# Properties

 Label 336.4.bc.d.17.1 Level $336$ Weight $4$ Character 336.17 Analytic conductor $19.825$ Analytic rank $0$ Dimension $12$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$336 = 2^{4} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 336.bc (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$19.8246417619$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ Defining polynomial: $$x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441$$ x^12 - x^11 - 29*x^9 + 6*x^8 - 49*x^7 + 1564*x^6 - 441*x^5 + 486*x^4 - 21141*x^3 - 59049*x + 531441 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{4}\cdot 3^{3}$$ Twist minimal: no (minimal twist has level 21) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 17.1 Root $$-2.59957 + 1.49740i$$ of defining polynomial Character $$\chi$$ $$=$$ 336.17 Dual form 336.4.bc.d.257.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-5.19615 + 0.00519496i) q^{3} +(8.05907 + 13.9587i) q^{5} +(5.67909 + 17.6280i) q^{7} +(26.9999 - 0.0539876i) q^{9} +O(q^{10})$$ $$q+(-5.19615 + 0.00519496i) q^{3} +(8.05907 + 13.9587i) q^{5} +(5.67909 + 17.6280i) q^{7} +(26.9999 - 0.0539876i) q^{9} +(30.8296 + 17.7995i) q^{11} -7.40831i q^{13} +(-41.9486 - 72.4897i) q^{15} +(14.4601 - 25.0457i) q^{17} +(-30.4580 + 17.5849i) q^{19} +(-29.6010 - 91.5685i) q^{21} +(48.0017 - 27.7138i) q^{23} +(-67.3971 + 116.735i) q^{25} +(-140.295 + 0.420792i) q^{27} +68.1510i q^{29} +(154.734 + 89.3356i) q^{31} +(-160.288 - 92.3286i) q^{33} +(-200.297 + 221.338i) q^{35} +(116.838 + 202.370i) q^{37} +(0.0384859 + 38.4947i) q^{39} -370.068 q^{41} +187.068 q^{43} +(218.348 + 376.449i) q^{45} +(-87.3726 - 151.334i) q^{47} +(-278.496 + 200.222i) q^{49} +(-75.0068 + 130.216i) q^{51} +(235.715 + 136.090i) q^{53} +573.789i q^{55} +(158.173 - 91.5321i) q^{57} +(-48.4354 + 83.8926i) q^{59} +(-333.882 + 192.767i) q^{61} +(154.287 + 475.650i) q^{63} +(103.411 - 59.7041i) q^{65} +(-509.009 + 881.630i) q^{67} +(-249.280 + 144.254i) q^{69} -125.333i q^{71} +(195.346 + 112.783i) q^{73} +(349.599 - 606.924i) q^{75} +(-138.686 + 644.550i) q^{77} +(-532.154 - 921.718i) q^{79} +(728.994 - 2.91533i) q^{81} -601.040 q^{83} +466.140 q^{85} +(-0.354042 - 354.123i) q^{87} +(-752.606 - 1303.55i) q^{89} +(130.594 - 42.0725i) q^{91} +(-804.484 - 463.397i) q^{93} +(-490.926 - 283.436i) q^{95} +327.463i q^{97} +(833.358 + 478.920i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q + 3 q^{3} + 56 q^{7} - 3 q^{9}+O(q^{10})$$ 12 * q + 3 * q^3 + 56 * q^7 - 3 * q^9 $$12 q + 3 q^{3} + 56 q^{7} - 3 q^{9} - 6 q^{15} - 300 q^{19} + 357 q^{21} - 42 q^{25} + 930 q^{31} - 855 q^{33} + 764 q^{37} + 426 q^{39} + 1012 q^{43} + 2367 q^{45} - 336 q^{49} + 1341 q^{51} + 270 q^{57} + 2358 q^{61} - 1071 q^{63} - 792 q^{67} - 2904 q^{73} + 2418 q^{75} - 1674 q^{79} + 837 q^{81} + 348 q^{85} - 1638 q^{87} + 1218 q^{91} - 1479 q^{93} + 3354 q^{99}+O(q^{100})$$ 12 * q + 3 * q^3 + 56 * q^7 - 3 * q^9 - 6 * q^15 - 300 * q^19 + 357 * q^21 - 42 * q^25 + 930 * q^31 - 855 * q^33 + 764 * q^37 + 426 * q^39 + 1012 * q^43 + 2367 * q^45 - 336 * q^49 + 1341 * q^51 + 270 * q^57 + 2358 * q^61 - 1071 * q^63 - 792 * q^67 - 2904 * q^73 + 2418 * q^75 - 1674 * q^79 + 837 * q^81 + 348 * q^85 - 1638 * q^87 + 1218 * q^91 - 1479 * q^93 + 3354 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$$.

 $$n$$ $$85$$ $$113$$ $$127$$ $$241$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 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 0
$$3$$ −5.19615 + 0.00519496i −1.00000 + 0.000999771i
$$4$$ 0 0
$$5$$ 8.05907 + 13.9587i 0.720825 + 1.24851i 0.960670 + 0.277694i $$0.0895701\pi$$
−0.239845 + 0.970811i $$0.577097\pi$$
$$6$$ 0 0
$$7$$ 5.67909 + 17.6280i 0.306642 + 0.951825i
$$8$$ 0 0
$$9$$ 26.9999 0.0539876i 0.999998 0.00199954i
$$10$$ 0 0
$$11$$ 30.8296 + 17.7995i 0.845043 + 0.487886i 0.858975 0.512017i $$-0.171102\pi$$
−0.0139322 + 0.999903i $$0.504435\pi$$
$$12$$ 0 0
$$13$$ 7.40831i 0.158054i −0.996872 0.0790268i $$-0.974819\pi$$
0.996872 0.0790268i $$-0.0251813\pi$$
$$14$$ 0 0
$$15$$ −41.9486 72.4897i −0.722073 1.24778i
$$16$$ 0 0
$$17$$ 14.4601 25.0457i 0.206300 0.357322i −0.744246 0.667905i $$-0.767191\pi$$
0.950546 + 0.310584i $$0.100524\pi$$
$$18$$ 0 0
$$19$$ −30.4580 + 17.5849i −0.367765 + 0.212329i −0.672482 0.740114i $$-0.734772\pi$$
0.304716 + 0.952443i $$0.401438\pi$$
$$20$$ 0 0
$$21$$ −29.6010 91.5685i −0.307593 0.951518i
$$22$$ 0 0
$$23$$ 48.0017 27.7138i 0.435175 0.251249i −0.266374 0.963870i $$-0.585825\pi$$
0.701549 + 0.712621i $$0.252492\pi$$
$$24$$ 0 0
$$25$$ −67.3971 + 116.735i −0.539177 + 0.933881i
$$26$$ 0 0
$$27$$ −140.295 + 0.420792i −0.999996 + 0.00299931i
$$28$$ 0 0
$$29$$ 68.1510i 0.436390i 0.975905 + 0.218195i $$0.0700169\pi$$
−0.975905 + 0.218195i $$0.929983\pi$$
$$30$$ 0 0
$$31$$ 154.734 + 89.3356i 0.896484 + 0.517585i 0.876058 0.482206i $$-0.160164\pi$$
0.0204262 + 0.999791i $$0.493498\pi$$
$$32$$ 0 0
$$33$$ −160.288 92.3286i −0.845530 0.487041i
$$34$$ 0 0
$$35$$ −200.297 + 221.338i −0.967323 + 1.06894i
$$36$$ 0 0
$$37$$ 116.838 + 202.370i 0.519137 + 0.899172i 0.999753 + 0.0222405i $$0.00707996\pi$$
−0.480615 + 0.876931i $$0.659587\pi$$
$$38$$ 0 0
$$39$$ 0.0384859 + 38.4947i 0.000158017 + 0.158053i
$$40$$ 0 0
$$41$$ −370.068 −1.40963 −0.704816 0.709390i $$-0.748970\pi$$
−0.704816 + 0.709390i $$0.748970\pi$$
$$42$$ 0 0
$$43$$ 187.068 0.663432 0.331716 0.943379i $$-0.392372\pi$$
0.331716 + 0.943379i $$0.392372\pi$$
$$44$$ 0 0
$$45$$ 218.348 + 376.449i 0.723320 + 1.24706i
$$46$$ 0 0
$$47$$ −87.3726 151.334i −0.271162 0.469666i 0.697998 0.716100i $$-0.254075\pi$$
−0.969160 + 0.246434i $$0.920741\pi$$
$$48$$ 0 0
$$49$$ −278.496 + 200.222i −0.811942 + 0.583739i
$$50$$ 0 0
$$51$$ −75.0068 + 130.216i −0.205942 + 0.357528i
$$52$$ 0 0
$$53$$ 235.715 + 136.090i 0.610905 + 0.352706i 0.773319 0.634017i $$-0.218595\pi$$
−0.162415 + 0.986723i $$0.551928\pi$$
$$54$$ 0 0
$$55$$ 573.789i 1.40672i
$$56$$ 0 0
$$57$$ 158.173 91.5321i 0.367553 0.212697i
$$58$$ 0 0
$$59$$ −48.4354 + 83.8926i −0.106877 + 0.185117i −0.914504 0.404578i $$-0.867419\pi$$
0.807626 + 0.589695i $$0.200752\pi$$
$$60$$ 0 0
$$61$$ −333.882 + 192.767i −0.700807 + 0.404611i −0.807648 0.589665i $$-0.799260\pi$$
0.106841 + 0.994276i $$0.465927\pi$$
$$62$$ 0 0
$$63$$ 154.287 + 475.650i 0.308544 + 0.951210i
$$64$$ 0 0
$$65$$ 103.411 59.7041i 0.197331 0.113929i
$$66$$ 0 0
$$67$$ −509.009 + 881.630i −0.928140 + 1.60759i −0.141708 + 0.989908i $$0.545259\pi$$
−0.786432 + 0.617677i $$0.788074\pi$$
$$68$$ 0 0
$$69$$ −249.280 + 144.254i −0.434924 + 0.251684i
$$70$$ 0 0
$$71$$ 125.333i 0.209497i −0.994499 0.104749i $$-0.966596\pi$$
0.994499 0.104749i $$-0.0334038\pi$$
$$72$$ 0 0
$$73$$ 195.346 + 112.783i 0.313199 + 0.180825i 0.648357 0.761337i $$-0.275456\pi$$
−0.335158 + 0.942162i $$0.608790\pi$$
$$74$$ 0 0
$$75$$ 349.599 606.924i 0.538243 0.934420i
$$76$$ 0 0
$$77$$ −138.686 + 644.550i −0.205256 + 0.953939i
$$78$$ 0 0
$$79$$ −532.154 921.718i −0.757874 1.31268i −0.943933 0.330138i $$-0.892905\pi$$
0.186059 0.982539i $$-0.440428\pi$$
$$80$$ 0 0
$$81$$ 728.994 2.91533i 0.999992 0.00399908i
$$82$$ 0 0
$$83$$ −601.040 −0.794852 −0.397426 0.917634i $$-0.630096\pi$$
−0.397426 + 0.917634i $$0.630096\pi$$
$$84$$ 0 0
$$85$$ 466.140 0.594824
$$86$$ 0 0
$$87$$ −0.354042 354.123i −0.000436290 0.436390i
$$88$$ 0 0
$$89$$ −752.606 1303.55i −0.896360 1.55254i −0.832112 0.554607i $$-0.812869\pi$$
−0.0642474 0.997934i $$-0.520465\pi$$
$$90$$ 0 0
$$91$$ 130.594 42.0725i 0.150439 0.0484658i
$$92$$ 0 0
$$93$$ −804.484 463.397i −0.897001 0.516689i
$$94$$ 0 0
$$95$$ −490.926 283.436i −0.530189 0.306105i
$$96$$ 0 0
$$97$$ 327.463i 0.342771i 0.985204 + 0.171386i $$0.0548244\pi$$
−0.985204 + 0.171386i $$0.945176\pi$$
$$98$$ 0 0
$$99$$ 833.358 + 478.920i 0.846017 + 0.486195i
$$100$$ 0 0
$$101$$ 547.845 948.895i 0.539729 0.934837i −0.459190 0.888338i $$-0.651860\pi$$
0.998918 0.0464990i $$-0.0148064\pi$$
$$102$$ 0 0
$$103$$ −179.848 + 103.835i −0.172048 + 0.0993318i −0.583551 0.812076i $$-0.698337\pi$$
0.411503 + 0.911408i $$0.365004\pi$$
$$104$$ 0 0
$$105$$ 1039.62 1151.15i 0.966254 1.06991i
$$106$$ 0 0
$$107$$ 1561.25 901.391i 1.41058 0.814399i 0.415138 0.909759i $$-0.363733\pi$$
0.995443 + 0.0953593i $$0.0304000\pi$$
$$108$$ 0 0
$$109$$ −141.825 + 245.647i −0.124627 + 0.215860i −0.921587 0.388172i $$-0.873107\pi$$
0.796960 + 0.604032i $$0.206440\pi$$
$$110$$ 0 0
$$111$$ −608.160 1050.94i −0.520036 0.898652i
$$112$$ 0 0
$$113$$ 1037.39i 0.863627i 0.901963 + 0.431814i $$0.142126\pi$$
−0.901963 + 0.431814i $$0.857874\pi$$
$$114$$ 0 0
$$115$$ 773.697 + 446.694i 0.627371 + 0.362213i
$$116$$ 0 0
$$117$$ −0.399957 200.024i −0.000316035 0.158053i
$$118$$ 0 0
$$119$$ 523.626 + 112.667i 0.403368 + 0.0867915i
$$120$$ 0 0
$$121$$ −31.8573 55.1785i −0.0239349 0.0414564i
$$122$$ 0 0
$$123$$ 1922.93 1.92249i 1.40963 0.00140931i
$$124$$ 0 0
$$125$$ −157.864 −0.112958
$$126$$ 0 0
$$127$$ −1645.81 −1.14994 −0.574968 0.818176i $$-0.694985\pi$$
−0.574968 + 0.818176i $$0.694985\pi$$
$$128$$ 0 0
$$129$$ −972.033 + 0.971811i −0.663432 + 0.000663281i
$$130$$ 0 0
$$131$$ 314.185 + 544.184i 0.209545 + 0.362943i 0.951571 0.307428i $$-0.0994683\pi$$
−0.742026 + 0.670371i $$0.766135\pi$$
$$132$$ 0 0
$$133$$ −482.961 437.048i −0.314873 0.284939i
$$134$$ 0 0
$$135$$ −1136.52 1954.95i −0.724566 1.24634i
$$136$$ 0 0
$$137$$ −432.079 249.461i −0.269453 0.155569i 0.359186 0.933266i $$-0.383054\pi$$
−0.628639 + 0.777697i $$0.716388\pi$$
$$138$$ 0 0
$$139$$ 1216.65i 0.742410i 0.928551 + 0.371205i $$0.121055\pi$$
−0.928551 + 0.371205i $$0.878945\pi$$
$$140$$ 0 0
$$141$$ 454.788 + 785.900i 0.271631 + 0.469395i
$$142$$ 0 0
$$143$$ 131.864 228.395i 0.0771121 0.133562i
$$144$$ 0 0
$$145$$ −951.300 + 549.233i −0.544835 + 0.314561i
$$146$$ 0 0
$$147$$ 1446.07 1041.83i 0.811358 0.584550i
$$148$$ 0 0
$$149$$ 2010.18 1160.58i 1.10524 0.638111i 0.167648 0.985847i $$-0.446383\pi$$
0.937592 + 0.347736i $$0.113050\pi$$
$$150$$ 0 0
$$151$$ 488.726 846.497i 0.263390 0.456205i −0.703750 0.710447i $$-0.748493\pi$$
0.967141 + 0.254242i $$0.0818260\pi$$
$$152$$ 0 0
$$153$$ 389.070 677.012i 0.205585 0.357733i
$$154$$ 0 0
$$155$$ 2879.85i 1.49235i
$$156$$ 0 0
$$157$$ −143.752 82.9950i −0.0730740 0.0421893i 0.463018 0.886349i $$-0.346767\pi$$
−0.536092 + 0.844160i $$0.680100\pi$$
$$158$$ 0 0
$$159$$ −1225.52 705.920i −0.611257 0.352095i
$$160$$ 0 0
$$161$$ 761.145 + 688.786i 0.372588 + 0.337168i
$$162$$ 0 0
$$163$$ 488.511 + 846.127i 0.234743 + 0.406587i 0.959198 0.282735i $$-0.0912417\pi$$
−0.724455 + 0.689322i $$0.757908\pi$$
$$164$$ 0 0
$$165$$ −2.98081 2981.49i −0.00140640 1.40672i
$$166$$ 0 0
$$167$$ 1.00709 0.000466651 0.000233326 1.00000i $$-0.499926\pi$$
0.000233326 1.00000i $$0.499926\pi$$
$$168$$ 0 0
$$169$$ 2142.12 0.975019
$$170$$ 0 0
$$171$$ −821.414 + 476.436i −0.367340 + 0.213064i
$$172$$ 0 0
$$173$$ 1978.27 + 3426.47i 0.869395 + 1.50584i 0.862616 + 0.505860i $$0.168825\pi$$
0.00677983 + 0.999977i $$0.497842\pi$$
$$174$$ 0 0
$$175$$ −2440.57 525.130i −1.05423 0.226835i
$$176$$ 0 0
$$177$$ 251.242 436.170i 0.106692 0.185224i
$$178$$ 0 0
$$179$$ −2423.54 1399.23i −1.01198 0.584266i −0.100208 0.994967i $$-0.531951\pi$$
−0.911770 + 0.410701i $$0.865284\pi$$
$$180$$ 0 0
$$181$$ 1506.74i 0.618758i 0.950939 + 0.309379i $$0.100121\pi$$
−0.950939 + 0.309379i $$0.899879\pi$$
$$182$$ 0 0
$$183$$ 1733.90 1003.38i 0.700403 0.405312i
$$184$$ 0 0
$$185$$ −1883.21 + 3261.82i −0.748414 + 1.29629i
$$186$$ 0 0
$$187$$ 891.599 514.765i 0.348664 0.201301i
$$188$$ 0 0
$$189$$ −804.168 2470.75i −0.309495 0.950901i
$$190$$ 0 0
$$191$$ 3184.51 1838.58i 1.20640 0.696518i 0.244433 0.969666i $$-0.421398\pi$$
0.961972 + 0.273148i $$0.0880650\pi$$
$$192$$ 0 0
$$193$$ 64.7335 112.122i 0.0241431 0.0418171i −0.853701 0.520763i $$-0.825648\pi$$
0.877845 + 0.478946i $$0.158981\pi$$
$$194$$ 0 0
$$195$$ −537.026 + 310.769i −0.197217 + 0.114126i
$$196$$ 0 0
$$197$$ 3044.81i 1.10119i −0.834774 0.550593i $$-0.814402\pi$$
0.834774 0.550593i $$-0.185598\pi$$
$$198$$ 0 0
$$199$$ −3458.29 1996.64i −1.23192 0.711248i −0.264488 0.964389i $$-0.585203\pi$$
−0.967429 + 0.253141i $$0.918536\pi$$
$$200$$ 0 0
$$201$$ 2640.31 4583.73i 0.926532 1.60851i
$$202$$ 0 0
$$203$$ −1201.37 + 387.035i −0.415367 + 0.133815i
$$204$$ 0 0
$$205$$ −2982.40 5165.67i −1.01610 1.75993i
$$206$$ 0 0
$$207$$ 1294.55 750.862i 0.434672 0.252118i
$$208$$ 0 0
$$209$$ −1252.01 −0.414370
$$210$$ 0 0
$$211$$ 4383.67 1.43026 0.715129 0.698992i $$-0.246368\pi$$
0.715129 + 0.698992i $$0.246368\pi$$
$$212$$ 0 0
$$213$$ 0.651100 + 651.249i 0.000209449 + 0.209497i
$$214$$ 0 0
$$215$$ 1507.59 + 2611.23i 0.478219 + 0.828299i
$$216$$ 0 0
$$217$$ −696.065 + 3235.00i −0.217751 + 1.01201i
$$218$$ 0 0
$$219$$ −1015.63 585.022i −0.313379 0.180512i
$$220$$ 0 0
$$221$$ −185.546 107.125i −0.0564759 0.0326064i
$$222$$ 0 0
$$223$$ 4851.53i 1.45687i 0.685114 + 0.728436i $$0.259753\pi$$
−0.685114 + 0.728436i $$0.740247\pi$$
$$224$$ 0 0
$$225$$ −1813.42 + 3155.48i −0.537308 + 0.934958i
$$226$$ 0 0
$$227$$ −1184.05 + 2050.83i −0.346203 + 0.599642i −0.985572 0.169259i $$-0.945863\pi$$
0.639368 + 0.768901i $$0.279196\pi$$
$$228$$ 0 0
$$229$$ −3737.27 + 2157.72i −1.07845 + 0.622646i −0.930479 0.366345i $$-0.880609\pi$$
−0.147975 + 0.988991i $$0.547276\pi$$
$$230$$ 0 0
$$231$$ 717.285 3349.90i 0.204303 0.954144i
$$232$$ 0 0
$$233$$ 4826.98 2786.86i 1.35719 0.783576i 0.367949 0.929846i $$-0.380060\pi$$
0.989245 + 0.146270i $$0.0467267\pi$$
$$234$$ 0 0
$$235$$ 1408.28 2439.22i 0.390920 0.677094i
$$236$$ 0 0
$$237$$ 2769.94 + 4786.62i 0.759186 + 1.31192i
$$238$$ 0 0
$$239$$ 4683.70i 1.26763i −0.773485 0.633814i $$-0.781488\pi$$
0.773485 0.633814i $$-0.218512\pi$$
$$240$$ 0 0
$$241$$ −1896.77 1095.10i −0.506977 0.292703i 0.224613 0.974448i $$-0.427888\pi$$
−0.731590 + 0.681745i $$0.761222\pi$$
$$242$$ 0 0
$$243$$ −3787.95 + 18.9356i −0.999988 + 0.00499884i
$$244$$ 0 0
$$245$$ −5039.26 2273.84i −1.31407 0.592940i
$$246$$ 0 0
$$247$$ 130.275 + 225.642i 0.0335594 + 0.0581266i
$$248$$ 0 0
$$249$$ 3123.09 3.12238i 0.794851 0.000794670i
$$250$$ 0 0
$$251$$ 2240.70 0.563473 0.281736 0.959492i $$-0.409090\pi$$
0.281736 + 0.959492i $$0.409090\pi$$
$$252$$ 0 0
$$253$$ 1973.16 0.490323
$$254$$ 0 0
$$255$$ −2422.13 + 2.42158i −0.594823 + 0.000594688i
$$256$$ 0 0
$$257$$ 555.785 + 962.648i 0.134898 + 0.233651i 0.925559 0.378604i $$-0.123596\pi$$
−0.790660 + 0.612255i $$0.790263\pi$$
$$258$$ 0 0
$$259$$ −2903.85 + 3208.90i −0.696665 + 0.769851i
$$260$$ 0 0
$$261$$ 3.67931 + 1840.07i 0.000872580 + 0.436389i
$$262$$ 0 0
$$263$$ 1782.86 + 1029.34i 0.418007 + 0.241337i 0.694224 0.719759i $$-0.255748\pi$$
−0.276217 + 0.961095i $$0.589081\pi$$
$$264$$ 0 0
$$265$$ 4387.04i 1.01696i
$$266$$ 0 0
$$267$$ 3917.42 + 6769.54i 0.897912 + 1.55164i
$$268$$ 0 0
$$269$$ 2414.62 4182.24i 0.547294 0.947940i −0.451165 0.892441i $$-0.648991\pi$$
0.998459 0.0554999i $$-0.0176752\pi$$
$$270$$ 0 0
$$271$$ 191.772 110.720i 0.0429865 0.0248183i −0.478353 0.878168i $$-0.658766\pi$$
0.521339 + 0.853350i $$0.325433\pi$$
$$272$$ 0 0
$$273$$ −678.368 + 219.293i −0.150391 + 0.0486162i
$$274$$ 0 0
$$275$$ −4155.65 + 2399.27i −0.911255 + 0.526113i
$$276$$ 0 0
$$277$$ −1233.58 + 2136.62i −0.267576 + 0.463455i −0.968235 0.250041i $$-0.919556\pi$$
0.700660 + 0.713496i $$0.252889\pi$$
$$278$$ 0 0
$$279$$ 4182.63 + 2403.70i 0.897517 + 0.515792i
$$280$$ 0 0
$$281$$ 4174.76i 0.886282i 0.896452 + 0.443141i $$0.146136\pi$$
−0.896452 + 0.443141i $$0.853864\pi$$
$$282$$ 0 0
$$283$$ 5628.39 + 3249.55i 1.18224 + 0.682565i 0.956531 0.291630i $$-0.0941977\pi$$
0.225706 + 0.974195i $$0.427531\pi$$
$$284$$ 0 0
$$285$$ 2552.40 + 1470.23i 0.530494 + 0.305574i
$$286$$ 0 0
$$287$$ −2101.65 6523.57i −0.432252 1.34172i
$$288$$ 0 0
$$289$$ 2038.31 + 3530.46i 0.414881 + 0.718595i
$$290$$ 0 0
$$291$$ −1.70116 1701.55i −0.000342693 0.342771i
$$292$$ 0 0
$$293$$ −5637.32 −1.12401 −0.562007 0.827133i $$-0.689970\pi$$
−0.562007 + 0.827133i $$0.689970\pi$$
$$294$$ 0 0
$$295$$ −1561.38 −0.308159
$$296$$ 0 0
$$297$$ −4332.74 2484.21i −0.846503 0.485349i
$$298$$ 0 0
$$299$$ −205.312 355.611i −0.0397108 0.0687810i
$$300$$ 0 0
$$301$$ 1062.38 + 3297.64i 0.203436 + 0.631472i
$$302$$ 0 0
$$303$$ −2841.75 + 4933.45i −0.538794 + 0.935376i
$$304$$ 0 0
$$305$$ −5381.56 3107.05i −1.01032 0.583308i
$$306$$ 0 0
$$307$$ 3442.95i 0.640064i 0.947407 + 0.320032i $$0.103694\pi$$
−0.947407 + 0.320032i $$0.896306\pi$$
$$308$$ 0 0
$$309$$ 933.976 540.477i 0.171948 0.0995037i
$$310$$ 0 0
$$311$$ −75.7324 + 131.172i −0.0138083 + 0.0239167i −0.872847 0.487994i $$-0.837729\pi$$
0.859039 + 0.511911i $$0.171062\pi$$
$$312$$ 0 0
$$313$$ 8335.31 4812.40i 1.50524 0.869050i 0.505257 0.862969i $$-0.331398\pi$$
0.999982 0.00608123i $$-0.00193573\pi$$
$$314$$ 0 0
$$315$$ −5396.05 + 5986.94i −0.965184 + 1.07087i
$$316$$ 0 0
$$317$$ −7866.93 + 4541.98i −1.39385 + 0.804741i −0.993739 0.111726i $$-0.964362\pi$$
−0.400112 + 0.916466i $$0.631029\pi$$
$$318$$ 0 0
$$319$$ −1213.05 + 2101.07i −0.212909 + 0.368768i
$$320$$ 0 0
$$321$$ −8107.83 + 4691.87i −1.40977 + 0.815809i
$$322$$ 0 0
$$323$$ 1017.12i 0.175214i
$$324$$ 0 0
$$325$$ 864.811 + 499.299i 0.147603 + 0.0852188i
$$326$$ 0 0
$$327$$ 735.666 1277.16i 0.124411 0.215985i
$$328$$ 0 0
$$329$$ 2171.52 2399.65i 0.363890 0.402118i
$$330$$ 0 0
$$331$$ −702.788 1217.26i −0.116703 0.202136i 0.801756 0.597651i $$-0.203899\pi$$
−0.918459 + 0.395516i $$0.870566\pi$$
$$332$$ 0 0
$$333$$ 3165.55 + 5457.66i 0.520934 + 0.898132i
$$334$$ 0 0
$$335$$ −16408.6 −2.67611
$$336$$ 0 0
$$337$$ 7983.35 1.29045 0.645223 0.763994i $$-0.276764\pi$$
0.645223 + 0.763994i $$0.276764\pi$$
$$338$$ 0 0
$$339$$ −5.38923 5390.46i −0.000863430 0.863627i
$$340$$ 0 0
$$341$$ 3180.25 + 5508.36i 0.505045 + 0.874764i
$$342$$ 0 0
$$343$$ −5111.13 3772.26i −0.804592 0.593828i
$$344$$ 0 0
$$345$$ −4022.57 2317.07i −0.627732 0.361585i
$$346$$ 0 0
$$347$$ 2268.41 + 1309.67i 0.350935 + 0.202612i 0.665097 0.746757i $$-0.268390\pi$$
−0.314162 + 0.949369i $$0.601724\pi$$
$$348$$ 0 0
$$349$$ 6032.33i 0.925224i −0.886561 0.462612i $$-0.846912\pi$$
0.886561 0.462612i $$-0.153088\pi$$
$$350$$ 0 0
$$351$$ 3.11736 + 1039.35i 0.000474052 + 0.158053i
$$352$$ 0 0
$$353$$ 2658.15 4604.06i 0.400791 0.694190i −0.593031 0.805180i $$-0.702069\pi$$
0.993822 + 0.110990i $$0.0354020\pi$$
$$354$$ 0 0
$$355$$ 1749.49 1010.07i 0.261558 0.151011i
$$356$$ 0 0
$$357$$ −2721.43 582.715i −0.403454 0.0863881i
$$358$$ 0 0
$$359$$ 1612.51 930.982i 0.237061 0.136867i −0.376764 0.926309i $$-0.622963\pi$$
0.613825 + 0.789442i $$0.289630\pi$$
$$360$$ 0 0
$$361$$ −2811.04 + 4868.87i −0.409832 + 0.709851i
$$362$$ 0 0
$$363$$ 165.822 + 286.550i 0.0239763 + 0.0414325i
$$364$$ 0 0
$$365$$ 3635.70i 0.521373i
$$366$$ 0 0
$$367$$ 1675.89 + 967.574i 0.238367 + 0.137621i 0.614426 0.788975i $$-0.289388\pi$$
−0.376059 + 0.926596i $$0.622721\pi$$
$$368$$ 0 0
$$369$$ −9991.81 + 19.9791i −1.40963 + 0.00281862i
$$370$$ 0 0
$$371$$ −1060.36 + 4928.06i −0.148385 + 0.689629i
$$372$$ 0 0
$$373$$ −3871.04 6704.83i −0.537359 0.930732i −0.999045 0.0436892i $$-0.986089\pi$$
0.461687 0.887043i $$-0.347244\pi$$
$$374$$ 0 0
$$375$$ 820.284 0.820097i 0.112958 0.000112932i
$$376$$ 0 0
$$377$$ 504.884 0.0689730
$$378$$ 0 0
$$379$$ 3722.15 0.504470 0.252235 0.967666i $$-0.418834\pi$$
0.252235 + 0.967666i $$0.418834\pi$$
$$380$$ 0 0
$$381$$ 8551.86 8.54991i 1.14994 0.00114967i
$$382$$ 0 0
$$383$$ 3546.73 + 6143.12i 0.473184 + 0.819578i 0.999529 0.0306926i $$-0.00977131\pi$$
−0.526345 + 0.850271i $$0.676438\pi$$
$$384$$ 0 0
$$385$$ −10114.8 + 3258.60i −1.33895 + 0.431359i
$$386$$ 0 0
$$387$$ 5050.82 10.0994i 0.663431 0.00132656i
$$388$$ 0 0
$$389$$ 6173.12 + 3564.05i 0.804601 + 0.464537i 0.845077 0.534644i $$-0.179554\pi$$
−0.0404765 + 0.999180i $$0.512888\pi$$
$$390$$ 0 0
$$391$$ 1602.98i 0.207330i
$$392$$ 0 0
$$393$$ −1635.38 2826.03i −0.209908 0.362733i
$$394$$ 0 0
$$395$$ 8577.33 14856.4i 1.09259 1.89242i
$$396$$ 0 0
$$397$$ 7738.99 4468.11i 0.978360 0.564857i 0.0765855 0.997063i $$-0.475598\pi$$
0.901775 + 0.432206i $$0.142265\pi$$
$$398$$ 0 0
$$399$$ 2511.81 + 2268.46i 0.315157 + 0.284624i
$$400$$ 0 0
$$401$$ 7719.60 4456.91i 0.961343 0.555032i 0.0647568 0.997901i $$-0.479373\pi$$
0.896586 + 0.442869i $$0.146039\pi$$
$$402$$ 0 0
$$403$$ 661.826 1146.32i 0.0818062 0.141692i
$$404$$ 0 0
$$405$$ 5915.71 + 10152.3i 0.725812 + 1.24561i
$$406$$ 0 0
$$407$$ 8318.63i 1.01312i
$$408$$ 0 0
$$409$$ −2680.13 1547.37i −0.324019 0.187073i 0.329163 0.944273i $$-0.393233\pi$$
−0.653183 + 0.757200i $$0.726567\pi$$
$$410$$ 0 0
$$411$$ 2246.44 + 1293.99i 0.269608 + 0.155299i
$$412$$ 0 0
$$413$$ −1753.93 377.389i −0.208972 0.0449639i
$$414$$ 0 0
$$415$$ −4843.82 8389.74i −0.572949 0.992377i
$$416$$ 0 0
$$417$$ −6.32046 6321.90i −0.000742240 0.742409i
$$418$$ 0 0
$$419$$ 7234.25 0.843476 0.421738 0.906718i $$-0.361420\pi$$
0.421738 + 0.906718i $$0.361420\pi$$
$$420$$ 0 0
$$421$$ 406.124 0.0470148 0.0235074 0.999724i $$-0.492517\pi$$
0.0235074 + 0.999724i $$0.492517\pi$$
$$422$$ 0 0
$$423$$ −2367.23 4081.29i −0.272101 0.469123i
$$424$$ 0 0
$$425$$ 1949.14 + 3376.01i 0.222464 + 0.385319i
$$426$$ 0 0
$$427$$ −5294.25 4790.95i −0.600016 0.542975i
$$428$$ 0 0
$$429$$ −683.999 + 1187.46i −0.0769785 + 0.133639i
$$430$$ 0 0
$$431$$ 10590.4 + 6114.37i 1.18358 + 0.683338i 0.956839 0.290618i $$-0.0938609\pi$$
0.226737 + 0.973956i $$0.427194\pi$$
$$432$$ 0 0
$$433$$ 3252.79i 0.361014i −0.983574 0.180507i $$-0.942226\pi$$
0.983574 0.180507i $$-0.0577738\pi$$
$$434$$ 0 0
$$435$$ 4940.24 2858.84i 0.544521 0.315105i
$$436$$ 0 0
$$437$$ −974.689 + 1688.21i −0.106695 + 0.184801i
$$438$$ 0 0
$$439$$ 13036.8 7526.81i 1.41734 0.818303i 0.421278 0.906932i $$-0.361582\pi$$
0.996065 + 0.0886287i $$0.0282485\pi$$
$$440$$ 0 0
$$441$$ −7508.57 + 5421.03i −0.810773 + 0.585361i
$$442$$ 0 0
$$443$$ 204.373 117.995i 0.0219189 0.0126549i −0.489001 0.872283i $$-0.662638\pi$$
0.510919 + 0.859629i $$0.329305\pi$$
$$444$$ 0 0
$$445$$ 12130.6 21010.8i 1.29224 2.23822i
$$446$$ 0 0
$$447$$ −10439.2 + 6040.99i −1.10460 + 0.639215i
$$448$$ 0 0
$$449$$ 5874.66i 0.617466i −0.951149 0.308733i $$-0.900095\pi$$
0.951149 0.308733i $$-0.0999049\pi$$
$$450$$ 0 0
$$451$$ −11409.0 6587.02i −1.19120 0.687739i
$$452$$ 0 0
$$453$$ −2535.09 + 4401.07i −0.262934 + 0.456468i
$$454$$ 0 0
$$455$$ 1639.74 + 1483.86i 0.168950 + 0.152889i
$$456$$ 0 0
$$457$$ −153.883 266.533i −0.0157513 0.0272821i 0.858042 0.513579i $$-0.171681\pi$$
−0.873794 + 0.486297i $$0.838347\pi$$
$$458$$ 0 0
$$459$$ −2018.15 + 3519.88i −0.205227 + 0.357939i
$$460$$ 0 0
$$461$$ 4752.26 0.480119 0.240060 0.970758i $$-0.422833\pi$$
0.240060 + 0.970758i $$0.422833\pi$$
$$462$$ 0 0
$$463$$ 9529.43 0.956523 0.478261 0.878218i $$-0.341267\pi$$
0.478261 + 0.878218i $$0.341267\pi$$
$$464$$ 0 0
$$465$$ −14.9607 14964.1i −0.00149201 1.49235i
$$466$$ 0 0
$$467$$ −3269.28 5662.56i −0.323949 0.561097i 0.657350 0.753586i $$-0.271677\pi$$
−0.981299 + 0.192489i $$0.938344\pi$$
$$468$$ 0 0
$$469$$ −18432.1 3965.99i −1.81475 0.390474i
$$470$$ 0 0
$$471$$ 747.386 + 430.508i 0.0731162 + 0.0421162i
$$472$$ 0 0
$$473$$ 5767.23 + 3329.71i 0.560629 + 0.323679i
$$474$$ 0 0
$$475$$ 4740.69i 0.457932i
$$476$$ 0 0
$$477$$ 6371.64 + 3661.70i 0.611609 + 0.351484i
$$478$$ 0 0
$$479$$ 3671.28 6358.85i 0.350199 0.606562i −0.636085 0.771619i $$-0.719447\pi$$
0.986284 + 0.165057i $$0.0527807\pi$$
$$480$$ 0 0
$$481$$ 1499.22 865.574i 0.142117 0.0820515i
$$482$$ 0 0
$$483$$ −3958.60 3575.08i −0.372925 0.336795i
$$484$$ 0 0
$$485$$ −4570.96 + 2639.05i −0.427952 + 0.247078i
$$486$$ 0 0
$$487$$ 3508.78 6077.39i 0.326485 0.565489i −0.655327 0.755345i $$-0.727469\pi$$
0.981812 + 0.189857i $$0.0608024\pi$$
$$488$$ 0 0
$$489$$ −2542.77 4394.06i −0.235150 0.406352i
$$490$$ 0 0
$$491$$ 224.222i 0.0206089i 0.999947 + 0.0103045i $$0.00328007\pi$$
−0.999947 + 0.0103045i $$0.996720\pi$$
$$492$$ 0 0
$$493$$ 1706.89 + 985.471i 0.155932 + 0.0900272i
$$494$$ 0 0
$$495$$ 30.9775 + 15492.3i 0.00281280 + 1.40672i
$$496$$ 0 0
$$497$$ 2209.38 711.777i 0.199405 0.0642406i
$$498$$ 0 0
$$499$$ −10396.1 18006.6i −0.932651 1.61540i −0.778770 0.627309i $$-0.784156\pi$$
−0.153881 0.988089i $$-0.549177\pi$$
$$500$$ 0 0
$$501$$ −5.23298 + 0.00523178i −0.000466651 + 4.66545e-7i
$$502$$ 0 0
$$503$$ −7341.52 −0.650780 −0.325390 0.945580i $$-0.605496\pi$$
−0.325390 + 0.945580i $$0.605496\pi$$
$$504$$ 0 0
$$505$$ 17660.5 1.55620
$$506$$ 0 0
$$507$$ −11130.8 + 11.1282i −0.975019 + 0.000974796i
$$508$$ 0 0
$$509$$ −9956.11 17244.5i −0.866988 1.50167i −0.865060 0.501669i $$-0.832720\pi$$
−0.00192778 0.999998i $$-0.500614\pi$$
$$510$$ 0 0
$$511$$ −878.757 + 4084.07i −0.0760742 + 0.353559i
$$512$$ 0 0
$$513$$ 4265.72 2479.90i 0.367127 0.213431i
$$514$$ 0 0
$$515$$ −2898.81 1673.63i −0.248032 0.143202i
$$516$$ 0 0
$$517$$ 6220.75i 0.529184i
$$518$$ 0 0
$$519$$ −10297.2 17794.2i −0.870900 1.50497i
$$520$$ 0 0
$$521$$ −3745.90 + 6488.08i −0.314992 + 0.545582i −0.979436 0.201756i $$-0.935335\pi$$
0.664444 + 0.747338i $$0.268668\pi$$
$$522$$ 0 0
$$523$$ −249.515 + 144.058i −0.0208614 + 0.0120444i −0.510394 0.859940i $$-0.670501\pi$$
0.489533 + 0.871985i $$0.337167\pi$$
$$524$$ 0 0
$$525$$ 12684.3 + 2715.97i 1.05445 + 0.225781i
$$526$$ 0 0
$$527$$ 4474.94 2583.61i 0.369889 0.213555i
$$528$$ 0 0
$$529$$ −4547.39 + 7876.32i −0.373748 + 0.647351i
$$530$$ 0 0
$$531$$ −1303.23 + 2267.71i −0.106507 + 0.185330i
$$532$$ 0 0
$$533$$ 2741.58i 0.222797i
$$534$$ 0 0
$$535$$ 25164.5 + 14528.7i 2.03356 + 1.17408i
$$536$$ 0 0
$$537$$ 12600.4 + 7258.03i 1.01256 + 0.583254i
$$538$$ 0 0
$$539$$ −12149.8 + 1215.69i −0.970923 + 0.0971496i
$$540$$ 0 0
$$541$$ −7400.87 12818.7i −0.588149 1.01870i −0.994475 0.104975i $$-0.966524\pi$$
0.406326 0.913728i $$-0.366810\pi$$
$$542$$ 0 0
$$543$$ −7.82747 7829.25i −0.000618616 0.618758i
$$544$$ 0 0
$$545$$ −4571.90 −0.359337
$$546$$ 0 0
$$547$$ 4036.80 0.315541 0.157771 0.987476i $$-0.449569\pi$$
0.157771 + 0.987476i $$0.449569\pi$$
$$548$$ 0 0
$$549$$ −9004.40 + 5222.73i −0.699997 + 0.406012i
$$550$$ 0 0
$$551$$ −1198.43 2075.74i −0.0926585 0.160489i
$$552$$ 0 0
$$553$$ 13225.9 14615.4i 1.01704 1.12388i
$$554$$ 0 0
$$555$$ 9768.51 16958.7i 0.747117 1.29704i
$$556$$ 0 0
$$557$$ 14891.1 + 8597.36i 1.13277 + 0.654007i 0.944631 0.328135i $$-0.106420\pi$$
0.188142 + 0.982142i $$0.439754\pi$$
$$558$$ 0 0
$$559$$ 1385.86i 0.104858i
$$560$$ 0 0
$$561$$ −4630.21 + 2679.43i −0.348463 + 0.201650i
$$562$$ 0 0
$$563$$ −9453.63 + 16374.2i −0.707678 + 1.22573i 0.258038 + 0.966135i $$0.416924\pi$$
−0.965716 + 0.259600i $$0.916409\pi$$
$$564$$ 0 0
$$565$$ −14480.7 + 8360.43i −1.07824 + 0.622524i
$$566$$ 0 0
$$567$$ 4191.41 + 12834.2i 0.310446 + 0.950591i
$$568$$ 0 0
$$569$$ −6255.57 + 3611.66i −0.460891 + 0.266096i −0.712419 0.701754i $$-0.752400\pi$$
0.251528 + 0.967850i $$0.419067\pi$$
$$570$$ 0 0
$$571$$ −4965.17 + 8599.93i −0.363898 + 0.630290i −0.988599 0.150574i $$-0.951888\pi$$
0.624700 + 0.780865i $$0.285221\pi$$
$$572$$ 0 0
$$573$$ −16537.7 + 9570.08i −1.20571 + 0.697724i
$$574$$ 0 0
$$575$$ 7471.31i 0.541870i
$$576$$ 0 0
$$577$$ 7254.16 + 4188.19i 0.523388 + 0.302178i 0.738320 0.674451i $$-0.235620\pi$$
−0.214932 + 0.976629i $$0.568953\pi$$
$$578$$ 0 0
$$579$$ −335.782 + 582.937i −0.0241013 + 0.0418412i
$$580$$ 0 0
$$581$$ −3413.36 10595.2i −0.243735 0.756560i
$$582$$ 0 0
$$583$$ 4844.67 + 8391.21i 0.344161 + 0.596104i
$$584$$ 0 0
$$585$$ 2788.85 1617.59i 0.197102 0.114323i
$$586$$ 0 0
$$587$$ 21277.2 1.49609 0.748043 0.663650i $$-0.230994\pi$$
0.748043 + 0.663650i $$0.230994\pi$$
$$588$$ 0 0
$$589$$ −6283.84 −0.439594
$$590$$ 0 0
$$591$$ 15.8177 + 15821.3i 0.00110093 + 1.10118i
$$592$$ 0 0
$$593$$ −1424.49 2467.29i −0.0986454 0.170859i 0.812479 0.582991i $$-0.198118\pi$$
−0.911124 + 0.412132i $$0.864784\pi$$
$$594$$ 0 0
$$595$$ 2647.25 + 8217.14i 0.182398 + 0.566168i
$$596$$ 0 0
$$597$$ 17980.2 + 10356.9i 1.23263 + 0.710016i
$$598$$ 0 0
$$599$$ −3844.40 2219.57i −0.262234 0.151401i 0.363119 0.931743i $$-0.381712\pi$$
−0.625353 + 0.780342i $$0.715045\pi$$
$$600$$ 0 0
$$601$$ 7868.29i 0.534033i 0.963692 + 0.267017i $$0.0860379\pi$$
−0.963692 + 0.267017i $$0.913962\pi$$
$$602$$ 0 0
$$603$$ −13695.6 + 23831.4i −0.924924 + 1.60944i
$$604$$ 0 0
$$605$$ 513.480 889.374i 0.0345057 0.0597656i
$$606$$ 0 0
$$607$$ 15144.9 8743.92i 1.01271 0.584686i 0.100724 0.994914i $$-0.467884\pi$$
0.911983 + 0.410228i $$0.134551\pi$$
$$608$$ 0 0
$$609$$ 6240.48 2017.33i 0.415233 0.134231i
$$610$$ 0 0
$$611$$ −1121.13 + 647.284i −0.0742324 + 0.0428581i
$$612$$ 0 0
$$613$$ −6422.07 + 11123.3i −0.423140 + 0.732900i −0.996245 0.0865820i $$-0.972406\pi$$
0.573105 + 0.819482i $$0.305739\pi$$
$$614$$ 0 0
$$615$$ 15523.8 + 26826.1i 1.01786 + 1.75892i
$$616$$ 0 0
$$617$$ 23625.5i 1.54153i 0.637117 + 0.770767i $$0.280127\pi$$
−0.637117 + 0.770767i $$0.719873\pi$$
$$618$$ 0 0
$$619$$ −16529.1 9543.05i −1.07328 0.619657i −0.144202 0.989548i $$-0.546062\pi$$
−0.929075 + 0.369891i $$0.879395\pi$$
$$620$$ 0 0
$$621$$ −6722.75 + 3908.32i −0.434420 + 0.252553i
$$622$$ 0 0
$$623$$ 18704.9 20669.9i 1.20289 1.32925i
$$624$$ 0 0
$$625$$ 7152.40 + 12388.3i 0.457754 + 0.792853i
$$626$$ 0 0
$$627$$ 6505.63 6.50415i 0.414370 0.000414275i
$$628$$ 0 0
$$629$$ 6757.98 0.428391
$$630$$ 0 0
$$631$$ −32.3893 −0.00204342 −0.00102171 0.999999i $$-0.500325\pi$$
−0.00102171 + 0.999999i $$0.500325\pi$$
$$632$$ 0 0
$$633$$ −22778.2 + 22.7730i −1.43026 + 0.00142993i
$$634$$ 0 0
$$635$$ −13263.7 22973.4i −0.828902 1.43570i
$$636$$ 0 0
$$637$$ 1483.31 + 2063.19i 0.0922620 + 0.128330i
$$638$$ 0 0
$$639$$ −6.76643 3383.98i −0.000418898 0.209497i
$$640$$ 0 0
$$641$$ −18742.7 10821.1i −1.15490 0.666784i −0.204827 0.978798i $$-0.565663\pi$$
−0.950078 + 0.312014i $$0.898996\pi$$
$$642$$ 0 0
$$643$$ 19867.3i 1.21849i −0.792982 0.609246i $$-0.791472\pi$$
0.792982 0.609246i $$-0.208528\pi$$
$$644$$ 0 0
$$645$$ −7847.24 13560.5i −0.479046 0.827820i
$$646$$ 0 0
$$647$$ −11212.2 + 19420.1i −0.681294 + 1.18004i 0.293293 + 0.956023i $$0.405249\pi$$
−0.974586 + 0.224012i $$0.928084\pi$$
$$648$$ 0 0
$$649$$ −2986.49 + 1724.25i −0.180632 + 0.104288i
$$650$$ 0 0
$$651$$ 3600.05 16813.2i 0.216739 1.01223i
$$652$$ 0 0
$$653$$ 17358.5 10021.9i 1.04026 0.600594i 0.120353 0.992731i $$-0.461597\pi$$
0.919907 + 0.392137i $$0.128264\pi$$
$$654$$ 0 0
$$655$$ −5064.07 + 8771.22i −0.302091 + 0.523237i
$$656$$ 0 0
$$657$$ 5280.41 + 3034.59i 0.313559 + 0.180199i
$$658$$ 0 0
$$659$$ 13217.9i 0.781327i −0.920533 0.390664i $$-0.872246\pi$$
0.920533 0.390664i $$-0.127754\pi$$
$$660$$ 0 0
$$661$$ 8470.90 + 4890.68i 0.498457 + 0.287784i 0.728076 0.685496i $$-0.240415\pi$$
−0.229619 + 0.973281i $$0.573748\pi$$
$$662$$ 0 0
$$663$$ 964.682 + 555.674i 0.0565085 + 0.0325499i
$$664$$ 0 0
$$665$$ 2208.41 10263.7i 0.128780 0.598511i
$$666$$ 0 0
$$667$$ 1888.72 + 3271.36i 0.109642 + 0.189906i
$$668$$ 0 0
$$669$$ −25.2035 25209.3i −0.00145654 1.45687i
$$670$$ 0 0
$$671$$ −13724.6 −0.789617
$$672$$ 0 0
$$673$$ −4670.73 −0.267524 −0.133762 0.991014i $$-0.542706\pi$$
−0.133762 + 0.991014i $$0.542706\pi$$
$$674$$ 0 0
$$675$$ 9406.39 16405.8i 0.536373 0.935494i
$$676$$ 0 0
$$677$$ −13521.0 23419.1i −0.767584 1.32949i −0.938870 0.344273i $$-0.888125\pi$$
0.171286 0.985221i $$-0.445208\pi$$
$$678$$ 0 0
$$679$$ −5772.53 + 1859.69i −0.326258 + 0.105108i
$$680$$ 0 0
$$681$$ 6141.85 10662.6i 0.345604 0.599988i
$$682$$ 0 0
$$683$$ −11596.9 6695.45i −0.649694 0.375101i 0.138645 0.990342i $$-0.455725\pi$$
−0.788339 + 0.615241i $$0.789059\pi$$
$$684$$ 0 0
$$685$$ 8041.69i 0.448551i
$$686$$ 0 0
$$687$$ 19408.2 11231.2i 1.07783 0.623724i
$$688$$ 0 0
$$689$$ 1008.20 1746.25i 0.0557464 0.0965557i
$$690$$ 0 0
$$691$$ −26837.3 + 15494.6i −1.47748 + 0.853025i −0.999676 0.0254396i $$-0.991901\pi$$
−0.477807 + 0.878465i $$0.658568\pi$$
$$692$$ 0 0
$$693$$ −3709.72 + 17410.3i −0.203348 + 0.954348i
$$694$$ 0 0
$$695$$ −16982.9 + 9805.07i −0.926903 + 0.535147i
$$696$$ 0 0
$$697$$ −5351.23 + 9268.60i −0.290807 + 0.503692i
$$698$$ 0 0
$$699$$ −25067.3 + 14506.0i −1.35641 + 0.784933i
$$700$$ 0 0
$$701$$ 2892.67i 0.155855i 0.996959 + 0.0779277i $$0.0248303\pi$$
−0.996959 + 0.0779277i $$0.975170\pi$$
$$702$$ 0 0
$$703$$ −7117.31 4109.18i −0.381841 0.220456i
$$704$$ 0 0
$$705$$ −7304.98 + 12681.9i −0.390243 + 0.677485i
$$706$$ 0 0
$$707$$ 19838.4 + 4268.57i 1.05530 + 0.227067i
$$708$$ 0 0
$$709$$ −7965.19 13796.1i −0.421917 0.730781i 0.574210 0.818708i $$-0.305309\pi$$
−0.996127 + 0.0879267i $$0.971976\pi$$
$$710$$ 0 0
$$711$$ −14417.9 24857.6i −0.760497 1.31116i
$$712$$ 0 0
$$713$$ 9903.30 0.520171
$$714$$ 0 0
$$715$$ 4250.81 0.222337
$$716$$ 0 0
$$717$$ 24.3316 + 24337.2i 0.00126734 + 1.26763i
$$718$$ 0 0
$$719$$ 5938.87 + 10286.4i 0.308042 + 0.533545i 0.977934 0.208914i $$-0.0669928\pi$$
−0.669892 + 0.742459i $$0.733659\pi$$
$$720$$ 0 0
$$721$$ −2851.78 2580.67i −0.147303 0.133300i
$$722$$ 0 0
$$723$$ 9861.57 + 5680.44i 0.507270 + 0.292196i
$$724$$ 0 0
$$725$$ −7955.61 4593.18i −0.407537 0.235291i
$$726$$ 0 0
$$727$$ 16795.8i 0.856839i 0.903580 + 0.428419i $$0.140929\pi$$
−0.903580 + 0.428419i $$0.859071\pi$$
$$728$$ 0 0
$$729$$ 19682.6 118.070i 0.999982 0.00599859i
$$730$$ 0 0
$$731$$ 2705.03 4685.24i 0.136866 0.237059i
$$732$$ 0 0
$$733$$ 22048.4 12729.7i 1.11102 0.641447i 0.171926 0.985110i $$-0.445001\pi$$
0.939093 + 0.343663i $$0.111668\pi$$
$$734$$ 0 0
$$735$$ 26196.6 + 11789.0i 1.31466 + 0.591626i
$$736$$ 0 0
$$737$$ −31385.1 + 18120.2i −1.56864 + 0.905653i
$$738$$ 0 0
$$739$$ −9319.48 + 16141.8i −0.463901 + 0.803499i −0.999151 0.0411940i $$-0.986884\pi$$
0.535251 + 0.844693i $$0.320217\pi$$
$$740$$ 0 0
$$741$$ −678.099 1171.79i −0.0336175 0.0580930i
$$742$$ 0 0
$$743$$ 14043.3i 0.693401i 0.937976 + 0.346700i $$0.112698\pi$$
−0.937976 + 0.346700i $$0.887302\pi$$
$$744$$ 0 0
$$745$$ 32400.4 + 18706.4i 1.59337 + 0.919932i
$$746$$ 0 0
$$747$$ −16228.0 + 32.4487i −0.794850 + 0.00158934i
$$748$$ 0 0
$$749$$ 24756.3 + 22402.8i 1.20771 + 1.09290i
$$750$$ 0 0
$$751$$ 8115.13 + 14055.8i 0.394308 + 0.682961i 0.993013 0.118009i $$-0.0376510\pi$$
−0.598705 + 0.800970i $$0.704318\pi$$
$$752$$ 0 0
$$753$$ −11643.0 + 11.6404i −0.563473 + 0.000563344i
$$754$$ 0 0
$$755$$ 15754.7 0.759433
$$756$$ 0 0
$$757$$ −33345.7 −1.60102 −0.800508 0.599322i $$-0.795437\pi$$
−0.800508 + 0.599322i $$0.795437\pi$$
$$758$$ 0 0
$$759$$ −10252.8 + 10.2505i −0.490322 + 0.000490211i
$$760$$ 0 0
$$761$$ 5394.02 + 9342.71i 0.256942 + 0.445037i 0.965421 0.260695i $$-0.0839517\pi$$
−0.708479 + 0.705732i $$0.750618\pi$$
$$762$$ 0 0
$$763$$ −5135.72 1105.04i −0.243677 0.0524313i
$$764$$ 0 0
$$765$$ 12585.8 25.1658i 0.594822 0.00118937i
$$766$$ 0 0
$$767$$ 621.503 + 358.825i 0.0292584 + 0.0168923i
$$768$$ 0 0
$$769$$ 35799.6i 1.67876i 0.543543 + 0.839381i $$0.317082\pi$$
−0.543543 + 0.839381i $$0.682918\pi$$
$$770$$ 0 0
$$771$$ −2892.94 4999.17i −0.135132 0.233516i
$$772$$ 0 0
$$773$$ −18306.3 + 31707.5i −0.851788 + 1.47534i 0.0278053 + 0.999613i $$0.491148\pi$$
−0.879593 + 0.475727i $$0.842185\pi$$
$$774$$ 0 0
$$775$$ −20857.2 + 12041.9i −0.966727 + 0.558140i
$$776$$ 0 0
$$777$$ 15072.2 16689.0i 0.695895 0.770548i
$$778$$ 0 0
$$779$$ 11271.5 6507.62i 0.518414 0.299306i
$$780$$ 0 0
$$781$$ 2230.86 3863.97i 0.102211 0.177034i
$$782$$ 0 0
$$783$$ −28.6773 9561.27i −0.00130887 0.436388i
$$784$$ 0 0
$$785$$ 2675.45i 0.121644i
$$786$$ 0 0
$$787$$ 34874.9 + 20135.0i 1.57961 + 0.911990i 0.994913 + 0.100742i $$0.0321216\pi$$
0.584701 + 0.811249i $$0.301212\pi$$
$$788$$ 0 0
$$789$$ −9269.36 5339.32i −0.418248