LMFDB - Embedded newform 315.4.j.c.226.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,4,Mod(46,315)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("315.46"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(315, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 4, names="a")

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

Newform invariants

comment:select newform

sage:traces = [4,-6,0,-6,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$18.5856016518$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	315.226
Dual form			315.4.j.c.46.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.20711 + 3.82282i) q^{2} +(-5.74264 - 9.94655i) q^{4} +(2.50000 - 4.33013i) q^{5} +(16.1066 + 9.14207i) q^{7} +15.3848 q^{8} +(11.0355 + 19.1141i) q^{10} +(-0.0710678 - 0.123093i) q^{11} -32.1421 q^{13} +(-70.4975 + 41.3951i) q^{14} +(11.9853 - 20.7591i) q^{16} +(-57.1838 - 99.0452i) q^{17} +(-21.6152 + 37.4387i) q^{19} -57.4264 q^{20} +0.627417 q^{22} +(77.2315 - 133.769i) q^{23} +(-12.5000 - 21.6506i) q^{25} +(70.9411 - 122.874i) q^{26} +(-1.56245 - 212.705i) q^{28} +40.1472 q^{29} +(-37.7107 - 65.3168i) q^{31} +(114.445 + 198.224i) q^{32} +504.843 q^{34} +(79.8528 - 46.8885i) q^{35} +(200.167 - 346.699i) q^{37} +(-95.4142 - 165.262i) q^{38} +(38.4619 - 66.6180i) q^{40} +95.4264 q^{41} -340.071 q^{43} +(-0.816234 + 1.41376i) q^{44} +(340.916 + 590.484i) q^{46} +(-3.74517 + 6.48682i) q^{47} +(175.845 + 294.495i) q^{49} +110.355 q^{50} +(184.581 + 319.703i) q^{52} +(-338.409 - 586.142i) q^{53} -0.710678 q^{55} +(247.796 + 140.649i) q^{56} +(-88.6091 + 153.476i) q^{58} +(398.090 + 689.513i) q^{59} +(378.551 - 655.669i) q^{61} +332.926 q^{62} -818.602 q^{64} +(-80.3553 + 139.180i) q^{65} +(370.290 + 641.362i) q^{67} +(-656.772 + 1137.56i) q^{68} +(3.00253 + 408.751i) q^{70} -37.0253 q^{71} +(-40.4386 - 70.0417i) q^{73} +(883.578 + 1530.40i) q^{74} +496.514 q^{76} +(-0.0193360 - 2.63232i) q^{77} +(158.679 - 274.840i) q^{79} +(-59.9264 - 103.796i) q^{80} +(-210.616 + 364.798i) q^{82} +945.929 q^{83} -571.838 q^{85} +(750.573 - 1300.03i) q^{86} +(-1.09336 - 1.89376i) q^{88} +(391.603 - 678.276i) q^{89} +(-517.701 - 293.846i) q^{91} -1774.05 q^{92} +(-16.5320 - 28.6342i) q^{94} +(108.076 + 187.193i) q^{95} +393.107 q^{97} +(-1513.91 + 22.2424i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} - 6 q^{4} + 10 q^{5} + 22 q^{7} - 12 q^{8} + 30 q^{10} + 28 q^{11} - 72 q^{13} - 84 q^{14} + 14 q^{16} - 76 q^{17} - 160 q^{19} - 60 q^{20} - 88 q^{22} - 22 q^{23} - 50 q^{25} + 148 q^{26}+ \cdots - 3066 q^{98}+O(q^{100}) $ 4 * q - 6 * q^2 - 6 * q^4 + 10 * q^5 + 22 * q^7 - 12 * q^8 + 30 * q^10 + 28 * q^11 - 72 * q^13 - 84 * q^14 + 14 * q^16 - 76 * q^17 - 160 * q^19 - 60 * q^20 - 88 * q^22 - 22 * q^23 - 50 * q^25 + 148 * q^26 + 138 * q^28 + 500 * q^29 + 132 * q^31 + 42 * q^32 + 888 * q^34 - 20 * q^35 + 416 * q^37 - 376 * q^38 - 30 * q^40 + 212 * q^41 - 1332 * q^43 - 156 * q^44 + 402 * q^46 - 196 * q^47 - 230 * q^49 + 300 * q^50 + 348 * q^52 - 952 * q^53 + 280 * q^55 + 714 * q^56 - 510 * q^58 + 840 * q^59 - 98 * q^61 + 8 * q^62 - 1204 * q^64 - 180 * q^65 + 1286 * q^67 - 1524 * q^68 + 210 * q^70 - 2128 * q^71 + 172 * q^73 + 1792 * q^74 - 288 * q^76 + 724 * q^77 + 1240 * q^79 - 70 * q^80 - 438 * q^82 + 3812 * q^83 - 760 * q^85 + 2018 * q^86 - 604 * q^88 + 650 * q^89 - 996 * q^91 - 5484 * q^92 - 332 * q^94 + 800 * q^95 - 1256 * q^97 - 3066 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	−2.20711	+	3.82282i	−0.780330	+	1.35157i	0.151419	+	0.988470i	$0.451616\pi$
$2$	−2.20711	+	3.82282i	−0.780330	+	1.35157i	−0.931749	+	0.363102i	$0.881718\pi$
$3$		0			0
$3$		0			0
$4$	−5.74264	−	9.94655i	−0.717830	−	1.24332i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$		0			0
$7$	16.1066	+	9.14207i	0.869675	+	0.493625i
$7$	16.1066	+	9.14207i	0.869675	+	0.493625i
$8$	15.3848			0.679917
$9$		0			0
$10$	11.0355	+	19.1141i	0.348974	+	0.604441i
$11$	−0.0710678	−	0.123093i	−0.00194798	−	0.00337400i	0.865050	−	0.501686i	$-0.167287\pi$
$11$	−0.0710678	−	0.123093i	−0.00194798	−	0.00337400i	−0.866998	+	0.498312i	$0.833953\pi$
$12$		0			0
$13$	−32.1421			−0.685740			−0.342870	−	0.939383i	$-0.611399\pi$
$13$	−32.1421			−0.685740			−0.342870	+	0.939383i	$0.611399\pi$
$14$	−70.4975	+	41.3951i	−1.34580	+	0.790237i
$15$		0			0
$16$	11.9853	−	20.7591i	0.187270	−	0.324361i
$17$	−57.1838	−	99.0452i	−0.815829	−	1.41306i	−0.908731	−	0.417383i	$-0.862947\pi$
$17$	−57.1838	−	99.0452i	−0.815829	−	1.41306i	0.0929014	−	0.995675i	$-0.470386\pi$
$18$		0			0
$19$	−21.6152	+	37.4387i	−0.260993	+	0.452054i	−0.966506	−	0.256643i	$-0.917383\pi$
$19$	−21.6152	+	37.4387i	−0.260993	+	0.452054i	0.705513	+	0.708697i	$0.250717\pi$
$20$	−57.4264			−0.642047
$21$		0			0
$22$	0.627417			0.00608026
$23$	77.2315	−	133.769i	0.700169	−	1.21273i	−0.268238	−	0.963353i	$-0.586441\pi$
$23$	77.2315	−	133.769i	0.700169	−	1.21273i	0.968407	−	0.249375i	$-0.0802252\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	70.9411	−	122.874i	0.535104	−	0.926827i
$27$		0			0
$28$	−1.56245	−	212.705i	−0.0105455	−	1.43562i
$29$	40.1472			0.257074			0.128537	−	0.991705i	$-0.458972\pi$
$29$	40.1472			0.257074			0.128537	+	0.991705i	$0.458972\pi$
$30$		0			0
$31$	−37.7107	−	65.3168i	−0.218485	−	0.378427i	0.735860	−	0.677134i	$-0.236778\pi$
$31$	−37.7107	−	65.3168i	−0.218485	−	0.378427i	−0.954345	+	0.298707i	$0.903445\pi$
$32$	114.445	+	198.224i	0.632224	+	1.09504i
$33$		0			0
$34$	504.843			2.54647
$35$	79.8528	−	46.8885i	0.385645	−	0.226446i
$36$		0			0
$37$	200.167	−	346.699i	0.889383	−	1.54046i	0.0487770	−	0.998810i	$-0.484468\pi$
$37$	200.167	−	346.699i	0.889383	−	1.54046i	0.840606	−	0.541647i	$-0.182199\pi$
$38$	−95.4142	−	165.262i	−0.407322	−	0.705502i
$39$		0			0
$40$	38.4619	−	66.6180i	0.152034	−	0.263331i
$41$	95.4264			0.363490			0.181745	−	0.983346i	$-0.441825\pi$
$41$	95.4264			0.363490			0.181745	+	0.983346i	$0.441825\pi$
$42$		0			0
$43$	−340.071			−1.20605			−0.603027	−	0.797721i	$-0.706039\pi$
$43$	−340.071			−1.20605			−0.603027	+	0.797721i	$0.706039\pi$
$44$	−0.816234	+	1.41376i	−0.00279663	+	0.00484391i
$45$		0			0
$46$	340.916	+	590.484i	1.09273	+	1.89266i
$47$	−3.74517	+	6.48682i	−0.0116232	+	0.0201319i	−0.871778	−	0.489900i	$-0.837033\pi$
$47$	−3.74517	+	6.48682i	−0.0116232	+	0.0201319i	0.860155	+	0.510032i	$0.170367\pi$
$48$		0			0
$49$	175.845	+	294.495i	0.512668	+	0.858587i
$50$	110.355			0.312132
$51$		0			0
$52$	184.581	+	319.703i	0.492245	+	0.852593i
$53$	−338.409	−	586.142i	−0.877058	−	1.51911i	−0.854554	−	0.519362i	$-0.826170\pi$
$53$	−338.409	−	586.142i	−0.877058	−	1.51911i	−0.0225038	−	0.999747i	$-0.507164\pi$
$54$		0			0
$55$	−0.710678			−0.00174232
$56$	247.796	+	140.649i	0.591307	+	0.335624i
$57$		0			0
$58$	−88.6091	+	153.476i	−0.200603	+	0.347454i
$59$	398.090	+	689.513i	0.878423	+	1.52147i	0.853071	+	0.521795i	$0.174737\pi$
$59$	398.090	+	689.513i	0.878423	+	1.52147i	0.0253519	+	0.999679i	$0.491929\pi$
$60$		0			0
$61$	378.551	−	655.669i	0.794565	−	1.37623i	−0.128550	−	0.991703i	$-0.541032\pi$
$61$	378.551	−	655.669i	0.794565	−	1.37623i	0.923115	−	0.384524i	$-0.125634\pi$
$62$	332.926			0.681962
$63$		0			0
$64$	−818.602			−1.59883
$65$	−80.3553	+	139.180i	−0.153336	+	0.265586i
$66$		0			0
$67$	370.290	+	641.362i	0.675197	+	1.16947i	0.976411	+	0.215918i	$0.0692745\pi$
$67$	370.290	+	641.362i	0.675197	+	1.16947i	−0.301215	+	0.953556i	$0.597392\pi$
$68$	−656.772	+	1137.56i	−1.17125	+	2.02867i
$69$		0			0
$70$	3.00253	+	408.751i	0.00512672	+	0.697930i
$71$	−37.0253			−0.0618886			−0.0309443	−	0.999521i	$-0.509851\pi$
$71$	−37.0253			−0.0618886			−0.0309443	+	0.999521i	$0.509851\pi$
$72$		0			0
$73$	−40.4386	−	70.0417i	−0.0648353	−	0.112298i	0.831786	−	0.555097i	$-0.187319\pi$
$73$	−40.4386	−	70.0417i	−0.0648353	−	0.112298i	−0.896621	+	0.442799i	$0.853986\pi$
$74$	883.578	+	1530.40i	1.38802	+	2.40413i
$75$		0			0
$76$	496.514			0.749395
$77$	−0.0193360	−	2.63232i	−2.86174e−5	−	0.00389585i
$78$		0			0
$79$	158.679	−	274.840i	0.225985	−	0.391417i	−0.730630	−	0.682774i	$-0.760773\pi$
$79$	158.679	−	274.840i	0.225985	−	0.391417i	0.956614	+	0.291357i	$0.0941067\pi$
$80$	−59.9264	−	103.796i	−0.0837497	−	0.145059i
$81$		0			0
$82$	−210.616	+	364.798i	−0.283642	+	0.491283i
$83$	945.929			1.25095			0.625477	−	0.780243i	$-0.284904\pi$
$83$	945.929			1.25095			0.625477	+	0.780243i	$0.284904\pi$
$84$		0			0
$85$	−571.838			−0.729700
$86$	750.573	−	1300.03i	0.941121	−	1.63007i
$87$		0			0
$88$	−1.09336	−	1.89376i	−0.00132446	−	0.00229404i
$89$	391.603	−	678.276i	0.466402	−	0.807832i	−0.532861	−	0.846203i	$-0.678883\pi$
$89$	391.603	−	678.276i	0.466402	−	0.807832i	0.999264	+	0.0383703i	$0.0122166\pi$
$90$		0			0
$91$	−517.701	−	293.846i	−0.596371	−	0.338499i
$92$	−1774.05			−2.01041
$93$		0			0
$94$	−16.5320	−	28.6342i	−0.0181398	−	0.0314191i
$95$	108.076	+	187.193i	0.116720	+	0.202165i
$96$		0			0
$97$	393.107			0.411484			0.205742	−	0.978606i	$-0.434039\pi$
$97$	393.107			0.411484			0.205742	+	0.978606i	$0.434039\pi$
$98$	−1513.91	+	22.2424i	−1.56049	+	0.0229268i
$99$		0			0
$100$	−143.566	+	248.664i	−0.143566	+	0.248664i
$101$	227.221	+	393.558i	0.223855	+	0.387728i	0.955975	−	0.293448i	$-0.0948026\pi$
$101$	227.221	+	393.558i	0.223855	+	0.387728i	−0.732121	+	0.681175i	$0.761469\pi$
$102$		0			0
$103$	351.850	−	609.422i	0.336590	−	0.582991i	−0.647199	−	0.762321i	$-0.724060\pi$
$103$	351.850	−	609.422i	0.336590	−	0.582991i	0.983789	+	0.179330i	$0.0573930\pi$
$104$	−494.500			−0.466247
$105$		0			0
$106$	2987.62			2.73758
$107$	477.499	−	827.052i	0.431416	−	0.747235i	−0.565579	−	0.824694i	$-0.691347\pi$
$107$	477.499	−	827.052i	0.431416	−	0.747235i	0.996996	+	0.0774592i	$0.0246808\pi$
$108$		0			0
$109$	−144.463	−	250.218i	−0.126946	−	0.219876i	0.795546	−	0.605893i	$-0.207184\pi$
$109$	−144.463	−	250.218i	−0.126946	−	0.219876i	−0.922492	+	0.386017i	$0.873851\pi$
$110$	1.56854	−	2.71680i	0.00135959	−	0.00235488i
$111$		0			0
$112$	382.823	−	224.789i	0.322977	−	0.189648i
$113$	−1251.24			−1.04165			−0.520826	−	0.853663i	$-0.674376\pi$
$113$	−1251.24			−1.04165			−0.520826	+	0.853663i	$0.674376\pi$
$114$		0			0
$115$	−386.157	−	668.844i	−0.313125	−	0.542348i
$116$	−230.551	−	399.326i	−0.184535	−	0.319625i
$117$		0			0
$118$	−3514.51			−2.74184
$119$	−15.5584	−	2118.06i	−0.0119852	−	1.63161i
$120$		0			0
$121$	665.490	−	1152.66i	0.499992	−	0.866012i
$122$	1671.00	+	2894.26i	1.24005	+	2.14782i
$123$		0			0
$124$	−433.118	+	750.182i	−0.313670	+	0.543293i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−1947.62			−1.36082			−0.680408	−	0.732833i	$-0.738198\pi$
$127$	−1947.62			−1.36082			−0.680408	+	0.732833i	$0.738198\pi$
$128$	891.185	−	1543.58i	0.615393	−	1.06589i
$129$		0			0
$130$	−354.706	−	614.368i	−0.239306	−	0.414490i
$131$	530.823	−	919.412i	0.354032	−	0.613201i	−0.632920	−	0.774217i	$-0.718144\pi$
$131$	530.823	−	919.412i	0.354032	−	0.613201i	0.986952	+	0.161016i	$0.0514771\pi$
$132$		0			0
$133$	−690.415	+	405.402i	−0.450124	+	0.264307i
$134$	−3269.08			−2.10750
$135$		0			0
$136$	−879.759	−	1523.79i	−0.554697	−	0.960763i
$137$	−719.671	−	1246.51i	−0.448800	−	0.777345i	0.549508	−	0.835489i	$-0.314815\pi$
$137$	−719.671	−	1246.51i	−0.448800	−	0.777345i	−0.998308	+	0.0581435i	$0.981482\pi$
$138$		0			0
$139$	662.132			0.404038			0.202019	−	0.979382i	$-0.435250\pi$
$139$	662.132			0.404038			0.202019	+	0.979382i	$0.435250\pi$
$140$	−924.944	−	524.996i	−0.558372	−	0.316930i
$141$		0			0
$142$	81.7187	−	141.541i	0.0482935	−	0.0836468i
$143$	2.28427	+	3.95647i	0.00133581	+	0.00231369i
$144$		0			0
$145$	100.368	−	173.842i	0.0574835	−	0.0995643i
$146$	357.009			0.202372
$147$		0			0
$148$	−4597.94			−2.55370
$149$	−393.555	+	681.657i	−0.216384	+	0.374789i	−0.953700	−	0.300760i	$-0.902760\pi$
$149$	−393.555	+	681.657i	−0.216384	+	0.374789i	0.737315	+	0.675549i	$0.236093\pi$
$150$		0			0
$151$	424.177	+	734.697i	0.228603	+	0.395952i	0.957394	−	0.288784i	$-0.0932509\pi$
$151$	424.177	+	734.697i	0.228603	+	0.395952i	−0.728791	+	0.684736i	$0.759918\pi$
$152$	−332.545	+	575.985i	−0.177454	+	0.307359i
$153$		0			0
$154$	10.1056	+	5.73589i	0.00528785	+	0.00300137i
$155$	−377.107			−0.195419
$156$		0			0
$157$	−477.461	−	826.987i	−0.242710	−	0.420387i	0.718775	−	0.695243i	$-0.244703\pi$
$157$	−477.461	−	826.987i	−0.242710	−	0.420387i	−0.961485	+	0.274856i	$0.911370\pi$
$158$	700.444	+	1213.20i	0.352685	+	0.610869i
$159$		0			0
$160$	1144.45			0.565478
$161$	2466.86	−	1448.51i	1.20755	−	0.709058i
$162$		0			0
$163$	3.68211	−	6.37760i	0.00176936	−	0.00306461i	−0.865139	−	0.501532i	$-0.832770\pi$
$163$	3.68211	−	6.37760i	0.00176936	−	0.00306461i	0.866909	+	0.498467i	$0.166103\pi$
$164$	−548.000	−	949.163i	−0.260924	−	0.451934i
$165$		0			0
$166$	−2087.77	+	3616.12i	−0.976157	+	1.69075i
$167$	−2921.40			−1.35368			−0.676841	−	0.736129i	$-0.736651\pi$
$167$	−2921.40			−1.35368			−0.676841	+	0.736129i	$0.736651\pi$
$168$		0			0
$169$	−1163.88			−0.529760
$170$	1262.11	−	2186.03i	0.569407	−	0.986242i
$171$		0			0
$172$	1952.91	+	3382.53i	0.865742	+	1.49951i
$173$	−1984.78	+	3437.75i	−0.872256	+	1.51079i	−0.0125990	+	0.999921i	$0.504011\pi$
$173$	−1984.78	+	3437.75i	−0.872256	+	1.51079i	−0.859657	+	0.510871i	$0.829323\pi$
$174$		0			0
$175$	−3.40097	−	462.994i	−0.00146908	−	0.199995i
$176$	−3.40707			−0.00145919
$177$		0			0
$178$	1728.62	+	2994.05i	0.727895	+	1.26075i
$179$	−552.976	−	957.782i	−0.230901	−	0.399933i	0.727172	−	0.686455i	$-0.240834\pi$
$179$	−552.976	−	957.782i	−0.230901	−	0.399933i	−0.958074	+	0.286522i	$0.907501\pi$
$180$		0			0
$181$	−117.214			−0.0481349			−0.0240674	−	0.999710i	$-0.507662\pi$
$181$	−117.214			−0.0481349			−0.0240674	+	0.999710i	$0.507662\pi$
$182$	2265.94	−	1330.53i	0.922871	−	0.541897i
$183$		0			0
$184$	1188.19	−	2058.00i	0.476057	−	0.824555i
$185$	−1000.83	−	1733.49i	−0.397744	−	0.688913i
$186$		0			0
$187$	−8.12785	+	14.0778i	−0.00317843	+	0.00550521i
$188$	86.0286			0.0333738
$189$		0			0
$190$	−954.142			−0.364320
$191$	501.300	−	868.277i	0.189910	−	0.328933i	−0.755310	−	0.655368i	$-0.772514\pi$
$191$	501.300	−	868.277i	0.189910	−	0.328933i	0.945220	+	0.326434i	$0.105847\pi$
$192$		0			0
$193$	−1628.88	−	2821.30i	−0.607510	−	1.05224i	−0.991649	−	0.128963i	$-0.958835\pi$
$193$	−1628.88	−	2821.30i	−0.607510	−	1.05224i	0.384140	−	0.923275i	$-0.374498\pi$
$194$	−867.629	+	1502.78i	−0.321093	+	0.556150i
$195$		0			0
$196$	1919.39	−	3440.23i	0.699488	−	1.25373i
$197$	41.6955			0.0150796			0.00753981	−	0.999972i	$-0.497600\pi$
$197$	41.6955			0.0150796			0.00753981	+	0.999972i	$0.497600\pi$
$198$		0			0
$199$	−1202.81	−	2083.32i	−0.428466	−	0.742125i	0.568271	−	0.822841i	$-0.307612\pi$
$199$	−1202.81	−	2083.32i	−0.428466	−	0.742125i	−0.996737	+	0.0807167i	$0.974279\pi$
$200$	−192.310	−	333.090i	−0.0679917	−	0.117765i
$201$		0			0
$202$	−2006.00			−0.698722
$203$	646.635	+	367.028i	0.223571	+	0.126898i
$204$		0			0
$205$	238.566	−	413.208i	0.0812789	−	0.140779i
$206$	1553.14	+	2690.12i	0.525303	+	0.909851i
$207$		0			0
$208$	−385.233	+	667.242i	−0.128419	+	0.222428i
$209$	6.14459			0.00203364
$210$		0			0
$211$	1211.24			0.395190			0.197595	−	0.980284i	$-0.436687\pi$
$211$	1211.24			0.395190			0.197595	+	0.980284i	$0.436687\pi$
$212$	−3886.72	+	6732.00i	−1.25916	+	2.18092i
$213$		0			0
$214$	2107.78	+	3650.78i	0.673294	+	1.16618i
$215$	−850.178	+	1472.55i	−0.269682	+	0.467103i
$216$		0			0
$217$	−10.2602	−	1396.79i	−0.00320973	−	0.436958i
$218$	1275.38			0.396238
$219$		0			0
$220$	4.08117	+	7.06879i	0.00125069	+	0.00216626i
$221$	1838.01	+	3183.52i	0.559447	+	0.968991i
$222$		0			0
$223$	4164.99			1.25071			0.625354	−	0.780341i	$-0.284954\pi$
$223$	4164.99			1.25071			0.625354	+	0.780341i	$0.284954\pi$
$224$	31.1379	+	4238.98i	0.00928789	+	1.26441i
$225$		0			0
$226$	2761.62	−	4783.26i	0.812832	−	1.40787i
$227$	1178.12	+	2040.57i	0.344470	+	0.596639i	0.985257	−	0.171079i	$-0.0547254\pi$
$227$	1178.12	+	2040.57i	0.344470	+	0.596639i	−0.640788	+	0.767718i	$0.721392\pi$
$228$		0			0
$229$	−2172.58	+	3763.02i	−0.626935	+	1.08588i	0.361228	+	0.932477i	$0.382358\pi$
$229$	−2172.58	+	3763.02i	−0.626935	+	1.08588i	−0.988163	+	0.153406i	$0.950976\pi$
$230$	3409.16			0.977363
$231$		0			0
$232$	617.655			0.174789
$233$	1229.12	−	2128.91i	0.345591	−	0.598581i	−0.639870	−	0.768483i	$-0.721012\pi$
$233$	1229.12	−	2128.91i	0.345591	−	0.598581i	0.985461	+	0.169902i	$0.0543452\pi$
$234$		0			0
$235$	18.7258	+	32.4341i	0.00519804	+	0.00900326i
$236$	4572.18	−	7919.25i	1.26112	−	2.18432i
$237$		0			0
$238$	8131.30	+	4615.31i	2.21460	+	1.25700i
$239$	−322.304			−0.0872307			−0.0436154	−	0.999048i	$-0.513888\pi$
$239$	−322.304			−0.0872307			−0.0436154	+	0.999048i	$0.513888\pi$
$240$		0			0
$241$	2505.62	+	4339.86i	0.669714	+	1.15998i	0.977984	+	0.208680i	$0.0669168\pi$
$241$	2505.62	+	4339.86i	0.669714	+	1.15998i	−0.308270	+	0.951299i	$0.599750\pi$
$242$	2937.61	+	5088.10i	0.780318	+	1.35155i
$243$		0			0
$244$	−8695.53			−2.28145
$245$	1714.81	−	25.1941i	0.447165	−	0.00656976i
$246$		0			0
$247$	694.759	−	1203.36i	0.178974	−	0.309991i
$248$	−580.170	−	1004.88i	−0.148552	−	0.257299i
$249$		0			0
$250$	275.888	−	477.853i	0.0697948	−	0.120888i
$251$	−3936.95			−0.990031			−0.495015	−	0.868884i	$-0.664838\pi$
$251$	−3936.95			−0.990031			−0.495015	+	0.868884i	$0.664838\pi$
$252$		0			0
$253$	−21.9547			−0.00545565
$254$	4298.62	−	7445.42i	1.06189	−	1.83924i
$255$		0			0
$256$	659.471	+	1142.24i	0.161004	+	0.278867i
$257$	−1813.08	+	3140.35i	−0.440066	+	0.762216i	−0.997694	−	0.0678748i	$-0.978378\pi$
$257$	−1813.08	+	3140.35i	−0.440066	+	0.762216i	0.557628	+	0.830091i	$0.311711\pi$
$258$		0			0
$259$	6393.54	−	3754.20i	1.53388	−	0.900674i
$260$	1845.81			0.440277
$261$		0			0
$262$	2343.16	+	4058.48i	0.552523	+	0.956999i
$263$	−393.278	−	681.177i	−0.0922074	−	0.159708i	0.816232	−	0.577724i	$-0.196059\pi$
$263$	−393.278	−	681.177i	−0.0922074	−	0.159708i	−0.908440	+	0.418016i	$0.862726\pi$
$264$		0			0
$265$	−3384.09			−0.784465
$266$	−25.9601	−	3534.10i	−0.00598389	−	0.814622i
$267$		0			0
$268$	4252.89	−	7366.22i	0.969353	−	1.67897i
$269$	2028.97	+	3514.28i	0.459883	+	0.796541i	0.998954	−	0.0457192i	$-0.0145580\pi$
$269$	2028.97	+	3514.28i	0.459883	+	0.796541i	−0.539071	+	0.842260i	$0.681225\pi$
$270$		0			0
$271$	−1449.71	+	2510.97i	−0.324958	+	0.562844i	−0.981504	−	0.191442i	$-0.938684\pi$
$271$	−1449.71	+	2510.97i	−0.324958	+	0.562844i	0.656546	+	0.754286i	$0.272017\pi$
$272$	−2741.45			−0.611122
$273$		0			0
$274$	6353.56			1.40085
$275$	−1.77670	+	3.07733i	−0.000389595	+	0.000674799i
$276$		0			0
$277$	−2646.98	−	4584.70i	−0.574157	−	0.994470i	−0.996133	−	0.0878623i	$-0.971996\pi$
$277$	−2646.98	−	4584.70i	−0.574157	−	0.994470i	0.421975	−	0.906607i	$-0.361337\pi$
$278$	−1461.40	+	2531.21i	−0.315283	+	0.546086i
$279$		0			0
$280$	1228.52	−	721.369i	0.262207	−	0.153964i
$281$	−2359.40			−0.500890			−0.250445	−	0.968131i	$-0.580577\pi$
$281$	−2359.40			−0.500890			−0.250445	+	0.968131i	$0.580577\pi$
$282$		0			0
$283$	1440.67	+	2495.32i	0.302612	+	0.524139i	0.976727	−	0.214487i	$-0.0688081\pi$
$283$	1440.67	+	2495.32i	0.302612	+	0.524139i	−0.674115	+	0.738626i	$0.735475\pi$
$284$	212.623	+	368.273i	0.0444255	+	0.0769472i
$285$		0			0
$286$	−20.1665			−0.00416948
$287$	1537.00	+	872.395i	0.316118	+	0.179428i
$288$		0			0
$289$	−4083.47	+	7072.77i	−0.831155	+	1.43960i
$290$	443.046	+	767.378i	0.0897122	+	0.155386i
$291$		0			0
$292$	−464.449	+	804.449i	−0.0930815	+	0.161222i
$293$	−760.730			−0.151680			−0.0758402	−	0.997120i	$-0.524164\pi$
$293$	−760.730			−0.151680			−0.0758402	+	0.997120i	$0.524164\pi$
$294$		0			0
$295$	3980.90			0.785685
$296$	3079.52	−	5333.88i	0.604707	−	1.04738i
$297$		0			0
$298$	−1737.24	−	3008.98i	−0.337703	−	0.584918i
$299$	−2482.39	+	4299.62i	−0.480134	+	0.831616i
$300$		0			0
$301$	−5477.39	−	3108.95i	−1.04888	−	0.595339i
$302$	−3744.82			−0.713544
$303$		0			0
$304$	518.129	+	897.426i	0.0977524	+	0.169312i
$305$	−1892.75	−	3278.35i	−0.355340	−	0.615467i
$306$		0			0
$307$	−4968.57			−0.923685			−0.461842	−	0.886962i	$-0.652811\pi$
$307$	−4968.57			−0.923685			−0.461842	+	0.886962i	$0.652811\pi$
$308$	−26.0714	+	15.3088i	−0.00482324	+	0.00283214i
$309$		0			0
$310$	832.315	−	1441.61i	0.152491	−	0.264123i
$311$	−2516.98	−	4359.54i	−0.458922	−	0.794877i	0.539982	−	0.841677i	$-0.318431\pi$
$311$	−2516.98	−	4359.54i	−0.458922	−	0.794877i	−0.998904	+	0.0467998i	$0.985098\pi$
$312$		0			0
$313$	−1799.60	+	3117.00i	−0.324983	+	0.562886i	−0.981509	−	0.191417i	$-0.938692\pi$
$313$	−1799.60	+	3117.00i	−0.324983	+	0.562886i	0.656526	+	0.754303i	$0.272025\pi$
$314$	4215.23			0.757577
$315$		0			0
$316$	−3644.95			−0.648875
$317$	1770.78	−	3067.08i	0.313744	−	0.543420i	−0.665426	−	0.746464i	$-0.731750\pi$
$317$	1770.78	−	3067.08i	0.313744	−	0.543420i	0.979170	+	0.203044i	$0.0650834\pi$
$318$		0			0
$319$	−2.85317	−	4.94184i	−0.000500774	−	0.000867367i
$320$	−2046.51	+	3544.65i	−0.357510	+	0.619225i
$321$		0			0
$322$	92.7558	+	12627.4i	0.0160530	+	2.18539i
$323$	4944.16			0.851704
$324$		0			0
$325$	401.777	+	695.898i	0.0685740	+	0.118774i
$326$	16.2536	+	28.1521i	0.00276136	+	0.00478282i
$327$		0			0
$328$	1468.11			0.247143
$329$	−119.625	+	70.2420i	−0.0200460	+	0.0117707i
$330$		0			0
$331$	3678.98	−	6372.18i	0.610922	−	1.05815i	−0.380164	−	0.924919i	$-0.624132\pi$
$331$	3678.98	−	6372.18i	0.610922	−	1.05815i	0.991085	−	0.133228i	$-0.0425342\pi$
$332$	−5432.13	−	9408.73i	−0.897972	−	1.55533i
$333$		0			0
$334$	6447.85	−	11168.0i	1.05632	−	1.82960i
$335$	3702.90			0.603914
$336$		0			0
$337$	−2323.24			−0.375534			−0.187767	−	0.982214i	$-0.560125\pi$
$337$	−2323.24			−0.375534			−0.187767	+	0.982214i	$0.560125\pi$
$338$	2568.81	−	4449.32i	0.413388	−	0.716009i
$339$		0			0
$340$	3283.86	+	5687.81i	0.523801	+	0.907249i
$341$	−5.36003	+	9.28385i	−0.000851208	+	0.00147434i
$342$		0			0
$343$	139.974	+	6350.91i	0.0220347	+	0.999757i
$344$	−5231.92			−0.820018
$345$		0			0
$346$	−8761.26	−	15174.9i	−1.36130	−	2.35783i
$347$	−2723.89	−	4717.92i	−0.421401	−	0.729889i	0.574675	−	0.818381i	$-0.305128\pi$
$347$	−2723.89	−	4717.92i	−0.421401	−	0.729889i	−0.996077	+	0.0884927i	$0.971795\pi$
$348$		0			0
$349$	−1227.84			−0.188324			−0.0941618	−	0.995557i	$-0.530017\pi$
$349$	−1227.84			−0.188324			−0.0941618	+	0.995557i	$0.530017\pi$
$350$	1777.45	+	1008.88i	0.271453	+	0.154076i
$351$		0			0
$352$	16.2667	−	28.1747i	0.00246311	−	0.00426624i
$353$	990.931	+	1716.34i	0.149411	+	0.258787i	0.931010	−	0.364994i	$-0.118929\pi$
$353$	990.931	+	1716.34i	0.149411	+	0.258787i	−0.781599	+	0.623781i	$0.785596\pi$
$354$		0			0
$355$	−92.5631	+	160.324i	−0.0138387	+	0.0239693i
$356$	−8995.33			−1.33919
$357$		0			0
$358$	4881.90			0.720717
$359$	−6109.03	+	10581.1i	−0.898112	+	1.55557i	−0.0682058	+	0.997671i	$0.521727\pi$
$359$	−6109.03	+	10581.1i	−0.898112	+	1.55557i	−0.829906	+	0.557904i	$0.811606\pi$
$360$		0			0
$361$	2495.06	+	4321.58i	0.363765	+	0.630059i
$362$	258.703	−	448.086i	0.0375611	−	0.0650577i
$363$		0			0
$364$	50.2203	+	6836.78i	0.00723149	+	0.984464i
$365$	−404.386			−0.0579905
$366$		0			0
$367$	−6823.85	−	11819.3i	−0.970577	−	1.68109i	−0.693818	−	0.720150i	$-0.744073\pi$
$367$	−6823.85	−	11819.3i	−0.970577	−	1.68109i	−0.276759	−	0.960939i	$-0.589260\pi$
$368$	−1851.28	−	3206.52i	−0.262241	−	0.454215i
$369$		0			0
$370$	8835.78			1.24149
$371$	−92.0737	−	12534.5i	−0.0128847	−	1.75407i
$372$		0			0
$373$	2772.01	−	4801.27i	0.384797	−	0.666488i	−0.606944	−	0.794745i	$-0.707605\pi$
$373$	2772.01	−	4801.27i	0.384797	−	0.666488i	0.991741	+	0.128256i	$0.0409380\pi$
$374$	−35.8781	−	62.1426i	−0.00496046	−	0.00859176i
$375$		0			0
$376$	−57.6185	+	99.7982i	−0.00790279	+	0.0136880i
$377$	−1290.42			−0.176286
$378$		0			0
$379$	−634.243			−0.0859601			−0.0429801	−	0.999076i	$-0.513685\pi$
$379$	−634.243			−0.0859601			−0.0429801	+	0.999076i	$0.513685\pi$
$380$	1241.28	−	2149.97i	0.167570	−	0.290240i
$381$		0			0
$382$	2212.84	+	3832.76i	0.296385	+	0.513353i
$383$	2895.47	−	5015.09i	0.386296	−	0.669084i	−0.605652	−	0.795730i	$-0.707088\pi$
$383$	2895.47	−	5015.09i	0.386296	−	0.669084i	0.991948	+	0.126645i	$0.0404210\pi$
$384$		0			0
$385$	−11.4466	−	6.49707i	−0.00151526	−	0.000860055i
$386$	14380.5			1.89623
$387$		0			0
$388$	−2257.47	−	3910.05i	−0.295376	−	0.511606i
$389$	758.496	+	1313.75i	0.0988619	+	0.171234i	0.911214	−	0.411934i	$-0.135146\pi$
$389$	758.496	+	1313.75i	0.0988619	+	0.171234i	−0.812352	+	0.583168i	$0.801813\pi$
$390$		0			0
$391$	−17665.6			−2.28487
$392$	2705.34	+	4530.74i	0.348572	+	0.583768i
$393$		0			0
$394$	−92.0265	+	159.395i	−0.0117671	+	0.0203812i
$395$	−793.396	−	1374.20i	−0.101063	−	0.175047i
$396$		0			0
$397$	3937.47	−	6819.90i	0.497773	−	0.862169i	−0.502223	−	0.864738i	$-0.667484\pi$
$397$	3937.47	−	6819.90i	0.497773	−	0.862169i	0.999997	+	0.00256925i	$0.000817820\pi$
$398$	10618.9			1.33738
$399$		0			0
$400$	−599.264			−0.0749080
$401$	−5555.64	+	9622.65i	−0.691859	+	1.19833i	0.279369	+	0.960184i	$0.409875\pi$
$401$	−5555.64	+	9622.65i	−0.691859	+	1.19833i	−0.971228	+	0.238151i	$0.923459\pi$
$402$		0			0
$403$	1212.10	+	2099.42i	0.149824	+	0.259503i
$404$	2609.69	−	4520.12i	0.321379	−	0.556645i
$405$		0			0
$406$	−2830.28	+	1661.90i	−0.345971	+	0.203149i
$407$	−56.9016			−0.00692999
$408$		0			0
$409$	5355.07	+	9275.25i	0.647411	+	1.12135i	0.983739	+	0.179603i	$0.0574814\pi$
$409$	5355.07	+	9275.25i	0.647411	+	1.12135i	−0.336328	+	0.941745i	$0.609185\pi$
$410$	1053.08	+	1823.99i	0.126849	+	0.219708i
$411$		0			0
$412$	−8082.19			−0.966458
$413$	108.312	+	14745.1i	0.0129048	+	1.75680i
$414$		0			0
$415$	2364.82	−	4095.99i	0.279722	−	0.484492i
$416$	−3678.50	−	6371.34i	−0.433541	−	0.750915i
$417$		0			0
$418$	−13.5618	+	23.4897i	−0.00158691	+	0.00274860i
$419$	−8615.98			−1.00458			−0.502289	−	0.864700i	$-0.667509\pi$
$419$	−8615.98			−1.00458			−0.502289	+	0.864700i	$0.667509\pi$
$420$		0			0
$421$	6689.72			0.774435			0.387217	−	0.921988i	$-0.373436\pi$
$421$	6689.72			0.774435			0.387217	+	0.921988i	$0.373436\pi$
$422$	−2673.33	+	4630.35i	−0.308379	+	0.534128i
$423$		0			0
$424$	−5206.35	−	9017.66i	−0.596327	−	1.03287i
$425$	−1429.59	+	2476.13i	−0.163166	+	0.282612i
$426$		0			0
$427$	12091.3	−	7099.87i	1.37035	−	0.804653i
$428$	−10968.4			−1.23873
$429$		0			0
$430$	−3752.87	−	6500.15i	−0.420882	−	0.728989i
$431$	3085.32	+	5343.93i	0.344814	+	0.597235i	0.985320	−	0.170718i	$-0.0546088\pi$
$431$	3085.32	+	5343.93i	0.344814	+	0.597235i	−0.640506	+	0.767953i	$0.721275\pi$
$432$		0			0
$433$	14001.1			1.55392			0.776961	−	0.629548i	$-0.216760\pi$
$433$	14001.1			1.55392			0.776961	+	0.629548i	$0.216760\pi$
$434$	5362.31	+	3043.63i	0.593085	+	0.336634i
$435$		0			0
$436$	−1659.20	+	2873.82i	−0.182251	+	0.315668i
$437$	3338.75	+	5782.89i	0.365479	+	0.633028i
$438$		0			0
$439$	−6103.49	+	10571.6i	−0.663562	+	1.14932i	0.316111	+	0.948722i	$0.397623\pi$
$439$	−6103.49	+	10571.6i	−0.663562	+	1.14932i	−0.979673	+	0.200601i	$0.935711\pi$
$440$	−10.9336			−0.00118464
$441$		0			0
$442$	−16226.7			−1.74621
$443$	613.882	−	1063.27i	0.0658384	−	0.114035i	−0.831227	−	0.555933i	$-0.812361\pi$
$443$	613.882	−	1063.27i	0.0658384	−	0.114035i	0.897066	+	0.441897i	$0.145694\pi$
$444$		0			0
$445$	−1958.01	−	3391.38i	−0.208581	−	0.361274i
$446$	−9192.57	+	15922.0i	−0.975966	+	1.69042i
$447$		0			0
$448$	−13184.9	−	7483.72i	−1.39046	−	0.789224i
$449$	1151.70			0.121051			0.0605257	−	0.998167i	$-0.480722\pi$
$449$	1151.70			0.121051			0.0605257	+	0.998167i	$0.480722\pi$
$450$		0			0
$451$	−6.78175	−	11.7463i	−0.000708071	−	0.00122641i
$452$	7185.41	+	12445.5i	0.747729	+	1.29510i
$453$		0			0
$454$	−10401.0			−1.07520
$455$	−2566.64	+	1507.10i	−0.264453	+	0.155283i
$456$		0			0
$457$	−9356.91	+	16206.6i	−0.957763	+	1.65889i	−0.229849	+	0.973226i	$0.573823\pi$
$457$	−9356.91	+	16206.6i	−0.957763	+	1.65889i	−0.727914	+	0.685668i	$0.759510\pi$
$458$	−9590.23	−	16610.8i	−0.978433	−	1.69470i
$459$		0			0
$460$	−4435.13	+	7681.87i	−0.449541	+	0.778628i
$461$	3154.57			0.318705			0.159352	−	0.987222i	$-0.449059\pi$
$461$	3154.57			0.318705			0.159352	+	0.987222i	$0.449059\pi$
$462$		0			0
$463$	4051.11			0.406633			0.203316	−	0.979113i	$-0.434828\pi$
$463$	4051.11			0.406633			0.203316	+	0.979113i	$0.434828\pi$
$464$	481.175	−	833.420i	0.0481422	−	0.0833848i
$465$		0			0
$466$	5425.62	+	9397.45i	0.539350	+	0.934181i
$467$	8170.80	−	14152.2i	0.809635	−	1.40233i	−0.103482	−	0.994631i	$-0.532998\pi$
$467$	8170.80	−	14152.2i	0.809635	−	1.40233i	0.913117	−	0.407697i	$-0.133668\pi$
$468$		0			0
$469$	100.748	+	13715.4i	0.00991920	+	1.35036i
$470$	−165.320			−0.0162247
$471$		0			0
$472$	6124.53	+	10608.0i	0.597255	+	1.03448i
$473$	24.1681	+	41.8604i	0.00234937	+	0.00406922i
$474$		0			0
$475$	1080.76			0.104397
$476$	−20978.0	+	12318.0i	−2.02001	+	1.18612i
$477$		0			0
$478$	711.360	−	1232.11i	0.0680688	−	0.117899i
$479$	1265.72	+	2192.30i	0.120736	+	0.209121i	0.920058	−	0.391782i	$-0.128141\pi$
$479$	1265.72	+	2192.30i	0.120736	+	0.209121i	−0.799322	+	0.600903i	$0.794808\pi$
$480$		0			0
$481$	−6433.78	+	11143.6i	−0.609886	+	1.05635i
$482$	−22120.7			−2.09039
$483$		0			0
$484$	−15286.7			−1.43564
$485$	982.767	−	1702.20i	0.0920106	−	0.159367i
$486$		0			0
$487$	4221.09	+	7311.14i	0.392763	+	0.680286i	0.992813	−	0.119677i	$-0.0381858\pi$
$487$	4221.09	+	7311.14i	0.392763	+	0.680286i	−0.600050	+	0.799963i	$0.704852\pi$
$488$	5823.92	−	10087.3i	0.540239	−	0.935721i
$489$		0			0
$490$	−3688.47	+	6611.04i	−0.340057	+	0.609502i
$491$	15223.9			1.39928			0.699640	−	0.714496i	$-0.253344\pi$
$491$	15223.9			1.39928			0.699640	+	0.714496i	$0.253344\pi$
$492$		0			0
$493$	−2295.77	−	3976.39i	−0.209729	−	0.363260i
$494$	3066.82	+	5311.88i	0.279317	+	0.483791i
$495$		0			0
$496$	−1807.89			−0.163663
$497$	−596.351	−	338.487i	−0.0538229	−	0.0305498i
$498$		0			0
$499$	8311.32	−	14395.6i	0.745623	−	1.29146i	−0.204280	−	0.978913i	$-0.565485\pi$
$499$	8311.32	−	14395.6i	0.745623	−	1.29146i	0.949903	−	0.312545i	$-0.101181\pi$
$500$	717.830	+	1243.32i	0.0642047	+	0.111206i
$501$		0			0
$502$	8689.26	−	15050.2i	0.772551	−	1.33810i
$503$	17506.6			1.55185			0.775923	−	0.630828i	$-0.217285\pi$
$503$	17506.6			1.55185			0.775923	+	0.630828i	$0.217285\pi$
$504$		0			0
$505$	2272.21			0.200222
$506$	48.4564	−	83.9289i	0.00425721	−	0.00737370i
$507$		0			0
$508$	11184.5	+	19372.1i	0.976835	+	1.69193i
$509$	6191.58	−	10724.1i	0.539169	−	0.933867i	−0.459780	−	0.888033i	$-0.652072\pi$
$509$	6191.58	−	10724.1i	0.539169	−	0.933867i	0.998949	−	0.0458348i	$-0.0145948\pi$
$510$		0			0
$511$	−11.0025	−	1497.83i	−0.000952485	−	0.129667i
$512$	8436.86			0.728242
$513$		0			0
$514$	−8003.33	−	13862.2i	−0.686793	−	1.18956i
$515$	−1759.25	−	3047.11i	−0.150528	−	0.260722i
$516$		0			0
$517$	1.06464			9.05666e−5
$518$	240.402	+	32727.3i	0.0203912	+	2.77597i
$519$		0			0
$520$	−1236.25	+	2141.25i	−0.104256	+	0.180577i
$521$	−7489.50	−	12972.2i	−0.629790	−	1.09083i	−0.987594	−	0.157032i	$-0.949807\pi$
$521$	−7489.50	−	12972.2i	−0.629790	−	1.09083i	0.357803	−	0.933797i	$-0.383526\pi$
$522$		0			0
$523$	−1859.56	+	3220.85i	−0.155474	+	0.269288i	−0.933231	−	0.359276i	$-0.883024\pi$
$523$	−1859.56	+	3220.85i	−0.155474	+	0.269288i	0.777758	+	0.628564i	$0.216357\pi$
$524$	−12193.3			−1.01654
$525$		0			0
$526$	3472.02			0.287809
$527$	−4312.88	+	7470.12i	−0.356493	+	0.617464i
$528$		0			0
$529$	−5845.91	−	10125.4i	−0.480472	−	0.832203i
$530$	7469.05	−	12936.8i	0.612141	−	1.06026i
$531$		0			0
$532$	7997.15	+	4539.16i	0.651730	+	0.369920i
$533$	−3067.21			−0.249260
$534$		0			0
$535$	−2387.49	−	4135.26i	−0.192935	−	0.334173i
$536$	5696.83	+	9867.21i	0.459078	+	0.795146i
$537$		0			0
$538$	−17912.6			−1.43544
$539$	23.7534	−	42.5745i	0.00189820	−	0.00340225i
$540$		0			0
$541$	122.363	−	211.939i	0.00972420	−	0.0168428i	−0.861122	−	0.508398i	$-0.830238\pi$
$541$	122.363	−	211.939i	0.00972420	−	0.0168428i	0.870847	+	0.491555i	$0.163571\pi$
$542$	−6399.33	−	11084.0i	−0.507149	−	0.878408i
$543$		0			0
$544$	13088.8	−	22670.4i	1.03157	−	1.78674i
$545$	−1444.63			−0.113544
$546$		0			0
$547$	−12685.4			−0.991568			−0.495784	−	0.868446i	$-0.665119\pi$
$547$	−12685.4			−0.991568			−0.495784	+	0.868446i	$0.665119\pi$
$548$	−8265.63	+	14316.5i	−0.644325	+	1.11600i
$549$		0			0
$550$	−7.84271	−	13.5840i	−0.000608026	−	0.00105313i
$551$	−867.790	+	1503.06i	−0.0670946	+	0.116211i
$552$		0			0
$553$	5068.39	−	2976.09i	0.389747	−	0.228854i
$554$	23368.7			1.79213
$555$		0			0
$556$	−3802.39	−	6585.93i	−0.290031	−	0.502348i
$557$	−11031.4	−	19106.9i	−0.839164	−	1.45347i	−0.890595	−	0.454798i	$-0.849711\pi$
$557$	−11031.4	−	19106.9i	−0.839164	−	1.45347i	0.0514307	−	0.998677i	$-0.483622\pi$
$558$		0			0
$559$	10930.6			0.827040
$560$	−16.3047	−	2219.65i	−0.00123035	−	0.167495i
$561$		0			0
$562$	5207.45	−	9019.57i	0.390859	−	0.676988i
$563$	3931.10	+	6808.86i	0.294274	+	0.509697i	0.974816	−	0.223012i	$-0.0715890\pi$
$563$	3931.10	+	6808.86i	0.294274	+	0.509697i	−0.680542	+	0.732709i	$0.738256\pi$
$564$		0			0
$565$	−3128.10	+	5418.02i	−0.232920	+	0.403430i
$566$	−12718.9			−0.944549
$567$		0			0
$568$	−569.625			−0.0420791
$569$	10470.8	−	18135.9i	0.771453	−	1.33620i	−0.165313	−	0.986241i	$-0.552864\pi$
$569$	10470.8	−	18135.9i	0.771453	−	1.33620i	0.936766	−	0.349955i	$-0.113803\pi$
$570$		0			0
$571$	3565.83	+	6176.20i	0.261341	+	0.452655i	0.966598	−	0.256296i	$-0.0825021\pi$
$571$	3565.83	+	6176.20i	0.261341	+	0.452655i	−0.705258	+	0.708951i	$0.749169\pi$
$572$	26.2355	−	45.4412i	0.00191776	−	0.00332167i
$573$		0			0
$574$	−6727.32	+	3950.19i	−0.489186	+	0.287243i
$575$	−3861.57			−0.280067
$576$		0			0
$577$	7816.51	+	13538.6i	0.563961	+	0.976809i	0.997146	+	0.0755039i	$0.0240565\pi$
$577$	7816.51	+	13538.6i	0.563961	+	0.976809i	−0.433184	+	0.901305i	$0.642610\pi$
$578$	−18025.3	−	31220.7i	−1.29715	−	2.24673i
$579$		0			0
$580$	−2305.51			−0.165054
$581$	15235.7	+	8647.75i	1.08792	+	0.617502i
$582$		0			0
$583$	−48.1000	+	83.3116i	−0.00341698	+	0.00591838i
$584$	−622.139	−	1077.58i	−0.0440827	−	0.0763534i
$585$		0			0
$586$	1679.01	−	2908.14i	0.118361	−	0.205007i
$587$	19406.2			1.36453			0.682266	−	0.731104i	$-0.260995\pi$
$587$	19406.2			1.36453			0.682266	+	0.731104i	$0.260995\pi$
$588$		0			0
$589$	3260.50			0.228093
$590$	−8786.28	+	15218.3i	−0.613094	+	1.06191i
$591$		0			0
$592$	−4798.10	−	8310.56i	−0.333110	−	0.576963i
$593$	−7429.82	+	12868.8i	−0.514513	+	0.891162i	0.485346	+	0.874322i	$0.338694\pi$
$593$	−7429.82	+	12868.8i	−0.514513	+	0.891162i	−0.999858	+	0.0168395i	$0.994640\pi$
$594$		0			0
$595$	−9210.36	−	5227.78i	−0.634602	−	0.360198i
$596$	9040.18			0.621309
$597$		0			0
$598$	−10957.8	−	18979.4i	−0.749326	−	1.29787i
$599$	−5264.93	−	9119.13i	−0.359131	−	0.622032i	0.628685	−	0.777660i	$-0.283593\pi$
$599$	−5264.93	−	9119.13i	−0.359131	−	0.622032i	−0.987816	+	0.155627i	$0.950260\pi$
$600$		0			0
$601$	11595.2			0.786984			0.393492	−	0.919328i	$-0.371267\pi$
$601$	11595.2			0.786984			0.393492	+	0.919328i	$0.371267\pi$
$602$	23974.2	−	14077.3i	1.62311	−	0.953069i
$603$		0			0
$604$	4871.80	−	8438.20i	0.328196	−	0.568453i
$605$	−3327.45	−	5763.31i	−0.223603	−	0.387292i
$606$		0			0
$607$	11641.0	−	20162.9i	0.778411	−	1.34825i	−0.154446	−	0.988001i	$-0.549359\pi$
$607$	11641.0	−	20162.9i	0.778411	−	1.34825i	0.932857	−	0.360246i	$-0.117307\pi$
$608$	−9894.99			−0.660024
$609$		0			0
$610$	16710.0			1.10913
$611$	120.378	−	208.500i	0.00797047	−	0.0138053i
$612$		0			0
$613$	3693.99	+	6398.18i	0.243391	+	0.421566i	0.961678	−	0.274181i	$-0.0884068\pi$
$613$	3693.99	+	6398.18i	0.243391	+	0.421566i	−0.718287	+	0.695747i	$0.755073\pi$
$614$	10966.2	−	18993.9i	0.720779	−	1.24843i
$615$		0			0
$616$	−0.297480	−	40.4976i	−1.94575e−5	−	0.00264886i
$617$	−667.085			−0.0435265			−0.0217632	−	0.999763i	$-0.506928\pi$
$617$	−667.085			−0.0435265			−0.0217632	+	0.999763i	$0.506928\pi$
$618$		0			0
$619$	4712.89	+	8162.96i	0.306021	+	0.530044i	0.977488	−	0.210990i	$-0.0676689\pi$
$619$	4712.89	+	8162.96i	0.306021	+	0.530044i	−0.671467	+	0.741034i	$0.734336\pi$
$620$	2165.59	+	3750.91i	0.140278	+	0.242968i
$621$		0			0
$622$	22221.0			1.43244
$623$	12508.2	−	7344.66i	0.804385	−	0.472323i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−7943.83	−	13759.1i	−0.507187	−	0.878474i
$627$		0			0
$628$	−5483.77	+	9498.17i	−0.348450	+	0.603532i
$629$	−45785.1			−2.90234
$630$		0			0
$631$	28047.3			1.76949			0.884744	−	0.466078i	$-0.154333\pi$
$631$	28047.3			1.76949			0.884744	+	0.466078i	$0.154333\pi$
$632$	2441.24	−	4228.36i	0.153651	−	0.266131i
$633$		0			0
$634$	7816.59	+	13538.7i	0.489647	+	0.848094i
$635$	−4869.06	+	8433.46i	−0.304288	+	0.527042i
$636$		0			0
$637$	−5652.04	−	9465.71i	−0.351557	−	0.588768i
$638$	25.1890			0.00156308
$639$		0			0
$640$	−4455.92	−	7717.89i	−0.275212	−	0.476682i
$641$	11604.2	+	20099.0i	0.715034	+	1.23847i	0.962947	+	0.269692i	$0.0869220\pi$
$641$	11604.2	+	20099.0i	0.715034	+	1.23847i	−0.247913	+	0.968782i	$0.579745\pi$
$642$		0			0
$643$	−4294.22			−0.263371			−0.131686	−	0.991292i	$-0.542039\pi$
$643$	−4294.22			−0.263371			−0.131686	+	0.991292i	$0.542039\pi$
$644$	−28573.9	−	16218.5i	−1.74840	−	0.992388i
$645$		0			0
$646$	−10912.3	+	18900.6i	−0.664610	+	1.15114i
$647$	−8696.69	−	15063.1i	−0.528443	−	0.915289i	−0.999450	−	0.0331602i	$-0.989443\pi$
$647$	−8696.69	−	15063.1i	−0.528443	−	0.915289i	0.471007	−	0.882129i	$-0.343890\pi$
$648$		0			0
$649$	56.5828	−	98.0043i	0.00342230	−	0.00592759i
$650$	−3547.06			−0.214042
$651$		0			0
$652$	−84.5801			−0.00508039
$653$	7237.72	−	12536.1i	0.433743	−	0.751265i	−0.563449	−	0.826151i	$-0.690526\pi$
$653$	7237.72	−	12536.1i	0.433743	−	0.751265i	0.997192	+	0.0748861i	$0.0238593\pi$
$654$		0			0
$655$	−2654.11	−	4597.06i	−0.158328	−	0.274232i
$656$	1143.71	−	1980.97i	0.0680708	−	0.117902i
$657$		0			0
$658$	−4.49798	−	612.336i	−0.000266489	−	0.0362786i
$659$	−620.113			−0.0366558			−0.0183279	−	0.999832i	$-0.505834\pi$
$659$	−620.113			−0.0366558			−0.0183279	+	0.999832i	$0.505834\pi$
$660$		0			0
$661$	−3052.75	−	5287.52i	−0.179634	−	0.311135i	0.762121	−	0.647434i	$-0.224158\pi$
$661$	−3052.75	−	5287.52i	−0.179634	−	0.311135i	−0.941755	+	0.336299i	$0.890825\pi$
$662$	16239.8	+	28128.2i	0.953441	+	1.65141i
$663$		0			0
$664$	14552.9			0.850546
$665$	29.4051	+	4003.09i	0.00171471	+	0.233433i
$666$		0			0
$667$	3100.63	−	5370.44i	0.179995	−	0.311761i
$668$	16776.6	+	29057.9i	0.971713	+	1.68306i
$669$		0			0
$670$	−8172.70	+	14155.5i	−0.471252	+	0.816233i
$671$	−107.611			−0.00619118
$672$		0			0
$673$	−16302.5			−0.933754			−0.466877	−	0.884322i	$-0.654621\pi$
$673$	−16302.5			−0.933754			−0.466877	+	0.884322i	$0.654621\pi$
$674$	5127.64	−	8881.33i	0.293040	−	0.507561i
$675$		0			0
$676$	6683.76	+	11576.6i	0.380278	+	0.658660i
$677$	−2409.55	+	4173.46i	−0.136789	+	0.236926i	−0.926280	−	0.376837i	$-0.877012\pi$
$677$	−2409.55	+	4173.46i	−0.136789	+	0.236926i	0.789490	+	0.613763i	$0.210345\pi$
$678$		0			0
$679$	6331.61	+	3593.81i	0.357857	+	0.203119i
$680$	−8797.59			−0.496136
$681$		0			0
$682$	−23.6603	−	40.9809i	−0.00132845	−	0.00230094i
$683$	−4095.16	−	7093.03i	−0.229425	−	0.397375i	0.728213	−	0.685351i	$-0.240351\pi$
$683$	−4095.16	−	7093.03i	−0.229425	−	0.397375i	−0.957638	+	0.287976i	$0.907018\pi$
$684$		0			0
$685$	−7196.71			−0.401419
$686$	−24587.3	−	13482.0i	−1.36844	−	0.750359i
$687$		0			0
$688$	−4075.85	+	7059.57i	−0.225858	+	0.391197i
$689$	10877.2	+	18839.9i	0.601434	+	1.04171i
$690$		0			0
$691$	−238.487	+	413.071i	−0.0131295	+	0.0227409i	−0.872515	−	0.488586i	$-0.837513\pi$
$691$	−238.487	+	413.071i	−0.0131295	+	0.0227409i	0.859386	+	0.511327i	$0.170846\pi$
$692$	45591.6			2.50453
$693$		0			0
$694$	24047.7			1.31533
$695$	1655.33	−	2867.12i	0.0903457	−	0.156483i
$696$		0			0
$697$	−5456.84	−	9451.53i	−0.296546	−	0.513633i
$698$	2709.98	−	4693.82i	0.146955	−	0.254533i
$699$		0			0
$700$	−4585.66	+	2692.64i	−0.247602	+	0.145389i
$701$	20366.7			1.09735			0.548673	−	0.836037i	$-0.315133\pi$
$701$	20366.7			1.09735			0.548673	+	0.836037i	$0.315133\pi$
$702$		0			0
$703$	8653.29	+	14987.9i	0.464246	+	0.804098i
$704$	58.1763	+	100.764i	0.00311449	+	0.00539445i
$705$		0			0
$706$	−8748.36			−0.466358
$707$	61.8218	+	8416.15i	0.00328861	+	0.447697i
$708$		0			0
$709$	−11207.5	+	19412.0i	−0.593664	+	1.02826i	0.400070	+	0.916484i	$0.368986\pi$
$709$	−11207.5	+	19412.0i	−0.593664	+	1.02826i	−0.993734	+	0.111771i	$0.964348\pi$
$710$	−408.593	−	707.705i	−0.0215975	−	0.0374080i
$711$		0			0
$712$	6024.72	−	10435.1i	0.317115	−	0.549259i
$713$	−11649.8			−0.611906
$714$		0			0
$715$	22.8427			0.00119478
$716$	−6351.08	+	11000.4i	−0.331496	+	0.574168i
$717$		0			0
$718$	−26966.5	−	46707.4i	−1.40165	−	2.42772i
$719$	−13078.0	+	22651.7i	−0.678340	+	1.17492i	0.297141	+	0.954834i	$0.403967\pi$
$719$	−13078.0	+	22651.7i	−0.678340	+	1.17492i	−0.975481	+	0.220085i	$0.929366\pi$
$720$		0			0
$721$	11238.5	−	6599.08i	0.580503	−	0.340863i
$722$	−22027.5			−1.13543
$723$		0			0
$724$	673.115	+	1165.87i	0.0345527	+	0.0598470i
$725$	−501.840	−	869.212i	−0.0257074	−	0.0445265i
$726$		0			0
$727$	−13666.2			−0.697184			−0.348592	−	0.937275i	$-0.613340\pi$
$727$	−13666.2			−0.697184			−0.348592	+	0.937275i	$0.613340\pi$
$728$	−7964.71	−	4520.75i	−0.405483	−	0.230151i
$729$		0			0
$730$	892.523	−	1545.90i	0.0452517	−	0.0783783i
$731$	19446.5	+	33682.4i	0.983935	+	1.70423i
$732$		0			0
$733$	−12519.1	+	21683.7i	−0.630836	+	1.09264i	0.356545	+	0.934278i	$0.383955\pi$
$733$	−12519.1	+	21683.7i	−0.630836	+	1.09264i	−0.987381	+	0.158362i	$0.949379\pi$
$734$	60243.8			3.02948
$735$		0			0
$736$	35354.9			1.77065
$737$	52.6315	−	91.1603i	0.00263054	−	0.00455622i
$738$		0			0
$739$	−1627.60	−	2819.08i	−0.0810178	−	0.140327i	0.822670	−	0.568520i	$-0.192484\pi$
$739$	−1627.60	−	2819.08i	−0.0810178	−	0.140327i	−0.903687	+	0.428193i	$0.859150\pi$
$740$	−11494.8	+	19909.7i	−0.571026	+	0.989045i
$741$		0			0
$742$	48120.4	+	27313.0i	2.38080	+	1.35134i
$743$	8366.48			0.413104			0.206552	−	0.978436i	$-0.433776\pi$
$743$	8366.48			0.413104			0.206552	+	0.978436i	$0.433776\pi$
$744$		0			0
$745$	1967.78	+	3408.29i	0.0967701	+	0.167611i
$746$	12236.3	+	21193.8i	0.600538	+	1.04016i
$747$		0			0
$748$	186.701			0.00912630
$749$	15251.8	−	8955.67i	0.744046	−	0.436893i
$750$		0			0
$751$	5082.23	−	8802.69i	0.246942	−	0.427716i	−0.715734	−	0.698373i	$-0.753908\pi$
$751$	5082.23	−	8802.69i	0.246942	−	0.427716i	0.962676	+	0.270657i	$0.0872410\pi$
$752$	89.7737	+	155.493i	0.00435334	+	0.00754021i
$753$		0			0
$754$	2848.09	−	4933.03i	0.137561	−	0.238263i
$755$	4241.77			0.204469
$756$		0			0
$757$	9031.23			0.433614			0.216807	−	0.976214i	$-0.430436\pi$
$757$	9031.23			0.433614			0.216807	+	0.976214i	$0.430436\pi$
$758$	1399.84	−	2424.60i	0.0670773	−	0.116181i
$759$		0			0
$760$	1662.73	+	2879.93i	0.0793598	+	0.137455i
$761$	−16217.3	+	28089.3i	−0.772508	+	1.33802i	0.163677	+	0.986514i	$0.447665\pi$
$761$	−16217.3	+	28089.3i	−0.772508	+	1.33802i	−0.936185	+	0.351509i	$0.885669\pi$
$762$		0			0
$763$	−39.3053	−	5350.86i	−0.00186494	−	0.253885i
$764$	−11515.1			−0.545292
$765$		0			0
$766$	12781.2	+	22137.7i	0.602877	+	1.04421i
$767$	−12795.5	−	22162.4i	−0.602370	−	1.04334i
$768$		0			0
$769$	−22629.4			−1.06117			−0.530583	−	0.847633i	$-0.678027\pi$
$769$	−22629.4			−1.06117			−0.530583	+	0.847633i	$0.678027\pi$
$770$	50.1010	−	29.4186i	0.00234482	−	0.00137685i
$771$		0			0
$772$	−18708.2	+	32403.5i	−0.872178	+	1.51066i
$773$	1353.50	+	2344.34i	0.0629782	+	0.109081i	0.895795	−	0.444467i	$-0.146607\pi$
$773$	1353.50	+	2344.34i	0.0629782	+	0.109081i	−0.832817	+	0.553548i	$0.813273\pi$
$774$		0			0
$775$	−942.767	+	1632.92i	−0.0436970	+	0.0756855i
$776$	6047.86			0.279775
$777$		0			0
$778$	−6696.33			−0.308580
$779$	−2062.66	+	3572.64i	−0.0948685	+	0.164317i
$780$		0			0
$781$	2.63130	+	4.55755i	0.000120558	+	0.000208812i
$782$	38989.8	−	67532.2i	1.78296	−	3.08817i
$783$		0			0
$784$	8221.02	−	120.783i	0.374500	−	0.00550215i
$785$	−4774.61			−0.217087
$786$		0			0
$787$	12542.3	+	21723.9i	0.568088	+	0.983958i	0.996755	+	0.0804951i	$0.0256501\pi$
$787$	12542.3	+	21723.9i	0.568088	+	0.983958i	−0.428667	+	0.903463i	$0.641017\pi$
$788$	−239.442	−	414.726i	−0.0108246	−	0.0187488i
$789$		0			0
$790$	7004.44			0.315451
$791$	−20153.2	−	11438.9i	−0.905898	−	0.514186i
$792$		0			0
$793$	−12167.4	+	21074.6i	−0.544865	+	0.943734i
$794$	17380.8	+	30104.5i	0.776855	+	1.34555i
$795$		0			0
$796$	−13814.6	+	23927.5i	−0.615131	+	1.06544i
$797$	−7374.99			−0.327774			−0.163887	−	0.986479i	$-0.552403\pi$
$797$	−7374.99			−0.327774			−0.163887	+	0.986479i	$0.552403\pi$
$798$		0			0
$799$	856.651			0.0379301
$800$	2861.12	−	4955.60i	0.126445	−	0.219009i
$801$		0			0
$802$	−24523.8	−	42476.4i	−1.07976	−	1.87019i
$803$	−5.74777	+	9.95542i	−0.000252596	+	0.000437508i
$804$		0			0
$805$	−105.065	−	14303.1i	−0.00460006	−	0.626233i
$806$	−10701.0			−0.467649
$807$		0			0
$808$	3495.74	+	6054.80i	0.152203	+	0.263623i
$809$	1157.19	+	2004.30i	0.0502899	+	0.0871046i	0.890075	−	0.455815i	$-0.150652\pi$
$809$	1157.19	+	2004.30i	0.0502899	+	0.0871046i	−0.839785	+	0.542920i	$0.817319\pi$
$810$		0			0
$811$	38300.1			1.65832			0.829160	−	0.559011i	$-0.188819\pi$
$811$	38300.1			1.65832			0.829160	+	0.559011i	$0.188819\pi$
$812$	−62.7278	−	8539.49i	−0.00271098	−	0.369061i
$813$		0			0
$814$	125.588	−	217.525i	0.00540768	−	0.00936638i
$815$	−18.4105	−	31.8880i	−0.000791280	−	0.00137054i
$816$		0			0
$817$	7350.71	−	12731.8i	0.314772	−	0.545201i
$818$	−47276.8			−2.02078
$819$		0			0
$820$	−5480.00			−0.233378
$821$	1971.47	−	3414.68i	0.0838059	−	0.145156i	−0.821076	−	0.570819i	$-0.806626\pi$
$821$	1971.47	−	3414.68i	0.0838059	−	0.145156i	0.904882	+	0.425663i	$0.139959\pi$
$822$		0			0
$823$	−9251.41	−	16023.9i	−0.391839	−	0.678686i	0.600853	−	0.799360i	$-0.294828\pi$
$823$	−9251.41	−	16023.9i	−0.391839	−	0.678686i	−0.992692	+	0.120674i	$0.961494\pi$
$824$	5413.13	−	9375.81i	0.228853	−	0.396386i
$825$		0			0
$826$	−56606.8	−	32129.9i	−2.38451	−	1.35344i
$827$	11965.2			0.503110			0.251555	−	0.967843i	$-0.419058\pi$
$827$	11965.2			0.503110			0.251555	+	0.967843i	$0.419058\pi$
$828$		0			0
$829$	17981.5	+	31144.8i	0.753344	+	1.30483i	0.946193	+	0.323602i	$0.104894\pi$
$829$	17981.5	+	31144.8i	0.753344	+	1.30483i	−0.192849	+	0.981228i	$0.561773\pi$
$830$	10438.8	+	18080.6i	0.436551	+	0.756128i
$831$		0			0
$832$	26311.6			1.09638
$833$	19112.8	−	34257.0i	0.794983	−	1.42489i
$834$		0			0
$835$	−7303.50	+	12650.0i	−0.302692	+	0.524279i
$836$	−35.2862	−	61.1174i	−0.00145981	−	0.00252846i
$837$		0			0
$838$	19016.4	−	32937.3i	0.783902	−	1.35776i
$839$	20174.0			0.830137			0.415069	−	0.909790i	$-0.363758\pi$
$839$	20174.0			0.830137			0.415069	+	0.909790i	$0.363758\pi$
$840$		0			0
$841$	−22777.2			−0.933913
$842$	−14764.9	+	25573.6i	−0.604315	+	1.04670i
$843$		0			0
$844$	−6955.71	−	12047.6i	−0.283679	−	0.491347i
$845$	−2909.71	+	5039.76i	−0.118458	+	0.205175i
$846$		0			0
$847$	21256.5	−	12481.5i	0.862316	−	0.506340i
$848$	−16223.7			−0.656987
$849$		0			0
$850$	−6310.53	−	10930.2i	−0.254647	−	0.441061i
$851$	−30918.3	−	53552.1i	−1.24544	−	2.15716i
$852$		0			0
$853$	25297.5			1.01544			0.507719	−	0.861523i	$-0.330489\pi$
$853$	25297.5			1.01544			0.507719	+	0.861523i	$0.330489\pi$
$854$	454.643	+	61893.2i	0.0182173	+	2.48003i
$855$		0			0
$856$	7346.21	−	12724.0i	0.293327	−	0.508058i
$857$	19634.5	+	34008.0i	0.782617	+	1.35553i	0.930412	+	0.366514i	$0.119449\pi$
$857$	19634.5	+	34008.0i	0.782617	+	1.35553i	−0.147795	+	0.989018i	$0.547218\pi$
$858$		0			0
$859$	7249.55	−	12556.6i	0.287953	−	0.498749i	−0.685368	−	0.728197i	$-0.740359\pi$
$859$	7249.55	−	12556.6i	0.287953	−	0.498749i	0.973321	+	0.229448i	$0.0736921\pi$
$860$	19529.1			0.774343
$861$		0			0
$862$	−27238.5			−1.07627
$863$	−12205.6	+	21140.8i	−0.481442	+	0.833882i	−0.999773	−	0.0212980i	$-0.993220\pi$
$863$	−12205.6	+	21140.8i	−0.481442	+	0.833882i	0.518331	+	0.855180i	$0.326553\pi$
$864$		0			0
$865$	9923.92	+	17188.7i	0.390085	+	0.675647i
$866$	−30901.9	+	53523.6i	−1.21257	+	2.10024i
$867$		0			0
$868$	−13834.3	+	8123.29i	−0.540974	+	0.317653i
$869$	−45.1079			−0.00176085
$870$		0			0
$871$	−11901.9	−	20614.7i	−0.463010	−	0.801956i
$872$	−2222.54	−	3849.55i	−0.0863126	−	0.149498i
$873$		0			0
$874$	−29475.9			−1.14078
$875$	−2013.33	−	1142.76i	−0.0777861	−	0.0441512i
$876$		0			0
$877$	2528.32	−	4379.18i	0.0973494	−	0.168614i	−0.813237	−	0.581932i	$-0.802297\pi$
$877$	2528.32	−	4379.18i	0.0973494	−	0.168614i	0.910587	+	0.413318i	$0.135630\pi$
$878$	−26942.1	−	46665.1i	−1.03559	−	1.79370i
$879$		0			0
$880$	−8.51768	+	14.7530i	−0.000326285	+	0.000565142i
$881$	−13233.9			−0.506086			−0.253043	−	0.967455i	$-0.581431\pi$
$881$	−13233.9			−0.506086			−0.253043	+	0.967455i	$0.581431\pi$
$882$		0			0
$883$	−13824.2			−0.526866			−0.263433	−	0.964678i	$-0.584855\pi$
$883$	−13824.2			−0.526866			−0.263433	+	0.964678i	$0.584855\pi$
$884$	21110.0	−	36563.7i	0.803176	−	1.39114i
$885$		0			0
$886$	2709.81	+	4693.52i	0.102751	+	0.177971i
$887$	−18909.7	+	32752.5i	−0.715811	+	1.23982i	0.246835	+	0.969057i	$0.420609\pi$
$887$	−18909.7	+	32752.5i	−0.715811	+	1.23982i	−0.962646	+	0.270763i	$0.912724\pi$
$888$		0			0
$889$	−31369.6	−	17805.3i	−1.18347	−	0.671734i
$890$	17286.2			0.651049
$891$		0			0
$892$	−23918.0	−	41427.2i	−0.897796	−	1.55503i
$893$	−161.905	−	280.428i	−0.00606713	−	0.0105086i
$894$		0			0
$895$	−5529.76			−0.206524
$896$	28465.4	−	16714.5i	1.06134	−	0.623206i
$897$		0			0
$898$	−2541.92	+	4402.74i	−0.0944600	+	0.163609i
$899$	−1513.98	−	2622.29i	−0.0561668	−	0.0972838i
$900$		0			0
$901$	−38703.0	+	67035.6i	−1.43106	+	2.47867i
$902$	59.8721			0.00221012
$903$		0			0
$904$	−19250.0			−0.708237
$905$	−293.034	+	507.550i	−0.0107633	+	0.0186426i
$906$		0			0
$907$	−526.377	−	911.711i	−0.0192702	−	0.0333769i	0.856230	−	0.516596i	$-0.172801\pi$
$907$	−526.377	−	911.711i	−0.0192702	−	0.0333769i	−0.875500	+	0.483219i	$0.839468\pi$
$908$	13531.1	−	23436.5i	0.494542	−	0.856571i
$909$		0			0
$910$	−96.5076	−	13138.1i	−0.00351560	−	0.478598i
$911$	−7854.40			−0.285651			−0.142825	−	0.989748i	$-0.545619\pi$
$911$	−7854.40			−0.285651			−0.142825	+	0.989748i	$0.545619\pi$
$912$		0			0
$913$	−67.2251	−	116.437i	−0.00243683	−	0.00422071i
$914$	−41303.4	−	71539.6i	−1.49474	−	2.58897i
$915$		0			0
$916$	49905.4			1.80013
$917$	16955.1	−	9955.78i	0.610584	−	0.358527i
$918$		0			0
$919$	−2467.92	+	4274.57i	−0.0885846	+	0.153433i	−0.906913	−	0.421318i	$-0.861568\pi$
$919$	−2467.92	+	4274.57i	−0.0885846	+	0.153433i	0.818328	+	0.574751i	$0.194901\pi$
$920$	−5940.95	−	10290.0i	−0.212899	−	0.368752i
$921$		0			0
$922$	−6962.47	+	12059.4i	−0.248695	+	0.430752i
$923$	1190.07			0.0424395
$924$		0			0
$925$	−10008.3			−0.355753
$926$	−8941.22	+	15486.7i	−0.317308	+	0.549593i
$927$		0			0
$928$	4594.63	+	7958.14i	0.162528	+	0.281507i
$929$	−7852.51	+	13600.9i	−0.277322	+	0.480336i	−0.970718	−	0.240220i	$-0.922780\pi$
$929$	−7852.51	+	13600.9i	−0.277322	+	0.480336i	0.693396	+	0.720557i	$0.256114\pi$
$930$		0			0
$931$	−14826.4	+	217.830i	−0.521930	+	0.00766821i
$932$	−28233.7			−0.992302
$933$		0			0
$934$	36067.7	+	62471.0i	1.26356	+	2.18856i
$935$	40.6393	+	70.3892i	0.00142144	+	0.00246200i
$936$		0			0
$937$	−43806.5			−1.52732			−0.763658	−	0.645621i	$-0.776599\pi$
$937$	−43806.5			−1.52732			−0.763658	+	0.645621i	$0.776599\pi$
$938$	−52653.8	−	29886.2i	−1.83284	−	1.04032i
$939$		0			0
$940$	215.071	−	372.515i	0.00746261	−	0.0129256i
$941$	2031.21	+	3518.16i	0.0703672	+	0.121880i	0.899062	−	0.437821i	$-0.144250\pi$
$941$	2031.21	+	3518.16i	0.0703672	+	0.121880i	−0.828695	+	0.559700i	$0.810916\pi$
$942$		0			0
$943$	7369.92	−	12765.1i	0.254504	−	0.440815i
$944$	19084.9			0.658009
$945$		0			0
$946$	−213.366			−0.00733313
$947$	−2430.06	+	4208.99i	−0.0833859	+	0.144429i	−0.904702	−	0.426044i	$-0.859907\pi$
$947$	−2430.06	+	4208.99i	−0.0833859	+	0.144429i	0.821316	+	0.570473i	$0.193240\pi$
$948$		0			0
$949$	1299.78	+	2251.29i	0.0444602	+	0.0770073i
$950$	−2385.36	+	4131.56i	−0.0814644	+	0.141100i
$951$		0			0
$952$	−239.363	−	32585.9i	−0.00814895	−	1.10936i
$953$	18999.6			0.645811			0.322906	−	0.946431i	$-0.395340\pi$
$953$	18999.6			0.645811			0.322906	+	0.946431i	$0.395340\pi$
$954$		0			0
$955$	−2506.50	−	4341.38i	−0.0849303	−	0.147104i
$956$	1850.88	+	3205.82i	0.0626168	+	0.108456i
$957$		0			0
$958$	−11174.4			−0.376855
$959$	−195.807	−	26656.3i	−0.00659325	−	0.897577i
$960$		0			0
$961$	12051.3	−	20873.5i	0.404529	−	0.700664i
$962$	−28400.1	−	49190.4i	−0.951825	−	1.64861i
$963$		0			0
$964$	28777.7	−	49844.5i	0.961482	−	1.66534i
$965$	−16288.8			−0.543373
$966$		0			0
$967$	−32695.1			−1.08728			−0.543641	−	0.839318i	$-0.682955\pi$
$967$	−32695.1			−1.08728			−0.543641	+	0.839318i	$0.682955\pi$
$968$	10238.4	−	17733.5i	0.339954	−	0.588817i
$969$		0			0
$970$	4338.14	+	7513.88i	0.143597	+	0.248718i
$971$	−3094.85	+	5360.43i	−0.102285	+	0.177162i	−0.912626	−	0.408797i	$-0.865949\pi$
$971$	−3094.85	+	5360.43i	−0.102285	+	0.177162i	0.810341	+	0.585959i	$0.199282\pi$
$972$		0			0
$973$	10664.7	+	6053.26i	0.351382	+	0.199443i
$974$	−37265.6			−1.22594
$975$		0			0
$976$	−9074.08	−	15716.8i	−0.297596	−	0.515452i
$977$	1071.22	+	1855.41i	0.0350782	+	0.0607572i	0.883032	−	0.469314i	$-0.155499\pi$
$977$	1071.22	+	1855.41i	0.0350782	+	0.0607572i	−0.847953	+	0.530071i	$0.822165\pi$
$978$		0			0
$979$	−111.321			−0.00363416
$980$	−10098.2	−	16911.8i	−0.329157	−	0.551253i
$981$		0			0
$982$	−33600.8	+	58198.4i	−1.09190	+	1.89123i
$983$	8404.11	+	14556.4i	0.272685	+	0.472305i	0.969549	−	0.244899i	$-0.0787549\pi$
$983$	8404.11	+	14556.4i	0.272685	+	0.472305i	−0.696863	+	0.717204i	$0.745422\pi$
$984$		0			0
$985$	104.239	−	180.547i	0.00337190	−	0.00584031i
$986$	20268.0			0.654630
$987$		0			0
$988$	−15959.0			−0.513891
$989$	−26264.2	+	45490.9i	−0.844442	+	1.46262i
$990$		0			0
$991$	−10625.4	−	18403.7i	−0.340593	−	0.589924i	0.643950	−	0.765067i	$-0.277294\pi$
$991$	−10625.4	−	18403.7i	−0.340593	−	0.589924i	−0.984543	+	0.175144i	$0.943961\pi$
$992$	8631.57	−	14950.3i	0.276263	−	0.478501i
$993$		0			0
$994$	2610.19	−	1532.67i	0.0832898	−	0.0489066i
$995$	−12028.1			−0.383231
$996$		0			0
$997$	18820.0	+	32597.1i	0.597828	+	1.03547i	0.993141	+	0.116922i	$0.0373028\pi$
$997$	18820.0	+	32597.1i	0.597828	+	1.03547i	−0.395313	+	0.918546i	$0.629364\pi$
$998$	36688.0	+	63545.4i	1.16366	+	2.01553i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.4.j.c.226.1		4
3.2	odd	2		35.4.e.b.16.2	yes	4
7.2	even	3		2205.4.a.bf.1.2		2
7.4	even	3	inner	315.4.j.c.46.1		4
7.5	odd	6		2205.4.a.bg.1.2		2
12.11	even	2		560.4.q.i.401.2		4
15.2	even	4		175.4.k.c.149.4		8
15.8	even	4		175.4.k.c.149.1		8
15.14	odd	2		175.4.e.c.51.1		4
21.2	odd	6		245.4.a.g.1.1		2
21.5	even	6		245.4.a.h.1.1		2
21.11	odd	6		35.4.e.b.11.2	✓	4
21.17	even	6		245.4.e.l.116.2		4
21.20	even	2		245.4.e.l.226.2		4
84.11	even	6		560.4.q.i.81.2		4
105.32	even	12		175.4.k.c.74.1		8
105.44	odd	6		1225.4.a.x.1.2		2
105.53	even	12		175.4.k.c.74.4		8
105.74	odd	6		175.4.e.c.151.1		4
105.89	even	6		1225.4.a.v.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.b.11.2	✓	4	21.11	odd	6
35.4.e.b.16.2	yes	4	3.2	odd	2
175.4.e.c.51.1		4	15.14	odd	2
175.4.e.c.151.1		4	105.74	odd	6
175.4.k.c.74.1		8	105.32	even	12
175.4.k.c.74.4		8	105.53	even	12
175.4.k.c.149.1		8	15.8	even	4
175.4.k.c.149.4		8	15.2	even	4
245.4.a.g.1.1		2	21.2	odd	6
245.4.a.h.1.1		2	21.5	even	6
245.4.e.l.116.2		4	21.17	even	6
245.4.e.l.226.2		4	21.20	even	2
315.4.j.c.46.1		4	7.4	even	3	inner
315.4.j.c.226.1		4	1.1	even	1	trivial
560.4.q.i.81.2		4	84.11	even	6
560.4.q.i.401.2		4	12.11	even	2
1225.4.a.v.1.2		2	105.89	even	6
1225.4.a.x.1.2		2	105.44	odd	6
2205.4.a.bf.1.2		2	7.2	even	3
2205.4.a.bg.1.2		2	7.5	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-2.20711 + 3.82282i) q^{2} +(-5.74264 - 9.94655i) q^{4} +(2.50000 - 4.33013i) q^{5} +(16.1066 + 9.14207i) q^{7} +15.3848 q^{8} +(11.0355 + 19.1141i) q^{10} +(-0.0710678 - 0.123093i) q^{11} -32.1421 q^{13} +(-70.4975 + 41.3951i) q^{14} +(11.9853 - 20.7591i) q^{16} +(-57.1838 - 99.0452i) q^{17} +(-21.6152 + 37.4387i) q^{19} -57.4264 q^{20} +0.627417 q^{22} +(77.2315 - 133.769i) q^{23} +(-12.5000 - 21.6506i) q^{25} +(70.9411 - 122.874i) q^{26} +(-1.56245 - 212.705i) q^{28} +40.1472 q^{29} +(-37.7107 - 65.3168i) q^{31} +(114.445 + 198.224i) q^{32} +504.843 q^{34} +(79.8528 - 46.8885i) q^{35} +(200.167 - 346.699i) q^{37} +(-95.4142 - 165.262i) q^{38} +(38.4619 - 66.6180i) q^{40} +95.4264 q^{41} -340.071 q^{43} +(-0.816234 + 1.41376i) q^{44} +(340.916 + 590.484i) q^{46} +(-3.74517 + 6.48682i) q^{47} +(175.845 + 294.495i) q^{49} +110.355 q^{50} +(184.581 + 319.703i) q^{52} +(-338.409 - 586.142i) q^{53} -0.710678 q^{55} +(247.796 + 140.649i) q^{56} +(-88.6091 + 153.476i) q^{58} +(398.090 + 689.513i) q^{59} +(378.551 - 655.669i) q^{61} +332.926 q^{62} -818.602 q^{64} +(-80.3553 + 139.180i) q^{65} +(370.290 + 641.362i) q^{67} +(-656.772 + 1137.56i) q^{68} +(3.00253 + 408.751i) q^{70} -37.0253 q^{71} +(-40.4386 - 70.0417i) q^{73} +(883.578 + 1530.40i) q^{74} +496.514 q^{76} +(-0.0193360 - 2.63232i) q^{77} +(158.679 - 274.840i) q^{79} +(-59.9264 - 103.796i) q^{80} +(-210.616 + 364.798i) q^{82} +945.929 q^{83} -571.838 q^{85} +(750.573 - 1300.03i) q^{86} +(-1.09336 - 1.89376i) q^{88} +(391.603 - 678.276i) q^{89} +(-517.701 - 293.846i) q^{91} -1774.05 q^{92} +(-16.5320 - 28.6342i) q^{94} +(108.076 + 187.193i) q^{95} +393.107 q^{97} +(-1513.91 + 22.2424i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} - 6 q^{4} + 10 q^{5} + 22 q^{7} - 12 q^{8} + 30 q^{10} + 28 q^{11} - 72 q^{13} - 84 q^{14} + 14 q^{16} - 76 q^{17} - 160 q^{19} - 60 q^{20} - 88 q^{22} - 22 q^{23} - 50 q^{25} + 148 q^{26}+ \cdots - 3066 q^{98}+O(q^{100}) \) 4 * q - 6 * q^2 - 6 * q^4 + 10 * q^5 + 22 * q^7 - 12 * q^8 + 30 * q^10 + 28 * q^11 - 72 * q^13 - 84 * q^14 + 14 * q^16 - 76 * q^17 - 160 * q^19 - 60 * q^20 - 88 * q^22 - 22 * q^23 - 50 * q^25 + 148 * q^26 + 138 * q^28 + 500 * q^29 + 132 * q^31 + 42 * q^32 + 888 * q^34 - 20 * q^35 + 416 * q^37 - 376 * q^38 - 30 * q^40 + 212 * q^41 - 1332 * q^43 - 156 * q^44 + 402 * q^46 - 196 * q^47 - 230 * q^49 + 300 * q^50 + 348 * q^52 - 952 * q^53 + 280 * q^55 + 714 * q^56 - 510 * q^58 + 840 * q^59 - 98 * q^61 + 8 * q^62 - 1204 * q^64 - 180 * q^65 + 1286 * q^67 - 1524 * q^68 + 210 * q^70 - 2128 * q^71 + 172 * q^73 + 1792 * q^74 - 288 * q^76 + 724 * q^77 + 1240 * q^79 - 70 * q^80 - 438 * q^82 + 3812 * q^83 - 760 * q^85 + 2018 * q^86 - 604 * q^88 + 650 * q^89 - 996 * q^91 - 5484 * q^92 - 332 * q^94 + 800 * q^95 - 1256 * q^97 - 3066 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more