LMFDB - Embedded newform 74.8.b.a.73.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,8,Mod(73,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("74.73");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	74.b (of order $2$, degree $1$, 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:	$23.1164918858$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			73.8
Character	$\chi$	$=$	74.73
Dual form			74.8.b.a.73.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-8.00000i q^{2} +14.3858 q^{3} -64.0000 q^{4} +303.371i q^{5} -115.086i q^{6} +76.6627 q^{7} +512.000i q^{8} -1980.05 q^{9} +2426.97 q^{10} +969.796 q^{11} -920.689 q^{12} -10523.6i q^{13} -613.301i q^{14} +4364.23i q^{15} +4096.00 q^{16} -6840.58i q^{17} +15840.4i q^{18} -56955.9i q^{19} -19415.8i q^{20} +1102.85 q^{21} -7758.37i q^{22} -30093.0i q^{23} +7365.51i q^{24} -13909.1 q^{25} -84189.1 q^{26} -59946.2 q^{27} -4906.41 q^{28} +114922. i q^{29} +34913.8 q^{30} -110397. i q^{31} -32768.0i q^{32} +13951.3 q^{33} -54724.6 q^{34} +23257.3i q^{35} +126723. q^{36} +(-190668. - 242028. i) q^{37} -455647. q^{38} -151391. i q^{39} -155326. q^{40} -384466. q^{41} -8822.81i q^{42} -48082.4i q^{43} -62067.0 q^{44} -600690. i q^{45} -240744. q^{46} +329501. q^{47} +58924.1 q^{48} -817666. q^{49} +111273. i q^{50} -98406.9i q^{51} +673513. i q^{52} -1.29994e6 q^{53} +479569. i q^{54} +294208. i q^{55} +39251.3i q^{56} -819354. i q^{57} +919376. q^{58} +316983. i q^{59} -279310. i q^{60} -1.54587e6i q^{61} -883178. q^{62} -151796. q^{63} -262144. q^{64} +3.19257e6 q^{65} -111610. i q^{66} +4.60848e6 q^{67} +437797. i q^{68} -432910. i q^{69} +186058. q^{70} +2.95688e6 q^{71} -1.01379e6i q^{72} +2.87820e6 q^{73} +(-1.93622e6 + 1.52535e6i) q^{74} -200093. q^{75} +3.64518e6i q^{76} +74347.2 q^{77} -1.21112e6 q^{78} -1.05741e6i q^{79} +1.24261e6i q^{80} +3.46800e6 q^{81} +3.07573e6i q^{82} -7.53870e6 q^{83} -70582.5 q^{84} +2.07523e6 q^{85} -384659. q^{86} +1.65324e6i q^{87} +496536. i q^{88} +2.20030e6i q^{89} -4.80552e6 q^{90} -806770. i q^{91} +1.92595e6i q^{92} -1.58815e6i q^{93} -2.63601e6i q^{94} +1.72788e7 q^{95} -471393. i q^{96} +1.16988e7i q^{97} +6.54133e6i q^{98} -1.92025e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 106 q^{3} - 1536 q^{4} + 104 q^{7} + 17554 q^{9} + 1136 q^{10} + 366 q^{11} + 6784 q^{12} + 98304 q^{16} - 239820 q^{21} - 675570 q^{25} + 97008 q^{26} + 338780 q^{27} - 6656 q^{28} + 350400 q^{30}+ \cdots - 53279900 q^{99}+O(q^{100}) $ 24 * q - 106 * q^3 - 1536 * q^4 + 104 * q^7 + 17554 * q^9 + 1136 * q^10 + 366 * q^11 + 6784 * q^12 + 98304 * q^16 - 239820 * q^21 - 675570 * q^25 + 97008 * q^26 + 338780 * q^27 - 6656 * q^28 + 350400 * q^30 - 763792 * q^33 + 713632 * q^34 - 1123456 * q^36 + 41652 * q^37 - 30816 * q^38 - 72704 * q^40 + 1729722 * q^41 - 23424 * q^44 - 488496 * q^46 + 114756 * q^47 - 434176 * q^48 + 4003056 * q^49 - 1115964 * q^53 - 2075632 * q^58 + 3248208 * q^62 - 2350900 * q^63 - 6291456 * q^64 - 5246556 * q^65 - 2717994 * q^67 - 5649440 * q^70 + 10643280 * q^71 - 10450370 * q^73 - 1064064 * q^74 - 17737980 * q^75 + 11665236 * q^77 + 8431856 * q^78 + 47300176 * q^81 + 555912 * q^83 + 15348480 * q^84 - 4853096 * q^85 - 12070464 * q^86 + 32064160 * q^90 - 58516956 * q^95 - 53279900 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$-1$

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 $

$2$		−	8.00000i		−	0.707107i
$2$		−	8.00000i		−	0.707107i
$3$	14.3858			0.307616			0.153808	−	0.988101i	$-0.450846\pi$
$3$	14.3858			0.307616			0.153808	+	0.988101i	$0.450846\pi$
$4$	−64.0000			−0.500000
$5$			303.371i			1.08537i	0.839935	+	0.542687i	$0.182593\pi$
$5$			303.371i			1.08537i	−0.839935	+	0.542687i	$0.817407\pi$
$6$		−	115.086i		−	0.217517i
$7$	76.6627			0.0844775			0.0422387	−	0.999108i	$-0.486551\pi$
$7$	76.6627			0.0844775			0.0422387	+	0.999108i	$0.486551\pi$
$8$			512.000i			0.353553i
$9$	−1980.05			−0.905373
$10$	2426.97			0.767475
$11$	969.796			0.219688			0.109844	−	0.993949i	$-0.464965\pi$
$11$	969.796			0.219688			0.109844	+	0.993949i	$0.464965\pi$
$12$	−920.689			−0.153808
$13$		−	10523.6i		−	1.32851i	−0.747507	−	0.664254i	$-0.768749\pi$
$13$		−	10523.6i		−	1.32851i	0.747507	−	0.664254i	$-0.231251\pi$
$14$		−	613.301i		−	0.0597346i
$15$			4364.23i			0.333878i
$16$	4096.00			0.250000
$17$		−	6840.58i		−	0.337693i	−0.985642	−	0.168846i	$-0.945996\pi$
$17$		−	6840.58i		−	0.337693i	0.985642	−	0.168846i	$-0.0540042\pi$
$18$			15840.4i			0.640195i
$19$		−	56955.9i		−	1.90503i	−0.304495	−	0.952514i	$-0.598488\pi$
$19$		−	56955.9i		−	1.90503i	0.304495	−	0.952514i	$-0.401512\pi$
$20$		−	19415.8i		−	0.542687i
$21$	1102.85			0.0259866
$22$		−	7758.37i		−	0.155343i
$23$		−	30093.0i		−	0.515724i	−0.966182	−	0.257862i	$-0.916982\pi$
$23$		−	30093.0i		−	0.515724i	0.966182	−	0.257862i	$-0.0830181\pi$
$24$			7365.51i			0.108759i
$25$	−13909.1			−0.178036
$26$	−84189.1			−0.939397
$27$	−59946.2			−0.586122
$28$	−4906.41			−0.0422387
$29$			114922.i			0.875004i	0.899217	+	0.437502i	$0.144137\pi$
$29$			114922.i			0.875004i	−0.899217	+	0.437502i	$0.855863\pi$
$30$	34913.8			0.236087
$31$		−	110397.i		−	0.665568i	−0.943003	−	0.332784i	$-0.892012\pi$
$31$		−	110397.i		−	0.665568i	0.943003	−	0.332784i	$-0.107988\pi$
$32$		−	32768.0i		−	0.176777i
$33$	13951.3			0.0675795
$34$	−54724.6			−0.238785
$35$			23257.3i			0.0916896i
$36$	126723.			0.452686
$37$	−190668.	−	242028.i	−0.618832	−	0.785524i
$37$	−190668.	−	242028.i	−0.618832	−	0.785524i
$38$	−455647.			−1.34706
$39$		−	151391.i		−	0.408670i
$40$	−155326.			−0.383738
$41$	−384466.			−0.871193			−0.435596	−	0.900142i	$-0.643463\pi$
$41$	−384466.			−0.871193			−0.435596	+	0.900142i	$0.643463\pi$
$42$		−	8822.81i		−	0.0183753i
$43$		−	48082.4i		−	0.0922246i	−0.998936	−	0.0461123i	$-0.985317\pi$
$43$		−	48082.4i		−	0.0922246i	0.998936	−	0.0461123i	$-0.0146832\pi$
$44$	−62067.0			−0.109844
$45$		−	600690.i		−	0.982668i
$46$	−240744.			−0.364672
$47$	329501.			0.462929			0.231464	−	0.972843i	$-0.425648\pi$
$47$	329501.			0.462929			0.231464	+	0.972843i	$0.425648\pi$
$48$	58924.1			0.0769039
$49$	−817666.			−0.992864
$50$			111273.i			0.125891i
$51$		−	98406.9i		−	0.103880i
$52$			673513.i			0.664254i
$53$	−1.29994e6			−1.19938			−0.599689	−	0.800233i	$-0.704709\pi$
$53$	−1.29994e6			−1.19938			−0.599689	+	0.800233i	$0.704709\pi$
$54$			479569.i			0.414451i
$55$			294208.i			0.238444i
$56$			39251.3i			0.0298673i
$57$		−	819354.i		−	0.586016i
$58$	919376.			0.618721
$59$			316983.i			0.200934i	0.994940	+	0.100467i	$0.0320337\pi$
$59$			316983.i			0.200934i	−0.994940	+	0.100467i	$0.967966\pi$
$60$		−	279310.i		−	0.166939i
$61$		−	1.54587e6i		−	0.872004i	−0.899946	−	0.436002i	$-0.856394\pi$
$61$		−	1.54587e6i		−	0.872004i	0.899946	−	0.436002i	$-0.143606\pi$
$62$	−883178.			−0.470628
$63$	−151796.			−0.0764836
$64$	−262144.			−0.125000
$65$	3.19257e6			1.44193
$66$		−	111610.i		−	0.0477859i
$67$	4.60848e6			1.87196			0.935980	−	0.352054i	$-0.114517\pi$
$67$	4.60848e6			1.87196			0.935980	+	0.352054i	$0.114517\pi$
$68$			437797.i			0.168846i
$69$		−	432910.i		−	0.158645i
$70$	186058.			0.0648344
$71$	2.95688e6			0.980460			0.490230	−	0.871593i	$-0.336913\pi$
$71$	2.95688e6			0.980460			0.490230	+	0.871593i	$0.336913\pi$
$72$		−	1.01379e6i		−	0.320098i
$73$	2.87820e6			0.865947			0.432973	−	0.901407i	$-0.357464\pi$
$73$	2.87820e6			0.865947			0.432973	+	0.901407i	$0.357464\pi$
$74$	−1.93622e6	+	1.52535e6i	−0.555449	+	0.437580i
$75$	−200093.			−0.0547668
$76$			3.64518e6i			0.952514i
$77$	74347.2			0.0185587
$78$	−1.21112e6			−0.288973
$79$		−	1.05741e6i		−	0.241295i	−0.992695	−	0.120647i	$-0.961503\pi$
$79$		−	1.05741e6i		−	0.241295i	0.992695	−	0.120647i	$-0.0384970\pi$
$80$			1.24261e6i			0.271343i
$81$	3.46800e6			0.725072
$82$			3.07573e6i			0.616026i
$83$	−7.53870e6			−1.44718			−0.723591	−	0.690229i	$-0.757510\pi$
$83$	−7.53870e6			−1.44718			−0.723591	+	0.690229i	$0.757510\pi$
$84$	−70582.5			−0.0129933
$85$	2.07523e6			0.366523
$86$	−384659.			−0.0652126
$87$			1.65324e6i			0.269165i
$88$			496536.i			0.0776714i
$89$			2.20030e6i			0.330840i	0.986223	+	0.165420i	$0.0528979\pi$
$89$			2.20030e6i			0.330840i	−0.986223	+	0.165420i	$0.947102\pi$
$90$	−4.80552e6			−0.694851
$91$		−	806770.i		−	0.112229i
$92$			1.92595e6i			0.257862i
$93$		−	1.58815e6i		−	0.204739i
$94$		−	2.63601e6i		−	0.327340i
$95$	1.72788e7			2.06767
$96$		−	471393.i		−	0.0543793i
$97$			1.16988e7i			1.30149i	0.759297	+	0.650744i	$0.225543\pi$
$97$			1.16988e7i			1.30149i	−0.759297	+	0.650744i	$0.774457\pi$
$98$			6.54133e6i			0.702061i
$99$	−1.92025e6			−0.198899
$100$	890182.			0.0890182
$101$	−5.63785e6			−0.544488			−0.272244	−	0.962228i	$-0.587766\pi$
$101$	−5.63785e6			−0.544488			−0.272244	+	0.962228i	$0.587766\pi$
$102$	−787255.			−0.0734539
$103$		−	1.39728e6i		−	0.125995i	−0.998014	−	0.0629973i	$-0.979934\pi$
$103$		−	1.39728e6i		−	0.125995i	0.998014	−	0.0629973i	$-0.0200660\pi$
$104$	5.38810e6			0.469698
$105$			334573.i			0.0282052i
$106$			1.03995e7i			0.848089i
$107$	−3.65843e6			−0.288704			−0.144352	−	0.989526i	$-0.546110\pi$
$107$	−3.65843e6			−0.288704			−0.144352	+	0.989526i	$0.546110\pi$
$108$	3.83656e6			0.293061
$109$		−	1.33252e7i		−	0.985554i	−0.870156	−	0.492777i	$-0.835982\pi$
$109$		−	1.33252e7i		−	0.985554i	0.870156	−	0.492777i	$-0.164018\pi$
$110$	2.35367e6			0.168605
$111$	−2.74291e6	−	3.48175e6i	−0.190362	−	0.241639i
$112$	314010.			0.0211194
$113$		−	3.02877e7i		−	1.97465i	−0.158697	−	0.987327i	$-0.550729\pi$
$113$		−	3.02877e7i		−	1.97465i	0.158697	−	0.987327i	$-0.449271\pi$
$114$	−6.55483e6			−0.414376
$115$	9.12934e6			0.559754
$116$		−	7.35500e6i		−	0.437502i
$117$			2.08373e7i			1.20279i
$118$	2.53586e6			0.142082
$119$		−	524417.i		−	0.0285274i
$120$	−2.23448e6			−0.118044
$121$	−1.85467e7			−0.951737
$122$	−1.23670e7			−0.616600
$123$	−5.53084e6			−0.267993
$124$			7.06543e6i			0.332784i
$125$			1.94813e7i			0.892138i
$126$			1.21437e6i			0.0540821i
$127$	−1.14906e7			−0.497773			−0.248886	−	0.968533i	$-0.580065\pi$
$127$	−1.14906e7			−0.497773			−0.248886	+	0.968533i	$0.580065\pi$
$128$			2.09715e6i			0.0883883i
$129$		−	691702.i		−	0.0283697i
$130$		−	2.55405e7i		−	1.01960i
$131$		−	1.55640e7i		−	0.604882i	−0.953168	−	0.302441i	$-0.902198\pi$
$131$		−	1.55640e7i		−	0.604882i	0.953168	−	0.302441i	$-0.0978015\pi$
$132$	−892881.			−0.0337897
$133$		−	4.36639e6i		−	0.160932i
$134$		−	3.68679e7i		−	1.32367i
$135$		−	1.81859e7i		−	0.636162i
$136$	3.50238e6			0.119392
$137$	2.65380e7			0.881753			0.440876	−	0.897568i	$-0.354668\pi$
$137$	2.65380e7			0.881753			0.440876	+	0.897568i	$0.354668\pi$
$138$	−3.46328e6			−0.112179
$139$	−4.58788e7			−1.44897			−0.724487	−	0.689289i	$-0.757923\pi$
$139$	−4.58788e7			−1.44897			−0.724487	+	0.689289i	$0.757923\pi$
$140$		−	1.48846e6i		−	0.0458448i
$141$	4.74012e6			0.142404
$142$		−	2.36551e7i		−	0.693290i
$143$		−	1.02058e7i		−	0.291857i
$144$	−8.11028e6			−0.226343
$145$	−3.48640e7			−0.949706
$146$		−	2.30256e7i		−	0.612317i
$147$	−1.17627e7			−0.305420
$148$	1.22028e7	+	1.54898e7i	0.309416	+	0.392762i
$149$	1.82942e7			0.453065			0.226533	−	0.974004i	$-0.427261\pi$
$149$	1.82942e7			0.453065			0.226533	+	0.974004i	$0.427261\pi$
$150$			1.60074e6i			0.0387260i
$151$	−6.74262e7			−1.59371			−0.796855	−	0.604170i	$-0.793505\pi$
$151$	−6.74262e7			−1.59371			−0.796855	+	0.604170i	$0.793505\pi$
$152$	2.91614e7			0.673529
$153$			1.35447e7i			0.305738i
$154$		−	594778.i		−	0.0131230i
$155$	3.34914e7			0.722390
$156$			9.68899e6i			0.204335i
$157$	6.33668e7			1.30681			0.653406	−	0.757008i	$-0.273340\pi$
$157$	6.33668e7			1.30681			0.653406	+	0.757008i	$0.273340\pi$
$158$	−8.45926e6			−0.170621
$159$	−1.87006e7			−0.368948
$160$	9.94087e6			0.191869
$161$		−	2.30701e6i		−	0.0435671i
$162$		−	2.77440e7i		−	0.512703i
$163$			5.89098e7i			1.06545i	0.846290	+	0.532723i	$0.178831\pi$
$163$			5.89098e7i			1.06545i	−0.846290	+	0.532723i	$0.821169\pi$
$164$	2.46058e7			0.435596
$165$			4.23241e6i			0.0733490i
$166$			6.03096e7i			1.02331i
$167$		−	2.87873e7i		−	0.478291i	−0.970984	−	0.239146i	$-0.923133\pi$
$167$		−	2.87873e7i		−	0.478291i	0.970984	−	0.239146i	$-0.0768674\pi$
$168$			564660.i			0.00918765i
$169$	−4.79984e7			−0.764933
$170$		−	1.66019e7i		−	0.259171i
$171$			1.12776e8i			1.72476i
$172$			3.07728e6i			0.0461123i
$173$	−4.16794e7			−0.612013			−0.306006	−	0.952029i	$-0.598993\pi$
$173$	−4.16794e7			−0.612013			−0.306006	+	0.952029i	$0.598993\pi$
$174$	1.32259e7			0.190328
$175$	−1.06631e6			−0.0150401
$176$	3.97229e6			0.0549220
$177$			4.56004e6i			0.0618105i
$178$	1.76024e7			0.233939
$179$			1.02139e8i			1.33108i	0.746362	+	0.665541i	$0.231799\pi$
$179$			1.02139e8i			1.33108i	−0.746362	+	0.665541i	$0.768201\pi$
$180$			3.84442e7i			0.491334i
$181$	−4.10966e7			−0.515146			−0.257573	−	0.966259i	$-0.582923\pi$
$181$	−4.10966e7			−0.515146			−0.257573	+	0.966259i	$0.582923\pi$
$182$	−6.45416e6			−0.0793579
$183$		−	2.22385e7i		−	0.268242i
$184$	1.54076e7			0.182336
$185$	7.34243e7	−	5.78433e7i	0.852587	−	0.671664i
$186$	−1.27052e7			−0.144772
$187$		−	6.63397e6i		−	0.0741870i
$188$	−2.10881e7			−0.231464
$189$	−4.59564e6			−0.0495141
$190$		−	1.38230e8i		−	1.46206i
$191$			1.05775e8i			1.09841i	0.835687	+	0.549206i	$0.185070\pi$
$191$			1.05775e8i			1.09841i	−0.835687	+	0.549206i	$0.814930\pi$
$192$	−3.77114e6			−0.0384520
$193$			4.88570e7i			0.489189i	0.969625	+	0.244594i	$0.0786548\pi$
$193$			4.88570e7i			0.489189i	−0.969625	+	0.244594i	$0.921345\pi$
$194$	9.35903e7			0.920291
$195$	4.59275e7			0.443560
$196$	5.23306e7			0.496432
$197$	1.17028e8			1.09058			0.545292	−	0.838246i	$-0.316419\pi$
$197$	1.17028e8			1.09058			0.545292	+	0.838246i	$0.316419\pi$
$198$			1.53620e7i			0.140643i
$199$		−	1.77633e7i		−	0.159785i	−0.996803	−	0.0798927i	$-0.974542\pi$
$199$		−	1.77633e7i		−	0.159785i	0.996803	−	0.0798927i	$-0.0254578\pi$
$200$		−	7.12145e6i		−	0.0629454i
$201$	6.62966e7			0.575844
$202$			4.51028e7i			0.385011i
$203$			8.81022e6i			0.0739181i
$204$			6.29804e6i			0.0519398i
$205$		−	1.16636e8i		−	0.945570i
$206$	−1.11782e7			−0.0890917
$207$			5.95856e7i			0.466923i
$208$		−	4.31048e7i		−	0.332127i
$209$		−	5.52357e7i		−	0.418512i
$210$	2.67659e6			0.0199441
$211$	1.01923e8			0.746933			0.373467	−	0.927644i	$-0.378169\pi$
$211$	1.01923e8			0.746933			0.373467	+	0.927644i	$0.378169\pi$
$212$	8.31959e7			0.599689
$213$	4.25370e7			0.301605
$214$			2.92675e7i			0.204144i
$215$	1.45868e7			0.100098
$216$		−	3.06924e7i		−	0.207226i
$217$		−	8.46335e6i		−	0.0562255i
$218$	−1.06602e8			−0.696892
$219$	4.14051e7			0.266379
$220$		−	1.88293e7i		−	0.119222i
$221$	−7.19878e7			−0.448627
$222$	−2.78540e7	+	2.19433e7i	−0.170865	+	0.134606i
$223$	−4.10431e7			−0.247841			−0.123920	−	0.992292i	$-0.539547\pi$
$223$	−4.10431e7			−0.247841			−0.123920	+	0.992292i	$0.539547\pi$
$224$		−	2.51208e6i		−	0.0149336i
$225$	2.75407e7			0.161189
$226$	−2.42301e8			−1.39629
$227$			1.98424e8i			1.12591i	0.826488	+	0.562954i	$0.190335\pi$
$227$			1.98424e8i			1.12591i	−0.826488	+	0.562954i	$0.809665\pi$
$228$			5.24387e7i			0.293008i
$229$	−2.01547e8			−1.10905			−0.554527	−	0.832166i	$-0.687101\pi$
$229$	−2.01547e8			−1.10905			−0.554527	+	0.832166i	$0.687101\pi$
$230$		−	7.30347e7i		−	0.395806i
$231$	1.06954e6			0.00570894
$232$	−5.88400e7			−0.309361
$233$	2.32614e8			1.20473			0.602366	−	0.798220i	$-0.294225\pi$
$233$	2.32614e8			1.20473			0.602366	+	0.798220i	$0.294225\pi$
$234$	1.66699e8			0.850504
$235$			9.99611e7i			0.502451i
$236$		−	2.02869e7i		−	0.100467i
$237$		−	1.52116e7i		−	0.0742260i
$238$	−4.19534e6			−0.0201719
$239$		−	1.56112e8i		−	0.739682i	−0.929095	−	0.369841i	$-0.879412\pi$
$239$		−	1.56112e8i		−	0.739682i	0.929095	−	0.369841i	$-0.120588\pi$
$240$			1.78759e7i			0.0834695i
$241$		−	2.58351e8i		−	1.18891i	−0.804128	−	0.594457i	$-0.797367\pi$
$241$		−	2.58351e8i		−	1.18891i	0.804128	−	0.594457i	$-0.202633\pi$
$242$			1.48373e8i			0.672980i
$243$	1.80992e8			0.809166
$244$			9.89357e7i			0.436002i
$245$		−	2.48056e8i		−	1.07763i
$246$			4.42467e7i			0.189499i
$247$	−5.99383e8			−2.53084
$248$	5.65234e7			0.235314
$249$	−1.08450e8			−0.445176
$250$	1.55850e8			0.630837
$251$		−	1.82736e8i		−	0.729400i	−0.931125	−	0.364700i	$-0.881172\pi$
$251$		−	1.82736e8i		−	0.729400i	0.931125	−	0.364700i	$-0.118828\pi$
$252$	9.71494e6			0.0382418
$253$		−	2.91841e7i		−	0.113298i
$254$			9.19251e7i			0.351978i
$255$	2.98538e7			0.112748
$256$	1.67772e7			0.0625000
$257$			2.85517e8i			1.04922i	0.851343	+	0.524610i	$0.175789\pi$
$257$			2.85517e8i			1.04922i	−0.851343	+	0.524610i	$0.824211\pi$
$258$	−5.53362e6			−0.0200604
$259$	−1.46171e7	−	1.85545e7i	−0.0522773	−	0.0663591i
$260$	−2.04324e8			−0.720964
$261$		−	2.27551e8i		−	0.792205i
$262$	−1.24512e8			−0.427716
$263$	−5.54351e8			−1.87906			−0.939528	−	0.342471i	$-0.888736\pi$
$263$	−5.54351e8			−1.87906			−0.939528	+	0.342471i	$0.888736\pi$
$264$			7.14305e6i			0.0238929i
$265$		−	3.94363e8i		−	1.30177i
$266$	−3.49312e7			−0.113796
$267$			3.16530e7i			0.101771i
$268$	−2.94943e8			−0.935980
$269$	2.50262e8			0.783901			0.391950	−	0.919986i	$-0.371800\pi$
$269$	2.50262e8			0.783901			0.391950	+	0.919986i	$0.371800\pi$
$270$	−1.45488e8			−0.449834
$271$	2.05974e8			0.628667			0.314333	−	0.949313i	$-0.398219\pi$
$271$	2.05974e8			0.628667			0.314333	+	0.949313i	$0.398219\pi$
$272$		−	2.80190e7i		−	0.0844232i
$273$		−	1.16060e7i		−	0.0345234i
$274$		−	2.12304e8i		−	0.623493i
$275$	−1.34890e7			−0.0391124
$276$			2.77063e7i			0.0793225i
$277$		−	1.32409e8i		−	0.374316i	−0.982330	−	0.187158i	$-0.940072\pi$
$277$		−	1.32409e8i		−	0.374316i	0.982330	−	0.187158i	$-0.0599276\pi$
$278$			3.67031e8i			1.02458i
$279$			2.18592e8i			0.602587i
$280$	−1.19077e7			−0.0324172
$281$		−	9.73790e7i		−	0.261814i	−0.991395	−	0.130907i	$-0.958211\pi$
$281$		−	9.73790e7i		−	0.261814i	0.991395	−	0.130907i	$-0.0417890\pi$
$282$		−	3.79210e7i		−	0.100695i
$283$		−	2.84385e7i		−	0.0745856i	−0.999304	−	0.0372928i	$-0.988127\pi$
$283$		−	2.84385e7i		−	0.0745856i	0.999304	−	0.0372928i	$-0.0118734\pi$
$284$	−1.89241e8			−0.490230
$285$	2.48569e8			0.636047
$286$	−8.16463e7			−0.206374
$287$	−2.94742e7			−0.0735962
$288$			6.48823e7i			0.160049i
$289$	3.63545e8			0.885964
$290$			2.78912e8i			0.671544i
$291$			1.68296e8i			0.400358i
$292$	−1.84205e8			−0.432973
$293$	−2.05178e8			−0.476534			−0.238267	−	0.971200i	$-0.576579\pi$
$293$	−2.05178e8			−0.476534			−0.238267	+	0.971200i	$0.576579\pi$
$294$			9.41020e7i			0.215965i
$295$	−9.61635e7			−0.218089
$296$	1.23918e8	−	9.76222e7i	0.277725	−	0.218790i
$297$	−5.81356e7			−0.128764
$298$		−	1.46353e8i		−	0.320366i
$299$	−3.16688e8			−0.685144
$300$	1.28059e7			0.0273834
$301$		−	3.68613e6i		−	0.00779090i
$302$			5.39410e8i			1.12692i
$303$	−8.11047e7			−0.167493
$304$		−	2.33291e8i		−	0.476257i
$305$	4.68973e8			0.946451
$306$	1.08357e8			0.216189
$307$	3.77499e8			0.744614			0.372307	−	0.928110i	$-0.378567\pi$
$307$	3.77499e8			0.744614			0.372307	+	0.928110i	$0.378567\pi$
$308$	−4.75822e6			−0.00927934
$309$		−	2.01009e7i		−	0.0387579i
$310$		−	2.67931e8i		−	0.510807i
$311$		−	3.96966e8i		−	0.748328i	−0.927363	−	0.374164i	$-0.877930\pi$
$311$		−	3.96966e8i		−	0.748328i	0.927363	−	0.374164i	$-0.122070\pi$
$312$	7.75120e7			0.144487
$313$		−	6.64097e8i		−	1.22413i	−0.790808	−	0.612064i	$-0.790340\pi$
$313$		−	6.64097e8i		−	1.22413i	0.790808	−	0.612064i	$-0.209660\pi$
$314$		−	5.06934e8i		−	0.924055i
$315$		−	4.60505e7i		−	0.0830133i
$316$			6.76741e7i			0.120647i
$317$	9.79448e8			1.72693			0.863463	−	0.504411i	$-0.168291\pi$
$317$	9.79448e8			1.72693			0.863463	+	0.504411i	$0.168291\pi$
$318$			1.49605e8i			0.260885i
$319$			1.11451e8i			0.192228i
$320$		−	7.95269e7i		−	0.135672i
$321$	−5.26294e7			−0.0888097
$322$	−1.84561e7			−0.0308066
$323$	−3.89611e8			−0.643314
$324$	−2.21952e8			−0.362536
$325$			1.46374e8i			0.236523i
$326$	4.71279e8			0.753384
$327$		−	1.91693e8i		−	0.303172i
$328$		−	1.96847e8i		−	0.308013i
$329$	2.52604e7			0.0391070
$330$	3.38593e7			0.0518656
$331$			7.40239e8i			1.12195i	0.827832	+	0.560976i	$0.189574\pi$
$331$			7.40239e8i			1.12195i	−0.827832	+	0.560976i	$0.810426\pi$
$332$	4.82477e8			0.723591
$333$	3.77533e8	+	4.79227e8i	0.560273	+	0.711192i
$334$	−2.30298e8			−0.338203
$335$			1.39808e9i			2.03178i
$336$	4.51728e6			0.00649665
$337$	4.56122e8			0.649197			0.324599	−	0.945852i	$-0.394771\pi$
$337$	4.56122e8			0.649197			0.324599	+	0.945852i	$0.394771\pi$
$338$			3.83987e8i			0.540889i
$339$		−	4.35711e8i		−	0.607435i
$340$	−1.32815e8			−0.183261
$341$		−	1.07063e8i		−	0.146217i
$342$	9.02205e8			1.21959
$343$	−1.25819e8			−0.168352
$344$	2.46182e7			0.0326063
$345$	1.31333e8			0.172189
$346$			3.33436e8i			0.432758i
$347$		−	7.14958e8i		−	0.918601i	−0.888281	−	0.459301i	$-0.848100\pi$
$347$		−	7.14958e8i		−	0.918601i	0.888281	−	0.459301i	$-0.151900\pi$
$348$		−	1.05807e8i		−	0.134582i
$349$	2.16908e8			0.273141			0.136570	−	0.990630i	$-0.456392\pi$
$349$	2.16908e8			0.273141			0.136570	+	0.990630i	$0.456392\pi$
$350$			8.53047e6i			0.0106349i
$351$			6.30852e8i			0.778668i
$352$		−	3.17783e7i		−	0.0388357i
$353$			1.20749e6i			0.00146108i	1.00000		0.000730538i	$0.000232537\pi$
$353$			1.20749e6i			0.00146108i	−1.00000		0.000730538i	$0.999767\pi$
$354$	3.64803e7			0.0437066
$355$			8.97033e8i			1.06417i
$356$		−	1.40819e8i		−	0.165420i
$357$		−	7.54414e6i		−	0.00877548i
$358$	8.17109e8			0.941217
$359$	9.30859e8			1.06183			0.530913	−	0.847426i	$-0.321849\pi$
$359$	9.30859e8			1.06183			0.530913	+	0.847426i	$0.321849\pi$
$360$	3.07553e8			0.347426
$361$	−2.35011e9			−2.62913
$362$			3.28773e8i			0.364263i
$363$	−2.66808e8			−0.292769
$364$			5.16333e7i			0.0561145i
$365$			8.73163e8i			0.939876i
$366$	−1.77908e8			−0.189676
$367$	−8.96938e8			−0.947177			−0.473588	−	0.880746i	$-0.657042\pi$
$367$	−8.96938e8			−0.947177			−0.473588	+	0.880746i	$0.657042\pi$
$368$		−	1.23261e8i		−	0.128931i
$369$	7.61262e8			0.788754
$370$	−4.62746e8	−	5.87394e8i	−0.474938	−	0.602870i
$371$	−9.96566e7			−0.101320
$372$			1.01642e8i			0.102370i
$373$	−1.08626e9			−1.08381			−0.541904	−	0.840441i	$-0.682296\pi$
$373$	−1.08626e9			−1.08381			−0.541904	+	0.840441i	$0.682296\pi$
$374$	−5.30718e7			−0.0524581
$375$			2.80253e8i			0.274436i
$376$			1.68704e8i			0.163670i
$377$	1.20940e9			1.16245
$378$			3.67651e7i			0.0350118i
$379$	−1.42519e8			−0.134473			−0.0672366	−	0.997737i	$-0.521418\pi$
$379$	−1.42519e8			−0.134473			−0.0672366	+	0.997737i	$0.521418\pi$
$380$	−1.10584e9			−1.03383
$381$	−1.65302e8			−0.153123
$382$	8.46199e8			0.776695
$383$			1.34836e9i			1.22634i	0.789951	+	0.613170i	$0.210106\pi$
$383$			1.34836e9i			1.22634i	−0.789951	+	0.613170i	$0.789894\pi$
$384$			3.01691e7i			0.0271896i
$385$			2.25548e7i			0.0201431i
$386$	3.90856e8			0.345909
$387$			9.52056e7i			0.0834976i
$388$		−	7.48723e8i		−	0.650744i
$389$		−	4.61882e8i		−	0.397839i	−0.980016	−	0.198920i	$-0.936257\pi$
$389$		−	4.61882e8i		−	0.397839i	0.980016	−	0.198920i	$-0.0637432\pi$
$390$		−	3.67420e8i		−	0.313644i
$391$	−2.05853e8			−0.174156
$392$		−	4.18645e8i		−	0.351030i
$393$		−	2.23899e8i		−	0.186071i
$394$		−	9.36227e8i		−	0.771160i
$395$	3.20787e8			0.261895
$396$	1.22896e8			0.0994497
$397$	−3.72153e8			−0.298507			−0.149254	−	0.988799i	$-0.547687\pi$
$397$	−3.72153e8			−0.298507			−0.149254	+	0.988799i	$0.547687\pi$
$398$	−1.42106e8			−0.112985
$399$		−	6.28139e7i		−	0.0495052i
$400$	−5.69716e7			−0.0445091
$401$			5.73275e8i			0.443974i	0.975050	+	0.221987i	$0.0712543\pi$
$401$			5.73275e8i			0.443974i	−0.975050	+	0.221987i	$0.928746\pi$
$402$		−	5.30372e8i		−	0.407183i
$403$	−1.16178e9			−0.884213
$404$	3.60822e8			0.272244
$405$			1.05209e9i			0.786974i
$406$	7.04818e7			0.0522680
$407$	−1.84909e8	−	2.34718e8i	−0.135950	−	0.172570i
$408$	5.03843e7			0.0367270
$409$		−	1.99617e9i		−	1.44267i	−0.692589	−	0.721333i	$-0.743530\pi$
$409$		−	1.99617e9i		−	1.44267i	0.692589	−	0.721333i	$-0.256470\pi$
$410$	−9.33087e8			−0.668619
$411$	3.81770e8			0.271241
$412$			8.94257e7i			0.0629973i
$413$			2.43008e7i			0.0169744i
$414$	4.76685e8			0.330164
$415$		−	2.28702e9i		−	1.57073i
$416$	−3.44839e8			−0.234849
$417$	−6.60002e8			−0.445727
$418$	−4.41885e8			−0.295932
$419$	−2.91379e8			−0.193513			−0.0967563	−	0.995308i	$-0.530847\pi$
$419$	−2.91379e8			−0.193513			−0.0967563	+	0.995308i	$0.530847\pi$
$420$		−	2.14127e7i		−	0.0141026i
$421$		−	1.79420e9i		−	1.17188i	−0.810353	−	0.585942i	$-0.800725\pi$
$421$		−	1.79420e9i		−	1.17188i	0.810353	−	0.585942i	$-0.199275\pi$
$422$		−	8.15380e8i		−	0.528161i
$423$	−6.52428e8			−0.419123
$424$		−	6.65567e8i		−	0.424044i
$425$			9.51462e7i			0.0601216i
$426$		−	3.40296e8i		−	0.213267i
$427$		−	1.18511e8i		−	0.0736647i
$428$	2.34140e8			0.144352
$429$		−	1.46818e8i		−	0.0897798i
$430$		−	1.16695e8i		−	0.0707801i
$431$			2.60384e9i			1.56655i	0.621677	+	0.783274i	$0.286452\pi$
$431$			2.60384e9i			1.56655i	−0.621677	+	0.783274i	$0.713548\pi$
$432$	−2.45540e8			−0.146531
$433$	5.58880e8			0.330834			0.165417	−	0.986224i	$-0.447103\pi$
$433$	5.58880e8			0.330834			0.165417	+	0.986224i	$0.447103\pi$
$434$	−6.77068e7			−0.0397574
$435$	−5.01545e8			−0.292145
$436$			8.52812e8i			0.492777i
$437$	−1.71397e9			−0.982469
$438$		−	3.31241e8i		−	0.188358i
$439$		−	2.86537e8i		−	0.161642i	−0.996729	−	0.0808211i	$-0.974246\pi$
$439$		−	2.86537e8i		−	0.161642i	0.996729	−	0.0808211i	$-0.0257542\pi$
$440$	−1.50635e8			−0.0843025
$441$	1.61902e9			0.898911
$442$			5.75902e8i			0.317227i
$443$	−7.81293e7			−0.0426973			−0.0213487	−	0.999772i	$-0.506796\pi$
$443$	−7.81293e7			−0.0426973			−0.0213487	+	0.999772i	$0.506796\pi$
$444$	1.75546e8	+	2.22832e8i	0.0951811	+	0.120820i
$445$	−6.67508e8			−0.359085
$446$			3.28345e8i			0.175250i
$447$	2.63176e8			0.139370
$448$	−2.00967e7			−0.0105597
$449$		−	7.37008e8i		−	0.384247i	−0.981371	−	0.192123i	$-0.938463\pi$
$449$		−	7.37008e8i		−	0.384247i	0.981371	−	0.192123i	$-0.0615374\pi$
$450$		−	2.20326e8i		−	0.113978i
$451$	−3.72854e8			−0.191391
$452$			1.93841e9i			0.987327i
$453$	−9.69977e8			−0.490250
$454$	1.58739e9			0.796138
$455$	2.44751e8			0.121810
$456$	4.19509e8			0.207188
$457$		−	1.67674e9i		−	0.821785i	−0.911684	−	0.410893i	$-0.865217\pi$
$457$		−	1.67674e9i		−	0.821785i	0.911684	−	0.410893i	$-0.134783\pi$
$458$			1.61238e9i			0.784219i
$459$			4.10067e8i			0.197929i
$460$	−5.84278e8			−0.279877
$461$		−	2.36757e9i		−	1.12551i	−0.826623	−	0.562756i	$-0.809741\pi$
$461$		−	2.36757e9i		−	1.12551i	0.826623	−	0.562756i	$-0.190259\pi$
$462$		−	8.55633e6i		−	0.00403683i
$463$		−	1.26126e9i		−	0.590570i	−0.955409	−	0.295285i	$-0.904585\pi$
$463$		−	1.26126e9i		−	0.590570i	0.955409	−	0.295285i	$-0.0954146\pi$
$464$			4.70720e8i			0.218751i
$465$	4.81799e8			0.222219
$466$		−	1.86091e9i		−	0.851874i
$467$			1.73825e9i			0.789777i	0.918729	+	0.394888i	$0.129217\pi$
$467$			1.73825e9i			0.789777i	−0.918729	+	0.394888i	$0.870783\pi$
$468$		−	1.33359e9i		−	0.601397i
$469$	3.53299e8			0.158138
$470$	7.99689e8			0.355286
$471$	9.11579e8			0.401996
$472$	−1.62295e8			−0.0710410
$473$		−	4.66302e7i		−	0.0202606i
$474$	−1.21693e8			−0.0524857
$475$			7.92205e8i			0.339164i
$476$			3.35627e7i			0.0142637i
$477$	2.57394e9			1.08588
$478$	−1.24890e9			−0.523034
$479$		−	4.35936e9i		−	1.81238i	−0.422874	−	0.906188i	$-0.638979\pi$
$479$		−	4.35936e9i		−	1.81238i	0.422874	−	0.906188i	$-0.361021\pi$
$480$	1.43007e8			0.0590218
$481$	−2.54701e9	+	2.00652e9i	−1.04357	+	0.822123i
$482$	−2.06681e9			−0.840689
$483$		−	3.31881e7i		−	0.0134019i
$484$	1.18699e9			0.475869
$485$	−3.54908e9			−1.41260
$486$		−	1.44794e9i		−	0.572167i
$487$			4.39964e9i			1.72610i	0.505120	+	0.863049i	$0.331448\pi$
$487$			4.39964e9i			1.72610i	−0.505120	+	0.863049i	$0.668552\pi$
$488$	7.91486e8			0.308300
$489$			8.47463e8i			0.327748i
$490$	−1.98445e9			−0.761998
$491$	2.99002e9			1.13996			0.569979	−	0.821659i	$-0.306951\pi$
$491$	2.99002e9			1.13996			0.569979	+	0.821659i	$0.306951\pi$
$492$	3.53973e8			0.133996
$493$	7.86133e8			0.295482
$494$			4.79507e9i			1.78958i
$495$		−	5.82547e8i		−	0.215880i
$496$		−	4.52187e8i		−	0.166392i
$497$	2.26683e8			0.0828268
$498$			8.67599e8i			0.314787i
$499$			5.17455e8i			0.186432i	0.995646	+	0.0932161i	$0.0297147\pi$
$499$			5.17455e8i			0.186432i	−0.995646	+	0.0932161i	$0.970285\pi$
$500$		−	1.24680e9i		−	0.446069i
$501$		−	4.14127e8i		−	0.147130i
$502$	−1.46189e9			−0.515763
$503$			7.73903e8i			0.271143i	0.990768	+	0.135572i	$0.0432871\pi$
$503$			7.73903e8i			0.271143i	−0.990768	+	0.135572i	$0.956713\pi$
$504$		−	7.77195e7i		−	0.0270410i
$505$		−	1.71036e9i		−	0.590973i
$506$	−2.33473e8			−0.0801141
$507$	−6.90494e8			−0.235305
$508$	7.35401e8			0.248886
$509$	3.95232e9			1.32843			0.664217	−	0.747540i	$-0.268765\pi$
$509$	3.95232e9			1.32843			0.664217	+	0.747540i	$0.268765\pi$
$510$		−	2.38831e8i		−	0.0797250i
$511$	2.20651e8			0.0731530
$512$		−	1.34218e8i		−	0.0441942i
$513$			3.41429e9i			1.11658i
$514$	2.28414e9			0.741911
$515$	4.23893e8			0.136751
$516$			4.42689e7i			0.0141849i
$517$	3.19549e8			0.101700
$518$	−1.48436e8	+	1.16937e8i	−0.0469229	+	0.0369657i
$519$	−5.99591e8			−0.188265
$520$			1.63460e9i			0.509798i
$521$	3.17154e9			0.982511			0.491256	−	0.871015i	$-0.336538\pi$
$521$	3.17154e9			0.982511			0.491256	+	0.871015i	$0.336538\pi$
$522$	−1.82041e9			−0.560173
$523$		−	1.03110e8i		−	0.0315171i	−0.999876	−	0.0157585i	$-0.994984\pi$
$523$		−	1.03110e8i		−	0.0315171i	0.999876	−	0.0157585i	$-0.00501631\pi$
$524$			9.96094e8i			0.302441i
$525$	−1.53397e7			−0.00462656
$526$			4.43481e9i			1.32869i
$527$	−7.55181e8			−0.224757
$528$	5.71444e7			0.0168949
$529$	2.49924e9			0.734028
$530$	−3.15491e9			−0.920494
$531$		−	6.27642e8i		−	0.181920i
$532$			2.79449e8i			0.0804660i
$533$			4.04598e9i			1.15739i
$534$	2.53224e8			0.0719633
$535$		−	1.10986e9i		−	0.313351i
$536$			2.35954e9i			0.661837i
$537$			1.46934e9i			0.409461i
$538$		−	2.00209e9i		−	0.554302i
$539$	−7.92969e8			−0.218120
$540$			1.16390e9i			0.318081i
$541$			4.13795e9i			1.12356i	0.827288	+	0.561778i	$0.189883\pi$
$541$			4.13795e9i			1.12356i	−0.827288	+	0.561778i	$0.810117\pi$
$542$		−	1.64779e9i		−	0.444534i
$543$	−5.91205e8			−0.158467
$544$	−2.24152e8			−0.0596962
$545$	4.04248e9			1.06969
$546$	−9.28480e7			−0.0244117
$547$		−	5.79115e9i		−	1.51290i	−0.654054	−	0.756448i	$-0.726933\pi$
$547$		−	5.79115e9i		−	1.51290i	0.654054	−	0.756448i	$-0.273067\pi$
$548$	−1.69843e9			−0.440876
$549$			3.06090e9i			0.789489i
$550$			1.07912e8i			0.0276567i
$551$	6.54549e9			1.66691
$552$	2.21650e8			0.0560895
$553$		−	8.10637e7i		−	0.0203840i
$554$	−1.05927e9			−0.264681
$555$	1.05626e9	−	8.32120e8i	0.262269	−	0.206614i
$556$	2.93624e9			0.724487
$557$		−	3.59091e9i		−	0.880462i	−0.897884	−	0.440231i	$-0.854896\pi$
$557$		−	3.59091e9i		−	0.880462i	0.897884	−	0.440231i	$-0.145104\pi$
$558$	1.74874e9			0.426093
$559$	−5.06002e8			−0.122521
$560$			9.52617e7i			0.0229224i
$561$		−	9.54347e7i		−	0.0228211i
$562$	−7.79032e8			−0.185131
$563$		−	7.40755e9i		−	1.74942i	−0.484643	−	0.874712i	$-0.661050\pi$
$563$		−	7.40755e9i		−	1.74942i	0.484643	−	0.874712i	$-0.338950\pi$
$564$	−3.03368e8			−0.0712021
$565$	9.18840e9			2.14324
$566$	−2.27508e8			−0.0527400
$567$	2.65866e8			0.0612523
$568$			1.51392e9i			0.346645i
$569$		−	3.57033e9i		−	0.812485i	−0.913765	−	0.406243i	$-0.866839\pi$
$569$		−	3.57033e9i		−	0.812485i	0.913765	−	0.406243i	$-0.133161\pi$
$570$		−	1.98855e9i		−	0.449753i
$571$	−2.45218e9			−0.551222			−0.275611	−	0.961269i	$-0.588880\pi$
$571$	−2.45218e9			−0.551222			−0.275611	+	0.961269i	$0.588880\pi$
$572$			6.53170e8i			0.145929i
$573$			1.52165e9i			0.337889i
$574$			2.35794e8i			0.0520404i
$575$			4.18566e8i			0.0918177i
$576$	5.19058e8			0.113172
$577$			6.75658e8i			0.146424i	0.997316	+	0.0732119i	$0.0233249\pi$
$577$			6.75658e8i			0.146424i	−0.997316	+	0.0732119i	$0.976675\pi$
$578$		−	2.90836e9i		−	0.626471i
$579$			7.02845e8i			0.150482i
$580$	2.23130e9			0.474853
$581$	−5.77937e8			−0.122254
$582$	1.34637e9			0.283096
$583$	−1.26067e9			−0.263489
$584$			1.47364e9i			0.306158i
$585$	−6.32145e9			−1.30548
$586$			1.64142e9i			0.336960i
$587$		−	5.25561e9i		−	1.07248i	−0.844065	−	0.536240i	$-0.819844\pi$
$587$		−	5.25561e9i		−	1.07248i	0.844065	−	0.536240i	$-0.180156\pi$
$588$	7.52816e8			0.152710
$589$	−6.28778e9			−1.26793
$590$			7.69308e8i			0.154212i
$591$	1.68354e9			0.335481
$592$	−7.80977e8	−	9.91346e8i	−0.154708	−	0.196381i
$593$	−4.90622e9			−0.966175			−0.483088	−	0.875572i	$-0.660485\pi$
$593$	−4.90622e9			−0.966175			−0.483088	+	0.875572i	$0.660485\pi$
$594$			4.65085e8i			0.0910499i
$595$	1.59093e8			0.0309629
$596$	−1.17083e9			−0.226533
$597$		−	2.55538e8i		−	0.0491525i
$598$			2.53350e9i			0.484470i
$599$	6.93042e9			1.31754			0.658772	−	0.752342i	$-0.271076\pi$
$599$	6.93042e9			1.31754			0.658772	+	0.752342i	$0.271076\pi$
$600$		−	1.02448e8i		−	0.0193630i
$601$	−8.76361e9			−1.64673			−0.823365	−	0.567512i	$-0.807906\pi$
$601$	−8.76361e9			−1.64673			−0.823365	+	0.567512i	$0.807906\pi$
$602$	−2.94890e7			−0.00550900
$603$	−9.12503e9			−1.69482
$604$	4.31528e9			0.796855
$605$		−	5.62652e9i		−	1.03299i
$606$			6.48838e8i			0.118436i
$607$			1.82720e9i			0.331608i	0.986159	+	0.165804i	$0.0530219\pi$
$607$			1.82720e9i			0.331608i	−0.986159	+	0.165804i	$0.946978\pi$
$608$	−1.86633e9			−0.336764
$609$			1.26742e8i			0.0227384i
$610$		−	3.75178e9i		−	0.669242i
$611$		−	3.46755e9i		−	0.615004i
$612$		−	8.66860e8i		−	0.152869i
$613$	−7.12745e9			−1.24975			−0.624874	−	0.780725i	$-0.714850\pi$
$613$	−7.12745e9			−1.24975			−0.624874	+	0.780725i	$0.714850\pi$
$614$		−	3.01999e9i		−	0.526522i
$615$		−	1.67790e9i		−	0.290872i
$616$			3.80658e7i			0.00656148i
$617$	3.34754e9			0.573757			0.286878	−	0.957967i	$-0.407382\pi$
$617$	3.34754e9			0.573757			0.286878	+	0.957967i	$0.407382\pi$
$618$	−1.60807e8			−0.0274060
$619$	1.11248e10			1.88527			0.942635	−	0.333826i	$-0.108340\pi$
$619$	1.11248e10			1.88527			0.942635	+	0.333826i	$0.108340\pi$
$620$	−2.14345e9			−0.361195
$621$			1.80396e9i			0.302278i
$622$	−3.17573e9			−0.529148
$623$			1.68681e8i			0.0279485i
$624$		−	6.20096e8i		−	0.102167i
$625$	−6.99670e9			−1.14634
$626$	−5.31278e9			−0.865589
$627$		−	7.94607e8i		−	0.128741i
$628$	−4.05547e9			−0.653406
$629$	−1.65561e9	+	1.30428e9i	−0.265266	+	0.208975i
$630$	−3.68404e8			−0.0586993
$631$			8.68011e9i			1.37538i	0.726005	+	0.687690i	$0.241375\pi$
$631$			8.68011e9i			1.37538i	−0.726005	+	0.687690i	$0.758625\pi$
$632$	5.41393e8			0.0853105
$633$	1.46623e9			0.229768
$634$		−	7.83558e9i		−	1.22112i
$635$		−	3.48593e9i		−	0.540269i
$636$	1.19684e9			0.184474
$637$			8.60482e9i			1.31903i
$638$	8.91607e8			0.135926
$639$	−5.85478e9			−0.887682
$640$	−6.36216e8			−0.0959344
$641$	1.35809e9			0.203670			0.101835	−	0.994801i	$-0.467529\pi$
$641$	1.35809e9			0.203670			0.101835	+	0.994801i	$0.467529\pi$
$642$			4.21035e8i			0.0627980i
$643$			3.88042e9i			0.575626i	0.957687	+	0.287813i	$0.0929281\pi$
$643$			3.88042e9i			0.575626i	−0.957687	+	0.287813i	$0.907072\pi$
$644$			1.47649e8i			0.0217835i
$645$	2.09843e8			0.0307918
$646$			3.11689e9i			0.454892i
$647$			5.46475e9i			0.793241i	0.917983	+	0.396621i	$0.129817\pi$
$647$			5.46475e9i			0.793241i	−0.917983	+	0.396621i	$0.870183\pi$
$648$			1.77561e9i			0.256352i
$649$			3.07409e8i			0.0441428i
$650$	1.17099e9			0.167247
$651$		−	1.21752e8i		−	0.0172958i
$652$		−	3.77023e9i		−	0.532723i
$653$		−	1.03020e10i		−	1.44786i	−0.689875	−	0.723929i	$-0.742334\pi$
$653$		−	1.03020e10i		−	1.44786i	0.689875	−	0.723929i	$-0.257666\pi$
$654$	−1.53354e9			−0.214375
$655$	4.72166e9			0.656523
$656$	−1.57477e9			−0.217798
$657$	−5.69898e9			−0.784004
$658$		−	2.02083e8i		−	0.0276529i
$659$	−1.12114e10			−1.52602			−0.763011	−	0.646386i	$-0.776280\pi$
$659$	−1.12114e10			−1.52602			−0.763011	+	0.646386i	$0.776280\pi$
$660$		−	2.70874e8i		−	0.0366745i
$661$			6.79897e9i			0.915669i	0.889038	+	0.457834i	$0.151375\pi$
$661$			6.79897e9i			0.915669i	−0.889038	+	0.457834i	$0.848625\pi$
$662$	5.92191e9			0.793339
$663$	−1.03560e9			−0.138005
$664$		−	3.85981e9i		−	0.511656i
$665$	1.32464e9			0.174671
$666$	3.83382e9	−	3.02026e9i	0.502888	−	0.396173i
$667$	3.45834e9			0.451261
$668$			1.84238e9i			0.239146i
$669$	−5.90436e8			−0.0762397
$670$	1.11847e10			1.43668
$671$		−	1.49918e9i		−	0.191569i
$672$		−	3.61382e7i		−	0.00459382i
$673$	5.94304e9			0.751547			0.375773	−	0.926712i	$-0.377377\pi$
$673$	5.94304e9			0.751547			0.375773	+	0.926712i	$0.377377\pi$
$674$		−	3.64898e9i		−	0.459052i
$675$	8.33797e8			0.104351
$676$	3.07190e9			0.382467
$677$	−1.16219e10			−1.43952			−0.719759	−	0.694224i	$-0.755748\pi$
$677$	−1.16219e10			−1.43952			−0.719759	+	0.694224i	$0.755748\pi$
$678$	−3.48569e9			−0.429521
$679$			8.96861e8i			0.109946i
$680$			1.06252e9i			0.129585i
$681$			2.85448e9i			0.346347i
$682$	−8.56503e8			−0.103391
$683$		−	1.19655e10i		−	1.43701i	−0.695523	−	0.718503i	$-0.744827\pi$
$683$		−	1.19655e10i		−	1.43701i	0.695523	−	0.718503i	$-0.255173\pi$
$684$		−	7.21764e9i		−	0.862380i
$685$			8.05088e9i			0.957031i
$686$			1.00656e9i			0.119043i
$687$	−2.89941e9			−0.341162
$688$		−	1.96946e8i		−	0.0230561i
$689$			1.36801e10i			1.59338i
$690$		−	1.05066e9i		−	0.121756i
$691$	1.52706e10			1.76069			0.880344	−	0.474336i	$-0.157312\pi$
$691$	1.52706e10			1.76069			0.880344	+	0.474336i	$0.157312\pi$
$692$	2.66748e9			0.306006
$693$	−1.47211e8			−0.0168025
$694$	−5.71966e9			−0.649549
$695$		−	1.39183e10i		−	1.57268i
$696$	−8.46459e8			−0.0951642
$697$			2.62997e9i			0.294195i
$698$		−	1.73526e9i		−	0.193140i
$699$	3.34633e9			0.370594
$700$	6.82437e7			0.00752003
$701$			9.98256e9i			1.09453i	0.836959	+	0.547266i	$0.184331\pi$
$701$			9.98256e9i			1.09453i	−0.836959	+	0.547266i	$0.815669\pi$
$702$	5.04682e9			0.550602
$703$	−1.37849e10	+	1.08597e10i	−1.49644	+	1.17889i
$704$	−2.54226e8			−0.0274610
$705$			1.43802e9i			0.154562i
$706$	9.65993e6			0.00103314
$707$	−4.32213e8			−0.0459970
$708$		−	2.91843e8i		−	0.0309052i
$709$		−	1.06532e10i		−	1.12258i	−0.827620	−	0.561289i	$-0.810306\pi$
$709$		−	1.06532e10i		−	1.12258i	0.827620	−	0.561289i	$-0.189694\pi$
$710$	7.17627e9			0.752479
$711$			2.09372e9i			0.218461i
$712$	−1.12655e9			−0.116969
$713$	−3.32218e9			−0.343250
$714$	−6.03531e7			−0.00620520
$715$	3.09614e9			0.316774
$716$		−	6.53687e9i		−	0.665541i
$717$		−	2.24580e9i		−	0.227538i
$718$		−	7.44687e9i		−	0.750824i
$719$	3.96005e9			0.397329			0.198664	−	0.980068i	$-0.436340\pi$
$719$	3.96005e9			0.397329			0.198664	+	0.980068i	$0.436340\pi$
$720$		−	2.46043e9i		−	0.245667i
$721$		−	1.07119e8i		−	0.0106437i
$722$			1.88008e10i			1.85908i
$723$		−	3.71657e9i		−	0.365728i
$724$	2.63018e9			0.257573
$725$		−	1.59846e9i		−	0.155782i
$726$			2.13446e9i			0.207019i
$727$			1.19431e10i			1.15278i	0.817176	+	0.576389i	$0.195539\pi$
$727$			1.19431e10i			1.15278i	−0.817176	+	0.576389i	$0.804461\pi$
$728$	4.13066e8			0.0396789
$729$	−4.98080e9			−0.476160
$730$	6.98531e9			0.664593
$731$	−3.28912e8			−0.0311436
$732$			1.42327e9i			0.134121i
$733$	3.10085e9			0.290815			0.145408	−	0.989372i	$-0.453551\pi$
$733$	3.10085e9			0.290815			0.145408	+	0.989372i	$0.453551\pi$
$734$			7.17550e9i			0.669755i
$735$		−	3.56848e9i		−	0.331495i
$736$	−9.86087e8			−0.0911681
$737$	4.46929e9			0.411247
$738$		−	6.09009e9i		−	0.557733i
$739$	1.08720e10			0.990951			0.495476	−	0.868622i	$-0.334994\pi$
$739$	1.08720e10			0.990951			0.495476	+	0.868622i	$0.334994\pi$
$740$	−4.69915e9	+	3.70197e9i	−0.426293	+	0.335832i
$741$	−8.62259e9			−0.778527
$742$			7.97253e8i			0.0716444i
$743$	−1.13930e10			−1.01901			−0.509503	−	0.860469i	$-0.670171\pi$
$743$	−1.13930e10			−1.01901			−0.509503	+	0.860469i	$0.670171\pi$
$744$	8.13132e8			0.0723862
$745$			5.54993e9i			0.491745i
$746$			8.69006e9i			0.766367i
$747$	1.49270e10			1.31024
$748$			4.24574e8i			0.0370935i
$749$	−2.80465e8			−0.0243889
$750$	2.24202e9			0.194055
$751$	2.17926e10			1.87745			0.938725	−	0.344667i	$-0.112008\pi$
$751$	2.17926e10			1.87745			0.938725	+	0.344667i	$0.112008\pi$
$752$	1.34964e9			0.115732
$753$		−	2.62879e9i		−	0.224375i
$754$		−	9.67518e9i		−	0.821976i
$755$		−	2.04552e10i		−	1.72977i
$756$	2.94121e8			0.0247571
$757$		−	3.05892e6i		−	0.000256290i	−1.00000		0.000128145i	$-0.999959\pi$
$757$		−	3.05892e6i		−	0.000256290i	1.00000		0.000128145i	$-4.07899e-5\pi$
$758$			1.14015e9i			0.0950869i
$759$		−	4.19835e8i		−	0.0348524i
$760$			8.84674e9i			0.731031i
$761$	1.42694e10			1.17370			0.586852	−	0.809695i	$-0.300367\pi$
$761$	1.42694e10			1.17370			0.586852	+	0.809695i	$0.300367\pi$
$762$			1.32241e9i			0.108274i
$763$		−	1.02154e9i		−	0.0832571i
$764$		−	6.76959e9i		−	0.549206i
$765$	−4.10907e9			−0.331840
$766$	1.07869e10			0.867154
$767$	3.33581e9			0.266943
$768$	2.41353e8			0.0192260
$769$			9.54592e8i			0.0756965i	0.999283	+	0.0378482i	$0.0120503\pi$
$769$			9.54592e8i			0.0756965i	−0.999283	+	0.0378482i	$0.987950\pi$
$770$	1.80438e8			0.0142433
$771$			4.10739e9i			0.322757i
$772$		−	3.12685e9i		−	0.244594i
$773$	8.17089e9			0.636270			0.318135	−	0.948045i	$-0.396944\pi$
$773$	8.17089e9			0.636270			0.318135	+	0.948045i	$0.396944\pi$
$774$	7.61645e8			0.0590417
$775$			1.53553e9i			0.118495i
$776$	−5.98978e9			−0.460145
$777$	−2.10279e8	−	2.66921e8i	−0.0160813	−	0.0204131i
$778$	−3.69506e9			−0.281315
$779$			2.18976e10i			1.65965i
$780$	−2.93936e9			−0.221780
$781$	2.86758e9			0.215395
$782$			1.64683e9i			0.123147i
$783$		−	6.88913e9i		−	0.512859i
$784$	−3.34916e9			−0.248216
$785$			1.92237e10i			1.41838i
$786$	−1.79120e9			−0.131572
$787$	1.45631e10			1.06498			0.532492	−	0.846435i	$-0.321256\pi$
$787$	1.45631e10			1.06498			0.532492	+	0.846435i	$0.321256\pi$
$788$	−7.48982e9			−0.545292
$789$	−7.97476e9			−0.578027
$790$		−	2.56630e9i		−	0.185188i
$791$		−	2.32193e9i		−	0.166814i
$792$		−	9.83166e8i		−	0.0703216i
$793$	−1.62682e10			−1.15846
$794$			2.97722e9i			0.211076i
$795$		−	5.67321e9i		−	0.400446i
$796$			1.13685e9i			0.0798927i
$797$			2.97098e9i			0.207872i	0.994584	+	0.103936i	$0.0331437\pi$
$797$			2.97098e9i			0.207872i	−0.994584	+	0.103936i	$0.966856\pi$
$798$	−5.02511e8			−0.0350054
$799$		−	2.25398e9i		−	0.156328i
$800$			4.55773e8i			0.0314727i
$801$		−	4.35671e9i		−	0.299533i
$802$	4.58620e9			0.313937
$803$	2.79127e9			0.190238
$804$	−4.24298e9			−0.287922
$805$	6.99880e8			0.0472866
$806$			9.29425e9i			0.625233i
$807$	3.60020e9			0.241140
$808$		−	2.88658e9i		−	0.192506i
$809$			4.88772e9i			0.324554i	0.986745	+	0.162277i	$0.0518838\pi$
$809$			4.88772e9i			0.324554i	−0.986745	+	0.162277i	$0.948116\pi$
$810$	8.41672e9			0.556475
$811$	−1.44236e9			−0.0949511			−0.0474756	−	0.998872i	$-0.515118\pi$
$811$	−1.44236e9			−0.0949511			−0.0474756	+	0.998872i	$0.515118\pi$
$812$		−	5.63854e8i		−	0.0369591i
$813$	2.96310e9			0.193388
$814$	−1.87774e9	+	1.47928e9i	−0.122025	+	0.0961311i
$815$	−1.78715e10			−1.15641
$816$		−	4.03075e8i		−	0.0259699i
$817$	−2.73858e9			−0.175690
$818$	−1.59693e10			−1.02012
$819$			1.59745e9i			0.101609i
$820$			7.46470e9i			0.472785i
$821$	1.44977e10			0.914321			0.457161	−	0.889384i	$-0.348866\pi$
$821$	1.44977e10			0.914321			0.457161	+	0.889384i	$0.348866\pi$
$822$		−	3.05416e9i		−	0.191796i
$823$	−1.48319e10			−0.927463			−0.463732	−	0.885976i	$-0.653490\pi$
$823$	−1.48319e10			−0.927463			−0.463732	+	0.885976i	$0.653490\pi$
$824$	7.15405e8			0.0445458
$825$	−1.94049e8			−0.0120316
$826$	1.94406e8			0.0120027
$827$		−	1.34376e10i		−	0.826135i	−0.910700	−	0.413067i	$-0.864457\pi$
$827$		−	1.34376e10i		−	0.826135i	0.910700	−	0.413067i	$-0.135543\pi$
$828$		−	3.81348e9i		−	0.233461i
$829$			1.76816e9i			0.107791i	0.998547	+	0.0538954i	$0.0171637\pi$
$829$			1.76816e9i			0.107791i	−0.998547	+	0.0538954i	$0.982836\pi$
$830$	−1.82962e10			−1.11068
$831$		−	1.90480e9i		−	0.115145i
$832$			2.75871e9i			0.166063i
$833$			5.59331e9i			0.335283i
$834$			5.28001e9i			0.315177i
$835$	8.73322e9			0.519125
$836$			3.53508e9i			0.209256i
$837$			6.61790e9i			0.390104i
$838$			2.33103e9i			0.136834i
$839$	−2.67966e10			−1.56644			−0.783219	−	0.621746i	$-0.786424\pi$
$839$	−2.67966e10			−1.56644			−0.783219	+	0.621746i	$0.786424\pi$
$840$	−1.71302e8			−0.00997203
$841$	4.04282e9			0.234368
$842$	−1.43536e10			−0.828647
$843$		−	1.40087e9i		−	0.0805382i
$844$	−6.52304e9			−0.373467
$845$		−	1.45613e10i		−	0.830239i
$846$			5.21943e9i			0.296365i
$847$	−1.42184e9			−0.0804003
$848$	−5.32454e9			−0.299845
$849$		−	4.09110e8i		−	0.0229437i
$850$	7.61170e8			0.0425124
$851$	−7.28334e9	+	5.73778e9i	−0.405114	+	0.319147i
$852$	−2.72237e9			−0.150802
$853$			9.12131e9i			0.503194i	0.967832	+	0.251597i	$0.0809558\pi$
$853$			9.12131e9i			0.503194i	−0.967832	+	0.251597i	$0.919044\pi$
$854$	−9.48084e8			−0.0520888
$855$	−3.42129e10			−1.87201
$856$		−	1.87312e9i		−	0.102072i
$857$		−	2.82440e10i		−	1.53283i	−0.642348	−	0.766413i	$-0.722040\pi$
$857$		−	2.82440e10i		−	1.53283i	0.642348	−	0.766413i	$-0.277960\pi$
$858$	−1.17454e9			−0.0634839
$859$		−	8.24724e9i		−	0.443948i	−0.975053	−	0.221974i	$-0.928750\pi$
$859$		−	8.24724e9i		−	0.443948i	0.975053	−	0.221974i	$-0.0712501\pi$
$860$	−9.33557e8			−0.0500491
$861$	−4.24009e8			−0.0226393
$862$	2.08307e10			1.10772
$863$	1.59406e10			0.844240			0.422120	−	0.906540i	$-0.361286\pi$
$863$	1.59406e10			0.844240			0.422120	+	0.906540i	$0.361286\pi$
$864$			1.96432e9i			0.103613i
$865$		−	1.26443e10i		−	0.664263i
$866$		−	4.47104e9i		−	0.233935i
$867$	5.22987e9			0.272536
$868$			5.41655e8i			0.0281128i
$869$		−	1.02547e9i		−	0.0530095i
$870$			4.01236e9i			0.206577i
$871$		−	4.84980e10i		−	2.48691i
$872$	6.82250e9			0.348446
$873$		−	2.31642e10i		−	1.17833i
$874$			1.37118e10i			0.694711i
$875$			1.49349e9i			0.0753655i
$876$	−2.64993e9			−0.133189
$877$	1.79597e10			0.899087			0.449543	−	0.893258i	$-0.351587\pi$
$877$	1.79597e10			0.899087			0.449543	+	0.893258i	$0.351587\pi$
$878$	−2.29229e9			−0.114298
$879$	−2.95164e9			−0.146589
$880$			1.20508e9i			0.0596109i
$881$	9.39202e9			0.462747			0.231373	−	0.972865i	$-0.425678\pi$
$881$	9.39202e9			0.462747			0.231373	+	0.972865i	$0.425678\pi$
$882$		−	1.29522e10i		−	0.635626i
$883$		−	2.63143e10i		−	1.28626i	−0.765755	−	0.643132i	$-0.777635\pi$
$883$		−	2.63143e10i		−	1.28626i	0.765755	−	0.643132i	$-0.222365\pi$
$884$	4.60722e9			0.224314
$885$	−1.38338e9			−0.0670875
$886$			6.25034e8i			0.0301916i
$887$	−3.06311e9			−0.147377			−0.0736885	−	0.997281i	$-0.523477\pi$
$887$	−3.06311e9			−0.147377			−0.0736885	+	0.997281i	$0.523477\pi$
$888$	1.78266e9	−	1.40437e9i	0.0854324	−	0.0673032i
$889$	−8.80903e8			−0.0420506
$890$			5.34007e9i			0.253911i
$891$	3.36325e9			0.159290
$892$	2.62676e9			0.123920
$893$		−	1.87670e10i		−	0.881892i
$894$		−	2.10540e9i		−	0.0985495i
$895$	−3.09859e10			−1.44472
$896$			1.60773e8i			0.00746682i
$897$	−4.55579e9			−0.210761
$898$	−5.89607e9			−0.271704
$899$	1.26871e10			0.582375
$900$	−1.76260e9			−0.0805946
$901$			8.89231e9i			0.405021i
$902$			2.98283e9i			0.135334i
$903$		−	5.30278e7i		−	0.00239660i
$904$	1.55073e10			0.698146
$905$		−	1.24675e10i		−	0.559126i
$906$			7.75982e9i			0.346659i
$907$			3.77092e10i			1.67812i	0.544041	+	0.839058i	$0.316893\pi$
$907$			3.77092e10i			1.67812i	−0.544041	+	0.839058i	$0.683107\pi$
$908$		−	1.26991e10i		−	0.562954i
$909$	1.11632e10			0.492965
$910$		−	1.95801e9i		−	0.0861330i
$911$			1.62520e10i			0.712183i	0.934451	+	0.356091i	$0.115891\pi$
$911$			1.62520e10i			0.712183i	−0.934451	+	0.356091i	$0.884109\pi$
$912$		−	3.35608e9i		−	0.146504i
$913$	−7.31100e9			−0.317928
$914$	−1.34139e10			−0.581090
$915$	6.74653e9			0.291143
$916$	1.28990e10			0.554527
$917$		−	1.19318e9i		−	0.0510989i
$918$	3.28053e9			0.139957
$919$			2.69483e10i			1.14532i	0.819793	+	0.572660i	$0.194088\pi$
$919$			2.69483e10i			1.14532i	−0.819793	+	0.572660i	$0.805912\pi$
$920$			4.67422e9i			0.197903i
$921$	5.43061e9			0.229055
$922$	−1.89406e10			−0.795857
$923$		−	3.11172e10i		−	1.30255i
$924$	−6.84506e7			−0.00285447
$925$	2.65202e9	+	3.36639e9i	0.110175	+	0.139852i
$926$	−1.00901e10			−0.417596
$927$			2.76668e9i			0.114072i
$928$	3.76576e9			0.154680
$929$	−2.50422e10			−1.02475			−0.512374	−	0.858763i	$-0.671234\pi$
$929$	−2.50422e10			−1.02475			−0.512374	+	0.858763i	$0.671234\pi$
$930$		−	3.85439e9i		−	0.157132i
$931$			4.65709e10i			1.89143i
$932$	−1.48873e10			−0.602366
$933$		−	5.71066e9i		−	0.230197i
$934$	1.39060e10			0.558456
$935$	2.01256e9			0.0805206
$936$	−1.06687e10			−0.425252
$937$	3.50866e10			1.39333			0.696664	−	0.717398i	$-0.254667\pi$
$937$	3.50866e10			1.39333			0.696664	+	0.717398i	$0.254667\pi$
$938$		−	2.82639e9i		−	0.111821i
$939$		−	9.55355e9i		−	0.376561i
$940$		−	6.39751e9i		−	0.251225i
$941$	3.21248e10			1.25683			0.628416	−	0.777877i	$-0.283703\pi$
$941$	3.21248e10			1.25683			0.628416	+	0.777877i	$0.283703\pi$
$942$		−	7.29264e9i		−	0.284254i
$943$			1.15697e10i			0.449296i
$944$			1.29836e9i			0.0502335i
$945$		−	1.39418e9i		−	0.0537414i
$946$	−3.73041e8			−0.0143264
$947$			1.87259e10i			0.716502i	0.933625	+	0.358251i	$0.116627\pi$
$947$			1.87259e10i			0.716502i	−0.933625	+	0.358251i	$0.883373\pi$
$948$			9.73543e8i			0.0371130i
$949$		−	3.02891e10i		−	1.15042i
$950$	6.33764e9			0.239825
$951$	1.40901e10			0.531230
$952$	2.68502e8			0.0100860
$953$	−3.28075e10			−1.22786			−0.613928	−	0.789362i	$-0.710412\pi$
$953$	−3.28075e10			−1.22786			−0.613928	+	0.789362i	$0.710412\pi$
$954$		−	2.05915e10i		−	0.767837i
$955$	−3.20890e10			−1.19219
$956$			9.99120e9i			0.369841i
$957$			1.60331e9i			0.0591323i
$958$	−3.48749e10			−1.28154
$959$	2.03448e9			0.0744882
$960$		−	1.14406e9i		−	0.0417347i
$961$	1.53250e10			0.557019
$962$	1.60522e10	+	2.03761e10i	0.581329	+	0.737919i
$963$	7.24388e9			0.261384
$964$			1.65345e10i			0.594457i
$965$	−1.48218e10			−0.530953
$966$	−2.65505e8			−0.00947659
$967$			8.77361e9i			0.312022i	0.987755	+	0.156011i	$0.0498636\pi$
$967$			8.77361e9i			0.312022i	−0.987755	+	0.156011i	$0.950136\pi$
$968$		−	9.49589e9i		−	0.336490i
$969$	−5.60486e9			−0.197893
$970$			2.83926e10i			0.998859i
$971$	4.17553e10			1.46368			0.731838	−	0.681479i	$-0.238663\pi$
$971$	4.17553e10			1.46368			0.731838	+	0.681479i	$0.238663\pi$
$972$	−1.15835e10			−0.404583
$973$	−3.51719e9			−0.122406
$974$	3.51971e10			1.22054
$975$			2.10570e9i			0.0727581i
$976$		−	6.33188e9i		−	0.218001i
$977$		−	1.62656e10i		−	0.558005i	−0.960290	−	0.279002i	$-0.909996\pi$
$977$		−	1.62656e10i		−	0.558005i	0.960290	−	0.279002i	$-0.0900037\pi$
$978$	6.77970e9			0.231753
$979$			2.13385e9i			0.0726815i
$980$			1.58756e10i			0.538814i
$981$			2.63845e10i			0.892294i
$982$		−	2.39202e10i		−	0.806072i
$983$	−3.96751e9			−0.133224			−0.0666118	−	0.997779i	$-0.521219\pi$
$983$	−3.96751e9			−0.133224			−0.0666118	+	0.997779i	$0.521219\pi$
$984$		−	2.83179e9i		−	0.0947497i
$985$			3.55030e10i			1.18369i
$986$		−	6.28906e9i		−	0.208938i
$987$	3.63390e8			0.0120299
$988$	3.83605e10			1.26542
$989$	−1.44694e9			−0.0475625
$990$	−4.66038e9			−0.152650
$991$		−	1.00915e10i		−	0.329379i	−0.986345	−	0.164690i	$-0.947338\pi$
$991$		−	1.00915e10i		−	0.329379i	0.986345	−	0.164690i	$-0.0526622\pi$
$992$	−3.61750e9			−0.117657
$993$			1.06489e10i			0.345130i
$994$		−	1.81346e9i		−	0.0585674i
$995$	5.38886e9			0.173427
$996$	6.94079e9			0.222588
$997$		−	4.86477e10i		−	1.55464i	−0.629107	−	0.777319i	$-0.716579\pi$
$997$		−	4.86477e10i		−	1.55464i	0.629107	−	0.777319i	$-0.283421\pi$
$998$	4.13964e9			0.131827
$999$	1.14298e10	+	1.45086e10i	0.362711	+	0.460413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.8.b.a.73.8	✓	24
37.36	even	2	inner	74.8.b.a.73.20	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.8.b.a.73.8	✓	24	1.1	even	1	trivial
74.8.b.a.73.20	yes	24	37.36	even	2	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	74.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-8.00000i q^{2} +14.3858 q^{3} -64.0000 q^{4} +303.371i q^{5} -115.086i q^{6} +76.6627 q^{7} +512.000i q^{8} -1980.05 q^{9} +2426.97 q^{10} +969.796 q^{11} -920.689 q^{12} -10523.6i q^{13} -613.301i q^{14} +4364.23i q^{15} +4096.00 q^{16} -6840.58i q^{17} +15840.4i q^{18} -56955.9i q^{19} -19415.8i q^{20} +1102.85 q^{21} -7758.37i q^{22} -30093.0i q^{23} +7365.51i q^{24} -13909.1 q^{25} -84189.1 q^{26} -59946.2 q^{27} -4906.41 q^{28} +114922. i q^{29} +34913.8 q^{30} -110397. i q^{31} -32768.0i q^{32} +13951.3 q^{33} -54724.6 q^{34} +23257.3i q^{35} +126723. q^{36} +(-190668. - 242028. i) q^{37} -455647. q^{38} -151391. i q^{39} -155326. q^{40} -384466. q^{41} -8822.81i q^{42} -48082.4i q^{43} -62067.0 q^{44} -600690. i q^{45} -240744. q^{46} +329501. q^{47} +58924.1 q^{48} -817666. q^{49} +111273. i q^{50} -98406.9i q^{51} +673513. i q^{52} -1.29994e6 q^{53} +479569. i q^{54} +294208. i q^{55} +39251.3i q^{56} -819354. i q^{57} +919376. q^{58} +316983. i q^{59} -279310. i q^{60} -1.54587e6i q^{61} -883178. q^{62} -151796. q^{63} -262144. q^{64} +3.19257e6 q^{65} -111610. i q^{66} +4.60848e6 q^{67} +437797. i q^{68} -432910. i q^{69} +186058. q^{70} +2.95688e6 q^{71} -1.01379e6i q^{72} +2.87820e6 q^{73} +(-1.93622e6 + 1.52535e6i) q^{74} -200093. q^{75} +3.64518e6i q^{76} +74347.2 q^{77} -1.21112e6 q^{78} -1.05741e6i q^{79} +1.24261e6i q^{80} +3.46800e6 q^{81} +3.07573e6i q^{82} -7.53870e6 q^{83} -70582.5 q^{84} +2.07523e6 q^{85} -384659. q^{86} +1.65324e6i q^{87} +496536. i q^{88} +2.20030e6i q^{89} -4.80552e6 q^{90} -806770. i q^{91} +1.92595e6i q^{92} -1.58815e6i q^{93} -2.63601e6i q^{94} +1.72788e7 q^{95} -471393. i q^{96} +1.16988e7i q^{97} +6.54133e6i q^{98} -1.92025e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 106 q^{3} - 1536 q^{4} + 104 q^{7} + 17554 q^{9} + 1136 q^{10} + 366 q^{11} + 6784 q^{12} + 98304 q^{16} - 239820 q^{21} - 675570 q^{25} + 97008 q^{26} + 338780 q^{27} - 6656 q^{28} + 350400 q^{30}+ \cdots - 53279900 q^{99}+O(q^{100}) \) 24 * q - 106 * q^3 - 1536 * q^4 + 104 * q^7 + 17554 * q^9 + 1136 * q^10 + 366 * q^11 + 6784 * q^12 + 98304 * q^16 - 239820 * q^21 - 675570 * q^25 + 97008 * q^26 + 338780 * q^27 - 6656 * q^28 + 350400 * q^30 - 763792 * q^33 + 713632 * q^34 - 1123456 * q^36 + 41652 * q^37 - 30816 * q^38 - 72704 * q^40 + 1729722 * q^41 - 23424 * q^44 - 488496 * q^46 + 114756 * q^47 - 434176 * q^48 + 4003056 * q^49 - 1115964 * q^53 - 2075632 * q^58 + 3248208 * q^62 - 2350900 * q^63 - 6291456 * q^64 - 5246556 * q^65 - 2717994 * q^67 - 5649440 * q^70 + 10643280 * q^71 - 10450370 * q^73 - 1064064 * q^74 - 17737980 * q^75 + 11665236 * q^77 + 8431856 * q^78 + 47300176 * q^81 + 555912 * q^83 + 15348480 * q^84 - 4853096 * q^85 - 12070464 * q^86 + 32064160 * q^90 - 58516956 * q^95 - 53279900 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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