i) q^{21} +(8142.88 + 15417.6i) q^{22} +(12231.8 + 7062.01i) q^{23} +(-40.9834 - 94.1532i) q^{24} +(148.647 - 257.465i) q^{25} +(92.9615 - 2465.76i) q^{26} -292.407i q^{27} +(24970.5 + 17045.3i) q^{28} +(16660.6 - 28857.0i) q^{29} +(-198.501 - 7.48369i) q^{30} -18943.4i q^{31} +(24806.9 + 21409.3i) q^{32} +(218.558 + 378.553i) q^{33} +(20450.0 + 12857.7i) q^{34} +(50649.8 - 29242.7i) q^{35} +(20218.3 + 42044.7i) q^{36} +69217.6 q^{37} +(-51797.1 - 18110.6i) q^{38} -61.8601i q^{39} +(58120.8 - 25299.1i) q^{40} +(23561.1 + 40809.1i) q^{41} +(641.661 + 403.436i) q^{42} +(-35418.9 + 20449.1i) q^{43} +(-115205. - 78641.2i) q^{44} +90248.9 q^{45} +(-112912. - 4256.90i) q^{46} +(95828.6 + 55326.7i) q^{47} +(641.686 + 512.918i) q^{48} -105512. q^{49} +(-89.6029 + 2376.67i) q^{50} +(524.460 + 302.797i) q^{51} +(8554.81 + 17790.0i) q^{52} +(76973.8 - 133323. i) q^{53} +(1092.48 + 2068.48i) q^{54} +(-233681. + 134916. i) q^{55} +(-240324. - 27284.9i) q^{56} +(-1314.73 - 404.786i) q^{57} +(-10042.8 + 266381. i) q^{58} +(239112. - 138051. i) q^{59} +(1432.15 - 688.689i) q^{60} +(191134. - 331054. i) q^{61} +(70775.4 + 134006. i) q^{62} +(-298224. - 172180. i) q^{63} +(-255472. - 58766.8i) q^{64} +38186.2 q^{65} +(-2960.40 - 1861.32i) q^{66} +(-111625. - 64446.7i) q^{67} +(-192701. - 14550.8i) q^{68} -2832.70 q^{69} +(-249041. + 396097. i) q^{70} +(-122698. + 70839.9i) q^{71} +(-300109. - 221885. i) q^{72} +(30653.2 + 53092.9i) q^{73} +(-489644. + 258607. i) q^{74} +59.6251i q^{75} +(434076. - 65407.8i) q^{76} +1.02959e6 q^{77} +(231.118 + 437.597i) q^{78} +(-409950. + 236685. i) q^{79} +(-316624. + 396113. i) q^{80} +(-265677. - 460165. i) q^{81} +(-319140. - 200655. i) q^{82} -71180.1i q^{83} +(-6046.40 - 456.560i) q^{84} +(-186917. + 323749. i) q^{85} +(174152. - 276987. i) q^{86} +6682.88i q^{87} +(1.10877e6 + 125883. i) q^{88} +(230679. - 399548. i) q^{89} +(-638419. + 337183. i) q^{90} +(-126185. - 72853.0i) q^{91} +(814641. - 391742. i) q^{92} +(1899.64 + 3290.27i) q^{93} +(-884599. - 33350.3i) q^{94} +(249874. - 811584. i) q^{95} +(-6455.61 - 1230.94i) q^{96} +(703631. + 1.21872e6i) q^{97} +(746388. - 394207. i) q^{98} +(1.37590e6 + 794379. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - q^{2} - 67 q^{4} - 2 q^{5} + 33 q^{6} + 962 q^{8} + 12660 q^{9}+O(q^{10}) $ 116 * q - q^2 - 67 * q^4 - 2 * q^5 + 33 * q^6 + 962 * q^8 + 12660 * q^9	\( 116 q - q^{2} - 67 q^{4} - 2 q^{5} + 33 q^{6} + 962 q^{8} + 12660 q^{9} - 812 q^{10} - 1462 q^{12} + 2518 q^{13} - 2742 q^{14} + 461 q^{16} + 6838 q^{17} - 13948 q^{18} - 24396 q^{20} + 11176 q^{21} + 22293 q^{22} + 33905 q^{24} - 156252 q^{25} - 78080 q^{26} - 34362 q^{28} - 2 q^{29} + 208344 q^{30} - 10941 q^{32} + 110316 q^{33} + 64648 q^{34} + 78574 q^{36} + 55432 q^{37} + 221994 q^{38} + 242590 q^{40} - 9126 q^{41} + 187550 q^{42} + 138081 q^{44} + 59576 q^{45} - 686052 q^{46} - 141617 q^{48} - 1306636 q^{49} + 167498 q^{50} - 35414 q^{52} + 60758 q^{53} - 348601 q^{54} + 543732 q^{56} - 466566 q^{57} + 1208536 q^{58} - 319142 q^{60} - 839474 q^{61} + 628548 q^{62} - 470026 q^{64} + 151836 q^{65} + 1471119 q^{66} + 341484 q^{68} - 2169836 q^{69} - 68364 q^{70} + 1236042 q^{72} + 207538 q^{73} + 336144 q^{74} - 97437 q^{76} + 1977632 q^{77} - 2740948 q^{78} + 1250050 q^{80} - 3334682 q^{81} - 2244893 q^{82} - 2404612 q^{84} + 788426 q^{85} + 910490 q^{86} + 5123058 q^{88} + 360166 q^{89} + 2446616 q^{90} + 2518692 q^{92} + 2079592 q^{93} - 2221200 q^{94} - 5927450 q^{96} + 3567778 q^{97} + 5270703 q^{98}+O(q^{100}) \) 116 * q - q^2 - 67 * q^4 - 2 * q^5 + 33 * q^6 + 962 * q^8 + 12660 * q^9 - 812 * q^10 - 1462 * q^12 + 2518 * q^13 - 2742 * q^14 + 461 * q^16 + 6838 * q^17 - 13948 * q^18 - 24396 * q^20 + 11176 * q^21 + 22293 * q^22 + 33905 * q^24 - 156252 * q^25 - 78080 * q^26 - 34362 * q^28 - 2 * q^29 + 208344 * q^30 - 10941 * q^32 + 110316 * q^33 + 64648 * q^34 + 78574 * q^36 + 55432 * q^37 + 221994 * q^38 + 242590 * q^40 - 9126 * q^41 + 187550 * q^42 + 138081 * q^44 + 59576 * q^45 - 686052 * q^46 - 141617 * q^48 - 1306636 * q^49 + 167498 * q^50 - 35414 * q^52 + 60758 * q^53 - 348601 * q^54 + 543732 * q^56 - 466566 * q^57 + 1208536 * q^58 - 319142 * q^60 - 839474 * q^61 + 628548 * q^62 - 470026 * q^64 + 151836 * q^65 + 1471119 * q^66 + 341484 * q^68 - 2169836 * q^69 - 68364 * q^70 + 1236042 * q^72 + 207538 * q^73 + 336144 * q^74 - 97437 * q^76 + 1977632 * q^77 - 2740948 * q^78 + 1250050 * q^80 - 3334682 * q^81 - 2244893 * q^82 - 2404612 * q^84 + 788426 * q^85 + 910490 * q^86 + 5123058 * q^88 + 360166 * q^89 + 2446616 * q^90 + 2518692 * q^92 + 2079592 * q^93 - 2221200 * q^94 - 5927450 * q^96 + 3567778 * q^97 + 5270703 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−7.07398	+	3.73615i	−0.884248	+	0.467018i
$2$	−7.07398	+	3.73615i	−0.884248	+	0.467018i
$3$	−0.173689	+	0.100280i	−0.00643294	+	0.00371406i	−0.503213	−	0.864162i	$-0.667849\pi$
$3$	−0.173689	+	0.100280i	−0.00643294	+	0.00371406i	0.496780	+	0.867876i	$0.334516\pi$
$4$	36.0824	−	52.8588i	0.563788	−	0.825919i
$5$	−61.9026	−	107.218i	−0.495220	−	0.857747i	0.504764	−	0.863257i	$-0.331579\pi$
$5$	−61.9026	−	107.218i	−0.495220	−	0.857747i	−0.999985	+	0.00551019i	$0.998246\pi$
$6$	0.854016	−	1.35830i	0.00395378	−	0.00628844i
$7$			472.399i			1.37726i	0.725115	+	0.688628i	$0.241787\pi$
$7$			472.399i			1.37726i	−0.725115	+	0.688628i	$0.758213\pi$
$8$	−57.7582	+	508.732i	−0.112809	+	0.993617i
$9$	−364.480	+	631.298i	−0.499972	+	0.865978i
$10$	838.481	+	527.184i	0.838481	+	0.527184i
$11$		−	2179.49i		−	1.63748i	−0.574165	−	0.818740i	$-0.694673\pi$
$11$		−	2179.49i		−	1.63748i	0.574165	−	0.818740i	$-0.305327\pi$
$12$	−0.966471	+	12.7993i	−0.000559300	+	0.00740703i
$13$	−154.219	+	267.115i	−0.0701953	+	0.121582i	−0.898987	−	0.437976i	$-0.855696\pi$
$13$	−154.219	+	267.115i	−0.0701953	+	0.121582i	0.828791	+	0.559558i	$0.189029\pi$
$14$	−1764.95	−	3341.74i	−0.643204	−	1.21784i
$15$	21.5036	+	12.4151i	0.00637144	+	0.00367855i
$16$	−1492.12	−	3814.55i	−0.364286	−	0.931287i
$17$	−1509.76	−	2614.99i	−0.307300	−	0.532259i	0.670471	−	0.741936i	$-0.266092\pi$
$17$	−1509.76	−	2614.99i	−0.307300	−	0.532259i	−0.977771	+	0.209677i	$0.932759\pi$
$18$	219.704	−	5827.54i	0.0376722	−	0.999235i
$19$	4667.94	+	5025.55i	0.680557	+	0.732695i
$19$	4667.94	+	5025.55i	0.680557	+	0.732695i
$20$	−7901.03	−	596.602i	−0.987629	−	0.0745753i
$21$	−47.3719	−	82.0506i	−0.00511521	−	0.00885980i
$22$	8142.88	+	15417.6i	0.764733	+	1.44794i
$23$	12231.8	+	7062.01i	1.00532	+	0.580423i	0.909819	−	0.415006i	$-0.136221\pi$
$23$	12231.8	+	7062.01i	1.00532	+	0.580423i	0.0955036	+	0.995429i	$0.469554\pi$
$24$	−40.9834	−	94.1532i	−0.00296466	−	0.00681085i
$25$	148.647	−	257.465i	0.00951343	−	0.0164777i
$26$	92.9615	−	2465.76i	0.00528912	−	0.140291i
$27$		−	292.407i		−	0.0148558i
$28$	24970.5	+	17045.3i	1.13750	+	0.776481i
$29$	16660.6	−	28857.0i	0.683120	−	1.18320i	−0.290904	−	0.956752i	$-0.593956\pi$
$29$	16660.6	−	28857.0i	0.683120	−	1.18320i	0.974024	−	0.226446i	$-0.0727108\pi$
$30$	−198.501	−	7.48369i	−0.00735188	−	0.000277174i
$31$		−	18943.4i		−	0.635878i	−0.948111	−	0.317939i	$-0.897009\pi$
$31$		−	18943.4i		−	0.635878i	0.948111	−	0.317939i	$-0.102991\pi$
$32$	24806.9	+	21409.3i	0.757047	+	0.653360i
$33$	218.558	+	378.553i	0.00608169	+	0.0105338i
$34$	20450.0	+	12857.7i	0.520304	+	0.327134i
$35$	50649.8	−	29242.7i	1.18134	−	0.682045i
$36$	20218.3	+	42044.7i	0.433349	+	0.901165i
$37$	69217.6			1.36651			0.683253	−	0.730182i	$-0.260565\pi$
$37$	69217.6			1.36651			0.683253	+	0.730182i	$0.260565\pi$
$38$	−51797.1	−	18110.6i	−0.943963	−	0.330051i
$39$		−	61.8601i		−	0.00104284i
$40$	58120.8	−	25299.1i	0.908137	−	0.395298i
$41$	23561.1	+	40809.1i	0.341857	+	0.592114i	0.984778	−	0.173819i	$-0.0556107\pi$
$41$	23561.1	+	40809.1i	0.341857	+	0.592114i	−0.642920	+	0.765933i	$0.722277\pi$
$42$	641.661	+	403.436i	0.00866080	+	0.00544536i
$43$	−35418.9	+	20449.1i	−0.445481	+	0.257199i	−0.705920	−	0.708292i	$-0.749466\pi$
$43$	−35418.9	+	20449.1i	−0.445481	+	0.257199i	0.260439	+	0.965490i	$0.416133\pi$
$44$	−115205.	−	78641.2i	−1.35243	−	0.923192i
$45$	90248.9			0.990386
$46$	−112912.	−	4256.90i	−1.16002	−	0.0437340i
$47$	95828.6	+	55326.7i	0.923000	+	0.532894i	0.884591	−	0.466368i	$-0.154438\pi$
$47$	95828.6	+	55326.7i	0.923000	+	0.532894i	0.0384092	+	0.999262i	$0.487771\pi$
$48$	641.686	+	512.918i	0.00580228	+	0.00463793i
$49$	−105512.			−0.896834
$50$	−89.6029	+	2376.67i	−0.000716823	+	0.0190133i
$51$	524.460	+	302.797i	0.00395368	+	0.00228266i
$52$	8554.81	+	17790.0i	0.0608416	+	0.126522i
$53$	76973.8	−	133323.i	0.517030	−	0.895522i	−0.482775	−	0.875745i	$-0.660371\pi$
$53$	76973.8	−	133323.i	0.517030	−	0.895522i	0.999804	−	0.0197772i	$-0.00629569\pi$
$54$	1092.48	+	2068.48i	0.00693794	+	0.0131362i
$55$	−233681.	+	134916.i	−1.40454	+	0.810913i
$56$	−240324.	−	27284.9i	−1.36846	−	0.155367i
$57$	−1314.73	−	404.786i	−0.00709925	−	0.00218575i
$58$	−10042.8	+	266381.i	−0.0514721	+	1.36527i
$59$	239112.	−	138051.i	1.16425	−	0.672179i	0.211929	−	0.977285i	$-0.432025\pi$
$59$	239112.	−	138051.i	1.16425	−	0.672179i	0.952318	+	0.305107i	$0.0986921\pi$
$60$	1432.15	−	688.689i	0.00663033	−	0.00318837i
$61$	191134.	−	331054.i	0.842072	−	1.45851i	−0.0460685	−	0.998938i	$-0.514669\pi$
$61$	191134.	−	331054.i	0.842072	−	1.45851i	0.888140	−	0.459573i	$-0.151997\pi$
$62$	70775.4	+	134006.i	0.296966	+	0.562273i
$63$	−298224.	−	172180.i	−1.19267	−	0.688590i
$64$	−255472.	−	58766.8i	−0.974548	−	0.224178i
$65$	38186.2			0.139049
$66$	−2960.40	−	1861.32i	−0.0102972	−	0.00647423i
$67$	−111625.	−	64446.7i	−0.371139	−	0.214277i	0.302817	−	0.953049i	$-0.402073\pi$
$67$	−111625.	−	64446.7i	−0.371139	−	0.214277i	−0.673956	+	0.738772i	$0.735406\pi$
$68$	−192701.	−	14550.8i	−0.612855	−	0.0462763i
$69$	−2832.70			−0.00862290
$70$	−249041.	+	396097.i	−0.726067	+	1.15480i
$71$	−122698.	+	70839.9i	−0.342818	+	0.197926i	−0.661517	−	0.749930i	$-0.730087\pi$
$71$	−122698.	+	70839.9i	−0.342818	+	0.197926i	0.318700	+	0.947856i	$0.396754\pi$
$72$	−300109.	−	221885.i	−0.804048	−	0.594471i
$73$	30653.2	+	53092.9i	0.0787965	+	0.136480i	0.902731	−	0.430206i	$-0.141559\pi$
$73$	30653.2	+	53092.9i	0.0787965	+	0.136480i	−0.823934	+	0.566685i	$0.808226\pi$
$74$	−489644.	+	258607.i	−1.20833	+	0.638183i
$75$			59.6251i			0.000141334i
$76$	434076.	−	65407.8i	0.988837	−	0.149001i
$77$	1.02959e6			2.25523
$78$	231.118	+	437.597i	0.000487024	+	0.000922127i
$79$	−409950.	+	236685.i	−0.831475	+	0.480052i	−0.854357	−	0.519686i	$-0.826049\pi$
$79$	−409950.	+	236685.i	−0.831475	+	0.480052i	0.0228824	+	0.999738i	$0.492716\pi$
$80$	−316624.	+	396113.i	−0.618407	+	0.773658i
$81$	−265677.	−	460165.i	−0.499917	−	0.865882i
$82$	−319140.	−	200655.i	−0.578815	−	0.363922i
$83$		−	71180.1i		−	0.124487i	−0.998061	−	0.0622436i	$-0.980174\pi$
$83$		−	71180.1i		−	0.124487i	0.998061	−	0.0622436i	$-0.0198256\pi$
$84$	−6046.40	−	456.560i	−0.0102014	−	0.000770300i
$85$	−186917.	+	323749.i	−0.304362	+	0.527171i
$86$	174152.	−	276987.i	0.273799	−	0.435475i
$87$			6682.88i			0.0101486i
$88$	1.10877e6	+	125883.i	1.62703	+	0.184722i
$89$	230679.	−	399548.i	0.327219	−	0.566759i	−0.654740	−	0.755854i	$-0.727222\pi$
$89$	230679.	−	399548.i	0.327219	−	0.566759i	0.981959	+	0.189095i	$0.0605553\pi$
$90$	−638419.	+	337183.i	−0.875747	+	0.462528i
$91$	−126185.	−	72853.0i	−0.167449	−	0.0966770i
$92$	814641.	−	391742.i	1.04617	−	0.503080i
$93$	1899.64	+	3290.27i	0.00236169	+	0.00409056i
$94$	−884599.	−	33350.3i	−1.06503	−	0.0401528i
$95$	249874.	−	811584.i	0.291441	−	0.946591i
$96$	−6455.61	−	1230.94i	−0.00729665	−	0.00139131i
$97$	703631.	+	1.21872e6i	0.770956	+	1.33534i	0.937039	+	0.349224i	$0.113555\pi$
$97$	703631.	+	1.21872e6i	0.770956	+	1.33534i	−0.166083	+	0.986112i	$0.553112\pi$
$98$	746388.	−	394207.i	0.793024	−	0.418838i
$99$	1.37590e6	+	794379.i	1.41802	+	0.818695i
$100$	−8245.73	−	17147.3i	−0.00824573	−	0.0171473i
$101$	−688441.	+	1.19241e6i	−0.668194	+	1.15735i	0.310215	+	0.950666i	$0.399599\pi$
$101$	−688441.	+	1.19241e6i	−0.668194	+	1.15735i	−0.978409	+	0.206679i	$0.933734\pi$
$102$	−4841.31	−	182.522i	−0.00456208	−	0.000171995i
$103$			438419.i			0.401216i	0.979672	+	0.200608i	$0.0642917\pi$
$103$			438419.i			0.401216i	−0.979672	+	0.200608i	$0.935708\pi$
$104$	−126983.	−	93884.3i	−0.112887	−	0.0834628i
$105$	−5864.89	+	10158.3i	−0.00506631	+	0.00877511i
$106$	−46398.9	+	1.23071e6i	−0.0389574	+	1.03333i
$107$			966422.i			0.788888i	0.918920	+	0.394444i	$0.129063\pi$
$107$			966422.i			0.788888i	−0.918920	+	0.394444i	$0.870937\pi$
$108$	−15456.3	−	10550.8i	−0.0122697	−	0.00837553i
$109$	−1.19464e6	−	2.06919e6i	−0.922485	−	1.59779i	−0.795557	−	0.605879i	$-0.792822\pi$
$109$	−1.19464e6	−	2.06919e6i	−0.922485	−	1.59779i	−0.126928	−	0.991912i	$-0.540512\pi$
$110$	1.14899e6	−	1.82746e6i	0.863253	−	1.37300i
$111$	−12022.4	+	6941.11i	−0.00879064	+	0.00507528i
$112$	1.80199e6	−	704874.i	1.28262	−	0.501715i
$113$	1.52405e6			1.05625			0.528123	−	0.849168i	$-0.322896\pi$
$113$	1.52405e6			1.05625			0.528123	+	0.849168i	$0.322896\pi$
$114$	10812.7	−	2048.58i	0.00729828	−	0.00138273i
$115$		−	1.74863e6i		−	1.14975i
$116$	−924194.	−	1.92189e6i	−0.592092	−	1.23128i
$117$	−112420.	−	194716.i	−0.0701915	−	0.121575i
$118$	−1.17569e6	+	1.86993e6i	−0.715564	+	1.13810i
$119$	1.23532e6	−	713211.i	0.733057	−	0.423231i
$120$	−7557.98	+	10222.5i	−0.00437383	+	0.00591580i
$121$	−2.97860e6			−1.68134
$122$	−115214.	+	3.05598e6i	−0.0634489	+	1.68295i
$123$	−8184.64	−	4725.40i	−0.00439829	−	0.00253936i
$124$	−1.00133e6	−	683525.i	−0.525184	−	0.358500i
$125$	−1.97126e6			−1.00929
$126$	2.75292e6	+	103788.i	1.37620	+	0.0518843i
$127$	−1.02526e6	−	591936.i	−0.500523	−	0.288977i	0.228406	−	0.973566i	$-0.426649\pi$
$127$	−1.02526e6	−	591936.i	−0.500523	−	0.288977i	−0.728930	+	0.684589i	$0.759982\pi$
$128$	2.02677e6	−	538765.i	0.966437	−	0.256903i
$129$	4101.25	−	7103.58i	0.00191050	−	0.00330908i
$130$	−270129.	+	142669.i	−0.122953	+	0.0649383i
$131$	−832025.	+	480370.i	−0.370103	+	0.213679i	−0.673503	−	0.739184i	$-0.735211\pi$
$131$	−832025.	+	480370.i	−0.370103	+	0.213679i	0.303400	+	0.952863i	$0.401878\pi$
$132$	27896.0	+	2106.41i	0.0121289	+	0.000915843i
$133$	−2.37407e6	+	2.20513e6i	−1.00911	+	0.937302i
$134$	1.03041e6	+	38847.7i	0.428250	+	0.0161455i
$135$	−31351.4	+	18100.7i	−0.0127425	+	0.00735690i
$136$	1.41753e6	−	617028.i	0.563528	−	0.245295i
$137$	1.46264e6	−	2.53336e6i	0.568820	−	0.985225i	−0.427863	−	0.903844i	$-0.640733\pi$
$137$	1.46264e6	−	2.53336e6i	0.568820	−	0.985225i	0.996683	−	0.0813817i	$-0.0259333\pi$
$138$	20038.5	−	10583.4i	0.00762478	−	0.00402705i
$139$	4.29498e6	+	2.47971e6i	1.59925	+	0.923328i	0.991632	+	0.129099i	$0.0412086\pi$
$139$	4.29498e6	+	2.47971e6i	1.59925	+	0.923328i	0.607619	+	0.794229i	$0.292125\pi$
$140$	281834.	−	3.73244e6i	0.102709	−	1.36022i
$141$	−22192.5			−0.00791680
$142$	603297.	−	959539.i	0.210701	−	0.335118i
$143$	582174.	+	336118.i	0.199088	+	0.114943i
$144$	2.95196e6	+	448358.i	0.988607	+	0.150154i
$145$	−4.12534e6			−1.35318
$146$	−415203.	−	261053.i	−0.133414	−	0.0838823i
$147$	18326.2	−	10580.7i	0.00576928	−	0.00333089i
$148$	2.49754e6	−	3.65876e6i	0.770419	−	1.12862i
$149$	3.13895e6	+	5.43682e6i	0.948912	+	1.64356i	0.747723	+	0.664011i	$0.231147\pi$
$149$	3.13895e6	+	5.43682e6i	0.948912	+	1.64356i	0.201189	+	0.979552i	$0.435520\pi$
$150$	−222.768	−	421.787i	−6.60054e−5	−	0.000124974i
$151$			495659.i			0.143964i	0.997406	+	0.0719818i	$0.0229323\pi$
$151$			495659.i			0.143964i	−0.997406	+	0.0719818i	$0.977068\pi$
$152$	−2.82627e6	+	2.08446e6i	−0.804791	+	0.593558i
$153$	2.20111e6			0.614566
$154$	−7.28328e6	+	3.84668e6i	−1.99418	+	1.05323i
$155$	−2.03108e6	+	1.17265e6i	−0.545422	+	0.314900i
$156$	−3269.85	−	2232.06i	−0.000861300	−	0.000587940i
$157$	−37935.8	−	65706.7i	−0.00980279	−	0.0169789i	0.861082	−	0.508465i	$-0.169787\pi$
$157$	−37935.8	−	65706.7i	−0.00980279	−	0.0169789i	−0.870885	+	0.491487i	$0.836454\pi$
$158$	2.01569e6	−	3.20593e6i	0.511037	−	0.812799i
$159$			30875.6i			0.00768111i
$160$	759860.	−	3.98505e6i	0.185513	−	0.972912i
$161$	−3.33608e6	+	5.77827e6i	−0.799391	+	1.38459i
$162$	3.59863e6	+	2.26259e6i	0.846433	+	0.532184i
$163$		−	27157.7i		−	0.00627089i	−0.999995	−	0.00313545i	$-0.999002\pi$
$163$		−	27157.7i		−	0.00627089i	0.999995	−	0.00313545i	$-0.000998045\pi$
$164$	3.00727e6	+	227077.i	0.681774	+	0.0514803i
$165$	27058.6	−	46866.8i	0.00602356	−	0.0104331i
$166$	265939.	+	503527.i	0.0581378	+	0.110078i
$167$	−6.81486e6	−	3.93456e6i	−1.46321	−	0.844786i	−0.464054	−	0.885807i	$-0.653606\pi$
$167$	−6.81486e6	−	3.93456e6i	−1.46321	−	0.844786i	−0.999158	+	0.0410205i	$0.986939\pi$
$168$	44477.9	−	19360.5i	0.00938029	−	0.00408309i
$169$	2.36584e6	+	4.09775e6i	0.490145	+	0.848956i
$170$	112671.	−	2.98854e6i	0.0229333	−	0.608293i
$171$	−4.87399e6	+	1.11515e6i	−0.974757	+	0.223020i
$172$	−197084.	+	2.61005e6i	−0.0387316	+	0.512937i
$173$	−1.95780e6	−	3.39100e6i	−0.378119	−	0.654922i	0.612669	−	0.790339i	$-0.290096\pi$
$173$	−1.95780e6	−	3.39100e6i	−0.378119	−	0.654922i	−0.990789	+	0.135417i	$0.956762\pi$
$174$	−24968.2	−	47274.5i	−0.00473957	−	0.00897387i
$175$	121626.	+	70220.8i	0.0226941	+	0.0131024i
$176$	−8.31376e6	+	3.25204e6i	−1.52496	+	0.596511i
$177$	−27687.5	+	47956.1i	−0.00499302	+	0.00864816i
$178$	−139051.	+	3.68824e6i	−0.0246554	+	0.653973i
$179$		−	8.96409e6i		−	1.56296i	−0.623932	−	0.781479i	$-0.714466\pi$
$179$		−	8.96409e6i		−	1.56296i	0.623932	−	0.781479i	$-0.285534\pi$
$180$	3.25640e6	−	4.77046e6i	0.558368	−	0.817979i
$181$	777391.	−	1.34648e6i	0.131100	−	0.227072i	−0.793001	−	0.609221i	$-0.791482\pi$
$181$	777391.	−	1.34648e6i	0.131100	−	0.227072i	0.924101	+	0.382148i	$0.124816\pi$
$182$	1.16482e6	+	43914.9i	0.193217	+	0.00728447i
$183$			76667.4i			0.0125100i
$184$	−4.29915e6	+	5.81479e6i	−0.690127	+	0.933428i
$185$	−4.28475e6	−	7.42140e6i	−0.676721	−	1.17212i
$186$	−25730.9	−	16178.0i	−0.00399868	−	0.00251412i
$187$	−5.69933e6	+	3.29051e6i	−0.871563	+	0.503197i
$188$	6.38224e6	−	3.06907e6i	0.960504	−	0.461884i
$189$	138133.			0.0204603
$190$	1.26459e6	+	6.67470e6i	0.184369	+	0.973130i
$191$		−	2.38390e6i		−	0.342128i	−0.985260	−	0.171064i	$-0.945280\pi$
$191$		−	2.38390e6i		−	0.342128i	0.985260	−	0.171064i	$-0.0547204\pi$
$192$	50265.9	−	15411.4i	0.00710181	−	0.00217741i
$193$	−218166.	−	377874.i	−0.0303469	−	0.0525624i	0.850453	−	0.526051i	$-0.176328\pi$
$193$	−218166.	−	377874.i	−0.0303469	−	0.0525624i	−0.880800	+	0.473489i	$0.842995\pi$
$194$	−9.53081e6	−	5.99237e6i	−1.30534	−	0.820717i
$195$	−6632.54	+	3829.30i	−0.000894491	+	0.000516435i
$196$	−3.80712e6	+	5.57722e6i	−0.505624	+	0.740713i
$197$	−4.81234e6			−0.629445			−0.314722	−	0.949184i	$-0.601911\pi$
$197$	−4.81234e6			−0.629445			−0.314722	+	0.949184i	$0.601911\pi$
$198$	−1.27010e7	−	478842.i	−1.63623	−	0.0616875i
$199$	9.45717e6	+	5.46010e6i	1.20006	+	0.692853i	0.960568	−	0.278046i	$-0.0896867\pi$
$199$	9.45717e6	+	5.46010e6i	1.20006	+	0.692853i	0.239489	+	0.970899i	$0.423020\pi$
$200$	122395.	+	90492.3i	0.0152994	+	0.0113115i
$201$	25850.7			0.00318335
$202$	414984.	−	1.10072e7i	0.0503474	−	1.33544i
$203$	1.36320e7	+	7.87046e6i	1.62957	+	0.940831i
$204$	34929.3	−	16796.7i	0.00411433	−	0.00197849i
$205$	2.91699e6	−	5.05238e6i	0.338589	−	0.586454i
$206$	−1.63800e6	−	3.10137e6i	−0.187375	−	0.354774i
$207$	−8.91646e6	+	5.14792e6i	−1.00527	+	0.580391i
$208$	1.24904e6	+	189710.i	0.138799	+	0.0210814i
$209$	1.09531e7	−	1.01737e7i	1.19977	−	1.11440i
$210$	3535.29	−	93771.6i	0.000381739	−	0.0101254i
$211$	−6.83719e6	+	3.94746e6i	−0.727831	+	0.420213i	−0.817628	−	0.575747i	$-0.804711\pi$
$211$	−6.83719e6	+	3.94746e6i	−0.727831	+	0.420213i	0.0897971	+	0.995960i	$0.471378\pi$
$212$	−4.26988e6	−	8.87935e6i	−0.448134	−	0.931909i
$213$	14207.6	−	24608.3i	0.00147022	−	0.00254649i
$214$	−3.61069e6	−	6.83645e6i	−0.368425	−	0.697573i
$215$	4.38504e6	+	2.53170e6i	0.441223	+	0.254740i
$216$	148757.	+	16888.9i	0.0147610	+	0.00167587i
$217$	8.94886e6			0.875767
$218$	1.61817e7	+	1.01740e7i	1.56190	+	0.982026i
$219$	−10648.3	−	6147.77i	−0.00101379	−	0.000585309i
$220$	−1.30029e6	+	1.72202e7i	−0.122116	+	1.61722i
$221$	931338.			0.0862841
$222$	59112.9	−	94018.5i	0.00540286	−	0.00859319i
$223$	6.66934e6	−	3.85055e6i	0.601407	−	0.347222i	−0.168188	−	0.985755i	$-0.553792\pi$
$223$	6.66934e6	−	3.85055e6i	0.601407	−	0.347222i	0.769595	+	0.638533i	$0.220458\pi$
$224$	−1.01137e7	+	1.17188e7i	−0.899844	+	1.04265i
$225$	108358.	+	187681.i	0.00951290	+	0.0164768i
$226$	−1.07811e7	+	5.69409e6i	−0.933983	+	0.493286i
$227$		−	1.30505e7i		−	1.11570i	−0.829941	−	0.557851i	$-0.811626\pi$
$227$		−	1.30505e7i		−	1.11570i	0.829941	−	0.557851i	$-0.188374\pi$
$228$	−68835.2	+	54889.5i	−0.00580773	+	0.00463111i
$229$	2.43190e6			0.202507			0.101253	−	0.994861i	$-0.467715\pi$
$229$	2.43190e6			0.202507			0.101253	+	0.994861i	$0.467715\pi$
$230$	6.53312e6	+	1.23697e7i	0.536954	+	1.01666i
$231$	−178828.	+	103246.i	−0.0145077	+	0.00837605i
$232$	1.37182e7	+	1.01425e7i	1.09858	+	0.812235i
$233$	7.27809e6	+	1.26060e7i	0.575373	+	0.996576i	0.996001	+	0.0893424i	$0.0284765\pi$
$233$	7.27809e6	+	1.26060e7i	0.575373	+	0.996576i	−0.420628	+	0.907233i	$0.638190\pi$
$234$	1.52274e6	+	957405.i	0.118844	+	0.0747219i
$235$		−	1.36995e7i		−	1.05560i
$236$	1.33051e6	−	1.76204e7i	0.101223	−	1.34054i
$237$	47469.2	−	82219.1i	0.00356588	−	0.00617629i
$238$	−6.07395e6	+	9.66057e6i	−0.450547	+	0.716592i
$239$		−	1.19806e7i		−	0.877575i	−0.898591	−	0.438787i	$-0.855408\pi$
$239$		−	1.19806e7i		−	0.877575i	0.898591	−	0.438787i	$-0.144592\pi$
$240$	15272.2	−	100551.i	0.00110476	−	0.00727369i
$241$	−698077.	+	1.20910e6i	−0.0498715	+	0.0863799i	−0.889883	−	0.456188i	$-0.849215\pi$
$241$	−698077.	+	1.20910e6i	−0.0498715	+	0.0863799i	0.840012	+	0.542568i	$0.182548\pi$
$242$	2.10705e7	−	1.11285e7i	1.48672	−	0.785216i
$243$	276896.	+	159866.i	0.0192974	+	0.0111414i
$244$	−1.06026e7	−	2.20484e7i	−0.729863	−	1.51777i
$245$	6.53144e6	+	1.13128e7i	0.444131	+	0.769257i
$246$	75552.8	+	2848.42i	0.00507511	+	0.000191337i
$247$	−2.06229e6	+	471843.i	−0.136854	+	0.0313117i
$248$	9.63713e6	+	1.09414e6i	0.631819	+	0.0717327i
$249$	7137.91	+	12363.2i	0.000462352	+	0.000800818i
$250$	1.39447e7	−	7.36492e6i	0.892459	−	0.471355i
$251$	1.15666e7	+	6.67798e6i	0.731450	+	0.422303i	0.818953	−	0.573861i	$-0.194555\pi$
$251$	1.15666e7	+	6.67798e6i	0.731450	+	0.422303i	−0.0875022	+	0.996164i	$0.527888\pi$
$252$	−1.98619e7	+	9.55112e6i	−1.24113	+	0.596833i
$253$	1.53915e7	−	2.66589e7i	0.950431	−	1.64619i
$254$	9.46425e6	+	356812.i	0.577544	+	0.0217740i
$255$		−	74975.6i		−	0.00452168i
$256$	−1.23244e7	+	1.13835e7i	−0.734591	+	0.678510i
$257$	1.10528e7	−	1.91440e7i	0.651136	−	1.12780i	−0.331711	−	0.943381i	$-0.607626\pi$
$257$	1.10528e7	−	1.91440e7i	0.651136	−	1.12780i	0.982847	−	0.184420i	$-0.0590407\pi$
$258$	−2472.19	+	65573.4i	−0.000143953	+	0.00381829i
$259$			3.26983e7i			1.88203i
$260$	1.37785e6	−	2.01848e6i	0.0783940	−	0.114843i
$261$	1.21449e7	+	2.10356e7i	0.683082	+	1.18313i
$262$	4.09100e6	−	6.50670e6i	0.227471	−	0.361790i
$263$	2.40428e7	−	1.38811e7i	1.32166	−	0.763058i	0.337662	−	0.941267i	$-0.390364\pi$
$263$	2.40428e7	−	1.38811e7i	1.32166	−	0.763058i	0.983993	+	0.178209i	$0.0570304\pi$
$264$	−205206.	+	89322.8i	−0.0111526	+	0.00485457i
$265$	−1.90595e7			−1.02417
$266$	8.55541e6	−	2.44689e7i	0.454565	−	1.30008i
$267$			92529.5i			0.00486123i
$268$	−7.43427e6	+	3.57497e6i	−0.386219	+	0.185724i
$269$	−7.88458e6	−	1.36565e7i	−0.405062	−	0.701588i	0.589267	−	0.807939i	$-0.299417\pi$
$269$	−7.88458e6	−	1.36565e7i	−0.405062	−	0.701588i	−0.994329	+	0.106350i	$0.966083\pi$
$270$	154152.	−	245178.i	0.00783175	−	0.0124563i
$271$	2.03474e6	−	1.17476e6i	0.102236	−	0.0590257i	−0.448010	−	0.894028i	$-0.647867\pi$
$271$	2.03474e6	−	1.17476e6i	0.102236	−	0.0590257i	0.550246	+	0.835003i	$0.314534\pi$
$272$	−7.72227e6	+	9.66094e6i	−0.383741	+	0.480079i
$273$	29222.6			0.00143626
$274$	−881661.	+	2.33856e7i	−0.0428598	+	1.13683i
$275$	−561141.	−	323975.i	−0.0269820	−	0.0155780i
$276$	−102211.	+	149733.i	−0.00486149	+	0.00712182i
$277$	2.41185e7			1.13478			0.567388	−	0.823450i	$-0.307954\pi$
$277$	2.41185e7			1.13478			0.567388	+	0.823450i	$0.307954\pi$
$278$	−3.96471e7	−	1.49474e6i	−1.84534	−	0.0695714i
$279$	1.19589e7	+	6.90450e6i	0.550656	+	0.317921i
$280$	1.19512e7	+	2.74562e7i	0.544426	+	1.25074i
$281$	−8.48170e6	+	1.46907e7i	−0.382264	+	0.662101i	−0.991386	−	0.130976i	$-0.958189\pi$
$281$	−8.48170e6	+	1.46907e7i	−0.382264	+	0.662101i	0.609121	+	0.793077i	$0.291522\pi$
$282$	156990.	−	82914.6i	0.00700041	−	0.00369729i
$283$	−2.49973e7	+	1.44322e7i	−1.10289	+	0.636756i	−0.936979	−	0.349385i	$-0.886391\pi$
$283$	−2.49973e7	+	1.44322e7i	−1.10289	+	0.636756i	−0.165914	+	0.986140i	$0.553057\pi$
$284$	−682738.	+	9.04177e6i	−0.0298057	+	0.394728i
$285$	37984.8	+	166021.i	0.00164087	+	0.00717179i
$286$	−5.37408e6	−	202608.i	−0.229724	−	0.00866082i
$287$	−1.92782e7	+	1.11303e7i	−0.815493	+	0.470825i
$288$	−2.25573e7	+	7.85729e6i	−0.944298	+	0.328924i
$289$	7.51001e6	−	1.30077e7i	0.311134	−	0.538899i
$290$	2.91826e7	−	1.54129e7i	1.19655	−	0.631960i
$291$	−244426.	−	141120.i	−0.00991903	−	0.00572675i
$292$	3.91247e6	+	295428.i	0.157146	+	0.0118660i
$293$	−2.09383e7			−0.832412			−0.416206	−	0.909270i	$-0.636640\pi$
$293$	−2.09383e7			−0.832412			−0.416206	+	0.909270i	$0.636640\pi$
$294$	−90108.6	+	143317.i	−0.00354588	+	0.00563969i
$295$	−2.96033e7	−	1.70915e7i	−1.15312	−	0.665753i
$296$	−3.99788e6	+	3.52132e7i	−0.154154	+	1.35778i
$297$	−637297.			−0.0243261
$298$	−4.25176e7	−	2.67324e7i	−1.60665	−	1.01016i
$299$	−3.77274e6	+	2.17819e6i	−0.141138	+	0.0814860i
$300$	3151.72	+	2151.42i	0.000116730	+	7.96822e-5i
$301$	−9.66013e6	−	1.67318e7i	−0.354228	−	0.613542i
$302$	−1.85186e6	−	3.50628e6i	−0.0672336	−	0.127299i
$303$		−	276146.i		−	0.00992684i
$304$	1.22051e7	−	2.53048e7i	0.434432	−	0.900705i
$305$	−4.73268e7			−1.66804
$306$	−1.55706e7	+	8.22368e6i	−0.543428	+	0.287013i
$307$	2.31726e7	−	1.33787e7i	0.800866	−	0.462380i	−0.0429080	−	0.999079i	$-0.513662\pi$
$307$	2.31726e7	−	1.33787e7i	0.800866	−	0.462380i	0.843774	+	0.536699i	$0.180329\pi$
$308$	3.71500e7	−	5.44228e7i	1.27147	−	1.86264i
$309$	−43964.5	−	76148.7i	−0.00149014	−	0.00258099i
$310$	9.98667e6	−	1.58837e7i	0.335225	−	0.533171i
$311$		−	4.72364e7i		−	1.57035i	−0.619276	−	0.785174i	$-0.712574\pi$
$311$		−	4.72364e7i		−	1.57035i	0.619276	−	0.785174i	$-0.287426\pi$
$312$	31470.2	+	3572.93i	0.00103618	+	0.000117641i
$313$	3.40424e6	−	5.89632e6i	0.111016	−	0.192286i	−0.805164	−	0.593052i	$-0.797923\pi$
$313$	3.40424e6	−	5.89632e6i	0.111016	−	0.192286i	0.916180	+	0.400766i	$0.131256\pi$
$314$	513847.	+	323074.i	0.0165976	+	0.0104355i
$315$			4.26335e7i			1.36402i
$316$	−2.28111e6	+	3.02096e7i	−0.0722911	+	0.957379i
$317$	−4.51794e6	+	7.82530e6i	−0.141828	+	0.245654i	−0.928185	−	0.372119i	$-0.878631\pi$
$317$	−4.51794e6	+	7.82530e6i	−0.141828	+	0.245654i	0.786357	+	0.617772i	$0.211965\pi$
$318$	−115356.	−	218413.i	−0.00358722	−	0.00679201i
$319$	−6.28935e7	−	3.63116e7i	−1.93746	−	1.11860i
$320$	9.51348e6	+	3.10291e7i	0.290329	+	0.946933i
$321$	−96912.4	−	167857.i	−0.00292998	−	0.00507487i
$322$	2.01095e6	−	5.33395e7i	0.0602330	−	1.59765i
$323$	6.09427e6	−	1.97940e7i	0.180848	−	0.587390i
$324$	−3.39101e7	−	2.56053e6i	−0.996996	−	0.0752826i
$325$	45848.5	+	79412.0i	0.00133560	+	0.00231332i
$326$	101465.	+	192113.i	0.00292862	+	0.00554502i
$327$	414994.	+	239597.i	0.0118686	+	0.00685232i
$328$	−2.21217e7	+	9.62925e6i	−0.626899	+	0.272879i
$329$	−2.61363e7	+	4.52693e7i	−0.733932	+	1.27121i
$330$	−16310.6	+	432630.i	−0.000453866	+	0.0120386i
$331$			4.18461e7i			1.15391i	0.816777	+	0.576954i	$0.195759\pi$
$331$			4.18461e7i			1.15391i	−0.816777	+	0.576954i	$0.804241\pi$
$332$	−3.76250e6	−	2.56835e6i	−0.102816	−	0.0701844i
$333$	−2.52284e7	+	4.36969e7i	−0.683215	+	1.18336i
$334$	6.29083e7	+	2.37171e6i	1.68837	+	0.0636534i
$335$			1.59577e7i			0.424458i
$336$	−242302.	+	303132.i	−0.00638762	+	0.00799123i
$337$	1.48759e7	+	2.57659e7i	0.388682	+	0.673217i	0.992273	−	0.124078i	$-0.0395972\pi$
$337$	1.48759e7	+	2.57659e7i	0.388682	+	0.673217i	−0.603591	+	0.797294i	$0.706264\pi$
$338$	−3.20457e7	−	2.01483e7i	−0.829888	−	0.521781i
$339$	−264712.	+	152831.i	−0.00679476	+	0.00392296i
$340$	1.03686e7	+	2.15618e7i	0.263805	+	0.548592i
$341$	−4.12869e7			−1.04124
$342$	3.03122e7	−	2.60985e7i	0.757772	−	0.652434i
$343$			5.73367e6i			0.142086i
$344$	−8.35737e6	−	1.91998e7i	−0.205303	−	0.471652i
$345$	175351.	+	303717.i	0.00427024	+	0.00739626i
$346$	2.65187e7	+	1.66733e7i	0.640212	+	0.402525i
$347$	6.00976e6	−	3.46974e6i	0.143836	−	0.0830440i	−0.426355	−	0.904556i	$-0.640202\pi$
$347$	6.00976e6	−	3.46974e6i	0.143836	−	0.0830440i	0.570191	+	0.821512i	$0.306869\pi$
$348$	353249.	+	241134.i	0.00838192	+	0.00572165i
$349$	4.15516e7			0.977489			0.488745	−	0.872427i	$-0.337455\pi$
$349$	4.15516e7			0.977489			0.488745	+	0.872427i	$0.337455\pi$
$350$	−1.12274e6	−	42328.3i	−0.0261862	−	0.000987249i
$351$	78106.4	+	45094.8i	0.00180620	+	0.00104281i
$352$	4.66613e7	−	5.40663e7i	1.06986	−	1.23965i
$353$	4.49849e7			1.02269			0.511343	−	0.859377i	$-0.329148\pi$
$353$	4.49849e7			1.02269			0.511343	+	0.859377i	$0.329148\pi$
$354$	16689.7	−	442685.i	0.000376217	−	0.00997895i
$355$	1.51907e7	+	8.77034e6i	0.339541	+	0.196034i
$356$	−1.27962e7	−	2.66101e7i	−0.283616	−	0.589788i
$357$	−143041.	+	247754.i	−0.00314380	+	0.00544523i
$358$	3.34911e7	+	6.34118e7i	0.729929	+	1.38204i
$359$	−9.18921e6	+	5.30539e6i	−0.198607	+	0.114666i	−0.596006	−	0.802980i	$-0.703246\pi$
$359$	−9.18921e6	+	5.30539e6i	−0.198607	+	0.114666i	0.397399	+	0.917646i	$0.369913\pi$
$360$	−5.21261e6	+	4.59125e7i	−0.111724	+	0.984064i
$361$	−3.46652e6	+	4.69180e7i	−0.0736838	+	0.997282i
$362$	−468602.	+	1.24294e7i	−0.00987822	+	0.262014i
$363$	517350.	−	298692.i	0.0108160	−	0.00624459i
$364$	−8.40399e6	+	4.04128e6i	−0.174253	+	0.0837944i
$365$	3.79502e6	−	6.57317e6i	0.0780433	−	0.135175i
$366$	−286441.	−	542344.i	−0.00584240	−	0.0110619i
$367$	9.51997e6	+	5.49636e6i	0.192592	+	0.111193i	0.593195	−	0.805059i	$-0.297866\pi$
$367$	9.51997e6	+	5.49636e6i	0.192592	+	0.111193i	−0.400604	+	0.916251i	$0.631200\pi$
$368$	8.68720e6	−	5.71960e7i	0.174316	−	1.14768i
$369$	−3.43503e7			−0.683677
$370$	5.80376e7	+	3.64904e7i	1.14579	+	0.720399i
$371$	6.29814e7	+	3.63624e7i	1.23336	+	0.712082i
$372$	242464.	+	18308.3i	0.00470996	+	0.000355647i
$373$	−2.67119e7			−0.514728			−0.257364	−	0.966315i	$-0.582854\pi$
$373$	−2.67119e7			−0.514728			−0.257364	+	0.966315i	$0.582854\pi$
$374$	2.80231e7	−	4.45705e7i	0.535676	−	0.851987i
$375$	342387.	−	197677.i	0.00649267	−	0.00374855i
$376$	−3.36813e7	+	4.55555e7i	−0.633615	+	0.856993i
$377$	5.13877e6	+	8.90062e6i	0.0959037	+	0.166110i
$378$	−977149.	+	516084.i	−0.0180919	+	0.00955532i
$379$			1.37299e6i			0.0252202i	0.999920	+	0.0126101i	$0.00401403\pi$
$379$			1.37299e6i			0.0252202i	−0.999920	+	0.0126101i	$0.995986\pi$
$380$	−3.38833e7	−	4.24920e7i	−0.617497	−	0.774384i
$381$	237436.			0.00429311
$382$	8.90660e6	+	1.68637e7i	0.159780	+	0.302526i
$383$	−708043.	+	408789.i	−0.0126027	+	0.00727616i	−0.506288	−	0.862364i	$-0.668983\pi$
$383$	−708043.	+	408789.i	−0.0126027	+	0.00727616i	0.493685	+	0.869641i	$0.335649\pi$
$384$	−298000.	+	296821.i	−0.00526287	+	0.00524204i
$385$	−6.37340e7	−	1.10391e8i	−1.11684	−	1.93442i
$386$	2.95509e6	+	1.85798e6i	0.0513818	+	0.0323056i
$387$		−	2.98131e7i		−	0.514369i
$388$	8.98091e7	+	6.78143e6i	1.53754	+	0.116098i
$389$	7.14765e6	−	1.23801e7i	0.121427	−	0.210317i	−0.798904	−	0.601459i	$-0.794586\pi$
$389$	7.14765e6	−	1.23801e7i	0.121427	−	0.210317i	0.920331	+	0.391142i	$0.127920\pi$
$390$	32611.7	−	51868.5i	0.000549767	−	0.000874400i
$391$		−	4.26479e7i		−	0.713456i
$392$	6.09416e6	−	5.36771e7i	0.101171	−	0.891109i
$393$	96342.6	−	166870.i	0.00158723	−	0.00274917i
$394$	3.40424e7	−	1.79796e7i	0.556585	−	0.293962i
$395$	5.07539e7	+	2.93028e7i	0.823527	+	0.475463i
$396$	9.16359e7	−	4.40656e7i	1.47564	−	0.709601i
$397$	−4.74999e7	−	8.22722e7i	−0.759138	−	1.31487i	−0.943291	−	0.331968i	$-0.892287\pi$
$397$	−4.74999e7	−	8.22722e7i	−0.759138	−	1.31487i	0.184152	−	0.982898i	$-0.441046\pi$
$398$	−8.72996e7	−	3.29128e6i	−1.38472	−	0.0522055i
$399$	191220.	−	621078.i	0.00301034	−	0.00977749i
$400$	−1.20391e6	−	182856.i	−0.0188111	−	0.00285712i
$401$	1.60760e7	+	2.78444e7i	0.249313	+	0.431822i	0.963335	−	0.268301i	$-0.0864620\pi$
$401$	1.60760e7	+	2.78444e7i	0.249313	+	0.431822i	−0.714023	+	0.700123i	$0.753129\pi$
$402$	−182868.	+	96582.1i	−0.00281487	+	0.00148668i
$403$	5.06008e6	+	2.92144e6i	0.0773112	+	0.0446357i
$404$	3.81890e7	+	7.94154e7i	0.579154	+	1.20437i
$405$	−3.28921e7	+	5.69708e7i	−0.495138	+	0.857605i
$406$	−1.25838e8	−	4.74422e6i	−1.88033	−	0.0708903i
$407$		−	1.50859e8i		−	2.23762i
$408$	−184334.	+	249320.i	−0.00271410	+	0.00367094i
$409$	2.27918e6	−	3.94766e6i	0.0333127	−	0.0576992i	−0.848888	−	0.528572i	$-0.822728\pi$
$409$	2.27918e6	−	3.94766e6i	0.0333127	−	0.0576992i	0.882201	+	0.470873i	$0.156061\pi$
$410$	−1.75833e6	+	4.66387e7i	−0.0255122	+	0.676698i
$411$			586690.i			0.00845052i
$412$	2.31743e7	+	1.58192e7i	0.331372	+	0.226201i
$413$	6.52153e7	+	1.12956e8i	0.925762	+	1.60347i
$414$	4.38415e7	−	6.97295e7i	0.617852	−	0.982687i
$415$	−7.63182e6	+	4.40623e6i	−0.106778	+	0.0616486i
$416$	−9.54446e6	+	3.32458e6i	−0.132578	+	0.0461804i
$417$	−994655.			−0.0137172
$418$	−3.94717e7	+	1.12891e8i	−0.540452	+	1.54572i
$419$			3.98464e7i			0.541685i	0.962624	+	0.270843i	$0.0873023\pi$
$419$			3.98464e7i			0.541685i	−0.962624	+	0.270843i	$0.912698\pi$
$420$	325336.	+	676547.i	0.00439121	+	0.00913167i
$421$	−3.99938e7	−	6.92712e7i	−0.535977	−	0.928339i	−0.999115	−	0.0420531i	$-0.986610\pi$
$421$	−3.99938e7	−	6.92712e7i	−0.535977	−	0.928339i	0.463139	−	0.886286i	$-0.346723\pi$
$422$	3.36179e7	−	5.34690e7i	0.447336	−	0.711483i
$423$	−6.98552e7	+	4.03309e7i	−0.922949	+	0.532865i
$424$	6.33796e7	+	4.68595e7i	0.831480	+	0.614752i
$425$	−897689.			−0.0116939
$426$	−8564.17	+	227160.i	−0.000110779	+	0.00293835i
$427$	1.56390e8	+	9.02916e7i	2.00874	+	1.15975i
$428$	5.10840e7	+	3.48709e7i	0.651558	+	0.444766i
$429$	−134823.			−0.00170763
$430$	−4.04785e7	−	1.52608e6i	−0.509118	−	0.0191943i
$431$	−4.92870e7	−	2.84559e7i	−0.615603	−	0.355418i	0.159552	−	0.987189i	$-0.448995\pi$
$431$	−4.92870e7	−	2.84559e7i	−0.615603	−	0.355418i	−0.775155	+	0.631771i	$0.782328\pi$
$432$	−1.11540e6	+	436305.i	−0.0138350	+	0.00541177i
$433$	5.74446e7	−	9.94969e7i	0.707596	−	1.22559i	−0.258151	−	0.966105i	$-0.583113\pi$
$433$	5.74446e7	−	9.94969e7i	0.707596	−	1.22559i	0.965747	−	0.259487i	$-0.0835535\pi$
$434$	−6.33040e7	+	3.34342e7i	−0.774395	+	0.408999i
$435$	716527.	−	413687.i	0.00870492	−	0.00502579i
$436$	−1.52480e8	−	1.15137e7i	−1.83973	−	0.138917i
$437$	2.16066e7	+	9.44364e7i	0.258906	+	1.13161i
$438$	98294.5	+	3705.81i	0.00116979	+	4.41022e-5i
$439$	−5.29010e7	+	3.05424e7i	−0.625274	+	0.361002i	−0.778919	−	0.627124i	$-0.784232\pi$
$439$	−5.29010e7	+	3.05424e7i	−0.625274	+	0.361002i	0.153646	+	0.988126i	$0.450899\pi$
$440$	−5.51389e7	−	1.26673e8i	−0.647292	−	1.48706i
$441$	3.84569e7	−	6.66093e7i	0.448392	−	0.776638i
$442$	−6.58827e6	+	3.47962e6i	−0.0762965	+	0.0402962i
$443$	−3.71626e7	−	2.14559e7i	−0.427460	−	0.246794i	0.270804	−	0.962634i	$-0.412710\pi$
$443$	−3.71626e7	−	2.14559e7i	−0.427460	−	0.246794i	−0.698264	+	0.715840i	$0.746044\pi$
$444$	−66896.8	+	885940.i	−0.000764287	+	0.0101217i
$445$	−5.71185e7			−0.648181
$446$	−3.27926e7	+	5.21563e7i	−0.369633	+	0.587899i
$447$	−1.09040e6	−	629545.i	−0.0122086	−	0.00704862i
$448$	2.77614e7	−	1.20685e8i	0.308750	−	1.34220i
$449$	7.87129e7			0.869574			0.434787	−	0.900533i	$-0.356824\pi$
$449$	7.87129e7			0.869574			0.434787	+	0.900533i	$0.356824\pi$
$450$	−1.46773e6	−	922814.i	−0.0161067	−	0.0101269i
$451$	8.89429e7	−	5.13512e7i	0.969575	−	0.559784i
$452$	5.49916e7	−	8.05597e7i	0.595499	−	0.872374i
$453$	−49704.5	−	86090.7i	−0.000534689	−	0.000926108i
$454$	4.87584e7	+	9.23187e7i	0.521053	+	0.986557i
$455$			1.80391e7i			0.191506i
$456$	281864.	−	645466.i	0.00297266	−	0.00680736i
$457$	9.92701e7			1.04009			0.520043	−	0.854140i	$-0.325916\pi$
$457$	9.92701e7			1.04009			0.520043	+	0.854140i	$0.325916\pi$
$458$	−1.72032e7	+	9.08593e6i	−0.179066	+	0.0945742i
$459$	−764641.	+	441466.i	−0.00790714	+	0.00456519i
$460$	−9.24303e7	−	6.30947e7i	−0.949601	−	0.648215i
$461$	7.79443e6	+	1.35004e7i	0.0795576	+	0.137798i	0.903059	−	0.429516i	$-0.141316\pi$
$461$	7.79443e6	+	1.35004e7i	0.0795576	+	0.137798i	−0.823502	+	0.567314i	$0.807983\pi$
$462$	879283.	−	1.39849e6i	0.00891667	−	0.0141819i
$463$			1.40107e8i			1.41162i	0.708403	+	0.705808i	$0.249416\pi$
$463$			1.40107e8i			1.41162i	−0.708403	+	0.705808i	$0.750584\pi$
$464$	−1.34936e8	−	2.04948e7i	−1.35075	−	0.205158i
$465$	235185.	−	407352.i	0.00233911	−	0.00405146i
$466$	−9.85830e7	−	6.19828e7i	−0.974191	−	0.612510i
$467$			3.79919e7i			0.373027i	0.982452	+	0.186514i	$0.0597189\pi$
$467$			3.79919e7i			0.373027i	−0.982452	+	0.186514i	$0.940281\pi$
$468$	−1.43489e7	−	1.08347e6i	−0.139984	−	0.0105701i
$469$	3.04445e7	−	5.27315e7i	0.295115	−	0.511153i
$470$	5.11832e7	+	9.69097e7i	0.492985	+	0.933413i
$471$	13178.1	+	7608.36i	0.000126121	+	7.28163e-5i
$472$	5.64204e7	+	1.29617e8i	0.536550	+	1.23264i
$473$	4.45685e7	+	7.71949e7i	0.421158	+	0.729466i
$474$	−28613.9	+	758968.i	−0.000268684	+	0.00712670i
$475$	1.98778e6	−	454795.i	0.0185476	−	0.00424360i
$476$	6.87376e6	−	9.10318e7i	0.0637343	−	0.844058i
$477$	5.61108e7	+	9.71868e7i	0.517001	+	0.895472i
$478$	4.47612e7	+	8.47504e7i	0.409843	+	0.775993i
$479$	−4.37187e7	−	2.52410e7i	−0.397796	−	0.229668i	0.287736	−	0.957710i	$-0.407097\pi$
$479$	−4.37187e7	−	2.52410e7i	−0.397796	−	0.229668i	−0.685533	+	0.728042i	$0.740431\pi$
$480$	267639.	+	768359.i	0.00242006	+	0.00694769i
$481$	−1.06747e7	+	1.84891e7i	−0.0959223	+	0.166142i
$482$	420793.	−	1.11613e7i	0.00375774	−	0.0996721i
$483$		−	1.33816e6i		−	0.0118759i
$484$	−1.07475e8	+	1.57445e8i	−0.947920	+	1.38865i
$485$	8.71131e7	−	1.50884e8i	0.763587	−	1.32257i
$486$	−2.55604e6	−	96365.5i	−0.0222669	−	0.000839485i
$487$		−	2.06196e8i		−	1.78523i	−0.450822	−	0.892614i	$-0.648869\pi$
$487$		−	2.06196e8i		−	1.78523i	0.450822	−	0.892614i	$-0.351131\pi$
$488$	1.57378e8	+	1.16357e8i	1.35421	+	1.00123i
$489$	2723.36	+	4716.99i	2.32905e−5	+	4.03403e-5i
$490$	−8.84695e7	−	5.56240e7i	−0.751978	−	0.472797i
$491$	−1.81159e8	+	1.04592e8i	−1.53044	+	0.883598i	−0.531095	+	0.847312i	$0.678219\pi$
$491$	−1.81159e8	+	1.04592e8i	−1.53044	+	0.883598i	−0.999341	+	0.0362857i	$0.988447\pi$
$492$	−545101.	+	262126.i	−0.00457701	+	0.00220098i
$493$	−1.00614e8			−0.839691
$494$	1.28257e7	−	1.10428e7i	0.106390	−	0.0916008i
$495$		−	1.96696e8i		−	1.62174i
$496$	−7.22607e7	+	2.82658e7i	−0.592185	+	0.231641i
$497$	−3.34647e7	−	5.79625e7i	−0.272595	−	0.472148i
$498$	−96684.3	−	60789.0i	−0.000782831	−	0.000492194i
$499$	−5.39997e7	+	3.11767e7i	−0.434600	+	0.250916i	−0.701304	−	0.712862i	$-0.747399\pi$
$499$	−5.39997e7	+	3.11767e7i	−0.434600	+	0.250916i	0.266704	+	0.963778i	$0.414065\pi$
$500$	−7.11279e7	+	1.04199e8i	−0.569023	+	0.833589i
$501$	1.57822e6			0.0125503
$502$	−1.06772e8	−	4.02541e6i	−0.844007	−	0.0318199i
$503$	−1.11296e8	−	6.42570e7i	−0.874535	−	0.504913i	−0.00568238	−	0.999984i	$-0.501809\pi$
$503$	−1.11296e8	−	6.42570e7i	−0.874535	−	0.504913i	−0.868853	+	0.495071i	$0.835142\pi$
$504$	1.04818e8	−	1.41771e8i	0.818739	−	1.10738i
$505$	1.70465e8			1.32361
$506$	−9.27784e6	+	2.46090e8i	−0.0716136	+	1.89951i
$507$	−821841.	−	474490.i	−0.00630615	−	0.00364085i
$508$	−6.82831e7	+	3.28357e7i	−0.520861	+	0.250470i
$509$	8.82216e7	−	1.52804e8i	0.668993	−	1.15873i	−0.309193	−	0.950999i	$-0.600059\pi$
$509$	8.82216e7	−	1.52804e8i	0.668993	−	1.15873i	0.978186	−	0.207730i	$-0.0666076\pi$
$510$	280120.	+	530376.i	0.00211170	+	0.00399828i
$511$	−2.50810e7	+	1.44805e7i	−0.187967	+	0.108523i
$512$	4.46521e7	−	1.26572e8i	0.332684	−	0.943038i
$513$	1.46951e6	−	1.36494e6i	0.0108848	−	0.0101102i
$514$	−6.66248e6	+	1.76719e8i	−0.0490622	+	1.30135i
$515$	4.70066e7	−	2.71393e7i	0.344142	−	0.198690i
$516$	−227504.	−	473102.i	−0.00165592	−	0.00344354i
$517$	1.20584e8	−	2.08857e8i	0.872604	−	1.51139i
$518$	−1.22166e8	−	2.31307e8i	−0.878941	−	1.66418i
$519$	680096.	+	392654.i	0.00486484	+	0.00280871i
$520$	−2.20557e6	+	1.94266e7i	−0.0156859	+	0.138161i
$521$	−6.81179e7			−0.481669			−0.240834	−	0.970566i	$-0.577421\pi$
$521$	−6.81179e7			−0.481669			−0.240834	+	0.970566i	$0.577421\pi$
$522$	−1.64505e8	−	1.03430e8i	−1.15656	−	0.727171i
$523$	−1.70592e8	−	9.84916e7i	−1.19249	−	0.688484i	−0.233619	−	0.972328i	$-0.575057\pi$
$523$	−1.70592e8	−	9.84916e7i	−1.19249	−	0.688484i	−0.958871	+	0.283844i	$0.908390\pi$
$524$	−4.62969e6	+	6.13128e7i	−0.0321780	+	0.426145i
$525$	−28166.8			−0.000194653
$526$	−1.18217e8	+	1.88022e8i	−0.812309	+	1.29197i
$527$	−4.95369e7	+	2.86001e7i	−0.338452	+	0.195405i
$528$	1.11790e6	−	1.39855e6i	0.00759452	−	0.00950112i
$529$	2.57260e7	+	4.45587e7i	0.173782	+	0.300999i
$530$	1.34827e8	−	7.12091e7i	0.905624	−	0.478308i
$531$			2.01268e8i			1.34428i
$532$	3.08986e7	+	2.05057e8i	0.205212	+	1.36188i
$533$	−1.45343e7			−0.0959872
$534$	−345704.	−	654552.i	−0.00227028	−	0.00429853i
$535$	1.03618e8	−	5.98240e7i	0.676667	−	0.390674i
$536$	3.92333e7	−	5.30648e7i	0.254777	−	0.344598i
$537$	898915.	+	1.55697e6i	0.00580491	+	0.0100544i
$538$	1.06798e8	+	6.71478e7i	0.685830	+	0.431206i
$539$			2.29961e8i			1.46855i
$540$	−174451.	+	2.31032e6i	−0.00110788	+	0.0146720i
$541$	−1.25851e8	+	2.17981e8i	−0.794814	+	1.37666i	0.128144	+	0.991756i	$0.459098\pi$
$541$	−1.25851e8	+	2.17981e8i	−0.794814	+	1.37666i	−0.922957	+	0.384902i	$0.874235\pi$
$542$	−1.00047e7	+	1.59123e7i	−0.0628354	+	0.0999392i
$543$			311826.i			0.00194766i
$544$	1.85325e7	−	9.71928e7i	0.115116	−	0.603723i
$545$	−1.47903e8	+	2.56176e8i	−0.913667	+	1.58252i
$546$	−206720.	+	109180.i	−0.00127001	+	0.000670757i
$547$	2.02702e8	+	1.17030e8i	1.23850	+	0.715049i	0.968788	−	0.247892i	$-0.0797379\pi$
$547$	2.02702e8	+	1.17030e8i	1.23850	+	0.715049i	0.269713	+	0.962941i	$0.413071\pi$
$548$	−8.11351e7	−	1.68723e8i	−0.493023	−	1.02526i
$549$	1.39329e8	+	2.41325e8i	0.842025	+	1.45843i
$550$	5.17991e6	+	195288.i	0.0311340	+	0.00117378i
$551$	2.22793e8	−	5.09741e7i	1.33183	−	0.304716i
$552$	163612.	−	1.44108e6i	0.000972740	−	0.00856786i
$553$	−1.11809e8	−	1.93660e8i	−0.661155	−	1.14515i
$554$	−1.70614e8	+	9.01101e7i	−1.00342	+	0.529961i
$555$	1.48843e6	+	859345.i	0.00870661	+	0.00502676i
$556$	2.86048e8	−	1.37554e8i	1.66423	−	0.800291i
$557$	8.14340e7	−	1.41048e8i	0.471238	−	0.816208i	−0.528221	−	0.849107i	$-0.677141\pi$
$557$	8.14340e7	−	1.41048e8i	0.471238	−	0.816208i	0.999459	+	0.0328994i	$0.0104741\pi$
$558$	−1.10394e8	−	4.16195e6i	−0.635391	−	0.0239549i
$559$		−	1.26146e7i		−	0.0722166i
$560$	−1.87123e8	−	1.49573e8i	−1.06552	−	0.851705i
$561$	659942.	−	1.14305e6i	0.00373781	−	0.00647407i
$562$	5.11267e6	−	1.35611e8i	0.0288031	−	0.763986i
$563$			1.39235e8i			0.780230i	0.920766	+	0.390115i	$0.127565\pi$
$563$			1.39235e8i			0.780230i	−0.920766	+	0.390115i	$0.872435\pi$
$564$	−800761.	+	1.17307e6i	−0.00446340	+	0.00653864i
$565$	−9.43428e7	−	1.63407e8i	−0.523075	−	0.905992i
$566$	1.22910e8	−	1.95486e8i	0.677854	−	1.07812i
$567$	2.17382e8	−	1.25505e8i	1.19254	−	0.688514i
$568$	−2.89517e7	−	6.65121e7i	−0.157990	−	0.362957i
$569$	−2.51329e8			−1.36429			−0.682144	−	0.731218i	$-0.738952\pi$
$569$	−2.51329e8			−1.36429			−0.682144	+	0.731218i	$0.738952\pi$
$570$	−888981.	−	1.03251e6i	−0.00480029	−	0.00557532i
$571$			6.16459e7i			0.331128i	0.986199	+	0.165564i	$0.0529444\pi$
$571$			6.16459e7i			0.331128i	−0.986199	+	0.165564i	$0.947056\pi$
$572$	3.87731e7	−	1.86451e7i	0.207177	−	0.0996268i
$573$	239056.	+	414058.i	0.00127068	+	0.00220088i
$574$	9.47892e7	−	1.50761e8i	0.501214	−	0.797176i
$575$	3.63644e6	−	2.09950e6i	0.0191281	−	0.0110436i
$576$	1.30214e8	−	1.39860e8i	0.681380	−	0.731854i
$577$	−1.66342e8			−0.865912			−0.432956	−	0.901415i	$-0.642530\pi$
$577$	−1.66342e8			−0.865912			−0.432956	+	0.901415i	$0.642530\pi$
$578$	−4.52695e6	+	1.20075e8i	−0.0234435	+	0.621825i
$579$	75786.1	+	43755.1i	0.000390440	+	0.000225420i
$580$	−1.48852e8	+	2.18061e8i	−0.762907	+	1.11762i
$581$	3.36254e7			0.171451
$582$	2.25631e6	+	85065.3i	0.0114454	+	0.000431502i
$583$	−2.90575e8	−	1.67763e8i	−1.46640	−	0.846626i
$584$	−2.87805e7	+	1.25277e7i	−0.144497	+	0.0628974i
$585$	−1.39181e7	+	2.41069e7i	−0.0695205	+	0.120413i
$586$	1.48117e8	−	7.82285e7i	0.736058	−	0.388751i
$587$	1.32455e8	−	7.64731e7i	0.654870	−	0.378089i	−0.135450	−	0.990784i	$-0.543248\pi$
$587$	1.32455e8	−	7.64731e7i	0.654870	−	0.378089i	0.790320	+	0.612695i	$0.209915\pi$
$588$	101974.	−	1.35048e6i	0.000501600	−	0.00664288i
$589$	9.52013e7	−	8.84269e7i	0.465904	−	0.432751i
$590$	2.73269e8	+	1.03025e7i	1.33056	+	0.0501635i
$591$	835852.	−	482579.i	0.00404918	−	0.00233779i
$592$	−1.03281e8	−	2.64034e8i	−0.497799	−	1.27261i
$593$	−1.30220e7	+	2.25548e7i	−0.0624475	+	0.108162i	−0.895559	−	0.444943i	$-0.853224\pi$
$593$	−1.30220e7	+	2.25548e7i	−0.0624475	+	0.108162i	0.833111	+	0.553105i	$0.186557\pi$
$594$	4.50823e6	−	2.38103e6i	0.0215103	−	0.0113607i
$595$	−1.52939e8	−	8.82991e7i	−0.726049	−	0.419185i
$596$	4.00645e8	+	3.02525e7i	1.89244	+	0.142897i
$597$	−2.19014e6			−0.0102932
$598$	1.85503e7	−	2.95040e7i	0.0867454	−	0.137968i
$599$	9.92902e7	+	5.73252e7i	0.461983	+	0.266726i	0.712878	−	0.701288i	$-0.247391\pi$
$599$	9.92902e7	+	5.73252e7i	0.461983	+	0.266726i	−0.250895	+	0.968014i	$0.580725\pi$
$600$	−30333.2	−	3443.84i	−0.000140431	−	1.59437e-5i
$601$	−2.91572e8			−1.34314			−0.671571	−	0.740940i	$-0.734380\pi$
$601$	−2.91572e8			−1.34314			−0.671571	+	0.740940i	$0.734380\pi$
$602$	1.30848e8	+	8.22690e7i	0.599761	+	0.377092i
$603$	8.13701e7	−	4.69790e7i	0.371119	−	0.214265i
$604$	2.62000e7	+	1.78846e7i	0.118902	+	0.0811649i
$605$	1.84383e8	+	3.19360e8i	0.832634	+	1.44216i
$606$	1.03172e6	+	1.95345e6i	0.00463601	+	0.00877778i
$607$		−	1.61303e8i		−	0.721236i	−0.932714	−	0.360618i	$-0.882566\pi$
$607$		−	1.61303e8i		−	0.721236i	0.932714	−	0.360618i	$-0.117434\pi$
$608$	8.20359e6	+	2.24606e8i	0.0365000	+	0.999334i
$609$	−3.15698e6			−0.0139772
$610$	3.34789e8	−	1.76820e8i	1.47496	−	0.779007i
$611$	−2.95572e7	+	1.70649e7i	−0.129581	+	0.0748134i
$612$	7.94216e7	−	1.16348e8i	0.346485	−	0.507582i
$613$	7.27528e7	+	1.26012e8i	0.315841	+	0.547053i	0.979616	−	0.200880i	$-0.0643801\pi$
$613$	7.27528e7	+	1.26012e8i	0.315841	+	0.547053i	−0.663775	+	0.747932i	$0.731047\pi$
$614$	−1.13938e8	+	1.81217e8i	−0.492224	+	0.782877i
$615$			1.17006e6i			0.00503016i
$616$	−5.94670e7	+	5.23783e8i	−0.254410	+	2.24083i
$617$	−8.60260e7	+	1.49001e8i	−0.366247	+	0.634358i	−0.988975	−	0.148080i	$-0.952691\pi$
$617$	−8.60260e7	+	1.49001e8i	−0.366247	+	0.634358i	0.622728	+	0.782438i	$0.286024\pi$
$618$	595507.	+	374417.i	0.00252302	+	0.00158632i
$619$		−	8.10104e7i		−	0.341561i	−0.985309	−	0.170781i	$-0.945371\pi$
$619$		−	8.10104e7i		−	0.341561i	0.985309	−	0.170781i	$-0.0546290\pi$
$620$	−1.13017e7	+	1.49673e8i	−0.0474208	+	0.628012i
$621$	2.06498e6	−	3.57665e6i	0.00862266	−	0.0149349i
$622$	1.76482e8	+	3.34150e8i	0.733381	+	1.38858i
$623$	1.88746e8	+	1.08972e8i	0.780572	+	0.450664i
$624$	−235969.	+	92302.4i	−0.000971182	+	0.000379891i
$625$	1.19704e8	+	2.07333e8i	0.490306	+	0.849234i
$626$	−2.05204e6	+	5.44292e7i	−0.00836493	+	0.221875i
$627$	−882225.	+	2.86544e6i	−0.00357912	+	0.0116249i
$628$	−4.84199e6	−	365616.i	−0.0195499	−	0.00147620i
$629$	−1.04502e8	−	1.81003e8i	−0.419927	−	0.727335i
$630$	−1.59285e8	−	3.01589e8i	−0.637020	−	1.20613i
$631$	8.30584e7	+	4.79538e7i	0.330594	+	0.190869i	0.656105	−	0.754670i	$-0.272203\pi$
$631$	8.30584e7	+	4.79538e7i	0.330594	+	0.190869i	−0.325511	+	0.945538i	$0.605536\pi$
$632$	−9.67310e7	−	2.22225e8i	−0.383190	−	0.880322i
$633$	791698.	−	1.37126e6i	0.00312139	−	0.00540641i
$634$	2.72336e6	−	7.22357e7i	0.0106866	−	0.283455i
$635$			1.46569e8i			0.572430i
$636$	1.63205e6	+	1.11407e6i	0.00634398	+	0.00433052i
$637$	1.62719e7	−	2.81838e7i	0.0629536	−	0.109039i
$638$	5.80573e8	+	2.18882e7i	2.23560	+	0.0842845i
$639$		−	1.03279e8i		−	0.395830i
$640$	−1.83227e8	−	1.83956e8i	−0.698957	−	0.701735i
$641$	1.81053e8	+	3.13592e8i	0.687433	+	1.19067i	0.972665	+	0.232211i	$0.0745960\pi$
$641$	1.81053e8	+	3.13592e8i	0.687433	+	1.19067i	−0.285232	+	0.958458i	$0.592071\pi$
$642$	1.31269e6	+	825340.i	0.00496088	+	0.00311909i
$643$	−9.28119e7	+	5.35850e7i	−0.349117	+	0.201563i	−0.664296	−	0.747469i	$-0.731269\pi$
$643$	−9.28119e7	+	5.35850e7i	−0.349117	+	0.201563i	0.315179	+	0.949032i	$0.397935\pi$
$644$	1.85059e8	+	3.84836e8i	0.692869	+	1.44085i
$645$	−1.01551e6			−0.00378448
$646$	3.08425e7	+	1.62792e8i	0.114407	+	0.603857i
$647$			1.70331e8i			0.628899i	0.949274	+	0.314449i	$0.101820\pi$
$647$			1.70331e8i			0.628899i	−0.949274	+	0.314449i	$0.898180\pi$
$648$	2.49446e8	−	1.08580e8i	0.916750	−	0.399047i
$649$	−3.00881e8	−	5.21141e8i	−1.10068	−	1.90643i
$650$	−621026.	−	390462.i	−0.00226136	−	0.00142180i
$651$	−1.55432e6	+	897387.i	−0.00563375	+	0.00325265i
$652$	−1.43552e6	−	979914.i	−0.00517925	−	0.00353545i
$653$	−4.72114e8			−1.69554			−0.847769	−	0.530366i	$-0.822054\pi$
$653$	−4.72114e8			−1.69554			−0.847769	+	0.530366i	$0.822054\pi$
$654$	−3.83083e6	−	144426.i	−0.0136949	−	0.000516313i
$655$	1.03009e8	+	5.94723e7i	0.366565	+	0.211636i
$656$	1.20513e8	−	1.50767e8i	0.426895	−	0.534066i
$657$	−4.46899e7			−0.157584
$658$	1.57546e7	−	4.17883e8i	0.0553007	−	1.46682i
$659$	3.91977e8	+	2.26308e8i	1.36963	+	0.790758i	0.990881	−	0.134740i	$-0.0430200\pi$
$659$	3.91977e8	+	2.26308e8i	1.36963	+	0.790758i	0.378752	+	0.925498i	$0.376353\pi$
$660$	−1.50099e6	−	3.12135e6i	−0.00522090	−	0.0108570i
$661$	1.24253e8	−	2.15212e8i	0.430231	−	0.745181i	−0.566662	−	0.823950i	$-0.691766\pi$
$661$	1.24253e8	−	2.15212e8i	0.430231	−	0.745181i	0.996893	+	0.0787690i	$0.0250989\pi$
$662$	−1.56343e8	−	2.96019e8i	−0.538896	−	1.02034i
$663$	−161763.	+	93394.2i	−0.000555060	+	0.000320464i
$664$	3.62116e7	+	4.11124e6i	0.123693	+	0.0140433i
$665$	3.83391e8	+	1.18040e8i	1.30370	+	0.401389i
$666$	1.52074e7	−	4.03368e8i	0.0514793	−	1.36546i
$667$	4.07577e8	−	2.35315e8i	1.37351	−	0.792997i
$668$	−4.53873e8	+	2.18257e8i	−1.52267	+	0.732215i
$669$	−772262.	+	1.33760e6i	−0.00257921	+	0.00446732i
$670$	−5.96201e7	−	1.12884e8i	−0.198230	−	0.375326i
$671$	−7.21528e8	−	4.16574e8i	−2.38828	−	1.37888i
$672$	581495.	−	3.04962e6i	0.00191619	−	0.0100494i
$673$	2.89037e8			0.948217			0.474109	−	0.880466i	$-0.342770\pi$
$673$	2.89037e8			0.948217			0.474109	+	0.880466i	$0.342770\pi$
$674$	−2.01497e8	−	1.26689e8i	−0.658096	−	0.413769i
$675$	−75284.5	−	43465.5i	−0.000244790	−	0.000141330i
$676$	3.01968e8	+	2.28014e7i	0.977508	+	0.0738110i
$677$	−4.65624e8			−1.50062			−0.750308	−	0.661088i	$-0.770095\pi$
$677$	−4.65624e8			−1.50062			−0.750308	+	0.661088i	$0.770095\pi$
$678$	1.30157e6	−	2.07013e6i	0.00417616	−	0.00664214i
$679$	−5.75724e8	+	3.32394e8i	−1.83910	+	1.06180i
$680$	−1.53905e8	−	1.13790e8i	−0.489471	−	0.361889i
$681$	1.30869e6	+	2.26672e6i	0.00414378	+	0.00717724i
$682$	2.92063e8	−	1.54254e8i	0.920711	−	0.486277i
$683$			5.83905e8i			1.83265i	0.400432	+	0.916326i	$0.368860\pi$
$683$			5.83905e8i			1.83265i	−0.400432	+	0.916326i	$0.631140\pi$
$684$	−1.16920e8	+	2.97871e8i	−0.365360	+	0.930807i
$685$	−3.62164e8			−1.12677
$686$	−2.14218e7	−	4.05599e7i	−0.0663566	−	0.125639i
$687$	−422395.	+	243870.i	−0.00130271	+	0.000752121i
$688$	1.30853e8	+	1.04595e8i	0.401808	+	0.321177i
$689$	2.37417e7	+	4.11218e7i	0.0725862	+	0.125723i
$690$	−2.37516e6	−	1.49335e6i	−0.00723014	−	0.00454585i
$691$		−	9.20647e7i		−	0.279035i	−0.990220	−	0.139518i	$-0.955445\pi$
$691$		−	9.20647e7i		−	0.279035i	0.990220	−	0.139518i	$-0.0445552\pi$
$692$	−2.49886e8	−	1.88688e7i	−0.754092	−	0.0569410i
$693$	−3.75264e8	+	6.49976e8i	−1.12755	+	1.95298i
$694$	−2.95495e7	+	4.69982e7i	−0.0884039	+	0.140606i
$695$		−	6.14001e8i		−	1.82900i
$696$	−3.39979e6	−	385991.i	−0.0100838	−	0.00114485i
$697$	7.11436e7	−	1.23224e8i	0.210105	−	0.363913i
$698$	−2.93936e8	+	1.55243e8i	−0.864342	+	0.456505i
$699$	−2.52825e6	−	1.45969e6i	−0.00740268	−	0.00427394i
$700$	8.10035e6	−	3.89527e6i	0.0236162	−	0.0113565i
$701$	−1.14553e6	−	1.98412e6i	−0.00332547	−	0.00575989i	0.864358	−	0.502877i	$-0.167725\pi$
$701$	−1.14553e6	−	1.98412e6i	−0.00332547	−	0.00575989i	−0.867683	+	0.497117i	$0.834392\pi$
$702$	−721004.	−	27182.6i	−0.00208414	−	7.85742e-5i
$703$	3.23104e8	+	3.47857e8i	0.929985	+	1.00123i
$704$	−1.28081e8	+	5.56798e8i	−0.367086	+	1.59580i
$705$	1.37377e6	+	2.37945e6i	0.00392056	+	0.00679061i
$706$	−3.18222e8	+	1.68070e8i	−0.904308	+	0.477613i
$707$	−5.63295e8	−	3.25219e8i	−1.59396	−	0.920274i
$708$	1.53587e6	+	3.19390e6i	0.00432768	+	0.00899956i
$709$	−1.38344e8	+	2.39618e8i	−0.388169	+	0.672328i	−0.992203	−	0.124630i	$-0.960226\pi$
$709$	−1.38344e8	+	2.39618e8i	−0.388169	+	0.672328i	0.604035	+	0.796958i	$0.293559\pi$
$710$	−1.40226e8	−	5.28666e6i	−0.391790	−	0.0147709i
$711$		−	3.45067e8i		−	0.960052i
$712$	1.89939e8	+	1.40431e8i	0.526228	+	0.389065i
$713$	1.33779e8	−	2.31711e8i	0.369078	−	0.639262i
$714$	86223.4	−	2.28703e6i	0.000236881	−	0.00628315i
$715$		−	8.32264e7i		−	0.227689i
$716$	−4.73831e8	−	3.23446e8i	−1.29088	−	0.881177i
$717$	1.20141e6	+	2.08090e6i	0.00325936	+	0.00564538i
$718$	4.51826e7	−	7.18625e7i	0.122067	−	0.194146i
$719$	−3.37120e8	+	1.94636e8i	−0.906981	+	0.523646i	−0.879458	−	0.475976i	$-0.842095\pi$
$719$	−3.37120e8	+	1.94636e8i	−0.906981	+	0.523646i	−0.0275222	+	0.999621i	$0.508762\pi$
$720$	−1.34662e8	−	3.44259e8i	−0.360784	−	0.922334i
$721$	−2.07109e8			−0.552577
$722$	−1.50770e8	−	3.44848e8i	−0.400594	−	0.916256i
$723$		−	280011.i		−	0.000740902i
$724$	−4.31233e7	−	8.96763e7i	−0.113631	−	0.236299i
$725$	−4.95311e6	−	8.57904e6i	−0.0129976	−	0.0225125i
$726$	−2.54377e6	+	4.04584e6i	−0.00664764	+	0.0105730i
$727$	−1.38646e8	+	8.00472e7i	−0.360831	+	0.208326i	−0.669445	−	0.742861i	$-0.733468\pi$
$727$	−1.38646e8	+	8.00472e7i	−0.360831	+	0.208326i	0.308614	+	0.951187i	$0.400135\pi$
$728$	4.43508e7	−	5.99865e7i	0.114950	−	0.155475i
$729$	3.87292e8			0.999669
$730$	−2.28759e6	+	6.06772e7i	−0.00588045	+	0.155976i
$731$	1.06948e8	+	6.17466e7i	0.273793	+	0.158074i
$732$	4.05255e6	+	2.76635e6i	0.0103323	+	0.00705299i
$733$	7.68741e8			1.95195			0.975974	−	0.217886i	$-0.0699161\pi$
$733$	7.68741e8			1.95195			0.975974	+	0.217886i	$0.0699161\pi$
$734$	−8.78793e7	−	3.31314e6i	−0.222228	−	0.00837822i
$735$	−2.26888e6	−	1.30994e6i	−0.00571413	−	0.00329905i
$736$	1.52239e8	+	4.37060e8i	0.381851	+	1.09625i
$737$	−1.40461e8	+	2.43285e8i	−0.350875	+	0.607733i
$738$	2.42993e8	−	1.28338e8i	0.604540	−	0.319290i
$739$	−4.06994e8	+	2.34978e8i	−1.00845	+	0.582229i	−0.910738	−	0.412985i	$-0.864486\pi$
$739$	−4.06994e8	+	2.34978e8i	−1.00845	+	0.582229i	−0.0977132	+	0.995215i	$0.531153\pi$
$740$	−5.46891e8	−	4.12954e7i	−1.34960	−	0.101908i
$741$	310881.	−	288759.i	0.000764082	−	0.000709711i
$742$	−5.81385e8	−	2.19188e7i	−1.42315	−	0.0536544i
$743$	−1.27789e8	+	7.37791e7i	−0.311550	+	0.179873i	−0.647620	−	0.761964i	$-0.724235\pi$
$743$	−1.27789e8	+	7.37791e7i	−0.311550	+	0.179873i	0.336070	+	0.941837i	$0.390902\pi$
$744$	−1.78359e6	+	776367.i	−0.00433087	+	0.00188516i
$745$	3.88618e8	−	6.73107e8i	0.939841	−	1.62785i
$746$	1.88959e8	−	9.97994e7i	0.455147	−	0.240387i
$747$	4.49359e7	+	2.59437e7i	0.107803	+	0.0622402i
$748$	−3.17132e7	+	4.19990e8i	−0.0757765	+	1.00354i
$749$	−4.56537e8			−1.08650
$750$	−1.68349e6	+	2.67757e6i	−0.00399049	+	0.00634684i
$751$	2.82626e7	+	1.63174e7i	0.0667257	+	0.0385241i	0.532992	−	0.846120i	$-0.321068\pi$
$751$	2.82626e7	+	1.63174e7i	0.0667257	+	0.0385241i	−0.466266	+	0.884645i	$0.654401\pi$
$752$	6.80592e7	−	4.48097e8i	0.160042	−	1.05370i
$753$	−2.67866e6			−0.00627383
$754$	−6.96056e7	−	4.37636e7i	−0.162379	−	0.102094i
$755$	5.31438e7	−	3.06826e7i	0.123484	−	0.0712937i
$756$	4.98417e6	−	7.30154e6i	0.0115353	−	0.0168985i
$757$	−5.35723e7	−	9.27899e7i	−0.123496	−	0.213901i	0.797648	−	0.603123i	$-0.206077\pi$
$757$	−5.35723e7	−	9.27899e7i	−0.123496	−	0.213901i	−0.921144	+	0.389222i	$0.872744\pi$
$758$	−5.12968e6	−	9.71248e6i	−0.0117783	−	0.0223009i
$759$			6.17383e6i			0.0141198i
$760$	3.98446e8	+	1.73995e8i	0.907672	+	0.396365i
$761$	3.74849e8			0.850554			0.425277	−	0.905063i	$-0.360177\pi$
$761$	3.74849e8			0.850554			0.425277	+	0.905063i	$0.360177\pi$
$762$	−1.67962e6	+	887096.i	−0.00379617	+	0.00200496i
$763$	9.77481e8	−	5.64349e8i	2.20057	−	1.27050i
$764$	−1.26010e8	−	8.60170e7i	−0.282570	−	0.192887i
$765$	−1.36255e8	−	2.36000e8i	−0.304346	−	0.527142i
$766$	3.48139e6	−	5.53711e6i	0.00774580	−	0.0123196i
$767$			8.51607e7i			0.188735i
$768$	999083.	−	3.21308e6i	0.00220556	−	0.00709312i
$769$	3.33638e8	−	5.77877e8i	0.733662	−	1.27074i	−0.221646	−	0.975127i	$-0.571143\pi$
$769$	3.33638e8	−	5.77877e8i	0.733662	−	1.27074i	0.955308	−	0.295613i	$-0.0955237\pi$
$770$	8.63289e8	+	5.42781e8i	1.89097	+	1.18892i
$771$			4.43347e6i			0.00967343i
$772$	−2.78459e7	−	2.10263e6i	−0.0605216	−	0.00456995i
$773$	1.04443e8	−	1.80901e8i	0.226122	−	0.391654i	−0.730534	−	0.682877i	$-0.760729\pi$
$773$	1.04443e8	−	1.80901e8i	0.226122	−	0.391654i	0.956655	+	0.291222i	$0.0940619\pi$
$774$	1.11386e8	+	2.10898e8i	0.240220	+	0.454830i
$775$	−4.87727e6	−	2.81589e6i	−0.0104778	−	0.00604938i
$776$	−6.60644e8	+	2.87568e8i	−1.41378	+	0.615397i
$777$	−3.27897e6	−	5.67934e6i	−0.00698996	−	0.0121070i
$778$	−4.30852e6	+	1.14281e8i	−0.00914933	+	0.242681i
$779$	−9.51063e7	+	3.08902e8i	−0.201186	+	0.653445i
$780$	−36905.9	+	488759.i	−7.77700e−5	+	0.00102994i
$781$	1.54395e8	+	2.67419e8i	0.324100	+	0.561357i
$782$	1.59339e8	+	3.01690e8i	0.333197	+	0.630872i
$783$	−8.43800e6	−	4.87168e6i	−0.0175774	−	0.0101483i
$784$	1.57436e8	+	4.02480e8i	0.326704	+	0.835210i
$785$	−4.69664e6	+	8.13482e6i	−0.00970909	+	0.0168166i
$786$	−58074.2	+	1.54039e6i	−0.000119596	+	0.00317221i
$787$		−	5.44919e8i		−	1.11791i	−0.829197	−	0.558956i	$-0.811202\pi$
$787$		−	5.44919e8i		−	1.11791i	0.829197	−	0.558956i	$-0.188798\pi$
$788$	−1.73641e8	+	2.54375e8i	−0.354873	+	0.519871i
$789$	−2.78399e6	+	4.82201e6i	−0.00566808	+	0.00981740i
$790$	−4.68511e8	−	1.76634e7i	−0.950252	−	0.0358255i
$791$			7.19961e8i			1.45472i
$792$	−4.83595e8	+	6.54084e8i	−0.973434	+	1.31661i
$793$	5.89531e7	+	1.02110e8i	0.118219	+	0.204761i
$794$	6.43394e8	+	4.04526e8i	1.28533	+	0.808136i
$795$	3.31043e6	−	1.91128e6i	0.00658845	−	0.00380384i
$796$	6.29852e8	−	3.02881e8i	1.24882	−	0.600528i
$797$	4.76059e8			0.940343			0.470171	−	0.882575i	$-0.344192\pi$
$797$	4.76059e8			0.940343			0.470171	+	0.882575i	$0.344192\pi$
$798$	967747.	+	5.10792e6i	0.00190438	+	0.0100516i
$799$		−	3.34121e8i		−	0.655033i
$800$	9.19962e6	−	3.20447e6i	0.0179680	−	0.00625873i
$801$	1.68156e8	+	2.91254e8i	0.327201	+	0.566728i
$802$	−2.17752e8	−	1.36909e8i	−0.422123	−	0.265404i
$803$	1.15715e8	−	6.68082e7i	0.223482	−	0.129028i
$804$	932757.	−	1.36644e6i	0.00179474	−	0.00262919i
$805$	8.26049e8			1.58350
$806$	−4.67099e7	−	1.76101e6i	−0.0892079	−	0.00336323i
$807$	2.73893e6	+	1.58132e6i	0.00521148	+	0.00300885i
$808$	−5.66856e8	−	4.19103e8i	−1.07458	−	0.794487i
$809$	−4.42568e8			−0.835861			−0.417931	−	0.908479i	$-0.637245\pi$
$809$	−4.42568e8			−0.835861			−0.417931	+	0.908479i	$0.637245\pi$
$810$	1.98270e7	−	5.25900e8i	0.0373080	−	0.989574i
$811$	4.05271e8	+	2.33984e8i	0.759772	+	0.438655i	0.829214	−	0.558931i	$-0.188788\pi$
$811$	4.05271e8	+	2.33984e8i	0.759772	+	0.438655i	−0.0694417	+	0.997586i	$0.522122\pi$
$812$	9.07900e8	−	4.36588e8i	1.69578	−	0.815462i
$813$	−235609.	+	408086.i	−0.000438450	+	0.000759417i
$814$	5.63630e8	+	1.06717e9i	1.04501	+	1.97861i
$815$	−2.91180e6	+	1.68113e6i	−0.00537884	+	0.00310547i
$816$	372480.	−	2.45239e6i	0.000685540	−	0.00451355i
$817$	−2.68101e8	−	8.25443e7i	−0.491624	−	0.151363i
$818$	−1.37387e6	+	3.64410e7i	−0.00251006	+	0.0665780i
$819$	9.19838e7	−	5.31069e7i	0.167440	−	0.0966716i
$820$	−1.61811e8	−	3.36491e8i	−0.293471	−	0.610284i
$821$	3.64554e8	−	6.31426e8i	0.658768	−	1.14102i	−0.322167	−	0.946683i	$-0.604411\pi$
$821$	3.64554e8	−	6.31426e8i	0.658768	−	1.14102i	0.980935	−	0.194337i	$-0.0622554\pi$
$822$	−2.19196e6	−	4.15024e6i	−0.00394655	−	0.00747235i
$823$	4.87658e8	+	2.81549e8i	0.874814	+	0.505074i	0.868945	−	0.494909i	$-0.164798\pi$
$823$	4.87658e8	+	2.81549e8i	0.874814	+	0.505074i	0.00586908	+	0.999983i	$0.498132\pi$
$824$	−2.23038e8	−	2.53223e7i	−0.398655	−	0.0452607i
$825$	129952.			0.000231431
$826$	−8.83353e8	−	5.55396e8i	−1.56745	−	0.985514i
$827$	−7.22363e8	−	4.17056e8i	−1.27714	−	0.737358i	−0.300819	−	0.953681i	$-0.597260\pi$
$827$	−7.22363e8	−	4.17056e8i	−1.27714	−	0.737358i	−0.976322	+	0.216324i	$0.930593\pi$
$828$	−4.96145e7	+	6.57063e8i	−0.0874012	+	1.15749i
$829$	3.09276e8			0.542854			0.271427	−	0.962459i	$-0.412504\pi$
$829$	3.09276e8			0.542854			0.271427	+	0.962459i	$0.412504\pi$
$830$	3.75250e7	−	5.96832e7i	0.0656276	−	0.104380i
$831$	−4.18912e6	+	2.41859e6i	−0.00729995	+	0.00421463i
$832$	5.50962e7	−	5.91775e7i	0.0956647	−	0.102751i
$833$	1.59298e8	+	2.75912e8i	0.275597	+	0.477348i
$834$	7.03617e6	−	3.71618e6i	0.0121294	−	0.00640617i
$835$			9.74237e8i			1.67342i
$836$	−1.42555e8	−	9.46062e8i	−0.243986	−	1.61920i
$837$	−5.53919e6			−0.00944648
$838$	−1.48872e8	−	2.81873e8i	−0.252977	−	0.478984i
$839$	−2.53791e7	+	1.46526e7i	−0.0429724	+	0.0248101i	−0.521332	−	0.853354i	$-0.674565\pi$
$839$	−2.53791e7	+	1.46526e7i	−0.0429724	+	0.0248101i	0.478360	+	0.878164i	$0.341231\pi$
$840$	−4.82910e6	−	3.57038e6i	−0.00814757	−	0.00602388i
$841$	−2.57741e8	−	4.46420e8i	−0.433306	−	0.750508i
$842$	5.41722e8	+	3.40601e8i	0.907487	+	0.570571i
$843$		−	3.40216e6i		−	0.00567900i
$844$	−3.80447e7	+	5.03840e8i	−0.0632800	+	0.838041i
$845$	2.92903e8	−	5.07322e8i	0.485460	−	0.840841i
$846$	3.43472e8	−	5.46290e8i	0.567258	−	0.902219i
$847$		−	1.40709e9i		−	2.31564i
$848$	−6.23420e8	−	9.46880e7i	−1.02233	−	0.155277i
$849$	2.89451e6	−	5.01343e6i	0.00472989	−	0.00819241i
$850$	6.35024e6	−	3.35390e6i	0.0103403	−	0.00546126i
$851$	8.46653e8	+	4.88815e8i	1.37378	+	0.793151i
$852$	−788120.	−	1.63892e6i	−0.00127431	−	0.00264996i
$853$	−2.50527e8	−	4.33926e8i	−0.403653	−	0.699147i	0.590511	−	0.807030i	$-0.298926\pi$
$853$	−2.50527e8	−	4.33926e8i	−0.403653	−	0.699147i	−0.994164	+	0.107883i	$0.965593\pi$
$854$	−1.44364e9	−	5.44267e7i	−2.31785	−	0.0873854i
$855$	4.21277e8	+	4.53551e8i	0.674014	+	0.725651i
$856$	−4.91650e8	−	5.58188e7i	−0.783853	−	0.0889936i
$857$	5.36565e8	+	9.29357e8i	0.852471	+	1.47652i	0.878972	+	0.476874i	$0.158230\pi$
$857$	5.36565e8	+	9.29357e8i	0.852471	+	1.47652i	−0.0265009	+	0.999649i	$0.508436\pi$
$858$	953737.	−	503719.i	0.00150996	−	0.000797492i
$859$	1.90431e8	+	1.09945e8i	0.300440	+	0.173459i	0.642641	−	0.766168i	$-0.277839\pi$
$859$	1.90431e8	+	1.09945e8i	0.300440	+	0.173459i	−0.342200	+	0.939627i	$0.611172\pi$
$860$	2.92046e8	−	1.40438e8i	0.459151	−	0.220795i
$861$	2.23227e6	−	3.86641e6i	0.00349734	−	0.00605757i
$862$	4.54970e8	+	1.71529e7i	0.710332	+	0.0267803i
$863$		−	6.56933e8i		−	1.02209i	−0.859554	−	0.511044i	$-0.829259\pi$
$863$		−	6.56933e8i		−	1.02209i	0.859554	−	0.511044i	$-0.170741\pi$
$864$	6.26023e6	−	7.25372e6i	0.00970620	−	0.0112466i
$865$	−2.42385e8	+	4.19823e8i	−0.374505	+	0.648662i
$866$	−3.46269e7	+	9.18461e8i	−0.0533163	+	1.41419i
$867$			3.01240e6i			0.00462227i
$868$	3.22897e8	−	4.73026e8i	0.493747	−	0.723313i
$869$	5.15851e8	+	8.93479e8i	0.786076	+	1.36152i
$870$	−3.52310e6	+	5.60346e6i	−0.00535017	+	0.00850940i
$871$	3.44294e7	−	1.98778e7i	0.0521045	−	0.0300825i
$872$	1.12166e9	−	4.88241e8i	1.69166	−	0.736351i
$873$	−1.02584e9			−1.54183
$874$	−5.05673e8	−	5.87316e8i	−0.757418	−	0.879706i
$875$		−	9.31222e8i		−	1.39005i
$876$	−709179.	+	341028.i	−0.00105498	+	0.000507315i
$877$	−2.04208e8	−	3.53699e8i	−0.302743	−	0.524367i	0.674013	−	0.738720i	$-0.264569\pi$
$877$	−2.04208e8	−	3.53699e8i	−0.302743	−	0.524367i	−0.976756	+	0.214353i	$0.931236\pi$
$878$	2.60110e8	−	4.13702e8i	0.384302	−	0.611229i
$879$	3.63676e6	−	2.09968e6i	0.00535485	−	0.00309163i
$880$	8.63322e8	+	6.90078e8i	1.26685	+	1.01263i
$881$	−4.04246e8			−0.591178			−0.295589	−	0.955315i	$-0.595516\pi$
$881$	−4.04246e8			−0.591178			−0.295589	+	0.955315i	$0.595516\pi$
$882$	−2.31814e7	+	6.14873e8i	−0.0337857	+	0.896148i
$883$	−1.04733e8	−	6.04677e7i	−0.152125	−	0.0878296i	0.422005	−	0.906593i	$-0.361326\pi$
$883$	−1.04733e8	−	6.04677e7i	−0.152125	−	0.0878296i	−0.574130	+	0.818764i	$0.694660\pi$
$884$	3.36050e7	−	4.92295e7i	0.0486459	−	0.0712637i
$885$	6.85570e6			0.00989058
$886$	3.43050e8	+	1.29333e7i	0.493238	+	0.0185956i
$887$	9.91490e8	+	5.72437e8i	1.42075	+	0.820270i	0.996363	−	0.0852116i	$-0.0271566\pi$
$887$	9.91490e8	+	5.72437e8i	1.42075	+	0.820270i	0.424386	+	0.905481i	$0.360490\pi$
$888$	−2.83677e6	−	6.51706e6i	−0.00405122	−	0.00930706i
$889$	2.79630e8	−	4.84333e8i	0.397996	−	0.689349i
$890$	4.04055e8	−	2.13403e8i	0.573153	−	0.302712i
$891$	−1.00292e9	+	5.79038e8i	−1.41786	+	0.818604i
$892$	3.71107e7	−	4.91471e8i	0.0522883	−	0.692474i
$893$	1.69275e8	+	7.39854e8i	0.237705	+	1.03894i
$894$	1.00656e7	+	379483.i	0.0140872	+	0.000531104i
$895$	−9.61115e8	+	5.54900e8i	−1.34062	+	0.774008i
$896$	2.54512e8	+	9.57442e8i	0.353821	+	1.33103i
$897$	436857.	−	756658.i	0.000605287	−	0.00104839i
$898$	−5.56813e8	+	2.94083e8i	−0.768919	+	0.406107i
$899$	−5.46651e8	−	3.15609e8i	−0.752370	−	0.434381i
$900$	1.38304e7	+	1.04433e6i	0.0189718	+	0.00143255i
$901$	−4.64849e8			−0.635533
$902$	−4.37325e8	+	6.95561e8i	−0.595915	+	0.947797i
$903$	3.35572e6	+	1.93743e6i	0.00455746	+	0.00263125i
$904$	−8.80266e7	+	7.75335e8i	−0.119154	+	1.04950i
$905$	−1.92490e8			−0.259694
$906$	673256.	+	423301.i	0.000905306	+	0.000569200i
$907$	4.04379e8	−	2.33468e8i	0.541960	−	0.312900i	−0.203913	−	0.978989i	$-0.565366\pi$
$907$	4.04379e8	−	2.33468e8i	0.541960	−	0.312900i	0.745873	+	0.666088i	$0.232033\pi$
$908$	−6.89832e8	−	4.70892e8i	−0.921480	−	0.629019i
$909$	−5.01845e8	−	8.69222e8i	−0.668157	−	1.15728i
$910$	−6.73968e7	−	1.27609e8i	−0.0894366	−	0.169338i
$911$		−	1.00256e9i		−	1.32603i	−0.748606	−	0.663015i	$-0.769276\pi$
$911$		−	1.00256e9i		−	1.32603i	0.748606	−	0.663015i	$-0.230724\pi$
$912$	417655.	+	5.61910e6i	0.000550596	+	0.00740768i
$913$	−1.55136e8			−0.203845
$914$	−7.02235e8	+	3.70887e8i	−0.919695	+	0.485740i
$915$	8.22016e6	−	4.74591e6i	0.0107304	−	0.00619521i
$916$	8.77488e7	−	1.28547e8i	0.114171	−	0.167254i
$917$	−2.26926e8	−	3.93048e8i	−0.294291	−	0.509727i
$918$	3.75968e6	−	5.97973e6i	0.00485985	−	0.00772954i
$919$			9.43197e8i			1.21522i	0.794235	+	0.607611i	$0.207872\pi$
$919$			9.43197e8i			1.21522i	−0.794235	+	0.607611i	$0.792128\pi$
$920$	8.89581e8	+	1.00997e8i	1.14241	+	0.129702i
$921$	−2.68322e6	+	4.64748e6i	−0.00343461	+	0.00594892i
$922$	−1.05577e8	−	6.63801e7i	−0.134703	−	0.0846926i
$923$		−	4.36995e7i		−	0.0555739i
$924$	−995065.	+	1.31780e7i	−0.00126135	+	0.0167045i
$925$	1.02890e7	−	1.78211e7i	0.0130001	−	0.0225169i
$926$	−5.23460e8	−	9.91114e8i	−0.659250	−	1.24822i
$927$	−2.76773e8	−	1.59795e8i	−0.347444	−	0.200597i
$928$	1.03111e9	−	3.59162e8i	1.29021	−	0.449414i
$929$	−3.62292e8	−	6.27507e8i	−0.451867	−	0.782657i	0.546635	−	0.837371i	$-0.315909\pi$
$929$	−3.62292e8	−	6.27507e8i	−0.451867	−	0.782657i	−0.998502	+	0.0547139i	$0.982575\pi$
$930$	−141767.	+	3.76029e6i	−0.000176249	+	0.00467490i
$931$	−4.92522e8	−	5.30255e8i	−0.610347	−	0.657106i
$932$	9.28951e8	+	7.01445e7i	1.14748	+	0.0866455i
$933$	4.73685e6	+	8.20446e6i	0.00583236	+	0.0101019i
$934$	−1.41943e8	−	2.68754e8i	−0.174211	−	0.329849i
$935$	7.05606e8	+	4.07382e8i	0.863232	+	0.498387i
$936$	1.05552e8	−	4.59449e7i	0.128717	−	0.0560287i
$937$	−6.68310e8	+	1.15755e9i	−0.812380	+	1.40708i	0.0988136	+	0.995106i	$0.468495\pi$
$937$	−6.68310e8	+	1.15755e9i	−0.812380	+	1.40708i	−0.911194	+	0.411978i	$0.864838\pi$
$938$	−1.83516e7	+	4.86767e8i	−0.0222365	+	0.589810i
$939$			1.36550e6i			0.00164929i
$940$	−7.24137e8	−	4.94310e8i	−0.871841	−	0.595135i
$941$	4.15602e8	−	7.19844e8i	0.498780	−	0.863912i	−0.501219	−	0.865320i	$-0.667115\pi$
$941$	4.15602e8	−	7.19844e8i	0.498780	−	0.863912i	0.999999	+	0.00140821i	$0.000448247\pi$
$942$	−121647.	−	4586.23i	−0.000145529	−	5.48660e-6i
$943$			6.65556e8i			0.793688i
$944$	−8.83387e8	−	7.06116e8i	−1.05011	−	0.839383i
$945$	−8.55077e6	−	1.48104e7i	−0.0101323	−	0.0175497i
$946$	−6.03688e8	−	3.79561e8i	−0.713082	−	0.448341i
$947$	−9.67259e8	+	5.58447e8i	−1.13892	+	0.657555i	−0.946163	−	0.323691i	$-0.895076\pi$
$947$	−9.67259e8	+	5.58447e8i	−1.13892	+	0.657555i	−0.192757	+	0.981247i	$0.561743\pi$
$948$	−2.63320e6	−	5.47583e6i	−0.00309072	−	0.00642725i
$949$	−1.89092e7			−0.0221246
$950$	−1.23623e7	+	1.06438e7i	−0.0144188	+	0.0124145i
$951$		−	1.81223e6i		−	0.00210703i
$952$	2.91483e8	+	6.69639e8i	0.337834	+	0.776122i
$953$	2.73043e8	+	4.72924e8i	0.315466	+	0.546402i	0.979536	−	0.201267i	$-0.0645060\pi$
$953$	2.73043e8	+	4.72924e8i	0.315466	+	0.546402i	−0.664071	+	0.747670i	$0.731173\pi$
$954$	−7.60031e8	−	4.77860e8i	−0.875359	−	0.550370i
$955$	−2.55598e8	+	1.47570e8i	−0.293459	+	0.169429i
$956$	−6.33280e8	−	4.32288e8i	−0.724806	−	0.494766i
$957$	1.45652e7			0.0166181
$958$	4.03570e8	+	1.52150e7i	0.459010	+	0.0173051i
$959$	1.19676e9	+	6.90948e8i	1.35691	+	0.783411i
$960$	−4.76397e6	−	4.43541e6i	−0.00538463	−	0.00501326i
$961$	5.28650e8			0.595659
$962$	6.43457e6	−	1.70674e8i	0.00722761	−	0.191708i
$963$	−6.10100e8	−	3.52241e8i	−0.683160	−	0.394422i
$964$	3.87236e7	+	8.05270e7i	0.0432259	+	0.0898898i
$965$	−2.70100e7	+	4.67828e7i	−0.0300568	+	0.0520600i
$966$	4.99957e6	+	9.46615e6i	0.00554628	+	0.0105013i
$967$	−9.21502e8	+	5.32030e8i	−1.01910	+	0.588378i	−0.913843	−	0.406067i	$-0.866900\pi$
$967$	−9.21502e8	+	5.32030e8i	−1.01910	+	0.588378i	−0.105257	+	0.994445i	$0.533567\pi$
$968$	1.72038e8	−	1.51531e9i	0.189670	−	1.67061i
$969$	926425.	+	4.04914e6i	0.00101821	+	0.00445032i
$970$	−5.25108e7	+	1.39282e9i	−0.0575352	+	1.52609i
$971$	1.01807e9	−	5.87783e8i	1.11204	−	0.642035i	0.172682	−	0.984978i	$-0.444757\pi$
$971$	1.01807e9	−	5.87783e8i	1.11204	−	0.642035i	0.939356	+	0.342942i	$0.111424\pi$
$972$	1.84414e7	−	8.86806e6i	0.0200815	−	0.00965673i
$973$	−1.17141e9	+	2.02894e9i	−1.27166	+	2.20258i
$974$	7.70379e8	+	1.45863e9i	0.833734	+	1.57858i
$975$	−15926.8	−	9195.34i	−1.71836e−5	−	9.92096e-6i
$976$	−1.54802e9	−	2.35120e8i	−1.66505	−	0.252895i
$977$	−3.64887e8			−0.391269			−0.195634	−	0.980677i	$-0.562677\pi$
$977$	−3.64887e8			−0.391269			−0.195634	+	0.980677i	$0.562677\pi$
$978$	−36888.3	−	23193.1i	−3.94342e−5	−	2.47937e-5i
$979$	−8.70808e8	−	5.02761e8i	−0.928057	−	0.535814i
$980$	8.33651e8	+	6.29485e7i	0.885740	+	0.0668817i
$981$	1.74170e9			1.84487
$982$	8.90744e8	−	1.41672e9i	0.940629	−	1.49606i
$983$	−7.00738e7	+	4.04571e7i	−0.0737726	+	0.0425926i	−0.536433	−	0.843943i	$-0.680228\pi$
$983$	−7.00738e7	+	4.04571e7i	−0.0737726	+	0.0425926i	0.462660	+	0.886536i	$0.346895\pi$
$984$	2.87669e6	−	3.89085e6i	0.00301931	−	0.00408375i
$985$	2.97896e8	+	5.15971e8i	0.311714	+	0.539904i
$986$	7.11744e8	−	3.75910e8i	0.742495	−	0.392151i
$987$		−	1.04837e7i		−	0.0109035i
$988$	−4.94714e7	+	1.26035e8i	−0.0512960	+	0.130684i
$989$	−5.77647e8			−0.597136
$990$	7.34886e8	+	1.39143e9i	0.757381	+	1.43402i
$991$	−8.70772e8	+	5.02740e8i	−0.894712	+	0.516562i	−0.875481	−	0.483253i	$-0.839455\pi$
$991$	−8.70772e8	+	5.02740e8i	−0.894712	+	0.516562i	−0.0192313	+	0.999815i	$0.506122\pi$
$992$	4.05566e8	−	4.69928e8i	0.415457	−	0.481389i
$993$	−4.19631e6	−	7.26822e6i	−0.00428568	−	0.00742302i
$994$	4.53285e8	+	2.84997e8i	0.461543	+	0.290189i
$995$		−	1.35198e9i		−	1.37246i
$996$	911059.	+	68793.5i	0.000922080	+	6.96257e-5i
$997$	−4.80578e8	+	8.32385e8i	−0.484929	+	0.839922i	−0.999850	−	0.0173158i	$-0.994488\pi$
$997$	−4.80578e8	+	8.32385e8i	−0.484929	+	0.839922i	0.514921	+	0.857238i	$0.327821\pi$
$998$	2.65512e8	−	4.22294e8i	0.267112	−	0.424838i
$999$		−	2.02397e7i		−	0.0203006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.g.a.7.8	✓	116
4.3	odd	2	inner	76.7.g.a.7.48	yes	116
19.11	even	3	inner	76.7.g.a.11.48	yes	116
76.11	odd	6	inner	76.7.g.a.11.8	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.g.a.7.8	✓	116	1.1	even	1	trivial
76.7.g.a.7.48	yes	116	4.3	odd	2	inner
76.7.g.a.11.8	yes	116	76.11	odd	6	inner
76.7.g.a.11.48	yes	116	19.11	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.07398 + 3.73615i) q^{2} +(-0.173689 + 0.100280i) q^{3} +(36.0824 - 52.8588i) q^{4} +(-61.9026 - 107.218i) q^{5} +(0.854016 - 1.35830i) q^{6} +472.399i q^{7} +(-57.7582 + 508.732i) q^{8} +(-364.480 + 631.298i) q^{9} +O(q^{10})\)	\(q+(-7.07398 + 3.73615i) q^{2} +(-0.173689 + 0.100280i) q^{3} +(36.0824 - 52.8588i) q^{4} +(-61.9026 - 107.218i) q^{5} +(0.854016 - 1.35830i) q^{6} +472.399i q^{7} +(-57.7582 + 508.732i) q^{8} +(-364.480 + 631.298i) q^{9} +(838.481 + 527.184i) q^{10} -2179.49i q^{11} +(-0.966471 + 12.7993i) q^{12} +(-154.219 + 267.115i) q^{13} +(-1764.95 - 3341.74i) q^{14} +(21.5036 + 12.4151i) q^{15} +(-1492.12 - 3814.55i) q^{16} +(-1509.76 - 2614.99i) q^{17} +(219.704 - 5827.54i) q^{18} +(4667.94 + 5025.55i) q^{19} +(-7901.03 - 596.602i) q^{20} +(-47.3719 - 82.0506i) q^{21} +(8142.88 + 15417.6i) q^{22} +(12231.8 + 7062.01i) q^{23} +(-40.9834 - 94.1532i) q^{24} +(148.647 - 257.465i) q^{25} +(92.9615 - 2465.76i) q^{26} -292.407i q^{27} +(24970.5 + 17045.3i) q^{28} +(16660.6 - 28857.0i) q^{29} +(-198.501 - 7.48369i) q^{30} -18943.4i q^{31} +(24806.9 + 21409.3i) q^{32} +(218.558 + 378.553i) q^{33} +(20450.0 + 12857.7i) q^{34} +(50649.8 - 29242.7i) q^{35} +(20218.3 + 42044.7i) q^{36} +69217.6 q^{37} +(-51797.1 - 18110.6i) q^{38} -61.8601i q^{39} +(58120.8 - 25299.1i) q^{40} +(23561.1 + 40809.1i) q^{41} +(641.661 + 403.436i) q^{42} +(-35418.9 + 20449.1i) q^{43} +(-115205. - 78641.2i) q^{44} +90248.9 q^{45} +(-112912. - 4256.90i) q^{46} +(95828.6 + 55326.7i) q^{47} +(641.686 + 512.918i) q^{48} -105512. q^{49} +(-89.6029 + 2376.67i) q^{50} +(524.460 + 302.797i) q^{51} +(8554.81 + 17790.0i) q^{52} +(76973.8 - 133323. i) q^{53} +(1092.48 + 2068.48i) q^{54} +(-233681. + 134916. i) q^{55} +(-240324. - 27284.9i) q^{56} +(-1314.73 - 404.786i) q^{57} +(-10042.8 + 266381. i) q^{58} +(239112. - 138051. i) q^{59} +(1432.15 - 688.689i) q^{60} +(191134. - 331054. i) q^{61} +(70775.4 + 134006. i) q^{62} +(-298224. - 172180. i) q^{63} +(-255472. - 58766.8i) q^{64} +38186.2 q^{65} +(-2960.40 - 1861.32i) q^{66} +(-111625. - 64446.7i) q^{67} +(-192701. - 14550.8i) q^{68} -2832.70 q^{69} +(-249041. + 396097. i) q^{70} +(-122698. + 70839.9i) q^{71} +(-300109. - 221885. i) q^{72} +(30653.2 + 53092.9i) q^{73} +(-489644. + 258607. i) q^{74} +59.6251i q^{75} +(434076. - 65407.8i) q^{76} +1.02959e6 q^{77} +(231.118 + 437.597i) q^{78} +(-409950. + 236685. i) q^{79} +(-316624. + 396113. i) q^{80} +(-265677. - 460165. i) q^{81} +(-319140. - 200655. i) q^{82} -71180.1i q^{83} +(-6046.40 - 456.560i) q^{84} +(-186917. + 323749. i) q^{85} +(174152. - 276987. i) q^{86} +6682.88i q^{87} +(1.10877e6 + 125883. i) q^{88} +(230679. - 399548. i) q^{89} +(-638419. + 337183. i) q^{90} +(-126185. - 72853.0i) q^{91} +(814641. - 391742. i) q^{92} +(1899.64 + 3290.27i) q^{93} +(-884599. - 33350.3i) q^{94} +(249874. - 811584. i) q^{95} +(-6455.61 - 1230.94i) q^{96} +(703631. + 1.21872e6i) q^{97} +(746388. - 394207. i) q^{98} +(1.37590e6 + 794379. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - q^{2} - 67 q^{4} - 2 q^{5} + 33 q^{6} + 962 q^{8} + 12660 q^{9}+O(q^{10}) \) 116 * q - q^2 - 67 * q^4 - 2 * q^5 + 33 * q^6 + 962 * q^8 + 12660 * q^9	\( 116 q - q^{2} - 67 q^{4} - 2 q^{5} + 33 q^{6} + 962 q^{8} + 12660 q^{9} - 812 q^{10} - 1462 q^{12} + 2518 q^{13} - 2742 q^{14} + 461 q^{16} + 6838 q^{17} - 13948 q^{18} - 24396 q^{20} + 11176 q^{21} + 22293 q^{22} + 33905 q^{24} - 156252 q^{25} - 78080 q^{26} - 34362 q^{28} - 2 q^{29} + 208344 q^{30} - 10941 q^{32} + 110316 q^{33} + 64648 q^{34} + 78574 q^{36} + 55432 q^{37} + 221994 q^{38} + 242590 q^{40} - 9126 q^{41} + 187550 q^{42} + 138081 q^{44} + 59576 q^{45} - 686052 q^{46} - 141617 q^{48} - 1306636 q^{49} + 167498 q^{50} - 35414 q^{52} + 60758 q^{53} - 348601 q^{54} + 543732 q^{56} - 466566 q^{57} + 1208536 q^{58} - 319142 q^{60} - 839474 q^{61} + 628548 q^{62} - 470026 q^{64} + 151836 q^{65} + 1471119 q^{66} + 341484 q^{68} - 2169836 q^{69} - 68364 q^{70} + 1236042 q^{72} + 207538 q^{73} + 336144 q^{74} - 97437 q^{76} + 1977632 q^{77} - 2740948 q^{78} + 1250050 q^{80} - 3334682 q^{81} - 2244893 q^{82} - 2404612 q^{84} + 788426 q^{85} + 910490 q^{86} + 5123058 q^{88} + 360166 q^{89} + 2446616 q^{90} + 2518692 q^{92} + 2079592 q^{93} - 2221200 q^{94} - 5927450 q^{96} + 3567778 q^{97} + 5270703 q^{98}+O(q^{100}) \) 116 * q - q^2 - 67 * q^4 - 2 * q^5 + 33 * q^6 + 962 * q^8 + 12660 * q^9 - 812 * q^10 - 1462 * q^12 + 2518 * q^13 - 2742 * q^14 + 461 * q^16 + 6838 * q^17 - 13948 * q^18 - 24396 * q^20 + 11176 * q^21 + 22293 * q^22 + 33905 * q^24 - 156252 * q^25 - 78080 * q^26 - 34362 * q^28 - 2 * q^29 + 208344 * q^30 - 10941 * q^32 + 110316 * q^33 + 64648 * q^34 + 78574 * q^36 + 55432 * q^37 + 221994 * q^38 + 242590 * q^40 - 9126 * q^41 + 187550 * q^42 + 138081 * q^44 + 59576 * q^45 - 686052 * q^46 - 141617 * q^48 - 1306636 * q^49 + 167498 * q^50 - 35414 * q^52 + 60758 * q^53 - 348601 * q^54 + 543732 * q^56 - 466566 * q^57 + 1208536 * q^58 - 319142 * q^60 - 839474 * q^61 + 628548 * q^62 - 470026 * q^64 + 151836 * q^65 + 1471119 * q^66 + 341484 * q^68 - 2169836 * q^69 - 68364 * q^70 + 1236042 * q^72 + 207538 * q^73 + 336144 * q^74 - 97437 * q^76 + 1977632 * q^77 - 2740948 * q^78 + 1250050 * q^80 - 3334682 * q^81 - 2244893 * q^82 - 2404612 * q^84 + 788426 * q^85 + 910490 * q^86 + 5123058 * q^88 + 360166 * q^89 + 2446616 * q^90 + 2518692 * q^92 + 2079592 * q^93 - 2221200 * q^94 - 5927450 * q^96 + 3567778 * q^97 + 5270703 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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