LMFDB - Embedded newform 35.5.d.a.6.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(6,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("35.6");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.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:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 109 x^{10} + 570 x^{9} + 5814 x^{8} - 22512 x^{7} - 151120 x^{6} + 300288 x^{5} + \cdots + 205833600 $ x^12 - 6x^11 - 109x^10 + 570x^9 + 5814x^8 - 22512x^7 - 151120x^6 + 300288x^5 + 2661184x^4 - 1881600x^3 - 12922560x^2 + 25948800*x + 205833600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			6.10
Root			$5.81769 - 2.23607i$ of defining polynomial
Character	$\chi$	$=$	35.6
Dual form			35.5.d.a.6.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.81769 q^{2} +14.5704i q^{3} +7.21016 q^{4} -11.1803i q^{5} +70.1957i q^{6} +(44.8989 + 19.6236i) q^{7} -42.3467 q^{8} -131.296 q^{9} +O(q^{10})$	\(q+4.81769 q^{2} +14.5704i q^{3} +7.21016 q^{4} -11.1803i q^{5} +70.1957i q^{6} +(44.8989 + 19.6236i) q^{7} -42.3467 q^{8} -131.296 q^{9} -53.8634i q^{10} +201.717 q^{11} +105.055i q^{12} -258.711i q^{13} +(216.309 + 94.5404i) q^{14} +162.902 q^{15} -319.376 q^{16} -242.930i q^{17} -632.545 q^{18} +253.614i q^{19} -80.6121i q^{20} +(-285.923 + 654.195i) q^{21} +971.808 q^{22} -323.663 q^{23} -617.009i q^{24} -125.000 q^{25} -1246.39i q^{26} -732.838i q^{27} +(323.729 + 141.489i) q^{28} -331.107 q^{29} +784.812 q^{30} +278.747i q^{31} -861.108 q^{32} +2939.09i q^{33} -1170.36i q^{34} +(219.398 - 501.985i) q^{35} -946.668 q^{36} -322.518 q^{37} +1221.84i q^{38} +3769.52 q^{39} +473.451i q^{40} +578.646i q^{41} +(-1377.49 + 3151.71i) q^{42} -1524.82 q^{43} +1454.41 q^{44} +1467.94i q^{45} -1559.31 q^{46} -389.432i q^{47} -4653.44i q^{48} +(1630.83 + 1762.16i) q^{49} -602.212 q^{50} +3539.59 q^{51} -1865.35i q^{52} +1071.73 q^{53} -3530.59i q^{54} -2255.26i q^{55} +(-1901.32 - 830.995i) q^{56} -3695.26 q^{57} -1595.17 q^{58} +1030.67i q^{59} +1174.55 q^{60} -6681.90i q^{61} +1342.92i q^{62} +(-5895.07 - 2576.51i) q^{63} +961.463 q^{64} -2892.47 q^{65} +14159.6i q^{66} -4053.08 q^{67} -1751.57i q^{68} -4715.90i q^{69} +(1056.99 - 2418.41i) q^{70} +3210.95 q^{71} +5559.97 q^{72} +2238.66i q^{73} -1553.79 q^{74} -1821.30i q^{75} +1828.60i q^{76} +(9056.86 + 3958.40i) q^{77} +18160.4 q^{78} -5234.87 q^{79} +3570.73i q^{80} +42.7274 q^{81} +2787.74i q^{82} +3799.88i q^{83} +(-2061.55 + 4716.85i) q^{84} -2716.04 q^{85} -7346.12 q^{86} -4824.37i q^{87} -8542.04 q^{88} +13693.9i q^{89} +7072.07i q^{90} +(5076.83 - 11615.8i) q^{91} -2333.66 q^{92} -4061.45 q^{93} -1876.16i q^{94} +2835.49 q^{95} -12546.7i q^{96} -18557.4i q^{97} +(7856.83 + 8489.53i) q^{98} -26484.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 122 q^{4} - 50 q^{7} - 186 q^{8} - 434 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 + 122 * q^4 - 50 * q^7 - 186 * q^8 - 434 * q^9	$ 12 q - 6 q^{2} + 122 q^{4} - 50 q^{7} - 186 q^{8} - 434 q^{9} + 126 q^{11} + 78 q^{14} + 50 q^{15} + 578 q^{16} + 734 q^{18} - 642 q^{21} + 2264 q^{22} - 756 q^{23} - 1500 q^{25} + 1414 q^{28} - 2190 q^{29} + 1600 q^{30} - 8682 q^{32} - 150 q^{35} - 3582 q^{36} + 5564 q^{37} + 8634 q^{39} + 5580 q^{42} + 3944 q^{43} - 11196 q^{44} + 7844 q^{46} - 8796 q^{49} + 750 q^{50} + 7206 q^{51} + 11760 q^{53} - 6606 q^{56} - 12900 q^{57} - 18496 q^{58} - 11700 q^{60} - 4310 q^{63} + 20146 q^{64} - 750 q^{65} - 24096 q^{67} + 14400 q^{70} - 5664 q^{71} + 39214 q^{72} + 17604 q^{74} + 26904 q^{77} + 20100 q^{78} - 1590 q^{79} - 11912 q^{81} - 43128 q^{84} + 1050 q^{85} + 17604 q^{86} - 7268 q^{88} - 7182 q^{91} - 60252 q^{92} - 70980 q^{93} - 3000 q^{95} + 57714 q^{98} + 23084 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 + 122 * q^4 - 50 * q^7 - 186 * q^8 - 434 * q^9 + 126 * q^11 + 78 * q^14 + 50 * q^15 + 578 * q^16 + 734 * q^18 - 642 * q^21 + 2264 * q^22 - 756 * q^23 - 1500 * q^25 + 1414 * q^28 - 2190 * q^29 + 1600 * q^30 - 8682 * q^32 - 150 * q^35 - 3582 * q^36 + 5564 * q^37 + 8634 * q^39 + 5580 * q^42 + 3944 * q^43 - 11196 * q^44 + 7844 * q^46 - 8796 * q^49 + 750 * q^50 + 7206 * q^51 + 11760 * q^53 - 6606 * q^56 - 12900 * q^57 - 18496 * q^58 - 11700 * q^60 - 4310 * q^63 + 20146 * q^64 - 750 * q^65 - 24096 * q^67 + 14400 * q^70 - 5664 * q^71 + 39214 * q^72 + 17604 * q^74 + 26904 * q^77 + 20100 * q^78 - 1590 * q^79 - 11912 * q^81 - 43128 * q^84 + 1050 * q^85 + 17604 * q^86 - 7268 * q^88 - 7182 * q^91 - 60252 * q^92 - 70980 * q^93 - 3000 * q^95 + 57714 * q^98 + 23084 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$1$	$-1$

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 $

$2$	4.81769			1.20442			0.602212	−	0.798337i	$-0.294286\pi$
$2$	4.81769			1.20442			0.602212	+	0.798337i	$0.294286\pi$
$3$			14.5704i			1.61893i	0.587166	+	0.809466i	$0.300243\pi$
$3$			14.5704i			1.61893i	−0.587166	+	0.809466i	$0.699757\pi$
$4$	7.21016			0.450635
$5$		−	11.1803i		−	0.447214i
$5$		−	11.1803i		−	0.447214i
$6$			70.1957i			1.94988i
$7$	44.8989	+	19.6236i	0.916305	+	0.400481i
$7$	44.8989	+	19.6236i	0.916305	+	0.400481i
$8$	−42.3467			−0.661668
$9$	−131.296			−1.62094
$10$		−	53.8634i		−	0.538634i
$11$	201.717			1.66708			0.833539	−	0.552460i	$-0.186311\pi$
$11$	201.717			1.66708			0.833539	+	0.552460i	$0.186311\pi$
$12$			105.055i			0.729548i
$13$		−	258.711i		−	1.53083i	−0.643535	−	0.765416i	$-0.722533\pi$
$13$		−	258.711i		−	1.53083i	0.643535	−	0.765416i	$-0.277467\pi$
$14$	216.309	+	94.5404i	1.10362	+	0.482349i
$15$	162.902			0.724009
$16$	−319.376			−1.24756
$17$		−	242.930i		−	0.840588i	−0.907388	−	0.420294i	$-0.861927\pi$
$17$		−	242.930i		−	0.840588i	0.907388	−	0.420294i	$-0.138073\pi$
$18$	−632.545			−1.95230
$19$			253.614i			0.702533i	0.936276	+	0.351266i	$0.114249\pi$
$19$			253.614i			0.702533i	−0.936276	+	0.351266i	$0.885751\pi$
$20$		−	80.6121i		−	0.201530i
$21$	−285.923	+	654.195i	−0.648352	+	1.48344i
$22$	971.808			2.00787
$23$	−323.663			−0.611840			−0.305920	−	0.952057i	$-0.598964\pi$
$23$	−323.663			−0.611840			−0.305920	+	0.952057i	$0.598964\pi$
$24$		−	617.009i		−	1.07120i
$25$	−125.000			−0.200000
$26$		−	1246.39i		−	1.84377i
$27$		−	732.838i		−	1.00526i
$28$	323.729	+	141.489i	0.412919	+	0.180471i
$29$	−331.107			−0.393707			−0.196853	−	0.980433i	$-0.563072\pi$
$29$	−331.107			−0.393707			−0.196853	+	0.980433i	$0.563072\pi$
$30$	784.812			0.872013
$31$			278.747i			0.290059i	0.989427	+	0.145030i	$0.0463277\pi$
$31$			278.747i			0.290059i	−0.989427	+	0.145030i	$0.953672\pi$
$32$	−861.108			−0.840926
$33$			2939.09i			2.69889i
$34$		−	1170.36i		−	1.01242i
$35$	219.398	−	501.985i	0.179101	−	0.409784i
$36$	−946.668			−0.730454
$37$	−322.518			−0.235587			−0.117793	−	0.993038i	$-0.537582\pi$
$37$	−322.518			−0.235587			−0.117793	+	0.993038i	$0.537582\pi$
$38$			1221.84i			0.846147i
$39$	3769.52			2.47831
$40$			473.451i			0.295907i
$41$			578.646i			0.344227i	0.985077	+	0.172114i	$0.0550596\pi$
$41$			578.646i			0.344227i	−0.985077	+	0.172114i	$0.944940\pi$
$42$	−1377.49	+	3151.71i	−0.780891	+	1.78668i
$43$	−1524.82			−0.824674			−0.412337	−	0.911031i	$-0.635287\pi$
$43$	−1524.82			−0.824674			−0.412337	+	0.911031i	$0.635287\pi$
$44$	1454.41			0.751244
$45$			1467.94i			0.724908i
$46$	−1559.31			−0.736914
$47$		−	389.432i		−	0.176293i	−0.996108	−	0.0881467i	$-0.971906\pi$
$47$		−	389.432i		−	0.176293i	0.996108	−	0.0881467i	$-0.0280944\pi$
$48$		−	4653.44i		−	2.01972i
$49$	1630.83	+	1762.16i	0.679229	+	0.733926i
$50$	−602.212			−0.240885
$51$	3539.59			1.36086
$52$		−	1865.35i		−	0.689847i
$53$	1071.73			0.381535			0.190768	−	0.981635i	$-0.438902\pi$
$53$	1071.73			0.381535			0.190768	+	0.981635i	$0.438902\pi$
$54$		−	3530.59i		−	1.21076i
$55$		−	2255.26i		−	0.745540i
$56$	−1901.32	−	830.995i	−0.606289	−	0.264986i
$57$	−3695.26			−1.13735
$58$	−1595.17			−0.474190
$59$			1030.67i			0.296085i	0.988981	+	0.148042i	$0.0472972\pi$
$59$			1030.67i			0.296085i	−0.988981	+	0.148042i	$0.952703\pi$
$60$	1174.55			0.326264
$61$		−	6681.90i		−	1.79573i	−0.440273	−	0.897864i	$-0.645118\pi$
$61$		−	6681.90i		−	1.79573i	0.440273	−	0.897864i	$-0.354882\pi$
$62$			1342.92i			0.349354i
$63$	−5895.07	−	2576.51i	−1.48528	−	0.649157i
$64$	961.463			0.234732
$65$	−2892.47			−0.684609
$66$			14159.6i			3.25060i
$67$	−4053.08			−0.902892			−0.451446	−	0.892299i	$-0.649092\pi$
$67$	−4053.08			−0.902892			−0.451446	+	0.892299i	$0.649092\pi$
$68$		−	1751.57i		−	0.378799i
$69$		−	4715.90i		−	0.990527i
$70$	1056.99	−	2418.41i	0.215713	−	0.493553i
$71$	3210.95			0.636967			0.318483	−	0.947928i	$-0.396827\pi$
$71$	3210.95			0.636967			0.318483	+	0.947928i	$0.396827\pi$
$72$	5559.97			1.07253
$73$			2238.66i			0.420091i	0.977692	+	0.210045i	$0.0673612\pi$
$73$			2238.66i			0.420091i	−0.977692	+	0.210045i	$0.932639\pi$
$74$	−1553.79			−0.283746
$75$		−	1821.30i		−	0.323787i
$76$			1828.60i			0.316586i
$77$	9056.86	+	3958.40i	1.52755	+	0.667634i
$78$	18160.4			2.98494
$79$	−5234.87			−0.838787			−0.419393	−	0.907805i	$-0.637757\pi$
$79$	−5234.87			−0.838787			−0.419393	+	0.907805i	$0.637757\pi$
$80$			3570.73i			0.557927i
$81$	42.7274			0.00651233
$82$			2787.74i			0.414595i
$83$			3799.88i			0.551587i	0.961217	+	0.275793i	$0.0889405\pi$
$83$			3799.88i			0.551587i	−0.961217	+	0.275793i	$0.911059\pi$
$84$	−2061.55	+	4716.85i	−0.292170	+	0.668488i
$85$	−2716.04			−0.375923
$86$	−7346.12			−0.993256
$87$		−	4824.37i		−	0.637385i
$88$	−8542.04			−1.10305
$89$			13693.9i			1.72881i	0.502799	+	0.864403i	$0.332304\pi$
$89$			13693.9i			1.72881i	−0.502799	+	0.864403i	$0.667696\pi$
$90$			7072.07i			0.873095i
$91$	5076.83	−	11615.8i	0.613070	−	1.40271i
$92$	−2333.66			−0.275716
$93$	−4061.45			−0.469586
$94$		−	1876.16i		−	0.212332i
$95$	2835.49			0.314182
$96$		−	12546.7i		−	1.36140i
$97$		−	18557.4i		−	1.97230i	−0.165847	−	0.986152i	$-0.553036\pi$
$97$		−	18557.4i		−	1.97230i	0.165847	−	0.986152i	$-0.446964\pi$
$98$	7856.83	+	8489.53i	0.818079	+	0.883958i
$99$	−26484.6			−2.70224
$100$	−901.270			−0.0901270
$101$			3882.89i			0.380639i	0.981722	+	0.190319i	$0.0609523\pi$
$101$			3882.89i			0.380639i	−0.981722	+	0.190319i	$0.939048\pi$
$102$	17052.6			1.63905
$103$		−	5551.06i		−	0.523241i	−0.965171	−	0.261620i	$-0.915743\pi$
$103$		−	5551.06i		−	0.523241i	0.965171	−	0.261620i	$-0.0842569\pi$
$104$			10955.6i			1.01290i
$105$	7314.12	+	3196.72i	0.663413	+	0.289952i
$106$	5163.28			0.459530
$107$	−1207.91			−0.105504			−0.0527518	−	0.998608i	$-0.516799\pi$
$107$	−1207.91			−0.105504			−0.0527518	+	0.998608i	$0.516799\pi$
$108$		−	5283.88i		−	0.453007i
$109$	4780.21			0.402341			0.201170	−	0.979556i	$-0.435526\pi$
$109$	4780.21			0.402341			0.201170	+	0.979556i	$0.435526\pi$
$110$		−	10865.1i		−	0.897946i
$111$		−	4699.22i		−	0.381399i
$112$	−14339.7	−	6267.31i	−1.14315	−	0.499626i
$113$	17585.2			1.37718			0.688590	−	0.725151i	$-0.258230\pi$
$113$	17585.2			1.37718			0.688590	+	0.725151i	$0.258230\pi$
$114$	−17802.6			−1.36985
$115$			3618.66i			0.273623i
$116$	−2387.34			−0.177418
$117$			33967.8i			2.48139i
$118$			4965.45i			0.356611i
$119$	4767.16	−	10907.3i	0.336640	−	0.770235i
$120$	−6898.37			−0.479053
$121$	26048.6			1.77915
$122$		−	32191.4i		−	2.16282i
$123$	−8431.10			−0.557281
$124$			2009.81i			0.130711i
$125$			1397.54i			0.0894427i
$126$	−28400.6	−	12412.8i	−1.78890	−	0.781860i
$127$	12120.0			0.751439			0.375720	−	0.926733i	$-0.377396\pi$
$127$	12120.0			0.751439			0.375720	+	0.926733i	$0.377396\pi$
$128$	18409.8			1.12364
$129$		−	22217.2i		−	1.33509i
$130$	−13935.0			−0.824559
$131$			30779.1i			1.79355i	0.442486	+	0.896776i	$0.354097\pi$
$131$			30779.1i			1.79355i	−0.442486	+	0.896776i	$0.645903\pi$
$132$			21191.3i			1.21621i
$133$	−4976.82	+	11387.0i	−0.281351	+	0.643734i
$134$	−19526.5			−1.08746
$135$	−8193.37			−0.449568
$136$			10287.3i			0.556190i
$137$	−25010.4			−1.33254			−0.666268	−	0.745712i	$-0.732109\pi$
$137$	−25010.4			−1.33254			−0.666268	+	0.745712i	$0.732109\pi$
$138$		−	22719.8i		−	1.19301i
$139$			5006.55i			0.259125i	0.991571	+	0.129562i	$0.0413573\pi$
$139$			5006.55i			0.259125i	−0.991571	+	0.129562i	$0.958643\pi$
$140$	1581.90	−	3619.40i	0.0807091	−	0.184663i
$141$	5674.18			0.285407
$142$	15469.4			0.767177
$143$		−	52186.2i		−	2.55202i
$144$	41932.9			2.02223
$145$			3701.89i			0.176071i
$146$			10785.2i			0.505967i
$147$	−25675.3	+	23761.8i	−1.18818	+	1.09963i
$148$	−2325.41			−0.106164
$149$	26261.1			1.18288			0.591439	−	0.806350i	$-0.298560\pi$
$149$	26261.1			1.18288			0.591439	+	0.806350i	$0.298560\pi$
$150$		−	8774.46i		−	0.389976i
$151$	14133.8			0.619876			0.309938	−	0.950757i	$-0.399692\pi$
$151$	14133.8			0.619876			0.309938	+	0.950757i	$0.399692\pi$
$152$		−	10739.7i		−	0.464843i
$153$			31895.8i			1.36255i
$154$	43633.2	+	19070.4i	1.83982	+	0.804114i
$155$	3116.48			0.129718
$156$	27178.8			1.11682
$157$			17409.6i			0.706300i	0.935567	+	0.353150i	$0.114889\pi$
$157$			17409.6i			0.706300i	−0.935567	+	0.353150i	$0.885111\pi$
$158$	−25220.0			−1.01025
$159$			15615.6i			0.617680i
$160$			9627.49i			0.376074i
$161$	−14532.1	−	6351.43i	−0.560632	−	0.245030i
$162$	205.847			0.00784360
$163$	−41569.3			−1.56458			−0.782290	−	0.622915i	$-0.785948\pi$
$163$	−41569.3			−1.56458			−0.782290	+	0.622915i	$0.785948\pi$
$164$			4172.13i			0.155121i
$165$	32860.0			1.20698
$166$			18306.7i			0.664344i
$167$			16314.1i			0.584967i	0.956271	+	0.292483i	$0.0944817\pi$
$167$			16314.1i			0.584967i	−0.956271	+	0.292483i	$0.905518\pi$
$168$	12107.9	−	27703.0i	0.428994	−	0.981542i
$169$	−38370.2			−1.34345
$170$	−13085.0			−0.452770
$171$		−	33298.6i		−	1.13877i
$172$	−10994.2			−0.371627
$173$			23077.3i			0.771069i	0.922693	+	0.385535i	$0.125983\pi$
$173$			23077.3i			0.771069i	−0.922693	+	0.385535i	$0.874017\pi$
$174$		−	23242.3i		−	0.767681i
$175$	−5612.37	−	2452.95i	−0.183261	−	0.0800963i
$176$	−64423.5			−2.07979
$177$	−15017.3			−0.479341
$178$			65972.9i			2.08222i
$179$	4029.02			0.125746			0.0628729	−	0.998022i	$-0.479974\pi$
$179$	4029.02			0.125746			0.0628729	+	0.998022i	$0.479974\pi$
$180$			10584.1i			0.326669i
$181$		−	4726.94i		−	0.144286i	−0.997394	−	0.0721428i	$-0.977016\pi$
$181$		−	4726.94i		−	0.144286i	0.997394	−	0.0721428i	$-0.0229837\pi$
$182$	24458.6	−	55961.5i	0.738396	−	1.68946i
$183$	97358.0			2.90716
$184$	13706.1			0.404835
$185$			3605.87i			0.105358i
$186$	−19566.8			−0.565580
$187$		−	49003.0i		−	1.40133i
$188$		−	2807.87i		−	0.0794440i
$189$	14380.9	−	32903.6i	0.402590	−	0.921128i
$190$	13660.5			0.378408
$191$	99.8028			0.00273575			0.00136787	−	0.999999i	$-0.499565\pi$
$191$	99.8028			0.00273575			0.00136787	+	0.999999i	$0.499565\pi$
$192$			14008.9i			0.380015i
$193$	−27603.3			−0.741047			−0.370524	−	0.928823i	$-0.620822\pi$
$193$	−27603.3			−0.741047			−0.370524	+	0.928823i	$0.620822\pi$
$194$		−	89403.8i		−	2.37549i
$195$		−	42144.5i		−	1.10834i
$196$	11758.5	+	12705.4i	0.306085	+	0.330733i
$197$	−17085.7			−0.440251			−0.220125	−	0.975472i	$-0.570647\pi$
$197$	−17085.7			−0.440251			−0.220125	+	0.975472i	$0.570647\pi$
$198$	−127595.			−3.25464
$199$		−	12618.2i		−	0.318634i	−0.987227	−	0.159317i	$-0.949071\pi$
$199$		−	12618.2i		−	0.318634i	0.987227	−	0.159317i	$-0.0509292\pi$
$200$	5293.34			0.132334
$201$		−	59055.0i		−	1.46172i
$202$			18706.6i			0.458450i
$203$	−14866.4	−	6497.52i	−0.360756	−	0.157672i
$204$	25521.0			0.613250
$205$	6469.46			0.153943
$206$		−	26743.3i		−	0.630203i
$207$	42495.8			0.991757
$208$			82626.0i			1.90981i
$209$			51158.2i			1.17118i
$210$	35237.2	+	15400.8i	0.799030	+	0.349225i
$211$	27000.1			0.606458			0.303229	−	0.952918i	$-0.401935\pi$
$211$	27000.1			0.606458			0.303229	+	0.952918i	$0.401935\pi$
$212$	7727.36			0.171933
$213$			46784.8i			1.03121i
$214$	−5819.34			−0.127071
$215$			17048.0i			0.368805i
$216$			31033.3i			0.665151i
$217$	−5470.01	+	12515.4i	−0.116163	+	0.265783i
$218$	23029.6			0.484588
$219$	−32618.2			−0.680099
$220$		−	16260.8i		−	0.335967i
$221$	−62848.6			−1.28680
$222$		−	22639.4i		−	0.459366i
$223$		−	63568.7i		−	1.27830i	−0.769081	−	0.639152i	$-0.779286\pi$
$223$		−	63568.7i		−	1.27830i	0.769081	−	0.639152i	$-0.220714\pi$
$224$	−38662.9	−	16898.0i	−0.770545	−	0.336775i
$225$	16412.0			0.324189
$226$	84720.2			1.65871
$227$			74171.9i			1.43942i	0.694275	+	0.719710i	$0.255725\pi$
$227$			74171.9i			1.43942i	−0.694275	+	0.719710i	$0.744275\pi$
$228$	−26643.4			−0.512531
$229$			79719.2i			1.52017i	0.649824	+	0.760084i	$0.274842\pi$
$229$			79719.2i			1.52017i	−0.649824	+	0.760084i	$0.725158\pi$
$230$			17433.6i			0.329558i
$231$	−57675.5	+	131962.i	−1.08085	+	2.47300i
$232$	14021.3			0.260503
$233$	34612.6			0.637562			0.318781	−	0.947828i	$-0.396727\pi$
$233$	34612.6			0.637562			0.318781	+	0.947828i	$0.396727\pi$
$234$			163646.i			2.98865i
$235$	−4353.98			−0.0788408
$236$			7431.30i			0.133426i
$237$		−	76274.1i		−	1.35794i
$238$	22966.7	−	52548.0i	0.405457	−	0.927689i
$239$	76161.8			1.33334			0.666671	−	0.745352i	$-0.267719\pi$
$239$	76161.8			1.33334			0.666671	+	0.745352i	$0.267719\pi$
$240$	−52027.0			−0.903246
$241$		−	57912.8i		−	0.997103i	−0.866860	−	0.498552i	$-0.833865\pi$
$241$		−	57912.8i		−	0.997103i	0.866860	−	0.498552i	$-0.166135\pi$
$242$	125494.			2.14285
$243$		−	58737.3i		−	0.994721i
$244$		−	48177.6i		−	0.809218i
$245$	19701.5	−	18233.2i	0.328222	−	0.303761i
$246$	−40618.4			−0.671202
$247$	65612.7			1.07546
$248$		−	11804.0i		−	0.191923i
$249$	−55365.8			−0.892982
$250$			6732.93i			0.107727i
$251$			36981.7i			0.587002i	0.955959	+	0.293501i	$0.0948203\pi$
$251$			36981.7i			0.587002i	−0.955959	+	0.293501i	$0.905180\pi$
$252$	−42504.4	−	18577.0i	−0.669318	−	0.292533i
$253$	−65288.2			−1.01998
$254$	58390.3			0.905051
$255$		−	39573.8i		−	0.608593i
$256$	73309.2			1.11861
$257$		−	75229.5i		−	1.13900i	−0.821993	−	0.569498i	$-0.807138\pi$
$257$		−	75229.5i		−	1.13900i	0.821993	−	0.569498i	$-0.192862\pi$
$258$		−	107036.i		−	1.60801i
$259$	−14480.7	−	6328.97i	−0.215869	−	0.0943482i
$260$	−20855.2			−0.308509
$261$	43473.2			0.638176
$262$			148284.i			2.16019i
$263$	−31641.9			−0.457458			−0.228729	−	0.973490i	$-0.573457\pi$
$263$	−31641.9			−0.457458			−0.228729	+	0.973490i	$0.573457\pi$
$264$		−	124461.i		−	1.78577i
$265$		−	11982.3i		−	0.170628i
$266$	−23976.8	+	54859.1i	−0.338866	+	0.775328i
$267$	−199525.			−2.79882
$268$	−29223.4			−0.406875
$269$		−	79641.8i		−	1.10062i	−0.834961	−	0.550309i	$-0.814510\pi$
$269$		−	79641.8i		−	1.10062i	0.834961	−	0.550309i	$-0.185490\pi$
$270$	−39473.2			−0.541470
$271$			40912.1i			0.557075i	0.960425	+	0.278537i	$0.0898496\pi$
$271$			40912.1i			0.557075i	−0.960425	+	0.278537i	$0.910150\pi$
$272$			77586.1i			1.04869i
$273$	169247.	+	73971.5i	2.27089	+	0.992519i
$274$	−120492.			−1.60494
$275$	−25214.6			−0.333416
$276$		−	34002.4i		−	0.446366i
$277$	−120604.			−1.57182			−0.785911	−	0.618340i	$-0.787806\pi$
$277$	−120604.			−1.57182			−0.785911	+	0.618340i	$0.787806\pi$
$278$			24120.0i			0.312096i
$279$		−	36598.4i		−	0.470169i
$280$	−9290.81	+	21257.4i	−0.118505	+	0.271141i
$281$	−48206.6			−0.610512			−0.305256	−	0.952270i	$-0.598742\pi$
$281$	−48206.6			−0.610512			−0.305256	+	0.952270i	$0.598742\pi$
$282$	27336.5			0.343751
$283$		−	45809.5i		−	0.571982i	−0.958232	−	0.285991i	$-0.907677\pi$
$283$		−	45809.5i		−	0.571982i	0.958232	−	0.285991i	$-0.0923228\pi$
$284$	23151.5			0.287040
$285$			41314.3i			0.508640i
$286$		−	251417.i		−	3.07371i
$287$	−11355.1	+	25980.6i	−0.137857	+	0.315417i
$288$	113060.			1.36309
$289$	24506.0			0.293411
$290$			17834.6i			0.212064i
$291$	270389.			3.19303
$292$			16141.1i			0.189308i
$293$			73600.8i			0.857328i	0.903464	+	0.428664i	$0.141016\pi$
$293$			73600.8i			0.857328i	−0.903464	+	0.428664i	$0.858984\pi$
$294$	−123696.	+	114477.i	−1.43107	+	1.32442i
$295$	11523.2			0.132413
$296$	13657.6			0.155880
$297$		−	147825.i		−	1.67585i
$298$	126518.			1.42468
$299$			83735.1i			0.936624i
$300$		−	13131.9i		−	0.145910i
$301$	−68462.9	−	29922.5i	−0.755652	−	0.330266i
$302$	68092.3			0.746594
$303$	−56575.3			−0.616228
$304$		−	80998.4i		−	0.876454i
$305$	−74706.0			−0.803074
$306$			153664.i			1.64108i
$307$		−	4729.94i		−	0.0501856i	−0.999685	−	0.0250928i	$-0.992012\pi$
$307$		−	4729.94i		−	0.0501856i	0.999685	−	0.0250928i	$-0.00798812\pi$
$308$	65301.4	+	28540.7i	0.688369	+	0.300859i
$309$	80881.2			0.847092
$310$	15014.3			0.156236
$311$		−	90455.7i		−	0.935223i	−0.883934	−	0.467611i	$-0.845115\pi$
$311$		−	90455.7i		−	0.935223i	0.883934	−	0.467611i	$-0.154885\pi$
$312$	−159627.			−1.63982
$313$		−	108219.i		−	1.10462i	−0.833638	−	0.552312i	$-0.813746\pi$
$313$		−	108219.i		−	1.10462i	0.833638	−	0.552312i	$-0.186254\pi$
$314$			83874.0i			0.850684i
$315$	−28806.2	+	65908.9i	−0.290312	+	0.664236i
$316$	−37744.2			−0.377987
$317$	117203.			1.16633			0.583163	−	0.812356i	$-0.301815\pi$
$317$	117203.			1.16633			0.583163	+	0.812356i	$0.301815\pi$
$318$			75231.0i			0.743948i
$319$	−66789.9			−0.656340
$320$		−	10749.5i		−	0.104975i
$321$		−	17599.7i		−	0.170803i
$322$	−70011.4	−	30599.3i	−0.675238	−	0.295120i
$323$	61610.5			0.590541
$324$	308.071			0.00293468
$325$			32338.8i			0.306167i
$326$	−200268.			−1.88442
$327$			69649.5i			0.651362i
$328$		−	24503.8i		−	0.227764i
$329$	7642.06	−	17485.1i	0.0706022	−	0.161538i
$330$	158309.			1.45371
$331$	−59340.4			−0.541619			−0.270810	−	0.962633i	$-0.587291\pi$
$331$	−59340.4			−0.541619			−0.270810	+	0.962633i	$0.587291\pi$
$332$			27397.8i			0.248564i
$333$	42345.5			0.381873
$334$			78596.5i			0.704548i
$335$			45314.8i			0.403785i
$336$	91317.1	−	208934.i	0.808861	−	1.85068i
$337$	157384.			1.38580			0.692902	−	0.721032i	$-0.256332\pi$
$337$	157384.			1.38580			0.692902	+	0.721032i	$0.256332\pi$
$338$	−184856.			−1.61808
$339$			256223.i			2.22956i
$340$	−19583.1			−0.169404
$341$			56227.8i			0.483551i
$342$		−	160423.i		−	1.37156i
$343$	38642.7	+	111122.i	0.328457	+	0.944519i
$344$	64571.2			0.545660
$345$	−52725.4			−0.442977
$346$			111180.i			0.928694i
$347$	165575.			1.37510			0.687551	−	0.726136i	$-0.258686\pi$
$347$	165575.			1.37510			0.687551	+	0.726136i	$0.258686\pi$
$348$		−	34784.5i		−	0.287228i
$349$		−	187470.i		−	1.53915i	−0.638558	−	0.769574i	$-0.720469\pi$
$349$		−	187470.i		−	1.53915i	0.638558	−	0.769574i	$-0.279531\pi$
$350$	−27038.7	−	11817.6i	−0.220724	−	0.0964698i
$351$	−189593.			−1.53889
$352$	−173700.			−1.40189
$353$		−	132192.i		−	1.06085i	−0.847731	−	0.530426i	$-0.822032\pi$
$353$		−	132192.i		−	1.06085i	0.847731	−	0.530426i	$-0.177968\pi$
$354$	−72348.6			−0.577329
$355$		−	35899.5i		−	0.284860i
$356$			98735.1i			0.779061i
$357$	158924.	+	69459.4i	1.24696	+	0.544998i
$358$	19410.6			0.151451
$359$	−216123.			−1.67692			−0.838459	−	0.544965i	$-0.816543\pi$
$359$	−216123.			−1.67692			−0.838459	+	0.544965i	$0.816543\pi$
$360$		−	62162.4i		−	0.479648i
$361$	66000.8			0.506448
$362$		−	22772.9i		−	0.173781i
$363$			379538.i			2.88033i
$364$	36604.8	−	83752.1i	0.276271	−	0.632110i
$365$	25029.0			0.187870
$366$	469041.			3.50145
$367$			36676.9i			0.272308i	0.990688	+	0.136154i	$0.0434742\pi$
$367$			36676.9i			0.272308i	−0.990688	+	0.136154i	$0.956526\pi$
$368$	103370.			0.763309
$369$		−	75974.1i		−	0.557973i
$370$			17372.0i			0.126895i
$371$	48119.6	+	21031.2i	0.349602	+	0.152798i
$372$	−29283.7			−0.211612
$373$	−250019.			−1.79703			−0.898517	−	0.438940i	$-0.855354\pi$
$373$	−250019.			−1.79703			−0.898517	+	0.438940i	$0.855354\pi$
$374$		−	236081.i		−	1.68779i
$375$	−20362.7			−0.144802
$376$			16491.2i			0.116648i
$377$			85661.1i			0.602699i
$378$	69282.8	−	158520.i	0.484888	−	1.10943i
$379$	159502.			1.11042			0.555211	−	0.831710i	$-0.312638\pi$
$379$	159502.			1.11042			0.555211	+	0.831710i	$0.312638\pi$
$380$	20444.4			0.141582
$381$			176593.i			1.21653i
$382$	480.819			0.00329500
$383$		−	237902.i		−	1.62181i	−0.585178	−	0.810905i	$-0.698975\pi$
$383$		−	237902.i		−	1.62181i	0.585178	−	0.810905i	$-0.301025\pi$
$384$			268238.i			1.81910i
$385$	44256.3	−	101259.i	0.298575	−	0.683142i
$386$	−132984.			−0.892534
$387$	200203.			1.33675
$388$		−	133802.i		−	0.888789i
$389$	−487.890			−0.00322420			−0.00161210	−	0.999999i	$-0.500513\pi$
$389$	−487.890			−0.00322420			−0.00161210	+	0.999999i	$0.500513\pi$
$390$		−	203039.i		−	1.33491i
$391$			78627.5i			0.514305i
$392$	−69060.3	−	74621.6i	−0.449424	−	0.485615i
$393$	−448464.			−2.90364
$394$	−82313.6			−0.530248
$395$			58527.6i			0.375117i
$396$	−190959.			−1.21772
$397$			213503.i			1.35464i	0.735689	+	0.677319i	$0.236858\pi$
$397$			213503.i			1.35464i	−0.735689	+	0.677319i	$0.763142\pi$
$398$		−	60790.7i		−	0.383770i
$399$	−165913.	−	72514.3i	−1.04216	−	0.455489i
$400$	39922.0			0.249513
$401$	−195733.			−1.21724			−0.608619	−	0.793463i	$-0.708276\pi$
$401$	−195733.			−1.21724			−0.608619	+	0.793463i	$0.708276\pi$
$402$		−	284509.i		−	1.76053i
$403$	72114.8			0.444032
$404$			27996.3i			0.171529i
$405$		−	477.707i		−	0.00291240i
$406$	−71621.6	−	31303.0i	−0.434502	−	0.189904i
$407$	−65057.3			−0.392742
$408$	−149890.			−0.900434
$409$		−	61109.4i		−	0.365310i	−0.983177	−	0.182655i	$-0.941531\pi$
$409$		−	61109.4i		−	0.365310i	0.983177	−	0.182655i	$-0.0584692\pi$
$410$	31167.9			0.185413
$411$		−	364411.i		−	2.15729i
$412$		−	40024.1i		−	0.235791i
$413$	−20225.5	+	46276.0i	−0.118576	+	0.271304i
$414$	204732.			1.19450
$415$	42484.0			0.246677
$416$			222778.i			1.28732i
$417$	−72947.4			−0.419506
$418$			246464.i			1.41059i
$419$		−	131493.i		−	0.748988i	−0.927229	−	0.374494i	$-0.877816\pi$
$419$		−	131493.i		−	0.748988i	0.927229	−	0.374494i	$-0.122184\pi$
$420$	52736.0	+	23048.9i	0.298957	+	0.130663i
$421$	−35202.6			−0.198615			−0.0993073	−	0.995057i	$-0.531663\pi$
$421$	−35202.6			−0.198615			−0.0993073	+	0.995057i	$0.531663\pi$
$422$	130078.			0.730432
$423$			51131.0i			0.285761i
$424$	−45384.4			−0.252449
$425$			30366.3i			0.168118i
$426$			225395.i			1.24201i
$427$	131123.	−	300010.i	0.719156	−	1.64543i
$428$	−8709.23			−0.0475436
$429$	760374.			4.13155
$430$			82132.1i			0.444198i
$431$	285348.			1.53610			0.768052	−	0.640388i	$-0.221226\pi$
$431$	285348.			1.53610			0.768052	+	0.640388i	$0.221226\pi$
$432$			234051.i			1.25413i
$433$		−	255078.i		−	1.36050i	−0.732982	−	0.680248i	$-0.761872\pi$
$433$		−	255078.i		−	1.36050i	0.732982	−	0.680248i	$-0.238128\pi$
$434$	−26352.8	+	60295.5i	−0.139910	+	0.320115i
$435$	−53938.1			−0.285047
$436$	34466.1			0.181309
$437$		−	82085.6i		−	0.429837i
$438$	−157145.			−0.819127
$439$			190309.i			0.987482i	0.869609	+	0.493741i	$0.164371\pi$
$439$			190309.i			0.987482i	−0.869609	+	0.493741i	$0.835629\pi$
$440$			95502.9i			0.493300i
$441$	−214122.	−	231365.i	−1.10099	−	1.18965i
$442$	−302785.			−1.54985
$443$	119088.			0.606822			0.303411	−	0.952860i	$-0.401875\pi$
$443$	119088.			0.606822			0.303411	+	0.952860i	$0.401875\pi$
$444$		−	33882.1i		−	0.171872i
$445$	153102.			0.773146
$446$		−	306255.i		−	1.53962i
$447$			382634.i			1.91500i
$448$	43168.7	+	18867.4i	0.215086	+	0.0940059i
$449$	170376.			0.845114			0.422557	−	0.906336i	$-0.361133\pi$
$449$	170376.			0.845114			0.422557	+	0.906336i	$0.361133\pi$
$450$	79068.2			0.390460
$451$			116722.i			0.573854i
$452$	126792.			0.620606
$453$			205935.i			1.00354i
$454$			357337.i			1.73367i
$455$	−129869.	−	56760.7i	−0.627311	−	0.274173i
$456$	156482.			0.752550
$457$	−341751.			−1.63635			−0.818176	−	0.574967i	$-0.805015\pi$
$457$	−341751.			−1.63635			−0.818176	+	0.574967i	$0.805015\pi$
$458$			384062.i			1.83093i
$459$	−178028.			−0.845013
$460$			26091.2i			0.123304i
$461$			220317.i			1.03668i	0.855174	+	0.518342i	$0.173450\pi$
$461$			220317.i			1.03668i	−0.855174	+	0.518342i	$0.826550\pi$
$462$	−277863.	+	635752.i	−1.30181	+	2.97854i
$463$	334907.			1.56229			0.781145	−	0.624349i	$-0.214636\pi$
$463$	334907.			1.56229			0.781145	+	0.624349i	$0.214636\pi$
$464$	105748.			0.491174
$465$			45408.4i			0.210005i
$466$	166753.			0.767895
$467$		−	331727.i		−	1.52106i	−0.649302	−	0.760531i	$-0.724939\pi$
$467$		−	331727.i		−	1.52106i	0.649302	−	0.760531i	$-0.275061\pi$
$468$			244913.i			1.11820i
$469$	−181979.	−	79536.0i	−0.827324	−	0.361591i
$470$	−20976.2			−0.0949577
$471$	−253665.			−1.14345
$472$		−	43645.5i		−	0.195910i
$473$	−307582.			−1.37480
$474$		−	367465.i		−	1.63553i
$475$		−	31701.8i		−	0.140507i
$476$	34372.0	−	78643.4i	0.151702	−	0.347095i
$477$	−140715.			−0.618447
$478$	366924.			1.60591
$479$		−	339790.i		−	1.48095i	−0.672085	−	0.740474i	$-0.734601\pi$
$479$		−	339790.i		−	1.48095i	0.672085	−	0.740474i	$-0.265399\pi$
$480$	−140276.			−0.608838
$481$			83439.0i			0.360644i
$482$		−	279006.i		−	1.20093i
$483$	92542.9	−	211739.i	0.396688	−	0.907625i
$484$	187814.			0.801748
$485$	−207478.			−0.882041
$486$		−	282978.i		−	1.19807i
$487$	74140.1			0.312605			0.156302	−	0.987709i	$-0.450043\pi$
$487$	74140.1			0.312605			0.156302	+	0.987709i	$0.450043\pi$
$488$			282957.i			1.18818i
$489$		−	605681.i		−	2.53295i
$490$	94915.8	−	87842.1i	0.395318	−	0.365856i
$491$	−1259.76			−0.00522547			−0.00261273	−	0.999997i	$-0.500832\pi$
$491$	−1259.76			−0.00522547			−0.00261273	+	0.999997i	$0.500832\pi$
$492$	−60789.6			−0.251130
$493$			80436.0i			0.330945i
$494$	316102.			1.29531
$495$			296107.i			1.20848i
$496$		−	89025.1i		−	0.361867i
$497$	144168.	+	63010.4i	0.583656	+	0.255093i
$498$	−266735.			−1.07553
$499$	−77913.9			−0.312906			−0.156453	−	0.987685i	$-0.550006\pi$
$499$	−77913.9			−0.312906			−0.156453	+	0.987685i	$0.550006\pi$
$500$			10076.5i			0.0403060i
$501$	−237703.			−0.947022
$502$			178166.i			0.706998i
$503$		−	221665.i		−	0.876116i	−0.898947	−	0.438058i	$-0.855666\pi$
$503$		−	221665.i		−	0.876116i	0.898947	−	0.438058i	$-0.144334\pi$
$504$	249637.	+	109107.i	0.982760	+	0.429527i
$505$	43412.1			0.170227
$506$	−314539.			−1.22849
$507$		−	559069.i		−	2.17495i
$508$	87386.9			0.338625
$509$			339130.i			1.30897i	0.756074	+	0.654486i	$0.227115\pi$
$509$			339130.i			1.30897i	−0.756074	+	0.654486i	$0.772885\pi$
$510$		−	190654.i		−	0.733004i
$511$	−43930.6	+	100514.i	−0.168239	+	0.384931i
$512$	58624.9			0.223636
$513$	185858.			0.706231
$514$		−	362433.i		−	1.37183i
$515$	−62062.8			−0.234000
$516$		−	160190.i		−	0.601639i
$517$		−	78554.9i		−	0.293895i
$518$	−69763.7	−	30491.0i	−0.259998	−	0.113635i
$519$	−336246.			−1.24831
$520$	122487.			0.452984
$521$			342794.i			1.26287i	0.775430	+	0.631433i	$0.217533\pi$
$521$			342794.i			1.26287i	−0.775430	+	0.631433i	$0.782467\pi$
$522$	209441.			0.768634
$523$			174970.i			0.639676i	0.947472	+	0.319838i	$0.103628\pi$
$523$			174970.i			0.639676i	−0.947472	+	0.319838i	$0.896372\pi$
$524$			221923.i			0.808237i
$525$	35740.4	−	81774.4i	0.129670	−	0.296687i
$526$	−152441.			−0.550973
$527$	67716.0			0.243820
$528$		−	938675.i		−	3.36703i
$529$	−175083.			−0.625652
$530$		−	57727.2i		−	0.205508i
$531$		−	135323.i		−	0.479936i
$532$	−35883.7	+	82102.2i	−0.126787	+	0.290089i
$533$	149702.			0.526954
$534$	−961251.			−3.37097
$535$			13504.8i			0.0471826i
$536$	171635.			0.597414
$537$			58704.4i			0.203574i
$538$		−	383690.i		−	1.32561i
$539$	328965.	+	355456.i	1.13233	+	1.22351i
$540$	−59075.6			−0.202591
$541$	316083.			1.07996			0.539978	−	0.841679i	$-0.318433\pi$
$541$	316083.			1.07996			0.539978	+	0.841679i	$0.318433\pi$
$542$			197102.i			0.670954i
$543$	68873.4			0.233589
$544$			209189.i			0.706873i
$545$		−	53444.4i		−	0.179932i
$546$	815382.	+	356372.i	2.73511	+	1.19541i
$547$	94365.5			0.315383			0.157692	−	0.987488i	$-0.449595\pi$
$547$	94365.5			0.315383			0.157692	+	0.987488i	$0.449595\pi$
$548$	−180329.			−0.600488
$549$			877310.i			2.91077i
$550$	−121476.			−0.401574
$551$		−	83973.6i		−	0.276592i
$552$			199703.i			0.655400i
$553$	−235040.	−	102727.i	−0.768584	−	0.335918i
$554$	−581035.			−1.89314
$555$	−52538.9			−0.170567
$556$			36098.1i			0.116771i
$557$	−135243.			−0.435916			−0.217958	−	0.975958i	$-0.569940\pi$
$557$	−135243.			−0.435916			−0.217958	+	0.975958i	$0.569940\pi$
$558$		−	176320.i		−	0.566283i
$559$			394488.i			1.26244i
$560$	−70070.6	+	160322.i	−0.223439	+	0.511231i
$561$	713993.			2.26865
$562$	−232245.			−0.735315
$563$			243317.i			0.767637i	0.923408	+	0.383819i	$0.125391\pi$
$563$			243317.i			0.767637i	−0.923408	+	0.383819i	$0.874609\pi$
$564$	40911.8			0.128614
$565$		−	196609.i		−	0.615894i
$566$		−	220696.i		−	0.688909i
$567$	1918.41	+	838.465i	0.00596728	+	0.00260807i
$568$	−135973.			−0.421460
$569$	139613.			0.431222			0.215611	−	0.976479i	$-0.430826\pi$
$569$	139613.			0.431222			0.215611	+	0.976479i	$0.430826\pi$
$570$			199039.i			0.612617i
$571$	−548346.			−1.68183			−0.840915	−	0.541167i	$-0.817983\pi$
$571$	−548346.			−1.68183			−0.840915	+	0.541167i	$0.817983\pi$
$572$		−	376271.i		−	1.15003i
$573$			1454.17i			0.00442899i
$574$	−54705.4	+	125166.i	−0.166038	+	0.379896i
$575$	40457.9			0.122368
$576$	−126237.			−0.380487
$577$			445087.i			1.33688i	0.743764	+	0.668442i	$0.233038\pi$
$577$			445087.i			1.33688i	−0.743764	+	0.668442i	$0.766962\pi$
$578$	118062.			0.353391
$579$		−	402190.i		−	1.19971i
$580$			26691.3i			0.0793438i
$581$	−74567.3	+	170611.i	−0.220900	+	0.505422i
$582$	1.30265e6			3.84575
$583$	216186.			0.636049
$584$		−	94800.1i		−	0.277961i
$585$	379771.			1.10971
$586$			354586.i			1.03259i
$587$		−	143426.i		−	0.416248i	−0.978102	−	0.208124i	$-0.933264\pi$
$587$		−	143426.i		−	0.416248i	0.978102	−	0.208124i	$-0.0667358\pi$
$588$	−185123.	+	171327.i	−0.535434	+	0.495530i
$589$	−70694.2			−0.203776
$590$	55515.4			0.159481
$591$		−	248945.i		−	0.712736i
$592$	103005.			0.293909
$593$		−	299727.i		−	0.852347i	−0.904642	−	0.426173i	$-0.859861\pi$
$593$		−	299727.i		−	0.852347i	0.904642	−	0.426173i	$-0.140139\pi$
$594$		−	712178.i		−	2.01844i
$595$	−121947.	−	53298.5i	−0.344460	−	0.150550i
$596$	189346.			0.533046
$597$	183852.			0.515847
$598$			403410.i			1.12809i
$599$	−439671.			−1.22539			−0.612694	−	0.790320i	$-0.709914\pi$
$599$	−439671.			−1.22539			−0.612694	+	0.790320i	$0.709914\pi$
$600$			77126.1i			0.214239i
$601$			188484.i			0.521827i	0.965362	+	0.260913i	$0.0840237\pi$
$601$			188484.i			0.521827i	−0.965362	+	0.260913i	$0.915976\pi$
$602$	−329833.	−	144157.i	−0.910125	−	0.397781i
$603$	532155.			1.46354
$604$	101907.			0.279338
$605$		−	291232.i		−	0.795661i
$606$	−272562.			−0.742200
$607$			10230.2i			0.0277656i	0.999904	+	0.0138828i	$0.00441917\pi$
$607$			10230.2i			0.0277656i	−0.999904	+	0.0138828i	$0.995581\pi$
$608$		−	218389.i		−	0.590778i
$609$	94671.4	−	216609.i	0.255261	−	0.584039i
$610$	−359910.			−0.967241
$611$	−100750.			−0.269876
$612$			229974.i			0.614011i
$613$	436819.			1.16247			0.581233	−	0.813737i	$-0.302571\pi$
$613$	436819.			1.16247			0.581233	+	0.813737i	$0.302571\pi$
$614$		−	22787.4i		−	0.0604447i
$615$			94262.5i			0.249223i
$616$	−383528.	−	167625.i	−1.01073	−	0.441752i
$617$	26556.4			0.0697588			0.0348794	−	0.999392i	$-0.488895\pi$
$617$	26556.4			0.0697588			0.0348794	+	0.999392i	$0.488895\pi$
$618$	389661.			1.02026
$619$			510737.i			1.33296i	0.745525	+	0.666478i	$0.232199\pi$
$619$			510737.i			1.33296i	−0.745525	+	0.666478i	$0.767801\pi$
$620$	22470.4			0.0584557
$621$			237193.i			0.615061i
$622$		−	435788.i		−	1.12640i
$623$	−268723.	+	614841.i	−0.692355	+	1.58411i
$624$	−1.20389e6			−3.09185
$625$	15625.0			0.0400000
$626$		−	521365.i		−	1.33043i
$627$	−745395.			−1.89606
$628$			125526.i			0.318284i
$629$			78349.4i			0.198032i
$630$	−138779.	+	317529.i	−0.349659	+	0.800022i
$631$	−3641.38			−0.00914550			−0.00457275	−	0.999990i	$-0.501456\pi$
$631$	−3641.38			−0.00914550			−0.00457275	+	0.999990i	$0.501456\pi$
$632$	221680.			0.554998
$633$			393403.i			0.981815i
$634$	564647.			1.40475
$635$		−	135505.i		−	0.336054i
$636$			112591.i			0.278348i
$637$	455889.	−	421913.i	1.12352	−	1.03979i
$638$	−321773.			−0.790512
$639$	−421586.			−1.03249
$640$		−	205827.i		−	0.502508i
$641$	330651.			0.804736			0.402368	−	0.915478i	$-0.368187\pi$
$641$	330651.			0.804736			0.402368	+	0.915478i	$0.368187\pi$
$642$		−	84790.0i		−	0.205719i
$643$			75104.8i			0.181654i	0.995867	+	0.0908272i	$0.0289511\pi$
$643$			75104.8i			0.181654i	−0.995867	+	0.0908272i	$0.971049\pi$
$644$	−104779.	−	45794.9i	−0.252640	−	0.110419i
$645$	−248396.			−0.597071
$646$	296821.			0.711261
$647$			381648.i			0.911706i	0.890055	+	0.455853i	$0.150666\pi$
$647$			381648.i			0.911706i	−0.890055	+	0.455853i	$0.849334\pi$
$648$	−1809.37			−0.00430900
$649$			207903.i			0.493596i
$650$			155799.i			0.368754i
$651$	−182355.	−	79700.3i	−0.430284	−	0.188061i
$652$	−299722.			−0.705055
$653$	462477.			1.08458			0.542292	−	0.840190i	$-0.317557\pi$
$653$	462477.			1.08458			0.542292	+	0.840190i	$0.317557\pi$
$654$			335550.i			0.784516i
$655$	344121.			0.802100
$656$		−	184806.i		−	0.429445i
$657$		−	293929.i		−	0.680943i
$658$	36817.1	−	84237.8i	0.0850350	−	0.194561i
$659$	−187187.			−0.431028			−0.215514	−	0.976501i	$-0.569143\pi$
$659$	−187187.			−0.431028			−0.215514	+	0.976501i	$0.569143\pi$
$660$	236926.			0.543907
$661$		−	95871.7i		−	0.219426i	−0.993963	−	0.109713i	$-0.965007\pi$
$661$		−	95871.7i		−	0.219426i	0.993963	−	0.109713i	$-0.0349931\pi$
$662$	−285884.			−0.652339
$663$		−	915729.i		−	2.08324i
$664$		−	160913.i		−	0.364967i
$665$	127311.	+	55642.6i	0.287887	+	0.125824i
$666$	204008.			0.459936
$667$	107167.			0.240885
$668$			117628.i			0.263607i
$669$	926221.			2.06949
$670$			218313.i			0.486328i
$671$		−	1.34785e6i		−	2.99362i
$672$	246211.	−	563333.i	0.545217	−	1.24746i
$673$	−118770.			−0.262226			−0.131113	−	0.991367i	$-0.541855\pi$
$673$	−118770.			−0.262226			−0.131113	+	0.991367i	$0.541855\pi$
$674$	758230.			1.66909
$675$			91604.7i			0.201053i
$676$	−276656.			−0.605405
$677$			340700.i			0.743352i	0.928363	+	0.371676i	$0.121217\pi$
$677$			340700.i			0.743352i	−0.928363	+	0.371676i	$0.878783\pi$
$678$			1.23441e6i			2.68534i
$679$	364163.	−	833208.i	0.789871	−	1.80723i
$680$	115015.			0.248736
$681$	−1.08071e6			−2.33032
$682$			270888.i			0.582401i
$683$	−148626.			−0.318605			−0.159303	−	0.987230i	$-0.550925\pi$
$683$	−148626.			−0.318605			−0.159303	+	0.987230i	$0.550925\pi$
$684$		−	240089.i		−	0.513168i
$685$			279624.i			0.595928i
$686$	186168.	+	535350.i	0.395601	+	1.13760i
$687$	−1.16154e6			−2.46105
$688$	486992.			1.02883
$689$		−	277269.i		−	0.584066i
$690$	−254015.			−0.533532
$691$			68328.5i			0.143102i	0.997437	+	0.0715510i	$0.0227949\pi$
$691$			68328.5i			0.143102i	−0.997437	+	0.0715510i	$0.977205\pi$
$692$			166391.i			0.347471i
$693$	−1.18913e6	−	519724.i	−2.47607	−	1.08220i
$694$	797688.			1.65620
$695$	55974.9			0.115884
$696$			204296.i			0.421737i
$697$	140570.			0.289353
$698$		−	903171.i		−	1.85378i
$699$			504319.i			1.03217i
$700$	−40466.1	−	17686.2i	−0.0825838	−	0.0360942i
$701$	−8208.96			−0.0167052			−0.00835261	−	0.999965i	$-0.502659\pi$
$701$	−8208.96			−0.0167052			−0.00835261	+	0.999965i	$0.502659\pi$
$702$	−913401.			−1.85348
$703$		−	81795.3i		−	0.165507i
$704$	193943.			0.391317
$705$		−	63439.2i		−	0.127638i
$706$		−	636859.i		−	1.27772i
$707$	−76196.3	+	174338.i	−0.152439	+	0.348781i
$708$	−108277.			−0.216008
$709$	−678427.			−1.34962			−0.674808	−	0.737993i	$-0.735774\pi$
$709$	−678427.			−1.34962			−0.674808	+	0.737993i	$0.735774\pi$
$710$		−	172953.i		−	0.343092i
$711$	687319.			1.35962
$712$		−	579891.i		−	1.14390i
$713$		−	90220.1i		−	0.177470i
$714$	765645.	+	334634.i	1.50187	+	0.656408i
$715$	−583460.			−1.14130
$716$	29049.9			0.0566655
$717$			1.10971e6i			2.15859i
$718$	−1.04121e6			−2.01972
$719$		−	589061.i		−	1.13947i	−0.821829	−	0.569735i	$-0.807046\pi$
$719$		−	589061.i		−	1.13947i	0.821829	−	0.569735i	$-0.192954\pi$
$720$		−	468824.i		−	0.904368i
$721$	108932.	−	249237.i	0.209548	−	0.479448i
$722$	317972.			0.609978
$723$	843812.			1.61424
$724$		−	34082.0i		−	0.0650201i
$725$	41388.4			0.0787414
$726$			1.82850e6i			3.46913i
$727$			705964.i			1.33571i	0.744289	+	0.667857i	$0.232788\pi$
$727$			705964.i			1.33571i	−0.744289	+	0.667857i	$0.767212\pi$
$728$	−214987.	+	491893.i	−0.405649	+	0.928128i
$729$	859286.			1.61690
$730$	120582.			0.226275
$731$			370425.i			0.693211i
$732$	701967.			1.31007
$733$			318582.i			0.592944i	0.955042	+	0.296472i	$0.0958101\pi$
$733$			318582.i			0.592944i	−0.955042	+	0.296472i	$0.904190\pi$
$734$			176698.i			0.327974i
$735$	265665.	+	287059.i	0.491768	+	0.531369i
$736$	278709.			0.514512
$737$	−817573.			−1.50519
$738$		−	366020.i		−	0.672035i
$739$	−547274.			−1.00211			−0.501055	−	0.865415i	$-0.667055\pi$
$739$	−547274.			−1.00211			−0.501055	+	0.865415i	$0.667055\pi$
$740$			25998.9i			0.0474779i
$741$			956003.i			1.74110i
$742$	231826.	+	101322.i	0.421069	+	0.184033i
$743$	233435.			0.422851			0.211426	−	0.977394i	$-0.432189\pi$
$743$	233435.			0.422851			0.211426	+	0.977394i	$0.432189\pi$
$744$	171989.			0.310710
$745$		−	293608.i		−	0.528999i
$746$	−1.20452e6			−2.16439
$747$		−	498910.i		−	0.894090i
$748$		−	353320.i		−	0.631487i
$749$	−54233.9	−	23703.5i	−0.0966734	−	0.0422522i
$750$	−98101.4			−0.174403
$751$	495140.			0.877906			0.438953	−	0.898510i	$-0.355349\pi$
$751$	495140.			0.877906			0.438953	+	0.898510i	$0.355349\pi$
$752$			124375.i			0.219937i
$753$	−538838.			−0.950316
$754$			412689.i			0.725905i
$755$		−	158021.i		−	0.277217i
$756$	103689.	−	237241.i	0.181421	−	0.415093i
$757$	124849.			0.217868			0.108934	−	0.994049i	$-0.465256\pi$
$757$	124849.			0.217868			0.108934	+	0.994049i	$0.465256\pi$
$758$	768432.			1.33742
$759$		−	951275.i		−	1.65129i
$760$	−120074.			−0.207884
$761$			892015.i			1.54029i	0.637868	+	0.770146i	$0.279817\pi$
$761$			892015.i			1.54029i	−0.637868	+	0.770146i	$0.720183\pi$
$762$			850769.i			1.46522i
$763$	214626.	+	93804.9i	0.368667	+	0.161130i
$764$	719.595			0.00123282
$765$	356606.			0.609349
$766$		−	1.14614e6i		−	1.95335i
$767$	266645.			0.453256
$768$			1.06814e6i			1.81095i
$769$		−	105869.i		−	0.179026i	−0.995986	−	0.0895132i	$-0.971469\pi$
$769$		−	105869.i		−	0.179026i	0.995986	−	0.0895132i	$-0.0285311\pi$
$770$	213213.	−	487834.i	0.359611	−	0.822792i
$771$	1.09612e6			1.84396
$772$	−199024.			−0.333942
$773$		−	255665.i		−	0.427870i	−0.976848	−	0.213935i	$-0.931372\pi$
$773$		−	255665.i		−	0.427870i	0.976848	−	0.213935i	$-0.0686281\pi$
$774$	964519.			1.61001
$775$		−	34843.4i		−	0.0580118i
$776$			785845.i			1.30501i
$777$	92215.6	−	210990.i	0.152743	−	0.349478i
$778$	−2350.50			−0.00388331
$779$	−146753.			−0.241831
$780$		−	303869.i		−	0.499455i
$781$	647702.			1.06187
$782$			378803.i			0.619441i
$783$			242648.i			0.395779i
$784$	−520848.	−	562791.i	−0.847381	−	0.915619i
$785$	194645.			0.315867
$786$	−2.16056e6			−3.49721
$787$		−	754940.i		−	1.21889i	−0.792830	−	0.609443i	$-0.791393\pi$
$787$		−	754940.i		−	1.21889i	0.792830	−	0.609443i	$-0.208607\pi$
$788$	−123191.			−0.198392
$789$		−	461035.i		−	0.740594i
$790$			281968.i			0.451799i
$791$	789557.	+	345085.i	1.26192	+	0.551535i
$792$	1.12154e6			1.78798
$793$	−1.72868e6			−2.74896
$794$			1.02859e6i			1.63156i
$795$	174587.			0.276235
$796$		−	90979.5i		−	0.143588i
$797$		−	360915.i		−	0.568183i	−0.958797	−	0.284091i	$-0.908308\pi$
$797$		−	360915.i		−	0.568183i	0.958797	−	0.284091i	$-0.0916919\pi$
$798$	−799319.	−	349351.i	−1.25520	−	0.548601i
$799$	−94604.8			−0.148190
$800$	107639.			0.168185
$801$		−	1.79796e6i		−	2.80230i
$802$	−942981.			−1.46607
$803$			451576.i			0.700325i
$804$		−	425796.i		−	0.658703i
$805$	−71011.2	+	162474.i	−0.109581	+	0.250722i
$806$	347427.			0.534802
$807$	1.16041e6			1.78183
$808$		−	164428.i		−	0.251856i
$809$	52604.1			0.0803754			0.0401877	−	0.999192i	$-0.487204\pi$
$809$	52604.1			0.0803754			0.0401877	+	0.999192i	$0.487204\pi$
$810$		−	2301.44i		−	0.00350776i
$811$			284790.i			0.432996i	0.976283	+	0.216498i	$0.0694634\pi$
$811$			284790.i			0.432996i	−0.976283	+	0.216498i	$0.930537\pi$
$812$	−107189.	−	46848.2i	−0.162569	−	0.0710527i
$813$	−596106.			−0.901867
$814$	−313426.			−0.473027
$815$			464759.i			0.699701i
$816$	−1.13046e6			−1.69775
$817$		−	386716.i		−	0.579360i
$818$		−	294407.i		−	0.439988i
$819$	−666570.	+	1.52512e6i	−0.993751	+	2.27371i
$820$	46645.8			0.0693722
$821$	−459269.			−0.681366			−0.340683	−	0.940178i	$-0.610658\pi$
$821$	−459269.			−0.681366			−0.340683	+	0.940178i	$0.610658\pi$
$822$		−	1.75562e6i		−	2.59829i
$823$	−750048.			−1.10736			−0.553680	−	0.832729i	$-0.686777\pi$
$823$	−750048.			−1.10736			−0.553680	+	0.832729i	$0.686777\pi$
$824$			235069.i			0.346212i
$825$		−	367386.i		−	0.539778i
$826$	−97440.0	+	222944.i	−0.142816	+	0.326764i
$827$	−892076.			−1.30434			−0.652170	−	0.758072i	$-0.726141\pi$
$827$	−892076.			−1.30434			−0.652170	+	0.758072i	$0.726141\pi$
$828$	306402.			0.446921
$829$		−	965908.i		−	1.40549i	−0.711443	−	0.702743i	$-0.751958\pi$
$829$		−	965908.i		−	1.40549i	0.711443	−	0.702743i	$-0.248042\pi$
$830$	204675.			0.297104
$831$		−	1.75725e6i		−	2.54467i
$832$		−	248741.i		−	0.359336i
$833$	428081.	−	396177.i	0.616930	−	0.570952i
$834$	−351438.			−0.505262
$835$	182398.			0.261605
$836$			368859.i			0.527774i
$837$	204276.			0.291586
$838$		−	633493.i		−	0.902098i
$839$			1.19914e6i			1.70351i	0.523938	+	0.851757i	$0.324463\pi$
$839$			1.19914e6i			1.70351i	−0.523938	+	0.851757i	$0.675537\pi$
$840$	−309729.	−	135371.i	−0.438959	−	0.191852i
$841$	−597649.			−0.844995
$842$	−169595.			−0.239216
$843$		−	702389.i		−	0.988377i
$844$	194675.			0.273291
$845$			428992.i			0.600809i
$846$			246334.i			0.344178i
$847$	1.16955e6	+	511166.i	1.63025	+	0.712517i
$848$	−342286.			−0.475989
$849$	667462.			0.926000
$850$			146295.i			0.202485i
$851$	104387.			0.144141
$852$			337326.i			0.464698i
$853$			517748.i			0.711575i	0.934567	+	0.355787i	$0.115787\pi$
$853$			517748.i			0.711575i	−0.934567	+	0.355787i	$0.884213\pi$
$854$	631710.	−	1.44536e6i	0.866168	−	1.98180i
$855$	−372290.			−0.509271
$856$	51151.0			0.0698083
$857$		−	1446.87i		−	0.00197001i	−1.00000		0.000985004i	$-0.999686\pi$
$857$		−	1446.87i		−	0.00197001i	1.00000		0.000985004i	$-0.000313536\pi$
$858$	3.66325e6			4.97613
$859$		−	217289.i		−	0.294477i	−0.989101	−	0.147239i	$-0.952961\pi$
$859$		−	217289.i		−	0.294477i	0.989101	−	0.147239i	$-0.0470385\pi$
$860$			122919.i			0.166197i
$861$	−378547.	−	165448.i	−0.510639	−	0.223181i
$862$	1.37472e6			1.85012
$863$	608808.			0.817446			0.408723	−	0.912658i	$-0.365974\pi$
$863$	608808.			0.817446			0.408723	+	0.912658i	$0.365974\pi$
$864$			631053.i			0.845353i
$865$	258012.			0.344833
$866$		−	1.22889e6i		−	1.63861i
$867$			357062.i			0.475013i
$868$	−39439.7	+	90238.3i	−0.0523473	+	0.119771i
$869$	−1.05596e6			−1.39832
$870$	−259857.			−0.343317
$871$			1.04858e6i			1.38218i
$872$	−202426.			−0.266216
$873$			2.43652e6i			3.19699i
$874$		−	395463.i		−	0.517706i
$875$	−27424.8	+	62748.2i	−0.0358202	+	0.0819568i
$876$	−235183.			−0.306477
$877$	461213.			0.599657			0.299828	−	0.953993i	$-0.403071\pi$
$877$	461213.			0.599657			0.299828	+	0.953993i	$0.403071\pi$
$878$			916848.i			1.18935i
$879$	−1.07239e6			−1.38796
$880$			720276.i			0.930109i
$881$		−	468049.i		−	0.603031i	−0.953461	−	0.301515i	$-0.902508\pi$
$881$		−	468049.i		−	0.603031i	0.953461	−	0.301515i	$-0.0974925\pi$
$882$	−1.03157e6	−	1.11464e6i	−1.32606	−	1.43284i
$883$	−1.35057e6			−1.73218			−0.866092	−	0.499884i	$-0.833376\pi$
$883$	−1.35057e6			−1.73218			−0.866092	+	0.499884i	$0.833376\pi$
$884$	−453149.			−0.579877
$885$			167898.i			0.214368i
$886$	573730.			0.730870
$887$			417192.i			0.530259i	0.964213	+	0.265130i	$0.0854148\pi$
$887$			417192.i			0.530259i	−0.964213	+	0.265130i	$0.914585\pi$
$888$			198997.i			0.252360i
$889$	544174.	+	237837.i	0.688547	+	0.300937i
$890$	737599.			0.931195
$891$	8618.82			0.0108566
$892$		−	458341.i		−	0.576048i
$893$	98765.5			0.123852
$894$			1.84341e6i			2.30647i
$895$		−	45045.8i		−	0.0562352i
$896$	826579.	+	361266.i	1.02960	+	0.449998i
$897$	−1.22005e6			−1.51633
$898$	820819.			1.01788
$899$		−	92295.2i		−	0.114198i
$900$	118334.			0.146091
$901$		−	260356.i		−	0.320714i
$902$			562333.i			0.691163i
$903$	435982.	−	997531.i	0.534679	−	1.22335i
$904$	−744676.			−0.911236
$905$	−52848.8			−0.0645265
$906$			992132.i			1.20868i
$907$	−207532.			−0.252273			−0.126137	−	0.992013i	$-0.540258\pi$
$907$	−207532.			−0.252273			−0.126137	+	0.992013i	$0.540258\pi$
$908$			534792.i			0.648654i
$909$		−	509810.i		−	0.616993i
$910$	−625669.	−	273456.i	−0.755548	−	0.330221i
$911$	1.34881e6			1.62522			0.812612	−	0.582805i	$-0.198045\pi$
$911$	1.34881e6			1.62522			0.812612	+	0.582805i	$0.198045\pi$
$912$	1.18018e6			1.41892
$913$			766499.i			0.919538i
$914$	−1.64645e6			−1.97086
$915$		−	1.08850e6i		−	1.30012i
$916$			574788.i			0.685042i
$917$	−603997.	+	1.38195e6i	−0.718284	+	1.64344i
$918$	−857686.			−1.01775
$919$	352887.			0.417835			0.208918	−	0.977933i	$-0.433006\pi$
$919$	352887.			0.417835			0.208918	+	0.977933i	$0.433006\pi$
$920$		−	153239.i		−	0.181048i
$921$	68917.1			0.0812471
$922$			1.06142e6i			1.24861i
$923$		−	830707.i		−	0.975089i
$924$	−415850.	+	951467.i	−0.487071	+	1.11442i
$925$	40314.8			0.0471174
$926$	1.61348e6			1.88166
$927$			728834.i			0.848143i
$928$	285119.			0.331078
$929$		−	382601.i		−	0.443317i	−0.975124	−	0.221658i	$-0.928853\pi$
$929$		−	382601.i		−	0.443317i	0.975124	−	0.221658i	$-0.0711470\pi$
$930$			218764.i			0.252935i
$931$	−446908.	+	413602.i	−0.515607	+	0.477181i
$932$	249563.			0.287308
$933$	1.31797e6			1.51406
$934$		−	1.59816e6i		−	1.83200i
$935$	−547870.			−0.626693
$936$		−	1.43842e6i		−	1.64186i
$937$		−	1.43975e6i		−	1.63987i	−0.572460	−	0.819933i	$-0.694011\pi$
$937$		−	1.43975e6i		−	1.63987i	0.572460	−	0.819933i	$-0.305989\pi$
$938$	−876719.	−	383180.i	−0.996448	−	0.435509i
$939$	1.57679e6			1.78831
$940$	−31392.9			−0.0355284
$941$		−	829098.i		−	0.936326i	−0.883642	−	0.468163i	$-0.844916\pi$
$941$		−	829098.i		−	0.936326i	0.883642	−	0.468163i	$-0.155084\pi$
$942$	−1.22208e6			−1.37720
$943$		−	187286.i		−	0.210612i
$944$		−	329171.i		−	0.369384i
$945$	−367874.	−	160783.i	−0.411941	−	0.180044i
$946$	−1.48183e6			−1.65584
$947$	−1.43840e6			−1.60391			−0.801957	−	0.597382i	$-0.796208\pi$
$947$	−1.43840e6			−1.60391			−0.801957	+	0.597382i	$0.796208\pi$
$948$		−	549948.i		−	0.611935i
$949$	579167.			0.643089
$950$		−	152729.i		−	0.169229i
$951$			1.70769e6i			1.88820i
$952$	−201874.	+	461889.i	−0.222744	+	0.509640i
$953$	1.38772e6			1.52797			0.763985	−	0.645235i	$-0.223240\pi$
$953$	1.38772e6			1.52797			0.763985	+	0.645235i	$0.223240\pi$
$954$	−677919.			−0.744871
$955$		−	1115.83i		−	0.00122346i
$956$	549139.			0.600851
$957$		−	973154.i		−	1.06257i
$958$		−	1.63700e6i		−	1.78369i
$959$	−1.12294e6	−	490793.i	−1.22101	−	0.533656i
$960$	156624.			0.169948
$961$	845821.			0.915866
$962$			401983.i			0.434368i
$963$	158594.			0.171015
$964$		−	417560.i		−	0.449330i
$965$			308614.i			0.331406i
$966$	445843.	−	1.02009e6i	0.477780	−	1.09316i
$967$	1.67888e6			1.79542			0.897711	−	0.440586i	$-0.145229\pi$
$967$	1.67888e6			1.79542			0.897711	+	0.440586i	$0.145229\pi$
$968$	−1.10307e6			−1.17721
$969$			897690.i			0.956046i
$970$	−999565.			−1.06235
$971$		−	9746.54i		−	0.0103374i	−0.999987	−	0.00516871i	$-0.998355\pi$
$971$		−	9746.54i		−	0.0103374i	0.999987	−	0.00516871i	$-0.00164526\pi$
$972$		−	423505.i		−	0.448256i
$973$	−98246.5	+	224789.i	−0.103775	+	0.237437i
$974$	357184.			0.376508
$975$	−471190.			−0.495663
$976$			2.13404e6i			2.24028i
$977$	1.26088e6			1.32095			0.660473	−	0.750850i	$-0.270356\pi$
$977$	1.26088e6			1.32095			0.660473	+	0.750850i	$0.270356\pi$
$978$		−	2.91799e6i		−	3.05074i
$979$			2.76228e6i			2.88206i
$980$	142051.	−	131465.i	0.147908	−	0.136885i
$981$	−627624.			−0.652171
$982$	−6069.14			−0.00629368
$983$		−	1.04613e6i		−	1.08263i	−0.840819	−	0.541316i	$-0.817926\pi$
$983$		−	1.04613e6i		−	1.08263i	0.840819	−	0.541316i	$-0.182074\pi$
$984$	357029.			0.368735
$985$			191024.i			0.196886i
$986$			387516.i			0.398598i
$987$	254765.	+	111348.i	0.261520	+	0.114300i
$988$	473078.			0.484640
$989$	493529.			0.504568
$990$			1.42655e6i			1.45552i
$991$	−587932.			−0.598659			−0.299330	−	0.954150i	$-0.596763\pi$
$991$	−587932.			−0.598659			−0.299330	+	0.954150i	$0.596763\pi$
$992$		−	240031.i		−	0.243918i
$993$		−	864612.i		−	0.876845i
$994$	694558.	+	303565.i	0.702968	+	0.307240i
$995$	−141076.			−0.142497
$996$	−399196.			−0.402409
$997$		−	480094.i		−	0.482988i	−0.970402	−	0.241494i	$-0.922363\pi$
$997$		−	480094.i		−	0.482988i	0.970402	−	0.241494i	$-0.0776374\pi$
$998$	−375365.			−0.376871
$999$			236354.i			0.236827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.d.a.6.10	yes	12
3.2	odd	2		315.5.h.a.181.4		12
4.3	odd	2		560.5.f.b.321.2		12
5.2	odd	4		175.5.c.d.174.2		24
5.3	odd	4		175.5.c.d.174.23		24
5.4	even	2		175.5.d.i.76.3		12
7.6	odd	2	inner	35.5.d.a.6.9	✓	12
21.20	even	2		315.5.h.a.181.3		12
28.27	even	2		560.5.f.b.321.11		12
35.13	even	4		175.5.c.d.174.1		24
35.27	even	4		175.5.c.d.174.24		24
35.34	odd	2		175.5.d.i.76.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.d.a.6.9	✓	12	7.6	odd	2	inner
35.5.d.a.6.10	yes	12	1.1	even	1	trivial
175.5.c.d.174.1		24	35.13	even	4
175.5.c.d.174.2		24	5.2	odd	4
175.5.c.d.174.23		24	5.3	odd	4
175.5.c.d.174.24		24	35.27	even	4
175.5.d.i.76.3		12	5.4	even	2
175.5.d.i.76.4		12	35.34	odd	2
315.5.h.a.181.3		12	21.20	even	2
315.5.h.a.181.4		12	3.2	odd	2
560.5.f.b.321.2		12	4.3	odd	2
560.5.f.b.321.11		12	28.27	even	2

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.81769 q^{2} +14.5704i q^{3} +7.21016 q^{4} -11.1803i q^{5} +70.1957i q^{6} +(44.8989 + 19.6236i) q^{7} -42.3467 q^{8} -131.296 q^{9} +O(q^{10})\)	\(q+4.81769 q^{2} +14.5704i q^{3} +7.21016 q^{4} -11.1803i q^{5} +70.1957i q^{6} +(44.8989 + 19.6236i) q^{7} -42.3467 q^{8} -131.296 q^{9} -53.8634i q^{10} +201.717 q^{11} +105.055i q^{12} -258.711i q^{13} +(216.309 + 94.5404i) q^{14} +162.902 q^{15} -319.376 q^{16} -242.930i q^{17} -632.545 q^{18} +253.614i q^{19} -80.6121i q^{20} +(-285.923 + 654.195i) q^{21} +971.808 q^{22} -323.663 q^{23} -617.009i q^{24} -125.000 q^{25} -1246.39i q^{26} -732.838i q^{27} +(323.729 + 141.489i) q^{28} -331.107 q^{29} +784.812 q^{30} +278.747i q^{31} -861.108 q^{32} +2939.09i q^{33} -1170.36i q^{34} +(219.398 - 501.985i) q^{35} -946.668 q^{36} -322.518 q^{37} +1221.84i q^{38} +3769.52 q^{39} +473.451i q^{40} +578.646i q^{41} +(-1377.49 + 3151.71i) q^{42} -1524.82 q^{43} +1454.41 q^{44} +1467.94i q^{45} -1559.31 q^{46} -389.432i q^{47} -4653.44i q^{48} +(1630.83 + 1762.16i) q^{49} -602.212 q^{50} +3539.59 q^{51} -1865.35i q^{52} +1071.73 q^{53} -3530.59i q^{54} -2255.26i q^{55} +(-1901.32 - 830.995i) q^{56} -3695.26 q^{57} -1595.17 q^{58} +1030.67i q^{59} +1174.55 q^{60} -6681.90i q^{61} +1342.92i q^{62} +(-5895.07 - 2576.51i) q^{63} +961.463 q^{64} -2892.47 q^{65} +14159.6i q^{66} -4053.08 q^{67} -1751.57i q^{68} -4715.90i q^{69} +(1056.99 - 2418.41i) q^{70} +3210.95 q^{71} +5559.97 q^{72} +2238.66i q^{73} -1553.79 q^{74} -1821.30i q^{75} +1828.60i q^{76} +(9056.86 + 3958.40i) q^{77} +18160.4 q^{78} -5234.87 q^{79} +3570.73i q^{80} +42.7274 q^{81} +2787.74i q^{82} +3799.88i q^{83} +(-2061.55 + 4716.85i) q^{84} -2716.04 q^{85} -7346.12 q^{86} -4824.37i q^{87} -8542.04 q^{88} +13693.9i q^{89} +7072.07i q^{90} +(5076.83 - 11615.8i) q^{91} -2333.66 q^{92} -4061.45 q^{93} -1876.16i q^{94} +2835.49 q^{95} -12546.7i q^{96} -18557.4i q^{97} +(7856.83 + 8489.53i) q^{98} -26484.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 122 q^{4} - 50 q^{7} - 186 q^{8} - 434 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 + 122 * q^4 - 50 * q^7 - 186 * q^8 - 434 * q^9	\( 12 q - 6 q^{2} + 122 q^{4} - 50 q^{7} - 186 q^{8} - 434 q^{9} + 126 q^{11} + 78 q^{14} + 50 q^{15} + 578 q^{16} + 734 q^{18} - 642 q^{21} + 2264 q^{22} - 756 q^{23} - 1500 q^{25} + 1414 q^{28} - 2190 q^{29} + 1600 q^{30} - 8682 q^{32} - 150 q^{35} - 3582 q^{36} + 5564 q^{37} + 8634 q^{39} + 5580 q^{42} + 3944 q^{43} - 11196 q^{44} + 7844 q^{46} - 8796 q^{49} + 750 q^{50} + 7206 q^{51} + 11760 q^{53} - 6606 q^{56} - 12900 q^{57} - 18496 q^{58} - 11700 q^{60} - 4310 q^{63} + 20146 q^{64} - 750 q^{65} - 24096 q^{67} + 14400 q^{70} - 5664 q^{71} + 39214 q^{72} + 17604 q^{74} + 26904 q^{77} + 20100 q^{78} - 1590 q^{79} - 11912 q^{81} - 43128 q^{84} + 1050 q^{85} + 17604 q^{86} - 7268 q^{88} - 7182 q^{91} - 60252 q^{92} - 70980 q^{93} - 3000 q^{95} + 57714 q^{98} + 23084 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 122 * q^4 - 50 * q^7 - 186 * q^8 - 434 * q^9 + 126 * q^11 + 78 * q^14 + 50 * q^15 + 578 * q^16 + 734 * q^18 - 642 * q^21 + 2264 * q^22 - 756 * q^23 - 1500 * q^25 + 1414 * q^28 - 2190 * q^29 + 1600 * q^30 - 8682 * q^32 - 150 * q^35 - 3582 * q^36 + 5564 * q^37 + 8634 * q^39 + 5580 * q^42 + 3944 * q^43 - 11196 * q^44 + 7844 * q^46 - 8796 * q^49 + 750 * q^50 + 7206 * q^51 + 11760 * q^53 - 6606 * q^56 - 12900 * q^57 - 18496 * q^58 - 11700 * q^60 - 4310 * q^63 + 20146 * q^64 - 750 * q^65 - 24096 * q^67 + 14400 * q^70 - 5664 * q^71 + 39214 * q^72 + 17604 * q^74 + 26904 * q^77 + 20100 * q^78 - 1590 * q^79 - 11912 * q^81 - 43128 * q^84 + 1050 * q^85 + 17604 * q^86 - 7268 * q^88 - 7182 * q^91 - 60252 * q^92 - 70980 * q^93 - 3000 * q^95 + 57714 * q^98 + 23084 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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