# Properties

 Label 1638.2.bj.f.127.2 Level $1638$ Weight $2$ Character 1638.127 Analytic conductor $13.079$ Analytic rank $0$ Dimension $8$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1638.bj (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

comment: select newform

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

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

 Self dual: no Analytic conductor: $$13.0794958511$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: 8.0.195105024.2 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81$$ x^8 - 4*x^7 + 5*x^6 + 4*x^5 - 20*x^4 + 12*x^3 + 45*x^2 - 108*x + 81 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 546) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 127.2 Root $$-1.58726 + 0.693255i$$ of defining polynomial Character $$\chi$$ $$=$$ 1638.127 Dual form 1638.2.bj.f.1135.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.78801i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.78801i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.894007 - 1.54846i) q^{10} +(-2.74922 + 1.58726i) q^{11} +(1.47952 + 3.28801i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.78052 + 4.81599i) q^{17} +(-5.36028 - 3.09476i) q^{19} +(1.54846 + 0.894007i) q^{20} +(1.58726 - 2.74922i) q^{22} +(-3.06678 - 5.31181i) q^{23} +1.80301 q^{25} +(-2.92531 - 2.10774i) q^{26} +(0.866025 - 0.500000i) q^{28} +(1.03880 + 1.79925i) q^{29} -5.63862i q^{31} +(0.866025 + 0.500000i) q^{32} -5.56103i q^{34} +(-0.894007 + 1.54846i) q^{35} +(-2.68202 + 1.54846i) q^{37} +6.18952 q^{38} -1.78801 q^{40} +(1.29768 - 0.749217i) q^{41} +(-4.81931 + 8.34729i) q^{43} +3.17452i q^{44} +(5.31181 + 3.06678i) q^{46} -10.5086i q^{47} +(0.500000 + 0.866025i) q^{49} +(-1.56145 + 0.901504i) q^{50} +(3.58726 + 0.362708i) q^{52} -3.60200 q^{53} +(-2.83804 - 4.91564i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-1.79925 - 1.03880i) q^{58} +(2.40874 + 1.39069i) q^{59} +(-0.844395 + 1.46254i) q^{61} +(2.81931 + 4.88319i) q^{62} -1.00000 q^{64} +(-5.87901 + 2.64539i) q^{65} +(-10.0064 + 5.77720i) q^{67} +(2.78052 + 4.81599i) q^{68} -1.78801i q^{70} +(0.518313 + 0.299248i) q^{71} -0.423973i q^{73} +(1.54846 - 2.68202i) q^{74} +(-5.36028 + 3.09476i) q^{76} -3.17452 q^{77} +6.96254 q^{79} +(1.54846 - 0.894007i) q^{80} +(-0.749217 + 1.29768i) q^{82} -4.30228i q^{83} +(-8.61106 - 4.97160i) q^{85} -9.63862i q^{86} +(-1.58726 - 2.74922i) q^{88} +(14.1102 - 8.14654i) q^{89} +(-0.362708 + 3.58726i) q^{91} -6.13356 q^{92} +(5.25429 + 9.10069i) q^{94} +(5.53347 - 9.58425i) q^{95} +(-15.1461 - 8.74462i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 4 q^{4}+O(q^{10})$$ 8 * q + 4 * q^4 $$8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97}+O(q^{100})$$ 8 * q + 4 * q^4 + 6 * q^10 - 6 * q^11 + 12 * q^13 - 8 * q^14 - 4 * q^16 - 2 * q^17 - 12 * q^19 + 6 * q^20 - 4 * q^22 - 8 * q^23 - 24 * q^25 - 6 * q^26 - 2 * q^29 + 6 * q^35 + 18 * q^37 + 4 * q^38 + 12 * q^40 - 12 * q^41 - 8 * q^43 + 18 * q^46 + 4 * q^49 - 12 * q^50 + 12 * q^52 + 12 * q^53 - 22 * q^55 - 4 * q^56 - 24 * q^58 - 18 * q^59 - 8 * q^61 - 8 * q^62 - 8 * q^64 - 46 * q^65 + 18 * q^67 + 2 * q^68 - 6 * q^71 + 6 * q^74 - 12 * q^76 + 8 * q^77 - 4 * q^79 + 6 * q^80 + 10 * q^82 - 54 * q^85 + 4 * q^88 + 18 * q^89 + 6 * q^91 - 16 * q^92 - 2 * q^94 + 50 * q^95 - 54 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$$.

 $$n$$ $$379$$ $$703$$ $$911$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 + 0.500000i −0.612372 + 0.353553i
$$3$$ 0 0
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 1.78801i 0.799624i 0.916597 + 0.399812i $$0.130925\pi$$
−0.916597 + 0.399812i $$0.869075\pi$$
$$6$$ 0 0
$$7$$ 0.866025 + 0.500000i 0.327327 + 0.188982i
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ −0.894007 1.54846i −0.282710 0.489668i
$$11$$ −2.74922 + 1.58726i −0.828920 + 0.478577i −0.853483 0.521121i $$-0.825514\pi$$
0.0245627 + 0.999698i $$0.492181\pi$$
$$12$$ 0 0
$$13$$ 1.47952 + 3.28801i 0.410344 + 0.911931i
$$14$$ −1.00000 −0.267261
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −2.78052 + 4.81599i −0.674374 + 1.16805i 0.302277 + 0.953220i $$0.402253\pi$$
−0.976651 + 0.214830i $$0.931080\pi$$
$$18$$ 0 0
$$19$$ −5.36028 3.09476i −1.22973 0.709986i −0.262758 0.964862i $$-0.584632\pi$$
−0.966974 + 0.254875i $$0.917966\pi$$
$$20$$ 1.54846 + 0.894007i 0.346247 + 0.199906i
$$21$$ 0 0
$$22$$ 1.58726 2.74922i 0.338405 0.586135i
$$23$$ −3.06678 5.31181i −0.639467 1.10759i −0.985550 0.169386i $$-0.945822\pi$$
0.346083 0.938204i $$-0.387512\pi$$
$$24$$ 0 0
$$25$$ 1.80301 0.360602
$$26$$ −2.92531 2.10774i −0.573700 0.413363i
$$27$$ 0 0
$$28$$ 0.866025 0.500000i 0.163663 0.0944911i
$$29$$ 1.03880 + 1.79925i 0.192900 + 0.334112i 0.946210 0.323553i $$-0.104877\pi$$
−0.753310 + 0.657665i $$0.771544\pi$$
$$30$$ 0 0
$$31$$ 5.63862i 1.01273i −0.862320 0.506363i $$-0.830989\pi$$
0.862320 0.506363i $$-0.169011\pi$$
$$32$$ 0.866025 + 0.500000i 0.153093 + 0.0883883i
$$33$$ 0 0
$$34$$ 5.56103i 0.953709i
$$35$$ −0.894007 + 1.54846i −0.151115 + 0.261738i
$$36$$ 0 0
$$37$$ −2.68202 + 1.54846i −0.440921 + 0.254566i −0.703988 0.710211i $$-0.748599\pi$$
0.263067 + 0.964778i $$0.415266\pi$$
$$38$$ 6.18952 1.00407
$$39$$ 0 0
$$40$$ −1.78801 −0.282710
$$41$$ 1.29768 0.749217i 0.202664 0.117008i −0.395234 0.918581i $$-0.629336\pi$$
0.597897 + 0.801573i $$0.296003\pi$$
$$42$$ 0 0
$$43$$ −4.81931 + 8.34729i −0.734938 + 1.27295i 0.219812 + 0.975542i $$0.429456\pi$$
−0.954750 + 0.297408i $$0.903878\pi$$
$$44$$ 3.17452i 0.478577i
$$45$$ 0 0
$$46$$ 5.31181 + 3.06678i 0.783184 + 0.452172i
$$47$$ 10.5086i 1.53283i −0.642344 0.766416i $$-0.722038\pi$$
0.642344 0.766416i $$-0.277962\pi$$
$$48$$ 0 0
$$49$$ 0.500000 + 0.866025i 0.0714286 + 0.123718i
$$50$$ −1.56145 + 0.901504i −0.220823 + 0.127492i
$$51$$ 0 0
$$52$$ 3.58726 + 0.362708i 0.497464 + 0.0502985i
$$53$$ −3.60200 −0.494773 −0.247386 0.968917i $$-0.579572\pi$$
−0.247386 + 0.968917i $$0.579572\pi$$
$$54$$ 0 0
$$55$$ −2.83804 4.91564i −0.382682 0.662824i
$$56$$ −0.500000 + 0.866025i −0.0668153 + 0.115728i
$$57$$ 0 0
$$58$$ −1.79925 1.03880i −0.236253 0.136401i
$$59$$ 2.40874 + 1.39069i 0.313592 + 0.181052i 0.648533 0.761187i $$-0.275383\pi$$
−0.334941 + 0.942239i $$0.608716\pi$$
$$60$$ 0 0
$$61$$ −0.844395 + 1.46254i −0.108114 + 0.187259i −0.915006 0.403440i $$-0.867814\pi$$
0.806892 + 0.590699i $$0.201148\pi$$
$$62$$ 2.81931 + 4.88319i 0.358053 + 0.620166i
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ −5.87901 + 2.64539i −0.729202 + 0.328121i
$$66$$ 0 0
$$67$$ −10.0064 + 5.77720i −1.22248 + 0.705797i −0.965445 0.260606i $$-0.916078\pi$$
−0.257031 + 0.966403i $$0.582744\pi$$
$$68$$ 2.78052 + 4.81599i 0.337187 + 0.584025i
$$69$$ 0 0
$$70$$ 1.78801i 0.213708i
$$71$$ 0.518313 + 0.299248i 0.0615124 + 0.0355142i 0.530441 0.847722i $$-0.322026\pi$$
−0.468928 + 0.883236i $$0.655360\pi$$
$$72$$ 0 0
$$73$$ 0.423973i 0.0496223i −0.999692 0.0248112i $$-0.992102\pi$$
0.999692 0.0248112i $$-0.00789845\pi$$
$$74$$ 1.54846 2.68202i 0.180005 0.311778i
$$75$$ 0 0
$$76$$ −5.36028 + 3.09476i −0.614866 + 0.354993i
$$77$$ −3.17452 −0.361770
$$78$$ 0 0
$$79$$ 6.96254 0.783346 0.391673 0.920104i $$-0.371896\pi$$
0.391673 + 0.920104i $$0.371896\pi$$
$$80$$ 1.54846 0.894007i 0.173124 0.0999530i
$$81$$ 0 0
$$82$$ −0.749217 + 1.29768i −0.0827372 + 0.143305i
$$83$$ 4.30228i 0.472237i −0.971724 0.236118i $$-0.924125\pi$$
0.971724 0.236118i $$-0.0758753\pi$$
$$84$$ 0 0
$$85$$ −8.61106 4.97160i −0.934001 0.539246i
$$86$$ 9.63862i 1.03936i
$$87$$ 0 0
$$88$$ −1.58726 2.74922i −0.169203 0.293068i
$$89$$ 14.1102 8.14654i 1.49568 0.863532i 0.495693 0.868498i $$-0.334914\pi$$
0.999988 + 0.00496618i $$0.00158079\pi$$
$$90$$ 0 0
$$91$$ −0.362708 + 3.58726i −0.0380221 + 0.376047i
$$92$$ −6.13356 −0.639467
$$93$$ 0 0
$$94$$ 5.25429 + 9.10069i 0.541938 + 0.938665i
$$95$$ 5.53347 9.58425i 0.567722 0.983323i
$$96$$ 0 0
$$97$$ −15.1461 8.74462i −1.53786 0.887881i −0.998964 0.0455062i $$-0.985510\pi$$
−0.538892 0.842375i $$-0.681157\pi$$
$$98$$ −0.866025 0.500000i −0.0874818 0.0505076i
$$99$$ 0 0
$$100$$ 0.901504 1.56145i 0.0901504 0.156145i
$$101$$ 2.03433 + 3.52357i 0.202424 + 0.350608i 0.949309 0.314345i $$-0.101785\pi$$
−0.746885 + 0.664953i $$0.768452\pi$$
$$102$$ 0 0
$$103$$ −18.0768 −1.78116 −0.890578 0.454831i $$-0.849700\pi$$
−0.890578 + 0.454831i $$0.849700\pi$$
$$104$$ −3.28801 + 1.47952i −0.322416 + 0.145079i
$$105$$ 0 0
$$106$$ 3.11942 1.80100i 0.302985 0.174929i
$$107$$ −0.770847 1.33515i −0.0745206 0.129073i 0.826357 0.563146i $$-0.190409\pi$$
−0.900878 + 0.434073i $$0.857076\pi$$
$$108$$ 0 0
$$109$$ 7.37731i 0.706618i −0.935507 0.353309i $$-0.885056\pi$$
0.935507 0.353309i $$-0.114944\pi$$
$$110$$ 4.91564 + 2.83804i 0.468688 + 0.270597i
$$111$$ 0 0
$$112$$ 1.00000i 0.0944911i
$$113$$ −4.95660 + 8.58509i −0.466278 + 0.807617i −0.999258 0.0385104i $$-0.987739\pi$$
0.532980 + 0.846128i $$0.321072\pi$$
$$114$$ 0 0
$$115$$ 9.49759 5.48344i 0.885655 0.511333i
$$116$$ 2.07759 0.192900
$$117$$ 0 0
$$118$$ −2.78138 −0.256047
$$119$$ −4.81599 + 2.78052i −0.441481 + 0.254889i
$$120$$ 0 0
$$121$$ −0.461204 + 0.798828i −0.0419276 + 0.0726208i
$$122$$ 1.68879i 0.152896i
$$123$$ 0 0
$$124$$ −4.88319 2.81931i −0.438524 0.253182i
$$125$$ 12.1639i 1.08797i
$$126$$ 0 0
$$127$$ 9.17452 + 15.8907i 0.814107 + 1.41008i 0.909967 + 0.414680i $$0.136107\pi$$
−0.0958600 + 0.995395i $$0.530560\pi$$
$$128$$ 0.866025 0.500000i 0.0765466 0.0441942i
$$129$$ 0 0
$$130$$ 3.76868 5.23048i 0.330535 0.458744i
$$131$$ −5.91928 −0.517170 −0.258585 0.965989i $$-0.583256\pi$$
−0.258585 + 0.965989i $$0.583256\pi$$
$$132$$ 0 0
$$133$$ −3.09476 5.36028i −0.268350 0.464795i
$$134$$ 5.77720 10.0064i 0.499074 0.864421i
$$135$$ 0 0
$$136$$ −4.81599 2.78052i −0.412968 0.238427i
$$137$$ −7.62363 4.40150i −0.651331 0.376046i 0.137635 0.990483i $$-0.456050\pi$$
−0.788966 + 0.614437i $$0.789383\pi$$
$$138$$ 0 0
$$139$$ −9.48720 + 16.4323i −0.804694 + 1.39377i 0.111804 + 0.993730i $$0.464337\pi$$
−0.916498 + 0.400040i $$0.868996\pi$$
$$140$$ 0.894007 + 1.54846i 0.0755574 + 0.130869i
$$141$$ 0 0
$$142$$ −0.598496 −0.0502247
$$143$$ −9.28645 6.69108i −0.776572 0.559537i
$$144$$ 0 0
$$145$$ −3.21708 + 1.85738i −0.267164 + 0.154247i
$$146$$ 0.211987 + 0.367172i 0.0175441 + 0.0303873i
$$147$$ 0 0
$$148$$ 3.09693i 0.254566i
$$149$$ −12.0919 6.98127i −0.990608 0.571928i −0.0851520 0.996368i $$-0.527138\pi$$
−0.905456 + 0.424440i $$0.860471\pi$$
$$150$$ 0 0
$$151$$ 17.8426i 1.45201i −0.687688 0.726006i $$-0.741374\pi$$
0.687688 0.726006i $$-0.258626\pi$$
$$152$$ 3.09476 5.36028i 0.251018 0.434776i
$$153$$ 0 0
$$154$$ 2.74922 1.58726i 0.221538 0.127905i
$$155$$ 10.0819 0.809800
$$156$$ 0 0
$$157$$ 4.57916 0.365457 0.182728 0.983163i $$-0.441507\pi$$
0.182728 + 0.983163i $$0.441507\pi$$
$$158$$ −6.02973 + 3.48127i −0.479700 + 0.276955i
$$159$$ 0 0
$$160$$ −0.894007 + 1.54846i −0.0706774 + 0.122417i
$$161$$ 6.13356i 0.483392i
$$162$$ 0 0
$$163$$ 10.6267 + 6.13531i 0.832344 + 0.480554i 0.854655 0.519197i $$-0.173769\pi$$
−0.0223103 + 0.999751i $$0.507102\pi$$
$$164$$ 1.49843i 0.117008i
$$165$$ 0 0
$$166$$ 2.15114 + 3.72589i 0.166961 + 0.289185i
$$167$$ −14.4610 + 8.34904i −1.11902 + 0.646068i −0.941151 0.337985i $$-0.890255\pi$$
−0.177872 + 0.984054i $$0.556921\pi$$
$$168$$ 0 0
$$169$$ −8.62206 + 9.72934i −0.663236 + 0.748411i
$$170$$ 9.94320 0.762609
$$171$$ 0 0
$$172$$ 4.81931 + 8.34729i 0.367469 + 0.636475i
$$173$$ −3.68865 + 6.38894i −0.280443 + 0.485742i −0.971494 0.237064i $$-0.923815\pi$$
0.691051 + 0.722806i $$0.257148\pi$$
$$174$$ 0 0
$$175$$ 1.56145 + 0.901504i 0.118035 + 0.0681473i
$$176$$ 2.74922 + 1.58726i 0.207230 + 0.119644i
$$177$$ 0 0
$$178$$ −8.14654 + 14.1102i −0.610609 + 1.05761i
$$179$$ −9.91008 17.1648i −0.740714 1.28295i −0.952171 0.305567i $$-0.901154\pi$$
0.211457 0.977387i $$-0.432179\pi$$
$$180$$ 0 0
$$181$$ −18.3266 −1.36220 −0.681102 0.732189i $$-0.738499\pi$$
−0.681102 + 0.732189i $$0.738499\pi$$
$$182$$ −1.47952 3.28801i −0.109669 0.243724i
$$183$$ 0 0
$$184$$ 5.31181 3.06678i 0.391592 0.226086i
$$185$$ −2.76868 4.79549i −0.203557 0.352571i
$$186$$ 0 0
$$187$$ 17.6536i 1.29096i
$$188$$ −9.10069 5.25429i −0.663736 0.383208i
$$189$$ 0 0
$$190$$ 11.0669i 0.802880i
$$191$$ −7.51518 + 13.0167i −0.543779 + 0.941854i 0.454903 + 0.890541i $$0.349674\pi$$
−0.998683 + 0.0513127i $$0.983659\pi$$
$$192$$ 0 0
$$193$$ −4.72408 + 2.72745i −0.340047 + 0.196326i −0.660293 0.751008i $$-0.729568\pi$$
0.320246 + 0.947334i $$0.396234\pi$$
$$194$$ 17.4892 1.25565
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ 6.60751 3.81485i 0.470766 0.271797i −0.245795 0.969322i $$-0.579049\pi$$
0.716560 + 0.697525i $$0.245716\pi$$
$$198$$ 0 0
$$199$$ 2.99512 5.18769i 0.212318 0.367746i −0.740121 0.672473i $$-0.765232\pi$$
0.952440 + 0.304727i $$0.0985653\pi$$
$$200$$ 1.80301i 0.127492i
$$201$$ 0 0
$$202$$ −3.52357 2.03433i −0.247917 0.143135i
$$203$$ 2.07759i 0.145818i
$$204$$ 0 0
$$205$$ 1.33961 + 2.32027i 0.0935624 + 0.162055i
$$206$$ 15.6549 9.03838i 1.09073 0.629734i
$$207$$ 0 0
$$208$$ 2.10774 2.92531i 0.146146 0.202833i
$$209$$ 19.6488 1.35913
$$210$$ 0 0
$$211$$ 1.38651 + 2.40150i 0.0954512 + 0.165326i 0.909797 0.415054i $$-0.136237\pi$$
−0.814346 + 0.580380i $$0.802904\pi$$
$$212$$ −1.80100 + 3.11942i −0.123693 + 0.214243i
$$213$$ 0 0
$$214$$ 1.33515 + 0.770847i 0.0912687 + 0.0526940i
$$215$$ −14.9251 8.61699i −1.01788 0.587674i
$$216$$ 0 0
$$217$$ 2.81931 4.88319i 0.191387 0.331493i
$$218$$ 3.68865 + 6.38894i 0.249827 + 0.432713i
$$219$$ 0 0
$$220$$ −5.67609 −0.382682
$$221$$ −19.9489 2.01703i −1.34191 0.135680i
$$222$$ 0 0
$$223$$ 19.5163 11.2677i 1.30691 0.754542i 0.325327 0.945602i $$-0.394526\pi$$
0.981578 + 0.191060i $$0.0611924\pi$$
$$224$$ 0.500000 + 0.866025i 0.0334077 + 0.0578638i
$$225$$ 0 0
$$226$$ 9.91321i 0.659417i
$$227$$ 1.58616 + 0.915773i 0.105277 + 0.0607820i 0.551714 0.834033i $$-0.313974\pi$$
−0.446437 + 0.894815i $$0.647307\pi$$
$$228$$ 0 0
$$229$$ 22.6060i 1.49385i −0.664910 0.746924i $$-0.731530\pi$$
0.664910 0.746924i $$-0.268470\pi$$
$$230$$ −5.48344 + 9.49759i −0.361567 + 0.626253i
$$231$$ 0 0
$$232$$ −1.79925 + 1.03880i −0.118126 + 0.0682003i
$$233$$ 9.43897 0.618367 0.309184 0.951002i $$-0.399944\pi$$
0.309184 + 0.951002i $$0.399944\pi$$
$$234$$ 0 0
$$235$$ 18.7895 1.22569
$$236$$ 2.40874 1.39069i 0.156796 0.0905262i
$$237$$ 0 0
$$238$$ 2.78052 4.81599i 0.180234 0.312175i
$$239$$ 15.8757i 1.02692i 0.858115 + 0.513458i $$0.171636\pi$$
−0.858115 + 0.513458i $$0.828364\pi$$
$$240$$ 0 0
$$241$$ 20.7197 + 11.9625i 1.33467 + 0.770575i 0.986012 0.166674i $$-0.0533027\pi$$
0.348662 + 0.937248i $$0.386636\pi$$
$$242$$ 0.922407i 0.0592946i
$$243$$ 0 0
$$244$$ 0.844395 + 1.46254i 0.0540569 + 0.0936293i
$$245$$ −1.54846 + 0.894007i −0.0989278 + 0.0571160i
$$246$$ 0 0
$$247$$ 2.24499 22.2034i 0.142845 1.41277i
$$248$$ 5.63862 0.358053
$$249$$ 0 0
$$250$$ −6.08193 10.5342i −0.384655 0.666243i
$$251$$ 10.2618 17.7739i 0.647718 1.12188i −0.335949 0.941880i $$-0.609057\pi$$
0.983667 0.180000i $$-0.0576098\pi$$
$$252$$ 0 0
$$253$$ 16.8625 + 9.73555i 1.06013 + 0.612069i
$$254$$ −15.8907 9.17452i −0.997074 0.575661i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 0.413344 + 0.715933i 0.0257837 + 0.0446587i 0.878629 0.477504i $$-0.158459\pi$$
−0.852846 + 0.522163i $$0.825125\pi$$
$$258$$ 0 0
$$259$$ −3.09693 −0.192434
$$260$$ −0.648527 + 6.41407i −0.0402199 + 0.397784i
$$261$$ 0 0
$$262$$ 5.12624 2.95964i 0.316700 0.182847i
$$263$$ 10.1805 + 17.6331i 0.627754 + 1.08730i 0.988001 + 0.154445i $$0.0493588\pi$$
−0.360248 + 0.932857i $$0.617308\pi$$
$$264$$ 0 0
$$265$$ 6.44042i 0.395632i
$$266$$ 5.36028 + 3.09476i 0.328660 + 0.189752i
$$267$$ 0 0
$$268$$ 11.5544i 0.705797i
$$269$$ −10.2587 + 17.7687i −0.625487 + 1.08338i 0.362959 + 0.931805i $$0.381766\pi$$
−0.988446 + 0.151570i $$0.951567\pi$$
$$270$$ 0 0
$$271$$ −10.5495 + 6.09076i −0.640837 + 0.369988i −0.784937 0.619576i $$-0.787305\pi$$
0.144100 + 0.989563i $$0.453971\pi$$
$$272$$ 5.56103 0.337187
$$273$$ 0 0
$$274$$ 8.80301 0.531809
$$275$$ −4.95686 + 2.86185i −0.298910 + 0.172576i
$$276$$ 0 0
$$277$$ 4.31242 7.46933i 0.259108 0.448789i −0.706895 0.707318i $$-0.749905\pi$$
0.966003 + 0.258530i $$0.0832380\pi$$
$$278$$ 18.9744i 1.13801i
$$279$$ 0 0
$$280$$ −1.54846 0.894007i −0.0925385 0.0534271i
$$281$$ 24.2922i 1.44915i 0.689194 + 0.724577i $$0.257965\pi$$
−0.689194 + 0.724577i $$0.742035\pi$$
$$282$$ 0 0
$$283$$ 5.36054 + 9.28472i 0.318651 + 0.551919i 0.980207 0.197976i $$-0.0634369\pi$$
−0.661556 + 0.749896i $$0.730104\pi$$
$$284$$ 0.518313 0.299248i 0.0307562 0.0177571i
$$285$$ 0 0
$$286$$ 11.3878 + 1.15142i 0.673377 + 0.0680852i
$$287$$ 1.49843 0.0884498
$$288$$ 0 0
$$289$$ −6.96254 12.0595i −0.409561 0.709380i
$$290$$ 1.85738 3.21708i 0.109069 0.188913i
$$291$$ 0 0
$$292$$ −0.367172 0.211987i −0.0214871 0.0124056i
$$293$$ 18.5571 + 10.7139i 1.08412 + 0.625914i 0.932004 0.362449i $$-0.118059\pi$$
0.152112 + 0.988363i $$0.451393\pi$$
$$294$$ 0 0
$$295$$ −2.48657 + 4.30687i −0.144774 + 0.250755i
$$296$$ −1.54846 2.68202i −0.0900027 0.155889i
$$297$$ 0 0
$$298$$ 13.9625 0.808828
$$299$$ 12.9280 17.9425i 0.747644 1.03764i
$$300$$ 0 0
$$301$$ −8.34729 + 4.81931i −0.481130 + 0.277781i
$$302$$ 8.92131 + 15.4522i 0.513364 + 0.889172i
$$303$$ 0 0
$$304$$ 6.18952i 0.354993i
$$305$$ −2.61503 1.50979i −0.149736 0.0864503i
$$306$$ 0 0
$$307$$ 7.59364i 0.433392i 0.976239 + 0.216696i $$0.0695280\pi$$
−0.976239 + 0.216696i $$0.930472\pi$$
$$308$$ −1.58726 + 2.74922i −0.0904426 + 0.156651i
$$309$$ 0 0
$$310$$ −8.73121 + 5.04097i −0.495899 + 0.286308i
$$311$$ −25.6355 −1.45366 −0.726828 0.686820i $$-0.759006\pi$$
−0.726828 + 0.686820i $$0.759006\pi$$
$$312$$ 0 0
$$313$$ −1.71308 −0.0968293 −0.0484146 0.998827i $$-0.515417\pi$$
−0.0484146 + 0.998827i $$0.515417\pi$$
$$314$$ −3.96567 + 2.28958i −0.223796 + 0.129208i
$$315$$ 0 0
$$316$$ 3.48127 6.02973i 0.195837 0.339199i
$$317$$ 33.2098i 1.86525i 0.360850 + 0.932624i $$0.382487\pi$$
−0.360850 + 0.932624i $$0.617513\pi$$
$$318$$ 0 0
$$319$$ −5.71175 3.29768i −0.319797 0.184635i
$$320$$ 1.78801i 0.0999530i
$$321$$ 0 0
$$322$$ 3.06678 + 5.31181i 0.170905 + 0.296016i
$$323$$ 29.8087 17.2101i 1.65860 0.957593i
$$324$$ 0 0
$$325$$ 2.66758 + 5.92832i 0.147971 + 0.328844i
$$326$$ −12.2706 −0.679606
$$327$$ 0 0
$$328$$ 0.749217 + 1.29768i 0.0413686 + 0.0716525i
$$329$$ 5.25429 9.10069i 0.289678 0.501737i
$$330$$ 0 0
$$331$$ 4.29537 + 2.47994i 0.236095 + 0.136310i 0.613381 0.789787i $$-0.289809\pi$$
−0.377286 + 0.926097i $$0.623142\pi$$
$$332$$ −3.72589 2.15114i −0.204485 0.118059i
$$333$$ 0 0
$$334$$ 8.34904 14.4610i 0.456839 0.791269i
$$335$$ −10.3297 17.8916i −0.564372 0.977521i
$$336$$ 0 0
$$337$$ 23.6174 1.28652 0.643260 0.765648i $$-0.277581\pi$$
0.643260 + 0.765648i $$0.277581\pi$$
$$338$$ 2.60226 12.7369i 0.141544 0.692795i
$$339$$ 0 0
$$340$$ −8.61106 + 4.97160i −0.467000 + 0.269623i
$$341$$ 8.94997 + 15.5018i 0.484668 + 0.839470i
$$342$$ 0 0
$$343$$ 1.00000i 0.0539949i
$$344$$ −8.34729 4.81931i −0.450056 0.259840i
$$345$$ 0 0
$$346$$ 7.37731i 0.396607i
$$347$$ −3.58483 + 6.20911i −0.192444 + 0.333323i −0.946060 0.323993i $$-0.894975\pi$$
0.753616 + 0.657315i $$0.228308\pi$$
$$348$$ 0 0
$$349$$ 10.7155 6.18662i 0.573590 0.331162i −0.184992 0.982740i $$-0.559226\pi$$
0.758582 + 0.651578i $$0.225893\pi$$
$$350$$ −1.80301 −0.0963749
$$351$$ 0 0
$$352$$ −3.17452 −0.169203
$$353$$ −22.7018 + 13.1069i −1.20830 + 0.697610i −0.962387 0.271683i $$-0.912420\pi$$
−0.245909 + 0.969293i $$0.579087\pi$$
$$354$$ 0 0
$$355$$ −0.535059 + 0.926750i −0.0283980 + 0.0491868i
$$356$$ 16.2931i 0.863532i
$$357$$ 0 0
$$358$$ 17.1648 + 9.91008i 0.907186 + 0.523764i
$$359$$ 3.61956i 0.191033i −0.995428 0.0955165i $$-0.969550\pi$$
0.995428 0.0955165i $$-0.0304503\pi$$
$$360$$ 0 0
$$361$$ 9.65506 + 16.7231i 0.508161 + 0.880161i
$$362$$ 15.8713 9.16329i 0.834176 0.481612i
$$363$$ 0 0
$$364$$ 2.92531 + 2.10774i 0.153328 + 0.110476i
$$365$$ 0.758070 0.0396792
$$366$$ 0 0
$$367$$ 4.03245 + 6.98440i 0.210492 + 0.364583i 0.951869 0.306506i $$-0.0991601\pi$$
−0.741377 + 0.671089i $$0.765827\pi$$
$$368$$ −3.06678 + 5.31181i −0.159867 + 0.276897i
$$369$$ 0 0
$$370$$ 4.79549 + 2.76868i 0.249306 + 0.143937i
$$371$$ −3.11942 1.80100i −0.161952 0.0935032i
$$372$$ 0 0
$$373$$ −14.5851 + 25.2621i −0.755187 + 1.30802i 0.190094 + 0.981766i $$0.439121\pi$$
−0.945281 + 0.326257i $$0.894213\pi$$
$$374$$ 8.82681 + 15.2885i 0.456423 + 0.790549i
$$375$$ 0 0
$$376$$ 10.5086 0.541938
$$377$$ −4.37904 + 6.07759i −0.225532 + 0.313012i
$$378$$ 0 0
$$379$$ −23.3797 + 13.4983i −1.20094 + 0.693361i −0.960763 0.277369i $$-0.910538\pi$$
−0.240173 + 0.970730i $$0.577204\pi$$
$$380$$ −5.53347 9.58425i −0.283861 0.491662i
$$381$$ 0 0
$$382$$ 15.0304i 0.769020i
$$383$$ −22.6159 13.0573i −1.15562 0.667197i −0.205368 0.978685i $$-0.565839\pi$$
−0.950250 + 0.311488i $$0.899173\pi$$
$$384$$ 0 0
$$385$$ 5.67609i 0.289280i
$$386$$ 2.72745 4.72408i 0.138824 0.240450i
$$387$$ 0 0
$$388$$ −15.1461 + 8.74462i −0.768928 + 0.443941i
$$389$$ 32.7110 1.65852 0.829258 0.558866i $$-0.188764\pi$$
0.829258 + 0.558866i $$0.188764\pi$$
$$390$$ 0 0
$$391$$ 34.1089 1.72496
$$392$$ −0.866025 + 0.500000i −0.0437409 + 0.0252538i
$$393$$ 0 0
$$394$$ −3.81485 + 6.60751i −0.192189 + 0.332882i
$$395$$ 12.4491i 0.626383i
$$396$$ 0 0
$$397$$ −0.524826 0.303008i −0.0263403 0.0152076i 0.486772 0.873529i $$-0.338174\pi$$
−0.513112 + 0.858321i $$0.671508\pi$$
$$398$$ 5.99023i 0.300263i
$$399$$ 0 0
$$400$$ −0.901504 1.56145i −0.0450752 0.0780726i
$$401$$ −8.83963 + 5.10356i −0.441430 + 0.254860i −0.704204 0.709998i $$-0.748696\pi$$
0.262774 + 0.964857i $$0.415363\pi$$
$$402$$ 0 0
$$403$$ 18.5399 8.34244i 0.923537 0.415566i
$$404$$ 4.06866 0.202424
$$405$$ 0 0
$$406$$ −1.03880 1.79925i −0.0515546 0.0892952i
$$407$$ 4.91564 8.51413i 0.243659 0.422030i
$$408$$ 0 0
$$409$$ 8.01863 + 4.62956i 0.396496 + 0.228917i 0.684971 0.728570i $$-0.259815\pi$$
−0.288475 + 0.957487i $$0.593148\pi$$
$$410$$ −2.32027 1.33961i −0.114590 0.0661586i
$$411$$ 0 0
$$412$$ −9.03838 + 15.6549i −0.445289 + 0.771263i
$$413$$ 1.39069 + 2.40874i 0.0684313 + 0.118527i
$$414$$ 0 0
$$415$$ 7.69254 0.377612
$$416$$ −0.362708 + 3.58726i −0.0177832 + 0.175880i
$$417$$ 0 0
$$418$$ −17.0163 + 9.82438i −0.832296 + 0.480526i
$$419$$ 6.42444 + 11.1275i 0.313855 + 0.543612i 0.979193 0.202930i $$-0.0650462\pi$$
−0.665339 + 0.746542i $$0.731713\pi$$
$$420$$ 0 0
$$421$$ 7.21371i 0.351575i 0.984428 + 0.175787i $$0.0562471\pi$$
−0.984428 + 0.175787i $$0.943753\pi$$
$$422$$ −2.40150 1.38651i −0.116903 0.0674942i
$$423$$ 0 0
$$424$$ 3.60200i 0.174929i
$$425$$ −5.01329 + 8.68328i −0.243180 + 0.421201i
$$426$$ 0 0
$$427$$ −1.46254 + 0.844395i −0.0707771 + 0.0408632i
$$428$$ −1.54169 −0.0745206
$$429$$ 0 0
$$430$$ 17.2340 0.831097
$$431$$ 5.17941 2.99033i 0.249483 0.144039i −0.370044 0.929014i $$-0.620658\pi$$
0.619528 + 0.784975i $$0.287324\pi$$
$$432$$ 0 0
$$433$$ 6.30144 10.9144i 0.302828 0.524513i −0.673947 0.738779i $$-0.735403\pi$$
0.976775 + 0.214266i $$0.0687359\pi$$
$$434$$ 5.63862i 0.270663i
$$435$$ 0 0
$$436$$ −6.38894 3.68865i −0.305975 0.176655i
$$437$$ 37.9637i 1.81605i
$$438$$ 0 0
$$439$$ 9.77965 + 16.9389i 0.466757 + 0.808447i 0.999279 0.0379690i $$-0.0120888\pi$$
−0.532522 + 0.846416i $$0.678755\pi$$
$$440$$ 4.91564 2.83804i 0.234344 0.135298i
$$441$$ 0 0
$$442$$ 18.2847 8.22764i 0.869717 0.391349i
$$443$$ 40.2601 1.91281 0.956407 0.292038i $$-0.0943335\pi$$
0.956407 + 0.292038i $$0.0943335\pi$$
$$444$$ 0 0
$$445$$ 14.5661 + 25.2293i 0.690500 + 1.19598i
$$446$$ −11.2677 + 19.5163i −0.533542 + 0.924121i
$$447$$ 0 0
$$448$$ −0.866025 0.500000i −0.0409159 0.0236228i
$$449$$ 24.7821 + 14.3079i 1.16954 + 0.675234i 0.953571 0.301167i $$-0.0973762\pi$$
0.215967 + 0.976401i $$0.430710\pi$$
$$450$$ 0 0
$$451$$ −2.37841 + 4.11952i −0.111995 + 0.193981i
$$452$$ 4.95660 + 8.58509i 0.233139 + 0.403809i
$$453$$ 0 0
$$454$$ −1.83155 −0.0859587
$$455$$ −6.41407 0.648527i −0.300696 0.0304034i
$$456$$ 0 0
$$457$$ 5.49961 3.17520i 0.257261 0.148530i −0.365824 0.930684i $$-0.619213\pi$$
0.623084 + 0.782155i $$0.285879\pi$$
$$458$$ 11.3030 + 19.5774i 0.528155 + 0.914791i
$$459$$ 0 0
$$460$$ 10.9669i 0.511333i
$$461$$ −20.9785 12.1119i −0.977065 0.564109i −0.0756821 0.997132i $$-0.524113\pi$$
−0.901383 + 0.433023i $$0.857447\pi$$
$$462$$ 0 0
$$463$$ 17.3851i 0.807954i 0.914769 + 0.403977i $$0.132372\pi$$
−0.914769 + 0.403977i $$0.867628\pi$$
$$464$$ 1.03880 1.79925i 0.0482249 0.0835280i
$$465$$ 0 0
$$466$$ −8.17439 + 4.71948i −0.378671 + 0.218626i
$$467$$ 14.8537 0.687349 0.343675 0.939089i $$-0.388328\pi$$
0.343675 + 0.939089i $$0.388328\pi$$
$$468$$ 0 0
$$469$$ −11.5544 −0.533532
$$470$$ −16.2722 + 9.39473i −0.750579 + 0.433347i
$$471$$ 0 0
$$472$$ −1.39069 + 2.40874i −0.0640117 + 0.110871i
$$473$$ 30.5980i 1.40690i
$$474$$ 0 0
$$475$$ −9.66463 5.57988i −0.443444 0.256022i
$$476$$ 5.56103i 0.254889i
$$477$$ 0 0
$$478$$ −7.93787 13.7488i −0.363070 0.628855i
$$479$$ 33.5014 19.3420i 1.53072 0.883759i 0.531387 0.847129i $$-0.321671\pi$$
0.999329 0.0366302i $$-0.0116624\pi$$
$$480$$ 0 0
$$481$$ −9.05947 6.52754i −0.413076 0.297630i
$$482$$ −23.9251 −1.08976
$$483$$ 0 0
$$484$$ 0.461204 + 0.798828i 0.0209638 + 0.0363104i
$$485$$ 15.6355 27.0815i 0.709971 1.22971i
$$486$$ 0 0
$$487$$ 22.2780 + 12.8622i 1.00951 + 0.582843i 0.911049 0.412298i $$-0.135274\pi$$
0.0984640 + 0.995141i $$0.468607\pi$$
$$488$$ −1.46254 0.844395i −0.0662059 0.0382240i
$$489$$ 0 0
$$490$$ 0.894007 1.54846i 0.0403871 0.0699525i
$$491$$ 9.17452 + 15.8907i 0.414040 + 0.717139i 0.995327 0.0965597i $$-0.0307839\pi$$
−0.581287 + 0.813699i $$0.697451\pi$$
$$492$$ 0 0
$$493$$ −11.5536 −0.520346
$$494$$ 9.15749 + 20.3512i 0.412015 + 0.915644i
$$495$$ 0 0
$$496$$ −4.88319 + 2.81931i −0.219262 + 0.126591i
$$497$$ 0.299248 + 0.518313i 0.0134231 + 0.0232495i
$$498$$ 0 0
$$499$$ 17.8096i 0.797269i −0.917110 0.398635i $$-0.869484\pi$$
0.917110 0.398635i $$-0.130516\pi$$
$$500$$ 10.5342 + 6.08193i 0.471105 + 0.271992i
$$501$$ 0 0
$$502$$ 20.5236i 0.916012i
$$503$$ 15.4711 26.7967i 0.689823 1.19481i −0.282072 0.959393i $$-0.591022\pi$$
0.971895 0.235415i $$-0.0756448\pi$$
$$504$$ 0 0
$$505$$ −6.30019 + 3.63741i −0.280355 + 0.161863i
$$506$$ −19.4711 −0.865596
$$507$$ 0 0
$$508$$ 18.3490 0.814107
$$509$$ −11.9583 + 6.90414i −0.530044 + 0.306021i −0.741034 0.671467i $$-0.765664\pi$$
0.210991 + 0.977488i $$0.432331\pi$$
$$510$$ 0 0
$$511$$ 0.211987 0.367172i 0.00937774 0.0162427i
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ −0.715933 0.413344i −0.0315784 0.0182318i
$$515$$ 32.3215i 1.42425i
$$516$$ 0 0
$$517$$ 16.6798 + 28.8903i 0.733579 + 1.27060i
$$518$$ 2.68202 1.54846i 0.117841 0.0680356i
$$519$$ 0 0
$$520$$ −2.64539 5.87901i −0.116008 0.257812i
$$521$$ 11.4549 0.501848 0.250924 0.968007i $$-0.419266\pi$$
0.250924 + 0.968007i $$0.419266\pi$$
$$522$$ 0 0
$$523$$ −0.465198 0.805747i −0.0203417 0.0352329i 0.855675 0.517513i $$-0.173142\pi$$
−0.876017 + 0.482280i $$0.839809\pi$$
$$524$$ −2.95964 + 5.12624i −0.129292 + 0.223941i
$$525$$ 0 0
$$526$$ −17.6331 10.1805i −0.768838 0.443889i
$$527$$ 27.1556 + 15.6783i 1.18292 + 0.682957i
$$528$$ 0 0
$$529$$ −7.31025 + 12.6617i −0.317837 + 0.550510i
$$530$$ 3.22021 + 5.57757i 0.139877 + 0.242274i
$$531$$ 0 0
$$532$$ −6.18952 −0.268350
$$533$$ 4.38338 + 3.15832i 0.189865 + 0.136802i
$$534$$ 0 0
$$535$$ 2.38726 1.37828i 0.103210 0.0595884i
$$536$$ −5.77720 10.0064i −0.249537 0.432211i
$$537$$ 0 0
$$538$$ 20.5175i 0.884572i
$$539$$ −2.74922 1.58726i −0.118417 0.0683682i
$$540$$ 0 0
$$541$$ 22.7965i 0.980097i −0.871695 0.490048i $$-0.836979\pi$$
0.871695 0.490048i $$-0.163021\pi$$
$$542$$ 6.09076 10.5495i 0.261621 0.453140i
$$543$$ 0 0
$$544$$ −4.81599 + 2.78052i −0.206484 + 0.119214i
$$545$$ 13.1907 0.565029
$$546$$ 0 0
$$547$$ 31.6698 1.35410 0.677052 0.735935i $$-0.263257\pi$$
0.677052 + 0.735935i $$0.263257\pi$$
$$548$$ −7.62363 + 4.40150i −0.325665 + 0.188023i
$$549$$ 0 0
$$550$$ 2.86185 4.95686i 0.122029 0.211361i
$$551$$ 12.8593i 0.547824i
$$552$$ 0 0
$$553$$ 6.02973 + 3.48127i 0.256410 + 0.148039i
$$554$$ 8.62484i 0.366434i
$$555$$ 0 0
$$556$$ 9.48720 + 16.4323i 0.402347 + 0.696885i
$$557$$ 9.38623 5.41914i 0.397707 0.229616i −0.287787 0.957694i $$-0.592920\pi$$
0.685494 + 0.728078i $$0.259586\pi$$
$$558$$ 0 0
$$559$$ −34.5763 3.49601i −1.46242 0.147865i
$$560$$ 1.78801 0.0755574
$$561$$ 0 0
$$562$$ −12.1461 21.0377i −0.512353 0.887422i
$$563$$ −7.73626 + 13.3996i −0.326044 + 0.564725i −0.981723 0.190315i $$-0.939049\pi$$
0.655679 + 0.755040i $$0.272383\pi$$
$$564$$ 0 0
$$565$$ −15.3503 8.86247i −0.645790 0.372847i
$$566$$ −9.28472 5.36054i −0.390266 0.225320i
$$567$$ 0 0
$$568$$ −0.299248 + 0.518313i −0.0125562 + 0.0217479i
$$569$$ −16.8667 29.2139i −0.707088 1.22471i −0.965933 0.258793i $$-0.916675\pi$$
0.258845 0.965919i $$-0.416658\pi$$
$$570$$ 0 0
$$571$$ −43.6140 −1.82519 −0.912594 0.408868i $$-0.865924\pi$$
−0.912594 + 0.408868i $$0.865924\pi$$
$$572$$ −10.4379 + 4.69676i −0.436429 + 0.196381i
$$573$$ 0 0
$$574$$ −1.29768 + 0.749217i −0.0541642 + 0.0312717i
$$575$$ −5.52943 9.57725i −0.230593 0.399399i
$$576$$ 0 0
$$577$$ 10.8368i 0.451143i 0.974227 + 0.225571i $$0.0724249\pi$$
−0.974227 + 0.225571i $$0.927575\pi$$
$$578$$ 12.0595 + 6.96254i 0.501608 + 0.289603i
$$579$$ 0 0
$$580$$ 3.71476i 0.154247i
$$581$$ 2.15114 3.72589i 0.0892444 0.154576i
$$582$$ 0 0
$$583$$ 9.90268 5.71731i 0.410127 0.236787i
$$584$$ 0.423973 0.0175441
$$585$$ 0 0
$$586$$ −21.4278 −0.885176
$$587$$ −22.5632 + 13.0269i −0.931284 + 0.537677i −0.887217 0.461352i $$-0.847365\pi$$
−0.0440666 + 0.999029i $$0.514031\pi$$
$$588$$ 0 0
$$589$$ −17.4502 + 30.2246i −0.719022 + 1.24538i
$$590$$ 4.97314i 0.204741i
$$591$$ 0 0
$$592$$ 2.68202 + 1.54846i 0.110230 + 0.0636415i
$$593$$ 1.68393i 0.0691509i 0.999402 + 0.0345754i $$0.0110079\pi$$
−0.999402 + 0.0345754i $$0.988992\pi$$
$$594$$ 0 0
$$595$$ −4.97160 8.61106i −0.203816 0.353019i
$$596$$ −12.0919 + 6.98127i −0.495304 + 0.285964i
$$597$$ 0 0
$$598$$ −2.22469 + 22.0027i −0.0909743 + 0.899756i
$$599$$ 6.54081 0.267250 0.133625 0.991032i $$-0.457338\pi$$
0.133625 + 0.991032i $$0.457338\pi$$
$$600$$ 0 0
$$601$$ −19.2387 33.3224i −0.784763 1.35925i −0.929140 0.369727i $$-0.879451\pi$$
0.144377 0.989523i $$-0.453882\pi$$
$$602$$ 4.81931 8.34729i 0.196420 0.340210i
$$603$$ 0 0
$$604$$ −15.4522 8.92131i −0.628740 0.363003i
$$605$$ −1.42832 0.824638i −0.0580693 0.0335263i
$$606$$ 0 0
$$607$$ 4.71797 8.17176i 0.191496 0.331682i −0.754250 0.656587i $$-0.771999\pi$$
0.945746 + 0.324906i $$0.105333\pi$$
$$608$$ −3.09476 5.36028i −0.125509 0.217388i
$$609$$ 0 0
$$610$$ 3.01958 0.122259
$$611$$ 34.5523 15.5476i 1.39784 0.628989i
$$612$$ 0 0
$$613$$ −22.0191 + 12.7127i −0.889342 + 0.513462i −0.873727 0.486416i $$-0.838304\pi$$
−0.0156146 + 0.999878i $$0.504970\pi$$
$$614$$ −3.79682 6.57628i −0.153227 0.265397i
$$615$$ 0 0
$$616$$ 3.17452i 0.127905i
$$617$$ −24.8545 14.3497i −1.00060 0.577699i −0.0921772 0.995743i $$-0.529383\pi$$
−0.908427 + 0.418044i $$0.862716\pi$$
$$618$$ 0 0
$$619$$ 9.61494i 0.386457i −0.981154 0.193229i $$-0.938104\pi$$
0.981154 0.193229i $$-0.0618959\pi$$
$$620$$ 5.04097 8.73121i 0.202450 0.350654i
$$621$$ 0 0
$$622$$ 22.2010 12.8177i 0.890178 0.513945i
$$623$$ 16.2931 0.652769
$$624$$ 0 0
$$625$$ −12.7341 −0.509365
$$626$$ 1.48357 0.856542i 0.0592956 0.0342343i
$$627$$ 0 0
$$628$$ 2.28958 3.96567i 0.0913642 0.158247i
$$629$$ 17.2221i 0.686691i
$$630$$ 0 0
$$631$$ 29.9445 + 17.2885i 1.19207 + 0.688244i 0.958776 0.284162i $$-0.0917153\pi$$
0.233297 + 0.972406i $$0.425049\pi$$
$$632$$ 6.96254i 0.276955i
$$633$$ 0 0
$$634$$ −16.6049 28.7605i −0.659465 1.14223i
$$635$$ −28.4129 + 16.4042i −1.12753 + 0.650980i
$$636$$ 0 0
$$637$$ −2.10774 + 2.92531i −0.0835119 + 0.115905i
$$638$$ 6.59536 0.261113
$$639$$ 0 0
$$640$$ 0.894007 + 1.54846i 0.0353387 + 0.0612085i
$$641$$ −3.25646 + 5.64035i −0.128622 + 0.222780i −0.923143 0.384457i $$-0.874389\pi$$
0.794521 + 0.607237i $$0.207722\pi$$
$$642$$ 0 0
$$643$$ −21.8991 12.6435i −0.863617 0.498609i 0.00160504 0.999999i $$-0.499489\pi$$
−0.865222 + 0.501389i $$0.832822\pi$$
$$644$$ −5.31181 3.06678i −0.209315 0.120848i
$$645$$ 0 0
$$646$$ −17.2101 + 29.8087i −0.677120 + 1.17281i
$$647$$ −5.95794 10.3194i −0.234231 0.405699i 0.724818 0.688940i $$-0.241924\pi$$
−0.959049 + 0.283241i $$0.908590\pi$$
$$648$$ 0 0
$$649$$ −8.82955 −0.346590
$$650$$ −5.27435 3.80028i −0.206877 0.149059i
$$651$$ 0 0
$$652$$ 10.6267 6.13531i 0.416172 0.240277i
$$653$$ 20.7508 + 35.9415i 0.812043 + 1.40650i 0.911432 + 0.411451i $$0.134978\pi$$
−0.0993891 + 0.995049i $$0.531689\pi$$
$$654$$ 0 0
$$655$$ 10.5837i 0.413541i
$$656$$ −1.29768 0.749217i −0.0506660 0.0292520i
$$657$$ 0 0
$$658$$ 10.5086i 0.409667i
$$659$$ 7.86778 13.6274i 0.306485 0.530848i −0.671106 0.741362i $$-0.734180\pi$$
0.977591 + 0.210514i $$0.0675137\pi$$
$$660$$ 0 0
$$661$$ −22.6071 + 13.0522i −0.879315 + 0.507673i −0.870432 0.492288i $$-0.836161\pi$$
−0.00888248 + 0.999961i $$0.502827\pi$$
$$662$$ −4.95987 −0.192771
$$663$$ 0 0
$$664$$ 4.30228 0.166961
$$665$$ 9.58425 5.53347i 0.371661 0.214579i
$$666$$ 0 0
$$667$$ 6.37151 11.0358i 0.246706 0.427307i
$$668$$ 16.6981i 0.646068i
$$669$$ 0 0
$$670$$ 17.8916 + 10.3297i 0.691212 + 0.399071i
$$671$$ 5.36110i 0.206963i
$$672$$ 0 0
$$673$$ 0.620853 + 1.07535i 0.0239321 + 0.0414516i 0.877743 0.479131i $$-0.159048\pi$$
−0.853811 + 0.520583i $$0.825715\pi$$
$$674$$ −20.4532 + 11.8087i −0.787829 + 0.454853i
$$675$$ 0 0
$$676$$ 4.11482 + 12.3316i 0.158262 + 0.474292i
$$677$$ −29.2845 −1.12550 −0.562748 0.826629i $$-0.690256\pi$$
−0.562748 + 0.826629i $$0.690256\pi$$
$$678$$ 0 0
$$679$$ −8.74462 15.1461i −0.335588 0.581255i
$$680$$ 4.97160 8.61106i 0.190652 0.330219i
$$681$$ 0 0
$$682$$ −15.5018 8.94997i −0.593595 0.342712i
$$683$$ 37.0486 + 21.3900i 1.41762 + 0.818466i 0.996090 0.0883461i $$-0.0281581\pi$$
0.421535 + 0.906812i $$0.361491\pi$$
$$684$$ 0 0
$$685$$ 7.86995 13.6311i 0.300695 0.520819i
$$686$$ −0.500000 0.866025i −0.0190901 0.0330650i
$$687$$ 0 0
$$688$$ 9.63862 0.367469
$$689$$ −5.32922 11.8434i −0.203027 0.451198i
$$690$$ 0 0
$$691$$ −16.3649 + 9.44827i −0.622549 + 0.359429i −0.777861 0.628437i $$-0.783695\pi$$
0.155312 + 0.987866i $$0.450362\pi$$
$$692$$ 3.68865 + 6.38894i 0.140222 + 0.242871i
$$693$$ 0 0
$$694$$ 7.16967i 0.272157i
$$695$$ −29.3812 16.9632i −1.11449 0.643452i
$$696$$ 0 0
$$697$$ 8.33284i 0.315629i
$$698$$ −6.18662 + 10.7155i −0.234167 + 0.405589i
$$699$$ 0 0
$$700$$ 1.56145 0.901504i 0.0590173 0.0340737i
$$701$$ 3.35161 0.126589 0.0632943 0.997995i $$-0.479839\pi$$
0.0632943 + 0.997995i $$0.479839\pi$$
$$702$$ 0 0
$$703$$ 19.1685 0.722954
$$704$$ 2.74922 1.58726i 0.103615 0.0598222i
$$705$$ 0 0
$$706$$ 13.1069 22.7018i 0.493285 0.854395i
$$707$$ 4.06866i 0.153018i
$$708$$ 0 0
$$709$$ 31.8468 + 18.3867i 1.19603 + 0.690529i 0.959668 0.281136i $$-0.0907113\pi$$
0.236363 + 0.971665i $$0.424045\pi$$
$$710$$ 1.07012i 0.0401608i
$$711$$ 0 0
$$712$$ 8.14654 + 14.1102i 0.305305 + 0.528803i
$$713$$ −29.9513 + 17.2924i −1.12169 + 0.647606i
$$714$$ 0 0
$$715$$ 11.9637 16.6043i 0.447419 0.620965i
$$716$$ −19.8202 −0.740714
$$717$$ 0 0
$$718$$ 1.80978 + 3.13463i 0.0675404 + 0.116983i
$$719$$ −8.08486 + 14.0034i −0.301514 + 0.522238i −0.976479 0.215612i $$-0.930825\pi$$
0.674965 + 0.737850i $$0.264159\pi$$
$$720$$ 0 0
$$721$$ −15.6549 9.03838i −0.583020 0.336607i
$$722$$ −16.7231 9.65506i −0.622368 0.359324i
$$723$$ 0 0
$$724$$ −9.16329 + 15.8713i −0.340551 + 0.589851i
$$725$$ 1.87296 + 3.24406i 0.0695599 + 0.120481i
$$726$$ 0 0
$$727$$ 27.2522 1.01073 0.505363 0.862907i $$-0.331358\pi$$
0.505363 + 0.862907i $$0.331358\pi$$
$$728$$ −3.58726 0.362708i −0.132953 0.0134429i
$$729$$ 0 0
$$730$$ −0.656508 + 0.379035i −0.0242984 + 0.0140287i
$$731$$ −26.8003 46.4196i −0.991247 1.71689i
$$732$$ 0 0
$$733$$ 39.6734i 1.46537i −0.680567 0.732686i $$-0.738267\pi$$
0.680567 0.732686i $$-0.261733\pi$$
$$734$$ −6.98440 4.03245i −0.257799 0.148840i
$$735$$ 0 0
$$736$$ 6.13356i 0.226086i
$$737$$ 18.3398 31.7655i 0.675557 1.17010i
$$738$$ 0 0
$$739$$ −22.0125 + 12.7089i −0.809742 + 0.467505i −0.846866 0.531806i $$-0.821514\pi$$
0.0371244 + 0.999311i $$0.488180\pi$$
$$740$$ −5.53735 −0.203557
$$741$$ 0 0
$$742$$ 3.60200 0.132234
$$743$$ 21.5143 12.4213i 0.789285 0.455694i −0.0504260 0.998728i $$-0.516058\pi$$
0.839711 + 0.543034i $$0.182725\pi$$
$$744$$ 0 0
$$745$$ 12.4826 21.6205i 0.457327 0.792114i
$$746$$ 29.1702i 1.06800i
$$747$$ 0 0
$$748$$ −15.2885 8.82681i −0.559002 0.322740i
$$749$$ 1.54169i 0.0563323i
$$750$$ 0 0
$$751$$ −22.7211 39.3540i −0.829103 1.43605i −0.898743 0.438476i $$-0.855518\pi$$
0.0696398 0.997572i $$-0.477815\pi$$
$$752$$ −9.10069 + 5.25429i −0.331868 + 0.191604i
$$753$$ 0 0
$$754$$ 0.753559 7.45287i 0.0274430 0.271417i
$$755$$ 31.9028 1.16106
$$756$$ 0 0
$$757$$ −3.20643 5.55369i −0.116540 0.201852i 0.801855 0.597519i $$-0.203847\pi$$
−0.918394 + 0.395667i $$0.870514\pi$$
$$758$$ 13.4983 23.3797i 0.490280 0.849190i
$$759$$ 0 0
$$760$$ 9.58425 + 5.53347i 0.347657 + 0.200720i
$$761$$ −27.8313 16.0684i −1.00888 0.582479i −0.0980185 0.995185i $$-0.531250\pi$$
−0.910864 + 0.412706i $$0.864584\pi$$
$$762$$ 0 0
$$763$$ 3.68865 6.38894i 0.133538 0.231295i
$$764$$ 7.51518 + 13.0167i 0.271890 + 0.470927i
$$765$$ 0 0
$$766$$ 26.1146 0.943558
$$767$$ −1.00883 + 9.97753i −0.0364267 + 0.360268i
$$768$$ 0 0
$$769$$ −33.7551 + 19.4885i −1.21724 + 0.702774i −0.964327 0.264714i $$-0.914722\pi$$
−0.252914 + 0.967489i $$0.581389\pi$$
$$770$$ 2.83804 + 4.91564i 0.102276 + 0.177147i
$$771$$ 0 0
$$772$$ 5.45490i 0.196326i
$$773$$ −2.09922 1.21199i −0.0755038 0.0435921i 0.461773 0.886998i $$-0.347214\pi$$
−0.537277 + 0.843406i $$0.680547\pi$$
$$774$$ 0 0
$$775$$ 10.1665i 0.365191i
$$776$$ 8.74462 15.1461i 0.313913 0.543714i
$$777$$ 0 0
$$778$$ −28.3286 + 16.3555i −1.01563 + 0.586374i
$$779$$ −9.27458 −0.332296
$$780$$ 0 0
$$781$$ −1.89994 −0.0679851
$$782$$ −29.5392 + 17.0544i −1.05632 + 0.609866i