LMFDB - Embedded newform 72.7.p.b.43.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,Mod(43,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("72.43");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.p (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:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.6
Character	$\chi$	$=$	72.43
Dual form			72.7.p.b.67.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.72049 + 2.09618i) q^{2} +(26.9984 - 0.294271i) q^{3} +(55.2120 - 32.3671i) q^{4} +(109.916 - 63.4600i) q^{5} +(-207.824 + 58.8655i) q^{6} +(509.750 + 294.305i) q^{7} +(-358.417 + 365.625i) q^{8} +(728.827 - 15.8897i) q^{9} +O(q^{10})$	\(q+(-7.72049 + 2.09618i) q^{2} +(26.9984 - 0.294271i) q^{3} +(55.2120 - 32.3671i) q^{4} +(109.916 - 63.4600i) q^{5} +(-207.824 + 58.8655i) q^{6} +(509.750 + 294.305i) q^{7} +(-358.417 + 365.625i) q^{8} +(728.827 - 15.8897i) q^{9} +(-715.581 + 720.346i) q^{10} +(691.611 - 1197.91i) q^{11} +(1481.11 - 890.108i) q^{12} +(-1390.60 + 802.866i) q^{13} +(-4552.44 - 1203.65i) q^{14} +(2948.88 - 1745.66i) q^{15} +(2000.74 - 3574.11i) q^{16} -338.300 q^{17} +(-5593.59 + 1650.43i) q^{18} -10341.9 q^{19} +(4014.66 - 7061.42i) q^{20} +(13849.0 + 7795.75i) q^{21} +(-2828.55 + 10698.2i) q^{22} +(5623.63 - 3246.80i) q^{23} +(-9569.08 + 9976.76i) q^{24} +(241.831 - 418.863i) q^{25} +(9053.20 - 9113.48i) q^{26} +(19672.5 - 643.468i) q^{27} +(37670.2 - 250.017i) q^{28} +(11237.9 + 6488.21i) q^{29} +(-19107.6 + 19658.8i) q^{30} +(29361.9 - 16952.1i) q^{31} +(-7954.67 + 31787.8i) q^{32} +(18319.9 - 32545.0i) q^{33} +(2611.84 - 709.140i) q^{34} +74706.2 q^{35} +(39725.7 - 24467.3i) q^{36} +58938.1i q^{37} +(79844.3 - 21678.4i) q^{38} +(-37307.8 + 22085.3i) q^{39} +(-16193.1 + 62933.1i) q^{40} +(-50586.0 - 87617.5i) q^{41} +(-123263. - 31156.8i) q^{42} +(-44708.4 + 77437.2i) q^{43} +(-587.536 - 88524.3i) q^{44} +(79101.3 - 47997.8i) q^{45} +(-36611.3 + 36855.1i) q^{46} +(81283.4 + 46929.0i) q^{47} +(52964.9 - 97084.0i) q^{48} +(114406. + 198157. i) q^{49} +(-989.039 + 3740.75i) q^{50} +(-9133.56 + 99.5519i) q^{51} +(-50791.6 + 89337.7i) q^{52} -142561. i q^{53} +(-150532. + 46205.0i) q^{54} -175558. i q^{55} +(-290308. + 80893.8i) q^{56} +(-279214. + 3043.31i) q^{57} +(-100363. - 26535.4i) q^{58} +(-162378. - 281247. i) q^{59} +(106311. - 191828. i) q^{60} +(-95732.7 - 55271.3i) q^{61} +(-191154. + 192427. i) q^{62} +(376196. + 206397. i) q^{63} +(-5219.13 - 262092. i) q^{64} +(-101900. + 176495. i) q^{65} +(-73218.1 + 289666. i) q^{66} +(-65902.4 - 114146. i) q^{67} +(-18678.2 + 10949.8i) q^{68} +(150874. - 89313.4i) q^{69} +(-576769. + 156598. i) q^{70} +23795.6i q^{71} +(-255414. + 272172. i) q^{72} +461863. q^{73} +(-123545. - 455031. i) q^{74} +(6405.79 - 11379.8i) q^{75} +(-570995. + 334737. i) q^{76} +(705098. - 407089. i) q^{77} +(241740. - 248713. i) q^{78} +(-57215.7 - 33033.5i) q^{79} +(-6900.38 - 519818. i) q^{80} +(530936. - 23161.7i) q^{81} +(574211. + 570413. i) q^{82} +(-489251. + 847408. i) q^{83} +(1.01696e6 - 17835.3i) q^{84} +(-37184.6 + 21468.5i) q^{85} +(182848. - 691571. i) q^{86} +(305315. + 171864. i) q^{87} +(190099. + 682219. i) q^{88} +577675. q^{89} +(-510088. + 536378. i) q^{90} -945148. q^{91} +(205402. - 361283. i) q^{92} +(787737. - 466321. i) q^{93} +(-725920. - 191930. i) q^{94} +(-1.13673e6 + 656294. i) q^{95} +(-205409. + 860561. i) q^{96} +(-58141.9 + 100705. i) q^{97} +(-1.29864e6 - 1.29005e6i) q^{98} +(485030. - 884055. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9}+O(q^{10}) $ 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9	\( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9} - 132 q^{10} + 2336 q^{11} - 2796 q^{12} + 2346 q^{14} + 8191 q^{16} - 3460 q^{17} + 6306 q^{18} - 4972 q^{19} + 3588 q^{20} - 18577 q^{22} - 50553 q^{24} + 224998 q^{25} + 38352 q^{26} - 27792 q^{27} - 8196 q^{28} - 107130 q^{30} - 191717 q^{32} - 42852 q^{33} + 6125 q^{34} - 62508 q^{35} + 87339 q^{36} + 250223 q^{38} - 27126 q^{40} - 145084 q^{41} - 107478 q^{42} + 74912 q^{43} - 1118662 q^{44} + 22296 q^{46} + 690903 q^{48} + 1210102 q^{49} - 844727 q^{50} + 830778 q^{51} + 62952 q^{52} + 860925 q^{54} - 587718 q^{56} + 748686 q^{57} + 221136 q^{58} + 98960 q^{59} - 960810 q^{60} - 1062312 q^{62} - 784646 q^{64} - 62502 q^{65} + 802866 q^{66} + 596624 q^{67} + 681953 q^{68} + 86334 q^{70} - 2246001 q^{72} - 1186276 q^{73} - 782586 q^{74} + 3451098 q^{75} - 273235 q^{76} - 3340578 q^{78} + 2446320 q^{80} - 621690 q^{81} - 3119398 q^{82} - 179350 q^{83} - 227136 q^{84} + 917117 q^{86} - 1184629 q^{88} + 253712 q^{89} - 4940256 q^{90} - 470604 q^{91} + 1731894 q^{92} + 2055426 q^{94} + 8439666 q^{96} - 1822756 q^{97} + 6531850 q^{98} + 2509818 q^{99}+O(q^{100}) \) 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9 - 132 * q^10 + 2336 * q^11 - 2796 * q^12 + 2346 * q^14 + 8191 * q^16 - 3460 * q^17 + 6306 * q^18 - 4972 * q^19 + 3588 * q^20 - 18577 * q^22 - 50553 * q^24 + 224998 * q^25 + 38352 * q^26 - 27792 * q^27 - 8196 * q^28 - 107130 * q^30 - 191717 * q^32 - 42852 * q^33 + 6125 * q^34 - 62508 * q^35 + 87339 * q^36 + 250223 * q^38 - 27126 * q^40 - 145084 * q^41 - 107478 * q^42 + 74912 * q^43 - 1118662 * q^44 + 22296 * q^46 + 690903 * q^48 + 1210102 * q^49 - 844727 * q^50 + 830778 * q^51 + 62952 * q^52 + 860925 * q^54 - 587718 * q^56 + 748686 * q^57 + 221136 * q^58 + 98960 * q^59 - 960810 * q^60 - 1062312 * q^62 - 784646 * q^64 - 62502 * q^65 + 802866 * q^66 + 596624 * q^67 + 681953 * q^68 + 86334 * q^70 - 2246001 * q^72 - 1186276 * q^73 - 782586 * q^74 + 3451098 * q^75 - 273235 * q^76 - 3340578 * q^78 + 2446320 * q^80 - 621690 * q^81 - 3119398 * q^82 - 179350 * q^83 - 227136 * q^84 + 917117 * q^86 - 1184629 * q^88 + 253712 * q^89 - 4940256 * q^90 - 470604 * q^91 + 1731894 * q^92 + 2055426 * q^94 + 8439666 * q^96 - 1822756 * q^97 + 6531850 * q^98 + 2509818 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−7.72049	+	2.09618i	−0.965062	+	0.262023i
$2$	−7.72049	+	2.09618i	−0.965062	+	0.262023i
$3$	26.9984	−	0.294271i	0.999941	−	0.0108989i
$3$	26.9984	−	0.294271i	0.999941	−	0.0108989i
$4$	55.2120	−	32.3671i	0.862688	−	0.505737i
$5$	109.916	−	63.4600i	0.879327	−	0.507680i	0.00889047	−	0.999960i	$-0.497170\pi$
$5$	109.916	−	63.4600i	0.879327	−	0.507680i	0.870436	+	0.492281i	$0.163837\pi$
$6$	−207.824	+	58.8655i	−0.962149	+	0.272526i
$7$	509.750	+	294.305i	1.48615	+	0.858031i	0.999876	−	0.0157737i	$-0.00502115\pi$
$7$	509.750	+	294.305i	1.48615	+	0.858031i	0.486277	+	0.873805i	$0.338354\pi$
$8$	−358.417	+	365.625i	−0.700032	+	0.714111i
$9$	728.827	−	15.8897i	0.999762	−	0.0217965i
$10$	−715.581	+	720.346i	−0.715581	+	0.720346i
$11$	691.611	−	1197.91i	0.519618	−	0.900004i	−0.480122	−	0.877202i	$-0.659408\pi$
$11$	691.611	−	1197.91i	0.519618	−	0.900004i	0.999740	−	0.0228026i	$-0.00725893\pi$
$12$	1481.11	−	890.108i	0.857125	−	0.515109i
$13$	−1390.60	+	802.866i	−0.632956	+	0.365437i	−0.781896	−	0.623409i	$-0.785747\pi$
$13$	−1390.60	+	802.866i	−0.632956	+	0.365437i	0.148940	+	0.988846i	$0.452414\pi$
$14$	−4552.44	−	1203.65i	−1.65905	−	0.438646i
$15$	2948.88	−	1745.66i	0.873741	−	0.517233i
$16$	2000.74	−	3574.11i	0.488461	−	0.872586i
$17$	−338.300			−0.0688582			−0.0344291	−	0.999407i	$-0.510961\pi$
$17$	−338.300			−0.0688582			−0.0344291	+	0.999407i	$0.510961\pi$
$18$	−5593.59	+	1650.43i	−0.959121	+	0.282996i
$19$	−10341.9			−1.50778			−0.753890	−	0.657001i	$-0.771825\pi$
$19$	−10341.9			−1.50778			−0.753890	+	0.657001i	$0.771825\pi$
$20$	4014.66	−	7061.42i	0.501832	−	0.882677i
$21$	13849.0	+	7795.75i	1.49542	+	0.841782i
$22$	−2828.55	+	10698.2i	−0.265641	+	1.00471i
$23$	5623.63	−	3246.80i	0.462203	−	0.266853i	−0.250767	−	0.968048i	$-0.580683\pi$
$23$	5623.63	−	3246.80i	0.462203	−	0.266853i	0.712970	+	0.701194i	$0.247349\pi$
$24$	−9569.08	+	9976.76i	−0.692208	+	0.721698i
$25$	241.831	−	418.863i	0.0154772	−	0.0268073i
$26$	9053.20	−	9113.48i	0.515089	−	0.518519i
$27$	19672.5	−	643.468i	0.999465	−	0.0326916i
$28$	37670.2	−	250.017i	1.71602	−	0.0113893i
$29$	11237.9	+	6488.21i	0.460778	+	0.266030i	0.712371	−	0.701803i	$-0.247621\pi$
$29$	11237.9	+	6488.21i	0.460778	+	0.266030i	−0.251594	+	0.967833i	$0.580955\pi$
$30$	−19107.6	+	19658.8i	−0.707687	+	0.728102i
$31$	29361.9	−	16952.1i	0.985598	−	0.569035i	0.0816423	−	0.996662i	$-0.473983\pi$
$31$	29361.9	−	16952.1i	0.985598	−	0.569035i	0.903955	+	0.427627i	$0.140650\pi$
$32$	−7954.67	+	31787.8i	−0.242757	+	0.970087i
$33$	18319.9	−	32545.0i	0.509778	−	0.905614i
$34$	2611.84	−	709.140i	0.0664524	−	0.0180424i
$35$	74706.2			1.74242
$36$	39725.7	−	24467.3i	0.851460	−	0.524420i
$37$			58938.1i			1.16357i	0.813344	+	0.581783i	$0.197645\pi$
$37$			58938.1i			1.16357i	−0.813344	+	0.581783i	$0.802355\pi$
$38$	79844.3	−	21678.4i	1.45510	−	0.395073i
$39$	−37307.8	+	22085.3i	−0.628936	+	0.372314i
$40$	−16193.1	+	62933.1i	−0.253018	+	0.983329i
$41$	−50586.0	−	87617.5i	−0.733971	−	1.27128i	−0.955173	−	0.296047i	$-0.904331\pi$
$41$	−50586.0	−	87617.5i	−0.733971	−	1.27128i	0.221202	−	0.975228i	$-0.429002\pi$
$42$	−123263.	−	31156.8i	−1.66374	−	0.420538i
$43$	−44708.4	+	77437.2i	−0.562320	+	0.973967i	0.434973	+	0.900443i	$0.356758\pi$
$43$	−44708.4	+	77437.2i	−0.562320	+	0.973967i	−0.997293	+	0.0735239i	$0.976575\pi$
$44$	−587.536	−	88524.3i	−0.00689726	−	1.03921i
$45$	79101.3	−	47997.8i	0.868052	−	0.526725i
$46$	−36611.3	+	36855.1i	−0.376133	+	0.378638i
$47$	81283.4	+	46929.0i	0.782904	+	0.452010i	0.837458	−	0.546501i	$-0.184041\pi$
$47$	81283.4	+	46929.0i	0.782904	+	0.452010i	−0.0545548	+	0.998511i	$0.517374\pi$
$48$	52964.9	−	97084.0i	0.478922	−	0.877858i
$49$	114406.	+	198157.i	0.972434	+	1.68430i
$50$	−989.039	+	3740.75i	−0.00791231	+	0.0299260i
$51$	−9133.56	+	99.5519i	−0.0688541	+	0.000750480i
$52$	−50791.6	+	89337.7i	−0.361228	+	0.635367i
$53$		−	142561.i		−	0.957576i	−0.877931	−	0.478788i	$-0.841076\pi$
$53$		−	142561.i		−	0.957576i	0.877931	−	0.478788i	$-0.158924\pi$
$54$	−150532.	+	46205.0i	−0.955980	+	0.293432i
$55$		−	175558.i		−	1.05520i
$56$	−290308.	+	80893.8i	−1.65308	+	0.460629i
$57$	−279214.	+	3043.31i	−1.50769	+	0.0164332i
$58$	−100363.	−	26535.4i	−0.514385	−	0.136001i
$59$	−162378.	−	281247.i	−0.790628	−	1.36941i	−0.925579	−	0.378555i	$-0.876421\pi$
$59$	−162378.	−	281247.i	−0.790628	−	1.36941i	0.134951	−	0.990852i	$-0.456912\pi$
$60$	106311.	−	191828.i	0.492182	−	0.888094i
$61$	−95732.7	−	55271.3i	−0.421765	−	0.243506i	0.274067	−	0.961711i	$-0.411631\pi$
$61$	−95732.7	−	55271.3i	−0.421765	−	0.243506i	−0.695832	+	0.718204i	$0.744964\pi$
$62$	−191154.	+	192427.i	−0.802062	+	0.807403i
$63$	376196.	+	206397.i	1.50450	+	0.825434i
$64$	−5219.13	−	262092.i	−0.0199094	−	0.999802i
$65$	−101900.	+	176495.i	−0.371050	+	0.642678i
$66$	−73218.1	+	289666.i	−0.254675	+	1.00755i
$67$	−65902.4	−	114146.i	−0.219117	−	0.379522i	0.735421	−	0.677610i	$-0.236984\pi$
$67$	−65902.4	−	114146.i	−0.219117	−	0.379522i	−0.954538	+	0.298088i	$0.903651\pi$
$68$	−18678.2	+	10949.8i	−0.0594031	+	0.0348241i
$69$	150874.	−	89313.4i	0.459268	−	0.271875i
$70$	−576769.	+	156598.i	−1.68154	+	0.456554i
$71$			23795.6i			0.0664848i	0.999447	+	0.0332424i	$0.0105833\pi$
$71$			23795.6i			0.0664848i	−0.999447	+	0.0332424i	$0.989417\pi$
$72$	−255414.	+	272172.i	−0.684301	+	0.729200i
$73$	461863.			1.18726			0.593629	−	0.804739i	$-0.297695\pi$
$73$	461863.			1.18726			0.593629	+	0.804739i	$0.297695\pi$
$74$	−123545.	−	455031.i	−0.304881	−	1.12291i
$75$	6405.79	−	11379.8i	0.0151841	−	0.0269743i
$76$	−570995.	+	334737.i	−1.30074	+	0.762539i
$77$	705098.	−	407089.i	1.54446	−	0.891696i
$78$	241740.	−	248713.i	0.509407	−	0.524102i
$79$	−57215.7	−	33033.5i	−0.116047	−	0.0669998i	0.440853	−	0.897579i	$-0.354676\pi$
$79$	−57215.7	−	33033.5i	−0.116047	−	0.0669998i	−0.556900	+	0.830580i	$0.688009\pi$
$80$	−6900.38	−	519818.i	−0.0134773	−	1.01527i
$81$	530936.	−	23161.7i	0.999050	−	0.0435827i
$82$	574211.	+	570413.i	1.04143	+	1.03454i
$83$	−489251.	+	847408.i	−0.855653	+	1.48203i	0.0203855	+	0.999792i	$0.493511\pi$
$83$	−489251.	+	847408.i	−0.855653	+	1.48203i	−0.876038	+	0.482242i	$0.839823\pi$
$84$	1.01696e6	−	17835.3i	1.71580	−	0.0300914i
$85$	−37184.6	+	21468.5i	−0.0605488	+	0.0349579i
$86$	182848.	−	691571.i	0.287472	−	1.08728i
$87$	305315.	+	171864.i	0.463650	+	0.260992i
$88$	190099.	+	682219.i	0.278954	+	1.00110i
$89$	577675.			0.819433			0.409717	−	0.912213i	$-0.365628\pi$
$89$	577675.			0.819433			0.409717	+	0.912213i	$0.365628\pi$
$90$	−510088.	+	536378.i	−0.699710	+	0.735772i
$91$	−945148.			−1.25423
$92$	205402.	−	361283.i	0.263780	−	0.463964i
$93$	787737.	−	466321.i	0.979337	−	0.579743i
$94$	−725920.	−	191930.i	−0.873987	−	0.231078i
$95$	−1.13673e6	+	656294.i	−1.32583	+	0.765469i
$96$	−205409.	+	860561.i	−0.232170	+	0.972675i
$97$	−58141.9	+	100705.i	−0.0637051	+	0.110341i	−0.896119	−	0.443814i	$-0.853625\pi$
$97$	−58141.9	+	100705.i	−0.0637051	+	0.110341i	0.832414	+	0.554155i	$0.186958\pi$
$98$	−1.29864e6	−	1.29005e6i	−1.37978	−	1.37066i
$99$	485030.	−	884055.i	0.499877	−	0.911116i
$100$	−205.440	−	30953.7i	−0.000205440	−	0.0309537i
$101$	−160731.	−	92798.0i	−0.156004	−	0.0900688i	0.419966	−	0.907540i	$-0.362042\pi$
$101$	−160731.	−	92798.0i	−0.156004	−	0.0900688i	−0.575970	+	0.817471i	$0.695375\pi$
$102$	70306.9	−	19914.2i	0.0662518	−	0.0187656i
$103$	−1.64022e6	+	946981.i	−1.50103	+	0.866622i	−0.501034	+	0.865428i	$0.667047\pi$
$103$	−1.64022e6	+	946981.i	−1.50103	+	0.866622i	−0.999999	+	0.00119395i	$0.999620\pi$
$104$	204868.	−	796200.i	0.182127	−	0.707819i
$105$	2.01695e6	−	21983.9i	1.74232	−	0.0189905i
$106$	298834.	+	1.10064e6i	0.250907	+	0.924120i
$107$	−1.10058e6			−0.898403			−0.449201	−	0.893430i	$-0.648291\pi$
$107$	−1.10058e6			−0.898403			−0.449201	+	0.893430i	$0.648291\pi$
$108$	1.06533e6	−	672269.i	0.845693	−	0.533669i
$109$		−	1.70368e6i		−	1.31555i	−0.753213	−	0.657776i	$-0.771497\pi$
$109$		−	1.70368e6i		−	1.31555i	0.753213	−	0.657776i	$-0.228503\pi$
$110$	368003.	+	1.35540e6i	0.276486	+	1.01833i
$111$	17343.8	+	1.59123e6i	0.0126816	+	1.16350i
$112$	2.07175e6	−	1.23308e6i	1.47463	−	0.877682i
$113$	−219765.	−	380644.i	−0.152308	−	0.263805i	0.779768	−	0.626069i	$-0.215337\pi$
$113$	−219765.	−	380644.i	−0.152308	−	0.263805i	−0.932076	+	0.362264i	$0.882004\pi$
$114$	2.14929e6	−	608779.i	1.45071	−	0.410908i
$115$	412084.	−	713750.i	0.270952	−	0.469303i
$116$	830472.	−	5511.85i	0.532048	−	0.00353121i
$117$	−1.00075e6	+	607246.i	−0.624840	+	0.379147i
$118$	1.84319e6	+	1.83099e6i	1.12182	+	1.11440i
$119$	−172449.	−	99563.3i	−0.102334	−	0.0590824i
$120$	−418669.	+	1.70386e6i	−0.242285	+	0.986028i
$121$	−70871.3	−	122753.i	−0.0400050	−	0.0692907i
$122$	854963.	+	226048.i	0.470834	+	0.124486i
$123$	−1.39152e6	−	2.35065e6i	−0.747783	−	1.26320i
$124$	1.07244e6	−	1.88632e6i	0.562481	−	0.989353i
$125$			1.92174e6i			0.983929i
$126$	−3.33707e6	−	804912.i	−1.66822	−	0.402381i
$127$			1.23692e6i			0.603850i	0.953332	+	0.301925i	$0.0976293\pi$
$127$			1.23692e6i			0.603850i	−0.953332	+	0.301925i	$0.902371\pi$
$128$	589687.	+	2.01254e6i	0.281185	+	0.959654i
$129$	−1.18427e6	+	2.10384e6i	−0.551672	+	0.980038i
$130$	416749.	−	1.57623e6i	0.189690	−	0.717447i
$131$	−1.34139e6	−	2.32335e6i	−0.596679	−	1.03348i	−0.993308	−	0.115499i	$-0.963153\pi$
$131$	−1.34139e6	−	2.32335e6i	−0.596679	−	1.03348i	0.396629	−	0.917979i	$-0.370180\pi$
$132$	−41912.6	−	2.38984e6i	−0.0182231	−	1.03908i
$133$	−5.27177e6	−	3.04366e6i	−2.24079	−	1.29372i
$134$	748070.	+	743122.i	0.310905	+	0.308849i
$135$	2.12148e6	−	1.31914e6i	0.862260	−	0.536155i
$136$	121252.	−	123691.i	0.0482030	−	0.0491724i
$137$	−384242.	+	665527.i	−0.149432	+	0.258824i	−0.931018	−	0.364974i	$-0.881078\pi$
$137$	−384242.	+	665527.i	−0.149432	+	0.258824i	0.781586	+	0.623798i	$0.214411\pi$
$138$	−977601.	+	1.00580e6i	−0.371984	+	0.382715i
$139$	1.97615e6	+	3.42280e6i	0.735828	+	1.27449i	0.954359	+	0.298662i	$0.0965403\pi$
$139$	1.97615e6	+	3.42280e6i	0.735828	+	1.27449i	−0.218531	+	0.975830i	$0.570126\pi$
$140$	4.12468e6	−	2.41803e6i	1.50316	−	0.881205i
$141$	2.20833e6	+	1.24309e6i	0.787783	+	0.443450i
$142$	−49880.0	−	183714.i	−0.0174205	−	0.0641619i
$143$			2.22108e6i			0.759551i
$144$	1.40140e6	−	2.63670e6i	0.469325	−	0.883025i
$145$	1.64697e6			0.540232
$146$	−3.56581e6	+	968151.i	−1.14578	+	0.311089i
$147$	3.14709e6	+	5.31625e6i	0.990733	+	1.67361i
$148$	1.90766e6	+	3.25409e6i	0.588458	+	1.00379i
$149$	−2.49407e6	+	1.43995e6i	−0.753961	+	0.435300i	−0.827123	−	0.562020i	$-0.810024\pi$
$149$	−2.49407e6	+	1.43995e6i	−0.753961	+	0.435300i	0.0731622	+	0.997320i	$0.476691\pi$
$150$	−25601.7	+	101285.i	−0.00758568	+	0.0300105i
$151$	−2.83213e6	−	1.63513e6i	−0.822587	−	0.474921i	0.0287207	−	0.999587i	$-0.490857\pi$
$151$	−2.83213e6	−	1.63513e6i	−0.822587	−	0.474921i	−0.851308	+	0.524667i	$0.824190\pi$
$152$	3.70669e6	−	3.78124e6i	1.05549	−	1.07672i
$153$	−246562.	+	5375.48i	−0.0688418	+	0.00150087i
$154$	−4.59037e6	+	4.62094e6i	−1.25686	+	1.26523i
$155$	2.15156e6	−	3.72662e6i	0.577775	−	1.00074i
$156$	−1.34500e6	+	2.42692e6i	−0.354282	+	0.639267i
$157$	4.64414e6	−	2.68129e6i	1.20007	−	0.692860i	0.239498	−	0.970897i	$-0.423017\pi$
$157$	4.64414e6	−	2.68129e6i	1.20007	−	0.692860i	0.960570	+	0.278037i	$0.0896837\pi$
$158$	510978.	+	135100.i	0.129548	+	0.0342519i
$159$	−41951.5	−	3.84892e6i	−0.0104365	−	0.957519i
$160$	1.14291e6	+	3.99879e6i	0.279030	+	0.976267i
$161$	3.82220e6			0.915873
$162$	−4.05054e6	+	1.29176e6i	−0.952725	+	0.303834i
$163$	−4.46796e6			−1.03168			−0.515842	−	0.856684i	$-0.672521\pi$
$163$	−4.46796e6			−1.03168			−0.515842	+	0.856684i	$0.672521\pi$
$164$	−5.62889e6	−	3.20022e6i	−1.27612	−	0.725518i
$165$	−51661.7	−	4.73980e6i	−0.0115005	−	1.05513i
$166$	2.00094e6	−	7.56797e6i	0.437431	−	1.65445i
$167$	−7.22825e6	+	4.17323e6i	−1.55197	+	0.896031i	−0.553991	+	0.832523i	$0.686896\pi$
$167$	−7.22825e6	+	4.17323e6i	−1.55197	+	0.896031i	−0.997981	+	0.0635087i	$0.979771\pi$
$168$	−7.81405e6	+	2.26943e6i	−1.64797	+	0.478619i
$169$	−1.12422e6	+	1.94720e6i	−0.232911	+	0.403414i
$170$	242081.	−	243693.i	0.0492736	−	0.0496017i
$171$	−7.53743e6	+	164329.i	−1.50742	+	0.0328644i
$172$	37980.6	+	5.72255e6i	0.00746408	+	1.12462i
$173$	−1.40890e6	−	813429.i	−0.272108	−	0.157102i	0.357737	−	0.933822i	$-0.383548\pi$
$173$	−1.40890e6	−	813429.i	−0.272108	−	0.157102i	−0.629845	+	0.776720i	$0.716882\pi$
$174$	−2.71744e6	−	686881.i	−0.515837	−	0.130387i
$175$	246547.	−	142344.i	0.0460029	−	0.0265598i
$176$	−2.89772e6	−	4.86859e6i	−0.531518	−	0.893028i
$177$	−4.46672e6	−	7.54545e6i	−0.805506	−	1.36071i
$178$	−4.45994e6	+	1.21091e6i	−0.790804	+	0.214710i
$179$	620318.			0.108157			0.0540785	−	0.998537i	$-0.482778\pi$
$179$	620318.			0.108157			0.0540785	+	0.998537i	$0.482778\pi$
$180$	2.81379e6	−	5.21034e6i	0.482474	−	0.893405i
$181$			2.15663e6i			0.363696i	0.983327	+	0.181848i	$0.0582079\pi$
$181$			2.15663e6i			0.363696i	−0.983327	+	0.181848i	$0.941792\pi$
$182$	7.29701e6	−	1.98120e6i	1.21041	−	0.328636i
$183$	−2.60090e6	−	1.46407e6i	−0.424394	−	0.238895i
$184$	−828490.	+	3.21985e6i	−0.132994	+	0.516871i
$185$	3.74021e6	+	6.47823e6i	0.590718	+	1.02315i
$186$	−5.10422e6	+	5.25147e6i	−0.793215	+	0.816097i
$187$	−233972.	+	405252.i	−0.0357799	+	0.0619726i
$188$	6.00678e6	−	39867.0i	0.903999	−	0.00599985i
$189$	1.02174e7	+	5.46169e6i	1.51341	+	0.808987i
$190$	7.40044e6	−	7.44972e6i	1.07894	−	1.08612i
$191$	6.90798e6	+	3.98832e6i	0.991404	+	0.572387i	0.905694	−	0.423933i	$-0.139351\pi$
$191$	6.90798e6	+	3.98832e6i	0.991404	+	0.572387i	0.0857104	+	0.996320i	$0.472684\pi$
$192$	−218034.	−	7.07453e6i	−0.0308050	−	0.999525i
$193$	−4.72974e6	−	8.19215e6i	−0.657908	−	1.13953i	−0.981156	−	0.193216i	$-0.938108\pi$
$193$	−4.72974e6	−	8.19215e6i	−0.657908	−	1.13953i	0.323248	−	0.946314i	$-0.395225\pi$
$194$	237789.	−	899367.i	0.0325676	−	0.123178i
$195$	−2.69919e6	+	4.79508e6i	−0.364024	+	0.646684i
$196$	1.27303e7	+	7.23764e6i	1.69072	+	0.961234i
$197$			5.50085e6i			0.719501i	0.933049	+	0.359751i	$0.117138\pi$
$197$			5.50085e6i			0.719501i	−0.933049	+	0.359751i	$0.882862\pi$
$198$	−1.89153e6	+	7.84205e6i	−0.243679	+	1.01026i
$199$		−	1.11340e7i		−	1.41284i	−0.707794	−	0.706419i	$-0.750309\pi$
$199$		−	1.11340e7i		−	1.41284i	0.707794	−	0.706419i	$-0.249691\pi$
$200$	66470.7	+	238547.i	0.00830884	+	0.0298184i
$201$	−1.81285e6	−	3.06237e6i	−0.223241	−	0.377112i
$202$	1.43544e6	+	379525.i	0.174153	+	0.0460454i
$203$	3.81902e6	+	6.61473e6i	0.456524	+	0.790723i
$204$	−501060.	+	301124.i	−0.0590200	+	0.0354695i
$205$	−1.11204e7	−	6.42037e6i	−1.29080	−	0.745244i
$206$	1.06783e7	−	1.07494e7i	1.22151	−	1.22965i
$207$	4.04706e6	−	2.45572e6i	0.456277	−	0.276864i
$208$	87300.4	+	6.57650e6i	0.00970121	+	0.730810i
$209$	−7.15255e6	+	1.23886e7i	−0.783469	+	1.35701i
$210$	−1.55258e7	+	4.39762e6i	−1.67647	+	0.474854i
$211$	−7.91445e6	−	1.37082e7i	−0.842506	−	1.45926i	−0.887769	−	0.460289i	$-0.847746\pi$
$211$	−7.91445e6	−	1.37082e7i	−0.842506	−	1.45926i	0.0452629	−	0.998975i	$-0.485587\pi$
$212$	−4.61429e6	−	7.87108e6i	−0.484281	−	0.826089i
$213$	7002.36	+	642444.i	0.000724612	+	0.0664808i
$214$	8.49704e6	−	2.30702e6i	0.867014	−	0.235402i
$215$			1.13488e7i			1.14191i
$216$	−6.81567e6	+	7.42338e6i	−0.676313	+	0.736615i
$217$	1.99564e7			1.95300
$218$	3.57122e6	+	1.31532e7i	0.344705	+	1.26959i
$219$	1.24696e7	−	135913.i	1.18719	−	0.0129398i
$220$	−5.68233e6	−	9.69294e6i	−0.533652	−	0.910306i
$221$	470442.	−	271610.i	0.0435842	−	0.0251633i
$222$	−3.46942e6	−	1.22488e7i	−0.317101	−	1.11952i
$223$	1.38905e7	+	8.01971e6i	1.25258	+	0.723176i	0.971621	−	0.236544i	$-0.0760148\pi$
$223$	1.38905e7	+	8.01971e6i	1.25258	+	0.723176i	0.280957	+	0.959720i	$0.409348\pi$
$224$	−1.34102e7	+	1.38628e7i	−1.19314	+	1.23340i
$225$	169597.	−	309121.i	0.0148892	−	0.0271382i
$226$	2.49459e6	+	2.47809e6i	0.216110	+	0.214680i
$227$	7.41569e6	−	1.28444e7i	0.633978	−	1.09808i	−0.352753	−	0.935716i	$-0.614754\pi$
$227$	7.41569e6	−	1.28444e7i	0.633978	−	1.09808i	0.986731	−	0.162365i	$-0.0519123\pi$
$228$	−1.53174e7	+	9.20538e6i	−1.29236	+	0.776671i
$229$	6.46091e6	−	3.73021e6i	0.538006	−	0.310618i	−0.206264	−	0.978496i	$-0.566131\pi$
$229$	6.46091e6	−	3.73021e6i	0.538006	−	0.310618i	0.744271	+	0.667878i	$0.232797\pi$
$230$	−1.68534e6	+	6.37431e6i	−0.138517	+	0.523902i
$231$	1.89167e7	−	1.11982e7i	1.53465	−	0.908476i
$232$	−6.40010e6	+	1.78338e6i	−0.512534	+	0.142817i
$233$	3.81957e6			0.301958			0.150979	−	0.988537i	$-0.451757\pi$
$233$	3.81957e6			0.301958			0.150979	+	0.988537i	$0.451757\pi$
$234$	6.45340e6	−	6.78600e6i	0.503664	−	0.529623i
$235$	1.19124e7			0.917904
$236$	−1.80684e7	−	1.02725e7i	−1.37462	−	0.781522i
$237$	−1.55445e6	−	875015.i	−0.116770	−	0.0657310i
$238$	1.54009e6	+	407194.i	0.114239	+	0.0302044i
$239$	−9.97819e6	+	5.76091e6i	−0.730900	+	0.421985i	−0.818751	−	0.574148i	$-0.805333\pi$
$239$	−9.97819e6	+	5.76091e6i	−0.730900	+	0.421985i	0.0878512	+	0.996134i	$0.472000\pi$
$240$	−339266.	−	1.40322e7i	−0.0245418	−	1.01506i
$241$	3.69830e6	−	6.40565e6i	0.264211	−	0.457627i	−0.703145	−	0.711046i	$-0.748222\pi$
$241$	3.69830e6	−	6.40565e6i	0.264211	−	0.457627i	0.967357	+	0.253419i	$0.0815551\pi$
$242$	804474.	+	799152.i	0.0567631	+	0.0563876i
$243$	1.43276e7	−	781566.i	0.998515	−	0.0544687i
$244$	−7.07457e6	+	46954.0i	−0.487002	+	0.00323224i
$245$	2.51500e7	+	1.45204e7i	1.71017	+	0.987369i
$246$	1.56706e7	+	1.52313e7i	1.05264	+	1.02313i
$247$	1.43814e7	−	8.30313e6i	0.954358	−	0.550999i
$248$	−4.32569e6	+	1.68114e7i	−0.283596	+	1.10217i
$249$	−1.29596e7	+	2.30226e7i	−0.839449	+	1.49127i
$250$	−4.02831e6	−	1.48368e7i	−0.257812	−	0.949553i
$251$	−9.35209e6			−0.591408			−0.295704	−	0.955280i	$-0.595554\pi$
$251$	−9.35209e6			−0.591408			−0.295704	+	0.955280i	$0.595554\pi$
$252$	2.74510e7	−	780786.i	1.71537	−	0.0487899i
$253$		−	8.98210e6i		−	0.554647i
$254$	−2.59281e6	−	9.54961e6i	−0.158223	−	0.582753i
$255$	−997606.	+	590558.i	−0.0601642	+	0.0356157i
$256$	−8.77133e6	−	1.43017e7i	−0.522812	−	0.852448i
$257$	−1.14254e7	−	1.97893e7i	−0.673087	−	1.16582i	−0.977024	−	0.213129i	$-0.931634\pi$
$257$	−1.14254e7	−	1.97893e7i	−0.673087	−	1.16582i	0.303937	−	0.952692i	$-0.401699\pi$
$258$	4.73310e6	−	1.87251e7i	0.275605	−	1.09035i
$259$	−1.73457e7	+	3.00437e7i	−0.998375	+	1.72924i
$260$	86565.6	+	1.30429e7i	0.00492522	+	0.742084i
$261$	8.29358e6	+	4.55021e6i	0.466467	+	0.255924i
$262$	1.52264e7	+	1.51256e7i	0.846627	+	0.841027i
$263$	−1.51356e7	−	8.73854e6i	−0.832017	−	0.480365i	0.0225259	−	0.999746i	$-0.492829\pi$
$263$	−1.51356e7	−	8.73854e6i	−0.832017	−	0.480365i	−0.854543	+	0.519381i	$0.826163\pi$
$264$	5.33313e6	+	1.83629e7i	0.289848	+	0.997997i
$265$	−9.04691e6	−	1.56697e7i	−0.486142	−	0.842022i
$266$	4.70807e7	+	1.24479e7i	2.50149	+	0.661382i
$267$	1.55963e7	−	169993.i	0.819385	−	0.00893094i
$268$	−7.33319e6	−	4.16917e6i	−0.380968	−	0.216594i
$269$			9.33403e6i			0.479526i	0.970831	+	0.239763i	$0.0770698\pi$
$269$			9.33403e6i			0.479526i	−0.970831	+	0.239763i	$0.922930\pi$
$270$	−1.36137e7	+	1.46314e7i	−0.691649	+	0.743354i
$271$			2.35058e7i			1.18105i	0.807020	+	0.590524i	$0.201079\pi$
$271$			2.35058e7i			1.18105i	−0.807020	+	0.590524i	$0.798921\pi$
$272$	−676849.	+	1.20912e6i	−0.0336345	+	0.0600847i
$273$	−2.55175e7	+	278130.i	−1.25415	+	0.0136697i
$274$	1.57147e6	−	5.94364e6i	0.0763932	−	0.288935i
$275$	−334506.	−	579381.i	−0.0160844	−	0.0278590i
$276$	5.43921e6	−	9.81452e6i	0.258707	−	0.466812i
$277$	−3.12755e6	−	1.80569e6i	−0.147152	−	0.0849580i	0.424616	−	0.905373i	$-0.360409\pi$
$277$	−3.12755e6	−	1.80569e6i	−0.147152	−	0.0849580i	−0.571768	+	0.820415i	$0.693742\pi$
$278$	−2.24317e7	−	2.22833e7i	−1.04407	−	1.03716i
$279$	2.11304e7	−	1.28217e7i	0.972961	−	0.590383i
$280$	−2.67759e7	+	2.73145e7i	−1.21975	+	1.24428i
$281$	2.66168e6	−	4.61016e6i	0.119960	−	0.207777i	−0.799792	−	0.600278i	$-0.795057\pi$
$281$	2.66168e6	−	4.61016e6i	0.119960	−	0.207777i	0.919752	+	0.392501i	$0.128390\pi$
$282$	−1.96551e7	−	4.96818e6i	−0.876454	−	0.221539i
$283$	4.02372e6	+	6.96929e6i	0.177529	+	0.307489i	0.941033	−	0.338313i	$-0.109856\pi$
$283$	4.02372e6	+	6.96929e6i	0.177529	+	0.307489i	−0.763505	+	0.645802i	$0.776523\pi$
$284$	770197.	+	1.31380e6i	0.0336238	+	0.0573556i
$285$	−3.04969e7	+	1.80534e7i	−1.31741	+	0.779874i
$286$	−4.65580e6	−	1.71479e7i	−0.199020	−	0.733013i
$287$		−	5.95508e7i		−	2.51908i
$288$	−5.29248e6	+	2.32942e7i	−0.221555	+	0.975148i
$289$	−2.40231e7			−0.995259
$290$	−1.27154e7	+	3.45234e6i	−0.521357	+	0.141553i
$291$	−1.54010e6	+	2.73598e6i	−0.0624987	+	0.111028i
$292$	2.55004e7	−	1.49492e7i	1.02423	−	0.600440i
$293$	1.12062e7	−	6.46988e6i	0.445506	−	0.257213i	−0.260424	−	0.965494i	$-0.583862\pi$
$293$	1.12062e7	−	6.46988e6i	0.445506	−	0.257213i	0.705931	+	0.708281i	$0.250529\pi$
$294$	−3.54409e7	−	3.44472e7i	−1.39464	−	1.35554i
$295$	−3.56959e7	−	2.06090e7i	−1.39044	−	0.802771i
$296$	−2.15492e7	−	2.11244e7i	−0.830915	−	0.814533i
$297$	1.28349e7	−	2.40108e7i	0.489917	−	0.916510i
$298$	1.62370e7	−	1.63451e7i	0.613560	−	0.617646i
$299$	−5.21350e6	+	9.03004e6i	−0.195036	+	0.337813i
$300$	−14655.3	−	835639.i	−0.000542789	−	0.0309496i
$301$	−4.55803e7	+	2.63158e7i	−1.67139	+	0.964976i
$302$	2.52930e7	+	6.68735e6i	0.918287	+	0.242791i
$303$	−4.36678e6	−	2.45810e6i	−0.156976	−	0.0883632i
$304$	−2.06913e7	+	3.69630e7i	−0.736491	+	1.31567i
$305$	−1.40301e7			−0.494493
$306$	1.89231e6	−	558341.i	0.0660433	−	0.0194866i
$307$	8.45078e6			0.292066			0.146033	−	0.989280i	$-0.453349\pi$
$307$	8.45078e6			0.292066			0.146033	+	0.989280i	$0.453349\pi$
$308$	2.57536e7	−	4.52982e7i	0.881426	−	1.55035i
$309$	−4.40046e7	+	2.60496e7i	−1.49150	+	0.882930i
$310$	−8.79945e6	+	3.32814e7i	−0.295373	+	1.11716i
$311$	−3.15180e7	+	1.81969e7i	−1.04780	+	0.604947i	−0.922032	−	0.387113i	$-0.873472\pi$
$311$	−3.15180e7	+	1.81969e7i	−1.04780	+	0.604947i	−0.125766	+	0.992060i	$0.540139\pi$
$312$	5.29681e6	−	2.15564e7i	0.174402	−	0.709762i
$313$	328987.	−	569822.i	0.0107287	−	0.0185826i	−0.860611	−	0.509263i	$-0.829918\pi$
$313$	328987.	−	569822.i	0.0107287	−	0.0185826i	0.871340	+	0.490680i	$0.163252\pi$
$314$	−3.02345e7	+	3.04359e7i	−0.976595	+	0.983098i
$315$	5.44479e7	−	1.18706e6i	1.74200	−	0.0379787i
$316$	−4.22820e6	+	28062.6i	−0.133997	+	0.000889337i
$317$	−4.28880e6	−	2.47614e6i	−0.134635	−	0.0777315i	0.431170	−	0.902271i	$-0.358101\pi$
$317$	−4.28880e6	−	2.47614e6i	−0.134635	−	0.0777315i	−0.565805	+	0.824539i	$0.691434\pi$
$318$	8.39193e6	+	2.96276e7i	0.260964	+	0.921330i
$319$	1.55445e7	−	8.97463e6i	0.478856	−	0.276468i
$320$	−1.72060e7	−	2.84769e7i	−0.525086	−	0.869045i
$321$	−2.97140e7	+	323869.i	−0.898350	+	0.00979162i
$322$	−2.95092e7	+	8.01203e6i	−0.883874	+	0.239980i
$323$	3.49865e6			0.103823
$324$	2.85644e7	−	1.84637e7i	0.839827	−	0.542854i
$325$			776631.i			0.0226238i
$326$	3.44949e7	−	9.36568e6i	0.995639	−	0.270325i
$327$	−501343.	−	4.59966e7i	−0.0143381	−	1.31547i
$328$	5.01660e7	+	1.29081e7i	1.42164	+	0.365797i
$329$	2.76228e7	+	4.78441e7i	0.775676	+	1.34351i
$330$	1.03343e7	+	3.64853e7i	0.287568	+	1.01526i
$331$	−1.95612e7	+	3.38811e7i	−0.539402	+	0.934271i	0.459535	+	0.888160i	$0.348016\pi$
$331$	−1.95612e7	+	3.38811e7i	−0.539402	+	0.934271i	−0.998936	+	0.0461112i	$0.985317\pi$
$332$	415628.	+	6.26228e7i	0.0113577	+	1.71127i
$333$	936507.	+	4.29556e7i	0.0253617	+	1.16329i
$334$	4.70578e7	−	4.73712e7i	1.26297	−	1.27138i
$335$	−1.44874e7	−	8.36432e6i	−0.385351	−	0.222483i
$336$	5.55712e7	−	3.39008e7i	1.46498	−	0.893701i
$337$	1.94546e7	+	3.36963e7i	0.508314	+	0.880425i	0.999954	+	0.00962668i	$0.00306431\pi$
$337$	1.94546e7	+	3.36963e7i	0.508314	+	0.880425i	−0.491640	+	0.870799i	$0.663602\pi$
$338$	4.59782e6	−	1.73899e7i	0.119070	−	0.450347i
$339$	−6.04531e6	−	1.02121e7i	−0.155174	−	0.262129i
$340$	−1.35816e6	+	2.38888e6i	−0.0345553	+	0.0607795i
$341$		−	4.68971e7i		−	1.18272i
$342$	5.78482e7	−	1.70685e7i	1.44614	−	0.426695i
$343$			6.54314e7i			1.62145i
$344$	−1.22887e7	−	4.41013e7i	−0.301879	−	1.08337i
$345$	1.09156e7	−	1.93914e7i	0.265821	−	0.472228i
$346$	1.25825e7	+	3.32676e6i	0.303766	+	0.0803143i
$347$	−2.65465e7	−	4.59798e7i	−0.635358	−	1.10047i	−0.986439	−	0.164127i	$-0.947519\pi$
$347$	−2.65465e7	−	4.59798e7i	−0.635358	−	1.10047i	0.351081	−	0.936345i	$-0.385814\pi$
$348$	2.24198e7	−	393195.i	0.531978	−	0.00932975i
$349$	−3.37312e7	−	1.94747e7i	−0.793516	−	0.458137i	0.0476829	−	0.998863i	$-0.484816\pi$
$349$	−3.37312e7	−	1.94747e7i	−0.793516	−	0.458137i	−0.841199	+	0.540726i	$0.818150\pi$
$350$	−1.60508e6	+	1.61577e6i	−0.0374364	+	0.0376856i
$351$	−2.68400e7	+	1.66892e7i	−0.620671	+	0.385934i
$352$	3.25773e7	+	3.15137e7i	0.746941	+	0.722557i
$353$	−1.74021e7	+	3.01413e7i	−0.395619	+	0.685232i	−0.993180	−	0.116591i	$-0.962803\pi$
$353$	−1.74021e7	+	3.01413e7i	−0.395619	+	0.685232i	0.597561	+	0.801824i	$0.296137\pi$
$354$	5.03019e7	+	4.88915e7i	1.13390	+	1.10211i
$355$	1.51007e6	+	2.61552e6i	0.0337530	+	0.0584618i
$356$	3.18946e7	−	1.86977e7i	0.706915	−	0.414418i
$357$	−4.68514e6	−	2.63730e6i	−0.102972	−	0.0579636i
$358$	−4.78916e6	+	1.30030e6i	−0.104378	+	0.0283396i
$359$			2.14401e7i			0.463387i	0.972789	+	0.231693i	$0.0744266\pi$
$359$			2.14401e7i			0.463387i	−0.972789	+	0.231693i	$0.925573\pi$
$360$	−1.08020e7	+	4.61246e7i	−0.231524	+	0.988611i
$361$	5.99082e7			1.27340
$362$	−4.52068e6	−	1.66502e7i	−0.0952968	−	0.350989i
$363$	−1.94953e6	−	3.29327e6i	−0.0407578	−	0.0688506i
$364$	−5.21835e7	+	3.05918e7i	−1.08201	+	0.634308i
$365$	5.07661e7	−	2.93098e7i	1.04399	−	0.602747i
$366$	2.31491e7	+	5.85135e6i	0.472163	+	0.119347i
$367$	6.65003e7	+	3.83939e7i	1.34532	+	0.776720i	0.987582	−	0.157103i	$-0.0502153\pi$
$367$	6.65003e7	+	3.83939e7i	1.34532	+	0.776720i	0.357736	+	0.933823i	$0.383549\pi$
$368$	−353044.	−	2.65955e7i	−0.00708412	−	0.533660i
$369$	−3.82607e7	−	6.30542e7i	−0.761506	−	1.25497i
$370$	−4.24558e7	−	4.21750e7i	−0.838170	−	0.832625i
$371$	4.19564e7	−	7.26705e7i	0.821629	−	1.42310i
$372$	2.83991e7	−	5.12433e7i	0.551665	−	0.995424i
$373$	3.63529e7	−	2.09884e7i	0.700507	−	0.404438i	−0.107029	−	0.994256i	$-0.534134\pi$
$373$	3.63529e7	−	2.09884e7i	0.700507	−	0.404438i	0.807536	+	0.589818i	$0.200800\pi$
$374$	956899.	−	3.61919e6i	0.0182916	−	0.0691826i
$375$	565511.	+	5.18838e7i	0.0107238	+	0.983871i
$376$	−4.62917e7	+	1.28991e7i	−0.870843	+	0.242659i
$377$	−2.08366e7			−0.388869
$378$	−9.03323e7	−	2.07493e7i	−1.67251	−	0.384175i
$379$	−1.38912e7			−0.255166			−0.127583	−	0.991828i	$-0.540722\pi$
$379$	−1.38912e7			−0.255166			−0.127583	+	0.991828i	$0.540722\pi$
$380$	−4.15190e7	+	7.30282e7i	−0.756653	+	1.33088i
$381$	363989.	+	3.33948e7i	0.00658132	+	0.603814i
$382$	−6.16932e7	−	1.63114e7i	−1.10674	−	0.292618i
$383$	1.21581e7	−	7.01947e6i	0.216406	−	0.124942i	−0.387879	−	0.921710i	$-0.626792\pi$
$383$	1.21581e7	−	7.01947e6i	0.216406	−	0.124942i	0.604285	+	0.796768i	$0.293459\pi$
$384$	1.65128e7	+	5.41618e7i	0.291627	+	0.956532i
$385$	5.16676e7	−	8.94910e7i	0.905392	−	1.56818i
$386$	5.36882e7	+	5.33330e7i	0.933505	+	0.927330i
$387$	−3.13542e7	+	5.71487e7i	−0.540958	+	0.985993i
$388$	49392.6	+	7.44200e6i	0.000845604	+	0.127407i
$389$	3.27424e7	+	1.89038e7i	0.556239	+	0.321145i	0.751635	−	0.659580i	$-0.229266\pi$
$389$	3.27424e7	+	1.89038e7i	0.556239	+	0.321145i	−0.195395	+	0.980725i	$0.562599\pi$
$390$	1.07877e7	−	4.26784e7i	0.181859	−	0.719472i
$391$	−1.90248e6	+	1.09839e6i	−0.0318265	+	0.0183750i
$392$	−1.13456e8	−	2.91930e7i	−1.88352	−	0.484642i
$393$	−3.68990e7	−	6.23321e7i	−0.607907	−	1.02691i
$394$	−1.15308e7	−	4.24693e7i	−0.188526	−	0.694363i
$395$	−8.38522e6			−0.136058
$396$	−1.83483e6	−	6.45095e7i	−0.0295469	−	1.03882i
$397$			2.33718e6i			0.0373526i	0.999826	+	0.0186763i	$0.00594519\pi$
$397$			2.33718e6i			0.0373526i	−0.999826	+	0.0186763i	$0.994055\pi$
$398$	2.33389e7	+	8.59601e7i	0.370196	+	1.36348i
$399$	−1.43225e8	−	8.06225e7i	−2.25476	−	1.26922i
$400$	−1.01322e6	−	1.70237e6i	−0.0158316	−	0.0265995i
$401$	3.85494e7	+	6.67694e7i	0.597839	+	1.03549i	0.993140	+	0.116935i	$0.0373070\pi$
$401$	3.85494e7	+	6.67694e7i	0.597839	+	1.03549i	−0.395301	+	0.918552i	$0.629360\pi$
$402$	2.04154e7	+	1.98430e7i	0.314253	+	0.305442i
$403$	−2.72206e7	+	4.71474e7i	−0.415893	+	0.720348i
$404$	−1.18779e7	+	78833.6i	−0.180134	+	0.00119555i
$405$	5.68885e7	−	3.62390e7i	0.856365	−	0.545521i
$406$	−4.33504e7	−	4.30636e7i	−0.647761	−	0.643476i
$407$	7.06022e7	+	4.07622e7i	1.04721	+	0.604609i
$408$	3.23722e6	−	3.37514e6i	0.0476642	−	0.0496948i
$409$	3.43481e7	+	5.94926e7i	0.502033	+	0.869547i	0.999997	+	0.00234939i	$0.000747834\pi$
$409$	3.43481e7	+	5.94926e7i	0.502033	+	0.869547i	−0.497964	+	0.867198i	$0.665919\pi$
$410$	9.93133e7	+	2.62580e7i	1.44097	+	0.380987i
$411$	−1.01781e7	+	1.80812e7i	−0.146602	+	0.260437i
$412$	−5.99088e7	+	1.05374e8i	−0.856641	+	1.50675i
$413$		−	1.91155e8i		−	2.71353i
$414$	−2.60977e7	+	2.74427e7i	−0.367791	+	0.386746i
$415$			1.24191e8i			1.73759i
$416$	−1.44595e7	−	5.05908e7i	−0.200851	−	0.702735i
$417$	5.43602e7	+	9.18286e7i	0.749675	+	1.26640i
$418$	2.92525e7	−	1.10639e8i	0.400528	−	1.51488i
$419$	−4.75381e7	−	8.23384e7i	−0.646249	−	1.11934i	−0.984012	−	0.178105i	$-0.943003\pi$
$419$	−4.75381e7	−	8.23384e7i	−0.646249	−	1.11934i	0.337763	−	0.941231i	$-0.390330\pi$
$420$	1.10648e8	−	6.64966e7i	1.49347	−	0.897536i
$421$	2.74912e7	+	1.58721e7i	0.368424	+	0.212710i	0.672770	−	0.739852i	$-0.265104\pi$
$421$	2.74912e7	+	1.58721e7i	0.368424	+	0.212710i	−0.304346	+	0.952562i	$0.598438\pi$
$422$	8.98384e7	+	8.92441e7i	1.19543	+	1.18752i
$423$	5.99872e7	+	3.29115e7i	0.792570	+	0.434838i
$424$	5.21239e7	+	5.10962e7i	0.683815	+	0.670334i
$425$	−81811.4	+	141702.i	−0.00106573	+	0.00184590i
$426$	−1.40074e6	−	4.94531e6i	−0.0181188	−	0.0639682i
$427$	−3.25332e7	−	5.63492e7i	−0.417872	−	0.723775i
$428$	−6.07654e7	+	3.56227e7i	−0.775041	+	0.454355i
$429$	653600.	+	5.99657e7i	0.00827828	+	0.759506i
$430$	−2.37891e7	−	8.76181e7i	−0.299208	−	1.10202i
$431$		−	1.33851e8i		−	1.67182i	−0.548866	−	0.835911i	$-0.684940\pi$
$431$		−	1.33851e8i		−	1.67182i	0.548866	−	0.835911i	$-0.315060\pi$
$432$	3.70596e7	−	7.15990e7i	0.459674	−	0.888088i
$433$	−4.21597e7			−0.519319			−0.259659	−	0.965700i	$-0.583610\pi$
$433$	−4.21597e7			−0.519319			−0.259659	+	0.965700i	$0.583610\pi$
$434$	−1.54073e8	+	4.18322e7i	−1.88476	+	0.511731i
$435$	4.44654e7	−	484654.i	0.540200	−	0.00588795i
$436$	−5.51432e7	−	9.40635e7i	−0.665323	−	1.13491i
$437$	−5.81588e7	+	3.35780e7i	−0.696901	+	0.402356i
$438$	−9.59863e7	+	2.71878e7i	−1.14232	+	0.323558i
$439$	9.30377e7	+	5.37153e7i	1.09968	+	0.634899i	0.936136	−	0.351638i	$-0.114375\pi$
$439$	9.30377e7	+	5.37153e7i	1.09968	+	0.634899i	0.163541	+	0.986537i	$0.447708\pi$
$440$	6.41885e7	+	6.29230e7i	0.753528	+	0.738672i
$441$	8.65307e7	+	1.42604e8i	1.00891	+	1.66271i
$442$	−3.06270e6	+	3.08309e6i	−0.0354681	+	0.0357042i
$443$	−1.58714e6	+	2.74900e6i	−0.0182559	+	0.0316201i	−0.875009	−	0.484107i	$-0.839145\pi$
$443$	−1.58714e6	+	2.74900e6i	−0.0182559	+	0.0316201i	0.856753	+	0.515727i	$0.172478\pi$
$444$	5.24613e7	+	8.72938e7i	0.599363	+	0.997320i
$445$	6.34957e7	−	3.66592e7i	0.720550	−	0.416010i
$446$	−1.24053e8	−	3.27990e7i	−1.39830	−	0.369705i
$447$	−6.69120e7	+	3.96102e7i	−0.749172	+	0.443491i
$448$	7.44744e7	−	1.35138e8i	0.828272	−	1.50294i
$449$	2.70606e7			0.298950			0.149475	−	0.988766i	$-0.452242\pi$
$449$	2.70606e7			0.298950			0.149475	+	0.988766i	$0.452242\pi$
$450$	−661399.	+	2.74208e6i	−0.00725815	+	0.0300914i
$451$	−1.39943e8			−1.52554
$452$	−2.44540e7	−	1.39029e7i	−0.264810	−	0.150554i
$453$	−7.69441e7	−	4.33125e7i	−0.827714	−	0.465927i
$454$	−3.03287e7	+	1.14709e8i	−0.324105	+	1.22583i
$455$	−1.03887e8	+	5.99791e7i	−1.10287	+	0.636745i
$456$	9.89621e7	−	1.03178e8i	1.04370	−	1.08816i
$457$	4.72979e7	−	8.19224e7i	0.495557	−	0.858329i	−0.504430	−	0.863453i	$-0.668297\pi$
$457$	4.72979e7	−	8.19224e7i	0.495557	−	0.858329i	0.999987	+	0.00512306i	$0.00163073\pi$
$458$	−4.20622e7	+	4.23423e7i	−0.437820	+	0.440736i
$459$	−6.65520e6	+	217686.i	−0.0688214	+	0.00225108i
$460$	−350073.	−	5.27456e7i	−0.00359654	−	0.541892i
$461$	1.40881e8	+	8.13379e7i	1.43797	+	0.830214i	0.997709	−	0.0676541i	$-0.0215514\pi$
$461$	1.40881e8	+	8.13379e7i	1.43797	+	0.830214i	0.440264	+	0.897868i	$0.354885\pi$
$462$	−1.22573e8	+	1.26109e8i	−1.24299	+	1.27885i
$463$	−2.02888e7	+	1.17138e7i	−0.204416	+	0.118019i	−0.598713	−	0.800963i	$-0.704321\pi$
$463$	−2.02888e7	+	1.17138e7i	−0.204416	+	0.118019i	0.394298	+	0.918983i	$0.370988\pi$
$464$	4.56737e7	−	2.71843e7i	0.457206	−	0.272123i
$465$	5.69921e7	−	1.01246e8i	0.566834	−	1.00697i
$466$	−2.94889e7	+	8.00651e6i	−0.291408	+	0.0791199i
$467$	−8.22983e7			−0.808054			−0.404027	−	0.914747i	$-0.632390\pi$
$467$	−8.22983e7			−0.808054			−0.404027	+	0.914747i	$0.632390\pi$
$468$	−3.55987e7	+	6.59188e7i	−0.347294	+	0.643090i
$469$		−	7.75815e7i		−	0.752037i
$470$	−9.19700e7	+	2.49707e7i	−0.885834	+	0.240512i
$471$	1.24595e8	−	7.37573e7i	1.19245	−	0.705898i
$472$	1.61030e8	+	4.14342e7i	1.53137	+	0.394033i
$473$	6.18417e7	+	1.07113e8i	0.584383	+	1.01218i
$474$	1.38353e7	+	3.49713e6i	0.129914	+	0.0328380i
$475$	−2.50098e6	+	4.33183e6i	−0.0233362	+	0.0404194i
$476$	−1.27438e7	+	84580.8i	−0.118162	+	0.000784244i
$477$	−2.26525e6	−	1.03902e8i	−0.0208718	−	0.957348i
$478$	6.49606e7	−	6.53932e7i	0.594794	−	0.598755i
$479$	−5.21280e7	−	3.00961e7i	−0.474313	−	0.273844i	0.243731	−	0.969843i	$-0.421629\pi$
$479$	−5.21280e7	−	3.00961e7i	−0.474313	−	0.273844i	−0.718043	+	0.695998i	$0.754962\pi$
$480$	3.20334e7	+	1.07625e8i	0.289654	+	0.973167i
$481$	−4.73194e7	−	8.19595e7i	−0.425210	−	0.736486i
$482$	−1.51253e7	+	5.72071e7i	−0.135071	+	0.510868i
$483$	1.03193e8	−	1.12476e6i	0.915819	−	0.00998203i
$484$	−7.88610e6	−	4.48352e6i	−0.0695547	−	0.0395443i
$485$			1.47587e7i			0.129367i
$486$	−1.08978e8	+	3.60674e7i	−0.949357	+	0.314200i
$487$		−	1.48134e8i		−	1.28253i	−0.767319	−	0.641265i	$-0.778410\pi$
$487$		−	1.48134e8i		−	1.28253i	0.767319	−	0.641265i	$-0.221590\pi$
$488$	5.45208e7	−	1.51921e7i	0.469140	−	0.130725i
$489$	−1.20628e8	+	1.31479e6i	−1.03162	+	0.0112442i
$490$	−2.24608e8	−	5.93854e7i	−1.90914	−	0.504767i
$491$	8.33192e6	+	1.44313e7i	0.0703884	+	0.121916i	0.899072	−	0.437802i	$-0.144243\pi$
$491$	8.33192e6	+	1.44313e7i	0.0703884	+	0.121916i	−0.828683	+	0.559718i	$0.810909\pi$
$492$	−1.52913e8	−	8.47443e7i	−1.28395	−	0.711566i
$493$	−3.80179e6	−	2.19496e6i	−0.0317283	−	0.0183183i
$494$	−9.36269e7	+	9.42504e7i	−0.776640	+	0.781812i
$495$	−2.78957e6	−	1.27952e8i	−0.0229997	−	1.05495i
$496$	−1.84331e6	−	1.38860e8i	−0.0151061	−	1.13797i
$497$	−7.00316e6	+	1.21298e7i	−0.0570460	+	0.0988065i
$498$	5.17951e7	−	2.04912e8i	0.419373	−	1.65912i
$499$	1.54043e6	+	2.66811e6i	0.0123977	+	0.0214735i	0.872158	−	0.489225i	$-0.162720\pi$
$499$	1.54043e6	+	2.66811e6i	0.0123977	+	0.0214735i	−0.859760	+	0.510698i	$0.829387\pi$
$500$	6.22012e7	+	1.06103e8i	0.497609	+	0.848824i
$501$	−1.93923e8	+	1.14798e8i	−1.54211	+	0.912893i
$502$	7.22027e7	−	1.96037e7i	0.570745	−	0.154963i
$503$			1.46797e8i			1.15349i	0.816924	+	0.576745i	$0.195677\pi$
$503$			1.46797e8i			1.15349i	−0.816924	+	0.576745i	$0.804323\pi$
$504$	−2.10299e8	+	6.35705e7i	−1.64265	+	0.496551i
$505$	−2.35558e7			−0.182904
$506$	1.88281e7	+	6.93463e7i	0.145330	+	0.535268i
$507$	−2.97791e7	+	5.29022e7i	−0.228501	+	0.405928i
$508$	4.00355e7	+	6.82927e7i	0.305389	+	0.520934i
$509$	1.27313e8	−	7.35043e7i	0.965428	−	0.557390i	0.0675889	−	0.997713i	$-0.478469\pi$
$509$	1.27313e8	−	7.35043e7i	0.965428	−	0.557390i	0.897839	+	0.440323i	$0.145136\pi$
$510$	6.46409e6	−	6.65056e6i	0.0487301	−	0.0501358i
$511$	2.35435e8	+	1.35929e8i	1.76445	+	1.01870i
$512$	9.76980e7	+	9.20299e7i	0.727907	+	0.685676i
$513$	−2.03450e8	+	6.65466e6i	−1.50697	+	0.0492917i
$514$	1.29692e8	+	1.28834e8i	0.955043	+	0.948725i
$515$	−1.20191e8	+	2.08176e8i	−0.879932	+	1.52409i
$516$	2.70939e6	+	1.54488e8i	0.0197207	+	1.12447i
$517$	1.12433e8	−	6.49132e7i	0.813621	−	0.469744i
$518$	7.09405e7	−	2.68312e8i	0.510394	−	1.93042i
$519$	−3.82774e7	−	2.15467e7i	−0.273805	−	0.154127i
$520$	−2.80086e7	−	1.00516e8i	−0.199196	−	0.714866i
$521$	1.21368e8			0.858205			0.429102	−	0.903256i	$-0.358830\pi$
$521$	1.21368e8			0.858205			0.429102	+	0.903256i	$0.358830\pi$
$522$	−7.35686e7	−	1.77450e7i	−0.517227	−	0.124757i
$523$	8.18350e7			0.572050			0.286025	−	0.958222i	$-0.407666\pi$
$523$	8.18350e7			0.572050			0.286025	+	0.958222i	$0.407666\pi$
$524$	−1.49261e8	−	8.48601e7i	−1.03742	−	0.589807i
$525$	6.61448e6	−	3.91561e6i	0.0457107	−	0.0270596i
$526$	1.35172e8	+	3.57388e7i	0.928814	+	0.245574i
$527$	−9.93315e6	+	5.73491e6i	−0.0678665	+	0.0391827i
$528$	−7.96664e7	−	1.30591e8i	−0.541219	−	0.887182i
$529$	−5.29345e7	+	9.16852e7i	−0.357579	+	0.619344i
$530$	1.02693e8	+	1.02014e8i	0.689786	+	0.685223i
$531$	−1.22815e8	−	2.02401e8i	−0.820288	−	1.35185i
$532$	−3.89579e8	+	2.58564e6i	−2.58739	+	0.0171725i
$533$	1.40690e8	+	8.12276e7i	0.929143	+	0.536441i
$534$	−1.20055e8	+	3.40051e7i	−0.788417	+	0.223317i
$535$	−1.20971e8	+	6.98429e7i	−0.789990	+	0.456101i
$536$	6.53552e7	+	1.68164e7i	0.424410	+	0.109204i
$537$	1.67476e7	−	182541.i	0.108151	−	0.00117880i
$538$	−1.95658e7	−	7.20633e7i	−0.125647	−	0.462772i
$539$	3.16497e8			2.02117
$540$	7.44345e7	−	1.41499e8i	0.472708	−	0.898611i
$541$			8.83914e7i			0.558237i	0.960257	+	0.279118i	$0.0900422\pi$
$541$			8.83914e7i			0.558237i	−0.960257	+	0.279118i	$0.909958\pi$
$542$	−4.92725e7	−	1.81477e8i	−0.309462	−	1.13978i
$543$	634632.	+	5.82254e7i	0.00396390	+	0.363675i
$544$	2.69107e6	−	1.07538e7i	0.0167158	−	0.0667984i
$545$	−1.08115e8	−	1.87261e8i	−0.667879	−	1.15680i
$546$	1.96425e8	−	5.56366e7i	1.20675	−	0.341809i
$547$	9.92391e7	−	1.71887e8i	0.606346	−	1.05022i	−0.385491	−	0.922712i	$-0.625968\pi$
$547$	9.92391e7	−	1.71887e8i	0.606346	−	1.05022i	0.991837	−	0.127511i	$-0.0406988\pi$
$548$	326421.	+	4.91819e7i	0.00198352	+	0.298857i
$549$	−7.06508e7	−	3.87621e7i	−0.426973	−	0.234256i
$550$	3.79704e6	+	3.77192e6i	0.0228222	+	0.0226712i
$551$	−1.16221e8	−	6.71001e7i	−0.694751	−	0.401115i
$552$	−2.14204e7	+	8.71745e7i	−0.127353	+	0.518289i
$553$	−1.94438e7	−	3.36777e7i	−0.114976	−	0.199144i
$554$	2.79313e7	+	7.38491e6i	0.164271	+	0.0434326i
$555$	1.02886e8	+	1.73801e8i	0.601835	+	1.01666i
$556$	2.19894e8	+	1.25017e8i	1.27935	+	0.727354i
$557$		−	5.91077e7i		−	0.342041i	−0.985267	−	0.171020i	$-0.945294\pi$
$557$		−	5.91077e7i		−	0.342041i	0.985267	−	0.171020i	$-0.0547064\pi$
$558$	−1.36260e8	+	1.43283e8i	−0.784273	+	0.824694i
$559$		−	1.43579e8i		−	0.821971i
$560$	1.49467e8	−	2.67008e8i	0.851103	−	1.52041i
$561$	−6.19762e6	+	1.10100e7i	−0.0351024	+	0.0623589i
$562$	−1.08857e7	+	4.11720e7i	−0.0613264	+	0.231950i
$563$	−1.80880e7	−	3.13293e7i	−0.101359	−	0.175560i	0.810886	−	0.585205i	$-0.198986\pi$
$563$	−1.80880e7	−	3.13293e7i	−0.101359	−	0.175560i	−0.912245	+	0.409645i	$0.865653\pi$
$564$	1.62162e8	−	2.84397e6i	0.903880	−	0.0158521i
$565$	−4.83112e7	−	2.78925e7i	−0.267857	−	0.154647i
$566$	−4.56740e7	−	4.53719e7i	−0.251895	−	0.250229i
$567$	2.77461e8	+	1.44450e8i	1.52214	+	0.792445i
$568$	−8.70028e6	−	8.52875e6i	−0.0474775	−	0.0465415i
$569$	3.42665e7	−	5.93512e7i	0.186008	−	0.322176i	−0.757908	−	0.652362i	$-0.773778\pi$
$569$	3.42665e7	−	5.93512e7i	0.186008	−	0.322176i	0.943916	+	0.330186i	$0.107112\pi$
$570$	1.97608e8	−	2.03308e8i	1.06704	−	1.09782i
$571$	8.35101e7	+	1.44644e8i	0.448570	+	0.776947i	0.998293	−	0.0584004i	$-0.0186000\pi$
$571$	8.35101e7	+	1.44644e8i	0.448570	+	0.776947i	−0.549723	+	0.835347i	$0.685267\pi$
$572$	7.18901e7	+	1.22631e8i	0.384133	+	0.655255i
$573$	1.87678e8	+	1.05645e8i	0.997584	+	0.561548i
$574$	1.24829e8	+	4.59761e8i	0.660057	+	2.43107i
$575$		−	3.14071e6i		−	0.0165205i
$576$	−7.96840e6	−	1.90937e8i	−0.0416969	−	0.999130i
$577$	3.03248e8			1.57859			0.789296	−	0.614013i	$-0.210446\pi$
$577$	3.03248e8			1.57859			0.789296	+	0.614013i	$0.210446\pi$
$578$	1.85470e8	−	5.03569e7i	0.960486	−	0.260781i
$579$	−1.30106e8	−	2.19783e8i	−0.670289	−	1.13229i
$580$	9.09323e7	−	5.33076e7i	0.466052	−	0.273215i
$581$	−4.98792e8	+	2.87978e8i	−2.54326	+	1.46835i
$582$	6.15526e6	−	2.43514e7i	0.0312232	−	0.123525i
$583$	−1.70775e8	−	9.85968e7i	−0.861822	−	0.497573i
$584$	−1.65540e8	+	1.68869e8i	−0.831119	+	0.847834i
$585$	−7.14627e7	+	1.30254e8i	−0.356954	+	0.650613i
$586$	−7.29550e7	+	7.34408e7i	−0.362545	+	0.364959i
$587$	1.26837e8	−	2.19688e8i	0.627093	−	1.08616i	−0.361039	−	0.932551i	$-0.617578\pi$
$587$	1.26837e8	−	2.19688e8i	0.627093	−	1.08616i	0.988132	−	0.153606i	$-0.0490886\pi$
$588$	3.45829e8	+	1.91659e8i	1.70110	+	0.942750i
$589$	−3.03657e8	+	1.75317e8i	−1.48606	+	0.857980i
$590$	3.18790e8	+	8.42868e7i	1.55221	+	0.410396i
$591$	1.61874e6	+	1.48514e8i	0.00784179	+	0.719458i
$592$	2.10651e8	+	1.17919e8i	1.01531	+	0.568356i
$593$	1.77204e8			0.849784			0.424892	−	0.905244i	$-0.360312\pi$
$593$	1.77204e8			0.849784			0.424892	+	0.905244i	$0.360312\pi$
$594$	−4.87606e7	+	2.12280e8i	−0.232654	+	1.01286i
$595$	−2.52731e7			−0.119980
$596$	−9.10953e7	+	1.60228e8i	−0.430286	+	0.756834i
$597$	−3.27642e6	−	3.00601e8i	−0.0153984	−	1.41275i
$598$	2.13221e7	−	8.06448e7i	0.0997073	−	0.377114i
$599$	−1.46503e8	+	8.45838e7i	−0.681659	+	0.393556i	−0.800480	−	0.599359i	$-0.795422\pi$
$599$	−1.46503e8	+	8.45838e7i	−0.681659	+	0.393556i	0.118821	+	0.992916i	$0.462089\pi$
$600$	1.86480e6	+	6.42082e6i	0.00863333	+	0.0297260i
$601$	−1.38979e7	+	2.40719e7i	−0.0640215	+	0.110889i	−0.896260	−	0.443530i	$-0.853726\pi$
$601$	−1.38979e7	+	2.40719e7i	−0.0640215	+	0.110889i	0.832238	+	0.554419i	$0.187059\pi$
$602$	2.96739e8	−	2.98715e8i	1.36015	−	1.36920i
$603$	−4.98452e7	−	8.21457e7i	−0.227337	−	0.374656i
$604$	−2.09292e8	+	1.38907e6i	−0.949821	+	0.00630397i
$605$	−1.55798e7	−	8.99498e6i	−0.0703550	−	0.0406195i
$606$	3.88664e7	+	9.82416e6i	0.174645	+	0.0441446i
$607$	−1.31731e8	+	7.60552e7i	−0.589011	+	0.340066i	−0.764706	−	0.644379i	$-0.777116\pi$
$607$	−1.31731e8	+	7.60552e7i	−0.589011	+	0.340066i	0.175695	+	0.984445i	$0.443783\pi$
$608$	8.22661e7	−	3.28745e8i	0.366024	−	1.46268i
$609$	1.05054e8	+	1.77463e8i	0.465115	+	0.785700i
$610$	1.08319e8	−	2.94096e7i	0.477216	−	0.129569i
$611$	−1.50711e8			−0.660725
$612$	−1.34392e7	+	8.27731e6i	−0.0586300	+	0.0361106i
$613$			8.92988e7i			0.387672i	0.981034	+	0.193836i	$0.0620929\pi$
$613$			8.92988e7i			0.387672i	−0.981034	+	0.193836i	$0.937907\pi$
$614$	−6.52442e7	+	1.77144e7i	−0.281862	+	0.0765281i
$615$	−3.02123e8	−	1.70067e8i	−1.29885	−	0.731132i
$616$	−1.03877e8	+	4.03709e8i	−0.444404	+	1.72713i
$617$	−1.15319e8	−	1.99738e8i	−0.490958	−	0.850364i	0.508988	−	0.860774i	$-0.330020\pi$
$617$	−1.15319e8	−	1.99738e8i	−0.490958	−	0.850364i	−0.999946	+	0.0104097i	$0.996686\pi$
$618$	2.85133e8	−	2.93358e8i	1.20804	−	1.24289i
$619$	−1.15520e8	+	2.00086e8i	−0.487063	+	0.843617i	−0.999889	−	0.0148750i	$-0.995265\pi$
$619$	−1.15520e8	+	2.00086e8i	−0.487063	+	0.843617i	0.512827	+	0.858492i	$0.328598\pi$
$620$	−1.82779e6	−	2.75394e8i	−0.00766923	−	1.15552i
$621$	1.08542e8	−	6.74913e7i	0.453233	−	0.281821i
$622$	2.05191e8	−	2.06557e8i	0.852680	−	0.858358i
$623$	2.94470e8	+	1.70012e8i	1.21780	+	0.703099i
$624$	4.29224e6	+	1.77529e8i	0.0176657	+	0.730661i
$625$	1.25732e8	+	2.17774e8i	0.514998	+	0.892003i
$626$	−1.34549e6	+	5.08892e6i	−0.00548476	+	0.0207445i
$627$	−1.89462e8	+	3.36576e8i	−0.768632	+	1.36547i
$628$	1.69626e8	−	2.98357e8i	0.684880	−	1.20464i
$629$		−	1.99388e7i		−	0.0801210i
$630$	−4.17876e8	+	1.23297e8i	−1.67119	+	0.493097i
$631$		−	3.53642e8i		−	1.40759i	−0.710404	−	0.703794i	$-0.751488\pi$
$631$		−	3.53642e8i		−	1.40759i	0.710404	−	0.703794i	$-0.248512\pi$
$632$	3.25849e7	−	9.07973e6i	0.129082	−	0.0359685i
$633$	−2.17711e8	−	3.67771e8i	−0.858361	−	1.44999i
$634$	3.83021e7	+	1.01269e7i	0.150298	+	0.0397382i
$635$	7.84947e7	+	1.35957e8i	0.306563	+	0.530982i
$636$	−1.26895e8	−	2.11149e8i	−0.493256	−	0.820762i
$637$	−3.18187e8	−	1.83705e8i	−1.23102	−	0.710727i
$638$	−1.01199e8	+	1.01873e8i	−0.389685	+	0.392280i
$639$	378105.	+	1.73429e7i	0.00144914	+	0.0664690i
$640$	1.92532e8	+	1.83788e8i	0.734450	+	0.701097i
$641$	−1.11038e8	+	1.92324e8i	−0.421598	+	0.730230i	−0.996096	−	0.0882764i	$-0.971864\pi$
$641$	−1.11038e8	+	1.92324e8i	−0.421598	+	0.730230i	0.574498	+	0.818506i	$0.305197\pi$
$642$	2.28728e8	−	6.47863e7i	0.864397	−	0.244838i
$643$	−1.27203e8	−	2.20322e8i	−0.478482	−	0.828754i	0.521214	−	0.853426i	$-0.325479\pi$
$643$	−1.27203e8	−	2.20322e8i	−0.478482	−	0.828754i	−0.999696	+	0.0246716i	$0.992146\pi$
$644$	2.11031e8	−	1.23714e8i	0.790113	−	0.463191i
$645$	3.33961e6	+	3.06399e8i	0.0124456	+	1.14185i
$646$	−2.70113e7	+	7.33382e6i	−0.100196	+	0.0272040i
$647$		−	2.57184e8i		−	0.949578i	−0.880100	−	0.474789i	$-0.842524\pi$
$647$		−	2.57184e8i		−	0.949578i	0.880100	−	0.474789i	$-0.157476\pi$
$648$	−1.81828e8	+	2.02425e8i	−0.668244	+	0.743942i
$649$	−4.49211e8			−1.64330
$650$	−1.62796e6	−	5.99597e6i	−0.00592794	−	0.0218333i
$651$	5.38790e8	−	5.87257e6i	1.95288	−	0.0212856i
$652$	−2.46685e8	+	1.44615e8i	−0.890022	+	0.521761i
$653$	−2.28727e8	+	1.32055e8i	−0.821443	+	0.474260i	−0.850914	−	0.525305i	$-0.823951\pi$
$653$	−2.28727e8	+	1.32055e8i	−0.821443	+	0.474260i	0.0294709	+	0.999566i	$0.490618\pi$
$654$	1.00288e8	+	3.54065e8i	0.358522	+	1.26576i
$655$	−2.94880e8	−	1.70249e8i	−1.04935	−	0.605844i
$656$	−4.14364e8	+	5.50052e6i	−1.46781	+	0.0194846i
$657$	3.36618e8	−	7.33886e6i	1.18698	−	0.0258781i
$658$	−3.13552e8	−	3.11478e8i	−1.10061	−	1.09333i
$659$	−1.33669e8	+	2.31522e8i	−0.467062	+	0.808976i	−0.999292	−	0.0376242i	$-0.988021\pi$
$659$	−1.33669e8	+	2.31522e8i	−0.467062	+	0.808976i	0.532230	+	0.846600i	$0.321354\pi$
$660$	−1.56266e8	−	2.60022e8i	−0.543542	−	0.904436i
$661$	1.33226e8	−	7.69178e7i	0.461300	−	0.266331i	−0.251291	−	0.967912i	$-0.580855\pi$
$661$	1.33226e8	−	7.69178e7i	0.461300	−	0.266331i	0.712591	+	0.701580i	$0.247522\pi$
$662$	8.00015e7	−	3.02582e8i	0.275755	−	1.04296i
$663$	1.26212e7	−	7.47146e6i	0.0433074	−	0.0256369i
$664$	−1.34478e8	−	4.82607e8i	−0.459352	−	1.64850i
$665$	−7.72601e8			−2.62718
$666$	−9.72732e7	−	3.29676e8i	−0.329284	−	1.11600i
$667$	8.42638e7			0.283964
$668$	−2.64011e8	+	4.64371e8i	−0.885712	+	1.55788i
$669$	3.77382e8	+	2.12432e8i	1.26039	+	0.709481i
$670$	1.29383e8	+	3.42084e7i	0.430183	+	0.113739i
$671$	−1.32420e8	+	7.64525e7i	−0.438314	+	0.253060i
$672$	−3.57974e8	+	3.78218e8i	−1.17963	+	1.24634i
$673$	8.94805e7	−	1.54985e8i	0.293551	−	0.508445i	−0.681096	−	0.732194i	$-0.738496\pi$
$673$	8.94805e7	−	1.54985e8i	0.293551	−	0.508445i	0.974647	+	0.223749i	$0.0718297\pi$
$674$	−2.20832e8	−	2.19372e8i	−0.721246	−	0.716475i
$675$	4.48789e6	−	8.39569e6i	0.0145925	−	0.0272989i
$676$	955043.	+	1.43897e8i	0.00309160	+	0.465812i
$677$	−3.50282e7	−	2.02235e7i	−0.112889	−	0.0651765i	0.442492	−	0.896772i	$-0.354094\pi$
$677$	−3.50282e7	−	2.02235e7i	−0.112889	−	0.0651765i	−0.555381	+	0.831596i	$0.687428\pi$
$678$	6.80792e7	+	6.61703e7i	0.218436	+	0.212312i
$679$	−5.92758e7	+	3.42229e7i	−0.189351	+	0.109322i
$680$	5.47814e6	−	2.12903e7i	0.0174223	−	0.0677103i
$681$	1.96432e8	−	3.48959e8i	0.621972	−	1.10493i
$682$	9.83050e7	+	3.62069e8i	0.309901	+	1.14140i
$683$	1.35074e8			0.423945			0.211972	−	0.977276i	$-0.432011\pi$
$683$	1.35074e8			0.423945			0.211972	+	0.977276i	$0.432011\pi$
$684$	−4.10838e8	+	2.53038e8i	−1.28381	+	0.790710i
$685$			9.75360e7i			0.303454i
$686$	−1.37156e8	−	5.05162e8i	−0.424857	−	1.56480i
$687$	1.73337e8	−	1.02611e8i	0.534589	−	0.316463i
$688$	1.87320e8	+	3.14724e8i	0.575199	+	0.966418i
$689$	1.14457e8	+	1.98246e8i	0.349934	+	0.606103i
$690$	−4.36257e7	+	1.72592e8i	−0.132799	+	0.525380i
$691$	−4.49918e7	+	7.79282e7i	−0.136364	+	0.236189i	−0.926118	−	0.377235i	$-0.876875\pi$
$691$	−4.49918e7	+	7.79282e7i	−0.136364	+	0.236189i	0.789754	+	0.613424i	$0.210208\pi$
$692$	−1.04117e8	+	691023.i	−0.314197	+	0.00208533i
$693$	5.07426e8	−	3.07901e8i	1.52466	−	0.925148i
$694$	3.01334e8	+	2.99341e8i	0.901509	+	0.895545i
$695$	4.34422e8	+	2.50813e8i	1.29407	+	0.747130i
$696$	−1.72268e8	+	5.00317e7i	−0.510947	+	0.148394i
$697$	1.71133e7	+	2.96410e7i	0.0505399	+	0.0875377i
$698$	3.01244e8	+	7.96477e7i	0.885834	+	0.234211i
$699$	1.03122e8	−	1.12399e6i	0.301940	−	0.00329101i
$700$	9.00508e6	−	1.58391e7i	0.0262539	−	0.0461782i
$701$			1.53340e8i			0.445146i	0.974916	+	0.222573i	$0.0714456\pi$
$701$			1.53340e8i			0.445146i	−0.974916	+	0.222573i	$0.928554\pi$
$702$	1.72235e8	−	1.85110e8i	0.497862	−	0.535080i
$703$		−	6.09529e8i		−	1.75440i
$704$	−3.17571e8	−	1.75014e8i	−0.910171	−	0.501596i
$705$	3.21617e8	−	3.50549e6i	0.917850	−	0.0100042i
$706$	7.11710e7	−	2.69184e8i	0.202250	−	0.764953i
$707$	−5.46218e7	−	9.46077e7i	−0.154564	−	0.267712i
$708$	−4.90841e8	−	2.72025e8i	−1.38306	−	0.766493i
$709$	8.47014e7	+	4.89024e7i	0.237658	+	0.137212i	0.614100	−	0.789228i	$-0.289519\pi$
$709$	8.47014e7	+	4.89024e7i	0.237658	+	0.137212i	−0.376442	+	0.926440i	$0.622853\pi$
$710$	−1.71411e7	−	1.70277e7i	−0.0478920	−	0.0475752i
$711$	−4.22252e7	−	2.31666e7i	−0.117480	−	0.0644544i
$712$	−2.07048e8	+	2.11212e8i	−0.573630	+	0.585166i
$713$	1.10080e8	−	1.90665e8i	0.303698	−	0.526020i
$714$	4.16998e7	+	1.05404e7i	0.114562	+	0.0289575i
$715$	1.40950e8	+	2.44132e8i	0.385608	+	0.667893i
$716$	3.42490e7	−	2.00779e7i	0.0933058	−	0.0546990i
$717$	−2.67700e8	+	1.58472e8i	−0.726258	+	0.429926i
$718$	−4.49424e7	−	1.65528e8i	−0.121418	−	0.447197i
$719$		−	1.63539e8i		−	0.439981i	−0.975502	−	0.219990i	$-0.929397\pi$
$719$		−	1.63539e8i		−	0.439981i	0.975502	−	0.219990i	$-0.0706026\pi$
$720$	−1.32889e7	−	3.78748e8i	−0.0356035	−	1.01473i
$721$	−1.11480e9			−2.97435
$722$	−4.62521e8	+	1.25579e8i	−1.22891	+	0.333660i
$723$	9.79632e7	−	1.74031e8i	0.259208	−	0.460480i
$724$	6.98038e7	+	1.19072e8i	0.183935	+	0.313756i
$725$	5.43535e6	−	3.13810e6i	0.0142631	−	0.00823479i
$726$	2.19547e7	+	2.13391e7i	0.0573742	+	0.0557656i
$727$	8.68710e7	+	5.01550e7i	0.226085	+	0.130530i	0.608765	−	0.793351i	$-0.291665\pi$
$727$	8.68710e7	+	5.01550e7i	0.226085	+	0.130530i	−0.382680	+	0.923881i	$0.624999\pi$
$728$	3.38757e8	−	3.45570e8i	0.877999	−	0.895657i
$729$	3.86592e8	−	2.53172e7i	0.997863	−	0.0653482i
$730$	−3.30501e8	+	3.32701e8i	−0.849579	+	0.855236i
$731$	1.51249e7	−	2.61970e7i	0.0387204	−	0.0670656i
$732$	−1.90988e8	+	3.34952e6i	−0.486938	+	0.00853984i
$733$	7.41990e7	−	4.28388e7i	0.188402	−	0.108774i	−0.402832	−	0.915274i	$-0.631974\pi$
$733$	7.41990e7	−	4.28388e7i	0.188402	−	0.108774i	0.591234	+	0.806500i	$0.298641\pi$
$734$	−5.93896e8	−	1.57023e8i	−1.50183	−	0.397078i
$735$	6.83284e8	+	3.84626e8i	1.72083	+	0.968672i
$736$	5.84747e7	+	2.04590e8i	0.146668	+	0.513158i
$737$	−1.82315e8			−0.455429
$738$	4.27564e8	+	4.06608e8i	1.06373	+	1.01160i
$739$	6.69513e8			1.65892			0.829461	−	0.558565i	$-0.188648\pi$
$739$	6.69513e8			1.65892			0.829461	+	0.558565i	$0.188648\pi$
$740$	4.16186e8	+	2.36616e8i	1.02705	+	0.583915i
$741$	3.85832e8	−	2.28403e8i	0.948296	−	0.561368i
$742$	−1.71593e8	+	6.49001e8i	−0.420037	+	1.58867i
$743$	5.93263e8	−	3.42520e8i	1.44637	−	0.835065i	0.448111	−	0.893978i	$-0.352097\pi$
$743$	5.93263e8	−	3.42520e8i	1.44637	−	0.835065i	0.998263	+	0.0589133i	$0.0187635\pi$
$744$	−1.11840e8	+	4.55153e8i	−0.271567	+	1.10519i
$745$	−1.82758e8	+	3.16546e8i	−0.441986	+	0.765541i
$746$	−2.36667e8	+	2.38243e8i	−0.570060	+	0.573857i
$747$	−3.43114e8	+	6.25388e8i	−0.823146	+	1.50033i
$748$	198764.	+	2.99478e7i	0.000474933	+	0.0715583i
$749$	−5.61022e8	−	3.23906e8i	−1.33516	−	0.770857i
$750$	−1.13124e8	−	3.99383e8i	−0.268146	−	0.946686i
$751$	−2.62854e8	+	1.51759e8i	−0.620576	+	0.358290i	−0.777093	−	0.629385i	$-0.783307\pi$
$751$	−2.62854e8	+	1.51759e8i	−0.620576	+	0.358290i	0.156517	+	0.987675i	$0.449973\pi$
$752$	3.30356e8	−	1.96623e8i	0.776835	−	0.462362i
$753$	−2.52491e8	+	2.75205e6i	−0.591373	+	0.00644571i
$754$	1.60869e8	−	4.36774e7i	0.375283	−	0.101893i
$755$	−4.15061e8			−0.964431
$756$	7.40904e8	−	2.91580e7i	1.71473	−	0.0674827i
$757$			3.19853e8i			0.737330i	0.929562	+	0.368665i	$0.120185\pi$
$757$			3.19853e8i			0.737330i	−0.929562	+	0.368665i	$0.879815\pi$
$758$	1.07247e8	−	2.91186e7i	0.246251	−	0.0668594i
$759$	−2.64317e6	−	2.42502e8i	−0.00604505	−	0.554614i
$760$	1.67467e8	−	6.50845e8i	0.381495	−	1.48264i
$761$	−1.99215e8	−	3.45050e8i	−0.452030	−	0.782939i	0.546482	−	0.837471i	$-0.315967\pi$
$761$	−1.99215e8	−	3.45050e8i	−0.452030	−	0.782939i	−0.998512	+	0.0545318i	$0.982633\pi$
$762$	−7.28118e7	−	2.57061e8i	−0.164565	−	0.580994i
$763$	5.01400e8	−	8.68451e8i	1.12878	−	1.95511i
$764$	5.10494e8	−	3.38815e6i	1.14475	−	0.00759771i
$765$	−2.67600e7	+	1.62377e7i	−0.0597725	+	0.0362693i
$766$	−7.91522e7	+	7.96793e7i	−0.176107	+	0.177280i
$767$	4.51608e8	+	2.60736e8i	1.00087	+	0.577850i
$768$	−2.41020e8	−	3.83542e8i	−0.532072	−	0.846699i
$769$	3.05488e8	+	5.29121e8i	0.671762	+	1.16353i	0.977404	+	0.211380i	$0.0677957\pi$
$769$	3.05488e8	+	5.29121e8i	0.671762	+	1.16353i	−0.305642	+	0.952147i	$0.598871\pi$
$770$	−2.11310e8	+	7.99219e8i	−0.462858	+	1.75063i
$771$	−3.14290e8	−	5.30918e8i	−0.685754	−	1.15842i
$772$	−5.26295e8	−	2.99217e8i	−1.14387	−	0.650331i
$773$			5.34595e8i			1.15741i	0.815537	+	0.578704i	$0.196441\pi$
$773$			5.34595e8i			1.15741i	−0.815537	+	0.578704i	$0.803559\pi$
$774$	1.22276e8	−	5.06941e8i	0.263705	−	1.09329i
$775$		−	1.63982e7i		−	0.0352282i
$776$	−1.59811e7	−	5.73524e7i	−0.0341997	−	0.122734i
$777$	−4.59466e8	+	8.16236e8i	−0.979469	+	1.74001i
$778$	−2.92413e8	−	7.73128e7i	−0.620953	−	0.164177i
$779$	5.23153e8	+	9.06128e8i	1.10667	+	1.91680i
$780$	6.17527e6	+	3.52111e8i	0.0130128	+	0.741986i
$781$	2.85049e7	+	1.64573e7i	0.0598366	+	0.0345467i
$782$	1.23856e7	−	1.24681e7i	0.0258998	−	0.0260723i
$783$	2.25252e8	+	1.20408e8i	0.469228	+	0.250824i
$784$	9.37130e8	−	1.24400e7i	1.94470	−	0.0258151i
$785$	3.40310e8	−	5.89433e8i	0.703502	−	1.21850i
$786$	4.15538e8	+	4.03887e8i	0.855743	+	0.831749i
$787$	−6.01819e7	−	1.04238e8i	−0.123464	−	0.213847i	0.797667	−	0.603098i	$-0.206067\pi$
$787$	−6.01819e7	−	1.04238e8i	−0.123464	−	0.213847i	−0.921132	+	0.389251i	$0.872734\pi$
$788$	1.78047e8	+	3.03713e8i	0.363878	+	0.620705i
$789$	−4.11208e8	−	2.31473e8i	−0.837203	−	0.471269i
$790$	6.47380e7	−	1.75770e7i	0.131304	−	0.0356502i
$791$		−	2.58711e8i		−	0.522740i
$792$	1.49390e8	+	4.94199e8i	0.300708	+	0.994779i
$793$	1.77502e8			0.355945
$794$	−4.89916e6	−	1.80442e7i	−0.00978723	−	0.0360475i
$795$	−2.48863e8	−	4.20395e8i	−0.495290	−	0.836674i
$796$	−3.60376e8	−	6.14732e8i	−0.714524	−	1.21884i
$797$	−1.11652e8	+	6.44622e7i	−0.220542	+	0.127330i	−0.606201	−	0.795311i	$-0.707307\pi$
$797$	−1.11652e8	+	6.44622e7i	−0.220542	+	0.127330i	0.385659	+	0.922641i	$0.373974\pi$
$798$	1.27477e9	+	3.22220e8i	2.50855	+	0.634079i
$799$	−2.74982e7	−	1.58761e7i	−0.0539093	−	0.0311246i
$800$	1.13911e7	+	1.10192e7i	0.0222482	+	0.0215219i
$801$	4.21025e8	−	9.17907e6i	0.819239	−	0.0178608i
$802$	−4.37581e8	−	4.34686e8i	−0.848273	−	0.842661i
$803$	3.19430e8	−	5.53269e8i	0.616920	−	1.06854i
$804$	−1.99211e8	−	1.10403e8i	−0.383306	−	0.212429i
$805$	4.20120e8	−	2.42556e8i	0.805352	−	0.464970i
$806$	1.11327e8	−	4.21060e8i	0.212615	−	0.804154i
$807$	2.74673e6	+	2.52004e8i	0.00522632	+	0.479498i
$808$	9.15379e7	−	2.55069e7i	0.173527	−	0.0483530i
$809$	7.79015e8			1.47130			0.735648	−	0.677364i	$-0.236878\pi$
$809$	7.79015e8			1.47130			0.735648	+	0.677364i	$0.236878\pi$
$810$	−3.63243e8	+	3.99032e8i	−0.683506	+	0.750848i
$811$	9.75630e8			1.82904			0.914519	−	0.404544i	$-0.132570\pi$
$811$	9.75630e8			1.82904			0.914519	+	0.404544i	$0.132570\pi$
$812$	4.24956e8	+	2.41602e8i	0.793735	+	0.451266i
$813$	6.91708e6	+	6.34620e8i	0.0128722	+	1.18098i
$814$	−6.30529e8	−	1.66709e8i	−1.16905	−	0.309091i
$815$	−4.91100e8	+	2.83537e8i	−0.907188	+	0.523765i
$816$	−1.79180e7	+	3.28436e7i	−0.0329777	+	0.0604477i
$817$	4.62368e8	−	8.00845e8i	0.847855	−	1.46853i
$818$	−3.89892e8	−	3.87312e8i	−0.712334	−	0.707622i
$819$	−6.88849e8	+	1.50181e7i	−1.25393	+	0.0273378i
$820$	−8.21790e8	+	5.45422e6i	−1.49046	+	0.00989217i
$821$	6.77546e8	+	3.91181e8i	1.22436	+	0.706885i	0.965845	−	0.259122i	$-0.0834332\pi$
$821$	6.77546e8	+	3.91181e8i	1.22436	+	0.706885i	0.258516	+	0.966007i	$0.416767\pi$
$822$	4.06782e7	−	1.60931e8i	0.0732396	−	0.289751i
$823$	−1.73224e8	+	1.00011e8i	−0.310749	+	0.179411i	−0.647261	−	0.762268i	$-0.724086\pi$
$823$	−1.73224e8	+	1.00011e8i	−0.310749	+	0.179411i	0.336513	+	0.941679i	$0.390752\pi$
$824$	2.41642e8	−	9.39119e8i	0.431907	−	1.67857i
$825$	−9.20162e6	−	1.55439e7i	−0.0163871	−	0.0276821i
$826$	4.00695e8	+	1.47581e9i	0.711008	+	2.61873i
$827$	−4.99277e8			−0.882724			−0.441362	−	0.897329i	$-0.645505\pi$
$827$	−4.99277e8			−0.882724			−0.441362	+	0.897329i	$0.645505\pi$
$828$	1.43962e8	−	2.66577e8i	0.253604	−	0.469604i
$829$		−	1.97967e8i		−	0.347480i	−0.984792	−	0.173740i	$-0.944415\pi$
$829$		−	1.97967e8i		−	0.347480i	0.984792	−	0.173740i	$-0.0555852\pi$
$830$	−2.60328e8	−	9.58819e8i	−0.455288	−	1.67688i
$831$	−8.49702e7	−	4.78304e7i	−0.148069	−	0.0833492i
$832$	2.17682e8	+	3.60276e8i	0.377967	+	0.625555i
$833$	−3.87035e7	−	6.70365e7i	−0.0669600	−	0.115978i
$834$	−6.12177e8	−	5.95013e8i	−1.05531	−	1.02572i
$835$	−5.29666e8	+	9.17409e8i	−0.909794	+	1.57581i
$836$	6.07622e6	+	9.15506e8i	0.0103995	+	1.56690i
$837$	5.66714e8	−	3.52384e8i	0.966468	−	0.600952i
$838$	5.39614e8	+	5.36045e8i	0.916962	+	0.910896i
$839$	−5.73383e8	−	3.31043e8i	−0.970865	−	0.560529i	−0.0713654	−	0.997450i	$-0.522736\pi$
$839$	−5.73383e8	−	3.31043e8i	−0.970865	−	0.560529i	−0.899500	+	0.436921i	$0.856069\pi$
$840$	−7.14870e8	+	7.45326e8i	−1.20612	+	1.25750i
$841$	−2.13218e8	−	3.69304e8i	−0.358456	−	0.620864i
$842$	−2.45517e8	−	6.49136e7i	−0.411287	−	0.108742i
$843$	7.05043e7	−	1.25250e8i	0.117688	−	0.209072i
$844$	−8.80669e8	−	5.00691e8i	−1.46482	−	0.832803i
$845$			2.85371e8i			0.472977i
$846$	−5.32119e8	−	1.28349e8i	−0.878816	−	0.211974i
$847$		−	8.34310e7i		−	0.137302i
$848$	−5.09529e8	−	2.85227e8i	−0.835567	−	0.467738i
$849$	1.10685e8	+	1.86976e8i	0.180869	+	0.305536i
$850$	334592.	−	1.26550e6i	0.000544827	−	0.00206065i
$851$	1.91360e8	+	3.31446e8i	0.310501	+	0.537804i
$852$	2.11807e7	+	3.52440e7i	0.0342469	+	0.0569857i
$853$	7.37499e8	+	4.25795e8i	1.18827	+	0.686047i	0.957913	−	0.287060i	$-0.0926779\pi$
$853$	7.37499e8	+	4.25795e8i	1.18827	+	0.686047i	0.230355	+	0.973107i	$0.426011\pi$
$854$	3.69291e8	+	3.66848e8i	0.592918	+	0.588996i
$855$	−8.18054e8	+	4.96387e8i	−1.30883	+	0.794186i
$856$	3.94467e8	−	4.02400e8i	0.628911	−	0.641560i
$857$	1.28480e8	−	2.22535e8i	0.204124	−	0.353554i	−0.745729	−	0.666249i	$-0.767899\pi$
$857$	1.28480e8	−	2.22535e8i	0.204124	−	0.353554i	0.949853	+	0.312696i	$0.101232\pi$
$858$	−1.30745e8	−	4.61595e8i	−0.206997	−	0.730801i
$859$	−3.23583e8	−	5.60462e8i	−0.510512	−	0.884233i	−0.999926	−	0.0121813i	$-0.996122\pi$
$859$	−3.23583e8	−	5.60462e8i	−0.510512	−	0.884233i	0.489414	−	0.872052i	$-0.337211\pi$
$860$	3.67327e8	+	6.26589e8i	0.577508	+	0.985116i
$861$	−1.75241e7	−	1.60778e9i	−0.0274552	−	2.51893i
$862$	2.80576e8	+	1.03340e9i	0.438056	+	1.61341i
$863$			2.58107e8i			0.401575i	0.979635	+	0.200788i	$0.0643501\pi$
$863$			2.58107e8i			0.401575i	−0.979635	+	0.200788i	$0.935650\pi$
$864$	−1.36034e8	+	6.30464e8i	−0.210914	+	0.977505i
$865$	−2.06481e8			−0.319030
$866$	3.25494e8	−	8.83745e7i	0.501174	−	0.136073i
$867$	−6.48586e8	+	7.06930e6i	−0.995199	+	0.0108472i
$868$	1.10183e9	−	6.45930e8i	1.68483	−	0.987703i
$869$	−7.91420e7	+	4.56927e7i	−0.120600	+	0.0696285i
$870$	−3.42279e8	+	9.69495e7i	−0.519784	+	0.147227i
$871$	1.83288e8	+	1.05822e8i	0.277383	+	0.160147i
$872$	6.22907e8	+	6.10627e8i	0.939451	+	0.920929i
$873$	−4.07752e7	+	7.43202e7i	−0.0612849	+	0.111703i
$874$	3.78629e8	−	3.81150e8i	0.567126	−	0.570902i
$875$	−5.65576e8	+	9.79606e8i	−0.844242	+	1.46227i
$876$	6.84071e8	−	4.11109e8i	1.01763	−	0.611567i
$877$	4.28121e8	−	2.47176e8i	0.634699	−	0.366444i	−0.147871	−	0.989007i	$-0.547242\pi$
$877$	4.28121e8	−	2.47176e8i	0.634699	−	0.366444i	0.782570	+	0.622563i	$0.213909\pi$
$878$	−8.30894e8	−	2.19685e8i	−1.22761	−	0.324576i
$879$	3.00644e8	−	1.77974e8i	0.442677	−	0.262053i
$880$	−6.27465e8	−	3.51246e8i	−0.920750	−	0.515422i
$881$	1.58137e8			0.231263			0.115632	−	0.993292i	$-0.463111\pi$
$881$	1.58137e8			0.231263			0.115632	+	0.993292i	$0.463111\pi$
$882$	−9.66984e8	−	9.19589e8i	−1.40933	−	1.34026i
$883$	−1.08852e9			−1.58109			−0.790543	−	0.612406i	$-0.790202\pi$
$883$	−1.08852e9			−1.58109			−0.790543	+	0.612406i	$0.790202\pi$
$884$	1.71828e7	−	3.02230e7i	0.0248735	−	0.0437502i
$885$	−9.69797e8	−	5.45907e8i	−1.39911	−	0.787569i
$886$	6.49107e6	−	2.45506e7i	0.00933286	−	0.0352989i
$887$	2.48354e8	−	1.43387e8i	0.355877	−	0.205465i	−0.311394	−	0.950281i	$-0.600796\pi$
$887$	2.48354e8	−	1.43387e8i	0.355877	−	0.205465i	0.667270	+	0.744815i	$0.267463\pi$
$888$	−5.88011e8	−	5.63983e8i	−0.839743	−	0.805429i
$889$	−3.64030e8	+	6.30519e8i	−0.518122	+	0.897414i
$890$	−4.13373e8	+	4.16126e8i	−0.586371	+	0.590276i
$891$	3.39456e8	−	6.52030e8i	0.479899	−	0.921795i
$892$	1.02650e9	−	6.81289e6i	1.44632	−	0.00959924i
$893$	−8.40622e8	−	4.85333e8i	−1.18045	−	0.681531i
$894$	4.33563e8	−	4.46071e8i	0.606792	−	0.624297i
$895$	6.81827e7	−	3.93653e7i	0.0951054	−	0.0549092i
$896$	−2.91706e8	+	1.19944e9i	−0.405529	+	1.66746i
$897$	−1.38099e8	+	2.45331e8i	−0.191343	+	0.339918i
$898$	−2.08921e8	+	5.67240e7i	−0.288505	+	0.0783318i
$899$	4.39956e8			0.605522
$900$	−641574.	−	2.25566e7i	−0.000880074	−	0.0309418i
$901$			4.82284e7i			0.0659369i
$902$	1.08043e9	−	2.93347e8i	1.47224	−	0.399726i
$903$	−1.22285e9	+	7.23897e8i	−1.66077	+	0.983135i
$904$	2.17940e8	+	5.60775e7i	0.295007	+	0.0759073i
$905$	1.36859e8	+	2.37047e8i	0.184641	+	0.319808i
$906$	6.84837e8	+	1.73105e8i	0.920879	+	0.232768i
$907$	−2.73502e8	+	4.73720e8i	−0.366555	+	0.634892i	−0.989024	−	0.147752i	$-0.952796\pi$
$907$	−2.73502e8	+	4.73720e8i	−0.366555	+	0.634892i	0.622469	+	0.782644i	$0.286130\pi$
$908$	−6.29977e6	−	9.49188e8i	−0.00841525	−	1.26793i
$909$	−1.18620e8	−	6.50797e7i	−0.157930	−	0.0866471i
$910$	6.76330e8	−	6.80834e8i	0.897500	−	0.903477i
$911$	6.62466e8	+	3.82475e8i	0.876210	+	0.505880i	0.869407	−	0.494097i	$-0.164501\pi$
$911$	6.62466e8	+	3.82475e8i	0.876210	+	0.505880i	0.00680322	+	0.999977i	$0.497834\pi$
$912$	−5.47756e8	+	1.00403e9i	−0.722108	+	1.32362i
$913$	6.76743e8	+	1.17215e9i	0.889224	+	1.54018i
$914$	−1.93439e8	+	7.31626e8i	−0.253341	+	0.958188i
$915$	−3.78789e8	+	4.12864e6i	−0.494464	+	0.00538944i
$916$	2.35984e8	−	4.15074e8i	0.307041	−	0.540056i
$917$		−	1.57911e9i		−	2.04788i
$918$	5.09251e7	−	1.56312e7i	0.0658270	−	0.0202052i
$919$			9.34657e8i			1.20422i	0.798413	+	0.602110i	$0.205673\pi$
$919$			9.34657e8i			1.20422i	−0.798413	+	0.602110i	$0.794327\pi$
$920$	1.13267e8	+	4.06488e8i	0.145459	+	0.522017i
$921$	2.28157e8	−	2.48682e6i	0.292049	−	0.00318321i
$922$	−1.25817e9	−	3.32655e8i	−1.60527	−	0.424426i
$923$	−1.91047e7	−	3.30903e7i	−0.0242960	−	0.0420819i
$924$	6.81976e8	−	1.23056e9i	0.864476	−	1.55986i
$925$	2.46870e7	+	1.42530e7i	0.0311920	+	0.0180087i
$926$	1.32086e8	−	1.32965e8i	0.166350	−	0.167458i
$927$	−1.18039e9	+	7.16248e8i	−1.48179	+	0.899133i
$928$	−2.95640e8	+	3.05617e8i	−0.369929	+	0.382414i
$929$	−9.00685e7	+	1.56003e8i	−0.112338	+	0.194575i	−0.916712	−	0.399548i	$-0.869167\pi$
$929$	−9.00685e7	+	1.56003e8i	−0.112338	+	0.194575i	0.804375	+	0.594122i	$0.202501\pi$
$930$	−2.27777e8	+	9.01133e8i	−0.283179	+	1.12031i
$931$	−1.18317e9	−	2.04931e9i	−1.46622	−	2.53956i
$932$	2.10886e8	−	1.23628e8i	0.260495	−	0.152711i
$933$	−8.45581e8	+	5.00563e8i	−1.04114	+	0.616331i
$934$	6.35383e8	−	1.72512e8i	0.779822	−	0.211729i
$935$			5.93915e7i			0.0726590i
$936$	1.36662e8	−	5.83547e8i	0.166656	−	0.711620i
$937$	4.06402e7			0.0494011			0.0247006	−	0.999695i	$-0.492137\pi$
$937$	4.06402e7			0.0494011			0.0247006	+	0.999695i	$0.492137\pi$
$938$	1.62625e8	+	5.98967e8i	0.197051	+	0.725762i
$939$	8.71444e6	−	1.54811e7i	0.0105255	−	0.0186984i
$940$	6.57710e8	−	3.85572e8i	0.791865	−	0.464218i
$941$	9.22940e8	−	5.32860e8i	1.10766	−	0.639505i	0.169434	−	0.985541i	$-0.445806\pi$
$941$	9.22940e8	−	5.32860e8i	1.10766	−	0.639505i	0.938221	+	0.346036i	$0.112473\pi$
$942$	−8.07328e8	+	8.30617e8i	−0.965822	+	0.993684i
$943$	−5.68954e8	−	3.28486e8i	−0.678488	−	0.391725i
$944$	−1.33009e9	+	1.76564e7i	−1.58112	+	0.0209887i
$945$	1.46966e9	−	4.80711e7i	1.74149	−	0.0569624i
$946$	−7.01976e8	−	6.97333e8i	−0.829180	−	0.823695i
$947$	−8.60234e7	+	1.48997e8i	−0.101290	+	0.175440i	−0.912216	−	0.409709i	$-0.865630\pi$
$947$	−8.60234e7	+	1.48997e8i	−0.101290	+	0.175440i	0.810926	+	0.585148i	$0.198964\pi$
$948$	−1.14146e8	+	2.00188e6i	−0.133979	+	0.00234970i
$949$	−6.42269e8	+	3.70814e8i	−0.751482	+	0.433868i
$950$	1.02285e7	−	3.86864e7i	0.0119300	−	0.0451219i
$951$	−1.16519e8	−	6.55897e7i	−0.135474	−	0.0762595i
$952$	9.82113e7	−	2.73664e7i	0.113828	−	0.0317181i
$953$	4.36004e8			0.503747			0.251873	−	0.967760i	$-0.418953\pi$
$953$	4.36004e8			0.503747			0.251873	+	0.967760i	$0.418953\pi$
$954$	2.35287e8	+	7.97428e8i	0.270990	+	0.918431i
$955$	1.01239e9			1.16236
$956$	−3.64452e8	+	6.41037e8i	−0.417125	+	0.733685i
$957$	4.17036e8	−	2.46875e8i	0.475815	−	0.281670i
$958$	4.65541e8	+	1.23087e8i	0.529494	+	0.139996i
$959$	−3.91735e8	+	2.26168e8i	−0.444157	+	0.256434i
$960$	−4.72915e8	−	7.63766e8i	−0.534526	−	0.863270i
$961$	1.30997e8	−	2.26894e8i	0.147602	−	0.255654i
$962$	5.37131e8	+	5.33578e8i	0.603330	+	0.599339i
$963$	−8.02134e8	+	1.74879e7i	−0.898190	+	0.0195821i
$964$	−3.14178e6	−	4.73372e8i	−0.00350707	−	0.528411i
$965$	−1.03975e9	−	6.00298e8i	−1.15703	−	0.668013i
$966$	−7.94345e8	+	2.24996e8i	−0.881206	+	0.249599i
$967$	9.25340e8	−	5.34246e8i	1.02335	−	0.590829i	0.108274	−	0.994121i	$-0.465468\pi$
$967$	9.25340e8	−	5.34246e8i	1.02335	−	0.590829i	0.915071	+	0.403293i	$0.132134\pi$
$968$	7.02829e7	+	1.80843e7i	0.0774861	+	0.0199377i
$969$	9.44580e7	−	1.02955e6i	0.103817	−	0.00113156i
$970$	−3.09370e7	−	1.13945e8i	−0.0338972	−	0.124847i
$971$	1.30528e9			1.42575			0.712877	−	0.701289i	$-0.247392\pi$
$971$	1.30528e9			1.42575			0.712877	+	0.701289i	$0.247392\pi$
$972$	7.65759e8	−	5.06896e8i	0.833860	−	0.551975i
$973$			2.32637e9i			2.52545i
$974$	3.10516e8	+	1.14367e9i	0.336053	+	1.23772i
$975$	228540.	+	2.09678e7i	0.000246574	+	0.0226224i
$976$	−3.89082e8	+	2.31576e8i	−0.418496	+	0.249083i
$977$	−4.89104e8	−	8.47153e8i	−0.524466	−	0.908402i	−0.999594	−	0.0284853i	$-0.990932\pi$
$977$	−4.89104e8	−	8.47153e8i	−0.524466	−	0.908402i	0.475128	−	0.879917i	$-0.342402\pi$
$978$	9.28551e8	−	2.63009e8i	0.992634	−	0.281160i
$979$	3.99527e8	−	6.92000e8i	0.425792	−	0.737493i
$980$	1.85857e9	−	1.23353e7i	1.97470	−	0.0131061i
$981$	−2.70709e7	−	1.24169e9i	−0.0286745	−	1.31524i
$982$	−9.45772e7	−	9.39516e7i	−0.0998739	−	0.0992133i
$983$	−4.01669e8	−	2.31904e8i	−0.422871	−	0.244145i	0.273434	−	0.961891i	$-0.411841\pi$
$983$	−4.01669e8	−	2.31904e8i	−0.422871	−	0.244145i	−0.696305	+	0.717746i	$0.745174\pi$
$984$	1.35820e9	+	3.33735e8i	1.42554	+	0.350281i
$985$	3.49084e8	+	6.04631e8i	0.365276	+	0.632677i
$986$	3.39527e7	+	8.97695e6i	0.0354196	+	0.00936479i
$987$	7.59851e8	+	1.28359e9i	0.790273	+	1.33498i
$988$	5.25280e8	−	9.23918e8i	0.544653	−	0.957994i
$989$			5.80638e8i			0.600228i
$990$	2.89747e8	+	9.82003e8i	0.298616	+	1.01206i
$991$		−	1.33655e9i		−	1.37330i	−0.726989	−	0.686649i	$-0.759081\pi$
$991$		−	1.33655e9i		−	1.37330i	0.726989	−	0.686649i	$-0.240919\pi$
$992$	3.05306e8	+	1.06820e9i	0.312753	+	1.09425i
$993$	−5.18152e8	+	9.20490e8i	−0.529187	+	0.940094i
$994$	2.86415e7	−	1.08328e8i	0.0291633	−	0.110302i
$995$	−7.06564e8	−	1.22380e9i	−0.717269	−	1.24235i
$996$	2.96493e7	+	1.69059e9i	0.0300080	+	1.71104i
$997$	−7.53024e8	−	4.34759e8i	−0.759842	−	0.438695i	0.0693969	−	0.997589i	$-0.477893\pi$
$997$	−7.53024e8	−	4.34759e8i	−0.759842	−	0.438695i	−0.829239	+	0.558894i	$0.811226\pi$
$998$	−1.74858e7	−	1.73701e7i	−0.0175911	−	0.0174747i
$999$	3.79248e7	+	1.15946e9i	0.0380388	+	1.16294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.p.b.43.6	✓	136
8.3	odd	2	inner	72.7.p.b.43.42	yes	136
9.4	even	3	inner	72.7.p.b.67.42	yes	136
72.67	odd	6	inner	72.7.p.b.67.6	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.p.b.43.6	✓	136	1.1	even	1	trivial
72.7.p.b.43.42	yes	136	8.3	odd	2	inner
72.7.p.b.67.6	yes	136	72.67	odd	6	inner
72.7.p.b.67.42	yes	136	9.4	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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.72049 + 2.09618i) q^{2} +(26.9984 - 0.294271i) q^{3} +(55.2120 - 32.3671i) q^{4} +(109.916 - 63.4600i) q^{5} +(-207.824 + 58.8655i) q^{6} +(509.750 + 294.305i) q^{7} +(-358.417 + 365.625i) q^{8} +(728.827 - 15.8897i) q^{9} +O(q^{10})\)	\(q+(-7.72049 + 2.09618i) q^{2} +(26.9984 - 0.294271i) q^{3} +(55.2120 - 32.3671i) q^{4} +(109.916 - 63.4600i) q^{5} +(-207.824 + 58.8655i) q^{6} +(509.750 + 294.305i) q^{7} +(-358.417 + 365.625i) q^{8} +(728.827 - 15.8897i) q^{9} +(-715.581 + 720.346i) q^{10} +(691.611 - 1197.91i) q^{11} +(1481.11 - 890.108i) q^{12} +(-1390.60 + 802.866i) q^{13} +(-4552.44 - 1203.65i) q^{14} +(2948.88 - 1745.66i) q^{15} +(2000.74 - 3574.11i) q^{16} -338.300 q^{17} +(-5593.59 + 1650.43i) q^{18} -10341.9 q^{19} +(4014.66 - 7061.42i) q^{20} +(13849.0 + 7795.75i) q^{21} +(-2828.55 + 10698.2i) q^{22} +(5623.63 - 3246.80i) q^{23} +(-9569.08 + 9976.76i) q^{24} +(241.831 - 418.863i) q^{25} +(9053.20 - 9113.48i) q^{26} +(19672.5 - 643.468i) q^{27} +(37670.2 - 250.017i) q^{28} +(11237.9 + 6488.21i) q^{29} +(-19107.6 + 19658.8i) q^{30} +(29361.9 - 16952.1i) q^{31} +(-7954.67 + 31787.8i) q^{32} +(18319.9 - 32545.0i) q^{33} +(2611.84 - 709.140i) q^{34} +74706.2 q^{35} +(39725.7 - 24467.3i) q^{36} +58938.1i q^{37} +(79844.3 - 21678.4i) q^{38} +(-37307.8 + 22085.3i) q^{39} +(-16193.1 + 62933.1i) q^{40} +(-50586.0 - 87617.5i) q^{41} +(-123263. - 31156.8i) q^{42} +(-44708.4 + 77437.2i) q^{43} +(-587.536 - 88524.3i) q^{44} +(79101.3 - 47997.8i) q^{45} +(-36611.3 + 36855.1i) q^{46} +(81283.4 + 46929.0i) q^{47} +(52964.9 - 97084.0i) q^{48} +(114406. + 198157. i) q^{49} +(-989.039 + 3740.75i) q^{50} +(-9133.56 + 99.5519i) q^{51} +(-50791.6 + 89337.7i) q^{52} -142561. i q^{53} +(-150532. + 46205.0i) q^{54} -175558. i q^{55} +(-290308. + 80893.8i) q^{56} +(-279214. + 3043.31i) q^{57} +(-100363. - 26535.4i) q^{58} +(-162378. - 281247. i) q^{59} +(106311. - 191828. i) q^{60} +(-95732.7 - 55271.3i) q^{61} +(-191154. + 192427. i) q^{62} +(376196. + 206397. i) q^{63} +(-5219.13 - 262092. i) q^{64} +(-101900. + 176495. i) q^{65} +(-73218.1 + 289666. i) q^{66} +(-65902.4 - 114146. i) q^{67} +(-18678.2 + 10949.8i) q^{68} +(150874. - 89313.4i) q^{69} +(-576769. + 156598. i) q^{70} +23795.6i q^{71} +(-255414. + 272172. i) q^{72} +461863. q^{73} +(-123545. - 455031. i) q^{74} +(6405.79 - 11379.8i) q^{75} +(-570995. + 334737. i) q^{76} +(705098. - 407089. i) q^{77} +(241740. - 248713. i) q^{78} +(-57215.7 - 33033.5i) q^{79} +(-6900.38 - 519818. i) q^{80} +(530936. - 23161.7i) q^{81} +(574211. + 570413. i) q^{82} +(-489251. + 847408. i) q^{83} +(1.01696e6 - 17835.3i) q^{84} +(-37184.6 + 21468.5i) q^{85} +(182848. - 691571. i) q^{86} +(305315. + 171864. i) q^{87} +(190099. + 682219. i) q^{88} +577675. q^{89} +(-510088. + 536378. i) q^{90} -945148. q^{91} +(205402. - 361283. i) q^{92} +(787737. - 466321. i) q^{93} +(-725920. - 191930. i) q^{94} +(-1.13673e6 + 656294. i) q^{95} +(-205409. + 860561. i) q^{96} +(-58141.9 + 100705. i) q^{97} +(-1.29864e6 - 1.29005e6i) q^{98} +(485030. - 884055. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9}+O(q^{10}) \) 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9	\( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9} - 132 q^{10} + 2336 q^{11} - 2796 q^{12} + 2346 q^{14} + 8191 q^{16} - 3460 q^{17} + 6306 q^{18} - 4972 q^{19} + 3588 q^{20} - 18577 q^{22} - 50553 q^{24} + 224998 q^{25} + 38352 q^{26} - 27792 q^{27} - 8196 q^{28} - 107130 q^{30} - 191717 q^{32} - 42852 q^{33} + 6125 q^{34} - 62508 q^{35} + 87339 q^{36} + 250223 q^{38} - 27126 q^{40} - 145084 q^{41} - 107478 q^{42} + 74912 q^{43} - 1118662 q^{44} + 22296 q^{46} + 690903 q^{48} + 1210102 q^{49} - 844727 q^{50} + 830778 q^{51} + 62952 q^{52} + 860925 q^{54} - 587718 q^{56} + 748686 q^{57} + 221136 q^{58} + 98960 q^{59} - 960810 q^{60} - 1062312 q^{62} - 784646 q^{64} - 62502 q^{65} + 802866 q^{66} + 596624 q^{67} + 681953 q^{68} + 86334 q^{70} - 2246001 q^{72} - 1186276 q^{73} - 782586 q^{74} + 3451098 q^{75} - 273235 q^{76} - 3340578 q^{78} + 2446320 q^{80} - 621690 q^{81} - 3119398 q^{82} - 179350 q^{83} - 227136 q^{84} + 917117 q^{86} - 1184629 q^{88} + 253712 q^{89} - 4940256 q^{90} - 470604 q^{91} + 1731894 q^{92} + 2055426 q^{94} + 8439666 q^{96} - 1822756 q^{97} + 6531850 q^{98} + 2509818 q^{99}+O(q^{100}) \) 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9 - 132 * q^10 + 2336 * q^11 - 2796 * q^12 + 2346 * q^14 + 8191 * q^16 - 3460 * q^17 + 6306 * q^18 - 4972 * q^19 + 3588 * q^20 - 18577 * q^22 - 50553 * q^24 + 224998 * q^25 + 38352 * q^26 - 27792 * q^27 - 8196 * q^28 - 107130 * q^30 - 191717 * q^32 - 42852 * q^33 + 6125 * q^34 - 62508 * q^35 + 87339 * q^36 + 250223 * q^38 - 27126 * q^40 - 145084 * q^41 - 107478 * q^42 + 74912 * q^43 - 1118662 * q^44 + 22296 * q^46 + 690903 * q^48 + 1210102 * q^49 - 844727 * q^50 + 830778 * q^51 + 62952 * q^52 + 860925 * q^54 - 587718 * q^56 + 748686 * q^57 + 221136 * q^58 + 98960 * q^59 - 960810 * q^60 - 1062312 * q^62 - 784646 * q^64 - 62502 * q^65 + 802866 * q^66 + 596624 * q^67 + 681953 * q^68 + 86334 * q^70 - 2246001 * q^72 - 1186276 * q^73 - 782586 * q^74 + 3451098 * q^75 - 273235 * q^76 - 3340578 * q^78 + 2446320 * q^80 - 621690 * q^81 - 3119398 * q^82 - 179350 * q^83 - 227136 * q^84 + 917117 * q^86 - 1184629 * q^88 + 253712 * q^89 - 4940256 * q^90 - 470604 * q^91 + 1731894 * q^92 + 2055426 * q^94 + 8439666 * q^96 - 1822756 * q^97 + 6531850 * q^98 + 2509818 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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