LMFDB - Embedded newform 304.5.r.c.145.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,5,Mod(65,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("304.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	304.r (of order $6$, degree $2$, not 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:	$31.4244687775$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 1024 x^{14} - 7028 x^{13} + 404698 x^{12} - 2337188 x^{11} + 77836288 x^{10} + \cdots + 23840536514409 $ x^16 - 8x^15 + 1024x^14 - 7028x^13 + 404698x^12 - 2337188x^11 + 77836288x^10 - 367923764x^9 + 7565874847x^8 - 28081380444x^7 + 352870494000x^6 - 961846520868x^5 + 6856327325898x^4 - 12141615583188x^3 + 32749209391860x^2 - 26834137576128*x + 23840536514409
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.4
Root			$0.500000 + 0.961202i$ of defining polynomial
Character	$\chi$	$=$	304.145
Dual form			304.5.r.c.65.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30717 + 0.754695i) q^{3} +(1.35492 + 2.34679i) q^{5} -79.4947 q^{7} +(-39.3609 + 68.1750i) q^{9} +O(q^{10})$	\(q+(-1.30717 + 0.754695i) q^{3} +(1.35492 + 2.34679i) q^{5} -79.4947 q^{7} +(-39.3609 + 68.1750i) q^{9} -109.030 q^{11} +(269.920 + 155.839i) q^{13} +(-3.54222 - 2.04510i) q^{15} +(-212.438 - 367.953i) q^{17} +(333.675 + 137.776i) q^{19} +(103.913 - 59.9943i) q^{21} +(132.097 - 228.798i) q^{23} +(308.828 - 534.906i) q^{25} -241.082i q^{27} +(-203.478 - 117.478i) q^{29} -648.147i q^{31} +(142.521 - 82.2843i) q^{33} +(-107.709 - 186.557i) q^{35} +626.819i q^{37} -470.442 q^{39} +(-415.611 + 239.953i) q^{41} +(622.065 + 1077.45i) q^{43} -213.323 q^{45} +(822.028 - 1423.79i) q^{47} +3918.41 q^{49} +(555.384 + 320.651i) q^{51} +(-4118.24 - 2377.67i) q^{53} +(-147.727 - 255.870i) q^{55} +(-540.148 + 71.7266i) q^{57} +(4227.83 - 2440.94i) q^{59} +(3545.36 - 6140.74i) q^{61} +(3128.98 - 5419.56i) q^{63} +844.594i q^{65} +(-51.8915 - 29.9596i) q^{67} +398.771i q^{69} +(-5416.15 + 3127.02i) q^{71} +(-1209.33 - 2094.62i) q^{73} +932.285i q^{75} +8667.30 q^{77} +(3684.36 - 2127.16i) q^{79} +(-3006.29 - 5207.04i) q^{81} +6643.06 q^{83} +(575.671 - 997.091i) q^{85} +354.640 q^{87} +(8489.61 + 4901.48i) q^{89} +(-21457.2 - 12388.3i) q^{91} +(489.153 + 847.239i) q^{93} +(128.772 + 969.738i) q^{95} +(-4066.41 + 2347.74i) q^{97} +(4291.51 - 7433.11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9}+O(q^{10}) $ 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9	$ 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9} + 84 q^{11} + 450 q^{13} + 390 q^{15} + 606 q^{17} + 306 q^{19} - 2160 q^{21} + 54 q^{23} - 434 q^{25} - 4914 q^{29} + 7890 q^{33} - 2328 q^{35} - 7620 q^{39} - 1692 q^{41} + 7402 q^{43} - 16720 q^{45} - 3198 q^{47} + 24816 q^{49} - 10710 q^{51} + 3870 q^{53} + 13588 q^{55} + 3702 q^{57} + 18288 q^{59} - 6522 q^{61} + 15676 q^{63} + 30168 q^{67} - 35874 q^{71} - 8080 q^{73} + 34560 q^{77} + 30738 q^{79} - 30920 q^{81} + 1476 q^{83} + 33626 q^{85} - 113100 q^{87} + 19782 q^{89} + 34260 q^{91} - 4272 q^{93} + 23706 q^{95} - 9936 q^{97} - 3848 q^{99}+O(q^{100}) $ 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9 + 84 * q^11 + 450 * q^13 + 390 * q^15 + 606 * q^17 + 306 * q^19 - 2160 * q^21 + 54 * q^23 - 434 * q^25 - 4914 * q^29 + 7890 * q^33 - 2328 * q^35 - 7620 * q^39 - 1692 * q^41 + 7402 * q^43 - 16720 * q^45 - 3198 * q^47 + 24816 * q^49 - 10710 * q^51 + 3870 * q^53 + 13588 * q^55 + 3702 * q^57 + 18288 * q^59 - 6522 * q^61 + 15676 * q^63 + 30168 * q^67 - 35874 * q^71 - 8080 * q^73 + 34560 * q^77 + 30738 * q^79 - 30920 * q^81 + 1476 * q^83 + 33626 * q^85 - 113100 * q^87 + 19782 * q^89 + 34260 * q^91 - 4272 * q^93 + 23706 * q^95 - 9936 * q^97 - 3848 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.30717	+	0.754695i	−0.145241	+	0.0838550i	−0.570860	−	0.821048i	$-0.693390\pi$
$3$	−1.30717	+	0.754695i	−0.145241	+	0.0838550i	0.425618	+	0.904903i	$0.360057\pi$
$4$		0			0
$5$	1.35492	+	2.34679i	0.0541967	+	0.0938715i	0.891851	−	0.452329i	$-0.149407\pi$
$5$	1.35492	+	2.34679i	0.0541967	+	0.0938715i	−0.837654	+	0.546201i	$0.816074\pi$
$6$		0			0
$7$	−79.4947			−1.62234			−0.811171	−	0.584809i	$-0.801169\pi$
$7$	−79.4947			−1.62234			−0.811171	+	0.584809i	$0.801169\pi$
$8$		0			0
$9$	−39.3609	+	68.1750i	−0.485937	+	0.841667i
$10$		0			0
$11$	−109.030			−0.901073			−0.450537	−	0.892758i	$-0.648767\pi$
$11$	−109.030			−0.901073			−0.450537	+	0.892758i	$0.648767\pi$
$12$		0			0
$13$	269.920	+	155.839i	1.59716	+	0.922121i	0.992031	+	0.125995i	$0.0402123\pi$
$13$	269.920	+	155.839i	1.59716	+	0.922121i	0.605130	+	0.796126i	$0.293121\pi$
$14$		0			0
$15$	−3.54222	−	2.04510i	−0.0157432	−	0.00908933i
$16$		0			0
$17$	−212.438	−	367.953i	−0.735078	−	1.27319i	−0.954689	−	0.297605i	$-0.903812\pi$
$17$	−212.438	−	367.953i	−0.735078	−	1.27319i	0.219611	−	0.975587i	$-0.429521\pi$
$18$		0			0
$19$	333.675	+	137.776i	0.924307	+	0.381650i
$19$	333.675	+	137.776i	0.924307	+	0.381650i
$20$		0			0
$21$	103.913	−	59.9943i	0.235631	−	0.136041i
$22$		0			0
$23$	132.097	−	228.798i	0.249710	−	0.432510i	−0.713735	−	0.700416i	$-0.752998\pi$
$23$	132.097	−	228.798i	0.249710	−	0.432510i	0.963445	+	0.267905i	$0.0863314\pi$
$24$		0			0
$25$	308.828	−	534.906i	0.494125	−	0.855850i
$26$		0			0
$27$		−	241.082i		−	0.330703i
$28$		0			0
$29$	−203.478	−	117.478i	−0.241947	−	0.139688i	0.374124	−	0.927379i	$-0.377943\pi$
$29$	−203.478	−	117.478i	−0.241947	−	0.139688i	−0.616071	+	0.787690i	$0.711277\pi$
$30$		0			0
$31$		−	648.147i		−	0.674451i	−0.941424	−	0.337225i	$-0.890512\pi$
$31$		−	648.147i		−	0.674451i	0.941424	−	0.337225i	$-0.109488\pi$
$32$		0			0
$33$	142.521	−	82.2843i	0.130873	−	0.0755595i
$34$		0			0
$35$	−107.709	−	186.557i	−0.0879256	−	0.152292i
$36$		0			0
$37$			626.819i			0.457866i	0.973442	+	0.228933i	$0.0735237\pi$
$37$			626.819i			0.457866i	−0.973442	+	0.228933i	$0.926476\pi$
$38$		0			0
$39$	−470.442			−0.309298
$40$		0			0
$41$	−415.611	+	239.953i	−0.247240	+	0.142744i	−0.618500	−	0.785785i	$-0.712259\pi$
$41$	−415.611	+	239.953i	−0.247240	+	0.142744i	0.371260	+	0.928529i	$0.378926\pi$
$42$		0			0
$43$	622.065	+	1077.45i	0.336433	+	0.582720i	0.983759	−	0.179494i	$-0.0574460\pi$
$43$	622.065	+	1077.45i	0.336433	+	0.582720i	−0.647326	+	0.762213i	$0.724113\pi$
$44$		0			0
$45$	−213.323			−0.105345
$46$		0			0
$47$	822.028	−	1423.79i	0.372127	−	0.644542i	−0.617766	−	0.786362i	$-0.711962\pi$
$47$	822.028	−	1423.79i	0.372127	−	0.644542i	0.989892	+	0.141820i	$0.0452954\pi$
$48$		0			0
$49$	3918.41			1.63199
$50$		0			0
$51$	555.384	+	320.651i	0.213527	+	0.123280i
$52$		0			0
$53$	−4118.24	−	2377.67i	−1.46609	−	0.846447i	−0.466808	−	0.884359i	$-0.654596\pi$
$53$	−4118.24	−	2377.67i	−1.46609	−	0.846447i	−0.999281	+	0.0379118i	$0.987929\pi$
$54$		0			0
$55$	−147.727	−	255.870i	−0.0488352	−	0.0845851i
$56$		0			0
$57$	−540.148	+	71.7266i	−0.166251	+	0.0220765i
$58$		0			0
$59$	4227.83	−	2440.94i	1.21455	−	0.701219i	0.250800	−	0.968039i	$-0.419306\pi$
$59$	4227.83	−	2440.94i	1.21455	−	0.701219i	0.963746	+	0.266820i	$0.0859731\pi$
$60$		0			0
$61$	3545.36	−	6140.74i	0.952797	−	1.65029i	0.213467	−	0.976950i	$-0.431524\pi$
$61$	3545.36	−	6140.74i	0.952797	−	1.65029i	0.739330	−	0.673343i	$-0.235142\pi$
$62$		0			0
$63$	3128.98	−	5419.56i	0.788355	−	1.36547i
$64$		0			0
$65$			844.594i			0.199904i
$66$		0			0
$67$	−51.8915	−	29.9596i	−0.0115597	−	0.00667400i	0.494209	−	0.869343i	$-0.335458\pi$
$67$	−51.8915	−	29.9596i	−0.0115597	−	0.00667400i	−0.505769	+	0.862669i	$0.668791\pi$
$68$		0			0
$69$			398.771i			0.0837577i
$70$		0			0
$71$	−5416.15	+	3127.02i	−1.07442	+	0.620317i	−0.929386	−	0.369110i	$-0.879663\pi$
$71$	−5416.15	+	3127.02i	−1.07442	+	0.620317i	−0.145035	+	0.989427i	$0.546329\pi$
$72$		0			0
$73$	−1209.33	−	2094.62i	−0.226934	−	0.393061i	0.729964	−	0.683486i	$-0.239537\pi$
$73$	−1209.33	−	2094.62i	−0.226934	−	0.393061i	−0.956898	+	0.290424i	$0.906204\pi$
$74$		0			0
$75$			932.285i			0.165740i
$76$		0			0
$77$	8667.30			1.46185
$78$		0			0
$79$	3684.36	−	2127.16i	0.590347	−	0.340837i	−0.174888	−	0.984588i	$-0.555956\pi$
$79$	3684.36	−	2127.16i	0.590347	−	0.340837i	0.765235	+	0.643751i	$0.222623\pi$
$80$		0			0
$81$	−3006.29	−	5207.04i	−0.458206	−	0.793635i
$82$		0			0
$83$	6643.06			0.964299			0.482150	−	0.876089i	$-0.339856\pi$
$83$	6643.06			0.964299			0.482150	+	0.876089i	$0.339856\pi$
$84$		0			0
$85$	575.671	−	997.091i	0.0796776	−	0.138006i
$86$		0			0
$87$	354.640			0.0468542
$88$		0			0
$89$	8489.61	+	4901.48i	1.07179	+	0.618796i	0.928669	−	0.370910i	$-0.120954\pi$
$89$	8489.61	+	4901.48i	1.07179	+	0.618796i	0.143117	+	0.989706i	$0.454288\pi$
$90$		0			0
$91$	−21457.2	−	12388.3i	−2.59114	−	1.49600i
$92$		0			0
$93$	489.153	+	847.239i	0.0565561	+	0.0979580i
$94$		0			0
$95$	128.772	+	969.738i	0.0142684	+	0.107450i
$96$		0			0
$97$	−4066.41	+	2347.74i	−0.432183	+	0.249521i	−0.700276	−	0.713872i	$-0.746940\pi$
$97$	−4066.41	+	2347.74i	−0.432183	+	0.249521i	0.268093	+	0.963393i	$0.413606\pi$
$98$		0			0
$99$	4291.51	−	7433.11i	0.437865	−	0.758404i
$100$		0			0
$101$	6044.15	−	10468.8i	0.592506	−	1.02625i	−0.401388	−	0.915908i	$-0.631472\pi$
$101$	6044.15	−	10468.8i	0.592506	−	1.02625i	0.993894	−	0.110342i	$-0.0351947\pi$
$102$		0			0
$103$			5955.85i			0.561396i	0.959796	+	0.280698i	$0.0905660\pi$
$103$			5955.85i			0.561396i	−0.959796	+	0.280698i	$0.909434\pi$
$104$		0			0
$105$	281.588	+	162.575i	0.0255408	+	0.0147460i
$106$		0			0
$107$		−	565.173i		−	0.0493644i	−0.999695	−	0.0246822i	$-0.992143\pi$
$107$		−	565.173i		−	0.0493644i	0.999695	−	0.0246822i	$-0.00785738\pi$
$108$		0			0
$109$	1522.49	−	879.012i	0.128145	−	0.0739847i	−0.434557	−	0.900644i	$-0.643095\pi$
$109$	1522.49	−	879.012i	0.128145	−	0.0739847i	0.562702	+	0.826660i	$0.309762\pi$
$110$		0			0
$111$	−473.057	−	819.359i	−0.0383944	−	0.0665010i
$112$		0			0
$113$			9913.95i			0.776408i	0.921574	+	0.388204i	$0.126904\pi$
$113$			9913.95i			0.776408i	−0.921574	+	0.388204i	$0.873096\pi$
$114$		0			0
$115$	715.920			0.0541339
$116$		0			0
$117$	−21248.6	+	12267.9i	−1.55224	+	0.896185i
$118$		0			0
$119$	16887.7	+	29250.3i	1.19255	+	2.06555i
$120$		0			0
$121$	−2753.49			−0.188067
$122$		0			0
$123$	362.183	−	627.319i	0.0239396	−	0.0414647i
$124$		0			0
$125$	3367.40			0.215513
$126$		0			0
$127$	12784.5	+	7381.12i	0.792639	+	0.457630i	0.840891	−	0.541205i	$-0.182032\pi$
$127$	12784.5	+	7381.12i	0.792639	+	0.457630i	−0.0482521	+	0.998835i	$0.515365\pi$
$128$		0			0
$129$	−1626.29	−	938.939i	−0.0977279	−	0.0564232i
$130$		0			0
$131$	3378.16	+	5851.14i	0.196851	+	0.340956i	0.947506	−	0.319739i	$-0.103595\pi$
$131$	3378.16	+	5851.14i	0.196851	+	0.340956i	−0.750655	+	0.660695i	$0.770262\pi$
$132$		0			0
$133$	−26525.4	−	10952.4i	−1.49954	−	0.619167i
$134$		0			0
$135$	565.769	−	326.647i	0.0310436	−	0.0179230i
$136$		0			0
$137$	4112.96	−	7123.85i	0.219136	−	0.379554i	−0.735408	−	0.677624i	$-0.763010\pi$
$137$	4112.96	−	7123.85i	0.219136	−	0.379554i	0.954544	+	0.298070i	$0.0963429\pi$
$138$		0			0
$139$	3781.52	−	6549.79i	0.195721	−	0.338999i	−0.751416	−	0.659829i	$-0.770629\pi$
$139$	3781.52	−	6549.79i	0.195721	−	0.338999i	0.947137	+	0.320831i	$0.103962\pi$
$140$		0			0
$141$			2481.52i			0.124819i
$142$		0			0
$143$	−29429.4	−	16991.1i	−1.43916	−	0.830899i
$144$		0			0
$145$		−	636.691i		−	0.0302826i
$146$		0			0
$147$	−5122.03	+	2957.21i	−0.237032	+	0.136851i
$148$		0			0
$149$	−5962.37	−	10327.1i	−0.268563	−	0.465165i	0.699928	−	0.714214i	$-0.253215\pi$
$149$	−5962.37	−	10327.1i	−0.268563	−	0.465165i	−0.968491	+	0.249048i	$0.919882\pi$
$150$		0			0
$151$		−	28967.0i		−	1.27043i	−0.772336	−	0.635214i	$-0.780912\pi$
$151$		−	28967.0i		−	1.27043i	0.772336	−	0.635214i	$-0.219088\pi$
$152$		0			0
$153$	33446.9			1.42881
$154$		0			0
$155$	1521.06	−	878.187i	0.0633117	−	0.0365530i
$156$		0			0
$157$	−3199.97	−	5542.52i	−0.129822	−	0.224858i	0.793786	−	0.608198i	$-0.208107\pi$
$157$	−3199.97	−	5542.52i	−0.129822	−	0.224858i	−0.923607	+	0.383340i	$0.874774\pi$
$158$		0			0
$159$	7177.66			0.283915
$160$		0			0
$161$	−10501.0	+	18188.2i	−0.405115	+	0.701680i
$162$		0			0
$163$	5001.30			0.188238			0.0941191	−	0.995561i	$-0.469997\pi$
$163$	5001.30			0.188238			0.0941191	+	0.995561i	$0.469997\pi$
$164$		0			0
$165$	386.207	+	222.977i	0.0141858	+	0.00819015i
$166$		0			0
$167$	−21896.3	−	12641.8i	−0.785122	−	0.453290i	0.0531207	−	0.998588i	$-0.483083\pi$
$167$	−21896.3	−	12641.8i	−0.785122	−	0.453290i	−0.838242	+	0.545298i	$0.816417\pi$
$168$		0			0
$169$	34290.8	+	59393.4i	1.20062	+	2.07953i
$170$		0			0
$171$	−22526.6	+	17325.3i	−0.770377	+	0.592501i
$172$		0			0
$173$	−8946.68	+	5165.37i	−0.298930	+	0.172587i	−0.641962	−	0.766736i	$-0.721879\pi$
$173$	−8946.68	+	5165.37i	−0.298930	+	0.172587i	0.343032	+	0.939324i	$0.388546\pi$
$174$		0			0
$175$	−24550.2	+	42522.3i	−0.801640	+	1.38848i
$176$		0			0
$177$	−3684.33	+	6381.45i	−0.117601	+	0.203691i
$178$		0			0
$179$			51529.9i			1.60825i	0.594460	+	0.804125i	$0.297366\pi$
$179$			51529.9i			1.60825i	−0.594460	+	0.804125i	$0.702634\pi$
$180$		0			0
$181$	−6016.05	−	3473.37i	−0.183635	−	0.106022i	0.405365	−	0.914155i	$-0.367145\pi$
$181$	−6016.05	−	3473.37i	−0.183635	−	0.106022i	−0.588999	+	0.808134i	$0.700478\pi$
$182$		0			0
$183$			10702.7i			0.319587i
$184$		0			0
$185$	−1471.01	+	849.289i	−0.0429806	+	0.0248149i
$186$		0			0
$187$	23162.0	+	40117.8i	0.662359	+	1.14724i
$188$		0			0
$189$			19164.8i			0.536513i
$190$		0			0
$191$	−51066.6			−1.39981			−0.699906	−	0.714235i	$-0.746775\pi$
$191$	−51066.6			−1.39981			−0.699906	+	0.714235i	$0.746775\pi$
$192$		0			0
$193$	−32396.3	+	18704.0i	−0.869723	+	0.502135i	−0.867256	−	0.497862i	$-0.834118\pi$
$193$	−32396.3	+	18704.0i	−0.869723	+	0.502135i	−0.00246664	+	0.999997i	$0.500785\pi$
$194$		0			0
$195$	−637.411	−	1104.03i	−0.0167629	−	0.0290343i
$196$		0			0
$197$	717.559			0.0184895			0.00924475	−	0.999957i	$-0.497057\pi$
$197$	717.559			0.0184895			0.00924475	+	0.999957i	$0.497057\pi$
$198$		0			0
$199$	36697.8	−	63562.4i	0.926688	−	1.60507i	0.137863	−	0.990451i	$-0.455977\pi$
$199$	36697.8	−	63562.4i	0.926688	−	1.60507i	0.788824	−	0.614619i	$-0.210690\pi$
$200$		0			0
$201$	90.4414			0.00223859
$202$		0			0
$203$	16175.4	+	9338.87i	0.392521	+	0.226622i
$204$		0			0
$205$	−1126.24	−	650.234i	−0.0267992	−	0.0154725i
$206$		0			0
$207$	10398.9	+	18011.4i	0.242687	+	0.420345i
$208$		0			0
$209$	−36380.5	−	15021.7i	−0.832868	−	0.343895i
$210$		0			0
$211$	−47735.6	+	27560.2i	−1.07221	+	0.619038i	−0.928783	−	0.370624i	$-0.879144\pi$
$211$	−47735.6	+	27560.2i	−1.07221	+	0.619038i	−0.143422	+	0.989662i	$0.545811\pi$
$212$		0			0
$213$	4719.89	−	8175.09i	0.104033	−	0.180191i
$214$		0			0
$215$	−1685.70	+	2919.71i	−0.0364672	+	0.0631630i
$216$		0			0
$217$			51524.3i			1.09419i
$218$		0			0
$219$	3161.60	+	1825.35i	0.0659203	+	0.0380591i
$220$		0			0
$221$		−	132424.i		−	2.71132i
$222$		0			0
$223$	46662.3	−	26940.5i	0.938333	−	0.541747i	0.0488954	−	0.998804i	$-0.484430\pi$
$223$	46662.3	−	26940.5i	0.938333	−	0.541747i	0.889437	+	0.457057i	$0.151097\pi$
$224$		0			0
$225$	24311.5	+	42108.8i	0.480227	+	0.831778i
$226$		0			0
$227$		−	68480.7i		−	1.32897i	−0.747300	−	0.664487i	$-0.768650\pi$
$227$		−	68480.7i		−	1.32897i	0.747300	−	0.664487i	$-0.231350\pi$
$228$		0			0
$229$	−31051.4			−0.592120			−0.296060	−	0.955169i	$-0.595673\pi$
$229$	−31051.4			−0.592120			−0.296060	+	0.955169i	$0.595673\pi$
$230$		0			0
$231$	−11329.6	+	6541.17i	−0.212321	+	0.122583i
$232$		0			0
$233$	−8921.34	−	15452.2i	−0.164330	−	0.284629i	0.772087	−	0.635517i	$-0.219213\pi$
$233$	−8921.34	−	15452.2i	−0.164330	−	0.284629i	−0.936417	+	0.350888i	$0.885880\pi$
$234$		0			0
$235$	4455.12			0.0806722
$236$		0			0
$237$	−3210.72	+	5561.13i	−0.0571618	+	0.0990071i
$238$		0			0
$239$	−76980.4			−1.34767			−0.673837	−	0.738880i	$-0.735355\pi$
$239$	−76980.4			−1.34767			−0.673837	+	0.738880i	$0.735355\pi$
$240$		0			0
$241$	52604.0	+	30371.0i	0.905701	+	0.522907i	0.879046	−	0.476738i	$-0.158181\pi$
$241$	52604.0	+	30371.0i	0.905701	+	0.522907i	0.0266557	+	0.999645i	$0.491514\pi$
$242$		0			0
$243$	24770.9	+	14301.5i	0.419498	+	0.242197i
$244$		0			0
$245$	5309.13	+	9195.69i	0.0884487	+	0.153198i
$246$		0			0
$247$	68594.8	+	89187.8i	1.12434	+	1.46188i
$248$		0			0
$249$	−8683.60	+	5013.48i	−0.140056	+	0.0808613i
$250$		0			0
$251$	19773.1	−	34248.0i	0.313853	−	0.543610i	−0.665340	−	0.746541i	$-0.731713\pi$
$251$	19773.1	−	34248.0i	0.313853	−	0.543610i	0.979193	+	0.202931i	$0.0650466\pi$
$252$		0			0
$253$	−14402.5	+	24945.8i	−0.225007	+	0.389724i
$254$		0			0
$255$			1737.82i			0.0267255i
$256$		0			0
$257$	−29307.4	−	16920.7i	−0.443723	−	0.256183i	0.261453	−	0.965216i	$-0.415798\pi$
$257$	−29307.4	−	16920.7i	−0.443723	−	0.256183i	−0.705175	+	0.709033i	$0.749132\pi$
$258$		0			0
$259$		−	49828.8i		−	0.742816i
$260$		0			0
$261$	16018.1	−	9248.06i	0.235142	−	0.135759i
$262$		0			0
$263$	−48919.2	−	84730.5i	−0.707241	−	1.22498i	−0.965877	−	0.259003i	$-0.916606\pi$
$263$	−48919.2	−	84730.5i	−0.707241	−	1.22498i	0.258635	−	0.965975i	$-0.416727\pi$
$264$		0			0
$265$		−	12886.2i		−	0.183499i
$266$		0			0
$267$	−14796.5			−0.207556
$268$		0			0
$269$	540.509	−	312.063i	0.00746962	−	0.00431259i	−0.496261	−	0.868174i	$-0.665294\pi$
$269$	540.509	−	312.063i	0.00746962	−	0.00431259i	0.503730	+	0.863861i	$0.331961\pi$
$270$		0			0
$271$	27056.1	+	46862.5i	0.368406	+	0.638097i	0.989316	−	0.145784i	$-0.0465704\pi$
$271$	27056.1	+	46862.5i	0.368406	+	0.638097i	−0.620911	+	0.783881i	$0.713237\pi$
$272$		0			0
$273$	37397.7			0.501787
$274$		0			0
$275$	−33671.5	+	58320.8i	−0.445243	+	0.771184i
$276$		0			0
$277$	−56774.7			−0.739938			−0.369969	−	0.929044i	$-0.620632\pi$
$277$	−56774.7			−0.739938			−0.369969	+	0.929044i	$0.620632\pi$
$278$		0			0
$279$	44187.5	+	25511.6i	0.567663	+	0.327740i
$280$		0			0
$281$	97544.0	+	56317.0i	1.23534	+	0.713226i	0.968139	−	0.250414i	$-0.0805667\pi$
$281$	97544.0	+	56317.0i	1.23534	+	0.713226i	0.267205	+	0.963640i	$0.413900\pi$
$282$		0			0
$283$	−30039.8	−	52030.4i	−0.375080	−	0.649658i	0.615259	−	0.788325i	$-0.289051\pi$
$283$	−30039.8	−	52030.4i	−0.375080	−	0.649658i	−0.990339	+	0.138667i	$0.955718\pi$
$284$		0			0
$285$	−900.184	−	1170.43i	−0.0110826	−	0.0144097i
$286$		0			0
$287$	33038.9	−	19075.0i	0.401108	−	0.231580i
$288$		0			0
$289$	−48498.9	+	84002.5i	−0.580679	+	1.00577i
$290$		0			0
$291$	3543.66	−	6137.79i	0.0418471	−	0.0724814i
$292$		0			0
$293$		−	143559.i		−	1.67223i	−0.548555	−	0.836115i	$-0.684822\pi$
$293$		−	143559.i		−	1.67223i	0.548555	−	0.836115i	$-0.315178\pi$
$294$		0			0
$295$	11456.7	+	6614.55i	0.131649	+	0.0760075i
$296$		0			0
$297$			26285.2i			0.297988i
$298$		0			0
$299$	71311.1	−	41171.5i	0.797654	−	0.460526i
$300$		0			0
$301$	−49450.9	−	85651.5i	−0.545810	−	0.945370i
$302$		0			0
$303$			18246.0i			0.198738i
$304$		0			0
$305$	19214.7			0.206554
$306$		0			0
$307$	−46012.3	+	26565.2i	−0.488200	+	0.281862i	−0.723827	−	0.689981i	$-0.757619\pi$
$307$	−46012.3	+	26565.2i	−0.488200	+	0.281862i	0.235628	+	0.971843i	$0.424285\pi$
$308$		0			0
$309$	−4494.85	−	7785.31i	−0.0470759	−	0.0815378i
$310$		0			0
$311$	74095.4			0.766074			0.383037	−	0.923733i	$-0.374878\pi$
$311$	74095.4			0.766074			0.383037	+	0.923733i	$0.374878\pi$
$312$		0			0
$313$	70166.3	−	121532.i	0.716209	−	1.24051i	−0.246282	−	0.969198i	$-0.579209\pi$
$313$	70166.3	−	121532.i	0.716209	−	1.24051i	0.962491	−	0.271313i	$-0.0874577\pi$
$314$		0			0
$315$	16958.1			0.170905
$316$		0			0
$317$	−88820.2	−	51280.4i	−0.883880	−	0.510308i	−0.0119442	−	0.999929i	$-0.503802\pi$
$317$	−88820.2	−	51280.4i	−0.883880	−	0.510308i	−0.871936	+	0.489620i	$0.837135\pi$
$318$		0			0
$319$	22185.1	+	12808.6i	0.218012	+	0.125869i
$320$		0			0
$321$	426.533	+	738.777i	0.00413945	+	0.00716974i
$322$		0			0
$323$	−20190.2	−	152045.i	−0.193524	−	1.45736i
$324$		0			0
$325$	166718.	−	96254.7i	1.57840	−	0.911287i
$326$		0			0
$327$	−1326.77	+	2298.04i	−0.0124080	+	0.0214912i
$328$		0			0
$329$	−65346.9	+	113184.i	−0.603717	+	1.04567i
$330$		0			0
$331$			34528.3i			0.315152i	0.987507	+	0.157576i	$0.0503679\pi$
$331$			34528.3i			0.315152i	−0.987507	+	0.157576i	$0.949632\pi$
$332$		0			0
$333$	−42733.4	−	24672.1i	−0.385371	−	0.222494i
$334$		0			0
$335$		−	162.371i		−	0.00144684i
$336$		0			0
$337$	155389.	−	89714.0i	1.36824	−	0.789951i	0.377533	−	0.925996i	$-0.376773\pi$
$337$	155389.	−	89714.0i	1.36824	−	0.789951i	0.990703	+	0.136045i	$0.0434392\pi$
$338$		0			0
$339$	−7482.01	−	12959.2i	−0.0651057	−	0.112766i
$340$		0			0
$341$			70667.4i			0.607730i
$342$		0			0
$343$	−120626.			−1.02531
$344$		0			0
$345$	−935.829	+	540.301i	−0.00786246	+	0.00453939i
$346$		0			0
$347$	−96226.4	−	166669.i	−0.799163	−	1.38419i	−0.920162	−	0.391538i	$-0.871943\pi$
$347$	−96226.4	−	166669.i	−0.799163	−	1.38419i	0.120999	−	0.992653i	$-0.461390\pi$
$348$		0			0
$349$	91163.6			0.748463			0.374232	−	0.927335i	$-0.377906\pi$
$349$	91163.6			0.748463			0.374232	+	0.927335i	$0.377906\pi$
$350$		0			0
$351$	37569.9	−	65073.0i	0.304948	−	0.528186i
$352$		0			0
$353$	126024.			1.01136			0.505678	−	0.862722i	$-0.331242\pi$
$353$	126024.			1.01136			0.505678	+	0.862722i	$0.331242\pi$
$354$		0			0
$355$	−14676.9	−	8473.71i	−0.116460	−	0.0672383i
$356$		0			0
$357$	−44150.1	−	25490.1i	−0.346414	−	0.200002i
$358$		0			0
$359$	−32340.5	−	56015.4i	−0.250933	−	0.434629i	0.712850	−	0.701317i	$-0.247404\pi$
$359$	−32340.5	−	56015.4i	−0.250933	−	0.434629i	−0.963783	+	0.266688i	$0.914071\pi$
$360$		0			0
$361$	92356.8	+	91944.5i	0.708687	+	0.705523i
$362$		0			0
$363$	3599.28	−	2078.04i	0.0273150	−	0.0157703i
$364$		0			0
$365$	3277.09	−	5676.09i	0.0245982	−	0.0426053i
$366$		0			0
$367$	83548.4	−	144710.i	0.620306	−	1.07440i	−0.369123	−	0.929381i	$-0.620342\pi$
$367$	83548.4	−	144710.i	0.620306	−	1.07440i	0.989429	−	0.145021i	$-0.0463249\pi$
$368$		0			0
$369$		−	37779.1i		−	0.277459i
$370$		0			0
$371$	327379.	+	189012.i	2.37850	+	1.37323i
$372$		0			0
$373$			115820.i			0.832467i	0.909258	+	0.416234i	$0.136650\pi$
$373$			115820.i			0.832467i	−0.909258	+	0.416234i	$0.863350\pi$
$374$		0			0
$375$	−4401.76	+	2541.36i	−0.0313014	+	0.0180719i
$376$		0			0
$377$	−36615.1	−	63419.3i	−0.257619	−	0.446209i
$378$		0			0
$379$			90727.2i			0.631624i	0.948822	+	0.315812i	$0.102277\pi$
$379$			90727.2i			0.631624i	−0.948822	+	0.315812i	$0.897723\pi$
$380$		0			0
$381$	−22282.0			−0.153498
$382$		0			0
$383$	−26744.8	+	15441.1i	−0.182323	+	0.105264i	−0.588384	−	0.808582i	$-0.700236\pi$
$383$	−26744.8	+	15441.1i	−0.182323	+	0.105264i	0.406061	+	0.913846i	$0.366902\pi$
$384$		0			0
$385$	11743.5	+	20340.3i	0.0792274	+	0.137226i
$386$		0			0
$387$	−97940.1			−0.653941
$388$		0			0
$389$	55857.2	−	96747.4i	0.369130	−	0.639352i	−0.620300	−	0.784365i	$-0.712989\pi$
$389$	55857.2	−	96747.4i	0.369130	−	0.639352i	0.989430	+	0.145013i	$0.0463223\pi$
$390$		0			0
$391$	−112249.			−0.734225
$392$		0			0
$393$	−8831.66	−	5098.96i	−0.0571817	−	0.0330139i
$394$		0			0
$395$	9984.00	+	5764.27i	0.0639898	+	0.0369445i
$396$		0			0
$397$	−96824.6	−	167705.i	−0.614334	−	1.06406i	−0.990501	−	0.137506i	$-0.956091\pi$
$397$	−96824.6	−	167705.i	−0.614334	−	1.06406i	0.376167	−	0.926552i	$-0.377242\pi$
$398$		0			0
$399$	42938.9	−	5701.88i	0.269715	−	0.0358156i
$400$		0			0
$401$	35967.6	−	20765.9i	0.223678	−	0.129140i	−0.383974	−	0.923344i	$-0.625445\pi$
$401$	35967.6	−	20765.9i	0.223678	−	0.129140i	0.607652	+	0.794203i	$0.292112\pi$
$402$		0			0
$403$	101006.	−	174948.i	0.621926	−	1.07721i
$404$		0			0
$405$	8146.55	−	14110.2i	0.0496665	−	0.0860249i
$406$		0			0
$407$		−	68342.0i		−	0.412571i
$408$		0			0
$409$	−120340.	−	69478.3i	−0.719388	−	0.415339i	0.0951394	−	0.995464i	$-0.469670\pi$
$409$	−120340.	−	69478.3i	−0.719388	−	0.415339i	−0.814527	+	0.580125i	$0.803004\pi$
$410$		0			0
$411$			12416.1i			0.0735025i
$412$		0			0
$413$	−336091.	+	194042.i	−1.97041	+	1.13762i
$414$		0			0
$415$	9000.80	+	15589.8i	0.0522619	+	0.0905202i
$416$		0			0
$417$			11415.6i			0.0656487i
$418$		0			0
$419$	265295.			1.51113			0.755563	−	0.655075i	$-0.227363\pi$
$419$	265295.			1.51113			0.755563	+	0.655075i	$0.227363\pi$
$420$		0			0
$421$	78399.4	−	45263.9i	0.442332	−	0.255381i	−0.262254	−	0.964999i	$-0.584466\pi$
$421$	78399.4	−	45263.9i	0.442332	−	0.255381i	0.704586	+	0.709618i	$0.251133\pi$
$422$		0			0
$423$	64711.4	+	112084.i	0.361660	+	0.626413i
$424$		0			0
$425$	−262427.			−1.45288
$426$		0			0
$427$	−281837.	+	488157.i	−1.54576	+	2.67734i
$428$		0			0
$429$	51292.2			0.278700
$430$		0			0
$431$	−102698.	−	59292.7i	−0.552850	−	0.319188i	0.197421	−	0.980319i	$-0.436743\pi$
$431$	−102698.	−	59292.7i	−0.552850	−	0.319188i	−0.750271	+	0.661131i	$0.770077\pi$
$432$		0			0
$433$	−134033.	−	77384.1i	−0.714885	−	0.412739i	0.0979820	−	0.995188i	$-0.468761\pi$
$433$	−134033.	−	77384.1i	−0.714885	−	0.412739i	−0.812867	+	0.582449i	$0.802095\pi$
$434$		0			0
$435$	480.508	+	832.264i	0.00253935	+	0.00439828i
$436$		0			0
$437$	75600.1	−	58144.4i	0.395876	−	0.304471i
$438$		0			0
$439$	104458.	−	60308.7i	0.542015	−	0.312933i	−0.203880	−	0.978996i	$-0.565355\pi$
$439$	104458.	−	60308.7i	0.542015	−	0.312933i	0.745895	+	0.666063i	$0.232022\pi$
$440$		0			0
$441$	−154232.	+	267138.i	−0.793045	+	1.37359i
$442$		0			0
$443$	−59838.7	+	103644.i	−0.304912	+	0.528123i	−0.977242	−	0.212129i	$-0.931960\pi$
$443$	−59838.7	+	103644.i	−0.304912	+	0.528123i	0.672330	+	0.740252i	$0.265294\pi$
$444$		0			0
$445$			26564.4i			0.134147i
$446$		0			0
$447$	15587.7	+	8999.54i	0.0780128	+	0.0450407i
$448$		0			0
$449$			361353.i			1.79242i	0.443632	+	0.896209i	$0.353690\pi$
$449$			361353.i			1.79242i	−0.443632	+	0.896209i	$0.646310\pi$
$450$		0			0
$451$	45314.0	−	26162.1i	0.222782	−	0.128623i
$452$		0			0
$453$	21861.3	+	37864.8i	0.106532	+	0.184518i
$454$		0			0
$455$		−	67140.8i		−	0.324312i
$456$		0			0
$457$	247568.			1.18539			0.592695	−	0.805427i	$-0.298064\pi$
$457$	247568.			1.18539			0.592695	+	0.805427i	$0.298064\pi$
$458$		0			0
$459$	−88706.9	+	51214.9i	−0.421048	+	0.243092i
$460$		0			0
$461$	34100.9	+	59064.5i	0.160459	+	0.277923i	0.935033	−	0.354560i	$-0.115369\pi$
$461$	34100.9	+	59064.5i	0.160459	+	0.277923i	−0.774574	+	0.632483i	$0.782036\pi$
$462$		0			0
$463$	−265413.			−1.23811			−0.619057	−	0.785346i	$-0.712485\pi$
$463$	−265413.			−1.23811			−0.619057	+	0.785346i	$0.712485\pi$
$464$		0			0
$465$	−1325.53	+	2295.88i	−0.00613031	+	0.0106180i
$466$		0			0
$467$	−44511.7			−0.204099			−0.102049	−	0.994779i	$-0.532540\pi$
$467$	−44511.7			−0.204099			−0.102049	+	0.994779i	$0.532540\pi$
$468$		0			0
$469$	4125.10	+	2381.63i	0.0187538	+	0.0108275i
$470$		0			0
$471$	8365.82	+	4830.01i	0.0377109	+	0.0217724i
$472$		0			0
$473$	−67823.7	−	117474.i	−0.303151	−	0.525073i
$474$		0			0
$475$	176745.	−	135936.i	0.783359	−	0.602486i
$476$		0			0
$477$	324195.	−	187174.i	1.42485	−	0.822639i
$478$		0			0
$479$	−110281.	+	191012.i	−0.480650	+	0.832511i	−0.999754	−	0.0222009i	$-0.992933\pi$
$479$	−110281.	+	191012.i	−0.480650	+	0.832511i	0.519103	+	0.854712i	$0.326266\pi$
$480$		0			0
$481$	−97682.6	+	169191.i	−0.422208	+	0.731286i
$482$		0			0
$483$		−	31700.2i		−	0.135884i
$484$		0			0
$485$	−11019.3	−	6361.99i	−0.0468458	−	0.0270464i
$486$		0			0
$487$			291672.i			1.22981i	0.788602	+	0.614904i	$0.210805\pi$
$487$			291672.i			1.22981i	−0.788602	+	0.614904i	$0.789195\pi$
$488$		0			0
$489$	−6537.55	+	3774.46i	−0.0273399	+	0.0157847i
$490$		0			0
$491$	−155315.	−	269013.i	−0.644243	−	1.11586i	−0.984476	−	0.175521i	$-0.943839\pi$
$491$	−155315.	−	269013.i	−0.644243	−	1.11586i	0.340233	−	0.940341i	$-0.389494\pi$
$492$		0			0
$493$			99826.8i			0.410727i
$494$		0			0
$495$	23258.6			0.0949233
$496$		0			0
$497$	430556.	−	248581.i	1.74308	−	1.00637i
$498$		0			0
$499$	−184973.	−	320383.i	−0.742862	−	1.28667i	−0.951187	−	0.308615i	$-0.900134\pi$
$499$	−184973.	−	320383.i	−0.742862	−	1.28667i	0.208325	−	0.978060i	$-0.433199\pi$
$500$		0			0
$501$	38162.8			0.152043
$502$		0			0
$503$	109000.	−	188793.i	0.430814	−	0.746192i	−0.566130	−	0.824316i	$-0.691560\pi$
$503$	109000.	−	188793.i	0.430814	−	0.746192i	0.996944	+	0.0781244i	$0.0248931\pi$
$504$		0			0
$505$	32757.3			0.128448
$506$		0			0
$507$	−89647.8	−	51758.2i	−0.348758	−	0.201355i
$508$		0			0
$509$	−217588.	−	125625.i	−0.839847	−	0.484886i	0.0173655	−	0.999849i	$-0.494472\pi$
$509$	−217588.	−	125625.i	−0.839847	−	0.484886i	−0.857212	+	0.514964i	$0.827805\pi$
$510$		0			0
$511$	96135.5	+	166512.i	0.368165	+	0.637680i
$512$		0			0
$513$	33215.3	−	80443.1i	0.126213	−	0.305671i
$514$		0			0
$515$	−13977.1	+	8069.69i	−0.0526991	+	0.0304258i
$516$		0			0
$517$	−89625.6	+	155236.i	−0.335313	+	0.580780i
$518$		0			0
$519$	7796.55	−	13504.0i	0.0289446	−	0.0501336i
$520$		0			0
$521$			102324.i			0.376968i	0.982076	+	0.188484i	$0.0603573\pi$
$521$			102324.i			0.376968i	−0.982076	+	0.188484i	$0.939643\pi$
$522$		0			0
$523$	190819.	+	110169.i	0.697618	+	0.402770i	0.806460	−	0.591289i	$-0.201381\pi$
$523$	190819.	+	110169.i	0.697618	+	0.402770i	−0.108841	+	0.994059i	$0.534714\pi$
$524$		0			0
$525$		−	74111.7i		−	0.268886i
$526$		0			0
$527$	−238487.	+	137691.i	−0.858706	+	0.495774i
$528$		0			0
$529$	105021.	+	181903.i	0.375290	+	0.650021i
$530$		0			0
$531$			384310.i			1.36299i
$532$		0			0
$533$	−149576.			−0.526510
$534$		0			0
$535$	1326.34	−	765.763i	0.00463391	−	0.00267539i
$536$		0			0
$537$	−38889.4	−	67358.4i	−0.134860	−	0.233584i
$538$		0			0
$539$	−427224.			−1.47055
$540$		0			0
$541$	−203815.	+	353017.i	−0.696372	+	1.20615i	0.273344	+	0.961916i	$0.411870\pi$
$541$	−203815.	+	353017.i	−0.696372	+	1.20615i	−0.969716	+	0.244235i	$0.921463\pi$
$542$		0			0
$543$	10485.3			0.0355617
$544$		0			0
$545$	4125.71	+	2381.98i	0.0138901	+	0.00801946i
$546$		0			0
$547$	96394.7	+	55653.5i	0.322165	+	0.186002i	0.652357	−	0.757912i	$-0.273780\pi$
$547$	96394.7	+	55653.5i	0.322165	+	0.186002i	−0.330192	+	0.943914i	$0.607114\pi$
$548$		0			0
$549$	279097.	+	483410.i	0.925998	+	1.60388i
$550$		0			0
$551$	−51709.8	−	67233.6i	−0.170321	−	0.221454i
$552$		0			0
$553$	−292887.	+	169098.i	−0.957745	+	0.552954i
$554$		0			0
$555$	1281.91	−	2220.33i	0.00416170	−	0.00720828i
$556$		0			0
$557$	−175783.	+	304466.i	−0.566588	+	0.981360i	0.430312	+	0.902680i	$0.358404\pi$
$557$	−175783.	+	304466.i	−0.566588	+	0.981360i	−0.996900	+	0.0786795i	$0.974930\pi$
$558$		0			0
$559$			387767.i			1.24093i
$560$		0			0
$561$	−60553.4	−	34960.5i	−0.192404	−	0.111084i
$562$		0			0
$563$			328649.i			1.03685i	0.855124	+	0.518424i	$0.173481\pi$
$563$			328649.i			1.03685i	−0.855124	+	0.518424i	$0.826519\pi$
$564$		0			0
$565$	−23265.9	+	13432.6i	−0.0728825	+	0.0420788i
$566$		0			0
$567$	238984.	+	413932.i	0.743366	+	1.28755i
$568$		0			0
$569$		−	388285.i		−	1.19929i	−0.800264	−	0.599647i	$-0.795308\pi$
$569$		−	388285.i		−	1.19929i	0.800264	−	0.599647i	$-0.204692\pi$
$570$		0			0
$571$	−16892.4			−0.0518107			−0.0259054	−	0.999664i	$-0.508247\pi$
$571$	−16892.4			−0.0518107			−0.0259054	+	0.999664i	$0.508247\pi$
$572$		0			0
$573$	66752.7	−	38539.7i	0.203310	−	0.117381i
$574$		0			0
$575$	−81590.4	−	141319.i	−0.246776	−	0.427429i
$576$		0			0
$577$	−522045.			−1.56804			−0.784018	−	0.620738i	$-0.786833\pi$
$577$	−522045.			−1.56804			−0.784018	+	0.620738i	$0.786833\pi$
$578$		0			0
$579$	28231.6	−	48898.6i	0.0842130	−	0.145861i
$580$		0			0
$581$	−528088.			−1.56442
$582$		0			0
$583$	449012.	+	259237.i	1.32105	+	0.762711i
$584$		0			0
$585$	−57580.2	−	33243.9i	−0.168252	−	0.0971406i
$586$		0			0
$587$	−200724.	−	347665.i	−0.582538	−	1.00898i	−0.995177	−	0.0980906i	$-0.968727\pi$
$587$	−200724.	−	347665.i	−0.582538	−	1.00898i	0.412640	−	0.910894i	$-0.364607\pi$
$588$		0			0
$589$	89298.9	−	216270.i	0.257404	−	0.623400i
$590$		0			0
$591$	−937.972	+	541.538i	−0.00268544	+	0.00155044i
$592$		0			0
$593$	171949.	−	297824.i	0.488979	−	0.846936i	−0.510941	−	0.859616i	$-0.670703\pi$
$593$	171949.	−	297824.i	0.488979	−	0.846936i	0.999920	+	0.0126797i	$0.00403619\pi$
$594$		0			0
$595$	−45762.8	+	79263.5i	−0.129264	+	0.223892i
$596$		0			0
$597$			110782.i			0.310830i
$598$		0			0
$599$	−73567.3	−	42474.1i	−0.205036	−	0.118378i	0.393966	−	0.919125i	$-0.371103\pi$
$599$	−73567.3	−	42474.1i	−0.205036	−	0.118378i	−0.599003	+	0.800747i	$0.704436\pi$
$600$		0			0
$601$		−	40436.4i		−	0.111950i	−0.998432	−	0.0559749i	$-0.982173\pi$
$601$		−	40436.4i		−	0.111950i	0.998432	−	0.0559749i	$-0.0178267\pi$
$602$		0			0
$603$	4084.99	−	2358.47i	0.0112346	−	0.00648628i
$604$		0			0
$605$	−3730.75	−	6461.85i	−0.0101926	−	0.0176541i
$606$		0			0
$607$		−	484179.i		−	1.31410i	−0.753847	−	0.657050i	$-0.771804\pi$
$607$		−	484179.i		−	1.31410i	0.753847	−	0.657050i	$-0.228196\pi$
$608$		0			0
$609$	−28192.0			−0.0760136
$610$		0			0
$611$	443764.	−	256207.i	1.18869	−	0.686292i
$612$		0			0
$613$	154104.	+	266916.i	0.410102	+	0.710318i	0.994901	−	0.100861i	$-0.0321596\pi$
$613$	154104.	+	266916.i	0.410102	+	0.710318i	−0.584798	+	0.811179i	$0.698826\pi$
$614$		0			0
$615$	1962.91			0.00518980
$616$		0			0
$617$	290312.	−	502835.i	0.762596	−	1.32086i	−0.178912	−	0.983865i	$-0.557258\pi$
$617$	290312.	−	502835.i	0.762596	−	1.32086i	0.941508	−	0.336990i	$-0.109409\pi$
$618$		0			0
$619$	137052.			0.357688			0.178844	−	0.983877i	$-0.442764\pi$
$619$	137052.			0.357688			0.178844	+	0.983877i	$0.442764\pi$
$620$		0			0
$621$	−55159.2	−	31846.2i	−0.143032	−	0.0825798i
$622$		0			0
$623$	−674880.	−	389642.i	−1.73880	−	1.00390i
$624$		0			0
$625$	−188455.	−	326414.i	−0.482445	−	0.835620i
$626$		0			0
$627$	58892.3	−	7820.34i	0.149804	−	0.0198925i
$628$		0			0
$629$	230640.	−	133160.i	0.582952	−	0.336567i
$630$		0			0
$631$	78369.0	−	135739.i	0.196827	−	0.340915i	−0.750671	−	0.660677i	$-0.770270\pi$
$631$	78369.0	−	135739.i	0.196827	−	0.340915i	0.947498	+	0.319762i	$0.103603\pi$
$632$		0			0
$633$	41599.1	−	72051.7i	0.103819	−	0.179820i
$634$		0			0
$635$			40003.2i			0.0992082i
$636$		0			0
$637$	1.05766e6	+	610640.i	2.60656	+	1.50490i
$638$		0			0
$639$		−	492329.i		−	1.20574i
$640$		0			0
$641$	−158874.	+	91726.2i	−0.386668	+	0.223243i	−0.680715	−	0.732548i	$-0.738331\pi$
$641$	−158874.	+	91726.2i	−0.386668	+	0.223243i	0.294047	+	0.955791i	$0.404998\pi$
$642$		0			0
$643$	176524.	+	305749.i	0.426955	+	0.739508i	0.996601	−	0.0823825i	$-0.0262529\pi$
$643$	176524.	+	305749.i	0.426955	+	0.739508i	−0.569646	+	0.821890i	$0.692920\pi$
$644$		0			0
$645$		−	5088.74i		−	0.0122318i
$646$		0			0
$647$	523782.			1.25124			0.625622	−	0.780126i	$-0.284845\pi$
$647$	523782.			1.25124			0.625622	+	0.780126i	$0.284845\pi$
$648$		0			0
$649$	−460960.	+	266136.i	−1.09440	+	0.631849i
$650$		0			0
$651$	−38885.1	−	67351.0i	−0.0917533	−	0.158921i
$652$		0			0
$653$	522720.			1.22587			0.612933	−	0.790135i	$-0.289990\pi$
$653$	522720.			1.22587			0.612933	+	0.790135i	$0.289990\pi$
$654$		0			0
$655$	−9154.26	+	15855.6i	−0.0213374	+	0.0369574i
$656$		0			0
$657$	190401.			0.441102
$658$		0			0
$659$	−209686.	−	121062.i	−0.482834	−	0.278764i	0.238763	−	0.971078i	$-0.423258\pi$
$659$	−209686.	−	121062.i	−0.482834	−	0.278764i	−0.721597	+	0.692314i	$0.756592\pi$
$660$		0			0
$661$	114420.	+	66060.4i	0.261878	+	0.151195i	0.625191	−	0.780472i	$-0.285021\pi$
$661$	114420.	+	66060.4i	0.261878	+	0.151195i	−0.363313	+	0.931667i	$0.618354\pi$
$662$		0			0
$663$	99939.6	+	173100.i	0.227358	+	0.393796i
$664$		0			0
$665$	−10236.7	−	77089.1i	−0.0231482	−	0.174321i
$666$		0			0
$667$	−53757.4	+	31036.8i	−0.120833	+	0.0697631i
$668$		0			0
$669$	−40663.7	+	70431.7i	−0.0908563	+	0.157368i
$670$		0			0
$671$	−386550.	+	669524.i	−0.858540	+	1.48704i
$672$		0			0
$673$			427834.i			0.944594i	0.881440	+	0.472297i	$0.156575\pi$
$673$			427834.i			0.944594i	−0.881440	+	0.472297i	$0.843425\pi$
$674$		0			0
$675$	−128957.	−	74453.1i	−0.283032	−	0.163409i
$676$		0			0
$677$		−	605243.i		−	1.32054i	−0.751027	−	0.660272i	$-0.770441\pi$
$677$		−	605243.i		−	1.32054i	0.751027	−	0.660272i	$-0.229559\pi$
$678$		0			0
$679$	323258.	−	186633.i	0.701148	−	0.404808i
$680$		0			0
$681$	51682.0	+	89515.9i	0.111441	+	0.193022i
$682$		0			0
$683$		−	638680.i		−	1.36912i	−0.728956	−	0.684561i	$-0.759994\pi$
$683$		−	638680.i		−	1.36912i	0.728956	−	0.684561i	$-0.240006\pi$
$684$		0			0
$685$	22290.9			0.0475058
$686$		0			0
$687$	40589.4	−	23434.3i	0.0860002	−	0.0496523i
$688$		0			0
$689$	−741065.	−	1.28356e6i	−1.56105	−	2.70382i
$690$		0			0
$691$	586931.			1.22922			0.614612	−	0.788829i	$-0.289312\pi$
$691$	586931.			1.22922			0.614612	+	0.788829i	$0.289312\pi$
$692$		0			0
$693$	−341153.	+	590894.i	−0.710366	+	1.23039i
$694$		0			0
$695$	20494.6			0.0424297
$696$		0			0
$697$	176583.	+	101950.i	0.363482	+	0.209856i
$698$		0			0
$699$	23323.4	+	13465.8i	0.0477351	+	0.0275599i
$700$		0			0
$701$	16565.6	+	28692.4i	0.0337109	+	0.0583890i	0.882389	−	0.470521i	$-0.155934\pi$
$701$	16565.6	+	28692.4i	0.0337109	+	0.0583890i	−0.848678	+	0.528910i	$0.822601\pi$
$702$		0			0
$703$	−86360.4	+	209154.i	−0.174745	+	0.423209i
$704$		0			0
$705$	−5823.60	+	3362.26i	−0.0117169	+	0.00676476i
$706$		0			0
$707$	−480478.	+	832213.i	−0.961247	+	1.66493i
$708$		0			0
$709$	209345.	−	362596.i	0.416457	−	0.721324i	−0.579124	−	0.815240i	$-0.696605\pi$
$709$	209345.	−	362596.i	0.416457	−	0.721324i	0.995580	+	0.0939159i	$0.0299385\pi$
$710$		0			0
$711$			334908.i			0.662501i
$712$		0			0
$713$	−148295.	−	85618.0i	−0.291707	−	0.168417i
$714$		0			0
$715$		−	92086.0i		−	0.180128i
$716$		0			0
$717$	100627.	−	58096.7i	0.195738	−	0.113009i
$718$		0			0
$719$	−408717.	−	707919.i	−0.790616	−	1.36939i	−0.925586	−	0.378537i	$-0.876427\pi$
$719$	−408717.	−	707919.i	−0.790616	−	1.36939i	0.134971	−	0.990850i	$-0.456906\pi$
$720$		0			0
$721$		−	473459.i		−	0.910777i
$722$		0			0
$723$	−91683.2			−0.175393
$724$		0			0
$725$	−125679.	+	72561.0i	−0.239105	+	0.138047i
$726$		0			0
$727$	−118045.	−	204459.i	−0.223346	−	0.386846i	0.732476	−	0.680793i	$-0.238365\pi$
$727$	−118045.	−	204459.i	−0.223346	−	0.386846i	−0.955822	+	0.293947i	$0.905031\pi$
$728$		0			0
$729$	443845.			0.835173
$730$		0			0
$731$	264300.	−	457781.i	0.494609	−	0.856689i
$732$		0			0
$733$	−388188.			−0.722494			−0.361247	−	0.932470i	$-0.617649\pi$
$733$	−388188.			−0.722494			−0.361247	+	0.932470i	$0.617649\pi$
$734$		0			0
$735$	−13879.9	−	8013.55i	−0.0256928	−	0.0148337i
$736$		0			0
$737$	5657.73	+	3266.49i	0.0104161	+	0.00601376i
$738$		0			0
$739$	119148.	+	206371.i	0.218172	+	0.377886i	0.954249	−	0.299012i	$-0.0966572\pi$
$739$	119148.	+	206371.i	0.218172	+	0.377886i	−0.736077	+	0.676898i	$0.763324\pi$
$740$		0			0
$741$	−156975.	−	64815.5i	−0.285886	−	0.118044i
$742$		0			0
$743$	531342.	−	306771.i	0.962491	−	0.555694i	0.0655522	−	0.997849i	$-0.479119\pi$
$743$	531342.	−	306771.i	0.962491	−	0.555694i	0.896939	+	0.442155i	$0.145786\pi$
$744$		0			0
$745$	16157.1	−	27984.8i	0.0291105	−	0.0504209i
$746$		0			0
$747$	−261477.	+	452891.i	−0.468588	+	0.811619i
$748$		0			0
$749$			44928.3i			0.0800859i
$750$		0			0
$751$	−640541.	−	369816.i	−1.13571	−	0.655701i	−0.190344	−	0.981717i	$-0.560960\pi$
$751$	−640541.	−	369816.i	−1.13571	−	0.655701i	−0.945364	+	0.326016i	$0.894294\pi$
$752$		0			0
$753$			59690.6i			0.105273i
$754$		0			0
$755$	67979.4	−	39247.9i	0.119257	−	0.0688530i
$756$		0			0
$757$	−166628.	−	288609.i	−0.290775	−	0.503637i	0.683218	−	0.730214i	$-0.260580\pi$
$757$	−166628.	−	288609.i	−0.290775	−	0.503637i	−0.973993	+	0.226577i	$0.927246\pi$
$758$		0			0
$759$		−	43477.9i		−	0.0754718i
$760$		0			0
$761$	502308.			0.867362			0.433681	−	0.901066i	$-0.357214\pi$
$761$	502308.			0.867362			0.433681	+	0.901066i	$0.357214\pi$
$762$		0			0
$763$	−121030.	+	69876.9i	−0.207895	+	0.120028i
$764$		0			0
$765$	45317.8	+	78492.8i	0.0774366	+	0.134124i
$766$		0			0
$767$	1.52157e6			2.58643
$768$		0			0
$769$	−227459.	+	393970.i	−0.384636	+	0.666210i	−0.991719	−	0.128429i	$-0.959006\pi$
$769$	−227459.	+	393970.i	−0.384636	+	0.666210i	0.607082	+	0.794639i	$0.292340\pi$
$770$		0			0
$771$	51079.7			0.0859290
$772$		0			0
$773$	618605.	+	357152.i	1.03527	+	0.597714i	0.918490	−	0.395443i	$-0.129409\pi$
$773$	618605.	+	357152.i	1.03527	+	0.597714i	0.116781	+	0.993158i	$0.462742\pi$
$774$		0			0
$775$	−346698.	−	200166.i	−0.577229	−	0.333263i
$776$		0			0
$777$	37605.6	+	65134.7i	0.0622888	+	0.107887i
$778$		0			0
$779$	−171739.	+	22805.3i	−0.283004	+	0.0375803i
$780$		0			0
$781$	590523.	−	340938.i	0.968132	−	0.558951i
$782$		0			0
$783$	−28321.8	+	49054.9i	−0.0461953	+	0.0800126i
$784$		0			0
$785$	8671.41	−	15019.3i	0.0140718	−	0.0243731i
$786$		0			0
$787$		−	414479.i		−	0.669196i	−0.942361	−	0.334598i	$-0.891399\pi$
$787$		−	414479.i		−	0.669196i	0.942361	−	0.334598i	$-0.108601\pi$
$788$		0			0
$789$	127891.	+	73838.1i	0.205441	+	0.118611i
$790$		0			0
$791$		−	788107.i		−	1.25960i
$792$		0			0
$793$	1.91393e6	−	1.10501e6i	3.04354	−	1.75719i
$794$		0			0
$795$	9725.14	+	16844.4i	0.0153873	+	0.0266515i
$796$		0			0
$797$			444827.i			0.700285i	0.936696	+	0.350143i	$0.113867\pi$
$797$			444827.i			0.700285i	−0.936696	+	0.350143i	$0.886133\pi$
$798$		0			0
$799$	−698518.			−1.09417
$800$		0			0
$801$	−668317.	+	385853.i	−1.04164	+	0.601391i
$802$		0			0
$803$	131853.	+	228377.i	0.204484	+	0.354177i
$804$		0			0
$805$	−56911.9			−0.0878236
$806$		0			0
$807$	−471.025	+	815.839i	−0.000723264	+	0.00125273i
$808$		0			0
$809$	−23210.9			−0.0354646			−0.0177323	−	0.999843i	$-0.505645\pi$
$809$	−23210.9			−0.0354646			−0.0177323	+	0.999843i	$0.505645\pi$
$810$		0			0
$811$	397137.	+	229287.i	0.603808	+	0.348609i	0.770538	−	0.637394i	$-0.219988\pi$
$811$	397137.	+	229287.i	0.603808	+	0.348609i	−0.166730	+	0.986003i	$0.553321\pi$
$812$		0			0
$813$	−70733.8	−	40838.2i	−0.107015	−	0.0617853i
$814$		0			0
$815$	6776.35	+	11737.0i	0.0102019	+	0.0176702i
$816$		0			0
$817$	59121.4	+	445223.i	0.0885728	+	0.667012i
$818$		0			0
$819$	1.68915e6	−	975232.i	2.51826	−	1.45392i
$820$		0			0
$821$	153601.	−	266045.i	0.227881	−	0.394702i	−0.729299	−	0.684196i	$-0.760153\pi$
$821$	153601.	−	266045.i	0.227881	−	0.394702i	0.957180	+	0.289493i	$0.0934868\pi$
$822$		0			0
$823$	18258.2	−	31624.2i	0.0269562	−	0.0466895i	−0.852233	−	0.523163i	$-0.824752\pi$
$823$	18258.2	−	31624.2i	0.0269562	−	0.0466895i	0.879189	+	0.476474i	$0.158085\pi$
$824$		0			0
$825$		−	101647.i		−	0.149343i
$826$		0			0
$827$	−310653.	−	179355.i	−0.454218	−	0.262243i	0.255392	−	0.966838i	$-0.417795\pi$
$827$	−310653.	−	179355.i	−0.454218	−	0.262243i	−0.709610	+	0.704595i	$0.751129\pi$
$828$		0			0
$829$		−	468345.i		−	0.681485i	−0.940157	−	0.340743i	$-0.889322\pi$
$829$		−	468345.i		−	0.681485i	0.940157	−	0.340743i	$-0.110678\pi$
$830$		0			0
$831$	74214.2	−	42847.6i	0.107469	−	0.0620475i
$832$		0			0
$833$	−832418.	−	1.44179e6i	−1.19964	−	2.07784i
$834$		0			0
$835$		−	68514.5i		−	0.0982674i
$836$		0			0
$837$	−156257.			−0.223043
$838$		0			0
$839$	−269666.	+	155692.i	−0.383091	+	0.221178i	−0.679162	−	0.733988i	$-0.737657\pi$
$839$	−269666.	+	155692.i	−0.383091	+	0.221178i	0.296071	+	0.955166i	$0.404323\pi$
$840$		0			0
$841$	−326038.	−	564715.i	−0.460974	−	0.798431i
$842$		0			0
$843$	−170009.			−0.239230
$844$		0			0
$845$	−92922.4	+	160946.i	−0.130139	+	0.225407i
$846$		0			0
$847$	218888.			0.305109
$848$		0			0
$849$	78534.2	+	45341.8i	0.108954	+	0.0629047i
$850$		0			0
$851$	143415.	+	82800.7i	0.198032	+	0.114334i
$852$		0			0
$853$	301187.	+	521671.i	0.413940	+	0.716966i	0.995317	−	0.0966690i	$-0.0308188\pi$
$853$	301187.	+	521671.i	0.413940	+	0.716966i	−0.581376	+	0.813635i	$0.697485\pi$
$854$		0			0
$855$	−71180.5	−	29390.7i	−0.0973708	−	0.0402048i
$856$		0			0
$857$	−1.06472e6	+	614717.i	−1.44969	+	0.836977i	−0.998462	−	0.0554328i	$-0.982346\pi$
$857$	−1.06472e6	+	614717.i	−1.44969	+	0.836977i	−0.451225	+	0.892410i	$0.649013\pi$
$858$		0			0
$859$	−580962.	+	1.00626e6i	−0.787338	+	1.36371i	0.140254	+	0.990116i	$0.455208\pi$
$859$	−580962.	+	1.00626e6i	−0.787338	+	1.36371i	−0.927592	+	0.373595i	$0.878125\pi$
$860$		0			0
$861$	−28791.6	+	49868.6i	−0.0388383	+	0.0672699i
$862$		0			0
$863$			23780.8i			0.0319304i	0.999873	+	0.0159652i	$0.00508210\pi$
$863$			23780.8i			0.0319304i	−0.999873	+	0.0159652i	$0.994918\pi$
$864$		0			0
$865$	−24244.0	−	13997.3i	−0.0324021	−	0.0187073i
$866$		0			0
$867$		−	146407.i		−	0.194771i
$868$		0			0
$869$	−401705.	+	231924.i	−0.531946	+	0.307119i
$870$		0			0
$871$	−9337.71	−	16173.4i	−0.0123085	−	0.0213189i
$872$		0			0
$873$		−	369637.i		−	0.485005i
$874$		0			0
$875$	−267690.			−0.349636
$876$		0			0
$877$	−731385.	+	422265.i	−0.950927	+	0.549018i	−0.893369	−	0.449324i	$-0.851665\pi$
$877$	−731385.	+	422265.i	−0.950927	+	0.549018i	−0.0575579	+	0.998342i	$0.518331\pi$
$878$		0			0
$879$	108343.	+	187656.i	0.140225	+	0.242876i
$880$		0			0
$881$	519810.			0.669719			0.334860	−	0.942268i	$-0.391311\pi$
$881$	519810.			0.669719			0.334860	+	0.942268i	$0.391311\pi$
$882$		0			0
$883$	576930.	−	999273.i	0.739949	−	1.28163i	−0.212568	−	0.977146i	$-0.568183\pi$
$883$	576930.	−	999273.i	0.739949	−	1.28163i	0.952518	−	0.304484i	$-0.0984839\pi$
$884$		0			0
$885$	−19967.9			−0.0254944
$886$		0			0
$887$	631174.	+	364409.i	0.802236	+	0.463171i	0.844252	−	0.535946i	$-0.180045\pi$
$887$	631174.	+	364409.i	0.802236	+	0.463171i	−0.0420166	+	0.999117i	$0.513378\pi$
$888$		0			0
$889$	−1.01630e6	−	586760.i	−1.28593	−	0.742432i
$890$		0			0
$891$	327775.	+	567723.i	0.412877	+	0.715124i
$892$		0			0
$893$	470454.	−	361829.i	0.589949	−	0.453733i
$894$		0			0
$895$	−120930.	+	69818.9i	−0.150969	+	0.0871619i
$896$		0			0
$897$	−62143.8	+	107636.i	−0.0772348	+	0.133775i
$898$		0			0
$899$	−76142.9	+	131883.i	−0.0942129	+	0.163181i
$900$		0			0
$901$			2.02042e6i			2.48882i
$902$		0			0
$903$	129282.	+	74640.7i	0.158548	+	0.0915378i
$904$		0			0
$905$		−	18824.5i		−	0.0229841i
$906$		0			0
$907$	−800625.	+	462241.i	−0.973228	+	0.561893i	−0.900219	−	0.435438i	$-0.856594\pi$
$907$	−800625.	+	462241.i	−0.973228	+	0.561893i	−0.0730091	+	0.997331i	$0.523260\pi$
$908$		0			0
$909$	475806.	+	824121.i	0.575841	+	0.997386i
$910$		0			0
$911$			1.60442e6i			1.93322i	0.256257	+	0.966609i	$0.417511\pi$
$911$			1.60442e6i			1.93322i	−0.256257	+	0.966609i	$0.582489\pi$
$912$		0			0
$913$	−724292.			−0.868904
$914$		0			0
$915$	−25116.9	+	14501.2i	−0.0300001	+	0.0173206i
$916$		0			0
$917$	−268546.	−	465135.i	−0.319360	−	0.553147i
$918$		0			0
$919$	126222.			0.149453			0.0747264	−	0.997204i	$-0.476192\pi$
$919$	126222.			0.149453			0.0747264	+	0.997204i	$0.476192\pi$
$920$		0			0
$921$	40097.3	−	69450.5i	0.0472711	−	0.0818759i
$922$		0			0
$923$	−1.94924e6			−2.28803
$924$		0			0
$925$	335290.	+	193580.i	0.391865	+	0.226243i
$926$		0			0
$927$	−406041.	−	234428.i	−0.472509	−	0.272803i
$928$		0			0
$929$	109861.	+	190286.i	0.127296	+	0.220483i	0.922628	−	0.385691i	$-0.126037\pi$
$929$	109861.	+	190286.i	0.127296	+	0.220483i	−0.795332	+	0.606174i	$0.792704\pi$
$930$		0			0
$931$	1.30748e6	+	539862.i	1.50846	+	0.622850i
$932$		0			0
$933$	−96855.3	+	55919.4i	−0.111265	+	0.0642391i
$934$		0			0
$935$	−62765.3	+	108713.i	−0.0717954	+	0.124353i
$936$		0			0
$937$	63546.7	−	110066.i	0.0723792	−	0.125365i	−0.827564	−	0.561371i	$-0.810274\pi$
$937$	63546.7	−	110066.i	0.0723792	−	0.125365i	0.899944	+	0.436006i	$0.143607\pi$
$938$		0			0
$939$			211817.i			0.240231i
$940$		0			0
$941$	677172.	+	390965.i	0.764751	+	0.441529i	0.830999	−	0.556274i	$-0.187770\pi$
$941$	677172.	+	390965.i	0.764751	+	0.441529i	−0.0662482	+	0.997803i	$0.521103\pi$
$942$		0			0
$943$			126788.i			0.142579i
$944$		0			0
$945$	−44975.7	+	25966.7i	−0.0503633	+	0.0290772i
$946$		0			0
$947$	−778015.	−	1.34756e6i	−0.867537	−	1.50262i	−0.864506	−	0.502622i	$-0.832369\pi$
$947$	−778015.	−	1.34756e6i	−0.867537	−	1.50262i	−0.00303020	−	0.999995i	$-0.500965\pi$
$948$		0			0
$949$		−	753842.i		−	0.837043i
$950$		0			0
$951$	154804.			0.171168
$952$		0			0
$953$	−651018.	+	375865.i	−0.716815	+	0.413853i	−0.813579	−	0.581454i	$-0.802484\pi$
$953$	−651018.	+	375865.i	−0.716815	+	0.413853i	0.0967642	+	0.995307i	$0.469151\pi$
$954$		0			0
$955$	−69191.0	−	119842.i	−0.0758652	−	0.131402i
$956$		0			0
$957$	−38666.3			−0.0422191
$958$		0			0
$959$	−326959.	+	566309.i	−0.355513	+	0.615767i
$960$		0			0
$961$	503426.			0.545116
$962$		0			0
$963$	38530.7	+	22245.7i	0.0415484	+	0.0239880i
$964$		0			0
$965$	−87788.7	−	50684.8i	−0.0942723	−	0.0544281i
$966$		0			0
$967$	609402.	+	1.05552e6i	0.651705	+	1.12879i	0.982709	+	0.185157i	$0.0592792\pi$
$967$	609402.	+	1.05552e6i	0.651705	+	1.12879i	−0.331004	+	0.943629i	$0.607387\pi$
$968$		0			0
$969$	141140.	+	183512.i	0.150315	+	0.195441i
$970$		0			0
$971$	47714.5	−	27548.0i	0.0506072	−	0.0292181i	−0.474483	−	0.880265i	$-0.657365\pi$
$971$	47714.5	−	27548.0i	0.0506072	−	0.0292181i	0.525090	+	0.851047i	$0.324032\pi$
$972$		0			0
$973$	−300611.	+	520674.i	−0.317526	+	0.549971i
$974$		0			0
$975$	−145286.	+	251643.i	−0.152832	+	0.264713i
$976$		0			0
$977$			722803.i			0.757236i	0.925553	+	0.378618i	$0.123601\pi$
$977$			722803.i			0.757236i	−0.925553	+	0.378618i	$0.876399\pi$
$978$		0			0
$979$	−925622.	−	534408.i	−0.965758	−	0.557580i
$980$		0			0
$981$			138395.i			0.143808i
$982$		0			0
$983$	345011.	−	199192.i	0.357048	−	0.206142i	−0.310737	−	0.950496i	$-0.600576\pi$
$983$	345011.	−	199192.i	0.357048	−	0.206142i	0.667785	+	0.744354i	$0.267243\pi$
$984$		0			0
$985$	972.234	+	1683.96i	0.00100207	+	0.00173564i
$986$		0			0
$987$		−	197268.i		−	0.202499i
$988$		0			0
$989$	328691.			0.336043
$990$		0			0
$991$	−1.00784e6	+	581876.i	−1.02623	+	0.592493i	−0.915902	−	0.401402i	$-0.868523\pi$
$991$	−1.00784e6	+	581876.i	−1.02623	+	0.592493i	−0.110327	+	0.993895i	$0.535190\pi$
$992$		0			0
$993$	−26058.4	−	45134.4i	−0.0264270	−	0.0457730i
$994$		0			0
$995$	198890.			0.200894
$996$		0			0
$997$	152584.	−	264284.i	0.153504	−	0.265877i	−0.779009	−	0.627012i	$-0.784278\pi$
$997$	152584.	−	264284.i	0.153504	−	0.265877i	0.932513	+	0.361136i	$0.117611\pi$
$998$		0			0
$999$	151115.			0.151418

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.c.145.4		16
4.3	odd	2		38.5.d.a.31.3	yes	16
12.11	even	2		342.5.m.c.145.6		16
19.8	odd	6	inner	304.5.r.c.65.4		16
76.27	even	6		38.5.d.a.27.3	✓	16
228.179	odd	6		342.5.m.c.217.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.d.a.27.3	✓	16	76.27	even	6
38.5.d.a.31.3	yes	16	4.3	odd	2
304.5.r.c.65.4		16	19.8	odd	6	inner
304.5.r.c.145.4		16	1.1	even	1	trivial
342.5.m.c.145.6		16	12.11	even	2
342.5.m.c.217.6		16	228.179	odd	6

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	304.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30717 + 0.754695i) q^{3} +(1.35492 + 2.34679i) q^{5} -79.4947 q^{7} +(-39.3609 + 68.1750i) q^{9} +O(q^{10})\)	\(q+(-1.30717 + 0.754695i) q^{3} +(1.35492 + 2.34679i) q^{5} -79.4947 q^{7} +(-39.3609 + 68.1750i) q^{9} -109.030 q^{11} +(269.920 + 155.839i) q^{13} +(-3.54222 - 2.04510i) q^{15} +(-212.438 - 367.953i) q^{17} +(333.675 + 137.776i) q^{19} +(103.913 - 59.9943i) q^{21} +(132.097 - 228.798i) q^{23} +(308.828 - 534.906i) q^{25} -241.082i q^{27} +(-203.478 - 117.478i) q^{29} -648.147i q^{31} +(142.521 - 82.2843i) q^{33} +(-107.709 - 186.557i) q^{35} +626.819i q^{37} -470.442 q^{39} +(-415.611 + 239.953i) q^{41} +(622.065 + 1077.45i) q^{43} -213.323 q^{45} +(822.028 - 1423.79i) q^{47} +3918.41 q^{49} +(555.384 + 320.651i) q^{51} +(-4118.24 - 2377.67i) q^{53} +(-147.727 - 255.870i) q^{55} +(-540.148 + 71.7266i) q^{57} +(4227.83 - 2440.94i) q^{59} +(3545.36 - 6140.74i) q^{61} +(3128.98 - 5419.56i) q^{63} +844.594i q^{65} +(-51.8915 - 29.9596i) q^{67} +398.771i q^{69} +(-5416.15 + 3127.02i) q^{71} +(-1209.33 - 2094.62i) q^{73} +932.285i q^{75} +8667.30 q^{77} +(3684.36 - 2127.16i) q^{79} +(-3006.29 - 5207.04i) q^{81} +6643.06 q^{83} +(575.671 - 997.091i) q^{85} +354.640 q^{87} +(8489.61 + 4901.48i) q^{89} +(-21457.2 - 12388.3i) q^{91} +(489.153 + 847.239i) q^{93} +(128.772 + 969.738i) q^{95} +(-4066.41 + 2347.74i) q^{97} +(4291.51 - 7433.11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9}+O(q^{10}) \) 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9	\( 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9} + 84 q^{11} + 450 q^{13} + 390 q^{15} + 606 q^{17} + 306 q^{19} - 2160 q^{21} + 54 q^{23} - 434 q^{25} - 4914 q^{29} + 7890 q^{33} - 2328 q^{35} - 7620 q^{39} - 1692 q^{41} + 7402 q^{43} - 16720 q^{45} - 3198 q^{47} + 24816 q^{49} - 10710 q^{51} + 3870 q^{53} + 13588 q^{55} + 3702 q^{57} + 18288 q^{59} - 6522 q^{61} + 15676 q^{63} + 30168 q^{67} - 35874 q^{71} - 8080 q^{73} + 34560 q^{77} + 30738 q^{79} - 30920 q^{81} + 1476 q^{83} + 33626 q^{85} - 113100 q^{87} + 19782 q^{89} + 34260 q^{91} - 4272 q^{93} + 23706 q^{95} - 9936 q^{97} - 3848 q^{99}+O(q^{100}) \) 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9 + 84 * q^11 + 450 * q^13 + 390 * q^15 + 606 * q^17 + 306 * q^19 - 2160 * q^21 + 54 * q^23 - 434 * q^25 - 4914 * q^29 + 7890 * q^33 - 2328 * q^35 - 7620 * q^39 - 1692 * q^41 + 7402 * q^43 - 16720 * q^45 - 3198 * q^47 + 24816 * q^49 - 10710 * q^51 + 3870 * q^53 + 13588 * q^55 + 3702 * q^57 + 18288 * q^59 - 6522 * q^61 + 15676 * q^63 + 30168 * q^67 - 35874 * q^71 - 8080 * q^73 + 34560 * q^77 + 30738 * q^79 - 30920 * q^81 + 1476 * q^83 + 33626 * q^85 - 113100 * q^87 + 19782 * q^89 + 34260 * q^91 - 4272 * q^93 + 23706 * q^95 - 9936 * q^97 - 3848 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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