LMFDB - Embedded newform 88.6.i.b.9.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [88,6,Mod(9,88)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(88, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("88.9");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 88 = 2^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	88.i (of order $5$, degree $4$, 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:	$14.1137761435$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			9.3
Character	$\chi$	$=$	88.9
Dual form			88.6.i.b.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-9.46729 + 6.87839i) q^{3} +(-7.68277 - 23.6451i) q^{5} +(61.8852 + 44.9623i) q^{7} +(-32.7737 + 100.867i) q^{9} +(-400.374 + 27.4184i) q^{11} +(131.830 - 405.731i) q^{13} +(235.375 + 171.010i) q^{15} +(-686.043 - 2111.42i) q^{17} +(1630.92 - 1184.93i) q^{19} -895.154 q^{21} +2677.09 q^{23} +(2028.11 - 1473.51i) q^{25} +(-1262.26 - 3884.83i) q^{27} +(-4166.32 - 3027.01i) q^{29} +(149.776 - 460.962i) q^{31} +(3601.86 - 3013.51i) q^{33} +(587.688 - 1808.72i) q^{35} +(-4795.74 - 3484.31i) q^{37} +(1542.71 + 4747.96i) q^{39} +(-10034.1 + 7290.18i) q^{41} +134.028 q^{43} +2636.81 q^{45} +(5647.18 - 4102.91i) q^{47} +(-3385.47 - 10419.4i) q^{49} +(21018.2 + 15270.6i) q^{51} +(-2336.12 + 7189.84i) q^{53} +(3724.29 + 9256.24i) q^{55} +(-7289.96 + 22436.2i) q^{57} +(-8139.39 - 5913.62i) q^{59} +(-5501.10 - 16930.6i) q^{61} +(-6563.43 + 4768.61i) q^{63} -10606.4 q^{65} +37247.9 q^{67} +(-25344.8 + 18414.1i) q^{69} +(21593.6 + 66458.1i) q^{71} +(-2884.18 - 2095.48i) q^{73} +(-9065.35 + 27900.3i) q^{75} +(-26010.0 - 16304.9i) q^{77} +(-22443.0 + 69072.5i) q^{79} +(17821.5 + 12948.1i) q^{81} +(-17291.9 - 53218.9i) q^{83} +(-44654.1 + 32443.1i) q^{85} +60264.7 q^{87} +22393.0 q^{89} +(26400.9 - 19181.4i) q^{91} +(1752.71 + 5394.28i) q^{93} +(-40547.8 - 29459.7i) q^{95} +(-4818.33 + 14829.3i) q^{97} +(10356.1 - 41283.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 21 q^{3} + 37 q^{5} - 181 q^{7} - 1123 q^{9} + 563 q^{11} - 753 q^{13} - 1731 q^{15} + 3153 q^{17} - 2022 q^{19} - 2282 q^{21} + 4516 q^{23} - 2551 q^{25} + 11538 q^{27} + 7829 q^{29} - 7643 q^{31}+ \cdots + 689815 q^{99}+O(q^{100}) $ 32 * q - 21 * q^3 + 37 * q^5 - 181 * q^7 - 1123 * q^9 + 563 * q^11 - 753 * q^13 - 1731 * q^15 + 3153 * q^17 - 2022 * q^19 - 2282 * q^21 + 4516 * q^23 - 2551 * q^25 + 11538 * q^27 + 7829 * q^29 - 7643 * q^31 - 20846 * q^33 - 47237 * q^35 - 30139 * q^37 + 15155 * q^39 + 17377 * q^41 + 37862 * q^43 + 46556 * q^45 - 7053 * q^47 - 43539 * q^49 - 55812 * q^51 - 17637 * q^53 + 81511 * q^55 + 137684 * q^57 + 58662 * q^59 + 32619 * q^61 - 29128 * q^63 - 103034 * q^65 + 20982 * q^67 - 183982 * q^69 + 43641 * q^71 + 94725 * q^73 - 14162 * q^75 + 143529 * q^77 + 111121 * q^79 - 97990 * q^81 - 117894 * q^83 + 123843 * q^85 - 154438 * q^87 + 13394 * q^89 - 378075 * q^91 - 83153 * q^93 + 362641 * q^95 - 332002 * q^97 + 689815 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$.

$n$	$23$	$45$	$57$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−9.46729	+	6.87839i	−0.607327	+	0.441249i	−0.848472	−	0.529240i	$-0.822477\pi$
$3$	−9.46729	+	6.87839i	−0.607327	+	0.441249i	0.241145	+	0.970489i	$0.422477\pi$
$4$		0			0
$5$	−7.68277	−	23.6451i	−0.137434	−	0.422977i	0.858527	−	0.512768i	$-0.171380\pi$
$5$	−7.68277	−	23.6451i	−0.137434	−	0.422977i	−0.995961	+	0.0897913i	$0.971380\pi$
$6$		0			0
$7$	61.8852	+	44.9623i	0.477355	+	0.346819i	0.800301	−	0.599599i	$-0.204673\pi$
$7$	61.8852	+	44.9623i	0.477355	+	0.346819i	−0.322945	+	0.946418i	$0.604673\pi$
$8$		0			0
$9$	−32.7737	+	100.867i	−0.134871	+	0.415091i
$10$		0			0
$11$	−400.374	+	27.4184i	−0.997663	+	0.0683219i
$11$	−400.374	+	27.4184i	−0.997663	+	0.0683219i
$12$		0			0
$13$	131.830	−	405.731i	0.216350	−	0.665856i	−0.782705	−	0.622392i	$-0.786161\pi$
$13$	131.830	−	405.731i	0.216350	−	0.665856i	0.999055	−	0.0434634i	$-0.0138392\pi$
$14$		0			0
$15$	235.375	+	171.010i	0.270105	+	0.196243i
$16$		0			0
$17$	−686.043	−	2111.42i	−0.575743	−	1.77196i	−0.633635	−	0.773632i	$-0.718438\pi$
$17$	−686.043	−	2111.42i	−0.575743	−	1.77196i	0.0578914	−	0.998323i	$-0.481562\pi$
$18$		0			0
$19$	1630.92	−	1184.93i	1.03645	−	0.753025i	0.0668608	−	0.997762i	$-0.478702\pi$
$19$	1630.92	−	1184.93i	1.03645	−	0.753025i	0.969589	+	0.244737i	$0.0787017\pi$
$20$		0			0
$21$	−895.154			−0.442945
$22$		0			0
$23$	2677.09			1.05522			0.527611	−	0.849486i	$-0.323088\pi$
$23$	2677.09			1.05522			0.527611	+	0.849486i	$0.323088\pi$
$24$		0			0
$25$	2028.11	−	1473.51i	0.648995	−	0.471523i
$26$		0			0
$27$	−1262.26	−	3884.83i	−0.333226	−	1.02556i
$28$		0			0
$29$	−4166.32	−	3027.01i	−0.919936	−	0.668373i	0.0235720	−	0.999722i	$-0.492496\pi$
$29$	−4166.32	−	3027.01i	−0.919936	−	0.668373i	−0.943508	+	0.331349i	$0.892496\pi$
$30$		0			0
$31$	149.776	−	460.962i	0.0279922	−	0.0861511i	−0.936084	−	0.351775i	$-0.885578\pi$
$31$	149.776	−	460.962i	0.0279922	−	0.0861511i	0.964077	+	0.265624i	$0.0855781\pi$
$32$		0			0
$33$	3601.86	−	3013.51i	0.575761	−	0.481712i
$34$		0			0
$35$	587.688	−	1808.72i	0.0810918	−	0.249575i
$36$		0			0
$37$	−4795.74	−	3484.31i	−0.575906	−	0.418420i	0.261340	−	0.965247i	$-0.415836\pi$
$37$	−4795.74	−	3484.31i	−0.575906	−	0.418420i	−0.837246	+	0.546827i	$0.815836\pi$
$38$		0			0
$39$	1542.71	+	4747.96i	0.162413	+	0.499857i
$40$		0			0
$41$	−10034.1	+	7290.18i	−0.932218	+	0.677296i	−0.946535	−	0.322601i	$-0.895443\pi$
$41$	−10034.1	+	7290.18i	−0.932218	+	0.677296i	0.0143169	+	0.999898i	$0.495443\pi$
$42$		0			0
$43$	134.028			0.0110541			0.00552706	−	0.999985i	$-0.498241\pi$
$43$	134.028			0.0110541			0.00552706	+	0.999985i	$0.498241\pi$
$44$		0			0
$45$	2636.81			0.194110
$46$		0			0
$47$	5647.18	−	4102.91i	0.372895	−	0.270924i	−0.385515	−	0.922701i	$-0.625976\pi$
$47$	5647.18	−	4102.91i	0.372895	−	0.270924i	0.758410	+	0.651777i	$0.225976\pi$
$48$		0			0
$49$	−3385.47	−	10419.4i	−0.201432	−	0.619945i
$50$		0			0
$51$	21018.2	+	15270.6i	1.13154	+	0.822111i
$52$		0			0
$53$	−2336.12	+	7189.84i	−0.114237	+	0.351584i	−0.991787	−	0.127900i	$-0.959176\pi$
$53$	−2336.12	+	7189.84i	−0.114237	+	0.351584i	0.877550	+	0.479484i	$0.159176\pi$
$54$		0			0
$55$	3724.29	+	9256.24i	0.166011	+	0.412599i
$56$		0			0
$57$	−7289.96	+	22436.2i	−0.297193	+	0.914665i
$58$		0			0
$59$	−8139.39	−	5913.62i	−0.304412	−	0.221168i	0.425083	−	0.905154i	$-0.360245\pi$
$59$	−8139.39	−	5913.62i	−0.304412	−	0.221168i	−0.729495	+	0.683986i	$0.760245\pi$
$60$		0			0
$61$	−5501.10	−	16930.6i	−0.189289	−	0.582571i	0.810707	−	0.585452i	$-0.199083\pi$
$61$	−5501.10	−	16930.6i	−0.189289	−	0.582571i	−0.999996	+	0.00288119i	$0.999083\pi$
$62$		0			0
$63$	−6563.43	+	4768.61i	−0.208343	+	0.151370i
$64$		0			0
$65$	−10606.4			−0.311375
$66$		0			0
$67$	37247.9			1.01371			0.506856	−	0.862031i	$-0.330808\pi$
$67$	37247.9			1.01371			0.506856	+	0.862031i	$0.330808\pi$
$68$		0			0
$69$	−25344.8	+	18414.1i	−0.640865	+	0.465616i
$70$		0			0
$71$	21593.6	+	66458.1i	0.508368	+	1.56460i	0.795033	+	0.606566i	$0.207453\pi$
$71$	21593.6	+	66458.1i	0.508368	+	1.56460i	−0.286665	+	0.958031i	$0.592547\pi$
$72$		0			0
$73$	−2884.18	−	2095.48i	−0.0633453	−	0.0460231i	0.555662	−	0.831408i	$-0.312465\pi$
$73$	−2884.18	−	2095.48i	−0.0633453	−	0.0460231i	−0.619007	+	0.785385i	$0.712465\pi$
$74$		0			0
$75$	−9065.35	+	27900.3i	−0.186094	+	0.572737i
$76$		0			0
$77$	−26010.0	−	16304.9i	−0.499935	−	0.313395i
$78$		0			0
$79$	−22443.0	+	69072.5i	−0.404588	+	1.24519i	0.516650	+	0.856196i	$0.327179\pi$
$79$	−22443.0	+	69072.5i	−0.404588	+	1.24519i	−0.921239	+	0.388998i	$0.872821\pi$
$80$		0			0
$81$	17821.5	+	12948.1i	0.301809	+	0.219277i
$82$		0			0
$83$	−17291.9	−	53218.9i	−0.275516	−	0.847951i	−0.989082	−	0.147363i	$-0.952921\pi$
$83$	−17291.9	−	53218.9i	−0.275516	−	0.847951i	0.713567	−	0.700587i	$-0.247079\pi$
$84$		0			0
$85$	−44654.1	+	32443.1i	−0.670370	+	0.487052i
$86$		0			0
$87$	60264.7			0.853621
$88$		0			0
$89$	22393.0			0.299666			0.149833	−	0.988711i	$-0.452126\pi$
$89$	22393.0			0.299666			0.149833	+	0.988711i	$0.452126\pi$
$90$		0			0
$91$	26400.9	−	19181.4i	0.334207	−	0.242816i
$92$		0			0
$93$	1752.71	+	5394.28i	0.0210137	+	0.0646734i
$94$		0			0
$95$	−40547.8	−	29459.7i	−0.460955	−	0.334904i
$96$		0			0
$97$	−4818.33	+	14829.3i	−0.0519957	+	0.160026i	−0.973683	−	0.227908i	$-0.926811\pi$
$97$	−4818.33	+	14829.3i	−0.0519957	+	0.160026i	0.921687	+	0.387935i	$0.126811\pi$
$98$		0			0
$99$	10356.1	−	41283.2i	0.106196	−	0.423336i
$100$		0			0
$101$	62901.1	−	193590.i	0.613557	−	1.88833i	0.192511	−	0.981295i	$-0.438337\pi$
$101$	62901.1	−	193590.i	0.613557	−	1.88833i	0.421046	−	0.907039i	$-0.361663\pi$
$102$		0			0
$103$	−140440.	−	102035.i	−1.30436	−	0.947671i	−0.304369	−	0.952554i	$-0.598446\pi$
$103$	−140440.	−	102035.i	−1.30436	−	0.947671i	−0.999988	+	0.00488317i	$0.998446\pi$
$104$		0			0
$105$	6877.26	+	21166.0i	0.0608754	+	0.187355i
$106$		0			0
$107$	−40934.8	+	29740.9i	−0.345647	+	0.251127i	−0.747041	−	0.664778i	$-0.768526\pi$
$107$	−40934.8	+	29740.9i	−0.345647	+	0.251127i	0.401393	+	0.915906i	$0.368526\pi$
$108$		0			0
$109$	149343.			1.20398			0.601989	−	0.798504i	$-0.294375\pi$
$109$	149343.			1.20398			0.601989	+	0.798504i	$0.294375\pi$
$110$		0			0
$111$	69369.2			0.534391
$112$		0			0
$113$	−26392.2	+	19175.1i	−0.194437	+	0.141267i	−0.680744	−	0.732521i	$-0.738344\pi$
$113$	−26392.2	+	19175.1i	−0.194437	+	0.141267i	0.486307	+	0.873788i	$0.338344\pi$
$114$		0			0
$115$	−20567.5	−	63300.2i	−0.145023	−	0.446334i
$116$		0			0
$117$	36604.4	+	26594.7i	0.247212	+	0.179610i
$118$		0			0
$119$	52478.4	−	161512.i	0.339714	−	1.04553i
$120$		0			0
$121$	159547.	−	21955.2i	0.990664	−	0.136325i
$122$		0			0
$123$	44850.8	−	138037.i	0.267305	−	0.822681i
$124$		0			0
$125$	−113278.	−	82301.5i	−0.648443	−	0.471121i
$126$		0			0
$127$	−43296.6	−	133253.i	−0.238201	−	0.733109i	−0.996681	−	0.0814114i	$-0.974057\pi$
$127$	−43296.6	−	133253.i	−0.238201	−	0.733109i	0.758479	−	0.651697i	$-0.225943\pi$
$128$		0			0
$129$	−1268.88	+	921.897i	−0.00671347	+	0.00487762i
$130$		0			0
$131$	−376094.			−1.91478			−0.957389	−	0.288801i	$-0.906743\pi$
$131$	−376094.			−1.91478			−0.957389	+	0.288801i	$0.906743\pi$
$132$		0			0
$133$	154207.			0.755919
$134$		0			0
$135$	−82159.7	+	59692.5i	−0.387994	+	0.281894i
$136$		0			0
$137$	97047.7	+	298682.i	0.441758	+	1.35959i	0.886001	+	0.463684i	$0.153473\pi$
$137$	97047.7	+	298682.i	0.441758	+	1.35959i	−0.444243	+	0.895906i	$0.646527\pi$
$138$		0			0
$139$	39232.8	+	28504.3i	0.172231	+	0.125133i	0.670561	−	0.741854i	$-0.266053\pi$
$139$	39232.8	+	28504.3i	0.172231	+	0.125133i	−0.498330	+	0.866987i	$0.666053\pi$
$140$		0			0
$141$	−25242.0	+	77687.0i	−0.106924	+	0.329079i
$142$		0			0
$143$	−41656.8	+	166059.i	−0.170352	+	0.679081i
$144$		0			0
$145$	−39565.1	+	121769.i	−0.156276	+	0.480969i
$146$		0			0
$147$	103720.	+	75357.0i	0.395885	+	0.287627i
$148$		0			0
$149$	−123729.	−	380798.i	−0.456568	−	1.40517i	−0.869284	−	0.494312i	$-0.835420\pi$
$149$	−123729.	−	380798.i	−0.456568	−	1.40517i	0.412716	−	0.910860i	$-0.364580\pi$
$150$		0			0
$151$	7896.14	−	5736.88i	0.0281821	−	0.0204755i	−0.573605	−	0.819132i	$-0.694456\pi$
$151$	7896.14	−	5736.88i	0.0281821	−	0.0204755i	0.601787	+	0.798657i	$0.294456\pi$
$152$		0			0
$153$	235457.			0.813175
$154$		0			0
$155$	−12050.2			−0.0402870
$156$		0			0
$157$	−343416.	+	249506.i	−1.11191	+	0.807853i	−0.982964	−	0.183798i	$-0.941161\pi$
$157$	−343416.	+	249506.i	−1.11191	+	0.807853i	−0.128950	+	0.991651i	$0.541161\pi$
$158$		0			0
$159$	−27337.8	−	84137.1i	−0.0857572	−	0.263933i
$160$		0			0
$161$	165672.	+	120368.i	0.503716	+	0.365971i
$162$		0			0
$163$	−52437.7	+	161387.i	−0.154588	+	0.475772i	−0.998119	−	0.0613082i	$-0.980473\pi$
$163$	−52437.7	+	161387.i	−0.154588	+	0.475772i	0.843531	+	0.537080i	$0.180473\pi$
$164$		0			0
$165$	−98927.0	−	62014.4i	−0.282882	−	0.177330i
$166$		0			0
$167$	−40190.3	+	123693.i	−0.111514	+	0.343206i	−0.991204	−	0.132342i	$-0.957750\pi$
$167$	−40190.3	+	123693.i	−0.111514	+	0.343206i	0.879690	+	0.475548i	$0.157750\pi$
$168$		0			0
$169$	153144.	+	111265.i	0.412460	+	0.299670i
$170$		0			0
$171$	66069.5	+	203341.i	0.172787	+	0.531783i
$172$		0			0
$173$	46050.0	−	33457.3i	0.116981	−	0.0849914i	−0.527757	−	0.849396i	$-0.676967\pi$
$173$	46050.0	−	33457.3i	0.116981	−	0.0849914i	0.644737	+	0.764404i	$0.276967\pi$
$174$		0			0
$175$	191762.			0.473335
$176$		0			0
$177$	117734.			0.282468
$178$		0			0
$179$	−260607.	+	189342.i	−0.607931	+	0.441687i	−0.848685	−	0.528899i	$-0.822605\pi$
$179$	−260607.	+	189342.i	−0.607931	+	0.441687i	0.240754	+	0.970586i	$0.422605\pi$
$180$		0			0
$181$	−85690.3	−	263728.i	−0.194417	−	0.598355i	−0.999983	−	0.00584857i	$-0.998138\pi$
$181$	−85690.3	−	263728.i	−0.194417	−	0.598355i	0.805565	−	0.592507i	$-0.201862\pi$
$182$		0			0
$183$	168536.	+	122449.i	0.372019	+	0.270288i
$184$		0			0
$185$	−45542.4	+	140165.i	−0.0978333	+	0.301100i
$186$		0			0
$187$	332565.	+	826548.i	0.695461	+	1.72848i
$188$		0			0
$189$	96555.6	−	297168.i	0.196618	−	0.605128i
$190$		0			0
$191$	−696956.	−	506368.i	−1.38236	−	1.00435i	−0.996655	−	0.0817238i	$-0.973957\pi$
$191$	−696956.	−	506368.i	−1.38236	−	1.00435i	−0.385707	−	0.922621i	$-0.626043\pi$
$192$		0			0
$193$	191332.	+	588860.i	0.369739	+	1.13794i	0.946960	+	0.321351i	$0.104137\pi$
$193$	191332.	+	588860.i	0.369739	+	1.13794i	−0.577221	+	0.816588i	$0.695863\pi$
$194$		0			0
$195$	100414.	−	72954.9i	0.189107	−	0.137394i
$196$		0			0
$197$	−156011.			−0.286412			−0.143206	−	0.989693i	$-0.545741\pi$
$197$	−156011.			−0.286412			−0.143206	+	0.989693i	$0.545741\pi$
$198$		0			0
$199$	679607.			1.21654			0.608269	−	0.793731i	$-0.291864\pi$
$199$	679607.			1.21654			0.608269	+	0.793731i	$0.291864\pi$
$200$		0			0
$201$	−352637.	+	256206.i	−0.615655	+	0.447300i
$202$		0			0
$203$	−121733.	−	374654.i	−0.207332	−	0.638103i
$204$		0			0
$205$	249467.	+	181248.i	0.414599	+	0.301224i
$206$		0			0
$207$	−87738.3	+	270031.i	−0.142319	+	0.438013i
$208$		0			0
$209$	−620489.	+	519133.i	−0.982580	+	0.822078i
$210$		0			0
$211$	191091.	−	588118.i	0.295484	−	0.909407i	−0.687574	−	0.726114i	$-0.741324\pi$
$211$	191091.	−	588118.i	0.295484	−	0.909407i	0.983058	−	0.183293i	$-0.0586757\pi$
$212$		0			0
$213$	−661558.	−	480650.i	−0.999122	−	0.725905i
$214$		0			0
$215$	−1029.71	−	3169.11i	−0.00151921	−	0.00467564i
$216$		0			0
$217$	29994.8	−	21792.5i	0.0432411	−	0.0314165i
$218$		0			0
$219$	41718.8			0.0587790
$220$		0			0
$221$	−947111.			−1.30443
$222$		0			0
$223$	27734.4	−	20150.2i	0.0373471	−	0.0271342i	−0.568955	−	0.822369i	$-0.692652\pi$
$223$	27734.4	−	20150.2i	0.0373471	−	0.0271342i	0.606302	+	0.795234i	$0.292652\pi$
$224$		0			0
$225$	82159.9	+	252862.i	0.108194	+	0.332987i
$226$		0			0
$227$	545031.	+	395988.i	0.702032	+	0.510056i	0.880593	−	0.473873i	$-0.157144\pi$
$227$	545031.	+	395988.i	0.702032	+	0.510056i	−0.178561	+	0.983929i	$0.557144\pi$
$228$		0			0
$229$	282869.	−	870580.i	0.356448	−	1.09703i	−0.598718	−	0.800960i	$-0.704323\pi$
$229$	282869.	−	870580.i	0.356448	−	1.09703i	0.955165	−	0.296073i	$-0.0956772\pi$
$230$		0			0
$231$	358396.	−	24543.7i	0.441910	−	0.0302628i
$232$		0			0
$233$	447545.	−	1.37740e6i	0.540066	−	1.66215i	−0.192373	−	0.981322i	$-0.561618\pi$
$233$	447545.	−	1.37740e6i	0.540066	−	1.66215i	0.732440	−	0.680832i	$-0.238382\pi$
$234$		0			0
$235$	−140400.	−	102006.i	−0.165843	−	0.120492i
$236$		0			0
$237$	−262633.	−	808301.i	−0.303723	−	0.934765i
$238$		0			0
$239$	35614.3	−	25875.3i	0.0403301	−	0.0293015i	−0.567438	−	0.823416i	$-0.692065\pi$
$239$	35614.3	−	25875.3i	0.0403301	−	0.0293015i	0.607768	+	0.794115i	$0.292065\pi$
$240$		0			0
$241$	840694.			0.932385			0.466193	−	0.884683i	$-0.345625\pi$
$241$	840694.			0.932385			0.466193	+	0.884683i	$0.345625\pi$
$242$		0			0
$243$	734812.			0.798290
$244$		0			0
$245$	−220358.	+	160100.i	−0.234539	+	0.170402i
$246$		0			0
$247$	−265760.	−	817925.i	−0.277171	−	0.853043i
$248$		0			0
$249$	529768.	+	384899.i	0.541486	+	0.393412i
$250$		0			0
$251$	88667.7	−	272891.i	0.0888344	−	0.273404i	−0.896763	−	0.442510i	$-0.854088\pi$
$251$	88667.7	−	272891.i	0.0888344	−	0.273404i	0.985598	+	0.169106i	$0.0540881\pi$
$252$		0			0
$253$	−1.07184e6	+	73401.5i	−1.05276	+	0.0720948i
$254$		0			0
$255$	199597.	−	614297.i	0.192223	−	0.591600i
$256$		0			0
$257$	134112.	+	97438.4i	0.126659	+	0.0920232i	0.649311	−	0.760523i	$-0.275057\pi$
$257$	134112.	+	97438.4i	0.126659	+	0.0920232i	−0.522652	+	0.852546i	$0.675057\pi$
$258$		0			0
$259$	−140123.	−	431255.i	−0.129796	−	0.399470i
$260$		0			0
$261$	441872.	−	321039.i	0.401509	−	0.291713i
$262$		0			0
$263$	31735.7			0.0282917			0.0141458	−	0.999900i	$-0.495497\pi$
$263$	31735.7			0.0282917			0.0141458	+	0.999900i	$0.495497\pi$
$264$		0			0
$265$	187952.			0.164412
$266$		0			0
$267$	−212001.	+	154028.i	−0.181995	+	0.132227i
$268$		0			0
$269$	−618701.	−	1.90417e6i	−0.521315	−	1.60444i	−0.771490	−	0.636241i	$-0.780488\pi$
$269$	−618701.	−	1.90417e6i	−0.521315	−	1.60444i	0.250175	−	0.968201i	$-0.419512\pi$
$270$		0			0
$271$	1.51141e6	+	1.09810e6i	1.25014	+	0.908278i	0.998230	−	0.0594731i	$-0.0189421\pi$
$271$	1.51141e6	+	1.09810e6i	1.25014	+	0.908278i	0.251908	+	0.967751i	$0.418942\pi$
$272$		0			0
$273$	−118008.	+	363192.i	−0.0958309	+	0.294937i
$274$		0			0
$275$	−771601.	+	645562.i	−0.615264	+	0.514762i
$276$		0			0
$277$	170834.	−	525774.i	0.133775	−	0.411718i	−0.861622	−	0.507550i	$-0.830551\pi$
$277$	170834.	−	525774.i	0.133775	−	0.411718i	0.995397	+	0.0958323i	$0.0305513\pi$
$278$		0			0
$279$	41587.2	+	30214.9i	0.0319852	+	0.0232386i
$280$		0			0
$281$	−569160.	−	1.75169e6i	−0.430000	−	1.32340i	−0.898125	−	0.439741i	$-0.855070\pi$
$281$	−569160.	−	1.75169e6i	−0.430000	−	1.32340i	0.468125	−	0.883662i	$-0.344930\pi$
$282$		0			0
$283$	126924.	−	92215.5i	0.0942056	−	0.0684444i	−0.539685	−	0.841867i	$-0.681457\pi$
$283$	126924.	−	92215.5i	0.0942056	−	0.0684444i	0.633891	+	0.773422i	$0.281457\pi$
$284$		0			0
$285$	586514.			0.427727
$286$		0			0
$287$	−948744.			−0.679899
$288$		0			0
$289$	−2.83876e6	+	2.06248e6i	−1.99933	+	1.45260i
$290$		0			0
$291$	−56385.1	−	173536.i	−0.0390330	−	0.120131i
$292$		0			0
$293$	566919.	+	411891.i	0.385791	+	0.280293i	0.763728	−	0.645538i	$-0.223367\pi$
$293$	566919.	+	411891.i	0.385791	+	0.280293i	−0.377938	+	0.925831i	$0.623367\pi$
$294$		0			0
$295$	−77295.1	+	237890.i	−0.0517127	+	0.159155i
$296$		0			0
$297$	611891.	+	1.52078e6i	0.402516	+	1.00040i
$298$		0			0
$299$	352921.	−	1.08618e6i	0.228297	−	0.702626i
$300$		0			0
$301$	8294.36	+	6026.20i	0.00527675	+	0.00383378i
$302$		0			0
$303$	736083.	+	2.26543e6i	0.460596	+	1.41757i
$304$		0			0
$305$	−358063.	+	260148.i	−0.220399	+	0.160129i
$306$		0			0
$307$	1.06175e6			0.642946			0.321473	−	0.946919i	$-0.395822\pi$
$307$	1.06175e6			0.642946			0.321473	+	0.946919i	$0.395822\pi$
$308$		0			0
$309$	2.03142e6			1.21033
$310$		0			0
$311$	−2.20475e6	+	1.60184e6i	−1.29258	+	0.939116i	−0.999854	−	0.0170794i	$-0.994563\pi$
$311$	−2.20475e6	+	1.60184e6i	−1.29258	+	0.939116i	−0.292728	+	0.956196i	$0.594563\pi$
$312$		0			0
$313$	716009.	+	2.20365e6i	0.413103	+	1.27140i	0.913937	+	0.405856i	$0.133026\pi$
$313$	716009.	+	2.20365e6i	0.413103	+	1.27140i	−0.500835	+	0.865543i	$0.666974\pi$
$314$		0			0
$315$	163180.	+	118557.i	0.0926594	+	0.0673210i
$316$		0			0
$317$	−865070.	+	2.66241e6i	−0.483507	+	1.48808i	0.350624	+	0.936516i	$0.385970\pi$
$317$	−865070.	+	2.66241e6i	−0.483507	+	1.48808i	−0.834131	+	0.551566i	$0.814030\pi$
$318$		0			0
$319$	1.75108e6	+	1.09770e6i	0.963451	+	0.603959i
$320$		0			0
$321$	182972.	−	563131.i	0.0991113	−	0.305033i
$322$		0			0
$323$	−3.62077e6	−	2.63065e6i	−1.93106	−	1.40299i
$324$		0			0
$325$	−330483.	−	1.01712e6i	−0.173556	−	0.534151i
$326$		0			0
$327$	−1.41387e6	+	1.02724e6i	−0.731208	+	0.531254i
$328$		0			0
$329$	533953.			0.271965
$330$		0			0
$331$	−1.00178e6			−0.502577			−0.251289	−	0.967912i	$-0.580854\pi$
$331$	−1.00178e6			−0.502577			−0.251289	+	0.967912i	$0.580854\pi$
$332$		0			0
$333$	508627.	−	369539.i	0.251356	−	0.182621i
$334$		0			0
$335$	−286167.	−	880731.i	−0.139318	−	0.428777i
$336$		0			0
$337$	2.12803e6	+	1.54611e6i	1.02071	+	0.741591i	0.966429	−	0.256934i	$-0.0827123\pi$
$337$	2.12803e6	+	1.54611e6i	1.02071	+	0.741591i	0.0542841	+	0.998526i	$0.482712\pi$
$338$		0			0
$339$	117969.	−	363072.i	0.0557531	−	0.171590i
$340$		0			0
$341$	−47327.4	+	188664.i	−0.0220408	+	0.0878622i
$342$		0			0
$343$	656254.	−	2.01974e6i	0.301187	−	0.926959i
$344$		0			0
$345$	630122.	+	457810.i	0.285021	+	0.207080i
$346$		0			0
$347$	569132.	+	1.75161e6i	0.253740	+	0.780932i	0.994075	+	0.108694i	$0.0346669\pi$
$347$	569132.	+	1.75161e6i	0.253740	+	0.780932i	−0.740335	+	0.672238i	$0.765333\pi$
$348$		0			0
$349$	−788139.	+	572617.i	−0.346369	+	0.251652i	−0.747344	−	0.664437i	$-0.768671\pi$
$349$	−788139.	+	572617.i	−0.346369	+	0.251652i	0.400975	+	0.916089i	$0.368671\pi$
$350$		0			0
$351$	−1.74260e6			−0.754971
$352$		0			0
$353$	3.34261e6			1.42774			0.713870	−	0.700278i	$-0.246941\pi$
$353$	3.34261e6			1.42774			0.713870	+	0.700278i	$0.246941\pi$
$354$		0			0
$355$	1.40551e6	−	1.02116e6i	0.591921	−	0.430056i
$356$		0			0
$357$	614114.	+	1.89005e6i	0.255022	+	0.784878i
$358$		0			0
$359$	−1.14919e6	−	834936.i	−0.470604	−	0.341914i	0.327072	−	0.944999i	$-0.393938\pi$
$359$	−1.14919e6	−	834936.i	−0.470604	−	0.341914i	−0.797677	+	0.603085i	$0.793938\pi$
$360$		0			0
$361$	490677.	−	1.51015e6i	0.198165	−	0.609890i
$362$		0			0
$363$	−1.35947e6	+	1.30529e6i	−0.541504	+	0.519923i
$364$		0			0
$365$	−27389.3	+	84295.7i	−0.0107609	+	0.0331187i
$366$		0			0
$367$	−1.79789e6	−	1.30624e6i	−0.696784	−	0.506243i	0.182099	−	0.983280i	$-0.441711\pi$
$367$	−1.79789e6	−	1.30624e6i	−0.696784	−	0.506243i	−0.878883	+	0.477037i	$0.841711\pi$
$368$		0			0
$369$	−406486.	−	1.25103e6i	−0.155410	−	0.478303i
$370$		0			0
$371$	−467843.	+	339908.i	−0.176468	+	0.128211i
$372$		0			0
$373$	−1.35037e6			−0.502552			−0.251276	−	0.967915i	$-0.580850\pi$
$373$	−1.35037e6			−0.502552			−0.251276	+	0.967915i	$0.580850\pi$
$374$		0			0
$375$	1.63854e6			0.601699
$376$		0			0
$377$	−1.77740e6	+	1.29136e6i	−0.644068	+	0.467943i
$378$		0			0
$379$	750525.	+	2.30988e6i	0.268390	+	0.826021i	0.990893	+	0.134652i	$0.0429918\pi$
$379$	750525.	+	2.30988e6i	0.268390	+	0.826021i	−0.722503	+	0.691368i	$0.757008\pi$
$380$		0			0
$381$	1.32647e6	+	963736.i	0.468150	+	0.340131i
$382$		0			0
$383$	42837.4	−	131840.i	0.0149220	−	0.0459251i	−0.943318	−	0.331889i	$-0.892314\pi$
$383$	42837.4	−	131840.i	0.0149220	−	0.0459251i	0.958240	+	0.285964i	$0.0923139\pi$
$384$		0			0
$385$	−185703.	+	740277.i	−0.0638509	+	0.254532i
$386$		0			0
$387$	−4392.60	+	13519.0i	−0.00149089	+	0.00458847i
$388$		0			0
$389$	22122.3	+	16072.8i	0.00741236	+	0.00538539i	0.591485	−	0.806316i	$-0.298542\pi$
$389$	22122.3	+	16072.8i	0.00741236	+	0.00538539i	−0.584073	+	0.811701i	$0.698542\pi$
$390$		0			0
$391$	−1.83660e6	−	5.65247e6i	−0.607537	−	1.86981i
$392$		0			0
$393$	3.56060e6	−	2.58692e6i	1.16290	−	0.844894i
$394$		0			0
$395$	1.80565e6			0.582293
$396$		0			0
$397$	1.84875e6			0.588711			0.294356	−	0.955696i	$-0.404895\pi$
$397$	1.84875e6			0.588711			0.294356	+	0.955696i	$0.404895\pi$
$398$		0			0
$399$	−1.45992e6	+	1.06070e6i	−0.459090	+	0.333548i
$400$		0			0
$401$	−1.60483e6	−	4.93914e6i	−0.498387	−	1.53388i	−0.811611	−	0.584198i	$-0.801409\pi$
$401$	−1.60483e6	−	4.93914e6i	−0.498387	−	1.53388i	0.313224	−	0.949679i	$-0.398591\pi$
$402$		0			0
$403$	−167282.	−	121537.i	−0.0513081	−	0.0372775i
$404$		0			0
$405$	169240.	−	520869.i	0.0512704	−	0.157794i
$406$		0			0
$407$	2.01562e6	+	1.26354e6i	0.603147	+	0.378095i
$408$		0			0
$409$	−734993.	+	2.26208e6i	−0.217258	+	0.668650i	0.781728	+	0.623620i	$0.214339\pi$
$409$	−734993.	+	2.26208e6i	−0.217258	+	0.668650i	−0.998986	+	0.0450308i	$0.985661\pi$
$410$		0			0
$411$	−2.97323e6	−	2.16018e6i	−0.868209	−	0.630791i
$412$		0			0
$413$	−237819.	−	731931.i	−0.0686074	−	0.211152i
$414$		0			0
$415$	−1.12552e6	+	817737.i	−0.320798	+	0.233074i
$416$		0			0
$417$	−567492.			−0.159816
$418$		0			0
$419$	3.99504e6			1.11170			0.555848	−	0.831284i	$-0.312394\pi$
$419$	3.99504e6			1.11170			0.555848	+	0.831284i	$0.312394\pi$
$420$		0			0
$421$	−4.05542e6	+	2.94644e6i	−1.11514	+	0.810199i	−0.983466	−	0.181093i	$-0.942036\pi$
$421$	−4.05542e6	+	2.94644e6i	−1.11514	+	0.810199i	−0.131678	+	0.991293i	$0.542036\pi$
$422$		0			0
$423$	228770.	+	704083.i	0.0621654	+	0.191325i
$424$		0			0
$425$	−4.50257e6	−	3.27131e6i	−1.20917	−	0.878515i
$426$		0			0
$427$	420803.	−	1.29510e6i	0.111689	−	0.343742i
$428$		0			0
$429$	−747840.	−	1.85866e6i	−0.196185	−	0.487592i
$430$		0			0
$431$	966422.	−	2.97434e6i	0.250596	−	0.771254i	−0.744070	−	0.668102i	$-0.767107\pi$
$431$	966422.	−	2.97434e6i	0.250596	−	0.771254i	0.994666	−	0.103152i	$-0.0328929\pi$
$432$		0			0
$433$	−1.90703e6	−	1.38554e6i	−0.488808	−	0.355140i	0.315917	−	0.948787i	$-0.397688\pi$
$433$	−1.90703e6	−	1.38554e6i	−0.488808	−	0.355140i	−0.804726	+	0.593647i	$0.797688\pi$
$434$		0			0
$435$	−463000.	−	1.42497e6i	−0.117316	−	0.361062i
$436$		0			0
$437$	4.36612e6	−	3.17217e6i	1.09368	−	0.794609i
$438$		0			0
$439$	4.25642e6			1.05410			0.527051	−	0.849833i	$-0.323297\pi$
$439$	4.25642e6			1.05410			0.527051	+	0.849833i	$0.323297\pi$
$440$		0			0
$441$	1.16193e6			0.284501
$442$		0			0
$443$	−354101.	+	257270.i	−0.0857271	+	0.0622844i	−0.629823	−	0.776738i	$-0.716873\pi$
$443$	−354101.	+	257270.i	−0.0857271	+	0.0622844i	0.544096	+	0.839023i	$0.316873\pi$
$444$		0			0
$445$	−172040.	−	529486.i	−0.0411842	−	0.126752i
$446$		0			0
$447$	3.79066e6	+	2.75407e6i	0.897317	+	0.651939i
$448$		0			0
$449$	−42521.4	+	130868.i	−0.00995387	+	0.0306349i	−0.955910	−	0.293659i	$-0.905127\pi$
$449$	−42521.4	+	130868.i	−0.00995387	+	0.0306349i	0.945956	+	0.324294i	$0.105127\pi$
$450$		0			0
$451$	3.81749e6	−	3.19391e6i	0.883766	−	0.739404i
$452$		0			0
$453$	−35294.6	+	108626.i	−0.00808095	+	0.0248706i
$454$		0			0
$455$	−656379.	−	476887.i	−0.148637	−	0.107991i
$456$		0			0
$457$	−2.12811e6	−	6.54966e6i	−0.476655	−	1.46699i	−0.843712	−	0.536795i	$-0.819635\pi$
$457$	−2.12811e6	−	6.54966e6i	−0.476655	−	1.46699i	0.367057	−	0.930198i	$-0.380365\pi$
$458$		0			0
$459$	−7.33656e6	+	5.33032e6i	−1.62540	+	1.18092i
$460$		0			0
$461$	2.87490e6			0.630042			0.315021	−	0.949085i	$-0.397988\pi$
$461$	2.87490e6			0.630042			0.315021	+	0.949085i	$0.397988\pi$
$462$		0			0
$463$	−3.45632e6			−0.749311			−0.374655	−	0.927164i	$-0.622239\pi$
$463$	−3.45632e6			−0.749311			−0.374655	+	0.927164i	$0.622239\pi$
$464$		0			0
$465$	114083.	−	82885.9i	0.0244674	−	0.0177766i
$466$		0			0
$467$	2.01178e6	+	6.19161e6i	0.426862	+	1.31375i	0.901200	+	0.433404i	$0.142688\pi$
$467$	2.01178e6	+	6.19161e6i	0.426862	+	1.31375i	−0.474338	+	0.880343i	$0.657312\pi$
$468$		0			0
$469$	2.30509e6	+	1.67475e6i	0.483901	+	0.351575i
$470$		0			0
$471$	1.53502e6	−	4.72430e6i	0.318831	−	0.981262i
$472$		0			0
$473$	−53661.3	+	3674.83i	−0.0110283	+	0.000755239i
$474$		0			0
$475$	1.56168e6	−	4.80635e6i	0.317583	−	0.977420i
$476$		0			0
$477$	−648655.	−	471276.i	−0.130532	−	0.0948373i
$478$		0			0
$479$	2.73593e6	+	8.42034e6i	0.544837	+	1.67684i	0.721376	+	0.692543i	$0.243510\pi$
$479$	2.73593e6	+	8.42034e6i	0.544837	+	1.67684i	−0.176539	+	0.984294i	$0.556490\pi$
$480$		0			0
$481$	−2.04592e6	+	1.48645e6i	−0.403205	+	0.292945i
$482$		0			0
$483$	−2.39641e6			−0.467405
$484$		0			0
$485$	387659.			0.0748333
$486$		0			0
$487$	7.35532e6	−	5.34395e6i	1.40533	−	1.02103i	0.411352	−	0.911476i	$-0.365057\pi$
$487$	7.35532e6	−	5.34395e6i	1.40533	−	1.02103i	0.993980	−	0.109558i	$-0.0349434\pi$
$488$		0			0
$489$	−613638.	−	1.88858e6i	−0.116049	−	0.357161i
$490$		0			0
$491$	2.38054e6	+	1.72956e6i	0.445627	+	0.323767i	0.787867	−	0.615846i	$-0.211186\pi$
$491$	2.38054e6	+	1.72956e6i	0.445627	+	0.323767i	−0.342240	+	0.939613i	$0.611186\pi$
$492$		0			0
$493$	−3.53302e6	+	1.08735e7i	−0.654680	+	2.01490i
$494$		0			0
$495$	−1.05571e6	+	72297.1i	−0.193656	+	0.0132620i
$496$		0			0
$497$	−1.65179e6	+	5.08367e6i	−0.299959	+	0.923180i
$498$		0			0
$499$	1.01075e6	+	734352.i	0.181716	+	0.132024i	0.674924	−	0.737887i	$-0.264176\pi$
$499$	1.01075e6	+	734352.i	0.181716	+	0.132024i	−0.493209	+	0.869911i	$0.664176\pi$
$500$		0			0
$501$	−470316.	−	1.44748e6i	−0.0837135	−	0.257644i
$502$		0			0
$503$	−3.33541e6	+	2.42331e6i	−0.587799	+	0.427061i	−0.841527	−	0.540215i	$-0.818343\pi$
$503$	−3.33541e6	+	2.42331e6i	−0.587799	+	0.427061i	0.253728	+	0.967276i	$0.418343\pi$
$504$		0			0
$505$	−5.06071e6			−0.883045
$506$		0			0
$507$	−2.21518e6			−0.382727
$508$		0			0
$509$	383970.	−	278970.i	0.0656905	−	0.0477270i	−0.554455	−	0.832213i	$-0.687073\pi$
$509$	383970.	−	278970.i	0.0656905	−	0.0477270i	0.620146	+	0.784486i	$0.287073\pi$
$510$		0			0
$511$	−84270.5	−	259358.i	−0.0142766	−	0.0439387i
$512$		0			0
$513$	−6.66190e6	−	4.84016e6i	−1.11765	−	0.812019i
$514$		0			0
$515$	−1.33367e6	+	4.10463e6i	−0.221581	+	0.681955i
$516$		0			0
$517$	−2.14849e6	+	1.79754e6i	−0.353514	+	0.295768i
$518$		0			0
$519$	−205836.	+	633499.i	−0.0335431	+	0.103235i
$520$		0			0
$521$	5.55566e6	+	4.03643e6i	0.896689	+	0.651482i	0.937613	−	0.347680i	$-0.113030\pi$
$521$	5.55566e6	+	4.03643e6i	0.896689	+	0.651482i	−0.0409248	+	0.999162i	$0.513030\pi$
$522$		0			0
$523$	3.16641e6	+	9.74520e6i	0.506189	+	1.55789i	0.798762	+	0.601647i	$0.205488\pi$
$523$	3.16641e6	+	9.74520e6i	0.506189	+	1.55789i	−0.292573	+	0.956243i	$0.594512\pi$
$524$		0			0
$525$	−1.81547e6	+	1.31902e6i	−0.287469	+	0.208858i
$526$		0			0
$527$	−1.07604e6			−0.168772
$528$		0			0
$529$	730479.			0.113493
$530$		0			0
$531$	863248.	−	627187.i	0.132862	−	0.0965296i
$532$		0			0
$533$	1.63506e6	+	5.03220e6i	0.249296	+	0.767256i
$534$		0			0
$535$	1.01772e6	+	739416.i	0.153725	+	0.111688i
$536$		0			0
$537$	1.16488e6	−	3.58512e6i	0.174319	−	0.536498i
$538$		0			0
$539$	1.64114e6	+	4.07883e6i	0.243317	+	0.604734i
$540$		0			0
$541$	−2.77347e6	+	8.53587e6i	−0.407409	+	1.25388i	0.511458	+	0.859308i	$0.329106\pi$
$541$	−2.77347e6	+	8.53587e6i	−0.407409	+	1.25388i	−0.918867	+	0.394568i	$0.870894\pi$
$542$		0			0
$543$	2.62528e6	+	1.90738e6i	0.382099	+	0.277611i
$544$		0			0
$545$	−1.14737e6	−	3.53123e6i	−0.165467	−	0.509255i
$546$		0			0
$547$	1.01091e6	−	734468.i	0.144459	−	0.104955i	−0.513209	−	0.858264i	$-0.671543\pi$
$547$	1.01091e6	−	734468.i	0.144459	−	0.104955i	0.657667	+	0.753309i	$0.271543\pi$
$548$		0			0
$549$	1.88804e6			0.267350
$550$		0			0
$551$	−1.03817e7			−1.45677
$552$		0			0
$553$	−4.49454e6	+	3.26548e6i	−0.624990	+	0.454081i
$554$		0			0
$555$	−532947.	−	1.64024e6i	−0.0734432	−	0.226035i
$556$		0			0
$557$	7.79233e6	+	5.66146e6i	1.06422	+	0.773198i	0.974864	−	0.222802i	$-0.0715204\pi$
$557$	7.79233e6	+	5.66146e6i	1.06422	+	0.773198i	0.0893519	+	0.996000i	$0.471520\pi$
$558$		0			0
$559$	17668.9	−	54379.4i	0.00239156	−	0.00736046i
$560$		0			0
$561$	−8.83382e6	−	5.53766e6i	−1.18506	−	0.742881i
$562$		0			0
$563$	3.51888e6	−	1.08300e7i	0.467879	−	1.43998i	−0.387447	−	0.921892i	$-0.626643\pi$
$563$	3.51888e6	−	1.08300e7i	0.467879	−	1.43998i	0.855326	−	0.518090i	$-0.173357\pi$
$564$		0			0
$565$	656162.	+	476729.i	0.0864748	+	0.0628276i
$566$		0			0
$567$	520713.	+	1.60259e6i	0.0680206	+	0.209346i
$568$		0			0
$569$	4.19760e6	−	3.04974e6i	0.543527	−	0.394895i	−0.281867	−	0.959454i	$-0.590954\pi$
$569$	4.19760e6	−	3.04974e6i	0.543527	−	0.394895i	0.825393	+	0.564558i	$0.190954\pi$
$570$		0			0
$571$	−2.66568e6			−0.342151			−0.171076	−	0.985258i	$-0.554724\pi$
$571$	−2.66568e6			−0.342151			−0.171076	+	0.985258i	$0.554724\pi$
$572$		0			0
$573$	1.00813e7			1.28271
$574$		0			0
$575$	5.42944e6	−	3.94472e6i	0.684834	−	0.497561i
$576$		0			0
$577$	−1.41136e6	−	4.34372e6i	−0.176481	−	0.543154i	0.823217	−	0.567727i	$-0.192177\pi$
$577$	−1.41136e6	−	4.34372e6i	−0.176481	−	0.543154i	−0.999698	+	0.0245737i	$0.992177\pi$
$578$		0			0
$579$	−5.86181e6	−	4.25886e6i	−0.726667	−	0.527955i
$580$		0			0
$581$	1.32273e6	−	4.07094e6i	0.162566	−	0.500328i
$582$		0			0
$583$	738188.	−	2.94268e6i	0.0899488	−	0.358568i
$584$		0			0
$585$	347611.	−	1.06984e6i	0.0419956	−	0.129249i
$586$		0			0
$587$	1.01066e7	+	7.34290e6i	1.21063	+	0.879574i	0.995288	−	0.0969652i	$-0.0309135\pi$
$587$	1.01066e7	+	7.34290e6i	1.21063	+	0.879574i	0.215341	+	0.976539i	$0.430914\pi$
$588$		0			0
$589$	−301937.	−	929265.i	−0.0358614	−	0.110370i
$590$		0			0
$591$	1.47701e6	−	1.07311e6i	0.173946	−	0.126379i
$592$		0			0
$593$	1.01646e7			1.18700			0.593502	−	0.804832i	$-0.297745\pi$
$593$	1.01646e7			1.18700			0.593502	+	0.804832i	$0.297745\pi$
$594$		0			0
$595$	−4.22215e6			−0.488924
$596$		0			0
$597$	−6.43404e6	+	4.67461e6i	−0.738836	+	0.536796i
$598$		0			0
$599$	365715.	+	1.12556e6i	0.0416463	+	0.128174i	0.969718	−	0.244228i	$-0.0785344\pi$
$599$	365715.	+	1.12556e6i	0.0416463	+	0.128174i	−0.928072	+	0.372402i	$0.878534\pi$
$600$		0			0
$601$	−1.05084e7	−	7.63479e6i	−1.18672	−	0.862206i	−0.193810	−	0.981039i	$-0.562085\pi$
$601$	−1.05084e7	−	7.63479e6i	−1.18672	−	0.862206i	−0.992914	+	0.118834i	$0.962085\pi$
$602$		0			0
$603$	−1.22075e6	+	3.75709e6i	−0.136721	+	0.420783i
$604$		0			0
$605$	−1.74490e6	−	3.60384e6i	−0.193813	−	0.400293i
$606$		0			0
$607$	−3.30827e6	+	1.01818e7i	−0.364442	+	1.12164i	0.585887	+	0.810392i	$0.300746\pi$
$607$	−3.30827e6	+	1.01818e7i	−0.364442	+	1.12164i	−0.950330	+	0.311245i	$0.899254\pi$
$608$		0			0
$609$	3.72950e6	+	2.70964e6i	0.407481	+	0.296052i
$610$		0			0
$611$	−920213.	−	2.83212e6i	−0.0997207	−	0.306909i
$612$		0			0
$613$	1.41576e7	−	1.02861e7i	1.52173	−	1.10560i	0.561108	−	0.827742i	$-0.310375\pi$
$613$	1.41576e7	−	1.02861e7i	1.52173	−	1.10560i	0.960622	−	0.277859i	$-0.0896249\pi$
$614$		0			0
$615$	−3.60847e6			−0.384712
$616$		0			0
$617$	−4.51576e6			−0.477549			−0.238775	−	0.971075i	$-0.576746\pi$
$617$	−4.51576e6			−0.477549			−0.238775	+	0.971075i	$0.576746\pi$
$618$		0			0
$619$	7.19956e6	−	5.23079e6i	0.755230	−	0.548707i	−0.142214	−	0.989836i	$-0.545422\pi$
$619$	7.19956e6	−	5.23079e6i	0.755230	−	0.548707i	0.897444	+	0.441129i	$0.145422\pi$
$620$		0			0
$621$	−3.37918e6	−	1.04001e7i	−0.351627	−	1.08220i
$622$		0			0
$623$	1.38580e6	+	1.00684e6i	0.143047	+	0.103930i
$624$		0			0
$625$	1.34510e6	−	4.13980e6i	0.137739	−	0.423916i
$626$		0			0
$627$	2.30355e6	−	9.18275e6i	0.234007	−	0.932833i
$628$		0			0
$629$	−4.06677e6	+	1.25162e7i	−0.409848	+	1.26138i
$630$		0			0
$631$	−1.58694e7	−	1.15298e7i	−1.58667	−	1.15279i	−0.908500	−	0.417886i	$-0.862771\pi$
$631$	−1.58694e7	−	1.15298e7i	−1.58667	−	1.15279i	−0.678175	−	0.734901i	$-0.737229\pi$
$632$		0			0
$633$	2.23619e6	+	6.88229e6i	0.221819	+	0.682690i
$634$		0			0
$635$	−2.81815e6	+	2.04751e6i	−0.277351	+	0.201507i
$636$		0			0
$637$	−4.67379e6			−0.456374
$638$		0			0
$639$	−7.41115e6			−0.718015
$640$		0			0
$641$	1.57149e7	−	1.14176e7i	1.51066	−	1.09756i	0.544779	−	0.838580i	$-0.316614\pi$
$641$	1.57149e7	−	1.14176e7i	1.51066	−	1.09756i	0.965883	−	0.258980i	$-0.0833863\pi$
$642$		0			0
$643$	−3.87447e6	−	1.19244e7i	−0.369560	−	1.13739i	−0.947076	−	0.321009i	$-0.895978\pi$
$643$	−3.87447e6	−	1.19244e7i	−0.369560	−	1.13739i	0.577516	−	0.816379i	$-0.304022\pi$
$644$		0			0
$645$	31546.9	+	22920.2i	0.00298578	+	0.00216930i
$646$		0			0
$647$	2.62893e6	−	8.09100e6i	0.246898	−	0.759874i	−0.748420	−	0.663225i	$-0.769187\pi$
$647$	2.62893e6	−	8.09100e6i	0.246898	−	0.759874i	0.995318	−	0.0966494i	$-0.0308125\pi$
$648$		0			0
$649$	3.42094e6	+	2.14449e6i	0.318812	+	0.199854i
$650$		0			0
$651$	−134072.	+	412632.i	−0.0123990	+	0.0381601i
$652$		0			0
$653$	1.49686e7	+	1.08753e7i	1.37372	+	0.998068i	0.997436	+	0.0715648i	$0.0227993\pi$
$653$	1.49686e7	+	1.08753e7i	1.37372	+	0.998068i	0.376287	+	0.926503i	$0.377201\pi$
$654$		0			0
$655$	2.88945e6	+	8.89280e6i	0.263155	+	0.809907i
$656$		0			0
$657$	305890.	−	222242.i	0.0276472	−	0.0200869i
$658$		0			0
$659$	−3.09897e6			−0.277974			−0.138987	−	0.990294i	$-0.544385\pi$
$659$	−3.09897e6			−0.277974			−0.138987	+	0.990294i	$0.544385\pi$
$660$		0			0
$661$	−1.64845e7			−1.46748			−0.733738	−	0.679432i	$-0.762226\pi$
$661$	−1.64845e7			−1.46748			−0.733738	+	0.679432i	$0.762226\pi$
$662$		0			0
$663$	8.96658e6	−	6.51460e6i	0.792215	−	0.575578i
$664$		0			0
$665$	−1.18474e6	−	3.64625e6i	−0.103889	−	0.319736i
$666$		0			0
$667$	−1.11536e7	−	8.10358e6i	−0.970737	−	0.705281i
$668$		0			0
$669$	−123969.	+	381536.i	−0.0107089	+	0.0329587i
$670$		0			0
$671$	2.66671e6	+	6.62775e6i	0.228649	+	0.568277i
$672$		0			0
$673$	−1.13267e6	+	3.48600e6i	−0.0963976	+	0.296681i	−0.987615	−	0.156894i	$-0.949852\pi$
$673$	−1.13267e6	+	3.48600e6i	−0.0963976	+	0.296681i	0.891218	+	0.453576i	$0.149852\pi$
$674$		0			0
$675$	−8.28433e6	−	6.01892e6i	−0.699839	−	0.508463i
$676$		0			0
$677$	1.84410e6	+	5.67556e6i	0.154637	+	0.475924i	0.998124	−	0.0612260i	$-0.0195010\pi$
$677$	1.84410e6	+	5.67556e6i	0.154637	+	0.475924i	−0.843487	+	0.537150i	$0.819501\pi$
$678$		0			0
$679$	−964942.	+	701071.i	−0.0803205	+	0.0583563i
$680$		0			0
$681$	−7.88374e6			−0.651425
$682$		0			0
$683$	−1.65497e7			−1.35750			−0.678749	−	0.734371i	$-0.737477\pi$
$683$	−1.65497e7			−1.35750			−0.678749	+	0.734371i	$0.737477\pi$
$684$		0			0
$685$	6.31678e6	−	4.58941e6i	0.514363	−	0.373707i
$686$		0			0
$687$	3.31019e6	+	1.01877e7i	0.267585	+	0.823541i
$688$		0			0
$689$	2.60917e6	+	1.89567e6i	0.209389	+	0.152130i
$690$		0			0
$691$	4.86132e6	−	1.49616e7i	0.387311	−	1.19202i	−0.547480	−	0.836819i	$-0.684413\pi$
$691$	4.86132e6	−	1.49616e7i	0.387311	−	1.19202i	0.934790	−	0.355200i	$-0.115587\pi$
$692$		0			0
$693$	2.49708e6	−	2.08918e6i	0.197514	−	0.165251i
$694$		0			0
$695$	372571.	−	1.14666e6i	0.0292582	−	0.0900474i
$696$		0			0
$697$	2.22764e7	+	1.61848e7i	1.73686	+	1.26190i
$698$		0			0
$699$	5.23727e6	+	1.61187e7i	0.405427	+	1.24777i
$700$		0			0
$701$	2.00451e7	−	1.45636e7i	1.54068	−	1.11937i	0.590777	−	0.806835i	$-0.298821\pi$
$701$	2.00451e7	−	1.45636e7i	1.54068	−	1.11937i	0.949906	−	0.312536i	$-0.101179\pi$
$702$		0			0
$703$	−1.19501e7			−0.911979
$704$		0			0
$705$	2.03085e6			0.153888
$706$		0			0
$707$	1.25969e7	−	9.15217e6i	0.947795	−	0.688613i
$708$		0			0
$709$	6.02268e6	+	1.85359e7i	0.449960	+	1.38484i	0.876951	+	0.480579i	$0.159574\pi$
$709$	6.02268e6	+	1.85359e7i	0.449960	+	1.38484i	−0.426991	+	0.904256i	$0.640426\pi$
$710$		0			0
$711$	−6.23160e6	−	4.52753e6i	−0.462302	−	0.335882i
$712$		0			0
$713$	400963.	−	1.23404e6i	0.0295380	−	0.0909085i
$714$		0			0
$715$	4.24652e6	−	290810.i	0.310648	−	0.0212738i
$716$		0			0
$717$	−159190.	+	489938.i	−0.0115643	+	0.0355912i
$718$		0			0
$719$	304649.	+	221340.i	0.0219775	+	0.0159676i	0.598720	−	0.800959i	$-0.295676\pi$
$719$	304649.	+	221340.i	0.0219775	+	0.0159676i	−0.576742	+	0.816926i	$0.695676\pi$
$720$		0			0
$721$	−4.10340e6	−	1.26290e7i	−0.293972	−	0.904752i
$722$		0			0
$723$	−7.95910e6	+	5.78262e6i	−0.566263	+	0.411414i
$724$		0			0
$725$	−1.29101e7			−0.912187
$726$		0			0
$727$	1.23377e7			0.865760			0.432880	−	0.901452i	$-0.357497\pi$
$727$	1.23377e7			0.865760			0.432880	+	0.901452i	$0.357497\pi$
$728$		0			0
$729$	−1.12873e7	+	8.20071e6i	−0.786632	+	0.571521i
$730$		0			0
$731$	−91948.9	−	282990.i	−0.00636434	−	0.0195874i
$732$		0			0
$733$	−1.40572e7	−	1.02132e7i	−0.966362	−	0.702103i	−0.0117422	−	0.999931i	$-0.503738\pi$
$733$	−1.40572e7	−	1.02132e7i	−0.966362	−	0.702103i	−0.954619	+	0.297828i	$0.903738\pi$
$734$		0			0
$735$	984969.	−	3.03142e6i	0.0672519	−	0.206980i
$736$		0			0
$737$	−1.49131e7	+	1.02128e6i	−1.01134	+	0.0692588i
$738$		0			0
$739$	−886593.	+	2.72865e6i	−0.0597191	+	0.183797i	−0.976466	−	0.215673i	$-0.930806\pi$
$739$	−886593.	+	2.72865e6i	−0.0597191	+	0.183797i	0.916747	+	0.399469i	$0.130806\pi$
$740$		0			0
$741$	8.14204e6	+	5.91554e6i	0.544738	+	0.395775i
$742$		0			0
$743$	2.54079e6	+	7.81975e6i	0.168848	+	0.519662i	0.999299	−	0.0374301i	$-0.0119172\pi$
$743$	2.54079e6	+	7.81975e6i	0.168848	+	0.519662i	−0.830451	+	0.557092i	$0.811917\pi$
$744$		0			0
$745$	−8.05345e6	+	5.85117e6i	−0.531608	+	0.386235i
$746$		0			0
$747$	5.93476e6			0.389136
$748$		0			0
$749$	−3.87048e6			−0.252092
$750$		0			0
$751$	−7.73146e6	+	5.61723e6i	−0.500220	+	0.363431i	−0.809101	−	0.587669i	$-0.800046\pi$
$751$	−7.73146e6	+	5.61723e6i	−0.500220	+	0.363431i	0.308881	+	0.951101i	$0.400046\pi$
$752$		0			0
$753$	1.03761e6	+	3.19343e6i	0.0666878	+	0.205244i
$754$		0			0
$755$	−196314.	−	142630.i	−0.0125338	−	0.00910634i
$756$		0			0
$757$	−7.25370e6	+	2.23246e7i	−0.460066	+	1.41594i	0.405018	+	0.914309i	$0.367265\pi$
$757$	−7.25370e6	+	2.23246e7i	−0.460066	+	1.41594i	−0.865084	+	0.501628i	$0.832735\pi$
$758$		0			0
$759$	9.64252e6	−	8.06743e6i	0.607556	−	0.508313i
$760$		0			0
$761$	−4.34256e6	+	1.33650e7i	−0.271822	+	0.836582i	0.718221	+	0.695815i	$0.244957\pi$
$761$	−4.34256e6	+	1.33650e7i	−0.271822	+	0.836582i	−0.990043	+	0.140767i	$0.955043\pi$
$762$		0			0
$763$	9.24212e6	+	6.71479e6i	0.574725	+	0.417562i
$764$		0			0
$765$	−1.80896e6	−	5.56742e6i	−0.111757	−	0.343954i
$766$		0			0
$767$	−3.47236e6	+	2.52282e6i	−0.213126	+	0.154845i
$768$		0			0
$769$	2.45947e7			1.49977			0.749887	−	0.661566i	$-0.230108\pi$
$769$	2.45947e7			1.49977			0.749887	+	0.661566i	$0.230108\pi$
$770$		0			0
$771$	−1.93990e6			−0.117529
$772$		0			0
$773$	2.75859e6	−	2.00423e6i	0.166050	−	0.120642i	−0.501657	−	0.865067i	$-0.667276\pi$
$773$	2.75859e6	−	2.00423e6i	0.166050	−	0.120642i	0.667707	+	0.744424i	$0.267276\pi$
$774$		0			0
$775$	−375470.	−	1.15558e6i	−0.0224554	−	0.0691106i
$776$		0			0
$777$	4.29293e6	+	3.11899e6i	0.255094	+	0.185337i
$778$		0			0
$779$	−7.72639e6	+	2.37794e7i	−0.456177	+	1.40397i
$780$		0			0
$781$	−1.04677e7	−	2.60160e7i	−0.614076	−	1.52621i
$782$		0			0
$783$	−6.50045e6	+	2.00063e7i	−0.378912	+	1.16617i
$784$		0			0
$785$	8.53799e6	+	6.20322e6i	0.494518	+	0.359288i
$786$		0			0
$787$	8.35031e6	+	2.56996e7i	0.480580	+	1.47907i	0.838282	+	0.545237i	$0.183560\pi$
$787$	8.35031e6	+	2.56996e7i	0.480580	+	1.47907i	−0.357702	+	0.933836i	$0.616440\pi$
$788$		0			0
$789$	−300451.	+	218290.i	−0.0171823	+	0.0124837i
$790$		0			0
$791$	−2.49544e6			−0.141810
$792$		0			0
$793$	−7.59450e6			−0.428861
$794$		0			0
$795$	−1.77940e6	+	1.29281e6i	−0.0998519	+	0.0725466i
$796$		0			0
$797$	4.08218e6	+	1.25636e7i	0.227639	+	0.700600i	0.998013	+	0.0630078i	$0.0200693\pi$
$797$	4.08218e6	+	1.25636e7i	0.227639	+	0.700600i	−0.770374	+	0.637592i	$0.779931\pi$
$798$		0			0
$799$	−1.25372e7	−	9.10880e6i	−0.694758	−	0.504771i
$800$		0			0
$801$	−733903.	+	2.25872e6i	−0.0404164	+	0.124389i
$802$		0			0
$803$	1.21220e6	+	759894.i	0.0663417	+	0.0415876i
$804$		0			0
$805$	1.57330e6	−	4.84211e6i	0.0855698	−	0.263357i
$806$		0			0
$807$	1.89550e7	+	1.37716e7i	1.02457	+	0.744392i
$808$		0			0
$809$	−3.91590e6	−	1.20519e7i	−0.210359	−	0.647418i	−0.999451	−	0.0331426i	$-0.989448\pi$
$809$	−3.91590e6	−	1.20519e7i	−0.210359	−	0.647418i	0.789092	−	0.614275i	$-0.210552\pi$
$810$		0			0
$811$	1.03083e7	−	7.48940e6i	0.550343	−	0.399848i	−0.277569	−	0.960706i	$-0.589529\pi$
$811$	1.03083e7	−	7.48940e6i	0.550343	−	0.399848i	0.827912	+	0.560858i	$0.189529\pi$
$812$		0			0
$813$	−2.18621e7			−1.16002
$814$		0			0
$815$	4.21888e6			0.222486
$816$		0			0
$817$	218589.	−	158814.i	0.0114571	−	0.00832404i
$818$		0			0
$819$	1.06952e6	+	3.29163e6i	0.0557157	+	0.171475i
$820$		0			0
$821$	−2.31549e7	−	1.68230e7i	−1.19890	−	0.871054i	−0.204727	−	0.978819i	$-0.565631\pi$
$821$	−2.31549e7	−	1.68230e7i	−1.19890	−	0.871054i	−0.994176	+	0.107765i	$0.965631\pi$
$822$		0			0
$823$	1.89202e6	−	5.82305e6i	0.0973703	−	0.299675i	−0.890494	−	0.454995i	$-0.849641\pi$
$823$	1.89202e6	−	5.82305e6i	0.0973703	−	0.299675i	0.987864	+	0.155320i	$0.0496409\pi$
$824$		0			0
$825$	2.86455e6	−	1.14191e7i	0.146528	−	0.584113i
$826$		0			0
$827$	−6.98451e6	+	2.14961e7i	−0.355118	+	1.09294i	0.600823	+	0.799382i	$0.294839\pi$
$827$	−6.98451e6	+	2.14961e7i	−0.355118	+	1.09294i	−0.955941	+	0.293558i	$0.905161\pi$
$828$		0			0
$829$	−6.61899e6	−	4.80898e6i	−0.334507	−	0.243034i	0.407833	−	0.913056i	$-0.366284\pi$
$829$	−6.61899e6	−	4.80898e6i	−0.334507	−	0.243034i	−0.742341	+	0.670023i	$0.766284\pi$
$830$		0			0
$831$	1.99914e6	+	6.15272e6i	0.100425	+	0.309075i
$832$		0			0
$833$	−1.96772e7	+	1.42963e7i	−0.982541	+	0.713858i
$834$		0			0
$835$	3.23351e6			0.160494
$836$		0			0
$837$	−1.97981e6			−0.0976812
$838$		0			0
$839$	2.75797e7	−	2.00378e7i	1.35265	−	0.982756i	0.353773	−	0.935331i	$-0.384898\pi$
$839$	2.75797e7	−	2.00378e7i	1.35265	−	0.982756i	0.998875	−	0.0474253i	$-0.0151016\pi$
$840$		0			0
$841$	1.85715e6	+	5.71572e6i	0.0905434	+	0.278664i
$842$		0			0
$843$	1.74372e7	+	1.26689e7i	0.845101	+	0.614002i
$844$		0			0
$845$	1.45432e6	−	4.47592e6i	0.0700676	−	0.215646i
$846$		0			0
$847$	1.08608e7	+	5.81491e6i	0.520179	+	0.278506i
$848$		0			0
$849$	−567330.	+	1.74606e6i	−0.0270126	+	0.0831363i
$850$		0			0
$851$	−1.28386e7	−	9.32782e6i	−0.607708	−	0.441526i
$852$		0			0
$853$	−5.49879e6	−	1.69236e7i	−0.258759	−	0.796377i	−0.993066	−	0.117560i	$-0.962493\pi$
$853$	−5.49879e6	−	1.69236e7i	−0.258759	−	0.796377i	0.734307	−	0.678817i	$-0.237507\pi$
$854$		0			0
$855$	4.30043e6	−	3.12444e6i	0.201185	−	0.146170i
$856$		0			0
$857$	−184993.			−0.00860404			−0.00430202	−	0.999991i	$-0.501369\pi$
$857$	−184993.			−0.00860404			−0.00430202	+	0.999991i	$0.501369\pi$
$858$		0			0
$859$	−1.38415e7			−0.640031			−0.320015	−	0.947412i	$-0.603688\pi$
$859$	−1.38415e7			−0.640031			−0.320015	+	0.947412i	$0.603688\pi$
$860$		0			0
$861$	8.98203e6	−	6.52583e6i	0.412921	−	0.300005i
$862$		0			0
$863$	−5.85356e6	−	1.80154e7i	−0.267543	−	0.823412i	−0.991097	−	0.133144i	$-0.957493\pi$
$863$	−5.85356e6	−	1.80154e7i	−0.267543	−	0.823412i	0.723554	−	0.690268i	$-0.242507\pi$
$864$		0			0
$865$	−1.14489e6	−	831813.i	−0.0520265	−	0.0377994i
$866$		0			0
$867$	1.26888e7	−	3.90522e7i	0.573290	−	1.76440i
$868$		0			0
$869$	7.09174e6	−	2.82702e7i	0.318569	−	1.26993i
$870$		0			0
$871$	4.91039e6	−	1.51126e7i	0.219316	−	0.674986i
$872$		0			0
$873$	−1.33787e6	−	972023.i	−0.0594128	−	0.0431659i
$874$		0			0
$875$	−3.30979e6	−	1.01865e7i	−0.146144	−	0.449785i
$876$		0			0
$877$	−4.59702e6	+	3.33993e6i	−0.201826	+	0.146635i	−0.684108	−	0.729381i	$-0.739808\pi$
$877$	−4.59702e6	+	3.33993e6i	−0.201826	+	0.146635i	0.482282	+	0.876016i	$0.339808\pi$
$878$		0			0
$879$	−8.20033e6			−0.357980
$880$		0			0
$881$	4.81474e6			0.208994			0.104497	−	0.994525i	$-0.466677\pi$
$881$	4.81474e6			0.208994			0.104497	+	0.994525i	$0.466677\pi$
$882$		0			0
$883$	2.72522e7	−	1.97999e7i	1.17625	−	0.854595i	0.184505	−	0.982832i	$-0.440932\pi$
$883$	2.72522e7	−	1.97999e7i	1.17625	−	0.854595i	0.991744	+	0.128237i	$0.0409318\pi$
$884$		0			0
$885$	−904525.	−	2.78384e6i	−0.0388206	−	0.119478i
$886$		0			0
$887$	−1.32275e7	−	9.61033e6i	−0.564506	−	0.410137i	0.268599	−	0.963252i	$-0.413439\pi$
$887$	−1.32275e7	−	9.61033e6i	−0.564506	−	0.410137i	−0.833105	+	0.553114i	$0.813439\pi$
$888$		0			0
$889$	3.31194e6	−	1.01931e7i	0.140549	−	0.432566i
$890$		0			0
$891$	−7.49028e6	−	4.69543e6i	−0.316085	−	0.198144i
$892$		0			0
$893$	4.34841e6	−	1.33830e7i	0.182475	−	0.561599i
$894$		0			0
$895$	6.47921e6	+	4.70742e6i	0.270374	+	0.196438i
$896$		0			0
$897$	4.12996e6	+	1.27107e7i	0.171382	+	0.527459i
$898$		0			0
$899$	−2.01935e6	+	1.46714e6i	−0.0833320	+	0.0605443i
$900$		0			0
$901$	1.67835e7			0.688763
$902$		0			0
$903$	−119976.			−0.00489637
$904$		0			0
$905$	−5.57753e6	+	4.05232e6i	−0.226371	+	0.164468i
$906$		0			0
$907$	1.38189e7	+	4.25302e7i	0.557770	+	1.71664i	0.688514	+	0.725223i	$0.258263\pi$
$907$	1.38189e7	+	4.25302e7i	0.557770	+	1.71664i	−0.130745	+	0.991416i	$0.541737\pi$
$908$		0			0
$909$	1.74653e7	+	1.26893e7i	0.701080	+	0.509364i
$910$		0			0
$911$	−6.78676e6	+	2.08875e7i	−0.270936	+	0.833855i	0.719330	+	0.694668i	$0.244449\pi$
$911$	−6.78676e6	+	2.08875e7i	−0.270936	+	0.833855i	−0.990266	+	0.139187i	$0.955551\pi$
$912$		0			0
$913$	8.38239e6	+	2.08333e7i	0.332806	+	0.827145i
$914$		0			0
$915$	1.60049e6	−	4.92580e6i	0.0631975	−	0.194502i
$916$		0			0
$917$	−2.32747e7	−	1.69100e7i	−0.914030	−	0.664082i
$918$		0			0
$919$	−8.34354e6	−	2.56788e7i	−0.325883	−	1.00296i	−0.971041	−	0.238915i	$-0.923208\pi$
$919$	−8.34354e6	−	2.56788e7i	−0.325883	−	1.00296i	0.645158	−	0.764049i	$-0.276792\pi$
$920$		0			0
$921$	−1.00519e7	+	7.30310e6i	−0.390479	+	0.283699i
$922$		0			0
$923$	2.98108e7			1.15178
$924$		0			0
$925$	−1.48605e7			−0.571055
$926$		0			0
$927$	1.48948e7	−	1.08217e7i	0.569290	−	0.413614i
$928$		0			0
$929$	−1.35875e6	−	4.18179e6i	−0.0516534	−	0.158973i	0.921902	−	0.387422i	$-0.126634\pi$
$929$	−1.35875e6	−	4.18179e6i	−0.0516534	−	0.158973i	−0.973556	+	0.228449i	$0.926634\pi$
$930$		0			0
$931$	−1.78677e7	−	1.29817e7i	−0.675608	−	0.490858i
$932$		0			0
$933$	9.85490e6	−	3.03303e7i	0.370636	−	1.14070i
$934$		0			0
$935$	1.69888e7	−	1.42137e7i	0.635527	−	0.531715i
$936$		0			0
$937$	−2.40296e6	+	7.39556e6i	−0.0894124	+	0.275183i	−0.985757	−	0.168174i	$-0.946213\pi$
$937$	−2.40296e6	+	7.39556e6i	−0.0894124	+	0.275183i	0.896345	+	0.443358i	$0.146213\pi$
$938$		0			0
$939$	−2.19362e7	−	1.59376e7i	−0.811892	−	0.589874i
$940$		0			0
$941$	−5.69714e6	−	1.75340e7i	−0.209741	−	0.645516i	−0.999485	−	0.0320801i	$-0.989787\pi$
$941$	−5.69714e6	−	1.75340e7i	−0.209741	−	0.645516i	0.789744	−	0.613436i	$-0.210213\pi$
$942$		0			0
$943$	−2.68621e7	+	1.95165e7i	−0.983697	+	0.714697i
$944$		0			0
$945$	−7.76838e6			−0.282977
$946$		0			0
$947$	1.27595e7			0.462338			0.231169	−	0.972914i	$-0.425745\pi$
$947$	1.27595e7			0.462338			0.231169	+	0.972914i	$0.425745\pi$
$948$		0			0
$949$	−1.23042e6	+	893954.i	−0.0443495	+	0.0322218i
$950$		0			0
$951$	−1.01232e7	−	3.11561e7i	−0.362968	−	1.11710i
$952$		0			0
$953$	3.33967e6	+	2.42641e6i	0.119116	+	0.0865431i	0.645748	−	0.763550i	$-0.276545\pi$
$953$	3.33967e6	+	2.42641e6i	0.119116	+	0.0865431i	−0.526632	+	0.850093i	$0.676545\pi$
$954$		0			0
$955$	−6.61859e6	+	2.03699e7i	−0.234832	+	0.722738i
$956$		0			0
$957$	−2.41284e7	+	1.65236e6i	−0.851627	+	0.0583210i
$958$		0			0
$959$	−7.42360e6	+	2.28475e7i	−0.260656	+	0.802218i
$960$		0			0
$961$	2.29714e7	+	1.66897e7i	0.802379	+	0.582962i
$962$		0			0
$963$	−1.65829e6	−	5.10370e6i	−0.0576229	−	0.177345i
$964$		0			0
$965$	1.24537e7	−	9.04816e6i	0.430508	−	0.312782i
$966$		0			0
$967$	−2.59567e7			−0.892655			−0.446328	−	0.894870i	$-0.647268\pi$
$967$	−2.59567e7			−0.892655			−0.446328	+	0.894870i	$0.647268\pi$
$968$		0			0
$969$	5.23735e7			1.79185
$970$		0			0
$971$	−2.81302e7	+	2.04378e7i	−0.957469	+	0.695642i	−0.952562	−	0.304346i	$-0.901562\pi$
$971$	−2.81302e7	+	2.04378e7i	−0.957469	+	0.695642i	−0.00490733	+	0.999988i	$0.501562\pi$
$972$		0			0
$973$	1.14631e6	+	3.52799e6i	0.0388169	+	0.119466i
$974$		0			0
$975$	1.01249e7	+	7.35620e6i	0.341099	+	0.247823i
$976$		0			0
$977$	−7.02266e6	+	2.16135e7i	−0.235378	+	0.724418i	0.761693	+	0.647938i	$0.224368\pi$
$977$	−7.02266e6	+	2.16135e7i	−0.235378	+	0.724418i	−0.997071	+	0.0764803i	$0.975632\pi$
$978$		0			0
$979$	−8.96558e6	+	613980.i	−0.298966	+	0.0204738i
$980$		0			0
$981$	−4.89453e6	+	1.50638e7i	−0.162382	+	0.499761i
$982$		0			0
$983$	−3.30261e7	−	2.39949e7i	−1.09012	−	0.792018i	−0.110699	−	0.993854i	$-0.535309\pi$
$983$	−3.30261e7	−	2.39949e7i	−1.09012	−	0.792018i	−0.979419	+	0.201836i	$0.935309\pi$
$984$		0			0
$985$	1.19860e6	+	3.68891e6i	0.0393626	+	0.121146i
$986$		0			0
$987$	−5.05509e6	+	3.67274e6i	−0.165172	+	0.120004i
$988$		0			0
$989$	358805.			0.0116646
$990$		0			0
$991$	5.50363e7			1.78019			0.890093	−	0.455779i	$-0.150639\pi$
$991$	5.50363e7			1.78019			0.890093	+	0.455779i	$0.150639\pi$
$992$		0			0
$993$	9.48416e6	−	6.89064e6i	0.305229	−	0.221762i
$994$		0			0
$995$	−5.22127e6	−	1.60694e7i	−0.167193	−	0.514567i
$996$		0			0
$997$	5.10996e6	+	3.71260e6i	0.162809	+	0.118288i	0.666207	−	0.745767i	$-0.267917\pi$
$997$	5.10996e6	+	3.71260e6i	0.162809	+	0.118288i	−0.503397	+	0.864055i	$0.667917\pi$
$998$		0			0
$999$	−7.48250e6	+	2.30288e7i	−0.237210	+	0.730057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.6.i.b.9.3	✓	32
11.4	even	5		968.6.a.q.1.11		16
11.5	even	5	inner	88.6.i.b.49.3	yes	32
11.7	odd	10		968.6.a.p.1.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.6.i.b.9.3	✓	32	1.1	even	1	trivial
88.6.i.b.49.3	yes	32	11.5	even	5	inner
968.6.a.p.1.11		16	11.7	odd	10
968.6.a.q.1.11		16	11.4	even	5

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:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	88.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.46729 + 6.87839i) q^{3} +(-7.68277 - 23.6451i) q^{5} +(61.8852 + 44.9623i) q^{7} +(-32.7737 + 100.867i) q^{9} +(-400.374 + 27.4184i) q^{11} +(131.830 - 405.731i) q^{13} +(235.375 + 171.010i) q^{15} +(-686.043 - 2111.42i) q^{17} +(1630.92 - 1184.93i) q^{19} -895.154 q^{21} +2677.09 q^{23} +(2028.11 - 1473.51i) q^{25} +(-1262.26 - 3884.83i) q^{27} +(-4166.32 - 3027.01i) q^{29} +(149.776 - 460.962i) q^{31} +(3601.86 - 3013.51i) q^{33} +(587.688 - 1808.72i) q^{35} +(-4795.74 - 3484.31i) q^{37} +(1542.71 + 4747.96i) q^{39} +(-10034.1 + 7290.18i) q^{41} +134.028 q^{43} +2636.81 q^{45} +(5647.18 - 4102.91i) q^{47} +(-3385.47 - 10419.4i) q^{49} +(21018.2 + 15270.6i) q^{51} +(-2336.12 + 7189.84i) q^{53} +(3724.29 + 9256.24i) q^{55} +(-7289.96 + 22436.2i) q^{57} +(-8139.39 - 5913.62i) q^{59} +(-5501.10 - 16930.6i) q^{61} +(-6563.43 + 4768.61i) q^{63} -10606.4 q^{65} +37247.9 q^{67} +(-25344.8 + 18414.1i) q^{69} +(21593.6 + 66458.1i) q^{71} +(-2884.18 - 2095.48i) q^{73} +(-9065.35 + 27900.3i) q^{75} +(-26010.0 - 16304.9i) q^{77} +(-22443.0 + 69072.5i) q^{79} +(17821.5 + 12948.1i) q^{81} +(-17291.9 - 53218.9i) q^{83} +(-44654.1 + 32443.1i) q^{85} +60264.7 q^{87} +22393.0 q^{89} +(26400.9 - 19181.4i) q^{91} +(1752.71 + 5394.28i) q^{93} +(-40547.8 - 29459.7i) q^{95} +(-4818.33 + 14829.3i) q^{97} +(10356.1 - 41283.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 21 q^{3} + 37 q^{5} - 181 q^{7} - 1123 q^{9} + 563 q^{11} - 753 q^{13} - 1731 q^{15} + 3153 q^{17} - 2022 q^{19} - 2282 q^{21} + 4516 q^{23} - 2551 q^{25} + 11538 q^{27} + 7829 q^{29} - 7643 q^{31}+ \cdots + 689815 q^{99}+O(q^{100}) \) 32 * q - 21 * q^3 + 37 * q^5 - 181 * q^7 - 1123 * q^9 + 563 * q^11 - 753 * q^13 - 1731 * q^15 + 3153 * q^17 - 2022 * q^19 - 2282 * q^21 + 4516 * q^23 - 2551 * q^25 + 11538 * q^27 + 7829 * q^29 - 7643 * q^31 - 20846 * q^33 - 47237 * q^35 - 30139 * q^37 + 15155 * q^39 + 17377 * q^41 + 37862 * q^43 + 46556 * q^45 - 7053 * q^47 - 43539 * q^49 - 55812 * q^51 - 17637 * q^53 + 81511 * q^55 + 137684 * q^57 + 58662 * q^59 + 32619 * q^61 - 29128 * q^63 - 103034 * q^65 + 20982 * q^67 - 183982 * q^69 + 43641 * q^71 + 94725 * q^73 - 14162 * q^75 + 143529 * q^77 + 111121 * q^79 - 97990 * q^81 - 117894 * q^83 + 123843 * q^85 - 154438 * q^87 + 13394 * q^89 - 378075 * q^91 - 83153 * q^93 + 362641 * q^95 - 332002 * q^97 + 689815 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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