LMFDB - Embedded newform 76.8.d.a.75.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,8,Mod(75,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("76.75");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	76.d (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:	$23.7412619368$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.18
Character	$\chi$	$=$	76.75
Dual form			76.8.d.a.75.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.73771 + 8.25396i) q^{2} -29.6173 q^{3} +(-8.25557 - 127.733i) q^{4} -224.326 q^{5} +(229.170 - 244.460i) q^{6} +1196.17i q^{7} +(1118.19 + 920.224i) q^{8} -1309.82 q^{9} +O(q^{10})$	\(q+(-7.73771 + 8.25396i) q^{2} -29.6173 q^{3} +(-8.25557 - 127.733i) q^{4} -224.326 q^{5} +(229.170 - 244.460i) q^{6} +1196.17i q^{7} +(1118.19 + 920.224i) q^{8} -1309.82 q^{9} +(1735.77 - 1851.58i) q^{10} +8011.66i q^{11} +(244.507 + 3783.12i) q^{12} +825.227i q^{13} +(-9873.15 - 9255.64i) q^{14} +6643.93 q^{15} +(-16247.7 + 2109.03i) q^{16} -2801.94 q^{17} +(10135.0 - 10811.2i) q^{18} +(-28454.1 + 9178.01i) q^{19} +(1851.94 + 28654.0i) q^{20} -35427.4i q^{21} +(-66127.9 - 61991.9i) q^{22} -1752.08i q^{23} +(-33117.6 - 27254.5i) q^{24} -27802.7 q^{25} +(-6811.39 - 6385.37i) q^{26} +103566. q^{27} +(152791. - 9875.08i) q^{28} +102545. i q^{29} +(-51408.8 + 54838.7i) q^{30} +89910.0 q^{31} +(108312. - 150427. i) q^{32} -237283. i q^{33} +(21680.6 - 23127.1i) q^{34} -268333. i q^{35} +(10813.3 + 167308. i) q^{36} -30843.0i q^{37} +(144415. - 305876. i) q^{38} -24441.0i q^{39} +(-250838. - 206430. i) q^{40} -658946. i q^{41} +(292416. + 274127. i) q^{42} -231513. i q^{43} +(1.02336e6 - 66140.8i) q^{44} +293827. q^{45} +(14461.6 + 13557.1i) q^{46} +563190. i q^{47} +(481212. - 62463.6i) q^{48} -607285. q^{49} +(215130. - 229482. i) q^{50} +82985.9 q^{51} +(105409. - 6812.72i) q^{52} -630479. i q^{53} +(-801365. + 854831. i) q^{54} -1.79723e6i q^{55} +(-1.10075e6 + 1.33754e6i) q^{56} +(842733. - 271828. i) q^{57} +(-846403. - 793465. i) q^{58} -1.62223e6 q^{59} +(-54849.4 - 848652. i) q^{60} -518123. q^{61} +(-695698. + 742113. i) q^{62} -1.56677e6i q^{63} +(403527. + 2.05796e6i) q^{64} -185120. i q^{65} +(1.95853e6 + 1.83603e6i) q^{66} +2.22768e6 q^{67} +(23131.6 + 357902. i) q^{68} +51891.8i q^{69} +(2.21481e6 + 2.07628e6i) q^{70} +2.63710e6 q^{71} +(-1.46462e6 - 1.20533e6i) q^{72} -5.93909e6 q^{73} +(254577. + 238655. i) q^{74} +823441. q^{75} +(1.40724e6 + 3.55877e6i) q^{76} -9.58333e6 q^{77} +(201735. + 189117. i) q^{78} -3.46606e6 q^{79} +(3.64478e6 - 473110. i) q^{80} -202776. q^{81} +(5.43891e6 + 5.09873e6i) q^{82} -4.18480e6i q^{83} +(-4.52526e6 + 292473. i) q^{84} +628549. q^{85} +(1.91090e6 + 1.79138e6i) q^{86} -3.03711e6i q^{87} +(-7.37252e6 + 8.95852e6i) q^{88} +8.19473e6i q^{89} +(-2.27355e6 + 2.42523e6i) q^{90} -987114. q^{91} +(-223799. + 14464.4i) q^{92} -2.66289e6 q^{93} +(-4.64854e6 - 4.35780e6i) q^{94} +(6.38300e6 - 2.05887e6i) q^{95} +(-3.20791e6 + 4.45523e6i) q^{96} +1.12198e7i q^{97} +(4.69900e6 - 5.01251e6i) q^{98} -1.04938e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9}+O(q^{10}) $ 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9	$ 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9} + 13050 q^{16} + 23968 q^{17} - 79660 q^{20} - 232154 q^{24} + 937496 q^{25} - 391242 q^{26} - 37666 q^{28} - 468496 q^{30} - 1128652 q^{36} - 530466 q^{38} + 651806 q^{42} + 1433776 q^{44} - 321252 q^{45} - 4014380 q^{49} + 1697586 q^{54} + 137420 q^{57} + 2227894 q^{58} - 3042164 q^{61} + 2261524 q^{62} + 9825150 q^{64} - 749476 q^{66} - 11176962 q^{68} + 598424 q^{73} - 6195964 q^{74} - 1714536 q^{76} - 2556764 q^{77} + 16623216 q^{80} + 43726748 q^{81} - 20460388 q^{82} + 27222844 q^{85} - 61733582 q^{92} + 17778200 q^{93} - 36370886 q^{96}+O(q^{100}) $ 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9 + 13050 * q^16 + 23968 * q^17 - 79660 * q^20 - 232154 * q^24 + 937496 * q^25 - 391242 * q^26 - 37666 * q^28 - 468496 * q^30 - 1128652 * q^36 - 530466 * q^38 + 651806 * q^42 + 1433776 * q^44 - 321252 * q^45 - 4014380 * q^49 + 1697586 * q^54 + 137420 * q^57 + 2227894 * q^58 - 3042164 * q^61 + 2261524 * q^62 + 9825150 * q^64 - 749476 * q^66 - 11176962 * q^68 + 598424 * q^73 - 6195964 * q^74 - 1714536 * q^76 - 2556764 * q^77 + 16623216 * q^80 + 43726748 * q^81 - 20460388 * q^82 + 27222844 * q^85 - 61733582 * q^92 + 17778200 * q^93 - 36370886 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−7.73771	+	8.25396i	−0.683924	+	0.729554i
$2$	−7.73771	+	8.25396i	−0.683924	+	0.729554i
$3$	−29.6173			−0.633316			−0.316658	−	0.948540i	$-0.602561\pi$
$3$	−29.6173			−0.633316			−0.316658	+	0.948540i	$0.602561\pi$
$4$	−8.25557	−	127.733i	−0.0644966	−	0.997918i
$5$	−224.326			−0.802574			−0.401287	−	0.915952i	$-0.631437\pi$
$5$	−224.326			−0.802574			−0.401287	+	0.915952i	$0.631437\pi$
$6$	229.170	−	244.460i	0.433140	−	0.462038i
$7$			1196.17i			1.31811i	0.752096	+	0.659053i	$0.229043\pi$
$7$			1196.17i			1.31811i	−0.752096	+	0.659053i	$0.770957\pi$
$8$	1118.19	+	920.224i	0.772145	+	0.635446i
$9$	−1309.82			−0.598911
$10$	1735.77	−	1851.58i	0.548899	−	0.585521i
$11$			8011.66i			1.81488i	0.420181	+	0.907440i	$0.361967\pi$
$11$			8011.66i			1.81488i	−0.420181	+	0.907440i	$0.638033\pi$
$12$	244.507	+	3783.12i	0.0408468	+	0.631998i
$13$			825.227i			0.104177i	0.998642	+	0.0520885i	$0.0165878\pi$
$13$			825.227i			0.104177i	−0.998642	+	0.0520885i	$0.983412\pi$
$14$	−9873.15	−	9255.64i	−0.961630	−	0.901485i
$15$	6643.93			0.508283
$16$	−16247.7	+	2109.03i	−0.991680	+	0.128725i
$17$	−2801.94			−0.138321			−0.0691605	−	0.997606i	$-0.522032\pi$
$17$	−2801.94			−0.138321			−0.0691605	+	0.997606i	$0.522032\pi$
$18$	10135.0	−	10811.2i	0.409609	−	0.436937i
$19$	−28454.1	+	9178.01i	−0.951716	+	0.306981i
$19$	−28454.1	+	9178.01i	−0.951716	+	0.306981i
$20$	1851.94	+	28654.0i	0.0517633	+	0.800903i
$21$		−	35427.4i		−	0.834778i
$22$	−66127.9	−	61991.9i	−1.32405	−	1.24124i
$23$		−	1752.08i		−	0.0300266i	−0.999887	−	0.0150133i	$-0.995221\pi$
$23$		−	1752.08i		−	0.0300266i	0.999887	−	0.0150133i	$-0.00477907\pi$
$24$	−33117.6	−	27254.5i	−0.489012	−	0.402438i
$25$	−27802.7			−0.355875
$26$	−6811.39	−	6385.37i	−0.0760027	−	0.0712491i
$27$	103566.			1.01262
$28$	152791.	−	9875.08i	1.31536	−	0.0850135i
$29$			102545.i			0.780768i	0.920652	+	0.390384i	$0.127658\pi$
$29$			102545.i			0.780768i	−0.920652	+	0.390384i	$0.872342\pi$
$30$	−51408.8	+	54838.7i	−0.347627	+	0.370820i
$31$	89910.0			0.542054			0.271027	−	0.962572i	$-0.412637\pi$
$31$	89910.0			0.542054			0.271027	+	0.962572i	$0.412637\pi$
$32$	108312.	−	150427.i	0.584322	−	0.811522i
$33$		−	237283.i		−	1.14939i
$34$	21680.6	−	23127.1i	0.0946010	−	0.100913i
$35$		−	268333.i		−	1.05788i
$36$	10813.3	+	167308.i	0.0386277	+	0.597664i
$37$		−	30843.0i		−	0.100104i	−0.998747	−	0.0500519i	$-0.984061\pi$
$37$		−	30843.0i		−	0.100104i	0.998747	−	0.0500519i	$-0.0159387\pi$
$38$	144415.	−	305876.i	0.426942	−	0.904279i
$39$		−	24441.0i		−	0.0659770i
$40$	−250838.	−	206430.i	−0.619704	−	0.509993i
$41$		−	658946.i		−	1.49316i	−0.665296	−	0.746580i	$-0.731695\pi$
$41$		−	658946.i		−	1.49316i	0.665296	−	0.746580i	$-0.268305\pi$
$42$	292416.	+	274127.i	0.609015	+	0.570925i
$43$		−	231513.i		−	0.444054i	−0.975041	−	0.222027i	$-0.928733\pi$
$43$		−	231513.i		−	0.444054i	0.975041	−	0.222027i	$-0.0712673\pi$
$44$	1.02336e6	−	66140.8i	1.81110	−	0.117054i
$45$	293827.			0.480670
$46$	14461.6	+	13557.1i	0.0219060	+	0.0205359i
$47$			563190.i			0.791247i	0.918413	+	0.395623i	$0.129471\pi$
$47$			563190.i			0.791247i	−0.918413	+	0.395623i	$0.870529\pi$
$48$	481212.	−	62463.6i	0.628047	−	0.0815234i
$49$	−607285.			−0.737406
$50$	215130.	−	229482.i	0.243391	−	0.259630i
$51$	82985.9			0.0876009
$52$	105409.	−	6812.72i	0.103960	−	0.00671907i
$53$		−	630479.i		−	0.581708i	−0.956767	−	0.290854i	$-0.906061\pi$
$53$		−	630479.i		−	0.581708i	0.956767	−	0.290854i	$-0.0939394\pi$
$54$	−801365.	+	854831.i	−0.692552	+	0.738757i
$55$		−	1.79723e6i		−	1.45658i
$56$	−1.10075e6	+	1.33754e6i	−0.837586	+	1.01777i
$57$	842733.	−	271828.i	0.602737	−	0.194416i
$58$	−846403.	−	793465.i	−0.569612	−	0.533986i
$59$	−1.62223e6			−1.02833			−0.514164	−	0.857692i	$-0.671898\pi$
$59$	−1.62223e6			−1.02833			−0.514164	+	0.857692i	$0.671898\pi$
$60$	−54849.4	−	848652.i	−0.0327825	−	0.507225i
$61$	−518123.			−0.292266			−0.146133	−	0.989265i	$-0.546683\pi$
$61$	−518123.			−0.292266			−0.146133	+	0.989265i	$0.546683\pi$
$62$	−695698.	+	742113.i	−0.370723	+	0.395457i
$63$		−	1.56677e6i		−	0.789428i
$64$	403527.	+	2.05796e6i	0.192417	+	0.981313i
$65$		−	185120.i		−	0.0836098i
$66$	1.95853e6	+	1.83603e6i	0.838544	+	0.786097i
$67$	2.22768e6			0.904879			0.452439	−	0.891795i	$-0.350554\pi$
$67$	2.22768e6			0.904879			0.452439	+	0.891795i	$0.350554\pi$
$68$	23131.6	+	357902.i	0.00892124	+	0.138033i
$69$			51891.8i			0.0190163i
$70$	2.21481e6	+	2.07628e6i	0.771779	+	0.723508i
$71$	2.63710e6			0.874424			0.437212	−	0.899358i	$-0.355966\pi$
$71$	2.63710e6			0.874424			0.437212	+	0.899358i	$0.355966\pi$
$72$	−1.46462e6	−	1.20533e6i	−0.462446	−	0.380575i
$73$	−5.93909e6			−1.78686			−0.893428	−	0.449206i	$-0.851707\pi$
$73$	−5.93909e6			−1.78686			−0.893428	+	0.449206i	$0.851707\pi$
$74$	254577.	+	238655.i	0.0730311	+	0.0684634i
$75$	823441.			0.225381
$76$	1.40724e6	+	3.55877e6i	0.367724	+	0.929935i
$77$	−9.58333e6			−2.39221
$78$	201735.	+	189117.i	0.0481337	+	0.0451232i
$79$	−3.46606e6			−0.790935			−0.395468	−	0.918480i	$-0.629417\pi$
$79$	−3.46606e6			−0.790935			−0.395468	+	0.918480i	$0.629417\pi$
$80$	3.64478e6	−	473110.i	0.795897	−	0.103311i
$81$	−202776.			−0.0423953
$82$	5.43891e6	+	5.09873e6i	1.08934	+	1.02121i
$83$		−	4.18480e6i		−	0.803344i	−0.915784	−	0.401672i	$-0.868429\pi$
$83$		−	4.18480e6i		−	0.803344i	0.915784	−	0.401672i	$-0.131571\pi$
$84$	−4.52526e6	+	292473.i	−0.833040	+	0.0538404i
$85$	628549.			0.111013
$86$	1.91090e6	+	1.79138e6i	0.323961	+	0.303699i
$87$		−	3.03711e6i		−	0.494473i
$88$	−7.37252e6	+	8.95852e6i	−1.15326	+	1.40135i
$89$			8.19473e6i			1.23217i	0.787681	+	0.616084i	$0.211282\pi$
$89$			8.19473e6i			1.23217i	−0.787681	+	0.616084i	$0.788718\pi$
$90$	−2.27355e6	+	2.42523e6i	−0.328742	+	0.350675i
$91$	−987114.			−0.137316
$92$	−223799.	+	14464.4i	−0.0299641	+	0.00193662i
$93$	−2.66289e6			−0.343291
$94$	−4.64854e6	−	4.35780e6i	−0.577257	−	0.541153i
$95$	6.38300e6	−	2.05887e6i	0.763822	−	0.246375i
$96$	−3.20791e6	+	4.45523e6i	−0.370061	+	0.513950i
$97$			1.12198e7i			1.24820i	0.781345	+	0.624099i	$0.214534\pi$
$97$			1.12198e7i			1.24820i	−0.781345	+	0.624099i	$0.785466\pi$
$98$	4.69900e6	−	5.01251e6i	0.504329	−	0.537977i
$99$		−	1.04938e7i		−	1.08695i
$100$	229527.	+	3.55134e6i	0.0229527	+	0.355134i
$101$	1.44678e7			1.39726			0.698632	−	0.715481i	$-0.253792\pi$
$101$	1.44678e7			1.39726			0.698632	+	0.715481i	$0.253792\pi$
$102$	−642121.	+	684962.i	−0.0599123	+	0.0639095i
$103$	−4.31089e6			−0.388720			−0.194360	−	0.980930i	$-0.562263\pi$
$103$	−4.31089e6			−0.388720			−0.194360	+	0.980930i	$0.562263\pi$
$104$	−759394.	+	922757.i	−0.0661989	+	0.0804398i
$105$			7.94729e6i			0.669971i
$106$	5.20394e6	+	4.87847e6i	0.424387	+	0.397844i
$107$	1.84161e7			1.45330			0.726648	−	0.687010i	$-0.241077\pi$
$107$	1.84161e7			1.45330			0.726648	+	0.687010i	$0.241077\pi$
$108$	−854998.	−	1.32289e7i	−0.0653103	−	1.01051i
$109$		−	1.72565e7i		−	1.27632i	−0.769903	−	0.638161i	$-0.779695\pi$
$109$		−	1.72565e7i		−	1.27632i	0.769903	−	0.638161i	$-0.220305\pi$
$110$	1.48342e7	+	1.39064e7i	1.06265	+	0.996187i
$111$			913486.i			0.0633974i
$112$	−2.52276e6	−	1.94350e7i	−0.169673	−	1.30714i
$113$		−	1.56714e7i		−	1.02173i	−0.859662	−	0.510863i	$-0.829326\pi$
$113$		−	1.56714e7i		−	1.02173i	0.859662	−	0.510863i	$-0.170674\pi$
$114$	−4.27717e6	+	9.05920e6i	−0.270389	+	0.572694i
$115$			393038.i			0.0240986i
$116$	1.30985e7	−	846569.i	0.779143	−	0.0503569i
$117$		−	1.08090e6i		−	0.0623927i
$118$	1.25524e7	−	1.33899e7i	0.703298	−	0.750220i
$119$		−	3.35161e6i		−	0.182322i
$120$	7.42915e6	+	6.11391e6i	0.392468	+	0.322986i
$121$	−4.46995e7			−2.29379
$122$	4.00909e6	−	4.27656e6i	0.199888	−	0.213224i
$123$			1.95162e7i			0.945642i
$124$	−742258.	−	1.14845e7i	−0.0349606	−	0.540925i
$125$	2.37624e7			1.08819
$126$	1.29320e7	+	1.21232e7i	0.575930	+	0.539909i
$127$	−3.53016e7			−1.52926			−0.764629	−	0.644471i	$-0.777078\pi$
$127$	−3.53016e7			−1.52926			−0.764629	+	0.644471i	$0.777078\pi$
$128$	−2.01087e7	−	1.25932e7i	−0.847519	−	0.530765i
$129$			6.85678e6i			0.281227i
$130$	1.52797e6	+	1.43241e6i	0.0609978	+	0.0571827i
$131$		−	7.61619e6i		−	0.295998i	−0.988988	−	0.147999i	$-0.952717\pi$
$131$		−	7.61619e6i		−	0.295998i	0.988988	−	0.147999i	$-0.0472832\pi$
$132$	−3.03090e7	+	1.95891e6i	−1.14700	+	0.0741320i
$133$	−1.09785e7	−	3.40360e7i	−0.404633	−	1.25446i
$134$	−1.72371e7	+	1.83871e7i	−0.618868	+	0.660158i
$135$	−2.32326e7			−0.812699
$136$	−3.13309e6	−	2.57842e6i	−0.106804	−	0.0878955i
$137$	2.36783e7			0.786735			0.393367	−	0.919381i	$-0.371310\pi$
$137$	2.36783e7			0.786735			0.393367	+	0.919381i	$0.371310\pi$
$138$	−428313.	−	401524.i	−0.0138734	−	0.0130057i
$139$			2.03663e7i			0.643220i	0.946872	+	0.321610i	$0.104224\pi$
$139$			2.03663e7i			0.643220i	−0.946872	+	0.321610i	$0.895776\pi$
$140$	−3.42751e7	+	2.21524e6i	−1.05568	+	0.0682296i
$141$		−	1.66801e7i		−	0.501109i
$142$	−2.04051e7	+	2.17665e7i	−0.598039	+	0.637939i
$143$	−6.61144e6			−0.189069
$144$	2.12815e7	−	2.76244e6i	0.593928	−	0.0770946i
$145$		−	2.30036e7i		−	0.626624i
$146$	4.59549e7	−	4.90209e7i	1.22207	−	1.30361i
$147$	1.79861e7			0.467011
$148$	−3.93969e6	+	254627.i	−0.0998955	+	0.00645636i
$149$	6.81516e7			1.68781			0.843906	−	0.536491i	$-0.180250\pi$
$149$	6.81516e7			1.68781			0.843906	+	0.536491i	$0.180250\pi$
$150$	−6.37155e6	+	6.79664e6i	−0.154144	+	0.164428i
$151$	6.98980e7			1.65214			0.826068	−	0.563571i	$-0.190573\pi$
$151$	6.98980e7			1.65214			0.826068	+	0.563571i	$0.190573\pi$
$152$	−4.02628e7	−	1.59214e7i	−0.929932	−	0.367730i
$153$	3.67003e6			0.0828419
$154$	7.41530e7	−	7.91004e7i	1.63609	−	1.74524i
$155$	−2.01692e7			−0.435038
$156$	−3.12193e6	+	201774.i	−0.0658396	+	0.00425529i
$157$	−1.34971e7			−0.278350			−0.139175	−	0.990268i	$-0.544445\pi$
$157$	−1.34971e7			−0.278350			−0.139175	+	0.990268i	$0.544445\pi$
$158$	2.68194e7	−	2.86087e7i	0.540939	−	0.577029i
$159$			1.86731e7i			0.368405i
$160$	−2.42973e7	+	3.37447e7i	−0.468962	+	0.651306i
$161$	2.09579e6			0.0395783
$162$	1.56902e6	−	1.67370e6i	0.0289952	−	0.0309297i
$163$			9.16053e7i			1.65678i	0.560154	+	0.828389i	$0.310742\pi$
$163$			9.16053e7i			1.65678i	−0.560154	+	0.828389i	$0.689258\pi$
$164$	−8.41695e7	+	5.43997e6i	−1.49005	+	0.0963038i
$165$			5.32289e7i			0.922473i
$166$	3.45412e7	+	3.23808e7i	0.586082	+	0.549426i
$167$	−1.14773e8			−1.90692			−0.953459	−	0.301523i	$-0.902505\pi$
$167$	−1.14773e8			−1.90692			−0.953459	+	0.301523i	$0.902505\pi$
$168$	3.26011e7	−	3.96144e7i	0.530457	−	0.644570i
$169$	6.20675e7			0.989147
$170$	−4.86354e6	+	5.18802e6i	−0.0759243	+	0.0809898i
$171$	3.72697e7	−	1.20215e7i	0.569993	−	0.183854i
$172$	−2.95720e7	+	1.91127e6i	−0.443129	+	0.0286400i
$173$			5.94261e7i			0.872601i	0.899801	+	0.436300i	$0.143712\pi$
$173$			5.94261e7i			0.872601i	−0.899801	+	0.436300i	$0.856288\pi$
$174$	2.50681e7	+	2.35003e7i	0.360745	+	0.338182i
$175$		−	3.32568e7i		−	0.469081i
$176$	−1.68968e7	−	1.30171e8i	−0.233620	−	1.79978i
$177$	4.80462e7			0.651257
$178$	−6.76389e7	−	6.34085e7i	−0.898932	−	0.842708i
$179$	5.98900e7			0.780493			0.390246	−	0.920711i	$-0.372390\pi$
$179$	5.98900e7			0.780493			0.390246	+	0.920711i	$0.372390\pi$
$180$	−2.42570e6	−	3.75315e7i	−0.0310016	−	0.479669i
$181$			6.04569e7i			0.757828i	0.925432	+	0.378914i	$0.123702\pi$
$181$			6.04569e7i			0.757828i	−0.925432	+	0.378914i	$0.876298\pi$
$182$	7.63801e6	−	8.14760e6i	0.0939140	−	0.100180i
$183$	1.53454e7			0.185097
$184$	1.61231e6	−	1.95915e6i	0.0190803	−	0.0231849i
$185$			6.91890e6i			0.0803408i
$186$	2.06047e7	−	2.19794e7i	0.234785	−	0.250449i
$187$		−	2.24482e7i		−	0.251036i
$188$	7.19382e7	−	4.64945e6i	0.789600	−	0.0510328i
$189$			1.23883e8i			1.33474i
$190$	−3.23960e7	+	6.86160e7i	−0.342653	+	0.725751i
$191$			1.33174e8i			1.38293i	0.722408	+	0.691467i	$0.243035\pi$
$191$			1.33174e8i			1.38293i	−0.722408	+	0.691467i	$0.756965\pi$
$192$	−1.19514e7	−	6.09512e7i	−0.121861	−	0.621482i
$193$		−	4.32762e7i		−	0.433310i	−0.976248	−	0.216655i	$-0.930485\pi$
$193$		−	4.32762e7i		−	0.433310i	0.976248	−	0.216655i	$-0.0695146\pi$
$194$	−9.26076e7	−	8.68155e7i	−0.910627	−	0.853672i
$195$			5.48275e6i			0.0529514i
$196$	5.01349e6	+	7.75707e7i	0.0475602	+	0.735871i
$197$	7.79341e7			0.726266			0.363133	−	0.931737i	$-0.381707\pi$
$197$	7.79341e7			0.726266			0.363133	+	0.931737i	$0.381707\pi$
$198$	8.66155e7	+	8.11981e7i	0.792989	+	0.743392i
$199$			3.17396e6i			0.0285506i	0.999898	+	0.0142753i	$0.00454413\pi$
$199$			3.17396e6i			0.0285506i	−0.999898	+	0.0142753i	$0.995456\pi$
$200$	−3.10886e7	−	2.55847e7i	−0.274787	−	0.226139i
$201$	−6.59777e7			−0.573074
$202$	−1.11948e8	+	1.19417e8i	−0.955622	+	1.01938i
$203$	−1.22662e8			−1.02914
$204$	−685096.	−	1.06001e7i	−0.00564996	−	0.0874185i
$205$			1.47819e8i			1.19837i
$206$	3.33565e7	−	3.55819e7i	0.265855	−	0.283592i
$207$			2.29491e6i			0.0179833i
$208$	−1.74043e6	−	1.34080e7i	−0.0134102	−	0.103310i
$209$	−7.35311e7	−	2.27965e8i	−0.557133	−	1.72725i
$210$	−6.55966e7	−	6.14938e7i	−0.488780	−	0.458209i
$211$	−7.97004e7			−0.584080			−0.292040	−	0.956406i	$-0.594334\pi$
$211$	−7.97004e7			−0.584080			−0.292040	+	0.956406i	$0.594334\pi$
$212$	−8.05333e7	+	5.20496e6i	−0.580497	+	0.0375182i
$213$	−7.81036e7			−0.553787
$214$	−1.42498e8	+	1.52006e8i	−0.993943	+	1.06026i
$215$			5.19345e7i			0.356386i
$216$	1.15806e8	+	9.53041e7i	0.781887	+	0.643463i
$217$			1.07548e8i			0.714484i
$218$	1.42435e8	+	1.33526e8i	0.931146	+	0.872907i
$219$	1.75899e8			1.13164
$220$	−2.29566e8	+	1.48371e7i	−1.45354	+	0.0939443i
$221$		−	2.31224e6i		−	0.0144099i
$222$	−7.53987e6	−	7.06829e6i	−0.0462518	−	0.0433590i
$223$	−1.37754e8			−0.831833			−0.415917	−	0.909403i	$-0.636539\pi$
$223$	−1.37754e8			−0.831833			−0.415917	+	0.909403i	$0.636539\pi$
$224$	1.79936e8	+	1.29560e8i	1.06967	+	0.770199i
$225$	3.64165e7			0.213137
$226$	1.29351e8	+	1.21261e8i	0.745404	+	0.698783i
$227$	−2.44762e7			−0.138884			−0.0694422	−	0.997586i	$-0.522122\pi$
$227$	−2.44762e7			−0.138884			−0.0694422	+	0.997586i	$0.522122\pi$
$228$	−4.16787e7	−	1.05401e8i	−0.232885	−	0.588943i
$229$	−7.82558e7			−0.430618			−0.215309	−	0.976546i	$-0.569076\pi$
$229$	−7.82558e7			−0.430618			−0.215309	+	0.976546i	$0.569076\pi$
$230$	−3.24412e6	−	3.04121e6i	−0.0175812	−	0.0164816i
$231$	2.83832e8			1.51502
$232$	−9.43645e7	+	1.14665e8i	−0.496136	+	0.602867i
$233$	−2.30517e8			−1.19387			−0.596936	−	0.802289i	$-0.703615\pi$
$233$	−2.30517e8			−1.19387			−0.596936	+	0.802289i	$0.703615\pi$
$234$	8.92168e6	+	8.36367e6i	0.0455188	+	0.0426719i
$235$		−	1.26338e8i		−	0.635034i
$236$	1.33925e7	+	2.07214e8i	0.0663237	+	1.02619i
$237$	1.02655e8			0.500912
$238$	2.76640e7	+	2.59338e7i	0.133014	+	0.124694i
$239$		−	3.21970e8i		−	1.52554i	−0.646672	−	0.762768i	$-0.723840\pi$
$239$		−	3.21970e8i		−	1.52554i	0.646672	−	0.762768i	$-0.276160\pi$
$240$	−1.07949e8	+	1.40122e7i	−0.504054	+	0.0654286i
$241$		−	2.69150e8i		−	1.23861i	−0.785151	−	0.619305i	$-0.787414\pi$
$241$		−	2.69150e8i		−	1.23861i	0.785151	−	0.619305i	$-0.212586\pi$
$242$	3.45872e8	−	3.68948e8i	1.56878	−	1.67344i
$243$	−2.20494e8			−0.985766
$244$	4.27740e6	+	6.61817e7i	0.0188502	+	0.291658i
$245$	1.36230e8			0.591823
$246$	−1.61086e8	−	1.51011e8i	−0.689896	−	0.646747i
$247$	−7.57394e6	−	2.34811e7i	−0.0319803	−	0.0991469i
$248$	1.00536e8	+	8.27374e7i	0.418544	+	0.344446i
$249$			1.23942e8i			0.508771i
$250$	−1.83866e8	+	1.96134e8i	−0.744239	+	0.793893i
$251$			1.68968e8i			0.674444i	0.941425	+	0.337222i	$0.109487\pi$
$251$			1.68968e8i			0.674444i	−0.941425	+	0.337222i	$0.890513\pi$
$252$	−2.00129e8	+	1.29346e7i	−0.787785	+	0.0509155i
$253$	1.40371e7			0.0544948
$254$	2.73153e8	−	2.91377e8i	1.04590	−	1.11568i
$255$	−1.86159e7			−0.0703062
$256$	2.59539e8	−	6.85336e7i	0.966860	−	0.255307i
$257$		−	3.78899e8i		−	1.39238i	−0.717858	−	0.696190i	$-0.754877\pi$
$257$		−	3.78899e8i		−	1.39238i	0.717858	−	0.696190i	$-0.245123\pi$
$258$	−5.65956e7	−	5.30558e7i	−0.205170	−	0.192338i
$259$	3.68936e7			0.131948
$260$	−2.36460e7	+	1.52827e6i	−0.0834357	+	0.00539255i
$261$		−	1.34315e8i		−	0.467610i
$262$	6.28637e7	+	5.89319e7i	0.215946	+	0.202440i
$263$			1.61921e8i			0.548856i	0.961608	+	0.274428i	$0.0884885\pi$
$263$			1.61921e8i			0.548856i	−0.961608	+	0.274428i	$0.911511\pi$
$264$	2.18354e8	−	2.65327e8i	0.730377	−	0.887499i
$265$			1.41433e8i			0.466864i
$266$	3.65880e8	+	1.72745e8i	1.19194	+	0.562756i
$267$		−	2.42705e8i		−	0.780351i
$268$	−1.83907e7	−	2.84549e8i	−0.0583616	−	0.902995i
$269$		−	4.78441e8i		−	1.49863i	−0.662213	−	0.749316i	$-0.730382\pi$
$269$		−	4.78441e8i		−	1.49863i	0.662213	−	0.749316i	$-0.269618\pi$
$270$	1.79767e8	−	1.91761e8i	0.555824	−	0.592908i
$271$		−	1.94325e8i		−	0.593112i	−0.955015	−	0.296556i	$-0.904162\pi$
$271$		−	1.94325e8i		−	0.593112i	0.955015	−	0.296556i	$-0.0958382\pi$
$272$	4.55251e7	−	5.90937e6i	0.137170	−	0.0178053i
$273$	2.92356e7			0.0869647
$274$	−1.83216e8	+	1.95439e8i	−0.538066	+	0.573965i
$275$		−	2.22746e8i		−	0.645870i
$276$	6.62832e6	−	428397.i	0.0189768	−	0.00122649i
$277$	−7.36153e7			−0.208108			−0.104054	−	0.994572i	$-0.533181\pi$
$277$	−7.36153e7			−0.208108			−0.104054	+	0.994572i	$0.533181\pi$
$278$	−1.68102e8	−	1.57588e8i	−0.469264	−	0.439914i
$279$	−1.17766e8			−0.324642
$280$	2.46926e8	−	3.00046e8i	0.672225	−	0.816836i
$281$			4.29773e8i			1.15549i	0.816216	+	0.577747i	$0.196068\pi$
$281$			4.29773e8i			1.15549i	−0.816216	+	0.577747i	$0.803932\pi$
$282$	1.37677e8	+	1.29066e8i	0.365586	+	0.342721i
$283$		−	3.48325e7i		−	0.0913550i	−0.998956	−	0.0456775i	$-0.985455\pi$
$283$		−	3.48325e7i		−	0.0913550i	0.998956	−	0.0456775i	$-0.0145447\pi$
$284$	−2.17707e7	−	3.36846e8i	−0.0563974	−	0.872603i
$285$	−1.89047e8	+	6.09781e7i	−0.483741	+	0.156033i
$286$	5.11574e7	−	5.45705e7i	0.129309	−	0.137936i
$287$	7.88213e8			1.96814
$288$	−1.41869e8	+	1.97032e8i	−0.349957	+	0.486029i
$289$	−4.02488e8			−0.980867
$290$	1.89870e8	+	1.77995e8i	0.457156	+	0.428563i
$291$		−	3.32299e8i		−	0.790504i
$292$	4.90305e7	+	7.58620e8i	0.115246	+	1.78314i
$293$		−	8.10466e8i		−	1.88234i	−0.337932	−	0.941170i	$-0.609727\pi$
$293$		−	8.10466e8i		−	1.88234i	0.337932	−	0.941170i	$-0.390273\pi$
$294$	−1.39172e8	+	1.48457e8i	−0.319400	+	0.340710i
$295$	3.63910e8			0.825309
$296$	2.83825e7	−	3.44882e7i	0.0636106	−	0.0772948i
$297$			8.29737e8i			1.83778i
$298$	−5.27338e8	+	5.62520e8i	−1.15434	+	1.23135i
$299$	1.44586e6			0.00312808
$300$	−6.79797e6	−	1.05181e8i	−0.0145363	−	0.224912i
$301$	2.76929e8			0.585311
$302$	−5.40851e8	+	5.76935e8i	−1.12993	+	1.20532i
$303$	−4.28498e8			−0.884910
$304$	4.42957e8	−	2.09132e8i	0.904282	−	0.426936i
$305$	1.16229e8			0.234565
$306$	−2.83977e7	+	3.02923e7i	−0.0566575	+	0.0604376i
$307$	7.20855e8			1.42188			0.710941	−	0.703252i	$-0.248269\pi$
$307$	7.20855e8			1.42188			0.710941	+	0.703252i	$0.248269\pi$
$308$	7.91158e7	+	1.22411e9i	0.154289	+	2.38723i
$309$	1.27677e8			0.246183
$310$	1.56063e8	−	1.66476e8i	0.297533	−	0.317384i
$311$		−	5.73920e8i		−	1.08191i	−0.841052	−	0.540954i	$-0.818063\pi$
$311$		−	5.73920e8i		−	1.08191i	0.841052	−	0.540954i	$-0.181937\pi$
$312$	2.24912e7	−	2.73296e7i	0.0419248	−	0.0509438i
$313$	−4.23398e8			−0.780447			−0.390224	−	0.920720i	$-0.627602\pi$
$313$	−4.23398e8			−0.780447			−0.390224	+	0.920720i	$0.627602\pi$
$314$	1.04437e8	−	1.11404e8i	0.190370	−	0.203071i
$315$			3.51467e8i			0.633575i
$316$	2.86143e7	+	4.42732e8i	0.0510126	+	0.789288i
$317$		−	2.67590e8i		−	0.471804i	−0.971777	−	0.235902i	$-0.924196\pi$
$317$		−	2.67590e8i		−	0.471804i	0.971777	−	0.235902i	$-0.0758045\pi$
$318$	−1.54127e8	−	1.44487e8i	−0.268771	−	0.251961i
$319$	−8.21557e8			−1.41700
$320$	−9.05217e7	−	4.61655e8i	−0.154429	−	0.787577i
$321$	−5.45434e8			−0.920396
$322$	−1.62166e7	+	1.72986e7i	−0.0270685	+	0.0288745i
$323$	7.97268e7	−	2.57163e7i	0.131642	−	0.0424618i
$324$	1.67403e6	+	2.59012e7i	0.00273436	+	0.0423071i
$325$		−	2.29436e7i		−	0.0370740i
$326$	−7.56106e8	−	7.08816e8i	−1.20871	−	1.13311i
$327$			5.11091e8i			0.808316i
$328$	6.06378e8	−	7.36824e8i	0.948822	−	1.15294i
$329$	−6.73672e8			−1.04295
$330$	−4.39349e8	−	4.11870e8i	−0.672994	−	0.630901i
$331$	−5.11928e8			−0.775909			−0.387955	−	0.921679i	$-0.626818\pi$
$331$	−5.11928e8			−0.775909			−0.387955	+	0.921679i	$0.626818\pi$
$332$	−5.34539e8	+	3.45479e7i	−0.801671	+	0.0518130i
$333$			4.03987e7i			0.0599533i
$334$	8.88080e8	−	9.47331e8i	1.30419	−	1.39120i
$335$	−4.99727e8			−0.726232
$336$	7.47172e7	+	5.75613e8i	0.107457	+	0.827833i
$337$			1.02170e8i			0.145419i	0.997353	+	0.0727093i	$0.0231645\pi$
$337$			1.02170e8i			0.145419i	−0.997353	+	0.0727093i	$0.976835\pi$
$338$	−4.80261e8	+	5.12303e8i	−0.676501	+	0.721636i
$339$			4.64145e8i			0.647076i
$340$	−5.18903e6	−	8.02868e7i	−0.00715995	−	0.110782i
$341$			7.20329e8i			0.983763i
$342$	−1.89157e8	+	4.00641e8i	−0.255700	+	0.541582i
$343$			2.58681e8i			0.346127i
$344$	2.13044e8	−	2.58875e8i	0.282172	−	0.342874i
$345$		−	1.16407e7i		−	0.0152620i
$346$	−4.90500e8	−	4.59822e8i	−0.636609	−	0.596792i
$347$			3.78889e8i			0.486810i	0.969925	+	0.243405i	$0.0782644\pi$
$347$			3.78889e8i			0.486810i	−0.969925	+	0.243405i	$0.921736\pi$
$348$	−3.87940e8	+	2.50730e7i	−0.493444	+	0.0318919i
$349$	−1.05939e9			−1.33403			−0.667016	−	0.745044i	$-0.732429\pi$
$349$	−1.05939e9			−1.33403			−0.667016	+	0.745044i	$0.732429\pi$
$350$	2.74501e8	+	2.57332e8i	0.342220	+	0.320816i
$351$			8.54656e7i			0.105491i
$352$	1.20517e9	+	8.67760e8i	1.47282	+	1.06048i
$353$	1.40502e9			1.70009			0.850046	−	0.526708i	$-0.176574\pi$
$353$	1.40502e9			1.70009			0.850046	+	0.526708i	$0.176574\pi$
$354$	−3.71767e8	+	3.96571e8i	−0.445410	+	0.475127i
$355$	−5.91570e8			−0.701790
$356$	1.04674e9	−	6.76522e7i	1.22960	−	0.0794706i
$357$			9.92654e7i			0.115467i
$358$	−4.63412e8	+	4.94329e8i	−0.533797	+	0.569411i
$359$		−	1.83786e8i		−	0.209643i	−0.994491	−	0.104822i	$-0.966573\pi$
$359$		−	1.83786e8i		−	0.209643i	0.994491	−	0.104822i	$-0.0334272\pi$
$360$	3.28553e8	+	2.70386e8i	0.371147	+	0.305440i
$361$	7.25400e8	−	5.22304e8i	0.811526	−	0.584316i
$362$	−4.99009e8	−	4.67798e8i	−0.552876	−	0.518297i
$363$	1.32388e9			1.45270
$364$	8.14919e6	+	1.26088e8i	0.00885645	+	0.137031i
$365$	1.33229e9			1.43408
$366$	−1.18738e8	+	1.26660e8i	−0.126592	+	0.135038i
$367$		−	6.52735e8i		−	0.689296i	−0.938732	−	0.344648i	$-0.887998\pi$
$367$		−	6.52735e8i		−	0.689296i	0.938732	−	0.344648i	$-0.112002\pi$
$368$	3.69518e6	+	2.84673e7i	0.00386517	+	0.0297768i
$369$			8.63099e8i			0.894269i
$370$	−5.71083e7	−	5.35365e7i	−0.0586129	−	0.0549470i
$371$	7.54161e8			0.766753
$372$	2.19837e7	+	3.40140e8i	0.0221411	+	0.342576i
$373$			1.54475e9i			1.54127i	0.637277	+	0.770634i	$0.280061\pi$
$373$			1.54475e9i			1.54127i	−0.637277	+	0.770634i	$0.719939\pi$
$374$	1.85287e8	+	1.73698e8i	0.183144	+	0.171690i
$375$	−7.03776e8			−0.689168
$376$	−5.18261e8	+	6.29751e8i	−0.502795	+	0.610958i
$377$	−8.46231e7			−0.0813381
$378$	−1.02252e9	−	9.58571e8i	−0.973761	−	0.912858i
$379$	3.14221e8			0.296481			0.148241	−	0.988951i	$-0.452639\pi$
$379$	3.14221e8			0.296481			0.148241	+	0.988951i	$0.452639\pi$
$380$	−3.15682e8	−	7.98326e8i	−0.295126	−	0.746342i
$381$	1.04554e9			0.968504
$382$	−1.09921e9	−	1.03046e9i	−1.00892	−	0.945822i
$383$	−1.85992e9			−1.69160			−0.845801	−	0.533499i	$-0.820877\pi$
$383$	−1.85992e9			−1.69160			−0.845801	+	0.533499i	$0.820877\pi$
$384$	5.95565e8	+	3.72977e8i	0.536747	+	0.336142i
$385$	2.14979e9			1.91992
$386$	3.57200e8	+	3.34859e8i	0.316123	+	0.296351i
$387$			3.03240e8i			0.265949i
$388$	1.43314e9	−	9.26257e7i	1.24560	−	0.0805046i
$389$	−7.06755e8			−0.608759			−0.304380	−	0.952551i	$-0.598449\pi$
$389$	−7.06755e8			−0.608759			−0.304380	+	0.952551i	$0.598449\pi$
$390$	−4.52544e7	−	4.24240e7i	−0.0386309	−	0.0362147i
$391$			4.90923e6i			0.00415331i
$392$	−6.79058e8	−	5.58839e8i	−0.569384	−	0.468582i
$393$			2.25571e8i			0.187460i
$394$	−6.03032e8	+	6.43265e8i	−0.496711	+	0.529850i
$395$	7.77528e8			0.634784
$396$	−1.34041e9	+	8.66324e7i	−1.08469	+	0.0701047i
$397$	−1.18422e9			−0.949871			−0.474936	−	0.880021i	$-0.657529\pi$
$397$	−1.18422e9			−0.949871			−0.474936	+	0.880021i	$0.657529\pi$
$398$	−2.61977e7	−	2.45592e7i	−0.0208292	−	0.0195265i
$399$	3.25153e8	+	1.00805e9i	0.256261	+	0.794472i
$400$	4.51730e8	−	5.86366e7i	0.352914	−	0.0458099i
$401$		−	1.00410e9i		−	0.777630i	−0.921316	−	0.388815i	$-0.872884\pi$
$401$		−	1.00410e9i		−	0.777630i	0.921316	−	0.388815i	$-0.127116\pi$
$402$	5.10517e8	−	5.44577e8i	0.391939	−	0.418088i
$403$			7.41962e7i			0.0564695i
$404$	−1.19440e8	−	1.84803e9i	−0.0901189	−	1.39436i
$405$	4.54879e7			0.0340254
$406$	9.49121e8	−	1.01244e9i	0.703851	−	0.750810i
$407$	2.47104e8			0.181677
$408$	9.27936e7	+	7.63656e7i	0.0676406	+	0.0556656i
$409$		−	7.47723e8i		−	0.540392i	−0.962805	−	0.270196i	$-0.912911\pi$
$409$		−	7.47723e8i		−	0.540392i	0.962805	−	0.270196i	$-0.0870885\pi$
$410$	−1.22009e9	−	1.14378e9i	−0.874276	−	0.819594i
$411$	−7.01286e8			−0.498252
$412$	3.55889e7	+	5.50645e8i	0.0250711	+	0.387911i
$413$		−	1.94047e9i		−	1.35545i
$414$	−1.89420e7	−	1.77573e7i	−0.0131198	−	0.0122992i
$415$			9.38761e8i			0.644743i
$416$	1.24136e8	+	8.93822e7i	0.0845419	+	0.0608729i
$417$		−	6.03193e8i		−	0.407362i
$418$	2.45057e9	+	1.15700e9i	1.64116	+	0.774849i
$419$			2.48449e9i			1.65002i	0.565119	+	0.825009i	$0.308830\pi$
$419$			2.48449e9i			1.65002i	−0.565119	+	0.825009i	$0.691170\pi$
$420$	1.01513e9	−	6.56094e7i	0.668577	−	0.0432109i
$421$			2.75596e9i			1.80005i	0.435834	+	0.900027i	$0.356453\pi$
$421$			2.75596e9i			1.80005i	−0.435834	+	0.900027i	$0.643547\pi$
$422$	6.16699e8	−	6.57844e8i	0.399466	−	0.426117i
$423$		−	7.37676e8i		−	0.473886i
$424$	5.80182e8	−	7.04993e8i	0.369644	−	0.449163i
$425$	7.79016e7			0.0492250
$426$	6.04344e8	−	6.44664e8i	0.378748	−	0.404017i
$427$		−	6.19764e8i		−	0.385238i
$428$	−1.52035e8	−	2.35235e9i	−0.0937327	−	1.45027i
$429$	1.95813e8			0.119740
$430$	−4.28665e8	−	4.01854e8i	−0.260003	−	0.243741i
$431$	−1.80224e9			−1.08428			−0.542140	−	0.840288i	$-0.682386\pi$
$431$	−1.80224e9			−1.08428			−0.542140	+	0.840288i	$0.682386\pi$
$432$	−1.68271e9	+	2.18424e8i	−1.00419	+	0.130349i
$433$		−	4.50244e8i		−	0.266527i	−0.991081	−	0.133263i	$-0.957454\pi$
$433$		−	4.50244e8i		−	0.266527i	0.991081	−	0.133263i	$-0.0425456\pi$
$434$	−8.87695e8	−	8.32175e8i	−0.521255	−	0.488653i
$435$			6.81303e8i			0.396851i
$436$	−2.20424e9	+	1.42462e8i	−1.27367	+	0.0823185i
$437$	1.60806e7	+	4.98539e7i	0.00921759	+	0.0285768i
$438$	−1.36106e9	+	1.45187e9i	−0.773959	+	0.825595i
$439$	5.73109e8			0.323304			0.161652	−	0.986848i	$-0.448318\pi$
$439$	5.73109e8			0.323304			0.161652	+	0.986848i	$0.448318\pi$
$440$	1.65385e9	−	2.00963e9i	0.925576	−	1.12469i
$441$	7.95433e8			0.441640
$442$	1.90851e7	+	1.78914e7i	0.0105128	+	0.00985525i
$443$			6.95298e8i			0.379978i	0.981786	+	0.189989i	$0.0608452\pi$
$443$			6.95298e8i			0.379978i	−0.981786	+	0.189989i	$0.939155\pi$
$444$	1.16683e8	−	7.54135e6i	0.0632654	−	0.00408892i
$445$		−	1.83829e9i		−	0.988905i
$446$	1.06590e9	−	1.13701e9i	0.568911	−	0.606867i
$447$	−2.01846e9			−1.06892
$448$	−2.46168e9	+	4.82688e8i	−1.29348	+	0.253626i
$449$		−	1.09272e9i		−	0.569702i	−0.958572	−	0.284851i	$-0.908056\pi$
$449$		−	1.09272e9i		−	0.569702i	0.958572	−	0.284851i	$-0.0919441\pi$
$450$	−2.81780e8	+	3.00580e8i	−0.145770	+	0.155495i
$451$	5.27925e9			2.70991
$452$	−2.00177e9	+	1.29377e8i	−1.01960	+	0.0658979i
$453$	−2.07019e9			−1.04632
$454$	1.89390e8	−	2.02025e8i	0.0949863	−	0.101324i
$455$	2.21436e8			0.110207
$456$	1.19247e9	+	4.71549e8i	0.588941	+	0.232890i
$457$	9.08856e7			0.0445439			0.0222719	−	0.999752i	$-0.492910\pi$
$457$	9.08856e7			0.0445439			0.0222719	+	0.999752i	$0.492910\pi$
$458$	6.05521e8	−	6.45920e8i	0.294510	−	0.314159i
$459$	−2.90186e8			−0.140066
$460$	5.02041e7	−	3.24475e6i	0.0240484	−	0.00155428i
$461$	6.32011e7			0.0300449			0.0150225	−	0.999887i	$-0.495218\pi$
$461$	6.32011e7			0.0300449			0.0150225	+	0.999887i	$0.495218\pi$
$462$	−2.19621e9	+	2.34274e9i	−1.03616	+	1.10529i
$463$		−	3.45564e9i		−	1.61806i	−0.587766	−	0.809031i	$-0.699993\pi$
$463$		−	3.45564e9i		−	1.61806i	0.587766	−	0.809031i	$-0.300007\pi$
$464$	−2.16270e8	−	1.66612e9i	−0.100504	−	0.774273i
$465$	5.97356e8			0.275517
$466$	1.78368e9	−	1.90268e9i	0.816517	−	0.870993i
$467$			5.07197e8i			0.230445i	0.993340	+	0.115222i	$0.0367581\pi$
$467$			5.07197e8i			0.230445i	−0.993340	+	0.115222i	$0.963242\pi$
$468$	−1.38067e8	+	8.92342e6i	−0.0622628	+	0.00402412i
$469$			2.66469e9i			1.19273i
$470$	1.04279e9	+	9.77569e8i	0.463291	+	0.434315i
$471$	3.99747e8			0.176284
$472$	−1.81396e9	−	1.49282e9i	−0.794019	−	0.653447i
$473$	1.85480e9			0.805905
$474$	−7.94316e8	+	8.47311e8i	−0.342586	+	0.365442i
$475$	7.91101e8	−	2.55174e8i	0.338692	−	0.109247i
$476$	−4.28112e8	+	2.76694e7i	−0.181942	+	0.0117591i
$477$			8.25812e8i			0.348391i
$478$	2.65752e9	+	2.49131e9i	1.11296	+	1.04335i
$479$			1.89559e9i			0.788079i	0.919094	+	0.394039i	$0.128923\pi$
$479$			1.89559e9i			0.788079i	−0.919094	+	0.394039i	$0.871077\pi$
$480$	7.19619e8	−	9.99425e8i	0.297001	−	0.412483i
$481$	2.54525e7			0.0104285
$482$	2.22155e9	+	2.08260e9i	0.903632	+	0.847115i
$483$	−6.20716e7			−0.0250656
$484$	3.69020e8	+	5.70963e9i	0.147942	+	2.28902i
$485$		−	2.51689e9i		−	1.00177i
$486$	1.70612e9	−	1.81994e9i	0.674189	−	0.719169i
$487$	−4.00715e9			−1.57212			−0.786058	−	0.618153i	$-0.787881\pi$
$487$	−4.00715e9			−1.57212			−0.786058	+	0.618153i	$0.787881\pi$
$488$	−5.79358e8	−	4.76789e8i	−0.225672	−	0.185719i
$489$		−	2.71310e9i		−	1.04926i
$490$	−1.05411e9	+	1.12444e9i	−0.404762	+	0.431766i
$491$			1.35445e9i			0.516390i	0.966093	+	0.258195i	$0.0831276\pi$
$491$			1.35445e9i			0.516390i	−0.966093	+	0.258195i	$0.916872\pi$
$492$	2.49287e9	−	1.61117e8i	0.943673	−	0.0609907i
$493$		−	2.87326e8i		−	0.107997i
$494$	2.52417e8	+	1.19175e8i	0.0942051	+	0.0444776i
$495$			2.35404e9i			0.872359i
$496$	−1.46083e9	+	1.89623e8i	−0.537544	+	0.0697757i
$497$			3.15442e9i			1.15258i
$498$	−1.02301e9	−	9.59031e8i	−0.371175	−	0.347960i
$499$		−	4.50384e9i		−	1.62267i	−0.584580	−	0.811336i	$-0.698741\pi$
$499$		−	4.50384e9i		−	1.62267i	0.584580	−	0.811336i	$-0.301259\pi$
$500$	−1.96172e8	−	3.03525e9i	−0.0701846	−	1.08592i
$501$	3.39926e9			1.20768
$502$	−1.39465e9	−	1.30742e9i	−0.492043	−	0.461268i
$503$			2.18660e9i			0.766092i	0.923729	+	0.383046i	$0.125125\pi$
$503$			2.18660e9i			0.766092i	−0.923729	+	0.383046i	$0.874875\pi$
$504$	1.44178e9	−	1.75194e9i	0.501639	−	0.609553i
$505$	−3.24551e9			−1.12141
$506$	−1.08615e8	+	1.15861e8i	−0.0372703	+	0.0397568i
$507$	−1.83827e9			−0.626443
$508$	2.91434e8	+	4.50919e9i	0.0986320	+	1.52607i
$509$		−	4.11191e9i		−	1.38207i	−0.722819	−	0.691037i	$-0.757154\pi$
$509$		−	4.11191e9i		−	1.38207i	0.722819	−	0.691037i	$-0.242846\pi$
$510$	1.44045e8	−	1.53655e8i	0.0480841	−	0.0512921i
$511$		−	7.10417e9i		−	2.35527i
$512$	−1.44257e9	+	2.67252e9i	−0.474998	+	0.879987i
$513$	−2.94688e9	+	9.50531e8i	−0.963723	+	0.310853i
$514$	3.12742e9	+	2.93181e9i	1.01582	+	0.952282i
$515$	9.67047e8			0.311977
$516$	8.75841e8	−	5.66066e7i	0.280641	−	0.0181382i
$517$	−4.51208e9			−1.43602
$518$	−2.85472e8	+	3.04518e8i	−0.0902421	+	0.0962629i
$519$		−	1.76004e9i		−	0.552632i
$520$	1.70352e8	−	2.06999e8i	0.0531295	−	0.0645589i
$521$			4.17673e9i			1.29391i	0.762528	+	0.646956i	$0.223958\pi$
$521$			4.17673e9i			1.29391i	−0.762528	+	0.646956i	$0.776042\pi$
$522$	1.10863e9	+	1.03929e9i	0.341147	+	0.319810i
$523$	2.69141e9			0.822666			0.411333	−	0.911485i	$-0.365063\pi$
$523$	2.69141e9			0.822666			0.411333	+	0.911485i	$0.365063\pi$
$524$	−9.72843e8	+	6.28760e7i	−0.295381	+	0.0190909i
$525$			9.84977e8i			0.297077i
$526$	−1.33649e9	−	1.25290e9i	−0.400420	−	0.375376i
$527$	−2.51923e8			−0.0749774
$528$	5.00437e8	+	3.85531e9i	0.147955	+	1.13983i
$529$	3.40176e9			0.999098
$530$	−1.16738e9	−	1.09437e9i	−0.340602	−	0.319299i
$531$	2.12483e9			0.615877
$532$	−4.25691e9	+	1.68331e9i	−1.22575	+	0.484699i
$533$	5.43780e8			0.155553
$534$	2.00328e9	+	1.87799e9i	0.569308	+	0.533701i
$535$	−4.13121e9			−1.16638
$536$	2.49096e9	+	2.04996e9i	0.698698	+	0.575002i
$537$	−1.77378e9			−0.494299
$538$	3.94903e9	+	3.70204e9i	1.09333	+	1.02495i
$539$		−	4.86536e9i		−	1.33830i
$540$	1.91798e8	+	2.96758e9i	0.0524164	+	0.811007i
$541$	−4.55157e9			−1.23587			−0.617933	−	0.786231i	$-0.712030\pi$
$541$	−4.55157e9			−1.23587			−0.617933	+	0.786231i	$0.712030\pi$
$542$	1.60395e9	+	1.50363e9i	0.432707	+	0.405644i
$543$		−	1.79057e9i		−	0.479945i
$544$	−3.03485e8	+	4.21487e8i	−0.0808240	+	0.112250i
$545$			3.87109e9i			1.02434i
$546$	−2.26217e8	+	2.41310e8i	−0.0594772	+	0.0634454i
$547$	3.08692e9			0.806437			0.403218	−	0.915104i	$-0.367892\pi$
$547$	3.08692e9			0.806437			0.403218	+	0.915104i	$0.367892\pi$
$548$	−1.95478e8	−	3.02451e9i	−0.0507417	−	0.785096i
$549$	6.78647e8			0.175041
$550$	1.83854e9	+	1.72354e9i	0.471197	+	0.441726i
$551$	−9.41160e8	−	2.91783e9i	−0.239681	−	0.743070i
$552$	−4.77521e7	+	5.80247e7i	−0.0120839	+	0.0146834i
$553$		−	4.14600e9i		−	1.04254i
$554$	5.69614e8	−	6.07618e8i	0.142330	−	0.151826i
$555$		−	2.04919e8i		−	0.0508811i
$556$	2.60145e9	−	1.68135e8i	0.641881	−	0.0414855i
$557$	−5.77832e9			−1.41680			−0.708400	−	0.705812i	$-0.750583\pi$
$557$	−5.77832e9			−1.41680			−0.708400	+	0.705812i	$0.750583\pi$
$558$	9.11238e8	−	9.72033e8i	0.222030	−	0.236843i
$559$	1.91051e8			0.0462602
$560$	5.65921e8	+	4.35979e9i	0.136175	+	1.04908i
$561$			6.64855e8i			0.158985i
$562$	−3.54733e9	−	3.32546e9i	−0.842994	−	0.790269i
$563$	3.94816e9			0.932429			0.466214	−	0.884672i	$-0.345618\pi$
$563$	3.94816e9			0.932429			0.466214	+	0.884672i	$0.345618\pi$
$564$	−2.13061e9	+	1.37704e8i	−0.500066	+	0.0323199i
$565$			3.51552e9i			0.820011i
$566$	2.87506e8	+	2.69524e8i	0.0666483	+	0.0624798i
$567$		−	2.42555e8i		−	0.0558816i
$568$	2.94877e9	+	2.42672e9i	0.675182	+	0.555649i
$569$			2.64752e9i			0.602486i	0.953547	+	0.301243i	$0.0974015\pi$
$569$			2.64752e9i			0.602486i	−0.953547	+	0.301243i	$0.902599\pi$
$570$	9.59482e8	−	2.03222e9i	0.217008	−	0.459630i
$571$			6.54027e9i			1.47018i	0.677971	+	0.735088i	$0.262859\pi$
$571$			6.54027e9i			1.47018i	−0.677971	+	0.735088i	$0.737141\pi$
$572$	5.45812e7	+	8.44502e8i	0.0121943	+	0.188675i
$573$		−	3.94424e9i		−	0.875835i
$574$	−6.09897e9	+	6.50587e9i	−1.34606	+	1.43587i
$575$			4.87126e7i			0.0106857i
$576$	−5.28547e8	−	2.69556e9i	−0.115240	−	0.587719i
$577$	−8.00716e9			−1.73525			−0.867627	−	0.497215i	$-0.834356\pi$
$577$	−8.00716e9			−1.73525			−0.867627	+	0.497215i	$0.834356\pi$
$578$	3.11434e9	−	3.32212e9i	0.670838	−	0.715595i
$579$			1.28172e9i			0.274422i
$580$	−2.93833e9	+	1.89908e8i	−0.625320	+	0.0404152i
$581$	5.00574e9			1.05889
$582$	2.74278e9	+	2.57124e9i	0.576715	+	0.540645i
$583$	5.05118e9			1.05573
$584$	−6.64100e9	−	5.46529e9i	−1.37971	−	1.13545i
$585$			2.42474e8i			0.0500748i
$586$	6.68955e9	+	6.27116e9i	1.37327	+	1.28738i
$587$			1.57397e9i			0.321190i	0.987020	+	0.160595i	$0.0513413\pi$
$587$			1.57397e9i			0.321190i	−0.987020	+	0.160595i	$0.948659\pi$
$588$	−1.48486e8	−	2.29743e9i	−0.0301206	−	0.466039i
$589$	−2.55831e9	+	8.25195e8i	−0.515881	+	0.166400i
$590$	−2.81583e9	+	3.00370e9i	−0.564449	+	0.602107i
$591$	−2.30820e9			−0.459956
$592$	6.50487e7	+	5.01128e8i	0.0128858	+	0.0992711i
$593$	1.85858e9			0.366008			0.183004	−	0.983112i	$-0.441418\pi$
$593$	1.85858e9			0.366008			0.183004	+	0.983112i	$0.441418\pi$
$594$	−6.84861e9	−	6.42027e9i	−1.34076	−	1.25690i
$595$			7.51853e8i			0.146327i
$596$	−5.62630e8	−	8.70524e9i	−0.108858	−	1.68430i
$597$		−	9.40040e7i		−	0.0180816i
$598$	−1.11877e7	+	1.19341e7i	−0.00213937	+	0.00228210i
$599$	−3.02396e8			−0.0574886			−0.0287443	−	0.999587i	$-0.509151\pi$
$599$	−3.02396e8			−0.0574886			−0.0287443	+	0.999587i	$0.509151\pi$
$600$	9.20760e8	+	7.57750e8i	0.174027	+	0.143218i
$601$		−	3.34218e9i		−	0.628013i	−0.949421	−	0.314007i	$-0.898329\pi$
$601$		−	3.34218e9i		−	0.628013i	0.949421	−	0.314007i	$-0.101671\pi$
$602$	−2.14280e9	+	2.28576e9i	−0.400308	+	0.427015i
$603$	−2.91785e9			−0.541942
$604$	−5.77048e8	−	8.92832e9i	−0.106557	−	1.64870i
$605$	1.00273e10			1.84094
$606$	3.31559e9	−	3.53680e9i	0.605211	−	0.645589i
$607$	−7.43759e8			−0.134981			−0.0674904	−	0.997720i	$-0.521499\pi$
$607$	−7.43759e8			−0.134981			−0.0674904	+	0.997720i	$0.521499\pi$
$608$	−1.70131e9	+	5.27435e9i	−0.306987	+	0.951714i
$609$	3.63290e9			0.651768
$610$	−8.99344e8	+	9.59346e8i	−0.160425	+	0.171128i
$611$	−4.64759e8			−0.0824297
$612$	−3.02982e7	−	4.68786e8i	−0.00534302	−	0.0826694i
$613$	−1.40956e9			−0.247156			−0.123578	−	0.992335i	$-0.539437\pi$
$613$	−1.40956e9			−0.247156			−0.123578	+	0.992335i	$0.539437\pi$
$614$	−5.57777e9	+	5.94990e9i	−0.972459	+	1.03734i
$615$		−	4.37799e9i		−	0.758948i
$616$	−1.07159e10	−	8.81881e9i	−1.84713	−	1.52012i
$617$	−1.47246e9			−0.252374			−0.126187	−	0.992006i	$-0.540274\pi$
$617$	−1.47246e9			−0.252374			−0.126187	+	0.992006i	$0.540274\pi$
$618$	−9.87927e8	+	1.05384e9i	−0.168370	+	0.179603i
$619$		−	4.43297e9i		−	0.751238i	−0.926774	−	0.375619i	$-0.877430\pi$
$619$		−	4.43297e9i		−	0.751238i	0.926774	−	0.375619i	$-0.122570\pi$
$620$	1.66508e8	+	2.57628e9i	0.0280585	+	0.434132i
$621$		−	1.81456e8i		−	0.0304054i
$622$	4.73711e9	+	4.44083e9i	0.789309	+	0.739942i
$623$	−9.80231e9			−1.62413
$624$	5.15466e7	+	3.97109e8i	0.00849287	+	0.0654281i
$625$	−3.15844e9			−0.517478
$626$	3.27613e9	−	3.49471e9i	0.533767	−	0.569378i
$627$	2.17779e9	+	6.75169e9i	0.352841	+	1.09390i
$628$	1.11426e8	+	1.72403e9i	0.0179527	+	0.277771i
$629$			8.64204e7i			0.0138465i
$630$	−2.90099e9	−	2.71955e9i	−0.462227	−	0.433317i
$631$			5.08136e9i			0.805150i	0.915387	+	0.402575i	$0.131885\pi$
$631$			5.08136e9i			0.805150i	−0.915387	+	0.402575i	$0.868115\pi$
$632$	−3.87570e9	−	3.18955e9i	−0.610717	−	0.502597i
$633$	2.36051e9			0.369907
$634$	2.20867e9	+	2.07053e9i	0.344207	+	0.322678i
$635$	7.91907e9			1.22734
$636$	2.38518e9	−	1.54157e8i	0.367638	−	0.0237609i
$637$		−	5.01148e8i		−	0.0768207i
$638$	6.35697e9	−	6.78109e9i	0.969121	−	1.03378i
$639$	−3.45412e9			−0.523702
$640$	4.51091e9	+	2.82499e9i	0.680197	+	0.425978i
$641$			2.28502e9i			0.342679i	0.985212	+	0.171340i	$0.0548095\pi$
$641$			2.28502e9i			0.342679i	−0.985212	+	0.171340i	$0.945190\pi$
$642$	4.22041e9	−	4.50199e9i	0.629480	−	0.671478i
$643$			3.25318e9i			0.482581i	0.970453	+	0.241290i	$0.0775706\pi$
$643$			3.25318e9i			0.482581i	−0.970453	+	0.241290i	$0.922429\pi$
$644$	−1.73019e7	−	2.67703e8i	−0.00255267	−	0.0394959i
$645$		−	1.53816e9i		−	0.225705i
$646$	−4.04642e8	+	8.57046e8i	−0.0590551	+	0.125081i
$647$			5.58016e9i			0.809994i	0.914318	+	0.404997i	$0.132727\pi$
$647$			5.58016e9i			0.809994i	−0.914318	+	0.404997i	$0.867273\pi$
$648$	−2.26741e8	−	1.86599e8i	−0.0327354	−	0.0269399i
$649$		−	1.29968e10i		−	1.86629i
$650$	1.89375e8	+	1.77531e8i	0.0270474	+	0.0253558i
$651$		−	3.18527e9i		−	0.452495i
$652$	1.17011e10	−	7.56254e8i	1.65333	−	0.106857i
$653$	−3.96601e9			−0.557388			−0.278694	−	0.960380i	$-0.589901\pi$
$653$	−3.96601e9			−0.557388			−0.278694	+	0.960380i	$0.589901\pi$
$654$	−4.21852e9	−	3.95468e9i	−0.589710	−	0.552826i
$655$			1.70851e9i			0.237560i
$656$	1.38973e9	+	1.07063e10i	0.192206	+	1.48074i
$657$	7.77912e9			1.07017
$658$	5.21268e9	−	5.56046e9i	0.713297	−	0.760886i
$659$	1.36049e10			1.85181			0.925904	−	0.377758i	$-0.123305\pi$
$659$	1.36049e10			1.85181			0.925904	+	0.377758i	$0.123305\pi$
$660$	6.79912e9	−	4.39435e8i	0.920553	−	0.0594964i
$661$		−	2.11912e9i		−	0.285397i	−0.989766	−	0.142699i	$-0.954422\pi$
$661$		−	2.11912e9i		−	0.285397i	0.989766	−	0.142699i	$-0.0455780\pi$
$662$	3.96115e9	−	4.22543e9i	0.530663	−	0.566067i
$663$			6.84822e7i			0.00912600i
$664$	3.85096e9	−	4.67939e9i	0.510482	−	0.620298i
$665$	2.46276e9	+	7.63517e9i	0.324748	+	1.00680i
$666$	−3.33449e8	−	3.12594e8i	−0.0437391	−	0.0410035i
$667$	1.79667e8			0.0234438
$668$	9.47516e8	+	1.46604e10i	0.122990	+	1.90295i
$669$	4.07989e9			0.526814
$670$	3.86674e9	−	4.12472e9i	0.496688	−	0.529825i
$671$		−	4.15103e9i		−	0.530428i
$672$	−5.32922e9	−	3.83721e9i	−0.677441	−	0.487780i
$673$		−	7.20831e9i		−	0.911551i	−0.890095	−	0.455776i	$-0.849362\pi$
$673$		−	7.20831e9i		−	0.911551i	0.890095	−	0.455776i	$-0.150638\pi$
$674$	−8.43309e8	−	7.90565e8i	−0.106091	−	0.0994553i
$675$	−2.87942e9			−0.360365
$676$	−5.12403e8	−	7.92810e9i	−0.0637967	−	0.987088i
$677$		−	2.94409e9i		−	0.364662i	−0.983237	−	0.182331i	$-0.941636\pi$
$677$		−	2.94409e9i		−	0.364662i	0.983237	−	0.182331i	$-0.0583643\pi$
$678$	−3.83103e9	−	3.59142e9i	−0.472076	−	0.442550i
$679$	−1.34208e10			−1.64526
$680$	7.02835e8	+	5.78406e8i	0.0857180	+	0.0705427i
$681$	7.24918e8			0.0879577
$682$	−5.94556e9	−	5.57370e9i	−0.717707	−	0.672819i
$683$	−1.07261e10			−1.28815			−0.644077	−	0.764961i	$-0.722758\pi$
$683$	−1.07261e10			−1.28815			−0.644077	+	0.764961i	$0.722758\pi$
$684$	−1.84323e9	−	4.66134e9i	−0.220234	−	0.556948i
$685$	−5.31166e9			−0.631413
$686$	−2.13514e9	−	2.00160e9i	−0.252518	−	0.236725i
$687$	2.31772e9			0.272717
$688$	4.88267e8	+	3.76155e9i	0.0571607	+	0.440360i
$689$	5.20288e8			0.0606006
$690$	9.60818e7	+	9.00724e7i	0.0111345	+	0.0104381i
$691$		−	1.38137e10i		−	1.59271i	−0.604832	−	0.796353i	$-0.706760\pi$
$691$		−	1.38137e10i		−	1.59271i	0.604832	−	0.796353i	$-0.293240\pi$
$692$	7.59070e9	−	4.90596e8i	0.870784	−	0.0562798i
$693$	1.25524e10			1.43272
$694$	−3.12734e9	−	2.93174e9i	−0.355154	−	0.332941i
$695$		−	4.56869e9i		−	0.516232i
$696$	2.79482e9	−	3.39605e9i	0.314211	−	0.381805i
$697$			1.84633e9i			0.206535i
$698$	8.19724e9	−	8.74414e9i	0.912376	−	0.973247i
$699$	6.82729e9			0.756098
$700$	−4.24801e9	+	2.74554e8i	−0.468104	+	0.0302542i
$701$	6.17128e9			0.676647			0.338323	−	0.941030i	$-0.390140\pi$
$701$	6.17128e9			0.676647			0.338323	+	0.941030i	$0.390140\pi$
$702$	−7.05430e8	−	6.61309e8i	−0.0769615	−	0.0721480i
$703$	2.83078e8	+	8.77611e8i	0.0307299	+	0.0952705i
$704$	−1.64877e10	+	3.23292e9i	−1.78097	+	0.349213i
$705$			3.74179e9i			0.402177i
$706$	−1.08717e10	+	1.15970e10i	−1.16273	+	1.24031i
$707$			1.73060e10i			1.84174i
$708$	−3.96648e8	−	6.13710e9i	−0.0420039	−	0.649901i
$709$	1.64415e10			1.73253			0.866263	−	0.499588i	$-0.166515\pi$
$709$	1.64415e10			1.73253			0.866263	+	0.499588i	$0.166515\pi$
$710$	4.57740e9	−	4.88280e9i	0.479971	−	0.511993i
$711$	4.53990e9			0.473699
$712$	−7.54099e9	+	9.16323e9i	−0.782976	+	0.951412i
$713$		−	1.57530e8i		−	0.0162760i
$714$	−8.19332e8	−	7.68087e8i	−0.0842396	−	0.0789709i
$715$	1.48312e9			0.151742
$716$	−4.94426e8	−	7.64996e9i	−0.0503391	−	0.778868i
$717$			9.53586e9i			0.966147i
$718$	1.51696e9	+	1.42208e9i	0.152946	+	0.143380i
$719$			1.35463e10i			1.35915i	0.733604	+	0.679577i	$0.237837\pi$
$719$			1.35463e10i			1.35915i	−0.733604	+	0.679577i	$0.762163\pi$
$720$	−4.77400e9	+	6.19688e8i	−0.476671	+	0.0618741i
$721$		−	5.15657e9i		−	0.512375i
$722$	−1.30186e9	+	1.00289e10i	−0.128732	+	0.991679i
$723$			7.97148e9i			0.784432i
$724$	7.72237e9	−	4.99106e8i	0.756251	−	0.0488774i
$725$		−	2.85103e9i		−	0.277856i
$726$	−1.02438e10	+	1.09272e10i	−0.993533	+	1.05982i
$727$		−	6.66020e9i		−	0.642861i	−0.946933	−	0.321431i	$-0.895836\pi$
$727$		−	6.66020e9i		−	0.642861i	0.946933	−	0.321431i	$-0.104164\pi$
$728$	−1.10378e9	−	9.08366e8i	−0.106028	−	0.0872572i
$729$	6.97389e9			0.666697
$730$	−1.03089e10	+	1.09967e10i	−0.980804	+	1.04624i
$731$			6.48686e8i			0.0614220i
$732$	−1.26685e8	−	1.96012e9i	−0.0119381	−	0.184711i
$733$	−2.39047e9			−0.224192			−0.112096	−	0.993697i	$-0.535756\pi$
$733$	−2.39047e9			−0.224192			−0.112096	+	0.993697i	$0.535756\pi$
$734$	5.38765e9	+	5.05068e9i	0.502878	+	0.471426i
$735$	−4.03476e9			−0.374811
$736$	−2.63560e8	−	1.89772e8i	−0.0243673	−	0.0175452i
$737$			1.78474e10i			1.64225i
$738$	−7.12398e9	−	6.67841e9i	−0.652417	−	0.611612i
$739$			5.36355e9i			0.488874i	0.969665	+	0.244437i	$0.0786031\pi$
$739$			5.36355e9i			0.488874i	−0.969665	+	0.244437i	$0.921397\pi$
$740$	8.83776e8	−	5.71195e7i	0.0801735	−	0.00518171i
$741$	2.24319e8	+	6.95446e8i	0.0202536	+	0.0627913i
$742$	−5.83549e9	+	6.22482e9i	−0.524401	+	0.559388i
$743$	−1.07944e10			−0.965469			−0.482735	−	0.875767i	$-0.660356\pi$
$743$	−1.07944e10			−0.965469			−0.482735	+	0.875767i	$0.660356\pi$
$744$	−2.97760e9	−	2.45045e9i	−0.265071	−	0.218143i
$745$	−1.52882e10			−1.35459
$746$	−1.27503e10	−	1.19529e10i	−1.12444	−	1.05411i
$747$			5.48133e9i			0.481131i
$748$	−2.86739e9	+	1.85323e8i	−0.250513	+	0.0161910i
$749$			2.20288e10i			1.91560i
$750$	5.44562e9	−	5.80894e9i	0.471339	−	0.502785i
$751$	−1.49468e10			−1.28769			−0.643843	−	0.765158i	$-0.722661\pi$
$751$	−1.49468e10			−1.28769			−0.643843	+	0.765158i	$0.722661\pi$
$752$	−1.18778e9	−	9.15053e9i	−0.101853	−	0.784664i
$753$		−	5.00436e9i		−	0.427136i
$754$	6.54789e8	−	6.98475e8i	0.0556291	−	0.0593405i
$755$	−1.56800e10			−1.32596
$756$	1.58240e10	−	1.02272e9i	1.33196	−	0.0860860i
$757$	−1.21228e10			−1.01571			−0.507853	−	0.861444i	$-0.669561\pi$
$757$	−1.21228e10			−1.01571			−0.507853	+	0.861444i	$0.669561\pi$
$758$	−2.43135e9	+	2.59356e9i	−0.202771	+	0.216299i
$759$	−4.15740e8			−0.0345124
$760$	9.03200e9	+	3.57160e9i	0.746340	+	0.295131i
$761$	−1.96748e10			−1.61832			−0.809158	−	0.587591i	$-0.800076\pi$
$761$	−1.96748e10			−1.61832			−0.809158	+	0.587591i	$0.800076\pi$
$762$	−8.09005e9	+	8.62980e9i	−0.662383	+	0.706575i
$763$	2.06418e10			1.68233
$764$	1.70107e10	−	1.09942e9i	1.38005	−	0.0891946i
$765$	−8.23285e8			−0.0664868
$766$	1.43915e10	−	1.53517e10i	1.15693	−	1.23411i
$767$		−	1.33871e9i		−	0.107128i
$768$	−7.68685e9	+	2.02978e9i	−0.612328	+	0.161690i
$769$	−2.14307e9			−0.169939			−0.0849696	−	0.996384i	$-0.527079\pi$
$769$	−2.14307e9			−0.169939			−0.0849696	+	0.996384i	$0.527079\pi$
$770$	−1.66345e10	+	1.77443e10i	−1.31308	+	1.40069i
$771$			1.12220e10i			0.881817i
$772$	−5.52782e9	+	3.57270e8i	−0.432408	+	0.0279470i
$773$		−	1.96871e10i		−	1.53304i	−0.642221	−	0.766520i	$-0.721987\pi$
$773$		−	1.96871e10i		−	1.53304i	0.642221	−	0.766520i	$-0.278013\pi$
$774$	−2.50293e9	−	2.34638e9i	−0.194024	−	0.181889i
$775$	−2.49974e9			−0.192903
$776$	−1.03247e10	+	1.25458e10i	−0.793163	+	0.963790i
$777$	−1.09269e9			−0.0835646
$778$	5.46867e9	−	5.83353e9i	0.416345	−	0.444122i
$779$	6.04781e9	+	1.87497e10i	0.458371	+	1.42106i
$780$	7.00331e8	−	4.52632e7i	0.0528412	−	0.00341519i
$781$			2.11275e10i			1.58698i
$782$	−4.05206e7	−	3.79862e7i	−0.00303006	−	0.00284055i
$783$			1.06202e10i			0.790618i
$784$	9.86699e9	−	1.28078e9i	0.731271	−	0.0949223i
$785$	3.02775e9			0.223397
$786$	−1.86185e9	−	1.74540e9i	−0.136762	−	0.128208i
$787$	9.20369e9			0.673055			0.336527	−	0.941674i	$-0.390748\pi$
$787$	9.20369e9			0.673055			0.336527	+	0.941674i	$0.390748\pi$
$788$	−6.43390e8	−	9.95480e9i	−0.0468417	−	0.724754i
$789$		−	4.79566e9i		−	0.347599i
$790$	−6.01629e9	+	6.41768e9i	−0.434144	+	0.463109i
$791$	1.87457e10			1.34674
$792$	9.65666e9	−	1.17340e10i	0.690699	−	0.839284i
$793$		−	4.27569e8i		−	0.0304474i
$794$	9.16313e9	−	9.77448e9i	0.649639	−	0.692982i
$795$		−	4.18886e9i		−	0.295672i
$796$	4.05421e8	−	2.62029e7i	0.0284912	−	0.00184142i
$797$			1.37515e10i			0.962154i	0.876678	+	0.481077i	$0.159754\pi$
$797$			1.37515e10i			0.962154i	−0.876678	+	0.481077i	$0.840246\pi$
$798$	−1.08364e10	−	5.11624e9i	−0.754872	−	0.356402i
$799$		−	1.57802e9i		−	0.109446i
$800$	−3.01137e9	+	4.18227e9i	−0.207946	+	0.288800i
$801$		−	1.07336e10i		−	0.737958i
$802$	8.28783e9	+	7.76947e9i	0.567323	+	0.531840i
$803$		−	4.75819e10i		−	3.24293i
$804$	5.44683e8	+	8.42756e9i	0.0369614	+	0.571881i
$805$	−4.70141e8			−0.0317645
$806$	−6.12412e8	−	5.74109e8i	−0.0411975	−	0.0386208i
$807$			1.41701e10i			0.949108i
$808$	1.61777e10	+	1.33136e10i	1.07889	+	0.887886i
$809$	−9.89408e8			−0.0656985			−0.0328493	−	0.999460i	$-0.510458\pi$
$809$	−9.89408e8			−0.0656985			−0.0328493	+	0.999460i	$0.510458\pi$
$810$	−3.51972e8	+	3.75455e8i	−0.0232708	+	0.0248233i
$811$	9.40415e9			0.619080			0.309540	−	0.950886i	$-0.399825\pi$
$811$	9.40415e9			0.619080			0.309540	+	0.950886i	$0.399825\pi$
$812$	1.01264e9	+	1.56680e10i	0.0663758	+	1.02699i
$813$			5.75539e9i			0.375628i
$814$	−1.91202e9	+	2.03958e9i	−0.124253	+	0.132543i
$815$		−	2.05495e10i		−	1.32969i
$816$	−1.34833e9	+	1.75019e8i	−0.0868721	+	0.0112764i
$817$	2.12483e9	+	6.58749e9i	0.136316	+	0.422613i
$818$	6.17167e9	+	5.78566e9i	0.394245	+	0.369587i
$819$	1.29294e9			0.0822403
$820$	1.88814e10	−	1.22033e9i	1.19588	−	0.0772909i
$821$	1.99388e10			1.25747			0.628736	−	0.777618i	$-0.283572\pi$
$821$	1.99388e10			1.25747			0.628736	+	0.777618i	$0.283572\pi$
$822$	5.42635e9	−	5.78838e9i	0.340766	−	0.363501i
$823$		−	1.76346e10i		−	1.10273i	−0.834266	−	0.551363i	$-0.814108\pi$
$823$		−	1.76346e10i		−	1.10273i	0.834266	−	0.551363i	$-0.185892\pi$
$824$	−4.82038e9	−	3.96699e9i	−0.300148	−	0.247011i
$825$			6.59713e9i			0.409040i
$826$	1.60166e10	+	1.50148e10i	0.988871	+	0.927022i
$827$	−1.20529e10			−0.741009			−0.370504	−	0.928831i	$-0.620815\pi$
$827$	−1.20529e10			−0.741009			−0.370504	+	0.928831i	$0.620815\pi$
$828$	2.93136e8	−	1.89458e7i	0.0179458	−	0.00115986i
$829$		−	2.02987e10i		−	1.23745i	−0.785608	−	0.618725i	$-0.787650\pi$
$829$		−	2.02987e10i		−	1.23745i	0.785608	−	0.618725i	$-0.212350\pi$
$830$	−7.74849e9	−	7.26386e9i	−0.470375	−	0.440955i
$831$	2.18028e9			0.131798
$832$	−1.69829e9	+	3.33002e8i	−0.102230	+	0.0200454i
$833$	1.70158e9			0.101999
$834$	4.97873e9	+	4.66734e9i	0.297192	+	0.278604i
$835$	2.57466e10			1.53044
$836$	−2.85117e10	+	1.12744e10i	−1.68772	+	0.667375i
$837$	9.31164e9			0.548892
$838$	−2.05069e10	−	1.92243e10i	−1.20378	−	1.12849i
$839$	−1.72932e10			−1.01090			−0.505450	−	0.862856i	$-0.668674\pi$
$839$	−1.72932e10			−1.01090			−0.505450	+	0.862856i	$0.668674\pi$
$840$	−7.31328e9	+	8.88654e9i	−0.425731	+	0.517315i
$841$	6.73437e9			0.390401
$842$	−2.27476e10	−	2.13248e10i	−1.31324	−	1.23110i
$843$		−	1.27287e10i		−	0.731793i
$844$	6.57972e8	+	1.01804e10i	0.0376712	+	0.582864i
$845$	−1.39234e10			−0.793864
$846$	6.08874e9	+	5.70792e9i	0.345725	+	0.324102i
$847$		−	5.34683e10i		−	3.02346i
$848$	1.32970e9	+	1.02438e10i	0.0748802	+	0.576868i
$849$			1.03164e9i			0.0578566i
$850$	−6.02781e8	+	6.42997e8i	−0.0336661	+	0.0359122i
$851$	−5.40395e7			−0.00300578
$852$	6.44790e8	+	9.97645e9i	0.0357174	+	0.552634i
$853$	−9.83277e9			−0.542443			−0.271222	−	0.962517i	$-0.587428\pi$
$853$	−9.83277e9			−0.542443			−0.271222	+	0.962517i	$0.587428\pi$
$854$	5.11551e9	+	4.79556e9i	0.281052	+	0.263473i
$855$	−8.36057e9	+	2.69674e9i	−0.457461	+	0.147556i
$856$	2.05926e10	+	1.69469e10i	1.12216	+	0.923491i
$857$			1.81378e10i			0.984358i	0.870494	+	0.492179i	$0.163799\pi$
$857$			1.81378e10i			0.984358i	−0.870494	+	0.492179i	$0.836201\pi$
$858$	−1.51514e9	+	1.61623e9i	−0.0818933	+	0.0873570i
$859$		−	1.40941e8i		−	0.00758684i	−0.999993	−	0.00379342i	$-0.998793\pi$
$859$		−	1.40941e8i		−	0.00758684i	0.999993	−	0.00379342i	$-0.00120749\pi$
$860$	6.63377e9	−	4.28748e8i	0.355644	−	0.0229857i
$861$	−2.33447e10			−1.24646
$862$	1.39452e10	−	1.48756e10i	0.741565	−	0.791041i
$863$	−1.70361e10			−0.902259			−0.451129	−	0.892459i	$-0.648979\pi$
$863$	−1.70361e10			−0.902259			−0.451129	+	0.892459i	$0.648979\pi$
$864$	1.12175e10	−	1.55791e10i	0.591694	−	0.821760i
$865$		−	1.33308e10i		−	0.700327i
$866$	3.71630e9	+	3.48386e9i	0.194445	+	0.182284i
$867$	1.19206e10			0.621199
$868$	1.37375e10	−	8.87869e8i	0.712997	−	0.0460818i
$869$		−	2.77689e10i		−	1.43545i
$870$	−5.62344e9	−	5.27173e9i	−0.289524	−	0.271416i
$871$			1.83834e9i			0.0942676i
$872$	1.58799e10	−	1.92960e10i	0.811034	−	0.985507i
$873$		−	1.46959e10i		−	0.747559i
$874$	−5.35919e8	−	2.53026e8i	−0.0271524	−	0.0128196i
$875$			2.84239e10i			1.43435i
$876$	−1.45215e9	−	2.24683e10i	−0.0729873	−	1.12929i
$877$		−	5.33127e8i		−	0.0266890i	−0.999911	−	0.0133445i	$-0.995752\pi$
$877$		−	5.33127e8i		−	0.0266890i	0.999911	−	0.0133445i	$-0.00424781\pi$
$878$	−4.43455e9	+	4.73041e9i	−0.221115	+	0.235868i
$879$			2.40038e10i			1.19212i
$880$	3.79039e9	+	2.92008e10i	0.187497	+	1.44446i
$881$	−2.62723e9			−0.129444			−0.0647220	−	0.997903i	$-0.520616\pi$
$881$	−2.62723e9			−0.129444			−0.0647220	+	0.997903i	$0.520616\pi$
$882$	−6.15483e9	+	6.56547e9i	−0.302048	+	0.322200i
$883$		−	3.35468e9i		−	0.163979i	−0.996633	−	0.0819895i	$-0.973873\pi$
$883$		−	3.35468e9i		−	0.163979i	0.996633	−	0.0819895i	$-0.0261274\pi$
$884$	−2.95350e8	+	1.90889e7i	−0.0143799	+	0.000929388i
$885$	−1.07780e10			−0.522682
$886$	−5.73896e9	−	5.38002e9i	−0.277214	−	0.259876i
$887$	−5.22452e9			−0.251370			−0.125685	−	0.992070i	$-0.540113\pi$
$887$	−5.22452e9			−0.251370			−0.125685	+	0.992070i	$0.540113\pi$
$888$	−8.40612e8	+	1.02145e9i	−0.0402856	+	0.0489520i
$889$		−	4.22267e10i		−	2.01573i
$890$	1.51732e10	+	1.42242e10i	0.721459	+	0.676336i
$891$		−	1.62457e9i		−	0.0769425i
$892$	1.13724e9	+	1.75958e10i	0.0536505	+	0.830102i
$893$	−5.16896e9	−	1.60251e10i	−0.242897	−	0.753042i
$894$	1.56183e10	−	1.66603e10i	0.731059	−	0.779834i
$895$	−1.34349e10			−0.626403
$896$	1.50637e10	−	2.40535e10i	0.699605	−	1.11712i
$897$	−4.28226e7			−0.00198107
$898$	9.01928e9	+	8.45517e9i	0.415628	+	0.389633i
$899$			9.21984e9i			0.423218i
$900$	−3.00639e8	−	4.65161e9i	−0.0137466	−	0.212693i
$901$			1.76657e9i			0.0804624i
$902$	−4.08493e10	+	4.35747e10i	−1.85337	+	1.97702i
$903$	−8.20189e9			−0.370687
$904$	1.44212e10	−	1.75236e10i	0.649252	−	0.788921i
$905$		−	1.35621e10i		−	0.608213i
$906$	1.60185e10	−	1.70872e10i	0.715606	−	0.763349i
$907$	6.79914e9			0.302572			0.151286	−	0.988490i	$-0.451659\pi$
$907$	6.79914e9			0.302572			0.151286	+	0.988490i	$0.451659\pi$
$908$	2.02065e8	+	3.12643e9i	0.00895758	+	0.138595i
$909$	−1.89502e10			−0.836837
$910$	−1.71341e9	+	1.82772e9i	−0.0753729	+	0.0804016i
$911$	1.63109e10			0.714767			0.357384	−	0.933958i	$-0.383669\pi$
$911$	1.63109e10			0.714767			0.357384	+	0.933958i	$0.383669\pi$
$912$	−1.31192e10	+	6.19391e9i	−0.572696	+	0.270385i
$913$	3.35272e10			1.45797
$914$	−7.03246e8	+	7.50165e8i	−0.0304646	+	0.0324972i
$915$	−3.44237e9			−0.148554
$916$	6.46046e8	+	9.99588e9i	0.0277734	+	0.429721i
$917$	9.11028e9			0.390157
$918$	2.24538e9	−	2.39519e9i	0.0957945	−	0.102186i
$919$		−	2.44503e9i		−	0.103916i	−0.998649	−	0.0519578i	$-0.983454\pi$
$919$		−	2.44503e9i		−	0.103916i	0.998649	−	0.0519578i	$-0.0165461\pi$
$920$	−3.61683e8	+	4.39489e8i	−0.0153134	+	0.0186076i
$921$	−2.13497e10			−0.900501
$922$	−4.89032e8	+	5.21659e8i	−0.0205485	+	0.0219194i
$923$			2.17621e9i			0.0910949i
$924$	−2.34319e9	−	3.62548e10i	−0.0977139	−	1.51187i
$925$			8.57520e8i			0.0356245i
$926$	2.85227e10	+	2.67388e10i	1.18046	+	1.10663i
$927$	5.64648e9			0.232809
$928$	1.54255e10	+	1.11069e10i	0.633610	+	0.456220i
$929$	2.32916e9			0.0953113			0.0476556	−	0.998864i	$-0.484825\pi$
$929$	2.32916e9			0.0953113			0.0476556	+	0.998864i	$0.484825\pi$
$930$	−4.62217e9	+	4.93055e9i	−0.188432	+	0.201004i
$931$	1.72798e10	−	5.57367e9i	0.701801	−	0.226369i
$932$	1.90305e9	+	2.94448e10i	0.0770007	+	1.19139i
$933$			1.69979e10i			0.685190i
$934$	−4.18638e9	−	3.92454e9i	−0.168122	−	0.157607i
$935$			5.03572e9i			0.201475i
$936$	9.94668e8	−	1.20864e9i	0.0396472	−	0.0481762i
$937$	−1.45387e10			−0.577346			−0.288673	−	0.957428i	$-0.593214\pi$
$937$	−1.45387e10			−0.577346			−0.288673	+	0.957428i	$0.593214\pi$
$938$	−2.19942e10	−	2.06186e10i	−0.870158	−	0.815734i
$939$	1.25399e10			0.494270
$940$	−1.61376e10	+	1.04299e9i	−0.633712	+	0.0409576i
$941$			1.69156e10i			0.661796i	0.943666	+	0.330898i	$0.107352\pi$
$941$			1.69156e10i			0.661796i	−0.943666	+	0.330898i	$0.892648\pi$
$942$	−3.09313e9	+	3.29949e9i	−0.120565	+	0.128608i
$943$	−1.15453e9			−0.0448345
$944$	2.63576e10	−	3.42133e9i	1.01977	−	0.132371i
$945$		−	2.77902e10i		−	1.07122i
$946$	−1.43519e10	+	1.53095e10i	−0.551178	+	0.587951i
$947$		−	7.67277e9i		−	0.293580i	−0.989168	−	0.146790i	$-0.953106\pi$
$947$		−	7.67277e9i		−	0.293580i	0.989168	−	0.146790i	$-0.0468942\pi$
$948$	−8.47476e8	−	1.31125e10i	−0.0323071	−	0.499869i
$949$		−	4.90110e9i		−	0.186149i
$950$	−4.01513e9	+	8.50418e9i	−0.151938	+	0.321810i
$951$			7.92527e9i			0.298801i
$952$	3.08423e9	−	3.74772e9i	0.115856	−	0.140779i
$953$			1.64859e10i			0.617002i	0.951224	+	0.308501i	$0.0998273\pi$
$953$			1.64859e10i			0.617002i	−0.951224	+	0.308501i	$0.900173\pi$
$954$	−6.81622e9	−	6.38990e9i	−0.254170	−	0.238273i
$955$		−	2.98744e10i		−	1.10991i
$956$	−4.11263e10	+	2.65804e9i	−1.52236	+	0.0983919i
$957$	2.43323e10			0.897410
$958$	−1.56461e10	−	1.46675e10i	−0.574946	−	0.538986i
$959$			2.83233e10i			1.03700i
$960$	2.68101e9	+	1.36730e10i	0.0978022	+	0.498785i
$961$	−1.94288e10			−0.706178
$962$	−1.96944e8	+	2.10084e8i	−0.00713231	+	0.00760817i
$963$	−2.41217e10			−0.870394
$964$	−3.43795e10	+	2.22199e9i	−1.23603	+	0.0798862i
$965$			9.70799e9i			0.347763i
$966$	4.80292e8	−	5.12336e8i	0.0171429	−	0.0182867i
$967$		−	4.88003e10i		−	1.73552i	−0.496984	−	0.867760i	$-0.665559\pi$
$967$		−	4.88003e10i		−	1.73552i	0.496984	−	0.867760i	$-0.334441\pi$
$968$	−4.99824e10	−	4.11336e10i	−1.77114	−	1.45758i
$969$	−2.36129e9	+	7.61645e8i	−0.0833712	+	0.0268918i
$970$	2.07743e10	+	1.94750e10i	0.730846	+	0.685135i
$971$	5.21393e10			1.82767			0.913835	−	0.406087i	$-0.133107\pi$
$971$	5.21393e10			1.82767			0.913835	+	0.406087i	$0.133107\pi$
$972$	1.82030e9	+	2.81644e10i	0.0635786	+	0.983714i
$973$	−2.43616e10			−0.847833
$974$	3.10062e10	−	3.30749e10i	1.07521	−	1.14694i
$975$			6.79526e8i			0.0234795i
$976$	8.41830e9	−	1.09273e9i	0.289835	−	0.0376219i
$977$			2.97443e10i			1.02040i	0.860054	+	0.510202i	$0.170430\pi$
$977$			2.97443e10i			1.02040i	−0.860054	+	0.510202i	$0.829570\pi$
$978$	2.23938e10	+	2.09932e10i	0.765494	+	0.717617i
$979$	−6.56534e10			−2.23624
$980$	−1.12466e9	−	1.74011e10i	−0.0381706	−	0.590591i
$981$			2.26029e10i			0.764403i
$982$	−1.11796e10	−	1.04803e10i	−0.376734	−	0.353171i
$983$	−7.23985e9			−0.243104			−0.121552	−	0.992585i	$-0.538787\pi$
$983$	−7.23985e9			−0.243104			−0.121552	+	0.992585i	$0.538787\pi$
$984$	−1.79593e10	+	2.18227e10i	−0.600904	+	0.730173i
$985$	−1.74827e10			−0.582882
$986$	2.37157e9	+	2.22324e9i	0.0787893	+	0.0738615i
$987$	1.99523e10			0.660516
$988$	−2.93680e9	+	1.16130e9i	−0.0968778	+	0.0383084i
$989$	−4.05629e8			−0.0133334
$990$	−1.94301e10	−	1.82149e10i	−0.636433	−	0.596627i
$991$	−3.29375e10			−1.07506			−0.537530	−	0.843245i	$-0.680642\pi$
$991$	−3.29375e10			−1.07506			−0.537530	+	0.843245i	$0.680642\pi$
$992$	9.73835e9	−	1.35249e10i	0.316734	−	0.439888i
$993$	1.51619e10			0.491396
$994$	−2.60365e10	−	2.44080e10i	−0.840872	−	0.788280i
$995$		−	7.12003e8i		−	0.0229140i
$996$	1.58316e10	−	1.02321e9i	0.507711	−	0.0328140i
$997$	4.15340e10			1.32730			0.663652	−	0.748042i	$-0.269006\pi$
$997$	4.15340e10			1.32730			0.663652	+	0.748042i	$0.269006\pi$
$998$	3.71745e10	+	3.48494e10i	1.18383	+	1.10978i
$999$		−	3.19429e9i		−	0.101367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.d.a.75.18	yes	68
4.3	odd	2	inner	76.8.d.a.75.52	yes	68
19.18	odd	2	inner	76.8.d.a.75.51	yes	68
76.75	even	2	inner	76.8.d.a.75.17	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.d.a.75.17	✓	68	76.75	even	2	inner
76.8.d.a.75.18	yes	68	1.1	even	1	trivial
76.8.d.a.75.51	yes	68	19.18	odd	2	inner
76.8.d.a.75.52	yes	68	4.3	odd	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	76.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.73771 + 8.25396i) q^{2} -29.6173 q^{3} +(-8.25557 - 127.733i) q^{4} -224.326 q^{5} +(229.170 - 244.460i) q^{6} +1196.17i q^{7} +(1118.19 + 920.224i) q^{8} -1309.82 q^{9} +O(q^{10})\)	\(q+(-7.73771 + 8.25396i) q^{2} -29.6173 q^{3} +(-8.25557 - 127.733i) q^{4} -224.326 q^{5} +(229.170 - 244.460i) q^{6} +1196.17i q^{7} +(1118.19 + 920.224i) q^{8} -1309.82 q^{9} +(1735.77 - 1851.58i) q^{10} +8011.66i q^{11} +(244.507 + 3783.12i) q^{12} +825.227i q^{13} +(-9873.15 - 9255.64i) q^{14} +6643.93 q^{15} +(-16247.7 + 2109.03i) q^{16} -2801.94 q^{17} +(10135.0 - 10811.2i) q^{18} +(-28454.1 + 9178.01i) q^{19} +(1851.94 + 28654.0i) q^{20} -35427.4i q^{21} +(-66127.9 - 61991.9i) q^{22} -1752.08i q^{23} +(-33117.6 - 27254.5i) q^{24} -27802.7 q^{25} +(-6811.39 - 6385.37i) q^{26} +103566. q^{27} +(152791. - 9875.08i) q^{28} +102545. i q^{29} +(-51408.8 + 54838.7i) q^{30} +89910.0 q^{31} +(108312. - 150427. i) q^{32} -237283. i q^{33} +(21680.6 - 23127.1i) q^{34} -268333. i q^{35} +(10813.3 + 167308. i) q^{36} -30843.0i q^{37} +(144415. - 305876. i) q^{38} -24441.0i q^{39} +(-250838. - 206430. i) q^{40} -658946. i q^{41} +(292416. + 274127. i) q^{42} -231513. i q^{43} +(1.02336e6 - 66140.8i) q^{44} +293827. q^{45} +(14461.6 + 13557.1i) q^{46} +563190. i q^{47} +(481212. - 62463.6i) q^{48} -607285. q^{49} +(215130. - 229482. i) q^{50} +82985.9 q^{51} +(105409. - 6812.72i) q^{52} -630479. i q^{53} +(-801365. + 854831. i) q^{54} -1.79723e6i q^{55} +(-1.10075e6 + 1.33754e6i) q^{56} +(842733. - 271828. i) q^{57} +(-846403. - 793465. i) q^{58} -1.62223e6 q^{59} +(-54849.4 - 848652. i) q^{60} -518123. q^{61} +(-695698. + 742113. i) q^{62} -1.56677e6i q^{63} +(403527. + 2.05796e6i) q^{64} -185120. i q^{65} +(1.95853e6 + 1.83603e6i) q^{66} +2.22768e6 q^{67} +(23131.6 + 357902. i) q^{68} +51891.8i q^{69} +(2.21481e6 + 2.07628e6i) q^{70} +2.63710e6 q^{71} +(-1.46462e6 - 1.20533e6i) q^{72} -5.93909e6 q^{73} +(254577. + 238655. i) q^{74} +823441. q^{75} +(1.40724e6 + 3.55877e6i) q^{76} -9.58333e6 q^{77} +(201735. + 189117. i) q^{78} -3.46606e6 q^{79} +(3.64478e6 - 473110. i) q^{80} -202776. q^{81} +(5.43891e6 + 5.09873e6i) q^{82} -4.18480e6i q^{83} +(-4.52526e6 + 292473. i) q^{84} +628549. q^{85} +(1.91090e6 + 1.79138e6i) q^{86} -3.03711e6i q^{87} +(-7.37252e6 + 8.95852e6i) q^{88} +8.19473e6i q^{89} +(-2.27355e6 + 2.42523e6i) q^{90} -987114. q^{91} +(-223799. + 14464.4i) q^{92} -2.66289e6 q^{93} +(-4.64854e6 - 4.35780e6i) q^{94} +(6.38300e6 - 2.05887e6i) q^{95} +(-3.20791e6 + 4.45523e6i) q^{96} +1.12198e7i q^{97} +(4.69900e6 - 5.01251e6i) q^{98} -1.04938e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9}+O(q^{10}) \) 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9	\( 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9} + 13050 q^{16} + 23968 q^{17} - 79660 q^{20} - 232154 q^{24} + 937496 q^{25} - 391242 q^{26} - 37666 q^{28} - 468496 q^{30} - 1128652 q^{36} - 530466 q^{38} + 651806 q^{42} + 1433776 q^{44} - 321252 q^{45} - 4014380 q^{49} + 1697586 q^{54} + 137420 q^{57} + 2227894 q^{58} - 3042164 q^{61} + 2261524 q^{62} + 9825150 q^{64} - 749476 q^{66} - 11176962 q^{68} + 598424 q^{73} - 6195964 q^{74} - 1714536 q^{76} - 2556764 q^{77} + 16623216 q^{80} + 43726748 q^{81} - 20460388 q^{82} + 27222844 q^{85} - 61733582 q^{92} + 17778200 q^{93} - 36370886 q^{96}+O(q^{100}) \) 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9 + 13050 * q^16 + 23968 * q^17 - 79660 * q^20 - 232154 * q^24 + 937496 * q^25 - 391242 * q^26 - 37666 * q^28 - 468496 * q^30 - 1128652 * q^36 - 530466 * q^38 + 651806 * q^42 + 1433776 * q^44 - 321252 * q^45 - 4014380 * q^49 + 1697586 * q^54 + 137420 * q^57 + 2227894 * q^58 - 3042164 * q^61 + 2261524 * q^62 + 9825150 * q^64 - 749476 * q^66 - 11176962 * q^68 + 598424 * q^73 - 6195964 * q^74 - 1714536 * q^76 - 2556764 * q^77 + 16623216 * q^80 + 43726748 * q^81 - 20460388 * q^82 + 27222844 * q^85 - 61733582 * q^92 + 17778200 * q^93 - 36370886 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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