LMFDB - Embedded newform 315.4.j.g.226.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,4,Mod(46,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("315.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	315.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.5856016518$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 38 x^{8} - 5 x^{7} + 1102 x^{6} - 137 x^{5} + 11161 x^{4} + 10784 x^{3} + 81600 x^{2} + \cdots + 4096 $ x^10 - x^9 + 38x^8 - 5x^7 + 1102x^6 - 137x^5 + 11161x^4 + 10784x^3 + 81600x^2 + 18432x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.2
Root			$-1.39853 + 2.42233i$ of defining polynomial
Character	$\chi$	$=$	315.226
Dual form			315.4.j.g.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39853 + 2.42233i) q^{2} +(0.0882227 + 0.152806i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-16.7384 - 7.92622i) q^{7} -22.8700 q^{8} +O(q^{10})$	\(q+(-1.39853 + 2.42233i) q^{2} +(0.0882227 + 0.152806i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-16.7384 - 7.92622i) q^{7} -22.8700 q^{8} +(-6.99265 - 12.1116i) q^{10} +(-24.8012 - 42.9569i) q^{11} +71.6575 q^{13} +(42.6091 - 29.4609i) q^{14} +(31.2787 - 54.1762i) q^{16} +(23.1490 + 40.0953i) q^{17} +(-27.0947 + 46.9293i) q^{19} -0.882227 q^{20} +138.741 q^{22} +(76.4532 - 132.421i) q^{23} +(-12.5000 - 21.6506i) q^{25} +(-100.215 + 173.578i) q^{26} +(-0.265533 - 3.25701i) q^{28} +38.5268 q^{29} +(-51.7027 - 89.5517i) q^{31} +(-3.99177 - 6.91395i) q^{32} -129.499 q^{34} +(76.1676 - 52.6640i) q^{35} +(-26.7415 + 46.3176i) q^{37} +(-75.7854 - 131.264i) q^{38} +(57.1751 - 99.0301i) q^{40} -40.4953 q^{41} +377.195 q^{43} +(4.37605 - 7.57954i) q^{44} +(213.844 + 370.389i) q^{46} +(194.784 - 337.375i) q^{47} +(217.350 + 265.345i) q^{49} +69.9265 q^{50} +(6.32181 + 10.9497i) q^{52} +(164.410 + 284.766i) q^{53} +248.012 q^{55} +(382.808 + 181.273i) q^{56} +(-53.8809 + 93.3244i) q^{58} +(-19.8422 - 34.3676i) q^{59} +(-98.7300 + 171.005i) q^{61} +289.231 q^{62} +522.789 q^{64} +(-179.144 + 310.286i) q^{65} +(-486.113 - 841.972i) q^{67} +(-4.08454 + 7.07463i) q^{68} +(21.0465 + 258.155i) q^{70} -386.897 q^{71} +(109.860 + 190.283i) q^{73} +(-74.7976 - 129.553i) q^{74} -9.56145 q^{76} +(74.6466 + 915.610i) q^{77} +(193.237 - 334.696i) q^{79} +(156.393 + 270.881i) q^{80} +(56.6339 - 98.0928i) q^{82} +1376.83 q^{83} -231.490 q^{85} +(-527.518 + 913.688i) q^{86} +(567.203 + 982.424i) q^{88} +(375.027 - 649.566i) q^{89} +(-1199.43 - 567.973i) q^{91} +26.9796 q^{92} +(544.822 + 943.660i) q^{94} +(-135.473 - 234.647i) q^{95} +533.467 q^{97} +(-946.723 + 155.399i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - 35 q^{4} - 25 q^{5} - 62 q^{7} - 66 q^{8}+O(q^{10}) $ 10 * q + q^2 - 35 * q^4 - 25 * q^5 - 62 * q^7 - 66 * q^8	$ 10 q + q^{2} - 35 q^{4} - 25 q^{5} - 62 q^{7} - 66 q^{8} + 5 q^{10} + 47 q^{11} + 2 q^{13} - 7 q^{14} - 171 q^{16} - 2 q^{17} + 21 q^{19} + 350 q^{20} + 1046 q^{22} + 201 q^{23} - 125 q^{25} - 47 q^{26} + 597 q^{28} - 380 q^{29} - 388 q^{31} - 95 q^{32} + 260 q^{34} + 95 q^{35} + 145 q^{37} + 835 q^{38} + 165 q^{40} + 562 q^{41} + 1136 q^{43} + 1091 q^{44} - 337 q^{46} - 473 q^{47} + 998 q^{49} - 50 q^{50} + 379 q^{52} + 351 q^{53} - 470 q^{55} + 1338 q^{56} - 1818 q^{58} + 708 q^{59} - 1944 q^{61} - 896 q^{62} - 250 q^{64} - 5 q^{65} - 1118 q^{67} - 3118 q^{68} + 865 q^{70} - 1728 q^{71} + 1652 q^{73} - 3285 q^{74} + 1382 q^{76} - 787 q^{77} - 218 q^{79} - 855 q^{80} - 1027 q^{82} + 3004 q^{83} + 20 q^{85} - 4264 q^{86} - 2131 q^{88} + 2322 q^{89} + 524 q^{91} + 5914 q^{92} + 2677 q^{94} + 105 q^{95} + 1196 q^{97} - 2971 q^{98}+O(q^{100}) $ 10 * q + q^2 - 35 * q^4 - 25 * q^5 - 62 * q^7 - 66 * q^8 + 5 * q^10 + 47 * q^11 + 2 * q^13 - 7 * q^14 - 171 * q^16 - 2 * q^17 + 21 * q^19 + 350 * q^20 + 1046 * q^22 + 201 * q^23 - 125 * q^25 - 47 * q^26 + 597 * q^28 - 380 * q^29 - 388 * q^31 - 95 * q^32 + 260 * q^34 + 95 * q^35 + 145 * q^37 + 835 * q^38 + 165 * q^40 + 562 * q^41 + 1136 * q^43 + 1091 * q^44 - 337 * q^46 - 473 * q^47 + 998 * q^49 - 50 * q^50 + 379 * q^52 + 351 * q^53 - 470 * q^55 + 1338 * q^56 - 1818 * q^58 + 708 * q^59 - 1944 * q^61 - 896 * q^62 - 250 * q^64 - 5 * q^65 - 1118 * q^67 - 3118 * q^68 + 865 * q^70 - 1728 * q^71 + 1652 * q^73 - 3285 * q^74 + 1382 * q^76 - 787 * q^77 - 218 * q^79 - 855 * q^80 - 1027 * q^82 + 3004 * q^83 + 20 * q^85 - 4264 * q^86 - 2131 * q^88 + 2322 * q^89 + 524 * q^91 + 5914 * q^92 + 2677 * q^94 + 105 * q^95 + 1196 * q^97 - 2971 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.39853	+	2.42233i	−0.494455	+	0.856422i	−0.999980	−	0.00639063i	$-0.997966\pi$
$2$	−1.39853	+	2.42233i	−0.494455	+	0.856422i	0.505524	+	0.862812i	$0.331299\pi$
$3$		0			0
$3$		0			0
$4$	0.0882227	+	0.152806i	0.0110278	+	0.0191008i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	−16.7384	−	7.92622i	−0.903790	−	0.427976i
$7$	−16.7384	−	7.92622i	−0.903790	−	0.427976i
$8$	−22.8700			−1.01072
$9$		0			0
$10$	−6.99265	−	12.1116i	−0.221127	−	0.383003i
$11$	−24.8012	−	42.9569i	−0.679803	−	1.17745i	−0.975040	−	0.222029i	$-0.928732\pi$
$11$	−24.8012	−	42.9569i	−0.679803	−	1.17745i	0.295237	−	0.955424i	$-0.404601\pi$
$12$		0			0
$13$	71.6575			1.52879			0.764393	−	0.644751i	$-0.223039\pi$
$13$	71.6575			1.52879			0.764393	+	0.644751i	$0.223039\pi$
$14$	42.6091	−	29.4609i	0.813412	−	0.562411i
$15$		0			0
$16$	31.2787	−	54.1762i	0.488729	−	0.846503i
$17$	23.1490	+	40.0953i	0.330263	+	0.572032i	0.982563	−	0.185928i	$-0.0595293\pi$
$17$	23.1490	+	40.0953i	0.330263	+	0.572032i	−0.652300	+	0.757961i	$0.726196\pi$
$18$		0			0
$19$	−27.0947	+	46.9293i	−0.327155	+	0.566649i	−0.981946	−	0.189161i	$-0.939423\pi$
$19$	−27.0947	+	46.9293i	−0.327155	+	0.566649i	0.654791	+	0.755810i	$0.272756\pi$
$20$	−0.882227			−0.00986359
$21$		0			0
$22$	138.741			1.34453
$23$	76.4532	−	132.421i	0.693113	−	1.20051i	−0.277700	−	0.960668i	$-0.589572\pi$
$23$	76.4532	−	132.421i	0.693113	−	1.20051i	0.970813	−	0.239839i	$-0.0770945\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−100.215	+	173.578i	−0.755916	+	1.30929i
$27$		0			0
$28$	−0.265533	−	3.25701i	−0.00179218	−	0.0219827i
$29$	38.5268			0.246698			0.123349	−	0.992363i	$-0.460637\pi$
$29$	38.5268			0.246698			0.123349	+	0.992363i	$0.460637\pi$
$30$		0			0
$31$	−51.7027	−	89.5517i	−0.299551	−	0.518837i	0.676482	−	0.736459i	$-0.263503\pi$
$31$	−51.7027	−	89.5517i	−0.299551	−	0.518837i	−0.976033	+	0.217622i	$0.930170\pi$
$32$	−3.99177	−	6.91395i	−0.0220516	−	0.0381945i
$33$		0			0
$34$	−129.499			−0.653201
$35$	76.1676	−	52.6640i	0.367848	−	0.254338i
$36$		0			0
$37$	−26.7415	+	46.3176i	−0.118818	+	0.205799i	−0.919300	−	0.393558i	$-0.871244\pi$
$37$	−26.7415	+	46.3176i	−0.118818	+	0.205799i	0.800481	+	0.599358i	$0.204577\pi$
$38$	−75.7854	−	131.264i	−0.323527	−	0.560365i
$39$		0			0
$40$	57.1751	−	99.0301i	0.226004	−	0.391451i
$41$	−40.4953			−0.154251			−0.0771256	−	0.997021i	$-0.524574\pi$
$41$	−40.4953			−0.154251			−0.0771256	+	0.997021i	$0.524574\pi$
$42$		0			0
$43$	377.195			1.33771			0.668856	−	0.743392i	$-0.266784\pi$
$43$	377.195			1.33771			0.668856	+	0.743392i	$0.266784\pi$
$44$	4.37605	−	7.57954i	0.0149935	−	0.0259695i
$45$		0			0
$46$	213.844	+	370.389i	0.685427	+	1.18719i
$47$	194.784	−	337.375i	0.604514	−	1.04705i	−0.387615	−	0.921822i	$-0.626701\pi$
$47$	194.784	−	337.375i	0.604514	−	1.04705i	0.992128	−	0.125227i	$-0.0399658\pi$
$48$		0			0
$49$	217.350	+	265.345i	0.633673	+	0.773601i
$50$	69.9265			0.197782
$51$		0			0
$52$	6.32181	+	10.9497i	0.0168592	+	0.0292010i
$53$	164.410	+	284.766i	0.426102	+	0.738031i	0.996523	−	0.0833220i	$-0.0265530\pi$
$53$	164.410	+	284.766i	0.426102	+	0.738031i	−0.570420	+	0.821353i	$0.693220\pi$
$54$		0			0
$55$	248.012			0.608034
$56$	382.808	+	181.273i	0.913480	+	0.432565i
$57$		0			0
$58$	−53.8809	+	93.3244i	−0.121981	+	0.211278i
$59$	−19.8422	−	34.3676i	−0.0437836	−	0.0758353i	0.843303	−	0.537438i	$-0.180608\pi$
$59$	−19.8422	−	34.3676i	−0.0437836	−	0.0758353i	−0.887087	+	0.461603i	$0.847275\pi$
$60$		0			0
$61$	−98.7300	+	171.005i	−0.207231	+	0.358934i	−0.950841	−	0.309679i	$-0.899778\pi$
$61$	−98.7300	+	171.005i	−0.207231	+	0.358934i	0.743610	+	0.668613i	$0.233112\pi$
$62$	289.231			0.592458
$63$		0			0
$64$	522.789			1.02107
$65$	−179.144	+	310.286i	−0.341847	+	0.592096i
$66$		0			0
$67$	−486.113	−	841.972i	−0.886390	−	1.53527i	−0.844112	−	0.536167i	$-0.819872\pi$
$67$	−486.113	−	841.972i	−0.886390	−	1.53527i	−0.0422784	−	0.999106i	$-0.513462\pi$
$68$	−4.08454	+	7.07463i	−0.00728417	+	0.0126165i
$69$		0			0
$70$	21.0465	+	258.155i	0.0359363	+	0.440792i
$71$	−386.897			−0.646708			−0.323354	−	0.946278i	$-0.604810\pi$
$71$	−386.897			−0.646708			−0.323354	+	0.946278i	$0.604810\pi$
$72$		0			0
$73$	109.860	+	190.283i	0.176139	+	0.305082i	0.940555	−	0.339642i	$-0.110306\pi$
$73$	109.860	+	190.283i	0.176139	+	0.305082i	−0.764416	+	0.644724i	$0.776972\pi$
$74$	−74.7976	−	129.553i	−0.117501	−	0.203517i
$75$		0			0
$76$	−9.56145			−0.0144312
$77$	74.6466	+	915.610i	0.110478	+	1.35511i
$78$		0			0
$79$	193.237	−	334.696i	0.275201	−	0.476662i	−0.694985	−	0.719024i	$-0.744589\pi$
$79$	193.237	−	334.696i	0.275201	−	0.476662i	0.970186	+	0.242362i	$0.0779223\pi$
$80$	156.393	+	270.881i	0.218566	+	0.378568i
$81$		0			0
$82$	56.6339	−	98.0928i	0.0762704	−	0.132104i
$83$	1376.83			1.82081			0.910404	−	0.413721i	$-0.135771\pi$
$83$	1376.83			1.82081			0.910404	+	0.413721i	$0.135771\pi$
$84$		0			0
$85$	−231.490			−0.295396
$86$	−527.518	+	913.688i	−0.661439	+	1.14565i
$87$		0			0
$88$	567.203	+	982.424i	0.687091	+	1.19008i
$89$	375.027	−	649.566i	0.446661	−	0.773639i	−0.551506	−	0.834171i	$-0.685946\pi$
$89$	375.027	−	649.566i	0.446661	−	0.773639i	0.998166	+	0.0605322i	$0.0192798\pi$
$90$		0			0
$91$	−1199.43	−	567.973i	−1.38170	−	0.654283i
$92$	26.9796			0.0305741
$93$		0			0
$94$	544.822	+	943.660i	0.597810	+	1.03544i
$95$	−135.473	−	234.647i	−0.146308	−	0.253413i
$96$		0			0
$97$	533.467			0.558406			0.279203	−	0.960232i	$-0.409930\pi$
$97$	533.467			0.558406			0.279203	+	0.960232i	$0.409930\pi$
$98$	−946.723	+	155.399i	−0.975852	+	0.160181i
$99$		0			0
$100$	2.20557	−	3.82015i	0.00220557	−	0.00382015i
$101$	−660.745	−	1144.44i	−0.650956	−	1.12749i	−0.982891	−	0.184187i	$-0.941035\pi$
$101$	−660.745	−	1144.44i	−0.650956	−	1.12749i	0.331935	−	0.943302i	$-0.392299\pi$
$102$		0			0
$103$	745.646	−	1291.50i	0.713308	−	1.23549i	−0.250301	−	0.968168i	$-0.580529\pi$
$103$	745.646	−	1291.50i	0.713308	−	1.23549i	0.963609	−	0.267317i	$-0.0861372\pi$
$104$	−1638.81			−1.54518
$105$		0			0
$106$	−919.729			−0.842754
$107$	−219.758	+	380.632i	−0.198550	+	0.343898i	−0.948058	−	0.318096i	$-0.896956\pi$
$107$	−219.758	+	380.632i	−0.198550	+	0.343898i	0.749509	+	0.661994i	$0.230290\pi$
$108$		0			0
$109$	−731.548	−	1267.08i	−0.642840	−	1.11343i	−0.984796	−	0.173716i	$-0.944423\pi$
$109$	−731.548	−	1267.08i	−0.642840	−	1.11343i	0.341955	−	0.939716i	$-0.388911\pi$
$110$	−346.852	+	600.765i	−0.300646	+	0.520734i
$111$		0			0
$112$	−952.968	+	658.903i	−0.803991	+	0.555897i
$113$	1270.15			1.05740			0.528699	−	0.848809i	$-0.322680\pi$
$113$	1270.15			1.05740			0.528699	+	0.848809i	$0.322680\pi$
$114$		0			0
$115$	382.266	+	662.104i	0.309969	+	0.536883i
$116$	3.39893	+	5.88713i	0.00272054	+	0.00471212i
$117$		0			0
$118$	111.000			0.0865960
$119$	−69.6741	−	854.617i	−0.0536724	−	0.658341i
$120$		0			0
$121$	−564.695	+	978.080i	−0.424264	+	0.734846i
$122$	−276.154	−	478.313i	−0.204933	−	0.354954i
$123$		0			0
$124$	9.12270	−	15.8010i	0.00660679	−	0.0114433i
$125$	125.000			0.0894427
$126$		0			0
$127$	−675.261			−0.471809			−0.235904	−	0.971776i	$-0.575805\pi$
$127$	−675.261			−0.471809			−0.235904	+	0.971776i	$0.575805\pi$
$128$	−699.202	+	1211.05i	−0.482823	+	0.836274i
$129$		0			0
$130$	−501.076	−	867.889i	−0.338056	−	0.585530i
$131$	347.464	−	601.826i	0.231741	−	0.401388i	−0.726579	−	0.687083i	$-0.758891\pi$
$131$	347.464	−	601.826i	0.231741	−	0.401388i	0.958321	+	0.285695i	$0.0922244\pi$
$132$		0			0
$133$	825.494	−	570.765i	0.538191	−	0.372117i
$134$	2719.38			1.75312
$135$		0			0
$136$	−529.419	−	916.981i	−0.333804	−	0.578165i
$137$	−1259.55	−	2181.60i	−0.785478	−	1.36049i	−0.928713	−	0.370799i	$-0.879084\pi$
$137$	−1259.55	−	2181.60i	−0.785478	−	1.36049i	0.143235	−	0.989689i	$-0.454249\pi$
$138$		0			0
$139$	−1711.61			−1.04444			−0.522219	−	0.852812i	$-0.674896\pi$
$139$	−1711.61			−1.04444			−0.522219	+	0.852812i	$0.674896\pi$
$140$	14.7671	+	6.99273i	0.00891462	+	0.00422138i
$141$		0			0
$142$	541.088	−	937.191i	0.319768	−	0.553855i
$143$	−1777.19	−	3078.18i	−1.03927	−	1.80007i
$144$		0			0
$145$	−96.3169	+	166.826i	−0.0551633	+	0.0955457i
$146$	−614.571			−0.348372
$147$		0			0
$148$	−9.43683			−0.00524123
$149$	−360.688	+	624.731i	−0.198314	+	0.343490i	−0.947982	−	0.318325i	$-0.896880\pi$
$149$	−360.688	+	624.731i	−0.198314	+	0.343490i	0.749668	+	0.661814i	$0.230213\pi$
$150$		0			0
$151$	−465.346	−	806.003i	−0.250790	−	0.434381i	0.712953	−	0.701211i	$-0.247357\pi$
$151$	−465.346	−	806.003i	−0.250790	−	0.434381i	−0.963744	+	0.266830i	$0.914024\pi$
$152$	619.655	−	1073.27i	0.330662	−	0.572724i
$153$		0			0
$154$	−2322.30	−	1099.69i	−1.21517	−	0.575426i
$155$	517.027			0.267926
$156$		0			0
$157$	−1133.33	−	1962.98i	−0.576111	−	0.997854i	−0.995920	−	0.0902412i	$-0.971236\pi$
$157$	−1133.33	−	1962.98i	−0.576111	−	0.997854i	0.419809	−	0.907613i	$-0.362097\pi$
$158$	540.496	+	936.166i	0.272149	+	0.471376i
$159$		0			0
$160$	39.9177			0.0197236
$161$	−2329.30	+	1610.53i	−1.14022	+	0.788370i
$162$		0			0
$163$	−1597.15	+	2766.34i	−0.767474	+	1.32930i	0.171454	+	0.985192i	$0.445153\pi$
$163$	−1597.15	+	2766.34i	−0.767474	+	1.32930i	−0.938928	+	0.344112i	$0.888180\pi$
$164$	−3.57260	−	6.18793i	−0.00170106	−	0.00294632i
$165$		0			0
$166$	−1925.54	+	3335.14i	−0.900308	+	1.55938i
$167$	611.079			0.283154			0.141577	−	0.989927i	$-0.454783\pi$
$167$	611.079			0.283154			0.141577	+	0.989927i	$0.454783\pi$
$168$		0			0
$169$	2937.79			1.33718
$170$	323.747	−	560.745i	0.146060	−	0.252984i
$171$		0			0
$172$	33.2771	+	57.6377i	0.0147521	+	0.0255513i
$173$	4.40560	−	7.63073i	0.00193614	−	0.00335349i	−0.865056	−	0.501676i	$-0.832717\pi$
$173$	4.40560	−	7.63073i	0.00193614	−	0.00335349i	0.866992	+	0.498322i	$0.166050\pi$
$174$		0			0
$175$	37.6225	+	461.475i	0.0162514	+	0.199339i
$176$	−3102.99			−1.32896
$177$		0			0
$178$	1048.97	+	1816.88i	0.441708	+	0.765060i
$179$	−625.080	−	1082.67i	−0.261009	−	0.452081i	0.705501	−	0.708709i	$-0.250722\pi$
$179$	−625.080	−	1082.67i	−0.261009	−	0.452081i	−0.966510	+	0.256628i	$0.917389\pi$
$180$		0			0
$181$	−2448.02			−1.00531			−0.502653	−	0.864488i	$-0.667643\pi$
$181$	−2448.02			−1.00531			−0.502653	+	0.864488i	$0.667643\pi$
$182$	3053.26	−	2111.09i	1.24353	−	0.859805i
$183$		0			0
$184$	−1748.49	+	3028.47i	−0.700544	+	1.21338i
$185$	−133.708	−	231.588i	−0.0531371	−	0.0920362i
$186$		0			0
$187$	1148.25	−	1988.82i	0.449027	−	0.777738i
$188$	68.7374			0.0266659
$189$		0			0
$190$	757.854			0.289371
$191$	−2534.16	+	4389.30i	−0.960030	+	1.66282i	−0.237616	+	0.971359i	$0.576366\pi$
$191$	−2534.16	+	4389.30i	−0.960030	+	1.66282i	−0.722414	+	0.691461i	$0.756967\pi$
$192$		0			0
$193$	−1722.28	−	2983.08i	−0.642345	−	1.11257i	−0.984908	−	0.173079i	$-0.944628\pi$
$193$	−1722.28	−	2983.08i	−0.642345	−	1.11257i	0.342563	−	0.939495i	$-0.388705\pi$
$194$	−746.071	+	1292.23i	−0.276107	+	0.478231i
$195$		0			0
$196$	−21.3712	+	56.6219i	−0.00778833	+	0.0206348i
$197$	1769.61			0.639998			0.319999	−	0.947418i	$-0.396317\pi$
$197$	1769.61			0.639998			0.319999	+	0.947418i	$0.396317\pi$
$198$		0			0
$199$	−102.986	−	178.377i	−0.0366858	−	0.0635416i	0.847100	−	0.531434i	$-0.178347\pi$
$199$	−102.986	−	178.377i	−0.0366858	−	0.0635416i	−0.883785	+	0.467893i	$0.845013\pi$
$200$	285.875	+	495.151i	0.101072	+	0.175062i
$201$		0			0
$202$	3696.29			1.28748
$203$	−644.877	−	305.372i	−0.222963	−	0.105581i
$204$		0			0
$205$	101.238	−	175.350i	0.0344916	−	0.0597413i
$206$	2085.62	+	3612.40i	0.705398	+	1.22178i
$207$		0			0
$208$	2241.35	−	3882.13i	0.747162	−	1.29412i
$209$	2687.91			0.889603
$210$		0			0
$211$	4973.82			1.62281			0.811403	−	0.584488i	$-0.198704\pi$
$211$	4973.82			1.62281			0.811403	+	0.584488i	$0.198704\pi$
$212$	−29.0093	+	50.2457i	−0.00939797	+	0.0162778i
$213$		0			0
$214$	−614.677	−	1064.65i	−0.196348	−	0.340084i
$215$	−942.986	+	1633.30i	−0.299122	+	0.518094i
$216$		0			0
$217$	155.615	+	1908.76i	0.0486812	+	0.597121i
$218$	4092.37			1.27142
$219$		0			0
$220$	21.8802	+	37.8977i	0.00670530	+	0.0116139i
$221$	1658.80	+	2873.13i	0.504901	+	0.874514i
$222$		0			0
$223$	3355.68			1.00768			0.503841	−	0.863796i	$-0.331920\pi$
$223$	3355.68			1.00768			0.503841	+	0.863796i	$0.331920\pi$
$224$	12.0144	+	147.368i	0.00358370	+	0.0439574i
$225$		0			0
$226$	−1776.35	+	3076.73i	−0.522836	+	0.905579i
$227$	−1041.55	−	1804.01i	−0.304537	−	0.527474i	0.672621	−	0.739987i	$-0.265168\pi$
$227$	−1041.55	−	1804.01i	−0.304537	−	0.527474i	−0.977158	+	0.212513i	$0.931835\pi$
$228$		0			0
$229$	2505.88	−	4340.31i	0.723114	−	1.25247i	−0.236632	−	0.971599i	$-0.576044\pi$
$229$	2505.88	−	4340.31i	0.723114	−	1.25247i	0.959746	−	0.280870i	$-0.0906231\pi$
$230$	−2138.44			−0.613064
$231$		0			0
$232$	−881.108			−0.249343
$233$	575.322	−	996.487i	0.161762	−	0.280180i	−0.773739	−	0.633505i	$-0.781616\pi$
$233$	575.322	−	996.487i	0.161762	−	0.280180i	0.935501	+	0.353325i	$0.114949\pi$
$234$		0			0
$235$	973.919	+	1686.88i	0.270347	+	0.468254i
$236$	3.50106	−	6.06401i	0.000965675	−	0.00167260i
$237$		0			0
$238$	2167.60	+	1026.44i	0.590357	+	0.279554i
$239$	−1919.63			−0.519543			−0.259771	−	0.965670i	$-0.583647\pi$
$239$	−1919.63			−0.519543			−0.259771	+	0.965670i	$0.583647\pi$
$240$		0			0
$241$	125.085	+	216.653i	0.0334332	+	0.0579080i	0.882258	−	0.470766i	$-0.156023\pi$
$241$	125.085	+	216.653i	0.0334332	+	0.0579080i	−0.848825	+	0.528674i	$0.822689\pi$
$242$	−1579.49	−	2735.75i	−0.419559	−	0.726697i
$243$		0			0
$244$	−34.8409			−0.00914123
$245$	−1692.35	+	277.790i	−0.441308	+	0.0724382i
$246$		0			0
$247$	−1941.53	+	3362.84i	−0.500149	+	0.866284i
$248$	1182.44	+	2048.05i	0.302763	+	0.524400i
$249$		0			0
$250$	−174.816	+	302.791i	−0.0442254	+	0.0766007i
$251$	−2905.43			−0.730634			−0.365317	−	0.930883i	$-0.619039\pi$
$251$	−2905.43			−0.730634			−0.365317	+	0.930883i	$0.619039\pi$
$252$		0			0
$253$	−7584.51			−1.88472
$254$	944.373	−	1635.70i	0.233288	−	0.404067i
$255$		0			0
$256$	135.444	+	234.595i	0.0330673	+	0.0572742i
$257$	744.648	−	1289.77i	0.180739	−	0.313049i	−0.761394	−	0.648290i	$-0.775484\pi$
$257$	744.648	−	1289.77i	0.180739	−	0.313049i	0.942132	+	0.335241i	$0.108818\pi$
$258$		0			0
$259$	814.735	−	563.325i	0.195464	−	0.135148i
$260$	−63.2181			−0.0150793
$261$		0			0
$262$	971.880	+	1683.34i	0.229171	+	0.396937i
$263$	1654.93	+	2866.42i	0.388013	+	0.672058i	0.992182	−	0.124798i	$-0.0398284\pi$
$263$	1654.93	+	2866.42i	0.388013	+	0.672058i	−0.604170	+	0.796856i	$0.706495\pi$
$264$		0			0
$265$	−1644.10			−0.381118
$266$	228.099	+	2797.85i	0.0525777	+	0.644914i
$267$		0			0
$268$	85.7724	−	148.562i	0.0195499	−	0.0338615i
$269$	2055.03	+	3559.41i	0.465789	+	0.806769i	0.999237	−	0.0390633i	$-0.0124374\pi$
$269$	2055.03	+	3559.41i	0.465789	+	0.806769i	−0.533448	+	0.845833i	$0.679104\pi$
$270$		0			0
$271$	864.137	−	1496.73i	0.193700	−	0.335498i	−0.752774	−	0.658279i	$-0.771285\pi$
$271$	864.137	−	1496.73i	0.193700	−	0.335498i	0.946473	+	0.322782i	$0.104618\pi$
$272$	2896.28			0.645636
$273$		0			0
$274$	7046.07			1.55353
$275$	−620.029	+	1073.92i	−0.135961	+	0.235491i
$276$		0			0
$277$	2274.07	+	3938.81i	0.493270	+	0.854368i	0.999970	−	0.00775399i	$-0.00246820\pi$
$277$	2274.07	+	3938.81i	0.493270	+	0.854368i	−0.506700	+	0.862122i	$0.669135\pi$
$278$	2393.74	−	4146.08i	0.516428	−	0.894479i
$279$		0			0
$280$	−1741.96	+	1204.43i	−0.371792	+	0.257065i
$281$	3781.62			0.802821			0.401410	−	0.915898i	$-0.368520\pi$
$281$	3781.62			0.802821			0.401410	+	0.915898i	$0.368520\pi$
$282$		0			0
$283$	−476.994	−	826.178i	−0.100192	−	0.173538i	0.811572	−	0.584253i	$-0.198612\pi$
$283$	−476.994	−	826.178i	−0.100192	−	0.173538i	−0.911764	+	0.410715i	$0.865279\pi$
$284$	−34.1331	−	59.1203i	−0.00713179	−	0.0123526i
$285$		0			0
$286$	9941.81			2.05550
$287$	677.828	+	320.975i	0.139411	+	0.0660158i
$288$		0			0
$289$	1384.74	−	2398.45i	0.281853	−	0.488184i
$290$	−269.404	−	466.622i	−0.0545516	−	0.0944862i
$291$		0			0
$292$	−19.3843	+	33.5746i	−0.00388487	+	0.00672879i
$293$	−4463.04			−0.889875			−0.444938	−	0.895562i	$-0.646774\pi$
$293$	−4463.04			−0.889875			−0.444938	+	0.895562i	$0.646774\pi$
$294$		0			0
$295$	198.422			0.0391612
$296$	611.579	−	1059.29i	0.120092	−	0.208006i
$297$		0			0
$298$	−1008.87	−	1747.41i	−0.196115	−	0.339680i
$299$	5478.44	−	9488.94i	1.05962	−	1.83532i
$300$		0			0
$301$	−6313.64	−	2989.73i	−1.20901	−	0.572509i
$302$	2603.20			0.496018
$303$		0			0
$304$	1694.97	+	2935.77i	0.319780	+	0.553875i
$305$	−493.650	−	855.027i	−0.0926765	−	0.160520i
$306$		0			0
$307$	6617.48			1.23023			0.615113	−	0.788439i	$-0.289110\pi$
$307$	6617.48			1.23023			0.615113	+	0.788439i	$0.289110\pi$
$308$	−133.325	+	92.1840i	−0.0246653	+	0.0170541i
$309$		0			0
$310$	−723.078	+	1252.41i	−0.132478	+	0.229458i
$311$	84.2817	+	145.980i	0.0153671	+	0.0266166i	0.873607	−	0.486633i	$-0.161775\pi$
$311$	84.2817	+	145.980i	0.0153671	+	0.0266166i	−0.858240	+	0.513249i	$0.828442\pi$
$312$		0			0
$313$	−3750.93	+	6496.80i	−0.677364	+	1.17323i	0.298407	+	0.954439i	$0.403545\pi$
$313$	−3750.93	+	6496.80i	−0.677364	+	1.17323i	−0.975772	+	0.218791i	$0.929789\pi$
$314$	6339.98			1.13944
$315$		0			0
$316$	68.1915			0.0121395
$317$	1712.58	−	2966.27i	0.303432	−	0.525560i	−0.673479	−	0.739206i	$-0.735201\pi$
$317$	1712.58	−	2966.27i	0.303432	−	0.525560i	0.976911	+	0.213647i	$0.0685341\pi$
$318$		0			0
$319$	−955.508	−	1654.99i	−0.167706	−	0.290475i
$320$	−1306.97	+	2263.74i	−0.228319	+	0.395459i
$321$		0			0
$322$	−643.629	−	7894.71i	−0.111391	−	1.36632i
$323$	−2508.86			−0.432188
$324$		0			0
$325$	−895.719	−	1551.43i	−0.152879	−	0.264793i
$326$	−4467.32	−	7737.63i	−0.758964	−	1.31456i
$327$		0			0
$328$	926.128			0.155905
$329$	−5934.49	+	4103.23i	−0.994465	+	0.687595i
$330$		0			0
$331$	−547.737	+	948.708i	−0.0909557	+	0.157540i	−0.907914	−	0.419158i	$-0.862325\pi$
$331$	−547.737	+	948.708i	−0.0909557	+	0.157540i	0.816958	+	0.576697i	$0.195659\pi$
$332$	121.468	+	210.388i	0.0200796	+	0.0347788i
$333$		0			0
$334$	−854.613	+	1480.23i	−0.140007	+	0.242499i
$335$	4861.13			0.792812
$336$		0			0
$337$	4241.92			0.685673			0.342837	−	0.939395i	$-0.388612\pi$
$337$	4241.92			0.685673			0.342837	+	0.939395i	$0.388612\pi$
$338$	−4108.60	+	7116.30i	−0.661178	+	1.14519i
$339$		0			0
$340$	−20.4227	−	35.3732i	−0.00325758	−	0.00564229i
$341$	−2564.57	+	4441.97i	−0.407271	+	0.705414i
$342$		0			0
$343$	−1534.91	−	6164.22i	−0.241625	−	0.970370i
$344$	−8626.45			−1.35206
$345$		0			0
$346$	12.3227	+	21.3436i	0.00191467	+	0.00331630i
$347$	39.0835	+	67.6945i	0.00604643	+	0.0104727i	0.869033	−	0.494755i	$-0.164742\pi$
$347$	39.0835	+	67.6945i	0.00604643	+	0.0104727i	−0.862986	+	0.505227i	$0.831409\pi$
$348$		0			0
$349$	−167.845			−0.0257436			−0.0128718	−	0.999917i	$-0.504097\pi$
$349$	−167.845			−0.0257436			−0.0128718	+	0.999917i	$0.504097\pi$
$350$	−1170.46	−	554.254i	−0.178754	−	0.0846460i
$351$		0			0
$352$	−198.001	+	342.948i	−0.0299815	+	0.0519295i
$353$	−2436.41	−	4219.98i	−0.367357	−	0.636280i	0.621795	−	0.783180i	$-0.286404\pi$
$353$	−2436.41	−	4219.98i	−0.367357	−	0.636280i	−0.989151	+	0.146900i	$0.953070\pi$
$354$		0			0
$355$	967.243	−	1675.31i	0.144608	−	0.250469i
$356$	132.344			0.0197028
$357$		0			0
$358$	3496.77			0.516230
$359$	4224.76	−	7317.50i	0.621099	−	1.07577i	−0.368183	−	0.929753i	$-0.620020\pi$
$359$	4224.76	−	7317.50i	0.621099	−	1.07577i	0.989281	−	0.146021i	$-0.0466468\pi$
$360$		0			0
$361$	1961.26	+	3397.00i	0.285940	+	0.495262i
$362$	3423.64	−	5929.92i	0.497079	−	0.860965i
$363$		0			0
$364$	−19.0274	−	233.389i	−0.00273986	−	0.0336069i
$365$	−1098.60			−0.157544
$366$		0			0
$367$	2400.60	+	4157.96i	0.341445	+	0.591400i	0.984701	−	0.174251i	$-0.0557503\pi$
$367$	2400.60	+	4157.96i	0.341445	+	0.591400i	−0.643256	+	0.765651i	$0.722417\pi$
$368$	−4782.71	−	8283.89i	−0.677488	−	1.17344i
$369$		0			0
$370$	747.976			0.105096
$371$	−494.841	−	6069.69i	−0.0692477	−	0.849387i
$372$		0			0
$373$	−3249.31	+	5627.97i	−0.451053	+	0.781247i	−0.998452	−	0.0556250i	$-0.982285\pi$
$373$	−3249.31	+	5627.97i	−0.451053	+	0.781247i	0.547399	+	0.836872i	$0.315618\pi$
$374$	3211.72	+	5562.85i	0.444048	+	0.769113i
$375$		0			0
$376$	−4454.71	+	7715.78i	−0.610995	+	1.05827i
$377$	2760.73			0.377148
$378$		0			0
$379$	−11049.4			−1.49754			−0.748770	−	0.662830i	$-0.769355\pi$
$379$	−11049.4			−1.49754			−0.748770	+	0.662830i	$0.769355\pi$
$380$	23.9036	−	41.4023i	0.00322692	−	0.00558919i
$381$		0			0
$382$	−7088.21	−	12277.1i	−0.949384	−	1.64438i
$383$	−4049.26	+	7013.53i	−0.540229	+	0.935703i	0.458662	+	0.888611i	$0.348329\pi$
$383$	−4049.26	+	7013.53i	−0.540229	+	0.935703i	−0.998891	+	0.0470925i	$0.985004\pi$
$384$		0			0
$385$	−4151.32	−	1965.80i	−0.549535	−	0.260224i
$386$	9634.66			1.27044
$387$		0			0
$388$	47.0639	+	81.5171i	0.00615801	+	0.0106660i
$389$	2948.71	+	5107.32i	0.384333	+	0.665685i	0.991676	−	0.128755i	$-0.0410981\pi$
$389$	2948.71	+	5107.32i	0.384333	+	0.665685i	−0.607343	+	0.794440i	$0.707765\pi$
$390$		0			0
$391$	7079.27			0.915637
$392$	−4970.80	−	6068.45i	−0.640467	−	0.781895i
$393$		0			0
$394$	−2474.86	+	4286.58i	−0.316451	+	0.548108i
$395$	966.185	+	1673.48i	0.123074	+	0.213170i
$396$		0			0
$397$	5780.71	−	10012.5i	0.730795	−	1.26577i	−0.225749	−	0.974185i	$-0.572483\pi$
$397$	5780.71	−	10012.5i	0.730795	−	1.26577i	0.956544	−	0.291588i	$-0.0941837\pi$
$398$	576.115			0.0725579
$399$		0			0
$400$	−1563.93			−0.195492
$401$	−6534.58	+	11318.2i	−0.813769	+	1.40949i	0.0964391	+	0.995339i	$0.469255\pi$
$401$	−6534.58	+	11318.2i	−0.813769	+	1.40949i	−0.910208	+	0.414151i	$0.864079\pi$
$402$		0			0
$403$	−3704.88	−	6417.05i	−0.457949	−	0.793191i
$404$	116.585	−	201.932i	0.0143573	−	0.0248675i
$405$		0			0
$406$	1641.59	−	1135.03i	0.200667	−	0.138746i
$407$	2652.88			0.323092
$408$		0			0
$409$	219.866	+	380.820i	0.0265812	+	0.0460399i	0.879010	−	0.476803i	$-0.158205\pi$
$409$	219.866	+	380.820i	0.0265812	+	0.0460399i	−0.852429	+	0.522843i	$0.824871\pi$
$410$	283.170	+	490.464i	0.0341091	+	0.0590788i
$411$		0			0
$412$	263.132			0.0314650
$413$	59.7210	+	732.534i	0.00711545	+	0.0872775i
$414$		0			0
$415$	−3442.08	+	5961.86i	−0.407145	+	0.705196i
$416$	−286.040	−	495.436i	−0.0337122	−	0.0583912i
$417$		0			0
$418$	−3759.13	+	6511.01i	−0.439869	+	0.761875i
$419$	−1673.71			−0.195146			−0.0975730	−	0.995228i	$-0.531108\pi$
$419$	−1673.71			−0.195146			−0.0975730	+	0.995228i	$0.531108\pi$
$420$		0			0
$421$	805.413			0.0932385			0.0466192	−	0.998913i	$-0.485155\pi$
$421$	805.413			0.0932385			0.0466192	+	0.998913i	$0.485155\pi$
$422$	−6956.04	+	12048.2i	−0.802405	+	1.38981i
$423$		0			0
$424$	−3760.06	−	6512.61i	−0.430671	−	0.745944i
$425$	578.726	−	1002.38i	0.0660526	−	0.114406i
$426$		0			0
$427$	3008.01	−	2079.81i	0.340909	−	0.235712i
$428$	−77.5506			−0.00875829
$429$		0			0
$430$	−2637.59	−	4568.44i	−0.295805	−	0.512348i
$431$	454.158	+	786.624i	0.0507564	+	0.0879127i	0.890287	−	0.455399i	$-0.150503\pi$
$431$	454.158	+	786.624i	0.0507564	+	0.0879127i	−0.839531	+	0.543312i	$0.817170\pi$
$432$		0			0
$433$	1464.37			0.162524			0.0812621	−	0.996693i	$-0.474105\pi$
$433$	1464.37			0.162524			0.0812621	+	0.996693i	$0.474105\pi$
$434$	−4841.28	−	2292.51i	−0.535458	−	0.253558i
$435$		0			0
$436$	129.078	−	223.570i	0.0141783	−	0.0245575i
$437$	4142.95	+	7175.79i	0.453510	+	0.785503i
$438$		0			0
$439$	3706.93	−	6420.59i	0.403012	−	0.698037i	−0.591076	−	0.806616i	$-0.701297\pi$
$439$	3706.93	−	6420.59i	0.403012	−	0.698037i	0.994088	+	0.108579i	$0.0346300\pi$
$440$	−5672.03			−0.614553
$441$		0			0
$442$	−9279.54			−0.998604
$443$	4328.45	−	7497.10i	0.464223	−	0.804058i	−0.534943	−	0.844888i	$-0.679667\pi$
$443$	4328.45	−	7497.10i	0.464223	−	0.804058i	0.999166	+	0.0408298i	$0.0130002\pi$
$444$		0			0
$445$	1875.14	+	3247.83i	0.199753	+	0.345982i
$446$	−4693.02	+	8128.56i	−0.498254	+	0.863001i
$447$		0			0
$448$	−8750.66	−	4143.74i	−0.922835	−	0.436994i
$449$	−7138.71			−0.750326			−0.375163	−	0.926959i	$-0.622413\pi$
$449$	−7138.71			−0.750326			−0.375163	+	0.926959i	$0.622413\pi$
$450$		0			0
$451$	1004.33	+	1739.55i	0.104860	+	0.181624i
$452$	112.056	+	194.087i	0.0116608	+	0.0201971i
$453$		0			0
$454$	5826.55			0.602320
$455$	5457.98	−	3773.77i	0.562361	−	0.388828i
$456$		0			0
$457$	−4977.80	+	8621.80i	−0.509522	+	0.882518i	0.490417	+	0.871488i	$0.336845\pi$
$457$	−4977.80	+	8621.80i	−0.509522	+	0.882518i	−0.999939	+	0.0110305i	$0.996489\pi$
$458$	7009.09	+	12140.1i	0.715095	+	1.23858i
$459$		0			0
$460$	−67.4490	+	116.825i	−0.00683658	+	0.0118413i
$461$	10380.2			1.04870			0.524351	−	0.851502i	$-0.324308\pi$
$461$	10380.2			1.04870			0.524351	+	0.851502i	$0.324308\pi$
$462$		0			0
$463$	−2851.77			−0.286249			−0.143124	−	0.989705i	$-0.545715\pi$
$463$	−2851.77			−0.286249			−0.143124	+	0.989705i	$0.545715\pi$
$464$	1205.07	−	2087.23i	0.120568	−	0.208831i
$465$		0			0
$466$	1609.21	+	2787.24i	0.159968	+	0.277073i
$467$	−6284.24	+	10884.6i	−0.622698	+	1.07854i	0.366283	+	0.930503i	$0.380630\pi$
$467$	−6284.24	+	10884.6i	−0.622698	+	1.07854i	−0.988981	+	0.148041i	$0.952703\pi$
$468$		0			0
$469$	1463.10	+	17946.3i	0.144051	+	1.76692i
$470$	−5448.22			−0.534697
$471$		0			0
$472$	453.791	+	785.989i	0.0442530	+	0.0766484i
$473$	−9354.86	−	16203.1i	−0.909381	−	1.57509i
$474$		0			0
$475$	1354.73			0.130862
$476$	124.444	−	86.0432i	0.0119829	−	0.00828526i
$477$		0			0
$478$	2684.66	−	4649.98i	0.256891	−	0.444948i
$479$	2769.77	+	4797.38i	0.264204	+	0.457615i	0.967355	−	0.253426i	$-0.0815574\pi$
$479$	2769.77	+	4797.38i	0.264204	+	0.457615i	−0.703151	+	0.711041i	$0.748224\pi$
$480$		0			0
$481$	−1916.23	+	3319.01i	−0.181648	+	0.314623i
$482$	−699.738			−0.0661249
$483$		0			0
$484$	−199.276			−0.0187148
$485$	−1333.67	+	2309.98i	−0.124863	+	0.216270i
$486$		0			0
$487$	5474.94	+	9482.88i	0.509432	+	0.882362i	0.999940	+	0.0109252i	$0.00347768\pi$
$487$	5474.94	+	9482.88i	0.509432	+	0.882362i	−0.490509	+	0.871436i	$0.663189\pi$
$488$	2257.96	−	3910.90i	0.209453	−	0.362783i
$489$		0			0
$490$	1693.91	−	4487.93i	0.156169	−	0.413763i
$491$	−5381.76			−0.494654			−0.247327	−	0.968932i	$-0.579552\pi$
$491$	−5381.76			−0.494654			−0.247327	+	0.968932i	$0.579552\pi$
$492$		0			0
$493$	891.858	+	1544.74i	0.0814752	+	0.141119i
$494$	−5430.59	−	9406.06i	−0.494603	−	0.856678i
$495$		0			0
$496$	−6468.76			−0.585597
$497$	6476.05	+	3066.63i	0.584488	+	0.276775i
$498$		0			0
$499$	−6571.38	+	11382.0i	−0.589530	+	1.02110i	0.404764	+	0.914421i	$0.367354\pi$
$499$	−6571.38	+	11382.0i	−0.589530	+	1.02110i	−0.994294	+	0.106674i	$0.965980\pi$
$500$	11.0278	+	19.1008i	0.000986359	+	0.00170842i
$501$		0			0
$502$	4063.34	−	7037.91i	0.361266	−	0.625731i
$503$	5172.75			0.458532			0.229266	−	0.973364i	$-0.426367\pi$
$503$	5172.75			0.458532			0.229266	+	0.973364i	$0.426367\pi$
$504$		0			0
$505$	6607.45			0.582233
$506$	10607.2	−	18372.2i	0.931910	−	1.61411i
$507$		0			0
$508$	−59.5733	−	103.184i	−0.00520303	−	0.00901191i
$509$	−2743.72	+	4752.27i	−0.238926	+	0.413832i	−0.960406	−	0.278603i	$-0.910129\pi$
$509$	−2743.72	+	4752.27i	−0.238926	+	0.413832i	0.721480	+	0.692435i	$0.243462\pi$
$510$		0			0
$511$	−330.657	−	4055.82i	−0.0286251	−	0.351113i
$512$	−11944.9			−1.03105
$513$		0			0
$514$	2082.83	+	3607.56i	0.178735	+	0.309577i
$515$	3728.23	+	6457.49i	0.319001	+	0.552526i
$516$		0			0
$517$	−19323.5			−1.64380
$518$	225.126	+	2761.38i	0.0190955	+	0.234224i
$519$		0			0
$520$	4097.02	−	7096.25i	0.345512	−	0.598444i
$521$	−4955.64	−	8583.42i	−0.416719	−	0.721778i	0.578889	−	0.815407i	$-0.303487\pi$
$521$	−4955.64	−	8583.42i	−0.416719	−	0.721778i	−0.995607	+	0.0936289i	$0.970153\pi$
$522$		0			0
$523$	−164.483	+	284.893i	−0.0137521	+	0.0238193i	−0.872820	−	0.488043i	$-0.837711\pi$
$523$	−164.483	+	284.893i	−0.0137521	+	0.0238193i	0.859067	+	0.511862i	$0.171044\pi$
$524$	122.617			0.0102224
$525$		0			0
$526$	−9257.88			−0.767420
$527$	2393.74	−	4146.07i	0.197861	−	0.342705i
$528$		0			0
$529$	−5606.68	−	9711.06i	−0.460810	−	0.798147i
$530$	2299.32	−	3982.54i	0.188446	−	0.326397i
$531$		0			0
$532$	160.044	+	75.7862i	0.0130428	+	0.00617622i
$533$	−2901.79			−0.235817
$534$		0			0
$535$	−1098.79	−	1903.16i	−0.0887941	−	0.153796i
$536$	11117.4	+	19255.9i	0.895894	+	1.55173i
$537$		0			0
$538$	−11496.1			−0.921247
$539$	6007.86	−	15917.5i	0.480106	−	1.27202i
$540$		0			0
$541$	5617.73	−	9730.19i	0.446442	−	0.773260i	−0.551709	−	0.834036i	$-0.686024\pi$
$541$	5617.73	−	9730.19i	0.446442	−	0.773260i	0.998151	+	0.0607763i	$0.0193576\pi$
$542$	2417.04	+	4186.44i	0.191552	+	0.331777i
$543$		0			0
$544$	184.811	−	320.103i	0.0145657	−	0.0252285i
$545$	7315.48			0.574974
$546$		0			0
$547$	−19423.1			−1.51823			−0.759115	−	0.650957i	$-0.774368\pi$
$547$	−19423.1			−1.51823			−0.759115	+	0.650957i	$0.774368\pi$
$548$	222.241	−	384.933i	0.0173242	−	0.0300065i
$549$		0			0
$550$	−1734.26	−	3003.83i	−0.134453	−	0.232879i
$551$	−1043.87	+	1808.03i	−0.0807084	+	0.139791i
$552$		0			0
$553$	−5887.36	+	4070.65i	−0.452724	+	0.313023i
$554$	−12721.4			−0.975600
$555$		0			0
$556$	−151.003	−	261.544i	−0.0115179	−	0.0199496i
$557$	6456.19	+	11182.5i	0.491127	+	0.850656i	0.999948	−	0.0102158i	$-0.00325185\pi$
$557$	6456.19	+	11182.5i	0.491127	+	0.850656i	−0.508821	+	0.860872i	$0.669919\pi$
$558$		0			0
$559$	27028.8			2.04508
$560$	−470.713	−	5773.73i	−0.0355201	−	0.435687i
$561$		0			0
$562$	−5288.71	+	9160.32i	−0.396959	+	0.687553i
$563$	2941.92	+	5095.56i	0.220226	+	0.381442i	0.954876	−	0.297003i	$-0.0959872\pi$
$563$	2941.92	+	5095.56i	0.220226	+	0.381442i	−0.734651	+	0.678446i	$0.762654\pi$
$564$		0			0
$565$	−3175.38	+	5499.93i	−0.236441	+	0.409528i
$566$	2668.36			0.198162
$567$		0			0
$568$	8848.35			0.653642
$569$	1518.77	−	2630.59i	0.111899	−	0.193814i	−0.804637	−	0.593767i	$-0.797640\pi$
$569$	1518.77	−	2630.59i	0.111899	−	0.193814i	0.916536	+	0.399953i	$0.130973\pi$
$570$		0			0
$571$	−7842.33	−	13583.3i	−0.574766	−	0.995523i	−0.996067	−	0.0886027i	$-0.971760\pi$
$571$	−7842.33	−	13583.3i	−0.574766	−	0.995523i	0.421301	−	0.906921i	$-0.361573\pi$
$572$	313.577	−	543.131i	0.0229218	−	0.0397018i
$573$		0			0
$574$	−1725.47	+	1193.03i	−0.125470	+	0.0867526i
$575$	−3822.66			−0.277245
$576$		0			0
$577$	8091.99	+	14015.7i	0.583837	+	1.01124i	0.995019	+	0.0996821i	$0.0317826\pi$
$577$	8091.99	+	14015.7i	0.583837	+	1.01124i	−0.411182	+	0.911553i	$0.634884\pi$
$578$	3873.21	+	6708.60i	0.278727	+	0.482770i
$579$		0			0
$580$	−33.9893			−0.00243333
$581$	−23046.0	−	10913.1i	−1.64563	−	0.779262i
$582$		0			0
$583$	8155.11	−	14125.1i	0.579331	−	1.00343i
$584$	−2512.50	−	4351.78i	−0.178028	−	0.308353i
$585$		0			0
$586$	6241.70	−	10810.9i	0.440004	−	0.762108i
$587$	−9256.04			−0.650831			−0.325415	−	0.945571i	$-0.605504\pi$
$587$	−9256.04			−0.650831			−0.325415	+	0.945571i	$0.605504\pi$
$588$		0			0
$589$	5603.46			0.391998
$590$	−277.499	+	480.642i	−0.0193635	+	0.0335385i
$591$		0			0
$592$	1672.88	+	2897.51i	0.116140	+	0.201160i
$593$	9577.26	−	16588.3i	0.663223	−	1.14874i	−0.316541	−	0.948579i	$-0.602522\pi$
$593$	9577.26	−	16588.3i	0.663223	−	1.14874i	0.979764	−	0.200156i	$-0.0641450\pi$
$594$		0			0
$595$	3874.79	+	1834.85i	0.266976	+	0.126422i
$596$	−127.284			−0.00874788
$597$		0			0
$598$	15323.5	+	26541.2i	1.04787	+	1.81496i
$599$	10442.2	+	18086.5i	0.712285	+	1.23371i	0.963997	+	0.265911i	$0.0856728\pi$
$599$	10442.2	+	18086.5i	0.712285	+	1.23371i	−0.251713	+	0.967802i	$0.580994\pi$
$600$		0			0
$601$	−8569.93			−0.581655			−0.290828	−	0.956775i	$-0.593931\pi$
$601$	−8569.93			−0.581655			−0.290828	+	0.956775i	$0.593931\pi$
$602$	16071.9	−	11112.5i	1.08811	−	0.752344i
$603$		0			0
$604$	82.1081	−	142.215i	0.00553134	−	0.00958057i
$605$	−2823.47	−	4890.40i	−0.189736	−	0.328633i
$606$		0			0
$607$	9680.48	−	16767.1i	0.647313	−	1.12118i	−0.336450	−	0.941701i	$-0.609226\pi$
$607$	9680.48	−	16767.1i	0.647313	−	1.12118i	0.983762	−	0.179477i	$-0.0574405\pi$
$608$	432.622			0.0288572
$609$		0			0
$610$	2761.54			0.183298
$611$	13957.7	−	24175.5i	0.924172	−	1.60071i
$612$		0			0
$613$	7953.59	+	13776.0i	0.524050	+	0.907680i	0.999608	+	0.0279963i	$0.00891268\pi$
$613$	7953.59	+	13776.0i	0.524050	+	0.907680i	−0.475558	+	0.879684i	$0.657754\pi$
$614$	−9254.75	+	16029.7i	−0.608292	+	1.05359i
$615$		0			0
$616$	−1707.17	−	20940.0i	−0.111662	−	1.36964i
$617$	−17496.4			−1.14162			−0.570810	−	0.821082i	$-0.693371\pi$
$617$	−17496.4			−1.14162			−0.570810	+	0.821082i	$0.693371\pi$
$618$		0			0
$619$	−11454.3	−	19839.4i	−0.743758	−	1.28823i	−0.950773	−	0.309889i	$-0.899708\pi$
$619$	−11454.3	−	19839.4i	−0.743758	−	1.28823i	0.207014	−	0.978338i	$-0.433625\pi$
$620$	45.6135	+	79.0049i	0.00295465	+	0.00511760i
$621$		0			0
$622$	−471.482			−0.0303934
$623$	−11426.0	+	7900.17i	−0.734786	+	0.508047i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−10491.6	−	18172.0i	−0.669853	−	1.16022i
$627$		0			0
$628$	199.971	−	346.359i	0.0127065	−	0.0220083i
$629$	−2476.16			−0.156965
$630$		0			0
$631$	27379.1			1.72733			0.863665	−	0.504066i	$-0.168163\pi$
$631$	27379.1			1.72733			0.863665	+	0.504066i	$0.168163\pi$
$632$	−4419.34	+	7654.51i	−0.278151	+	0.481772i
$633$		0			0
$634$	4790.19	+	8296.85i	0.300067	+	0.519732i
$635$	1688.15	−	2923.97i	0.105500	−	0.182731i
$636$		0			0
$637$	15574.7	+	19014.0i	0.968750	+	1.18267i
$638$	5345.23			0.331692
$639$		0			0
$640$	−3496.01	−	6055.27i	−0.215925	−	0.373993i
$641$	−4408.05	−	7634.97i	−0.271619	−	0.470457i	0.697658	−	0.716431i	$-0.254226\pi$
$641$	−4408.05	−	7634.97i	−0.271619	−	0.470457i	−0.969276	+	0.245974i	$0.920892\pi$
$642$		0			0
$643$	25760.8			1.57995			0.789975	−	0.613139i	$-0.210094\pi$
$643$	25760.8			1.57995			0.789975	+	0.613139i	$0.210094\pi$
$644$	−451.596	−	213.847i	−0.0276326	−	0.0130850i
$645$		0			0
$646$	3508.72	−	6077.28i	0.213698	−	0.370135i
$647$	−10809.1	−	18721.8i	−0.656797	−	1.13761i	−0.981440	−	0.191769i	$-0.938577\pi$
$647$	−10809.1	−	18721.8i	−0.656797	−	1.13761i	0.324643	−	0.945837i	$-0.394756\pi$
$648$		0			0
$649$	−984.217	+	1704.71i	−0.0595284	+	0.103106i
$650$	5010.76			0.302366
$651$		0			0
$652$	−563.619			−0.0338543
$653$	−12504.1	+	21657.8i	−0.749349	+	1.29791i	0.198786	+	0.980043i	$0.436300\pi$
$653$	−12504.1	+	21657.8i	−0.749349	+	1.29791i	−0.948135	+	0.317867i	$0.897033\pi$
$654$		0			0
$655$	1737.32	+	3009.13i	0.103638	+	0.179506i
$656$	−1266.64	+	2193.88i	−0.0753871	+	0.130574i
$657$		0			0
$658$	−1639.81	−	20113.8i	−0.0971526	−	1.19167i
$659$	29424.3			1.73932			0.869658	−	0.493655i	$-0.164340\pi$
$659$	29424.3			1.73932			0.869658	+	0.493655i	$0.164340\pi$
$660$		0			0
$661$	10511.2	+	18205.9i	0.618513	+	1.07130i	0.989757	+	0.142761i	$0.0455981\pi$
$661$	10511.2	+	18205.9i	0.618513	+	1.07130i	−0.371244	+	0.928535i	$0.621069\pi$
$662$	−1532.05	−	2653.59i	−0.0899470	−	0.155793i
$663$		0			0
$664$	−31488.2			−1.84033
$665$	407.748	+	5001.41i	0.0237771	+	0.291648i
$666$		0			0
$667$	2945.49	−	5101.75i	0.170989	−	0.296162i
$668$	53.9110	+	93.3767i	0.00312258	+	0.00540846i
$669$		0			0
$670$	−6798.44	+	11775.2i	−0.392010	+	0.678981i
$671$	9794.48			0.563504
$672$		0			0
$673$	5241.08			0.300192			0.150096	−	0.988671i	$-0.452042\pi$
$673$	5241.08			0.300192			0.150096	+	0.988671i	$0.452042\pi$
$674$	−5932.45	+	10275.3i	−0.339035	+	0.587225i
$675$		0			0
$676$	259.180	+	448.913i	0.0147463	+	0.0255413i
$677$	2674.13	−	4631.73i	0.151810	−	0.262942i	−0.780083	−	0.625676i	$-0.784823\pi$
$677$	2674.13	−	4631.73i	0.151810	−	0.262942i	0.931893	+	0.362734i	$0.118157\pi$
$678$		0			0
$679$	−8929.40	−	4228.38i	−0.504682	−	0.238984i
$680$	5294.19			0.298563
$681$		0			0
$682$	−7173.27	−	12424.5i	−0.402755	−	0.697591i
$683$	8987.22	+	15566.3i	0.503494	+	0.872077i	0.999992	+	0.00403932i	$0.00128576\pi$
$683$	8987.22	+	15566.3i	0.503494	+	0.872077i	−0.496498	+	0.868038i	$0.665381\pi$
$684$		0			0
$685$	12595.5			0.702553
$686$	17078.4	+	4902.80i	0.950519	+	0.272871i
$687$		0			0
$688$	11798.1	−	20435.0i	0.653779	−	1.13238i
$689$	11781.2	+	20405.6i	0.651419	+	1.12829i
$690$		0			0
$691$	−11867.0	+	20554.3i	−0.653319	+	1.13158i	0.328994	+	0.944332i	$0.393290\pi$
$691$	−11867.0	+	20554.3i	−0.653319	+	1.13158i	−0.982312	+	0.187249i	$0.940043\pi$
$692$	1.55470			8.54056e−5
$693$		0			0
$694$	−218.638			−0.0119587
$695$	4279.02	−	7411.49i	0.233543	−	0.404509i
$696$		0			0
$697$	−937.427	−	1623.67i	−0.0509435	−	0.0882367i
$698$	234.736	−	406.575i	0.0127291	−	0.0220474i
$699$		0			0
$700$	−67.1971	+	46.4615i	−0.00362830	+	0.00250869i
$701$	31094.0			1.67533			0.837664	−	0.546186i	$-0.183921\pi$
$701$	31094.0			1.67533			0.837664	+	0.546186i	$0.183921\pi$
$702$		0			0
$703$	−1449.10	−	2509.92i	−0.0777439	−	0.134656i
$704$	−12965.8	−	22457.4i	−0.694128	−	1.20226i
$705$		0			0
$706$	13629.6			0.726566
$707$	1988.71	+	24393.4i	0.105790	+	1.29761i
$708$		0			0
$709$	4526.97	−	7840.94i	0.239794	−	0.415335i	−0.720861	−	0.693080i	$-0.756253\pi$
$709$	4526.97	−	7840.94i	0.239794	−	0.415335i	0.960655	+	0.277744i	$0.0895868\pi$
$710$	2705.44	+	4685.96i	0.143005	+	0.247691i
$711$		0			0
$712$	−8576.88	+	14855.6i	−0.451450	+	0.781934i
$713$	−15811.3			−0.830490
$714$		0			0
$715$	17771.9			0.929554
$716$	110.292	−	191.032i	0.00575673	−	0.00997095i
$717$		0			0
$718$	11816.9	+	20467.5i	0.614211	+	1.06385i
$719$	−550.907	+	954.198i	−0.0285749	+	0.0494932i	−0.879959	−	0.475049i	$-0.842430\pi$
$719$	−550.907	+	954.198i	−0.0285749	+	0.0494932i	0.851384	+	0.524542i	$0.175764\pi$
$720$		0			0
$721$	−22717.6	+	15707.5i	−1.17344	+	0.811341i
$722$	−10971.5			−0.565537
$723$		0			0
$724$	−215.971	−	374.073i	−0.0110863	−	0.0192021i
$725$	−481.585	−	834.129i	−0.0246698	−	0.0427293i
$726$		0			0
$727$	−6476.47			−0.330397			−0.165199	−	0.986260i	$-0.552827\pi$
$727$	−6476.47			−0.330397			−0.165199	+	0.986260i	$0.552827\pi$
$728$	27431.1	+	12989.6i	1.39652	+	0.661298i
$729$		0			0
$730$	1536.43	−	2661.17i	0.0778983	−	0.134924i
$731$	8731.69	+	15123.7i	0.441797	+	0.765214i
$732$		0			0
$733$	8055.97	−	13953.4i	0.405940	−	0.703109i	−0.588490	−	0.808504i	$-0.700277\pi$
$733$	8055.97	−	13953.4i	0.405940	−	0.703109i	0.994430	+	0.105395i	$0.0336108\pi$
$734$	−13429.3			−0.675317
$735$		0			0
$736$	−1220.73			−0.0611370
$737$	−24112.3	+	41763.8i	−1.20514	+	2.08737i
$738$		0			0
$739$	4586.13	+	7943.42i	0.228286	+	0.395404i	0.957300	−	0.289095i	$-0.0933544\pi$
$739$	4586.13	+	7943.42i	0.228286	+	0.395404i	−0.729014	+	0.684499i	$0.760021\pi$
$740$	23.5921	−	40.8627i	0.00117198	−	0.00202992i
$741$		0			0
$742$	15394.8	+	7289.98i	0.761673	+	0.360679i
$743$	−3249.07			−0.160426			−0.0802131	−	0.996778i	$-0.525560\pi$
$743$	−3249.07			−0.160426			−0.0802131	+	0.996778i	$0.525560\pi$
$744$		0			0
$745$	−1803.44	−	3123.65i	−0.0886886	−	0.153613i
$746$	−9088.52	−	15741.8i	−0.446051	−	0.772584i
$747$		0			0
$748$	405.205			0.0198072
$749$	6695.38	−	4629.33i	0.326627	−	0.225837i
$750$		0			0
$751$	12095.8	−	20950.5i	0.587726	−	1.01797i	−0.406804	−	0.913515i	$-0.633357\pi$
$751$	12095.8	−	20950.5i	0.587726	−	1.01797i	0.994530	−	0.104455i	$-0.0333099\pi$
$752$	−12185.2	−	21105.3i	−0.590887	−	1.02345i
$753$		0			0
$754$	−3860.97	+	6687.39i	−0.186483	+	0.322998i
$755$	4653.46			0.224313
$756$		0			0
$757$	−21282.7			−1.02184			−0.510919	−	0.859629i	$-0.670695\pi$
$757$	−21282.7			−1.02184			−0.510919	+	0.859629i	$0.670695\pi$
$758$	15452.9	−	26765.2i	0.740467	−	1.28253i
$759$		0			0
$760$	3098.28	+	5366.37i	0.147877	+	0.256130i
$761$	16112.2	−	27907.2i	0.767501	−	1.32935i	−0.171413	−	0.985199i	$-0.554833\pi$
$761$	16112.2	−	27907.2i	0.767501	−	1.32935i	0.938914	−	0.344152i	$-0.111834\pi$
$762$		0			0
$763$	2201.82	+	27007.3i	0.104471	+	1.28143i
$764$	−894.283			−0.0423482
$765$		0			0
$766$	−11326.0	−	19617.3i	−0.534238	−	0.925327i
$767$	−1421.84	−	2462.70i	−0.0669357	−	0.115936i
$768$		0			0
$769$	−25116.5			−1.17780			−0.588898	−	0.808208i	$-0.700438\pi$
$769$	−25116.5			−1.17780			−0.588898	+	0.808208i	$0.700438\pi$
$770$	10567.6	−	7306.64i	0.494582	−	0.341965i
$771$		0			0
$772$	303.889	−	526.350i	0.0141673	−	0.0245386i
$773$	−5912.37	−	10240.5i	−0.275101	−	0.476489i	0.695060	−	0.718952i	$-0.255378\pi$
$773$	−5912.37	−	10240.5i	−0.275101	−	0.476489i	−0.970161	+	0.242463i	$0.922045\pi$
$774$		0			0
$775$	−1292.57	+	2238.79i	−0.0599102	+	0.103767i
$776$	−12200.4			−0.564393
$777$		0			0
$778$	−16495.5			−0.760142
$779$	1097.21	−	1900.42i	0.0504640	−	0.0874063i
$780$		0			0
$781$	9595.50	+	16619.9i	0.439634	+	0.761468i
$782$	−9900.58	+	17148.3i	−0.452742	+	0.784172i
$783$		0			0
$784$	21173.8	−	3475.56i	0.964550	−	0.158325i
$785$	11333.3			0.515289
$786$		0			0
$787$	10145.5	+	17572.5i	0.459527	+	0.795923i	0.998936	−	0.0461203i	$-0.0146858\pi$
$787$	10145.5	+	17572.5i	0.459527	+	0.795923i	−0.539409	+	0.842044i	$0.681352\pi$
$788$	156.120	+	270.408i	0.00705779	+	0.0122245i
$789$		0			0
$790$	−5404.96			−0.243417
$791$	−21260.4	−	10067.5i	−0.955666	−	0.452541i
$792$		0			0
$793$	−7074.74	+	12253.8i	−0.316812	+	0.548734i
$794$	16169.0	+	28005.5i	0.722691	+	1.25174i
$795$		0			0
$796$	18.1714	−	31.4737i	0.000809129	−	0.00140145i
$797$	37140.0			1.65065			0.825325	−	0.564658i	$-0.190992\pi$
$797$	37140.0			1.65065			0.825325	+	0.564658i	$0.190992\pi$
$798$		0			0
$799$	18036.2			0.798594
$800$	−99.7942	+	172.849i	−0.00441032	+	0.00763890i
$801$		0			0
$802$	−18277.6	−	31657.8i	−0.804745	−	1.39386i
$803$	5449.32	−	9438.49i	0.239480	−	0.414791i
$804$		0			0
$805$	−1150.55	−	14112.5i	−0.0503744	−	0.617889i
$806$	20725.6			0.905741
$807$		0			0
$808$	15111.3	+	26173.5i	0.657936	+	1.13958i
$809$	−1917.48	−	3321.17i	−0.0833311	−	0.144334i	0.821348	−	0.570428i	$-0.193223\pi$
$809$	−1917.48	−	3321.17i	−0.0833311	−	0.144334i	−0.904679	+	0.426094i	$0.859889\pi$
$810$		0			0
$811$	−19628.9			−0.849894			−0.424947	−	0.905218i	$-0.639707\pi$
$811$	−19628.9			−0.849894			−0.424947	+	0.905218i	$0.639707\pi$
$812$	−10.2301	−	125.482i	−0.000442127	−	0.00542310i
$813$		0			0
$814$	−3710.14	+	6426.14i	−0.159755	+	0.276703i
$815$	−7985.74	−	13831.7i	−0.343225	−	0.594483i
$816$		0			0
$817$	−10220.0	+	17701.5i	−0.437639	+	0.758013i
$818$	−1229.96			−0.0525728
$819$		0			0
$820$	35.7260			0.00152147
$821$	−6112.71	+	10587.5i	−0.259848	+	0.450070i	−0.966201	−	0.257790i	$-0.917006\pi$
$821$	−6112.71	+	10587.5i	−0.259848	+	0.450070i	0.706353	+	0.707860i	$0.250339\pi$
$822$		0			0
$823$	−12547.2	−	21732.4i	−0.531431	−	0.920465i	−0.999327	−	0.0366818i	$-0.988321\pi$
$823$	−12547.2	−	21732.4i	−0.531431	−	0.920465i	0.467896	−	0.883783i	$-0.345012\pi$
$824$	−17052.9	+	29536.6i	−0.720956	+	1.24873i
$825$		0			0
$826$	−1857.96	−	879.807i	−0.0782647	−	0.0370610i
$827$	−36846.0			−1.54929			−0.774644	−	0.632397i	$-0.782071\pi$
$827$	−36846.0			−1.54929			−0.774644	+	0.632397i	$0.782071\pi$
$828$		0			0
$829$	17563.0	+	30420.1i	0.735814	+	1.27447i	0.954365	+	0.298642i	$0.0965336\pi$
$829$	17563.0	+	30420.1i	0.735814	+	1.27447i	−0.218551	+	0.975825i	$0.570133\pi$
$830$	−9627.71	−	16675.7i	−0.402630	−	0.697375i
$831$		0			0
$832$	37461.7			1.56100
$833$	−5607.65	+	14857.2i	−0.233246	+	0.617973i
$834$		0			0
$835$	−1527.70	+	2646.05i	−0.0633152	+	0.109665i
$836$	237.135	+	410.730i	0.00981039	+	0.0169921i
$837$		0			0
$838$	2340.74	−	4054.28i	0.0964910	−	0.167127i
$839$	−20946.7			−0.861931			−0.430965	−	0.902368i	$-0.641827\pi$
$839$	−20946.7			−0.861931			−0.430965	+	0.902368i	$0.641827\pi$
$840$		0			0
$841$	−22904.7			−0.939140
$842$	−1126.39	+	1950.97i	−0.0461023	+	0.0798515i
$843$		0			0
$844$	438.804	+	760.030i	0.0178960	+	0.0309968i
$845$	−7344.49	+	12721.0i	−0.299004	+	0.517889i
$846$		0			0
$847$	17204.6	−	11895.6i	0.697942	−	0.482572i
$848$	20570.1			0.832994
$849$		0			0
$850$	1618.73	+	2803.73i	0.0653201	+	0.113138i
$851$	4088.95	+	7082.26i	0.164709	+	0.285284i
$852$		0			0
$853$	−30591.5			−1.22794			−0.613969	−	0.789330i	$-0.710428\pi$
$853$	−30591.5			−1.22794			−0.613969	+	0.789330i	$0.710428\pi$
$854$	831.169	+	10195.1i	0.0333045	+	0.408510i
$855$		0			0
$856$	5025.87	−	8705.06i	0.200678	−	0.347585i
$857$	−3242.25	−	5615.74i	−0.129233	−	0.223839i	0.794146	−	0.607727i	$-0.207918\pi$
$857$	−3242.25	−	5615.74i	−0.129233	−	0.223839i	−0.923380	+	0.383888i	$0.874585\pi$
$858$		0			0
$859$	21799.0	−	37756.9i	0.865857	−	1.49971i	−0.000336687	−	1.00000i	$-0.500107\pi$
$859$	21799.0	−	37756.9i	0.865857	−	1.49971i	0.866194	−	0.499708i	$-0.166559\pi$
$860$	−332.771			−0.0131947
$861$		0			0
$862$	−2540.61			−0.100387
$863$	−2701.47	+	4679.09i	−0.106558	+	0.184563i	−0.914373	−	0.404872i	$-0.867316\pi$
$863$	−2701.47	+	4679.09i	−0.106558	+	0.184563i	0.807816	+	0.589435i	$0.200650\pi$
$864$		0			0
$865$	22.0280	+	38.1537i	0.000865867	+	0.00149973i
$866$	−2047.96	+	3547.18i	−0.0803610	+	0.139189i
$867$		0			0
$868$	−277.942	+	192.175i	−0.0108686	+	0.00751480i
$869$	−19170.0			−0.748329
$870$		0			0
$871$	−34833.6	−	60333.6i	−1.35510	−	2.34710i
$872$	16730.5	+	28978.1i	0.649733	+	1.12537i
$873$		0			0
$874$	−23176.1			−0.896962
$875$	−2092.30	−	990.778i	−0.0808374	−	0.0382793i
$876$		0			0
$877$	−24490.9	+	42419.5i	−0.942987	+	1.63330i	−0.183254	+	0.983066i	$0.558663\pi$
$877$	−24490.9	+	42419.5i	−0.942987	+	1.63330i	−0.759733	+	0.650235i	$0.774670\pi$
$878$	10368.5	+	17958.8i	0.398543	+	0.690296i
$879$		0			0
$880$	7757.47	−	13436.3i	0.297164	−	0.514703i
$881$	−13125.8			−0.501952			−0.250976	−	0.967993i	$-0.580752\pi$
$881$	−13125.8			−0.501952			−0.250976	+	0.967993i	$0.580752\pi$
$882$		0			0
$883$	−7496.22			−0.285694			−0.142847	−	0.989745i	$-0.545626\pi$
$883$	−7496.22			−0.285694			−0.142847	+	0.989745i	$0.545626\pi$
$884$	−292.688	+	506.950i	−0.0111359	+	0.0192880i
$885$		0			0
$886$	12106.9	+	20969.8i	0.459075	+	0.795142i
$887$	23013.9	−	39861.2i	0.871173	−	1.50892i	0.0103881	−	0.999946i	$-0.496693\pi$
$887$	23013.9	−	39861.2i	0.871173	−	1.50892i	0.860785	−	0.508969i	$-0.169973\pi$
$888$		0			0
$889$	11302.8	+	5352.27i	0.426416	+	0.201923i
$890$	−10489.7			−0.395075
$891$		0			0
$892$	296.047	+	512.769i	0.0111125	+	0.0192475i
$893$	10555.2	+	18282.1i	0.395539	+	0.685094i
$894$		0			0
$895$	6250.80			0.233454
$896$	21302.6	−	14729.1i	0.794276	−	0.549179i
$897$		0			0
$898$	9983.71	−	17292.3i	0.371003	−	0.642596i
$899$	−1991.94	−	3450.14i	−0.0738986	−	0.127996i
$900$		0			0
$901$	−7611.86	+	13184.1i	−0.281452	+	0.487488i
$902$	−5618.35			−0.207395
$903$		0			0
$904$	−29048.4			−1.06874
$905$	6120.06	−	10600.3i	0.224793	−	0.389353i
$906$		0			0
$907$	−5884.68	−	10192.6i	−0.215433	−	0.373141i	0.737974	−	0.674830i	$-0.235783\pi$
$907$	−5884.68	−	10192.6i	−0.215433	−	0.373141i	−0.953406	+	0.301689i	$0.902450\pi$
$908$	183.776	−	318.310i	0.00671677	−	0.0116338i
$909$		0			0
$910$	1508.14	+	18498.7i	0.0549389	+	0.673876i
$911$	−4591.84			−0.166997			−0.0834986	−	0.996508i	$-0.526609\pi$
$911$	−4591.84			−0.166997			−0.0834986	+	0.996508i	$0.526609\pi$
$912$		0			0
$913$	−34147.0	−	59144.4i	−1.23779	−	2.14391i
$914$	−13923.2	−	24115.7i	−0.503872	−	0.872732i
$915$		0			0
$916$	884.301			0.0318975
$917$	−10586.2	+	7319.54i	−0.381230	+	0.263591i
$918$		0			0
$919$	−2722.20	+	4714.99i	−0.0977118	+	0.169242i	−0.910737	−	0.412987i	$-0.864486\pi$
$919$	−2722.20	+	4714.99i	−0.0977118	+	0.169242i	0.813025	+	0.582228i	$0.197819\pi$
$920$	−8742.43	−	15142.3i	−0.313293	−	0.542639i
$921$		0			0
$922$	−14517.0	+	25144.1i	−0.518537	+	0.898132i
$923$	−27724.1			−0.988677
$924$		0			0
$925$	1337.08			0.0475273
$926$	3988.29	−	6907.92i	0.141537	−	0.245149i
$927$		0			0
$928$	−153.790	−	266.372i	−0.00544009	−	0.00942251i
$929$	11057.2	−	19151.7i	0.390502	−	0.676369i	−0.602014	−	0.798486i	$-0.705635\pi$
$929$	11057.2	−	19151.7i	0.390502	−	0.676369i	0.992516	+	0.122117i	$0.0389682\pi$
$930$		0			0
$931$	−18341.5	+	3010.65i	−0.645669	+	0.105983i
$932$	203.026			0.00713555
$933$		0			0
$934$	−17577.4	−	30445.0i	−0.615793	−	1.06658i
$935$	5741.23	+	9944.10i	0.200811	+	0.347815i
$936$		0			0
$937$	−38332.7			−1.33647			−0.668236	−	0.743949i	$-0.732950\pi$
$937$	−38332.7			−1.33647			−0.668236	+	0.743949i	$0.732950\pi$
$938$	−45518.1	−	21554.4i	−1.58445	−	0.750294i
$939$		0			0
$940$	−171.843	+	297.642i	−0.00596268	+	0.0103277i
$941$	−20670.3	−	35802.1i	−0.716082	−	1.24029i	−0.962541	−	0.271137i	$-0.912600\pi$
$941$	−20670.3	−	35802.1i	−0.716082	−	1.24029i	0.246458	−	0.969153i	$-0.420733\pi$
$942$		0			0
$943$	−3095.99	+	5362.42i	−0.106914	+	0.185180i
$944$	−2482.54			−0.0855932
$945$		0			0
$946$	52332.3			1.79859
$947$	−2208.67	+	3825.53i	−0.0757889	+	0.131270i	−0.901429	−	0.432927i	$-0.857481\pi$
$947$	−2208.67	+	3825.53i	−0.0757889	+	0.131270i	0.825640	+	0.564197i	$0.190814\pi$
$948$		0			0
$949$	7872.30	+	13635.2i	0.269279	+	0.466405i
$950$	−1894.64	+	3281.60i	−0.0647054	+	0.112073i
$951$		0			0
$952$	1593.45	+	19545.1i	0.0542478	+	0.665400i
$953$	1981.88			0.0673656			0.0336828	−	0.999433i	$-0.489276\pi$
$953$	1981.88			0.0673656			0.0336828	+	0.999433i	$0.489276\pi$
$954$		0			0
$955$	−12670.8	−	21946.5i	−0.429338	−	0.743636i
$956$	−169.355	−	293.332i	−0.00572943	−	0.00992366i
$957$		0			0
$958$	−15494.4			−0.522549
$959$	3790.99	+	46500.0i	0.127651	+	1.56576i
$960$		0			0
$961$	9549.17	−	16539.6i	0.320539	−	0.555189i
$962$	−5359.81	−	9283.46i	−0.179633	−	0.311134i
$963$		0			0
$964$	−22.0706	+	38.2274i	−0.000737392	+	0.00127720i
$965$	17222.8			0.574531
$966$		0			0
$967$	12406.6			0.412586			0.206293	−	0.978490i	$-0.433860\pi$
$967$	12406.6			0.412586			0.206293	+	0.978490i	$0.433860\pi$
$968$	12914.6	−	22368.7i	0.428812	−	0.742725i
$969$		0			0
$970$	−3730.35	−	6461.16i	−0.123479	−	0.213871i
$971$	−11095.6	+	19218.1i	−0.366709	+	0.635159i	−0.989049	−	0.147589i	$-0.952849\pi$
$971$	−11095.6	+	19218.1i	−0.366709	+	0.635159i	0.622340	+	0.782747i	$0.286182\pi$
$972$		0			0
$973$	28649.7	+	13566.6i	0.943952	+	0.446994i
$974$	−30627.5			−1.00756
$975$		0			0
$976$	6176.28	+	10697.6i	0.202559	+	0.350843i
$977$	−650.409	−	1126.54i	−0.0212983	−	0.0368897i	0.855180	−	0.518331i	$-0.173447\pi$
$977$	−650.409	−	1126.54i	−0.0212983	−	0.0368897i	−0.876478	+	0.481442i	$0.840113\pi$
$978$		0			0
$979$	−37204.4			−1.21456
$980$	−191.752	−	234.095i	−0.00625030	−	0.00763048i
$981$		0			0
$982$	7526.55	−	13036.4i	0.244584	−	0.423633i
$983$	−19449.8	−	33688.1i	−0.631082	−	1.09307i	−0.987331	−	0.158675i	$-0.949278\pi$
$983$	−19449.8	−	33688.1i	−0.631082	−	1.09307i	0.356249	−	0.934391i	$-0.384055\pi$
$984$		0			0
$985$	−4424.03	+	7662.65i	−0.143108	+	0.247870i
$986$	−4989.16			−0.161143
$987$		0			0
$988$	−685.149			−0.0220623
$989$	28837.7	−	49948.4i	0.927185	−	1.60593i
$990$		0			0
$991$	1356.61	+	2349.72i	0.0434856	+	0.0753192i	0.886949	−	0.461867i	$-0.152820\pi$
$991$	1356.61	+	2349.72i	0.0434856	+	0.0753192i	−0.843463	+	0.537187i	$0.819487\pi$
$992$	−412.770	+	714.939i	−0.0132112	+	0.0228824i
$993$		0			0
$994$	−16485.3	+	11398.3i	−0.526040	+	0.363715i
$995$	1029.86			0.0328127
$996$		0			0
$997$	−25524.1	−	44209.0i	−0.810788	−	1.40433i	−0.912313	−	0.409493i	$-0.865706\pi$
$997$	−25524.1	−	44209.0i	−0.810788	−	1.40433i	0.101526	−	0.994833i	$-0.467628\pi$
$998$	−18380.6	−	31836.0i	−0.582992	−	1.00977i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.4.j.g.226.2		10
3.2	odd	2		35.4.e.c.16.4	yes	10
7.2	even	3		2205.4.a.bu.1.4		5
7.4	even	3	inner	315.4.j.g.46.2		10
7.5	odd	6		2205.4.a.bt.1.4		5
12.11	even	2		560.4.q.n.401.5		10
15.2	even	4		175.4.k.d.149.7		20
15.8	even	4		175.4.k.d.149.4		20
15.14	odd	2		175.4.e.d.51.2		10
21.2	odd	6		245.4.a.m.1.2		5
21.5	even	6		245.4.a.n.1.2		5
21.11	odd	6		35.4.e.c.11.4	✓	10
21.17	even	6		245.4.e.o.116.4		10
21.20	even	2		245.4.e.o.226.4		10
84.11	even	6		560.4.q.n.81.5		10
105.32	even	12		175.4.k.d.74.4		20
105.44	odd	6		1225.4.a.bg.1.4		5
105.53	even	12		175.4.k.d.74.7		20
105.74	odd	6		175.4.e.d.151.2		10
105.89	even	6		1225.4.a.bf.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.c.11.4	✓	10	21.11	odd	6
35.4.e.c.16.4	yes	10	3.2	odd	2
175.4.e.d.51.2		10	15.14	odd	2
175.4.e.d.151.2		10	105.74	odd	6
175.4.k.d.74.4		20	105.32	even	12
175.4.k.d.74.7		20	105.53	even	12
175.4.k.d.149.4		20	15.8	even	4
175.4.k.d.149.7		20	15.2	even	4
245.4.a.m.1.2		5	21.2	odd	6
245.4.a.n.1.2		5	21.5	even	6
245.4.e.o.116.4		10	21.17	even	6
245.4.e.o.226.4		10	21.20	even	2
315.4.j.g.46.2		10	7.4	even	3	inner
315.4.j.g.226.2		10	1.1	even	1	trivial
560.4.q.n.81.5		10	84.11	even	6
560.4.q.n.401.5		10	12.11	even	2
1225.4.a.bf.1.4		5	105.89	even	6
1225.4.a.bg.1.4		5	105.44	odd	6
2205.4.a.bt.1.4		5	7.5	odd	6
2205.4.a.bu.1.4		5	7.2	even	3

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	315.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39853 + 2.42233i) q^{2} +(0.0882227 + 0.152806i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-16.7384 - 7.92622i) q^{7} -22.8700 q^{8} +O(q^{10})\)	\(q+(-1.39853 + 2.42233i) q^{2} +(0.0882227 + 0.152806i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-16.7384 - 7.92622i) q^{7} -22.8700 q^{8} +(-6.99265 - 12.1116i) q^{10} +(-24.8012 - 42.9569i) q^{11} +71.6575 q^{13} +(42.6091 - 29.4609i) q^{14} +(31.2787 - 54.1762i) q^{16} +(23.1490 + 40.0953i) q^{17} +(-27.0947 + 46.9293i) q^{19} -0.882227 q^{20} +138.741 q^{22} +(76.4532 - 132.421i) q^{23} +(-12.5000 - 21.6506i) q^{25} +(-100.215 + 173.578i) q^{26} +(-0.265533 - 3.25701i) q^{28} +38.5268 q^{29} +(-51.7027 - 89.5517i) q^{31} +(-3.99177 - 6.91395i) q^{32} -129.499 q^{34} +(76.1676 - 52.6640i) q^{35} +(-26.7415 + 46.3176i) q^{37} +(-75.7854 - 131.264i) q^{38} +(57.1751 - 99.0301i) q^{40} -40.4953 q^{41} +377.195 q^{43} +(4.37605 - 7.57954i) q^{44} +(213.844 + 370.389i) q^{46} +(194.784 - 337.375i) q^{47} +(217.350 + 265.345i) q^{49} +69.9265 q^{50} +(6.32181 + 10.9497i) q^{52} +(164.410 + 284.766i) q^{53} +248.012 q^{55} +(382.808 + 181.273i) q^{56} +(-53.8809 + 93.3244i) q^{58} +(-19.8422 - 34.3676i) q^{59} +(-98.7300 + 171.005i) q^{61} +289.231 q^{62} +522.789 q^{64} +(-179.144 + 310.286i) q^{65} +(-486.113 - 841.972i) q^{67} +(-4.08454 + 7.07463i) q^{68} +(21.0465 + 258.155i) q^{70} -386.897 q^{71} +(109.860 + 190.283i) q^{73} +(-74.7976 - 129.553i) q^{74} -9.56145 q^{76} +(74.6466 + 915.610i) q^{77} +(193.237 - 334.696i) q^{79} +(156.393 + 270.881i) q^{80} +(56.6339 - 98.0928i) q^{82} +1376.83 q^{83} -231.490 q^{85} +(-527.518 + 913.688i) q^{86} +(567.203 + 982.424i) q^{88} +(375.027 - 649.566i) q^{89} +(-1199.43 - 567.973i) q^{91} +26.9796 q^{92} +(544.822 + 943.660i) q^{94} +(-135.473 - 234.647i) q^{95} +533.467 q^{97} +(-946.723 + 155.399i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - 35 q^{4} - 25 q^{5} - 62 q^{7} - 66 q^{8}+O(q^{10}) \) 10 * q + q^2 - 35 * q^4 - 25 * q^5 - 62 * q^7 - 66 * q^8	\( 10 q + q^{2} - 35 q^{4} - 25 q^{5} - 62 q^{7} - 66 q^{8} + 5 q^{10} + 47 q^{11} + 2 q^{13} - 7 q^{14} - 171 q^{16} - 2 q^{17} + 21 q^{19} + 350 q^{20} + 1046 q^{22} + 201 q^{23} - 125 q^{25} - 47 q^{26} + 597 q^{28} - 380 q^{29} - 388 q^{31} - 95 q^{32} + 260 q^{34} + 95 q^{35} + 145 q^{37} + 835 q^{38} + 165 q^{40} + 562 q^{41} + 1136 q^{43} + 1091 q^{44} - 337 q^{46} - 473 q^{47} + 998 q^{49} - 50 q^{50} + 379 q^{52} + 351 q^{53} - 470 q^{55} + 1338 q^{56} - 1818 q^{58} + 708 q^{59} - 1944 q^{61} - 896 q^{62} - 250 q^{64} - 5 q^{65} - 1118 q^{67} - 3118 q^{68} + 865 q^{70} - 1728 q^{71} + 1652 q^{73} - 3285 q^{74} + 1382 q^{76} - 787 q^{77} - 218 q^{79} - 855 q^{80} - 1027 q^{82} + 3004 q^{83} + 20 q^{85} - 4264 q^{86} - 2131 q^{88} + 2322 q^{89} + 524 q^{91} + 5914 q^{92} + 2677 q^{94} + 105 q^{95} + 1196 q^{97} - 2971 q^{98}+O(q^{100}) \) 10 * q + q^2 - 35 * q^4 - 25 * q^5 - 62 * q^7 - 66 * q^8 + 5 * q^10 + 47 * q^11 + 2 * q^13 - 7 * q^14 - 171 * q^16 - 2 * q^17 + 21 * q^19 + 350 * q^20 + 1046 * q^22 + 201 * q^23 - 125 * q^25 - 47 * q^26 + 597 * q^28 - 380 * q^29 - 388 * q^31 - 95 * q^32 + 260 * q^34 + 95 * q^35 + 145 * q^37 + 835 * q^38 + 165 * q^40 + 562 * q^41 + 1136 * q^43 + 1091 * q^44 - 337 * q^46 - 473 * q^47 + 998 * q^49 - 50 * q^50 + 379 * q^52 + 351 * q^53 - 470 * q^55 + 1338 * q^56 - 1818 * q^58 + 708 * q^59 - 1944 * q^61 - 896 * q^62 - 250 * q^64 - 5 * q^65 - 1118 * q^67 - 3118 * q^68 + 865 * q^70 - 1728 * q^71 + 1652 * q^73 - 3285 * q^74 + 1382 * q^76 - 787 * q^77 - 218 * q^79 - 855 * q^80 - 1027 * q^82 + 3004 * q^83 + 20 * q^85 - 4264 * q^86 - 2131 * q^88 + 2322 * q^89 + 524 * q^91 + 5914 * q^92 + 2677 * q^94 + 105 * q^95 + 1196 * q^97 - 2971 * q^98

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